LMFDB - Embedded newform 105.2.p.a.59.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(59,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("105.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.p (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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.11
Character	$\chi$	$=$	105.59
Dual form			105.2.p.a.89.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25399 + 2.17197i) q^{2} +(-1.51966 + 0.831052i) q^{3} +(-2.14497 + 3.71520i) q^{4} +(-0.00874528 - 2.23605i) q^{5} +(-3.71065 - 2.25852i) q^{6} +(1.65993 + 2.06025i) q^{7} -5.74313 q^{8} +(1.61871 - 2.52582i) q^{9} +(4.84567 - 2.82298i) q^{10} +(1.48843 + 0.859346i) q^{11} +(0.172094 - 7.42841i) q^{12} -0.360784 q^{13} +(-2.39327 + 6.18885i) q^{14} +(1.87156 + 3.39076i) q^{15} +(-2.91187 - 5.04351i) q^{16} +(-2.20219 - 1.27144i) q^{17} +(7.51586 + 0.348428i) q^{18} +(4.93492 - 2.84918i) q^{19} +(8.32614 + 4.76378i) q^{20} +(-4.23470 - 1.75138i) q^{21} +4.31044i q^{22} +(-1.25399 - 2.17197i) q^{23} +(8.72758 - 4.77284i) q^{24} +(-4.99985 + 0.0391098i) q^{25} +(-0.452418 - 0.783611i) q^{26} +(-0.360784 + 5.18361i) q^{27} +(-11.2147 + 1.74780i) q^{28} -3.76228i q^{29} +(-5.01771 + 8.31695i) q^{30} +(-2.41187 - 1.39249i) q^{31} +(1.55977 - 2.70160i) q^{32} +(-2.97606 - 0.0689466i) q^{33} -6.37747i q^{34} +(4.59231 - 3.72971i) q^{35} +(5.91187 + 11.4316i) q^{36} +(2.86279 - 1.65283i) q^{37} +(12.3767 + 7.14567i) q^{38} +(0.548267 - 0.299830i) q^{39} +(0.0502252 + 12.8419i) q^{40} -2.63477 q^{41} +(-1.50631 - 11.3939i) q^{42} -10.0606i q^{43} +(-6.38529 + 3.68655i) q^{44} +(-5.66203 - 3.59742i) q^{45} +(3.14497 - 5.44725i) q^{46} +(-5.04290 + 2.91152i) q^{47} +(8.61645 + 5.24448i) q^{48} +(-1.48925 + 6.83975i) q^{49} +(-6.35469 - 10.8105i) q^{50} +(4.40320 + 0.102009i) q^{51} +(0.773871 - 1.34038i) q^{52} +(0.727175 - 1.25950i) q^{53} +(-11.7111 + 5.71658i) q^{54} +(1.90853 - 3.33572i) q^{55} +(-9.53320 - 11.8323i) q^{56} +(-5.13156 + 8.43094i) q^{57} +(8.17157 - 4.71786i) q^{58} +(-3.42928 + 5.93969i) q^{59} +(-16.6118 - 0.319848i) q^{60} +(1.38882 - 0.801836i) q^{61} -6.98468i q^{62} +(7.89077 - 0.857759i) q^{63} -3.82374 q^{64} +(0.00315515 + 0.806730i) q^{65} +(-3.58220 - 6.55038i) q^{66} +(-2.15712 - 1.24541i) q^{67} +(9.44729 - 5.45439i) q^{68} +(3.71065 + 2.25852i) q^{69} +(13.8595 + 5.29735i) q^{70} +13.1790i q^{71} +(-9.29643 + 14.5061i) q^{72} +(-5.82187 + 10.0838i) q^{73} +(7.17980 + 4.14526i) q^{74} +(7.56554 - 4.21457i) q^{75} +24.4456i q^{76} +(0.700227 + 4.49300i) q^{77} +(1.33874 + 0.814836i) q^{78} +(6.93492 + 12.0116i) q^{79} +(-11.2521 + 6.55519i) q^{80} +(-3.75958 - 8.17713i) q^{81} +(-3.30396 - 5.72264i) q^{82} -3.50427i q^{83} +(15.5900 - 11.9761i) q^{84} +(-2.82374 + 4.93534i) q^{85} +(21.8514 - 12.6159i) q^{86} +(3.12665 + 5.71737i) q^{87} +(-8.54825 - 4.93534i) q^{88} +(-6.10392 - 10.5723i) q^{89} +(0.713373 - 16.8089i) q^{90} +(-0.598876 - 0.743304i) q^{91} +10.7591 q^{92} +(4.82244 + 0.111722i) q^{93} +(-12.6475 - 7.30202i) q^{94} +(-6.41406 - 11.0098i) q^{95} +(-0.125143 + 5.40176i) q^{96} +8.18747 q^{97} +(-16.7232 + 5.34234i) q^{98} +(4.57989 - 2.36849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 6 q^{21} + 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} - 72 q^{40} - 18 q^{45} + 36 q^{46} - 12 q^{49} - 12 q^{51} - 36 q^{54} + 12 q^{60}+ \cdots - 48 q^{99}+O(q^{100}) $ 24 * q - 12 * q^4 - 6 * q^9 - 24 * q^15 - 12 * q^16 - 6 * q^21 + 18 * q^24 - 12 * q^25 + 18 * q^30 + 84 * q^36 - 12 * q^39 - 72 * q^40 - 18 * q^45 + 36 * q^46 - 12 * q^49 - 12 * q^51 - 36 * q^54 + 12 * q^60 + 36 * q^61 + 24 * q^64 - 72 * q^66 + 108 * q^70 + 72 * q^75 + 48 * q^79 - 6 * q^81 + 48 * q^84 + 48 * q^85 - 96 * q^91 - 72 * q^94 - 90 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.25399	+	2.17197i	0.886704	+	1.53582i	0.843749	+	0.536739i	$0.180344\pi$
$2$	1.25399	+	2.17197i	0.886704	+	1.53582i	0.0429549	+	0.999077i	$0.486323\pi$
$3$	−1.51966	+	0.831052i	−0.877374	+	0.479808i
$3$	−1.51966	+	0.831052i	−0.877374	+	0.479808i
$4$	−2.14497	+	3.71520i	−1.07249	+	1.85760i
$5$	−0.00874528	−	2.23605i	−0.00391101	−	0.999992i
$5$	−0.00874528	−	2.23605i	−0.00391101	−	0.999992i
$6$	−3.71065	−	2.25852i	−1.51487	−	0.922036i
$7$	1.65993	+	2.06025i	0.627395	+	0.778701i
$7$	1.65993	+	2.06025i	0.627395	+	0.778701i
$8$	−5.74313			−2.03050
$9$	1.61871	−	2.52582i	0.539569	−	0.841942i
$10$	4.84567	−	2.82298i	1.53234	−	0.892703i
$11$	1.48843	+	0.859346i	0.448779	+	0.259103i	0.707314	−	0.706899i	$-0.249907\pi$
$11$	1.48843	+	0.859346i	0.448779	+	0.259103i	−0.258535	+	0.966002i	$0.583240\pi$
$12$	0.172094	−	7.42841i	0.0496794	−	2.14440i
$13$	−0.360784			−0.100063			−0.0500317	−	0.998748i	$-0.515932\pi$
$13$	−0.360784			−0.100063			−0.0500317	+	0.998748i	$0.515932\pi$
$14$	−2.39327	+	6.18885i	−0.639628	+	1.65404i
$15$	1.87156	+	3.39076i	0.483236	+	0.875490i
$16$	−2.91187	−	5.04351i	−0.727967	−	1.26088i
$17$	−2.20219	−	1.27144i	−0.534110	−	0.308369i	0.208578	−	0.978006i	$-0.433116\pi$
$17$	−2.20219	−	1.27144i	−0.534110	−	0.308369i	−0.742689	+	0.669637i	$0.766450\pi$
$18$	7.51586	+	0.348428i	1.77150	+	0.0821252i
$19$	4.93492	−	2.84918i	1.13215	−	0.653646i	0.187674	−	0.982231i	$-0.439905\pi$
$19$	4.93492	−	2.84918i	1.13215	−	0.653646i	0.944474	+	0.328586i	$0.106572\pi$
$20$	8.32614	+	4.76378i	1.86178	+	1.06521i
$21$	−4.23470	−	1.75138i	−0.924087	−	0.382182i
$22$			4.31044i			0.918989i
$23$	−1.25399	−	2.17197i	−0.261475	−	0.452887i	0.705159	−	0.709049i	$-0.250875\pi$
$23$	−1.25399	−	2.17197i	−0.261475	−	0.452887i	−0.966634	+	0.256162i	$0.917542\pi$
$24$	8.72758	−	4.77284i	1.78151	−	0.974251i
$25$	−4.99985	+	0.0391098i	−0.999969	+	0.00782195i
$26$	−0.452418	−	0.783611i	−0.0887265	−	0.153679i
$27$	−0.360784	+	5.18361i	−0.0694328	+	0.997587i
$28$	−11.2147	+	1.74780i	−2.11939	+	0.330303i
$29$		−	3.76228i		−	0.698638i	−0.937004	−	0.349319i	$-0.886413\pi$
$29$		−	3.76228i		−	0.698638i	0.937004	−	0.349319i	$-0.113587\pi$
$30$	−5.01771	+	8.31695i	−0.916105	+	1.51846i
$31$	−2.41187	−	1.39249i	−0.433185	−	0.250099i	0.267518	−	0.963553i	$-0.413797\pi$
$31$	−2.41187	−	1.39249i	−0.433185	−	0.250099i	−0.700702	+	0.713454i	$0.747130\pi$
$32$	1.55977	−	2.70160i	0.275731	−	0.477580i
$33$	−2.97606	−	0.0689466i	−0.518066	−	0.0120021i
$34$		−	6.37747i		−	1.09373i
$35$	4.59231	−	3.72971i	0.776241	−	0.630436i
$36$	5.91187	+	11.4316i	0.985312	+	1.90527i
$37$	2.86279	−	1.65283i	0.470639	−	0.271724i	−0.245868	−	0.969303i	$-0.579073\pi$
$37$	2.86279	−	1.65283i	0.470639	−	0.271724i	0.716507	+	0.697580i	$0.245740\pi$
$38$	12.3767	+	7.14567i	2.00776	+	1.15918i
$39$	0.548267	−	0.299830i	0.0877929	−	0.0480112i
$40$	0.0502252	+	12.8419i	0.00794131	+	2.03049i
$41$	−2.63477			−0.411481			−0.205741	−	0.978607i	$-0.565960\pi$
$41$	−2.63477			−0.411481			−0.205741	+	0.978607i	$0.565960\pi$
$42$	−1.50631	−	11.3939i	−0.232429	−	1.75811i
$43$		−	10.0606i		−	1.53423i	−0.641510	−	0.767114i	$-0.721692\pi$
$43$		−	10.0606i		−	1.53423i	0.641510	−	0.767114i	$-0.278308\pi$
$44$	−6.38529	+	3.68655i	−0.962618	+	0.555768i
$45$	−5.66203	−	3.59742i	−0.844045	−	0.536272i
$46$	3.14497	−	5.44725i	0.463701	−	0.803154i
$47$	−5.04290	+	2.91152i	−0.735583	+	0.424689i	−0.820461	−	0.571702i	$-0.806283\pi$
$47$	−5.04290	+	2.91152i	−0.735583	+	0.424689i	0.0848783	+	0.996391i	$0.472950\pi$
$48$	8.61645	+	5.24448i	1.24368	+	0.756975i
$49$	−1.48925	+	6.83975i	−0.212751	+	0.977107i
$50$	−6.35469	−	10.8105i	−0.898689	−	1.52883i
$51$	4.40320	+	0.102009i	0.616572	+	0.0142842i
$52$	0.773871	−	1.34038i	0.107317	−	0.185878i
$53$	0.727175	−	1.25950i	0.0998852	−	0.173006i	−0.811752	−	0.584003i	$-0.801486\pi$
$53$	0.727175	−	1.25950i	0.0998852	−	0.173006i	0.911637	+	0.410996i	$0.134819\pi$
$54$	−11.7111	+	5.71658i	−1.59368	+	0.777928i
$55$	1.90853	−	3.33572i	0.257345	−	0.449789i
$56$	−9.53320	−	11.8323i	−1.27393	−	1.58115i
$57$	−5.13156	+	8.43094i	−0.679692	+	1.11671i
$58$	8.17157	−	4.71786i	1.07298	−	0.619485i
$59$	−3.42928	+	5.93969i	−0.446454	+	0.773282i	−0.998152	−	0.0607624i	$-0.980647\pi$
$59$	−3.42928	+	5.93969i	−0.446454	+	0.773282i	0.551698	+	0.834044i	$0.313980\pi$
$60$	−16.6118	−	0.319848i	−2.14458	−	0.0412922i
$61$	1.38882	−	0.801836i	0.177820	−	0.102665i	−0.408448	−	0.912782i	$-0.633930\pi$
$61$	1.38882	−	0.801836i	0.177820	−	0.102665i	0.586268	+	0.810117i	$0.300596\pi$
$62$		−	6.98468i		−	0.887055i
$63$	7.89077	−	0.857759i	0.994144	−	0.108067i
$64$	−3.82374			−0.477967
$65$	0.00315515	+	0.806730i	0.000391348	+	0.100063i
$66$	−3.58220	−	6.55038i	−0.440938	−	0.806296i
$67$	−2.15712	−	1.24541i	−0.263534	−	0.152151i	0.362412	−	0.932018i	$-0.381953\pi$
$67$	−2.15712	−	1.24541i	−0.263534	−	0.152151i	−0.625946	+	0.779867i	$0.715287\pi$
$68$	9.44729	−	5.45439i	1.14565	−	0.661442i
$69$	3.71065	+	2.25852i	0.446710	+	0.271894i
$70$	13.8595	+	5.29735i	1.65653	+	0.633154i
$71$			13.1790i			1.56406i	0.623243	+	0.782028i	$0.285815\pi$
$71$			13.1790i			1.56406i	−0.623243	+	0.782028i	$0.714185\pi$
$72$	−9.29643	+	14.5061i	−1.09560	+	1.70956i
$73$	−5.82187	+	10.0838i	−0.681398	+	1.18022i	0.293156	+	0.956065i	$0.405294\pi$
$73$	−5.82187	+	10.0838i	−0.681398	+	1.18022i	−0.974554	+	0.224151i	$0.928039\pi$
$74$	7.17980	+	4.14526i	0.834635	+	0.481877i
$75$	7.56554	−	4.21457i	0.873594	−	0.486656i
$76$			24.4456i			2.80410i
$77$	0.700227	+	4.49300i	0.0797982	+	0.512024i
$78$	1.33874	+	0.814836i	0.151583	+	0.0922621i
$79$	6.93492	+	12.0116i	0.780239	+	1.35141i	0.931802	+	0.362966i	$0.118236\pi$
$79$	6.93492	+	12.0116i	0.780239	+	1.35141i	−0.151563	+	0.988448i	$0.548431\pi$
$80$	−11.2521	+	6.55519i	−1.25802	+	0.732893i
$81$	−3.75958	−	8.17713i	−0.417732	−	0.908571i
$82$	−3.30396	−	5.72264i	−0.364862	−	0.631959i
$83$		−	3.50427i		−	0.384644i	−0.981332	−	0.192322i	$-0.938398\pi$
$83$		−	3.50427i		−	0.384644i	0.981332	−	0.192322i	$-0.0616018\pi$
$84$	15.5900	−	11.9761i	1.70101	−	1.30670i
$85$	−2.82374	+	4.93534i	−0.306277	+	0.535312i
$86$	21.8514	−	12.6159i	2.35629	−	1.36041i
$87$	3.12665	+	5.71737i	0.335212	+	0.612967i
$88$	−8.54825	−	4.93534i	−0.911247	−	0.526108i
$89$	−6.10392	−	10.5723i	−0.647014	−	1.12066i	−0.983832	−	0.179092i	$-0.942684\pi$
$89$	−6.10392	−	10.5723i	−0.647014	−	1.12066i	0.336818	−	0.941570i	$-0.390649\pi$
$90$	0.713373	−	16.8089i	0.0751962	−	1.77181i
$91$	−0.598876	−	0.743304i	−0.0627793	−	0.0779194i
$92$	10.7591			1.12171
$93$	4.82244	+	0.111722i	0.500064	+	0.0115850i
$94$	−12.6475	−	7.30202i	−1.30449	−	0.753146i
$95$	−6.41406	−	11.0098i	−0.658069	−	1.12958i
$96$	−0.125143	+	5.40176i	−0.0127723	+	0.551314i
$97$	8.18747			0.831311			0.415656	−	0.909522i	$-0.363552\pi$
$97$	8.18747			0.831311			0.415656	+	0.909522i	$0.363552\pi$
$98$	−16.7232	+	5.34234i	−1.68930	+	0.539658i
$99$	4.57989	−	2.36849i	0.460296	−	0.238042i
$100$	10.5792	−	18.6593i	1.05792	−	1.86593i
$101$	−0.623467	+	1.07988i	−0.0620372	+	0.107452i	−0.895376	−	0.445311i	$-0.853093\pi$
$101$	−0.623467	+	1.07988i	−0.0620372	+	0.107452i	0.833339	+	0.552763i	$0.186426\pi$
$102$	5.30001	+	9.69155i	0.524779	+	0.959607i
$103$	2.07302	+	3.59057i	0.204261	+	0.353790i	0.949897	−	0.312563i	$-0.101188\pi$
$103$	2.07302	+	3.59057i	0.204261	+	0.353790i	−0.745636	+	0.666353i	$0.767854\pi$
$104$	2.07203			0.203179
$105$	−3.87914	+	9.48432i	−0.378565	+	0.925575i
$106$	3.64748			0.354274
$107$	0.553762	+	0.959143i	0.0535342	+	0.0927239i	0.891551	−	0.452921i	$-0.149618\pi$
$107$	0.553762	+	0.959143i	0.0535342	+	0.0927239i	−0.838016	+	0.545645i	$0.816285\pi$
$108$	−18.4843	−	12.4591i	−1.77865	−	1.19888i
$109$	4.55684	−	7.89268i	0.436466	−	0.755982i	−0.560948	−	0.827851i	$-0.689563\pi$
$109$	4.55684	−	7.89268i	0.436466	−	0.755982i	0.997414	+	0.0718694i	$0.0228965\pi$
$110$	9.63836	−	0.0376960i	0.918982	−	0.00359417i
$111$	−2.97686	+	4.89086i	−0.282551	+	0.464220i
$112$	5.55738	−	14.3711i	0.525123	−	1.35794i
$113$	3.79282			0.356799			0.178399	−	0.983958i	$-0.442908\pi$
$113$	3.79282			0.356799			0.178399	+	0.983958i	$0.442908\pi$
$114$	−24.7467	−	0.573307i	−2.31774	−	0.0536952i
$115$	−4.84567	+	2.82298i	−0.451861	+	0.263244i
$116$	13.9776	+	8.06999i	1.29779	+	0.749280i
$117$	−0.584002	+	0.911276i	−0.0539910	+	0.0842475i
$118$	−17.2011			−1.58349
$119$	−1.03601	−	6.64757i	−0.0949712	−	0.609381i
$120$	−10.7486	−	19.4736i	−0.981211	−	1.77769i
$121$	−4.02305	−	6.96812i	−0.365732	−	0.633466i
$122$	3.48313	+	2.01099i	0.315348	+	0.182066i
$123$	4.00394	−	2.18963i	0.361023	−	0.197432i
$124$	10.3468	−	5.97372i	0.929169	−	0.536456i
$125$	0.131176	+	11.1796i	0.0117328	+	0.999931i
$126$	11.7580	+	16.0629i	1.04748	+	1.43100i
$127$		−	5.98643i		−	0.531210i	−0.964082	−	0.265605i	$-0.914428\pi$
$127$		−	5.98643i		−	0.531210i	0.964082	−	0.265605i	$-0.0855716\pi$
$128$	−7.91447	−	13.7083i	−0.699547	−	1.21165i
$129$	8.36089	+	15.2887i	0.736135	+	1.34609i
$130$	−1.74824	+	1.01848i	−0.153331	+	0.0893269i
$131$	7.29012	+	12.6269i	0.636941	+	1.10321i	0.986100	+	0.166151i	$0.0531339\pi$
$131$	7.29012	+	12.6269i	0.636941	+	1.10321i	−0.349159	+	0.937063i	$0.613533\pi$
$132$	6.63973	−	10.9088i	0.577914	−	0.949488i
$133$	14.0616	+	5.43772i	1.21930	+	0.471510i
$134$		−	6.24693i		−	0.539653i
$135$	11.5940	+	0.761398i	0.997851	+	0.0655307i
$136$	12.6475	+	7.30202i	1.08451	+	0.626143i
$137$	7.85666	−	13.6081i	0.671240	−	1.16262i	−0.306313	−	0.951931i	$-0.599095\pi$
$137$	7.85666	−	13.6081i	0.671240	−	1.16262i	0.977553	−	0.210691i	$-0.0675713\pi$
$138$	−0.252326	+	10.8916i	−0.0214794	+	0.927153i
$139$		−	14.7324i		−	1.24959i	−0.780790	−	0.624794i	$-0.785183\pi$
$139$		−	14.7324i		−	1.24959i	0.780790	−	0.624794i	$-0.214817\pi$
$140$	4.00625	+	25.0615i	0.338590	+	2.11808i
$141$	5.24385	−	8.61542i	0.441612	−	0.725549i
$142$	−28.6243	+	16.5263i	−2.40210	+	1.38685i
$143$	−0.537001	−	0.310038i	−0.0449063	−	0.0259267i
$144$	−17.4525	−	0.809079i	−1.45437	−	0.0674232i
$145$	−8.41266	+	0.0329022i	−0.698633	+	0.00273238i
$146$	−29.2022			−2.41679
$147$	−3.42103	−	11.6317i	−0.282162	−	0.959367i
$148$			14.1811i			1.16568i
$149$	11.0008	−	6.35130i	0.901219	−	0.520319i	0.0236233	−	0.999721i	$-0.492480\pi$
$149$	11.0008	−	6.35130i	0.901219	−	0.520319i	0.877595	+	0.479402i	$0.159146\pi$
$150$	18.6410	+	11.1471i	1.52203	+	0.910159i
$151$	−8.34679	+	14.4571i	−0.679252	+	1.17650i	0.295955	+	0.955202i	$0.404362\pi$
$151$	−8.34679	+	14.4571i	−0.679252	+	1.17650i	−0.975207	+	0.221297i	$0.928971\pi$
$152$	−28.3419	+	16.3632i	−2.29883	+	1.32723i
$153$	−6.77613	+	3.50427i	−0.547818	+	0.283304i
$154$	−8.88058	+	7.15503i	−0.715618	+	0.576569i
$155$	−3.09259	+	5.40524i	−0.248403	+	0.434159i
$156$	−0.0620888	+	2.68005i	−0.00497108	+	0.214576i
$157$	0.721567	−	1.24979i	0.0575873	−	0.0997442i	−0.835795	−	0.549042i	$-0.814993\pi$
$157$	0.721567	−	1.24979i	0.0575873	−	0.0997442i	0.893382	+	0.449298i	$0.148326\pi$
$158$	−17.3926	+	30.1249i	−1.38368	+	2.39661i
$159$	−0.0583424	+	2.51833i	−0.00462685	+	0.199717i
$160$	−6.05456	−	3.46410i	−0.478655	−	0.273861i
$161$	2.39327	−	6.18885i	0.188616	−	0.487750i
$162$	13.0460	−	18.4197i	1.02499	−	1.44719i
$163$	−14.6028	+	8.43094i	−1.14378	+	0.660362i	−0.947364	−	0.320158i	$-0.896264\pi$
$163$	−14.6028	+	8.43094i	−1.14378	+	0.660362i	−0.196417	+	0.980521i	$0.562931\pi$
$164$	5.65150	−	9.78869i	0.441308	−	0.764368i
$165$	−0.128142	+	6.65523i	−0.00997582	+	0.518109i
$166$	7.61118	−	4.39432i	0.590742	−	0.341065i
$167$			7.20879i			0.557833i	0.960315	+	0.278916i	$0.0899752\pi$
$167$			7.20879i			0.557833i	−0.960315	+	0.278916i	$0.910025\pi$
$168$	24.3204	+	10.0584i	1.87636	+	0.776022i
$169$	−12.8698			−0.989987
$170$	−14.2603	+	0.0557727i	−1.09372	+	0.00427757i
$171$	0.791659	−	17.0767i	0.0605397	−	1.30589i
$172$	37.3772	+	21.5797i	2.84998	+	1.64544i
$173$	−7.78210	+	4.49300i	−0.591662	+	0.341596i	−0.765754	−	0.643133i	$-0.777634\pi$
$173$	−7.78210	+	4.49300i	−0.591662	+	0.341596i	0.174093	+	0.984729i	$0.444301\pi$
$174$	−8.49719	+	13.9605i	−0.644170	+	1.05834i
$175$	−8.37998	−	10.2360i	−0.633467	−	0.773770i
$176$		−	10.0092i		−	0.754473i
$177$	0.275136	−	11.8762i	0.0206805	−	0.892669i
$178$	15.3085	−	26.5151i	1.14742	−	1.98739i
$179$	9.49333	+	5.48098i	0.709565	+	0.409667i	0.810900	−	0.585185i	$-0.198978\pi$
$179$	9.49333	+	5.48098i	0.709565	+	0.409667i	−0.101335	+	0.994852i	$0.532311\pi$
$180$	25.5100	−	13.3192i	1.90141	−	0.992756i
$181$		−	5.39306i		−	0.400863i	−0.979708	−	0.200431i	$-0.935766\pi$
$181$		−	5.39306i		−	0.400863i	0.979708	−	0.200431i	$-0.0642344\pi$
$182$	0.863452	−	2.23284i	0.0640033	−	0.165509i
$183$	−1.44416	+	2.37270i	−0.106756	+	0.175395i
$184$	7.20181	+	12.4739i	0.530925	+	0.919589i
$185$	−3.72085	−	6.38688i	−0.273562	−	0.469573i
$186$	5.80463	+	10.6143i	0.425616	+	0.778279i
$187$	−2.18521	−	3.78489i	−0.159798	−	0.276779i
$188$		−	24.9805i		−	1.82189i
$189$	−11.2784	+	7.86114i	−0.820384	+	0.571814i
$190$	15.8698	−	27.7373i	1.15132	−	2.01228i
$191$	−18.4619	+	10.6590i	−1.33586	+	0.771259i	−0.986191	−	0.165614i	$-0.947039\pi$
$191$	−18.4619	+	10.6590i	−1.33586	+	0.771259i	−0.349669	+	0.936873i	$0.613706\pi$
$192$	5.81077	−	3.17773i	0.419356	−	0.229333i
$193$	−12.0690	−	6.96805i	−0.868747	−	0.501571i	−0.00181508	−	0.999998i	$-0.500578\pi$
$193$	−12.0690	−	6.96805i	−0.868747	−	0.501571i	−0.866932	+	0.498427i	$0.833911\pi$
$194$	10.2670	+	17.7829i	0.737127	+	1.27674i
$195$	−0.675229	−	1.22333i	−0.0483542	−	0.0876045i
$196$	−22.2166	−	20.2039i	−1.58690	−	1.44314i
$197$	−2.01202			−0.143350			−0.0716752	−	0.997428i	$-0.522835\pi$
$197$	−2.01202			−0.143350			−0.0716752	+	0.997428i	$0.522835\pi$
$198$	10.8874	+	6.97733i	0.773735	+	0.495857i
$199$	6.90207	+	3.98491i	0.489275	+	0.282483i	0.724274	−	0.689513i	$-0.242175\pi$
$199$	6.90207	+	3.98491i	0.489275	+	0.282483i	−0.234999	+	0.971996i	$0.575509\pi$
$200$	28.7148	−	0.224612i	2.03044	−	0.0158825i
$201$	4.31308	+	0.0999214i	0.304221	+	0.00704791i
$202$	−3.12728			−0.220035
$203$	7.75124	−	6.24513i	0.544030	−	0.438322i
$204$	−9.82374	+	16.1400i	−0.687799	+	1.13003i
$205$	0.0230418	+	5.89147i	0.00160931	+	0.411478i
$206$	−5.19908	+	9.00507i	−0.362237	+	0.627413i
$207$	−7.51586	−	0.348428i	−0.522388	−	0.0242174i
$208$	1.05055	+	1.81961i	0.0728428	+	0.126168i
$209$	9.79371			0.677445
$210$	−25.4641	+	3.46784i	−1.75719	+	0.239303i
$211$	−4.95390			−0.341041			−0.170520	−	0.985354i	$-0.554545\pi$
$211$	−4.95390			−0.341041			−0.170520	+	0.985354i	$0.554545\pi$
$212$	3.11954	+	5.40321i	0.214251	+	0.371094i
$213$	−10.9524	−	20.0275i	−0.750447	−	1.37226i
$214$	−1.38882	+	2.40551i	−0.0949379	+	0.164437i
$215$	−22.4960	+	0.0879828i	−1.53422	+	0.00600038i
$216$	2.07203	−	29.7701i	0.140984	−	2.02560i
$217$	−1.13465	−	7.28050i	−0.0770254	−	0.494232i
$218$	22.8569			1.54806
$219$	0.467097	−	20.1621i	0.0315635	−	1.36243i
$220$	8.29915	+	14.2456i	0.559529	+	0.960437i
$221$	0.794515	+	0.458713i	0.0534449	+	0.0308564i
$222$	−14.3558	−	0.332581i	−0.963495	−	0.0223213i
$223$	15.6534			1.04823			0.524114	−	0.851648i	$-0.324397\pi$
$223$	15.6534			1.04823			0.524114	+	0.851648i	$0.324397\pi$
$224$	8.15509	−	1.27096i	0.544885	−	0.0849195i
$225$	−7.99450	+	12.6920i	−0.532966	+	0.846136i
$226$	4.75615	+	8.23790i	0.316374	+	0.547977i
$227$	−10.9223	−	6.30600i	−0.724939	−	0.418544i	0.0916289	−	0.995793i	$-0.470793\pi$
$227$	−10.9223	−	6.30600i	−0.724939	−	0.418544i	−0.816568	+	0.577250i	$0.804126\pi$
$228$	−20.3156	−	37.1489i	−1.34543	−	2.46025i
$229$	−5.18951	+	2.99617i	−0.342933	+	0.197992i	−0.661568	−	0.749885i	$-0.730109\pi$
$229$	−5.18951	+	2.99617i	−0.342933	+	0.197992i	0.318636	+	0.947877i	$0.396775\pi$
$230$	−12.2078	−	6.98468i	−0.804961	−	0.460556i
$231$	−4.79802	−	6.24588i	−0.315686	−	0.410949i
$232$			21.6073i			1.41859i
$233$	10.9016	+	18.8822i	0.714190	+	1.23701i	0.963271	+	0.268531i	$0.0865381\pi$
$233$	10.9016	+	18.8822i	0.714190	+	1.23701i	−0.249081	+	0.968483i	$0.580129\pi$
$234$	−2.71160	−	0.125707i	−0.177263	−	0.00821772i
$235$	6.55441	+	11.2507i	0.427563	+	0.733916i
$236$	−14.7114	−	25.4809i	−0.957632	−	1.65867i
$237$	−20.5210	−	12.4903i	−1.33298	−	0.811330i
$238$	13.1392	−	10.5862i	0.851686	−	0.686199i
$239$		−	24.9069i		−	1.61109i	−0.592533	−	0.805546i	$-0.701872\pi$
$239$		−	24.9069i		−	1.61109i	0.592533	−	0.805546i	$-0.298128\pi$
$240$	11.6516	−	19.3127i	0.752105	−	1.24663i
$241$	14.7454	+	8.51326i	0.949835	+	0.548388i	0.893030	−	0.449998i	$-0.148575\pi$
$241$	14.7454	+	8.51326i	0.949835	+	0.548388i	0.0568054	+	0.998385i	$0.481909\pi$
$242$	10.0897	−	17.4759i	0.648591	−	1.12339i
$243$	12.5089	+	9.30202i	0.802446	+	0.596725i
$244$			6.87967i			0.440426i
$245$	15.3070	+	3.27023i	0.977931	+	0.208928i
$246$	9.77670	+	5.95067i	0.623339	+	0.379401i
$247$	−1.78044	+	1.02794i	−0.113286	+	0.0654060i
$248$	13.8517	+	7.99727i	0.879582	+	0.507827i
$249$	2.91223	+	5.32529i	0.184555	+	0.337476i
$250$	−24.1172	+	14.3040i	−1.52531	+	0.904662i
$251$	27.3925			1.72900			0.864501	−	0.502631i	$-0.167635\pi$
$251$	27.3925			1.72900			0.864501	+	0.502631i	$0.167635\pi$
$252$	−13.7387	+	31.1557i	−0.865459	+	1.96262i
$253$		−	4.31044i		−	0.270995i
$254$	13.0024	−	7.50691i	0.815840	−	0.471026i
$255$	0.189591	−	9.84668i	0.0118726	−	0.616623i
$256$	16.0256	−	27.7571i	1.00160	−	1.73482i
$257$	26.3170	−	15.1941i	1.64161	−	0.947783i	0.661347	−	0.750080i	$-0.269985\pi$
$257$	26.3170	−	15.1941i	1.64161	−	0.947783i	0.980262	−	0.197703i	$-0.0633482\pi$
$258$	−22.7221	+	37.3314i	−1.41461	+	2.32415i
$259$	8.15728	+	3.15447i	0.506868	+	0.196009i
$260$	−3.00393	−	1.71869i	−0.186296	−	0.106589i
$261$	−9.50287	−	6.09003i	−0.588213	−	0.376963i
$262$	−18.2835	+	31.6679i	−1.12956	+	1.95645i
$263$	−9.66832	+	16.7460i	−0.596174	+	1.03260i	0.397206	+	0.917729i	$0.369980\pi$
$263$	−9.66832	+	16.7460i	−0.596174	+	1.03260i	−0.993380	+	0.114874i	$0.963354\pi$
$264$	17.0919	+	0.395969i	1.05193	+	0.0243702i
$265$	−2.82268	−	1.61499i	−0.173396	−	0.0992078i
$266$	5.82255	+	37.3603i	0.357003	+	2.29071i
$267$	18.0620	+	10.9936i	1.10538	+	0.672796i
$268$	9.25392	−	5.34275i	0.565273	−	0.326361i
$269$	−11.0008	+	19.0539i	−0.670729	+	1.16174i	0.306969	+	0.951720i	$0.400685\pi$
$269$	−11.0008	+	19.0539i	−0.670729	+	1.16174i	−0.977698	+	0.210017i	$0.932648\pi$
$270$	12.8850	+	26.1366i	0.784154	+	1.59062i
$271$	−13.0404	+	7.52886i	−0.792146	+	0.457345i	−0.840717	−	0.541474i	$-0.817866\pi$
$271$	−13.0404	+	7.52886i	−0.792146	+	0.457345i	0.0485718	+	0.998820i	$0.484533\pi$
$272$			14.8090i			0.897929i
$273$	1.52781	+	0.631869i	0.0924672	+	0.0382425i
$274$	39.4086			2.38076
$275$	−7.47554	−	4.23839i	−0.450792	−	0.255584i
$276$	−16.3501	+	8.94135i	−0.984160	+	0.538206i
$277$	−1.45145	−	0.837995i	−0.0872092	−	0.0503502i	0.455761	−	0.890102i	$-0.349367\pi$
$277$	−1.45145	−	0.837995i	−0.0872092	−	0.0503502i	−0.542970	+	0.839752i	$0.682700\pi$
$278$	31.9984	−	18.4743i	1.91914	−	1.10801i
$279$	−7.42130	+	3.83792i	−0.444302	+	0.229770i
$280$	−26.3742	+	21.4202i	−1.57616	+	1.28010i
$281$		−	2.10086i		−	0.125327i	−0.998035	−	0.0626633i	$-0.980041\pi$
$281$		−	2.10086i		−	0.125327i	0.998035	−	0.0626633i	$-0.0199594\pi$
$282$	25.2882	+	0.585852i	1.50589	+	0.0348870i
$283$	2.50200	−	4.33360i	0.148729	−	0.257606i	−0.782029	−	0.623242i	$-0.785815\pi$
$283$	2.50200	−	4.33360i	0.148729	−	0.257606i	0.930758	+	0.365636i	$0.119149\pi$
$284$	−48.9625	−	28.2685i	−2.90539	−	1.67743i
$285$	18.8969	+	11.4007i	1.11935	+	0.675319i
$286$		−	1.55514i		−	0.0919571i
$287$	−4.37353	−	5.42827i	−0.258161	−	0.320421i
$288$	−4.29897	−	8.31281i	−0.253319	−	0.489837i
$289$	−5.26690	−	9.12253i	−0.309817	−	0.536620i
$290$	−10.6208	−	18.2308i	−0.623677	−	1.07055i
$291$	−12.4421	+	6.80421i	−0.729371	+	0.398870i
$292$	−24.9755	−	43.2588i	−1.46158	−	2.53153i
$293$		−	17.2734i		−	1.00912i	−0.863376	−	0.504561i	$-0.831654\pi$
$293$		−	17.2734i		−	1.00912i	0.863376	−	0.504561i	$-0.168346\pi$
$294$	20.9738	−	22.0164i	1.22322	−	1.28402i
$295$	13.3114	+	7.61610i	0.775022	+	0.443427i
$296$	−16.4414	+	9.49242i	−0.955634	+	0.551736i
$297$	−4.99152	+	7.40541i	−0.289637	+	0.429706i
$298$	27.5897	+	15.9289i	1.59823	+	0.922737i
$299$	0.452418	+	0.783611i	0.0261640	+	0.0453174i
$300$	−0.569922	+	37.1476i	−0.0329045	+	2.14472i
$301$	20.7274	−	16.6999i	1.19471	−	0.962568i
$302$	−41.8671			−2.40918
$303$	0.0500217	−	2.15917i	0.00287367	−	0.124041i
$304$	−28.7397	−	16.5929i	−1.64833	−	0.951666i
$305$	−1.80509	−	3.09846i	−0.103359	−	0.177417i
$306$	−16.1084	−	10.3232i	−0.920854	−	0.590140i
$307$	10.2324			0.583994			0.291997	−	0.956419i	$-0.405680\pi$
$307$	10.2324			0.583994			0.291997	+	0.956419i	$0.405680\pi$
$308$	−18.1943	−	7.03587i	−1.03672	−	0.400906i
$309$	−6.13423	−	3.73365i	−0.348964	−	0.212400i
$310$	−15.6181	+	0.0610830i	−0.887049	+	0.00346928i
$311$	5.23895	−	9.07413i	0.297074	−	0.514547i	−0.678391	−	0.734701i	$-0.737323\pi$
$311$	5.23895	−	9.07413i	0.297074	−	0.514547i	0.975465	+	0.220154i	$0.0706559\pi$
$312$	−3.14877	+	1.72196i	−0.178264	+	0.0974868i
$313$	0.128088	+	0.221855i	0.00723997	+	0.0125400i	0.869623	−	0.493717i	$-0.164362\pi$
$313$	0.128088	+	0.221855i	0.00723997	+	0.0125400i	−0.862383	+	0.506257i	$0.831029\pi$
$314$	3.61935			0.204252
$315$	−1.98700	−	17.6367i	−0.111955	−	0.993713i
$316$	−59.5008			−3.34718
$317$	15.4693	+	26.7935i	0.868840	+	1.50487i	0.863183	+	0.504890i	$0.168467\pi$
$317$	15.4693	+	26.7935i	0.868840	+	1.50487i	0.00565618	+	0.999984i	$0.498200\pi$
$318$	−5.54291	+	3.03124i	−0.310831	+	0.169984i
$319$	3.23310	−	5.59990i	0.181019	−	0.313534i
$320$	0.0334396	+	8.55007i	0.00186933	+	0.477964i
$321$	−1.63862	−	0.997363i	−0.0914591	−	0.0556674i
$322$	16.4431	−	2.56264i	0.916340	−	0.142810i
$323$	−14.4902			−0.806256
$324$	38.4439	+	3.57212i	2.13577	+	0.198451i
$325$	1.80386	−	0.0141102i	0.100060	−	0.000782691i
$326$	−36.6235	−	21.1446i	−2.02839	−	1.17109i
$327$	−0.365602	+	15.7811i	−0.0202179	+	0.872698i
$328$	15.1318			0.835514
$329$	−14.3693	−	5.55671i	−0.792207	−	0.306351i
$330$	−14.6157	+	8.06726i	−0.804566	+	0.444088i
$331$	4.18951	+	7.25645i	0.230276	+	0.398850i	0.957889	−	0.287137i	$-0.0927036\pi$
$331$	4.18951	+	7.25645i	0.230276	+	0.398850i	−0.727613	+	0.685988i	$0.759370\pi$
$332$	13.0191	+	7.51657i	0.714515	+	0.412525i
$333$	0.459248	−	9.90635i	0.0251666	−	0.542865i
$334$	−15.6573	+	9.03973i	−0.856728	+	0.494632i
$335$	−2.76594	+	4.83432i	−0.151120	+	0.264127i
$336$	3.49779	+	26.4575i	0.190820	+	1.44338i
$337$		−	11.7454i		−	0.639810i	−0.947450	−	0.319905i	$-0.896349\pi$
$337$		−	11.7454i		−	0.639810i	0.947450	−	0.319905i	$-0.103651\pi$
$338$	−16.1386	−	27.9529i	−0.877825	−	1.52044i
$339$	−5.76378	+	3.15203i	−0.313046	+	0.171195i
$340$	−12.2789	−	21.0769i	−0.665918	−	1.14306i
$341$	−2.39327	−	4.14526i	−0.129603	−	0.224478i
$342$	38.0829	−	19.6945i	2.05929	−	1.06496i
$343$	−16.5636	+	8.28527i	−0.894353	+	0.447363i
$344$			57.7794i			3.11526i
$345$	5.01771	−	8.31695i	0.270145	−	0.447770i
$346$	−19.5173	−	11.2683i	−1.04926	−	0.605789i
$347$	0.221030	−	0.382835i	0.0118655	−	0.0205516i	−0.860032	−	0.510241i	$-0.829556\pi$
$347$	0.221030	−	0.382835i	0.0118655	−	0.0205516i	0.871897	+	0.489689i	$0.162890\pi$
$348$	−27.9478	−	0.647468i	−1.49816	−	0.0347079i
$349$			21.7405i			1.16374i	0.813282	+	0.581870i	$0.197679\pi$
$349$			21.7405i			1.16374i	−0.813282	+	0.581870i	$0.802321\pi$
$350$	11.7239	−	31.0369i	0.626670	−	1.65899i
$351$	0.130165	−	1.87016i	0.00694768	−	0.0998219i
$352$	4.64322	−	2.68077i	0.247485	−	0.142885i
$353$	19.7311	+	11.3917i	1.05018	+	0.606321i	0.922700	−	0.385520i	$-0.125978\pi$
$353$	19.7311	+	11.3917i	1.05018	+	0.606321i	0.127480	+	0.991841i	$0.459311\pi$
$354$	26.1398	−	14.2950i	1.38931	−	0.759771i
$355$	29.4688	−	0.115254i	1.56404	−	0.00611703i
$356$	52.3709			2.77565
$357$	7.09885	+	9.24103i	0.375711	+	0.489087i
$358$			27.4923i			1.45301i
$359$	−21.6706	+	12.5115i	−1.14373	+	0.660333i	−0.947351	−	0.320195i	$-0.896251\pi$
$359$	−21.6706	+	12.5115i	−1.14373	+	0.660333i	−0.196378	+	0.980528i	$0.562918\pi$
$360$	32.5178	+	20.6604i	1.71384	+	1.08890i
$361$	6.73561	−	11.6664i	0.354506	−	0.614022i
$362$	11.7136	−	6.76283i	0.615651	−	0.355447i
$363$	11.9045	+	7.24579i	0.624825	+	0.380305i
$364$	4.04610	−	0.630578i	0.212073	−	0.0330513i
$365$	22.5987	+	12.9298i	1.18287	+	0.676777i
$366$	−6.96439	−	0.161344i	−0.364035	−	0.00843361i
$367$	10.6736	−	18.4872i	0.557156	−	0.965023i	−0.440576	−	0.897715i	$-0.645226\pi$
$367$	10.6736	−	18.4872i	0.557156	−	0.965023i	0.997732	−	0.0673073i	$-0.0214408\pi$
$368$	−7.30290	+	12.6490i	−0.380690	+	0.659374i
$369$	−4.26491	+	6.65496i	−0.222022	+	0.346443i
$370$	9.20623	−	16.0907i	0.478609	−	0.836513i
$371$	3.80196	−	0.592529i	0.197388	−	0.0307626i
$372$	−10.7591	+	17.6767i	−0.557832	+	0.916495i
$373$	−12.2411	+	7.06740i	−0.633820	+	0.365936i	−0.782230	−	0.622990i	$-0.785918\pi$
$373$	−12.2411	+	7.06740i	−0.633820	+	0.365936i	0.148410	+	0.988926i	$0.452584\pi$
$374$	5.48045	−	9.49242i	0.283387	−	0.490841i
$375$	−9.49015	−	16.8801i	−0.490069	−	0.871684i
$376$	28.9620	−	16.7212i	1.49360	−	0.862332i
$377$			1.35737i			0.0699081i
$378$	−31.2172	−	14.6386i	−1.60564	−	0.752929i
$379$	−9.53880			−0.489975			−0.244988	−	0.969526i	$-0.578784\pi$
$379$	−9.53880			−0.489975			−0.244988	+	0.969526i	$0.578784\pi$
$380$	54.6616	−	0.213784i	2.80408	−	0.0109669i
$381$	4.97503	+	9.09731i	0.254879	+	0.466069i
$382$	−46.3021	−	26.7325i	−2.36902	−	1.36776i
$383$	−13.6576	+	7.88522i	−0.697870	+	0.402916i	−0.806554	−	0.591161i	$-0.798670\pi$
$383$	−13.6576	+	7.88522i	−0.697870	+	0.402916i	0.108683	+	0.994076i	$0.465337\pi$
$384$	23.4195	+	14.2545i	1.19512	+	0.727422i
$385$	10.0404	−	1.60503i	0.511708	−	0.0818001i
$386$		−	34.9514i		−	1.77898i
$387$	−25.4113	−	16.2852i	−1.29173	−	0.827822i
$388$	−17.5619	+	30.4181i	−0.891570	+	1.54424i
$389$	29.5749	+	17.0751i	1.49951	+	0.865740i	1.00000		0.000570006i	$-0.000181439\pi$
$389$	29.5749	+	17.0751i	1.49951	+	0.865740i	0.499506	+	0.866310i	$0.333515\pi$
$390$	1.81031	−	3.00062i	0.0916685	−	0.151942i
$391$			6.37747i			0.322522i
$392$	8.55298	−	39.2815i	0.431991	−	1.98402i
$393$	−21.5721	−	13.1300i	−1.08817	−	0.662322i
$394$	−2.52305	−	4.37005i	−0.127109	−	0.220160i
$395$	26.7980	−	15.6119i	1.34835	−	0.785519i
$396$	−1.02433	+	22.0956i	−0.0514744	+	1.11034i
$397$	−2.14122	−	3.70870i	−0.107465	−	0.186134i	0.807278	−	0.590172i	$-0.200940\pi$
$397$	−2.14122	−	3.70870i	−0.107465	−	0.186134i	−0.914743	+	0.404037i	$0.867607\pi$
$398$			19.9881i			1.00191i
$399$	−25.8879	+	3.42248i	−1.29601	+	0.171338i
$400$	14.7562	+	25.1029i	0.737808	+	1.25514i
$401$	−10.8316	+	6.25361i	−0.540903	+	0.312290i	−0.745445	−	0.666568i	$-0.767763\pi$
$401$	−10.8316	+	6.25361i	−0.540903	+	0.312290i	0.204542	+	0.978858i	$0.434429\pi$
$402$	5.19152	+	9.49319i	0.258930	+	0.473477i
$403$	0.870163	+	0.502389i	0.0433459	+	0.0250258i
$404$	−2.67464	−	4.63261i	−0.133068	−	0.230481i
$405$	−18.2516	+	8.47813i	−0.906930	+	0.421282i
$406$	23.2842	+	9.00415i	1.15558	+	0.446868i
$407$	5.68142			0.281617
$408$	−25.2882	−	0.585852i	−1.25195	−	0.0290040i
$409$	5.59219	+	3.22865i	0.276516	+	0.159647i	0.631845	−	0.775095i	$-0.282298\pi$
$409$	5.59219	+	3.22865i	0.276516	+	0.159647i	−0.355329	+	0.934741i	$0.615631\pi$
$410$	−12.7672	+	7.43788i	−0.630528	+	0.367331i
$411$	−0.630352	+	27.2090i	−0.0310930	+	1.34212i
$412$	−17.7863			−0.876267
$413$	−17.9296	+	2.79430i	−0.882258	+	0.137499i
$414$	−8.66802	−	16.7611i	−0.426010	−	0.823766i
$415$	−7.83573	+	0.0306458i	−0.384641	+	0.00150434i
$416$	−0.562740	+	0.974694i	−0.0275906	+	0.0477883i
$417$	12.2434	+	22.3882i	0.599562	+	1.09636i
$418$	12.2812	+	21.2717i	0.600693	+	1.04043i
$419$	−10.0144			−0.489233			−0.244617	−	0.969620i	$-0.578662\pi$
$419$	−10.0144			−0.489233			−0.244617	+	0.969620i	$0.578662\pi$
$420$	−26.9155	−	34.7554i	−1.31334	−	1.69589i
$421$	17.7858			0.866825			0.433413	−	0.901196i	$-0.357309\pi$
$421$	17.7858			0.866825			0.433413	+	0.901196i	$0.357309\pi$
$422$	−6.21214	−	10.7597i	−0.302402	−	0.523776i
$423$	−0.808982	+	17.4504i	−0.0393341	+	0.848467i
$424$	−4.17626	+	7.23350i	−0.202817	+	0.351290i
$425$	11.0604	+	6.27086i	0.536506	+	0.304182i
$426$	29.7649	−	48.9025i	1.44212	−	2.36934i
$427$	3.95733	+	1.53032i	0.191509	+	0.0740576i
$428$	−4.75121			−0.229659
$429$	1.07371	+	0.0248748i	0.0518394	+	0.00120097i
$430$	−28.4009	−	48.7504i	−1.36961	−	2.35095i
$431$	−2.54530	−	1.46953i	−0.122603	−	0.0707847i	0.437444	−	0.899245i	$-0.355884\pi$
$431$	−2.54530	−	1.46953i	−0.122603	−	0.0707847i	−0.560047	+	0.828461i	$0.689217\pi$
$432$	27.1941	−	13.2744i	1.30838	−	0.638664i
$433$	31.6675			1.52184			0.760922	−	0.648843i	$-0.224747\pi$
$433$	31.6675			1.52184			0.760922	+	0.648843i	$0.224747\pi$
$434$	14.3902	−	11.5941i	0.690751	−	0.556534i
$435$	12.7570	−	7.04135i	0.611651	−	0.337607i
$436$	19.5486	+	33.8592i	0.936208	+	1.62156i
$437$	−12.3767	−	7.14567i	−0.592056	−	0.341824i
$438$	44.3773	−	24.2685i	2.12043	−	1.15960i
$439$	−18.6152	+	10.7475i	−0.888457	+	0.512951i	−0.873437	−	0.486936i	$-0.838114\pi$
$439$	−18.6152	+	10.7475i	−0.888457	+	0.512951i	−0.0150195	+	0.999887i	$0.504781\pi$
$440$	−10.9609	+	19.1575i	−0.522541	+	0.913297i
$441$	14.8653	+	14.8331i	0.707873	+	0.706340i
$442$			2.30088i			0.109442i
$443$	−13.1347	−	22.7499i	−0.624048	−	1.08088i	−0.988724	−	0.149748i	$-0.952154\pi$
$443$	−13.1347	−	22.7499i	−0.624048	−	1.08088i	0.364676	−	0.931134i	$-0.381180\pi$
$444$	−11.7852	−	21.5504i	−0.559303	−	1.02274i
$445$	−23.5868	+	13.7411i	−1.11812	+	0.651392i
$446$	19.6291	+	33.9987i	0.929467	+	1.60988i
$447$	−11.4391	+	18.7940i	−0.541052	+	0.888926i
$448$	−6.34714	−	7.87786i	−0.299874	−	0.372194i
$449$			36.0069i			1.69927i	0.527369	+	0.849636i	$0.323179\pi$
$449$			36.0069i			1.69927i	−0.527369	+	0.849636i	$0.676821\pi$
$450$	−37.5918	−	1.44814i	−1.77209	−	0.0682660i
$451$	−3.92167	−	2.26418i	−0.184664	−	0.106616i
$452$	−8.13550	+	14.0911i	−0.382662	+	0.662789i
$453$	0.669675	−	28.9064i	0.0314641	−	1.35814i
$454$		−	31.6306i		−	1.48450i
$455$	−1.65683	+	1.34562i	−0.0776733	+	0.0630835i
$456$	29.4712	−	48.4200i	1.38012	−	2.26747i
$457$	15.8020	−	9.12327i	0.739185	−	0.426768i	−0.0825881	−	0.996584i	$-0.526319\pi$
$457$	15.8020	−	9.12327i	0.739185	−	0.426768i	0.821773	+	0.569815i	$0.192985\pi$
$458$	−13.0152	−	7.51431i	−0.608159	−	0.351121i
$459$	7.38515	−	10.9566i	0.344709	−	0.511410i
$460$	−0.0940911	−	24.0579i	−0.00438702	−	1.12170i
$461$	−22.8072			−1.06224			−0.531119	−	0.847298i	$-0.678228\pi$
$461$	−22.8072			−1.06224			−0.531119	+	0.847298i	$0.678228\pi$
$462$	7.54922	−	18.2534i	0.351221	−	0.849226i
$463$		−	23.3718i		−	1.08618i	−0.839674	−	0.543090i	$-0.817254\pi$
$463$		−	23.3718i		−	1.08618i	0.839674	−	0.543090i	$-0.182746\pi$
$464$	−18.9751	+	10.9553i	−0.880897	+	0.508586i
$465$	0.207642	−	10.7842i	0.00962917	−	0.500106i
$466$	−27.3411	+	47.3561i	−1.26655	+	2.19373i
$467$	−9.43053	+	5.44472i	−0.436393	+	0.251951i	−0.702066	−	0.712112i	$-0.747739\pi$
$467$	−9.43053	+	5.44472i	−0.436393	+	0.251951i	0.265674	+	0.964063i	$0.414406\pi$
$468$	−2.13291	−	4.12435i	−0.0985936	−	0.190648i
$469$	−1.01481	−	6.51150i	−0.0468595	−	0.300673i
$470$	−16.2171	+	28.3443i	−0.748039	+	1.30742i
$471$	−0.0578924	+	2.49891i	−0.00266754	+	0.115144i
$472$	19.6948	−	34.1124i	0.906527	−	1.57015i
$473$	8.64555	−	14.9745i	0.397523	−	0.688530i
$474$	1.39544	−	60.2336i	0.0640945	−	2.76662i
$475$	−24.5624	+	14.4384i	−1.12700	+	0.662481i
$476$	26.9193	+	10.4098i	1.23384	+	0.477135i
$477$	−2.00421	−	3.87549i	−0.0917663	−	0.177446i
$478$	54.0970	−	31.2329i	2.47434	−	1.42856i
$479$	−5.13835	+	8.89989i	−0.234777	+	0.406646i	−0.959208	−	0.282701i	$-0.908769\pi$
$479$	−5.13835	+	8.89989i	−0.234777	+	0.406646i	0.724431	+	0.689348i	$0.242103\pi$
$480$	12.0797	+	0.232586i	0.551360	+	0.0106160i
$481$	−1.03285	+	0.596314i	−0.0470938	+	0.0271896i
$482$			42.7021i			1.94503i
$483$	1.50631	+	11.3939i	0.0685397	+	0.518438i
$484$	34.5173			1.56897
$485$	−0.0716017	−	18.3076i	−0.00325126	−	0.831305i
$486$	−4.51771	+	38.8336i	−0.204928	+	1.76153i
$487$	11.9923	+	6.92377i	0.543424	+	0.313746i	0.746466	−	0.665424i	$-0.231749\pi$
$487$	11.9923	+	6.92377i	0.543424	+	0.313746i	−0.203041	+	0.979170i	$0.565083\pi$
$488$	−7.97618	+	4.60505i	−0.361065	+	0.208461i
$489$	15.1847	−	24.9478i	0.686676	−	1.12818i
$490$	12.0920	+	37.3473i	0.546261	+	1.68718i
$491$		−	13.5981i		−	0.613672i	−0.951762	−	0.306836i	$-0.900730\pi$
$491$		−	13.5981i		−	0.613672i	0.951762	−	0.306836i	$-0.0992704\pi$
$492$	−0.453428	+	19.5721i	−0.0204421	+	0.882379i
$493$	−4.78350	+	8.28527i	−0.215438	+	0.373150i
$494$	−4.46529	−	2.57804i	−0.200903	−	0.115991i
$495$	−5.33611	−	10.2202i	−0.239840	−	0.459362i
$496$			16.2190i			0.728256i
$497$	−27.1520	+	21.8762i	−1.21793	+	0.981281i
$498$	−7.91447	+	13.0031i	−0.354656	+	0.582684i
$499$	−18.1054	−	31.3595i	−0.810511	−	1.40385i	−0.912507	−	0.409061i	$-0.865856\pi$
$499$	−18.1054	−	31.3595i	−0.810511	−	1.40385i	0.101996	−	0.994785i	$-0.467477\pi$
$500$	−41.8157	−	23.4925i	−1.87006	−	1.05062i
$501$	−5.99087	−	10.9549i	−0.267653	−	0.489428i
$502$	34.3499	+	59.4958i	1.53311	+	2.65543i
$503$		−	0.513189i		−	0.0228819i	−0.999935	−	0.0114410i	$-0.996358\pi$
$503$		−	0.513189i		−	0.0228819i	0.999935	−	0.0114410i	$-0.00364185\pi$
$504$	−45.3177	+	4.92622i	−2.01861	+	0.219431i
$505$	2.42011	+	1.38466i	0.107693	+	0.0616165i
$506$	9.36215	−	5.40524i	0.416198	−	0.240292i
$507$	19.5577	−	10.6955i	0.868589	−	0.475004i
$508$	22.2408	+	12.8407i	0.986776	+	0.569715i
$509$	−9.40202	−	16.2848i	−0.416737	−	0.721810i	0.578872	−	0.815419i	$-0.303493\pi$
$509$	−9.40202	−	16.2848i	−0.416737	−	0.721810i	−0.995609	+	0.0936084i	$0.970160\pi$
$510$	21.6245	−	11.9358i	0.957547	−	0.528528i
$511$	−30.4390	+	4.74387i	−1.34654	+	0.209856i
$512$	48.7256			2.15339
$513$	12.9886	+	26.6086i	0.573460	+	1.17480i
$514$	66.0024	+	38.1065i	2.91124	+	1.68081i
$515$	8.01058	−	4.66678i	0.352988	−	0.205643i
$516$	−74.7343	−	1.73137i	−3.29000	−	0.0762195i
$517$	−10.0080			−0.440152
$518$	3.37771	+	21.6730i	0.148408	+	0.952258i
$519$	8.09219	−	13.2951i	0.355208	−	0.583591i
$520$	−0.0181204	−	4.63316i	−0.000794634	−	0.203177i
$521$	15.1847	−	26.3007i	0.665254	−	1.15225i	−0.313963	−	0.949435i	$-0.601657\pi$
$521$	15.1847	−	26.3007i	0.665254	−	1.15225i	0.979216	−	0.202818i	$-0.0650100\pi$
$522$	1.31088	−	28.2768i	0.0573758	−	1.23764i
$523$	−19.5144	−	33.7999i	−0.853305	−	1.47797i	−0.878208	−	0.478278i	$-0.841261\pi$
$523$	−19.5144	−	33.7999i	−0.853305	−	1.47797i	0.0249028	−	0.999690i	$-0.492072\pi$
$524$	−62.5485			−2.73244
$525$	21.2413	+	8.59101i	0.927048	+	0.374943i
$526$	−48.4958			−2.11452
$527$	3.54093	+	6.13308i	0.154246	+	0.267161i
$528$	8.31818	+	15.2106i	0.362002	+	0.661955i
$529$	8.35503	−	14.4713i	0.363262	−	0.629188i
$530$	−0.0318982	−	8.15594i	−0.00138557	−	0.354272i
$531$	9.45162	+	18.2764i	0.410165	+	0.793127i
$532$	−50.3641	+	40.5781i	−2.18356	+	1.75928i
$533$	0.950580			0.0411742
$534$	−1.22822	+	53.0159i	−0.0531504	+	2.29422i
$535$	2.13985	−	1.24663i	0.0925138	−	0.0538964i
$536$	12.3886	+	7.15257i	0.535106	+	0.308944i
$537$	−18.9816	−	0.439747i	−0.819115	−	0.0189765i
$538$	−55.1794			−2.37895
$539$	−8.09436	+	8.90071i	−0.348649	+	0.383381i
$540$	−27.6975	+	41.4408i	−1.19191	+	1.78333i
$541$	5.25615	+	9.10392i	0.225980	+	0.391408i	0.956613	−	0.291362i	$-0.0941084\pi$
$541$	5.25615	+	9.10392i	0.225980	+	0.391408i	−0.730633	+	0.682770i	$0.760775\pi$
$542$	−32.7049	−	18.8822i	−1.40480	−	0.811060i
$543$	4.48191	+	8.19559i	0.192337	+	0.351706i
$544$	−6.86984	+	3.96630i	−0.294542	+	0.170054i
$545$	−17.6883	−	10.1203i	−0.757683	−	0.433506i
$546$	0.543453	+	4.11071i	0.0232577	+	0.175922i
$547$			25.2465i			1.07946i	0.841837	+	0.539731i	$0.181474\pi$
$547$			25.2465i			1.07946i	−0.841837	+	0.539731i	$0.818526\pi$
$548$	33.7046	+	58.3782i	1.43979	+	2.49379i
$549$	0.222795	−	4.80586i	0.00950864	−	0.205109i
$550$	−0.168580	−	21.5515i	−0.00718829	−	0.918961i
$551$	−10.7194	−	18.5666i	−0.456662	−	0.790962i
$552$	−21.3107	−	12.9710i	−0.907045	−	0.552081i
$553$	−13.2355	+	34.2261i	−0.562829	+	1.45544i
$554$		−	4.20334i		−	0.178583i
$555$	10.9622	+	6.61364i	0.465321	+	0.280734i
$556$	54.7339	+	31.6007i	2.32124	+	1.34017i
$557$	−10.1745	+	17.6227i	−0.431106	+	0.746697i	−0.996969	−	0.0778021i	$-0.975210\pi$
$557$	−10.1745	+	17.6227i	−0.431106	+	0.746697i	0.565863	+	0.824499i	$0.308543\pi$
$558$	−17.6421	−	11.3061i	−0.746849	−	0.478627i
$559$			3.62970i			0.153520i
$560$	−32.1830	−	12.3009i	−1.35998	−	0.519808i
$561$	6.46621	+	3.93571i	0.273003	+	0.166166i
$562$	4.56300	−	2.63445i	0.192479	−	0.111128i
$563$	30.8870	+	17.8326i	1.30173	+	0.751555i	0.980701	−	0.195514i	$-0.0626376\pi$
$563$	30.8870	+	17.8326i	1.30173	+	0.751555i	0.321030	+	0.947069i	$0.395971\pi$
$564$	20.7601	+	37.9618i	0.874158	+	1.59848i
$565$	−0.0331693	−	8.48094i	−0.00139544	−	0.356796i
$566$	12.5499			0.527513
$567$	10.6063	−	21.3192i	0.445422	−	0.895321i
$568$		−	75.6885i		−	3.17582i
$569$	21.8018	−	12.5873i	0.913977	−	0.527685i	0.0322687	−	0.999479i	$-0.489727\pi$
$569$	21.8018	−	12.5873i	0.913977	−	0.527685i	0.881709	+	0.471794i	$0.156393\pi$
$570$	−1.06553	+	55.3398i	−0.0446301	+	2.31793i
$571$	−2.49020	+	4.31316i	−0.104212	+	0.180500i	−0.913416	−	0.407028i	$-0.866565\pi$
$571$	−2.49020	+	4.31316i	−0.104212	+	0.180500i	0.809204	+	0.587528i	$0.199899\pi$
$572$	2.30371	−	1.33005i	0.0963228	−	0.0556120i
$573$	19.1976	−	31.5409i	0.801992	−	1.31764i
$574$	6.30570	−	16.3062i	0.263195	−	0.680607i
$575$	6.35469	+	10.8105i	0.265009	+	0.450828i
$576$	−6.18951	+	9.65809i	−0.257896	+	0.402421i
$577$	−10.9662	+	18.9939i	−0.456527	+	0.790728i	−0.998775	−	0.0494908i	$-0.984240\pi$
$577$	−10.9662	+	18.9939i	−0.456527	+	0.790728i	0.542248	+	0.840219i	$0.317573\pi$
$578$	13.2093	−	22.8791i	0.549432	−	0.951645i
$579$	24.1316	+	0.559057i	1.00287	+	0.0232336i
$580$	17.9227	−	31.3253i	0.744199	−	1.30071i
$581$	7.21968	−	5.81685i	0.299523	−	0.241324i
$582$	−30.3808	−	18.4915i	−1.25933	−	0.766499i
$583$	2.16470	−	1.24979i	0.0896528	−	0.0517610i
$584$	33.4357	−	57.9124i	1.38358	−	2.39643i
$585$	2.04277	+	1.29789i	0.0844580	+	0.0536611i
$586$	37.5173	−	21.6606i	1.54983	−	0.894792i
$587$		−	31.8719i		−	1.31549i	−0.753240	−	0.657746i	$-0.771510\pi$
$587$		−	31.8719i		−	1.31549i	0.753240	−	0.657746i	$-0.228490\pi$
$588$	50.5521	+	12.2399i	2.08474	+	0.504764i
$589$	−15.8698			−0.653905
$590$	0.150428	+	38.4626i	0.00619304	+	1.58348i
$591$	3.05758	−	1.67209i	0.125772	−	0.0687807i
$592$	−16.6721	−	9.62566i	−0.685220	−	0.395612i
$593$	28.4985	−	16.4536i	1.17029	−	0.675669i	0.216545	−	0.976273i	$-0.430521\pi$
$593$	28.4985	−	16.4536i	1.17029	−	0.675669i	0.953749	+	0.300603i	$0.0971880\pi$
$594$	−22.3436	−	1.55514i	−0.916771	−	0.0638080i
$595$	−14.8552	+	2.37471i	−0.609005	+	0.0973537i
$596$			54.4935i			2.23214i
$597$	−13.8004	−	0.319716i	−0.564814	−	0.0130851i
$598$	−1.13465	+	1.96528i	−0.0463995	+	0.0803662i
$599$	18.8935	+	10.9082i	0.771968	+	0.445696i	0.833576	−	0.552404i	$-0.186290\pi$
$599$	18.8935	+	10.9082i	0.771968	+	0.445696i	−0.0616082	+	0.998100i	$0.519623\pi$
$600$	−43.4499	+	24.2048i	−1.77383	+	0.988156i
$601$		−	23.9262i		−	0.975969i	−0.872852	−	0.487985i	$-0.837732\pi$
$601$		−	23.9262i		−	0.975969i	0.872852	−	0.487985i	$-0.162268\pi$
$602$	62.2636	+	24.0777i	2.53768	+	0.981335i
$603$	−6.63744	+	3.43255i	−0.270297	+	0.139784i
$604$	−35.8073	−	62.0200i	−1.45698	−	2.52356i
$605$	−15.5459	+	9.05668i	−0.632031	+	0.368206i
$606$	4.75239	−	2.59893i	0.193053	−	0.105574i
$607$	22.1491	+	38.3634i	0.899005	+	1.55712i	0.828769	+	0.559591i	$0.189042\pi$
$607$	22.1491	+	38.3634i	0.899005	+	1.55712i	0.0702358	+	0.997530i	$0.477625\pi$
$608$		−	17.7763i		−	0.720922i
$609$	−6.58919	+	15.9321i	−0.267007	+	0.645603i
$610$	4.46621	−	7.80604i	0.180831	−	0.316057i
$611$	1.81940	−	1.05043i	0.0736049	−	0.0424958i
$612$	1.51553	−	32.6913i	0.0612618	−	1.32147i
$613$	6.96484	+	4.02115i	0.281307	+	0.162413i	0.634015	−	0.773321i	$-0.281406\pi$
$613$	6.96484	+	4.02115i	0.281307	+	0.162413i	−0.352708	+	0.935733i	$0.614739\pi$
$614$	12.8313	+	22.2245i	0.517829	+	0.896907i
$615$	−4.93113	−	8.93386i	−0.198842	−	0.360248i
$616$	−4.02149	−	25.8038i	−0.162030	−	1.03967i
$617$	−13.1311			−0.528637			−0.264318	−	0.964435i	$-0.585147\pi$
$617$	−13.1311			−0.528637			−0.264318	+	0.964435i	$0.585147\pi$
$618$	0.417130	−	18.0053i	0.0167794	−	0.724280i
$619$	−21.7909	−	12.5810i	−0.875850	−	0.505672i	−0.00656210	−	0.999978i	$-0.502089\pi$
$619$	−21.7909	−	12.5810i	−0.875850	−	0.505672i	−0.869288	+	0.494306i	$0.835422\pi$
$620$	−13.4480	−	23.0837i	−0.540086	−	0.927064i
$621$	11.7111	−	5.71658i	0.469949	−	0.229398i
$622$	26.2783			1.05367
$623$	11.6495	−	30.1249i	0.466727	−	1.20693i
$624$	−3.10867	−	1.89212i	−0.124447	−	0.0757455i
$625$	24.9969	−	0.391086i	0.999878	−	0.0156434i
$626$	−0.321242	+	0.556407i	−0.0128394	+	0.0222385i
$627$	−14.8831	+	8.13908i	−0.594373	+	0.325044i
$628$	3.09548	+	5.36153i	0.123523	+	0.213948i
$629$	−8.40588			−0.335164
$630$	35.8146	−	26.4319i	1.42689	−	1.05307i
$631$	−9.42011			−0.375009			−0.187504	−	0.982264i	$-0.560040\pi$
$631$	−9.42011			−0.375009			−0.187504	+	0.982264i	$0.560040\pi$
$632$	−39.8281	−	68.9843i	−1.58428	−	2.74405i
$633$	7.52823	−	4.11695i	0.299220	−	0.163634i
$634$	−38.7965	+	67.1975i	−1.54081	+	2.66875i
$635$	−13.3860	+	0.0523530i	−0.531206	+	0.00207756i
$636$	−9.23097	−	5.61851i	−0.366032	−	0.222788i
$637$	0.537299	−	2.46767i	0.0212885	−	0.0977725i
$638$	16.2171			0.642041
$639$	33.2878	+	21.3329i	1.31684	+	0.843915i
$640$	−30.5831	+	17.8170i	−1.20890	+	0.704280i
$641$	−4.25254	−	2.45520i	−0.167965	−	0.0969747i	0.413661	−	0.910431i	$-0.364250\pi$
$641$	−4.25254	−	2.45520i	−0.167965	−	0.0969747i	−0.581626	+	0.813456i	$0.697583\pi$
$642$	0.111427	−	4.80973i	0.00439768	−	0.189825i
$643$	−8.98926			−0.354502			−0.177251	−	0.984166i	$-0.556720\pi$
$643$	−8.98926			−0.354502			−0.177251	+	0.984166i	$0.556720\pi$
$644$	17.8593	+	22.1664i	0.703756	+	0.873478i
$645$	34.1131	−	18.8291i	1.34320	−	0.741394i
$646$	−18.1705	−	31.4723i	−0.714910	−	1.23826i
$647$	−0.206934	−	0.119473i	−0.00813542	−	0.00469699i	0.495927	−	0.868364i	$-0.334828\pi$
$647$	−0.206934	−	0.119473i	−0.00813542	−	0.00469699i	−0.504062	+	0.863667i	$0.668162\pi$
$648$	21.5918	+	46.9623i	0.848205	+	1.84485i
$649$	−10.2085	+	5.89388i	−0.400719	+	0.231355i
$650$	2.29267	+	3.90024i	0.0899259	+	0.152980i
$651$	7.77475	+	10.1209i	0.304717	+	0.396669i
$652$		−	72.3365i		−	2.83292i
$653$	−0.979061	−	1.69578i	−0.0383136	−	0.0663611i	0.846233	−	0.532813i	$-0.178865\pi$
$653$	−0.979061	−	1.69578i	−0.0383136	−	0.0663611i	−0.884546	+	0.466452i	$0.845532\pi$
$654$	−34.7346	+	18.9953i	−1.35823	+	0.742774i
$655$	28.1706	−	16.4115i	1.10071	−	0.641251i
$656$	7.67209	+	13.2885i	0.299545	+	0.518827i
$657$	16.0459	+	31.0277i	0.626012	+	1.21050i
$658$	−5.94996	−	38.1778i	−0.231953	−	1.48833i
$659$		−	31.6741i		−	1.23385i	−0.787023	−	0.616924i	$-0.788379\pi$
$659$		−	31.6741i		−	1.23385i	0.787023	−	0.616924i	$-0.211621\pi$
$660$	−24.4507	−	14.7514i	−0.951741	−	0.574196i
$661$	−24.8549	−	14.3500i	−0.966744	−	0.558150i	−0.0685020	−	0.997651i	$-0.521822\pi$
$661$	−24.8549	−	14.3500i	−0.966744	−	0.558150i	−0.898242	+	0.439501i	$0.855155\pi$
$662$	−10.5072	+	18.1990i	−0.408374	+	0.707324i
$663$	−1.58860	−	0.0368033i	−0.0616963	−	0.00142932i
$664$			20.1255i			0.781020i
$665$	12.0361	−	31.4901i	0.466738	−	1.22113i
$666$	22.0922	−	11.4250i	0.856055	−	0.442709i
$667$	−8.17157	+	4.71786i	−0.316404	+	0.182676i
$668$	−26.7821	−	15.4626i	−1.03623	−	0.598268i
$669$	−23.7877	+	13.0088i	−0.919687	+	0.502948i
$670$	−13.9685	+	0.0546311i	−0.539649	+	0.00211059i
$671$	2.75622			0.106403
$672$	−11.3367	+	8.70872i	−0.437322	+	0.335946i
$673$			33.9688i			1.30940i	0.755889	+	0.654700i	$0.227205\pi$
$673$			33.9688i			1.30940i	−0.755889	+	0.654700i	$0.772795\pi$
$674$	25.5106	−	14.7285i	0.982631	−	0.567322i
$675$	1.60113	−	25.9314i	0.0616276	−	0.998099i
$676$	27.6054	−	47.8140i	1.06175	−	1.83900i
$677$	−6.22623	+	3.59472i	−0.239294	+	0.138156i	−0.614852	−	0.788643i	$-0.710784\pi$
$677$	−6.22623	+	3.59472i	−0.239294	+	0.138156i	0.375558	+	0.926799i	$0.377451\pi$
$678$	−14.0738	−	8.56616i	−0.540502	−	0.328981i
$679$	13.5906	+	16.8682i	0.521561	+	0.647343i
$680$	16.2171	−	28.3443i	0.621897	−	1.08695i
$681$	21.8388	+	0.505940i	0.836863	+	0.0193876i
$682$	6.00226	−	10.3962i	0.229838	−	0.398092i
$683$	−4.02013	+	6.96307i	−0.153826	+	0.266435i	−0.932631	−	0.360832i	$-0.882493\pi$
$683$	−4.02013	+	6.96307i	−0.153826	+	0.266435i	0.778805	+	0.627266i	$0.215826\pi$
$684$	61.7454	+	39.5703i	2.36089	+	1.51301i
$685$	−30.4972	−	17.4489i	−1.16524	−	0.666688i
$686$	−38.7660	−	25.5861i	−1.48009	−	0.976883i
$687$	5.39630	−	8.86589i	0.205882	−	0.338255i
$688$	−50.7407	+	29.2952i	−1.93447	+	1.11687i
$689$	−0.262353	+	0.454409i	−0.00999485	+	0.0173116i
$690$	24.3563	+	0.468964i	0.927230	+	0.0178531i
$691$	38.3278	−	22.1286i	1.45806	−	0.841810i	0.459142	−	0.888363i	$-0.348157\pi$
$691$	38.3278	−	22.1286i	1.45806	−	0.841810i	0.998916	+	0.0465523i	$0.0148234\pi$
$692$		−	38.5494i		−	1.46543i
$693$	12.4820	+	5.50419i	0.474151	+	0.209087i
$694$	1.10867			0.0420847
$695$	−32.9425	+	0.128839i	−1.24958	+	0.00488715i
$696$	−17.9568	−	32.8356i	−0.680649	−	1.24463i
$697$	5.80226	+	3.34994i	0.219776	+	0.126888i
$698$	−47.2197	+	27.2623i	−1.78729	+	1.03189i
$699$	−32.2588	−	19.6346i	−1.22014	−	0.742649i
$700$	56.0037	−	9.17735i	2.11674	−	0.346871i
$701$			0.779307i			0.0294340i	0.999892	+	0.0147170i	$0.00468474\pi$
$701$			0.779307i			0.0294340i	−0.999892	+	0.0147170i	$0.995315\pi$
$702$	4.22516	−	2.06245i	0.159468	−	0.0778420i
$703$	9.41841	−	16.3132i	0.355222	−	0.615263i
$704$	−5.69137	−	3.28592i	−0.214502	−	0.123843i
$705$	−19.3104	−	11.6502i	−0.727271	−	0.438771i
$706$			57.1404i			2.15051i
$707$	−3.25973	+	0.508023i	−0.122595	+	0.0191062i
$708$	43.5323	+	26.4963i	1.63604	+	0.995792i
$709$	4.63267	+	8.02402i	0.173984	+	0.301348i	0.939809	−	0.341700i	$-0.111003\pi$
$709$	4.63267	+	8.02402i	0.173984	+	0.301348i	−0.765825	+	0.643048i	$0.777669\pi$
$710$	37.2039	+	63.8610i	1.39624	+	2.39666i
$711$	41.5649	+	1.92691i	1.55880	+	0.0722646i
$712$	35.0556	+	60.7181i	1.31376	+	2.27551i
$713$			6.98468i			0.261578i
$714$	−11.1694	+	27.0066i	−0.418003	+	1.01070i
$715$	−0.688564	+	1.20347i	−0.0257508	+	0.0450074i
$716$	−40.7259	+	23.5131i	−1.52200	+	0.878725i
$717$	20.6989	+	37.8499i	0.773015	+	1.41353i
$718$	−54.3493	−	31.3786i	−2.02830	−	1.17104i
$719$	9.09980	+	15.7613i	0.339365	+	0.587798i	0.984313	−	0.176428i	$-0.0564544\pi$
$719$	9.09980	+	15.7613i	0.339365	+	0.587798i	−0.644948	+	0.764226i	$0.723121\pi$
$720$	−1.65652	+	39.0317i	−0.0617347	+	1.45463i
$721$	−3.95641	+	10.2310i	−0.147344	+	0.381024i
$722$	33.7855			1.25737
$723$	−29.4829	−	0.683032i	−1.09648	−	0.0254022i
$724$	20.0363	+	11.5680i	0.744643	+	0.429920i
$725$	0.147142	+	18.8108i	0.00546472	+	0.698617i
$726$	−0.809513	+	34.9424i	−0.0300438	+	1.29683i
$727$	−31.6357			−1.17330			−0.586652	−	0.809839i	$-0.699554\pi$
$727$	−31.6357			−1.17330			−0.586652	+	0.809839i	$0.699554\pi$
$728$	3.43942	+	4.26889i	0.127473	+	0.158216i
$729$	−26.7397	−	3.74032i	−0.990358	−	0.138531i
$730$	0.255381	+	65.2976i	0.00945209	+	2.41677i
$731$	−12.7914	+	22.1554i	−0.473108	+	0.819447i
$732$	−5.71736	−	10.4547i	−0.211320	−	0.386418i
$733$	8.50426	+	14.7298i	0.314112	+	0.544058i	0.979248	−	0.202664i	$-0.0649599\pi$
$733$	8.50426	+	14.7298i	0.314112	+	0.544058i	−0.665136	+	0.746722i	$0.731627\pi$
$734$	53.5381			1.97613
$735$	−25.9792	+	7.75132i	−0.958256	+	0.285912i
$736$	−7.82374			−0.288387
$737$	−2.14048	−	3.70742i	−0.0788457	−	0.136565i
$738$	−19.8025	−	0.918025i	−0.728941	−	0.0337930i
$739$	9.49020	−	16.4375i	0.349103	−	0.604664i	−0.636988	−	0.770874i	$-0.719820\pi$
$739$	9.49020	−	16.4375i	0.349103	−	0.604664i	0.986090	+	0.166210i	$0.0531531\pi$
$740$	31.7097	−	0.124018i	1.16567	−	0.00455898i
$741$	1.85138	−	3.04174i	0.0680123	−	0.111741i
$742$	6.05456	+	7.51471i	0.222270	+	0.275874i
$743$	3.80063			0.139432			0.0697159	−	0.997567i	$-0.477791\pi$
$743$	3.80063			0.139432			0.0697159	+	0.997567i	$0.477791\pi$
$744$	−27.6959	−	0.641633i	−1.01538	−	0.0235234i
$745$	−14.2980	−	24.5427i	−0.523840	−	0.899177i
$746$	−30.7004	−	17.7249i	−1.12402	−	0.648953i
$747$	−8.85118	−	5.67239i	−0.323848	−	0.207542i
$748$	18.7489			0.685526
$749$	−1.05687	+	2.73300i	−0.0386171	+	0.0998616i
$750$	24.7625	−	41.7797i	0.904199	−	1.52558i
$751$	6.32279	+	10.9514i	0.230722	+	0.399622i	0.958021	−	0.286699i	$-0.0925579\pi$
$751$	6.32279	+	10.9514i	0.230722	+	0.399622i	−0.727299	+	0.686321i	$0.759225\pi$
$752$	29.3685	+	16.9559i	1.07096	+	0.618319i
$753$	−41.6272	+	22.7646i	−1.51698	+	0.829589i
$754$	−2.94817	+	1.70213i	−0.107366	+	0.0619878i
$755$	32.3997	+	18.5374i	1.17915	+	0.674645i
$756$	−5.01383	−	58.7635i	−0.182351	−	2.13721i
$757$		−	6.50118i		−	0.236289i	−0.992996	−	0.118145i	$-0.962305\pi$
$757$		−	6.50118i		−	0.236289i	0.992996	−	0.118145i	$-0.0376947\pi$
$758$	−11.9615	−	20.7180i	−0.434463	−	0.752512i
$759$	3.58220	+	6.55038i	0.130026	+	0.237764i
$760$	36.8368	+	63.2307i	1.33621	+	2.29362i
$761$	−21.8912	−	37.9167i	−0.793556	−	1.37448i	−0.923752	−	0.382992i	$-0.874894\pi$
$761$	−21.8912	−	37.9167i	−0.793556	−	1.37448i	0.130195	−	0.991488i	$-0.458440\pi$
$762$	−13.5205	+	22.2135i	−0.489795	+	0.804712i
$763$	23.8249	−	3.71308i	0.862521	−	0.134423i
$764$		−	91.4531i		−	3.30866i
$765$	7.89499	+	15.1211i	0.285444	+	0.546705i
$766$	−34.2529	−	19.7759i	−1.23761	−	0.714533i
$767$	1.23723	−	2.14294i	0.0446737	−	0.0773771i
$768$	−1.28575	+	55.4993i	−0.0463957	+	2.00266i
$769$			33.3141i			1.20134i	0.799498	+	0.600668i	$0.205099\pi$
$769$			33.3141i			1.20134i	−0.799498	+	0.600668i	$0.794901\pi$
$770$	16.0767	+	19.7949i	0.579363	+	0.713357i
$771$	−27.3657	+	44.9606i	−0.985550	+	1.61922i
$772$	51.7754	−	29.8925i	1.86344	−	1.07586i
$773$	−36.6610	−	21.1662i	−1.31860	−	0.761296i	−0.335099	−	0.942183i	$-0.608770\pi$
$773$	−36.6610	−	21.1662i	−1.31860	−	0.761296i	−0.983504	+	0.180887i	$0.942103\pi$
$774$	3.50539	−	75.6141i	0.125999	−	2.71789i
$775$	12.1134	+	6.86793i	0.435128	+	0.246703i
$776$	−47.0217			−1.68798
$777$	−15.0178	+	1.98541i	−0.538760	+	0.0712262i
$778$			85.6477i			3.07062i
$779$	−13.0024	+	7.50691i	−0.465858	+	0.268963i
$780$	5.99327	+	0.115396i	0.214593	+	0.00413184i
$781$	−11.3253	+	19.6160i	−0.405251	+	0.701915i
$782$	−13.8517	+	7.99727i	−0.495335	+	0.285982i
$783$	19.5022	+	1.35737i	0.696952	+	0.0485084i
$784$	38.8328	−	12.4054i	1.38689	−	0.443049i
$785$	−2.80091	−	1.60253i	−0.0999686	−	0.0571968i
$786$	1.46691	−	63.3188i	0.0523229	−	2.25851i
$787$	12.9551	−	22.4388i	0.461799	−	0.799859i	−0.537252	−	0.843422i	$-0.680538\pi$
$787$	12.9551	−	22.4388i	0.461799	−	0.799859i	0.999051	+	0.0435632i	$0.0138710\pi$
$788$	4.31573	−	7.47506i	0.153741	−	0.266288i
$789$	0.775704	−	33.4830i	0.0276158	−	1.19203i
$790$	67.5129	+	38.6273i	2.40200	+	1.37430i
$791$	6.29582	+	7.81416i	0.223854	+	0.277839i
$792$	−26.3029	+	13.6025i	−0.934633	+	0.483345i
$793$	−0.501064	+	0.289289i	−0.0177933	+	0.0102730i
$794$	5.37013	−	9.30134i	0.190579	−	0.330092i
$795$	5.63163	+	0.108433i	0.199733	+	0.00384572i
$796$	−29.6095	+	17.0951i	−1.04948	+	0.605918i
$797$		−	27.5780i		−	0.976865i	−0.872602	−	0.488432i	$-0.837569\pi$
$797$		−	27.5780i		−	0.976865i	0.872602	−	0.488432i	$-0.162431\pi$
$798$	−39.8966	−	51.9360i	−1.41233	−	1.83851i
$799$	14.8073			0.523843
$800$	−7.69296	+	13.5686i	−0.271987	+	0.479723i
$801$	−36.5842	−	1.69601i	−1.29264	−	0.0599255i
$802$	−27.1653	−	15.6839i	−0.959240	−	0.553818i
$803$	−17.3309	+	10.0060i	−0.611594	+	0.353104i
$804$	−9.62267	+	15.8096i	−0.339365	+	0.557563i
$805$	−13.8595	−	5.29735i	−0.488484	−	0.186707i
$806$			2.51996i			0.0887617i
$807$	0.882609	−	38.0976i	0.0310693	−	1.34110i
$808$	3.58065	−	6.20187i	0.125967	−	0.218181i
$809$	−27.0106	−	15.5946i	−0.949641	−	0.548275i	−0.0566716	−	0.998393i	$-0.518049\pi$
$809$	−27.0106	−	15.5946i	−0.949641	−	0.548275i	−0.892969	+	0.450117i	$0.851382\pi$
$810$	−41.3016	−	29.0105i	−1.45119	−	1.01932i
$811$			17.5174i			0.615120i	0.951529	+	0.307560i	$0.0995124\pi$
$811$			17.5174i			0.615120i	−0.951529	+	0.307560i	$0.900488\pi$
$812$	6.57572	+	42.1931i	0.230763	+	1.48069i
$813$	13.5600	−	22.2785i	0.475569	−	0.781341i
$814$	7.12443	+	12.3399i	0.249711	+	0.432512i
$815$	18.9797	+	32.5789i	0.664830	+	1.14119i
$816$	−12.3071	−	22.5046i	−0.430834	−	0.787820i
$817$	−28.6645	−	49.6483i	−1.00284	−	1.73697i
$818$			16.1948i			0.566237i
$819$	−2.84686	+	0.309465i	−0.0994773	+	0.0108136i
$820$	−21.9374	−	12.5514i	−0.766088	−	0.438315i
$821$	30.7324	−	17.7433i	1.07257	−	0.619247i	0.143685	−	0.989623i	$-0.454105\pi$
$821$	30.7324	−	17.7433i	1.07257	−	0.619247i	0.928882	+	0.370377i	$0.120771\pi$
$822$	−59.8876	+	32.7506i	−2.08882	+	1.14231i
$823$	−26.0214	−	15.0235i	−0.907050	−	0.523686i	−0.0275693	−	0.999620i	$-0.508777\pi$
$823$	−26.0214	−	15.0235i	−0.907050	−	0.523686i	−0.879481	+	0.475934i	$0.842110\pi$
$824$	−11.9056	−	20.6211i	−0.414752	−	0.718371i
$825$	14.8826	+	0.228329i	0.518144	+	0.00794941i
$826$	−28.5527	−	35.4386i	−0.993474	−	1.23307i
$827$	21.6751			0.753717			0.376859	−	0.926271i	$-0.377004\pi$
$827$	21.6751			0.753717			0.376859	+	0.926271i	$0.377004\pi$
$828$	17.4158	−	27.1756i	0.605240	−	0.944416i
$829$	−7.93492	−	4.58123i	−0.275591	−	0.159113i	0.355835	−	0.934549i	$-0.384197\pi$
$829$	−7.93492	−	4.58123i	−0.275591	−	0.159113i	−0.631426	+	0.775436i	$0.717530\pi$
$830$	−9.89248	−	16.9806i	−0.343373	−	0.589404i
$831$	2.90212	+	0.0672336i	0.100673	+	0.00233231i
$832$	1.37954			0.0478270
$833$	11.9759	−	13.1689i	0.414941	−	0.456277i
$834$	−33.2735	+	54.6669i	−1.15217	+	1.89296i
$835$	16.1192	−	0.0630428i	0.557828	−	0.00218169i
$836$	−21.0072	+	36.3856i	−0.726551	+	1.25842i
$837$	8.08831	−	11.9998i	0.279573	−	0.414774i
$838$	−12.5579	−	21.7509i	−0.433805	−	0.751372i
$839$	31.7155			1.09494			0.547471	−	0.836825i	$-0.315591\pi$
$839$	31.7155			1.09494			0.547471	+	0.836825i	$0.315591\pi$
$840$	22.2784	−	54.4696i	0.768678	−	1.87938i
$841$	14.8452			0.511904
$842$	22.3031	+	38.6302i	0.768617	+	1.33128i
$843$	1.74592	+	3.19258i	0.0601327	+	0.109958i
$844$	10.6260	−	18.4047i	0.365762	−	0.633518i
$845$	0.112550	+	28.7776i	0.00387185	+	0.989980i
$846$	−38.9162	+	20.1255i	−1.33797	+	0.691928i
$847$	7.67809	−	19.8551i	0.263822	−	0.682229i
$848$	−8.46976			−0.290853
$849$	−0.200740	+	8.66487i	−0.00688936	+	0.297378i
$850$	0.249421	+	31.8864i	0.00855508	+	1.09369i
$851$	−7.17980	−	4.14526i	−0.246120	−	0.142098i
$852$	97.8988	+	2.26803i	3.35396	+	0.0777013i
$853$	−10.2006			−0.349262			−0.174631	−	0.984634i	$-0.555873\pi$
$853$	−10.2006			−0.349262			−0.174631	+	0.984634i	$0.555873\pi$
$854$	1.63862	+	10.5142i	0.0560726	+	0.359789i
$855$	−38.1913	−	1.62085i	−1.30612	−	0.0554319i
$856$	−3.18032	−	5.50848i	−0.108701	−	0.188276i
$857$	−1.56368	−	0.902790i	−0.0534142	−	0.0308387i	0.473055	−	0.881033i	$-0.343151\pi$
$857$	−1.56368	−	0.902790i	−0.0534142	−	0.0308387i	−0.526469	+	0.850194i	$0.676484\pi$
$858$	1.29240	+	2.36327i	0.0441218	+	0.0806807i
$859$	6.67971	−	3.85653i	0.227909	−	0.131583i	−0.381698	−	0.924287i	$-0.624661\pi$
$859$	6.67971	−	3.85653i	0.227909	−	0.131583i	0.609607	+	0.792704i	$0.291327\pi$
$860$	47.9265	−	83.7660i	1.63428	−	2.85640i
$861$	11.1574	+	4.61448i	0.380244	+	0.157261i
$862$		−	7.37109i		−	0.251060i
$863$	11.1766	+	19.3584i	0.380455	+	0.658967i	0.991127	−	0.132916i	$-0.0424342\pi$
$863$	11.1766	+	19.3584i	0.380455	+	0.658967i	−0.610673	+	0.791883i	$0.709101\pi$
$864$	13.4413	+	9.05994i	0.457283	+	0.308226i
$865$	10.1146	+	17.3619i	0.343907	+	0.590321i
$866$	39.7107	+	68.7809i	1.34942	+	2.33727i
$867$	15.5852	+	9.48604i	0.529300	+	0.322163i
$868$	29.4823	+	11.4010i	1.00069	+	0.386975i
$869$			23.8380i			0.808648i
$870$	31.2907	+	18.8781i	1.06086	+	0.640026i
$871$	0.778253	+	0.449324i	0.0263701	+	0.0152248i
$872$	−26.1705	+	45.3287i	−0.886246	+	1.53502i
$873$	13.2531	−	20.6801i	0.448549	−	0.699916i
$874$		−	35.8423i		−	1.21238i
$875$	−22.8150	+	18.8276i	−0.771286	+	0.636488i
$876$	73.9045	+	44.9826i	2.49700	+	1.51982i
$877$	44.8106	−	25.8714i	1.51315	−	0.873615i	0.513264	−	0.858231i	$-0.328436\pi$
$877$	44.8106	−	25.8714i	1.51315	−	0.873615i	0.999882	−	0.0153839i	$-0.00489705\pi$
$878$	−46.6866	−	26.9545i	−1.57560	−	0.909671i
$879$	14.3551	+	26.2496i	0.484185	+	0.885377i
$880$	−22.3811	+	0.0875333i	−0.754467	+	0.00295075i
$881$	−40.9882			−1.38093			−0.690464	−	0.723367i	$-0.742594\pi$
$881$	−40.9882			−1.38093			−0.690464	+	0.723367i	$0.742594\pi$
$882$	−13.5762	+	50.8877i	−0.457134	+	1.71348i
$883$		−	10.6943i		−	0.359891i	−0.983677	−	0.179945i	$-0.942408\pi$
$883$		−	10.6943i		−	0.359891i	0.983677	−	0.179945i	$-0.0575921\pi$
$884$	−3.40843	+	1.96786i	−0.114638	+	0.0661861i
$885$	−26.5582	−	0.511358i	−0.892743	−	0.0171891i
$886$	32.9415	−	57.0563i	1.10669	−	1.91684i
$887$	40.7766	−	23.5424i	1.36914	−	0.790476i	0.378326	−	0.925672i	$-0.376500\pi$
$887$	40.7766	−	23.5424i	1.36914	−	0.790476i	0.990819	+	0.135196i	$0.0431665\pi$
$888$	17.0965	−	28.0888i	0.573721	−	0.942599i
$889$	12.3335	−	9.93706i	0.413654	−	0.333278i
$890$	−59.4229	−	33.9987i	−1.99186	−	1.13964i
$891$	1.43111	−	15.4019i	0.0479439	−	0.515983i
$892$	−33.5760	+	58.1554i	−1.12421	+	1.94719i
$893$	−16.5909	+	28.7362i	−0.555192	+	0.961621i
$894$	−55.1646	−	1.27800i	−1.84498	−	0.0427427i
$895$	12.1727	−	21.2755i	0.406889	−	0.711161i
$896$	15.1050	−	39.0605i	0.504621	−	1.30492i
$897$	−1.33874	−	0.814836i	−0.0446993	−	0.0272066i
$898$	−78.2061	+	45.1523i	−2.60977	+	1.50675i
$899$	−5.23895	+	9.07413i	−0.174729	+	0.302639i
$900$	−30.0055	−	56.9253i	−1.00018	−	1.89751i
$901$	−3.20276	+	1.84912i	−0.106699	+	0.0616030i
$902$		−	11.3570i		−	0.378147i
$903$	−17.6200	+	42.6037i	−0.586355	+	1.41776i
$904$	−21.7827			−0.724480
$905$	−12.0592	+	0.0471638i	−0.400860	+	0.00156778i
$906$	63.6236	−	34.7937i	2.11375	−	1.15594i
$907$	−7.55017	−	4.35909i	−0.250699	−	0.144741i	0.369385	−	0.929276i	$-0.379568\pi$
$907$	−7.55017	−	4.35909i	−0.250699	−	0.144741i	−0.620084	+	0.784535i	$0.712902\pi$
$908$	46.8561	−	27.0524i	1.55497	−	0.897765i
$909$	1.71837	+	3.32277i	0.0569947	+	0.110209i
$910$	−5.00029	−	1.91119i	−0.165758	−	0.0633555i
$911$		−	4.85314i		−	0.160792i	−0.996763	−	0.0803958i	$-0.974382\pi$
$911$		−	4.85314i		−	0.160792i	0.996763	−	0.0803958i	$-0.0256184\pi$
$912$	57.4639	+	1.33127i	1.90282	+	0.0440827i
$913$	3.01138	−	5.21587i	0.0996622	−	0.172620i
$914$	39.6310	+	22.8809i	1.31088	+	0.756834i
$915$	5.31810	+	3.20847i	0.175811	+	0.106069i
$916$		−	25.7068i		−	0.849376i
$917$	−13.9134	+	35.9792i	−0.459460	+	1.18814i
$918$	33.0583	+	2.30088i	1.09109	+	0.0759405i
$919$	17.9292	+	31.0543i	0.591429	+	1.02439i	0.994040	+	0.109014i	$0.0347694\pi$
$919$	17.9292	+	31.0543i	0.591429	+	1.02439i	−0.402611	+	0.915371i	$0.631897\pi$
$920$	27.8293	−	16.2127i	0.917505	−	0.534517i
$921$	−15.5497	+	8.50365i	−0.512381	+	0.280205i
$922$	−28.6000	−	49.5366i	−0.941889	−	1.63140i
$923$		−	4.75475i		−	0.156505i
$924$	33.4963	−	4.42835i	1.10195	−	0.145682i
$925$	−14.2489	+	8.37587i	−0.468500	+	0.275397i
$926$	50.7629	−	29.3080i	1.66817	−	0.963120i
$927$	12.4248	+	0.576000i	0.408083	+	0.0189183i
$928$	−10.1642	−	5.86830i	−0.333656	−	0.192636i
$929$	−12.7001	−	21.9973i	−0.416678	−	0.721707i	0.578925	−	0.815381i	$-0.303472\pi$
$929$	−12.7001	−	21.9973i	−0.416678	−	0.721707i	−0.995603	+	0.0936737i	$0.970139\pi$
$930$	23.6834	−	13.0723i	0.776608	−	0.428657i
$931$	12.1383	+	37.9967i	0.397816	+	1.24529i
$932$	−93.5349			−3.06384
$933$	−0.420329	+	18.1434i	−0.0137610	+	0.593988i
$934$	−23.6515	−	13.6552i	−0.773902	−	0.446813i
$935$	−8.44410	+	4.91934i	−0.276152	+	0.160880i
$936$	3.35400	−	5.23357i	0.109629	−	0.171065i
$937$	−40.3037			−1.31667			−0.658333	−	0.752727i	$-0.728738\pi$
$937$	−40.3037			−1.31667			−0.658333	+	0.752727i	$0.728738\pi$
$938$	12.8702	−	10.3695i	0.420228	−	0.338576i
$939$	−0.379023	−	0.230695i	−0.0123689	−	0.00752846i
$940$	−55.8577	+	0.218462i	−1.82188	+	0.00712543i
$941$	−9.12065	+	15.7974i	−0.297325	+	0.514982i	−0.975523	−	0.219897i	$-0.929428\pi$
$941$	−9.12065	+	15.7974i	−0.297325	+	0.514982i	0.678198	+	0.734879i	$0.262761\pi$
$942$	−5.50016	+	3.00786i	−0.179205	+	0.0980015i
$943$	3.30396	+	5.72264i	0.107592	+	0.186355i
$944$	39.9425			1.30002
$945$	17.6765	+	25.1503i	0.575018	+	0.818141i
$946$	43.3657			1.40994
$947$	9.42425	+	16.3233i	0.306247	+	0.530435i	0.977538	−	0.210759i	$-0.0675934\pi$
$947$	9.42425	+	16.3233i	0.306247	+	0.530435i	−0.671291	+	0.741194i	$0.734260\pi$
$948$	90.4208	−	49.4483i	2.93673	−	1.60601i
$949$	2.10043	−	3.63806i	0.0681830	−	0.118096i
$950$	−62.1609	−	35.2432i	−2.01676	−	1.14344i
$951$	−45.7747	−	27.8612i	−1.48435	−	0.903461i
$952$	5.94996	+	38.1778i	0.192839	+	1.23735i
$953$	−25.3110			−0.819903			−0.409952	−	0.912107i	$-0.634454\pi$
$953$	−25.3110			−0.819903			−0.409952	+	0.912107i	$0.634454\pi$
$954$	5.90419	−	9.21289i	0.191155	−	0.298278i
$955$	23.9955	+	41.1886i	0.776478	+	1.33283i
$956$	92.5341	+	53.4246i	2.99277	+	1.72787i
$957$	−0.259397	+	11.1968i	−0.00838511	+	0.361941i
$958$	−25.7737			−0.832712
$959$	41.0777	−	6.40189i	1.32647	−	0.206728i
$960$	−7.15637	−	12.9654i	−0.230971	−	0.418456i
$961$	−11.6219	−	20.1298i	−0.374901	−	0.649347i
$962$	−2.59035	−	1.49554i	−0.0835164	−	0.0482182i
$963$	3.31901	+	0.153866i	0.106953	+	0.00495825i
$964$	−63.2570	+	36.5214i	−2.03737	+	1.17628i
$965$	−15.4754	+	27.0479i	−0.498170	+	0.870702i
$966$	−22.8582	+	17.5594i	−0.735451	+	0.564965i
$967$			32.2840i			1.03818i	0.854718	+	0.519092i	$0.173730\pi$
$967$			32.2840i			1.03818i	−0.854718	+	0.519092i	$0.826270\pi$
$968$	23.1049	+	40.0188i	0.742619	+	1.28625i
$969$	22.0201	−	12.0421i	0.707387	−	0.386848i
$970$	39.6738	−	23.1130i	1.27385	−	0.742114i
$971$	0.693916	+	1.20190i	0.0222688	+	0.0385707i	0.876945	−	0.480591i	$-0.159578\pi$
$971$	0.693916	+	1.20190i	0.0222688	+	0.0385707i	−0.854676	+	0.519161i	$0.826244\pi$
$972$	−61.3901	+	26.5205i	−1.96909	+	0.850645i
$973$	30.3525	−	24.4548i	0.973056	−	0.783986i
$974$			34.7293i			1.11280i
$975$	−2.72952	+	1.52055i	−0.0874147	+	0.0486964i
$976$	−8.08813	−	4.66968i	−0.258895	−	0.149473i
$977$	28.9058	−	50.0663i	0.924779	−	1.60176i	0.132863	−	0.991134i	$-0.457583\pi$
$977$	28.9058	−	50.0663i	0.924779	−	1.60176i	0.791916	−	0.610630i	$-0.209084\pi$
$978$	73.2274	+	1.69646i	2.34155	+	0.0542469i
$979$		−	20.9815i		−	0.670572i
$980$	−44.9828	+	49.8542i	−1.43692	+	1.59253i
$981$	−12.5593	−	24.2857i	−0.400989	−	0.775383i
$982$	29.5346	−	17.0518i	0.942487	−	0.544145i
$983$	22.5265	+	13.0057i	0.718485	+	0.414818i	0.814195	−	0.580592i	$-0.197179\pi$
$983$	22.5265	+	13.0057i	0.718485	+	0.414818i	−0.0957097	+	0.995409i	$0.530512\pi$
$984$	−22.9951	+	12.5753i	−0.733058	+	0.400886i
$985$	0.0175957	+	4.49898i	0.000560644	+	0.143349i
$986$	−23.9938			−0.764119
$987$	26.4543	−	3.49737i	0.842051	−	0.111323i
$988$		−	8.81958i		−	0.280588i
$989$	−21.8514	+	12.6159i	−0.694833	+	0.401162i
$990$	15.5065	−	24.4058i	0.492828	−	0.775668i
$991$	18.1162	−	31.3782i	0.575480	−	0.996760i	−0.420510	−	0.907288i	$-0.638149\pi$
$991$	18.1162	−	31.3782i	0.575480	−	0.996760i	0.995989	−	0.0894720i	$-0.0285180\pi$
$992$	−7.52393	+	4.34394i	−0.238885	+	0.137920i
$993$	−12.3971	−	7.54560i	−0.393410	−	0.239452i
$994$	−81.5627	−	31.5408i	−2.58701	−	1.00041i
$995$	8.85011	−	15.4682i	0.280567	−	0.490376i
$996$	−26.0312	−	0.603066i	−0.824829	−	0.0191089i
$997$	−17.2974	+	29.9600i	−0.547814	+	0.948842i	0.450610	+	0.892721i	$0.351207\pi$
$997$	−17.2974	+	29.9600i	−0.547814	+	0.948842i	−0.998424	+	0.0561210i	$0.982127\pi$
$998$	45.4080	−	78.6490i	1.43737	−	2.48959i
$999$	7.53479	+	15.4359i	0.238390	+	0.488370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.p.a.59.11	yes	24
3.2	odd	2	inner	105.2.p.a.59.1	✓	24
5.2	odd	4		525.2.t.j.101.2		24
5.3	odd	4		525.2.t.j.101.11		24
5.4	even	2	inner	105.2.p.a.59.2	yes	24
7.2	even	3		735.2.p.f.509.11		24
7.3	odd	6		735.2.g.b.734.1		24
7.4	even	3		735.2.g.b.734.4		24
7.5	odd	6	inner	105.2.p.a.89.12	yes	24
7.6	odd	2		735.2.p.f.374.12		24
15.2	even	4		525.2.t.j.101.12		24
15.8	even	4		525.2.t.j.101.1		24
15.14	odd	2	inner	105.2.p.a.59.12	yes	24
21.2	odd	6		735.2.p.f.509.1		24
21.5	even	6	inner	105.2.p.a.89.2	yes	24
21.11	odd	6		735.2.g.b.734.23		24
21.17	even	6		735.2.g.b.734.22		24
21.20	even	2		735.2.p.f.374.2		24
35.4	even	6		735.2.g.b.734.21		24
35.9	even	6		735.2.p.f.509.2		24
35.12	even	12		525.2.t.j.26.12		24
35.19	odd	6	inner	105.2.p.a.89.1	yes	24
35.24	odd	6		735.2.g.b.734.24		24
35.33	even	12		525.2.t.j.26.1		24
35.34	odd	2		735.2.p.f.374.1		24
105.44	odd	6		735.2.p.f.509.12		24
105.47	odd	12		525.2.t.j.26.2		24
105.59	even	6		735.2.g.b.734.3		24
105.68	odd	12		525.2.t.j.26.11		24
105.74	odd	6		735.2.g.b.734.2		24
105.89	even	6	inner	105.2.p.a.89.11	yes	24
105.104	even	2		735.2.p.f.374.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.1	✓	24	3.2	odd	2	inner
105.2.p.a.59.2	yes	24	5.4	even	2	inner
105.2.p.a.59.11	yes	24	1.1	even	1	trivial
105.2.p.a.59.12	yes	24	15.14	odd	2	inner
105.2.p.a.89.1	yes	24	35.19	odd	6	inner
105.2.p.a.89.2	yes	24	21.5	even	6	inner
105.2.p.a.89.11	yes	24	105.89	even	6	inner
105.2.p.a.89.12	yes	24	7.5	odd	6	inner
525.2.t.j.26.1		24	35.33	even	12
525.2.t.j.26.2		24	105.47	odd	12
525.2.t.j.26.11		24	105.68	odd	12
525.2.t.j.26.12		24	35.12	even	12
525.2.t.j.101.1		24	15.8	even	4
525.2.t.j.101.2		24	5.2	odd	4
525.2.t.j.101.11		24	5.3	odd	4
525.2.t.j.101.12		24	15.2	even	4
735.2.g.b.734.1		24	7.3	odd	6
735.2.g.b.734.2		24	105.74	odd	6
735.2.g.b.734.3		24	105.59	even	6
735.2.g.b.734.4		24	7.4	even	3
735.2.g.b.734.21		24	35.4	even	6
735.2.g.b.734.22		24	21.17	even	6
735.2.g.b.734.23		24	21.11	odd	6
735.2.g.b.734.24		24	35.24	odd	6
735.2.p.f.374.1		24	35.34	odd	2
735.2.p.f.374.2		24	21.20	even	2
735.2.p.f.374.11		24	105.104	even	2
735.2.p.f.374.12		24	7.6	odd	2
735.2.p.f.509.1		24	21.2	odd	6
735.2.p.f.509.2		24	35.9	even	6
735.2.p.f.509.11		24	7.2	even	3
735.2.p.f.509.12		24	105.44	odd	6

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25399 + 2.17197i) q^{2} +(-1.51966 + 0.831052i) q^{3} +(-2.14497 + 3.71520i) q^{4} +(-0.00874528 - 2.23605i) q^{5} +(-3.71065 - 2.25852i) q^{6} +(1.65993 + 2.06025i) q^{7} -5.74313 q^{8} +(1.61871 - 2.52582i) q^{9} +(4.84567 - 2.82298i) q^{10} +(1.48843 + 0.859346i) q^{11} +(0.172094 - 7.42841i) q^{12} -0.360784 q^{13} +(-2.39327 + 6.18885i) q^{14} +(1.87156 + 3.39076i) q^{15} +(-2.91187 - 5.04351i) q^{16} +(-2.20219 - 1.27144i) q^{17} +(7.51586 + 0.348428i) q^{18} +(4.93492 - 2.84918i) q^{19} +(8.32614 + 4.76378i) q^{20} +(-4.23470 - 1.75138i) q^{21} +4.31044i q^{22} +(-1.25399 - 2.17197i) q^{23} +(8.72758 - 4.77284i) q^{24} +(-4.99985 + 0.0391098i) q^{25} +(-0.452418 - 0.783611i) q^{26} +(-0.360784 + 5.18361i) q^{27} +(-11.2147 + 1.74780i) q^{28} -3.76228i q^{29} +(-5.01771 + 8.31695i) q^{30} +(-2.41187 - 1.39249i) q^{31} +(1.55977 - 2.70160i) q^{32} +(-2.97606 - 0.0689466i) q^{33} -6.37747i q^{34} +(4.59231 - 3.72971i) q^{35} +(5.91187 + 11.4316i) q^{36} +(2.86279 - 1.65283i) q^{37} +(12.3767 + 7.14567i) q^{38} +(0.548267 - 0.299830i) q^{39} +(0.0502252 + 12.8419i) q^{40} -2.63477 q^{41} +(-1.50631 - 11.3939i) q^{42} -10.0606i q^{43} +(-6.38529 + 3.68655i) q^{44} +(-5.66203 - 3.59742i) q^{45} +(3.14497 - 5.44725i) q^{46} +(-5.04290 + 2.91152i) q^{47} +(8.61645 + 5.24448i) q^{48} +(-1.48925 + 6.83975i) q^{49} +(-6.35469 - 10.8105i) q^{50} +(4.40320 + 0.102009i) q^{51} +(0.773871 - 1.34038i) q^{52} +(0.727175 - 1.25950i) q^{53} +(-11.7111 + 5.71658i) q^{54} +(1.90853 - 3.33572i) q^{55} +(-9.53320 - 11.8323i) q^{56} +(-5.13156 + 8.43094i) q^{57} +(8.17157 - 4.71786i) q^{58} +(-3.42928 + 5.93969i) q^{59} +(-16.6118 - 0.319848i) q^{60} +(1.38882 - 0.801836i) q^{61} -6.98468i q^{62} +(7.89077 - 0.857759i) q^{63} -3.82374 q^{64} +(0.00315515 + 0.806730i) q^{65} +(-3.58220 - 6.55038i) q^{66} +(-2.15712 - 1.24541i) q^{67} +(9.44729 - 5.45439i) q^{68} +(3.71065 + 2.25852i) q^{69} +(13.8595 + 5.29735i) q^{70} +13.1790i q^{71} +(-9.29643 + 14.5061i) q^{72} +(-5.82187 + 10.0838i) q^{73} +(7.17980 + 4.14526i) q^{74} +(7.56554 - 4.21457i) q^{75} +24.4456i q^{76} +(0.700227 + 4.49300i) q^{77} +(1.33874 + 0.814836i) q^{78} +(6.93492 + 12.0116i) q^{79} +(-11.2521 + 6.55519i) q^{80} +(-3.75958 - 8.17713i) q^{81} +(-3.30396 - 5.72264i) q^{82} -3.50427i q^{83} +(15.5900 - 11.9761i) q^{84} +(-2.82374 + 4.93534i) q^{85} +(21.8514 - 12.6159i) q^{86} +(3.12665 + 5.71737i) q^{87} +(-8.54825 - 4.93534i) q^{88} +(-6.10392 - 10.5723i) q^{89} +(0.713373 - 16.8089i) q^{90} +(-0.598876 - 0.743304i) q^{91} +10.7591 q^{92} +(4.82244 + 0.111722i) q^{93} +(-12.6475 - 7.30202i) q^{94} +(-6.41406 - 11.0098i) q^{95} +(-0.125143 + 5.40176i) q^{96} +8.18747 q^{97} +(-16.7232 + 5.34234i) q^{98} +(4.57989 - 2.36849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 6 q^{21} + 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} - 72 q^{40} - 18 q^{45} + 36 q^{46} - 12 q^{49} - 12 q^{51} - 36 q^{54} + 12 q^{60}+ \cdots - 48 q^{99}+O(q^{100}) \) 24 * q - 12 * q^4 - 6 * q^9 - 24 * q^15 - 12 * q^16 - 6 * q^21 + 18 * q^24 - 12 * q^25 + 18 * q^30 + 84 * q^36 - 12 * q^39 - 72 * q^40 - 18 * q^45 + 36 * q^46 - 12 * q^49 - 12 * q^51 - 36 * q^54 + 12 * q^60 + 36 * q^61 + 24 * q^64 - 72 * q^66 + 108 * q^70 + 72 * q^75 + 48 * q^79 - 6 * q^81 + 48 * q^84 + 48 * q^85 - 96 * q^91 - 72 * q^94 - 90 * q^96 - 48 * q^99

Introduction

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