LMFDB - Embedded newform 105.2.p.a.59.1

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			59.1
Character	$\chi$	$=$	105.59
Dual form			105.2.p.a.89.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25399 - 2.17197i) q^{2} +(0.0401158 + 1.73159i) 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} +(-2.99678 + 0.138928i) q^{9} +(4.84567 - 2.82298i) q^{10} +(-1.48843 - 0.859346i) q^{11} +(-6.51924 - 3.56517i) q^{12} -0.360784 q^{13} +(2.39327 - 6.18885i) q^{14} +(-3.87156 + 0.104844i) q^{15} +(-2.91187 - 5.04351i) q^{16} +(2.20219 + 1.27144i) q^{17} +(4.05968 + 6.33471i) q^{18} +(4.93492 - 2.84918i) q^{19} +(-8.32614 - 4.76378i) q^{20} +(-3.50091 + 2.95696i) q^{21} +4.31044i q^{22} +(1.25399 + 2.17197i) q^{23} +(0.230390 + 9.94472i) 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} +(5.08261 + 8.27745i) q^{30} +(-2.41187 - 1.39249i) q^{31} +(-1.55977 + 2.70160i) q^{32} +(1.42832 - 2.61182i) 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} +(-0.0144731 - 0.624728i) q^{39} +(0.0502252 + 12.8419i) q^{40} +2.63477 q^{41} +(10.8125 + 3.89588i) q^{42} -10.0606i q^{43} +(6.38529 - 3.68655i) q^{44} +(-0.336857 - 6.69974i) 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} +(-2.11326 + 3.86429i) q^{51} +(0.773871 - 1.34038i) q^{52} +(-0.727175 + 1.25950i) q^{53} +(-10.8062 + 7.28380i) 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} +(7.91488 - 14.6085i) q^{60} +(1.38882 - 0.801836i) q^{61} +6.98468i q^{62} +(-5.26068 - 5.94351i) q^{63} -3.82374 q^{64} +(-0.00315515 - 0.806730i) q^{65} +(-7.46390 + 0.172917i) 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} +(-17.2109 + 0.797880i) q^{72} +(-5.82187 + 10.0838i) q^{73} +(-7.17980 - 4.14526i) q^{74} +(-0.268295 - 8.65610i) 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} +(8.96140 - 0.832672i) q^{81} +(-3.30396 - 5.72264i) q^{82} +3.50427i q^{83} +(-3.47636 - 19.3492i) q^{84} +(-2.82374 + 4.93534i) q^{85} +(-21.8514 + 12.6159i) q^{86} +(-6.51472 + 0.150927i) q^{87} +(-8.54825 - 4.93534i) q^{88} +(6.10392 + 10.5723i) q^{89} +(-14.1292 + 9.13304i) q^{90} +(-0.598876 - 0.743304i) q^{91} -10.7591 q^{92} +(2.31447 - 4.23222i) q^{93} +(-12.6475 - 7.30202i) q^{94} +(6.41406 + 11.0098i) q^{95} +(-4.74063 - 2.59250i) 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	$-0.819656\pi$
$2$	−1.25399	−	2.17197i	−0.886704	−	1.53582i	−0.0429549	−	0.999077i	$-0.513677\pi$
$3$	0.0401158	+	1.73159i	0.0231608	+	0.999732i
$3$	0.0401158	+	1.73159i	0.0231608	+	0.999732i
$4$	−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
$9$	−2.99678	+	0.138928i	−0.998927	+	0.0463093i
$10$	4.84567	−	2.82298i	1.53234	−	0.892703i
$11$	−1.48843	−	0.859346i	−0.448779	−	0.259103i	0.258535	−	0.966002i	$-0.416760\pi$
$11$	−1.48843	−	0.859346i	−0.448779	−	0.259103i	−0.707314	+	0.706899i	$0.750093\pi$
$12$	−6.51924	−	3.56517i	−1.88194	−	1.02917i
$13$	−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
$15$	−3.87156	+	0.104844i	−0.999634	+	0.0270706i
$16$	−2.91187	−	5.04351i	−0.727967	−	1.26088i
$17$	2.20219	+	1.27144i	0.534110	+	0.308369i	0.742689	−	0.669637i	$-0.233550\pi$
$17$	2.20219	+	1.27144i	0.534110	+	0.308369i	−0.208578	+	0.978006i	$0.566884\pi$
$18$	4.05968	+	6.33471i	0.956875	+	1.49311i
$19$	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
$21$	−3.50091	+	2.95696i	−0.763961	+	0.645262i
$22$			4.31044i			0.918989i
$23$	1.25399	+	2.17197i	0.261475	+	0.452887i	0.966634	−	0.256162i	$-0.0824579\pi$
$23$	1.25399	+	2.17197i	0.261475	+	0.452887i	−0.705159	+	0.709049i	$0.749125\pi$
$24$	0.230390	+	9.94472i	0.0470281	+	2.02996i
$25$	−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	$0.113587\pi$
$29$			3.76228i			0.698638i	−0.937004	+	0.349319i	$0.886413\pi$
$30$	5.08261	+	8.27745i	0.927954	+	1.51125i
$31$	−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
$33$	1.42832	−	2.61182i	0.248639	−	0.454660i
$34$		−	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
$39$	−0.0144731	−	0.624728i	−0.00231755	−	0.100037i
$40$	0.0502252	+	12.8419i	0.00794131	+	2.03049i
$41$	2.63477			0.411481			0.205741	−	0.978607i	$-0.434040\pi$
$41$	2.63477			0.411481			0.205741	+	0.978607i	$0.434040\pi$
$42$	10.8125	+	3.89588i	1.66841	+	0.601147i
$43$		−	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
$45$	−0.336857	−	6.69974i	−0.0502157	−	0.998738i
$46$	3.14497	−	5.44725i	0.463701	−	0.803154i
$47$	5.04290	−	2.91152i	0.735583	−	0.424689i	−0.0848783	−	0.996391i	$-0.527050\pi$
$47$	5.04290	−	2.91152i	0.735583	−	0.424689i	0.820461	+	0.571702i	$0.193717\pi$
$48$	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
$51$	−2.11326	+	3.86429i	−0.295916	+	0.541109i
$52$	0.773871	−	1.34038i	0.107317	−	0.185878i
$53$	−0.727175	+	1.25950i	−0.0998852	+	0.173006i	−0.911637	−	0.410996i	$-0.865181\pi$
$53$	−0.727175	+	1.25950i	−0.0998852	+	0.173006i	0.811752	+	0.584003i	$0.198514\pi$
$54$	−10.8062	+	7.28380i	−1.47054	+	0.991200i
$55$	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	−0.551698	−	0.834044i	$-0.686020\pi$
$59$	3.42928	−	5.93969i	0.446454	−	0.773282i	0.998152	+	0.0607624i	$0.0193532\pi$
$60$	7.91488	−	14.6085i	1.02181	−	1.88595i
$61$	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
$63$	−5.26068	−	5.94351i	−0.662783	−	0.748811i
$64$	−3.82374			−0.477967
$65$	−0.00315515	−	0.806730i	−0.000391348	−	0.100063i
$66$	−7.46390	+	0.172917i	−0.918742	+	0.0212846i
$67$	−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	$-0.714185\pi$
$71$		−	13.1790i		−	1.56406i	0.623243	−	0.782028i	$-0.285815\pi$
$72$	−17.2109	+	0.797880i	−2.02832	+	0.0940310i
$73$	−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
$75$	−0.268295	−	8.65610i	−0.0309800	−	0.999520i
$76$			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
$81$	8.96140	−	0.832672i	0.995711	−	0.0925191i
$82$	−3.30396	−	5.72264i	−0.364862	−	0.631959i
$83$			3.50427i			0.384644i	0.981332	+	0.192322i	$0.0616018\pi$
$83$			3.50427i			0.384644i	−0.981332	+	0.192322i	$0.938398\pi$
$84$	−3.47636	−	19.3492i	−0.379302	−	2.11117i
$85$	−2.82374	+	4.93534i	−0.306277	+	0.535312i
$86$	−21.8514	+	12.6159i	−2.35629	+	1.36041i
$87$	−6.51472	+	0.150927i	−0.698451	+	0.0161811i
$88$	−8.54825	−	4.93534i	−0.911247	−	0.526108i
$89$	6.10392	+	10.5723i	0.647014	+	1.12066i	0.983832	+	0.179092i	$0.0573158\pi$
$89$	6.10392	+	10.5723i	0.647014	+	1.12066i	−0.336818	+	0.941570i	$0.609351\pi$
$90$	−14.1292	+	9.13304i	−1.48935	+	0.962707i
$91$	−0.598876	−	0.743304i	−0.0627793	−	0.0779194i
$92$	−10.7591			−1.12171
$93$	2.31447	−	4.23222i	0.239999	−	0.438861i
$94$	−12.6475	−	7.30202i	−1.30449	−	0.753146i
$95$	6.41406	+	11.0098i	0.658069	+	1.12958i
$96$	−4.74063	−	2.59250i	−0.483839	−	0.264596i
$97$	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	−0.833339	−	0.552763i	$-0.813574\pi$
$101$	0.623467	−	1.07988i	0.0620372	−	0.107452i	0.895376	+	0.445311i	$0.146907\pi$
$102$	11.0431	−	0.255837i	1.09343	−	0.0253316i
$103$	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
$105$	−6.64254	−	7.80235i	−0.648245	−	0.761432i
$106$	3.64748			0.354274
$107$	−0.553762	−	0.959143i	−0.0535342	−	0.0927239i	0.838016	−	0.545645i	$-0.183715\pi$
$107$	−0.553762	−	0.959143i	−0.0535342	−	0.0927239i	−0.891551	+	0.452921i	$0.850382\pi$
$108$	20.0320	+	9.77832i	1.92758	+	0.940920i
$109$	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	$-0.557092\pi$
$113$	−3.79282			−0.356799			−0.178399	+	0.983958i	$0.557092\pi$
$114$	11.8768	−	21.7179i	1.11237	−	2.03407i
$115$	−4.84567	+	2.82298i	−0.451861	+	0.263244i
$116$	−13.9776	−	8.06999i	−1.29779	−	0.749280i
$117$	1.08119	−	0.0501228i	0.0999560	−	0.00463386i
$118$	−17.2011			−1.58349
$119$	1.03601	+	6.64757i	0.0949712	+	0.609381i
$120$	−22.2349	+	0.602133i	−2.02976	+	0.0549670i
$121$	−4.02305	−	6.96812i	−0.365732	−	0.633466i
$122$	−3.48313	−	2.01099i	−0.315348	−	0.182066i
$123$	0.105696	+	4.56232i	0.00953025	+	0.411371i
$124$	10.3468	−	5.97372i	0.929169	−	0.536456i
$125$	−0.131176	−	11.1796i	−0.0117328	−	0.999931i
$126$	−6.31230	+	18.8791i	−0.562344	+	1.68189i
$127$		−	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
$129$	17.4208	−	0.403589i	1.53382	−	0.0355340i
$130$	−1.74824	+	1.01848i	−0.153331	+	0.0893269i
$131$	−7.29012	−	12.6269i	−0.636941	−	1.10321i	−0.986100	−	0.166151i	$-0.946866\pi$
$131$	−7.29012	−	12.6269i	−0.636941	−	1.10321i	0.349159	−	0.937063i	$-0.386467\pi$
$132$	6.63973	+	10.9088i	0.577914	+	0.949488i
$133$	14.0616	+	5.43772i	1.21930	+	0.471510i
$134$			6.24693i			0.539653i
$135$	11.5877	−	0.852062i	0.997307	−	0.0733339i
$136$	12.6475	+	7.30202i	1.08451	+	0.626143i
$137$	−7.85666	+	13.6081i	−0.671240	+	1.16262i	0.306313	+	0.951931i	$0.400905\pi$
$137$	−7.85666	+	13.6081i	−0.671240	+	1.16262i	−0.977553	+	0.210691i	$0.932429\pi$
$138$	9.55855	+	5.22727i	0.813678	+	0.444975i
$139$		−	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
$144$	9.42692	+	14.7097i	0.785577	+	1.22581i
$145$	−8.41266	+	0.0329022i	−0.698633	+	0.00273238i
$146$	29.2022			2.41679
$147$	−11.9034	−	2.30439i	−0.981772	−	0.190063i
$148$			14.1811i			1.16568i
$149$	−11.0008	+	6.35130i	−0.901219	+	0.520319i	−0.877595	−	0.479402i	$-0.840854\pi$
$149$	−11.0008	+	6.35130i	−0.901219	+	0.520319i	−0.0236233	+	0.999721i	$0.507520\pi$
$150$	−18.4644	+	11.4374i	−1.50761	+	0.933857i
$151$	−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
$156$	2.35203	+	1.28625i	0.188313	+	0.102983i
$157$	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
$159$	−2.21011	−	1.20864i	−0.175273	−	0.0958515i
$160$	−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
$165$	5.85265	+	3.17096i	0.455629	+	0.246859i
$166$	7.61118	−	4.39432i	0.590742	−	0.341065i
$167$		−	7.20879i		−	0.557833i	−0.960315	−	0.278916i	$-0.910025\pi$
$167$		−	7.20879i		−	0.557833i	0.960315	−	0.278916i	$-0.0899752\pi$
$168$	−20.1062	+	16.9822i	−1.55122	+	1.31021i
$169$	−12.8698			−0.989987
$170$	14.2603	−	0.0557727i	1.09372	−	0.00427757i
$171$	−14.3930	+	9.22395i	−1.10066	+	0.705373i
$172$	37.3772	+	21.5797i	2.84998	+	1.64544i
$173$	7.78210	−	4.49300i	0.591662	−	0.341596i	−0.174093	−	0.984729i	$-0.555699\pi$
$173$	7.78210	−	4.49300i	0.591662	−	0.341596i	0.765754	+	0.643133i	$0.222366\pi$
$174$	8.49719	+	13.9605i	0.644170	+	1.05834i
$175$	−8.37998	−	10.2360i	−0.633467	−	0.773770i
$176$			10.0092i			0.754473i
$177$	10.4227	+	5.69982i	0.783414	+	0.428425i
$178$	15.3085	−	26.5151i	1.14742	−	1.98739i
$179$	−9.49333	−	5.48098i	−0.709565	−	0.409667i	0.101335	−	0.994852i	$-0.467689\pi$
$179$	−9.49333	−	5.48098i	−0.709565	−	0.409667i	−0.810900	+	0.585185i	$0.801022\pi$
$180$	25.6134	+	13.1193i	1.90911	+	0.977852i
$181$		−	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
$186$	−12.0946	+	0.280196i	−0.886817	+	0.0205449i
$187$	−2.18521	−	3.78489i	−0.159798	−	0.276779i
$188$			24.9805i			1.82189i
$189$	10.0807	−	9.34775i	0.733260	−	0.679948i
$190$	15.8698	−	27.7373i	1.15132	−	2.01228i
$191$	18.4619	−	10.6590i	1.33586	−	0.771259i	0.349669	−	0.936873i	$-0.386294\pi$
$191$	18.4619	−	10.6590i	1.33586	−	0.771259i	0.986191	+	0.165614i	$0.0529607\pi$
$192$	−0.153392	−	6.62113i	−0.0110701	−	0.477839i
$193$	−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
$195$	1.39680	−	0.0378260i	0.100027	−	0.00270878i
$196$	−22.2166	−	20.2039i	−1.58690	−	1.44314i
$197$	2.01202			0.143350			0.0716752	−	0.997428i	$-0.477165\pi$
$197$	2.01202			0.143350			0.0716752	+	0.997428i	$0.477165\pi$
$198$	−0.598840	−	12.9174i	−0.0425577	−	0.918003i
$199$	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
$201$	2.07001	−	3.78520i	0.146007	−	0.266987i
$202$	−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
$207$	−4.05968	−	6.33471i	−0.282167	−	0.440293i
$208$	1.05055	+	1.81961i	0.0728428	+	0.126168i
$209$	−9.79371			−0.677445
$210$	−8.61682	+	24.2115i	−0.594617	+	1.67075i
$211$	−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
$213$	22.8205	−	0.528684i	1.56364	−	0.0362248i
$214$	−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
$219$	−17.6945	−	9.67655i	−1.19568	−	0.653880i
$220$	8.29915	+	14.2456i	0.559529	+	0.960437i
$221$	−0.794515	−	0.458713i	−0.0534449	−	0.0308564i
$222$	6.88985	−	12.5987i	0.462417	−	0.845572i
$223$	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
$225$	14.9780	−	0.811821i	0.998534	−	0.0541214i
$226$	4.75615	+	8.23790i	0.316374	+	0.547977i
$227$	10.9223	+	6.30600i	0.724939	+	0.418544i	0.816568	−	0.577250i	$-0.195874\pi$
$227$	10.9223	+	6.30600i	0.724939	+	0.418544i	−0.0916289	+	0.995793i	$0.529207\pi$
$228$	−42.3297	+	0.980654i	−2.80335	+	0.0649454i
$229$	−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
$231$	7.75192	−	1.39274i	0.510039	−	0.0916357i
$232$			21.6073i			1.41859i
$233$	−10.9016	−	18.8822i	−0.714190	−	1.23701i	−0.963271	−	0.268531i	$-0.913462\pi$
$233$	−10.9016	−	18.8822i	−0.714190	−	1.23701i	0.249081	−	0.968483i	$-0.419871\pi$
$234$	−1.46466	−	2.28546i	−0.0957481	−	0.149405i
$235$	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	$0.298128\pi$
$239$			24.9069i			1.61109i	−0.592533	+	0.805546i	$0.701872\pi$
$240$	11.8023	+	19.2210i	0.761833	+	1.24071i
$241$	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
$243$	1.80134	+	15.4840i	0.115556	+	0.993301i
$244$			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
$249$	−6.06795	+	0.140577i	−0.384541	+	0.00890868i
$250$	−24.1172	+	14.3040i	−1.52531	+	0.904662i
$251$	−27.3925			−1.72900			−0.864501	−	0.502631i	$-0.832365\pi$
$251$	−27.3925			−1.72900			−0.864501	+	0.502631i	$0.832365\pi$
$252$	33.3653	−	6.79582i	2.10182	−	0.428096i
$253$		−	4.31044i		−	0.270995i
$254$	−13.0024	+	7.50691i	−0.815840	+	0.471026i
$255$	−8.65923	−	4.69156i	−0.542262	−	0.293797i
$256$	16.0256	−	27.7571i	1.00160	−	1.73482i
$257$	−26.3170	+	15.1941i	−1.64161	+	0.947783i	−0.661347	+	0.750080i	$0.730015\pi$
$257$	−26.3170	+	15.1941i	−1.64161	+	0.947783i	−0.980262	+	0.197703i	$0.936652\pi$
$258$	−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
$261$	−0.522685	−	11.2747i	−0.0323534	−	0.697889i
$262$	−18.2835	+	31.6679i	−1.12956	+	1.95645i
$263$	9.66832	−	16.7460i	0.596174	−	1.03260i	−0.397206	−	0.917729i	$-0.630020\pi$
$263$	9.66832	−	16.7460i	0.596174	−	1.03260i	0.993380	−	0.114874i	$-0.0366465\pi$
$264$	8.20304	−	15.0000i	0.504862	−	0.923187i
$265$	−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	$-0.599315\pi$
$269$	11.0008	−	19.0539i	0.670729	−	1.16174i	0.977698	−	0.210017i	$-0.0673520\pi$
$270$	−16.3815	−	24.0996i	−0.996943	−	1.46665i
$271$	−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
$273$	1.26307	−	1.06682i	0.0764445	−	0.0645671i
$274$	39.4086			2.38076
$275$	7.47554	+	4.23839i	0.450792	+	0.255584i
$276$	−0.431609	−	18.6303i	−0.0259798	−	1.12141i
$277$	−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	$0.0199594\pi$
$281$			2.10086i			0.125327i	−0.998035	+	0.0626633i	$0.980041\pi$
$282$	12.1367	−	22.1931i	0.722731	−	1.32158i
$283$	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
$285$	−18.8071	+	11.5482i	−1.11404	+	0.684054i
$286$		−	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
$291$	0.328446	+	14.1773i	0.0192539	+	0.831088i
$292$	−24.9755	−	43.2588i	−1.46158	−	2.53153i
$293$			17.2734i			1.00912i	0.863376	+	0.504561i	$0.168346\pi$
$293$			17.2734i			1.00912i	−0.863376	+	0.504561i	$0.831654\pi$
$294$	9.92159	+	28.7434i	0.578639	+	1.67635i
$295$	13.3114	+	7.61610i	0.775022	+	0.443427i
$296$	16.4414	−	9.49242i	0.955634	−	0.551736i
$297$	−3.91752	+	8.02549i	−0.227317	+	0.465686i
$298$	27.5897	+	15.9289i	1.59823	+	0.922737i
$299$	−0.452418	−	0.783611i	−0.0261640	−	0.0453174i
$300$	32.7346	+	17.5703i	1.88993	+	1.01442i
$301$	20.7274	−	16.6999i	1.19471	−	0.962568i
$302$	41.8671			2.40918
$303$	1.89491	+	1.03627i	0.108860	+	0.0595319i
$304$	−28.7397	−	16.5929i	−1.64833	−	0.951666i
$305$	1.80509	+	3.09846i	0.103359	+	0.177417i
$306$	0.886007	+	19.1119i	0.0506497	+	1.09255i
$307$	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	−0.975465	−	0.220154i	$-0.929344\pi$
$311$	−5.23895	+	9.07413i	−0.297074	+	0.514547i	0.678391	+	0.734701i	$0.262677\pi$
$312$	−0.0831209	−	3.58789i	−0.00470579	−	0.203124i
$313$	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
$315$	13.2440	−	11.8151i	0.746214	−	0.665707i
$316$	−59.5008			−3.34718
$317$	−15.4693	−	26.7935i	−0.868840	−	1.50487i	−0.863183	−	0.504890i	$-0.831533\pi$
$317$	−15.4693	−	26.7935i	−0.868840	−	1.50487i	−0.00565618	−	0.999984i	$-0.501800\pi$
$318$	0.146321	+	6.31592i	0.00820529	+	0.354179i
$319$	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
$324$	−16.1284	+	35.0795i	−0.896023	+	1.94886i
$325$	1.80386	−	0.0141102i	0.100060	−	0.000782691i
$326$	36.6235	+	21.1446i	2.02839	+	1.17109i
$327$	13.8497	+	7.57394i	0.765888	+	0.418840i
$328$	15.1318			0.835514
$329$	14.3693	+	5.55671i	0.792207	+	0.306351i
$330$	−0.451924	−	16.6881i	−0.0248776	−	0.918652i
$331$	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
$333$	−8.34952	+	5.35089i	−0.457551	+	0.293227i
$334$	−15.6573	+	9.03973i	−0.856728	+	0.494632i
$335$	2.76594	−	4.83432i	0.151120	−	0.264127i
$336$	25.1077	+	9.04657i	1.36973	+	0.493531i
$337$		−	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
$339$	−0.152152	−	6.56759i	−0.00826375	−	0.356703i
$340$	−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
$345$	−5.08261	−	8.27745i	−0.273639	−	0.445643i
$346$	−19.5173	−	11.2683i	−1.04926	−	0.605789i
$347$	−0.221030	+	0.382835i	−0.0118655	+	0.0205516i	−0.871897	−	0.489689i	$-0.837110\pi$
$347$	−0.221030	+	0.382835i	−0.0118655	+	0.0205516i	0.860032	+	0.510241i	$0.170444\pi$
$348$	13.4132	−	24.5272i	0.719021	−	1.31480i
$349$			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	−0.127480	−	0.991841i	$-0.540689\pi$
$353$	−19.7311	−	11.3917i	−1.05018	−	0.606321i	−0.922700	+	0.385520i	$0.874022\pi$
$354$	−0.690035	−	29.7852i	−0.0366750	−	1.58307i
$355$	29.4688	−	0.115254i	1.56404	−	0.00611703i
$356$	−52.3709			−2.77565
$357$	−11.4693	+	2.06062i	−0.607018	+	0.109059i
$358$			27.4923i			1.45301i
$359$	21.6706	−	12.5115i	1.14373	−	0.660333i	0.196378	−	0.980528i	$-0.437082\pi$
$359$	21.6706	−	12.5115i	1.14373	−	0.660333i	0.947351	+	0.320195i	$0.103749\pi$
$360$	−1.93461	−	38.4775i	−0.101963	−	2.02794i
$361$	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
$366$	3.34247	−	6.11201i	0.174714	−	0.319480i
$367$	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
$369$	−7.89582	+	0.366042i	−0.411040	+	0.0190554i
$370$	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
$375$	19.3531	−	0.675620i	0.999391	−	0.0348889i
$376$	28.9620	−	16.7212i	1.49360	−	0.862332i
$377$		−	1.35737i		−	0.0699081i
$378$	−32.9441	−	10.1729i	−1.69446	−	0.523239i
$379$	−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
$381$	10.3660	−	0.240150i	0.531067	−	0.0123033i
$382$	−46.3021	−	26.7325i	−2.36902	−	1.36776i
$383$	13.6576	−	7.88522i	0.697870	−	0.402916i	−0.108683	−	0.994076i	$-0.534663\pi$
$383$	13.6576	−	7.88522i	0.697870	−	0.402916i	0.806554	+	0.591161i	$0.201330\pi$
$384$	−23.4195	+	14.2545i	−1.19512	+	0.727422i
$385$	10.0404	−	1.60503i	0.511708	−	0.0818001i
$386$			34.9514i			1.77898i
$387$	1.39770	+	30.1495i	0.0710490	+	1.53258i
$388$	−17.5619	+	30.4181i	−0.891570	+	1.54424i
$389$	−29.5749	−	17.0751i	−1.49951	−	0.865740i	−0.499506	−	0.866310i	$-0.666485\pi$
$389$	−29.5749	−	17.0751i	−1.49951	−	0.865740i	−1.00000		0.000570006i	$0.999819\pi$
$390$	−1.83372	−	2.98637i	−0.0928542	−	0.151221i
$391$			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
$396$	−18.6231	+	11.9349i	−0.935848	+	0.599750i
$397$	−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
$399$	−8.85179	+	24.5671i	−0.443144	+	1.22989i
$400$	14.7562	+	25.1029i	0.737808	+	1.25514i
$401$	10.8316	−	6.25361i	0.540903	−	0.312290i	−0.204542	−	0.978858i	$-0.565571\pi$
$401$	10.8316	−	6.25361i	0.540903	−	0.312290i	0.745445	+	0.666568i	$0.232237\pi$
$402$	−10.8171	+	0.250600i	−0.539508	+	0.0124988i
$403$	0.870163	+	0.502389i	0.0433459	+	0.0250258i
$404$	2.67464	+	4.63261i	0.133068	+	0.230481i
$405$	1.94027	+	20.0309i	0.0964127	+	0.995341i
$406$	23.2842	+	9.00415i	1.15558	+	0.446868i
$407$	−5.68142			−0.281617
$408$	−12.1367	+	22.1931i	−0.600857	+	1.09872i
$409$	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
$411$	−23.8788	−	13.0586i	−1.17786	−	0.644132i
$412$	−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
$417$	25.5105	−	0.591002i	1.24925	−	0.0289415i
$418$	12.2812	+	21.2717i	0.600693	+	1.04043i
$419$	10.0144			0.489233			0.244617	−	0.969620i	$-0.421338\pi$
$419$	10.0144			0.489233			0.244617	+	0.969620i	$0.421338\pi$
$420$	43.2354	−	7.94253i	2.10967	−	0.387556i
$421$	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
$423$	−14.7080	+	9.42579i	−0.715127	+	0.458298i
$424$	−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
$429$	−0.515315	+	0.942302i	−0.0248797	+	0.0454948i
$430$	−28.4009	−	48.7504i	−1.36961	−	2.35095i
$431$	2.54530	+	1.46953i	0.122603	+	0.0707847i	0.560047	−	0.828461i	$-0.310783\pi$
$431$	2.54530	+	1.46953i	0.122603	+	0.0707847i	−0.437444	+	0.899245i	$0.644116\pi$
$432$	−25.0930	+	16.9136i	−1.20729	+	0.813757i
$433$	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
$435$	−0.394453	−	14.5659i	−0.0189126	−	0.698382i
$436$	19.5486	+	33.8592i	0.936208	+	1.62156i
$437$	12.3767	+	7.14567i	0.592056	+	0.341824i
$438$	1.17147	+	50.5661i	0.0559749	+	2.41614i
$439$	−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
$441$	3.51274	−	20.7041i	0.167273	−	0.985911i
$442$			2.30088i			0.109442i
$443$	13.1347	+	22.7499i	0.624048	+	1.08088i	0.988724	+	0.149748i	$0.0478463\pi$
$443$	13.1347	+	22.7499i	0.624048	+	1.08088i	−0.364676	+	0.931134i	$0.618820\pi$
$444$	−24.5558	+	0.568886i	−1.16537	+	0.0269981i
$445$	−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	$-0.676821\pi$
$449$		−	36.0069i		−	1.69927i	0.527369	−	0.849636i	$-0.323179\pi$
$450$	−20.5455	−	31.5138i	−0.968524	−	1.48557i
$451$	−3.92167	−	2.26418i	−0.184664	−	0.106616i
$452$	8.13550	−	14.0911i	0.382662	−	0.662789i
$453$	−25.3685	−	13.8732i	−1.19192	−	0.651821i
$454$		−	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
$459$	5.79612	−	11.8740i	0.270540	−	0.554232i
$460$	−0.0940911	−	24.0579i	−0.00438702	−	1.12170i
$461$	22.8072			1.06224			0.531119	−	0.847298i	$-0.321772\pi$
$461$	22.8072			1.06224			0.531119	+	0.847298i	$0.321772\pi$
$462$	−12.7458	−	15.0905i	−0.592989	−	0.702072i
$463$		−	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
$465$	9.48370	+	5.13826i	0.439796	+	0.238281i
$466$	−27.3411	+	47.3561i	−1.26655	+	2.19373i
$467$	9.43053	−	5.44472i	0.436393	−	0.251951i	−0.265674	−	0.964063i	$-0.585594\pi$
$467$	9.43053	−	5.44472i	0.436393	−	0.251951i	0.702066	+	0.712112i	$0.252261\pi$
$468$	−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
$471$	2.19307	+	1.19932i	0.101051	+	0.0552617i
$472$	19.6948	−	34.1124i	0.906527	−	1.57015i
$473$	−8.64555	+	14.9745i	−0.397523	+	0.688530i
$474$	52.8615	+	28.9083i	2.42801	+	1.32780i
$475$	−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	−0.724431	−	0.689348i	$-0.757897\pi$
$479$	5.13835	−	8.89989i	0.234777	−	0.406646i	0.959208	+	0.282701i	$0.0912305\pi$
$480$	5.75551	−	10.6230i	0.262702	−	0.484870i
$481$	−1.03285	+	0.596314i	−0.0470938	+	0.0271896i
$482$		−	42.7021i		−	1.94503i
$483$	−10.8125	−	3.89588i	−0.491988	−	0.177269i
$484$	34.5173			1.56897
$485$	0.0716017	+	18.3076i	0.00325126	+	0.831305i
$486$	31.3720	−	23.3292i	1.42306	−	1.05824i
$487$	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	$0.0992704\pi$
$491$			13.5981i			0.613672i	−0.951762	+	0.306836i	$0.900730\pi$
$492$	−17.1767	−	9.39338i	−0.774384	−	0.423486i
$493$	−4.78350	+	8.28527i	−0.215438	+	0.373150i
$494$	4.46529	+	2.57804i	0.200903	+	0.115991i
$495$	−5.25601	+	10.2616i	−0.236240	+	0.461224i
$496$			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
$501$	12.4826	−	0.289186i	0.557683	−	0.0129199i
$502$	34.3499	+	59.4958i	1.53311	+	2.65543i
$503$			0.513189i			0.0228819i	0.999935	+	0.0114410i	$0.00364185\pi$
$503$			0.513189i			0.0228819i	−0.999935	+	0.0114410i	$0.996358\pi$
$504$	−30.2127	−	34.1343i	−1.34578	−	1.52046i
$505$	2.42011	+	1.38466i	0.107693	+	0.0616165i
$506$	−9.36215	+	5.40524i	−0.416198	+	0.240292i
$507$	−0.516283	−	22.2852i	−0.0229289	−	0.989722i
$508$	22.2408	+	12.8407i	0.986776	+	0.569715i
$509$	9.40202	+	16.2848i	0.416737	+	0.721810i	0.995609	−	0.0936084i	$-0.0298402\pi$
$509$	9.40202	+	16.2848i	0.416737	+	0.721810i	−0.578872	+	0.815419i	$0.696507\pi$
$510$	0.668639	+	24.6908i	0.0296079	+	1.09333i
$511$	−30.4390	+	4.74387i	−1.34654	+	0.209856i
$512$	−48.7256			−2.15339
$513$	−16.5495	−	24.5528i	−0.730677	−	1.08403i
$514$	66.0024	+	38.1065i	2.91124	+	1.68081i
$515$	−8.01058	+	4.66678i	−0.352988	+	0.205643i
$516$	−35.8678	+	65.5875i	−1.57899	+	2.88733i
$517$	−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	$0.398343\pi$
$521$	−15.1847	+	26.3007i	−0.665254	+	1.15225i	−0.979216	+	0.202818i	$0.934990\pi$
$522$	−23.8330	+	15.2736i	−1.04314	+	0.668509i
$523$	−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
$525$	17.3884	−	14.9213i	0.758891	−	0.651218i
$526$	−48.4958			−2.11452
$527$	−3.54093	−	6.13308i	−0.154246	−	0.267161i
$528$	−17.3318	+	0.401527i	−0.754271	+	0.0174742i
$529$	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
$534$	46.5272	+	25.4443i	2.01343	+	1.10108i
$535$	2.13985	−	1.24663i	0.0925138	−	0.0538964i
$536$	−12.3886	−	7.15257i	−0.535106	−	0.308944i
$537$	9.10995	−	16.6584i	0.393123	−	0.718862i
$538$	−55.1794			−2.37895
$539$	8.09436	−	8.90071i	0.348649	−	0.383381i
$540$	−21.6896	+	44.8782i	−0.933374	+	1.93125i
$541$	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
$543$	9.33855	−	0.216347i	0.400755	−	0.00928432i
$544$	−6.86984	+	3.96630i	−0.294542	+	0.170054i
$545$	17.6883	+	10.1203i	0.757683	+	0.433506i
$546$	−3.90099	−	1.40557i	−0.166947	−	0.0601528i
$547$			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
$549$	−4.05060	+	2.59587i	−0.172875	+	0.110789i
$550$	−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
$555$	−10.9102	+	6.69919i	−0.463111	+	0.284365i
$556$	54.7339	+	31.6007i	2.32124	+	1.34017i
$557$	10.1745	−	17.6227i	0.431106	−	0.746697i	−0.565863	−	0.824499i	$-0.691457\pi$
$557$	10.1745	−	17.6227i	0.431106	−	0.746697i	0.996969	+	0.0778021i	$0.0247902\pi$
$558$	−0.970366	−	20.9316i	−0.0410789	−	0.886104i
$559$			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	−0.321030	−	0.947069i	$-0.604029\pi$
$563$	−30.8870	−	17.8326i	−1.30173	−	0.751555i	−0.980701	+	0.195514i	$0.937362\pi$
$564$	−43.2559	+	1.00211i	−1.82140	+	0.0421966i
$565$	−0.0331693	−	8.48094i	−0.00139544	−	0.356796i
$566$	−12.5499			−0.527513
$567$	16.5908	+	17.0805i	0.696749	+	0.717315i
$568$		−	75.6885i		−	3.17582i
$569$	−21.8018	+	12.5873i	−0.913977	+	0.527685i	−0.881709	−	0.471794i	$-0.843607\pi$
$569$	−21.8018	+	12.5873i	−0.913977	+	0.527685i	−0.0322687	+	0.999479i	$0.510273\pi$
$570$	48.6662	+	26.3673i	2.03840	+	1.10440i
$571$	−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
$576$	11.4589	−	0.531223i	0.477455	−	0.0221343i
$577$	−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
$579$	11.5816	−	21.1781i	0.481316	−	0.880130i
$580$	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
$585$	0.121533	+	2.41716i	0.00502475	+	0.0999371i
$586$	37.5173	−	21.6606i	1.54983	−	0.894792i
$587$			31.8719i			1.31549i	0.753240	+	0.657746i	$0.228490\pi$
$587$			31.8719i			1.31549i	−0.753240	+	0.657746i	$0.771510\pi$
$588$	34.0936	−	39.2805i	1.40600	−	1.61990i
$589$	−15.8698			−0.653905
$590$	−0.150428	−	38.4626i	−0.00619304	−	1.58348i
$591$	0.0807137	+	3.48398i	0.00332012	+	0.143312i
$592$	−16.6721	−	9.62566i	−0.685220	−	0.395612i
$593$	−28.4985	+	16.4536i	−1.17029	+	0.675669i	−0.953749	−	0.300603i	$-0.902812\pi$
$593$	−28.4985	+	16.4536i	−1.17029	+	0.675669i	−0.216545	+	0.976273i	$0.569479\pi$
$594$	22.3436	−	1.55514i	0.916771	−	0.0638080i
$595$	−14.8552	+	2.37471i	−0.609005	+	0.0973537i
$596$		−	54.4935i		−	2.23214i
$597$	−6.62334	+	12.1114i	−0.271075	+	0.495686i
$598$	−1.13465	+	1.96528i	−0.0463995	+	0.0803662i
$599$	−18.8935	−	10.9082i	−0.771968	−	0.445696i	0.0616082	−	0.998100i	$-0.480377\pi$
$599$	−18.8935	−	10.9082i	−0.771968	−	0.445696i	−0.833576	+	0.552404i	$0.813710\pi$
$600$	−1.54085	−	49.7131i	−0.0629049	−	2.02953i
$601$		−	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
$606$	−0.125453	−	5.41515i	−0.00509619	−	0.219976i
$607$	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
$609$	−11.1249	−	13.1714i	−0.450805	−	0.533733i
$610$	4.46621	−	7.80604i	0.180831	−	0.316057i
$611$	−1.81940	+	1.05043i	−0.0736049	+	0.0424958i
$612$	27.5537	−	17.6581i	1.11379	−	0.713787i
$613$	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
$615$	−10.2007	+	0.276240i	−0.411330	+	0.0111391i
$616$	−4.02149	−	25.8038i	−0.162030	−	1.03967i
$617$	13.1311			0.528637			0.264318	−	0.964435i	$-0.414853\pi$
$617$	13.1311			0.528637			0.264318	+	0.964435i	$0.414853\pi$
$618$	15.8016	+	8.64141i	0.635635	+	0.347609i
$619$	−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
$621$	10.8062	−	7.28380i	0.433639	−	0.292289i
$622$	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
$627$	−0.392882	−	16.9587i	−0.0156902	−	0.677264i
$628$	3.09548	+	5.36153i	0.123523	+	0.213948i
$629$	8.40588			0.335164
$630$	−42.2699	−	13.9495i	−1.68407	−	0.555762i
$631$	−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
$633$	−0.198730	−	8.57811i	−0.00789879	−	0.340949i
$634$	−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
$639$	1.83092	+	39.4945i	0.0724303	+	1.56238i
$640$	−30.5831	+	17.8170i	−1.20890	+	0.704280i
$641$	4.25254	+	2.45520i	0.167965	+	0.0969747i	0.581626	−	0.813456i	$-0.302417\pi$
$641$	4.25254	+	2.45520i	0.167965	+	0.0969747i	−0.413661	+	0.910431i	$0.635750\pi$
$642$	−4.22106	−	2.30836i	−0.166592	−	0.0911039i
$643$	−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
$645$	1.05480	+	38.9503i	0.0415325	+	1.53367i
$646$	−18.1705	−	31.4723i	−0.714910	−	1.23826i
$647$	0.206934	+	0.119473i	0.00813542	+	0.00469699i	0.504062	−	0.863667i	$-0.331838\pi$
$647$	0.206934	+	0.119473i	0.00813542	+	0.00469699i	−0.495927	+	0.868364i	$0.665172\pi$
$648$	51.4665	−	4.78214i	2.02179	−	0.187860i
$649$	−10.2085	+	5.89388i	−0.400719	+	0.231355i
$650$	−2.29267	−	3.90024i	−0.0899259	−	0.152980i
$651$	12.5613	−	2.25681i	0.492316	−	0.0884515i
$652$		−	72.3365i		−	2.83292i
$653$	0.979061	+	1.69578i	0.0383136	+	0.0663611i	0.884546	−	0.466452i	$-0.154468\pi$
$653$	0.979061	+	1.69578i	0.0383136	+	0.0663611i	−0.846233	+	0.532813i	$0.821135\pi$
$654$	−0.916922	−	39.5787i	−0.0358545	−	1.54765i
$655$	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	$0.211621\pi$
$659$			31.6741i			1.23385i	−0.787023	+	0.616924i	$0.788379\pi$
$660$	−24.3345	+	14.9422i	−0.947221	+	0.581623i
$661$	−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
$663$	0.762429	−	1.39417i	0.0296103	−	0.0541452i
$664$			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
$669$	0.627947	+	27.1052i	0.0242778	+	1.04795i
$670$	−13.9685	+	0.0546311i	−0.539649	+	0.00211059i
$671$	−2.75622			−0.106403
$672$	−2.52792	−	14.0703i	−0.0975167	−	0.542772i
$673$			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
$675$	2.00659	+	25.9032i	0.0772338	+	0.997013i
$676$	27.6054	−	47.8140i	1.06175	−	1.83900i
$677$	6.22623	−	3.59472i	0.239294	−	0.138156i	−0.375558	−	0.926799i	$-0.622549\pi$
$677$	6.22623	−	3.59472i	0.239294	−	0.138156i	0.614852	+	0.788643i	$0.289216\pi$
$678$	−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
$681$	−10.4812	+	19.1659i	−0.401641	+	0.734438i
$682$	6.00226	−	10.3962i	0.229838	−	0.398092i
$683$	4.02013	−	6.96307i	0.153826	−	0.266435i	−0.778805	−	0.627266i	$-0.784174\pi$
$683$	4.02013	−	6.96307i	0.153826	−	0.266435i	0.932631	+	0.360832i	$0.117507\pi$
$684$	−3.39617	−	73.2582i	−0.129856	−	2.80110i
$685$	−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
$690$	−11.6049	+	21.4191i	−0.441789	+	0.815412i
$691$	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
$693$	2.72263	+	13.3672i	0.103424	+	0.507780i
$694$	1.10867			0.0420847
$695$	32.9425	−	0.128839i	1.24958	−	0.00488715i
$696$	−37.4149	+	0.866792i	−1.41821	+	0.0328557i
$697$	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	$-0.995315\pi$
$701$		−	0.779307i		−	0.0294340i	0.999892	−	0.0147170i	$-0.00468474\pi$
$702$	3.89871	−	2.62787i	0.147147	−	0.0991827i
$703$	9.41841	−	16.3132i	0.355222	−	0.615263i
$704$	5.69137	+	3.28592i	0.214502	+	0.123843i
$705$	−19.2187	+	11.8009i	−0.723817	+	0.444446i
$706$			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
$711$	−22.4512	−	35.0328i	−0.841985	−	1.31383i
$712$	35.0556	+	60.7181i	1.31376	+	2.27551i
$713$		−	6.98468i		−	0.261578i
$714$	18.8579	+	22.3269i	0.705740	+	0.835565i
$715$	−0.688564	+	1.20347i	−0.0257508	+	0.0450074i
$716$	40.7259	−	23.5131i	1.52200	−	0.878725i
$717$	−43.1284	+	0.999158i	−1.61066	+	0.0373142i
$718$	−54.3493	−	31.3786i	−2.02830	−	1.17104i
$719$	−9.09980	−	15.7613i	−0.339365	−	0.587798i	0.644948	−	0.764226i	$-0.276879\pi$
$719$	−9.09980	−	15.7613i	−0.339365	−	0.587798i	−0.984313	+	0.176428i	$0.943546\pi$
$720$	−32.8093	+	21.2077i	−1.22273	+	0.790365i
$721$	−3.95641	+	10.2310i	−0.147344	+	0.381024i
$722$	−33.7855			−1.25737
$723$	−14.1499	+	25.8745i	−0.526241	+	0.962281i
$724$	20.0363	+	11.5680i	0.744643	+	0.429920i
$725$	−0.147142	−	18.8108i	−0.00546472	−	0.698617i
$726$	−30.6658	−	16.7701i	−1.13811	−	0.622398i
$727$	−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
$732$	−11.9127	+	0.275983i	−0.440307	+	0.0102006i
$733$	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
$735$	5.04864	−	26.6367i	0.186222	−	0.982508i
$736$	−7.82374			−0.288387
$737$	2.14048	+	3.70742i	0.0788457	+	0.136565i
$738$	10.6963	+	16.6905i	0.393736	+	0.614385i
$739$	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	$-0.522209\pi$
$743$	−3.80063			−0.139432			−0.0697159	+	0.997567i	$0.522209\pi$
$744$	13.2923	−	24.3062i	0.487319	−	0.891108i
$745$	−14.2980	−	24.5427i	−0.523840	−	0.899177i
$746$	30.7004	+	17.7249i	1.12402	+	0.648953i
$747$	−0.486841	−	10.5015i	−0.0178126	−	0.384231i
$748$	18.7489			0.685526
$749$	1.05687	−	2.73300i	0.0386171	−	0.0998616i
$750$	−25.7360	−	41.1872i	−0.939747	−	1.50394i
$751$	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
$753$	−1.09887	−	47.4325i	−0.0400451	−	1.72854i
$754$	−2.94817	+	1.70213i	−0.107366	+	0.0619878i
$755$	−32.3997	−	18.5374i	−1.17915	−	0.674645i
$756$	13.1060	+	57.5023i	0.476661	+	2.09134i
$757$		−	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
$759$	7.46390	−	0.172917i	0.270922	−	0.00627647i
$760$	36.8368	+	63.2307i	1.33621	+	2.29362i
$761$	21.8912	+	37.9167i	0.793556	+	1.37448i	0.923752	+	0.382992i	$0.125106\pi$
$761$	21.8912	+	37.9167i	0.793556	+	1.37448i	−0.130195	+	0.991488i	$0.541560\pi$
$762$	−13.5205	−	22.2135i	−0.489795	−	0.804712i
$763$	23.8249	−	3.71308i	0.862521	−	0.134423i
$764$			91.4531i			3.30866i
$765$	7.77647	−	15.1824i	0.281159	−	0.548921i
$766$	−34.2529	−	19.7759i	−1.23761	−	0.714533i
$767$	−1.23723	+	2.14294i	−0.0446737	+	0.0773771i
$768$	48.7066	+	26.6361i	1.75755	+	0.961149i
$769$			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	0.983504	−	0.180887i	$-0.0578968\pi$
$773$	36.6610	+	21.1662i	1.31860	+	0.761296i	0.335099	+	0.942183i	$0.391230\pi$
$774$	63.7310	−	40.8428i	2.29077	−	1.46806i
$775$	12.1134	+	6.86793i	0.435128	+	0.246703i
$776$	47.0217			1.68798
$777$	−5.13500	+	14.2516i	−0.184217	+	0.511272i
$778$			85.6477i			3.07062i
$779$	13.0024	−	7.50691i	0.465858	−	0.268963i
$780$	−2.85556	+	5.27052i	−0.102245	+	0.188715i
$781$	−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
$786$	−55.5691	−	30.3890i	−1.98208	−	1.08394i
$787$	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
$789$	29.3850	+	16.0697i	1.04613	+	0.572098i
$790$	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
$795$	2.68325	−	4.95249i	0.0951652	−	0.175647i
$796$	−29.6095	+	17.0951i	−1.04948	+	0.605918i
$797$			27.5780i			0.976865i	0.872602	+	0.488432i	$0.162431\pi$
$797$			27.5780i			0.976865i	−0.872602	+	0.488432i	$0.837569\pi$
$798$	64.4590	−	11.5810i	2.28182	−	0.409962i
$799$	14.8073			0.523843
$800$	7.69296	−	13.5686i	0.271987	−	0.479723i
$801$	−19.7609	−	30.8349i	−0.698217	−	1.08950i
$802$	−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
$807$	33.4348	+	18.2844i	1.17696	+	0.643642i
$808$	3.58065	−	6.20187i	0.125967	−	0.218181i
$809$	27.0106	+	15.5946i	0.949641	+	0.548275i	0.892969	−	0.450117i	$-0.148618\pi$
$809$	27.0106	+	15.5946i	0.949641	+	0.548275i	0.0566716	+	0.998393i	$0.481951\pi$
$810$	41.0734	−	29.3327i	1.44317	−	1.03064i
$811$			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
$816$	25.6431	−	0.594075i	0.897689	−	0.0207968i
$817$	−28.6645	−	49.6483i	−1.00284	−	1.73697i
$818$		−	16.1948i		−	0.566237i
$819$	1.89797	+	2.14432i	0.0663203	+	0.0749286i
$820$	−21.9374	−	12.5514i	−0.766088	−	0.438315i
$821$	−30.7324	+	17.7433i	−1.07257	+	0.619247i	−0.928882	−	0.370377i	$-0.879229\pi$
$821$	−30.7324	+	17.7433i	−1.07257	+	0.619247i	−0.143685	+	0.989623i	$0.545895\pi$
$822$	1.58091	+	68.2395i	0.0551405	+	2.38012i
$823$	−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
$825$	−7.03925	+	13.1146i	−0.245075	+	0.456590i
$826$	−28.5527	−	35.4386i	−0.993474	−	1.23307i
$827$	−21.6751			−0.753717			−0.376859	−	0.926271i	$-0.622996\pi$
$827$	−21.6751			−0.753717			−0.376859	+	0.926271i	$0.622996\pi$
$828$	32.2426	−	1.49473i	1.12051	−	0.0519456i
$829$	−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
$831$	1.39283	−	2.54693i	0.0483169	−	0.0883519i
$832$	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
$837$	−6.34798	+	13.0046i	−0.219418	+	0.449504i
$838$	−12.5579	−	21.7509i	−0.433805	−	0.751372i
$839$	−31.7155			−1.09494			−0.547471	−	0.836825i	$-0.684409\pi$
$839$	−31.7155			−1.09494			−0.547471	+	0.836825i	$0.684409\pi$
$840$	−38.1489	−	44.8099i	−1.31626	−	1.54609i
$841$	14.8452			0.511904
$842$	−22.3031	−	38.6302i	−0.768617	−	1.33128i
$843$	−3.63782	+	0.0842775i	−0.125293	+	0.00290267i
$844$	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
$849$	7.60437	+	4.15859i	0.260981	+	0.142722i
$850$	0.249421	+	31.8864i	0.00855508	+	1.09369i
$851$	7.17980	+	4.14526i	0.246120	+	0.142098i
$852$	−46.9852	+	85.9168i	−1.60969	+	2.94346i
$853$	−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
$855$	−20.7511	−	32.1029i	−0.709673	−	1.09790i
$856$	−3.18032	−	5.50848i	−0.108701	−	0.188276i
$857$	1.56368	+	0.902790i	0.0534142	+	0.0308387i	0.526469	−	0.850194i	$-0.323516\pi$
$857$	1.56368	+	0.902790i	0.0534142	+	0.0308387i	−0.473055	+	0.881033i	$0.656849\pi$
$858$	2.69285	−	0.0623854i	0.0919324	−	0.00212980i
$859$	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
$861$	−9.22408	+	7.79090i	−0.314356	+	0.265513i
$862$		−	7.37109i		−	0.251060i
$863$	−11.1766	−	19.3584i	−0.380455	−	0.658967i	0.610673	−	0.791883i	$-0.290899\pi$
$863$	−11.1766	−	19.3584i	−0.380455	−	0.658967i	−0.991127	+	0.132916i	$0.957566\pi$
$864$	14.5668	+	7.11056i	0.495573	+	0.241906i
$865$	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
$870$	−31.1421	+	19.1222i	−1.05582	+	0.648304i
$871$	0.778253	+	0.449324i	0.0263701	+	0.0152248i
$872$	26.1705	−	45.3287i	0.886246	−	1.53502i
$873$	−24.5361	+	1.13747i	−0.830420	+	0.0384974i
$874$		−	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
$879$	−29.9104	+	0.692935i	−1.00885	+	0.0233721i
$880$	−22.3811	+	0.0875333i	−0.754467	+	0.00295075i
$881$	40.9882			1.38093			0.690464	−	0.723367i	$-0.257406\pi$
$881$	40.9882			1.38093			0.690464	+	0.723367i	$0.257406\pi$
$882$	−49.3737	+	18.3332i	−1.66250	+	0.617309i
$883$		−	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
$885$	−12.6539	+	23.3554i	−0.425357	+	0.785084i
$886$	32.9415	−	57.0563i	1.10669	−	1.91684i
$887$	−40.7766	+	23.5424i	−1.36914	+	0.790476i	−0.990819	−	0.135196i	$-0.956833\pi$
$887$	−40.7766	+	23.5424i	−1.36914	+	0.790476i	−0.378326	+	0.925672i	$0.623500\pi$
$888$	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
$891$	−14.0540	−	6.46157i	−0.470826	−	0.216471i
$892$	−33.5760	+	58.1554i	−1.12421	+	1.94719i
$893$	16.5909	−	28.7362i	0.555192	−	0.961621i
$894$	−26.4755	+	48.4129i	−0.885473	+	1.61917i
$895$	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
$900$	−29.1114	+	57.3877i	−0.970378	+	1.91292i
$901$	−3.20276	+	1.84912i	−0.106699	+	0.0616030i
$902$			11.3570i			0.378147i
$903$	29.7489	+	35.2213i	0.989980	+	1.17209i
$904$	−21.7827			−0.724480
$905$	12.0592	−	0.0471638i	0.400860	−	0.00156778i
$906$	1.67953	+	72.4965i	0.0557986	+	2.40853i
$907$	−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	$0.0256184\pi$
$911$			4.85314i			0.160792i	−0.996763	+	0.0803958i	$0.974382\pi$
$912$	27.5790	−	50.4309i	0.913234	−	1.66993i
$913$	3.01138	−	5.21587i	0.0996622	−	0.172620i
$914$	−39.6310	−	22.8809i	−1.31088	−	0.756834i
$915$	−5.29284	+	3.24997i	−0.174976	+	0.107441i
$916$		−	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
$921$	0.410480	+	17.7183i	0.0135258	+	0.583837i
$922$	−28.6000	−	49.5366i	−0.941889	−	1.63140i
$923$			4.75475i			0.156505i
$924$	−11.4533	+	31.7873i	−0.376787	+	1.04573i
$925$	−14.2489	+	8.37587i	−0.468500	+	0.275397i
$926$	−50.7629	+	29.3080i	−1.66817	+	0.963120i
$927$	−6.71121	−	10.4722i	−0.220425	−	0.343951i
$928$	−10.1642	−	5.86830i	−0.333656	−	0.192636i
$929$	12.7001	+	21.9973i	0.416678	+	0.721707i	0.995603	−	0.0936737i	$-0.0298611\pi$
$929$	12.7001	+	21.9973i	0.416678	+	0.721707i	−0.578925	+	0.815381i	$0.696528\pi$
$930$	−0.732302	−	27.0416i	−0.0240131	−	0.886730i
$931$	12.1383	+	37.9967i	0.397816	+	1.24529i
$932$	93.5349			3.06384
$933$	−15.9228	−	8.70768i	−0.521289	−	0.285077i
$934$	−23.6515	−	13.6552i	−0.773902	−	0.446813i
$935$	8.44410	−	4.91934i	0.276152	−	0.160880i
$936$	6.20941	−	0.287862i	0.202961	−	0.00940906i
$937$	−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	−0.678198	−	0.734879i	$-0.737239\pi$
$941$	9.12065	−	15.7974i	0.297325	−	0.514982i	0.975523	+	0.219897i	$0.0705723\pi$
$942$	−0.145193	−	6.26721i	−0.00473064	−	0.204197i
$943$	3.30396	+	5.72264i	0.107592	+	0.186355i
$944$	−39.9425			−1.30002
$945$	20.9902	+	22.4591i	0.682811	+	0.730595i
$946$	43.3657			1.40994
$947$	−9.42425	−	16.3233i	−0.306247	−	0.530435i	0.671291	−	0.741194i	$-0.265740\pi$
$947$	−9.42425	−	16.3233i	−0.306247	−	0.530435i	−0.977538	+	0.210759i	$0.932407\pi$
$948$	−2.38692	−	103.031i	−0.0775236	−	3.34629i
$949$	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	$-0.365546\pi$
$953$	25.3110			0.819903			0.409952	+	0.912107i	$0.365546\pi$
$954$	−10.9307	+	0.506736i	−0.353894	+	0.0164062i
$955$	23.9955	+	41.1886i	0.776478	+	1.33283i
$956$	−92.5341	−	53.4246i	−2.99277	−	1.72787i
$957$	9.82641	+	5.37375i	0.317643	+	0.173709i
$958$	−25.7737			−0.832712
$959$	−41.0777	+	6.40189i	−1.32647	+	0.206728i
$960$	14.8038	−	0.400896i	0.477792	−	0.0129389i
$961$	−11.6219	−	20.1298i	−0.374901	−	0.649347i
$962$	2.59035	+	1.49554i	0.0835164	+	0.0482182i
$963$	1.79275	+	2.79741i	0.0577707	+	0.0901453i
$964$	−63.2570	+	36.5214i	−2.03737	+	1.17628i
$965$	15.4754	−	27.0479i	0.498170	−	0.870702i
$966$	5.09706	+	28.3699i	0.163995	+	0.912787i
$967$			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
$969$	0.581285	+	25.0910i	0.0186736	+	0.806039i
$970$	39.6738	−	23.1130i	1.27385	−	0.742114i
$971$	−0.693916	−	1.20190i	−0.0222688	−	0.0385707i	0.854676	−	0.519161i	$-0.173756\pi$
$971$	−0.693916	−	1.20190i	−0.0222688	−	0.0385707i	−0.876945	+	0.480591i	$0.840422\pi$
$972$	−61.3901	−	26.5205i	−1.96909	−	0.850645i
$973$	30.3525	−	24.4548i	0.973056	−	0.783986i
$974$		−	34.7293i		−	1.11280i
$975$	0.0967962	+	3.12298i	0.00309996	+	0.100015i
$976$	−8.08813	−	4.66968i	−0.258895	−	0.149473i
$977$	−28.9058	+	50.0663i	−0.924779	+	1.60176i	−0.132863	+	0.991134i	$0.542417\pi$
$977$	−28.9058	+	50.0663i	−0.924779	+	1.60176i	−0.791916	+	0.610630i	$0.790916\pi$
$978$	−35.1445	+	64.2650i	−1.12380	+	2.05497i
$979$		−	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	0.0957097	−	0.995409i	$-0.469488\pi$
$983$	−22.5265	−	13.0057i	−0.718485	−	0.414818i	−0.814195	+	0.580592i	$0.802821\pi$
$984$	0.607023	+	26.2020i	0.0193512	+	0.835290i
$985$	0.0175957	+	4.49898i	0.000560644	+	0.143349i
$986$	23.9938			0.764119
$987$	−9.04549	+	25.1046i	−0.287921	+	0.799090i
$988$		−	8.81958i		−	0.280588i
$989$	21.8514	−	12.6159i	0.694833	−	0.401162i
$990$	28.8788	−	1.45200i	0.917829	−	0.0461477i
$991$	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
$996$	12.4933	−	22.8452i	0.395866	−	0.723878i
$997$	−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
$999$	−9.60048	−	14.2433i	−0.303746	−	0.450637i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.1	✓	24	1.1	even	1	trivial
105.2.p.a.59.2	yes	24	15.14	odd	2	inner
105.2.p.a.59.11	yes	24	3.2	odd	2	inner
105.2.p.a.59.12	yes	24	5.4	even	2	inner
105.2.p.a.89.1	yes	24	105.89	even	6	inner
105.2.p.a.89.2	yes	24	7.5	odd	6	inner
105.2.p.a.89.11	yes	24	35.19	odd	6	inner
105.2.p.a.89.12	yes	24	21.5	even	6	inner
525.2.t.j.26.1		24	105.68	odd	12
525.2.t.j.26.2		24	35.12	even	12
525.2.t.j.26.11		24	35.33	even	12
525.2.t.j.26.12		24	105.47	odd	12
525.2.t.j.101.1		24	5.3	odd	4
525.2.t.j.101.2		24	15.2	even	4
525.2.t.j.101.11		24	15.8	even	4
525.2.t.j.101.12		24	5.2	odd	4
735.2.g.b.734.1		24	21.17	even	6
735.2.g.b.734.2		24	35.4	even	6
735.2.g.b.734.3		24	35.24	odd	6
735.2.g.b.734.4		24	21.11	odd	6
735.2.g.b.734.21		24	105.74	odd	6
735.2.g.b.734.22		24	7.3	odd	6
735.2.g.b.734.23		24	7.4	even	3
735.2.g.b.734.24		24	105.59	even	6
735.2.p.f.374.1		24	105.104	even	2
735.2.p.f.374.2		24	7.6	odd	2
735.2.p.f.374.11		24	35.34	odd	2
735.2.p.f.374.12		24	21.20	even	2
735.2.p.f.509.1		24	7.2	even	3
735.2.p.f.509.2		24	105.44	odd	6
735.2.p.f.509.11		24	21.2	odd	6
735.2.p.f.509.12		24	35.9	even	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} +(0.0401158 + 1.73159i) 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} +(-2.99678 + 0.138928i) q^{9} +(4.84567 - 2.82298i) q^{10} +(-1.48843 - 0.859346i) q^{11} +(-6.51924 - 3.56517i) q^{12} -0.360784 q^{13} +(2.39327 - 6.18885i) q^{14} +(-3.87156 + 0.104844i) q^{15} +(-2.91187 - 5.04351i) q^{16} +(2.20219 + 1.27144i) q^{17} +(4.05968 + 6.33471i) q^{18} +(4.93492 - 2.84918i) q^{19} +(-8.32614 - 4.76378i) q^{20} +(-3.50091 + 2.95696i) q^{21} +4.31044i q^{22} +(1.25399 + 2.17197i) q^{23} +(0.230390 + 9.94472i) 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} +(5.08261 + 8.27745i) q^{30} +(-2.41187 - 1.39249i) q^{31} +(-1.55977 + 2.70160i) q^{32} +(1.42832 - 2.61182i) 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} +(-0.0144731 - 0.624728i) q^{39} +(0.0502252 + 12.8419i) q^{40} +2.63477 q^{41} +(10.8125 + 3.89588i) q^{42} -10.0606i q^{43} +(6.38529 - 3.68655i) q^{44} +(-0.336857 - 6.69974i) 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} +(-2.11326 + 3.86429i) q^{51} +(0.773871 - 1.34038i) q^{52} +(-0.727175 + 1.25950i) q^{53} +(-10.8062 + 7.28380i) 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} +(7.91488 - 14.6085i) q^{60} +(1.38882 - 0.801836i) q^{61} +6.98468i q^{62} +(-5.26068 - 5.94351i) q^{63} -3.82374 q^{64} +(-0.00315515 - 0.806730i) q^{65} +(-7.46390 + 0.172917i) 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} +(-17.2109 + 0.797880i) q^{72} +(-5.82187 + 10.0838i) q^{73} +(-7.17980 - 4.14526i) q^{74} +(-0.268295 - 8.65610i) 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} +(8.96140 - 0.832672i) q^{81} +(-3.30396 - 5.72264i) q^{82} +3.50427i q^{83} +(-3.47636 - 19.3492i) q^{84} +(-2.82374 + 4.93534i) q^{85} +(-21.8514 + 12.6159i) q^{86} +(-6.51472 + 0.150927i) q^{87} +(-8.54825 - 4.93534i) q^{88} +(6.10392 + 10.5723i) q^{89} +(-14.1292 + 9.13304i) q^{90} +(-0.598876 - 0.743304i) q^{91} -10.7591 q^{92} +(2.31447 - 4.23222i) q^{93} +(-12.6475 - 7.30202i) q^{94} +(6.41406 + 11.0098i) q^{95} +(-4.74063 - 2.59250i) 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

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