LMFDB - Embedded newform 105.2.j.a.92.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(8,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("105.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.j (of order $4$, 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 $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			92.5
Character	$\chi$	$=$	105.92
Dual form			105.2.j.a.8.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.347054 + 0.347054i) q^{2} +(1.72305 - 0.176396i) q^{3} +1.75911i q^{4} +(-1.16790 + 1.90683i) q^{5} +(-0.536770 + 0.659208i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.30461 - 1.30461i) q^{8} +(2.93777 - 0.607876i) q^{9} +O(q^{10})$	\(q+(-0.347054 + 0.347054i) q^{2} +(1.72305 - 0.176396i) q^{3} +1.75911i q^{4} +(-1.16790 + 1.90683i) q^{5} +(-0.536770 + 0.659208i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.30461 - 1.30461i) q^{8} +(2.93777 - 0.607876i) q^{9} +(-0.256447 - 1.06710i) q^{10} -2.67137i q^{11} +(0.310299 + 3.03102i) q^{12} +(2.14945 - 2.14945i) q^{13} +0.490808 q^{14} +(-1.67599 + 3.49157i) q^{15} -2.61267 q^{16} +(3.26719 - 3.26719i) q^{17} +(-0.808598 + 1.23053i) q^{18} +5.24329i q^{19} +(-3.35432 - 2.05447i) q^{20} +(-1.34311 - 1.09365i) q^{21} +(0.927108 + 0.927108i) q^{22} +(-2.54815 - 2.54815i) q^{23} +(-2.47803 - 2.01778i) q^{24} +(-2.27200 - 4.45399i) q^{25} +1.49195i q^{26} +(4.95468 - 1.56561i) q^{27} +(1.24388 - 1.24388i) q^{28} -2.86924 q^{29} +(-0.630101 - 1.79342i) q^{30} -5.28599 q^{31} +(3.51596 - 3.51596i) q^{32} +(-0.471218 - 4.60289i) q^{33} +2.26778i q^{34} +(2.17417 - 0.522500i) q^{35} +(1.06932 + 5.16785i) q^{36} +(-2.14286 - 2.14286i) q^{37} +(-1.81970 - 1.81970i) q^{38} +(3.32444 - 4.08274i) q^{39} +(4.01133 - 0.964012i) q^{40} +11.5768i q^{41} +(0.845684 - 0.0865765i) q^{42} +(0.759108 - 0.759108i) q^{43} +4.69922 q^{44} +(-2.27192 + 6.31177i) q^{45} +1.76869 q^{46} +(-7.66034 + 7.66034i) q^{47} +(-4.50176 + 0.460865i) q^{48} +1.00000i q^{49} +(2.33428 + 0.757266i) q^{50} +(5.05320 - 6.20584i) q^{51} +(3.78111 + 3.78111i) q^{52} +(4.43577 + 4.43577i) q^{53} +(-1.17619 + 2.26289i) q^{54} +(5.09384 + 3.11990i) q^{55} +1.84500i q^{56} +(0.924894 + 9.03442i) q^{57} +(0.995779 - 0.995779i) q^{58} +0.159437 q^{59} +(-6.14204 - 2.94825i) q^{60} +4.72534 q^{61} +(1.83452 - 1.83452i) q^{62} +(-2.50715 - 1.64748i) q^{63} -2.78490i q^{64} +(1.58828 + 6.60897i) q^{65} +(1.76099 + 1.43391i) q^{66} +(-5.41156 - 5.41156i) q^{67} +(5.74734 + 5.74734i) q^{68} +(-4.84006 - 3.94109i) q^{69} +(-0.573216 + 0.935887i) q^{70} -13.5880i q^{71} +(-4.62569 - 3.03961i) q^{72} +(4.16486 - 4.16486i) q^{73} +1.48737 q^{74} +(-4.70043 - 7.27365i) q^{75} -9.22351 q^{76} +(-1.88894 + 1.88894i) q^{77} +(0.263173 + 2.57069i) q^{78} +3.89710i q^{79} +(3.05135 - 4.98193i) q^{80} +(8.26097 - 3.57160i) q^{81} +(-4.01778 - 4.01778i) q^{82} +(4.03778 + 4.03778i) q^{83} +(1.92384 - 2.36267i) q^{84} +(2.41421 + 10.0457i) q^{85} +0.526902i q^{86} +(-4.94383 + 0.506122i) q^{87} +(-3.48510 + 3.48510i) q^{88} +3.95125 q^{89} +(-1.40205 - 2.97900i) q^{90} -3.03977 q^{91} +(4.48247 - 4.48247i) q^{92} +(-9.10800 + 0.932426i) q^{93} -5.31710i q^{94} +(-9.99806 - 6.12366i) q^{95} +(5.43796 - 6.67836i) q^{96} +(-1.86878 - 1.86878i) q^{97} +(-0.347054 - 0.347054i) q^{98} +(-1.62386 - 7.84786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3}+O(q^{10}) $ 24 * q - 4 * q^3	$ 24 q - 4 q^{3} - 16 q^{10} + 16 q^{12} - 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 4 q^{21} + 8 q^{22} - 16 q^{25} - 16 q^{27} + 20 q^{30} + 28 q^{33} + 16 q^{36} - 16 q^{37} + 64 q^{40} - 20 q^{42} - 40 q^{43} + 20 q^{45} - 64 q^{46} + 16 q^{48} - 20 q^{51} + 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} + 32 q^{61} - 8 q^{63} - 16 q^{66} + 24 q^{67} - 8 q^{70} - 8 q^{72} + 32 q^{73} - 60 q^{75} + 32 q^{76} + 60 q^{78} + 52 q^{81} - 80 q^{82} + 24 q^{85} + 4 q^{87} + 96 q^{88} - 24 q^{90} - 24 q^{91} - 76 q^{93} - 96 q^{96} + 24 q^{97}+O(q^{100}) $ 24 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 - 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 4 * q^21 + 8 * q^22 - 16 * q^25 - 16 * q^27 + 20 * q^30 + 28 * q^33 + 16 * q^36 - 16 * q^37 + 64 * q^40 - 20 * q^42 - 40 * q^43 + 20 * q^45 - 64 * q^46 + 16 * q^48 - 20 * q^51 + 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 + 32 * q^61 - 8 * q^63 - 16 * q^66 + 24 * q^67 - 8 * q^70 - 8 * q^72 + 32 * q^73 - 60 * q^75 + 32 * q^76 + 60 * q^78 + 52 * q^81 - 80 * q^82 + 24 * q^85 + 4 * q^87 + 96 * q^88 - 24 * q^90 - 24 * q^91 - 76 * q^93 - 96 * q^96 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.347054	+	0.347054i	−0.245404	+	0.245404i	−0.819081	−	0.573677i	$-0.805516\pi$
$2$	−0.347054	+	0.347054i	−0.245404	+	0.245404i	0.573677	+	0.819081i	$0.305516\pi$
$3$	1.72305	−	0.176396i	0.994801	−	0.101842i
$3$	1.72305	−	0.176396i	0.994801	−	0.101842i
$4$			1.75911i			0.879554i
$5$	−1.16790	+	1.90683i	−0.522302	+	0.852760i
$5$	−1.16790	+	1.90683i	−0.522302	+	0.852760i
$6$	−0.536770	+	0.659208i	−0.219135	+	0.269120i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−1.30461	−	1.30461i	−0.461250	−	0.461250i
$9$	2.93777	−	0.607876i	0.979256	−	0.202625i
$10$	−0.256447	−	1.06710i	−0.0810957	−	0.337446i
$11$		−	2.67137i		−	0.805448i	−0.915322	−	0.402724i	$-0.868064\pi$
$11$		−	2.67137i		−	0.805448i	0.915322	−	0.402724i	$-0.131936\pi$
$12$	0.310299	+	3.03102i	0.0895757	+	0.874981i
$13$	2.14945	−	2.14945i	0.596149	−	0.596149i	−0.343137	−	0.939285i	$-0.611489\pi$
$13$	2.14945	−	2.14945i	0.596149	−	0.596149i	0.939285	+	0.343137i	$0.111489\pi$
$14$	0.490808			0.131174
$15$	−1.67599	+	3.49157i	−0.432740	+	0.901519i
$16$	−2.61267			−0.653169
$17$	3.26719	−	3.26719i	0.792410	−	0.792410i	−0.189475	−	0.981886i	$-0.560679\pi$
$17$	3.26719	−	3.26719i	0.792410	−	0.792410i	0.981886	+	0.189475i	$0.0606787\pi$
$18$	−0.808598	+	1.23053i	−0.190588	+	0.290038i
$19$			5.24329i			1.20289i	0.798913	+	0.601446i	$0.205409\pi$
$19$			5.24329i			1.20289i	−0.798913	+	0.601446i	$0.794591\pi$
$20$	−3.35432	−	2.05447i	−0.750049	−	0.459393i
$21$	−1.34311	−	1.09365i	−0.293090	−	0.238653i
$22$	0.927108	+	0.927108i	0.197660	+	0.197660i
$23$	−2.54815	−	2.54815i	−0.531326	−	0.531326i	0.389641	−	0.920967i	$-0.372599\pi$
$23$	−2.54815	−	2.54815i	−0.531326	−	0.531326i	−0.920967	+	0.389641i	$0.872599\pi$
$24$	−2.47803	−	2.01778i	−0.505826	−	0.411877i
$25$	−2.27200	−	4.45399i	−0.454400	−	0.890798i
$26$			1.49195i			0.292595i
$27$	4.95468	−	1.56561i	0.953529	−	0.301301i
$28$	1.24388	−	1.24388i	0.235071	−	0.235071i
$29$	−2.86924			−0.532804			−0.266402	−	0.963862i	$-0.585835\pi$
$29$	−2.86924			−0.532804			−0.266402	+	0.963862i	$0.585835\pi$
$30$	−0.630101	−	1.79342i	−0.115040	−	0.327432i
$31$	−5.28599			−0.949391			−0.474696	−	0.880150i	$-0.657442\pi$
$31$	−5.28599			−0.949391			−0.474696	+	0.880150i	$0.657442\pi$
$32$	3.51596	−	3.51596i	0.621540	−	0.621540i
$33$	−0.471218	−	4.60289i	−0.0820286	−	0.801260i
$34$			2.26778i			0.388921i
$35$	2.17417	−	0.522500i	0.367501	−	0.0883186i
$36$	1.06932	+	5.16785i	0.178220	+	0.861309i
$37$	−2.14286	−	2.14286i	−0.352284	−	0.352284i	0.508675	−	0.860959i	$-0.330136\pi$
$37$	−2.14286	−	2.14286i	−0.352284	−	0.352284i	−0.860959	+	0.508675i	$0.830136\pi$
$38$	−1.81970	−	1.81970i	−0.295195	−	0.295195i
$39$	3.32444	−	4.08274i	0.532336	−	0.653762i
$40$	4.01133	−	0.964012i	0.634248	−	0.152424i
$41$			11.5768i			1.80800i	0.427537	+	0.903998i	$0.359381\pi$
$41$			11.5768i			1.80800i	−0.427537	+	0.903998i	$0.640619\pi$
$42$	0.845684	−	0.0865765i	0.130492	−	0.0133590i
$43$	0.759108	−	0.759108i	0.115763	−	0.115763i	−0.646852	−	0.762615i	$-0.723915\pi$
$43$	0.759108	−	0.759108i	0.115763	−	0.115763i	0.762615	+	0.646852i	$0.223915\pi$
$44$	4.69922			0.708434
$45$	−2.27192	+	6.31177i	−0.338677	+	0.940903i
$46$	1.76869			0.260779
$47$	−7.66034	+	7.66034i	−1.11738	+	1.11738i	−0.125250	+	0.992125i	$0.539973\pi$
$47$	−7.66034	+	7.66034i	−1.11738	+	1.11738i	−0.992125	+	0.125250i	$0.960027\pi$
$48$	−4.50176	+	0.460865i	−0.649773	+	0.0665201i
$49$			1.00000i			0.142857i
$50$	2.33428	+	0.757266i	0.330117	+	0.107094i
$51$	5.05320	−	6.20584i	0.707589	−	0.868991i
$52$	3.78111	+	3.78111i	0.524345	+	0.524345i
$53$	4.43577	+	4.43577i	0.609300	+	0.609300i	0.942763	−	0.333463i	$-0.108217\pi$
$53$	4.43577	+	4.43577i	0.609300	+	0.609300i	−0.333463	+	0.942763i	$0.608217\pi$
$54$	−1.17619	+	2.26289i	−0.160059	+	0.307940i
$55$	5.09384	+	3.11990i	0.686854	+	0.420687i
$56$			1.84500i			0.246548i
$57$	0.924894	+	9.03442i	0.122505	+	1.19664i
$58$	0.995779	−	0.995779i	0.130752	−	0.130752i
$59$	0.159437			0.0207569			0.0103785	−	0.999946i	$-0.496696\pi$
$59$	0.159437			0.0207569			0.0103785	+	0.999946i	$0.496696\pi$
$60$	−6.14204	−	2.94825i	−0.792934	−	0.380618i
$61$	4.72534			0.605018			0.302509	−	0.953147i	$-0.402176\pi$
$61$	4.72534			0.605018			0.302509	+	0.953147i	$0.402176\pi$
$62$	1.83452	−	1.83452i	0.232984	−	0.232984i
$63$	−2.50715	−	1.64748i	−0.315871	−	0.207563i
$64$		−	2.78490i		−	0.348112i
$65$	1.58828	+	6.60897i	0.197002	+	0.819742i
$66$	1.76099	+	1.43391i	0.216762	+	0.176502i
$67$	−5.41156	−	5.41156i	−0.661127	−	0.661127i	0.294519	−	0.955646i	$-0.404841\pi$
$67$	−5.41156	−	5.41156i	−0.661127	−	0.661127i	−0.955646	+	0.294519i	$0.904841\pi$
$68$	5.74734	+	5.74734i	0.696967	+	0.696967i
$69$	−4.84006	−	3.94109i	−0.582675	−	0.474452i
$70$	−0.573216	+	0.935887i	−0.0685125	+	0.111860i
$71$		−	13.5880i		−	1.61260i	−0.591508	−	0.806299i	$-0.701467\pi$
$71$		−	13.5880i		−	1.61260i	0.591508	−	0.806299i	$-0.298533\pi$
$72$	−4.62569	−	3.03961i	−0.545143	−	0.358221i
$73$	4.16486	−	4.16486i	0.487460	−	0.487460i	−0.420044	−	0.907504i	$-0.637985\pi$
$73$	4.16486	−	4.16486i	0.487460	−	0.487460i	0.907504	+	0.420044i	$0.137985\pi$
$74$	1.48737			0.172904
$75$	−4.70043	−	7.27365i	−0.542758	−	0.839889i
$76$	−9.22351			−1.05801
$77$	−1.88894	+	1.88894i	−0.215265	+	0.215265i
$78$	0.263173	+	2.57069i	0.0297985	+	0.291073i
$79$			3.89710i			0.438458i	0.975673	+	0.219229i	$0.0703542\pi$
$79$			3.89710i			0.438458i	−0.975673	+	0.219229i	$0.929646\pi$
$80$	3.05135	−	4.98193i	0.341152	−	0.556996i
$81$	8.26097	−	3.57160i	0.917886	−	0.396844i
$82$	−4.01778	−	4.01778i	−0.443689	−	0.443689i
$83$	4.03778	+	4.03778i	0.443204	+	0.443204i	0.893087	−	0.449883i	$-0.148534\pi$
$83$	4.03778	+	4.03778i	0.443204	+	0.443204i	−0.449883	+	0.893087i	$0.648534\pi$
$84$	1.92384	−	2.36267i	0.209908	−	0.257789i
$85$	2.41421	+	10.0457i	0.261858	+	1.08961i
$86$			0.526902i			0.0568173i
$87$	−4.94383	+	0.506122i	−0.530034	+	0.0542619i
$88$	−3.48510	+	3.48510i	−0.371513	+	0.371513i
$89$	3.95125			0.418832			0.209416	−	0.977827i	$-0.432844\pi$
$89$	3.95125			0.418832			0.209416	+	0.977827i	$0.432844\pi$
$90$	−1.40205	−	2.97900i	−0.147789	−	0.314014i
$91$	−3.03977			−0.318655
$92$	4.48247	−	4.48247i	0.467330	−	0.467330i
$93$	−9.10800	+	0.932426i	−0.944455	+	0.0966881i
$94$		−	5.31710i		−	0.548417i
$95$	−9.99806	−	6.12366i	−1.02578	−	0.628274i
$96$	5.43796	−	6.67836i	0.555009	−	0.681607i
$97$	−1.86878	−	1.86878i	−0.189746	−	0.189746i	0.605840	−	0.795586i	$-0.292837\pi$
$97$	−1.86878	−	1.86878i	−0.189746	−	0.189746i	−0.795586	+	0.605840i	$0.792837\pi$
$98$	−0.347054	−	0.347054i	−0.0350577	−	0.0350577i
$99$	−1.62386	−	7.84786i	−0.163204	−	0.788740i
$100$	7.83504	−	3.99670i	0.783504	−	0.399670i
$101$			3.76115i			0.374249i	0.982336	+	0.187124i	$0.0599167\pi$
$101$			3.76115i			0.374249i	−0.982336	+	0.187124i	$0.940083\pi$
$102$	0.400027	+	3.90749i	0.0396086	+	0.386899i
$103$	−8.85701	+	8.85701i	−0.872707	+	0.872707i	−0.992767	−	0.120060i	$-0.961691\pi$
$103$	−8.85701	+	8.85701i	−0.872707	+	0.872707i	0.120060	+	0.992767i	$0.461691\pi$
$104$	−5.60838			−0.549947
$105$	3.65402	−	1.28380i	0.356596	−	0.125286i
$106$	−3.07890			−0.299049
$107$	−0.710397	+	0.710397i	−0.0686766	+	0.0686766i	−0.740611	−	0.671934i	$-0.765464\pi$
$107$	−0.710397	+	0.710397i	−0.0686766	+	0.0686766i	0.671934	+	0.740611i	$0.265464\pi$
$108$	2.75407	+	8.71582i	0.265011	+	0.838680i
$109$			19.0144i			1.82125i	0.413237	+	0.910623i	$0.364398\pi$
$109$			19.0144i			1.82125i	−0.413237	+	0.910623i	$0.635602\pi$
$110$	−2.85061	+	0.685064i	−0.271795	+	0.0653183i
$111$	−4.07024	−	3.31425i	−0.386330	−	0.314575i
$112$	1.84744	+	1.84744i	0.174567	+	0.174567i
$113$	−5.69132	−	5.69132i	−0.535394	−	0.535394i	0.386779	−	0.922173i	$-0.373588\pi$
$113$	−5.69132	−	5.69132i	−0.535394	−	0.535394i	−0.922173	+	0.386779i	$0.873588\pi$
$114$	−3.45642	−	2.81444i	−0.323723	−	0.263597i
$115$	7.83488	−	1.88289i	0.730607	−	0.175581i
$116$		−	5.04730i		−	0.468630i
$117$	5.00798	−	7.62117i	0.462988	−	0.704577i
$118$	−0.0553332	+	0.0553332i	−0.00509383	+	0.00509383i
$119$	−4.62051			−0.423561
$120$	6.74166	−	2.36862i	0.615427	−	0.216224i
$121$	3.86380			0.351254
$122$	−1.63995	+	1.63995i	−0.148474	+	0.148474i
$123$	2.04210	+	19.9474i	0.184130	+	1.79859i
$124$		−	9.29862i		−	0.835041i
$125$	11.1465	+	0.869508i	0.996971	+	0.0777712i
$126$	1.44188	−	0.298350i	0.128453	−	0.0265792i
$127$	−12.1366	−	12.1366i	−1.07695	−	1.07695i	−0.996781	−	0.0801668i	$-0.974455\pi$
$127$	−12.1366	−	12.1366i	−1.07695	−	1.07695i	−0.0801668	−	0.996781i	$-0.525545\pi$
$128$	7.99843	+	7.99843i	0.706968	+	0.706968i
$129$	1.17407	−	1.44188i	0.103371	−	0.126950i
$130$	−2.84489	−	1.74245i	−0.249513	−	0.152823i
$131$		−	9.94280i		−	0.868706i	−0.900743	−	0.434353i	$-0.856977\pi$
$131$		−	9.94280i		−	0.868706i	0.900743	−	0.434353i	$-0.143023\pi$
$132$	8.09697	−	0.828923i	0.704751	−	0.0721485i
$133$	3.70756	−	3.70756i	0.321487	−	0.321487i
$134$	3.75620			0.324486
$135$	−2.80124	+	11.2762i	−0.241093	+	0.970502i
$136$	−8.52483			−0.730998
$137$	−13.6645	+	13.6645i	−1.16744	+	1.16744i	−0.184630	+	0.982808i	$0.559109\pi$
$137$	−13.6645	+	13.6645i	−1.16744	+	1.16744i	−0.982808	+	0.184630i	$0.940891\pi$
$138$	3.04753	−	0.311989i	0.259423	−	0.0265583i
$139$		−	16.7933i		−	1.42439i	−0.701982	−	0.712195i	$-0.747701\pi$
$139$		−	16.7933i		−	1.42439i	0.701982	−	0.712195i	$-0.252299\pi$
$140$	0.919133	+	3.82459i	0.0776809	+	0.323237i
$141$	−11.8479	+	14.5504i	−0.997770	+	1.22536i
$142$	4.71576	+	4.71576i	0.395738	+	0.395738i
$143$	−5.74196	−	5.74196i	−0.480167	−	0.480167i
$144$	−7.67544	+	1.58818i	−0.639620	+	0.132349i
$145$	3.35099	−	5.47115i	0.278285	−	0.454354i
$146$			2.89086i			0.239249i
$147$	0.176396	+	1.72305i	0.0145489	+	0.142114i
$148$	3.76952	−	3.76952i	0.309853	−	0.309853i
$149$	−9.31256			−0.762915			−0.381458	−	0.924386i	$-0.624578\pi$
$149$	−9.31256			−0.762915			−0.381458	+	0.924386i	$0.624578\pi$
$150$	4.15565	+	0.893047i	0.339307	+	0.0729169i
$151$	20.3868			1.65905			0.829527	−	0.558466i	$-0.188610\pi$
$151$	20.3868			1.65905			0.829527	+	0.558466i	$0.188610\pi$
$152$	6.84046	−	6.84046i	0.554834	−	0.554834i
$153$	7.61221	−	11.5843i	0.615410	−	0.936535i
$154$		−	1.31113i		−	0.105654i
$155$	6.17353	−	10.0795i	0.495869	−	0.809603i
$156$	7.18199	+	5.84804i	0.575019	+	0.468218i
$157$	6.32887	+	6.32887i	0.505098	+	0.505098i	0.913018	−	0.407919i	$-0.133746\pi$
$157$	6.32887	+	6.32887i	0.505098	+	0.505098i	−0.407919	+	0.913018i	$0.633746\pi$
$158$	−1.35250	−	1.35250i	−0.107599	−	0.107599i
$159$	8.42549	+	6.86058i	0.668185	+	0.544080i
$160$	2.59804	+	10.8106i	0.205393	+	0.854657i
$161$			3.60363i			0.284006i
$162$	−1.62746	+	4.10654i	−0.127866	+	0.322640i
$163$	−6.45638	+	6.45638i	−0.505703	+	0.505703i	−0.913205	−	0.407502i	$-0.866400\pi$
$163$	−6.45638	+	6.45638i	−0.505703	+	0.505703i	0.407502	+	0.913205i	$0.366400\pi$
$164$	−20.3649			−1.59023
$165$	9.32726	+	4.47720i	0.726126	+	0.348549i
$166$	−2.80266			−0.217528
$167$	−1.58004	+	1.58004i	−0.122268	+	0.122268i	−0.765593	−	0.643325i	$-0.777554\pi$
$167$	−1.58004	+	1.58004i	−0.122268	+	0.122268i	0.643325	+	0.765593i	$0.277554\pi$
$168$	0.325450	+	3.17902i	0.0251090	+	0.245267i
$169$			3.75977i			0.289213i
$170$	−4.32427	−	2.64855i	−0.331657	−	0.203134i
$171$	3.18727	+	15.4036i	0.243737	+	1.17794i
$172$	1.33535	+	1.33535i	0.101820	+	0.101820i
$173$	1.69970	+	1.69970i	0.129226	+	0.129226i	0.768761	−	0.639536i	$-0.220873\pi$
$173$	1.69970	+	1.69970i	0.129226	+	0.129226i	−0.639536	+	0.768761i	$0.720873\pi$
$174$	1.54012	−	1.89142i	0.116756	−	0.143388i
$175$	−1.54290	+	4.75599i	−0.116632	+	0.359519i
$176$			6.97941i			0.526093i
$177$	0.274717	−	0.0281240i	0.0206490	−	0.00211393i
$178$	−1.37130	+	1.37130i	−0.102783	+	0.102783i
$179$	8.44380			0.631119			0.315560	−	0.948906i	$-0.397808\pi$
$179$	8.44380			0.631119			0.315560	+	0.948906i	$0.397808\pi$
$180$	−11.1031	−	3.99654i	−0.827575	−	0.297885i
$181$	5.51483			0.409914			0.204957	−	0.978771i	$-0.434295\pi$
$181$	5.51483			0.409914			0.204957	+	0.978771i	$0.434295\pi$
$182$	1.05496	−	1.05496i	0.0781992	−	0.0781992i
$183$	8.14198	−	0.833531i	0.601872	−	0.0616164i
$184$			6.64869i			0.490148i
$185$	6.58872	−	1.58342i	0.484413	−	0.116415i
$186$	2.83736	−	3.48456i	0.208045	−	0.255501i
$187$	−8.72787	−	8.72787i	−0.638245	−	0.638245i
$188$	−13.4754	−	13.4754i	−0.982792	−	0.982792i
$189$	−4.61054	−	2.39644i	−0.335368	−	0.174315i
$190$	5.59510	−	1.34463i	0.405911	−	0.0975494i
$191$		−	0.559524i		−	0.0404858i	−0.999795	−	0.0202429i	$-0.993556\pi$
$191$		−	0.559524i		−	0.0404858i	0.999795	−	0.0202429i	$-0.00644395\pi$
$192$	−0.491244	−	4.79850i	−0.0354525	−	0.346302i
$193$	7.05199	−	7.05199i	0.507613	−	0.507613i	−0.406180	−	0.913793i	$-0.633139\pi$
$193$	7.05199	−	7.05199i	0.507613	−	0.507613i	0.913793	+	0.406180i	$0.133139\pi$
$194$	1.29713			0.0931287
$195$	3.90248	+	11.1074i	0.279462	+	0.795417i
$196$	−1.75911			−0.125651
$197$	10.1505	−	10.1505i	0.723190	−	0.723190i	−0.246064	−	0.969254i	$-0.579137\pi$
$197$	10.1505	−	10.1505i	0.723190	−	0.723190i	0.969254	+	0.246064i	$0.0791372\pi$
$198$	3.28719	+	2.16006i	0.233611	+	0.153509i
$199$			11.6748i			0.827604i	0.910367	+	0.413802i	$0.135799\pi$
$199$			11.6748i			0.827604i	−0.910367	+	0.413802i	$0.864201\pi$
$200$	−2.84664	+	8.77481i	−0.201288	+	0.620472i
$201$	−10.2789	−	8.36978i	−0.725020	−	0.590359i
$202$	−1.30532	−	1.30532i	−0.0918421	−	0.0918421i
$203$	2.02886	+	2.02886i	0.142398	+	0.142398i
$204$	10.9167	+	8.88912i	0.764324	+	0.622363i
$205$	−22.0750	−	13.5206i	−1.54179	−	0.944320i
$206$		−	6.14771i		−	0.428332i
$207$	−9.03483	−	5.93692i	−0.627964	−	0.412644i
$208$	−5.61580	+	5.61580i	−0.389386	+	0.389386i
$209$	14.0067			0.968867
$210$	−0.822591	+	1.71369i	−0.0567642	+	0.118256i
$211$	−0.777102			−0.0534979			−0.0267490	−	0.999642i	$-0.508515\pi$
$211$	−0.777102			−0.0534979			−0.0267490	+	0.999642i	$0.508515\pi$
$212$	−7.80300	+	7.80300i	−0.535912	+	0.535912i
$213$	−2.39687	−	23.4127i	−0.164231	−	1.60421i
$214$		−	0.493091i		−	0.0337070i
$215$	0.560925	+	2.33405i	0.0382547	+	0.159181i
$216$	−8.50645	−	4.42142i	−0.578790	−	0.300840i
$217$	3.73776	+	3.73776i	0.253736	+	0.253736i
$218$	−6.59901	−	6.59901i	−0.446941	−	0.446941i
$219$	6.44157	−	7.91090i	0.435281	−	0.534569i
$220$	−5.48824	+	8.96062i	−0.370017	+	0.604125i
$221$		−	14.0453i		−	0.944789i
$222$	2.56281	−	0.262367i	0.172005	−	0.0176089i
$223$	−3.33811	+	3.33811i	−0.223536	+	0.223536i	−0.809986	−	0.586450i	$-0.800525\pi$
$223$	−3.33811	+	3.33811i	−0.223536	+	0.223536i	0.586450	+	0.809986i	$0.300525\pi$
$224$	−4.97232			−0.332227
$225$	−9.38209	−	11.7037i	−0.625473	−	0.780246i
$226$	3.95038			0.262776
$227$	−0.242326	+	0.242326i	−0.0160838	+	0.0160838i	−0.715103	−	0.699019i	$-0.753620\pi$
$227$	−0.242326	+	0.242326i	−0.0160838	+	0.0160838i	0.699019	+	0.715103i	$0.253620\pi$
$228$	−15.8925	+	1.62699i	−1.05251	+	0.107750i
$229$		−	13.4793i		−	0.890735i	−0.895348	−	0.445368i	$-0.853073\pi$
$229$		−	13.4793i		−	0.890735i	0.895348	−	0.445368i	$-0.146927\pi$
$230$	−2.06566	+	3.37259i	−0.136205	+	0.222382i
$231$	−2.92153	+	3.58793i	−0.192223	+	0.236069i
$232$	3.74324	+	3.74324i	0.245756	+	0.245756i
$233$	−1.19260	−	1.19260i	−0.0781301	−	0.0781301i	0.666962	−	0.745092i	$-0.267594\pi$
$233$	−1.19260	−	1.19260i	−0.0781301	−	0.0781301i	−0.745092	+	0.666962i	$0.767594\pi$
$234$	0.906918	+	4.38299i	0.0592871	+	0.286525i
$235$	−5.66043	−	23.5535i	−0.369246	−	1.53646i
$236$			0.280467i			0.0182568i
$237$	0.687432	+	6.71488i	0.0446535	+	0.436178i
$238$	1.60356	−	1.60356i	0.103944	−	0.103944i
$239$	−5.15325			−0.333336			−0.166668	−	0.986013i	$-0.553301\pi$
$239$	−5.15325			−0.333336			−0.166668	+	0.986013i	$0.553301\pi$
$240$	4.37883	−	9.12233i	0.282652	−	0.588844i
$241$	−14.9174			−0.960914			−0.480457	−	0.877018i	$-0.659529\pi$
$241$	−14.9174			−0.960914			−0.480457	+	0.877018i	$0.659529\pi$
$242$	−1.34094	+	1.34094i	−0.0861992	+	0.0861992i
$243$	13.6040	−	7.61123i	0.872698	−	0.488261i
$244$			8.31238i			0.532146i
$245$	−1.90683	−	1.16790i	−0.121823	−	0.0746146i
$246$	−7.63153	−	6.21409i	−0.486569	−	0.396196i
$247$	11.2702	+	11.2702i	0.717103	+	0.717103i
$248$	6.89616	+	6.89616i	0.437907	+	0.437907i
$249$	7.66953	+	6.24504i	0.486037	+	0.395763i
$250$	−4.17019	+	3.56666i	−0.263746	+	0.225575i
$251$		−	4.30303i		−	0.271605i	−0.990736	−	0.135802i	$-0.956639\pi$
$251$		−	4.30303i		−	0.271605i	0.990736	−	0.135802i	$-0.0433613\pi$
$252$	2.89810	−	4.41035i	0.182563	−	0.277826i
$253$	−6.80704	+	6.80704i	−0.427955	+	0.427955i
$254$	8.42409			0.528575
$255$	5.93183	+	16.8834i	0.371465	+	1.05728i
$256$	0.0180230			0.00112644
$257$	5.82885	−	5.82885i	0.363594	−	0.363594i	−0.501540	−	0.865134i	$-0.667233\pi$
$257$	5.82885	−	5.82885i	0.363594	−	0.363594i	0.865134	+	0.501540i	$0.167233\pi$
$258$	0.0929433	+	0.907876i	0.00578640	+	0.0565219i
$259$			3.03046i			0.188304i
$260$	−11.6259	+	2.79396i	−0.721007	+	0.173274i
$261$	−8.42916	+	1.74414i	−0.521752	+	0.107960i
$262$	3.45068	+	3.45068i	0.213184	+	0.213184i
$263$	0.0624909	+	0.0624909i	0.00385335	+	0.00385335i	0.709031	−	0.705177i	$-0.249133\pi$
$263$	0.0624909	+	0.0624909i	0.00385335	+	0.00385335i	−0.705177	+	0.709031i	$0.749133\pi$
$264$	−5.39022	+	6.61974i	−0.331745	+	0.407417i
$265$	−13.6388	+	3.27771i	−0.837826	+	0.201348i
$266$			2.57345i			0.157788i
$267$	6.80819	−	0.696985i	0.416654	−	0.0426548i
$268$	9.51951	−	9.51951i	0.581497	−	0.581497i
$269$	29.6699			1.80901			0.904504	−	0.426465i	$-0.140241\pi$
$269$	29.6699			1.80901			0.904504	+	0.426465i	$0.140241\pi$
$270$	−2.94127	−	4.88563i	−0.179000	−	0.297330i
$271$	22.6377			1.37514			0.687571	−	0.726117i	$-0.258677\pi$
$271$	22.6377			1.37514			0.687571	+	0.726117i	$0.258677\pi$
$272$	−8.53611	+	8.53611i	−0.517578	+	0.517578i
$273$	−5.23767	+	0.536204i	−0.316998	+	0.0324525i
$274$		−	9.48463i		−	0.572988i
$275$	−11.8982	+	6.06935i	−0.717491	+	0.365996i
$276$	6.93281	−	8.51419i	0.417306	−	0.512494i
$277$	4.21136	+	4.21136i	0.253036	+	0.253036i	0.822214	−	0.569178i	$-0.192738\pi$
$277$	4.21136	+	4.21136i	0.253036	+	0.253036i	−0.569178	+	0.822214i	$0.692738\pi$
$278$	5.82817	+	5.82817i	0.349551	+	0.349551i
$279$	−15.5290	+	3.21323i	−0.929698	+	0.192371i
$280$	−3.51810	−	2.15478i	−0.210247	−	0.128773i
$281$			22.0093i			1.31297i	0.754341	+	0.656483i	$0.227957\pi$
$281$			22.0093i			1.31297i	−0.754341	+	0.656483i	$0.772043\pi$
$282$	−0.937914	−	9.16160i	−0.0558520	−	0.545565i
$283$	9.59899	−	9.59899i	0.570601	−	0.570601i	−0.361695	−	0.932296i	$-0.617802\pi$
$283$	9.59899	−	9.59899i	0.570601	−	0.570601i	0.932296	+	0.361695i	$0.117802\pi$
$284$	23.9027			1.41837
$285$	−18.3073	−	8.78772i	−1.08443	−	0.520540i
$286$	3.98553			0.235670
$287$	8.18605	−	8.18605i	0.483207	−	0.483207i
$288$	8.19181	−	12.4664i	0.482707	−	0.734587i
$289$		−	4.34908i		−	0.255828i
$290$	0.735807	+	3.06176i	0.0432081	+	0.179792i
$291$	−3.54963	−	2.89034i	−0.208083	−	0.169435i
$292$	7.32643	+	7.32643i	0.428747	+	0.428747i
$293$	−3.56359	−	3.56359i	−0.208187	−	0.208187i	0.595309	−	0.803497i	$-0.297030\pi$
$293$	−3.56359	−	3.56359i	−0.208187	−	0.208187i	−0.803497	+	0.595309i	$0.797030\pi$
$294$	−0.659208	−	0.536770i	−0.0384458	−	0.0313051i
$295$	−0.186207	+	0.304019i	−0.0108414	+	0.0177007i
$296$			5.59120i			0.324982i
$297$	−4.18231	−	13.2358i	−0.242683	−	0.768018i
$298$	3.23196	−	3.23196i	0.187222	−	0.187222i
$299$	−10.9542			−0.633499
$300$	12.7951	−	8.26856i	0.738727	−	0.477385i
$301$	−1.07354			−0.0618778
$302$	−7.07531	+	7.07531i	−0.407139	+	0.407139i
$303$	0.663452	+	6.48063i	0.0381143	+	0.372303i
$304$		−	13.6990i		−	0.785692i
$305$	−5.51874	+	9.01042i	−0.316002	+	0.515935i
$306$	1.37853	+	6.66222i	0.0788053	+	0.380854i
$307$	10.4746	+	10.4746i	0.597814	+	0.597814i	0.939730	−	0.341916i	$-0.111076\pi$
$307$	10.4746	+	10.4746i	0.597814	+	0.597814i	−0.341916	+	0.939730i	$0.611076\pi$
$308$	−3.32285	−	3.32285i	−0.189337	−	0.189337i
$309$	−13.6987	+	16.8234i	−0.779291	+	0.957048i
$310$	1.35558	+	5.64066i	0.0769915	+	0.320368i
$311$			20.4344i			1.15873i	0.815068	+	0.579365i	$0.196699\pi$
$311$			20.4344i			1.15873i	−0.815068	+	0.579365i	$0.803301\pi$
$312$	−9.66350	+	0.989296i	−0.547088	+	0.0560078i
$313$	−16.4829	+	16.4829i	−0.931670	+	0.931670i	−0.997810	−	0.0661408i	$-0.978931\pi$
$313$	−16.4829	+	16.4829i	−0.931670	+	0.931670i	0.0661408	+	0.997810i	$0.478931\pi$
$314$	−4.39291			−0.247906
$315$	6.06958	−	2.85661i	0.341982	−	0.160952i
$316$	−6.85542			−0.385647
$317$	22.9540	−	22.9540i	1.28922	−	1.28922i	0.353965	−	0.935259i	$-0.384833\pi$
$317$	22.9540	−	22.9540i	1.28922	−	1.28922i	0.935259	−	0.353965i	$-0.115167\pi$
$318$	−5.30509	+	0.543105i	−0.297494	+	0.0304558i
$319$			7.66479i			0.429146i
$320$	5.31032	+	3.25249i	0.296856	+	0.181820i
$321$	−1.09873	+	1.34936i	−0.0613254	+	0.0753137i
$322$	−1.25065	−	1.25065i	−0.0696961	−	0.0696961i
$323$	17.1308	+	17.1308i	0.953185	+	0.953185i
$324$	6.28283	+	14.5319i	0.349046	+	0.807330i
$325$	−14.4571	−	4.69006i	−0.801938	−	0.260158i
$326$		−	4.48142i		−	0.248203i
$327$	3.35406	+	32.7626i	0.185480	+	1.81178i
$328$	15.1033	−	15.1033i	0.833938	−	0.833938i
$329$	10.8334			0.597262
$330$	−4.79089	+	1.68323i	−0.263730	+	0.0926589i
$331$	−2.21461			−0.121726			−0.0608631	−	0.998146i	$-0.519385\pi$
$331$	−2.21461			−0.121726			−0.0608631	+	0.998146i	$0.519385\pi$
$332$	−7.10290	+	7.10290i	−0.389822	+	0.389822i
$333$	−7.59782	−	4.99263i	−0.416358	−	0.273595i
$334$		−	1.09672i		−	0.0600099i
$335$	16.6391	−	3.99874i	0.909091	−	0.218475i
$336$	3.50910	+	2.85734i	0.191437	+	0.155881i
$337$	10.8541	+	10.8541i	0.591263	+	0.591263i	0.937972	−	0.346710i	$-0.112701\pi$
$337$	10.8541	+	10.8541i	0.591263	+	0.591263i	−0.346710	+	0.937972i	$0.612701\pi$
$338$	−1.30484	−	1.30484i	−0.0709741	−	0.0709741i
$339$	−10.8103	−	8.80247i	−0.587136	−	0.478085i
$340$	−17.6715	+	4.24686i	−0.958374	+	0.230318i
$341$			14.1208i			0.764685i
$342$	−6.45202	−	4.23971i	−0.348885	−	0.229257i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−1.98068			−0.106791
$345$	13.1677	−	4.62635i	0.708926	−	0.249075i
$346$	−1.17977			−0.0634251
$347$	5.06341	−	5.06341i	0.271818	−	0.271818i	−0.558014	−	0.829832i	$-0.688436\pi$
$347$	5.06341	−	5.06341i	0.271818	−	0.271818i	0.829832	+	0.558014i	$0.188436\pi$
$348$	−0.890323	−	8.69672i	−0.0477263	−	0.466193i
$349$		−	7.42733i		−	0.397576i	−0.980043	−	0.198788i	$-0.936300\pi$
$349$		−	7.42733i		−	0.397576i	0.980043	−	0.198788i	$-0.0637005\pi$
$350$	−1.11512	−	2.18605i	−0.0596055	−	0.116849i
$351$	7.28463	−	14.0150i	0.388825	−	0.748066i
$352$	−9.39243	−	9.39243i	−0.500618	−	0.500618i
$353$	−9.09032	−	9.09032i	−0.483829	−	0.483829i	0.422523	−	0.906352i	$-0.361144\pi$
$353$	−9.09032	−	9.09032i	−0.483829	−	0.483829i	−0.906352	+	0.422523i	$0.861144\pi$
$354$	−0.0855810	+	0.105102i	−0.00454858	+	0.00558611i
$355$	25.9100	+	15.8695i	1.37516	+	0.842264i
$356$			6.95068i			0.368385i
$357$	−7.96134	+	0.815038i	−0.421359	+	0.0431364i
$358$	−2.93045	+	2.93045i	−0.154879	+	0.154879i
$359$	−25.2640			−1.33338			−0.666692	−	0.745333i	$-0.732290\pi$
$359$	−25.2640			−1.33338			−0.666692	+	0.745333i	$0.732290\pi$
$360$	11.1984	−	5.27044i	0.590206	−	0.277776i
$361$	−8.49208			−0.446951
$362$	−1.91394	+	1.91394i	−0.100594	+	0.100594i
$363$	6.65750	−	0.681558i	0.349428	−	0.0357725i
$364$		−	5.34729i		−	0.280274i
$365$	3.07752	+	12.8058i	0.161085	+	0.670288i
$366$	−2.53642	+	3.11498i	−0.132581	+	0.162823i
$367$	1.61189	+	1.61189i	0.0841399	+	0.0841399i	0.747924	−	0.663784i	$-0.231051\pi$
$367$	1.61189	+	1.61189i	0.0841399	+	0.0841399i	−0.663784	+	0.747924i	$0.731051\pi$
$368$	6.65749	+	6.65749i	0.347045	+	0.347045i
$369$	7.03727	+	34.0100i	0.366346	+	1.77049i
$370$	−1.73711	+	2.83617i	−0.0903081	+	0.147445i
$371$		−	6.27313i		−	0.325685i
$372$	−1.64024	−	16.0219i	−0.0850424	−	0.830699i
$373$	13.0455	−	13.0455i	0.675469	−	0.675469i	−0.283502	−	0.958972i	$-0.591496\pi$
$373$	13.0455	−	13.0455i	0.675469	−	0.675469i	0.958972	+	0.283502i	$0.0914964\pi$
$374$	6.05808			0.313256
$375$	19.3593	−	0.467991i	0.999708	−	0.0241669i
$376$	19.9875			1.03078
$377$	−6.16727	+	6.16727i	−0.317630	+	0.317630i
$378$	2.43180	−	0.768413i	0.125078	−	0.0395229i
$379$		−	19.0635i		−	0.979228i	−0.871939	−	0.489614i	$-0.837138\pi$
$379$		−	19.0635i		−	0.979228i	0.871939	−	0.489614i	$-0.162862\pi$
$380$	10.7722	−	17.5877i	0.552601	−	0.902228i
$381$	−23.0527	−	18.7710i	−1.18103	−	0.961670i
$382$	0.194185	+	0.194185i	0.00993537	+	0.00993537i
$383$	−17.7244	−	17.7244i	−0.905673	−	0.905673i	0.0902463	−	0.995919i	$-0.471235\pi$
$383$	−17.7244	−	17.7244i	−0.905673	−	0.905673i	−0.995919	+	0.0902463i	$0.971235\pi$
$384$	15.1925	+	12.3708i	0.775291	+	0.631293i
$385$	−1.39579	−	5.80799i	−0.0711360	−	0.296003i
$386$			4.89484i			0.249141i
$387$	1.76864	−	2.69153i	0.0899050	−	0.136818i
$388$	3.28738	−	3.28738i	0.166892	−	0.166892i
$389$	−18.3513			−0.930446			−0.465223	−	0.885193i	$-0.654026\pi$
$389$	−18.3513			−0.930446			−0.465223	+	0.885193i	$0.654026\pi$
$390$	−5.20923	−	2.50049i	−0.263779	−	0.126617i
$391$	−16.6506			−0.842056
$392$	1.30461	−	1.30461i	0.0658928	−	0.0658928i
$393$	−1.75387	−	17.1319i	−0.0884710	−	0.864189i
$394$			7.04550i			0.354947i
$395$	−7.43110	−	4.55144i	−0.373899	−	0.229008i
$396$	13.8052	−	2.85655i	0.693739	−	0.143547i
$397$	−10.9124	−	10.9124i	−0.547679	−	0.547679i	0.378090	−	0.925769i	$-0.376581\pi$
$397$	−10.9124	−	10.9124i	−0.547679	−	0.547679i	−0.925769	+	0.378090i	$0.876581\pi$
$398$	−4.05178	−	4.05178i	−0.203097	−	0.203097i
$399$	5.73430	−	7.04230i	0.287074	−	0.352556i
$400$	5.93600	+	11.6368i	0.296800	+	0.581841i
$401$		−	34.4243i		−	1.71907i	−0.511079	−	0.859534i	$-0.670754\pi$
$401$		−	34.4243i		−	1.71907i	0.511079	−	0.859534i	$-0.329246\pi$
$402$	6.47210	−	0.662578i	0.322799	−	0.0330464i
$403$	−11.3619	+	11.3619i	−0.565979	+	0.565979i
$404$	−6.61627			−0.329172
$405$	−2.83759	+	19.9236i	−0.141001	+	0.990009i
$406$	−1.40824			−0.0698900
$407$	−5.72437	+	5.72437i	−0.283746	+	0.283746i
$408$	−14.6887	+	1.50375i	−0.727198	+	0.0744465i
$409$		−	7.59254i		−	0.375427i	−0.982224	−	0.187714i	$-0.939892\pi$
$409$		−	7.59254i		−	0.375427i	0.982224	−	0.187714i	$-0.0601077\pi$
$410$	12.3536	−	2.96884i	0.610101	−	0.146621i
$411$	−21.1342	+	25.9549i	−1.04247	+	1.28026i
$412$	−15.5804	−	15.5804i	−0.767593	−	0.767593i
$413$	−0.112739	−	0.112739i	−0.00554752	−	0.00554752i
$414$	5.19600	−	1.07514i	0.255369	−	0.0528404i
$415$	−12.4151	+	2.98363i	−0.609434	+	0.146460i
$416$		−	15.1147i		−	0.741061i
$417$	−2.96227	−	28.9356i	−0.145063	−	1.41698i
$418$	−4.86109	+	4.86109i	−0.237764	+	0.237764i
$419$	−6.20644			−0.303204			−0.151602	−	0.988442i	$-0.548443\pi$
$419$	−6.20644			−0.303204			−0.151602	+	0.988442i	$0.548443\pi$
$420$	2.25835	+	6.42781i	0.110196	+	0.313645i
$421$	25.1339			1.22495			0.612474	−	0.790490i	$-0.290174\pi$
$421$	25.1339			1.22495			0.612474	+	0.790490i	$0.290174\pi$
$422$	0.269696	−	0.269696i	0.0131286	−	0.0131286i
$423$	−17.8478	+	27.1608i	−0.867788	+	1.32061i
$424$		−	11.5739i		−	0.562079i
$425$	−21.9751	−	7.12897i	−1.06595	−	0.345806i
$426$	8.95731	+	7.29363i	0.433983	+	0.353377i
$427$	−3.34132	−	3.34132i	−0.161698	−	0.161698i
$428$	−1.24966	−	1.24966i	−0.0604048	−	0.0604048i
$429$	−10.9065	−	8.88079i	−0.526571	−	0.428769i
$430$	−1.00471	−	0.615371i	−0.0484515	−	0.0296758i
$431$			8.43225i			0.406167i	0.979161	+	0.203084i	$0.0650963\pi$
$431$			8.43225i			0.406167i	−0.979161	+	0.203084i	$0.934904\pi$
$432$	−12.9450	+	4.09043i	−0.622815	+	0.196801i
$433$	−18.8277	+	18.8277i	−0.904802	+	0.904802i	−0.995847	−	0.0910444i	$-0.970979\pi$
$433$	−18.8277	+	18.8277i	−0.904802	+	0.904802i	0.0910444	+	0.995847i	$0.470979\pi$
$434$	−2.59440			−0.124535
$435$	4.80882	−	10.0181i	0.230566	−	0.480333i
$436$	−33.4483			−1.60188
$437$	13.3607	−	13.3607i	0.639128	−	0.639128i
$438$	0.509935	+	4.98108i	0.0243657	+	0.238005i
$439$		−	4.88270i		−	0.233039i	−0.993188	−	0.116519i	$-0.962826\pi$
$439$		−	4.88270i		−	0.233039i	0.993188	−	0.116519i	$-0.0371737\pi$
$440$	−2.57523	−	10.7157i	−0.122769	−	0.510853i
$441$	0.607876	+	2.93777i	0.0289465	+	0.139894i
$442$	4.87447	+	4.87447i	0.231855	+	0.231855i
$443$	23.8960	+	23.8960i	1.13534	+	1.13534i	0.989276	+	0.146059i	$0.0466590\pi$
$443$	23.8960	+	23.8960i	1.13534	+	1.13534i	0.146059	+	0.989276i	$0.453341\pi$
$444$	5.83013	−	7.15998i	0.276686	−	0.339798i
$445$	−4.61468	+	7.53437i	−0.218757	+	0.357163i
$446$		−	2.31700i		−	0.109713i
$447$	−16.0460	+	1.64270i	−0.758948	+	0.0776970i
$448$	−1.96922	+	1.96922i	−0.0930368	+	0.0930368i
$449$	−23.6736			−1.11723			−0.558613	−	0.829428i	$-0.688666\pi$
$449$	−23.6736			−1.11723			−0.558613	+	0.829428i	$0.688666\pi$
$450$	7.31790	+	0.805721i	0.344969	+	0.0379820i
$451$	30.9259			1.45625
$452$	10.0116	−	10.0116i	0.470908	−	0.470908i
$453$	35.1274	−	3.59615i	1.65043	−	0.168962i
$454$		−	0.168200i		−	0.00789404i
$455$	3.55016	−	5.79633i	0.166434	−	0.271736i
$456$	10.5798	−	12.9930i	0.495444	−	0.608455i
$457$	10.2580	+	10.2580i	0.479849	+	0.479849i	0.905083	−	0.425234i	$-0.139808\pi$
$457$	10.2580	+	10.2580i	0.479849	+	0.479849i	−0.425234	+	0.905083i	$0.639808\pi$
$458$	4.67803	+	4.67803i	0.218590	+	0.218590i
$459$	11.0728	−	21.3030i	0.516832	−	0.994341i
$460$	3.31221	+	13.7824i	0.154433	+	0.642608i
$461$		−	23.3153i		−	1.08590i	−0.839764	−	0.542951i	$-0.817307\pi$
$461$		−	23.3153i		−	1.08590i	0.839764	−	0.542951i	$-0.182693\pi$
$462$	−0.231278	−	2.25913i	−0.0107600	−	0.105104i
$463$	−17.0563	+	17.0563i	−0.792672	+	0.792672i	−0.981928	−	0.189256i	$-0.939392\pi$
$463$	−17.0563	+	17.0563i	−0.792672	+	0.792672i	0.189256	+	0.981928i	$0.439392\pi$
$464$	7.49639			0.348011
$465$	8.85928	−	18.4564i	0.410839	−	0.855894i
$466$	0.827796			0.0383469
$467$	−8.00621	+	8.00621i	−0.370483	+	0.370483i	−0.867653	−	0.497170i	$-0.834373\pi$
$467$	−8.00621	+	8.00621i	−0.370483	+	0.370483i	0.497170	+	0.867653i	$0.334373\pi$
$468$	13.4065	+	8.80957i	0.619714	+	0.407223i
$469$			7.65310i			0.353387i
$470$	10.1388	+	6.20986i	0.467668	+	0.286439i
$471$	12.0213	+	9.78854i	0.553913	+	0.451032i
$472$	−0.208003	−	0.208003i	−0.00957413	−	0.00957413i
$473$	−2.02786	−	2.02786i	−0.0932409	−	0.0932409i
$474$	−2.56900	−	2.09185i	−0.117998	−	0.0960817i
$475$	23.3535	−	11.9128i	1.07153	−	0.546595i
$476$		−	8.12797i		−	0.372545i
$477$	15.7277	+	10.3349i	0.720121	+	0.473201i
$478$	1.78845	−	1.78845i	0.0818019	−	0.0818019i
$479$	−20.1199			−0.919304			−0.459652	−	0.888099i	$-0.652026\pi$
$479$	−20.1199			−0.919304			−0.459652	+	0.888099i	$0.652026\pi$
$480$	6.38349	+	18.1689i	0.291365	+	0.829295i
$481$	−9.21192			−0.420027
$482$	5.17713	−	5.17713i	0.235812	−	0.235812i
$483$	0.635665	+	6.20921i	0.0289238	+	0.282529i
$484$			6.79683i			0.308947i
$485$	5.74600	−	1.38089i	0.260912	−	0.0627030i
$486$	−2.07982	+	7.36283i	−0.0943425	+	0.333985i
$487$	7.77959	+	7.77959i	0.352527	+	0.352527i	0.861049	−	0.508522i	$-0.169808\pi$
$487$	7.77959	+	7.77959i	0.352527	+	0.352527i	−0.508522	+	0.861049i	$0.669808\pi$
$488$	−6.16474	−	6.16474i	−0.279064	−	0.279064i
$489$	−9.98576	+	12.2635i	−0.451572	+	0.554576i
$490$	1.06710	−	0.256447i	0.0482065	−	0.0115851i
$491$			2.29546i			0.103593i	0.998658	+	0.0517963i	$0.0164947\pi$
$491$			2.29546i			0.103593i	−0.998658	+	0.0517963i	$0.983505\pi$
$492$	−35.0896	+	3.59228i	−1.58196	+	0.161952i
$493$	−9.37435	+	9.37435i	−0.422199	+	0.422199i
$494$	−7.82270			−0.351960
$495$	16.8610	+	6.06912i	0.757848	+	0.272787i
$496$	13.8106			0.620113
$497$	−9.60816	+	9.60816i	−0.430985	+	0.430985i
$498$	−4.82910	+	0.494377i	−0.216397	+	0.0221536i
$499$		−	12.3264i		−	0.551806i	−0.961185	−	0.275903i	$-0.911023\pi$
$499$		−	12.3264i		−	0.551806i	0.961185	−	0.275903i	$-0.0889769\pi$
$500$	−1.52956	+	19.6079i	−0.0684039	+	0.876890i
$501$	−2.44378	+	3.00120i	−0.109180	+	0.134084i
$502$	1.49338	+	1.49338i	0.0666529	+	0.0666529i
$503$	4.62523	+	4.62523i	0.206229	+	0.206229i	0.802662	−	0.596434i	$-0.203416\pi$
$503$	4.62523	+	4.62523i	0.206229	+	0.206229i	−0.596434	+	0.802662i	$0.703416\pi$
$504$	1.12153	+	5.42018i	0.0499570	+	0.241434i
$505$	−7.17188	−	4.39266i	−0.319144	−	0.195471i
$506$		−	4.72482i		−	0.210044i
$507$	0.663208	+	6.47826i	0.0294541	+	0.287709i
$508$	21.3496	−	21.3496i	0.947234	−	0.947234i
$509$	13.6161			0.603525			0.301762	−	0.953383i	$-0.402425\pi$
$509$	13.6161			0.603525			0.301762	+	0.953383i	$0.402425\pi$
$510$	−7.91811	−	3.80079i	−0.350620	−	0.168302i
$511$	−5.89000			−0.260558
$512$	−16.0031	+	16.0031i	−0.707245	+	0.707245i
$513$	8.20894	+	25.9788i	0.362433	+	1.14699i
$514$			4.04585i			0.178455i
$515$	−6.54468	−	27.2329i	−0.288393	−	1.20003i
$516$	2.53642	+	2.06532i	0.111660	+	0.0909207i
$517$	20.4636	+	20.4636i	0.899987	+	0.899987i
$518$	−1.05173	−	1.05173i	−0.0462105	−	0.0462105i
$519$	3.22848	+	2.62884i	0.141715	+	0.115393i
$520$	6.55005	−	10.6942i	0.287239	−	0.468973i
$521$			18.3870i			0.805550i	0.915299	+	0.402775i	$0.131954\pi$
$521$			18.3870i			0.805550i	−0.915299	+	0.402775i	$0.868046\pi$
$522$	2.32006	−	3.53068i	0.101546	−	0.154534i
$523$	−8.91043	+	8.91043i	−0.389626	+	0.389626i	−0.874554	−	0.484928i	$-0.838846\pi$
$523$	−8.91043	+	8.91043i	−0.389626	+	0.389626i	0.484928	+	0.874554i	$0.338846\pi$
$524$	17.4905			0.764074
$525$	−1.81954	+	8.46695i	−0.0794114	+	0.369528i
$526$	−0.0433754			−0.00189126
$527$	−17.2703	+	17.2703i	−0.752308	+	0.752308i
$528$	1.23114	+	12.0258i	0.0535785	+	0.523358i
$529$		−	10.0139i		−	0.435385i
$530$	3.59586	−	5.87094i	0.156194	−	0.255017i
$531$	0.468389	−	0.0969179i	0.0203264	−	0.00420588i
$532$	6.52201	+	6.52201i	0.282765	+	0.282765i
$533$	24.8837	+	24.8837i	1.07783	+	1.07783i
$534$	−2.12091	+	2.60470i	−0.0917810	+	0.112716i
$535$	−0.524931	−	2.18428i	−0.0226947	−	0.0944347i
$536$			14.1200i			0.609889i
$537$	14.5491	−	1.48945i	0.627838	−	0.0642746i
$538$	−10.2971	+	10.2971i	−0.443938	+	0.443938i
$539$	2.67137			0.115064
$540$	−19.8361	−	4.92769i	−0.853609	−	0.212054i
$541$	27.8258			1.19632			0.598162	−	0.801375i	$-0.295898\pi$
$541$	27.8258			1.19632			0.598162	+	0.801375i	$0.295898\pi$
$542$	−7.85649	+	7.85649i	−0.337465	+	0.337465i
$543$	9.50229	−	0.972793i	0.407783	−	0.0417465i
$544$		−	22.9746i		−	0.985030i
$545$	−36.2572	−	22.2070i	−1.55309	−	0.951242i
$546$	1.63166	−	2.00384i	0.0698286	−	0.0857566i
$547$	−13.2773	−	13.2773i	−0.567695	−	0.567695i	0.363787	−	0.931482i	$-0.381483\pi$
$547$	−13.2773	−	13.2773i	−0.567695	−	0.567695i	−0.931482	+	0.363787i	$0.881483\pi$
$548$	−24.0373	−	24.0373i	−1.02682	−	1.02682i
$549$	13.8820	−	2.87242i	0.592468	−	0.122592i
$550$	2.02294	−	6.23572i	0.0862583	−	0.265892i
$551$		−	15.0442i		−	0.640906i
$552$	1.17280	+	11.4560i	0.0499178	+	0.487600i
$553$	2.75566	−	2.75566i	0.117183	−	0.117183i
$554$	−2.92314			−0.124192
$555$	11.0734	−	3.89052i	0.470038	−	0.165143i
$556$	29.5412			1.25283
$557$	−10.4002	+	10.4002i	−0.440672	+	0.440672i	−0.892238	−	0.451566i	$-0.850866\pi$
$557$	−10.4002	+	10.4002i	−0.440672	+	0.440672i	0.451566	+	0.892238i	$0.350866\pi$
$558$	4.27424	−	6.50456i	0.180943	−	0.275360i
$559$		−	3.26332i		−	0.138024i
$560$	−5.68039	+	1.36512i	−0.240040	+	0.0576869i
$561$	−16.5781	−	13.4990i	−0.699927	−	0.569926i
$562$	−7.63842	−	7.63842i	−0.322207	−	0.322207i
$563$	10.1623	+	10.1623i	0.428291	+	0.428291i	0.888046	−	0.459755i	$-0.152063\pi$
$563$	10.1623	+	10.1623i	0.428291	+	0.428291i	−0.459755	+	0.888046i	$0.652063\pi$
$564$	−25.5957	−	20.8417i	−1.07777	−	0.877592i
$565$	17.4993	−	4.20546i	0.736200	−	0.176925i
$566$			6.66273i			0.280055i
$567$	−8.36689	−	3.31589i	−0.351376	−	0.139254i
$568$	−17.7271	+	17.7271i	−0.743811	+	0.743811i
$569$	39.8275			1.66965			0.834827	−	0.550512i	$-0.185567\pi$
$569$	39.8275			1.66965			0.834827	+	0.550512i	$0.185567\pi$
$570$	9.40342	−	3.30380i	0.393866	−	0.138381i
$571$	−43.8314			−1.83429			−0.917143	−	0.398558i	$-0.869511\pi$
$571$	−43.8314			−1.83429			−0.917143	+	0.398558i	$0.869511\pi$
$572$	10.1007	−	10.1007i	0.422332	−	0.422332i
$573$	−0.0986978	−	0.964086i	−0.00412316	−	0.0402753i
$574$			5.68199i			0.237162i
$575$	−5.56003	+	17.1388i	−0.231869	+	0.714739i
$576$	−1.69287	−	8.18138i	−0.0705363	−	0.340891i
$577$	−27.8182	−	27.8182i	−1.15809	−	1.15809i	−0.984886	−	0.173202i	$-0.944589\pi$
$577$	−27.8182	−	27.8182i	−1.15809	−	1.15809i	−0.173202	−	0.984886i	$-0.555411\pi$
$578$	1.50936	+	1.50936i	0.0627812	+	0.0627812i
$579$	10.9070	−	13.3948i	0.453278	−	0.556670i
$580$	9.62434	+	5.89476i	0.399629	+	0.244767i
$581$		−	5.71029i		−	0.236903i
$582$	2.23502	−	0.228809i	0.0926445	−	0.00948443i
$583$	11.8496	−	11.8496i	0.490759	−	0.490759i
$584$	−10.8670			−0.449681
$585$	8.68344	+	18.4502i	0.359016	+	0.762820i
$586$	2.47352			0.102180
$587$	27.2778	−	27.2778i	1.12588	−	1.12588i	0.135034	−	0.990841i	$-0.456886\pi$
$587$	27.2778	−	27.2778i	1.12588	−	1.12588i	0.990841	−	0.135034i	$-0.0431144\pi$
$588$	−3.03102	+	0.310299i	−0.124997	+	0.0127965i
$589$		−	27.7160i		−	1.14202i
$590$	−0.0408871	−	0.170135i	−0.00168330	−	0.00700434i
$591$	15.6992	−	19.2802i	0.645779	−	0.793081i
$592$	5.59860	+	5.59860i	0.230101	+	0.230101i
$593$	−1.21000	−	1.21000i	−0.0496886	−	0.0496886i	0.681826	−	0.731515i	$-0.261186\pi$
$593$	−1.21000	−	1.21000i	−0.0496886	−	0.0496886i	−0.731515	+	0.681826i	$0.761186\pi$
$594$	6.04501	+	3.14204i	0.248030	+	0.128919i
$595$	5.39631	−	8.81052i	0.221227	−	0.361196i
$596$		−	16.3818i		−	0.671025i
$597$	2.05939	+	20.1162i	0.0842850	+	0.823301i
$598$	3.80170	−	3.80170i	0.155463	−	0.155463i
$599$	−15.6005			−0.637421			−0.318710	−	0.947852i	$-0.603250\pi$
$599$	−15.6005			−0.637421			−0.318710	+	0.947852i	$0.603250\pi$
$600$	−3.35706	+	15.6215i	−0.137051	+	0.637746i
$601$	14.2954			0.583122			0.291561	−	0.956552i	$-0.405825\pi$
$601$	14.2954			0.583122			0.291561	+	0.956552i	$0.405825\pi$
$602$	0.372576	−	0.372576i	0.0151851	−	0.0151851i
$603$	−19.1875	−	12.6083i	−0.781374	−	0.513452i
$604$			35.8626i			1.45923i
$605$	−4.51254	+	7.36760i	−0.183461	+	0.299536i
$606$	−2.47938	−	2.01887i	−0.100718	−	0.0820111i
$607$	−26.8784	−	26.8784i	−1.09096	−	1.09096i	−0.995426	−	0.0955365i	$-0.969543\pi$
$607$	−26.8784	−	26.8784i	−1.09096	−	1.09096i	−0.0955365	−	0.995426i	$-0.530457\pi$
$608$	18.4352	+	18.4352i	0.747646	+	0.747646i
$609$	3.85369	+	3.13793i	0.156160	+	0.127155i
$610$	−1.21180	−	5.04240i	−0.0490643	−	0.204161i
$611$			32.9310i			1.33224i
$612$	20.3780	+	13.3907i	0.823733	+	0.541287i
$613$	2.77744	−	2.77744i	0.112180	−	0.112180i	−0.648789	−	0.760969i	$-0.724724\pi$
$613$	2.77744	−	2.77744i	0.112180	−	0.112180i	0.760969	+	0.648789i	$0.224724\pi$
$614$	−7.27046			−0.293412
$615$	−40.4212	−	19.4027i	−1.62994	−	0.782392i
$616$	4.92867			0.198582
$617$	−3.21465	+	3.21465i	−0.129417	+	0.129417i	−0.768848	−	0.639431i	$-0.779170\pi$
$617$	−3.21465	+	3.21465i	−0.129417	+	0.129417i	0.639431	+	0.768848i	$0.279170\pi$
$618$	−1.08443	−	10.5928i	−0.0436222	−	0.426104i
$619$			48.7011i			1.95746i	0.205146	+	0.978731i	$0.434233\pi$
$619$			48.7011i			1.95746i	−0.205146	+	0.978731i	$0.565767\pi$
$620$	17.7309	+	10.8599i	0.712090	+	0.436144i
$621$	−16.6147	−	8.63587i	−0.666724	−	0.346545i
$622$	−7.09184	−	7.09184i	−0.284357	−	0.284357i
$623$	−2.79396	−	2.79396i	−0.111938	−	0.111938i
$624$	−8.68567	+	10.6669i	−0.347705	+	0.427017i
$625$	−14.6760	+	20.2389i	−0.587041	+	0.809557i
$626$		−	11.4409i		−	0.457271i
$627$	24.1343	−	2.47073i	0.963830	−	0.0986716i
$628$	−11.1332	+	11.1332i	−0.444261	+	0.444261i
$629$	−14.0023			−0.558307
$630$	−1.11507	+	3.09786i	−0.0444256	+	0.123422i
$631$	15.0588			0.599480			0.299740	−	0.954021i	$-0.403100\pi$
$631$	15.0588			0.599480			0.299740	+	0.954021i	$0.403100\pi$
$632$	5.08420	−	5.08420i	0.202239	−	0.202239i
$633$	−1.33898	+	0.137078i	−0.0532197	+	0.00544834i
$634$			15.9325i			0.632761i
$635$	37.3168	−	8.96805i	1.48087	−	0.355886i
$636$	−12.0685	+	14.8213i	−0.478547	+	0.587704i
$637$	2.14945	+	2.14945i	0.0851641	+	0.0851641i
$638$	−2.66009	−	2.66009i	−0.105314	−	0.105314i
$639$	−8.25981	−	39.9184i	−0.326753	−	1.57915i
$640$	−24.5930	+	5.91025i	−0.972126	+	0.233623i
$641$			45.9720i			1.81578i	0.419204	+	0.907892i	$0.362309\pi$
$641$			45.9720i			1.81578i	−0.419204	+	0.907892i	$0.637691\pi$
$642$	−0.0869793	−	0.849619i	−0.00343280	−	0.0335318i
$643$	−5.91991	+	5.91991i	−0.233458	+	0.233458i	−0.814135	−	0.580676i	$-0.802788\pi$
$643$	−5.91991	+	5.91991i	−0.233458	+	0.233458i	0.580676	+	0.814135i	$0.302788\pi$
$644$	−6.33917			−0.249798
$645$	1.37822	+	3.92274i	0.0542672	+	0.154458i
$646$	−11.8906			−0.467831
$647$	−11.1176	+	11.1176i	−0.437079	+	0.437079i	−0.891028	−	0.453949i	$-0.850015\pi$
$647$	−11.1176	+	11.1176i	−0.437079	+	0.437079i	0.453949	+	0.891028i	$0.350015\pi$
$648$	−15.4369	−	6.11781i	−0.606419	−	0.240330i
$649$		−	0.425915i		−	0.0167186i
$650$	6.64511	−	3.38970i	0.260642	−	0.132955i
$651$	7.09965	+	5.78100i	0.278257	+	0.226575i
$652$	−11.3575	−	11.3575i	−0.444793	−	0.444793i
$653$	−30.6500	−	30.6500i	−1.19943	−	1.19943i	−0.974339	−	0.225088i	$-0.927733\pi$
$653$	−30.6500	−	30.6500i	−1.19943	−	1.19943i	−0.225088	−	0.974339i	$-0.572267\pi$
$654$	−12.5344	−	10.2063i	−0.490135	−	0.399100i
$655$	18.9592	+	11.6122i	0.740798	+	0.453727i
$656$		−	30.2465i		−	1.18093i
$657$	9.70367	−	14.7671i	0.378576	−	0.576120i
$658$	−3.75976	+	3.75976i	−0.146571	+	0.146571i
$659$	50.9397			1.98433			0.992165	−	0.124933i	$-0.0398714\pi$
$659$	50.9397			1.98433			0.992165	+	0.124933i	$0.0398714\pi$
$660$	−7.87587	+	16.4077i	−0.306568	+	0.638667i
$661$	−20.5394			−0.798889			−0.399445	−	0.916757i	$-0.630797\pi$
$661$	−20.5394			−0.798889			−0.399445	+	0.916757i	$0.630797\pi$
$662$	0.768589	−	0.768589i	0.0298721	−	0.0298721i
$663$	−2.47753	−	24.2007i	−0.0962194	−	0.939877i
$664$		−	10.5355i		−	0.408856i
$665$	2.73962	+	11.3998i	0.106238	+	0.442064i
$666$	4.36956	−	0.904139i	0.169317	−	0.0350347i
$667$	7.31125	+	7.31125i	0.283093	+	0.283093i
$668$	−2.77947	−	2.77947i	−0.107541	−	0.107541i
$669$	−5.16288	+	6.34054i	−0.199609	+	0.245139i
$670$	−4.38688	+	7.16244i	−0.169480	+	0.276709i
$671$		−	12.6231i		−	0.487310i
$672$	−8.56753	+	0.877097i	−0.330500	+	0.0338347i
$673$	25.4635	−	25.4635i	0.981544	−	0.981544i	−0.0182887	−	0.999833i	$-0.505822\pi$
$673$	25.4635	−	25.4635i	0.981544	−	0.981544i	0.999833	+	0.0182887i	$0.00582181\pi$
$674$	−7.53394			−0.290196
$675$	−18.2302	−	18.5110i	−0.701682	−	0.712490i
$676$	−6.61384			−0.254379
$677$	8.67613	−	8.67613i	0.333451	−	0.333451i	−0.520445	−	0.853895i	$-0.674234\pi$
$677$	8.67613	−	8.67613i	0.333451	−	0.333451i	0.853895	+	0.520445i	$0.174234\pi$
$678$	6.80669	−	0.696831i	0.261409	−	0.0267616i
$679$			2.64285i			0.101423i
$680$	9.95618	−	16.2554i	0.381802	−	0.623366i
$681$	−0.374794	+	0.460284i	−0.0143621	+	0.0176381i
$682$	−4.90068	−	4.90068i	−0.187657	−	0.187657i
$683$	−24.0010	−	24.0010i	−0.918373	−	0.918373i	0.0785378	−	0.996911i	$-0.474975\pi$
$683$	−24.0010	−	24.0010i	−0.918373	−	0.918373i	−0.996911	+	0.0785378i	$0.974975\pi$
$684$	−27.0965	+	5.60675i	−1.03606	+	0.214379i
$685$	−10.0971	−	42.0147i	−0.385789	−	1.60530i
$686$			0.490808i			0.0187391i
$687$	−2.37769	−	23.2254i	−0.0907145	−	0.886104i
$688$	−1.98330	+	1.98330i	−0.0756127	+	0.0756127i
$689$	19.0689			0.726467
$690$	−2.96431	+	6.17550i	−0.112849	+	0.235097i
$691$	−32.5680			−1.23894			−0.619472	−	0.785019i	$-0.712653\pi$
$691$	−32.5680			−1.23894			−0.619472	+	0.785019i	$0.712653\pi$
$692$	−2.98996	+	2.98996i	−0.113661	+	0.113661i
$693$	−4.40103	+	6.69752i	−0.167181	+	0.254418i
$694$			3.51455i			0.133410i
$695$	32.0220	+	19.6130i	1.21466	+	0.743962i
$696$	7.11007	+	5.78948i	0.269506	+	0.219450i
$697$	37.8237	+	37.8237i	1.43267	+	1.43267i
$698$	2.57768	+	2.57768i	0.0975667	+	0.0975667i
$699$	−2.26528	−	1.84454i	−0.0856808	−	0.0697670i
$700$	−8.36630	−	2.71412i	−0.316217	−	0.102584i
$701$		−	2.43359i		−	0.0919155i	−0.998943	−	0.0459577i	$-0.985366\pi$
$701$		−	2.43359i		−	0.0919155i	0.998943	−	0.0459577i	$-0.0146340\pi$
$702$	2.33580	+	7.39211i	0.0881592	+	0.278997i
$703$	11.2356	−	11.2356i	0.423760	−	0.423760i
$704$	−7.43948			−0.280386
$705$	−13.9079	−	39.5853i	−0.523802	−	1.49087i
$706$	6.30965			0.237467
$707$	2.65954	−	2.65954i	0.100022	−	0.100022i
$708$	0.0494732	+	0.483257i	0.00185932	+	0.0181619i
$709$			12.3477i			0.463728i	0.972748	+	0.231864i	$0.0744825\pi$
$709$			12.3477i			0.463728i	−0.972748	+	0.231864i	$0.925518\pi$
$710$	−14.4997	+	3.48460i	−0.544164	+	0.130775i
$711$	2.36895	+	11.4488i	0.0888427	+	0.429363i
$712$	−5.15485	−	5.15485i	−0.193186	−	0.193186i
$713$	13.4695	+	13.4695i	0.504436	+	0.504436i
$714$	2.48015	−	3.04587i	0.0928173	−	0.113989i
$715$	17.6550	−	4.24288i	0.660259	−	0.158675i
$716$			14.8536i			0.555103i
$717$	−8.87927	+	0.909011i	−0.331603	+	0.0339476i
$718$	8.76797	−	8.76797i	0.327218	−	0.327218i
$719$	24.2165			0.903125			0.451562	−	0.892240i	$-0.350867\pi$
$719$	24.2165			0.903125			0.451562	+	0.892240i	$0.350867\pi$
$720$	5.93578	−	16.4906i	0.221213	−	0.614568i
$721$	12.5257			0.466482
$722$	2.94721	−	2.94721i	0.109684	−	0.109684i
$723$	−25.7033	+	2.63137i	−0.955917	+	0.0978616i
$724$			9.70117i			0.360541i
$725$	6.51891	+	12.7795i	0.242106	+	0.474621i
$726$	−2.07397	+	2.54704i	−0.0769723	+	0.0945297i
$727$	−25.8923	−	25.8923i	−0.960293	−	0.960293i	0.0389483	−	0.999241i	$-0.487599\pi$
$727$	−25.8923	−	25.8923i	−0.960293	−	0.960293i	−0.999241	+	0.0389483i	$0.987599\pi$
$728$	3.96573	+	3.96573i	0.146980	+	0.146980i
$729$	22.0977	−	15.5142i	0.818435	−	0.574599i
$730$	−5.51237	−	3.37624i	−0.204022	−	0.124960i
$731$		−	4.96030i		−	0.183463i
$732$	1.46627	+	14.3226i	0.0541949	+	0.529379i
$733$	13.4535	−	13.4535i	0.496918	−	0.496918i	−0.413559	−	0.910477i	$-0.635715\pi$
$733$	13.4535	−	13.4535i	0.496918	−	0.496918i	0.910477	+	0.413559i	$0.135715\pi$
$734$	−1.11882			−0.0412965
$735$	−3.49157	−	1.67599i	−0.128788	−	0.0618200i
$736$	−17.9184			−0.660481
$737$	−14.4563	+	14.4563i	−0.532503	+	0.532503i
$738$	−14.2456	−	9.36099i	−0.524388	−	0.344583i
$739$			1.96813i			0.0723987i	0.999345	+	0.0361994i	$0.0115251\pi$
$739$			1.96813i			0.0723987i	−0.999345	+	0.0361994i	$0.988475\pi$
$740$	2.78540	+	11.5903i	0.102393	+	0.426067i
$741$	21.4070	+	17.4310i	0.786406	+	0.640343i
$742$	2.17711	+	2.17711i	0.0799243	+	0.0799243i
$743$	−4.54680	−	4.54680i	−0.166806	−	0.166806i	0.618768	−	0.785574i	$-0.287632\pi$
$743$	−4.54680	−	4.54680i	−0.166806	−	0.166806i	−0.785574	+	0.618768i	$0.787632\pi$
$744$	13.0989	+	10.6659i	0.480227	+	0.391032i
$745$	10.8762	−	17.7575i	0.398472	−	0.650584i
$746$			9.05496i			0.331526i
$747$	14.3166	+	9.40761i	0.523815	+	0.344206i
$748$	15.3533	−	15.3533i	0.561371	−	0.561371i
$749$	1.00465			0.0367092
$750$	−6.55628	+	6.88112i	−0.239402	+	0.251263i
$751$	−0.491718			−0.0179430			−0.00897152	−	0.999960i	$-0.502856\pi$
$751$	−0.491718			−0.0179430			−0.00897152	+	0.999960i	$0.502856\pi$
$752$	20.0140	−	20.0140i	0.729835	−	0.729835i
$753$	−0.759037	−	7.41432i	−0.0276609	−	0.270193i
$754$		−	4.28075i		−	0.155896i
$755$	−23.8098	+	38.8742i	−0.866528	+	1.41478i
$756$	4.21559	−	8.11044i	0.153320	−	0.294974i
$757$	3.50957	+	3.50957i	0.127558	+	0.127558i	0.768003	−	0.640446i	$-0.221250\pi$
$757$	3.50957	+	3.50957i	0.127558	+	0.127558i	−0.640446	+	0.768003i	$0.721250\pi$
$758$	6.61607	+	6.61607i	0.240306	+	0.240306i
$759$	−10.5281	+	12.9296i	−0.382146	+	0.469314i
$760$	5.05459	+	21.0326i	0.183349	+	0.762932i
$761$			26.9220i			0.975922i	0.872865	+	0.487961i	$0.162259\pi$
$761$			26.9220i			0.975922i	−0.872865	+	0.487961i	$0.837741\pi$
$762$	14.5151	−	1.48598i	0.525826	−	0.0538312i
$763$	13.4452	−	13.4452i	0.486749	−	0.486749i
$764$	0.984264			0.0356094
$765$	13.1990	+	28.0445i	0.477210	+	1.01395i
$766$	12.3026			0.444512
$767$	0.342701	−	0.342701i	0.0123742	−	0.0123742i
$768$	0.0310544	−	0.00317918i	0.00112058	−	0.000114719i
$769$			31.3935i			1.13208i	0.824378	+	0.566040i	$0.191525\pi$
$769$			31.3935i			1.13208i	−0.824378	+	0.566040i	$0.808475\pi$
$770$	2.50010	+	1.53127i	0.0900973	+	0.0551832i
$771$	9.01519	−	11.0716i	0.324674	−	0.398733i
$772$	12.4052	+	12.4052i	0.446473	+	0.446473i
$773$	13.3925	+	13.3925i	0.481693	+	0.481693i	0.905672	−	0.423979i	$-0.139367\pi$
$773$	13.3925	+	13.3925i	0.481693	+	0.481693i	−0.423979	+	0.905672i	$0.639367\pi$
$774$	0.320291	+	1.54792i	0.0115126	+	0.0556387i
$775$	12.0098	+	23.5437i	0.431404	+	0.845716i
$776$			4.87606i			0.175040i
$777$	0.534561	+	5.22162i	0.0191773	+	0.187325i
$778$	6.36887	−	6.36887i	0.228335	−	0.228335i
$779$	−60.7006			−2.17482
$780$	−19.5391	+	6.86488i	−0.699612	+	0.245802i
$781$	−36.2985			−1.29886
$782$	5.77865	−	5.77865i	0.206644	−	0.206644i
$783$	−14.2162	+	4.49210i	−0.508044	+	0.160535i
$784$		−	2.61267i		−	0.0933098i
$785$	−19.4596	+	4.67657i	−0.694542	+	0.166914i
$786$	6.55437	+	5.33700i	0.233787	+	0.190364i
$787$	22.4712	+	22.4712i	0.801011	+	0.801011i	0.983254	−	0.182243i	$-0.0583358\pi$
$787$	22.4712	+	22.4712i	0.801011	+	0.801011i	−0.182243	+	0.983254i	$0.558336\pi$
$788$	17.8557	+	17.8557i	0.636085	+	0.636085i
$789$	0.118698	+	0.0966515i	0.00422575	+	0.00344088i
$790$	4.15858	−	0.999399i	0.147956	−	0.0355570i
$791$			8.04874i			0.286180i
$792$	−8.11990	+	12.3569i	−0.288528	+	0.439084i
$793$	10.1569	−	10.1569i	0.360681	−	0.360681i
$794$	7.57440			0.268805
$795$	−22.9221	+	8.05347i	−0.812964	+	0.285627i
$796$	−20.5372			−0.727922
$797$	7.83907	−	7.83907i	0.277674	−	0.277674i	−0.554506	−	0.832180i	$-0.687093\pi$
$797$	7.83907	−	7.83907i	0.277674	−	0.277674i	0.832180	+	0.554506i	$0.187093\pi$
$798$	0.453945	+	4.43417i	0.0160695	+	0.156968i
$799$			50.0556i			1.77084i
$800$	−23.6483	−	7.67178i	−0.836094	−	0.271238i
$801$	11.6079	−	2.40187i	0.410144	−	0.0848660i
$802$	11.9471	+	11.9471i	0.421866	+	0.421866i
$803$	−11.1259	−	11.1259i	−0.392623	−	0.392623i
$804$	14.7233	−	18.0817i	0.519252	−	0.637694i
$805$	−6.87151	−	4.20869i	−0.242189	−	0.148337i
$806$		−	7.88640i		−	0.277787i
$807$	51.1227	−	5.23366i	1.79960	−	0.184233i
$808$	4.90684	−	4.90684i	0.172622	−	0.172622i
$809$	−6.27026			−0.220451			−0.110225	−	0.993907i	$-0.535157\pi$
$809$	−6.27026			−0.220451			−0.110225	+	0.993907i	$0.535157\pi$
$810$	−5.92975	−	7.89934i	−0.208350	−	0.277554i
$811$	−8.90138			−0.312570			−0.156285	−	0.987712i	$-0.549952\pi$
$811$	−8.90138			−0.312570			−0.156285	+	0.987712i	$0.549952\pi$
$812$	−3.56898	+	3.56898i	−0.125247	+	0.125247i
$813$	39.0058	−	3.99320i	1.36799	−	0.140048i
$814$		−	3.97332i		−	0.139265i
$815$	−4.77079	−	19.8517i	−0.167114	−	0.695373i
$816$	−13.2024	+	16.2138i	−0.462175	+	0.567598i
$817$	3.98022	+	3.98022i	0.139250	+	0.139250i
$818$	2.63502	+	2.63502i	0.0921313	+	0.0921313i
$819$	−8.93015	+	1.84781i	−0.312045	+	0.0645676i
$820$	23.7842	−	38.8324i	0.830581	−	1.35608i
$821$		−	16.8442i		−	0.587867i	−0.955826	−	0.293934i	$-0.905036\pi$
$821$		−	16.8442i		−	0.587867i	0.955826	−	0.293934i	$-0.0949645\pi$
$822$	−1.67305	−	16.3425i	−0.0583543	−	0.570008i
$823$	32.4880	−	32.4880i	1.13246	−	1.13246i	0.142695	−	0.989767i	$-0.454423\pi$
$823$	32.4880	−	32.4880i	1.13246	−	1.13246i	0.989767	−	0.142695i	$-0.0455767\pi$
$824$	23.1099			0.805072
$825$	−19.4306	+	12.5566i	−0.676486	+	0.437164i
$826$	0.0782529			0.00272277
$827$	−4.87454	+	4.87454i	−0.169504	+	0.169504i	−0.786762	−	0.617257i	$-0.788244\pi$
$827$	−4.87454	+	4.87454i	−0.169504	+	0.169504i	0.617257	+	0.786762i	$0.288244\pi$
$828$	10.4437	−	15.8932i	0.362943	−	0.552329i
$829$			9.82522i			0.341244i	0.985337	+	0.170622i	$0.0545777\pi$
$829$			9.82522i			0.341244i	−0.985337	+	0.170622i	$0.945422\pi$
$830$	3.27323	−	5.34419i	0.113616	−	0.185499i
$831$	7.99924	+	6.51350i	0.277490	+	0.225951i
$832$	−5.98598	−	5.98598i	−0.207527	−	0.207527i
$833$	3.26719	+	3.26719i	0.113201	+	0.113201i
$834$	11.0703	+	9.01414i	0.383332	+	0.312134i
$835$	−1.16754	−	4.85822i	−0.0404043	−	0.168126i
$836$			24.6394i			0.852171i
$837$	−26.1904	+	8.27579i	−0.905272	+	0.286053i
$838$	2.15397	−	2.15397i	0.0744075	−	0.0744075i
$839$	13.0314			0.449893			0.224947	−	0.974371i	$-0.427779\pi$
$839$	13.0314			0.449893			0.224947	+	0.974371i	$0.427779\pi$
$840$	−6.44194	−	3.09221i	−0.222268	−	0.106691i
$841$	−20.7675			−0.716120
$842$	−8.72279	+	8.72279i	−0.300607	+	0.300607i
$843$	3.88235	+	37.9231i	0.133715	+	1.30614i
$844$		−	1.36701i		−	0.0470543i
$845$	−7.16925	−	4.39105i	−0.246630	−	0.151057i
$846$	−3.23214	−	15.6204i	−0.111123	−	0.537041i
$847$	−2.73212	−	2.73212i	−0.0938766	−	0.0938766i
$848$	−11.5892	−	11.5892i	−0.397976	−	0.397976i
$849$	14.8463	−	18.2327i	0.509523	−	0.625745i
$850$	10.1007	−	5.15240i	0.346450	−	0.176726i
$851$			10.9207i			0.374355i
$852$	41.1855	−	4.21634i	1.41099	−	0.144450i
$853$	−36.7177	+	36.7177i	−1.25719	+	1.25719i	−0.304761	+	0.952429i	$0.598576\pi$
$853$	−36.7177	+	36.7177i	−1.25719	+	1.25719i	−0.952429	+	0.304761i	$0.901424\pi$
$854$	2.31923			0.0793626
$855$	−33.0944	−	11.9123i	−1.13181	−	0.407392i
$856$	1.85358			0.0633542
$857$	−25.5867	+	25.5867i	−0.874024	+	0.874024i	−0.992908	−	0.118884i	$-0.962068\pi$
$857$	−25.5867	+	25.5867i	−0.874024	+	0.874024i	0.118884	+	0.992908i	$0.462068\pi$
$858$	6.86725	−	0.703032i	0.234444	−	0.0240011i
$859$		−	15.7133i		−	0.536132i	−0.963401	−	0.268066i	$-0.913615\pi$
$859$		−	15.7133i		−	0.536132i	0.963401	−	0.268066i	$-0.0863845\pi$
$860$	−4.10585	+	0.986727i	−0.140008	+	0.0336471i
$861$	12.6609	−	15.5489i	0.431484	−	0.529906i
$862$	−2.92644	−	2.92644i	−0.0996751	−	0.0996751i
$863$	11.1088	+	11.1088i	0.378147	+	0.378147i	0.870433	−	0.492286i	$-0.163839\pi$
$863$	11.1088	+	11.1088i	0.378147	+	0.378147i	−0.492286	+	0.870433i	$0.663839\pi$
$864$	11.9159	−	22.9251i	0.405386	−	0.779927i
$865$	−5.22613	+	1.25595i	−0.177694	+	0.0427037i
$866$		−	13.0685i		−	0.444084i
$867$	−0.767159	−	7.49366i	−0.0260541	−	0.254498i
$868$	−6.57512	+	6.57512i	−0.223174	+	0.223174i
$869$	10.4106			0.353155
$870$	1.80791	+	5.14575i	0.0612939	+	0.174457i
$871$	−23.2637			−0.788260
$872$	24.8064	−	24.8064i	0.840050	−	0.840050i
$873$	−6.62602	−	4.35405i	−0.224257	−	0.147362i
$874$			9.27375i			0.313689i
$875$	−7.26691	−	8.49658i	−0.245667	−	0.287237i
$876$	13.9161	+	11.3314i	0.470182	+	0.382853i
$877$	−20.7301	−	20.7301i	−0.700006	−	0.700006i	0.264405	−	0.964412i	$-0.414824\pi$
$877$	−20.7301	−	20.7301i	−0.700006	−	0.700006i	−0.964412	+	0.264405i	$0.914824\pi$
$878$	1.69456	+	1.69456i	0.0571886	+	0.0571886i
$879$	−6.76884	−	5.51163i	−0.228307	−	0.185903i
$880$	−13.3086	−	8.15128i	−0.448631	−	0.274780i
$881$		−	26.4774i		−	0.892045i	−0.895022	−	0.446023i	$-0.852840\pi$
$881$		−	26.4774i		−	0.892045i	0.895022	−	0.446023i	$-0.147160\pi$
$882$	−1.23053	−	0.808598i	−0.0414341	−	0.0272269i
$883$	−26.9720	+	26.9720i	−0.907681	+	0.907681i	−0.996085	−	0.0884037i	$-0.971823\pi$
$883$	−26.9720	+	26.9720i	−0.907681	+	0.907681i	0.0884037	+	0.996085i	$0.471823\pi$
$884$	24.7072			0.830993
$885$	−0.267215	+	0.556685i	−0.00898235	+	0.0187128i
$886$	−16.5864			−0.557231
$887$	−1.34997	+	1.34997i	−0.0453275	+	0.0453275i	−0.729407	−	0.684080i	$-0.760204\pi$
$887$	−1.34997	+	1.34997i	−0.0453275	+	0.0453275i	0.684080	+	0.729407i	$0.260204\pi$
$888$	0.986265	+	9.63389i	0.0330969	+	0.323292i
$889$			17.1637i			0.575653i
$890$	−1.01329	−	4.21637i	−0.0339655	−	0.141333i
$891$	−9.54105	−	22.0681i	−0.319637	−	0.739309i
$892$	−5.87209	−	5.87209i	−0.196612	−	0.196612i
$893$	−40.1654	−	40.1654i	−1.34408	−	1.34408i
$894$	4.99871	−	6.13892i	0.167182	−	0.205316i
$895$	−9.86155	+	16.1009i	−0.329635	+	0.538194i
$896$		−	11.3115i		−	0.377890i
$897$	−18.8746	+	1.93228i	−0.630205	+	0.0645169i
$898$	8.21601	−	8.21601i	0.274172	−	0.274172i
$899$	15.1668			0.505840
$900$	20.5881	−	16.5041i	0.686268	−	0.550137i
$901$	28.9850			0.965631
$902$	−10.7330	+	10.7330i	−0.357368	+	0.357368i
$903$	−1.84976	+	0.189368i	−0.0615561	+	0.00630178i
$904$			14.8499i			0.493901i
$905$	−6.44079	+	10.5158i	−0.214099	+	0.349558i
$906$	−10.9430	+	13.4391i	−0.363558	+	0.446486i
$907$	−28.6846	−	28.6846i	−0.952456	−	0.952456i	0.0464640	−	0.998920i	$-0.485205\pi$
$907$	−28.6846	−	28.6846i	−0.952456	−	0.952456i	−0.998920	+	0.0464640i	$0.985205\pi$
$908$	−0.426278	−	0.426278i	−0.0141465	−	0.0141465i
$909$	2.28631	+	11.0494i	0.0758322	+	0.366485i
$910$	0.779541	+	3.24374i	0.0258415	+	0.107529i
$911$		−	34.0874i		−	1.12937i	−0.825307	−	0.564684i	$-0.808998\pi$
$911$		−	34.0874i		−	1.12937i	0.825307	−	0.564684i	$-0.191002\pi$
$912$	−2.41645	−	23.6040i	−0.0800166	−	0.781607i
$913$	10.7864	−	10.7864i	0.356978	−	0.356978i
$914$	−7.12016			−0.235514
$915$	−7.91964	+	16.4989i	−0.261815	+	0.545435i
$916$	23.7115			0.783450
$917$	−7.03062	+	7.03062i	−0.232172	+	0.232172i
$918$	3.55046	+	11.2361i	0.117183	+	0.370848i
$919$			2.19661i			0.0724593i	0.999343	+	0.0362297i	$0.0115348\pi$
$919$			2.19661i			0.0724593i	−0.999343	+	0.0362297i	$0.988465\pi$
$920$	−12.6779	−	7.76503i	−0.417979	−	0.256006i
$921$	19.8958	+	16.2005i	0.655589	+	0.533823i
$922$	8.09166	+	8.09166i	0.266485	+	0.266485i
$923$	−29.2066	−	29.2066i	−0.961348	−	0.961348i
$924$	−6.31156	−	5.13929i	−0.207635	−	0.169070i
$925$	−4.67569	+	14.4129i	−0.153736	+	0.473892i
$926$		−	11.8389i		−	0.389049i
$927$	−20.6359	+	31.4038i	−0.677771	+	1.03144i
$928$	−10.0881	+	10.0881i	−0.331159	+	0.331159i
$929$	−51.2981			−1.68304			−0.841518	−	0.540230i	$-0.818337\pi$
$929$	−51.2981			−1.68304			−0.841518	+	0.540230i	$0.818337\pi$
$930$	3.33071	+	9.48000i	0.109218	+	0.310861i
$931$	−5.24329			−0.171842
$932$	2.09792	−	2.09792i	0.0687197	−	0.0687197i
$933$	3.60455	+	35.2094i	0.118008	+	1.15271i
$934$		−	5.55717i		−	0.181836i
$935$	26.8359	−	6.44925i	0.877627	−	0.210913i
$936$	−16.4761	+	3.40920i	−0.538539	+	0.111433i
$937$	16.4279	+	16.4279i	0.536675	+	0.536675i	0.922551	−	0.385876i	$-0.126101\pi$
$937$	16.4279	+	16.4279i	0.536675	+	0.536675i	−0.385876	+	0.922551i	$0.626101\pi$
$938$	−2.65603	−	2.65603i	−0.0867226	−	0.0867226i
$939$	−25.4933	+	31.3083i	−0.831942	+	1.02171i
$940$	41.4332	−	9.95730i	1.35140	−	0.324771i
$941$		−	57.2870i		−	1.86750i	−0.357922	−	0.933752i	$-0.616515\pi$
$941$		−	57.2870i		−	1.86750i	0.357922	−	0.933752i	$-0.383485\pi$
$942$	−7.56918	+	0.774891i	−0.246617	+	0.0252473i
$943$	29.4995	−	29.4995i	0.960635	−	0.960635i
$944$	−0.416557			−0.0135578
$945$	9.95427	−	5.99271i	0.323812	−	0.194943i
$946$	1.40755			0.0457634
$947$	35.8300	−	35.8300i	1.16432	−	1.16432i	0.180799	−	0.983520i	$-0.442132\pi$
$947$	35.8300	−	35.8300i	1.16432	−	1.16432i	0.983520	−	0.180799i	$-0.0578684\pi$
$948$	−11.8122	+	1.20927i	−0.383642	+	0.0392752i
$949$		−	17.9043i		−	0.581197i
$950$	−3.97056	+	12.2393i	−0.128822	+	0.397095i
$951$	35.5017	−	43.5997i	1.15122	−	1.41382i
$952$	6.02797	+	6.02797i	0.195368	+	0.195368i
$953$	−35.4764	−	35.4764i	−1.14919	−	1.14919i	−0.986712	−	0.162481i	$-0.948050\pi$
$953$	−35.4764	−	35.4764i	−1.14919	−	1.14919i	−0.162481	−	0.986712i	$-0.551950\pi$
$954$	−9.04510	+	1.87159i	−0.292846	+	0.0605950i
$955$	1.06692	+	0.653471i	0.0345247	+	0.0211458i
$956$		−	9.06511i		−	0.293187i
$957$	1.35204	+	13.2068i	0.0437051	+	0.426914i
$958$	6.98270	−	6.98270i	0.225601	−	0.225601i
$959$	19.3245			0.624022
$960$	9.72365	+	4.66747i	0.313830	+	0.150642i
$961$	−3.05833			−0.0986558
$962$	3.19703	−	3.19703i	0.103076	−	0.103076i
$963$	−1.65515	+	2.51881i	−0.0533364	+	0.0811677i
$964$		−	26.2413i		−	0.845175i
$965$	5.21090	+	21.6830i	0.167745	+	0.698000i
$966$	−2.37554	−	1.93432i	−0.0764317	−	0.0622357i
$967$	−21.0372	−	21.0372i	−0.676511	−	0.676511i	0.282698	−	0.959209i	$-0.408771\pi$
$967$	−21.0372	−	21.0372i	−0.676511	−	0.676511i	−0.959209	+	0.282698i	$0.908771\pi$
$968$	−5.04075	−	5.04075i	−0.162016	−	0.162016i
$969$	32.5390	+	26.4954i	1.04530	+	0.851154i
$970$	−1.51493	+	2.47341i	−0.0486413	+	0.0794164i
$971$			23.4561i			0.752742i	0.926469	+	0.376371i	$0.122828\pi$
$971$			23.4561i			0.752742i	−0.926469	+	0.376371i	$0.877172\pi$
$972$	13.3890	+	23.9309i	0.429451	+	0.767585i
$973$	−11.8747	+	11.8747i	−0.380684	+	0.380684i
$974$	−5.39987			−0.173023
$975$	−25.7376	−	5.53100i	−0.824264	−	0.177134i
$976$	−12.3458			−0.395179
$977$	9.03422	−	9.03422i	0.289030	−	0.289030i	−0.547666	−	0.836697i	$-0.684484\pi$
$977$	9.03422	−	9.03422i	0.289030	−	0.289030i	0.836697	+	0.547666i	$0.184484\pi$
$978$	−0.790504	−	7.72169i	−0.0252775	−	0.246913i
$979$		−	10.5552i		−	0.337347i
$980$	2.05447	−	3.35432i	0.0656276	−	0.107150i
$981$	11.5584	+	55.8598i	0.369031	+	1.78347i
$982$	−0.796647	−	0.796647i	−0.0254220	−	0.0254220i
$983$	−3.13374	−	3.13374i	−0.0999509	−	0.0999509i	0.655363	−	0.755314i	$-0.272516\pi$
$983$	−3.13374	−	3.13374i	−0.0999509	−	0.0999509i	−0.755314	+	0.655363i	$0.772516\pi$
$984$	23.3594	−	28.6877i	0.744672	−	0.914532i
$985$	7.50044	+	31.2099i	0.238984	+	0.994432i
$986$		−	6.50680i		−	0.207219i
$987$	18.6664	−	1.91096i	0.594157	−	0.0608265i
$988$	−19.8254	+	19.8254i	−0.630731	+	0.630731i
$989$	−3.86864			−0.123016
$990$	−7.95800	+	3.74538i	−0.252922	+	0.119036i
$991$	−29.2283			−0.928467			−0.464233	−	0.885713i	$-0.653670\pi$
$991$	−29.2283			−0.928467			−0.464233	+	0.885713i	$0.653670\pi$
$992$	−18.5853	+	18.5853i	−0.590085	+	0.590085i
$993$	−3.81588	+	0.390649i	−0.121093	+	0.0123969i
$994$		−	6.66909i		−	0.211531i
$995$	−22.2618	−	13.6350i	−0.705748	−	0.432260i
$996$	−10.9857	+	13.4915i	−0.348095	+	0.427496i
$997$	−4.57510	−	4.57510i	−0.144895	−	0.144895i	0.630938	−	0.775833i	$-0.282670\pi$
$997$	−4.57510	−	4.57510i	−0.144895	−	0.144895i	−0.775833	+	0.630938i	$0.782670\pi$
$998$	4.27793	+	4.27793i	0.135415	+	0.135415i
$999$	−13.9721	−	7.26231i	−0.442057	−	0.229769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.j.a.92.5	yes	24
3.2	odd	2	inner	105.2.j.a.92.8	yes	24
5.2	odd	4		525.2.j.b.218.5		24
5.3	odd	4	inner	105.2.j.a.8.8	yes	24
5.4	even	2		525.2.j.b.407.8		24
7.2	even	3		735.2.y.j.557.8		48
7.3	odd	6		735.2.y.g.422.5		48
7.4	even	3		735.2.y.j.422.5		48
7.5	odd	6		735.2.y.g.557.8		48
7.6	odd	2		735.2.j.h.197.5		24
15.2	even	4		525.2.j.b.218.8		24
15.8	even	4	inner	105.2.j.a.8.5	✓	24
15.14	odd	2		525.2.j.b.407.5		24
21.2	odd	6		735.2.y.j.557.5		48
21.5	even	6		735.2.y.g.557.5		48
21.11	odd	6		735.2.y.j.422.8		48
21.17	even	6		735.2.y.g.422.8		48
21.20	even	2		735.2.j.h.197.8		24
35.3	even	12		735.2.y.g.128.5		48
35.13	even	4		735.2.j.h.638.8		24
35.18	odd	12		735.2.y.j.128.5		48
35.23	odd	12		735.2.y.j.263.8		48
35.33	even	12		735.2.y.g.263.8		48
105.23	even	12		735.2.y.j.263.5		48
105.38	odd	12		735.2.y.g.128.8		48
105.53	even	12		735.2.y.j.128.8		48
105.68	odd	12		735.2.y.g.263.5		48
105.83	odd	4		735.2.j.h.638.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.5	✓	24	15.8	even	4	inner
105.2.j.a.8.8	yes	24	5.3	odd	4	inner
105.2.j.a.92.5	yes	24	1.1	even	1	trivial
105.2.j.a.92.8	yes	24	3.2	odd	2	inner
525.2.j.b.218.5		24	5.2	odd	4
525.2.j.b.218.8		24	15.2	even	4
525.2.j.b.407.5		24	15.14	odd	2
525.2.j.b.407.8		24	5.4	even	2
735.2.j.h.197.5		24	7.6	odd	2
735.2.j.h.197.8		24	21.20	even	2
735.2.j.h.638.5		24	105.83	odd	4
735.2.j.h.638.8		24	35.13	even	4
735.2.y.g.128.5		48	35.3	even	12
735.2.y.g.128.8		48	105.38	odd	12
735.2.y.g.263.5		48	105.68	odd	12
735.2.y.g.263.8		48	35.33	even	12
735.2.y.g.422.5		48	7.3	odd	6
735.2.y.g.422.8		48	21.17	even	6
735.2.y.g.557.5		48	21.5	even	6
735.2.y.g.557.8		48	7.5	odd	6
735.2.y.j.128.5		48	35.18	odd	12
735.2.y.j.128.8		48	105.53	even	12
735.2.y.j.263.5		48	105.23	even	12
735.2.y.j.263.8		48	35.23	odd	12
735.2.y.j.422.5		48	7.4	even	3
735.2.y.j.422.8		48	21.11	odd	6
735.2.y.j.557.5		48	21.2	odd	6
735.2.y.j.557.8		48	7.2	even	3

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.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.347054 + 0.347054i) q^{2} +(1.72305 - 0.176396i) q^{3} +1.75911i q^{4} +(-1.16790 + 1.90683i) q^{5} +(-0.536770 + 0.659208i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.30461 - 1.30461i) q^{8} +(2.93777 - 0.607876i) q^{9} +O(q^{10})\)	\(q+(-0.347054 + 0.347054i) q^{2} +(1.72305 - 0.176396i) q^{3} +1.75911i q^{4} +(-1.16790 + 1.90683i) q^{5} +(-0.536770 + 0.659208i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.30461 - 1.30461i) q^{8} +(2.93777 - 0.607876i) q^{9} +(-0.256447 - 1.06710i) q^{10} -2.67137i q^{11} +(0.310299 + 3.03102i) q^{12} +(2.14945 - 2.14945i) q^{13} +0.490808 q^{14} +(-1.67599 + 3.49157i) q^{15} -2.61267 q^{16} +(3.26719 - 3.26719i) q^{17} +(-0.808598 + 1.23053i) q^{18} +5.24329i q^{19} +(-3.35432 - 2.05447i) q^{20} +(-1.34311 - 1.09365i) q^{21} +(0.927108 + 0.927108i) q^{22} +(-2.54815 - 2.54815i) q^{23} +(-2.47803 - 2.01778i) q^{24} +(-2.27200 - 4.45399i) q^{25} +1.49195i q^{26} +(4.95468 - 1.56561i) q^{27} +(1.24388 - 1.24388i) q^{28} -2.86924 q^{29} +(-0.630101 - 1.79342i) q^{30} -5.28599 q^{31} +(3.51596 - 3.51596i) q^{32} +(-0.471218 - 4.60289i) q^{33} +2.26778i q^{34} +(2.17417 - 0.522500i) q^{35} +(1.06932 + 5.16785i) q^{36} +(-2.14286 - 2.14286i) q^{37} +(-1.81970 - 1.81970i) q^{38} +(3.32444 - 4.08274i) q^{39} +(4.01133 - 0.964012i) q^{40} +11.5768i q^{41} +(0.845684 - 0.0865765i) q^{42} +(0.759108 - 0.759108i) q^{43} +4.69922 q^{44} +(-2.27192 + 6.31177i) q^{45} +1.76869 q^{46} +(-7.66034 + 7.66034i) q^{47} +(-4.50176 + 0.460865i) q^{48} +1.00000i q^{49} +(2.33428 + 0.757266i) q^{50} +(5.05320 - 6.20584i) q^{51} +(3.78111 + 3.78111i) q^{52} +(4.43577 + 4.43577i) q^{53} +(-1.17619 + 2.26289i) q^{54} +(5.09384 + 3.11990i) q^{55} +1.84500i q^{56} +(0.924894 + 9.03442i) q^{57} +(0.995779 - 0.995779i) q^{58} +0.159437 q^{59} +(-6.14204 - 2.94825i) q^{60} +4.72534 q^{61} +(1.83452 - 1.83452i) q^{62} +(-2.50715 - 1.64748i) q^{63} -2.78490i q^{64} +(1.58828 + 6.60897i) q^{65} +(1.76099 + 1.43391i) q^{66} +(-5.41156 - 5.41156i) q^{67} +(5.74734 + 5.74734i) q^{68} +(-4.84006 - 3.94109i) q^{69} +(-0.573216 + 0.935887i) q^{70} -13.5880i q^{71} +(-4.62569 - 3.03961i) q^{72} +(4.16486 - 4.16486i) q^{73} +1.48737 q^{74} +(-4.70043 - 7.27365i) q^{75} -9.22351 q^{76} +(-1.88894 + 1.88894i) q^{77} +(0.263173 + 2.57069i) q^{78} +3.89710i q^{79} +(3.05135 - 4.98193i) q^{80} +(8.26097 - 3.57160i) q^{81} +(-4.01778 - 4.01778i) q^{82} +(4.03778 + 4.03778i) q^{83} +(1.92384 - 2.36267i) q^{84} +(2.41421 + 10.0457i) q^{85} +0.526902i q^{86} +(-4.94383 + 0.506122i) q^{87} +(-3.48510 + 3.48510i) q^{88} +3.95125 q^{89} +(-1.40205 - 2.97900i) q^{90} -3.03977 q^{91} +(4.48247 - 4.48247i) q^{92} +(-9.10800 + 0.932426i) q^{93} -5.31710i q^{94} +(-9.99806 - 6.12366i) q^{95} +(5.43796 - 6.67836i) q^{96} +(-1.86878 - 1.86878i) q^{97} +(-0.347054 - 0.347054i) q^{98} +(-1.62386 - 7.84786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3}+O(q^{10}) \) 24 * q - 4 * q^3	\( 24 q - 4 q^{3} - 16 q^{10} + 16 q^{12} - 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 4 q^{21} + 8 q^{22} - 16 q^{25} - 16 q^{27} + 20 q^{30} + 28 q^{33} + 16 q^{36} - 16 q^{37} + 64 q^{40} - 20 q^{42} - 40 q^{43} + 20 q^{45} - 64 q^{46} + 16 q^{48} - 20 q^{51} + 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} + 32 q^{61} - 8 q^{63} - 16 q^{66} + 24 q^{67} - 8 q^{70} - 8 q^{72} + 32 q^{73} - 60 q^{75} + 32 q^{76} + 60 q^{78} + 52 q^{81} - 80 q^{82} + 24 q^{85} + 4 q^{87} + 96 q^{88} - 24 q^{90} - 24 q^{91} - 76 q^{93} - 96 q^{96} + 24 q^{97}+O(q^{100}) \) 24 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 - 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 4 * q^21 + 8 * q^22 - 16 * q^25 - 16 * q^27 + 20 * q^30 + 28 * q^33 + 16 * q^36 - 16 * q^37 + 64 * q^40 - 20 * q^42 - 40 * q^43 + 20 * q^45 - 64 * q^46 + 16 * q^48 - 20 * q^51 + 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 + 32 * q^61 - 8 * q^63 - 16 * q^66 + 24 * q^67 - 8 * q^70 - 8 * q^72 + 32 * q^73 - 60 * q^75 + 32 * q^76 + 60 * q^78 + 52 * q^81 - 80 * q^82 + 24 * q^85 + 4 * q^87 + 96 * q^88 - 24 * q^90 - 24 * q^91 - 76 * q^93 - 96 * q^96 + 24 * q^97

Introduction

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