LMFDB - Embedded newform 105.2.j.a.8.8

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			8.8
Character	$\chi$	$=$	105.8
Dual form			105.2.j.a.92.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347054 + 0.347054i) q^{2} +(0.176396 + 1.72305i) q^{3} -1.75911i q^{4} +(1.16790 + 1.90683i) q^{5} +(-0.536770 + 0.659208i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.30461 - 1.30461i) q^{8} +(-2.93777 + 0.607876i) q^{9} +O(q^{10})$	\(q+(0.347054 + 0.347054i) q^{2} +(0.176396 + 1.72305i) 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} +(3.03102 - 0.310299i) q^{12} +(2.14945 + 2.14945i) q^{13} -0.490808 q^{14} +(-3.07954 + 2.34871i) q^{15} -2.61267 q^{16} +(-3.26719 - 3.26719i) q^{17} +(-1.23053 - 0.808598i) 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} +(-1.56561 - 4.95468i) q^{27} +(1.24388 + 1.24388i) q^{28} +2.86924 q^{29} +(-1.88389 - 0.253638i) q^{30} -5.28599 q^{31} +(-3.51596 - 3.51596i) q^{32} +(4.60289 - 0.471218i) 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} +(-0.0865765 - 0.845684i) q^{42} +(0.759108 + 0.759108i) q^{43} -4.69922 q^{44} +(-4.59015 - 4.89189i) q^{45} +1.76869 q^{46} +(7.66034 + 7.66034i) q^{47} +(-0.460865 - 4.50176i) 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} +(9.03442 - 0.924894i) q^{57} +(0.995779 + 0.995779i) q^{58} -0.159437 q^{59} +(4.13163 + 5.41724i) q^{60} +4.72534 q^{61} +(-1.83452 - 1.83452i) q^{62} +(1.64748 - 2.50715i) 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} +(-3.03961 + 4.62569i) q^{72} +(4.16486 + 4.16486i) q^{73} -1.48737 q^{74} +(-8.07519 - 3.12910i) q^{75} -9.22351 q^{76} +(1.88894 + 1.88894i) q^{77} +(-2.57069 + 0.263173i) 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} +(0.506122 + 4.94383i) q^{87} +(-3.48510 - 3.48510i) q^{88} -3.95125 q^{89} +(0.104719 - 3.29077i) q^{90} -3.03977 q^{91} +(-4.48247 - 4.48247i) q^{92} +(-0.932426 - 9.10800i) 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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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	$-0.194484\pi$
$2$	0.347054	+	0.347054i	0.245404	+	0.245404i	−0.573677	+	0.819081i	$0.694484\pi$
$3$	0.176396	+	1.72305i	0.101842	+	0.994801i
$3$	0.176396	+	1.72305i	0.101842	+	0.994801i
$4$		−	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	$-0.131936\pi$
$12$	3.03102	−	0.310299i	0.874981	−	0.0895757i
$13$	2.14945	+	2.14945i	0.596149	+	0.596149i	0.939285	−	0.343137i	$-0.111489\pi$
$13$	2.14945	+	2.14945i	0.596149	+	0.596149i	−0.343137	+	0.939285i	$0.611489\pi$
$14$	−0.490808			−0.131174
$15$	−3.07954	+	2.34871i	−0.795134	+	0.606434i
$16$	−2.61267			−0.653169
$17$	−3.26719	−	3.26719i	−0.792410	−	0.792410i	0.189475	−	0.981886i	$-0.439321\pi$
$17$	−3.26719	−	3.26719i	−0.792410	−	0.792410i	−0.981886	+	0.189475i	$0.939321\pi$
$18$	−1.23053	−	0.808598i	−0.290038	−	0.190588i
$19$		−	5.24329i		−	1.20289i	−0.798913	−	0.601446i	$-0.794591\pi$
$19$		−	5.24329i		−	1.20289i	0.798913	−	0.601446i	$-0.205409\pi$
$20$	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	$-0.627401\pi$
$23$	2.54815	−	2.54815i	0.531326	−	0.531326i	0.920967	+	0.389641i	$0.127401\pi$
$24$	2.47803	+	2.01778i	0.505826	+	0.411877i
$25$	−2.27200	+	4.45399i	−0.454400	+	0.890798i
$26$			1.49195i			0.292595i
$27$	−1.56561	−	4.95468i	−0.301301	−	0.953529i
$28$	1.24388	+	1.24388i	0.235071	+	0.235071i
$29$	2.86924			0.532804			0.266402	−	0.963862i	$-0.414165\pi$
$29$	2.86924			0.532804			0.266402	+	0.963862i	$0.414165\pi$
$30$	−1.88389	−	0.253638i	−0.343950	−	0.0463078i
$31$	−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
$33$	4.60289	−	0.471218i	0.801260	−	0.0820286i
$34$		−	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	−0.860959	−	0.508675i	$-0.830136\pi$
$37$	−2.14286	+	2.14286i	−0.352284	+	0.352284i	0.508675	+	0.860959i	$0.330136\pi$
$38$	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	$0.640619\pi$
$42$	−0.0865765	−	0.845684i	−0.0133590	−	0.130492i
$43$	0.759108	+	0.759108i	0.115763	+	0.115763i	0.762615	−	0.646852i	$-0.223915\pi$
$43$	0.759108	+	0.759108i	0.115763	+	0.115763i	−0.646852	+	0.762615i	$0.723915\pi$
$44$	−4.69922			−0.708434
$45$	−4.59015	−	4.89189i	−0.684259	−	0.729239i
$46$	1.76869			0.260779
$47$	7.66034	+	7.66034i	1.11738	+	1.11738i	0.992125	+	0.125250i	$0.0399734\pi$
$47$	7.66034	+	7.66034i	1.11738	+	1.11738i	0.125250	+	0.992125i	$0.460027\pi$
$48$	−0.460865	−	4.50176i	−0.0665201	−	0.649773i
$49$		−	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	$-0.891783\pi$
$53$	−4.43577	+	4.43577i	−0.609300	+	0.609300i	0.333463	+	0.942763i	$0.391783\pi$
$54$	1.17619	−	2.26289i	0.160059	−	0.307940i
$55$	5.09384	−	3.11990i	0.686854	−	0.420687i
$56$			1.84500i			0.246548i
$57$	9.03442	−	0.924894i	1.19664	−	0.122505i
$58$	0.995779	+	0.995779i	0.130752	+	0.130752i
$59$	−0.159437			−0.0207569			−0.0103785	−	0.999946i	$-0.503304\pi$
$59$	−0.159437			−0.0207569			−0.0103785	+	0.999946i	$0.503304\pi$
$60$	4.13163	+	5.41724i	0.533391	+	0.699363i
$61$	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
$63$	1.64748	−	2.50715i	0.207563	−	0.315871i
$64$			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	−0.955646	−	0.294519i	$-0.904841\pi$
$67$	−5.41156	+	5.41156i	−0.661127	+	0.661127i	0.294519	+	0.955646i	$0.404841\pi$
$68$	−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	$-0.298533\pi$
$72$	−3.03961	+	4.62569i	−0.358221	+	0.545143i
$73$	4.16486	+	4.16486i	0.487460	+	0.487460i	0.907504	−	0.420044i	$-0.137985\pi$
$73$	4.16486	+	4.16486i	0.487460	+	0.487460i	−0.420044	+	0.907504i	$0.637985\pi$
$74$	−1.48737			−0.172904
$75$	−8.07519	−	3.12910i	−0.932443	−	0.361317i
$76$	−9.22351			−1.05801
$77$	1.88894	+	1.88894i	0.215265	+	0.215265i
$78$	−2.57069	+	0.263173i	−0.291073	+	0.0297985i
$79$		−	3.89710i		−	0.438458i	−0.975673	−	0.219229i	$-0.929646\pi$
$79$		−	3.89710i		−	0.438458i	0.975673	−	0.219229i	$-0.0703542\pi$
$80$	−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	$-0.851466\pi$
$83$	−4.03778	+	4.03778i	−0.443204	+	0.443204i	0.449883	+	0.893087i	$0.351466\pi$
$84$	−1.92384	+	2.36267i	−0.209908	+	0.257789i
$85$	2.41421	−	10.0457i	0.261858	−	1.08961i
$86$			0.526902i			0.0568173i
$87$	0.506122	+	4.94383i	0.0542619	+	0.530034i
$88$	−3.48510	−	3.48510i	−0.371513	−	0.371513i
$89$	−3.95125			−0.418832			−0.209416	−	0.977827i	$-0.567156\pi$
$89$	−3.95125			−0.418832			−0.209416	+	0.977827i	$0.567156\pi$
$90$	0.104719	−	3.29077i	0.0110384	−	0.346878i
$91$	−3.03977			−0.318655
$92$	−4.48247	−	4.48247i	−0.467330	−	0.467330i
$93$	−0.932426	−	9.10800i	−0.0966881	−	0.944455i
$94$			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	−0.795586	−	0.605840i	$-0.792837\pi$
$97$	−1.86878	+	1.86878i	−0.189746	+	0.189746i	0.605840	+	0.795586i	$0.292837\pi$
$98$	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	$0.940083\pi$
$102$	3.90749	−	0.400027i	0.386899	−	0.0396086i
$103$	−8.85701	−	8.85701i	−0.872707	−	0.872707i	0.120060	−	0.992767i	$-0.461691\pi$
$103$	−8.85701	−	8.85701i	−0.872707	−	0.872707i	−0.992767	+	0.120060i	$0.961691\pi$
$104$	5.60838			0.549947
$105$	0.516777	−	3.83835i	0.0504323	−	0.374585i
$106$	−3.07890			−0.299049
$107$	0.710397	+	0.710397i	0.0686766	+	0.0686766i	0.740611	−	0.671934i	$-0.234536\pi$
$107$	0.710397	+	0.710397i	0.0686766	+	0.0686766i	−0.671934	+	0.740611i	$0.734536\pi$
$108$	−8.71582	+	2.75407i	−0.838680	+	0.265011i
$109$		−	19.0144i		−	1.82125i	−0.413237	−	0.910623i	$-0.635602\pi$
$109$		−	19.0144i		−	1.82125i	0.413237	−	0.910623i	$-0.364398\pi$
$110$	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	$-0.626412\pi$
$113$	5.69132	−	5.69132i	0.535394	−	0.535394i	0.922173	+	0.386779i	$0.126412\pi$
$114$	3.45642	+	2.81444i	0.323723	+	0.263597i
$115$	7.83488	+	1.88289i	0.730607	+	0.175581i
$116$		−	5.04730i		−	0.468630i
$117$	−7.62117	−	5.00798i	−0.704577	−	0.462988i
$118$	−0.0553332	−	0.0553332i	−0.00509383	−	0.00509383i
$119$	4.62051			0.423561
$120$	−0.953453	+	7.08176i	−0.0870380	+	0.646473i
$121$	3.86380			0.351254
$122$	1.63995	+	1.63995i	0.148474	+	0.148474i
$123$	−19.9474	+	2.04210i	−1.79859	+	0.184130i
$124$			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	−0.0801668	+	0.996781i	$0.525545\pi$
$127$	−12.1366	+	12.1366i	−1.07695	+	1.07695i	−0.996781	+	0.0801668i	$0.974455\pi$
$128$	−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	$-0.143023\pi$
$132$	−0.828923	−	8.09697i	−0.0721485	−	0.704751i
$133$	3.70756	+	3.70756i	0.321487	+	0.321487i
$134$	−3.75620			−0.324486
$135$	7.61926	−	8.77194i	0.655761	−	0.754968i
$136$	−8.52483			−0.730998
$137$	13.6645	+	13.6645i	1.16744	+	1.16744i	0.982808	+	0.184630i	$0.0591086\pi$
$137$	13.6645	+	13.6645i	1.16744	+	1.16744i	0.184630	+	0.982808i	$0.440891\pi$
$138$	0.311989	+	3.04753i	0.0265583	+	0.259423i
$139$			16.7933i			1.42439i	0.701982	+	0.712195i	$0.252299\pi$
$139$			16.7933i			1.42439i	−0.701982	+	0.712195i	$0.747701\pi$
$140$	−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
$147$	1.72305	−	0.176396i	0.142114	−	0.0145489i
$148$	3.76952	+	3.76952i	0.309853	+	0.309853i
$149$	9.31256			0.762915			0.381458	−	0.924386i	$-0.375422\pi$
$149$	9.31256			0.762915			0.381458	+	0.924386i	$0.375422\pi$
$150$	−1.71656	−	3.88849i	−0.140157	−	0.317494i
$151$	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
$153$	11.5843	+	7.61221i	0.936535	+	0.615410i
$154$			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	−0.407919	−	0.913018i	$-0.633746\pi$
$157$	6.32887	−	6.32887i	0.505098	−	0.505098i	0.913018	+	0.407919i	$0.133746\pi$
$158$	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
$162$	4.10654	+	1.62746i	0.322640	+	0.127866i
$163$	−6.45638	−	6.45638i	−0.505703	−	0.505703i	0.407502	−	0.913205i	$-0.366400\pi$
$163$	−6.45638	−	6.45638i	−0.505703	−	0.505703i	−0.913205	+	0.407502i	$0.866400\pi$
$164$	20.3649			1.59023
$165$	6.27426	+	8.22658i	0.488451	+	0.640439i
$166$	−2.80266			−0.217528
$167$	1.58004	+	1.58004i	0.122268	+	0.122268i	0.765593	−	0.643325i	$-0.222446\pi$
$167$	1.58004	+	1.58004i	0.122268	+	0.122268i	−0.643325	+	0.765593i	$0.722446\pi$
$168$	−3.17902	+	0.325450i	−0.245267	+	0.0251090i
$169$		−	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	$-0.779127\pi$
$173$	−1.69970	+	1.69970i	−0.129226	+	0.129226i	0.639536	+	0.768761i	$0.279127\pi$
$174$	−1.54012	+	1.89142i	−0.116756	+	0.143388i
$175$	−1.54290	−	4.75599i	−0.116632	−	0.359519i
$176$			6.97941i			0.526093i
$177$	−0.0281240	−	0.274717i	−0.00211393	−	0.0206490i
$178$	−1.37130	−	1.37130i	−0.102783	−	0.102783i
$179$	−8.44380			−0.631119			−0.315560	−	0.948906i	$-0.602192\pi$
$179$	−8.44380			−0.631119			−0.315560	+	0.948906i	$0.602192\pi$
$180$	−8.60535	+	8.07456i	−0.641405	+	0.601842i
$181$	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
$183$	0.833531	+	8.14198i	0.0616164	+	0.601872i
$184$		−	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	$-0.00644395\pi$
$192$	−4.79850	+	0.491244i	−0.346302	+	0.0354525i
$193$	7.05199	+	7.05199i	0.507613	+	0.507613i	0.913793	−	0.406180i	$-0.133139\pi$
$193$	7.05199	+	7.05199i	0.507613	+	0.507613i	−0.406180	+	0.913793i	$0.633139\pi$
$194$	−1.29713			−0.0931287
$195$	−11.6677	−	1.57089i	−0.835543	−	0.112493i
$196$	−1.75911			−0.125651
$197$	−10.1505	−	10.1505i	−0.723190	−	0.723190i	0.246064	−	0.969254i	$-0.420863\pi$
$197$	−10.1505	−	10.1505i	−0.723190	−	0.723190i	−0.969254	+	0.246064i	$0.920863\pi$
$198$	−2.16006	+	3.28719i	−0.153509	+	0.233611i
$199$		−	11.6748i		−	0.827604i	−0.910367	−	0.413802i	$-0.864201\pi$
$199$		−	11.6748i		−	0.827604i	0.910367	−	0.413802i	$-0.135799\pi$
$200$	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
$207$	−5.93692	+	9.03483i	−0.412644	+	0.627964i
$208$	−5.61580	−	5.61580i	−0.389386	−	0.389386i
$209$	−14.0067			−0.968867
$210$	1.51146	−	1.15276i	0.104301	−	0.0795483i
$211$	−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
$213$	23.4127	−	2.39687i	1.60421	−	0.164231i
$214$			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
$222$	−0.262367	−	2.56281i	−0.0176089	−	0.172005i
$223$	−3.33811	−	3.33811i	−0.223536	−	0.223536i	0.586450	−	0.809986i	$-0.300525\pi$
$223$	−3.33811	−	3.33811i	−0.223536	−	0.223536i	−0.809986	+	0.586450i	$0.800525\pi$
$224$	4.97232			0.332227
$225$	3.96714	−	14.4659i	0.264476	−	0.964392i
$226$	3.95038			0.262776
$227$	0.242326	+	0.242326i	0.0160838	+	0.0160838i	0.715103	−	0.699019i	$-0.246380\pi$
$227$	0.242326	+	0.242326i	0.0160838	+	0.0160838i	−0.699019	+	0.715103i	$0.746380\pi$
$228$	−1.62699	−	15.8925i	−0.107750	−	1.05251i
$229$			13.4793i			0.890735i	0.895348	+	0.445368i	$0.146927\pi$
$229$			13.4793i			0.890735i	−0.895348	+	0.445368i	$0.853073\pi$
$230$	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	$-0.732406\pi$
$233$	1.19260	−	1.19260i	0.0781301	−	0.0781301i	0.745092	+	0.666962i	$0.232406\pi$
$234$	−0.906918	−	4.38299i	−0.0592871	−	0.286525i
$235$	−5.66043	+	23.5535i	−0.369246	+	1.53646i
$236$			0.280467i			0.0182568i
$237$	6.71488	−	0.687432i	0.436178	−	0.0446535i
$238$	1.60356	+	1.60356i	0.103944	+	0.103944i
$239$	5.15325			0.333336			0.166668	−	0.986013i	$-0.446699\pi$
$239$	5.15325			0.333336			0.166668	+	0.986013i	$0.446699\pi$
$240$	8.04584	−	6.13641i	0.519357	−	0.396104i
$241$	−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
$243$	7.61123	+	13.6040i	0.488261	+	0.872698i
$244$		−	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	$-0.0433613\pi$
$252$	−4.41035	−	2.89810i	−0.277826	−	0.182563i
$253$	−6.80704	−	6.80704i	−0.427955	−	0.427955i
$254$	−8.42409			−0.528575
$255$	17.7351	+	2.38777i	1.11062	+	0.149528i
$256$	0.0180230			0.00112644
$257$	−5.82885	−	5.82885i	−0.363594	−	0.363594i	0.501540	−	0.865134i	$-0.332767\pi$
$257$	−5.82885	−	5.82885i	−0.363594	−	0.363594i	−0.865134	+	0.501540i	$0.832767\pi$
$258$	−0.907876	+	0.0929433i	−0.0565219	+	0.00578640i
$259$		−	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	$-0.750867\pi$
$263$	−0.0624909	+	0.0624909i	−0.00385335	+	0.00385335i	0.705177	+	0.709031i	$0.250867\pi$
$264$	5.39022	−	6.61974i	0.331745	−	0.407417i
$265$	−13.6388	−	3.27771i	−0.837826	−	0.201348i
$266$			2.57345i			0.157788i
$267$	−0.696985	−	6.80819i	−0.0426548	−	0.416654i
$268$	9.51951	+	9.51951i	0.581497	+	0.581497i
$269$	−29.6699			−1.80901			−0.904504	−	0.426465i	$-0.859759\pi$
$269$	−29.6699			−1.80901			−0.904504	+	0.426465i	$0.859759\pi$
$270$	5.68862	−	0.400043i	0.346199	−	0.0243459i
$271$	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
$273$	−0.536204	−	5.23767i	−0.0324525	−	0.316998i
$274$			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	−0.569178	−	0.822214i	$-0.692738\pi$
$277$	4.21136	−	4.21136i	0.253036	−	0.253036i	0.822214	+	0.569178i	$0.192738\pi$
$278$	−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	$0.772043\pi$
$282$	−9.16160	+	0.937914i	−0.545565	+	0.0558520i
$283$	9.59899	+	9.59899i	0.570601	+	0.570601i	0.932296	−	0.361695i	$-0.117802\pi$
$283$	9.59899	+	9.59899i	0.570601	+	0.570601i	−0.361695	+	0.932296i	$0.617802\pi$
$284$	−23.9027			−1.41837
$285$	12.3150	+	16.1469i	0.729475	+	0.956461i
$286$	3.98553			0.235670
$287$	−8.18605	−	8.18605i	−0.483207	−	0.483207i
$288$	12.4664	+	8.19181i	0.734587	+	0.482707i
$289$			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	$-0.702970\pi$
$293$	3.56359	−	3.56359i	0.208187	−	0.208187i	0.803497	+	0.595309i	$0.202970\pi$
$294$	0.659208	+	0.536770i	0.0384458	+	0.0313051i
$295$	−0.186207	−	0.304019i	−0.0108414	−	0.0177007i
$296$			5.59120i			0.324982i
$297$	−13.2358	+	4.18231i	−0.768018	+	0.242683i
$298$	3.23196	+	3.23196i	0.187222	+	0.187222i
$299$	10.9542			0.633499
$300$	−5.50442	+	14.2051i	−0.317798	+	0.820134i
$301$	−1.07354			−0.0618778
$302$	7.07531	+	7.07531i	0.407139	+	0.407139i
$303$	−6.48063	+	0.663452i	−0.372303	+	0.0381143i
$304$			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	−0.341916	−	0.939730i	$-0.611076\pi$
$307$	10.4746	−	10.4746i	0.597814	−	0.597814i	0.939730	+	0.341916i	$0.111076\pi$
$308$	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	$0.803301\pi$
$312$	0.989296	+	9.66350i	0.0560078	+	0.547088i
$313$	−16.4829	−	16.4829i	−0.931670	−	0.931670i	0.0661408	−	0.997810i	$-0.478931\pi$
$313$	−16.4829	−	16.4829i	−0.931670	−	0.931670i	−0.997810	+	0.0661408i	$0.978931\pi$
$314$	4.39291			0.247906
$315$	6.70481	+	0.213361i	0.377773	+	0.0120215i
$316$	−6.85542			−0.385647
$317$	−22.9540	−	22.9540i	−1.28922	−	1.28922i	−0.935259	−	0.353965i	$-0.884833\pi$
$317$	−22.9540	−	22.9540i	−1.28922	−	1.28922i	−0.353965	−	0.935259i	$-0.615167\pi$
$318$	−0.543105	−	5.30509i	−0.0304558	−	0.297494i
$319$		−	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
$327$	32.7626	−	3.35406i	1.81178	−	0.185480i
$328$	15.1033	+	15.1033i	0.833938	+	0.833938i
$329$	−10.8334			−0.597262
$330$	−0.677561	+	5.03257i	−0.0372985	+	0.277034i
$331$	−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
$333$	4.99263	−	7.59782i	0.273595	−	0.416358i
$334$			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	−0.346710	−	0.937972i	$-0.612701\pi$
$337$	10.8541	−	10.8541i	0.591263	−	0.591263i	0.937972	+	0.346710i	$0.112701\pi$
$338$	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
$342$	−4.23971	+	6.45202i	−0.229257	+	0.348885i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	1.98068			0.106791
$345$	−1.86227	+	13.8320i	−0.100261	+	0.744689i
$346$	−1.17977			−0.0634251
$347$	−5.06341	−	5.06341i	−0.271818	−	0.271818i	0.558014	−	0.829832i	$-0.311564\pi$
$347$	−5.06341	−	5.06341i	−0.271818	−	0.271818i	−0.829832	+	0.558014i	$0.811564\pi$
$348$	8.69672	−	0.890323i	0.466193	−	0.0477263i
$349$			7.42733i			0.397576i	0.980043	+	0.198788i	$0.0637005\pi$
$349$			7.42733i			0.397576i	−0.980043	+	0.198788i	$0.936300\pi$
$350$	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	$-0.638856\pi$
$353$	9.09032	−	9.09032i	0.483829	−	0.483829i	0.906352	+	0.422523i	$0.138856\pi$
$354$	0.0855810	−	0.105102i	0.00454858	−	0.00558611i
$355$	25.9100	−	15.8695i	1.37516	−	0.842264i
$356$			6.95068i			0.368385i
$357$	0.815038	+	7.96134i	0.0431364	+	0.421359i
$358$	−2.93045	−	2.93045i	−0.154879	−	0.154879i
$359$	25.2640			1.33338			0.666692	−	0.745333i	$-0.267710\pi$
$359$	25.2640			1.33338			0.666692	+	0.745333i	$0.267710\pi$
$360$	−12.3704	−	0.393650i	−0.651976	−	0.0207472i
$361$	−8.49208			−0.446951
$362$	1.91394	+	1.91394i	0.100594	+	0.100594i
$363$	0.681558	+	6.65750i	0.0357725	+	0.349428i
$364$			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	−0.663784	−	0.747924i	$-0.731051\pi$
$367$	1.61189	−	1.61189i	0.0841399	−	0.0841399i	0.747924	+	0.663784i	$0.231051\pi$
$368$	−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
$372$	−16.0219	+	1.64024i	−0.830699	+	0.0850424i
$373$	13.0455	+	13.0455i	0.675469	+	0.675469i	0.958972	−	0.283502i	$-0.0914964\pi$
$373$	13.0455	+	13.0455i	0.675469	+	0.675469i	−0.283502	+	0.958972i	$0.591496\pi$
$374$	−6.05808			−0.313256
$375$	−3.46439	−	19.0525i	−0.178901	−	0.983867i
$376$	19.9875			1.03078
$377$	6.16727	+	6.16727i	0.317630	+	0.317630i
$378$	0.768413	+	2.43180i	0.0395229	+	0.125078i
$379$			19.0635i			0.979228i	0.871939	+	0.489614i	$0.162862\pi$
$379$			19.0635i			0.979228i	−0.871939	+	0.489614i	$0.837138\pi$
$380$	−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	$-0.528765\pi$
$383$	17.7244	−	17.7244i	0.905673	−	0.905673i	0.995919	+	0.0902463i	$0.0287654\pi$
$384$	−15.1925	−	12.3708i	−0.775291	−	0.631293i
$385$	−1.39579	+	5.80799i	−0.0711360	+	0.296003i
$386$			4.89484i			0.249141i
$387$	−2.69153	−	1.76864i	−0.136818	−	0.0899050i
$388$	3.28738	+	3.28738i	0.166892	+	0.166892i
$389$	18.3513			0.930446			0.465223	−	0.885193i	$-0.345974\pi$
$389$	18.3513			0.930446			0.465223	+	0.885193i	$0.345974\pi$
$390$	−3.50414	−	4.59451i	−0.177439	−	0.232652i
$391$	−16.6506			−0.842056
$392$	−1.30461	−	1.30461i	−0.0658928	−	0.0658928i
$393$	17.1319	−	1.75387i	0.864189	−	0.0884710i
$394$		−	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	−0.925769	−	0.378090i	$-0.876581\pi$
$397$	−10.9124	+	10.9124i	−0.547679	+	0.547679i	0.378090	+	0.925769i	$0.376581\pi$
$398$	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	$-0.329246\pi$
$402$	−0.662578	−	6.47210i	−0.0330464	−	0.322799i
$403$	−11.3619	−	11.3619i	−0.565979	−	0.565979i
$404$	6.61627			0.329172
$405$	16.4585	+	11.5810i	0.817827	+	0.575464i
$406$	−1.40824			−0.0698900
$407$	5.72437	+	5.72437i	0.283746	+	0.283746i
$408$	−1.50375	−	14.6887i	−0.0744465	−	0.727198i
$409$			7.59254i			0.375427i	0.982224	+	0.187714i	$0.0601077\pi$
$409$			7.59254i			0.375427i	−0.982224	+	0.187714i	$0.939892\pi$
$410$	−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
$417$	−28.9356	+	2.96227i	−1.41698	+	0.145063i
$418$	−4.86109	−	4.86109i	−0.237764	−	0.237764i
$419$	6.20644			0.303204			0.151602	−	0.988442i	$-0.451557\pi$
$419$	6.20644			0.303204			0.151602	+	0.988442i	$0.451557\pi$
$420$	−6.75207	−	0.909066i	−0.329467	−	0.0443579i
$421$	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
$423$	−27.1608	−	17.8478i	−1.32061	−	0.867788i
$424$			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	$0.934904\pi$
$432$	4.09043	+	12.9450i	0.196801	+	0.622815i
$433$	−18.8277	−	18.8277i	−0.904802	−	0.904802i	0.0910444	−	0.995847i	$-0.470979\pi$
$433$	−18.8277	−	18.8277i	−0.904802	−	0.904802i	−0.995847	+	0.0910444i	$0.970979\pi$
$434$	2.59440			0.124535
$435$	−8.83593	+	6.73900i	−0.423651	+	0.323110i
$436$	−33.4483			−1.60188
$437$	−13.3607	−	13.3607i	−0.639128	−	0.639128i
$438$	−4.98108	+	0.509935i	−0.238005	+	0.0243657i
$439$			4.88270i			0.233039i	0.993188	+	0.116519i	$0.0371737\pi$
$439$			4.88270i			0.233039i	−0.993188	+	0.116519i	$0.962826\pi$
$440$	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	−0.146059	+	0.989276i	$0.546659\pi$
$443$	−23.8960	+	23.8960i	−1.13534	+	1.13534i	−0.989276	+	0.146059i	$0.953341\pi$
$444$	−5.83013	+	7.15998i	−0.276686	+	0.339798i
$445$	−4.61468	−	7.53437i	−0.218757	−	0.357163i
$446$		−	2.31700i		−	0.109713i
$447$	1.64270	+	16.0460i	0.0776970	+	0.758948i
$448$	−1.96922	−	1.96922i	−0.0930368	−	0.0930368i
$449$	23.6736			1.11723			0.558613	−	0.829428i	$-0.311334\pi$
$449$	23.6736			1.11723			0.558613	+	0.829428i	$0.311334\pi$
$450$	6.39725	−	3.64363i	0.301569	−	0.171762i
$451$	30.9259			1.45625
$452$	−10.0116	−	10.0116i	−0.470908	−	0.470908i
$453$	3.59615	+	35.1274i	0.168962	+	1.65043i
$454$			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	−0.425234	−	0.905083i	$-0.639808\pi$
$457$	10.2580	−	10.2580i	0.479849	−	0.479849i	0.905083	+	0.425234i	$0.139808\pi$
$458$	−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	$-0.182693\pi$
$462$	−2.25913	+	0.231278i	−0.105104	+	0.0107600i
$463$	−17.0563	−	17.0563i	−0.792672	−	0.792672i	0.189256	−	0.981928i	$-0.439392\pi$
$463$	−17.0563	−	17.0563i	−0.792672	−	0.792672i	−0.981928	+	0.189256i	$0.939392\pi$
$464$	−7.49639			−0.348011
$465$	16.2784	−	12.4152i	0.754893	−	0.575743i
$466$	0.827796			0.0383469
$467$	8.00621	+	8.00621i	0.370483	+	0.370483i	0.867653	−	0.497170i	$-0.165627\pi$
$467$	8.00621	+	8.00621i	0.370483	+	0.370483i	−0.497170	+	0.867653i	$0.665627\pi$
$468$	−8.80957	+	13.4065i	−0.407223	+	0.619714i
$469$		−	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
$477$	10.3349	−	15.7277i	0.473201	−	0.720121i
$478$	1.78845	+	1.78845i	0.0818019	+	0.0818019i
$479$	20.1199			0.919304			0.459652	−	0.888099i	$-0.347974\pi$
$479$	20.1199			0.919304			0.459652	+	0.888099i	$0.347974\pi$
$480$	19.0855	+	2.56958i	0.871131	+	0.117285i
$481$	−9.21192			−0.420027
$482$	−5.17713	−	5.17713i	−0.235812	−	0.235812i
$483$	−6.20921	+	0.635665i	−0.282529	+	0.0289238i
$484$		−	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	−0.508522	−	0.861049i	$-0.669808\pi$
$487$	7.77959	−	7.77959i	0.352527	−	0.352527i	0.861049	+	0.508522i	$0.169808\pi$
$488$	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	$0.983505\pi$
$492$	3.59228	+	35.0896i	0.161952	+	1.58196i
$493$	−9.37435	−	9.37435i	−0.422199	−	0.422199i
$494$	7.82270			0.351960
$495$	−13.0680	+	12.2620i	−0.587364	+	0.551135i
$496$	13.8106			0.620113
$497$	9.60816	+	9.60816i	0.430985	+	0.430985i
$498$	−0.494377	−	4.82910i	−0.0221536	−	0.216397i
$499$			12.3264i			0.551806i	0.961185	+	0.275903i	$0.0889769\pi$
$499$			12.3264i			0.551806i	−0.961185	+	0.275903i	$0.911023\pi$
$500$	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	$-0.796584\pi$
$503$	−4.62523	+	4.62523i	−0.206229	+	0.206229i	0.596434	+	0.802662i	$0.296584\pi$
$504$	−1.12153	−	5.42018i	−0.0499570	−	0.241434i
$505$	−7.17188	+	4.39266i	−0.319144	+	0.195471i
$506$		−	4.72482i		−	0.210044i
$507$	6.47826	−	0.663208i	0.287709	−	0.0294541i
$508$	21.3496	+	21.3496i	0.947234	+	0.947234i
$509$	−13.6161			−0.603525			−0.301762	−	0.953383i	$-0.597575\pi$
$509$	−13.6161			−0.603525			−0.301762	+	0.953383i	$0.597575\pi$
$510$	5.32635	+	6.98372i	0.235855	+	0.309244i
$511$	−5.89000			−0.260558
$512$	16.0031	+	16.0031i	0.707245	+	0.707245i
$513$	−25.9788	+	8.20894i	−1.14699	+	0.362433i
$514$		−	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	$0.868046\pi$
$522$	−3.53068	−	2.32006i	−0.154534	−	0.101546i
$523$	−8.91043	−	8.91043i	−0.389626	−	0.389626i	0.484928	−	0.874554i	$-0.338846\pi$
$523$	−8.91043	−	8.91043i	−0.389626	−	0.389626i	−0.874554	+	0.484928i	$0.838846\pi$
$524$	−17.4905			−0.764074
$525$	7.92263	−	3.49742i	0.345772	−	0.152640i
$526$	−0.0433754			−0.00189126
$527$	17.2703	+	17.2703i	0.752308	+	0.752308i
$528$	−12.0258	+	1.23114i	−0.523358	+	0.0535785i
$529$			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
$537$	−1.48945	−	14.5491i	−0.0642746	−	0.627838i
$538$	−10.2971	−	10.2971i	−0.443938	−	0.443938i
$539$	−2.67137			−0.115064
$540$	−15.4308	−	13.4031i	−0.664035	−	0.576777i
$541$	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
$543$	0.972793	+	9.50229i	0.0417465	+	0.407783i
$544$			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	−0.931482	−	0.363787i	$-0.881483\pi$
$547$	−13.2773	+	13.2773i	−0.567695	+	0.567695i	0.363787	+	0.931482i	$0.381483\pi$
$548$	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
$552$	11.4560	−	1.17280i	0.487600	−	0.0499178i
$553$	2.75566	+	2.75566i	0.117183	+	0.117183i
$554$	2.92314			0.124192
$555$	1.56607	−	11.6320i	0.0664761	−	0.493750i
$556$	29.5412			1.25283
$557$	10.4002	+	10.4002i	0.440672	+	0.440672i	0.892238	−	0.451566i	$-0.149134\pi$
$557$	10.4002	+	10.4002i	0.440672	+	0.440672i	−0.451566	+	0.892238i	$0.649134\pi$
$558$	6.50456	+	4.27424i	0.275360	+	0.180943i
$559$			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	$-0.847937\pi$
$563$	−10.1623	+	10.1623i	−0.428291	+	0.428291i	0.459755	+	0.888046i	$0.347937\pi$
$564$	25.5957	+	20.8417i	1.07777	+	0.877592i
$565$	17.4993	+	4.20546i	0.736200	+	0.176925i
$566$			6.66273i			0.280055i
$567$	−3.31589	+	8.36689i	−0.139254	+	0.351376i
$568$	−17.7271	−	17.7271i	−0.743811	−	0.743811i
$569$	−39.8275			−1.66965			−0.834827	−	0.550512i	$-0.814433\pi$
$569$	−39.8275			−1.66965			−0.834827	+	0.550512i	$0.814433\pi$
$570$	−1.32990	+	9.87780i	−0.0557033	+	0.413735i
$571$	−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
$573$	0.964086	−	0.0986978i	0.0402753	−	0.00412316i
$574$		−	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	−0.173202	+	0.984886i	$0.555411\pi$
$577$	−27.8182	+	27.8182i	−1.15809	+	1.15809i	−0.984886	+	0.173202i	$0.944589\pi$
$578$	−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
$582$	−0.228809	−	2.23502i	−0.00948443	−	0.0926445i
$583$	11.8496	+	11.8496i	0.490759	+	0.490759i
$584$	10.8670			0.449681
$585$	0.648568	−	20.3811i	0.0268150	−	0.842655i
$586$	2.47352			0.102180
$587$	−27.2778	−	27.2778i	−1.12588	−	1.12588i	−0.990841	−	0.135034i	$-0.956886\pi$
$587$	−27.2778	−	27.2778i	−1.12588	−	1.12588i	−0.135034	−	0.990841i	$-0.543114\pi$
$588$	−0.310299	−	3.03102i	−0.0127965	−	0.124997i
$589$			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	$-0.738814\pi$
$593$	1.21000	−	1.21000i	0.0496886	−	0.0496886i	0.731515	+	0.681826i	$0.238814\pi$
$594$	−6.04501	−	3.14204i	−0.248030	−	0.128919i
$595$	5.39631	+	8.81052i	0.221227	+	0.361196i
$596$		−	16.3818i		−	0.671025i
$597$	20.1162	−	2.05939i	0.823301	−	0.0842850i
$598$	3.80170	+	3.80170i	0.155463	+	0.155463i
$599$	15.6005			0.637421			0.318710	−	0.947852i	$-0.396750\pi$
$599$	15.6005			0.637421			0.318710	+	0.947852i	$0.396750\pi$
$600$	−14.6172	+	6.45274i	−0.596747	+	0.263432i
$601$	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
$603$	12.6083	−	19.1875i	0.513452	−	0.781374i
$604$		−	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	−0.0955365	+	0.995426i	$0.530457\pi$
$607$	−26.8784	+	26.8784i	−1.09096	+	1.09096i	−0.995426	+	0.0955365i	$0.969543\pi$
$608$	−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
$612$	13.3907	−	20.3780i	0.541287	−	0.823733i
$613$	2.77744	+	2.77744i	0.112180	+	0.112180i	0.760969	−	0.648789i	$-0.224724\pi$
$613$	2.77744	+	2.77744i	0.112180	+	0.112180i	−0.648789	+	0.760969i	$0.724724\pi$
$614$	7.27046			0.293412
$615$	−27.1906	−	35.6513i	−1.09643	−	1.43760i
$616$	4.92867			0.198582
$617$	3.21465	+	3.21465i	0.129417	+	0.129417i	0.768848	−	0.639431i	$-0.220830\pi$
$617$	3.21465	+	3.21465i	0.129417	+	0.129417i	−0.639431	+	0.768848i	$0.720830\pi$
$618$	10.5928	−	1.08443i	0.426104	−	0.0436222i
$619$		−	48.7011i		−	1.95746i	−0.205146	−	0.978731i	$-0.565767\pi$
$619$		−	48.7011i		−	1.95746i	0.205146	−	0.978731i	$-0.434233\pi$
$620$	−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
$627$	−2.47073	−	24.1343i	−0.0986716	−	0.963830i
$628$	−11.1332	−	11.1332i	−0.444261	−	0.444261i
$629$	14.0023			0.558307
$630$	2.25288	+	2.40098i	0.0897569	+	0.0956572i
$631$	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
$633$	−0.137078	−	1.33898i	−0.00544834	−	0.0532197i
$634$		−	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	$0.637691\pi$
$642$	−0.849619	+	0.0869793i	−0.0335318	+	0.00343280i
$643$	−5.91991	−	5.91991i	−0.233458	−	0.233458i	0.580676	−	0.814135i	$-0.302788\pi$
$643$	−5.91991	−	5.91991i	−0.233458	−	0.233458i	−0.814135	+	0.580676i	$0.802788\pi$
$644$	6.33917			0.249798
$645$	−4.12062	−	0.554781i	−0.162249	−	0.0218445i
$646$	−11.8906			−0.467831
$647$	11.1176	+	11.1176i	0.437079	+	0.437079i	0.891028	−	0.453949i	$-0.149985\pi$
$647$	11.1176	+	11.1176i	0.437079	+	0.437079i	−0.453949	+	0.891028i	$0.649985\pi$
$648$	6.11781	−	15.4369i	0.240330	−	0.606419i
$649$			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	0.225088	−	0.974339i	$-0.427733\pi$
$653$	30.6500	−	30.6500i	1.19943	−	1.19943i	0.974339	−	0.225088i	$-0.0722669\pi$
$654$	12.5344	+	10.2063i	0.490135	+	0.399100i
$655$	18.9592	−	11.6122i	0.740798	−	0.453727i
$656$		−	30.2465i		−	1.18093i
$657$	−14.7671	−	9.70367i	−0.576120	−	0.378576i
$658$	−3.75976	−	3.75976i	−0.146571	−	0.146571i
$659$	−50.9397			−1.98433			−0.992165	−	0.124933i	$-0.960129\pi$
$659$	−50.9397			−1.98433			−0.992165	+	0.124933i	$0.960129\pi$
$660$	14.4714	−	11.0371i	0.563300	−	0.429619i
$661$	−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
$663$	24.2007	−	2.47753i	0.939877	−	0.0962194i
$664$			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
$672$	0.877097	+	8.56753i	0.0338347	+	0.330500i
$673$	25.4635	+	25.4635i	0.981544	+	0.981544i	0.999833	−	0.0182887i	$-0.00582181\pi$
$673$	25.4635	+	25.4635i	0.981544	+	0.981544i	−0.0182887	+	0.999833i	$0.505822\pi$
$674$	7.53394			0.290196
$675$	25.6252	+	4.28384i	0.986313	+	0.164885i
$676$	−6.61384			−0.254379
$677$	−8.67613	−	8.67613i	−0.333451	−	0.333451i	0.520445	−	0.853895i	$-0.325766\pi$
$677$	−8.67613	−	8.67613i	−0.333451	−	0.333451i	−0.853895	+	0.520445i	$0.825766\pi$
$678$	0.696831	+	6.80669i	0.0267616	+	0.261409i
$679$		−	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	$-0.525025\pi$
$683$	24.0010	−	24.0010i	0.918373	−	0.918373i	0.996911	+	0.0785378i	$0.0250251\pi$
$684$	27.0965	−	5.60675i	1.03606	−	0.214379i
$685$	−10.0971	+	42.0147i	−0.385789	+	1.60530i
$686$			0.490808i			0.0187391i
$687$	−23.2254	+	2.37769i	−0.886104	+	0.0907145i
$688$	−1.98330	−	1.98330i	−0.0756127	−	0.0756127i
$689$	−19.0689			−0.726467
$690$	−5.44675	+	4.15413i	−0.207354	+	0.158145i
$691$	−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
$693$	−6.69752	−	4.40103i	−0.254418	−	0.167181i
$694$		−	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	$-0.0146340\pi$
$702$	7.39211	−	2.33580i	0.278997	−	0.0881592i
$703$	11.2356	+	11.2356i	0.423760	+	0.423760i
$704$	7.43948			0.280386
$705$	−41.5822	−	5.59843i	−1.56608	−	0.210849i
$706$	6.30965			0.237467
$707$	−2.65954	−	2.65954i	−0.100022	−	0.100022i
$708$	−0.483257	+	0.0494732i	−0.0181619	+	0.00185932i
$709$		−	12.3477i		−	0.463728i	−0.972748	−	0.231864i	$-0.925518\pi$
$709$		−	12.3477i		−	0.463728i	0.972748	−	0.231864i	$-0.0744825\pi$
$710$	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
$717$	0.909011	+	8.87927i	0.0339476	+	0.331603i
$718$	8.76797	+	8.76797i	0.327218	+	0.327218i
$719$	−24.2165			−0.903125			−0.451562	−	0.892240i	$-0.649133\pi$
$719$	−24.2165			−0.903125			−0.451562	+	0.892240i	$0.649133\pi$
$720$	11.9926	+	12.7809i	0.446936	+	0.476316i
$721$	12.5257			0.466482
$722$	−2.94721	−	2.94721i	−0.109684	−	0.109684i
$723$	−2.63137	−	25.7033i	−0.0978616	−	0.955917i
$724$		−	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	−0.999241	−	0.0389483i	$-0.987599\pi$
$727$	−25.8923	+	25.8923i	−0.960293	+	0.960293i	0.0389483	+	0.999241i	$0.487599\pi$
$728$	−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
$732$	14.3226	−	1.46627i	0.529379	−	0.0541949i
$733$	13.4535	+	13.4535i	0.496918	+	0.496918i	0.910477	−	0.413559i	$-0.135715\pi$
$733$	13.4535	+	13.4535i	0.496918	+	0.496918i	−0.413559	+	0.910477i	$0.635715\pi$
$734$	1.11882			0.0412965
$735$	2.34871	+	3.07954i	0.0866334	+	0.113591i
$736$	−17.9184			−0.660481
$737$	14.4563	+	14.4563i	0.532503	+	0.532503i
$738$	9.36099	−	14.2456i	0.344583	−	0.524388i
$739$		−	1.96813i		−	0.0723987i	−0.999345	−	0.0361994i	$-0.988475\pi$
$739$		−	1.96813i		−	0.0723987i	0.999345	−	0.0361994i	$-0.0115251\pi$
$740$	−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	$-0.712368\pi$
$743$	4.54680	−	4.54680i	0.166806	−	0.166806i	0.785574	+	0.618768i	$0.212368\pi$
$744$	−13.0989	−	10.6659i	−0.480227	−	0.391032i
$745$	10.8762	+	17.7575i	0.398472	+	0.650584i
$746$			9.05496i			0.331526i
$747$	9.40761	−	14.3166i	0.344206	−	0.523815i
$748$	15.3533	+	15.3533i	0.561371	+	0.561371i
$749$	−1.00465			−0.0367092
$750$	5.40991	−	7.81457i	0.197542	−	0.285348i
$751$	−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
$753$	7.41432	−	0.759037i	0.270193	−	0.0276609i
$754$			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	−0.640446	−	0.768003i	$-0.721250\pi$
$757$	3.50957	−	3.50957i	0.127558	−	0.127558i	0.768003	+	0.640446i	$0.221250\pi$
$758$	−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	$0.837741\pi$
$762$	−1.48598	−	14.5151i	−0.0538312	−	0.525826i
$763$	13.4452	+	13.4452i	0.486749	+	0.486749i
$764$	−0.984264			−0.0356094
$765$	−0.985834	+	30.9796i	−0.0356429	+	1.12007i
$766$	12.3026			0.444512
$767$	−0.342701	−	0.342701i	−0.0123742	−	0.0123742i
$768$	0.00317918	+	0.0310544i	0.000114719	+	0.00112058i
$769$		−	31.3935i		−	1.13208i	−0.824378	−	0.566040i	$-0.808475\pi$
$769$		−	31.3935i		−	1.13208i	0.824378	−	0.566040i	$-0.191525\pi$
$770$	−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	$-0.860633\pi$
$773$	−13.3925	+	13.3925i	−0.481693	+	0.481693i	0.423979	+	0.905672i	$0.360633\pi$
$774$	−0.320291	−	1.54792i	−0.0115126	−	0.0556387i
$775$	12.0098	−	23.5437i	0.431404	−	0.845716i
$776$			4.87606i			0.175040i
$777$	5.22162	−	0.534561i	0.187325	−	0.0191773i
$778$	6.36887	+	6.36887i	0.228335	+	0.228335i
$779$	60.7006			2.17482
$780$	−2.76336	+	20.5248i	−0.0989440	+	0.734905i
$781$	−36.2985			−1.29886
$782$	−5.77865	−	5.77865i	−0.206644	−	0.206644i
$783$	−4.49210	−	14.2162i	−0.160535	−	0.508044i
$784$			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	−0.182243	−	0.983254i	$-0.558336\pi$
$787$	22.4712	−	22.4712i	0.801011	−	0.801011i	0.983254	+	0.182243i	$0.0583358\pi$
$788$	−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
$792$	12.3569	+	8.11990i	0.439084	+	0.288528i
$793$	10.1569	+	10.1569i	0.360681	+	0.360681i
$794$	−7.57440			−0.268805
$795$	3.24181	−	24.0785i	0.114975	−	0.853975i
$796$	−20.5372			−0.727922
$797$	−7.83907	−	7.83907i	−0.277674	−	0.277674i	0.554506	−	0.832180i	$-0.312907\pi$
$797$	−7.83907	−	7.83907i	−0.277674	−	0.277674i	−0.832180	+	0.554506i	$0.812907\pi$
$798$	−4.43417	+	0.453945i	−0.156968	+	0.0160695i
$799$		−	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
$807$	−5.23366	−	51.1227i	−0.184233	−	1.79960i
$808$	4.90684	+	4.90684i	0.172622	+	0.172622i
$809$	6.27026			0.220451			0.110225	−	0.993907i	$-0.464843\pi$
$809$	6.27026			0.220451			0.110225	+	0.993907i	$0.464843\pi$
$810$	1.69274	+	9.73119i	0.0594769	+	0.341919i
$811$	−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
$813$	3.99320	+	39.0058i	0.140048	+	1.36799i
$814$			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	$-0.0949645\pi$
$822$	−16.3425	+	1.67305i	−0.570008	+	0.0583543i
$823$	32.4880	+	32.4880i	1.13246	+	1.13246i	0.989767	+	0.142695i	$0.0455767\pi$
$823$	32.4880	+	32.4880i	1.13246	+	1.13246i	0.142695	+	0.989767i	$0.454423\pi$
$824$	−23.1099			−0.805072
$825$	−8.35897	+	21.5718i	−0.291022	+	0.751034i
$826$	0.0782529			0.00272277
$827$	4.87454	+	4.87454i	0.169504	+	0.169504i	0.786762	−	0.617257i	$-0.211756\pi$
$827$	4.87454	+	4.87454i	0.169504	+	0.169504i	−0.617257	+	0.786762i	$0.711756\pi$
$828$	15.8932	+	10.4437i	0.552329	+	0.362943i
$829$		−	9.82522i		−	0.341244i	−0.985337	−	0.170622i	$-0.945422\pi$
$829$		−	9.82522i		−	0.341244i	0.985337	−	0.170622i	$-0.0545777\pi$
$830$	−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
$837$	8.27579	+	26.1904i	0.286053	+	0.905272i
$838$	2.15397	+	2.15397i	0.0744075	+	0.0744075i
$839$	−13.0314			−0.449893			−0.224947	−	0.974371i	$-0.572221\pi$
$839$	−13.0314			−0.449893			−0.224947	+	0.974371i	$0.572221\pi$
$840$	−4.33337	−	5.68175i	−0.149515	−	0.196039i
$841$	−20.7675			−0.716120
$842$	8.72279	+	8.72279i	0.300607	+	0.300607i
$843$	−37.9231	+	3.88235i	−1.30614	+	0.133715i
$844$			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
$852$	−4.21634	−	41.1855i	−0.144450	−	1.41099i
$853$	−36.7177	−	36.7177i	−1.25719	−	1.25719i	−0.952429	−	0.304761i	$-0.901424\pi$
$853$	−36.7177	−	36.7177i	−1.25719	−	1.25719i	−0.304761	−	0.952429i	$-0.598576\pi$
$854$	−2.31923			−0.0793626
$855$	−25.6496	+	24.0675i	−0.877197	+	0.823090i
$856$	1.85358			0.0633542
$857$	25.5867	+	25.5867i	0.874024	+	0.874024i	0.992908	−	0.118884i	$-0.0379318\pi$
$857$	25.5867	+	25.5867i	0.874024	+	0.874024i	−0.118884	+	0.992908i	$0.537932\pi$
$858$	0.703032	+	6.86725i	0.0240011	+	0.234444i
$859$			15.7133i			0.536132i	0.963401	+	0.268066i	$0.0863845\pi$
$859$			15.7133i			0.536132i	−0.963401	+	0.268066i	$0.913615\pi$
$860$	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	$-0.836161\pi$
$863$	−11.1088	+	11.1088i	−0.378147	+	0.378147i	0.492286	+	0.870433i	$0.336161\pi$
$864$	−11.9159	+	22.9251i	−0.405386	+	0.779927i
$865$	−5.22613	−	1.25595i	−0.177694	−	0.0427037i
$866$		−	13.0685i		−	0.444084i
$867$	−7.49366	+	0.767159i	−0.254498	+	0.0260541i
$868$	−6.57512	−	6.57512i	−0.223174	−	0.223174i
$869$	−10.4106			−0.353155
$870$	−5.40534	−	0.727748i	−0.183258	−	0.0246730i
$871$	−23.2637			−0.788260
$872$	−24.8064	−	24.8064i	−0.840050	−	0.840050i
$873$	4.35405	−	6.62602i	0.147362	−	0.224257i
$874$		−	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	−0.964412	−	0.264405i	$-0.914824\pi$
$877$	−20.7301	+	20.7301i	−0.700006	+	0.700006i	0.264405	+	0.964412i	$0.414824\pi$
$878$	−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	$-0.147160\pi$
$882$	−0.808598	+	1.23053i	−0.0272269	+	0.0414341i
$883$	−26.9720	−	26.9720i	−0.907681	−	0.907681i	0.0884037	−	0.996085i	$-0.471823\pi$
$883$	−26.9720	−	26.9720i	−0.907681	−	0.907681i	−0.996085	+	0.0884037i	$0.971823\pi$
$884$	−24.7072			−0.830993
$885$	0.490993	−	0.374471i	0.0165045	−	0.0125877i
$886$	−16.5864			−0.557231
$887$	1.34997	+	1.34997i	0.0453275	+	0.0453275i	0.729407	−	0.684080i	$-0.239796\pi$
$887$	1.34997	+	1.34997i	0.0453275	+	0.0453275i	−0.684080	+	0.729407i	$0.739796\pi$
$888$	−9.63389	+	0.986265i	−0.323292	+	0.0330969i
$889$		−	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
$897$	1.93228	+	18.8746i	0.0645169	+	0.630205i
$898$	8.21601	+	8.21601i	0.274172	+	0.274172i
$899$	−15.1668			−0.505840
$900$	−25.4470	−	6.97863i	−0.848235	−	0.232621i
$901$	28.9850			0.965631
$902$	10.7330	+	10.7330i	0.357368	+	0.357368i
$903$	−0.189368	−	1.84976i	−0.00630178	−	0.0615561i
$904$		−	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	−0.998920	−	0.0464640i	$-0.985205\pi$
$907$	−28.6846	+	28.6846i	−0.952456	+	0.952456i	0.0464640	+	0.998920i	$0.485205\pi$
$908$	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	$-0.191002\pi$
$912$	−23.6040	+	2.41645i	−0.781607	+	0.0800166i
$913$	10.7864	+	10.7864i	0.356978	+	0.356978i
$914$	7.12016			0.235514
$915$	−14.5519	+	11.0984i	−0.481070	+	0.366903i
$916$	23.7115			0.783450
$917$	7.03062	+	7.03062i	0.232172	+	0.232172i
$918$	−11.2361	+	3.55046i	−0.370848	+	0.117183i
$919$		−	2.19661i		−	0.0724593i	−0.999343	−	0.0362297i	$-0.988465\pi$
$919$		−	2.19661i		−	0.0724593i	0.999343	−	0.0362297i	$-0.0115348\pi$
$920$	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
$927$	31.4038	+	20.6359i	1.03144	+	0.677771i
$928$	−10.0881	−	10.0881i	−0.331159	−	0.331159i
$929$	51.2981			1.68304			0.841518	−	0.540230i	$-0.181663\pi$
$929$	51.2981			1.68304			0.841518	+	0.540230i	$0.181663\pi$
$930$	9.95824	+	1.34073i	0.326543	+	0.0439642i
$931$	−5.24329			−0.171842
$932$	−2.09792	−	2.09792i	−0.0687197	−	0.0687197i
$933$	−35.2094	+	3.60455i	−1.15271	+	0.118008i
$934$			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	−0.385876	−	0.922551i	$-0.626101\pi$
$937$	16.4279	−	16.4279i	0.536675	−	0.536675i	0.922551	+	0.385876i	$0.126101\pi$
$938$	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	$-0.383485\pi$
$942$	0.774891	+	7.56918i	0.0252473	+	0.246617i
$943$	29.4995	+	29.4995i	0.960635	+	0.960635i
$944$	0.416557			0.0135578
$945$	0.815071	+	11.5903i	0.0265143	+	0.377033i
$946$	1.40755			0.0457634
$947$	−35.8300	−	35.8300i	−1.16432	−	1.16432i	−0.983520	−	0.180799i	$-0.942132\pi$
$947$	−35.8300	−	35.8300i	−1.16432	−	1.16432i	−0.180799	−	0.983520i	$-0.557868\pi$
$948$	−1.20927	−	11.8122i	−0.0392752	−	0.383642i
$949$			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	0.162481	−	0.986712i	$-0.448050\pi$
$953$	35.4764	−	35.4764i	1.14919	−	1.14919i	0.986712	−	0.162481i	$-0.0519496\pi$
$954$	9.04510	−	1.87159i	0.292846	−	0.0605950i
$955$	1.06692	−	0.653471i	0.0345247	−	0.0211458i
$956$		−	9.06511i		−	0.293187i
$957$	13.2068	−	1.35204i	0.426914	−	0.0437051i
$958$	6.98270	+	6.98270i	0.225601	+	0.225601i
$959$	−19.3245			−0.624022
$960$	−6.54091	−	8.57620i	−0.211107	−	0.276796i
$961$	−3.05833			−0.0986558
$962$	−3.19703	−	3.19703i	−0.103076	−	0.103076i
$963$	−2.51881	−	1.65515i	−0.0811677	−	0.0533364i
$964$			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	−0.959209	−	0.282698i	$-0.908771\pi$
$967$	−21.0372	+	21.0372i	−0.676511	+	0.676511i	0.282698	+	0.959209i	$0.408771\pi$
$968$	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	$0.877172\pi$
$972$	23.9309	−	13.3890i	0.767585	−	0.429451i
$973$	−11.8747	−	11.8747i	−0.380684	−	0.380684i
$974$	5.39987			0.173023
$975$	−10.6314	−	24.0830i	−0.340476	−	0.771273i
$976$	−12.3458			−0.395179
$977$	−9.03422	−	9.03422i	−0.289030	−	0.289030i	0.547666	−	0.836697i	$-0.315516\pi$
$977$	−9.03422	−	9.03422i	−0.289030	−	0.289030i	−0.836697	+	0.547666i	$0.815516\pi$
$978$	7.72169	−	0.790504i	0.246913	−	0.0252775i
$979$			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	$-0.727484\pi$
$983$	3.13374	−	3.13374i	0.0999509	−	0.0999509i	0.755314	+	0.655363i	$0.227484\pi$
$984$	−23.3594	+	28.6877i	−0.744672	+	0.914532i
$985$	7.50044	−	31.2099i	0.238984	−	0.994432i
$986$		−	6.50680i		−	0.207219i
$987$	−1.91096	−	18.6664i	−0.0608265	−	0.594157i
$988$	−19.8254	−	19.8254i	−0.630731	−	0.630731i
$989$	3.86864			0.123016
$990$	−8.79086	−	0.279743i	−0.279392	−	0.00889082i
$991$	−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
$993$	−0.390649	−	3.81588i	−0.0123969	−	0.121093i
$994$			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	−0.775833	−	0.630938i	$-0.782670\pi$
$997$	−4.57510	+	4.57510i	−0.144895	+	0.144895i	0.630938	+	0.775833i	$0.282670\pi$
$998$	−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.8.8	yes	24
3.2	odd	2	inner	105.2.j.a.8.5	✓	24
5.2	odd	4	inner	105.2.j.a.92.5	yes	24
5.3	odd	4		525.2.j.b.407.8		24
5.4	even	2		525.2.j.b.218.5		24
7.2	even	3		735.2.y.j.263.8		48
7.3	odd	6		735.2.y.g.128.5		48
7.4	even	3		735.2.y.j.128.5		48
7.5	odd	6		735.2.y.g.263.8		48
7.6	odd	2		735.2.j.h.638.8		24
15.2	even	4	inner	105.2.j.a.92.8	yes	24
15.8	even	4		525.2.j.b.407.5		24
15.14	odd	2		525.2.j.b.218.8		24
21.2	odd	6		735.2.y.j.263.5		48
21.5	even	6		735.2.y.g.263.5		48
21.11	odd	6		735.2.y.j.128.8		48
21.17	even	6		735.2.y.g.128.8		48
21.20	even	2		735.2.j.h.638.5		24
35.2	odd	12		735.2.y.j.557.8		48
35.12	even	12		735.2.y.g.557.8		48
35.17	even	12		735.2.y.g.422.5		48
35.27	even	4		735.2.j.h.197.5		24
35.32	odd	12		735.2.y.j.422.5		48
105.2	even	12		735.2.y.j.557.5		48
105.17	odd	12		735.2.y.g.422.8		48
105.32	even	12		735.2.y.j.422.8		48
105.47	odd	12		735.2.y.g.557.5		48
105.62	odd	4		735.2.j.h.197.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.5	✓	24	3.2	odd	2	inner
105.2.j.a.8.8	yes	24	1.1	even	1	trivial
105.2.j.a.92.5	yes	24	5.2	odd	4	inner
105.2.j.a.92.8	yes	24	15.2	even	4	inner
525.2.j.b.218.5		24	5.4	even	2
525.2.j.b.218.8		24	15.14	odd	2
525.2.j.b.407.5		24	15.8	even	4
525.2.j.b.407.8		24	5.3	odd	4
735.2.j.h.197.5		24	35.27	even	4
735.2.j.h.197.8		24	105.62	odd	4
735.2.j.h.638.5		24	21.20	even	2
735.2.j.h.638.8		24	7.6	odd	2
735.2.y.g.128.5		48	7.3	odd	6
735.2.y.g.128.8		48	21.17	even	6
735.2.y.g.263.5		48	21.5	even	6
735.2.y.g.263.8		48	7.5	odd	6
735.2.y.g.422.5		48	35.17	even	12
735.2.y.g.422.8		48	105.17	odd	12
735.2.y.g.557.5		48	105.47	odd	12
735.2.y.g.557.8		48	35.12	even	12
735.2.y.j.128.5		48	7.4	even	3
735.2.y.j.128.8		48	21.11	odd	6
735.2.y.j.263.5		48	21.2	odd	6
735.2.y.j.263.8		48	7.2	even	3
735.2.y.j.422.5		48	35.32	odd	12
735.2.y.j.422.8		48	105.32	even	12
735.2.y.j.557.5		48	105.2	even	12
735.2.y.j.557.8		48	35.2	odd	12

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)

\(f(q)\)	\(=\)	\(q+(0.347054 + 0.347054i) q^{2} +(0.176396 + 1.72305i) q^{3} -1.75911i q^{4} +(1.16790 + 1.90683i) q^{5} +(-0.536770 + 0.659208i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.30461 - 1.30461i) q^{8} +(-2.93777 + 0.607876i) q^{9} +O(q^{10})\)	\(q+(0.347054 + 0.347054i) q^{2} +(0.176396 + 1.72305i) 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} +(3.03102 - 0.310299i) q^{12} +(2.14945 + 2.14945i) q^{13} -0.490808 q^{14} +(-3.07954 + 2.34871i) q^{15} -2.61267 q^{16} +(-3.26719 - 3.26719i) q^{17} +(-1.23053 - 0.808598i) 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} +(-1.56561 - 4.95468i) q^{27} +(1.24388 + 1.24388i) q^{28} +2.86924 q^{29} +(-1.88389 - 0.253638i) q^{30} -5.28599 q^{31} +(-3.51596 - 3.51596i) q^{32} +(4.60289 - 0.471218i) 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} +(-0.0865765 - 0.845684i) q^{42} +(0.759108 + 0.759108i) q^{43} -4.69922 q^{44} +(-4.59015 - 4.89189i) q^{45} +1.76869 q^{46} +(7.66034 + 7.66034i) q^{47} +(-0.460865 - 4.50176i) 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} +(9.03442 - 0.924894i) q^{57} +(0.995779 + 0.995779i) q^{58} -0.159437 q^{59} +(4.13163 + 5.41724i) q^{60} +4.72534 q^{61} +(-1.83452 - 1.83452i) q^{62} +(1.64748 - 2.50715i) 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} +(-3.03961 + 4.62569i) q^{72} +(4.16486 + 4.16486i) q^{73} -1.48737 q^{74} +(-8.07519 - 3.12910i) q^{75} -9.22351 q^{76} +(1.88894 + 1.88894i) q^{77} +(-2.57069 + 0.263173i) 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} +(0.506122 + 4.94383i) q^{87} +(-3.48510 - 3.48510i) q^{88} -3.95125 q^{89} +(0.104719 - 3.29077i) q^{90} -3.03977 q^{91} +(-4.48247 - 4.48247i) q^{92} +(-0.932426 - 9.10800i) 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

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