LMFDB - Embedded newform 315.2.r.b.184.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(184,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("315.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			184.20
Character	$\chi$	$=$	315.184
Dual form			315.2.r.b.214.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.257756i q^{2} +(0.745098 - 1.56359i) q^{3} +1.93356 q^{4} +(-1.95987 - 1.07653i) q^{5} +(-0.403026 - 0.192053i) q^{6} +(-2.46150 + 0.970066i) q^{7} -1.01390i q^{8} +(-1.88966 - 2.33006i) q^{9} +O(q^{10})$	\(q-0.257756i q^{2} +(0.745098 - 1.56359i) q^{3} +1.93356 q^{4} +(-1.95987 - 1.07653i) q^{5} +(-0.403026 - 0.192053i) q^{6} +(-2.46150 + 0.970066i) q^{7} -1.01390i q^{8} +(-1.88966 - 2.33006i) q^{9} +(-0.277481 + 0.505168i) q^{10} +(2.68286 - 4.64685i) q^{11} +(1.44069 - 3.02331i) q^{12} +(-0.977775 - 0.564519i) q^{13} +(0.250040 + 0.634466i) q^{14} +(-3.14355 + 2.26233i) q^{15} +3.60579 q^{16} +(3.53516 - 2.04103i) q^{17} +(-0.600588 + 0.487070i) q^{18} +(-2.85185 + 4.93955i) q^{19} +(-3.78953 - 2.08153i) q^{20} +(-0.317269 + 4.57158i) q^{21} +(-1.19775 - 0.691523i) q^{22} +(0.884981 - 0.510944i) q^{23} +(-1.58533 - 0.755454i) q^{24} +(2.68218 + 4.21970i) q^{25} +(-0.145508 + 0.252027i) q^{26} +(-5.05126 + 1.21853i) q^{27} +(-4.75946 + 1.87568i) q^{28} +(1.94717 + 3.37259i) q^{29} +(0.583128 + 0.810268i) q^{30} +4.67081 q^{31} -2.95721i q^{32} +(-5.26680 - 7.65727i) q^{33} +(-0.526087 - 0.911209i) q^{34} +(5.86852 + 0.748663i) q^{35} +(-3.65377 - 4.50532i) q^{36} +(-0.294141 - 0.169822i) q^{37} +(1.27320 + 0.735081i) q^{38} +(-1.61122 + 1.10822i) q^{39} +(-1.09149 + 1.98711i) q^{40} +(-2.80446 + 4.85747i) q^{41} +(1.17835 + 0.0817779i) q^{42} +(10.0115 - 5.78014i) q^{43} +(5.18748 - 8.98497i) q^{44} +(1.19511 + 6.60089i) q^{45} +(-0.131699 - 0.228109i) q^{46} +5.90341i q^{47} +(2.68667 - 5.63799i) q^{48} +(5.11795 - 4.77563i) q^{49} +(1.08765 - 0.691349i) q^{50} +(-0.557295 - 7.04833i) q^{51} +(-1.89059 - 1.09153i) q^{52} +(-3.75049 + 2.16535i) q^{53} +(0.314083 + 1.30199i) q^{54} +(-10.2605 + 6.21906i) q^{55} +(0.983548 + 2.49571i) q^{56} +(5.59854 + 8.13958i) q^{57} +(0.869305 - 0.501893i) q^{58} -7.12991 q^{59} +(-6.07824 + 4.37435i) q^{60} +0.247835 q^{61} -1.20393i q^{62} +(6.91170 + 3.90236i) q^{63} +6.44933 q^{64} +(1.30859 + 2.15898i) q^{65} +(-1.97371 + 1.35755i) q^{66} +9.95311i q^{67} +(6.83546 - 3.94645i) q^{68} +(-0.139511 - 1.76446i) q^{69} +(0.192972 - 1.51264i) q^{70} -4.81763 q^{71} +(-2.36245 + 1.91592i) q^{72} +(4.12066 - 2.37906i) q^{73} +(-0.0437727 + 0.0758166i) q^{74} +(8.59640 - 1.04976i) q^{75} +(-5.51422 + 9.55092i) q^{76} +(-2.09611 + 14.0408i) q^{77} +(0.285651 + 0.415301i) q^{78} +3.79776 q^{79} +(-7.06687 - 3.88172i) q^{80} +(-1.85840 + 8.80604i) q^{81} +(1.25204 + 0.722866i) q^{82} +(13.7872 - 7.96002i) q^{83} +(-0.613459 + 8.83943i) q^{84} +(-9.12568 + 0.194455i) q^{85} +(-1.48986 - 2.58052i) q^{86} +(6.72419 - 0.531666i) q^{87} +(-4.71144 - 2.72015i) q^{88} +(-4.60534 + 7.97667i) q^{89} +(1.70142 - 0.308046i) q^{90} +(2.95441 + 0.441056i) q^{91} +(1.71117 - 0.987942i) q^{92} +(3.48022 - 7.30326i) q^{93} +1.52164 q^{94} +(10.9068 - 6.61078i) q^{95} +(-4.62388 - 2.20341i) q^{96} +(3.15766 - 1.82307i) q^{97} +(-1.23095 - 1.31918i) q^{98} +(-15.8971 + 2.52972i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	0.257756i		−	0.182261i	−0.995839	−	0.0911305i	$-0.970952\pi$
$2$		−	0.257756i		−	0.182261i	0.995839	−	0.0911305i	$-0.0290480\pi$
$3$	0.745098	−	1.56359i	0.430183	−	0.902742i
$3$	0.745098	−	1.56359i	0.430183	−	0.902742i
$4$	1.93356			0.966781
$5$	−1.95987	−	1.07653i	−0.876481	−	0.481437i
$5$	−1.95987	−	1.07653i	−0.876481	−	0.481437i
$6$	−0.403026	−	0.192053i	−0.164535	−	0.0784055i
$7$	−2.46150	+	0.970066i	−0.930359	+	0.366650i
$7$	−2.46150	+	0.970066i	−0.930359	+	0.366650i
$8$		−	1.01390i		−	0.358467i
$9$	−1.88966	−	2.33006i	−0.629886	−	0.776688i
$10$	−0.277481	+	0.505168i	−0.0877471	+	0.159748i
$11$	2.68286	−	4.64685i	0.808913	−	1.40108i	−0.104705	−	0.994503i	$-0.533390\pi$
$11$	2.68286	−	4.64685i	0.808913	−	1.40108i	0.913617	−	0.406575i	$-0.133277\pi$
$12$	1.44069	−	3.02331i	0.415893	−	0.872754i
$13$	−0.977775	−	0.564519i	−0.271186	−	0.156569i	0.358241	−	0.933629i	$-0.383377\pi$
$13$	−0.977775	−	0.564519i	−0.271186	−	0.156569i	−0.629426	+	0.777060i	$0.716710\pi$
$14$	0.250040	+	0.634466i	0.0668260	+	0.169568i
$15$	−3.14355	+	2.26233i	−0.811660	+	0.584130i
$16$	3.60579			0.901446
$17$	3.53516	−	2.04103i	0.857403	−	0.495022i	−0.00573854	−	0.999984i	$-0.501827\pi$
$17$	3.53516	−	2.04103i	0.857403	−	0.495022i	0.863142	+	0.504961i	$0.168493\pi$
$18$	−0.600588	+	0.487070i	−0.141560	+	0.114804i
$19$	−2.85185	+	4.93955i	−0.654259	+	1.13321i	0.327820	+	0.944740i	$0.393686\pi$
$19$	−2.85185	+	4.93955i	−0.654259	+	1.13321i	−0.982079	+	0.188469i	$0.939647\pi$
$20$	−3.78953	−	2.08153i	−0.847365	−	0.465444i
$21$	−0.317269	+	4.57158i	−0.0692338	+	0.997600i
$22$	−1.19775	−	0.691523i	−0.255362	−	0.147433i
$23$	0.884981	−	0.510944i	0.184531	−	0.106539i	−0.404889	−	0.914366i	$-0.632690\pi$
$23$	0.884981	−	0.510944i	0.184531	−	0.106539i	0.589420	+	0.807827i	$0.299356\pi$
$24$	−1.58533	−	0.755454i	−0.323603	−	0.154206i
$25$	2.68218	+	4.21970i	0.536437	+	0.843940i
$26$	−0.145508	+	0.252027i	−0.0285365	+	0.0494266i
$27$	−5.05126	+	1.21853i	−0.972115	+	0.234506i
$28$	−4.75946	+	1.87568i	−0.899453	+	0.354471i
$29$	1.94717	+	3.37259i	0.361580	+	0.626274i	0.988221	−	0.153034i	$-0.0489043\pi$
$29$	1.94717	+	3.37259i	0.361580	+	0.626274i	−0.626641	+	0.779308i	$0.715571\pi$
$30$	0.583128	+	0.810268i	0.106464	+	0.147934i
$31$	4.67081			0.838903			0.419451	−	0.907778i	$-0.362222\pi$
$31$	4.67081			0.838903			0.419451	+	0.907778i	$0.362222\pi$
$32$		−	2.95721i		−	0.522766i
$33$	−5.26680	−	7.65727i	−0.916831	−	1.33296i
$34$	−0.526087	−	0.911209i	−0.0902232	−	0.156271i
$35$	5.86852	+	0.748663i	0.991961	+	0.126547i
$36$	−3.65377	−	4.50532i	−0.608961	−	0.750887i
$37$	−0.294141	−	0.169822i	−0.0483565	−	0.0279186i	0.475627	−	0.879647i	$-0.342221\pi$
$37$	−0.294141	−	0.169822i	−0.0483565	−	0.0279186i	−0.523983	+	0.851729i	$0.675555\pi$
$38$	1.27320	+	0.735081i	0.206540	+	0.119246i
$39$	−1.61122	+	1.10822i	−0.258001	+	0.177457i
$40$	−1.09149	+	1.98711i	−0.172579	+	0.314190i
$41$	−2.80446	+	4.85747i	−0.437983	+	0.758609i	−0.997534	−	0.0701872i	$-0.977640\pi$
$41$	−2.80446	+	4.85747i	−0.437983	+	0.758609i	0.559551	+	0.828796i	$0.310974\pi$
$42$	1.17835	+	0.0817779i	0.181824	+	0.0126186i
$43$	10.0115	−	5.78014i	1.52674	−	0.881462i	0.527242	−	0.849715i	$-0.323226\pi$
$43$	10.0115	−	5.78014i	1.52674	−	0.881462i	0.999496	−	0.0317471i	$-0.0101071\pi$
$44$	5.18748	−	8.98497i	0.782042	−	1.35454i
$45$	1.19511	+	6.60089i	0.178156	+	0.984002i
$46$	−0.131699	−	0.228109i	−0.0194179	−	0.0336328i
$47$			5.90341i			0.861101i	0.902567	+	0.430550i	$0.141681\pi$
$47$			5.90341i			0.861101i	−0.902567	+	0.430550i	$0.858319\pi$
$48$	2.68667	−	5.63799i	0.387787	−	0.813773i
$49$	5.11795	−	4.77563i	0.731135	−	0.682233i
$50$	1.08765	−	0.691349i	0.153817	−	0.0977715i
$51$	−0.557295	−	7.04833i	−0.0780369	−	0.986964i
$52$	−1.89059	−	1.09153i	−0.262177	−	0.151368i
$53$	−3.75049	+	2.16535i	−0.515169	+	0.297433i	−0.734956	−	0.678115i	$-0.762797\pi$
$53$	−3.75049	+	2.16535i	−0.515169	+	0.297433i	0.219787	+	0.975548i	$0.429464\pi$
$54$	0.314083	+	1.30199i	0.0427413	+	0.177179i
$55$	−10.2605	+	6.21906i	−1.38353	+	0.838577i
$56$	0.983548	+	2.49571i	0.131432	+	0.333503i
$57$	5.59854	+	8.13958i	0.741545	+	1.07811i
$58$	0.869305	−	0.501893i	0.114145	−	0.0659018i
$59$	−7.12991			−0.928235			−0.464117	−	0.885774i	$-0.653628\pi$
$59$	−7.12991			−0.928235			−0.464117	+	0.885774i	$0.653628\pi$
$60$	−6.07824	+	4.37435i	−0.784698	+	0.564726i
$61$	0.247835			0.0317320			0.0158660	−	0.999874i	$-0.494949\pi$
$61$	0.247835			0.0317320			0.0158660	+	0.999874i	$0.494949\pi$
$62$		−	1.20393i		−	0.152899i
$63$	6.91170	+	3.90236i	0.870792	+	0.491651i
$64$	6.44933			0.806167
$65$	1.30859	+	2.15898i	0.162311	+	0.267789i
$66$	−1.97371	+	1.35755i	−0.242946	+	0.167103i
$67$			9.95311i			1.21597i	0.793950	+	0.607983i	$0.208021\pi$
$67$			9.95311i			1.21597i	−0.793950	+	0.607983i	$0.791979\pi$
$68$	6.83546	−	3.94645i	0.828921	−	0.478578i
$69$	−0.139511	−	1.76446i	−0.0167952	−	0.212415i
$70$	0.192972	−	1.51264i	0.0230646	−	0.180796i
$71$	−4.81763			−0.571748			−0.285874	−	0.958267i	$-0.592284\pi$
$71$	−4.81763			−0.571748			−0.285874	+	0.958267i	$0.592284\pi$
$72$	−2.36245	+	1.91592i	−0.278417	+	0.225793i
$73$	4.12066	−	2.37906i	0.482287	−	0.278448i	−0.239082	−	0.970999i	$-0.576847\pi$
$73$	4.12066	−	2.37906i	0.482287	−	0.278448i	0.721369	+	0.692551i	$0.243513\pi$
$74$	−0.0437727	+	0.0758166i	−0.00508848	+	0.00881350i
$75$	8.59640	−	1.04976i	0.992626	−	0.121215i
$76$	−5.51422	+	9.55092i	−0.632525	+	1.09557i
$77$	−2.09611	+	14.0408i	−0.238873	+	1.60009i
$78$	0.285651	+	0.415301i	0.0323436	+	0.0470235i
$79$	3.79776			0.427281			0.213641	−	0.976912i	$-0.431468\pi$
$79$	3.79776			0.427281			0.213641	+	0.976912i	$0.431468\pi$
$80$	−7.06687	−	3.88172i	−0.790100	−	0.433990i
$81$	−1.85840	+	8.80604i	−0.206488	+	0.978449i
$82$	1.25204	+	0.722866i	0.138265	+	0.0798272i
$83$	13.7872	−	7.96002i	1.51334	−	0.873725i	0.513458	−	0.858115i	$-0.328364\pi$
$83$	13.7872	−	7.96002i	1.51334	−	0.873725i	0.999878	−	0.0156106i	$-0.00496922\pi$
$84$	−0.613459	+	8.83943i	−0.0669339	+	0.964461i
$85$	−9.12568	+	0.194455i	−0.989819	+	0.0210916i
$86$	−1.48986	−	2.58052i	−0.160656	−	0.278265i
$87$	6.72419	−	0.531666i	0.720909	−	0.0570006i
$88$	−4.71144	−	2.72015i	−0.502241	−	0.289969i
$89$	−4.60534	+	7.97667i	−0.488165	+	0.845526i	−0.999907	−	0.0136129i	$-0.995667\pi$
$89$	−4.60534	+	7.97667i	−0.488165	+	0.845526i	0.511743	+	0.859139i	$0.329000\pi$
$90$	1.70142	−	0.308046i	0.179345	−	0.0324709i
$91$	2.95441	+	0.441056i	0.309706	+	0.0462352i
$92$	1.71117	−	0.987942i	0.178401	−	0.103000i
$93$	3.48022	−	7.30326i	0.360882	−	0.757313i
$94$	1.52164			0.156945
$95$	10.9068	−	6.61078i	1.11901	−	0.678252i
$96$	−4.62388	−	2.20341i	−0.471922	−	0.224885i
$97$	3.15766	−	1.82307i	0.320611	−	0.185105i	−0.331054	−	0.943612i	$-0.607404\pi$
$97$	3.15766	−	1.82307i	0.320611	−	0.185105i	0.651665	+	0.758507i	$0.274071\pi$
$98$	−1.23095	−	1.31918i	−0.124344	−	0.133257i
$99$	−15.8971	+	2.52972i	−1.59772	+	0.254246i
$100$	5.18617	+	8.15906i	0.518617	+	0.815906i
$101$	4.20869	−	7.28967i	0.418780	−	0.725349i	−0.577037	−	0.816718i	$-0.695791\pi$
$101$	4.20869	−	7.28967i	0.418780	−	0.725349i	0.995817	+	0.0913693i	$0.0291244\pi$
$102$	−1.81675	+	0.143646i	−0.179885	+	0.0142231i
$103$	−9.32209	+	5.38211i	−0.918533	+	0.530315i	−0.883167	−	0.469059i	$-0.844593\pi$
$103$	−9.32209	+	5.38211i	−0.918533	+	0.530315i	−0.0353661	+	0.999374i	$0.511260\pi$
$104$	−0.572365	+	0.991365i	−0.0561250	+	0.0972113i
$105$	5.54323	−	8.61816i	0.540964	−	0.841046i
$106$	0.558130	+	0.966710i	0.0542104	+	0.0938952i
$107$	5.21609	+	3.01151i	0.504258	+	0.291134i	0.730470	−	0.682944i	$-0.239301\pi$
$107$	5.21609	+	3.01151i	0.504258	+	0.291134i	−0.226212	+	0.974078i	$0.572634\pi$
$108$	−9.76692	+	2.35610i	−0.939822	+	0.226716i
$109$	3.49133	+	6.04717i	0.334409	+	0.579214i	0.983371	−	0.181607i	$-0.0581300\pi$
$109$	3.49133	+	6.04717i	0.334409	+	0.579214i	−0.648962	+	0.760821i	$0.724797\pi$
$110$	1.60300	+	2.64471i	0.152840	+	0.252163i
$111$	−0.484698	+	0.333383i	−0.0460055	+	0.0316433i
$112$	−8.87563	+	3.49785i	−0.838669	+	0.330516i
$113$	−13.5334	−	7.81354i	−1.27312	−	0.735036i	−0.297546	−	0.954708i	$-0.596168\pi$
$113$	−13.5334	−	7.81354i	−1.27312	−	0.735036i	−0.975574	+	0.219671i	$0.929501\pi$
$114$	2.09803	−	1.44306i	0.196498	−	0.135155i
$115$	−2.28449	+	0.0486792i	−0.213030	+	0.00453936i
$116$	3.76496	+	6.52111i	0.349568	+	0.605470i
$117$	0.532294	+	3.34502i	0.0492106	+	0.309248i
$118$			1.83778i			0.169181i
$119$	−6.72187	+	8.45333i	−0.616193	+	0.774915i
$120$	2.29377	+	3.18724i	0.209391	+	0.290954i
$121$	−8.89548	−	15.4074i	−0.808680	−	1.40067i
$122$		−	0.0638810i		−	0.00578351i
$123$	5.50551	+	8.00433i	0.496415	+	0.721726i
$124$	9.03131			0.811035
$125$	−0.714116	−	11.1575i	−0.0638724	−	0.997958i
$126$	1.00586	−	1.78153i	0.0896087	−	0.158711i
$127$			11.3213i			1.00460i	0.864692	+	0.502302i	$0.167513\pi$
$127$			11.3213i			1.00460i	−0.864692	+	0.502302i	$0.832487\pi$
$128$		−	7.57677i		−	0.669698i
$129$	−1.57824	−	19.9607i	−0.138957	−	1.75744i
$130$	0.556491	−	0.337298i	0.0488075	−	0.0295830i
$131$	−0.314761	−	0.545182i	−0.0275008	−	0.0476328i	0.851947	−	0.523627i	$-0.175422\pi$
$131$	−0.314761	−	0.545182i	−0.0275008	−	0.0476328i	−0.879448	+	0.475995i	$0.842088\pi$
$132$	−10.1837	−	14.8058i	−0.886375	−	1.28868i
$133$	2.22813	−	14.9252i	0.193204	−	1.29418i
$134$	2.56547			0.221623
$135$	11.2116	+	3.04965i	0.964940	+	0.262472i
$136$	−2.06940	−	3.58430i	−0.177449	−	0.307351i
$137$	−16.1810	−	9.34210i	−1.38244	−	0.798150i	−0.389988	−	0.920820i	$-0.627521\pi$
$137$	−16.1810	−	9.34210i	−1.38244	−	0.798150i	−0.992448	+	0.122670i	$0.960854\pi$
$138$	−0.454799	+	0.0359599i	−0.0387150	+	0.00306111i
$139$	9.02774	−	15.6365i	0.765723	−	1.32627i	−0.174141	−	0.984721i	$-0.555715\pi$
$139$	9.02774	−	15.6365i	0.765723	−	1.32627i	0.939864	−	0.341550i	$-0.110952\pi$
$140$	11.3471	+	1.44759i	0.959009	+	0.122343i
$141$	9.23054	+	4.39862i	0.777352	+	0.370431i
$142$			1.24177i			0.104207i
$143$	−5.24647	+	3.02905i	−0.438732	+	0.253302i
$144$	−6.81370	−	8.40171i	−0.567808	−	0.700143i
$145$	−0.185512	−	8.70601i	−0.0154060	−	0.722995i
$146$	−0.613218	−	1.06212i	−0.0507502	−	0.0879020i
$147$	−3.65378	−	11.5607i	−0.301358	−	0.953511i
$148$	−0.568740	−	0.328362i	−0.0467501	−	0.0269912i
$149$	3.75859	+	6.51007i	0.307916	+	0.533326i	0.977906	−	0.209044i	$-0.0670351\pi$
$149$	3.75859	+	6.51007i	0.307916	+	0.533326i	−0.669990	+	0.742370i	$0.733702\pi$
$150$	−0.270581	−	2.21577i	−0.0220928	−	0.180917i
$151$	−8.62712	+	14.9426i	−0.702065	+	1.21601i	0.265676	+	0.964062i	$0.414405\pi$
$151$	−8.62712	+	14.9426i	−0.702065	+	1.21601i	−0.967740	+	0.251949i	$0.918928\pi$
$152$	5.00820	+	2.89148i	0.406219	+	0.234530i
$153$	−11.4360	−	4.38032i	−0.924544	−	0.354128i
$154$	3.61909	+	0.540284i	0.291635	+	0.0435373i
$155$	−9.15419	−	5.02825i	−0.735282	−	0.403879i
$156$	−3.11539	+	2.14282i	−0.249431	+	0.171563i
$157$		−	12.2141i		−	0.974795i	−0.873180	−	0.487398i	$-0.837946\pi$
$157$		−	12.2141i		−	0.974795i	0.873180	−	0.487398i	$-0.162054\pi$
$158$		−	0.978894i		−	0.0778767i
$159$	0.591240	+	7.47764i	0.0468883	+	0.593015i
$160$	−3.18351	+	5.79575i	−0.251679	+	0.458194i
$161$	−1.68273	+	2.11618i	−0.132618	+	0.166778i
$162$	2.26981	+	0.479012i	0.178333	+	0.0376348i
$163$	15.1590	+	8.75206i	1.18735	+	0.685514i	0.957702	−	0.287761i	$-0.0929109\pi$
$163$	15.1590	+	8.75206i	1.18735	+	0.685514i	0.229643	+	0.973275i	$0.426244\pi$
$164$	−5.42260	+	9.39221i	−0.423434	+	0.733409i
$165$	2.07899	+	20.6771i	0.161849	+	1.60971i
$166$	−2.05174	−	3.55372i	−0.159246	−	0.275822i
$167$	2.79354	+	1.61285i	0.216171	+	0.124806i	0.604176	−	0.796851i	$-0.293502\pi$
$167$	2.79354	+	1.61285i	0.216171	+	0.124806i	−0.388005	+	0.921657i	$0.626836\pi$
$168$	4.63512	+	0.321679i	0.357607	+	0.0248180i
$169$	−5.86264	−	10.1544i	−0.450972	−	0.781107i
$170$	0.0501219	+	2.35220i	0.00384418	+	0.180405i
$171$	16.8985	−	2.68906i	1.29226	−	0.205637i
$172$	19.3578	−	11.1762i	1.47602	−	0.852181i
$173$			11.4463i			0.870249i	0.900370	+	0.435125i	$0.143296\pi$
$173$			11.4463i			0.870249i	−0.900370	+	0.435125i	$0.856704\pi$
$174$	−0.137040	−	1.73320i	−0.0103890	−	0.131394i
$175$	−10.6956	−	7.78489i	−0.808510	−	0.588483i
$176$	9.67382	−	16.7555i	0.729192	−	1.26300i
$177$	−5.31248	+	11.1483i	−0.399311	+	0.837956i
$178$	2.05603	+	1.18705i	0.154106	+	0.0889733i
$179$	1.96106	+	3.39665i	0.146576	+	0.253878i	0.929960	−	0.367661i	$-0.119841\pi$
$179$	1.96106	+	3.39665i	0.146576	+	0.253878i	−0.783384	+	0.621538i	$0.786508\pi$
$180$	2.31082	+	12.7632i	0.172238	+	0.951315i
$181$	−25.0287			−1.86037			−0.930185	−	0.367092i	$-0.880354\pi$
$181$	−25.0287			−1.86037			−0.930185	+	0.367092i	$0.880354\pi$
$182$	0.113685	−	0.761517i	0.00842687	−	0.0564474i
$183$	0.184662	−	0.387514i	0.0136506	−	0.0286458i
$184$	−0.518045	−	0.897281i	−0.0381908	−	0.0661484i
$185$	0.393660	+	0.649481i	0.0289425	+	0.0477508i
$186$	−1.88246	−	0.897046i	−0.138028	−	0.0657746i
$187$		−	21.9032i		−	1.60172i
$188$			11.4146i			0.832496i
$189$	11.2516	−	7.89946i	0.818434	−	0.574601i
$190$	−1.70397	−	2.81129i	−0.123619	−	0.203953i
$191$	−5.14437			−0.372233			−0.186117	−	0.982528i	$-0.559590\pi$
$191$	−5.14437			−0.372233			−0.186117	+	0.982528i	$0.559590\pi$
$192$	4.80539	−	10.0841i	0.346799	−	0.727760i
$193$		−	12.1686i		−	0.875918i	−0.898995	−	0.437959i	$-0.855701\pi$
$193$		−	12.1686i		−	0.875918i	0.898995	−	0.437959i	$-0.144299\pi$
$194$	−0.469908	−	0.813904i	−0.0337374	−	0.0584349i
$195$	4.35081	−	0.437454i	0.311568	−	0.0313268i
$196$	9.89586	−	9.23397i	0.706847	−	0.659570i
$197$			2.36581i			0.168557i	0.996442	+	0.0842787i	$0.0268586\pi$
$197$			2.36581i			0.168557i	−0.996442	+	0.0842787i	$0.973141\pi$
$198$	0.652049	+	4.09758i	0.0463391	+	0.291202i
$199$	0.135602	+	0.234869i	0.00961255	+	0.0166494i	0.870792	−	0.491652i	$-0.163607\pi$
$199$	0.135602	+	0.234869i	0.00961255	+	0.0166494i	−0.861179	+	0.508302i	$0.830274\pi$
$200$	4.27835	−	2.71946i	0.302525	−	0.192295i
$201$	15.5626	+	7.41605i	1.09770	+	0.523088i
$202$	−1.87895	−	1.08481i	−0.132203	−	0.0763273i
$203$	−8.06458	−	6.41274i	−0.566022	−	0.450086i
$204$	−1.07756	−	13.6284i	−0.0754446	−	0.954178i
$205$	10.7256	−	6.50093i	0.749106	−	0.454045i
$206$	1.38727	+	2.40282i	0.0966557	+	0.167413i
$207$	−2.86284	−	1.09655i	−0.198981	−	0.0762157i
$208$	−3.52565	−	2.03553i	−0.244460	−	0.141139i
$209$	15.3022	+	26.5042i	1.05848	+	1.83334i
$210$	−2.22138	−	1.42880i	−0.153290	−	0.0985966i
$211$	−2.51581	+	4.35752i	−0.173196	+	0.299984i	−0.939535	−	0.342452i	$-0.888743\pi$
$211$	−2.51581	+	4.35752i	−0.173196	+	0.299984i	0.766340	+	0.642436i	$0.222076\pi$
$212$	−7.25180	+	4.18683i	−0.498056	+	0.287553i
$213$	−3.58961	+	7.53283i	−0.245956	+	0.516141i
$214$	0.776234	−	1.34448i	0.0530623	−	0.0919066i
$215$	−25.8437	+	0.550691i	−1.76252	+	0.0375568i
$216$	1.23547	+	5.12146i	0.0840628	+	0.348471i
$217$	−11.4972	+	4.53100i	−0.780481	+	0.307584i
$218$	1.55869	−	0.899912i	0.105568	−	0.0609497i
$219$	−0.649594	−	8.21568i	−0.0438955	−	0.555164i
$220$	−19.8393	+	12.0249i	−1.33757	+	0.810721i
$221$	−4.60879			−0.310021
$222$	0.0859314	+	0.124934i	0.00576734	+	0.00838500i
$223$	−12.0345	+	6.94811i	−0.805888	+	0.465280i	−0.845526	−	0.533934i	$-0.820713\pi$
$223$	−12.0345	+	6.94811i	−0.805888	+	0.465280i	0.0396376	+	0.999214i	$0.487380\pi$
$224$	2.86869	+	7.27917i	0.191672	+	0.486360i
$225$	4.76377	−	14.2234i	0.317585	−	0.948230i
$226$	−2.01399	+	3.48833i	−0.133968	+	0.232040i
$227$	−11.6381	−	6.71924i	−0.772446	−	0.445972i	0.0613004	−	0.998119i	$-0.480475\pi$
$227$	−11.6381	−	6.71924i	−0.772446	−	0.445972i	−0.833747	+	0.552147i	$0.813809\pi$
$228$	10.8251	+	15.7384i	0.716911	+	1.04230i
$229$	−9.85209	−	17.0643i	−0.651045	−	1.12764i	−0.982870	−	0.184301i	$-0.940998\pi$
$229$	−9.85209	−	17.0643i	−0.651045	−	1.12764i	0.331825	−	0.943341i	$-0.392336\pi$
$230$	0.0125474	+	0.588841i	0.000827348	+	0.0388271i
$231$	20.3923	+	13.7392i	1.34171	+	0.903974i
$232$	3.41946	−	1.97423i	0.224499	−	0.129614i
$233$	−8.27673	−	4.77857i	−0.542226	−	0.313055i	0.203754	−	0.979022i	$-0.434686\pi$
$233$	−8.27673	−	4.77857i	−0.542226	−	0.313055i	−0.745981	+	0.665968i	$0.768019\pi$
$234$	0.862200	−	0.137202i	0.0563638	−	0.00896917i
$235$	6.35517	−	11.5699i	0.414566	−	0.754738i
$236$	−13.7861			−0.897400
$237$	2.82970	−	5.93815i	0.183809	−	0.385725i
$238$	2.17889	+	1.73260i	0.141237	+	0.112308i
$239$	−14.2555	+	24.6913i	−0.922114	+	1.59715i	−0.125976	+	0.992033i	$0.540206\pi$
$239$	−14.2555	+	24.6913i	−0.922114	+	1.59715i	−0.796138	+	0.605115i	$0.793127\pi$
$240$	−11.3350	+	8.15746i	−0.731668	+	0.526562i
$241$	1.89253	−	3.27796i	0.121909	−	0.211152i	−0.798612	−	0.601847i	$-0.794432\pi$
$241$	1.89253	−	3.27796i	0.121909	−	0.211152i	0.920520	+	0.390695i	$0.127765\pi$
$242$	−3.97135	+	2.29286i	−0.255288	+	0.147391i
$243$	12.3844	+	9.46715i	0.794459	+	0.607318i
$244$	0.479205			0.0306779
$245$	−15.1716	+	3.85001i	−0.969278	+	0.245968i
$246$	2.06316	−	1.41908i	0.131542	−	0.0904771i
$247$	5.57693	−	3.21984i	0.354852	−	0.204874i
$248$		−	4.73573i		−	0.300719i
$249$	−2.17345	−	27.4885i	−0.137737	−	1.74201i
$250$	−2.87591	+	0.184067i	−0.181889	+	0.0116414i
$251$	4.64726			0.293333			0.146666	−	0.989186i	$-0.453146\pi$
$251$	4.64726			0.293333			0.146666	+	0.989186i	$0.453146\pi$
$252$	13.3642	+	7.54545i	0.841866	+	0.475319i
$253$		−	5.48317i		−	0.344724i
$254$	2.91814			0.183100
$255$	−6.49548	+	14.4138i	−0.406763	+	0.902625i
$256$	10.9457			0.684107
$257$	−7.82060	+	4.51523i	−0.487836	+	0.281652i	−0.723676	−	0.690140i	$-0.757549\pi$
$257$	−7.82060	+	4.51523i	−0.487836	+	0.281652i	0.235840	+	0.971792i	$0.424216\pi$
$258$	−5.14498	+	0.406802i	−0.320313	+	0.0253264i
$259$	0.888767	+	0.132681i	0.0552253	+	0.00824442i
$260$	2.53025	+	4.17453i	0.156919	+	0.258893i
$261$	4.17887	−	10.9101i	0.258666	−	0.675315i
$262$	−0.140524	+	0.0811315i	−0.00868159	+	0.00501232i
$263$	0.394218	+	0.227602i	0.0243085	+	0.0140345i	0.512105	−	0.858923i	$-0.328866\pi$
$263$	0.394218	+	0.227602i	0.0243085	+	0.0140345i	−0.487796	+	0.872957i	$0.662199\pi$
$264$	−7.76369	+	5.34000i	−0.477822	+	0.328654i
$265$	9.68152	−	0.206299i	0.594731	−	0.0126729i
$266$	−3.84705	−	0.574315i	−0.235878	−	0.0352135i
$267$	9.04086	+	13.1443i	0.553291	+	0.804417i
$268$			19.2450i			1.17557i
$269$	2.40196	+	4.16032i	0.146450	+	0.253659i	0.929913	−	0.367779i	$-0.119882\pi$
$269$	2.40196	+	4.16032i	0.146450	+	0.253659i	−0.783463	+	0.621439i	$0.786548\pi$
$270$	0.786064	−	2.88985i	0.0478383	−	0.175871i
$271$	2.84594	−	4.92932i	0.172879	−	0.299435i	−0.766546	−	0.642189i	$-0.778026\pi$
$271$	2.84594	−	4.92932i	0.172879	−	0.299435i	0.939425	+	0.342754i	$0.111360\pi$
$272$	12.7470	−	7.35951i	0.772903	−	0.446236i
$273$	2.89096	−	4.29087i	0.174969	−	0.259695i
$274$	−2.40798	+	4.17075i	−0.145472	+	0.251964i
$275$	26.8043	−	1.14284i	1.61636	−	0.0689157i
$276$	−0.269754	−	3.41168i	−0.0162373	−	0.205359i
$277$	17.6842	+	10.2099i	1.06254	+	0.613456i	0.926133	−	0.377197i	$-0.123112\pi$
$277$	17.6842	+	10.2099i	1.06254	+	0.613456i	0.136405	+	0.990653i	$0.456445\pi$
$278$	−4.03040	−	2.32695i	−0.241727	−	0.139561i
$279$	−8.82623	−	10.8833i	−0.528413	−	0.651566i
$280$	0.759069	−	5.95008i	0.0453630	−	0.355585i
$281$	−2.52860	−	4.37967i	−0.150844	−	0.261269i	0.780694	−	0.624913i	$-0.214866\pi$
$281$	−2.52860	−	4.37967i	−0.150844	−	0.261269i	−0.931538	+	0.363644i	$0.881532\pi$
$282$	1.13377	−	2.37923i	0.0675151	−	0.141681i
$283$			7.98703i			0.474780i	0.971414	+	0.237390i	$0.0762919\pi$
$283$			7.98703i			0.474780i	−0.971414	+	0.237390i	$0.923708\pi$
$284$	−9.31519			−0.552755
$285$	−2.20994	−	21.9795i	−0.130906	−	1.30195i
$286$	0.780755	+	1.35231i	0.0461670	+	0.0799636i
$287$	2.19111	−	14.6772i	0.129337	−	0.866365i
$288$	−6.89049	+	5.58811i	−0.406026	+	0.329283i
$289$	−0.168408	+	0.291691i	−0.00990635	+	0.0171583i
$290$	−2.24403	+	0.0478169i	−0.131774	+	0.00280791i
$291$	−0.497783	−	6.29566i	−0.0291806	−	0.369058i
$292$	7.96755	−	4.60007i	0.466266	−	0.269199i
$293$	21.5890	+	12.4644i	1.26124	+	0.728178i	0.973315	−	0.229475i	$-0.0737010\pi$
$293$	21.5890	+	12.4644i	1.26124	+	0.728178i	0.287926	+	0.957653i	$0.407034\pi$
$294$	−2.97984	+	0.941782i	−0.173788	+	0.0549258i
$295$	13.9737	+	7.67553i	0.813580	+	0.446887i
$296$	−0.172183	+	0.298229i	−0.0100079	+	0.0173342i
$297$	−7.88949	+	26.7416i	−0.457794	+	1.55170i
$298$	1.67801	−	0.968799i	0.0972045	−	0.0561210i
$299$	−1.15375			−0.0667231
$300$	16.6217	−	2.02977i	0.959652	−	0.117189i
$301$	−19.0361	+	23.9396i	−1.09723	+	1.37986i
$302$	3.85154	+	2.22369i	0.221631	+	0.127959i
$303$	−8.26219	−	12.0122i	−0.474651	−	0.690083i
$304$	−10.2832	+	17.8109i	−0.589779	+	1.02153i
$305$	−0.485725	−	0.266801i	−0.0278125	−	0.0152770i
$306$	−1.12905	+	2.94769i	−0.0645436	+	0.168508i
$307$			28.9466i			1.65207i	0.563620	+	0.826034i	$0.309408\pi$
$307$			28.9466i			1.65207i	−0.563620	+	0.826034i	$0.690592\pi$
$308$	−4.05295	+	27.1487i	−0.230938	+	1.54694i
$309$	1.46957	+	18.5862i	0.0836007	+	1.05733i
$310$	−1.29606	+	2.35955i	−0.0736113	+	0.134013i
$311$	32.8085			1.86040			0.930199	−	0.367055i	$-0.119634\pi$
$311$	32.8085			1.86040			0.930199	+	0.367055i	$0.119634\pi$
$312$	1.12362	+	1.63361i	0.0636127	+	0.0924850i
$313$			7.02270i			0.396947i	0.980106	+	0.198473i	$0.0635983\pi$
$313$			7.02270i			0.396947i	−0.980106	+	0.198473i	$0.936402\pi$
$314$	−3.14827			−0.177667
$315$	−9.34505	−	15.0887i	−0.526534	−	0.850154i
$316$	7.34320			0.413087
$317$		−	22.0012i		−	1.23571i	−0.786293	−	0.617854i	$-0.788002\pi$
$317$		−	22.0012i		−	1.23571i	0.786293	−	0.617854i	$-0.211998\pi$
$318$	1.92741	−	0.152395i	0.108084	−	0.00854591i
$319$	20.8959			1.16995
$320$	−12.6399	−	6.94287i	−0.706589	−	0.388118i
$321$	8.59528	−	5.91197i	0.479742	−	0.329974i
$322$	0.545457	+	0.433733i	0.0303971	+	0.0241710i
$323$			23.2828i			1.29549i
$324$	−3.59332	+	17.0270i	−0.199629	+	0.945946i
$325$	−0.240472	−	5.64006i	−0.0133390	−	0.312854i
$326$	2.25589	−	3.90732i	0.124942	−	0.216407i
$327$	12.0567	−	0.953296i	0.666737	−	0.0527174i
$328$	4.92498	+	2.84344i	0.271936	+	0.157003i
$329$	−5.72670	−	14.5312i	−0.315723	−	0.801133i
$330$	5.32964	−	0.535872i	0.293387	−	0.0294988i
$331$	−23.9826			−1.31820			−0.659101	−	0.752054i	$-0.729063\pi$
$331$	−23.9826			−1.31820			−0.659101	+	0.752054i	$0.729063\pi$
$332$	26.6583	−	15.3912i	1.46306	−	0.844701i
$333$	0.160129	+	1.00627i	0.00877499	+	0.0551435i
$334$	0.415722	−	0.720052i	0.0227473	−	0.0393995i
$335$	10.7148	−	19.5068i	0.585411	−	1.06577i
$336$	−1.14400	+	16.4841i	−0.0624105	+	0.899283i
$337$	−20.7827	−	11.9989i	−1.13211	−	0.653622i	−0.187643	−	0.982237i	$-0.560085\pi$
$337$	−20.7827	−	11.9989i	−1.13211	−	0.653622i	−0.944464	+	0.328615i	$0.893418\pi$
$338$	−2.61735	+	1.51113i	−0.142365	+	0.0821946i
$339$	−22.3010	+	15.3390i	−1.21122	+	0.833099i
$340$	−17.6451	+	0.375991i	−0.956939	+	0.0203910i
$341$	12.5311	−	21.7046i	0.678599	−	1.17537i
$342$	−0.693120	−	4.35568i	−0.0374796	−	0.235528i
$343$	−7.96514	+	16.7199i	−0.430077	+	0.902792i
$344$	−5.86047	−	10.1506i	−0.315975	−	0.547286i
$345$	−1.62606	+	3.60829i	−0.0875440	+	0.194264i
$346$	2.95036			0.158612
$347$			26.9404i			1.44624i	0.690725	+	0.723118i	$0.257292\pi$
$347$			26.9404i			1.44624i	−0.690725	+	0.723118i	$0.742708\pi$
$348$	13.0016	−	1.02801i	0.696961	−	0.0551071i
$349$	−2.02632	−	3.50969i	−0.108467	−	0.187870i	0.806683	−	0.590985i	$-0.201261\pi$
$349$	−2.02632	−	3.50969i	−0.108467	−	0.187870i	−0.915149	+	0.403115i	$0.867927\pi$
$350$	−2.00660	+	2.75685i	−0.107257	+	0.147360i
$351$	5.62687	+	1.66008i	0.300340	+	0.0886085i
$352$	−13.7417	−	7.93378i	−0.732436	−	0.422872i
$353$	−6.42883	−	3.71169i	−0.342172	−	0.197553i	0.319060	−	0.947735i	$-0.396633\pi$
$353$	−6.42883	−	3.71169i	−0.342172	−	0.197553i	−0.661232	+	0.750181i	$0.729966\pi$
$354$	2.87354	+	1.36932i	0.152727	+	0.0727787i
$355$	9.44194	+	5.18631i	0.501126	+	0.275261i
$356$	−8.90470	+	15.4234i	−0.471948	+	0.817438i
$357$	8.20913	+	16.8088i	0.434473	+	0.889618i
$358$	0.875507	−	0.505474i	0.0462720	−	0.0267151i
$359$	−8.36553	+	14.4895i	−0.441516	+	0.764727i	−0.997802	−	0.0662631i	$-0.978892\pi$
$359$	−8.36553	+	14.4895i	−0.441516	+	0.764727i	0.556287	+	0.830991i	$0.312226\pi$
$360$	6.69263	−	1.21172i	0.352733	−	0.0638632i
$361$	−6.76608	−	11.7192i	−0.356109	−	0.616799i
$362$			6.45130i			0.339073i
$363$	−30.7190	+	2.42888i	−1.61233	+	0.127483i
$364$	5.71254	+	0.852808i	0.299418	+	0.0446993i
$365$	−10.6371	+	0.226661i	−0.556770	+	0.0118640i
$366$	−0.0998839	−	0.0475976i	−0.00522102	−	0.00248797i
$367$	4.18589	+	2.41673i	0.218502	+	0.126152i	0.605256	−	0.796031i	$-0.293071\pi$
$367$	4.18589	+	2.41673i	0.218502	+	0.126152i	−0.386755	+	0.922183i	$0.626404\pi$
$368$	3.19105	−	1.84235i	0.166345	−	0.0960394i
$369$	16.6177	−	2.64437i	0.865082	−	0.137661i
$370$	0.167407	−	0.101468i	0.00870310	−	0.00527508i
$371$	7.13129	−	8.96821i	0.370238	−	0.465606i
$372$	6.72921	−	14.1213i	0.348893	−	0.732155i
$373$	2.76209	−	1.59469i	0.143016	−	0.0825701i	−0.426785	−	0.904353i	$-0.640354\pi$
$373$	2.76209	−	1.59469i	0.143016	−	0.0825701i	0.569800	+	0.821783i	$0.307020\pi$
$374$	−5.64567			−0.291931
$375$	−17.9779	−	7.19686i	−0.928375	−	0.371644i
$376$	5.98546			0.308677
$377$		−	4.39684i		−	0.226449i
$378$	−2.03613	−	2.90017i	−0.104727	−	0.149168i
$379$	36.3293			1.86611			0.933056	−	0.359731i	$-0.117132\pi$
$379$	36.3293			1.86611			0.933056	+	0.359731i	$0.117132\pi$
$380$	21.0890	−	12.7824i	1.08184	−	0.655721i
$381$	17.7019	+	8.43549i	0.906898	+	0.432163i
$382$			1.32599i			0.0678436i
$383$	−13.0688	+	7.54526i	−0.667783	+	0.385545i	−0.795236	−	0.606300i	$-0.792653\pi$
$383$	−13.0688	+	7.54526i	−0.667783	+	0.385545i	0.127453	+	0.991845i	$0.459320\pi$
$384$	−11.8470	−	5.64544i	−0.604565	−	0.288093i
$385$	19.2233	−	25.2616i	0.979712	−	1.28745i
$386$	−3.13654			−0.159646
$387$	−32.3864	−	12.4049i	−1.64629	−	0.630578i
$388$	6.10552	−	3.52503i	0.309961	−	0.178956i
$389$	−1.55112	+	2.68662i	−0.0786450	+	0.136217i	−0.902666	−	0.430343i	$-0.858393\pi$
$389$	−1.55112	+	2.68662i	−0.0786450	+	0.136217i	0.824021	+	0.566560i	$0.191726\pi$
$390$	−0.112756	−	1.12145i	−0.00570964	−	0.0567866i
$391$	2.08570	−	3.61254i	0.105479	−	0.182694i
$392$	−4.84200	−	5.18908i	−0.244558	−	0.262088i
$393$	−1.08697	+	0.0859443i	−0.0548304	+	0.00433532i
$394$	0.609803			0.0307214
$395$	−7.44311	−	4.08838i	−0.374504	−	0.205709i
$396$	−30.7381	+	4.89136i	−1.54465	+	0.245800i
$397$	−22.3062	−	12.8785i	−1.11952	−	0.646352i	−0.178238	−	0.983987i	$-0.557040\pi$
$397$	−22.3062	−	12.8785i	−1.11952	−	0.646352i	−0.941277	+	0.337635i	$0.890373\pi$
$398$	0.0605389	−	0.0349521i	0.00303454	−	0.00175199i
$399$	−21.6767	−	14.6046i	−1.08519	−	0.731145i
$400$	9.67138	+	15.2153i	0.483569	+	0.760767i
$401$	−7.10930	−	12.3137i	−0.355022	−	0.614915i	0.632100	−	0.774887i	$-0.282193\pi$
$401$	−7.10930	−	12.3137i	−0.355022	−	0.614915i	−0.987122	+	0.159971i	$0.948860\pi$
$402$	1.91153	−	4.01136i	0.0953384	−	0.200068i
$403$	−4.56700	−	2.63676i	−0.227499	−	0.131346i
$404$	8.13776	−	14.0950i	0.404869	−	0.701253i
$405$	13.1221	−	15.2581i	0.652045	−	0.758181i
$406$	−1.65292	+	2.07869i	−0.0820332	+	0.103164i
$407$	−1.57828	+	0.911220i	−0.0782324	+	0.0451675i
$408$	−7.14629	+	0.565041i	−0.353794	+	0.0279737i
$409$	29.8656			1.47676			0.738378	−	0.674387i	$-0.235592\pi$
$409$	29.8656			1.47676			0.738378	+	0.674387i	$0.235592\pi$
$410$	−1.67565	−	2.76458i	−0.0827546	−	0.136533i
$411$	−26.6637	+	18.3397i	−1.31522	+	0.904632i
$412$	−18.0248	+	10.4066i	−0.888020	+	0.512699i
$413$	17.5503	−	6.91648i	0.863591	−	0.340338i
$414$	−0.282643	+	0.737914i	−0.0138912	+	0.0362665i
$415$	−35.5902	+	0.758375i	−1.74705	+	0.0372272i
$416$	−1.66940	+	2.89149i	−0.0818491	+	0.141767i
$417$	−17.7226	−	25.7665i	−0.867879	−	1.26179i
$418$	6.83162	−	3.94424i	0.334145	−	0.192919i
$419$	6.69434	−	11.5949i	0.327040	−	0.566449i	−0.654883	−	0.755730i	$-0.727282\pi$
$419$	6.69434	−	11.5949i	0.327040	−	0.566449i	0.981923	+	0.189281i	$0.0606156\pi$
$420$	10.7182	−	16.6637i	0.522994	−	0.813107i
$421$	−10.1790	−	17.6305i	−0.496092	−	0.859257i	0.503898	−	0.863763i	$-0.331899\pi$
$421$	−10.1790	−	17.6305i	−0.496092	−	0.859257i	−0.999990	+	0.00450634i	$0.998566\pi$
$422$	1.12318	+	0.648466i	0.0546753	+	0.0315668i
$423$	13.7553	−	11.1554i	0.668807	−	0.542395i
$424$	2.19544	+	3.80262i	0.106620	+	0.184671i
$425$	18.0945	+	9.44293i	0.877712	+	0.458049i
$426$	1.94163	+	0.925243i	0.0940723	+	0.0448282i
$427$	−0.610046	+	0.240416i	−0.0295222	+	0.0116346i
$428$	10.0856	+	5.82294i	0.487507	+	0.281462i
$429$	0.827071	+	10.4603i	0.0399313	+	0.505027i
$430$	0.141944	+	6.66136i	0.00684514	+	0.321239i
$431$	−16.3814	−	28.3734i	−0.789064	−	1.36670i	−0.926541	−	0.376194i	$-0.877233\pi$
$431$	−16.3814	−	28.3734i	−0.789064	−	1.36670i	0.137477	−	0.990505i	$-0.456101\pi$
$432$	−18.2137	+	4.39376i	−0.876309	+	0.211395i
$433$		−	8.52240i		−	0.409560i	−0.978808	−	0.204780i	$-0.934352\pi$
$433$		−	8.52240i		−	0.409560i	0.978808	−	0.204780i	$-0.0656480\pi$
$434$	1.16789	+	2.96347i	0.0560605	+	0.142251i
$435$	−13.7509	−	6.19677i	−0.659305	−	0.297112i
$436$	6.75071	+	11.6926i	0.323300	+	0.559973i
$437$			5.82854i			0.278817i
$438$	−2.11764	+	0.167437i	−0.101185	+	0.00800044i
$439$	28.2761			1.34954			0.674771	−	0.738027i	$-0.264242\pi$
$439$	28.2761			1.34954			0.674771	+	0.738027i	$0.264242\pi$
$440$	6.30549	+	10.4031i	0.300603	+	0.495949i
$441$	−20.7987	−	2.90084i	−0.990413	−	0.138135i
$442$			1.18794i			0.0565047i
$443$			34.4261i			1.63563i	0.575479	+	0.817817i	$0.304816\pi$
$443$			34.4261i			1.63563i	−0.575479	+	0.817817i	$0.695184\pi$
$444$	−0.937193	+	0.644617i	−0.0444772	+	0.0305922i
$445$	17.6130	−	10.6755i	0.834934	−	0.506067i
$446$	1.79092	+	3.10196i	0.0848023	+	0.146882i
$447$	12.9796	−	1.02627i	0.613916	−	0.0485409i
$448$	−15.8750	+	6.25628i	−0.750024	+	0.295581i
$449$	14.1363			0.667132			0.333566	−	0.942727i	$-0.391748\pi$
$449$	14.1363			0.667132			0.333566	+	0.942727i	$0.391748\pi$
$450$	−3.66618	−	1.22789i	−0.172825	−	0.0578833i
$451$	15.0479	+	26.0638i	0.708580	+	1.22730i
$452$	−26.1678	−	15.1080i	−1.23083	−	0.710619i
$453$	16.9361	+	24.6230i	0.795729	+	1.15689i
$454$	−1.73192	+	2.99978i	−0.0812833	+	0.140787i
$455$	−5.31545	−	4.04491i	−0.249192	−	0.189628i
$456$	8.25271	−	5.67635i	0.386469	−	0.265820i
$457$			11.2025i			0.524031i	0.965064	+	0.262015i	$0.0843871\pi$
$457$			11.2025i			0.524031i	−0.965064	+	0.262015i	$0.915613\pi$
$458$	−4.39843	+	2.53943i	−0.205525	+	0.118660i
$459$	−15.3700	+	14.6175i	−0.717409	+	0.682285i
$460$	−4.41721	+	0.0941243i	−0.205953	+	0.00438857i
$461$	13.4181	+	23.2408i	0.624942	+	1.08243i	0.988552	+	0.150880i	$0.0482108\pi$
$461$	13.4181	+	23.2408i	0.624942	+	1.08243i	−0.363610	+	0.931551i	$0.618456\pi$
$462$	3.54136	−	5.25622i	0.164759	−	0.244542i
$463$	−16.9274	−	9.77304i	−0.786683	−	0.454192i	0.0521105	−	0.998641i	$-0.483405\pi$
$463$	−16.9274	−	9.77304i	−0.786683	−	0.454192i	−0.838794	+	0.544450i	$0.816739\pi$
$464$	7.02106	+	12.1608i	0.325945	+	0.564553i
$465$	−14.6829	+	10.5669i	−0.680904	+	0.490028i
$466$	−1.23170	+	2.13337i	−0.0570576	+	0.0988267i
$467$	31.3519	+	18.1010i	1.45079	+	0.837615i	0.998526	−	0.0542684i	$-0.0172827\pi$
$467$	31.3519	+	18.1010i	1.45079	+	0.837615i	0.452265	+	0.891883i	$0.350616\pi$
$468$	1.02922	+	6.46781i	0.0475759	+	0.298975i
$469$	−9.65517	−	24.4996i	−0.445834	−	1.13128i
$470$	−2.98221	−	1.63808i	−0.137559	−	0.0755591i
$471$	−19.0980	−	9.10074i	−0.879988	−	0.419340i
$472$			7.22900i			0.332742i
$473$		−	62.0292i		−	2.85211i
$474$	−1.53059	−	0.729373i	−0.0703025	−	0.0335012i
$475$	−28.4926	+	1.21482i	−1.30733	+	0.0557399i
$476$	−12.9972	+	16.3450i	−0.595723	+	0.749173i
$477$	12.1325	+	4.64712i	0.555510	+	0.212777i
$478$	6.36433	+	3.67445i	0.291098	+	0.168065i
$479$	6.66384	−	11.5421i	0.304479	−	0.527373i	−0.672666	−	0.739946i	$-0.734851\pi$
$479$	6.66384	−	11.5421i	0.304479	−	0.527373i	0.977145	+	0.212573i	$0.0681844\pi$
$480$	6.69017	+	9.29613i	0.305363	+	0.424308i
$481$	0.191736	+	0.332096i	0.00874240	+	0.0151423i
$482$	−0.844914	−	0.487812i	−0.0384848	−	0.0222192i
$483$	2.05504	+	4.20787i	0.0935078	+	0.191465i
$484$	−17.2000	−	29.7912i	−0.781817	−	1.35415i
$485$	−8.15118	+	0.173690i	−0.370126	+	0.00788685i
$486$	2.44021	−	3.19215i	0.110690	−	0.144799i
$487$	21.9643	−	12.6811i	0.995297	−	0.574635i	0.0884437	−	0.996081i	$-0.471811\pi$
$487$	21.9643	−	12.6811i	0.995297	−	0.574635i	0.906853	+	0.421446i	$0.138477\pi$
$488$		−	0.251280i		−	0.0113749i
$489$	24.9796	−	17.1814i	1.12962	−	0.776970i
$490$	0.992364	+	3.91057i	0.0448304	+	0.176661i
$491$	7.08802	−	12.2768i	0.319878	−	0.554045i	−0.660584	−	0.750752i	$-0.729691\pi$
$491$	7.08802	−	12.2768i	0.319878	−	0.554045i	0.980462	+	0.196707i	$0.0630247\pi$
$492$	10.6452	+	15.4769i	0.479925	+	0.697751i
$493$	13.7671	+	7.94844i	0.620039	+	0.357980i
$494$	−0.829933	−	1.43749i	−0.0373405	−	0.0646756i
$495$	33.8796	+	12.1558i	1.52278	+	0.546361i
$496$	16.8420			0.756226
$497$	11.8586	−	4.67342i	0.531931	−	0.209632i
$498$	−7.08532	+	0.560220i	−0.317501	+	0.0251041i
$499$	10.2035	+	17.6730i	0.456771	+	0.791151i	0.998788	−	0.0492165i	$-0.0156724\pi$
$499$	10.2035	+	17.6730i	0.456771	+	0.791151i	−0.542017	+	0.840368i	$0.682339\pi$
$500$	−1.38079	−	21.5737i	−0.0617507	−	0.964807i
$501$	4.60331	−	3.16623i	0.205661	−	0.141457i
$502$		−	1.19786i		−	0.0534631i
$503$		−	7.51280i		−	0.334979i	−0.985874	−	0.167490i	$-0.946434\pi$
$503$		−	7.51280i		−	0.334979i	0.985874	−	0.167490i	$-0.0535661\pi$
$504$	3.95659	−	7.00776i	0.176241	−	0.312151i
$505$	−16.0960	+	9.75604i	−0.716263	+	0.434138i
$506$	−1.41332			−0.0628297
$507$	−20.2456	+	1.60077i	−0.899138	+	0.0710928i
$508$			21.8905i			0.971232i
$509$	−3.55519	−	6.15776i	−0.157581	−	0.272938i	0.776415	−	0.630222i	$-0.217036\pi$
$509$	−3.55519	−	6.15776i	−0.157581	−	0.272938i	−0.933996	+	0.357284i	$0.883703\pi$
$510$	3.71523	+	1.67425i	0.164513	+	0.0741370i
$511$	−7.83515	+	9.85337i	−0.346606	+	0.435887i
$512$		−	17.9749i		−	0.794384i
$513$	8.38643	−	28.4260i	0.370270	−	1.25504i
$514$	1.16383	+	2.01581i	0.0513342	+	0.0889134i
$515$	24.0641	−	0.512770i	1.06039	−	0.0225954i
$516$	−3.05163	−	38.5952i	−0.134341	−	1.69906i
$517$	27.4323	+	15.8380i	1.20647	+	0.696556i
$518$	0.0341994	−	0.229085i	0.00150264	−	0.0100654i
$519$	17.8974	+	8.52865i	0.785610	+	0.374366i
$520$	2.18899	−	1.32678i	0.0959936	−	0.0581832i
$521$	−3.72233	−	6.44727i	−0.163078	−	0.282460i	0.772893	−	0.634537i	$-0.218809\pi$
$521$	−3.72233	−	6.44727i	−0.163078	−	0.282460i	−0.935971	+	0.352077i	$0.885476\pi$
$522$	−2.81213	−	1.07713i	−0.123084	−	0.0471447i
$523$	−28.2805	−	16.3278i	−1.23662	−	0.713964i	−0.268220	−	0.963358i	$-0.586435\pi$
$523$	−28.2805	−	16.3278i	−1.23662	−	0.713964i	−0.968402	+	0.249394i	$0.919769\pi$
$524$	−0.608610	−	1.05414i	−0.0265872	−	0.0460504i
$525$	−20.1417	+	10.9230i	−0.879055	+	0.476721i
$526$	0.0586657	−	0.101612i	0.00255795	−	0.00443050i
$527$	16.5121	−	9.53326i	0.719278	−	0.415275i
$528$	−18.9909	−	27.6105i	−0.826474	−	1.20159i
$529$	−10.9779	+	19.0142i	−0.477299	+	0.826706i
$530$	−0.0531748	−	2.49547i	−0.00230977	−	0.108396i
$531$	13.4731	+	16.6131i	0.584682	+	0.720949i
$532$	4.30824	−	28.8587i	0.186786	−	1.25118i
$533$	5.48426	−	3.16634i	0.237550	−	0.137149i
$534$	3.38802	−	2.33033i	0.146614	−	0.100843i
$535$	−6.98089	−	11.5174i	−0.301810	−	0.497941i
$536$	10.0914			0.435884
$537$	6.77217	−	0.535460i	0.292241	−	0.0231068i
$538$	1.07235	−	0.619120i	0.0462322	−	0.0266922i
$539$	−8.46090	−	36.5947i	−0.364437	−	1.57624i
$540$	21.6783	+	5.89668i	0.932885	+	0.253753i
$541$	1.16573	−	2.01911i	0.0501187	−	0.0868082i	−0.839878	−	0.542776i	$-0.817373\pi$
$541$	1.16573	−	2.01911i	0.0501187	−	0.0868082i	0.889996	+	0.455968i	$0.150707\pi$
$542$	−1.27056	−	0.733558i	−0.0545752	−	0.0315090i
$543$	−18.6489	+	39.1348i	−0.800299	+	1.67943i
$544$	−6.03575	−	10.4542i	−0.258781	−	0.448221i
$545$	−0.332630	−	15.6102i	−0.0142483	−	0.668666i
$546$	−1.10600	−	0.745162i	−0.0473323	−	0.0318900i
$547$	−8.21585	+	4.74342i	−0.351284	+	0.202814i	−0.665251	−	0.746620i	$-0.731675\pi$
$547$	−8.21585	+	4.74342i	−0.351284	+	0.202814i	0.313966	+	0.949434i	$0.398342\pi$
$548$	−31.2870	−	18.0635i	−1.33651	−	0.771636i
$549$	−0.468323	−	0.577472i	−0.0199876	−	0.0246459i
$550$	−0.294573	−	6.90895i	−0.0125606	−	0.294599i
$551$	−22.2121			−0.946266
$552$	−1.78898	+	0.141450i	−0.0761440	+	0.00602053i
$553$	−9.34817	+	3.68407i	−0.397525	+	0.156663i
$554$	2.63167	−	4.55819i	0.111809	−	0.193659i
$555$	1.30884	−	0.131598i	0.0555572	−	0.00558603i
$556$	17.4557	−	30.2341i	0.740286	−	1.28221i
$557$	−9.66838	+	5.58204i	−0.409663	+	0.236519i	−0.690645	−	0.723194i	$-0.742673\pi$
$557$	−9.66838	+	5.58204i	−0.409663	+	0.236519i	0.280982	+	0.959713i	$0.409340\pi$
$558$	−2.80523	+	2.27501i	−0.118755	+	0.0963090i
$559$	−13.0520			−0.552040
$560$	21.1606	+	2.69952i	0.894199	+	0.114075i
$561$	−34.2477	−	16.3200i	−1.44594	−	0.689032i
$562$	−1.12889	+	0.651762i	−0.0476192	+	0.0274929i
$563$			23.8134i			1.00361i	0.864979	+	0.501807i	$0.167331\pi$
$563$			23.8134i			1.00361i	−0.864979	+	0.501807i	$0.832669\pi$
$564$	17.8478	+	8.50501i	0.751529	+	0.358125i
$565$	18.1123	+	29.8826i	0.761991	+	1.25717i
$566$	2.05870			0.0865338
$567$	−3.96800	−	23.4788i	−0.166640	−	0.986018i
$568$			4.88459i			0.204953i
$569$	5.29241			0.221869			0.110935	−	0.993828i	$-0.464616\pi$
$569$	5.29241			0.221869			0.110935	+	0.993828i	$0.464616\pi$
$570$	−5.66535	+	0.569626i	−0.237295	+	0.0238590i
$571$	−3.95575			−0.165543			−0.0827715	−	0.996569i	$-0.526377\pi$
$571$	−3.95575			−0.165543			−0.0827715	+	0.996569i	$0.526377\pi$
$572$	−10.1444	+	5.85685i	−0.424157	+	0.244887i
$573$	−3.83306	+	8.04371i	−0.160128	+	0.336031i
$574$	−3.78312	−	0.564772i	−0.157905	−	0.0235731i
$575$	4.52971	+	2.36391i	0.188902	+	0.0985819i
$576$	−12.1870	−	15.0274i	−0.507793	−	0.626140i
$577$	−6.68392	+	3.85896i	−0.278255	+	0.160651i	−0.632633	−	0.774451i	$-0.718026\pi$
$577$	−6.68392	+	3.85896i	−0.278255	+	0.160651i	0.354378	+	0.935102i	$0.384693\pi$
$578$	0.0751851	+	0.0434081i	0.00312729	+	0.00180554i
$579$	−19.0268	−	9.06684i	−0.790728	−	0.376805i
$580$	−0.358700	−	16.8336i	−0.0148942	−	0.698978i
$581$	−26.2153	+	32.9680i	−1.08759	+	1.36774i
$582$	−1.62274	+	0.128307i	−0.0672649	+	0.00531848i
$583$			23.2373i			0.962390i
$584$	−2.41213	−	4.17793i	−0.0998146	−	0.172884i
$585$	2.55778	−	7.12884i	0.105751	−	0.294741i
$586$	3.21277	−	5.56468i	0.132718	−	0.229875i
$587$	−14.8297	+	8.56191i	−0.612086	+	0.353388i	−0.773781	−	0.633453i	$-0.781637\pi$
$587$	−14.8297	+	8.56191i	−0.612086	+	0.353388i	0.161696	+	0.986841i	$0.448304\pi$
$588$	−7.06480	−	22.3533i	−0.291347	−	0.921836i
$589$	−13.3204	+	23.0717i	−0.548860	+	0.950653i
$590$	1.97841	−	3.60180i	0.0814499	−	0.148284i
$591$	3.69918	+	1.76276i	0.152164	+	0.0725105i
$592$	−1.06061	−	0.612343i	−0.0435908	−	0.0251672i
$593$	16.1568	+	9.32814i	0.663481	+	0.383061i	0.793602	−	0.608437i	$-0.208203\pi$
$593$	16.1568	+	9.32814i	0.663481	+	0.383061i	−0.130121	+	0.991498i	$0.541537\pi$
$594$	6.89280	+	2.03356i	0.282815	+	0.0834380i
$595$	22.2742	−	9.33116i	0.913154	−	0.382540i
$596$	7.26747	+	12.5876i	0.297687	+	0.515609i
$597$	0.468277	−	0.0370255i	0.0191653	−	0.00151535i
$598$			0.297386i			0.0121610i
$599$	16.7313			0.683623			0.341811	−	0.939769i	$-0.388960\pi$
$599$	16.7313			0.683623			0.341811	+	0.939769i	$0.388960\pi$
$600$	−1.06435	−	8.71587i	−0.0434517	−	0.355824i
$601$	18.4820	+	32.0118i	0.753897	+	1.30579i	0.945921	+	0.324398i	$0.105162\pi$
$601$	18.4820	+	32.0118i	0.753897	+	1.30579i	−0.192024	+	0.981390i	$0.561505\pi$
$602$	6.17057	+	4.90668i	0.251494	+	0.199981i
$603$	23.1914	−	18.8080i	0.944426	−	0.765919i
$604$	−16.6811	+	28.8925i	−0.678743	+	1.17562i
$605$	0.847500	+	39.7728i	0.0344558	+	1.61699i
$606$	−3.09622	+	2.12963i	−0.125775	+	0.0865103i
$607$	14.2868	−	8.24849i	0.579884	−	0.334796i	−0.181204	−	0.983446i	$-0.557999\pi$
$607$	14.2868	−	8.24849i	0.579884	−	0.334796i	0.761087	+	0.648650i	$0.224666\pi$
$608$	14.6073	+	8.43351i	0.592403	+	0.342024i
$609$	−16.0358	+	7.83160i	−0.649805	+	0.317353i
$610$	−0.0687695	+	0.125198i	−0.00278440	+	0.00506913i
$611$	3.33258	−	5.77221i	0.134822	−	0.233518i
$612$	−22.1122	−	8.46961i	−0.893831	−	0.342364i
$613$	−9.48847	+	5.47817i	−0.383236	+	0.221261i	−0.679225	−	0.733930i	$-0.737684\pi$
$613$	−9.48847	+	5.47817i	−0.383236	+	0.221261i	0.295990	+	0.955191i	$0.404351\pi$
$614$	7.46115			0.301108
$615$	−2.17322	−	21.6143i	−0.0876327	−	0.871572i
$616$	14.2359	+	2.12524i	0.573581	+	0.0856283i
$617$	−20.1328	−	11.6237i	−0.810516	−	0.467951i	0.0366192	−	0.999329i	$-0.488341\pi$
$617$	−20.1328	−	11.6237i	−0.810516	−	0.467951i	−0.847135	+	0.531378i	$0.821674\pi$
$618$	4.79069	−	0.378789i	0.192710	−	0.0152371i
$619$	−1.60021	+	2.77165i	−0.0643180	+	0.111402i	−0.896391	−	0.443264i	$-0.853821\pi$
$619$	−1.60021	+	2.77165i	−0.0643180	+	0.111402i	0.832073	+	0.554666i	$0.187154\pi$
$620$	−17.7002	−	9.72243i	−0.710857	−	0.390462i
$621$	−3.84766	+	3.65929i	−0.154401	+	0.146842i
$622$		−	8.45658i		−	0.339078i
$623$	3.59813	−	24.1020i	0.144156	−	0.965628i
$624$	−5.80970	+	3.99601i	−0.232574	+	0.159968i
$625$	−10.6118	+	22.6360i	−0.424471	+	0.905442i
$626$	1.81014			0.0723479
$627$	52.8435	−	4.17822i	2.11037	−	0.166862i
$628$		−	23.6168i		−	0.942413i
$629$	−1.38645			−0.0552814
$630$	−3.88921	+	2.40874i	−0.154950	+	0.0959666i
$631$	24.5995			0.979290			0.489645	−	0.871922i	$-0.337126\pi$
$631$	24.5995			0.979290			0.489645	+	0.871922i	$0.337126\pi$
$632$		−	3.85054i		−	0.153166i
$633$	4.93886	+	7.18049i	0.196302	+	0.285399i
$634$	−5.67093			−0.225221
$635$	12.1877	−	22.1883i	0.483654	−	0.880516i
$636$	1.14320	+	14.4585i	0.0453308	+	0.573316i
$637$	−7.70013	+	1.78032i	−0.305090	+	0.0705386i
$638$		−	5.38604i		−	0.213235i
$639$	9.10367	+	11.2254i	0.360136	+	0.444070i
$640$	−8.15659	+	14.8495i	−0.322418	+	0.586978i
$641$	−6.00214	+	10.3960i	−0.237070	+	0.410618i	−0.959872	−	0.280437i	$-0.909521\pi$
$641$	−6.00214	+	10.3960i	−0.237070	+	0.410618i	0.722802	+	0.691055i	$0.242854\pi$
$642$	−1.52385	−	2.21548i	−0.0601414	−	0.0874382i
$643$	14.9130	+	8.61003i	0.588112	+	0.339546i	0.764351	−	0.644801i	$-0.223060\pi$
$643$	14.9130	+	8.61003i	0.588112	+	0.339546i	−0.176239	+	0.984347i	$0.556393\pi$
$644$	−3.25366	+	4.09176i	−0.128212	+	0.161238i
$645$	−18.3950	+	40.8194i	−0.724304	+	1.60726i
$646$	6.00128			0.236117
$647$	−14.8537	+	8.57577i	−0.583958	+	0.337148i	−0.762705	−	0.646747i	$-0.776129\pi$
$647$	−14.8537	+	8.57577i	−0.583958	+	0.337148i	0.178747	+	0.983895i	$0.442796\pi$
$648$	8.92843	+	1.88422i	0.350742	+	0.0740193i
$649$	−19.1285	+	33.1316i	−0.750861	+	1.30053i
$650$	−1.45376	+	0.0619831i	−0.0570211	+	0.00243118i
$651$	−1.48190	+	21.3530i	−0.0580804	+	0.836890i
$652$	29.3109	+	16.9226i	1.14790	+	0.662742i
$653$	−25.0256	+	14.4485i	−0.979326	+	0.565414i	−0.902067	−	0.431597i	$-0.857950\pi$
$653$	−25.0256	+	14.4485i	−0.979326	+	0.565414i	−0.0772595	+	0.997011i	$0.524617\pi$
$654$	−0.245718	−	3.10769i	−0.00960832	−	0.121520i
$655$	0.0299882	+	1.40733i	0.00117174	+	0.0549891i
$656$	−10.1123	+	17.5150i	−0.394818	+	0.683845i
$657$	−13.3300	−	5.10579i	−0.520053	−	0.199196i
$658$	−3.74551	+	1.47609i	−0.146015	+	0.0575440i
$659$	0.716983	+	1.24185i	0.0279297	+	0.0483756i	0.879652	−	0.475617i	$-0.157775\pi$
$659$	0.716983	+	1.24185i	0.0279297	+	0.0483756i	−0.851723	+	0.523993i	$0.824442\pi$
$660$	4.01986	+	39.9804i	0.156473	+	1.55624i
$661$	13.8369			0.538194			0.269097	−	0.963113i	$-0.413275\pi$
$661$	13.8369			0.538194			0.269097	+	0.963113i	$0.413275\pi$
$662$			6.18165i			0.240257i
$663$	−3.43400	+	7.20628i	−0.133366	+	0.279869i
$664$	−8.07065	−	13.9788i	−0.313202	−	0.542482i
$665$	−20.4342	+	26.8527i	−0.792403	+	1.04130i
$666$	0.259373	−	0.0412741i	0.0100505	−	0.00159934i
$667$	3.44641	+	1.98979i	0.133445	+	0.0770448i
$668$	5.40148	+	3.11855i	0.208990	+	0.120660i
$669$	1.89716	+	23.9941i	0.0733483	+	0.927665i
$670$	−5.02799	−	2.76180i	−0.194248	−	0.106698i
$671$	0.664907	−	1.15165i	0.0256685	−	0.0444591i
$672$	13.5191	+	0.938231i	0.521511	+	0.0361930i
$673$	3.80527	−	2.19698i	0.146683	−	0.0846872i	−0.424863	−	0.905258i	$-0.639678\pi$
$673$	3.80527	−	2.19698i	0.146683	−	0.0846872i	0.571545	+	0.820571i	$0.306344\pi$
$674$	−3.09279	+	5.35687i	−0.119130	+	0.206339i
$675$	−18.6902	−	18.0465i	−0.719387	−	0.694609i
$676$	−11.3358	−	19.6341i	−0.435991	−	0.755159i
$677$		−	21.0480i		−	0.808939i	−0.914552	−	0.404469i	$-0.867456\pi$
$677$		−	21.0480i		−	0.808939i	0.914552	−	0.404469i	$-0.132544\pi$
$678$	3.95371	+	5.74820i	0.151841	+	0.220758i
$679$	−6.00406	+	7.55062i	−0.230415	+	0.289766i
$680$	0.197158	+	9.25252i	0.00756065	+	0.354818i
$681$	−19.1777	+	13.1907i	−0.734891	+	0.505470i
$682$	−5.59448	−	3.22997i	−0.214224	−	0.123682i
$683$	39.3977	−	22.7462i	1.50751	−	0.870361i	0.507548	−	0.861624i	$-0.330552\pi$
$683$	39.3977	−	22.7462i	1.50751	−	0.870361i	0.999962	−	0.00873721i	$-0.00278118\pi$
$684$	32.6742	−	5.19946i	1.24933	−	0.198806i
$685$	21.6556	+	35.7286i	0.827420	+	1.36512i
$686$	4.30966	+	2.05306i	0.164544	+	0.0783862i
$687$	−34.0225	+	2.69008i	−1.29804	+	0.102633i
$688$	36.0993	−	20.8419i	1.37627	−	0.794591i
$689$	4.88951			0.186276
$690$	0.930058	+	0.419126i	0.0354067	+	0.0159558i
$691$	−0.402702			−0.0153195			−0.00765976	−	0.999971i	$-0.502438\pi$
$691$	−0.402702			−0.0153195			−0.00765976	+	0.999971i	$0.502438\pi$
$692$			22.1322i			0.841340i
$693$	36.6768	−	21.6482i	1.39324	−	0.822346i
$694$	6.94404			0.263592
$695$	−34.5263	+	20.9269i	−1.30966	+	0.793803i
$696$	−0.539056	−	6.81765i	−0.0204329	−	0.258422i
$697$			22.8959i			0.867245i
$698$	−0.904644	+	0.522297i	−0.0342413	+	0.0197692i
$699$	−13.6387	+	9.38094i	−0.515864	+	0.354820i
$700$	−20.6806	−	15.0526i	−0.781652	−	0.568934i
$701$	−12.1053			−0.457209			−0.228605	−	0.973519i	$-0.573416\pi$
$701$	−12.1053			−0.457209			−0.228605	+	0.973519i	$0.573416\pi$
$702$	0.427895	−	1.45036i	0.0161499	−	0.0547403i
$703$	1.67769	−	0.968616i	0.0632753	−	0.0365320i
$704$	17.3027	−	29.9691i	0.652119	−	1.12950i
$705$	−13.3554	−	18.5576i	−0.502995	−	0.698921i
$706$	−0.956709	+	1.65707i	−0.0360062	+	0.0623646i
$707$	−3.28823	+	22.0262i	−0.123667	+	0.828381i
$708$	−10.2720	+	21.5559i	−0.386046	+	0.810120i
$709$	−8.99021			−0.337635			−0.168817	−	0.985647i	$-0.553995\pi$
$709$	−8.99021			−0.337635			−0.168817	+	0.985647i	$0.553995\pi$
$710$	1.33680	−	2.43371i	0.0501692	−	0.0913357i
$711$	−7.17646	−	8.84902i	−0.269138	−	0.331864i
$712$	8.08754	+	4.66934i	0.303093	+	0.174991i
$713$	4.13358	−	2.38652i	0.154804	−	0.0893760i
$714$	4.33258	−	2.11595i	0.162143	−	0.0791874i
$715$	13.5432	−	0.288587i	0.506489	−	0.0107925i
$716$	3.79183	+	6.56764i	0.141707	+	0.245444i
$717$	27.9854	+	40.6873i	1.04513	+	1.51950i
$718$	3.73476	+	2.15626i	0.139380	+	0.0804710i
$719$	−5.34809	+	9.26316i	−0.199450	+	0.345457i	−0.948350	−	0.317225i	$-0.897249\pi$
$719$	−5.34809	+	9.26316i	−0.199450	+	0.345457i	0.748900	+	0.662683i	$0.230582\pi$
$720$	4.30930	+	23.8014i	0.160598	+	0.887025i
$721$	17.7253	−	22.2911i	0.660125	−	0.830164i
$722$	−3.02069	+	1.74400i	−0.112418	+	0.0649048i
$723$	−3.71528	−	5.40156i	−0.138173	−	0.200886i
$724$	−48.3946			−1.79857
$725$	−9.00867	+	17.2624i	−0.334573	+	0.641108i
$726$	0.626058	+	7.91800i	0.0232352	+	0.293864i
$727$	−2.11504	+	1.22112i	−0.0784424	+	0.0452887i	−0.538708	−	0.842492i	$-0.681087\pi$
$727$	−2.11504	+	1.22112i	−0.0784424	+	0.0452887i	0.460266	+	0.887781i	$0.347754\pi$
$728$	0.447186	−	2.99547i	0.0165738	−	0.111020i
$729$	24.0304	−	12.3102i	0.890014	−	0.455934i
$730$	0.0584231	+	2.74177i	0.00216234	+	0.101477i
$731$	23.5948	−	40.8675i	0.872687	−	1.51154i
$732$	0.357055	−	0.749282i	0.0131971	−	0.0276942i
$733$	18.8143	−	10.8624i	0.694922	−	0.401214i	−0.110531	−	0.993873i	$-0.535255\pi$
$733$	18.8143	−	10.8624i	0.694922	−	0.401214i	0.805453	+	0.592659i	$0.201922\pi$
$734$	0.622925	−	1.07894i	0.0229926	−	0.0398243i
$735$	−5.28447	+	26.5909i	−0.194921	+	0.980819i
$736$	−1.51097	−	2.61707i	−0.0556950	−	0.0964666i
$737$	46.2506	+	26.7028i	1.70366	+	0.983610i
$738$	−0.681603	−	4.28330i	−0.0250901	−	0.157671i
$739$	−15.6123	−	27.0414i	−0.574309	−	0.994733i	−0.996116	−	0.0880471i	$-0.971937\pi$
$739$	−15.6123	−	27.0414i	−0.574309	−	0.994733i	0.421807	−	0.906686i	$-0.361396\pi$
$740$	0.761166	+	1.25581i	0.0279810	+	0.0461645i
$741$	−0.879166	−	11.1192i	−0.0322970	−	0.408473i
$742$	−2.31161	−	1.83813i	−0.0848619	−	0.0674800i
$743$	39.7464	+	22.9476i	1.45816	+	0.841866i	0.998921	−	0.0464485i	$-0.0147903\pi$
$743$	39.7464	+	22.9476i	1.45816	+	0.841866i	0.459235	+	0.888315i	$0.348124\pi$
$744$	−7.40476	−	3.52859i	−0.271472	−	0.129364i
$745$	−0.358093	−	16.8051i	−0.0131195	−	0.615692i
$746$	−0.411042	−	0.711945i	−0.0150493	−	0.0260662i
$747$	−44.6003	−	17.0832i	−1.63184	−	0.625043i
$748$		−	42.3511i		−	1.54851i
$749$	−15.7607	−	2.35288i	−0.575885	−	0.0859723i
$750$	−1.85503	+	4.63391i	−0.0677362	+	0.169207i
$751$	−17.4701	−	30.2591i	−0.637493	−	1.10417i	−0.985981	−	0.166857i	$-0.946638\pi$
$751$	−17.4701	−	30.2591i	−0.637493	−	1.10417i	0.348488	−	0.937313i	$-0.386695\pi$
$752$			21.2864i			0.776236i
$753$	3.46267	−	7.26643i	0.126187	−	0.264804i
$754$	−1.13331			−0.0412728
$755$	32.9941	−	19.9983i	1.20078	−	0.727811i
$756$	21.7557	−	15.2741i	0.791246	−	0.555513i
$757$		−	31.7733i		−	1.15482i	−0.816455	−	0.577409i	$-0.804064\pi$
$757$		−	31.7733i		−	1.15482i	0.816455	−	0.577409i	$-0.195936\pi$
$758$		−	9.36409i		−	0.340119i
$759$	−8.57345	−	4.08550i	−0.311197	−	0.148294i
$760$	−6.70266	−	11.0584i	−0.243131	−	0.401130i
$761$	5.95672	+	10.3173i	0.215931	+	0.374003i	0.953560	−	0.301203i	$-0.0973881\pi$
$761$	5.95672	+	10.3173i	0.215931	+	0.374003i	−0.737629	+	0.675206i	$0.764055\pi$
$762$	2.17430	−	4.56278i	0.0787665	−	0.165292i
$763$	−14.4601	−	11.4983i	−0.523489	−	0.416265i
$764$	−9.94695			−0.359868
$765$	17.6975	+	20.8960i	0.639855	+	0.755496i
$766$	1.94483	+	3.36855i	0.0702697	+	0.121711i
$767$	6.97144	+	4.02496i	0.251724	+	0.145333i
$768$	8.15563	−	17.1147i	0.294291	−	0.617572i
$769$	−16.9530	+	29.3634i	−0.611340	+	1.05887i	0.379675	+	0.925120i	$0.376036\pi$
$769$	−16.9530	+	29.3634i	−0.611340	+	1.05887i	−0.991015	+	0.133752i	$0.957298\pi$
$770$	−6.51132	−	4.95493i	−0.234652	−	0.178563i
$771$	1.23287	+	15.5925i	0.0444006	+	0.561552i
$772$		−	23.5288i		−	0.846821i
$773$	−35.6140	+	20.5617i	−1.28095	+	0.739554i	−0.977021	−	0.213142i	$-0.931630\pi$
$773$	−35.6140	+	20.5617i	−1.28095	+	0.739554i	−0.303924	+	0.952696i	$0.598297\pi$
$774$	−3.19745	+	8.34777i	−0.114930	+	0.300055i
$775$	12.5280	+	19.7094i	0.450018	+	0.707984i
$776$	−1.84841	−	3.20154i	−0.0663541	−	0.114929i
$777$	0.869679	−	1.29081i	0.0311996	−	0.0463076i
$778$	0.692492	+	0.399811i	0.0248271	+	0.0143339i
$779$	−15.9958	−	27.7055i	−0.573109	−	0.992653i
$780$	8.41255	−	0.845845i	0.301218	−	0.0302861i
$781$	−12.9250	+	22.3868i	−0.462494	+	0.801064i
$782$	−0.931154	−	0.537602i	−0.0332980	−	0.0192246i
$783$	−13.9452	−	14.6631i	−0.498362	−	0.524018i
$784$	18.4542	−	17.2199i	0.659079	−	0.614996i
$785$	−13.1488	+	23.9381i	−0.469302	+	0.854389i
$786$	0.0221526	+	0.280173i	0.000790159	+	0.00999345i
$787$		−	0.817396i		−	0.0291370i	−0.999894	−	0.0145685i	$-0.995363\pi$
$787$		−	0.817396i		−	0.0291370i	0.999894	−	0.0145685i	$-0.00463747\pi$
$788$			4.57445i			0.162958i
$789$	0.649609	−	0.446812i	0.0231267	−	0.0159069i
$790$	−1.05381	+	1.91851i	−0.0374927	+	0.0682574i
$791$	40.8922	+	6.10468i	1.45396	+	0.217057i
$792$	2.56488	+	16.1181i	0.0911389	+	0.572732i
$793$	−0.242327	−	0.139908i	−0.00860528	−	0.00496826i
$794$	−3.31950	+	5.74955i	−0.117805	+	0.204044i
$795$	6.89112	−	15.2917i	0.244403	−	0.542340i
$796$	0.262194	+	0.454134i	0.00929323	+	0.0160963i
$797$	−1.03641	−	0.598374i	−0.0367117	−	0.0211955i	0.481532	−	0.876429i	$-0.340081\pi$
$797$	−1.03641	−	0.598374i	−0.0367117	−	0.0211955i	−0.518244	+	0.855233i	$0.673414\pi$
$798$	−3.76443	+	5.58730i	−0.133259	+	0.197788i
$799$	12.0490	+	20.8695i	0.426264	+	0.738311i
$800$	12.4785	−	7.93178i	0.441183	−	0.280431i
$801$	27.2887	−	4.34245i	0.964198	−	0.153433i
$802$	−3.17392	+	1.83246i	−0.112075	+	0.0647066i
$803$		−	25.5308i		−	0.900962i
$804$	30.0913	+	14.3394i	1.06124	+	0.505711i
$805$	5.57605	−	2.33593i	0.196530	−	0.0823308i
$806$	−0.679641	+	1.17717i	−0.0239393	+	0.0414641i
$807$	8.29476	−	0.655847i	0.291989	−	0.0230869i
$808$	−7.39098	−	4.26719i	−0.260014	−	0.150119i
$809$	16.3677	+	28.3497i	0.575458	+	0.996723i	0.995992	+	0.0894461i	$0.0285097\pi$
$809$	16.3677	+	28.3497i	0.575458	+	0.996723i	−0.420533	+	0.907277i	$0.638157\pi$
$810$	−3.93286	−	3.38231i	−0.138187	−	0.118842i
$811$	−13.2174			−0.464124			−0.232062	−	0.972701i	$-0.574547\pi$
$811$	−13.2174			−0.464124			−0.232062	+	0.972701i	$0.574547\pi$
$812$	−15.5934	−	12.3994i	−0.547220	−	0.435135i
$813$	−5.58695	−	8.12272i	−0.195943	−	0.284876i
$814$	0.234872	+	0.406811i	0.00823227	+	0.0142587i
$815$	−20.2879	−	33.4720i	−0.710653	−	1.17247i
$816$	−2.00949	−	25.4148i	−0.0703461	−	0.889695i
$817$			65.9363i			2.30682i
$818$		−	7.69802i		−	0.269155i
$819$	−4.55513	−	7.71741i	−0.159169	−	0.269668i
$820$	20.7385	−	12.5700i	0.724221	−	0.438962i
$821$	−1.09221			−0.0381184			−0.0190592	−	0.999818i	$-0.506067\pi$
$821$	−1.09221			−0.0381184			−0.0190592	+	0.999818i	$0.506067\pi$
$822$	4.72717	+	6.87273i	0.164879	+	0.239714i
$823$			24.5845i			0.856961i	0.903551	+	0.428480i	$0.140951\pi$
$823$			24.5845i			0.856961i	−0.903551	+	0.428480i	$0.859049\pi$
$824$	5.45692	+	9.45165i	0.190101	+	0.329264i
$825$	18.1849	−	42.7625i	0.633116	−	1.48880i
$826$	−1.78276	−	4.52368i	−0.0620302	−	0.157399i
$827$		−	24.2297i		−	0.842549i	−0.906933	−	0.421275i	$-0.861583\pi$
$827$		−	24.2297i		−	0.842549i	0.906933	−	0.421275i	$-0.138417\pi$
$828$	−5.53548	−	2.12025i	−0.192371	−	0.0736839i
$829$	−13.5596	−	23.4858i	−0.470943	−	0.815697i	0.528505	−	0.848930i	$-0.322753\pi$
$829$	−13.5596	−	23.4858i	−0.470943	−	0.815697i	−0.999448	+	0.0332333i	$0.989420\pi$
$830$	0.195476	+	9.17358i	0.00678506	+	0.318420i
$831$	29.1407	−	20.0434i	1.01088	−	0.695299i
$832$	−6.30600	−	3.64077i	−0.218621	−	0.126221i
$833$	8.34558	−	27.3285i	0.289157	−	0.946877i
$834$	−6.64145	+	4.56810i	−0.229975	+	0.158180i
$835$	−3.73870	−	6.16830i	−0.129383	−	0.213463i
$836$	29.5878	+	51.2476i	1.02332	+	1.77243i
$837$	−23.5935	+	5.69153i	−0.815510	+	0.196728i
$838$	−2.98866	−	1.72550i	−0.103242	−	0.0596066i
$839$	−22.2145	−	38.4767i	−0.766930	−	1.32836i	−0.939220	−	0.343316i	$-0.888450\pi$
$839$	−22.2145	−	38.4767i	−0.766930	−	1.32836i	0.172290	−	0.985046i	$-0.444883\pi$
$840$	−8.73794	−	5.62027i	−0.301487	−	0.193918i
$841$	6.91709	−	11.9808i	0.238521	−	0.413130i
$842$	−4.54436	+	2.62369i	−0.156609	+	0.0904182i
$843$	−8.73209	+	0.690426i	−0.300749	+	0.0237795i
$844$	−4.86448	+	8.42553i	−0.167442	+	0.290019i
$845$	0.558551	+	26.2126i	0.0192148	+	0.901740i
$846$	−2.87537	−	3.54552i	−0.0988574	−	0.121897i
$847$	36.8424	+	29.2961i	1.26592	+	1.00663i
$848$	−13.5235	+	7.80777i	−0.464397	+	0.268120i
$849$	12.4885	+	5.95113i	0.428604	+	0.204242i
$850$	2.43397	−	4.66396i	0.0834845	−	0.159973i
$851$	−0.347079			−0.0118977
$852$	−6.94074	+	14.5652i	−0.237786	+	0.498995i
$853$	32.3311	−	18.6664i	1.10700	−	0.639125i	0.168947	−	0.985625i	$-0.445963\pi$
$853$	32.3311	−	18.6664i	1.10700	−	0.639125i	0.938050	+	0.346501i	$0.112630\pi$
$854$	0.0619687	+	0.157243i	0.00212053	+	0.00538074i
$855$	−36.0137	−	12.9214i	−1.23164	−	0.441904i
$856$	3.05337	−	5.28858i	0.104362	−	0.180760i
$857$	−14.3777	−	8.30095i	−0.491132	−	0.283555i	0.233912	−	0.972258i	$-0.424847\pi$
$857$	−14.3777	−	8.30095i	−0.491132	−	0.283555i	−0.725044	+	0.688703i	$0.758181\pi$
$858$	2.69620	−	0.213182i	0.0920468	−	0.00727792i
$859$	−10.1645	−	17.6055i	−0.346809	−	0.600690i	0.638872	−	0.769313i	$-0.279401\pi$
$859$	−10.1645	−	17.6055i	−0.346809	−	0.600690i	−0.985681	+	0.168623i	$0.946068\pi$
$860$	−49.9704	+	1.06480i	−1.70398	+	0.0363092i
$861$	−21.3165	−	14.3619i	−0.726465	−	0.489453i
$862$	−7.31341	+	4.22240i	−0.249096	+	0.143816i
$863$	−35.2221	−	20.3355i	−1.19897	−	0.692227i	−0.238647	−	0.971106i	$-0.576704\pi$
$863$	−35.2221	−	20.3355i	−1.19897	−	0.692227i	−0.960326	+	0.278879i	$0.910037\pi$
$864$	3.60345	+	14.9376i	0.122592	+	0.508188i
$865$	12.3223	−	22.4333i	0.418970	−	0.762757i
$866$	−2.19670			−0.0746469
$867$	0.330606	+	0.480661i	0.0112280	+	0.0163241i
$868$	−22.2305	+	8.76096i	−0.754554	+	0.297366i
$869$	10.1889	−	17.6476i	0.345633	−	0.598654i
$870$	−1.59725	+	3.54437i	−0.0541520	+	0.120166i
$871$	5.61871	−	9.73190i	0.190383	−	0.329753i
$872$	6.13121	−	3.53986i	0.207629	−	0.119875i
$873$	−10.2148	−	3.91256i	−0.345717	−	0.132420i
$874$	1.50234			0.0508174
$875$	12.5813	+	26.7715i	0.425326	+	0.905040i
$876$	−1.25603	−	15.8855i	−0.0424374	−	0.536722i
$877$	0.0135817	−	0.00784141i	0.000458622	−	0.000264786i	−0.499771	−	0.866158i	$-0.666582\pi$
$877$	0.0135817	−	0.00784141i	0.000458622	−	0.000264786i	0.500229	+	0.865893i	$0.333249\pi$
$878$		−	7.28832i		−	0.245969i
$879$	35.5752	−	24.4692i	1.19992	−	0.825325i
$880$	−36.9972	+	22.4246i	−1.24718	+	0.755933i
$881$	−27.0051			−0.909823			−0.454912	−	0.890537i	$-0.650329\pi$
$881$	−27.0051			−0.909823			−0.454912	+	0.890537i	$0.650329\pi$
$882$	−0.747709	+	5.36098i	−0.0251767	+	0.180514i
$883$		−	6.45745i		−	0.217310i	−0.994079	−	0.108655i	$-0.965346\pi$
$883$		−	6.45745i		−	0.217310i	0.994079	−	0.108655i	$-0.0346544\pi$
$884$	−8.91139			−0.299722
$885$	22.4132	−	16.1302i	0.753411	−	0.542210i
$886$	8.87353			0.298112
$887$	−29.2131	+	16.8662i	−0.980880	+	0.566311i	−0.902536	−	0.430615i	$-0.858297\pi$
$887$	−29.2131	+	16.8662i	−0.980880	+	0.566311i	−0.0783444	+	0.996926i	$0.524963\pi$
$888$	0.338017	+	0.491434i	0.0113431	+	0.0164915i
$889$	−10.9824	−	27.8674i	−0.368338	−	0.934642i
$890$	−2.75167	−	4.53984i	−0.0922362	−	0.152176i
$891$	35.9345	+	32.2611i	1.20385	+	1.08079i
$892$	−23.2694	+	13.4346i	−0.779118	+	0.449824i
$893$	−29.1602	−	16.8356i	−0.975808	−	0.563383i
$894$	−0.264527	−	3.34558i	−0.00884711	−	0.111893i
$895$	−0.186836	−	8.76813i	−0.00624524	−	0.293086i
$896$	7.34997	+	18.6502i	0.245545	+	0.623060i
$897$	−0.859657	+	1.80400i	−0.0287031	+	0.0602337i
$898$		−	3.64371i		−	0.121592i
$899$	9.09485	+	15.7527i	0.303330	+	0.525383i
$900$	9.21104	−	27.5019i	0.307035	−	0.916731i
$901$	−8.83906	+	15.3097i	−0.294472	+	0.510040i
$902$	6.71810	−	3.87870i	0.223688	−	0.129146i
$903$	23.2480	+	47.6022i	0.773646	+	1.58410i
$904$	−7.92214	+	13.7215i	−0.263486	+	0.456372i
$905$	49.0530	+	26.9441i	1.63058	+	0.895651i
$906$	6.34673	−	4.36539i	0.210856	−	0.145030i
$907$	−24.5689	−	14.1849i	−0.815796	−	0.471000i	0.0331683	−	0.999450i	$-0.489440\pi$
$907$	−24.5689	−	14.1849i	−0.815796	−	0.471000i	−0.848965	+	0.528449i	$0.822774\pi$
$908$	−22.5029	−	12.9921i	−0.746786	−	0.431157i
$909$	−24.9384	+	3.96845i	−0.827153	+	0.131625i
$910$	−1.04260	+	1.37009i	−0.0345618	+	0.0454180i
$911$	8.96916	+	15.5350i	0.297162	+	0.514699i	0.975485	−	0.220064i	$-0.0706267\pi$
$911$	8.96916	+	15.5350i	0.297162	+	0.514699i	−0.678324	+	0.734763i	$0.737293\pi$
$912$	20.1871	+	29.3496i	0.668463	+	0.971862i
$913$		−	85.4224i		−	2.82707i
$914$	2.88751			0.0955103
$915$	−0.779081	+	0.560684i	−0.0257556	+	0.0185356i
$916$	−19.0496	−	32.9949i	−0.629417	−	1.09018i
$917$	1.30365	+	1.03663i	0.0430502	+	0.0342324i
$918$	3.76774	+	3.96170i	0.124354	+	0.130756i
$919$	28.3996	−	49.1896i	0.936818	−	1.62262i	0.165458	−	0.986217i	$-0.447090\pi$
$919$	28.3996	−	49.1896i	0.936818	−	1.62262i	0.771360	−	0.636400i	$-0.219577\pi$
$920$	0.0493558	+	2.31624i	0.00162721	+	0.0763643i
$921$	45.2607	+	21.5681i	1.49139	+	0.710691i
$922$	5.99045	−	3.45859i	0.197285	−	0.113903i
$923$	4.71056	+	2.71964i	0.155050	+	0.0895182i
$924$	39.4297	+	26.5656i	1.29714	+	0.873945i
$925$	−0.0723405	−	1.69668i	−0.00237854	−	0.0557866i
$926$	−2.51906	+	4.36314i	−0.0827814	+	0.143382i
$927$	30.1562	+	11.5507i	0.990460	+	0.379376i
$928$	9.97345	−	5.75818i	0.327395	−	0.189021i
$929$	−45.0348			−1.47755			−0.738773	−	0.673955i	$-0.764594\pi$
$929$	−45.0348			−1.47755			−0.738773	+	0.673955i	$0.764594\pi$
$930$	2.72368	+	3.78461i	0.0893130	+	0.124102i
$931$	8.99384	+	38.8997i	0.294761	+	1.27489i
$932$	−16.0036	−	9.23966i	−0.524214	−	0.302655i
$933$	24.4456	−	51.2992i	0.800311	−	1.67946i
$934$	4.66564	−	8.08113i	0.152664	−	0.264423i
$935$	−23.5793	+	42.9274i	−0.771127	+	1.40388i
$936$	3.39152	−	0.539693i	0.110855	−	0.0176404i
$937$		−	28.0807i		−	0.917355i	−0.888603	−	0.458678i	$-0.848323\pi$
$937$		−	28.0807i		−	0.917355i	0.888603	−	0.458678i	$-0.151677\pi$
$938$	−6.31490	+	2.48868i	−0.206189	+	0.0812582i
$939$	10.9807	+	5.23260i	0.358340	+	0.170760i
$940$	12.2881	−	22.3712i	0.400794	−	0.729667i
$941$	−55.2630			−1.80152			−0.900761	−	0.434315i	$-0.856990\pi$
$941$	−55.2630			−1.80152			−0.900761	+	0.434315i	$0.856990\pi$
$942$	−2.34577	+	4.92262i	−0.0764293	+	0.160387i
$943$			5.73169i			0.186649i
$944$	−25.7089			−0.836754
$945$	−30.5557	+	3.36928i	−0.993975	+	0.109603i
$946$	−15.9884			−0.519827
$947$		−	6.80967i		−	0.221284i	−0.993860	−	0.110642i	$-0.964709\pi$
$947$		−	6.80967i		−	0.221284i	0.993860	−	0.110642i	$-0.0352908\pi$
$948$	5.47141	−	11.4818i	0.177703	−	0.372911i
$949$	−5.37210			−0.174386
$950$	0.313128	+	7.34413i	0.0101592	+	0.238275i
$951$	−34.4009	−	16.3930i	−1.11553	−	0.531580i
$952$	8.57082	+	6.81529i	0.277782	+	0.220885i
$953$		−	8.21719i		−	0.266181i	−0.991104	−	0.133090i	$-0.957510\pi$
$953$		−	8.21719i		−	0.266181i	0.991104	−	0.133090i	$-0.0424901\pi$
$954$	1.19782	−	3.12723i	0.0387809	−	0.101248i
$955$	10.0823	+	5.53805i	0.326255	+	0.179207i
$956$	−27.5640	+	47.7422i	−0.891482	+	1.54409i
$957$	15.5695	−	32.6727i	0.503290	−	1.05616i
$958$	−2.97505	−	1.71764i	−0.0961194	−	0.0554946i
$959$	48.8919	+	7.29894i	1.57880	+	0.235695i
$960$	−20.2738	+	14.5905i	−0.654333	+	0.470906i
$961$	−9.18350			−0.296242
$962$	0.0855998	−	0.0494210i	0.00275985	−	0.00159340i
$963$	−2.83960	−	17.8445i	−0.0915050	−	0.575032i
$964$	3.65933	−	6.33815i	0.117859	−	0.204138i
$965$	−13.0999	+	23.8490i	−0.421700	+	0.767726i
$966$	1.08460	−	0.529700i	0.0348965	−	0.0170428i
$967$	−46.2872	−	26.7239i	−1.48850	−	0.859384i	−0.488583	−	0.872517i	$-0.662486\pi$
$967$	−46.2872	−	26.7239i	−1.48850	−	0.859384i	−0.999914	+	0.0131335i	$0.995819\pi$
$968$	−15.6216	+	9.01912i	−0.502096	+	0.289885i
$969$	36.4049	+	17.3480i	1.16949	+	0.557298i
$970$	0.0447696	+	2.10101i	0.00143746	+	0.0674595i
$971$	9.93424	−	17.2066i	0.318805	−	0.552186i	−0.661434	−	0.750003i	$-0.730052\pi$
$971$	9.93424	−	17.2066i	0.318805	−	0.552186i	0.980239	+	0.197817i	$0.0633852\pi$
$972$	23.9460	+	18.3053i	0.768068	+	0.587143i
$973$	−7.05333	+	47.2467i	−0.226119	+	1.51466i
$974$	−3.26863	−	5.66143i	−0.104734	−	0.181404i
$975$	−8.99795	−	3.82640i	−0.288165	−	0.122543i
$976$	0.893640			0.0286047
$977$			15.0890i			0.482740i	0.970433	+	0.241370i	$0.0775968\pi$
$977$			15.0890i			0.482740i	−0.970433	+	0.241370i	$0.922403\pi$
$978$	−4.42861	−	6.43864i	−0.141611	−	0.205885i
$979$	24.7109	+	42.8006i	0.789765	+	1.36791i
$980$	−29.3352	+	7.44424i	−0.937079	+	0.237798i
$981$	7.49286	−	19.5621i	0.239229	−	0.624570i
$982$	−3.16442	−	1.82698i	−0.100981	−	0.0583013i
$983$	32.8028	+	18.9387i	1.04625	+	0.604051i	0.921596	−	0.388150i	$-0.126886\pi$
$983$	32.8028	+	18.9387i	1.04625	+	0.604051i	0.124651	+	0.992201i	$0.460219\pi$
$984$	8.11558	−	5.58203i	0.258715	−	0.177949i
$985$	2.54686	−	4.63669i	0.0811497	−	0.147737i
$986$	2.04876	−	3.54855i	0.0652457	−	0.113009i
$987$	−26.9879	−	1.87297i	−0.859035	−	0.0596172i
$988$	10.7833	−	6.22576i	0.343064	−	0.198068i
$989$	5.90665	−	10.2306i	0.187821	−	0.325315i
$990$	3.13322	−	8.73268i	0.0995803	−	0.277543i
$991$	0.941984	+	1.63156i	0.0299231	+	0.0518283i	0.880599	−	0.473862i	$-0.157140\pi$
$991$	0.941984	+	1.63156i	0.0299231	+	0.0518283i	−0.850676	+	0.525690i	$0.823807\pi$
$992$		−	13.8126i		−	0.438550i
$993$	−17.8694	+	37.4991i	−0.567068	+	1.19000i
$994$	−1.20460	−	3.05662i	−0.0382076	−	0.0969502i
$995$	−0.0129192	−	0.606292i	−0.000409566	−	0.0192207i
$996$	−4.20251	−	53.1507i	−0.133161	−	1.68415i
$997$	1.68174	+	0.970952i	0.0532612	+	0.0307504i	0.526394	−	0.850241i	$-0.323544\pi$
$997$	1.68174	+	0.970952i	0.0532612	+	0.0307504i	−0.473133	+	0.880991i	$0.656877\pi$
$998$	4.55531	−	2.63001i	0.144196	−	0.0832516i
$999$	1.69272	+	0.499397i	0.0535552	+	0.0158002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.r.b.184.20	✓	84
3.2	odd	2		945.2.r.b.604.23		84
5.4	even	2	inner	315.2.r.b.184.23	yes	84
7.4	even	3		315.2.bo.b.4.23	yes	84
9.2	odd	6		945.2.bo.b.289.23		84
9.7	even	3		315.2.bo.b.79.20	yes	84
15.14	odd	2		945.2.r.b.604.20		84
21.11	odd	6		945.2.bo.b.739.20		84
35.4	even	6		315.2.bo.b.4.20	yes	84
45.29	odd	6		945.2.bo.b.289.20		84
45.34	even	6		315.2.bo.b.79.23	yes	84
63.11	odd	6		945.2.r.b.424.23		84
63.25	even	3	inner	315.2.r.b.214.20	yes	84
105.74	odd	6		945.2.bo.b.739.23		84
315.74	odd	6		945.2.r.b.424.20		84
315.214	even	6	inner	315.2.r.b.214.23	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.20	✓	84	1.1	even	1	trivial
315.2.r.b.184.23	yes	84	5.4	even	2	inner
315.2.r.b.214.20	yes	84	63.25	even	3	inner
315.2.r.b.214.23	yes	84	315.214	even	6	inner
315.2.bo.b.4.20	yes	84	35.4	even	6
315.2.bo.b.4.23	yes	84	7.4	even	3
315.2.bo.b.79.20	yes	84	9.7	even	3
315.2.bo.b.79.23	yes	84	45.34	even	6
945.2.r.b.424.20		84	315.74	odd	6
945.2.r.b.424.23		84	63.11	odd	6
945.2.r.b.604.20		84	15.14	odd	2
945.2.r.b.604.23		84	3.2	odd	2
945.2.bo.b.289.20		84	45.29	odd	6
945.2.bo.b.289.23		84	9.2	odd	6
945.2.bo.b.739.20		84	21.11	odd	6
945.2.bo.b.739.23		84	105.74	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.257756i q^{2} +(0.745098 - 1.56359i) q^{3} +1.93356 q^{4} +(-1.95987 - 1.07653i) q^{5} +(-0.403026 - 0.192053i) q^{6} +(-2.46150 + 0.970066i) q^{7} -1.01390i q^{8} +(-1.88966 - 2.33006i) q^{9} +O(q^{10})\)	\(q-0.257756i q^{2} +(0.745098 - 1.56359i) q^{3} +1.93356 q^{4} +(-1.95987 - 1.07653i) q^{5} +(-0.403026 - 0.192053i) q^{6} +(-2.46150 + 0.970066i) q^{7} -1.01390i q^{8} +(-1.88966 - 2.33006i) q^{9} +(-0.277481 + 0.505168i) q^{10} +(2.68286 - 4.64685i) q^{11} +(1.44069 - 3.02331i) q^{12} +(-0.977775 - 0.564519i) q^{13} +(0.250040 + 0.634466i) q^{14} +(-3.14355 + 2.26233i) q^{15} +3.60579 q^{16} +(3.53516 - 2.04103i) q^{17} +(-0.600588 + 0.487070i) q^{18} +(-2.85185 + 4.93955i) q^{19} +(-3.78953 - 2.08153i) q^{20} +(-0.317269 + 4.57158i) q^{21} +(-1.19775 - 0.691523i) q^{22} +(0.884981 - 0.510944i) q^{23} +(-1.58533 - 0.755454i) q^{24} +(2.68218 + 4.21970i) q^{25} +(-0.145508 + 0.252027i) q^{26} +(-5.05126 + 1.21853i) q^{27} +(-4.75946 + 1.87568i) q^{28} +(1.94717 + 3.37259i) q^{29} +(0.583128 + 0.810268i) q^{30} +4.67081 q^{31} -2.95721i q^{32} +(-5.26680 - 7.65727i) q^{33} +(-0.526087 - 0.911209i) q^{34} +(5.86852 + 0.748663i) q^{35} +(-3.65377 - 4.50532i) q^{36} +(-0.294141 - 0.169822i) q^{37} +(1.27320 + 0.735081i) q^{38} +(-1.61122 + 1.10822i) q^{39} +(-1.09149 + 1.98711i) q^{40} +(-2.80446 + 4.85747i) q^{41} +(1.17835 + 0.0817779i) q^{42} +(10.0115 - 5.78014i) q^{43} +(5.18748 - 8.98497i) q^{44} +(1.19511 + 6.60089i) q^{45} +(-0.131699 - 0.228109i) q^{46} +5.90341i q^{47} +(2.68667 - 5.63799i) q^{48} +(5.11795 - 4.77563i) q^{49} +(1.08765 - 0.691349i) q^{50} +(-0.557295 - 7.04833i) q^{51} +(-1.89059 - 1.09153i) q^{52} +(-3.75049 + 2.16535i) q^{53} +(0.314083 + 1.30199i) q^{54} +(-10.2605 + 6.21906i) q^{55} +(0.983548 + 2.49571i) q^{56} +(5.59854 + 8.13958i) q^{57} +(0.869305 - 0.501893i) q^{58} -7.12991 q^{59} +(-6.07824 + 4.37435i) q^{60} +0.247835 q^{61} -1.20393i q^{62} +(6.91170 + 3.90236i) q^{63} +6.44933 q^{64} +(1.30859 + 2.15898i) q^{65} +(-1.97371 + 1.35755i) q^{66} +9.95311i q^{67} +(6.83546 - 3.94645i) q^{68} +(-0.139511 - 1.76446i) q^{69} +(0.192972 - 1.51264i) q^{70} -4.81763 q^{71} +(-2.36245 + 1.91592i) q^{72} +(4.12066 - 2.37906i) q^{73} +(-0.0437727 + 0.0758166i) q^{74} +(8.59640 - 1.04976i) q^{75} +(-5.51422 + 9.55092i) q^{76} +(-2.09611 + 14.0408i) q^{77} +(0.285651 + 0.415301i) q^{78} +3.79776 q^{79} +(-7.06687 - 3.88172i) q^{80} +(-1.85840 + 8.80604i) q^{81} +(1.25204 + 0.722866i) q^{82} +(13.7872 - 7.96002i) q^{83} +(-0.613459 + 8.83943i) q^{84} +(-9.12568 + 0.194455i) q^{85} +(-1.48986 - 2.58052i) q^{86} +(6.72419 - 0.531666i) q^{87} +(-4.71144 - 2.72015i) q^{88} +(-4.60534 + 7.97667i) q^{89} +(1.70142 - 0.308046i) q^{90} +(2.95441 + 0.441056i) q^{91} +(1.71117 - 0.987942i) q^{92} +(3.48022 - 7.30326i) q^{93} +1.52164 q^{94} +(10.9068 - 6.61078i) q^{95} +(-4.62388 - 2.20341i) q^{96} +(3.15766 - 1.82307i) q^{97} +(-1.23095 - 1.31918i) q^{98} +(-15.8971 + 2.52972i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

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