LMFDB - Embedded newform 930.2.o.d.161.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.14
Character	$\chi$	$=$	930.161
Dual form			930.2.o.d.491.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.118080 - 1.72802i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.72802 + 0.118080i) q^{6} +(0.295093 + 0.511116i) q^{7} -1.00000i q^{8} +(-2.97211 - 0.408090i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.118080 - 1.72802i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.72802 + 0.118080i) q^{6} +(0.295093 + 0.511116i) q^{7} -1.00000i q^{8} +(-2.97211 - 0.408090i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.33844 + 4.05030i) q^{11} +(-0.118080 + 1.72802i) q^{12} +(2.48977 + 1.43747i) q^{13} +(-0.511116 + 0.295093i) q^{14} +(0.966271 - 1.43747i) q^{15} +1.00000 q^{16} +(1.50350 + 2.60413i) q^{17} +(0.408090 - 2.97211i) q^{18} +(1.44058 + 2.49515i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.918064 - 0.449574i) q^{21} +(-4.05030 - 2.33844i) q^{22} +0.585340 q^{23} +(-1.72802 - 0.118080i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.43747 + 2.48977i) q^{26} +(-1.05614 + 5.08769i) q^{27} +(-0.295093 - 0.511116i) q^{28} -5.47269 q^{29} +(1.43747 + 0.966271i) q^{30} +(4.99514 + 2.45939i) q^{31} +1.00000i q^{32} +(6.72288 + 4.51914i) q^{33} +(-2.60413 + 1.50350i) q^{34} +0.590186i q^{35} +(2.97211 + 0.408090i) q^{36} +(4.88163 - 2.81841i) q^{37} +(-2.49515 + 1.44058i) q^{38} +(2.77797 - 4.13264i) q^{39} +(0.500000 - 0.866025i) q^{40} +(4.52658 + 2.61342i) q^{41} +(0.449574 + 0.918064i) q^{42} +(2.86939 - 1.65664i) q^{43} +(2.33844 - 4.05030i) q^{44} +(-2.36988 - 1.83947i) q^{45} +0.585340i q^{46} +5.89031i q^{47} +(0.118080 - 1.72802i) q^{48} +(3.32584 - 5.76052i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(4.67753 - 2.29058i) q^{51} +(-2.48977 - 1.43747i) q^{52} +(0.900907 - 1.56042i) q^{53} +(-5.08769 - 1.05614i) q^{54} +(-4.05030 + 2.33844i) q^{55} +(0.511116 - 0.295093i) q^{56} +(4.48178 - 2.19472i) q^{57} -5.47269i q^{58} +(2.70209 - 1.56005i) q^{59} +(-0.966271 + 1.43747i) q^{60} +3.09464i q^{61} +(-2.45939 + 4.99514i) q^{62} +(-0.668468 - 1.63952i) q^{63} -1.00000 q^{64} +(1.43747 + 2.48977i) q^{65} +(-4.51914 + 6.72288i) q^{66} +(-5.77223 + 9.99779i) q^{67} +(-1.50350 - 2.60413i) q^{68} +(0.0691170 - 1.01148i) q^{69} -0.590186 q^{70} +(-1.46261 - 0.844440i) q^{71} +(-0.408090 + 2.97211i) q^{72} +(2.55082 + 1.47272i) q^{73} +(2.81841 + 4.88163i) q^{74} +(1.55555 - 0.761750i) q^{75} +(-1.44058 - 2.49515i) q^{76} -2.76023 q^{77} +(4.13264 + 2.77797i) q^{78} +(0.835902 - 0.482609i) q^{79} +(0.866025 + 0.500000i) q^{80} +(8.66692 + 2.42578i) q^{81} +(-2.61342 + 4.52658i) q^{82} +(-5.93914 + 10.2869i) q^{83} +(-0.918064 + 0.449574i) q^{84} +3.00699i q^{85} +(1.65664 + 2.86939i) q^{86} +(-0.646216 + 9.45692i) q^{87} +(4.05030 + 2.33844i) q^{88} -0.409193 q^{89} +(1.83947 - 2.36988i) q^{90} +1.69675i q^{91} -0.585340 q^{92} +(4.83970 - 8.34130i) q^{93} -5.89031 q^{94} +2.88115i q^{95} +(1.72802 + 0.118080i) q^{96} -12.7800 q^{97} +(5.76052 + 3.32584i) q^{98} +(8.60300 - 11.0837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) $ 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9	$ 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9} - 18 q^{10} + 36 q^{16} - 4 q^{18} - 4 q^{19} + 72 q^{21} - 18 q^{22} + 18 q^{25} + 8 q^{28} + 52 q^{31} - 36 q^{33} + 18 q^{34} - 8 q^{36} - 54 q^{37} - 8 q^{39} + 18 q^{40} + 12 q^{42} - 18 q^{43} + 4 q^{45} - 62 q^{49} - 10 q^{51} - 18 q^{55} + 12 q^{57} + 88 q^{63} - 36 q^{64} - 4 q^{66} + 10 q^{67} + 46 q^{69} + 16 q^{70} + 4 q^{72} + 24 q^{73} + 4 q^{76} + 92 q^{78} + 42 q^{79} + 4 q^{81} - 12 q^{82} - 72 q^{84} - 16 q^{87} + 18 q^{88} + 8 q^{90} + 48 q^{93} - 92 q^{94} - 80 q^{97} - 18 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9 - 18 * q^10 + 36 * q^16 - 4 * q^18 - 4 * q^19 + 72 * q^21 - 18 * q^22 + 18 * q^25 + 8 * q^28 + 52 * q^31 - 36 * q^33 + 18 * q^34 - 8 * q^36 - 54 * q^37 - 8 * q^39 + 18 * q^40 + 12 * q^42 - 18 * q^43 + 4 * q^45 - 62 * q^49 - 10 * q^51 - 18 * q^55 + 12 * q^57 + 88 * q^63 - 36 * q^64 - 4 * q^66 + 10 * q^67 + 46 * q^69 + 16 * q^70 + 4 * q^72 + 24 * q^73 + 4 * q^76 + 92 * q^78 + 42 * q^79 + 4 * q^81 - 12 * q^82 - 72 * q^84 - 16 * q^87 + 18 * q^88 + 8 * q^90 + 48 * q^93 - 92 * q^94 - 80 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.118080	−	1.72802i	0.0681736	−	0.997673i
$3$	0.118080	−	1.72802i	0.0681736	−	0.997673i
$4$	−1.00000			−0.500000
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	1.72802	+	0.118080i	0.705462	+	0.0482060i
$7$	0.295093	+	0.511116i	0.111535	+	0.193184i	0.916389	−	0.400288i	$-0.131090\pi$
$7$	0.295093	+	0.511116i	0.111535	+	0.193184i	−0.804855	+	0.593472i	$0.797757\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.97211	−	0.408090i	−0.990705	−	0.136030i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.33844	+	4.05030i	−0.705067	+	1.22121i	0.261601	+	0.965176i	$0.415750\pi$
$11$	−2.33844	+	4.05030i	−0.705067	+	1.22121i	−0.966668	+	0.256035i	$0.917584\pi$
$12$	−0.118080	+	1.72802i	−0.0340868	+	0.498837i
$13$	2.48977	+	1.43747i	0.690538	+	0.398682i	0.803814	−	0.594881i	$-0.202801\pi$
$13$	2.48977	+	1.43747i	0.690538	+	0.398682i	−0.113275	+	0.993564i	$0.536134\pi$
$14$	−0.511116	+	0.295093i	−0.136601	+	0.0788669i
$15$	0.966271	−	1.43747i	0.249490	−	0.371153i
$16$	1.00000			0.250000
$17$	1.50350	+	2.60413i	0.364651	+	0.631595i	0.988720	−	0.149775i	$-0.0478549\pi$
$17$	1.50350	+	2.60413i	0.364651	+	0.631595i	−0.624069	+	0.781369i	$0.714522\pi$
$18$	0.408090	−	2.97211i	0.0961878	−	0.700534i
$19$	1.44058	+	2.49515i	0.330491	+	0.572427i	0.982608	−	0.185691i	$-0.0594524\pi$
$19$	1.44058	+	2.49515i	0.330491	+	0.572427i	−0.652117	+	0.758118i	$0.726119\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	0.918064	−	0.449574i	0.200338	−	0.0981051i
$22$	−4.05030	−	2.33844i	−0.863527	−	0.498557i
$23$	0.585340			0.122052			0.0610259	−	0.998136i	$-0.480563\pi$
$23$	0.585340			0.122052			0.0610259	+	0.998136i	$0.480563\pi$
$24$	−1.72802	−	0.118080i	−0.352731	−	0.0241030i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−1.43747	+	2.48977i	−0.281911	+	0.488284i
$27$	−1.05614	+	5.08769i	−0.203254	+	0.979126i
$28$	−0.295093	−	0.511116i	−0.0557673	−	0.0965918i
$29$	−5.47269			−1.01625			−0.508126	−	0.861283i	$-0.669662\pi$
$29$	−5.47269			−1.01625			−0.508126	+	0.861283i	$0.669662\pi$
$30$	1.43747	+	0.966271i	0.262445	+	0.176416i
$31$	4.99514	+	2.45939i	0.897154	+	0.441719i
$31$	4.99514	+	2.45939i	0.897154	+	0.441719i
$32$			1.00000i			0.176777i
$33$	6.72288	+	4.51914i	1.17030	+	0.786681i
$34$	−2.60413	+	1.50350i	−0.446605	+	0.257847i
$35$			0.590186i			0.0997596i
$36$	2.97211	+	0.408090i	0.495352	+	0.0680150i
$37$	4.88163	−	2.81841i	0.802536	−	0.463344i	−0.0418213	−	0.999125i	$-0.513316\pi$
$37$	4.88163	−	2.81841i	0.802536	−	0.463344i	0.844357	+	0.535781i	$0.179983\pi$
$38$	−2.49515	+	1.44058i	−0.404767	+	0.233692i
$39$	2.77797	−	4.13264i	0.444831	−	0.661752i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	4.52658	+	2.61342i	0.706932	+	0.408148i	0.809924	−	0.586535i	$-0.199508\pi$
$41$	4.52658	+	2.61342i	0.706932	+	0.408148i	−0.102992	+	0.994682i	$0.532842\pi$
$42$	0.449574	+	0.918064i	0.0693708	+	0.141660i
$43$	2.86939	−	1.65664i	0.437578	−	0.252635i	−0.264992	−	0.964251i	$-0.585369\pi$
$43$	2.86939	−	1.65664i	0.437578	−	0.252635i	0.702570	+	0.711615i	$0.252036\pi$
$44$	2.33844	−	4.05030i	0.352533	−	0.610606i
$45$	−2.36988	−	1.83947i	−0.353281	−	0.274213i
$46$			0.585340i			0.0863036i
$47$			5.89031i			0.859191i	0.903022	+	0.429595i	$0.141344\pi$
$47$			5.89031i			0.859191i	−0.903022	+	0.429595i	$0.858656\pi$
$48$	0.118080	−	1.72802i	0.0170434	−	0.249418i
$49$	3.32584	−	5.76052i	0.475120	−	0.822932i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	4.67753	−	2.29058i	0.654985	−	0.320745i
$52$	−2.48977	−	1.43747i	−0.345269	−	0.199341i
$53$	0.900907	−	1.56042i	0.123749	−	0.214340i	−0.797494	−	0.603327i	$-0.793842\pi$
$53$	0.900907	−	1.56042i	0.123749	−	0.214340i	0.921243	+	0.388987i	$0.127175\pi$
$54$	−5.08769	−	1.05614i	−0.692347	−	0.143722i
$55$	−4.05030	+	2.33844i	−0.546142	+	0.315315i
$56$	0.511116	−	0.295093i	0.0683007	−	0.0394334i
$57$	4.48178	−	2.19472i	0.593626	−	0.290697i
$58$		−	5.47269i		−	0.718599i
$59$	2.70209	−	1.56005i	0.351783	−	0.203102i	−0.313687	−	0.949526i	$-0.601564\pi$
$59$	2.70209	−	1.56005i	0.351783	−	0.203102i	0.665470	+	0.746424i	$0.268231\pi$
$60$	−0.966271	+	1.43747i	−0.124745	+	0.185577i
$61$			3.09464i			0.396228i	0.980179	+	0.198114i	$0.0634816\pi$
$61$			3.09464i			0.396228i	−0.980179	+	0.198114i	$0.936518\pi$
$62$	−2.45939	+	4.99514i	−0.312342	+	0.634383i
$63$	−0.668468	−	1.63952i	−0.0842191	−	0.206560i
$64$	−1.00000			−0.125000
$65$	1.43747	+	2.48977i	0.178296	+	0.308818i
$66$	−4.51914	+	6.72288i	−0.556267	+	0.827529i
$67$	−5.77223	+	9.99779i	−0.705190	+	1.22142i	0.261433	+	0.965222i	$0.415805\pi$
$67$	−5.77223	+	9.99779i	−0.705190	+	1.22142i	−0.966623	+	0.256203i	$0.917528\pi$
$68$	−1.50350	−	2.60413i	−0.182326	−	0.315797i
$69$	0.0691170	−	1.01148i	0.00832071	−	0.121768i
$70$	−0.590186			−0.0705407
$71$	−1.46261	−	0.844440i	−0.173580	−	0.100217i	0.410693	−	0.911774i	$-0.365287\pi$
$71$	−1.46261	−	0.844440i	−0.173580	−	0.100217i	−0.584273	+	0.811557i	$0.698620\pi$
$72$	−0.408090	+	2.97211i	−0.0480939	+	0.350267i
$73$	2.55082	+	1.47272i	0.298551	+	0.172369i	0.641792	−	0.766879i	$-0.278191\pi$
$73$	2.55082	+	1.47272i	0.298551	+	0.172369i	−0.343241	+	0.939248i	$0.611525\pi$
$74$	2.81841	+	4.88163i	0.327634	+	0.567479i
$75$	1.55555	−	0.761750i	0.179619	−	0.0879593i
$76$	−1.44058	−	2.49515i	−0.165245	−	0.286213i
$77$	−2.76023			−0.314557
$78$	4.13264	+	2.77797i	0.467929	+	0.314543i
$79$	0.835902	−	0.482609i	0.0940464	−	0.0542977i	−0.452239	−	0.891897i	$-0.649375\pi$
$79$	0.835902	−	0.482609i	0.0940464	−	0.0542977i	0.546286	+	0.837599i	$0.316041\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$	8.66692	+	2.42578i	0.962992	+	0.269531i
$82$	−2.61342	+	4.52658i	−0.288604	+	0.499877i
$83$	−5.93914	+	10.2869i	−0.651905	+	1.12913i	0.330755	+	0.943717i	$0.392697\pi$
$83$	−5.93914	+	10.2869i	−0.651905	+	1.12913i	−0.982660	+	0.185416i	$0.940637\pi$
$84$	−0.918064	+	0.449574i	−0.100169	+	0.0490525i
$85$			3.00699i			0.326154i
$86$	1.65664	+	2.86939i	0.178640	+	0.309414i
$87$	−0.646216	+	9.45692i	−0.0692816	+	1.01389i
$88$	4.05030	+	2.33844i	0.431763	+	0.249279i
$89$	−0.409193			−0.0433744			−0.0216872	−	0.999765i	$-0.506904\pi$
$89$	−0.409193			−0.0433744			−0.0216872	+	0.999765i	$0.506904\pi$
$90$	1.83947	−	2.36988i	0.193898	−	0.249807i
$91$			1.69675i			0.177868i
$92$	−0.585340			−0.0610259
$93$	4.83970	−	8.34130i	0.501853	−	0.864953i
$94$	−5.89031			−0.607539
$95$			2.88115i			0.295600i
$96$	1.72802	+	0.118080i	0.176365	+	0.0120515i
$97$	−12.7800			−1.29761			−0.648805	−	0.760954i	$-0.724731\pi$
$97$	−12.7800			−1.29761			−0.648805	+	0.760954i	$0.724731\pi$
$98$	5.76052	+	3.32584i	0.581901	+	0.335961i
$99$	8.60300	−	11.0837i	0.864634	−	1.11395i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$		−	5.87075i		−	0.584161i	−0.956394	−	0.292081i	$-0.905652\pi$
$101$		−	5.87075i		−	0.584161i	0.956394	−	0.292081i	$-0.0943476\pi$
$102$	2.29058	+	4.67753i	0.226801	+	0.463144i
$103$	−2.59197	+	4.48942i	−0.255394	+	0.442355i	−0.965002	−	0.262241i	$-0.915539\pi$
$103$	−2.59197	+	4.48942i	−0.255394	+	0.442355i	0.709608	+	0.704596i	$0.248872\pi$
$104$	1.43747	−	2.48977i	0.140956	−	0.244142i
$105$	1.01985	+	0.0696893i	0.0995275	+	0.00680097i
$106$	1.56042	+	0.900907i	0.151561	+	0.0875038i
$107$	8.33944	−	4.81478i	0.806204	−	0.465462i	−0.0394317	−	0.999222i	$-0.512555\pi$
$107$	8.33944	−	4.81478i	0.806204	−	0.465462i	0.845636	+	0.533760i	$0.179221\pi$
$108$	1.05614	−	5.08769i	0.101627	−	0.489563i
$109$	−12.5936			−1.20625			−0.603126	−	0.797646i	$-0.706078\pi$
$109$	−12.5936			−1.20625			−0.603126	+	0.797646i	$0.706078\pi$
$110$	−2.33844	−	4.05030i	−0.222962	−	0.386181i
$111$	−4.29385	−	8.76837i	−0.407554	−	0.832257i
$112$	0.295093	+	0.511116i	0.0278837	+	0.0482959i
$113$	5.55484	+	3.20709i	0.522555	+	0.301697i	0.737979	−	0.674823i	$-0.235780\pi$
$113$	5.55484	+	3.20709i	0.522555	+	0.301697i	−0.215424	+	0.976521i	$0.569113\pi$
$114$	2.19472	+	4.48178i	0.205554	+	0.419757i
$115$	0.506919	+	0.292670i	0.0472704	+	0.0272916i
$116$	5.47269			0.508126
$117$	−6.81327	−	5.28838i	−0.629887	−	0.488911i
$118$	1.56005	+	2.70209i	0.143615	+	0.248748i
$119$	−0.887342	+	1.53692i	−0.0813425	+	0.140889i
$120$	−1.43747	−	0.966271i	−0.131222	−	0.0882081i
$121$	−5.43661	−	9.41649i	−0.494238	−	0.856045i
$122$	−3.09464			−0.280175
$123$	5.05054	−	7.51342i	0.455392	−	0.677463i
$124$	−4.99514	−	2.45939i	−0.448577	−	0.220859i
$125$			1.00000i			0.0894427i
$126$	1.63952	−	0.668468i	0.146060	−	0.0595519i
$127$	−13.1713	+	7.60444i	−1.16876	+	0.674785i	−0.953388	−	0.301746i	$-0.902430\pi$
$127$	−13.1713	+	7.60444i	−1.16876	+	0.674785i	−0.215374	+	0.976532i	$0.569097\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−2.52389	−	5.15398i	−0.222216	−	0.453783i
$130$	−2.48977	+	1.43747i	−0.218367	+	0.126074i
$131$	0.744839	−	0.430033i	0.0650769	−	0.0375721i	−0.467109	−	0.884200i	$-0.654704\pi$
$131$	0.744839	−	0.430033i	0.0650769	−	0.0375721i	0.532185	+	0.846628i	$0.321371\pi$
$132$	−6.72288	−	4.51914i	−0.585151	−	0.393340i
$133$	−0.850207	+	1.47260i	−0.0737223	+	0.127691i
$134$	−9.99779	−	5.77223i	−0.863678	−	0.498645i
$135$	−3.45849	+	3.87800i	−0.297659	+	0.333765i
$136$	2.60413	−	1.50350i	0.223302	−	0.128924i
$137$	7.56206	−	13.0979i	0.646071	−	1.11903i	−0.337982	−	0.941152i	$-0.609744\pi$
$137$	7.56206	−	13.0979i	0.646071	−	1.11903i	0.984053	−	0.177875i	$-0.0569222\pi$
$138$	1.01148	+	0.0691170i	0.0861028	+	0.00588363i
$139$		−	6.63378i		−	0.562670i	−0.959610	−	0.281335i	$-0.909223\pi$
$139$		−	6.63378i		−	0.562670i	0.959610	−	0.281335i	$-0.0907772\pi$
$140$		−	0.590186i		−	0.0498798i
$141$	10.1786	+	0.695530i	0.857192	+	0.0585742i
$142$	0.844440	−	1.46261i	0.0708639	−	0.122740i
$143$	−11.6444	+	6.72288i	−0.973751	+	0.562195i
$144$	−2.97211	−	0.408090i	−0.247676	−	0.0340075i
$145$	−4.73949	−	2.73634i	−0.393593	−	0.227241i
$146$	−1.47272	+	2.55082i	−0.121883	+	0.211108i
$147$	−9.56159	−	6.42733i	−0.788627	−	0.530117i
$148$	−4.88163	+	2.81841i	−0.401268	+	0.231672i
$149$	18.2286	−	10.5243i	1.49334	−	0.862182i	0.493373	−	0.869818i	$-0.335764\pi$
$149$	18.2286	−	10.5243i	1.49334	−	0.862182i	0.999971	+	0.00763584i	$0.00243059\pi$
$150$	0.761750	+	1.55555i	0.0621966	+	0.127010i
$151$		−	16.8681i		−	1.37271i	−0.727268	−	0.686353i	$-0.759210\pi$
$151$		−	16.8681i		−	1.37271i	0.727268	−	0.686353i	$-0.240790\pi$
$152$	2.49515	−	1.44058i	0.202383	−	0.116846i
$153$	−3.40584	−	8.35334i	−0.275346	−	0.675327i
$154$		−	2.76023i		−	0.222426i
$155$	3.09622	+	4.62746i	0.248695	+	0.371687i
$156$	−2.77797	+	4.13264i	−0.222416	+	0.330876i
$157$	1.10936			0.0885362			0.0442681	−	0.999020i	$-0.485904\pi$
$157$	1.10936			0.0885362			0.0442681	+	0.999020i	$0.485904\pi$
$158$	0.482609	+	0.835902i	0.0383943	+	0.0665008i
$159$	−2.59005	−	1.74104i	−0.205405	−	0.138074i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	0.172730	+	0.299176i	0.0136130	+	0.0235784i
$162$	−2.42578	+	8.66692i	−0.190587	+	0.680938i
$163$	−9.25474			−0.724887			−0.362444	−	0.932006i	$-0.618057\pi$
$163$	−9.25474			−0.724887			−0.362444	+	0.932006i	$0.618057\pi$
$164$	−4.52658	−	2.61342i	−0.353466	−	0.204074i
$165$	3.56262	+	7.27513i	0.277349	+	0.566368i
$166$	−10.2869	−	5.93914i	−0.798418	−	0.460967i
$167$	4.64334	+	8.04251i	0.359313	+	0.622348i	0.987846	−	0.155435i	$-0.0496778\pi$
$167$	4.64334	+	8.04251i	0.359313	+	0.622348i	−0.628533	+	0.777783i	$0.716344\pi$
$168$	−0.449574	−	0.918064i	−0.0346854	−	0.0708301i
$169$	−2.36736	−	4.10039i	−0.182105	−	0.315414i
$170$	−3.00699			−0.230626
$171$	−3.26331	−	8.00376i	−0.249551	−	0.612062i
$172$	−2.86939	+	1.65664i	−0.218789	+	0.126318i
$173$	−20.5960	−	11.8911i	−1.56588	−	0.904064i	−0.996641	−	0.0818953i	$-0.973903\pi$
$173$	−20.5960	−	11.8911i	−1.56588	−	0.904064i	−0.569244	−	0.822169i	$-0.692764\pi$
$174$	−9.45692	−	0.646216i	−0.716927	−	0.0489895i
$175$	−0.295093	+	0.511116i	−0.0223069	+	0.0386367i
$176$	−2.33844	+	4.05030i	−0.176267	+	0.305303i
$177$	−2.37674	−	4.85349i	−0.178647	−	0.364810i
$178$		−	0.409193i		−	0.0306703i
$179$	8.98349	+	15.5599i	0.671458	+	1.16300i	0.977491	+	0.210978i	$0.0676648\pi$
$179$	8.98349	+	15.5599i	0.671458	+	1.16300i	−0.306033	+	0.952021i	$0.599002\pi$
$180$	2.36988	+	1.83947i	0.176641	+	0.137106i
$181$	−0.555527	−	0.320734i	−0.0412920	−	0.0238399i	0.479212	−	0.877699i	$-0.340923\pi$
$181$	−0.555527	−	0.320734i	−0.0412920	−	0.0238399i	−0.520504	+	0.853859i	$0.674256\pi$
$182$	−1.69675			−0.125771
$183$	5.34760	+	0.365416i	0.395306	+	0.0270123i
$184$		−	0.585340i		−	0.0431518i
$185$	5.63683			0.414428
$186$	8.34130	+	4.83970i	0.611614	+	0.354864i
$187$	−14.0633			−1.02841
$188$		−	5.89031i		−	0.429595i
$189$	−2.91206	+	0.961533i	−0.211821	+	0.0699412i
$190$	−2.88115			−0.209021
$191$	−16.3559	−	9.44308i	−1.18347	−	0.683277i	−0.226656	−	0.973975i	$-0.572779\pi$
$191$	−16.3559	−	9.44308i	−1.18347	−	0.683277i	−0.956815	+	0.290698i	$0.906113\pi$
$192$	−0.118080	+	1.72802i	−0.00852171	+	0.124709i
$193$	−3.18956	−	5.52448i	−0.229590	−	0.397661i	0.728097	−	0.685474i	$-0.240405\pi$
$193$	−3.18956	−	5.52448i	−0.229590	−	0.397661i	−0.957687	+	0.287813i	$0.907072\pi$
$194$		−	12.7800i		−	0.917549i
$195$	4.47211	−	2.18999i	0.320255	−	0.156828i
$196$	−3.32584	+	5.76052i	−0.237560	+	0.411466i
$197$	6.47331	−	11.2121i	0.461204	−	0.798829i	−0.537817	−	0.843061i	$-0.680751\pi$
$197$	6.47331	−	11.2121i	0.461204	−	0.798829i	0.999021	+	0.0442328i	$0.0140843\pi$
$198$	11.0837	+	8.60300i	0.787681	+	0.611389i
$199$	12.4215	+	7.17157i	0.880539	+	0.508379i	0.870836	−	0.491574i	$-0.163578\pi$
$199$	12.4215	+	7.17157i	0.880539	+	0.508379i	0.00970264	+	0.999953i	$0.496912\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	16.5948	+	11.1551i	1.17051	+	0.786818i
$202$	5.87075			0.413064
$203$	−1.61495	−	2.79718i	−0.113347	−	0.196323i
$204$	−4.67753	+	2.29058i	−0.327492	+	0.160372i
$205$	2.61342	+	4.52658i	0.182529	+	0.316150i
$206$	−4.48942	−	2.59197i	−0.312793	−	0.180591i
$207$	−1.73970	−	0.238871i	−0.120917	−	0.0166027i
$208$	2.48977	+	1.43747i	0.172635	+	0.0996706i
$209$	−13.4748			−0.932072
$210$	−0.0696893	+	1.01985i	−0.00480902	+	0.0703766i
$211$	0.525922	+	0.910924i	0.0362060	+	0.0627106i	0.883561	−	0.468317i	$-0.155139\pi$
$211$	0.525922	+	0.910924i	0.0362060	+	0.0627106i	−0.847355	+	0.531027i	$0.821806\pi$
$212$	−0.900907	+	1.56042i	−0.0618746	+	0.107170i
$213$	−1.63192	+	2.42772i	−0.111817	+	0.166344i
$214$	4.81478	+	8.33944i	0.329132	+	0.570073i
$215$	3.31328			0.225964
$216$	5.08769	+	1.05614i	0.346173	+	0.0718610i
$217$	0.216999	+	3.27884i	0.0147308	+	0.222582i
$218$		−	12.5936i		−	0.852949i
$219$	2.84609	−	4.23398i	0.192321	−	0.286106i
$220$	4.05030	−	2.33844i	0.273071	−	0.157658i
$221$			8.64492i			0.581520i
$222$	8.76837	−	4.29385i	0.588494	−	0.288185i
$223$	−6.76345	+	3.90488i	−0.452914	+	0.261490i	−0.709060	−	0.705148i	$-0.750881\pi$
$223$	−6.76345	+	3.90488i	−0.452914	+	0.261490i	0.256146	+	0.966638i	$0.417547\pi$
$224$	−0.511116	+	0.295093i	−0.0341504	+	0.0197167i
$225$	−1.13264	−	2.77797i	−0.0755094	−	0.185198i
$226$	−3.20709	+	5.55484i	−0.213332	+	0.369502i
$227$	18.1094	+	10.4554i	1.20196	+	0.693952i	0.960991	−	0.276581i	$-0.0892013\pi$
$227$	18.1094	+	10.4554i	1.20196	+	0.693952i	0.240970	+	0.970533i	$0.422535\pi$
$228$	−4.48178	+	2.19472i	−0.296813	+	0.145349i
$229$	12.3777	−	7.14624i	0.817938	−	0.472237i	−0.0317667	−	0.999495i	$-0.510113\pi$
$229$	12.3777	−	7.14624i	0.817938	−	0.472237i	0.849705	+	0.527258i	$0.176780\pi$
$230$	−0.292670	+	0.506919i	−0.0192981	+	0.0334253i
$231$	−0.325928	+	4.76973i	−0.0214445	+	0.313825i
$232$			5.47269i			0.359300i
$233$		−	16.5863i		−	1.08661i	−0.839537	−	0.543303i	$-0.817173\pi$
$233$		−	16.5863i		−	1.08661i	0.839537	−	0.543303i	$-0.182827\pi$
$234$	5.28838	−	6.81327i	0.345712	−	0.445397i
$235$	−2.94516	+	5.10116i	−0.192121	+	0.332763i
$236$	−2.70209	+	1.56005i	−0.175891	+	0.101551i
$237$	−0.735254	−	1.50144i	−0.0477599	−	0.0975292i
$238$	−1.53692	−	0.887342i	−0.0996238	−	0.0575178i
$239$	−2.30620	+	3.99446i	−0.149176	+	0.258380i	−0.930923	−	0.365215i	$-0.880995\pi$
$239$	−2.30620	+	3.99446i	−0.149176	+	0.258380i	0.781747	+	0.623596i	$0.214329\pi$
$240$	0.966271	−	1.43747i	0.0623725	−	0.0927883i
$241$	18.4433	−	10.6482i	1.18804	−	0.685913i	0.230176	−	0.973149i	$-0.426070\pi$
$241$	18.4433	−	10.6482i	1.18804	−	0.685913i	0.957860	+	0.287236i	$0.0927365\pi$
$242$	9.41649	−	5.43661i	0.605315	−	0.349479i
$243$	5.21519	−	14.6902i	0.334555	−	0.942376i
$244$		−	3.09464i		−	0.198114i
$245$	5.76052	−	3.32584i	0.368026	−	0.212480i
$246$	7.51342	+	5.05054i	0.479038	+	0.322011i
$247$			8.28314i			0.527043i
$248$	2.45939	−	4.99514i	0.156171	−	0.317192i
$249$	17.0747	+	11.4776i	1.08206	+	0.727366i
$250$	−1.00000			−0.0632456
$251$	−13.6875	−	23.7075i	−0.863949	−	1.49640i	−0.868087	−	0.496412i	$-0.834650\pi$
$251$	−13.6875	−	23.7075i	−0.863949	−	1.49640i	0.00413772	−	0.999991i	$-0.498683\pi$
$252$	0.668468	+	1.63952i	0.0421095	+	0.103280i
$253$	−1.36878	+	2.37080i	−0.0860546	+	0.149051i
$254$	−7.60444	−	13.1713i	−0.477145	−	0.826440i
$255$	5.19614	+	0.355066i	0.325395	+	0.0222351i
$256$	1.00000			0.0625000
$257$	7.08285	+	4.08929i	0.441816	+	0.255083i	0.704368	−	0.709835i	$-0.251231\pi$
$257$	7.08285	+	4.08929i	0.441816	+	0.255083i	−0.262552	+	0.964918i	$0.584564\pi$
$258$	5.15398	−	2.52389i	0.320873	−	0.157131i
$259$	2.88107	+	1.66339i	0.179021	+	0.103358i
$260$	−1.43747	−	2.48977i	−0.0891481	−	0.154409i
$261$	16.2655	+	2.23335i	1.00681	+	0.138241i
$262$	0.430033	+	0.744839i	0.0265675	+	0.0460163i
$263$	1.95456			0.120523			0.0602617	−	0.998183i	$-0.480806\pi$
$263$	1.95456			0.120523			0.0602617	+	0.998183i	$0.480806\pi$
$264$	4.51914	−	6.72288i	0.278134	−	0.413765i
$265$	1.56042	−	0.900907i	0.0958557	−	0.0553423i
$266$	−1.47260	−	0.850207i	−0.0902910	−	0.0521295i
$267$	−0.0483176	+	0.707095i	−0.00295699	+	0.0432735i
$268$	5.77223	−	9.99779i	0.352595	−	0.610712i
$269$	2.52744	−	4.37765i	0.154101	−	0.266910i	−0.778631	−	0.627483i	$-0.784085\pi$
$269$	2.52744	−	4.37765i	0.154101	−	0.266910i	0.932731	+	0.360572i	$0.117419\pi$
$270$	−3.87800	−	3.45849i	−0.236008	−	0.210477i
$271$			9.67395i			0.587651i	0.955859	+	0.293825i	$0.0949284\pi$
$271$			9.67395i			0.587651i	−0.955859	+	0.293825i	$0.905072\pi$
$272$	1.50350	+	2.60413i	0.0911628	+	0.157899i
$273$	2.93202	+	0.200352i	0.177454	+	0.0121259i
$274$	13.0979	+	7.56206i	0.791272	+	0.456841i
$275$	−4.67688			−0.282027
$276$	−0.0691170	+	1.01148i	−0.00416036	+	0.0608839i
$277$			16.9377i			1.01769i	0.860859	+	0.508843i	$0.169927\pi$
$277$			16.9377i			1.01769i	−0.860859	+	0.508843i	$0.830073\pi$
$278$	6.63378			0.397868
$279$	−13.8425	−	9.34804i	−0.828727	−	0.559653i
$280$	0.590186			0.0352703
$281$		−	23.8706i		−	1.42400i	−0.702180	−	0.711999i	$-0.747790\pi$
$281$		−	23.8706i		−	1.42400i	0.702180	−	0.711999i	$-0.252210\pi$
$282$	−0.695530	+	10.1786i	−0.0414182	+	0.606126i
$283$	−25.8177			−1.53470			−0.767352	−	0.641226i	$-0.778426\pi$
$283$	−25.8177			−1.53470			−0.767352	+	0.641226i	$0.778426\pi$
$284$	1.46261	+	0.844440i	0.0867902	+	0.0501083i
$285$	4.97869	+	0.340207i	0.294912	+	0.0201521i
$286$	−6.72288	−	11.6444i	−0.397532	−	0.688546i
$287$			3.08481i			0.182090i
$288$	0.408090	−	2.97211i	0.0240469	−	0.175134i
$289$	3.97900	−	6.89183i	0.234059	−	0.405402i
$290$	2.73634	−	4.73949i	0.160684	−	0.278312i
$291$	−1.50906	+	22.0841i	−0.0884629	+	1.29459i
$292$	−2.55082	−	1.47272i	−0.149276	−	0.0861844i
$293$	14.1888	−	8.19189i	0.828917	−	0.478575i	−0.0245650	−	0.999698i	$-0.507820\pi$
$293$	14.1888	−	8.19189i	0.828917	−	0.478575i	0.853482	+	0.521123i	$0.174487\pi$
$294$	6.42733	−	9.56159i	0.374849	−	0.557643i
$295$	3.12011			0.181660
$296$	−2.81841	−	4.88163i	−0.163817	−	0.283739i
$297$	−18.1369	−	16.1749i	−1.05241	−	0.938565i
$298$	10.5243	+	18.2286i	0.609655	+	1.05595i
$299$	1.45736	+	0.841408i	0.0842814	+	0.0486599i
$300$	−1.55555	+	0.761750i	−0.0898097	+	0.0439797i
$301$	1.69347	+	0.977726i	0.0976101	+	0.0563552i
$302$	16.8681			0.970650
$303$	−10.1448	−	0.693219i	−0.582802	−	0.0398244i
$304$	1.44058	+	2.49515i	0.0826227	+	0.143107i
$305$	−1.54732	+	2.68004i	−0.0885993	+	0.153458i
$306$	8.35334	−	3.40584i	0.477528	−	0.194699i
$307$	−11.2930	−	19.5601i	−0.644527	−	1.11635i	−0.984411	−	0.175886i	$-0.943721\pi$
$307$	−11.2930	−	19.5601i	−0.644527	−	1.11635i	0.339884	−	0.940467i	$-0.389612\pi$
$308$	2.76023			0.157279
$309$	7.45175	+	5.00908i	0.423915	+	0.284957i
$310$	−4.62746	+	3.09622i	−0.262822	+	0.175854i
$311$			7.76670i			0.440409i	0.975454	+	0.220205i	$0.0706725\pi$
$311$			7.76670i			0.440409i	−0.975454	+	0.220205i	$0.929327\pi$
$312$	−4.13264	−	2.77797i	−0.233965	−	0.157272i
$313$	−21.0679	+	12.1635i	−1.19083	+	0.687523i	−0.958494	−	0.285113i	$-0.907969\pi$
$313$	−21.0679	+	12.1635i	−1.19083	+	0.687523i	−0.232332	+	0.972637i	$0.574635\pi$
$314$			1.10936i			0.0626045i
$315$	0.240849	−	1.75410i	0.0135703	−	0.0988323i
$316$	−0.835902	+	0.482609i	−0.0470232	+	0.0271489i
$317$	−10.8728	+	6.27740i	−0.610676	+	0.352574i	−0.773230	−	0.634126i	$-0.781360\pi$
$317$	−10.8728	+	6.27740i	−0.610676	+	0.352574i	0.162554	+	0.986700i	$0.448027\pi$
$318$	1.74104	−	2.59005i	0.0976327	−	0.145243i
$319$	12.7976	−	22.1660i	0.716526	−	1.24106i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−7.33532	−	14.9793i	−0.409417	−	0.836061i
$322$	−0.299176	+	0.172730i	−0.0166724	+	0.00962584i
$323$	−4.33180	+	7.50289i	−0.241028	+	0.417472i
$324$	−8.66692	−	2.42578i	−0.481496	−	0.134766i
$325$			2.87494i			0.159473i
$326$		−	9.25474i		−	0.512573i
$327$	−1.48706	+	21.7621i	−0.0822346	+	1.20345i
$328$	2.61342	−	4.52658i	0.144302	−	0.249938i
$329$	−3.01063	+	1.73819i	−0.165982	+	0.0958295i
$330$	−7.27513	+	3.56262i	−0.400482	+	0.196116i
$331$	−21.1683	−	12.2215i	−1.16352	−	0.671757i	−0.211372	−	0.977406i	$-0.567793\pi$
$331$	−21.1683	−	12.2215i	−1.16352	−	0.671757i	−0.952144	+	0.305649i	$0.901127\pi$
$332$	5.93914	−	10.2869i	0.325953	−	0.564566i
$333$	−15.6589	+	6.38450i	−0.858105	+	0.349868i
$334$	−8.04251	+	4.64334i	−0.440066	+	0.254072i
$335$	−9.99779	+	5.77223i	−0.546238	+	0.315370i
$336$	0.918064	−	0.449574i	0.0500845	−	0.0245263i
$337$			7.97132i			0.434225i	0.976147	+	0.217113i	$0.0696639\pi$
$337$			7.97132i			0.434225i	−0.976147	+	0.217113i	$0.930336\pi$
$338$	4.10039	−	2.36736i	0.223032	−	0.128767i
$339$	6.19783	−	9.22018i	0.336620	−	0.500772i
$340$		−	3.00699i		−	0.163077i
$341$	−21.6421	+	14.4807i	−1.17198	+	0.784173i
$342$	8.00376	−	3.26331i	0.432794	−	0.176460i
$343$	8.05703			0.435039
$344$	−1.65664	−	2.86939i	−0.0893201	−	0.154707i
$345$	0.565597	−	0.841408i	0.0304507	−	0.0452999i
$346$	11.8911	−	20.5960i	0.639270	−	1.10725i
$347$	15.3080	+	26.5142i	0.821775	+	1.42336i	0.904359	+	0.426772i	$0.140349\pi$
$347$	15.3080	+	26.5142i	0.821775	+	1.42336i	−0.0825838	+	0.996584i	$0.526317\pi$
$348$	0.646216	−	9.45692i	0.0346408	−	0.506944i
$349$	21.2775			1.13896			0.569479	−	0.822006i	$-0.307145\pi$
$349$	21.2775			1.13896			0.569479	+	0.822006i	$0.307145\pi$
$350$	−0.511116	−	0.295093i	−0.0273203	−	0.0157734i
$351$	−9.94294	+	11.1490i	−0.530715	+	0.595090i
$352$	−4.05030	−	2.33844i	−0.215882	−	0.124639i
$353$	11.3691	+	19.6918i	0.605115	+	1.04809i	0.992033	+	0.125976i	$0.0402061\pi$
$353$	11.3691	+	19.6918i	0.605115	+	1.04809i	−0.386919	+	0.922114i	$0.626461\pi$
$354$	4.85349	−	2.37674i	0.257960	−	0.126323i
$355$	−0.844440	−	1.46261i	−0.0448182	−	0.0776275i
$356$	0.409193			0.0216872
$357$	2.55105	+	1.71483i	0.135016	+	0.0907582i
$358$	−15.5599	+	8.98349i	−0.822364	+	0.474792i
$359$	1.29984	+	0.750465i	0.0686031	+	0.0396080i	0.533909	−	0.845542i	$-0.320722\pi$
$359$	1.29984	+	0.750465i	0.0686031	+	0.0396080i	−0.465306	+	0.885150i	$0.654056\pi$
$360$	−1.83947	+	2.36988i	−0.0969488	+	0.124904i
$361$	5.34948	−	9.26558i	0.281552	−	0.487662i
$362$	0.320734	−	0.555527i	0.0168574	−	0.0291979i
$363$	−16.9139	+	8.28268i	−0.887747	+	0.434728i
$364$		−	1.69675i		−	0.0889338i
$365$	1.47272	+	2.55082i	0.0770857	+	0.133516i
$366$	−0.365416	+	5.34760i	−0.0191006	+	0.279524i
$367$	−2.43304	−	1.40472i	−0.127004	−	0.0733256i	0.435152	−	0.900357i	$-0.356695\pi$
$367$	−2.43304	−	1.40472i	−0.127004	−	0.0733256i	−0.562156	+	0.827031i	$0.690028\pi$
$368$	0.585340			0.0305129
$369$	−12.3870	−	9.61463i	−0.644841	−	0.500518i
$370$			5.63683i			0.293045i
$371$	1.06341			0.0552092
$372$	−4.83970	+	8.34130i	−0.250927	+	0.432476i
$373$	21.9797			1.13807			0.569033	−	0.822315i	$-0.307318\pi$
$373$	21.9797			1.13807			0.569033	+	0.822315i	$0.307318\pi$
$374$		−	14.0633i		−	0.727198i
$375$	1.72802	+	0.118080i	0.0892346	+	0.00609764i
$376$	5.89031			0.303770
$377$	−13.6257	−	7.86682i	−0.701761	−	0.405162i
$378$	−0.961533	−	2.91206i	−0.0494559	−	0.149780i
$379$	−10.2057	−	17.6768i	−0.524232	−	0.907997i	−0.999602	−	0.0282108i	$-0.991019\pi$
$379$	−10.2057	−	17.6768i	−0.524232	−	0.907997i	0.475370	−	0.879786i	$-0.342314\pi$
$380$		−	2.88115i		−	0.147800i
$381$	11.5854	+	23.6582i	0.593536	+	1.21205i
$382$	9.44308	−	16.3559i	0.483150	−	0.836840i
$383$	16.0251	−	27.7563i	0.818845	−	1.41828i	−0.0876892	−	0.996148i	$-0.527948\pi$
$383$	16.0251	−	27.7563i	0.818845	−	1.41828i	0.906534	−	0.422133i	$-0.138718\pi$
$384$	−1.72802	−	0.118080i	−0.0881827	−	0.00602576i
$385$	−2.39043	−	1.38011i	−0.121828	−	0.0703371i
$386$	5.52448	−	3.18956i	0.281189	−	0.162344i
$387$	−9.20421	+	3.75276i	−0.467876	+	0.190763i
$388$	12.7800			0.648805
$389$	18.6651	+	32.3290i	0.946360	+	1.63914i	0.753005	+	0.658015i	$0.228604\pi$
$389$	18.6651	+	32.3290i	0.946360	+	1.63914i	0.193356	+	0.981129i	$0.438063\pi$
$390$	2.18999	+	4.47211i	0.110894	+	0.226454i
$391$	0.880056	+	1.52430i	0.0445063	+	0.0770872i
$392$	−5.76052	−	3.32584i	−0.290950	−	0.167980i
$393$	−0.655155	−	1.33788i	−0.0330482	−	0.0674869i
$394$	11.2121	+	6.47331i	0.564857	+	0.326120i
$395$	0.965217			0.0485653
$396$	−8.60300	+	11.0837i	−0.432317	+	0.556975i
$397$	18.0304	+	31.2296i	0.904921	+	1.56737i	0.821024	+	0.570894i	$0.193403\pi$
$397$	18.0304	+	31.2296i	0.904921	+	1.56737i	0.0838969	+	0.996474i	$0.473263\pi$
$398$	−7.17157	+	12.4215i	−0.359478	+	0.622635i
$399$	2.44429	+	1.64306i	0.122368	+	0.0822559i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−36.7308			−1.83425			−0.917125	−	0.398599i	$-0.869496\pi$
$401$	−36.7308			−1.83425			−0.917125	+	0.398599i	$0.869496\pi$
$402$	−11.1551	+	16.5948i	−0.556364	+	0.827674i
$403$	8.90146	+	13.3037i	0.443413	+	0.662703i
$404$			5.87075i			0.292081i
$405$	6.29289	+	6.43425i	0.312696	+	0.319720i
$406$	2.79718	−	1.61495i	0.138822	−	0.0801487i
$407$			26.3628i			1.30675i
$408$	−2.29058	−	4.67753i	−0.113400	−	0.231572i
$409$	29.9703	−	17.3034i	1.48194	−	0.855597i	0.482148	−	0.876090i	$-0.339857\pi$
$409$	29.9703	−	17.3034i	1.48194	−	0.855597i	0.999790	+	0.0204926i	$0.00652345\pi$
$410$	−4.52658	+	2.61342i	−0.223552	+	0.129068i
$411$	−21.7405	−	14.6140i	−1.07238	−	0.720856i
$412$	2.59197	−	4.48942i	0.127697	−	0.221178i
$413$	1.59474	+	0.920722i	0.0784719	+	0.0453058i
$414$	0.238871	−	1.73970i	0.0117399	−	0.0855014i
$415$	−10.2869	+	5.93914i	−0.504964	+	0.291541i
$416$	−1.43747	+	2.48977i	−0.0704778	+	0.122071i
$417$	−11.4633	−	0.783318i	−0.561361	−	0.0383593i
$418$		−	13.4748i		−	0.659074i
$419$			2.99848i			0.146485i	0.997314	+	0.0732426i	$0.0233347\pi$
$419$			2.99848i			0.146485i	−0.997314	+	0.0732426i	$0.976665\pi$
$420$	−1.01985	−	0.0696893i	−0.0497637	−	0.00340049i
$421$	−9.94262	+	17.2211i	−0.484574	+	0.839306i	−0.999843	−	0.0177220i	$-0.994359\pi$
$421$	−9.94262	+	17.2211i	−0.484574	+	0.839306i	0.515269	+	0.857028i	$0.327692\pi$
$422$	−0.910924	+	0.525922i	−0.0443431	+	0.0256015i
$423$	2.40378	−	17.5067i	0.116876	−	0.851204i
$424$	−1.56042	−	0.900907i	−0.0757806	−	0.0437519i
$425$	−1.50350	+	2.60413i	−0.0729303	+	0.126319i
$426$	−2.42772	−	1.63192i	−0.117623	−	0.0790666i
$427$	−1.58172	+	0.913206i	−0.0765447	+	0.0441931i
$428$	−8.33944	+	4.81478i	−0.403102	+	0.232731i
$429$	10.2423	+	20.9156i	0.494503	+	1.00981i
$430$			3.31328i			0.159781i
$431$	5.57553	−	3.21903i	0.268564	−	0.155055i	−0.359671	−	0.933079i	$-0.617111\pi$
$431$	5.57553	−	3.21903i	0.268564	−	0.155055i	0.628235	+	0.778024i	$0.283778\pi$
$432$	−1.05614	+	5.08769i	−0.0508134	+	0.244782i
$433$			29.7643i			1.43038i	0.698929	+	0.715191i	$0.253661\pi$
$433$			29.7643i			1.43038i	−0.698929	+	0.715191i	$0.746339\pi$
$434$	−3.27884	+	0.216999i	−0.157389	+	0.0104163i
$435$	−5.28810	+	7.86682i	−0.253545	+	0.377185i
$436$	12.5936			0.603126
$437$	0.843226	+	1.46051i	0.0403370	+	0.0698657i
$438$	4.23398	+	2.84609i	0.202307	+	0.135992i
$439$	19.7500	−	34.2079i	0.942614	−	1.63266i	0.182155	−	0.983270i	$-0.441693\pi$
$439$	19.7500	−	34.2079i	0.942614	−	1.63266i	0.760459	−	0.649386i	$-0.224974\pi$
$440$	2.33844	+	4.05030i	0.111481	+	0.193090i
$441$	−12.2356	+	15.7637i	−0.582647	+	0.750652i
$442$	−8.64492			−0.411197
$443$	−10.5606	−	6.09717i	−0.501750	−	0.289685i	0.227686	−	0.973735i	$-0.426884\pi$
$443$	−10.5606	−	6.09717i	−0.501750	−	0.289685i	−0.729436	+	0.684049i	$0.760217\pi$
$444$	4.29385	+	8.76837i	0.203777	+	0.416128i
$445$	−0.354372	−	0.204597i	−0.0167988	−	0.00969881i
$446$	−3.90488	−	6.76345i	−0.184902	−	0.320259i
$447$	−16.0337	−	32.7421i	−0.758370	−	1.54865i
$448$	−0.295093	−	0.511116i	−0.0139418	−	0.0241480i
$449$	1.10717			0.0522506			0.0261253	−	0.999659i	$-0.491683\pi$
$449$	1.10717			0.0522506			0.0261253	+	0.999659i	$0.491683\pi$
$450$	2.77797	−	1.13264i	0.130955	−	0.0533932i
$451$	−21.1703	+	12.2227i	−0.996869	+	0.575542i
$452$	−5.55484	−	3.20709i	−0.261278	−	0.150849i
$453$	−29.1484	−	1.99179i	−1.36951	−	0.0935824i
$454$	−10.4554	+	18.1094i	−0.490698	+	0.849914i
$455$	−0.848374	+	1.46943i	−0.0397724	+	0.0688878i
$456$	−2.19472	−	4.48178i	−0.102777	−	0.209878i
$457$			8.27976i			0.387311i	0.981070	+	0.193655i	$0.0620344\pi$
$457$			8.27976i			0.387311i	−0.981070	+	0.193655i	$0.937966\pi$
$458$	7.14624	+	12.3777i	0.333922	+	0.578370i
$459$	−14.8369	+	4.89900i	−0.692527	+	0.228666i
$460$	−0.506919	−	0.292670i	−0.0236352	−	0.0136458i
$461$	−19.4170			−0.904338			−0.452169	−	0.891932i	$-0.649350\pi$
$461$	−19.4170			−0.904338			−0.452169	+	0.891932i	$0.649350\pi$
$462$	−4.76973	−	0.325928i	−0.221908	−	0.0151636i
$463$		−	34.1138i		−	1.58540i	−0.609610	−	0.792702i	$-0.708674\pi$
$463$		−	34.1138i		−	1.58540i	0.609610	−	0.792702i	$-0.291326\pi$
$464$	−5.47269			−0.254063
$465$	8.36195	−	4.80393i	0.387776	−	0.222777i
$466$	16.5863			0.768347
$467$			25.2788i			1.16976i	0.811118	+	0.584882i	$0.198859\pi$
$467$			25.2788i			1.16976i	−0.811118	+	0.584882i	$0.801141\pi$
$468$	6.81327	+	5.28838i	0.314943	+	0.244455i
$469$	−6.81337			−0.314612
$470$	−5.10116	−	2.94516i	−0.235299	−	0.135850i
$471$	0.130993	−	1.91699i	0.00603583	−	0.0883302i
$472$	−1.56005	−	2.70209i	−0.0718073	−	0.124374i
$473$			15.4958i			0.712499i
$474$	1.50144	−	0.735254i	0.0689636	−	0.0337713i
$475$	−1.44058	+	2.49515i	−0.0660981	+	0.114485i
$476$	0.887342	−	1.53692i	0.0406712	−	0.0704446i
$477$	−3.31439	+	4.27009i	−0.151755	+	0.195514i
$478$	−3.99446	−	2.30620i	−0.182702	−	0.105483i
$479$	16.1197	−	9.30670i	0.736527	−	0.425234i	−0.0842784	−	0.996442i	$-0.526859\pi$
$479$	16.1197	−	9.30670i	0.736527	−	0.425234i	0.820805	+	0.571208i	$0.193525\pi$
$480$	1.43747	+	0.966271i	0.0656112	+	0.0441040i
$481$	16.2055			0.738909
$482$	10.6482	+	18.4433i	0.485013	+	0.840068i
$483$	0.537379	−	0.263154i	0.0244516	−	0.0119739i
$484$	5.43661	+	9.41649i	0.247119	+	0.428022i
$485$	−11.0678	−	6.38999i	−0.502562	−	0.290155i
$486$	14.6902	+	5.21519i	0.666361	+	0.236566i
$487$	6.09365	+	3.51817i	0.276130	+	0.159424i	0.631670	−	0.775237i	$-0.282370\pi$
$487$	6.09365	+	3.51817i	0.276130	+	0.159424i	−0.355540	+	0.934661i	$0.615703\pi$
$488$	3.09464			0.140088
$489$	−1.09280	+	15.9924i	−0.0494182	+	0.723201i
$490$	3.32584	+	5.76052i	0.150246	+	0.260234i
$491$	−13.2084	+	22.8777i	−0.596088	+	1.03245i	0.397304	+	0.917687i	$0.369946\pi$
$491$	−13.2084	+	22.8777i	−0.596088	+	1.03245i	−0.993392	+	0.114768i	$0.963388\pi$
$492$	−5.05054	+	7.51342i	−0.227696	+	0.338731i
$493$	−8.22816	−	14.2516i	−0.370578	−	0.641860i
$494$	−8.28314			−0.372676
$495$	12.9922	−	5.29723i	0.583958	−	0.238093i
$496$	4.99514	+	2.45939i	0.224288	+	0.110430i
$497$		−	0.996753i		−	0.0447105i
$498$	−11.4776	+	17.0747i	−0.514325	+	0.765134i
$499$	10.7088	−	6.18273i	0.479392	−	0.276777i	−0.240771	−	0.970582i	$-0.577400\pi$
$499$	10.7088	−	6.18273i	0.479392	−	0.276777i	0.720163	+	0.693805i	$0.244067\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	14.4459	−	7.07413i	0.645396	−	0.316049i
$502$	23.7075	−	13.6875i	1.05812	−	0.610904i
$503$	−14.3552	+	8.28798i	−0.640067	+	0.369543i	−0.784640	−	0.619951i	$-0.787152\pi$
$503$	−14.3552	+	8.28798i	−0.640067	+	0.369543i	0.144574	+	0.989494i	$0.453819\pi$
$504$	−1.63952	+	0.668468i	−0.0730300	+	0.0297759i
$505$	2.93537	−	5.08422i	0.130622	−	0.226245i
$506$	−2.37080	−	1.36878i	−0.105395	−	0.0608498i
$507$	−7.36509	+	3.60667i	−0.327095	+	0.160178i
$508$	13.1713	−	7.60444i	0.584381	−	0.337393i
$509$	−19.8929	+	34.4556i	−0.881739	+	1.52722i	−0.0323336	+	0.999477i	$0.510294\pi$
$509$	−19.8929	+	34.4556i	−0.881739	+	1.52722i	−0.849406	+	0.527740i	$0.823039\pi$
$510$	−0.355066	+	5.19614i	−0.0157226	+	0.230089i
$511$			1.73836i			0.0769003i
$512$			1.00000i			0.0441942i
$513$	−14.2160	+	4.69398i	−0.627651	+	0.207244i
$514$	−4.08929	+	7.08285i	−0.180371	+	0.312411i
$515$	−4.48942	+	2.59197i	−0.197827	+	0.114216i
$516$	2.52389	+	5.15398i	0.111108	+	0.226891i
$517$	−23.8575	−	13.7742i	−1.04925	−	0.605787i
$518$	−1.66339	+	2.88107i	−0.0730850	+	0.126587i
$519$	−22.9801	+	34.1862i	−1.00871	+	1.50061i
$520$	2.48977	−	1.43747i	0.109184	−	0.0630372i
$521$	26.6298	−	15.3747i	1.16667	−	0.673578i	0.213778	−	0.976882i	$-0.431423\pi$
$521$	26.6298	−	15.3747i	1.16667	−	0.673578i	0.952894	+	0.303304i	$0.0980897\pi$
$522$	−2.23335	+	16.2655i	−0.0977511	+	0.711919i
$523$			13.9900i			0.611740i	0.952073	+	0.305870i	$0.0989473\pi$
$523$			13.9900i			0.611740i	−0.952073	+	0.305870i	$0.901053\pi$
$524$	−0.744839	+	0.430033i	−0.0325384	+	0.0187861i
$525$	0.848374	+	0.570279i	0.0370261	+	0.0248890i
$526$			1.95456i			0.0852229i
$527$	1.10561	+	16.7057i	0.0481610	+	0.727711i
$528$	6.72288	+	4.51914i	0.292576	+	0.196670i
$529$	−22.6574			−0.985103
$530$	0.900907	+	1.56042i	0.0391329	+	0.0677802i
$531$	−8.66758	+	3.53396i	−0.376141	+	0.153361i
$532$	0.850207	−	1.47260i	0.0368612	−	0.0638454i
$533$	7.51342	+	13.0136i	0.325443	+	0.563683i
$534$	−0.707095	−	0.0483176i	−0.0305990	−	0.00209091i
$535$	9.62956			0.416322
$536$	9.99779	+	5.77223i	0.431839	+	0.249322i
$537$	27.9485	−	13.6863i	1.20607	−	0.590610i
$538$	4.37765	+	2.52744i	0.188734	+	0.108966i
$539$	15.5546	+	26.9413i	0.669983	+	1.16044i
$540$	3.45849	−	3.87800i	0.148830	−	0.166883i
$541$	1.99719	+	3.45923i	0.0858657	+	0.148724i	0.905760	−	0.423791i	$-0.139301\pi$
$541$	1.99719	+	3.45923i	0.0858657	+	0.148724i	−0.819894	+	0.572515i	$0.805968\pi$
$542$	−9.67395			−0.415532
$543$	−0.619831	+	0.922090i	−0.0265995	+	0.0395707i
$544$	−2.60413	+	1.50350i	−0.111651	+	0.0644618i
$545$	−10.9064	−	6.29682i	−0.467179	−	0.269726i
$546$	−0.200352	+	2.93202i	−0.00857429	+	0.125479i
$547$	11.5236	−	19.9595i	0.492714	−	0.853407i	−0.507250	−	0.861799i	$-0.669338\pi$
$547$	11.5236	−	19.9595i	0.492714	−	0.853407i	0.999965	+	0.00839225i	$0.00267137\pi$
$548$	−7.56206	+	13.0979i	−0.323035	+	0.559514i
$549$	1.26289	−	9.19762i	0.0538989	−	0.392545i
$550$		−	4.67688i		−	0.199423i
$551$	−7.88382	−	13.6552i	−0.335862	−	0.581730i
$552$	−1.01148	−	0.0691170i	−0.0430514	−	0.00294182i
$553$	0.493338	+	0.284829i	0.0209789	+	0.0121121i
$554$	−16.9377			−0.719613
$555$	0.665598	−	9.74056i	0.0282530	−	0.413464i
$556$			6.63378i			0.281335i
$557$	11.0586			0.468570			0.234285	−	0.972168i	$-0.424725\pi$
$557$	11.0586			0.468570			0.234285	+	0.972168i	$0.424725\pi$
$558$	9.34804	−	13.8425i	0.395734	−	0.585999i
$559$	9.52549			0.402885
$560$			0.590186i			0.0249399i
$561$	−1.66060	+	24.3018i	−0.0701107	+	1.02602i
$562$	23.8706			1.00692
$563$	−34.4726	−	19.9027i	−1.45285	−	0.838801i	−0.454204	−	0.890898i	$-0.650076\pi$
$563$	−34.4726	−	19.9027i	−1.45285	−	0.838801i	−0.998642	+	0.0520969i	$0.983410\pi$
$564$	−10.1786	−	0.695530i	−0.428596	−	0.0292871i
$565$	3.20709	+	5.55484i	0.134923	+	0.233694i
$566$		−	25.8177i		−	1.08520i
$567$	1.31769	+	5.14563i	0.0553379	+	0.216096i
$568$	−0.844440	+	1.46261i	−0.0354319	+	0.0613699i
$569$	23.4121	−	40.5509i	0.981485	−	1.69998i	0.324863	−	0.945761i	$-0.394682\pi$
$569$	23.4121	−	40.5509i	0.981485	−	1.69998i	0.656622	−	0.754220i	$-0.271985\pi$
$570$	−0.340207	+	4.97869i	−0.0142497	+	0.208534i
$571$	−33.4816	−	19.3306i	−1.40116	−	0.808962i	−0.406651	−	0.913584i	$-0.633303\pi$
$571$	−33.4816	−	19.3306i	−1.40116	−	0.808962i	−0.994512	+	0.104622i	$0.966637\pi$
$572$	11.6444	−	6.72288i	0.486875	−	0.281098i
$573$	−18.2491	+	27.1483i	−0.762369	+	1.13414i
$574$	−3.08481			−0.128757
$575$	0.292670	+	0.506919i	0.0122052	+	0.0211400i
$576$	2.97211	+	0.408090i	0.123838	+	0.0170038i
$577$	11.0818	+	19.1942i	0.461340	+	0.799064i	0.999028	−	0.0440797i	$-0.0140356\pi$
$577$	11.0818	+	19.1942i	0.461340	+	0.799064i	−0.537688	+	0.843144i	$0.680702\pi$
$578$	6.89183	+	3.97900i	0.286662	+	0.165505i
$579$	−9.92304	+	4.85930i	−0.412388	+	0.201945i
$580$	4.73949	+	2.73634i	0.196796	+	0.113620i
$581$	−7.01039			−0.290840
$582$	−22.0841	−	1.50906i	−0.915415	−	0.0625527i
$583$	4.21344	+	7.29789i	0.174503	+	0.302248i
$584$	1.47272	−	2.55082i	0.0609416	−	0.105554i
$585$	−3.25627	−	7.98650i	−0.134630	−	0.330201i
$586$	8.19189	+	14.1888i	0.338404	+	0.586133i
$587$	21.7332			0.897027			0.448513	−	0.893776i	$-0.351954\pi$
$587$	21.7332			0.897027			0.448513	+	0.893776i	$0.351954\pi$
$588$	9.56159	+	6.42733i	0.394313	+	0.265058i
$589$	1.05934	+	16.0066i	0.0436492	+	0.659539i
$590$			3.12011i			0.128453i
$591$	−18.6104	−	12.5099i	−0.765528	−	0.514590i
$592$	4.88163	−	2.81841i	0.200634	−	0.115836i
$593$		−	13.3440i		−	0.547971i	−0.961734	−	0.273986i	$-0.911658\pi$
$593$		−	13.3440i		−	0.547971i	0.961734	−	0.273986i	$-0.0883421\pi$
$594$	16.1749	−	18.1369i	0.663665	−	0.744168i
$595$	−1.53692	+	0.887342i	−0.0630076	+	0.0363775i
$596$	−18.2286	+	10.5243i	−0.746672	+	0.431091i
$597$	13.8594	−	20.6178i	0.567226	−	0.843832i
$598$	−0.841408	+	1.45736i	−0.0344077	+	0.0595960i
$599$	24.6222	+	14.2156i	1.00603	+	0.580834i	0.910028	−	0.414547i	$-0.136060\pi$
$599$	24.6222	+	14.2156i	1.00603	+	0.580834i	0.0960062	+	0.995381i	$0.469393\pi$
$600$	−0.761750	−	1.55555i	−0.0310983	−	0.0635051i
$601$	−18.4011	+	10.6239i	−0.750596	+	0.433357i	−0.825909	−	0.563803i	$-0.809338\pi$
$601$	−18.4011	+	10.6239i	−0.750596	+	0.433357i	0.0753129	+	0.997160i	$0.476004\pi$
$602$	−0.977726	+	1.69347i	−0.0398491	+	0.0690207i
$603$	21.2357	−	27.3590i	0.864785	−	1.11414i
$604$			16.8681i			0.686353i
$605$		−	10.8732i		−	0.442060i
$606$	0.693219	−	10.1448i	0.0281601	−	0.412103i
$607$	20.5818	−	35.6487i	0.835389	−	1.44694i	−0.0583248	−	0.998298i	$-0.518576\pi$
$607$	20.5818	−	35.6487i	0.835389	−	1.44694i	0.893714	−	0.448638i	$-0.148091\pi$
$608$	−2.49515	+	1.44058i	−0.101192	+	0.0584231i
$609$	−5.02427	+	2.46038i	−0.203594	+	0.0996995i
$610$	−2.68004	−	1.54732i	−0.108511	−	0.0626491i
$611$	−8.46715	+	14.6655i	−0.342544	+	0.593304i
$612$	3.40584	+	8.35334i	0.137673	+	0.337664i
$613$	20.0322	−	11.5656i	0.809091	−	0.467129i	−0.0375491	−	0.999295i	$-0.511955\pi$
$613$	20.0322	−	11.5656i	0.809091	−	0.467129i	0.846640	+	0.532166i	$0.178622\pi$
$614$	19.5601	−	11.2930i	0.789381	−	0.455749i
$615$	8.13061	−	3.98154i	0.327858	−	0.160551i
$616$			2.76023i			0.111213i
$617$	18.4259	−	10.6382i	0.741800	−	0.428278i	−0.0809236	−	0.996720i	$-0.525787\pi$
$617$	18.4259	−	10.6382i	0.741800	−	0.428278i	0.822723	+	0.568442i	$0.192454\pi$
$618$	−5.00908	+	7.45175i	−0.201495	+	0.299753i
$619$			10.3600i			0.416402i	0.978086	+	0.208201i	$0.0667609\pi$
$619$			10.3600i			0.416402i	−0.978086	+	0.208201i	$0.933239\pi$
$620$	−3.09622	−	4.62746i	−0.124347	−	0.185843i
$621$	−0.618199	+	2.97803i	−0.0248075	+	0.119504i
$622$	−7.76670			−0.311416
$623$	−0.120750	−	0.209145i	−0.00483775	−	0.00837922i
$624$	2.77797	−	4.13264i	0.111208	−	0.165438i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−12.1635	−	21.0679i	−0.486152	−	0.842041i
$627$	−1.59111	+	23.2847i	−0.0635427	+	0.929903i
$628$	−1.10936			−0.0442681
$629$	14.6790	+	8.47494i	0.585291	+	0.337918i
$630$	1.75410	+	0.240849i	0.0698850	+	0.00959565i
$631$	33.6528	+	19.4294i	1.33970	+	0.773474i	0.986762	−	0.162174i	$-0.0518506\pi$
$631$	33.6528	+	19.4294i	1.33970	+	0.773474i	0.352934	+	0.935648i	$0.385184\pi$
$632$	−0.482609	−	0.835902i	−0.0191971	−	0.0332504i
$633$	1.63620	−	0.801242i	0.0650330	−	0.0318465i
$634$	−6.27740	−	10.8728i	−0.249307	−	0.431813i
$635$	−15.2089			−0.603546
$636$	2.59005	+	1.74104i	0.102702	+	0.0690368i
$637$	16.5612	−	9.56159i	0.656177	−	0.378844i
$638$	22.1660	+	12.7976i	0.877561	+	0.506660i
$639$	4.00245	+	3.10665i	0.158334	+	0.122897i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	4.55356	−	7.88700i	0.179855	−	0.311518i	−0.761976	−	0.647606i	$-0.775771\pi$
$641$	4.55356	−	7.88700i	0.179855	−	0.311518i	0.941831	+	0.336088i	$0.109104\pi$
$642$	14.9793	−	7.33532i	0.591184	−	0.289502i
$643$			11.1693i			0.440473i	0.975446	+	0.220237i	$0.0706830\pi$
$643$			11.1693i			0.440473i	−0.975446	+	0.220237i	$0.929317\pi$
$644$	−0.172730	−	0.299176i	−0.00680650	−	0.0117892i
$645$	0.391233	−	5.72542i	0.0154048	−	0.225438i
$646$	−7.50289	−	4.33180i	−0.295197	−	0.170432i
$647$	18.5912			0.730894			0.365447	−	0.930832i	$-0.380916\pi$
$647$	18.5912			0.730894			0.365447	+	0.930832i	$0.380916\pi$
$648$	2.42578	−	8.66692i	0.0952937	−	0.340469i
$649$			14.5924i			0.572801i
$650$	−2.87494			−0.112764
$651$	5.69153	+	0.0121882i	0.223069	+	0.000477692i
$652$	9.25474			0.362444
$653$		−	42.6892i		−	1.67056i	−0.549826	−	0.835279i	$-0.685306\pi$
$653$		−	42.6892i		−	1.67056i	0.549826	−	0.835279i	$-0.314694\pi$
$654$	−21.7621	−	1.48706i	−0.850964	−	0.0581486i
$655$	0.860066			0.0336055
$656$	4.52658	+	2.61342i	0.176733	+	0.102037i
$657$	−6.98034	−	5.41806i	−0.272329	−	0.211379i
$658$	−1.73819	−	3.01063i	−0.0677617	−	0.117367i
$659$			12.6930i			0.494449i	0.968958	+	0.247225i	$0.0795185\pi$
$659$			12.6930i			0.494449i	−0.968958	+	0.247225i	$0.920481\pi$
$660$	−3.56262	−	7.27513i	−0.138675	−	0.283184i
$661$	18.7942	−	32.5526i	0.731011	−	1.26615i	−0.225440	−	0.974257i	$-0.572382\pi$
$661$	18.7942	−	32.5526i	0.731011	−	1.26615i	0.956451	−	0.291892i	$-0.0942847\pi$
$662$	12.2215	−	21.1683i	0.475004	−	0.822731i
$663$	14.9386	+	1.02079i	0.580167	+	0.0396444i
$664$	10.2869	+	5.93914i	0.399209	+	0.230483i
$665$	−1.47260	+	0.850207i	−0.0571050	+	0.0329696i
$666$	−6.38450	−	15.6589i	−0.247394	−	0.606772i
$667$	−3.20338			−0.124035
$668$	−4.64334	−	8.04251i	−0.179656	−	0.311174i
$669$	5.94909	+	12.1485i	0.230005	+	0.469687i
$670$	−5.77223	−	9.99779i	−0.223001	−	0.386248i
$671$	−12.5342	−	7.23663i	−0.483878	−	0.279367i
$672$	0.449574	+	0.918064i	0.0173427	+	0.0354151i
$673$	7.30862	+	4.21963i	0.281726	+	0.162655i	0.634205	−	0.773165i	$-0.281328\pi$
$673$	7.30862	+	4.21963i	0.281726	+	0.162655i	−0.352478	+	0.935820i	$0.614661\pi$
$674$	−7.97132			−0.307044
$675$	−4.93414	+	1.62920i	−0.189915	+	0.0627081i
$676$	2.36736	+	4.10039i	0.0910523	+	0.157707i
$677$	−1.34626	+	2.33179i	−0.0517410	+	0.0896180i	−0.890736	−	0.454521i	$-0.849810\pi$
$677$	−1.34626	+	2.33179i	−0.0517410	+	0.0896180i	0.838995	+	0.544139i	$0.183144\pi$
$678$	9.22018	+	6.19783i	0.354099	+	0.238026i
$679$	−3.77128	−	6.53205i	−0.144729	−	0.250677i
$680$	3.00699			0.115313
$681$	20.2056	−	30.0588i	0.774280	−	1.15185i
$682$	−14.4807	−	21.6421i	−0.554494	−	0.828718i
$683$			14.9285i			0.571223i	0.958345	+	0.285612i	$0.0921967\pi$
$683$			14.9285i			0.571223i	−0.958345	+	0.285612i	$0.907803\pi$
$684$	3.26331	+	8.00376i	0.124776	+	0.306031i
$685$	13.0979	−	7.56206i	0.500444	−	0.288932i
$686$			8.05703i			0.307619i
$687$	−10.8873	−	22.2327i	−0.415376	−	0.848229i
$688$	2.86939	−	1.65664i	0.109394	−	0.0631589i
$689$	4.48611	−	2.59005i	0.170907	−	0.0986732i
$690$	0.841408	+	0.565597i	0.0320319	+	0.0215319i
$691$	−1.72141	+	2.98157i	−0.0654856	+	0.113424i	−0.896909	−	0.442215i	$-0.854193\pi$
$691$	−1.72141	+	2.98157i	−0.0654856	+	0.113424i	0.831424	+	0.555639i	$0.187526\pi$
$692$	20.5960	+	11.8911i	0.782942	+	0.452032i
$693$	8.20372	+	1.12642i	0.311633	+	0.0427892i
$694$	−26.5142	+	15.3080i	−1.00647	+	0.581083i
$695$	3.31689	−	5.74502i	0.125817	−	0.217921i
$696$	9.45692	+	0.646216i	0.358464	+	0.0244948i
$697$			15.7171i			0.595326i
$698$			21.2775i			0.805364i
$699$	−28.6615	−	1.95852i	−1.08408	−	0.0740779i
$700$	0.295093	−	0.511116i	0.0111535	−	0.0193184i
$701$	−12.4708	+	7.20002i	−0.471015	+	0.271941i	−0.716665	−	0.697418i	$-0.754332\pi$
$701$	−12.4708	+	7.20002i	−0.471015	+	0.271941i	0.245649	+	0.969359i	$0.420999\pi$
$702$	−11.1490	−	9.94294i	−0.420793	−	0.375272i
$703$	14.0647	+	8.12027i	0.530461	+	0.306262i
$704$	2.33844	−	4.05030i	0.0881333	−	0.152651i
$705$	8.46715	+	5.69164i	0.318891	+	0.214360i
$706$	−19.6918	+	11.3691i	−0.741111	+	0.427881i
$707$	3.00063	−	1.73242i	0.112850	−	0.0651542i
$708$	2.37674	+	4.85349i	0.0893235	+	0.182405i
$709$			29.8336i			1.12043i	0.828349	+	0.560213i	$0.189281\pi$
$709$			29.8336i			1.12043i	−0.828349	+	0.560213i	$0.810719\pi$
$710$	1.46261	−	0.844440i	0.0548909	−	0.0316913i
$711$	−2.68135	+	1.09324i	−0.100558	+	0.0409999i
$712$			0.409193i			0.0153352i
$713$	2.92385	+	1.43958i	0.109499	+	0.0539126i
$714$	−1.71483	+	2.55105i	−0.0641757	+	0.0954708i
$715$	−13.4458			−0.502843
$716$	−8.98349	−	15.5599i	−0.335729	−	0.581499i
$717$	6.63020	+	4.45684i	0.247609	+	0.166444i
$718$	−0.750465	+	1.29984i	−0.0280071	+	0.0485097i
$719$	−6.94656	−	12.0318i	−0.259063	−	0.448710i	0.706928	−	0.707285i	$-0.250080\pi$
$719$	−6.94656	−	12.0318i	−0.259063	−	0.448710i	−0.965991	+	0.258575i	$0.916747\pi$
$720$	−2.36988	−	1.83947i	−0.0883203	−	0.0685531i
$721$	−3.05948			−0.113941
$722$	9.26558	+	5.34948i	0.344829	+	0.199087i
$723$	−16.2226	−	33.1277i	−0.603324	−	1.23203i
$724$	0.555527	+	0.320734i	0.0206460	+	0.0119200i
$725$	−2.73634	−	4.73949i	−0.101625	−	0.176020i
$726$	−8.28268	−	16.9139i	−0.307399	−	0.627732i
$727$	0.865765	+	1.49955i	0.0321095	+	0.0556152i	0.881634	−	0.471935i	$-0.156444\pi$
$727$	0.865765	+	1.49955i	0.0321095	+	0.0556152i	−0.849524	+	0.527550i	$0.823111\pi$
$728$	1.69675			0.0628857
$729$	−24.7692	−	10.7466i	−0.917376	−	0.398022i
$730$	−2.55082	+	1.47272i	−0.0944103	+	0.0545078i
$731$	8.62822	+	4.98151i	0.319126	+	0.184248i
$732$	−5.34760	−	0.365416i	−0.197653	−	0.0135062i
$733$	16.9702	−	29.3932i	0.626808	−	1.08566i	−0.361380	−	0.932419i	$-0.617694\pi$
$733$	16.9702	−	29.3932i	0.626808	−	1.08566i	0.988188	−	0.153245i	$-0.0489724\pi$
$734$	1.40472	−	2.43304i	0.0518490	−	0.0898051i
$735$	−5.06692	−	10.3470i	−0.186896	−	0.381656i
$736$			0.585340i			0.0215759i
$737$	−26.9960	−	46.7585i	−0.994412	−	1.72237i
$738$	9.61463	−	12.3870i	0.353919	−	0.455971i
$739$	−25.3227	−	14.6201i	−0.931511	−	0.537808i	−0.0442221	−	0.999022i	$-0.514081\pi$
$739$	−25.3227	−	14.6201i	−0.931511	−	0.537808i	−0.887289	+	0.461213i	$0.847414\pi$
$740$	−5.63683			−0.207214
$741$	14.3134	+	0.978075i	0.525817	+	0.0359305i
$742$			1.06341i			0.0390388i
$743$	50.4374			1.85037			0.925184	−	0.379519i	$-0.123910\pi$
$743$	50.4374			1.85037			0.925184	+	0.379519i	$0.123910\pi$
$744$	−8.34130	−	4.83970i	−0.305807	−	0.177432i
$745$	21.0486			0.771159
$746$			21.9797i			0.804734i
$747$	21.8498	−	28.1501i	0.799442	−	1.02996i
$748$	14.0633			0.514207
$749$	4.92182	+	2.84161i	0.179839	+	0.103830i
$750$	−0.118080	+	1.72802i	−0.00431168	+	0.0630984i
$751$	20.3241	+	35.2024i	0.741637	+	1.28455i	0.951749	+	0.306876i	$0.0992837\pi$
$751$	20.3241	+	35.2024i	0.741637	+	1.28455i	−0.210112	+	0.977677i	$0.567383\pi$
$752$			5.89031i			0.214798i
$753$	−42.5833	+	20.8530i	−1.55182	+	0.759924i
$754$	7.86682	−	13.6257i	0.286493	−	0.496220i
$755$	8.43405	−	14.6082i	0.306946	−	0.531647i
$756$	2.91206	−	0.961533i	0.105910	−	0.0349706i
$757$	−9.92590	−	5.73072i	−0.360763	−	0.208287i	0.308652	−	0.951175i	$-0.400122\pi$
$757$	−9.92590	−	5.73072i	−0.360763	−	0.208287i	−0.669415	+	0.742888i	$0.733455\pi$
$758$	17.6768	−	10.2057i	0.642051	−	0.370688i
$759$	3.93517	+	2.64523i	0.142838	+	0.0960158i
$760$	2.88115			0.104510
$761$	12.8069	+	22.1823i	0.464251	+	0.804106i	0.999167	−	0.0407988i	$-0.0129903\pi$
$761$	12.8069	+	22.1823i	0.464251	+	0.804106i	−0.534917	+	0.844905i	$0.679657\pi$
$762$	−23.6582	+	11.5854i	−0.857046	+	0.419694i
$763$	−3.71629	−	6.43681i	−0.134539	−	0.233028i
$764$	16.3559	+	9.44308i	0.591735	+	0.341639i
$765$	1.22712	−	8.93712i	0.0443668	−	0.323122i
$766$	27.7563	+	16.0251i	1.00288	+	0.579011i
$767$	8.97013			0.323893
$768$	0.118080	−	1.72802i	0.00426085	−	0.0623546i
$769$	−23.5436	−	40.7787i	−0.849004	−	1.47052i	−0.882098	−	0.471067i	$-0.843869\pi$
$769$	−23.5436	−	40.7787i	−0.849004	−	1.47052i	0.0330933	−	0.999452i	$-0.489464\pi$
$770$	1.38011	−	2.39043i	0.0497359	−	0.0861451i
$771$	7.90272	−	11.7565i	0.284609	−	0.423398i
$772$	3.18956	+	5.52448i	0.114795	+	0.198830i
$773$	−0.831188			−0.0298958			−0.0149479	−	0.999888i	$-0.504758\pi$
$773$	−0.831188			−0.0298958			−0.0149479	+	0.999888i	$0.504758\pi$
$774$	−3.75276	−	9.20421i	−0.134890	−	0.330838i
$775$	0.367679	+	5.55561i	0.0132074	+	0.199563i
$776$			12.7800i			0.458775i
$777$	3.21457	−	4.78214i	0.115322	−	0.171558i
$778$	−32.3290	+	18.6651i	−1.15905	+	0.669178i
$779$			15.0593i			0.539556i
$780$	−4.47211	+	2.18999i	−0.160127	+	0.0784141i
$781$	6.84047	−	3.94935i	0.244771	−	0.141319i
$782$	−1.52430	+	0.880056i	−0.0545089	+	0.0314707i
$783$	5.77990	−	27.8433i	0.206557	−	0.995039i
$784$	3.32584	−	5.76052i	0.118780	−	0.205733i
$785$	0.960730	+	0.554678i	0.0342899	+	0.0197973i
$786$	1.33788	−	0.655155i	0.0477204	−	0.0233686i
$787$	25.4996	−	14.7222i	0.908961	−	0.524789i	0.0288644	−	0.999583i	$-0.490811\pi$
$787$	25.4996	−	14.7222i	0.908961	−	0.524789i	0.880097	+	0.474794i	$0.157478\pi$
$788$	−6.47331	+	11.2121i	−0.230602	+	0.399414i
$789$	0.230795	−	3.37752i	0.00821651	−	0.120243i
$790$			0.965217i			0.0343409i
$791$			3.78555i			0.134599i
$792$	−11.0837	−	8.60300i	−0.393841	−	0.305694i
$793$	−4.44845	+	7.70494i	−0.157969	+	0.273611i
$794$	−31.2296	+	18.0304i	−1.10830	+	0.639876i
$795$	−1.37253	−	2.80281i	−0.0486787	−	0.0994055i
$796$	−12.4215	−	7.17157i	−0.440269	−	0.254190i
$797$	13.6953	−	23.7209i	0.485111	−	0.840237i	−0.514742	−	0.857345i	$-0.672112\pi$
$797$	13.6953	−	23.7209i	0.485111	−	0.840237i	0.999854	+	0.0171076i	$0.00544579\pi$
$798$	−1.64306	+	2.44429i	−0.0581637	+	0.0865271i
$799$	−15.3391	+	8.85606i	−0.542660	+	0.313305i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	1.21617	+	0.166988i	0.0429712	+	0.00590022i
$802$		−	36.7308i		−	1.29701i
$803$	−11.9299	+	6.88773i	−0.420997	+	0.243063i
$804$	−16.5948	−	11.1551i	−0.585254	−	0.393409i
$805$			0.345459i			0.0121758i
$806$	−13.3037	+	8.90146i	−0.468602	+	0.313541i
$807$	−7.26624	−	4.88438i	−0.255784	−	0.171938i
$808$	−5.87075			−0.206532
$809$	−3.74578	−	6.48788i	−0.131695	−	0.228102i	0.792635	−	0.609696i	$-0.208709\pi$
$809$	−3.74578	−	6.48788i	−0.131695	−	0.228102i	−0.924330	+	0.381594i	$0.875375\pi$
$810$	−6.43425	+	6.29289i	−0.226077	+	0.221109i
$811$	0.458412	−	0.793993i	0.0160970	−	0.0278809i	−0.857865	−	0.513876i	$-0.828209\pi$
$811$	0.458412	−	0.793993i	0.0160970	−	0.0278809i	0.873962	+	0.485995i	$0.161543\pi$
$812$	1.61495	+	2.79718i	0.0566737	+	0.0981617i
$813$	16.7168	+	1.14230i	0.586283	+	0.0400623i
$814$	−26.3628			−0.924015
$815$	−8.01484	−	4.62737i	−0.280748	−	0.162090i
$816$	4.67753	−	2.29058i	0.163746	−	0.0801862i
$817$	8.26714	+	4.77303i	0.289231	+	0.166987i
$818$	17.3034	+	29.9703i	0.604999	+	1.04789i
$819$	0.692426	−	5.04293i	0.0241953	−	0.176214i
$820$	−2.61342	−	4.52658i	−0.0912646	−	0.158075i
$821$	−1.80737			−0.0630775			−0.0315388	−	0.999503i	$-0.510041\pi$
$821$	−1.80737			−0.0630775			−0.0315388	+	0.999503i	$0.510041\pi$
$822$	14.6140	−	21.7405i	0.509722	−	0.758286i
$823$	20.8385	−	12.0311i	0.726386	−	0.419379i	−0.0907129	−	0.995877i	$-0.528915\pi$
$823$	20.8385	−	12.0311i	0.726386	−	0.419379i	0.817098	+	0.576498i	$0.195581\pi$
$824$	4.48942	+	2.59197i	0.156396	+	0.0902954i
$825$	−0.552247	+	8.08175i	−0.0192268	+	0.281370i
$826$	−0.920722	+	1.59474i	−0.0320360	+	0.0554880i
$827$	−26.1422	+	45.2796i	−0.909052	+	1.57452i	−0.0936684	+	0.995603i	$0.529859\pi$
$827$	−26.1422	+	45.2796i	−0.909052	+	1.57452i	−0.815384	+	0.578921i	$0.803474\pi$
$828$	1.73970	+	0.238871i	0.0604586	+	0.00830136i
$829$			32.6536i			1.13411i	0.823681	+	0.567054i	$0.191917\pi$
$829$			32.6536i			1.13411i	−0.823681	+	0.567054i	$0.808083\pi$
$830$	−5.93914	−	10.2869i	−0.206151	−	0.357063i
$831$	29.2687	+	2.00000i	1.01532	+	0.0693794i
$832$	−2.48977	−	1.43747i	−0.0863173	−	0.0498353i
$833$	20.0015			0.693013
$834$	0.783318	−	11.4633i	0.0271241	−	0.396942i
$835$			9.28669i			0.321379i
$836$	13.4748			0.466036
$837$	−17.7881	+	22.8163i	−0.614848	+	0.788646i
$838$	−2.99848			−0.103581
$839$		−	28.5391i		−	0.985281i	−0.870233	−	0.492640i	$-0.836032\pi$
$839$		−	28.5391i		−	0.985281i	0.870233	−	0.492640i	$-0.163968\pi$
$840$	0.0696893	−	1.01985i	0.00240451	−	0.0351883i
$841$	0.950308			0.0327692
$842$	−17.2211	−	9.94262i	−0.593479	−	0.342645i
$843$	−41.2488	−	2.81864i	−1.42069	−	0.0970792i
$844$	−0.525922	−	0.910924i	−0.0181030	−	0.0313553i
$845$		−	4.73472i		−	0.162879i
$846$	17.5067	+	2.40378i	0.601892	+	0.0826436i
$847$	3.20861	−	5.55748i	0.110249	−	0.190957i
$848$	0.900907	−	1.56042i	0.0309373	−	0.0535849i
$849$	−3.04856	+	44.6136i	−0.104626	+	1.53113i
$850$	−2.60413	−	1.50350i	−0.0893210	−	0.0515695i
$851$	2.85741	−	1.64973i	0.0979509	−	0.0565520i
$852$	1.63192	−	2.42772i	0.0559085	−	0.0831722i
$853$	17.2191			0.589572			0.294786	−	0.955563i	$-0.404752\pi$
$853$	17.2191			0.589572			0.294786	+	0.955563i	$0.404752\pi$
$854$	−0.913206	−	1.58172i	−0.0312493	−	0.0541253i
$855$	1.17577	−	8.56311i	0.0402105	−	0.292852i
$856$	−4.81478	−	8.33944i	−0.164566	−	0.285036i
$857$	−43.7696	−	25.2704i	−1.49514	−	0.863221i	−0.495158	−	0.868803i	$-0.664890\pi$
$857$	−43.7696	−	25.2704i	−1.49514	−	0.863221i	−0.999984	+	0.00558224i	$0.998223\pi$
$858$	−20.9156	+	10.2423i	−0.714045	+	0.349667i
$859$	1.79144	+	1.03429i	0.0611230	+	0.0352894i	0.530250	−	0.847841i	$-0.322098\pi$
$859$	1.79144	+	1.03429i	0.0611230	+	0.0352894i	−0.469127	+	0.883131i	$0.655431\pi$
$860$	−3.31328			−0.112982
$861$	5.33061	+	0.364254i	0.181667	+	0.0124138i
$862$	3.21903	+	5.57553i	0.109641	+	0.189903i
$863$	3.41935	−	5.92248i	0.116396	−	0.201604i	−0.801941	−	0.597403i	$-0.796199\pi$
$863$	3.41935	−	5.92248i	0.116396	−	0.201604i	0.918337	+	0.395800i	$0.129533\pi$
$864$	−5.08769	−	1.05614i	−0.173087	−	0.0359305i
$865$	−11.8911	−	20.5960i	−0.404310	−	0.700285i
$866$	−29.7643			−1.01143
$867$	−11.4394	−	7.68959i	−0.388502	−	0.261152i
$868$	−0.216999	−	3.27884i	−0.00736541	−	0.111291i
$869$			4.51421i			0.153134i
$870$	−7.86682	−	5.28810i	−0.266710	−	0.179283i
$871$	−28.7431	+	16.5948i	−0.973921	+	0.562294i
$872$			12.5936i			0.426474i
$873$	37.9836	+	5.21539i	1.28555	+	0.176514i
$874$	−1.46051	+	0.843226i	−0.0494025	+	0.0285225i
$875$	−0.511116	+	0.295093i	−0.0172789	+	0.00997596i
$876$	−2.84609	+	4.23398i	−0.0961605	+	0.143053i
$877$	21.8766	−	37.8914i	0.738721	−	1.27950i	−0.214350	−	0.976757i	$-0.568763\pi$
$877$	21.8766	−	37.8914i	0.738721	−	1.27950i	0.953071	−	0.302746i	$-0.0979034\pi$
$878$	34.2079	+	19.7500i	1.15446	+	0.666529i
$879$	−12.4803	−	25.4858i	−0.420952	−	0.859614i
$880$	−4.05030	+	2.33844i	−0.136536	+	0.0788288i
$881$	11.3488	−	19.6568i	0.382352	−	0.662253i	−0.609046	−	0.793135i	$-0.708447\pi$
$881$	11.3488	−	19.6568i	0.382352	−	0.662253i	0.991398	+	0.130882i	$0.0417808\pi$
$882$	−15.7637	−	12.2356i	−0.530791	−	0.411994i
$883$			31.4192i			1.05734i	0.848828	+	0.528670i	$0.177309\pi$
$883$			31.4192i			1.05734i	−0.848828	+	0.528670i	$0.822691\pi$
$884$		−	8.64492i		−	0.290760i
$885$	0.368423	−	5.39162i	0.0123844	−	0.181237i
$886$	6.09717	−	10.5606i	0.204839	−	0.354791i
$887$	0.322462	−	0.186174i	0.0108272	−	0.00625110i	−0.494577	−	0.869134i	$-0.664677\pi$
$887$	0.322462	−	0.186174i	0.0108272	−	0.00625110i	0.505404	+	0.862883i	$0.331344\pi$
$888$	−8.76837	+	4.29385i	−0.294247	+	0.144092i
$889$	−7.77350	−	4.48803i	−0.260715	−	0.150524i
$890$	0.204597	−	0.354372i	0.00685810	−	0.0118786i
$891$	−30.0922	+	29.4311i	−1.00813	+	0.985979i
$892$	6.76345	−	3.90488i	0.226457	−	0.130745i
$893$	−14.6972	+	8.48544i	−0.491824	+	0.283954i
$894$	32.7421	−	16.0337i	1.09506	−	0.536248i
$895$			17.9670i			0.600570i
$896$	0.511116	−	0.295093i	0.0170752	−	0.00985836i
$897$	1.62606	−	2.41900i	0.0542925	−	0.0807680i
$898$			1.10717i			0.0369468i
$899$	−27.3368	−	13.4595i	−0.911735	−	0.448898i
$900$	1.13264	+	2.77797i	0.0377547	+	0.0925990i
$901$	5.41804			0.180501
$902$	−12.2227	−	21.1703i	−0.406970	−	0.704893i
$903$	1.88950	−	2.81090i	0.0628785	−	0.0935410i
$904$	3.20709	−	5.55484i	0.106666	−	0.184751i
$905$	−0.320734	−	0.555527i	−0.0106615	−	0.0184663i
$906$	1.99179	−	29.1484i	0.0661727	−	0.968392i
$907$	8.92989			0.296512			0.148256	−	0.988949i	$-0.452634\pi$
$907$	8.92989			0.296512			0.148256	+	0.988949i	$0.452634\pi$
$908$	−18.1094	−	10.4554i	−0.600980	−	0.346976i
$909$	−2.39580	+	17.4485i	−0.0794635	+	0.578731i
$910$	−1.46943	−	0.848374i	−0.0487110	−	0.0281233i
$911$	−0.293706	−	0.508715i	−0.00973093	−	0.0168545i	0.861119	−	0.508404i	$-0.169764\pi$
$911$	−0.293706	−	0.508715i	−0.00973093	−	0.0168545i	−0.870850	+	0.491549i	$0.836431\pi$
$912$	4.48178	−	2.19472i	0.148406	−	0.0726743i
$913$	−27.7767	−	48.1106i	−0.919273	−	1.59223i
$914$	−8.27976			−0.273870
$915$	4.44845	+	2.99026i	0.147061	+	0.0988550i
$916$	−12.3777	+	7.14624i	−0.408969	+	0.236118i
$917$	0.439593	+	0.253799i	0.0145166	+	0.00838119i
$918$	−4.89900	−	14.8369i	−0.161691	−	0.489691i
$919$	−7.00363	+	12.1306i	−0.231028	+	0.400153i	−0.958111	−	0.286397i	$-0.907542\pi$
$919$	−7.00363	+	12.1306i	−0.231028	+	0.400153i	0.727083	+	0.686550i	$0.240876\pi$
$920$	0.292670	−	0.506919i	0.00964904	−	0.0167126i
$921$	−35.1337	+	17.2049i	−1.15770	+	0.566921i
$922$		−	19.4170i		−	0.639463i
$923$	−2.42772	−	4.20493i	−0.0799092	−	0.138407i
$924$	0.325928	−	4.76973i	0.0107223	−	0.156913i
$925$	4.88163	+	2.81841i	0.160507	+	0.0926689i
$926$	34.1138			1.12105
$927$	9.53571	−	12.2853i	0.313194	−	0.403502i
$928$		−	5.47269i		−	0.179650i
$929$	1.83007			0.0600427			0.0300214	−	0.999549i	$-0.490442\pi$
$929$	1.83007			0.0600427			0.0300214	+	0.999549i	$0.490442\pi$
$930$	4.80393	+	8.36195i	0.157527	+	0.274199i
$931$	19.1645			0.628091
$932$			16.5863i			0.543303i
$933$	13.4210	+	0.917094i	0.439385	+	0.0300243i
$934$	−25.2788			−0.827148
$935$	−12.1792	−	7.03167i	−0.398303	−	0.229960i
$936$	−5.28838	+	6.81327i	−0.172856	+	0.222699i
$937$	6.77296	+	11.7311i	0.221263	+	0.383239i	0.955192	−	0.295988i	$-0.0956487\pi$
$937$	6.77296	+	11.7311i	0.221263	+	0.383239i	−0.733929	+	0.679226i	$0.762315\pi$
$938$		−	6.81337i		−	0.222464i
$939$	18.5311	+	37.8420i	0.604741	+	1.23493i
$940$	2.94516	−	5.10116i	0.0960604	−	0.166382i
$941$	−8.67450	+	15.0247i	−0.282781	+	0.489790i	−0.972069	−	0.234697i	$-0.924590\pi$
$941$	−8.67450	+	15.0247i	−0.282781	+	0.489790i	0.689288	+	0.724487i	$0.257923\pi$
$942$	1.91699	+	0.130993i	0.0624589	+	0.00426798i
$943$	2.64958	+	1.52974i	0.0862823	+	0.0498151i
$944$	2.70209	−	1.56005i	0.0879457	−	0.0507755i
$945$	−3.00268	−	0.623317i	−0.0976772	−	0.0202765i
$946$	−15.4958			−0.503813
$947$	−7.70416	−	13.3440i	−0.250352	−	0.433622i	0.713271	−	0.700888i	$-0.247213\pi$
$947$	−7.70416	−	13.3440i	−0.250352	−	0.433622i	−0.963623	+	0.267267i	$0.913880\pi$
$948$	0.735254	+	1.50144i	0.0238799	+	0.0487646i
$949$	4.23398	+	7.33347i	0.137441	+	0.238054i
$950$	−2.49515	−	1.44058i	−0.0809534	−	0.0467384i
$951$	9.56362	+	19.5296i	0.310122	+	0.633292i
$952$	1.53692	+	0.887342i	0.0498119	+	0.0287589i
$953$	11.3217			0.366744			0.183372	−	0.983044i	$-0.441299\pi$
$953$	11.3217			0.366744			0.183372	+	0.983044i	$0.441299\pi$
$954$	−4.27009	−	3.31439i	−0.138249	−	0.107307i
$955$	−9.44308	−	16.3559i	−0.305571	−	0.529264i
$956$	2.30620	−	3.99446i	0.0745880	−	0.129190i
$957$	−36.7922	−	24.7318i	−1.18932	−	0.799466i
$958$	9.30670	+	16.1197i	0.300686	+	0.520803i
$959$	8.92604			0.288237
$960$	−0.966271	+	1.43747i	−0.0311863	+	0.0463941i
$961$	18.9028	+	24.5700i	0.609769	+	0.792579i
$962$			16.2055i			0.522488i
$963$	−26.7506	+	10.9068i	−0.862027	+	0.351468i
$964$	−18.4433	+	10.6482i	−0.594018	+	0.342956i
$965$		−	6.37912i		−	0.205351i
$966$	0.263154	+	0.537379i	0.00846683	+	0.0172899i
$967$	−22.2534	+	12.8480i	−0.715620	+	0.413163i	−0.813138	−	0.582070i	$-0.802243\pi$
$967$	−22.2534	+	12.8480i	−0.715620	+	0.413163i	0.0975186	+	0.995234i	$0.468909\pi$
$968$	−9.41649	+	5.43661i	−0.302658	+	0.174739i
$969$	12.4537	+	8.37138i	0.400069	+	0.268928i
$970$	6.38999	−	11.0678i	0.205170	−	0.355365i
$971$	−13.0504	−	7.53462i	−0.418806	−	0.241798i	0.275761	−	0.961226i	$-0.411070\pi$
$971$	−13.0504	−	7.53462i	−0.418806	−	0.241798i	−0.694566	+	0.719429i	$0.744404\pi$
$972$	−5.21519	+	14.6902i	−0.167277	+	0.471188i
$973$	3.39063	−	1.95758i	0.108699	−	0.0627572i
$974$	−3.51817	+	6.09365i	−0.112730	+	0.195253i
$975$	4.96796	+	0.339474i	0.159102	+	0.0108719i
$976$			3.09464i			0.0990570i
$977$		−	45.0714i		−	1.44196i	−0.692956	−	0.720980i	$-0.743692\pi$
$977$		−	45.0714i		−	1.44196i	0.692956	−	0.720980i	$-0.256308\pi$
$978$	−15.9924	−	1.09280i	−0.511380	−	0.0349439i
$979$	0.956875	−	1.65736i	0.0305818	−	0.0529693i
$980$	−5.76052	+	3.32584i	−0.184013	+	0.106240i
$981$	37.4297	+	5.13934i	1.19504	+	0.164086i
$982$	−22.8777	−	13.2084i	−0.730056	−	0.421498i
$983$	−19.1329	+	33.1392i	−0.610245	+	1.05697i	0.380954	+	0.924594i	$0.375596\pi$
$983$	−19.1329	+	33.1392i	−0.610245	+	1.05697i	−0.991199	+	0.132381i	$0.957738\pi$
$984$	−7.51342	−	5.05054i	−0.239519	−	0.161005i
$985$	11.2121	−	6.47331i	0.357247	−	0.206257i
$986$	14.2516	−	8.22816i	0.453863	−	0.262038i
$987$	2.64813	+	5.40768i	0.0842910	+	0.172128i
$988$		−	8.28314i		−	0.263522i
$989$	1.67957	−	0.969698i	0.0534071	−	0.0308346i
$990$	5.29723	+	12.9922i	0.168357	+	0.412921i
$991$		−	25.5729i		−	0.812351i	−0.913795	−	0.406176i	$-0.866862\pi$
$991$		−	25.5729i		−	0.812351i	0.913795	−	0.406176i	$-0.133138\pi$
$992$	−2.45939	+	4.99514i	−0.0780856	+	0.158596i
$993$	−23.6186	+	35.1362i	−0.749515	+	1.11501i
$994$	0.996753			0.0316151
$995$	7.17157	+	12.4215i	0.227354	+	0.393789i
$996$	−17.0747	−	11.4776i	−0.541032	−	0.363683i
$997$	−16.6915	+	28.9106i	−0.528626	+	0.915607i	0.470817	+	0.882231i	$0.343959\pi$
$997$	−16.6915	+	28.9106i	−0.528626	+	0.915607i	−0.999443	+	0.0333761i	$0.989374\pi$
$998$	6.18273	+	10.7088i	0.195711	+	0.338981i
$999$	9.18354	+	27.8129i	0.290554	+	0.879960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.d.161.14	yes	36
3.2	odd	2	inner	930.2.o.d.161.8	✓	36
31.26	odd	6	inner	930.2.o.d.491.17	yes	36
93.26	even	6	inner	930.2.o.d.491.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.d.161.8	✓	36	3.2	odd	2	inner
930.2.o.d.161.14	yes	36	1.1	even	1	trivial
930.2.o.d.491.5	yes	36	93.26	even	6	inner
930.2.o.d.491.17	yes	36	31.26	odd	6	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.118080 - 1.72802i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.72802 + 0.118080i) q^{6} +(0.295093 + 0.511116i) q^{7} -1.00000i q^{8} +(-2.97211 - 0.408090i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.118080 - 1.72802i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.72802 + 0.118080i) q^{6} +(0.295093 + 0.511116i) q^{7} -1.00000i q^{8} +(-2.97211 - 0.408090i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.33844 + 4.05030i) q^{11} +(-0.118080 + 1.72802i) q^{12} +(2.48977 + 1.43747i) q^{13} +(-0.511116 + 0.295093i) q^{14} +(0.966271 - 1.43747i) q^{15} +1.00000 q^{16} +(1.50350 + 2.60413i) q^{17} +(0.408090 - 2.97211i) q^{18} +(1.44058 + 2.49515i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.918064 - 0.449574i) q^{21} +(-4.05030 - 2.33844i) q^{22} +0.585340 q^{23} +(-1.72802 - 0.118080i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.43747 + 2.48977i) q^{26} +(-1.05614 + 5.08769i) q^{27} +(-0.295093 - 0.511116i) q^{28} -5.47269 q^{29} +(1.43747 + 0.966271i) q^{30} +(4.99514 + 2.45939i) q^{31} +1.00000i q^{32} +(6.72288 + 4.51914i) q^{33} +(-2.60413 + 1.50350i) q^{34} +0.590186i q^{35} +(2.97211 + 0.408090i) q^{36} +(4.88163 - 2.81841i) q^{37} +(-2.49515 + 1.44058i) q^{38} +(2.77797 - 4.13264i) q^{39} +(0.500000 - 0.866025i) q^{40} +(4.52658 + 2.61342i) q^{41} +(0.449574 + 0.918064i) q^{42} +(2.86939 - 1.65664i) q^{43} +(2.33844 - 4.05030i) q^{44} +(-2.36988 - 1.83947i) q^{45} +0.585340i q^{46} +5.89031i q^{47} +(0.118080 - 1.72802i) q^{48} +(3.32584 - 5.76052i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(4.67753 - 2.29058i) q^{51} +(-2.48977 - 1.43747i) q^{52} +(0.900907 - 1.56042i) q^{53} +(-5.08769 - 1.05614i) q^{54} +(-4.05030 + 2.33844i) q^{55} +(0.511116 - 0.295093i) q^{56} +(4.48178 - 2.19472i) q^{57} -5.47269i q^{58} +(2.70209 - 1.56005i) q^{59} +(-0.966271 + 1.43747i) q^{60} +3.09464i q^{61} +(-2.45939 + 4.99514i) q^{62} +(-0.668468 - 1.63952i) q^{63} -1.00000 q^{64} +(1.43747 + 2.48977i) q^{65} +(-4.51914 + 6.72288i) q^{66} +(-5.77223 + 9.99779i) q^{67} +(-1.50350 - 2.60413i) q^{68} +(0.0691170 - 1.01148i) q^{69} -0.590186 q^{70} +(-1.46261 - 0.844440i) q^{71} +(-0.408090 + 2.97211i) q^{72} +(2.55082 + 1.47272i) q^{73} +(2.81841 + 4.88163i) q^{74} +(1.55555 - 0.761750i) q^{75} +(-1.44058 - 2.49515i) q^{76} -2.76023 q^{77} +(4.13264 + 2.77797i) q^{78} +(0.835902 - 0.482609i) q^{79} +(0.866025 + 0.500000i) q^{80} +(8.66692 + 2.42578i) q^{81} +(-2.61342 + 4.52658i) q^{82} +(-5.93914 + 10.2869i) q^{83} +(-0.918064 + 0.449574i) q^{84} +3.00699i q^{85} +(1.65664 + 2.86939i) q^{86} +(-0.646216 + 9.45692i) q^{87} +(4.05030 + 2.33844i) q^{88} -0.409193 q^{89} +(1.83947 - 2.36988i) q^{90} +1.69675i q^{91} -0.585340 q^{92} +(4.83970 - 8.34130i) q^{93} -5.89031 q^{94} +2.88115i q^{95} +(1.72802 + 0.118080i) q^{96} -12.7800 q^{97} +(5.76052 + 3.32584i) q^{98} +(8.60300 - 11.0837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) \) 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9	\( 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9} - 18 q^{10} + 36 q^{16} - 4 q^{18} - 4 q^{19} + 72 q^{21} - 18 q^{22} + 18 q^{25} + 8 q^{28} + 52 q^{31} - 36 q^{33} + 18 q^{34} - 8 q^{36} - 54 q^{37} - 8 q^{39} + 18 q^{40} + 12 q^{42} - 18 q^{43} + 4 q^{45} - 62 q^{49} - 10 q^{51} - 18 q^{55} + 12 q^{57} + 88 q^{63} - 36 q^{64} - 4 q^{66} + 10 q^{67} + 46 q^{69} + 16 q^{70} + 4 q^{72} + 24 q^{73} + 4 q^{76} + 92 q^{78} + 42 q^{79} + 4 q^{81} - 12 q^{82} - 72 q^{84} - 16 q^{87} + 18 q^{88} + 8 q^{90} + 48 q^{93} - 92 q^{94} - 80 q^{97} - 18 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9 - 18 * q^10 + 36 * q^16 - 4 * q^18 - 4 * q^19 + 72 * q^21 - 18 * q^22 + 18 * q^25 + 8 * q^28 + 52 * q^31 - 36 * q^33 + 18 * q^34 - 8 * q^36 - 54 * q^37 - 8 * q^39 + 18 * q^40 + 12 * q^42 - 18 * q^43 + 4 * q^45 - 62 * q^49 - 10 * q^51 - 18 * q^55 + 12 * q^57 + 88 * q^63 - 36 * q^64 - 4 * q^66 + 10 * q^67 + 46 * q^69 + 16 * q^70 + 4 * q^72 + 24 * q^73 + 4 * q^76 + 92 * q^78 + 42 * q^79 + 4 * q^81 - 12 * q^82 - 72 * q^84 - 16 * q^87 + 18 * q^88 + 8 * q^90 + 48 * q^93 - 92 * q^94 - 80 * q^97 - 18 * q^99

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