LMFDB - Embedded newform 930.2.o.e.161.19

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:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.19
Character	$\chi$	$=$	930.161
Dual form			930.2.o.e.491.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.41853 + 0.993862i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.993862 + 1.41853i) q^{6} +(-1.64767 - 2.85385i) q^{7} -1.00000i q^{8} +(1.02448 + 2.81965i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.41853 + 0.993862i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.993862 + 1.41853i) q^{6} +(-1.64767 - 2.85385i) q^{7} -1.00000i q^{8} +(1.02448 + 2.81965i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.34247 - 4.05727i) q^{11} +(-1.41853 - 0.993862i) q^{12} +(-3.57649 - 2.06489i) q^{13} +(2.85385 - 1.64767i) q^{14} +(-0.731555 - 1.56998i) q^{15} +1.00000 q^{16} +(-3.02223 - 5.23465i) q^{17} +(-2.81965 + 1.02448i) q^{18} +(-1.11458 - 1.93051i) q^{19} +(0.866025 + 0.500000i) q^{20} +(0.499058 - 5.68585i) q^{21} +(4.05727 + 2.34247i) q^{22} +0.244780 q^{23} +(0.993862 - 1.41853i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.06489 - 3.57649i) q^{26} +(-1.34909 + 5.01796i) q^{27} +(1.64767 + 2.85385i) q^{28} +2.05814 q^{29} +(1.56998 - 0.731555i) q^{30} +(-5.16785 - 2.07204i) q^{31} +1.00000i q^{32} +(7.35524 - 3.42729i) q^{33} +(5.23465 - 3.02223i) q^{34} +3.29535i q^{35} +(-1.02448 - 2.81965i) q^{36} +(-7.39979 + 4.27227i) q^{37} +(1.93051 - 1.11458i) q^{38} +(-3.02115 - 6.48364i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(6.83739 + 3.94757i) q^{41} +(5.68585 + 0.499058i) q^{42} +(10.0366 - 5.79463i) q^{43} +(-2.34247 + 4.05727i) q^{44} +(0.522605 - 2.95413i) q^{45} +0.244780i q^{46} -3.99299i q^{47} +(1.41853 + 0.993862i) q^{48} +(-1.92965 + 3.34226i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(0.915391 - 10.4292i) q^{51} +(3.57649 + 2.06489i) q^{52} +(0.996554 - 1.72608i) q^{53} +(-5.01796 - 1.34909i) q^{54} +(-4.05727 + 2.34247i) q^{55} +(-2.85385 + 1.64767i) q^{56} +(0.337591 - 3.84623i) q^{57} +2.05814i q^{58} +(-0.641535 + 0.370390i) q^{59} +(0.731555 + 1.56998i) q^{60} +6.30131i q^{61} +(2.07204 - 5.16785i) q^{62} +(6.35888 - 7.56957i) q^{63} -1.00000 q^{64} +(2.06489 + 3.57649i) q^{65} +(3.42729 + 7.35524i) q^{66} +(1.90767 - 3.30418i) q^{67} +(3.02223 + 5.23465i) q^{68} +(0.347229 + 0.243278i) q^{69} -3.29535 q^{70} +(8.36971 + 4.83225i) q^{71} +(2.81965 - 1.02448i) q^{72} +(0.290365 + 0.167642i) q^{73} +(-4.27227 - 7.39979i) q^{74} +(-0.151443 + 1.72542i) q^{75} +(1.11458 + 1.93051i) q^{76} -15.4385 q^{77} +(6.48364 - 3.02115i) q^{78} +(-11.1206 + 6.42046i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-6.90090 + 5.77733i) q^{81} +(-3.94757 + 6.83739i) q^{82} +(-1.42255 + 2.46393i) q^{83} +(-0.499058 + 5.68585i) q^{84} +6.04445i q^{85} +(5.79463 + 10.0366i) q^{86} +(2.91954 + 2.04551i) q^{87} +(-4.05727 - 2.34247i) q^{88} -0.149606 q^{89} +(2.95413 + 0.522605i) q^{90} +13.6090i q^{91} -0.244780 q^{92} +(-5.27144 - 8.07539i) q^{93} +3.99299 q^{94} +2.22916i q^{95} +(-0.993862 + 1.41853i) q^{96} -7.67331 q^{97} +(-3.34226 - 1.92965i) q^{98} +(13.8399 + 2.44837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * 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
$3$	1.41853	+	0.993862i	0.818991	+	0.573807i
$3$	1.41853	+	0.993862i	0.818991	+	0.573807i
$4$	−1.00000			−0.500000
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−0.993862	+	1.41853i	−0.405743	+	0.579114i
$7$	−1.64767	−	2.85385i	−0.622762	−	1.07866i	−0.988969	−	0.148122i	$-0.952677\pi$
$7$	−1.64767	−	2.85385i	−0.622762	−	1.07866i	0.366207	−	0.930533i	$-0.380656\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.02448	+	2.81965i	0.341492	+	0.939885i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	2.34247	−	4.05727i	0.706281	−	1.22331i	−0.259947	−	0.965623i	$-0.583705\pi$
$11$	2.34247	−	4.05727i	0.706281	−	1.22331i	0.966227	−	0.257691i	$-0.0829616\pi$
$12$	−1.41853	−	0.993862i	−0.409495	−	0.286903i
$13$	−3.57649	−	2.06489i	−0.991939	−	0.572696i	−0.0860855	−	0.996288i	$-0.527436\pi$
$13$	−3.57649	−	2.06489i	−0.991939	−	0.572696i	−0.905853	+	0.423592i	$0.860769\pi$
$14$	2.85385	−	1.64767i	0.762725	−	0.440359i
$15$	−0.731555	−	1.56998i	−0.188887	−	0.405366i
$16$	1.00000			0.250000
$17$	−3.02223	−	5.23465i	−0.732998	−	1.26959i	−0.955596	−	0.294679i	$-0.904787\pi$
$17$	−3.02223	−	5.23465i	−0.732998	−	1.26959i	0.222598	−	0.974910i	$-0.428546\pi$
$18$	−2.81965	+	1.02448i	−0.664599	+	0.241471i
$19$	−1.11458	−	1.93051i	−0.255702	−	0.442889i	0.709384	−	0.704822i	$-0.248973\pi$
$19$	−1.11458	−	1.93051i	−0.255702	−	0.442889i	−0.965086	+	0.261933i	$0.915640\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	0.499058	−	5.68585i	0.108903	−	1.24075i
$22$	4.05727	+	2.34247i	0.865014	+	0.499416i
$23$	0.244780			0.0510402			0.0255201	−	0.999674i	$-0.491876\pi$
$23$	0.244780			0.0510402			0.0255201	+	0.999674i	$0.491876\pi$
$24$	0.993862	−	1.41853i	0.202871	−	0.289557i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	2.06489	−	3.57649i	0.404957	−	0.701407i
$27$	−1.34909	+	5.01796i	−0.259633	+	0.965707i
$28$	1.64767	+	2.85385i	0.311381	+	0.539328i
$29$	2.05814			0.382188			0.191094	−	0.981572i	$-0.438797\pi$
$29$	2.05814			0.382188			0.191094	+	0.981572i	$0.438797\pi$
$30$	1.56998	−	0.731555i	0.286637	−	0.133563i
$31$	−5.16785	−	2.07204i	−0.928173	−	0.372149i
$31$	−5.16785	−	2.07204i	−0.928173	−	0.372149i
$32$			1.00000i			0.176777i
$33$	7.35524	−	3.42729i	1.28038	−	0.596614i
$34$	5.23465	−	3.02223i	0.897735	−	0.518308i
$35$			3.29535i			0.557015i
$36$	−1.02448	−	2.81965i	−0.170746	−	0.469942i
$37$	−7.39979	+	4.27227i	−1.21652	+	0.702357i	−0.964172	−	0.265280i	$-0.914536\pi$
$37$	−7.39979	+	4.27227i	−1.21652	+	0.702357i	−0.252347	+	0.967637i	$0.581202\pi$
$38$	1.93051	−	1.11458i	0.313170	−	0.180809i
$39$	−3.02115	−	6.48364i	−0.483772	−	1.03821i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	6.83739	+	3.94757i	1.06782	+	0.616507i	0.927585	−	0.373611i	$-0.121881\pi$
$41$	6.83739	+	3.94757i	1.06782	+	0.616507i	0.140236	+	0.990118i	$0.455214\pi$
$42$	5.68585	+	0.499058i	0.877345	+	0.0770063i
$43$	10.0366	−	5.79463i	1.53057	−	0.883672i	0.531230	−	0.847228i	$-0.321730\pi$
$43$	10.0366	−	5.79463i	1.53057	−	0.883672i	0.999336	−	0.0364445i	$-0.0116032\pi$
$44$	−2.34247	+	4.05727i	−0.353140	+	0.611657i
$45$	0.522605	−	2.95413i	0.0779054	−	0.440376i
$46$			0.244780i			0.0360909i
$47$		−	3.99299i		−	0.582437i	−0.956656	−	0.291219i	$-0.905939\pi$
$47$		−	3.99299i		−	0.582437i	0.956656	−	0.291219i	$-0.0940607\pi$
$48$	1.41853	+	0.993862i	0.204748	+	0.143452i
$49$	−1.92965	+	3.34226i	−0.275665	+	0.477466i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	0.915391	−	10.4292i	0.128180	−	1.46038i
$52$	3.57649	+	2.06489i	0.495969	+	0.286348i
$53$	0.996554	−	1.72608i	0.136887	−	0.237096i	−0.789430	−	0.613841i	$-0.789624\pi$
$53$	0.996554	−	1.72608i	0.136887	−	0.237096i	0.926317	+	0.376746i	$0.122957\pi$
$54$	−5.01796	−	1.34909i	−0.682858	−	0.183589i
$55$	−4.05727	+	2.34247i	−0.547083	+	0.315858i
$56$	−2.85385	+	1.64767i	−0.381362	+	0.220180i
$57$	0.337591	−	3.84623i	0.0447150	−	0.509446i
$58$			2.05814i			0.270247i
$59$	−0.641535	+	0.370390i	−0.0835207	+	0.0482207i	−0.541179	−	0.840908i	$-0.682022\pi$
$59$	−0.641535	+	0.370390i	−0.0835207	+	0.0482207i	0.457658	+	0.889128i	$0.348688\pi$
$60$	0.731555	+	1.56998i	0.0944434	+	0.202683i
$61$			6.30131i			0.806801i	0.915024	+	0.403400i	$0.132172\pi$
$61$			6.30131i			0.806801i	−0.915024	+	0.403400i	$0.867828\pi$
$62$	2.07204	−	5.16785i	0.263149	−	0.656317i
$63$	6.35888	−	7.56957i	0.801144	−	0.953676i
$64$	−1.00000			−0.125000
$65$	2.06489	+	3.57649i	0.256117	+	0.443608i
$66$	3.42729	+	7.35524i	0.421870	+	0.905367i
$67$	1.90767	−	3.30418i	0.233059	−	0.403669i	−0.725648	−	0.688066i	$-0.758460\pi$
$67$	1.90767	−	3.30418i	0.233059	−	0.403669i	0.958707	+	0.284397i	$0.0917933\pi$
$68$	3.02223	+	5.23465i	0.366499	+	0.634795i
$69$	0.347229	+	0.243278i	0.0418014	+	0.0292872i
$70$	−3.29535			−0.393869
$71$	8.36971	+	4.83225i	0.993302	+	0.573483i	0.906260	−	0.422722i	$-0.138925\pi$
$71$	8.36971	+	4.83225i	0.993302	+	0.573483i	0.0870422	+	0.996205i	$0.472259\pi$
$72$	2.81965	−	1.02448i	0.332299	−	0.120736i
$73$	0.290365	+	0.167642i	0.0339847	+	0.0196211i	0.516896	−	0.856048i	$-0.327087\pi$
$73$	0.290365	+	0.167642i	0.0339847	+	0.0196211i	−0.482911	+	0.875669i	$0.660421\pi$
$74$	−4.27227	−	7.39979i	−0.496642	−	0.860208i
$75$	−0.151443	+	1.72542i	−0.0174871	+	0.199234i
$76$	1.11458	+	1.93051i	0.127851	+	0.221444i
$77$	−15.4385			−1.75938
$78$	6.48364	−	3.02115i	0.734128	−	0.342078i
$79$	−11.1206	+	6.42046i	−1.25116	+	0.722358i	−0.971340	−	0.237695i	$-0.923608\pi$
$79$	−11.1206	+	6.42046i	−1.25116	+	0.722358i	−0.279820	+	0.960052i	$0.590275\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	−6.90090	+	5.77733i	−0.766767	+	0.641926i
$82$	−3.94757	+	6.83739i	−0.435936	+	0.755063i
$83$	−1.42255	+	2.46393i	−0.156145	+	0.270451i	−0.933475	−	0.358642i	$-0.883240\pi$
$83$	−1.42255	+	2.46393i	−0.156145	+	0.270451i	0.777330	+	0.629093i	$0.216573\pi$
$84$	−0.499058	+	5.68585i	−0.0544516	+	0.620377i
$85$			6.04445i			0.655613i
$86$	5.79463	+	10.0366i	0.624851	+	1.08227i
$87$	2.91954	+	2.04551i	0.313008	+	0.219302i
$88$	−4.05727	−	2.34247i	−0.432507	−	0.249708i
$89$	−0.149606			−0.0158582			−0.00792909	−	0.999969i	$-0.502524\pi$
$89$	−0.149606			−0.0158582			−0.00792909	+	0.999969i	$0.502524\pi$
$90$	2.95413	+	0.522605i	0.311393	+	0.0550874i
$91$			13.6090i			1.42661i
$92$	−0.244780			−0.0255201
$93$	−5.27144	−	8.07539i	−0.546623	−	0.837379i
$94$	3.99299			0.411845
$95$			2.22916i			0.228707i
$96$	−0.993862	+	1.41853i	−0.101436	+	0.144778i
$97$	−7.67331			−0.779107			−0.389553	−	0.921004i	$-0.627371\pi$
$97$	−7.67331			−0.779107			−0.389553	+	0.921004i	$0.627371\pi$
$98$	−3.34226	−	1.92965i	−0.337619	−	0.194925i
$99$	13.8399	+	2.44837i	1.39096	+	0.246071i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$		−	5.06959i		−	0.504443i	−0.967669	−	0.252222i	$-0.918839\pi$
$101$		−	5.06959i		−	0.504443i	0.967669	−	0.252222i	$-0.0811612\pi$
$102$	10.4292	+	0.915391i	1.03265	+	0.0906372i
$103$	9.37875	−	16.2445i	0.924115	−	1.60061i	0.131138	−	0.991364i	$-0.458137\pi$
$103$	9.37875	−	16.2445i	0.924115	−	1.60061i	0.792978	−	0.609251i	$-0.208530\pi$
$104$	−2.06489	+	3.57649i	−0.202479	+	0.350703i
$105$	−3.27512	+	4.67456i	−0.319619	+	0.456190i
$106$	1.72608	+	0.996554i	0.167652	+	0.0967939i
$107$	−3.66151	+	2.11397i	−0.353971	+	0.204366i	−0.666433	−	0.745565i	$-0.732180\pi$
$107$	−3.66151	+	2.11397i	−0.353971	+	0.204366i	0.312462	+	0.949930i	$0.398846\pi$
$108$	1.34909	−	5.01796i	0.129817	−	0.482854i
$109$	5.84653			0.559996			0.279998	−	0.960001i	$-0.409666\pi$
$109$	5.84653			0.559996			0.279998	+	0.960001i	$0.409666\pi$
$110$	−2.34247	−	4.05727i	−0.223346	−	0.386846i
$111$	−14.7429	−	1.29401i	−1.39933	−	0.122822i
$112$	−1.64767	−	2.85385i	−0.155690	−	0.269664i
$113$	5.58805	+	3.22626i	0.525679	+	0.303501i	0.739255	−	0.673425i	$-0.235178\pi$
$113$	5.58805	+	3.22626i	0.525679	+	0.303501i	−0.213576	+	0.976926i	$0.568511\pi$
$114$	3.84623	+	0.337591i	0.360232	+	0.0316183i
$115$	−0.211986	−	0.122390i	−0.0197678	−	0.0114129i
$116$	−2.05814			−0.191094
$117$	2.15824	−	12.1999i	0.199529	−	1.12788i
$118$	−0.370390	−	0.641535i	−0.0340972	−	0.0590580i
$119$	−9.95929	+	17.2500i	−0.912966	+	1.58130i
$120$	−1.56998	+	0.731555i	−0.143319	+	0.0667815i
$121$	−5.47431	−	9.48178i	−0.497665	−	0.861980i
$122$	−6.30131			−0.570494
$123$	5.77573	+	12.3952i	0.520780	+	1.11764i
$124$	5.16785	+	2.07204i	0.464086	+	0.186075i
$125$		−	1.00000i		−	0.0894427i
$126$	7.56957	+	6.35888i	0.674351	+	0.566494i
$127$	0.366646	−	0.211683i	0.0325346	−	0.0187839i	−0.483644	−	0.875265i	$-0.660687\pi$
$127$	0.366646	−	0.211683i	0.0325346	−	0.0187839i	0.516179	+	0.856481i	$0.327354\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	19.9963	+	1.75511i	1.76058	+	0.154529i
$130$	−3.57649	+	2.06489i	−0.313679	+	0.181102i
$131$	−1.79983	+	1.03913i	−0.157252	+	0.0907895i	−0.576561	−	0.817054i	$-0.695606\pi$
$131$	−1.79983	+	1.03913i	−0.157252	+	0.0907895i	0.419309	+	0.907844i	$0.362272\pi$
$132$	−7.35524	+	3.42729i	−0.640191	+	0.298307i
$133$	−3.67293	+	6.36169i	−0.318483	+	0.551629i
$134$	3.30418	+	1.90767i	0.285437	+	0.164797i
$135$	3.67733	−	3.67114i	0.316494	−	0.315961i
$136$	−5.23465	+	3.02223i	−0.448868	+	0.259154i
$137$	9.76518	−	16.9138i	0.834296	−	1.44504i	−0.0603063	−	0.998180i	$-0.519208\pi$
$137$	9.76518	−	16.9138i	0.834296	−	1.44504i	0.894602	−	0.446863i	$-0.147459\pi$
$138$	−0.243278	+	0.347229i	−0.0207092	+	0.0295581i
$139$		−	22.5295i		−	1.91092i	−0.295114	−	0.955462i	$-0.595358\pi$
$139$		−	22.5295i		−	1.91092i	0.295114	−	0.955462i	$-0.404642\pi$
$140$		−	3.29535i		−	0.278508i
$141$	3.96848	−	5.66419i	0.334206	−	0.477011i
$142$	−4.83225	+	8.36971i	−0.405514	+	0.702370i
$143$	−16.7556	+	9.67385i	−1.40117	+	0.808968i
$144$	1.02448	+	2.81965i	0.0853730	+	0.234971i
$145$	−1.78240	−	1.02907i	−0.148021	−	0.0854597i
$146$	−0.167642	+	0.290365i	−0.0138742	+	0.0240308i
$147$	−6.05903	+	2.82330i	−0.499740	+	0.232862i
$148$	7.39979	−	4.27227i	0.608259	−	0.351179i
$149$	13.4165	−	7.74601i	1.09912	−	0.634578i	0.163131	−	0.986604i	$-0.447841\pi$
$149$	13.4165	−	7.74601i	1.09912	−	0.634578i	0.935990	+	0.352027i	$0.114507\pi$
$150$	−1.72542	−	0.151443i	−0.140880	−	0.0123653i
$151$			18.2693i			1.48673i	0.668884	+	0.743367i	$0.266772\pi$
$151$			18.2693i			1.48673i	−0.668884	+	0.743367i	$0.733228\pi$
$152$	−1.93051	+	1.11458i	−0.156585	+	0.0904043i
$153$	11.6637	−	13.8844i	0.942955	−	1.12249i
$154$		−	15.4385i		−	1.24407i
$155$	3.43947	+	4.37836i	0.276265	+	0.351679i
$156$	3.02115	+	6.48364i	0.241886	+	0.519107i
$157$	−18.3537			−1.46478			−0.732391	−	0.680885i	$-0.761596\pi$
$157$	−18.3537			−1.46478			−0.732391	+	0.680885i	$0.761596\pi$
$158$	−6.42046	−	11.1206i	−0.510784	−	0.884704i
$159$	3.12913	−	1.45807i	0.248156	−	0.115632i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−0.403318	−	0.698566i	−0.0317859	−	0.0550548i
$162$	−5.77733	−	6.90090i	−0.453910	−	0.542186i
$163$	1.70445			0.133503			0.0667515	−	0.997770i	$-0.478737\pi$
$163$	1.70445			0.133503			0.0667515	+	0.997770i	$0.478737\pi$
$164$	−6.83739	−	3.94757i	−0.533910	−	0.308253i
$165$	−8.08347	−	0.709501i	−0.629297	−	0.0552346i
$166$	−2.46393	−	1.42255i	−0.191238	−	0.110411i
$167$	6.28618	+	10.8880i	0.486439	+	0.842537i	0.999878	−	0.0155887i	$-0.00496225\pi$
$167$	6.28618	+	10.8880i	0.486439	+	0.842537i	−0.513439	+	0.858126i	$0.671629\pi$
$168$	−5.68585	−	0.499058i	−0.438673	−	0.0385031i
$169$	2.02750	+	3.51174i	0.155962	+	0.270134i
$170$	−6.04445			−0.463588
$171$	4.30151	−	5.12049i	0.328944	−	0.391573i
$172$	−10.0366	+	5.79463i	−0.765283	+	0.441836i
$173$	2.25868	+	1.30405i	0.171724	+	0.0991450i	0.583399	−	0.812186i	$-0.301723\pi$
$173$	2.25868	+	1.30405i	0.171724	+	0.0991450i	−0.411674	+	0.911331i	$0.635056\pi$
$174$	−2.04551	+	2.91954i	−0.155070	+	0.221330i
$175$	1.64767	−	2.85385i	0.124552	−	0.215731i
$176$	2.34247	−	4.05727i	0.176570	−	0.305828i
$177$	−1.27816	−	0.112186i	−0.0960720	−	0.00843242i
$178$		−	0.149606i		−	0.0112134i
$179$	9.49768	+	16.4505i	0.709890	+	1.22957i	0.964898	+	0.262626i	$0.0845886\pi$
$179$	9.49768	+	16.4505i	0.709890	+	1.22957i	−0.255008	+	0.966939i	$0.582078\pi$
$180$	−0.522605	+	2.95413i	−0.0389527	+	0.220188i
$181$	−14.3763	−	8.30014i	−1.06858	−	0.616944i	−0.140786	−	0.990040i	$-0.544963\pi$
$181$	−14.3763	−	8.30014i	−1.06858	−	0.616944i	−0.927793	+	0.373096i	$0.878296\pi$
$182$	−13.6090			−1.00877
$183$	−6.26264	+	8.93863i	−0.462948	+	0.660762i
$184$		−	0.244780i		−	0.0180454i
$185$	8.54454			0.628207
$186$	8.07539	−	5.27144i	0.592116	−	0.386521i
$187$	−28.3179			−2.07081
$188$			3.99299i			0.291219i
$189$	16.5434	−	4.41784i	1.20336	−	0.321351i
$190$	−2.22916			−0.161720
$191$	14.6036	+	8.43140i	1.05668	+	0.610074i	0.924512	−	0.381153i	$-0.124473\pi$
$191$	14.6036	+	8.43140i	1.05668	+	0.610074i	0.132168	+	0.991227i	$0.457806\pi$
$192$	−1.41853	−	0.993862i	−0.102374	−	0.0717258i
$193$	−3.46345	−	5.99887i	−0.249305	−	0.431808i	0.714028	−	0.700117i	$-0.246869\pi$
$193$	−3.46345	−	5.99887i	−0.249305	−	0.431808i	−0.963333	+	0.268308i	$0.913535\pi$
$194$		−	7.67331i		−	0.550912i
$195$	−0.625425	+	7.12558i	−0.0447876	+	0.510273i
$196$	1.92965	−	3.34226i	0.137832	−	0.238733i
$197$	7.40933	−	12.8333i	0.527893	−	0.914337i	−0.471579	−	0.881824i	$-0.656316\pi$
$197$	7.40933	−	12.8333i	0.527893	−	0.914337i	0.999471	−	0.0325129i	$-0.0103510\pi$
$198$	−2.44837	+	13.8399i	−0.173998	+	0.983559i
$199$	−16.4647	−	9.50589i	−1.16715	−	0.673855i	−0.214143	−	0.976802i	$-0.568696\pi$
$199$	−16.4647	−	9.50589i	−1.16715	−	0.673855i	−0.953007	+	0.302947i	$0.902029\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	5.98999	−	2.79113i	0.422501	−	0.196871i
$202$	5.06959			0.356695
$203$	−3.39115	−	5.87364i	−0.238012	−	0.412249i
$204$	−0.915391	+	10.4292i	−0.0640902	+	0.730191i
$205$	−3.94757	−	6.83739i	−0.275710	−	0.477544i
$206$	16.2445	+	9.37875i	1.13181	+	0.653448i
$207$	0.250771	+	0.690195i	0.0174298	+	0.0479719i
$208$	−3.57649	−	2.06489i	−0.247985	−	0.143174i
$209$	−10.4435			−0.722390
$210$	−4.67456	−	3.27512i	−0.322575	−	0.226005i
$211$	−0.159771	−	0.276731i	−0.0109991	−	0.0190509i	0.860473	−	0.509495i	$-0.170168\pi$
$211$	−0.159771	−	0.276731i	−0.0109991	−	0.0190509i	−0.871473	+	0.490444i	$0.836835\pi$
$212$	−0.996554	+	1.72608i	−0.0684436	+	0.118548i
$213$	7.07012	+	15.1731i	0.484437	+	1.03964i
$214$	−2.11397	−	3.66151i	−0.144508	−	0.250296i
$215$	−11.5893			−0.790381
$216$	5.01796	+	1.34909i	0.341429	+	0.0917943i
$217$	2.60163	+	18.1623i	0.176610	+	1.23294i
$218$			5.84653i			0.395977i
$219$	0.245279	+	0.526389i	0.0165744	+	0.0355701i
$220$	4.05727	−	2.34247i	0.273541	−	0.157929i
$221$			24.9622i			1.67914i
$222$	1.29401	−	14.7429i	0.0868484	−	0.989479i
$223$	−1.19955	+	0.692562i	−0.0803279	+	0.0463774i	−0.539626	−	0.841905i	$-0.681434\pi$
$223$	−1.19955	+	0.692562i	−0.0803279	+	0.0463774i	0.459298	+	0.888282i	$0.348101\pi$
$224$	2.85385	−	1.64767i	0.190681	−	0.110090i
$225$	−1.92965	+	2.29705i	−0.128644	+	0.153137i
$226$	−3.22626	+	5.58805i	−0.214608	+	0.371711i
$227$	7.88419	+	4.55194i	0.523292	+	0.302123i	0.738281	−	0.674494i	$-0.235638\pi$
$227$	7.88419	+	4.55194i	0.523292	+	0.302123i	−0.214988	+	0.976617i	$0.568971\pi$
$228$	−0.337591	+	3.84623i	−0.0223575	+	0.254723i
$229$	6.91782	−	3.99401i	0.457143	−	0.263931i	−0.253699	−	0.967283i	$-0.581647\pi$
$229$	6.91782	−	3.99401i	0.457143	−	0.263931i	0.710842	+	0.703352i	$0.248314\pi$
$230$	0.122390	−	0.211986i	0.00807016	−	0.0139779i
$231$	−21.9000	−	15.3437i	−1.44092	−	1.00954i
$232$		−	2.05814i		−	0.135124i
$233$			15.9529i			1.04511i	0.852606	+	0.522554i	$0.175021\pi$
$233$			15.9529i			1.04511i	−0.852606	+	0.522554i	$0.824979\pi$
$234$	12.1999	+	2.15824i	0.797531	+	0.141089i
$235$	−1.99650	+	3.45803i	−0.130237	+	0.225577i
$236$	0.641535	−	0.370390i	0.0417603	−	0.0241103i
$237$	−22.1559	−	1.94467i	−1.43918	−	0.126320i
$238$	−17.2500	−	9.95929i	−1.11815	−	0.645565i
$239$	4.52292	−	7.83393i	0.292564	−	0.506735i	−0.681852	−	0.731491i	$-0.738825\pi$
$239$	4.52292	−	7.83393i	0.292564	−	0.506735i	0.974415	+	0.224756i	$0.0721584\pi$
$240$	−0.731555	−	1.56998i	−0.0472217	−	0.101342i
$241$	13.3621	−	7.71462i	0.860730	−	0.496943i	−0.00352685	−	0.999994i	$-0.501123\pi$
$241$	13.3621	−	7.71462i	0.860730	−	0.496943i	0.864257	+	0.503051i	$0.167789\pi$
$242$	9.48178	−	5.47431i	0.609512	−	0.351902i
$243$	−15.5310	+	1.33680i	−0.996316	+	0.0857557i
$244$		−	6.30131i		−	0.403400i
$245$	3.34226	−	1.92965i	0.213529	−	0.123281i
$246$	−12.3952	+	5.77573i	−0.790288	+	0.368247i
$247$			9.20591i			0.585758i
$248$	−2.07204	+	5.16785i	−0.131575	+	0.328159i
$249$	−4.46673	+	2.08134i	−0.283068	+	0.131900i
$250$	1.00000			0.0632456
$251$	−1.89792	−	3.28729i	−0.119795	−	0.207492i	0.799891	−	0.600145i	$-0.204891\pi$
$251$	−1.89792	−	3.28729i	−0.119795	−	0.207492i	−0.919687	+	0.392653i	$0.871557\pi$
$252$	−6.35888	+	7.56957i	−0.400572	+	0.476838i
$253$	0.573389	−	0.993140i	0.0360487	−	0.0624382i
$254$	0.211683	+	0.366646i	0.0132822	+	0.0230054i
$255$	−6.00736	+	8.57426i	−0.376195	+	0.536941i
$256$	1.00000			0.0625000
$257$	−26.8650	−	15.5105i	−1.67579	−	0.967518i	−0.964296	−	0.264828i	$-0.914685\pi$
$257$	−26.8650	−	15.5105i	−1.67579	−	0.967518i	−0.711495	−	0.702691i	$-0.751982\pi$
$258$	−1.75511	+	19.9963i	−0.109269	+	1.24492i
$259$	24.3849	+	14.0786i	1.51520	+	0.874803i
$260$	−2.06489	−	3.57649i	−0.128059	−	0.221804i
$261$	2.10852	+	5.80325i	0.130514	+	0.359212i
$262$	−1.03913	−	1.79983i	−0.0641979	−	0.111194i
$263$	−21.5086			−1.32627			−0.663137	−	0.748498i	$-0.730775\pi$
$263$	−21.5086			−1.32627			−0.663137	+	0.748498i	$0.730775\pi$
$264$	−3.42729	−	7.35524i	−0.210935	−	0.452684i
$265$	−1.72608	+	0.996554i	−0.106032	+	0.0612178i
$266$	−6.36169	−	3.67293i	−0.390060	−	0.225202i
$267$	−0.212221	−	0.148688i	−0.0129877	−	0.00909953i
$268$	−1.90767	+	3.30418i	−0.116529	+	0.201835i
$269$	−13.5212	+	23.4194i	−0.824401	+	1.42791i	0.0779746	+	0.996955i	$0.475155\pi$
$269$	−13.5212	+	23.4194i	−0.824401	+	1.42791i	−0.902376	+	0.430950i	$0.858179\pi$
$270$	3.67114	+	3.67733i	0.223418	+	0.223795i
$271$			16.9825i			1.03162i	0.856704	+	0.515808i	$0.172508\pi$
$271$			16.9825i			1.03162i	−0.856704	+	0.515808i	$0.827492\pi$
$272$	−3.02223	−	5.23465i	−0.183249	−	0.317397i
$273$	−13.5255	+	19.3049i	−0.818600	+	1.16838i
$274$	16.9138	+	9.76518i	1.02180	+	0.589936i
$275$	4.68494			0.282512
$276$	−0.347229	−	0.243278i	−0.0209007	−	0.0146436i
$277$		−	23.1214i		−	1.38923i	−0.719381	−	0.694616i	$-0.755574\pi$
$277$		−	23.1214i		−	1.38923i	0.719381	−	0.694616i	$-0.244426\pi$
$278$	22.5295			1.35123
$279$	0.548100	−	16.6943i	0.0328139	−	0.999461i
$280$	3.29535			0.196935
$281$		−	26.0722i		−	1.55534i	−0.628674	−	0.777669i	$-0.716402\pi$
$281$		−	26.0722i		−	1.55534i	0.628674	−	0.777669i	$-0.283598\pi$
$282$	5.66419	+	3.96848i	0.337298	+	0.236320i
$283$	14.5905			0.867315			0.433657	−	0.901078i	$-0.357223\pi$
$283$	14.5905			0.867315			0.433657	+	0.901078i	$0.357223\pi$
$284$	−8.36971	−	4.83225i	−0.496651	−	0.286742i
$285$	−2.21548	+	3.16214i	−0.131234	+	0.187309i
$286$	−9.67385	−	16.7556i	−0.572027	−	0.990780i
$287$		−	26.0172i		−	1.53575i
$288$	−2.81965	+	1.02448i	−0.166150	+	0.0603678i
$289$	−9.76772	+	16.9182i	−0.574571	+	0.995187i
$290$	1.02907	−	1.78240i	0.0604292	−	0.104666i
$291$	−10.8849	−	7.62622i	−0.638081	−	0.447057i
$292$	−0.290365	−	0.167642i	−0.0169923	−	0.00981053i
$293$	24.7303	−	14.2780i	1.44476	−	0.834132i	0.446598	−	0.894735i	$-0.352636\pi$
$293$	24.7303	−	14.2780i	1.44476	−	0.834132i	0.998162	+	0.0606026i	$0.0193022\pi$
$294$	−2.82330	−	6.05903i	−0.164658	−	0.353370i
$295$	0.740780			0.0431299
$296$	4.27227	+	7.39979i	0.248321	+	0.430104i
$297$	17.1990	+	17.2281i	0.997989	+	0.999673i
$298$	7.74601	+	13.4165i	0.448714	+	0.777196i
$299$	−0.875452	−	0.505443i	−0.0506287	−	0.0292305i
$300$	0.151443	−	1.72542i	0.00874357	−	0.0996170i
$301$	−33.0740	−	19.0953i	−1.90636	−	1.10064i
$302$	−18.2693			−1.05128
$303$	5.03848	−	7.19139i	0.289453	−	0.413134i
$304$	−1.11458	−	1.93051i	−0.0639255	−	0.110722i
$305$	3.15066	−	5.45710i	0.180406	−	0.312473i
$306$	13.8844	+	11.6637i	0.793719	+	0.666770i
$307$	4.69037	+	8.12397i	0.267694	+	0.463659i	0.968266	−	0.249922i	$-0.0804051\pi$
$307$	4.69037	+	8.12397i	0.267694	+	0.463659i	−0.700572	+	0.713582i	$0.747072\pi$
$308$	15.4385			0.879689
$309$	29.4488	−	13.7221i	1.67529	−	0.780625i
$310$	−4.37836	+	3.43947i	−0.248674	+	0.195349i
$311$			1.63457i			0.0926879i	0.998926	+	0.0463440i	$0.0147570\pi$
$311$			1.63457i			0.0926879i	−0.998926	+	0.0463440i	$0.985243\pi$
$312$	−6.48364	+	3.02115i	−0.367064	+	0.171039i
$313$	10.6934	−	6.17384i	0.604427	−	0.348966i	−0.166354	−	0.986066i	$-0.553200\pi$
$313$	10.6934	−	6.17384i	0.604427	−	0.348966i	0.770781	+	0.637100i	$0.219866\pi$
$314$		−	18.3537i		−	1.03576i
$315$	−9.29174	+	3.37600i	−0.523530	+	0.190216i
$316$	11.1206	−	6.42046i	0.625580	−	0.361179i
$317$	−29.5244	+	17.0459i	−1.65825	+	0.957393i	−0.684732	+	0.728795i	$0.740081\pi$
$317$	−29.5244	+	17.0459i	−1.65825	+	0.957393i	−0.973521	+	0.228598i	$0.926586\pi$
$318$	1.45807	+	3.12913i	0.0817644	+	0.175473i
$319$	4.82113	−	8.35045i	0.269932	−	0.467535i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−7.29497	−	0.640293i	−0.407166	−	0.0357377i
$322$	0.698566	−	0.403318i	0.0389296	−	0.0224760i
$323$	−6.73702	+	11.6689i	−0.374858	+	0.649273i
$324$	6.90090	−	5.77733i	0.383383	−	0.320963i
$325$		−	4.12977i		−	0.229078i
$326$			1.70445i			0.0944009i
$327$	8.29350	+	5.81064i	0.458631	+	0.321329i
$328$	3.94757	−	6.83739i	0.217968	−	0.377532i
$329$	−11.3954	+	6.57914i	−0.628249	+	0.362720i
$330$	0.709501	−	8.08347i	0.0390568	−	0.444980i
$331$	19.1972	+	11.0835i	1.05517	+	0.609205i	0.924093	−	0.382167i	$-0.124822\pi$
$331$	19.1972	+	11.0835i	1.05517	+	0.609205i	0.131080	+	0.991372i	$0.458155\pi$
$332$	1.42255	−	2.46393i	0.0780725	−	0.135225i
$333$	−19.6272	−	16.4880i	−1.07557	−	0.903538i
$334$	−10.8880	+	6.28618i	−0.595764	+	0.343964i
$335$	−3.30418	+	1.90767i	−0.180526	+	0.104227i
$336$	0.499058	−	5.68585i	0.0272258	−	0.310188i
$337$			24.0073i			1.30776i	0.756597	+	0.653881i	$0.226860\pi$
$337$			24.0073i			1.30776i	−0.756597	+	0.653881i	$0.773140\pi$
$338$	−3.51174	+	2.02750i	−0.191013	+	0.110282i
$339$	4.72038	+	10.1303i	0.256376	+	0.550203i
$340$		−	6.04445i		−	0.327807i
$341$	−20.5123	+	16.1137i	−1.11081	+	0.872605i
$342$	5.12049	+	4.30151i	0.276884	+	0.232599i
$343$	−10.3497			−0.558829
$344$	−5.79463	−	10.0366i	−0.312425	−	0.541137i
$345$	−0.179070	−	0.384299i	−0.00964081	−	0.0206900i
$346$	−1.30405	+	2.25868i	−0.0701061	+	0.121427i
$347$	14.1185	+	24.4539i	0.757919	+	1.31275i	0.943910	+	0.330202i	$0.107117\pi$
$347$	14.1185	+	24.4539i	0.757919	+	1.31275i	−0.185992	+	0.982551i	$0.559550\pi$
$348$	−2.91954	−	2.04551i	−0.156504	−	0.109651i
$349$	14.1084			0.755205			0.377602	−	0.925968i	$-0.376749\pi$
$349$	14.1084			0.755205			0.377602	+	0.925968i	$0.376749\pi$
$350$	2.85385	+	1.64767i	0.152545	+	0.0880718i
$351$	15.1865	−	15.1609i	0.810597	−	0.809231i
$352$	4.05727	+	2.34247i	0.216253	+	0.124854i
$353$	11.1592	+	19.3283i	0.593943	+	1.02874i	0.993695	+	0.112116i	$0.0357628\pi$
$353$	11.1592	+	19.3283i	0.593943	+	1.02874i	−0.399752	+	0.916623i	$0.630904\pi$
$354$	0.112186	−	1.27816i	0.00596262	−	0.0679332i
$355$	−4.83225	−	8.36971i	−0.256469	−	0.444218i
$356$	0.149606			0.00792909
$357$	−31.2717	+	14.5715i	−1.65507	+	0.771207i
$358$	−16.4505	+	9.49768i	−0.869434	+	0.501968i
$359$	4.93899	+	2.85152i	0.260670	+	0.150498i	0.624640	−	0.780913i	$-0.285246\pi$
$359$	4.93899	+	2.85152i	0.260670	+	0.150498i	−0.363970	+	0.931411i	$0.618579\pi$
$360$	−2.95413	−	0.522605i	−0.155696	−	0.0275437i
$361$	7.01543	−	12.1511i	0.369233	−	0.639530i
$362$	8.30014	−	14.3763i	0.436245	−	0.755599i
$363$	1.65809	−	18.8909i	0.0870273	−	0.991517i
$364$		−	13.6090i		−	0.713307i
$365$	−0.167642	−	0.290365i	−0.00877480	−	0.0151984i
$366$	−8.93863	−	6.26264i	−0.467229	−	0.327353i
$367$	27.7580	+	16.0261i	1.44896	+	0.836555i	0.998419	−	0.0562025i	$-0.0178992\pi$
$367$	27.7580	+	16.0261i	1.44896	+	0.836555i	0.450537	+	0.892758i	$0.351233\pi$
$368$	0.244780			0.0127600
$369$	−4.12604	+	23.3233i	−0.214793	+	1.21416i
$370$			8.54454i			0.444210i
$371$	−6.56798			−0.340993
$372$	5.27144	+	8.07539i	0.273312	+	0.418689i
$373$	−22.0309			−1.14072			−0.570359	−	0.821396i	$-0.693196\pi$
$373$	−22.0309			−1.14072			−0.570359	+	0.821396i	$0.693196\pi$
$374$		−	28.3179i		−	1.46428i
$375$	0.993862	−	1.41853i	0.0513228	−	0.0732528i
$376$	−3.99299			−0.205923
$377$	−7.36092	−	4.24983i	−0.379107	−	0.218877i
$378$	4.41784	+	16.5434i	0.227229	+	0.850901i
$379$	11.4743	+	19.8741i	0.589397	+	1.02087i	0.994312	+	0.106511i	$0.0339679\pi$
$379$	11.4743	+	19.8741i	0.589397	+	1.02087i	−0.404915	+	0.914355i	$0.632699\pi$
$380$		−	2.22916i		−	0.114353i
$381$	0.730484	+	0.0641160i	0.0374238	+	0.00328476i
$382$	−8.43140	+	14.6036i	−0.431388	+	0.747186i
$383$	5.15835	−	8.93453i	0.263579	−	0.456533i	−0.703611	−	0.710585i	$-0.748430\pi$
$383$	5.15835	−	8.93453i	0.263579	−	0.456533i	0.967190	+	0.254052i	$0.0817635\pi$
$384$	0.993862	−	1.41853i	0.0507178	−	0.0723892i
$385$	13.3701	+	7.71924i	0.681404	+	0.393409i
$386$	5.99887	−	3.46345i	0.305335	−	0.176285i
$387$	26.6211	+	22.3633i	1.35323	+	1.13679i
$388$	7.67331			0.389553
$389$	−12.7371	−	22.0613i	−0.645798	−	1.11855i	−0.984117	−	0.177523i	$-0.943192\pi$
$389$	−12.7371	−	22.0613i	−0.645798	−	1.11855i	0.338319	−	0.941031i	$-0.390142\pi$
$390$	−7.12558	−	0.625425i	−0.360818	−	0.0316696i
$391$	−0.739781	−	1.28134i	−0.0374123	−	0.0648001i
$392$	3.34226	+	1.92965i	0.168810	+	0.0974623i
$393$	−3.58588	−	0.314739i	−0.180884	−	0.0158765i
$394$	12.8333	+	7.40933i	0.646534	+	0.373276i
$395$	12.8409			0.646096
$396$	−13.8399	−	2.44837i	−0.695482	−	0.123035i
$397$	3.16333	+	5.47906i	0.158763	+	0.274986i	0.934423	−	0.356165i	$-0.115916\pi$
$397$	3.16333	+	5.47906i	0.158763	+	0.274986i	−0.775660	+	0.631151i	$0.782583\pi$
$398$	9.50589	−	16.4647i	0.476487	−	0.825300i
$399$	−11.5328	+	5.37389i	−0.577363	+	0.269031i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	25.4504			1.27093			0.635465	−	0.772130i	$-0.280808\pi$
$401$	25.4504			1.27093			0.635465	+	0.772130i	$0.280808\pi$
$402$	2.79113	+	5.98999i	0.139209	+	0.298753i
$403$	14.2042	+	18.0816i	0.707562	+	0.900710i
$404$			5.06959i			0.252222i
$405$	8.86502	−	1.55287i	0.440506	−	0.0771626i
$406$	5.87364	−	3.39115i	0.291504	−	0.168300i
$407$			40.0306i			1.98425i
$408$	−10.4292	−	0.915391i	−0.516323	−	0.0453186i
$409$	31.9037	−	18.4196i	1.57754	−	0.910790i	0.582333	−	0.812950i	$-0.302140\pi$
$409$	31.9037	−	18.4196i	1.57754	−	0.910790i	0.995202	−	0.0978399i	$-0.0311933\pi$
$410$	6.83739	−	3.94757i	0.337675	−	0.194957i
$411$	30.6622	−	14.2875i	1.51246	−	0.704752i
$412$	−9.37875	+	16.2445i	−0.462058	+	0.800307i
$413$	2.11408	+	1.22056i	0.104027	+	0.0600600i
$414$	−0.690195	+	0.250771i	−0.0339212	+	0.0123247i
$415$	2.46393	−	1.42255i	0.120949	−	0.0698301i
$416$	2.06489	−	3.57649i	0.101239	−	0.175352i
$417$	22.3912	−	31.9588i	1.09650	−	1.56503i
$418$		−	10.4435i		−	0.510807i
$419$			8.72337i			0.426164i	0.977034	+	0.213082i	$0.0683502\pi$
$419$			8.72337i			0.426164i	−0.977034	+	0.213082i	$0.931650\pi$
$420$	3.27512	−	4.67456i	0.159810	−	0.228095i
$421$	−2.19810	+	3.80721i	−0.107129	+	0.185552i	−0.914606	−	0.404347i	$-0.867499\pi$
$421$	−2.19810	+	3.80721i	−0.107129	+	0.185552i	0.807477	+	0.589899i	$0.200832\pi$
$422$	0.276731	−	0.159771i	0.0134711	−	0.00777752i
$423$	11.2589	−	4.09072i	0.547424	−	0.198898i
$424$	−1.72608	−	0.996554i	−0.0838260	−	0.0483969i
$425$	3.02223	−	5.23465i	0.146600	−	0.253918i
$426$	−15.1731	+	7.07012i	−0.735137	+	0.342548i
$427$	17.9830	−	10.3825i	0.870260	−	0.502445i
$428$	3.66151	−	2.11397i	0.176986	−	0.102183i
$429$	−33.3829	−	2.93008i	−1.61174	−	0.141465i
$430$		−	11.5893i		−	0.558883i
$431$	12.3311	−	7.11935i	0.593967	−	0.342927i	−0.172698	−	0.984975i	$-0.555248\pi$
$431$	12.3311	−	7.11935i	0.593967	−	0.342927i	0.766665	+	0.642048i	$0.221915\pi$
$432$	−1.34909	+	5.01796i	−0.0649084	+	0.241427i
$433$		−	16.3649i		−	0.786448i	−0.919443	−	0.393224i	$-0.871360\pi$
$433$		−	16.3649i		−	0.786448i	0.919443	−	0.393224i	$-0.128640\pi$
$434$	−18.1623	+	2.60163i	−0.871820	+	0.124882i
$435$	−1.50564	−	3.23124i	−0.0721901	−	0.154926i
$436$	−5.84653			−0.279998
$437$	−0.272827	−	0.472550i	−0.0130511	−	0.0226051i
$438$	−0.526389	+	0.245279i	−0.0251519	+	0.0117199i
$439$	−6.66688	+	11.5474i	−0.318193	+	0.551126i	−0.980111	−	0.198450i	$-0.936409\pi$
$439$	−6.66688	+	11.5474i	−0.318193	+	0.551126i	0.661918	+	0.749576i	$0.269743\pi$
$440$	2.34247	+	4.05727i	0.111673	+	0.193423i
$441$	−11.4009	−	2.01689i	−0.542900	−	0.0960426i
$442$	−24.9622			−1.18733
$443$	−18.7900	−	10.8484i	−0.892742	−	0.515425i	−0.0179037	−	0.999840i	$-0.505699\pi$
$443$	−18.7900	−	10.8484i	−0.892742	−	0.515425i	−0.874838	+	0.484415i	$0.839033\pi$
$444$	14.7429	+	1.29401i	0.699667	+	0.0614111i
$445$	0.129562	+	0.0748029i	0.00614185	+	0.00354600i
$446$	−0.692562	−	1.19955i	−0.0327937	−	0.0568004i
$447$	26.7302	+	2.34616i	1.26429	+	0.110970i
$448$	1.64767	+	2.85385i	0.0778452	+	0.134832i
$449$	−5.51787			−0.260405			−0.130202	−	0.991487i	$-0.541563\pi$
$449$	−5.51787			−0.260405			−0.130202	+	0.991487i	$0.541563\pi$
$450$	−2.29705	−	1.92965i	−0.108284	−	0.0909648i
$451$	32.0327	−	18.4941i	1.50836	−	0.870854i
$452$	−5.58805	−	3.22626i	−0.262840	−	0.151751i
$453$	−18.1572	+	25.9156i	−0.853097	+	1.21762i
$454$	−4.55194	+	7.88419i	−0.213633	+	0.370024i
$455$	6.80451	−	11.7858i	0.319000	−	0.552525i
$456$	−3.84623	−	0.337591i	−0.180116	−	0.0158091i
$457$		−	17.8127i		−	0.833241i	−0.909081	−	0.416620i	$-0.863214\pi$
$457$		−	17.8127i		−	0.833241i	0.909081	−	0.416620i	$-0.136786\pi$
$458$	3.99401	+	6.91782i	0.186628	+	0.323249i
$459$	30.3446	−	8.10338i	1.41636	−	0.378233i
$460$	0.211986	+	0.122390i	0.00988389	+	0.00570646i
$461$	10.7060			0.498630			0.249315	−	0.968422i	$-0.419795\pi$
$461$	10.7060			0.498630			0.249315	+	0.968422i	$0.419795\pi$
$462$	15.3437	−	21.9000i	0.713855	−	1.01888i
$463$		−	23.2499i		−	1.08051i	−0.841500	−	0.540257i	$-0.818327\pi$
$463$		−	23.2499i		−	1.08051i	0.841500	−	0.540257i	$-0.181673\pi$
$464$	2.05814			0.0955469
$465$	0.527512	+	9.62921i	0.0244628	+	0.446544i
$466$	−15.9529			−0.739003
$467$		−	1.78177i		−	0.0824507i	−0.999150	−	0.0412253i	$-0.986874\pi$
$467$		−	1.78177i		−	0.0824507i	0.999150	−	0.0412253i	$-0.0131262\pi$
$468$	−2.15824	+	12.1999i	−0.0997647	+	0.563940i
$469$	−12.5728			−0.580560
$470$	−3.45803	−	1.99650i	−0.159507	−	0.0920914i
$471$	−26.0353	−	18.2410i	−1.19964	−	0.840501i
$472$	0.370390	+	0.641535i	0.0170486	+	0.0295290i
$473$		−	54.2949i		−	2.49648i
$474$	1.94467	−	22.1559i	0.0893216	−	1.01766i
$475$	1.11458	−	1.93051i	0.0511404	−	0.0885778i
$476$	9.95929	−	17.2500i	0.456483	−	0.790652i
$477$	5.88790	+	1.04161i	0.269588	+	0.0476920i
$478$	7.83393	+	4.52292i	0.358316	+	0.206874i
$479$	30.8844	−	17.8311i	1.41115	−	0.814725i	0.415649	−	0.909525i	$-0.363555\pi$
$479$	30.8844	−	17.8311i	1.41115	−	0.814725i	0.995496	+	0.0948002i	$0.0302212\pi$
$480$	1.56998	−	0.731555i	0.0716593	−	0.0333908i
$481$	35.2870			1.60895
$482$	7.71462	+	13.3621i	0.351391	+	0.608628i
$483$	0.122159	−	1.39178i	0.00555844	−	0.0633283i
$484$	5.47431	+	9.48178i	0.248832	+	0.430990i
$485$	6.64528	+	3.83666i	0.301747	+	0.174214i
$486$	−1.33680	−	15.5310i	−0.0606384	−	0.704502i
$487$	9.14547	+	5.28014i	0.414421	+	0.239266i	0.692687	−	0.721238i	$-0.256427\pi$
$487$	9.14547	+	5.28014i	0.414421	+	0.239266i	−0.278267	+	0.960504i	$0.589760\pi$
$488$	6.30131			0.285247
$489$	2.41782	+	1.69399i	0.109338	+	0.0766049i
$490$	1.92965	+	3.34226i	0.0871729	+	0.150988i
$491$	8.01143	−	13.8762i	0.361551	−	0.626224i	−0.626665	−	0.779288i	$-0.715581\pi$
$491$	8.01143	−	13.8762i	0.361551	−	0.626224i	0.988216	+	0.153064i	$0.0489141\pi$
$492$	−5.77573	−	12.3952i	−0.260390	−	0.558818i
$493$	−6.22018	−	10.7737i	−0.280143	−	0.485221i
$494$	−9.20591			−0.414194
$495$	−10.7615	−	9.04031i	−0.483695	−	0.406332i
$496$	−5.16785	−	2.07204i	−0.232043	−	0.0930373i
$497$		−	31.8479i		−	1.42857i
$498$	−2.08134	−	4.46673i	−0.0932673	−	0.200159i
$499$	15.8026	−	9.12364i	0.707422	−	0.408430i	−0.102684	−	0.994714i	$-0.532743\pi$
$499$	15.8026	−	9.12364i	0.707422	−	0.408430i	0.810106	+	0.586284i	$0.199410\pi$
$500$			1.00000i			0.0447214i
$501$	−1.90400	+	21.6926i	−0.0850643	+	0.969152i
$502$	3.28729	−	1.89792i	0.146719	−	0.0847082i
$503$	30.0423	−	17.3449i	1.33952	−	0.773371i	0.352782	−	0.935706i	$-0.385236\pi$
$503$	30.0423	−	17.3449i	1.33952	−	0.773371i	0.986736	+	0.162335i	$0.0519024\pi$
$504$	−7.56957	−	6.35888i	−0.337176	−	0.283247i
$505$	−2.53480	+	4.39040i	−0.112797	+	0.195370i
$506$	0.993140	+	0.573389i	0.0441504	+	0.0254903i
$507$	−0.614102	+	6.99657i	−0.0272732	+	0.310729i
$508$	−0.366646	+	0.211683i	−0.0162673	+	0.00939193i
$509$	9.89991	−	17.1472i	0.438806	−	0.760034i	−0.558792	−	0.829308i	$-0.688735\pi$
$509$	9.89991	−	17.1472i	0.438806	−	0.760034i	0.997598	+	0.0692738i	$0.0220682\pi$
$510$	−8.57426	−	6.00736i	−0.379675	−	0.266010i
$511$		−	1.10488i		−	0.0488770i
$512$			1.00000i			0.0441942i
$513$	11.1909	−	2.98848i	0.494090	−	0.131945i
$514$	15.5105	−	26.8650i	0.684139	−	1.18496i
$515$	−16.2445	+	9.37875i	−0.715817	+	0.413277i
$516$	−19.9963	−	1.75511i	−0.880288	−	0.0772645i
$517$	−16.2007	−	9.35345i	−0.712504	−	0.411364i
$518$	−14.0786	+	24.3849i	−0.618579	+	1.07141i
$519$	1.90797	+	4.09465i	0.0837505	+	0.179735i
$520$	3.57649	−	2.06489i	0.156839	−	0.0905512i
$521$	−27.2181	+	15.7144i	−1.19245	+	0.688460i	−0.958861	−	0.283876i	$-0.908380\pi$
$521$	−27.2181	+	15.7144i	−1.19245	+	0.688460i	−0.233587	+	0.972336i	$0.575046\pi$
$522$	−5.80325	+	2.10852i	−0.254001	+	0.0922873i
$523$			30.9522i			1.35345i	0.736237	+	0.676723i	$0.236601\pi$
$523$			30.9522i			1.35345i	−0.736237	+	0.676723i	$0.763399\pi$
$524$	1.79983	−	1.03913i	0.0786260	−	0.0453947i
$525$	5.17362	−	2.41073i	0.225795	−	0.105213i
$526$		−	21.5086i		−	0.937818i
$527$	4.77201	+	33.3141i	0.207872	+	1.45118i
$528$	7.35524	−	3.42729i	0.320096	−	0.149154i
$529$	−22.9401			−0.997395
$530$	−0.996554	−	1.72608i	−0.0432875	−	0.0749762i
$531$	−1.70161	−	1.42945i	−0.0738435	−	0.0620328i
$532$	3.67293	−	6.36169i	0.159242	−	0.275814i
$533$	−16.3026	−	28.2369i	−0.706142	−	1.22307i
$534$	0.148688	−	0.212221i	0.00643434	−	0.00918370i
$535$	4.22795			0.182790
$536$	−3.30418	−	1.90767i	−0.142719	−	0.0823987i
$537$	−2.87672	+	32.7749i	−0.124139	+	1.41434i
$538$	−23.4194	−	13.5212i	−1.00968	−	0.582940i
$539$	9.04031	+	15.6583i	0.389394	+	0.674449i
$540$	−3.67733	+	3.67114i	−0.158247	+	0.157981i
$541$	21.6449	+	37.4901i	0.930588	+	1.61183i	0.782318	+	0.622879i	$0.214037\pi$
$541$	21.6449	+	37.4901i	0.930588	+	1.61183i	0.148270	+	0.988947i	$0.452630\pi$
$542$	−16.9825			−0.729463
$543$	−12.1440	−	26.0620i	−0.521149	−	1.11843i
$544$	5.23465	−	3.02223i	0.224434	−	0.129577i
$545$	−5.06324	−	2.92326i	−0.216885	−	0.125219i
$546$	−19.3049	−	13.5255i	−0.826172	−	0.578838i
$547$	2.09475	−	3.62821i	0.0895650	−	0.155131i	−0.817762	−	0.575556i	$-0.804786\pi$
$547$	2.09475	−	3.62821i	0.0895650	−	0.155131i	0.907327	+	0.420425i	$0.138119\pi$
$548$	−9.76518	+	16.9138i	−0.417148	+	0.722522i
$549$	−17.7675	+	6.45554i	−0.758300	+	0.275516i
$550$			4.68494i			0.199766i
$551$	−2.29396	−	3.97326i	−0.0977261	−	0.169267i
$552$	0.243278	−	0.347229i	0.0103546	−	0.0147790i
$553$	36.6461	+	21.1576i	1.55835	+	0.899714i
$554$	23.1214			0.982336
$555$	12.1207	+	8.49210i	0.514496	+	0.360470i
$556$			22.5295i			0.955462i
$557$	−33.3611			−1.41356			−0.706778	−	0.707435i	$-0.749852\pi$
$557$	−33.3611			−1.41356			−0.706778	+	0.707435i	$0.749852\pi$
$558$	16.6943	+	0.548100i	0.706726	+	0.0232029i
$559$	−47.8610			−2.02430
$560$			3.29535i			0.139254i
$561$	−40.1699	−	28.1441i	−1.69597	−	1.18824i
$562$	26.0722			1.09979
$563$	−3.50089	−	2.02124i	−0.147545	−	0.0851851i	0.424410	−	0.905470i	$-0.360482\pi$
$563$	−3.50089	−	2.02124i	−0.147545	−	0.0851851i	−0.571955	+	0.820285i	$0.693815\pi$
$564$	−3.96848	+	5.66419i	−0.167103	+	0.238505i
$565$	−3.22626	−	5.58805i	−0.135730	−	0.235091i
$566$			14.5905i			0.613284i
$567$	27.8581	+	10.1750i	1.16993	+	0.427310i
$568$	4.83225	−	8.36971i	0.202757	−	0.351185i
$569$	1.92967	−	3.34229i	0.0808961	−	0.140116i	−0.822739	−	0.568419i	$-0.807555\pi$
$569$	1.92967	−	3.34229i	0.0808961	−	0.140116i	0.903635	+	0.428303i	$0.140888\pi$
$570$	−3.16214	−	2.21548i	−0.132447	−	0.0927961i
$571$	27.2167	+	15.7136i	1.13898	+	0.657593i	0.946179	−	0.323644i	$-0.104908\pi$
$571$	27.2167	+	15.7136i	1.13898	+	0.657593i	0.192805	+	0.981237i	$0.438241\pi$
$572$	16.7556	−	9.67385i	0.700587	−	0.404484i
$573$	12.3361	+	26.4742i	0.515346	+	1.10598i
$574$	26.0172			1.08594
$575$	0.122390	+	0.211986i	0.00510402	+	0.00884042i
$576$	−1.02448	−	2.81965i	−0.0426865	−	0.117486i
$577$	0.696828	+	1.20694i	0.0290093	+	0.0502457i	0.880166	−	0.474667i	$-0.157431\pi$
$577$	0.696828	+	1.20694i	0.0290093	+	0.0502457i	−0.851156	+	0.524912i	$0.824098\pi$
$578$	−16.9182	−	9.76772i	−0.703703	−	0.406283i
$579$	1.04903	−	11.9518i	0.0435963	−	0.496700i
$580$	1.78240	+	1.02907i	0.0740103	+	0.0427299i
$581$	9.37558			0.388965
$582$	7.62622	−	10.8849i	0.316117	−	0.451192i
$583$	−4.66879	−	8.08658i	−0.193362	−	0.334912i
$584$	0.167642	−	0.290365i	0.00693709	−	0.0120154i
$585$	−7.96903	+	9.48628i	−0.329479	+	0.392210i
$586$	14.2780	+	24.7303i	0.589821	+	1.02160i
$587$	−44.2243			−1.82533			−0.912666	−	0.408706i	$-0.865980\pi$
$587$	−44.2243			−1.82533			−0.912666	+	0.408706i	$0.865980\pi$
$588$	6.05903	−	2.82330i	0.249870	−	0.116431i
$589$	1.75989	+	12.2860i	0.0725149	+	0.506237i
$590$			0.740780i			0.0304974i
$591$	23.2649	−	10.8407i	0.956992	−	0.445925i
$592$	−7.39979	+	4.27227i	−0.304130	+	0.175589i
$593$		−	14.8656i		−	0.610459i	−0.952279	−	0.305229i	$-0.901267\pi$
$593$		−	14.8656i		−	0.610459i	0.952279	−	0.305229i	$-0.0987332\pi$
$594$	−17.2281	+	17.1990i	−0.706876	+	0.705685i
$595$	17.2500	−	9.95929i	0.707181	−	0.408291i
$596$	−13.4165	+	7.74601i	−0.549560	+	0.317289i
$597$	−13.9082	−	29.8481i	−0.569223	−	1.22160i
$598$	0.505443	−	0.875452i	0.0206691	−	0.0357999i
$599$	23.8479	+	13.7686i	0.974397	+	0.562568i	0.900574	−	0.434703i	$-0.143147\pi$
$599$	23.8479	+	13.7686i	0.974397	+	0.562568i	0.0738230	+	0.997271i	$0.476480\pi$
$600$	1.72542	+	0.151443i	0.0704399	+	0.00618264i
$601$	−30.8947	+	17.8371i	−1.26022	+	0.727589i	−0.973117	−	0.230310i	$-0.926026\pi$
$601$	−30.8947	+	17.8371i	−1.26022	+	0.727589i	−0.287105	+	0.957899i	$0.592693\pi$
$602$	19.0953	−	33.0740i	0.778266	−	1.34800i
$603$	11.2710	+	1.99391i	0.458990	+	0.0811984i
$604$		−	18.2693i		−	0.743367i
$605$			10.9486i			0.445125i
$606$	7.19139	+	5.03848i	0.292130	+	0.204674i
$607$	22.4644	−	38.9094i	0.911801	−	1.57929i	0.100282	−	0.994959i	$-0.468025\pi$
$607$	22.4644	−	38.9094i	0.911801	−	1.57929i	0.811519	−	0.584327i	$-0.198641\pi$
$608$	1.93051	−	1.11458i	0.0782924	−	0.0452022i
$609$	1.02713	−	11.7023i	0.0416215	−	0.474201i
$610$	5.45710	+	3.15066i	0.220951	+	0.127566i
$611$	−8.24507	+	14.2809i	−0.333560	+	0.577742i
$612$	−11.6637	+	13.8844i	−0.471477	+	0.561244i
$613$	36.0994	−	20.8420i	1.45804	−	0.841800i	0.459125	−	0.888372i	$-0.348163\pi$
$613$	36.0994	−	20.8420i	1.45804	−	0.841800i	0.998915	+	0.0465721i	$0.0148297\pi$
$614$	−8.12397	+	4.69037i	−0.327857	+	0.189288i
$615$	1.19566	−	13.6224i	0.0482138	−	0.549309i
$616$			15.4385i			0.622034i
$617$	37.6159	−	21.7175i	1.51436	−	0.874316i	0.514501	−	0.857490i	$-0.327977\pi$
$617$	37.6159	−	21.7175i	1.51436	−	0.874316i	0.999858	−	0.0168256i	$-0.00535600\pi$
$618$	13.7221	+	29.4488i	0.551985	+	1.18461i
$619$			38.4345i			1.54481i	0.635129	+	0.772406i	$0.280947\pi$
$619$			38.4345i			1.54481i	−0.635129	+	0.772406i	$0.719053\pi$
$620$	−3.43947	−	4.37836i	−0.138132	−	0.175839i
$621$	−0.330231	+	1.22830i	−0.0132517	+	0.0492899i
$622$	−1.63457			−0.0655403
$623$	0.246502	+	0.426953i	0.00987587	+	0.0171055i
$624$	−3.02115	−	6.48364i	−0.120943	−	0.259553i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	6.17384	+	10.6934i	0.246756	+	0.427394i
$627$	−14.8144	−	10.3794i	−0.591630	−	0.414512i
$628$	18.3537			0.732391
$629$	44.7277	+	25.8236i	1.78341	+	1.02965i
$630$	−3.37600	−	9.29174i	−0.134503	−	0.370192i
$631$	5.86942	+	3.38871i	0.233658	+	0.134902i	0.612258	−	0.790658i	$-0.290261\pi$
$631$	5.86942	+	3.38871i	0.233658	+	0.134902i	−0.378601	+	0.925560i	$0.623595\pi$
$632$	6.42046	+	11.1206i	0.255392	+	0.442352i
$633$	0.0483923	−	0.551342i	0.00192342	−	0.0219139i
$634$	−17.0459	−	29.5244i	−0.676979	−	1.17256i
$635$	−0.423367			−0.0168008
$636$	−3.12913	+	1.45807i	−0.124078	+	0.0578162i
$637$	13.8028	−	7.96903i	0.546885	−	0.315744i
$638$	8.35045	+	4.82113i	0.330597	+	0.190870i
$639$	−5.05072	+	28.5502i	−0.199803	+	1.12943i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−1.51314	+	2.62083i	−0.0597653	+	0.103517i	−0.894360	−	0.447348i	$-0.852369\pi$
$641$	−1.51314	+	2.62083i	−0.0597653	+	0.103517i	0.834595	+	0.550865i	$0.185702\pi$
$642$	0.640293	−	7.29497i	0.0252704	−	0.287910i
$643$			8.47085i			0.334058i	0.985952	+	0.167029i	$0.0534173\pi$
$643$			8.47085i			0.334058i	−0.985952	+	0.167029i	$0.946583\pi$
$644$	0.403318	+	0.698566i	0.0158929	+	0.0275274i
$645$	−16.4397	−	11.5181i	−0.647314	−	0.453526i
$646$	−11.6689	−	6.73702i	−0.459106	−	0.265065i
$647$	−30.7071			−1.20722			−0.603611	−	0.797279i	$-0.706272\pi$
$647$	−30.7071			−1.20722			−0.603611	+	0.797279i	$0.706272\pi$
$648$	5.77733	+	6.90090i	0.226955	+	0.271093i
$649$			3.47051i			0.136229i
$650$	4.12977			0.161983
$651$	−14.3604	+	28.3495i	−0.562827	+	1.11111i
$652$	−1.70445			−0.0667515
$653$			20.6155i			0.806748i	0.915035	+	0.403374i	$0.132163\pi$
$653$			20.6155i			0.806748i	−0.915035	+	0.403374i	$0.867837\pi$
$654$	−5.81064	+	8.29350i	−0.227214	+	0.324301i
$655$	2.07827			0.0812046
$656$	6.83739	+	3.94757i	0.266955	+	0.154127i
$657$	−0.175222	+	0.990475i	−0.00683604	+	0.0386421i
$658$	−6.57914	−	11.3954i	−0.256482	−	0.444239i
$659$			45.9699i			1.79073i	0.445331	+	0.895366i	$0.353086\pi$
$659$			45.9699i			1.79073i	−0.445331	+	0.895366i	$0.646914\pi$
$660$	8.08347	+	0.709501i	0.314649	+	0.0276173i
$661$	−1.62902	+	2.82155i	−0.0633616	+	0.109745i	−0.895966	−	0.444123i	$-0.853515\pi$
$661$	−1.62902	+	2.82155i	−0.0633616	+	0.109745i	0.832604	+	0.553868i	$0.186849\pi$
$662$	−11.0835	+	19.1972i	−0.430773	+	0.746121i
$663$	−24.8090	+	35.4097i	−0.963502	+	1.37520i
$664$	2.46393	+	1.42255i	0.0956189	+	0.0552056i
$665$	6.36169	−	3.67293i	0.246696	−	0.142430i
$666$	16.4880	−	19.6272i	0.638898	−	0.760540i
$667$	0.503792			0.0195069
$668$	−6.28618	−	10.8880i	−0.243220	−	0.421269i
$669$	−2.38992	−	0.209767i	−0.0923995	−	0.00811008i
$670$	−1.90767	−	3.30418i	−0.0736996	−	0.127651i
$671$	25.5662	+	14.7606i	0.986970	+	0.569828i
$672$	5.68585	+	0.499058i	0.219336	+	0.0192516i
$673$	−28.5117	−	16.4612i	−1.09905	−	0.634534i	−0.163076	−	0.986614i	$-0.552141\pi$
$673$	−28.5117	−	16.4612i	−1.09905	−	0.634534i	−0.935970	+	0.352079i	$0.885475\pi$
$674$	−24.0073			−0.924727
$675$	−5.02023	+	1.34063i	−0.193229	+	0.0516009i
$676$	−2.02750	−	3.51174i	−0.0779808	−	0.135067i
$677$	−2.98095	+	5.16316i	−0.114567	+	0.198436i	−0.917607	−	0.397490i	$-0.869882\pi$
$677$	−2.98095	+	5.16316i	−0.114567	+	0.198436i	0.803039	+	0.595926i	$0.203215\pi$
$678$	−10.1303	+	4.72038i	−0.389052	+	0.181285i
$679$	12.6431	+	21.8985i	0.485198	+	0.840388i
$680$	6.04445			0.231794
$681$	6.65999	+	14.2929i	0.255211	+	0.547705i
$682$	−16.1137	−	20.5123i	−0.617025	−	0.785458i
$683$			32.4819i			1.24289i	0.783459	+	0.621443i	$0.213453\pi$
$683$			32.4819i			1.24289i	−0.783459	+	0.621443i	$0.786547\pi$
$684$	−4.30151	+	5.12049i	−0.164472	+	0.195787i
$685$	−16.9138	+	9.76518i	−0.646243	+	0.373109i
$686$		−	10.3497i		−	0.395152i
$687$	13.7827	+	1.20973i	0.525841	+	0.0461541i
$688$	10.0366	−	5.79463i	0.382641	−	0.220918i
$689$	−7.12832	+	4.11554i	−0.271567	+	0.156790i
$690$	0.384299	−	0.179070i	0.0146300	−	0.00681708i
$691$	8.97812	−	15.5506i	0.341544	−	0.591571i	−0.643176	−	0.765719i	$-0.722384\pi$
$691$	8.97812	−	15.5506i	0.341544	−	0.591571i	0.984720	+	0.174147i	$0.0557169\pi$
$692$	−2.25868	−	1.30405i	−0.0858621	−	0.0495725i
$693$	−15.8164	−	43.5312i	−0.600814	−	1.65361i
$694$	−24.4539	+	14.1185i	−0.928257	+	0.535929i
$695$	−11.2647	+	19.5111i	−0.427296	+	0.740098i
$696$	2.04551	−	2.91954i	0.0775349	−	0.110665i
$697$		−	47.7218i		−	1.80759i
$698$			14.1084i			0.534010i
$699$	−15.8550	+	22.6297i	−0.599690	+	0.855933i
$700$	−1.64767	+	2.85385i	−0.0622762	+	0.107866i
$701$	17.0045	−	9.81756i	0.642251	−	0.370804i	−0.143230	−	0.989689i	$-0.545749\pi$
$701$	17.0045	−	9.81756i	0.642251	−	0.370804i	0.785481	+	0.618885i	$0.212416\pi$
$702$	15.1609	+	15.1865i	0.572213	+	0.573179i
$703$	16.4953	+	9.52357i	0.622133	+	0.359188i
$704$	−2.34247	+	4.05727i	−0.0882851	+	0.152914i
$705$	−6.26890	+	2.92109i	−0.236100	+	0.110015i
$706$	−19.3283	+	11.1592i	−0.727428	+	0.419981i
$707$	−14.4679	+	8.35303i	−0.544120	+	0.314148i
$708$	1.27816	+	0.112186i	0.0480360	+	0.00421621i
$709$		−	2.09339i		−	0.0786187i	−0.999227	−	0.0393094i	$-0.987484\pi$
$709$		−	2.09339i		−	0.0786187i	0.999227	−	0.0393094i	$-0.0125158\pi$
$710$	8.36971	−	4.83225i	0.314110	−	0.181351i
$711$	−29.4962	−	24.7785i	−1.10619	−	0.929267i
$712$			0.149606i			0.00560672i
$713$	−1.26499	−	0.507194i	−0.0473741	−	0.0189946i
$714$	−14.5715	−	31.2717i	−0.545326	−	1.17031i
$715$	19.3477			0.723563
$716$	−9.49768	−	16.4505i	−0.354945	−	0.614783i
$717$	14.2018	−	6.61753i	0.530375	−	0.247136i
$718$	−2.85152	+	4.93899i	−0.106418	+	0.184321i
$719$	4.88475	+	8.46063i	0.182170	+	0.315528i	0.942619	−	0.333869i	$-0.108354\pi$
$719$	4.88475	+	8.46063i	0.182170	+	0.315528i	−0.760449	+	0.649398i	$0.775021\pi$
$720$	0.522605	−	2.95413i	0.0194763	−	0.110094i
$721$	−61.8124			−2.30202
$722$	12.1511	+	7.01543i	0.452216	+	0.261087i
$723$	26.6219	+	2.33665i	0.990079	+	0.0869011i
$724$	14.3763	+	8.30014i	0.534289	+	0.308472i
$725$	1.02907	+	1.78240i	0.0382188	+	0.0661968i
$726$	18.8909	+	1.65809i	0.701109	+	0.0615376i
$727$	−9.42776	−	16.3294i	−0.349656	−	0.605622i	0.636532	−	0.771250i	$-0.280368\pi$
$727$	−9.42776	−	16.3294i	−0.349656	−	0.605622i	−0.986188	+	0.165628i	$0.947035\pi$
$728$	13.6090			0.504384
$729$	−23.3599	−	13.5394i	−0.865181	−	0.501460i
$730$	0.290365	−	0.167642i	0.0107469	−	0.00620472i
$731$	−60.6657	−	35.0254i	−2.24380	−	1.29546i
$732$	6.26264	−	8.93863i	0.231474	−	0.330381i
$733$	−7.30224	+	12.6479i	−0.269714	+	0.467159i	−0.968788	−	0.247891i	$-0.920263\pi$
$733$	−7.30224	+	12.6479i	−0.269714	+	0.467159i	0.699074	+	0.715050i	$0.253596\pi$
$734$	−16.0261	+	27.7580i	−0.591534	+	1.02457i
$735$	6.65892	+	0.584466i	0.245618	+	0.0215583i
$736$			0.244780i			0.00902271i
$737$	−8.93730	−	15.4799i	−0.329210	−	0.570208i
$738$	−23.3233	−	4.12604i	−0.858541	−	0.151882i
$739$	−41.8282	−	24.1495i	−1.53868	−	0.888355i	−0.998917	−	0.0465355i	$-0.985182\pi$
$739$	−41.8282	−	24.1495i	−1.53868	−	0.888355i	−0.539759	−	0.841819i	$-0.681485\pi$
$740$	−8.54454			−0.314104
$741$	−9.14941	+	13.0589i	−0.336112	+	0.479731i
$742$		−	6.56798i		−	0.241118i
$743$	−6.41688			−0.235412			−0.117706	−	0.993048i	$-0.537554\pi$
$743$	−6.41688			−0.235412			−0.117706	+	0.993048i	$0.537554\pi$
$744$	−8.07539	+	5.27144i	−0.296058	+	0.193261i
$745$	−15.4920			−0.567584
$746$		−	22.0309i		−	0.806609i
$747$	−8.40478	−	1.48686i	−0.307515	−	0.0544014i
$748$	28.3179			1.03540
$749$	12.0659	+	6.96627i	0.440880	+	0.254542i
$750$	1.41853	+	0.993862i	0.0517975	+	0.0362907i
$751$	−8.51988	−	14.7569i	−0.310895	−	0.538486i	0.667661	−	0.744465i	$-0.267295\pi$
$751$	−8.51988	−	14.7569i	−0.310895	−	0.538486i	−0.978556	+	0.205979i	$0.933962\pi$
$752$		−	3.99299i		−	0.145609i
$753$	0.574853	−	6.54940i	0.0209488	−	0.238673i
$754$	4.24983	−	7.36092i	0.154770	−	0.268069i
$755$	9.13464	−	15.8217i	0.332444	−	0.575809i
$756$	−16.5434	+	4.41784i	−0.601678	+	0.160675i
$757$	17.9616	+	10.3701i	0.652826	+	0.376909i	0.789538	−	0.613701i	$-0.210320\pi$
$757$	17.9616	+	10.3701i	0.652826	+	0.376909i	−0.136712	+	0.990611i	$0.543653\pi$
$758$	−19.8741	+	11.4743i	−0.721861	+	0.416767i
$759$	1.80042	−	0.838932i	0.0653510	−	0.0304513i
$760$	2.22916			0.0808601
$761$	11.5689	+	20.0379i	0.419372	+	0.726373i	0.995876	−	0.0907205i	$-0.0289170\pi$
$761$	11.5689	+	20.0379i	0.419372	+	0.726373i	−0.576504	+	0.817094i	$0.695584\pi$
$762$	−0.0641160	+	0.730484i	−0.00232268	+	0.0264626i
$763$	−9.63317	−	16.6851i	−0.348744	−	0.604043i
$764$	−14.6036	−	8.43140i	−0.528340	−	0.305037i
$765$	−17.0433	+	6.19240i	−0.616201	+	0.223887i
$766$	8.93453	+	5.15835i	0.322818	+	0.186379i
$767$	3.05925			0.110463
$768$	1.41853	+	0.993862i	0.0511869	+	0.0358629i
$769$	19.5619	+	33.8822i	0.705420	+	1.22182i	0.966540	+	0.256517i	$0.0825749\pi$
$769$	19.5619	+	33.8822i	0.705420	+	1.22182i	−0.261120	+	0.965306i	$0.584092\pi$
$770$	−7.71924	+	13.3701i	−0.278182	+	0.481826i
$771$	−22.6936	−	48.7023i	−0.817289	−	1.75397i
$772$	3.46345	+	5.99887i	0.124652	+	0.215904i
$773$	−17.0109			−0.611839			−0.305920	−	0.952057i	$-0.598964\pi$
$773$	−17.0109			−0.611839			−0.305920	+	0.952057i	$0.598964\pi$
$774$	−22.3633	+	26.6211i	−0.803831	+	0.956875i
$775$	−0.789485	−	5.51151i	−0.0283592	−	0.197979i
$776$			7.67331i			0.275456i
$777$	20.5986	+	44.2062i	0.738969	+	1.58589i
$778$	22.0613	−	12.7371i	0.790937	−	0.456648i
$779$		−	17.5995i		−	0.630568i
$780$	0.625425	−	7.12558i	0.0223938	−	0.255137i
$781$	39.2116	−	22.6388i	1.40310	−	0.810080i
$782$	1.28134	−	0.739781i	0.0458206	−	0.0264545i
$783$	−2.77663	+	10.3277i	−0.0992286	+	0.369081i
$784$	−1.92965	+	3.34226i	−0.0689162	+	0.119366i
$785$	15.8947	+	9.17683i	0.567307	+	0.327535i
$786$	0.314739	−	3.58588i	0.0112264	−	0.127904i
$787$	12.8119	−	7.39695i	0.456695	−	0.263673i	−0.253959	−	0.967215i	$-0.581733\pi$
$787$	12.8119	−	7.39695i	0.456695	−	0.263673i	0.710653	+	0.703542i	$0.248399\pi$
$788$	−7.40933	+	12.8333i	−0.263946	+	0.457168i
$789$	−30.5106	−	21.3765i	−1.08621	−	0.761025i
$790$			12.8409i			0.456859i
$791$		−	21.2633i		−	0.756036i
$792$	2.44837	−	13.8399i	0.0869991	−	0.491780i
$793$	13.0115	−	22.5366i	0.462052	−	0.800297i
$794$	−5.47906	+	3.16333i	−0.194444	+	0.112263i
$795$	−3.43894	−	0.301843i	−0.121967	−	0.0107053i
$796$	16.4647	+	9.50589i	0.583575	+	0.336927i
$797$	−11.4621	+	19.8529i	−0.406007	+	0.703226i	−0.994438	−	0.105322i	$-0.966413\pi$
$797$	−11.4621	+	19.8529i	−0.406007	+	0.703226i	0.588431	+	0.808548i	$0.299746\pi$
$798$	−5.37389	−	11.5328i	−0.190234	−	0.408257i
$799$	−20.9019	+	12.0677i	−0.739456	+	0.426925i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−0.153268	−	0.421837i	−0.00541544	−	0.0149049i
$802$			25.4504i			0.898683i
$803$	1.36034	−	0.785394i	0.0480054	−	0.0277159i
$804$	−5.98999	+	2.79113i	−0.211250	+	0.0984354i
$805$			0.806635i			0.0284302i
$806$	−18.0816	+	14.2042i	−0.636898	+	0.500322i
$807$	−42.4559	+	19.7830i	−1.49452	+	0.696394i
$808$	−5.06959			−0.178348
$809$	−25.3510	−	43.9092i	−0.891294	−	1.54377i	−0.838325	−	0.545170i	$-0.816465\pi$
$809$	−25.3510	−	43.9092i	−0.891294	−	1.54377i	−0.0529687	−	0.998596i	$-0.516868\pi$
$810$	1.55287	+	8.86502i	0.0545622	+	0.311485i
$811$	−8.64545	+	14.9744i	−0.303583	+	0.525821i	−0.976945	−	0.213492i	$-0.931516\pi$
$811$	−8.64545	+	14.9744i	−0.303583	+	0.525821i	0.673362	+	0.739313i	$0.264850\pi$
$812$	3.39115	+	5.87364i	0.119006	+	0.206124i
$813$	−16.8783	+	24.0903i	−0.591948	+	0.844884i
$814$	−40.0306			−1.40307
$815$	−1.47610	−	0.852226i	−0.0517055	−	0.0298522i
$816$	0.915391	−	10.4292i	0.0320451	−	0.365095i
$817$	−22.3732	−	12.9171i	−0.782737	−	0.451914i
$818$	18.4196	+	31.9037i	0.644026	+	1.11549i
$819$	−38.3727	+	13.9421i	−1.34085	+	0.487177i
$820$	3.94757	+	6.83739i	0.137855	+	0.238772i
$821$	37.4349			1.30649			0.653244	−	0.757147i	$-0.273407\pi$
$821$	37.4349			1.30649			0.653244	+	0.757147i	$0.273407\pi$
$822$	14.2875	+	30.6622i	0.498335	+	1.06947i
$823$	−28.5790	+	16.5001i	−0.996202	+	0.575157i	−0.907122	−	0.420867i	$-0.861726\pi$
$823$	−28.5790	+	16.5001i	−0.996202	+	0.575157i	−0.0890794	+	0.996025i	$0.528393\pi$
$824$	−16.2445	−	9.37875i	−0.565903	−	0.326724i
$825$	6.64574	+	4.65618i	0.231375	+	0.162107i
$826$	−1.22056	+	2.11408i	−0.0424689	+	0.0735582i
$827$	21.9755	−	38.0628i	0.764165	−	1.32357i	−0.176523	−	0.984297i	$-0.556485\pi$
$827$	21.9755	−	38.0628i	0.764165	−	1.32357i	0.940687	−	0.339275i	$-0.110182\pi$
$828$	−0.250771	−	0.690195i	−0.00871490	−	0.0239859i
$829$		−	8.72147i		−	0.302909i	−0.988464	−	0.151455i	$-0.951604\pi$
$829$		−	8.72147i		−	0.302909i	0.988464	−	0.151455i	$-0.0483957\pi$
$830$	1.42255	+	2.46393i	0.0493774	+	0.0855241i
$831$	22.9795	−	32.7985i	0.797151	−	1.13777i
$832$	3.57649	+	2.06489i	0.123992	+	0.0715870i
$833$	23.3274			0.808247
$834$	31.9588	+	22.3912i	1.10664	+	0.775343i
$835$		−	12.5724i		−	0.435084i
$836$	10.4435			0.361195
$837$	17.3693	−	23.1367i	0.600372	−	0.799721i
$838$	−8.72337			−0.301344
$839$		−	42.4663i		−	1.46610i	−0.680175	−	0.733050i	$-0.738096\pi$
$839$		−	42.4663i		−	1.46610i	0.680175	−	0.733050i	$-0.261904\pi$
$840$	4.67456	+	3.27512i	0.161288	+	0.113002i
$841$	−24.7640			−0.853933
$842$	−3.80721	−	2.19810i	−0.131205	−	0.0757514i
$843$	25.9122	−	36.9843i	0.892463	−	1.27381i
$844$	0.159771	+	0.276731i	0.00549953	+	0.00952547i
$845$		−	4.05500i		−	0.139496i
$846$	4.09072	+	11.2589i	0.140642	+	0.387087i
$847$	−18.0398	+	31.2458i	−0.619853	+	1.07362i
$848$	0.996554	−	1.72608i	0.0342218	−	0.0592739i
$849$	20.6971	+	14.5009i	0.710323	+	0.497671i
$850$	5.23465	+	3.02223i	0.179547	+	0.103662i
$851$	−1.81132	+	1.04577i	−0.0620913	+	0.0358484i
$852$	−7.07012	−	15.1731i	−0.242218	−	0.519820i
$853$	21.4819			0.735525			0.367762	−	0.929920i	$-0.380124\pi$
$853$	21.4819			0.735525			0.367762	+	0.929920i	$0.380124\pi$
$854$	10.3825	+	17.9830i	0.355282	+	0.615367i
$855$	−6.28546	+	2.28372i	−0.214958	+	0.0781015i
$856$	2.11397	+	3.66151i	0.0722541	+	0.125148i
$857$	16.4246	+	9.48276i	0.561054	+	0.323925i	0.753569	−	0.657369i	$-0.228331\pi$
$857$	16.4246	+	9.48276i	0.561054	+	0.323925i	−0.192514	+	0.981294i	$0.561664\pi$
$858$	2.93008	−	33.3829i	0.100031	−	1.13967i
$859$	−30.8514	−	17.8121i	−1.05264	−	0.607741i	−0.129251	−	0.991612i	$-0.541257\pi$
$859$	−30.8514	−	17.8121i	−1.05264	−	0.607741i	−0.923387	+	0.383871i	$0.874591\pi$
$860$	11.5893			0.395190
$861$	25.8575	−	36.9063i	0.881222	−	1.25776i
$862$	7.11935	+	12.3311i	0.242486	+	0.419998i
$863$	−2.53731	+	4.39475i	−0.0863710	+	0.149599i	−0.905975	−	0.423332i	$-0.860860\pi$
$863$	−2.53731	+	4.39475i	−0.0863710	+	0.149599i	0.819604	+	0.572931i	$0.194194\pi$
$864$	−5.01796	−	1.34909i	−0.170715	−	0.0458971i
$865$	−1.30405	−	2.25868i	−0.0443390	−	0.0767974i
$866$	16.3649			0.556103
$867$	−30.6702	+	14.2912i	−1.04161	+	0.485356i
$868$	−2.60163	−	18.1623i	−0.0883050	−	0.616470i
$869$			60.1588i			2.04075i
$870$	3.23124	−	1.50564i	0.109549	−	0.0510461i
$871$	−13.6455	+	7.87823i	−0.462360	+	0.266943i
$872$		−	5.84653i		−	0.197988i
$873$	−7.86112	−	21.6361i	−0.266059	−	0.732271i
$874$	0.472550	−	0.272827i	0.0159842	−	0.00922851i
$875$	−2.85385	+	1.64767i	−0.0964779	+	0.0557015i
$876$	−0.245279	−	0.526389i	−0.00828722	−	0.0177850i
$877$	17.7228	−	30.6968i	0.598456	−	1.03656i	−0.394593	−	0.918856i	$-0.629114\pi$
$877$	17.7228	−	30.6968i	0.598456	−	1.03656i	0.993049	−	0.117700i	$-0.0375522\pi$
$878$	−11.5474	−	6.66688i	−0.389705	−	0.224996i
$879$	49.2712	+	4.32462i	1.66188	+	0.145866i
$880$	−4.05727	+	2.34247i	−0.136771	+	0.0789646i
$881$	3.31664	−	5.74459i	0.111741	−	0.193540i	−0.804732	−	0.593639i	$-0.797691\pi$
$881$	3.31664	−	5.74459i	0.111741	−	0.193540i	0.916472	+	0.400099i	$0.131024\pi$
$882$	2.01689	−	11.4009i	0.0679124	−	0.383888i
$883$			35.2519i			1.18632i	0.805084	+	0.593160i	$0.202120\pi$
$883$			35.2519i			1.18632i	−0.805084	+	0.593160i	$0.797880\pi$
$884$		−	24.9622i		−	0.839570i
$885$	1.05082	+	0.736234i	0.0353230	+	0.0247482i
$886$	10.8484	−	18.7900i	0.364460	−	0.631264i
$887$	−2.63299	+	1.52016i	−0.0884070	+	0.0510418i	−0.543552	−	0.839376i	$-0.682921\pi$
$887$	−2.63299	+	1.52016i	−0.0884070	+	0.0510418i	0.455145	+	0.890417i	$0.349588\pi$
$888$	−1.29401	+	14.7429i	−0.0434242	+	0.494739i
$889$	−1.20823	−	0.697570i	−0.0405226	−	0.0233957i
$890$	−0.0748029	+	0.129562i	−0.00250740	+	0.00434294i
$891$	7.27509	+	41.5321i	0.243725	+	1.39138i
$892$	1.19955	−	0.692562i	0.0401640	−	0.0231887i
$893$	−7.70850	+	4.45050i	−0.257955	+	0.148930i
$894$	−2.34616	+	26.7302i	−0.0784673	+	0.893991i
$895$		−	18.9954i		−	0.634945i
$896$	−2.85385	+	1.64767i	−0.0953406	+	0.0550449i
$897$	−0.739518	−	1.58707i	−0.0246918	−	0.0529906i
$898$		−	5.51787i		−	0.184134i
$899$	−10.6362	−	4.26455i	−0.354736	−	0.142231i
$900$	1.92965	−	2.29705i	0.0643218	−	0.0765683i
$901$	−12.0473			−0.401352
$902$	18.4941	+	32.0327i	0.615786	+	1.06657i
$903$	−27.9385	−	59.9584i	−0.929736	−	1.99529i
$904$	3.22626	−	5.58805i	0.107304	−	0.185856i
$905$	8.30014	+	14.3763i	0.275906	+	0.477883i
$906$	−25.9156	−	18.1572i	−0.860988	−	0.603231i
$907$	−7.96679			−0.264533			−0.132267	−	0.991214i	$-0.542225\pi$
$907$	−7.96679			−0.264533			−0.132267	+	0.991214i	$0.542225\pi$
$908$	−7.88419	−	4.55194i	−0.261646	−	0.151061i
$909$	14.2945	−	5.19367i	0.474119	−	0.172263i
$910$	11.7858	+	6.80451i	0.390694	+	0.225567i
$911$	21.6226	+	37.4515i	0.716390	+	1.24082i	0.962421	+	0.271561i	$0.0875400\pi$
$911$	21.6226	+	37.4515i	0.716390	+	1.24082i	−0.246031	+	0.969262i	$0.579127\pi$
$912$	0.337591	−	3.84623i	0.0111787	−	0.127361i
$913$	6.66455	+	11.5433i	0.220564	+	0.382029i
$914$	17.8127			0.589190
$915$	9.89292	−	4.60976i	0.327050	−	0.152394i
$916$	−6.91782	+	3.99401i	−0.228571	+	0.131966i
$917$	5.93107	+	3.42430i	0.195861	+	0.113080i
$918$	8.10338	+	30.3446i	0.267451	+	1.00152i
$919$	8.39359	−	14.5381i	0.276879	−	0.479569i	−0.693728	−	0.720237i	$-0.744033\pi$
$919$	8.39359	−	14.5381i	0.276879	−	0.479569i	0.970607	+	0.240668i	$0.0773665\pi$
$920$	−0.122390	+	0.211986i	−0.00403508	+	0.00698896i
$921$	−1.42065	+	16.1857i	−0.0468120	+	0.533337i
$922$			10.7060i			0.352585i
$923$	−19.9561	−	34.5650i	−0.656863	−	1.13772i
$924$	21.9000	+	15.3437i	0.720458	+	0.504772i
$925$	−7.39979	−	4.27227i	−0.243304	−	0.140471i
$926$	23.2499			0.764038
$927$	55.4121	+	9.80276i	1.81997	+	0.321965i
$928$			2.05814i			0.0675618i
$929$	−27.8352			−0.913242			−0.456621	−	0.889661i	$-0.650940\pi$
$929$	−27.8352			−0.913242			−0.456621	+	0.889661i	$0.650940\pi$
$930$	−9.62921	+	0.527512i	−0.315754	+	0.0172978i
$931$	8.60301			0.281952
$932$		−	15.9529i		−	0.522554i
$933$	−1.62454	+	2.31869i	−0.0531850	+	0.0759106i
$934$	1.78177			0.0583014
$935$	24.5240	+	14.1589i	0.802021	+	0.463047i
$936$	−12.1999	−	2.15824i	−0.398765	−	0.0705443i
$937$	19.2733	+	33.3823i	0.629630	+	1.09055i	0.987626	+	0.156828i	$0.0501267\pi$
$937$	19.2733	+	33.3823i	0.629630	+	1.09055i	−0.357996	+	0.933723i	$0.616540\pi$
$938$		−	12.5728i		−	0.410518i
$939$	21.3049	+	1.86997i	0.695259	+	0.0610242i
$940$	1.99650	−	3.45803i	0.0651185	−	0.112789i
$941$	−6.88657	+	11.9279i	−0.224496	+	0.388838i	−0.956168	−	0.292818i	$-0.905407\pi$
$941$	−6.88657	+	11.9279i	−0.224496	+	0.388838i	0.731672	+	0.681657i	$0.238740\pi$
$942$	18.2410	−	26.0353i	0.594324	−	0.848275i
$943$	1.67366	+	0.966286i	0.0545018	+	0.0314666i
$944$	−0.641535	+	0.370390i	−0.0208802	+	0.0120552i
$945$	−16.5359	−	4.44573i	−0.537914	−	0.144620i
$946$	54.2949			1.76528
$947$	10.9849	+	19.0264i	0.356960	+	0.618273i	0.987451	−	0.157923i	$-0.0504798\pi$
$947$	10.9849	+	19.0264i	0.356960	+	0.618273i	−0.630491	+	0.776196i	$0.717146\pi$
$948$	22.1559	+	1.94467i	0.719591	+	0.0631599i
$949$	−0.692325	−	1.19914i	−0.0224738	−	0.0389258i
$950$	1.93051	+	1.11458i	0.0626340	+	0.0361617i
$951$	−58.8226	−	5.16297i	−1.90745	−	0.167421i
$952$	17.2500	+	9.95929i	0.559075	+	0.322782i
$953$	−44.4966			−1.44138			−0.720692	−	0.693255i	$-0.756176\pi$
$953$	−44.4966			−1.44138			−0.720692	+	0.693255i	$0.756176\pi$
$954$	−1.04161	+	5.88790i	−0.0337233	+	0.190628i
$955$	−8.43140	−	14.6036i	−0.272834	−	0.472562i
$956$	−4.52292	+	7.83393i	−0.146282	+	0.253367i
$957$	15.1381	−	7.05385i	0.489346	−	0.228019i
$958$	17.8311	+	30.8844i	0.576098	+	0.997830i
$959$	−64.3593			−2.07827
$960$	0.731555	+	1.56998i	0.0236108	+	0.0506708i
$961$	22.4133	+	21.4160i	0.723010	+	0.690838i
$962$			35.2870i			1.13770i
$963$	−9.71180	−	8.15848i	−0.312958	−	0.262903i
$964$	−13.3621	+	7.71462i	−0.430365	+	0.248471i
$965$			6.92690i			0.222985i
$966$	1.39178	+	0.122159i	0.0447799	+	0.00393041i
$967$	−46.3539	+	26.7624i	−1.49064	+	0.860621i	−0.999943	−	0.0107092i	$-0.996591\pi$
$967$	−46.3539	+	26.7624i	−1.49064	+	0.860621i	−0.490697	+	0.871330i	$0.663258\pi$
$968$	−9.48178	+	5.47431i	−0.304756	+	0.175951i
$969$	−21.1539	+	9.85701i	−0.679563	+	0.316653i
$970$	−3.83666	+	6.64528i	−0.123188	+	0.213367i
$971$	42.9055	+	24.7715i	1.37690	+	0.794955i	0.991785	−	0.127912i	$-0.0408276\pi$
$971$	42.9055	+	24.7715i	1.37690	+	0.794955i	0.385118	+	0.922868i	$0.374161\pi$
$972$	15.5310	−	1.33680i	0.498158	−	0.0428779i
$973$	−64.2958	+	37.1212i	−2.06123	+	1.19005i
$974$	−5.28014	+	9.14547i	−0.169187	+	0.293040i
$975$	4.10442	−	5.85822i	0.131447	−	0.187613i
$976$			6.30131i			0.201700i
$977$		−	9.46739i		−	0.302888i	−0.988466	−	0.151444i	$-0.951608\pi$
$977$		−	9.46739i		−	0.302888i	0.988466	−	0.151444i	$-0.0483924\pi$
$978$	−1.69399	+	2.41782i	−0.0541678	+	0.0773134i
$979$	−0.350447	+	0.606992i	−0.0112003	+	0.0193995i
$980$	−3.34226	+	1.92965i	−0.106765	+	0.0616405i
$981$	5.98963	+	16.4852i	0.191234	+	0.526332i
$982$	13.8762	+	8.01143i	0.442807	+	0.255655i
$983$	10.1810	−	17.6341i	0.324725	−	0.562440i	−0.656732	−	0.754124i	$-0.728062\pi$
$983$	10.1810	−	17.6341i	0.324725	−	0.562440i	0.981457	+	0.191684i	$0.0613949\pi$
$984$	12.3952	−	5.77573i	0.395144	−	0.184124i
$985$	−12.8333	+	7.40933i	−0.408904	+	0.236081i
$986$	10.7737	−	6.22018i	0.343103	−	0.198091i
$987$	−22.7035	−	1.99273i	−0.722661	−	0.0634294i
$988$		−	9.20591i		−	0.292879i
$989$	2.45676	−	1.41841i	0.0781203	−	0.0451028i
$990$	9.04031	−	10.7615i	0.287320	−	0.342024i
$991$		−	53.4053i		−	1.69647i	−0.529617	−	0.848237i	$-0.677664\pi$
$991$		−	53.4053i		−	1.69647i	0.529617	−	0.848237i	$-0.322336\pi$
$992$	2.07204	−	5.16785i	0.0657873	−	0.164079i
$993$	16.2164	+	34.8017i	0.514612	+	1.10440i
$994$	31.8479			1.01015
$995$	9.50589	+	16.4647i	0.301357	+	0.521966i
$996$	4.46673	−	2.08134i	0.141534	−	0.0659499i
$997$	27.9449	−	48.4020i	0.885024	−	1.53291i	0.0393377	−	0.999226i	$-0.487475\pi$
$997$	27.9449	−	48.4020i	0.885024	−	1.53291i	0.845686	−	0.533680i	$-0.179191\pi$
$998$	9.12364	+	15.8026i	0.288804	+	0.500223i
$999$	−11.4551	−	42.8956i	−0.362423	−	1.35716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.e.161.19	yes	40
3.2	odd	2	inner	930.2.o.e.161.5	✓	40
31.26	odd	6	inner	930.2.o.e.491.15	yes	40
93.26	even	6	inner	930.2.o.e.491.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.e.161.5	✓	40	3.2	odd	2	inner
930.2.o.e.161.19	yes	40	1.1	even	1	trivial
930.2.o.e.491.9	yes	40	93.26	even	6	inner
930.2.o.e.491.15	yes	40	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.41853 + 0.993862i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.993862 + 1.41853i) q^{6} +(-1.64767 - 2.85385i) q^{7} -1.00000i q^{8} +(1.02448 + 2.81965i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.41853 + 0.993862i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.993862 + 1.41853i) q^{6} +(-1.64767 - 2.85385i) q^{7} -1.00000i q^{8} +(1.02448 + 2.81965i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.34247 - 4.05727i) q^{11} +(-1.41853 - 0.993862i) q^{12} +(-3.57649 - 2.06489i) q^{13} +(2.85385 - 1.64767i) q^{14} +(-0.731555 - 1.56998i) q^{15} +1.00000 q^{16} +(-3.02223 - 5.23465i) q^{17} +(-2.81965 + 1.02448i) q^{18} +(-1.11458 - 1.93051i) q^{19} +(0.866025 + 0.500000i) q^{20} +(0.499058 - 5.68585i) q^{21} +(4.05727 + 2.34247i) q^{22} +0.244780 q^{23} +(0.993862 - 1.41853i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.06489 - 3.57649i) q^{26} +(-1.34909 + 5.01796i) q^{27} +(1.64767 + 2.85385i) q^{28} +2.05814 q^{29} +(1.56998 - 0.731555i) q^{30} +(-5.16785 - 2.07204i) q^{31} +1.00000i q^{32} +(7.35524 - 3.42729i) q^{33} +(5.23465 - 3.02223i) q^{34} +3.29535i q^{35} +(-1.02448 - 2.81965i) q^{36} +(-7.39979 + 4.27227i) q^{37} +(1.93051 - 1.11458i) q^{38} +(-3.02115 - 6.48364i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(6.83739 + 3.94757i) q^{41} +(5.68585 + 0.499058i) q^{42} +(10.0366 - 5.79463i) q^{43} +(-2.34247 + 4.05727i) q^{44} +(0.522605 - 2.95413i) q^{45} +0.244780i q^{46} -3.99299i q^{47} +(1.41853 + 0.993862i) q^{48} +(-1.92965 + 3.34226i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(0.915391 - 10.4292i) q^{51} +(3.57649 + 2.06489i) q^{52} +(0.996554 - 1.72608i) q^{53} +(-5.01796 - 1.34909i) q^{54} +(-4.05727 + 2.34247i) q^{55} +(-2.85385 + 1.64767i) q^{56} +(0.337591 - 3.84623i) q^{57} +2.05814i q^{58} +(-0.641535 + 0.370390i) q^{59} +(0.731555 + 1.56998i) q^{60} +6.30131i q^{61} +(2.07204 - 5.16785i) q^{62} +(6.35888 - 7.56957i) q^{63} -1.00000 q^{64} +(2.06489 + 3.57649i) q^{65} +(3.42729 + 7.35524i) q^{66} +(1.90767 - 3.30418i) q^{67} +(3.02223 + 5.23465i) q^{68} +(0.347229 + 0.243278i) q^{69} -3.29535 q^{70} +(8.36971 + 4.83225i) q^{71} +(2.81965 - 1.02448i) q^{72} +(0.290365 + 0.167642i) q^{73} +(-4.27227 - 7.39979i) q^{74} +(-0.151443 + 1.72542i) q^{75} +(1.11458 + 1.93051i) q^{76} -15.4385 q^{77} +(6.48364 - 3.02115i) q^{78} +(-11.1206 + 6.42046i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-6.90090 + 5.77733i) q^{81} +(-3.94757 + 6.83739i) q^{82} +(-1.42255 + 2.46393i) q^{83} +(-0.499058 + 5.68585i) q^{84} +6.04445i q^{85} +(5.79463 + 10.0366i) q^{86} +(2.91954 + 2.04551i) q^{87} +(-4.05727 - 2.34247i) q^{88} -0.149606 q^{89} +(2.95413 + 0.522605i) q^{90} +13.6090i q^{91} -0.244780 q^{92} +(-5.27144 - 8.07539i) q^{93} +3.99299 q^{94} +2.22916i q^{95} +(-0.993862 + 1.41853i) q^{96} -7.67331 q^{97} +(-3.34226 - 1.92965i) q^{98} +(13.8399 + 2.44837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

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