LMFDB - Embedded newform 930.2.s.d.439.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

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([0, 3, 4]))

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

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.8
Character	$\chi$	$=$	930.439
Dual form			930.2.s.d.769.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-2.21417 - 0.312164i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.24405 - 0.718253i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-2.21417 - 0.312164i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.24405 - 0.718253i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.312164 - 2.21417i) q^{10} +(1.06533 + 1.84520i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.930742 + 0.537364i) q^{13} +(0.718253 - 1.24405i) q^{14} +(1.76145 + 1.37743i) q^{15} +1.00000 q^{16} +(-3.17135 - 1.83098i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(1.71542 - 2.97119i) q^{19} +(2.21417 + 0.312164i) q^{20} +(0.718253 + 1.24405i) q^{21} +(-1.84520 + 1.06533i) q^{22} +0.935664i q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.80511 + 1.38237i) q^{25} +(-0.537364 - 0.930742i) q^{26} -1.00000i q^{27} +(1.24405 + 0.718253i) q^{28} +3.18722 q^{29} +(-1.37743 + 1.76145i) q^{30} +(5.36078 - 1.50401i) q^{31} +1.00000i q^{32} -2.13066i q^{33} +(1.83098 - 3.17135i) q^{34} +(2.53033 + 1.97868i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.50380 + 2.02292i) q^{37} +(2.97119 + 1.71542i) q^{38} +1.07473 q^{39} +(-0.312164 + 2.21417i) q^{40} +(5.85951 + 10.1490i) q^{41} +(-1.24405 + 0.718253i) q^{42} +(8.03235 + 4.63748i) q^{43} +(-1.06533 - 1.84520i) q^{44} +(-0.836743 - 2.07361i) q^{45} -0.935664 q^{46} +7.84412i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-2.46823 - 4.27509i) q^{49} +(-1.38237 + 4.80511i) q^{50} +(1.83098 + 3.17135i) q^{51} +(0.930742 - 0.537364i) q^{52} +(9.23106 - 5.32956i) q^{53} +1.00000 q^{54} +(-1.78281 - 4.41816i) q^{55} +(-0.718253 + 1.24405i) q^{56} +(-2.97119 + 1.71542i) q^{57} +3.18722i q^{58} +(-1.43328 + 2.48251i) q^{59} +(-1.76145 - 1.37743i) q^{60} +3.56112 q^{61} +(1.50401 + 5.36078i) q^{62} -1.43651i q^{63} -1.00000 q^{64} +(2.22857 - 0.899272i) q^{65} +2.13066 q^{66} +(-1.09406 + 0.631657i) q^{67} +(3.17135 + 1.83098i) q^{68} +(0.467832 - 0.810309i) q^{69} +(-1.97868 + 2.53033i) q^{70} +(-0.0395679 - 0.0685336i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-2.91552 + 1.68327i) q^{73} +(-2.02292 + 3.50380i) q^{74} +(-3.47016 - 3.59972i) q^{75} +(-1.71542 + 2.97119i) q^{76} -3.06070i q^{77} +1.07473i q^{78} +(5.23529 - 9.06779i) q^{79} +(-2.21417 - 0.312164i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-10.1490 + 5.85951i) q^{82} +(-11.0179 + 6.36117i) q^{83} +(-0.718253 - 1.24405i) q^{84} +(6.45034 + 5.04408i) q^{85} +(-4.63748 + 8.03235i) q^{86} +(-2.76021 - 1.59361i) q^{87} +(1.84520 - 1.06533i) q^{88} +1.28384 q^{89} +(2.07361 - 0.836743i) q^{90} +1.54385 q^{91} -0.935664i q^{92} +(-5.39458 - 1.37788i) q^{93} -7.84412 q^{94} +(-4.72573 + 6.04324i) q^{95} +(0.500000 - 0.866025i) q^{96} -15.8799i q^{97} +(4.27509 - 2.46823i) q^{98} +(-1.06533 + 1.84520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9	$ 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9} + 4 q^{10} + 2 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} - 14 q^{24} - 14 q^{25} - 12 q^{26} + 24 q^{29} + 4 q^{30} + 10 q^{34} + 8 q^{35} - 14 q^{36} + 24 q^{39} - 4 q^{40} + 20 q^{41} - 2 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{49} - 8 q^{50} + 10 q^{51} + 28 q^{54} + 6 q^{55} + 8 q^{56} - 20 q^{59} + 8 q^{60} + 32 q^{61} - 28 q^{64} - 12 q^{65} + 4 q^{66} - 6 q^{69} - 16 q^{70} - 16 q^{71} - 6 q^{74} - 8 q^{75} - 4 q^{76} + 10 q^{79} + 2 q^{80} - 14 q^{81} + 8 q^{84} + 72 q^{85} + 18 q^{86} - 80 q^{89} - 4 q^{90} + 32 q^{91} - 12 q^{94} - 32 q^{95} + 14 q^{96} - 2 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9 + 4 * q^10 + 2 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 - 14 * q^24 - 14 * q^25 - 12 * q^26 + 24 * q^29 + 4 * q^30 + 10 * q^34 + 8 * q^35 - 14 * q^36 + 24 * q^39 - 4 * q^40 + 20 * q^41 - 2 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^49 - 8 * q^50 + 10 * q^51 + 28 * q^54 + 6 * q^55 + 8 * q^56 - 20 * q^59 + 8 * q^60 + 32 * q^61 - 28 * q^64 - 12 * q^65 + 4 * q^66 - 6 * q^69 - 16 * q^70 - 16 * q^71 - 6 * q^74 - 8 * q^75 - 4 * q^76 + 10 * q^79 + 2 * q^80 - 14 * q^81 + 8 * q^84 + 72 * q^85 + 18 * q^86 - 80 * q^89 - 4 * q^90 + 32 * q^91 - 12 * q^94 - 32 * q^95 + 14 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−1.00000			−0.500000
$5$	−2.21417	−	0.312164i	−0.990207	−	0.139604i
$5$	−2.21417	−	0.312164i	−0.990207	−	0.139604i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−1.24405	−	0.718253i	−0.470207	−	0.271474i	0.246119	−	0.969239i	$-0.420844\pi$
$7$	−1.24405	−	0.718253i	−0.470207	−	0.271474i	−0.716326	+	0.697765i	$0.754178\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.312164	−	2.21417i	0.0987150	−	0.700182i
$11$	1.06533	+	1.84520i	0.321209	+	0.556350i	0.980738	−	0.195329i	$-0.0625775\pi$
$11$	1.06533	+	1.84520i	0.321209	+	0.556350i	−0.659529	+	0.751679i	$0.729244\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−0.930742	+	0.537364i	−0.258141	+	0.149038i	−0.623486	−	0.781834i	$-0.714284\pi$
$13$	−0.930742	+	0.537364i	−0.258141	+	0.149038i	0.365345	+	0.930872i	$0.380951\pi$
$14$	0.718253	−	1.24405i	0.191961	−	0.332486i
$15$	1.76145	+	1.37743i	0.454803	+	0.355650i
$16$	1.00000			0.250000
$17$	−3.17135	−	1.83098i	−0.769165	−	0.444078i	0.0634118	−	0.997987i	$-0.479802\pi$
$17$	−3.17135	−	1.83098i	−0.769165	−	0.444078i	−0.832577	+	0.553910i	$0.813135\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	1.71542	−	2.97119i	0.393544	−	0.681638i	−0.599370	−	0.800472i	$-0.704582\pi$
$19$	1.71542	−	2.97119i	0.393544	−	0.681638i	0.992914	+	0.118834i	$0.0379155\pi$
$20$	2.21417	+	0.312164i	0.495104	+	0.0698020i
$21$	0.718253	+	1.24405i	0.156736	+	0.271474i
$22$	−1.84520	+	1.06533i	−0.393399	+	0.227129i
$23$			0.935664i			0.195099i	0.995231	+	0.0975497i	$0.0311005\pi$
$23$			0.935664i			0.195099i	−0.995231	+	0.0975497i	$0.968900\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	4.80511	+	1.38237i	0.961021	+	0.276474i
$26$	−0.537364	−	0.930742i	−0.105386	−	0.182534i
$27$		−	1.00000i		−	0.192450i
$28$	1.24405	+	0.718253i	0.235103	+	0.135737i
$29$	3.18722			0.591851			0.295926	−	0.955211i	$-0.404372\pi$
$29$	3.18722			0.591851			0.295926	+	0.955211i	$0.404372\pi$
$30$	−1.37743	+	1.76145i	−0.251483	+	0.321595i
$31$	5.36078	−	1.50401i	0.962824	−	0.270129i
$31$	5.36078	−	1.50401i	0.962824	−	0.270129i
$32$			1.00000i			0.176777i
$33$		−	2.13066i		−	0.370900i
$34$	1.83098	−	3.17135i	0.314010	−	0.543882i
$35$	2.53033	+	1.97868i	0.427703	+	0.334458i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	3.50380	+	2.02292i	0.576021	+	0.332566i	0.759551	−	0.650448i	$-0.225419\pi$
$37$	3.50380	+	2.02292i	0.576021	+	0.332566i	−0.183529	+	0.983014i	$0.558752\pi$
$38$	2.97119	+	1.71542i	0.481991	+	0.278278i
$39$	1.07473			0.172094
$40$	−0.312164	+	2.21417i	−0.0493575	+	0.350091i
$41$	5.85951	+	10.1490i	0.915102	+	1.58500i	0.806751	+	0.590891i	$0.201224\pi$
$41$	5.85951	+	10.1490i	0.915102	+	1.58500i	0.108351	+	0.994113i	$0.465443\pi$
$42$	−1.24405	+	0.718253i	−0.191961	+	0.110829i
$43$	8.03235	+	4.63748i	1.22492	+	0.707209i	0.965963	−	0.258679i	$-0.0832872\pi$
$43$	8.03235	+	4.63748i	1.22492	+	0.707209i	0.258959	+	0.965888i	$0.416621\pi$
$44$	−1.06533	−	1.84520i	−0.160604	−	0.278175i
$45$	−0.836743	−	2.07361i	−0.124734	−	0.309116i
$46$	−0.935664			−0.137956
$47$			7.84412i			1.14418i	0.820190	+	0.572092i	$0.193868\pi$
$47$			7.84412i			1.14418i	−0.820190	+	0.572092i	$0.806132\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−2.46823	−	4.27509i	−0.352604	−	0.610728i
$50$	−1.38237	+	4.80511i	−0.195497	+	0.679545i
$51$	1.83098	+	3.17135i	0.256388	+	0.444078i
$52$	0.930742	−	0.537364i	0.129071	−	0.0745190i
$53$	9.23106	−	5.32956i	1.26798	−	0.732071i	0.293378	−	0.955997i	$-0.405221\pi$
$53$	9.23106	−	5.32956i	1.26798	−	0.732071i	0.974606	+	0.223925i	$0.0718872\pi$
$54$	1.00000			0.136083
$55$	−1.78281	−	4.41816i	−0.240395	−	0.595744i
$56$	−0.718253	+	1.24405i	−0.0959806	+	0.166243i
$57$	−2.97119	+	1.71542i	−0.393544	+	0.227213i
$58$			3.18722i			0.418502i
$59$	−1.43328	+	2.48251i	−0.186597	+	0.323195i	−0.944113	−	0.329621i	$-0.893079\pi$
$59$	−1.43328	+	2.48251i	−0.186597	+	0.323195i	0.757517	+	0.652816i	$0.226412\pi$
$60$	−1.76145	−	1.37743i	−0.227402	−	0.177825i
$61$	3.56112			0.455955			0.227978	−	0.973666i	$-0.426789\pi$
$61$	3.56112			0.455955			0.227978	+	0.973666i	$0.426789\pi$
$62$	1.50401	+	5.36078i	0.191010	+	0.680820i
$63$		−	1.43651i		−	0.180983i
$64$	−1.00000			−0.125000
$65$	2.22857	−	0.899272i	0.276420	−	0.111541i
$66$	2.13066			0.262266
$67$	−1.09406	+	0.631657i	−0.133661	+	0.0771692i	−0.565340	−	0.824858i	$-0.691255\pi$
$67$	−1.09406	+	0.631657i	−0.133661	+	0.0771692i	0.431678	+	0.902028i	$0.357922\pi$
$68$	3.17135	+	1.83098i	0.384582	+	0.222039i
$69$	0.467832	−	0.810309i	0.0563203	−	0.0975497i
$70$	−1.97868	+	2.53033i	−0.236498	+	0.302432i
$71$	−0.0395679	−	0.0685336i	−0.00469585	−	0.00813345i	0.863668	−	0.504061i	$-0.168161\pi$
$71$	−0.0395679	−	0.0685336i	−0.00469585	−	0.00813345i	−0.868364	+	0.495928i	$0.834828\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−2.91552	+	1.68327i	−0.341236	+	0.197012i	−0.660818	−	0.750546i	$-0.729791\pi$
$73$	−2.91552	+	1.68327i	−0.341236	+	0.197012i	0.319583	+	0.947558i	$0.396457\pi$
$74$	−2.02292	+	3.50380i	−0.235160	+	0.407309i
$75$	−3.47016	−	3.59972i	−0.400700	−	0.415660i
$76$	−1.71542	+	2.97119i	−0.196772	+	0.340819i
$77$		−	3.06070i		−	0.348799i
$78$			1.07473i			0.121689i
$79$	5.23529	−	9.06779i	0.589016	−	1.02021i	−0.405345	−	0.914164i	$-0.632849\pi$
$79$	5.23529	−	9.06779i	0.589016	−	1.02021i	0.994362	−	0.106043i	$-0.0338180\pi$
$80$	−2.21417	−	0.312164i	−0.247552	−	0.0349010i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−10.1490	+	5.85951i	−1.12077	+	0.647075i
$83$	−11.0179	+	6.36117i	−1.20937	+	0.698229i	−0.962621	−	0.270851i	$-0.912695\pi$
$83$	−11.0179	+	6.36117i	−1.20937	+	0.698229i	−0.246747	+	0.969080i	$0.579362\pi$
$84$	−0.718253	−	1.24405i	−0.0783678	−	0.135737i
$85$	6.45034	+	5.04408i	0.699638	+	0.547107i
$86$	−4.63748	+	8.03235i	−0.500072	+	0.866151i
$87$	−2.76021	−	1.59361i	−0.295926	−	0.170853i
$88$	1.84520	−	1.06533i	0.196699	−	0.113564i
$89$	1.28384			0.136087			0.0680435	−	0.997682i	$-0.478324\pi$
$89$	1.28384			0.136087			0.0680435	+	0.997682i	$0.478324\pi$
$90$	2.07361	−	0.836743i	0.218578	−	0.0882005i
$91$	1.54385			0.161840
$92$		−	0.935664i		−	0.0975497i
$93$	−5.39458	−	1.37788i	−0.559392	−	0.142879i
$94$	−7.84412			−0.809060
$95$	−4.72573	+	6.04324i	−0.484850	+	0.620023i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	15.8799i		−	1.61236i	−0.591672	−	0.806179i	$-0.701532\pi$
$97$		−	15.8799i		−	1.61236i	0.591672	−	0.806179i	$-0.298468\pi$
$98$	4.27509	−	2.46823i	0.431850	−	0.249328i
$99$	−1.06533	+	1.84520i	−0.107070	+	0.185450i
$100$	−4.80511	−	1.38237i	−0.480511	−	0.138237i
$101$	−0.545325			−0.0542618			−0.0271309	−	0.999632i	$-0.508637\pi$
$101$	−0.545325			−0.0542618			−0.0271309	+	0.999632i	$0.508637\pi$
$102$	−3.17135	+	1.83098i	−0.314010	+	0.181294i
$103$	7.67910	−	4.43353i	0.756645	−	0.436849i	−0.0714451	−	0.997445i	$-0.522761\pi$
$103$	7.67910	−	4.43353i	0.756645	−	0.436849i	0.828090	+	0.560596i	$0.189428\pi$
$104$	0.537364	+	0.930742i	0.0526929	+	0.0912668i
$105$	−1.20199	−	2.97875i	−0.117302	−	0.290697i
$106$	5.32956	+	9.23106i	0.517652	+	0.896600i
$107$	−2.53308	−	1.46247i	−0.244882	−	0.141383i	0.372537	−	0.928018i	$-0.378488\pi$
$107$	−2.53308	−	1.46247i	−0.244882	−	0.141383i	−0.617418	+	0.786635i	$0.711821\pi$
$108$			1.00000i			0.0962250i
$109$	2.32922			0.223099			0.111549	−	0.993759i	$-0.464419\pi$
$109$	2.32922			0.223099			0.111549	+	0.993759i	$0.464419\pi$
$110$	4.41816	−	1.78281i	0.421255	−	0.169985i
$111$	−2.02292	−	3.50380i	−0.192007	−	0.332566i
$112$	−1.24405	−	0.718253i	−0.117552	−	0.0678685i
$113$	11.0269	−	6.36640i	1.03733	−	0.598900i	0.118251	−	0.992984i	$-0.462271\pi$
$113$	11.0269	−	6.36640i	1.03733	−	0.598900i	0.919075	+	0.394084i	$0.128938\pi$
$114$	−1.71542	−	2.97119i	−0.160664	−	0.278278i
$115$	0.292081	−	2.07172i	0.0272367	−	0.193189i
$116$	−3.18722			−0.295926
$117$	−0.930742	−	0.537364i	−0.0860471	−	0.0496793i
$118$	−2.48251	−	1.43328i	−0.228534	−	0.131944i
$119$	2.63021	+	4.55566i	0.241111	+	0.417617i
$120$	1.37743	−	1.76145i	0.125741	−	0.160797i
$121$	3.23015	−	5.59478i	0.293650	−	0.508616i
$122$			3.56112i			0.322409i
$123$		−	11.7190i		−	1.05667i
$124$	−5.36078	+	1.50401i	−0.481412	+	0.135064i
$125$	−10.2078	−	4.56078i	−0.913014	−	0.407929i
$126$	1.43651			0.127974
$127$	7.64763	+	4.41536i	0.678618	+	0.391800i	0.799334	−	0.600887i	$-0.205186\pi$
$127$	7.64763	+	4.41536i	0.678618	+	0.391800i	−0.120716	+	0.992687i	$0.538519\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−4.63748	−	8.03235i	−0.408307	−	0.707209i
$130$	0.899272	+	2.22857i	0.0788714	+	0.195458i
$131$	−10.8255	+	18.7503i	−0.945826	+	1.63822i	−0.191738	+	0.981446i	$0.561413\pi$
$131$	−10.8255	+	18.7503i	−0.945826	+	1.63822i	−0.754088	+	0.656773i	$0.771921\pi$
$132$			2.13066i			0.185450i
$133$	−4.26813	+	2.46421i	−0.370094	+	0.213674i
$134$	−0.631657	−	1.09406i	−0.0545669	−	0.0945126i
$135$	−0.312164	+	2.21417i	−0.0268668	+	0.190566i
$136$	−1.83098	+	3.17135i	−0.157005	+	0.271941i
$137$	5.43383	−	3.13722i	0.464243	−	0.268031i	−0.249583	−	0.968353i	$-0.580294\pi$
$137$	5.43383	−	3.13722i	0.464243	−	0.268031i	0.713827	+	0.700322i	$0.246960\pi$
$138$	0.810309	+	0.467832i	0.0689781	+	0.0398245i
$139$	−17.3868			−1.47473			−0.737363	−	0.675496i	$-0.763929\pi$
$139$	−17.3868			−1.47473			−0.737363	+	0.675496i	$0.763929\pi$
$140$	−2.53033	−	1.97868i	−0.213852	−	0.167229i
$141$	3.92206	−	6.79321i	0.330297	−	0.572092i
$142$	0.0685336	−	0.0395679i	0.00575121	−	0.00332047i
$143$	−1.98309	−	1.14494i	−0.165835	−	0.0957446i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−7.05704	−	0.994935i	−0.586056	−	0.0826248i
$146$	−1.68327	−	2.91552i	−0.139309	−	0.241290i
$147$			4.93645i			0.407152i
$148$	−3.50380	−	2.02292i	−0.288011	−	0.166283i
$149$	−3.75724	+	6.50774i	−0.307805	+	0.533135i	−0.977882	−	0.209157i	$-0.932928\pi$
$149$	−3.75724	+	6.50774i	−0.307805	+	0.533135i	0.670077	+	0.742292i	$0.266261\pi$
$150$	3.59972	−	3.47016i	0.293916	−	0.283337i
$151$	20.8731			1.69863			0.849316	−	0.527884i	$-0.177015\pi$
$151$	20.8731			1.69863			0.849316	+	0.527884i	$0.177015\pi$
$152$	−2.97119	−	1.71542i	−0.240996	−	0.139139i
$153$		−	3.66196i		−	0.296052i
$154$	3.06070			0.246638
$155$	−12.3392	+	1.65670i	−0.991107	+	0.133069i
$156$	−1.07473			−0.0860471
$157$		−	16.5885i		−	1.32391i	−0.749546	−	0.661953i	$-0.769728\pi$
$157$		−	16.5885i		−	1.32391i	0.749546	−	0.661953i	$-0.230272\pi$
$158$	9.06779	+	5.23529i	0.721395	+	0.416497i
$159$	−10.6591			−0.845323
$160$	0.312164	−	2.21417i	0.0246787	−	0.175046i
$161$	0.672043	−	1.16401i	0.0529644	−	0.0917371i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$			8.13701i			0.637340i	0.947866	+	0.318670i	$0.103236\pi$
$163$			8.13701i			0.637340i	−0.947866	+	0.318670i	$0.896764\pi$
$164$	−5.85951	−	10.1490i	−0.457551	−	0.792502i
$165$	−0.665115	+	4.71764i	−0.0517791	+	0.367268i
$166$	−6.36117	−	11.0179i	−0.493722	−	0.855152i
$167$	6.78726	+	3.91863i	0.525214	+	0.303233i	0.739065	−	0.673634i	$-0.235267\pi$
$167$	6.78726	+	3.91863i	0.525214	+	0.303233i	−0.213851	+	0.976866i	$0.568601\pi$
$168$	1.24405	−	0.718253i	0.0959806	−	0.0554144i
$169$	−5.92248	+	10.2580i	−0.455575	+	0.789080i
$170$	−5.04408	+	6.45034i	−0.386863	+	0.494719i
$171$	3.43084			0.262363
$172$	−8.03235	−	4.63748i	−0.612461	−	0.353605i
$173$	11.4098	−	6.58742i	0.867467	−	0.500833i	0.000961620	−	1.00000i	$-0.499694\pi$
$173$	11.4098	−	6.58742i	0.867467	−	0.500833i	0.866506	+	0.499167i	$0.166361\pi$
$174$	1.59361	−	2.76021i	0.120811	−	0.209251i
$175$	−4.98490	−	5.17102i	−0.376823	−	0.390892i
$176$	1.06533	+	1.84520i	0.0803022	+	0.139088i
$177$	2.48251	−	1.43328i	0.186597	−	0.107732i
$178$			1.28384i			0.0962281i
$179$	−5.76518	+	9.98558i	−0.430910	+	0.746357i	−0.996952	−	0.0780189i	$-0.975141\pi$
$179$	−5.76518	+	9.98558i	−0.430910	+	0.746357i	0.566042	+	0.824376i	$0.308474\pi$
$180$	0.836743	+	2.07361i	0.0623672	+	0.154558i
$181$	4.85938	+	8.41670i	0.361195	+	0.625608i	0.988158	−	0.153441i	$-0.0490355\pi$
$181$	4.85938	+	8.41670i	0.361195	+	0.625608i	−0.626963	+	0.779049i	$0.715702\pi$
$182$			1.54385i			0.114438i
$183$	−3.08402	−	1.78056i	−0.227978	−	0.131623i
$184$	0.935664			0.0689781
$185$	−7.12653	−	5.57285i	−0.523953	−	0.409724i
$186$	1.37788	−	5.39458i	0.101031	−	0.395550i
$187$		−	7.80238i		−	0.570566i
$188$		−	7.84412i		−	0.572092i
$189$	−0.718253	+	1.24405i	−0.0522452	+	0.0904913i
$190$	−6.04324	−	4.72573i	−0.438423	−	0.342841i
$191$	−0.603738	−	1.04570i	−0.0436849	−	0.0756645i	0.843356	−	0.537355i	$-0.180576\pi$
$191$	−0.603738	−	1.04570i	−0.0436849	−	0.0756645i	−0.887041	+	0.461690i	$0.847243\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	9.40763	+	5.43150i	0.677176	+	0.390968i	0.798790	−	0.601610i	$-0.205474\pi$
$193$	9.40763	+	5.43150i	0.677176	+	0.390968i	−0.121614	+	0.992577i	$0.538807\pi$
$194$	15.8799			1.14011
$195$	−2.37963	−	0.335492i	−0.170409	−	0.0240250i
$196$	2.46823	+	4.27509i	0.176302	+	0.305364i
$197$	−1.79030	+	1.03363i	−0.127554	+	0.0736431i	−0.562419	−	0.826852i	$-0.690129\pi$
$197$	−1.79030	+	1.03363i	−0.127554	+	0.0736431i	0.434866	+	0.900495i	$0.356796\pi$
$198$	−1.84520	−	1.06533i	−0.131133	−	0.0757096i
$199$	−2.42343	−	4.19751i	−0.171792	−	0.297553i	0.767254	−	0.641343i	$-0.221623\pi$
$199$	−2.42343	−	4.19751i	−0.171792	−	0.297553i	−0.939047	+	0.343790i	$0.888289\pi$
$200$	1.38237	−	4.80511i	0.0977483	−	0.339772i
$201$	1.26331			0.0891074
$202$		−	0.545325i		−	0.0383689i
$203$	−3.96506	−	2.28923i	−0.278292	−	0.160672i
$204$	−1.83098	−	3.17135i	−0.128194	−	0.222039i
$205$	−9.80582	−	24.3007i	−0.684868	−	1.69723i
$206$	4.43353	+	7.67910i	0.308899	+	0.535029i
$207$	−0.810309	+	0.467832i	−0.0563203	+	0.0325166i
$208$	−0.930742	+	0.537364i	−0.0645353	+	0.0372595i
$209$	7.30994			0.505639
$210$	2.97875	−	1.20199i	0.205553	−	0.0829450i
$211$	−6.99794	+	12.1208i	−0.481758	+	0.834430i	−0.999781	−	0.0209372i	$-0.993335\pi$
$211$	−6.99794	+	12.1208i	−0.481758	+	0.834430i	0.518023	+	0.855367i	$0.326668\pi$
$212$	−9.23106	+	5.32956i	−0.633992	+	0.366036i
$213$			0.0791358i			0.00542230i
$214$	1.46247	−	2.53308i	0.0999726	−	0.173158i
$215$	−16.3373	−	12.7756i	−1.11420	−	0.871288i
$216$	−1.00000			−0.0680414
$217$	−7.74934	−	1.97933i	−0.526059	−	0.134365i
$218$			2.32922i			0.157755i
$219$	3.36655			0.227490
$220$	1.78281	+	4.41816i	0.120197	+	0.297872i
$221$	3.93561			0.264738
$222$	3.50380	−	2.02292i	0.235160	−	0.135770i
$223$	−6.14831	−	3.54973i	−0.411722	−	0.237708i	0.279808	−	0.960056i	$-0.409729\pi$
$223$	−6.14831	−	3.54973i	−0.411722	−	0.237708i	−0.691529	+	0.722349i	$0.743063\pi$
$224$	0.718253	−	1.24405i	0.0479903	−	0.0831216i
$225$	1.20539	+	4.85253i	0.0803591	+	0.323502i
$226$	6.36640	+	11.0269i	0.423486	+	0.733500i
$227$	16.7766	−	9.68597i	1.11350	−	0.642881i	0.173768	−	0.984787i	$-0.444406\pi$
$227$	16.7766	−	9.68597i	1.11350	−	0.642881i	0.939734	+	0.341906i	$0.111072\pi$
$228$	2.97119	−	1.71542i	0.196772	−	0.113606i
$229$	7.26939	−	12.5910i	0.480375	−	0.832034i	−0.519371	−	0.854549i	$-0.673834\pi$
$229$	7.26939	−	12.5910i	0.480375	−	0.832034i	0.999747	+	0.0225146i	$0.00716723\pi$
$230$	2.07172	+	0.292081i	0.136605	+	0.0192592i
$231$	−1.53035	+	2.65065i	−0.100690	+	0.174400i
$232$		−	3.18722i		−	0.209251i
$233$			1.47599i			0.0966951i	0.998831	+	0.0483475i	$0.0153955\pi$
$233$			1.47599i			0.0966951i	−0.998831	+	0.0483475i	$0.984605\pi$
$234$	0.537364	−	0.930742i	0.0351286	−	0.0608445i
$235$	2.44865	−	17.3682i	0.159733	−	1.13298i
$236$	1.43328	−	2.48251i	0.0932984	−	0.161598i
$237$	−9.06779	+	5.23529i	−0.589016	+	0.340069i
$238$	−4.55566	+	2.63021i	−0.295299	+	0.170491i
$239$	0.901318	+	1.56113i	0.0583014	+	0.100981i	0.893703	−	0.448659i	$-0.148098\pi$
$239$	0.901318	+	1.56113i	0.0583014	+	0.100981i	−0.835402	+	0.549640i	$0.814765\pi$
$240$	1.76145	+	1.37743i	0.113701	+	0.0889126i
$241$	0.887042	−	1.53640i	0.0571394	−	0.0989684i	−0.836041	−	0.548667i	$-0.815135\pi$
$241$	0.887042	−	1.53640i	0.0571394	−	0.0989684i	0.893180	+	0.449699i	$0.148469\pi$
$242$	5.59478	+	3.23015i	0.359646	+	0.207642i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−3.56112			−0.227978
$245$	4.13054	+	10.2363i	0.263891	+	0.653972i
$246$	11.7190			0.747178
$247$			3.68722i			0.234612i
$248$	−1.50401	−	5.36078i	−0.0955050	−	0.340410i
$249$	12.7223			0.806245
$250$	4.56078	−	10.2078i	0.288449	−	0.645598i
$251$	−6.72206	+	11.6429i	−0.424293	+	0.734896i	−0.996354	−	0.0853143i	$-0.972811\pi$
$251$	−6.72206	+	11.6429i	−0.424293	+	0.734896i	0.572061	+	0.820211i	$0.306144\pi$
$252$			1.43651i			0.0904913i
$253$	−1.72649	+	0.996790i	−0.108544	+	0.0626676i
$254$	−4.41536	+	7.64763i	−0.277045	+	0.479855i
$255$	−3.06412	−	7.59347i	−0.191883	−	0.475522i
$256$	1.00000			0.0625000
$257$	2.39555	−	1.38307i	0.149430	−	0.0862737i	−0.423420	−	0.905933i	$-0.639171\pi$
$257$	2.39555	−	1.38307i	0.149430	−	0.0862737i	0.572851	+	0.819660i	$0.305837\pi$
$258$	8.03235	−	4.63748i	0.500072	−	0.288717i
$259$	−2.90594	−	5.03323i	−0.180566	−	0.312750i
$260$	−2.22857	+	0.899272i	−0.138210	+	0.0557705i
$261$	1.59361	+	2.76021i	0.0986419	+	0.170853i
$262$	−18.7503	−	10.8255i	−1.15840	−	0.668800i
$263$		−	13.7423i		−	0.847386i	−0.905806	−	0.423693i	$-0.860733\pi$
$263$		−	13.7423i		−	0.847386i	0.905806	−	0.423693i	$-0.139267\pi$
$264$	−2.13066			−0.131133
$265$	−22.1029	+	8.91895i	−1.35777	+	0.547886i
$266$	−2.46421	−	4.26813i	−0.151090	−	0.261696i
$267$	−1.11184	−	0.641921i	−0.0680435	−	0.0392849i
$268$	1.09406	−	0.631657i	0.0668305	−	0.0385846i
$269$	3.62554	+	6.27962i	0.221053	+	0.382875i	0.955128	−	0.296193i	$-0.0957173\pi$
$269$	3.62554	+	6.27962i	0.221053	+	0.382875i	−0.734075	+	0.679068i	$0.762384\pi$
$270$	−2.21417	−	0.312164i	−0.134750	−	0.0189977i
$271$	−16.7720			−1.01882			−0.509412	−	0.860523i	$-0.670137\pi$
$271$	−16.7720			−1.01882			−0.509412	+	0.860523i	$0.670137\pi$
$272$	−3.17135	−	1.83098i	−0.192291	−	0.111019i
$273$	−1.33702	−	0.771926i	−0.0809199	−	0.0467191i
$274$	3.13722	+	5.43383i	0.189527	+	0.328270i
$275$	2.56827	+	10.3391i	0.154872	+	0.623470i
$276$	−0.467832	+	0.810309i	−0.0281602	+	0.0487748i
$277$		−	8.25596i		−	0.496053i	−0.968753	−	0.248026i	$-0.920218\pi$
$277$		−	8.25596i		−	0.496053i	0.968753	−	0.248026i	$-0.0797820\pi$
$278$		−	17.3868i		−	1.04279i
$279$	3.98290	+	3.89056i	0.238450	+	0.232922i
$280$	1.97868	−	2.53033i	0.118249	−	0.151216i
$281$	30.7433			1.83399			0.916996	−	0.398898i	$-0.130607\pi$
$281$	30.7433			1.83399			0.916996	+	0.398898i	$0.130607\pi$
$282$	6.79321	+	3.92206i	0.404530	+	0.233555i
$283$			14.9246i			0.887177i	0.896231	+	0.443588i	$0.146295\pi$
$283$			14.9246i			0.887177i	−0.896231	+	0.443588i	$0.853705\pi$
$284$	0.0395679	+	0.0685336i	0.00234792	+	0.00406672i
$285$	7.11422	−	2.87073i	0.421410	−	0.170047i
$286$	1.14494	−	1.98309i	0.0677017	−	0.117263i
$287$		−	16.8345i		−	0.993706i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−1.79504	−	3.10909i	−0.105590	−	0.182888i
$290$	0.994935	−	7.05704i	0.0584246	−	0.414404i
$291$	−7.93994	+	13.7524i	−0.465448	+	0.806179i
$292$	2.91552	−	1.68327i	0.170618	−	0.0985062i
$293$	−25.0938	−	14.4879i	−1.46600	−	0.846394i	−0.466720	−	0.884405i	$-0.654565\pi$
$293$	−25.0938	−	14.4879i	−1.46600	−	0.846394i	−0.999277	+	0.0380108i	$0.987898\pi$
$294$	−4.93645			−0.287900
$295$	3.94847	−	5.04928i	0.229889	−	0.293981i
$296$	2.02292	−	3.50380i	0.117580	−	0.203654i
$297$	1.84520	−	1.06533i	0.107070	−	0.0618167i
$298$	−6.50774	−	3.75724i	−0.376983	−	0.217651i
$299$	−0.502792	−	0.870862i	−0.0290772	−	0.0503632i
$300$	3.47016	+	3.59972i	0.200350	+	0.207830i
$301$	−6.66177	−	11.5385i	−0.383978	−	0.665069i
$302$			20.8731i			1.20111i
$303$	0.472265	+	0.272662i	0.0271309	+	0.0156640i
$304$	1.71542	−	2.97119i	0.0983860	−	0.170410i
$305$	−7.88494	−	1.11166i	−0.451490	−	0.0636532i
$306$	3.66196			0.209340
$307$	17.5661	+	10.1418i	1.00255	+	0.578822i	0.909002	−	0.416792i	$-0.136846\pi$
$307$	17.5661	+	10.1418i	1.00255	+	0.578822i	0.0935480	+	0.995615i	$0.470179\pi$
$308$			3.06070i			0.174400i
$309$	−8.86707			−0.504430
$310$	−1.65670	−	12.3392i	−0.0940943	−	0.700818i
$311$	17.1444			0.972169			0.486085	−	0.873912i	$-0.338425\pi$
$311$	17.1444			0.972169			0.486085	+	0.873912i	$0.338425\pi$
$312$		−	1.07473i		−	0.0608445i
$313$	6.05166	+	3.49393i	0.342060	+	0.197489i	0.661183	−	0.750225i	$-0.270055\pi$
$313$	6.05166	+	3.49393i	0.342060	+	0.197489i	−0.319122	+	0.947713i	$0.603388\pi$
$314$	16.5885			0.936142
$315$	−0.448425	+	3.18067i	−0.0252659	+	0.179210i
$316$	−5.23529	+	9.06779i	−0.294508	+	0.510103i
$317$	18.9222	+	10.9247i	1.06278	+	0.613594i	0.926199	−	0.377035i	$-0.123056\pi$
$317$	18.9222	+	10.9247i	1.06278	+	0.613594i	0.136577	+	0.990629i	$0.456390\pi$
$318$		−	10.6591i		−	0.597734i
$319$	3.39543	+	5.88107i	0.190108	+	0.329276i
$320$	2.21417	+	0.312164i	0.123776	+	0.0174505i
$321$	1.46247	+	2.53308i	0.0816273	+	0.141383i
$322$	1.16401	+	0.672043i	0.0648679	+	0.0374515i
$323$	−10.8804	+	6.28179i	−0.605401	+	0.349528i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−5.21515	+	1.29546i	−0.289284	+	0.0718593i
$326$	−8.13701			−0.450667
$327$	−2.01716	−	1.16461i	−0.111549	−	0.0644031i
$328$	10.1490	−	5.85951i	0.560384	−	0.323538i
$329$	5.63406	−	9.75848i	0.310616	−	0.538003i
$330$	−4.71764	−	0.665115i	−0.259698	−	0.0366134i
$331$	−2.85802	−	4.95024i	−0.157091	−	0.272090i	0.776727	−	0.629837i	$-0.216878\pi$
$331$	−2.85802	−	4.95024i	−0.157091	−	0.272090i	−0.933818	+	0.357747i	$0.883545\pi$
$332$	11.0179	−	6.36117i	0.604684	−	0.349115i
$333$			4.04584i			0.221711i
$334$	−3.91863	+	6.78726i	−0.214418	+	0.371383i
$335$	2.61962	−	1.05707i	0.143125	−	0.0577539i
$336$	0.718253	+	1.24405i	0.0391839	+	0.0678685i
$337$		−	10.2739i		−	0.559653i	−0.960051	−	0.279826i	$-0.909723\pi$
$337$		−	10.2739i		−	0.559653i	0.960051	−	0.279826i	$-0.0902769\pi$
$338$	−10.2580	−	5.92248i	−0.557964	−	0.322140i
$339$	−12.7328			−0.691550
$340$	−6.45034	−	5.04408i	−0.349819	−	0.273554i
$341$	8.48621	+	8.28946i	0.459554	+	0.448899i
$342$			3.43084i			0.185518i
$343$			17.1468i			0.925839i
$344$	4.63748	−	8.03235i	0.250036	−	0.433075i
$345$	−1.28881	+	1.64812i	−0.0693872	+	0.0887319i
$346$	6.58742	+	11.4098i	0.354142	+	0.613392i
$347$	8.98356	+	5.18666i	0.482263	+	0.278435i	0.721359	−	0.692561i	$-0.243518\pi$
$347$	8.98356	+	5.18666i	0.482263	+	0.278435i	−0.239096	+	0.970996i	$0.576851\pi$
$348$	2.76021	+	1.59361i	0.147963	+	0.0854264i
$349$	1.54492			0.0826976			0.0413488	−	0.999145i	$-0.486835\pi$
$349$	1.54492			0.0826976			0.0413488	+	0.999145i	$0.486835\pi$
$350$	5.17102	−	4.98490i	0.276403	−	0.266454i
$351$	0.537364	+	0.930742i	0.0286824	+	0.0496793i
$352$	−1.84520	+	1.06533i	−0.0983497	+	0.0567822i
$353$	−0.916329	−	0.529043i	−0.0487712	−	0.0281581i	0.475416	−	0.879761i	$-0.342298\pi$
$353$	−0.916329	−	0.529043i	−0.0487712	−	0.0281581i	−0.524187	+	0.851603i	$0.675631\pi$
$354$	1.43328	+	2.48251i	0.0761779	+	0.131944i
$355$	0.0662164	+	0.164097i	0.00351440	+	0.00870936i
$356$	−1.28384			−0.0680435
$357$		−	5.26042i		−	0.278411i
$358$	−9.98558	−	5.76518i	−0.527754	−	0.304699i
$359$	−14.8705	−	25.7564i	−0.784833	−	1.35937i	−0.929099	−	0.369831i	$-0.879415\pi$
$359$	−14.8705	−	25.7564i	−0.784833	−	1.35937i	0.144266	−	0.989539i	$-0.453918\pi$
$360$	−2.07361	+	0.836743i	−0.109289	+	0.0441003i
$361$	3.61468	+	6.26080i	0.190246	+	0.329516i
$362$	−8.41670	+	4.85938i	−0.442372	+	0.255404i
$363$	−5.59478	+	3.23015i	−0.293650	+	0.169539i
$364$	−1.54385			−0.0809199
$365$	6.98091	−	2.81694i	0.365398	−	0.147445i
$366$	1.78056	−	3.08402i	0.0930715	−	0.161205i
$367$	−0.454524	+	0.262420i	−0.0237260	+	0.0136982i	−0.511816	−	0.859095i	$-0.671027\pi$
$367$	−0.454524	+	0.262420i	−0.0237260	+	0.0136982i	0.488090	+	0.872793i	$0.337694\pi$
$368$			0.935664i			0.0487748i
$369$	−5.85951	+	10.1490i	−0.305034	+	0.528335i
$370$	5.57285	−	7.12653i	0.289719	−	0.370491i
$371$	−15.3119			−0.794953
$372$	5.39458	+	1.37788i	0.279696	+	0.0714395i
$373$			13.8842i			0.718896i	0.933165	+	0.359448i	$0.117035\pi$
$373$			13.8842i			0.718896i	−0.933165	+	0.359448i	$0.882965\pi$
$374$	7.80238			0.403451
$375$	6.55982	+	9.05366i	0.338748	+	0.467529i
$376$	7.84412			0.404530
$377$	−2.96648	+	1.71270i	−0.152781	+	0.0882083i
$378$	−1.24405	−	0.718253i	−0.0639870	−	0.0369429i
$379$	−16.4095	+	28.4221i	−0.842901	+	1.45995i	0.0445307	+	0.999008i	$0.485821\pi$
$379$	−16.4095	+	28.4221i	−0.842901	+	1.45995i	−0.887432	+	0.460939i	$0.847513\pi$
$380$	4.72573	−	6.04324i	0.242425	−	0.310012i
$381$	−4.41536	−	7.64763i	−0.226206	−	0.391800i
$382$	1.04570	−	0.603738i	0.0535029	−	0.0308899i
$383$	−26.3009	+	15.1848i	−1.34391	+	0.775908i	−0.987379	−	0.158375i	$-0.949375\pi$
$383$	−26.3009	+	15.1848i	−1.34391	+	0.775908i	−0.356533	+	0.934283i	$0.616041\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−0.955441	+	6.77692i	−0.0486938	+	0.345384i
$386$	−5.43150	+	9.40763i	−0.276456	+	0.478836i
$387$			9.27496i			0.471473i
$388$			15.8799i			0.806179i
$389$	8.09813	−	14.0264i	0.410591	−	0.711165i	−0.584363	−	0.811492i	$-0.698656\pi$
$389$	8.09813	−	14.0264i	0.410591	−	0.711165i	0.994955	+	0.100327i	$0.0319889\pi$
$390$	0.335492	−	2.37963i	0.0169883	−	0.120497i
$391$	1.71318	−	2.96732i	0.0866393	−	0.150064i
$392$	−4.27509	+	2.46823i	−0.215925	+	0.124664i
$393$	18.7503	−	10.8255i	0.945826	−	0.546073i
$394$	−1.03363	−	1.79030i	−0.0520735	−	0.0901940i
$395$	−14.4225	+	18.4434i	−0.725673	+	0.927987i
$396$	1.06533	−	1.84520i	0.0535348	−	0.0927250i
$397$	29.4183	+	16.9847i	1.47646	+	0.852437i	0.999647	−	0.0265662i	$-0.00845728\pi$
$397$	29.4183	+	16.9847i	1.47646	+	0.852437i	0.476817	+	0.879003i	$0.341791\pi$
$398$	4.19751	−	2.42343i	0.210402	−	0.121476i
$399$	4.92842			0.246729
$400$	4.80511	+	1.38237i	0.240255	+	0.0691185i
$401$	−22.9279			−1.14497			−0.572483	−	0.819917i	$-0.694020\pi$
$401$	−22.9279			−1.14497			−0.572483	+	0.819917i	$0.694020\pi$
$402$			1.26331i			0.0630084i
$403$	−4.18130	+	4.28054i	−0.208285	+	0.213229i
$404$	0.545325			0.0271309
$405$	1.37743	−	1.76145i	0.0684449	−	0.0875270i
$406$	2.28923	−	3.96506i	0.113612	−	0.196783i
$407$			8.62030i			0.427293i
$408$	3.17135	−	1.83098i	0.157005	−	0.0906469i
$409$	1.07304	−	1.85857i	0.0530586	−	0.0919001i	−0.838276	−	0.545246i	$-0.816436\pi$
$409$	1.07304	−	1.85857i	0.0530586	−	0.0919001i	0.891335	+	0.453346i	$0.149770\pi$
$410$	24.3007	−	9.80582i	1.20013	−	0.484275i
$411$	−6.27445			−0.309496
$412$	−7.67910	+	4.43353i	−0.378322	+	0.218424i
$413$	3.56614	−	2.05891i	0.175478	−	0.101312i
$414$	−0.467832	−	0.810309i	−0.0229927	−	0.0398245i
$415$	26.3812	−	10.6453i	1.29500	−	0.522559i
$416$	−0.537364	−	0.930742i	−0.0263464	−	0.0456334i
$417$	15.0574	+	8.69339i	0.737363	+	0.425717i
$418$			7.30994i			0.357541i
$419$	−4.10306			−0.200448			−0.100224	−	0.994965i	$-0.531956\pi$
$419$	−4.10306			−0.200448			−0.100224	+	0.994965i	$0.531956\pi$
$420$	1.20199	+	2.97875i	0.0586509	+	0.145348i
$421$	6.62810	+	11.4802i	0.323034	+	0.559511i	0.981113	−	0.193438i	$-0.0619638\pi$
$421$	6.62810	+	11.4802i	0.323034	+	0.559511i	−0.658078	+	0.752949i	$0.728630\pi$
$422$	−12.1208	−	6.99794i	−0.590031	−	0.340655i
$423$	−6.79321	+	3.92206i	−0.330297	+	0.190697i
$424$	−5.32956	−	9.23106i	−0.258826	−	0.448300i
$425$	−12.7076	−	13.1820i	−0.616408	−	0.639422i
$426$	−0.0791358			−0.00383414
$427$	−4.43022	−	2.55779i	−0.214393	−	0.123780i
$428$	2.53308	+	1.46247i	0.122441	+	0.0706913i
$429$	1.14494	+	1.98309i	0.0552782	+	0.0957446i
$430$	12.7756	−	16.3373i	0.616094	−	0.787857i
$431$	5.72068	−	9.90850i	0.275555	−	0.477276i	−0.694720	−	0.719281i	$-0.744472\pi$
$431$	5.72068	−	9.90850i	0.275555	−	0.477276i	0.970275	+	0.242005i	$0.0778049\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			1.28380i			0.0616954i	0.999524	+	0.0308477i	$0.00982069\pi$
$433$			1.28380i			0.0616954i	−0.999524	+	0.0308477i	$0.990179\pi$
$434$	1.97933	−	7.74934i	0.0950107	−	0.371980i
$435$	5.61411	+	4.39016i	0.269176	+	0.210492i
$436$	−2.32922			−0.111549
$437$	2.78004	+	1.60506i	0.132987	+	0.0767802i
$438$			3.36655i			0.160860i
$439$	1.47912	+	2.56192i	0.0705948	+	0.122274i	0.899162	−	0.437616i	$-0.144177\pi$
$439$	1.47912	+	2.56192i	0.0705948	+	0.122274i	−0.828567	+	0.559889i	$0.810844\pi$
$440$	−4.41816	+	1.78281i	−0.210627	+	0.0849923i
$441$	2.46823	−	4.27509i	0.117535	−	0.203576i
$442$			3.93561i			0.187198i
$443$	−27.4282	+	15.8357i	−1.30315	+	0.752375i	−0.980943	−	0.194293i	$-0.937759\pi$
$443$	−27.4282	+	15.8357i	−1.30315	+	0.752375i	−0.322209	+	0.946669i	$0.604425\pi$
$444$	2.02292	+	3.50380i	0.0960036	+	0.166283i
$445$	−2.84265	−	0.400770i	−0.134754	−	0.0189983i
$446$	3.54973	−	6.14831i	0.168085	−	0.291131i
$447$	6.50774	−	3.75724i	0.307805	−	0.177712i
$448$	1.24405	+	0.718253i	0.0587758	+	0.0339343i
$449$	3.86496			0.182399			0.0911994	−	0.995833i	$-0.470930\pi$
$449$	3.86496			0.182399			0.0911994	+	0.995833i	$0.470930\pi$
$450$	−4.85253	+	1.20539i	−0.228750	+	0.0568225i
$451$	−12.4846	+	21.6240i	−0.587878	+	1.01823i
$452$	−11.0269	+	6.36640i	−0.518663	+	0.299450i
$453$	−18.0767	−	10.4366i	−0.849316	−	0.490353i
$454$	9.68597	+	16.7766i	0.454585	+	0.787365i
$455$	−3.41835	−	0.481935i	−0.160255	−	0.0225935i
$456$	1.71542	+	2.97119i	0.0803319	+	0.139139i
$457$			10.5057i			0.491436i	0.969341	+	0.245718i	$0.0790237\pi$
$457$			10.5057i			0.491436i	−0.969341	+	0.245718i	$0.920976\pi$
$458$	12.5910	+	7.26939i	0.588337	+	0.339676i
$459$	−1.83098	+	3.17135i	−0.0854628	+	0.148026i
$460$	−0.292081	+	2.07172i	−0.0136183	+	0.0965944i
$461$	19.7600			0.920315			0.460157	−	0.887837i	$-0.347793\pi$
$461$	19.7600			0.920315			0.460157	+	0.887837i	$0.347793\pi$
$462$	−2.65065	−	1.53035i	−0.123319	−	0.0711984i
$463$			32.8265i			1.52558i	0.646649	+	0.762788i	$0.276170\pi$
$463$			32.8265i			1.52558i	−0.646649	+	0.762788i	$0.723830\pi$
$464$	3.18722			0.147963
$465$	11.5144	+	4.73484i	0.533967	+	0.219573i
$466$	−1.47599			−0.0683737
$467$			20.9567i			0.969758i	0.874581	+	0.484879i	$0.161136\pi$
$467$			20.9567i			0.969758i	−0.874581	+	0.484879i	$0.838864\pi$
$468$	0.930742	+	0.537364i	0.0430236	+	0.0248397i
$469$	1.81476			0.0837978
$470$	17.3682	+	2.44865i	0.801137	+	0.112948i
$471$	−8.29424	+	14.3660i	−0.382178	+	0.661953i
$472$	2.48251	+	1.43328i	0.114267	+	0.0659720i
$473$			19.7618i			0.908647i
$474$	−5.23529	−	9.06779i	−0.240465	−	0.416497i
$475$	12.3501	−	11.9056i	0.566660	−	0.546264i
$476$	−2.63021	−	4.55566i	−0.120556	−	0.208808i
$477$	9.23106	+	5.32956i	0.422661	+	0.244024i
$478$	−1.56113	+	0.901318i	−0.0714043	+	0.0412253i
$479$	−1.51772	+	2.62877i	−0.0693465	+	0.120112i	−0.898614	−	0.438740i	$-0.855425\pi$
$479$	−1.51772	+	2.62877i	−0.0693465	+	0.120112i	0.829267	+	0.558852i	$0.188758\pi$
$480$	−1.37743	+	1.76145i	−0.0628707	+	0.0803987i
$481$	−4.34818			−0.198260
$482$	1.53640	+	0.887042i	0.0699812	+	0.0404037i
$483$	−1.16401	+	0.672043i	−0.0529644	+	0.0305790i
$484$	−3.23015	+	5.59478i	−0.146825	+	0.254308i
$485$	−4.95713	+	35.1608i	−0.225092	+	1.59657i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	17.5378	−	10.1255i	0.794715	−	0.458829i	−0.0469048	−	0.998899i	$-0.514936\pi$
$487$	17.5378	−	10.1255i	0.794715	−	0.458829i	0.841620	+	0.540070i	$0.181602\pi$
$488$		−	3.56112i		−	0.161205i
$489$	4.06851	−	7.04686i	0.183984	−	0.318670i
$490$	−10.2363	+	4.13054i	−0.462428	+	0.186599i
$491$	4.95735	+	8.58639i	0.223722	+	0.387498i	0.955935	−	0.293577i	$-0.0948458\pi$
$491$	4.95735	+	8.58639i	0.223722	+	0.387498i	−0.732213	+	0.681076i	$0.761512\pi$
$492$			11.7190i			0.528335i
$493$	−10.1078	−	5.83573i	−0.455231	−	0.262828i
$494$	−3.68722			−0.165896
$495$	2.93483	−	3.75304i	0.131911	−	0.168687i
$496$	5.36078	−	1.50401i	0.240706	−	0.0675322i
$497$			0.113679i			0.00509920i
$498$			12.7223i			0.570102i
$499$	−1.77449	+	3.07351i	−0.0794371	+	0.137589i	−0.903007	−	0.429625i	$-0.858646\pi$
$499$	−1.77449	+	3.07351i	−0.0794371	+	0.137589i	0.823570	+	0.567214i	$0.191979\pi$
$500$	10.2078	+	4.56078i	0.456507	+	0.203964i
$501$	−3.91863	−	6.78726i	−0.175071	−	0.303233i
$502$	−11.6429	−	6.72206i	−0.519650	−	0.300020i
$503$	18.4227	+	10.6364i	0.821430	+	0.474253i	0.850909	−	0.525313i	$-0.176052\pi$
$503$	18.4227	+	10.6364i	0.821430	+	0.474253i	−0.0294796	+	0.999565i	$0.509385\pi$
$504$	−1.43651			−0.0639870
$505$	1.20744	+	0.170231i	0.0537305	+	0.00757517i
$506$	−0.996790	−	1.72649i	−0.0443127	−	0.0767519i
$507$	10.2580	−	5.92248i	0.455575	−	0.263027i
$508$	−7.64763	−	4.41536i	−0.339309	−	0.195900i
$509$	−9.47768	−	16.4158i	−0.420091	−	0.727618i	0.575857	−	0.817550i	$-0.304668\pi$
$509$	−9.47768	−	16.4158i	−0.420091	−	0.727618i	−0.995948	+	0.0899320i	$0.971335\pi$
$510$	7.59347	−	3.06412i	0.336245	−	0.135681i
$511$	4.83607			0.213935
$512$			1.00000i			0.0441942i
$513$	−2.97119	−	1.71542i	−0.131181	−	0.0757376i
$514$	1.38307	+	2.39555i	0.0610047	+	0.105663i
$515$	−18.3868	+	7.41946i	−0.810221	+	0.326940i
$516$	4.63748	+	8.03235i	0.204154	+	0.353605i
$517$	−14.4740	+	8.35657i	−0.636566	+	0.367522i
$518$	5.03323	−	2.90594i	0.221147	−	0.127680i
$519$	−13.1748			−0.578312
$520$	−0.899272	−	2.22857i	−0.0394357	−	0.0977292i
$521$	17.6576	−	30.5839i	0.773594	−	1.33990i	−0.161987	−	0.986793i	$-0.551790\pi$
$521$	17.6576	−	30.5839i	0.773594	−	1.33990i	0.935581	−	0.353112i	$-0.114876\pi$
$522$	−2.76021	+	1.59361i	−0.120811	+	0.0697503i
$523$			37.5941i			1.64388i	0.569577	+	0.821938i	$0.307107\pi$
$523$			37.5941i			1.64388i	−0.569577	+	0.821938i	$0.692893\pi$
$524$	10.8255	−	18.7503i	0.472913	−	0.819110i
$525$	1.73154	+	6.97069i	0.0755708	+	0.304226i
$526$	13.7423			0.599193
$527$	−19.7547	−	5.04572i	−0.860529	−	0.219795i
$528$		−	2.13066i		−	0.0927250i
$529$	22.1245			0.961936
$530$	−8.91895	−	22.1029i	−0.387414	−	0.960087i
$531$	−2.86656			−0.124398
$532$	4.26813	−	2.46421i	0.185047	−	0.106837i
$533$	−10.9074	−	6.29739i	−0.472452	−	0.272770i
$534$	0.641921	−	1.11184i	0.0277786	−	0.0481140i
$535$	5.15214	+	4.02890i	0.222746	+	0.174185i
$536$	0.631657	+	1.09406i	0.0272834	+	0.0472563i
$537$	9.98558	−	5.76518i	0.430910	−	0.248786i
$538$	−6.27962	+	3.62554i	−0.270734	+	0.156308i
$539$	5.25895	−	9.10876i	0.226519	−	0.392342i
$540$	0.312164	−	2.21417i	0.0134334	−	0.0952828i
$541$	−19.1200	+	33.1167i	−0.822031	+	1.42380i	0.0821363	+	0.996621i	$0.473826\pi$
$541$	−19.1200	+	33.1167i	−0.822031	+	1.42380i	−0.904167	+	0.427178i	$0.859508\pi$
$542$		−	16.7720i		−	0.720417i
$543$		−	9.71877i		−	0.417072i
$544$	1.83098	−	3.17135i	0.0785026	−	0.135970i
$545$	−5.15729	−	0.727099i	−0.220914	−	0.0311455i
$546$	0.771926	−	1.33702i	0.0330354	−	0.0572190i
$547$	8.29105	−	4.78684i	0.354500	−	0.204671i	−0.312166	−	0.950028i	$-0.601054\pi$
$547$	8.29105	−	4.78684i	0.354500	−	0.204671i	0.666665	+	0.745357i	$0.267721\pi$
$548$	−5.43383	+	3.13722i	−0.232122	+	0.134016i
$549$	1.78056	+	3.08402i	0.0759925	+	0.131623i
$550$	−10.3391	+	2.56827i	−0.440860	+	0.109511i
$551$	5.46741	−	9.46984i	0.232920	−	0.403429i
$552$	−0.810309	−	0.467832i	−0.0344890	−	0.0199122i
$553$	−13.0259	+	7.52053i	−0.553919	+	0.319805i
$554$	8.25596			0.350762
$555$	3.38533	+	8.38950i	0.143699	+	0.356114i
$556$	17.3868			0.737363
$557$		−	20.5825i		−	0.872107i	−0.899921	−	0.436054i	$-0.856376\pi$
$557$		−	20.5825i		−	0.872107i	0.899921	−	0.436054i	$-0.143624\pi$
$558$	−3.89056	+	3.98290i	−0.164701	+	0.168610i
$559$	−9.96806			−0.421604
$560$	2.53033	+	1.97868i	0.106926	+	0.0836146i
$561$	−3.90119	+	6.75706i	−0.164708	+	0.285283i
$562$			30.7433i			1.29683i
$563$	15.3785	−	8.87876i	0.648125	−	0.374195i	−0.139612	−	0.990206i	$-0.544586\pi$
$563$	15.3785	−	8.87876i	0.648125	−	0.374195i	0.787738	+	0.616011i	$0.211252\pi$
$564$	−3.92206	+	6.79321i	−0.165149	+	0.286046i
$565$	−26.4029	+	10.6541i	−1.11078	+	0.448221i
$566$	−14.9246			−0.627329
$567$	1.24405	−	0.718253i	0.0522452	−	0.0301638i
$568$	−0.0685336	+	0.0395679i	−0.00287561	+	0.00166023i
$569$	−3.73865	−	6.47552i	−0.156732	−	0.271468i	0.776956	−	0.629555i	$-0.216763\pi$
$569$	−3.73865	−	6.47552i	−0.156732	−	0.271468i	−0.933688	+	0.358087i	$0.883429\pi$
$570$	2.87073	+	7.11422i	0.120242	+	0.297982i
$571$	−16.8446	−	29.1757i	−0.704925	−	1.22097i	−0.966719	−	0.255842i	$-0.917647\pi$
$571$	−16.8446	−	29.1757i	−0.704925	−	1.22097i	0.261794	−	0.965124i	$-0.415686\pi$
$572$	1.98309	+	1.14494i	0.0829173	+	0.0478723i
$573$			1.20748i			0.0504430i
$574$	16.8345			0.702656
$575$	−1.29343	+	4.49596i	−0.0539399	+	0.187495i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−10.6585	−	6.15371i	−0.443720	−	0.256182i	0.261454	−	0.965216i	$-0.415798\pi$
$577$	−10.6585	−	6.15371i	−0.443720	−	0.256182i	−0.705174	+	0.709034i	$0.749131\pi$
$578$	3.10909	−	1.79504i	0.129321	−	0.0746636i
$579$	−5.43150	−	9.40763i	−0.225725	−	0.390968i
$580$	7.05704	+	0.994935i	0.293028	+	0.0413124i
$581$	18.2757			0.758204
$582$	−13.7524	−	7.93994i	−0.570055	−	0.329121i
$583$	19.6682	+	11.3555i	0.814575	+	0.470295i
$584$	1.68327	+	2.91552i	0.0696544	+	0.120645i
$585$	1.89308	+	1.48036i	0.0782691	+	0.0612054i
$586$	14.4879	−	25.0938i	0.598491	−	1.03662i
$587$			1.74474i			0.0720132i	0.999352	+	0.0360066i	$0.0114637\pi$
$587$			1.74474i			0.0720132i	−0.999352	+	0.0360066i	$0.988536\pi$
$588$		−	4.93645i		−	0.203576i
$589$	4.72727	−	18.5079i	0.194784	−	0.762606i
$590$	5.04928	+	3.94847i	0.207876	+	0.162556i
$591$	2.06726			0.0850357
$592$	3.50380	+	2.02292i	0.144005	+	0.0831415i
$593$		−	27.0311i		−	1.11003i	−0.831839	−	0.555016i	$-0.812712\pi$
$593$		−	27.0311i		−	1.11003i	0.831839	−	0.555016i	$-0.187288\pi$
$594$	1.06533	+	1.84520i	0.0437110	+	0.0757096i
$595$	−4.40162	−	10.9081i	−0.180449	−	0.447187i
$596$	3.75724	−	6.50774i	0.153903	−	0.266567i
$597$			4.84686i			0.198369i
$598$	0.870862	−	0.502792i	0.0356122	−	0.0205607i
$599$	−1.54348	−	2.67338i	−0.0630648	−	0.109231i	0.832769	−	0.553620i	$-0.186754\pi$
$599$	−1.54348	−	2.67338i	−0.0630648	−	0.109231i	−0.895834	+	0.444389i	$0.853421\pi$
$600$	−3.59972	+	3.47016i	−0.146958	+	0.141669i
$601$	14.7316	−	25.5159i	0.600915	−	1.04082i	−0.391767	−	0.920064i	$-0.628136\pi$
$601$	14.7316	−	25.5159i	0.600915	−	1.04082i	0.992683	−	0.120752i	$-0.0385305\pi$
$602$	11.5385	−	6.66177i	0.470275	−	0.271513i
$603$	−1.09406	−	0.631657i	−0.0445537	−	0.0257231i
$604$	−20.8731			−0.849316
$605$	−8.89859	+	11.3795i	−0.361779	+	0.462641i
$606$	−0.272662	+	0.472265i	−0.0110761	+	0.0191845i
$607$	33.7512	−	19.4863i	1.36992	−	0.790924i	0.379003	−	0.925395i	$-0.376267\pi$
$607$	33.7512	−	19.4863i	1.36992	−	0.790924i	0.990917	+	0.134472i	$0.0429337\pi$
$608$	2.97119	+	1.71542i	0.120498	+	0.0695694i
$609$	2.28923	+	3.96506i	0.0927642	+	0.160672i
$610$	1.11166	−	7.88494i	0.0450096	−	0.319252i
$611$	−4.21515	−	7.30085i	−0.170527	−	0.295361i
$612$			3.66196i			0.148026i
$613$	16.8373	+	9.72099i	0.680050	+	0.392627i	0.799874	−	0.600168i	$-0.204900\pi$
$613$	16.8373	+	9.72099i	0.680050	+	0.392627i	−0.119824	+	0.992795i	$0.538233\pi$
$614$	−10.1418	+	17.5661i	−0.409289	+	0.708910i
$615$	−3.65826	+	25.9479i	−0.147515	+	1.04632i
$616$	−3.06070			−0.123319
$617$	−11.0402	−	6.37405i	−0.444461	−	0.256609i	0.261027	−	0.965331i	$-0.415939\pi$
$617$	−11.0402	−	6.37405i	−0.444461	−	0.256609i	−0.705488	+	0.708722i	$0.749272\pi$
$618$		−	8.86707i		−	0.356686i
$619$	21.2823			0.855410			0.427705	−	0.903918i	$-0.359322\pi$
$619$	21.2823			0.855410			0.427705	+	0.903918i	$0.359322\pi$
$620$	12.3392	−	1.65670i	0.495553	−	0.0665347i
$621$	0.935664			0.0375469
$622$			17.1444i			0.687427i
$623$	−1.59716	−	0.922123i	−0.0639890	−	0.0369441i
$624$	1.07473			0.0430236
$625$	21.1781	+	13.2849i	0.847124	+	0.531395i
$626$	−3.49393	+	6.05166i	−0.139645	+	0.241873i
$627$	−6.33060	−	3.65497i	−0.252820	−	0.145966i
$628$			16.5885i			0.661953i
$629$	−7.40785	−	12.8308i	−0.295370	−	0.511596i
$630$	−3.18067	−	0.448425i	−0.126721	−	0.0178657i
$631$	−9.44908	−	16.3663i	−0.376162	−	0.651532i	0.614338	−	0.789043i	$-0.289423\pi$
$631$	−9.44908	−	16.3663i	−0.376162	−	0.651532i	−0.990500	+	0.137511i	$0.956090\pi$
$632$	−9.06779	−	5.23529i	−0.360697	−	0.208249i
$633$	12.1208	−	6.99794i	0.481758	−	0.278143i
$634$	−10.9247	+	18.9222i	−0.433877	+	0.751496i
$635$	−15.5548	−	12.1637i	−0.617275	−	0.482701i
$636$	10.6591			0.422661
$637$	4.59456	+	2.65267i	0.182043	+	0.105103i
$638$	−5.88107	+	3.39543i	−0.232834	+	0.134427i
$639$	0.0395679	−	0.0685336i	0.00156528	−	0.00271115i
$640$	−0.312164	+	2.21417i	−0.0123394	+	0.0875228i
$641$	−5.95384	−	10.3123i	−0.235162	−	0.407313i	0.724157	−	0.689635i	$-0.242229\pi$
$641$	−5.95384	−	10.3123i	−0.235162	−	0.407313i	−0.959320	+	0.282321i	$0.908896\pi$
$642$	−2.53308	+	1.46247i	−0.0999726	+	0.0577192i
$643$			32.3221i			1.27466i	0.770592	+	0.637329i	$0.219961\pi$
$643$			32.3221i			1.27466i	−0.770592	+	0.637329i	$0.780039\pi$
$644$	−0.672043	+	1.16401i	−0.0264822	+	0.0458685i
$645$	7.76076	+	19.2327i	0.305580	+	0.757285i
$646$	−6.28179	−	10.8804i	−0.247154	−	0.428083i
$647$		−	25.4783i		−	1.00166i	−0.865547	−	0.500828i	$-0.833029\pi$
$647$		−	25.4783i		−	1.00166i	0.865547	−	0.500828i	$-0.166971\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−6.10765			−0.239746
$650$	−1.29546	−	5.21515i	−0.0508122	−	0.204555i
$651$	5.72146	+	5.58882i	0.224242	+	0.219043i
$652$		−	8.13701i		−	0.318670i
$653$			1.34114i			0.0524828i	0.999656	+	0.0262414i	$0.00835385\pi$
$653$			1.34114i			0.0524828i	−0.999656	+	0.0262414i	$0.991646\pi$
$654$	1.16461	−	2.01716i	0.0455399	−	0.0788774i
$655$	29.8226	−	38.1370i	1.16527	−	1.49014i
$656$	5.85951	+	10.1490i	0.228776	+	0.396251i
$657$	−2.91552	−	1.68327i	−0.113745	−	0.0656708i
$658$	9.75848	+	5.63406i	0.380425	+	0.219639i
$659$	22.9784			0.895111			0.447556	−	0.894256i	$-0.352295\pi$
$659$	22.9784			0.895111			0.447556	+	0.894256i	$0.352295\pi$
$660$	0.665115	−	4.71764i	0.0258896	−	0.183634i
$661$	9.27586	+	16.0663i	0.360789	+	0.624905i	0.988091	−	0.153871i	$-0.0491741\pi$
$661$	9.27586	+	16.0663i	0.360789	+	0.624905i	−0.627302	+	0.778776i	$0.715841\pi$
$662$	4.95024	−	2.85802i	0.192397	−	0.111080i
$663$	−3.40834	−	1.96780i	−0.132369	−	0.0764232i
$664$	6.36117	+	11.0179i	0.246861	+	0.427576i
$665$	10.2196	−	4.12382i	0.396300	−	0.159915i
$666$	−4.04584			−0.156773
$667$			2.98216i			0.115470i
$668$	−6.78726	−	3.91863i	−0.262607	−	0.151616i
$669$	3.54973	+	6.14831i	0.137241	+	0.237708i
$670$	1.05707	+	2.61962i	0.0408382	+	0.101205i
$671$	3.79377	+	6.57100i	0.146457	+	0.253671i
$672$	−1.24405	+	0.718253i	−0.0479903	+	0.0277072i
$673$	3.03699	−	1.75341i	0.117067	−	0.0675888i	−0.440323	−	0.897839i	$-0.645136\pi$
$673$	3.03699	−	1.75341i	0.117067	−	0.0675888i	0.557390	+	0.830251i	$0.311803\pi$
$674$	10.2739			0.395734
$675$	1.38237	−	4.80511i	0.0532074	−	0.184949i
$676$	5.92248	−	10.2580i	0.227788	−	0.394540i
$677$	−18.2004	+	10.5080i	−0.699498	+	0.403855i	−0.807160	−	0.590332i	$-0.798997\pi$
$677$	−18.2004	+	10.5080i	−0.699498	+	0.403855i	0.107663	+	0.994187i	$0.465663\pi$
$678$		−	12.7328i		−	0.489000i
$679$	−11.4058	+	19.7554i	−0.437713	+	0.758142i
$680$	5.04408	−	6.45034i	0.193432	−	0.247359i
$681$	−19.3719			−0.742335
$682$	−8.28946	+	8.48621i	−0.317420	+	0.324954i
$683$		−	29.0446i		−	1.11136i	−0.831396	−	0.555681i	$-0.812458\pi$
$683$		−	29.0446i		−	1.11136i	0.831396	−	0.555681i	$-0.187542\pi$
$684$	−3.43084			−0.131181
$685$	−13.0108	+	5.25010i	−0.497116	+	0.200596i
$686$	−17.1468			−0.654667
$687$	−12.5910	+	7.26939i	−0.480375	+	0.277345i
$688$	8.03235	+	4.63748i	0.306231	+	0.176802i
$689$	−5.72783	+	9.92089i	−0.218213	+	0.377956i
$690$	−1.64812	−	1.28881i	−0.0627429	−	0.0490641i
$691$	16.1961	+	28.0525i	0.616130	+	1.06717i	0.990185	+	0.139762i	$0.0446336\pi$
$691$	16.1961	+	28.0525i	0.616130	+	1.06717i	−0.374056	+	0.927406i	$0.622033\pi$
$692$	−11.4098	+	6.58742i	−0.433734	+	0.250416i
$693$	2.65065	−	1.53035i	0.100690	−	0.0581332i
$694$	−5.18666	+	8.98356i	−0.196883	+	0.341011i
$695$	38.4973	+	5.42753i	1.46029	+	0.205878i
$696$	−1.59361	+	2.76021i	−0.0604056	+	0.104626i
$697$		−	42.9146i		−	1.62551i
$698$			1.54492i			0.0584760i
$699$	0.737993	−	1.27824i	0.0279135	−	0.0483475i
$700$	4.98490	+	5.17102i	0.188412	+	0.195446i
$701$	−14.9239	+	25.8490i	−0.563670	+	0.976304i	0.433502	+	0.901152i	$0.357278\pi$
$701$	−14.9239	+	25.8490i	−0.563670	+	0.976304i	−0.997172	+	0.0751520i	$0.976056\pi$
$702$	−0.930742	+	0.537364i	−0.0351286	+	0.0202815i
$703$	12.0210	−	6.94031i	0.453380	−	0.261759i
$704$	−1.06533	−	1.84520i	−0.0401511	−	0.0695438i
$705$	−10.8047	+	13.8170i	−0.406929	+	0.520378i
$706$	0.529043	−	0.916329i	0.0199108	−	0.0344865i
$707$	0.678411	+	0.391681i	0.0255143	+	0.0147307i
$708$	−2.48251	+	1.43328i	−0.0932984	+	0.0538659i
$709$	26.3607			0.989995			0.494998	−	0.868894i	$-0.335169\pi$
$709$	26.3607			0.989995			0.494998	+	0.868894i	$0.335169\pi$
$710$	−0.164097	+	0.0662164i	−0.00615845	+	0.00248506i
$711$	10.4706			0.392678
$712$		−	1.28384i		−	0.0481140i
$713$	1.40725	+	5.01589i	0.0527020	+	0.187846i
$714$	5.26042			0.196866
$715$	4.03350	+	3.15414i	0.150844	+	0.117958i
$716$	5.76518	−	9.98558i	0.215455	−	0.373179i
$717$		−	1.80264i		−	0.0673207i
$718$	25.7564	−	14.8705i	0.961220	−	0.554961i
$719$	−2.57901	+	4.46697i	−0.0961807	+	0.166590i	−0.910101	−	0.414387i	$-0.863996\pi$
$719$	−2.57901	+	4.46697i	−0.0961807	+	0.166590i	0.813920	+	0.580977i	$0.197329\pi$
$720$	−0.836743	−	2.07361i	−0.0311836	−	0.0772789i
$721$	−12.7376			−0.474373
$722$	−6.26080	+	3.61468i	−0.233003	+	0.134524i
$723$	−1.53640	+	0.887042i	−0.0571394	+	0.0329895i
$724$	−4.85938	−	8.41670i	−0.180598	−	0.312804i
$725$	15.3149	+	4.40591i	0.568782	+	0.163631i
$726$	−3.23015	−	5.59478i	−0.119882	−	0.207642i
$727$	−20.8575	−	12.0421i	−0.773561	−	0.446615i	0.0605827	−	0.998163i	$-0.480704\pi$
$727$	−20.8575	−	12.0421i	−0.773561	−	0.446615i	−0.834143	+	0.551548i	$0.814037\pi$
$728$		−	1.54385i		−	0.0572190i
$729$	−1.00000			−0.0370370
$730$	2.81694	+	6.98091i	0.104260	+	0.258375i
$731$	−16.9823	−	29.4141i	−0.628111	−	1.08792i
$732$	3.08402	+	1.78056i	0.113989	+	0.0658115i
$733$	−10.1774	+	5.87592i	−0.375911	+	0.217032i	−0.676038	−	0.736867i	$-0.736304\pi$
$733$	−10.1774	+	5.87592i	−0.375911	+	0.217032i	0.300127	+	0.953899i	$0.402971\pi$
$734$	−0.262420	−	0.454524i	−0.00968608	−	0.0167768i
$735$	1.54098	−	10.9301i	0.0568400	−	0.403165i
$736$	−0.935664			−0.0344890
$737$	−2.33107	−	1.34585i	−0.0858662	−	0.0495749i
$738$	−10.1490	−	5.85951i	−0.373589	−	0.215692i
$739$	−22.5607	−	39.0762i	−0.829907	−	1.43744i	−0.898110	−	0.439770i	$-0.855060\pi$
$739$	−22.5607	−	39.0762i	−0.829907	−	1.43744i	0.0682033	−	0.997671i	$-0.478273\pi$
$740$	7.12653	+	5.57285i	0.261977	+	0.204862i
$741$	1.84361	−	3.19322i	0.0677267	−	0.117306i
$742$		−	15.3119i		−	0.562117i
$743$		−	32.5800i		−	1.19525i	−0.801777	−	0.597623i	$-0.796112\pi$
$743$		−	32.5800i		−	1.19525i	0.801777	−	0.597623i	$-0.203888\pi$
$744$	−1.37788	+	5.39458i	−0.0505154	+	0.197775i
$745$	10.3507	−	13.2364i	0.379219	−	0.484943i
$746$	−13.8842			−0.508337
$747$	−11.0179	−	6.36117i	−0.403123	−	0.232743i
$748$			7.80238i			0.285283i
$749$	2.10085	+	3.63878i	0.0767634	+	0.132958i
$750$	−9.05366	+	6.55982i	−0.330593	+	0.239531i
$751$	3.02224	−	5.23468i	0.110283	−	0.191016i	−0.805601	−	0.592458i	$-0.798158\pi$
$751$	3.02224	−	5.23468i	0.110283	−	0.191016i	0.915884	+	0.401442i	$0.131491\pi$
$752$			7.84412i			0.286046i
$753$	11.6429	−	6.72206i	0.424293	−	0.244965i
$754$	−1.71270	−	2.96648i	−0.0623727	−	0.108033i
$755$	−46.2167	−	6.51585i	−1.68200	−	0.237136i
$756$	0.718253	−	1.24405i	0.0261226	−	0.0452457i
$757$	19.9199	−	11.5008i	0.724002	−	0.418003i	−0.0922218	−	0.995738i	$-0.529397\pi$
$757$	19.9199	−	11.5008i	0.724002	−	0.418003i	0.816224	+	0.577736i	$0.196064\pi$
$758$	−28.4221	−	16.4095i	−1.03234	−	0.596021i
$759$	1.99358			0.0723624
$760$	6.04324	+	4.72573i	0.219211	+	0.171420i
$761$	20.0204	−	34.6763i	0.725738	−	1.25702i	−0.232931	−	0.972493i	$-0.574832\pi$
$761$	20.0204	−	34.6763i	0.725738	−	1.25702i	0.958669	−	0.284522i	$-0.0918350\pi$
$762$	7.64763	−	4.41536i	0.277045	−	0.159952i
$763$	−2.89767	−	1.67297i	−0.104903	−	0.0605655i
$764$	0.603738	+	1.04570i	0.0218425	+	0.0378323i
$765$	−1.14313	+	8.10820i	−0.0413300	+	0.293153i
$766$	−15.1848	−	26.3009i	−0.548650	−	0.950289i
$767$		−	3.08077i		−	0.111240i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−22.4021	+	38.8016i	−0.807842	+	1.39922i	0.106514	+	0.994311i	$0.466031\pi$
$769$	−22.4021	+	38.8016i	−0.807842	+	1.39922i	−0.914356	+	0.404912i	$0.867302\pi$
$770$	−6.77692	−	0.955441i	−0.244223	−	0.0344317i
$771$	−2.76615			−0.0996203
$772$	−9.40763	−	5.43150i	−0.338588	−	0.195484i
$773$		−	17.8526i		−	0.642113i	−0.947060	−	0.321056i	$-0.895962\pi$
$773$		−	17.8526i		−	0.642113i	0.947060	−	0.321056i	$-0.104038\pi$
$774$	−9.27496			−0.333382
$775$	27.8382	+	0.183630i	0.999978	+	0.00659618i
$776$	−15.8799			−0.570055
$777$			5.81187i			0.208500i
$778$	14.0264	+	8.09813i	0.502870	+	0.290332i
$779$	40.2061			1.44053
$780$	2.37963	+	0.335492i	0.0852045	+	0.0120125i
$781$	0.0843057	−	0.146022i	0.00301669	−	0.00522507i
$782$	2.96732	+	1.71318i	0.106111	+	0.0612632i
$783$		−	3.18722i		−	0.113902i
$784$	−2.46823	−	4.27509i	−0.0881509	−	0.152682i
$785$	−5.17833	+	36.7297i	−0.184822	+	1.31094i
$786$	10.8255	+	18.7503i	0.386132	+	0.668800i
$787$	30.7258	+	17.7395i	1.09526	+	0.632346i	0.934971	−	0.354724i	$-0.115425\pi$
$787$	30.7258	+	17.7395i	1.09526	+	0.632346i	0.160285	+	0.987071i	$0.448759\pi$
$788$	1.79030	−	1.03363i	0.0637768	−	0.0368215i
$789$	−6.87115	+	11.9012i	−0.244619	+	0.423693i
$790$	−18.4434	−	14.4225i	−0.656186	−	0.513129i
$791$	−18.2907			−0.650343
$792$	1.84520	+	1.06533i	0.0655665	+	0.0378548i
$793$	−3.31449	+	1.91362i	−0.117701	+	0.0679547i
$794$	−16.9847	+	29.4183i	−0.602764	+	1.04402i
$795$	23.6011	+	3.32739i	0.837045	+	0.118010i
$796$	2.42343	+	4.19751i	0.0858962	+	0.148777i
$797$	−36.3322	+	20.9764i	−1.28695	+	0.743023i	−0.978110	−	0.208089i	$-0.933276\pi$
$797$	−36.3322	+	20.9764i	−1.28695	+	0.743023i	−0.308844	+	0.951113i	$0.599942\pi$
$798$			4.92842i			0.174464i
$799$	14.3624	−	24.8764i	0.508106	−	0.880065i
$800$	−1.38237	+	4.80511i	−0.0488741	+	0.169886i
$801$	0.641921	+	1.11184i	0.0226812	+	0.0392849i
$802$		−	22.9279i		−	0.809613i
$803$	−6.21197	−	3.58648i	−0.219216	−	0.126564i
$804$	−1.26331			−0.0445537
$805$	−1.85138	+	2.36754i	−0.0652526	+	0.0834447i
$806$	−4.28054	−	4.18130i	−0.150776	−	0.147280i
$807$		−	7.25108i		−	0.255250i
$808$			0.545325i			0.0191845i
$809$	−22.6928	+	39.3050i	−0.797835	+	1.38189i	0.123188	+	0.992383i	$0.460688\pi$
$809$	−22.6928	+	39.3050i	−0.797835	+	1.38189i	−0.921023	+	0.389508i	$0.872645\pi$
$810$	1.76145	+	1.37743i	0.0618909	+	0.0483979i
$811$	−16.7715	−	29.0491i	−0.588928	−	1.02005i	−0.994373	−	0.105933i	$-0.966217\pi$
$811$	−16.7715	−	29.0491i	−0.588928	−	1.02005i	0.405446	−	0.914119i	$-0.367116\pi$
$812$	3.96506	+	2.28923i	0.139146	+	0.0803361i
$813$	14.5249	+	8.38598i	0.509412	+	0.294109i
$814$	−8.62030			−0.302142
$815$	2.54008	−	18.0167i	0.0889752	−	0.631099i
$816$	1.83098	+	3.17135i	0.0640971	+	0.111019i
$817$	27.5577	−	15.9104i	0.964122	−	0.556636i
$818$	1.85857	+	1.07304i	0.0649832	+	0.0375181i
$819$	0.771926	+	1.33702i	0.0269733	+	0.0467191i
$820$	9.80582	+	24.3007i	0.342434	+	0.848617i
$821$	36.2245			1.26424			0.632122	−	0.774869i	$-0.282184\pi$
$821$	36.2245			1.26424			0.632122	+	0.774869i	$0.282184\pi$
$822$		−	6.27445i		−	0.218846i
$823$	−14.6202	−	8.44100i	−0.509629	−	0.294235i	0.223052	−	0.974807i	$-0.428398\pi$
$823$	−14.6202	−	8.44100i	−0.509629	−	0.294235i	−0.732681	+	0.680572i	$0.761731\pi$
$824$	−4.43353	−	7.67910i	−0.154449	−	0.267514i
$825$	2.94536	−	10.2380i	0.102544	−	0.356443i
$826$	2.05891	+	3.56614i	0.0716387	+	0.124082i
$827$	31.6551	−	18.2761i	1.10075	−	0.635521i	0.164335	−	0.986405i	$-0.447452\pi$
$827$	31.6551	−	18.2761i	1.10075	−	0.635521i	0.936419	+	0.350884i	$0.114119\pi$
$828$	0.810309	−	0.467832i	0.0281602	−	0.0162583i
$829$	33.3984			1.15997			0.579986	−	0.814626i	$-0.303058\pi$
$829$	33.3984			1.15997			0.579986	+	0.814626i	$0.303058\pi$
$830$	10.6453	+	26.3812i	0.369505	+	0.915704i
$831$	−4.12798	+	7.14987i	−0.143198	+	0.248026i
$832$	0.930742	−	0.537364i	0.0322677	−	0.0186297i
$833$			18.0771i			0.626334i
$834$	−8.69339	+	15.0574i	−0.301027	+	0.521395i
$835$	−13.8049	−	10.7953i	−0.477739	−	0.373585i
$836$	−7.30994			−0.252820
$837$	−1.50401	−	5.36078i	−0.0519863	−	0.185296i
$838$		−	4.10306i		−	0.141738i
$839$	46.1460			1.59314			0.796568	−	0.604549i	$-0.206647\pi$
$839$	46.1460			1.59314			0.796568	+	0.604549i	$0.206647\pi$
$840$	−2.97875	+	1.20199i	−0.102777	+	0.0414725i
$841$	−18.8417			−0.649712
$842$	−11.4802	+	6.62810i	−0.395634	+	0.228420i
$843$	−26.6245	−	15.3716i	−0.916996	−	0.529428i
$844$	6.99794	−	12.1208i	0.240879	−	0.417215i
$845$	16.3156	−	20.8643i	0.561273	−	0.717752i
$846$	−3.92206	−	6.79321i	−0.134843	−	0.233555i
$847$	−8.03693	+	4.64012i	−0.276152	+	0.159437i
$848$	9.23106	−	5.32956i	0.316996	−	0.183018i
$849$	7.46231	−	12.9251i	0.256106	−	0.443588i
$850$	13.1820	−	12.7076i	0.452140	−	0.435866i
$851$	−1.89277	+	3.27838i	−0.0648834	+	0.112381i
$852$		−	0.0791358i		−	0.00271115i
$853$		−	53.9629i		−	1.84766i	−0.382808	−	0.923828i	$-0.625043\pi$
$853$		−	53.9629i		−	1.84766i	0.382808	−	0.923828i	$-0.374957\pi$
$854$	2.55779	−	4.43022i	0.0875257	−	0.151599i
$855$	−7.59646	−	1.07098i	−0.259794	−	0.0366269i
$856$	−1.46247	+	2.53308i	−0.0499863	+	0.0865788i
$857$	−8.72406	+	5.03684i	−0.298008	+	0.172055i	−0.641548	−	0.767083i	$-0.721707\pi$
$857$	−8.72406	+	5.03684i	−0.298008	+	0.172055i	0.343540	+	0.939138i	$0.388374\pi$
$858$	−1.98309	+	1.14494i	−0.0677017	+	0.0390876i
$859$	−24.8414	−	43.0266i	−0.847578	−	1.46805i	−0.883364	−	0.468688i	$-0.844727\pi$
$859$	−24.8414	−	43.0266i	−0.847578	−	1.46805i	0.0357863	−	0.999359i	$-0.488606\pi$
$860$	16.3373	+	12.7756i	0.557099	+	0.435644i
$861$	−8.41723	+	14.5791i	−0.286858	+	0.496853i
$862$	9.90850	+	5.72068i	0.337485	+	0.194847i
$863$	−46.0787	+	26.6036i	−1.56854	+	0.905596i	−0.572198	+	0.820116i	$0.693909\pi$
$863$	−46.0787	+	26.6036i	−1.56854	+	0.905596i	−0.996340	+	0.0854801i	$0.972758\pi$
$864$	1.00000			0.0340207
$865$	−27.3195	+	11.0240i	−0.928891	+	0.374826i
$866$	−1.28380			−0.0436252
$867$			3.59007i			0.121925i
$868$	7.74934	+	1.97933i	0.263030	+	0.0671827i
$869$	22.3092			0.756789
$870$	−4.39016	+	5.61411i	−0.148840	+	0.190336i
$871$	0.678860	−	1.17582i	0.0230023	−	0.0398411i
$872$		−	2.32922i		−	0.0788774i
$873$	13.7524	−	7.93994i	0.465448	−	0.268726i
$874$	−1.60506	+	2.78004i	−0.0542918	+	0.0940362i
$875$	9.42322	+	13.0056i	0.318563	+	0.439670i
$876$	−3.36655			−0.113745
$877$	−44.4299	+	25.6516i	−1.50029	+	0.866193i	−0.500290	+	0.865858i	$0.666773\pi$
$877$	−44.4299	+	25.6516i	−1.50029	+	0.866193i	−1.00000		0.000334977i	$0.999893\pi$
$878$	−2.56192	+	1.47912i	−0.0864606	+	0.0499180i
$879$	14.4879	+	25.0938i	0.488666	+	0.846394i
$880$	−1.78281	−	4.41816i	−0.0600987	−	0.148936i
$881$	−17.8528	−	30.9220i	−0.601478	−	1.04179i	−0.992598	−	0.121450i	$-0.961246\pi$
$881$	−17.8528	−	30.9220i	−0.601478	−	1.04179i	0.391120	−	0.920340i	$-0.372088\pi$
$882$	4.27509	+	2.46823i	0.143950	+	0.0831095i
$883$			16.0006i			0.538464i	0.963075	+	0.269232i	$0.0867698\pi$
$883$			16.0006i			0.538464i	−0.963075	+	0.269232i	$0.913230\pi$
$884$	−3.93561			−0.132369
$885$	−5.94412	+	2.39857i	−0.199809	+	0.0806271i
$886$	−15.8357	−	27.4282i	−0.532010	−	0.921468i
$887$	−12.1344	−	7.00579i	−0.407433	−	0.235232i	0.282253	−	0.959340i	$-0.408918\pi$
$887$	−12.1344	−	7.00579i	−0.407433	−	0.235232i	−0.689686	+	0.724108i	$0.742252\pi$
$888$	−3.50380	+	2.02292i	−0.117580	+	0.0678848i
$889$	−6.34269	−	10.9859i	−0.212727	−	0.368454i
$890$	0.400770	−	2.84265i	0.0134338	−	0.0952857i
$891$	−2.13066			−0.0713797
$892$	6.14831	+	3.54973i	0.205861	+	0.118854i
$893$	23.3064	+	13.4560i	0.779919	+	0.450286i
$894$	3.75724	+	6.50774i	0.125661	+	0.217651i
$895$	15.8822	−	20.3101i	0.530884	−	0.678892i
$896$	−0.718253	+	1.24405i	−0.0239951	+	0.0415608i
$897$			1.00558i			0.0335755i
$898$			3.86496i			0.128975i
$899$	17.0860	−	4.79362i	0.569849	−	0.159876i
$900$	−1.20539	−	4.85253i	−0.0401795	−	0.161751i
$901$	−39.0332			−1.30039
$902$	−21.6240	−	12.4846i	−0.720001	−	0.415693i
$903$			13.3235i			0.443379i
$904$	−6.36640	−	11.0269i	−0.211743	−	0.366750i
$905$	−8.13211	−	20.1529i	−0.270321	−	0.669906i
$906$	10.4366	−	18.0767i	0.346732	−	0.600557i
$907$			18.2979i			0.607573i	0.952740	+	0.303786i	$0.0982509\pi$
$907$			18.2979i			0.607573i	−0.952740	+	0.303786i	$0.901749\pi$
$908$	−16.7766	+	9.68597i	−0.556751	+	0.321440i
$909$	−0.272662	−	0.472265i	−0.00904364	−	0.0156640i
$910$	0.481935	−	3.41835i	0.0159760	−	0.113317i
$911$	−12.2113	+	21.1506i	−0.404578	+	0.700750i	−0.994272	−	0.106876i	$-0.965915\pi$
$911$	−12.2113	+	21.1506i	−0.404578	+	0.700750i	0.589694	+	0.807627i	$0.299248\pi$
$912$	−2.97119	+	1.71542i	−0.0983860	+	0.0568032i
$913$	−23.4753	−	13.5535i	−0.776919	−	0.448555i
$914$	−10.5057			−0.347498
$915$	6.27273	+	4.90519i	0.207370	+	0.162161i
$916$	−7.26939	+	12.5910i	−0.240188	+	0.416017i
$917$	26.9349	−	15.5509i	0.889468	−	0.513535i
$918$	−3.17135	−	1.83098i	−0.104670	−	0.0604313i
$919$	8.73880	+	15.1361i	0.288267	+	0.499292i	0.973396	−	0.229129i	$-0.0735877\pi$
$919$	8.73880	+	15.1361i	0.288267	+	0.499292i	−0.685130	+	0.728421i	$0.740254\pi$
$920$	−2.07172	−	0.292081i	−0.0683026	−	0.00962961i
$921$	−10.1418	−	17.5661i	−0.334183	−	0.578822i
$922$			19.7600i			0.650761i
$923$	0.0736550	+	0.0425247i	0.00242438	+	0.00139972i
$924$	1.53035	−	2.65065i	0.0503449	−	0.0871999i
$925$	14.0397	+	14.5639i	0.461623	+	0.478858i
$926$	−32.8265			−1.07874
$927$	7.67910	+	4.43353i	0.252215	+	0.145616i
$928$			3.18722i			0.104626i
$929$	−57.2978			−1.87988			−0.939939	−	0.341342i	$-0.889119\pi$
$929$	−57.2978			−1.87988			−0.939939	+	0.341342i	$0.889119\pi$
$930$	−4.73484	+	11.5144i	−0.155262	+	0.377572i
$931$	−16.9362			−0.555060
$932$		−	1.47599i		−	0.0483475i
$933$	−14.8475	−	8.57220i	−0.486085	−	0.280641i
$934$	−20.9567			−0.685723
$935$	−2.43562	+	17.2758i	−0.0796534	+	0.564979i
$936$	−0.537364	+	0.930742i	−0.0175643	+	0.0304223i
$937$	−19.4868	−	11.2507i	−0.636605	−	0.367544i	0.146701	−	0.989181i	$-0.453135\pi$
$937$	−19.4868	−	11.2507i	−0.636605	−	0.367544i	−0.783306	+	0.621637i	$0.786468\pi$
$938$			1.81476i			0.0592540i
$939$	−3.49393	−	6.05166i	−0.114020	−	0.197489i
$940$	−2.44865	+	17.3682i	−0.0798663	+	0.566489i
$941$	−26.8644	−	46.5306i	−0.875756	−	1.51685i	−0.855956	−	0.517049i	$-0.827030\pi$
$941$	−26.8644	−	46.5306i	−0.875756	−	1.51685i	−0.0197998	−	0.999804i	$-0.506303\pi$
$942$	−14.3660	−	8.29424i	−0.468071	−	0.270241i
$943$	−9.49603	+	5.48254i	−0.309233	+	0.178536i
$944$	−1.43328	+	2.48251i	−0.0466492	+	0.0807988i
$945$	1.97868	−	2.53033i	0.0643665	−	0.0823116i
$946$	−19.7618			−0.642511
$947$	−21.3904	−	12.3497i	−0.695094	−	0.401313i	0.110424	−	0.993885i	$-0.464779\pi$
$947$	−21.3904	−	12.3497i	−0.695094	−	0.401313i	−0.805517	+	0.592572i	$0.798113\pi$
$948$	9.06779	−	5.23529i	0.294508	−	0.170034i
$949$	1.80906	−	3.13339i	0.0587247	−	0.101714i
$950$	11.9056	+	12.3501i	0.386267	+	0.400689i
$951$	−10.9247	−	18.9222i	−0.354259	−	0.613594i
$952$	4.55566	−	2.63021i	0.147650	−	0.0852456i
$953$		−	47.4761i		−	1.53790i	−0.639308	−	0.768950i	$-0.720779\pi$
$953$		−	47.4761i		−	1.53790i	0.639308	−	0.768950i	$-0.279221\pi$
$954$	−5.32956	+	9.23106i	−0.172551	+	0.298867i
$955$	1.01035	+	2.50383i	0.0326941	+	0.0810222i
$956$	−0.901318	−	1.56113i	−0.0291507	−	0.0504905i
$957$		−	6.79087i		−	0.219518i
$958$	−2.62877	−	1.51772i	−0.0849318	−	0.0490354i
$959$	−9.01328			−0.291054
$960$	−1.76145	−	1.37743i	−0.0568504	−	0.0444563i
$961$	26.4759	−	16.1254i	0.854061	−	0.520173i
$962$		−	4.34818i		−	0.140191i
$963$		−	2.92495i		−	0.0942551i
$964$	−0.887042	+	1.53640i	−0.0285697	+	0.0494842i
$965$	−19.1346	−	14.9630i	−0.615964	−	0.481675i
$966$	−0.672043	−	1.16401i	−0.0216226	−	0.0374515i
$967$	−29.0205	−	16.7550i	−0.933238	−	0.538805i	−0.0454036	−	0.998969i	$-0.514457\pi$
$967$	−29.0205	−	16.7550i	−0.933238	−	0.538805i	−0.887834	+	0.460164i	$0.847791\pi$
$968$	−5.59478	−	3.23015i	−0.179823	−	0.103821i
$969$	12.5636			0.403600
$970$	−35.1608	−	4.95713i	−1.12894	−	0.159164i
$971$	−9.09649	−	15.7556i	−0.291920	−	0.505620i	0.682344	−	0.731032i	$-0.260961\pi$
$971$	−9.09649	−	15.7556i	−0.291920	−	0.505620i	−0.974264	+	0.225411i	$0.927627\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	21.6300	+	12.4881i	0.693426	+	0.400350i
$974$	10.1255	+	17.5378i	0.324441	+	0.561948i
$975$	5.16418	+	1.48567i	0.165386	+	0.0475796i
$976$	3.56112			0.113989
$977$			16.6162i			0.531599i	0.964028	+	0.265799i	$0.0856359\pi$
$977$			16.6162i			0.531599i	−0.964028	+	0.265799i	$0.914364\pi$
$978$	7.04686	+	4.06851i	0.225334	+	0.130096i
$979$	1.36771	+	2.36895i	0.0437124	+	0.0757120i
$980$	−4.13054	−	10.2363i	−0.131945	−	0.326986i
$981$	1.16461	+	2.01716i	0.0371831	+	0.0644031i
$982$	−8.58639	+	4.95735i	−0.274003	+	0.158196i
$983$	−5.79650	+	3.34661i	−0.184880	+	0.106740i	−0.589583	−	0.807708i	$-0.700708\pi$
$983$	−5.79650	+	3.34661i	−0.184880	+	0.106740i	0.404704	+	0.914448i	$0.367375\pi$
$984$	−11.7190			−0.373589
$985$	4.28669	−	1.72977i	0.136585	−	0.0551149i
$986$	5.83573	−	10.1078i	0.185847	−	0.321897i
$987$	−9.75848	+	5.63406i	−0.310616	+	0.179334i
$988$		−	3.68722i		−	0.117306i
$989$	−4.33912	+	7.51558i	−0.137976	+	0.238982i
$990$	3.75304	+	2.93483i	0.119279	+	0.0932749i
$991$	−15.4166			−0.489723			−0.244862	−	0.969558i	$-0.578743\pi$
$991$	−15.4166			−0.489723			−0.244862	+	0.969558i	$0.578743\pi$
$992$	1.50401	+	5.36078i	0.0477525	+	0.170205i
$993$			5.71604i			0.181393i
$994$	−0.113679			−0.00360568
$995$	4.05558	+	10.0505i	0.128571	+	0.318622i
$996$	−12.7223			−0.403123
$997$	−35.4330	+	20.4572i	−1.12217	+	0.647887i	−0.941955	−	0.335739i	$-0.891014\pi$
$997$	−35.4330	+	20.4572i	−1.12217	+	0.647887i	−0.180219	+	0.983627i	$0.557681\pi$
$998$	−3.07351	−	1.77449i	−0.0972901	−	0.0561705i
$999$	2.02292	−	3.50380i	0.0640024	−	0.110855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.d.439.8	yes	28
5.4	even	2	inner	930.2.s.d.439.5	✓	28
31.25	even	3	inner	930.2.s.d.769.12	yes	28
155.149	even	6	inner	930.2.s.d.769.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.d.439.5	✓	28	5.4	even	2	inner
930.2.s.d.439.8	yes	28	1.1	even	1	trivial
930.2.s.d.769.1	yes	28	155.149	even	6	inner
930.2.s.d.769.12	yes	28	31.25	even	3	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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-2.21417 - 0.312164i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.24405 - 0.718253i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-2.21417 - 0.312164i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.24405 - 0.718253i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.312164 - 2.21417i) q^{10} +(1.06533 + 1.84520i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.930742 + 0.537364i) q^{13} +(0.718253 - 1.24405i) q^{14} +(1.76145 + 1.37743i) q^{15} +1.00000 q^{16} +(-3.17135 - 1.83098i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(1.71542 - 2.97119i) q^{19} +(2.21417 + 0.312164i) q^{20} +(0.718253 + 1.24405i) q^{21} +(-1.84520 + 1.06533i) q^{22} +0.935664i q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.80511 + 1.38237i) q^{25} +(-0.537364 - 0.930742i) q^{26} -1.00000i q^{27} +(1.24405 + 0.718253i) q^{28} +3.18722 q^{29} +(-1.37743 + 1.76145i) q^{30} +(5.36078 - 1.50401i) q^{31} +1.00000i q^{32} -2.13066i q^{33} +(1.83098 - 3.17135i) q^{34} +(2.53033 + 1.97868i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.50380 + 2.02292i) q^{37} +(2.97119 + 1.71542i) q^{38} +1.07473 q^{39} +(-0.312164 + 2.21417i) q^{40} +(5.85951 + 10.1490i) q^{41} +(-1.24405 + 0.718253i) q^{42} +(8.03235 + 4.63748i) q^{43} +(-1.06533 - 1.84520i) q^{44} +(-0.836743 - 2.07361i) q^{45} -0.935664 q^{46} +7.84412i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-2.46823 - 4.27509i) q^{49} +(-1.38237 + 4.80511i) q^{50} +(1.83098 + 3.17135i) q^{51} +(0.930742 - 0.537364i) q^{52} +(9.23106 - 5.32956i) q^{53} +1.00000 q^{54} +(-1.78281 - 4.41816i) q^{55} +(-0.718253 + 1.24405i) q^{56} +(-2.97119 + 1.71542i) q^{57} +3.18722i q^{58} +(-1.43328 + 2.48251i) q^{59} +(-1.76145 - 1.37743i) q^{60} +3.56112 q^{61} +(1.50401 + 5.36078i) q^{62} -1.43651i q^{63} -1.00000 q^{64} +(2.22857 - 0.899272i) q^{65} +2.13066 q^{66} +(-1.09406 + 0.631657i) q^{67} +(3.17135 + 1.83098i) q^{68} +(0.467832 - 0.810309i) q^{69} +(-1.97868 + 2.53033i) q^{70} +(-0.0395679 - 0.0685336i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-2.91552 + 1.68327i) q^{73} +(-2.02292 + 3.50380i) q^{74} +(-3.47016 - 3.59972i) q^{75} +(-1.71542 + 2.97119i) q^{76} -3.06070i q^{77} +1.07473i q^{78} +(5.23529 - 9.06779i) q^{79} +(-2.21417 - 0.312164i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-10.1490 + 5.85951i) q^{82} +(-11.0179 + 6.36117i) q^{83} +(-0.718253 - 1.24405i) q^{84} +(6.45034 + 5.04408i) q^{85} +(-4.63748 + 8.03235i) q^{86} +(-2.76021 - 1.59361i) q^{87} +(1.84520 - 1.06533i) q^{88} +1.28384 q^{89} +(2.07361 - 0.836743i) q^{90} +1.54385 q^{91} -0.935664i q^{92} +(-5.39458 - 1.37788i) q^{93} -7.84412 q^{94} +(-4.72573 + 6.04324i) q^{95} +(0.500000 - 0.866025i) q^{96} -15.8799i q^{97} +(4.27509 - 2.46823i) q^{98} +(-1.06533 + 1.84520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9	\( 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9} + 4 q^{10} + 2 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} - 14 q^{24} - 14 q^{25} - 12 q^{26} + 24 q^{29} + 4 q^{30} + 10 q^{34} + 8 q^{35} - 14 q^{36} + 24 q^{39} - 4 q^{40} + 20 q^{41} - 2 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{49} - 8 q^{50} + 10 q^{51} + 28 q^{54} + 6 q^{55} + 8 q^{56} - 20 q^{59} + 8 q^{60} + 32 q^{61} - 28 q^{64} - 12 q^{65} + 4 q^{66} - 6 q^{69} - 16 q^{70} - 16 q^{71} - 6 q^{74} - 8 q^{75} - 4 q^{76} + 10 q^{79} + 2 q^{80} - 14 q^{81} + 8 q^{84} + 72 q^{85} + 18 q^{86} - 80 q^{89} - 4 q^{90} + 32 q^{91} - 12 q^{94} - 32 q^{95} + 14 q^{96} - 2 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9 + 4 * q^10 + 2 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 - 14 * q^24 - 14 * q^25 - 12 * q^26 + 24 * q^29 + 4 * q^30 + 10 * q^34 + 8 * q^35 - 14 * q^36 + 24 * q^39 - 4 * q^40 + 20 * q^41 - 2 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^49 - 8 * q^50 + 10 * q^51 + 28 * q^54 + 6 * q^55 + 8 * q^56 - 20 * q^59 + 8 * q^60 + 32 * q^61 - 28 * q^64 - 12 * q^65 + 4 * q^66 - 6 * q^69 - 16 * q^70 - 16 * q^71 - 6 * q^74 - 8 * q^75 - 4 * q^76 + 10 * q^79 + 2 * q^80 - 14 * q^81 + 8 * q^84 + 72 * q^85 + 18 * q^86 - 80 * q^89 - 4 * q^90 + 32 * q^91 - 12 * q^94 - 32 * q^95 + 14 * q^96 - 2 * q^99

Introduction

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