LMFDB - Embedded newform 930.2.s.d.439.5

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			439.5
Character	$\chi$	$=$	930.439
Dual form			930.2.s.d.769.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(0.836743 - 2.07361i) q^{5} +(0.500000 - 0.866025i) q^{6} +(1.24405 + 0.718253i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(0.836743 - 2.07361i) q^{5} +(0.500000 - 0.866025i) q^{6} +(1.24405 + 0.718253i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.07361 - 0.836743i) 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} +(-0.836743 + 2.07361i) q^{20} +(0.718253 + 1.24405i) q^{21} +(1.84520 - 1.06533i) q^{22} -0.935664i q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.59972 - 3.47016i) 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} +(2.07361 + 0.836743i) 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} +(2.21417 - 0.312164i) q^{45} -0.935664 q^{46} -7.84412i q^{47} +(0.866025 + 0.500000i) q^{48} +(-2.46823 - 4.27509i) q^{49} +(-3.47016 + 3.59972i) q^{50} +(1.83098 + 3.17135i) q^{51} +(-0.930742 + 0.537364i) q^{52} +(-9.23106 + 5.32956i) q^{53} +1.00000 q^{54} +(4.71764 - 0.665115i) 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} +(-0.335492 - 2.37963i) 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} +(-1.38237 - 4.80511i) q^{75} +(-1.71542 + 2.97119i) q^{76} +3.06070i q^{77} -1.07473i q^{78} +(5.23529 - 9.06779i) q^{79} +(0.836743 - 2.07361i) 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} +(-0.312164 - 2.21417i) 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
$5$	0.836743	−	2.07361i	0.374203	−	0.927347i
$5$	0.836743	−	2.07361i	0.374203	−	0.927347i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	1.24405	+	0.718253i	0.470207	+	0.271474i	0.716326	−	0.697765i	$-0.245822\pi$
$7$	1.24405	+	0.718253i	0.470207	+	0.271474i	−0.246119	+	0.969239i	$0.579156\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.07361	−	0.836743i	−0.655733	−	0.264602i
$11$	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	−0.365345	−	0.930872i	$-0.619049\pi$
$13$	0.930742	−	0.537364i	0.258141	−	0.149038i	0.623486	+	0.781834i	$0.285716\pi$
$14$	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	0.832577	−	0.553910i	$-0.186865\pi$
$17$	3.17135	+	1.83098i	0.769165	+	0.444078i	−0.0634118	+	0.997987i	$0.520198\pi$
$18$	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	$0.0379155\pi$
$20$	−0.836743	+	2.07361i	−0.187102	+	0.463673i
$21$	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	$-0.968900\pi$
$23$		−	0.935664i		−	0.195099i	0.995231	−	0.0975497i	$-0.0311005\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−3.59972	−	3.47016i	−0.719944	−	0.694032i
$26$	−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	0.183529	−	0.983014i	$-0.441248\pi$
$37$	−3.50380	−	2.02292i	−0.576021	−	0.332566i	−0.759551	+	0.650448i	$0.774581\pi$
$38$	−2.97119	−	1.71542i	−0.481991	−	0.278278i
$39$	1.07473			0.172094
$40$	2.07361	+	0.836743i	0.327867	+	0.132301i
$41$	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	−0.258959	−	0.965888i	$-0.583379\pi$
$43$	−8.03235	−	4.63748i	−1.22492	−	0.707209i	−0.965963	+	0.258679i	$0.916713\pi$
$44$	−1.06533	−	1.84520i	−0.160604	−	0.278175i
$45$	2.21417	−	0.312164i	0.330069	−	0.0465347i
$46$	−0.935664			−0.137956
$47$		−	7.84412i		−	1.14418i	−0.820190	−	0.572092i	$-0.806132\pi$
$47$		−	7.84412i		−	1.14418i	0.820190	−	0.572092i	$-0.193868\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−2.46823	−	4.27509i	−0.352604	−	0.610728i
$50$	−3.47016	+	3.59972i	−0.490755	+	0.509077i
$51$	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	−0.974606	−	0.223925i	$-0.928113\pi$
$53$	−9.23106	+	5.32956i	−1.26798	+	0.732071i	−0.293378	+	0.955997i	$0.594779\pi$
$54$	1.00000			0.136083
$55$	4.71764	−	0.665115i	0.636127	−	0.0896841i
$56$	−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
$65$	−0.335492	−	2.37963i	−0.0416126	−	0.295157i
$66$	2.13066			0.262266
$67$	1.09406	−	0.631657i	0.133661	−	0.0771692i	−0.431678	−	0.902028i	$-0.642078\pi$
$67$	1.09406	−	0.631657i	0.133661	−	0.0771692i	0.565340	+	0.824858i	$0.308745\pi$
$68$	−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	−0.319583	−	0.947558i	$-0.603543\pi$
$73$	2.91552	−	1.68327i	0.341236	−	0.197012i	0.660818	+	0.750546i	$0.270209\pi$
$74$	−2.02292	+	3.50380i	−0.235160	+	0.407309i
$75$	−1.38237	−	4.80511i	−0.159622	−	0.554846i
$76$	−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	$-0.0338180\pi$
$80$	0.836743	−	2.07361i	0.0935508	−	0.231837i
$81$	−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	0.246747	−	0.969080i	$-0.420638\pi$
$83$	11.0179	−	6.36117i	1.20937	−	0.698229i	0.962621	+	0.270851i	$0.0873051\pi$
$84$	−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	$0.478324\pi$
$90$	−0.312164	−	2.21417i	−0.0329050	−	0.233394i
$91$	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	$0.298468\pi$
$97$			15.8799i			1.61236i	−0.591672	+	0.806179i	$0.701532\pi$
$98$	−4.27509	+	2.46823i	−0.431850	+	0.249328i
$99$	−1.06533	+	1.84520i	−0.107070	+	0.185450i
$100$	3.59972	+	3.47016i	0.359972	+	0.347016i
$101$	−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	−0.828090	−	0.560596i	$-0.810572\pi$
$103$	−7.67910	+	4.43353i	−0.756645	+	0.436849i	0.0714451	+	0.997445i	$0.477239\pi$
$104$	0.537364	+	0.930742i	0.0526929	+	0.0912668i
$105$	3.18067	−	0.448425i	0.310402	−	0.0437618i
$106$	5.32956	+	9.23106i	0.517652	+	0.896600i
$107$	2.53308	+	1.46247i	0.244882	+	0.141383i	0.617418	−	0.786635i	$-0.288179\pi$
$107$	2.53308	+	1.46247i	0.244882	+	0.141383i	−0.372537	+	0.928018i	$0.621512\pi$
$108$		−	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	$0.464419\pi$
$110$	−0.665115	−	4.71764i	−0.0634162	−	0.449810i
$111$	−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	−0.919075	−	0.394084i	$-0.871062\pi$
$113$	−11.0269	+	6.36640i	−1.03733	+	0.598900i	−0.118251	+	0.992984i	$0.537729\pi$
$114$	−1.71542	−	2.97119i	−0.160664	−	0.278278i
$115$	−1.94020	−	0.782911i	−0.180925	−	0.0730068i
$116$	−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	0.120716	−	0.992687i	$-0.461481\pi$
$127$	−7.64763	−	4.41536i	−0.678618	−	0.391800i	−0.799334	+	0.600887i	$0.794814\pi$
$128$			1.00000i			0.0883883i
$129$	−4.63748	−	8.03235i	−0.408307	−	0.707209i
$130$	−2.37963	+	0.335492i	−0.208708	+	0.0294246i
$131$	−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
$135$	2.07361	+	0.836743i	0.178468	+	0.0720154i
$136$	−1.83098	+	3.17135i	−0.157005	+	0.271941i
$137$	−5.43383	+	3.13722i	−0.464243	+	0.268031i	−0.713827	−	0.700322i	$-0.753040\pi$
$137$	−5.43383	+	3.13722i	−0.464243	+	0.268031i	0.249583	+	0.968353i	$0.419706\pi$
$138$	−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
$145$	2.66688	−	6.60905i	0.221473	−	0.548851i
$146$	−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	$0.266261\pi$
$150$	−4.80511	+	1.38237i	−0.392335	+	0.112870i
$151$	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
$155$	1.36686	−	12.3746i	0.109789	−	0.993955i
$156$	−1.07473			−0.0860471
$157$			16.5885i			1.32391i	0.749546	+	0.661953i	$0.230272\pi$
$157$			16.5885i			1.32391i	−0.749546	+	0.661953i	$0.769728\pi$
$158$	−9.06779	−	5.23529i	−0.721395	−	0.416497i
$159$	−10.6591			−0.845323
$160$	−2.07361	−	0.836743i	−0.163933	−	0.0661504i
$161$	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	$-0.896764\pi$
$163$		−	8.13701i		−	0.637340i	0.947866	−	0.318670i	$-0.103236\pi$
$164$	−5.85951	−	10.1490i	−0.457551	−	0.792502i
$165$	4.41816	+	1.78281i	0.343953	+	0.138792i
$166$	−6.36117	−	11.0179i	−0.493722	−	0.855152i
$167$	−6.78726	−	3.91863i	−0.525214	−	0.303233i	0.213851	−	0.976866i	$-0.431399\pi$
$167$	−6.78726	−	3.91863i	−0.525214	−	0.303233i	−0.739065	+	0.673634i	$0.764733\pi$
$168$	−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	−0.866506	−	0.499167i	$-0.833639\pi$
$173$	−11.4098	+	6.58742i	−0.867467	+	0.500833i	−0.000961620		1.00000i	$0.500306\pi$
$174$	1.59361	−	2.76021i	0.120811	−	0.209251i
$175$	−1.98578	−	6.90256i	−0.150111	−	0.521785i
$176$	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	$0.308474\pi$
$180$	−2.21417	+	0.312164i	−0.165035	+	0.0232673i
$181$	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	0.121614	−	0.992577i	$-0.461193\pi$
$193$	−9.40763	−	5.43150i	−0.677176	−	0.390968i	−0.798790	+	0.601610i	$0.794526\pi$
$194$	15.8799			1.14011
$195$	0.899272	−	2.22857i	0.0643982	−	0.159591i
$196$	2.46823	+	4.27509i	0.176302	+	0.305364i
$197$	1.79030	−	1.03363i	0.127554	−	0.0736431i	−0.434866	−	0.900495i	$-0.643204\pi$
$197$	1.79030	−	1.03363i	0.127554	−	0.0736431i	0.562419	+	0.826852i	$0.309871\pi$
$198$	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	$0.888289\pi$
$200$	3.47016	−	3.59972i	0.245377	−	0.254539i
$201$	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
$205$	25.9479	−	3.65826i	1.81228	−	0.255504i
$206$	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
$210$	−0.448425	−	3.18067i	−0.0309443	−	0.219487i
$211$	−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
$220$	−4.71764	+	0.665115i	−0.318063	+	0.0448420i
$221$	3.93561			0.264738
$222$	−3.50380	+	2.02292i	−0.235160	+	0.135770i
$223$	6.14831	+	3.54973i	0.411722	+	0.237708i	0.691529	−	0.722349i	$-0.256937\pi$
$223$	6.14831	+	3.54973i	0.411722	+	0.237708i	−0.279808	+	0.960056i	$0.590271\pi$
$224$	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	−0.939734	−	0.341906i	$-0.888928\pi$
$227$	−16.7766	+	9.68597i	−1.11350	+	0.642881i	−0.173768	+	0.984787i	$0.555594\pi$
$228$	−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	$0.00716723\pi$
$230$	−0.782911	+	1.94020i	−0.0516236	+	0.127933i
$231$	−1.53035	+	2.65065i	−0.100690	+	0.174400i
$232$			3.18722i			0.209251i
$233$		−	1.47599i		−	0.0966951i	−0.998831	−	0.0483475i	$-0.984605\pi$
$233$		−	1.47599i		−	0.0966951i	0.998831	−	0.0483475i	$-0.0153955\pi$
$234$	0.537364	−	0.930742i	0.0351286	−	0.0608445i
$235$	−16.2657	−	6.56352i	−1.06105	−	0.428157i
$236$	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
$245$	−10.9301	+	1.54098i	−0.698302	+	0.0984498i
$246$	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
$255$	8.10820	−	1.14313i	0.507755	−	0.0715857i
$256$	1.00000			0.0625000
$257$	−2.39555	+	1.38307i	−0.149430	+	0.0862737i	−0.572851	−	0.819660i	$-0.694163\pi$
$257$	−2.39555	+	1.38307i	−0.149430	+	0.0862737i	0.423420	+	0.905933i	$0.360829\pi$
$258$	−8.03235	+	4.63748i	−0.500072	+	0.288717i
$259$	−2.90594	−	5.03323i	−0.180566	−	0.312750i
$260$	0.335492	+	2.37963i	0.0208063	+	0.147579i
$261$	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	$0.139267\pi$
$263$			13.7423i			0.847386i	−0.905806	+	0.423693i	$0.860733\pi$
$264$	−2.13066			−0.131133
$265$	3.32739	+	23.6011i	0.204400	+	1.44980i
$266$	−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	$0.762384\pi$
$270$	0.836743	−	2.07361i	0.0509226	−	0.126196i
$271$	−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	$0.0797820\pi$
$277$			8.25596i			0.496053i	−0.968753	+	0.248026i	$0.920218\pi$
$278$			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	$-0.853705\pi$
$283$		−	14.9246i		−	0.887177i	0.896231	−	0.443588i	$-0.146295\pi$
$284$	0.0395679	+	0.0685336i	0.00234792	+	0.00406672i
$285$	−1.07098	−	7.59646i	−0.0634396	−	0.449976i
$286$	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
$290$	−6.60905	−	2.66688i	−0.388097	−	0.156605i
$291$	−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	0.999277	−	0.0380108i	$-0.0121021\pi$
$293$	25.0938	+	14.4879i	1.46600	+	0.846394i	0.466720	+	0.884405i	$0.345435\pi$
$294$	−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
$300$	1.38237	+	4.80511i	0.0798111	+	0.277423i
$301$	−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
$305$	2.97975	−	7.38439i	0.170620	−	0.422829i
$306$	3.66196			0.209340
$307$	−17.5661	−	10.1418i	−1.00255	−	0.578822i	−0.0935480	−	0.995615i	$-0.529821\pi$
$307$	−17.5661	−	10.1418i	−1.00255	−	0.578822i	−0.909002	+	0.416792i	$0.863154\pi$
$308$		−	3.06070i		−	0.174400i
$309$	−8.86707			−0.504430
$310$	−12.3746	−	1.36686i	−0.702832	−	0.0776323i
$311$	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	0.319122	−	0.947713i	$-0.396612\pi$
$313$	−6.05166	−	3.49393i	−0.342060	−	0.197489i	−0.661183	+	0.750225i	$0.729945\pi$
$314$	16.5885			0.936142
$315$	2.97875	+	1.20199i	0.167834	+	0.0677243i
$316$	−5.23529	+	9.06779i	−0.294508	+	0.510103i
$317$	−18.9222	−	10.9247i	−1.06278	−	0.613594i	−0.136577	−	0.990629i	$-0.543610\pi$
$317$	−18.9222	−	10.9247i	−1.06278	−	0.613594i	−0.926199	+	0.377035i	$0.876944\pi$
$318$			10.6591i			0.597734i
$319$	3.39543	+	5.88107i	0.190108	+	0.329276i
$320$	−0.836743	+	2.07361i	−0.0467754	+	0.115918i
$321$	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
$330$	1.78281	−	4.41816i	0.0981407	−	0.243211i
$331$	−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
$335$	−0.394362	−	2.79719i	−0.0215463	−	0.152827i
$336$	0.718253	+	1.24405i	0.0391839	+	0.0678685i
$337$			10.2739i			0.559653i	0.960051	+	0.279826i	$0.0902769\pi$
$337$			10.2739i			0.559653i	−0.960051	+	0.279826i	$0.909723\pi$
$338$	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	0.239096	−	0.970996i	$-0.423149\pi$
$347$	−8.98356	−	5.18666i	−0.482263	−	0.278435i	−0.721359	+	0.692561i	$0.756482\pi$
$348$	−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	$0.486835\pi$
$350$	−6.90256	+	1.98578i	−0.368958	+	0.106144i
$351$	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	0.524187	−	0.851603i	$-0.324369\pi$
$353$	0.916329	+	0.529043i	0.0487712	+	0.0281581i	−0.475416	+	0.879761i	$0.657702\pi$
$354$	1.43328	+	2.48251i	0.0761779	+	0.131944i
$355$	−0.175220	+	0.0247034i	−0.00929972	+	0.00131112i
$356$	−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	$-0.453918\pi$
$360$	0.312164	+	2.21417i	0.0164525	+	0.116697i
$361$	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
$365$	−1.05092	−	7.45412i	−0.0550075	−	0.390166i
$366$	1.78056	−	3.08402i	0.0930715	−	0.161205i
$367$	0.454524	−	0.262420i	0.0237260	−	0.0136982i	−0.488090	−	0.872793i	$-0.662306\pi$
$367$	0.454524	−	0.262420i	0.0237260	−	0.0136982i	0.511816	+	0.859095i	$0.328973\pi$
$368$		−	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	$-0.882965\pi$
$373$		−	13.8842i		−	0.718896i	0.933165	−	0.359448i	$-0.117035\pi$
$374$	7.80238			0.403451
$375$	−11.1206	−	1.15415i	−0.574266	−	0.0595999i
$376$	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	0.356533	−	0.934283i	$-0.383959\pi$
$383$	26.3009	−	15.1848i	1.34391	−	0.775908i	0.987379	+	0.158375i	$0.0506254\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	6.34670	+	2.56102i	0.323458	+	0.130522i
$386$	−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	$0.0319889\pi$
$390$	−2.22857	−	0.899272i	−0.112848	−	0.0455364i
$391$	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	−0.476817	−	0.879003i	$-0.658209\pi$
$397$	−29.4183	−	16.9847i	−1.47646	−	0.852437i	−0.999647	+	0.0265662i	$0.991543\pi$
$398$	−4.19751	+	2.42343i	−0.210402	+	0.121476i
$399$	4.92842			0.246729
$400$	−3.59972	−	3.47016i	−0.179986	−	0.173508i
$401$	−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	$0.149770\pi$
$410$	−3.65826	−	25.9479i	−0.180669	−	1.28148i
$411$	−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
$415$	−3.97146	−	28.1694i	−0.194951	−	1.38278i
$416$	−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	$0.531956\pi$
$420$	−3.18067	+	0.448425i	−0.155201	+	0.0218809i
$421$	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
$425$	−5.06218	−	17.5961i	−0.245552	−	0.853536i
$426$	−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	$-0.990179\pi$
$433$		−	1.28380i		−	0.0616954i	0.999524	−	0.0308477i	$-0.00982069\pi$
$434$	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	$0.810844\pi$
$440$	0.665115	+	4.71764i	0.0317081	+	0.224905i
$441$	2.46823	−	4.27509i	0.117535	−	0.203576i
$442$		−	3.93561i		−	0.187198i
$443$	27.4282	−	15.8357i	1.30315	−	0.752375i	0.322209	−	0.946669i	$-0.395575\pi$
$443$	27.4282	−	15.8357i	1.30315	−	0.752375i	0.980943	+	0.194293i	$0.0622413\pi$
$444$	2.02292	+	3.50380i	0.0960036	+	0.166283i
$445$	1.07425	−	2.66219i	0.0509242	−	0.126200i
$446$	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
$455$	1.29181	−	3.20135i	0.0605609	−	0.150082i
$456$	1.71542	+	2.97119i	0.0803319	+	0.139139i
$457$		−	10.5057i		−	0.491436i	−0.969341	−	0.245718i	$-0.920976\pi$
$457$		−	10.5057i		−	0.491436i	0.969341	−	0.245718i	$-0.0790237\pi$
$458$	−12.5910	−	7.26939i	−0.588337	−	0.339676i
$459$	−1.83098	+	3.17135i	−0.0854628	+	0.148026i
$460$	1.94020	+	0.782911i	0.0904624	+	0.0365034i
$461$	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	$-0.723830\pi$
$463$		−	32.8265i		−	1.52558i	0.646649	−	0.762788i	$-0.276170\pi$
$464$	3.18722			0.147963
$465$	7.37105	−	10.0333i	0.341824	−	0.465284i
$466$	−1.47599			−0.0683737
$467$		−	20.9567i		−	0.969758i	−0.874581	−	0.484879i	$-0.838864\pi$
$467$		−	20.9567i		−	0.969758i	0.874581	−	0.484879i	$-0.161136\pi$
$468$	−0.930742	−	0.537364i	−0.0430236	−	0.0248397i
$469$	1.81476			0.0837978
$470$	−6.56352	+	16.2657i	−0.302753	+	0.750279i
$471$	−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
$475$	−16.4855	+	4.74269i	−0.756409	+	0.217609i
$476$	−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
$485$	32.9287	+	13.2874i	1.49522	+	0.603349i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−17.5378	+	10.1255i	−0.794715	+	0.458829i	−0.841620	−	0.540070i	$-0.818398\pi$
$487$	−17.5378	+	10.1255i	−0.794715	+	0.458829i	0.0469048	+	0.998899i	$0.485064\pi$
$488$			3.56112i			0.161205i
$489$	4.06851	−	7.04686i	0.183984	−	0.318670i
$490$	1.54098	+	10.9301i	0.0696145	+	0.493774i
$491$	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	0.0294796	−	0.999565i	$-0.490615\pi$
$503$	−18.4227	−	10.6364i	−0.821430	−	0.474253i	−0.850909	+	0.525313i	$0.823948\pi$
$504$	−1.43651			−0.0639870
$505$	−0.456297	+	1.13079i	−0.0203049	+	0.0503195i
$506$	−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	$0.971335\pi$
$510$	−1.14313	−	8.10820i	−0.0506187	−	0.359037i
$511$	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
$515$	2.76798	+	19.6332i	0.121972	+	0.865142i
$516$	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
$520$	2.37963	−	0.335492i	0.104354	−	0.0147123i
$521$	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	$-0.692893\pi$
$523$		−	37.5941i		−	1.64388i	0.569577	−	0.821938i	$-0.307107\pi$
$524$	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
$530$	23.6011	−	3.32739i	1.02517	−	0.144533i
$531$	−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
$540$	−2.07361	−	0.836743i	−0.0892340	−	0.0360077i
$541$	−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
$545$	1.94896	−	4.82990i	0.0834843	−	0.206890i
$546$	0.771926	−	1.33702i	0.0330354	−	0.0572190i
$547$	−8.29105	+	4.78684i	−0.354500	+	0.204671i	−0.666665	−	0.745357i	$-0.732279\pi$
$547$	−8.29105	+	4.78684i	−0.354500	+	0.204671i	0.312166	+	0.950028i	$0.398946\pi$
$548$	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
$555$	−8.95818	+	1.26297i	−0.380254	+	0.0536099i
$556$	17.3868			0.737363
$557$			20.5825i			0.872107i	0.899921	+	0.436054i	$0.143624\pi$
$557$			20.5825i			0.872107i	−0.899921	+	0.436054i	$0.856376\pi$
$558$	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	−0.787738	−	0.616011i	$-0.788748\pi$
$563$	−15.3785	+	8.87876i	−0.648125	+	0.374195i	0.139612	+	0.990206i	$0.455414\pi$
$564$	−3.92206	+	6.79321i	−0.165149	+	0.286046i
$565$	3.97472	+	28.1926i	0.167218	+	1.18607i
$566$	−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	$0.883429\pi$
$570$	−7.59646	+	1.07098i	−0.318181	+	0.0448586i
$571$	−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
$575$	−3.24690	+	3.36813i	−0.135405	+	0.140461i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	10.6585	+	6.15371i	0.443720	+	0.256182i	0.705174	−	0.709034i	$-0.250869\pi$
$577$	10.6585	+	6.15371i	0.443720	+	0.256182i	−0.261454	+	0.965216i	$0.584202\pi$
$578$	−3.10909	+	1.79504i	−0.129321	+	0.0746636i
$579$	−5.43150	−	9.40763i	−0.225725	−	0.390968i
$580$	−2.66688	+	6.60905i	−0.110736	+	0.274426i
$581$	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	$-0.988536\pi$
$587$		−	1.74474i		−	0.0720132i	0.999352	−	0.0360066i	$-0.0114637\pi$
$588$			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	$0.187288\pi$
$593$			27.0311i			1.11003i	−0.831839	+	0.555016i	$0.812712\pi$
$594$	1.06533	+	1.84520i	0.0437110	+	0.0757096i
$595$	11.6475	−	1.64211i	0.477500	−	0.0673201i
$596$	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	$0.853421\pi$
$600$	4.80511	−	1.38237i	0.196168	−	0.0564350i
$601$	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	−0.990917	−	0.134472i	$-0.957066\pi$
$607$	−33.7512	+	19.4863i	−1.36992	+	0.790924i	−0.379003	+	0.925395i	$0.623733\pi$
$608$	−2.97119	−	1.71542i	−0.120498	−	0.0695694i
$609$	2.28923	+	3.96506i	0.0927642	+	0.160672i
$610$	−7.38439	−	2.97975i	−0.298985	−	0.120646i
$611$	−4.21515	−	7.30085i	−0.170527	−	0.295361i
$612$		−	3.66196i		−	0.148026i
$613$	−16.8373	−	9.72099i	−0.680050	−	0.392627i	0.119824	−	0.992795i	$-0.461767\pi$
$613$	−16.8373	−	9.72099i	−0.680050	−	0.392627i	−0.799874	+	0.600168i	$0.795100\pi$
$614$	−10.1418	+	17.5661i	−0.409289	+	0.708910i
$615$	24.3007	+	9.80582i	0.979899	+	0.395409i
$616$	−3.06070			−0.123319
$617$	11.0402	+	6.37405i	0.444461	+	0.256609i	0.705488	−	0.708722i	$-0.250728\pi$
$617$	11.0402	+	6.37405i	0.444461	+	0.256609i	−0.261027	+	0.965331i	$0.584061\pi$
$618$			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	$0.359322\pi$
$620$	−1.36686	+	12.3746i	−0.0548943	+	0.496977i
$621$	0.935664			0.0375469
$622$		−	17.1444i		−	0.687427i
$623$	1.59716	+	0.922123i	0.0639890	+	0.0369441i
$624$	1.07473			0.0430236
$625$	0.915977	+	24.9832i	0.0366391	+	0.999329i
$626$	−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
$630$	1.20199	−	2.97875i	0.0478883	−	0.118676i
$631$	−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
$640$	2.07361	+	0.836743i	0.0819667	+	0.0330752i
$641$	−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	$-0.780039\pi$
$643$		−	32.3221i		−	1.27466i	0.770592	−	0.637329i	$-0.219961\pi$
$644$	−0.672043	+	1.16401i	−0.0264822	+	0.0458685i
$645$	−20.5364	+	2.89531i	−0.808618	+	0.114003i
$646$	−6.28179	−	10.8804i	−0.247154	−	0.428083i
$647$			25.4783i			1.00166i	0.865547	+	0.500828i	$0.166971\pi$
$647$			25.4783i			1.00166i	−0.865547	+	0.500828i	$0.833029\pi$
$648$	−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	$-0.991646\pi$
$653$		−	1.34114i		−	0.0524828i	0.999656	−	0.0262414i	$-0.00835385\pi$
$654$	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	$0.352295\pi$
$660$	−4.41816	−	1.78281i	−0.171976	−	0.0693960i
$661$	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
$665$	−1.53848	−	10.9124i	−0.0596595	−	0.423163i
$666$	−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
$670$	−2.79719	+	0.394362i	−0.108065	+	0.0152355i
$671$	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	−0.557390	−	0.830251i	$-0.688197\pi$
$673$	−3.03699	+	1.75341i	−0.117067	+	0.0675888i	0.440323	+	0.897839i	$0.354864\pi$
$674$	10.2739			0.395734
$675$	3.47016	−	3.59972i	0.133567	−	0.138553i
$676$	5.92248	−	10.2580i	0.227788	−	0.394540i
$677$	18.2004	−	10.5080i	0.699498	−	0.403855i	−0.107663	−	0.994187i	$-0.534337\pi$
$677$	18.2004	−	10.5080i	0.699498	−	0.403855i	0.807160	+	0.590332i	$0.201003\pi$
$678$			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	$0.187542\pi$
$683$			29.0446i			1.11136i	−0.831396	+	0.555681i	$0.812458\pi$
$684$	−3.43084			−0.131181
$685$	1.95866	+	13.8927i	0.0748364	+	0.530813i
$686$	−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
$695$	−14.5483	+	36.0534i	−0.551847	+	1.36758i
$696$	−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
$700$	1.98578	+	6.90256i	0.0750555	+	0.260892i
$701$	−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	$0.335169\pi$
$710$	0.0247034	+	0.175220i	0.000927101	+	0.00657590i
$711$	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	$0.197329\pi$
$720$	2.21417	−	0.312164i	0.0825173	−	0.0116337i
$721$	−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
$725$	−11.4731	−	11.0602i	−0.426100	−	0.410764i
$726$	−3.23015	−	5.59478i	−0.119882	−	0.207642i
$727$	20.8575	+	12.0421i	0.773561	+	0.446615i	0.834143	−	0.551548i	$-0.185963\pi$
$727$	20.8575	+	12.0421i	0.773561	+	0.446615i	−0.0605827	+	0.998163i	$0.519296\pi$
$728$			1.54385i			0.0572190i
$729$	−1.00000			−0.0370370
$730$	−7.45412	+	1.05092i	−0.275889	+	0.0388961i
$731$	−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	−0.300127	−	0.953899i	$-0.597029\pi$
$733$	10.1774	−	5.87592i	0.375911	−	0.217032i	0.676038	+	0.736867i	$0.263696\pi$
$734$	−0.262420	−	0.454524i	−0.00968608	−	0.0167768i
$735$	−10.2363	−	4.13054i	−0.377571	−	0.152357i
$736$	−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	$0.203888\pi$
$743$			32.5800i			1.19525i	−0.801777	+	0.597623i	$0.796112\pi$
$744$	−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
$750$	−1.15415	+	11.1206i	−0.0421435	+	0.406067i
$751$	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
$755$	17.4655	−	43.2828i	0.635633	−	1.57522i
$756$	0.718253	−	1.24405i	0.0261226	−	0.0452457i
$757$	−19.9199	+	11.5008i	−0.724002	+	0.418003i	−0.816224	−	0.577736i	$-0.803936\pi$
$757$	−19.9199	+	11.5008i	−0.724002	+	0.418003i	0.0922218	+	0.995738i	$0.470603\pi$
$758$	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
$765$	7.59347	+	3.06412i	0.274543	+	0.110783i
$766$	−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	$0.867302\pi$
$770$	2.56102	−	6.34670i	0.0922929	−	0.228719i
$771$	−2.76615			−0.0996203
$772$	9.40763	+	5.43150i	0.338588	+	0.195484i
$773$			17.8526i			0.642113i	0.947060	+	0.321056i	$0.104038\pi$
$773$			17.8526i			0.642113i	−0.947060	+	0.321056i	$0.895962\pi$
$774$	−9.27496			−0.333382
$775$	−24.5165	−	13.1887i	−0.880658	−	0.473753i
$776$	−15.8799			−0.570055
$777$		−	5.81187i		−	0.208500i
$778$	−14.0264	−	8.09813i	−0.502870	−	0.290332i
$779$	40.2061			1.44053
$780$	−0.899272	+	2.22857i	−0.0321991	+	0.0797955i
$781$	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
$785$	34.3981	+	13.8803i	1.22772	+	0.495409i
$786$	10.8255	+	18.7503i	0.386132	+	0.668800i
$787$	−30.7258	−	17.7395i	−1.09526	−	0.632346i	−0.160285	−	0.987071i	$-0.551241\pi$
$787$	−30.7258	−	17.7395i	−1.09526	−	0.632346i	−0.934971	+	0.354724i	$0.884575\pi$
$788$	−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
$795$	−8.91895	+	22.1029i	−0.316322	+	0.783907i
$796$	2.42343	+	4.19751i	0.0858962	+	0.148777i
$797$	36.3322	−	20.9764i	1.28695	−	0.743023i	0.308844	−	0.951113i	$-0.400058\pi$
$797$	36.3322	−	20.9764i	1.28695	−	0.743023i	0.978110	+	0.208089i	$0.0667245\pi$
$798$		−	4.92842i		−	0.174464i
$799$	14.3624	−	24.8764i	0.508106	−	0.880065i
$800$	−3.47016	+	3.59972i	−0.122689	+	0.127269i
$801$	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
$815$	−16.8730	−	6.80859i	−0.591035	−	0.238495i
$816$	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
$820$	−25.9479	+	3.65826i	−0.906141	+	0.127752i
$821$	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	0.732681	−	0.680572i	$-0.238269\pi$
$823$	14.6202	+	8.44100i	0.509629	+	0.294235i	−0.223052	+	0.974807i	$0.571602\pi$
$824$	−4.43353	−	7.67910i	−0.154449	−	0.267514i
$825$	7.39373	−	7.66977i	0.257416	−	0.267027i
$826$	2.05891	+	3.56614i	0.0716387	+	0.124082i
$827$	−31.6551	+	18.2761i	−1.10075	+	0.635521i	−0.936419	−	0.350884i	$-0.885881\pi$
$827$	−31.6551	+	18.2761i	−1.10075	+	0.635521i	−0.164335	+	0.986405i	$0.552548\pi$
$828$	−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	$0.303058\pi$
$830$	−28.1694	+	3.97146i	−0.977775	+	0.137851i
$831$	−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	$0.206647\pi$
$840$	0.448425	+	3.18067i	0.0154721	+	0.109744i
$841$	−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
$850$	−17.5961	+	5.06218i	−0.603541	+	0.173631i
$851$	−1.89277	+	3.27838i	−0.0648834	+	0.112381i
$852$			0.0791358i			0.00271115i
$853$			53.9629i			1.84766i	0.382808	+	0.923828i	$0.374957\pi$
$853$			53.9629i			1.84766i	−0.382808	+	0.923828i	$0.625043\pi$
$854$	2.55779	−	4.43022i	0.0875257	−	0.151599i
$855$	2.87073	−	7.11422i	0.0981769	−	0.243301i
$856$	−1.46247	+	2.53308i	−0.0499863	+	0.0865788i
$857$	8.72406	−	5.03684i	0.298008	−	0.172055i	−0.343540	−	0.939138i	$-0.611626\pi$
$857$	8.72406	−	5.03684i	0.298008	−	0.172055i	0.641548	+	0.767083i	$0.278293\pi$
$858$	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	$-0.306091\pi$
$863$	46.0787	−	26.6036i	1.56854	−	0.905596i	0.996340	−	0.0854801i	$-0.0272424\pi$
$864$	1.00000			0.0340207
$865$	4.11271	+	29.1714i	0.139836	+	0.991856i
$866$	−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
$875$	−15.9748	−	1.65794i	−0.540047	−	0.0560485i
$876$	−3.36655			−0.113745
$877$	44.4299	−	25.6516i	1.50029	−	0.866193i	0.500290	−	0.865858i	$-0.333227\pi$
$877$	44.4299	−	25.6516i	1.50029	−	0.866193i	1.00000		0.000334977i	$-0.000106626\pi$
$878$	2.56192	−	1.47912i	0.0864606	−	0.0499180i
$879$	14.4879	+	25.0938i	0.488666	+	0.846394i
$880$	4.71764	−	0.665115i	0.159032	−	0.0224210i
$881$	−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	$-0.913230\pi$
$883$		−	16.0006i		−	0.538464i	0.963075	−	0.269232i	$-0.0867698\pi$
$884$	−3.93561			−0.132369
$885$	0.894836	+	6.34704i	0.0300796	+	0.213354i
$886$	−15.8357	−	27.4282i	−0.532010	−	0.921468i
$887$	12.1344	+	7.00579i	0.407433	+	0.235232i	0.689686	−	0.724108i	$-0.257748\pi$
$887$	12.1344	+	7.00579i	0.407433	+	0.235232i	−0.282253	+	0.959340i	$0.591082\pi$
$888$	3.50380	−	2.02292i	0.117580	−	0.0678848i
$889$	−6.34269	−	10.9859i	−0.212727	−	0.368454i
$890$	−2.66219	−	1.07425i	−0.0892368	−	0.0360088i
$891$	−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
$905$	21.5190	−	3.03385i	0.715316	−	0.100849i
$906$	10.4366	−	18.0767i	0.346732	−	0.600557i
$907$		−	18.2979i		−	0.607573i	−0.952740	−	0.303786i	$-0.901749\pi$
$907$		−	18.2979i		−	0.607573i	0.952740	−	0.303786i	$-0.0982509\pi$
$908$	16.7766	−	9.68597i	0.556751	−	0.321440i
$909$	−0.272662	−	0.472265i	−0.00904364	−	0.0156640i
$910$	−3.20135	−	1.29181i	−0.106124	−	0.0428230i
$911$	−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	$0.740254\pi$
$920$	0.782911	−	1.94020i	0.0258118	−	0.0639666i
$921$	−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
$925$	5.59285	+	19.4407i	0.183892	+	0.639206i
$926$	−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	$0.889119\pi$
$930$	−10.0333	−	7.37105i	−0.329006	−	0.241706i
$931$	−16.9362			−0.555060
$932$			1.47599i			0.0483475i
$933$	14.8475	+	8.57220i	0.486085	+	0.280641i
$934$	−20.9567			−0.685723
$935$	16.1791	+	6.52859i	0.529113	+	0.213508i
$936$	−0.537364	+	0.930742i	−0.0175643	+	0.0304223i
$937$	19.4868	+	11.2507i	0.636605	+	0.367544i	0.783306	−	0.621637i	$-0.213532\pi$
$937$	19.4868	+	11.2507i	0.636605	+	0.367544i	−0.146701	+	0.989181i	$0.546865\pi$
$938$		−	1.81476i		−	0.0592540i
$939$	−3.49393	−	6.05166i	−0.114020	−	0.197489i
$940$	16.2657	+	6.56352i	0.530527	+	0.214078i
$941$	−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	0.805517	−	0.592572i	$-0.201887\pi$
$947$	21.3904	+	12.3497i	0.695094	+	0.401313i	−0.110424	+	0.993885i	$0.535221\pi$
$948$	−9.06779	+	5.23529i	−0.294508	+	0.170034i
$949$	1.80906	−	3.13339i	0.0587247	−	0.101714i
$950$	4.74269	+	16.4855i	0.153873	+	0.534862i
$951$	−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	$0.279221\pi$
$953$			47.4761i			1.53790i	−0.639308	+	0.768950i	$0.720779\pi$
$954$	−5.32956	+	9.23106i	−0.172551	+	0.298867i
$955$	−2.67356	+	0.376930i	−0.0865143	+	0.0121972i
$956$	−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	0.887834	−	0.460164i	$-0.152209\pi$
$967$	29.0205	+	16.7550i	0.933238	+	0.538805i	0.0454036	+	0.998969i	$0.485543\pi$
$968$	5.59478	+	3.23015i	0.179823	+	0.103821i
$969$	12.5636			0.403600
$970$	13.2874	−	32.9287i	0.426632	−	1.05728i
$971$	−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
$975$	−3.86872	−	3.72948i	−0.123898	−	0.119439i
$976$	3.56112			0.113989
$977$		−	16.6162i		−	0.531599i	−0.964028	−	0.265799i	$-0.914364\pi$
$977$		−	16.6162i		−	0.531599i	0.964028	−	0.265799i	$-0.0856359\pi$
$978$	−7.04686	−	4.06851i	−0.225334	−	0.130096i
$979$	1.36771	+	2.36895i	0.0437124	+	0.0757120i
$980$	10.9301	−	1.54098i	0.349151	−	0.0492249i
$981$	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	−0.404704	−	0.914448i	$-0.632625\pi$
$983$	5.79650	−	3.34661i	0.184880	−	0.106740i	0.589583	+	0.807708i	$0.299292\pi$
$984$	−11.7190			−0.373589
$985$	−0.645324	−	4.57727i	−0.0205617	−	0.145844i
$986$	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
$995$	−10.7318	+	1.51302i	−0.340220	+	0.0479658i
$996$	−12.7223			−0.403123
$997$	35.4330	−	20.4572i	1.12217	−	0.647887i	0.180219	−	0.983627i	$-0.442319\pi$
$997$	35.4330	−	20.4572i	1.12217	−	0.647887i	0.941955	+	0.335739i	$0.108986\pi$
$998$	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.439.5	✓	28
5.4	even	2	inner	930.2.s.d.439.8	yes	28
31.25	even	3	inner	930.2.s.d.769.1	yes	28
155.149	even	6	inner	930.2.s.d.769.12	yes	28

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(0.836743 - 2.07361i) q^{5} +(0.500000 - 0.866025i) q^{6} +(1.24405 + 0.718253i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(0.836743 - 2.07361i) q^{5} +(0.500000 - 0.866025i) q^{6} +(1.24405 + 0.718253i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.07361 - 0.836743i) 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} +(-0.836743 + 2.07361i) q^{20} +(0.718253 + 1.24405i) q^{21} +(1.84520 - 1.06533i) q^{22} -0.935664i q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.59972 - 3.47016i) 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} +(2.07361 + 0.836743i) 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} +(2.21417 - 0.312164i) q^{45} -0.935664 q^{46} -7.84412i q^{47} +(0.866025 + 0.500000i) q^{48} +(-2.46823 - 4.27509i) q^{49} +(-3.47016 + 3.59972i) q^{50} +(1.83098 + 3.17135i) q^{51} +(-0.930742 + 0.537364i) q^{52} +(-9.23106 + 5.32956i) q^{53} +1.00000 q^{54} +(4.71764 - 0.665115i) 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} +(-0.335492 - 2.37963i) 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} +(-1.38237 - 4.80511i) q^{75} +(-1.71542 + 2.97119i) q^{76} +3.06070i q^{77} -1.07473i q^{78} +(5.23529 - 9.06779i) q^{79} +(0.836743 - 2.07361i) 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} +(-0.312164 - 2.21417i) 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

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