LMFDB - Embedded newform 570.2.q.c.49.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(49,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, 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("570.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.q (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 $ x^20 - 49x^16 - 8x^15 + 72x^13 + 2145x^12 - 648x^11 + 32x^10 - 7056x^9 - 11968x^8 + 10368x^7 + 9344x^6 + 18176x^5 + 56320x^4 + 28160x^3 + 8192x^2 + 4096*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.10
Root			$0.320085 + 1.19457i$ of defining polynomial
Character	$\chi$	$=$	570.49
Dual form			570.2.q.c.349.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.21950 + 0.271659i) q^{5} +(-0.500000 - 0.866025i) q^{6} -4.03495i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.21950 + 0.271659i) q^{5} +(-0.500000 - 0.866025i) q^{6} -4.03495i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.78632 + 1.34502i) q^{10} -1.47054 q^{11} -1.00000i q^{12} +(4.38320 - 2.53064i) q^{13} +(2.01747 - 3.49437i) q^{14} +(-1.78632 - 1.34502i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.0812933 + 0.0469347i) q^{17} +1.00000i q^{18} +(-4.00172 - 1.72807i) q^{19} +(0.874489 + 2.05798i) q^{20} +(-2.01747 + 3.49437i) q^{21} +(-1.27352 - 0.735269i) q^{22} +(2.22178 - 1.28274i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.85240 + 1.20590i) q^{25} +5.06128 q^{26} -1.00000i q^{27} +(3.49437 - 2.01747i) q^{28} +(2.10491 + 3.64581i) q^{29} +(-0.874489 - 2.05798i) q^{30} +4.26558 q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.27352 + 0.735269i) q^{33} +(0.0469347 + 0.0812933i) q^{34} +(1.09613 - 8.95558i) q^{35} +(-0.500000 + 0.866025i) q^{36} -1.53807i q^{37} +(-2.60156 - 3.49741i) q^{38} -5.06128 q^{39} +(-0.271659 + 2.21950i) q^{40} +(-3.88123 + 6.72248i) q^{41} +(-3.49437 + 2.01747i) q^{42} +(3.97202 + 2.29325i) q^{43} +(-0.735269 - 1.27352i) q^{44} +(0.874489 + 2.05798i) q^{45} +2.56549 q^{46} +(-3.49530 + 2.01801i) q^{47} +(0.866025 - 0.500000i) q^{48} -9.28080 q^{49} +(3.59936 + 3.47054i) q^{50} +(-0.0469347 - 0.0812933i) q^{51} +(4.38320 + 2.53064i) q^{52} +(9.22964 - 5.32873i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-3.26387 - 0.399485i) q^{55} +4.03495 q^{56} +(2.60156 + 3.49741i) q^{57} +4.20982i q^{58} +(-3.07599 + 5.32777i) q^{59} +(0.271659 - 2.21950i) q^{60} +(0.653722 + 1.13228i) q^{61} +(3.69410 + 2.13279i) q^{62} +(3.49437 - 2.01747i) q^{63} -1.00000 q^{64} +(10.4160 - 4.42603i) q^{65} +(0.735269 + 1.27352i) q^{66} +(-9.31187 + 5.37621i) q^{67} +0.0938694i q^{68} -2.56549 q^{69} +(5.42707 - 7.20770i) q^{70} +(4.33806 - 7.51373i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(-11.0108 - 6.35711i) q^{73} +(0.769037 - 1.33201i) q^{74} +(-3.59936 - 3.47054i) q^{75} +(-0.504306 - 4.32963i) q^{76} +5.93355i q^{77} +(-4.38320 - 2.53064i) q^{78} +(-6.48112 + 11.2256i) q^{79} +(-1.34502 + 1.78632i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.72248 + 3.88123i) q^{82} +2.06328i q^{83} -4.03495 q^{84} +(0.167681 + 0.126256i) q^{85} +(2.29325 + 3.97202i) q^{86} -4.20982i q^{87} -1.47054i q^{88} +(-0.813846 - 1.40962i) q^{89} +(-0.271659 + 2.21950i) q^{90} +(-10.2110 - 17.6860i) q^{91} +(2.22178 + 1.28274i) q^{92} +(-3.69410 - 2.13279i) q^{93} -4.03603 q^{94} +(-8.41239 - 4.92257i) q^{95} +1.00000 q^{96} +(-10.3479 - 5.97438i) q^{97} +(-8.03741 - 4.64040i) q^{98} +(-0.735269 - 1.27352i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9	$ 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9} - 2 q^{10} + 12 q^{11} + 10 q^{14} + 2 q^{15} - 10 q^{16} + 6 q^{19} - 10 q^{21} + 10 q^{24} + 14 q^{25} + 8 q^{29} + 40 q^{31} + 12 q^{34} + 2 q^{35} - 10 q^{36} + 2 q^{40} - 14 q^{41} + 6 q^{44} + 44 q^{46} - 8 q^{49} - 8 q^{50} - 12 q^{51} + 10 q^{54} + 20 q^{56} + 8 q^{59} - 2 q^{60} + 16 q^{61} - 20 q^{64} + 40 q^{65} - 6 q^{66} - 44 q^{69} + 8 q^{70} - 4 q^{71} + 26 q^{74} + 8 q^{75} + 8 q^{79} - 10 q^{81} - 20 q^{84} - 16 q^{85} - 20 q^{86} - 2 q^{89} + 2 q^{90} - 44 q^{91} - 32 q^{94} - 80 q^{95} + 20 q^{96} + 6 q^{99}+O(q^{100}) $ 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9 - 2 * q^10 + 12 * q^11 + 10 * q^14 + 2 * q^15 - 10 * q^16 + 6 * q^19 - 10 * q^21 + 10 * q^24 + 14 * q^25 + 8 * q^29 + 40 * q^31 + 12 * q^34 + 2 * q^35 - 10 * q^36 + 2 * q^40 - 14 * q^41 + 6 * q^44 + 44 * q^46 - 8 * q^49 - 8 * q^50 - 12 * q^51 + 10 * q^54 + 20 * q^56 + 8 * q^59 - 2 * q^60 + 16 * q^61 - 20 * q^64 + 40 * q^65 - 6 * q^66 - 44 * q^69 + 8 * q^70 - 4 * q^71 + 26 * q^74 + 8 * q^75 + 8 * q^79 - 10 * q^81 - 20 * q^84 - 16 * q^85 - 20 * q^86 - 2 * q^89 + 2 * q^90 - 44 * q^91 - 32 * q^94 - 80 * q^95 + 20 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.21950	+	0.271659i	0.992593	+	0.121490i
$5$	2.21950	+	0.271659i	0.992593	+	0.121490i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$		−	4.03495i		−	1.52507i	−0.646949	−	0.762533i	$-0.723955\pi$
$7$		−	4.03495i		−	1.52507i	0.646949	−	0.762533i	$-0.276045\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.78632	+	1.34502i	0.564883	+	0.425331i
$11$	−1.47054			−0.443384			−0.221692	−	0.975117i	$-0.571158\pi$
$11$	−1.47054			−0.443384			−0.221692	+	0.975117i	$0.571158\pi$
$12$		−	1.00000i		−	0.288675i
$13$	4.38320	−	2.53064i	1.21568	−	0.701874i	0.251690	−	0.967808i	$-0.419014\pi$
$13$	4.38320	−	2.53064i	1.21568	−	0.701874i	0.963991	+	0.265934i	$0.0856805\pi$
$14$	2.01747	−	3.49437i	0.539192	−	0.933909i
$15$	−1.78632	−	1.34502i	−0.461225	−	0.347282i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.0812933	+	0.0469347i	0.0197165	+	0.0113833i	0.509826	−	0.860278i	$-0.329710\pi$
$17$	0.0812933	+	0.0469347i	0.0197165	+	0.0113833i	−0.490109	+	0.871661i	$0.663043\pi$
$18$			1.00000i			0.235702i
$19$	−4.00172	−	1.72807i	−0.918058	−	0.396447i
$19$	−4.00172	−	1.72807i	−0.918058	−	0.396447i
$20$	0.874489	+	2.05798i	0.195542	+	0.460178i
$21$	−2.01747	+	3.49437i	−0.440249	+	0.762533i
$22$	−1.27352	−	0.735269i	−0.271516	−	0.156760i
$23$	2.22178	−	1.28274i	0.463273	−	0.267471i	−0.250147	−	0.968208i	$-0.580479\pi$
$23$	2.22178	−	1.28274i	0.463273	−	0.267471i	0.713419	+	0.700737i	$0.247145\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	4.85240	+	1.20590i	0.970481	+	0.241179i
$26$	5.06128			0.992599
$27$		−	1.00000i		−	0.192450i
$28$	3.49437	−	2.01747i	0.660373	−	0.381267i
$29$	2.10491	+	3.64581i	0.390872	+	0.677011i	0.992565	−	0.121717i	$-0.0388401\pi$
$29$	2.10491	+	3.64581i	0.390872	+	0.677011i	−0.601693	+	0.798728i	$0.705507\pi$
$30$	−0.874489	−	2.05798i	−0.159659	−	0.375733i
$31$	4.26558			0.766120			0.383060	−	0.923723i	$-0.374870\pi$
$31$	4.26558			0.766120			0.383060	+	0.923723i	$0.374870\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.27352	+	0.735269i	0.221692	+	0.127994i
$34$	0.0469347	+	0.0812933i	0.00804924	+	0.0139417i
$35$	1.09613	−	8.95558i	0.185280	−	1.51377i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$		−	1.53807i		−	0.252858i	−0.991976	−	0.126429i	$-0.959648\pi$
$37$		−	1.53807i		−	0.252858i	0.991976	−	0.126429i	$-0.0403515\pi$
$38$	−2.60156	−	3.49741i	−0.422028	−	0.567356i
$39$	−5.06128			−0.810454
$40$	−0.271659	+	2.21950i	−0.0429531	+	0.350935i
$41$	−3.88123	+	6.72248i	−0.606146	+	1.04987i	0.385724	+	0.922614i	$0.373952\pi$
$41$	−3.88123	+	6.72248i	−0.606146	+	1.04987i	−0.991869	+	0.127261i	$0.959382\pi$
$42$	−3.49437	+	2.01747i	−0.539192	+	0.311303i
$43$	3.97202	+	2.29325i	0.605727	+	0.349717i	0.771291	−	0.636482i	$-0.219611\pi$
$43$	3.97202	+	2.29325i	0.605727	+	0.349717i	−0.165564	+	0.986199i	$0.552944\pi$
$44$	−0.735269	−	1.27352i	−0.110846	−	0.191991i
$45$	0.874489	+	2.05798i	0.130361	+	0.306785i
$46$	2.56549			0.378261
$47$	−3.49530	+	2.01801i	−0.509842	+	0.294358i	−0.732769	−	0.680478i	$-0.761772\pi$
$47$	−3.49530	+	2.01801i	−0.509842	+	0.294358i	0.222927	+	0.974835i	$0.428439\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−9.28080			−1.32583
$50$	3.59936	+	3.47054i	0.509026	+	0.490808i
$51$	−0.0469347	−	0.0812933i	−0.00657218	−	0.0113833i
$52$	4.38320	+	2.53064i	0.607840	+	0.350937i
$53$	9.22964	−	5.32873i	1.26779	−	0.731958i	0.293219	−	0.956045i	$-0.405273\pi$
$53$	9.22964	−	5.32873i	1.26779	−	0.731958i	0.974569	+	0.224087i	$0.0719401\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−3.26387	−	0.399485i	−0.440100	−	0.0538666i
$56$	4.03495			0.539192
$57$	2.60156	+	3.49741i	0.344584	+	0.463244i
$58$			4.20982i			0.552777i
$59$	−3.07599	+	5.32777i	−0.400460	+	0.693617i	−0.993781	−	0.111349i	$-0.964483\pi$
$59$	−3.07599	+	5.32777i	−0.400460	+	0.693617i	0.593321	+	0.804966i	$0.297816\pi$
$60$	0.271659	−	2.21950i	0.0350710	−	0.286537i
$61$	0.653722	+	1.13228i	0.0837005	+	0.144974i	0.904837	−	0.425759i	$-0.139993\pi$
$61$	0.653722	+	1.13228i	0.0837005	+	0.144974i	−0.821136	+	0.570732i	$0.806659\pi$
$62$	3.69410	+	2.13279i	0.469151	+	0.270864i
$63$	3.49437	−	2.01747i	0.440249	−	0.254178i
$64$	−1.00000			−0.125000
$65$	10.4160	−	4.42603i	1.29195	−	0.548982i
$66$	0.735269	+	1.27352i	0.0905054	+	0.156760i
$67$	−9.31187	+	5.37621i	−1.13763	+	0.656808i	−0.945842	−	0.324629i	$-0.894761\pi$
$67$	−9.31187	+	5.37621i	−1.13763	+	0.656808i	−0.191784	+	0.981437i	$0.561427\pi$
$68$			0.0938694i			0.0113833i
$69$	−2.56549			−0.308849
$70$	5.42707	−	7.20770i	0.648659	−	0.861485i
$71$	4.33806	−	7.51373i	0.514833	−	0.891716i	−0.485019	−	0.874503i	$-0.661187\pi$
$71$	4.33806	−	7.51373i	0.514833	−	0.891716i	0.999852	−	0.0172126i	$-0.00547923\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−11.0108	−	6.35711i	−1.28872	−	0.744044i	−0.310296	−	0.950640i	$-0.600428\pi$
$73$	−11.0108	−	6.35711i	−1.28872	−	0.744044i	−0.978426	+	0.206596i	$0.933761\pi$
$74$	0.769037	−	1.33201i	0.0893987	−	0.154843i
$75$	−3.59936	−	3.47054i	−0.415618	−	0.400743i
$76$	−0.504306	−	4.32963i	−0.0578479	−	0.496642i
$77$			5.93355i			0.676190i
$78$	−4.38320	−	2.53064i	−0.496300	−	0.286539i
$79$	−6.48112	+	11.2256i	−0.729183	+	1.26298i	0.228046	+	0.973650i	$0.426766\pi$
$79$	−6.48112	+	11.2256i	−0.729183	+	1.26298i	−0.957229	+	0.289332i	$0.906567\pi$
$80$	−1.34502	+	1.78632i	−0.150377	+	0.199716i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−6.72248	+	3.88123i	−0.742374	+	0.428610i
$83$			2.06328i			0.226475i	0.993568	+	0.113237i	$0.0361221\pi$
$83$			2.06328i			0.226475i	−0.993568	+	0.113237i	$0.963878\pi$
$84$	−4.03495			−0.440249
$85$	0.167681	+	0.126256i	0.0181875	+	0.0136944i
$86$	2.29325	+	3.97202i	0.247287	+	0.428314i
$87$		−	4.20982i		−	0.451340i
$88$		−	1.47054i		−	0.156760i
$89$	−0.813846	−	1.40962i	−0.0862675	−	0.149420i	0.819663	−	0.572846i	$-0.194161\pi$
$89$	−0.813846	−	1.40962i	−0.0862675	−	0.149420i	−0.905931	+	0.423426i	$0.860827\pi$
$90$	−0.271659	+	2.21950i	−0.0286354	+	0.233956i
$91$	−10.2110	−	17.6860i	−1.07040	−	1.85399i
$92$	2.22178	+	1.28274i	0.231636	+	0.133735i
$93$	−3.69410	−	2.13279i	−0.383060	−	0.221160i
$94$	−4.03603			−0.416285
$95$	−8.41239	−	4.92257i	−0.863093	−	0.505045i
$96$	1.00000			0.102062
$97$	−10.3479	−	5.97438i	−1.05067	−	0.606607i	−0.127836	−	0.991795i	$-0.540803\pi$
$97$	−10.3479	−	5.97438i	−1.05067	−	0.606607i	−0.922838	+	0.385188i	$0.874136\pi$
$98$	−8.03741	−	4.64040i	−0.811901	−	0.468751i
$99$	−0.735269	−	1.27352i	−0.0738974	−	0.127994i
$100$	1.38186	+	4.80525i	0.138186	+	0.480525i
$101$	−0.252103	−	0.436656i	−0.0250852	−	0.0434489i	0.853210	−	0.521567i	$-0.174652\pi$
$101$	−0.252103	−	0.436656i	−0.0250852	−	0.0434489i	−0.878295	+	0.478118i	$0.841319\pi$
$102$		−	0.0938694i		−	0.00929446i
$103$		−	5.33797i		−	0.525966i	−0.964800	−	0.262983i	$-0.915294\pi$
$103$		−	5.33797i		−	0.525966i	0.964800	−	0.262983i	$-0.0847063\pi$
$104$	2.53064	+	4.38320i	0.248150	+	0.429808i
$105$	−5.42707	+	7.20770i	−0.529628	+	0.703399i
$106$	10.6575			1.03514
$107$			17.9275i			1.73312i	0.499076	+	0.866558i	$0.333673\pi$
$107$			17.9275i			1.73312i	−0.499076	+	0.866558i	$0.666327\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−4.43631	+	7.68392i	−0.424922	+	0.735986i	−0.996413	−	0.0846222i	$-0.973032\pi$
$109$	−4.43631	+	7.68392i	−0.424922	+	0.735986i	0.571492	+	0.820608i	$0.306365\pi$
$110$	−2.62685	−	1.97790i	−0.250460	−	0.188585i
$111$	−0.769037	+	1.33201i	−0.0729937	+	0.126429i
$112$	3.49437	+	2.01747i	0.330187	+	0.190633i
$113$			15.8667i			1.49261i	0.665603	+	0.746306i	$0.268174\pi$
$113$			15.8667i			1.49261i	−0.665603	+	0.746306i	$0.731826\pi$
$114$	0.504306	+	4.32963i	0.0472326	+	0.405507i
$115$	5.27972	−	2.24349i	0.492336	−	0.209207i
$116$	−2.10491	+	3.64581i	−0.195436	+	0.338505i
$117$	4.38320	+	2.53064i	0.405227	+	0.233958i
$118$	−5.32777	+	3.07599i	−0.490461	+	0.283168i
$119$	0.189379	−	0.328014i	0.0173604	−	0.0300690i
$120$	1.34502	−	1.78632i	0.122783	−	0.163068i
$121$	−8.83752			−0.803410
$122$			1.30744i			0.118370i
$123$	6.72248	−	3.88123i	0.606146	−	0.349958i
$124$	2.13279	+	3.69410i	0.191530	+	0.331740i
$125$	10.4423	+	3.99469i	0.933991	+	0.357296i
$126$	4.03495			0.359462
$127$	−5.77290	+	3.33298i	−0.512262	+	0.295755i	−0.733763	−	0.679406i	$-0.762238\pi$
$127$	−5.77290	+	3.33298i	−0.512262	+	0.295755i	0.221501	+	0.975160i	$0.428904\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−2.29325	−	3.97202i	−0.201909	−	0.349717i
$130$	11.2335	+	1.37494i	0.985247	+	0.120590i
$131$	−3.53784	+	6.12771i	−0.309102	+	0.535381i	−0.978166	−	0.207824i	$-0.933362\pi$
$131$	−3.53784	+	6.12771i	−0.309102	+	0.535381i	0.669064	+	0.743205i	$0.266695\pi$
$132$			1.47054i			0.127994i
$133$	−6.97268	+	16.1467i	−0.604608	+	1.40010i
$134$	−10.7524			−0.928867
$135$	0.271659	−	2.21950i	0.0233807	−	0.191025i
$136$	−0.0469347	+	0.0812933i	−0.00402462	+	0.00697084i
$137$	−16.3302	+	9.42826i	−1.39519	+	0.805511i	−0.993883	−	0.110435i	$-0.964775\pi$
$137$	−16.3302	+	9.42826i	−1.39519	+	0.805511i	−0.401302	+	0.915946i	$0.631442\pi$
$138$	−2.22178	−	1.28274i	−0.189130	−	0.109194i
$139$	−9.99616	−	17.3139i	−0.847864	−	1.46854i	−0.883111	−	0.469164i	$-0.844555\pi$
$139$	−9.99616	−	17.3139i	−0.847864	−	1.46854i	0.0352474	−	0.999379i	$-0.488778\pi$
$140$	8.30383	−	3.52852i	0.701802	−	0.298214i
$141$	4.03603			0.339895
$142$	7.51373	−	4.33806i	0.630538	−	0.364042i
$143$	−6.44566	+	3.72141i	−0.539014	+	0.311200i
$144$	−1.00000			−0.0833333
$145$	3.68144	+	8.66372i	0.305727	+	0.719483i
$146$	−6.35711	−	11.0108i	−0.526119	−	0.911264i
$147$	8.03741	+	4.64040i	0.662914	+	0.382734i
$148$	1.33201	−	0.769037i	0.109491	−	0.0632144i
$149$	6.10397	−	10.5724i	0.500056	−	0.866123i	−0.499944	−	0.866058i	$-0.666646\pi$
$149$	6.10397	−	10.5724i	0.500056	−	0.866123i	1.00000		6.51503e-5i	$-2.07380e-5\pi$
$150$	−1.38186	−	4.80525i	−0.112829	−	0.392347i
$151$	19.9109			1.62032			0.810161	−	0.586207i	$-0.199380\pi$
$151$	19.9109			1.62032			0.810161	+	0.586207i	$0.199380\pi$
$152$	1.72807	−	4.00172i	0.140165	−	0.324582i
$153$			0.0938694i			0.00758889i
$154$	−2.96677	+	5.13860i	−0.239069	+	0.414080i
$155$	9.46747	+	1.15878i	0.760445	+	0.0930756i
$156$	−2.53064	−	4.38320i	−0.202613	−	0.350937i
$157$	−14.0594	−	8.11721i	−1.12206	−	0.647824i	−0.180137	−	0.983641i	$-0.557654\pi$
$157$	−14.0594	−	8.11721i	−1.12206	−	0.647824i	−0.941927	+	0.335817i	$0.890988\pi$
$158$	−11.2256	+	6.48112i	−0.893063	+	0.515610i
$159$	−10.6575			−0.845192
$160$	−2.05798	+	0.874489i	−0.162697	+	0.0691344i
$161$	−5.17581	−	8.96476i	−0.407911	−	0.706522i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$			2.05750i			0.161156i	0.996748	+	0.0805780i	$0.0256766\pi$
$163$			2.05750i			0.161156i	−0.996748	+	0.0805780i	$0.974323\pi$
$164$	−7.76245			−0.606146
$165$	2.62685	+	1.97790i	0.204500	+	0.153979i
$166$	−1.03164	+	1.78686i	−0.0800709	+	0.138687i
$167$	18.8169	−	10.8639i	1.45609	−	0.840676i	0.457278	−	0.889324i	$-0.348824\pi$
$167$	18.8169	−	10.8639i	1.45609	−	0.840676i	0.998816	+	0.0486476i	$0.0154911\pi$
$168$	−3.49437	−	2.01747i	−0.269596	−	0.155651i
$169$	6.30829	−	10.9263i	0.485253	−	0.840483i
$170$	0.0820878	+	0.193181i	0.00629584	+	0.0148163i
$171$	−0.504306	−	4.32963i	−0.0385652	−	0.331095i
$172$			4.58649i			0.349717i
$173$	20.0963	+	11.6026i	1.52790	+	0.882132i	0.999450	+	0.0331655i	$0.0105588\pi$
$173$	20.0963	+	11.6026i	1.52790	+	0.882132i	0.528447	+	0.848966i	$0.322774\pi$
$174$	2.10491	−	3.64581i	0.159573	−	0.276388i
$175$	4.86573	−	19.5792i	0.367815	−	1.48005i
$176$	0.735269	−	1.27352i	0.0554230	−	0.0959955i
$177$	5.32777	−	3.07599i	0.400460	−	0.231206i
$178$		−	1.62769i		−	0.122001i
$179$	−6.37559			−0.476534			−0.238267	−	0.971200i	$-0.576579\pi$
$179$	−6.37559			−0.476534			−0.238267	+	0.971200i	$0.576579\pi$
$180$	−1.34502	+	1.78632i	−0.100252	+	0.133144i
$181$	4.39603	+	7.61415i	0.326755	+	0.565955i	0.981866	−	0.189577i	$-0.0607116\pi$
$181$	4.39603	+	7.61415i	0.326755	+	0.565955i	−0.655111	+	0.755532i	$0.727378\pi$
$182$		−	20.4220i		−	1.51378i
$183$		−	1.30744i		−	0.0966491i
$184$	1.28274	+	2.22178i	0.0945652	+	0.163792i
$185$	0.417831	−	3.41376i	0.0307196	−	0.250985i
$186$	−2.13279	−	3.69410i	−0.156384	−	0.270864i
$187$	−0.119545	−	0.0690193i	−0.00874200	−	0.00504719i
$188$	−3.49530	−	2.01801i	−0.254921	−	0.147179i
$189$	−4.03495			−0.293499
$190$	−4.82406	−	8.46926i	−0.349974	−	0.614425i
$191$	12.9659			0.938177			0.469088	−	0.883151i	$-0.344583\pi$
$191$	12.9659			0.938177			0.469088	+	0.883151i	$0.344583\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	5.29710	+	3.05828i	0.381294	+	0.220140i	0.678381	−	0.734710i	$-0.262682\pi$
$193$	5.29710	+	3.05828i	0.381294	+	0.220140i	−0.297087	+	0.954850i	$0.596015\pi$
$194$	−5.97438	−	10.3479i	−0.428936	−	0.742939i
$195$	−11.2335	−	1.37494i	−0.804451	−	0.0984617i
$196$	−4.64040	−	8.03741i	−0.331457	−	0.574101i
$197$		−	7.34941i		−	0.523624i	−0.965119	−	0.261812i	$-0.915680\pi$
$197$		−	7.34941i		−	0.523624i	0.965119	−	0.261812i	$-0.0843200\pi$
$198$		−	1.47054i		−	0.104507i
$199$	1.71780	+	2.97531i	0.121771	+	0.210914i	0.920466	−	0.390822i	$-0.127809\pi$
$199$	1.71780	+	2.97531i	0.121771	+	0.210914i	−0.798695	+	0.601736i	$0.794476\pi$
$200$	−1.20590	+	4.85240i	−0.0852698	+	0.343117i
$201$	10.7524			0.758417
$202$		−	0.504207i		−	0.0354759i
$203$	14.7107	−	8.49321i	1.03249	−	0.596106i
$204$	0.0469347	−	0.0812933i	0.00328609	−	0.00569167i
$205$	−10.4406	+	13.8662i	−0.729205	+	0.968458i
$206$	2.66899	−	4.62282i	0.185957	−	0.322087i
$207$	2.22178	+	1.28274i	0.154424	+	0.0891569i
$208$			5.06128i			0.350937i
$209$	5.88469	+	2.54120i	0.407052	+	0.175778i
$210$	−8.30383	+	3.52852i	−0.573019	+	0.243491i
$211$	2.01970	−	3.49822i	0.139042	−	0.240827i	−0.788092	−	0.615557i	$-0.788931\pi$
$211$	2.01970	−	3.49822i	0.139042	−	0.240827i	0.927134	+	0.374730i	$0.122264\pi$
$212$	9.22964	+	5.32873i	0.633894	+	0.365979i
$213$	−7.51373	+	4.33806i	−0.514833	+	0.297239i
$214$	−8.96375	+	15.5257i	−0.612749	+	1.06131i
$215$	8.19293	+	6.16891i	0.558754	+	0.420716i
$216$	1.00000			0.0680414
$217$		−	17.2114i		−	1.16838i
$218$	−7.68392	+	4.43631i	−0.520421	+	0.300465i
$219$	6.35711	+	11.0108i	0.429574	+	0.744044i
$220$	−1.28597	−	3.02634i	−0.0867001	−	0.204035i
$221$	0.475100			0.0319587
$222$	−1.33201	+	0.769037i	−0.0893987	+	0.0516144i
$223$	15.6334	+	9.02593i	1.04689	+	0.604421i	0.921776	−	0.387722i	$-0.126738\pi$
$223$	15.6334	+	9.02593i	1.04689	+	0.604421i	0.125111	+	0.992143i	$0.460071\pi$
$224$	2.01747	+	3.49437i	0.134798	+	0.233477i
$225$	1.38186	+	4.80525i	0.0921243	+	0.320350i
$226$	−7.93334	+	13.7409i	−0.527718	+	0.914034i
$227$		−	26.8513i		−	1.78219i	−0.453820	−	0.891093i	$-0.649939\pi$
$227$		−	26.8513i		−	1.78219i	0.453820	−	0.891093i	$-0.350061\pi$
$228$	−1.72807	+	4.00172i	−0.114444	+	0.265020i
$229$	13.7131			0.906190			0.453095	−	0.891462i	$-0.350320\pi$
$229$	13.7131			0.906190			0.453095	+	0.891462i	$0.350320\pi$
$230$	5.69412	+	0.696938i	0.375459	+	0.0459548i
$231$	2.96677	−	5.13860i	0.195199	−	0.338095i
$232$	−3.64581	+	2.10491i	−0.239359	+	0.138194i
$233$	0.00572506	+	0.00330537i	0.000375061	+	0.000216542i	0.500188	−	0.865917i	$-0.333264\pi$
$233$	0.00572506	+	0.00330537i	0.000375061	+	0.000216542i	−0.499812	+	0.866134i	$0.666598\pi$
$234$	2.53064	+	4.38320i	0.165433	+	0.286539i
$235$	−8.30605	+	3.52946i	−0.541827	+	0.230237i
$236$	−6.15198			−0.400460
$237$	11.2256	−	6.48112i	0.729183	−	0.420994i
$238$	0.328014	−	0.189379i	0.0212620	−	0.0122756i
$239$	4.67499			0.302400			0.151200	−	0.988503i	$-0.451686\pi$
$239$	4.67499			0.302400			0.151200	+	0.988503i	$0.451686\pi$
$240$	2.05798	−	0.874489i	0.132842	−	0.0564480i
$241$	13.9044	+	24.0831i	0.895659	+	1.55133i	0.832987	+	0.553292i	$0.186629\pi$
$241$	13.9044	+	24.0831i	0.895659	+	1.55133i	0.0626717	+	0.998034i	$0.480038\pi$
$242$	−7.65351	−	4.41876i	−0.491986	−	0.284049i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−0.653722	+	1.13228i	−0.0418503	+	0.0724868i
$245$	−20.5988	−	2.52121i	−1.31601	−	0.161074i
$246$	7.76245			0.494916
$247$	−21.9135	+	2.55244i	−1.39432	+	0.162408i
$248$			4.26558i			0.270864i
$249$	1.03164	−	1.78686i	0.0653776	−	0.113237i
$250$	7.04598	+	8.68068i	0.445627	+	0.549014i
$251$	3.03259	+	5.25259i	0.191415	+	0.331541i	0.945719	−	0.324984i	$-0.105359\pi$
$251$	3.03259	+	5.25259i	0.191415	+	0.331541i	−0.754304	+	0.656525i	$0.772026\pi$
$252$	3.49437	+	2.01747i	0.220124	+	0.127089i
$253$	−3.26721	+	1.88633i	−0.205408	+	0.118592i
$254$	−6.66597			−0.418260
$255$	−0.0820878	−	0.193181i	−0.00514054	−	0.0120975i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.11707	−	0.644941i	0.0696809	−	0.0402303i	−0.464755	−	0.885439i	$-0.653858\pi$
$257$	1.11707	−	0.644941i	0.0696809	−	0.0402303i	0.534436	+	0.845209i	$0.320524\pi$
$258$		−	4.58649i		−	0.285543i
$259$	−6.20604			−0.385625
$260$	9.04106	+	6.80751i	0.560703	+	0.422184i
$261$	−2.10491	+	3.64581i	−0.130291	+	0.225670i
$262$	−6.12771	+	3.53784i	−0.378571	+	0.218568i
$263$	−24.4863	−	14.1372i	−1.50989	−	0.871737i	−0.999933	−	0.0115378i	$-0.996327\pi$
$263$	−24.4863	−	14.1372i	−1.50989	−	0.871737i	−0.509959	−	0.860199i	$-0.670339\pi$
$264$	−0.735269	+	1.27352i	−0.0452527	+	0.0783800i
$265$	21.9328	−	9.31984i	1.34732	−	0.572513i
$266$	−14.1119	+	10.4971i	−0.865255	+	0.643621i
$267$			1.62769i			0.0996131i
$268$	−9.31187	−	5.37621i	−0.568813	−	0.328404i
$269$	−13.8782	+	24.0377i	−0.846169	+	1.46561i	0.0384337	+	0.999261i	$0.487763\pi$
$269$	−13.8782	+	24.0377i	−0.846169	+	1.46561i	−0.884602	+	0.466346i	$0.845570\pi$
$270$	1.34502	−	1.78632i	0.0818551	−	0.108712i
$271$	−5.42826	+	9.40202i	−0.329743	+	0.571132i	−0.982461	−	0.186469i	$-0.940296\pi$
$271$	−5.42826	+	9.40202i	−0.329743	+	0.571132i	0.652718	+	0.757601i	$0.273629\pi$
$272$	−0.0812933	+	0.0469347i	−0.00492913	+	0.00284584i
$273$			20.4220i			1.23600i
$274$	−18.8565			−1.13916
$275$	−7.13565	−	1.77332i	−0.430296	−	0.106935i
$276$	−1.28274	−	2.22178i	−0.0772122	−	0.133735i
$277$		−	24.5237i		−	1.47349i	−0.676173	−	0.736743i	$-0.736363\pi$
$277$		−	24.5237i		−	1.47349i	0.676173	−	0.736743i	$-0.263637\pi$
$278$		−	19.9923i		−	1.19906i
$279$	2.13279	+	3.69410i	0.127687	+	0.221160i
$280$	8.95558	+	1.09613i	0.535199	+	0.0655063i
$281$	3.29709	+	5.71073i	0.196688	+	0.340674i	0.947453	−	0.319896i	$-0.103648\pi$
$281$	3.29709	+	5.71073i	0.196688	+	0.340674i	−0.750765	+	0.660570i	$0.770315\pi$
$282$	3.49530	+	2.01801i	0.208142	+	0.120171i
$283$	20.4709	+	11.8189i	1.21687	+	0.702559i	0.964247	−	0.265006i	$-0.0853740\pi$
$283$	20.4709	+	11.8189i	1.21687	+	0.702559i	0.252621	+	0.967565i	$0.418707\pi$
$284$	8.67611			0.514833
$285$	4.82406	+	8.46926i	0.285753	+	0.501676i
$286$	−7.44281			−0.440103
$287$	27.1248	+	15.6605i	1.60113	+	0.924412i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	−8.49559	−	14.7148i	−0.499741	−	0.865577i
$290$	−1.14364	+	9.34372i	−0.0671567	+	0.548682i
$291$	5.97438	+	10.3479i	0.350225	+	0.606607i
$292$		−	12.7142i		−	0.744044i
$293$		−	23.0123i		−	1.34439i	−0.740374	−	0.672195i	$-0.765352\pi$
$293$		−	23.0123i		−	1.34439i	0.740374	−	0.672195i	$-0.234648\pi$
$294$	4.64040	+	8.03741i	0.270634	+	0.468751i
$295$	−8.27451	+	10.9894i	−0.481761	+	0.639827i
$296$	1.53807			0.0893987
$297$			1.47054i			0.0853293i
$298$	10.5724	−	6.10397i	0.612442	−	0.353593i
$299$	6.49233	−	11.2451i	0.375461	−	0.650318i
$300$	1.20590	−	4.85240i	0.0696225	−	0.280154i
$301$	9.25313	−	16.0269i	0.533341	−	0.923774i
$302$	17.2433	+	9.95543i	0.992241	+	0.572870i
$303$			0.504207i			0.0289659i
$304$	3.49741	−	2.60156i	0.200590	−	0.149209i
$305$	1.14335	+	2.69069i	0.0654678	+	0.154068i
$306$	−0.0469347	+	0.0812933i	−0.00268308	+	0.00464723i
$307$	22.0807	+	12.7483i	1.26021	+	0.727584i	0.973116	−	0.230318i	$-0.0739765\pi$
$307$	22.0807	+	12.7483i	1.26021	+	0.727584i	0.287097	+	0.957902i	$0.407310\pi$
$308$	−5.13860	+	2.96677i	−0.292799	+	0.169048i
$309$	−2.66899	+	4.62282i	−0.151833	+	0.262983i
$310$	7.61968	+	5.73727i	0.432768	+	0.325855i
$311$	−30.3172			−1.71913			−0.859565	−	0.511027i	$-0.829265\pi$
$311$	−30.3172			−1.71913			−0.859565	+	0.511027i	$0.829265\pi$
$312$		−	5.06128i		−	0.286539i
$313$	−6.54063	+	3.77623i	−0.369698	+	0.213445i	−0.673327	−	0.739345i	$-0.735135\pi$
$313$	−6.54063	+	3.77623i	−0.369698	+	0.213445i	0.303628	+	0.952791i	$0.401802\pi$
$314$	−8.11721	−	14.0594i	−0.458081	−	0.793419i
$315$	8.30383	−	3.52852i	0.467868	−	0.198809i
$316$	−12.9622			−0.729183
$317$	12.1344	−	7.00579i	0.681535	−	0.393484i	−0.118898	−	0.992906i	$-0.537936\pi$
$317$	12.1344	−	7.00579i	0.681535	−	0.393484i	0.800433	+	0.599422i	$0.204603\pi$
$318$	−9.22964	−	5.32873i	−0.517572	−	0.298821i
$319$	−3.09535	−	5.36131i	−0.173307	−	0.300176i
$320$	−2.21950	−	0.271659i	−0.124074	−	0.0151862i
$321$	8.96375	−	15.5257i	0.500308	−	0.866558i
$322$		−	10.3516i		−	0.576873i
$323$	−0.244207	−	0.328300i	−0.0135880	−	0.0182671i
$324$	−1.00000			−0.0555556
$325$	24.3207	−	6.99400i	1.34907	−	0.387957i
$326$	−1.02875	+	1.78185i	−0.0569773	+	0.0986875i
$327$	7.68392	−	4.43631i	0.424922	−	0.245329i
$328$	−6.72248	−	3.88123i	−0.371187	−	0.214305i
$329$	8.14258	+	14.1034i	0.448915	+	0.777544i
$330$	1.28597	+	3.02634i	0.0707903	+	0.166594i
$331$	−2.20541			−0.121220			−0.0606102	−	0.998162i	$-0.519305\pi$
$331$	−2.20541			−0.121220			−0.0606102	+	0.998162i	$0.519305\pi$
$332$	−1.78686	+	1.03164i	−0.0980665	+	0.0566187i
$333$	1.33201	−	0.769037i	0.0729937	−	0.0421429i
$334$	21.7279			1.18890
$335$	−22.1282	+	9.40287i	−1.20899	+	0.513734i
$336$	−2.01747	−	3.49437i	−0.110062	−	0.190633i
$337$	3.35026	+	1.93428i	0.182500	+	0.105367i	0.588467	−	0.808521i	$-0.299732\pi$
$337$	3.35026	+	1.93428i	0.182500	+	0.105367i	−0.405966	+	0.913888i	$0.633065\pi$
$338$	10.9263	−	6.30829i	0.594311	−	0.343126i
$339$	7.93334	−	13.7409i	0.430880	−	0.746306i
$340$	−0.0255005	+	0.208344i	−0.00138296	+	0.0112990i
$341$	−6.27270			−0.339685
$342$	1.72807	−	4.00172i	0.0934434	−	0.216388i
$343$			9.20290i			0.496910i
$344$	−2.29325	+	3.97202i	−0.123644	+	0.214157i
$345$	−5.69412	−	0.696938i	−0.306561	−	0.0375219i
$346$	11.6026	+	20.0963i	0.623761	+	1.08039i
$347$	10.6406	+	6.14337i	0.571219	+	0.329793i	0.757636	−	0.652677i	$-0.226354\pi$
$347$	10.6406	+	6.14337i	0.571219	+	0.329793i	−0.186417	+	0.982471i	$0.559688\pi$
$348$	3.64581	−	2.10491i	0.195436	−	0.112835i
$349$	23.1329			1.23828			0.619139	−	0.785282i	$-0.287482\pi$
$349$	23.1329			1.23828			0.619139	+	0.785282i	$0.287482\pi$
$350$	14.0034	−	14.5232i	0.748515	−	0.776298i
$351$	−2.53064	−	4.38320i	−0.135076	−	0.233958i
$352$	1.27352	−	0.735269i	0.0678791	−	0.0391900i
$353$			2.27216i			0.120935i	0.998170	+	0.0604674i	$0.0192591\pi$
$353$			2.27216i			0.120935i	−0.998170	+	0.0604674i	$0.980741\pi$
$354$	6.15198			0.326974
$355$	11.6695	−	15.4983i	0.619353	−	0.822564i
$356$	0.813846	−	1.40962i	0.0431338	−	0.0747098i
$357$	−0.328014	+	0.189379i	−0.0173604	+	0.0100230i
$358$	−5.52142	−	3.18779i	−0.291816	−	0.168480i
$359$	−10.3404	+	17.9101i	−0.545746	+	0.945260i	0.452813	+	0.891605i	$0.350420\pi$
$359$	−10.3404	+	17.9101i	−0.545746	+	0.945260i	−0.998560	+	0.0536549i	$0.982913\pi$
$360$	−2.05798	+	0.874489i	−0.108465	+	0.0460896i
$361$	13.0275	+	13.8305i	0.685660	+	0.727922i
$362$			8.79207i			0.462101i
$363$	7.65351	+	4.41876i	0.401705	+	0.231925i
$364$	10.2110	−	17.6860i	0.535202	−	0.926997i
$365$	−22.7117	−	17.1008i	−1.18878	−	0.895099i
$366$	0.653722	−	1.13228i	0.0341706	−	0.0591852i
$367$	−31.7744	+	18.3450i	−1.65861	+	0.957600i	−0.685255	+	0.728304i	$0.740309\pi$
$367$	−31.7744	+	18.3450i	−1.65861	+	0.957600i	−0.973357	+	0.229296i	$0.926358\pi$
$368$			2.56549i			0.133735i
$369$	−7.76245			−0.404097
$370$	2.06873	−	2.74749i	0.107548	−	0.142835i
$371$	−21.5012	−	37.2411i	−1.11628	−	1.93346i
$372$		−	4.26558i		−	0.221160i
$373$		−	19.5380i		−	1.01164i	−0.862640	−	0.505819i	$-0.831190\pi$
$373$		−	19.5380i		−	1.01164i	0.862640	−	0.505819i	$-0.168810\pi$
$374$	−0.0690193	−	0.119545i	−0.00356890	−	0.00618152i
$375$	−7.04598	−	8.68068i	−0.363853	−	0.448268i
$376$	−2.01801	−	3.49530i	−0.104071	−	0.180256i
$377$	18.4525	+	10.6536i	0.950352	+	0.548686i
$378$	−3.49437	−	2.01747i	−0.179731	−	0.103768i
$379$	−3.46802			−0.178140			−0.0890701	−	0.996025i	$-0.528390\pi$
$379$	−3.46802			−0.178140			−0.0890701	+	0.996025i	$0.528390\pi$
$380$	0.0568730	−	9.74663i	0.00291752	−	0.499991i
$381$	6.66597			0.341508
$382$	11.2288	+	6.48293i	0.574514	+	0.331696i
$383$	−21.7388	−	12.5509i	−1.11080	−	0.641322i	−0.171765	−	0.985138i	$-0.554947\pi$
$383$	−21.7388	−	12.5509i	−1.11080	−	0.641322i	−0.939037	+	0.343816i	$0.888280\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−1.61190	+	13.1695i	−0.0821501	+	0.671182i
$386$	3.05828	+	5.29710i	0.155662	+	0.269615i
$387$			4.58649i			0.233145i
$388$		−	11.9488i		−	0.606607i
$389$	7.02074	+	12.1603i	0.355965	+	0.616550i	0.987283	−	0.158974i	$-0.0508188\pi$
$389$	7.02074	+	12.1603i	0.355965	+	0.616550i	−0.631317	+	0.775525i	$0.717485\pi$
$390$	−9.04106	−	6.80751i	−0.457812	−	0.344711i
$391$	0.240821			0.0121788
$392$		−	9.28080i		−	0.468751i
$393$	6.12771	−	3.53784i	0.309102	−	0.178460i
$394$	3.67471	−	6.36478i	0.185129	−	0.320653i
$395$	−17.4344	+	23.1547i	−0.877221	+	1.16504i
$396$	0.735269	−	1.27352i	0.0369487	−	0.0639970i
$397$	−26.6267	−	15.3729i	−1.33635	−	0.771544i	−0.350089	−	0.936716i	$-0.613849\pi$
$397$	−26.6267	−	15.3729i	−1.33635	−	0.771544i	−0.986265	+	0.165172i	$0.947182\pi$
$398$			3.43559i			0.172211i
$399$	14.1119	−	10.4971i	0.706478	−	0.525514i
$400$	−3.47054	+	3.59936i	−0.173527	+	0.179968i
$401$	−19.3518	+	33.5183i	−0.966381	+	1.67382i	−0.260525	+	0.965467i	$0.583896\pi$
$401$	−19.3518	+	33.5183i	−0.966381	+	1.67382i	−0.705857	+	0.708355i	$0.749438\pi$
$402$	9.31187	+	5.37621i	0.464434	+	0.268141i
$403$	18.6969	−	10.7946i	0.931357	−	0.537719i
$404$	0.252103	−	0.436656i	0.0125426	−	0.0217244i
$405$	−1.34502	+	1.78632i	−0.0668344	+	0.0887629i
$406$	16.9864			0.843022
$407$			2.26180i			0.112113i
$408$	0.0812933	−	0.0469347i	0.00402462	−	0.00232361i
$409$	−10.3920	−	17.9994i	−0.513850	−	0.890014i	−0.999871	−	0.0160671i	$-0.994885\pi$
$409$	−10.3920	−	17.9994i	−0.513850	−	0.890014i	0.486021	−	0.873947i	$-0.338448\pi$
$410$	−15.9749	+	6.78818i	−0.788946	+	0.335244i
$411$	18.8565			0.930123
$412$	4.62282	−	2.66899i	0.227750	−	0.131491i
$413$	21.4973	+	12.4115i	1.05781	+	0.610728i
$414$	1.28274	+	2.22178i	0.0630435	+	0.109194i
$415$	−0.560510	+	4.57947i	−0.0275143	+	0.224797i
$416$	−2.53064	+	4.38320i	−0.124075	+	0.214904i
$417$			19.9923i			0.979029i
$418$	3.82569	+	5.14308i	0.187121	+	0.251556i
$419$	36.2672			1.77177			0.885883	−	0.463908i	$-0.153553\pi$
$419$	36.2672			1.77177			0.885883	+	0.463908i	$0.153553\pi$
$420$	−8.95558	−	1.09613i	−0.436988	−	0.0534857i
$421$	10.7212	−	18.5697i	0.522519	−	0.905030i	−0.477137	−	0.878829i	$-0.658326\pi$
$421$	10.7212	−	18.5697i	0.522519	−	0.905030i	0.999657	−	0.0262013i	$-0.00834109\pi$
$422$	3.49822	−	2.01970i	0.170291	−	0.0983174i
$423$	−3.49530	−	2.01801i	−0.169947	−	0.0981192i
$424$	5.32873	+	9.22964i	0.258786	+	0.448231i
$425$	0.337869	+	0.325778i	0.0163891	+	0.0158025i
$426$	−8.67611			−0.420359
$427$	4.56869	−	2.63773i	0.221094	−	0.127649i
$428$	−15.5257	+	8.96375i	−0.750461	+	0.433279i
$429$	7.44281			0.359342
$430$	4.01084	+	9.43890i	0.193420	+	0.455184i
$431$	2.91216	+	5.04400i	0.140274	+	0.242961i	0.927600	−	0.373576i	$-0.121868\pi$
$431$	2.91216	+	5.04400i	0.140274	+	0.242961i	−0.787326	+	0.616537i	$0.788535\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	27.3690	−	15.8015i	1.31527	−	0.759371i	0.332305	−	0.943172i	$-0.392174\pi$
$433$	27.3690	−	15.8015i	1.31527	−	0.759371i	0.982963	+	0.183801i	$0.0588403\pi$
$434$	8.60569	−	14.9055i	0.413086	−	0.715486i
$435$	1.14364	−	9.34372i	0.0548332	−	0.447997i
$436$	−8.87262			−0.424922
$437$	−11.1076	+	1.29379i	−0.531349	+	0.0618904i
$438$			12.7142i			0.607509i
$439$	−0.932951	+	1.61592i	−0.0445273	+	0.0771236i	−0.887430	−	0.460942i	$-0.847512\pi$
$439$	−0.932951	+	1.61592i	−0.0445273	+	0.0771236i	0.842903	+	0.538066i	$0.180845\pi$
$440$	0.399485	−	3.26387i	0.0190447	−	0.155599i
$441$	−4.64040	−	8.03741i	−0.220971	−	0.382734i
$442$	0.411448	+	0.237550i	0.0195706	+	0.0112991i
$443$	−13.6368	+	7.87318i	−0.647902	+	0.374066i	−0.787652	−	0.616121i	$-0.788703\pi$
$443$	−13.6368	+	7.87318i	−0.647902	+	0.374066i	0.139750	+	0.990187i	$0.455370\pi$
$444$	−1.53807			−0.0729937
$445$	−1.42340	−	3.34975i	−0.0674755	−	0.158794i
$446$	9.02593	+	15.6334i	0.427390	+	0.740262i
$447$	−10.5724	+	6.10397i	−0.500056	+	0.288708i
$448$			4.03495i			0.190633i
$449$	−29.7436			−1.40369			−0.701845	−	0.712330i	$-0.747640\pi$
$449$	−29.7436			−1.40369			−0.701845	+	0.712330i	$0.747640\pi$
$450$	−1.20590	+	4.85240i	−0.0568465	+	0.228744i
$451$	5.70749	−	9.88567i	0.268755	−	0.465498i
$452$	−13.7409	+	7.93334i	−0.646320	+	0.373153i
$453$	−17.2433	−	9.95543i	−0.810161	−	0.467747i
$454$	13.4257	−	23.2539i	0.630098	−	1.09136i
$455$	−17.8588	−	42.0280i	−0.837234	−	1.97030i
$456$	−3.49741	+	2.60156i	−0.163781	+	0.121829i
$457$			12.7891i			0.598250i	0.954214	+	0.299125i	$0.0966948\pi$
$457$			12.7891i			0.598250i	−0.954214	+	0.299125i	$0.903305\pi$
$458$	11.8759	+	6.85657i	0.554926	+	0.320387i
$459$	0.0469347	−	0.0812933i	0.00219073	−	0.00379445i
$460$	4.58278	+	3.45062i	0.213673	+	0.160886i
$461$	5.96303	−	10.3283i	0.277726	−	0.481035i	−0.693093	−	0.720848i	$-0.743753\pi$
$461$	5.96303	−	10.3283i	0.277726	−	0.481035i	0.970819	+	0.239813i	$0.0770860\pi$
$462$	5.13860	−	2.96677i	0.239069	−	0.138027i
$463$			19.3208i			0.897913i	0.893554	+	0.448956i	$0.148204\pi$
$463$			19.3208i			0.897913i	−0.893554	+	0.448956i	$0.851796\pi$
$464$	−4.20982			−0.195436
$465$	−7.61968	−	5.73727i	−0.353354	−	0.266059i
$466$	0.00330537	+	0.00572506i	0.000153118	+	0.000265208i
$467$		−	26.7009i		−	1.23557i	−0.786347	−	0.617785i	$-0.788030\pi$
$467$		−	26.7009i		−	1.23557i	0.786347	−	0.617785i	$-0.211970\pi$
$468$			5.06128i			0.233958i
$469$	21.6927	+	37.5729i	1.00168	+	1.73496i
$470$	−8.95798	−	1.09642i	−0.413201	−	0.0505742i
$471$	8.11721	+	14.0594i	0.374021	+	0.647824i
$472$	−5.32777	−	3.07599i	−0.245231	−	0.141584i
$473$	−5.84101	−	3.37231i	−0.268570	−	0.155059i
$474$	12.9622			0.595375
$475$	−17.3341	−	13.2110i	−0.795342	−	0.606161i
$476$	0.378758			0.0173604
$477$	9.22964	+	5.32873i	0.422596	+	0.243986i
$478$	4.04866	+	2.33750i	0.185182	+	0.106915i
$479$	−6.79124	−	11.7628i	−0.310299	−	0.537454i	0.668128	−	0.744047i	$-0.267096\pi$
$479$	−6.79124	−	11.7628i	−0.310299	−	0.537454i	−0.978427	+	0.206592i	$0.933763\pi$
$480$	2.21950	+	0.271659i	0.101306	+	0.0123995i
$481$	−3.89231	−	6.74168i	−0.177474	−	0.307394i
$482$			27.8087i			1.26665i
$483$			10.3516i			0.471015i
$484$	−4.41876	−	7.65351i	−0.200853	−	0.347887i
$485$	−21.3443	−	16.0713i	−0.969195	−	0.729760i
$486$	1.00000			0.0453609
$487$		−	8.03640i		−	0.364164i	−0.983283	−	0.182082i	$-0.941716\pi$
$487$		−	8.03640i		−	0.364164i	0.983283	−	0.182082i	$-0.0582837\pi$
$488$	−1.13228	+	0.653722i	−0.0512559	+	0.0295926i
$489$	1.02875	−	1.78185i	0.0465217	−	0.0805780i
$490$	−16.5785	−	12.4828i	−0.748938	−	0.563916i
$491$	10.3390	−	17.9077i	0.466593	−	0.808163i	−0.532679	−	0.846317i	$-0.678815\pi$
$491$	10.3390	−	17.9077i	0.466593	−	0.808163i	0.999272	+	0.0381546i	$0.0121479\pi$
$492$	6.72248	+	3.88123i	0.303073	+	0.174979i
$493$			0.395174i			0.0177977i
$494$	−20.2538	−	8.74626i	−0.911263	−	0.393513i
$495$	−1.28597	−	3.02634i	−0.0578000	−	0.136024i
$496$	−2.13279	+	3.69410i	−0.0957650	+	0.165870i
$497$	−30.3175	−	17.5038i	−1.35993	−	0.785154i
$498$	1.78686	−	1.03164i	0.0800709	−	0.0462290i
$499$	−0.551160	+	0.954638i	−0.0246733	+	0.0427355i	−0.878098	−	0.478480i	$-0.841188\pi$
$499$	−0.551160	+	0.954638i	−0.0246733	+	0.0427355i	0.853425	+	0.521216i	$0.174521\pi$
$500$	1.76166	+	11.0407i	0.0787840	+	0.493754i
$501$	−21.7279			−0.970729
$502$			6.06517i			0.270702i
$503$	21.0518	−	12.1543i	0.938653	−	0.541932i	0.0491154	−	0.998793i	$-0.484360\pi$
$503$	21.0518	−	12.1543i	0.938653	−	0.541932i	0.889538	+	0.456861i	$0.151026\pi$
$504$	2.01747	+	3.49437i	0.0898654	+	0.155651i
$505$	−0.440923	−	1.03765i	−0.0196208	−	0.0461746i
$506$	−3.77265			−0.167715
$507$	−10.9263	+	6.30829i	−0.485253	+	0.280161i
$508$	−5.77290	−	3.33298i	−0.256131	−	0.147877i
$509$	−4.96728	−	8.60358i	−0.220171	−	0.381347i	0.734689	−	0.678404i	$-0.237328\pi$
$509$	−4.96728	−	8.60358i	−0.220171	−	0.381347i	−0.954860	+	0.297057i	$0.903995\pi$
$510$	0.0255005	−	0.208344i	0.00112918	−	0.00922561i
$511$	−25.6506	+	44.4282i	−1.13472	+	1.96539i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.72807	+	4.00172i	−0.0762962	+	0.176680i
$514$	1.28988			0.0568942
$515$	1.45011	−	11.8477i	0.0638994	−	0.522070i
$516$	2.29325	−	3.97202i	0.100955	−	0.174858i
$517$	5.13998	−	2.96757i	0.226056	−	0.130513i
$518$	−5.37459	−	3.10302i	−0.236146	−	0.136339i
$519$	−11.6026	−	20.0963i	−0.509299	−	0.882132i
$520$	4.42603	+	10.4160i	0.194094	+	0.456772i
$521$	−20.9057			−0.915895			−0.457947	−	0.888979i	$-0.651415\pi$
$521$	−20.9057			−0.915895			−0.457947	+	0.888979i	$0.651415\pi$
$522$	−3.64581	+	2.10491i	−0.159573	+	0.0921295i
$523$	27.3676	−	15.8007i	1.19670	−	0.690916i	0.236883	−	0.971538i	$-0.423874\pi$
$523$	27.3676	−	15.8007i	1.19670	−	0.690916i	0.959818	+	0.280622i	$0.0905408\pi$
$524$	−7.07568			−0.309102
$525$	−14.0034	+	14.5232i	−0.611160	+	0.633845i
$526$	−14.1372	−	24.4863i	−0.616411	−	1.06766i
$527$	0.346763	+	0.200204i	0.0151052	+	0.00872101i
$528$	−1.27352	+	0.735269i	−0.0554230	+	0.0319985i
$529$	−8.20913	+	14.2186i	−0.356919	+	0.618202i
$530$	23.6543	+	2.89520i	1.02748	+	0.125759i
$531$	−6.15198			−0.266973
$532$	−17.4698	+	2.03485i	−0.757413	+	0.0882218i
$533$			39.2880i			1.70175i
$534$	−0.813846	+	1.40962i	−0.0352186	+	0.0610003i
$535$	−4.87017	+	39.7902i	−0.210556	+	1.72028i
$536$	−5.37621	−	9.31187i	−0.232217	−	0.402211i
$537$	5.52142	+	3.18779i	0.238267	+	0.137563i
$538$	−24.0377	+	13.8782i	−1.03634	+	0.598332i
$539$	13.6478			0.587851
$540$	2.05798	−	0.874489i	0.0885612	−	0.0376320i
$541$	−2.50615	−	4.34078i	−0.107748	−	0.186625i	0.807110	−	0.590402i	$-0.201031\pi$
$541$	−2.50615	−	4.34078i	−0.107748	−	0.186625i	−0.914858	+	0.403777i	$0.867697\pi$
$542$	−9.40202	+	5.42826i	−0.403851	+	0.233164i
$543$		−	8.79207i		−	0.377304i
$544$	−0.0938694			−0.00402462
$545$	−11.9338	+	15.8493i	−0.511189	+	0.678911i
$546$	−10.2110	+	17.6860i	−0.436991	+	0.756890i
$547$	−30.7554	+	17.7566i	−1.31500	+	0.759218i	−0.982920	−	0.184032i	$-0.941085\pi$
$547$	−30.7554	+	17.7566i	−1.31500	+	0.759218i	−0.332084	+	0.943250i	$0.607752\pi$
$548$	−16.3302	−	9.42826i	−0.697593	−	0.402755i
$549$	−0.653722	+	1.13228i	−0.0279002	+	0.0483245i
$550$	−5.29299	−	5.10356i	−0.225694	−	0.217617i
$551$	−2.12304	−	18.2270i	−0.0904445	−	0.776495i
$552$		−	2.56549i		−	0.109194i
$553$	45.2948	+	26.1510i	1.92613	+	1.11205i
$554$	12.2618	−	21.2381i	0.520956	−	0.902322i
$555$	−2.06873	+	2.74749i	−0.0878128	+	0.116624i
$556$	9.99616	−	17.3139i	0.423932	−	0.734271i
$557$	−8.45640	+	4.88231i	−0.358309	+	0.206870i	−0.668339	−	0.743857i	$-0.732994\pi$
$557$	−8.45640	+	4.88231i	−0.358309	+	0.206870i	0.310030	+	0.950727i	$0.399661\pi$
$558$			4.26558i			0.180576i
$559$	23.2135			0.981828
$560$	7.20770	+	5.42707i	0.304581	+	0.229336i
$561$	0.0690193	+	0.119545i	0.00291400	+	0.00504719i
$562$			6.59418i			0.278159i
$563$		−	11.5237i		−	0.485665i	−0.970068	−	0.242833i	$-0.921923\pi$
$563$		−	11.5237i		−	0.485665i	0.970068	−	0.242833i	$-0.0780766\pi$
$564$	2.01801	+	3.49530i	0.0849737	+	0.147179i
$565$	−4.31033	+	35.2162i	−0.181337	+	1.48156i
$566$	11.8189	+	20.4709i	0.496784	+	0.860456i
$567$	3.49437	+	2.01747i	0.146750	+	0.0847259i
$568$	7.51373	+	4.33806i	0.315269	+	0.182021i
$569$	−1.93925			−0.0812978			−0.0406489	−	0.999173i	$-0.512943\pi$
$569$	−1.93925			−0.0812978			−0.0406489	+	0.999173i	$0.512943\pi$
$570$	−0.0568730	+	9.74663i	−0.00238215	+	0.408241i
$571$	−38.0052			−1.59047			−0.795235	−	0.606301i	$-0.792652\pi$
$571$	−38.0052			−1.59047			−0.795235	+	0.606301i	$0.792652\pi$
$572$	−6.44566	−	3.72141i	−0.269507	−	0.155600i
$573$	−11.2288	−	6.48293i	−0.469088	−	0.270828i
$574$	15.6605	+	27.1248i	0.653658	+	1.13217i
$575$	12.3278	−	3.54516i	0.514106	−	0.147843i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$		−	28.3094i		−	1.17854i	−0.807938	−	0.589268i	$-0.799416\pi$
$577$		−	28.3094i		−	1.17854i	0.807938	−	0.589268i	$-0.200584\pi$
$578$		−	16.9912i		−	0.706740i
$579$	−3.05828	−	5.29710i	−0.127098	−	0.220140i
$580$	−5.66228	+	7.52008i	−0.235113	+	0.312254i
$581$	8.32524			0.345389
$582$			11.9488i			0.495292i
$583$	−13.5725	+	7.83611i	−0.562117	+	0.324539i
$584$	6.35711	−	11.0108i	0.263059	−	0.455632i
$585$	9.04106	+	6.80751i	0.373802	+	0.281456i
$586$	11.5061	−	19.9292i	0.475314	−	0.823267i
$587$	9.39980	+	5.42698i	0.387971	+	0.223995i	0.681281	−	0.732022i	$-0.261423\pi$
$587$	9.39980	+	5.42698i	0.387971	+	0.223995i	−0.293309	+	0.956018i	$0.594757\pi$
$588$			9.28080i			0.382734i
$589$	−17.0696	−	7.37122i	−0.703342	−	0.303726i
$590$	−12.6606	+	5.37984i	−0.521230	+	0.221484i
$591$	−3.67471	+	6.36478i	−0.151157	+	0.261812i
$592$	1.33201	+	0.769037i	0.0547453	+	0.0316072i
$593$	−24.0190	+	13.8674i	−0.986341	+	0.569464i	−0.904179	−	0.427155i	$-0.859516\pi$
$593$	−24.0190	+	13.8674i	−0.986341	+	0.569464i	−0.0821625	+	0.996619i	$0.526183\pi$
$594$	−0.735269	+	1.27352i	−0.0301685	+	0.0522533i
$595$	0.509436	−	0.676583i	0.0208848	−	0.0277372i
$596$	12.2079			0.500056
$597$		−	3.43559i		−	0.140609i
$598$	11.2451	−	6.49233i	0.459844	−	0.265491i
$599$	15.6071	+	27.0323i	0.637690	+	1.10451i	0.985938	+	0.167109i	$0.0534433\pi$
$599$	15.6071	+	27.0323i	0.637690	+	1.10451i	−0.348248	+	0.937402i	$0.613223\pi$
$600$	3.47054	−	3.59936i	0.141684	−	0.146943i
$601$	42.3271			1.72656			0.863280	−	0.504726i	$-0.168406\pi$
$601$	42.3271			1.72656			0.863280	+	0.504726i	$0.168406\pi$
$602$	16.0269	−	9.25313i	0.653207	−	0.377129i
$603$	−9.31187	−	5.37621i	−0.379209	−	0.218936i
$604$	9.95543	+	17.2433i	0.405081	+	0.701620i
$605$	−19.6149	−	2.40079i	−0.797459	−	0.0976060i
$606$	−0.252103	+	0.436656i	−0.0102410	+	0.0177379i
$607$		−	12.9882i		−	0.527176i	−0.964635	−	0.263588i	$-0.915094\pi$
$607$		−	12.9882i		−	0.527176i	0.964635	−	0.263588i	$-0.0849059\pi$
$608$	4.32963	−	0.504306i	0.175590	−	0.0204523i
$609$	−16.9864			−0.688324
$610$	−0.355179	+	2.90188i	−0.0143808	+	0.117494i
$611$	−10.2137	+	17.6907i	−0.413204	+	0.715690i
$612$	−0.0812933	+	0.0469347i	−0.00328609	+	0.00189722i
$613$	−23.2303	−	13.4120i	−0.938264	−	0.541707i	−0.0488484	−	0.998806i	$-0.515555\pi$
$613$	−23.2303	−	13.4120i	−0.938264	−	0.541707i	−0.889416	+	0.457099i	$0.848888\pi$
$614$	12.7483	+	22.0807i	0.514480	+	0.891105i
$615$	15.9749	−	6.78818i	0.644172	−	0.273726i
$616$	−5.93355			−0.239069
$617$	11.9663	−	6.90877i	0.481747	−	0.278136i	−0.239398	−	0.970922i	$-0.576950\pi$
$617$	11.9663	−	6.90877i	0.481747	−	0.278136i	0.721144	+	0.692785i	$0.243617\pi$
$618$	−4.62282	+	2.66899i	−0.185957	+	0.107362i
$619$	36.2091			1.45537			0.727684	−	0.685912i	$-0.240597\pi$
$619$	36.2091			1.45537			0.727684	+	0.685912i	$0.240597\pi$
$620$	3.73020	+	8.77846i	0.149808	+	0.352551i
$621$	−1.28274	−	2.22178i	−0.0514748	−	0.0891569i
$622$	−26.2555	−	15.1586i	−1.05275	−	0.607804i
$623$	−5.68775	+	3.28383i	−0.227875	+	0.131564i
$624$	2.53064	−	4.38320i	0.101307	−	0.175468i
$625$	22.0916	+	11.7030i	0.883665	+	0.468120i
$626$	−7.55247			−0.301857
$627$	−3.82569	−	5.14308i	−0.152783	−	0.205395i
$628$		−	16.2344i		−	0.647824i
$629$	0.0721890	−	0.125035i	0.00287837	−	0.00498547i
$630$	8.95558	+	1.09613i	0.356799	+	0.0436709i
$631$	−1.00438	−	1.73963i	−0.0399836	−	0.0692536i	0.845341	−	0.534227i	$-0.179397\pi$
$631$	−1.00438	−	1.73963i	−0.0399836	−	0.0692536i	−0.885325	+	0.464973i	$0.846064\pi$
$632$	−11.2256	−	6.48112i	−0.446532	−	0.257805i
$633$	−3.49822	+	2.01970i	−0.139042	+	0.0802758i
$634$	14.0116			0.556471
$635$	−13.7184	+	5.82932i	−0.544399	+	0.231329i
$636$	−5.32873	−	9.22964i	−0.211298	−	0.365979i
$637$	−40.6796	+	23.4864i	−1.61178	+	0.930564i
$638$		−	6.19071i		−	0.245093i
$639$	8.67611			0.343222
$640$	−1.78632	−	1.34502i	−0.0706104	−	0.0531664i
$641$	−8.04795	+	13.9395i	−0.317875	+	0.550575i	−0.980044	−	0.198779i	$-0.936302\pi$
$641$	−8.04795	+	13.9395i	−0.317875	+	0.550575i	0.662170	+	0.749354i	$0.269636\pi$
$642$	15.5257	−	8.96375i	0.612749	−	0.353771i
$643$	−34.6016	−	19.9773i	−1.36455	−	0.787826i	−0.374328	−	0.927296i	$-0.622127\pi$
$643$	−34.6016	−	19.9773i	−1.36455	−	0.787826i	−0.990226	+	0.139470i	$0.955460\pi$
$644$	5.17581	−	8.96476i	0.203955	−	0.353261i
$645$	−4.01084	−	9.43890i	−0.157927	−	0.371656i
$646$	−0.0473389	−	0.406420i	−0.00186252	−	0.0159904i
$647$			32.2985i			1.26979i	0.772600	+	0.634893i	$0.218956\pi$
$647$			32.2985i			1.26979i	−0.772600	+	0.634893i	$0.781044\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	4.52336	−	7.83470i	0.177558	−	0.307539i
$650$	24.5594	+	6.10339i	0.963298	+	0.239394i
$651$	−8.60569	+	14.9055i	−0.337283	+	0.584192i
$652$	−1.78185	+	1.02875i	−0.0697826	+	0.0402890i
$653$			25.3382i			0.991559i	0.868448	+	0.495780i	$0.165118\pi$
$653$			25.3382i			0.991559i	−0.868448	+	0.495780i	$0.834882\pi$
$654$	8.87262			0.346947
$655$	−9.51690	+	12.6394i	−0.371856	+	0.493862i
$656$	−3.88123	−	6.72248i	−0.151536	−	0.262469i
$657$		−	12.7142i		−	0.496029i
$658$			16.2852i			0.634862i
$659$	2.44914	+	4.24204i	0.0954051	+	0.165247i	0.909778	−	0.415096i	$-0.136252\pi$
$659$	2.44914	+	4.24204i	0.0954051	+	0.165247i	−0.814372	+	0.580343i	$0.802919\pi$
$660$	−0.399485	+	3.26387i	−0.0155499	+	0.127046i
$661$	−24.1271	−	41.7893i	−0.938435	−	1.62542i	−0.768391	−	0.639980i	$-0.778942\pi$
$661$	−24.1271	−	41.7893i	−0.938435	−	1.62542i	−0.170044	−	0.985437i	$-0.554391\pi$
$662$	−1.90994	−	1.10271i	−0.0742320	−	0.0428579i
$663$	−0.411448	−	0.237550i	−0.0159793	−	0.00922567i
$664$	−2.06328			−0.0800709
$665$	−19.8623	+	33.9436i	−0.770227	+	1.31627i
$666$	1.53807			0.0595991
$667$	9.35330	+	5.40013i	0.362161	+	0.209094i
$668$	18.8169	+	10.8639i	0.728047	+	0.420338i
$669$	−9.02593	−	15.6334i	−0.348963	−	0.604421i
$670$	−23.8650	−	2.92099i	−0.921987	−	0.112848i
$671$	−0.961324	−	1.66506i	−0.0371115	−	0.0642790i
$672$		−	4.03495i		−	0.155651i
$673$		−	11.3374i		−	0.437025i	−0.975834	−	0.218512i	$-0.929880\pi$
$673$		−	11.3374i		−	0.437025i	0.975834	−	0.218512i	$-0.0701204\pi$
$674$	1.93428	+	3.35026i	0.0745055	+	0.129047i
$675$	1.20590	−	4.85240i	0.0464150	−	0.186769i
$676$	12.6166			0.485253
$677$		−	30.8182i		−	1.18444i	−0.805776	−	0.592220i	$-0.798252\pi$
$677$		−	30.8182i		−	1.18444i	0.805776	−	0.592220i	$-0.201748\pi$
$678$	13.7409	−	7.93334i	0.527718	−	0.304678i
$679$	−24.1063	+	41.7534i	−0.925116	+	1.60235i
$680$	−0.126256	+	0.167681i	−0.00484169	+	0.00643026i
$681$	−13.4257	+	23.2539i	−0.514473	+	0.891093i
$682$	−5.43231	−	3.13635i	−0.208014	−	0.120097i
$683$			10.5683i			0.404386i	0.979346	+	0.202193i	$0.0648069\pi$
$683$			10.5683i			0.404386i	−0.979346	+	0.202193i	$0.935193\pi$
$684$	3.49741	−	2.60156i	0.133727	−	0.0994730i
$685$	−38.8063	+	16.4898i	−1.48271	+	0.630043i
$686$	−4.60145	+	7.96995i	−0.175684	+	0.304294i
$687$	−11.8759	−	6.85657i	−0.453095	−	0.261595i
$688$	−3.97202	+	2.29325i	−0.151432	+	0.0874292i
$689$	26.9702	−	46.7138i	1.02748	−	1.77965i
$690$	−4.58278	−	3.45062i	−0.174463	−	0.131363i
$691$	−0.570970			−0.0217207			−0.0108604	−	0.999941i	$-0.503457\pi$
$691$	−0.570970			−0.0217207			−0.0108604	+	0.999941i	$0.503457\pi$
$692$			23.2053i			0.882132i
$693$	−5.13860	+	2.96677i	−0.195199	+	0.112698i
$694$	6.14337	+	10.6406i	0.233199	+	0.403913i
$695$	−17.4831	−	41.1438i	−0.663171	−	1.56067i
$696$	4.20982			0.159573
$697$	−0.631035	+	0.364328i	−0.0239022	+	0.0137999i
$698$	20.0337	+	11.5665i	0.758287	+	0.437797i
$699$	−0.00330537	−	0.00572506i	−0.000125020	−	0.000216542i
$700$	19.3889	−	5.57575i	0.732833	−	0.210743i
$701$	3.36247	−	5.82398i	0.126999	−	0.219969i	−0.795514	−	0.605936i	$-0.792799\pi$
$701$	3.36247	−	5.82398i	0.126999	−	0.219969i	0.922513	+	0.385967i	$0.126132\pi$
$702$		−	5.06128i		−	0.191026i
$703$	−2.65790	+	6.15494i	−0.100245	+	0.232138i
$704$	1.47054			0.0554230
$705$	8.95798	+	1.09642i	0.337377	+	0.0412937i
$706$	−1.13608	+	1.96775i	−0.0427569	+	0.0740571i
$707$	−1.76188	+	1.01722i	−0.0662625	+	0.0382566i
$708$	5.32777	+	3.07599i	0.200230	+	0.115603i
$709$	−15.4517	−	26.7632i	−0.580302	−	1.00511i	−0.995443	−	0.0953554i	$-0.969601\pi$
$709$	−15.4517	−	26.7632i	−0.580302	−	1.00511i	0.415141	−	0.909757i	$-0.363732\pi$
$710$	17.8552	−	7.58716i	0.670095	−	0.284741i
$711$	−12.9622			−0.486122
$712$	1.40962	−	0.813846i	0.0528278	−	0.0305002i
$713$	9.47717	−	5.47164i	0.354923	−	0.204915i
$714$	−0.378758			−0.0141747
$715$	−15.3171	+	6.50866i	−0.572828	+	0.243410i
$716$	−3.18779	−	5.52142i	−0.119133	−	0.206345i
$717$	−4.04866	−	2.33750i	−0.151200	−	0.0872954i
$718$	−17.9101	+	10.3404i	−0.668400	+	0.385901i
$719$	−11.7185	+	20.2970i	−0.437025	+	0.756949i	−0.997458	−	0.0712504i	$-0.977301\pi$
$719$	−11.7185	+	20.2970i	−0.437025	+	0.756949i	0.560434	+	0.828199i	$0.310634\pi$
$720$	−2.21950	−	0.271659i	−0.0827161	−	0.0101241i
$721$	−21.5384			−0.802133
$722$	4.36691	+	18.4914i	0.162520	+	0.688177i
$723$		−	27.8087i		−	1.03422i
$724$	−4.39603	+	7.61415i	−0.163377	+	0.282978i
$725$	5.81740	+	20.2293i	0.216053	+	0.751296i
$726$	4.41876	+	7.65351i	0.163995	+	0.284049i
$727$	34.0238	+	19.6436i	1.26187	+	0.728543i	0.973437	−	0.228957i	$-0.0735314\pi$
$727$	34.0238	+	19.6436i	1.26187	+	0.728543i	0.288436	+	0.957499i	$0.406865\pi$
$728$	17.6860	−	10.2110i	0.655486	−	0.378445i
$729$	−1.00000			−0.0370370
$730$	−11.1184	−	26.1656i	−0.411512	−	0.968432i
$731$	0.215266	+	0.372851i	0.00796189	+	0.0137904i
$732$	1.13228	−	0.653722i	0.0418503	−	0.0241623i
$733$		−	45.2875i		−	1.67273i	−0.548171	−	0.836366i	$-0.684676\pi$
$733$		−	45.2875i		−	1.67273i	0.548171	−	0.836366i	$-0.315324\pi$
$734$	−36.6899			−1.35425
$735$	16.5785	+	12.4828i	0.611506	+	0.460436i
$736$	−1.28274	+	2.22178i	−0.0472826	+	0.0818959i
$737$	13.6935	−	7.90592i	0.504405	−	0.291218i
$738$	−6.72248	−	3.88123i	−0.247458	−	0.142870i
$739$	15.7422	−	27.2663i	0.579086	−	1.00301i	−0.416499	−	0.909136i	$-0.636743\pi$
$739$	15.7422	−	27.2663i	0.579086	−	1.00301i	0.995585	−	0.0938695i	$-0.0299237\pi$
$740$	3.16532	−	1.34503i	0.116359	−	0.0494442i
$741$	20.2538	+	8.74626i	0.744043	+	0.321302i
$742$		−	43.0023i		−	1.57866i
$743$	−40.4415	−	23.3489i	−1.48365	−	0.856587i	−0.483826	−	0.875164i	$-0.660753\pi$
$743$	−40.4415	−	23.3489i	−1.48365	−	0.856587i	−0.999827	+	0.0185770i	$0.994086\pi$
$744$	2.13279	−	3.69410i	0.0781918	−	0.135432i
$745$	16.4199	−	21.8073i	0.601577	−	0.798956i
$746$	9.76898	−	16.9204i	0.357668	−	0.619499i
$747$	−1.78686	+	1.03164i	−0.0653776	+	0.0377458i
$748$		−	0.138039i		−	0.00504719i
$749$	72.3365			2.64312
$750$	−1.76166	−	11.0407i	−0.0643268	−	0.403149i
$751$	−14.8807	−	25.7741i	−0.543004	−	0.940510i	−0.998730	−	0.0503901i	$-0.983954\pi$
$751$	−14.8807	−	25.7741i	−0.543004	−	0.940510i	0.455726	−	0.890120i	$-0.349380\pi$
$752$		−	4.03603i		−	0.147179i
$753$		−	6.06517i		−	0.221027i
$754$	10.6536	+	18.4525i	0.387980	+	0.672000i
$755$	44.1922	+	5.40896i	1.60832	+	0.196852i
$756$	−2.01747	−	3.49437i	−0.0733748	−	0.127089i
$757$	−11.2784	−	6.51161i	−0.409922	−	0.236668i	0.280834	−	0.959756i	$-0.409389\pi$
$757$	−11.2784	−	6.51161i	−0.409922	−	0.236668i	−0.690756	+	0.723088i	$0.742722\pi$
$758$	−3.00339	−	1.73401i	−0.109088	−	0.0629820i
$759$	3.77265			0.136939
$760$	4.92257	−	8.41239i	0.178560	−	0.305150i
$761$	43.4538			1.57520			0.787600	−	0.616187i	$-0.211324\pi$
$761$	43.4538			1.57520			0.787600	+	0.616187i	$0.211324\pi$
$762$	5.77290	+	3.33298i	0.209130	+	0.120741i
$763$	31.0042	+	17.9003i	1.12243	+	0.648034i
$764$	6.48293	+	11.2288i	0.234544	+	0.406242i
$765$	−0.0255005	+	0.208344i	−0.000921972	+	0.00753268i
$766$	−12.5509	−	21.7388i	−0.453483	−	0.785456i
$767$			31.1369i			1.12429i
$768$			1.00000i			0.0360844i
$769$	−23.6418	−	40.9487i	−0.852544	−	1.47665i	−0.878905	−	0.476996i	$-0.841725\pi$
$769$	−23.6418	−	40.9487i	−0.852544	−	1.47665i	0.0263617	−	0.999652i	$-0.491608\pi$
$770$	−7.98072	+	10.5992i	−0.287605	+	0.381969i
$771$	−1.28988			−0.0464539
$772$			6.11656i			0.220140i
$773$	11.4692	−	6.62172i	0.412517	−	0.238167i	−0.279354	−	0.960188i	$-0.590120\pi$
$773$	11.4692	−	6.62172i	0.412517	−	0.238167i	0.691871	+	0.722022i	$0.256787\pi$
$774$	−2.29325	+	3.97202i	−0.0824290	+	0.142771i
$775$	20.6983	+	5.14385i	0.743505	+	0.184772i
$776$	5.97438	−	10.3479i	0.214468	−	0.371469i
$777$	5.37459	+	3.10302i	0.192812	+	0.111320i
$778$			14.0415i			0.503411i
$779$	27.1485	−	20.1944i	0.972696	−	0.723541i
$780$	−4.42603	−	10.4160i	−0.158477	−	0.372953i
$781$	−6.37928	+	11.0492i	−0.228269	+	0.395373i
$782$	0.208557	+	0.120411i	0.00745799	+	0.00430587i
$783$	3.64581	−	2.10491i	0.130291	−	0.0752234i
$784$	4.64040	−	8.03741i	0.165729	−	0.287050i
$785$	−28.9999	−	21.8356i	−1.03505	−	0.779345i
$786$	7.07568			0.252381
$787$			21.7913i			0.776775i	0.921496	+	0.388388i	$0.126968\pi$
$787$			21.7913i			0.776775i	−0.921496	+	0.388388i	$0.873032\pi$
$788$	6.36478	−	3.67471i	0.226736	−	0.130906i
$789$	14.1372	+	24.4863i	0.503297	+	0.871737i
$790$	−26.6760	+	11.3353i	−0.949089	+	0.403293i
$791$	64.0212			2.27633
$792$	1.27352	−	0.735269i	0.0452527	−	0.0261267i
$793$	5.73079	+	3.30867i	0.203506	+	0.117494i
$794$	−15.3729	−	26.6267i	−0.545564	−	0.944945i
$795$	−23.6543	−	2.89520i	−0.838932	−	0.102682i
$796$	−1.71780	+	2.97531i	−0.0608857	+	0.105457i
$797$		−	14.8524i		−	0.526099i	−0.964782	−	0.263049i	$-0.915272\pi$
$797$		−	14.8524i		−	0.526099i	0.964782	−	0.263049i	$-0.0847283\pi$
$798$	17.4698	−	2.03485i	0.618425	−	0.0720328i
$799$	−0.378860			−0.0134031
$800$	−4.80525	+	1.38186i	−0.169891	+	0.0488563i
$801$	0.813846	−	1.40962i	0.0287558	−	0.0498066i
$802$	−33.5183	+	19.3518i	−1.18357	+	0.683335i
$803$	16.1919	+	9.34838i	0.571399	+	0.329897i
$804$	5.37621	+	9.31187i	0.189604	+	0.328404i
$805$	−9.05237	−	21.3034i	−0.319054	−	0.750846i
$806$	21.5893			0.760450
$807$	24.0377	−	13.8782i	0.846169	−	0.488536i
$808$	0.436656	−	0.252103i	0.0153615	−	0.00886897i
$809$	0.338772			0.0119106			0.00595530	−	0.999982i	$-0.498104\pi$
$809$	0.338772			0.0119106			0.00595530	+	0.999982i	$0.498104\pi$
$810$	−2.05798	+	0.874489i	−0.0723099	+	0.0307264i
$811$	−2.04652	−	3.54467i	−0.0718629	−	0.124470i	0.827855	−	0.560942i	$-0.189561\pi$
$811$	−2.04652	−	3.54467i	−0.0718629	−	0.124470i	−0.899718	+	0.436472i	$0.856228\pi$
$812$	14.7107	+	8.49321i	0.516243	+	0.298053i
$813$	9.40202	−	5.42826i	0.329743	−	0.190377i
$814$	−1.13090	+	1.95877i	−0.0396380	+	0.0686550i
$815$	−0.558939	+	4.56664i	−0.0195788	+	0.159962i
$816$	0.0938694			0.00328609
$817$	−11.9320	−	16.0409i	−0.417448	−	0.561199i
$818$		−	20.7839i		−	0.726694i
$819$	10.2110	−	17.6860i	0.356801	−	0.617998i
$820$	−17.2288	−	2.10874i	−0.601656	−	0.0736404i
$821$	17.2054	+	29.8007i	0.600474	+	1.04005i	0.992749	+	0.120203i	$0.0383547\pi$
$821$	17.2054	+	29.8007i	0.600474	+	1.04005i	−0.392275	+	0.919848i	$0.628312\pi$
$822$	16.3302	+	9.42826i	0.569582	+	0.328848i
$823$	10.3009	−	5.94720i	0.359065	−	0.207306i	−0.309605	−	0.950865i	$-0.600197\pi$
$823$	10.3009	−	5.94720i	0.359065	−	0.207306i	0.668671	+	0.743559i	$0.266864\pi$
$824$	5.33797			0.185957
$825$	5.29299	+	5.10356i	0.184278	+	0.177683i
$826$	12.4115	+	21.4973i	0.431850	+	0.747986i
$827$	−10.5632	+	6.09865i	−0.367318	+	0.212071i	−0.672286	−	0.740292i	$-0.734687\pi$
$827$	−10.5632	+	6.09865i	−0.367318	+	0.212071i	0.304968	+	0.952363i	$0.401354\pi$
$828$			2.56549i			0.0891569i
$829$	33.0048			1.14631			0.573153	−	0.819449i	$-0.305720\pi$
$829$	33.0048			1.14631			0.573153	+	0.819449i	$0.305720\pi$
$830$	−2.77515	+	3.68568i	−0.0963268	+	0.127932i
$831$	−12.2618	+	21.2381i	−0.425358	+	0.736743i
$832$	−4.38320	+	2.53064i	−0.151960	+	0.0877342i
$833$	−0.754467	−	0.435592i	−0.0261407	−	0.0150924i
$834$	−9.99616	+	17.3139i	−0.346139	+	0.599530i
$835$	44.7154	−	19.0008i	1.54744	−	0.657549i
$836$	0.741602	+	6.36689i	0.0256488	+	0.220203i
$837$		−	4.26558i		−	0.147440i
$838$	31.4083	+	18.1336i	1.08498	+	0.626414i
$839$	−8.97119	+	15.5386i	−0.309720	+	0.536451i	−0.978301	−	0.207189i	$-0.933569\pi$
$839$	−8.97119	+	15.5386i	−0.309720	+	0.536451i	0.668581	+	0.743639i	$0.266902\pi$
$840$	−7.20770	−	5.42707i	−0.248689	−	0.187252i
$841$	5.63869	−	9.76650i	0.194438	−	0.336776i
$842$	18.5697	−	10.7212i	0.639953	−	0.369477i
$843$		−	6.59418i		−	0.227116i
$844$	4.03940			0.139042
$845$	16.9695	−	22.5372i	0.583769	−	0.775304i
$846$	−2.01801	−	3.49530i	−0.0693808	−	0.120171i
$847$			35.6589i			1.22525i
$848$			10.6575i			0.365979i
$849$	−11.8189	−	20.4709i	−0.405623	−	0.702559i
$850$	0.129715	+	0.451066i	0.00444918	+	0.0154714i
$851$	−1.97295	−	3.41726i	−0.0676320	−	0.117142i
$852$	−7.51373	−	4.33806i	−0.257416	−	0.148619i
$853$	19.4891	+	11.2520i	0.667295	+	0.385263i	0.795051	−	0.606543i	$-0.207444\pi$
$853$	19.4891	+	11.2520i	0.667295	+	0.385263i	−0.127756	+	0.991806i	$0.540777\pi$
$854$	5.27547			0.180523
$855$	0.0568730	−	9.74663i	0.00194501	−	0.333328i
$856$	−17.9275			−0.612749
$857$	−1.71631	−	0.990914i	−0.0586281	−	0.0338490i	0.470399	−	0.882454i	$-0.344110\pi$
$857$	−1.71631	−	0.990914i	−0.0586281	−	0.0338490i	−0.529028	+	0.848605i	$0.677443\pi$
$858$	6.44566	+	3.72141i	0.220051	+	0.127047i
$859$	−16.4673	−	28.5223i	−0.561858	−	0.973167i	−0.997334	−	0.0729670i	$-0.976753\pi$
$859$	−16.4673	−	28.5223i	−0.561858	−	0.973167i	0.435476	−	0.900200i	$-0.356580\pi$
$860$	−1.24596	+	10.1797i	−0.0424870	+	0.347126i
$861$	−15.6605	−	27.1248i	−0.533710	−	0.924412i
$862$			5.82431i			0.198377i
$863$			1.13901i			0.0387723i	0.999812	+	0.0193862i	$0.00617119\pi$
$863$			1.13901i			0.0387723i	−0.999812	+	0.0193862i	$0.993829\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	41.4520	+	31.2114i	1.40941	+	1.06122i
$866$	31.6030			1.07391
$867$			16.9912i			0.577051i
$868$	14.9055	−	8.60569i	0.505925	−	0.292096i
$869$	9.53074	−	16.5077i	0.323308	−	0.559986i
$870$	5.66228	−	7.52008i	0.191969	−	0.254955i
$871$	−27.2105	+	47.1300i	−0.921993	+	1.59694i
$872$	−7.68392	−	4.43631i	−0.260210	−	0.150232i
$873$		−	11.9488i		−	0.404405i
$874$	−10.2664	−	4.43335i	−0.347265	−	0.149960i
$875$	16.1184	−	42.1343i	0.544901	−	1.42440i
$876$	−6.35711	+	11.0108i	−0.214787	+	0.372022i
$877$	19.9508	+	11.5186i	0.673692	+	0.388956i	0.797474	−	0.603353i	$-0.206169\pi$
$877$	19.9508	+	11.5186i	0.673692	+	0.388956i	−0.123782	+	0.992309i	$0.539502\pi$
$878$	−1.61592	+	0.932951i	−0.0545346	+	0.0314856i
$879$	−11.5061	+	19.9292i	−0.388092	+	0.672195i
$880$	1.97790	−	2.62685i	0.0666749	−	0.0885511i
$881$	−6.22555			−0.209744			−0.104872	−	0.994486i	$-0.533443\pi$
$881$	−6.22555			−0.209744			−0.104872	+	0.994486i	$0.533443\pi$
$882$		−	9.28080i		−	0.312501i
$883$	−28.2402	+	16.3045i	−0.950360	+	0.548691i	−0.893193	−	0.449674i	$-0.851540\pi$
$883$	−28.2402	+	16.3045i	−0.950360	+	0.548691i	−0.0571672	+	0.998365i	$0.518207\pi$
$884$	0.237550	+	0.411448i	0.00798967	+	0.0138385i
$885$	12.6606	−	5.37984i	0.425583	−	0.180841i
$886$	−15.7464			−0.529009
$887$	−3.26261	+	1.88367i	−0.109548	+	0.0632474i	−0.553773	−	0.832668i	$-0.686812\pi$
$887$	−3.26261	+	1.88367i	−0.109548	+	0.0632474i	0.444225	+	0.895915i	$0.353479\pi$
$888$	−1.33201	−	0.769037i	−0.0446993	−	0.0258072i
$889$	13.4484	+	23.2933i	0.451045	+	0.781234i
$890$	0.442177	−	3.61267i	0.0148218	−	0.121097i
$891$	0.735269	−	1.27352i	0.0246325	−	0.0426647i
$892$			18.0519i			0.604421i
$893$	17.4745	−	2.03539i	0.584762	−	0.0681118i
$894$	−12.2079			−0.408294
$895$	−14.1506	−	1.73199i	−0.473004	−	0.0578939i
$896$	−2.01747	+	3.49437i	−0.0673991	+	0.116739i
$897$	−11.2451	+	6.49233i	−0.375461	+	0.216773i
$898$	−25.7588	−	14.8718i	−0.859581	−	0.496279i
$899$	8.97866	+	15.5515i	0.299455	+	0.518671i
$900$	−3.47054	+	3.59936i	−0.115685	+	0.119979i
$901$	1.00041			0.0333285
$902$	9.88567	−	5.70749i	0.329157	−	0.190039i
$903$	−16.0269	+	9.25313i	−0.533341	+	0.307925i
$904$	−15.8667			−0.527718
$905$	7.68856	+	18.0939i	0.255576	+	0.601461i
$906$	−9.95543	−	17.2433i	−0.330747	−	0.572870i
$907$	−8.85151	−	5.11042i	−0.293910	−	0.169689i	0.345794	−	0.938310i	$-0.387610\pi$
$907$	−8.85151	−	5.11042i	−0.293910	−	0.169689i	−0.639704	+	0.768622i	$0.720943\pi$
$908$	23.2539	−	13.4257i	0.771709	−	0.445547i
$909$	0.252103	−	0.436656i	0.00836174	−	0.0144830i
$910$	5.54782	−	45.3267i	0.183909	−	1.50257i
$911$	−18.6042			−0.616383			−0.308192	−	0.951324i	$-0.599724\pi$
$911$	−18.6042			−0.616383			−0.308192	+	0.951324i	$0.599724\pi$
$912$	−4.32963	+	0.504306i	−0.143368	+	0.0166992i
$913$		−	3.03414i		−	0.100415i
$914$	−6.39456	+	11.0757i	−0.211513	+	0.366352i
$915$	0.355179	−	2.90188i	0.0117419	−	0.0959332i
$916$	6.85657	+	11.8759i	0.226548	+	0.392392i
$917$	24.7250	+	14.2750i	0.816492	+	0.471402i
$918$	0.0812933	−	0.0469347i	0.00268308	−	0.00154908i
$919$	35.5145			1.17152			0.585758	−	0.810486i	$-0.300797\pi$
$919$	35.5145			1.17152			0.585758	+	0.810486i	$0.300797\pi$
$920$	2.24349	+	5.27972i	0.0739657	+	0.174067i
$921$	−12.7483	−	22.0807i	−0.420071	−	0.727584i
$922$	10.3283	−	5.96303i	0.340143	−	0.196382i
$923$		−	43.9123i		−	1.44539i
$924$	5.93355			0.195199
$925$	1.85476	−	7.46335i	0.0609841	−	0.245393i
$926$	−9.66039	+	16.7323i	−0.317460	+	0.549857i
$927$	4.62282	−	2.66899i	0.151833	−	0.0876610i
$928$	−3.64581	−	2.10491i	−0.119680	−	0.0690971i
$929$	2.13612	−	3.69987i	0.0700838	−	0.121389i	−0.828854	−	0.559465i	$-0.811007\pi$
$929$	2.13612	−	3.69987i	0.0700838	−	0.121389i	0.898938	+	0.438076i	$0.144340\pi$
$930$	−3.73020	−	8.77846i	−0.122318	−	0.287857i
$931$	37.1392	+	16.0379i	1.21719	+	0.525621i
$932$			0.00661073i			0.000216542i
$933$	26.2555	+	15.1586i	0.859565	+	0.496270i
$934$	13.3504	−	23.1237i	0.436840	−	0.756629i
$935$	−0.246581	−	0.185664i	−0.00806406	−	0.00607187i
$936$	−2.53064	+	4.38320i	−0.0827166	+	0.143269i
$937$	44.5676	−	25.7311i	1.45596	−	0.840599i	0.457152	−	0.889389i	$-0.348870\pi$
$937$	44.5676	−	25.7311i	1.45596	−	0.840599i	0.998809	+	0.0487891i	$0.0155362\pi$
$938$			43.3854i			1.41658i
$939$	7.55247			0.246465
$940$	−7.20963	−	5.42852i	−0.235152	−	0.177059i
$941$	−30.2442	−	52.3845i	−0.985934	−	1.70769i	−0.637712	−	0.770275i	$-0.720119\pi$
$941$	−30.2442	−	52.3845i	−0.985934	−	1.70769i	−0.348222	−	0.937412i	$-0.613214\pi$
$942$			16.2344i			0.528946i
$943$			19.9145i			0.648505i
$944$	−3.07599	−	5.32777i	−0.100115	−	0.173404i
$945$	−8.95558	−	1.09613i	−0.291325	−	0.0356571i
$946$	−3.37231	−	5.84101i	−0.109643	−	0.189908i
$947$	10.0415	+	5.79749i	0.326306	+	0.188393i	0.654200	−	0.756322i	$-0.273005\pi$
$947$	10.0415	+	5.79749i	0.326306	+	0.188393i	−0.327894	+	0.944715i	$0.606339\pi$
$948$	11.2256	+	6.48112i	0.364592	+	0.210497i
$949$	−64.3503			−2.08890
$950$	−8.40627	−	20.1081i	−0.272736	−	0.652392i
$951$	−14.0116			−0.454357
$952$	0.328014	+	0.189379i	0.0106310	+	0.00613781i
$953$	−22.5443	−	13.0160i	−0.730282	−	0.421629i	0.0882433	−	0.996099i	$-0.471875\pi$
$953$	−22.5443	−	13.0160i	−0.730282	−	0.421629i	−0.818525	+	0.574470i	$0.805208\pi$
$954$	5.32873	+	9.22964i	0.172524	+	0.298821i
$955$	28.7778	+	3.52229i	0.931227	+	0.113979i
$956$	2.33750	+	4.04866i	0.0756000	+	0.130943i
$957$			6.19071i			0.200117i
$958$		−	13.5825i		−	0.438830i
$959$	38.0425	+	65.8916i	1.22846	+	2.12775i
$960$	1.78632	+	1.34502i	0.0576532	+	0.0434102i
$961$	−12.8049			−0.413060
$962$		−	7.78462i		−	0.250986i
$963$	−15.5257	+	8.96375i	−0.500308	+	0.288853i
$964$	−13.9044	+	24.0831i	−0.447829	+	0.775663i
$965$	10.9261	+	8.22688i	0.351725	+	0.264833i
$966$	−5.17581	+	8.96476i	−0.166529	+	0.288436i
$967$	14.9595	+	8.63685i	0.481064	+	0.277743i	0.720860	−	0.693081i	$-0.243747\pi$
$967$	14.9595	+	8.63685i	0.481064	+	0.277743i	−0.239796	+	0.970823i	$0.577080\pi$
$968$		−	8.83752i		−	0.284049i
$969$	0.0473389	+	0.406420i	0.00152075	+	0.0130561i
$970$	−10.4491	−	24.5903i	−0.335499	−	0.789547i
$971$	5.47052	−	9.47522i	0.175557	−	0.304074i	−0.764797	−	0.644272i	$-0.777161\pi$
$971$	5.47052	−	9.47522i	0.175557	−	0.304074i	0.940354	+	0.340198i	$0.110494\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	−69.8605	+	40.3340i	−2.23963	+	1.29305i
$974$	4.01820	−	6.95973i	0.128752	−	0.223004i
$975$	−24.5594	−	6.10339i	−0.786530	−	0.195465i
$976$	−1.30744			−0.0418503
$977$			9.01488i			0.288412i	0.989548	+	0.144206i	$0.0460627\pi$
$977$			9.01488i			0.288412i	−0.989548	+	0.144206i	$0.953937\pi$
$978$	1.78185	−	1.02875i	0.0569773	−	0.0328958i
$979$	1.19679	+	2.07290i	0.0382496	+	0.0662503i
$980$	−8.11595	−	19.0997i	−0.259255	−	0.610117i
$981$	−8.87262			−0.283281
$982$	17.9077	−	10.3390i	0.571457	−	0.329931i
$983$	−12.8956	−	7.44527i	−0.411305	−	0.237467i	0.280045	−	0.959987i	$-0.409651\pi$
$983$	−12.8956	−	7.44527i	−0.411305	−	0.237467i	−0.691350	+	0.722520i	$0.742984\pi$
$984$	3.88123	+	6.72248i	0.123729	+	0.214305i
$985$	1.99653	−	16.3121i	0.0636149	−	0.519745i
$986$	−0.197587	+	0.342231i	−0.00629245	+	0.0108988i
$987$		−	16.2852i		−	0.518362i
$988$	−13.1672	−	17.7014i	−0.418905	−	0.563157i
$989$	11.7666			0.374156
$990$	0.399485	−	3.26387i	0.0126965	−	0.103733i
$991$	−23.1717	+	40.1346i	−0.736075	+	1.27492i	0.218176	+	0.975910i	$0.429989\pi$
$991$	−23.1717	+	40.1346i	−0.736075	+	1.27492i	−0.954250	+	0.299009i	$0.903344\pi$
$992$	−3.69410	+	2.13279i	−0.117288	+	0.0677161i
$993$	1.90994	+	1.10271i	0.0606102	+	0.0349933i
$994$	−17.5038	−	30.3175i	−0.555188	−	0.961613i
$995$	3.00439	+	7.07037i	0.0952454	+	0.224146i
$996$	2.06328			0.0653776
$997$	26.1990	−	15.1260i	0.829730	−	0.479045i	−0.0240304	−	0.999711i	$-0.507650\pi$
$997$	26.1990	−	15.1260i	0.829730	−	0.479045i	0.853760	+	0.520667i	$0.174317\pi$
$998$	−0.954638	+	0.551160i	−0.0302185	+	0.0174467i
$999$	−1.53807			−0.0486625

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.q.c.49.10	yes	20
3.2	odd	2		1710.2.t.c.1189.1		20
5.4	even	2	inner	570.2.q.c.49.2	✓	20
15.14	odd	2		1710.2.t.c.1189.9		20
19.7	even	3	inner	570.2.q.c.349.2	yes	20
57.26	odd	6		1710.2.t.c.919.9		20
95.64	even	6	inner	570.2.q.c.349.10	yes	20
285.254	odd	6		1710.2.t.c.919.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.c.49.2	✓	20	5.4	even	2	inner
570.2.q.c.49.10	yes	20	1.1	even	1	trivial
570.2.q.c.349.2	yes	20	19.7	even	3	inner
570.2.q.c.349.10	yes	20	95.64	even	6	inner
1710.2.t.c.919.1		20	285.254	odd	6
1710.2.t.c.919.9		20	57.26	odd	6
1710.2.t.c.1189.1		20	3.2	odd	2
1710.2.t.c.1189.9		20	15.14	odd	2

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.21950 + 0.271659i) q^{5} +(-0.500000 - 0.866025i) q^{6} -4.03495i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.21950 + 0.271659i) q^{5} +(-0.500000 - 0.866025i) q^{6} -4.03495i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.78632 + 1.34502i) q^{10} -1.47054 q^{11} -1.00000i q^{12} +(4.38320 - 2.53064i) q^{13} +(2.01747 - 3.49437i) q^{14} +(-1.78632 - 1.34502i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.0812933 + 0.0469347i) q^{17} +1.00000i q^{18} +(-4.00172 - 1.72807i) q^{19} +(0.874489 + 2.05798i) q^{20} +(-2.01747 + 3.49437i) q^{21} +(-1.27352 - 0.735269i) q^{22} +(2.22178 - 1.28274i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.85240 + 1.20590i) q^{25} +5.06128 q^{26} -1.00000i q^{27} +(3.49437 - 2.01747i) q^{28} +(2.10491 + 3.64581i) q^{29} +(-0.874489 - 2.05798i) q^{30} +4.26558 q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.27352 + 0.735269i) q^{33} +(0.0469347 + 0.0812933i) q^{34} +(1.09613 - 8.95558i) q^{35} +(-0.500000 + 0.866025i) q^{36} -1.53807i q^{37} +(-2.60156 - 3.49741i) q^{38} -5.06128 q^{39} +(-0.271659 + 2.21950i) q^{40} +(-3.88123 + 6.72248i) q^{41} +(-3.49437 + 2.01747i) q^{42} +(3.97202 + 2.29325i) q^{43} +(-0.735269 - 1.27352i) q^{44} +(0.874489 + 2.05798i) q^{45} +2.56549 q^{46} +(-3.49530 + 2.01801i) q^{47} +(0.866025 - 0.500000i) q^{48} -9.28080 q^{49} +(3.59936 + 3.47054i) q^{50} +(-0.0469347 - 0.0812933i) q^{51} +(4.38320 + 2.53064i) q^{52} +(9.22964 - 5.32873i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-3.26387 - 0.399485i) q^{55} +4.03495 q^{56} +(2.60156 + 3.49741i) q^{57} +4.20982i q^{58} +(-3.07599 + 5.32777i) q^{59} +(0.271659 - 2.21950i) q^{60} +(0.653722 + 1.13228i) q^{61} +(3.69410 + 2.13279i) q^{62} +(3.49437 - 2.01747i) q^{63} -1.00000 q^{64} +(10.4160 - 4.42603i) q^{65} +(0.735269 + 1.27352i) q^{66} +(-9.31187 + 5.37621i) q^{67} +0.0938694i q^{68} -2.56549 q^{69} +(5.42707 - 7.20770i) q^{70} +(4.33806 - 7.51373i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(-11.0108 - 6.35711i) q^{73} +(0.769037 - 1.33201i) q^{74} +(-3.59936 - 3.47054i) q^{75} +(-0.504306 - 4.32963i) q^{76} +5.93355i q^{77} +(-4.38320 - 2.53064i) q^{78} +(-6.48112 + 11.2256i) q^{79} +(-1.34502 + 1.78632i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.72248 + 3.88123i) q^{82} +2.06328i q^{83} -4.03495 q^{84} +(0.167681 + 0.126256i) q^{85} +(2.29325 + 3.97202i) q^{86} -4.20982i q^{87} -1.47054i q^{88} +(-0.813846 - 1.40962i) q^{89} +(-0.271659 + 2.21950i) q^{90} +(-10.2110 - 17.6860i) q^{91} +(2.22178 + 1.28274i) q^{92} +(-3.69410 - 2.13279i) q^{93} -4.03603 q^{94} +(-8.41239 - 4.92257i) q^{95} +1.00000 q^{96} +(-10.3479 - 5.97438i) q^{97} +(-8.03741 - 4.64040i) q^{98} +(-0.735269 - 1.27352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9	\( 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9} - 2 q^{10} + 12 q^{11} + 10 q^{14} + 2 q^{15} - 10 q^{16} + 6 q^{19} - 10 q^{21} + 10 q^{24} + 14 q^{25} + 8 q^{29} + 40 q^{31} + 12 q^{34} + 2 q^{35} - 10 q^{36} + 2 q^{40} - 14 q^{41} + 6 q^{44} + 44 q^{46} - 8 q^{49} - 8 q^{50} - 12 q^{51} + 10 q^{54} + 20 q^{56} + 8 q^{59} - 2 q^{60} + 16 q^{61} - 20 q^{64} + 40 q^{65} - 6 q^{66} - 44 q^{69} + 8 q^{70} - 4 q^{71} + 26 q^{74} + 8 q^{75} + 8 q^{79} - 10 q^{81} - 20 q^{84} - 16 q^{85} - 20 q^{86} - 2 q^{89} + 2 q^{90} - 44 q^{91} - 32 q^{94} - 80 q^{95} + 20 q^{96} + 6 q^{99}+O(q^{100}) \) 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9 - 2 * q^10 + 12 * q^11 + 10 * q^14 + 2 * q^15 - 10 * q^16 + 6 * q^19 - 10 * q^21 + 10 * q^24 + 14 * q^25 + 8 * q^29 + 40 * q^31 + 12 * q^34 + 2 * q^35 - 10 * q^36 + 2 * q^40 - 14 * q^41 + 6 * q^44 + 44 * q^46 - 8 * q^49 - 8 * q^50 - 12 * q^51 + 10 * q^54 + 20 * q^56 + 8 * q^59 - 2 * q^60 + 16 * q^61 - 20 * q^64 + 40 * q^65 - 6 * q^66 - 44 * q^69 + 8 * q^70 - 4 * q^71 + 26 * q^74 + 8 * q^75 + 8 * q^79 - 10 * q^81 - 20 * q^84 - 16 * q^85 - 20 * q^86 - 2 * q^89 + 2 * q^90 - 44 * q^91 - 32 * q^94 - 80 * q^95 + 20 * q^96 + 6 * q^99

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