LMFDB - Embedded newform 546.2.bk.c.25.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(25,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("546.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bk (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:	$4.35983195036$
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} - 26 x^{18} + 431 x^{16} - 4370 x^{14} + 32381 x^{12} - 160412 x^{10} + 573820 x^{8} + \cdots + 810000 $ x^20 - 26x^18 + 431x^16 - 4370x^14 + 32381x^12 - 160412x^10 + 573820x^8 - 1203000x^6 + 1802736x^4 - 1479600*x^2 + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.8
Root			$0.935588 + 0.540162i$ of defining polynomial
Character	$\chi$	$=$	546.25
Dual form			546.2.bk.c.415.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.935588 - 0.540162i) q^{5} -1.00000i q^{6} +(1.55401 - 2.14127i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.935588 - 0.540162i) q^{5} -1.00000i q^{6} +(1.55401 - 2.14127i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.540162 - 0.935588i) q^{10} +(-4.99823 - 2.88573i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.235018 + 3.59788i) q^{13} +(0.275179 - 2.63140i) q^{14} -1.08032i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.54960 + 2.68399i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(5.93381 - 3.42589i) q^{19} -1.08032i q^{20} +(-1.07739 - 2.41645i) q^{21} -5.77146 q^{22} +(2.46605 + 4.27133i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.91645 + 3.31939i) q^{25} +(2.00247 + 2.99835i) q^{26} -1.00000 q^{27} +(-1.07739 - 2.41645i) q^{28} +7.05400 q^{29} +(-0.540162 - 0.935588i) q^{30} +(-3.33574 - 1.92589i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.99823 + 2.88573i) q^{33} +3.09920i q^{34} +(0.297283 - 2.84277i) q^{35} -1.00000 q^{36} +(-2.06396 + 1.19163i) q^{37} +(3.42589 - 5.93381i) q^{38} +(3.23337 + 1.59541i) q^{39} +(-0.540162 - 0.935588i) q^{40} -8.58166i q^{41} +(-2.14127 - 1.55401i) q^{42} +9.19577 q^{43} +(-4.99823 + 2.88573i) q^{44} +(-0.935588 - 0.540162i) q^{45} +(4.27133 + 2.46605i) q^{46} +(0.297903 - 0.171994i) q^{47} -1.00000 q^{48} +(-2.17009 - 6.65513i) q^{49} +3.83290i q^{50} +(1.54960 + 2.68399i) q^{51} +(3.23337 + 1.59541i) q^{52} +(-5.09788 + 8.82979i) q^{53} +(-0.866025 + 0.500000i) q^{54} -6.23504 q^{55} +(-2.14127 - 1.55401i) q^{56} -6.85178i q^{57} +(6.10894 - 3.52700i) q^{58} +(-9.94051 - 5.73915i) q^{59} +(-0.935588 - 0.540162i) q^{60} +(2.01964 + 3.49811i) q^{61} -3.85178 q^{62} +(-2.63140 - 0.275179i) q^{63} -1.00000 q^{64} +(2.16332 + 3.23919i) q^{65} +(-2.88573 + 4.99823i) q^{66} +(10.8620 + 6.27120i) q^{67} +(1.54960 + 2.68399i) q^{68} +4.93210 q^{69} +(-1.16393 - 2.61055i) q^{70} +11.4987i q^{71} +(-0.866025 + 0.500000i) q^{72} +(6.41044 + 3.70107i) q^{73} +(-1.19163 + 2.06396i) q^{74} +(1.91645 + 3.31939i) q^{75} -6.85178i q^{76} +(-13.9464 + 6.21810i) q^{77} +(3.59788 - 0.235018i) q^{78} +(1.98734 + 3.44217i) q^{79} +(-0.935588 - 0.540162i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.29083 - 7.43194i) q^{82} +10.2400i q^{83} +(-2.63140 - 0.275179i) q^{84} +3.34814i q^{85} +(7.96377 - 4.59788i) q^{86} +(3.52700 - 6.10894i) q^{87} +(-2.88573 + 4.99823i) q^{88} +(8.96805 - 5.17771i) q^{89} -1.08032 q^{90} +(8.06927 + 5.08792i) q^{91} +4.93210 q^{92} +(-3.33574 + 1.92589i) q^{93} +(0.171994 - 0.297903i) q^{94} +(3.70107 - 6.41044i) q^{95} +(-0.866025 + 0.500000i) q^{96} +2.93158i q^{97} +(-5.20691 - 4.67847i) q^{98} +5.77146i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{3} + 10 q^{4} - 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^3 + 10 * q^4 - 10 * q^9	$ 20 q + 10 q^{3} + 10 q^{4} - 10 q^{9} + 4 q^{10} - 10 q^{12} + 4 q^{13} - 2 q^{14} - 10 q^{16} - 6 q^{17} - 12 q^{22} - 16 q^{23} + 2 q^{25} - 4 q^{26} - 20 q^{27} - 28 q^{29} - 4 q^{30} + 16 q^{35} - 20 q^{36} + 10 q^{38} + 2 q^{39} - 4 q^{40} - 10 q^{42} + 24 q^{43} - 20 q^{48} + 2 q^{49} + 6 q^{51} + 2 q^{52} - 22 q^{53} + 88 q^{55} - 10 q^{56} + 14 q^{61} + 40 q^{62} - 20 q^{64} + 20 q^{65} - 6 q^{66} + 6 q^{68} - 32 q^{69} + 24 q^{74} - 2 q^{75} - 28 q^{77} - 8 q^{78} + 4 q^{79} - 10 q^{81} + 12 q^{82} - 14 q^{87} - 6 q^{88} - 8 q^{90} + 68 q^{91} - 32 q^{92} - 18 q^{94} + 8 q^{95}+O(q^{100}) $ 20 * q + 10 * q^3 + 10 * q^4 - 10 * q^9 + 4 * q^10 - 10 * q^12 + 4 * q^13 - 2 * q^14 - 10 * q^16 - 6 * q^17 - 12 * q^22 - 16 * q^23 + 2 * q^25 - 4 * q^26 - 20 * q^27 - 28 * q^29 - 4 * q^30 + 16 * q^35 - 20 * q^36 + 10 * q^38 + 2 * q^39 - 4 * q^40 - 10 * q^42 + 24 * q^43 - 20 * q^48 + 2 * q^49 + 6 * q^51 + 2 * q^52 - 22 * q^53 + 88 * q^55 - 10 * q^56 + 14 * q^61 + 40 * q^62 - 20 * q^64 + 20 * q^65 - 6 * q^66 + 6 * q^68 - 32 * q^69 + 24 * q^74 - 2 * q^75 - 28 * q^77 - 8 * q^78 + 4 * q^79 - 10 * q^81 + 12 * q^82 - 14 * q^87 - 6 * q^88 - 8 * q^90 + 68 * q^91 - 32 * q^92 - 18 * q^94 + 8 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.935588	−	0.540162i	0.418407	−	0.241568i	−0.275988	−	0.961161i	$-0.589005\pi$
$5$	0.935588	−	0.540162i	0.418407	−	0.241568i	0.694396	+	0.719593i	$0.255672\pi$
$6$		−	1.00000i		−	0.408248i
$7$	1.55401	−	2.14127i	0.587362	−	0.809324i
$7$	1.55401	−	2.14127i	0.587362	−	0.809324i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.540162	−	0.935588i	0.170814	−	0.295859i
$11$	−4.99823	−	2.88573i	−1.50702	−	0.870080i	−0.999967	−	0.00816615i	$-0.997401\pi$
$11$	−4.99823	−	2.88573i	−1.50702	−	0.870080i	−0.507055	−	0.861913i	$-0.669266\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.235018	+	3.59788i	0.0651821	+	0.997873i
$13$	0.235018	+	3.59788i	0.0651821	+	0.997873i
$14$	0.275179	−	2.63140i	0.0735448	−	0.703272i
$15$		−	1.08032i		−	0.278938i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.54960	+	2.68399i	−0.375833	+	0.650962i	−0.990451	−	0.137862i	$-0.955977\pi$
$17$	−1.54960	+	2.68399i	−0.375833	+	0.650962i	0.614618	+	0.788825i	$0.289310\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	5.93381	−	3.42589i	1.36131	−	0.785953i	0.371512	−	0.928428i	$-0.378839\pi$
$19$	5.93381	−	3.42589i	1.36131	−	0.785953i	0.989798	+	0.142475i	$0.0455061\pi$
$20$		−	1.08032i		−	0.241568i
$21$	−1.07739	−	2.41645i	−0.235105	−	0.527313i
$22$	−5.77146			−1.23048
$23$	2.46605	+	4.27133i	0.514207	+	0.890633i	0.999864	+	0.0164835i	$0.00524710\pi$
$23$	2.46605	+	4.27133i	0.514207	+	0.890633i	−0.485657	+	0.874149i	$0.661420\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−1.91645	+	3.31939i	−0.383290	+	0.663878i
$26$	2.00247	+	2.99835i	0.392717	+	0.588025i
$27$	−1.00000			−0.192450
$28$	−1.07739	−	2.41645i	−0.203607	−	0.456666i
$29$	7.05400			1.30989			0.654947	−	0.755675i	$-0.272691\pi$
$29$	7.05400			1.30989			0.654947	+	0.755675i	$0.272691\pi$
$30$	−0.540162	−	0.935588i	−0.0986196	−	0.170814i
$31$	−3.33574	−	1.92589i	−0.599116	−	0.345900i	0.169578	−	0.985517i	$-0.445760\pi$
$31$	−3.33574	−	1.92589i	−0.599116	−	0.345900i	−0.768694	+	0.639617i	$0.779093\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−4.99823	+	2.88573i	−0.870080	+	0.502341i
$34$			3.09920i			0.531509i
$35$	0.297283	−	2.84277i	0.0502499	−	0.480515i
$36$	−1.00000			−0.166667
$37$	−2.06396	+	1.19163i	−0.339314	+	0.195903i	−0.659968	−	0.751293i	$-0.729430\pi$
$37$	−2.06396	+	1.19163i	−0.339314	+	0.195903i	0.320655	+	0.947196i	$0.396097\pi$
$38$	3.42589	−	5.93381i	0.555753	−	0.962592i
$39$	3.23337	+	1.59541i	0.517753	+	0.255470i
$40$	−0.540162	−	0.935588i	−0.0854071	−	0.147929i
$41$		−	8.58166i		−	1.34023i	−0.742257	−	0.670115i	$-0.766245\pi$
$41$		−	8.58166i		−	1.34023i	0.742257	−	0.670115i	$-0.233755\pi$
$42$	−2.14127	−	1.55401i	−0.330405	−	0.239789i
$43$	9.19577			1.40234			0.701171	−	0.712993i	$-0.252661\pi$
$43$	9.19577			1.40234			0.701171	+	0.712993i	$0.252661\pi$
$44$	−4.99823	+	2.88573i	−0.753511	+	0.435040i
$45$	−0.935588	−	0.540162i	−0.139469	−	0.0805226i
$46$	4.27133	+	2.46605i	0.629773	+	0.363599i
$47$	0.297903	−	0.171994i	0.0434536	−	0.0250880i	−0.478116	−	0.878297i	$-0.658680\pi$
$47$	0.297903	−	0.171994i	0.0434536	−	0.0250880i	0.521569	+	0.853209i	$0.325347\pi$
$48$	−1.00000			−0.144338
$49$	−2.17009	−	6.65513i	−0.310012	−	0.950733i
$50$			3.83290i			0.542054i
$51$	1.54960	+	2.68399i	0.216987	+	0.375833i
$52$	3.23337	+	1.59541i	0.448387	+	0.221244i
$53$	−5.09788	+	8.82979i	−0.700248	+	1.21287i	0.268131	+	0.963382i	$0.413594\pi$
$53$	−5.09788	+	8.82979i	−0.700248	+	1.21287i	−0.968379	+	0.249483i	$0.919739\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−6.23504			−0.840732
$56$	−2.14127	−	1.55401i	−0.286139	−	0.207664i
$57$		−	6.85178i		−	0.907540i
$58$	6.10894	−	3.52700i	0.802143	−	0.463118i
$59$	−9.94051	−	5.73915i	−1.29414	−	0.747174i	−0.314758	−	0.949172i	$-0.601923\pi$
$59$	−9.94051	−	5.73915i	−1.29414	−	0.747174i	−0.979386	+	0.201998i	$0.935257\pi$
$60$	−0.935588	−	0.540162i	−0.120784	−	0.0697346i
$61$	2.01964	+	3.49811i	0.258588	+	0.447887i	0.965864	−	0.259050i	$-0.0834095\pi$
$61$	2.01964	+	3.49811i	0.258588	+	0.447887i	−0.707276	+	0.706938i	$0.750076\pi$
$62$	−3.85178			−0.489176
$63$	−2.63140	−	0.275179i	−0.331525	−	0.0346693i
$64$	−1.00000			−0.125000
$65$	2.16332	+	3.23919i	0.268327	+	0.401772i
$66$	−2.88573	+	4.99823i	−0.355209	+	0.615239i
$67$	10.8620	+	6.27120i	1.32701	+	0.766148i	0.984836	−	0.173489i	$-0.0555041\pi$
$67$	10.8620	+	6.27120i	1.32701	+	0.766148i	0.342172	+	0.939637i	$0.388837\pi$
$68$	1.54960	+	2.68399i	0.187917	+	0.325481i
$69$	4.93210			0.593755
$70$	−1.16393	−	2.61055i	−0.139116	−	0.312020i
$71$			11.4987i			1.36465i	0.731051	+	0.682323i	$0.239030\pi$
$71$			11.4987i			1.36465i	−0.731051	+	0.682323i	$0.760970\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	6.41044	+	3.70107i	0.750285	+	0.433177i	0.825797	−	0.563968i	$-0.190726\pi$
$73$	6.41044	+	3.70107i	0.750285	+	0.433177i	−0.0755118	+	0.997145i	$0.524059\pi$
$74$	−1.19163	+	2.06396i	−0.138524	+	0.239931i
$75$	1.91645	+	3.31939i	0.221293	+	0.383290i
$76$		−	6.85178i		−	0.785953i
$77$	−13.9464	+	6.21810i	−1.58934	+	0.708618i
$78$	3.59788	−	0.235018i	0.407380	−	0.0266105i
$79$	1.98734	+	3.44217i	0.223593	+	0.387274i	0.955896	−	0.293704i	$-0.0948881\pi$
$79$	1.98734	+	3.44217i	0.223593	+	0.387274i	−0.732304	+	0.680978i	$0.761555\pi$
$80$	−0.935588	−	0.540162i	−0.104602	−	0.0603919i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.29083	−	7.43194i	−0.473843	−	0.820720i
$83$			10.2400i			1.12398i	0.827143	+	0.561992i	$0.189965\pi$
$83$			10.2400i			1.12398i	−0.827143	+	0.561992i	$0.810035\pi$
$84$	−2.63140	−	0.275179i	−0.287109	−	0.0300245i
$85$			3.34814i			0.363157i
$86$	7.96377	−	4.59788i	0.858755	−	0.495803i
$87$	3.52700	−	6.10894i	0.378134	−	0.654947i
$88$	−2.88573	+	4.99823i	−0.307620	+	0.532813i
$89$	8.96805	−	5.17771i	0.950612	−	0.548836i	0.0573410	−	0.998355i	$-0.481738\pi$
$89$	8.96805	−	5.17771i	0.950612	−	0.548836i	0.893271	+	0.449519i	$0.148404\pi$
$90$	−1.08032			−0.113876
$91$	8.06927	+	5.08792i	0.845889	+	0.533359i
$92$	4.93210			0.514207
$93$	−3.33574	+	1.92589i	−0.345900	+	0.199705i
$94$	0.171994	−	0.297903i	0.0177399	−	0.0307263i
$95$	3.70107	−	6.41044i	0.379722	−	0.657697i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$			2.93158i			0.297657i	0.988863	+	0.148829i	$0.0475502\pi$
$97$			2.93158i			0.297657i	−0.988863	+	0.148829i	$0.952450\pi$
$98$	−5.20691	−	4.67847i	−0.525978	−	0.472597i
$99$			5.77146i			0.580053i
$100$	1.91645	+	3.31939i	0.191645	+	0.331939i
$101$	3.26202	−	5.64998i	0.324583	−	0.562194i	−0.656845	−	0.754026i	$-0.728109\pi$
$101$	3.26202	−	5.64998i	0.324583	−	0.562194i	0.981428	+	0.191832i	$0.0614428\pi$
$102$	2.68399	+	1.54960i	0.265754	+	0.153433i
$103$	−3.22110	−	5.57910i	−0.317384	−	0.549725i	0.662557	−	0.749011i	$-0.269471\pi$
$103$	−3.22110	−	5.57910i	−0.317384	−	0.549725i	−0.979941	+	0.199286i	$0.936138\pi$
$104$	3.59788	−	0.235018i	0.352802	−	0.0230454i
$105$	−2.31327	−	1.67884i	−0.225752	−	0.163838i
$106$			10.1958i			0.990300i
$107$	−5.17978	−	8.97165i	−0.500749	−	0.867322i	−1.00000		0.000864682i	$-0.999725\pi$
$107$	−5.17978	−	8.97165i	−0.500749	−	0.867322i	0.499251	−	0.866457i	$-0.333609\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	4.36054	+	2.51756i	0.417664	+	0.241139i	0.694077	−	0.719900i	$-0.255813\pi$
$109$	4.36054	+	2.51756i	0.417664	+	0.241139i	−0.276413	+	0.961039i	$0.589146\pi$
$110$	−5.39970	+	3.11752i	−0.514841	+	0.297244i
$111$			2.38326i			0.226209i
$112$	−2.63140	−	0.275179i	−0.248644	−	0.0260020i
$113$	−18.0933			−1.70207			−0.851036	−	0.525108i	$-0.824025\pi$
$113$	−18.0933			−1.70207			−0.851036	+	0.525108i	$0.824025\pi$
$114$	−3.42589	−	5.93381i	−0.320864	−	0.555753i
$115$	4.61441	+	2.66413i	0.430296	+	0.248432i
$116$	3.52700	−	6.10894i	0.327474	−	0.567201i
$117$	2.99835	−	2.00247i	0.277198	−	0.185129i
$118$	−11.4783			−1.05666
$119$	3.33904	+	7.48907i	0.306090	+	0.686522i
$120$	−1.08032			−0.0986196
$121$	11.1548	+	19.3208i	1.01408	+	1.75643i
$122$	3.49811	+	2.01964i	0.316704	+	0.182849i
$123$	−7.43194	−	4.29083i	−0.670115	−	0.386891i
$124$	−3.33574	+	1.92589i	−0.299558	+	0.172950i
$125$			9.54239i			0.853497i
$126$	−2.41645	+	1.07739i	−0.215275	+	0.0959814i
$127$	17.2950			1.53468			0.767340	−	0.641240i	$-0.221580\pi$
$127$	17.2950			1.53468			0.767340	+	0.641240i	$0.221580\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	4.59788	−	7.96377i	0.404821	−	0.701171i
$130$	3.49308	+	1.72356i	0.306364	+	0.151166i
$131$	4.35254	+	7.53881i	0.380283	+	0.658669i	0.991103	−	0.133100i	$-0.0424933\pi$
$131$	4.35254	+	7.53881i	0.380283	+	0.658669i	−0.610820	+	0.791770i	$0.709160\pi$
$132$			5.77146i			0.502341i
$133$	1.88547	−	18.0298i	0.163491	−	1.56338i
$134$	12.5424			1.08350
$135$	−0.935588	+	0.540162i	−0.0805226	+	0.0464897i
$136$	2.68399	+	1.54960i	0.230150	+	0.132877i
$137$	−6.82036	−	3.93773i	−0.582702	−	0.336423i	0.179504	−	0.983757i	$-0.442551\pi$
$137$	−6.82036	−	3.93773i	−0.582702	−	0.336423i	−0.762207	+	0.647334i	$0.775884\pi$
$138$	4.27133	−	2.46605i	0.363599	−	0.209924i
$139$	−17.1252			−1.45254			−0.726272	−	0.687408i	$-0.758749\pi$
$139$	−17.1252			−1.45254			−0.726272	+	0.687408i	$0.758749\pi$
$140$	−2.31327	−	1.67884i	−0.195507	−	0.141888i
$141$		−	0.343989i		−	0.0289691i
$142$	5.74935	+	9.95817i	0.482475	+	0.835671i
$143$	9.20784	−	18.6612i	0.769998	−	1.56053i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	6.59963	−	3.81030i	0.548070	−	0.316428i
$146$	7.40214			0.612605
$147$	−6.84855	−	1.44821i	−0.564859	−	0.119447i
$148$			2.38326i			0.195903i
$149$	−17.1530	+	9.90329i	−1.40523	+	0.811309i	−0.994923	−	0.100639i	$-0.967911\pi$
$149$	−17.1530	+	9.90329i	−1.40523	+	0.811309i	−0.410305	+	0.911948i	$0.634578\pi$
$150$	3.31939	+	1.91645i	0.271027	+	0.156478i
$151$	−1.40531	−	0.811357i	−0.114363	−	0.0660273i	0.441728	−	0.897149i	$-0.354366\pi$
$151$	−1.40531	−	0.811357i	−0.114363	−	0.0660273i	−0.556090	+	0.831122i	$0.687699\pi$
$152$	−3.42589	−	5.93381i	−0.277876	−	0.481296i
$153$	3.09920			0.250556
$154$	−8.96892	+	12.3583i	−0.722736	+	0.995856i
$155$	−4.16117			−0.334233
$156$	2.99835	−	2.00247i	0.240060	−	0.160326i
$157$	−0.349550	+	0.605438i	−0.0278971	+	0.0483192i	−0.879637	−	0.475646i	$-0.842214\pi$
$157$	−0.349550	+	0.605438i	−0.0278971	+	0.0483192i	0.851740	+	0.523965i	$0.175548\pi$
$158$	3.44217	+	1.98734i	0.273844	+	0.158104i
$159$	5.09788	+	8.82979i	0.404288	+	0.700248i
$160$	−1.08032			−0.0854071
$161$	12.9783	+	1.35721i	1.02284	+	0.106963i
$162$			1.00000i			0.0785674i
$163$	−9.04024	+	5.21939i	−0.708087	+	0.408814i	−0.810352	−	0.585943i	$-0.800724\pi$
$163$	−9.04024	+	5.21939i	−0.708087	+	0.408814i	0.102266	+	0.994757i	$0.467391\pi$
$164$	−7.43194	−	4.29083i	−0.580337	−	0.335058i
$165$	−3.11752	+	5.39970i	−0.242699	+	0.420366i
$166$	5.11999	+	8.86808i	0.397388	+	0.688296i
$167$		−	5.53642i		−	0.428421i	−0.976788	−	0.214210i	$-0.931282\pi$
$167$		−	5.53642i		−	0.428421i	0.976788	−	0.214210i	$-0.0687178\pi$
$168$	−2.41645	+	1.07739i	−0.186433	+	0.0831223i
$169$	−12.8895	+	1.69113i	−0.991503	+	0.130087i
$170$	1.67407	+	2.89957i	0.128395	+	0.222387i
$171$	−5.93381	−	3.42589i	−0.453770	−	0.261984i
$172$	4.59788	−	7.96377i	0.350585	−	0.607232i
$173$	−1.79455	−	3.10826i	−0.136437	−	0.236317i	0.789708	−	0.613483i	$-0.210232\pi$
$173$	−1.79455	−	3.10826i	−0.136437	−	0.236317i	−0.926146	+	0.377166i	$0.876899\pi$
$174$		−	7.05400i		−	0.534762i
$175$	4.12952	+	9.26202i	0.312163	+	0.700143i
$176$			5.77146i			0.435040i
$177$	−9.94051	+	5.73915i	−0.747174	+	0.431381i
$178$	5.17771	−	8.96805i	0.388086	−	0.672184i
$179$	−5.12190	+	8.87138i	−0.382828	+	0.663078i	−0.991465	−	0.130371i	$-0.958383\pi$
$179$	−5.12190	+	8.87138i	−0.382828	+	0.663078i	0.608637	+	0.793449i	$0.291717\pi$
$180$	−0.935588	+	0.540162i	−0.0697346	+	0.0402613i
$181$	−12.8223			−0.953074			−0.476537	−	0.879154i	$-0.658108\pi$
$181$	−12.8223			−0.953074			−0.476537	+	0.879154i	$0.658108\pi$
$182$	9.53215	+	0.371637i	0.706570	+	0.0275476i
$183$	4.03927			0.298592
$184$	4.27133	−	2.46605i	0.314886	−	0.181800i
$185$	−1.28735	+	2.22975i	−0.0946475	+	0.163934i
$186$	−1.92589	+	3.33574i	−0.141213	+	0.244588i
$187$	15.4905	−	8.94345i	1.13278	−	0.654010i
$188$		−	0.343989i		−	0.0250880i
$189$	−1.55401	+	2.14127i	−0.113038	+	0.155755i
$190$		−	7.40214i		−	0.537007i
$191$	−3.88688	−	6.73227i	−0.281245	−	0.487130i	0.690447	−	0.723383i	$-0.257414\pi$
$191$	−3.88688	−	6.73227i	−0.281245	−	0.487130i	−0.971692	+	0.236253i	$0.924081\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−10.4923	−	6.05772i	−0.755251	−	0.436044i	0.0723371	−	0.997380i	$-0.476954\pi$
$193$	−10.4923	−	6.05772i	−0.755251	−	0.436044i	−0.827588	+	0.561336i	$0.810288\pi$
$194$	1.46579	+	2.53882i	0.105238	+	0.182277i
$195$	3.88688	−	0.253895i	0.278345	−	0.0181818i
$196$	−6.84855	−	1.44821i	−0.489182	−	0.103444i
$197$			10.6227i			0.756837i	0.925635	+	0.378419i	$0.123532\pi$
$197$			10.6227i			0.756837i	−0.925635	+	0.378419i	$0.876468\pi$
$198$	2.88573	+	4.99823i	0.205080	+	0.355209i
$199$	12.7960	−	22.1633i	0.907083	−	1.57111i	0.0889875	−	0.996033i	$-0.471637\pi$
$199$	12.7960	−	22.1633i	0.907083	−	1.57111i	0.818096	−	0.575082i	$-0.195030\pi$
$200$	3.31939	+	1.91645i	0.234716	+	0.135514i
$201$	10.8620	−	6.27120i	0.766148	−	0.442336i
$202$		−	6.52403i		−	0.459029i
$203$	10.9620	−	15.1045i	0.769382	−	1.06013i
$204$	3.09920			0.216987
$205$	−4.63549	−	8.02890i	−0.323756	−	0.560762i
$206$	−5.57910	−	3.22110i	−0.388715	−	0.224424i
$207$	2.46605	−	4.27133i	0.171402	−	0.296878i
$208$	2.99835	−	2.00247i	0.207898	−	0.138847i
$209$	−39.5447			−2.73537
$210$	−2.84277	−	0.297283i	−0.196169	−	0.0205145i
$211$	16.5582			1.13991			0.569955	−	0.821676i	$-0.306961\pi$
$211$	16.5582			1.13991			0.569955	+	0.821676i	$0.306961\pi$
$212$	5.09788	+	8.82979i	0.350124	+	0.606433i
$213$	9.95817	+	5.74935i	0.682323	+	0.393939i
$214$	−8.97165	−	5.17978i	−0.613289	−	0.354083i
$215$	8.60345	−	4.96720i	0.586750	−	0.338760i
$216$			1.00000i			0.0680414i
$217$	−9.30763	+	4.14986i	−0.631843	+	0.281711i
$218$	5.03512			0.341021
$219$	6.41044	−	3.70107i	0.433177	−	0.250095i
$220$	−3.11752	+	5.39970i	−0.210183	+	0.364048i
$221$	−10.0209	−	4.94450i	−0.674076	−	0.332603i
$222$	1.19163	+	2.06396i	0.0799770	+	0.138524i
$223$		−	1.63865i		−	0.109732i	−0.998494	−	0.0548661i	$-0.982527\pi$
$223$		−	1.63865i		−	0.109732i	0.998494	−	0.0548661i	$-0.0174732\pi$
$224$	−2.41645	+	1.07739i	−0.161456	+	0.0719861i
$225$	3.83290			0.255527
$226$	−15.6692	+	9.04663i	−1.04230	+	0.601773i
$227$	−9.53213	−	5.50338i	−0.632670	−	0.365272i	0.149115	−	0.988820i	$-0.452357\pi$
$227$	−9.53213	−	5.50338i	−0.632670	−	0.365272i	−0.781785	+	0.623548i	$0.785691\pi$
$228$	−5.93381	−	3.42589i	−0.392976	−	0.226885i
$229$	−15.1031	+	8.71978i	−0.998041	+	0.576219i	−0.907668	−	0.419689i	$-0.862139\pi$
$229$	−15.1031	+	8.71978i	−0.998041	+	0.576219i	−0.0903729	+	0.995908i	$0.528806\pi$
$230$	5.32827			0.351335
$231$	−1.58818	+	15.1870i	−0.104495	+	0.999232i
$232$		−	7.05400i		−	0.463118i
$233$	1.57065	+	2.72044i	0.102896	+	0.178222i	0.912877	−	0.408235i	$-0.133856\pi$
$233$	1.57065	+	2.72044i	0.102896	+	0.178222i	−0.809980	+	0.586457i	$0.800522\pi$
$234$	1.59541	−	3.23337i	0.104295	−	0.211372i
$235$	0.185810	−	0.321832i	0.0121209	−	0.0209940i
$236$	−9.94051	+	5.73915i	−0.647072	+	0.373587i
$237$	3.97467			0.258183
$238$	6.63623	+	4.81620i	0.430163	+	0.312188i
$239$		−	16.3029i		−	1.05455i	−0.849695	−	0.527275i	$-0.823214\pi$
$239$		−	16.3029i		−	1.05455i	0.849695	−	0.527275i	$-0.176786\pi$
$240$	−0.935588	+	0.540162i	−0.0603919	+	0.0348673i
$241$	−3.48604	−	2.01266i	−0.224555	−	0.129647i	0.383502	−	0.923540i	$-0.374718\pi$
$241$	−3.48604	−	2.01266i	−0.224555	−	0.129647i	−0.608058	+	0.793893i	$0.708051\pi$
$242$	19.3208	+	11.1548i	1.24199	+	0.717061i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	4.03927			0.258588
$245$	−5.62515	−	5.05426i	−0.359378	−	0.322905i
$246$	−8.58166			−0.547147
$247$	13.7205	+	20.5440i	0.873015	+	1.30719i
$248$	−1.92589	+	3.33574i	−0.122294	+	0.211820i
$249$	8.86808	+	5.11999i	0.561992	+	0.324466i
$250$	4.77120	+	8.26395i	0.301757	+	0.522658i
$251$	9.74843			0.615315			0.307658	−	0.951497i	$-0.400455\pi$
$251$	9.74843			0.615315			0.307658	+	0.951497i	$0.400455\pi$
$252$	−1.55401	+	2.14127i	−0.0978936	+	0.134887i
$253$		−	28.4654i		−	1.78960i
$254$	14.9779	−	8.64748i	0.939796	−	0.542591i
$255$	2.89957	+	1.67407i	0.181578	+	0.104834i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.40807	−	2.43885i	−0.0878329	−	0.152131i	0.818762	−	0.574133i	$-0.194661\pi$
$257$	−1.40807	−	2.43885i	−0.0878329	−	0.152131i	−0.906595	+	0.422002i	$0.861328\pi$
$258$		−	9.19577i		−	0.572503i
$259$	−0.655824	+	6.27131i	−0.0407509	+	0.389681i
$260$	3.88688	−	0.253895i	0.241054	−	0.0157459i
$261$	−3.52700	−	6.10894i	−0.218316	−	0.378134i
$262$	7.53881	+	4.35254i	0.465750	+	0.268901i
$263$	−3.59390	+	6.22482i	−0.221609	+	0.383839i	−0.955297	−	0.295648i	$-0.904464\pi$
$263$	−3.59390	+	6.22482i	−0.221609	+	0.383839i	0.733687	+	0.679487i	$0.237798\pi$
$264$	2.88573	+	4.99823i	0.177604	+	0.307620i
$265$			11.0147i			0.676629i
$266$	−7.38203	−	16.5570i	−0.452621	−	1.01517i
$267$		−	10.3554i		−	0.633741i
$268$	10.8620	−	6.27120i	0.663504	−	0.383074i
$269$	−3.63417	+	6.29456i	−0.221579	+	0.383786i	−0.955288	−	0.295678i	$-0.904454\pi$
$269$	−3.63417	+	6.29456i	−0.221579	+	0.383786i	0.733709	+	0.679464i	$0.237788\pi$
$270$	−0.540162	+	0.935588i	−0.0328732	+	0.0569380i
$271$	−22.8520	+	13.1936i	−1.38816	+	0.801455i	−0.993108	−	0.117203i	$-0.962607\pi$
$271$	−22.8520	+	13.1936i	−1.38816	+	0.801455i	−0.395053	+	0.918658i	$0.629274\pi$
$272$	3.09920			0.187917
$273$	8.44090	−	4.44423i	0.510867	−	0.268977i
$274$	−7.87547			−0.475775
$275$	19.1577	−	11.0607i	1.15525	−	0.666986i
$276$	2.46605	−	4.27133i	0.148439	−	0.257104i
$277$	7.99431	−	13.8465i	0.480331	−	0.831958i	−0.519414	−	0.854523i	$-0.673850\pi$
$277$	7.99431	−	13.8465i	0.480331	−	0.831958i	0.999745	+	0.0225644i	$0.00718310\pi$
$278$	−14.8309	+	8.56262i	−0.889498	+	0.513552i
$279$			3.85178i			0.230600i
$280$	−2.84277	−	0.297283i	−0.169888	−	0.0177660i
$281$		−	12.7062i		−	0.757988i	−0.925399	−	0.378994i	$-0.876270\pi$
$281$		−	12.7062i		−	0.757988i	0.925399	−	0.378994i	$-0.123730\pi$
$282$	−0.171994	−	0.297903i	−0.0102421	−	0.0177399i
$283$	−8.89947	+	15.4143i	−0.529019	+	0.916287i	0.470409	+	0.882449i	$0.344106\pi$
$283$	−8.89947	+	15.4143i	−0.529019	+	0.916287i	−0.999427	+	0.0338384i	$0.989227\pi$
$284$	9.95817	+	5.74935i	0.590909	+	0.341161i
$285$	−3.70107	−	6.41044i	−0.219232	−	0.379722i
$286$	−1.35639	−	20.7650i	−0.0802052	−	1.22786i
$287$	−18.3757	−	13.3360i	−1.08468	−	0.787200i
$288$			1.00000i			0.0589256i
$289$	3.69748	+	6.40422i	0.217499	+	0.376719i
$290$	3.81030	−	6.59963i	0.223749	−	0.387544i
$291$	2.53882	+	1.46579i	0.148829	+	0.0859262i
$292$	6.41044	−	3.70107i	0.375143	−	0.216589i
$293$		−	14.7839i		−	0.863684i	−0.901949	−	0.431842i	$-0.857864\pi$
$293$		−	14.7839i		−	0.863684i	0.901949	−	0.431842i	$-0.142136\pi$
$294$	−6.65513	+	2.17009i	−0.388135	+	0.126562i
$295$	−12.4003			−0.721973
$296$	1.19163	+	2.06396i	0.0692621	+	0.119965i
$297$	4.99823	+	2.88573i	0.290027	+	0.167447i
$298$	−9.90329	+	17.1530i	−0.573682	+	0.993646i
$299$	−14.7882	+	9.87640i	−0.855222	+	0.571167i
$300$	3.83290			0.221293
$301$	14.2903	−	19.6906i	0.823682	−	1.13495i
$302$	−1.62271			−0.0933767
$303$	−3.26202	−	5.64998i	−0.187398	−	0.324583i
$304$	−5.93381	−	3.42589i	−0.340328	−	0.196488i
$305$	3.77909	+	2.18186i	0.216390	+	0.124933i
$306$	2.68399	−	1.54960i	0.153433	−	0.0885848i
$307$			4.87132i			0.278021i	0.990291	+	0.139010i	$0.0443922\pi$
$307$			4.87132i			0.278021i	−0.990291	+	0.139010i	$0.955608\pi$
$308$	−1.58818	+	15.1870i	−0.0904952	+	0.865361i
$309$	−6.44219			−0.366484
$310$	−3.60368	+	2.08058i	−0.204675	+	0.118169i
$311$	15.4208	−	26.7097i	0.874436	−	1.51457i	0.0170738	−	0.999854i	$-0.494565\pi$
$311$	15.4208	−	26.7097i	0.874436	−	1.51457i	0.857362	−	0.514713i	$-0.172102\pi$
$312$	1.59541	−	3.23337i	0.0903223	−	0.183053i
$313$	−16.7341	−	28.9843i	−0.945868	−	1.63829i	−0.754004	−	0.656870i	$-0.771880\pi$
$313$	−16.7341	−	28.9843i	−0.945868	−	1.63829i	−0.191864	−	0.981421i	$-0.561453\pi$
$314$			0.699100i			0.0394525i
$315$	−2.61055	+	1.16393i	−0.147088	+	0.0655799i
$316$	3.97467			0.223593
$317$	17.6927	−	10.2149i	0.993723	−	0.573726i	0.0873379	−	0.996179i	$-0.472164\pi$
$317$	17.6927	−	10.2149i	0.993723	−	0.573726i	0.906385	+	0.422453i	$0.138831\pi$
$318$	8.82979	+	5.09788i	0.495150	+	0.285875i
$319$	−35.2575	−	20.3559i	−1.97404	−	1.13971i
$320$	−0.935588	+	0.540162i	−0.0523009	+	0.0301960i
$321$	−10.3596			−0.578215
$322$	11.9182	−	5.31379i	0.664174	−	0.296126i
$323$			21.2350i			1.18155i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−12.3932	−	6.11505i	−0.687450	−	0.339202i
$326$	−5.21939	+	9.04024i	−0.289075	+	0.500693i
$327$	4.36054	−	2.51756i	0.241139	−	0.139221i
$328$	−8.58166			−0.473843
$329$	0.0946586	−	0.905172i	0.00521870	−	0.0499038i
$330$			6.23504i			0.343228i
$331$	−13.4250	+	7.75093i	−0.737905	+	0.426030i	−0.821307	−	0.570486i	$-0.806755\pi$
$331$	−13.4250	+	7.75093i	−0.737905	+	0.426030i	0.0834022	+	0.996516i	$0.473421\pi$
$332$	8.86808	+	5.11999i	0.486699	+	0.280996i
$333$	2.06396	+	1.19163i	0.113105	+	0.0653009i
$334$	−2.76821	−	4.79468i	−0.151470	−	0.262353i
$335$	13.5498			0.740307
$336$	−1.55401	+	2.14127i	−0.0847784	+	0.116816i
$337$	−15.5114			−0.844959			−0.422480	−	0.906372i	$-0.638840\pi$
$337$	−15.5114			−0.844959			−0.422480	+	0.906372i	$0.638840\pi$
$338$	−10.3171	+	7.90933i	−0.561176	+	0.430211i
$339$	−9.04663	+	15.6692i	−0.491346	+	0.851036i
$340$	2.89957	+	1.67407i	0.157251	+	0.0907892i
$341$	11.1152	+	19.2521i	0.601921	+	1.04256i
$342$	−6.85178			−0.370502
$343$	−17.6228	−	5.69541i	−0.951540	−	0.307524i
$344$		−	9.19577i		−	0.495803i
$345$	4.61441	−	2.66413i	0.248432	−	0.143432i
$346$	−3.10826	−	1.79455i	−0.167101	−	0.0964759i
$347$	5.13018	−	8.88574i	0.275403	−	0.477011i	−0.694834	−	0.719170i	$-0.744522\pi$
$347$	5.13018	−	8.88574i	0.275403	−	0.477011i	0.970237	+	0.242159i	$0.0778555\pi$
$348$	−3.52700	−	6.10894i	−0.189067	−	0.327474i
$349$		−	12.1017i		−	0.647790i	−0.946093	−	0.323895i	$-0.895008\pi$
$349$		−	12.1017i		−	0.647790i	0.946093	−	0.323895i	$-0.104992\pi$
$350$	8.20728	+	5.95638i	0.438698	+	0.318382i
$351$	−0.235018	−	3.59788i	−0.0125443	−	0.192041i
$352$	2.88573	+	4.99823i	0.153810	+	0.266406i
$353$	9.57822	+	5.52999i	0.509797	+	0.294331i	0.732750	−	0.680498i	$-0.238236\pi$
$353$	9.57822	+	5.52999i	0.509797	+	0.294331i	−0.222953	+	0.974829i	$0.571570\pi$
$354$	−5.73915	+	9.94051i	−0.305033	+	0.528332i
$355$	6.21116	+	10.7580i	0.329654	+	0.570978i
$356$		−	10.3554i		−	0.548836i
$357$	8.15524	+	0.852836i	0.431621	+	0.0451369i
$358$			10.2438i			0.541401i
$359$	2.65373	−	1.53213i	0.140059	−	0.0808629i	−0.428333	−	0.903621i	$-0.640899\pi$
$359$	2.65373	−	1.53213i	0.140059	−	0.0808629i	0.568392	+	0.822758i	$0.307566\pi$
$360$	−0.540162	+	0.935588i	−0.0284690	+	0.0493098i
$361$	13.9734	−	24.2027i	0.735444	−	1.27383i
$362$	−11.1044	+	6.41115i	−0.583636	+	0.336963i
$363$	22.3097			1.17096
$364$	8.44090	−	4.44423i	0.442424	−	0.232941i
$365$	7.99670			0.418567
$366$	3.49811	−	2.01964i	0.182849	−	0.105568i
$367$	13.9194	−	24.1092i	0.726589	−	1.25849i	−0.231728	−	0.972781i	$-0.574438\pi$
$367$	13.9194	−	24.1092i	0.726589	−	1.25849i	0.958317	−	0.285708i	$-0.0922287\pi$
$368$	2.46605	−	4.27133i	0.128552	−	0.222658i
$369$	−7.43194	+	4.29083i	−0.386891	+	0.223372i
$370$			2.57469i			0.133852i
$371$	10.9848	+	24.6376i	0.570303	+	1.27912i
$372$			3.85178i			0.199705i
$373$	14.3103	+	24.7862i	0.740960	+	1.28338i	0.952058	+	0.305916i	$0.0989627\pi$
$373$	14.3103	+	24.7862i	0.740960	+	1.28338i	−0.211098	+	0.977465i	$0.567704\pi$
$374$	8.94345	−	15.4905i	0.462455	−	0.800995i
$375$	8.26395	+	4.77120i	0.426749	+	0.246383i
$376$	−0.171994	−	0.297903i	−0.00886993	−	0.0153632i
$377$	1.65781	+	25.3795i	0.0853817	+	1.30711i
$378$	−0.275179	+	2.63140i	−0.0141537	+	0.135345i
$379$		−	33.5171i		−	1.72166i	−0.508894	−	0.860829i	$-0.669946\pi$
$379$		−	33.5171i		−	1.72166i	0.508894	−	0.860829i	$-0.330054\pi$
$380$	−3.70107	−	6.41044i	−0.189861	−	0.328849i
$381$	8.64748	−	14.9779i	0.443024	−	0.767340i
$382$	−6.73227	−	3.88688i	−0.344453	−	0.198870i
$383$	−0.418503	+	0.241623i	−0.0213845	+	0.0123463i	−0.510654	−	0.859786i	$-0.670597\pi$
$383$	−0.418503	+	0.241623i	−0.0213845	+	0.0123463i	0.489270	+	0.872133i	$0.337263\pi$
$384$			1.00000i			0.0510310i
$385$	−9.68933	+	13.3509i	−0.493814	+	0.680425i
$386$	−12.1154			−0.616660
$387$	−4.59788	−	7.96377i	−0.233724	−	0.404821i
$388$	2.53882	+	1.46579i	0.128889	+	0.0744143i
$389$	−9.52029	+	16.4896i	−0.482698	+	0.836057i	−0.999803	−	0.0198650i	$-0.993676\pi$
$389$	−9.52029	+	16.4896i	−0.482698	+	0.836057i	0.517105	+	0.855922i	$0.327010\pi$
$390$	3.23919	−	2.16332i	0.164023	−	0.109544i
$391$	−15.2856			−0.773025
$392$	−6.65513	+	2.17009i	−0.336135	+	0.109606i
$393$	8.70507			0.439113
$394$	5.31136	+	9.19954i	0.267582	+	0.463466i
$395$	3.71865	+	2.14697i	0.187106	+	0.108026i
$396$	4.99823	+	2.88573i	0.251170	+	0.145013i
$397$	23.0428	−	13.3038i	1.15648	−	0.667696i	0.206025	−	0.978547i	$-0.433947\pi$
$397$	23.0428	−	13.3038i	1.15648	−	0.667696i	0.950459	+	0.310850i	$0.100614\pi$
$398$		−	25.5920i		−	1.28281i
$399$	−14.6715	−	10.6478i	−0.734495	−	0.533054i
$400$	3.83290			0.191645
$401$	4.56360	−	2.63480i	0.227896	−	0.131576i	−0.381705	−	0.924284i	$-0.624663\pi$
$401$	4.56360	−	2.63480i	0.227896	−	0.131576i	0.609601	+	0.792709i	$0.291330\pi$
$402$	6.27120	−	10.8620i	0.312779	−	0.541749i
$403$	6.14517	−	12.4542i	0.306113	−	0.620389i
$404$	−3.26202	−	5.64998i	−0.162291	−	0.281097i
$405$			1.08032i			0.0536817i
$406$	1.94111	−	18.5619i	0.0963359	−	0.921212i
$407$	13.7549			0.681804
$408$	2.68399	−	1.54960i	0.132877	−	0.0767167i
$409$	−6.07095	−	3.50506i	−0.300189	−	0.173314i	0.342339	−	0.939577i	$-0.388781\pi$
$409$	−6.07095	−	3.50506i	−0.300189	−	0.173314i	−0.642528	+	0.766262i	$0.722114\pi$
$410$	−8.02890	−	4.63549i	−0.396519	−	0.228930i
$411$	−6.82036	+	3.93773i	−0.336423	+	0.194234i
$412$	−6.44219			−0.317384
$413$	−27.7368	+	12.3666i	−1.36484	+	0.608521i
$414$		−	4.93210i		−	0.242400i
$415$	5.53124	+	9.58039i	0.271518	+	0.470283i
$416$	1.59541	−	3.23337i	0.0782214	−	0.158529i
$417$	−8.56262	+	14.8309i	−0.419313	+	0.726272i
$418$	−34.2467	+	19.7724i	−1.67506	+	0.967098i
$419$	22.7139			1.10965			0.554823	−	0.831969i	$-0.312786\pi$
$419$	22.7139			1.10965			0.554823	+	0.831969i	$0.312786\pi$
$420$	−2.61055	+	1.16393i	−0.127382	+	0.0567939i
$421$			0.689615i			0.0336098i	0.999859	+	0.0168049i	$0.00534942\pi$
$421$			0.689615i			0.0336098i	−0.999859	+	0.0168049i	$0.994651\pi$
$422$	14.3398	−	8.27908i	0.698050	−	0.403019i
$423$	−0.297903	−	0.171994i	−0.0144845	−	0.00836265i
$424$	8.82979	+	5.09788i	0.428813	+	0.247575i
$425$	−5.93947	−	10.2875i	−0.288106	−	0.499015i
$426$	11.4987			0.557114
$427$	10.6289	+	1.11152i	0.514371	+	0.0537904i
$428$	−10.3596			−0.500749
$429$	−11.5572	−	17.3048i	−0.557986	−	0.835486i
$430$	4.96720	−	8.60345i	0.239540	−	0.414895i
$431$	2.01402	+	1.16279i	0.0970119	+	0.0560098i	0.547721	−	0.836661i	$-0.315496\pi$
$431$	2.01402	+	1.16279i	0.0970119	+	0.0560098i	−0.450709	+	0.892671i	$0.648829\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−6.69113			−0.321555			−0.160778	−	0.986991i	$-0.551400\pi$
$433$	−6.69113			−0.321555			−0.160778	+	0.986991i	$0.551400\pi$
$434$	−5.98572	+	8.24770i	−0.287324	+	0.395902i
$435$		−	7.62060i		−	0.365380i
$436$	4.36054	−	2.51756i	0.208832	−	0.120569i
$437$	29.2662	+	16.8968i	1.39999	+	0.808285i
$438$	3.70107	−	6.41044i	0.176844	−	0.306303i
$439$	−10.3585	−	17.9414i	−0.494384	−	0.856298i	0.505595	−	0.862771i	$-0.331273\pi$
$439$	−10.3585	−	17.9414i	−0.494384	−	0.856298i	−0.999979	+	0.00647301i	$0.997940\pi$
$440$			6.23504i			0.297244i
$441$	−4.67847	+	5.20691i	−0.222784	+	0.247948i
$442$	−11.1506	+	0.728367i	−0.530378	+	0.0346449i
$443$	−0.373195	−	0.646393i	−0.0177310	−	0.0307111i	0.857024	−	0.515277i	$-0.172311\pi$
$443$	−0.373195	−	0.646393i	−0.0177310	−	0.0307111i	−0.874755	+	0.484566i	$0.838978\pi$
$444$	2.06396	+	1.19163i	0.0979514	+	0.0565523i
$445$	5.59360	−	9.68840i	0.265162	−	0.459274i
$446$	−0.819325	−	1.41911i	−0.0387962	−	0.0671969i
$447$			19.8066i			0.936819i
$448$	−1.55401	+	2.14127i	−0.0734202	+	0.101166i
$449$			35.3286i			1.66726i	0.552324	+	0.833629i	$0.313741\pi$
$449$			35.3286i			1.66726i	−0.552324	+	0.833629i	$0.686259\pi$
$450$	3.31939	−	1.91645i	0.156478	−	0.0903423i
$451$	−24.7643	+	42.8931i	−1.16611	+	2.01976i
$452$	−9.04663	+	15.6692i	−0.425518	+	0.737019i
$453$	−1.40531	+	0.811357i	−0.0660273	+	0.0381209i
$454$	−11.0068			−0.516573
$455$	10.2978	+	0.401489i	0.482769	+	0.0188221i
$456$	−6.85178			−0.320864
$457$	−29.0667	+	16.7817i	−1.35968	+	0.785014i	−0.989581	−	0.143977i	$-0.954011\pi$
$457$	−29.0667	+	16.7817i	−1.35968	+	0.785014i	−0.370102	+	0.928991i	$0.620677\pi$
$458$	−8.71978	+	15.1031i	−0.407449	+	0.705722i
$459$	1.54960	−	2.68399i	0.0723292	−	0.125278i
$460$	4.61441	−	2.66413i	0.215148	−	0.124216i
$461$		−	0.974793i		−	0.0454006i	−0.999742	−	0.0227003i	$-0.992774\pi$
$461$		−	0.974793i		−	0.0454006i	0.999742	−	0.0227003i	$-0.00722635\pi$
$462$	6.21810	+	13.9464i	0.289292	+	0.648847i
$463$			12.4376i			0.578024i	0.957325	+	0.289012i	$0.0933267\pi$
$463$			12.4376i			0.578024i	−0.957325	+	0.289012i	$0.906673\pi$
$464$	−3.52700	−	6.10894i	−0.163737	−	0.283600i
$465$	−2.08058	+	3.60368i	−0.0964847	+	0.167116i
$466$	2.72044	+	1.57065i	0.126022	+	0.0727588i
$467$	6.58082	+	11.3983i	0.304524	+	0.527451i	0.977155	−	0.212527i	$-0.0681692\pi$
$467$	6.58082	+	11.3983i	0.304524	+	0.527451i	−0.672631	+	0.739978i	$0.734836\pi$
$468$	−0.235018	−	3.59788i	−0.0108637	−	0.166312i
$469$	30.3081	−	13.5130i	1.39950	−	0.623974i
$470$		−	0.371619i		−	0.0171415i
$471$	0.349550	+	0.605438i	0.0161064	+	0.0278971i
$472$	−5.73915	+	9.94051i	−0.264166	+	0.457549i
$473$	−45.9625	−	26.5365i	−2.11336	−	1.22015i
$474$	3.44217	−	1.98734i	0.158104	−	0.0912813i
$475$			26.2622i			1.20499i
$476$	8.15524	+	0.852836i	0.373795	+	0.0390897i
$477$	10.1958			0.466832
$478$	−8.15147	−	14.1188i	−0.372839	−	0.645777i
$479$	−12.7473	−	7.35964i	−0.582438	−	0.336271i	0.179664	−	0.983728i	$-0.442499\pi$
$479$	−12.7473	−	7.35964i	−0.582438	−	0.336271i	−0.762102	+	0.647458i	$0.775832\pi$
$480$	−0.540162	+	0.935588i	−0.0246549	+	0.0427035i
$481$	−4.77241	−	7.14585i	−0.217603	−	0.325823i
$482$	−4.02533			−0.183349
$483$	7.66455	−	10.5610i	0.348749	−	0.480541i
$484$	22.3097			1.01408
$485$	1.58353	+	2.74275i	0.0719043	+	0.124542i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	15.7836	+	9.11264i	0.715222	+	0.412933i	0.812991	−	0.582276i	$-0.197838\pi$
$487$	15.7836	+	9.11264i	0.715222	+	0.412933i	−0.0977699	+	0.995209i	$0.531171\pi$
$488$	3.49811	−	2.01964i	0.158352	−	0.0914246i
$489$			10.4388i			0.472058i
$490$	−7.39865	−	1.56454i	−0.334237	−	0.0706787i
$491$	6.69377			0.302085			0.151043	−	0.988527i	$-0.451737\pi$
$491$	6.69377			0.302085			0.151043	+	0.988527i	$0.451737\pi$
$492$	−7.43194	+	4.29083i	−0.335058	+	0.193446i
$493$	−10.9309	+	18.9328i	−0.492302	+	0.852692i
$494$	22.1543	+	10.9314i	0.996770	+	0.491827i
$495$	3.11752	+	5.39970i	0.140122	+	0.242699i
$496$			3.85178i			0.172950i
$497$	24.6218	+	17.8691i	1.10444	+	0.801540i
$498$	10.2400			0.458864
$499$	12.8211	−	7.40229i	0.573953	−	0.331372i	−0.184773	−	0.982781i	$-0.559155\pi$
$499$	12.8211	−	7.40229i	0.573953	−	0.331372i	0.758727	+	0.651409i	$0.225822\pi$
$500$	8.26395	+	4.77120i	0.369575	+	0.213374i
$501$	−4.79468	−	2.76821i	−0.214210	−	0.123674i
$502$	8.44239	−	4.87421i	0.376802	−	0.217547i
$503$	29.2584			1.30457			0.652283	−	0.757975i	$-0.273811\pi$
$503$	29.2584			1.30457			0.652283	+	0.757975i	$0.273811\pi$
$504$	−0.275179	+	2.63140i	−0.0122575	+	0.117212i
$505$		−	7.04807i		−	0.313635i
$506$	−14.2327	−	24.6518i	−0.632721	−	1.09590i
$507$	−4.98020	+	12.0082i	−0.221179	+	0.533304i
$508$	8.64748	−	14.9779i	0.383670	−	0.664536i
$509$	−6.75683	+	3.90106i	−0.299491	+	0.172911i	−0.642214	−	0.766525i	$-0.721984\pi$
$509$	−6.75683	+	3.90106i	−0.299491	+	0.172911i	0.342723	+	0.939436i	$0.388651\pi$
$510$	3.34814			0.148258
$511$	17.8869	−	7.97498i	0.791270	−	0.352792i
$512$			1.00000i			0.0441942i
$513$	−5.93381	+	3.42589i	−0.261984	+	0.151257i
$514$	−2.43885	−	1.40807i	−0.107573	−	0.0621073i
$515$	−6.02724	−	3.47983i	−0.265592	−	0.153339i
$516$	−4.59788	−	7.96377i	−0.202411	−	0.350585i
$517$	−1.98532			−0.0873141
$518$	2.56770	+	5.75903i	0.112818	+	0.253037i
$519$	−3.58911			−0.157544
$520$	3.23919	−	2.16332i	0.142048	−	0.0948678i
$521$	−11.9207	+	20.6472i	−0.522255	+	0.904572i	0.477410	+	0.878681i	$0.341576\pi$
$521$	−11.9207	+	20.6472i	−0.522255	+	0.904572i	−0.999665	+	0.0258915i	$0.991758\pi$
$522$	−6.10894	−	3.52700i	−0.267381	−	0.154373i
$523$	−1.03664	−	1.79551i	−0.0453290	−	0.0785121i	0.842471	−	0.538742i	$-0.181100\pi$
$523$	−1.03664	−	1.79551i	−0.0453290	−	0.0785121i	−0.887800	+	0.460230i	$0.847767\pi$
$524$	8.70507			0.380283
$525$	10.0859	+	1.05474i	0.440185	+	0.0460324i
$526$			7.18780i			0.313403i
$527$	10.3381	−	5.96872i	0.450336	−	0.260001i
$528$	4.99823	+	2.88573i	0.217520	+	0.125585i
$529$	−0.662816	+	1.14803i	−0.0288181	+	0.0499144i
$530$	5.50736	+	9.53903i	0.239225	+	0.414349i
$531$			11.4783i			0.498116i
$532$	−14.6715	−	10.6478i	−0.636091	−	0.461639i
$533$	30.8758	−	2.01684i	1.33738	−	0.0873591i
$534$	−5.17771	−	8.96805i	−0.224061	−	0.388086i
$535$	−9.69228	−	5.59584i	−0.419034	−	0.241929i
$536$	6.27120	−	10.8620i	0.270874	−	0.469168i
$537$	5.12190	+	8.87138i	0.221026	+	0.382828i
$538$			7.26834i			0.313360i
$539$	−8.35831	+	39.5261i	−0.360018	+	1.70251i
$540$			1.08032i			0.0464897i
$541$	−29.6976	+	17.1459i	−1.27680	+	0.737161i	−0.976259	−	0.216608i	$-0.930501\pi$
$541$	−29.6976	+	17.1459i	−1.27680	+	0.737161i	−0.300542	+	0.953769i	$0.597167\pi$
$542$	−13.1936	+	22.8520i	−0.566715	+	0.981578i
$543$	−6.41115	+	11.1044i	−0.275129	+	0.476537i
$544$	2.68399	−	1.54960i	0.115075	−	0.0664386i
$545$	5.43956			0.233005
$546$	5.08792	−	8.06927i	0.217743	−	0.345333i
$547$	−44.6606			−1.90955			−0.954774	−	0.297334i	$-0.903903\pi$
$547$	−44.6606			−1.90955			−0.954774	+	0.297334i	$0.903903\pi$
$548$	−6.82036	+	3.93773i	−0.291351	+	0.168212i
$549$	2.01964	−	3.49811i	0.0861959	−	0.149296i
$550$	11.0607	−	19.1577i	0.471630	−	0.816887i
$551$	41.8571	−	24.1662i	1.78317	−	1.02952i
$552$		−	4.93210i		−	0.209924i
$553$	10.4590	+	1.09375i	0.444760	+	0.0465109i
$554$		−	15.9886i		−	0.679291i
$555$	1.28735	+	2.22975i	0.0546448	+	0.0946475i
$556$	−8.56262	+	14.8309i	−0.363136	+	0.628970i
$557$	−17.4377	−	10.0677i	−0.738860	−	0.426581i	0.0827944	−	0.996567i	$-0.473616\pi$
$557$	−17.4377	−	10.0677i	−0.738860	−	0.426581i	−0.821655	+	0.569985i	$0.806949\pi$
$558$	1.92589	+	3.33574i	0.0815294	+	0.141213i
$559$	2.16117	+	33.0853i	0.0914076	+	1.39936i
$560$	−2.61055	+	1.16393i	−0.110316	+	0.0491849i
$561$		−	17.8869i		−	0.755185i
$562$	−6.35310	−	11.0039i	−0.267989	−	0.464171i
$563$	−10.0473	+	17.4024i	−0.423443	+	0.733424i	−0.996274	−	0.0862494i	$-0.972512\pi$
$563$	−10.0473	+	17.4024i	−0.423443	+	0.733424i	0.572831	+	0.819674i	$0.305845\pi$
$564$	−0.297903	−	0.171994i	−0.0125440	−	0.00724227i
$565$	−16.9278	+	9.77329i	−0.712159	+	0.411165i
$566$			17.7989i			0.748145i
$567$	1.07739	+	2.41645i	0.0452461	+	0.101481i
$568$	11.4987			0.482475
$569$	3.88217	+	6.72412i	0.162749	+	0.281890i	0.935854	−	0.352389i	$-0.114631\pi$
$569$	3.88217	+	6.72412i	0.162749	+	0.281890i	−0.773105	+	0.634279i	$0.781297\pi$
$570$	−6.41044	−	3.70107i	−0.268504	−	0.155021i
$571$	−12.3342	+	21.3635i	−0.516171	+	0.894034i	0.483653	+	0.875260i	$0.339310\pi$
$571$	−12.3342	+	21.3635i	−0.516171	+	0.894034i	−0.999824	+	0.0187744i	$0.994024\pi$
$572$	−11.5572	−	17.3048i	−0.483230	−	0.723552i
$573$	−7.77376			−0.324753
$574$	−22.5818	−	2.36150i	−0.942546	−	0.0985669i
$575$	−18.9043			−0.788362
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	28.8021	+	16.6289i	1.19905	+	0.692271i	0.960343	−	0.278821i	$-0.0899435\pi$
$577$	28.8021	+	16.6289i	1.19905	+	0.692271i	0.238706	+	0.971092i	$0.423277\pi$
$578$	6.40422	+	3.69748i	0.266380	+	0.153795i
$579$	−10.4923	+	6.05772i	−0.436044	+	0.251750i
$580$		−	7.62060i		−	0.316428i
$581$	21.9266	+	15.9131i	0.909667	+	0.660185i
$582$	2.93158			0.121518
$583$	50.9608	−	29.4222i	2.11058	−	1.21854i
$584$	3.70107	−	6.41044i	0.153151	−	0.265266i
$585$	1.72356	−	3.49308i	0.0712604	−	0.144421i
$586$	−7.39194	−	12.8032i	−0.305358	−	0.528896i
$587$			13.3541i			0.551183i	0.961275	+	0.275592i	$0.0888737\pi$
$587$			13.3541i			0.551183i	−0.961275	+	0.275592i	$0.911126\pi$
$588$	−4.67847	+	5.20691i	−0.192937	+	0.214729i
$589$	−26.3915			−1.08744
$590$	−10.7390	+	6.20014i	−0.442116	+	0.255256i
$591$	9.19954	+	5.31136i	0.378419	+	0.218480i
$592$	2.06396	+	1.19163i	0.0848284	+	0.0489757i
$593$	−15.9633	+	9.21644i	−0.655536	+	0.378474i	−0.790574	−	0.612367i	$-0.790218\pi$
$593$	−15.9633	+	9.21644i	−0.655536	+	0.378474i	0.135038	+	0.990840i	$0.456884\pi$
$594$	5.77146			0.236806
$595$	7.16927	+	5.20305i	0.293912	+	0.213304i
$596$			19.8066i			0.811309i
$597$	−12.7960	−	22.1633i	−0.523705	−	0.907083i
$598$	−7.86873	+	15.9473i	−0.321776	+	0.652134i
$599$	−1.08926	+	1.88666i	−0.0445061	+	0.0770869i	−0.887420	−	0.460961i	$-0.847505\pi$
$599$	−1.08926	+	1.88666i	−0.0445061	+	0.0770869i	0.842914	+	0.538048i	$0.180838\pi$
$600$	3.31939	−	1.91645i	0.135514	−	0.0782388i
$601$	18.5021			0.754717			0.377359	−	0.926067i	$-0.376832\pi$
$601$	18.5021			0.754717			0.377359	+	0.926067i	$0.376832\pi$
$602$	2.53048	−	24.1978i	0.103135	−	0.986227i
$603$		−	12.5424i		−	0.510766i
$604$	−1.40531	+	0.811357i	−0.0571813	+	0.0330136i
$605$	20.8727	+	12.0508i	0.848595	+	0.489936i
$606$	−5.64998	−	3.26202i	−0.229515	−	0.132510i
$607$	−1.74668	−	3.02535i	−0.0708958	−	0.122795i	0.828398	−	0.560139i	$-0.189252\pi$
$607$	−1.74668	−	3.02535i	−0.0708958	−	0.122795i	−0.899294	+	0.437344i	$0.855919\pi$
$608$	−6.85178			−0.277876
$609$	−7.59990	−	17.0456i	−0.307963	−	0.690724i
$610$	4.36372			0.176682
$611$	0.688828	+	1.03140i	0.0278670	+	0.0417259i
$612$	1.54960	−	2.68399i	0.0626389	−	0.108494i
$613$	8.91698	+	5.14822i	0.360153	+	0.207935i	0.669148	−	0.743129i	$-0.266659\pi$
$613$	8.91698	+	5.14822i	0.360153	+	0.207935i	−0.308995	+	0.951064i	$0.599993\pi$
$614$	2.43566	+	4.21869i	0.0982952	+	0.170252i
$615$	−9.27097			−0.373842
$616$	6.21810	+	13.9464i	0.250534	+	0.561918i
$617$			17.1451i			0.690236i	0.938559	+	0.345118i	$0.112161\pi$
$617$			17.1451i			0.690236i	−0.938559	+	0.345118i	$0.887839\pi$
$618$	−5.57910	+	3.22110i	−0.224424	+	0.129572i
$619$	−40.9700	−	23.6541i	−1.64672	−	0.950737i	−0.978362	−	0.206900i	$-0.933662\pi$
$619$	−40.9700	−	23.6541i	−1.64672	−	0.950737i	−0.668362	−	0.743836i	$-0.733004\pi$
$620$	−2.08058	+	3.60368i	−0.0835582	+	0.144727i
$621$	−2.46605	−	4.27133i	−0.0989592	−	0.171402i
$622$		−	30.8417i		−	1.23664i
$623$	2.84960	−	27.2493i	0.114167	−	1.09172i
$624$	−0.235018	−	3.59788i	−0.00940823	−	0.144031i
$625$	−4.42782	−	7.66921i	−0.177113	−	0.306768i
$626$	−28.9843	−	16.7341i	−1.15845	−	0.668830i
$627$	−19.7724	+	34.2467i	−0.789632	+	1.36768i
$628$	0.349550	+	0.605438i	0.0139486	+	0.0241596i
$629$		−	7.38620i		−	0.294507i
$630$	−1.67884	+	2.31327i	−0.0668865	+	0.0921627i
$631$			19.1671i			0.763030i	0.924363	+	0.381515i	$0.124598\pi$
$631$			19.1671i			0.763030i	−0.924363	+	0.381515i	$0.875402\pi$
$632$	3.44217	−	1.98734i	0.136922	−	0.0790520i
$633$	8.27908	−	14.3398i	0.329064	−	0.569955i
$634$	10.2149	−	17.6927i	0.405686	−	0.702668i
$635$	16.1810	−	9.34208i	0.642122	−	0.370729i
$636$	10.1958			0.404288
$637$	23.4344	−	9.37179i	0.928503	−	0.371324i
$638$	−40.7118			−1.61180
$639$	9.95817	−	5.74935i	0.393939	−	0.227441i
$640$	−0.540162	+	0.935588i	−0.0213518	+	0.0369823i
$641$	−2.65616	+	4.60061i	−0.104912	+	0.181713i	−0.913702	−	0.406384i	$-0.866789\pi$
$641$	−2.65616	+	4.60061i	−0.104912	+	0.181713i	0.808790	+	0.588097i	$0.200123\pi$
$642$	−8.97165	+	5.17978i	−0.354083	+	0.204430i
$643$			0.135981i			0.00536255i	0.999996	+	0.00268128i	$0.000853478\pi$
$643$			0.135981i			0.00536255i	−0.999996	+	0.00268128i	$0.999147\pi$
$644$	7.66455	−	10.5610i	0.302026	−	0.416160i
$645$		−	9.93440i		−	0.391167i
$646$	10.6175	+	18.3901i	0.417741	+	0.723548i
$647$	14.6938	−	25.4504i	0.577672	−	1.00056i	−0.418073	−	0.908413i	$-0.637294\pi$
$647$	14.6938	−	25.4504i	0.577672	−	1.00056i	0.995746	−	0.0921446i	$-0.0293722\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	33.1233	+	57.3712i	1.30020	+	2.25202i
$650$	−13.7903	+	0.900799i	−0.540901	+	0.0353322i
$651$	−1.05993	+	10.1356i	−0.0415419	+	0.397245i
$652$			10.4388i			0.408814i
$653$	−4.90119	−	8.48911i	−0.191798	−	0.332205i	0.754048	−	0.656819i	$-0.228099\pi$
$653$	−4.90119	−	8.48911i	−0.191798	−	0.332205i	−0.945846	+	0.324615i	$0.894765\pi$
$654$	2.51756	−	4.36054i	0.0984444	−	0.170511i
$655$	8.14436	+	4.70215i	0.318226	+	0.183728i
$656$	−7.43194	+	4.29083i	−0.290168	+	0.167529i
$657$		−	7.40214i		−	0.288785i
$658$	−0.370610	−	0.831232i	−0.0144479	−	0.0324048i
$659$	−7.36005			−0.286707			−0.143353	−	0.989672i	$-0.545789\pi$
$659$	−7.36005			−0.286707			−0.143353	+	0.989672i	$0.545789\pi$
$660$	3.11752	+	5.39970i	0.121349	+	0.210183i
$661$	41.3452	+	23.8706i	1.60814	+	0.928460i	0.989786	+	0.142561i	$0.0455338\pi$
$661$	41.3452	+	23.8706i	1.60814	+	0.928460i	0.618355	+	0.785899i	$0.287800\pi$
$662$	−7.75093	+	13.4250i	−0.301248	+	0.521778i
$663$	−9.29249	+	6.20607i	−0.360890	+	0.241024i
$664$	10.2400			0.397388
$665$	−7.97498	−	17.8869i	−0.309256	−	0.693624i
$666$	2.38326			0.0923494
$667$	17.3955	+	30.1299i	0.673557	+	1.16664i
$668$	−4.79468	−	2.76821i	−0.185512	−	0.107105i
$669$	−1.41911	−	0.819325i	−0.0548661	−	0.0316769i
$670$	11.7345	−	6.77492i	0.453343	−	0.261738i
$671$		−	23.3125i		−	0.899968i
$672$	−0.275179	+	2.63140i	−0.0106153	+	0.101509i
$673$	36.4374			1.40456			0.702279	−	0.711902i	$-0.252166\pi$
$673$	36.4374			1.40456			0.702279	+	0.711902i	$0.252166\pi$
$674$	−13.4333	+	7.75570i	−0.517430	+	0.298738i
$675$	1.91645	−	3.31939i	0.0737642	−	0.127763i
$676$	−4.98020	+	12.0082i	−0.191546	+	0.461855i
$677$	11.8072	+	20.4507i	0.453789	+	0.785986i	0.998618	−	0.0525617i	$-0.0167386\pi$
$677$	11.8072	+	20.4507i	0.453789	+	0.785986i	−0.544829	+	0.838547i	$0.683405\pi$
$678$			18.0933i			0.694868i
$679$	6.27731	+	4.55572i	0.240901	+	0.174832i
$680$	3.34814			0.128395
$681$	−9.53213	+	5.50338i	−0.365272	+	0.210890i
$682$	19.2521	+	11.1152i	0.737200	+	0.425622i
$683$	−8.45985	−	4.88430i	−0.323707	−	0.186892i	0.329337	−	0.944213i	$-0.393175\pi$
$683$	−8.45985	−	4.88430i	−0.323707	−	0.186892i	−0.653044	+	0.757320i	$0.726508\pi$
$684$	−5.93381	+	3.42589i	−0.226885	+	0.130992i
$685$	−8.50805			−0.325076
$686$	−18.1095	+	3.87901i	−0.691423	+	0.148101i
$687$			17.4396i			0.665361i
$688$	−4.59788	−	7.96377i	−0.175293	−	0.303616i
$689$	−32.9667	−	16.2664i	−1.25593	−	0.619702i
$690$	2.66413	−	4.61441i	0.101422	−	0.175668i
$691$	−29.7884	+	17.1983i	−1.13320	+	0.654256i	−0.944739	−	0.327824i	$-0.893685\pi$
$691$	−29.7884	+	17.1983i	−1.13320	+	0.654256i	−0.188465	+	0.982080i	$0.560351\pi$
$692$	−3.58911			−0.136437
$693$	12.3583	+	8.96892i	0.469451	+	0.340701i
$694$		−	10.2604i		−	0.389478i
$695$	−16.0222	+	9.25040i	−0.607755	+	0.350888i
$696$	−6.10894	−	3.52700i	−0.231559	−	0.133691i
$697$	23.0331	+	13.2981i	0.872440	+	0.503703i
$698$	−6.05086	−	10.4804i	−0.229028	−	0.396689i
$699$	3.14129			0.118815
$700$	10.0859	+	1.05474i	0.381211	+	0.0398652i
$701$	28.6811			1.08327			0.541636	−	0.840613i	$-0.317805\pi$
$701$	28.6811			1.08327			0.541636	+	0.840613i	$0.317805\pi$
$702$	−2.00247	−	2.99835i	−0.0755785	−	0.113165i
$703$	−8.16478	+	14.1418i	−0.307941	+	0.533369i
$704$	4.99823	+	2.88573i	0.188378	+	0.108760i
$705$	−0.185810	−	0.321832i	−0.00699799	−	0.0121209i
$706$	11.0600			0.416248
$707$	−7.02892	−	15.7650i	−0.264350	−	0.592904i
$708$			11.4783i			0.431381i
$709$	−2.70101	+	1.55943i	−0.101439	+	0.0585657i	−0.549861	−	0.835256i	$-0.685319\pi$
$709$	−2.70101	+	1.55943i	−0.101439	+	0.0585657i	0.448422	+	0.893822i	$0.351986\pi$
$710$	10.7580	+	6.21116i	0.403742	+	0.233101i
$711$	1.98734	−	3.44217i	0.0745309	−	0.129091i
$712$	−5.17771	−	8.96805i	−0.194043	−	0.336092i
$713$		−	18.9974i		−	0.711457i
$714$	7.48907	−	3.33904i	0.280271	−	0.124961i
$715$	−1.46534	−	22.4329i	−0.0548007	−	0.838944i
$716$	5.12190	+	8.87138i	0.191414	+	0.331539i
$717$	−14.1188	−	8.15147i	−0.527275	−	0.304422i
$718$	1.53213	−	2.65373i	0.0571787	−	0.0990364i
$719$	−9.38820	−	16.2608i	−0.350121	−	0.606427i	0.636150	−	0.771566i	$-0.280526\pi$
$719$	−9.38820	−	16.2608i	−0.350121	−	0.606427i	−0.986270	+	0.165139i	$0.947193\pi$
$720$			1.08032i			0.0402613i
$721$	−16.9520	−	1.77276i	−0.631325	−	0.0660210i
$722$		−	27.9469i		−	1.04007i
$723$	−3.48604	+	2.01266i	−0.129647	+	0.0748518i
$724$	−6.41115	+	11.1044i	−0.238268	+	0.412693i
$725$	−13.5186	+	23.4150i	−0.502070	+	0.869610i
$726$	19.3208	−	11.1548i	0.717061	−	0.413995i
$727$	−16.2413			−0.602357			−0.301179	−	0.953568i	$-0.597380\pi$
$727$	−16.2413			−0.602357			−0.301179	+	0.953568i	$0.597380\pi$
$728$	5.08792	−	8.06927i	0.188571	−	0.299067i
$729$	1.00000			0.0370370
$730$	6.92535	−	3.99835i	0.256319	−	0.147986i
$731$	−14.2498	+	24.6813i	−0.527047	+	0.912871i
$732$	2.01964	−	3.49811i	0.0746479	−	0.129294i
$733$	−22.5436	+	13.0156i	−0.832668	+	0.480741i	−0.854765	−	0.519015i	$-0.826299\pi$
$733$	−22.5436	+	13.0156i	−0.832668	+	0.480741i	0.0220975	+	0.999756i	$0.492966\pi$
$734$		−	27.8389i		−	1.02755i
$735$	−7.18969	+	2.34439i	−0.265196	+	0.0864743i
$736$		−	4.93210i		−	0.181800i
$737$	−36.1939	−	62.6897i	−1.33322	−	2.30921i
$738$	−4.29083	+	7.43194i	−0.157948	+	0.273573i
$739$	1.29518	+	0.747775i	0.0476441	+	0.0275073i	0.523633	−	0.851944i	$-0.324576\pi$
$739$	1.29518	+	0.747775i	0.0476441	+	0.0275073i	−0.475989	+	0.879451i	$0.657910\pi$
$740$	1.28735	+	2.22975i	0.0473238	+	0.0819672i
$741$	24.6519	−	1.61029i	0.905610	−	0.0591554i
$742$	21.8319	+	15.8444i	0.801474	+	0.581665i
$743$		−	15.2009i		−	0.557667i	−0.960339	−	0.278834i	$-0.910052\pi$
$743$		−	15.2009i		−	0.557667i	0.960339	−	0.278834i	$-0.0899478\pi$
$744$	1.92589	+	3.33574i	0.0706065	+	0.122294i
$745$	−10.6988	+	18.5308i	−0.391972	+	0.678915i
$746$	24.7862	+	14.3103i	0.907487	+	0.523938i
$747$	8.86808	−	5.11999i	0.324466	−	0.187331i
$748$		−	17.8869i		−	0.654010i
$749$	−27.2602	−	2.85074i	−0.996066	−	0.104164i
$750$	9.54239			0.348439
$751$	−18.5713	−	32.1664i	−0.677676	−	1.17377i	−0.975679	−	0.219205i	$-0.929654\pi$
$751$	−18.5713	−	32.1664i	−0.677676	−	1.17377i	0.298003	−	0.954565i	$-0.403680\pi$
$752$	−0.297903	−	0.171994i	−0.0108634	−	0.00627199i
$753$	4.87421	−	8.44239i	0.177626	−	0.307658i
$754$	14.1254	+	21.1504i	0.514418	+	0.770250i
$755$	−1.75306			−0.0638002
$756$	1.07739	+	2.41645i	0.0391842	+	0.0878855i
$757$	−35.9035			−1.30494			−0.652468	−	0.757816i	$-0.726266\pi$
$757$	−35.9035			−1.30494			−0.652468	+	0.757816i	$0.726266\pi$
$758$	−16.7586	−	29.0267i	−0.608698	−	1.05430i
$759$	−24.6518	−	14.2327i	−0.894802	−	0.516614i
$760$	−6.41044	−	3.70107i	−0.232531	−	0.134252i
$761$	23.7043	−	13.6857i	0.859280	−	0.496105i	−0.00449130	−	0.999990i	$-0.501430\pi$
$761$	23.7043	−	13.6857i	0.859280	−	0.496105i	0.863771	+	0.503885i	$0.168096\pi$
$762$		−	17.2950i		−	0.626531i
$763$	12.1671	−	5.42478i	0.440479	−	0.196390i
$764$	−7.77376			−0.281245
$765$	2.89957	−	1.67407i	0.104834	−	0.0605261i
$766$	−0.241623	+	0.418503i	−0.00873018	+	0.0151211i
$767$	18.3126	−	37.1136i	0.661230	−	1.34009i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$		−	26.0250i		−	0.938487i	−0.883069	−	0.469243i	$-0.844527\pi$
$769$		−	26.0250i		−	0.938487i	0.883069	−	0.469243i	$-0.155473\pi$
$770$	−1.71575	+	16.4069i	−0.0618315	+	0.591263i
$771$	−2.81614			−0.101421
$772$	−10.4923	+	6.05772i	−0.377625	+	0.218022i
$773$	17.6596	+	10.1958i	0.635171	+	0.366716i	0.782752	−	0.622334i	$-0.213815\pi$
$773$	17.6596	+	10.1958i	0.635171	+	0.366716i	−0.147581	+	0.989050i	$0.547149\pi$
$774$	−7.96377	−	4.59788i	−0.286252	−	0.165268i
$775$	12.7856	−	7.38174i	0.459271	−	0.265160i
$776$	2.93158			0.105238
$777$	5.10321	+	3.70362i	0.183076	+	0.132867i
$778$			19.0406i			0.682638i
$779$	−29.3998	−	50.9220i	−1.05336	−	1.82447i
$780$	1.72356	−	3.49308i	0.0617133	−	0.125072i
$781$	33.1821	−	57.4731i	1.18735	−	2.05655i
$782$	−13.2377	+	7.64279i	−0.473379	+	0.273306i
$783$	−7.05400			−0.252089
$784$	−4.67847	+	5.20691i	−0.167088	+	0.185961i
$785$			0.755254i			0.0269562i
$786$	7.53881	−	4.35254i	0.268901	−	0.155250i
$787$	−6.05807	−	3.49763i	−0.215947	−	0.124677i	0.388125	−	0.921607i	$-0.373123\pi$
$787$	−6.05807	−	3.49763i	−0.215947	−	0.124677i	−0.604072	+	0.796930i	$0.706456\pi$
$788$	9.19954	+	5.31136i	0.327720	+	0.189209i
$789$	3.59390	+	6.22482i	0.127946	+	0.221609i
$790$	4.29393			0.152771
$791$	−28.1172	+	38.7426i	−0.999732	+	1.37753i
$792$	5.77146			0.205080
$793$	−12.1111	+	8.08853i	−0.430079	+	0.287232i
$794$	13.3038	−	23.0428i	0.472133	−	0.817758i
$795$	9.53903	+	5.50736i	0.338315	+	0.195326i
$796$	−12.7960	−	22.1633i	−0.453542	−	0.785557i
$797$	44.9462			1.59208			0.796038	−	0.605246i	$-0.206925\pi$
$797$	44.9462			1.59208			0.796038	+	0.605246i	$0.206925\pi$
$798$	−18.0298	−	1.88547i	−0.638247	−	0.0667448i
$799$			1.06609i			0.0377156i
$800$	3.31939	−	1.91645i	0.117358	−	0.0677568i
$801$	−8.96805	−	5.17771i	−0.316871	−	0.182945i
$802$	2.63480	−	4.56360i	0.0930380	−	0.161146i
$803$	−21.3606	−	36.9976i	−0.753797	−	1.30562i
$804$		−	12.5424i		−	0.442336i
$805$	12.8755	−	5.74061i	0.453801	−	0.202330i
$806$	−0.905236	−	13.8583i	−0.0318856	−	0.488136i
$807$	3.63417	+	6.29456i	0.127929	+	0.221579i
$808$	−5.64998	−	3.26202i	−0.198766	−	0.114757i
$809$	13.8100	−	23.9196i	0.485533	−	0.840968i	−0.514328	−	0.857593i	$-0.671959\pi$
$809$	13.8100	−	23.9196i	0.485533	−	0.840968i	0.999862	+	0.0166248i	$0.00529210\pi$
$810$	0.540162	+	0.935588i	0.0189793	+	0.0328732i
$811$		−	4.21568i		−	0.148033i	−0.997257	−	0.0740164i	$-0.976418\pi$
$811$		−	4.21568i		−	0.148033i	0.997257	−	0.0740164i	$-0.0235817\pi$
$812$	−7.59990	−	17.0456i	−0.266704	−	0.598185i
$813$			26.3872i			0.925441i
$814$	11.9121	−	6.87744i	0.417518	−	0.241054i
$815$	−5.63863	+	9.76639i	−0.197512	+	0.342102i
$816$	1.54960	−	2.68399i	0.0542469	−	0.0939583i
$817$	54.5660	−	31.5037i	1.90902	−	1.10217i
$818$	−7.01012			−0.245103
$819$	0.371637	−	9.53215i	0.0129861	−	0.333080i
$820$	−9.27097			−0.323756
$821$	−1.66789	+	0.962958i	−0.0582098	+	0.0336075i	−0.528822	−	0.848732i	$-0.677366\pi$
$821$	−1.66789	+	0.962958i	−0.0582098	+	0.0336075i	0.470613	+	0.882340i	$0.344033\pi$
$822$	−3.93773	+	6.82036i	−0.137344	+	0.237887i
$823$	3.49898	−	6.06041i	0.121967	−	0.211253i	−0.798576	−	0.601893i	$-0.794413\pi$
$823$	3.49898	−	6.06041i	0.121967	−	0.211253i	0.920543	+	0.390641i	$0.127747\pi$
$824$	−5.57910	+	3.22110i	−0.194357	+	0.112212i
$825$		−	22.1214i		−	0.770169i
$826$	−17.8374	+	24.5782i	−0.620644	+	0.855184i
$827$			12.8119i			0.445513i	0.974874	+	0.222756i	$0.0715055\pi$
$827$			12.8119i			0.445513i	−0.974874	+	0.222756i	$0.928495\pi$
$828$	−2.46605	−	4.27133i	−0.0857012	−	0.148439i
$829$	−9.14750	+	15.8439i	−0.317706	+	0.550283i	−0.980009	−	0.198953i	$-0.936246\pi$
$829$	−9.14750	+	15.8439i	−0.317706	+	0.550283i	0.662303	+	0.749236i	$0.269579\pi$
$830$	9.58039	+	5.53124i	0.332540	+	0.191992i
$831$	−7.99431	−	13.8465i	−0.277319	−	0.480331i
$832$	−0.235018	−	3.59788i	−0.00814777	−	0.124734i
$833$	21.2250	+	4.48831i	0.735404	+	0.155511i
$834$			17.1252i			0.592998i
$835$	−2.99056	−	5.17980i	−0.103493	−	0.179254i
$836$	−19.7724	+	34.2467i	−0.683842	+	1.18445i
$837$	3.33574	+	1.92589i	0.115300	+	0.0665685i
$838$	19.6708	−	11.3569i	0.679516	−	0.392319i
$839$		−	44.7849i		−	1.54615i	−0.634316	−	0.773074i	$-0.718718\pi$
$839$		−	44.7849i		−	1.54615i	0.634316	−	0.773074i	$-0.281282\pi$
$840$	−1.67884	+	2.31327i	−0.0579254	+	0.0798152i
$841$	20.7589			0.715824
$842$	0.344808	+	0.597224i	0.0118829	+	0.0205817i
$843$	−11.0039	−	6.35310i	−0.378994	−	0.218812i
$844$	8.27908	−	14.3398i	0.284978	−	0.493596i
$845$	−11.1458	+	8.54463i	−0.383427	+	0.293944i
$846$	−0.343989			−0.0118266
$847$	58.7058	+	6.13917i	2.01715	+	0.210944i
$848$	10.1958			0.350124
$849$	8.89947	+	15.4143i	0.305429	+	0.529019i
$850$	−10.2875	−	5.93947i	−0.352857	−	0.203722i
$851$	−10.1797	−	5.87724i	−0.348955	−	0.201469i
$852$	9.95817	−	5.74935i	0.341161	−	0.196970i
$853$		−	1.72370i		−	0.0590182i	−0.999565	−	0.0295091i	$-0.990606\pi$
$853$		−	1.72370i		−	0.0590182i	0.999565	−	0.0295091i	$-0.00939441\pi$
$854$	9.76070	−	4.35187i	0.334004	−	0.148918i
$855$	−7.40214			−0.253148
$856$	−8.97165	+	5.17978i	−0.306645	+	0.177041i
$857$	−9.26063	+	16.0399i	−0.316337	+	0.547912i	−0.979721	−	0.200368i	$-0.935786\pi$
$857$	−9.26063	+	16.0399i	−0.316337	+	0.547912i	0.663384	+	0.748279i	$0.269120\pi$
$858$	−18.6612	−	9.20784i	−0.637084	−	0.314351i
$859$	−6.15239	−	10.6563i	−0.209917	−	0.363587i	0.741771	−	0.670653i	$-0.233986\pi$
$859$	−6.15239	−	10.6563i	−0.209917	−	0.363587i	−0.951688	+	0.307066i	$0.900653\pi$
$860$		−	9.93440i		−	0.338760i
$861$	−20.7372	+	9.24579i	−0.706721	+	0.315096i
$862$	2.32559			0.0792099
$863$	−21.4530	+	12.3859i	−0.730270	+	0.421621i	−0.818521	−	0.574477i	$-0.805206\pi$
$863$	−21.4530	+	12.3859i	−0.730270	+	0.421621i	0.0882511	+	0.996098i	$0.471872\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	−3.35793	−	1.93870i	−0.114173	−	0.0659178i
$866$	−5.79469	+	3.34557i	−0.196912	+	0.113687i
$867$	7.39495			0.251146
$868$	−1.05993	+	10.1356i	−0.0359764	+	0.344024i
$869$		−	22.9396i		−	0.778174i
$870$	−3.81030	−	6.59963i	−0.129181	−	0.223749i
$871$	−20.0103	+	40.5542i	−0.678022	+	1.37413i
$872$	2.51756	−	4.36054i	0.0852553	−	0.147667i
$873$	2.53882	−	1.46579i	0.0859262	−	0.0496095i
$874$	33.7937			1.14309
$875$	20.4328	+	14.8290i	0.690756	+	0.501312i
$876$		−	7.40214i		−	0.250095i
$877$	42.1142	−	24.3147i	1.42210	−	0.821048i	0.425619	−	0.904903i	$-0.360057\pi$
$877$	42.1142	−	24.3147i	1.42210	−	0.821048i	0.996478	+	0.0838547i	$0.0267232\pi$
$878$	−17.9414	−	10.3585i	−0.605494	−	0.349582i
$879$	−12.8032	−	7.39194i	−0.431842	−	0.249324i
$880$	3.11752	+	5.39970i	0.105092	+	0.182024i
$881$	46.4194			1.56391			0.781955	−	0.623335i	$-0.214223\pi$
$881$	46.4194			1.56391			0.781955	+	0.623335i	$0.214223\pi$
$882$	−1.44821	+	6.84855i	−0.0487639	+	0.230603i
$883$	−5.00657			−0.168485			−0.0842423	−	0.996445i	$-0.526847\pi$
$883$	−5.00657			−0.168485			−0.0842423	+	0.996445i	$0.526847\pi$
$884$	−9.29249	+	6.20607i	−0.312540	+	0.208733i
$885$	−6.20014	+	10.7390i	−0.208416	+	0.360986i
$886$	−0.646393	−	0.373195i	−0.0217160	−	0.0125377i
$887$	−1.00078	−	1.73341i	−0.0336031	−	0.0582022i	0.848735	−	0.528819i	$-0.177365\pi$
$887$	−1.00078	−	1.73341i	−0.0336031	−	0.0582022i	−0.882338	+	0.470617i	$0.844032\pi$
$888$	2.38326			0.0799770
$889$	26.8766	−	37.0332i	0.901413	−	1.24205i
$890$		−	11.1872i		−	0.374996i
$891$	4.99823	−	2.88573i	0.167447	−	0.0966755i
$892$	−1.41911	−	0.819325i	−0.0475154	−	0.0274330i
$893$	1.17847	−	2.04116i	0.0394359	−	0.0683050i
$894$	9.90329	+	17.1530i	0.331215	+	0.573682i
$895$			11.0666i			0.369916i
$896$	−0.275179	+	2.63140i	−0.00919310	+	0.0879090i
$897$	1.15913	+	17.7451i	0.0387022	+	0.592493i
$898$	17.6643	+	30.5954i	0.589465	+	1.02098i
$899$	−23.5303	−	13.5852i	−0.784779	−	0.453092i
$900$	1.91645	−	3.31939i	0.0638817	−	0.110646i
$901$	−15.7994	−	27.3653i	−0.526353	−	0.911670i
$902$			49.5287i			1.64912i
$903$	−9.90742	−	22.2211i	−0.329698	−	0.739472i
$904$			18.0933i			0.601773i
$905$	−11.9964	+	6.92612i	−0.398773	+	0.230232i
$906$	−0.811357	+	1.40531i	−0.0269555	+	0.0466883i
$907$	−8.96407	+	15.5262i	−0.297647	+	0.515540i	−0.975597	−	0.219568i	$-0.929535\pi$
$907$	−8.96407	+	15.5262i	−0.297647	+	0.515540i	0.677950	+	0.735108i	$0.262869\pi$
$908$	−9.53213	+	5.50338i	−0.316335	+	0.182636i
$909$	−6.52403			−0.216389
$910$	9.11891	−	4.80120i	0.302289	−	0.159158i
$911$	11.9040			0.394396			0.197198	−	0.980364i	$-0.436816\pi$
$911$	11.9040			0.394396			0.197198	+	0.980364i	$0.436816\pi$
$912$	−5.93381	+	3.42589i	−0.196488	+	0.113443i
$913$	29.5498	−	51.1817i	0.977955	−	1.69387i
$914$	−16.7817	+	29.0667i	−0.555088	+	0.961441i
$915$	3.77909	−	2.18186i	0.124933	−	0.0721301i
$916$			17.4396i			0.576219i
$917$	22.9065	+	2.39546i	0.756441	+	0.0791049i
$918$		−	3.09920i		−	0.102289i
$919$	−4.79363	−	8.30281i	−0.158127	−	0.273884i	0.776066	−	0.630652i	$-0.217212\pi$
$919$	−4.79363	−	8.30281i	−0.158127	−	0.273884i	−0.934193	+	0.356767i	$0.883879\pi$
$920$	2.66413	−	4.61441i	0.0878339	−	0.152133i
$921$	4.21869	+	2.43566i	0.139010	+	0.0802577i
$922$	−0.487396	−	0.844195i	−0.0160515	−	0.0278021i
$923$	−41.3710	+	2.70240i	−1.36174	+	0.0889505i
$924$	12.3583	+	8.96892i	0.406557	+	0.295056i
$925$		−	9.13480i		−	0.300350i
$926$	6.21880	+	10.7713i	0.204362	+	0.353966i
$927$	−3.22110	+	5.57910i	−0.105795	+	0.183242i
$928$	−6.10894	−	3.52700i	−0.200536	−	0.115779i
$929$	26.6876	−	15.4081i	0.875592	−	0.505523i	0.00638924	−	0.999980i	$-0.497966\pi$
$929$	26.6876	−	15.4081i	0.875592	−	0.505523i	0.869202	+	0.494457i	$0.164633\pi$
$930$			4.16117i			0.136450i
$931$	−35.6766	−	32.0558i	−1.16925	−	1.05059i
$932$	3.14129			0.102896
$933$	−15.4208	−	26.7097i	−0.504856	−	0.874436i
$934$	11.3983	+	6.58082i	0.372964	+	0.215331i
$935$	9.66182	−	16.7348i	0.315975	−	0.547285i
$936$	−2.00247	−	2.99835i	−0.0654529	−	0.0980041i
$937$	0.430950			0.0140785			0.00703927	−	0.999975i	$-0.497759\pi$
$937$	0.430950			0.0140785			0.00703927	+	0.999975i	$0.497759\pi$
$938$	19.4910	−	26.8567i	0.636405	−	0.876901i
$939$	−33.4682			−1.09219
$940$	−0.185810	−	0.321832i	−0.00606044	−	0.0104970i
$941$	8.00176	+	4.61982i	0.260850	+	0.150602i	0.624722	−	0.780847i	$-0.285212\pi$
$941$	8.00176	+	4.61982i	0.260850	+	0.150602i	−0.363872	+	0.931449i	$0.618546\pi$
$942$	0.605438	+	0.349550i	0.0197262	+	0.0113890i
$943$	36.6551	−	21.1628i	1.19365	−	0.689156i
$944$			11.4783i			0.373587i
$945$	−0.297283	+	2.84277i	−0.00967061	+	0.0924752i
$946$	−53.0730			−1.72555
$947$	5.35898	−	3.09401i	0.174143	−	0.100542i	−0.410395	−	0.911908i	$-0.634609\pi$
$947$	5.35898	−	3.09401i	0.174143	−	0.100542i	0.584538	+	0.811366i	$0.301276\pi$
$948$	1.98734	−	3.44217i	0.0645457	−	0.111796i
$949$	−11.8094	+	23.9338i	−0.383351	+	0.776925i
$950$	13.1311	+	22.7437i	0.426029	+	0.737904i
$951$		−	20.4298i		−	0.662482i
$952$	7.48907	−	3.33904i	0.242722	−	0.108219i
$953$	−8.22046			−0.266287			−0.133143	−	0.991097i	$-0.542507\pi$
$953$	−8.22046			−0.266287			−0.133143	+	0.991097i	$0.542507\pi$
$954$	8.82979	−	5.09788i	0.285875	−	0.165050i
$955$	−7.27303	−	4.19909i	−0.235350	−	0.135879i
$956$	−14.1188	−	8.15147i	−0.456633	−	0.263637i
$957$	−35.2575	+	20.3559i	−1.13971	+	0.658013i
$958$	−14.7193			−0.475558
$959$	−19.0307	+	8.48494i	−0.614533	+	0.273993i
$960$			1.08032i			0.0348673i
$961$	−8.08190	−	13.9983i	−0.260706	−	0.451557i
$962$	−7.70595	−	3.80228i	−0.248450	−	0.122590i
$963$	−5.17978	+	8.97165i	−0.166916	+	0.289107i
$964$	−3.48604	+	2.01266i	−0.112278	+	0.0648236i
$965$	−13.0886			−0.421337
$966$	1.35721	−	12.9783i	0.0436676	−	0.417571i
$967$		−	15.3760i		−	0.494459i	−0.968957	−	0.247229i	$-0.920480\pi$
$967$		−	15.3760i		−	0.494459i	0.968957	−	0.247229i	$-0.0795201\pi$
$968$	19.3208	−	11.1548i	0.620993	−	0.358530i
$969$	18.3901	+	10.6175i	0.590775	+	0.341084i
$970$	2.74275	+	1.58353i	0.0880645	+	0.0508440i
$971$	15.9985	+	27.7102i	0.513415	+	0.889261i	0.999879	+	0.0155604i	$0.00495324\pi$
$971$	15.9985	+	27.7102i	0.513415	+	0.889261i	−0.486464	+	0.873701i	$0.661713\pi$
$972$	1.00000			0.0320750
$973$	−26.6128	+	36.6698i	−0.853169	+	1.17558i
$974$	18.2253			0.583976
$975$	−11.4924	+	7.67528i	−0.368051	+	0.245806i
$976$	2.01964	−	3.49811i	0.0646470	−	0.111972i
$977$	30.5708	+	17.6501i	0.978048	+	0.564676i	0.901680	−	0.432404i	$-0.142334\pi$
$977$	30.5708	+	17.6501i	0.978048	+	0.564676i	0.0763675	+	0.997080i	$0.475668\pi$
$978$	5.21939	+	9.04024i	0.166898	+	0.289075i
$979$	−59.7658			−1.91012
$980$	−7.18969	+	2.34439i	−0.229666	+	0.0748889i
$981$		−	5.03512i		−	0.160759i
$982$	5.79697	−	3.34688i	0.184989	−	0.106803i
$983$	−49.6359	−	28.6573i	−1.58314	−	0.914026i	−0.994397	−	0.105706i	$-0.966290\pi$
$983$	−49.6359	−	28.6573i	−1.58314	−	0.914026i	−0.588743	−	0.808320i	$-0.700377\pi$
$984$	−4.29083	+	7.43194i	−0.136787	+	0.236921i
$985$	5.73798	+	9.93848i	0.182827	+	0.316666i
$986$			21.8618i			0.696220i
$987$	−0.736573	−	0.534563i	−0.0234454	−	0.0170153i
$988$	24.6519	−	1.61029i	0.784281	−	0.0512301i
$989$	22.6772	+	39.2781i	0.721094	+	1.24897i
$990$	5.39970	+	3.11752i	0.171614	+	0.0990813i
$991$	20.7591	−	35.9558i	0.659434	−	1.14217i	−0.321328	−	0.946968i	$-0.604129\pi$
$991$	20.7591	−	35.9558i	0.659434	−	1.14217i	0.980762	−	0.195206i	$-0.0625375\pi$
$992$	1.92589	+	3.33574i	0.0611470	+	0.105910i
$993$			15.5019i			0.491937i
$994$	30.2577	+	3.16421i	0.959716	+	0.100362i
$995$		−	27.6476i		−	0.876488i
$996$	8.86808	−	5.11999i	0.280996	−	0.162233i
$997$	−4.21969	+	7.30871i	−0.133639	+	0.231469i	−0.925077	−	0.379780i	$-0.876000\pi$
$997$	−4.21969	+	7.30871i	−0.133639	+	0.231469i	0.791438	+	0.611250i	$0.209333\pi$
$998$	7.40229	−	12.8211i	0.234315	−	0.405846i
$999$	2.06396	−	1.19163i	0.0653009	−	0.0377015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bk.c.25.8	yes	20
3.2	odd	2		1638.2.dm.e.1117.3		20
7.2	even	3	inner	546.2.bk.c.415.3	yes	20
7.3	odd	6		3822.2.c.n.883.8		10
7.4	even	3		3822.2.c.m.883.8		10
13.12	even	2	inner	546.2.bk.c.25.3	✓	20
21.2	odd	6		1638.2.dm.e.415.8		20
39.38	odd	2		1638.2.dm.e.1117.8		20
91.25	even	6		3822.2.c.m.883.3		10
91.38	odd	6		3822.2.c.n.883.3		10
91.51	even	6	inner	546.2.bk.c.415.8	yes	20
273.233	odd	6		1638.2.dm.e.415.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.c.25.3	✓	20	13.12	even	2	inner
546.2.bk.c.25.8	yes	20	1.1	even	1	trivial
546.2.bk.c.415.3	yes	20	7.2	even	3	inner
546.2.bk.c.415.8	yes	20	91.51	even	6	inner
1638.2.dm.e.415.3		20	273.233	odd	6
1638.2.dm.e.415.8		20	21.2	odd	6
1638.2.dm.e.1117.3		20	3.2	odd	2
1638.2.dm.e.1117.8		20	39.38	odd	2
3822.2.c.m.883.3		10	91.25	even	6
3822.2.c.m.883.8		10	7.4	even	3
3822.2.c.n.883.3		10	91.38	odd	6
3822.2.c.n.883.8		10	7.3	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.935588 - 0.540162i) q^{5} -1.00000i q^{6} +(1.55401 - 2.14127i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.935588 - 0.540162i) q^{5} -1.00000i q^{6} +(1.55401 - 2.14127i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.540162 - 0.935588i) q^{10} +(-4.99823 - 2.88573i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.235018 + 3.59788i) q^{13} +(0.275179 - 2.63140i) q^{14} -1.08032i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.54960 + 2.68399i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(5.93381 - 3.42589i) q^{19} -1.08032i q^{20} +(-1.07739 - 2.41645i) q^{21} -5.77146 q^{22} +(2.46605 + 4.27133i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.91645 + 3.31939i) q^{25} +(2.00247 + 2.99835i) q^{26} -1.00000 q^{27} +(-1.07739 - 2.41645i) q^{28} +7.05400 q^{29} +(-0.540162 - 0.935588i) q^{30} +(-3.33574 - 1.92589i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.99823 + 2.88573i) q^{33} +3.09920i q^{34} +(0.297283 - 2.84277i) q^{35} -1.00000 q^{36} +(-2.06396 + 1.19163i) q^{37} +(3.42589 - 5.93381i) q^{38} +(3.23337 + 1.59541i) q^{39} +(-0.540162 - 0.935588i) q^{40} -8.58166i q^{41} +(-2.14127 - 1.55401i) q^{42} +9.19577 q^{43} +(-4.99823 + 2.88573i) q^{44} +(-0.935588 - 0.540162i) q^{45} +(4.27133 + 2.46605i) q^{46} +(0.297903 - 0.171994i) q^{47} -1.00000 q^{48} +(-2.17009 - 6.65513i) q^{49} +3.83290i q^{50} +(1.54960 + 2.68399i) q^{51} +(3.23337 + 1.59541i) q^{52} +(-5.09788 + 8.82979i) q^{53} +(-0.866025 + 0.500000i) q^{54} -6.23504 q^{55} +(-2.14127 - 1.55401i) q^{56} -6.85178i q^{57} +(6.10894 - 3.52700i) q^{58} +(-9.94051 - 5.73915i) q^{59} +(-0.935588 - 0.540162i) q^{60} +(2.01964 + 3.49811i) q^{61} -3.85178 q^{62} +(-2.63140 - 0.275179i) q^{63} -1.00000 q^{64} +(2.16332 + 3.23919i) q^{65} +(-2.88573 + 4.99823i) q^{66} +(10.8620 + 6.27120i) q^{67} +(1.54960 + 2.68399i) q^{68} +4.93210 q^{69} +(-1.16393 - 2.61055i) q^{70} +11.4987i q^{71} +(-0.866025 + 0.500000i) q^{72} +(6.41044 + 3.70107i) q^{73} +(-1.19163 + 2.06396i) q^{74} +(1.91645 + 3.31939i) q^{75} -6.85178i q^{76} +(-13.9464 + 6.21810i) q^{77} +(3.59788 - 0.235018i) q^{78} +(1.98734 + 3.44217i) q^{79} +(-0.935588 - 0.540162i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.29083 - 7.43194i) q^{82} +10.2400i q^{83} +(-2.63140 - 0.275179i) q^{84} +3.34814i q^{85} +(7.96377 - 4.59788i) q^{86} +(3.52700 - 6.10894i) q^{87} +(-2.88573 + 4.99823i) q^{88} +(8.96805 - 5.17771i) q^{89} -1.08032 q^{90} +(8.06927 + 5.08792i) q^{91} +4.93210 q^{92} +(-3.33574 + 1.92589i) q^{93} +(0.171994 - 0.297903i) q^{94} +(3.70107 - 6.41044i) q^{95} +(-0.866025 + 0.500000i) q^{96} +2.93158i q^{97} +(-5.20691 - 4.67847i) q^{98} +5.77146i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{3} + 10 q^{4} - 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^3 + 10 * q^4 - 10 * q^9	\( 20 q + 10 q^{3} + 10 q^{4} - 10 q^{9} + 4 q^{10} - 10 q^{12} + 4 q^{13} - 2 q^{14} - 10 q^{16} - 6 q^{17} - 12 q^{22} - 16 q^{23} + 2 q^{25} - 4 q^{26} - 20 q^{27} - 28 q^{29} - 4 q^{30} + 16 q^{35} - 20 q^{36} + 10 q^{38} + 2 q^{39} - 4 q^{40} - 10 q^{42} + 24 q^{43} - 20 q^{48} + 2 q^{49} + 6 q^{51} + 2 q^{52} - 22 q^{53} + 88 q^{55} - 10 q^{56} + 14 q^{61} + 40 q^{62} - 20 q^{64} + 20 q^{65} - 6 q^{66} + 6 q^{68} - 32 q^{69} + 24 q^{74} - 2 q^{75} - 28 q^{77} - 8 q^{78} + 4 q^{79} - 10 q^{81} + 12 q^{82} - 14 q^{87} - 6 q^{88} - 8 q^{90} + 68 q^{91} - 32 q^{92} - 18 q^{94} + 8 q^{95}+O(q^{100}) \) 20 * q + 10 * q^3 + 10 * q^4 - 10 * q^9 + 4 * q^10 - 10 * q^12 + 4 * q^13 - 2 * q^14 - 10 * q^16 - 6 * q^17 - 12 * q^22 - 16 * q^23 + 2 * q^25 - 4 * q^26 - 20 * q^27 - 28 * q^29 - 4 * q^30 + 16 * q^35 - 20 * q^36 + 10 * q^38 + 2 * q^39 - 4 * q^40 - 10 * q^42 + 24 * q^43 - 20 * q^48 + 2 * q^49 + 6 * q^51 + 2 * q^52 - 22 * q^53 + 88 * q^55 - 10 * q^56 + 14 * q^61 + 40 * q^62 - 20 * q^64 + 20 * q^65 - 6 * q^66 + 6 * q^68 - 32 * q^69 + 24 * q^74 - 2 * q^75 - 28 * q^77 - 8 * q^78 + 4 * q^79 - 10 * q^81 + 12 * q^82 - 14 * q^87 - 6 * q^88 - 8 * q^90 + 68 * q^91 - 32 * q^92 - 18 * q^94 + 8 * q^95

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