LMFDB - Embedded newform 950.2.h.c.381.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			381.2
Character	$\chi$	$=$	950.381
Dual form			950.2.h.c.571.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-1.83642 + 1.33424i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.65745 + 1.50096i) q^{5} +(-1.83642 - 1.33424i) q^{6} +4.52091 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.665206 - 2.04729i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-1.83642 + 1.33424i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.65745 + 1.50096i) q^{5} +(-1.83642 - 1.33424i) q^{6} +4.52091 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.665206 - 2.04729i) q^{9} +(-1.93967 - 1.11250i) q^{10} +(-1.44013 - 4.43227i) q^{11} +(0.701452 - 2.15885i) q^{12} +(1.69670 - 5.22191i) q^{13} +(1.39704 + 4.29964i) q^{14} +(1.04114 - 4.96783i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-5.72408 - 4.15879i) q^{17} +2.15265 q^{18} +(0.809017 + 0.587785i) q^{19} +(0.458661 - 2.18852i) q^{20} +(-8.30231 + 6.03198i) q^{21} +(3.77031 - 2.73929i) q^{22} +(0.440649 + 1.35618i) q^{23} +2.26995 q^{24} +(0.494253 - 4.97551i) q^{25} +5.49064 q^{26} +(-0.594373 - 1.82929i) q^{27} +(-3.65749 + 2.65732i) q^{28} +(3.33603 - 2.42377i) q^{29} +(5.04641 - 0.544964i) q^{30} +(-3.16639 - 2.30052i) q^{31} +1.00000 q^{32} +(8.55840 + 6.21804i) q^{33} +(2.18640 - 6.72906i) q^{34} +(-7.49316 + 6.78569i) q^{35} +(0.665206 + 2.04729i) q^{36} +(0.259769 - 0.799487i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(3.85142 + 11.8535i) q^{39} +(2.22314 - 0.240078i) q^{40} +(-1.04708 + 3.22258i) q^{41} +(-8.30231 - 6.03198i) q^{42} +2.84236 q^{43} +(3.77031 + 2.73929i) q^{44} +(1.97036 + 4.39173i) q^{45} +(-1.15363 + 0.838165i) q^{46} +(1.88812 - 1.37180i) q^{47} +(0.701452 + 2.15885i) q^{48} +13.4386 q^{49} +(4.88473 - 1.06745i) q^{50} +16.0607 q^{51} +(1.69670 + 5.22191i) q^{52} +(-4.07929 + 2.96377i) q^{53} +(1.55609 - 1.13057i) q^{54} +(9.03958 + 5.18467i) q^{55} +(-3.65749 - 2.65732i) q^{56} -2.26995 q^{57} +(3.33603 + 2.42377i) q^{58} +(-2.21139 + 6.80596i) q^{59} +(2.07772 + 4.63102i) q^{60} +(-2.35356 - 7.24351i) q^{61} +(1.20945 - 3.72232i) q^{62} +(3.00734 - 9.25563i) q^{63} +(0.309017 + 0.951057i) q^{64} +(5.02567 + 11.2017i) q^{65} +(-3.26902 + 10.0610i) q^{66} +(-11.6997 - 8.50035i) q^{67} +7.07536 q^{68} +(-2.61869 - 1.90259i) q^{69} +(-8.76909 - 5.02952i) q^{70} +(9.32964 - 6.77838i) q^{71} +(-1.74153 + 1.26530i) q^{72} +(-0.582569 - 1.79296i) q^{73} +0.840631 q^{74} +(5.73087 + 9.79660i) q^{75} -1.00000 q^{76} +(-6.51070 - 20.0379i) q^{77} +(-10.0831 + 7.32584i) q^{78} +(0.0773743 - 0.0562157i) q^{79} +(0.915316 + 2.04015i) q^{80} +(8.75684 + 6.36221i) q^{81} -3.38842 q^{82} +(-10.7767 - 7.82970i) q^{83} +(3.17120 - 9.75995i) q^{84} +(15.7295 - 1.69864i) q^{85} +(0.878337 + 2.70324i) q^{86} +(-2.89248 + 8.90214i) q^{87} +(-1.44013 + 4.43227i) q^{88} +(4.69209 + 14.4408i) q^{89} +(-3.56790 + 3.23104i) q^{90} +(7.67063 - 23.6078i) q^{91} +(-1.15363 - 0.838165i) q^{92} +8.88428 q^{93} +(1.88812 + 1.37180i) q^{94} +(-2.22314 + 0.240078i) q^{95} +(-1.83642 + 1.33424i) q^{96} +(-10.5820 + 7.68826i) q^{97} +(4.15276 + 12.7809i) q^{98} -10.0321 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9}+O(q^{10}) $ 44 * q - 11 * q^2 + q^3 - 11 * q^4 - q^5 + q^6 + 18 * q^7 - 11 * q^8 - 8 * q^9	\( 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} + 2 q^{13} + 3 q^{14} - 4 q^{15} - 11 q^{16} + 11 q^{17} + 42 q^{18} + 11 q^{19} - 6 q^{20} + 3 q^{21} - 6 q^{22} - 3 q^{23} + 6 q^{24} - 11 q^{25} + 22 q^{26} - 23 q^{27} - 12 q^{28} + 36 q^{29} - 4 q^{30} + 11 q^{31} + 44 q^{32} + 2 q^{33} - 19 q^{34} + 67 q^{35} - 8 q^{36} + 3 q^{37} + 11 q^{38} + 47 q^{39} + 4 q^{40} + 2 q^{41} + 3 q^{42} + 70 q^{43} - 6 q^{44} - 28 q^{45} - 8 q^{46} - 11 q^{47} - 4 q^{48} + 22 q^{49} + 14 q^{50} + 38 q^{51} + 2 q^{52} - 9 q^{53} + 32 q^{54} + 8 q^{55} - 12 q^{56} - 6 q^{57} + 36 q^{58} - 62 q^{59} + 11 q^{60} - 28 q^{61} - 29 q^{62} + 10 q^{63} - 11 q^{64} - 39 q^{65} - 8 q^{66} + 25 q^{67} + 16 q^{68} - 81 q^{69} - 43 q^{70} - 34 q^{71} - 13 q^{72} + 6 q^{73} + 8 q^{74} - 39 q^{75} - 44 q^{76} - 21 q^{77} - 58 q^{78} + 19 q^{79} - q^{80} - 22 q^{81} + 2 q^{82} - 50 q^{83} - 7 q^{84} + 102 q^{85} - 10 q^{86} + 47 q^{87} - q^{88} - 4 q^{89} - 38 q^{90} - 8 q^{91} - 8 q^{92} + 60 q^{93} - 11 q^{94} - 4 q^{95} + q^{96} + 8 q^{97} + 7 q^{98} - 12 q^{99}+O(q^{100}) \) 44 * q - 11 * q^2 + q^3 - 11 * q^4 - q^5 + q^6 + 18 * q^7 - 11 * q^8 - 8 * q^9 + 4 * q^10 - q^11 - 4 * q^12 + 2 * q^13 + 3 * q^14 - 4 * q^15 - 11 * q^16 + 11 * q^17 + 42 * q^18 + 11 * q^19 - 6 * q^20 + 3 * q^21 - 6 * q^22 - 3 * q^23 + 6 * q^24 - 11 * q^25 + 22 * q^26 - 23 * q^27 - 12 * q^28 + 36 * q^29 - 4 * q^30 + 11 * q^31 + 44 * q^32 + 2 * q^33 - 19 * q^34 + 67 * q^35 - 8 * q^36 + 3 * q^37 + 11 * q^38 + 47 * q^39 + 4 * q^40 + 2 * q^41 + 3 * q^42 + 70 * q^43 - 6 * q^44 - 28 * q^45 - 8 * q^46 - 11 * q^47 - 4 * q^48 + 22 * q^49 + 14 * q^50 + 38 * q^51 + 2 * q^52 - 9 * q^53 + 32 * q^54 + 8 * q^55 - 12 * q^56 - 6 * q^57 + 36 * q^58 - 62 * q^59 + 11 * q^60 - 28 * q^61 - 29 * q^62 + 10 * q^63 - 11 * q^64 - 39 * q^65 - 8 * q^66 + 25 * q^67 + 16 * q^68 - 81 * q^69 - 43 * q^70 - 34 * q^71 - 13 * q^72 + 6 * q^73 + 8 * q^74 - 39 * q^75 - 44 * q^76 - 21 * q^77 - 58 * q^78 + 19 * q^79 - q^80 - 22 * q^81 + 2 * q^82 - 50 * q^83 - 7 * q^84 + 102 * q^85 - 10 * q^86 + 47 * q^87 - q^88 - 4 * q^89 - 38 * q^90 - 8 * q^91 - 8 * q^92 + 60 * q^93 - 11 * q^94 - 4 * q^95 + q^96 + 8 * q^97 + 7 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−1.83642	+	1.33424i	−1.06026	+	0.770324i	−0.974136	−	0.225960i	$-0.927448\pi$
$3$	−1.83642	+	1.33424i	−1.06026	+	0.770324i	−0.0861237	+	0.996284i	$0.527448\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−1.65745	+	1.50096i	−0.741232	+	0.671249i
$5$	−1.65745	+	1.50096i	−0.741232	+	0.671249i
$6$	−1.83642	−	1.33424i	−0.749717	−	0.544701i
$7$	4.52091			1.70874			0.854371	−	0.519663i	$-0.173943\pi$
$7$	4.52091			1.70874			0.854371	+	0.519663i	$0.173943\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	0.665206	−	2.04729i	0.221735	−	0.682431i
$10$	−1.93967	−	1.11250i	−0.613379	−	0.351804i
$11$	−1.44013	−	4.43227i	−0.434216	−	1.33638i	−0.893888	−	0.448290i	$-0.852033\pi$
$11$	−1.44013	−	4.43227i	−0.434216	−	1.33638i	0.459672	−	0.888089i	$-0.347967\pi$
$12$	0.701452	−	2.15885i	0.202492	−	0.623205i
$13$	1.69670	−	5.22191i	0.470580	−	1.44830i	−0.381246	−	0.924473i	$-0.624505\pi$
$13$	1.69670	−	5.22191i	0.470580	−	1.44830i	0.851827	−	0.523824i	$-0.175495\pi$
$14$	1.39704	+	4.29964i	0.373374	+	1.14913i
$15$	1.04114	−	4.96783i	0.268820	−	1.28269i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−5.72408	−	4.15879i	−1.38829	−	1.00865i	−0.996050	−	0.0887933i	$-0.971699\pi$
$17$	−5.72408	−	4.15879i	−1.38829	−	1.00865i	−0.392244	−	0.919861i	$-0.628301\pi$
$18$	2.15265			0.507385
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$20$	0.458661	−	2.18852i	0.102560	−	0.489368i
$21$	−8.30231	+	6.03198i	−1.81171	+	1.31629i
$22$	3.77031	−	2.73929i	0.803833	−	0.584019i
$23$	0.440649	+	1.35618i	0.0918817	+	0.282783i	0.986428	−	0.164192i	$-0.0525015\pi$
$23$	0.440649	+	1.35618i	0.0918817	+	0.282783i	−0.894547	+	0.446974i	$0.852502\pi$
$24$	2.26995			0.463351
$25$	0.494253	−	4.97551i	0.0988507	−	0.995102i
$26$	5.49064			1.07680
$27$	−0.594373	−	1.82929i	−0.114387	−	0.352048i
$28$	−3.65749	+	2.65732i	−0.691201	+	0.502187i
$29$	3.33603	−	2.42377i	0.619486	−	0.450083i	−0.233256	−	0.972415i	$-0.574938\pi$
$29$	3.33603	−	2.42377i	0.619486	−	0.450083i	0.852742	+	0.522333i	$0.174938\pi$
$30$	5.04641	−	0.544964i	0.921345	−	0.0994963i
$31$	−3.16639	−	2.30052i	−0.568701	−	0.413185i	0.265932	−	0.963992i	$-0.414320\pi$
$31$	−3.16639	−	2.30052i	−0.568701	−	0.413185i	−0.834633	+	0.550807i	$0.814320\pi$
$32$	1.00000			0.176777
$33$	8.55840	+	6.21804i	1.48983	+	1.08242i
$34$	2.18640	−	6.72906i	0.374965	−	1.15402i
$35$	−7.49316	+	6.78569i	−1.26658	+	1.14699i
$36$	0.665206	+	2.04729i	0.110868	+	0.341216i
$37$	0.259769	−	0.799487i	0.0427058	−	0.131435i	−0.927430	−	0.373996i	$-0.877987\pi$
$37$	0.259769	−	0.799487i	0.0427058	−	0.131435i	0.970136	+	0.242561i	$0.0779874\pi$
$38$	−0.309017	+	0.951057i	−0.0501292	+	0.154282i
$39$	3.85142	+	11.8535i	0.616721	+	1.89807i
$40$	2.22314	−	0.240078i	0.351510	−	0.0379596i
$41$	−1.04708	+	3.22258i	−0.163526	+	0.503282i	−0.998925	−	0.0463629i	$-0.985237\pi$
$41$	−1.04708	+	3.22258i	−0.163526	+	0.503282i	0.835398	+	0.549645i	$0.185237\pi$
$42$	−8.30231	−	6.03198i	−1.28107	−	0.930754i
$43$	2.84236			0.433456			0.216728	−	0.976232i	$-0.430462\pi$
$43$	2.84236			0.433456			0.216728	+	0.976232i	$0.430462\pi$
$44$	3.77031	+	2.73929i	0.568396	+	0.412964i
$45$	1.97036	+	4.39173i	0.293724	+	0.654680i
$46$	−1.15363	+	0.838165i	−0.170094	+	0.123581i
$47$	1.88812	−	1.37180i	0.275411	−	0.200098i	−0.441502	−	0.897260i	$-0.645554\pi$
$47$	1.88812	−	1.37180i	0.275411	−	0.200098i	0.716913	+	0.697162i	$0.245554\pi$
$48$	0.701452	+	2.15885i	0.101246	+	0.311603i
$49$	13.4386			1.91980
$50$	4.88473	−	1.06745i	0.690804	−	0.150961i
$51$	16.0607			2.24894
$52$	1.69670	+	5.22191i	0.235290	+	0.724149i
$53$	−4.07929	+	2.96377i	−0.560333	+	0.407106i	−0.831581	−	0.555404i	$-0.812564\pi$
$53$	−4.07929	+	2.96377i	−0.560333	+	0.407106i	0.271248	+	0.962510i	$0.412564\pi$
$54$	1.55609	−	1.13057i	0.211757	−	0.153850i
$55$	9.03958	+	5.18467i	1.21890	+	0.699100i
$56$	−3.65749	−	2.65732i	−0.488753	−	0.355100i
$57$	−2.26995			−0.300662
$58$	3.33603	+	2.42377i	0.438043	+	0.318257i
$59$	−2.21139	+	6.80596i	−0.287899	+	0.886061i	0.697616	+	0.716472i	$0.254244\pi$
$59$	−2.21139	+	6.80596i	−0.287899	+	0.886061i	−0.985515	+	0.169589i	$0.945756\pi$
$60$	2.07772	+	4.63102i	0.268232	+	0.597862i
$61$	−2.35356	−	7.24351i	−0.301342	−	0.927436i	−0.981017	−	0.193923i	$-0.937879\pi$
$61$	−2.35356	−	7.24351i	−0.301342	−	0.927436i	0.679674	−	0.733514i	$-0.262121\pi$
$62$	1.20945	−	3.72232i	0.153601	−	0.472735i
$63$	3.00734	−	9.25563i	0.378889	−	1.16610i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	5.02567	+	11.2017i	0.623358	+	1.38940i
$66$	−3.26902	+	10.0610i	−0.402388	+	1.23842i
$67$	−11.6997	−	8.50035i	−1.42935	−	1.03848i	−0.990137	−	0.140100i	$-0.955258\pi$
$67$	−11.6997	−	8.50035i	−1.42935	−	1.03848i	−0.439212	−	0.898383i	$-0.644742\pi$
$68$	7.07536			0.858013
$69$	−2.61869	−	1.90259i	−0.315253	−	0.229045i
$70$	−8.76909	−	5.02952i	−1.04811	−	0.601143i
$71$	9.32964	−	6.77838i	1.10722	−	0.804446i	0.125001	−	0.992157i	$-0.460107\pi$
$71$	9.32964	−	6.77838i	1.10722	−	0.804446i	0.982224	+	0.187711i	$0.0601067\pi$
$72$	−1.74153	+	1.26530i	−0.205242	+	0.149117i
$73$	−0.582569	−	1.79296i	−0.0681846	−	0.209851i	0.911159	−	0.412056i	$-0.135189\pi$
$73$	−0.582569	−	1.79296i	−0.0681846	−	0.209851i	−0.979343	+	0.202205i	$0.935189\pi$
$74$	0.840631			0.0977213
$75$	5.73087	+	9.79660i	0.661744	+	1.13121i
$76$	−1.00000			−0.114708
$77$	−6.51070	−	20.0379i	−0.741963	−	2.28353i
$78$	−10.0831	+	7.32584i	−1.14169	+	0.829488i
$79$	0.0773743	−	0.0562157i	0.00870529	−	0.00632476i	−0.583424	−	0.812168i	$-0.698287\pi$
$79$	0.0773743	−	0.0562157i	0.00870529	−	0.00632476i	0.592129	+	0.805843i	$0.298287\pi$
$80$	0.915316	+	2.04015i	0.102335	+	0.228095i
$81$	8.75684	+	6.36221i	0.972982	+	0.706913i
$82$	−3.38842			−0.374188
$83$	−10.7767	−	7.82970i	−1.18289	−	0.859422i	−0.190398	−	0.981707i	$-0.560978\pi$
$83$	−10.7767	−	7.82970i	−1.18289	−	0.859422i	−0.992495	+	0.122285i	$0.960978\pi$
$84$	3.17120	−	9.75995i	0.346006	−	1.06490i
$85$	15.7295	−	1.69864i	1.70611	−	0.184243i
$86$	0.878337	+	2.70324i	0.0947135	+	0.291498i
$87$	−2.89248	+	8.90214i	−0.310106	+	0.954410i
$88$	−1.44013	+	4.43227i	−0.153518	+	0.472481i
$89$	4.69209	+	14.4408i	0.497361	+	1.53072i	0.813245	+	0.581922i	$0.197699\pi$
$89$	4.69209	+	14.4408i	0.497361	+	1.53072i	−0.315884	+	0.948798i	$0.602301\pi$
$90$	−3.56790	+	3.23104i	−0.376090	+	0.340581i
$91$	7.67063	−	23.6078i	0.804101	−	2.47477i
$92$	−1.15363	−	0.838165i	−0.120275	−	0.0873847i
$93$	8.88428			0.921257
$94$	1.88812	+	1.37180i	0.194745	+	0.141491i
$95$	−2.22314	+	0.240078i	−0.228090	+	0.0246315i
$96$	−1.83642	+	1.33424i	−0.187429	+	0.136175i
$97$	−10.5820	+	7.68826i	−1.07444	+	0.780625i	−0.976705	−	0.214588i	$-0.931159\pi$
$97$	−10.5820	+	7.68826i	−1.07444	+	0.780625i	−0.0977333	+	0.995213i	$0.531159\pi$
$98$	4.15276	+	12.7809i	0.419492	+	1.29106i
$99$	−10.0321			−1.00827
$100$	2.52467	+	4.31579i	0.252467	+	0.431579i
$101$	5.05365			0.502857			0.251428	−	0.967876i	$-0.419100\pi$
$101$	5.05365			0.502857			0.251428	+	0.967876i	$0.419100\pi$
$102$	4.96302	+	15.2746i	0.491412	+	1.51241i
$103$	9.43268	−	6.85324i	0.929429	−	0.675270i	−0.0164238	−	0.999865i	$-0.505228\pi$
$103$	9.43268	−	6.85324i	0.929429	−	0.675270i	0.945853	+	0.324595i	$0.105228\pi$
$104$	−4.44202	+	3.22732i	−0.435576	+	0.316465i
$105$	4.70688	−	22.4591i	0.459344	−	2.19178i
$106$	−4.07929	−	2.96377i	−0.396215	−	0.287867i
$107$	−13.3442			−1.29003			−0.645017	−	0.764169i	$-0.723150\pi$
$107$	−13.3442			−1.29003			−0.645017	+	0.764169i	$0.723150\pi$
$108$	1.55609	+	1.13057i	0.149735	+	0.108789i
$109$	−0.771068	+	2.37310i	−0.0738549	+	0.227302i	−0.981169	−	0.193152i	$-0.938129\pi$
$109$	−0.771068	+	2.37310i	−0.0738549	+	0.227302i	0.907314	+	0.420454i	$0.138129\pi$
$110$	−2.13753	+	10.1993i	−0.203805	+	0.972466i
$111$	0.589662	+	1.81479i	0.0559682	+	0.172253i
$112$	1.39704	−	4.29964i	0.132008	−	0.406278i
$113$	−3.67177	+	11.3005i	−0.345411	+	1.06306i	0.615953	+	0.787783i	$0.288771\pi$
$113$	−3.67177	+	11.3005i	−0.345411	+	1.06306i	−0.961364	+	0.275282i	$0.911229\pi$
$114$	−0.701452	−	2.15885i	−0.0656970	−	0.202194i
$115$	−2.76592	−	1.58640i	−0.257923	−	0.147932i
$116$	−1.27425	+	3.92174i	−0.118311	+	0.364125i
$117$	−9.56213	−	6.94729i	−0.884019	−	0.642278i
$118$	−7.15621			−0.658783
$119$	−25.8781	−	18.8015i	−2.37224	−	1.72353i
$120$	−3.76231	+	3.40709i	−0.343450	+	0.311023i
$121$	−8.67183	+	6.30045i	−0.788348	+	0.572768i
$122$	6.16170	−	4.47674i	0.557854	−	0.405305i
$123$	−2.37681	−	7.31507i	−0.214310	−	0.659578i
$124$	3.91387			0.351476
$125$	6.64883	+	8.98849i	0.594690	+	0.803955i
$126$	9.73194			0.866990
$127$	0.810934	+	2.49580i	0.0719587	+	0.221466i	0.980567	−	0.196182i	$-0.0628544\pi$
$127$	0.810934	+	2.49580i	0.0719587	+	0.221466i	−0.908609	+	0.417648i	$0.862854\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−5.21978	+	3.79239i	−0.459576	+	0.333901i
$130$	−9.10044	+	8.24122i	−0.798161	+	0.722803i
$131$	−12.3853	−	8.99848i	−1.08211	−	0.786201i	−0.104062	−	0.994571i	$-0.533184\pi$
$131$	−12.3853	−	8.99848i	−1.08211	−	0.786201i	−0.978050	+	0.208370i	$0.933184\pi$
$132$	−10.5788			−0.920763
$133$	3.65749	+	2.65732i	0.317145	+	0.230419i
$134$	4.46890	−	13.7539i	0.386054	−	1.18815i
$135$	3.73083	+	2.13983i	0.321099	+	0.184167i
$136$	2.18640	+	6.72906i	0.187483	+	0.577012i
$137$	4.17980	−	12.8641i	0.357104	−	1.09905i	−0.597675	−	0.801739i	$-0.703909\pi$
$137$	4.17980	−	12.8641i	0.357104	−	1.09905i	0.954779	−	0.297316i	$-0.0960914\pi$
$138$	1.00025	−	3.07845i	0.0851469	−	0.262055i
$139$	−6.51304	−	20.0451i	−0.552429	−	1.70020i	−0.702638	−	0.711548i	$-0.747995\pi$
$139$	−6.51304	−	20.0451i	−0.552429	−	1.70020i	0.150209	−	0.988654i	$-0.452005\pi$
$140$	2.07356	−	9.89411i	0.175248	−	0.836205i
$141$	−1.63708	+	5.03843i	−0.137867	+	0.424312i
$142$	9.32964	+	6.77838i	0.782926	+	0.568829i
$143$	−25.5884			−2.13981
$144$	−1.74153	−	1.26530i	−0.145128	−	0.105441i
$145$	−1.89132	+	9.02451i	−0.157065	+	0.749445i
$146$	1.52519	−	1.10811i	0.126225	−	0.0917081i
$147$	−24.6790	+	17.9303i	−2.03549	+	1.47887i
$148$	0.259769	+	0.799487i	0.0213529	+	0.0657175i
$149$	5.15433			0.422259			0.211130	−	0.977458i	$-0.432286\pi$
$149$	5.15433			0.422259			0.211130	+	0.977458i	$0.432286\pi$
$150$	−7.54619	+	8.47770i	−0.616144	+	0.692201i
$151$	8.80446			0.716497			0.358248	−	0.933626i	$-0.383374\pi$
$151$	8.80446			0.716497			0.358248	+	0.933626i	$0.383374\pi$
$152$	−0.309017	−	0.951057i	−0.0250646	−	0.0771409i
$153$	−12.3220	+	8.95243i	−0.996171	+	0.723761i
$154$	17.0452	−	12.3841i	1.37354	−	0.997938i
$155$	8.70110	−	0.939635i	0.698889	−	0.0754733i
$156$	−10.0831	−	7.32584i	−0.807298	−	0.586536i
$157$	2.82404			0.225383			0.112692	−	0.993630i	$-0.464053\pi$
$157$	2.82404			0.225383			0.112692	+	0.993630i	$0.464053\pi$
$158$	0.0773743	+	0.0562157i	0.00615557	+	0.00447228i
$159$	3.53691	−	10.8855i	0.280495	−	0.863276i
$160$	−1.65745	+	1.50096i	−0.131033	+	0.118661i
$161$	1.99213	+	6.13116i	0.157002	+	0.483203i
$162$	−3.34481	+	10.2943i	−0.262793	+	0.808795i
$163$	−6.30800	+	19.4140i	−0.494081	+	1.52062i	0.324304	+	0.945953i	$0.394870\pi$
$163$	−6.30800	+	19.4140i	−0.494081	+	1.52062i	−0.818384	+	0.574671i	$0.805130\pi$
$164$	−1.04708	−	3.22258i	−0.0817631	−	0.251641i
$165$	−23.5181	+	2.53973i	−1.83088	+	0.197718i
$166$	4.11632	−	12.6687i	0.319488	−	0.983284i
$167$	−1.81958	−	1.32200i	−0.140803	−	0.102299i	0.515154	−	0.857098i	$-0.327735\pi$
$167$	−1.81958	−	1.32200i	−0.140803	−	0.102299i	−0.655957	+	0.754798i	$0.727735\pi$
$168$	10.2622			0.791747
$169$	−13.8723	−	10.0788i	−1.06710	−	0.775295i
$170$	6.47619	+	14.4348i	0.496701	+	1.10710i
$171$	1.74153	−	1.26530i	0.133178	−	0.0967597i
$172$	−2.29952	+	1.67070i	−0.175336	+	0.127389i
$173$	−3.67982	−	11.3253i	−0.279772	−	0.861049i	−0.987917	−	0.154982i	$-0.950468\pi$
$173$	−3.67982	−	11.3253i	−0.279772	−	0.861049i	0.708146	−	0.706066i	$-0.249532\pi$
$174$	−9.36026			−0.709600
$175$	2.23447	−	22.4938i	0.168910	−	1.70037i
$176$	−4.66036			−0.351288
$177$	−5.01974	−	15.4492i	−0.377307	−	1.16123i
$178$	−12.2841	+	8.92489i	−0.920729	+	0.668949i
$179$	5.23059	−	3.80025i	0.390953	−	0.284044i	−0.374893	−	0.927068i	$-0.622321\pi$
$179$	5.23059	−	3.80025i	0.390953	−	0.284044i	0.765846	+	0.643024i	$0.222321\pi$
$180$	−4.17544	−	2.39483i	−0.311219	−	0.178500i
$181$	11.7031	+	8.50283i	0.869887	+	0.632010i	0.930557	−	0.366148i	$-0.119324\pi$
$181$	11.7031	+	8.50283i	0.869887	+	0.632010i	−0.0606694	+	0.998158i	$0.519324\pi$
$182$	24.8227			1.83998
$183$	13.9867	+	10.1619i	1.03393	+	0.751193i
$184$	0.440649	−	1.35618i	0.0324851	−	0.0999788i
$185$	0.769443	+	1.71501i	0.0565706	+	0.126090i
$186$	2.74539	+	8.44945i	0.201302	+	0.619544i
$187$	−10.1894	+	31.3599i	−0.745125	+	2.29326i
$188$	−0.721200	+	2.21962i	−0.0525989	+	0.161883i
$189$	−2.68711	−	8.27007i	−0.195458	−	0.601559i
$190$	−0.915316	−	2.04015i	−0.0664040	−	0.148008i
$191$	5.28590	−	16.2683i	0.382475	−	1.17714i	−0.555821	−	0.831302i	$-0.687596\pi$
$191$	5.28590	−	16.2683i	0.382475	−	1.17714i	0.938296	−	0.345834i	$-0.112404\pi$
$192$	−1.83642	−	1.33424i	−0.132533	−	0.0962905i
$193$	27.4618			1.97675			0.988373	−	0.152048i	$-0.0485867\pi$
$193$	27.4618			1.97675			0.988373	+	0.152048i	$0.0485867\pi$
$194$	−10.5820	−	7.68826i	−0.759742	−	0.551985i
$195$	−24.1750	−	13.8656i	−1.73121	−	0.992939i
$196$	−10.8721	+	7.89902i	−0.776576	+	0.564215i
$197$	20.0276	−	14.5509i	1.42690	−	1.03671i	0.436321	−	0.899791i	$-0.356281\pi$
$197$	20.0276	−	14.5509i	1.42690	−	1.03671i	0.990583	−	0.136916i	$-0.0437190\pi$
$198$	−3.10010	−	9.54113i	−0.220315	−	0.678059i
$199$	20.6603			1.46457			0.732286	−	0.680997i	$-0.238453\pi$
$199$	20.6603			1.46457			0.732286	+	0.680997i	$0.238453\pi$
$200$	−3.32439	+	3.73476i	−0.235070	+	0.264087i
$201$	32.8272			2.31545
$202$	1.56166	+	4.80630i	0.109878	+	0.338170i
$203$	15.0819	−	10.9576i	1.05854	−	0.769076i
$204$	−12.9934	+	9.44023i	−0.909717	+	0.660948i
$205$	−3.10147	−	6.91287i	−0.216616	−	0.482816i
$206$	9.43268	+	6.85324i	0.657206	+	0.477488i
$207$	3.06962			0.213353
$208$	−4.44202	−	3.22732i	−0.307999	−	0.223774i
$209$	1.44013	−	4.43227i	0.0996159	−	0.306586i
$210$	22.8144	−	2.46373i	1.57434	−	0.170014i
$211$	−1.44227	−	4.43886i	−0.0992901	−	0.305584i	0.889058	−	0.457795i	$-0.151361\pi$
$211$	−1.44227	−	4.43886i	−0.0992901	−	0.305584i	−0.988348	+	0.152211i	$0.951361\pi$
$212$	1.55815	−	4.79549i	0.107014	−	0.329355i
$213$	−8.08919	+	24.8960i	−0.554262	+	1.70584i
$214$	−4.12359	−	12.6911i	−0.281883	−	0.867545i
$215$	−4.71106	+	4.26626i	−0.321291	+	0.290956i
$216$	−0.594373	+	1.82929i	−0.0404420	+	0.124468i
$217$	−14.3150	−	10.4004i	−0.971763	−	0.706027i
$218$	−2.49523			−0.168998
$219$	3.46209	+	2.51536i	0.233946	+	0.169972i
$220$	−10.3606	+	1.11885i	−0.698515	+	0.0754328i
$221$	−31.4289	+	22.8344i	−2.11414	+	1.53601i
$222$	−1.54375	+	1.12160i	−0.103610	+	0.0752771i
$223$	−1.95103	−	6.00466i	−0.130651	−	0.402102i	0.864237	−	0.503084i	$-0.167801\pi$
$223$	−1.95103	−	6.00466i	−0.130651	−	0.402102i	−0.994888	+	0.100982i	$0.967801\pi$
$224$	4.52091			0.302066
$225$	−9.85755	−	4.32162i	−0.657170	−	0.288108i
$226$	−11.8821			−0.790384
$227$	−4.42322	−	13.6133i	−0.293580	−	0.903545i	−0.983695	−	0.179846i	$-0.942440\pi$
$227$	−4.42322	−	13.6133i	−0.293580	−	0.903545i	0.690115	−	0.723699i	$-0.257560\pi$
$228$	1.83642	−	1.33424i	0.121620	−	0.0883622i
$229$	0.796321	−	0.578561i	0.0526224	−	0.0382324i	−0.561163	−	0.827705i	$-0.689646\pi$
$229$	0.796321	−	0.578561i	0.0526224	−	0.0382324i	0.613786	+	0.789473i	$0.289646\pi$
$230$	0.654037	−	3.12077i	0.0431260	−	0.205777i
$231$	38.6917	+	28.1112i	2.54573	+	1.84958i
$232$	−4.12356			−0.270725
$233$	−3.69877	−	2.68731i	−0.242314	−	0.176052i	0.459999	−	0.887919i	$-0.347850\pi$
$233$	−3.69877	−	2.68731i	−0.242314	−	0.176052i	−0.702314	+	0.711868i	$0.747850\pi$
$234$	3.65241	−	11.2410i	0.238765	−	0.734844i
$235$	−1.07045	+	5.10768i	−0.0698282	+	0.333189i
$236$	−2.21139	−	6.80596i	−0.143949	−	0.443031i
$237$	−0.0670868	+	0.206472i	−0.00435775	+	0.0134118i
$238$	9.88454	−	30.4215i	0.640719	−	1.97193i
$239$	5.06321	+	15.5829i	0.327512	+	1.00798i	0.970294	+	0.241928i	$0.0777799\pi$
$239$	5.06321	+	15.5829i	0.327512	+	1.00798i	−0.642782	+	0.766049i	$0.722220\pi$
$240$	−4.40295	−	2.52532i	−0.284210	−	0.163009i
$241$	−0.508376	+	1.56462i	−0.0327474	+	0.100786i	−0.966094	−	0.258190i	$-0.916874\pi$
$241$	−0.508376	+	1.56462i	−0.0327474	+	0.100786i	0.933347	+	0.358976i	$0.116874\pi$
$242$	−8.67183	−	6.30045i	−0.557446	−	0.405008i
$243$	−18.7997			−1.20600
$244$	6.16170	+	4.47674i	0.394462	+	0.286594i
$245$	−22.2738	+	20.1708i	−1.42302	+	1.28866i
$246$	6.22257	−	4.52096i	0.396737	−	0.288246i
$247$	4.44202	−	3.22732i	0.282639	−	0.205349i
$248$	1.20945	+	3.72232i	0.0768004	+	0.236367i
$249$	30.2372			1.91621
$250$	−6.49396	+	9.10101i	−0.410714	+	0.575599i
$251$	−5.30919			−0.335113			−0.167556	−	0.985862i	$-0.553588\pi$
$251$	−5.30919			−0.335113			−0.167556	+	0.985862i	$0.553588\pi$
$252$	3.00734	+	9.25563i	0.189444	+	0.583050i
$253$	5.37635	−	3.90615i	0.338009	−	0.245578i
$254$	−2.12305	+	1.54249i	−0.133212	+	0.0967843i
$255$	−26.6197	+	24.1064i	−1.66699	+	1.50960i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−17.5891			−1.09718			−0.548590	−	0.836092i	$-0.684835\pi$
$257$	−17.5891			−1.09718			−0.548590	+	0.836092i	$0.684835\pi$
$258$	−5.21978	−	3.79239i	−0.324969	−	0.236104i
$259$	1.17439	−	3.61441i	0.0729732	−	0.224588i
$260$	−10.6501	−	6.10836i	−0.660488	−	0.378824i
$261$	−2.74302	−	8.44215i	−0.169789	−	0.522556i
$262$	4.73078	−	14.5598i	0.292269	−	0.899510i
$263$	2.81861	−	8.67479i	0.173803	−	0.534910i	−0.825774	−	0.564001i	$-0.809261\pi$
$263$	2.81861	−	8.67479i	0.173803	−	0.534910i	0.999577	+	0.0290911i	$0.00926129\pi$
$264$	−3.26902	−	10.0610i	−0.201194	−	0.619212i
$265$	2.31270	−	11.0351i	0.142068	−	0.677883i
$266$	−1.39704	+	4.29964i	−0.0856579	+	0.263628i
$267$	−27.8842	−	20.2590i	−1.70648	−	1.23983i
$268$	14.4617			0.883387
$269$	19.2041	+	13.9526i	1.17089	+	0.850703i	0.991115	−	0.133004i	$-0.0424625\pi$
$269$	19.2041	+	13.9526i	1.17089	+	0.850703i	0.179777	+	0.983707i	$0.442462\pi$
$270$	−0.882204	+	4.20948i	−0.0536892	+	0.256181i
$271$	−15.2880	+	11.1074i	−0.928679	+	0.674724i	−0.945669	−	0.325131i	$-0.894592\pi$
$271$	−15.2880	+	11.1074i	−0.928679	+	0.674724i	0.0169904	+	0.999856i	$0.494592\pi$
$272$	−5.72408	+	4.15879i	−0.347073	+	0.252164i
$273$	17.4119	+	53.5884i	1.05382	+	3.24332i
$274$	13.5261			0.817142
$275$	−22.7646	+	4.97473i	−1.37276	+	0.299987i
$276$	3.23688			0.194837
$277$	0.952847	+	2.93256i	0.0572510	+	0.176201i	0.975593	−	0.219588i	$-0.0704713\pi$
$277$	0.952847	+	2.93256i	0.0572510	+	0.176201i	−0.918342	+	0.395789i	$0.870471\pi$
$278$	17.0514	−	12.3885i	1.02267	−	0.743015i
$279$	−6.81614	+	4.95221i	−0.408072	+	0.296481i
$280$	10.0506	−	1.08537i	0.600640	−	0.0648633i
$281$	8.85882	+	6.43631i	0.528473	+	0.383958i	0.819786	−	0.572670i	$-0.194092\pi$
$281$	8.85882	+	6.43631i	0.528473	+	0.383958i	−0.291313	+	0.956628i	$0.594092\pi$
$282$	−5.29771			−0.315474
$283$	−11.8815	−	8.63239i	−0.706279	−	0.513142i	0.175692	−	0.984445i	$-0.443784\pi$
$283$	−11.8815	−	8.63239i	−0.706279	−	0.513142i	−0.881971	+	0.471303i	$0.843784\pi$
$284$	−3.56361	+	10.9677i	−0.211461	+	0.650810i
$285$	3.76231	−	3.40709i	0.222860	−	0.201819i
$286$	−7.90724	−	24.3360i	−0.467565	−	1.43902i
$287$	−4.73375	+	14.5690i	−0.279424	+	0.859979i
$288$	0.665206	−	2.04729i	0.0391977	−	0.120638i
$289$	10.2163	+	31.4425i	0.600959	+	1.84956i
$290$	−9.16727	+	0.989976i	−0.538321	+	0.0581334i
$291$	9.17503	−	28.2378i	0.537850	−	1.65533i
$292$	1.52519	+	1.10811i	0.0892548	+	0.0648474i
$293$	−12.8976			−0.753489			−0.376744	−	0.926317i	$-0.622956\pi$
$293$	−12.8976			−0.753489			−0.376744	+	0.926317i	$0.622956\pi$
$294$	−24.6790	−	17.9303i	−1.43931	−	1.04572i
$295$	−6.55020	−	14.5997i	−0.381367	−	0.850029i
$296$	−0.680085	+	0.494110i	−0.0395291	+	0.0287196i
$297$	−7.25194	+	5.26884i	−0.420800	+	0.305729i
$298$	1.59278	+	4.90206i	0.0922670	+	0.283969i
$299$	7.82949			0.452791
$300$	−10.3947	−	4.55710i	−0.600137	−	0.263104i
$301$	12.8500			0.740664
$302$	2.72073	+	8.37354i	0.156560	+	0.481843i
$303$	−9.28064	+	6.74278i	−0.533159	+	0.387363i
$304$	0.809017	−	0.587785i	0.0464003	−	0.0337118i
$305$	14.7731	+	8.47313i	0.845905	+	0.485170i
$306$	−12.3220	−	8.95243i	−0.704400	−	0.511776i
$307$	−5.23148			−0.298576			−0.149288	−	0.988794i	$-0.547698\pi$
$307$	−5.23148			−0.298576			−0.149288	+	0.988794i	$0.547698\pi$
$308$	17.0452	+	12.3841i	0.971242	+	0.705649i
$309$	−8.17853	+	25.1709i	−0.465260	+	1.43192i
$310$	3.58243	+	7.98488i	0.203469	+	0.453510i
$311$	−8.38544	−	25.8077i	−0.475495	−	1.46342i	−0.845290	−	0.534308i	$-0.820572\pi$
$311$	−8.38544	−	25.8077i	−0.475495	−	1.46342i	0.369795	−	0.929113i	$-0.379428\pi$
$312$	3.85142	−	11.8535i	0.218044	−	0.671069i
$313$	7.58686	−	23.3499i	0.428835	−	1.31982i	−0.470440	−	0.882432i	$-0.655905\pi$
$313$	7.58686	−	23.3499i	0.428835	−	1.31982i	0.899274	−	0.437385i	$-0.144095\pi$
$314$	0.872677	+	2.68582i	0.0492480	+	0.151570i
$315$	8.90781	+	19.8546i	0.501898	+	1.11868i
$316$	−0.0295543	+	0.0909589i	−0.00166256	+	0.00511684i
$317$	16.0721	+	11.6770i	0.902697	+	0.655848i	0.939157	−	0.343487i	$-0.111608\pi$
$317$	16.0721	+	11.6770i	0.902697	+	0.655848i	−0.0364602	+	0.999335i	$0.511608\pi$
$318$	11.4457			0.641842
$319$	−15.5471	−	11.2956i	−0.870472	−	0.632435i
$320$	−1.93967	−	1.11250i	−0.108431	−	0.0621908i
$321$	24.5056	−	17.8044i	1.36777	−	0.993744i
$322$	−5.21548	+	3.78927i	−0.290647	+	0.211167i
$323$	−2.18640	−	6.72906i	−0.121655	−	0.374415i
$324$	−10.8240			−0.601336
$325$	−25.1431	−	11.0229i	−1.39469	−	0.611441i
$326$	−20.4131			−1.13058
$327$	−1.75028	−	5.38682i	−0.0967908	−	0.297892i
$328$	2.74129	−	1.99166i	0.151362	−	0.109971i
$329$	8.53604	−	6.20180i	0.470607	−	0.341916i
$330$	−9.68292	−	21.5822i	−0.533027	−	1.18806i
$331$	18.4708	+	13.4198i	1.01525	+	0.737619i	0.965303	−	0.261133i	$-0.0840960\pi$
$331$	18.4708	+	13.4198i	1.01525	+	0.737619i	0.0499430	+	0.998752i	$0.484096\pi$
$332$	13.3207			0.731068
$333$	−1.46399	−	1.06365i	−0.0802259	−	0.0582875i
$334$	0.695017	−	2.13904i	0.0380296	−	0.117043i
$335$	32.1503	−	3.47193i	1.75656	−	0.189692i
$336$	3.17120	+	9.75995i	0.173003	+	0.532449i
$337$	−2.53077	+	7.78892i	−0.137860	+	0.424289i	−0.996024	−	0.0890863i	$-0.971605\pi$
$337$	−2.53077	+	7.78892i	−0.137860	+	0.424289i	0.858164	+	0.513376i	$0.171605\pi$
$338$	5.29876	−	16.3079i	0.288214	−	0.887033i
$339$	−8.33471	−	25.6516i	−0.452679	−	1.39320i
$340$	−11.7270	+	10.6198i	−0.635987	+	0.575940i
$341$	−5.63649	+	17.3473i	−0.305233	+	0.939411i
$342$	1.74153	+	1.26530i	0.0941713	+	0.0684194i
$343$	29.1084			1.57170
$344$	−2.29952	−	1.67070i	−0.123982	−	0.0900779i
$345$	7.19604	−	0.777102i	0.387422	−	0.0418378i
$346$	9.63390	−	6.99944i	0.517922	−	0.376292i
$347$	9.57138	−	6.95401i	0.513819	−	0.373311i	−0.300452	−	0.953797i	$-0.597137\pi$
$347$	9.57138	−	6.95401i	0.513819	−	0.373311i	0.814270	+	0.580486i	$0.197137\pi$
$348$	−2.89248	−	8.90214i	−0.155053	−	0.477205i
$349$	−16.7255			−0.895297			−0.447649	−	0.894210i	$-0.647738\pi$
$349$	−16.7255			−0.895297			−0.447649	+	0.894210i	$0.647738\pi$
$350$	22.0834	−	4.82586i	1.18041	−	0.257953i
$351$	−10.5609			−0.563698
$352$	−1.44013	−	4.43227i	−0.0767592	−	0.236241i
$353$	−9.74295	+	7.07867i	−0.518565	+	0.376760i	−0.816063	−	0.577963i	$-0.803848\pi$
$353$	−9.74295	+	7.07867i	−0.518565	+	0.376760i	0.297498	+	0.954722i	$0.403848\pi$
$354$	13.1418	−	9.54811i	0.698481	−	0.507476i
$355$	−5.28931	+	25.2382i	−0.280728	+	1.33950i
$356$	−12.2841	−	8.92489i	−0.651054	−	0.473018i
$357$	72.6088			3.84287
$358$	5.23059	+	3.80025i	0.276445	+	0.200849i
$359$	5.43380	−	16.7235i	0.286785	−	0.882633i	−0.699073	−	0.715050i	$-0.746404\pi$
$359$	5.43380	−	16.7235i	0.286785	−	0.882633i	0.985858	−	0.167583i	$-0.0535962\pi$
$360$	0.987338	−	4.71113i	0.0520373	−	0.248298i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	−4.47020	+	13.7579i	−0.234949	+	0.723097i
$363$	7.51884	−	23.1406i	0.394637	−	1.21457i
$364$	7.67063	+	23.6078i	0.402050	+	1.23738i
$365$	3.65674	+	2.09733i	0.191403	+	0.109779i
$366$	−5.34245	+	16.4424i	−0.279254	+	0.859457i
$367$	12.0814	+	8.77765i	0.630644	+	0.458190i	0.856623	−	0.515943i	$-0.172558\pi$
$367$	12.0814	+	8.77765i	0.630644	+	0.458190i	−0.225979	+	0.974132i	$0.572558\pi$
$368$	1.42597			0.0743339
$369$	5.90104	+	4.28736i	0.307196	+	0.223191i
$370$	−1.39330	+	1.26175i	−0.0724342	+	0.0655953i
$371$	−18.4421	+	13.3990i	−0.957465	+	0.695639i
$372$	−7.18753	+	5.22205i	−0.372656	+	0.270751i
$373$	1.70214	+	5.23866i	0.0881336	+	0.271247i	0.985403	−	0.170235i	$-0.0544527\pi$
$373$	1.70214	+	5.23866i	0.0881336	+	0.271247i	−0.897270	+	0.441483i	$0.854453\pi$
$374$	−32.9737			−1.70503
$375$	−24.2029	−	7.63555i	−1.24983	−	0.394298i
$376$	−2.33385			−0.120359
$377$	−6.99646	−	21.5329i	−0.360336	−	1.10900i
$378$	7.03494	−	5.11118i	0.361838	−	0.262891i
$379$	−26.5658	+	19.3012i	−1.36459	+	0.991434i	−0.366454	+	0.930436i	$0.619428\pi$
$379$	−26.5658	+	19.3012i	−1.36459	+	0.991434i	−0.998138	+	0.0609976i	$0.980572\pi$
$380$	1.65745	−	1.50096i	0.0850252	−	0.0769975i
$381$	−4.81921	−	3.50136i	−0.246896	−	0.179380i
$382$	17.1055			0.875196
$383$	−13.4211	−	9.75097i	−0.685784	−	0.498251i	0.189487	−	0.981883i	$-0.439317\pi$
$383$	−13.4211	−	9.75097i	−0.685784	−	0.498251i	−0.875272	+	0.483632i	$0.839317\pi$
$384$	0.701452	−	2.15885i	0.0357958	−	0.110168i
$385$	40.8671	+	23.4394i	2.08278	+	1.19458i
$386$	8.48617	+	26.1178i	0.431935	+	1.32936i
$387$	1.89075	−	5.81914i	0.0961125	−	0.295804i
$388$	4.04196	−	12.4399i	0.205199	−	0.631539i
$389$	−9.20448	−	28.3285i	−0.466685	−	1.43631i	−0.856850	−	0.515565i	$-0.827582\pi$
$389$	−9.20448	−	28.3285i	−0.466685	−	1.43631i	0.390165	−	0.920745i	$-0.372418\pi$
$390$	5.71650	−	27.2766i	0.289466	−	1.38120i
$391$	3.11775	−	9.59545i	0.157671	−	0.485263i
$392$	−10.8721	−	7.89902i	−0.549122	−	0.398961i
$393$	34.7509			1.75295
$394$	20.0276	+	14.5509i	1.00897	+	0.733062i
$395$	−0.0438663	+	0.209310i	−0.00220715	+	0.0105315i
$396$	8.11617	−	5.89674i	0.407853	−	0.296323i
$397$	15.6925	−	11.4012i	0.787582	−	0.572212i	−0.119663	−	0.992815i	$-0.538181\pi$
$397$	15.6925	−	11.4012i	0.787582	−	0.572212i	0.907245	+	0.420603i	$0.138181\pi$
$398$	6.38440	+	19.6491i	0.320021	+	0.984923i
$399$	−10.2622			−0.513753
$400$	−4.57926	−	2.00758i	−0.228963	−	0.100379i
$401$	17.8951			0.893639			0.446820	−	0.894624i	$-0.352557\pi$
$401$	17.8951			0.893639			0.446820	+	0.894624i	$0.352557\pi$
$402$	10.1442	+	31.2205i	0.505945	+	1.55714i
$403$	−17.3855	+	12.6313i	−0.866034	+	0.629211i
$404$	−4.08849	+	2.97046i	−0.203410	+	0.147786i
$405$	−24.0634	+	2.59861i	−1.19572	+	0.129126i
$406$	15.0819	+	10.9576i	0.748502	+	0.543819i
$407$	−3.91764			−0.194190
$408$	−12.9934	−	9.44023i	−0.643267	−	0.467361i
$409$	−10.5874	+	32.5846i	−0.523513	+	1.61121i	0.243725	+	0.969844i	$0.421631\pi$
$409$	−10.5874	+	32.5846i	−0.523513	+	1.61121i	−0.767238	+	0.641362i	$0.778369\pi$
$410$	5.61612	−	5.08587i	0.277360	−	0.251173i
$411$	9.48792	+	29.2008i	0.468004	+	1.44037i
$412$	−3.60296	+	11.0888i	−0.177505	+	0.546305i
$413$	−9.99750	+	30.7691i	−0.491945	+	1.51405i
$414$	0.948565	+	2.91938i	0.0466194	+	0.143480i
$415$	29.6138	−	3.19800i	1.45368	−	0.156984i
$416$	1.69670	−	5.22191i	0.0831876	−	0.256025i
$417$	38.7057	+	28.1213i	1.89542	+	1.37711i
$418$	4.66036			0.227946
$419$	12.1725	+	8.84382i	0.594664	+	0.432049i	0.843981	−	0.536373i	$-0.180206\pi$
$419$	12.1725	+	8.84382i	0.594664	+	0.432049i	−0.249317	+	0.968422i	$0.580206\pi$
$420$	9.39317	+	20.9364i	0.458340	+	1.02159i
$421$	−1.26920	+	0.922131i	−0.0618573	+	0.0449419i	−0.618284	−	0.785955i	$-0.712172\pi$
$421$	−1.26920	+	0.922131i	−0.0618573	+	0.0449419i	0.556427	+	0.830897i	$0.312172\pi$
$422$	3.77592	−	2.74337i	0.183809	−	0.133545i
$423$	−1.55249	−	4.77808i	−0.0754847	−	0.232318i
$424$	5.04227			0.244875
$425$	−23.5213	+	26.4247i	−1.14095	+	1.28179i
$426$	−26.1772			−1.26829
$427$	−10.6402	−	32.7472i	−0.514917	−	1.58475i
$428$	10.7957	−	7.84353i	0.521829	−	0.379131i
$429$	46.9911	−	34.1410i	2.26875	−	1.64835i
$430$	−5.51325	−	3.16213i	−0.265873	−	0.152492i
$431$	−9.00985	−	6.54604i	−0.433989	−	0.315312i	0.349253	−	0.937029i	$-0.386435\pi$
$431$	−9.00985	−	6.54604i	−0.433989	−	0.315312i	−0.783242	+	0.621717i	$0.786435\pi$
$432$	−1.92343			−0.0925412
$433$	5.46233	+	3.96862i	0.262503	+	0.190720i	0.711250	−	0.702939i	$-0.248129\pi$
$433$	5.46233	+	3.96862i	0.262503	+	0.190720i	−0.448747	+	0.893659i	$0.648129\pi$
$434$	5.46783	−	16.8282i	0.262464	−	0.807782i
$435$	−8.56760	−	19.0963i	−0.410785	−	0.915598i
$436$	−0.771068	−	2.37310i	−0.0369275	−	0.113651i
$437$	−0.440649	+	1.35618i	−0.0210791	+	0.0648748i
$438$	−1.32240	+	4.06993i	−0.0631867	+	0.194469i
$439$	10.7180	+	32.9867i	0.511543	+	1.57437i	0.789485	+	0.613769i	$0.210348\pi$
$439$	10.7180	+	32.9867i	0.511543	+	1.57437i	−0.277943	+	0.960598i	$0.589652\pi$
$440$	−4.26571	−	9.50782i	−0.203360	−	0.453267i
$441$	8.93945	−	27.5128i	0.425688	−	1.31013i
$442$	−31.4289	−	22.8344i	−1.49492	−	1.08612i
$443$	−3.24411			−0.154132			−0.0770661	−	0.997026i	$-0.524555\pi$
$443$	−3.24411			−0.154132			−0.0770661	+	0.997026i	$0.524555\pi$
$444$	−1.54375	−	1.12160i	−0.0732634	−	0.0532290i
$445$	−29.4519	−	16.8922i	−1.39615	−	0.800766i
$446$	5.10787	−	3.71108i	0.241865	−	0.175725i
$447$	−9.46554	+	6.87712i	−0.447705	+	0.325276i
$448$	1.39704	+	4.29964i	0.0660038	+	0.203139i
$449$	−21.1271			−0.997048			−0.498524	−	0.866876i	$-0.666124\pi$
$449$	−21.1271			−0.997048			−0.498524	+	0.866876i	$0.666124\pi$
$450$	1.06396	−	10.7105i	0.0501553	−	0.504900i
$451$	15.7913			0.743581
$452$	−3.67177	−	11.3005i	−0.172705	−	0.531532i
$453$	−16.1687	+	11.7473i	−0.759673	+	0.551935i
$454$	11.5801	−	8.41347i	0.543483	−	0.394864i
$455$	22.7206	+	50.6419i	1.06516	+	2.37413i
$456$	1.83642	+	1.33424i	0.0859985	+	0.0624815i
$457$	−27.4628			−1.28465			−0.642327	−	0.766431i	$-0.722031\pi$
$457$	−27.4628			−1.28465			−0.642327	+	0.766431i	$0.722031\pi$
$458$	0.796321	+	0.578561i	0.0372096	+	0.0270344i
$459$	−4.20540	+	12.9429i	−0.196291	+	0.604123i
$460$	3.17014	−	0.342344i	0.147808	−	0.0159619i
$461$	5.32211	+	16.3798i	0.247875	+	0.762881i	0.995150	+	0.0983665i	$0.0313618\pi$
$461$	5.32211	+	16.3798i	0.247875	+	0.762881i	−0.747275	+	0.664515i	$0.768638\pi$
$462$	−14.7789	+	45.4849i	−0.687578	+	2.11615i
$463$	−1.04871	+	3.22761i	−0.0487378	+	0.150000i	−0.972464	−	0.233055i	$-0.925128\pi$
$463$	−1.04871	+	3.22761i	−0.0487378	+	0.150000i	0.923726	+	0.383054i	$0.125128\pi$
$464$	−1.27425	−	3.92174i	−0.0591556	−	0.182062i
$465$	−14.7252	+	13.3349i	−0.682866	+	0.618393i
$466$	1.41280	−	4.34816i	0.0654469	−	0.201425i
$467$	0.135248	+	0.0982638i	0.00625855	+	0.00454710i	0.590910	−	0.806737i	$-0.298769\pi$
$467$	0.135248	+	0.0982638i	0.00625855	+	0.00454710i	−0.584652	+	0.811284i	$0.698769\pi$
$468$	11.8194			0.546354
$469$	−52.8934	−	38.4293i	−2.44239	−	1.77450i
$470$	−5.18848	+	0.560306i	−0.239327	+	0.0258450i
$471$	−5.18614	+	3.76795i	−0.238965	+	0.173618i
$472$	5.78950	−	4.20632i	0.266483	−	0.193611i
$473$	−4.09337	−	12.5981i	−0.188213	−	0.579261i
$474$	−0.217097			−0.00997161
$475$	3.32439	−	3.73476i	0.152534	−	0.171362i
$476$	31.9870			1.46612
$477$	3.35415	+	10.3230i	0.153576	+	0.472659i
$478$	−13.2556	+	9.63079i	−0.606299	+	0.440502i
$479$	−19.9667	+	14.5067i	−0.912302	+	0.662826i	−0.941596	−	0.336744i	$-0.890674\pi$
$479$	−19.9667	+	14.5067i	−0.912302	+	0.662826i	0.0292937	+	0.999571i	$0.490674\pi$
$480$	1.04114	−	4.96783i	0.0475211	−	0.226749i
$481$	−3.73410	−	2.71298i	−0.170260	−	0.123701i
$482$	−1.64514			−0.0749340
$483$	−11.8388	−	8.60143i	−0.538686	−	0.391378i
$484$	3.31234	−	10.1943i	0.150561	−	0.463379i
$485$	5.99931	−	28.6260i	0.272415	−	1.29984i
$486$	−5.80942	−	17.8796i	−0.263521	−	0.811034i
$487$	4.22871	−	13.0146i	0.191621	−	0.589749i	−0.808378	−	0.588663i	$-0.799654\pi$
$487$	4.22871	−	13.0146i	0.191621	−	0.589749i	0.999999	−	0.00108584i	$-0.000345635\pi$
$488$	−2.35356	+	7.24351i	−0.106541	+	0.327898i
$489$	−14.3188	−	44.0688i	−0.647519	−	1.99286i
$490$	−26.0665	−	14.9505i	−1.17757	−	0.675395i
$491$	−9.76066	+	30.0402i	−0.440493	+	1.35570i	0.446859	+	0.894604i	$0.352542\pi$
$491$	−9.76066	+	30.0402i	−0.440493	+	1.35570i	−0.887352	+	0.461093i	$0.847458\pi$
$492$	6.22257	+	4.52096i	0.280535	+	0.203821i
$493$	−29.1757			−1.31401
$494$	4.44202	+	3.22732i	0.199856	+	0.145204i
$495$	16.6277	−	15.0578i	0.747361	−	0.676798i
$496$	−3.16639	+	2.30052i	−0.142175	+	0.103296i
$497$	42.1785	−	30.6444i	1.89196	−	1.37459i
$498$	9.34382	+	28.7573i	0.418707	+	1.28865i
$499$	36.3566			1.62754			0.813772	−	0.581184i	$-0.197410\pi$
$499$	36.3566			1.62754			0.813772	+	0.581184i	$0.197410\pi$
$500$	−10.6623	−	3.36376i	−0.476834	−	0.150432i
$501$	5.10538			0.228092
$502$	−1.64063	−	5.04934i	−0.0732248	−	0.225363i
$503$	10.7269	−	7.79356i	0.478289	−	0.347498i	−0.322374	−	0.946612i	$-0.604481\pi$
$503$	10.7269	−	7.79356i	0.478289	−	0.347498i	0.800663	+	0.599115i	$0.204481\pi$
$504$	−7.87331	+	5.72029i	−0.350705	+	0.254802i
$505$	−8.37615	+	7.58531i	−0.372734	+	0.337542i
$506$	5.37635	+	3.90615i	0.239008	+	0.173650i
$507$	38.9231			1.72863
$508$	−2.12305	−	1.54249i	−0.0941952	−	0.0684368i
$509$	−9.53105	+	29.3336i	−0.422456	+	1.30019i	0.482953	+	0.875647i	$0.339564\pi$
$509$	−9.53105	+	29.3336i	−0.422456	+	1.30019i	−0.905409	+	0.424540i	$0.860436\pi$
$510$	−31.1525	−	17.8675i	−1.37945	−	0.791188i
$511$	−2.63374	−	8.10583i	−0.116510	−	0.358581i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	0.594373	−	1.82929i	0.0262422	−	0.0807653i
$514$	−5.43534	−	16.7283i	−0.239742	−	0.737852i
$515$	−5.34773	+	25.5169i	−0.235649	+	1.12441i
$516$	1.99378	−	6.13622i	0.0877712	−	0.270132i
$517$	−8.79934	−	6.39310i	−0.386995	−	0.281168i
$518$	3.80041			0.166981
$519$	21.8684	+	15.8883i	0.959917	+	0.697421i
$520$	2.51834	−	12.0164i	0.110437	−	0.526954i
$521$	−7.72415	+	5.61192i	−0.338401	+	0.245863i	−0.743987	−	0.668194i	$-0.767068\pi$
$521$	−7.72415	+	5.61192i	−0.338401	+	0.245863i	0.405586	+	0.914057i	$0.367068\pi$
$522$	7.18132	−	5.21753i	0.314318	−	0.228365i
$523$	8.57452	+	26.3897i	0.374938	+	1.15394i	0.943521	+	0.331313i	$0.107492\pi$
$523$	8.57452	+	26.3897i	0.374938	+	1.15394i	−0.568583	+	0.822626i	$0.692508\pi$
$524$	15.3091			0.668782
$525$	25.9087	+	44.2895i	1.13075	+	1.93295i
$526$	9.12121			0.397704
$527$	8.55731	+	26.3367i	0.372762	+	1.14724i
$528$	8.55840	−	6.21804i	0.372457	−	0.270606i
$529$	16.9623	−	12.3239i	0.737493	−	0.535820i
$530$	11.2097	−	1.21054i	0.486918	−	0.0525824i
$531$	12.4628	+	9.05474i	0.540839	+	0.392942i
$532$	−4.52091			−0.196006
$533$	15.0514	+	10.9355i	0.651950	+	0.473669i
$534$	10.6508	−	32.7798i	0.460905	−	1.41852i
$535$	22.1173	−	20.0291i	0.956214	−	0.865933i
$536$	4.46890	+	13.7539i	0.193027	+	0.594076i
$537$	−4.53514	+	13.9577i	−0.195706	+	0.602321i
$538$	−7.33530	+	22.5757i	−0.316247	+	0.973309i
$539$	−19.3534	−	59.5635i	−0.833608	−	2.56558i
$540$	−4.27607	+	0.461774i	−0.184013	+	0.0198716i
$541$	−5.91123	+	18.1929i	−0.254143	+	0.782173i	0.739854	+	0.672768i	$0.234895\pi$
$541$	−5.91123	+	18.1929i	−0.254143	+	0.782173i	−0.993997	+	0.109405i	$0.965105\pi$
$542$	−15.2880	−	11.1074i	−0.656675	−	0.477102i
$543$	−32.8367			−1.40916
$544$	−5.72408	−	4.15879i	−0.245418	−	0.178307i
$545$	−2.28392	−	5.09063i	−0.0978326	−	0.218059i
$546$	−45.5850	+	33.1194i	−1.95086	+	1.41738i
$547$	6.22715	−	4.52429i	0.266254	−	0.193445i	−0.446646	−	0.894711i	$-0.647382\pi$
$547$	6.22715	−	4.52429i	0.266254	−	0.193445i	0.712899	+	0.701266i	$0.247382\pi$
$548$	4.17980	+	12.8641i	0.178552	+	0.549527i
$549$	−16.3952			−0.699730
$550$	−11.7659	−	20.1131i	−0.501699	−	0.857627i
$551$	4.12356			0.175670
$552$	1.00025	+	3.07845i	0.0425735	+	0.131028i
$553$	0.349802	−	0.254146i	0.0148751	−	0.0108074i
$554$	−2.49459	+	1.81242i	−0.105985	+	0.0770025i
$555$	−3.70126	−	2.12286i	−0.157110	−	0.0901105i
$556$	17.0514	+	12.3885i	0.723139	+	0.525391i
$557$	24.0280			1.01810			0.509049	−	0.860738i	$-0.329997\pi$
$557$	24.0280			1.01810			0.509049	+	0.860738i	$0.329997\pi$
$558$	−6.81614	−	4.95221i	−0.288550	−	0.209644i
$559$	4.82263	−	14.8425i	0.203976	−	0.627773i
$560$	4.13806	+	9.22331i	0.174865	+	0.389756i
$561$	−23.1295	−	71.1852i	−0.976527	−	3.00544i
$562$	−3.38377	+	10.4142i	−0.142736	+	0.439295i
$563$	10.2416	−	31.5203i	0.431631	−	1.32842i	−0.464870	−	0.885379i	$-0.653899\pi$
$563$	10.2416	−	31.5203i	0.431631	−	1.32842i	0.896500	−	0.443043i	$-0.146101\pi$
$564$	−1.63708	−	5.03843i	−0.0689337	−	0.212156i
$565$	−10.8759	−	24.2412i	−0.457551	−	1.01983i
$566$	4.53831	−	13.9675i	0.190760	−	0.587098i
$567$	39.5889	+	28.7630i	1.66258	+	1.20793i
$568$	−11.5321			−0.483875
$569$	30.2198	+	21.9559i	1.26688	+	0.920441i	0.999074	−	0.0430325i	$-0.0137019\pi$
$569$	30.2198	+	21.9559i	1.26688	+	0.920441i	0.267804	+	0.963473i	$0.413702\pi$
$570$	4.40295	+	2.52532i	0.184419	+	0.105774i
$571$	20.1055	−	14.6075i	0.841391	−	0.611306i	−0.0813680	−	0.996684i	$-0.525929\pi$
$571$	20.1055	−	14.6075i	0.841391	−	0.611306i	0.922759	+	0.385378i	$0.125929\pi$
$572$	20.7014	−	15.0405i	0.865570	−	0.628874i
$573$	11.9987	+	36.9282i	0.501254	+	1.54270i
$574$	−15.3187			−0.639391
$575$	6.96548	−	1.52216i	0.290480	−	0.0634784i
$576$	2.15265			0.0896939
$577$	−11.1677	−	34.3708i	−0.464919	−	1.43087i	−0.859084	−	0.511835i	$-0.828966\pi$
$577$	−11.1677	−	34.3708i	−0.464919	−	1.43087i	0.394165	−	0.919040i	$-0.371034\pi$
$578$	−26.7466	+	19.4326i	−1.11251	+	0.808288i
$579$	−50.4316	+	36.6407i	−2.09587	+	1.52274i
$580$	−3.77437	−	8.41267i	−0.156722	−	0.349317i
$581$	−48.7203	−	35.3974i	−2.02126	−	1.46853i
$582$	29.6910			1.23073
$583$	19.0109	+	13.8123i	0.787353	+	0.572045i
$584$	−0.582569	+	1.79296i	−0.0241069	+	0.0741934i
$585$	26.2763	−	2.83759i	1.08639	−	0.117320i
$586$	−3.98559	−	12.2664i	−0.164643	−	0.506720i
$587$	−13.4450	+	41.3794i	−0.554933	+	1.70791i	0.141187	+	0.989983i	$0.454908\pi$
$587$	−13.4450	+	41.3794i	−0.554933	+	1.70791i	−0.696120	+	0.717926i	$0.745092\pi$
$588$	9.42654	−	29.0119i	0.388744	−	1.19643i
$589$	−1.20945	−	3.72232i	−0.0498347	−	0.153375i
$590$	11.8610	−	10.7412i	0.488311	−	0.442207i
$591$	−17.3647	+	53.4431i	−0.714290	+	2.19836i
$592$	−0.680085	−	0.494110i	−0.0279513	−	0.0203078i
$593$	2.15823			0.0886278			0.0443139	−	0.999018i	$-0.485890\pi$
$593$	2.15823			0.0886278			0.0443139	+	0.999018i	$0.485890\pi$
$594$	−7.25194	−	5.26884i	−0.297551	−	0.216183i
$595$	71.1117	−	7.67938i	2.91530	−	0.314824i
$596$	−4.16994	+	3.02964i	−0.170807	+	0.124099i
$597$	−37.9412	+	27.5659i	−1.55283	+	1.12820i
$598$	2.41945	+	7.44629i	0.0989385	+	0.304501i
$599$	30.4532			1.24428			0.622141	−	0.782905i	$-0.286263\pi$
$599$	30.4532			1.24428			0.622141	+	0.782905i	$0.286263\pi$
$600$	1.12193	−	11.2941i	0.0458025	−	0.461081i
$601$	6.91887			0.282227			0.141113	−	0.989993i	$-0.454932\pi$
$601$	6.91887			0.282227			0.141113	+	0.989993i	$0.454932\pi$
$602$	3.97088	+	12.2211i	0.161841	+	0.498095i
$603$	−25.1855	+	18.2983i	−1.02563	+	0.745164i
$604$	−7.12296	+	5.17513i	−0.289829	+	0.210573i
$605$	4.91638	−	23.4587i	0.199879	−	0.953732i
$606$	−9.28064	−	6.74278i	−0.377000	−	0.273907i
$607$	−35.3021			−1.43287			−0.716433	−	0.697656i	$-0.754227\pi$
$607$	−35.3021			−1.43287			−0.716433	+	0.697656i	$0.754227\pi$
$608$	0.809017	+	0.587785i	0.0328100	+	0.0238378i
$609$	−13.0766	+	40.2458i	−0.529892	+	1.63084i
$610$	−3.49329	+	16.6684i	−0.141439	+	0.674883i
$611$	−3.95985	−	12.1872i	−0.160198	−	0.493040i
$612$	4.70657	−	14.4853i	0.190252	−	0.585535i
$613$	12.1927	−	37.5252i	0.492458	−	1.51563i	−0.328424	−	0.944530i	$-0.606517\pi$
$613$	12.1927	−	37.5252i	0.492458	−	1.51563i	0.820882	−	0.571099i	$-0.193483\pi$
$614$	−1.61662	−	4.97543i	−0.0652413	−	0.200792i
$615$	14.9191	+	8.55685i	0.601594	+	0.345045i
$616$	−6.51070	+	20.0379i	−0.262324	+	0.807349i
$617$	−6.31125	−	4.58539i	−0.254081	−	0.184601i	0.453452	−	0.891281i	$-0.350192\pi$
$617$	−6.31125	−	4.58539i	−0.254081	−	0.184601i	−0.707534	+	0.706680i	$0.750192\pi$
$618$	−26.4663			−1.06463
$619$	−1.48156	−	1.07642i	−0.0595490	−	0.0432649i	0.557613	−	0.830101i	$-0.311718\pi$
$619$	−1.48156	−	1.07642i	−0.0595490	−	0.0432649i	−0.617162	+	0.786836i	$0.711718\pi$
$620$	−6.48703	+	5.87456i	−0.260526	+	0.235928i
$621$	2.21894	−	1.61215i	0.0890429	−	0.0646935i
$622$	21.9534	−	15.9500i	0.880249	−	0.639539i
$623$	21.2125	+	65.2854i	0.849862	+	2.61561i
$624$	12.4635			0.498938
$625$	−24.5114	−	4.91833i	−0.980457	−	0.196733i
$626$	24.5516			0.981279
$627$	3.26902	+	10.0610i	0.130552	+	0.401798i
$628$	−2.28470	+	1.65993i	−0.0911694	+	0.0662384i
$629$	−4.81184	+	3.49601i	−0.191861	+	0.139395i
$630$	−16.1302	+	14.6072i	−0.642641	+	0.581966i
$631$	−26.7956	−	19.4681i	−1.06671	−	0.775013i	−0.0913953	−	0.995815i	$-0.529133\pi$
$631$	−26.7956	−	19.4681i	−1.06671	−	0.775013i	−0.975319	+	0.220802i	$0.929133\pi$
$632$	−0.0956399			−0.00380435
$633$	8.57113	+	6.22729i	0.340672	+	0.247513i
$634$	−6.13898	+	18.8938i	−0.243810	+	0.750370i
$635$	−5.09016	−	2.91947i	−0.201997	−	0.115856i
$636$	3.53691	+	10.8855i	0.140248	+	0.431638i
$637$	22.8013	−	70.1752i	0.903421	−	2.78044i
$638$	5.93847	−	18.2767i	0.235106	−	0.723583i
$639$	−7.67121	−	23.6095i	−0.303468	−	0.933979i
$640$	0.458661	−	2.18852i	0.0181302	−	0.0865089i
$641$	4.82949	−	14.8636i	0.190753	−	0.587078i	−0.809247	−	0.587469i	$-0.800124\pi$
$641$	4.82949	−	14.8636i	0.190753	−	0.587078i	1.00000		0.000390741i	$0.000124377\pi$
$642$	24.5056	+	17.8044i	0.967160	+	0.702683i
$643$	4.92924			0.194390			0.0971951	−	0.995265i	$-0.469013\pi$
$643$	4.92924			0.194390			0.0971951	+	0.995265i	$0.469013\pi$
$644$	−5.21548	−	3.78927i	−0.205519	−	0.149318i
$645$	2.95928	−	14.1203i	0.116522	−	0.555988i
$646$	5.72408	−	4.15879i	0.225211	−	0.163625i
$647$	0.765024	−	0.555823i	0.0300762	−	0.0218516i	−0.572646	−	0.819803i	$-0.694083\pi$
$647$	0.765024	−	0.555823i	0.0300762	−	0.0218516i	0.602722	+	0.797951i	$0.294083\pi$
$648$	−3.34481	−	10.2943i	−0.131397	−	0.404397i
$649$	33.3505			1.30912
$650$	2.71377	−	27.3187i	0.106443	−	1.07153i
$651$	40.1650			1.57419
$652$	−6.30800	−	19.4140i	−0.247040	−	0.760312i
$653$	−10.0362	+	7.29176i	−0.392748	+	0.285348i	−0.766581	−	0.642148i	$-0.778044\pi$
$653$	−10.0362	+	7.29176i	−0.392748	+	0.285348i	0.373832	+	0.927496i	$0.378044\pi$
$654$	4.58230	−	3.32924i	0.179182	−	0.130183i
$655$	34.0344	−	3.67538i	1.32983	−	0.143609i
$656$	2.74129	+	1.99166i	0.107029	+	0.0777613i
$657$	−4.05825			−0.158328
$658$	8.53604	+	6.20180i	0.332769	+	0.241771i
$659$	5.18853	−	15.9687i	0.202117	−	0.622051i	−0.797703	−	0.603051i	$-0.793952\pi$
$659$	5.18853	−	15.9687i	0.202117	−	0.622051i	0.999819	−	0.0190002i	$-0.00604831\pi$
$660$	17.5337	−	15.8783i	0.682500	−	0.618061i
$661$	−3.60370	−	11.0910i	−0.140168	−	0.431392i	0.856190	−	0.516660i	$-0.172825\pi$
$661$	−3.60370	−	11.0910i	−0.140168	−	0.431392i	−0.996358	+	0.0852690i	$0.972825\pi$
$662$	−7.05521	+	21.7137i	−0.274209	+	0.843927i
$663$	27.2502	−	83.8674i	1.05831	−	3.25714i
$664$	4.11632	+	12.6687i	0.159744	+	0.491642i
$665$	−10.0506	+	1.08537i	−0.389746	+	0.0420888i
$666$	0.559193	−	1.72102i	0.0216683	−	0.0666881i
$667$	4.75709	+	3.45622i	0.184195	+	0.133826i
$668$	2.24912			0.0870211
$669$	11.5946	+	8.42396i	0.448272	+	0.325689i
$670$	13.2370	+	29.5039i	0.511390	+	1.13984i
$671$	−28.7157	+	20.8632i	−1.10856	+	0.805415i
$672$	−8.30231	+	6.03198i	−0.320268	+	0.232689i
$673$	−0.230519	−	0.709466i	−0.00888587	−	0.0273479i	0.946515	−	0.322659i	$-0.104577\pi$
$673$	−0.230519	−	0.709466i	−0.00888587	−	0.0273479i	−0.955401	+	0.295311i	$0.904577\pi$
$674$	−8.18975			−0.315458
$675$	−9.39544	+	2.05318i	−0.361631	+	0.0790268i
$676$	17.1471			0.659505
$677$	0.928886	+	2.85882i	0.0357000	+	0.109873i	0.967319	−	0.253564i	$-0.0816030\pi$
$677$	0.928886	+	2.85882i	0.0357000	+	0.109873i	−0.931619	+	0.363438i	$0.881603\pi$
$678$	21.8205	−	15.8536i	0.838013	−	0.608852i
$679$	−47.8402	+	34.7579i	−1.83594	+	1.33389i
$680$	−13.7239	−	7.87136i	−0.526287	−	0.301853i
$681$	26.2863	+	19.0981i	1.00729	+	0.731841i
$682$	−18.2401			−0.698448
$683$	−30.2359	−	21.9677i	−1.15695	−	0.840570i	−0.167557	−	0.985862i	$-0.553588\pi$
$683$	−30.2359	−	21.9677i	−1.15695	−	0.840570i	−0.989389	+	0.145292i	$0.953588\pi$
$684$	−0.665206	+	2.04729i	−0.0254348	+	0.0782802i
$685$	12.3807	+	27.5952i	0.473041	+	1.05436i
$686$	8.99498	+	27.6837i	0.343430	+	1.05697i
$687$	−0.690444	+	2.12497i	−0.0263421	+	0.0810726i
$688$	0.878337	−	2.70324i	0.0334863	−	0.103060i
$689$	8.55523	+	26.3303i	0.325928	+	1.00310i
$690$	2.96277	+	6.60370i	0.112791	+	0.251399i
$691$	9.10992	−	28.0374i	0.346558	−	1.06659i	−0.614187	−	0.789160i	$-0.710516\pi$
$691$	9.10992	−	28.0374i	0.346558	−	1.06659i	0.960745	−	0.277434i	$-0.0894840\pi$
$692$	9.63390	+	6.99944i	0.366226	+	0.266079i
$693$	−45.3544			−1.72287
$694$	9.57138	+	6.95401i	0.363325	+	0.263971i
$695$	40.8818	+	23.4478i	1.55074	+	0.889427i
$696$	7.57261	−	5.50182i	0.287039	−	0.208546i
$697$	19.3956	−	14.0917i	0.734660	−	0.533762i
$698$	−5.16847	−	15.9069i	−0.195630	−	0.602086i
$699$	10.3780			0.392533
$700$	11.4138	+	19.5113i	0.431402	+	0.737457i
$701$	31.4283			1.18703			0.593515	−	0.804823i	$-0.297740\pi$
$701$	31.4283			1.18703			0.593515	+	0.804823i	$0.297740\pi$
$702$	−3.26349	−	10.0440i	−0.123173	−	0.379086i
$703$	0.680085	−	0.494110i	0.0256499	−	0.0186357i
$704$	3.77031	−	2.73929i	0.142099	−	0.103241i
$705$	−4.84908	−	10.8081i	−0.182627	−	0.407057i
$706$	−9.74295	−	7.07867i	−0.366681	−	0.266409i
$707$	22.8471			0.859253
$708$	13.1418	+	9.54811i	0.493901	+	0.358840i
$709$	5.22343	−	16.0761i	0.196170	−	0.603749i	−0.803791	−	0.594912i	$-0.797187\pi$
$709$	5.22343	−	16.0761i	0.196170	−	0.603749i	0.999961	−	0.00883731i	$-0.00281304\pi$
$710$	−25.6374	+	2.76860i	−0.962156	+	0.103904i
$711$	−0.0636202	−	0.195803i	−0.00238595	−	0.00734318i
$712$	4.69209	−	14.4408i	0.175844	−	0.541191i
$713$	1.72465	−	5.30791i	0.0645885	−	0.198783i
$714$	22.4374	+	69.0551i	0.839697	+	2.58432i
$715$	42.4113	−	38.4071i	1.58609	−	1.43634i
$716$	−1.99791	+	6.14893i	−0.0746653	+	0.229796i
$717$	−30.0896	−	21.8614i	−1.12372	−	0.816428i
$718$	17.5841			0.656234
$719$	13.9991	+	10.1710i	0.522080	+	0.379313i	0.817387	−	0.576089i	$-0.195422\pi$
$719$	13.9991	+	10.1710i	0.522080	+	0.379313i	−0.295307	+	0.955402i	$0.595422\pi$
$720$	4.78565	−	0.516804i	0.178351	−	0.0192602i
$721$	42.6443	−	30.9829i	1.58816	−	1.15386i
$722$	−0.809017	+	0.587785i	−0.0301085	+	0.0218751i
$723$	−1.15399	−	3.55160i	−0.0429172	−	0.132086i
$724$	−14.4659			−0.537620
$725$	−10.4106	−	17.7964i	−0.386642	−	0.660943i
$726$	24.3315			0.903026
$727$	4.74974	+	14.6182i	0.176158	+	0.542159i	0.999684	−	0.0251189i	$-0.00799645\pi$
$727$	4.74974	+	14.6182i	0.176158	+	0.542159i	−0.823526	+	0.567278i	$0.807996\pi$
$728$	−20.0820	+	14.5904i	−0.744287	+	0.540756i
$729$	8.25371	−	5.99667i	0.305693	−	0.222099i
$730$	−0.864684	+	4.12588i	−0.0320034	+	0.152706i
$731$	−16.2699	−	11.8208i	−0.601764	−	0.437207i
$732$	−17.2885			−0.639003
$733$	−6.10810	−	4.43779i	−0.225608	−	0.163914i	0.469240	−	0.883071i	$-0.344528\pi$
$733$	−6.10810	−	4.43779i	−0.225608	−	0.163914i	−0.694847	+	0.719157i	$0.744528\pi$
$734$	−4.61468	+	14.2025i	−0.170331	+	0.524225i
$735$	13.9914	−	66.7607i	0.516081	−	2.46250i
$736$	0.440649	+	1.35618i	0.0162425	+	0.0499894i
$737$	−20.8267	+	64.0979i	−0.767161	+	2.36108i
$738$	−2.25400	+	6.93709i	−0.0829708	+	0.255358i
$739$	0.582049	+	1.79136i	0.0214110	+	0.0658963i	0.961191	−	0.275883i	$-0.0889703\pi$
$739$	0.582049	+	1.79136i	0.0214110	+	0.0658963i	−0.939780	+	0.341780i	$0.888970\pi$
$740$	−1.63055	−	0.935204i	−0.0599402	−	0.0343788i
$741$	−3.85142	+	11.8535i	−0.141485	+	0.435447i
$742$	−18.4421	−	13.3990i	−0.677030	−	0.491891i
$743$	−11.6728			−0.428232			−0.214116	−	0.976808i	$-0.568687\pi$
$743$	−11.6728			−0.428232			−0.214116	+	0.976808i	$0.568687\pi$
$744$	−7.18753	−	5.22205i	−0.263508	−	0.191450i
$745$	−8.54302	+	7.73643i	−0.312992	+	0.283441i
$746$	−4.45627	+	3.23767i	−0.163156	+	0.118539i
$747$	−23.1984	+	16.8546i	−0.848785	+	0.616679i
$748$	−10.1894	−	31.3599i	−0.372563	−	1.14663i
$749$	−60.3279			−2.20433
$750$	−0.217268	−	25.3778i	−0.00793349	−	0.926667i
$751$	−40.9227			−1.49329			−0.746645	−	0.665223i	$-0.768337\pi$
$751$	−40.9227			−1.49329			−0.746645	+	0.665223i	$0.768337\pi$
$752$	−0.721200	−	2.21962i	−0.0262994	−	0.0809414i
$753$	9.74992	−	7.08373i	0.355307	−	0.258145i
$754$	18.3170	−	13.3080i	0.667064	−	0.484651i
$755$	−14.5929	+	13.2151i	−0.531091	+	0.480948i
$756$	7.03494	+	5.11118i	0.255858	+	0.185892i
$757$	−17.2100			−0.625509			−0.312754	−	0.949834i	$-0.601252\pi$
$757$	−17.2100			−0.625509			−0.312754	+	0.949834i	$0.601252\pi$
$758$	−26.5658	−	19.3012i	−0.964912	−	0.701050i
$759$	−4.66153	+	14.3467i	−0.169203	+	0.520752i
$760$	1.93967	+	1.11250i	0.0703594	+	0.0403547i
$761$	1.85245	+	5.70124i	0.0671511	+	0.206670i	0.979002	−	0.203853i	$-0.0653463\pi$
$761$	1.85245	+	5.70124i	0.0671511	+	0.206670i	−0.911850	+	0.410523i	$0.865346\pi$
$762$	1.84078	−	5.66532i	0.0666842	−	0.205233i
$763$	−3.48593	+	10.7286i	−0.126199	+	0.388401i
$764$	5.28590	+	16.2683i	0.191237	+	0.588568i
$765$	6.98577	−	33.3329i	0.252571	−	1.20515i
$766$	5.12639	−	15.7774i	0.185224	−	0.570061i
$767$	31.7881	+	23.0954i	1.14780	+	0.833926i
$768$	2.26995			0.0819096
$769$	−4.75198	−	3.45252i	−0.171361	−	0.124501i	0.498799	−	0.866718i	$-0.333775\pi$
$769$	−4.75198	−	3.45252i	−0.171361	−	0.124501i	−0.670160	+	0.742217i	$0.733775\pi$
$770$	−9.66356	+	46.1101i	−0.348251	+	1.66169i
$771$	32.3011	−	23.4681i	1.16330	−	0.845184i
$772$	−22.2171	+	16.1417i	−0.799611	+	0.580951i
$773$	16.8601	+	51.8900i	0.606415	+	1.86635i	0.486757	+	0.873538i	$0.338180\pi$
$773$	16.8601	+	51.8900i	0.606415	+	1.86635i	0.119658	+	0.992815i	$0.461820\pi$
$774$	6.11861			0.219929
$775$	−13.0113	+	14.6174i	−0.467378	+	0.525072i
$776$	13.0801			0.469547
$777$	2.66581	+	8.20451i	0.0956353	+	0.294335i
$778$	24.0976	−	17.5080i	0.863942	−	0.627690i
$779$	−2.74129	+	1.99166i	−0.0982168	+	0.0713587i
$780$	27.7080	−	2.99220i	0.992107	−	0.107138i
$781$	−43.4795	−	31.5897i	−1.55582	−	1.13037i
$782$	10.0893			0.360791
$783$	−6.41663	−	4.66196i	−0.229312	−	0.166605i
$784$	4.15276	−	12.7809i	0.148313	−	0.456460i
$785$	−4.68070	+	4.23877i	−0.167061	+	0.151288i
$786$	10.7386	+	33.0501i	0.383034	+	1.17886i
$787$	15.0456	−	46.3057i	0.536319	−	1.65062i	−0.204463	−	0.978874i	$-0.565545\pi$
$787$	15.0456	−	46.3057i	0.536319	−	1.65062i	0.740782	−	0.671745i	$-0.234455\pi$
$788$	−7.64985	+	23.5438i	−0.272514	+	0.838713i
$789$	6.39809	+	19.6913i	0.227778	+	0.701029i
$790$	−0.212621	+	0.0229610i	−0.00756472	+	0.000816916i
$791$	−16.5997	+	51.0887i	−0.590218	+	1.81650i
$792$	8.11617	+	5.89674i	0.288396	+	0.209532i
$793$	−41.8182			−1.48501
$794$	15.6925	+	11.4012i	0.556904	+	0.404615i
$795$	10.4764	+	23.3509i	0.371561	+	0.828170i
$796$	−16.7146	+	12.1438i	−0.592432	+	0.430427i
$797$	16.0632	−	11.6706i	0.568986	−	0.413393i	−0.265751	−	0.964042i	$-0.585620\pi$
$797$	16.0632	−	11.6706i	0.568986	−	0.413393i	0.834737	+	0.550649i	$0.185620\pi$
$798$	−3.17120	−	9.75995i	−0.112259	−	0.345498i
$799$	−16.5128			−0.584182
$800$	0.494253	−	4.97551i	0.0174745	−	0.175911i
$801$	32.6857			1.15489
$802$	5.52989	+	17.0193i	0.195267	+	0.600971i
$803$	−7.10792	+	5.16421i	−0.250833	+	0.182241i
$804$	−26.5577	+	19.2953i	−0.936620	+	0.680494i
$805$	−12.5045	−	7.17196i	−0.440725	−	0.252778i
$806$	−17.3855	−	12.6313i	−0.612379	−	0.444919i
$807$	−53.8829			−1.89677
$808$	−4.08849	−	2.97046i	−0.143832	−	0.104500i
$809$	2.86655	−	8.82233i	0.100782	−	0.310176i	−0.887935	−	0.459969i	$-0.847861\pi$
$809$	2.86655	−	8.82233i	0.100782	−	0.310176i	0.988717	+	0.149792i	$0.0478606\pi$
$810$	−9.90743	−	22.0826i	−0.348111	−	0.775905i
$811$	−11.6981	−	36.0029i	−0.410775	−	1.26423i	−0.915976	−	0.401233i	$-0.868582\pi$
$811$	−11.6981	−	36.0029i	−0.410775	−	1.26423i	0.505202	−	0.863001i	$-0.331418\pi$
$812$	−5.76077	+	17.7298i	−0.202163	+	0.622195i
$813$	13.2553	−	40.7957i	0.464884	−	1.43077i
$814$	−1.21062	−	3.72590i	−0.0424322	−	0.130593i
$815$	−18.6845	−	41.6457i	−0.654488	−	1.45879i
$816$	4.96302	−	15.2746i	0.173740	−	0.534718i
$817$	2.29952	+	1.67070i	0.0804499	+	0.0584503i
$818$	−34.2615			−1.19793
$819$	−43.2295	−	31.4081i	−1.51056	−	1.09749i
$820$	6.57243	+	3.76963i	0.229519	+	0.131641i
$821$	25.7612	−	18.7166i	0.899071	−	0.653213i	−0.0391564	−	0.999233i	$-0.512467\pi$
$821$	25.7612	−	18.7166i	0.899071	−	0.653213i	0.938227	+	0.346020i	$0.112467\pi$
$822$	−24.8397	+	18.0471i	−0.866384	+	0.629465i
$823$	12.4567	+	38.3378i	0.434214	+	1.33637i	0.893890	+	0.448286i	$0.147965\pi$
$823$	12.4567	+	38.3378i	0.434214	+	1.33637i	−0.459676	+	0.888086i	$0.652035\pi$
$824$	−11.6594			−0.406175
$825$	35.1680	−	39.5091i	1.22439	−	1.37553i
$826$	−32.3526			−1.12569
$827$	10.8921	+	33.5223i	0.378754	+	1.16569i	0.940911	+	0.338655i	$0.109972\pi$
$827$	10.8921	+	33.5223i	0.378754	+	1.16569i	−0.562156	+	0.827031i	$0.690028\pi$
$828$	−2.48337	+	1.80428i	−0.0863032	+	0.0627030i
$829$	−22.7015	+	16.4936i	−0.788454	+	0.572846i	−0.907504	−	0.420043i	$-0.862015\pi$
$829$	−22.7015	+	16.4936i	−0.788454	+	0.572846i	0.119050	+	0.992888i	$0.462015\pi$
$830$	12.1926	+	27.1761i	0.423213	+	0.943298i
$831$	−5.66258	−	4.11410i	−0.196433	−	0.142717i
$832$	5.49064			0.190354
$833$	−76.9237	−	55.8883i	−2.66525	−	1.93642i
$834$	−14.7843	+	45.5012i	−0.511937	+	1.57558i
$835$	5.00012	−	0.539965i	0.173036	−	0.0186862i
$836$	1.44013	+	4.43227i	0.0498080	+	0.153293i
$837$	−2.32630	+	7.15962i	−0.0804088	+	0.247473i
$838$	−4.64947	+	14.3096i	−0.160613	+	0.494317i
$839$	5.42695	+	16.7024i	0.187359	+	0.576632i	0.999981	−	0.00615910i	$-0.00196051\pi$
$839$	5.42695	+	16.7024i	0.187359	+	0.576632i	−0.812622	+	0.582791i	$0.801961\pi$
$840$	−17.0091	+	15.4031i	−0.586868	+	0.531459i
$841$	−3.70704	+	11.4091i	−0.127829	+	0.393417i
$842$	−1.26920	−	0.922131i	−0.0437397	−	0.0317787i
$843$	−24.8561			−0.856091
$844$	3.77592	+	2.74337i	0.129972	+	0.0944305i
$845$	38.1205	−	4.11665i	1.31139	−	0.141617i
$846$	4.06448	−	2.95302i	0.139740	−	0.101527i
$847$	−39.2045	+	28.4838i	−1.34708	+	0.978714i
$848$	1.55815	+	4.79549i	0.0535070	+	0.164678i
$849$	33.3371			1.14413
$850$	−32.3999	−	14.2043i	−1.11131	−	0.487205i
$851$	1.19871			0.0410914
$852$	−8.08919	−	24.8960i	−0.277131	−	0.852922i
$853$	−26.5506	+	19.2901i	−0.909075	+	0.660481i	−0.940781	−	0.339016i	$-0.889906\pi$
$853$	−26.5506	+	19.2901i	−0.909075	+	0.660481i	0.0317060	+	0.999497i	$0.489906\pi$
$854$	27.8565	−	20.2389i	0.953229	−	0.692561i
$855$	−0.987338	+	4.71113i	−0.0337662	+	0.161117i
$856$	10.7957	+	7.84353i	0.368989	+	0.268086i
$857$	−19.0105			−0.649388			−0.324694	−	0.945819i	$-0.605261\pi$
$857$	−19.0105			−0.649388			−0.324694	+	0.945819i	$0.605261\pi$
$858$	46.9911	+	34.1410i	1.60425	+	1.16556i
$859$	−6.70359	+	20.6315i	−0.228724	+	0.703939i	0.769169	+	0.639046i	$0.220671\pi$
$859$	−6.70359	+	20.6315i	−0.228724	+	0.703939i	−0.997892	+	0.0648929i	$0.979329\pi$
$860$	1.30368	−	6.22057i	0.0444551	−	0.212120i
$861$	−10.7453	−	33.0708i	−0.366200	−	1.12705i
$862$	3.44146	−	10.5917i	0.117216	−	0.360755i
$863$	−12.7066	+	39.1070i	−0.432539	+	1.33122i	0.463048	+	0.886333i	$0.346756\pi$
$863$	−12.7066	+	39.1070i	−0.432539	+	1.33122i	−0.895587	+	0.444886i	$0.853244\pi$
$864$	−0.594373	−	1.82929i	−0.0202210	−	0.0622338i
$865$	23.0979	+	13.2479i	0.785354	+	0.450441i
$866$	−2.08643	+	6.42136i	−0.0708996	+	0.218207i
$867$	−60.7134	−	44.1109i	−2.06193	−	1.49808i
$868$	17.6943			0.600583
$869$	−0.360592	−	0.261986i	−0.0122323	−	0.00888725i
$870$	15.5141	−	14.0494i	0.525978	−	0.476318i
$871$	−64.2390	+	46.6724i	−2.17666	+	1.58143i
$872$	2.01868	−	1.46666i	0.0683612	−	0.0496673i
$873$	8.70093	+	26.7787i	0.294482	+	0.906322i
$874$	−1.42597			−0.0482342
$875$	30.0588	+	40.6362i	1.01617	+	1.37375i
$876$	−4.27938			−0.144587
$877$	−3.34411	−	10.2921i	−0.112923	−	0.347540i	0.878585	−	0.477585i	$-0.158488\pi$
$877$	−3.34411	−	10.2921i	−0.112923	−	0.347540i	−0.991508	+	0.130045i	$0.958488\pi$
$878$	−28.0601	+	20.3869i	−0.946983	+	0.688024i
$879$	23.6856	−	17.2086i	0.798894	−	0.580431i
$880$	7.72430	−	6.99500i	0.260386	−	0.235802i
$881$	−18.5630	−	13.4868i	−0.625404	−	0.454383i	0.229401	−	0.973332i	$-0.426323\pi$
$881$	−18.5630	−	13.4868i	−0.625404	−	0.454383i	−0.854805	+	0.518949i	$0.826323\pi$
$882$	28.9287			0.974079
$883$	14.9173	+	10.8381i	0.502008	+	0.364730i	0.809784	−	0.586729i	$-0.199585\pi$
$883$	14.9173	+	10.8381i	0.502008	+	0.364730i	−0.307775	+	0.951459i	$0.599585\pi$
$884$	12.0048	−	36.9469i	0.403764	−	1.24266i
$885$	31.5085	+	18.0717i	1.05915	+	0.607475i
$886$	−1.00248	−	3.08533i	−0.0336791	−	0.103654i
$887$	16.4575	−	50.6508i	0.552587	−	1.70069i	−0.149644	−	0.988740i	$-0.547813\pi$
$887$	16.4575	−	50.6508i	0.552587	−	1.70069i	0.702231	−	0.711949i	$-0.252187\pi$
$888$	0.589662	−	1.81479i	0.0197878	−	0.0609005i
$889$	3.66616	+	11.2833i	0.122959	+	0.378429i
$890$	6.96428	−	33.2304i	0.233443	−	1.11389i
$891$	15.5880	−	47.9751i	0.522219	−	1.60722i
$892$	5.10787	+	3.71108i	0.171024	+	0.124256i
$893$	2.33385			0.0780993
$894$	−9.46554	−	6.87712i	−0.316575	−	0.230005i
$895$	−2.96541	+	14.1496i	−0.0991228	+	0.472969i
$896$	−3.65749	+	2.65732i	−0.122188	+	0.0887749i
$897$	−14.3783	+	10.4464i	−0.480077	+	0.348796i
$898$	−6.52862	−	20.0930i	−0.217863	−	0.670513i
$899$	−16.1391			−0.538269
$900$	10.5151	−	2.29786i	0.350504	−	0.0765953i
$901$	35.6759			1.18854
$902$	4.87977	+	15.0184i	0.162478	+	0.500057i
$903$	−23.5981	+	17.1450i	−0.785297	+	0.570551i
$904$	9.61281	−	6.98411i	0.319717	−	0.232288i
$905$	−32.1597	+	3.47294i	−1.06902	+	0.115444i
$906$	−16.1687	−	11.7473i	−0.537170	−	0.390277i
$907$	−19.2777			−0.640106			−0.320053	−	0.947400i	$-0.603701\pi$
$907$	−19.2777			−0.640106			−0.320053	+	0.947400i	$0.603701\pi$
$908$	11.5801	+	8.41347i	0.384301	+	0.279211i
$909$	3.36172	−	10.3463i	0.111501	−	0.343165i
$910$	−41.1423	+	37.2578i	−1.36385	+	1.23508i
$911$	−10.2292	−	31.4822i	−0.338908	−	1.04305i	−0.964765	−	0.263114i	$-0.915250\pi$
$911$	−10.2292	−	31.4822i	−0.338908	−	1.04305i	0.625857	−	0.779938i	$-0.284750\pi$
$912$	−0.701452	+	2.15885i	−0.0232274	+	0.0714865i
$913$	−19.1835	+	59.0409i	−0.634882	+	1.95397i
$914$	−8.48646	−	26.1187i	−0.280707	−	0.863928i
$915$	−38.4349	+	4.15059i	−1.27062	+	0.137214i
$916$	−0.304168	+	0.936131i	−0.0100500	+	0.0309307i
$917$	−55.9930	−	40.6813i	−1.84905	−	1.34341i
$918$	−13.6090			−0.449163
$919$	8.79886	+	6.39275i	0.290248	+	0.210877i	0.723375	−	0.690456i	$-0.242590\pi$
$919$	8.79886	+	6.39275i	0.290248	+	0.210877i	−0.433127	+	0.901333i	$0.642590\pi$
$920$	1.30521	+	2.90919i	0.0430317	+	0.0959131i
$921$	9.60721	−	6.98005i	0.316568	−	0.230000i
$922$	−13.9335	+	10.1232i	−0.458874	+	0.333391i
$923$	−19.5665	−	60.2194i	−0.644039	−	1.98215i
$924$	−47.8256			−1.57335
$925$	−3.84947	−	1.68763i	−0.126570	−	0.0554891i
$926$	−3.39371			−0.111524
$927$	−7.75592	−	23.8703i	−0.254738	−	0.784003i
$928$	3.33603	−	2.42377i	0.109511	−	0.0795641i
$929$	5.55534	−	4.03619i	0.182265	−	0.132423i	−0.492912	−	0.870079i	$-0.664067\pi$
$929$	5.55534	−	4.03619i	0.182265	−	0.132423i	0.675176	+	0.737656i	$0.264067\pi$
$930$	−17.2326	−	9.88379i	−0.565080	−	0.324102i
$931$	10.8721	+	7.89902i	0.356317	+	0.258880i
$932$	4.57193			0.149758
$933$	49.8329	+	36.2057i	1.63146	+	1.18532i
$934$	−0.0516603	+	0.158994i	−0.00169038	+	0.00520245i
$935$	−30.1814	−	67.2712i	−0.987037	−	2.20000i
$936$	3.65241	+	11.2410i	0.119383	+	0.367422i
$937$	−0.602422	+	1.85407i	−0.0196803	+	0.0605697i	−0.960414	−	0.278575i	$-0.910138\pi$
$937$	−0.602422	+	1.85407i	−0.0196803	+	0.0605697i	0.940734	+	0.339145i	$0.110138\pi$
$938$	20.2035	−	62.1799i	0.659667	−	2.03025i
$939$	17.2218	+	53.0031i	0.562011	+	1.72969i
$940$	−2.13621	−	4.76140i	−0.0696756	−	0.155300i
$941$	−1.22167	+	3.75992i	−0.0398254	+	0.122570i	−0.968993	−	0.247090i	$-0.920526\pi$
$941$	−1.22167	+	3.75992i	−0.0398254	+	0.122570i	0.929167	+	0.369660i	$0.120526\pi$
$942$	−5.18614	−	3.76795i	−0.168974	−	0.122766i
$943$	−4.83179			−0.157345
$944$	5.78950	+	4.20632i	0.188432	+	0.136904i
$945$	16.8668	+	9.67395i	0.548676	+	0.314694i
$946$	10.7166	−	7.78605i	0.348426	−	0.253146i
$947$	17.8275	−	12.9524i	0.579315	−	0.420897i	−0.259162	−	0.965834i	$-0.583446\pi$
$947$	17.8275	−	12.9524i	0.579315	−	0.420897i	0.838477	+	0.544937i	$0.183446\pi$
$948$	−0.0670868	−	0.206472i	−0.00217888	−	0.00670589i
$949$	−10.3511			−0.336012
$950$	4.57926	+	2.00758i	0.148571	+	0.0651345i
$951$	−45.0951			−1.46231
$952$	9.88454	+	30.4215i	0.320360	+	0.985966i
$953$	25.5765	−	18.5824i	0.828505	−	0.601944i	−0.0906313	−	0.995885i	$-0.528888\pi$
$953$	25.5765	−	18.5824i	0.828505	−	0.601944i	0.919136	+	0.393941i	$0.128888\pi$
$954$	−8.78128	+	6.37998i	−0.284305	+	0.206559i
$955$	15.6570	+	34.8978i	0.506648	+	1.12927i
$956$	−13.2556	−	9.63079i	−0.428718	−	0.311482i
$957$	43.6222			1.41011
$958$	−19.9667	−	14.5067i	−0.645095	−	0.468689i
$959$	18.8965	−	58.1574i	0.610199	−	1.87800i
$960$	5.04641	−	0.544964i	0.162872	−	0.0175886i
$961$	−4.84588	−	14.9141i	−0.156319	−	0.481099i
$962$	1.42630	−	4.38970i	0.0459857	−	0.141530i
$963$	−8.87665	+	27.3195i	−0.286046	+	0.880359i
$964$	−0.508376	−	1.56462i	−0.0163737	−	0.0503930i
$965$	−45.5165	+	41.2191i	−1.46523	+	1.32689i
$966$	4.52204	−	13.9174i	0.145494	−	0.447785i
$967$	−32.7347	−	23.7831i	−1.05268	−	0.764814i	−0.0799566	−	0.996798i	$-0.525478\pi$
$967$	−32.7347	−	23.7831i	−1.05268	−	0.764814i	−0.972720	+	0.231984i	$0.925478\pi$
$968$	10.7190			0.344521
$969$	12.9934	+	9.44023i	0.417407	+	0.303264i
$970$	29.0788	−	3.14023i	0.933665	−	0.100827i
$971$	5.12310	−	3.72215i	0.164408	−	0.119449i	−0.502539	−	0.864555i	$-0.667601\pi$
$971$	5.12310	−	3.72215i	0.164408	−	0.119449i	0.666947	+	0.745105i	$0.267601\pi$
$972$	15.2093	−	11.0502i	0.487838	−	0.354435i
$973$	−29.4449	−	90.6220i	−0.943959	−	2.90521i
$974$	13.6844			0.438476
$975$	60.8806	−	13.3042i	1.94974	−	0.426075i
$976$	−7.61628			−0.243791
$977$	−4.26972	−	13.1408i	−0.136600	−	0.420413i	0.859235	−	0.511581i	$-0.170940\pi$
$977$	−4.26972	−	13.1408i	−0.136600	−	0.420413i	−0.995836	+	0.0911682i	$0.970940\pi$
$978$	37.4872	−	27.2360i	1.19871	−	0.870912i
$979$	57.2482	−	41.5932i	1.82966	−	1.32933i
$980$	6.16377	−	29.4107i	0.196894	−	0.939490i
$981$	4.34552	+	3.15721i	0.138742	+	0.100802i
$982$	−31.5862			−1.00796
$983$	10.3962	+	7.55328i	0.331587	+	0.240912i	0.741104	−	0.671390i	$-0.234303\pi$
$983$	10.3962	+	7.55328i	0.331587	+	0.240912i	−0.409517	+	0.912303i	$0.634303\pi$
$984$	−2.37681	+	7.31507i	−0.0757700	+	0.233196i
$985$	−11.3543	+	54.1778i	−0.361780	+	1.72625i
$986$	−9.01578	−	27.7477i	−0.287121	−	0.883667i
$987$	−7.40110	+	22.7783i	−0.235580	+	0.725040i
$988$	−1.69670	+	5.22191i	−0.0539793	+	0.166131i
$989$	1.25248	+	3.85475i	0.0398266	+	0.122574i
$990$	19.4591	+	11.1608i	0.618450	+	0.354713i
$991$	4.36535	−	13.4352i	0.138670	−	0.426782i	−0.857473	−	0.514529i	$-0.827967\pi$
$991$	4.36535	−	13.4352i	0.138670	−	0.426782i	0.996143	+	0.0877471i	$0.0279667\pi$
$992$	−3.16639	−	2.30052i	−0.100533	−	0.0730415i
$993$	−51.8254			−1.64463
$994$	42.1785	+	30.6444i	1.33782	+	0.971983i
$995$	−34.2434	+	31.0103i	−1.08559	+	0.983092i
$996$	−24.4624	+	17.7730i	−0.775122	+	0.563159i
$997$	3.48104	−	2.52912i	0.110246	−	0.0800981i	−0.531297	−	0.847186i	$-0.678295\pi$
$997$	3.48104	−	2.52912i	0.110246	−	0.0800981i	0.641542	+	0.767088i	$0.278295\pi$
$998$	11.2348	+	34.5772i	0.355632	+	1.09452i
$999$	−1.61690			−0.0511563

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.c.381.2	✓	44
25.21	even	5	inner	950.2.h.c.571.2	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.c.381.2	✓	44	1.1	even	1	trivial
950.2.h.c.571.2	yes	44	25.21	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-1.83642 + 1.33424i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.65745 + 1.50096i) q^{5} +(-1.83642 - 1.33424i) q^{6} +4.52091 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.665206 - 2.04729i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-1.83642 + 1.33424i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.65745 + 1.50096i) q^{5} +(-1.83642 - 1.33424i) q^{6} +4.52091 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.665206 - 2.04729i) q^{9} +(-1.93967 - 1.11250i) q^{10} +(-1.44013 - 4.43227i) q^{11} +(0.701452 - 2.15885i) q^{12} +(1.69670 - 5.22191i) q^{13} +(1.39704 + 4.29964i) q^{14} +(1.04114 - 4.96783i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-5.72408 - 4.15879i) q^{17} +2.15265 q^{18} +(0.809017 + 0.587785i) q^{19} +(0.458661 - 2.18852i) q^{20} +(-8.30231 + 6.03198i) q^{21} +(3.77031 - 2.73929i) q^{22} +(0.440649 + 1.35618i) q^{23} +2.26995 q^{24} +(0.494253 - 4.97551i) q^{25} +5.49064 q^{26} +(-0.594373 - 1.82929i) q^{27} +(-3.65749 + 2.65732i) q^{28} +(3.33603 - 2.42377i) q^{29} +(5.04641 - 0.544964i) q^{30} +(-3.16639 - 2.30052i) q^{31} +1.00000 q^{32} +(8.55840 + 6.21804i) q^{33} +(2.18640 - 6.72906i) q^{34} +(-7.49316 + 6.78569i) q^{35} +(0.665206 + 2.04729i) q^{36} +(0.259769 - 0.799487i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(3.85142 + 11.8535i) q^{39} +(2.22314 - 0.240078i) q^{40} +(-1.04708 + 3.22258i) q^{41} +(-8.30231 - 6.03198i) q^{42} +2.84236 q^{43} +(3.77031 + 2.73929i) q^{44} +(1.97036 + 4.39173i) q^{45} +(-1.15363 + 0.838165i) q^{46} +(1.88812 - 1.37180i) q^{47} +(0.701452 + 2.15885i) q^{48} +13.4386 q^{49} +(4.88473 - 1.06745i) q^{50} +16.0607 q^{51} +(1.69670 + 5.22191i) q^{52} +(-4.07929 + 2.96377i) q^{53} +(1.55609 - 1.13057i) q^{54} +(9.03958 + 5.18467i) q^{55} +(-3.65749 - 2.65732i) q^{56} -2.26995 q^{57} +(3.33603 + 2.42377i) q^{58} +(-2.21139 + 6.80596i) q^{59} +(2.07772 + 4.63102i) q^{60} +(-2.35356 - 7.24351i) q^{61} +(1.20945 - 3.72232i) q^{62} +(3.00734 - 9.25563i) q^{63} +(0.309017 + 0.951057i) q^{64} +(5.02567 + 11.2017i) q^{65} +(-3.26902 + 10.0610i) q^{66} +(-11.6997 - 8.50035i) q^{67} +7.07536 q^{68} +(-2.61869 - 1.90259i) q^{69} +(-8.76909 - 5.02952i) q^{70} +(9.32964 - 6.77838i) q^{71} +(-1.74153 + 1.26530i) q^{72} +(-0.582569 - 1.79296i) q^{73} +0.840631 q^{74} +(5.73087 + 9.79660i) q^{75} -1.00000 q^{76} +(-6.51070 - 20.0379i) q^{77} +(-10.0831 + 7.32584i) q^{78} +(0.0773743 - 0.0562157i) q^{79} +(0.915316 + 2.04015i) q^{80} +(8.75684 + 6.36221i) q^{81} -3.38842 q^{82} +(-10.7767 - 7.82970i) q^{83} +(3.17120 - 9.75995i) q^{84} +(15.7295 - 1.69864i) q^{85} +(0.878337 + 2.70324i) q^{86} +(-2.89248 + 8.90214i) q^{87} +(-1.44013 + 4.43227i) q^{88} +(4.69209 + 14.4408i) q^{89} +(-3.56790 + 3.23104i) q^{90} +(7.67063 - 23.6078i) q^{91} +(-1.15363 - 0.838165i) q^{92} +8.88428 q^{93} +(1.88812 + 1.37180i) q^{94} +(-2.22314 + 0.240078i) q^{95} +(-1.83642 + 1.33424i) q^{96} +(-10.5820 + 7.68826i) q^{97} +(4.15276 + 12.7809i) q^{98} -10.0321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9}+O(q^{10}) \) 44 * q - 11 * q^2 + q^3 - 11 * q^4 - q^5 + q^6 + 18 * q^7 - 11 * q^8 - 8 * q^9	\( 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} + 2 q^{13} + 3 q^{14} - 4 q^{15} - 11 q^{16} + 11 q^{17} + 42 q^{18} + 11 q^{19} - 6 q^{20} + 3 q^{21} - 6 q^{22} - 3 q^{23} + 6 q^{24} - 11 q^{25} + 22 q^{26} - 23 q^{27} - 12 q^{28} + 36 q^{29} - 4 q^{30} + 11 q^{31} + 44 q^{32} + 2 q^{33} - 19 q^{34} + 67 q^{35} - 8 q^{36} + 3 q^{37} + 11 q^{38} + 47 q^{39} + 4 q^{40} + 2 q^{41} + 3 q^{42} + 70 q^{43} - 6 q^{44} - 28 q^{45} - 8 q^{46} - 11 q^{47} - 4 q^{48} + 22 q^{49} + 14 q^{50} + 38 q^{51} + 2 q^{52} - 9 q^{53} + 32 q^{54} + 8 q^{55} - 12 q^{56} - 6 q^{57} + 36 q^{58} - 62 q^{59} + 11 q^{60} - 28 q^{61} - 29 q^{62} + 10 q^{63} - 11 q^{64} - 39 q^{65} - 8 q^{66} + 25 q^{67} + 16 q^{68} - 81 q^{69} - 43 q^{70} - 34 q^{71} - 13 q^{72} + 6 q^{73} + 8 q^{74} - 39 q^{75} - 44 q^{76} - 21 q^{77} - 58 q^{78} + 19 q^{79} - q^{80} - 22 q^{81} + 2 q^{82} - 50 q^{83} - 7 q^{84} + 102 q^{85} - 10 q^{86} + 47 q^{87} - q^{88} - 4 q^{89} - 38 q^{90} - 8 q^{91} - 8 q^{92} + 60 q^{93} - 11 q^{94} - 4 q^{95} + q^{96} + 8 q^{97} + 7 q^{98} - 12 q^{99}+O(q^{100}) \) 44 * q - 11 * q^2 + q^3 - 11 * q^4 - q^5 + q^6 + 18 * q^7 - 11 * q^8 - 8 * q^9 + 4 * q^10 - q^11 - 4 * q^12 + 2 * q^13 + 3 * q^14 - 4 * q^15 - 11 * q^16 + 11 * q^17 + 42 * q^18 + 11 * q^19 - 6 * q^20 + 3 * q^21 - 6 * q^22 - 3 * q^23 + 6 * q^24 - 11 * q^25 + 22 * q^26 - 23 * q^27 - 12 * q^28 + 36 * q^29 - 4 * q^30 + 11 * q^31 + 44 * q^32 + 2 * q^33 - 19 * q^34 + 67 * q^35 - 8 * q^36 + 3 * q^37 + 11 * q^38 + 47 * q^39 + 4 * q^40 + 2 * q^41 + 3 * q^42 + 70 * q^43 - 6 * q^44 - 28 * q^45 - 8 * q^46 - 11 * q^47 - 4 * q^48 + 22 * q^49 + 14 * q^50 + 38 * q^51 + 2 * q^52 - 9 * q^53 + 32 * q^54 + 8 * q^55 - 12 * q^56 - 6 * q^57 + 36 * q^58 - 62 * q^59 + 11 * q^60 - 28 * q^61 - 29 * q^62 + 10 * q^63 - 11 * q^64 - 39 * q^65 - 8 * q^66 + 25 * q^67 + 16 * q^68 - 81 * q^69 - 43 * q^70 - 34 * q^71 - 13 * q^72 + 6 * q^73 + 8 * q^74 - 39 * q^75 - 44 * q^76 - 21 * q^77 - 58 * q^78 + 19 * q^79 - q^80 - 22 * q^81 + 2 * q^82 - 50 * q^83 - 7 * q^84 + 102 * q^85 - 10 * q^86 + 47 * q^87 - q^88 - 4 * q^89 - 38 * q^90 - 8 * q^91 - 8 * q^92 + 60 * q^93 - 11 * q^94 - 4 * q^95 + q^96 + 8 * q^97 + 7 * q^98 - 12 * q^99

Introduction

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