LMFDB - Embedded newform 414.2.e.d.139.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(139,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(6))

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("414.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.e (of order $3$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			139.1
Root			$0.187540 + 0.324828i$ of defining polynomial
Character	$\chi$	$=$	414.139
Dual form			414.2.e.d.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.61720 - 0.620220i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.536235 - 0.928786i) q^{5} +(-0.271473 - 1.71064i) q^{6} +(-0.121951 - 0.211225i) q^{7} -1.00000 q^{8} +(2.23065 + 2.00604i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.61720 - 0.620220i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.536235 - 0.928786i) q^{5} +(-0.271473 - 1.71064i) q^{6} +(-0.121951 - 0.211225i) q^{7} -1.00000 q^{8} +(2.23065 + 2.00604i) q^{9} +1.07247 q^{10} +(-0.317214 - 0.549430i) q^{11} +(1.34572 - 1.09042i) q^{12} +(2.75704 - 4.77533i) q^{13} +(0.121951 - 0.211225i) q^{14} +(-1.44325 + 1.16945i) q^{15} +(-0.500000 - 0.866025i) q^{16} +7.28484 q^{17} +(-0.621951 + 2.93482i) q^{18} +1.65567 q^{19} +(0.536235 + 0.928786i) q^{20} +(0.0662125 + 0.417228i) q^{21} +(0.317214 - 0.549430i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(1.61720 + 0.620220i) q^{24} +(1.92490 + 3.33403i) q^{25} +5.51408 q^{26} +(-2.36323 - 4.62765i) q^{27} +0.243901 q^{28} +(-2.59455 - 4.49390i) q^{29} +(-1.73439 - 0.665167i) q^{30} +(3.82951 - 6.63290i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.172230 + 1.08528i) q^{33} +(3.64242 + 6.30886i) q^{34} -0.261577 q^{35} +(-2.85261 + 0.928786i) q^{36} +4.11999 q^{37} +(0.827834 + 1.43385i) q^{38} +(-7.42043 + 6.01268i) q^{39} +(-0.536235 + 0.928786i) q^{40} +(-3.51163 + 6.08233i) q^{41} +(-0.328224 + 0.265956i) q^{42} +(2.73048 + 4.72934i) q^{43} +0.634427 q^{44} +(3.05933 - 0.996094i) q^{45} -1.00000 q^{46} +(2.39600 + 4.15000i) q^{47} +(0.271473 + 1.71064i) q^{48} +(3.47026 - 6.01066i) q^{49} +(-1.92490 + 3.33403i) q^{50} +(-11.7810 - 4.51820i) q^{51} +(2.75704 + 4.77533i) q^{52} -9.94555 q^{53} +(2.82605 - 4.36044i) q^{54} -0.680404 q^{55} +(0.121951 + 0.211225i) q^{56} +(-2.67754 - 1.02688i) q^{57} +(2.59455 - 4.49390i) q^{58} +(-5.47354 + 9.48045i) q^{59} +(-0.291146 - 1.83461i) q^{60} +(-6.02141 - 10.4294i) q^{61} +7.65902 q^{62} +(0.151694 - 0.715806i) q^{63} +1.00000 q^{64} +(-2.95684 - 5.12140i) q^{65} +(-0.853765 + 0.691795i) q^{66} +(-0.121951 + 0.211225i) q^{67} +(-3.64242 + 6.30886i) q^{68} +(1.34572 - 1.09042i) q^{69} +(-0.130788 - 0.226532i) q^{70} -7.03926 q^{71} +(-2.23065 - 2.00604i) q^{72} -0.0957368 q^{73} +(2.05999 + 3.56801i) q^{74} +(-1.04512 - 6.58565i) q^{75} +(-0.827834 + 1.43385i) q^{76} +(-0.0773688 + 0.134007i) q^{77} +(-8.91735 - 3.41994i) q^{78} +(-6.05031 - 10.4794i) q^{79} -1.07247 q^{80} +(0.951641 + 8.94955i) q^{81} -7.02327 q^{82} +(-4.66982 - 8.08836i) q^{83} +(-0.394436 - 0.151272i) q^{84} +(3.90639 - 6.76606i) q^{85} +(-2.73048 + 4.72934i) q^{86} +(1.40870 + 8.87671i) q^{87} +(0.317214 + 0.549430i) q^{88} +6.00860 q^{89} +(2.39231 + 2.15141i) q^{90} -1.34489 q^{91} +(-0.500000 - 0.866025i) q^{92} +(-10.3069 + 8.35158i) q^{93} +(-2.39600 + 4.15000i) q^{94} +(0.887827 - 1.53776i) q^{95} +(-1.34572 + 1.09042i) q^{96} +(4.59455 + 7.95800i) q^{97} +6.94051 q^{98} +(0.394582 - 1.86193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9	\( 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9} - 2 q^{10} - 11 q^{11} + 6 q^{13} - 5 q^{14} + 9 q^{15} - 5 q^{16} + 2 q^{17} - 6 q^{19} - q^{20} - 21 q^{21} + 11 q^{22} - 5 q^{23} + 3 q^{24} + 12 q^{26} + 27 q^{27} - 10 q^{28} - 8 q^{29} + 9 q^{30} + 4 q^{31} + 5 q^{32} - 24 q^{33} + q^{34} + 46 q^{35} + 3 q^{36} - 28 q^{37} - 3 q^{38} - 45 q^{39} + q^{40} - 24 q^{41} - 27 q^{42} + 27 q^{43} + 22 q^{44} + 27 q^{45} - 10 q^{46} - 9 q^{47} + 3 q^{48} - 12 q^{49} - 6 q^{51} + 6 q^{52} - 26 q^{53} + 18 q^{54} + 16 q^{55} - 5 q^{56} - 18 q^{57} + 8 q^{58} - 9 q^{59} + 3 q^{61} + 8 q^{62} + 42 q^{63} + 10 q^{64} + 5 q^{65} - 3 q^{66} + 5 q^{67} - q^{68} + 23 q^{70} + 54 q^{71} + 3 q^{72} + 34 q^{73} - 14 q^{74} - 45 q^{75} + 3 q^{76} - 13 q^{77} - 30 q^{78} - 11 q^{79} + 2 q^{80} + 33 q^{81} - 48 q^{82} - 23 q^{83} - 6 q^{84} + 23 q^{85} - 27 q^{86} + 63 q^{87} + 11 q^{88} + 78 q^{89} + 51 q^{90} - 30 q^{91} - 5 q^{92} - 27 q^{93} + 9 q^{94} - 37 q^{95} + 28 q^{97} - 24 q^{98} + 24 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9 - 2 * q^10 - 11 * q^11 + 6 * q^13 - 5 * q^14 + 9 * q^15 - 5 * q^16 + 2 * q^17 - 6 * q^19 - q^20 - 21 * q^21 + 11 * q^22 - 5 * q^23 + 3 * q^24 + 12 * q^26 + 27 * q^27 - 10 * q^28 - 8 * q^29 + 9 * q^30 + 4 * q^31 + 5 * q^32 - 24 * q^33 + q^34 + 46 * q^35 + 3 * q^36 - 28 * q^37 - 3 * q^38 - 45 * q^39 + q^40 - 24 * q^41 - 27 * q^42 + 27 * q^43 + 22 * q^44 + 27 * q^45 - 10 * q^46 - 9 * q^47 + 3 * q^48 - 12 * q^49 - 6 * q^51 + 6 * q^52 - 26 * q^53 + 18 * q^54 + 16 * q^55 - 5 * q^56 - 18 * q^57 + 8 * q^58 - 9 * q^59 + 3 * q^61 + 8 * q^62 + 42 * q^63 + 10 * q^64 + 5 * q^65 - 3 * q^66 + 5 * q^67 - q^68 + 23 * q^70 + 54 * q^71 + 3 * q^72 + 34 * q^73 - 14 * q^74 - 45 * q^75 + 3 * q^76 - 13 * q^77 - 30 * q^78 - 11 * q^79 + 2 * q^80 + 33 * q^81 - 48 * q^82 - 23 * q^83 - 6 * q^84 + 23 * q^85 - 27 * q^86 + 63 * q^87 + 11 * q^88 + 78 * q^89 + 51 * q^90 - 30 * q^91 - 5 * q^92 - 27 * q^93 + 9 * q^94 - 37 * q^95 + 28 * q^97 - 24 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.61720	−	0.620220i	−0.933689	−	0.358084i
$3$	−1.61720	−	0.620220i	−0.933689	−	0.358084i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.536235	−	0.928786i	0.239811	−	0.415366i	−0.720849	−	0.693093i	$-0.756248\pi$
$5$	0.536235	−	0.928786i	0.239811	−	0.415366i	0.960660	+	0.277727i	$0.0895810\pi$
$6$	−0.271473	−	1.71064i	−0.110828	−	0.698367i
$7$	−0.121951	−	0.211225i	−0.0460930	−	0.0798354i	0.842058	−	0.539386i	$-0.181344\pi$
$7$	−0.121951	−	0.211225i	−0.0460930	−	0.0798354i	−0.888151	+	0.459551i	$0.848010\pi$
$8$	−1.00000			−0.353553
$9$	2.23065	+	2.00604i	0.743552	+	0.668679i
$10$	1.07247			0.339145
$11$	−0.317214	−	0.549430i	−0.0956435	−	0.165659i	0.814233	−	0.580538i	$-0.197158\pi$
$11$	−0.317214	−	0.549430i	−0.0956435	−	0.165659i	−0.909877	+	0.414878i	$0.863824\pi$
$12$	1.34572	−	1.09042i	0.388477	−	0.314778i
$13$	2.75704	−	4.77533i	0.764665	−	1.32444i	−0.175759	−	0.984433i	$-0.556238\pi$
$13$	2.75704	−	4.77533i	0.764665	−	1.32444i	0.940424	−	0.340005i	$-0.110429\pi$
$14$	0.121951	−	0.211225i	0.0325927	−	0.0564521i
$15$	−1.44325	+	1.16945i	−0.372645	+	0.301950i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	7.28484			1.76683			0.883417	−	0.468588i	$-0.155237\pi$
$17$	7.28484			1.76683			0.883417	+	0.468588i	$0.155237\pi$
$18$	−0.621951	+	2.93482i	−0.146595	+	0.691744i
$19$	1.65567			0.379836			0.189918	−	0.981800i	$-0.439178\pi$
$19$	1.65567			0.379836			0.189918	+	0.981800i	$0.439178\pi$
$20$	0.536235	+	0.928786i	0.119906	+	0.207683i
$21$	0.0662125	+	0.417228i	0.0144487	+	0.0910466i
$22$	0.317214	−	0.549430i	0.0676302	−	0.117139i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	1.61720	+	0.620220i	0.330109	+	0.126602i
$25$	1.92490	+	3.33403i	0.384981	+	0.666807i
$26$	5.51408			1.08140
$27$	−2.36323	−	4.62765i	−0.454803	−	0.890592i
$28$	0.243901			0.0460930
$29$	−2.59455	−	4.49390i	−0.481796	−	0.834496i	0.517985	−	0.855390i	$-0.326682\pi$
$29$	−2.59455	−	4.49390i	−0.481796	−	0.834496i	−0.999782	+	0.0208936i	$0.993349\pi$
$30$	−1.73439	−	0.665167i	−0.316656	−	0.121442i
$31$	3.82951	−	6.63290i	0.687800	−	1.19130i	−0.284748	−	0.958602i	$-0.591910\pi$
$31$	3.82951	−	6.63290i	0.687800	−	1.19130i	0.972548	−	0.232702i	$-0.0747567\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.172230	+	1.08528i	0.0299813	+	0.188923i
$34$	3.64242	+	6.30886i	0.624670	+	1.08196i
$35$	−0.261577			−0.0442145
$36$	−2.85261	+	0.928786i	−0.475434	+	0.154798i
$37$	4.11999			0.677321			0.338661	−	0.940909i	$-0.390026\pi$
$37$	4.11999			0.677321			0.338661	+	0.940909i	$0.390026\pi$
$38$	0.827834	+	1.43385i	0.134292	+	0.232601i
$39$	−7.42043	+	6.01268i	−1.18822	+	0.962800i
$40$	−0.536235	+	0.928786i	−0.0847862	+	0.146854i
$41$	−3.51163	+	6.08233i	−0.548425	+	0.949900i	0.449958	+	0.893050i	$0.351439\pi$
$41$	−3.51163	+	6.08233i	−0.548425	+	0.949900i	−0.998383	+	0.0568502i	$0.981894\pi$
$42$	−0.328224	+	0.265956i	−0.0506460	+	0.0410379i
$43$	2.73048	+	4.72934i	0.416395	+	0.721217i	0.995574	−	0.0939833i	$-0.0299600\pi$
$43$	2.73048	+	4.72934i	0.416395	+	0.721217i	−0.579179	+	0.815201i	$0.696627\pi$
$44$	0.634427			0.0956435
$45$	3.05933	−	0.996094i	0.456058	−	0.148489i
$46$	−1.00000			−0.147442
$47$	2.39600	+	4.15000i	0.349493	+	0.605340i	0.986159	−	0.165800i	$-0.0530205\pi$
$47$	2.39600	+	4.15000i	0.349493	+	0.605340i	−0.636666	+	0.771139i	$0.719687\pi$
$48$	0.271473	+	1.71064i	0.0391837	+	0.246910i
$49$	3.47026	−	6.01066i	0.495751	−	0.858666i
$50$	−1.92490	+	3.33403i	−0.272223	+	0.471503i
$51$	−11.7810	−	4.51820i	−1.64967	−	0.632675i
$52$	2.75704	+	4.77533i	0.382332	+	0.662219i
$53$	−9.94555			−1.36613			−0.683063	−	0.730360i	$-0.739353\pi$
$53$	−9.94555			−1.36613			−0.683063	+	0.730360i	$0.739353\pi$
$54$	2.82605	−	4.36044i	0.384577	−	0.593381i
$55$	−0.680404			−0.0917456
$56$	0.121951	+	0.211225i	0.0162963	+	0.0282261i
$57$	−2.67754	−	1.02688i	−0.354649	−	0.136013i
$58$	2.59455	−	4.49390i	0.340682	−	0.590078i
$59$	−5.47354	+	9.48045i	−0.712595	+	1.23425i	0.251285	+	0.967913i	$0.419147\pi$
$59$	−5.47354	+	9.48045i	−0.712595	+	1.23425i	−0.963880	+	0.266337i	$0.914187\pi$
$60$	−0.291146	−	1.83461i	−0.0375868	−	0.236848i
$61$	−6.02141	−	10.4294i	−0.770963	−	1.33535i	−0.937036	−	0.349233i	$-0.886442\pi$
$61$	−6.02141	−	10.4294i	−0.770963	−	1.33535i	0.166073	−	0.986113i	$-0.446891\pi$
$62$	7.65902			0.972696
$63$	0.151694	−	0.715806i	0.0191117	−	0.0901831i
$64$	1.00000			0.125000
$65$	−2.95684	−	5.12140i	−0.366751	−	0.635231i
$66$	−0.853765	+	0.691795i	−0.105091	+	0.0851541i
$67$	−0.121951	+	0.211225i	−0.0148986	+	0.0258052i	−0.873379	−	0.487042i	$-0.838076\pi$
$67$	−0.121951	+	0.211225i	−0.0148986	+	0.0258052i	0.858480	+	0.512847i	$0.171409\pi$
$68$	−3.64242	+	6.30886i	−0.441709	+	0.765062i
$69$	1.34572	−	1.09042i	0.162006	−	0.131272i
$70$	−0.130788	−	0.226532i	−0.0156322	−	0.0270757i
$71$	−7.03926			−0.835406			−0.417703	−	0.908584i	$-0.637165\pi$
$71$	−7.03926			−0.835406			−0.417703	+	0.908584i	$0.637165\pi$
$72$	−2.23065	−	2.00604i	−0.262885	−	0.236414i
$73$	−0.0957368			−0.0112051			−0.00560257	−	0.999984i	$-0.501783\pi$
$73$	−0.0957368			−0.0112051			−0.00560257	+	0.999984i	$0.501783\pi$
$74$	2.05999	+	3.56801i	0.239469	+	0.414773i
$75$	−1.04512	−	6.58565i	−0.120680	−	0.760446i
$76$	−0.827834	+	1.43385i	−0.0949591	+	0.164474i
$77$	−0.0773688	+	0.134007i	−0.00881699	+	0.0152715i
$78$	−8.91735	−	3.41994i	−1.00969	−	0.387232i
$79$	−6.05031	−	10.4794i	−0.680713	−	1.17903i	−0.974764	−	0.223240i	$-0.928337\pi$
$79$	−6.05031	−	10.4794i	−0.680713	−	1.17903i	0.294050	−	0.955790i	$-0.404997\pi$
$80$	−1.07247			−0.119906
$81$	0.951641	+	8.94955i	0.105738	+	0.994394i
$82$	−7.02327			−0.775590
$83$	−4.66982	−	8.08836i	−0.512579	−	0.887813i	−0.999894	−	0.0145867i	$-0.995357\pi$
$83$	−4.66982	−	8.08836i	−0.512579	−	0.887813i	0.487314	−	0.873227i	$-0.337977\pi$
$84$	−0.394436	−	0.151272i	−0.0430365	−	0.0165052i
$85$	3.90639	−	6.76606i	0.423707	−	0.733882i
$86$	−2.73048	+	4.72934i	−0.294436	+	0.509978i
$87$	1.40870	+	8.87671i	0.151029	+	0.951684i
$88$	0.317214	+	0.549430i	0.0338151	+	0.0585695i
$89$	6.00860			0.636910			0.318455	−	0.947938i	$-0.396836\pi$
$89$	6.00860			0.636910			0.318455	+	0.947938i	$0.396836\pi$
$90$	2.39231	+	2.15141i	0.252172	+	0.226779i
$91$	−1.34489			−0.140983
$92$	−0.500000	−	0.866025i	−0.0521286	−	0.0902894i
$93$	−10.3069	+	8.35158i	−1.06878	+	0.866018i
$94$	−2.39600	+	4.15000i	−0.247129	+	0.428040i
$95$	0.887827	−	1.53776i	0.0910891	−	0.157771i
$96$	−1.34572	+	1.09042i	−0.137347	+	0.111291i
$97$	4.59455	+	7.95800i	0.466506	+	0.808012i	0.999268	−	0.0382527i	$-0.0121792\pi$
$97$	4.59455	+	7.95800i	0.466506	+	0.808012i	−0.532762	+	0.846265i	$0.678846\pi$
$98$	6.94051			0.701098
$99$	0.394582	−	1.86193i	0.0396570	−	0.187131i
$100$	−3.84981			−0.384981
$101$	3.37636	+	5.84803i	0.335961	+	0.581901i	0.983669	−	0.179988i	$-0.0576057\pi$
$101$	3.37636	+	5.84803i	0.335961	+	0.581901i	−0.647708	+	0.761889i	$0.724272\pi$
$102$	−1.97764	−	12.4618i	−0.195815	−	1.23390i
$103$	−7.59304	+	13.1515i	−0.748164	+	1.29586i	0.200538	+	0.979686i	$0.435731\pi$
$103$	−7.59304	+	13.1515i	−0.748164	+	1.29586i	−0.948702	+	0.316172i	$0.897602\pi$
$104$	−2.75704	+	4.77533i	−0.270350	+	0.468260i
$105$	0.423021	+	0.162235i	0.0412826	+	0.0158325i
$106$	−4.97277	−	8.61310i	−0.482998	−	0.836578i
$107$	−1.93613			−0.187173			−0.0935864	−	0.995611i	$-0.529833\pi$
$107$	−1.93613			−0.187173			−0.0935864	+	0.995611i	$0.529833\pi$
$108$	5.18928	+	0.267212i	0.499338	+	0.0257125i
$109$	13.8648			1.32801			0.664004	−	0.747729i	$-0.268856\pi$
$109$	13.8648			1.32801			0.664004	+	0.747729i	$0.268856\pi$
$110$	−0.340202	−	0.589247i	−0.0324370	−	0.0561825i
$111$	−6.66283	−	2.55530i	−0.632408	−	0.242538i
$112$	−0.121951	+	0.211225i	−0.0115232	+	0.0199588i
$113$	−5.65406	+	9.79311i	−0.531889	+	0.921258i	0.467418	+	0.884036i	$0.345184\pi$
$113$	−5.65406	+	9.79311i	−0.531889	+	0.921258i	−0.999307	+	0.0372221i	$0.988149\pi$
$114$	−0.449469	−	2.83226i	−0.0420966	−	0.265265i
$115$	0.536235	+	0.928786i	0.0500041	+	0.0866097i
$116$	5.18911			0.481796
$117$	15.7295	−	5.12140i	1.45419	−	0.473473i
$118$	−10.9471			−1.00776
$119$	−0.888391	−	1.53874i	−0.0814387	−	0.141056i
$120$	1.44325	−	1.16945i	0.131750	−	0.106755i
$121$	5.29875	−	9.17771i	0.481705	−	0.834337i
$122$	6.02141	−	10.4294i	0.545153	−	0.944233i
$123$	9.45139	−	7.65834i	0.852203	−	0.690529i
$124$	3.82951	+	6.63290i	0.343900	+	0.595652i
$125$	9.49115			0.848914
$126$	0.695754	−	0.226532i	0.0619827	−	0.0201811i
$127$	0.923965			0.0819886			0.0409943	−	0.999159i	$-0.486947\pi$
$127$	0.923965			0.0819886			0.0409943	+	0.999159i	$0.486947\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.48250	−	9.34177i	−0.130527	−	0.822497i
$130$	2.95684	−	5.12140i	0.259332	−	0.449176i
$131$	5.10713	−	8.84580i	0.446212	−	0.772861i	−0.551924	−	0.833894i	$-0.686106\pi$
$131$	5.10713	−	8.84580i	0.446212	−	0.772861i	0.998136	+	0.0610330i	$0.0194395\pi$
$132$	−1.02599	−	0.393484i	−0.0893013	−	0.0342484i
$133$	−0.201910	−	0.349718i	−0.0175078	−	0.0303244i
$134$	−0.243901			−0.0210698
$135$	−5.56534	−	0.286577i	−0.478988	−	0.0246646i
$136$	−7.28484			−0.624670
$137$	2.42256	+	4.19599i	0.206973	+	0.358488i	0.950760	−	0.309929i	$-0.100305\pi$
$137$	2.42256	+	4.19599i	0.206973	+	0.358488i	−0.743787	+	0.668417i	$0.766972\pi$
$138$	1.61720	+	0.620220i	0.137665	+	0.0527966i
$139$	−3.29429	+	5.70587i	−0.279418	+	0.483966i	−0.971240	−	0.238102i	$-0.923475\pi$
$139$	−3.29429	+	5.70587i	−0.279418	+	0.483966i	0.691822	+	0.722068i	$0.256808\pi$
$140$	0.130788	−	0.226532i	0.0110536	−	0.0191454i
$141$	−1.30090	−	8.19742i	−0.109555	−	0.690347i
$142$	−3.51963	−	6.09617i	−0.295361	−	0.511580i
$143$	−3.49828			−0.292541
$144$	0.621951	−	2.93482i	0.0518292	−	0.244568i
$145$	−5.56516			−0.462161
$146$	−0.0478684	−	0.0829105i	−0.00396162	−	0.00686172i
$147$	−9.34002	+	7.56810i	−0.770352	+	0.624207i
$148$	−2.05999	+	3.56801i	−0.169330	+	0.293289i
$149$	−6.79142	+	11.7631i	−0.556375	+	0.963669i	0.441421	+	0.897300i	$0.354475\pi$
$149$	−6.79142	+	11.7631i	−0.556375	+	0.963669i	−0.997795	+	0.0663687i	$0.978859\pi$
$150$	5.18078	−	4.19792i	0.423009	−	0.342759i
$151$	0.745405	+	1.29108i	0.0606602	+	0.105067i	0.894761	−	0.446546i	$-0.147346\pi$
$151$	0.745405	+	1.29108i	0.0606602	+	0.105067i	−0.834101	+	0.551613i	$0.814013\pi$
$152$	−1.65567			−0.134292
$153$	16.2500	+	14.6137i	1.31373	+	1.18144i
$154$	−0.154738			−0.0124691
$155$	−4.10703	−	7.11359i	−0.329885	−	0.571377i
$156$	−1.49692	−	9.43262i	−0.119850	−	0.755214i
$157$	−2.96847	+	5.14155i	−0.236910	+	0.410340i	−0.959826	−	0.280596i	$-0.909468\pi$
$157$	−2.96847	+	5.14155i	−0.236910	+	0.410340i	0.722916	+	0.690936i	$0.242801\pi$
$158$	6.05031	−	10.4794i	0.481337	−	0.833700i
$159$	16.0839	+	6.16842i	1.27554	+	0.489188i
$160$	−0.536235	−	0.928786i	−0.0423931	−	0.0734270i
$161$	0.243901			0.0192221
$162$	−7.27471	+	5.29892i	−0.571556	+	0.416322i
$163$	14.1999			1.11222			0.556112	−	0.831107i	$-0.312293\pi$
$163$	14.1999			1.11222			0.556112	+	0.831107i	$0.312293\pi$
$164$	−3.51163	−	6.08233i	−0.274213	−	0.474950i
$165$	1.10035	+	0.422000i	0.0856619	+	0.0328527i
$166$	4.66982	−	8.08836i	0.362448	−	0.627779i
$167$	−5.55335	+	9.61868i	−0.429731	+	0.744316i	−0.996849	−	0.0793207i	$-0.974725\pi$
$167$	−5.55335	+	9.61868i	−0.429731	+	0.744316i	0.567118	+	0.823636i	$0.308058\pi$
$168$	−0.0662125	−	0.417228i	−0.00510840	−	0.0321898i
$169$	−8.70252	−	15.0732i	−0.669425	−	1.15948i
$170$	7.81277			0.599212
$171$	3.69322	+	3.32133i	0.282428	+	0.253988i
$172$	−5.46097			−0.416395
$173$	7.20521	+	12.4798i	0.547802	+	0.948821i	0.998425	+	0.0561065i	$0.0178686\pi$
$173$	7.20521	+	12.4798i	0.547802	+	0.948821i	−0.450623	+	0.892714i	$0.648798\pi$
$174$	−6.98311	+	5.65833i	−0.529388	+	0.428957i
$175$	0.469486	−	0.813174i	0.0354898	−	0.0614702i
$176$	−0.317214	+	0.549430i	−0.0239109	+	0.0414149i
$177$	14.7318	−	11.9370i	1.10731	−	0.897237i
$178$	3.00430	+	5.20360i	0.225182	+	0.390026i
$179$	8.65567			0.646955			0.323478	−	0.946236i	$-0.395148\pi$
$179$	8.65567			0.646955			0.323478	+	0.946236i	$0.395148\pi$
$180$	−0.667023	+	3.14751i	−0.0497170	+	0.234601i
$181$	−17.7546			−1.31969			−0.659845	−	0.751402i	$-0.729378\pi$
$181$	−17.7546			−1.31969			−0.659845	+	0.751402i	$0.729378\pi$
$182$	−0.672445	−	1.16471i	−0.0498449	−	0.0863340i
$183$	3.26930	+	20.6010i	0.241673	+	1.52287i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	2.20928	−	3.82658i	0.162429	−	0.281336i
$186$	−12.3861	−	4.75027i	−0.908196	−	0.348307i
$187$	−2.31085	−	4.00251i	−0.168986	−	0.292693i
$188$	−4.79201			−0.349493
$189$	−0.689277	+	1.06352i	−0.0501375	+	0.0773594i
$190$	1.77565			0.128819
$191$	−2.70699	−	4.68865i	−0.195871	−	0.339259i	0.751315	−	0.659944i	$-0.229420\pi$
$191$	−2.70699	−	4.68865i	−0.195871	−	0.339259i	−0.947186	+	0.320685i	$0.896087\pi$
$192$	−1.61720	−	0.620220i	−0.116711	−	0.0447605i
$193$	−7.81654	+	13.5386i	−0.562647	+	0.974533i	0.434617	+	0.900615i	$0.356884\pi$
$193$	−7.81654	+	13.5386i	−0.562647	+	0.974533i	−0.997264	+	0.0739179i	$0.976450\pi$
$194$	−4.59455	+	7.95800i	−0.329870	+	0.571351i
$195$	1.60540	+	10.1162i	0.114965	+	0.724436i
$196$	3.47026	+	6.01066i	0.247875	+	0.429333i
$197$	0.282964			0.0201604			0.0100802	−	0.999949i	$-0.496791\pi$
$197$	0.282964			0.0201604			0.0100802	+	0.999949i	$0.496791\pi$
$198$	1.80977	−	0.589247i	0.128615	−	0.0418760i
$199$	6.51442			0.461795			0.230897	−	0.972978i	$-0.425834\pi$
$199$	6.51442			0.461795			0.230897	+	0.972978i	$0.425834\pi$
$200$	−1.92490	−	3.33403i	−0.136111	−	0.235752i
$201$	0.328224	−	0.265956i	0.0231511	−	0.0187591i
$202$	−3.37636	+	5.84803i	−0.237560	+	0.411466i
$203$	−0.632815	+	1.09607i	−0.0444149	+	0.0769288i
$204$	9.80340	−	7.94357i	0.686375	−	0.556161i
$205$	3.76612	+	6.52311i	0.263037	+	0.455594i
$206$	−15.1861			−1.05806
$207$	−2.85261	+	0.928786i	−0.198270	+	0.0645551i
$208$	−5.51408			−0.382332
$209$	−0.525201	−	0.909674i	−0.0363289	−	0.0629235i
$210$	0.0710108	+	0.447464i	0.00490021	+	0.0308780i
$211$	−8.53633	+	14.7854i	−0.587665	+	1.01787i	0.406872	+	0.913485i	$0.366619\pi$
$211$	−8.53633	+	14.7854i	−0.587665	+	1.01787i	−0.994537	+	0.104381i	$0.966714\pi$
$212$	4.97277	−	8.61310i	0.341531	−	0.591550i
$213$	11.3839	+	4.36589i	0.780010	+	0.299146i
$214$	−0.968065	−	1.67674i	−0.0661756	−	0.114619i
$215$	5.85672			0.399425
$216$	2.36323	+	4.62765i	0.160797	+	0.314872i
$217$	−1.86804			−0.126811
$218$	6.93241	+	12.0073i	0.469522	+	0.813236i
$219$	0.154825	+	0.0593779i	0.0104621	+	0.00401238i
$220$	0.340202	−	0.589247i	0.0229364	−	0.0397270i
$221$	20.0846	−	34.7875i	1.35104	−	2.34006i
$222$	−1.11846	−	7.04783i	−0.0750663	−	0.473019i
$223$	11.1983	+	19.3960i	0.749893	+	1.29885i	0.947874	+	0.318646i	$0.103228\pi$
$223$	11.1983	+	19.3960i	0.749893	+	1.29885i	−0.197981	+	0.980206i	$0.563438\pi$
$224$	−0.243901			−0.0162963
$225$	−2.39439	+	11.2985i	−0.159626	+	0.753234i
$226$	−11.3081			−0.752204
$227$	−6.44178	−	11.1575i	−0.427556	−	0.740548i	0.569099	−	0.822269i	$-0.307292\pi$
$227$	−6.44178	−	11.1575i	−0.427556	−	0.740548i	−0.996655	+	0.0817203i	$0.973959\pi$
$228$	2.22807	−	1.80538i	0.147558	−	0.119564i
$229$	5.03616	−	8.72289i	0.332799	−	0.576425i	−0.650261	−	0.759711i	$-0.725340\pi$
$229$	5.03616	−	8.72289i	0.332799	−	0.576425i	0.983060	+	0.183287i	$0.0586736\pi$
$230$	−0.536235	+	0.928786i	−0.0353583	+	0.0612423i
$231$	0.208234	−	0.168730i	0.0137008	−	0.0111016i
$232$	2.59455	+	4.49390i	0.170341	+	0.295039i
$233$	1.94779			0.127604			0.0638020	−	0.997963i	$-0.479677\pi$
$233$	1.94779			0.127604			0.0638020	+	0.997963i	$0.479677\pi$
$234$	12.3000	+	11.0614i	0.804076	+	0.723109i
$235$	5.13928			0.335250
$236$	−5.47354	−	9.48045i	−0.356297	−	0.617125i
$237$	3.28499	+	20.6999i	0.213383	+	1.34460i
$238$	0.888391	−	1.53874i	0.0575858	−	0.0997416i
$239$	−3.43217	+	5.94469i	−0.222009	+	0.384530i	−0.955418	−	0.295257i	$-0.904595\pi$
$239$	−3.43217	+	5.94469i	−0.222009	+	0.384530i	0.733409	+	0.679787i	$0.237928\pi$
$240$	1.73439	+	0.665167i	0.111955	+	0.0429363i
$241$	−5.23568	−	9.06847i	−0.337260	−	0.584151i	0.646656	−	0.762782i	$-0.276167\pi$
$241$	−5.23568	−	9.06847i	−0.337260	−	0.584151i	−0.983916	+	0.178630i	$0.942833\pi$
$242$	10.5975			0.681233
$243$	4.01169	−	15.0634i	0.257350	−	0.966318i
$244$	12.0428			0.770963
$245$	−3.72174	−	6.44625i	−0.237773	−	0.411836i
$246$	11.3580	+	4.35597i	0.724160	+	0.277726i
$247$	4.56474	−	7.90636i	0.290448	−	0.503070i
$248$	−3.82951	+	6.63290i	−0.243174	+	0.421190i
$249$	2.53546	+	15.9768i	0.160678	+	1.01249i
$250$	4.74557	+	8.21958i	0.300137	+	0.519852i
$251$	22.1052			1.39526			0.697632	−	0.716456i	$-0.254237\pi$
$251$	22.1052			1.39526			0.697632	+	0.716456i	$0.254237\pi$
$252$	0.544059	+	0.489274i	0.0342725	+	0.0308214i
$253$	0.634427			0.0398861
$254$	0.461982	+	0.800177i	0.0289874	+	0.0502076i
$255$	−10.5138	+	8.51924i	−0.658402	+	0.533495i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.9225	+	22.3825i	−0.806086	+	1.39618i	0.109469	+	0.993990i	$0.465085\pi$
$257$	−12.9225	+	22.3825i	−0.806086	+	1.39618i	−0.915555	+	0.402192i	$0.868248\pi$
$258$	7.34896	−	5.95477i	0.457526	−	0.370728i
$259$	−0.502435	−	0.870242i	−0.0312198	−	0.0540742i
$260$	5.91368			0.366751
$261$	3.22737	−	15.2291i	0.199769	−	0.942658i
$262$	10.2143			0.631039
$263$	−15.1587	−	26.2556i	−0.934725	−	1.61899i	−0.775124	−	0.631809i	$-0.782313\pi$
$263$	−15.1587	−	26.2556i	−0.934725	−	1.61899i	−0.159601	−	0.987182i	$-0.551021\pi$
$264$	−0.172230	−	1.08528i	−0.0106000	−	0.0667943i
$265$	−5.33315	+	9.23728i	−0.327613	+	0.567442i
$266$	0.201910	−	0.349718i	0.0123799	−	0.0214426i
$267$	−9.71709	−	3.72665i	−0.594676	−	0.228067i
$268$	−0.121951	−	0.211225i	−0.00744932	−	0.0129026i
$269$	−12.3343			−0.752033			−0.376017	−	0.926613i	$-0.622706\pi$
$269$	−12.3343			−0.752033			−0.376017	+	0.926613i	$0.622706\pi$
$270$	−2.53449	−	4.96302i	−0.154244	−	0.302039i
$271$	−9.37653			−0.569584			−0.284792	−	0.958589i	$-0.591924\pi$
$271$	−9.37653			−0.569584			−0.284792	+	0.958589i	$0.591924\pi$
$272$	−3.64242	−	6.30886i	−0.220854	−	0.382531i
$273$	2.17495	+	0.834127i	0.131634	+	0.0504837i
$274$	−2.42256	+	4.19599i	−0.146352	+	0.253489i
$275$	1.22121	−	2.11520i	0.0736419	−	0.127551i
$276$	0.271473	+	1.71064i	0.0163407	+	0.102969i
$277$	0.178175	+	0.308608i	0.0107055	+	0.0185425i	0.871329	−	0.490700i	$-0.163259\pi$
$277$	0.178175	+	0.308608i	0.0107055	+	0.0185425i	−0.860623	+	0.509243i	$0.829926\pi$
$278$	−6.58857			−0.395156
$279$	21.8481	−	7.11359i	1.30801	−	0.425879i
$280$	0.261577			0.0156322
$281$	−13.5595	−	23.4857i	−0.808891	−	1.40104i	−0.913632	−	0.406541i	$-0.866735\pi$
$281$	−13.5595	−	23.4857i	−0.808891	−	1.40104i	0.104741	−	0.994500i	$-0.466599\pi$
$282$	6.44872	−	5.22532i	0.384016	−	0.311163i
$283$	2.31470	−	4.00917i	0.137594	−	0.238321i	−0.788991	−	0.614405i	$-0.789396\pi$
$283$	2.31470	−	4.00917i	0.137594	−	0.238321i	0.926586	+	0.376084i	$0.122730\pi$
$284$	3.51963	−	6.09617i	0.208852	−	0.361741i
$285$	−2.38954	+	1.93622i	−0.141544	+	0.114692i
$286$	−1.74914	−	3.02960i	−0.103429	−	0.179144i
$287$	1.71298			0.101114
$288$	2.85261	−	0.928786i	0.168091	−	0.0547292i
$289$	36.0690			2.12170
$290$	−2.78258	−	4.81957i	−0.163399	−	0.283015i
$291$	−2.49459	−	15.7193i	−0.146235	−	0.921481i
$292$	0.0478684	−	0.0829105i	0.00280129	−	0.00485197i
$293$	−2.14833	+	3.72102i	−0.125507	+	0.217385i	−0.921931	−	0.387354i	$-0.873389\pi$
$293$	−2.14833	+	3.72102i	−0.125507	+	0.217385i	0.796424	+	0.604739i	$0.206722\pi$
$294$	−11.2242	−	4.30464i	−0.654607	−	0.251052i
$295$	5.87021	+	10.1675i	0.341777	+	0.591975i
$296$	−4.11999			−0.239469
$297$	−1.79292	+	2.76638i	−0.104036	+	0.160522i
$298$	−13.5828			−0.786832
$299$	2.75704	+	4.77533i	0.159444	+	0.276165i
$300$	6.22590	+	2.38773i	0.359453	+	0.137856i
$301$	0.665968	−	1.15349i	0.0383858	−	0.0664861i
$302$	−0.745405	+	1.29108i	−0.0428932	+	0.0742933i
$303$	−1.83318	−	11.5515i	−0.105313	−	0.663617i
$304$	−0.827834	−	1.43385i	−0.0474795	−	0.0822370i
$305$	−12.9156			−0.739543
$306$	−4.53081	+	21.3797i	−0.259009	+	1.22220i
$307$	−14.0398			−0.801292			−0.400646	−	0.916233i	$-0.631214\pi$
$307$	−14.0398			−0.801292			−0.400646	+	0.916233i	$0.631214\pi$
$308$	−0.0773688	−	0.134007i	−0.00440850	−	0.00763574i
$309$	20.4363	−	16.5593i	1.16258	−	0.942024i
$310$	4.10703	−	7.11359i	0.233264	−	0.404024i
$311$	0.0943154	−	0.163359i	0.00534813	−	0.00926324i	−0.863339	−	0.504624i	$-0.831631\pi$
$311$	0.0943154	−	0.163359i	0.00534813	−	0.00926324i	0.868687	+	0.495361i	$0.164964\pi$
$312$	7.42043	−	6.01268i	0.420099	−	0.340401i
$313$	−10.7871	−	18.6838i	−0.609724	−	1.05607i	−0.991286	−	0.131729i	$-0.957947\pi$
$313$	−10.7871	−	18.6838i	−0.609724	−	1.05607i	0.381562	−	0.924343i	$-0.375386\pi$
$314$	−5.93695			−0.335041
$315$	−0.583487	−	0.524732i	−0.0328758	−	0.0295653i
$316$	12.1006			0.680713
$317$	−9.55363	−	16.5474i	−0.536585	−	0.929393i	−0.999085	−	0.0427732i	$-0.986381\pi$
$317$	−9.55363	−	16.5474i	−0.536585	−	0.929393i	0.462500	−	0.886619i	$-0.346953\pi$
$318$	2.69994	+	17.0133i	0.151405	+	0.954058i
$319$	−1.64606	+	2.85105i	−0.0921614	+	0.159628i
$320$	0.536235	−	0.928786i	0.0299764	−	0.0519207i
$321$	3.13110	+	1.20083i	0.174761	+	0.0670236i
$322$	0.121951	+	0.211225i	0.00679604	+	0.0117711i
$323$	12.0613			0.671108
$324$	−8.22635	−	3.65063i	−0.457020	−	0.202813i
$325$	21.2281			1.17753
$326$	7.09996	+	12.2975i	0.393231	+	0.681095i
$327$	−22.4221	−	8.59923i	−1.23995	−	0.475539i
$328$	3.51163	−	6.08233i	0.193898	−	0.335840i
$329$	0.584388	−	1.01219i	0.0322184	−	0.0558038i
$330$	0.184711	+	1.16393i	0.0101680	+	0.0640722i
$331$	−2.14806	−	3.72054i	−0.118068	−	0.204499i	0.800934	−	0.598752i	$-0.204337\pi$
$331$	−2.14806	−	3.72054i	−0.118068	−	0.204499i	−0.919002	+	0.394253i	$0.871003\pi$
$332$	9.33964			0.512579
$333$	9.19026	+	8.26484i	0.503623	+	0.452910i
$334$	−11.1067			−0.607731
$335$	0.130788	+	0.226532i	0.00714573	+	0.0123768i
$336$	0.328224	−	0.265956i	0.0179061	−	0.0145091i
$337$	−16.0623	+	27.8207i	−0.874968	+	1.51549i	−0.0181715	+	0.999835i	$0.505784\pi$
$337$	−16.0623	+	27.8207i	−0.874968	+	1.51549i	−0.856797	+	0.515654i	$0.827549\pi$
$338$	8.70252	−	15.0732i	0.473355	−	0.819875i
$339$	15.2176	−	12.3306i	0.826507	−	0.669708i
$340$	3.90639	+	6.76606i	0.211854	+	0.366941i
$341$	−4.85909			−0.263134
$342$	−1.02974	+	4.85909i	−0.0556822	+	0.262750i
$343$	−3.40011			−0.183589
$344$	−2.73048	−	4.72934i	−0.147218	−	0.254989i
$345$	−0.291146	−	1.83461i	−0.0156748	−	0.0987723i
$346$	−7.20521	+	12.4798i	−0.387355	+	0.670918i
$347$	15.3887	−	26.6539i	0.826106	−	1.43086i	−0.0749643	−	0.997186i	$-0.523884\pi$
$347$	15.3887	−	26.6539i	0.826106	−	1.43086i	0.901071	−	0.433672i	$-0.142782\pi$
$348$	−8.39181	−	3.21839i	−0.449848	−	0.172524i
$349$	1.78306	+	3.08835i	0.0954451	+	0.165316i	0.909794	−	0.415059i	$-0.136239\pi$
$349$	1.78306	+	3.08835i	0.0954451	+	0.165316i	−0.814349	+	0.580375i	$0.802906\pi$
$350$	0.938973			0.0501902
$351$	−28.6141	−	1.47343i	−1.52731	−	0.0786459i
$352$	−0.634427			−0.0338151
$353$	4.61596	+	7.99509i	0.245683	+	0.425535i	0.962323	−	0.271907i	$-0.0876544\pi$
$353$	4.61596	+	7.99509i	0.245683	+	0.425535i	−0.716640	+	0.697443i	$0.754321\pi$
$354$	17.7036	+	6.78960i	0.940936	+	0.360863i
$355$	−3.77469	+	6.53796i	−0.200340	+	0.346999i
$356$	−3.00430	+	5.20360i	−0.159228	+	0.275790i
$357$	0.482347	+	3.03944i	0.0255285	+	0.160864i
$358$	4.32783	+	7.49603i	0.228733	+	0.396177i
$359$	32.4382			1.71202			0.856010	−	0.516959i	$-0.172936\pi$
$359$	32.4382			1.71202			0.856010	+	0.516959i	$0.172936\pi$
$360$	−3.05933	+	0.996094i	−0.161241	+	0.0524988i
$361$	−16.2588			−0.855724
$362$	−8.87730	−	15.3759i	−0.466581	−	0.808141i
$363$	−14.2613	+	11.5558i	−0.748525	+	0.606521i
$364$	0.672445	−	1.16471i	0.0352457	−	0.0610473i
$365$	−0.0513374	+	0.0889190i	−0.00268712	+	0.00465423i
$366$	−16.2063	+	13.1318i	−0.847118	+	0.686409i
$367$	10.6354	+	18.4210i	0.555162	+	0.961568i	0.997891	+	0.0649128i	$0.0206769\pi$
$367$	10.6354	+	18.4210i	0.555162	+	0.961568i	−0.442729	+	0.896655i	$0.645990\pi$
$368$	1.00000			0.0521286
$369$	−20.0346	+	6.52311i	−1.04296	+	0.339580i
$370$	4.41856			0.229710
$371$	1.21287	+	2.10074i	0.0629688	+	0.109065i
$372$	−2.07921	−	13.1018i	−0.107802	−	0.679299i
$373$	0.378111	−	0.654907i	0.0195778	−	0.0339098i	−0.856071	−	0.516859i	$-0.827101\pi$
$373$	0.378111	−	0.654907i	0.0195778	−	0.0339098i	0.875648	+	0.482949i	$0.160434\pi$
$374$	2.31085	−	4.00251i	0.119491	−	0.206965i
$375$	−15.3491	−	5.88660i	−0.792622	−	0.303983i
$376$	−2.39600	−	4.15000i	−0.123564	−	0.214020i
$377$	−28.6131			−1.47365
$378$	−1.26567	−	0.0651734i	−0.0650991	−	0.00335216i
$379$	−28.5110			−1.46451			−0.732257	−	0.681028i	$-0.761533\pi$
$379$	−28.5110			−1.46451			−0.732257	+	0.681028i	$0.761533\pi$
$380$	0.887827	+	1.53776i	0.0455446	+	0.0788855i
$381$	−1.49423	−	0.573061i	−0.0765519	−	0.0293588i
$382$	2.70699	−	4.68865i	0.138502	−	0.239892i
$383$	14.8573	−	25.7337i	0.759175	−	1.31493i	−0.184097	−	0.982908i	$-0.558936\pi$
$383$	14.8573	−	25.7337i	0.759175	−	1.31493i	0.943272	−	0.332022i	$-0.107731\pi$
$384$	−0.271473	−	1.71064i	−0.0138535	−	0.0872959i
$385$	0.0829756	+	0.143718i	0.00422883	+	0.00732455i
$386$	−15.6331			−0.795703
$387$	−3.39645	+	16.0270i	−0.172651	+	0.814697i
$388$	−9.18911			−0.466506
$389$	1.44866	+	2.50916i	0.0734501	+	0.127219i	0.900411	−	0.435040i	$-0.143266\pi$
$389$	1.44866	+	2.50916i	0.0734501	+	0.127219i	−0.826961	+	0.562259i	$0.809932\pi$
$390$	−7.95818	+	6.44842i	−0.402978	+	0.326528i
$391$	−3.64242	+	6.30886i	−0.184205	+	0.319053i
$392$	−3.47026	+	6.01066i	−0.175274	+	0.303584i
$393$	−13.7456	+	11.1379i	−0.693373	+	0.561831i
$394$	0.141482	+	0.245054i	0.00712777	+	0.0123457i
$395$	−12.9775			−0.652971
$396$	1.41519	+	1.27268i	0.0711159	+	0.0639548i
$397$	−7.30643			−0.366699			−0.183349	−	0.983048i	$-0.558694\pi$
$397$	−7.30643			−0.366699			−0.183349	+	0.983048i	$0.558694\pi$
$398$	3.25721	+	5.64165i	0.163269	+	0.282790i
$399$	0.109626	+	0.690791i	0.00548816	+	0.0345828i
$400$	1.92490	−	3.33403i	0.0962452	−	0.166702i
$401$	−8.44269	+	14.6232i	−0.421608	+	0.730246i	−0.996097	−	0.0882661i	$-0.971867\pi$
$401$	−8.44269	+	14.6232i	−0.421608	+	0.730246i	0.574489	+	0.818512i	$0.305201\pi$
$402$	0.394436	+	0.151272i	0.0196727	+	0.00754478i
$403$	−21.1162	−	36.5743i	−1.05187	−	1.82190i
$404$	−6.75273			−0.335961
$405$	8.82251	+	3.91519i	0.438394	+	0.194547i
$406$	−1.26563			−0.0628121
$407$	−1.30692	−	2.26364i	−0.0647814	−	0.112205i
$408$	11.7810	+	4.51820i	0.583248	+	0.223684i
$409$	−17.4429	+	30.2120i	−0.862497	+	1.49389i	0.00701441	+	0.999975i	$0.497767\pi$
$409$	−17.4429	+	30.2120i	−0.862497	+	1.49389i	−0.869511	+	0.493913i	$0.835566\pi$
$410$	−3.76612	+	6.52311i	−0.185995	+	0.322153i
$411$	−1.31532	−	8.28827i	−0.0648798	−	0.408830i
$412$	−7.59304	−	13.1515i	−0.374082	−	0.647929i
$413$	2.67001			0.131382
$414$	−2.23065	−	2.00604i	−0.109631	−	0.0985913i
$415$	−10.0165			−0.491689
$416$	−2.75704	−	4.77533i	−0.135175	−	0.234130i
$417$	8.86641	−	7.18434i	0.434190	−	0.351819i
$418$	0.525201	−	0.909674i	0.0256884	−	0.0444936i
$419$	−9.58756	+	16.6061i	−0.468383	+	0.811263i	−0.999347	−	0.0361313i	$-0.988497\pi$
$419$	−9.58756	+	16.6061i	−0.468383	+	0.811263i	0.530964	+	0.847394i	$0.321830\pi$
$420$	−0.352010	+	0.285229i	−0.0171763	+	0.0139178i
$421$	−8.99188	−	15.5744i	−0.438238	−	0.759050i	0.559316	−	0.828954i	$-0.311064\pi$
$421$	−8.99188	−	15.5744i	−0.438238	−	0.759050i	−0.997554	+	0.0699047i	$0.977730\pi$
$422$	−17.0727			−0.831084
$423$	−2.98039	+	14.0637i	−0.144912	+	0.683800i
$424$	9.94555			0.482998
$425$	14.0226	+	24.2879i	0.680197	+	1.17814i
$426$	1.91097	+	12.0417i	0.0925866	+	0.583420i
$427$	−1.46863	+	2.54374i	−0.0710719	+	0.123100i
$428$	0.968065	−	1.67674i	0.0467932	−	0.0810482i
$429$	5.65741	+	2.16970i	0.273142	+	0.104754i
$430$	2.92836	+	5.07207i	0.141218	+	0.244597i
$431$	−4.63953			−0.223478			−0.111739	−	0.993738i	$-0.535642\pi$
$431$	−4.63953			−0.223478			−0.111739	+	0.993738i	$0.535642\pi$
$432$	−2.82605	+	4.36044i	−0.135968	+	0.209792i
$433$	10.8517			0.521500			0.260750	−	0.965406i	$-0.416030\pi$
$433$	10.8517			0.521500			0.260750	+	0.965406i	$0.416030\pi$
$434$	−0.934021	−	1.61777i	−0.0448345	−	0.0776556i
$435$	8.99996	+	3.45162i	0.431515	+	0.165493i
$436$	−6.93241	+	12.0073i	−0.332002	+	0.575045i
$437$	−0.827834	+	1.43385i	−0.0396007	+	0.0685904i
$438$	0.0259899	+	0.163772i	0.00124185	+	0.00782531i
$439$	16.4402	+	28.4752i	0.784646	+	1.35905i	0.929210	+	0.369551i	$0.120489\pi$
$439$	16.4402	+	28.4752i	0.784646	+	1.35905i	−0.144564	+	0.989495i	$0.546178\pi$
$440$	0.680404			0.0324370
$441$	19.7985	−	6.44625i	0.942788	−	0.306964i
$442$	40.1692			1.91065
$443$	18.0418	+	31.2493i	0.857192	+	1.48470i	0.874596	+	0.484852i	$0.161127\pi$
$443$	18.0418	+	31.2493i	0.857192	+	1.48470i	−0.0174040	+	0.999849i	$0.505540\pi$
$444$	5.54437	−	4.49253i	0.263124	−	0.213206i
$445$	3.22202	−	5.58070i	0.152738	−	0.264551i
$446$	−11.1983	+	19.3960i	−0.530254	+	0.918427i
$447$	18.2788	−	14.8110i	0.864556	−	0.700539i
$448$	−0.121951	−	0.211225i	−0.00576162	−	0.00997942i
$449$	−27.0847			−1.27821			−0.639104	−	0.769120i	$-0.720695\pi$
$449$	−27.0847			−1.27821			−0.639104	+	0.769120i	$0.720695\pi$
$450$	−10.9820	+	3.57565i	−0.517696	+	0.168558i
$451$	4.45575			0.209813
$452$	−5.65406	−	9.79311i	−0.265944	−	0.460629i
$453$	−0.404714	−	2.55024i	−0.0190151	−	0.119821i
$454$	6.44178	−	11.1575i	0.302328	−	0.523647i
$455$	−0.721177	+	1.24911i	−0.0338093	+	0.0585594i
$456$	2.67754	+	1.02688i	0.125387	+	0.0480880i
$457$	−16.8341	−	29.1576i	−0.787468	−	1.36393i	−0.927514	−	0.373789i	$-0.878058\pi$
$457$	−16.8341	−	29.1576i	−0.787468	−	1.36393i	0.140046	−	0.990145i	$-0.455275\pi$
$458$	10.0723			0.470649
$459$	−17.2157	−	33.7117i	−0.803562	−	1.57353i
$460$	−1.07247			−0.0500041
$461$	−7.66607	−	13.2780i	−0.357045	−	0.618419i	0.630421	−	0.776253i	$-0.282882\pi$
$461$	−7.66607	−	13.2780i	−0.357045	−	0.618419i	−0.987466	+	0.157834i	$0.949549\pi$
$462$	0.250241	+	0.0959713i	0.0116423	+	0.00446499i
$463$	−17.8947	+	30.9945i	−0.831635	+	1.44043i	0.0651055	+	0.997878i	$0.479262\pi$
$463$	−17.8947	+	30.9945i	−0.831635	+	1.44043i	−0.896741	+	0.442556i	$0.854072\pi$
$464$	−2.59455	+	4.49390i	−0.120449	+	0.208624i
$465$	2.22989	+	14.0513i	0.103409	+	0.651615i
$466$	0.973895	+	1.68684i	0.0451148	+	0.0781412i
$467$	−3.45620			−0.159934			−0.0799670	−	0.996798i	$-0.525482\pi$
$467$	−3.45620			−0.159934			−0.0799670	+	0.996798i	$0.525482\pi$
$468$	−3.42948	+	16.1828i	−0.158528	+	0.748052i
$469$	0.0594878			0.00274689
$470$	2.56964	+	4.45075i	0.118529	+	0.205298i
$471$	7.98950	−	6.47379i	0.368137	−	0.298296i
$472$	5.47354	−	9.48045i	0.251940	−	0.436373i
$473$	1.73229	−	3.00042i	0.0796510	−	0.137960i
$474$	−16.2841	+	13.1948i	−0.747954	+	0.606058i
$475$	3.18700	+	5.52005i	0.146230	+	0.253277i
$476$	1.77678			0.0814387
$477$	−22.1851	−	19.9511i	−1.01579	−	0.913499i
$478$	−6.86434			−0.313968
$479$	−14.2875	−	24.7467i	−0.652814	−	1.13071i	−0.982437	−	0.186595i	$-0.940255\pi$
$479$	−14.2875	−	24.7467i	−0.652814	−	1.13071i	0.329623	−	0.944113i	$-0.393078\pi$
$480$	0.291146	+	1.83461i	0.0132889	+	0.0837383i
$481$	11.3590	−	19.6743i	0.517924	−	0.897071i
$482$	5.23568	−	9.06847i	0.238479	−	0.413057i
$483$	−0.394436	−	0.151272i	−0.0179475	−	0.00688313i
$484$	5.29875	+	9.17771i	0.240852	+	0.417168i
$485$	9.85504			0.447494
$486$	15.0511	−	4.05748i	0.682734	−	0.184051i
$487$	−14.2755			−0.646886			−0.323443	−	0.946248i	$-0.604840\pi$
$487$	−14.2755			−0.646886			−0.323443	+	0.946248i	$0.604840\pi$
$488$	6.02141	+	10.4294i	0.272576	+	0.472116i
$489$	−22.9641	−	8.80708i	−1.03847	−	0.398270i
$490$	3.72174	−	6.44625i	0.168131	−	0.291212i
$491$	−7.09647	+	12.2914i	−0.320259	+	0.554705i	−0.980541	−	0.196313i	$-0.937103\pi$
$491$	−7.09647	+	12.2914i	−0.320259	+	0.554705i	0.660282	+	0.751017i	$0.270437\pi$
$492$	1.90662	+	12.0143i	0.0859573	+	0.541647i
$493$	−18.9009	−	32.7373i	−0.851255	−	1.47442i
$494$	9.12948			0.410755
$495$	−1.51775	−	1.36491i	−0.0682176	−	0.0613483i
$496$	−7.65902			−0.343900
$497$	0.858441	+	1.48686i	0.0385064	+	0.0666950i
$498$	−12.5686	+	10.1842i	−0.563212	+	0.456363i
$499$	16.3122	−	28.2536i	0.730236	−	1.26481i	−0.226547	−	0.974000i	$-0.572744\pi$
$499$	16.3122	−	28.2536i	0.730236	−	1.26481i	0.956782	−	0.290805i	$-0.0939231\pi$
$500$	−4.74557	+	8.21958i	−0.212229	+	0.367591i
$501$	14.9466	−	12.1110i	0.667763	−	0.541080i
$502$	11.0526	+	19.1436i	0.493301	+	0.854422i
$503$	20.4118			0.910118			0.455059	−	0.890461i	$-0.349618\pi$
$503$	20.4118			0.910118			0.455059	+	0.890461i	$0.349618\pi$
$504$	−0.151694	+	0.715806i	−0.00675701	+	0.0318845i
$505$	7.24209			0.322269
$506$	0.317214	+	0.549430i	0.0141019	+	0.0244252i
$507$	4.72499	+	29.7738i	0.209844	+	1.32230i
$508$	−0.461982	+	0.800177i	−0.0204972	+	0.0355021i
$509$	−10.7960	+	18.6991i	−0.478522	+	0.828825i	−0.999697	−	0.0246252i	$-0.992161\pi$
$509$	−10.7960	+	18.6991i	−0.478522	+	0.828825i	0.521174	+	0.853450i	$0.325494\pi$
$510$	−12.6348	−	4.84564i	−0.559478	−	0.214568i
$511$	0.0116752	+	0.0202220i	0.000516478	+	0.000894567i
$512$	−1.00000			−0.0441942
$513$	−3.91272	−	7.66186i	−0.172751	−	0.338279i
$514$	−25.8451			−1.13998
$515$	8.14330	+	14.1046i	0.358837	+	0.621523i
$516$	8.83147	+	3.38700i	0.388784	+	0.149104i
$517$	1.52009	−	2.63287i	0.0668535	−	0.115794i
$518$	0.502435	−	0.870242i	0.0220757	−	0.0382362i
$519$	−3.91203	−	24.6511i	−0.171719	−	1.08206i
$520$	2.95684	+	5.12140i	0.129666	+	0.224588i
$521$	32.5067			1.42414			0.712072	−	0.702106i	$-0.247757\pi$
$521$	32.5067			1.42414			0.712072	+	0.702106i	$0.247757\pi$
$522$	14.8025	−	4.81957i	0.647887	−	0.210947i
$523$	1.66747			0.0729133			0.0364567	−	0.999335i	$-0.488393\pi$
$523$	1.66747			0.0729133			0.0364567	+	0.999335i	$0.488393\pi$
$524$	5.10713	+	8.84580i	0.223106	+	0.386431i
$525$	−1.26360	+	1.02388i	−0.0551480	+	0.0446857i
$526$	15.1587	−	26.2556i	0.660950	−	1.14480i
$527$	27.8974	−	48.3197i	1.21523	−	2.10484i
$528$	0.853765	−	0.691795i	0.0371553	−	0.0301065i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−10.6663			−0.463314
$531$	−31.2277	+	10.1675i	−1.35517	+	0.441232i
$532$	0.403819			0.0175078
$533$	19.3634	+	33.5384i	0.838723	+	1.45271i
$534$	−1.63117	−	10.2786i	−0.0705876	−	0.444797i
$535$	−1.03822	+	1.79825i	−0.0448862	+	0.0777451i
$536$	0.121951	−	0.211225i	0.00526746	−	0.00912351i
$537$	−13.9979	−	5.36842i	−0.604055	−	0.231664i
$538$	−6.16713	−	10.6818i	−0.265884	−	0.460524i
$539$	−4.40325			−0.189661
$540$	3.03085	−	4.67644i	0.130427	−	0.201242i
$541$	−8.04220			−0.345761			−0.172881	−	0.984943i	$-0.555307\pi$
$541$	−8.04220			−0.345761			−0.172881	+	0.984943i	$0.555307\pi$
$542$	−4.68826	−	8.12031i	−0.201378	−	0.348797i
$543$	28.7127	+	11.0118i	1.23218	+	0.472560i
$544$	3.64242	−	6.30886i	0.156168	−	0.270490i
$545$	7.43480	−	12.8774i	0.318472	−	0.551609i
$546$	0.365101	+	2.30063i	0.0156249	+	0.0984578i
$547$	21.5242	+	37.2810i	0.920308	+	1.59402i	0.798938	+	0.601413i	$0.205395\pi$
$547$	21.5242	+	37.2810i	0.920308	+	1.59402i	0.121370	+	0.992607i	$0.461271\pi$
$548$	−4.84512			−0.206973
$549$	7.49004	−	35.3435i	0.319667	−	1.50843i
$550$	2.44242			0.104145
$551$	−4.29572	−	7.44041i	−0.183004	−	0.316972i
$552$	−1.34572	+	1.09042i	−0.0572779	+	0.0464115i
$553$	−1.47568	+	2.55595i	−0.0627522	+	0.108690i
$554$	−0.178175	+	0.308608i	−0.00756993	+	0.0131115i
$555$	−5.94616	+	4.81810i	−0.252401	+	0.204517i
$556$	−3.29429	−	5.70587i	−0.139709	−	0.241983i
$557$	−27.7394			−1.17536			−0.587679	−	0.809094i	$-0.699958\pi$
$557$	−27.7394			−1.17536			−0.587679	+	0.809094i	$0.699958\pi$
$558$	17.0846	+	15.3643i	0.723250	+	0.650421i
$559$	30.1122			1.27361
$560$	0.130788	+	0.226532i	0.00552681	+	0.00957272i
$561$	1.25467	+	7.90609i	0.0529720	+	0.333795i
$562$	13.5595	−	23.4857i	0.571973	−	0.990686i
$563$	−4.17580	+	7.23270i	−0.175989	+	0.304822i	−0.940503	−	0.339785i	$-0.889646\pi$
$563$	−4.17580	+	7.23270i	−0.175989	+	0.304822i	0.764514	+	0.644607i	$0.222979\pi$
$564$	7.74962	+	2.97210i	0.326318	+	0.125148i
$565$	6.06380	+	10.5028i	0.255106	+	0.441857i
$566$	4.62939			0.194588
$567$	1.77431	−	1.29241i	0.0745141	−	0.0542762i
$568$	7.03926			0.295361
$569$	5.43472	+	9.41322i	0.227835	+	0.394623i	0.957166	−	0.289539i	$-0.0935018\pi$
$569$	5.43472	+	9.41322i	0.227835	+	0.394623i	−0.729331	+	0.684161i	$0.760169\pi$
$570$	−2.87158	−	1.10130i	−0.120277	−	0.0461282i
$571$	−5.18922	+	8.98800i	−0.217162	+	0.376136i	−0.953939	−	0.300000i	$-0.903013\pi$
$571$	−5.18922	+	8.98800i	−0.217162	+	0.376136i	0.736777	+	0.676136i	$0.236347\pi$
$572$	1.74914	−	3.02960i	0.0731352	−	0.126674i
$573$	1.46975	+	9.26140i	0.0613996	+	0.386901i
$574$	0.856491	+	1.48349i	0.0357493	+	0.0619195i
$575$	−3.84981			−0.160548
$576$	2.23065	+	2.00604i	0.0929439	+	0.0835848i
$577$	38.1317			1.58744			0.793721	−	0.608282i	$-0.208141\pi$
$577$	38.1317			1.58744			0.793721	+	0.608282i	$0.208141\pi$
$578$	18.0345	+	31.2366i	0.750135	+	1.29927i
$579$	21.0378	−	17.0467i	0.874302	−	0.708436i
$580$	2.78258	−	4.81957i	0.115540	−	0.200122i
$581$	−1.13897	+	1.97276i	−0.0472526	+	0.0818439i
$582$	12.3660	−	10.0200i	0.512588	−	0.415343i
$583$	3.15486	+	5.46438i	0.130661	+	0.226312i
$584$	0.0957368			0.00396162
$585$	3.67802	−	17.3556i	0.152067	−	0.717565i
$586$	−4.29667			−0.177494
$587$	16.5869	+	28.7293i	0.684614	+	1.18579i	0.973558	+	0.228440i	$0.0733625\pi$
$587$	16.5869	+	28.7293i	0.684614	+	1.18579i	−0.288944	+	0.957346i	$0.593304\pi$
$588$	−1.88416	−	11.8727i	−0.0777014	−	0.489624i
$589$	6.34040	−	10.9819i	0.261251	−	0.452501i
$590$	−5.87021	+	10.1675i	−0.241673	+	0.418589i
$591$	−0.457609	−	0.175500i	−0.0188235	−	0.00721911i
$592$	−2.05999	−	3.56801i	−0.0846652	−	0.146644i
$593$	21.7148			0.891721			0.445860	−	0.895103i	$-0.352898\pi$
$593$	21.7148			0.891721			0.445860	+	0.895103i	$0.352898\pi$
$594$	−3.29222	−	0.169527i	−0.135081	−	0.00695577i
$595$	−1.90554			−0.0781197
$596$	−6.79142	−	11.7631i	−0.278187	−	0.481835i
$597$	−10.5351	−	4.04037i	−0.431173	−	0.165361i
$598$	−2.75704	+	4.77533i	−0.112744	+	0.195278i
$599$	−9.16590	+	15.8758i	−0.374509	+	0.648668i	−0.990253	−	0.139278i	$-0.955522\pi$
$599$	−9.16590	+	15.8758i	−0.374509	+	0.648668i	0.615745	+	0.787946i	$0.288855\pi$
$600$	1.04512	+	6.58565i	0.0426667	+	0.268858i
$601$	−21.2017	−	36.7225i	−0.864837	−	1.49794i	−0.867209	−	0.497945i	$-0.834088\pi$
$601$	−21.2017	−	36.7225i	−0.864837	−	1.49794i	0.00237178	−	0.999997i	$-0.499245\pi$
$602$	1.33194			0.0542857
$603$	−0.695754	+	0.226532i	−0.0283333	+	0.00922509i
$604$	−1.49081			−0.0606602
$605$	−5.68275	−	9.84281i	−0.231037	−	0.400167i
$606$	9.08731	−	7.36334i	0.369147	−	0.299115i
$607$	−18.8618	+	32.6695i	−0.765575	+	1.32602i	0.174366	+	0.984681i	$0.444212\pi$
$607$	−18.8618	+	32.6695i	−0.765575	+	1.32602i	−0.939942	+	0.341335i	$0.889121\pi$
$608$	0.827834	−	1.43385i	0.0335731	−	0.0581503i
$609$	1.70319	−	1.38007i	0.0690167	−	0.0559234i
$610$	−6.45778	−	11.1852i	−0.261468	−	0.452876i
$611$	26.4235			1.06898
$612$	−20.7808	+	6.76606i	−0.840013	+	0.273502i
$613$	26.4133			1.06682			0.533411	−	0.845856i	$-0.320910\pi$
$613$	26.4133			1.06682			0.533411	+	0.845856i	$0.320910\pi$
$614$	−7.01988	−	12.1588i	−0.283299	−	0.490689i
$615$	−2.04480	−	12.8850i	−0.0824541	−	0.519573i
$616$	0.0773688	−	0.134007i	0.00311728	−	0.00539928i
$617$	−14.2445	+	24.6722i	−0.573462	+	0.993266i	0.422745	+	0.906249i	$0.361067\pi$
$617$	−14.2445	+	24.6722i	−0.573462	+	0.993266i	−0.996207	+	0.0870169i	$0.972267\pi$
$618$	24.5589	+	9.41870i	0.987903	+	0.378876i
$619$	−12.3771	−	21.4377i	−0.497476	−	0.861653i	0.502520	−	0.864566i	$-0.332406\pi$
$619$	−12.3771	−	21.4377i	−0.497476	−	0.861653i	−0.999996	+	0.00291240i	$0.999073\pi$
$620$	8.21406			0.329885
$621$	5.18928	+	0.267212i	0.208239	+	0.0107229i
$622$	0.188631			0.00756340
$623$	−0.732752	−	1.26916i	−0.0293571	−	0.0508480i
$624$	8.91735	+	3.41994i	0.356980	+	0.136907i
$625$	−4.53504	+	7.85492i	−0.181402	+	0.314197i
$626$	10.7871	−	18.6838i	0.431140	−	0.746756i
$627$	0.285155	+	1.79686i	0.0113880	+	0.0717598i
$628$	−2.96847	−	5.14155i	−0.118455	−	0.205170i
$629$	30.0135			1.19671
$630$	0.162688	−	0.767680i	0.00648163	−	0.0305851i
$631$	18.8354			0.749825			0.374912	−	0.927060i	$-0.377673\pi$
$631$	18.8354			0.749825			0.374912	+	0.927060i	$0.377673\pi$
$632$	6.05031	+	10.4794i	0.240668	+	0.416850i
$633$	22.9751	−	18.6164i	0.913178	−	0.739937i
$634$	9.55363	−	16.5474i	0.379423	−	0.657180i
$635$	0.495462	−	0.858165i	0.0196618	−	0.0340553i
$636$	−13.3840	+	10.8449i	−0.530709	+	0.430027i
$637$	−19.1353	−	33.1432i	−0.758167	−	1.31318i
$638$	−3.29211			−0.130336
$639$	−15.7022	−	14.1210i	−0.621167	−	0.558618i
$640$	1.07247			0.0423931
$641$	6.25470	+	10.8335i	0.247046	+	0.427896i	0.962705	−	0.270554i	$-0.0872068\pi$
$641$	6.25470	+	10.8335i	0.247046	+	0.427896i	−0.715659	+	0.698450i	$0.753874\pi$
$642$	0.525606	+	3.31203i	0.0207440	+	0.130715i
$643$	20.7317	−	35.9083i	0.817578	−	1.41609i	−0.0898837	−	0.995952i	$-0.528650\pi$
$643$	20.7317	−	35.9083i	0.817578	−	1.41609i	0.907462	−	0.420135i	$-0.138017\pi$
$644$	−0.121951	+	0.211225i	−0.00480553	+	0.00832341i
$645$	−9.47148	−	3.63246i	−0.372939	−	0.143028i
$646$	6.03064	+	10.4454i	0.237272	+	0.410968i
$647$	12.1904			0.479256			0.239628	−	0.970865i	$-0.422975\pi$
$647$	12.1904			0.479256			0.239628	+	0.970865i	$0.422975\pi$
$648$	−0.951641	−	8.94955i	−0.0373840	−	0.351571i
$649$	6.94513			0.272620
$650$	10.6141	+	18.3841i	0.416318	+	0.721084i
$651$	3.02099	+	1.15860i	0.118402	+	0.0454090i
$652$	−7.09996	+	12.2975i	−0.278056	+	0.481607i
$653$	1.31204	−	2.27253i	0.0513443	−	0.0889309i	−0.839211	−	0.543806i	$-0.816983\pi$
$653$	1.31204	−	2.27253i	0.0513443	−	0.0889309i	0.890555	+	0.454875i	$0.150316\pi$
$654$	−3.76392	−	23.7178i	−0.147181	−	0.927438i
$655$	−5.47724	−	9.48685i	−0.214013	−	0.370682i
$656$	7.02327			0.274213
$657$	−0.213556	−	0.192051i	−0.00833160	−	0.00749264i
$658$	1.16878			0.0455636
$659$	2.38826	+	4.13659i	0.0930335	+	0.161139i	0.908786	−	0.417262i	$-0.137010\pi$
$659$	2.38826	+	4.13659i	0.0930335	+	0.161139i	−0.815753	+	0.578401i	$0.803677\pi$
$660$	−0.915636	+	0.741929i	−0.0356411	+	0.0288795i
$661$	16.2194	−	28.0928i	0.630861	−	1.09268i	−0.356515	−	0.934290i	$-0.616035\pi$
$661$	16.2194	−	28.0928i	0.630861	−	1.09268i	0.987376	−	0.158394i	$-0.0506315\pi$
$662$	2.14806	−	3.72054i	0.0834865	−	0.144603i
$663$	−54.0567	+	43.8015i	−2.09939	+	1.70111i
$664$	4.66982	+	8.08836i	0.181224	+	0.313889i
$665$	−0.433084			−0.0167943
$666$	−2.56243	+	12.0914i	−0.0992920	+	0.468533i
$667$	5.18911			0.200923
$668$	−5.55335	−	9.61868i	−0.214865	−	0.372158i
$669$	−6.08005	−	38.3126i	−0.235068	−	1.48125i
$670$	−0.130788	+	0.226532i	−0.00505279	+	0.00875169i
$671$	−3.82015	+	6.61669i	−0.147475	+	0.255434i
$672$	0.394436	+	0.151272i	0.0152157	+	0.00583546i
$673$	10.7944	+	18.6964i	0.416092	+	0.720693i	0.995542	−	0.0943146i	$-0.0300660\pi$
$673$	10.7944	+	18.6964i	0.416092	+	0.720693i	−0.579450	+	0.815008i	$0.696733\pi$
$674$	−32.1246			−1.23739
$675$	10.8798	−	16.7869i	0.418762	−	0.646127i
$676$	17.4050			0.669425
$677$	21.8521	+	37.8489i	0.839844	+	1.45465i	0.890024	+	0.455913i	$0.150687\pi$
$677$	21.8521	+	37.8489i	0.839844	+	1.45465i	−0.0501801	+	0.998740i	$0.515980\pi$
$678$	18.2874	+	7.01351i	0.702325	+	0.269352i
$679$	1.12062	−	1.94097i	0.0430053	−	0.0744874i
$680$	−3.90639	+	6.76606i	−0.149803	+	0.259467i
$681$	3.49753	+	22.0392i	0.134026	+	0.844543i
$682$	−2.42954	−	4.20809i	−0.0930321	−	0.161136i
$683$	12.8281			0.490854			0.245427	−	0.969415i	$-0.421072\pi$
$683$	12.8281			0.490854			0.245427	+	0.969415i	$0.421072\pi$
$684$	−4.72297	+	1.53776i	−0.180587	+	0.0587978i
$685$	5.19624			0.198538
$686$	−1.70005	−	2.94458i	−0.0649083	−	0.112425i
$687$	−13.5546	+	10.9831i	−0.517139	+	0.419032i
$688$	2.73048	−	4.72934i	0.104099	−	0.180304i
$689$	−27.4203	+	47.4933i	−1.04463	+	1.80935i
$690$	1.44325	−	1.16945i	0.0549435	−	0.0445201i
$691$	5.34173	+	9.25215i	0.203209	+	0.351968i	0.949561	−	0.313583i	$-0.101530\pi$
$691$	5.34173	+	9.25215i	0.203209	+	0.351968i	−0.746352	+	0.665552i	$0.768196\pi$
$692$	−14.4104			−0.547802
$693$	−0.441405	+	0.143718i	−0.0167676	+	0.00545940i
$694$	30.7773			1.16829
$695$	3.53302	+	6.11937i	0.134015	+	0.232121i
$696$	−1.40870	−	8.87671i	−0.0533966	−	0.336471i
$697$	−25.5817	+	44.3088i	−0.968976	+	1.67832i
$698$	−1.78306	+	3.08835i	−0.0674899	+	0.116896i
$699$	−3.14996	−	1.20806i	−0.119142	−	0.0456930i
$700$	0.469486	+	0.813174i	0.0177449	+	0.0307351i
$701$	−32.8988			−1.24257			−0.621285	−	0.783585i	$-0.713389\pi$
$701$	−32.8988			−1.24257			−0.621285	+	0.783585i	$0.713389\pi$
$702$	−13.0310	−	25.5172i	−0.491824	−	0.963086i
$703$	6.82133			0.257271
$704$	−0.317214	−	0.549430i	−0.0119554	−	0.0207074i
$705$	−8.31123	−	3.18748i	−0.313019	−	0.120048i
$706$	−4.61596	+	7.99509i	−0.173724	+	0.300899i
$707$	0.823499	−	1.42634i	0.0309709	−	0.0536431i
$708$	2.97183	+	18.7266i	0.111688	+	0.703787i
$709$	1.01650	+	1.76063i	0.0381754	+	0.0661217i	0.884482	−	0.466575i	$-0.154512\pi$
$709$	1.01650	+	1.76063i	0.0381754	+	0.0661217i	−0.846306	+	0.532696i	$0.821179\pi$
$710$	−7.54939			−0.283323
$711$	7.52599	−	35.5132i	0.282247	−	1.33185i
$712$	−6.00860			−0.225182
$713$	3.82951	+	6.63290i	0.143416	+	0.248404i
$714$	−2.39106	+	1.93745i	−0.0894831	+	0.0725071i
$715$	−1.87590	+	3.24915i	−0.0701547	+	0.121511i
$716$	−4.32783	+	7.49603i	−0.161739	+	0.280140i
$717$	9.23751	−	7.48504i	0.344981	−	0.279534i
$718$	16.2191	+	28.0923i	0.605291	+	1.04839i
$719$	−31.9696			−1.19226			−0.596132	−	0.802886i	$-0.703297\pi$
$719$	−31.9696			−1.19226			−0.596132	+	0.802886i	$0.703297\pi$
$720$	−2.39231	−	2.15141i	−0.0891561	−	0.0801784i
$721$	3.70390			0.137940
$722$	−8.12938	−	14.0805i	−0.302544	−	0.524022i
$723$	2.84269	+	17.9128i	0.105721	+	0.666183i
$724$	8.87730	−	15.3759i	0.329922	−	0.571442i
$725$	9.98854	−	17.3007i	0.370965	−	0.642530i
$726$	−17.1383	−	6.57278i	−0.636060	−	0.243939i
$727$	10.7326	+	18.5894i	0.398050	+	0.689442i	0.993485	−	0.113961i	$-0.0363538\pi$
$727$	10.7326	+	18.5894i	0.398050	+	0.689442i	−0.595436	+	0.803403i	$0.703020\pi$
$728$	1.34489			0.0498449
$729$	−15.8303	+	21.8724i	−0.586308	+	0.810088i
$730$	−0.102675			−0.00380016
$731$	19.8912	+	34.4525i	0.735701	+	1.27427i
$732$	−19.4756	−	7.46920i	−0.719840	−	0.276069i
$733$	2.35869	−	4.08538i	0.0871204	−	0.150897i	−0.819172	−	0.573547i	$-0.805567\pi$
$733$	2.35869	−	4.08538i	0.0871204	−	0.150897i	0.906293	+	0.422650i	$0.138900\pi$
$734$	−10.6354	+	18.4210i	−0.392559	+	0.679931i
$735$	2.02070	+	12.7332i	0.0745347	+	0.469670i
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	0.154738			0.00569983
$738$	−15.6665	−	14.0889i	−0.576691	−	0.518621i
$739$	−49.1972			−1.80975			−0.904875	−	0.425678i	$-0.860036\pi$
$739$	−49.1972			−1.80975			−0.904875	+	0.425678i	$0.860036\pi$
$740$	2.20928	+	3.82658i	0.0812147	+	0.140668i
$741$	−12.2858	+	9.95501i	−0.451329	+	0.365706i
$742$	−1.21287	+	2.10074i	−0.0445257	+	0.0771207i
$743$	21.0439	−	36.4491i	0.772026	−	1.33719i	−0.164425	−	0.986390i	$-0.552577\pi$
$743$	21.0439	−	36.4491i	0.772026	−	1.33719i	0.936451	−	0.350799i	$-0.114090\pi$
$744$	10.3069	−	8.35158i	0.377870	−	0.306184i
$745$	7.28359	+	12.6155i	0.266850	+	0.462198i
$746$	0.756221			0.0276872
$747$	5.80879	−	27.4102i	0.212533	−	1.00289i
$748$	4.62170			0.168986
$749$	0.236112	+	0.408958i	0.00862735	+	0.0149430i
$750$	−2.57659	−	16.2360i	−0.0940836	−	0.592854i
$751$	15.9084	−	27.5542i	0.580506	−	1.00547i	−0.414913	−	0.909861i	$-0.636188\pi$
$751$	15.9084	−	27.5542i	0.580506	−	1.00547i	0.995419	−	0.0956050i	$-0.0304786\pi$
$752$	2.39600	−	4.15000i	0.0873733	−	0.151335i
$753$	−35.7484	−	13.7101i	−1.30274	−	0.499622i
$754$	−14.3066	−	24.7797i	−0.521014	−	0.902424i
$755$	1.59885			0.0581880
$756$	−0.576393	−	1.12869i	−0.0209632	−	0.0410500i
$757$	−51.0385			−1.85502			−0.927512	−	0.373793i	$-0.878057\pi$
$757$	−51.0385			−1.85502			−0.927512	+	0.373793i	$0.878057\pi$
$758$	−14.2555	−	24.6913i	−0.517784	−	0.896828i
$759$	−1.02599	−	0.393484i	−0.0372412	−	0.0142826i
$760$	−0.887827	+	1.53776i	−0.0322049	+	0.0557805i
$761$	−1.17926	+	2.04254i	−0.0427482	+	0.0740421i	−0.886608	−	0.462522i	$-0.846945\pi$
$761$	−1.17926	+	2.04254i	−0.0427482	+	0.0740421i	0.843860	+	0.536564i	$0.180278\pi$
$762$	−0.250831	−	1.58057i	−0.00908665	−	0.0572582i
$763$	−1.69082	−	2.92859i	−0.0612119	−	0.106022i
$764$	5.41399			0.195871
$765$	22.2868	−	7.25639i	0.805779	−	0.262355i
$766$	29.7147			1.07364
$767$	30.1815	+	52.2760i	1.08979	+	1.88758i
$768$	1.34572	−	1.09042i	0.0485597	−	0.0393473i
$769$	−17.2314	+	29.8456i	−0.621379	+	1.07626i	0.367850	+	0.929885i	$0.380094\pi$
$769$	−17.2314	+	29.8456i	−0.621379	+	1.07626i	−0.989229	+	0.146375i	$0.953239\pi$
$770$	−0.0829756	+	0.143718i	−0.00299023	+	0.00517924i
$771$	34.7804	−	28.1821i	1.25258	−	1.01495i
$772$	−7.81654	−	13.5386i	−0.281323	−	0.487267i
$773$	−15.1379			−0.544474			−0.272237	−	0.962230i	$-0.587763\pi$
$773$	−15.1379			−0.544474			−0.272237	+	0.962230i	$0.587763\pi$
$774$	−15.5780	+	5.07207i	−0.559939	+	0.182312i
$775$	29.4858			1.05916
$776$	−4.59455	−	7.95800i	−0.164935	−	0.285676i
$777$	0.272794	+	1.71897i	0.00978644	+	0.0616678i
$778$	−1.44866	+	2.50916i	−0.0519371	+	0.0899576i
$779$	−5.81410	+	10.0703i	−0.208312	+	0.360807i
$780$	−9.56359	−	3.66778i	−0.342431	−	0.131328i
$781$	2.23295	+	3.86758i	0.0799012	+	0.138393i
$782$	−7.28484			−0.260505
$783$	−14.6647	+	22.6268i	−0.524073	+	0.808615i
$784$	−6.94051			−0.247875
$785$	3.18360	+	5.51415i	0.113627	+	0.196809i
$786$	−16.5185	−	6.33508i	−0.589194	−	0.225965i
$787$	13.6703	−	23.6776i	0.487292	−	0.844015i	−0.512601	−	0.858627i	$-0.671318\pi$
$787$	13.6703	−	23.6776i	0.487292	−	0.844015i	0.999893	+	0.0146118i	$0.00465125\pi$
$788$	−0.141482	+	0.245054i	−0.00504009	+	0.00872970i
$789$	8.23034	+	51.8622i	0.293008	+	1.84634i
$790$	−6.48877	−	11.2389i	−0.230860	−	0.399862i
$791$	2.75806			0.0980654
$792$	−0.394582	+	1.86193i	−0.0140209	+	0.0661608i
$793$	−66.4051			−2.35811
$794$	−3.65321	−	6.32755i	−0.129648	−	0.224556i
$795$	14.3539	−	11.6308i	0.509080	−	0.412501i
$796$	−3.25721	+	5.64165i	−0.115449	+	0.199963i
$797$	13.6342	−	23.6151i	0.482947	−	0.836489i	−0.516861	−	0.856069i	$-0.672900\pi$
$797$	13.6342	−	23.6151i	0.482947	−	0.836489i	0.999808	+	0.0195803i	$0.00623299\pi$
$798$	−0.543430	+	0.440334i	−0.0192372	+	0.0155877i
$799$	17.4545	+	30.2321i	0.617496	+	1.06953i
$800$	3.84981			0.136111
$801$	13.4031	+	12.0535i	0.473576	+	0.425888i
$802$	−16.8854			−0.596243
$803$	0.0303690	+	0.0526007i	0.00107170	+	0.00185624i
$804$	0.0662125	+	0.417228i	0.00233513	+	0.0147145i
$805$	0.130788	−	0.226532i	0.00460968	−	0.00798420i
$806$	21.1162	−	36.5743i	0.743787	−	1.28828i
$807$	19.9469	+	7.64996i	0.702166	+	0.269291i
$808$	−3.37636	−	5.84803i	−0.118780	−	0.205733i
$809$	−30.6978			−1.07928			−0.539639	−	0.841897i	$-0.681439\pi$
$809$	−30.6978			−1.07928			−0.539639	+	0.841897i	$0.681439\pi$
$810$	1.02061	+	9.59811i	0.0358604	+	0.337243i
$811$	26.0002			0.912992			0.456496	−	0.889726i	$-0.349104\pi$
$811$	26.0002			0.912992			0.456496	+	0.889726i	$0.349104\pi$
$812$	−0.632815	−	1.09607i	−0.0222074	−	0.0384644i
$813$	15.1637	+	5.81551i	0.531814	+	0.203959i
$814$	1.30692	−	2.26364i	0.0458074	−	0.0793407i
$815$	7.61449	−	13.1887i	0.266724	−	0.461980i
$816$	1.97764	+	12.4618i	0.0692311	+	0.436249i
$817$	4.52078	+	7.83022i	0.158162	+	0.273945i
$818$	−34.8858			−1.21975
$819$	−2.99998	−	2.69790i	−0.104828	−	0.0942721i
$820$	−7.53224			−0.263037
$821$	5.46515	+	9.46593i	0.190735	+	0.330363i	0.945494	−	0.325639i	$-0.105579\pi$
$821$	5.46515	+	9.46593i	0.190735	+	0.330363i	−0.754759	+	0.656002i	$0.772246\pi$
$822$	6.52019	−	5.28323i	0.227418	−	0.184274i
$823$	25.8414	−	44.7586i	0.900774	−	1.56019i	0.0742833	−	0.997237i	$-0.476333\pi$
$823$	25.8414	−	44.7586i	0.900774	−	1.56019i	0.826491	−	0.562950i	$-0.190334\pi$
$824$	7.59304	−	13.1515i	0.264516	−	0.458155i
$825$	−3.28683	+	2.66328i	−0.114433	+	0.0927234i
$826$	1.33500	+	2.31229i	0.0464507	+	0.0804550i
$827$	19.9784			0.694718			0.347359	−	0.937732i	$-0.387078\pi$
$827$	19.9784			0.694718			0.347359	+	0.937732i	$0.387078\pi$
$828$	0.621951	−	2.93482i	0.0216143	−	0.101992i
$829$	21.6429			0.751690			0.375845	−	0.926683i	$-0.377352\pi$
$829$	21.6429			0.751690			0.375845	+	0.926683i	$0.377352\pi$
$830$	−5.00824	−	8.67452i	−0.173838	−	0.301097i
$831$	−0.0967392	−	0.609588i	−0.00335585	−	0.0211464i
$832$	2.75704	−	4.77533i	0.0955831	−	0.165555i
$833$	25.2803	−	43.7867i	0.875910	−	1.51712i
$834$	10.6550	+	4.08636i	0.368953	+	0.141499i
$835$	5.95579	+	10.3157i	0.206109	+	0.356991i
$836$	1.05040			0.0363289
$837$	−39.7448	−	2.04658i	−1.37378	−	0.0707403i
$838$	−19.1751			−0.662394
$839$	4.46956	+	7.74150i	0.154306	+	0.267266i	0.932806	−	0.360378i	$-0.117352\pi$
$839$	4.46956	+	7.74150i	0.154306	+	0.267266i	−0.778500	+	0.627645i	$0.784019\pi$
$840$	−0.423021	−	0.162235i	−0.0145956	−	0.00559764i
$841$	1.03658	−	1.79542i	0.0357443	−	0.0619109i
$842$	8.99188	−	15.5744i	0.309881	−	0.536729i
$843$	7.36206	+	46.3909i	0.253563	+	1.59779i
$844$	−8.53633	−	14.7854i	−0.293833	−	0.508933i
$845$	−18.6664			−0.642143
$846$	−13.6697	+	4.45075i	−0.469974	+	0.153020i
$847$	−2.58474			−0.0888128
$848$	4.97277	+	8.61310i	0.170766	+	0.295775i
$849$	−6.22989	+	5.04800i	−0.213809	+	0.173247i
$850$	−14.0226	+	24.2879i	−0.480972	+	0.833068i
$851$	−2.05999	+	3.56801i	−0.0706156	+	0.122310i
$852$	−9.47290	+	7.67577i	−0.324536	+	0.262968i
$853$	14.8203	+	25.6695i	0.507438	+	0.878908i	0.999963	+	0.00861009i	$0.00274071\pi$
$853$	14.8203	+	25.6695i	0.507438	+	0.878908i	−0.492525	+	0.870298i	$0.663926\pi$
$854$	−2.93726			−0.100511
$855$	5.06524	−	1.64920i	0.173228	−	0.0564015i
$856$	1.93613			0.0661756
$857$	−4.79864	−	8.31149i	−0.163918	−	0.283915i	0.772352	−	0.635195i	$-0.219080\pi$
$857$	−4.79864	−	8.31149i	−0.163918	−	0.283915i	−0.936271	+	0.351279i	$0.885747\pi$
$858$	0.949687	+	5.98431i	0.0324218	+	0.204301i
$859$	−4.99335	+	8.64873i	−0.170371	+	0.295091i	−0.938550	−	0.345145i	$-0.887830\pi$
$859$	−4.99335	+	8.64873i	−0.170371	+	0.295091i	0.768179	+	0.640235i	$0.221163\pi$
$860$	−2.92836	+	5.07207i	−0.0998563	+	0.172956i
$861$	−2.77023	−	1.06243i	−0.0944092	−	0.0362074i
$862$	−2.31977	−	4.01795i	−0.0790115	−	0.136852i
$863$	−14.0266			−0.477472			−0.238736	−	0.971084i	$-0.576733\pi$
$863$	−14.0266			−0.477472			−0.238736	+	0.971084i	$0.576733\pi$
$864$	−5.18928	−	0.267212i	−0.176543	−	0.00909075i
$865$	15.4547			0.525477
$866$	5.42586	+	9.39786i	0.184378	+	0.319352i
$867$	−58.3306	−	22.3707i	−1.98101	−	0.759748i
$868$	0.934021	−	1.61777i	0.0317028	−	0.0549108i
$869$	−3.83848	+	6.64845i	−0.130212	+	0.225533i
$870$	1.51079	+	9.52001i	0.0512205	+	0.322758i
$871$	0.672445	+	1.16471i	0.0227849	+	0.0394646i
$872$	−13.8648			−0.469522
$873$	−5.71517	+	26.9684i	−0.193429	+	0.912742i
$874$	−1.65567			−0.0560038
$875$	−1.15745	−	2.00476i	−0.0391290	−	0.0677734i
$876$	−0.128835	+	0.104394i	−0.00435294	+	0.00352714i
$877$	14.4747	−	25.0709i	0.488775	−	0.846584i	−0.511141	−	0.859497i	$-0.670777\pi$
$877$	14.4747	−	25.0709i	0.488775	−	0.846584i	0.999917	+	0.0129129i	$0.00411043\pi$
$878$	−16.4402	+	28.4752i	−0.554829	+	0.960991i
$879$	5.78213	−	4.68519i	0.195027	−	0.158028i
$880$	0.340202	+	0.589247i	0.0114682	+	0.0198635i
$881$	8.81103			0.296851			0.148426	−	0.988924i	$-0.452579\pi$
$881$	8.81103			0.296851			0.148426	+	0.988924i	$0.452579\pi$
$882$	15.4819	+	13.9229i	0.521302	+	0.468809i
$883$	−12.0696			−0.406175			−0.203088	−	0.979161i	$-0.565098\pi$
$883$	−12.0696			−0.406175			−0.203088	+	0.979161i	$0.565098\pi$
$884$	20.0846	+	34.7875i	0.675518	+	1.17003i
$885$	−3.18720	−	20.0837i	−0.107137	−	0.675105i
$886$	−18.0418	+	31.2493i	−0.606126	+	1.04984i
$887$	27.4426	−	47.5320i	0.921432	−	1.59597i	0.124231	−	0.992253i	$-0.460354\pi$
$887$	27.4426	−	47.5320i	0.921432	−	1.59597i	0.797201	−	0.603714i	$-0.206313\pi$
$888$	6.66283	+	2.55530i	0.223590	+	0.0857501i
$889$	−0.112678	−	0.195164i	−0.00377910	−	0.00654559i
$890$	6.44404			0.216005
$891$	4.61528	−	3.36178i	0.154618	−	0.112624i
$892$	−22.3966			−0.749893
$893$	3.96699	+	6.87102i	0.132750	+	0.229930i
$894$	21.9661	+	8.42434i	0.734657	+	0.281752i
$895$	4.64147	−	8.03926i	0.155147	−	0.268723i
$896$	0.121951	−	0.211225i	0.00407408	−	0.00705652i
$897$	−1.49692	−	9.43262i	−0.0499807	−	0.314946i
$898$	−13.5424	−	23.4561i	−0.451915	−	0.782739i
$899$	−39.7435			−1.32552
$900$	−8.58760	−	7.72286i	−0.286253	−	0.257429i
$901$	−72.4518			−2.41372
$902$	2.22788	+	3.85880i	0.0741802	+	0.128484i
$903$	−1.79242	+	1.45238i	−0.0596480	+	0.0483320i
$904$	5.65406	−	9.79311i	0.188051	−	0.325714i
$905$	−9.52064	+	16.4902i	−0.316477	+	0.548154i
$906$	2.00622	−	1.62561i	0.0666522	−	0.0540074i
$907$	20.1788	+	34.9508i	0.670027	+	1.16052i	0.977896	+	0.209092i	$0.0670510\pi$
$907$	20.1788	+	34.9508i	0.670027	+	1.16052i	−0.307869	+	0.951429i	$0.599616\pi$
$908$	12.8836			0.427556
$909$	−4.19986	+	19.8180i	−0.139301	+	0.657323i
$910$	−1.44235			−0.0478135
$911$	−23.6772	−	41.0102i	−0.784462	−	1.35873i	−0.929320	−	0.369276i	$-0.879606\pi$
$911$	−23.6772	−	41.0102i	−0.784462	−	1.35873i	0.144858	−	0.989453i	$-0.453728\pi$
$912$	0.449469	+	2.83226i	0.0148834	+	0.0937855i
$913$	−2.96266	+	5.13148i	−0.0980498	+	0.169827i
$914$	16.8341	−	29.1576i	0.556824	−	0.964447i
$915$	20.8870	+	8.01049i	0.690503	+	0.264818i
$916$	5.03616	+	8.72289i	0.166399	+	0.288212i
$917$	−2.49127			−0.0822689
$918$	20.5873	−	31.7651i	0.679484	−	1.04841i
$919$	13.9197			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$919$	13.9197			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$920$	−0.536235	−	0.928786i	−0.0176791	−	0.0306212i
$921$	22.7051	+	8.70774i	0.748157	+	0.286930i
$922$	7.66607	−	13.2780i	0.252469	−	0.437288i
$923$	−19.4075	+	33.6148i	−0.638806	+	1.10644i
$924$	0.0420070	+	0.264701i	0.00138193	+	0.00870802i
$925$	7.93058	+	13.7362i	0.260756	+	0.451642i
$926$	−35.7893			−1.17611
$927$	−43.3199	+	14.1046i	−1.42281	+	0.463256i
$928$	−5.18911			−0.170341
$929$	−14.3450	−	24.8463i	−0.470645	−	0.815181i	0.528792	−	0.848752i	$-0.322645\pi$
$929$	−14.3450	−	24.8463i	−0.470645	−	0.815181i	−0.999436	+	0.0335710i	$0.989312\pi$
$930$	−11.0539	+	8.95681i	−0.362471	+	0.293705i
$931$	5.74559	−	9.95166i	0.188304	−	0.326152i
$932$	−0.973895	+	1.68684i	−0.0319010	+	0.0552541i
$933$	−0.253845	+	0.205687i	−0.00831051	+	0.00673391i
$934$	−1.72810	−	2.99316i	−0.0565452	−	0.0979392i
$935$	−4.95664			−0.162099
$936$	−15.7295	+	5.12140i	−0.514134	+	0.167398i
$937$	35.6801			1.16562			0.582808	−	0.812610i	$-0.301954\pi$
$937$	35.6801			1.16562			0.582808	+	0.812610i	$0.301954\pi$
$938$	0.0297439	+	0.0515179i	0.000971172	+	0.00168212i
$939$	5.85681	+	36.9058i	0.191130	+	1.20438i
$940$	−2.56964	+	4.45075i	−0.0838124	+	0.145167i
$941$	17.8310	−	30.8841i	0.581272	−	1.00679i	−0.414056	−	0.910251i	$-0.635888\pi$
$941$	17.8310	−	30.8841i	0.581272	−	1.00679i	0.995329	−	0.0965422i	$-0.0307783\pi$
$942$	9.60121	+	3.68221i	0.312824	+	0.119973i
$943$	−3.51163	−	6.08233i	−0.114355	−	0.198068i
$944$	10.9471			0.356297
$945$	0.618164	+	1.21049i	0.0201089	+	0.0393771i
$946$	3.46459			0.112643
$947$	17.3529	+	30.0561i	0.563894	+	0.976693i	0.997152	+	0.0754228i	$0.0240307\pi$
$947$	17.3529	+	30.0561i	0.563894	+	0.976693i	−0.433258	+	0.901270i	$0.642636\pi$
$948$	−19.5691	−	7.50505i	−0.635575	−	0.243753i
$949$	−0.263950	+	0.457175i	−0.00856818	+	0.0148405i
$950$	−3.18700	+	5.52005i	−0.103400	+	0.179094i
$951$	5.18709	+	32.6857i	0.168203	+	1.05991i
$952$	0.888391	+	1.53874i	0.0287929	+	0.0498708i
$953$	−36.9247			−1.19611			−0.598054	−	0.801456i	$-0.704059\pi$
$953$	−36.9247			−1.19611			−0.598054	+	0.801456i	$0.704059\pi$
$954$	6.18564	−	29.1884i	0.200267	−	0.945009i
$955$	−5.80634			−0.187889
$956$	−3.43217	−	5.94469i	−0.111004	−	0.192265i
$957$	4.43028	−	3.58980i	0.143210	−	0.116042i
$958$	14.2875	−	24.7467i	0.461609	−	0.799531i
$959$	0.590865	−	1.02341i	0.0190800	−	0.0330476i
$960$	−1.44325	+	1.16945i	−0.0465807	+	0.0377437i
$961$	−13.8303	−	23.9547i	−0.446138	−	0.772733i
$962$	22.7179			0.732455
$963$	−4.31884	−	3.88395i	−0.139173	−	0.125158i
$964$	10.4714			0.337260
$965$	8.38300	+	14.5198i	0.269858	+	0.467408i
$966$	−0.0662125	−	0.417228i	−0.00213035	−	0.0134241i
$967$	−4.22863	+	7.32420i	−0.135984	+	0.235530i	−0.925973	−	0.377590i	$-0.876753\pi$
$967$	−4.22863	+	7.32420i	−0.135984	+	0.235530i	0.789989	+	0.613121i	$0.210086\pi$
$968$	−5.29875	+	9.17771i	−0.170308	+	0.294983i
$969$	−19.5055	−	7.48065i	−0.626606	−	0.240313i
$970$	4.92752	+	8.53471i	0.158213	+	0.274033i
$971$	−29.2898			−0.939953			−0.469977	−	0.882679i	$-0.655738\pi$
$971$	−29.2898			−0.939953			−0.469977	+	0.882679i	$0.655738\pi$
$972$	11.0394	+	11.0059i	0.354090	+	0.353016i
$973$	1.60696			0.0515168
$974$	−7.13777	−	12.3630i	−0.228709	−	0.396135i
$975$	−34.3301	−	13.1661i	−1.09944	−	0.421653i
$976$	−6.02141	+	10.4294i	−0.192741	+	0.333837i
$977$	−8.40274	+	14.5540i	−0.268827	+	0.465623i	−0.968559	−	0.248783i	$-0.919969\pi$
$977$	−8.40274	+	14.5540i	−0.268827	+	0.465623i	0.699732	+	0.714406i	$0.253303\pi$
$978$	−3.85489	−	24.2910i	−0.123266	−	0.776741i
$979$	−1.90601	−	3.30131i	−0.0609163	−	0.105510i
$980$	7.44349			0.237773
$981$	30.9276	+	27.8133i	0.987443	+	0.888011i
$982$	−14.1929			−0.452915
$983$	−21.4129	−	37.0883i	−0.682967	−	1.18293i	−0.974071	−	0.226242i	$-0.927356\pi$
$983$	−21.4129	−	37.0883i	−0.682967	−	1.18293i	0.291104	−	0.956691i	$-0.405977\pi$
$984$	−9.45139	+	7.65834i	−0.301299	+	0.244139i
$985$	0.151735	−	0.262813i	0.00483469	−	0.00837393i
$986$	18.9009	−	32.7373i	0.601928	−	1.04257i
$987$	−1.57285	+	1.27446i	−0.0500644	+	0.0405666i
$988$	4.56474	+	7.90636i	0.145224	+	0.251535i
$989$	−5.46097			−0.173649
$990$	0.423178	−	1.99686i	0.0134495	−	0.0634645i
$991$	57.4079			1.82362			0.911811	−	0.410610i	$-0.134684\pi$
$991$	57.4079			1.82362			0.911811	+	0.410610i	$0.134684\pi$
$992$	−3.82951	−	6.63290i	−0.121587	−	0.210595i
$993$	1.16628	+	7.34912i	0.0370107	+	0.233217i
$994$	−0.858441	+	1.48686i	−0.0272281	+	0.0471605i
$995$	3.49326	−	6.05050i	0.110744	−	0.191814i
$996$	−15.1040	−	5.79263i	−0.478590	−	0.183546i
$997$	−9.93587	−	17.2094i	−0.314672	−	0.545028i	0.664695	−	0.747114i	$-0.268561\pi$
$997$	−9.93587	−	17.2094i	−0.314672	−	0.545028i	−0.979368	+	0.202086i	$0.935228\pi$
$998$	32.6245			1.03271
$999$	−9.73646	−	19.0659i	−0.308048	−	0.603217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.d.139.1	✓	10
3.2	odd	2		1242.2.e.b.415.2		10
9.2	odd	6		1242.2.e.b.829.2		10
9.4	even	3		3726.2.a.r.1.2		5
9.5	odd	6		3726.2.a.u.1.4		5
9.7	even	3	inner	414.2.e.d.277.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.d.139.1	✓	10	1.1	even	1	trivial
414.2.e.d.277.1	yes	10	9.7	even	3	inner
1242.2.e.b.415.2		10	3.2	odd	2
1242.2.e.b.829.2		10	9.2	odd	6
3726.2.a.r.1.2		5	9.4	even	3
3726.2.a.u.1.4		5	9.5	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.61720 - 0.620220i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.536235 - 0.928786i) q^{5} +(-0.271473 - 1.71064i) q^{6} +(-0.121951 - 0.211225i) q^{7} -1.00000 q^{8} +(2.23065 + 2.00604i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.61720 - 0.620220i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.536235 - 0.928786i) q^{5} +(-0.271473 - 1.71064i) q^{6} +(-0.121951 - 0.211225i) q^{7} -1.00000 q^{8} +(2.23065 + 2.00604i) q^{9} +1.07247 q^{10} +(-0.317214 - 0.549430i) q^{11} +(1.34572 - 1.09042i) q^{12} +(2.75704 - 4.77533i) q^{13} +(0.121951 - 0.211225i) q^{14} +(-1.44325 + 1.16945i) q^{15} +(-0.500000 - 0.866025i) q^{16} +7.28484 q^{17} +(-0.621951 + 2.93482i) q^{18} +1.65567 q^{19} +(0.536235 + 0.928786i) q^{20} +(0.0662125 + 0.417228i) q^{21} +(0.317214 - 0.549430i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(1.61720 + 0.620220i) q^{24} +(1.92490 + 3.33403i) q^{25} +5.51408 q^{26} +(-2.36323 - 4.62765i) q^{27} +0.243901 q^{28} +(-2.59455 - 4.49390i) q^{29} +(-1.73439 - 0.665167i) q^{30} +(3.82951 - 6.63290i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.172230 + 1.08528i) q^{33} +(3.64242 + 6.30886i) q^{34} -0.261577 q^{35} +(-2.85261 + 0.928786i) q^{36} +4.11999 q^{37} +(0.827834 + 1.43385i) q^{38} +(-7.42043 + 6.01268i) q^{39} +(-0.536235 + 0.928786i) q^{40} +(-3.51163 + 6.08233i) q^{41} +(-0.328224 + 0.265956i) q^{42} +(2.73048 + 4.72934i) q^{43} +0.634427 q^{44} +(3.05933 - 0.996094i) q^{45} -1.00000 q^{46} +(2.39600 + 4.15000i) q^{47} +(0.271473 + 1.71064i) q^{48} +(3.47026 - 6.01066i) q^{49} +(-1.92490 + 3.33403i) q^{50} +(-11.7810 - 4.51820i) q^{51} +(2.75704 + 4.77533i) q^{52} -9.94555 q^{53} +(2.82605 - 4.36044i) q^{54} -0.680404 q^{55} +(0.121951 + 0.211225i) q^{56} +(-2.67754 - 1.02688i) q^{57} +(2.59455 - 4.49390i) q^{58} +(-5.47354 + 9.48045i) q^{59} +(-0.291146 - 1.83461i) q^{60} +(-6.02141 - 10.4294i) q^{61} +7.65902 q^{62} +(0.151694 - 0.715806i) q^{63} +1.00000 q^{64} +(-2.95684 - 5.12140i) q^{65} +(-0.853765 + 0.691795i) q^{66} +(-0.121951 + 0.211225i) q^{67} +(-3.64242 + 6.30886i) q^{68} +(1.34572 - 1.09042i) q^{69} +(-0.130788 - 0.226532i) q^{70} -7.03926 q^{71} +(-2.23065 - 2.00604i) q^{72} -0.0957368 q^{73} +(2.05999 + 3.56801i) q^{74} +(-1.04512 - 6.58565i) q^{75} +(-0.827834 + 1.43385i) q^{76} +(-0.0773688 + 0.134007i) q^{77} +(-8.91735 - 3.41994i) q^{78} +(-6.05031 - 10.4794i) q^{79} -1.07247 q^{80} +(0.951641 + 8.94955i) q^{81} -7.02327 q^{82} +(-4.66982 - 8.08836i) q^{83} +(-0.394436 - 0.151272i) q^{84} +(3.90639 - 6.76606i) q^{85} +(-2.73048 + 4.72934i) q^{86} +(1.40870 + 8.87671i) q^{87} +(0.317214 + 0.549430i) q^{88} +6.00860 q^{89} +(2.39231 + 2.15141i) q^{90} -1.34489 q^{91} +(-0.500000 - 0.866025i) q^{92} +(-10.3069 + 8.35158i) q^{93} +(-2.39600 + 4.15000i) q^{94} +(0.887827 - 1.53776i) q^{95} +(-1.34572 + 1.09042i) q^{96} +(4.59455 + 7.95800i) q^{97} +6.94051 q^{98} +(0.394582 - 1.86193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9	\( 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9} - 2 q^{10} - 11 q^{11} + 6 q^{13} - 5 q^{14} + 9 q^{15} - 5 q^{16} + 2 q^{17} - 6 q^{19} - q^{20} - 21 q^{21} + 11 q^{22} - 5 q^{23} + 3 q^{24} + 12 q^{26} + 27 q^{27} - 10 q^{28} - 8 q^{29} + 9 q^{30} + 4 q^{31} + 5 q^{32} - 24 q^{33} + q^{34} + 46 q^{35} + 3 q^{36} - 28 q^{37} - 3 q^{38} - 45 q^{39} + q^{40} - 24 q^{41} - 27 q^{42} + 27 q^{43} + 22 q^{44} + 27 q^{45} - 10 q^{46} - 9 q^{47} + 3 q^{48} - 12 q^{49} - 6 q^{51} + 6 q^{52} - 26 q^{53} + 18 q^{54} + 16 q^{55} - 5 q^{56} - 18 q^{57} + 8 q^{58} - 9 q^{59} + 3 q^{61} + 8 q^{62} + 42 q^{63} + 10 q^{64} + 5 q^{65} - 3 q^{66} + 5 q^{67} - q^{68} + 23 q^{70} + 54 q^{71} + 3 q^{72} + 34 q^{73} - 14 q^{74} - 45 q^{75} + 3 q^{76} - 13 q^{77} - 30 q^{78} - 11 q^{79} + 2 q^{80} + 33 q^{81} - 48 q^{82} - 23 q^{83} - 6 q^{84} + 23 q^{85} - 27 q^{86} + 63 q^{87} + 11 q^{88} + 78 q^{89} + 51 q^{90} - 30 q^{91} - 5 q^{92} - 27 q^{93} + 9 q^{94} - 37 q^{95} + 28 q^{97} - 24 q^{98} + 24 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9 - 2 * q^10 - 11 * q^11 + 6 * q^13 - 5 * q^14 + 9 * q^15 - 5 * q^16 + 2 * q^17 - 6 * q^19 - q^20 - 21 * q^21 + 11 * q^22 - 5 * q^23 + 3 * q^24 + 12 * q^26 + 27 * q^27 - 10 * q^28 - 8 * q^29 + 9 * q^30 + 4 * q^31 + 5 * q^32 - 24 * q^33 + q^34 + 46 * q^35 + 3 * q^36 - 28 * q^37 - 3 * q^38 - 45 * q^39 + q^40 - 24 * q^41 - 27 * q^42 + 27 * q^43 + 22 * q^44 + 27 * q^45 - 10 * q^46 - 9 * q^47 + 3 * q^48 - 12 * q^49 - 6 * q^51 + 6 * q^52 - 26 * q^53 + 18 * q^54 + 16 * q^55 - 5 * q^56 - 18 * q^57 + 8 * q^58 - 9 * q^59 + 3 * q^61 + 8 * q^62 + 42 * q^63 + 10 * q^64 + 5 * q^65 - 3 * q^66 + 5 * q^67 - q^68 + 23 * q^70 + 54 * q^71 + 3 * q^72 + 34 * q^73 - 14 * q^74 - 45 * q^75 + 3 * q^76 - 13 * q^77 - 30 * q^78 - 11 * q^79 + 2 * q^80 + 33 * q^81 - 48 * q^82 - 23 * q^83 - 6 * q^84 + 23 * q^85 - 27 * q^86 + 63 * q^87 + 11 * q^88 + 78 * q^89 + 51 * q^90 - 30 * q^91 - 5 * q^92 - 27 * q^93 + 9 * q^94 - 37 * q^95 + 28 * q^97 - 24 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more