LMFDB - Embedded newform 546.2.j.e.529.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(289,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.j (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 $ x^10 - 2x^9 + 15x^8 + 14x^7 + 110x^6 + 36x^5 + 233x^4 + 164x^3 + 345x^2 + 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.4
Root			$-0.623307 - 1.07960i$ of defining polynomial
Character	$\chi$	$=$	546.529
Dual form			546.2.j.e.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.623307 + 1.07960i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.30301 - 1.30235i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.623307 + 1.07960i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.30301 - 1.30235i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.623307 - 1.07960i) q^{10} +(1.24766 + 2.16101i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.785103 + 3.51904i) q^{13} +(-2.30301 + 1.30235i) q^{14} +(-0.623307 + 1.07960i) q^{15} +1.00000 q^{16} +0.495324 q^{17} +(0.500000 - 0.866025i) q^{18} +(3.83578 - 6.64376i) q^{19} +(0.623307 + 1.07960i) q^{20} +(2.27938 + 1.34329i) q^{21} +(-1.24766 - 2.16101i) q^{22} +0.448052 q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.72298 - 2.98428i) q^{25} +(0.785103 - 3.51904i) q^{26} -1.00000 q^{27} +(2.30301 - 1.30235i) q^{28} +(-3.71142 + 6.42837i) q^{29} +(0.623307 - 1.07960i) q^{30} +(-4.06448 + 7.03989i) q^{31} -1.00000 q^{32} +(-1.24766 + 2.16101i) q^{33} -0.495324 q^{34} +(2.84150 + 1.67457i) q^{35} +(-0.500000 + 0.866025i) q^{36} +2.74194 q^{37} +(-3.83578 + 6.64376i) q^{38} +(-3.44013 + 1.07960i) q^{39} +(-0.623307 - 1.07960i) q^{40} +(-1.87097 + 3.24061i) q^{41} +(-2.27938 - 1.34329i) q^{42} +(1.47532 + 2.55532i) q^{43} +(1.24766 + 2.16101i) q^{44} -1.24661 q^{45} -0.448052 q^{46} +(3.29729 + 5.71107i) q^{47} +(0.500000 + 0.866025i) q^{48} +(3.60775 - 5.99868i) q^{49} +(-1.72298 + 2.98428i) q^{50} +(0.247662 + 0.428963i) q^{51} +(-0.785103 + 3.51904i) q^{52} +(3.86750 - 6.69870i) q^{53} +1.00000 q^{54} +(-1.55535 + 2.69395i) q^{55} +(-2.30301 + 1.30235i) q^{56} +7.67156 q^{57} +(3.71142 - 6.42837i) q^{58} -1.45531 q^{59} +(-0.623307 + 1.07960i) q^{60} +(2.09967 - 3.63674i) q^{61} +(4.06448 - 7.03989i) q^{62} +(-0.0236360 + 2.64565i) q^{63} +1.00000 q^{64} +(-4.28851 + 1.34584i) q^{65} +(1.24766 - 2.16101i) q^{66} +(-0.0138047 - 0.0239105i) q^{67} +0.495324 q^{68} +(0.224026 + 0.388024i) q^{69} +(-2.84150 - 1.67457i) q^{70} +(4.68884 + 8.12130i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-5.07151 + 8.78412i) q^{73} -2.74194 q^{74} +3.44595 q^{75} +(3.83578 - 6.64376i) q^{76} +(5.68779 + 3.35195i) q^{77} +(3.44013 - 1.07960i) q^{78} +(-4.93545 - 8.54845i) q^{79} +(0.623307 + 1.07960i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.87097 - 3.24061i) q^{82} +7.42285 q^{83} +(2.27938 + 1.34329i) q^{84} +(0.308739 + 0.534751i) q^{85} +(-1.47532 - 2.55532i) q^{86} -7.42285 q^{87} +(-1.24766 - 2.16101i) q^{88} -11.4811 q^{89} +1.24661 q^{90} +(2.77493 + 9.12687i) q^{91} +0.448052 q^{92} -8.12896 q^{93} +(-3.29729 - 5.71107i) q^{94} +9.56347 q^{95} +(-0.500000 - 0.866025i) q^{96} +(-0.509831 - 0.883054i) q^{97} +(-3.60775 + 5.99868i) q^{98} -2.49532 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 5 q^{3} + 10 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} - 10 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 5 * q^3 + 10 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 - 10 * q^8 - 5 * q^9	\( 10 q - 10 q^{2} + 5 q^{3} + 10 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} - 10 q^{8} - 5 q^{9} + 2 q^{10} + 6 q^{11} + 5 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} + 10 q^{16} - 8 q^{17} + 5 q^{18} + 3 q^{19} - 2 q^{20} - 4 q^{21} - 6 q^{22} - 12 q^{23} - 5 q^{24} - q^{25} + 4 q^{26} - 10 q^{27} - 2 q^{28} - 2 q^{30} - 10 q^{31} - 10 q^{32} - 6 q^{33} + 8 q^{34} + 16 q^{35} - 5 q^{36} - 2 q^{37} - 3 q^{38} - 2 q^{39} + 2 q^{40} - 4 q^{41} + 4 q^{42} + 3 q^{43} + 6 q^{44} + 4 q^{45} + 12 q^{46} - 15 q^{47} + 5 q^{48} + 4 q^{49} + q^{50} - 4 q^{51} - 4 q^{52} - 17 q^{53} + 10 q^{54} + 3 q^{55} + 2 q^{56} + 6 q^{57} - 4 q^{59} + 2 q^{60} + 11 q^{61} + 10 q^{62} - 2 q^{63} + 10 q^{64} - 4 q^{65} + 6 q^{66} - q^{67} - 8 q^{68} - 6 q^{69} - 16 q^{70} + 18 q^{71} + 5 q^{72} + 12 q^{73} + 2 q^{74} - 2 q^{75} + 3 q^{76} + 18 q^{77} + 2 q^{78} - 4 q^{79} - 2 q^{80} - 5 q^{81} + 4 q^{82} - 4 q^{84} + q^{85} - 3 q^{86} - 6 q^{88} - 14 q^{89} - 4 q^{90} + 26 q^{91} - 12 q^{92} - 20 q^{93} + 15 q^{94} - 48 q^{95} - 5 q^{96} - 6 q^{97} - 4 q^{98} - 12 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 5 * q^3 + 10 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 - 10 * q^8 - 5 * q^9 + 2 * q^10 + 6 * q^11 + 5 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 + 10 * q^16 - 8 * q^17 + 5 * q^18 + 3 * q^19 - 2 * q^20 - 4 * q^21 - 6 * q^22 - 12 * q^23 - 5 * q^24 - q^25 + 4 * q^26 - 10 * q^27 - 2 * q^28 - 2 * q^30 - 10 * q^31 - 10 * q^32 - 6 * q^33 + 8 * q^34 + 16 * q^35 - 5 * q^36 - 2 * q^37 - 3 * q^38 - 2 * q^39 + 2 * q^40 - 4 * q^41 + 4 * q^42 + 3 * q^43 + 6 * q^44 + 4 * q^45 + 12 * q^46 - 15 * q^47 + 5 * q^48 + 4 * q^49 + q^50 - 4 * q^51 - 4 * q^52 - 17 * q^53 + 10 * q^54 + 3 * q^55 + 2 * q^56 + 6 * q^57 - 4 * q^59 + 2 * q^60 + 11 * q^61 + 10 * q^62 - 2 * q^63 + 10 * q^64 - 4 * q^65 + 6 * q^66 - q^67 - 8 * q^68 - 6 * q^69 - 16 * q^70 + 18 * q^71 + 5 * q^72 + 12 * q^73 + 2 * q^74 - 2 * q^75 + 3 * q^76 + 18 * q^77 + 2 * q^78 - 4 * q^79 - 2 * q^80 - 5 * q^81 + 4 * q^82 - 4 * q^84 + q^85 - 3 * q^86 - 6 * q^88 - 14 * q^89 - 4 * q^90 + 26 * q^91 - 12 * q^92 - 20 * q^93 + 15 * q^94 - 48 * q^95 - 5 * q^96 - 6 * q^97 - 4 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	0.623307	+	1.07960i	0.278751	+	0.482811i	0.971075	−	0.238776i	$-0.0767462\pi$
$5$	0.623307	+	1.07960i	0.278751	+	0.482811i	−0.692323	+	0.721587i	$0.743413\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	2.30301	−	1.30235i	0.870458	−	0.492243i
$7$	2.30301	−	1.30235i	0.870458	−	0.492243i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.623307	−	1.07960i	−0.197107	−	0.341399i
$11$	1.24766	+	2.16101i	0.376184	+	0.651570i	0.990504	−	0.137487i	$-0.0439026\pi$
$11$	1.24766	+	2.16101i	0.376184	+	0.651570i	−0.614319	+	0.789058i	$0.710569\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−0.785103	+	3.51904i	−0.217748	+	0.976005i
$13$	−0.785103	+	3.51904i	−0.217748	+	0.976005i
$14$	−2.30301	+	1.30235i	−0.615506	+	0.348069i
$15$	−0.623307	+	1.07960i	−0.160937	+	0.278751i
$16$	1.00000			0.250000
$17$	0.495324			0.120134			0.0600669	−	0.998194i	$-0.480869\pi$
$17$	0.495324			0.120134			0.0600669	+	0.998194i	$0.480869\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	3.83578	−	6.64376i	0.879988	−	1.52418i	0.0286358	−	0.999590i	$-0.490884\pi$
$19$	3.83578	−	6.64376i	0.879988	−	1.52418i	0.851352	−	0.524594i	$-0.175783\pi$
$20$	0.623307	+	1.07960i	0.139376	+	0.241406i
$21$	2.27938	+	1.34329i	0.497401	+	0.293130i
$22$	−1.24766	−	2.16101i	−0.266002	−	0.460730i
$23$	0.448052			0.0934253			0.0467127	−	0.998908i	$-0.485125\pi$
$23$	0.448052			0.0934253			0.0467127	+	0.998908i	$0.485125\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	1.72298	−	2.98428i	0.344595	−	0.596857i
$26$	0.785103	−	3.51904i	0.153971	−	0.690140i
$27$	−1.00000			−0.192450
$28$	2.30301	−	1.30235i	0.435229	−	0.246122i
$29$	−3.71142	+	6.42837i	−0.689194	+	1.19372i	0.282905	+	0.959148i	$0.408702\pi$
$29$	−3.71142	+	6.42837i	−0.689194	+	1.19372i	−0.972099	+	0.234571i	$0.924631\pi$
$30$	0.623307	−	1.07960i	0.113800	−	0.197107i
$31$	−4.06448	+	7.03989i	−0.730002	+	1.26440i	0.226879	+	0.973923i	$0.427148\pi$
$31$	−4.06448	+	7.03989i	−0.730002	+	1.26440i	−0.956882	+	0.290478i	$0.906186\pi$
$32$	−1.00000			−0.176777
$33$	−1.24766	+	2.16101i	−0.217190	+	0.376184i
$34$	−0.495324			−0.0849474
$35$	2.84150	+	1.67457i	0.480302	+	0.283053i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	2.74194			0.450772			0.225386	−	0.974270i	$-0.427636\pi$
$37$	2.74194			0.450772			0.225386	+	0.974270i	$0.427636\pi$
$38$	−3.83578	+	6.64376i	−0.622246	+	1.07776i
$39$	−3.44013	+	1.07960i	−0.550861	+	0.172874i
$40$	−0.623307	−	1.07960i	−0.0985534	−	0.170700i
$41$	−1.87097	+	3.24061i	−0.292196	+	0.506099i	−0.974329	−	0.225130i	$-0.927719\pi$
$41$	−1.87097	+	3.24061i	−0.292196	+	0.506099i	0.682133	+	0.731229i	$0.261053\pi$
$42$	−2.27938	−	1.34329i	−0.351716	−	0.207274i
$43$	1.47532	+	2.55532i	0.224983	+	0.389683i	0.956314	−	0.292340i	$-0.0944339\pi$
$43$	1.47532	+	2.55532i	0.224983	+	0.389683i	−0.731331	+	0.682023i	$0.761101\pi$
$44$	1.24766	+	2.16101i	0.188092	+	0.325785i
$45$	−1.24661			−0.185834
$46$	−0.448052			−0.0660617
$47$	3.29729	+	5.71107i	0.480959	+	0.833046i	0.999761	−	0.0218486i	$-0.00695519\pi$
$47$	3.29729	+	5.71107i	0.480959	+	0.833046i	−0.518802	+	0.854894i	$0.673622\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	3.60775	−	5.99868i	0.515393	−	0.856954i
$50$	−1.72298	+	2.98428i	−0.243666	+	0.422042i
$51$	0.247662	+	0.428963i	0.0346796	+	0.0600669i
$52$	−0.785103	+	3.51904i	−0.108874	+	0.488002i
$53$	3.86750	−	6.69870i	0.531241	−	0.920137i	−0.468094	−	0.883679i	$-0.655059\pi$
$53$	3.86750	−	6.69870i	0.531241	−	0.920137i	0.999335	−	0.0364583i	$-0.0116076\pi$
$54$	1.00000			0.136083
$55$	−1.55535	+	2.69395i	−0.209724	+	0.363252i
$56$	−2.30301	+	1.30235i	−0.307753	+	0.174034i
$57$	7.67156			1.01612
$58$	3.71142	−	6.42837i	0.487334	−	0.844087i
$59$	−1.45531			−0.189465			−0.0947324	−	0.995503i	$-0.530200\pi$
$59$	−1.45531			−0.189465			−0.0947324	+	0.995503i	$0.530200\pi$
$60$	−0.623307	+	1.07960i	−0.0804686	+	0.139376i
$61$	2.09967	−	3.63674i	0.268835	−	0.465636i	−0.699726	−	0.714411i	$-0.746695\pi$
$61$	2.09967	−	3.63674i	0.268835	−	0.465636i	0.968561	+	0.248775i	$0.0800279\pi$
$62$	4.06448	−	7.03989i	0.516190	−	0.894067i
$63$	−0.0236360	+	2.64565i	−0.00297786	+	0.333320i
$64$	1.00000			0.125000
$65$	−4.28851	+	1.34584i	−0.531924	+	0.166931i
$66$	1.24766	−	2.16101i	0.153577	−	0.266002i
$67$	−0.0138047	−	0.0239105i	−0.00168652	−	0.00292113i	0.865181	−	0.501460i	$-0.167204\pi$
$67$	−0.0138047	−	0.0239105i	−0.00168652	−	0.00292113i	−0.866867	+	0.498539i	$0.833870\pi$
$68$	0.495324			0.0600669
$69$	0.224026	+	0.388024i	0.0269696	+	0.0467127i
$70$	−2.84150	−	1.67457i	−0.339625	−	0.200149i
$71$	4.68884	+	8.12130i	0.556463	+	0.963821i	0.997788	+	0.0664743i	$0.0211751\pi$
$71$	4.68884	+	8.12130i	0.556463	+	0.963821i	−0.441326	+	0.897347i	$0.645492\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−5.07151	+	8.78412i	−0.593576	+	1.02810i	0.400170	+	0.916441i	$0.368951\pi$
$73$	−5.07151	+	8.78412i	−0.593576	+	1.02810i	−0.993746	+	0.111663i	$0.964382\pi$
$74$	−2.74194			−0.318744
$75$	3.44595			0.397905
$76$	3.83578	−	6.64376i	0.439994	−	0.762092i
$77$	5.68779	+	3.35195i	0.648184	+	0.381990i
$78$	3.44013	−	1.07960i	0.389518	−	0.122241i
$79$	−4.93545	−	8.54845i	−0.555282	−	0.961776i	−0.997882	−	0.0650567i	$-0.979277\pi$
$79$	−4.93545	−	8.54845i	−0.555282	−	0.961776i	0.442600	−	0.896719i	$-0.354056\pi$
$80$	0.623307	+	1.07960i	0.0696878	+	0.120703i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.87097	−	3.24061i	0.206614	−	0.357866i
$83$	7.42285			0.814763			0.407382	−	0.913258i	$-0.366442\pi$
$83$	7.42285			0.814763			0.407382	+	0.913258i	$0.366442\pi$
$84$	2.27938	+	1.34329i	0.248701	+	0.146565i
$85$	0.308739	+	0.534751i	0.0334874	+	0.0580019i
$86$	−1.47532	−	2.55532i	−0.159087	−	0.275547i
$87$	−7.42285			−0.795813
$88$	−1.24766	−	2.16101i	−0.133001	−	0.230365i
$89$	−11.4811			−1.21700			−0.608498	−	0.793555i	$-0.708228\pi$
$89$	−11.4811			−1.21700			−0.608498	+	0.793555i	$0.708228\pi$
$90$	1.24661			0.131405
$91$	2.77493	+	9.12687i	0.290891	+	0.956756i
$92$	0.448052			0.0467127
$93$	−8.12896			−0.842934
$94$	−3.29729	−	5.71107i	−0.340089	−	0.589052i
$95$	9.56347			0.981191
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−0.509831	−	0.883054i	−0.0517655	−	0.0896605i	0.838982	−	0.544160i	$-0.183152\pi$
$97$	−0.509831	−	0.883054i	−0.0517655	−	0.0896605i	−0.890747	+	0.454499i	$0.849818\pi$
$98$	−3.60775	+	5.99868i	−0.364438	+	0.605958i
$99$	−2.49532			−0.250790
$100$	1.72298	−	2.98428i	0.172298	−	0.298428i
$101$	−8.97127	−	15.5387i	−0.892675	−	1.54616i	−0.836656	−	0.547729i	$-0.815493\pi$
$101$	−8.97127	−	15.5387i	−0.892675	−	1.54616i	−0.0560191	−	0.998430i	$-0.517841\pi$
$102$	−0.247662	−	0.428963i	−0.0245222	−	0.0424737i
$103$	0.524685	+	0.908780i	0.0516987	+	0.0895448i	0.890717	−	0.454559i	$-0.150203\pi$
$103$	0.524685	+	0.908780i	0.0516987	+	0.0895448i	−0.839018	+	0.544104i	$0.816870\pi$
$104$	0.785103	−	3.51904i	0.0769857	−	0.345070i
$105$	−0.0294650	+	3.29810i	−0.00287549	+	0.321861i
$106$	−3.86750	+	6.69870i	−0.375644	+	0.650635i
$107$	−10.1830			−0.984432			−0.492216	−	0.870473i	$-0.663813\pi$
$107$	−10.1830			−0.984432			−0.492216	+	0.870473i	$0.663813\pi$
$108$	−1.00000			−0.0962250
$109$	9.92285	−	17.1869i	0.950436	−	1.64620i	0.205955	−	0.978562i	$-0.433970\pi$
$109$	9.92285	−	17.1869i	0.950436	−	1.64620i	0.744482	−	0.667643i	$-0.232697\pi$
$110$	1.55535	−	2.69395i	0.148297	−	0.256858i
$111$	1.37097	+	2.37459i	0.130127	+	0.225386i
$112$	2.30301	−	1.30235i	0.217614	−	0.123061i
$113$	−7.93440	−	13.7428i	−0.746406	−	1.29281i	−0.949535	−	0.313661i	$-0.898445\pi$
$113$	−7.93440	−	13.7428i	−0.746406	−	1.29281i	0.203129	−	0.979152i	$-0.434889\pi$
$114$	−7.67156			−0.718507
$115$	0.279274	+	0.483717i	0.0260424	+	0.0451068i
$116$	−3.71142	+	6.42837i	−0.344597	+	0.596860i
$117$	−2.65502	−	2.43944i	−0.245457	−	0.225526i
$118$	1.45531			0.133972
$119$	1.14074	−	0.645087i	0.104571	−	0.0591350i
$120$	0.623307	−	1.07960i	0.0568999	−	0.0985534i
$121$	2.38668	−	4.13385i	0.216971	−	0.375804i
$122$	−2.09967	+	3.63674i	−0.190095	+	0.329255i
$123$	−3.74194			−0.337399
$124$	−4.06448	+	7.03989i	−0.365001	+	0.632201i
$125$	10.5288			0.941728
$126$	0.0236360	−	2.64565i	0.00210567	−	0.235693i
$127$	4.23846	−	7.34124i	0.376103	−	0.651429i	−0.614389	−	0.789004i	$-0.710597\pi$
$127$	4.23846	−	7.34124i	0.376103	−	0.651429i	0.990491	+	0.137574i	$0.0439306\pi$
$128$	−1.00000			−0.0883883
$129$	−1.47532	+	2.55532i	−0.129894	+	0.224983i
$130$	4.28851	−	1.34584i	0.376127	−	0.118038i
$131$	−8.26678	−	14.3185i	−0.722272	−	1.25101i	−0.960087	−	0.279701i	$-0.909765\pi$
$131$	−8.26678	−	14.3185i	−0.722272	−	1.25101i	0.237816	−	0.971310i	$-0.423569\pi$
$132$	−1.24766	+	2.16101i	−0.108595	+	0.188092i
$133$	0.181325	−	20.2962i	0.0157229	−	1.75991i
$134$	0.0138047	+	0.0239105i	0.00119255	+	0.00206555i
$135$	−0.623307	−	1.07960i	−0.0536457	−	0.0929171i
$136$	−0.495324			−0.0424737
$137$	−0.856837			−0.0732045			−0.0366023	−	0.999330i	$-0.511653\pi$
$137$	−0.856837			−0.0732045			−0.0366023	+	0.999330i	$0.511653\pi$
$138$	−0.224026	−	0.388024i	−0.0190704	−	0.0330308i
$139$	4.74886	+	8.22528i	0.402793	+	0.697659i	0.994062	−	0.108816i	$-0.0347060\pi$
$139$	4.74886	+	8.22528i	0.402793	+	0.697659i	−0.591268	+	0.806475i	$0.701373\pi$
$140$	2.84150	+	1.67457i	0.240151	+	0.141527i
$141$	−3.29729	+	5.71107i	−0.277682	+	0.480959i
$142$	−4.68884	−	8.12130i	−0.393478	−	0.681525i
$143$	−8.58423	+	2.69395i	−0.717849	+	0.225279i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−9.25342			−0.768455
$146$	5.07151	−	8.78412i	0.419721	−	0.726979i
$147$	6.99888	+	0.125065i	0.577258	+	0.0103152i
$148$	2.74194			0.225386
$149$	2.36872	−	4.10274i	0.194053	−	0.336109i	−0.752537	−	0.658550i	$-0.771170\pi$
$149$	2.36872	−	4.10274i	0.194053	−	0.336109i	0.946590	+	0.322441i	$0.104503\pi$
$150$	−3.44595			−0.281361
$151$	−3.56085	+	6.16758i	−0.289778	+	0.501911i	−0.973757	−	0.227592i	$-0.926915\pi$
$151$	−3.56085	+	6.16758i	−0.289778	+	0.501911i	0.683978	+	0.729502i	$0.260248\pi$
$152$	−3.83578	+	6.64376i	−0.311123	+	0.538880i
$153$	−0.247662	+	0.428963i	−0.0200223	+	0.0346796i
$154$	−5.68779	−	3.35195i	−0.458335	−	0.270108i
$155$	−10.1337			−0.813956
$156$	−3.44013	+	1.07960i	−0.275431	+	0.0864371i
$157$	−7.52147	+	13.0276i	−0.600279	+	1.03971i	0.392500	+	0.919752i	$0.371610\pi$
$157$	−7.52147	+	13.0276i	−0.600279	+	1.03971i	−0.992779	+	0.119961i	$0.961723\pi$
$158$	4.93545	+	8.54845i	0.392643	+	0.680078i
$159$	7.73499			0.613425
$160$	−0.623307	−	1.07960i	−0.0492767	−	0.0853498i
$161$	1.03187	−	0.583522i	0.0813228	−	0.0459880i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	4.51485	−	7.81996i	0.353631	−	0.612506i	−0.633252	−	0.773946i	$-0.718280\pi$
$163$	4.51485	−	7.81996i	0.353631	−	0.612506i	0.986883	+	0.161439i	$0.0516137\pi$
$164$	−1.87097	+	3.24061i	−0.146098	+	0.253049i
$165$	−3.11070			−0.242168
$166$	−7.42285			−0.576125
$167$	1.42442	−	2.46716i	0.110225	−	0.190915i	−0.805636	−	0.592411i	$-0.798176\pi$
$167$	1.42442	−	2.46716i	0.110225	−	0.190915i	0.915861	+	0.401496i	$0.131510\pi$
$168$	−2.27938	−	1.34329i	−0.175858	−	0.103637i
$169$	−11.7672	−	5.52561i	−0.905171	−	0.425047i
$170$	−0.308739	−	0.534751i	−0.0236792	−	0.0410136i
$171$	3.83578	+	6.64376i	0.293329	+	0.508061i
$172$	1.47532	+	2.55532i	0.112492	+	0.194841i
$173$	12.7438	−	22.0729i	0.968891	−	1.67817i	0.270116	−	0.962828i	$-0.412938\pi$
$173$	12.7438	−	22.0729i	0.968891	−	1.67817i	0.698776	−	0.715341i	$-0.253729\pi$
$174$	7.42285			0.562725
$175$	0.0814487	−	9.11678i	0.00615695	−	0.689163i
$176$	1.24766	+	2.16101i	0.0940461	+	0.162893i
$177$	−0.727653	−	1.26033i	−0.0546938	−	0.0947324i
$178$	11.4811			0.860547
$179$	−9.10030	−	15.7622i	−0.680189	−	1.17812i	−0.974923	−	0.222542i	$-0.928565\pi$
$179$	−9.10030	−	15.7622i	−0.680189	−	1.17812i	0.294734	−	0.955579i	$-0.404769\pi$
$180$	−1.24661			−0.0929171
$181$	−13.7305			−1.02058			−0.510290	−	0.860003i	$-0.670462\pi$
$181$	−13.7305			−1.02058			−0.510290	+	0.860003i	$0.670462\pi$
$182$	−2.77493	−	9.12687i	−0.205691	−	0.676529i
$183$	4.19934			0.310424
$184$	−0.448052			−0.0330308
$185$	1.70907	+	2.96019i	0.125653	+	0.217638i
$186$	8.12896			0.596044
$187$	0.617997	+	1.07040i	0.0451924	+	0.0782756i
$188$	3.29729	+	5.71107i	0.240480	+	0.416523i
$189$	−2.30301	+	1.30235i	−0.167520	+	0.0947323i
$190$	−9.56347			−0.693807
$191$	−2.64294	+	4.57771i	−0.191236	+	0.331231i	−0.945660	−	0.325156i	$-0.894583\pi$
$191$	−2.64294	+	4.57771i	−0.191236	+	0.331231i	0.754424	+	0.656388i	$0.227916\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−2.40599	−	4.16729i	−0.173187	−	0.299968i	0.766346	−	0.642429i	$-0.222073\pi$
$193$	−2.40599	−	4.16729i	−0.173187	−	0.299968i	−0.939532	+	0.342461i	$0.888740\pi$
$194$	0.509831	+	0.883054i	0.0366038	+	0.0633996i
$195$	−3.30979	−	3.04103i	−0.237019	−	0.217773i
$196$	3.60775	−	5.99868i	0.257696	−	0.428477i
$197$	11.7743	−	20.3937i	0.838883	−	1.45299i	−0.0519458	−	0.998650i	$-0.516542\pi$
$197$	11.7743	−	20.3937i	0.838883	−	1.45299i	0.890829	−	0.454339i	$-0.150124\pi$
$198$	2.49532			0.177335
$199$	11.2797			0.799596			0.399798	−	0.916603i	$-0.369080\pi$
$199$	11.2797			0.799596			0.399798	+	0.916603i	$0.369080\pi$
$200$	−1.72298	+	2.98428i	−0.121833	+	0.211021i
$201$	0.0138047	−	0.0239105i	0.000973710	−	0.00168652i
$202$	8.97127	+	15.5387i	0.631217	+	1.09330i
$203$	−0.175447	+	19.6382i	−0.0123139	+	1.37833i
$204$	0.247662	+	0.428963i	0.0173398	+	0.0300334i
$205$	−4.66475			−0.325800
$206$	−0.524685	−	0.908780i	−0.0365565	−	0.0633177i
$207$	−0.224026	+	0.388024i	−0.0155709	+	0.0269696i
$208$	−0.785103	+	3.51904i	−0.0544371	+	0.244001i
$209$	19.1430			1.32415
$210$	0.0294650	−	3.29810i	0.00203328	−	0.227590i
$211$	−6.22021	+	10.7737i	−0.428217	+	0.741693i	−0.996715	−	0.0809915i	$-0.974191\pi$
$211$	−6.22021	+	10.7737i	−0.428217	+	0.741693i	0.568498	+	0.822685i	$0.307525\pi$
$212$	3.86750	−	6.69870i	0.265621	−	0.460069i
$213$	−4.68884	+	8.12130i	−0.321274	+	0.556463i
$214$	10.1830			0.696099
$215$	−1.83915	+	3.18550i	−0.125429	+	0.217249i
$216$	1.00000			0.0680414
$217$	−0.192136	+	21.5064i	−0.0130431	+	1.45995i
$218$	−9.92285	+	17.1869i	−0.672060	+	1.16404i
$219$	−10.1430			−0.685402
$220$	−1.55535	+	2.69395i	−0.104862	+	0.181626i
$221$	−0.388880	+	1.74306i	−0.0261589	+	0.117251i
$222$	−1.37097	−	2.37459i	−0.0920134	−	0.159372i
$223$	−10.4651	+	18.1260i	−0.700793	+	1.21381i	0.267396	+	0.963587i	$0.413837\pi$
$223$	−10.4651	+	18.1260i	−0.700793	+	1.21381i	−0.968188	+	0.250222i	$0.919496\pi$
$224$	−2.30301	+	1.30235i	−0.153877	+	0.0870172i
$225$	1.72298	+	2.98428i	0.114865	+	0.198952i
$226$	7.93440	+	13.7428i	0.527789	+	0.914157i
$227$	17.5810			1.16689			0.583447	−	0.812151i	$-0.301704\pi$
$227$	17.5810			1.16689			0.583447	+	0.812151i	$0.301704\pi$
$228$	7.67156			0.508061
$229$	7.24620	+	12.5508i	0.478842	+	0.829379i	0.999706	−	0.0242609i	$-0.00772324\pi$
$229$	7.24620	+	12.5508i	0.478842	+	0.829379i	−0.520863	+	0.853640i	$0.674390\pi$
$230$	−0.279274	−	0.483717i	−0.0184148	−	0.0318953i
$231$	−0.0589796	+	6.60174i	−0.00388057	+	0.434363i
$232$	3.71142	−	6.42837i	0.243667	−	0.422043i
$233$	−7.24897	−	12.5556i	−0.474896	−	0.822544i	0.524691	−	0.851293i	$-0.324181\pi$
$233$	−7.24897	−	12.5556i	−0.474896	−	0.822544i	−0.999587	+	0.0287492i	$0.990848\pi$
$234$	2.65502	+	2.43944i	0.173564	+	0.159471i
$235$	−4.11045	+	7.11950i	−0.268136	+	0.464425i
$236$	−1.45531			−0.0947324
$237$	4.93545	−	8.54845i	0.320592	−	0.555282i
$238$	−1.14074	+	0.645087i	−0.0739431	+	0.0418148i
$239$	3.15093			0.203817			0.101908	−	0.994794i	$-0.467505\pi$
$239$	3.15093			0.203817			0.101908	+	0.994794i	$0.467505\pi$
$240$	−0.623307	+	1.07960i	−0.0402343	+	0.0696878i
$241$	−24.8446			−1.60038			−0.800189	−	0.599747i	$-0.795268\pi$
$241$	−24.8446			−1.60038			−0.800189	+	0.599747i	$0.795268\pi$
$242$	−2.38668	+	4.13385i	−0.153422	+	0.265734i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	2.09967	−	3.63674i	0.134418	−	0.232818i
$245$	8.72490	+	0.155908i	0.557414	+	0.00996059i
$246$	3.74194			0.238577
$247$	20.3682	+	18.7143i	1.29600	+	1.19076i
$248$	4.06448	−	7.03989i	0.258095	−	0.447033i
$249$	3.71142	+	6.42837i	0.235202	+	0.407382i
$250$	−10.5288			−0.665902
$251$	−3.69421	−	6.39857i	−0.233177	−	0.403874i	0.725564	−	0.688154i	$-0.241579\pi$
$251$	−3.69421	−	6.39857i	−0.233177	−	0.403874i	−0.958741	+	0.284280i	$0.908245\pi$
$252$	−0.0236360	+	2.64565i	−0.00148893	+	0.166660i
$253$	0.559018	+	0.968247i	0.0351451	+	0.0608732i
$254$	−4.23846	+	7.34124i	−0.265945	+	0.460630i
$255$	−0.308739	+	0.534751i	−0.0193340	+	0.0334874i
$256$	1.00000			0.0625000
$257$	26.8892			1.67730			0.838650	−	0.544671i	$-0.183345\pi$
$257$	26.8892			1.67730			0.838650	+	0.544671i	$0.183345\pi$
$258$	1.47532	−	2.55532i	0.0918491	−	0.159087i
$259$	6.31472	−	3.57097i	0.392378	−	0.221889i
$260$	−4.28851	+	1.34584i	−0.265962	+	0.0834656i
$261$	−3.71142	−	6.42837i	−0.229731	−	0.397906i
$262$	8.26678	+	14.3185i	0.510723	+	0.884598i
$263$	1.46562	+	2.53852i	0.0903738	+	0.156532i	0.907668	−	0.419688i	$-0.137860\pi$
$263$	1.46562	+	2.53852i	0.0903738	+	0.156532i	−0.817295	+	0.576220i	$0.804527\pi$
$264$	1.24766	−	2.16101i	0.0767883	−	0.133001i
$265$	9.64254			0.592337
$266$	−0.181325	+	20.2962i	−0.0111178	+	1.24444i
$267$	−5.74056	−	9.94294i	−0.351317	−	0.608498i
$268$	−0.0138047	−	0.0239105i	−0.000843258	−	0.00146056i
$269$	2.14443			0.130748			0.0653741	−	0.997861i	$-0.479176\pi$
$269$	2.14443			0.130748			0.0653741	+	0.997861i	$0.479176\pi$
$270$	0.623307	+	1.07960i	0.0379332	+	0.0657023i
$271$	17.2844			1.04995			0.524976	−	0.851117i	$-0.324074\pi$
$271$	17.2844			1.04995			0.524976	+	0.851117i	$0.324074\pi$
$272$	0.495324			0.0300334
$273$	−6.51664	+	6.96659i	−0.394405	+	0.421637i
$274$	0.856837			0.0517634
$275$	8.59877			0.518526
$276$	0.224026	+	0.388024i	0.0134848	+	0.0233563i
$277$	−2.83381			−0.170267			−0.0851336	−	0.996370i	$-0.527132\pi$
$277$	−2.83381			−0.170267			−0.0851336	+	0.996370i	$0.527132\pi$
$278$	−4.74886	−	8.22528i	−0.284818	−	0.493319i
$279$	−4.06448	−	7.03989i	−0.243334	−	0.421467i
$280$	−2.84150	−	1.67457i	−0.169812	−	0.100074i
$281$	−28.5254			−1.70168			−0.850842	−	0.525422i	$-0.823907\pi$
$281$	−28.5254			−1.70168			−0.850842	+	0.525422i	$0.823907\pi$
$282$	3.29729	−	5.71107i	0.196351	−	0.340089i
$283$	2.29901	+	3.98201i	0.136662	+	0.236706i	0.926231	−	0.376956i	$-0.123029\pi$
$283$	2.29901	+	3.98201i	0.136662	+	0.236706i	−0.789569	+	0.613662i	$0.789696\pi$
$284$	4.68884	+	8.12130i	0.278231	+	0.481911i
$285$	4.78173	+	8.28221i	0.283245	+	0.490596i
$286$	8.58423	−	2.69395i	0.507596	−	0.159297i
$287$	−0.0884446	+	9.89984i	−0.00522072	+	0.584369i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−16.7547			−0.985568
$290$	9.25342			0.543380
$291$	0.509831	−	0.883054i	0.0298868	−	0.0517655i
$292$	−5.07151	+	8.78412i	−0.296788	+	0.514052i
$293$	3.19384	+	5.53189i	0.186586	+	0.323177i	0.944110	−	0.329631i	$-0.106924\pi$
$293$	3.19384	+	5.53189i	0.186586	+	0.323177i	−0.757524	+	0.652808i	$0.773591\pi$
$294$	−6.99888	−	0.125065i	−0.408183	−	0.00729395i
$295$	−0.907102	−	1.57115i	−0.0528135	−	0.0914757i
$296$	−2.74194			−0.159372
$297$	−1.24766	−	2.16101i	−0.0723967	−	0.125395i
$298$	−2.36872	+	4.10274i	−0.137216	+	0.237665i
$299$	−0.351767	+	1.57671i	−0.0203432	+	0.0911836i
$300$	3.44595			0.198952
$301$	6.72560	+	3.96356i	0.387657	+	0.228456i
$302$	3.56085	−	6.16758i	0.204904	−	0.354904i
$303$	8.97127	−	15.5387i	0.515386	−	0.892675i
$304$	3.83578	−	6.64376i	0.219997	−	0.381046i
$305$	5.23496			0.299753
$306$	0.247662	−	0.428963i	0.0141579	−	0.0245222i
$307$	−1.39899			−0.0798446			−0.0399223	−	0.999203i	$-0.512711\pi$
$307$	−1.39899			−0.0798446			−0.0399223	+	0.999203i	$0.512711\pi$
$308$	5.68779	+	3.35195i	0.324092	+	0.190995i
$309$	−0.524685	+	0.908780i	−0.0298483	+	0.0516987i
$310$	10.1337			0.575554
$311$	−8.55183	+	14.8122i	−0.484930	+	0.839923i	−0.999850	−	0.0173150i	$-0.994488\pi$
$311$	−8.55183	+	14.8122i	−0.484930	+	0.839923i	0.514920	+	0.857238i	$0.327822\pi$
$312$	3.44013	−	1.07960i	0.194759	−	0.0611203i
$313$	−5.81247	−	10.0675i	−0.328540	−	0.569048i	0.653682	−	0.756769i	$-0.273223\pi$
$313$	−5.81247	−	10.0675i	−0.328540	−	0.569048i	−0.982222	+	0.187721i	$0.939890\pi$
$314$	7.52147	−	13.0276i	0.424461	−	0.735188i
$315$	−2.87097	+	1.62353i	−0.161761	+	0.0914756i
$316$	−4.93545	−	8.54845i	−0.277641	−	0.480888i
$317$	−3.29277	−	5.70324i	−0.184940	−	0.320326i	0.758616	−	0.651538i	$-0.225876\pi$
$317$	−3.29277	−	5.70324i	−0.184940	−	0.320326i	−0.943556	+	0.331212i	$0.892543\pi$
$318$	−7.73499			−0.433757
$319$	−18.5224			−1.03706
$320$	0.623307	+	1.07960i	0.0348439	+	0.0603514i
$321$	−5.09152	−	8.81877i	−0.284181	−	0.492216i
$322$	−1.03187	+	0.583522i	−0.0575039	+	0.0325184i
$323$	1.89995	−	3.29082i	0.105716	−	0.183106i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	9.14909	+	8.40619i	0.507500	+	0.466292i
$326$	−4.51485	+	7.81996i	−0.250055	+	0.433107i
$327$	19.8457			1.09747
$328$	1.87097	−	3.24061i	0.103307	−	0.178933i
$329$	15.0315	+	8.85845i	0.828716	+	0.488382i
$330$	3.11070			0.171239
$331$	11.6343	−	20.1512i	0.639477	−	1.10761i	−0.346070	−	0.938209i	$-0.612484\pi$
$331$	11.6343	−	20.1512i	0.639477	−	1.10761i	0.985548	−	0.169399i	$-0.0541826\pi$
$332$	7.42285			0.407382
$333$	−1.37097	+	2.37459i	−0.0751286	+	0.130127i
$334$	−1.42442	+	2.46716i	−0.0779406	+	0.134997i
$335$	0.0172092	−	0.0298071i	0.000940236	−	0.00162854i
$336$	2.27938	+	1.34329i	0.124350	+	0.0732826i
$337$	19.4320			1.05853			0.529263	−	0.848458i	$-0.322468\pi$
$337$	19.4320			1.05853			0.529263	+	0.848458i	$0.322468\pi$
$338$	11.7672	+	5.52561i	0.640053	+	0.300554i
$339$	7.93440	−	13.7428i	0.430938	−	0.746406i
$340$	0.308739	+	0.534751i	0.0167437	+	0.0290010i
$341$	−20.2844			−1.09846
$342$	−3.83578	−	6.64376i	−0.207415	−	0.359254i
$343$	0.496304	−	18.5136i	0.0267979	−	0.999641i
$344$	−1.47532	−	2.55532i	−0.0795437	−	0.137774i
$345$	−0.279274	+	0.483717i	−0.0150356	+	0.0260424i
$346$	−12.7438	+	22.0729i	−0.685110	+	1.18664i
$347$	29.6707			1.59281			0.796404	−	0.604765i	$-0.206733\pi$
$347$	29.6707			1.59281			0.796404	+	0.604765i	$0.206733\pi$
$348$	−7.42285			−0.397906
$349$	−13.3023	+	23.0403i	−0.712058	+	1.23332i	0.252025	+	0.967721i	$0.418904\pi$
$349$	−13.3023	+	23.0403i	−0.712058	+	1.23332i	−0.964083	+	0.265600i	$0.914430\pi$
$350$	−0.0814487	+	9.11678i	−0.00435362	+	0.487312i
$351$	0.785103	−	3.51904i	0.0419057	−	0.187832i
$352$	−1.24766	−	2.16101i	−0.0665006	−	0.115182i
$353$	6.90939	+	11.9674i	0.367750	+	0.636961i	0.989213	−	0.146482i	$-0.0467950\pi$
$353$	6.90939	+	11.9674i	0.367750	+	0.636961i	−0.621464	+	0.783443i	$0.713462\pi$
$354$	0.727653	+	1.26033i	0.0386743	+	0.0669859i
$355$	−5.84517	+	10.1241i	−0.310229	+	0.537333i
$356$	−11.4811			−0.608498
$357$	1.12903	+	0.665365i	0.0597547	+	0.0352149i
$358$	9.10030	+	15.7622i	0.480966	+	0.833058i
$359$	1.38095	+	2.39188i	0.0728840	+	0.126239i	0.900164	−	0.435551i	$-0.143446\pi$
$359$	1.38095	+	2.39188i	0.0728840	+	0.126239i	−0.827280	+	0.561790i	$0.810113\pi$
$360$	1.24661			0.0657023
$361$	−19.9264	−	34.5135i	−1.04876	−	1.81650i
$362$	13.7305			0.721658
$363$	4.77336			0.250536
$364$	2.77493	+	9.12687i	0.145446	+	0.478378i
$365$	−12.6444			−0.661840
$366$	−4.19934			−0.219503
$367$	5.46151	+	9.45961i	0.285089	+	0.493788i	0.972631	−	0.232357i	$-0.0746437\pi$
$367$	5.46151	+	9.45961i	0.285089	+	0.493788i	−0.687542	+	0.726145i	$0.741310\pi$
$368$	0.448052			0.0233563
$369$	−1.87097	−	3.24061i	−0.0973987	−	0.168700i
$370$	−1.70907	−	2.96019i	−0.0888502	−	0.153893i
$371$	0.182825	−	20.4640i	0.00949178	−	1.06244i
$372$	−8.12896			−0.421467
$373$	−9.84303	+	17.0486i	−0.509653	+	0.882745i	0.490285	+	0.871562i	$0.336893\pi$
$373$	−9.84303	+	17.0486i	−0.509653	+	0.882745i	−0.999937	+	0.0111823i	$0.996440\pi$
$374$	−0.617997	−	1.07040i	−0.0319559	−	0.0553492i
$375$	5.26442	+	9.11824i	0.271854	+	0.470864i
$376$	−3.29729	−	5.71107i	−0.170045	−	0.294526i
$377$	−19.7078	−	18.1076i	−1.01501	−	0.932587i
$378$	2.30301	−	1.30235i	0.118454	−	0.0669858i
$379$	−8.31713	+	14.4057i	−0.427222	+	0.739970i	−0.996625	−	0.0820882i	$-0.973841\pi$
$379$	−8.31713	+	14.4057i	−0.427222	+	0.739970i	0.569403	+	0.822059i	$0.307174\pi$
$380$	9.56347			0.490596
$381$	8.47693			0.434286
$382$	2.64294	−	4.57771i	0.135225	−	0.234216i
$383$	−18.1834	+	31.4945i	−0.929127	+	1.60929i	−0.144341	+	0.989528i	$0.546106\pi$
$383$	−18.1834	+	31.4945i	−0.929127	+	1.60929i	−0.784786	+	0.619767i	$0.787227\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−0.0735247	+	8.22982i	−0.00374717	+	0.419431i
$386$	2.40599	+	4.16729i	0.122461	+	0.212109i
$387$	−2.95063			−0.149989
$388$	−0.509831	−	0.883054i	−0.0258828	−	0.0448303i
$389$	8.89008	−	15.3981i	0.450745	−	0.780713i	−0.547687	−	0.836683i	$-0.684492\pi$
$389$	8.89008	−	15.3981i	0.450745	−	0.780713i	0.998432	+	0.0559696i	$0.0178250\pi$
$390$	3.30979	+	3.04103i	0.167598	+	0.153989i
$391$	0.221931			0.0112235
$392$	−3.60775	+	5.99868i	−0.182219	+	0.302979i
$393$	8.26678	−	14.3185i	0.417004	−	0.722272i
$394$	−11.7743	+	20.3937i	−0.593180	+	1.02742i
$395$	6.15260	−	10.6566i	0.309571	−	0.536192i
$396$	−2.49532			−0.125395
$397$	−4.43952	+	7.68948i	−0.222813	+	0.385924i	−0.955661	−	0.294469i	$-0.904857\pi$
$397$	−4.43952	+	7.68948i	−0.222813	+	0.385924i	0.732848	+	0.680392i	$0.238191\pi$
$398$	−11.2797			−0.565400
$399$	17.6677	−	9.99108i	0.884492	−	0.500180i
$400$	1.72298	−	2.98428i	0.0861489	−	0.149214i
$401$	−30.1630			−1.50627			−0.753134	−	0.657867i	$-0.771459\pi$
$401$	−30.1630			−1.50627			−0.753134	+	0.657867i	$0.771459\pi$
$402$	−0.0138047	+	0.0239105i	−0.000688517	+	0.00119255i
$403$	−21.5826	−	19.8301i	−1.07511	−	0.987807i
$404$	−8.97127	−	15.5387i	−0.446338	−	0.773079i
$405$	0.623307	−	1.07960i	0.0309724	−	0.0536457i
$406$	0.175447	−	19.6382i	0.00870728	−	0.974629i
$407$	3.42101	+	5.92537i	0.169573	+	0.293709i
$408$	−0.247662	−	0.428963i	−0.0122611	−	0.0212368i
$409$	16.7720			0.829323			0.414662	−	0.909976i	$-0.363900\pi$
$409$	16.7720			0.829323			0.414662	+	0.909976i	$0.363900\pi$
$410$	4.66475			0.230376
$411$	−0.428418	−	0.742042i	−0.0211323	−	0.0366023i
$412$	0.524685	+	0.908780i	0.0258494	+	0.0447724i
$413$	−3.35159	+	1.89532i	−0.164921	+	0.0932628i
$414$	0.224026	−	0.388024i	0.0110103	−	0.0190704i
$415$	4.62671	+	8.01370i	0.227116	+	0.393377i
$416$	0.785103	−	3.51904i	0.0384928	−	0.172535i
$417$	−4.74886	+	8.22528i	−0.232553	+	0.402793i
$418$	−19.1430			−0.936316
$419$	−19.8098	+	34.3115i	−0.967770	+	1.67623i	−0.265788	+	0.964031i	$0.585632\pi$
$419$	−19.8098	+	34.3115i	−0.967770	+	1.67623i	−0.701982	+	0.712195i	$0.747701\pi$
$420$	−0.0294650	+	3.29810i	−0.00143775	+	0.160931i
$421$	−32.2271			−1.57065			−0.785326	−	0.619083i	$-0.787505\pi$
$421$	−32.2271			−1.57065			−0.785326	+	0.619083i	$0.787505\pi$
$422$	6.22021	−	10.7737i	0.302795	−	0.524456i
$423$	−6.59458			−0.320639
$424$	−3.86750	+	6.69870i	−0.187822	+	0.325318i
$425$	0.853432	−	1.47819i	0.0413975	−	0.0717027i
$426$	4.68884	−	8.12130i	0.227175	−	0.393478i
$427$	0.0992558	−	11.1100i	0.00480333	−	0.537649i
$428$	−10.1830			−0.492216
$429$	−6.62514	−	6.08719i	−0.319865	−	0.293892i
$430$	1.83915	−	3.18550i	0.0886916	−	0.153618i
$431$	−5.50063	−	9.52738i	−0.264956	−	0.458918i	0.702596	−	0.711589i	$-0.252024\pi$
$431$	−5.50063	−	9.52738i	−0.264956	−	0.458918i	−0.967552	+	0.252671i	$0.918691\pi$
$432$	−1.00000			−0.0481125
$433$	15.9643	+	27.6509i	0.767193	+	1.32882i	0.939079	+	0.343701i	$0.111681\pi$
$433$	15.9643	+	27.6509i	0.767193	+	1.32882i	−0.171886	+	0.985117i	$0.554986\pi$
$434$	0.192136	−	21.5064i	0.00922285	−	1.03234i
$435$	−4.62671	−	8.01370i	−0.221834	−	0.384227i
$436$	9.92285	−	17.1869i	0.475218	−	0.823102i
$437$	1.71863	−	2.97675i	0.0822132	−	0.142397i
$438$	10.1430			0.484653
$439$	−1.43526			−0.0685010			−0.0342505	−	0.999413i	$-0.510904\pi$
$439$	−1.43526			−0.0685010			−0.0342505	+	0.999413i	$0.510904\pi$
$440$	1.55535	−	2.69395i	0.0741485	−	0.128429i
$441$	3.39113	+	6.12374i	0.161482	+	0.291607i
$442$	0.388880	−	1.74306i	0.0184972	−	0.0829091i
$443$	5.72758	+	9.92047i	0.272126	+	0.471336i	0.969406	−	0.245463i	$-0.0789400\pi$
$443$	5.72758	+	9.92047i	0.272126	+	0.471336i	−0.697280	+	0.716799i	$0.745607\pi$
$444$	1.37097	+	2.37459i	0.0650633	+	0.112693i
$445$	−7.15626	−	12.3950i	−0.339239	−	0.587580i
$446$	10.4651	−	18.1260i	0.495535	−	0.858292i
$447$	4.73744			0.224073
$448$	2.30301	−	1.30235i	0.108807	−	0.0615304i
$449$	−17.3713	−	30.0880i	−0.819803	−	1.41994i	−0.905827	−	0.423647i	$-0.860750\pi$
$449$	−17.3713	−	30.0880i	−0.819803	−	1.41994i	0.0860243	−	0.996293i	$-0.472584\pi$
$450$	−1.72298	−	2.98428i	−0.0812219	−	0.140681i
$451$	−9.33735			−0.439679
$452$	−7.93440	−	13.7428i	−0.373203	−	0.646406i
$453$	−7.12171			−0.334607
$454$	−17.5810			−0.825119
$455$	−8.12373	+	8.68465i	−0.380846	+	0.407143i
$456$	−7.67156			−0.359254
$457$	36.8048			1.72166			0.860829	−	0.508894i	$-0.169946\pi$
$457$	36.8048			1.72166			0.860829	+	0.508894i	$0.169946\pi$
$458$	−7.24620	−	12.5508i	−0.338593	−	0.586460i
$459$	−0.495324			−0.0231198
$460$	0.279274	+	0.483717i	0.0130212	+	0.0225534i
$461$	−3.99129	−	6.91311i	−0.185893	−	0.321976i	0.757984	−	0.652273i	$-0.226184\pi$
$461$	−3.99129	−	6.91311i	−0.185893	−	0.321976i	−0.943877	+	0.330297i	$0.892851\pi$
$462$	0.0589796	−	6.60174i	0.00274398	−	0.307141i
$463$	26.4799			1.23063			0.615314	−	0.788282i	$-0.289029\pi$
$463$	26.4799			1.23063			0.615314	+	0.788282i	$0.289029\pi$
$464$	−3.71142	+	6.42837i	−0.172299	+	0.298430i
$465$	−5.06684	−	8.77602i	−0.234969	−	0.406978i
$466$	7.24897	+	12.5556i	0.335802	+	0.581626i
$467$	−3.12210	−	5.40764i	−0.144474	−	0.250236i	0.784703	−	0.619872i	$-0.212816\pi$
$467$	−3.12210	−	5.40764i	−0.144474	−	0.250236i	−0.929176	+	0.369636i	$0.879482\pi$
$468$	−2.65502	−	2.43944i	−0.122728	−	0.112763i
$469$	−0.0629324	−	0.0370876i	−0.00290595	−	0.00171254i
$470$	4.11045	−	7.11950i	0.189601	−	0.328398i
$471$	−15.0429			−0.693142
$472$	1.45531			0.0669859
$473$	−3.68139	+	6.37635i	−0.169270	+	0.293185i
$474$	−4.93545	+	8.54845i	−0.226693	+	0.392643i
$475$	−13.2179	−	22.8941i	−0.606480	−	1.05045i
$476$	1.14074	−	0.645087i	0.0522857	−	0.0295675i
$477$	3.86750	+	6.69870i	0.177080	+	0.306712i
$478$	−3.15093			−0.144120
$479$	−10.7862	−	18.6823i	−0.492836	−	0.853617i	0.507130	−	0.861869i	$-0.330706\pi$
$479$	−10.7862	−	18.6823i	−0.492836	−	0.853617i	−0.999966	+	0.00825291i	$0.997373\pi$
$480$	0.623307	−	1.07960i	0.0284499	−	0.0492767i
$481$	−2.15270	+	9.64898i	−0.0981548	+	0.439955i
$482$	24.8446			1.13164
$483$	1.02128	+	0.601865i	0.0464699	+	0.0273858i
$484$	2.38668	−	4.13385i	0.108485	−	0.187902i
$485$	0.635563	−	1.10083i	0.0288594	−	0.0499860i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	13.6151			0.616961			0.308481	−	0.951231i	$-0.400180\pi$
$487$	13.6151			0.616961			0.308481	+	0.951231i	$0.400180\pi$
$488$	−2.09967	+	3.63674i	−0.0950476	+	0.164627i
$489$	9.02971			0.408337
$490$	−8.72490	−	0.155908i	−0.394151	−	0.00704320i
$491$	6.14512	−	10.6437i	0.277326	−	0.480342i	−0.693394	−	0.720559i	$-0.743885\pi$
$491$	6.14512	−	10.6437i	0.277326	−	0.480342i	0.970719	+	0.240217i	$0.0772186\pi$
$492$	−3.74194			−0.168700
$493$	−1.83836	+	3.18413i	−0.0827955	+	0.143406i
$494$	−20.3682	−	18.7143i	−0.916407	−	0.841995i
$495$	−1.55535	−	2.69395i	−0.0699079	−	0.121084i
$496$	−4.06448	+	7.03989i	−0.182501	+	0.316100i
$497$	21.3753	+	12.5970i	0.958812	+	0.565051i
$498$	−3.71142	−	6.42837i	−0.166313	−	0.288062i
$499$	−7.11789	−	12.3285i	−0.318640	−	0.551901i	0.661564	−	0.749889i	$-0.269893\pi$
$499$	−7.11789	−	12.3285i	−0.318640	−	0.551901i	−0.980205	+	0.197987i	$0.936560\pi$
$500$	10.5288			0.470864
$501$	2.84883			0.127276
$502$	3.69421	+	6.39857i	0.164881	+	0.285582i
$503$	10.4692	+	18.1332i	0.466798	+	0.808518i	0.999281	−	0.0379227i	$-0.0120741\pi$
$503$	10.4692	+	18.1332i	0.466798	+	0.808518i	−0.532482	+	0.846441i	$0.678741\pi$
$504$	0.0236360	−	2.64565i	0.00105283	−	0.117846i
$505$	11.1837	−	19.3708i	0.497669	−	0.861987i
$506$	−0.559018	−	0.968247i	−0.0248514	−	0.0430438i
$507$	−1.09829	−	12.9535i	−0.0487770	−	0.575286i
$508$	4.23846	−	7.34124i	0.188051	−	0.325715i
$509$	13.9297			0.617423			0.308711	−	0.951156i	$-0.400102\pi$
$509$	13.9297			0.617423			0.308711	+	0.951156i	$0.400102\pi$
$510$	0.308739	−	0.534751i	0.0136712	−	0.0236792i
$511$	−0.239741	+	26.8349i	−0.0106055	+	1.18710i
$512$	−1.00000			−0.0441942
$513$	−3.83578	+	6.64376i	−0.169354	+	0.293329i
$514$	−26.8892			−1.18603
$515$	−0.654079	+	1.13290i	−0.0288222	+	0.0499214i
$516$	−1.47532	+	2.55532i	−0.0649471	+	0.112492i
$517$	−8.22781	+	14.2510i	−0.361859	+	0.626757i
$518$	−6.31472	+	3.57097i	−0.277453	+	0.156899i
$519$	25.4875			1.11878
$520$	4.28851	−	1.34584i	0.188063	−	0.0590191i
$521$	11.1502	−	19.3128i	0.488501	−	0.846109i	−0.511412	−	0.859336i	$-0.670877\pi$
$521$	11.1502	−	19.3128i	0.488501	−	0.846109i	0.999913	+	0.0132274i	$0.00421053\pi$
$522$	3.71142	+	6.42837i	0.162445	+	0.281362i
$523$	−27.7032			−1.21138			−0.605689	−	0.795702i	$-0.707102\pi$
$523$	−27.7032			−1.21138			−0.605689	+	0.795702i	$0.707102\pi$
$524$	−8.26678	−	14.3185i	−0.361136	−	0.625506i
$525$	7.93608	−	4.48785i	0.346359	−	0.195866i
$526$	−1.46562	−	2.53852i	−0.0639040	−	0.110685i
$527$	−2.01324	+	3.48703i	−0.0876979	+	0.151897i
$528$	−1.24766	+	2.16101i	−0.0542975	+	0.0940461i
$529$	−22.7992			−0.991272
$530$	−9.64254			−0.418845
$531$	0.727653	−	1.26033i	0.0315775	−	0.0546938i
$532$	0.181325	−	20.2962i	0.00786145	−	0.879953i
$533$	−9.93493	−	9.12822i	−0.430330	−	0.395387i
$534$	5.74056	+	9.94294i	0.248418	+	0.430273i
$535$	−6.34716	−	10.9936i	−0.274412	−	0.475295i
$536$	0.0138047	+	0.0239105i	0.000596273	+	0.00103278i
$537$	9.10030	−	15.7622i	0.392707	−	0.680189i
$538$	−2.14443			−0.0924530
$539$	17.4645	+	0.312078i	0.752248	+	0.0134422i
$540$	−0.623307	−	1.07960i	−0.0268229	−	0.0464585i
$541$	7.32108	+	12.6805i	0.314758	+	0.545177i	0.979386	−	0.201998i	$-0.0647434\pi$
$541$	7.32108	+	12.6805i	0.314758	+	0.545177i	−0.664628	+	0.747174i	$0.731410\pi$
$542$	−17.2844			−0.742428
$543$	−6.86524	−	11.8910i	−0.294616	−	0.510290i
$544$	−0.495324			−0.0212368
$545$	24.7399			1.05974
$546$	6.51664	−	6.96659i	0.278886	−	0.298143i
$547$	21.7401			0.929542			0.464771	−	0.885431i	$-0.346137\pi$
$547$	21.7401			0.929542			0.464771	+	0.885431i	$0.346137\pi$
$548$	−0.856837			−0.0366023
$549$	2.09967	+	3.63674i	0.0896118	+	0.155212i
$550$	−8.59877			−0.366653
$551$	28.4724	+	49.3157i	1.21297	+	2.10092i
$552$	−0.224026	−	0.388024i	−0.00953518	−	0.0165154i
$553$	−22.4995	−	13.2595i	−0.956777	−	0.563851i
$554$	2.83381			0.120397
$555$	−1.70907	+	2.96019i	−0.0725459	+	0.125653i
$556$	4.74886	+	8.22528i	0.201397	+	0.348829i
$557$	−2.23589	−	3.87267i	−0.0947375	−	0.164090i	0.814762	−	0.579796i	$-0.196868\pi$
$557$	−2.23589	−	3.87267i	−0.0947375	−	0.164090i	−0.909499	+	0.415706i	$0.863535\pi$
$558$	4.06448	+	7.03989i	0.172063	+	0.298022i
$559$	−10.1505	+	3.18550i	−0.429322	+	0.134732i
$560$	2.84150	+	1.67457i	0.120075	+	0.0707633i
$561$	−0.617997	+	1.07040i	−0.0260919	+	0.0451924i
$562$	28.5254			1.20327
$563$	−11.1580			−0.470253			−0.235126	−	0.971965i	$-0.575550\pi$
$563$	−11.1580			−0.470253			−0.235126	+	0.971965i	$0.575550\pi$
$564$	−3.29729	+	5.71107i	−0.138841	+	0.240480i
$565$	9.89113	−	17.1319i	0.416123	−	0.720746i
$566$	−2.29901	−	3.98201i	−0.0966347	−	0.167376i
$567$	−2.27938	−	1.34329i	−0.0957249	−	0.0564130i
$568$	−4.68884	−	8.12130i	−0.196739	−	0.340762i
$569$	−36.8818			−1.54617			−0.773083	−	0.634304i	$-0.781287\pi$
$569$	−36.8818			−1.54617			−0.773083	+	0.634304i	$0.781287\pi$
$570$	−4.78173	−	8.28221i	−0.200285	−	0.346903i
$571$	0.101526	−	0.175849i	0.00424874	−	0.00735904i	−0.863893	−	0.503675i	$-0.831981\pi$
$571$	0.101526	−	0.175849i	0.00424874	−	0.00735904i	0.868142	+	0.496316i	$0.165314\pi$
$572$	−8.58423	+	2.69395i	−0.358925	+	0.112640i
$573$	−5.28588			−0.220821
$574$	0.0884446	−	9.89984i	0.00369161	−	0.413211i
$575$	0.771984	−	1.33711i	0.0321939	−	0.0557615i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	10.4151	−	18.0396i	0.433588	−	0.750997i	−0.563591	−	0.826054i	$-0.690581\pi$
$577$	10.4151	−	18.0396i	0.433588	−	0.750997i	0.997179	+	0.0750570i	$0.0239139\pi$
$578$	16.7547			0.696902
$579$	2.40599	−	4.16729i	0.0999893	−	0.173187i
$580$	−9.25342			−0.384227
$581$	17.0949	−	9.66717i	0.709217	−	0.401062i
$582$	−0.509831	+	0.883054i	−0.0211332	+	0.0366038i
$583$	19.3013			0.799379
$584$	5.07151	−	8.78412i	0.209861	−	0.363489i
$585$	0.978720	−	4.38688i	0.0404651	−	0.181375i
$586$	−3.19384	−	5.53189i	−0.131936	−	0.228520i
$587$	−8.25511	+	14.2983i	−0.340725	+	0.590153i	−0.984568	−	0.175005i	$-0.944006\pi$
$587$	−8.25511	+	14.2983i	−0.340725	+	0.590153i	0.643843	+	0.765158i	$0.277339\pi$
$588$	6.99888	+	0.125065i	0.288629	+	0.00515760i
$589$	31.1809	+	54.0069i	1.28479	+	2.22532i
$590$	0.907102	+	1.57115i	0.0373448	+	0.0646831i
$591$	23.5486			0.968659
$592$	2.74194			0.112693
$593$	5.86959	+	10.1664i	0.241035	+	0.417485i	0.961009	−	0.276515i	$-0.0891797\pi$
$593$	5.86959	+	10.1664i	0.241035	+	0.417485i	−0.719974	+	0.694001i	$0.755846\pi$
$594$	1.24766	+	2.16101i	0.0511922	+	0.0886675i
$595$	1.40747	+	0.829453i	0.0577005	+	0.0340043i
$596$	2.36872	−	4.10274i	0.0970264	−	0.168055i
$597$	5.63984	+	9.76849i	0.230823	+	0.399798i
$598$	0.351767	−	1.57671i	0.0143848	−	0.0644765i
$599$	−21.8486	+	37.8430i	−0.892711	+	1.54622i	−0.0560993	+	0.998425i	$0.517866\pi$
$599$	−21.8486	+	37.8430i	−0.892711	+	1.54622i	−0.836612	+	0.547796i	$0.815467\pi$
$600$	−3.44595			−0.140681
$601$	2.84613	−	4.92964i	0.116096	−	0.201084i	−0.802121	−	0.597161i	$-0.796295\pi$
$601$	2.84613	−	4.92964i	0.116096	−	0.201084i	0.918217	+	0.396077i	$0.129629\pi$
$602$	−6.72560	−	3.96356i	−0.274115	−	0.161543i
$603$	0.0276094			0.00112434
$604$	−3.56085	+	6.16758i	−0.144889	+	0.250955i
$605$	5.95053			0.241924
$606$	−8.97127	+	15.5387i	−0.364433	+	0.631217i
$607$	12.5493	−	21.7360i	0.509360	−	0.882238i	−0.490581	−	0.871396i	$-0.663215\pi$
$607$	12.5493	−	21.7360i	0.509360	−	0.882238i	0.999941	−	0.0108424i	$-0.00345131\pi$
$608$	−3.83578	+	6.64376i	−0.155561	+	0.269440i
$609$	−17.0949	+	9.66717i	−0.692721	+	0.391734i
$610$	−5.23496			−0.211957
$611$	−22.6862	+	7.11950i	−0.917785	+	0.288024i
$612$	−0.247662	+	0.428963i	−0.0100111	+	0.0173398i
$613$	−1.29666	−	2.24587i	−0.0523715	−	0.0907100i	0.838651	−	0.544669i	$-0.183345\pi$
$613$	−1.29666	−	2.24587i	−0.0523715	−	0.0907100i	−0.891023	+	0.453959i	$0.850011\pi$
$614$	1.39899			0.0564587
$615$	−2.33237	−	4.03979i	−0.0940504	−	0.162900i
$616$	−5.68779	−	3.35195i	−0.229168	−	0.135054i
$617$	8.83438	+	15.3016i	0.355659	+	0.616019i	0.987231	−	0.159298i	$-0.0509231\pi$
$617$	8.83438	+	15.3016i	0.355659	+	0.616019i	−0.631572	+	0.775318i	$0.717590\pi$
$618$	0.524685	−	0.908780i	0.0211059	−	0.0365565i
$619$	20.4642	−	35.4450i	0.822525	−	1.42465i	−0.0812719	−	0.996692i	$-0.525898\pi$
$619$	20.4642	−	35.4450i	0.822525	−	1.42465i	0.903797	−	0.427962i	$-0.140768\pi$
$620$	−10.1337			−0.406978
$621$	−0.448052			−0.0179797
$622$	8.55183	−	14.8122i	0.342897	−	0.593915i
$623$	−26.4412	+	14.9525i	−1.05934	+	0.599058i
$624$	−3.44013	+	1.07960i	−0.137715	+	0.0432185i
$625$	−2.05219	−	3.55450i	−0.0820876	−	0.142180i
$626$	5.81247	+	10.0675i	0.232313	+	0.402378i
$627$	9.57151	+	16.5783i	0.382249	+	0.662075i
$628$	−7.52147	+	13.0276i	−0.300139	+	0.519857i
$629$	1.35815			0.0541529
$630$	2.87097	−	1.62353i	0.114382	−	0.0646830i
$631$	3.58097	+	6.20242i	0.142556	+	0.246914i	0.928459	−	0.371436i	$-0.121135\pi$
$631$	3.58097	+	6.20242i	0.142556	+	0.246914i	−0.785902	+	0.618351i	$0.787801\pi$
$632$	4.93545	+	8.54845i	0.196322	+	0.340039i
$633$	−12.4404			−0.494462
$634$	3.29277	+	5.70324i	0.130773	+	0.226505i
$635$	10.5675			0.419357
$636$	7.73499			0.306712
$637$	18.2771	+	17.4054i	0.724165	+	0.689626i
$638$	18.5224			0.733309
$639$	−9.37767			−0.370975
$640$	−0.623307	−	1.07960i	−0.0246384	−	0.0426749i
$641$	3.25919			0.128730			0.0643652	−	0.997926i	$-0.479498\pi$
$641$	3.25919			0.128730			0.0643652	+	0.997926i	$0.479498\pi$
$642$	5.09152	+	8.81877i	0.200946	+	0.348049i
$643$	−9.17027	−	15.8834i	−0.361640	−	0.626379i	0.626591	−	0.779348i	$-0.284450\pi$
$643$	−9.17027	−	15.8834i	−0.361640	−	0.626379i	−0.988231	+	0.152969i	$0.951116\pi$
$644$	1.03187	−	0.583522i	0.0406614	−	0.0229940i
$645$	−3.67830			−0.144833
$646$	−1.89995	+	3.29082i	−0.0747527	+	0.129475i
$647$	−21.9343	−	37.9913i	−0.862325	−	1.49359i	−0.869679	−	0.493618i	$-0.835674\pi$
$647$	−21.9343	−	37.9913i	−0.862325	−	1.49359i	0.00735417	−	0.999973i	$-0.497659\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−1.81573	−	3.14494i	−0.0712737	−	0.123450i
$650$	−9.14909	−	8.40619i	−0.358857	−	0.329718i
$651$	−18.7211	+	10.5868i	−0.733738	+	0.414929i
$652$	4.51485	−	7.81996i	0.176815	−	0.306253i
$653$	13.2804			0.519704			0.259852	−	0.965649i	$-0.416326\pi$
$653$	13.2804			0.519704			0.259852	+	0.965649i	$0.416326\pi$
$654$	−19.8457			−0.776028
$655$	10.3055	−	17.8496i	0.402668	−	0.697442i
$656$	−1.87097	+	3.24061i	−0.0730491	+	0.126525i
$657$	−5.07151	−	8.78412i	−0.197859	−	0.342701i
$658$	−15.0315	−	8.85845i	−0.585991	−	0.345338i
$659$	1.53479	+	2.65834i	0.0597871	+	0.103554i	0.894370	−	0.447328i	$-0.147624\pi$
$659$	1.53479	+	2.65834i	0.0597871	+	0.103554i	−0.834583	+	0.550883i	$0.814291\pi$
$660$	−3.11070			−0.121084
$661$	14.8034	+	25.6402i	0.575785	+	0.997290i	0.995956	+	0.0898443i	$0.0286370\pi$
$661$	14.8034	+	25.6402i	0.575785	+	0.997290i	−0.420170	+	0.907445i	$0.638030\pi$
$662$	−11.6343	+	20.1512i	−0.452179	+	0.783197i
$663$	−1.70398	+	0.534751i	−0.0661770	+	0.0207680i
$664$	−7.42285			−0.288062
$665$	22.0248	−	12.4550i	0.854085	−	0.482985i
$666$	1.37097	−	2.37459i	0.0531240	−	0.0920134i
$667$	−1.66291	+	2.88025i	−0.0643882	+	0.111524i
$668$	1.42442	−	2.46716i	0.0551123	−	0.0954573i
$669$	−20.9301			−0.809206
$670$	−0.0172092	+	0.0298071i	−0.000664848	+	0.00115155i
$671$	10.4787			0.404526
$672$	−2.27938	−	1.34329i	−0.0879289	−	0.0518186i
$673$	−4.54511	+	7.87235i	−0.175201	+	0.303457i	−0.940231	−	0.340538i	$-0.889391\pi$
$673$	−4.54511	+	7.87235i	−0.175201	+	0.303457i	0.765030	+	0.643995i	$0.222724\pi$
$674$	−19.4320			−0.748491
$675$	−1.72298	+	2.98428i	−0.0663174	+	0.114865i
$676$	−11.7672	−	5.52561i	−0.452586	−	0.212523i
$677$	8.92163	+	15.4527i	0.342886	+	0.593896i	0.984967	−	0.172741i	$-0.0552622\pi$
$677$	8.92163	+	15.4527i	0.342886	+	0.593896i	−0.642081	+	0.766636i	$0.721929\pi$
$678$	−7.93440	+	13.7428i	−0.304719	+	0.527789i
$679$	−2.32420	−	1.36970i	−0.0891945	−	0.0525645i
$680$	−0.308739	−	0.534751i	−0.0118396	−	0.0205068i
$681$	8.79052	+	15.2256i	0.336853	+	0.583447i
$682$	20.2844			0.776730
$683$	−12.3180			−0.471333			−0.235667	−	0.971834i	$-0.575727\pi$
$683$	−12.3180			−0.471333			−0.235667	+	0.971834i	$0.575727\pi$
$684$	3.83578	+	6.64376i	0.146665	+	0.254031i
$685$	−0.534072	−	0.925040i	−0.0204058	−	0.0353440i
$686$	−0.496304	+	18.5136i	−0.0189490	+	0.706853i
$687$	−7.24620	+	12.5508i	−0.276460	+	0.478842i
$688$	1.47532	+	2.55532i	0.0562459	+	0.0974207i
$689$	20.5366	+	18.8690i	0.782381	+	0.718853i
$690$	0.279274	−	0.483717i	0.0106318	−	0.0184148i
$691$	−27.1762			−1.03383			−0.516916	−	0.856036i	$-0.672920\pi$
$691$	−27.1762			−1.03383			−0.516916	+	0.856036i	$0.672920\pi$
$692$	12.7438	−	22.0729i	0.484446	−	0.839084i
$693$	−5.74677	+	3.24979i	−0.218302	+	0.123449i
$694$	−29.6707			−1.12629
$695$	−5.92000	+	10.2537i	−0.224558	+	0.388946i
$696$	7.42285			0.281362
$697$	−0.926736	+	1.60515i	−0.0351026	+	0.0607995i
$698$	13.3023	−	23.0403i	0.503501	−	0.872090i
$699$	7.24897	−	12.5556i	0.274181	−	0.474896i
$700$	0.0814487	−	9.11678i	0.00307847	−	0.344582i
$701$	38.0704			1.43790			0.718950	−	0.695062i	$-0.244623\pi$
$701$	38.0704			1.43790			0.718950	+	0.695062i	$0.244623\pi$
$702$	−0.785103	+	3.51904i	−0.0296318	+	0.132817i
$703$	10.5175	−	18.2168i	0.396674	−	0.687059i
$704$	1.24766	+	2.16101i	0.0470230	+	0.0814463i
$705$	−8.22089			−0.309617
$706$	−6.90939	−	11.9674i	−0.260038	−	0.450400i
$707$	−40.8979	−	24.1021i	−1.53812	−	0.906452i
$708$	−0.727653	−	1.26033i	−0.0273469	−	0.0473662i
$709$	20.7624	−	35.9616i	0.779750	−	1.35057i	−0.152336	−	0.988329i	$-0.548679\pi$
$709$	20.7624	−	35.9616i	0.779750	−	1.35057i	0.932086	−	0.362238i	$-0.117987\pi$
$710$	5.84517	−	10.1241i	0.219365	−	0.379952i
$711$	9.87090			0.370188
$712$	11.4811			0.430273
$713$	−1.82110	+	3.15424i	−0.0682007	+	0.118127i
$714$	−1.12903	−	0.665365i	−0.0422529	−	0.0249007i
$715$	−8.25899	−	7.58837i	−0.308869	−	0.283789i
$716$	−9.10030	−	15.7622i	−0.340094	−	0.589061i
$717$	1.57547	+	2.72879i	0.0588368	+	0.101908i
$718$	−1.38095	−	2.39188i	−0.0515368	−	0.0892643i
$719$	−8.30463	+	14.3840i	−0.309710	+	0.536434i	−0.978299	−	0.207198i	$-0.933565\pi$
$719$	−8.30463	+	14.3840i	−0.309710	+	0.536434i	0.668589	+	0.743633i	$0.266899\pi$
$720$	−1.24661			−0.0464585
$721$	2.39191	+	1.40961i	0.0890794	+	0.0524966i
$722$	19.9264	+	34.5135i	0.741584	+	1.28446i
$723$	−12.4223	−	21.5160i	−0.461990	−	0.800189i
$724$	−13.7305			−0.510290
$725$	12.7894	+	22.1519i	0.474986	+	0.822701i
$726$	−4.77336			−0.177156
$727$	−20.2421			−0.750737			−0.375368	−	0.926876i	$-0.622484\pi$
$727$	−20.2421			−0.750737			−0.375368	+	0.926876i	$0.622484\pi$
$728$	−2.77493	−	9.12687i	−0.102846	−	0.338264i
$729$	1.00000			0.0370370
$730$	12.6444			0.467991
$731$	0.730759	+	1.26571i	0.0270281	+	0.0468141i
$732$	4.19934			0.155212
$733$	−8.42173	−	14.5869i	−0.311064	−	0.538778i	0.667529	−	0.744584i	$-0.267352\pi$
$733$	−8.42173	−	14.5869i	−0.311064	−	0.538778i	−0.978593	+	0.205805i	$0.934019\pi$
$734$	−5.46151	−	9.45961i	−0.201588	−	0.349161i
$735$	4.22743	+	7.63394i	0.155931	+	0.281582i
$736$	−0.448052			−0.0165154
$737$	0.0344473	−	0.0596644i	0.00126888	−	0.00219777i
$738$	1.87097	+	3.24061i	0.0688713	+	0.119289i
$739$	24.0597	+	41.6726i	0.885049	+	1.53295i	0.845657	+	0.533726i	$0.179209\pi$
$739$	24.0597	+	41.6726i	0.885049	+	1.53295i	0.0393919	+	0.999224i	$0.487458\pi$
$740$	1.70907	+	2.96019i	0.0628266	+	0.108819i
$741$	−6.02296	+	26.9965i	−0.221259	+	0.991741i
$742$	−0.182825	+	20.4640i	−0.00671170	+	0.751259i
$743$	2.98460	−	5.16948i	0.109494	−	0.189650i	−0.806071	−	0.591819i	$-0.798410\pi$
$743$	2.98460	−	5.16948i	0.109494	−	0.189650i	0.915566	+	0.402169i	$0.131744\pi$
$744$	8.12896			0.298022
$745$	5.90575			0.216370
$746$	9.84303	−	17.0486i	0.360379	−	0.624195i
$747$	−3.71142	+	6.42837i	−0.135794	+	0.235202i
$748$	0.617997	+	1.07040i	0.0225962	+	0.0391378i
$749$	−23.4517	+	13.2619i	−0.856906	+	0.484580i
$750$	−5.26442	−	9.11824i	−0.192229	−	0.332951i
$751$	36.3054			1.32480			0.662401	−	0.749150i	$-0.269538\pi$
$751$	36.3054			1.32480			0.662401	+	0.749150i	$0.269538\pi$
$752$	3.29729	+	5.71107i	0.120240	+	0.208261i
$753$	3.69421	−	6.39857i	0.134625	−	0.233177i
$754$	19.7078	+	18.1076i	0.717717	+	0.659439i
$755$	−8.87802			−0.323104
$756$	−2.30301	+	1.30235i	−0.0837598	+	0.0473661i
$757$	−3.48399	+	6.03445i	−0.126628	+	0.219326i	−0.922368	−	0.386312i	$-0.873749\pi$
$757$	−3.48399	+	6.03445i	−0.126628	+	0.219326i	0.795740	+	0.605638i	$0.207082\pi$
$758$	8.31713	−	14.4057i	0.302092	−	0.523238i
$759$	−0.559018	+	0.968247i	−0.0202911	+	0.0351451i
$760$	−9.56347			−0.346903
$761$	1.47562	−	2.55585i	0.0534912	−	0.0926496i	−0.838040	−	0.545609i	$-0.816298\pi$
$761$	1.47562	−	2.55585i	0.0534912	−	0.0926496i	0.891531	+	0.452959i	$0.149632\pi$
$762$	−8.47693			−0.307087
$763$	0.469074	−	52.5047i	0.0169816	−	1.90080i
$764$	−2.64294	+	4.57771i	−0.0956182	+	0.165616i
$765$	−0.617478			−0.0223250
$766$	18.1834	−	31.4945i	0.656992	−	1.13794i
$767$	1.14257	−	5.12128i	0.0412556	−	0.184919i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−21.0168	+	36.4022i	−0.757885	+	1.31270i	0.186042	+	0.982542i	$0.440434\pi$
$769$	−21.0168	+	36.4022i	−0.757885	+	1.31270i	−0.943927	+	0.330154i	$0.892899\pi$
$770$	0.0735247	−	8.22982i	0.00264965	−	0.296582i
$771$	13.4446	+	23.2867i	0.484195	+	0.838650i
$772$	−2.40599	−	4.16729i	−0.0865933	−	0.149984i
$773$	−43.6310			−1.56930			−0.784650	−	0.619940i	$-0.787157\pi$
$773$	−43.6310			−1.56930			−0.784650	+	0.619940i	$0.787157\pi$
$774$	2.95063			0.106058
$775$	14.0060	+	24.2591i	0.503111	+	0.871414i
$776$	0.509831	+	0.883054i	0.0183019	+	0.0316998i
$777$	6.24991	+	3.68322i	0.224214	+	0.132135i
$778$	−8.89008	+	15.3981i	−0.318725	+	0.552048i
$779$	14.3532	+	24.8606i	0.514258	+	0.890722i
$780$	−3.30979	−	3.04103i	−0.118509	−	0.108887i
$781$	−11.7002	+	20.2653i	−0.418665	+	0.725149i
$782$	−0.221931			−0.00793624
$783$	3.71142	−	6.42837i	0.132635	−	0.229731i
$784$	3.60775	−	5.99868i	0.128848	−	0.214238i
$785$	−18.7527			−0.669314
$786$	−8.26678	+	14.3185i	−0.294866	+	0.510723i
$787$	24.3320			0.867341			0.433671	−	0.901071i	$-0.357218\pi$
$787$	24.3320			0.867341			0.433671	+	0.901071i	$0.357218\pi$
$788$	11.7743	−	20.3937i	0.419442	−	0.726494i
$789$	−1.46562	+	2.53852i	−0.0521774	+	0.0903738i
$790$	−6.15260	+	10.6566i	−0.218900	+	0.379145i
$791$	−36.1710	−	21.3164i	−1.28609	−	0.757925i
$792$	2.49532			0.0886675
$793$	11.1493	+	10.2440i	0.395925	+	0.363776i
$794$	4.43952	−	7.68948i	0.157553	−	0.272889i
$795$	4.82127	+	8.35069i	0.170993	+	0.296168i
$796$	11.2797			0.399798
$797$	−13.8223	−	23.9408i	−0.489609	−	0.848028i	0.510319	−	0.859985i	$-0.329527\pi$
$797$	−13.8223	−	23.9408i	−0.489609	−	0.848028i	−0.999929	+	0.0119569i	$0.996194\pi$
$798$	−17.6677	+	9.99108i	−0.625430	+	0.353680i
$799$	1.63323	+	2.82883i	0.0577794	+	0.100077i
$800$	−1.72298	+	2.98428i	−0.0609165	+	0.105510i
$801$	5.74056	−	9.94294i	0.202833	−	0.351317i
$802$	30.1630			1.06509
$803$	−25.3101			−0.893175
$804$	0.0138047	−	0.0239105i	0.000486855	−	0.000843258i
$805$	1.27314	+	0.750293i	0.0448723	+	0.0264443i
$806$	21.5826	+	19.8301i	0.760214	+	0.698485i
$807$	1.07222	+	1.85713i	0.0377438	+	0.0653741i
$808$	8.97127	+	15.5387i	0.315608	+	0.546650i
$809$	23.3835	+	40.5014i	0.822119	+	1.42395i	0.904101	+	0.427319i	$0.140542\pi$
$809$	23.3835	+	40.5014i	0.822119	+	1.42395i	−0.0819815	+	0.996634i	$0.526125\pi$
$810$	−0.623307	+	1.07960i	−0.0219008	+	0.0379332i
$811$	−33.4037			−1.17296			−0.586481	−	0.809963i	$-0.699487\pi$
$811$	−33.4037			−1.17296			−0.586481	+	0.809963i	$0.699487\pi$
$812$	−0.175447	+	19.6382i	−0.00615697	+	0.689167i
$813$	8.64220	+	14.9687i	0.303095	+	0.524976i
$814$	−3.42101	−	5.92537i	−0.119906	−	0.207684i
$815$	11.2566			0.394300
$816$	0.247662	+	0.428963i	0.00866991	+	0.0150167i
$817$	22.6359			0.791931
$818$	−16.7720			−0.586420
$819$	−9.29157	−	2.16028i	−0.324674	−	0.0754863i
$820$	−4.66475			−0.162900
$821$	37.4874			1.30832			0.654160	−	0.756356i	$-0.273022\pi$
$821$	37.4874			1.30832			0.654160	+	0.756356i	$0.273022\pi$
$822$	0.428418	+	0.742042i	0.0149428	+	0.0258817i
$823$	−49.7545			−1.73433			−0.867166	−	0.498020i	$-0.834061\pi$
$823$	−49.7545			−1.73433			−0.867166	+	0.498020i	$0.834061\pi$
$824$	−0.524685	−	0.908780i	−0.0182783	−	0.0316589i
$825$	4.29939	+	7.44676i	0.149685	+	0.259263i
$826$	3.35159	−	1.89532i	0.116617	−	0.0659467i
$827$	3.32250			0.115534			0.0577672	−	0.998330i	$-0.481602\pi$
$827$	3.32250			0.115534			0.0577672	+	0.998330i	$0.481602\pi$
$828$	−0.224026	+	0.388024i	−0.00778544	+	0.0134848i
$829$	8.25485	+	14.2978i	0.286703	+	0.496584i	0.973021	−	0.230718i	$-0.0741075\pi$
$829$	8.25485	+	14.2978i	0.286703	+	0.496584i	−0.686318	+	0.727302i	$0.740774\pi$
$830$	−4.62671	−	8.01370i	−0.160595	−	0.278160i
$831$	−1.41690	−	2.45415i	−0.0491519	−	0.0851336i
$832$	−0.785103	+	3.51904i	−0.0272185	+	0.122001i
$833$	1.78701	−	2.97129i	0.0619161	−	0.102949i
$834$	4.74886	−	8.22528i	0.164440	−	0.284818i
$835$	3.55139			0.122901
$836$	19.1430			0.662075
$837$	4.06448	−	7.03989i	0.140489	−	0.243334i
$838$	19.8098	−	34.3115i	0.684317	−	1.18527i
$839$	8.35299	+	14.4678i	0.288377	+	0.499484i	0.973423	−	0.229016i	$-0.0735510\pi$
$839$	8.35299	+	14.4678i	0.288377	+	0.499484i	−0.685045	+	0.728500i	$0.740218\pi$
$840$	0.0294650	−	3.29810i	0.00101664	−	0.113795i
$841$	−13.0493	−	22.6021i	−0.449977	−	0.779383i
$842$	32.2271			1.11062
$843$	−14.2627	−	24.7037i	−0.491234	−	0.850842i
$844$	−6.22021	+	10.7737i	−0.214108	+	0.370847i
$845$	−1.36915	−	16.1480i	−0.0471002	−	0.555509i
$846$	6.59458			0.226726
$847$	0.112823	−	12.6286i	0.00387665	−	0.433924i
$848$	3.86750	−	6.69870i	0.132810	−	0.230034i
$849$	−2.29901	+	3.98201i	−0.0789019	+	0.136662i
$850$	−0.853432	+	1.47819i	−0.0292725	+	0.0507014i
$851$	1.22853			0.0421135
$852$	−4.68884	+	8.12130i	−0.160637	+	0.278231i
$853$	27.5476			0.943212			0.471606	−	0.881809i	$-0.343674\pi$
$853$	27.5476			0.943212			0.471606	+	0.881809i	$0.343674\pi$
$854$	−0.0992558	+	11.1100i	−0.00339646	+	0.380175i
$855$	−4.78173	+	8.28221i	−0.163532	+	0.283245i
$856$	10.1830			0.348049
$857$	−9.17302	+	15.8881i	−0.313344	+	0.542729i	−0.979084	−	0.203455i	$-0.934783\pi$
$857$	−9.17302	+	15.8881i	−0.313344	+	0.542729i	0.665740	+	0.746184i	$0.268116\pi$
$858$	6.62514	+	6.08719i	0.226179	+	0.207813i
$859$	−21.5684	−	37.3575i	−0.735903	−	1.27462i	−0.954326	−	0.298767i	$-0.903425\pi$
$859$	−21.5684	−	37.3575i	−0.735903	−	1.27462i	0.218423	−	0.975854i	$-0.429909\pi$
$860$	−1.83915	+	3.18550i	−0.0627144	+	0.108625i
$861$	−8.61774	+	4.87333i	−0.293692	+	0.166082i
$862$	5.50063	+	9.52738i	0.187352	+	0.324504i
$863$	22.5095	+	38.9876i	0.766233	+	1.32715i	0.939592	+	0.342296i	$0.111204\pi$
$863$	22.5095	+	38.9876i	0.766233	+	1.32715i	−0.173359	+	0.984859i	$0.555462\pi$
$864$	1.00000			0.0340207
$865$	31.7731			1.08032
$866$	−15.9643	−	27.6509i	−0.542488	−	0.939616i
$867$	−8.37733	−	14.5100i	−0.284509	−	0.492784i
$868$	−0.192136	+	21.5064i	−0.00652154	+	0.729973i
$869$	12.3155	−	21.3312i	0.417776	−	0.723610i
$870$	4.62671	+	8.01370i	0.156860	+	0.271690i
$871$	0.0949800	−	0.0298071i	0.00321827	−	0.00100998i
$872$	−9.92285	+	17.1869i	−0.336030	+	0.582021i
$873$	1.01966			0.0345104
$874$	−1.71863	+	2.97675i	−0.0581335	+	0.100690i
$875$	24.2481	−	13.7123i	0.819734	−	0.463559i
$876$	−10.1430			−0.342701
$877$	10.9297	−	18.9309i	0.369071	−	0.639250i	−0.620349	−	0.784326i	$-0.713009\pi$
$877$	10.9297	−	18.9309i	0.369071	−	0.639250i	0.989421	+	0.145075i	$0.0463425\pi$
$878$	1.43526			0.0484376
$879$	−3.19384	+	5.53189i	−0.107726	+	0.186586i
$880$	−1.55535	+	2.69395i	−0.0524309	+	0.0908130i
$881$	0.975574	−	1.68974i	0.0328679	−	0.0569289i	−0.849124	−	0.528194i	$-0.822869\pi$
$881$	0.975574	−	1.68974i	0.0328679	−	0.0569289i	0.881991	+	0.471265i	$0.156203\pi$
$882$	−3.39113	−	6.12374i	−0.114185	−	0.206197i
$883$	−20.9397			−0.704677			−0.352338	−	0.935873i	$-0.614613\pi$
$883$	−20.9397			−0.704677			−0.352338	+	0.935873i	$0.614613\pi$
$884$	−0.388880	+	1.74306i	−0.0130795	+	0.0586256i
$885$	0.907102	−	1.57115i	0.0304919	−	0.0528135i
$886$	−5.72758	−	9.92047i	−0.192422	−	0.333285i
$887$	23.5772			0.791646			0.395823	−	0.918327i	$-0.370459\pi$
$887$	23.5772			0.791646			0.395823	+	0.918327i	$0.370459\pi$
$888$	−1.37097	−	2.37459i	−0.0460067	−	0.0796859i
$889$	0.200361	−	22.4270i	0.00671989	−	0.752176i
$890$	7.15626	+	12.3950i	0.239878	+	0.415482i
$891$	1.24766	−	2.16101i	0.0417983	−	0.0723967i
$892$	−10.4651	+	18.1260i	−0.350396	+	0.606904i
$893$	50.5907			1.69295
$894$	−4.73744			−0.158444
$895$	11.3446	−	19.6494i	0.379207	−	0.656806i
$896$	−2.30301	+	1.30235i	−0.0769383	+	0.0435086i
$897$	−1.54136	+	0.483717i	−0.0514644	+	0.0161508i
$898$	17.3713	+	30.0880i	0.579688	+	1.00405i
$899$	−30.1700	−	52.2560i	−1.00623	−	1.74284i
$900$	1.72298	+	2.98428i	0.0574326	+	0.0994761i
$901$	1.91566	−	3.31803i	0.0638200	−	0.110540i
$902$	9.33735			0.310900
$903$	−0.0697412	+	7.80632i	−0.00232084	+	0.259778i
$904$	7.93440	+	13.7428i	0.263894	+	0.457078i
$905$	−8.55831	−	14.8234i	−0.284488	−	0.492747i
$906$	7.12171			0.236603
$907$	−0.0707540	−	0.122550i	−0.00234935	−	0.00406919i	0.864848	−	0.502033i	$-0.167414\pi$
$907$	−0.0707540	−	0.122550i	−0.00234935	−	0.00406919i	−0.867198	+	0.497964i	$0.834081\pi$
$908$	17.5810			0.583447
$909$	17.9425			0.595117
$910$	8.12373	−	8.68465i	0.269299	−	0.287893i
$911$	48.1769			1.59617			0.798086	−	0.602543i	$-0.205846\pi$
$911$	48.1769			1.59617			0.798086	+	0.602543i	$0.205846\pi$
$912$	7.67156			0.254031
$913$	9.26121	+	16.0409i	0.306501	+	0.530876i
$914$	−36.8048			−1.21740
$915$	2.61748	+	4.53360i	0.0865311	+	0.149876i
$916$	7.24620	+	12.5508i	0.239421	+	0.414690i
$917$	−37.6862	−	22.2094i	−1.24451	−	0.733419i
$918$	0.495324			0.0163481
$919$	−19.8090	+	34.3102i	−0.653439	+	1.13179i	0.328844	+	0.944384i	$0.393341\pi$
$919$	−19.8090	+	34.3102i	−0.653439	+	1.13179i	−0.982283	+	0.187405i	$0.939992\pi$
$920$	−0.279274	−	0.483717i	−0.00920739	−	0.0159477i
$921$	−0.699495	−	1.21156i	−0.0230492	−	0.0399223i
$922$	3.99129	+	6.91311i	0.131446	+	0.227671i
$923$	−32.2604	+	10.1241i	−1.06186	+	0.333240i
$924$	−0.0589796	+	6.60174i	−0.00194029	+	0.217181i
$925$	4.72430	−	8.18272i	0.155334	−	0.269046i
$926$	−26.4799			−0.870185
$927$	−1.04937			−0.0344658
$928$	3.71142	−	6.42837i	0.121833	−	0.211022i
$929$	−18.0167	+	31.2059i	−0.591109	+	1.02383i	0.402974	+	0.915211i	$0.367976\pi$
$929$	−18.0167	+	31.2059i	−0.591109	+	1.02383i	−0.994083	+	0.108620i	$0.965357\pi$
$930$	5.06684	+	8.77602i	0.166148	+	0.287777i
$931$	−26.0153	−	46.9787i	−0.852616	−	1.53966i
$932$	−7.24897	−	12.5556i	−0.237448	−	0.411272i
$933$	−17.1037			−0.559949
$934$	3.12210	+	5.40764i	0.102158	+	0.176943i
$935$	−0.770404	+	1.33438i	−0.0251949	+	0.0436388i
$936$	2.65502	+	2.43944i	0.0867821	+	0.0797355i
$937$	−2.37671			−0.0776439			−0.0388219	−	0.999246i	$-0.512361\pi$
$937$	−2.37671			−0.0776439			−0.0388219	+	0.999246i	$0.512361\pi$
$938$	0.0629324	+	0.0370876i	0.00205481	+	0.00121095i
$939$	5.81247	−	10.0675i	0.189683	−	0.328540i
$940$	−4.11045	+	7.11950i	−0.134068	+	0.232213i
$941$	−19.3411	+	33.4998i	−0.630503	+	1.09206i	0.356946	+	0.934125i	$0.383818\pi$
$941$	−19.3411	+	33.4998i	−0.630503	+	1.09206i	−0.987449	+	0.157938i	$0.949515\pi$
$942$	15.0429			0.490125
$943$	−0.838291	+	1.45196i	−0.0272985	+	0.0472824i
$944$	−1.45531			−0.0473662
$945$	−2.84150	−	1.67457i	−0.0924341	−	0.0544736i
$946$	3.68139	−	6.37635i	0.119692	−	0.207313i
$947$	−14.7464			−0.479194			−0.239597	−	0.970872i	$-0.577015\pi$
$947$	−14.7464			−0.479194			−0.239597	+	0.970872i	$0.577015\pi$
$948$	4.93545	−	8.54845i	0.160296	−	0.277641i
$949$	−26.9300	−	24.7433i	−0.874184	−	0.803201i
$950$	13.2179	+	22.8941i	0.428846	+	0.742783i
$951$	3.29277	−	5.70324i	0.106775	−	0.184940i
$952$	−1.14074	+	0.645087i	−0.0369716	+	0.0209074i
$953$	8.54843	+	14.8063i	0.276911	+	0.479623i	0.970615	−	0.240636i	$-0.0773561\pi$
$953$	8.54843	+	14.8063i	0.276911	+	0.479623i	−0.693705	+	0.720259i	$0.744023\pi$
$954$	−3.86750	−	6.69870i	−0.125215	−	0.216878i
$955$	−6.58945			−0.213230
$956$	3.15093			0.101908
$957$	−9.26121	−	16.0409i	−0.299372	−	0.518528i
$958$	10.7862	+	18.6823i	0.348487	+	0.603598i
$959$	−1.97331	+	1.11590i	−0.0637214	+	0.0360344i
$960$	−0.623307	+	1.07960i	−0.0201171	+	0.0348439i
$961$	−17.5400	−	30.3802i	−0.565807	−	0.980006i
$962$	2.15270	−	9.64898i	0.0694059	−	0.311096i
$963$	5.09152	−	8.81877i	0.164072	−	0.284181i
$964$	−24.8446			−0.800189
$965$	2.99933	−	5.19500i	0.0965520	−	0.167233i
$966$	−1.02128	−	0.601865i	−0.0328592	−	0.0193647i
$967$	−7.90857			−0.254323			−0.127161	−	0.991882i	$-0.540587\pi$
$967$	−7.90857			−0.254323			−0.127161	+	0.991882i	$0.540587\pi$
$968$	−2.38668	+	4.13385i	−0.0767108	+	0.132867i
$969$	3.79991			0.122071
$970$	−0.635563	+	1.10083i	−0.0204067	+	0.0353454i
$971$	−1.95050	+	3.37836i	−0.0625944	+	0.108417i	−0.895624	−	0.444811i	$-0.853271\pi$
$971$	−1.95050	+	3.37836i	−0.0625944	+	0.108417i	0.833030	+	0.553228i	$0.186604\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	21.6489	+	12.7582i	0.694032	+	0.409010i
$974$	−13.6151			−0.436257
$975$	−2.70543	+	12.1264i	−0.0866431	+	0.388357i
$976$	2.09967	−	3.63674i	0.0672088	−	0.116409i
$977$	25.6949	+	44.5048i	0.822051	+	1.42383i	0.904152	+	0.427211i	$0.140504\pi$
$977$	25.6949	+	44.5048i	0.822051	+	1.42383i	−0.0821009	+	0.996624i	$0.526163\pi$
$978$	−9.02971			−0.288738
$979$	−14.3246	−	24.8109i	−0.457815	−	0.792959i
$980$	8.72490	+	0.155908i	0.278707	+	0.00498030i
$981$	9.92285	+	17.1869i	0.316812	+	0.548735i
$982$	−6.14512	+	10.6437i	−0.196099	+	0.339653i
$983$	7.32146	−	12.6811i	0.233518	−	0.404465i	−0.725323	−	0.688409i	$-0.758310\pi$
$983$	7.32146	−	12.6811i	0.233518	−	0.404465i	0.958841	+	0.283944i	$0.0916428\pi$
$984$	3.74194			0.119289
$985$	29.3560			0.935359
$986$	1.83836	−	3.18413i	0.0585452	−	0.101403i
$987$	−0.155870	+	17.4469i	−0.00496139	+	0.555342i
$988$	20.3682	+	18.7143i	0.647998	+	0.595381i
$989$	0.661018	+	1.14492i	0.0210192	+	0.0364062i
$990$	1.55535	+	2.69395i	0.0494323	+	0.0856193i
$991$	11.2664	+	19.5140i	0.357890	+	0.619884i	0.987608	−	0.156940i	$-0.0501630\pi$
$991$	11.2664	+	19.5140i	0.357890	+	0.619884i	−0.629718	+	0.776824i	$0.716830\pi$
$992$	4.06448	−	7.03989i	0.129047	−	0.223517i
$993$	23.2685			0.738405
$994$	−21.3753	−	12.5970i	−0.677982	−	0.399551i
$995$	7.03070	+	12.1775i	0.222888	+	0.386054i
$996$	3.71142	+	6.42837i	0.117601	+	0.203691i
$997$	−24.6033			−0.779194			−0.389597	−	0.920986i	$-0.627386\pi$
$997$	−24.6033			−0.779194			−0.389597	+	0.920986i	$0.627386\pi$
$998$	7.11789	+	12.3285i	0.225313	+	0.390253i
$999$	−2.74194			−0.0867511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.j.e.529.4	yes	10
3.2	odd	2		1638.2.m.k.1621.2		10
7.2	even	3		546.2.k.e.373.4	yes	10
13.3	even	3		546.2.k.e.445.4	yes	10
21.2	odd	6		1638.2.p.j.919.2		10
39.29	odd	6		1638.2.p.j.991.2		10
91.16	even	3	inner	546.2.j.e.289.4	✓	10
273.107	odd	6		1638.2.m.k.289.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.e.289.4	✓	10	91.16	even	3	inner
546.2.j.e.529.4	yes	10	1.1	even	1	trivial
546.2.k.e.373.4	yes	10	7.2	even	3
546.2.k.e.445.4	yes	10	13.3	even	3
1638.2.m.k.289.2		10	273.107	odd	6
1638.2.m.k.1621.2		10	3.2	odd	2
1638.2.p.j.919.2		10	21.2	odd	6
1638.2.p.j.991.2		10	39.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.623307 + 1.07960i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.30301 - 1.30235i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.623307 + 1.07960i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.30301 - 1.30235i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.623307 - 1.07960i) q^{10} +(1.24766 + 2.16101i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.785103 + 3.51904i) q^{13} +(-2.30301 + 1.30235i) q^{14} +(-0.623307 + 1.07960i) q^{15} +1.00000 q^{16} +0.495324 q^{17} +(0.500000 - 0.866025i) q^{18} +(3.83578 - 6.64376i) q^{19} +(0.623307 + 1.07960i) q^{20} +(2.27938 + 1.34329i) q^{21} +(-1.24766 - 2.16101i) q^{22} +0.448052 q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.72298 - 2.98428i) q^{25} +(0.785103 - 3.51904i) q^{26} -1.00000 q^{27} +(2.30301 - 1.30235i) q^{28} +(-3.71142 + 6.42837i) q^{29} +(0.623307 - 1.07960i) q^{30} +(-4.06448 + 7.03989i) q^{31} -1.00000 q^{32} +(-1.24766 + 2.16101i) q^{33} -0.495324 q^{34} +(2.84150 + 1.67457i) q^{35} +(-0.500000 + 0.866025i) q^{36} +2.74194 q^{37} +(-3.83578 + 6.64376i) q^{38} +(-3.44013 + 1.07960i) q^{39} +(-0.623307 - 1.07960i) q^{40} +(-1.87097 + 3.24061i) q^{41} +(-2.27938 - 1.34329i) q^{42} +(1.47532 + 2.55532i) q^{43} +(1.24766 + 2.16101i) q^{44} -1.24661 q^{45} -0.448052 q^{46} +(3.29729 + 5.71107i) q^{47} +(0.500000 + 0.866025i) q^{48} +(3.60775 - 5.99868i) q^{49} +(-1.72298 + 2.98428i) q^{50} +(0.247662 + 0.428963i) q^{51} +(-0.785103 + 3.51904i) q^{52} +(3.86750 - 6.69870i) q^{53} +1.00000 q^{54} +(-1.55535 + 2.69395i) q^{55} +(-2.30301 + 1.30235i) q^{56} +7.67156 q^{57} +(3.71142 - 6.42837i) q^{58} -1.45531 q^{59} +(-0.623307 + 1.07960i) q^{60} +(2.09967 - 3.63674i) q^{61} +(4.06448 - 7.03989i) q^{62} +(-0.0236360 + 2.64565i) q^{63} +1.00000 q^{64} +(-4.28851 + 1.34584i) q^{65} +(1.24766 - 2.16101i) q^{66} +(-0.0138047 - 0.0239105i) q^{67} +0.495324 q^{68} +(0.224026 + 0.388024i) q^{69} +(-2.84150 - 1.67457i) q^{70} +(4.68884 + 8.12130i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-5.07151 + 8.78412i) q^{73} -2.74194 q^{74} +3.44595 q^{75} +(3.83578 - 6.64376i) q^{76} +(5.68779 + 3.35195i) q^{77} +(3.44013 - 1.07960i) q^{78} +(-4.93545 - 8.54845i) q^{79} +(0.623307 + 1.07960i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.87097 - 3.24061i) q^{82} +7.42285 q^{83} +(2.27938 + 1.34329i) q^{84} +(0.308739 + 0.534751i) q^{85} +(-1.47532 - 2.55532i) q^{86} -7.42285 q^{87} +(-1.24766 - 2.16101i) q^{88} -11.4811 q^{89} +1.24661 q^{90} +(2.77493 + 9.12687i) q^{91} +0.448052 q^{92} -8.12896 q^{93} +(-3.29729 - 5.71107i) q^{94} +9.56347 q^{95} +(-0.500000 - 0.866025i) q^{96} +(-0.509831 - 0.883054i) q^{97} +(-3.60775 + 5.99868i) q^{98} -2.49532 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 5 q^{3} + 10 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} - 10 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 5 * q^3 + 10 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 - 10 * q^8 - 5 * q^9	\( 10 q - 10 q^{2} + 5 q^{3} + 10 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} - 10 q^{8} - 5 q^{9} + 2 q^{10} + 6 q^{11} + 5 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} + 10 q^{16} - 8 q^{17} + 5 q^{18} + 3 q^{19} - 2 q^{20} - 4 q^{21} - 6 q^{22} - 12 q^{23} - 5 q^{24} - q^{25} + 4 q^{26} - 10 q^{27} - 2 q^{28} - 2 q^{30} - 10 q^{31} - 10 q^{32} - 6 q^{33} + 8 q^{34} + 16 q^{35} - 5 q^{36} - 2 q^{37} - 3 q^{38} - 2 q^{39} + 2 q^{40} - 4 q^{41} + 4 q^{42} + 3 q^{43} + 6 q^{44} + 4 q^{45} + 12 q^{46} - 15 q^{47} + 5 q^{48} + 4 q^{49} + q^{50} - 4 q^{51} - 4 q^{52} - 17 q^{53} + 10 q^{54} + 3 q^{55} + 2 q^{56} + 6 q^{57} - 4 q^{59} + 2 q^{60} + 11 q^{61} + 10 q^{62} - 2 q^{63} + 10 q^{64} - 4 q^{65} + 6 q^{66} - q^{67} - 8 q^{68} - 6 q^{69} - 16 q^{70} + 18 q^{71} + 5 q^{72} + 12 q^{73} + 2 q^{74} - 2 q^{75} + 3 q^{76} + 18 q^{77} + 2 q^{78} - 4 q^{79} - 2 q^{80} - 5 q^{81} + 4 q^{82} - 4 q^{84} + q^{85} - 3 q^{86} - 6 q^{88} - 14 q^{89} - 4 q^{90} + 26 q^{91} - 12 q^{92} - 20 q^{93} + 15 q^{94} - 48 q^{95} - 5 q^{96} - 6 q^{97} - 4 q^{98} - 12 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 5 * q^3 + 10 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 - 10 * q^8 - 5 * q^9 + 2 * q^10 + 6 * q^11 + 5 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 + 10 * q^16 - 8 * q^17 + 5 * q^18 + 3 * q^19 - 2 * q^20 - 4 * q^21 - 6 * q^22 - 12 * q^23 - 5 * q^24 - q^25 + 4 * q^26 - 10 * q^27 - 2 * q^28 - 2 * q^30 - 10 * q^31 - 10 * q^32 - 6 * q^33 + 8 * q^34 + 16 * q^35 - 5 * q^36 - 2 * q^37 - 3 * q^38 - 2 * q^39 + 2 * q^40 - 4 * q^41 + 4 * q^42 + 3 * q^43 + 6 * q^44 + 4 * q^45 + 12 * q^46 - 15 * q^47 + 5 * q^48 + 4 * q^49 + q^50 - 4 * q^51 - 4 * q^52 - 17 * q^53 + 10 * q^54 + 3 * q^55 + 2 * q^56 + 6 * q^57 - 4 * q^59 + 2 * q^60 + 11 * q^61 + 10 * q^62 - 2 * q^63 + 10 * q^64 - 4 * q^65 + 6 * q^66 - q^67 - 8 * q^68 - 6 * q^69 - 16 * q^70 + 18 * q^71 + 5 * q^72 + 12 * q^73 + 2 * q^74 - 2 * q^75 + 3 * q^76 + 18 * q^77 + 2 * q^78 - 4 * q^79 - 2 * q^80 - 5 * q^81 + 4 * q^82 - 4 * q^84 + q^85 - 3 * q^86 - 6 * q^88 - 14 * q^89 - 4 * q^90 + 26 * q^91 - 12 * q^92 - 20 * q^93 + 15 * q^94 - 48 * q^95 - 5 * q^96 - 6 * q^97 - 4 * q^98 - 12 * q^99

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