LMFDB - Embedded newform 847.2.e.f.606.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(485,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, 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("847.485");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 11 x^{12} - 2 x^{11} + 88 x^{10} - 10 x^{9} + 310 x^{8} + 46 x^{7} + 791 x^{6} + 186 x^{5} + \cdots + 81 $ x^14 + 11x^12 - 2x^11 + 88x^10 - 10x^9 + 310x^8 + 46x^7 + 791x^6 + 186x^5 + 901x^4 + 567x^3 + 738x^2 + 243x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			606.6
Root			$-0.838875 - 1.45297i$ of defining polynomial
Character	$\chi$	$=$	847.606
Dual form			847.2.e.f.485.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.838875 + 1.45297i) q^{2} +(0.537398 - 0.930801i) q^{3} +(-0.407422 + 0.705675i) q^{4} +(0.752739 + 1.30378i) q^{5} +1.80324 q^{6} +(-2.64562 - 0.0259872i) q^{7} +1.98840 q^{8} +(0.922406 + 1.59765i) q^{9} +O(q^{10})$	\(q+(0.838875 + 1.45297i) q^{2} +(0.537398 - 0.930801i) q^{3} +(-0.407422 + 0.705675i) q^{4} +(0.752739 + 1.30378i) q^{5} +1.80324 q^{6} +(-2.64562 - 0.0259872i) q^{7} +1.98840 q^{8} +(0.922406 + 1.59765i) q^{9} +(-1.26291 + 2.18742i) q^{10} +(0.437896 + 0.758457i) q^{12} -0.492593 q^{13} +(-2.18159 - 3.86582i) q^{14} +1.61808 q^{15} +(2.48286 + 4.30044i) q^{16} +(-0.583532 + 1.01071i) q^{17} +(-1.54757 + 2.68046i) q^{18} +(2.56178 + 4.43713i) q^{19} -1.22673 q^{20} +(-1.44594 + 2.44858i) q^{21} +(3.89192 + 6.74100i) q^{23} +(1.06856 - 1.85080i) q^{24} +(1.36677 - 2.36731i) q^{25} +(-0.413224 - 0.715725i) q^{26} +5.20719 q^{27} +(1.09622 - 1.85636i) q^{28} -3.30872 q^{29} +(1.35737 + 2.35103i) q^{30} +(4.35726 - 7.54700i) q^{31} +(-2.17722 + 3.77105i) q^{32} -1.95804 q^{34} +(-1.95758 - 3.46888i) q^{35} -1.50323 q^{36} +(-1.55858 - 2.69954i) q^{37} +(-4.29803 + 7.44440i) q^{38} +(-0.264719 + 0.458506i) q^{39} +(1.49674 + 2.59244i) q^{40} -6.12510 q^{41} +(-4.77069 - 0.0468612i) q^{42} +4.59775 q^{43} +(-1.38866 + 2.40524i) q^{45} +(-6.52967 + 11.3097i) q^{46} +(-2.10275 - 3.64206i) q^{47} +5.33713 q^{48} +(6.99865 + 0.137505i) q^{49} +4.58619 q^{50} +(0.627178 + 1.08630i) q^{51} +(0.200693 - 0.347611i) q^{52} +(2.41269 - 4.17891i) q^{53} +(4.36818 + 7.56591i) q^{54} +(-5.26055 - 0.0516729i) q^{56} +5.50679 q^{57} +(-2.77560 - 4.80748i) q^{58} +(-4.82567 + 8.35830i) q^{59} +(-0.659242 + 1.14184i) q^{60} +(-4.79674 - 8.30819i) q^{61} +14.6208 q^{62} +(-2.39882 - 4.25076i) q^{63} +2.62578 q^{64} +(-0.370794 - 0.642235i) q^{65} +(-0.218716 + 0.378827i) q^{67} +(-0.475487 - 0.823568i) q^{68} +8.36604 q^{69} +(3.39802 - 5.75427i) q^{70} -15.1300 q^{71} +(1.83411 + 3.17677i) q^{72} +(1.45597 - 2.52181i) q^{73} +(2.61491 - 4.52916i) q^{74} +(-1.46900 - 2.54438i) q^{75} -4.17490 q^{76} -0.888264 q^{78} +(7.31855 + 12.6761i) q^{79} +(-3.73789 + 6.47422i) q^{80} +(0.0311138 - 0.0538906i) q^{81} +(-5.13819 - 8.89961i) q^{82} -13.5944 q^{83} +(-1.13880 - 2.01797i) q^{84} -1.75699 q^{85} +(3.85693 + 6.68040i) q^{86} +(-1.77810 + 3.07976i) q^{87} +(1.02743 + 1.77957i) q^{89} -4.65966 q^{90} +(1.30322 + 0.0128011i) q^{91} -6.34261 q^{92} +(-4.68317 - 8.11149i) q^{93} +(3.52788 - 6.11047i) q^{94} +(-3.85671 + 6.68001i) q^{95} +(2.34007 + 4.05312i) q^{96} -15.0226 q^{97} +(5.67120 + 10.2842i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{3} - 8 q^{4} - 4 q^{5} - 4 q^{6} + 2 q^{7} - 6 q^{8} - 10 q^{9}+O(q^{10}) $ 14 * q - 3 * q^3 - 8 * q^4 - 4 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 - 10 * q^9	$ 14 q - 3 q^{3} - 8 q^{4} - 4 q^{5} - 4 q^{6} + 2 q^{7} - 6 q^{8} - 10 q^{9} - 6 q^{10} - 13 q^{12} + 12 q^{13} + 12 q^{14} - 2 q^{15} - 6 q^{16} + 3 q^{17} - 14 q^{18} + 9 q^{19} + 4 q^{20} - 6 q^{21} + 6 q^{23} - 4 q^{24} - 7 q^{25} - 25 q^{26} + 24 q^{27} - 36 q^{28} + 12 q^{29} - 16 q^{30} - 14 q^{31} + 36 q^{32} + 16 q^{34} + 18 q^{35} - 4 q^{36} + 8 q^{37} + 10 q^{38} + 9 q^{39} - 18 q^{40} - 20 q^{41} - 8 q^{42} + 34 q^{43} - 12 q^{45} - 16 q^{46} - 30 q^{47} + 112 q^{48} + 14 q^{49} + 42 q^{50} + 20 q^{51} + 37 q^{52} + 10 q^{53} + 7 q^{54} - 33 q^{56} - 62 q^{57} + 13 q^{58} - 20 q^{59} - 42 q^{60} - 7 q^{61} + 52 q^{62} + 37 q^{63} + 42 q^{64} - 12 q^{65} - 7 q^{67} - 7 q^{68} + 18 q^{69} - 39 q^{70} - 22 q^{71} + q^{72} + 6 q^{73} - 8 q^{74} + q^{75} - 112 q^{76} + 30 q^{78} + 14 q^{79} - 12 q^{80} - 35 q^{81} + 7 q^{82} + 34 q^{83} + 40 q^{84} - 4 q^{85} + 15 q^{87} - 40 q^{89} + 136 q^{90} - 32 q^{91} - 52 q^{92} - 19 q^{94} - 20 q^{95} + 63 q^{96} - 44 q^{97} + 21 q^{98}+O(q^{100}) $ 14 * q - 3 * q^3 - 8 * q^4 - 4 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 - 10 * q^9 - 6 * q^10 - 13 * q^12 + 12 * q^13 + 12 * q^14 - 2 * q^15 - 6 * q^16 + 3 * q^17 - 14 * q^18 + 9 * q^19 + 4 * q^20 - 6 * q^21 + 6 * q^23 - 4 * q^24 - 7 * q^25 - 25 * q^26 + 24 * q^27 - 36 * q^28 + 12 * q^29 - 16 * q^30 - 14 * q^31 + 36 * q^32 + 16 * q^34 + 18 * q^35 - 4 * q^36 + 8 * q^37 + 10 * q^38 + 9 * q^39 - 18 * q^40 - 20 * q^41 - 8 * q^42 + 34 * q^43 - 12 * q^45 - 16 * q^46 - 30 * q^47 + 112 * q^48 + 14 * q^49 + 42 * q^50 + 20 * q^51 + 37 * q^52 + 10 * q^53 + 7 * q^54 - 33 * q^56 - 62 * q^57 + 13 * q^58 - 20 * q^59 - 42 * q^60 - 7 * q^61 + 52 * q^62 + 37 * q^63 + 42 * q^64 - 12 * q^65 - 7 * q^67 - 7 * q^68 + 18 * q^69 - 39 * q^70 - 22 * q^71 + q^72 + 6 * q^73 - 8 * q^74 + q^75 - 112 * q^76 + 30 * q^78 + 14 * q^79 - 12 * q^80 - 35 * q^81 + 7 * q^82 + 34 * q^83 + 40 * q^84 - 4 * q^85 + 15 * q^87 - 40 * q^89 + 136 * q^90 - 32 * q^91 - 52 * q^92 - 19 * q^94 - 20 * q^95 + 63 * q^96 - 44 * q^97 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.838875	+	1.45297i	0.593174	+	1.02741i	0.993802	+	0.111167i	$0.0354587\pi$
$2$	0.838875	+	1.45297i	0.593174	+	1.02741i	−0.400628	+	0.916241i	$0.631208\pi$
$3$	0.537398	−	0.930801i	0.310267	−	0.537398i	−0.668153	−	0.744024i	$-0.732915\pi$
$3$	0.537398	−	0.930801i	0.310267	−	0.537398i	0.978420	+	0.206626i	$0.0662482\pi$
$4$	−0.407422	+	0.705675i	−0.203711	+	0.352838i
$5$	0.752739	+	1.30378i	0.336635	+	0.583069i	0.983798	−	0.179283i	$-0.0573777\pi$
$5$	0.752739	+	1.30378i	0.336635	+	0.583069i	−0.647162	+	0.762352i	$0.724044\pi$
$6$	1.80324			0.736169
$7$	−2.64562	−	0.0259872i	−0.999952	−	0.00982224i
$7$	−2.64562	−	0.0259872i	−0.999952	−	0.00982224i
$8$	1.98840			0.703004
$9$	0.922406	+	1.59765i	0.307469	+	0.532552i
$10$	−1.26291	+	2.18742i	−0.399367	+	0.691723i
$11$		0			0
$11$		0			0
$12$	0.437896	+	0.758457i	0.126410	+	0.218948i
$13$	−0.492593			−0.136621			−0.0683104	−	0.997664i	$-0.521761\pi$
$13$	−0.492593			−0.136621			−0.0683104	+	0.997664i	$0.521761\pi$
$14$	−2.18159	−	3.86582i	−0.583054	−	1.03318i
$15$	1.61808			0.417787
$16$	2.48286	+	4.30044i	0.620715	+	1.07511i
$17$	−0.583532	+	1.01071i	−0.141527	+	0.245132i	−0.928072	−	0.372401i	$-0.878535\pi$
$17$	−0.583532	+	1.01071i	−0.141527	+	0.245132i	0.786545	+	0.617533i	$0.211868\pi$
$18$	−1.54757	+	2.68046i	−0.364765	+	0.631792i
$19$	2.56178	+	4.43713i	0.587713	+	1.01795i	0.994531	+	0.104439i	$0.0333048\pi$
$19$	2.56178	+	4.43713i	0.587713	+	1.01795i	−0.406818	+	0.913509i	$0.633362\pi$
$20$	−1.22673			−0.274305
$21$	−1.44594	+	2.44858i	−0.315530	+	0.534325i
$22$		0			0
$23$	3.89192	+	6.74100i	0.811521	+	1.40560i	0.911799	+	0.410637i	$0.134694\pi$
$23$	3.89192	+	6.74100i	0.811521	+	1.40560i	−0.100277	+	0.994960i	$0.531973\pi$
$24$	1.06856	−	1.85080i	0.218119	−	0.377793i
$25$	1.36677	−	2.36731i	0.273353	−	0.473462i
$26$	−0.413224	−	0.715725i	−0.0810399	−	0.140365i
$27$	5.20719			1.00212
$28$	1.09622	−	1.85636i	0.207167	−	0.350820i
$29$	−3.30872			−0.614413			−0.307207	−	0.951643i	$-0.599394\pi$
$29$	−3.30872			−0.614413			−0.307207	+	0.951643i	$0.599394\pi$
$30$	1.35737	+	2.35103i	0.247821	+	0.429238i
$31$	4.35726	−	7.54700i	0.782587	−	1.35548i	−0.147843	−	0.989011i	$-0.547233\pi$
$31$	4.35726	−	7.54700i	0.782587	−	1.35548i	0.930430	−	0.366470i	$-0.119434\pi$
$32$	−2.17722	+	3.77105i	−0.384882	+	0.666635i
$33$		0			0
$34$	−1.95804			−0.335801
$35$	−1.95758	−	3.46888i	−0.330892	−	0.586348i
$36$	−1.50323			−0.250539
$37$	−1.55858	−	2.69954i	−0.256229	−	0.443802i	0.708999	−	0.705209i	$-0.249147\pi$
$37$	−1.55858	−	2.69954i	−0.256229	−	0.443802i	−0.965229	+	0.261407i	$0.915814\pi$
$38$	−4.29803	+	7.44440i	−0.697232	+	1.20764i
$39$	−0.264719	+	0.458506i	−0.0423889	+	0.0734198i
$40$	1.49674	+	2.59244i	0.236656	+	0.409900i
$41$	−6.12510			−0.956580			−0.478290	−	0.878202i	$-0.658743\pi$
$41$	−6.12510			−0.956580			−0.478290	+	0.878202i	$0.658743\pi$
$42$	−4.77069	−	0.0468612i	−0.736134	−	0.00723083i
$43$	4.59775			0.701150			0.350575	−	0.936535i	$-0.385986\pi$
$43$	4.59775			0.701150			0.350575	+	0.936535i	$0.385986\pi$
$44$		0			0
$45$	−1.38866	+	2.40524i	−0.207010	+	0.358551i
$46$	−6.52967	+	11.3097i	−0.962747	+	1.66753i
$47$	−2.10275	−	3.64206i	−0.306717	−	0.531250i	0.670925	−	0.741525i	$-0.265897\pi$
$47$	−2.10275	−	3.64206i	−0.306717	−	0.531250i	−0.977642	+	0.210276i	$0.932564\pi$
$48$	5.33713			0.770349
$49$	6.99865	+	0.137505i	0.999807	+	0.0196435i
$50$	4.58619			0.648585
$51$	0.627178	+	1.08630i	0.0878224	+	0.152113i
$52$	0.200693	−	0.347611i	0.0278312	−	0.0482050i
$53$	2.41269	−	4.17891i	0.331409	−	0.574017i	−0.651379	−	0.758752i	$-0.725809\pi$
$53$	2.41269	−	4.17891i	0.331409	−	0.574017i	0.982788	+	0.184735i	$0.0591427\pi$
$54$	4.36818	+	7.56591i	0.594434	+	1.02959i
$55$		0			0
$56$	−5.26055	−	0.0516729i	−0.702970	−	0.00690508i
$57$	5.50679			0.729392
$58$	−2.77560	−	4.80748i	−0.364454	−	0.631253i
$59$	−4.82567	+	8.35830i	−0.628248	+	1.08816i	0.359655	+	0.933085i	$0.382894\pi$
$59$	−4.82567	+	8.35830i	−0.628248	+	1.08816i	−0.987903	+	0.155072i	$0.950439\pi$
$60$	−0.659242	+	1.14184i	−0.0851078	+	0.147411i
$61$	−4.79674	−	8.30819i	−0.614159	−	1.06376i	−0.990531	−	0.137287i	$-0.956162\pi$
$61$	−4.79674	−	8.30819i	−0.614159	−	1.06376i	0.376372	−	0.926469i	$-0.377171\pi$
$62$	14.6208			1.85684
$63$	−2.39882	−	4.25076i	−0.302223	−	0.535546i
$64$	2.62578			0.328222
$65$	−0.370794	−	0.642235i	−0.0459914	−	0.0796594i
$66$		0			0
$67$	−0.218716	+	0.378827i	−0.0267204	+	0.0462811i	−0.879076	−	0.476681i	$-0.841840\pi$
$67$	−0.218716	+	0.378827i	−0.0267204	+	0.0462811i	0.852356	+	0.522962i	$0.175173\pi$
$68$	−0.475487	−	0.823568i	−0.0576613	−	0.0998723i
$69$	8.36604			1.00715
$70$	3.39802	−	5.75427i	0.406142	−	0.687767i
$71$	−15.1300			−1.79560			−0.897799	−	0.440405i	$-0.854835\pi$
$71$	−15.1300			−1.79560			−0.897799	+	0.440405i	$0.854835\pi$
$72$	1.83411	+	3.17677i	0.216152	+	0.374386i
$73$	1.45597	−	2.52181i	0.170408	−	0.295155i	−0.768155	−	0.640264i	$-0.778825\pi$
$73$	1.45597	−	2.52181i	0.170408	−	0.295155i	0.938563	+	0.345109i	$0.112158\pi$
$74$	2.61491	−	4.52916i	0.303977	−	0.526504i
$75$	−1.46900	−	2.54438i	−0.169625	−	0.293799i
$76$	−4.17490			−0.478894
$77$		0			0
$78$	−0.888264			−0.100576
$79$	7.31855	+	12.6761i	0.823401	+	1.42617i	0.903135	+	0.429356i	$0.141259\pi$
$79$	7.31855	+	12.6761i	0.823401	+	1.42617i	−0.0797343	+	0.996816i	$0.525407\pi$
$80$	−3.73789	+	6.47422i	−0.417909	+	0.723839i
$81$	0.0311138	−	0.0538906i	0.00345709	−	0.00598785i
$82$	−5.13819	−	8.89961i	−0.567419	−	0.982798i
$83$	−13.5944			−1.49218			−0.746088	−	0.665847i	$-0.768070\pi$
$83$	−13.5944			−1.49218			−0.746088	+	0.665847i	$0.768070\pi$
$84$	−1.13880	−	2.01797i	−0.124253	−	0.220179i
$85$	−1.75699			−0.190572
$86$	3.85693	+	6.68040i	0.415904	+	0.720366i
$87$	−1.77810	+	3.07976i	−0.190632	+	0.330185i
$88$		0			0
$89$	1.02743	+	1.77957i	0.108908	+	0.188634i	0.915328	−	0.402709i	$-0.131931\pi$
$89$	1.02743	+	1.77957i	0.108908	+	0.188634i	−0.806420	+	0.591343i	$0.798598\pi$
$90$	−4.65966			−0.491171
$91$	1.30322	+	0.0128011i	0.136614	+	0.00134192i
$92$	−6.34261			−0.661263
$93$	−4.68317	−	8.11149i	−0.485622	−	0.841122i
$94$	3.52788	−	6.11047i	0.363873	−	0.630247i
$95$	−3.85671	+	6.68001i	−0.395690	+	0.685355i
$96$	2.34007	+	4.05312i	0.238832	+	0.413669i
$97$	−15.0226			−1.52531			−0.762656	−	0.646804i	$-0.776105\pi$
$97$	−15.0226			−1.52531			−0.762656	+	0.646804i	$0.776105\pi$
$98$	5.67120	+	10.2842i	0.572878	+	1.03886i
$99$		0			0
$100$	1.11370	+	1.92899i	0.111370	+	0.192899i
$101$	9.63338	−	16.6855i	0.958557	−	1.66027i	0.232547	−	0.972585i	$-0.425294\pi$
$101$	9.63338	−	16.6855i	0.958557	−	1.66027i	0.726010	−	0.687685i	$-0.241373\pi$
$102$	−1.05225	+	1.82255i	−0.104188	+	0.180459i
$103$	−8.84480	−	15.3196i	−0.871504	−	1.50949i	−0.860441	−	0.509551i	$-0.829812\pi$
$103$	−8.84480	−	15.3196i	−0.871504	−	1.50949i	−0.0110634	−	0.999939i	$-0.503522\pi$
$104$	−0.979470			−0.0960450
$105$	−4.28084	−	0.0420495i	−0.417767	−	0.00410361i
$106$	8.09579			0.786333
$107$	0.0794996	+	0.137697i	0.00768551	+	0.0133117i	0.869843	−	0.493329i	$-0.164220\pi$
$107$	0.0794996	+	0.137697i	0.00768551	+	0.0133117i	−0.862157	+	0.506641i	$0.830887\pi$
$108$	−2.12152	+	3.67458i	−0.204144	+	0.353587i
$109$	9.92873	−	17.1971i	0.951000	−	1.64718i	0.207732	−	0.978186i	$-0.433392\pi$
$109$	9.92873	−	17.1971i	0.951000	−	1.64718i	0.743268	−	0.668994i	$-0.233275\pi$
$110$		0			0
$111$	−3.35032			−0.317998
$112$	−6.45695	−	11.4419i	−0.610125	−	1.08115i
$113$	3.43717			0.323342			0.161671	−	0.986845i	$-0.448312\pi$
$113$	3.43717			0.323342			0.161671	+	0.986845i	$0.448312\pi$
$114$	4.61950	+	8.00121i	0.432656	+	0.749382i
$115$	−5.85920	+	10.1484i	−0.546373	+	0.946347i
$116$	1.34804	−	2.33488i	0.125163	−	0.216788i
$117$	−0.454371	−	0.786994i	−0.0420066	−	0.0727576i
$118$	−16.1925			−1.49064
$119$	1.57007	−	2.65878i	0.143928	−	0.243730i
$120$	3.21739			0.293706
$121$		0			0
$122$	8.04773	−	13.9391i	0.728607	−	1.26198i
$123$	−3.29162	+	5.70125i	−0.296795	+	0.514065i
$124$	3.55049	+	6.14962i	0.318843	+	0.552253i
$125$	11.6427			1.04135
$126$	4.16394	−	7.05128i	0.370953	−	0.628178i
$127$	−1.97264			−0.175043			−0.0875216	−	0.996163i	$-0.527895\pi$
$127$	−1.97264			−0.175043			−0.0875216	+	0.996163i	$0.527895\pi$
$128$	6.55714	+	11.3573i	0.579574	+	1.00385i
$129$	2.47082	−	4.27959i	0.217544	−	0.376797i
$130$	0.622100	−	1.07751i	0.0545618	−	0.0945038i
$131$	−2.04271	−	3.53807i	−0.178472	−	0.309123i	0.762885	−	0.646534i	$-0.223782\pi$
$131$	−2.04271	−	3.53807i	−0.178472	−	0.309123i	−0.941357	+	0.337411i	$0.890449\pi$
$132$		0			0
$133$	−6.66220	−	11.8056i	−0.577686	−	1.02367i
$134$	−0.733900			−0.0633993
$135$	3.91965	+	6.78904i	0.337350	+	0.584308i
$136$	−1.16029	+	2.00968i	−0.0994942	+	0.172329i
$137$	5.11092	−	8.85237i	0.436655	−	0.756309i	−0.560774	−	0.827969i	$-0.689496\pi$
$137$	5.11092	−	8.85237i	0.436655	−	0.756309i	0.997429	+	0.0716601i	$0.0228297\pi$
$138$	7.01806	+	12.1556i	0.597417	+	1.03476i
$139$	−11.9268			−1.01162			−0.505809	−	0.862645i	$-0.668806\pi$
$139$	−11.9268			−1.01162			−0.505809	+	0.862645i	$0.668806\pi$
$140$	3.24547	+	0.0318793i	0.274292	+	0.00269429i
$141$	−4.52005			−0.380657
$142$	−12.6922	−	21.9835i	−1.06510	−	1.84481i
$143$		0			0
$144$	−4.58041	+	7.93350i	−0.381701	+	0.661125i
$145$	−2.49060	−	4.31385i	−0.206833	−	0.358246i
$146$	4.88549			0.404326
$147$	3.88905	−	6.44045i	0.320764	−	0.531200i
$148$	2.54000			0.208787
$149$	5.07856	+	8.79633i	0.416052	+	0.720623i	0.995538	−	0.0943587i	$-0.0300800\pi$
$149$	5.07856	+	8.79633i	0.416052	+	0.720623i	−0.579486	+	0.814982i	$0.696747\pi$
$150$	2.46461	−	4.26883i	0.201234	−	0.348548i
$151$	2.24225	−	3.88369i	0.182472	−	0.316051i	−0.760250	−	0.649631i	$-0.774923\pi$
$151$	2.24225	−	3.88369i	0.182472	−	0.316051i	0.942722	+	0.333580i	$0.108257\pi$
$152$	5.09383	+	8.82278i	0.413164	+	0.715622i
$153$	−2.15301			−0.174061
$154$		0			0
$155$	13.1195			1.05379
$156$	−0.215704	−	0.373611i	−0.0172702	−	0.0299128i
$157$	1.96272	−	3.39954i	0.156642	−	0.271313i	−0.777013	−	0.629484i	$-0.783266\pi$
$157$	1.96272	−	3.39954i	0.156642	−	0.271313i	0.933656	+	0.358171i	$0.116600\pi$
$158$	−12.2787	+	21.2673i	−0.976840	+	1.69194i
$159$	−2.59315	−	4.49148i	−0.205651	−	0.356197i
$160$	−6.55551			−0.518259
$161$	−10.1214	−	17.9353i	−0.797676	−	1.41350i
$162$	0.104402			0.00820261
$163$	2.13252	+	3.69364i	0.167032	+	0.289308i	0.937375	−	0.348322i	$-0.113248\pi$
$163$	2.13252	+	3.69364i	0.167032	+	0.289308i	−0.770343	+	0.637630i	$0.779915\pi$
$164$	2.49550	−	4.32233i	0.194866	−	0.337518i
$165$		0			0
$166$	−11.4040	−	19.7523i	−0.885120	−	1.53307i
$167$	12.4869			0.966262			0.483131	−	0.875548i	$-0.339499\pi$
$167$	12.4869			0.966262			0.483131	+	0.875548i	$0.339499\pi$
$168$	−2.87511	+	4.86875i	−0.221819	+	0.375632i
$169$	−12.7574			−0.981335
$170$	−1.47389	−	2.55286i	−0.113042	−	0.195795i
$171$	−4.72601	+	8.18568i	−0.361407	+	0.625975i
$172$	−1.87322	+	3.24452i	−0.142832	+	0.247392i
$173$	−5.58167	−	9.66774i	−0.424367	−	0.735025i	0.571994	−	0.820258i	$-0.306170\pi$
$173$	−5.58167	−	9.66774i	−0.424367	−	0.735025i	−0.996361	+	0.0852329i	$0.972837\pi$
$174$	−5.96641			−0.452312
$175$	−3.67747	+	6.22749i	−0.277991	+	0.470754i
$176$		0			0
$177$	5.18661	+	8.98347i	0.389849	+	0.675239i
$178$	−1.72378	+	2.98567i	−0.129202	+	0.223785i
$179$	−7.01879	+	12.1569i	−0.524609	+	0.908649i	0.474981	+	0.879996i	$0.342455\pi$
$179$	−7.01879	+	12.1569i	−0.524609	+	0.908649i	−0.999589	+	0.0286527i	$0.990878\pi$
$180$	−1.13154	−	1.95989i	−0.0843403	−	0.146082i
$181$	21.1103			1.56911			0.784557	−	0.620057i	$-0.212891\pi$
$181$	21.1103			1.56911			0.784557	+	0.620057i	$0.212891\pi$
$182$	1.07464	+	1.90428i	0.0796573	+	0.141154i
$183$	−10.3110			−0.762214
$184$	7.73868	+	13.4038i	0.570503	+	0.988140i
$185$	2.34641	−	4.06411i	0.172512	−	0.298799i
$186$	7.85719	−	13.6090i	0.576117	−	0.997864i
$187$		0			0
$188$	3.42682			0.249927
$189$	−13.7763	−	0.135320i	−1.00208	−	0.00984310i
$190$	−12.9412			−0.938851
$191$	1.88453	+	3.26410i	0.136360	+	0.236182i	0.926116	−	0.377239i	$-0.123126\pi$
$191$	1.88453	+	3.26410i	0.136360	+	0.236182i	−0.789756	+	0.613421i	$0.789793\pi$
$192$	1.41109	−	2.44407i	0.101836	−	0.176386i
$193$	4.83458	−	8.37374i	0.348001	−	0.602755i	−0.637893	−	0.770125i	$-0.720194\pi$
$193$	4.83458	−	8.37374i	0.348001	−	0.602755i	0.985894	+	0.167370i	$0.0535273\pi$
$194$	−12.6021	−	21.8274i	−0.904776	−	1.56712i
$195$	−0.797057			−0.0570784
$196$	−2.94844	+	4.88275i	−0.210603	+	0.348768i
$197$	−14.6138			−1.04119			−0.520596	−	0.853803i	$-0.674290\pi$
$197$	−14.6138			−1.04119			−0.520596	+	0.853803i	$0.674290\pi$
$198$		0			0
$199$	6.74482	−	11.6824i	0.478127	−	0.828141i	−0.521558	−	0.853216i	$-0.674649\pi$
$199$	6.74482	−	11.6824i	0.478127	−	0.828141i	0.999686	+	0.0250749i	$0.00798242\pi$
$200$	2.71767	−	4.70715i	0.192169	−	0.332846i
$201$	0.235075	+	0.407162i	0.0165809	+	0.0287190i
$202$	32.3248			2.27436
$203$	8.75362	+	0.0859844i	0.614384	+	0.00603492i
$204$	−1.02210			−0.0715616
$205$	−4.61061	−	7.98580i	−0.322019	−	0.557753i
$206$	14.8394	−	25.7025i	1.03391	−	1.79078i
$207$	−7.17986	+	12.4359i	−0.499035	+	0.864354i
$208$	−1.22304	−	2.11837i	−0.0848025	−	0.146882i
$209$		0			0
$210$	−3.52999	−	6.25522i	−0.243593	−	0.431651i
$211$	−7.04689			−0.485128			−0.242564	−	0.970135i	$-0.577988\pi$
$211$	−7.04689			−0.485128			−0.242564	+	0.970135i	$0.577988\pi$
$212$	1.96597	+	3.40516i	0.135023	+	0.233867i
$213$	−8.13082	+	14.0830i	−0.557115	+	0.964951i
$214$	−0.133380	+	0.231022i	−0.00911769	+	0.0157923i
$215$	3.46090	+	5.99446i	0.236032	+	0.408819i
$216$	10.3539			0.704497
$217$	−11.7238	+	19.8533i	−0.795863	+	1.34773i
$218$	33.3158			2.25643
$219$	−1.56487	−	2.71043i	−0.105744	−	0.183154i
$220$		0			0
$221$	0.287444	−	0.497867i	0.0193356	−	0.0334902i
$222$	−2.81050	−	4.86792i	−0.188628	−	0.326714i
$223$	−3.07444			−0.205880			−0.102940	−	0.994688i	$-0.532825\pi$
$223$	−3.07444			−0.205880			−0.102940	+	0.994688i	$0.532825\pi$
$224$	5.85810	−	9.92021i	0.391411	−	0.662822i
$225$	5.04286			0.336191
$226$	2.88336	+	4.99412i	0.191798	+	0.332204i
$227$	7.45854	−	12.9186i	0.495041	−	0.857436i	−0.504943	−	0.863153i	$-0.668486\pi$
$227$	7.45854	−	12.9186i	0.495041	−	0.857436i	0.999984	+	0.00571713i	$0.00181983\pi$
$228$	−2.24358	+	3.88600i	−0.148585	+	0.257357i
$229$	7.32201	+	12.6821i	0.483852	+	0.838056i	0.999828	−	0.0185467i	$-0.00590393\pi$
$229$	7.32201	+	12.6821i	0.483852	+	0.838056i	−0.515976	+	0.856603i	$0.672571\pi$
$230$	−19.6606			−1.29638
$231$		0			0
$232$	−6.57904			−0.431935
$233$	3.52933	+	6.11297i	0.231214	+	0.400474i	0.958166	−	0.286214i	$-0.0923970\pi$
$233$	3.52933	+	6.11297i	0.231214	+	0.400474i	−0.726952	+	0.686689i	$0.759064\pi$
$234$	0.762321	−	1.32038i	0.0498345	−	0.0863159i
$235$	3.16564	−	5.48305i	0.206504	−	0.357675i
$236$	−3.93216	−	6.81071i	−0.255962	−	0.443339i
$237$	15.7319			1.02190
$238$	5.18024	+	0.0508840i	0.335785	+	0.00329832i
$239$	23.5686			1.52453			0.762263	−	0.647267i	$-0.224088\pi$
$239$	23.5686			1.52453			0.762263	+	0.647267i	$0.224088\pi$
$240$	4.01747	+	6.95846i	0.259327	+	0.449167i
$241$	7.28455	−	12.6172i	0.469239	−	0.812746i	−0.530142	−	0.847909i	$-0.677862\pi$
$241$	7.28455	−	12.6172i	0.469239	−	0.812746i	0.999382	+	0.0351624i	$0.0111948\pi$
$242$		0			0
$243$	7.77734	+	13.4707i	0.498917	+	0.864149i
$244$	7.81718			0.500444
$245$	5.08888	+	9.22822i	0.325117	+	0.589570i
$246$	−11.0450			−0.704205
$247$	−1.26192	−	2.18570i	−0.0802938	−	0.139073i
$248$	8.66396	−	15.0064i	0.550162	−	0.952908i
$249$	−7.30559	+	12.6537i	−0.462973	+	0.801893i
$250$	9.76674	+	16.9165i	0.617703	+	1.06989i
$251$	3.59896			0.227165			0.113582	−	0.993529i	$-0.463767\pi$
$251$	3.59896			0.227165			0.113582	+	0.993529i	$0.463767\pi$
$252$	3.97699	+	0.0390649i	0.250527	+	0.00246086i
$253$		0			0
$254$	−1.65480	−	2.86619i	−0.103831	−	0.179841i
$255$	−0.944202	+	1.63541i	−0.0591283	+	0.102413i
$256$	−8.37546	+	14.5067i	−0.523466	+	0.906670i
$257$	−7.67529	−	13.2940i	−0.478771	−	0.829256i	0.520932	−	0.853598i	$-0.325584\pi$
$257$	−7.67529	−	13.2940i	−0.478771	−	0.829256i	−0.999704	+	0.0243418i	$0.992251\pi$
$258$	8.29083			0.516165
$259$	4.05327	+	7.18248i	0.251858	+	0.446298i
$260$	0.604279			0.0374758
$261$	−3.05198	−	5.28619i	−0.188913	−	0.327207i
$262$	3.42715	−	5.93600i	0.211730	−	0.366727i
$263$	2.55468	−	4.42483i	0.157528	−	0.272847i	−0.776449	−	0.630181i	$-0.782981\pi$
$263$	2.55468	−	4.42483i	0.157528	−	0.272847i	0.933977	+	0.357334i	$0.116314\pi$
$264$		0			0
$265$	7.26452			0.446256
$266$	11.5644	−	19.5834i	0.709060	−	1.20073i
$267$	2.20856			0.135162
$268$	−0.178219	−	0.308685i	−0.0108865	−	0.0188559i
$269$	−8.06425	+	13.9677i	−0.491686	+	0.851626i	−0.999954	−	0.00957342i	$-0.996953\pi$
$269$	−8.06425	+	13.9677i	−0.491686	+	0.851626i	0.508268	+	0.861199i	$0.330286\pi$
$270$	−6.57620	+	11.3903i	−0.400215	+	0.693192i
$271$	−0.381221	−	0.660294i	−0.0231575	−	0.0401100i	0.854214	−	0.519921i	$-0.174039\pi$
$271$	−0.381221	−	0.660294i	−0.0231575	−	0.0401100i	−0.877372	+	0.479811i	$0.840705\pi$
$272$	−5.79531			−0.351392
$273$	0.712262	−	1.20616i	0.0431080	−	0.0729999i
$274$	17.1497			1.03605
$275$		0			0
$276$	−3.40851	+	5.90371i	−0.205168	+	0.355362i
$277$	−3.50951	+	6.07864i	−0.210866	+	0.365230i	−0.951986	−	0.306142i	$-0.900962\pi$
$277$	−3.50951	+	6.07864i	−0.210866	+	0.365230i	0.741120	+	0.671373i	$0.234295\pi$
$278$	−10.0051	−	17.3293i	−0.600066	−	1.03934i
$279$	16.0767			0.962485
$280$	−3.89245	−	6.89751i	−0.232618	−	0.412205i
$281$	10.4713			0.624668			0.312334	−	0.949972i	$-0.398889\pi$
$281$	10.4713			0.624668			0.312334	+	0.949972i	$0.398889\pi$
$282$	−3.79176	−	6.56751i	−0.225796	−	0.391090i
$283$	−5.31582	+	9.20727i	−0.315993	+	0.547315i	−0.979648	−	0.200723i	$-0.935671\pi$
$283$	−5.31582	+	9.20727i	−0.315993	+	0.547315i	0.663655	+	0.748039i	$0.269004\pi$
$284$	6.16428	−	10.6769i	0.365783	−	0.633555i
$285$	4.14517	+	7.17965i	0.245539	+	0.425286i
$286$		0			0
$287$	16.2047	+	0.159174i	0.956534	+	0.00939576i
$288$	−8.03312			−0.473356
$289$	7.81898	+	13.5429i	0.459940	+	0.796640i
$290$	4.17861	−	7.23756i	0.245376	−	0.425004i
$291$	−8.07311	+	13.9830i	−0.473254	+	0.819700i
$292$	1.18638	+	2.05488i	0.0694279	+	0.120253i
$293$	14.9062			0.870828			0.435414	−	0.900230i	$-0.356602\pi$
$293$	14.9062			0.870828			0.435414	+	0.900230i	$0.356602\pi$
$294$	12.6202	+	0.247954i	0.736027	+	0.0144610i
$295$	−14.5299			−0.845962
$296$	−3.09908	−	5.36776i	−0.180130	−	0.311995i
$297$		0			0
$298$	−8.52056	+	14.7580i	−0.493583	+	0.854910i
$299$	−1.91713	−	3.32057i	−0.110871	−	0.192034i
$300$	2.39400			0.138218
$301$	−12.1639	−	0.119483i	−0.701116	−	0.00688686i
$302$	7.52387			0.432950
$303$	−10.3539	−	17.9335i	−0.594817	−	1.03025i
$304$	−12.7211	+	22.0336i	−0.729604	+	1.26371i
$305$	7.22139	−	12.5078i	0.413495	−	0.716195i
$306$	−1.80611	−	3.12827i	−0.103248	−	0.178831i
$307$	−24.1498			−1.37830			−0.689150	−	0.724619i	$-0.742016\pi$
$307$	−24.1498			−1.37830			−0.689150	+	0.724619i	$0.742016\pi$
$308$		0			0
$309$	−19.0127			−1.08160
$310$	11.0056	+	19.0623i	0.625078	+	1.08267i
$311$	−5.99744	+	10.3879i	−0.340084	+	0.589042i	−0.984448	−	0.175676i	$-0.943789\pi$
$311$	−5.99744	+	10.3879i	−0.340084	+	0.589042i	0.644364	+	0.764719i	$0.277122\pi$
$312$	−0.526366	+	0.911692i	−0.0297996	+	0.0516144i
$313$	−0.680070	−	1.17792i	−0.0384398	−	0.0665797i	0.846165	−	0.532920i	$-0.178905\pi$
$313$	−0.680070	−	1.17792i	−0.0384398	−	0.0665797i	−0.884605	+	0.466341i	$0.845572\pi$
$314$	6.58592			0.371665
$315$	3.73639	−	6.32726i	0.210521	−	0.356501i
$316$	−11.9269			−0.670943
$317$	−11.3526	−	19.6632i	−0.637624	−	1.10440i	−0.985953	−	0.167025i	$-0.946584\pi$
$317$	−11.3526	−	19.6632i	−0.637624	−	1.10440i	0.348328	−	0.937373i	$-0.386750\pi$
$318$	4.35066	−	7.53557i	0.243973	−	0.422574i
$319$		0			0
$320$	1.97652	+	3.42344i	0.110491	+	0.191376i
$321$	0.170892			0.00953824
$322$	17.5690	−	29.7516i	0.979079	−	1.65799i
$323$	−5.97952			−0.332709
$324$	0.0253529	+	0.0439124i	0.00140849	+	0.00243958i
$325$	−0.673260	+	1.16612i	−0.0373458	+	0.0646848i
$326$	−3.57784	+	6.19700i	−0.198158	+	0.343220i
$327$	−10.6714	−	18.4833i	−0.590128	−	1.02213i
$328$	−12.1791			−0.672480
$329$	5.46843	+	9.69018i	0.301484	+	0.534237i
$330$		0			0
$331$	−2.82200	−	4.88785i	−0.155111	−	0.268660i	0.777988	−	0.628279i	$-0.216240\pi$
$331$	−2.82200	−	4.88785i	−0.155111	−	0.268660i	−0.933099	+	0.359618i	$0.882907\pi$
$332$	5.53864	−	9.59321i	0.303973	−	0.526496i
$333$	2.87529	−	4.98015i	0.157565	−	0.272911i
$334$	10.4749	+	18.1431i	0.573162	+	0.992745i
$335$	−0.658544			−0.0359801
$336$	−14.1201	−	0.138697i	−0.770312	−	0.00756656i
$337$	11.0378			0.601268			0.300634	−	0.953740i	$-0.402802\pi$
$337$	11.0378			0.601268			0.300634	+	0.953740i	$0.402802\pi$
$338$	−10.7018	−	18.5361i	−0.582102	−	1.00823i
$339$	1.84713	−	3.19932i	0.100322	−	0.173763i
$340$	0.715836	−	1.23986i	0.0388216	−	0.0672410i
$341$		0			0
$342$	−15.8581			−0.857508
$343$	−18.5122	−	0.545661i	−0.999566	−	0.0294629i
$344$	9.14214			0.492911
$345$	6.29745	+	10.9075i	0.339043	+	0.587240i
$346$	9.36465	−	16.2200i	0.503447	−	0.871995i
$347$	−4.31607	+	7.47565i	−0.231699	+	0.401314i	−0.958308	−	0.285737i	$-0.907762\pi$
$347$	−4.31607	+	7.47565i	−0.231699	+	0.401314i	0.726609	+	0.687051i	$0.241095\pi$
$348$	−1.44887	−	2.50952i	−0.0776677	−	0.134524i
$349$	11.4624			0.613569			0.306784	−	0.951779i	$-0.400747\pi$
$349$	11.4624			0.613569			0.306784	+	0.951779i	$0.400747\pi$
$350$	−12.1333	−	0.119182i	−0.648553	−	0.00637056i
$351$	−2.56503			−0.136911
$352$		0			0
$353$	−4.76869	+	8.25961i	−0.253812	+	0.439615i	−0.964572	−	0.263819i	$-0.915018\pi$
$353$	−4.76869	+	8.25961i	−0.253812	+	0.439615i	0.710760	+	0.703434i	$0.248351\pi$
$354$	−8.70183	+	15.0720i	−0.462497	+	0.801068i
$355$	−11.3889	−	19.7262i	−0.604462	−	1.04696i
$356$	−1.67440			−0.0887428
$357$	−1.63105	−	2.89025i	−0.0863241	−	0.152968i
$358$	−23.5515			−1.24474
$359$	12.8615	+	22.2768i	0.678805	+	1.17573i	0.975341	+	0.220703i	$0.0708353\pi$
$359$	12.8615	+	22.2768i	0.678805	+	1.17573i	−0.296536	+	0.955022i	$0.595831\pi$
$360$	−2.76121	+	4.78256i	−0.145529	+	0.252063i
$361$	−3.62544	+	6.27945i	−0.190813	+	0.330497i
$362$	17.7089	+	30.6727i	0.930758	+	1.61212i
$363$		0			0
$364$	−0.539992	+	0.914432i	−0.0283033	+	0.0479293i
$365$	4.38385			0.229461
$366$	−8.64967	−	14.9817i	−0.452125	−	0.783104i
$367$	10.8370	−	18.7702i	0.565685	−	0.979795i	−0.431301	−	0.902208i	$-0.641945\pi$
$367$	10.8370	−	18.7702i	0.565685	−	0.979795i	0.996986	−	0.0775868i	$-0.0247215\pi$
$368$	−19.3262	+	33.4739i	−1.00745	+	1.74495i
$369$	−5.64983	−	9.78580i	−0.294119	−	0.509428i
$370$	7.87339			0.409318
$371$	−6.49168	+	10.9931i	−0.337031	+	0.570734i
$372$	7.63210			0.395706
$373$	12.8071	+	22.1825i	0.663125	+	1.14857i	0.979790	+	0.200029i	$0.0641038\pi$
$373$	12.8071	+	22.1825i	0.663125	+	1.14857i	−0.316664	+	0.948538i	$0.602563\pi$
$374$		0			0
$375$	6.25675	−	10.8370i	0.323097	−	0.559621i
$376$	−4.18109	−	7.24186i	−0.215623	−	0.373471i
$377$	1.62985			0.0839417
$378$	−11.3599	−	20.1301i	−0.584292	−	1.03538i
$379$	−27.9609			−1.43625			−0.718127	−	0.695912i	$-0.755000\pi$
$379$	−27.9609			−1.43625			−0.718127	+	0.695912i	$0.755000\pi$
$380$	−3.14261	−	5.44317i	−0.161213	−	0.279228i
$381$	−1.06009	+	1.83613i	−0.0543101	+	0.0940679i
$382$	−3.16176	+	5.47633i	−0.161770	+	0.280194i
$383$	−2.57571	−	4.46127i	−0.131613	−	0.227960i	0.792686	−	0.609631i	$-0.208682\pi$
$383$	−2.57571	−	4.46127i	−0.131613	−	0.227960i	−0.924298	+	0.381671i	$0.875349\pi$
$384$	14.0952			0.719291
$385$		0			0
$386$	16.2224			0.825700
$387$	4.24099	+	7.34561i	0.215582	+	0.373398i
$388$	6.12053	−	10.6011i	0.310723	−	0.538188i
$389$	−17.8650	+	30.9431i	−0.905792	+	1.56888i	−0.0859413	+	0.996300i	$0.527390\pi$
$389$	−17.8650	+	30.9431i	−0.905792	+	1.56888i	−0.819851	+	0.572577i	$0.805944\pi$
$390$	−0.668631	−	1.15810i	−0.0338574	−	0.0586428i
$391$	−9.08423			−0.459409
$392$	13.9161	+	0.273414i	0.702868	+	0.0138095i
$393$	−4.39099			−0.221496
$394$	−12.2592	−	21.2335i	−0.617608	−	1.06973i
$395$	−11.0179	+	19.0836i	−0.554372	+	0.960200i
$396$		0			0
$397$	−4.86742	−	8.43062i	−0.244289	−	0.423121i	0.717643	−	0.696412i	$-0.245221\pi$
$397$	−4.86742	−	8.43062i	−0.244289	−	0.423121i	−0.961931	+	0.273291i	$0.911888\pi$
$398$	22.6322			1.13445
$399$	−14.5689	−	0.143106i	−0.729356	−	0.00716426i
$400$	13.5740			0.678698
$401$	−0.981109	−	1.69933i	−0.0489943	−	0.0848605i	0.840488	−	0.541830i	$-0.182268\pi$
$401$	−0.981109	−	1.69933i	−0.0489943	−	0.0848605i	−0.889482	+	0.456969i	$0.848935\pi$
$402$	−0.394397	+	0.683115i	−0.0196707	+	0.0340707i
$403$	−2.14636	+	3.71760i	−0.106918	+	0.185187i
$404$	7.84970	+	13.5961i	0.390537	+	0.676430i
$405$	0.0936822			0.00465511
$406$	7.21826	+	12.7909i	0.358236	+	0.634802i
$407$		0			0
$408$	1.24708	+	2.16000i	0.0617395	+	0.106936i
$409$	−13.5624	+	23.4908i	−0.670617	+	1.16154i	0.307112	+	0.951673i	$0.400637\pi$
$409$	−13.5624	+	23.4908i	−0.670617	+	1.16154i	−0.977729	+	0.209870i	$0.932696\pi$
$410$	7.73544	−	13.3982i	0.382026	−	0.661689i
$411$	−5.49319	−	9.51449i	−0.270959	−	0.469315i
$412$	14.4143			0.710140
$413$	12.9841	−	21.9875i	0.638906	−	1.08193i
$414$	−24.0920			−1.18406
$415$	−10.2330	−	17.7241i	−0.502319	−	0.870042i
$416$	1.07248	−	1.85760i	0.0525828	−	0.0910762i
$417$	−6.40944	+	11.1015i	−0.313872	+	0.543642i
$418$		0			0
$419$	7.05834			0.344822			0.172411	−	0.985025i	$-0.444844\pi$
$419$	7.05834			0.344822			0.172411	+	0.985025i	$0.444844\pi$
$420$	1.77378	−	3.00375i	0.0865516	−	0.146568i
$421$	−1.23795			−0.0603338			−0.0301669	−	0.999545i	$-0.509604\pi$
$421$	−1.23795			−0.0603338			−0.0301669	+	0.999545i	$0.509604\pi$
$422$	−5.91145	−	10.2389i	−0.287765	−	0.498424i
$423$	3.87917	−	6.71893i	0.188612	−	0.326685i
$424$	4.79739	−	8.30932i	0.232982	−	0.403536i
$425$	1.59510	+	2.76280i	0.0773739	+	0.134016i
$426$	−27.2830			−1.32186
$427$	12.4745	+	22.1050i	0.603681	+	1.06974i
$428$	−0.129559			−0.00626249
$429$		0			0
$430$	−5.80653	+	10.0572i	−0.280016	+	0.485001i
$431$	−0.644758	+	1.11675i	−0.0310569	+	0.0537922i	−0.881136	−	0.472863i	$-0.843221\pi$
$431$	−0.644758	+	1.11675i	−0.0310569	+	0.0537922i	0.850079	+	0.526655i	$0.176554\pi$
$432$	12.9287	+	22.3932i	0.622033	+	1.07739i
$433$	−23.3688			−1.12304			−0.561518	−	0.827465i	$-0.689782\pi$
$433$	−23.3688			−1.12304			−0.561518	+	0.827465i	$0.689782\pi$
$434$	−38.6811	−	0.379954i	−1.85675	−	0.0182384i
$435$	−5.35378			−0.256694
$436$	8.09036	+	14.0129i	0.387458	+	0.671097i
$437$	−19.9405	+	34.5379i	−0.953883	+	1.65217i
$438$	2.62545	−	4.54742i	0.125449	−	0.217284i
$439$	4.85965	+	8.41717i	0.231939	+	0.401729i	0.958379	−	0.285500i	$-0.0921598\pi$
$439$	4.85965	+	8.41717i	0.231939	+	0.401729i	−0.726440	+	0.687230i	$0.758826\pi$
$440$		0			0
$441$	6.23591	+	11.3083i	0.296948	+	0.538489i
$442$	0.964517			0.0458774
$443$	1.10531	+	1.91445i	0.0525148	+	0.0909582i	0.891088	−	0.453831i	$-0.149943\pi$
$443$	1.10531	+	1.91445i	0.0525148	+	0.0909582i	−0.838573	+	0.544789i	$0.816610\pi$
$444$	1.36499	−	2.36424i	0.0647797	−	0.112202i
$445$	−1.54678	+	2.67910i	−0.0733244	+	0.127002i
$446$	−2.57907	−	4.46708i	−0.122122	−	0.211522i
$447$	10.9168			0.516349
$448$	−6.94681	−	0.0682366i	−0.328206	−	0.00322388i
$449$	−40.6819			−1.91990			−0.959949	−	0.280176i	$-0.909607\pi$
$449$	−40.6819			−1.91990			−0.959949	+	0.280176i	$0.909607\pi$
$450$	4.23033	+	7.32714i	0.199420	+	0.345405i
$451$		0			0
$452$	−1.40038	+	2.42553i	−0.0658683	+	0.114087i
$453$	−2.40996	−	4.17418i	−0.113230	−	0.196120i
$454$	25.0271			1.17458
$455$	0.964293	+	1.70875i	0.0452067	+	0.0801073i
$456$	10.9497			0.512765
$457$	−12.0566	−	20.8827i	−0.563985	−	0.976851i	−0.997143	−	0.0755331i	$-0.975934\pi$
$457$	−12.0566	−	20.8827i	−0.563985	−	0.976851i	0.433158	−	0.901318i	$-0.357399\pi$
$458$	−12.2845	+	21.2774i	−0.574017	+	0.994227i
$459$	−3.03856	+	5.26294i	−0.141828	+	0.245653i
$460$	−4.77433	−	8.26939i	−0.222605	−	0.385562i
$461$	−6.96636			−0.324456			−0.162228	−	0.986753i	$-0.551868\pi$
$461$	−6.96636			−0.324456			−0.162228	+	0.986753i	$0.551868\pi$
$462$		0			0
$463$	−14.3806			−0.668323			−0.334161	−	0.942516i	$-0.608453\pi$
$463$	−14.3806			−0.668323			−0.334161	+	0.942516i	$0.608453\pi$
$464$	−8.21508	−	14.2289i	−0.381375	−	0.660562i
$465$	7.05041	−	12.2117i	0.326955	−	0.566303i
$466$	−5.92133	+	10.2560i	−0.274300	+	0.475102i
$467$	2.73959	+	4.74511i	0.126773	+	0.219577i	0.922425	−	0.386177i	$-0.126205\pi$
$467$	2.73959	+	4.74511i	0.126773	+	0.219577i	−0.795652	+	0.605755i	$0.792871\pi$
$468$	0.740483			0.0342288
$469$	0.588484	−	0.996549i	0.0271737	−	0.0460164i
$470$	10.6223			0.489970
$471$	−2.10953	−	3.65381i	−0.0972020	−	0.168359i
$472$	−9.59533	+	16.6196i	−0.441661	+	0.764979i
$473$		0			0
$474$	13.1971	+	22.8580i	0.606163	+	1.04990i
$475$	14.0054			0.642613
$476$	1.23656	+	2.19121i	0.0566775	+	0.100434i
$477$	8.90194			0.407592
$478$	19.7711	+	34.2446i	0.904309	+	1.56631i
$479$	−9.94891	+	17.2320i	−0.454577	+	0.787351i	−0.998664	−	0.0516782i	$-0.983543\pi$
$479$	−9.94891	+	17.2320i	−0.454577	+	0.787351i	0.544087	+	0.839029i	$0.316876\pi$
$480$	−3.52292	+	6.10188i	−0.160799	+	0.278511i
$481$	0.767747	+	1.32978i	0.0350063	+	0.0606326i
$482$	24.4433			1.11336
$483$	−22.1334	−	0.217410i	−1.00710	−	0.00989250i
$484$		0			0
$485$	−11.3081	−	19.5862i	−0.513474	−	0.889363i
$486$	−13.0484	+	22.6005i	−0.591889	+	1.02518i
$487$	−2.77235	+	4.80185i	−0.125627	+	0.217593i	−0.921978	−	0.387242i	$-0.873428\pi$
$487$	−2.77235	+	4.80185i	−0.125627	+	0.217593i	0.796351	+	0.604835i	$0.206761\pi$
$488$	−9.53781	−	16.5200i	−0.431756	−	0.747824i
$489$	4.58405			0.207298
$490$	−9.13943	+	15.1353i	−0.412877	+	0.683745i
$491$	10.2190			0.461175			0.230588	−	0.973052i	$-0.425935\pi$
$491$	10.2190			0.461175			0.230588	+	0.973052i	$0.425935\pi$
$492$	−2.68216	−	4.64563i	−0.120921	−	0.209441i
$493$	1.93074	−	3.34414i	0.0869562	−	0.150613i
$494$	2.11718	−	3.66706i	0.0952564	−	0.164989i
$495$		0			0
$496$	43.2739			1.94305
$497$	40.0282	+	0.393186i	1.79551	+	0.0176368i
$498$	−24.5139			−1.09849
$499$	2.93984	+	5.09196i	0.131605	+	0.227947i	0.924296	−	0.381677i	$-0.124653\pi$
$499$	2.93984	+	5.09196i	0.131605	+	0.227947i	−0.792690	+	0.609625i	$0.791320\pi$
$500$	−4.74348	+	8.21595i	−0.212135	+	0.367428i
$501$	6.71041	−	11.6228i	0.299799	−	0.519267i
$502$	3.01908	+	5.22920i	0.134748	+	0.233391i
$503$	25.6224			1.14245			0.571223	−	0.820795i	$-0.306469\pi$
$503$	25.6224			1.14245			0.571223	+	0.820795i	$0.306469\pi$
$504$	−4.76981	−	8.45220i	−0.212464	−	0.376491i
$505$	29.0057			1.29074
$506$		0			0
$507$	−6.85578	+	11.8746i	−0.304476	+	0.527368i
$508$	0.803696	−	1.39204i	0.0356582	−	0.0617619i
$509$	−9.13163	−	15.8165i	−0.404752	−	0.701052i	0.589540	−	0.807739i	$-0.299309\pi$
$509$	−9.13163	−	15.8165i	−0.404752	−	0.701052i	−0.994293	+	0.106687i	$0.965976\pi$
$510$	−3.16827			−0.140293
$511$	−3.91747	+	6.63392i	−0.173299	+	0.293467i
$512$	−1.87529			−0.0828771
$513$	13.3397	+	23.1050i	0.588961	+	1.02011i
$514$	12.8772	−	22.3040i	0.567989	−	0.983786i
$515$	13.3157	−	23.0634i	0.586758	−	1.01629i
$516$	2.01333	+	3.48719i	0.0886320	+	0.153515i
$517$		0			0
$518$	−7.03577	+	11.9145i	−0.309134	+	0.523493i
$519$	−11.9983			−0.526668
$520$	−0.737286	−	1.27702i	−0.0323321	−	0.0560009i
$521$	−12.5443	+	21.7274i	−0.549575	+	0.951893i	0.448728	+	0.893668i	$0.351877\pi$
$521$	−12.5443	+	21.7274i	−0.549575	+	0.951893i	−0.998304	+	0.0582243i	$0.981456\pi$
$522$	5.12046	−	8.86890i	0.224117	−	0.388181i
$523$	8.66542	+	15.0090i	0.378913	+	0.656296i	0.990904	−	0.134568i	$-0.0429648\pi$
$523$	8.66542	+	15.0090i	0.378913	+	0.656296i	−0.611992	+	0.790864i	$0.709631\pi$
$524$	3.32897			0.145427
$525$	3.82029	+	6.76964i	0.166731	+	0.295451i
$526$	8.57221			0.373766
$527$	5.08520	+	8.80782i	0.221515	+	0.383675i
$528$		0			0
$529$	−18.7941	+	32.5523i	−0.817134	+	1.41532i
$530$	6.09402	+	10.5552i	0.264707	+	0.458487i
$531$	−17.8049			−0.772667
$532$	11.0452	+	0.108494i	0.478871	+	0.00470381i
$533$	3.01719			0.130689
$534$	1.85271	+	3.20899i	0.0801745	+	0.138866i
$535$	−0.119685	+	0.207300i	−0.00517443	+	0.00896237i
$536$	−0.434893	+	0.753257i	−0.0187845	+	0.0325358i
$537$	7.54376	+	13.0662i	0.325537	+	0.563847i
$538$	−27.0596			−1.16662
$539$		0			0
$540$	−6.38781			−0.274888
$541$	−18.1536	−	31.4430i	−0.780485	−	1.35184i	−0.931659	−	0.363333i	$-0.881639\pi$
$541$	−18.1536	−	31.4430i	−0.780485	−	1.35184i	0.151174	−	0.988507i	$-0.451694\pi$
$542$	0.639593	−	1.10781i	0.0274729	−	0.0475844i
$543$	11.3446	−	19.6495i	0.486844	−	0.843239i
$544$	−2.54095	−	4.40106i	−0.108942	−	0.188694i
$545$	29.8950			1.28056
$546$	2.35001	+	0.0230835i	0.100571	+	0.000987882i
$547$	12.5122			0.534982			0.267491	−	0.963560i	$-0.413805\pi$
$547$	12.5122			0.534982			0.267491	+	0.963560i	$0.413805\pi$
$548$	4.16460	+	7.21330i	0.177903	+	0.308137i
$549$	8.84908	−	15.3271i	0.377670	−	0.654143i
$550$		0			0
$551$	−8.47621	−	14.6812i	−0.361099	−	0.625441i
$552$	16.6350			0.708033
$553$	−19.0327	−	33.7264i	−0.809353	−	1.43419i
$554$	−11.7761			−0.500320
$555$	−2.52192	−	4.36809i	−0.107049	−	0.185415i
$556$	4.85924	−	8.41645i	0.206078	−	0.356937i
$557$	13.7179	−	23.7601i	0.581246	−	1.00675i	−0.414086	−	0.910238i	$-0.635899\pi$
$557$	13.7179	−	23.7601i	0.581246	−	1.00675i	0.995332	−	0.0965095i	$-0.0307678\pi$
$558$	13.4863	+	23.3590i	0.570921	+	0.988864i
$559$	−2.26482			−0.0957916
$560$	10.0573	−	17.0312i	0.424998	−	0.719700i
$561$		0			0
$562$	8.78414	+	15.2146i	0.370537	+	0.641788i
$563$	−14.8816	+	25.7757i	−0.627185	+	1.08632i	0.360929	+	0.932593i	$0.382460\pi$
$563$	−14.8816	+	25.7757i	−0.627185	+	1.08632i	−0.988114	+	0.153723i	$0.950874\pi$
$564$	1.84157	−	3.18969i	0.0775440	−	0.134310i
$565$	2.58729	+	4.48132i	0.108848	+	0.188531i
$566$	−17.8372			−0.749755
$567$	−0.0837158	+	0.141766i	−0.00351573	+	0.00595360i
$568$	−30.0844			−1.26231
$569$	6.93502	+	12.0118i	0.290731	+	0.503561i	0.973983	−	0.226622i	$-0.0727681\pi$
$569$	6.93502	+	12.0118i	0.290731	+	0.503561i	−0.683252	+	0.730183i	$0.739435\pi$
$570$	−6.95456	+	12.0457i	−0.291295	+	0.504537i
$571$	3.47193	−	6.01355i	0.145296	−	0.251659i	−0.784188	−	0.620524i	$-0.786920\pi$
$571$	3.47193	−	6.01355i	0.145296	−	0.251659i	0.929483	+	0.368864i	$0.120253\pi$
$572$		0			0
$573$	4.05096			0.169231
$574$	13.3625	+	23.6786i	0.557738	+	0.988324i
$575$	21.2774			0.887329
$576$	2.42203	+	4.19508i	0.100918	+	0.174795i
$577$	15.5598	−	26.9504i	0.647765	−	1.12196i	−0.335891	−	0.941901i	$-0.609037\pi$
$577$	15.5598	−	26.9504i	0.647765	−	1.12196i	0.983656	−	0.180060i	$-0.0576293\pi$
$578$	−13.1183	+	22.7216i	−0.545649	+	0.945092i
$579$	−5.19619	−	9.00007i	−0.215946	−	0.374030i
$580$	4.05890			0.168537
$581$	35.9656	+	0.353280i	1.49210	+	0.0146565i
$582$	−27.0893			−1.12289
$583$		0			0
$584$	2.89504	−	5.01435i	0.119797	−	0.207495i
$585$	0.684046	−	1.18480i	0.0282818	−	0.0489856i
$586$	12.5044	+	21.6583i	0.516552	+	0.894695i
$587$	42.2631			1.74438			0.872192	−	0.489164i	$-0.162698\pi$
$587$	42.2631			1.74438			0.872192	+	0.489164i	$0.162698\pi$
$588$	2.96039	+	5.36839i	0.122084	+	0.221389i
$589$	44.6494			1.83975
$590$	−12.1887	−	21.1115i	−0.501803	−	0.869148i
$591$	−7.85344	+	13.6026i	−0.323047	+	0.559535i
$592$	7.73948	−	13.4052i	0.318091	−	0.550949i
$593$	−12.0931	−	20.9459i	−0.496605	−	0.860145i	0.503388	−	0.864061i	$-0.332087\pi$
$593$	−12.0931	−	20.9459i	−0.496605	−	0.860145i	−0.999992	+	0.00391598i	$0.998754\pi$
$594$		0			0
$595$	4.64833	+	0.0456592i	0.190563	+	0.00187185i
$596$	−8.27647			−0.339017
$597$	−7.24930	−	12.5562i	−0.296694	−	0.513889i
$598$	3.21647	−	5.57109i	0.131531	−	0.227819i
$599$	−7.05474	+	12.2192i	−0.288249	+	0.499262i	−0.973392	−	0.229147i	$-0.926406\pi$
$599$	−7.05474	+	12.2192i	−0.288249	+	0.499262i	0.685143	+	0.728409i	$0.259740\pi$
$600$	−2.92095	−	5.05923i	−0.119247	−	0.206542i
$601$	−36.5483			−1.49084			−0.745419	−	0.666596i	$-0.767751\pi$
$601$	−36.5483			−1.49084			−0.745419	+	0.666596i	$0.767751\pi$
$602$	−10.0304	−	17.7741i	−0.408808	−	0.724417i
$603$	−0.806979			−0.0328627
$604$	1.82708	+	3.16460i	0.0743430	+	0.128766i
$605$		0			0
$606$	17.3713	−	30.0880i	0.705660	−	1.22224i
$607$	−15.8421	−	27.4393i	−0.643009	−	1.11373i	−0.984757	−	0.173933i	$-0.944352\pi$
$607$	−15.8421	−	27.4393i	−0.643009	−	1.11373i	0.341748	−	0.939792i	$-0.388981\pi$
$608$	−22.3102			−0.904800
$609$	4.78421	−	8.10167i	0.193866	−	0.328296i
$610$	24.2314			0.981099
$611$	1.03580	+	1.79406i	0.0419039	+	0.0725798i
$612$	0.877185	−	1.51933i	0.0354581	−	0.0614152i
$613$	20.5350	−	35.5677i	0.829401	−	1.43656i	−0.0691077	−	0.997609i	$-0.522015\pi$
$613$	20.5350	−	35.5677i	0.829401	−	1.43656i	0.898509	−	0.438956i	$-0.144651\pi$
$614$	−20.2586	−	35.0890i	−0.817572	−	1.41608i
$615$	−9.91092			−0.399647
$616$		0			0
$617$	8.74510			0.352065			0.176032	−	0.984384i	$-0.443674\pi$
$617$	8.74510			0.352065			0.176032	+	0.984384i	$0.443674\pi$
$618$	−15.9493	−	27.6250i	−0.641575	−	1.11124i
$619$	−12.4849	+	21.6245i	−0.501811	+	0.869162i	0.498187	+	0.867070i	$0.333999\pi$
$619$	−12.4849	+	21.6245i	−0.501811	+	0.869162i	−0.999998	+	0.00209253i	$0.999334\pi$
$620$	−5.34518	+	9.25813i	−0.214668	+	0.371815i
$621$	20.2660	+	35.1017i	0.813245	+	1.40858i
$622$	−20.1244			−0.806915
$623$	−2.67196	−	4.73476i	−0.107050	−	0.189694i
$624$	−2.62904			−0.105246
$625$	1.93006	+	3.34296i	0.0772024	+	0.133718i
$626$	1.14099	−	1.97625i	0.0456030	−	0.0789867i
$627$		0			0
$628$	1.59931	+	2.77009i	0.0638196	+	0.110539i
$629$	3.63793			0.145054
$630$	12.3277	+	0.121092i	0.491147	+	0.00482440i
$631$	34.0049			1.35371			0.676857	−	0.736114i	$-0.263341\pi$
$631$	34.0049			1.35371			0.676857	+	0.736114i	$0.263341\pi$
$632$	14.5522	+	25.2051i	0.578854	+	1.00260i
$633$	−3.78698	+	6.55925i	−0.150519	+	0.260707i
$634$	19.0468	−	32.9900i	0.756445	−	1.31020i
$635$	−1.48488	−	2.57189i	−0.0589257	−	0.102062i
$636$	4.22603			0.167573
$637$	−3.44749	−	0.0677339i	−0.136594	−	0.00268372i
$638$		0			0
$639$	−13.9560	−	24.1725i	−0.552090	−	0.956249i
$640$	−9.87163	+	17.0982i	−0.390210	+	0.675864i
$641$	15.7093	−	27.2093i	0.620479	−	1.07470i	−0.368917	−	0.929462i	$-0.620271\pi$
$641$	15.7093	−	27.2093i	0.620479	−	1.07470i	0.989397	−	0.145239i	$-0.0463952\pi$
$642$	0.143357	+	0.248301i	0.00565784	+	0.00979966i
$643$	−2.51107			−0.0990269			−0.0495135	−	0.998773i	$-0.515767\pi$
$643$	−2.51107			−0.0990269			−0.0495135	+	0.998773i	$0.515767\pi$
$644$	16.7802	+	0.164827i	0.661231	+	0.00649509i
$645$	7.43953			0.292931
$646$	−5.01607	−	8.68809i	−0.197355	−	0.341828i
$647$	−21.0045	+	36.3809i	−0.825773	+	1.43028i	0.0755543	+	0.997142i	$0.475927\pi$
$647$	−21.0045	+	36.3809i	−0.825773	+	1.43028i	−0.901327	+	0.433139i	$0.857406\pi$
$648$	0.0618665	−	0.107156i	0.00243034	−	0.00420948i
$649$		0			0
$650$	−2.25912			−0.0886102
$651$	12.1791	+	21.5816i	0.477337	+	0.845851i
$652$	−3.47534			−0.136105
$653$	7.46340	+	12.9270i	0.292065	+	0.505872i	0.974298	−	0.225263i	$-0.0723242\pi$
$653$	7.46340	+	12.9270i	0.292065	+	0.505872i	−0.682233	+	0.731135i	$0.738991\pi$
$654$	17.9039	−	31.0104i	0.700097	−	1.21260i
$655$	3.07525	−	5.32649i	0.120160	−	0.208123i
$656$	−15.2078	−	26.3406i	−0.593763	−	1.02843i
$657$	5.37197			0.209580
$658$	−9.49224	+	16.0743i	−0.370046	+	0.626643i
$659$	36.6391			1.42726			0.713629	−	0.700524i	$-0.247050\pi$
$659$	36.6391			1.42726			0.713629	+	0.700524i	$0.247050\pi$
$660$		0			0
$661$	−22.5879	+	39.1234i	−0.878567	+	1.52172i	−0.0256538	+	0.999671i	$0.508167\pi$
$661$	−22.5879	+	39.1234i	−0.878567	+	1.52172i	−0.852913	+	0.522052i	$0.825167\pi$
$662$	4.73461	−	8.20058i	0.184016	−	0.318725i
$663$	−0.308944	−	0.535106i	−0.0119984	−	0.0207818i
$664$	−27.0310			−1.04901
$665$	10.3770	−	17.5726i	0.402402	−	0.681435i
$666$	9.64804			0.373854
$667$	−12.8773	−	22.3041i	−0.498610	−	0.863617i
$668$	−5.08742	+	8.81167i	−0.196838	+	0.340934i
$669$	−1.65220	+	2.86169i	−0.0638777	+	0.110639i
$670$	−0.552436	−	0.956847i	−0.0213425	−	0.0369662i
$671$		0			0
$672$	−6.08561	−	10.7838i	−0.234757	−	0.415995i
$673$	−13.9469			−0.537614			−0.268807	−	0.963194i	$-0.586629\pi$
$673$	−13.9469			−0.537614			−0.268807	+	0.963194i	$0.586629\pi$
$674$	9.25935	+	16.0377i	0.356657	+	0.617748i
$675$	7.11701	−	12.3270i	0.273934	−	0.474467i
$676$	5.19762	−	9.00255i	0.199909	−	0.346252i
$677$	−8.41730	−	14.5792i	−0.323503	−	0.560324i	0.657705	−	0.753275i	$-0.271527\pi$
$677$	−8.41730	−	14.5792i	−0.323503	−	0.560324i	−0.981208	+	0.192952i	$0.938194\pi$
$678$	6.19804			0.238034
$679$	39.7441	+	0.390395i	1.52524	+	0.0149820i
$680$	−3.49359			−0.133973
$681$	−8.01641	−	13.8848i	−0.307190	−	0.532068i
$682$		0			0
$683$	15.9850	−	27.6867i	0.611647	−	1.05940i	−0.379316	−	0.925267i	$-0.623841\pi$
$683$	15.9850	−	27.6867i	0.611647	−	1.05940i	0.990963	−	0.134137i	$-0.0428261\pi$
$684$	−3.85096	−	6.67005i	−0.147245	−	0.255036i
$685$	15.3888			0.587974
$686$	−14.7366	−	27.3555i	−0.562646	−	1.04444i
$687$	15.7393			0.600493
$688$	11.4156	+	19.7723i	0.435214	+	0.753812i
$689$	−1.18848	+	2.05850i	−0.0452774	+	0.0784227i
$690$	−10.5655	+	18.3001i	−0.402223	+	0.696671i
$691$	15.2134	+	26.3504i	0.578746	+	1.00242i	0.995624	+	0.0934544i	$0.0297909\pi$
$691$	15.2134	+	26.3504i	0.578746	+	1.00242i	−0.416878	+	0.908963i	$0.636876\pi$
$692$	9.09638			0.345793
$693$		0			0
$694$	−14.4826			−0.549751
$695$	−8.97777	−	15.5500i	−0.340546	−	0.589844i
$696$	−3.53556	+	6.12378i	−0.134015	+	0.232121i
$697$	3.57419	−	6.19068i	0.135382	−	0.234489i
$698$	9.61553	+	16.6546i	0.363953	+	0.630385i
$699$	7.58661			0.286952
$700$	−2.89631	−	5.13232i	−0.109470	−	0.193983i
$701$	−5.18313			−0.195764			−0.0978821	−	0.995198i	$-0.531207\pi$
$701$	−5.18313			−0.195764			−0.0978821	+	0.995198i	$0.531207\pi$
$702$	−2.15174	−	3.72692i	−0.0812120	−	0.140663i
$703$	7.98549	−	13.8313i	0.301179	−	0.521657i
$704$		0			0
$705$	−3.40242	−	5.89316i	−0.128143	−	0.221949i
$706$	−16.0013			−0.602218
$707$	−25.9199	+	43.8932i	−0.974818	+	1.65077i
$708$	−8.45255			−0.317666
$709$	−9.27484	−	16.0645i	−0.348324	−	0.603315i	0.637628	−	0.770345i	$-0.279916\pi$
$709$	−9.27484	−	16.0645i	−0.348324	−	0.603315i	−0.985952	+	0.167030i	$0.946582\pi$
$710$	19.1078	−	33.0956i	0.717102	−	1.24206i
$711$	−13.5014	+	23.3850i	−0.506340	+	0.877007i
$712$	2.04294	+	3.53848i	0.0765626	+	0.132610i
$713$	67.8325			2.54035
$714$	2.83121	−	4.79442i	0.105955	−	0.179427i
$715$		0			0
$716$	−5.71921	−	9.90597i	−0.213737	−	0.370203i
$717$	12.6657	−	21.9377i	0.473010	−	0.819278i
$718$	−21.5784	+	37.3749i	−0.805299	+	1.39482i
$719$	11.0689	+	19.1720i	0.412802	+	0.714993i	0.995195	−	0.0979138i	$-0.0312170\pi$
$719$	11.0689	+	19.1720i	0.412802	+	0.714993i	−0.582393	+	0.812907i	$0.697884\pi$
$720$	−13.7914			−0.513976
$721$	23.0019	+	40.7599i	0.856635	+	1.51798i
$722$	−12.1652			−0.452741
$723$	−7.82941	−	13.5609i	−0.291179	−	0.504337i
$724$	−8.60078	+	14.8970i	−0.319646	+	0.553642i
$725$	−4.52225	+	7.83276i	−0.167952	+	0.290901i
$726$		0			0
$727$	21.4358			0.795011			0.397506	−	0.917600i	$-0.369876\pi$
$727$	21.4358			0.795011			0.397506	+	0.917600i	$0.369876\pi$
$728$	2.59131	+	0.0254537i	0.0960403	+	0.000943377i
$729$	16.9048			0.626104
$730$	3.67750	+	6.36962i	0.136110	+	0.235750i
$731$	−2.68293	+	4.64697i	−0.0992317	+	0.171874i
$732$	4.20094	−	7.27624i	0.155271	−	0.268938i
$733$	21.3641	+	37.0036i	0.789099	+	1.36676i	0.926519	+	0.376247i	$0.122786\pi$
$733$	21.3641	+	37.0036i	0.789099	+	1.36676i	−0.137420	+	0.990513i	$0.543881\pi$
$734$	36.3634			1.34220
$735$	11.3244	+	0.222494i	0.417707	+	0.00820682i
$736$	−33.8943			−1.24936
$737$		0			0
$738$	9.47901	−	16.4181i	0.348927	−	0.604359i
$739$	11.3527	−	19.6635i	0.417617	−	0.723333i	−0.578082	−	0.815978i	$-0.696199\pi$
$739$	11.3527	−	19.6635i	0.417617	−	0.723333i	0.995699	+	0.0926449i	$0.0295321\pi$
$740$	1.91196	+	3.31161i	0.0702850	+	0.121737i
$741$	−2.71261			−0.0996501
$742$	−21.4184	−	0.210387i	−0.786295	−	0.00772355i
$743$	−31.2644			−1.14698			−0.573490	−	0.819212i	$-0.694411\pi$
$743$	−31.2644			−1.14698			−0.573490	+	0.819212i	$0.694411\pi$
$744$	−9.31199	−	16.1288i	−0.341394	−	0.591312i
$745$	−7.64567	+	13.2427i	−0.280116	+	0.485174i
$746$	−21.4871	+	37.2167i	−0.786698	+	1.36260i
$747$	−12.5395	−	21.7191i	−0.458798	−	0.794661i
$748$		0			0
$749$	−0.206748	−	0.366361i	−0.00755439	−	0.0133865i
$750$	20.9945			0.766611
$751$	3.94516	+	6.83322i	0.143961	+	0.249348i	0.928985	−	0.370118i	$-0.120683\pi$
$751$	3.94516	+	6.83322i	0.143961	+	0.249348i	−0.785024	+	0.619466i	$0.787349\pi$
$752$	10.4416	−	18.0855i	0.380768	−	0.659509i
$753$	1.93408	−	3.34992i	0.0704817	−	0.122078i
$754$	1.36724	+	2.36813i	0.0497920	+	0.0862423i
$755$	6.75132			0.245706
$756$	5.70824	−	9.66643i	0.207607	−	0.351565i
$757$	−2.80096			−0.101803			−0.0509014	−	0.998704i	$-0.516209\pi$
$757$	−2.80096			−0.101803			−0.0509014	+	0.998704i	$0.516209\pi$
$758$	−23.4557	−	40.6264i	−0.851949	−	1.47562i
$759$		0			0
$760$	−7.66866	+	13.2825i	−0.278171	+	0.481807i
$761$	12.7181	+	22.0284i	0.461030	+	0.798527i	0.999013	−	0.0444286i	$-0.0141467\pi$
$761$	12.7181	+	22.0284i	0.461030	+	0.798527i	−0.537983	+	0.842956i	$0.680813\pi$
$762$	−3.55714			−0.128861
$763$	−26.7146	+	45.2389i	−0.967133	+	1.63776i
$764$	−3.07119			−0.111112
$765$	−1.62066	−	2.80706i	−0.0585950	−	0.101490i
$766$	4.32140	−	7.48489i	0.156139	−	0.270440i
$767$	2.37709	−	4.11724i	0.0858318	−	0.148665i
$768$	9.00191	+	15.5918i	0.324828	+	0.562619i
$769$	28.3807			1.02343			0.511717	−	0.859154i	$-0.329010\pi$
$769$	28.3807			1.02343			0.511717	+	0.859154i	$0.329010\pi$
$770$		0			0
$771$	−16.4987			−0.594188
$772$	3.93943	+	6.82329i	0.141783	+	0.245576i
$773$	−6.44451	+	11.1622i	−0.231793	+	0.401477i	−0.958336	−	0.285644i	$-0.907792\pi$
$773$	−6.44451	+	11.1622i	−0.231793	+	0.401477i	0.726543	+	0.687121i	$0.241126\pi$
$774$	−7.11532	+	12.3241i	−0.255755	+	0.442980i
$775$	−11.9107	−	20.6300i	−0.427846	−	0.741051i
$776$	−29.8708			−1.07230
$777$	8.86368	+	0.0870654i	0.317983	+	0.00312345i
$778$	−59.9460			−2.14917
$779$	−15.6912	−	27.1779i	−0.562195	−	0.973750i
$780$	0.324738	−	0.562463i	0.0116275	−	0.0201394i
$781$		0			0
$782$	−7.62053	−	13.1992i	−0.272510	−	0.472001i
$783$	−17.2291			−0.615718
$784$	16.7853	+	30.4387i	0.599476	+	1.08709i
$785$	5.90968			0.210926
$786$	−3.68349	−	6.37999i	−0.131386	−	0.227567i
$787$	−26.9002	+	46.5925i	−0.958888	+	1.66084i	−0.233679	+	0.972314i	$0.575076\pi$
$787$	−26.9002	+	46.5925i	−0.958888	+	1.66084i	−0.725209	+	0.688528i	$0.758257\pi$
$788$	5.95399	−	10.3126i	0.212102	−	0.367372i
$789$	−2.74576	−	4.75579i	−0.0977515	−	0.169311i
$790$	−36.9706			−1.31536
$791$	−9.09346	−	0.0893225i	−0.323326	−	0.00317594i
$792$		0			0
$793$	2.36284	+	4.09256i	0.0839070	+	0.145331i
$794$	8.16631	−	14.1445i	0.289812	−	0.501968i
$795$	3.90394	−	6.76182i	0.138458	−	0.239817i
$796$	5.49597	+	9.51930i	0.194800	+	0.337403i
$797$	−7.52765			−0.266643			−0.133322	−	0.991073i	$-0.542564\pi$
$797$	−7.52765			−0.266643			−0.133322	+	0.991073i	$0.542564\pi$
$798$	−12.0135	−	21.2883i	−0.425275	−	0.753596i
$799$	4.90808			0.173635
$800$	5.95150	+	10.3083i	0.210417	+	0.364454i
$801$	−1.89542	+	3.28297i	−0.0669715	+	0.115998i
$802$	1.64606	−	2.85105i	0.0581242	−	0.100674i
$803$		0			0
$804$	−0.383099			−0.0135108
$805$	15.7650	−	26.6967i	0.555642	−	0.940934i
$806$	−7.20210			−0.253683
$807$	8.66743	+	15.0124i	0.305108	+	0.528463i
$808$	19.1550	−	33.1774i	0.673869	−	1.16718i
$809$	4.78489	−	8.28768i	0.168228	−	0.291379i	−0.769569	−	0.638564i	$-0.779529\pi$
$809$	4.78489	−	8.28768i	0.168228	−	0.291379i	0.937797	+	0.347184i	$0.112862\pi$
$810$	0.0785877	+	0.136118i	0.00276129	+	0.00478269i
$811$	−5.05315			−0.177440			−0.0887201	−	0.996057i	$-0.528278\pi$
$811$	−5.05315			−0.177440			−0.0887201	+	0.996057i	$0.528278\pi$
$812$	−3.62709	+	6.14218i	−0.127286	+	0.215548i
$813$	−0.819470			−0.0287401
$814$		0			0
$815$	−3.21047	+	5.56069i	−0.112458	+	0.194782i
$816$	−3.11439	+	5.39428i	−0.109025	+	0.188837i
$817$	11.7784	+	20.4008i	0.412075	+	0.713734i
$818$	−45.5086			−1.59117
$819$	1.18164	+	2.09390i	0.0412900	+	0.0731667i
$820$	7.51385			0.262395
$821$	3.27422	+	5.67112i	0.114271	+	0.197923i	0.917488	−	0.397763i	$-0.130213\pi$
$821$	3.27422	+	5.67112i	0.114271	+	0.197923i	−0.803217	+	0.595687i	$0.796880\pi$
$822$	9.21621	−	15.9629i	0.321452	−	0.556771i
$823$	15.1943	−	26.3174i	0.529642	−	0.917366i	−0.469761	−	0.882794i	$-0.655660\pi$
$823$	15.1943	−	26.3174i	0.529642	−	0.917366i	0.999402	−	0.0345722i	$-0.0110069\pi$
$824$	−17.5870	−	30.4615i	−0.612671	−	1.06118i
$825$		0			0
$826$	42.8393	+	0.420798i	1.49057	+	0.0146414i
$827$	−23.0405			−0.801197			−0.400599	−	0.916254i	$-0.631198\pi$
$827$	−23.0405			−0.801197			−0.400599	+	0.916254i	$0.631198\pi$
$828$	−5.85047	−	10.1333i	−0.203318	−	0.352157i
$829$	2.00599	−	3.47448i	0.0696711	−	0.120674i	−0.829085	−	0.559122i	$-0.811138\pi$
$829$	2.00599	−	3.47448i	0.0696711	−	0.120674i	0.898757	+	0.438448i	$0.144472\pi$
$830$	17.1684	−	29.7366i	0.595925	−	1.03217i
$831$	3.77200	+	6.53330i	0.130849	+	0.226638i
$832$	−1.29344			−0.0448420
$833$	−4.22291	+	6.99334i	−0.146315	+	0.242305i
$834$	−21.5069			−0.744722
$835$	9.39935	+	16.2801i	0.325278	+	0.563398i
$836$		0			0
$837$	22.6891	−	39.2986i	0.784249	−	1.35836i
$838$	5.92106	+	10.2556i	0.204540	+	0.354273i
$839$	8.17443			0.282213			0.141106	−	0.989994i	$-0.454934\pi$
$839$	8.17443			0.282213			0.141106	+	0.989994i	$0.454934\pi$
$840$	−8.51200	−	0.0836110i	−0.293692	−	0.00288485i
$841$	−18.0524			−0.622496
$842$	−1.03848	−	1.79870i	−0.0357885	−	0.0619874i
$843$	5.62728	−	9.74673i	0.193814	−	0.335695i
$844$	2.87106	−	4.97281i	0.0988258	−	0.171171i
$845$	−9.60296	−	16.6328i	−0.330352	−	0.572186i
$846$	13.0166			0.447519
$847$		0			0
$848$	23.9615			0.822842
$849$	5.71342	+	9.89594i	0.196084	+	0.339628i
$850$	−2.67618	+	4.63529i	−0.0917924	+	0.158989i
$851$	12.1318	−	21.0128i	0.415871	−	0.720310i
$852$	−6.62535	−	11.4754i	−0.226981	−	0.393142i
$853$	−8.00203			−0.273984			−0.136992	−	0.990572i	$-0.543744\pi$
$853$	−8.00203			−0.273984			−0.136992	+	0.990572i	$0.543744\pi$
$854$	−21.6535	+	36.6684i	−0.740967	+	1.25477i
$855$	−14.2298			−0.486649
$856$	0.158077	+	0.273797i	0.00540295	+	0.00935818i
$857$	17.3239	−	30.0058i	0.591772	−	1.02498i	−0.402222	−	0.915542i	$-0.631762\pi$
$857$	17.3239	−	30.0058i	0.591772	−	1.02498i	0.993994	−	0.109436i	$-0.0349046\pi$
$858$		0			0
$859$	−15.4657	−	26.7873i	−0.527681	−	0.913971i	−0.999479	−	0.0322644i	$-0.989728\pi$
$859$	−15.4657	−	26.7873i	−0.527681	−	0.913971i	0.471798	−	0.881707i	$-0.343605\pi$
$860$	−5.64019			−0.192329
$861$	8.85655	−	14.9978i	0.301830	−	0.511125i
$862$	−2.16349			−0.0736886
$863$	−6.03576	−	10.4542i	−0.205460	−	0.355867i	0.744819	−	0.667266i	$-0.232536\pi$
$863$	−6.03576	−	10.4542i	−0.205460	−	0.355867i	−0.950279	+	0.311399i	$0.899202\pi$
$864$	−11.3372	+	19.6366i	−0.385699	+	0.668050i
$865$	8.40309	−	14.5546i	0.285714	−	0.494870i
$866$	−19.6035	−	33.9543i	−0.666155	−	1.15381i
$867$	16.8076			0.570817
$868$	−9.23344	−	16.3619i	−0.313403	−	0.555358i
$869$		0			0
$870$	−4.49115	−	7.77890i	−0.152264	−	0.263729i
$871$	0.107738	−	0.186608i	0.00365056	−	0.00632296i
$872$	19.7422	−	34.1946i	0.668557	−	1.15797i
$873$	−13.8569	−	24.0009i	−0.468986	−	0.812307i
$874$	−66.9103			−2.26328
$875$	−30.8021	−	0.302561i	−1.04130	−	0.0102284i
$876$	2.55024			0.0861648
$877$	−10.2826	−	17.8100i	−0.347220	−	0.601402i	0.638535	−	0.769593i	$-0.279541\pi$
$877$	−10.2826	−	17.8100i	−0.347220	−	0.601402i	−0.985754	+	0.168191i	$0.946208\pi$
$878$	−8.15328	+	14.1219i	−0.275160	+	0.476591i
$879$	8.01055	−	13.8747i	0.270189	−	0.467981i
$880$		0			0
$881$	−19.3738			−0.652719			−0.326359	−	0.945246i	$-0.605822\pi$
$881$	−19.3738			−0.652719			−0.326359	+	0.945246i	$0.605822\pi$
$882$	−11.1995	+	18.5468i	−0.377105	+	0.624504i
$883$	−26.9916			−0.908340			−0.454170	−	0.890915i	$-0.650064\pi$
$883$	−26.9916			−0.908340			−0.454170	+	0.890915i	$0.650064\pi$
$884$	0.234222	+	0.405684i	0.00787773	+	0.0136446i
$885$	−7.80833	+	13.5244i	−0.262474	+	0.454618i
$886$	−1.85443	+	3.21197i	−0.0623008	+	0.107908i
$887$	5.16545	+	8.94682i	0.173439	+	0.300405i	0.939620	−	0.342220i	$-0.111179\pi$
$887$	5.16545	+	8.94682i	0.173439	+	0.300405i	−0.766181	+	0.642625i	$0.777845\pi$
$888$	−6.66176			−0.223554
$889$	5.21886	+	0.0512633i	0.175035	+	0.00171932i
$890$	−5.19022			−0.173976
$891$		0			0
$892$	1.25259	−	2.16956i	0.0419399	−	0.0726421i
$893$	10.7736	−	18.6603i	0.360523	−	0.624445i
$894$	9.15786	+	15.8619i	0.306285	+	0.530501i
$895$	−21.1333			−0.706407
$896$	−17.0526	−	30.2175i	−0.569686	−	1.00950i
$897$	−4.12106			−0.137598
$898$	−34.1270	−	59.1097i	−1.13883	−	1.97252i
$899$	−14.4169	+	24.9709i	−0.480832	+	0.832826i
$900$	−2.05457	+	3.55862i	−0.0684857	+	0.118621i
$901$	2.81577	+	4.87705i	0.0938068	+	0.162478i
$902$		0			0
$903$	−6.64807	+	11.2580i	−0.221234	+	0.374642i
$904$	6.83445			0.227311
$905$	15.8905	+	27.5232i	0.528219	+	0.914902i
$906$	4.04332	−	7.00323i	0.134330	−	0.232667i
$907$	11.5445	−	19.9957i	0.383329	−	0.663946i	−0.608207	−	0.793779i	$-0.708111\pi$
$907$	11.5445	−	19.9957i	0.383329	−	0.663946i	0.991536	+	0.129833i	$0.0414441\pi$
$908$	6.07754	+	10.5266i	0.201690	+	0.349338i
$909$	35.5436			1.17891
$910$	−1.67384	+	2.83452i	−0.0554874	+	0.0939633i
$911$	39.8213			1.31934			0.659669	−	0.751556i	$-0.270696\pi$
$911$	39.8213			1.31934			0.659669	+	0.751556i	$0.270696\pi$
$912$	13.6726	+	23.6816i	0.452744	+	0.784176i
$913$		0			0
$914$	20.2280	−	35.0359i	0.669083	−	1.15889i
$915$	−7.76152	−	13.4433i	−0.256588	−	0.444423i
$916$	−11.9326			−0.394264
$917$	5.31229	+	9.41349i	0.175427	+	0.310861i
$918$	−10.1959			−0.336514
$919$	−2.24299	−	3.88497i	−0.0739893	−	0.128153i	0.826657	−	0.562706i	$-0.190240\pi$
$919$	−2.24299	−	3.88497i	−0.0739893	−	0.128153i	−0.900646	+	0.434553i	$0.856906\pi$
$920$	−11.6504	+	20.1791i	−0.384103	+	0.665285i
$921$	−12.9780	+	22.4786i	−0.427641	+	0.740696i
$922$	−5.84390	−	10.1219i	−0.192459	−	0.333348i
$923$	7.45293			0.245316
$924$		0			0
$925$	−8.52088			−0.280165
$926$	−12.0635	−	20.8946i	−0.396432	−	0.686640i
$927$	16.3170	−	28.2619i	0.535921	−	0.928242i
$928$	7.20381	−	12.4774i	0.236476	−	0.409589i
$929$	−24.4907	−	42.4191i	−0.803512	−	1.39172i	−0.917291	−	0.398218i	$-0.869629\pi$
$929$	−24.4907	−	42.4191i	−0.803512	−	1.39172i	0.113779	−	0.993506i	$-0.463705\pi$
$930$	23.6576			0.775765
$931$	17.3189	+	31.4062i	0.567603	+	1.02930i
$932$	−5.75170			−0.188403
$933$	6.44603	+	11.1648i	0.211034	+	0.365521i
$934$	−4.59634	+	7.96110i	−0.150397	+	0.260495i
$935$		0			0
$936$	−0.903470	−	1.56486i	−0.0295308	−	0.0511489i
$937$	24.0986			0.787268			0.393634	−	0.919267i	$-0.371218\pi$
$937$	24.0986			0.787268			0.393634	+	0.919267i	$0.371218\pi$
$938$	1.94162	+	0.0190720i	0.0633963	+	0.000622724i
$939$	−1.46187			−0.0477064
$940$	2.57950	+	4.46783i	0.0841341	+	0.145725i
$941$	−2.65999	+	4.60724i	−0.0867133	+	0.150192i	−0.906120	−	0.423021i	$-0.860970\pi$
$941$	−2.65999	+	4.60724i	−0.0867133	+	0.150192i	0.819407	+	0.573213i	$0.194303\pi$
$942$	3.53926	−	6.13018i	0.115315	−	0.199732i
$943$	−23.8384	−	41.2893i	−0.776286	−	1.34457i
$944$	−47.9258			−1.55985
$945$	−10.1935	−	18.0631i	−0.331595	−	0.587593i
$946$		0			0
$947$	−15.2482	−	26.4107i	−0.495501	−	0.858233i	0.504485	−	0.863420i	$-0.331682\pi$
$947$	−15.2482	−	26.4107i	−0.495501	−	0.858233i	−0.999987	+	0.00518702i	$0.998349\pi$
$948$	−6.40952	+	11.1016i	−0.208172	+	0.360564i
$949$	−0.717199	+	1.24223i	−0.0232813	+	0.0403243i
$950$	11.7488	+	20.3495i	0.381181	+	0.660226i
$951$	−24.4034			−0.791335
$952$	3.12192	−	5.28671i	0.101182	−	0.171343i
$953$	40.4965			1.31181			0.655906	−	0.754843i	$-0.272287\pi$
$953$	40.4965			1.31181			0.655906	+	0.754843i	$0.272287\pi$
$954$	7.46761	+	12.9343i	0.241773	+	0.418763i
$955$	−2.83711	+	4.91403i	−0.0918069	+	0.159014i
$956$	−9.60236	+	16.6318i	−0.310563	+	0.537910i
$957$		0			0
$958$	−33.3836			−1.07857
$959$	−13.7516	+	23.2872i	−0.444063	+	0.751983i
$960$	4.24872			0.137127
$961$	−22.4715	−	38.9217i	−0.724886	−	1.25554i
$962$	−1.28809	+	2.23103i	−0.0415296	+	0.0719314i
$963$	−0.146662	+	0.254026i	−0.00472611	+	0.00818586i
$964$	5.93577	+	10.2811i	0.191178	+	0.331131i
$965$	14.5567			0.468597
$966$	−18.2513	−	32.3416i	−0.587225	−	1.04058i
$967$	25.6872			0.826044			0.413022	−	0.910721i	$-0.364473\pi$
$967$	25.6872			0.826044			0.413022	+	0.910721i	$0.364473\pi$
$968$		0			0
$969$	−3.21338	+	5.56574i	−0.103229	+	0.178797i
$970$	18.9721	−	32.8607i	0.609159	−	1.05509i
$971$	−9.43441	−	16.3409i	−0.302765	−	0.524404i	0.673997	−	0.738735i	$-0.264576\pi$
$971$	−9.43441	−	16.3409i	−0.302765	−	0.524404i	−0.976761	+	0.214331i	$0.931243\pi$
$972$	−12.6746			−0.406539
$973$	31.5538	+	0.309944i	1.01157	+	0.00993636i
$974$	−9.30262			−0.298075
$975$	0.723618	+	1.25334i	0.0231743	+	0.0401391i
$976$	23.8192	−	41.2561i	0.762435	−	1.32058i
$977$	−13.5601	+	23.4868i	−0.433826	+	0.751408i	−0.997199	−	0.0747942i	$-0.976170\pi$
$977$	−13.5601	+	23.4868i	−0.433826	+	0.751408i	0.563373	+	0.826203i	$0.309503\pi$
$978$	3.84545	+	6.66051i	0.122964	+	0.212980i
$979$		0			0
$980$	−8.58545	−	0.168681i	−0.274252	−	0.00538832i
$981$	36.6333			1.16961
$982$	8.57243	+	14.8479i	0.273557	+	0.473815i
$983$	4.80894	−	8.32933i	0.153381	−	0.265664i	−0.779087	−	0.626916i	$-0.784317\pi$
$983$	4.80894	−	8.32933i	0.153381	−	0.265664i	0.932469	+	0.361251i	$0.117650\pi$
$984$	−6.54504	+	11.3363i	−0.208648	+	0.361389i
$985$	−11.0004	−	19.0533i	−0.350502	−	0.607087i
$986$	6.47860			0.206321
$987$	11.9583	+	0.117463i	0.380638	+	0.00373890i
$988$	2.05653			0.0654269
$989$	17.8941	+	30.9934i	0.568998	+	0.985533i
$990$		0			0
$991$	−22.4657	+	38.9117i	−0.713646	+	1.23607i	0.249833	+	0.968289i	$0.419624\pi$
$991$	−22.4657	+	38.9117i	−0.713646	+	1.23607i	−0.963479	+	0.267783i	$0.913709\pi$
$992$	18.9734	+	32.8629i	0.602407	+	1.04340i
$993$	−6.06615			−0.192503
$994$	33.0074	+	58.4898i	1.04693	+	1.85518i
$995$	20.3084			0.643818
$996$	−5.95291	−	10.3108i	−0.188625	−	0.326709i
$997$	16.2745	−	28.1882i	0.515418	−	0.892731i	−0.484422	−	0.874835i	$-0.660970\pi$
$997$	16.2745	−	28.1882i	0.515418	−	0.892731i	0.999840	−	0.0178960i	$-0.00569679\pi$
$998$	−4.93232	+	8.54303i	−0.156130	+	0.270425i
$999$	−8.11583	−	14.0570i	−0.256774	−	0.444745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.e.f.606.6	yes	14
7.2	even	3	inner	847.2.e.f.485.6	✓	14
7.3	odd	6		5929.2.a.bo.1.2		7
7.4	even	3		5929.2.a.bp.1.2		7
11.2	odd	10		847.2.n.l.81.2		56
11.3	even	5		847.2.n.m.130.6		56
11.4	even	5		847.2.n.m.753.2		56
11.5	even	5		847.2.n.m.487.2		56
11.6	odd	10		847.2.n.l.487.6		56
11.7	odd	10		847.2.n.l.753.6		56
11.8	odd	10		847.2.n.l.130.2		56
11.9	even	5		847.2.n.m.81.6		56
11.10	odd	2		847.2.e.g.606.2	yes	14
77.2	odd	30		847.2.n.l.807.6		56
77.9	even	15		847.2.n.m.807.2		56
77.10	even	6		5929.2.a.bn.1.6		7
77.16	even	15		847.2.n.m.366.6		56
77.30	odd	30		847.2.n.l.9.6		56
77.32	odd	6		5929.2.a.bq.1.6		7
77.37	even	15		847.2.n.m.632.6		56
77.51	odd	30		847.2.n.l.632.2		56
77.58	even	15		847.2.n.m.9.2		56
77.65	odd	6		847.2.e.g.485.2	yes	14
77.72	odd	30		847.2.n.l.366.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.e.f.485.6	✓	14	7.2	even	3	inner
847.2.e.f.606.6	yes	14	1.1	even	1	trivial
847.2.e.g.485.2	yes	14	77.65	odd	6
847.2.e.g.606.2	yes	14	11.10	odd	2
847.2.n.l.9.6		56	77.30	odd	30
847.2.n.l.81.2		56	11.2	odd	10
847.2.n.l.130.2		56	11.8	odd	10
847.2.n.l.366.2		56	77.72	odd	30
847.2.n.l.487.6		56	11.6	odd	10
847.2.n.l.632.2		56	77.51	odd	30
847.2.n.l.753.6		56	11.7	odd	10
847.2.n.l.807.6		56	77.2	odd	30
847.2.n.m.9.2		56	77.58	even	15
847.2.n.m.81.6		56	11.9	even	5
847.2.n.m.130.6		56	11.3	even	5
847.2.n.m.366.6		56	77.16	even	15
847.2.n.m.487.2		56	11.5	even	5
847.2.n.m.632.6		56	77.37	even	15
847.2.n.m.753.2		56	11.4	even	5
847.2.n.m.807.2		56	77.9	even	15
5929.2.a.bn.1.6		7	77.10	even	6
5929.2.a.bo.1.2		7	7.3	odd	6
5929.2.a.bp.1.2		7	7.4	even	3
5929.2.a.bq.1.6		7	77.32	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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.838875 + 1.45297i) q^{2} +(0.537398 - 0.930801i) q^{3} +(-0.407422 + 0.705675i) q^{4} +(0.752739 + 1.30378i) q^{5} +1.80324 q^{6} +(-2.64562 - 0.0259872i) q^{7} +1.98840 q^{8} +(0.922406 + 1.59765i) q^{9} +O(q^{10})\)	\(q+(0.838875 + 1.45297i) q^{2} +(0.537398 - 0.930801i) q^{3} +(-0.407422 + 0.705675i) q^{4} +(0.752739 + 1.30378i) q^{5} +1.80324 q^{6} +(-2.64562 - 0.0259872i) q^{7} +1.98840 q^{8} +(0.922406 + 1.59765i) q^{9} +(-1.26291 + 2.18742i) q^{10} +(0.437896 + 0.758457i) q^{12} -0.492593 q^{13} +(-2.18159 - 3.86582i) q^{14} +1.61808 q^{15} +(2.48286 + 4.30044i) q^{16} +(-0.583532 + 1.01071i) q^{17} +(-1.54757 + 2.68046i) q^{18} +(2.56178 + 4.43713i) q^{19} -1.22673 q^{20} +(-1.44594 + 2.44858i) q^{21} +(3.89192 + 6.74100i) q^{23} +(1.06856 - 1.85080i) q^{24} +(1.36677 - 2.36731i) q^{25} +(-0.413224 - 0.715725i) q^{26} +5.20719 q^{27} +(1.09622 - 1.85636i) q^{28} -3.30872 q^{29} +(1.35737 + 2.35103i) q^{30} +(4.35726 - 7.54700i) q^{31} +(-2.17722 + 3.77105i) q^{32} -1.95804 q^{34} +(-1.95758 - 3.46888i) q^{35} -1.50323 q^{36} +(-1.55858 - 2.69954i) q^{37} +(-4.29803 + 7.44440i) q^{38} +(-0.264719 + 0.458506i) q^{39} +(1.49674 + 2.59244i) q^{40} -6.12510 q^{41} +(-4.77069 - 0.0468612i) q^{42} +4.59775 q^{43} +(-1.38866 + 2.40524i) q^{45} +(-6.52967 + 11.3097i) q^{46} +(-2.10275 - 3.64206i) q^{47} +5.33713 q^{48} +(6.99865 + 0.137505i) q^{49} +4.58619 q^{50} +(0.627178 + 1.08630i) q^{51} +(0.200693 - 0.347611i) q^{52} +(2.41269 - 4.17891i) q^{53} +(4.36818 + 7.56591i) q^{54} +(-5.26055 - 0.0516729i) q^{56} +5.50679 q^{57} +(-2.77560 - 4.80748i) q^{58} +(-4.82567 + 8.35830i) q^{59} +(-0.659242 + 1.14184i) q^{60} +(-4.79674 - 8.30819i) q^{61} +14.6208 q^{62} +(-2.39882 - 4.25076i) q^{63} +2.62578 q^{64} +(-0.370794 - 0.642235i) q^{65} +(-0.218716 + 0.378827i) q^{67} +(-0.475487 - 0.823568i) q^{68} +8.36604 q^{69} +(3.39802 - 5.75427i) q^{70} -15.1300 q^{71} +(1.83411 + 3.17677i) q^{72} +(1.45597 - 2.52181i) q^{73} +(2.61491 - 4.52916i) q^{74} +(-1.46900 - 2.54438i) q^{75} -4.17490 q^{76} -0.888264 q^{78} +(7.31855 + 12.6761i) q^{79} +(-3.73789 + 6.47422i) q^{80} +(0.0311138 - 0.0538906i) q^{81} +(-5.13819 - 8.89961i) q^{82} -13.5944 q^{83} +(-1.13880 - 2.01797i) q^{84} -1.75699 q^{85} +(3.85693 + 6.68040i) q^{86} +(-1.77810 + 3.07976i) q^{87} +(1.02743 + 1.77957i) q^{89} -4.65966 q^{90} +(1.30322 + 0.0128011i) q^{91} -6.34261 q^{92} +(-4.68317 - 8.11149i) q^{93} +(3.52788 - 6.11047i) q^{94} +(-3.85671 + 6.68001i) q^{95} +(2.34007 + 4.05312i) q^{96} -15.0226 q^{97} +(5.67120 + 10.2842i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{3} - 8 q^{4} - 4 q^{5} - 4 q^{6} + 2 q^{7} - 6 q^{8} - 10 q^{9}+O(q^{10}) \) 14 * q - 3 * q^3 - 8 * q^4 - 4 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 - 10 * q^9	\( 14 q - 3 q^{3} - 8 q^{4} - 4 q^{5} - 4 q^{6} + 2 q^{7} - 6 q^{8} - 10 q^{9} - 6 q^{10} - 13 q^{12} + 12 q^{13} + 12 q^{14} - 2 q^{15} - 6 q^{16} + 3 q^{17} - 14 q^{18} + 9 q^{19} + 4 q^{20} - 6 q^{21} + 6 q^{23} - 4 q^{24} - 7 q^{25} - 25 q^{26} + 24 q^{27} - 36 q^{28} + 12 q^{29} - 16 q^{30} - 14 q^{31} + 36 q^{32} + 16 q^{34} + 18 q^{35} - 4 q^{36} + 8 q^{37} + 10 q^{38} + 9 q^{39} - 18 q^{40} - 20 q^{41} - 8 q^{42} + 34 q^{43} - 12 q^{45} - 16 q^{46} - 30 q^{47} + 112 q^{48} + 14 q^{49} + 42 q^{50} + 20 q^{51} + 37 q^{52} + 10 q^{53} + 7 q^{54} - 33 q^{56} - 62 q^{57} + 13 q^{58} - 20 q^{59} - 42 q^{60} - 7 q^{61} + 52 q^{62} + 37 q^{63} + 42 q^{64} - 12 q^{65} - 7 q^{67} - 7 q^{68} + 18 q^{69} - 39 q^{70} - 22 q^{71} + q^{72} + 6 q^{73} - 8 q^{74} + q^{75} - 112 q^{76} + 30 q^{78} + 14 q^{79} - 12 q^{80} - 35 q^{81} + 7 q^{82} + 34 q^{83} + 40 q^{84} - 4 q^{85} + 15 q^{87} - 40 q^{89} + 136 q^{90} - 32 q^{91} - 52 q^{92} - 19 q^{94} - 20 q^{95} + 63 q^{96} - 44 q^{97} + 21 q^{98}+O(q^{100}) \) 14 * q - 3 * q^3 - 8 * q^4 - 4 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 - 10 * q^9 - 6 * q^10 - 13 * q^12 + 12 * q^13 + 12 * q^14 - 2 * q^15 - 6 * q^16 + 3 * q^17 - 14 * q^18 + 9 * q^19 + 4 * q^20 - 6 * q^21 + 6 * q^23 - 4 * q^24 - 7 * q^25 - 25 * q^26 + 24 * q^27 - 36 * q^28 + 12 * q^29 - 16 * q^30 - 14 * q^31 + 36 * q^32 + 16 * q^34 + 18 * q^35 - 4 * q^36 + 8 * q^37 + 10 * q^38 + 9 * q^39 - 18 * q^40 - 20 * q^41 - 8 * q^42 + 34 * q^43 - 12 * q^45 - 16 * q^46 - 30 * q^47 + 112 * q^48 + 14 * q^49 + 42 * q^50 + 20 * q^51 + 37 * q^52 + 10 * q^53 + 7 * q^54 - 33 * q^56 - 62 * q^57 + 13 * q^58 - 20 * q^59 - 42 * q^60 - 7 * q^61 + 52 * q^62 + 37 * q^63 + 42 * q^64 - 12 * q^65 - 7 * q^67 - 7 * q^68 + 18 * q^69 - 39 * q^70 - 22 * q^71 + q^72 + 6 * q^73 - 8 * q^74 + q^75 - 112 * q^76 + 30 * q^78 + 14 * q^79 - 12 * q^80 - 35 * q^81 + 7 * q^82 + 34 * q^83 + 40 * q^84 - 4 * q^85 + 15 * q^87 - 40 * q^89 + 136 * q^90 - 32 * q^91 - 52 * q^92 - 19 * q^94 - 20 * q^95 + 63 * q^96 - 44 * q^97 + 21 * q^98

Introduction

L-functions

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