LMFDB - Embedded newform 392.2.p.g.373.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(165,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.165"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-2,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.951588245534976.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64 $ x^12 - x^11 + 2x^10 - 9x^9 + 8x^8 - 13x^7 + 35x^6 - 26x^5 + 32x^4 - 72x^3 + 32x^2 - 32x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.4
Root			$1.41417 - 0.0105323i$ of defining polynomial
Character	$\chi$	$=$	392.373
Dual form			392.2.p.g.165.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.242117 + 1.39333i) q^{2} +(2.13038 - 1.22998i) q^{3} +(-1.88276 - 0.674701i) q^{4} +(-1.28690 - 0.742990i) q^{5} +(1.19797 + 3.26613i) q^{6} +(1.39593 - 2.45995i) q^{8} +(1.52569 - 2.64257i) q^{9} +(1.34681 - 1.61319i) q^{10} +(4.37021 - 2.52314i) q^{11} +(-4.84086 + 0.878379i) q^{12} -2.58633i q^{13} -3.65544 q^{15} +(3.08956 + 2.54060i) q^{16} +(0.629755 + 1.09077i) q^{17} +(3.31258 + 2.76560i) q^{18} +(2.68324 + 1.54917i) q^{19} +(1.92162 + 2.26714i) q^{20} +(2.45748 + 6.70006i) q^{22} +(0.697966 - 1.20891i) q^{23} +(-0.0518180 - 6.95761i) q^{24} +(-1.39593 - 2.41782i) q^{25} +(3.60362 + 0.626196i) q^{26} -0.126378i q^{27} -0.638384i q^{29} +(0.885046 - 5.09325i) q^{30} +(-1.82772 - 3.16571i) q^{31} +(-4.28794 + 3.68966i) q^{32} +(6.20682 - 10.7505i) q^{33} +(-1.67228 + 0.613365i) q^{34} +(-4.65544 + 3.94593i) q^{36} +(5.21370 + 3.01013i) q^{37} +(-2.80817 + 3.36357i) q^{38} +(-3.18113 - 5.50988i) q^{39} +(-3.62414 + 2.12854i) q^{40} -6.36226 q^{41} +1.02401i q^{43} +(-9.93042 + 1.80188i) q^{44} +(-3.92680 + 2.26714i) q^{45} +(1.51543 + 1.26520i) q^{46} +(-5.48316 + 9.49712i) q^{47} +(9.70682 + 1.61236i) q^{48} +(3.70682 - 1.35960i) q^{50} +(2.68324 + 1.54917i) q^{51} +(-1.74500 + 4.86944i) q^{52} +(-4.99481 + 2.88375i) q^{53} +(0.176087 + 0.0305984i) q^{54} -7.49868 q^{55} +7.62177 q^{57} +(0.889482 + 0.154564i) q^{58} +(-3.01720 + 1.74198i) q^{59} +(6.88231 + 2.46633i) q^{60} +(11.1614 + 6.44406i) q^{61} +(4.85341 - 1.78015i) q^{62} +(-4.10275 - 6.86786i) q^{64} +(-1.92162 + 3.32834i) q^{65} +(13.4763 + 11.2511i) q^{66} +(-0.443410 + 0.256003i) q^{67} +(-0.449735 - 2.47855i) q^{68} -3.43393i q^{69} -7.41363 q^{71} +(-4.37084 - 7.44196i) q^{72} +(4.94731 + 8.56899i) q^{73} +(-5.45644 + 6.53562i) q^{74} +(-5.94774 - 3.43393i) q^{75} +(-4.00667 - 4.72709i) q^{76} +(8.44731 - 3.09834i) q^{78} +(-4.35341 + 7.54032i) q^{79} +(-2.08830 - 5.56500i) q^{80} +(4.42162 + 7.65847i) q^{81} +(1.54041 - 8.86475i) q^{82} -2.97196i q^{83} -1.87161i q^{85} +(-1.42679 - 0.247931i) q^{86} +(-0.785198 - 1.36000i) q^{87} +(-0.106298 - 14.2727i) q^{88} +(-1.29186 + 2.23757i) q^{89} +(-2.20814 - 6.02026i) q^{90} +(-2.12976 + 1.80517i) q^{92} +(-7.78749 - 4.49611i) q^{93} +(-11.9051 - 9.93929i) q^{94} +(-2.30203 - 3.98724i) q^{95} +(-4.59674 + 13.1345i) q^{96} +1.57040 q^{97} -15.3981i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 8 q^{6} + 4 q^{8} + 8 q^{10} + 2 q^{12} - 20 q^{15} + 8 q^{16} + 2 q^{17} + 6 q^{18} - 8 q^{20} + 12 q^{22} + 2 q^{23} - 18 q^{24} - 4 q^{25} + 2 q^{26} + 14 q^{30} - 10 q^{31} - 12 q^{32}+ \cdots - 40 q^{97}+O(q^{100}) $ 12 * q - 2 * q^2 + 8 * q^6 + 4 * q^8 + 8 * q^10 + 2 * q^12 - 20 * q^15 + 8 * q^16 + 2 * q^17 + 6 * q^18 - 8 * q^20 + 12 * q^22 + 2 * q^23 - 18 * q^24 - 4 * q^25 + 2 * q^26 + 14 * q^30 - 10 * q^31 - 12 * q^32 + 14 * q^33 - 32 * q^34 - 32 * q^36 - 18 * q^38 + 4 * q^39 - 10 * q^40 + 8 * q^41 - 30 * q^44 - 4 * q^46 - 30 * q^47 + 56 * q^48 - 16 * q^50 + 32 * q^52 - 2 * q^54 - 4 * q^55 - 4 * q^57 - 22 * q^58 + 6 * q^60 + 28 * q^62 + 24 * q^64 + 8 * q^65 + 38 * q^66 - 4 * q^68 + 32 * q^71 + 20 * q^72 + 10 * q^73 + 18 * q^74 - 52 * q^76 + 52 * q^78 - 22 * q^79 - 36 * q^80 + 22 * q^81 + 26 * q^82 + 40 * q^86 + 20 * q^87 - 14 * q^88 + 10 * q^89 - 52 * q^90 - 20 * q^92 - 42 * q^94 - 34 * q^95 - 16 * q^96 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.242117	+	1.39333i	−0.171203	+	0.985236i
$2$	−0.242117	+	1.39333i	−0.171203	+	0.985236i
$3$	2.13038	−	1.22998i	1.22998	−	0.710128i	0.262952	−	0.964809i	$-0.415304\pi$
$3$	2.13038	−	1.22998i	1.22998	−	0.710128i	0.967025	+	0.254681i	$0.0819706\pi$
$4$	−1.88276	−	0.674701i	−0.941379	−	0.337350i
$5$	−1.28690	−	0.742990i	−0.575518	−	0.332275i	0.183832	−	0.982958i	$-0.441150\pi$
$5$	−1.28690	−	0.742990i	−0.575518	−	0.332275i	−0.759350	+	0.650682i	$0.774483\pi$
$6$	1.19797	+	3.26613i	0.489068	+	1.33339i
$7$		0			0
$7$		0			0
$8$	1.39593	−	2.45995i	0.493536	−	0.869725i
$9$	1.52569	−	2.64257i	0.508562	−	0.880856i
$10$	1.34681	−	1.61319i	0.425900	−	0.510134i
$11$	4.37021	−	2.52314i	1.31767	−	0.760756i	0.334315	−	0.942461i	$-0.391495\pi$
$11$	4.37021	−	2.52314i	1.31767	−	0.760756i	0.983353	+	0.181705i	$0.0581616\pi$
$12$	−4.84086	+	0.878379i	−1.39744	+	0.253566i
$13$		−	2.58633i		−	0.717320i	−0.933468	−	0.358660i	$-0.883234\pi$
$13$		−	2.58633i		−	0.717320i	0.933468	−	0.358660i	$-0.116766\pi$
$14$		0			0
$15$	−3.65544			−0.943831
$16$	3.08956	+	2.54060i	0.772389	+	0.635149i
$17$	0.629755	+	1.09077i	0.152738	+	0.264550i	0.932233	−	0.361858i	$-0.117858\pi$
$17$	0.629755	+	1.09077i	0.152738	+	0.264550i	−0.779495	+	0.626408i	$0.784524\pi$
$18$	3.31258	+	2.76560i	0.780783	+	0.651859i
$19$	2.68324	+	1.54917i	0.615577	+	0.355404i	0.775145	−	0.631783i	$-0.217677\pi$
$19$	2.68324	+	1.54917i	0.615577	+	0.355404i	−0.159568	+	0.987187i	$0.551010\pi$
$20$	1.92162	+	2.26714i	0.429687	+	0.506948i
$21$		0			0
$22$	2.45748	+	6.70006i	0.523936	+	1.42846i
$23$	0.697966	−	1.20891i	0.145536	−	0.252076i	−0.784037	−	0.620714i	$-0.786843\pi$
$23$	0.697966	−	1.20891i	0.145536	−	0.252076i	0.929573	+	0.368639i	$0.120176\pi$
$24$	−0.0518180	−	6.95761i	−0.0105773	−	1.42022i
$25$	−1.39593	−	2.41782i	−0.279186	−	0.483565i
$26$	3.60362	+	0.626196i	0.706729	+	0.122807i
$27$		−	0.126378i		−	0.0243215i
$28$		0			0
$29$		−	0.638384i		−	0.118545i	−0.998242	−	0.0592725i	$-0.981122\pi$
$29$		−	0.638384i		−	0.118545i	0.998242	−	0.0592725i	$-0.0188781\pi$
$30$	0.885046	−	5.09325i	0.161587	−	0.929896i
$31$	−1.82772	−	3.16571i	−0.328268	−	0.568578i	0.653900	−	0.756581i	$-0.273132\pi$
$31$	−1.82772	−	3.16571i	−0.328268	−	0.568578i	−0.982168	+	0.188003i	$0.939798\pi$
$32$	−4.28794	+	3.68966i	−0.758007	+	0.652246i
$33$	6.20682	−	10.7505i	1.08047	−	1.87143i
$34$	−1.67228	+	0.613365i	−0.286793	+	0.105191i
$35$		0			0
$36$	−4.65544	+	3.94593i	−0.775907	+	0.657656i
$37$	5.21370	+	3.01013i	0.857127	+	0.494862i	0.863049	−	0.505120i	$-0.168552\pi$
$37$	5.21370	+	3.01013i	0.857127	+	0.494862i	−0.00592229	+	0.999982i	$0.501885\pi$
$38$	−2.80817	+	3.36357i	−0.455545	+	0.545643i
$39$	−3.18113	−	5.50988i	−0.509388	−	0.882287i
$40$	−3.62414	+	2.12854i	−0.573027	+	0.336552i
$41$	−6.36226			−0.993618			−0.496809	−	0.867860i	$-0.665495\pi$
$41$	−6.36226			−0.993618			−0.496809	+	0.867860i	$0.665495\pi$
$42$		0			0
$43$			1.02401i			0.156160i	0.996947	+	0.0780801i	$0.0248790\pi$
$43$			1.02401i			0.156160i	−0.996947	+	0.0780801i	$0.975121\pi$
$44$	−9.93042	+	1.80188i	−1.49707	+	0.271644i
$45$	−3.92680	+	2.26714i	−0.585373	+	0.337965i
$46$	1.51543	+	1.26520i	0.223438	+	0.186543i
$47$	−5.48316	+	9.49712i	−0.799802	+	1.38530i	0.119943	+	0.992781i	$0.461729\pi$
$47$	−5.48316	+	9.49712i	−0.799802	+	1.38530i	−0.919745	+	0.392516i	$0.871605\pi$
$48$	9.70682	+	1.61236i	1.40106	+	0.232724i
$49$		0			0
$50$	3.70682	−	1.35960i	0.524223	−	0.192277i
$51$	2.68324	+	1.54917i	0.375729	+	0.216927i
$52$	−1.74500	+	4.86944i	−0.241988	+	0.675270i
$53$	−4.99481	+	2.88375i	−0.686089	+	0.396114i	−0.802145	−	0.597129i	$-0.796308\pi$
$53$	−4.99481	+	2.88375i	−0.686089	+	0.396114i	0.116056	+	0.993243i	$0.462975\pi$
$54$	0.176087	+	0.0305984i	0.0239624	+	0.00416391i
$55$	−7.49868			−1.01112
$56$		0			0
$57$	7.62177			1.00953
$58$	0.889482	+	0.154564i	0.116795	+	0.0202952i
$59$	−3.01720	+	1.74198i	−0.392806	+	0.226787i	−0.683375	−	0.730067i	$-0.739489\pi$
$59$	−3.01720	+	1.74198i	−0.392806	+	0.226787i	0.290569	+	0.956854i	$0.406155\pi$
$60$	6.88231	+	2.46633i	0.888503	+	0.318402i
$61$	11.1614	+	6.44406i	1.42908	+	0.825077i	0.997048	−	0.0767831i	$-0.0244649\pi$
$61$	11.1614	+	6.44406i	1.42908	+	0.825077i	0.432028	+	0.901860i	$0.357798\pi$
$62$	4.85341	−	1.78015i	0.616383	−	0.226080i
$63$		0			0
$64$	−4.10275	−	6.86786i	−0.512844	−	0.858482i
$65$	−1.92162	+	3.32834i	−0.238348	+	0.412830i
$66$	13.4763	+	11.2511i	1.65882	+	1.38491i
$67$	−0.443410	+	0.256003i	−0.0541711	+	0.0312757i	−0.526841	−	0.849964i	$-0.676624\pi$
$67$	−0.443410	+	0.256003i	−0.0541711	+	0.0312757i	0.472670	+	0.881240i	$0.343290\pi$
$68$	−0.449735	−	2.47855i	−0.0545384	−	0.300568i
$69$		−	3.43393i		−	0.413396i
$70$		0			0
$71$	−7.41363			−0.879836			−0.439918	−	0.898038i	$-0.644993\pi$
$71$	−7.41363			−0.879836			−0.439918	+	0.898038i	$0.644993\pi$
$72$	−4.37084	−	7.44196i	−0.515108	−	0.877044i
$73$	4.94731	+	8.56899i	0.579038	+	1.00292i	0.995590	+	0.0938118i	$0.0299052\pi$
$73$	4.94731	+	8.56899i	0.579038	+	1.00292i	−0.416552	+	0.909112i	$0.636761\pi$
$74$	−5.45644	+	6.53562i	−0.634299	+	0.759750i
$75$	−5.94774	−	3.43393i	−0.686786	−	0.396516i
$76$	−4.00667	−	4.72709i	−0.459596	−	0.542235i
$77$		0			0
$78$	8.44731	−	3.09834i	0.956469	−	0.350818i
$79$	−4.35341	+	7.54032i	−0.489797	+	0.848353i	−0.999931	−	0.0117420i	$-0.996262\pi$
$79$	−4.35341	+	7.54032i	−0.489797	+	0.848353i	0.510134	+	0.860095i	$0.329596\pi$
$80$	−2.08830	−	5.56500i	−0.233479	−	0.622185i
$81$	4.42162	+	7.65847i	0.491291	+	0.850941i
$82$	1.54041	−	8.86475i	0.170110	−	0.978948i
$83$		−	2.97196i		−	0.326215i	−0.986608	−	0.163107i	$-0.947848\pi$
$83$		−	2.97196i		−	0.326215i	0.986608	−	0.163107i	$-0.0521517\pi$
$84$		0			0
$85$		−	1.87161i		−	0.203004i
$86$	−1.42679	−	0.247931i	−0.153855	−	0.0267351i
$87$	−0.785198	−	1.36000i	−0.0841820	−	0.145808i
$88$	−0.106298	−	14.2727i	−0.0113314	−	1.52147i
$89$	−1.29186	+	2.23757i	−0.136937	+	0.237182i	−0.926336	−	0.376699i	$-0.877059\pi$
$89$	−1.29186	+	2.23757i	−0.136937	+	0.237182i	0.789399	+	0.613881i	$0.210393\pi$
$90$	−2.20814	−	6.02026i	−0.232758	−	0.634591i
$91$		0			0
$92$	−2.12976	+	1.80517i	−0.222042	+	0.188202i
$93$	−7.78749	−	4.49611i	−0.807525	−	0.466225i
$94$	−11.9051	−	9.93929i	−1.22792	−	1.02516i
$95$	−2.30203	−	3.98724i	−0.236184	−	0.409082i
$96$	−4.59674	+	13.1345i	−0.469153	+	1.34053i
$97$	1.57040			0.159449			0.0797247	−	0.996817i	$-0.474596\pi$
$97$	1.57040			0.159449			0.0797247	+	0.996817i	$0.474596\pi$
$98$		0			0
$99$		−	15.3981i		−	1.54757i
$100$	0.996894	+	5.49402i	0.0996894	+	0.549402i
$101$	−0.181183	+	0.104606i	−0.0180284	+	0.0104087i	−0.508987	−	0.860774i	$-0.669980\pi$
$101$	−0.181183	+	0.104606i	−0.0180284	+	0.0104087i	0.490959	+	0.871183i	$0.336647\pi$
$102$	−2.80817	+	3.36357i	−0.278050	+	0.333043i
$103$	3.43846	−	5.95558i	0.338801	−	0.586821i	−0.645406	−	0.763839i	$-0.723312\pi$
$103$	3.43846	−	5.95558i	0.338801	−	0.586821i	0.984207	+	0.177019i	$0.0566453\pi$
$104$	−6.36226	−	3.61034i	−0.623871	−	0.354023i
$105$		0			0
$106$	−2.80870	−	7.65764i	−0.272805	−	0.743776i
$107$	−11.2048	−	6.46908i	−1.08321	−	0.625389i	−0.151447	−	0.988465i	$-0.548393\pi$
$107$	−11.2048	−	6.46908i	−1.08321	−	0.625389i	−0.931759	+	0.363076i	$0.881726\pi$
$108$	−0.0852675	+	0.237940i	−0.00820487	+	0.0228958i
$109$	16.6430	−	9.60883i	1.59411	−	0.920359i	0.601517	−	0.798860i	$-0.294563\pi$
$109$	16.6430	−	9.60883i	1.59411	−	0.920359i	0.992591	−	0.121500i	$-0.0387703\pi$
$110$	1.81556	−	10.4482i	0.173107	−	0.996193i
$111$	14.8096			1.40566
$112$		0			0
$113$	−1.05137			−0.0989050			−0.0494525	−	0.998776i	$-0.515748\pi$
$113$	−1.05137			−0.0989050			−0.0494525	+	0.998776i	$0.515748\pi$
$114$	−1.84536	+	10.6197i	−0.172834	+	0.994623i
$115$	−1.79642	+	1.03716i	−0.167517	+	0.0967160i
$116$	−0.430718	+	1.20192i	−0.0399912	+	0.111596i
$117$	−6.83456	−	3.94593i	−0.631855	−	0.364802i
$118$	−1.69665	−	4.62573i	−0.156189	−	0.425833i
$119$		0			0
$120$	−5.10275	+	8.99222i	−0.465815	+	0.820874i
$121$	7.23250	−	12.5271i	0.657500	−	1.13882i
$122$	−11.6811	+	13.9914i	−1.05756	+	1.26672i
$123$	−13.5540	+	7.82543i	−1.22213	+	0.705595i
$124$	1.30525	+	7.19342i	0.117215	+	0.645989i
$125$			11.5786i			1.03562i
$126$		0			0
$127$	−7.20814			−0.639619			−0.319809	−	0.947482i	$-0.603619\pi$
$127$	−7.20814			−0.639619			−0.319809	+	0.947482i	$0.603619\pi$
$128$	10.5626	−	4.05367i	0.933608	−	0.358297i
$129$	1.25951	+	2.18154i	0.110894	+	0.192074i
$130$	−4.17223	−	3.48331i	−0.365929	−	0.305506i
$131$	−12.7767	−	7.37662i	−1.11630	−	0.644498i	−0.175849	−	0.984417i	$-0.556267\pi$
$131$	−12.7767	−	7.37662i	−1.11630	−	0.644498i	−0.940455	+	0.339919i	$0.889600\pi$
$132$	−18.9393	+	16.0529i	−1.64846	+	1.39722i
$133$		0			0
$134$	−0.249340	−	0.679801i	−0.0215397	−	0.0587258i
$135$	−0.0938978	+	0.162636i	−0.00808144	+	0.0139975i
$136$	3.56233	−	0.0265311i	0.305468	−	0.00227502i
$137$	4.68113	+	8.10795i	0.399936	+	0.692709i	0.993718	−	0.111917i	$-0.0356991\pi$
$137$	4.68113	+	8.10795i	0.399936	+	0.692709i	−0.593782	+	0.804626i	$0.702366\pi$
$138$	4.78461	+	0.831414i	0.407293	+	0.0707746i
$139$		−	1.69519i		−	0.143784i	−0.997412	−	0.0718921i	$-0.977096\pi$
$139$		−	1.69519i		−	0.143784i	0.997412	−	0.0718921i	$-0.0229037\pi$
$140$		0			0
$141$			26.9767i			2.27184i
$142$	1.79497	−	10.3297i	0.150630	−	0.866846i
$143$	−6.52569	−	11.3028i	−0.545705	−	0.945189i
$144$	11.4274	−	4.28821i	0.952283	−	0.357351i
$145$	−0.474313	+	0.821534i	−0.0393895	+	0.0682247i
$146$	−13.1373	+	4.81855i	−1.08725	+	0.398786i
$147$		0			0
$148$	−7.78520	−	9.18503i	−0.639939	−	0.755005i
$149$	−3.19276	−	1.84334i	−0.261561	−	0.151012i	0.363485	−	0.931600i	$-0.381587\pi$
$149$	−3.19276	−	1.84334i	−0.261561	−	0.151012i	−0.625047	+	0.780587i	$0.714920\pi$
$150$	6.22466	−	7.45577i	0.508241	−	0.608761i
$151$	7.13861	+	12.3644i	0.580932	+	1.00620i	0.995369	+	0.0961252i	$0.0306449\pi$
$151$	7.13861	+	12.3644i	0.580932	+	1.00620i	−0.414438	+	0.910078i	$0.636022\pi$
$152$	7.55650	−	4.43811i	0.612913	−	0.359978i
$153$	3.84324			0.310707
$154$		0			0
$155$			5.43191i			0.436302i
$156$	2.27178	+	12.5201i	0.181888	+	1.00241i
$157$	11.1614	−	6.44406i	0.890780	−	0.514292i	0.0165822	−	0.999863i	$-0.494721\pi$
$157$	11.1614	−	6.44406i	0.890780	−	0.514292i	0.874197	+	0.485571i	$0.161388\pi$
$158$	−9.45215	−	7.89139i	−0.751973	−	0.627806i
$159$	−7.09390	+	12.2870i	−0.562583	+	0.974422i
$160$	8.25951	−	1.56232i	0.652972	−	0.123512i
$161$		0			0
$162$	−11.7414	+	4.30654i	−0.922488	+	0.338354i
$163$	2.79831	+	1.61560i	0.219180	+	0.126544i	0.605571	−	0.795791i	$-0.292945\pi$
$163$	2.79831	+	1.61560i	0.219180	+	0.126544i	−0.386390	+	0.922335i	$0.626278\pi$
$164$	11.9786	+	4.29262i	0.935371	+	0.335197i
$165$	−15.9751	+	9.22320i	−1.24366	+	0.718026i
$166$	4.14093	+	0.719563i	0.321399	+	0.0558489i
$167$	14.0487			1.08712			0.543562	−	0.839369i	$-0.317075\pi$
$167$	14.0487			1.08712			0.543562	+	0.839369i	$0.317075\pi$
$168$		0			0
$169$	6.31088			0.485453
$170$	2.60777	+	0.453149i	0.200007	+	0.0347549i
$171$	8.18757	−	4.72709i	0.626119	−	0.361490i
$172$	0.690901	−	1.92797i	0.0526807	−	0.147006i
$173$	5.66273	+	3.26938i	0.430529	+	0.248566i	0.699572	−	0.714562i	$-0.253374\pi$
$173$	5.66273	+	3.26938i	0.430529	+	0.248566i	−0.269043	+	0.963128i	$0.586707\pi$
$174$	2.08505	−	0.764762i	0.158067	−	0.0579765i
$175$		0			0
$176$	19.9123	+	3.30755i	1.50095	+	0.249316i
$177$	−4.28520	+	7.42218i	−0.322095	+	0.557885i
$178$	−2.80490	−	2.34175i	−0.210236	−	0.175522i
$179$	−0.109447	+	0.0631891i	−0.00818044	+	0.00472298i	−0.504085	−	0.863654i	$-0.668170\pi$
$179$	−0.109447	+	0.0631891i	−0.00818044	+	0.00472298i	0.495904	+	0.868377i	$0.334837\pi$
$180$	8.92286	−	1.61906i	0.665071	−	0.120678i
$181$		−	2.71920i		−	0.202117i	−0.994880	−	0.101058i	$-0.967777\pi$
$181$		−	2.71920i		−	0.202117i	0.994880	−	0.101058i	$-0.0322229\pi$
$182$		0			0
$183$	31.7042			2.34364
$184$	−1.99956	−	3.40452i	−0.147409	−	0.250985i
$185$	−4.47299	−	7.74745i	−0.328861	−	0.569604i
$186$	8.15007	−	9.76199i	0.597592	−	0.715784i
$187$	5.50433	+	3.17793i	0.402516	+	0.232393i
$188$	16.7312	−	14.1813i	1.22025	−	1.03428i
$189$		0			0
$190$	6.11292	−	2.24212i	0.443478	−	0.162661i
$191$	1.22365	−	2.11943i	0.0885404	−	0.153357i	−0.818354	−	0.574715i	$-0.805113\pi$
$191$	1.22365	−	2.11943i	0.0885404	−	0.153357i	0.906894	+	0.421358i	$0.138446\pi$
$192$	−17.1877	−	9.58488i	−1.24042	−	0.691729i
$193$	−1.97431	−	3.41961i	−0.142114	−	0.246149i	0.786178	−	0.618000i	$-0.212057\pi$
$193$	−1.97431	−	3.41961i	−0.142114	−	0.246149i	−0.928293	+	0.371851i	$0.878723\pi$
$194$	−0.380220	+	2.18808i	−0.0272982	+	0.157095i
$195$			9.45419i			0.677029i
$196$		0			0
$197$		−	19.5468i		−	1.39265i	−0.717727	−	0.696325i	$-0.754817\pi$
$197$		−	19.5468i		−	1.39265i	0.717727	−	0.696325i	$-0.245183\pi$
$198$	21.4547	+	3.72815i	1.52472	+	0.264948i
$199$	10.3981	+	18.0101i	0.737103	+	1.27670i	0.953795	+	0.300460i	$0.0971401\pi$
$199$	10.3981	+	18.0101i	0.737103	+	1.27670i	−0.216692	+	0.976240i	$0.569527\pi$
$200$	−7.89636	+	0.0588095i	−0.558357	+	0.00415846i
$201$	−0.629755	+	1.09077i	−0.0444195	+	0.0769369i
$202$	−0.101884	−	0.277775i	−0.00716850	−	0.0195442i
$203$		0			0
$204$	−4.00667	−	4.72709i	−0.280523	−	0.330963i
$205$	8.18757	+	4.72709i	0.571845	+	0.330155i
$206$	7.46560	+	6.23287i	0.520153	+	0.434264i
$207$	−2.12976	−	3.68884i	−0.148028	−	0.256392i
$208$	6.57083	−	7.99062i	0.455605	−	0.554050i
$209$	15.6351			1.08150
$210$		0			0
$211$			17.2132i			1.18500i	0.805569	+	0.592502i	$0.201860\pi$
$211$			17.2132i			1.18500i	−0.805569	+	0.592502i	$0.798140\pi$
$212$	11.3497	−	2.05941i	0.779499	−	0.141441i
$213$	−15.7939	+	9.11860i	−1.08218	+	0.624796i
$214$	11.7265	−	14.0457i	0.801604	−	0.960145i
$215$	0.760830	−	1.31780i	0.0518882	−	0.0898730i
$216$	−0.310885	−	0.176415i	−0.0211530	−	0.0120036i
$217$		0			0
$218$	9.35875	+	25.5157i	0.633855	+	1.72814i
$219$	21.0793	+	12.1701i	1.42441	+	0.822382i
$220$	14.1182	+	5.05936i	0.951849	+	0.341102i
$221$	2.82109	−	1.62876i	0.189767	−	0.109562i
$222$	−3.58565	+	20.6347i	−0.240653	+	1.38491i
$223$	−17.5164			−1.17298			−0.586492	−	0.809955i	$-0.699491\pi$
$223$	−17.5164			−1.17298			−0.586492	+	0.809955i	$0.699491\pi$
$224$		0			0
$225$	−8.51902			−0.567935
$226$	0.254556	−	1.46492i	0.0169328	−	0.0974447i
$227$	11.4237	−	6.59546i	0.758215	−	0.437756i	−0.0704394	−	0.997516i	$-0.522440\pi$
$227$	11.4237	−	6.59546i	0.758215	−	0.437756i	0.828655	+	0.559760i	$0.189107\pi$
$228$	−14.3500	−	5.14241i	−0.950349	−	0.340565i
$229$	−14.8693	−	8.58482i	−0.982594	−	0.567301i	−0.0795417	−	0.996832i	$-0.525346\pi$
$229$	−14.8693	−	8.58482i	−0.982594	−	0.567301i	−0.903052	+	0.429531i	$0.858679\pi$
$230$	−1.01017	−	2.75413i	−0.0666087	−	0.181602i
$231$		0			0
$232$	−1.57040	−	0.891141i	−0.103102	−	0.0585062i
$233$	−12.4393	+	21.5455i	−0.814927	+	1.41149i	0.0944534	+	0.995529i	$0.469890\pi$
$233$	−12.4393	+	21.5455i	−0.814927	+	1.41149i	−0.909380	+	0.415966i	$0.863444\pi$
$234$	7.15277	−	8.56744i	0.467591	−	0.560071i
$235$	14.1125	−	8.14787i	0.920600	−	0.531508i
$236$	6.85598	−	1.24402i	0.446286	−	0.0809791i
$237$			21.4184i			1.39127i
$238$		0			0
$239$	−13.3242			−0.861872			−0.430936	−	0.902383i	$-0.641817\pi$
$239$	−13.3242			−0.861872			−0.430936	+	0.902383i	$0.641817\pi$
$240$	−11.2937	−	9.28701i	−0.729005	−	0.599474i
$241$	−11.1218	−	19.2635i	−0.716416	−	1.24087i	−0.962411	−	0.271598i	$-0.912448\pi$
$241$	−11.1218	−	19.2635i	−0.716416	−	1.24087i	0.245995	−	0.969271i	$-0.420885\pi$
$242$	15.7033	+	13.1103i	1.00944	+	0.842763i
$243$	19.1678	+	11.0665i	1.22962	+	0.709919i
$244$	−16.6665	−	19.6632i	−1.06696	−	1.25881i
$245$		0			0
$246$	−7.62177	−	20.7800i	−0.485946	−	1.32488i
$247$	4.00667	−	6.93975i	0.254938	−	0.441566i
$248$	−10.3389	+	0.0770004i	−0.656519	+	0.00488953i
$249$	−3.65544	−	6.33141i	−0.231654	−	0.401237i
$250$	−16.1328	−	2.80337i	−1.02033	−	0.177301i
$251$			27.4386i			1.73191i	0.500121	+	0.865955i	$0.333289\pi$
$251$			27.4386i			1.73191i	−0.500121	+	0.865955i	$0.666711\pi$
$252$		0			0
$253$		−	7.04427i		−	0.442870i
$254$	1.74522	−	10.0433i	0.109505	−	0.630175i
$255$	−2.30203	−	3.98724i	−0.144159	−	0.249691i
$256$	3.09074	+	15.6986i	0.193171	+	0.981165i
$257$	−12.0948	+	20.9487i	−0.754451	+	1.30675i	0.191196	+	0.981552i	$0.438763\pi$
$257$	−12.0948	+	20.9487i	−0.754451	+	1.30675i	−0.945647	+	0.325195i	$0.894570\pi$
$258$	−3.34456	+	1.22673i	−0.208223	+	0.0763729i
$259$		0			0
$260$	5.86358	−	4.96995i	0.363644	−	0.308223i
$261$	−1.68697	−	0.973974i	−0.104421	−	0.0602875i
$262$	13.3715	−	16.0162i	0.826097	−	0.989482i
$263$	5.43846	+	9.41968i	0.335350	+	0.580842i	0.983552	−	0.180626i	$-0.0578123\pi$
$263$	5.43846	+	9.41968i	0.335350	+	0.580842i	−0.648202	+	0.761468i	$0.724479\pi$
$264$	−17.7815	−	30.2755i	−1.09438	−	1.86333i
$265$	8.57040			0.526475
$266$		0			0
$267$			6.35585i			0.388972i
$268$	1.00756	−	0.182822i	0.0615465	−	0.0111677i
$269$	20.7887	−	12.0024i	1.26751	−	0.731796i	0.292992	−	0.956115i	$-0.405349\pi$
$269$	20.7887	−	12.0024i	1.26751	−	0.731796i	0.974516	+	0.224319i	$0.0720156\pi$
$270$	−0.203872	−	0.170208i	−0.0124072	−	0.0103585i
$271$	3.11160	−	5.38945i	0.189016	−	0.327386i	−0.755906	−	0.654680i	$-0.772803\pi$
$271$	3.11160	−	5.38945i	0.189016	−	0.327386i	0.944922	+	0.327294i	$0.106137\pi$
$272$	−0.825537	+	4.96995i	−0.0500555	+	0.301347i
$273$		0			0
$274$	−12.4305	+	4.55930i	−0.750952	+	0.275437i
$275$	−12.2010	−	7.04427i	−0.735750	−	0.424786i
$276$	−2.31687	+	6.46526i	−0.139459	+	0.389163i
$277$	−24.2493	+	14.0003i	−1.45700	+	0.841199i	−0.998863	−	0.0476832i	$-0.984816\pi$
$277$	−24.2493	+	14.0003i	−1.45700	+	0.841199i	−0.458136	+	0.888882i	$0.651483\pi$
$278$	2.36197	+	0.410435i	0.141661	+	0.0246163i
$279$	−11.1541			−0.667780
$280$		0			0
$281$	−16.7112			−0.996906			−0.498453	−	0.866917i	$-0.666098\pi$
$281$	−16.7112			−0.996906			−0.498453	+	0.866917i	$0.666098\pi$
$282$	−37.5875	−	6.53152i	−2.23830	−	0.388946i
$283$	−24.1193	+	13.9253i	−1.43374	+	0.827772i	−0.997404	−	0.0720102i	$-0.977059\pi$
$283$	−24.1193	+	13.9253i	−1.43374	+	0.827772i	−0.436339	+	0.899782i	$0.643725\pi$
$284$	13.9581	+	5.00198i	0.828260	+	0.296813i
$285$	−9.80843	−	5.66290i	−0.581001	−	0.335441i
$286$	17.3286	−	6.35585i	1.02466	−	0.375829i
$287$		0			0
$288$	3.20814	+	16.9604i	0.189041	+	0.999403i
$289$	7.70682	−	13.3486i	0.453342	−	0.785212i
$290$	−1.02983	−	0.859784i	−0.0604738	−	0.0504882i
$291$	3.34554	−	1.93155i	0.196119	−	0.113229i
$292$	−3.53308	−	19.4713i	−0.206758	−	1.13947i
$293$		−	20.1851i		−	1.17923i	−0.807685	−	0.589614i	$-0.799280\pi$
$293$		−	20.1851i		−	1.17923i	0.807685	−	0.589614i	$-0.200720\pi$
$294$		0			0
$295$	5.17710			0.301423
$296$	14.6828	−	8.62352i	0.853418	−	0.501232i
$297$	−0.318870	−	0.552300i	−0.0185027	−	0.0320477i
$298$	3.34141	−	4.00228i	0.193563	−	0.231846i
$299$	−3.12665	−	1.80517i	−0.180819	−	0.104396i
$300$	8.88128	+	10.4782i	0.512761	+	0.604959i
$301$		0			0
$302$	−18.9562	+	6.95282i	−1.09080	+	0.400090i
$303$	−0.257326	+	0.445702i	−0.0147830	+	0.0256049i
$304$	4.35421	+	11.6033i	0.249731	+	0.665494i
$305$	−9.57574	−	16.5857i	−0.548305	−	0.949693i
$306$	−0.930515	+	5.35491i	−0.0531940	+	0.306120i
$307$		−	17.8844i		−	1.02071i	−0.859962	−	0.510357i	$-0.829513\pi$
$307$		−	17.8844i		−	1.02071i	0.859962	−	0.510357i	$-0.170487\pi$
$308$		0			0
$309$		−	16.9169i		−	0.962368i
$310$	−7.56847	−	1.31516i	−0.429860	−	0.0746961i
$311$	−0.715667	−	1.23957i	−0.0405818	−	0.0702897i	0.845021	−	0.534733i	$-0.179588\pi$
$311$	−0.715667	−	1.23957i	−0.0405818	−	0.0702897i	−0.885603	+	0.464443i	$0.846254\pi$
$312$	−17.9947	+	0.134018i	−1.01875	+	0.00758730i
$313$	2.42829	−	4.20591i	0.137255	−	0.237732i	−0.789202	−	0.614134i	$-0.789505\pi$
$313$	2.42829	−	4.20591i	0.137255	−	0.237732i	0.926457	+	0.376402i	$0.122839\pi$
$314$	6.27635	+	17.1118i	0.354195	+	0.965676i
$315$		0			0
$316$	13.2839	−	11.2594i	0.747277	−	0.633389i
$317$	9.78002	+	5.64650i	0.549301	+	0.317139i	0.748840	−	0.662751i	$-0.230611\pi$
$317$	9.78002	+	5.64650i	0.549301	+	0.317139i	−0.199539	+	0.979890i	$0.563944\pi$
$318$	−15.4023	−	12.8591i	−0.863719	−	0.721100i
$319$	−1.61073	−	2.78987i	−0.0901838	−	0.156203i
$320$	0.177064	+	11.8865i	0.00989815	+	0.664477i
$321$	−31.8273			−1.77642
$322$		0			0
$323$			3.90239i			0.217135i
$324$	−3.15767	−	17.4023i	−0.175426	−	0.966795i
$325$	−6.25330	+	3.61034i	−0.346871	+	0.200266i
$326$	−2.92860	+	3.50781i	−0.162200	+	0.194280i
$327$	23.6373	−	40.9410i	1.30714	−	2.26404i
$328$	−8.88128	+	15.6509i	−0.490387	+	0.864174i
$329$		0			0
$330$	−8.98316	−	24.4917i	−0.494507	−	1.34822i
$331$	−20.6415	−	11.9174i	−1.13456	−	0.655039i	−0.189483	−	0.981884i	$-0.560681\pi$
$331$	−20.6415	−	11.9174i	−1.13456	−	0.655039i	−0.945078	+	0.326845i	$0.894014\pi$
$332$	−2.00518	+	5.59548i	−0.110049	+	0.307092i
$333$	15.9089	−	9.18503i	0.871805	−	0.503337i
$334$	−3.40144	+	19.5746i	−0.186119	+	1.07107i
$335$	0.760830			0.0415686
$336$		0			0
$337$	16.4650			0.896906			0.448453	−	0.893806i	$-0.351975\pi$
$337$	16.4650			0.896906			0.448453	+	0.893806i	$0.351975\pi$
$338$	−1.52797	+	8.79317i	−0.0831109	+	0.478285i
$339$	−2.23983	+	1.29317i	−0.121651	+	0.0702351i
$340$	−1.26277	+	3.52378i	−0.0684836	+	0.191104i
$341$	−15.9751	−	9.22320i	−0.865098	−	0.499465i
$342$	4.60407	+	12.5525i	0.248959	+	0.678763i
$343$		0			0
$344$	2.51902	+	1.42945i	0.135817	+	0.0770708i
$345$	−2.55137	+	4.41911i	−0.137361	+	0.237917i
$346$	−5.92638	+	7.09850i	−0.318604	+	0.381618i
$347$	2.78706	−	1.60911i	0.149617	−	0.0863817i	−0.423322	−	0.905979i	$-0.639136\pi$
$347$	2.78706	−	1.60911i	0.149617	−	0.0863817i	0.572940	+	0.819597i	$0.305803\pi$
$348$	0.560743	+	3.09033i	0.0300590	+	0.165659i
$349$		−	22.8716i		−	1.22429i	−0.790747	−	0.612143i	$-0.790308\pi$
$349$		−	22.8716i		−	1.22429i	0.790747	−	0.612143i	$-0.209692\pi$
$350$		0			0
$351$	−0.326856			−0.0174463
$352$	−9.42964	+	26.9437i	−0.502601	+	1.43610i
$353$	11.6608	+	20.1971i	0.620641	+	1.07498i	0.989367	+	0.145444i	$0.0464609\pi$
$353$	11.6608	+	20.1971i	0.620641	+	1.07498i	−0.368725	+	0.929538i	$0.620206\pi$
$354$	−9.30405	−	7.76775i	−0.494505	−	0.412851i
$355$	9.54058	+	5.50826i	0.506361	+	0.292348i
$356$	3.94196	−	3.34119i	0.208923	−	0.177083i
$357$		0			0
$358$	−0.0615446	−	0.167795i	−0.00325273	−	0.00886825i
$359$	2.55488	−	4.42518i	0.134841	−	0.233552i	−0.790696	−	0.612210i	$-0.790281\pi$
$359$	2.55488	−	4.42518i	0.134841	−	0.233552i	0.925537	+	0.378658i	$0.123614\pi$
$360$	0.0955128	+	12.8245i	0.00503397	+	0.675912i
$361$	−4.70015	−	8.14090i	−0.247376	−	0.428468i
$362$	3.78876	+	0.658366i	0.199133	+	0.0346030i
$363$		−	35.5833i		−	1.86764i
$364$		0			0
$365$		−	14.7032i		−	0.769600i
$366$	−7.67613	+	44.1745i	−0.401238	+	2.30904i
$367$	14.0779	+	24.3837i	0.734862	+	1.27282i	0.954784	+	0.297301i	$0.0960863\pi$
$367$	14.0779	+	24.3837i	0.734862	+	1.27282i	−0.219922	+	0.975517i	$0.570580\pi$
$368$	5.22777	−	1.96176i	0.272516	−	0.102264i
$369$	−9.70682	+	16.8127i	−0.505317	+	0.875234i
$370$	11.8778	−	4.35658i	0.617496	−	0.226488i
$371$		0			0
$372$	11.6284	+	13.7193i	0.602906	+	0.711313i
$373$	−6.10052	−	3.52214i	−0.315873	−	0.182369i	0.333679	−	0.942687i	$-0.391710\pi$
$373$	−6.10052	−	3.52214i	−0.315873	−	0.182369i	−0.649551	+	0.760318i	$0.725043\pi$
$374$	−5.76060	+	6.89994i	−0.297874	+	0.356787i
$375$	14.2414	+	24.6667i	0.735420	+	1.27379i
$376$	15.7084	+	26.7457i	0.810096	+	1.37930i
$377$	−1.65107			−0.0850346
$378$		0			0
$379$		−	13.1974i		−	0.677905i	−0.940803	−	0.338953i	$-0.889927\pi$
$379$		−	13.1974i		−	0.677905i	0.940803	−	0.338953i	$-0.110073\pi$
$380$	1.64398	+	9.06019i	0.0843344	+	0.464778i
$381$	−15.3561	+	8.86584i	−0.786716	+	0.454211i
$382$	2.65680	+	2.21811i	0.135934	+	0.113488i
$383$	−2.46546	+	4.27031i	−0.125979	+	0.218202i	−0.922115	−	0.386915i	$-0.873541\pi$
$383$	−2.46546	+	4.27031i	−0.125979	+	0.218202i	0.796136	+	0.605118i	$0.206874\pi$
$384$	17.5164	−	21.6276i	0.893879	−	1.10368i
$385$		0			0
$386$	5.24267	−	1.92293i	0.266845	−	0.0978746i
$387$	2.70602	+	1.56232i	0.137555	+	0.0794172i
$388$	−2.95667	−	1.05955i	−0.150102	−	0.0537903i
$389$	19.8735	−	11.4739i	1.00762	−	0.581752i	0.0971291	−	0.995272i	$-0.469034\pi$
$389$	19.8735	−	11.4739i	1.00762	−	0.581752i	0.910495	+	0.413520i	$0.135701\pi$
$390$	−13.1728	−	2.28902i	−0.667033	−	0.115909i
$391$	1.75819			0.0889155
$392$		0			0
$393$	−36.2923			−1.83070
$394$	27.2352	+	4.73261i	1.37209	+	0.238426i
$395$	11.2048	−	6.46908i	0.563773	−	0.325495i
$396$	−10.3891	+	28.9909i	−0.522073	+	1.45685i
$397$	25.9079	+	14.9579i	1.30028	+	0.750716i	0.980452	−	0.196760i	$-0.0630420\pi$
$397$	25.9079	+	14.9579i	1.30028	+	0.750716i	0.319827	+	0.947476i	$0.396375\pi$
$398$	−27.6116	+	10.1275i	−1.38404	+	0.507646i
$399$		0			0
$400$	1.82991	−	11.0165i	0.0914953	−	0.550826i
$401$	7.83525	−	13.5711i	0.391274	−	0.677706i	−0.601344	−	0.798990i	$-0.705368\pi$
$401$	7.83525	−	13.5711i	0.391274	−	0.677706i	0.992618	+	0.121284i	$0.0387012\pi$
$402$	−1.36733	−	1.14155i	−0.0681962	−	0.0569355i
$403$	−8.18757	+	4.72709i	−0.407852	+	0.235473i
$404$	0.411701	−	0.0747036i	0.0204829	−	0.00371664i
$405$		−	13.1409i		−	0.652975i
$406$		0			0
$407$	30.3800			1.50588
$408$	7.55650	−	4.43811i	0.374103	−	0.219719i
$409$	−13.0434	−	22.5918i	−0.644954	−	1.11709i	−0.984312	−	0.176436i	$-0.943543\pi$
$409$	−13.0434	−	22.5918i	−0.644954	−	1.11709i	0.339358	−	0.940657i	$-0.389790\pi$
$410$	−8.56877	+	10.2635i	−0.423182	+	0.506878i
$411$	19.9452	+	11.5154i	0.983824	+	0.568011i
$412$	−10.4920	+	8.89299i	−0.516904	+	0.438126i
$413$		0			0
$414$	5.65544	−	2.07433i	0.277950	−	0.101948i
$415$	−2.20814	+	3.82460i	−0.108393	+	0.187742i
$416$	9.54269	+	11.0900i	0.467869	+	0.543733i
$417$	−2.08505	−	3.61141i	−0.102105	−	0.176851i
$418$	−3.78553	+	21.7849i	−0.185156	+	1.06554i
$419$		−	0.252757i		−	0.0123480i	−0.999981	−	0.00617398i	$-0.998035\pi$
$419$		−	0.252757i		−	0.0123480i	0.999981	−	0.00617398i	$-0.00196525\pi$
$420$		0			0
$421$			18.3701i			0.895302i	0.894208	+	0.447651i	$0.147739\pi$
$421$			18.3701i			0.895302i	−0.894208	+	0.447651i	$0.852261\pi$
$422$	−23.9837	−	4.16761i	−1.16751	−	0.202876i
$423$	16.7312	+	28.9793i	0.813498	+	1.40902i
$424$	0.121490	+	16.3125i	0.00590009	+	0.792206i
$425$	1.75819	−	3.04528i	0.0852848	−	0.147718i
$426$	−8.88128	−	24.2139i	−0.430299	−	1.17317i
$427$		0			0
$428$	16.7312	+	19.7396i	0.808732	+	0.954148i
$429$	−27.8044	−	16.0529i	−1.34241	−	0.775041i
$430$	1.65192	+	1.37915i	0.0796627	+	0.0665086i
$431$	−13.7223	−	23.7678i	−0.660982	−	1.14485i	−0.980358	−	0.197226i	$-0.936807\pi$
$431$	−13.7223	−	23.7678i	−0.660982	−	1.14485i	0.319377	−	0.947628i	$-0.396527\pi$
$432$	0.321076	−	0.390453i	0.0154478	−	0.0187857i
$433$	7.26215			0.348997			0.174498	−	0.984657i	$-0.444170\pi$
$433$	7.26215			0.348997			0.174498	+	0.984657i	$0.444170\pi$
$434$		0			0
$435$			2.33358i			0.111886i
$436$	−37.8178	+	6.86207i	−1.81114	+	0.328634i
$437$	3.74562	−	2.16253i	0.179177	−	0.103448i
$438$	−22.0607	+	26.4239i	−1.05410	+	1.26258i
$439$	15.0022	−	25.9845i	0.716015	−	1.24017i	−0.246551	−	0.969130i	$-0.579297\pi$
$439$	15.0022	−	25.9845i	0.716015	−	1.24017i	0.962567	−	0.271045i	$-0.0873692\pi$
$440$	−10.4676	+	18.4464i	−0.499025	+	0.879398i
$441$		0			0
$442$	1.58637	+	4.32507i	0.0754558	+	0.205723i
$443$	30.3838	+	17.5421i	1.44358	+	0.833451i	0.998086	−	0.0618342i	$-0.0196950\pi$
$443$	30.3838	+	17.5421i	1.44358	+	0.833451i	0.445493	+	0.895285i	$0.353028\pi$
$444$	−27.8828	−	9.99202i	−1.32326	−	0.474200i
$445$	3.32499	−	1.91968i	0.157620	−	0.0910017i
$446$	4.24102	−	24.4062i	0.200818	−	1.15567i
$447$	−9.06908			−0.428953
$448$		0			0
$449$	−21.0107			−0.991556			−0.495778	−	0.868449i	$-0.665117\pi$
$449$	−21.0107			−0.991556			−0.495778	+	0.868449i	$0.665117\pi$
$450$	2.06260	−	11.8698i	0.0972320	−	0.559550i
$451$	−27.8044	+	16.0529i	−1.30926	+	0.755901i
$452$	1.97948	+	0.709363i	0.0931071	+	0.0333656i
$453$	30.4159	+	17.5606i	1.42906	+	0.825071i
$454$	6.42380	+	17.5139i	0.301484	+	0.821966i
$455$		0			0
$456$	10.6395	−	18.7492i	0.498239	−	0.878012i
$457$	−6.68780	+	11.5836i	−0.312842	+	0.541858i	−0.978976	−	0.203974i	$-0.934614\pi$
$457$	−6.68780	+	11.5836i	−0.312842	+	0.541858i	0.666135	+	0.745832i	$0.267948\pi$
$458$	15.5616	−	18.6394i	0.727148	−	0.870963i
$459$	0.137849	−	0.0795874i	0.00643426	−	0.00371482i
$460$	4.08200	−	0.740682i	0.190324	−	0.0345345i
$461$			2.68641i			0.125118i	0.998041	+	0.0625592i	$0.0199262\pi$
$461$			2.68641i			0.125118i	−0.998041	+	0.0625592i	$0.980074\pi$
$462$		0			0
$463$	−21.0380			−0.977721			−0.488860	−	0.872362i	$-0.662587\pi$
$463$	−21.0380			−0.977721			−0.488860	+	0.872362i	$0.662587\pi$
$464$	1.62188	−	1.97232i	0.0752937	−	0.0915629i
$465$	6.68113	+	11.5721i	0.309830	+	0.536641i
$466$	−27.0083	−	22.5487i	−1.25114	−	1.04455i
$467$	−21.3849	−	12.3466i	−0.989574	−	0.571331i	−0.0844270	−	0.996430i	$-0.526906\pi$
$467$	−21.3849	−	12.3466i	−0.989574	−	0.571331i	−0.905147	+	0.425099i	$0.860239\pi$
$468$	10.2055	+	12.0405i	0.471749	+	0.556573i
$469$		0			0
$470$	7.93582	+	21.6362i	0.366052	+	0.998004i
$471$	15.8521	−	27.4566i	0.730426	−	1.26513i
$472$	0.0733884	+	9.85387i	0.00337797	+	0.453561i
$473$	2.58373	+	4.47515i	0.118800	+	0.205767i
$474$	−29.8429	−	5.18576i	−1.37073	−	0.238190i
$475$		−	8.65014i		−	0.396896i
$476$		0			0
$477$			17.5988i			0.805794i
$478$	3.22602	−	18.5651i	0.147555	−	0.849147i
$479$	−20.4562	−	35.4311i	−0.934666	−	1.61889i	−0.775229	−	0.631680i	$-0.782366\pi$
$479$	−20.4562	−	35.4311i	−0.934666	−	1.61889i	−0.159437	−	0.987208i	$-0.550968\pi$
$480$	15.6743	−	13.4874i	0.715431	−	0.615610i
$481$	7.78520	−	13.4844i	0.354974	−	0.614834i
$482$	29.5332	−	10.8323i	1.34520	−	0.493399i
$483$		0			0
$484$	−22.0691	+	18.7057i	−1.00314	+	0.850257i
$485$	−2.02094	−	1.16679i	−0.0917660	−	0.0529811i
$486$	−20.0603	+	24.0278i	−0.909952	+	1.08992i
$487$	−8.76704	−	15.1850i	−0.397273	−	0.688096i	0.596116	−	0.802898i	$-0.296710\pi$
$487$	−8.76704	−	15.1850i	−0.397273	−	0.688096i	−0.993388	+	0.114802i	$0.963377\pi$
$488$	31.4327	−	18.4612i	1.42289	−	0.835697i
$489$	7.94863			0.359449
$490$		0			0
$491$		−	15.7509i		−	0.710830i	−0.934709	−	0.355415i	$-0.884340\pi$
$491$		−	15.7509i		−	0.710830i	0.934709	−	0.355415i	$-0.115660\pi$
$492$	30.7988	−	5.58847i	1.38852	−	0.251948i
$493$	0.696329	−	0.402026i	0.0313611	−	0.0181063i
$494$	8.69930	+	7.26286i	0.391400	+	0.326771i
$495$	−11.4406	+	19.8158i	−0.514219	+	0.890653i
$496$	2.39593	−	14.4241i	0.107581	−	0.647663i
$497$		0			0
$498$	9.70682	−	3.56031i	0.434973	−	0.159541i
$499$	8.82147	+	5.09308i	0.394903	+	0.227997i	0.684282	−	0.729217i	$-0.260116\pi$
$499$	8.82147	+	5.09308i	0.394903	+	0.227997i	−0.289379	+	0.957215i	$0.593449\pi$
$500$	7.81206	−	21.7996i	0.349366	−	0.974909i
$501$	29.9292	−	17.2796i	1.33714	−	0.771997i
$502$	−38.2312	−	6.64337i	−1.70634	−	0.296508i
$503$	−27.1001			−1.20833			−0.604167	−	0.796858i	$-0.706494\pi$
$503$	−27.1001			−1.20833			−0.604167	+	0.796858i	$0.706494\pi$
$504$		0			0
$505$	0.310885			0.0138342
$506$	9.81502	+	1.70554i	0.436331	+	0.0758205i
$507$	13.4446	−	7.76224i	0.597096	−	0.344733i
$508$	13.5712	+	4.86333i	0.602124	+	0.215776i
$509$	−19.4357	−	11.2212i	−0.861471	−	0.497371i	0.00303361	−	0.999995i	$-0.499034\pi$
$509$	−19.4357	−	11.2212i	−0.861471	−	0.497371i	−0.864505	+	0.502625i	$0.832368\pi$
$510$	6.11292	−	2.24212i	0.270685	−	0.0992828i
$511$		0			0
$512$	−22.6218	+	0.505513i	−0.999750	+	0.0223407i
$513$	0.195781	−	0.339103i	0.00864396	−	0.0149718i
$514$	−26.2602	−	21.9241i	−1.15829	−	0.967030i
$515$	−8.84987	+	5.10948i	−0.389972	+	0.225150i
$516$	−0.899470	−	4.95710i	−0.0395970	−	0.218224i
$517$			55.3392i			2.43382i
$518$		0			0
$519$	16.0850			0.706055
$520$	5.50512	+	9.37323i	0.241415	+	0.411043i
$521$	−5.13510	−	8.89426i	−0.224973	−	0.389664i	0.731338	−	0.682015i	$-0.238896\pi$
$521$	−5.13510	−	8.89426i	−0.224973	−	0.389664i	−0.956311	+	0.292350i	$0.905563\pi$
$522$	1.76552	−	2.11470i	0.0772746	−	0.0925579i
$523$	−15.4655	−	8.92903i	−0.676261	−	0.390439i	0.122184	−	0.992507i	$-0.461010\pi$
$523$	−15.4655	−	8.92903i	−0.676261	−	0.390439i	−0.798445	+	0.602068i	$0.794344\pi$
$524$	19.0784	+	22.5088i	0.833443	+	0.983302i
$525$		0			0
$526$	−14.4415	+	5.29692i	−0.629680	+	0.230956i
$527$	2.30203	−	3.98724i	0.100278	−	0.173687i
$528$	46.4891	−	17.4453i	2.02318	−	0.759211i
$529$	10.5257	+	18.2310i	0.457639	+	0.792653i
$530$	−2.07504	+	11.9414i	−0.0901341	+	0.518702i
$531$			10.6309i			0.461341i
$532$		0			0
$533$			16.4549i			0.712742i
$534$	−8.85582	−	1.53886i	−0.383229	−	0.0665931i
$535$	9.61292	+	16.6501i	0.415603	+	0.719845i
$536$	0.0107852	+	1.44813i	0.000465850	+	0.0625497i
$537$	−0.155442	+	0.269234i	−0.00670783	+	0.0116183i
$538$	11.6900	+	31.8716i	0.503991	+	1.37408i
$539$		0			0
$540$	0.286517	−	0.242851i	0.0123297	−	0.0104506i
$541$	19.9303	+	11.5067i	0.856869	+	0.494714i	0.862963	−	0.505268i	$-0.168606\pi$
$541$	19.9303	+	11.5067i	0.856869	+	0.494714i	−0.00609356	+	0.999981i	$0.501940\pi$
$542$	6.75593	+	5.64038i	0.290192	+	0.242275i
$543$	−3.34456	−	5.79294i	−0.143529	−	0.248599i
$544$	−6.72492	−	2.35356i	−0.288328	−	0.100908i
$545$	−28.5571			−1.22325
$546$		0			0
$547$		−	9.10136i		−	0.389146i	−0.980888	−	0.194573i	$-0.937668\pi$
$547$		−	9.10136i		−	0.389146i	0.980888	−	0.194573i	$-0.0623321\pi$
$548$	−3.34299	−	18.4237i	−0.142806	−	0.787021i
$549$	34.0577	−	19.6632i	1.45355	−	0.839206i
$550$	12.7691	−	15.2946i	0.544477	−	0.652163i
$551$	0.988965	−	1.71294i	0.0421313	−	0.0729736i
$552$	−8.44731	−	4.79353i	−0.359541	−	0.204026i
$553$		0			0
$554$	−13.6360	−	37.1771i	−0.579337	−	1.57950i
$555$	−19.0584	−	11.0034i	−0.808983	−	0.467067i
$556$	−1.14375	+	3.19164i	−0.0485057	+	0.135356i
$557$	−15.0016	+	8.66116i	−0.635637	+	0.366985i	−0.782932	−	0.622107i	$-0.786277\pi$
$557$	−15.0016	+	8.66116i	−0.635637	+	0.366985i	0.147295	+	0.989093i	$0.452943\pi$
$558$	2.70061	−	15.5414i	0.114326	−	0.657921i
$559$	2.64843			0.112017
$560$		0			0
$561$	15.6351			0.660115
$562$	4.04607	−	23.2843i	0.170673	−	0.982187i
$563$	−6.91560	+	3.99272i	−0.291458	+	0.168273i	−0.638599	−	0.769540i	$-0.720486\pi$
$563$	−6.91560	+	3.99272i	−0.291458	+	0.168273i	0.347141	+	0.937813i	$0.387152\pi$
$564$	18.2012	−	50.7905i	0.766408	−	2.13867i
$565$	1.35301	+	0.781160i	0.0569215	+	0.0328637i
$566$	−13.5629	−	36.9778i	−0.570090	−	1.55429i
$567$		0			0
$568$	−10.3489	+	18.2372i	−0.434231	+	0.765216i
$569$	−5.98535	+	10.3669i	−0.250919	+	0.434604i	−0.963779	−	0.266702i	$-0.914066\pi$
$569$	−5.98535	+	10.3669i	−0.250919	+	0.434604i	0.712860	+	0.701306i	$0.247399\pi$
$570$	10.2651	−	12.2953i	0.429958	−	0.514995i
$571$	−36.9016	+	21.3051i	−1.54428	+	0.891592i	−0.545722	+	0.837966i	$0.683745\pi$
$571$	−36.9016	+	21.3051i	−1.54428	+	0.891592i	−0.998561	+	0.0536265i	$0.982922\pi$
$572$	4.66027	+	25.6834i	0.194856	+	1.07388i
$573$		−	6.02026i		−	0.251500i
$574$		0			0
$575$	−3.89725			−0.162527
$576$	−24.4083	+	0.363590i	−1.01701	+	0.0151496i
$577$	−14.9650	−	25.9202i	−0.623001	−	1.07907i	−0.988924	−	0.148425i	$-0.952580\pi$
$577$	−14.9650	−	25.9202i	−0.623001	−	1.07907i	0.365922	−	0.930645i	$-0.380754\pi$
$578$	16.7331	+	13.9701i	0.696005	+	0.581079i
$579$	−8.41208	−	4.85672i	−0.349594	−	0.201838i
$580$	1.44731	−	1.22673i	0.0600961	−	0.0509372i
$581$		0			0
$582$	1.88128	+	5.12912i	0.0779816	+	0.212609i
$583$	−14.5522	+	25.2052i	−0.602692	+	1.04389i
$584$	27.9854	−	0.208426i	1.15804	−	0.00862473i
$585$	5.86358	+	10.1560i	0.242429	+	0.419900i
$586$	28.1246	+	4.88717i	1.16182	+	0.201887i
$587$		−	19.4269i		−	0.801833i	−0.916115	−	0.400916i	$-0.868692\pi$
$587$		−	19.4269i		−	0.801833i	0.916115	−	0.400916i	$-0.131308\pi$
$588$		0			0
$589$		−	11.3258i		−	0.466671i
$590$	−1.25347	+	7.21343i	−0.0516044	+	0.296972i
$591$	−24.0421	−	41.6421i	−0.988959	−	1.71293i
$592$	8.46050	+	22.5459i	0.347724	+	0.926630i
$593$	−9.07706	+	15.7219i	−0.372750	+	0.645622i	−0.989988	−	0.141155i	$-0.954919\pi$
$593$	−9.07706	+	15.7219i	−0.372750	+	0.645622i	0.617237	+	0.786777i	$0.288252\pi$
$594$	0.846742	−	0.310572i	0.0347423	−	0.0127429i
$595$		0			0
$596$	4.76750	+	5.62473i	0.195284	+	0.230398i
$597$	44.3039	+	25.5789i	1.81324	+	1.04687i
$598$	3.27222	−	3.91940i	0.133811	−	0.160276i
$599$	−5.59258	−	9.68663i	−0.228507	−	0.395785i	0.728859	−	0.684664i	$-0.240051\pi$
$599$	−5.59258	−	9.68663i	−0.228507	−	0.395785i	−0.957366	+	0.288879i	$0.906718\pi$
$600$	−16.7499	+	9.83763i	−0.683814	+	0.401620i
$601$	4.21883			0.172090			0.0860448	−	0.996291i	$-0.472577\pi$
$601$	4.21883			0.172090			0.0860448	+	0.996291i	$0.472577\pi$
$602$		0			0
$603$			1.56232i			0.0636226i
$604$	−5.09798	−	28.0957i	−0.207434	−	1.14320i
$605$	−18.6150	+	10.7474i	−0.756806	+	0.436942i
$606$	−0.558708	−	0.466453i	−0.0226960	−	0.0189484i
$607$	−13.6196	+	23.5898i	−0.552802	+	0.957481i	0.445269	+	0.895397i	$0.353108\pi$
$607$	−13.6196	+	23.5898i	−0.552802	+	0.957481i	−0.998071	+	0.0620841i	$0.980225\pi$
$608$	−17.2215	+	3.25751i	−0.698423	+	0.132110i
$609$		0			0
$610$	25.4278	−	9.32653i	1.02954	−	0.377620i
$611$	24.5627	+	14.1813i	0.993701	+	0.573713i
$612$	−7.23589	−	2.59304i	−0.292493	−	0.104817i
$613$	3.20401	−	1.84984i	0.129409	−	0.0747141i	−0.433898	−	0.900962i	$-0.642862\pi$
$613$	3.20401	−	1.84984i	0.129409	−	0.0747141i	0.563307	+	0.826248i	$0.309529\pi$
$614$	24.9189	+	4.33012i	1.00564	+	0.174749i
$615$	23.2569			0.937808
$616$		0			0
$617$	26.0487			1.04868			0.524341	−	0.851508i	$-0.324312\pi$
$617$	26.0487			1.04868			0.524341	+	0.851508i	$0.324312\pi$
$618$	23.5709	+	4.09587i	0.948159	+	0.164760i
$619$	27.7816	−	16.0397i	1.11664	−	0.644692i	0.176098	−	0.984373i	$-0.443652\pi$
$619$	27.7816	−	16.0397i	1.11664	−	0.644692i	0.940541	+	0.339681i	$0.110319\pi$
$620$	3.66492	−	10.2270i	0.147187	−	0.410725i
$621$	−0.152780	−	0.0882077i	−0.00613086	−	0.00353965i
$622$	1.90041	−	0.697042i	0.0761996	−	0.0279488i
$623$		0			0
$624$	4.17009	−	25.1051i	0.166937	−	1.00501i
$625$	1.62309	−	2.81127i	0.0649236	−	0.112451i
$626$	5.27231	+	4.40174i	0.210724	+	0.175929i
$627$	33.3088	−	19.2308i	1.33022	−	0.768005i
$628$	−25.3621	+	4.60198i	−1.01206	+	0.183639i
$629$			7.58258i			0.302337i
$630$		0			0
$631$	11.7538			0.467912			0.233956	−	0.972247i	$-0.424833\pi$
$631$	11.7538			0.467912			0.233956	+	0.972247i	$0.424833\pi$
$632$	12.4718	+	21.2350i	0.496101	+	0.844682i
$633$	21.1718	+	36.6707i	0.841504	+	1.45753i
$634$	−10.2354	+	12.2597i	−0.406499	+	0.486896i
$635$	9.27612	+	5.35557i	0.368112	+	0.212529i
$636$	21.6461	−	18.3472i	0.858325	−	0.727513i
$637$		0			0
$638$	4.27721	−	1.56881i	0.169336	−	0.0621099i
$639$	−11.3109	+	19.5910i	−0.447452	+	0.775009i
$640$	−16.6048	−	2.63122i	−0.656361	−	0.104008i
$641$	−20.9136	−	36.2235i	−0.826039	−	1.43074i	−0.901123	−	0.433564i	$-0.857256\pi$
$641$	−20.9136	−	36.2235i	−0.826039	−	1.43074i	0.0750839	−	0.997177i	$-0.476078\pi$
$642$	7.70593	−	44.3460i	0.304129	−	1.75020i
$643$			42.9368i			1.69326i	0.532180	+	0.846631i	$0.321373\pi$
$643$			42.9368i			1.69326i	−0.532180	+	0.846631i	$0.678627\pi$
$644$		0			0
$645$		−	3.74321i		−	0.147389i
$646$	−5.43733	−	0.944836i	−0.213929	−	0.0371741i
$647$	−4.55891	−	7.89626i	−0.179229	−	0.310434i	0.762388	−	0.647121i	$-0.224027\pi$
$647$	−4.55891	−	7.89626i	−0.179229	−	0.310434i	−0.941617	+	0.336687i	$0.890694\pi$
$648$	25.0118	−	0.186279i	0.982555	−	0.00731774i
$649$	−8.79054	+	15.2257i	−0.345059	+	0.597660i
$650$	−3.51638	−	9.58706i	−0.137924	−	0.376035i
$651$		0			0
$652$	−4.17849	−	4.92981i	−0.163642	−	0.193066i
$653$	−18.8716	−	10.8955i	−0.738502	−	0.426374i	0.0830227	−	0.996548i	$-0.473543\pi$
$653$	−18.8716	−	10.8955i	−0.738502	−	0.426374i	−0.821524	+	0.570174i	$0.806876\pi$
$654$	51.3215	+	42.8472i	2.00683	+	1.67546i
$655$	10.9615	+	18.9859i	0.428301	+	0.741840i
$656$	−19.6566	−	16.1639i	−0.767460	−	0.631096i
$657$	30.1922			1.17791
$658$		0			0
$659$		−	0.152682i		−	0.00594765i	−0.999996	−	0.00297383i	$-0.999053\pi$
$659$		−	0.152682i		−	0.00594765i	0.999996	−	0.00297383i	$-0.000946600\pi$
$660$	36.3001	−	6.58668i	1.41298	−	0.256386i
$661$	24.6004	−	14.2031i	0.956845	−	0.552435i	0.0616446	−	0.998098i	$-0.480365\pi$
$661$	24.6004	−	14.2031i	0.956845	−	0.552435i	0.895201	+	0.445663i	$0.147032\pi$
$662$	21.6026	−	25.8751i	0.839608	−	1.00567i
$663$	4.00667	−	6.93975i	0.155606	−	0.269518i
$664$	−7.31088	−	4.14865i	−0.283717	−	0.160999i
$665$		0			0
$666$	8.94599	+	24.3903i	0.346650	+	0.945106i
$667$	−0.771750	−	0.445570i	−0.0298823	−	0.0172525i
$668$	−26.4504	−	9.47869i	−1.02340	−	0.366742i
$669$	−37.3166	+	21.5447i	−1.44274	+	0.832968i
$670$	−0.184210	+	1.06009i	−0.00711666	+	0.0409549i
$671$	65.0371			2.51073
$672$		0			0
$673$	26.2542			1.01203			0.506013	−	0.862526i	$-0.331119\pi$
$673$	26.2542			1.01203			0.506013	+	0.862526i	$0.331119\pi$
$674$	−3.98646	+	22.9413i	−0.153553	+	0.883664i
$675$	−0.305561	+	0.176415i	−0.0117610	+	0.00679023i
$676$	−11.8819	−	4.25796i	−0.456995	−	0.163768i
$677$	4.00416	+	2.31180i	0.153892	+	0.0888498i	0.574969	−	0.818175i	$-0.305014\pi$
$677$	4.00416	+	2.31180i	0.153892	+	0.0888498i	−0.421076	+	0.907025i	$0.638348\pi$
$678$	−1.25951	−	3.43393i	−0.0483712	−	0.131879i
$679$		0			0
$680$	−4.60407	−	2.61264i	−0.176558	−	0.100190i
$681$	16.2245	−	28.1017i	0.621725	−	1.07686i
$682$	16.7188	−	20.0255i	0.640198	−	0.766816i
$683$	16.8469	−	9.72659i	0.644631	−	0.372178i	−0.141765	−	0.989900i	$-0.545278\pi$
$683$	16.8469	−	9.72659i	0.644631	−	0.372178i	0.786396	+	0.617723i	$0.211945\pi$
$684$	−18.6046	+	3.37582i	−0.711364	+	0.129078i
$685$		−	13.9121i		−	0.531555i
$686$		0			0
$687$	−42.2365			−1.61142
$688$	−2.60160	+	3.16374i	−0.0991851	+	0.120617i
$689$	7.45834	+	12.9182i	0.284140	+	0.492145i
$690$	−5.53956	−	4.62486i	−0.210888	−	0.176065i
$691$	−15.0449	−	8.68618i	−0.572335	−	0.330438i	0.185746	−	0.982598i	$-0.440530\pi$
$691$	−15.0449	−	8.68618i	−0.572335	−	0.330438i	−0.758081	+	0.652160i	$0.773863\pi$
$692$	−8.45570	−	9.97610i	−0.321438	−	0.379234i
$693$		0			0
$694$	1.56723	+	4.27290i	0.0594914	+	0.162197i
$695$	−1.25951	+	2.18154i	−0.0477760	+	0.0827504i
$696$	−4.44163	+	0.0330798i	−0.168359	+	0.00125388i
$697$	−4.00667	−	6.93975i	−0.151763	−	0.262862i
$698$	31.8677	+	5.53760i	1.20621	+	0.209601i
$699$			61.2003i			2.31481i
$700$		0			0
$701$		−	25.1180i		−	0.948695i	−0.880338	−	0.474348i	$-0.842684\pi$
$701$		−	25.1180i		−	0.948695i	0.880338	−	0.474348i	$-0.157316\pi$
$702$	0.0791376	−	0.455420i	0.00298686	−	0.0171887i
$703$	9.32640	+	16.1538i	0.351752	+	0.609252i
$704$	−35.2585	−	19.6622i	−1.32885	−	0.741046i
$705$	20.0434	−	34.7162i	0.754878	−	1.30749i
$706$	−30.9646	+	11.3573i	−1.16537	+	0.427438i
$707$		0			0
$708$	13.0757	−	11.0829i	0.491416	−	0.416523i
$709$	−17.4147	−	10.0544i	−0.654024	−	0.377601i	0.135972	−	0.990713i	$-0.456584\pi$
$709$	−17.4147	−	10.0544i	−0.654024	−	0.377601i	−0.789996	+	0.613112i	$0.789918\pi$
$710$	−9.98478	+	11.9596i	−0.374722	+	0.448834i
$711$	13.2839	+	23.0084i	0.498184	+	0.862881i
$712$	3.70097	+	6.30143i	0.138700	+	0.236156i
$713$	−5.10275			−0.191099
$714$		0			0
$715$			19.3941i			0.725297i
$716$	0.248696	−	0.0451260i	0.00929419	−	0.00168644i
$717$	−28.3857	+	16.3885i	−1.06008	+	0.612039i
$718$	5.54717	+	4.63121i	0.207019	+	0.172835i
$719$	−19.1966	+	33.2496i	−0.715914	+	1.24000i	0.246692	+	0.969094i	$0.420656\pi$
$719$	−19.1966	+	33.2496i	−0.715914	+	1.24000i	−0.962606	+	0.270906i	$0.912677\pi$
$720$	−17.8920	−	2.97196i	−0.666794	−	0.110758i
$721$		0			0
$722$	12.4810	−	4.57783i	0.464494	−	0.170369i
$723$	−47.3873	−	27.3590i	−1.76235	−	1.01749i
$724$	−1.83465	+	5.11960i	−0.0681842	+	0.190269i
$725$	−1.54350	+	0.891141i	−0.0573242	+	0.0330961i
$726$	49.5794	+	8.61532i	1.84006	+	0.319745i
$727$	−14.8679			−0.551422			−0.275711	−	0.961241i	$-0.588913\pi$
$727$	−14.8679			−0.551422			−0.275711	+	0.961241i	$0.588913\pi$
$728$		0			0
$729$	27.9167			1.03395
$730$	20.4865	+	3.55990i	0.758238	+	0.131758i
$731$	−1.11696	+	0.644877i	−0.0413122	+	0.0238516i
$732$	−59.6913	−	21.3908i	−2.20625	−	0.790628i
$733$	−36.4503	−	21.0446i	−1.34632	−	0.777300i	−0.358597	−	0.933492i	$-0.616745\pi$
$733$	−36.4503	−	21.0446i	−1.34632	−	0.777300i	−0.987727	+	0.156192i	$0.950078\pi$
$734$	−37.3831	+	13.7115i	−1.37984	+	0.506102i
$735$		0			0
$736$	1.46765	+	7.75900i	0.0540982	+	0.286000i
$737$	−1.29186	+	2.23757i	−0.0475864	+	0.0824221i
$738$	−21.0755	−	17.5955i	−0.775800	−	0.647699i
$739$	−10.9859	+	6.34270i	−0.404122	+	0.233320i	−0.688261	−	0.725463i	$-0.741626\pi$
$739$	−10.9859	+	6.34270i	−0.404122	+	0.233320i	0.284139	+	0.958783i	$0.408292\pi$
$740$	3.19435	+	17.6045i	0.117427	+	0.647155i
$741$		−	19.7124i		−	0.724154i
$742$		0			0
$743$	−25.7219			−0.943644			−0.471822	−	0.881694i	$-0.656404\pi$
$743$	−25.7219			−0.943644			−0.471822	+	0.881694i	$0.656404\pi$
$744$	−21.9310	+	12.8806i	−0.804031	+	0.472226i
$745$	2.73917	+	4.74438i	0.100355	+	0.173821i
$746$	6.38455	−	7.64729i	0.233755	−	0.279987i
$747$	−7.85360	−	4.53428i	−0.287348	−	0.165901i
$748$	−8.21917	−	9.69704i	−0.300523	−	0.354559i
$749$		0			0
$750$	−37.8171	+	13.8707i	−1.38089	+	0.506487i
$751$	−17.9305	+	31.0565i	−0.654292	+	1.13327i	0.327779	+	0.944755i	$0.393700\pi$
$751$	−17.9305	+	31.0565i	−0.654292	+	1.13327i	−0.982071	+	0.188513i	$0.939633\pi$
$752$	−41.0689	+	15.4114i	−1.49763	+	0.561995i
$753$	33.7489	+	58.4548i	1.22988	+	2.13021i
$754$	0.399754	−	2.30050i	0.0145582	−	0.0837791i
$755$		−	21.2157i		−	0.772117i
$756$		0			0
$757$			30.7289i			1.11686i	0.829551	+	0.558431i	$0.188597\pi$
$757$			30.7289i			1.11686i	−0.829551	+	0.558431i	$0.811403\pi$
$758$	18.3884	+	3.19532i	0.667896	+	0.116059i
$759$	−8.66429	−	15.0070i	−0.314494	−	0.544719i
$760$	−13.0219	+	0.0969829i	−0.472354	+	0.00351794i
$761$	22.5624	−	39.0792i	0.817887	−	1.41662i	−0.0893497	−	0.996000i	$-0.528479\pi$
$761$	22.5624	−	39.0792i	0.817887	−	1.41662i	0.907236	−	0.420621i	$-0.138188\pi$
$762$	−8.63510	−	23.5427i	−0.312817	−	0.852863i
$763$		0			0
$764$	−3.73382	+	3.16477i	−0.135085	+	0.114497i
$765$	−4.94585	−	2.85549i	−0.178818	−	0.103240i
$766$	−5.35303	−	4.46913i	−0.193413	−	0.161476i
$767$	4.50535	+	7.80349i	0.162679	+	0.281768i
$768$	25.8934	+	29.6426i	0.934348	+	1.06963i
$769$	28.0168			1.01031			0.505156	−	0.863028i	$-0.331435\pi$
$769$	28.0168			1.01031			0.505156	+	0.863028i	$0.331435\pi$
$770$		0			0
$771$			59.5051i			2.14302i
$772$	1.40994	+	7.77037i	0.0507449	+	0.279662i
$773$	−29.9953	+	17.3178i	−1.07886	+	0.622878i	−0.930588	−	0.366069i	$-0.880703\pi$
$773$	−29.9953	+	17.3178i	−1.07886	+	0.622878i	−0.148268	+	0.988947i	$0.547370\pi$
$774$	−2.83201	+	3.39212i	−0.101794	+	0.121927i
$775$	−5.10275	+	8.83822i	−0.183296	+	0.317478i
$776$	2.19216	−	3.86310i	0.0786941	−	0.138677i
$777$		0			0
$778$	11.1753	+	30.4684i	0.400655	+	1.09235i
$779$	−17.0715	−	9.85621i	−0.611649	−	0.353136i
$780$	6.37875	−	17.8000i	0.228396	−	0.637341i
$781$	−32.3992	+	18.7057i	−1.15933	+	0.669341i
$782$	−0.425689	+	2.44975i	−0.0152226	+	0.0876028i
$783$	−0.0806779			−0.00288319
$784$		0			0
$785$	−19.1515			−0.683546
$786$	8.78699	−	50.5673i	0.313422	−	1.80367i
$787$	29.6763	−	17.1336i	1.05784	−	0.610747i	0.133009	−	0.991115i	$-0.457536\pi$
$787$	29.6763	−	17.1336i	1.05784	−	0.610747i	0.924835	+	0.380368i	$0.124203\pi$
$788$	−13.1882	+	36.8018i	−0.469811	+	1.31101i
$789$	23.1720	+	13.3784i	0.824944	+	0.476282i
$790$	6.30071	+	17.1783i	0.224169	+	0.611175i
$791$		0			0
$792$	−37.8786	−	21.4947i	−1.34596	−	0.763781i
$793$	16.6665	−	28.8672i	0.591844	−	1.02510i
$794$	−27.1141	+	32.4767i	−0.962244	+	1.15256i
$795$	18.2582	−	10.5414i	0.647552	−	0.373865i
$796$	−7.42574	−	40.9242i	−0.263198	−	1.45052i
$797$		−	20.5838i		−	0.729114i	−0.931181	−	0.364557i	$-0.881220\pi$
$797$		−	20.5838i		−	0.729114i	0.931181	−	0.364557i	$-0.118780\pi$
$798$		0			0
$799$	−13.8122			−0.488641
$800$	14.9066	+	5.21696i	0.527029	+	0.184447i
$801$	3.94196	+	6.82767i	0.139282	+	0.241244i
$802$	17.0120	+	14.2029i	0.600713	+	0.501522i
$803$	43.2416	+	24.9655i	1.52596	+	0.881014i
$804$	1.92162	−	1.62876i	0.0677703	−	0.0574418i
$805$		0			0
$806$	−4.60407	−	12.5525i	−0.162171	−	0.442144i
$807$	29.5252	−	51.1392i	1.03934	−	1.80019i
$808$	0.00440697	+	0.591724i	0.000155037	+	0.0208168i
$809$	23.4504	+	40.6172i	0.824471	+	1.42802i	0.902323	+	0.431060i	$0.141860\pi$
$809$	23.4504	+	40.6172i	0.824471	+	1.42802i	−0.0778526	+	0.996965i	$0.524806\pi$
$810$	18.3096	+	3.18163i	0.643335	+	0.111791i
$811$		−	22.2462i		−	0.781168i	−0.920567	−	0.390584i	$-0.872273\pi$
$811$		−	22.2462i		−	0.781168i	0.920567	−	0.390584i	$-0.127727\pi$
$812$		0			0
$813$		−	15.3088i		−	0.536902i
$814$	−7.35552	+	42.3294i	−0.257811	+	1.48365i
$815$	−2.40076	−	4.15823i	−0.0840948	−	0.145656i
$816$	4.35421	+	11.6033i	0.152428	+	0.406196i
$817$	−1.58637	+	2.74767i	−0.0554999	+	0.0961287i
$818$	34.6360	−	12.7039i	1.21102	−	0.444182i
$819$		0			0
$820$	−12.2258	−	14.4241i	−0.426945	−	0.503713i
$821$	−28.4062	−	16.4003i	−0.991384	−	0.572376i	−0.0856966	−	0.996321i	$-0.527312\pi$
$821$	−28.4062	−	16.4003i	−0.991384	−	0.572376i	−0.905688	+	0.423945i	$0.860645\pi$
$822$	−20.8738	+	25.0022i	−0.728058	+	0.872053i
$823$	6.88576	+	11.9265i	0.240023	+	0.415731i	0.960720	−	0.277518i	$-0.0895118\pi$
$823$	6.88576	+	11.9265i	0.240023	+	0.415731i	−0.720698	+	0.693249i	$0.756178\pi$
$824$	−9.85060	−	16.7720i	−0.343162	−	0.584281i
$825$	−34.6572			−1.20661
$826$		0			0
$827$		−	22.0460i		−	0.766615i	−0.923621	−	0.383307i	$-0.874785\pi$
$827$		−	22.0460i		−	0.766615i	0.923621	−	0.383307i	$-0.125215\pi$
$828$	1.52095	+	8.38215i	0.0528566	+	0.291300i
$829$	−4.74751	+	2.74098i	−0.164888	+	0.0951980i	−0.580173	−	0.814493i	$-0.697015\pi$
$829$	−4.74751	+	2.74098i	−0.164888	+	0.0951980i	0.415285	+	0.909691i	$0.363682\pi$
$830$	−4.79432	−	4.00267i	−0.166413	−	0.138935i
$831$	−34.4402	+	59.6522i	−1.19472	+	2.06931i
$832$	−17.7626	+	10.6111i	−0.615806	+	0.367873i
$833$		0			0
$834$	5.53672	−	2.03078i	0.191721	−	0.0703202i
$835$	−18.0793	−	10.4381i	−0.625659	−	0.361224i
$836$	−29.4371	−	10.5490i	−1.01810	−	0.364845i
$837$	−0.400076	+	0.230984i	−0.0138287	+	0.00798398i
$838$	0.352174	+	0.0611968i	0.0121657	+	0.00211401i
$839$	−28.7512			−0.992601			−0.496301	−	0.868151i	$-0.665309\pi$
$839$	−28.7512			−0.992601			−0.496301	+	0.868151i	$0.665309\pi$
$840$		0			0
$841$	28.5925			0.985947
$842$	−25.5956	−	4.44771i	−0.882084	−	0.153278i
$843$	−35.6012	+	20.5544i	−1.22617	+	0.707930i
$844$	11.6137	−	32.4083i	0.399762	−	1.11554i
$845$	−8.12145	−	4.68892i	−0.279387	−	0.161304i
$846$	−44.4287	+	16.2957i	−1.52749	+	0.560259i
$847$		0			0
$848$	−22.7582	−	3.78027i	−0.781519	−	0.129815i
$849$	−34.2556	+	59.3324i	−1.17565	+	2.03628i
$850$	3.81740	+	3.18706i	0.130936	+	0.109315i
$851$	7.27797	−	4.20194i	0.249486	−	0.144041i
$852$	35.8884	−	6.51198i	1.22952	−	0.223097i
$853$			21.7605i			0.745064i	0.928019	+	0.372532i	$0.121510\pi$
$853$			21.7605i			0.745064i	−0.928019	+	0.372532i	$0.878490\pi$
$854$		0			0
$855$	−14.0487			−0.480457
$856$	−31.5547	+	18.5328i	−1.07852	+	0.633439i
$857$	5.89593	+	10.2121i	0.201401	+	0.348837i	0.948980	−	0.315336i	$-0.102117\pi$
$857$	5.89593	+	10.2121i	0.201401	+	0.348837i	−0.747579	+	0.664173i	$0.768784\pi$
$858$	29.0990	−	34.8542i	0.993422	−	1.18990i
$859$	−4.15132	−	2.39676i	−0.141641	−	0.0817766i	0.427505	−	0.904013i	$-0.359393\pi$
$859$	−4.15132	−	2.39676i	−0.141641	−	0.0817766i	−0.569146	+	0.822237i	$0.692726\pi$
$860$	−2.32158	+	1.96776i	−0.0791651	+	0.0671000i
$861$		0			0
$862$	36.4389	−	13.3652i	1.24111	−	0.455220i
$863$	0.0628642	−	0.108884i	0.00213992	−	0.00370646i	−0.864953	−	0.501852i	$-0.832652\pi$
$863$	0.0628642	−	0.108884i	0.00213992	−	0.00370646i	0.867093	+	0.498146i	$0.165986\pi$
$864$	0.466293	+	0.541902i	0.0158636	+	0.0184359i
$865$	−4.85823	−	8.41471i	−0.165185	−	0.286109i
$866$	−1.75829	+	10.1186i	−0.0597492	+	0.343844i
$867$		−	37.9168i		−	1.28772i
$868$		0			0
$869$			43.9371i			1.49046i
$870$	−3.25145	−	0.564999i	−0.110234	−	0.0191553i
$871$	0.662108	+	1.14681i	0.0224347	+	0.0388580i
$872$	−0.404812	−	54.3543i	−0.0137087	−	1.84067i
$873$	2.39593	−	4.14988i	0.0810900	−	0.140452i
$874$	2.10625	+	5.74249i	0.0712451	+	0.194242i
$875$		0			0
$876$	−31.4760	−	37.1357i	−1.06348	−	1.25470i
$877$	25.9534	+	14.9842i	0.876385	+	0.505981i	0.869465	−	0.493995i	$-0.164464\pi$
$877$	25.9534	+	14.9842i	0.876385	+	0.505981i	0.00692013	+	0.999976i	$0.497797\pi$
$878$	32.5729	+	27.1944i	1.09928	+	0.917765i
$879$	−24.8273	−	43.0021i	−0.837403	−	1.45042i
$880$	−23.1676	−	19.0511i	−0.780980	−	0.642213i
$881$	30.2728			1.01992			0.509959	−	0.860199i	$-0.329661\pi$
$881$	30.2728			1.01992			0.509959	+	0.860199i	$0.329661\pi$
$882$		0			0
$883$		−	43.3423i		−	1.45858i	−0.684203	−	0.729291i	$-0.739850\pi$
$883$		−	43.3423i		−	1.45858i	0.684203	−	0.729291i	$-0.260150\pi$
$884$	−6.41035	+	1.16316i	−0.215603	+	0.0391214i
$885$	11.0292	−	6.36772i	0.370743	−	0.214048i
$886$	−31.7985	+	38.0876i	−1.06829	+	1.27958i
$887$	7.56821	−	13.1085i	0.254116	−	0.440141i	−0.710539	−	0.703658i	$-0.751549\pi$
$887$	7.56821	−	13.1085i	0.254116	−	0.440141i	0.964655	+	0.263516i	$0.0848823\pi$
$888$	20.6731	−	36.4309i	0.693745	−	1.22254i
$889$		0			0
$890$	1.86972	+	5.09761i	0.0626732	+	0.170872i
$891$	38.6468	+	22.3128i	1.29472	+	0.747505i
$892$	32.9791	+	11.8183i	1.10422	+	0.395706i
$893$	−29.4253	+	16.9887i	−0.984680	+	0.568505i
$894$	2.19578	−	12.6362i	0.0734379	−	0.422619i
$895$	0.187796			0.00627731
$896$		0			0
$897$	−8.88128			−0.296537
$898$	5.08705	−	29.2749i	0.169757	−	0.976916i
$899$	−2.02094	+	1.16679i	−0.0674020	+	0.0389146i
$900$	16.0393	+	5.74779i	0.534642	+	0.191593i
$901$	−6.29101	−	3.63212i	−0.209584	−	0.121003i
$902$	−15.6351	−	42.6275i	−0.520592	−	1.41934i
$903$		0			0
$904$	−1.46765	+	2.58633i	−0.0488132	+	0.0860201i
$905$	−2.02034	+	3.49933i	−0.0671584	+	0.116322i
$906$	−31.8321	+	38.1278i	−1.05755	+	1.26671i
$907$	27.4761	−	15.8633i	0.912328	−	0.526733i	0.0311488	−	0.999515i	$-0.490083\pi$
$907$	27.4761	−	15.8633i	0.912328	−	0.526733i	0.881180	+	0.472782i	$0.156750\pi$
$908$	−25.9580	+	4.71009i	−0.861445	+	0.156310i
$909$			0.638384i			0.0211739i
$910$		0			0
$911$	29.4757			0.976574			0.488287	−	0.872683i	$-0.337622\pi$
$911$	29.4757			0.976574			0.488287	+	0.872683i	$0.337622\pi$
$912$	23.5479	+	19.3638i	0.779749	+	0.641201i
$913$	−7.49868	−	12.9881i	−0.248170	−	0.429843i
$914$	−14.5206	−	12.1229i	−0.480299	−	0.400991i
$915$	−40.8000	−	23.5559i	−1.34881	−	0.778734i
$916$	22.2032	+	26.1955i	0.733614	+	0.865524i
$917$		0			0
$918$	0.0775161	+	0.211340i	0.00255841	+	0.00697525i
$919$	−8.85875	+	15.3438i	−0.292223	+	0.506146i	−0.974335	−	0.225102i	$-0.927728\pi$
$919$	−8.85875	+	15.3438i	−0.292223	+	0.506146i	0.682112	+	0.731248i	$0.261062\pi$
$920$	0.0436949	+	5.86692i	0.00144058	+	0.193427i
$921$	−21.9974	−	38.1005i	−0.724838	−	1.25546i
$922$	−3.74306	−	0.650426i	−0.123271	−	0.0214206i
$923$			19.1741i			0.631124i
$924$		0			0
$925$		−	16.8077i		−	0.552635i
$926$	5.09368	−	29.3130i	0.167389	−	0.963285i
$927$	−10.4920	−	18.1727i	−0.344603	−	0.596870i
$928$	2.35542	+	2.73735i	0.0773205	+	0.0898579i
$929$	26.6338	−	46.1311i	0.873826	−	1.51351i	0.0158180	−	0.999875i	$-0.494965\pi$
$929$	26.6338	−	46.1311i	0.873826	−	1.51351i	0.858008	−	0.513636i	$-0.171702\pi$
$930$	−17.7414	+	6.50725i	−0.581762	+	0.213381i
$931$		0			0
$932$	37.9570	−	32.1722i	1.24332	−	1.05384i
$933$	−3.04929	−	1.76051i	−0.0998293	−	0.0576365i
$934$	22.3805	−	26.8069i	0.732313	−	0.877150i
$935$	−4.72233	−	8.17932i	−0.154437	−	0.267492i
$936$	−19.2474	+	11.3044i	−0.629121	+	0.369497i
$937$	38.2055			1.24812			0.624060	−	0.781377i	$-0.285482\pi$
$937$	38.2055			1.24812			0.624060	+	0.781377i	$0.285482\pi$
$938$		0			0
$939$		−	11.9469i		−	0.389874i
$940$	−32.0679	+	5.81874i	−1.04594	+	0.189786i
$941$	8.31195	−	4.79890i	0.270962	−	0.156440i	−0.358363	−	0.933582i	$-0.616665\pi$
$941$	8.31195	−	4.79890i	0.270962	−	0.156440i	0.629325	+	0.777143i	$0.283332\pi$
$942$	34.4182	+	28.7350i	1.12140	+	0.936236i
$943$	−4.44064	+	7.69141i	−0.144607	+	0.250467i
$944$	−13.7475	−	2.28354i	−0.447443	−	0.0743229i
$945$		0			0
$946$	−6.86094	+	2.51648i	−0.223068	+	0.0818179i
$947$	−14.3314	−	8.27425i	−0.465709	−	0.268877i	0.248733	−	0.968572i	$-0.419986\pi$
$947$	−14.3314	−	8.27425i	−0.465709	−	0.268877i	−0.714442	+	0.699695i	$0.753319\pi$
$948$	14.4510	−	40.3256i	0.469346	−	1.30972i
$949$	22.1622	−	12.7954i	0.719417	−	0.415356i
$950$	12.0525	+	2.09435i	0.391036	+	0.0679496i
$951$	27.7803			0.900837
$952$		0			0
$953$	6.08942			0.197256			0.0986278	−	0.995124i	$-0.468555\pi$
$953$	6.08942			0.197256			0.0986278	+	0.995124i	$0.468555\pi$
$954$	−24.5210	−	4.26098i	−0.793897	−	0.137954i
$955$	−3.14943	+	1.81832i	−0.101913	+	0.0588396i
$956$	25.0863	+	8.98986i	0.811348	+	0.290753i
$957$	−6.86296	−	3.96233i	−0.221848	−	0.128084i
$958$	54.3201	−	19.9238i	1.75500	−	0.643708i
$959$		0			0
$960$	14.9974	+	25.1051i	0.484038	+	0.810262i
$961$	8.81887	−	15.2747i	0.284480	−	0.492733i
$962$	16.9033	+	14.1122i	0.544984	+	0.454995i
$963$	−34.1899	+	19.7396i	−1.10176	+	0.636099i
$964$	7.94253	+	43.7723i	0.255812	+	1.40981i
$965$			5.86758i			0.188884i
$966$		0			0
$967$	21.5430			0.692778			0.346389	−	0.938091i	$-0.387408\pi$
$967$	21.5430			0.692778			0.346389	+	0.938091i	$0.387408\pi$
$968$	−20.7199	−	35.2786i	−0.665963	−	1.13390i
$969$	4.79985	+	8.31358i	0.154193	+	0.267071i
$970$	2.11503	−	2.53334i	0.0679095	−	0.0813406i
$971$	−2.27385	−	1.31281i	−0.0729715	−	0.0421301i	0.463070	−	0.886322i	$-0.346748\pi$
$971$	−2.27385	−	1.31281i	−0.0729715	−	0.0421301i	−0.536042	+	0.844191i	$0.680081\pi$
$972$	−28.6218	−	33.7682i	−0.918044	−	1.08311i
$973$		0			0
$974$	23.2804	−	8.53887i	0.745951	−	0.273603i
$975$	−8.88128	+	15.3828i	−0.284429	+	0.492645i
$976$	18.1122	+	48.2660i	0.579756	+	1.54496i
$977$	17.2338	+	29.8499i	0.551359	+	0.954982i	0.998177	+	0.0603567i	$0.0192238\pi$
$977$	17.2338	+	29.8499i	0.551359	+	0.954982i	−0.446818	+	0.894625i	$0.647443\pi$
$978$	−1.92450	+	11.0751i	−0.0615387	+	0.354142i
$979$			13.0382i			0.416704i
$980$		0			0
$981$		−	58.6403i		−	1.87224i
$982$	21.9463	+	3.81358i	0.700335	+	0.121696i
$983$	26.2210	+	45.4161i	0.836320	+	1.44855i	0.892951	+	0.450154i	$0.148631\pi$
$983$	26.2210	+	45.4161i	0.836320	+	1.44855i	−0.0566303	+	0.998395i	$0.518036\pi$
$984$	0.329679	+	44.2661i	0.0105098	+	1.41115i
$985$	−14.5230	+	25.1547i	−0.462743	+	0.801494i
$986$	0.391563	+	1.06756i	0.0124699	+	0.0339979i
$987$		0			0
$988$	−12.2258	+	10.3626i	−0.388956	+	0.329677i
$989$	1.23794	+	0.714725i	0.0393642	+	0.0227269i
$990$	−24.8400	−	20.7384i	−0.789467	−	0.659109i
$991$	8.08057	+	13.9960i	0.256688	+	0.444596i	0.965353	−	0.260949i	$-0.0840355\pi$
$991$	8.08057	+	13.9960i	0.256688	+	0.444596i	−0.708665	+	0.705545i	$0.750702\pi$
$992$	19.5175	+	6.83067i	0.619682	+	0.216874i
$993$	−58.6325			−1.86064
$994$		0			0
$995$		−	30.9028i		−	0.979684i
$996$	2.61051	+	14.3868i	0.0827171	+	0.455865i
$997$	−34.0954	+	19.6850i	−1.07981	+	0.623430i	−0.930846	−	0.365412i	$-0.880928\pi$
$997$	−34.0954	+	19.6850i	−1.07981	+	0.623430i	−0.148967	+	0.988842i	$0.547595\pi$
$998$	−9.23219	+	11.0581i	−0.292240	+	0.350039i
$999$	0.380415	−	0.658898i	0.0120358	−	0.0208466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.p.g.373.4		12
4.3	odd	2		1568.2.t.g.177.1		12
7.2	even	3		392.2.b.f.197.5		6
7.3	odd	6		56.2.p.a.53.2	yes	12
7.4	even	3	inner	392.2.p.g.165.2		12
7.5	odd	6		392.2.b.e.197.5		6
7.6	odd	2		56.2.p.a.37.4	yes	12
8.3	odd	2		1568.2.t.g.177.6		12
8.5	even	2	inner	392.2.p.g.373.2		12
21.17	even	6		504.2.cj.c.109.5		12
21.20	even	2		504.2.cj.c.37.3		12
28.3	even	6		224.2.t.a.81.1		12
28.11	odd	6		1568.2.t.g.753.6		12
28.19	even	6		1568.2.b.f.785.6		6
28.23	odd	6		1568.2.b.e.785.1		6
28.27	even	2		224.2.t.a.177.6		12
56.3	even	6		224.2.t.a.81.6		12
56.5	odd	6		392.2.b.e.197.6		6
56.11	odd	6		1568.2.t.g.753.1		12
56.13	odd	2		56.2.p.a.37.2	✓	12
56.19	even	6		1568.2.b.f.785.1		6
56.27	even	2		224.2.t.a.177.1		12
56.37	even	6		392.2.b.f.197.6		6
56.45	odd	6		56.2.p.a.53.4	yes	12
56.51	odd	6		1568.2.b.e.785.6		6
56.53	even	6	inner	392.2.p.g.165.4		12
84.59	odd	6		2016.2.cr.c.1873.5		12
84.83	odd	2		2016.2.cr.c.1297.2		12
168.59	odd	6		2016.2.cr.c.1873.2		12
168.83	odd	2		2016.2.cr.c.1297.5		12
168.101	even	6		504.2.cj.c.109.3		12
168.125	even	2		504.2.cj.c.37.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.2	✓	12	56.13	odd	2
56.2.p.a.37.4	yes	12	7.6	odd	2
56.2.p.a.53.2	yes	12	7.3	odd	6
56.2.p.a.53.4	yes	12	56.45	odd	6
224.2.t.a.81.1		12	28.3	even	6
224.2.t.a.81.6		12	56.3	even	6
224.2.t.a.177.1		12	56.27	even	2
224.2.t.a.177.6		12	28.27	even	2
392.2.b.e.197.5		6	7.5	odd	6
392.2.b.e.197.6		6	56.5	odd	6
392.2.b.f.197.5		6	7.2	even	3
392.2.b.f.197.6		6	56.37	even	6
392.2.p.g.165.2		12	7.4	even	3	inner
392.2.p.g.165.4		12	56.53	even	6	inner
392.2.p.g.373.2		12	8.5	even	2	inner
392.2.p.g.373.4		12	1.1	even	1	trivial
504.2.cj.c.37.3		12	21.20	even	2
504.2.cj.c.37.5		12	168.125	even	2
504.2.cj.c.109.3		12	168.101	even	6
504.2.cj.c.109.5		12	21.17	even	6
1568.2.b.e.785.1		6	28.23	odd	6
1568.2.b.e.785.6		6	56.51	odd	6
1568.2.b.f.785.1		6	56.19	even	6
1568.2.b.f.785.6		6	28.19	even	6
1568.2.t.g.177.1		12	4.3	odd	2
1568.2.t.g.177.6		12	8.3	odd	2
1568.2.t.g.753.1		12	56.11	odd	6
1568.2.t.g.753.6		12	28.11	odd	6
2016.2.cr.c.1297.2		12	84.83	odd	2
2016.2.cr.c.1297.5		12	168.83	odd	2
2016.2.cr.c.1873.2		12	168.59	odd	6
2016.2.cr.c.1873.5		12	84.59	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.242117 + 1.39333i) q^{2} +(2.13038 - 1.22998i) q^{3} +(-1.88276 - 0.674701i) q^{4} +(-1.28690 - 0.742990i) q^{5} +(1.19797 + 3.26613i) q^{6} +(1.39593 - 2.45995i) q^{8} +(1.52569 - 2.64257i) q^{9} +(1.34681 - 1.61319i) q^{10} +(4.37021 - 2.52314i) q^{11} +(-4.84086 + 0.878379i) q^{12} -2.58633i q^{13} -3.65544 q^{15} +(3.08956 + 2.54060i) q^{16} +(0.629755 + 1.09077i) q^{17} +(3.31258 + 2.76560i) q^{18} +(2.68324 + 1.54917i) q^{19} +(1.92162 + 2.26714i) q^{20} +(2.45748 + 6.70006i) q^{22} +(0.697966 - 1.20891i) q^{23} +(-0.0518180 - 6.95761i) q^{24} +(-1.39593 - 2.41782i) q^{25} +(3.60362 + 0.626196i) q^{26} -0.126378i q^{27} -0.638384i q^{29} +(0.885046 - 5.09325i) q^{30} +(-1.82772 - 3.16571i) q^{31} +(-4.28794 + 3.68966i) q^{32} +(6.20682 - 10.7505i) q^{33} +(-1.67228 + 0.613365i) q^{34} +(-4.65544 + 3.94593i) q^{36} +(5.21370 + 3.01013i) q^{37} +(-2.80817 + 3.36357i) q^{38} +(-3.18113 - 5.50988i) q^{39} +(-3.62414 + 2.12854i) q^{40} -6.36226 q^{41} +1.02401i q^{43} +(-9.93042 + 1.80188i) q^{44} +(-3.92680 + 2.26714i) q^{45} +(1.51543 + 1.26520i) q^{46} +(-5.48316 + 9.49712i) q^{47} +(9.70682 + 1.61236i) q^{48} +(3.70682 - 1.35960i) q^{50} +(2.68324 + 1.54917i) q^{51} +(-1.74500 + 4.86944i) q^{52} +(-4.99481 + 2.88375i) q^{53} +(0.176087 + 0.0305984i) q^{54} -7.49868 q^{55} +7.62177 q^{57} +(0.889482 + 0.154564i) q^{58} +(-3.01720 + 1.74198i) q^{59} +(6.88231 + 2.46633i) q^{60} +(11.1614 + 6.44406i) q^{61} +(4.85341 - 1.78015i) q^{62} +(-4.10275 - 6.86786i) q^{64} +(-1.92162 + 3.32834i) q^{65} +(13.4763 + 11.2511i) q^{66} +(-0.443410 + 0.256003i) q^{67} +(-0.449735 - 2.47855i) q^{68} -3.43393i q^{69} -7.41363 q^{71} +(-4.37084 - 7.44196i) q^{72} +(4.94731 + 8.56899i) q^{73} +(-5.45644 + 6.53562i) q^{74} +(-5.94774 - 3.43393i) q^{75} +(-4.00667 - 4.72709i) q^{76} +(8.44731 - 3.09834i) q^{78} +(-4.35341 + 7.54032i) q^{79} +(-2.08830 - 5.56500i) q^{80} +(4.42162 + 7.65847i) q^{81} +(1.54041 - 8.86475i) q^{82} -2.97196i q^{83} -1.87161i q^{85} +(-1.42679 - 0.247931i) q^{86} +(-0.785198 - 1.36000i) q^{87} +(-0.106298 - 14.2727i) q^{88} +(-1.29186 + 2.23757i) q^{89} +(-2.20814 - 6.02026i) q^{90} +(-2.12976 + 1.80517i) q^{92} +(-7.78749 - 4.49611i) q^{93} +(-11.9051 - 9.93929i) q^{94} +(-2.30203 - 3.98724i) q^{95} +(-4.59674 + 13.1345i) q^{96} +1.57040 q^{97} -15.3981i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 8 q^{6} + 4 q^{8} + 8 q^{10} + 2 q^{12} - 20 q^{15} + 8 q^{16} + 2 q^{17} + 6 q^{18} - 8 q^{20} + 12 q^{22} + 2 q^{23} - 18 q^{24} - 4 q^{25} + 2 q^{26} + 14 q^{30} - 10 q^{31} - 12 q^{32}+ \cdots - 40 q^{97}+O(q^{100}) \) 12 * q - 2 * q^2 + 8 * q^6 + 4 * q^8 + 8 * q^10 + 2 * q^12 - 20 * q^15 + 8 * q^16 + 2 * q^17 + 6 * q^18 - 8 * q^20 + 12 * q^22 + 2 * q^23 - 18 * q^24 - 4 * q^25 + 2 * q^26 + 14 * q^30 - 10 * q^31 - 12 * q^32 + 14 * q^33 - 32 * q^34 - 32 * q^36 - 18 * q^38 + 4 * q^39 - 10 * q^40 + 8 * q^41 - 30 * q^44 - 4 * q^46 - 30 * q^47 + 56 * q^48 - 16 * q^50 + 32 * q^52 - 2 * q^54 - 4 * q^55 - 4 * q^57 - 22 * q^58 + 6 * q^60 + 28 * q^62 + 24 * q^64 + 8 * q^65 + 38 * q^66 - 4 * q^68 + 32 * q^71 + 20 * q^72 + 10 * q^73 + 18 * q^74 - 52 * q^76 + 52 * q^78 - 22 * q^79 - 36 * q^80 + 22 * q^81 + 26 * q^82 + 40 * q^86 + 20 * q^87 - 14 * q^88 + 10 * q^89 - 52 * q^90 - 20 * q^92 - 42 * q^94 - 34 * q^95 - 16 * q^96 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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