LMFDB - Embedded newform 1568.2.t.g.753.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1568,2,Mod(177,1568)] 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("1568.177"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1568, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1568.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,0,0,0,0,0,0,20,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$12.5205430369$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			753.1
Root			$1.41417 - 0.0105323i$ of defining polynomial
Character	$\chi$	$=$	1568.753
Dual form			1568.2.t.g.177.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.13038 - 1.22998i) q^{3} +(-1.28690 + 0.742990i) q^{5} +(1.52569 + 2.64257i) q^{9} +(-4.37021 - 2.52314i) q^{11} +2.58633i q^{13} +3.65544 q^{15} +(0.629755 - 1.09077i) q^{17} +(-2.68324 + 1.54917i) q^{19} +(-0.697966 - 1.20891i) q^{23} +(-1.39593 + 2.41782i) q^{25} -0.126378i q^{27} +0.638384i q^{29} +(1.82772 - 3.16571i) q^{31} +(6.20682 + 10.7505i) q^{33} +(5.21370 - 3.01013i) q^{37} +(3.18113 - 5.50988i) q^{39} -6.36226 q^{41} +1.02401i q^{43} +(-3.92680 - 2.26714i) q^{45} +(5.48316 + 9.49712i) q^{47} +(-2.68324 + 1.54917i) q^{51} +(-4.99481 - 2.88375i) q^{53} +7.49868 q^{55} +7.62177 q^{57} +(3.01720 + 1.74198i) q^{59} +(11.1614 - 6.44406i) q^{61} +(-1.92162 - 3.32834i) q^{65} +(0.443410 + 0.256003i) q^{67} +3.43393i q^{69} +7.41363 q^{71} +(4.94731 - 8.56899i) q^{73} +(5.94774 - 3.43393i) q^{75} +(4.35341 + 7.54032i) q^{79} +(4.42162 - 7.65847i) q^{81} -2.97196i q^{83} +1.87161i q^{85} +(0.785198 - 1.36000i) q^{87} +(-1.29186 - 2.23757i) q^{89} +(-7.78749 + 4.49611i) q^{93} +(2.30203 - 3.98724i) q^{95} +1.57040 q^{97} -15.3981i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 20 q^{15} + 2 q^{17} - 2 q^{23} - 4 q^{25} + 10 q^{31} + 14 q^{33} - 4 q^{39} + 8 q^{41} + 30 q^{47} + 4 q^{55} - 4 q^{57} + 8 q^{65} - 32 q^{71} + 10 q^{73} + 22 q^{79} + 22 q^{81} - 20 q^{87} + 10 q^{89}+ \cdots - 40 q^{97}+O(q^{100}) $ 12 * q + 20 * q^15 + 2 * q^17 - 2 * q^23 - 4 * q^25 + 10 * q^31 + 14 * q^33 - 4 * q^39 + 8 * q^41 + 30 * q^47 + 4 * q^55 - 4 * q^57 + 8 * q^65 - 32 * q^71 + 10 * q^73 + 22 * q^79 + 22 * q^81 - 20 * q^87 + 10 * q^89 + 34 * q^95 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times$.

$n$	$197$	$1471$	$1473$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.13038	−	1.22998i	−1.22998	−	0.710128i	−0.262952	−	0.964809i	$-0.584696\pi$
$3$	−2.13038	−	1.22998i	−1.22998	−	0.710128i	−0.967025	+	0.254681i	$0.918029\pi$
$4$		0			0
$5$	−1.28690	+	0.742990i	−0.575518	+	0.332275i	−0.759350	−	0.650682i	$-0.774483\pi$
$5$	−1.28690	+	0.742990i	−0.575518	+	0.332275i	0.183832	+	0.982958i	$0.441150\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.52569	+	2.64257i	0.508562	+	0.880856i
$10$		0			0
$11$	−4.37021	−	2.52314i	−1.31767	−	0.760756i	−0.334315	−	0.942461i	$-0.608505\pi$
$11$	−4.37021	−	2.52314i	−1.31767	−	0.760756i	−0.983353	+	0.181705i	$0.941838\pi$
$12$		0			0
$13$			2.58633i			0.717320i	0.933468	+	0.358660i	$0.116766\pi$
$13$			2.58633i			0.717320i	−0.933468	+	0.358660i	$0.883234\pi$
$14$		0			0
$15$	3.65544			0.943831
$16$		0			0
$17$	0.629755	−	1.09077i	0.152738	−	0.264550i	−0.779495	−	0.626408i	$-0.784524\pi$
$17$	0.629755	−	1.09077i	0.152738	−	0.264550i	0.932233	+	0.361858i	$0.117858\pi$
$18$		0			0
$19$	−2.68324	+	1.54917i	−0.615577	+	0.355404i	−0.775145	−	0.631783i	$-0.782323\pi$
$19$	−2.68324	+	1.54917i	−0.615577	+	0.355404i	0.159568	+	0.987187i	$0.448990\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.697966	−	1.20891i	−0.145536	−	0.252076i	0.784037	−	0.620714i	$-0.213157\pi$
$23$	−0.697966	−	1.20891i	−0.145536	−	0.252076i	−0.929573	+	0.368639i	$0.879824\pi$
$24$		0			0
$25$	−1.39593	+	2.41782i	−0.279186	+	0.483565i
$26$		0			0
$27$		−	0.126378i		−	0.0243215i
$28$		0			0
$29$			0.638384i			0.118545i	0.998242	+	0.0592725i	$0.0188781\pi$
$29$			0.638384i			0.118545i	−0.998242	+	0.0592725i	$0.981122\pi$
$30$		0			0
$31$	1.82772	−	3.16571i	0.328268	−	0.568578i	−0.653900	−	0.756581i	$-0.726868\pi$
$31$	1.82772	−	3.16571i	0.328268	−	0.568578i	0.982168	+	0.188003i	$0.0602016\pi$
$32$		0			0
$33$	6.20682	+	10.7505i	1.08047	+	1.87143i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.21370	−	3.01013i	0.857127	−	0.494862i	−0.00592229	−	0.999982i	$-0.501885\pi$
$37$	5.21370	−	3.01013i	0.857127	−	0.494862i	0.863049	+	0.505120i	$0.168552\pi$
$38$		0			0
$39$	3.18113	−	5.50988i	0.509388	−	0.882287i
$40$		0			0
$41$	−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	$0.975121\pi$
$44$		0			0
$45$	−3.92680	−	2.26714i	−0.585373	−	0.337965i
$46$		0			0
$47$	5.48316	+	9.49712i	0.799802	+	1.38530i	0.919745	+	0.392516i	$0.128395\pi$
$47$	5.48316	+	9.49712i	0.799802	+	1.38530i	−0.119943	+	0.992781i	$0.538271\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.68324	+	1.54917i	−0.375729	+	0.216927i
$52$		0			0
$53$	−4.99481	−	2.88375i	−0.686089	−	0.396114i	0.116056	−	0.993243i	$-0.462975\pi$
$53$	−4.99481	−	2.88375i	−0.686089	−	0.396114i	−0.802145	+	0.597129i	$0.796308\pi$
$54$		0			0
$55$	7.49868			1.01112
$56$		0			0
$57$	7.62177			1.00953
$58$		0			0
$59$	3.01720	+	1.74198i	0.392806	+	0.226787i	0.683375	−	0.730067i	$-0.260511\pi$
$59$	3.01720	+	1.74198i	0.392806	+	0.226787i	−0.290569	+	0.956854i	$0.593845\pi$
$60$		0			0
$61$	11.1614	−	6.44406i	1.42908	−	0.825077i	0.432028	−	0.901860i	$-0.357798\pi$
$61$	11.1614	−	6.44406i	1.42908	−	0.825077i	0.997048	+	0.0767831i	$0.0244649\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.92162	−	3.32834i	−0.238348	−	0.412830i
$66$		0			0
$67$	0.443410	+	0.256003i	0.0541711	+	0.0312757i	0.526841	−	0.849964i	$-0.323376\pi$
$67$	0.443410	+	0.256003i	0.0541711	+	0.0312757i	−0.472670	+	0.881240i	$0.656710\pi$
$68$		0			0
$69$			3.43393i			0.413396i
$70$		0			0
$71$	7.41363			0.879836			0.439918	−	0.898038i	$-0.355007\pi$
$71$	7.41363			0.879836			0.439918	+	0.898038i	$0.355007\pi$
$72$		0			0
$73$	4.94731	−	8.56899i	0.579038	−	1.00292i	−0.416552	−	0.909112i	$-0.636761\pi$
$73$	4.94731	−	8.56899i	0.579038	−	1.00292i	0.995590	−	0.0938118i	$-0.0299052\pi$
$74$		0			0
$75$	5.94774	−	3.43393i	0.686786	−	0.396516i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.35341	+	7.54032i	0.489797	+	0.848353i	0.999931	−	0.0117420i	$-0.00373767\pi$
$79$	4.35341	+	7.54032i	0.489797	+	0.848353i	−0.510134	+	0.860095i	$0.670404\pi$
$80$		0			0
$81$	4.42162	−	7.65847i	0.491291	−	0.850941i
$82$		0			0
$83$		−	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
$86$		0			0
$87$	0.785198	−	1.36000i	0.0841820	−	0.145808i
$88$		0			0
$89$	−1.29186	−	2.23757i	−0.136937	−	0.237182i	0.789399	−	0.613881i	$-0.210393\pi$
$89$	−1.29186	−	2.23757i	−0.136937	−	0.237182i	−0.926336	+	0.376699i	$0.877059\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−7.78749	+	4.49611i	−0.807525	+	0.466225i
$94$		0			0
$95$	2.30203	−	3.98724i	0.236184	−	0.409082i
$96$		0			0
$97$	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			0
$101$	−0.181183	−	0.104606i	−0.0180284	−	0.0104087i	0.490959	−	0.871183i	$-0.336647\pi$
$101$	−0.181183	−	0.104606i	−0.0180284	−	0.0104087i	−0.508987	+	0.860774i	$0.669980\pi$
$102$		0			0
$103$	−3.43846	−	5.95558i	−0.338801	−	0.586821i	0.645406	−	0.763839i	$-0.276688\pi$
$103$	−3.43846	−	5.95558i	−0.338801	−	0.586821i	−0.984207	+	0.177019i	$0.943355\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.2048	−	6.46908i	1.08321	−	0.625389i	0.151447	−	0.988465i	$-0.451607\pi$
$107$	11.2048	−	6.46908i	1.08321	−	0.625389i	0.931759	+	0.363076i	$0.118274\pi$
$108$		0			0
$109$	16.6430	+	9.60883i	1.59411	+	0.920359i	0.992591	+	0.121500i	$0.0387703\pi$
$109$	16.6430	+	9.60883i	1.59411	+	0.920359i	0.601517	+	0.798860i	$0.294563\pi$
$110$		0			0
$111$	−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	$0.515748\pi$
$114$		0			0
$115$	1.79642	+	1.03716i	0.167517	+	0.0967160i
$116$		0			0
$117$	−6.83456	+	3.94593i	−0.631855	+	0.364802i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	7.23250	+	12.5271i	0.657500	+	1.13882i
$122$		0			0
$123$	13.5540	+	7.82543i	1.22213	+	0.705595i
$124$		0			0
$125$		−	11.5786i		−	1.03562i
$126$		0			0
$127$	7.20814			0.639619			0.319809	−	0.947482i	$-0.396381\pi$
$127$	7.20814			0.639619			0.319809	+	0.947482i	$0.396381\pi$
$128$		0			0
$129$	1.25951	−	2.18154i	0.110894	−	0.192074i
$130$		0			0
$131$	12.7767	−	7.37662i	1.11630	−	0.644498i	0.175849	−	0.984417i	$-0.443733\pi$
$131$	12.7767	−	7.37662i	1.11630	−	0.644498i	0.940455	+	0.339919i	$0.110400\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.0938978	+	0.162636i	0.00808144	+	0.0139975i
$136$		0			0
$137$	4.68113	−	8.10795i	0.399936	−	0.692709i	−0.593782	−	0.804626i	$-0.702366\pi$
$137$	4.68113	−	8.10795i	0.399936	−	0.692709i	0.993718	+	0.111917i	$0.0356991\pi$
$138$		0			0
$139$		−	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
$142$		0			0
$143$	6.52569	−	11.3028i	0.545705	−	0.945189i
$144$		0			0
$145$	−0.474313	−	0.821534i	−0.0393895	−	0.0682247i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.19276	+	1.84334i	−0.261561	+	0.151012i	−0.625047	−	0.780587i	$-0.714920\pi$
$149$	−3.19276	+	1.84334i	−0.261561	+	0.151012i	0.363485	+	0.931600i	$0.381587\pi$
$150$		0			0
$151$	−7.13861	+	12.3644i	−0.580932	+	1.00620i	0.414438	+	0.910078i	$0.363978\pi$
$151$	−7.13861	+	12.3644i	−0.580932	+	1.00620i	−0.995369	+	0.0961252i	$0.969355\pi$
$152$		0			0
$153$	3.84324			0.310707
$154$		0			0
$155$			5.43191i			0.436302i
$156$		0			0
$157$	11.1614	+	6.44406i	0.890780	+	0.514292i	0.874197	−	0.485571i	$-0.161388\pi$
$157$	11.1614	+	6.44406i	0.890780	+	0.514292i	0.0165822	+	0.999863i	$0.494721\pi$
$158$		0			0
$159$	7.09390	+	12.2870i	0.562583	+	0.974422i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−2.79831	+	1.61560i	−0.219180	+	0.126544i	−0.605571	−	0.795791i	$-0.707055\pi$
$163$	−2.79831	+	1.61560i	−0.219180	+	0.126544i	0.386390	+	0.922335i	$0.373722\pi$
$164$		0			0
$165$	−15.9751	−	9.22320i	−1.24366	−	0.718026i
$166$		0			0
$167$	−14.0487			−1.08712			−0.543562	−	0.839369i	$-0.682925\pi$
$167$	−14.0487			−1.08712			−0.543562	+	0.839369i	$0.682925\pi$
$168$		0			0
$169$	6.31088			0.485453
$170$		0			0
$171$	−8.18757	−	4.72709i	−0.626119	−	0.361490i
$172$		0			0
$173$	5.66273	−	3.26938i	0.430529	−	0.248566i	−0.269043	−	0.963128i	$-0.586707\pi$
$173$	5.66273	−	3.26938i	0.430529	−	0.248566i	0.699572	+	0.714562i	$0.253374\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.28520	−	7.42218i	−0.322095	−	0.557885i
$178$		0			0
$179$	0.109447	+	0.0631891i	0.00818044	+	0.00472298i	0.504085	−	0.863654i	$-0.331830\pi$
$179$	0.109447	+	0.0631891i	0.00818044	+	0.00472298i	−0.495904	+	0.868377i	$0.665163\pi$
$180$		0			0
$181$			2.71920i			0.202117i	0.994880	+	0.101058i	$0.0322229\pi$
$181$			2.71920i			0.202117i	−0.994880	+	0.101058i	$0.967777\pi$
$182$		0			0
$183$	−31.7042			−2.34364
$184$		0			0
$185$	−4.47299	+	7.74745i	−0.328861	+	0.569604i
$186$		0			0
$187$	−5.50433	+	3.17793i	−0.402516	+	0.232393i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.22365	−	2.11943i	−0.0885404	−	0.153357i	0.818354	−	0.574715i	$-0.194887\pi$
$191$	−1.22365	−	2.11943i	−0.0885404	−	0.153357i	−0.906894	+	0.421358i	$0.861554\pi$
$192$		0			0
$193$	−1.97431	+	3.41961i	−0.142114	+	0.246149i	−0.928293	−	0.371851i	$-0.878723\pi$
$193$	−1.97431	+	3.41961i	−0.142114	+	0.246149i	0.786178	+	0.618000i	$0.212057\pi$
$194$		0			0
$195$			9.45419i			0.677029i
$196$		0			0
$197$			19.5468i			1.39265i	0.717727	+	0.696325i	$0.245183\pi$
$197$			19.5468i			1.39265i	−0.717727	+	0.696325i	$0.754817\pi$
$198$		0			0
$199$	−10.3981	+	18.0101i	−0.737103	+	1.27670i	0.216692	+	0.976240i	$0.430473\pi$
$199$	−10.3981	+	18.0101i	−0.737103	+	1.27670i	−0.953795	+	0.300460i	$0.902860\pi$
$200$		0			0
$201$	−0.629755	−	1.09077i	−0.0444195	−	0.0769369i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	8.18757	−	4.72709i	0.571845	−	0.330155i
$206$		0			0
$207$	2.12976	−	3.68884i	0.148028	−	0.256392i
$208$		0			0
$209$	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	$0.798140\pi$
$212$		0			0
$213$	−15.7939	−	9.11860i	−1.08218	−	0.624796i
$214$		0			0
$215$	−0.760830	−	1.31780i	−0.0518882	−	0.0898730i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−21.0793	+	12.1701i	−1.42441	+	0.822382i
$220$		0			0
$221$	2.82109	+	1.62876i	0.189767	+	0.109562i
$222$		0			0
$223$	17.5164			1.17298			0.586492	−	0.809955i	$-0.300509\pi$
$223$	17.5164			1.17298			0.586492	+	0.809955i	$0.300509\pi$
$224$		0			0
$225$	−8.51902			−0.567935
$226$		0			0
$227$	−11.4237	−	6.59546i	−0.758215	−	0.437756i	0.0704394	−	0.997516i	$-0.477560\pi$
$227$	−11.4237	−	6.59546i	−0.758215	−	0.437756i	−0.828655	+	0.559760i	$0.810893\pi$
$228$		0			0
$229$	−14.8693	+	8.58482i	−0.982594	+	0.567301i	−0.903052	−	0.429531i	$-0.858679\pi$
$229$	−14.8693	+	8.58482i	−0.982594	+	0.567301i	−0.0795417	+	0.996832i	$0.525346\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.4393	−	21.5455i	−0.814927	−	1.41149i	−0.909380	−	0.415966i	$-0.863444\pi$
$233$	−12.4393	−	21.5455i	−0.814927	−	1.41149i	0.0944534	−	0.995529i	$-0.469890\pi$
$234$		0			0
$235$	−14.1125	−	8.14787i	−0.920600	−	0.531508i
$236$		0			0
$237$		−	21.4184i		−	1.39127i
$238$		0			0
$239$	13.3242			0.861872			0.430936	−	0.902383i	$-0.358183\pi$
$239$	13.3242			0.861872			0.430936	+	0.902383i	$0.358183\pi$
$240$		0			0
$241$	−11.1218	+	19.2635i	−0.716416	+	1.24087i	0.245995	+	0.969271i	$0.420885\pi$
$241$	−11.1218	+	19.2635i	−0.716416	+	1.24087i	−0.962411	+	0.271598i	$0.912448\pi$
$242$		0			0
$243$	−19.1678	+	11.0665i	−1.22962	+	0.709919i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.00667	−	6.93975i	−0.254938	−	0.441566i
$248$		0			0
$249$	−3.65544	+	6.33141i	−0.231654	+	0.401237i
$250$		0			0
$251$			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
$254$		0			0
$255$	2.30203	−	3.98724i	0.144159	−	0.249691i
$256$		0			0
$257$	−12.0948	−	20.9487i	−0.754451	−	1.30675i	−0.945647	−	0.325195i	$-0.894570\pi$
$257$	−12.0948	−	20.9487i	−0.754451	−	1.30675i	0.191196	−	0.981552i	$-0.438763\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.68697	+	0.973974i	−0.104421	+	0.0602875i
$262$		0			0
$263$	−5.43846	+	9.41968i	−0.335350	+	0.580842i	−0.983552	−	0.180626i	$-0.942188\pi$
$263$	−5.43846	+	9.41968i	−0.335350	+	0.580842i	0.648202	+	0.761468i	$0.275521\pi$
$264$		0			0
$265$	8.57040			0.526475
$266$		0			0
$267$			6.35585i			0.388972i
$268$		0			0
$269$	20.7887	+	12.0024i	1.26751	+	0.731796i	0.974516	−	0.224319i	$-0.0720156\pi$
$269$	20.7887	+	12.0024i	1.26751	+	0.731796i	0.292992	+	0.956115i	$0.405349\pi$
$270$		0			0
$271$	−3.11160	−	5.38945i	−0.189016	−	0.327386i	0.755906	−	0.654680i	$-0.227197\pi$
$271$	−3.11160	−	5.38945i	−0.189016	−	0.327386i	−0.944922	+	0.327294i	$0.893863\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	12.2010	−	7.04427i	0.735750	−	0.424786i
$276$		0			0
$277$	−24.2493	−	14.0003i	−1.45700	−	0.841199i	−0.458136	−	0.888882i	$-0.651483\pi$
$277$	−24.2493	−	14.0003i	−1.45700	−	0.841199i	−0.998863	+	0.0476832i	$0.984816\pi$
$278$		0			0
$279$	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	$0.666098\pi$
$282$		0			0
$283$	24.1193	+	13.9253i	1.43374	+	0.827772i	0.997404	−	0.0720102i	$-0.0229414\pi$
$283$	24.1193	+	13.9253i	1.43374	+	0.827772i	0.436339	+	0.899782i	$0.356275\pi$
$284$		0			0
$285$	−9.80843	+	5.66290i	−0.581001	+	0.335441i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.70682	+	13.3486i	0.453342	+	0.785212i
$290$		0			0
$291$	−3.34554	−	1.93155i	−0.196119	−	0.113229i
$292$		0			0
$293$			20.1851i			1.17923i	0.807685	+	0.589614i	$0.200720\pi$
$293$			20.1851i			1.17923i	−0.807685	+	0.589614i	$0.799280\pi$
$294$		0			0
$295$	−5.17710			−0.301423
$296$		0			0
$297$	−0.318870	+	0.552300i	−0.0185027	+	0.0320477i
$298$		0			0
$299$	3.12665	−	1.80517i	0.180819	−	0.104396i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.257326	+	0.445702i	0.0147830	+	0.0256049i
$304$		0			0
$305$	−9.57574	+	16.5857i	−0.548305	+	0.949693i
$306$		0			0
$307$		−	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
$310$		0			0
$311$	0.715667	−	1.23957i	0.0405818	−	0.0702897i	−0.845021	−	0.534733i	$-0.820412\pi$
$311$	0.715667	−	1.23957i	0.0405818	−	0.0702897i	0.885603	+	0.464443i	$0.153746\pi$
$312$		0			0
$313$	2.42829	+	4.20591i	0.137255	+	0.237732i	0.926457	−	0.376402i	$-0.122839\pi$
$313$	2.42829	+	4.20591i	0.137255	+	0.237732i	−0.789202	+	0.614134i	$0.789505\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.78002	−	5.64650i	0.549301	−	0.317139i	−0.199539	−	0.979890i	$-0.563944\pi$
$317$	9.78002	−	5.64650i	0.549301	−	0.317139i	0.748840	+	0.662751i	$0.230611\pi$
$318$		0			0
$319$	1.61073	−	2.78987i	0.0901838	−	0.156203i
$320$		0			0
$321$	−31.8273			−1.77642
$322$		0			0
$323$			3.90239i			0.217135i
$324$		0			0
$325$	−6.25330	−	3.61034i	−0.346871	−	0.200266i
$326$		0			0
$327$	−23.6373	−	40.9410i	−1.30714	−	2.26404i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	20.6415	−	11.9174i	1.13456	−	0.655039i	0.189483	−	0.981884i	$-0.439319\pi$
$331$	20.6415	−	11.9174i	1.13456	−	0.655039i	0.945078	+	0.326845i	$0.105986\pi$
$332$		0			0
$333$	15.9089	+	9.18503i	0.871805	+	0.503337i
$334$		0			0
$335$	−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	$0.351975\pi$
$338$		0			0
$339$	2.23983	+	1.29317i	0.121651	+	0.0702351i
$340$		0			0
$341$	−15.9751	+	9.22320i	−0.865098	+	0.499465i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2.55137	−	4.41911i	−0.137361	−	0.237917i
$346$		0			0
$347$	−2.78706	−	1.60911i	−0.149617	−	0.0863817i	0.423322	−	0.905979i	$-0.360864\pi$
$347$	−2.78706	−	1.60911i	−0.149617	−	0.0863817i	−0.572940	+	0.819597i	$0.694197\pi$
$348$		0			0
$349$			22.8716i			1.22429i	0.790747	+	0.612143i	$0.209692\pi$
$349$			22.8716i			1.22429i	−0.790747	+	0.612143i	$0.790308\pi$
$350$		0			0
$351$	0.326856			0.0174463
$352$		0			0
$353$	11.6608	−	20.1971i	0.620641	−	1.07498i	−0.368725	−	0.929538i	$-0.620206\pi$
$353$	11.6608	−	20.1971i	0.620641	−	1.07498i	0.989367	−	0.145444i	$-0.0464609\pi$
$354$		0			0
$355$	−9.54058	+	5.50826i	−0.506361	+	0.292348i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.55488	−	4.42518i	−0.134841	−	0.233552i	0.790696	−	0.612210i	$-0.209719\pi$
$359$	−2.55488	−	4.42518i	−0.134841	−	0.233552i	−0.925537	+	0.378658i	$0.876386\pi$
$360$		0			0
$361$	−4.70015	+	8.14090i	−0.247376	+	0.428468i
$362$		0			0
$363$		−	35.5833i		−	1.86764i
$364$		0			0
$365$			14.7032i			0.769600i
$366$		0			0
$367$	−14.0779	+	24.3837i	−0.734862	+	1.27282i	0.219922	+	0.975517i	$0.429420\pi$
$367$	−14.0779	+	24.3837i	−0.734862	+	1.27282i	−0.954784	+	0.297301i	$0.903914\pi$
$368$		0			0
$369$	−9.70682	−	16.8127i	−0.505317	−	0.875234i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−6.10052	+	3.52214i	−0.315873	+	0.182369i	−0.649551	−	0.760318i	$-0.725043\pi$
$373$	−6.10052	+	3.52214i	−0.315873	+	0.182369i	0.333679	+	0.942687i	$0.391710\pi$
$374$		0			0
$375$	−14.2414	+	24.6667i	−0.735420	+	1.27379i
$376$		0			0
$377$	−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	$-0.110073\pi$
$380$		0			0
$381$	−15.3561	−	8.86584i	−0.786716	−	0.454211i
$382$		0			0
$383$	2.46546	+	4.27031i	0.125979	+	0.218202i	0.922115	−	0.386915i	$-0.126459\pi$
$383$	2.46546	+	4.27031i	0.125979	+	0.218202i	−0.796136	+	0.605118i	$0.793126\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.70602	+	1.56232i	−0.137555	+	0.0794172i
$388$		0			0
$389$	19.8735	+	11.4739i	1.00762	+	0.581752i	0.910495	−	0.413520i	$-0.135701\pi$
$389$	19.8735	+	11.4739i	1.00762	+	0.581752i	0.0971291	+	0.995272i	$0.469034\pi$
$390$		0			0
$391$	−1.75819			−0.0889155
$392$		0			0
$393$	−36.2923			−1.83070
$394$		0			0
$395$	−11.2048	−	6.46908i	−0.563773	−	0.325495i
$396$		0			0
$397$	25.9079	−	14.9579i	1.30028	−	0.750716i	0.319827	−	0.947476i	$-0.396375\pi$
$397$	25.9079	−	14.9579i	1.30028	−	0.750716i	0.980452	+	0.196760i	$0.0630420\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.83525	+	13.5711i	0.391274	+	0.677706i	0.992618	−	0.121284i	$-0.0387012\pi$
$401$	7.83525	+	13.5711i	0.391274	+	0.677706i	−0.601344	+	0.798990i	$0.705368\pi$
$402$		0			0
$403$	8.18757	+	4.72709i	0.407852	+	0.235473i
$404$		0			0
$405$			13.1409i			0.652975i
$406$		0			0
$407$	−30.3800			−1.50588
$408$		0			0
$409$	−13.0434	+	22.5918i	−0.644954	+	1.11709i	0.339358	+	0.940657i	$0.389790\pi$
$409$	−13.0434	+	22.5918i	−0.644954	+	1.11709i	−0.984312	+	0.176436i	$0.943543\pi$
$410$		0			0
$411$	−19.9452	+	11.5154i	−0.983824	+	0.568011i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2.20814	+	3.82460i	0.108393	+	0.187742i
$416$		0			0
$417$	−2.08505	+	3.61141i	−0.102105	+	0.176851i
$418$		0			0
$419$		−	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	$-0.852261\pi$
$421$		−	18.3701i		−	0.895302i	0.894208	−	0.447651i	$-0.147739\pi$
$422$		0			0
$423$	−16.7312	+	28.9793i	−0.813498	+	1.40902i
$424$		0			0
$425$	1.75819	+	3.04528i	0.0852848	+	0.147718i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−27.8044	+	16.0529i	−1.34241	+	0.775041i
$430$		0			0
$431$	13.7223	−	23.7678i	0.660982	−	1.14485i	−0.319377	−	0.947628i	$-0.603473\pi$
$431$	13.7223	−	23.7678i	0.660982	−	1.14485i	0.980358	−	0.197226i	$-0.0631932\pi$
$432$		0			0
$433$	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
$436$		0			0
$437$	3.74562	+	2.16253i	0.179177	+	0.103448i
$438$		0			0
$439$	−15.0022	−	25.9845i	−0.716015	−	1.24017i	−0.962567	−	0.271045i	$-0.912631\pi$
$439$	−15.0022	−	25.9845i	−0.716015	−	1.24017i	0.246551	−	0.969130i	$-0.420703\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−30.3838	+	17.5421i	−1.44358	+	0.833451i	−0.998086	−	0.0618342i	$-0.980305\pi$
$443$	−30.3838	+	17.5421i	−1.44358	+	0.833451i	−0.445493	+	0.895285i	$0.646972\pi$
$444$		0			0
$445$	3.32499	+	1.91968i	0.157620	+	0.0910017i
$446$		0			0
$447$	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	$0.665117\pi$
$450$		0			0
$451$	27.8044	+	16.0529i	1.30926	+	0.755901i
$452$		0			0
$453$	30.4159	−	17.5606i	1.42906	−	0.825071i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−6.68780	−	11.5836i	−0.312842	−	0.541858i	0.666135	−	0.745832i	$-0.267948\pi$
$457$	−6.68780	−	11.5836i	−0.312842	−	0.541858i	−0.978976	+	0.203974i	$0.934614\pi$
$458$		0			0
$459$	−0.137849	−	0.0795874i	−0.00643426	−	0.00371482i
$460$		0			0
$461$		−	2.68641i		−	0.125118i	−0.998041	−	0.0625592i	$-0.980074\pi$
$461$		−	2.68641i		−	0.125118i	0.998041	−	0.0625592i	$-0.0199262\pi$
$462$		0			0
$463$	21.0380			0.977721			0.488860	−	0.872362i	$-0.337413\pi$
$463$	21.0380			0.977721			0.488860	+	0.872362i	$0.337413\pi$
$464$		0			0
$465$	6.68113	−	11.5721i	0.309830	−	0.536641i
$466$		0			0
$467$	21.3849	−	12.3466i	0.989574	−	0.571331i	0.0844270	−	0.996430i	$-0.473094\pi$
$467$	21.3849	−	12.3466i	0.989574	−	0.571331i	0.905147	+	0.425099i	$0.139761\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−15.8521	−	27.4566i	−0.730426	−	1.26513i
$472$		0			0
$473$	2.58373	−	4.47515i	0.118800	−	0.205767i
$474$		0			0
$475$		−	8.65014i		−	0.396896i
$476$		0			0
$477$		−	17.5988i		−	0.805794i
$478$		0			0
$479$	20.4562	−	35.4311i	0.934666	−	1.61889i	0.159437	−	0.987208i	$-0.449032\pi$
$479$	20.4562	−	35.4311i	0.934666	−	1.61889i	0.775229	−	0.631680i	$-0.217634\pi$
$480$		0			0
$481$	7.78520	+	13.4844i	0.354974	+	0.614834i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.02094	+	1.16679i	−0.0917660	+	0.0529811i
$486$		0			0
$487$	8.76704	−	15.1850i	0.397273	−	0.688096i	−0.596116	−	0.802898i	$-0.703290\pi$
$487$	8.76704	−	15.1850i	0.397273	−	0.688096i	0.993388	+	0.114802i	$0.0366234\pi$
$488$		0			0
$489$	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	$-0.115660\pi$
$492$		0			0
$493$	0.696329	+	0.402026i	0.0313611	+	0.0181063i
$494$		0			0
$495$	11.4406	+	19.8158i	0.514219	+	0.890653i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−8.82147	+	5.09308i	−0.394903	+	0.227997i	−0.684282	−	0.729217i	$-0.739884\pi$
$499$	−8.82147	+	5.09308i	−0.394903	+	0.227997i	0.289379	+	0.957215i	$0.406551\pi$
$500$		0			0
$501$	29.9292	+	17.2796i	1.33714	+	0.771997i
$502$		0			0
$503$	27.1001			1.20833			0.604167	−	0.796858i	$-0.293506\pi$
$503$	27.1001			1.20833			0.604167	+	0.796858i	$0.293506\pi$
$504$		0			0
$505$	0.310885			0.0138342
$506$		0			0
$507$	−13.4446	−	7.76224i	−0.597096	−	0.344733i
$508$		0			0
$509$	−19.4357	+	11.2212i	−0.861471	+	0.497371i	−0.864505	−	0.502625i	$-0.832368\pi$
$509$	−19.4357	+	11.2212i	−0.861471	+	0.497371i	0.00303361	+	0.999995i	$0.499034\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.195781	+	0.339103i	0.00864396	+	0.0149718i
$514$		0			0
$515$	8.84987	+	5.10948i	0.389972	+	0.225150i
$516$		0			0
$517$		−	55.3392i		−	2.43382i
$518$		0			0
$519$	−16.0850			−0.706055
$520$		0			0
$521$	−5.13510	+	8.89426i	−0.224973	+	0.389664i	−0.956311	−	0.292350i	$-0.905563\pi$
$521$	−5.13510	+	8.89426i	−0.224973	+	0.389664i	0.731338	+	0.682015i	$0.238896\pi$
$522$		0			0
$523$	15.4655	−	8.92903i	0.676261	−	0.390439i	−0.122184	−	0.992507i	$-0.538990\pi$
$523$	15.4655	−	8.92903i	0.676261	−	0.390439i	0.798445	+	0.602068i	$0.205656\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.30203	−	3.98724i	−0.100278	−	0.173687i
$528$		0			0
$529$	10.5257	−	18.2310i	0.457639	−	0.792653i
$530$		0			0
$531$			10.6309i			0.461341i
$532$		0			0
$533$		−	16.4549i		−	0.712742i
$534$		0			0
$535$	−9.61292	+	16.6501i	−0.415603	+	0.719845i
$536$		0			0
$537$	−0.155442	−	0.269234i	−0.00670783	−	0.0116183i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	19.9303	−	11.5067i	0.856869	−	0.494714i	−0.00609356	−	0.999981i	$-0.501940\pi$
$541$	19.9303	−	11.5067i	0.856869	−	0.494714i	0.862963	+	0.505268i	$0.168606\pi$
$542$		0			0
$543$	3.34456	−	5.79294i	0.143529	−	0.248599i
$544$		0			0
$545$	−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	$-0.0623321\pi$
$548$		0			0
$549$	34.0577	+	19.6632i	1.45355	+	0.839206i
$550$		0			0
$551$	−0.988965	−	1.71294i	−0.0421313	−	0.0729736i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	19.0584	−	11.0034i	0.808983	−	0.467067i
$556$		0			0
$557$	−15.0016	−	8.66116i	−0.635637	−	0.366985i	0.147295	−	0.989093i	$-0.452943\pi$
$557$	−15.0016	−	8.66116i	−0.635637	−	0.366985i	−0.782932	+	0.622107i	$0.786277\pi$
$558$		0			0
$559$	−2.64843			−0.112017
$560$		0			0
$561$	15.6351			0.660115
$562$		0			0
$563$	6.91560	+	3.99272i	0.291458	+	0.168273i	0.638599	−	0.769540i	$-0.279514\pi$
$563$	6.91560	+	3.99272i	0.291458	+	0.168273i	−0.347141	+	0.937813i	$0.612848\pi$
$564$		0			0
$565$	1.35301	−	0.781160i	0.0569215	−	0.0328637i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.98535	−	10.3669i	−0.250919	−	0.434604i	0.712860	−	0.701306i	$-0.247399\pi$
$569$	−5.98535	−	10.3669i	−0.250919	−	0.434604i	−0.963779	+	0.266702i	$0.914066\pi$
$570$		0			0
$571$	36.9016	+	21.3051i	1.54428	+	0.891592i	0.998561	+	0.0536265i	$0.0170780\pi$
$571$	36.9016	+	21.3051i	1.54428	+	0.891592i	0.545722	+	0.837966i	$0.316255\pi$
$572$		0			0
$573$			6.02026i			0.251500i
$574$		0			0
$575$	3.89725			0.162527
$576$		0			0
$577$	−14.9650	+	25.9202i	−0.623001	+	1.07907i	0.365922	+	0.930645i	$0.380754\pi$
$577$	−14.9650	+	25.9202i	−0.623001	+	1.07907i	−0.988924	+	0.148425i	$0.952580\pi$
$578$		0			0
$579$	8.41208	−	4.85672i	0.349594	−	0.201838i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	14.5522	+	25.2052i	0.602692	+	1.04389i
$584$		0			0
$585$	5.86358	−	10.1560i	0.242429	−	0.419900i
$586$		0			0
$587$		−	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
$590$		0			0
$591$	24.0421	−	41.6421i	0.988959	−	1.71293i
$592$		0			0
$593$	−9.07706	−	15.7219i	−0.372750	−	0.645622i	0.617237	−	0.786777i	$-0.288252\pi$
$593$	−9.07706	−	15.7219i	−0.372750	−	0.645622i	−0.989988	+	0.141155i	$0.954919\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	44.3039	−	25.5789i	1.81324	−	1.04687i
$598$		0			0
$599$	5.59258	−	9.68663i	0.228507	−	0.395785i	−0.728859	−	0.684664i	$-0.759949\pi$
$599$	5.59258	−	9.68663i	0.228507	−	0.395785i	0.957366	+	0.288879i	$0.0932824\pi$
$600$		0			0
$601$	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
$604$		0			0
$605$	−18.6150	−	10.7474i	−0.756806	−	0.436942i
$606$		0			0
$607$	13.6196	+	23.5898i	0.552802	+	0.957481i	0.998071	+	0.0620841i	$0.0197747\pi$
$607$	13.6196	+	23.5898i	0.552802	+	0.957481i	−0.445269	+	0.895397i	$0.646892\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−24.5627	+	14.1813i	−0.993701	+	0.573713i
$612$		0			0
$613$	3.20401	+	1.84984i	0.129409	+	0.0747141i	0.563307	−	0.826248i	$-0.309529\pi$
$613$	3.20401	+	1.84984i	0.129409	+	0.0747141i	−0.433898	+	0.900962i	$0.642862\pi$
$614$		0			0
$615$	−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	$0.324312\pi$
$618$		0			0
$619$	−27.7816	−	16.0397i	−1.11664	−	0.644692i	−0.176098	−	0.984373i	$-0.556348\pi$
$619$	−27.7816	−	16.0397i	−1.11664	−	0.644692i	−0.940541	+	0.339681i	$0.889681\pi$
$620$		0			0
$621$	−0.152780	+	0.0882077i	−0.00613086	+	0.00353965i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	1.62309	+	2.81127i	0.0649236	+	0.112451i
$626$		0			0
$627$	−33.3088	−	19.2308i	−1.33022	−	0.768005i
$628$		0			0
$629$		−	7.58258i		−	0.302337i
$630$		0			0
$631$	−11.7538			−0.467912			−0.233956	−	0.972247i	$-0.575167\pi$
$631$	−11.7538			−0.467912			−0.233956	+	0.972247i	$0.575167\pi$
$632$		0			0
$633$	21.1718	−	36.6707i	0.841504	−	1.45753i
$634$		0			0
$635$	−9.27612	+	5.35557i	−0.368112	+	0.212529i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	11.3109	+	19.5910i	0.447452	+	0.775009i
$640$		0			0
$641$	−20.9136	+	36.2235i	−0.826039	+	1.43074i	0.0750839	+	0.997177i	$0.476078\pi$
$641$	−20.9136	+	36.2235i	−0.826039	+	1.43074i	−0.901123	+	0.433564i	$0.857256\pi$
$642$		0			0
$643$			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
$646$		0			0
$647$	4.55891	−	7.89626i	0.179229	−	0.310434i	−0.762388	−	0.647121i	$-0.775973\pi$
$647$	4.55891	−	7.89626i	0.179229	−	0.310434i	0.941617	+	0.336687i	$0.109306\pi$
$648$		0			0
$649$	−8.79054	−	15.2257i	−0.345059	−	0.597660i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−18.8716	+	10.8955i	−0.738502	+	0.426374i	−0.821524	−	0.570174i	$-0.806876\pi$
$653$	−18.8716	+	10.8955i	−0.738502	+	0.426374i	0.0830227	+	0.996548i	$0.473543\pi$
$654$		0			0
$655$	−10.9615	+	18.9859i	−0.428301	+	0.741840i
$656$		0			0
$657$	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	$-0.000946600\pi$
$660$		0			0
$661$	24.6004	+	14.2031i	0.956845	+	0.552435i	0.895201	−	0.445663i	$-0.147032\pi$
$661$	24.6004	+	14.2031i	0.956845	+	0.552435i	0.0616446	+	0.998098i	$0.480365\pi$
$662$		0			0
$663$	−4.00667	−	6.93975i	−0.155606	−	0.269518i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.771750	−	0.445570i	0.0298823	−	0.0172525i
$668$		0			0
$669$	−37.3166	−	21.5447i	−1.44274	−	0.832968i
$670$		0			0
$671$	−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	$0.331119\pi$
$674$		0			0
$675$	0.305561	+	0.176415i	0.0117610	+	0.00679023i
$676$		0			0
$677$	4.00416	−	2.31180i	0.153892	−	0.0888498i	−0.421076	−	0.907025i	$-0.638348\pi$
$677$	4.00416	−	2.31180i	0.153892	−	0.0888498i	0.574969	+	0.818175i	$0.305014\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	16.2245	+	28.1017i	0.621725	+	1.07686i
$682$		0			0
$683$	−16.8469	−	9.72659i	−0.644631	−	0.372178i	0.141765	−	0.989900i	$-0.454722\pi$
$683$	−16.8469	−	9.72659i	−0.644631	−	0.372178i	−0.786396	+	0.617723i	$0.788055\pi$
$684$		0			0
$685$			13.9121i			0.531555i
$686$		0			0
$687$	42.2365			1.61142
$688$		0			0
$689$	7.45834	−	12.9182i	0.284140	−	0.492145i
$690$		0			0
$691$	15.0449	−	8.68618i	0.572335	−	0.330438i	−0.185746	−	0.982598i	$-0.559470\pi$
$691$	15.0449	−	8.68618i	0.572335	−	0.330438i	0.758081	+	0.652160i	$0.226137\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.25951	+	2.18154i	0.0477760	+	0.0827504i
$696$		0			0
$697$	−4.00667	+	6.93975i	−0.151763	+	0.262862i
$698$		0			0
$699$			61.2003i			2.31481i
$700$		0			0
$701$			25.1180i			0.948695i	0.880338	+	0.474348i	$0.157316\pi$
$701$			25.1180i			0.948695i	−0.880338	+	0.474348i	$0.842684\pi$
$702$		0			0
$703$	−9.32640	+	16.1538i	−0.351752	+	0.609252i
$704$		0			0
$705$	20.0434	+	34.7162i	0.754878	+	1.30749i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−17.4147	+	10.0544i	−0.654024	+	0.377601i	−0.789996	−	0.613112i	$-0.789918\pi$
$709$	−17.4147	+	10.0544i	−0.654024	+	0.377601i	0.135972	+	0.990713i	$0.456584\pi$
$710$		0			0
$711$	−13.2839	+	23.0084i	−0.498184	+	0.862881i
$712$		0			0
$713$	−5.10275			−0.191099
$714$		0			0
$715$			19.3941i			0.725297i
$716$		0			0
$717$	−28.3857	−	16.3885i	−1.06008	−	0.612039i
$718$		0			0
$719$	19.1966	+	33.2496i	0.715914	+	1.24000i	0.962606	+	0.270906i	$0.0873231\pi$
$719$	19.1966	+	33.2496i	0.715914	+	1.24000i	−0.246692	+	0.969094i	$0.579344\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	47.3873	−	27.3590i	1.76235	−	1.01749i
$724$		0			0
$725$	−1.54350	−	0.891141i	−0.0573242	−	0.0330961i
$726$		0			0
$727$	14.8679			0.551422			0.275711	−	0.961241i	$-0.411087\pi$
$727$	14.8679			0.551422			0.275711	+	0.961241i	$0.411087\pi$
$728$		0			0
$729$	27.9167			1.03395
$730$		0			0
$731$	1.11696	+	0.644877i	0.0413122	+	0.0238516i
$732$		0			0
$733$	−36.4503	+	21.0446i	−1.34632	+	0.777300i	−0.987727	−	0.156192i	$-0.950078\pi$
$733$	−36.4503	+	21.0446i	−1.34632	+	0.777300i	−0.358597	+	0.933492i	$0.616745\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.29186	−	2.23757i	−0.0475864	−	0.0824221i
$738$		0			0
$739$	10.9859	+	6.34270i	0.404122	+	0.233320i	0.688261	−	0.725463i	$-0.258374\pi$
$739$	10.9859	+	6.34270i	0.404122	+	0.233320i	−0.284139	+	0.958783i	$0.591708\pi$
$740$		0			0
$741$			19.7124i			0.724154i
$742$		0			0
$743$	25.7219			0.943644			0.471822	−	0.881694i	$-0.343596\pi$
$743$	25.7219			0.943644			0.471822	+	0.881694i	$0.343596\pi$
$744$		0			0
$745$	2.73917	−	4.74438i	0.100355	−	0.173821i
$746$		0			0
$747$	7.85360	−	4.53428i	0.287348	−	0.165901i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	17.9305	+	31.0565i	0.654292	+	1.13327i	0.982071	+	0.188513i	$0.0603667\pi$
$751$	17.9305	+	31.0565i	0.654292	+	1.13327i	−0.327779	+	0.944755i	$0.606300\pi$
$752$		0			0
$753$	33.7489	−	58.4548i	1.22988	−	2.13021i
$754$		0			0
$755$		−	21.2157i		−	0.772117i
$756$		0			0
$757$		−	30.7289i		−	1.11686i	−0.829551	−	0.558431i	$-0.811403\pi$
$757$		−	30.7289i		−	1.11686i	0.829551	−	0.558431i	$-0.188597\pi$
$758$		0			0
$759$	8.66429	−	15.0070i	0.314494	−	0.544719i
$760$		0			0
$761$	22.5624	+	39.0792i	0.817887	+	1.41662i	0.907236	+	0.420621i	$0.138188\pi$
$761$	22.5624	+	39.0792i	0.817887	+	1.41662i	−0.0893497	+	0.996000i	$0.528479\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−4.94585	+	2.85549i	−0.178818	+	0.103240i
$766$		0			0
$767$	−4.50535	+	7.80349i	−0.162679	+	0.281768i
$768$		0			0
$769$	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
$772$		0			0
$773$	−29.9953	−	17.3178i	−1.07886	−	0.622878i	−0.148268	−	0.988947i	$-0.547370\pi$
$773$	−29.9953	−	17.3178i	−1.07886	−	0.622878i	−0.930588	+	0.366069i	$0.880703\pi$
$774$		0			0
$775$	5.10275	+	8.83822i	0.183296	+	0.317478i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	17.0715	−	9.85621i	0.611649	−	0.353136i
$780$		0			0
$781$	−32.3992	−	18.7057i	−1.15933	−	0.669341i
$782$		0			0
$783$	0.0806779			0.00288319
$784$		0			0
$785$	−19.1515			−0.683546
$786$		0			0
$787$	−29.6763	−	17.1336i	−1.05784	−	0.610747i	−0.133009	−	0.991115i	$-0.542464\pi$
$787$	−29.6763	−	17.1336i	−1.05784	−	0.610747i	−0.924835	+	0.380368i	$0.875797\pi$
$788$		0			0
$789$	23.1720	−	13.3784i	0.824944	−	0.476282i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	16.6665	+	28.8672i	0.591844	+	1.02510i
$794$		0			0
$795$	−18.2582	−	10.5414i	−0.647552	−	0.373865i
$796$		0			0
$797$			20.5838i			0.729114i	0.931181	+	0.364557i	$0.118780\pi$
$797$			20.5838i			0.729114i	−0.931181	+	0.364557i	$0.881220\pi$
$798$		0			0
$799$	13.8122			0.488641
$800$		0			0
$801$	3.94196	−	6.82767i	0.139282	−	0.241244i
$802$		0			0
$803$	−43.2416	+	24.9655i	−1.52596	+	0.881014i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−29.5252	−	51.1392i	−1.03934	−	1.80019i
$808$		0			0
$809$	23.4504	−	40.6172i	0.824471	−	1.42802i	−0.0778526	−	0.996965i	$-0.524806\pi$
$809$	23.4504	−	40.6172i	0.824471	−	1.42802i	0.902323	−	0.431060i	$-0.141860\pi$
$810$		0			0
$811$		−	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
$814$		0			0
$815$	2.40076	−	4.15823i	0.0840948	−	0.145656i
$816$		0			0
$817$	−1.58637	−	2.74767i	−0.0554999	−	0.0961287i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−28.4062	+	16.4003i	−0.991384	+	0.572376i	−0.905688	−	0.423945i	$-0.860645\pi$
$821$	−28.4062	+	16.4003i	−0.991384	+	0.572376i	−0.0856966	+	0.996321i	$0.527312\pi$
$822$		0			0
$823$	−6.88576	+	11.9265i	−0.240023	+	0.415731i	−0.960720	−	0.277518i	$-0.910488\pi$
$823$	−6.88576	+	11.9265i	−0.240023	+	0.415731i	0.720698	+	0.693249i	$0.243822\pi$
$824$		0			0
$825$	−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	$-0.125215\pi$
$828$		0			0
$829$	−4.74751	−	2.74098i	−0.164888	−	0.0951980i	0.415285	−	0.909691i	$-0.363682\pi$
$829$	−4.74751	−	2.74098i	−0.164888	−	0.0951980i	−0.580173	+	0.814493i	$0.697015\pi$
$830$		0			0
$831$	34.4402	+	59.6522i	1.19472	+	2.06931i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	18.0793	−	10.4381i	0.625659	−	0.361224i
$836$		0			0
$837$	−0.400076	−	0.230984i	−0.0138287	−	0.00798398i
$838$		0			0
$839$	28.7512			0.992601			0.496301	−	0.868151i	$-0.334691\pi$
$839$	28.7512			0.992601			0.496301	+	0.868151i	$0.334691\pi$
$840$		0			0
$841$	28.5925			0.985947
$842$		0			0
$843$	35.6012	+	20.5544i	1.22617	+	0.707930i
$844$		0			0
$845$	−8.12145	+	4.68892i	−0.279387	+	0.161304i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−34.2556	−	59.3324i	−1.17565	−	2.03628i
$850$		0			0
$851$	−7.27797	−	4.20194i	−0.249486	−	0.144041i
$852$		0			0
$853$		−	21.7605i		−	0.745064i	−0.928019	−	0.372532i	$-0.878490\pi$
$853$		−	21.7605i		−	0.745064i	0.928019	−	0.372532i	$-0.121510\pi$
$854$		0			0
$855$	14.0487			0.480457
$856$		0			0
$857$	5.89593	−	10.2121i	0.201401	−	0.348837i	−0.747579	−	0.664173i	$-0.768784\pi$
$857$	5.89593	−	10.2121i	0.201401	−	0.348837i	0.948980	+	0.315336i	$0.102117\pi$
$858$		0			0
$859$	4.15132	−	2.39676i	0.141641	−	0.0817766i	−0.427505	−	0.904013i	$-0.640607\pi$
$859$	4.15132	−	2.39676i	0.141641	−	0.0817766i	0.569146	+	0.822237i	$0.307274\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.0628642	−	0.108884i	−0.00213992	−	0.00370646i	0.864953	−	0.501852i	$-0.167348\pi$
$863$	−0.0628642	−	0.108884i	−0.00213992	−	0.00370646i	−0.867093	+	0.498146i	$0.834014\pi$
$864$		0			0
$865$	−4.85823	+	8.41471i	−0.165185	+	0.286109i
$866$		0			0
$867$		−	37.9168i		−	1.28772i
$868$		0			0
$869$		−	43.9371i		−	1.49046i
$870$		0			0
$871$	−0.662108	+	1.14681i	−0.0224347	+	0.0388580i
$872$		0			0
$873$	2.39593	+	4.14988i	0.0810900	+	0.140452i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	25.9534	−	14.9842i	0.876385	−	0.505981i	0.00692013	−	0.999976i	$-0.497797\pi$
$877$	25.9534	−	14.9842i	0.876385	−	0.505981i	0.869465	+	0.493995i	$0.164464\pi$
$878$		0			0
$879$	24.8273	−	43.0021i	0.837403	−	1.45042i
$880$		0			0
$881$	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	$-0.260150\pi$
$884$		0			0
$885$	11.0292	+	6.36772i	0.370743	+	0.214048i
$886$		0			0
$887$	−7.56821	−	13.1085i	−0.254116	−	0.440141i	0.710539	−	0.703658i	$-0.248451\pi$
$887$	−7.56821	−	13.1085i	−0.254116	−	0.440141i	−0.964655	+	0.263516i	$0.915118\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−38.6468	+	22.3128i	−1.29472	+	0.747505i
$892$		0			0
$893$	−29.4253	−	16.9887i	−0.984680	−	0.568505i
$894$		0			0
$895$	−0.187796			−0.00627731
$896$		0			0
$897$	−8.88128			−0.296537
$898$		0			0
$899$	2.02094	+	1.16679i	0.0674020	+	0.0389146i
$900$		0			0
$901$	−6.29101	+	3.63212i	−0.209584	+	0.121003i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.02034	−	3.49933i	−0.0671584	−	0.116322i
$906$		0			0
$907$	−27.4761	−	15.8633i	−0.912328	−	0.526733i	−0.0311488	−	0.999515i	$-0.509917\pi$
$907$	−27.4761	−	15.8633i	−0.912328	−	0.526733i	−0.881180	+	0.472782i	$0.843250\pi$
$908$		0			0
$909$		−	0.638384i		−	0.0211739i
$910$		0			0
$911$	−29.4757			−0.976574			−0.488287	−	0.872683i	$-0.662378\pi$
$911$	−29.4757			−0.976574			−0.488287	+	0.872683i	$0.662378\pi$
$912$		0			0
$913$	−7.49868	+	12.9881i	−0.248170	+	0.429843i
$914$		0			0
$915$	40.8000	−	23.5559i	1.34881	−	0.778734i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	8.85875	+	15.3438i	0.292223	+	0.506146i	0.974335	−	0.225102i	$-0.0722716\pi$
$919$	8.85875	+	15.3438i	0.292223	+	0.506146i	−0.682112	+	0.731248i	$0.738938\pi$
$920$		0			0
$921$	−21.9974	+	38.1005i	−0.724838	+	1.25546i
$922$		0			0
$923$			19.1741i			0.631124i
$924$		0			0
$925$			16.8077i			0.552635i
$926$		0			0
$927$	10.4920	−	18.1727i	0.344603	−	0.596870i
$928$		0			0
$929$	26.6338	+	46.1311i	0.873826	+	1.51351i	0.858008	+	0.513636i	$0.171702\pi$
$929$	26.6338	+	46.1311i	0.873826	+	1.51351i	0.0158180	+	0.999875i	$0.494965\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−3.04929	+	1.76051i	−0.0998293	+	0.0576365i
$934$		0			0
$935$	4.72233	−	8.17932i	0.154437	−	0.267492i
$936$		0			0
$937$	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
$940$		0			0
$941$	8.31195	+	4.79890i	0.270962	+	0.156440i	0.629325	−	0.777143i	$-0.283332\pi$
$941$	8.31195	+	4.79890i	0.270962	+	0.156440i	−0.358363	+	0.933582i	$0.616665\pi$
$942$		0			0
$943$	4.44064	+	7.69141i	0.144607	+	0.250467i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.3314	−	8.27425i	0.465709	−	0.268877i	−0.248733	−	0.968572i	$-0.580014\pi$
$947$	14.3314	−	8.27425i	0.465709	−	0.268877i	0.714442	+	0.699695i	$0.246681\pi$
$948$		0			0
$949$	22.1622	+	12.7954i	0.719417	+	0.415356i
$950$		0			0
$951$	−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	$0.468555\pi$
$954$		0			0
$955$	3.14943	+	1.81832i	0.101913	+	0.0588396i
$956$		0			0
$957$	−6.86296	+	3.96233i	−0.221848	+	0.128084i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	8.81887	+	15.2747i	0.284480	+	0.492733i
$962$		0			0
$963$	34.1899	+	19.7396i	1.10176	+	0.636099i
$964$		0			0
$965$		−	5.86758i		−	0.188884i
$966$		0			0
$967$	−21.5430			−0.692778			−0.346389	−	0.938091i	$-0.612592\pi$
$967$	−21.5430			−0.692778			−0.346389	+	0.938091i	$0.612592\pi$
$968$		0			0
$969$	4.79985	−	8.31358i	0.154193	−	0.267071i
$970$		0			0
$971$	2.27385	−	1.31281i	0.0729715	−	0.0421301i	−0.463070	−	0.886322i	$-0.653252\pi$
$971$	2.27385	−	1.31281i	0.0729715	−	0.0421301i	0.536042	+	0.844191i	$0.319919\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	8.88128	+	15.3828i	0.284429	+	0.492645i
$976$		0			0
$977$	17.2338	−	29.8499i	0.551359	−	0.954982i	−0.446818	−	0.894625i	$-0.647443\pi$
$977$	17.2338	−	29.8499i	0.551359	−	0.954982i	0.998177	−	0.0603567i	$-0.0192238\pi$
$978$		0			0
$979$			13.0382i			0.416704i
$980$		0			0
$981$			58.6403i			1.87224i
$982$		0			0
$983$	−26.2210	+	45.4161i	−0.836320	+	1.44855i	0.0566303	+	0.998395i	$0.481964\pi$
$983$	−26.2210	+	45.4161i	−0.836320	+	1.44855i	−0.892951	+	0.450154i	$0.851369\pi$
$984$		0			0
$985$	−14.5230	−	25.1547i	−0.462743	−	0.801494i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.23794	−	0.714725i	0.0393642	−	0.0227269i
$990$		0			0
$991$	−8.08057	+	13.9960i	−0.256688	+	0.444596i	−0.965353	−	0.260949i	$-0.915964\pi$
$991$	−8.08057	+	13.9960i	−0.256688	+	0.444596i	0.708665	+	0.705545i	$0.249298\pi$
$992$		0			0
$993$	−58.6325			−1.86064
$994$		0			0
$995$		−	30.9028i		−	0.979684i
$996$		0			0
$997$	−34.0954	−	19.6850i	−1.07981	−	0.623430i	−0.148967	−	0.988842i	$-0.547595\pi$
$997$	−34.0954	−	19.6850i	−1.07981	−	0.623430i	−0.930846	+	0.365412i	$0.880928\pi$
$998$		0			0
$999$	−0.380415	−	0.658898i	−0.0120358	−	0.0208466i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.2	✓	12	28.19	even	6
56.2.p.a.37.4	yes	12	56.19	even	6
56.2.p.a.53.2	yes	12	56.27	even	2
56.2.p.a.53.4	yes	12	28.27	even	2
224.2.t.a.81.1		12	56.13	odd	2
224.2.t.a.81.6		12	7.6	odd	2
224.2.t.a.177.1		12	7.5	odd	6
224.2.t.a.177.6		12	56.5	odd	6
392.2.b.e.197.5		6	56.3	even	6
392.2.b.e.197.6		6	28.3	even	6
392.2.b.f.197.5		6	56.11	odd	6
392.2.b.f.197.6		6	28.11	odd	6
392.2.p.g.165.2		12	8.3	odd	2
392.2.p.g.165.4		12	4.3	odd	2
392.2.p.g.373.2		12	28.23	odd	6
392.2.p.g.373.4		12	56.51	odd	6
504.2.cj.c.37.3		12	168.131	odd	6
504.2.cj.c.37.5		12	84.47	odd	6
504.2.cj.c.109.3		12	84.83	odd	2
504.2.cj.c.109.5		12	168.83	odd	2
1568.2.b.e.785.1		6	56.53	even	6
1568.2.b.e.785.6		6	7.4	even	3
1568.2.b.f.785.1		6	7.3	odd	6
1568.2.b.f.785.6		6	56.45	odd	6
1568.2.t.g.177.1		12	56.37	even	6	inner
1568.2.t.g.177.6		12	7.2	even	3	inner
1568.2.t.g.753.1		12	1.1	even	1	trivial
1568.2.t.g.753.6		12	8.5	even	2	inner
2016.2.cr.c.1297.2		12	168.5	even	6
2016.2.cr.c.1297.5		12	21.5	even	6
2016.2.cr.c.1873.2		12	21.20	even	2
2016.2.cr.c.1873.5		12	168.125	even	2

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:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1568.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.13038 - 1.22998i) q^{3} +(-1.28690 + 0.742990i) q^{5} +(1.52569 + 2.64257i) q^{9} +(-4.37021 - 2.52314i) q^{11} +2.58633i q^{13} +3.65544 q^{15} +(0.629755 - 1.09077i) q^{17} +(-2.68324 + 1.54917i) q^{19} +(-0.697966 - 1.20891i) q^{23} +(-1.39593 + 2.41782i) q^{25} -0.126378i q^{27} +0.638384i q^{29} +(1.82772 - 3.16571i) q^{31} +(6.20682 + 10.7505i) q^{33} +(5.21370 - 3.01013i) q^{37} +(3.18113 - 5.50988i) q^{39} -6.36226 q^{41} +1.02401i q^{43} +(-3.92680 - 2.26714i) q^{45} +(5.48316 + 9.49712i) q^{47} +(-2.68324 + 1.54917i) q^{51} +(-4.99481 - 2.88375i) q^{53} +7.49868 q^{55} +7.62177 q^{57} +(3.01720 + 1.74198i) q^{59} +(11.1614 - 6.44406i) q^{61} +(-1.92162 - 3.32834i) q^{65} +(0.443410 + 0.256003i) q^{67} +3.43393i q^{69} +7.41363 q^{71} +(4.94731 - 8.56899i) q^{73} +(5.94774 - 3.43393i) q^{75} +(4.35341 + 7.54032i) q^{79} +(4.42162 - 7.65847i) q^{81} -2.97196i q^{83} +1.87161i q^{85} +(0.785198 - 1.36000i) q^{87} +(-1.29186 - 2.23757i) q^{89} +(-7.78749 + 4.49611i) q^{93} +(2.30203 - 3.98724i) q^{95} +1.57040 q^{97} -15.3981i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 20 q^{15} + 2 q^{17} - 2 q^{23} - 4 q^{25} + 10 q^{31} + 14 q^{33} - 4 q^{39} + 8 q^{41} + 30 q^{47} + 4 q^{55} - 4 q^{57} + 8 q^{65} - 32 q^{71} + 10 q^{73} + 22 q^{79} + 22 q^{81} - 20 q^{87} + 10 q^{89}+ \cdots - 40 q^{97}+O(q^{100}) \) 12 * q + 20 * q^15 + 2 * q^17 - 2 * q^23 - 4 * q^25 + 10 * q^31 + 14 * q^33 - 4 * q^39 + 8 * q^41 + 30 * q^47 + 4 * q^55 - 4 * q^57 + 8 * q^65 - 32 * q^71 + 10 * q^73 + 22 * q^79 + 22 * q^81 - 20 * q^87 + 10 * q^89 + 34 * q^95 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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