LMFDB - Embedded newform 224.2.t.a.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(81,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("224.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.78864900528$
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:	$\Z[a_1, \ldots, a_{7}]$
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			177.1
Root			$1.41417 + 0.0105323i$ of defining polynomial
Character	$\chi$	$=$	224.177
Dual form			224.2.t.a.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13038 + 1.22998i) q^{3} +(-1.28690 - 0.742990i) q^{5} +(-0.129755 - 2.64257i) q^{7} +(1.52569 - 2.64257i) q^{9} +O(q^{10})$	\(q+(-2.13038 + 1.22998i) q^{3} +(-1.28690 - 0.742990i) q^{5} +(-0.129755 - 2.64257i) q^{7} +(1.52569 - 2.64257i) q^{9} +(4.37021 - 2.52314i) q^{11} -2.58633i q^{13} +3.65544 q^{15} +(-0.629755 - 1.09077i) q^{17} +(-2.68324 - 1.54917i) q^{19} +(3.52673 + 5.47008i) q^{21} +(-0.697966 + 1.20891i) q^{23} +(-1.39593 - 2.41782i) q^{25} +0.126378i q^{27} +0.638384i q^{29} +(-1.82772 - 3.16571i) q^{31} +(-6.20682 + 10.7505i) q^{33} +(-1.79642 + 3.49712i) q^{35} +(-5.21370 - 3.01013i) q^{37} +(3.18113 + 5.50988i) q^{39} +6.36226 q^{41} +1.02401i q^{43} +(-3.92680 + 2.26714i) q^{45} +(-5.48316 + 9.49712i) q^{47} +(-6.96633 + 0.685774i) q^{49} +(2.68324 + 1.54917i) q^{51} +(4.99481 - 2.88375i) q^{53} -7.49868 q^{55} +7.62177 q^{57} +(3.01720 - 1.74198i) q^{59} +(11.1614 + 6.44406i) q^{61} +(-7.18113 - 3.68884i) q^{63} +(-1.92162 + 3.32834i) q^{65} +(-0.443410 + 0.256003i) q^{67} -3.43393i q^{69} +7.41363 q^{71} +(-4.94731 - 8.56899i) q^{73} +(5.94774 + 3.43393i) q^{75} +(-7.23463 - 11.2212i) q^{77} +(4.35341 - 7.54032i) q^{79} +(4.42162 + 7.65847i) q^{81} +2.97196i q^{83} +1.87161i q^{85} +(-0.785198 - 1.36000i) q^{87} +(1.29186 - 2.23757i) q^{89} +(-6.83456 + 0.335590i) q^{91} +(7.78749 + 4.49611i) q^{93} +(2.30203 + 3.98724i) q^{95} -1.57040 q^{97} -15.3981i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{7}+O(q^{10}) $ 12 * q + 4 * q^7	$ 12 q + 4 q^{7} + 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} - 12 q^{49} - 4 q^{55} - 4 q^{57} - 44 q^{63} + 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}+O(q^{100}) $ 12 * q + 4 * q^7 + 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 - 12 * q^49 - 4 * q^55 - 4 * q^57 - 44 * q^63 + 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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.13038	+	1.22998i	−1.22998	+	0.710128i	−0.967025	−	0.254681i	$-0.918029\pi$
$3$	−2.13038	+	1.22998i	−1.22998	+	0.710128i	−0.262952	+	0.964809i	$0.584696\pi$
$4$		0			0
$5$	−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	$0.774483\pi$
$6$		0			0
$7$	−0.129755	−	2.64257i	−0.0490429	−	0.998797i
$7$	−0.129755	−	2.64257i	−0.0490429	−	0.998797i
$8$		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	$-0.391495\pi$
$11$	4.37021	−	2.52314i	1.31767	−	0.760756i	0.983353	+	0.181705i	$0.0581616\pi$
$12$		0			0
$13$		−	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
$16$		0			0
$17$	−0.629755	−	1.09077i	−0.152738	−	0.264550i	0.779495	−	0.626408i	$-0.215476\pi$
$17$	−0.629755	−	1.09077i	−0.152738	−	0.264550i	−0.932233	+	0.361858i	$0.882142\pi$
$18$		0			0
$19$	−2.68324	−	1.54917i	−0.615577	−	0.355404i	0.159568	−	0.987187i	$-0.448990\pi$
$19$	−2.68324	−	1.54917i	−0.615577	−	0.355404i	−0.775145	+	0.631783i	$0.782323\pi$
$20$		0			0
$21$	3.52673	+	5.47008i	0.769595	+	1.19367i
$22$		0			0
$23$	−0.697966	+	1.20891i	−0.145536	+	0.252076i	−0.929573	−	0.368639i	$-0.879824\pi$
$23$	−0.697966	+	1.20891i	−0.145536	+	0.252076i	0.784037	+	0.620714i	$0.213157\pi$
$24$		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	$-0.273132\pi$
$31$	−1.82772	−	3.16571i	−0.328268	−	0.568578i	−0.982168	+	0.188003i	$0.939798\pi$
$32$		0			0
$33$	−6.20682	+	10.7505i	−1.08047	+	1.87143i
$34$		0			0
$35$	−1.79642	+	3.49712i	−0.303650	+	0.591121i
$36$		0			0
$37$	−5.21370	−	3.01013i	−0.857127	−	0.494862i	0.00592229	−	0.999982i	$-0.498115\pi$
$37$	−5.21370	−	3.01013i	−0.857127	−	0.494862i	−0.863049	+	0.505120i	$0.831448\pi$
$38$		0			0
$39$	3.18113	+	5.50988i	0.509388	+	0.882287i
$40$		0			0
$41$	6.36226			0.993618			0.496809	−	0.867860i	$-0.334505\pi$
$41$	6.36226			0.993618			0.496809	+	0.867860i	$0.334505\pi$
$42$		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	0.119943	+	0.992781i	$0.461729\pi$
$47$	−5.48316	+	9.49712i	−0.799802	+	1.38530i	−0.919745	+	0.392516i	$0.871605\pi$
$48$		0			0
$49$	−6.96633	+	0.685774i	−0.995190	+	0.0979677i
$50$		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	$-0.537025\pi$
$53$	4.99481	−	2.88375i	0.686089	−	0.396114i	0.802145	+	0.597129i	$0.203692\pi$
$54$		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	−0.290569	−	0.956854i	$-0.593845\pi$
$59$	3.01720	−	1.74198i	0.392806	−	0.226787i	0.683375	+	0.730067i	$0.260511\pi$
$60$		0			0
$61$	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	$0.357798\pi$
$62$		0			0
$63$	−7.18113	−	3.68884i	−0.904737	−	0.464751i
$64$		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	$-0.676624\pi$
$67$	−0.443410	+	0.256003i	−0.0541711	+	0.0312757i	0.472670	+	0.881240i	$0.343290\pi$
$68$		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	−0.995590	−	0.0938118i	$-0.970095\pi$
$73$	−4.94731	−	8.56899i	−0.579038	−	1.00292i	0.416552	−	0.909112i	$-0.363239\pi$
$74$		0			0
$75$	5.94774	+	3.43393i	0.686786	+	0.396516i
$76$		0			0
$77$	−7.23463	−	11.2212i	−0.824463	−	1.27877i
$78$		0			0
$79$	4.35341	−	7.54032i	0.489797	−	0.848353i	−0.510134	−	0.860095i	$-0.670404\pi$
$79$	4.35341	−	7.54032i	0.489797	−	0.848353i	0.999931	+	0.0117420i	$0.00373767\pi$
$80$		0			0
$81$	4.42162	+	7.65847i	0.491291	+	0.850941i
$82$		0			0
$83$			2.97196i			0.326215i	0.986608	+	0.163107i	$0.0521517\pi$
$83$			2.97196i			0.326215i	−0.986608	+	0.163107i	$0.947848\pi$
$84$		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	$-0.789607\pi$
$89$	1.29186	−	2.23757i	0.136937	−	0.237182i	0.926336	+	0.376699i	$0.122941\pi$
$90$		0			0
$91$	−6.83456	+	0.335590i	−0.716456	+	0.0351794i
$92$		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	$-0.525404\pi$
$97$	−1.57040			−0.159449			−0.0797247	+	0.996817i	$0.525404\pi$
$98$		0			0
$99$		−	15.3981i		−	1.54757i
$100$		0			0
$101$	−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	$0.336647\pi$
$102$		0			0
$103$	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	$0.0566453\pi$
$104$		0			0
$105$	−0.474313	−	9.65975i	−0.0462882	−	0.942695i
$106$		0			0
$107$	−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			0
$109$	−16.6430	+	9.60883i	−1.59411	+	0.920359i	−0.601517	+	0.798860i	$0.705437\pi$
$109$	−16.6430	+	9.60883i	−1.59411	+	0.920359i	−0.992591	+	0.121500i	$0.961230\pi$
$110$		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
$119$	−2.80071	+	1.80570i	−0.256741	+	0.165529i
$120$		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	0.940455	−	0.339919i	$-0.110400\pi$
$131$	12.7767	+	7.37662i	1.11630	+	0.644498i	0.175849	+	0.984417i	$0.443733\pi$
$132$		0			0
$133$	−3.74562	+	7.29165i	−0.324786	+	0.632267i
$134$		0			0
$135$	0.0938978	−	0.162636i	0.00808144	−	0.0139975i
$136$		0			0
$137$	4.68113	+	8.10795i	0.399936	+	0.692709i	0.993718	−	0.111917i	$-0.0356991\pi$
$137$	4.68113	+	8.10795i	0.399936	+	0.692709i	−0.593782	+	0.804626i	$0.702366\pi$
$138$		0			0
$139$			1.69519i			0.143784i	0.997412	+	0.0718921i	$0.0229037\pi$
$139$			1.69519i			0.143784i	−0.997412	+	0.0718921i	$0.977096\pi$
$140$		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
$147$	13.9975	−	10.0294i	1.15449	−	0.827210i
$148$		0			0
$149$	3.19276	+	1.84334i	0.261561	+	0.151012i	0.625047	−	0.780587i	$-0.285080\pi$
$149$	3.19276	+	1.84334i	0.261561	+	0.151012i	−0.363485	+	0.931600i	$0.618413\pi$
$150$		0			0
$151$	−7.13861	−	12.3644i	−0.580932	−	1.00620i	−0.995369	−	0.0961252i	$-0.969355\pi$
$151$	−7.13861	−	12.3644i	−0.580932	−	1.00620i	0.414438	−	0.910078i	$-0.363978\pi$
$152$		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	0.0165822	−	0.999863i	$-0.494721\pi$
$157$	11.1614	−	6.44406i	0.890780	−	0.514292i	0.874197	+	0.485571i	$0.161388\pi$
$158$		0			0
$159$	−7.09390	+	12.2870i	−0.562583	+	0.974422i
$160$		0			0
$161$	3.28520	+	1.68756i	0.258910	+	0.132998i
$162$		0			0
$163$	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	$0.626278\pi$
$164$		0			0
$165$	15.9751	−	9.22320i	1.24366	−	0.718026i
$166$		0			0
$167$	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
$170$		0			0
$171$	−8.18757	+	4.72709i	−0.626119	+	0.361490i
$172$		0			0
$173$	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	$0.586707\pi$
$174$		0			0
$175$	−6.20814	+	4.00257i	−0.469291	+	0.302566i
$176$		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	$-0.668170\pi$
$179$	−0.109447	+	0.0631891i	−0.00818044	+	0.00472298i	0.495904	+	0.868377i	$0.334837\pi$
$180$		0			0
$181$		−	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
$184$		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
$189$	0.333963	−	0.0163982i	0.0242922	−	0.00119280i
$190$		0			0
$191$	−1.22365	+	2.11943i	−0.0885404	+	0.153357i	−0.906894	−	0.421358i	$-0.861554\pi$
$191$	−1.22365	+	2.11943i	−0.0885404	+	0.153357i	0.818354	+	0.574715i	$0.194887\pi$
$192$		0			0
$193$	−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			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	0.953795	+	0.300460i	$0.0971401\pi$
$199$	10.3981	+	18.0101i	0.737103	+	1.27670i	−0.216692	+	0.976240i	$0.569527\pi$
$200$		0			0
$201$	0.629755	−	1.09077i	0.0444195	−	0.0769369i
$202$		0			0
$203$	1.68697	−	0.0828337i	0.118402	−	0.00581378i
$204$		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
$217$	−8.12844	+	5.24064i	−0.551794	+	0.355758i
$218$		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	$-0.699491\pi$
$223$	−17.5164			−1.17298			−0.586492	+	0.809955i	$0.699491\pi$
$224$		0			0
$225$	−8.51902			−0.567935
$226$		0			0
$227$	−11.4237	+	6.59546i	−0.758215	+	0.437756i	−0.828655	−	0.559760i	$-0.810893\pi$
$227$	−11.4237	+	6.59546i	−0.758215	+	0.437756i	0.0704394	+	0.997516i	$0.477560\pi$
$228$		0			0
$229$	−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	$0.858679\pi$
$230$		0			0
$231$	29.2143	+	15.0070i	1.92216	+	0.987388i
$232$		0			0
$233$	−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	$0.863444\pi$
$234$		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	0.962411	+	0.271598i	$0.0875521\pi$
$241$	11.1218	+	19.2635i	0.716416	+	1.24087i	−0.245995	+	0.969271i	$0.579115\pi$
$242$		0			0
$243$	−19.1678	−	11.0665i	−1.22962	−	0.709919i
$244$		0			0
$245$	9.47446	+	4.29339i	0.605301	+	0.274295i
$246$		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	$-0.666711\pi$
$251$		−	27.4386i		−	1.73191i	0.500121	−	0.865955i	$-0.333289\pi$
$252$		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	−0.191196	−	0.981552i	$-0.561237\pi$
$257$	12.0948	−	20.9487i	0.754451	−	1.30675i	0.945647	−	0.325195i	$-0.105430\pi$
$258$		0			0
$259$	−7.27797	+	14.1681i	−0.452231	+	0.880365i
$260$		0			0
$261$	1.68697	+	0.973974i	0.104421	+	0.0602875i
$262$		0			0
$263$	−5.43846	−	9.41968i	−0.335350	−	0.580842i	0.648202	−	0.761468i	$-0.275521\pi$
$263$	−5.43846	−	9.41968i	−0.335350	−	0.580842i	−0.983552	+	0.180626i	$0.942188\pi$
$264$		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	0.292992	−	0.956115i	$-0.405349\pi$
$269$	20.7887	−	12.0024i	1.26751	−	0.731796i	0.974516	+	0.224319i	$0.0720156\pi$
$270$		0			0
$271$	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			0
$273$	14.1475	−	9.12129i	0.856243	−	0.552045i
$274$		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	$-0.348517\pi$
$277$	24.2493	−	14.0003i	1.45700	−	0.841199i	0.998863	+	0.0476832i	$0.0151838\pi$
$278$		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	0.436339	−	0.899782i	$-0.356275\pi$
$283$	24.1193	−	13.9253i	1.43374	−	0.827772i	0.997404	+	0.0720102i	$0.0229414\pi$
$284$		0			0
$285$	−9.80843	−	5.66290i	−0.581001	−	0.335441i
$286$		0			0
$287$	−0.825537	−	16.8127i	−0.0487299	−	0.992422i
$288$		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	$-0.799280\pi$
$293$		−	20.1851i		−	1.17923i	0.807685	−	0.589614i	$-0.200720\pi$
$294$		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
$301$	2.70602	−	0.132871i	0.155972	−	0.00765855i
$302$		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	$0.170487\pi$
$307$			17.8844i			1.02071i	−0.859962	+	0.510357i	$0.829513\pi$
$308$		0			0
$309$			16.9169i			0.962368i
$310$		0			0
$311$	−0.715667	−	1.23957i	−0.0405818	−	0.0702897i	0.845021	−	0.534733i	$-0.179588\pi$
$311$	−0.715667	−	1.23957i	−0.0405818	−	0.0702897i	−0.885603	+	0.464443i	$0.846254\pi$
$312$		0			0
$313$	−2.42829	+	4.20591i	−0.137255	+	0.237732i	−0.926457	−	0.376402i	$-0.877161\pi$
$313$	−2.42829	+	4.20591i	−0.137255	+	0.237732i	0.789202	+	0.614134i	$0.210495\pi$
$314$		0			0
$315$	6.50060	+	10.0827i	0.366267	+	0.568094i
$316$		0			0
$317$	−9.78002	−	5.64650i	−0.549301	−	0.317139i	0.199539	−	0.979890i	$-0.436056\pi$
$317$	−9.78002	−	5.64650i	−0.549301	−	0.317139i	−0.748840	+	0.662751i	$0.769389\pi$
$318$		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
$329$	25.8082	+	13.2573i	1.42285	+	0.730900i
$330$		0			0
$331$	−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	$0.894014\pi$
$332$		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
$343$	2.71612	+	18.3200i	0.146657	+	0.989187i
$344$		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	$-0.639136\pi$
$347$	2.78706	−	1.60911i	0.149617	−	0.0863817i	0.572940	+	0.819597i	$0.305803\pi$
$348$		0			0
$349$		−	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
$352$		0			0
$353$	−11.6608	−	20.1971i	−0.620641	−	1.07498i	−0.989367	−	0.145444i	$-0.953539\pi$
$353$	−11.6608	−	20.1971i	−0.620641	−	1.07498i	0.368725	−	0.929538i	$-0.379794\pi$
$354$		0			0
$355$	−9.54058	−	5.50826i	−0.506361	−	0.292348i
$356$		0			0
$357$	3.74562	−	7.29165i	0.198239	−	0.385915i
$358$		0			0
$359$	−2.55488	+	4.42518i	−0.134841	+	0.233552i	−0.925537	−	0.378658i	$-0.876386\pi$
$359$	−2.55488	+	4.42518i	−0.134841	+	0.233552i	0.790696	+	0.612210i	$0.209719\pi$
$360$		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	0.954784	+	0.297301i	$0.0960863\pi$
$367$	14.0779	+	24.3837i	0.734862	+	1.27282i	−0.219922	+	0.975517i	$0.570580\pi$
$368$		0			0
$369$	9.70682	−	16.8127i	0.505317	−	0.875234i
$370$		0			0
$371$	−8.26861	−	12.8249i	−0.429285	−	0.665837i
$372$		0			0
$373$	6.10052	+	3.52214i	0.315873	+	0.182369i	0.649551	−	0.760318i	$-0.274957\pi$
$373$	6.10052	+	3.52214i	0.315873	+	0.182369i	−0.333679	+	0.942687i	$0.608290\pi$
$374$		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	$-0.873541\pi$
$383$	−2.46546	+	4.27031i	−0.125979	+	0.218202i	0.796136	+	0.605118i	$0.206874\pi$
$384$		0			0
$385$	0.972993	+	19.8158i	0.0495883	+	1.00991i
$386$		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	$-0.864299\pi$
$389$	−19.8735	+	11.4739i	−1.00762	+	0.581752i	−0.0971291	+	0.995272i	$0.530966\pi$
$390$		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	0.980452	−	0.196760i	$-0.0630420\pi$
$397$	25.9079	+	14.9579i	1.30028	+	0.750716i	0.319827	+	0.947476i	$0.396375\pi$
$398$		0			0
$399$	−0.988965	−	20.1410i	−0.0495102	−	1.00831i
$400$		0			0
$401$	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	$0.0387012\pi$
$402$		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	0.984312	+	0.176436i	$0.0564568\pi$
$409$	13.0434	+	22.5918i	0.644954	+	1.11709i	−0.339358	+	0.940657i	$0.610210\pi$
$410$		0			0
$411$	−19.9452	−	11.5154i	−0.983824	−	0.568011i
$412$		0			0
$413$	−4.99481	−	7.74713i	−0.245778	−	0.381211i
$414$		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	$0.00196525\pi$
$419$			0.252757i			0.0123480i	−0.999981	+	0.00617398i	$0.998035\pi$
$420$		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
$427$	15.5806	−	30.3310i	0.753998	−	1.46782i
$428$		0			0
$429$	27.8044	+	16.0529i	1.34241	+	0.775041i
$430$		0			0
$431$	13.7223	+	23.7678i	0.660982	+	1.14485i	0.980358	+	0.197226i	$0.0631932\pi$
$431$	13.7223	+	23.7678i	0.660982	+	1.14485i	−0.319377	+	0.947628i	$0.603473\pi$
$432$		0			0
$433$	−7.26215			−0.348997			−0.174498	−	0.984657i	$-0.555830\pi$
$433$	−7.26215			−0.348997			−0.174498	+	0.984657i	$0.555830\pi$
$434$		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	−0.246551	−	0.969130i	$-0.579297\pi$
$439$	15.0022	−	25.9845i	0.716015	−	1.24017i	0.962567	−	0.271045i	$-0.0873692\pi$
$440$		0			0
$441$	−8.81623	+	19.4553i	−0.419821	+	0.926441i
$442$		0			0
$443$	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	$0.353028\pi$
$444$		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
$455$	9.04471	+	4.64614i	0.424022	+	0.217814i
$456$		0			0
$457$	−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	$0.267948\pi$
$458$		0			0
$459$	0.137849	−	0.0795874i	0.00643426	−	0.00371482i
$460$		0			0
$461$			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	$-0.337413\pi$
$463$	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	0.905147	−	0.425099i	$-0.139761\pi$
$467$	21.3849	+	12.3466i	0.989574	+	0.571331i	0.0844270	+	0.996430i	$0.473094\pi$
$468$		0			0
$469$	0.734040	+	1.13852i	0.0338948	+	0.0525721i
$470$		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	−0.775229	−	0.631680i	$-0.782366\pi$
$479$	−20.4562	−	35.4311i	−0.934666	−	1.61889i	−0.159437	−	0.987208i	$-0.550968\pi$
$480$		0			0
$481$	−7.78520	+	13.4844i	−0.354974	+	0.614834i
$482$		0			0
$483$	−9.07439	+	0.445570i	−0.412899	+	0.0202741i
$484$		0			0
$485$	2.02094	+	1.16679i	0.0917660	+	0.0529811i
$486$		0			0
$487$	8.76704	+	15.1850i	0.397273	+	0.688096i	0.993388	−	0.114802i	$-0.0366234\pi$
$487$	8.76704	+	15.1850i	0.397273	+	0.688096i	−0.596116	+	0.802898i	$0.703290\pi$
$488$		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
$497$	−0.961958	−	19.5910i	−0.0431497	−	0.878778i
$498$		0			0
$499$	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	$0.593449\pi$
$500$		0			0
$501$	−29.9292	+	17.2796i	−1.33714	+	0.771997i
$502$		0			0
$503$	−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
$506$		0			0
$507$	−13.4446	+	7.76224i	−0.597096	+	0.344733i
$508$		0			0
$509$	−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	$0.832368\pi$
$510$		0			0
$511$	−22.0022	+	14.1855i	−0.973319	+	0.627528i
$512$		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	$-0.0944373\pi$
$521$	5.13510	+	8.89426i	0.224973	+	0.389664i	−0.731338	+	0.682015i	$0.761104\pi$
$522$		0			0
$523$	15.4655	+	8.92903i	0.676261	+	0.390439i	0.798445	−	0.602068i	$-0.205656\pi$
$523$	15.4655	+	8.92903i	0.676261	+	0.390439i	−0.122184	+	0.992507i	$0.538990\pi$
$524$		0			0
$525$	8.30264	−	16.1629i	0.362357	−	0.705406i
$526$		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
$539$	−28.7140	+	20.5740i	−1.23680	+	0.886186i
$540$		0			0
$541$	−19.9303	−	11.5067i	−0.856869	−	0.494714i	0.00609356	−	0.999981i	$-0.498060\pi$
$541$	−19.9303	−	11.5067i	−0.856869	−	0.494714i	−0.862963	+	0.505268i	$0.831394\pi$
$542$		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
$553$	−20.4907	−	10.5258i	−0.871353	−	0.447602i
$554$		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	$-0.547057\pi$
$557$	15.0016	−	8.66116i	0.635637	−	0.366985i	0.782932	+	0.622107i	$0.213723\pi$
$558$		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	−0.347141	−	0.937813i	$-0.612848\pi$
$563$	6.91560	−	3.99272i	0.291458	−	0.168273i	0.638599	+	0.769540i	$0.279514\pi$
$564$		0			0
$565$	1.35301	+	0.781160i	0.0569215	+	0.0328637i
$566$		0			0
$567$	19.6643	−	12.6782i	0.825823	−	0.532432i
$568$		0			0
$569$	−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	$0.247399\pi$
$570$		0			0
$571$	−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	$0.982922\pi$
$572$		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	0.988924	+	0.148425i	$0.0474203\pi$
$577$	14.9650	+	25.9202i	0.623001	+	1.07907i	−0.365922	+	0.930645i	$0.619246\pi$
$578$		0			0
$579$	8.41208	+	4.85672i	0.349594	+	0.201838i
$580$		0			0
$581$	7.85360	−	0.385627i	0.325822	−	0.0159985i
$582$		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	$0.131308\pi$
$587$			19.4269i			0.801833i	−0.916115	+	0.400916i	$0.868692\pi$
$588$		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	$-0.711748\pi$
$593$	9.07706	−	15.7219i	0.372750	−	0.645622i	0.989988	+	0.141155i	$0.0450815\pi$
$594$		0			0
$595$	4.94585	−	0.242851i	0.202760	−	0.00995592i
$596$		0			0
$597$	−44.3039	−	25.5789i	−1.81324	−	1.04687i
$598$		0			0
$599$	5.59258	+	9.68663i	0.228507	+	0.395785i	0.957366	−	0.288879i	$-0.0932824\pi$
$599$	5.59258	+	9.68663i	0.228507	+	0.395785i	−0.728859	+	0.684664i	$0.759949\pi$
$600$		0			0
$601$	−4.21883			−0.172090			−0.0860448	−	0.996291i	$-0.527423\pi$
$601$	−4.21883			−0.172090			−0.0860448	+	0.996291i	$0.527423\pi$
$602$		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	0.445269	+	0.895397i	$0.353108\pi$
$607$	−13.6196	+	23.5898i	−0.552802	+	0.957481i	−0.998071	+	0.0620841i	$0.980225\pi$
$608$		0			0
$609$	−3.49201	+	2.25141i	−0.141504	+	0.0912315i
$610$		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	$-0.690471\pi$
$613$	−3.20401	+	1.84984i	−0.129409	+	0.0747141i	0.433898	+	0.900962i	$0.357138\pi$
$614$		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	−0.940541	−	0.339681i	$-0.889681\pi$
$619$	−27.7816	+	16.0397i	−1.11664	+	0.644692i	−0.176098	+	0.984373i	$0.556348\pi$
$620$		0			0
$621$	−0.152780	−	0.0882077i	−0.00613086	−	0.00353965i
$622$		0			0
$623$	−6.08057	−	3.12350i	−0.243613	−	0.125140i
$624$		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
$637$	1.77364	+	18.0172i	0.0702742	+	0.713869i
$638$		0			0
$639$	11.3109	−	19.5910i	0.447452	−	0.775009i
$640$		0			0
$641$	−20.9136	−	36.2235i	−0.826039	−	1.43074i	−0.901123	−	0.433564i	$-0.857256\pi$
$641$	−20.9136	−	36.2235i	−0.826039	−	1.43074i	0.0750839	−	0.997177i	$-0.476078\pi$
$642$		0			0
$643$		−	42.9368i		−	1.69326i	−0.532180	−	0.846631i	$-0.678627\pi$
$643$		−	42.9368i		−	1.69326i	0.532180	−	0.846631i	$-0.321373\pi$
$644$		0			0
$645$			3.74321i			0.147389i
$646$		0			0
$647$	−4.55891	−	7.89626i	−0.179229	−	0.310434i	0.762388	−	0.647121i	$-0.224027\pi$
$647$	−4.55891	−	7.89626i	−0.179229	−	0.310434i	−0.941617	+	0.336687i	$0.890694\pi$
$648$		0			0
$649$	8.79054	−	15.2257i	0.345059	−	0.597660i
$650$		0			0
$651$	10.8708	−	21.1624i	0.426061	−	0.829419i
$652$		0			0
$653$	18.8716	+	10.8955i	0.738502	+	0.426374i	0.821524	−	0.570174i	$-0.193124\pi$
$653$	18.8716	+	10.8955i	0.738502	+	0.426374i	−0.0830227	+	0.996548i	$0.526457\pi$
$654$		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	0.0616446	−	0.998098i	$-0.480365\pi$
$661$	24.6004	−	14.2031i	0.956845	−	0.552435i	0.895201	+	0.445663i	$0.147032\pi$
$662$		0			0
$663$	4.00667	−	6.93975i	0.155606	−	0.269518i
$664$		0			0
$665$	10.2379	−	6.60065i	0.397007	−	0.255962i
$666$		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	0.574969	−	0.818175i	$-0.305014\pi$
$677$	4.00416	+	2.31180i	0.153892	+	0.0888498i	−0.421076	+	0.907025i	$0.638348\pi$
$678$		0			0
$679$	0.203767	+	4.14988i	0.00781986	+	0.159258i
$680$		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	$-0.545278\pi$
$683$	16.8469	−	9.72659i	0.644631	−	0.372178i	0.786396	+	0.617723i	$0.211945\pi$
$684$		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	0.758081	−	0.652160i	$-0.226137\pi$
$691$	15.0449	+	8.68618i	0.572335	+	0.330438i	−0.185746	+	0.982598i	$0.559470\pi$
$692$		0			0
$693$	−40.6905	+	1.99799i	−1.54571	+	0.0758972i
$694$		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
$707$	0.299938	+	0.465215i	0.0112803	+	0.0174962i
$708$		0			0
$709$	17.4147	+	10.0544i	0.654024	+	0.377601i	0.789996	−	0.613112i	$-0.210082\pi$
$709$	17.4147	+	10.0544i	0.654024	+	0.377601i	−0.135972	+	0.990713i	$0.543416\pi$
$710$		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	0.246692	+	0.969094i	$0.420656\pi$
$719$	−19.1966	+	33.2496i	−0.715914	+	1.24000i	−0.962606	+	0.270906i	$0.912677\pi$
$720$		0			0
$721$	−16.1842	−	8.31358i	−0.602730	−	0.309614i
$722$		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	$-0.588913\pi$
$727$	−14.8679			−0.551422			−0.275711	+	0.961241i	$0.588913\pi$
$728$		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	−0.358597	−	0.933492i	$-0.616745\pi$
$733$	−36.4503	−	21.0446i	−1.34632	−	0.777300i	−0.987727	+	0.156192i	$0.950078\pi$
$734$		0			0
$735$	−25.4650	+	2.50681i	−0.939291	+	0.0924650i
$736$		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	$-0.741626\pi$
$739$	−10.9859	+	6.34270i	−0.404122	+	0.233320i	0.284139	+	0.958783i	$0.408292\pi$
$740$		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
$749$	−15.6411	+	30.4488i	−0.571513	+	1.11257i
$750$		0			0
$751$	17.9305	−	31.0565i	0.654292	−	1.13327i	−0.327779	−	0.944755i	$-0.606300\pi$
$751$	17.9305	−	31.0565i	0.654292	−	1.13327i	0.982071	−	0.188513i	$-0.0603667\pi$
$752$		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	0.0893497	+	0.996000i	$0.471521\pi$
$761$	−22.5624	+	39.0792i	−0.817887	+	1.41662i	−0.907236	+	0.420621i	$0.861812\pi$
$762$		0			0
$763$	27.5515	+	42.7334i	0.997431	+	1.54705i
$764$		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	$-0.668565\pi$
$769$	−28.0168			−1.01031			−0.505156	+	0.863028i	$0.668565\pi$
$770$		0			0
$771$			59.5051i			2.14302i
$772$		0			0
$773$	−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	$0.547370\pi$
$774$		0			0
$775$	−5.10275	+	8.83822i	−0.183296	+	0.317478i
$776$		0			0
$777$	−1.92162	−	39.1353i	−0.0689377	−	1.40397i
$778$		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	−0.924835	−	0.380368i	$-0.875797\pi$
$787$	−29.6763	+	17.1336i	−1.05784	+	0.610747i	−0.133009	+	0.991115i	$0.542464\pi$
$788$		0			0
$789$	23.1720	+	13.3784i	0.824944	+	0.476282i
$790$		0			0
$791$	0.136421	+	2.77833i	0.00485058	+	0.0987860i
$792$		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	$-0.881220\pi$
$797$		−	20.5838i		−	0.729114i	0.931181	−	0.364557i	$-0.118780\pi$
$798$		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
$805$	−2.97387	−	4.61258i	−0.104815	−	0.162572i
$806$		0			0
$807$	−29.5252	+	51.1392i	−1.03934	+	1.80019i
$808$		0			0
$809$	23.4504	+	40.6172i	0.824471	+	1.42802i	0.902323	+	0.431060i	$0.141860\pi$
$809$	23.4504	+	40.6172i	0.824471	+	1.42802i	−0.0778526	+	0.996965i	$0.524806\pi$
$810$		0			0
$811$			22.2462i			0.781168i	0.920567	+	0.390584i	$0.127727\pi$
$811$			22.2462i			0.781168i	−0.920567	+	0.390584i	$0.872273\pi$
$812$		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
$819$	−9.54058	+	18.5728i	−0.333375	+	0.648986i
$820$		0			0
$821$	28.4062	+	16.4003i	0.991384	+	0.572376i	0.905688	−	0.423945i	$-0.139355\pi$
$821$	28.4062	+	16.4003i	0.991384	+	0.572376i	0.0856966	+	0.996321i	$0.472688\pi$
$822$		0			0
$823$	−6.88576	−	11.9265i	−0.240023	−	0.415731i	0.720698	−	0.693249i	$-0.243822\pi$
$823$	−6.88576	−	11.9265i	−0.240023	−	0.415731i	−0.960720	+	0.277518i	$0.910488\pi$
$824$		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	−0.580173	−	0.814493i	$-0.697015\pi$
$829$	−4.74751	+	2.74098i	−0.164888	+	0.0951980i	0.415285	+	0.909691i	$0.363682\pi$
$830$		0			0
$831$	−34.4402	+	59.6522i	−1.19472	+	2.06931i
$832$		0			0
$833$	5.13510	+	7.16678i	0.177921	+	0.248314i
$834$		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	$-0.665309\pi$
$839$	−28.7512			−0.992601			−0.496301	+	0.868151i	$0.665309\pi$
$840$		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
$847$	−34.0421	−	17.4869i	−1.16970	−	0.600858i
$848$		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	$0.121510\pi$
$853$			21.7605i			0.745064i	−0.928019	+	0.372532i	$0.878490\pi$
$854$		0			0
$855$	14.0487			0.480457
$856$		0			0
$857$	−5.89593	−	10.2121i	−0.201401	−	0.348837i	0.747579	−	0.664173i	$-0.231216\pi$
$857$	−5.89593	−	10.2121i	−0.201401	−	0.348837i	−0.948980	+	0.315336i	$0.897883\pi$
$858$		0			0
$859$	4.15132	+	2.39676i	0.141641	+	0.0817766i	0.569146	−	0.822237i	$-0.307274\pi$
$859$	4.15132	+	2.39676i	0.141641	+	0.0817766i	−0.427505	+	0.904013i	$0.640607\pi$
$860$		0			0
$861$	22.4379	+	34.8021i	0.764683	+	1.18605i
$862$		0			0
$863$	−0.0628642	+	0.108884i	−0.00213992	+	0.00370646i	−0.867093	−	0.498146i	$-0.834014\pi$
$863$	−0.0628642	+	0.108884i	−0.00213992	+	0.00370646i	0.864953	+	0.501852i	$0.167348\pi$
$864$		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
$875$	30.5971	−	1.50238i	1.03437	−	0.0507897i
$876$		0			0
$877$	−25.9534	−	14.9842i	−0.876385	−	0.505981i	−0.00692013	−	0.999976i	$-0.502203\pi$
$877$	−25.9534	−	14.9842i	−0.876385	−	0.505981i	−0.869465	+	0.493995i	$0.835536\pi$
$878$		0			0
$879$	24.8273	+	43.0021i	0.837403	+	1.45042i
$880$		0			0
$881$	−30.2728			−1.01992			−0.509959	−	0.860199i	$-0.670339\pi$
$881$	−30.2728			−1.01992			−0.509959	+	0.860199i	$0.670339\pi$
$882$		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	$-0.751549\pi$
$887$	7.56821	−	13.1085i	0.254116	−	0.440141i	0.964655	+	0.263516i	$0.0848823\pi$
$888$		0			0
$889$	−0.935294	−	19.0480i	−0.0313687	−	0.638849i
$890$		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
$903$	−5.60143	+	3.61141i	−0.186404	+	0.120180i
$904$		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	$-0.490083\pi$
$907$	27.4761	−	15.8633i	0.912328	−	0.526733i	0.881180	+	0.472782i	$0.156750\pi$
$908$		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
$917$	17.8354	−	34.7204i	0.588976	−	1.14657i
$918$		0			0
$919$	8.85875	−	15.3438i	0.292223	−	0.506146i	−0.682112	−	0.731248i	$-0.738938\pi$
$919$	8.85875	−	15.3438i	0.292223	−	0.506146i	0.974335	+	0.225102i	$0.0722716\pi$
$920$		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	−0.0158180	+	0.999875i	$0.505035\pi$
$929$	−26.6338	+	46.1311i	−0.873826	+	1.51351i	−0.858008	+	0.513636i	$0.828298\pi$
$930$		0			0
$931$	19.7547	+	8.95192i	0.647434	+	0.293387i
$932$		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	$-0.714518\pi$
$937$	−38.2055			−1.24812			−0.624060	+	0.781377i	$0.714518\pi$
$938$		0			0
$939$		−	11.9469i		−	0.389874i
$940$		0			0
$941$	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	$0.283332\pi$
$942$		0			0
$943$	−4.44064	+	7.69141i	−0.144607	+	0.250467i
$944$		0			0
$945$	−0.441960	−	0.227028i	−0.0143769	−	0.00738523i
$946$		0			0
$947$	−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	$0.753319\pi$
$948$		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
$959$	20.8184	−	13.4223i	0.672262	−	0.433427i
$960$		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	0.536042	−	0.844191i	$-0.319919\pi$
$971$	2.27385	+	1.31281i	0.0729715	+	0.0421301i	−0.463070	+	0.886322i	$0.653252\pi$
$972$		0			0
$973$	4.47966	−	0.219960i	0.143611	−	0.00705160i
$974$		0			0
$975$	8.88128	−	15.3828i	0.284429	−	0.492645i
$976$		0			0
$977$	17.2338	+	29.8499i	0.551359	+	0.954982i	0.998177	+	0.0603567i	$0.0192238\pi$
$977$	17.2338	+	29.8499i	0.551359	+	0.954982i	−0.446818	+	0.894625i	$0.647443\pi$
$978$		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	0.892951	+	0.450154i	$0.148631\pi$
$983$	26.2210	+	45.4161i	0.836320	+	1.44855i	−0.0566303	+	0.998395i	$0.518036\pi$
$984$		0			0
$985$	14.5230	−	25.1547i	0.462743	−	0.801494i
$986$		0			0
$987$	−71.2877	+	3.50036i	−2.26911	+	0.111418i
$988$		0			0
$989$	−1.23794	−	0.714725i	−0.0393642	−	0.0227269i
$990$		0			0
$991$	−8.08057	−	13.9960i	−0.256688	−	0.444596i	0.708665	−	0.705545i	$-0.249298\pi$
$991$	−8.08057	−	13.9960i	−0.256688	−	0.444596i	−0.965353	+	0.260949i	$0.915964\pi$
$992$		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	−0.930846	−	0.365412i	$-0.880928\pi$
$997$	−34.0954	+	19.6850i	−1.07981	+	0.623430i	−0.148967	+	0.988842i	$0.547595\pi$
$998$		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	224.2.t.a.177.1		12
3.2	odd	2		2016.2.cr.c.1297.5		12
4.3	odd	2		56.2.p.a.37.2	✓	12
7.2	even	3		1568.2.b.f.785.1		6
7.3	odd	6		1568.2.t.g.753.1		12
7.4	even	3	inner	224.2.t.a.81.6		12
7.5	odd	6		1568.2.b.e.785.6		6
7.6	odd	2		1568.2.t.g.177.6		12
8.3	odd	2		56.2.p.a.37.4	yes	12
8.5	even	2	inner	224.2.t.a.177.6		12
12.11	even	2		504.2.cj.c.37.5		12
21.11	odd	6		2016.2.cr.c.1873.2		12
24.5	odd	2		2016.2.cr.c.1297.2		12
24.11	even	2		504.2.cj.c.37.3		12
28.3	even	6		392.2.p.g.165.4		12
28.11	odd	6		56.2.p.a.53.4	yes	12
28.19	even	6		392.2.b.f.197.6		6
28.23	odd	6		392.2.b.e.197.6		6
28.27	even	2		392.2.p.g.373.2		12
56.3	even	6		392.2.p.g.165.2		12
56.5	odd	6		1568.2.b.e.785.1		6
56.11	odd	6		56.2.p.a.53.2	yes	12
56.13	odd	2		1568.2.t.g.177.1		12
56.19	even	6		392.2.b.f.197.5		6
56.27	even	2		392.2.p.g.373.4		12
56.37	even	6		1568.2.b.f.785.6		6
56.45	odd	6		1568.2.t.g.753.6		12
56.51	odd	6		392.2.b.e.197.5		6
56.53	even	6	inner	224.2.t.a.81.1		12
84.11	even	6		504.2.cj.c.109.3		12
168.11	even	6		504.2.cj.c.109.5		12
168.53	odd	6		2016.2.cr.c.1873.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.2	✓	12	4.3	odd	2
56.2.p.a.37.4	yes	12	8.3	odd	2
56.2.p.a.53.2	yes	12	56.11	odd	6
56.2.p.a.53.4	yes	12	28.11	odd	6
224.2.t.a.81.1		12	56.53	even	6	inner
224.2.t.a.81.6		12	7.4	even	3	inner
224.2.t.a.177.1		12	1.1	even	1	trivial
224.2.t.a.177.6		12	8.5	even	2	inner
392.2.b.e.197.5		6	56.51	odd	6
392.2.b.e.197.6		6	28.23	odd	6
392.2.b.f.197.5		6	56.19	even	6
392.2.b.f.197.6		6	28.19	even	6
392.2.p.g.165.2		12	56.3	even	6
392.2.p.g.165.4		12	28.3	even	6
392.2.p.g.373.2		12	28.27	even	2
392.2.p.g.373.4		12	56.27	even	2
504.2.cj.c.37.3		12	24.11	even	2
504.2.cj.c.37.5		12	12.11	even	2
504.2.cj.c.109.3		12	84.11	even	6
504.2.cj.c.109.5		12	168.11	even	6
1568.2.b.e.785.1		6	56.5	odd	6
1568.2.b.e.785.6		6	7.5	odd	6
1568.2.b.f.785.1		6	7.2	even	3
1568.2.b.f.785.6		6	56.37	even	6
1568.2.t.g.177.1		12	56.13	odd	2
1568.2.t.g.177.6		12	7.6	odd	2
1568.2.t.g.753.1		12	7.3	odd	6
1568.2.t.g.753.6		12	56.45	odd	6
2016.2.cr.c.1297.2		12	24.5	odd	2
2016.2.cr.c.1297.5		12	3.2	odd	2
2016.2.cr.c.1873.2		12	21.11	odd	6
2016.2.cr.c.1873.5		12	168.53	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.13038 + 1.22998i) q^{3} +(-1.28690 - 0.742990i) q^{5} +(-0.129755 - 2.64257i) q^{7} +(1.52569 - 2.64257i) q^{9} +O(q^{10})\)	\(q+(-2.13038 + 1.22998i) q^{3} +(-1.28690 - 0.742990i) q^{5} +(-0.129755 - 2.64257i) q^{7} +(1.52569 - 2.64257i) q^{9} +(4.37021 - 2.52314i) q^{11} -2.58633i q^{13} +3.65544 q^{15} +(-0.629755 - 1.09077i) q^{17} +(-2.68324 - 1.54917i) q^{19} +(3.52673 + 5.47008i) q^{21} +(-0.697966 + 1.20891i) q^{23} +(-1.39593 - 2.41782i) q^{25} +0.126378i q^{27} +0.638384i q^{29} +(-1.82772 - 3.16571i) q^{31} +(-6.20682 + 10.7505i) q^{33} +(-1.79642 + 3.49712i) q^{35} +(-5.21370 - 3.01013i) q^{37} +(3.18113 + 5.50988i) q^{39} +6.36226 q^{41} +1.02401i q^{43} +(-3.92680 + 2.26714i) q^{45} +(-5.48316 + 9.49712i) q^{47} +(-6.96633 + 0.685774i) q^{49} +(2.68324 + 1.54917i) q^{51} +(4.99481 - 2.88375i) q^{53} -7.49868 q^{55} +7.62177 q^{57} +(3.01720 - 1.74198i) q^{59} +(11.1614 + 6.44406i) q^{61} +(-7.18113 - 3.68884i) q^{63} +(-1.92162 + 3.32834i) q^{65} +(-0.443410 + 0.256003i) q^{67} -3.43393i q^{69} +7.41363 q^{71} +(-4.94731 - 8.56899i) q^{73} +(5.94774 + 3.43393i) q^{75} +(-7.23463 - 11.2212i) q^{77} +(4.35341 - 7.54032i) q^{79} +(4.42162 + 7.65847i) q^{81} +2.97196i q^{83} +1.87161i q^{85} +(-0.785198 - 1.36000i) q^{87} +(1.29186 - 2.23757i) q^{89} +(-6.83456 + 0.335590i) q^{91} +(7.78749 + 4.49611i) q^{93} +(2.30203 + 3.98724i) q^{95} -1.57040 q^{97} -15.3981i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{7}+O(q^{10}) \) 12 * q + 4 * q^7	\( 12 q + 4 q^{7} + 20 q^{15} - 2 q^{17} - 2 q^{23} - 4 q^{25} - 10 q^{31} - 14 q^{33} - 4 q^{39} - 8 q^{41} - 30 q^{47} - 12 q^{49} - 4 q^{55} - 4 q^{57} - 44 q^{63} + 8 q^{65} - 32 q^{71} - 10 q^{73} + 22 q^{79} + 22 q^{81} + 20 q^{87} - 10 q^{89} + 34 q^{95} + 40 q^{97}+O(q^{100}) \) 12 * q + 4 * q^7 + 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 - 12 * q^49 - 4 * q^55 - 4 * q^57 - 44 * q^63 + 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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