LMFDB - Embedded newform 845.2.l.f.699.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(654,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("845.654");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.l (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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			699.7
Character	$\chi$	$=$	845.699
Dual form			845.2.l.f.654.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.165418 + 0.286513i) q^{2} +(-2.33117 + 1.34590i) q^{3} +(0.945274 - 1.63726i) q^{4} +(-0.702335 + 2.12291i) q^{5} +(-0.771236 - 0.445274i) q^{6} +(-1.67674 + 2.90420i) q^{7} +1.28714 q^{8} +(2.12291 - 3.67698i) q^{9} +O(q^{10})$	\(q+(0.165418 + 0.286513i) q^{2} +(-2.33117 + 1.34590i) q^{3} +(0.945274 - 1.63726i) q^{4} +(-0.702335 + 2.12291i) q^{5} +(-0.771236 - 0.445274i) q^{6} +(-1.67674 + 2.90420i) q^{7} +1.28714 q^{8} +(2.12291 - 3.67698i) q^{9} +(-0.724419 + 0.149939i) q^{10} +(-2.81095 + 1.62291i) q^{11} +5.08898i q^{12} -1.10945 q^{14} +(-1.21996 - 5.89413i) q^{15} +(-1.67763 - 2.90574i) q^{16} +(1.68772 + 0.974404i) q^{17} +1.40467 q^{18} +(1.07890 + 0.622905i) q^{19} +(2.81185 + 3.15663i) q^{20} -9.02690i q^{21} +(-0.929966 - 0.536916i) q^{22} +(-2.33117 + 1.34590i) q^{23} +(-3.00053 + 1.73236i) q^{24} +(-4.01345 - 2.98198i) q^{25} +3.35348i q^{27} +(3.16995 + 5.49052i) q^{28} +(1.50000 + 2.59808i) q^{29} +(1.48694 - 1.32453i) q^{30} -3.78109i q^{31} +(1.84216 - 3.19071i) q^{32} +(4.36854 - 7.56654i) q^{33} +0.644737i q^{34} +(-4.98770 - 5.59927i) q^{35} +(-4.01345 - 6.95150i) q^{36} +(-0.974404 - 1.68772i) q^{37} +0.412160i q^{38} +(-0.904000 + 2.73247i) q^{40} +(-2.40850 + 1.39055i) q^{41} +(2.58632 - 1.49321i) q^{42} +(-7.56654 - 4.36854i) q^{43} +6.13636i q^{44} +(6.31489 + 7.08920i) q^{45} +(-0.771236 - 0.445274i) q^{46} -6.86960 q^{47} +(7.82169 + 4.51586i) q^{48} +(-2.12291 - 3.67698i) q^{49} +(0.190477 - 1.64318i) q^{50} -5.24581 q^{51} -12.8336i q^{53} +(-0.960814 + 0.554726i) q^{54} +(-1.47104 - 7.10721i) q^{55} +(-2.15819 + 3.73809i) q^{56} -3.35348 q^{57} +(-0.496255 + 0.859539i) q^{58} +(-2.19562 - 1.26764i) q^{59} +(-10.8034 - 3.57417i) q^{60} +(3.74581 - 6.48793i) q^{61} +(1.08333 - 0.625462i) q^{62} +(7.11911 + 12.3307i) q^{63} -5.49162 q^{64} +2.89055 q^{66} +(-2.00758 - 3.47722i) q^{67} +(3.19071 - 1.84216i) q^{68} +(3.62291 - 6.27506i) q^{69} +(0.779207 - 2.35526i) q^{70} +(4.54300 + 2.62291i) q^{71} +(2.73247 - 4.73277i) q^{72} +5.46493 q^{73} +(0.322368 - 0.558359i) q^{74} +(13.3695 + 1.54979i) q^{75} +(2.03972 - 1.17763i) q^{76} -10.8848i q^{77} -13.7811 q^{79} +(7.34688 - 1.52065i) q^{80} +(1.85526 + 3.21341i) q^{81} +(-0.796819 - 0.460044i) q^{82} +8.61955 q^{83} +(-14.7794 - 8.53289i) q^{84} +(-3.25391 + 2.89851i) q^{85} -2.89055i q^{86} +(-6.99351 - 4.03771i) q^{87} +(-3.61808 + 2.08890i) q^{88} +(-8.93425 + 5.15819i) q^{89} +(-0.986548 + 2.98198i) q^{90} +5.08898i q^{92} +(5.08898 + 8.81438i) q^{93} +(-1.13636 - 1.96823i) q^{94} +(-2.08012 + 1.85292i) q^{95} +9.91745i q^{96} +(-2.63304 + 4.56055i) q^{97} +(0.702335 - 1.21648i) q^{98} +13.7811i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4} + 12 q^{9}+O(q^{10}) $ 24 * q - 8 * q^4 + 12 * q^9	$ 24 q - 8 q^{4} + 12 q^{9} - 14 q^{10} - 88 q^{14} - 32 q^{16} + 4 q^{25} + 36 q^{29} - 8 q^{30} + 20 q^{35} + 4 q^{36} + 140 q^{40} - 12 q^{49} - 48 q^{51} - 52 q^{55} + 32 q^{56} + 12 q^{61} + 24 q^{64} + 8 q^{66} + 48 q^{69} + 16 q^{74} - 4 q^{75} - 208 q^{79} + 28 q^{81} - 124 q^{90} + 112 q^{94} - 40 q^{95}+O(q^{100}) $ 24 * q - 8 * q^4 + 12 * q^9 - 14 * q^10 - 88 * q^14 - 32 * q^16 + 4 * q^25 + 36 * q^29 - 8 * q^30 + 20 * q^35 + 4 * q^36 + 140 * q^40 - 12 * q^49 - 48 * q^51 - 52 * q^55 + 32 * q^56 + 12 * q^61 + 24 * q^64 + 8 * q^66 + 48 * q^69 + 16 * q^74 - 4 * q^75 - 208 * q^79 + 28 * q^81 - 124 * q^90 + 112 * q^94 - 40 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.165418	+	0.286513i	0.116968	+	0.202595i	0.918565	−	0.395270i	$-0.129349\pi$
$2$	0.165418	+	0.286513i	0.116968	+	0.202595i	−0.801597	+	0.597865i	$0.796016\pi$
$3$	−2.33117	+	1.34590i	−1.34590	+	0.777057i	−0.987666	−	0.156574i	$-0.949955\pi$
$3$	−2.33117	+	1.34590i	−1.34590	+	0.777057i	−0.358236	+	0.933631i	$0.616622\pi$
$4$	0.945274	−	1.63726i	0.472637	−	0.818631i
$5$	−0.702335	+	2.12291i	−0.314094	+	0.949392i
$5$	−0.702335	+	2.12291i	−0.314094	+	0.949392i
$6$	−0.771236	−	0.445274i	−0.314856	−	0.181782i
$7$	−1.67674	+	2.90420i	−0.633748	+	1.09768i	0.353031	+	0.935611i	$0.385151\pi$
$7$	−1.67674	+	2.90420i	−0.633748	+	1.09768i	−0.986779	+	0.162072i	$0.948182\pi$
$8$	1.28714			0.455071
$9$	2.12291	−	3.67698i	0.707635	−	1.22566i
$10$	−0.724419	+	0.149939i	−0.229081	+	0.0474150i
$11$	−2.81095	+	1.62291i	−0.847535	+	0.489324i	−0.859818	−	0.510600i	$-0.829423\pi$
$11$	−2.81095	+	1.62291i	−0.847535	+	0.489324i	0.0122837	+	0.999925i	$0.496090\pi$
$12$			5.08898i			1.46906i
$13$		0			0
$13$		0			0
$14$	−1.10945			−0.296514
$15$	−1.21996	−	5.89413i	−0.314992	−	1.52186i
$16$	−1.67763	−	2.90574i	−0.419408	−	0.726436i
$17$	1.68772	+	0.974404i	0.409332	+	0.236328i	0.690503	−	0.723330i	$-0.257389\pi$
$17$	1.68772	+	0.974404i	0.409332	+	0.236328i	−0.281171	+	0.959658i	$0.590723\pi$
$18$	1.40467			0.331084
$19$	1.07890	+	0.622905i	0.247517	+	0.142904i	0.618627	−	0.785685i	$-0.287689\pi$
$19$	1.07890	+	0.622905i	0.247517	+	0.142904i	−0.371110	+	0.928589i	$0.621023\pi$
$20$	2.81185	+	3.15663i	0.628750	+	0.705844i
$21$		−	9.02690i		−	1.96983i
$22$	−0.929966	−	0.536916i	−0.198269	−	0.114471i
$23$	−2.33117	+	1.34590i	−0.486083	+	0.280640i	−0.722948	−	0.690903i	$-0.757213\pi$
$23$	−2.33117	+	1.34590i	−0.486083	+	0.280640i	0.236865	+	0.971543i	$0.423880\pi$
$24$	−3.00053	+	1.73236i	−0.612481	+	0.353616i
$25$	−4.01345	−	2.98198i	−0.802690	−	0.596396i
$26$		0			0
$27$			3.35348i			0.645377i
$28$	3.16995	+	5.49052i	0.599065	+	1.03761i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	1.48694	−	1.32453i	0.271477	−	0.241825i
$31$		−	3.78109i		−	0.679105i	−0.940587	−	0.339552i	$-0.889724\pi$
$31$		−	3.78109i		−	0.679105i	0.940587	−	0.339552i	$-0.110276\pi$
$32$	1.84216	−	3.19071i	0.325650	−	0.564043i
$33$	4.36854	−	7.56654i	0.760466	−	1.31717i
$34$			0.644737i			0.110571i
$35$	−4.98770	−	5.59927i	−0.843076	−	0.946450i
$36$	−4.01345	−	6.95150i	−0.668909	−	1.15858i
$37$	−0.974404	−	1.68772i	−0.160191	−	0.277459i	0.774746	−	0.632273i	$-0.217878\pi$
$37$	−0.974404	−	1.68772i	−0.160191	−	0.277459i	−0.934937	+	0.354813i	$0.884544\pi$
$38$			0.412160i			0.0668611i
$39$		0			0
$40$	−0.904000	+	2.73247i	−0.142935	+	0.432041i
$41$	−2.40850	+	1.39055i	−0.376144	+	0.217167i	−0.676139	−	0.736774i	$-0.736348\pi$
$41$	−2.40850	+	1.39055i	−0.376144	+	0.217167i	0.299995	+	0.953941i	$0.403015\pi$
$42$	2.58632	−	1.49321i	0.399078	−	0.230408i
$43$	−7.56654	−	4.36854i	−1.15389	−	0.666197i	−0.204055	−	0.978959i	$-0.565412\pi$
$43$	−7.56654	−	4.36854i	−1.15389	−	0.666197i	−0.949831	+	0.312763i	$0.898745\pi$
$44$			6.13636i			0.925091i
$45$	6.31489	+	7.08920i	0.941368	+	1.05679i
$46$	−0.771236	−	0.445274i	−0.113713	−	0.0656520i
$47$	−6.86960			−1.00203			−0.501017	−	0.865437i	$-0.667041\pi$
$47$	−6.86960			−1.00203			−0.501017	+	0.865437i	$0.667041\pi$
$48$	7.82169	+	4.51586i	1.12896	+	0.651808i
$49$	−2.12291	−	3.67698i	−0.303272	−	0.525283i
$50$	0.190477	−	1.64318i	0.0269375	−	0.232381i
$51$	−5.24581			−0.734560
$52$		0			0
$53$		−	12.8336i		−	1.76282i	−0.472347	−	0.881412i	$-0.656593\pi$
$53$		−	12.8336i		−	1.76282i	0.472347	−	0.881412i	$-0.343407\pi$
$54$	−0.960814	+	0.554726i	−0.130750	+	0.0754887i
$55$	−1.47104	−	7.10721i	−0.198355	−	0.958336i
$56$	−2.15819	+	3.73809i	−0.288400	+	0.499524i
$57$	−3.35348			−0.444179
$58$	−0.496255	+	0.859539i	−0.0651614	+	0.112863i
$59$	−2.19562	−	1.26764i	−0.285845	−	0.165033i	0.350221	−	0.936667i	$-0.386106\pi$
$59$	−2.19562	−	1.26764i	−0.285845	−	0.165033i	−0.636067	+	0.771634i	$0.719440\pi$
$60$	−10.8034	−	3.57417i	−1.39472	−	0.461423i
$61$	3.74581	−	6.48793i	0.479602	−	0.830695i	−0.520124	−	0.854090i	$-0.674114\pi$
$61$	3.74581	−	6.48793i	0.479602	−	0.830695i	0.999726	+	0.0233957i	$0.00744777\pi$
$62$	1.08333	−	0.625462i	0.137583	−	0.0794338i
$63$	7.11911	+	12.3307i	0.896924	+	1.55352i
$64$	−5.49162			−0.686453
$65$		0			0
$66$	2.89055			0.355802
$67$	−2.00758	−	3.47722i	−0.245264	−	0.424810i	0.716942	−	0.697133i	$-0.245541\pi$
$67$	−2.00758	−	3.47722i	−0.245264	−	0.424810i	−0.962206	+	0.272323i	$0.912208\pi$
$68$	3.19071	−	1.84216i	0.386930	−	0.223394i
$69$	3.62291	−	6.27506i	0.436147	−	0.755428i
$70$	0.779207	−	2.35526i	0.0931331	−	0.281508i
$71$	4.54300	+	2.62291i	0.539155	+	0.311282i	0.744737	−	0.667359i	$-0.232575\pi$
$71$	4.54300	+	2.62291i	0.539155	+	0.311282i	−0.205581	+	0.978640i	$0.565908\pi$
$72$	2.73247	−	4.73277i	0.322024	−	0.557762i
$73$	5.46493			0.639622			0.319811	−	0.947481i	$-0.396381\pi$
$73$	5.46493			0.639622			0.319811	+	0.947481i	$0.396381\pi$
$74$	0.322368	−	0.558359i	0.0374746	−	0.0649079i
$75$	13.3695	+	1.54979i	1.54378	+	0.178954i
$76$	2.03972	−	1.17763i	0.233972	−	0.135084i
$77$		−	10.8848i		−	1.24043i
$78$		0			0
$79$	−13.7811			−1.55049			−0.775247	−	0.631658i	$-0.782375\pi$
$79$	−13.7811			−1.55049			−0.775247	+	0.631658i	$0.782375\pi$
$80$	7.34688	−	1.52065i	0.821406	−	0.170014i
$81$	1.85526	+	3.21341i	0.206140	+	0.357046i
$82$	−0.796819	−	0.460044i	−0.0879940	−	0.0508033i
$83$	8.61955			0.946119			0.473059	−	0.881031i	$-0.343150\pi$
$83$	8.61955			0.946119			0.473059	+	0.881031i	$0.343150\pi$
$84$	−14.7794	−	8.53289i	−1.61257	−	0.931015i
$85$	−3.25391	+	2.89851i	−0.352936	+	0.314387i
$86$		−	2.89055i		−	0.311696i
$87$	−6.99351	−	4.03771i	−0.749783	−	0.432888i
$88$	−3.61808	+	2.08890i	−0.385688	+	0.222677i
$89$	−8.93425	+	5.15819i	−0.947028	+	0.546767i	−0.892156	−	0.451726i	$-0.850808\pi$
$89$	−8.93425	+	5.15819i	−0.947028	+	0.546767i	−0.0548717	+	0.998493i	$0.517475\pi$
$90$	−0.986548	+	2.98198i	−0.103991	+	0.314328i
$91$		0			0
$92$			5.08898i			0.530563i
$93$	5.08898	+	8.81438i	0.527703	+	0.914008i
$94$	−1.13636	−	1.96823i	−0.117206	−	0.203007i
$95$	−2.08012	+	1.85292i	−0.213416	+	0.190106i
$96$			9.91745i			1.01220i
$97$	−2.63304	+	4.56055i	−0.267344	+	0.463054i	−0.968175	−	0.250273i	$-0.919479\pi$
$97$	−2.63304	+	4.56055i	−0.267344	+	0.463054i	0.700831	+	0.713328i	$0.252813\pi$
$98$	0.702335	−	1.21648i	0.0709465	−	0.122883i
$99$			13.7811i			1.38505i
$100$	−8.67609	+	3.75229i	−0.867609	+	0.375229i
$101$	2.85526	+	4.94546i	0.284109	+	0.492092i	0.972393	−	0.233350i	$-0.0749688\pi$
$101$	2.85526	+	4.94546i	0.284109	+	0.492092i	−0.688283	+	0.725442i	$0.741635\pi$
$102$	−0.867753	−	1.50299i	−0.0859203	−	0.148818i
$103$			7.36863i			0.726052i	0.931779	+	0.363026i	$0.118256\pi$
$103$			7.36863i			0.726052i	−0.931779	+	0.363026i	$0.881744\pi$
$104$		0			0
$105$	19.1633	+	6.33991i	1.87014	+	0.618712i
$106$	3.67698	−	2.12291i	0.357140	−	0.206195i
$107$	−7.42568	+	4.28722i	−0.717868	+	0.414461i	−0.813967	−	0.580911i	$-0.802697\pi$
$107$	−7.42568	+	4.28722i	−0.717868	+	0.414461i	0.0960996	+	0.995372i	$0.469363\pi$
$108$	5.49052	+	3.16995i	0.528326	+	0.305029i
$109$		−	8.49162i		−	0.813350i	−0.913573	−	0.406675i	$-0.866688\pi$
$109$		−	8.49162i		−	0.813350i	0.913573	−	0.406675i	$-0.133312\pi$
$110$	1.79297	−	1.59714i	0.170953	−	0.152281i
$111$	4.54300	+	2.62291i	0.431203	+	0.248955i
$112$	11.2518			1.06320
$113$	6.35006	+	3.66621i	0.597363	+	0.344888i	0.768004	−	0.640446i	$-0.221250\pi$
$113$	6.35006	+	3.66621i	0.597363	+	0.344888i	−0.170640	+	0.985333i	$0.554584\pi$
$114$	−0.554726	−	0.960814i	−0.0519549	−	0.0899885i
$115$	−1.21996	−	5.89413i	−0.113762	−	0.549630i
$116$	5.67164			0.526599
$117$		0			0
$118$		−	0.838765i		−	0.0772145i
$119$	−5.65972	+	3.26764i	−0.518826	+	0.299544i
$120$	−1.57025	−	7.58654i	−0.143344	−	0.692553i
$121$	−0.232358	+	0.402456i	−0.0211234	+	0.0365869i
$122$	2.47850			0.224393
$123$	3.74308	−	6.48321i	0.337502	−	0.584571i
$124$	−6.19064	−	3.57417i	−0.555936	−	0.320970i
$125$	9.14925	−	6.42583i	0.818333	−	0.574744i
$126$	−2.35526	+	4.07944i	−0.209824	+	0.363425i
$127$	−7.93599	+	4.58185i	−0.704205	+	0.406573i	−0.808912	−	0.587930i	$-0.799943\pi$
$127$	−7.93599	+	4.58185i	−0.704205	+	0.406573i	0.104707	+	0.994503i	$0.466610\pi$
$128$	−4.59273	−	7.95484i	−0.405944	−	0.703115i
$129$	23.5185			2.07069
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$	−8.25894	−	14.3049i	−0.718848	−	1.24508i
$133$	−3.61808	+	2.08890i	−0.313727	+	0.181130i
$134$	0.664179	−	1.15039i	0.0573763	−	0.0993787i
$135$	−7.11911	−	2.35526i	−0.612716	−	0.202709i
$136$	2.17232	+	1.25419i	0.186275	+	0.107546i
$137$	−8.42435	+	14.5914i	−0.719741	+	1.24663i	0.241361	+	0.970435i	$0.422406\pi$
$137$	−8.42435	+	14.5914i	−0.719741	+	1.24663i	−0.961102	+	0.276193i	$0.910927\pi$
$138$	2.39718			0.204061
$139$	−0.513452	+	0.889325i	−0.0435505	+	0.0754316i	−0.886979	−	0.461810i	$-0.847200\pi$
$139$	−0.513452	+	0.889325i	−0.0435505	+	0.0754316i	0.843429	+	0.537241i	$0.180534\pi$
$140$	−13.8822	+	2.87333i	−1.17326	+	0.242841i
$141$	16.0142	−	9.24581i	1.34864	−	0.778638i
$142$			1.73551i			0.145640i
$143$		0			0
$144$	−14.2458			−1.18715
$145$	−6.56897	+	1.35964i	−0.545523	+	0.112912i
$146$	0.904000	+	1.56577i	0.0748155	+	0.129584i
$147$	9.89771	+	5.71445i	0.816349	+	0.471319i
$148$	−3.68431			−0.302849
$149$	−13.7279	−	7.92583i	−1.12464	−	0.649309i	−0.182056	−	0.983288i	$-0.558275\pi$
$149$	−13.7279	−	7.92583i	−1.12464	−	0.649309i	−0.942581	+	0.333979i	$0.891609\pi$
$150$	1.76752	+	4.08690i	0.144318	+	0.333694i
$151$			14.5454i			1.18369i	0.806052	+	0.591845i	$0.201600\pi$
$151$			14.5454i			1.18369i	−0.806052	+	0.591845i	$0.798400\pi$
$152$	1.38869	+	0.801763i	0.112638	+	0.0650316i
$153$	7.16573	−	4.13713i	0.579315	−	0.334468i
$154$	3.11862	−	1.80054i	0.251306	−	0.145091i
$155$	8.02690	+	2.65559i	0.644736	+	0.213302i
$156$		0			0
$157$		−	10.9210i		−	0.871588i	−0.900047	−	0.435794i	$-0.856468\pi$
$157$		−	10.9210i		−	0.871588i	0.900047	−	0.435794i	$-0.143532\pi$
$158$	−2.27964	−	3.94846i	−0.181359	−	0.314123i
$159$	17.2727	+	29.9172i	1.36982	+	2.37259i
$160$	5.47976	+	6.15167i	0.433213	+	0.486332i
$161$		−	9.02690i		−	0.711420i
$162$	−0.613789	+	1.06311i	−0.0482238	+	0.0835261i
$163$	−2.08890	+	3.61808i	−0.163615	+	0.283390i	−0.936163	−	0.351567i	$-0.885649\pi$
$163$	−2.08890	+	3.61808i	−0.163615	+	0.283390i	0.772547	+	0.634957i	$0.218982\pi$
$164$			5.25779i			0.410564i
$165$	12.9949	+	14.5882i	1.01165	+	1.13569i
$166$	1.42583	+	2.46961i	0.110666	+	0.191679i
$167$	1.67674	+	2.90420i	0.129750	+	0.224733i	0.923580	−	0.383407i	$-0.125249\pi$
$167$	1.67674	+	2.90420i	0.129750	+	0.224733i	−0.793830	+	0.608140i	$0.791916\pi$
$168$		−	11.6188i		−	0.896413i
$169$		0			0
$170$	−1.36872	−	0.452821i	−0.104976	−	0.0347298i
$171$	4.58082	−	2.64474i	0.350304	−	0.202248i
$172$	−14.3049	+	8.25894i	−1.09074	+	0.629738i
$173$	7.56654	+	4.36854i	0.575273	+	0.332134i	0.759253	−	0.650796i	$-0.225565\pi$
$173$	7.56654	+	4.36854i	0.575273	+	0.332134i	−0.183979	+	0.982930i	$0.558898\pi$
$174$		−	2.67164i		−	0.202537i
$175$	15.3898	−	6.65585i	1.16336	−	0.503135i
$176$	9.43149	+	5.44527i	0.710925	+	0.410453i
$177$	6.82449			0.512960
$178$	−2.95577	−	1.70652i	−0.221545	−	0.127909i
$179$	9.00507	+	15.5972i	0.673071	+	1.16579i	0.977029	+	0.213107i	$0.0683584\pi$
$179$	9.00507	+	15.5972i	0.673071	+	1.16579i	−0.303958	+	0.952685i	$0.598308\pi$
$180$	17.5762	−	3.63790i	1.31005	−	0.271153i
$181$	−1.04366			−0.0775749			−0.0387875	−	0.999247i	$-0.512350\pi$
$181$	−1.04366			−0.0775749			−0.0387875	+	0.999247i	$0.512350\pi$
$182$		0			0
$183$			20.1660i			1.49071i
$184$	−3.00053	+	1.73236i	−0.221202	+	0.127711i
$185$	4.26722	−	0.883225i	0.313732	−	0.0649360i
$186$	−1.68362	+	2.91612i	−0.123449	+	0.213820i
$187$	−6.32546			−0.462564
$188$	−6.49365	+	11.2473i	−0.473598	+	0.820296i
$189$	−9.73916	−	5.62291i	−0.708419	−	0.409006i
$190$	−0.874976	−	0.289474i	−0.0634774	−	0.0210006i
$191$	−12.7593	+	22.0997i	−0.923228	+	1.59908i	−0.128841	+	0.991665i	$0.541126\pi$
$191$	−12.7593	+	22.0997i	−0.923228	+	1.59908i	−0.794387	+	0.607412i	$0.792208\pi$
$192$	12.8019	−	7.39118i	0.923898	−	0.533413i
$193$	−9.91035	−	17.1652i	−0.713362	−	1.23558i	−0.963588	−	0.267392i	$-0.913838\pi$
$193$	−9.91035	−	17.1652i	−0.713362	−	1.23558i	0.250225	−	0.968188i	$-0.419495\pi$
$194$	−1.74221			−0.125083
$195$		0			0
$196$	−8.02690			−0.573350
$197$	10.8260	+	18.7512i	0.771319	+	1.33596i	0.936840	+	0.349758i	$0.113736\pi$
$197$	10.8260	+	18.7512i	0.771319	+	1.33596i	−0.165521	+	0.986206i	$0.552930\pi$
$198$	−3.94846	+	2.27964i	−0.280605	+	0.162007i
$199$	−9.11453	+	15.7868i	−0.646112	+	1.11910i	0.337932	+	0.941171i	$0.390273\pi$
$199$	−9.11453	+	15.7868i	−0.646112	+	1.11910i	−0.984044	+	0.177928i	$0.943061\pi$
$200$	−5.16586	−	3.83821i	−0.365281	−	0.271402i
$201$	9.36000	+	5.40400i	0.660204	+	0.381169i
$202$	−0.944625	+	1.63614i	−0.0664636	+	0.115118i
$203$	−10.0604			−0.706104
$204$	−4.95873	+	8.58877i	−0.347180	+	0.601334i
$205$	−1.26043	−	6.08964i	−0.0880321	−	0.425319i
$206$	−2.11121	+	1.21891i	−0.147095	+	0.0849252i
$207$			11.4289i			0.794363i
$208$		0			0
$209$	−4.04366			−0.279706
$210$	1.35349	+	6.53926i	0.0933996	+	0.451252i
$211$	−9.64981	−	16.7140i	−0.664320	−	1.15064i	−0.979469	−	0.201594i	$-0.935388\pi$
$211$	−9.64981	−	16.7140i	−0.664320	−	1.15064i	0.315149	−	0.949042i	$-0.397946\pi$
$212$	−21.0119	−	12.1312i	−1.44310	−	0.833176i
$213$	−14.1207			−0.967534
$214$	−2.45669	−	1.41837i	−0.167936	−	0.0969577i
$215$	14.5882	−	12.9949i	0.994910	−	0.886242i
$216$			4.31638i			0.293692i
$217$	10.9810	+	6.33991i	0.745442	+	0.430381i
$218$	2.43296	−	1.40467i	0.164781	−	0.0951362i
$219$	−12.7397	+	7.35526i	−0.860868	+	0.497023i
$220$	−13.0269	−	4.30978i	−0.878274	−	0.290565i
$221$		0			0
$222$			1.73551i			0.116480i
$223$	−6.18537	−	10.7134i	−0.414203	−	0.717421i	0.581141	−	0.813803i	$-0.302606\pi$
$223$	−6.18537	−	10.7134i	−0.414203	−	0.717421i	−0.995344	+	0.0963818i	$0.969273\pi$
$224$	6.17763	+	10.7000i	0.412760	+	0.714922i
$225$	−19.4849	+	8.42692i	−1.29899	+	0.561795i
$226$			2.42583i			0.161364i
$227$	−3.08141	+	5.33715i	−0.204520	+	0.354239i	−0.949980	−	0.312311i	$-0.898897\pi$
$227$	−3.08141	+	5.33715i	−0.204520	+	0.354239i	0.745460	+	0.666551i	$0.232230\pi$
$228$	−3.16995	+	5.49052i	−0.209935	+	0.363619i
$229$			26.9832i			1.78310i	0.452920	+	0.891551i	$0.350382\pi$
$229$			26.9832i			1.78310i	−0.452920	+	0.891551i	$0.649618\pi$
$230$	1.48694	−	1.32453i	0.0980459	−	0.0873370i
$231$	14.6498	+	25.3742i	0.963887	+	1.66950i
$232$	1.93070	+	3.34408i	0.126757	+	0.219549i
$233$		−	0.824319i		−	0.0540029i	−0.999635	−	0.0270015i	$-0.991404\pi$
$233$		−	0.824319i		−	0.0540029i	0.999635	−	0.0270015i	$-0.00859588\pi$
$234$		0			0
$235$	4.82476	−	14.5835i	0.314733	−	0.951323i
$236$	−4.15092	+	2.39654i	−0.270202	+	0.156001i
$237$	32.1261	−	18.5480i	2.08681	−	1.20482i
$238$	−1.87244	−	1.08106i	−0.121372	−	0.0700744i
$239$			4.00000i			0.258738i	0.991596	+	0.129369i	$0.0412952\pi$
$239$			4.00000i			0.258738i	−0.991596	+	0.129369i	$0.958705\pi$
$240$	−15.0802	+	13.4331i	−0.973421	+	0.867101i
$241$	−19.6534	−	11.3469i	−1.26599	−	0.730917i	−0.291760	−	0.956492i	$-0.594241\pi$
$241$	−19.6534	−	11.3469i	−1.26599	−	0.730917i	−0.974226	+	0.225575i	$0.927574\pi$
$242$	−0.153745			−0.00988310
$243$	−17.3625	−	10.0242i	−1.11380	−	0.643054i
$244$	−7.08163	−	12.2657i	−0.453355	−	0.785234i
$245$	9.29687	−	1.92426i	0.593955	−	0.122936i
$246$	2.47670			0.157908
$247$		0			0
$248$		−	4.86678i		−	0.309041i
$249$	−20.0936	+	11.6011i	−1.27338	+	0.735188i
$250$	3.35454	+	1.55843i	0.212159	+	0.0985635i
$251$	9.51345	−	16.4778i	0.600484	−	1.04007i	−0.392264	−	0.919853i	$-0.628308\pi$
$251$	9.51345	−	16.4778i	0.600484	−	1.04007i	0.992748	−	0.120216i	$-0.0383586\pi$
$252$	26.9180			1.69568
$253$	4.36854	−	7.56654i	0.274648	−	0.475704i
$254$	−2.62552	−	1.51584i	−0.164739	−	0.0951124i
$255$	3.68431	−	11.1364i	0.230721	−	0.697386i
$256$	−3.97218	+	6.88001i	−0.248261	+	0.430001i
$257$	−1.82857	+	1.05573i	−0.114063	+	0.0658544i	−0.555946	−	0.831218i	$-0.687644\pi$
$257$	−1.82857	+	1.05573i	−0.114063	+	0.0658544i	0.441883	+	0.897073i	$0.354311\pi$
$258$	3.89039	+	6.73836i	0.242205	+	0.419512i
$259$	6.53528			0.406083
$260$		0			0
$261$	12.7374			0.788427
$262$	1.65418	+	2.86513i	0.102196	+	0.177008i
$263$	25.9092	−	14.9587i	1.59763	−	0.922391i	0.605685	−	0.795704i	$-0.292899\pi$
$263$	25.9092	−	14.9587i	1.59763	−	0.922391i	0.991943	−	0.126687i	$-0.0404343\pi$
$264$	5.62291	−	9.73916i	0.346066	−	0.599404i
$265$	27.2444	+	9.01345i	1.67361	+	0.553692i
$266$	−1.19699	−	0.691084i	−0.0733923	−	0.0423731i
$267$	13.8848	−	24.0492i	0.849738	−	1.47179i
$268$	−7.59083			−0.463684
$269$	9.29455	−	16.0986i	0.566699	−	0.981551i	−0.430191	−	0.902738i	$-0.641554\pi$
$269$	9.29455	−	16.0986i	0.566699	−	0.981551i	0.996889	−	0.0788127i	$-0.0251129\pi$
$270$	−0.502818	−	2.42932i	−0.0306006	−	0.147844i
$271$	5.04439	−	2.91238i	0.306425	−	0.176914i	−0.338901	−	0.940822i	$-0.610055\pi$
$271$	5.04439	−	2.91238i	0.306425	−	0.176914i	0.645326	+	0.763908i	$0.276722\pi$
$272$		−	6.53876i		−	0.396471i
$273$		0			0
$274$	−5.57417			−0.336748
$275$	16.1211	+	1.86875i	0.972139	+	0.112690i
$276$	−6.84927	−	11.8633i	−0.412278	−	0.714086i
$277$	11.7263	+	6.77017i	0.704564	+	0.406780i	0.809045	−	0.587747i	$-0.199985\pi$
$277$	11.7263	+	6.77017i	0.704564	+	0.406780i	−0.104481	+	0.994527i	$0.533318\pi$
$278$	−0.339738			−0.0203761
$279$	−13.9030	−	8.02690i	−0.832351	−	0.480558i
$280$	−6.41985	−	7.20702i	−0.383659	−	0.430702i
$281$		−	0.464716i		−	0.0277226i	−0.999904	−	0.0138613i	$-0.995588\pi$
$281$		−	0.464716i		−	0.0277226i	0.999904	−	0.0138613i	$-0.00441233\pi$
$282$	5.29809	+	3.05885i	0.315496	+	0.182152i
$283$	8.71259	−	5.03022i	0.517910	−	0.299015i	−0.218169	−	0.975911i	$-0.570009\pi$
$283$	8.71259	−	5.03022i	0.517910	−	0.299015i	0.736079	+	0.676896i	$0.236675\pi$
$284$	8.58877	−	4.95873i	0.509649	−	0.294246i
$285$	2.35526	−	7.11911i	0.139514	−	0.421700i
$286$		0			0
$287$		−	9.32634i		−	0.550516i
$288$	−7.82145	−	13.5471i	−0.460883	−	0.798273i
$289$	−6.60107	−	11.4334i	−0.388298	−	0.672553i
$290$	−1.47618	−	1.65719i	−0.0866844	−	0.0973133i
$291$		−	14.1752i		−	0.830967i
$292$	5.16586	−	8.94752i	0.302309	−	0.523614i
$293$	−6.72506	+	11.6481i	−0.392882	+	0.680492i	−0.992828	−	0.119548i	$-0.961855\pi$
$293$	−6.72506	+	11.6481i	−0.392882	+	0.680492i	0.599946	+	0.800040i	$0.295189\pi$
$294$			3.78109i			0.220518i
$295$	4.23314	−	3.77079i	0.246463	−	0.219544i
$296$	−1.25419	−	2.17232i	−0.0728983	−	0.126264i
$297$	−5.44238	−	9.42647i	−0.315799	−	0.546979i
$298$		−	5.24431i		−	0.303795i
$299$		0			0
$300$	15.1752	−	20.4244i	0.876143	−	1.17920i
$301$	25.3742	−	14.6498i	1.46255	−	0.844401i
$302$	−4.16745	+	2.40608i	−0.239810	+	0.138454i
$303$	−13.3122	−	7.68581i	−0.764767	−	0.441538i
$304$		−	4.18002i		−	0.239741i
$305$	11.1425	+	12.5087i	0.638015	+	0.716246i
$306$	2.37068	+	1.36872i	0.135523	+	0.0782442i
$307$	−24.6077			−1.40444			−0.702219	−	0.711961i	$-0.747807\pi$
$307$	−24.6077			−1.40444			−0.702219	+	0.711961i	$0.747807\pi$
$308$	−17.8212	−	10.2891i	−1.01546	−	0.586274i
$309$	−9.91745	−	17.1775i	−0.564184	−	0.977196i
$310$	0.566935	+	2.73909i	0.0321997	+	0.155570i
$311$	−2.43781			−0.138236			−0.0691178	−	0.997609i	$-0.522018\pi$
$311$	−2.43781			−0.138236			−0.0691178	+	0.997609i	$0.522018\pi$
$312$		0			0
$313$			19.2965i			1.09071i	0.838207	+	0.545353i	$0.183604\pi$
$313$			19.2965i			1.09071i	−0.838207	+	0.545353i	$0.816396\pi$
$314$	3.12900	−	1.80653i	0.176579	−	0.101948i
$315$	−31.1768	+	6.45295i	−1.75662	+	0.363583i
$316$	−13.0269	+	22.5633i	−0.732821	+	1.26928i
$317$	−28.8217			−1.61879			−0.809395	−	0.587265i	$-0.800205\pi$
$317$	−28.8217			−1.61879			−0.809395	+	0.587265i	$0.800205\pi$
$318$	−5.71445	+	9.89771i	−0.320450	+	0.555036i
$319$	−8.43286	−	4.86872i	−0.472150	−	0.272596i
$320$	3.85695	−	11.6582i	0.215610	−	0.651713i
$321$	11.5404	−	19.9885i	0.644120	−	1.11565i
$322$	2.58632	−	1.49321i	0.144130	−	0.0832136i
$323$	1.21392	+	2.10258i	0.0675445	+	0.116990i
$324$	7.01492			0.389718
$325$		0			0
$326$	−1.38217			−0.0765512
$327$	11.4289	+	19.7954i	0.632019	+	1.09469i
$328$	−3.10006	+	1.78982i	−0.171172	+	0.0988264i
$329$	11.5185	−	19.9507i	0.635037	−	1.09992i
$330$	−2.03013	+	6.13636i	−0.111755	+	0.337795i
$331$	−2.57478	−	1.48655i	−0.141522	−	0.0817081i	0.427567	−	0.903984i	$-0.359371\pi$
$331$	−2.57478	−	1.48655i	−0.141522	−	0.0817081i	−0.569089	+	0.822276i	$0.692704\pi$
$332$	8.14783	−	14.1125i	0.447171	−	0.774522i
$333$	−8.27427			−0.453427
$334$	−0.554726	+	0.960814i	−0.0303533	+	0.0525734i
$335$	8.79180	−	1.81972i	0.480347	−	0.0994218i
$336$	−26.2299	+	15.1438i	−1.43096	+	0.826163i
$337$		−	1.90370i		−	0.103701i	−0.998655	−	0.0518505i	$-0.983488\pi$
$337$		−	1.90370i		−	0.103701i	0.998655	−	0.0518505i	$-0.0165119\pi$
$338$		0			0
$339$	−19.7374			−1.07199
$340$	1.66978	+	8.06738i	0.0905565	+	0.437515i
$341$	6.13636	+	10.6285i	0.332302	+	0.575565i
$342$	1.51550	+	0.874976i	0.0819490	+	0.0473133i
$343$	−9.23611			−0.498703
$344$	−9.73916	−	5.62291i	−0.525100	−	0.303167i
$345$	10.7769	+	12.0983i	0.580206	+	0.651349i
$346$			2.89055i			0.155397i
$347$	10.9420	+	6.31735i	0.587396	+	0.339133i	0.764067	−	0.645137i	$-0.223200\pi$
$347$	10.9420	+	6.31735i	0.587396	+	0.339133i	−0.176671	+	0.984270i	$0.556533\pi$
$348$	−13.2216	+	7.63347i	−0.708750	+	0.409197i
$349$	−7.77093	+	4.48655i	−0.415968	+	0.240159i	−0.693351	−	0.720600i	$-0.743866\pi$
$349$	−7.77093	+	4.48655i	−0.415968	+	0.240159i	0.277383	+	0.960760i	$0.410533\pi$
$350$	4.45274	+	3.30837i	0.238009	+	0.176840i
$351$		0			0
$352$			11.9586i			0.637395i
$353$	−17.1252	−	29.6618i	−0.911484	−	1.57874i	−0.811969	−	0.583701i	$-0.801604\pi$
$353$	−17.1252	−	29.6618i	−0.911484	−	1.57874i	−0.0995150	−	0.995036i	$-0.531729\pi$
$354$	1.12890	+	1.95530i	0.0600001	+	0.103923i
$355$	−8.75889	+	7.80221i	−0.464874	+	0.414098i
$356$			19.5036i			1.03369i
$357$	8.79585	−	15.2349i	0.465526	−	0.806315i
$358$	−2.97921	+	5.16014i	−0.157456	+	0.272722i
$359$		−	22.4043i		−	1.18245i	−0.806505	−	0.591227i	$-0.798644\pi$
$359$		−	22.4043i		−	1.18245i	0.806505	−	0.591227i	$-0.201356\pi$
$360$	8.12812	+	9.12475i	0.428389	+	0.480917i
$361$	−8.72398	−	15.1104i	−0.459157	−	0.795283i
$362$	−0.172641	−	0.299023i	−0.00907381	−	0.0157163i
$363$		−	1.25092i		−	0.0656565i
$364$		0			0
$365$	−3.83821	+	11.6015i	−0.200901	+	0.607252i
$366$	−5.77781	+	3.33582i	−0.302011	+	0.174366i
$367$	−11.4273	+	6.59753i	−0.596498	+	0.344388i	−0.767663	−	0.640854i	$-0.778580\pi$
$367$	−11.4273	+	6.59753i	−0.596498	+	0.344388i	0.171165	+	0.985242i	$0.445247\pi$
$368$	7.82169	+	4.51586i	0.407734	+	0.235405i
$369$			11.8080i			0.614700i
$370$	0.958932	+	1.07651i	0.0498525	+	0.0559652i
$371$	37.2712	+	21.5185i	1.93502	+	1.11719i
$372$	19.2419			0.997647
$373$	−13.2168	−	7.63070i	−0.684338	−	0.395103i	0.117149	−	0.993114i	$-0.462624\pi$
$373$	−13.2168	−	7.63070i	−0.684338	−	0.395103i	−0.801488	+	0.598012i	$0.795958\pi$
$374$	−1.04635	−	1.81233i	−0.0541053	−	0.0937131i
$375$	−12.6799	+	27.2937i	−0.654788	+	1.40944i
$376$	−8.84210			−0.455997
$377$		0			0
$378$		−	3.72052i		−	0.191363i
$379$	15.7868	−	9.11453i	0.810915	−	0.468182i	−0.0363588	−	0.999339i	$-0.511576\pi$
$379$	15.7868	−	9.11453i	0.810915	−	0.468182i	0.847273	+	0.531157i	$0.178243\pi$
$380$	1.06744	+	5.15722i	0.0547583	+	0.264560i
$381$	12.3334	−	21.3621i	0.631861	−	1.09442i
$382$	−8.44246			−0.431954
$383$	0.720440	−	1.24784i	0.0368128	−	0.0637616i	−0.847032	−	0.531542i	$-0.821613\pi$
$383$	0.720440	−	1.24784i	0.0368128	−	0.0637616i	0.883845	+	0.467780i	$0.154946\pi$
$384$	21.4129	+	12.3627i	1.09272	+	0.630883i
$385$	23.1073	+	7.64474i	1.17766	+	0.389612i
$386$	3.27870	−	5.67888i	0.166882	−	0.289048i
$387$	−32.1261	+	18.5480i	−1.63306	+	0.942848i
$388$	4.97788	+	8.62194i	0.252714	+	0.437713i
$389$	−18.7912			−0.952754			−0.476377	−	0.879241i	$-0.658050\pi$
$389$	−18.7912			−0.952754			−0.476377	+	0.879241i	$0.658050\pi$
$390$		0			0
$391$	−5.24581			−0.265292
$392$	−2.73247	−	4.73277i	−0.138010	−	0.239041i
$393$	−23.3117	+	13.4590i	−1.17592	+	0.678918i
$394$	−3.58163	+	6.20357i	−0.180440	+	0.312531i
$395$	9.67894	−	29.2560i	0.487000	−	1.47203i
$396$	22.5633	+	13.0269i	1.13385	+	0.654627i
$397$	−8.54634	+	14.8027i	−0.428928	+	0.742926i	−0.996778	−	0.0802063i	$-0.974442\pi$
$397$	−8.54634	+	14.8027i	−0.428928	+	0.742926i	0.567850	+	0.823132i	$0.307775\pi$
$398$	−6.03084			−0.302298
$399$	5.62291	−	9.73916i	0.281497	−	0.487568i
$400$	−1.93177	+	16.6647i	−0.0965886	+	0.833236i
$401$	19.2276	−	11.1011i	0.960182	−	0.554361i	0.0639527	−	0.997953i	$-0.479629\pi$
$401$	19.2276	−	11.1011i	0.960182	−	0.554361i	0.896229	+	0.443592i	$0.146296\pi$
$402$			3.57568i			0.178339i
$403$		0			0
$404$	10.7960			0.537122
$405$	−8.12478	+	1.68166i	−0.403724	+	0.0835623i
$406$	−1.66418	−	2.88244i	−0.0825918	−	0.143053i
$407$	5.47801	+	3.16273i	0.271535	+	0.156771i
$408$	−6.75207			−0.334277
$409$	8.34221	+	4.81638i	0.412496	+	0.238155i	0.691862	−	0.722030i	$-0.256791\pi$
$409$	8.34221	+	4.81638i	0.412496	+	0.238155i	−0.279366	+	0.960185i	$0.590124\pi$
$410$	1.53626	−	1.36847i	0.0758706	−	0.0675838i
$411$		−	45.3534i		−	2.23712i
$412$	12.0644	+	6.96537i	0.594369	+	0.343159i
$413$	7.36296	−	4.25101i	0.362308	−	0.209178i
$414$	−3.27452	+	1.89055i	−0.160934	+	0.0929153i
$415$	−6.05381	+	18.2985i	−0.297170	+	0.898238i
$416$		0			0
$417$		−	2.76423i		−	0.135365i
$418$	−0.668896	−	1.15856i	−0.0327168	−	0.0566671i
$419$	−0.978168	−	1.69424i	−0.0477866	−	0.0827689i	0.841143	−	0.540813i	$-0.181883\pi$
$419$	−0.978168	−	1.69424i	−0.0477866	−	0.0827689i	−0.888929	+	0.458044i	$0.848550\pi$
$420$	28.4946	−	25.3823i	1.39039	−	1.23853i
$421$			12.0807i			0.588778i	0.955686	+	0.294389i	$0.0951161\pi$
$421$			12.0807i			0.588778i	−0.955686	+	0.294389i	$0.904884\pi$
$422$	3.19251	−	5.52959i	0.155409	−	0.269176i
$423$	−14.5835	+	25.2594i	−0.709075	+	1.22815i
$424$		−	16.5185i		−	0.802210i
$425$	−3.86792	−	8.94346i	−0.187622	−	0.433822i
$426$	−2.33582	−	4.04576i	−0.113171	−	0.196018i
$427$	12.5615	+	21.7571i	0.607893	+	1.05290i
$428$			16.2104i			0.783558i
$429$		0			0
$430$	6.13636	+	2.03013i	0.295921	+	0.0979016i
$431$	−21.2948	+	12.2945i	−1.02573	+	0.592207i	−0.915759	−	0.401727i	$-0.868410\pi$
$431$	−21.2948	+	12.2945i	−1.02573	+	0.592207i	−0.109974	+	0.993934i	$0.535077\pi$
$432$	9.74434	−	5.62590i	0.468825	−	0.270676i
$433$	31.2400	+	18.0364i	1.50130	+	0.866775i	0.999999	+	0.00150085i	$0.000477735\pi$
$433$	31.2400	+	18.0364i	1.50130	+	0.866775i	0.501299	+	0.865274i	$0.332856\pi$
$434$			4.19495i			0.201364i
$435$	13.4835	−	12.0107i	0.646482	−	0.575871i
$436$	−13.9030	−	8.02690i	−0.665833	−	0.384419i
$437$	−3.35348			−0.160419
$438$	−4.21475	−	2.43339i	−0.201389	−	0.116272i
$439$	−1.26764	−	2.19562i	−0.0605013	−	0.104791i	0.834188	−	0.551480i	$-0.185937\pi$
$439$	−1.26764	−	2.19562i	−0.0605013	−	0.104791i	−0.894690	+	0.446688i	$0.852603\pi$
$440$	−1.89343	−	9.14794i	−0.0902658	−	0.436111i
$441$	−18.0269			−0.858424
$442$		0			0
$443$			19.3579i			0.919721i	0.887991	+	0.459860i	$0.152101\pi$
$443$			19.3579i			0.919721i	−0.887991	+	0.459860i	$0.847899\pi$
$444$	8.58877	−	4.95873i	0.407605	−	0.235331i
$445$	−4.67552	−	22.5893i	−0.221641	−	1.07084i
$446$	2.04635	−	3.54438i	0.0968973	−	0.167831i
$447$	42.6696			2.01820
$448$	9.20801	−	15.9487i	0.435038	−	0.753507i
$449$	−21.4844	−	12.4040i	−1.01391	−	0.585381i	−0.101576	−	0.994828i	$-0.532388\pi$
$449$	−21.4844	−	12.4040i	−1.01391	−	0.585381i	−0.912334	+	0.409447i	$0.865722\pi$
$450$	−5.63757	−	4.18869i	−0.265758	−	0.197457i
$451$	4.51345	−	7.81753i	0.212530	−	0.368113i
$452$	12.0051	−	6.93114i	0.564672	−	0.326013i
$453$	−19.5767	−	33.9079i	−0.919795	−	1.59313i
$454$	−2.03888			−0.0956896
$455$		0			0
$456$	−4.31638			−0.202133
$457$	−3.78374	−	6.55363i	−0.176996	−	0.306566i	0.763854	−	0.645389i	$-0.223305\pi$
$457$	−3.78374	−	6.55363i	−0.176996	−	0.306566i	−0.940850	+	0.338823i	$0.889971\pi$
$458$	−7.73105	+	4.46352i	−0.361248	+	0.208567i
$459$	−3.26764	+	5.65972i	−0.152520	+	0.264173i
$460$	−10.8034	−	3.57417i	−0.503712	−	0.166646i
$461$	−10.6896	−	6.17164i	−0.497864	−	0.287442i	0.229967	−	0.973198i	$-0.426138\pi$
$461$	−10.6896	−	6.17164i	−0.497864	−	0.287442i	−0.727831	+	0.685756i	$0.759472\pi$
$462$	−4.84669	+	8.39472i	−0.225489	+	0.390558i
$463$	22.8578			1.06229			0.531146	−	0.847281i	$-0.321762\pi$
$463$	22.8578			1.06229			0.531146	+	0.847281i	$0.321762\pi$
$464$	5.03289	−	8.71723i	0.233646	−	0.404687i
$465$	−22.2863	+	4.61279i	−1.03350	+	0.213913i
$466$	0.236178	−	0.136357i	0.0109407	−	0.00631664i
$467$			15.2976i			0.707889i	0.935266	+	0.353945i	$0.115160\pi$
$467$			15.2976i			0.707889i	−0.935266	+	0.353945i	$0.884840\pi$
$468$		0			0
$469$	13.4647			0.621743
$470$	4.97647	−	1.03002i	0.229547	−	0.0475115i
$471$	14.6985	+	25.4586i	0.677273	+	1.17307i
$472$	−2.82606	−	1.63163i	−0.130080	−	0.0751017i
$473$	28.3589			1.30394
$474$	10.6285	+	6.13636i	0.488182	+	0.281852i
$475$	−2.47264	−	5.71727i	−0.113452	−	0.262326i
$476$			12.3553i			0.566303i
$477$	−47.1887	−	27.2444i	−2.16062	−	1.24744i
$478$	−1.14605	+	0.661673i	−0.0524192	+	0.0302642i
$479$	−21.0296	+	12.1414i	−0.960866	+	0.554756i	−0.896439	−	0.443166i	$-0.853855\pi$
$479$	−21.0296	+	12.1414i	−0.960866	+	0.554756i	−0.0644264	+	0.997922i	$0.520522\pi$
$480$	−21.0538	−	6.96537i	−0.960971	−	0.317924i
$481$		0			0
$482$		−	7.50793i		−	0.341977i
$483$	12.1493	+	21.0433i	0.552814	+	0.957501i
$484$	0.439284	+	0.760862i	0.0199674	+	0.0345846i
$485$	−7.83235	−	8.79272i	−0.355649	−	0.399257i
$486$		−	6.63276i		−	0.300868i
$487$	−18.4441	+	31.9462i	−0.835783	+	1.44762i	0.0576081	+	0.998339i	$0.481653\pi$
$487$	−18.4441	+	31.9462i	−0.835783	+	1.44762i	−0.893391	+	0.449280i	$0.851681\pi$
$488$	4.82136	−	8.35085i	0.218253	−	0.378025i
$489$		−	11.2458i		−	0.508553i
$490$	2.08920	+	2.34537i	0.0943803	+	0.105953i
$491$	−17.6767	−	30.6170i	−0.797739	−	1.38172i	−0.921085	−	0.389361i	$-0.872696\pi$
$491$	−17.6767	−	30.6170i	−0.797739	−	1.38172i	0.123346	−	0.992364i	$-0.460637\pi$
$492$	−7.07647	−	12.2568i	−0.319032	−	0.552580i
$493$			5.84642i			0.263310i
$494$		0			0
$495$	−29.2560	−	9.67894i	−1.31496	−	0.435036i
$496$	−10.9869	+	6.34328i	−0.493326	+	0.284822i
$497$	−15.2349	+	8.79585i	−0.683377	+	0.394548i
$498$	−6.64771	−	3.83806i	−0.297891	−	0.171988i
$499$			16.2189i			0.726058i	0.931778	+	0.363029i	$0.118257\pi$
$499$			16.2189i			0.726058i	−0.931778	+	0.363029i	$0.881743\pi$
$500$	−1.87223	−	21.0539i	−0.0837286	−	0.941558i
$501$	−7.81753	−	4.51345i	−0.349261	−	0.201646i
$502$	6.29480			0.280950
$503$	17.5270	+	10.1192i	0.781489	+	0.451193i	0.836958	−	0.547268i	$-0.184332\pi$
$503$	17.5270	+	10.1192i	0.781489	+	0.451193i	−0.0554688	+	0.998460i	$0.517665\pi$
$504$	9.16326	+	15.8712i	0.408164	+	0.706961i
$505$	−12.5041	+	2.58808i	−0.556425	+	0.115168i
$506$	2.89055			0.128500
$507$		0			0
$508$			17.3244i			0.768646i
$509$	−17.3526	+	10.0185i	−0.769140	+	0.444063i	−0.832568	−	0.553923i	$-0.813130\pi$
$509$	−17.3526	+	10.0185i	−0.769140	+	0.444063i	0.0634276	+	0.997986i	$0.479797\pi$
$510$	3.80016	−	0.786554i	0.168274	−	0.0348292i
$511$	−9.16326	+	15.8712i	−0.405359	+	0.702102i
$512$	−20.9992			−0.928042
$513$	−2.08890	+	3.61808i	−0.0922271	+	0.159742i
$514$	−0.604959	−	0.349273i	−0.0266836	−	0.0154058i
$515$	−15.6429	−	5.17524i	−0.689308	−	0.228048i
$516$	22.2314	−	38.5060i	0.978685	−	1.69513i
$517$	19.3101	−	11.1487i	0.849259	−	0.490320i
$518$	1.08106	+	1.87244i	0.0474988	+	0.0822704i
$519$	−23.5185			−1.03235
$520$		0			0
$521$	16.0269			0.702151			0.351076	−	0.936347i	$-0.385816\pi$
$521$	16.0269			0.702151			0.351076	+	0.936347i	$0.385816\pi$
$522$	2.10700	+	3.64944i	0.0922210	+	0.159732i
$523$	10.1654	−	5.86898i	0.444501	−	0.256633i	−0.261004	−	0.965338i	$-0.584054\pi$
$523$	10.1654	−	5.86898i	0.444501	−	0.256633i	0.705505	+	0.708705i	$0.250720\pi$
$524$	9.45274	−	16.3726i	0.412945	−	0.715241i
$525$	−26.9180	+	36.2291i	−1.17480	+	1.58117i
$526$	8.57170	+	4.94887i	0.373744	+	0.215781i
$527$	3.68431	−	6.38142i	0.160491	−	0.277979i
$528$	−29.3152			−1.27578
$529$	−7.87709	+	13.6435i	−0.342482	+	0.593197i
$530$	1.92426	+	9.29687i	0.0835844	+	0.403830i
$531$	−9.32219	+	5.38217i	−0.404548	+	0.233566i
$532$			7.89832i			0.342436i
$533$		0			0
$534$	9.18722			0.397570
$535$	−3.88605	−	18.7751i	−0.168008	−	0.811718i
$536$	−2.58402	−	4.47565i	−0.111613	−	0.193319i
$537$	−41.9847	−	24.2399i	−1.81177	−	1.04603i
$538$	6.14995			0.265143
$539$	11.9348	+	6.89055i	0.514067	+	0.296797i
$540$	−10.5857	+	9.42949i	−0.455536	+	0.405780i
$541$		−	21.8080i		−	0.937599i	−0.883305	−	0.468800i	$-0.844687\pi$
$541$		−	21.8080i		−	0.937599i	0.883305	−	0.468800i	$-0.155313\pi$
$542$	1.66887	+	0.963521i	0.0716840	+	0.0413868i
$543$	2.43296	−	1.40467i	0.104408	−	0.0602801i
$544$	6.21808	−	3.59001i	0.266598	−	0.153920i
$545$	18.0269	+	5.96396i	0.772188	+	0.255468i
$546$		0			0
$547$		−	6.30924i		−	0.269764i	−0.990862	−	0.134882i	$-0.956935\pi$
$547$		−	6.30924i		−	0.269764i	0.990862	−	0.134882i	$-0.0430655\pi$
$548$	15.9266	+	27.5858i	0.680352	+	1.17840i
$549$	−15.9040	−	27.5465i	−0.678766	−	1.17566i
$550$	2.13130	+	4.92803i	0.0908790	+	0.210132i
$551$			3.73743i			0.159220i
$552$	4.66317	−	8.07684i	0.198478	−	0.343773i
$553$	23.1073	−	40.0230i	0.982622	−	1.70195i
$554$			4.47964i			0.190322i
$555$	−8.75889	+	7.80221i	−0.371794	+	0.331185i
$556$	0.970706	+	1.68131i	0.0411671	+	0.0713035i
$557$	17.9189	+	31.0364i	0.759247	+	1.31506i	0.943235	+	0.332126i	$0.107766\pi$
$557$	17.9189	+	31.0364i	0.759247	+	1.31506i	−0.183987	+	0.982929i	$0.558901\pi$
$558$		−	5.31119i		−	0.224840i
$559$		0			0
$560$	−7.90253	+	23.8865i	−0.333943	+	1.00939i
$561$	14.7457	−	8.51345i	0.622565	−	0.359438i
$562$	0.133147	−	0.0768725i	0.00561647	−	0.00324267i
$563$	−4.33196	−	2.50106i	−0.182570	−	0.105407i	0.405929	−	0.913904i	$-0.366948\pi$
$563$	−4.33196	−	2.50106i	−0.182570	−	0.105407i	−0.588500	+	0.808497i	$0.700281\pi$
$564$		−	34.9593i		−	1.47205i
$565$	−12.2429	+	10.9057i	−0.515062	+	0.458805i
$566$	2.88244	+	1.66418i	0.121158	+	0.0699507i
$567$	−12.4432			−0.522564
$568$	5.84746	+	3.37603i	0.245354	+	0.141655i
$569$	6.58402	+	11.4039i	0.276017	+	0.478075i	0.970391	−	0.241539i	$-0.0776522\pi$
$569$	6.58402	+	11.4039i	0.276017	+	0.478075i	−0.694375	+	0.719614i	$0.744319\pi$
$570$	2.42932	−	0.502818i	0.101753	−	0.0210607i
$571$	−19.8349			−0.830065			−0.415032	−	0.909807i	$-0.636230\pi$
$571$	−19.8349			−0.830065			−0.415032	+	0.909807i	$0.636230\pi$
$572$		0			0
$573$		−	68.6909i		−	2.86960i
$574$	2.67212	−	1.54275i	0.111532	−	0.0643930i
$575$	13.3695	+	1.54979i	0.557547	+	0.0646307i
$576$	−11.6582	+	20.1926i	−0.485758	+	0.841357i
$577$	10.9210			0.454646			0.227323	−	0.973819i	$-0.427003\pi$
$577$	10.9210			0.454646			0.227323	+	0.973819i	$0.427003\pi$
$578$	2.18388	−	3.78258i	0.0908373	−	0.157335i
$579$	46.2054	+	26.6767i	1.92023	+	1.10865i
$580$	−3.98339	+	12.0404i	−0.165401	+	0.499949i
$581$	−14.4527	+	25.0329i	−0.599601	+	1.03854i
$582$	4.06139	−	2.34484i	0.168350	−	0.0971969i
$583$	20.8276	+	36.0745i	0.862593	+	1.49406i
$584$	7.03411			0.291073
$585$		0			0
$586$	−4.44979			−0.183819
$587$	−20.2247	−	35.0303i	−0.834764	−	1.44585i	−0.894222	−	0.447624i	$-0.852270\pi$
$587$	−20.2247	−	35.0303i	−0.834764	−	1.44585i	0.0594576	−	0.998231i	$-0.481063\pi$
$588$	18.7121	−	10.8034i	0.771673	−	0.445526i
$589$	2.35526	−	4.07944i	0.0970469	−	0.168090i
$590$	1.78062	+	0.589093i	0.0733069	+	0.0242526i
$591$	−50.4744	−	29.1414i	−2.07624	−	1.19872i
$592$	−3.26938	+	5.66274i	−0.134371	+	0.232737i
$593$	1.47709			0.0606569			0.0303284	−	0.999540i	$-0.490345\pi$
$593$	1.47709			0.0606569			0.0303284	+	0.999540i	$0.490345\pi$
$594$	1.80054	−	3.11862i	0.0738769	−	0.127959i
$595$	−2.96188	−	14.3100i	−0.121425	−	0.586654i
$596$	−25.9533	+	14.9842i	−1.06309	+	0.613775i
$597$		−	49.0690i		−	2.00826i
$598$		0			0
$599$	−2.27271			−0.0928606			−0.0464303	−	0.998922i	$-0.514785\pi$
$599$	−2.27271			−0.0928606			−0.0464303	+	0.998922i	$0.514785\pi$
$600$	17.2083	+	1.99479i	0.702528	+	0.0814369i
$601$	−3.70215	−	6.41231i	−0.151014	−	0.261563i	0.780587	−	0.625048i	$-0.214920\pi$
$601$	−3.70215	−	6.41231i	−0.151014	−	0.261563i	−0.931600	+	0.363484i	$0.881587\pi$
$602$	8.39472	+	4.84669i	0.342143	+	0.197536i
$603$	−17.0476			−0.694231
$604$	23.8147	+	13.7494i	0.969005	+	0.559456i
$605$	−0.691182	−	0.775932i	−0.0281006	−	0.0315461i
$606$		−	5.08549i		−	0.206584i
$607$	9.26059	+	5.34661i	0.375876	+	0.217012i	0.676022	−	0.736881i	$-0.263702\pi$
$607$	9.26059	+	5.34661i	0.375876	+	0.217012i	−0.300146	+	0.953893i	$0.597036\pi$
$608$	3.97502	−	2.29498i	0.161208	−	0.0930736i
$609$	23.4526	−	13.5404i	0.950347	−	0.548683i
$610$	−1.74074	+	5.26162i	−0.0704804	+	0.213037i
$611$		0			0
$612$		−	15.6429i		−	0.632327i
$613$	3.04075	+	5.26673i	0.122815	+	0.212721i	0.920877	−	0.389854i	$-0.127475\pi$
$613$	3.04075	+	5.26673i	0.122815	+	0.212721i	−0.798062	+	0.602575i	$0.794141\pi$
$614$	−4.07057	−	7.05043i	−0.164275	−	0.284532i
$615$	11.1343	+	12.4996i	0.448980	+	0.504032i
$616$		−	14.0101i		−	0.564485i
$617$	−15.9194	+	27.5732i	−0.640892	+	1.11006i	0.344342	+	0.938844i	$0.388102\pi$
$617$	−15.9194	+	27.5732i	−0.640892	+	1.11006i	−0.985234	+	0.171213i	$0.945231\pi$
$618$	3.28106	−	5.68295i	0.131983	−	0.228602i
$619$			26.4043i			1.06128i	0.847598	+	0.530639i	$0.178048\pi$
$619$			26.4043i			1.06128i	−0.847598	+	0.530639i	$0.821952\pi$
$620$	11.9355	−	10.6319i	0.479342	−	0.426987i
$621$	−4.51345	−	7.81753i	−0.181119	−	0.313707i
$622$	−0.403259	−	0.698464i	−0.0161692	−	0.0280059i
$623$		−	34.5957i		−	1.38605i
$624$		0			0
$625$	7.21560	+	23.9361i	0.288624	+	0.957443i
$626$	−5.52871	+	3.19200i	−0.220972	+	0.127578i
$627$	9.42647	−	5.44238i	0.376457	−	0.217348i
$628$	−17.8805	−	10.3233i	−0.713509	−	0.411944i
$629$		−	3.79785i		−	0.151430i
$630$	−7.00607	−	7.86513i	−0.279129	−	0.313354i
$631$	−30.4564	−	17.5840i	−1.21245	−	0.700009i	−0.249158	−	0.968463i	$-0.580154\pi$
$631$	−30.4564	−	17.5840i	−1.21245	−	0.700009i	−0.963293	+	0.268454i	$0.913487\pi$
$632$	−17.7381			−0.705585
$633$	44.9907	+	25.9754i	1.78822	+	1.03243i
$634$	−4.76764	−	8.25780i	−0.189347	−	0.327959i
$635$	−4.15310	−	20.0653i	−0.164811	−	0.796269i
$636$	65.3098			2.58970
$637$		0			0
$638$		−	3.22150i		−	0.127540i
$639$	19.2887	−	11.1364i	0.763051	−	0.440547i
$640$	20.1130	−	4.16297i	0.795036	−	0.164556i
$641$	2.76257	−	4.78491i	0.109115	−	0.188993i	−0.806297	−	0.591511i	$-0.798532\pi$
$641$	2.76257	−	4.78491i	0.109115	−	0.188993i	0.915412	+	0.402518i	$0.131865\pi$
$642$	7.63594			0.301367
$643$	−16.0776	+	27.8472i	−0.634039	+	1.09819i	0.352679	+	0.935744i	$0.385271\pi$
$643$	−16.0776	+	27.8472i	−0.634039	+	1.09819i	−0.986718	+	0.162444i	$0.948062\pi$
$644$	−14.7794	−	8.53289i	−0.582390	−	0.336243i
$645$	−16.5179	+	49.9276i	−0.650391	+	1.96590i
$646$	−0.401610	+	0.695609i	−0.0158011	+	0.0273684i
$647$	11.9376	−	6.89216i	0.469314	−	0.270959i	−0.246638	−	0.969108i	$-0.579326\pi$
$647$	11.9376	−	6.89216i	0.469314	−	0.270959i	0.715953	+	0.698149i	$0.245993\pi$
$648$	2.38797	+	4.13609i	0.0938085	+	0.162481i
$649$	8.22905			0.323019
$650$		0			0
$651$	−34.1316			−1.33772
$652$	3.94916	+	6.84015i	0.154661	+	0.267881i
$653$	−7.36296	+	4.25101i	−0.288135	+	0.166355i	−0.637100	−	0.770781i	$-0.719866\pi$
$653$	−7.36296	+	4.25101i	−0.288135	+	0.166355i	0.348965	+	0.937136i	$0.386533\pi$
$654$	−3.78109	+	6.54905i	−0.147852	+	0.256088i
$655$	−7.02335	+	21.2291i	−0.274425	+	0.829488i
$656$	8.08115	+	4.66565i	0.315516	+	0.182163i
$657$	11.6015	−	20.0944i	0.452619	−	0.783959i
$658$	7.62150			0.297117
$659$	2.02183	−	3.50192i	0.0787594	−	0.136415i	−0.823956	−	0.566654i	$-0.808237\pi$
$659$	2.02183	−	3.50192i	0.0787594	−	0.136415i	0.902715	+	0.430239i	$0.141571\pi$
$660$	36.1685	−	7.48611i	1.40786	−	0.291397i
$661$	27.0830	−	15.6364i	1.05341	−	0.608184i	0.129805	−	0.991540i	$-0.458565\pi$
$661$	27.0830	−	15.6364i	1.05341	−	0.608184i	0.923601	+	0.383356i	$0.125232\pi$
$662$		−	0.983609i		−	0.0382290i
$663$		0			0
$664$	11.0945			0.430551
$665$	−1.89343	−	9.14794i	−0.0734241	−	0.354742i
$666$	−1.36872	−	2.37068i	−0.0530366	−	0.0918622i
$667$	−6.99351	−	4.03771i	−0.270790	−	0.156341i
$668$	6.33991			0.245298
$669$	28.8383	+	16.6498i	1.11495	+	0.643719i
$670$	1.97570	+	2.21795i	0.0763278	+	0.0856869i
$671$			24.3164i			0.938723i
$672$	−28.8022	−	16.6290i	−1.11107	−	0.641477i
$673$	−27.7768	+	16.0370i	−1.07072	+	0.618179i	−0.928377	−	0.371639i	$-0.878796\pi$
$673$	−27.7768	+	16.0370i	−1.07072	+	0.618179i	−0.142340	+	0.989818i	$0.545463\pi$
$674$	0.545433	−	0.314906i	0.0210093	−	0.0121297i
$675$	10.0000	−	13.4590i	0.384900	−	0.518038i
$676$		0			0
$677$			14.2382i			0.547220i	0.961841	+	0.273610i	$0.0882177\pi$
$677$			14.2382i			0.547220i	−0.961841	+	0.273610i	$0.911782\pi$
$678$	−3.26493	−	5.65503i	−0.125389	−	0.217180i
$679$	−8.82983	−	15.2937i	−0.338858	−	0.586919i
$680$	−4.18822	+	3.73077i	−0.160611	+	0.143068i
$681$		−	16.5891i		−	0.635695i
$682$	−2.03013	+	3.51629i	−0.0777377	+	0.134646i
$683$	12.8923	−	22.3302i	0.493311	−	0.854440i	−0.506659	−	0.862146i	$-0.669120\pi$
$683$	12.8923	−	22.3302i	0.493311	−	0.854440i	0.999970	+	0.00770647i	$0.00245307\pi$
$684$		−	10.0000i		−	0.382360i
$685$	−25.0595	−	28.1322i	−0.957473	−	1.07487i
$686$	−1.52782	−	2.64626i	−0.0583325	−	0.101035i
$687$	−36.3168	−	62.9025i	−1.38557	−	2.39988i
$688$			29.3152i			1.11763i
$689$		0			0
$690$	−1.68362	+	5.08898i	−0.0640944	+	0.193734i
$691$	0.0378138	−	0.0218318i	0.00143851	−	0.000830522i	−0.499281	−	0.866440i	$-0.666402\pi$
$691$	0.0378138	−	0.0218318i	0.00143851	−	0.000830522i	0.500719	+	0.865610i	$0.333069\pi$
$692$	14.3049	−	8.25894i	0.543791	−	0.313958i
$693$	−40.0230	−	23.1073i	−1.52035	−	0.877774i
$694$			4.18002i			0.158671i
$695$	−1.52734	−	1.71461i	−0.0579352	−	0.0650390i
$696$	−9.00160	−	5.19707i	−0.341205	−	0.196995i
$697$	−5.41982			−0.205290
$698$	−2.57091	−	1.48431i	−0.0973103	−	0.0561821i
$699$	1.10945	+	1.92163i	0.0419634	+	0.0726827i
$700$	3.65016	−	31.4887i	0.137963	−	1.19016i
$701$	14.5454			0.549373			0.274687	−	0.961534i	$-0.411426\pi$
$701$	14.5454			0.549373			0.274687	+	0.961534i	$0.411426\pi$
$702$		0			0
$703$		−	2.42785i		−	0.0915679i
$704$	15.4367	−	8.91238i	0.581792	−	0.335898i
$705$	8.38064	+	40.4903i	0.315633	+	1.52495i
$706$	5.66565	−	9.81320i	0.213230	−	0.369325i
$707$	−19.1501			−0.720214
$708$	6.45101	−	11.1735i	0.242444	−	0.419925i
$709$	17.0025	+	9.81638i	0.638541	+	0.368662i	0.784052	−	0.620695i	$-0.213149\pi$
$709$	17.0025	+	9.81638i	0.638541	+	0.368662i	−0.145511	+	0.989357i	$0.546483\pi$
$710$	−3.68431	−	1.21891i	−0.138270	−	0.0457447i
$711$	−29.2560	+	50.6728i	−1.09718	+	1.90038i
$712$	−11.4996	+	6.63929i	−0.430965	+	0.248818i
$713$	5.08898	+	8.81438i	0.190584	+	0.330101i
$714$	5.81998			0.217807
$715$		0			0
$716$	34.0490			1.27247
$717$	−5.38361	−	9.32468i	−0.201055	−	0.348237i
$718$	6.41912	−	3.70608i	0.239559	−	0.138310i
$719$	−23.7156	+	41.0766i	−0.884443	+	1.53190i	−0.0380914	+	0.999274i	$0.512128\pi$
$719$	−23.7156	+	41.0766i	−0.884443	+	1.53190i	−0.846351	+	0.532625i	$0.821206\pi$
$720$	10.0053	−	30.2425i	0.372876	−	1.12707i
$721$	−21.3999	−	12.3553i	−0.796976	−	0.460134i
$722$	2.88621	−	4.99906i	0.107414	−	0.186046i
$723$	61.0872			2.27186
$724$	−0.986548	+	1.70875i	−0.0366648	+	0.0635052i
$725$	1.72723	−	14.9002i	0.0641477	−	0.553380i
$726$	0.358406	−	0.206926i	0.0133017	−	0.00767973i
$727$		−	34.0951i		−	1.26452i	−0.774757	−	0.632259i	$-0.782128\pi$
$727$		−	34.0951i		−	1.26452i	0.774757	−	0.632259i	$-0.217872\pi$
$728$		0			0
$729$	42.8349			1.58648
$730$	−3.95890	+	0.819409i	−0.146525	+	0.0303277i
$731$	−8.51345	−	14.7457i	−0.314881	−	0.545391i
$732$	33.0170	+	19.0624i	1.22034	+	0.704565i
$733$	14.3920			0.531580			0.265790	−	0.964031i	$-0.414367\pi$
$733$	14.3920			0.531580			0.265790	+	0.964031i	$0.414367\pi$
$734$	−3.78055	−	2.18270i	−0.139543	−	0.0805651i
$735$	−19.0827	+	16.9984i	−0.703877	+	0.626997i
$736$			9.91745i			0.365562i
$737$	11.2864	+	6.51621i	0.415740	+	0.240028i
$738$	−3.38314	+	1.95326i	−0.124535	+	0.0719004i
$739$	29.8328	−	17.2240i	1.09742	−	0.633594i	0.161876	−	0.986811i	$-0.448246\pi$
$739$	29.8328	−	17.2240i	1.09742	−	0.633594i	0.935541	+	0.353217i	$0.114912\pi$
$740$	2.58762	−	7.82145i	0.0951228	−	0.287522i
$741$		0			0
$742$			14.2382i			0.522702i
$743$	20.3567	+	35.2589i	0.746816	+	1.29352i	0.949342	+	0.314246i	$0.101752\pi$
$743$	20.3567	+	35.2589i	0.746816	+	1.29352i	−0.202526	+	0.979277i	$0.564915\pi$
$744$	6.55021	+	11.3453i	0.240142	+	0.415939i
$745$	26.4674	−	23.5765i	0.969690	−	0.863777i
$746$		−	5.04903i		−	0.184858i
$747$	18.2985	−	31.6939i	0.669507	−	1.15962i
$748$	−5.97929	+	10.3564i	−0.218625	+	0.378669i
$749$		−	28.7542i		−	1.05066i
$750$	−9.91748	+	0.881918i	−0.362135	+	0.0322031i
$751$	16.2509	+	28.1474i	0.593003	+	1.02711i	0.993825	+	0.110956i	$0.0353912\pi$
$751$	16.2509	+	28.1474i	0.593003	+	1.02711i	−0.400822	+	0.916156i	$0.631275\pi$
$752$	11.5247	+	19.9613i	0.420261	+	0.727914i
$753$			51.2167i			1.86644i
$754$		0			0
$755$	−30.8786	−	10.2158i	−1.12379	−	0.371790i
$756$	−18.4123	+	10.6304i	−0.669650	+	0.386623i
$757$	−11.2864	+	6.51621i	−0.410211	+	0.236836i	−0.690881	−	0.722969i	$-0.742777\pi$
$757$	−11.2864	+	6.51621i	−0.410211	+	0.236836i	0.280669	+	0.959805i	$0.409444\pi$
$758$	5.22286	+	3.01542i	0.189703	+	0.109525i
$759$			23.5185i			0.853668i
$760$	−2.67739	+	2.38496i	−0.0971193	+	0.0865116i
$761$	3.45532	+	1.99493i	0.125255	+	0.0723161i	0.561318	−	0.827600i	$-0.310294\pi$
$761$	3.45532	+	1.99493i	0.125255	+	0.0723161i	−0.436063	+	0.899916i	$0.643628\pi$
$762$	8.16070			0.295631
$763$	24.6613	+	14.2382i	0.892800	+	0.515458i
$764$	24.1220	+	41.7805i	0.872703	+	1.51157i
$765$	3.75001	+	18.1178i	0.135582	+	0.655051i
$766$	0.476696			0.0172237
$767$		0			0
$768$		−	21.3847i		−	0.771652i
$769$	5.77367	−	3.33343i	0.208204	−	0.120207i	−0.392272	−	0.919849i	$-0.628311\pi$
$769$	5.77367	−	3.33343i	0.208204	−	0.120207i	0.600476	+	0.799642i	$0.294978\pi$
$770$	1.63205	+	7.88512i	0.0588151	+	0.284160i
$771$	2.84181	−	4.92216i	0.102345	−	0.177267i
$772$	−37.4720			−1.34865
$773$	24.1675	−	41.8593i	0.869244	−	1.50557i	0.00647254	−	0.999979i	$-0.497940\pi$
$773$	24.1675	−	41.8593i	0.869244	−	1.50557i	0.862771	−	0.505595i	$-0.168727\pi$
$774$	−10.6285	−	6.13636i	−0.382033	−	0.220567i
$775$	−11.2751	+	15.1752i	−0.405015	+	0.545111i
$776$	−3.38907	+	5.87005i	−0.121661	+	0.210723i
$777$	−15.2349	+	8.79585i	−0.546548	+	0.315549i
$778$	−3.10841	−	5.38393i	−0.111442	−	0.193023i
$779$	−3.46472			−0.124136
$780$		0			0
$781$	−17.0269			−0.609271
$782$	−0.867753	−	1.50299i	−0.0310308	−	0.0537469i
$783$	−8.71259	+	5.03022i	−0.311363	+	0.179765i
$784$	−7.12291	+	12.3372i	−0.254389	+	0.440615i
$785$	23.1842	+	7.67017i	0.827478	+	0.273760i
$786$	−7.71236	−	4.45274i	−0.275091	−	0.158824i
$787$	−13.9806	+	24.2151i	−0.498355	+	0.863176i	−0.999998	−	0.00189876i	$-0.999396\pi$
$787$	−13.9806	+	24.2151i	−0.498355	+	0.863176i	0.501643	+	0.865074i	$0.332729\pi$
$788$	40.9341			1.45822
$789$	−40.2658	+	69.7424i	−1.43350	+	2.48290i
$790$	9.98328	−	2.06633i	0.355189	−	0.0735167i
$791$	−21.2948	+	12.2945i	−0.757155	+	0.437144i
$792$			17.7381i			0.630297i
$793$		0			0
$794$	−5.65488			−0.200684
$795$	−75.6426	+	15.6564i	−2.68277	+	0.555277i
$796$	17.2314	+	29.8457i	0.610752	+	1.05785i
$797$	32.2529	+	18.6212i	1.14246	+	0.659597i	0.947038	−	0.321123i	$-0.104060\pi$
$797$	32.2529	+	18.6212i	1.14246	+	0.659597i	0.195418	+	0.980720i	$0.437393\pi$
$798$	3.72052			0.131705
$799$	−11.5939	−	6.69377i	−0.410164	−	0.236808i
$800$	−16.9080	+	7.31249i	−0.597789	+	0.258535i
$801$			43.8014i			1.54765i
$802$	6.36120	+	3.67264i	0.224622	+	0.129685i
$803$	−15.3617	+	8.86907i	−0.542102	+	0.312983i
$804$	17.6955	−	10.2165i	0.624073	−	0.360309i
$805$	19.1633	+	6.33991i	0.675416	+	0.223452i
$806$		0			0
$807$			50.0382i			1.76143i
$808$	3.67511	+	6.36548i	0.129290	+	0.223937i
$809$	7.26434	+	12.5822i	0.255400	+	0.442367i	0.965004	−	0.262234i	$-0.0844594\pi$
$809$	7.26434	+	12.5822i	0.255400	+	0.442367i	−0.709604	+	0.704601i	$0.751126\pi$
$810$	−1.82580	−	2.04968i	−0.0641522	−	0.0720183i
$811$		−	44.0538i		−	1.54694i	−0.633834	−	0.773469i	$-0.718520\pi$
$811$		−	44.0538i		−	1.54694i	0.633834	−	0.773469i	$-0.281480\pi$
$812$	−9.50986	+	16.4716i	−0.333731	+	0.578039i
$813$	−7.83955	+	13.5785i	−0.274945	+	0.476219i
$814$			2.09269i			0.0733489i
$815$	−6.21373	−	6.97563i	−0.217657	−	0.244346i
$816$	8.80054	+	15.2430i	0.308080	+	0.533611i
$817$	−5.44238	−	9.42647i	−0.190405	−	0.329790i
$818$			3.18687i			0.111426i
$819$		0			0
$820$	−11.1618	−	3.69273i	−0.389787	−	0.128956i
$821$	−23.4060	+	13.5135i	−0.816875	+	0.471623i	−0.849337	−	0.527850i	$-0.822998\pi$
$821$	−23.4060	+	13.5135i	−0.816875	+	0.471623i	0.0324629	+	0.999473i	$0.489665\pi$
$822$	12.9943	−	7.50229i	0.453230	−	0.261672i
$823$	34.2914	+	19.7981i	1.19532	+	0.690120i	0.959509	−	0.281679i	$-0.0908912\pi$
$823$	34.2914	+	19.7981i	1.19532	+	0.690120i	0.235814	+	0.971798i	$0.424225\pi$
$824$			9.48442i			0.330405i
$825$	−40.0962	+	17.3410i	−1.39597	+	0.603737i
$826$	2.43594	+	1.40639i	0.0847571	+	0.0489345i
$827$	26.5639			0.923716			0.461858	−	0.886954i	$-0.347183\pi$
$827$	26.5639			0.923716			0.461858	+	0.886954i	$0.347183\pi$
$828$	18.7121	+	10.8034i	0.650290	+	0.375445i
$829$	−6.99162	−	12.1098i	−0.242829	−	0.420592i	0.718690	−	0.695331i	$-0.244742\pi$
$829$	−6.99162	−	12.1098i	−0.242829	−	0.420592i	−0.961519	+	0.274738i	$0.911409\pi$
$830$	−6.24416	+	1.29241i	−0.216738	+	0.0448602i
$831$	−36.4480			−1.26437
$832$		0			0
$833$		−	8.27427i		−	0.286686i
$834$	0.791986	−	0.457254i	0.0274242	−	0.0158334i
$835$	−7.34297	+	1.51984i	−0.254114	+	0.0525962i
$836$	−3.82237	+	6.62054i	−0.132199	+	0.228976i
$837$	12.6798			0.438278
$838$	0.323614	−	0.560515i	0.0111791	−	0.0193627i
$839$	12.4657	+	7.19707i	0.430364	+	0.248471i	0.699502	−	0.714631i	$-0.253405\pi$
$839$	12.4657	+	7.19707i	0.430364	+	0.248471i	−0.269138	+	0.963102i	$0.586739\pi$
$840$	24.6657	+	8.16032i	0.851048	+	0.281558i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−3.46128	+	1.99837i	−0.119284	+	0.0688684i
$843$	0.625462	+	1.08333i	0.0215421	+	0.0373119i
$844$	−36.4868			−1.25593
$845$		0			0
$846$	−9.64952			−0.331757
$847$	−0.779207	−	1.34963i	−0.0267739	−	0.0463737i
$848$	−37.2910	+	21.5300i	−1.28058	+	0.739343i
$849$	−13.5404	+	23.4526i	−0.464704	+	0.804891i
$850$	1.92259	−	2.58762i	0.0659444	−	0.0887547i
$851$	4.54300	+	2.62291i	0.155732	+	0.0899120i
$852$	−13.3479	+	23.1193i	−0.457292	+	0.792053i
$853$	−27.2633			−0.933478			−0.466739	−	0.884395i	$-0.654571\pi$
$853$	−27.2633			−0.933478			−0.466739	+	0.884395i	$0.654571\pi$
$854$	−4.15580	+	7.19806i	−0.142209	+	0.246312i
$855$	2.39726	+	11.5821i	0.0819845	+	0.396101i
$856$	−9.55786	+	5.51823i	−0.326681	+	0.188609i
$857$			50.6201i			1.72915i	0.502503	+	0.864575i	$0.332413\pi$
$857$			50.6201i			1.72915i	−0.502503	+	0.864575i	$0.667587\pi$
$858$		0			0
$859$	−1.27992			−0.0436702			−0.0218351	−	0.999762i	$-0.506951\pi$
$859$	−1.27992			−0.0436702			−0.0218351	+	0.999762i	$0.506951\pi$
$860$	−7.48611	−	36.1685i	−0.255274	−	1.23333i
$861$	12.5523	+	21.7413i	0.427782	+	0.740941i
$862$	−7.04509	−	4.06749i	−0.239957	−	0.138539i
$863$	−8.38448			−0.285411			−0.142706	−	0.989765i	$-0.545580\pi$
$863$	−8.38448			−0.285411			−0.142706	+	0.989765i	$0.545580\pi$
$864$	10.7000	+	6.17763i	0.364020	+	0.210167i
$865$	−14.5882	+	12.9949i	−0.496015	+	0.441839i
$866$			11.9342i			0.405541i
$867$	30.7765	+	17.7688i	1.04522	+	0.603460i
$868$	20.7602	−	11.9859i	0.704646	−	0.406828i
$869$	38.7380	−	22.3654i	1.31410	−	0.758695i
$870$	5.67164	+	1.87639i	0.192287	+	0.0636155i
$871$		0			0
$872$		−	10.9299i		−	0.370132i
$873$	11.1794	+	19.3632i	0.378365	+	0.655347i
$874$	−0.554726	−	0.960814i	−0.0187639	−	0.0325000i
$875$	3.32098	+	37.3456i	0.112270	+	1.26251i
$876$			27.8109i			0.939645i
$877$	27.9431	−	48.3989i	0.943572	−	1.63431i	0.184985	−	0.982741i	$-0.440776\pi$
$877$	27.9431	−	48.3989i	0.943572	−	1.63431i	0.758586	−	0.651573i	$-0.225890\pi$
$878$	0.419382	−	0.726391i	0.0141535	−	0.0245145i
$879$		−	36.2051i		−	1.22117i
$880$	−18.1839	+	16.1978i	−0.612978	+	0.546026i
$881$	12.5975	+	21.8195i	0.424420	+	0.735116i	0.996366	−	0.0851746i	$-0.0271448\pi$
$881$	12.5975	+	21.8195i	0.424420	+	0.735116i	−0.571946	+	0.820291i	$0.693811\pi$
$882$	−2.98198	−	5.16494i	−0.100408	−	0.173913i
$883$		−	30.7868i		−	1.03606i	−0.855363	−	0.518029i	$-0.826666\pi$
$883$		−	30.7868i		−	1.03606i	0.855363	−	0.518029i	$-0.173334\pi$
$884$		0			0
$885$	−4.79307	+	14.4877i	−0.161117	+	0.487000i
$886$	−5.54628	+	3.20215i	−0.186331	+	0.107578i
$887$	−10.8011	+	6.23603i	−0.362666	+	0.209385i	−0.670250	−	0.742136i	$-0.733813\pi$
$887$	−10.8011	+	6.23603i	−0.362666	+	0.209385i	0.307584	+	0.951521i	$0.400480\pi$
$888$	5.84746	+	3.37603i	0.196228	+	0.113292i
$889$		−	30.7302i		−	1.03066i
$890$	5.69872	−	5.07628i	0.191021	−	0.170157i
$891$	−10.4301	−	6.02183i	−0.349422	−	0.201739i
$892$	−23.3875			−0.783071
$893$	−7.41163	−	4.27911i	−0.248021	−	0.143195i
$894$	7.05833	+	12.2254i	0.236066	+	0.408878i
$895$	−39.4360	+	8.16243i	−1.31820	+	0.272840i
$896$	30.8032			1.02906
$897$		0			0
$898$		−	8.20739i		−	0.273884i
$899$	9.82357	−	5.67164i	0.327634	−	0.189160i
$900$	−4.62144	+	39.8676i	−0.154048	+	1.32892i
$901$	12.5051	−	21.6594i	0.416604	−	0.721580i
$902$	2.98643			0.0994372
$903$	−39.4344	+	68.3024i	−1.31230	+	2.27296i
$904$	8.17338	+	4.71891i	0.271843	+	0.156948i
$905$	0.733001	−	2.21560i	0.0243658	−	0.0736490i
$906$	6.47670	−	11.2180i	0.215174	−	0.372692i
$907$	33.6807	−	19.4455i	1.11835	−	0.645678i	0.177369	−	0.984144i	$-0.443241\pi$
$907$	33.6807	−	19.4455i	1.11835	−	0.645678i	0.940979	+	0.338466i	$0.109908\pi$
$908$	5.82555	+	10.0901i	0.193328	+	0.334853i
$909$	24.2458			0.804183
$910$		0			0
$911$	0.165096			0.00546989			0.00273494	−	0.999996i	$-0.499129\pi$
$911$	0.165096			0.00546989			0.00273494	+	0.999996i	$0.499129\pi$
$912$	5.62590	+	9.74434i	0.186292	+	0.322667i
$913$	−24.2292	+	13.9887i	−0.801868	+	0.462959i
$914$	1.25180	−	2.16818i	0.0414059	−	0.0717171i
$915$	−42.8105	−	14.1633i	−1.41527	−	0.468223i
$916$	44.1786	+	25.5065i	1.45970	+	0.842760i
$917$	−16.7674	+	29.0420i	−0.553708	+	0.959050i
$918$	−2.16211			−0.0713603
$919$	0.447663	−	0.775375i	0.0147670	−	0.0255773i	−0.858547	−	0.512734i	$-0.828633\pi$
$919$	0.447663	−	0.775375i	0.0147670	−	0.0255773i	0.873314	+	0.487157i	$0.161966\pi$
$920$	−1.57025	−	7.58654i	−0.0517697	−	0.250121i
$921$	57.3648	−	33.1196i	1.89024	−	1.09133i
$922$		−	4.08361i		−	0.134486i
$923$		0			0
$924$	55.3923			1.82227
$925$	−1.12201	+	9.67923i	−0.0368916	+	0.318251i
$926$	3.78109	+	6.54905i	0.124254	+	0.215215i
$927$	27.0943	+	15.6429i	0.889893	+	0.513780i
$928$	11.0529			0.362831
$929$	10.6430	+	6.14474i	0.349185	+	0.201602i	0.664326	−	0.747443i	$-0.268718\pi$
$929$	10.6430	+	6.14474i	0.349185	+	0.201602i	−0.315141	+	0.949045i	$0.602052\pi$
$930$	−5.00818	−	5.62226i	−0.164225	−	0.184361i
$931$		−	5.28947i		−	0.173356i
$932$	−1.34963	−	0.779207i	−0.0442085	−	0.0255238i
$933$	5.68295	−	3.28106i	0.186052	−	0.107417i
$934$	−4.38296	+	2.53051i	−0.143415	+	0.0828007i
$935$	4.44259	−	13.4284i	0.145288	−	0.439154i
$936$		0			0
$937$		−	5.77242i		−	0.188577i	−0.995545	−	0.0942884i	$-0.969942\pi$
$937$		−	5.77242i		−	0.188577i	0.995545	−	0.0942884i	$-0.0300576\pi$
$938$	2.22731	+	3.85781i	0.0727242	+	0.125962i
$939$	−25.9713	−	44.9835i	−0.847540	−	1.46798i
$940$	−19.3163	−	21.6848i	−0.630029	−	0.707280i
$941$			55.8887i			1.82192i	0.412495	+	0.910960i	$0.364658\pi$
$941$			55.8887i			1.82192i	−0.412495	+	0.910960i	$0.635342\pi$
$942$	−4.86282	+	8.42264i	−0.158439	+	0.274425i
$943$	3.74308	−	6.48321i	0.121891	−	0.211122i
$944$			8.50655i			0.276864i
$945$	18.7770	−	16.7261i	0.610817	−	0.544102i
$946$	4.69108	+	8.12520i	0.152520	+	0.264173i
$947$	−0.948188	−	1.64231i	−0.0308120	−	0.0533679i	0.850208	−	0.526447i	$-0.176476\pi$
$947$	−0.948188	−	1.64231i	−0.0308120	−	0.0533679i	−0.881020	+	0.473079i	$0.843143\pi$
$948$		−	70.1318i		−	2.27777i
$949$		0			0
$950$	1.22905	−	1.65418i	0.0398757	−	0.0536688i
$951$	67.1884	−	38.7912i	2.17873	−	1.25789i
$952$	−7.28483	+	4.20590i	−0.236103	+	0.136314i
$953$	−29.1438	−	16.8262i	−0.944059	−	0.545053i	−0.0528285	−	0.998604i	$-0.516824\pi$
$953$	−29.1438	−	16.8262i	−0.944059	−	0.545053i	−0.891230	+	0.453551i	$0.850157\pi$
$954$		−	18.0269i		−	0.583643i
$955$	−37.9543	−	42.6081i	−1.22817	−	1.37877i
$956$	6.54905	+	3.78109i	0.211811	+	0.122289i
$957$	26.2113			0.847290
$958$	−6.95735	−	4.01683i	−0.224782	−	0.129778i
$959$	−28.2509	−	48.9320i	−0.912269	−	1.58010i
$960$	6.69956	+	32.3683i	0.216227	+	1.04468i
$961$	16.7033			0.538817
$962$		0			0
$963$			36.4054i			1.17315i
$964$	−37.1556	+	21.4518i	−1.19670	+	0.690917i
$965$	43.4005	−	8.98300i	1.39711	−	0.289173i
$966$	−4.01944	+	6.96188i	−0.129323	+	0.223995i
$967$	−23.0493			−0.741216			−0.370608	−	0.928789i	$-0.620851\pi$
$967$	−23.0493			−0.741216			−0.370608	+	0.928789i	$0.620851\pi$
$968$	−0.299076	+	0.518015i	−0.00961267	+	0.0166496i
$969$	−5.65972	−	3.26764i	−0.181816	−	0.104972i
$970$	1.22361	−	3.69855i	0.0392879	−	0.118753i
$971$	−7.45964	+	12.9205i	−0.239391	+	0.414638i	−0.960540	−	0.278143i	$-0.910281\pi$
$971$	−7.45964	+	12.9205i	−0.239391	+	0.414638i	0.721148	+	0.692781i	$0.243615\pi$
$972$	−32.8246	+	18.9513i	−1.05285	+	0.607862i
$973$	−1.72185	−	2.98233i	−0.0552000	−	0.0956092i
$974$	−12.2040			−0.391041
$975$		0			0
$976$	−25.1364			−0.804595
$977$	11.6821	+	20.2339i	0.373742	+	0.647341i	0.990138	−	0.140096i	$-0.0447411\pi$
$977$	11.6821	+	20.2339i	0.373742	+	0.647341i	−0.616396	+	0.787437i	$0.711408\pi$
$978$	3.22207	−	1.86026i	0.103030	−	0.0594846i
$979$	16.7425	−	28.9989i	0.535093	−	0.926808i
$980$	5.63757	−	17.0404i	0.180086	−	0.544334i
$981$	−31.2235	−	18.0269i	−0.996890	−	0.575555i
$982$	5.84810	−	10.1292i	0.186620	−	0.323236i
$983$	5.31119			0.169401			0.0847003	−	0.996406i	$-0.473007\pi$
$983$	5.31119			0.169401			0.0847003	+	0.996406i	$0.473007\pi$
$984$	4.81785	−	8.34476i	0.153587	−	0.266021i
$985$	−47.4104	+	9.81295i	−1.51062	+	0.312667i
$986$	−1.67508	+	0.967105i	−0.0533453	+	0.0307989i
$987$			62.0112i			1.97384i
$988$		0			0
$989$	23.5185			0.747846
$990$	−2.06633	−	9.98328i	−0.0656723	−	0.317289i
$991$	12.0440	+	20.8607i	0.382589	+	0.662663i	0.991432	−	0.130628i	$-0.0416992\pi$
$991$	12.0440	+	20.8607i	0.382589	+	0.662663i	−0.608843	+	0.793291i	$0.708366\pi$
$992$	−12.0644	−	6.96537i	−0.383044	−	0.221151i
$993$	8.00299			0.253967
$994$	−5.04025	−	2.90999i	−0.159867	−	0.0922993i
$995$	−27.1125	−	30.4369i	−0.859523	−	0.964915i
$996$			43.8648i			1.38991i
$997$	−17.6755	−	10.2050i	−0.559790	−	0.323195i	0.193271	−	0.981145i	$-0.438090\pi$
$997$	−17.6755	−	10.2050i	−0.559790	−	0.323195i	−0.753061	+	0.657951i	$0.771424\pi$
$998$	−4.64692	+	2.68290i	−0.147096	+	0.0849258i
$999$	5.65972	−	3.26764i	0.179066	−	0.103384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.l.f.699.7		24
5.4	even	2	inner	845.2.l.f.699.6		24
13.2	odd	12		845.2.b.e.339.4		6
13.3	even	3		845.2.d.d.844.5		12
13.4	even	6	inner	845.2.l.f.654.6		24
13.5	odd	4		845.2.n.e.484.4		12
13.6	odd	12		845.2.n.e.529.3		12
13.7	odd	12		65.2.n.a.9.4	yes	12
13.8	odd	4		65.2.n.a.29.3	yes	12
13.9	even	3	inner	845.2.l.f.654.8		24
13.10	even	6		845.2.d.d.844.7		12
13.11	odd	12		845.2.b.d.339.3		6
13.12	even	2	inner	845.2.l.f.699.5		24
39.8	even	4		585.2.bs.a.289.4		12
39.20	even	12		585.2.bs.a.334.3		12
52.7	even	12		1040.2.dh.a.529.1		12
52.47	even	4		1040.2.dh.a.289.6		12
65.2	even	12		4225.2.a.bq.1.3		6
65.4	even	6	inner	845.2.l.f.654.7		24
65.7	even	12		325.2.e.e.126.3		12
65.8	even	4		325.2.e.e.276.4		12
65.9	even	6	inner	845.2.l.f.654.5		24
65.19	odd	12		845.2.n.e.529.4		12
65.24	odd	12		845.2.b.d.339.4		6
65.28	even	12		4225.2.a.bq.1.4		6
65.29	even	6		845.2.d.d.844.8		12
65.33	even	12		325.2.e.e.126.4		12
65.34	odd	4		65.2.n.a.29.4	yes	12
65.37	even	12		4225.2.a.br.1.4		6
65.44	odd	4		845.2.n.e.484.3		12
65.47	even	4		325.2.e.e.276.3		12
65.49	even	6		845.2.d.d.844.6		12
65.54	odd	12		845.2.b.e.339.3		6
65.59	odd	12		65.2.n.a.9.3	✓	12
65.63	even	12		4225.2.a.br.1.3		6
65.64	even	2	inner	845.2.l.f.699.8		24
195.59	even	12		585.2.bs.a.334.4		12
195.164	even	4		585.2.bs.a.289.3		12
260.59	even	12		1040.2.dh.a.529.6		12
260.99	even	4		1040.2.dh.a.289.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.3	✓	12	65.59	odd	12
65.2.n.a.9.4	yes	12	13.7	odd	12
65.2.n.a.29.3	yes	12	13.8	odd	4
65.2.n.a.29.4	yes	12	65.34	odd	4
325.2.e.e.126.3		12	65.7	even	12
325.2.e.e.126.4		12	65.33	even	12
325.2.e.e.276.3		12	65.47	even	4
325.2.e.e.276.4		12	65.8	even	4
585.2.bs.a.289.3		12	195.164	even	4
585.2.bs.a.289.4		12	39.8	even	4
585.2.bs.a.334.3		12	39.20	even	12
585.2.bs.a.334.4		12	195.59	even	12
845.2.b.d.339.3		6	13.11	odd	12
845.2.b.d.339.4		6	65.24	odd	12
845.2.b.e.339.3		6	65.54	odd	12
845.2.b.e.339.4		6	13.2	odd	12
845.2.d.d.844.5		12	13.3	even	3
845.2.d.d.844.6		12	65.49	even	6
845.2.d.d.844.7		12	13.10	even	6
845.2.d.d.844.8		12	65.29	even	6
845.2.l.f.654.5		24	65.9	even	6	inner
845.2.l.f.654.6		24	13.4	even	6	inner
845.2.l.f.654.7		24	65.4	even	6	inner
845.2.l.f.654.8		24	13.9	even	3	inner
845.2.l.f.699.5		24	13.12	even	2	inner
845.2.l.f.699.6		24	5.4	even	2	inner
845.2.l.f.699.7		24	1.1	even	1	trivial
845.2.l.f.699.8		24	65.64	even	2	inner
845.2.n.e.484.3		12	65.44	odd	4
845.2.n.e.484.4		12	13.5	odd	4
845.2.n.e.529.3		12	13.6	odd	12
845.2.n.e.529.4		12	65.19	odd	12
1040.2.dh.a.289.1		12	260.99	even	4
1040.2.dh.a.289.6		12	52.47	even	4
1040.2.dh.a.529.1		12	52.7	even	12
1040.2.dh.a.529.6		12	260.59	even	12
4225.2.a.bq.1.3		6	65.2	even	12
4225.2.a.bq.1.4		6	65.28	even	12
4225.2.a.br.1.3		6	65.63	even	12
4225.2.a.br.1.4		6	65.37	even	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.165418 + 0.286513i) q^{2} +(-2.33117 + 1.34590i) q^{3} +(0.945274 - 1.63726i) q^{4} +(-0.702335 + 2.12291i) q^{5} +(-0.771236 - 0.445274i) q^{6} +(-1.67674 + 2.90420i) q^{7} +1.28714 q^{8} +(2.12291 - 3.67698i) q^{9} +O(q^{10})\)	\(q+(0.165418 + 0.286513i) q^{2} +(-2.33117 + 1.34590i) q^{3} +(0.945274 - 1.63726i) q^{4} +(-0.702335 + 2.12291i) q^{5} +(-0.771236 - 0.445274i) q^{6} +(-1.67674 + 2.90420i) q^{7} +1.28714 q^{8} +(2.12291 - 3.67698i) q^{9} +(-0.724419 + 0.149939i) q^{10} +(-2.81095 + 1.62291i) q^{11} +5.08898i q^{12} -1.10945 q^{14} +(-1.21996 - 5.89413i) q^{15} +(-1.67763 - 2.90574i) q^{16} +(1.68772 + 0.974404i) q^{17} +1.40467 q^{18} +(1.07890 + 0.622905i) q^{19} +(2.81185 + 3.15663i) q^{20} -9.02690i q^{21} +(-0.929966 - 0.536916i) q^{22} +(-2.33117 + 1.34590i) q^{23} +(-3.00053 + 1.73236i) q^{24} +(-4.01345 - 2.98198i) q^{25} +3.35348i q^{27} +(3.16995 + 5.49052i) q^{28} +(1.50000 + 2.59808i) q^{29} +(1.48694 - 1.32453i) q^{30} -3.78109i q^{31} +(1.84216 - 3.19071i) q^{32} +(4.36854 - 7.56654i) q^{33} +0.644737i q^{34} +(-4.98770 - 5.59927i) q^{35} +(-4.01345 - 6.95150i) q^{36} +(-0.974404 - 1.68772i) q^{37} +0.412160i q^{38} +(-0.904000 + 2.73247i) q^{40} +(-2.40850 + 1.39055i) q^{41} +(2.58632 - 1.49321i) q^{42} +(-7.56654 - 4.36854i) q^{43} +6.13636i q^{44} +(6.31489 + 7.08920i) q^{45} +(-0.771236 - 0.445274i) q^{46} -6.86960 q^{47} +(7.82169 + 4.51586i) q^{48} +(-2.12291 - 3.67698i) q^{49} +(0.190477 - 1.64318i) q^{50} -5.24581 q^{51} -12.8336i q^{53} +(-0.960814 + 0.554726i) q^{54} +(-1.47104 - 7.10721i) q^{55} +(-2.15819 + 3.73809i) q^{56} -3.35348 q^{57} +(-0.496255 + 0.859539i) q^{58} +(-2.19562 - 1.26764i) q^{59} +(-10.8034 - 3.57417i) q^{60} +(3.74581 - 6.48793i) q^{61} +(1.08333 - 0.625462i) q^{62} +(7.11911 + 12.3307i) q^{63} -5.49162 q^{64} +2.89055 q^{66} +(-2.00758 - 3.47722i) q^{67} +(3.19071 - 1.84216i) q^{68} +(3.62291 - 6.27506i) q^{69} +(0.779207 - 2.35526i) q^{70} +(4.54300 + 2.62291i) q^{71} +(2.73247 - 4.73277i) q^{72} +5.46493 q^{73} +(0.322368 - 0.558359i) q^{74} +(13.3695 + 1.54979i) q^{75} +(2.03972 - 1.17763i) q^{76} -10.8848i q^{77} -13.7811 q^{79} +(7.34688 - 1.52065i) q^{80} +(1.85526 + 3.21341i) q^{81} +(-0.796819 - 0.460044i) q^{82} +8.61955 q^{83} +(-14.7794 - 8.53289i) q^{84} +(-3.25391 + 2.89851i) q^{85} -2.89055i q^{86} +(-6.99351 - 4.03771i) q^{87} +(-3.61808 + 2.08890i) q^{88} +(-8.93425 + 5.15819i) q^{89} +(-0.986548 + 2.98198i) q^{90} +5.08898i q^{92} +(5.08898 + 8.81438i) q^{93} +(-1.13636 - 1.96823i) q^{94} +(-2.08012 + 1.85292i) q^{95} +9.91745i q^{96} +(-2.63304 + 4.56055i) q^{97} +(0.702335 - 1.21648i) q^{98} +13.7811i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4} + 12 q^{9}+O(q^{10}) \) 24 * q - 8 * q^4 + 12 * q^9	\( 24 q - 8 q^{4} + 12 q^{9} - 14 q^{10} - 88 q^{14} - 32 q^{16} + 4 q^{25} + 36 q^{29} - 8 q^{30} + 20 q^{35} + 4 q^{36} + 140 q^{40} - 12 q^{49} - 48 q^{51} - 52 q^{55} + 32 q^{56} + 12 q^{61} + 24 q^{64} + 8 q^{66} + 48 q^{69} + 16 q^{74} - 4 q^{75} - 208 q^{79} + 28 q^{81} - 124 q^{90} + 112 q^{94} - 40 q^{95}+O(q^{100}) \) 24 * q - 8 * q^4 + 12 * q^9 - 14 * q^10 - 88 * q^14 - 32 * q^16 + 4 * q^25 + 36 * q^29 - 8 * q^30 + 20 * q^35 + 4 * q^36 + 140 * q^40 - 12 * q^49 - 48 * q^51 - 52 * q^55 + 32 * q^56 + 12 * q^61 + 24 * q^64 + 8 * q^66 + 48 * q^69 + 16 * q^74 - 4 * q^75 - 208 * q^79 + 28 * q^81 - 124 * q^90 + 112 * q^94 - 40 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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