LMFDB - Embedded newform 900.2.o.a.299.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(299,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.299"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,2,0,-6,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.7465802011608416256.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + x^{12} + 8x^{10} - 20x^{8} + 32x^{6} + 16x^{4} - 64x^{2} + 256 $ x^16 - x^14 + x^12 + 8x^10 - 20x^8 + 32x^6 + 16x^4 - 64*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.3
Root			$1.37379 + 0.335728i$ of defining polynomial
Character	$\chi$	$=$	900.299
Dual form			900.2.o.a.599.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.977642 - 1.02187i) q^{2} +(-1.07561 - 1.35760i) q^{3} +(-0.0884324 + 1.99804i) q^{4} +(-0.335728 + 2.42637i) q^{6} +(0.637910 - 1.10489i) q^{7} +(2.12819 - 1.86301i) q^{8} +(-0.686141 + 2.92048i) q^{9} +(0.252704 - 0.437696i) q^{11} +(2.80766 - 2.02905i) q^{12} +(-2.05446 + 1.18614i) q^{13} +(-1.75270 + 0.428329i) q^{14} +(-3.98436 - 0.353383i) q^{16} -0.792287 q^{17} +(3.65515 - 2.15404i) q^{18} +4.70285i q^{19} +(-2.18614 + 0.322405i) q^{21} +(-0.694322 + 0.169680i) q^{22} +(-2.78912 + 1.61030i) q^{23} +(-4.81831 - 0.885370i) q^{24} +(3.22060 + 0.939764i) q^{26} +(4.70285 - 2.20979i) q^{27} +(2.15121 + 1.37228i) q^{28} +(-2.18614 - 1.26217i) q^{29} +(-7.04069 + 4.06494i) q^{31} +(3.53417 + 4.41698i) q^{32} +(-0.866025 + 0.127719i) q^{33} +(0.774573 + 0.809613i) q^{34} +(-5.77457 - 1.62920i) q^{36} +6.74456i q^{37} +(4.80570 - 4.59771i) q^{38} +(3.82009 + 1.51330i) q^{39} +(5.87228 - 3.39036i) q^{41} +(2.46672 + 1.91875i) q^{42} +(-3.86473 + 6.69391i) q^{43} +(0.852189 + 0.543620i) q^{44} +(4.37228 + 1.27582i) q^{46} +(-1.03834 - 0.599485i) q^{47} +(3.80585 + 5.78926i) q^{48} +(2.68614 + 4.65253i) q^{49} +(0.852189 + 1.07561i) q^{51} +(-2.18828 - 4.20979i) q^{52} +1.87953 q^{53} +(-6.85582 - 2.64532i) q^{54} +(-0.700825 - 3.53986i) q^{56} +(6.38458 - 5.05842i) q^{57} +(0.847492 + 3.46790i) q^{58} +(6.18850 + 10.7188i) q^{59} +(1.18614 - 2.05446i) q^{61} +(11.0371 + 3.22060i) q^{62} +(2.78912 + 2.62112i) q^{63} +(1.05842 - 7.92967i) q^{64} +(0.977175 + 0.760101i) q^{66} +(-3.86473 - 6.69391i) q^{67} +(0.0700638 - 1.58302i) q^{68} +(5.18614 + 2.05446i) q^{69} +11.8716 q^{71} +(3.98063 + 7.49364i) q^{72} +3.37228i q^{73} +(6.89206 - 6.59377i) q^{74} +(-9.39651 - 0.415885i) q^{76} +(-0.322405 - 0.558422i) q^{77} +(-2.18828 - 5.38310i) q^{78} +(8.55691 + 4.94034i) q^{79} +(-8.05842 - 4.00772i) q^{81} +(-9.20550 - 2.68614i) q^{82} +(-6.61659 - 3.82009i) q^{83} +(-0.450854 - 4.39652i) q^{84} +(10.6186 - 2.59500i) q^{86} +(0.637910 + 4.32550i) q^{87} +(-0.277627 - 1.40229i) q^{88} -11.9769i q^{89} +3.02661i q^{91} +(-2.97080 - 5.71519i) q^{92} +(13.0916 + 5.18614i) q^{93} +(0.402528 + 1.64713i) q^{94} +(2.19510 - 9.54890i) q^{96} +(9.08385 + 5.24456i) q^{97} +(2.12819 - 7.29339i) q^{98} +(1.10489 + 1.03834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} - 6 q^{6} + 12 q^{9} - 24 q^{14} - 2 q^{16} - 12 q^{21} - 6 q^{24} - 12 q^{29} - 14 q^{34} - 66 q^{36} + 48 q^{41} + 24 q^{46} + 20 q^{49} - 78 q^{54} + 36 q^{56} - 4 q^{61} - 52 q^{64} - 48 q^{66}+ \cdots + 24 q^{96}+O(q^{100}) $ 16 * q + 2 * q^4 - 6 * q^6 + 12 * q^9 - 24 * q^14 - 2 * q^16 - 12 * q^21 - 6 * q^24 - 12 * q^29 - 14 * q^34 - 66 * q^36 + 48 * q^41 + 24 * q^46 + 20 * q^49 - 78 * q^54 + 36 * q^56 - 4 * q^61 - 52 * q^64 - 48 * q^66 + 60 * q^69 + 60 * q^74 - 6 * q^76 - 60 * q^81 - 60 * q^84 + 42 * q^86 + 36 * q^94 + 24 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.977642	−	1.02187i	−0.691297	−	0.722570i
$2$	−0.977642	−	1.02187i	−0.691297	−	0.722570i
$3$	−1.07561	−	1.35760i	−0.621002	−	0.783809i
$3$	−1.07561	−	1.35760i	−0.621002	−	0.783809i
$4$	−0.0884324	+	1.99804i	−0.0442162	+	0.999022i
$5$		0			0
$5$		0			0
$6$	−0.335728	+	2.42637i	−0.137061	+	0.990563i
$7$	0.637910	−	1.10489i	0.241107	−	0.417610i	−0.719923	−	0.694054i	$-0.755823\pi$
$7$	0.637910	−	1.10489i	0.241107	−	0.417610i	0.961030	+	0.276444i	$0.0891560\pi$
$8$	2.12819	−	1.86301i	0.752430	−	0.658672i
$9$	−0.686141	+	2.92048i	−0.228714	+	0.973494i
$10$		0			0
$11$	0.252704	−	0.437696i	0.0761931	−	0.131970i	−0.825411	−	0.564532i	$-0.809057\pi$
$11$	0.252704	−	0.437696i	0.0761931	−	0.131970i	0.901605	+	0.432561i	$0.142390\pi$
$12$	2.80766	−	2.02905i	0.810501	−	0.585737i
$13$	−2.05446	+	1.18614i	−0.569804	+	0.328976i	−0.757071	−	0.653333i	$-0.773370\pi$
$13$	−2.05446	+	1.18614i	−0.569804	+	0.328976i	0.187267	+	0.982309i	$0.440037\pi$
$14$	−1.75270	+	0.428329i	−0.468430	+	0.114476i
$15$		0			0
$16$	−3.98436	−	0.353383i	−0.996090	−	0.0883459i
$17$	−0.792287			−0.192158			−0.0960789	−	0.995374i	$-0.530630\pi$
$17$	−0.792287			−0.192158			−0.0960789	+	0.995374i	$0.530630\pi$
$18$	3.65515	−	2.15404i	0.861527	−	0.507712i
$19$			4.70285i			1.07891i	0.842015	+	0.539454i	$0.181369\pi$
$19$			4.70285i			1.07891i	−0.842015	+	0.539454i	$0.818631\pi$
$20$		0			0
$21$	−2.18614	+	0.322405i	−0.477055	+	0.0703546i
$22$	−0.694322	+	0.169680i	−0.148030	+	0.0361759i
$23$	−2.78912	+	1.61030i	−0.581572	+	0.335771i	−0.761758	−	0.647862i	$-0.775664\pi$
$23$	−2.78912	+	1.61030i	−0.581572	+	0.335771i	0.180186	+	0.983633i	$0.442330\pi$
$24$	−4.81831	−	0.885370i	−0.983534	−	0.180725i
$25$		0			0
$26$	3.22060	+	0.939764i	0.631612	+	0.184303i
$27$	4.70285	−	2.20979i	0.905065	−	0.425274i
$28$	2.15121	+	1.37228i	0.406541	+	0.259337i
$29$	−2.18614	−	1.26217i	−0.405956	−	0.234379i	0.283095	−	0.959092i	$-0.408639\pi$
$29$	−2.18614	−	1.26217i	−0.405956	−	0.234379i	−0.689051	+	0.724713i	$0.741972\pi$
$30$		0			0
$31$	−7.04069	+	4.06494i	−1.26455	+	0.730086i	−0.973951	−	0.226761i	$-0.927186\pi$
$31$	−7.04069	+	4.06494i	−1.26455	+	0.730086i	−0.290595	+	0.956846i	$0.593853\pi$
$32$	3.53417	+	4.41698i	0.624758	+	0.780818i
$33$	−0.866025	+	0.127719i	−0.150756	+	0.0222330i
$34$	0.774573	+	0.809613i	0.132838	+	0.138848i
$35$		0			0
$36$	−5.77457	−	1.62920i	−0.962429	−	0.271534i
$37$			6.74456i			1.10880i	0.832251	+	0.554400i	$0.187052\pi$
$37$			6.74456i			1.10880i	−0.832251	+	0.554400i	$0.812948\pi$
$38$	4.80570	−	4.59771i	0.779588	−	0.745847i
$39$	3.82009	+	1.51330i	0.611704	+	0.242322i
$40$		0			0
$41$	5.87228	−	3.39036i	0.917096	−	0.529486i	0.0343887	−	0.999409i	$-0.489052\pi$
$41$	5.87228	−	3.39036i	0.917096	−	0.529486i	0.882708	+	0.469923i	$0.155718\pi$
$42$	2.46672	+	1.91875i	0.380623	+	0.296070i
$43$	−3.86473	+	6.69391i	−0.589366	+	1.02081i	0.404950	+	0.914339i	$0.367289\pi$
$43$	−3.86473	+	6.69391i	−0.589366	+	1.02081i	−0.994316	+	0.106473i	$0.966044\pi$
$44$	0.852189	+	0.543620i	0.128472	+	0.0819538i
$45$		0			0
$46$	4.37228	+	1.27582i	0.644658	+	0.188110i
$47$	−1.03834	−	0.599485i	−0.151457	−	0.0874439i	0.422356	−	0.906430i	$-0.361203\pi$
$47$	−1.03834	−	0.599485i	−0.151457	−	0.0874439i	−0.573813	+	0.818986i	$0.694537\pi$
$48$	3.80585	+	5.78926i	0.549327	+	0.835607i
$49$	2.68614	+	4.65253i	0.383734	+	0.664647i
$50$		0			0
$51$	0.852189	+	1.07561i	0.119330	+	0.150615i
$52$	−2.18828	−	4.20979i	−0.303460	−	0.583792i
$53$	1.87953			0.258173			0.129086	−	0.991633i	$-0.458796\pi$
$53$	1.87953			0.258173			0.129086	+	0.991633i	$0.458796\pi$
$54$	−6.85582	−	2.64532i	−0.932959	−	0.359983i
$55$		0			0
$56$	−0.700825	−	3.53986i	−0.0936516	−	0.473033i
$57$	6.38458	−	5.05842i	0.845659	−	0.670004i
$58$	0.847492	+	3.46790i	0.111281	+	0.455357i
$59$	6.18850	+	10.7188i	0.805674	+	1.39547i	0.915835	+	0.401555i	$0.131530\pi$
$59$	6.18850	+	10.7188i	0.805674	+	1.39547i	−0.110161	+	0.993914i	$0.535137\pi$
$60$		0			0
$61$	1.18614	−	2.05446i	0.151870	−	0.263046i	−0.780045	−	0.625723i	$-0.784804\pi$
$61$	1.18614	−	2.05446i	0.151870	−	0.263046i	0.931915	+	0.362677i	$0.118137\pi$
$62$	11.0371	+	3.22060i	1.40172	+	0.409017i
$63$	2.78912	+	2.62112i	0.351397	+	0.330230i
$64$	1.05842	−	7.92967i	0.132303	−	0.991209i
$65$		0			0
$66$	0.977175	+	0.760101i	0.120282	+	0.0935620i
$67$	−3.86473	−	6.69391i	−0.472152	−	0.817791i	0.527340	−	0.849654i	$-0.323189\pi$
$67$	−3.86473	−	6.69391i	−0.472152	−	0.817791i	−0.999492	+	0.0318630i	$0.989856\pi$
$68$	0.0700638	−	1.58302i	0.00849648	−	0.191970i
$69$	5.18614	+	2.05446i	0.624338	+	0.247327i
$70$		0			0
$71$	11.8716			1.40890			0.704450	−	0.709754i	$-0.251194\pi$
$71$	11.8716			1.40890			0.704450	+	0.709754i	$0.251194\pi$
$72$	3.98063	+	7.49364i	0.469122	+	0.883133i
$73$			3.37228i			0.394696i	0.980334	+	0.197348i	$0.0632328\pi$
$73$			3.37228i			0.394696i	−0.980334	+	0.197348i	$0.936767\pi$
$74$	6.89206	−	6.59377i	0.801186	−	0.766510i
$75$		0			0
$76$	−9.39651	−	0.415885i	−1.07785	−	0.0477052i
$77$	−0.322405	−	0.558422i	−0.0367415	−	0.0636381i
$78$	−2.18828	−	5.38310i	−0.247774	−	0.609516i
$79$	8.55691	+	4.94034i	0.962728	+	0.555831i	0.897012	−	0.442007i	$-0.145733\pi$
$79$	8.55691	+	4.94034i	0.962728	+	0.555831i	0.0657165	+	0.997838i	$0.479067\pi$
$80$		0			0
$81$	−8.05842	−	4.00772i	−0.895380	−	0.445302i
$82$	−9.20550	−	2.68614i	−1.01658	−	0.296635i
$83$	−6.61659	−	3.82009i	−0.726265	−	0.419309i	0.0907894	−	0.995870i	$-0.471061\pi$
$83$	−6.61659	−	3.82009i	−0.726265	−	0.419309i	−0.817054	+	0.576561i	$0.804394\pi$
$84$	−0.450854	−	4.39652i	−0.0491922	−	0.479699i
$85$		0			0
$86$	10.6186	−	2.59500i	1.14504	−	0.279826i
$87$	0.637910	+	4.32550i	0.0683912	+	0.463742i
$88$	−0.277627	−	1.40229i	−0.0295952	−	0.149485i
$89$		−	11.9769i		−	1.26955i	−0.772698	−	0.634773i	$-0.781093\pi$
$89$		−	11.9769i		−	1.26955i	0.772698	−	0.634773i	$-0.218907\pi$
$90$		0			0
$91$			3.02661i			0.317274i
$92$	−2.97080	−	5.71519i	−0.309728	−	0.595850i
$93$	13.0916	+	5.18614i	1.35753	+	0.537778i
$94$	0.402528	+	1.64713i	0.0415176	+	0.169888i
$95$		0			0
$96$	2.19510	−	9.54890i	0.224037	−	0.974581i
$97$	9.08385	+	5.24456i	0.922325	+	0.532505i	0.884376	−	0.466775i	$-0.154584\pi$
$97$	9.08385	+	5.24456i	0.922325	+	0.532505i	0.0379490	+	0.999280i	$0.487918\pi$
$98$	2.12819	−	7.29339i	0.214980	−	0.736744i
$99$	1.10489	+	1.03834i	0.111046	+	0.104357i
$100$		0			0
$101$	1.06930	+	0.617359i	0.106399	+	0.0614295i	0.552255	−	0.833675i	$-0.313767\pi$
$101$	1.06930	+	0.617359i	0.106399	+	0.0614295i	−0.445856	+	0.895105i	$0.647101\pi$
$102$	0.265993	−	1.92238i	0.0263372	−	0.190344i
$103$	−0.237482	−	0.411331i	−0.0233998	−	0.0405297i	0.854088	−	0.520128i	$-0.174116\pi$
$103$	−0.237482	−	0.411331i	−0.0233998	−	0.0405297i	−0.877488	+	0.479598i	$0.840782\pi$
$104$	−2.16249	+	6.35180i	−0.212050	+	0.622845i
$105$		0			0
$106$	−1.83751	−	1.92063i	−0.178474	−	0.186548i
$107$			12.5652i			1.21472i	0.794427	+	0.607360i	$0.207771\pi$
$107$			12.5652i			1.21472i	−0.794427	+	0.607360i	$0.792229\pi$
$108$	3.99937	+	9.59193i	0.384839	+	0.922984i
$109$	−13.4891			−1.29202			−0.646012	−	0.763327i	$-0.723564\pi$
$109$	−13.4891			−1.29202			−0.646012	+	0.763327i	$0.723564\pi$
$110$		0			0
$111$	9.15640	−	7.25450i	0.869087	−	0.688566i
$112$	−2.93212	+	4.17686i	−0.277059	+	0.394677i
$113$	−3.63903	−	6.30298i	−0.342331	−	0.592935i	0.642534	−	0.766257i	$-0.277883\pi$
$113$	−3.63903	−	6.30298i	−0.342331	−	0.592935i	−0.984865	+	0.173322i	$0.944550\pi$
$114$	−11.4109	−	1.57888i	−1.06873	−	0.147876i
$115$		0			0
$116$	2.71519	−	4.25639i	0.252099	−	0.395196i
$117$	−2.05446	−	6.81386i	−0.189935	−	0.629942i
$118$	4.90307	−	16.8030i	0.451364	−	1.54684i
$119$	−0.505408	+	0.875393i	−0.0463307	+	0.0802471i
$120$		0			0
$121$	5.37228	+	9.30506i	0.488389	+	0.845915i
$122$	−3.25901	+	0.796442i	−0.295057	+	0.0721065i
$123$	−10.9190	−	4.32550i	−0.984534	−	0.390017i
$124$	−7.49931	−	14.4271i	−0.673458	−	1.29559i
$125$		0			0
$126$	−0.0483257	−	5.41263i	−0.00430520	−	0.482196i
$127$	7.65492			0.679265			0.339632	−	0.940558i	$-0.389697\pi$
$127$	7.65492			0.679265			0.339632	+	0.940558i	$0.389697\pi$
$128$	−9.13785	+	6.67081i	−0.807679	+	0.589622i
$129$	13.2446	−	1.95327i	1.16612	−	0.171975i
$130$		0			0
$131$	3.82009	+	6.61659i	0.333763	+	0.578094i	0.983246	−	0.182282i	$-0.0583483\pi$
$131$	3.82009	+	6.61659i	0.333763	+	0.578094i	−0.649484	+	0.760375i	$0.725015\pi$
$132$	−0.178603	−	1.74165i	−0.0155454	−	0.151591i
$133$	5.19615	+	3.00000i	0.450564	+	0.260133i
$134$	−3.06198	+	10.4935i	−0.264514	+	0.906500i
$135$		0			0
$136$	−1.68614	+	1.47603i	−0.144585	+	0.126569i
$137$	−2.74555	+	4.75544i	−0.234568	+	0.406284i	−0.959147	−	0.282908i	$-0.908701\pi$
$137$	−2.74555	+	4.75544i	−0.234568	+	0.406284i	0.724579	+	0.689192i	$0.242034\pi$
$138$	−2.97080	−	7.30808i	−0.252892	−	0.622105i
$139$	−13.3233	+	7.69219i	−1.13006	+	0.652443i	−0.943951	−	0.330085i	$-0.892923\pi$
$139$	−13.3233	+	7.69219i	−1.13006	+	0.652443i	−0.186114	+	0.982528i	$0.559589\pi$
$140$		0			0
$141$	0.302985	+	2.05446i	0.0255159	+	0.173016i
$142$	−11.6062	−	12.1312i	−0.973968	−	1.01803i
$143$			1.19897i			0.100263i
$144$	3.76588	−	11.3938i	0.313823	−	0.949481i
$145$		0			0
$146$	3.44603	−	3.29688i	0.285195	−	0.272852i
$147$	3.42703	−	8.65099i	0.282657	−	0.713522i
$148$	−13.4759	−	0.596438i	−1.10771	−	0.0490269i
$149$	11.1861	−	6.45832i	0.916404	−	0.529086i	0.0339182	−	0.999425i	$-0.489201\pi$
$149$	11.1861	−	6.45832i	0.916404	−	0.529086i	0.882486	+	0.470338i	$0.155868\pi$
$150$		0			0
$151$	2.62112	+	1.51330i	0.213304	+	0.123151i	0.602846	−	0.797858i	$-0.294033\pi$
$151$	2.62112	+	1.51330i	0.213304	+	0.123151i	−0.389542	+	0.921009i	$0.627367\pi$
$152$	8.76144	+	10.0086i	0.710647	+	0.811804i
$153$	0.543620	−	2.31386i	0.0439491	−	0.187064i
$154$	−0.255437	+	0.875393i	−0.0205837	+	0.0705411i
$155$		0			0
$156$	−3.36147	+	7.49888i	−0.269133	+	0.600391i
$157$	−10.2723	+	5.93070i	−0.819817	+	0.473322i	−0.850353	−	0.526212i	$-0.823612\pi$
$157$	−10.2723	+	5.93070i	−0.819817	+	0.473322i	0.0305363	+	0.999534i	$0.490278\pi$
$158$	−3.31722	−	13.5739i	−0.263904	−	1.07988i
$159$	−2.02163	−	2.55164i	−0.160326	−	0.202358i
$160$		0			0
$161$			4.10891i			0.323828i
$162$	3.78288	+	12.1528i	0.297212	+	0.954812i
$163$	1.75079			0.137132			0.0685660	−	0.997647i	$-0.478158\pi$
$163$	1.75079			0.137132			0.0685660	+	0.997647i	$0.478158\pi$
$164$	6.25480	+	12.0329i	0.488417	+	0.939611i
$165$		0			0
$166$	2.56502	+	10.4960i	0.199084	+	0.814645i
$167$	−15.1469	+	8.74507i	−1.17210	+	0.676714i	−0.954174	−	0.299251i	$-0.903263\pi$
$167$	−15.1469	+	8.74507i	−1.17210	+	0.676714i	−0.217928	+	0.975965i	$0.569930\pi$
$168$	−4.05189	+	4.75893i	−0.312610	+	0.367160i
$169$	−3.68614	+	6.38458i	−0.283549	+	0.491122i
$170$		0			0
$171$	−13.7346	−	3.22682i	−1.05031	−	0.246761i
$172$	−13.0330	−	8.31386i	−0.993754	−	0.633926i
$173$	−8.83518	+	15.3030i	−0.671726	+	1.16346i	0.305688	+	0.952132i	$0.401114\pi$
$173$	−8.83518	+	15.3030i	−0.671726	+	1.16346i	−0.977414	+	0.211333i	$0.932220\pi$
$174$	3.79644	−	4.88065i	0.287808	−	0.370001i
$175$		0			0
$176$	−1.16154	+	1.65464i	−0.0875543	+	0.124723i
$177$	7.89542	−	19.9307i	0.593456	−	1.49808i
$178$	−12.2388	+	11.7091i	−0.917337	+	0.877634i
$179$	−8.83915			−0.660669			−0.330334	−	0.943864i	$-0.607162\pi$
$179$	−8.83915			−0.660669			−0.330334	+	0.943864i	$0.607162\pi$
$180$		0			0
$181$	−4.00000			−0.297318			−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000			−0.297318			−0.148659	+	0.988889i	$0.547496\pi$
$182$	3.09279	−	2.95894i	0.229253	−	0.219331i
$183$	−4.06494	+	0.599485i	−0.300489	+	0.0443152i
$184$	−2.93580	+	8.62319i	−0.216430	+	0.635710i
$185$		0			0
$186$	−7.49931	−	18.4481i	−0.549876	−	1.35268i
$187$	−0.200214	+	0.346781i	−0.0146411	+	0.0253591i
$188$	1.28962	−	2.02163i	0.0940552	−	0.147443i
$189$	0.558422	−	6.60580i	0.0406192	−	0.480501i
$190$		0			0
$191$	−7.54610	+	13.0702i	−0.546017	+	0.945728i	0.452526	+	0.891751i	$0.350523\pi$
$191$	−7.54610	+	13.0702i	−0.546017	+	0.945728i	−0.998542	+	0.0539770i	$0.982810\pi$
$192$	−11.9038	+	7.09230i	−0.859079	+	0.511843i
$193$	6.70699	−	3.87228i	0.482780	−	0.278733i	−0.238795	−	0.971070i	$-0.576752\pi$
$193$	6.70699	−	3.87228i	0.482780	−	0.278733i	0.721574	+	0.692337i	$0.243419\pi$
$194$	−3.52150	−	14.4098i	−0.252829	−	1.03456i
$195$		0			0
$196$	−9.53351	+	4.95559i	−0.680965	+	0.353971i
$197$	−23.9538			−1.70663			−0.853317	−	0.521392i	$-0.825413\pi$
$197$	−23.9538			−1.70663			−0.853317	+	0.521392i	$0.825413\pi$
$198$	−0.0191439	−	2.14418i	−0.00136050	−	0.152380i
$199$		−	12.9073i		−	0.914973i	−0.889217	−	0.457486i	$-0.848750\pi$
$199$		−	12.9073i		−	0.914973i	0.889217	−	0.457486i	$-0.151250\pi$
$200$		0			0
$201$	−4.93070	+	12.4468i	−0.347785	+	0.877927i
$202$	−0.414530	−	1.69624i	−0.0291662	−	0.119347i
$203$	−2.78912	+	1.61030i	−0.195758	+	0.113021i
$204$	−2.22447	+	1.60759i	−0.155744	+	0.112554i
$205$		0			0
$206$	−0.188154	+	0.644810i	−0.0131093	+	0.0449261i
$207$	−2.78912	−	9.25048i	−0.193857	−	0.642953i
$208$	8.60485	−	4.00000i	0.596639	−	0.277350i
$209$	2.05842	+	1.18843i	0.142384	+	0.0822055i
$210$		0			0
$211$	−15.1863	+	8.76780i	−1.04547	+	0.603600i	−0.921377	−	0.388671i	$-0.872934\pi$
$211$	−15.1863	+	8.76780i	−1.04547	+	0.603600i	−0.124090	+	0.992271i	$0.539601\pi$
$212$	−0.166211	+	3.75538i	−0.0114154	+	0.257920i
$213$	−12.7692	−	16.1168i	−0.874929	−	1.10431i
$214$	12.8399	−	12.2842i	0.877720	−	0.839732i
$215$		0			0
$216$	5.89174	−	13.4643i	0.400882	−	0.916129i
$217$			10.3723i			0.704116i
$218$	13.1875	+	13.7841i	0.893173	+	0.933578i
$219$	4.57820	−	3.62725i	0.309366	−	0.245107i
$220$		0			0
$221$	1.62772	−	0.939764i	0.109492	−	0.0632154i
$222$	−16.3648	−	2.26434i	−1.09834	−	0.151973i
$223$	4.06494	−	7.04069i	0.272209	−	0.471479i	−0.697218	−	0.716859i	$-0.745579\pi$
$223$	4.06494	−	7.04069i	0.272209	−	0.471479i	0.969427	+	0.245379i	$0.0789125\pi$
$224$	7.13477	−	1.08724i	0.476712	−	0.0726443i
$225$		0			0
$226$	−2.88316	+	9.88067i	−0.191785	+	0.657253i
$227$	12.4696	+	7.19932i	0.827635	+	0.477835i	0.853042	−	0.521842i	$-0.174755\pi$
$227$	12.4696	+	7.19932i	0.827635	+	0.477835i	−0.0254070	+	0.999677i	$0.508088\pi$
$228$	9.54235	+	13.2040i	0.631957	+	0.874457i
$229$	1.81386	+	3.14170i	0.119863	+	0.207609i	0.919713	−	0.392591i	$-0.128421\pi$
$229$	1.81386	+	3.14170i	0.119863	+	0.207609i	−0.799850	+	0.600200i	$0.795088\pi$
$230$		0			0
$231$	−0.411331	+	1.03834i	−0.0270636	+	0.0683177i
$232$	−7.00396	+	1.38665i	−0.459832	+	0.0910381i
$233$	−4.84630			−0.317491			−0.158746	−	0.987320i	$-0.550745\pi$
$233$	−4.84630			−0.317491			−0.158746	+	0.987320i	$0.550745\pi$
$234$	−4.95435	+	8.76090i	−0.323876	+	0.572718i
$235$		0			0
$236$	−21.9639	+	11.4170i	−1.42973	+	0.743184i
$237$	−2.49689	−	16.9307i	−0.162190	−	1.09977i
$238$	1.38864	−	0.339360i	0.0900125	−	0.0219974i
$239$	−6.02987	−	10.4440i	−0.390040	−	0.675569i	0.602414	−	0.798184i	$-0.294206\pi$
$239$	−6.02987	−	10.4440i	−0.390040	−	0.675569i	−0.992454	+	0.122614i	$0.960872\pi$
$240$		0			0
$241$	3.24456	−	5.61975i	0.209001	−	0.362000i	−0.742399	−	0.669958i	$-0.766312\pi$
$241$	3.24456	−	5.61975i	0.209001	−	0.362000i	0.951400	+	0.307958i	$0.0996456\pi$
$242$	4.25639	−	14.5868i	0.273611	−	0.937674i
$243$	3.22682	+	15.2508i	0.207001	+	0.978341i
$244$	4.00000	+	2.55164i	0.256074	+	0.163352i
$245$		0			0
$246$	6.25480	+	15.3866i	0.398791	+	0.981013i
$247$	−5.57825	−	9.66181i	−0.354935	−	0.614766i
$248$	−7.41094	+	21.7678i	−0.470595	+	1.38226i
$249$	1.93070	+	13.0916i	0.122353	+	0.829645i
$250$		0			0
$251$	11.1780			0.705551			0.352776	−	0.935708i	$-0.385238\pi$
$251$	11.1780			0.705551			0.352776	+	0.935708i	$0.385238\pi$
$252$	−5.48376	+	5.34100i	−0.345444	+	0.336451i
$253$			1.62772i			0.102334i
$254$	−7.48378	−	7.82233i	−0.469574	−	0.490817i
$255$		0			0
$256$	15.7502	+	2.81601i	0.984390	+	0.176001i
$257$	−7.49927	−	12.9891i	−0.467792	−	0.810239i	0.531531	−	0.847039i	$-0.321617\pi$
$257$	−7.49927	−	12.9891i	−0.467792	−	0.810239i	−0.999323	+	0.0367996i	$0.988284\pi$
$258$	−14.9444	−	11.6246i	−0.930399	−	0.723717i
$259$	7.45202	+	4.30243i	0.463046	+	0.267340i
$260$		0			0
$261$	5.18614	−	5.51856i	0.321014	−	0.341590i
$262$	3.02661	−	10.3723i	0.186984	−	0.640802i
$263$	24.2267	+	13.9873i	1.49388	+	0.862494i	0.999975	−	0.00701993i	$-0.00223453\pi$
$263$	24.2267	+	13.9873i	1.49388	+	0.862494i	0.493908	+	0.869514i	$0.335568\pi$
$264$	−1.60513	+	1.88522i	−0.0987889	+	0.116027i
$265$		0			0
$266$	−2.01437	−	8.24271i	−0.123509	−	0.505393i
$267$	−16.2598	+	12.8824i	−0.995082	+	0.788391i
$268$	13.7165	−	7.12994i	0.837868	−	0.435531i
$269$		−	21.4843i		−	1.30992i	−0.755663	−	0.654961i	$-0.772685\pi$
$269$		−	21.4843i		−	1.30992i	0.755663	−	0.654961i	$-0.227315\pi$
$270$		0			0
$271$		−	29.9679i		−	1.82042i	−0.414146	−	0.910211i	$-0.635920\pi$
$271$		−	29.9679i		−	1.82042i	0.414146	−	0.910211i	$-0.364080\pi$
$272$	3.15676	+	0.279981i	0.191406	+	0.0169763i
$273$	4.10891	−	3.25544i	0.248683	−	0.197028i
$274$	7.54360	−	1.84352i	0.455726	−	0.111371i
$275$		0			0
$276$	−4.56352	+	10.1805i	−0.274691	+	0.612791i
$277$	5.51856	+	3.18614i	0.331578	+	0.191437i	0.656541	−	0.754290i	$-0.272019\pi$
$277$	5.51856	+	3.18614i	0.331578	+	0.191437i	−0.324963	+	0.945727i	$0.605352\pi$
$278$	20.8858	+	6.09442i	1.25265	+	0.365519i
$279$	−7.04069	−	23.3513i	−0.421515	−	1.39801i
$280$		0			0
$281$	−19.9307	−	11.5070i	−1.18897	−	0.686450i	−0.230894	−	0.972979i	$-0.574165\pi$
$281$	−19.9307	−	11.5070i	−1.18897	−	0.686450i	−0.958072	+	0.286529i	$0.907499\pi$
$282$	1.80317	−	2.31813i	0.107377	−	0.138043i
$283$	−4.94034	−	8.55691i	−0.293673	−	0.508656i	0.681003	−	0.732281i	$-0.261544\pi$
$283$	−4.94034	−	8.55691i	−0.293673	−	0.508656i	−0.974675	+	0.223625i	$0.928211\pi$
$284$	−1.04983	+	23.7200i	−0.0622961	+	1.40752i
$285$		0			0
$286$	1.22519	−	1.17216i	0.0724470	−	0.0693115i
$287$		−	8.65099i		−	0.510652i
$288$	−15.3246	+	7.29080i	−0.903012	+	0.429614i
$289$	−16.3723			−0.963075
$290$		0			0
$291$	−2.65064	−	17.9733i	−0.155384	−	1.05361i
$292$	−6.73797	−	0.298219i	−0.394310	−	0.0174519i
$293$	−11.6545	−	20.1861i	−0.680862	−	1.17929i	−0.974718	−	0.223437i	$-0.928272\pi$
$293$	−11.6545	−	20.1861i	−0.680862	−	1.17929i	0.293857	−	0.955850i	$-0.405061\pi$
$294$	−12.1906	+	4.95559i	−0.710970	+	0.289016i
$295$		0			0
$296$	12.5652	+	14.3537i	0.730335	+	0.834294i
$297$	0.221215	−	2.61684i	0.0128362	−	0.151845i
$298$	−17.5356	−	5.11684i	−1.01581	−	0.296411i
$299$	3.82009	−	6.61659i	0.220921	−	0.382647i
$300$		0			0
$301$	4.93070	+	8.54023i	0.284201	+	0.492251i
$302$	−1.01612	−	4.15791i	−0.0584710	−	0.239261i
$303$	−0.312018	−	2.11571i	−0.0179250	−	0.121544i
$304$	1.66191	−	18.7379i	0.0953171	−	1.07469i
$305$		0			0
$306$	−2.89593	+	1.70662i	−0.165549	+	0.0975608i
$307$	1.20128			0.0685609			0.0342805	−	0.999412i	$-0.489086\pi$
$307$	1.20128			0.0685609			0.0342805	+	0.999412i	$0.489086\pi$
$308$	1.14426	−	0.594797i	0.0652004	−	0.0338917i
$309$	−0.302985	+	0.764836i	−0.0172362	+	0.0435100i
$310$		0			0
$311$	−9.56773	−	16.5718i	−0.542536	−	0.939700i	−0.998758	−	0.0498340i	$-0.984131\pi$
$311$	−9.56773	−	16.5718i	−0.542536	−	0.939700i	0.456221	−	0.889866i	$-0.349203\pi$
$312$	10.9492	−	3.89624i	0.619875	−	0.220581i
$313$	16.0121	+	9.24456i	0.905055	+	0.522534i	0.878837	−	0.477123i	$-0.158320\pi$
$313$	16.0121	+	9.24456i	0.905055	+	0.522534i	0.0262180	+	0.999656i	$0.491654\pi$
$314$	16.1030	+	4.69882i	0.908746	+	0.265170i
$315$		0			0
$316$	−10.6277	+	16.6602i	−0.597856	+	0.937210i
$317$	−16.2607	+	28.1644i	−0.913293	+	1.58187i	−0.103911	+	0.994587i	$0.533136\pi$
$317$	−16.2607	+	28.1644i	−0.913293	+	1.58187i	−0.809381	+	0.587283i	$0.800197\pi$
$318$	−0.631011	+	4.56044i	−0.0353853	+	0.255737i
$319$	−1.10489	+	0.637910i	−0.0618621	+	0.0357161i
$320$		0			0
$321$	17.0584	−	13.5152i	0.952108	−	0.754343i
$322$	4.19877	−	4.01704i	0.233988	−	0.223861i
$323$		−	3.72601i		−	0.207321i
$324$	8.72023	−	15.7467i	0.484457	−	0.874815i
$325$		0			0
$326$	−1.71164	−	1.78907i	−0.0947990	−	0.0990876i
$327$	14.5090	+	18.3128i	0.802349	+	1.01270i
$328$	6.18109	−	18.1554i	0.341294	−	1.00247i
$329$	−1.32473	+	0.764836i	−0.0730350	+	0.0421667i
$330$		0			0
$331$	24.0254	+	13.8711i	1.32056	+	0.762424i	0.983817	−	0.179174i	$-0.0573426\pi$
$331$	24.0254	+	13.8711i	1.32056	+	0.762424i	0.336739	+	0.941598i	$0.390676\pi$
$332$	8.21782	−	12.8824i	0.451012	−	0.707014i
$333$	−19.6974	−	4.62772i	−1.07941	−	0.253597i
$334$	23.7446	+	6.92860i	1.29924	+	0.379116i
$335$		0			0
$336$	8.82430	−	0.512032i	0.481405	−	0.0279336i
$337$	13.6352	−	7.87228i	0.742756	−	0.428830i	−0.0803144	−	0.996770i	$-0.525592\pi$
$337$	13.6352	−	7.87228i	0.742756	−	0.428830i	0.823071	+	0.567939i	$0.192259\pi$
$338$	10.1279	−	2.47508i	0.550887	−	0.134627i
$339$	−4.64275	+	11.7199i	−0.252160	+	0.636536i
$340$		0			0
$341$			4.10891i			0.222510i
$342$	10.1301	+	17.1896i	0.547775	+	0.929509i
$343$	15.7848			0.852300
$344$	4.24589	+	21.4460i	0.228923	+	1.15629i
$345$		0			0
$346$	24.2753	−	5.93244i	1.30505	−	0.318930i
$347$	6.01594	−	3.47331i	0.322953	−	0.186457i	−0.329755	−	0.944066i	$-0.606966\pi$
$347$	6.01594	−	3.47331i	0.322953	−	0.186457i	0.652708	+	0.757610i	$0.273633\pi$
$348$	−8.69894	+	0.892059i	−0.466312	+	0.0478194i
$349$	−2.81386	+	4.87375i	−0.150622	+	0.260886i	−0.931456	−	0.363853i	$-0.881461\pi$
$349$	−2.81386	+	4.87375i	−0.150622	+	0.260886i	0.780834	+	0.624739i	$0.214794\pi$
$350$		0			0
$351$	−7.04069	+	10.1182i	−0.375804	+	0.540067i
$352$	2.82639	−	0.430703i	0.150647	−	0.0229566i
$353$	−4.18265	+	7.24456i	−0.222620	+	0.385589i	−0.955603	−	0.294658i	$-0.904794\pi$
$353$	−4.18265	+	7.24456i	−0.222620	+	0.385589i	0.732983	+	0.680247i	$0.238128\pi$
$354$	−28.0855	+	11.4170i	−1.49273	+	0.606807i
$355$		0			0
$356$	23.9303	+	1.05914i	1.26830	+	0.0561345i
$357$	1.73205	−	0.255437i	0.0916698	−	0.0135192i
$358$	8.64152	+	9.03245i	0.456719	+	0.477380i
$359$	1.38712			0.0732096			0.0366048	−	0.999330i	$-0.488346\pi$
$359$	1.38712			0.0732096			0.0366048	+	0.999330i	$0.488346\pi$
$360$		0			0
$361$	−3.11684			−0.164044
$362$	3.91057	+	4.08748i	0.205535	+	0.214833i
$363$	6.85407	−	17.3020i	0.359745	−	0.908119i
$364$	−6.04729	−	0.267650i	−0.316964	−	0.0140287i
$365$		0			0
$366$	4.58666	+	3.56776i	0.239748	+	0.186490i
$367$	−3.18955	+	5.52447i	−0.166493	+	0.288375i	−0.937185	−	0.348834i	$-0.886578\pi$
$367$	−3.18955	+	5.52447i	−0.166493	+	0.288375i	0.770691	+	0.637209i	$0.219911\pi$
$368$	11.6819	−	5.43039i	0.608962	−	0.283079i
$369$	5.87228	+	19.4762i	0.305699	+	1.01389i
$370$		0			0
$371$	1.19897	−	2.07668i	0.0622474	−	0.107816i
$372$	−11.5199	+	25.6989i	−0.597277	+	1.33243i
$373$	−17.2005	+	9.93070i	−0.890607	+	0.514192i	−0.874141	−	0.485672i	$-0.838575\pi$
$373$	−17.2005	+	9.93070i	−0.890607	+	0.514192i	−0.0164662	+	0.999864i	$0.505242\pi$
$374$	0.550103	−	0.134435i	0.0284451	−	0.00695147i
$375$		0			0
$376$	−3.32663	+	0.658610i	−0.171558	+	0.0339652i
$377$	5.98844			0.308420
$378$	−7.29620	+	5.88747i	−0.375276	+	0.302819i
$379$		−	6.45364i		−	0.331501i	−0.986168	−	0.165751i	$-0.946995\pi$
$379$		−	6.45364i		−	0.331501i	0.986168	−	0.165751i	$-0.0530047\pi$
$380$		0			0
$381$	−8.23369	−	10.3923i	−0.421825	−	0.532414i
$382$	20.7334	−	5.06688i	1.06082	−	0.259244i
$383$	7.49198	−	4.32550i	0.382822	−	0.221023i	−0.296223	−	0.955119i	$-0.595727\pi$
$383$	7.49198	−	4.32550i	0.382822	−	0.221023i	0.679045	+	0.734096i	$0.262394\pi$
$384$	18.8850	+	5.23034i	0.963722	+	0.266910i
$385$		0			0
$386$	−10.5140	−	3.06796i	−0.535148	−	0.156155i
$387$	−16.8977	−	15.8798i	−0.858958	−	0.807217i
$388$	−11.2822	+	17.6861i	−0.572766	+	0.897878i
$389$	−27.3030	−	15.7634i	−1.38432	−	0.799235i	−0.391649	−	0.920115i	$-0.628095\pi$
$389$	−27.3030	−	15.7634i	−1.38432	−	0.799235i	−0.992667	+	0.120879i	$0.961429\pi$
$390$		0			0
$391$	2.20979	−	1.27582i	0.111754	−	0.0645210i
$392$	14.3843	+	4.89720i	0.726518	+	0.247346i
$393$	4.87375	−	12.3030i	0.245848	−	0.620603i
$394$	23.4182	+	24.4776i	1.17979	+	1.23316i
$395$		0			0
$396$	−2.17235	+	2.11580i	−0.109165	+	0.106323i
$397$			18.7446i			0.940763i	0.882463	+	0.470381i	$0.155884\pi$
$397$			18.7446i			0.940763i	−0.882463	+	0.470381i	$0.844116\pi$
$398$	−13.1895	+	12.6187i	−0.661132	+	0.632518i
$399$	−1.51622	−	10.2811i	−0.0759062	−	0.514699i
$400$		0			0
$401$	3.98913	−	2.30312i	0.199207	−	0.115012i	−0.397078	−	0.917785i	$-0.629976\pi$
$401$	3.98913	−	2.30312i	0.199207	−	0.115012i	0.596286	+	0.802772i	$0.296643\pi$
$402$	17.5394	−	7.12994i	0.874787	−	0.355609i
$403$	9.64319	−	16.7025i	0.480362	−	0.832011i
$404$	−1.32807	+	2.08191i	−0.0660740	+	0.103579i
$405$		0			0
$406$	4.37228	+	1.27582i	0.216993	+	0.0633179i
$407$	2.95207	+	1.70438i	0.146329	+	0.0844829i
$408$	3.81749	+	0.701467i	0.188994	+	0.0347278i
$409$	6.87228	+	11.9031i	0.339812	+	0.588572i	0.984397	−	0.175960i	$-0.0563031\pi$
$409$	6.87228	+	11.9031i	0.339812	+	0.588572i	−0.644585	+	0.764533i	$0.722970\pi$
$410$		0			0
$411$	9.40910	−	1.38762i	0.464117	−	0.0684465i
$412$	0.842859	−	0.438125i	0.0415247	−	0.0215849i
$413$	15.7908			0.777016
$414$	−6.72601	+	11.8938i	−0.330565	+	0.584547i
$415$		0			0
$416$	−12.4999	−	4.88246i	−0.612860	−	0.239383i
$417$	24.7735	+	9.81386i	1.21316	+	0.480587i
$418$	−0.797979	−	3.26530i	−0.0390305	−	0.159711i
$419$	−13.4819	−	23.3513i	−0.658634	−	1.14079i	−0.980970	−	0.194162i	$-0.937801\pi$
$419$	−13.4819	−	23.3513i	−0.658634	−	1.14079i	0.322336	−	0.946625i	$-0.395532\pi$
$420$		0			0
$421$	5.30298	−	9.18504i	0.258452	−	0.447651i	−0.707376	−	0.706838i	$-0.750121\pi$
$421$	5.30298	−	9.18504i	0.258452	−	0.447651i	0.965827	+	0.259186i	$0.0834544\pi$
$422$	23.8063	+	6.94661i	1.15887	+	0.338156i
$423$	2.46323	−	2.62112i	0.119766	−	0.127443i
$424$	4.00000	−	3.50157i	0.194257	−	0.170051i
$425$		0			0
$426$	−3.98563	+	28.8049i	−0.193104	+	1.39560i
$427$	−1.51330	−	2.62112i	−0.0732339	−	0.126845i
$428$	−25.1057	−	1.11117i	−1.21353	−	0.0537103i
$429$	1.62772	−	1.28962i	0.0785870	−	0.0622635i
$430$		0			0
$431$	−31.1952			−1.50262			−0.751310	−	0.659949i	$-0.770578\pi$
$431$	−31.1952			−1.50262			−0.751310	+	0.659949i	$0.770578\pi$
$432$	−19.5188	+	7.14267i	−0.939097	+	0.343652i
$433$		−	8.62772i		−	0.414622i	−0.978275	−	0.207311i	$-0.933529\pi$
$433$		−	8.62772i		−	0.414622i	0.978275	−	0.207311i	$-0.0664712\pi$
$434$	10.5991	−	10.1404i	0.508774	−	0.486754i
$435$		0			0
$436$	1.19288	−	26.9519i	0.0571284	−	1.29076i
$437$	−7.57301	−	13.1168i	−0.362266	−	0.627464i
$438$	−8.18241	−	1.13217i	−0.390971	−	0.0540972i
$439$	−5.65357	−	3.26409i	−0.269830	−	0.155786i	0.358980	−	0.933345i	$-0.383124\pi$
$439$	−5.65357	−	3.26409i	−0.269830	−	0.155786i	−0.628810	+	0.777559i	$0.716458\pi$
$440$		0			0
$441$	−15.4307	+	4.65253i	−0.734795	+	0.221549i
$442$	−2.55164	−	0.744563i	−0.121369	−	0.0354152i
$443$	10.7188	+	6.18850i	0.509265	+	0.294025i	0.732532	−	0.680733i	$-0.238339\pi$
$443$	10.7188	+	6.18850i	0.509265	+	0.294025i	−0.223266	+	0.974758i	$0.571672\pi$
$444$	13.6851	+	18.9364i	0.649465	+	0.898683i
$445$		0			0
$446$	−11.1687	+	2.72943i	−0.528854	+	0.129242i
$447$	−20.7997	−	8.23966i	−0.983791	−	0.389723i
$448$	−8.08627	−	6.22787i	−0.382040	−	0.294239i
$449$			19.4024i			0.915657i	0.889041	+	0.457828i	$0.151373\pi$
$449$			19.4024i			0.915657i	−0.889041	+	0.457828i	$0.848627\pi$
$450$		0			0
$451$		−	3.42703i		−	0.161373i
$452$	12.9154	−	6.71355i	0.607492	−	0.315779i
$453$	−0.764836	−	5.18614i	−0.0359351	−	0.243666i
$454$	−4.83403	−	19.7806i	−0.226872	−	0.928351i
$455$		0			0
$456$	4.16377	−	22.6598i	0.194986	−	1.06114i
$457$	34.6222	+	19.9891i	1.61956	+	0.935052i	0.987034	+	0.160510i	$0.0513140\pi$
$457$	34.6222	+	19.9891i	1.61956	+	0.935052i	0.632523	+	0.774541i	$0.282019\pi$
$458$	1.43710	−	4.92498i	0.0671511	−	0.230129i
$459$	−3.72601	+	1.75079i	−0.173915	+	0.0817196i
$460$		0			0
$461$	0.302985	+	0.174928i	0.0141114	+	0.00814722i	0.507039	−	0.861923i	$-0.330740\pi$
$461$	0.302985	+	0.174928i	0.0141114	+	0.00814722i	−0.492928	+	0.870070i	$0.664073\pi$
$462$	1.46318	−	0.594797i	0.0680733	−	0.0276725i
$463$	2.38870	+	4.13734i	0.111012	+	0.192279i	0.916179	−	0.400770i	$-0.131257\pi$
$463$	2.38870	+	4.13734i	0.111012	+	0.192279i	−0.805167	+	0.593049i	$0.797924\pi$
$464$	8.26434	+	5.80148i	0.383662	+	0.269327i
$465$		0			0
$466$	4.73794	+	4.95228i	0.219481	+	0.229410i
$467$		−	5.11313i		−	0.236608i	−0.992977	−	0.118304i	$-0.962254\pi$
$467$		−	5.11313i		−	0.236608i	0.992977	−	0.118304i	$-0.0377457\pi$
$468$	13.7961	−	3.50233i	0.637724	−	0.161895i
$469$	−9.86141			−0.455357
$470$		0			0
$471$	19.1004	+	7.56651i	0.880102	+	0.348647i
$472$	33.1395	+	11.2825i	1.52537	+	0.519318i
$473$	1.95327	+	3.38316i	0.0898113	+	0.155558i
$474$	−14.8599	+	19.1037i	−0.682538	+	0.877460i
$475$		0			0
$476$	−1.70438	−	1.08724i	−0.0781201	−	0.0498336i
$477$	−1.28962	+	5.48913i	−0.0590477	+	0.251330i
$478$	−4.77739	+	16.3723i	−0.218513	+	0.748851i
$479$	−6.53528	+	11.3194i	−0.298605	+	0.517198i	−0.975817	−	0.218589i	$-0.929855\pi$
$479$	−6.53528	+	11.3194i	−0.298605	+	0.517198i	0.677212	+	0.735788i	$0.263188\pi$
$480$		0			0
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$	−8.91467	+	2.17858i	−0.406052	+	0.0992317i
$483$	5.57825	−	4.41957i	0.253819	−	0.201098i
$484$	−19.0670	+	9.91119i	−0.866682	+	0.450508i
$485$		0			0
$486$	12.4297	−	18.2072i	0.563821	−	0.825897i
$487$	42.8752			1.94286			0.971430	−	0.237325i	$-0.0762707\pi$
$487$	42.8752			1.94286			0.971430	+	0.237325i	$0.0762707\pi$
$488$	−1.30312	−	6.58207i	−0.0589897	−	0.297956i
$489$	−1.88316	−	2.37686i	−0.0851593	−	0.107485i
$490$		0			0
$491$	−6.88206	−	11.9201i	−0.310583	−	0.537946i	0.667906	−	0.744246i	$-0.267191\pi$
$491$	−6.88206	−	11.9201i	−0.310583	−	0.537946i	−0.978489	+	0.206300i	$0.933858\pi$
$492$	9.60812	−	21.4342i	0.433168	−	0.966326i
$493$	1.73205	+	1.00000i	0.0780076	+	0.0450377i
$494$	−4.41957	+	15.1460i	−0.198846	+	0.681452i
$495$		0			0
$496$	29.4891	−	13.7081i	1.32410	−	0.615513i
$497$	7.57301	−	13.1168i	0.339696	−	0.588371i
$498$	11.4903	−	14.7718i	0.514894	−	0.661940i
$499$	2.96790	−	1.71352i	0.132861	−	0.0767076i	−0.432096	−	0.901828i	$-0.642226\pi$
$499$	2.96790	−	1.71352i	0.132861	−	0.0767076i	0.564958	+	0.825120i	$0.308893\pi$
$500$		0			0
$501$	28.1644	+	11.1571i	1.25829	+	0.498464i
$502$	−10.9281	−	11.4225i	−0.487746	−	0.509810i
$503$		−	19.3236i		−	0.861597i	−0.902448	−	0.430799i	$-0.858232\pi$
$503$		−	19.3236i		−	0.861597i	0.902448	−	0.430799i	$-0.141768\pi$
$504$	10.8190	+	0.382095i	0.481914	+	0.0170199i
$505$		0			0
$506$	1.66332	−	1.59133i	0.0739434	−	0.0707431i
$507$	12.6325	−	1.86301i	0.561030	−	0.0827390i
$508$	−0.676943	+	15.2949i	−0.0300345	+	0.678600i
$509$	−12.8139	+	7.39809i	−0.567964	+	0.327914i	−0.756336	−	0.654183i	$-0.773012\pi$
$509$	−12.8139	+	7.39809i	−0.567964	+	0.327914i	0.188372	+	0.982098i	$0.439679\pi$
$510$		0			0
$511$	3.72601	+	2.15121i	0.164829	+	0.0951641i
$512$	−12.5205	−	18.8477i	−0.553333	−	0.832960i
$513$	10.3923	+	22.1168i	0.458831	+	0.976483i
$514$	−5.94158	+	20.3620i	−0.262072	+	0.898129i
$515$		0			0
$516$	2.73146	+	26.6360i	0.120246	+	1.17258i
$517$	−0.524785	+	0.302985i	−0.0230800	+	0.0133252i
$518$	−2.88889	−	11.8212i	−0.126931	−	0.519395i
$519$	30.2785	−	4.46537i	1.32908	−	0.196008i
$520$		0			0
$521$			26.0357i			1.14064i	0.821421	+	0.570322i	$0.193181\pi$
$521$			26.0357i			1.14064i	−0.821421	+	0.570322i	$0.806819\pi$
$522$	−10.7094	+	0.0956173i	−0.468739	+	0.00418505i
$523$	−9.40571			−0.411283			−0.205641	−	0.978627i	$-0.565928\pi$
$523$	−9.40571			−0.411283			−0.205641	+	0.978627i	$0.565928\pi$
$524$	−13.5580	+	7.04758i	−0.592286	+	0.307875i
$525$		0			0
$526$	−9.39187	−	38.4311i	−0.409505	−	1.67568i
$527$	5.57825	−	3.22060i	0.242992	−	0.140292i
$528$	3.49569	−	0.202838i	0.152130	−	0.00882739i
$529$	−6.31386	+	10.9359i	−0.274516	+	0.475475i
$530$		0			0
$531$	−35.5502	+	10.7188i	−1.54275	+	0.465156i
$532$	−6.45364	+	10.1168i	−0.279801	+	0.438621i
$533$	−8.04290	+	13.9307i	−0.348376	+	0.603406i
$534$	29.0604	+	4.02098i	1.25757	+	0.174005i
$535$		0			0
$536$	−20.6957	−	7.04593i	−0.893917	−	0.304338i
$537$	9.50744	+	12.0000i	0.410276	+	0.517838i
$538$	−21.9542	+	21.0040i	−0.946511	+	0.905546i
$539$	2.71519			0.116952
$540$		0			0
$541$	−8.97825			−0.386005			−0.193003	−	0.981198i	$-0.561823\pi$
$541$	−8.97825			−0.386005			−0.193003	+	0.981198i	$0.561823\pi$
$542$	−30.6233	+	29.2979i	−1.31538	+	1.25845i
$543$	4.30243	+	5.43039i	0.184635	+	0.233040i
$544$	−2.80007	−	3.49951i	−0.120052	−	0.150040i
$545$		0			0
$546$	−7.34368	−	1.01612i	−0.314280	−	0.0434858i
$547$	−11.1192	+	19.2591i	−0.475424	+	0.823458i	−0.999604	−	0.0281494i	$-0.991039\pi$
$547$	−11.1192	+	19.2591i	−0.475424	+	0.823458i	0.524180	+	0.851608i	$0.324372\pi$
$548$	−9.25878	−	5.90627i	−0.395515	−	0.252303i
$549$	5.18614	+	4.87375i	0.221339	+	0.208006i
$550$		0			0
$551$	5.93580	−	10.2811i	0.252873	−	0.437990i
$552$	14.8646	−	5.28953i	0.632678	−	0.225137i
$553$	10.9171	−	6.30298i	0.464242	−	0.268030i
$554$	−2.13936	−	8.75415i	−0.0908925	−	0.371928i
$555$		0			0
$556$	−14.1911	−	27.3007i	−0.601838	−	1.15781i
$557$	7.22316			0.306055			0.153027	−	0.988222i	$-0.451098\pi$
$557$	7.22316			0.306055			0.153027	+	0.988222i	$0.451098\pi$
$558$	−16.9787	+	30.0239i	−0.718767	+	1.27101i
$559$		−	18.3365i		−	0.775549i
$560$		0			0
$561$	0.686141	−	0.101190i	0.0289689	−	0.00427224i
$562$	7.72645	+	31.6163i	0.325921	+	1.33365i
$563$	−13.6709	+	7.89288i	−0.576158	+	0.332645i	−0.759605	−	0.650384i	$-0.774608\pi$
$563$	−13.6709	+	7.89288i	−0.576158	+	0.332645i	0.183447	+	0.983030i	$0.441274\pi$
$564$	−4.13169	+	0.423696i	−0.173975	+	0.0178408i
$565$		0			0
$566$	−3.91416	+	13.4140i	−0.164525	+	0.563831i
$567$	−9.56866	+	6.34713i	−0.401846	+	0.266554i
$568$	25.2651	−	22.1168i	1.06010	−	0.928002i
$569$	21.9891	+	12.6954i	0.921832	+	0.532220i	0.884219	−	0.467072i	$-0.154691\pi$
$569$	21.9891	+	12.6954i	0.921832	+	0.532220i	0.0376130	+	0.999292i	$0.488025\pi$
$570$		0			0
$571$	3.66146	−	2.11395i	0.153227	−	0.0884659i	−0.421426	−	0.906863i	$-0.638470\pi$
$571$	3.66146	−	2.11395i	0.153227	−	0.0884659i	0.574653	+	0.818397i	$0.305137\pi$
$572$	−2.39560	−	0.106028i	−0.100165	−	0.00443324i
$573$	25.8607	−	3.81386i	1.08035	−	0.159326i
$574$	−8.84018	+	8.45757i	−0.368982	+	0.353012i
$575$		0			0
$576$	22.4322	+	8.53197i	0.934677	+	0.355499i
$577$		−	31.8397i		−	1.32550i	−0.748840	−	0.662751i	$-0.769389\pi$
$577$		−	31.8397i		−	1.32550i	0.748840	−	0.662751i	$-0.230611\pi$
$578$	16.0062	+	16.7303i	0.665771	+	0.695890i
$579$	−12.4711	−	4.94034i	−0.518280	−	0.205313i
$580$		0			0
$581$	−8.44158	+	4.87375i	−0.350216	+	0.202197i
$582$	−15.7750	+	20.2801i	−0.653894	+	0.840635i
$583$	0.474964	−	0.822662i	0.0196710	−	0.0340712i
$584$	6.28258	+	7.17687i	0.259975	+	0.296981i
$585$		0			0
$586$	−9.23369	+	31.6442i	−0.381440	+	1.30721i
$587$	3.38977	+	1.95708i	0.139911	+	0.0807774i	0.568321	−	0.822807i	$-0.307593\pi$
$587$	3.38977	+	1.95708i	0.139911	+	0.0807774i	−0.428411	+	0.903584i	$0.640926\pi$
$588$	16.9820	+	7.61239i	0.700326	+	0.313930i
$589$	−19.1168	−	33.1113i	−0.787696	−	1.36433i
$590$		0			0
$591$	25.7648	+	32.5196i	1.05982	+	1.33768i
$592$	2.38342	−	26.8728i	0.0979578	−	1.10446i
$593$	8.80773			0.361690			0.180845	−	0.983512i	$-0.442117\pi$
$593$	8.80773			0.361690			0.180845	+	0.983512i	$0.442117\pi$
$594$	−2.89034	+	2.33228i	−0.118592	+	0.0956948i
$595$		0			0
$596$	11.9148	+	22.9215i	0.488049	+	0.938902i
$597$	−17.5229	+	13.8832i	−0.717164	+	0.568200i
$598$	−10.4960	+	2.56502i	−0.429212	+	0.104892i
$599$	−0.0940770	−	0.162946i	−0.00384388	−	0.00665780i	0.864097	−	0.503325i	$-0.167890\pi$
$599$	−0.0940770	−	0.162946i	−0.00384388	−	0.00665780i	−0.867941	+	0.496667i	$0.834557\pi$
$600$		0			0
$601$	−7.98913	+	13.8376i	−0.325883	+	0.564446i	−0.981691	−	0.190482i	$-0.938995\pi$
$601$	−7.98913	+	13.8376i	−0.325883	+	0.564446i	0.655807	+	0.754928i	$0.272328\pi$
$602$	3.90653	−	13.3878i	0.159218	−	0.545647i
$603$	22.2012	−	6.69391i	0.904102	−	0.272597i
$604$	−3.25544	+	5.10328i	−0.132462	+	0.207650i
$605$		0			0
$606$	−1.85694	+	2.38725i	−0.0754329	+	0.0969753i
$607$	1.98827	+	3.44378i	0.0807013	+	0.139779i	0.903551	−	0.428480i	$-0.140951\pi$
$607$	1.98827	+	3.44378i	0.0807013	+	0.139779i	−0.822850	+	0.568259i	$0.807617\pi$
$608$	−20.7724	+	16.6207i	−0.842432	+	0.674057i
$609$	5.18614	+	2.05446i	0.210153	+	0.0832508i
$610$		0			0
$611$	2.84429			0.115068
$612$	4.57512	+	1.29080i	0.184938	+	0.0521774i
$613$			4.23369i			0.170997i	0.996338	+	0.0854985i	$0.0272483\pi$
$613$			4.23369i			0.170997i	−0.996338	+	0.0854985i	$0.972752\pi$
$614$	−1.17443	−	1.22756i	−0.0473960	−	0.0495401i
$615$		0			0
$616$	−1.72648	−	0.587788i	−0.0695620	−	0.0236827i
$617$	2.45060	+	4.24456i	0.0986574	+	0.170880i	0.911129	−	0.412121i	$-0.135212\pi$
$617$	2.45060	+	4.24456i	0.0986574	+	0.170880i	−0.812472	+	0.583001i	$0.801879\pi$
$618$	1.07777	−	0.438125i	0.0433544	−	0.0176240i
$619$	8.08103	+	4.66559i	0.324804	+	0.187526i	0.653532	−	0.756899i	$-0.273287\pi$
$619$	8.08103	+	4.66559i	0.324804	+	0.187526i	−0.328728	+	0.944425i	$0.606620\pi$
$620$		0			0
$621$	−9.55842	+	13.7364i	−0.383566	+	0.551222i
$622$	−7.58039	+	25.9783i	−0.303946	+	1.04163i
$623$	−13.2332	−	7.64018i	−0.530176	−	0.306097i
$624$	−14.6858	−	7.37950i	−0.587904	−	0.295416i
$625$		0			0
$626$	−6.20732	−	25.4001i	−0.248095	−	1.01519i
$627$	−0.600642	−	4.07279i	−0.0239873	−	0.162652i
$628$	−10.9414	−	21.0489i	−0.436610	−	0.839944i
$629$		−	5.34363i		−	0.213064i
$630$		0			0
$631$		−	42.8752i		−	1.70683i	−0.521228	−	0.853417i	$-0.674526\pi$
$631$		−	42.8752i		−	1.70683i	0.521228	−	0.853417i	$-0.325474\pi$
$632$	27.4147	−	5.42758i	1.09050	−	0.215898i
$633$	28.2376	+	11.1861i	1.12234	+	0.444609i
$634$	44.6775	−	10.9184i	1.77437	−	0.433624i
$635$		0			0
$636$	5.27707	−	3.81366i	0.209249	−	0.151222i
$637$	−11.0371	−	6.37228i	−0.437306	−	0.252479i
$638$	1.73205	+	0.505408i	0.0685725	+	0.0200093i
$639$	−8.14558	+	34.6708i	−0.322234	+	1.37155i
$640$		0			0
$641$	18.1277	+	10.4660i	0.716002	+	0.413384i	0.813279	−	0.581873i	$-0.197680\pi$
$641$	18.1277	+	10.4660i	0.716002	+	0.413384i	−0.0972775	+	0.995257i	$0.531013\pi$
$642$	−30.4878	−	4.21848i	−1.20326	−	0.166490i
$643$	17.9733	+	31.1307i	0.708798	+	1.22767i	0.965303	+	0.261131i	$0.0840954\pi$
$643$	17.9733	+	31.1307i	0.708798	+	1.22767i	−0.256506	+	0.966543i	$0.582571\pi$
$644$	−8.20979	−	0.363361i	−0.323511	−	0.0143184i
$645$		0			0
$646$	−3.80749	+	3.64270i	−0.149804	+	0.143320i
$647$		−	46.0993i		−	1.81235i	−0.422904	−	0.906174i	$-0.638989\pi$
$647$		−	46.0993i		−	1.81235i	0.422904	−	0.906174i	$-0.361011\pi$
$648$	−24.6163	+	6.48367i	−0.967019	+	0.254703i
$649$	6.25544			0.245547
$650$		0			0
$651$	14.0814	−	11.1565i	0.551893	−	0.437258i
$652$	−0.154826	+	3.49815i	−0.00606346	+	0.136998i
$653$	2.20193	+	3.81386i	0.0861683	+	0.149248i	0.905888	−	0.423516i	$-0.139204\pi$
$653$	2.20193	+	3.81386i	0.0861683	+	0.149248i	−0.819720	+	0.572764i	$0.805871\pi$
$654$	4.52868	−	32.7297i	0.177085	−	1.27983i
$655$		0			0
$656$	−24.5954	+	11.4333i	−0.960288	+	0.446394i
$657$	−9.84868	−	2.31386i	−0.384234	−	0.0902723i
$658$	2.07668	+	0.605969i	0.0809573	+	0.0236231i
$659$	6.02987	−	10.4440i	0.234891	−	0.406842i	−0.724350	−	0.689432i	$-0.757860\pi$
$659$	6.02987	−	10.4440i	0.234891	−	0.406842i	0.959241	+	0.282590i	$0.0911935\pi$
$660$		0			0
$661$	−7.81386	−	13.5340i	−0.303924	−	0.526412i	0.673097	−	0.739554i	$-0.264964\pi$
$661$	−7.81386	−	13.5340i	−0.303924	−	0.526412i	−0.977021	+	0.213142i	$0.931630\pi$
$662$	−9.31383	−	38.1118i	−0.361992	−	1.48126i
$663$	−3.02661	−	1.19897i	−0.117544	−	0.0465641i
$664$	−21.1982	+	4.19685i	−0.822651	+	0.162869i
$665$		0			0
$666$	14.5281	+	24.6524i	0.562951	+	0.955260i
$667$	8.12989			0.314791
$668$	−16.1336	−	31.0375i	−0.624226	−	1.20088i
$669$	−13.9307	+	2.05446i	−0.538592	+	0.0794299i
$670$		0			0
$671$	−0.599485	−	1.03834i	−0.0231429	−	0.0400846i
$672$	−9.15024	−	8.51670i	−0.352978	−	0.328539i
$673$	−25.8607	−	14.9307i	−0.996858	−	0.575536i	−0.0895410	−	0.995983i	$-0.528540\pi$
$673$	−25.8607	−	14.9307i	−0.996858	−	0.575536i	−0.907317	+	0.420447i	$0.861873\pi$
$674$	−21.3748	−	6.23711i	−0.823326	−	0.240244i
$675$		0			0
$676$	−12.4307	−	7.92967i	−0.478104	−	0.304987i
$677$	−1.75950	+	3.04755i	−0.0676232	+	0.117127i	−0.897855	−	0.440292i	$-0.854875\pi$
$677$	−1.75950	+	3.04755i	−0.0676232	+	0.117127i	0.830231	+	0.557419i	$0.188208\pi$
$678$	16.5151	−	6.71355i	0.634259	−	0.257832i
$679$	11.5894	−	6.69112i	0.444759	−	0.256782i
$680$		0			0
$681$	−3.63859	−	24.6723i	−0.139431	−	0.945445i
$682$	4.19877	−	4.01704i	0.160779	−	0.153821i
$683$		−	20.0172i		−	0.765936i	−0.923762	−	0.382968i	$-0.874902\pi$
$683$		−	20.0172i		−	0.765936i	0.923762	−	0.382968i	$-0.125098\pi$
$684$	7.66191	−	27.1570i	0.292960	−	1.03837i
$685$		0			0
$686$	−15.4319	−	16.1300i	−0.589193	−	0.615847i
$687$	2.31416	−	5.84172i	0.0882907	−	0.222876i
$688$	17.7640	−	25.3052i	0.677246	−	0.964752i
$689$	−3.86141	+	2.22938i	−0.147108	+	0.0849328i
$690$		0			0
$691$	17.3961	+	10.0436i	0.661777	+	0.382077i	0.792954	−	0.609282i	$-0.208542\pi$
$691$	17.3961	+	10.0436i	0.661777	+	0.382077i	−0.131177	+	0.991359i	$0.541875\pi$
$692$	−29.7947	−	19.0064i	−1.13263	−	0.722513i
$693$	1.85208	−	0.558422i	0.0703546	−	0.0212127i
$694$	−9.43070	−	2.75186i	−0.357985	−	0.104459i
$695$		0			0
$696$	9.41602	+	8.01707i	0.356913	+	0.303886i
$697$	−4.65253	+	2.68614i	−0.176227	+	0.101745i
$698$	7.73128	−	1.88938i	0.292633	−	0.0715143i
$699$	5.21271	+	6.57932i	0.197163	+	0.248853i
$700$		0			0
$701$			32.7615i			1.23738i	0.785634	+	0.618692i	$0.212337\pi$
$701$			32.7615i			1.23738i	−0.785634	+	0.618692i	$0.787663\pi$
$702$	17.2227	−	2.69727i	0.650029	−	0.101802i
$703$	−31.7187			−1.19629
$704$	−3.20332	−	2.46713i	−0.120730	−	0.0929834i
$705$		0			0
$706$	11.4921	−	2.80847i	0.432512	−	0.105698i
$707$	1.36423	−	0.787639i	0.0513072	−	0.0296222i
$708$	39.1242	+	17.5379i	1.47038	+	0.659115i
$709$	11.9307	−	20.6646i	0.448067	−	0.776075i	−0.550193	−	0.835037i	$-0.685446\pi$
$709$	11.9307	−	20.6646i	0.448067	−	0.776075i	0.998260	+	0.0589626i	$0.0187793\pi$
$710$		0			0
$711$	−20.2994	+	21.6005i	−0.761287	+	0.810084i
$712$	−22.3130	−	25.4891i	−0.836215	−	0.955245i
$713$	13.0916	−	22.6753i	0.490283	−	0.849195i
$714$	−1.95435	−	1.52020i	−0.0731397	−	0.0568922i
$715$		0			0
$716$	0.781666	−	17.6610i	0.0292122	−	0.660023i
$717$	−7.69304	+	19.4198i	−0.287302	+	0.725247i
$718$	−1.35611	−	1.41746i	−0.0506096	−	0.0528991i
$719$	−16.2912			−0.607558			−0.303779	−	0.952743i	$-0.598248\pi$
$719$	−16.2912			−0.607558			−0.303779	+	0.952743i	$0.598248\pi$
$720$		0			0
$721$	−0.605969			−0.0225675
$722$	3.04716	+	3.18501i	0.113403	+	0.118534i
$723$	−11.1192	+	1.63983i	−0.413528	+	0.0609859i
$724$	0.353729	−	7.99218i	0.0131463	−	0.297027i
$725$		0			0
$726$	−24.3812	+	9.91119i	−0.904871	+	0.367839i
$727$	−19.0489	+	32.9937i	−0.706485	+	1.22367i	0.259668	+	0.965698i	$0.416387\pi$
$727$	−19.0489	+	32.9937i	−0.706485	+	1.22367i	−0.966153	+	0.257969i	$0.916947\pi$
$728$	5.63858	+	6.44121i	0.208980	+	0.238727i
$729$	17.2337	−	20.7846i	0.638285	−	0.769800i
$730$		0			0
$731$	3.06198	−	5.30350i	0.113251	−	0.196157i
$732$	−0.838325	−	8.17495i	−0.0309854	−	0.302155i
$733$	0.322405	−	0.186141i	0.0119083	−	0.00687526i	−0.494034	−	0.869443i	$-0.664478\pi$
$733$	0.322405	−	0.186141i	0.0119083	−	0.00687526i	0.505942	+	0.862567i	$0.331145\pi$
$734$	8.76352	−	2.14165i	0.323467	−	0.0790496i
$735$		0			0
$736$	−16.9699	−	6.62842i	−0.625518	−	0.244327i
$737$	−3.90653			−0.143899
$738$	14.1611	−	25.0414i	0.521277	−	0.921787i
$739$			6.45364i			0.237401i	0.992930	+	0.118700i	$0.0378728\pi$
$739$			6.45364i			0.237401i	−0.992930	+	0.118700i	$0.962127\pi$
$740$		0			0
$741$	−7.11684	+	17.9653i	−0.261444	+	0.659972i
$742$	−3.29426	+	0.805056i	−0.120936	+	0.0295546i
$743$	−18.3226	+	10.5785i	−0.672190	+	0.388089i	−0.796906	−	0.604103i	$-0.793531\pi$
$743$	−18.3226	+	10.5785i	−0.672190	+	0.388089i	0.124716	+	0.992193i	$0.460198\pi$
$744$	37.5232	−	13.3526i	1.37567	−	0.489528i
$745$		0			0
$746$	26.9638	+	7.86797i	0.987215	+	0.288067i
$747$	15.6964	−	16.7025i	0.574301	−	0.611112i
$748$	−0.675178	−	0.430703i	−0.0246870	−	0.0157481i
$749$	13.8832	+	8.01544i	0.507279	+	0.292878i
$750$		0			0
$751$	−18.7832	+	10.8445i	−0.685408	+	0.395721i	−0.801890	−	0.597472i	$-0.796172\pi$
$751$	−18.7832	+	10.8445i	−0.685408	+	0.395721i	0.116481	+	0.993193i	$0.462838\pi$
$752$	3.92527	+	2.75550i	0.143140	+	0.100483i
$753$	−12.0232	−	15.1753i	−0.438149	−	0.553017i
$754$	−5.85455	−	6.11940i	−0.213210	−	0.222855i
$755$		0			0
$756$	13.1493	+	1.69992i	0.478235	+	0.0618254i
$757$		−	14.0000i		−	0.508839i	−0.967094	−	0.254419i	$-0.918116\pi$
$757$		−	14.0000i		−	0.508839i	0.967094	−	0.254419i	$-0.0818843\pi$
$758$	−6.59477	+	6.30935i	−0.239533	+	0.229166i
$759$	2.20979	−	1.75079i	0.0802102	−	0.0635495i
$760$		0			0
$761$	15.0475	−	8.68771i	0.545473	−	0.314929i	−0.201821	−	0.979422i	$-0.564686\pi$
$761$	15.0475	−	8.68771i	0.545473	−	0.314929i	0.747294	+	0.664493i	$0.231353\pi$
$762$	−2.56997	+	18.5737i	−0.0931004	+	0.672854i
$763$	−8.60485	+	14.9040i	−0.311517	+	0.539563i
$764$	−25.4476	−	16.2333i	−0.920661	−	0.587299i
$765$		0			0
$766$	−11.7446	−	3.42703i	−0.424348	−	0.123824i
$767$	−25.4280	−	14.6809i	−0.918152	−	0.530095i
$768$	−13.1181	−	24.4114i	−0.473357	−	0.880871i
$769$	4.04755	+	7.01056i	0.145958	+	0.252807i	0.929730	−	0.368242i	$-0.120040\pi$
$769$	4.04755	+	7.01056i	0.145958	+	0.252807i	−0.783772	+	0.621049i	$0.786707\pi$
$770$		0			0
$771$	−9.56773	+	24.1522i	−0.344573	+	0.869820i
$772$	7.14387	+	13.7433i	0.257114	+	0.494632i
$773$	−0.699713			−0.0251669			−0.0125835	−	0.999921i	$-0.504006\pi$
$773$	−0.699713			−0.0251669			−0.0125835	+	0.999921i	$0.504006\pi$
$774$	0.292778	+	32.7920i	0.0105237	+	1.17868i
$775$		0			0
$776$	29.1028	−	5.76181i	1.04473	−	0.206837i
$777$	−2.17448	−	14.7446i	−0.0780091	−	0.528958i
$778$	10.5844	+	43.3110i	0.379470	+	1.55278i
$779$	15.9444	+	27.6165i	0.571267	+	0.989463i
$780$		0			0
$781$	3.00000	−	5.19615i	0.107348	−	0.185933i
$782$	−3.46410	−	1.01082i	−0.123876	−	0.0361467i
$783$	−13.0702	−	1.10489i	−0.467092	−	0.0394857i
$784$	−9.05842	−	19.4866i	−0.323515	−	0.695950i
$785$		0			0
$786$	−17.3368	+	7.04758i	−0.618384	+	0.251379i
$787$	−17.3727	−	30.0903i	−0.619268	−	1.07260i	−0.989620	−	0.143712i	$-0.954096\pi$
$787$	−17.3727	−	30.0903i	−0.619268	−	1.07260i	0.370351	−	0.928892i	$-0.379237\pi$
$788$	2.11829	−	47.8607i	0.0754609	−	1.70497i
$789$	−7.06930	−	47.9350i	−0.251674	−	1.70653i
$790$		0			0
$791$	−9.28550			−0.330154
$792$	4.28586	+	0.151364i	0.152291	+	0.00537850i
$793$			5.62772i			0.199846i
$794$	19.1545	−	18.3255i	0.679767	−	0.650347i
$795$		0			0
$796$	25.7893	+	1.14142i	0.914078	+	0.0404566i
$797$	−11.9494	−	20.6970i	−0.423270	−	0.733126i	0.572987	−	0.819565i	$-0.305785\pi$
$797$	−11.9494	−	20.6970i	−0.423270	−	0.733126i	−0.996257	+	0.0864387i	$0.972451\pi$
$798$	−9.02361	+	11.6006i	−0.319433	+	0.410657i
$799$	0.822662	+	0.474964i	0.0291037	+	0.0168030i
$800$		0			0
$801$	34.9783	+	8.21782i	1.23590	+	0.290363i
$802$	−6.25343	−	1.82473i	−0.220816	−	0.0644336i
$803$	1.47603	+	0.852189i	0.0520881	+	0.0300731i
$804$	−24.4331	−	10.9525i	−0.861690	−	0.386263i
$805$		0			0
$806$	−26.4954	+	6.47498i	−0.933259	+	0.228072i
$807$	−29.1671	+	23.1087i	−1.02673	+	0.813464i
$808$	3.42581	−	0.678246i	0.120520	−	0.0238606i
$809$			35.8381i			1.26000i	0.776595	+	0.630000i	$0.216945\pi$
$809$			35.8381i			1.26000i	−0.776595	+	0.630000i	$0.783055\pi$
$810$		0			0
$811$		−	1.20128i		−	0.0421828i	−0.999778	−	0.0210914i	$-0.993286\pi$
$811$		−	1.20128i		−	0.0421828i	0.999778	−	0.0210914i	$-0.00671410\pi$
$812$	−2.97080	−	5.71519i	−0.104255	−	0.200564i
$813$	−40.6844	+	32.2337i	−1.42686	+	1.13048i
$814$	−1.14442	−	4.68290i	−0.0401118	−	0.164136i
$815$		0			0
$816$	−3.01533	−	4.58675i	−0.105558	−	0.160568i
$817$	−31.4805	−	18.1753i	−1.10136	−	0.635872i
$818$	5.44482	−	18.6596i	0.190374	−	0.652417i
$819$	−8.83915	−	2.07668i	−0.308865	−	0.0725650i
$820$		0			0
$821$	−15.8139	−	9.13014i	−0.551907	−	0.318644i	0.197983	−	0.980205i	$-0.436561\pi$
$821$	−15.8139	−	9.13014i	−0.551907	−	0.318644i	−0.749891	+	0.661561i	$0.769894\pi$
$822$	−10.6167	−	8.25827i	−0.370300	−	0.288040i
$823$	−7.01701	−	12.1538i	−0.244598	−	0.423656i	0.717421	−	0.696640i	$-0.245323\pi$
$823$	−7.01701	−	12.1538i	−0.244598	−	0.423656i	−0.962018	+	0.272984i	$0.911989\pi$
$824$	−1.27172	−	0.432962i	−0.0443025	−	0.0150829i
$825$		0			0
$826$	−15.4378	−	16.1362i	−0.537149	−	0.561449i
$827$			47.4864i			1.65126i	0.564210	+	0.825632i	$0.309181\pi$
$827$			47.4864i			1.65126i	−0.564210	+	0.825632i	$0.690819\pi$
$828$	18.7295	−	4.75475i	0.650895	−	0.165239i
$829$	48.2337			1.67523			0.837613	−	0.546265i	$-0.183951\pi$
$829$	48.2337			1.67523			0.837613	+	0.546265i	$0.183951\pi$
$830$		0			0
$831$	−1.61030	−	10.9190i	−0.0558607	−	0.378776i
$832$	7.23123	+	17.5466i	0.250698	+	0.608319i
$833$	−2.12819	−	3.68614i	−0.0737376	−	0.127717i
$834$	−14.1911	−	34.9097i	−0.491399	−	1.20882i
$835$		0			0
$836$	−2.55657	+	4.00772i	−0.0884207	+	0.138610i
$837$	−24.1287	+	34.6753i	−0.834009	+	1.19855i
$838$	−10.6815	+	36.6060i	−0.368987	+	1.26453i
$839$	−21.3102	+	36.9104i	−0.735711	+	1.27429i	0.218700	+	0.975792i	$0.429818\pi$
$839$	−21.3102	+	36.9104i	−0.735711	+	1.27429i	−0.954411	+	0.298496i	$0.903515\pi$
$840$		0			0
$841$	−11.3139	−	19.5962i	−0.390133	−	0.675730i
$842$	−14.5703	+	3.56072i	−0.502127	+	0.122711i
$843$	5.81573	+	39.4349i	0.200304	+	1.35821i
$844$	−16.1755	−	31.1182i	−0.556783	−	1.07113i
$845$		0			0
$846$	−5.08660	+	0.0454148i	−0.174881	+	0.00156139i
$847$	13.7081			0.471017
$848$	−7.48871	−	0.664194i	−0.257163	−	0.0228085i
$849$	−6.30298	+	15.9109i	−0.216318	+	0.546059i
$850$		0			0
$851$	−10.8608	−	18.8114i	−0.372303	−	0.644847i
$852$	33.3314	−	24.0881i	1.14191	−	0.825245i
$853$	−38.6299	−	22.3030i	−1.32266	−	0.763640i	−0.338510	−	0.940963i	$-0.609923\pi$
$853$	−38.6299	−	22.3030i	−1.32266	−	0.763640i	−0.984153	+	0.177323i	$0.943256\pi$
$854$	−1.19897	+	4.10891i	−0.0410279	+	0.140604i
$855$		0			0
$856$	23.4090	+	26.7411i	0.800102	+	0.913992i
$857$	18.7851	−	32.5367i	0.641685	−	1.11143i	−0.343371	−	0.939200i	$-0.611569\pi$
$857$	18.7851	−	32.5367i	0.641685	−	1.11143i	0.985056	−	0.172232i	$-0.0550978\pi$
$858$	−2.90915	−	0.402528i	−0.0993167	−	0.0137421i
$859$	−1.58077	+	0.912661i	−0.0539353	+	0.0311396i	−0.526725	−	0.850036i	$-0.676580\pi$
$859$	−1.58077	+	0.912661i	−0.0539353	+	0.0311396i	0.472790	+	0.881175i	$0.343247\pi$
$860$		0			0
$861$	−11.7446	+	9.30506i	−0.400254	+	0.317116i
$862$	30.4977	+	31.8774i	1.03876	+	1.08575i
$863$			40.0344i			1.36279i	0.731918	+	0.681393i	$0.238625\pi$
$863$			40.0344i			1.36279i	−0.731918	+	0.681393i	$0.761375\pi$
$864$	26.3812	+	12.9626i	0.897508	+	0.440998i
$865$		0			0
$866$	−8.81640	+	8.43482i	−0.299593	+	0.286627i
$867$	17.6101	+	22.2270i	0.598072	+	0.754867i
$868$	−20.7243	−	0.917245i	−0.703428	−	0.0311333i
$869$	4.32473	−	2.49689i	0.146707	−	0.0847011i
$870$		0			0
$871$	15.8798	+	9.16823i	0.538068	+	0.310654i
$872$	−28.7075	+	25.1303i	−0.972158	+	0.851020i
$873$	−21.5494	+	22.9307i	−0.729338	+	0.776087i
$874$	−6.00000	+	20.5622i	−0.202953	+	0.695527i
$875$		0			0
$876$	6.84254	+	9.46821i	0.231188	+	0.319901i
$877$	−18.7302	+	10.8139i	−0.632472	+	0.365158i	−0.781709	−	0.623643i	$-0.785652\pi$
$877$	−18.7302	+	10.8139i	−0.632472	+	0.365158i	0.149237	+	0.988802i	$0.452318\pi$
$878$	2.19169	+	8.96831i	0.0739661	+	0.302666i
$879$	−14.8690	+	37.5344i	−0.501520	+	1.26600i
$880$		0			0
$881$		−	52.9562i		−	1.78414i	−0.451898	−	0.892070i	$-0.649253\pi$
$881$		−	52.9562i		−	1.78414i	0.451898	−	0.892070i	$-0.350747\pi$
$882$	19.8400	+	11.2196i	0.668047	+	0.377785i
$883$	20.0127			0.673481			0.336741	−	0.941597i	$-0.390675\pi$
$883$	20.0127			0.673481			0.336741	+	0.941597i	$0.390675\pi$
$884$	1.73375	+	3.33536i	0.0583122	+	0.112180i
$885$		0			0
$886$	−4.15531	−	17.0033i	−0.139600	−	0.571239i
$887$	16.8977	−	9.75588i	0.567369	−	0.327571i	−0.188729	−	0.982029i	$-0.560437\pi$
$887$	16.8977	−	9.75588i	0.567369	−	0.327571i	0.756098	+	0.654459i	$0.227103\pi$
$888$	5.97143	−	32.4974i	0.200388	−	1.09054i
$889$	4.88316	−	8.45787i	0.163776	−	0.283668i
$890$		0			0
$891$	−3.79056	+	2.51437i	−0.126989	+	0.0842347i
$892$	13.7081	+	8.74456i	0.458982	+	0.292790i
$893$	2.81929	−	4.88316i	0.0943440	−	0.163409i
$894$	11.9148	+	29.3100i	0.398490	+	0.980273i
$895$		0			0
$896$	1.54141	+	14.3517i	0.0514949	+	0.479458i
$897$	−13.0916	+	1.93070i	−0.437115	+	0.0644643i
$898$	19.8267	−	18.9686i	0.661626	−	0.632991i
$899$	20.5226			0.684467
$900$		0			0
$901$	−1.48913			−0.0496100
$902$	−3.50198	+	3.35041i	−0.116603	+	0.111557i
$903$	6.29069	−	15.8798i	0.209341	−	0.528448i
$904$	−19.4871	−	6.63444i	−0.648130	−	0.220658i
$905$		0			0
$906$	−4.55182	+	5.85175i	−0.151224	+	0.194411i
$907$	−14.9467	+	25.8884i	−0.496297	+	0.859611i	−0.999991	−	0.00427097i	$-0.998641\pi$
$907$	−14.9467	+	25.8884i	−0.496297	+	0.859611i	0.503694	+	0.863882i	$0.331974\pi$
$908$	−15.4873	+	24.2781i	−0.513963	+	0.805698i
$909$	−2.53667	+	2.69927i	−0.0841361	+	0.0895290i
$910$		0			0
$911$	−17.9015	+	31.0063i	−0.593102	+	1.02728i	0.400710	+	0.916205i	$0.368764\pi$
$911$	−17.9015	+	31.0063i	−0.593102	+	1.02728i	−0.993812	+	0.111078i	$0.964570\pi$
$912$	−27.2260	+	17.8984i	−0.901544	+	0.592674i
$913$	−3.34408	+	1.93070i	−0.110673	+	0.0638970i
$914$	−13.4218	−	54.9215i	−0.443955	−	1.81664i
$915$		0			0
$916$	−6.43765	+	3.34634i	−0.212706	+	0.110566i
$917$	9.74749			0.321891
$918$	5.43178	+	2.09585i	0.179275	+	0.0691735i
$919$			36.9711i			1.21956i	0.792570	+	0.609781i	$0.208743\pi$
$919$			36.9711i			1.21956i	−0.792570	+	0.609781i	$0.791257\pi$
$920$		0			0
$921$	−1.29211	−	1.63086i	−0.0425765	−	0.0537387i
$922$	−0.117457	−	0.480628i	−0.00386823	−	0.0158286i
$923$	−24.3897	+	14.0814i	−0.802796	+	0.463494i
$924$	−2.03827	−	0.913680i	−0.0670542	−	0.0300579i
$925$		0			0
$926$	1.89253	−	6.48577i	0.0621925	−	0.213136i
$927$	1.36423	−	0.411331i	0.0448072	−	0.0135099i
$928$	−2.15121	−	14.1168i	−0.0706170	−	0.463408i
$929$	−16.0693	−	9.27761i	−0.527217	−	0.304389i	0.212666	−	0.977125i	$-0.431785\pi$
$929$	−16.0693	−	9.27761i	−0.527217	−	0.304389i	−0.739882	+	0.672736i	$0.765119\pi$
$930$		0			0
$931$	−21.8802	+	12.6325i	−0.717094	+	0.414014i
$932$	0.428569	−	9.68311i	0.0140383	−	0.317181i
$933$	−12.2067	+	30.8139i	−0.399630	+	1.00880i
$934$	−5.22495	+	4.99882i	−0.170966	+	0.163566i
$935$		0			0
$936$	−17.0665	−	10.6738i	−0.557837	−	0.348883i
$937$		−	45.7228i		−	1.49370i	−0.664993	−	0.746850i	$-0.731565\pi$
$937$		−	45.7228i		−	1.49370i	0.664993	−	0.746850i	$-0.268435\pi$
$938$	9.64092	+	10.0771i	0.314787	+	0.329028i
$939$	−4.67228	−	31.6814i	−0.152474	−	1.03388i
$940$		0			0
$941$	11.6970	−	6.75327i	0.381312	−	0.220150i	−0.297077	−	0.954854i	$-0.596012\pi$
$941$	11.6970	−	6.75327i	0.381312	−	0.220150i	0.678389	+	0.734703i	$0.262678\pi$
$942$	−10.9414	−	26.9155i	−0.356490	−	0.876954i
$943$	−10.9190	+	18.9123i	−0.355572	+	0.615869i
$944$	−20.8694	−	44.8945i	−0.679240	−	1.46119i
$945$		0			0
$946$	1.54755	−	5.30350i	0.0503151	−	0.172432i
$947$	−5.69005	−	3.28515i	−0.184902	−	0.106753i	0.404692	−	0.914453i	$-0.367379\pi$
$947$	−5.69005	−	3.28515i	−0.184902	−	0.106753i	−0.589594	+	0.807700i	$0.700712\pi$
$948$	34.0491	−	3.49167i	1.10586	−	0.113404i
$949$	−4.00000	−	6.92820i	−0.129845	−	0.224899i
$950$		0			0
$951$	55.7260	−	8.21830i	1.80704	−	0.266497i
$952$	0.555254	+	2.80458i	0.0179959	+	0.0908971i
$953$	10.2997			0.333641			0.166821	−	0.985987i	$-0.446650\pi$
$953$	10.2997			0.333641			0.166821	+	0.985987i	$0.446650\pi$
$954$	6.86995	−	4.04858i	0.222423	−	0.131077i
$955$		0			0
$956$	21.4009	−	11.1244i	0.692155	−	0.359788i
$957$	2.05446	+	0.813859i	0.0664111	+	0.0263083i
$958$	17.9562	−	4.38816i	0.580137	−	0.141775i
$959$	3.50283	+	6.06709i	0.113112	+	0.195916i
$960$		0			0
$961$	17.5475	−	30.3932i	0.566050	−	0.980427i
$962$	−6.33830	+	21.7216i	−0.204355	+	0.700331i
$963$	−36.6963	−	8.62146i	−1.18252	−	0.277823i
$964$	10.9416	+	6.97975i	0.352404	+	0.224802i
$965$		0			0
$966$	−9.96975	−	1.37948i	−0.320772	−	0.0443840i
$967$	23.4259	+	40.5748i	0.753325	+	1.30480i	0.946203	+	0.323574i	$0.104885\pi$
$967$	23.4259	+	40.5748i	0.753325	+	1.30480i	−0.192878	+	0.981223i	$0.561782\pi$
$968$	28.7686	+	9.79440i	0.924659	+	0.314804i
$969$	−5.05842	+	4.00772i	−0.162500	+	0.128747i
$970$		0			0
$971$	37.0019			1.18745			0.593724	−	0.804669i	$-0.297657\pi$
$971$	37.0019			1.18745			0.593724	+	0.804669i	$0.297657\pi$
$972$	−30.7572	+	5.09866i	−0.986537	+	0.163540i
$973$			19.6277i			0.629236i
$974$	−41.9166	−	43.8128i	−1.34309	−	1.40385i
$975$		0			0
$976$	−5.45202	+	7.76653i	−0.174515	+	0.248601i
$977$	27.3441	+	47.3614i	0.874816	+	1.51523i	0.856959	+	0.515385i	$0.172351\pi$
$977$	27.3441	+	47.3614i	0.874816	+	1.51523i	0.0178572	+	0.999841i	$0.494316\pi$
$978$	−0.587788	+	4.24806i	−0.0187954	+	0.135838i
$979$	−5.24224	−	3.02661i	−0.167543	−	0.0967307i
$980$		0			0
$981$	9.25544	−	39.3947i	0.295503	−	1.25778i
$982$	−5.45257	+	18.6861i	−0.173998	+	0.596299i
$983$	−29.8050	−	17.2079i	−0.950631	−	0.548847i	−0.0573540	−	0.998354i	$-0.518266\pi$
$983$	−29.8050	−	17.2079i	−0.950631	−	0.548847i	−0.893277	+	0.449507i	$0.851600\pi$
$984$	−31.2962	+	11.1367i	−0.997686	+	0.355025i
$985$		0			0
$986$	−0.671457	−	2.74757i	−0.0213835	−	0.0875005i
$987$	2.46323	+	0.975793i	0.0784055	+	0.0310598i
$988$	19.7980	−	10.2912i	0.629859	−	0.327406i
$989$		−	24.8935i		−	0.791568i
$990$		0			0
$991$		−	7.65492i		−	0.243167i	−0.992581	−	0.121583i	$-0.961203\pi$
$991$		−	7.65492i		−	0.243167i	0.992581	−	0.121583i	$-0.0387972\pi$
$992$	−42.8377	−	16.7324i	−1.36010	−	0.531253i
$993$	−7.01056	−	47.5367i	−0.222473	−	1.50853i
$994$	−20.8074	+	5.08495i	−0.659970	+	0.161285i
$995$		0			0
$996$	−26.3283	+	2.69991i	−0.834243	+	0.0855500i
$997$	−20.9046	−	12.0693i	−0.662056	−	0.382238i	0.131004	−	0.991382i	$-0.458180\pi$
$997$	−20.9046	−	12.0693i	−0.662056	−	0.382238i	−0.793060	+	0.609143i	$0.791513\pi$
$998$	−4.65253	−	1.35760i	−0.147273	−	0.0429740i
$999$	14.9040	+	31.7187i	0.471543	+	1.00354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.o.a.299.3		16
4.3	odd	2	inner	900.2.o.a.299.8		16
5.2	odd	4		36.2.h.a.11.4	yes	8
5.3	odd	4		900.2.r.c.551.1		8
5.4	even	2	inner	900.2.o.a.299.6		16
9.5	odd	6	inner	900.2.o.a.599.1		16
15.2	even	4		108.2.h.a.35.1		8
20.3	even	4		900.2.r.c.551.2		8
20.7	even	4		36.2.h.a.11.3	✓	8
20.19	odd	2	inner	900.2.o.a.299.1		16
36.23	even	6	inner	900.2.o.a.599.6		16
40.27	even	4		576.2.s.f.191.1		8
40.37	odd	4		576.2.s.f.191.4		8
45.2	even	12		324.2.b.b.323.8		8
45.7	odd	12		324.2.b.b.323.1		8
45.14	odd	6	inner	900.2.o.a.599.8		16
45.22	odd	12		108.2.h.a.71.2		8
45.23	even	12		900.2.r.c.851.2		8
45.32	even	12		36.2.h.a.23.3	yes	8
60.47	odd	4		108.2.h.a.35.2		8
120.77	even	4		1728.2.s.f.575.2		8
120.107	odd	4		1728.2.s.f.575.1		8
180.7	even	12		324.2.b.b.323.7		8
180.23	odd	12		900.2.r.c.851.1		8
180.47	odd	12		324.2.b.b.323.2		8
180.59	even	6	inner	900.2.o.a.599.3		16
180.67	even	12		108.2.h.a.71.1		8
180.167	odd	12		36.2.h.a.23.4	yes	8
360.67	even	12		1728.2.s.f.1151.2		8
360.77	even	12		576.2.s.f.383.1		8
360.157	odd	12		1728.2.s.f.1151.1		8
360.187	even	12		5184.2.c.j.5183.8		8
360.227	odd	12		5184.2.c.j.5183.2		8
360.277	odd	12		5184.2.c.j.5183.7		8
360.317	even	12		5184.2.c.j.5183.1		8
360.347	odd	12		576.2.s.f.383.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.h.a.11.3	✓	8	20.7	even	4
36.2.h.a.11.4	yes	8	5.2	odd	4
36.2.h.a.23.3	yes	8	45.32	even	12
36.2.h.a.23.4	yes	8	180.167	odd	12
108.2.h.a.35.1		8	15.2	even	4
108.2.h.a.35.2		8	60.47	odd	4
108.2.h.a.71.1		8	180.67	even	12
108.2.h.a.71.2		8	45.22	odd	12
324.2.b.b.323.1		8	45.7	odd	12
324.2.b.b.323.2		8	180.47	odd	12
324.2.b.b.323.7		8	180.7	even	12
324.2.b.b.323.8		8	45.2	even	12
576.2.s.f.191.1		8	40.27	even	4
576.2.s.f.191.4		8	40.37	odd	4
576.2.s.f.383.1		8	360.77	even	12
576.2.s.f.383.4		8	360.347	odd	12
900.2.o.a.299.1		16	20.19	odd	2	inner
900.2.o.a.299.3		16	1.1	even	1	trivial
900.2.o.a.299.6		16	5.4	even	2	inner
900.2.o.a.299.8		16	4.3	odd	2	inner
900.2.o.a.599.1		16	9.5	odd	6	inner
900.2.o.a.599.3		16	180.59	even	6	inner
900.2.o.a.599.6		16	36.23	even	6	inner
900.2.o.a.599.8		16	45.14	odd	6	inner
900.2.r.c.551.1		8	5.3	odd	4
900.2.r.c.551.2		8	20.3	even	4
900.2.r.c.851.1		8	180.23	odd	12
900.2.r.c.851.2		8	45.23	even	12
1728.2.s.f.575.1		8	120.107	odd	4
1728.2.s.f.575.2		8	120.77	even	4
1728.2.s.f.1151.1		8	360.157	odd	12
1728.2.s.f.1151.2		8	360.67	even	12
5184.2.c.j.5183.1		8	360.317	even	12
5184.2.c.j.5183.2		8	360.227	odd	12
5184.2.c.j.5183.7		8	360.277	odd	12
5184.2.c.j.5183.8		8	360.187	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.977642 - 1.02187i) q^{2} +(-1.07561 - 1.35760i) q^{3} +(-0.0884324 + 1.99804i) q^{4} +(-0.335728 + 2.42637i) q^{6} +(0.637910 - 1.10489i) q^{7} +(2.12819 - 1.86301i) q^{8} +(-0.686141 + 2.92048i) q^{9} +(0.252704 - 0.437696i) q^{11} +(2.80766 - 2.02905i) q^{12} +(-2.05446 + 1.18614i) q^{13} +(-1.75270 + 0.428329i) q^{14} +(-3.98436 - 0.353383i) q^{16} -0.792287 q^{17} +(3.65515 - 2.15404i) q^{18} +4.70285i q^{19} +(-2.18614 + 0.322405i) q^{21} +(-0.694322 + 0.169680i) q^{22} +(-2.78912 + 1.61030i) q^{23} +(-4.81831 - 0.885370i) q^{24} +(3.22060 + 0.939764i) q^{26} +(4.70285 - 2.20979i) q^{27} +(2.15121 + 1.37228i) q^{28} +(-2.18614 - 1.26217i) q^{29} +(-7.04069 + 4.06494i) q^{31} +(3.53417 + 4.41698i) q^{32} +(-0.866025 + 0.127719i) q^{33} +(0.774573 + 0.809613i) q^{34} +(-5.77457 - 1.62920i) q^{36} +6.74456i q^{37} +(4.80570 - 4.59771i) q^{38} +(3.82009 + 1.51330i) q^{39} +(5.87228 - 3.39036i) q^{41} +(2.46672 + 1.91875i) q^{42} +(-3.86473 + 6.69391i) q^{43} +(0.852189 + 0.543620i) q^{44} +(4.37228 + 1.27582i) q^{46} +(-1.03834 - 0.599485i) q^{47} +(3.80585 + 5.78926i) q^{48} +(2.68614 + 4.65253i) q^{49} +(0.852189 + 1.07561i) q^{51} +(-2.18828 - 4.20979i) q^{52} +1.87953 q^{53} +(-6.85582 - 2.64532i) q^{54} +(-0.700825 - 3.53986i) q^{56} +(6.38458 - 5.05842i) q^{57} +(0.847492 + 3.46790i) q^{58} +(6.18850 + 10.7188i) q^{59} +(1.18614 - 2.05446i) q^{61} +(11.0371 + 3.22060i) q^{62} +(2.78912 + 2.62112i) q^{63} +(1.05842 - 7.92967i) q^{64} +(0.977175 + 0.760101i) q^{66} +(-3.86473 - 6.69391i) q^{67} +(0.0700638 - 1.58302i) q^{68} +(5.18614 + 2.05446i) q^{69} +11.8716 q^{71} +(3.98063 + 7.49364i) q^{72} +3.37228i q^{73} +(6.89206 - 6.59377i) q^{74} +(-9.39651 - 0.415885i) q^{76} +(-0.322405 - 0.558422i) q^{77} +(-2.18828 - 5.38310i) q^{78} +(8.55691 + 4.94034i) q^{79} +(-8.05842 - 4.00772i) q^{81} +(-9.20550 - 2.68614i) q^{82} +(-6.61659 - 3.82009i) q^{83} +(-0.450854 - 4.39652i) q^{84} +(10.6186 - 2.59500i) q^{86} +(0.637910 + 4.32550i) q^{87} +(-0.277627 - 1.40229i) q^{88} -11.9769i q^{89} +3.02661i q^{91} +(-2.97080 - 5.71519i) q^{92} +(13.0916 + 5.18614i) q^{93} +(0.402528 + 1.64713i) q^{94} +(2.19510 - 9.54890i) q^{96} +(9.08385 + 5.24456i) q^{97} +(2.12819 - 7.29339i) q^{98} +(1.10489 + 1.03834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} - 6 q^{6} + 12 q^{9} - 24 q^{14} - 2 q^{16} - 12 q^{21} - 6 q^{24} - 12 q^{29} - 14 q^{34} - 66 q^{36} + 48 q^{41} + 24 q^{46} + 20 q^{49} - 78 q^{54} + 36 q^{56} - 4 q^{61} - 52 q^{64} - 48 q^{66}+ \cdots + 24 q^{96}+O(q^{100}) \) 16 * q + 2 * q^4 - 6 * q^6 + 12 * q^9 - 24 * q^14 - 2 * q^16 - 12 * q^21 - 6 * q^24 - 12 * q^29 - 14 * q^34 - 66 * q^36 + 48 * q^41 + 24 * q^46 + 20 * q^49 - 78 * q^54 + 36 * q^56 - 4 * q^61 - 52 * q^64 - 48 * q^66 + 60 * q^69 + 60 * q^74 - 6 * q^76 - 60 * q^81 - 60 * q^84 + 42 * q^86 + 36 * q^94 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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