LMFDB - Embedded newform 675.2.ba.b.32.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] 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("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			32.10
Character	$\chi$	$=$	675.32
Dual form			675.2.ba.b.443.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0140240 - 0.160295i) q^{2} +(-0.850222 - 1.50901i) q^{3} +(1.94412 + 0.342800i) q^{4} +(-0.253811 + 0.115124i) q^{6} +(-1.66092 + 2.37204i) q^{7} +(0.165506 - 0.617675i) q^{8} +(-1.55424 + 2.56599i) q^{9} +(-1.48958 + 4.09258i) q^{11} +(-1.13564 - 3.22516i) q^{12} +(4.71104 - 0.412163i) q^{13} +(0.356933 + 0.299503i) q^{14} +(3.61342 + 1.31518i) q^{16} +(1.51857 + 5.66739i) q^{17} +(0.389520 + 0.285124i) q^{18} +(-0.695229 + 0.401391i) q^{19} +(4.99158 + 0.489589i) q^{21} +(0.635132 + 0.296167i) q^{22} +(-2.18347 + 1.52888i) q^{23} +(-1.07280 + 0.275411i) q^{24} -0.760939i q^{26} +(5.19357 + 0.163709i) q^{27} +(-4.04215 + 4.04215i) q^{28} +(-2.06994 + 1.73689i) q^{29} +(1.27517 - 7.23183i) q^{31} +(0.801990 - 1.71987i) q^{32} +(7.44223 - 1.23181i) q^{33} +(0.929752 - 0.163940i) q^{34} +(-3.90126 + 4.45580i) q^{36} +(-3.14033 + 0.841448i) q^{37} +(0.0545912 + 0.117071i) q^{38} +(-4.62739 - 6.75860i) q^{39} +(2.88706 - 3.44066i) q^{41} +(0.148481 - 0.793261i) q^{42} +(6.22917 - 2.90471i) q^{43} +(-4.29885 + 7.44583i) q^{44} +(0.214452 + 0.371442i) q^{46} +(-4.52886 - 3.17114i) q^{47} +(-1.08759 - 6.57090i) q^{48} +(-0.473765 - 1.30166i) q^{49} +(7.26104 - 7.11008i) q^{51} +(9.30011 + 0.813654i) q^{52} +(-1.70331 - 1.70331i) q^{53} +(0.0990765 - 0.830210i) q^{54} +(1.19026 + 1.41849i) q^{56} +(1.19680 + 0.707839i) q^{57} +(0.249386 + 0.356161i) q^{58} +(4.31439 - 1.57031i) q^{59} +(2.10123 + 11.9167i) q^{61} +(-1.14135 - 0.305823i) q^{62} +(-3.50516 - 7.94862i) q^{63} +(6.39585 + 3.69265i) q^{64} +(-0.0930836 - 1.21023i) q^{66} +(0.582021 + 6.65253i) q^{67} +(1.00950 + 11.5386i) q^{68} +(4.16355 + 1.99500i) q^{69} +(-5.61473 - 3.24167i) q^{71} +(1.32772 + 1.38470i) q^{72} +(9.31768 + 2.49666i) q^{73} +(0.0908402 + 0.515180i) q^{74} +(-1.48920 + 0.542026i) q^{76} +(-7.23368 - 10.3308i) q^{77} +(-1.14827 + 0.646967i) q^{78} +(0.322504 + 0.384345i) q^{79} +(-4.16865 - 7.97636i) q^{81} +(-0.511034 - 0.511034i) q^{82} +(-8.92110 - 0.780495i) q^{83} +(9.53639 + 2.66293i) q^{84} +(-0.378253 - 1.03924i) q^{86} +(4.38090 + 1.64683i) q^{87} +(2.28135 + 1.59742i) q^{88} +(6.84734 + 11.8599i) q^{89} +(-6.84699 + 11.8593i) q^{91} +(-4.76903 + 2.22384i) q^{92} +(-11.9971 + 4.22442i) q^{93} +(-0.571832 + 0.681483i) q^{94} +(-3.27718 + 0.252061i) q^{96} +(-3.08067 - 6.60652i) q^{97} +(-0.215294 + 0.0576878i) q^{98} +(-8.18637 - 10.1831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.0140240	−	0.160295i	0.00991648	−	0.113346i	−0.989623	−	0.143688i	$-0.954104\pi$
$2$	0.0140240	−	0.160295i	0.00991648	−	0.113346i	0.999540	+	0.0303416i	$0.00965952\pi$
$3$	−0.850222	−	1.50901i	−0.490876	−	0.871229i
$3$	−0.850222	−	1.50901i	−0.490876	−	0.871229i
$4$	1.94412	+	0.342800i	0.972059	+	0.171400i
$5$		0			0
$5$		0			0
$6$	−0.253811	+	0.115124i	−0.103618	+	0.0469993i
$7$	−1.66092	+	2.37204i	−0.627768	+	0.896545i	−0.999494	−	0.0317971i	$-0.989877\pi$
$7$	−1.66092	+	2.37204i	−0.627768	+	0.896545i	0.371727	+	0.928342i	$0.378766\pi$
$8$	0.165506	−	0.617675i	0.0585151	−	0.218381i
$9$	−1.55424	+	2.56599i	−0.518081	+	0.855331i
$10$		0			0
$11$	−1.48958	+	4.09258i	−0.449125	+	1.23396i	0.484210	+	0.874952i	$0.339107\pi$
$11$	−1.48958	+	4.09258i	−0.449125	+	1.23396i	−0.933335	+	0.359008i	$0.883115\pi$
$12$	−1.13564	−	3.22516i	−0.327832	−	0.931022i
$13$	4.71104	−	0.412163i	1.30661	−	0.114313i	0.587507	−	0.809219i	$-0.300109\pi$
$13$	4.71104	−	0.412163i	1.30661	−	0.114313i	0.719101	+	0.694905i	$0.244554\pi$
$14$	0.356933	+	0.299503i	0.0953945	+	0.0800455i
$15$		0			0
$16$	3.61342	+	1.31518i	0.903355	+	0.328794i
$17$	1.51857	+	5.66739i	0.368308	+	1.37454i	0.862881	+	0.505407i	$0.168658\pi$
$17$	1.51857	+	5.66739i	0.368308	+	1.37454i	−0.494573	+	0.869136i	$0.664676\pi$
$18$	0.389520	+	0.285124i	0.0918108	+	0.0672043i
$19$	−0.695229	+	0.401391i	−0.159497	+	0.0920854i	−0.577624	−	0.816303i	$-0.696020\pi$
$19$	−0.695229	+	0.401391i	−0.159497	+	0.0920854i	0.418127	+	0.908388i	$0.362687\pi$
$20$		0			0
$21$	4.99158	+	0.489589i	1.08925	+	0.106837i
$22$	0.635132	+	0.296167i	0.135411	+	0.0631430i
$23$	−2.18347	+	1.52888i	−0.455286	+	0.318794i	−0.778626	−	0.627488i	$-0.784083\pi$
$23$	−2.18347	+	1.52888i	−0.455286	+	0.318794i	0.323340	+	0.946283i	$0.395194\pi$
$24$	−1.07280	+	0.275411i	−0.218984	+	0.0562181i
$25$		0			0
$26$		−	0.760939i		−	0.149232i
$27$	5.19357	+	0.163709i	0.999504	+	0.0315057i
$28$	−4.04215	+	4.04215i	−0.763895	+	0.763895i
$29$	−2.06994	+	1.73689i	−0.384379	+	0.322532i	−0.814419	−	0.580278i	$-0.802944\pi$
$29$	−2.06994	+	1.73689i	−0.384379	+	0.322532i	0.430040	+	0.902810i	$0.358500\pi$
$30$		0			0
$31$	1.27517	−	7.23183i	0.229027	−	1.29887i	−0.625809	−	0.779976i	$-0.715231\pi$
$31$	1.27517	−	7.23183i	0.229027	−	1.29887i	0.854836	−	0.518899i	$-0.173658\pi$
$32$	0.801990	−	1.71987i	0.141773	−	0.304034i
$33$	7.44223	−	1.23181i	1.29553	−	0.214431i
$34$	0.929752	−	0.163940i	0.159451	−	0.0281155i
$35$		0			0
$36$	−3.90126	+	4.45580i	−0.650209	+	0.742633i
$37$	−3.14033	+	0.841448i	−0.516266	+	0.138333i	−0.507539	−	0.861629i	$-0.669445\pi$
$37$	−3.14033	+	0.841448i	−0.516266	+	0.138333i	−0.00872734	+	0.999962i	$0.502778\pi$
$38$	0.0545912	+	0.117071i	0.00885586	+	0.0189914i
$39$	−4.62739	−	6.75860i	−0.740976	−	1.08224i
$40$		0			0
$41$	2.88706	−	3.44066i	0.450883	−	0.537341i	−0.491943	−	0.870628i	$-0.663713\pi$
$41$	2.88706	−	3.44066i	0.450883	−	0.537341i	0.942826	+	0.333286i	$0.108158\pi$
$42$	0.148481	−	0.793261i	0.0229111	−	0.122403i
$43$	6.22917	−	2.90471i	0.949940	−	0.442964i	0.115037	−	0.993361i	$-0.463301\pi$
$43$	6.22917	−	2.90471i	0.949940	−	0.442964i	0.834903	+	0.550397i	$0.185524\pi$
$44$	−4.29885	+	7.44583i	−0.648076	+	1.12250i
$45$		0			0
$46$	0.214452	+	0.371442i	0.0316192	+	0.0547661i
$47$	−4.52886	−	3.17114i	−0.660602	−	0.462558i	0.194580	−	0.980887i	$-0.437666\pi$
$47$	−4.52886	−	3.17114i	−0.660602	−	0.462558i	−0.855182	+	0.518328i	$0.826555\pi$
$48$	−1.08759	−	6.57090i	−0.156980	−	0.948427i
$49$	−0.473765	−	1.30166i	−0.0676807	−	0.185951i
$50$		0			0
$51$	7.26104	−	7.11008i	1.01675	−	0.995611i
$52$	9.30011	+	0.813654i	1.28969	+	0.112834i
$53$	−1.70331	−	1.70331i	−0.233968	−	0.233968i	0.580379	−	0.814347i	$-0.302905\pi$
$53$	−1.70331	−	1.70331i	−0.233968	−	0.233968i	−0.814347	+	0.580379i	$0.802905\pi$
$54$	0.0990765	−	0.830210i	0.0134826	−	0.112977i
$55$		0			0
$56$	1.19026	+	1.41849i	0.159055	+	0.189554i
$57$	1.19680	+	0.707839i	0.158521	+	0.0937556i
$58$	0.249386	+	0.356161i	0.0327460	+	0.0467662i
$59$	4.31439	−	1.57031i	0.561686	−	0.204437i	−0.0455453	−	0.998962i	$-0.514503\pi$
$59$	4.31439	−	1.57031i	0.561686	−	0.204437i	0.607231	+	0.794525i	$0.292280\pi$
$60$		0			0
$61$	2.10123	+	11.9167i	0.269035	+	1.52577i	0.757294	+	0.653074i	$0.226521\pi$
$61$	2.10123	+	11.9167i	0.269035	+	1.52577i	−0.488259	+	0.872699i	$0.662368\pi$
$62$	−1.14135	−	0.305823i	−0.144951	−	0.0388395i
$63$	−3.50516	−	7.94862i	−0.441609	−	1.00143i
$64$	6.39585	+	3.69265i	0.799482	+	0.461581i
$65$		0			0
$66$	−0.0930836	−	1.21023i	−0.0114578	−	0.148969i
$67$	0.582021	+	6.65253i	0.0711052	+	0.812736i	0.945096	+	0.326793i	$0.105968\pi$
$67$	0.582021	+	6.65253i	0.0711052	+	0.812736i	−0.873991	+	0.485943i	$0.838476\pi$
$68$	1.00950	+	11.5386i	0.122420	+	1.39926i
$69$	4.16355	+	1.99500i	0.501232	+	0.240170i
$70$		0			0
$71$	−5.61473	−	3.24167i	−0.666346	−	0.384715i	0.128345	−	0.991730i	$-0.459034\pi$
$71$	−5.61473	−	3.24167i	−0.666346	−	0.384715i	−0.794691	+	0.607014i	$0.792367\pi$
$72$	1.32772	+	1.38470i	0.156473	+	0.163189i
$73$	9.31768	+	2.49666i	1.09055	+	0.292212i	0.758912	−	0.651194i	$-0.225731\pi$
$73$	9.31768	+	2.49666i	1.09055	+	0.292212i	0.331640	+	0.943406i	$0.392398\pi$
$74$	0.0908402	+	0.515180i	0.0105600	+	0.0598885i
$75$		0			0
$76$	−1.48920	+	0.542026i	−0.170823	+	0.0621747i
$77$	−7.23368	−	10.3308i	−0.824355	−	1.17730i
$78$	−1.14827	+	0.646967i	−0.130016	+	0.0732546i
$79$	0.322504	+	0.384345i	0.0362845	+	0.0432422i	0.783882	−	0.620910i	$-0.213237\pi$
$79$	0.322504	+	0.384345i	0.0362845	+	0.0432422i	−0.747597	+	0.664153i	$0.768792\pi$
$80$		0			0
$81$	−4.16865	−	7.97636i	−0.463184	−	0.886262i
$82$	−0.511034	−	0.511034i	−0.0564343	−	0.0564343i
$83$	−8.92110	−	0.780495i	−0.979218	−	0.0856704i	−0.413706	−	0.910411i	$-0.635766\pi$
$83$	−8.92110	−	0.780495i	−0.979218	−	0.0856704i	−0.565512	+	0.824740i	$0.691321\pi$
$84$	9.53639	+	2.66293i	1.04051	+	0.290550i
$85$		0			0
$86$	−0.378253	−	1.03924i	−0.0407881	−	0.112064i
$87$	4.38090	+	1.64683i	0.469682	+	0.176559i
$88$	2.28135	+	1.59742i	0.243193	+	0.170286i
$89$	6.84734	+	11.8599i	0.725816	+	1.25715i	0.958637	+	0.284631i	$0.0918711\pi$
$89$	6.84734	+	11.8599i	0.725816	+	1.25715i	−0.232821	+	0.972520i	$0.574796\pi$
$90$		0			0
$91$	−6.84699	+	11.8593i	−0.717759	+	1.24320i
$92$	−4.76903	+	2.22384i	−0.497206	+	0.231851i
$93$	−11.9971	+	4.22442i	−1.24404	+	0.438052i
$94$	−0.571832	+	0.681483i	−0.0589800	+	0.0702896i
$95$		0			0
$96$	−3.27718	+	0.252061i	−0.334476	+	0.0257259i
$97$	−3.08067	−	6.60652i	−0.312795	−	0.670790i	0.685567	−	0.728010i	$-0.259554\pi$
$97$	−3.08067	−	6.60652i	−0.312795	−	0.670790i	−0.998362	+	0.0572192i	$0.981777\pi$
$98$	−0.215294	+	0.0576878i	−0.0217480	+	0.00582735i
$99$	−8.18637	−	10.1831i	−0.822762	−	1.02344i
$100$		0			0
$101$	5.17835	−	0.913082i	0.515265	−	0.0908551i	0.0900315	−	0.995939i	$-0.471303\pi$
$101$	5.17835	−	0.913082i	0.515265	−	0.0908551i	0.425233	+	0.905084i	$0.360192\pi$
$102$	−1.03788	−	1.26362i	−0.102766	−	0.125117i
$103$	1.58805	−	3.40559i	0.156475	−	0.335562i	−0.812404	−	0.583094i	$-0.801842\pi$
$103$	1.58805	−	3.40559i	0.156475	−	0.335562i	0.968880	+	0.247532i	$0.0796195\pi$
$104$	0.525121	−	2.97811i	0.0514924	−	0.292028i
$105$		0			0
$106$	−0.296920	+	0.249146i	−0.0288395	+	0.0241992i
$107$	5.69179	−	5.69179i	0.550246	−	0.550246i	−0.376266	−	0.926512i	$-0.622792\pi$
$107$	5.69179	−	5.69179i	0.550246	−	0.550246i	0.926512	+	0.376266i	$0.122792\pi$
$108$	10.0408	+	2.09863i	0.966176	+	0.201941i
$109$		−	12.1610i		−	1.16481i	−0.812899	−	0.582405i	$-0.802112\pi$
$109$		−	12.1610i		−	1.16481i	0.812899	−	0.582405i	$-0.197888\pi$
$110$		0			0
$111$	3.93973	+	4.02338i	0.373943	+	0.381882i
$112$	−9.12124	+	6.38676i	−0.861876	+	0.603492i
$113$	−3.69017	−	1.72075i	−0.347142	−	0.161875i	0.241225	−	0.970469i	$-0.422451\pi$
$113$	−3.69017	−	1.72075i	−0.347142	−	0.161875i	−0.588366	+	0.808594i	$0.700229\pi$
$114$	0.130247	−	0.181915i	0.0121988	−	0.0170379i
$115$		0			0
$116$	−4.61962	+	2.66714i	−0.428921	+	0.247638i
$117$	−6.26450	+	12.7291i	−0.579153	+	1.17681i
$118$	−0.191208	−	0.713599i	−0.0176021	−	0.0656921i
$119$	−15.9655	−	5.81095i	−1.46355	−	0.532689i
$120$		0			0
$121$	−6.10389	−	5.12177i	−0.554899	−	0.465616i
$122$	1.93965	−	0.169698i	0.175608	−	0.0153637i
$123$	−7.64665	−	1.43128i	−0.689475	−	0.129054i
$124$	4.95815	−	13.6224i	0.445255	−	1.22333i
$125$		0			0
$126$	−1.32328	+	0.450389i	−0.117887	+	0.0401238i
$127$	0.200655	−	0.748856i	0.0178053	−	0.0664502i	−0.956452	−	0.291891i	$-0.905716\pi$
$127$	0.200655	−	0.748856i	0.0178053	−	0.0664502i	0.974257	+	0.225441i	$0.0723822\pi$
$128$	2.85853	−	4.08240i	0.252661	−	0.360837i
$129$	−9.67943	−	6.93025i	−0.852226	−	0.610175i
$130$		0			0
$131$	−7.46979	−	1.31713i	−0.652639	−	0.115078i	−0.162481	−	0.986712i	$-0.551950\pi$
$131$	−7.46979	−	1.31713i	−0.652639	−	0.115078i	−0.490158	+	0.871634i	$0.663061\pi$
$132$	14.8908	+	0.156414i	1.29608	+	0.0136141i
$133$	0.202605	−	2.31579i	0.0175681	−	0.200804i
$134$	1.07453			0.0928254
$135$		0			0
$136$	3.75194			0.321726
$137$	0.863173	−	9.86611i	0.0737459	−	0.842919i	−0.865776	−	0.500431i	$-0.833175\pi$
$137$	0.863173	−	9.86611i	0.0737459	−	0.842919i	0.939522	−	0.342488i	$-0.111270\pi$
$138$	0.378179	−	0.639419i	0.0321927	−	0.0544310i
$139$	−14.8464	−	2.61782i	−1.25926	−	0.222041i	−0.496105	−	0.868262i	$-0.665237\pi$
$139$	−14.8464	−	2.61782i	−1.25926	−	0.222041i	−0.763150	+	0.646222i	$0.776348\pi$
$140$		0			0
$141$	−0.934757	+	9.53029i	−0.0787208	+	0.802595i
$142$	−0.598365	+	0.854554i	−0.0502137	+	0.0717126i
$143$	−5.33066	+	19.8943i	−0.445772	+	1.66364i
$144$	−8.99088	+	7.22791i	−0.749240	+	0.602326i
$145$		0			0
$146$	0.530875	−	1.45857i	0.0439355	−	0.120712i
$147$	−1.56142	+	1.82162i	−0.128783	+	0.150244i
$148$	−6.39361	+	0.559369i	−0.525552	+	0.0459798i
$149$	11.3083	+	9.48879i	0.926412	+	0.777352i	0.975170	−	0.221459i	$-0.0710818\pi$
$149$	11.3083	+	9.48879i	0.926412	+	0.777352i	−0.0487579	+	0.998811i	$0.515526\pi$
$150$		0			0
$151$	−2.23835	−	0.814693i	−0.182154	−	0.0662987i	0.249333	−	0.968418i	$-0.419789\pi$
$151$	−2.23835	−	0.814693i	−0.182154	−	0.0662987i	−0.431487	+	0.902119i	$0.642011\pi$
$152$	0.132865	+	0.495858i	0.0107768	+	0.0402194i
$153$	−16.9027	−	4.91185i	−1.36650	−	0.397100i
$154$	−1.75742	+	1.01465i	−0.141617	+	0.0817626i
$155$		0			0
$156$	−6.67935	−	14.7258i	−0.534776	−	1.17901i
$157$	−7.10700	−	3.31405i	−0.567200	−	0.264490i	0.117794	−	0.993038i	$-0.462418\pi$
$157$	−7.10700	−	3.31405i	−0.567200	−	0.264490i	−0.684995	+	0.728548i	$0.740195\pi$
$158$	0.0661316	−	0.0463058i	0.00526114	−	0.00368389i
$159$	−1.12213	+	4.01852i	−0.0889905	+	0.318689i
$160$		0			0
$161$		−	7.71863i		−	0.608313i
$162$	−1.33703	+	0.556355i	−0.105047	+	0.0437114i
$163$	−10.1968	+	10.1968i	−0.798677	+	0.798677i	−0.982887	−	0.184210i	$-0.941027\pi$
$163$	−10.1968	+	10.1968i	−0.798677	+	0.798677i	0.184210	+	0.982887i	$0.441027\pi$
$164$	6.79225	−	5.69937i	0.530385	−	0.445046i
$165$		0			0
$166$	−0.250219	+	1.41906i	−0.0194208	+	0.110141i
$167$	−2.74303	+	5.88244i	−0.212262	+	0.455197i	−0.983395	−	0.181477i	$-0.941912\pi$
$167$	−2.74303	+	5.88244i	−0.212262	+	0.455197i	0.771133	+	0.636673i	$0.219690\pi$
$168$	1.12854	−	3.00215i	0.0870689	−	0.231621i
$169$	9.22155	−	1.62601i	0.709350	−	0.125078i
$170$		0			0
$171$	0.0505891	−	2.40781i	0.00386865	−	0.184130i
$172$	13.1060	−	3.51174i	0.999321	−	0.267767i
$173$	4.90021	+	10.5085i	0.372556	+	0.798949i	0.999797	+	0.0201240i	$0.00640610\pi$
$173$	4.90021	+	10.5085i	0.372556	+	0.798949i	−0.627242	+	0.778825i	$0.715816\pi$
$174$	0.325417	−	0.679143i	0.0246698	−	0.0514857i
$175$		0			0
$176$	−10.7649	+	12.8292i	−0.811438	+	0.967034i
$177$	−6.03781	−	5.17536i	−0.453829	−	0.389004i
$178$	1.99712	−	0.931272i	0.149690	−	0.0698018i
$179$	3.42048	−	5.92444i	0.255658	−	0.442813i	−0.709416	−	0.704790i	$-0.751041\pi$
$179$	3.42048	−	5.92444i	0.255658	−	0.442813i	0.965074	+	0.261977i	$0.0843744\pi$
$180$		0			0
$181$	−8.12103	−	14.0660i	−0.603631	−	1.04552i	−0.992266	−	0.124128i	$-0.960387\pi$
$181$	−8.12103	−	14.0660i	−0.603631	−	1.04552i	0.388635	−	0.921392i	$-0.372947\pi$
$182$	1.80497	+	1.26386i	0.133794	+	0.0936832i
$183$	16.1959	−	13.3026i	1.19724	−	0.983357i
$184$	0.582977	+	1.60172i	0.0429776	+	0.118080i
$185$		0			0
$186$	0.508907	+	1.98232i	0.0373149	+	0.145351i
$187$	−25.4563	−	2.22713i	−1.86155	−	0.162864i
$188$	−7.71757	−	7.71757i	−0.562861	−	0.562861i
$189$	−9.01442	+	12.0474i	−0.655702	+	0.876322i
$190$		0			0
$191$	−13.1571	−	15.6801i	−0.952017	−	1.13457i	−0.990802	−	0.135322i	$-0.956793\pi$
$191$	−13.1571	−	15.6801i	−0.952017	−	1.13457i	0.0387846	−	0.999248i	$-0.487651\pi$
$192$	0.134357	−	12.7910i	0.00969639	−	0.923111i
$193$	−4.46650	−	6.37883i	−0.321506	−	0.459158i	0.625570	−	0.780168i	$-0.284867\pi$
$193$	−4.46650	−	6.37883i	−0.321506	−	0.459158i	−0.947076	+	0.321010i	$0.895978\pi$
$194$	−1.10220	+	0.401167i	−0.0791332	+	0.0288021i
$195$		0			0
$196$	−0.474846	−	2.69298i	−0.0339176	−	0.192356i
$197$	5.11454	+	1.37044i	0.364396	+	0.0976395i	0.436371	−	0.899767i	$-0.356264\pi$
$197$	5.11454	+	1.37044i	0.364396	+	0.0976395i	−0.0719752	+	0.997406i	$0.522930\pi$
$198$	−1.74711	+	1.16943i	−0.124162	+	0.0831077i
$199$	24.0896	+	13.9081i	1.70766	+	0.985920i	0.937440	+	0.348148i	$0.113189\pi$
$199$	24.0896	+	13.9081i	1.70766	+	0.985920i	0.770225	+	0.637773i	$0.220144\pi$
$200$		0			0
$201$	9.54391	−	6.53441i	0.673176	−	0.460902i
$202$	−0.0737416	−	0.842870i	−0.00518844	−	0.0593041i
$203$	−0.681958	−	7.79481i	−0.0478640	−	0.547088i
$204$	16.5537	−	11.3338i	1.15899	−	0.793521i
$205$		0			0
$206$	−0.523629	−	0.302317i	−0.0364829	−	0.0210634i
$207$	−0.529459	−	7.97904i	−0.0368000	−	0.554582i
$208$	17.5651	+	4.70654i	1.21792	+	0.326340i
$209$	−0.607127	−	3.44319i	−0.0419958	−	0.238170i
$210$		0			0
$211$	8.85421	−	3.22267i	0.609549	−	0.221858i	−0.0187568	−	0.999824i	$-0.505971\pi$
$211$	8.85421	−	3.22267i	0.609549	−	0.221858i	0.628306	+	0.777966i	$0.283749\pi$
$212$	−2.72754	−	3.89534i	−0.187328	−	0.267533i
$213$	−0.117948	+	11.2288i	−0.00808168	+	0.769388i
$214$	−0.832546	−	0.992189i	−0.0569116	−	0.0678247i
$215$		0			0
$216$	0.960684	−	3.18085i	0.0653663	−	0.216429i
$217$	15.0362	+	15.0362i	1.02072	+	1.02072i
$218$	−1.94935	−	0.170546i	−0.132026	−	0.0115508i
$219$	−4.15460	−	16.1832i	−0.280742	−	1.09356i
$220$		0			0
$221$	9.48994	+	26.0734i	0.638363	+	1.75389i
$222$	0.700179	−	0.575097i	0.0469930	−	0.0385980i
$223$	8.50538	+	5.95553i	0.569562	+	0.398812i	0.822580	−	0.568650i	$-0.192534\pi$
$223$	8.50538	+	5.95553i	0.569562	+	0.398812i	−0.253017	+	0.967462i	$0.581423\pi$
$224$	2.74756	+	4.75892i	0.183579	+	0.317969i
$225$		0			0
$226$	−0.327580	+	0.567385i	−0.0217903	+	0.0377419i
$227$	−13.6725	+	6.37560i	−0.907477	+	0.423164i	−0.819579	−	0.572966i	$-0.805793\pi$
$227$	−13.6725	+	6.37560i	−0.907477	+	0.423164i	−0.0878980	+	0.996129i	$0.528015\pi$
$228$	2.08408	+	1.78639i	0.138022	+	0.118306i
$229$	−0.604581	+	0.720511i	−0.0399518	+	0.0476127i	−0.785650	−	0.618671i	$-0.787671\pi$
$229$	−0.604581	+	0.720511i	−0.0399518	+	0.0476127i	0.745699	+	0.666284i	$0.232116\pi$
$230$		0			0
$231$	−9.43903	+	19.6992i	−0.621043	+	1.29611i
$232$	0.730246	+	1.56602i	0.0479430	+	0.102814i
$233$	5.42572	−	1.45382i	0.355451	−	0.0952427i	−0.0766749	−	0.997056i	$-0.524430\pi$
$233$	5.42572	−	1.45382i	0.355451	−	0.0952427i	0.432126	+	0.901813i	$0.357764\pi$
$234$	1.95256	+	1.18268i	0.127643	+	0.0773145i
$235$		0			0
$236$	8.92598	−	1.57389i	0.581032	−	0.102452i
$237$	0.305782	−	0.813442i	0.0198627	−	0.0528387i
$238$	−1.15537	+	2.47770i	−0.0748914	+	0.160605i
$239$	2.69221	−	15.2683i	0.174144	−	0.987622i	−0.764982	−	0.644051i	$-0.777252\pi$
$239$	2.69221	−	15.2683i	0.174144	−	0.987622i	0.939127	−	0.343571i	$-0.111637\pi$
$240$		0			0
$241$	14.6302	−	12.2762i	0.942414	−	0.790779i	−0.0355896	−	0.999366i	$-0.511331\pi$
$241$	14.6302	−	12.2762i	0.942414	−	0.790779i	0.978004	+	0.208587i	$0.0668865\pi$
$242$	−0.906597	+	0.906597i	−0.0582783	+	0.0582783i
$243$	−8.49215	+	13.0722i	−0.544772	+	0.838584i
$244$			23.8877i			1.52925i
$245$		0			0
$246$	−0.336665	+	1.20565i	−0.0214650	+	0.0768695i
$247$	−3.10982	+	2.17752i	−0.197873	+	0.138552i
$248$	−4.25587	−	1.98455i	−0.270248	−	0.126019i
$249$	6.40714	+	14.1257i	0.406036	+	0.895177i
$250$		0			0
$251$	−10.8992	+	6.29267i	−0.687953	+	0.397190i	−0.802845	−	0.596188i	$-0.796681\pi$
$251$	−10.8992	+	6.29267i	−0.687953	+	0.397190i	0.114892	+	0.993378i	$0.463348\pi$
$252$	−4.08965	−	16.6546i	−0.257624	−	1.04914i
$253$	−3.00463	−	11.2134i	−0.188900	−	0.704983i
$254$	−0.117224	−	0.0426661i	−0.00735529	−	0.00267711i
$255$		0			0
$256$	10.7006	+	8.97889i	0.668789	+	0.561181i
$257$	29.5115	−	2.58192i	1.84088	−	0.161056i	0.887100	−	0.461576i	$-0.152716\pi$
$257$	29.5115	−	2.58192i	1.84088	−	0.161056i	0.953775	+	0.300521i	$0.0971604\pi$
$258$	−1.24663	+	1.45438i	−0.0776119	+	0.0905456i
$259$	3.21988	−	8.84654i	0.200073	−	0.549697i
$260$		0			0
$261$	−1.23965	−	8.01102i	−0.0767325	−	0.495869i
$262$	−0.315886	+	1.17890i	−0.0195155	+	0.0728328i
$263$	−0.339036	+	0.484194i	−0.0209059	+	0.0298567i	−0.829469	−	0.558553i	$-0.811357\pi$
$263$	−0.339036	+	0.484194i	−0.0209059	+	0.0298567i	0.808563	+	0.588410i	$0.200246\pi$
$264$	0.470872	−	4.80075i	0.0289801	−	0.295466i
$265$		0			0
$266$	−0.368368	−	0.0649533i	−0.0225861	−	0.00398254i
$267$	12.0750	−	20.4163i	0.738981	−	1.24946i
$268$	−1.14897	+	13.1328i	−0.0701847	+	0.802215i
$269$	−29.5187			−1.79979			−0.899894	−	0.436108i	$-0.856357\pi$
$269$	−29.5187			−1.79979			−0.899894	+	0.436108i	$0.856357\pi$
$270$		0			0
$271$	−9.45815			−0.574542			−0.287271	−	0.957849i	$-0.592748\pi$
$271$	−9.45815			−0.574542			−0.287271	+	0.957849i	$0.592748\pi$
$272$	−1.96638	+	22.4758i	−0.119229	+	1.36280i
$273$	23.7174	+	0.249128i	1.43544	+	0.0150779i
$274$	−1.56939	−	0.276725i	−0.0948101	−	0.0167176i
$275$		0			0
$276$	7.41054	+	5.30578i	0.446062	+	0.319370i
$277$	11.6968	−	16.7047i	0.702792	−	1.00369i	−0.296031	−	0.955178i	$-0.595663\pi$
$277$	11.6968	−	16.7047i	0.702792	−	1.00369i	0.998823	−	0.0485123i	$-0.0154480\pi$
$278$	−0.627831	+	2.34310i	−0.0376548	+	0.140530i
$279$	16.5749	+	14.5121i	0.992314	+	0.868816i
$280$		0			0
$281$	7.06656	−	19.4152i	0.421555	−	1.15821i	−0.529261	−	0.848459i	$-0.677531\pi$
$281$	7.06656	−	19.4152i	0.421555	−	1.15821i	0.950816	−	0.309755i	$-0.100247\pi$
$282$	1.51455	+	0.283490i	0.0901902	+	0.0168816i
$283$	−12.8473	+	1.12399i	−0.763693	+	0.0668145i	−0.462345	−	0.886700i	$-0.652992\pi$
$283$	−12.8473	+	1.12399i	−0.763693	+	0.0668145i	−0.301348	+	0.953514i	$0.597436\pi$
$284$	−9.80446	−	8.22692i	−0.581787	−	0.488178i
$285$		0			0
$286$	3.11420	+	1.13348i	0.184147	+	0.0670239i
$287$	3.36621	+	12.5629i	0.198701	+	0.741563i
$288$	3.16670	+	4.73101i	0.186599	+	0.278777i
$289$	−15.0908	+	8.71266i	−0.887692	+	0.512509i
$290$		0			0
$291$	−7.35007	+	10.2658i	−0.430869	+	0.601791i
$292$	17.2588	+	8.04791i	1.01000	+	0.470968i
$293$	27.6373	−	19.3518i	1.61459	−	1.13055i	0.710048	−	0.704153i	$-0.248673\pi$
$293$	27.6373	−	19.3518i	1.61459	−	1.13055i	0.904538	−	0.426392i	$-0.140216\pi$
$294$	0.270099	+	0.275834i	0.0157525	+	0.0160870i
$295$		0			0
$296$			2.07897i			0.120837i
$297$	−8.40622	+	21.0113i	−0.487778	+	1.21920i
$298$	1.67960	−	1.67960i	0.0972964	−	0.0972964i
$299$	−9.65629	+	8.10259i	−0.558438	+	0.468585i
$300$		0			0
$301$	−3.45606	+	19.6003i	−0.199204	+	1.12974i
$302$	−0.161982	+	0.347372i	−0.00932102	+	0.0199890i
$303$	−5.78060	−	7.03787i	−0.332087	−	0.404315i
$304$	−3.04006	+	0.536044i	−0.174359	+	0.0307442i
$305$		0			0
$306$	−1.02439	+	2.64054i	−0.0585605	+	0.150950i
$307$	9.73639	−	2.60886i	0.555685	−	0.148895i	0.0299620	−	0.999551i	$-0.490461\pi$
$307$	9.73639	−	2.60886i	0.555685	−	0.148895i	0.525723	+	0.850656i	$0.323795\pi$
$308$	−10.5217	−	22.5639i	−0.599532	−	1.28570i
$309$	−6.48927	+	0.499116i	−0.369162	+	0.0283937i
$310$		0			0
$311$	16.5976	−	19.7803i	0.941166	−	1.12164i	−0.0512465	−	0.998686i	$-0.516319\pi$
$311$	16.5976	−	19.7803i	0.941166	−	1.12164i	0.992413	−	0.122952i	$-0.0392361\pi$
$312$	−4.94048	+	1.73964i	−0.279700	+	0.0984878i
$313$	−5.10324	+	2.37968i	−0.288452	+	0.134508i	−0.561459	−	0.827505i	$-0.689760\pi$
$313$	−5.10324	+	2.37968i	−0.288452	+	0.134508i	0.273007	+	0.962012i	$0.411982\pi$
$314$	−0.630895	+	1.09274i	−0.0356035	+	0.0616670i
$315$		0			0
$316$	0.495232	+	0.857767i	0.0278590	+	0.0482532i
$317$	1.51852	+	1.06328i	0.0852886	+	0.0597197i	0.615443	−	0.788181i	$-0.288977\pi$
$317$	1.51852	+	1.06328i	0.0852886	+	0.0597197i	−0.530154	+	0.847901i	$0.677866\pi$
$318$	0.628413	+	0.236228i	0.0352396	+	0.0132470i
$319$	−4.02502	−	11.0586i	−0.225358	−	0.619165i
$320$		0			0
$321$	−13.4283	−	3.74970i	−0.749493	−	0.209288i
$322$	−1.23726	−	0.108246i	−0.0689498	−	0.00603233i
$323$	−3.33059	−	3.33059i	−0.185319	−	0.185319i
$324$	−5.37005	−	16.9360i	−0.298336	−	0.940889i
$325$		0			0
$326$	1.49150	+	1.77750i	0.0826067	+	0.0984469i
$327$	−18.3511	+	10.3395i	−1.01482	+	0.571777i
$328$	−1.64739	−	2.35271i	−0.0909618	−	0.129907i
$329$	15.0441	−	5.47561i	0.829409	−	0.301880i
$330$		0			0
$331$	−3.34434	−	18.9667i	−0.183822	−	1.04251i	−0.927460	−	0.373923i	$-0.878012\pi$
$331$	−3.34434	−	18.9667i	−0.183822	−	1.04251i	0.743638	−	0.668583i	$-0.233099\pi$
$332$	−17.0761	−	4.57553i	−0.937173	−	0.251115i
$333$	2.72168	−	9.36587i	0.149147	−	0.513247i
$334$	0.904459	+	0.522190i	0.0494898	+	0.0285730i
$335$		0			0
$336$	17.3928	+	8.33391i	0.948855	+	0.454652i
$337$	−0.300674	−	3.43672i	−0.0163788	−	0.187210i	−0.999977	−	0.00683487i	$-0.997824\pi$
$337$	−0.300674	−	3.43672i	−0.0163788	−	0.187210i	0.983598	−	0.180375i	$-0.0577312\pi$
$338$	−0.131318	−	1.50097i	−0.00714277	−	0.0816423i
$339$	0.540823	+	7.03154i	0.0293735	+	0.381901i
$340$		0			0
$341$	27.6974	+	15.9911i	1.49990	+	0.865966i
$342$	−0.385252	−	0.0418764i	−0.0208320	−	0.00226442i
$343$	−15.7049	−	4.20811i	−0.847984	−	0.227217i
$344$	−0.763205	−	4.32835i	−0.0411493	−	0.233369i
$345$		0			0
$346$	1.75319	−	0.638109i	0.0942520	−	0.0343049i
$347$	−4.96478	−	7.09044i	−0.266523	−	0.380635i	0.663475	−	0.748198i	$-0.269081\pi$
$347$	−4.96478	−	7.09044i	−0.266523	−	0.380635i	−0.929998	+	0.367564i	$0.880192\pi$
$348$	7.95246	+	4.70341i	0.426296	+	0.252129i
$349$	−6.93929	−	8.26992i	−0.371452	−	0.442679i	0.547645	−	0.836711i	$-0.315524\pi$
$349$	−6.93929	−	8.26992i	−0.371452	−	0.442679i	−0.919097	+	0.394032i	$0.871080\pi$
$350$		0			0
$351$	24.5346	−	1.36936i	1.30956	−	0.0730910i
$352$	5.84410	+	5.84410i	0.311491	+	0.311491i
$353$	26.6492	+	2.33150i	1.41839	+	0.124093i	0.770405	−	0.637555i	$-0.220054\pi$
$353$	26.6492	+	2.33150i	1.41839	+	0.124093i	0.647990	+	0.761649i	$0.275610\pi$
$354$	−0.914260	+	0.895253i	−0.0485924	+	0.0475822i
$355$		0			0
$356$	9.24644	+	25.4044i	0.490060	+	1.34643i
$357$	4.80539	+	29.0327i	0.254328	+	1.53657i
$358$	−0.901691	−	0.631371i	−0.0476559	−	0.0333690i
$359$	6.82588	+	11.8228i	0.360256	+	0.623982i	0.988003	−	0.154436i	$-0.0493560\pi$
$359$	6.82588	+	11.8228i	0.360256	+	0.623982i	−0.627747	+	0.778418i	$0.716023\pi$
$360$		0			0
$361$	−9.17777	+	15.8964i	−0.483041	+	0.836651i
$362$	−2.36861	+	1.10450i	−0.124491	+	0.0580513i
$363$	−2.53916	+	13.5655i	−0.133271	+	0.712004i
$364$	−17.3767	+	20.7088i	−0.910788	+	1.08544i
$365$		0			0
$366$	−1.90521	−	2.78268i	−0.0995871	−	0.145453i
$367$	−5.50814	−	11.8122i	−0.287523	−	0.616594i	0.708498	−	0.705712i	$-0.249373\pi$
$367$	−5.50814	−	11.8122i	−0.287523	−	0.616594i	−0.996021	+	0.0891181i	$0.971595\pi$
$368$	−9.90056	+	2.65285i	−0.516103	+	0.138289i
$369$	4.34153	+	12.7558i	0.226011	+	0.664041i
$370$		0			0
$371$	6.86938	−	1.21126i	0.356640	−	0.0628853i
$372$	−24.7719	+	4.10016i	−1.28436	+	0.212583i
$373$	0.799956	−	1.71551i	0.0414201	−	0.0888258i	−0.884509	−	0.466523i	$-0.845506\pi$
$373$	0.799956	−	1.71551i	0.0414201	−	0.0888258i	0.925929	+	0.377698i	$0.123284\pi$
$374$	−0.713999	+	4.04929i	−0.0369200	+	0.209384i
$375$		0			0
$376$	−2.70829	+	2.27252i	−0.139669	+	0.117196i
$377$	−9.03572	+	9.03572i	−0.465363	+	0.465363i
$378$	1.80473	+	1.61392i	0.0928252	+	0.0830112i
$379$			8.64900i			0.444270i	0.975016	+	0.222135i	$0.0713025\pi$
$379$			8.64900i			0.444270i	−0.975016	+	0.222135i	$0.928698\pi$
$380$		0			0
$381$	−1.30063	+	0.333902i	−0.0666335	+	0.0171063i
$382$	−2.69796	+	1.88913i	−0.138040	+	0.0966563i
$383$	15.4786	+	7.21777i	0.790917	+	0.368811i	0.775723	−	0.631074i	$-0.217386\pi$
$383$	15.4786	+	7.21777i	0.790917	+	0.368811i	0.0151943	+	0.999885i	$0.495163\pi$
$384$	−8.59078	−	0.842608i	−0.438397	−	0.0429992i
$385$		0			0
$386$	−1.08513	+	0.626503i	−0.0552319	+	0.0318881i
$387$	−2.22818	+	20.4986i	−0.113265	+	1.04200i
$388$	−3.72447	−	13.8999i	−0.189081	−	0.705661i
$389$	0.823821	+	0.299846i	0.0417694	+	0.0152028i	0.362820	−	0.931859i	$-0.381814\pi$
$389$	0.823821	+	0.299846i	0.0417694	+	0.0152028i	−0.321051	+	0.947062i	$0.604036\pi$
$390$		0			0
$391$	−11.9805	−	10.0529i	−0.605882	−	0.508395i
$392$	−0.882413	+	0.0772012i	−0.0445686	+	0.00389925i
$393$	4.36343	+	12.3919i	0.220106	+	0.625087i
$394$	0.291401	−	0.800617i	0.0146806	−	0.0403345i
$395$		0			0
$396$	−12.4245	−	22.6035i	−0.624354	−	1.13587i
$397$	0.598779	−	2.23467i	0.0300519	−	0.112155i	−0.949271	−	0.314460i	$-0.898177\pi$
$397$	0.598779	−	2.23467i	0.0300519	−	0.112155i	0.979323	+	0.202305i	$0.0648432\pi$
$398$	2.56724	−	3.66640i	0.128684	−	0.183780i
$399$	−3.66681	+	1.66320i	−0.183570	+	0.0832641i
$400$		0			0
$401$	6.34251	+	1.11835i	0.316730	+	0.0558480i	0.329753	−	0.944067i	$-0.393035\pi$
$401$	6.34251	+	1.11835i	0.316730	+	0.0558480i	−0.0130235	+	0.999915i	$0.504146\pi$
$402$	−0.913591	−	1.62148i	−0.0455658	−	0.0808722i
$403$	3.02667	−	34.5950i	0.150769	−	1.72330i
$404$	10.3803			0.516440
$405$		0			0
$406$	−1.25904			−0.0624849
$407$	1.23407	−	14.1054i	0.0611704	−	0.699181i
$408$	−3.18998	−	5.66172i	−0.157928	−	0.280297i
$409$	−27.7142	−	4.88676i	−1.37038	−	0.241635i	−0.560462	−	0.828180i	$-0.689376\pi$
$409$	−27.7142	−	4.88676i	−1.37038	−	0.241635i	−0.809916	+	0.586546i	$0.800487\pi$
$410$		0			0
$411$	−15.6220	+	7.08585i	−0.770576	+	0.349519i
$412$	4.25479	−	6.07648i	0.209619	−	0.299367i
$413$	−3.44101	+	12.8420i	−0.169321	+	0.631915i
$414$	−1.28643	−	0.0270284i	−0.0632245	−	0.00132837i
$415$		0			0
$416$	3.06934	−	8.43295i	0.150487	−	0.413459i
$417$	8.67242	+	24.6291i	0.424690	+	1.20609i
$418$	−0.560441	+	0.0490322i	−0.0274121	+	0.00239824i
$419$	28.5256	+	23.9358i	1.39357	+	1.16934i	0.963872	+	0.266365i	$0.0858226\pi$
$419$	28.5256	+	23.9358i	1.39357	+	1.16934i	0.429693	+	0.902975i	$0.358622\pi$
$420$		0			0
$421$	27.5767	+	10.0371i	1.34400	+	0.489178i	0.911071	−	0.412249i	$-0.135256\pi$
$421$	27.5767	+	10.0371i	1.34400	+	0.489178i	0.432933	+	0.901426i	$0.357479\pi$
$422$	−0.392407	−	1.46448i	−0.0191021	−	0.0712900i
$423$	15.1761	−	6.69230i	0.737886	−	0.325391i
$424$	−1.33400	+	0.770186i	−0.0647849	+	0.0374036i
$425$		0			0
$426$	1.79828	+	0.176380i	0.0871268	+	0.00854565i
$427$	−31.7567	−	14.8084i	−1.53682	−	0.716629i
$428$	13.0167	−	9.11436i	0.629184	−	0.440559i
$429$	34.5530	−	8.87053i	1.66823	−	0.428273i
$430$		0			0
$431$			0.480686i			0.0231538i	0.999933	+	0.0115769i	$0.00368513\pi$
$431$			0.480686i			0.0231538i	−0.999933	+	0.0115769i	$0.996315\pi$
$432$	18.5513	+	7.42202i	0.892548	+	0.357092i
$433$	5.55599	−	5.55599i	0.267004	−	0.267004i	−0.560888	−	0.827892i	$-0.689540\pi$
$433$	5.55599	−	5.55599i	0.267004	−	0.267004i	0.827892	+	0.560888i	$0.189540\pi$
$434$	2.62110	−	2.19937i	0.125817	−	0.105573i
$435$		0			0
$436$	4.16878	−	23.6423i	0.199648	−	1.13226i
$437$	0.904335	−	1.93935i	0.0432602	−	0.0927718i
$438$	−2.65236	+	0.439009i	−0.126735	+	0.0209767i
$439$	12.2268	−	2.15591i	0.583551	−	0.102896i	0.125924	−	0.992040i	$-0.459810\pi$
$439$	12.2268	−	2.15591i	0.583551	−	0.102896i	0.457627	+	0.889144i	$0.348699\pi$
$440$		0			0
$441$	4.07640	+	0.807416i	0.194114	+	0.0384484i
$442$	4.31253	−	1.15554i	0.205126	−	0.0549634i
$443$	−7.51833	−	16.1231i	−0.357207	−	0.766033i	0.642793	−	0.766040i	$-0.277775\pi$
$443$	−7.51833	−	16.1231i	−0.357207	−	0.766033i	−1.00000		7.21597e-6i	$0.999998\pi$
$444$	6.28009	+	9.17246i	0.298040	+	0.435306i
$445$		0			0
$446$	1.07392	−	1.27985i	0.0508517	−	0.0606028i
$447$	4.70414	−	25.1320i	0.222498	−	1.18870i
$448$	−19.3821	+	9.03801i	−0.915717	+	0.427006i
$449$	−1.91039	+	3.30889i	−0.0901568	+	0.156156i	−0.907577	−	0.419886i	$-0.862070\pi$
$449$	−1.91039	+	3.30889i	−0.0901568	+	0.156156i	0.817420	+	0.576042i	$0.195403\pi$
$450$		0			0
$451$	9.78070	+	16.9407i	0.460555	+	0.797705i
$452$	−6.58425	−	4.61034i	−0.309697	−	0.216852i
$453$	0.673713	+	4.07037i	0.0316538	+	0.191243i
$454$	0.830236	+	2.28105i	0.0389649	+	0.107055i
$455$		0			0
$456$	0.635292	−	0.622085i	0.0297503	−	0.0291318i
$457$	22.0047	+	1.92516i	1.02934	+	0.0900553i	0.589292	−	0.807920i	$-0.299407\pi$
$457$	22.0047	+	1.92516i	1.02934	+	0.0900553i	0.440045	+	0.897976i	$0.354962\pi$
$458$	0.107016	+	0.107016i	0.00500053	+	0.00500053i
$459$	6.95901	+	29.6826i	0.324819	+	1.38546i
$460$		0			0
$461$	4.15610	+	4.95304i	0.193569	+	0.230686i	0.854095	−	0.520116i	$-0.174111\pi$
$461$	4.15610	+	4.95304i	0.193569	+	0.230686i	−0.660527	+	0.750803i	$0.729667\pi$
$462$	3.02531	+	1.78929i	0.140750	+	0.0832455i
$463$	0.176051	+	0.251426i	0.00818177	+	0.0116848i	0.823222	−	0.567719i	$-0.192174\pi$
$463$	0.176051	+	0.251426i	0.00818177	+	0.0116848i	−0.815040	+	0.579404i	$0.803285\pi$
$464$	−9.76390	+	3.55377i	−0.453278	+	0.164980i
$465$		0			0
$466$	−0.156950	−	0.890106i	−0.00727056	−	0.0412334i
$467$	41.3450	+	11.0784i	1.91322	+	0.512645i	0.992470	+	0.122489i	$0.0390876\pi$
$467$	41.3450	+	11.0784i	1.91322	+	0.512645i	0.920749	+	0.390156i	$0.127579\pi$
$468$	−16.5425	+	22.5994i	−0.764676	+	1.04466i
$469$	−16.7467	−	9.66873i	−0.773292	−	0.446460i
$470$		0			0
$471$	1.04159	+	13.5422i	0.0479938	+	0.623993i
$472$	−0.255886	−	2.92479i	−0.0117781	−	0.134624i
$473$	2.60893	+	29.8202i	0.119959	+	1.37113i
$474$	−0.126103	−	0.0604232i	−0.00579209	−	0.00277533i
$475$		0			0
$476$	−29.0467	−	16.7701i	−1.33135	−	0.768658i
$477$	7.01805	−	1.72333i	0.321335	−	0.0789058i
$478$	−2.40968	−	0.645671i	−0.110216	−	0.0295323i
$479$	−7.22789	−	40.9914i	−0.330251	−	1.87295i	−0.469863	−	0.882740i	$-0.655697\pi$
$479$	−7.22789	−	40.9914i	−0.330251	−	1.87295i	0.139612	−	0.990206i	$-0.455415\pi$
$480$		0			0
$481$	−14.4474	+	5.25842i	−0.658745	+	0.239763i
$482$	−1.76264	−	2.51732i	−0.0802862	−	0.114661i
$483$	−11.6475	+	6.56255i	−0.529980	+	0.298606i
$484$	−10.1109	−	12.0497i	−0.459588	−	0.547716i
$485$		0			0
$486$	1.97632	+	1.54458i	0.0896479	+	0.0700635i
$487$	−16.8595	−	16.8595i	−0.763975	−	0.763975i	0.213064	−	0.977038i	$-0.431656\pi$
$487$	−16.8595	−	16.8595i	−0.763975	−	0.763975i	−0.977038	+	0.213064i	$0.931656\pi$
$488$	7.70840	+	0.674397i	0.348943	+	0.0305285i
$489$	24.0567	+	6.71758i	1.08788	+	0.303779i
$490$		0			0
$491$	−5.41828	−	14.8866i	−0.244524	−	0.671823i	−0.999864	−	0.0164907i	$-0.994751\pi$
$491$	−5.41828	−	14.8866i	−0.244524	−	0.671823i	0.755340	−	0.655333i	$-0.227472\pi$
$492$	−14.3753	−	5.40386i	−0.648091	−	0.243625i
$493$	−12.9870	−	9.09358i	−0.584904	−	0.409554i
$494$	0.305434	+	0.529027i	0.0137421	+	0.0238020i
$495$		0			0
$496$	14.1189	−	24.4546i	0.633955	−	1.09804i
$497$	17.0150	−	7.93420i	0.763225	−	0.355898i
$498$	2.35413	−	0.828936i	0.105491	−	0.0371455i
$499$	0.350248	−	0.417409i	0.0156792	−	0.0186858i	−0.758148	−	0.652083i	$-0.773895\pi$
$499$	0.350248	−	0.417409i	0.0156792	−	0.0186858i	0.773827	+	0.633397i	$0.218340\pi$
$500$		0			0
$501$	11.2089	−	0.862118i	0.500775	−	0.0385166i
$502$	0.855835	+	1.83534i	0.0381978	+	0.0819154i
$503$	18.7290	−	5.01841i	0.835083	−	0.223760i	0.184153	−	0.982898i	$-0.441046\pi$
$503$	18.7290	−	5.01841i	0.835083	−	0.223760i	0.650930	+	0.759138i	$0.274379\pi$
$504$	−5.48979	+	0.849509i	−0.244535	+	0.0378401i
$505$		0			0
$506$	−1.83960	+	0.324371i	−0.0817801	+	0.0144200i
$507$	−10.2940	−	12.5330i	−0.457174	−	0.556609i
$508$	0.646805	−	1.38708i	0.0286974	−	0.0615417i
$509$	4.57685	−	25.9566i	0.202865	−	1.15051i	−0.697898	−	0.716197i	$-0.745881\pi$
$509$	4.57685	−	25.9566i	0.202865	−	1.15051i	0.900764	−	0.434310i	$-0.143008\pi$
$510$		0			0
$511$	−21.3981	+	17.9551i	−0.946595	+	0.794287i
$512$	8.63735	−	8.63735i	0.381720	−	0.381720i
$513$	−3.67644	+	1.97084i	−0.162319	+	0.0870146i
$514$		−	4.76676i		−	0.210253i
$515$		0			0
$516$	−16.4423	−	16.7913i	−0.723830	−	0.739197i
$517$	19.7242	−	13.8111i	0.867471	−	0.607410i
$518$	−1.37290	−	0.640195i	−0.0603219	−	0.0281286i
$519$	11.6912	−	16.3291i	0.513189	−	0.716767i
$520$		0			0
$521$	−6.99745	+	4.03998i	−0.306564	+	0.176995i	−0.645388	−	0.763855i	$-0.723304\pi$
$521$	−6.99745	+	4.03998i	−0.306564	+	0.176995i	0.338824	+	0.940850i	$0.389971\pi$
$522$	−1.30151	+	0.0863636i	−0.0569657	+	0.00378003i
$523$	9.26181	+	34.5655i	0.404991	+	1.51145i	0.804073	+	0.594530i	$0.202662\pi$
$523$	9.26181	+	34.5655i	0.404991	+	1.51145i	−0.399083	+	0.916915i	$0.630671\pi$
$524$	−14.0706	−	5.12130i	−0.614679	−	0.223725i
$525$		0			0
$526$	0.0728594	+	0.0611363i	0.00317682	+	0.00266567i
$527$	42.9220	−	3.75519i	1.86971	−	0.163579i
$528$	28.5120	+	5.33681i	1.24082	+	0.232255i
$529$	−5.43640	+	14.9364i	−0.236365	+	0.649408i
$530$		0			0
$531$	−2.67621	+	13.5113i	−0.116137	+	0.586342i
$532$	1.18774	−	4.43271i	0.0514951	−	0.192182i
$533$	12.1830	−	17.3991i	0.527702	−	0.753637i
$534$	−3.10330	−	2.22189i	−0.134293	−	0.0961507i
$535$		0			0
$536$	4.20543	+	0.741531i	0.181647	+	0.0320293i
$537$	−11.8482	−	0.124454i	−0.511289	−	0.00537059i
$538$	−0.413971	+	4.73172i	−0.0178476	+	0.203999i
$539$	6.03285			0.259853
$540$		0			0
$541$	−6.99126			−0.300578			−0.150289	−	0.988642i	$-0.548020\pi$
$541$	−6.99126			−0.300578			−0.150289	+	0.988642i	$0.548020\pi$
$542$	−0.132641	+	1.51610i	−0.00569743	+	0.0651220i
$543$	−14.3212	+	24.2140i	−0.614580	+	1.03912i
$544$	10.9651	+	1.93344i	0.470123	+	0.0828954i
$545$		0			0
$546$	0.372547	−	3.79829i	0.0159435	−	0.162552i
$547$	−6.72270	+	9.60101i	−0.287442	+	0.410509i	−0.936741	−	0.350024i	$-0.886174\pi$
$547$	−6.72270	+	9.60101i	−0.287442	+	0.410509i	0.649299	+	0.760533i	$0.275062\pi$
$548$	5.06022	−	18.8850i	0.216162	−	0.806727i
$549$	−33.8439	−	13.1297i	−1.44442	−	0.560360i
$550$		0			0
$551$	0.741915	−	2.03839i	0.0316066	−	0.0868385i
$552$	1.92135	−	2.24154i	0.0817781	−	0.0954061i
$553$	−1.44733	+	0.126625i	−0.0615469	+	0.00538465i
$554$	−2.51366	−	2.10921i	−0.106795	−	0.0896117i
$555$		0			0
$556$	−27.9658	−	10.1787i	−1.18601	−	0.431673i
$557$	3.09577	+	11.5536i	0.131172	+	0.489541i	0.999984	−	0.00560082i	$-0.00178281\pi$
$557$	3.09577	+	11.5536i	0.131172	+	0.489541i	−0.868812	+	0.495142i	$0.835116\pi$
$558$	2.55867	−	2.45336i	0.108317	−	0.103859i
$559$	28.1487	−	16.2516i	1.19056	−	0.687371i
$560$		0			0
$561$	18.2827	+	40.3074i	0.771897	+	1.70178i
$562$	−3.01306	−	1.40502i	−0.127098	−	0.0592670i
$563$	−6.90509	+	4.83500i	−0.291015	+	0.203771i	−0.709962	−	0.704240i	$-0.751288\pi$
$563$	−6.90509	+	4.83500i	−0.291015	+	0.203771i	0.418947	+	0.908010i	$0.362399\pi$
$564$	−5.08426	+	18.2076i	−0.214086	+	0.766677i
$565$		0			0
$566$			2.07513i			0.0872241i
$567$	25.8440	+	3.35988i	1.08535	+	0.141102i
$568$	−2.93157	+	2.93157i	−0.123006	+	0.123006i
$569$	9.07677	−	7.61631i	0.380518	−	0.319292i	−0.432388	−	0.901688i	$-0.642329\pi$
$569$	9.07677	−	7.61631i	0.380518	−	0.319292i	0.812906	+	0.582395i	$0.197884\pi$
$570$		0			0
$571$	5.84395	−	33.1427i	0.244562	−	1.38698i	−0.576946	−	0.816782i	$-0.695756\pi$
$571$	5.84395	−	33.1427i	0.244562	−	1.38698i	0.821508	−	0.570197i	$-0.193133\pi$
$572$	−17.1832	+	36.8495i	−0.718465	+	1.54075i
$573$	−12.4749	+	33.1858i	−0.521148	+	1.38636i
$574$	2.06098	−	0.363406i	0.0860235	−	0.0151683i
$575$		0			0
$576$	−19.4160	+	10.6725i	−0.809001	+	0.444685i
$577$	−28.4975	+	7.63587i	−1.18637	+	0.317886i	−0.797448	−	0.603387i	$-0.793817\pi$
$577$	−28.4975	+	7.63587i	−1.18637	+	0.317886i	−0.388917	+	0.921273i	$0.627151\pi$
$578$	1.18497	+	2.54117i	0.0492881	+	0.105699i
$579$	−5.82821	+	12.1634i	−0.242212	+	0.505495i
$580$		0			0
$581$	16.6686	−	19.8648i	0.691529	−	0.824132i
$582$	1.54248	+	1.32215i	0.0639378	+	0.0548049i
$583$	9.50816	−	4.43373i	0.393788	−	0.183626i
$584$	3.08426	−	5.34209i	0.127627	−	0.221057i
$585$		0			0
$586$	−2.71442	−	4.70152i	−0.112132	−	0.194218i
$587$	−18.6182	−	13.0366i	−0.768453	−	0.538077i	0.122338	−	0.992488i	$-0.460961\pi$
$587$	−18.6182	−	13.0366i	−0.768453	−	0.538077i	−0.890792	+	0.454412i	$0.849850\pi$
$588$	−3.66003	+	3.00618i	−0.150937	+	0.123973i
$589$	2.01626	+	5.53962i	0.0830784	+	0.228256i
$590$		0			0
$591$	−2.28049	−	8.88308i	−0.0938067	−	0.365401i
$592$	−12.4540	−	1.08958i	−0.511855	−	0.0447815i
$593$	9.57575	+	9.57575i	0.393229	+	0.393229i	0.875837	−	0.482608i	$-0.160310\pi$
$593$	9.57575	+	9.57575i	0.393229	+	0.393229i	−0.482608	+	0.875837i	$0.660310\pi$
$594$	3.25012	+	1.64214i	0.133354	+	0.0673778i
$595$		0			0
$596$	18.7319	+	22.3238i	0.767288	+	0.914419i
$597$	0.506047	−	48.1765i	0.0207111	−	1.97173i
$598$	1.16339	+	1.66149i	0.0475744	+	0.0679433i
$599$	−13.5529	+	4.93284i	−0.553755	+	0.201550i	−0.603714	−	0.797201i	$-0.706313\pi$
$599$	−13.5529	+	4.93284i	−0.553755	+	0.201550i	0.0499591	+	0.998751i	$0.484091\pi$
$600$		0			0
$601$	4.30406	+	24.4095i	0.175566	+	0.995686i	0.937488	+	0.348017i	$0.113145\pi$
$601$	4.30406	+	24.4095i	0.175566	+	0.995686i	−0.761922	+	0.647669i	$0.775744\pi$
$602$	3.09337	+	0.828865i	0.126076	+	0.0337820i
$603$	−17.9750	−	8.84619i	−0.731997	−	0.360245i
$604$	−4.07234	−	2.35117i	−0.165701	−	0.0956676i
$605$		0			0
$606$	−1.20921	+	0.827904i	−0.0491206	+	0.0336313i
$607$	2.42989	+	27.7738i	0.0986264	+	1.12730i	0.870714	+	0.491789i	$0.163657\pi$
$607$	2.42989	+	27.7738i	0.0986264	+	1.12730i	−0.772088	+	0.635516i	$0.780788\pi$
$608$	0.132774	+	1.51762i	0.00538471	+	0.0615476i
$609$	−11.1827	+	7.65641i	−0.453144	+	0.310253i
$610$		0			0
$611$	−22.6427	−	13.0728i	−0.916025	−	0.528867i
$612$	−31.1771	−	15.3435i	−1.26026	−	0.620223i
$613$	−32.4313	−	8.68995i	−1.30989	−	0.350984i	−0.464708	−	0.885464i	$-0.653841\pi$
$613$	−32.4313	−	8.68995i	−1.30989	−	0.350984i	−0.845181	+	0.534480i	$0.820507\pi$
$614$	−0.281645	−	1.59729i	−0.0113662	−	0.0644612i
$615$		0			0
$616$	−7.57828	+	2.75827i	−0.305337	+	0.111134i
$617$	−16.2918	−	23.2671i	−0.655884	−	0.936700i	0.344113	−	0.938928i	$-0.388180\pi$
$617$	−16.2918	−	23.2671i	−0.655884	−	0.936700i	−0.999998	+	0.00222854i	$0.999291\pi$
$618$	−0.0109998	+	1.04720i	−0.000442478	+	0.0421246i
$619$	16.2376	+	19.3513i	0.652646	+	0.777793i	0.986310	−	0.164899i	$-0.0527299\pi$
$619$	16.2376	+	19.3513i	0.652646	+	0.777793i	−0.333665	+	0.942692i	$0.608285\pi$
$620$		0			0
$621$	−11.5903	+	7.58292i	−0.465103	+	0.304292i
$622$	−2.93792	−	2.93792i	−0.117800	−	0.117800i
$623$	−39.5050	−	3.45624i	−1.58274	−	0.138471i
$624$	−7.83197	−	30.5075i	−0.313530	−	1.22128i
$625$		0			0
$626$	0.309884	+	0.851399i	0.0123854	+	0.0340287i
$627$	−4.67962	+	3.84364i	−0.186886	+	0.153500i
$628$	−12.6808	−	8.87918i	−0.506018	−	0.354318i
$629$	−9.53762	−	16.5196i	−0.380290	−	0.658681i
$630$		0			0
$631$	2.76033	−	4.78103i	0.109887	−	0.190330i	−0.805837	−	0.592137i	$-0.798284\pi$
$631$	2.76033	−	4.78103i	0.109887	−	0.190330i	0.915724	+	0.401807i	$0.131618\pi$
$632$	0.290777	−	0.135591i	0.0115665	−	0.00539354i
$633$	−12.3911	−	10.6211i	−0.492502	−	0.422153i
$634$	0.191734	−	0.228500i	0.00761475	−	0.00907490i
$635$		0			0
$636$	−3.55910	+	7.42780i	−0.141127	+	0.294532i
$637$	−2.76842	−	5.93690i	−0.109689	−	0.235229i
$638$	−1.82910	+	0.490105i	−0.0724146	+	0.0194034i
$639$	17.0448	−	9.36903i	0.674280	−	0.370633i
$640$		0			0
$641$	−45.0144	+	7.93726i	−1.77796	+	0.313503i	−0.963699	−	0.266991i	$-0.913971\pi$
$641$	−45.0144	+	7.93726i	−1.77796	+	0.313503i	−0.814264	+	0.580494i	$0.802859\pi$
$642$	−0.789378	+	2.09990i	−0.0311543	+	0.0828766i
$643$	−6.68798	+	14.3424i	−0.263748	+	0.565610i	−0.992929	−	0.118711i	$-0.962124\pi$
$643$	−6.68798	+	14.3424i	−0.263748	+	0.565610i	0.729181	+	0.684321i	$0.239901\pi$
$644$	2.64595	−	15.0059i	0.104265	−	0.591316i
$645$		0			0
$646$	−0.580587	+	0.487170i	−0.0228429	+	0.0191675i
$647$	−8.27160	+	8.27160i	−0.325190	+	0.325190i	−0.850754	−	0.525564i	$-0.823854\pi$
$647$	−8.27160	+	8.27160i	−0.325190	+	0.325190i	0.525564	+	0.850754i	$0.323854\pi$
$648$	−5.61674	+	1.25474i	−0.220646	+	0.0492909i
$649$			19.9961i			0.784915i
$650$		0			0
$651$	9.90572	−	35.4740i	0.388236	−	1.39033i
$652$	−23.3193	+	16.3284i	−0.913255	+	0.639468i
$653$	−44.7948	−	20.8882i	−1.75296	−	0.817417i	−0.984012	−	0.178100i	$-0.943005\pi$
$653$	−44.7948	−	20.8882i	−1.75296	−	0.817417i	−0.768944	−	0.639316i	$-0.779217\pi$
$654$	1.40002	+	3.08659i	0.0547452	+	0.120695i
$655$		0			0
$656$	14.9572	−	8.63557i	0.583982	−	0.337162i
$657$	−20.8884	+	20.0287i	−0.814933	+	0.781393i
$658$	−0.666736	−	2.48829i	−0.0259921	−	0.0970037i
$659$	25.0705	+	9.12491i	0.976607	+	0.355456i	0.780520	−	0.625130i	$-0.214954\pi$
$659$	25.0705	+	9.12491i	0.976607	+	0.355456i	0.196087	+	0.980586i	$0.437176\pi$
$660$		0			0
$661$	−33.2465	−	27.8971i	−1.29314	−	1.08507i	−0.991287	−	0.131716i	$-0.957951\pi$
$661$	−33.2465	−	27.8971i	−1.29314	−	1.08507i	−0.301851	−	0.953355i	$-0.597604\pi$
$662$	−3.08718	+	0.270093i	−0.119987	+	0.0104975i
$663$	31.2766	−	36.4886i	1.21468	−	1.41710i
$664$	−1.95858	+	5.38117i	−0.0760078	+	0.208830i
$665$		0			0
$666$	−1.46314	−	0.567620i	−0.0566954	−	0.0219948i
$667$	1.86416	−	6.95716i	0.0721808	−	0.269382i
$668$	−7.34927	+	10.4958i	−0.284352	+	0.406096i
$669$	1.75551	−	17.8983i	0.0678720	−	0.691987i
$670$		0			0
$671$	−51.8999	−	9.15135i	−2.00357	−	0.353284i
$672$	4.84523	−	8.19225i	0.186909	−	0.316023i
$673$	−0.873070	+	9.97924i	−0.0336544	+	0.384671i	0.960624	+	0.277852i	$0.0896224\pi$
$673$	−0.873070	+	9.97924i	−0.0336544	+	0.384671i	−0.994278	+	0.106820i	$0.965933\pi$
$674$	−0.555107			−0.0213819
$675$		0			0
$676$	18.4852			0.710968
$677$	−3.14213	+	35.9148i	−0.120762	+	1.38032i	0.658010	+	0.753009i	$0.271398\pi$
$677$	−3.14213	+	35.9148i	−0.120762	+	1.38032i	−0.778772	+	0.627307i	$0.784157\pi$
$678$	1.13471	+	0.0119190i	0.0435782	+	0.000457747i
$679$	20.7876	+	3.66542i	0.797756	+	0.140666i
$680$		0			0
$681$	21.2456	+	15.2113i	0.814131	+	0.582900i
$682$	2.95173	−	4.21550i	0.113027	−	0.161420i
$683$	10.9399	−	40.8281i	0.418602	−	1.56224i	−0.358908	−	0.933373i	$-0.616851\pi$
$683$	10.9399	−	40.8281i	0.418602	−	1.56224i	0.777510	−	0.628871i	$-0.216483\pi$
$684$	0.923751	−	4.66373i	0.0353205	−	0.178322i
$685$		0			0
$686$	−0.894787	+	2.45841i	−0.0341631	+	0.0938624i
$687$	1.60129	+	0.299726i	0.0610930	+	0.0114352i
$688$	26.3288	−	2.30347i	1.00378	−	0.0878191i
$689$	−8.72642	−	7.32234i	−0.332450	−	0.278959i
$690$		0			0
$691$	−5.10153	−	1.85681i	−0.194071	−	0.0706362i	0.243156	−	0.969987i	$-0.421817\pi$
$691$	−5.10153	−	1.85681i	−0.194071	−	0.0706362i	−0.437227	+	0.899351i	$0.644040\pi$
$692$	5.92425	+	22.1096i	0.225206	+	0.840481i
$693$	37.7516	−	2.50506i	1.43406	−	0.0951592i
$694$	−1.20619	+	0.696395i	−0.0457864	+	0.0264348i
$695$		0			0
$696$	1.74227	−	2.43342i	0.0660406	−	0.0922384i
$697$	23.8838	+	11.1372i	0.904663	+	0.421851i
$698$	−1.42295	+	0.996358i	−0.0538593	+	0.0377127i
$699$	−6.80690	−	6.95142i	−0.257461	−	0.262927i
$700$		0			0
$701$			8.37641i			0.316373i	0.987409	+	0.158186i	$0.0505647\pi$
$701$			8.37641i			0.316373i	−0.987409	+	0.158186i	$0.949435\pi$
$702$	0.124572	−	3.95199i	0.00470167	−	0.149158i
$703$	1.84550	−	1.84550i	0.0696043	−	0.0696043i
$704$	−24.6396	+	20.6751i	−0.928639	+	0.779221i
$705$		0			0
$706$	0.747459	−	4.23905i	0.0281310	−	0.159539i
$707$	−6.43494	+	13.7998i	−0.242011	+	0.518994i
$708$	−9.96409	−	12.1313i	−0.374474	−	0.455921i
$709$	−27.2222	+	4.80001i	−1.02235	+	0.180268i	−0.659599	−	0.751617i	$-0.729274\pi$
$709$	−27.2222	+	4.80001i	−1.02235	+	0.180268i	−0.362752	+	0.931886i	$0.618163\pi$
$710$		0			0
$711$	−1.48748	+	0.230177i	−0.0557848	+	0.00863232i
$712$	8.45886	−	2.26655i	0.317009	−	0.0849424i
$713$	8.27234	+	17.7401i	0.309802	+	0.664372i
$714$	4.72120	−	0.363126i	0.176686	−	0.0135896i
$715$		0			0
$716$	8.68071	−	10.3453i	0.324413	−	0.386621i
$717$	−25.3290	+	8.91885i	−0.945929	+	0.333080i
$718$	1.99086	−	0.928354i	0.0742983	−	0.0346459i
$719$	−13.4438	+	23.2854i	−0.501371	+	0.868400i	0.498628	+	0.866816i	$0.333837\pi$
$719$	−13.4438	+	23.2854i	−0.501371	+	0.868400i	−0.999999	+	0.00158362i	$0.999496\pi$
$720$		0			0
$721$	5.44055	+	9.42331i	0.202617	+	0.350942i
$722$	2.41940	+	1.69408i	0.0900409	+	0.0630473i
$723$	−30.9639	−	11.6397i	−1.15156	−	0.432884i
$724$	−10.9664	−	30.1299i	−0.407563	−	1.11977i
$725$		0			0
$726$	2.13888	+	0.597258i	0.0793812	+	0.0221663i
$727$	19.0908	+	1.67023i	0.708040	+	0.0619455i	0.435487	−	0.900195i	$-0.356576\pi$
$727$	19.0908	+	1.67023i	0.708040	+	0.0619455i	0.272553	+	0.962141i	$0.412132\pi$
$728$	6.19200	+	6.19200i	0.229491	+	0.229491i
$729$	26.9464	+	1.70047i	0.998015	+	0.0629802i
$730$		0			0
$731$	25.9216	+	30.8921i	0.958743	+	1.14259i
$732$	36.0469	−	20.3099i	1.33233	−	0.750674i
$733$	−20.2855	−	28.9707i	−0.749261	−	1.07006i	−0.994917	−	0.100699i	$-0.967892\pi$
$733$	−20.2855	−	28.9707i	−0.749261	−	1.07006i	0.245656	−	0.969357i	$-0.420997\pi$
$734$	−1.97069	+	0.717274i	−0.0727397	+	0.0264751i
$735$		0			0
$736$	0.878364	+	4.98145i	0.0323769	+	0.183619i
$737$	−28.0930	−	7.52749i	−1.03482	−	0.277279i
$738$	2.10558	−	0.517039i	0.0775076	−	0.0190325i
$739$	−16.8271	−	9.71511i	−0.618993	−	0.357376i	0.157484	−	0.987522i	$-0.449662\pi$
$739$	−16.8271	−	9.71511i	−0.618993	−	0.357376i	−0.776477	+	0.630146i	$0.782995\pi$
$740$		0			0
$741$	5.92994	+	2.84138i	0.217842	+	0.104381i
$742$	−0.0978225	−	1.11812i	−0.00359118	−	0.0410473i
$743$	2.72437	+	31.1397i	0.0999474	+	1.14240i	0.866143	+	0.499796i	$0.166592\pi$
$743$	2.72437	+	31.1397i	0.0999474	+	1.14240i	−0.766195	+	0.642608i	$0.777853\pi$
$744$	0.623732	+	8.10948i	0.0228671	+	0.297308i
$745$		0			0
$746$	−0.263770	−	0.152288i	−0.00965730	−	0.00557564i
$747$	15.8683	−	21.6784i	0.580591	−	0.793171i
$748$	−48.7265	−	13.0562i	−1.78162	−	0.477383i
$749$	4.04754	+	22.9547i	0.147894	+	0.838747i
$750$		0			0
$751$	21.6560	−	7.88215i	0.790240	−	0.287624i	0.0848041	−	0.996398i	$-0.472974\pi$
$751$	21.6560	−	7.88215i	0.790240	−	0.287624i	0.705436	+	0.708774i	$0.250751\pi$
$752$	−12.1941	−	17.4149i	−0.444672	−	0.635057i
$753$	18.7625	+	11.0969i	0.683743	+	0.404394i
$754$	1.32167	+	1.57510i	0.0481322	+	0.0573618i
$755$		0			0
$756$	−21.6549	+	20.3315i	−0.787583	+	0.739449i
$757$	−10.7861	−	10.7861i	−0.392029	−	0.392029i	0.483381	−	0.875410i	$-0.339408\pi$
$757$	−10.7861	−	10.7861i	−0.392029	−	0.392029i	−0.875410	+	0.483381i	$0.839408\pi$
$758$	1.38640	+	0.121294i	0.0503561	+	0.00440559i
$759$	−14.3666	+	14.0679i	−0.521475	+	0.510634i
$760$		0			0
$761$	3.19211	+	8.77024i	0.115714	+	0.317921i	0.984007	−	0.178131i	$-0.0570049\pi$
$761$	3.19211	+	8.77024i	0.115714	+	0.317921i	−0.868293	+	0.496051i	$0.834783\pi$
$762$	0.0352829	+	0.213168i	0.00127816	+	0.00772228i
$763$	28.8462	+	20.1984i	1.04430	+	0.731229i
$764$	−20.2039	−	34.9942i	−0.730951	−	1.26604i
$765$		0			0
$766$	1.37405	−	2.37992i	0.0496463	−	0.0859899i
$767$	19.6781	−	9.17603i	0.710533	−	0.331327i
$768$	4.45136	−	23.7814i	0.160624	−	0.858139i
$769$	7.77292	−	9.26340i	0.280299	−	0.334047i	−0.607465	−	0.794346i	$-0.707814\pi$
$769$	7.77292	−	9.26340i	0.280299	−	0.334047i	0.887764	+	0.460300i	$0.152258\pi$
$770$		0			0
$771$	−28.9875	−	42.3380i	−1.04396	−	1.52477i
$772$	−6.49674	−	13.9323i	−0.233823	−	0.501435i
$773$	1.78767	−	0.479004i	0.0642980	−	0.0172286i	−0.226527	−	0.974005i	$-0.572737\pi$
$773$	1.78767	−	0.479004i	0.0642980	−	0.0172286i	0.290825	+	0.956776i	$0.406070\pi$
$774$	3.25459	+	0.644640i	0.116984	+	0.0231711i
$775$		0			0
$776$	−4.59055	+	0.809438i	−0.164791	+	0.0290571i
$777$	−16.0872	+	2.66269i	−0.577124	+	0.0955234i
$778$	0.0596173	−	0.127850i	0.00213738	−	0.00458363i
$779$	−0.626118	+	3.55089i	−0.0224330	+	0.127224i
$780$		0			0
$781$	21.6304	−	18.1500i	0.773996	−	0.649459i
$782$	−1.77944	+	1.77944i	−0.0636327	+	0.0636327i
$783$	−11.0348	+	8.68180i	−0.394350	+	0.310262i
$784$		−	5.32653i		−	0.190233i
$785$		0			0
$786$	2.04755	−	0.525653i	0.0730338	−	0.0187494i
$787$	13.9857	−	9.79291i	0.498537	−	0.349080i	−0.297106	−	0.954844i	$-0.596022\pi$
$787$	13.9857	−	9.79291i	0.498537	−	0.349080i	0.795644	+	0.605765i	$0.207133\pi$
$788$	9.47347	+	4.41755i	0.337479	+	0.157369i
$789$	1.01891	+	0.0999377i	0.0362742	+	0.00355788i
$790$		0			0
$791$	10.2108	−	5.89518i	0.363053	−	0.209609i
$792$	−7.64475	+	3.37116i	−0.271644	+	0.119789i
$793$	14.8106	+	55.2739i	0.525940	+	1.96283i
$794$	−0.349811	−	0.127321i	−0.0124143	−	0.00451844i
$795$		0			0
$796$	42.0652	+	35.2969i	1.49096	+	1.25107i
$797$	−16.8357	+	1.47293i	−0.596350	+	0.0521739i	−0.381335	−	0.924437i	$-0.624536\pi$
$797$	−16.8357	+	1.47293i	−0.596350	+	0.0521739i	−0.215015	+	0.976611i	$0.568980\pi$
$798$	0.215180	+	0.611097i	0.00761728	+	0.0216326i
$799$	11.0947	−	30.4824i	0.392502	−	1.07839i
$800$		0			0
$801$	−41.0750	−	0.863001i	−1.45131	−	0.0304926i
$802$	0.268215	−	1.00099i	0.00947098	−	0.0353462i
$803$	−24.0972	+	34.4144i	−0.850372	+	1.21446i
$804$	20.7945	−	9.43200i	0.733365	−	0.332641i
$805$		0			0
$806$	−5.50298	−	0.970323i	−0.193834	−	0.0341782i
$807$	25.0975	+	44.5442i	0.883473	+	1.56803i
$808$	0.293057	−	3.34966i	0.0103097	−	0.117841i
$809$	47.0271			1.65338			0.826692	−	0.562654i	$-0.190220\pi$
$809$	47.0271			1.65338			0.826692	+	0.562654i	$0.190220\pi$
$810$		0			0
$811$	−46.5510			−1.63463			−0.817314	−	0.576192i	$-0.804538\pi$
$811$	−46.5510			−1.63463			−0.817314	+	0.576192i	$0.804538\pi$
$812$	1.34626	−	15.3878i	0.0472444	−	0.540006i
$813$	8.04153	+	14.2725i	0.282029	+	0.500558i
$814$	−2.24373	−	0.395630i	−0.0786427	−	0.0138668i
$815$		0			0
$816$	35.5882	−	16.1422i	1.24584	−	0.565089i
$817$	−3.16478	+	4.51977i	−0.110722	+	0.158127i
$818$	−1.17199	+	4.37392i	−0.0409776	+	0.152931i
$819$	−19.7891	−	36.0016i	−0.691487	−	1.25800i
$820$		0			0
$821$	−11.2400	+	30.8817i	−0.392280	+	1.07778i	0.573678	+	0.819081i	$0.305516\pi$
$821$	−11.2400	+	30.8817i	−0.392280	+	1.07778i	−0.965958	+	0.258699i	$0.916706\pi$
$822$	0.916746	+	2.60350i	0.0319752	+	0.0908076i
$823$	−8.92506	+	0.780841i	−0.311108	+	0.0272184i	−0.241641	−	0.970366i	$-0.577686\pi$
$823$	−8.92506	+	0.780841i	−0.311108	+	0.0272184i	−0.0694673	+	0.997584i	$0.522130\pi$
$824$	−1.84072	−	1.54454i	−0.0641244	−	0.0538067i
$825$		0			0
$826$	2.01026	+	0.731675i	0.0699460	+	0.0254582i
$827$	−13.3446	−	49.8029i	−0.464039	−	1.73182i	−0.660057	−	0.751216i	$-0.729468\pi$
$827$	−13.3446	−	49.8029i	−0.464039	−	1.73182i	0.196018	−	0.980600i	$-0.437199\pi$
$828$	1.70589	−	15.6937i	0.0592836	−	0.545393i
$829$	−6.07560	+	3.50775i	−0.211014	+	0.121829i	−0.601783	−	0.798660i	$-0.705543\pi$
$829$	−6.07560	+	3.50775i	−0.211014	+	0.121829i	0.390768	+	0.920489i	$0.372209\pi$
$830$		0			0
$831$	−35.1526	−	3.44786i	−1.21943	−	0.119605i
$832$	31.6531	+	14.7601i	1.09737	+	0.511714i
$833$	6.65756	−	4.66167i	0.230671	−	0.161517i
$834$	4.06956	−	1.04475i	0.140917	−	0.0361767i
$835$		0			0
$836$		−	6.90208i		−	0.238713i
$837$	7.80658	−	37.3503i	0.269835	−	1.29101i
$838$	4.23684	−	4.23684i	0.146359	−	0.146359i
$839$	2.86722	−	2.40588i	0.0989873	−	0.0830602i	−0.591951	−	0.805974i	$-0.701642\pi$
$839$	2.86722	−	2.40588i	0.0989873	−	0.0830602i	0.690938	+	0.722914i	$0.257198\pi$
$840$		0			0
$841$	−3.76791	+	21.3689i	−0.129928	+	0.736858i
$842$	1.99563	−	4.27965i	0.0687741	−	0.147487i
$843$	−35.3059	+	5.84371i	−1.21600	+	0.201268i
$844$	18.3184	−	3.23002i	0.630544	−	0.111182i
$845$		0			0
$846$	−0.859915	−	2.52651i	−0.0295645	−	0.0868631i
$847$	22.2871	−	5.97181i	0.765793	−	0.205194i
$848$	−3.91463	−	8.39495i	−0.134429	−	0.288284i
$849$	12.6192	+	18.4311i	0.433089	+	0.632554i
$850$		0			0
$851$	5.57034	−	6.63847i	0.190949	−	0.227564i
$852$	−4.07856	+	21.7898i	−0.139729	+	0.746505i
$853$	39.4684	−	18.4044i	1.35137	−	0.630155i	0.394025	−	0.919100i	$-0.371082\pi$
$853$	39.4684	−	18.4044i	1.35137	−	0.630155i	0.957346	+	0.288945i	$0.0933044\pi$
$854$	−2.81908	+	4.88278i	−0.0964668	+	0.167085i
$855$		0			0
$856$	−2.57365	−	4.45770i	−0.0879657	−	0.152361i
$857$	39.0125	+	27.3168i	1.33264	+	0.933125i	0.999951	−	0.00991152i	$-0.00315499\pi$
$857$	39.0125	+	27.3168i	1.33264	+	0.933125i	0.332690	+	0.943036i	$0.392044\pi$
$858$	−0.937333	−	5.66308i	−0.0320000	−	0.193334i
$859$	14.5712	+	40.0340i	0.497162	+	1.36594i	0.894006	+	0.448055i	$0.147883\pi$
$859$	14.5712	+	40.0340i	0.497162	+	1.36594i	−0.396844	+	0.917886i	$0.629895\pi$
$860$		0			0
$861$	16.0955	−	15.7609i	0.548533	−	0.537130i
$862$	0.0770518	+	0.00674116i	0.00262439	+	0.000229605i
$863$	11.3790	+	11.3790i	0.387346	+	0.387346i	0.873740	−	0.486393i	$-0.161688\pi$
$863$	11.3790	+	11.3790i	0.387346	+	0.387346i	−0.486393	+	0.873740i	$0.661688\pi$
$864$	4.44675	−	8.80100i	0.151282	−	0.299416i
$865$		0			0
$866$	−0.812682	−	0.968517i	−0.0276161	−	0.0329115i
$867$	25.9780	+	15.3645i	0.882260	+	0.521805i
$868$	24.0777	+	34.3866i	0.817252	+	1.16716i
$869$	−2.05336	+	0.747362i	−0.0696554	+	0.0253525i
$870$		0			0
$871$	5.48385	+	31.1005i	0.185813	+	1.05380i
$872$	−7.51153	−	2.01271i	−0.254372	−	0.0681589i
$873$	21.7404	+	2.36316i	0.735801	+	0.0799807i
$874$	−0.298187	−	0.172158i	−0.0100863	−	0.00582334i
$875$		0			0
$876$	−2.52941	−	32.8863i	−0.0854610	−	1.11112i
$877$	−2.17490	−	24.8592i	−0.0734411	−	0.839435i	−0.940181	−	0.340675i	$-0.889344\pi$
$877$	−2.17490	−	24.8592i	−0.0734411	−	0.839435i	0.866740	−	0.498760i	$-0.166211\pi$
$878$	−0.174114	−	1.99013i	−0.00587605	−	0.0671635i
$879$	−52.7000	−	25.2517i	−1.77753	−	0.851717i
$880$		0			0
$881$	19.2496	+	11.1138i	0.648536	+	0.374432i	0.787895	−	0.615810i	$-0.211171\pi$
$881$	19.2496	+	11.1138i	0.648536	+	0.374432i	−0.139359	+	0.990242i	$0.544504\pi$
$882$	0.186593	−	0.642104i	0.00628290	−	0.0216208i
$883$	51.9401	+	13.9173i	1.74792	+	0.468355i	0.984181	−	0.177166i	$-0.0566930\pi$
$883$	51.9401	+	13.9173i	1.74792	+	0.468355i	0.763743	+	0.645521i	$0.223360\pi$
$884$	9.51159	+	53.9429i	0.319909	+	1.81430i
$885$		0			0
$886$	−2.68990	+	0.979043i	−0.0903689	+	0.0328916i
$887$	−27.3502	−	39.0601i	−0.918330	−	1.31151i	−0.950077	−	0.312015i	$-0.898996\pi$
$887$	−27.3502	−	39.0601i	−0.918330	−	1.31151i	0.0317472	−	0.999496i	$-0.489893\pi$
$888$	3.13719	−	1.76758i	0.105277	−	0.0593162i
$889$	1.44304	+	1.71975i	0.0483980	+	0.0576785i
$890$		0			0
$891$	38.8534	−	5.17915i	1.30164	−	0.173508i
$892$	14.4939	+	14.4939i	0.485292	+	0.485292i
$893$	4.42146	+	0.386828i	0.147959	+	0.0129447i
$894$	−3.96256	−	1.10650i	−0.132528	−	0.0370070i
$895$		0			0
$896$	4.93582	+	13.5611i	0.164894	+	0.453043i
$897$	20.4369	+	7.68247i	0.682368	+	0.256510i
$898$	0.503608	+	0.352630i	0.0168056	+	0.0117674i
$899$	9.92137	+	17.1843i	0.330896	+	0.573129i
$900$		0			0
$901$	7.06673	−	12.2399i	0.235427	−	0.407771i
$902$	2.85267	−	1.33022i	0.0949837	−	0.0442916i
$903$	32.5155	−	11.4494i	1.08205	−	0.381011i
$904$	−1.67361	+	1.99453i	−0.0556635	+	0.0663371i
$905$		0			0
$906$	0.661909	−	0.0509101i	0.0219905	−	0.00169137i
$907$	15.2342	+	32.6698i	0.505842	+	1.08478i	0.979010	+	0.203810i	$0.0653325\pi$
$907$	15.2342	+	32.6698i	0.505842	+	1.08478i	−0.473168	+	0.880972i	$0.656890\pi$
$908$	−28.7666	+	7.70797i	−0.954652	+	0.255798i
$909$	−5.70545	+	14.7068i	−0.189238	+	0.487792i
$910$		0			0
$911$	35.2604	−	6.21737i	1.16823	−	0.205991i	0.444310	−	0.895873i	$-0.353449\pi$
$911$	35.2604	−	6.21737i	1.16823	−	0.205991i	0.723921	+	0.689883i	$0.242338\pi$
$912$	3.39362	+	4.13173i	0.112374	+	0.136815i
$913$	16.4829	−	35.3477i	0.545505	−	1.16984i
$914$	0.617189	−	3.50025i	0.0204148	−	0.115778i
$915$		0			0
$916$	−1.42237	+	1.19351i	−0.0469964	+	0.0394346i
$917$	15.5310	−	15.5310i	0.512878	−	0.512878i
$918$	4.85557	−	0.699228i	0.160258	−	0.0230780i
$919$		−	10.8922i		−	0.359301i	−0.983730	−	0.179651i	$-0.942503\pi$
$919$		−	10.8922i		−	0.359301i	0.983730	−	0.179651i	$-0.0574967\pi$
$920$		0			0
$921$	−12.2149	−	12.4742i	−0.402495	−	0.411040i
$922$	0.852235	−	0.596741i	0.0280669	−	0.0196526i
$923$	−27.7873	−	12.9575i	−0.914632	−	0.426500i
$924$	−25.1035	+	35.0618i	−0.825844	+	1.15345i
$925$		0			0
$926$	0.0427714	−	0.0246941i	0.00140556	−	0.000811498i
$927$	6.27050	+	9.36804i	0.205950	+	0.307687i
$928$	1.32716	+	4.95301i	0.0435660	+	0.162591i
$929$	−0.624723	−	0.227381i	−0.0204965	−	0.00746012i	0.331752	−	0.943367i	$-0.392360\pi$
$929$	−0.624723	−	0.227381i	−0.0204965	−	0.00746012i	−0.352248	+	0.935907i	$0.614583\pi$
$930$		0			0
$931$	0.851849	+	0.714786i	0.0279182	+	0.0234262i
$932$	11.0466	−	0.966453i	0.361844	−	0.0316572i
$933$	−43.9604	−	8.22841i	−1.43920	−	0.269386i
$934$	2.35563	−	6.47205i	0.0770787	−	0.211772i
$935$		0			0
$936$	6.82565	+	5.97617i	0.223103	+	0.195337i
$937$	−8.19227	+	30.5740i	−0.267630	+	0.998808i	0.692991	+	0.720946i	$0.256292\pi$
$937$	−8.19227	+	30.5740i	−0.267630	+	0.998808i	−0.960621	+	0.277862i	$0.910374\pi$
$938$	−1.78471	+	2.54883i	−0.0582728	+	0.0832222i
$939$	7.92986	+	5.67760i	0.258781	+	0.185282i
$940$		0			0
$941$	15.3045	+	2.69859i	0.498911	+	0.0879715i	0.417441	−	0.908704i	$-0.362927\pi$
$941$	15.3045	+	2.69859i	0.498911	+	0.0879715i	0.0814707	+	0.996676i	$0.474038\pi$
$942$	2.18536	+	0.0229551i	0.0712030	+	0.000747919i
$943$	−1.04344	+	11.9266i	−0.0339791	+	0.388383i
$944$	17.6549			0.574619
$945$		0			0
$946$	4.81662			0.156602
$947$	2.28059	−	26.0673i	0.0741093	−	0.847074i	−0.864622	−	0.502423i	$-0.832442\pi$
$947$	2.28059	−	26.0673i	0.0741093	−	0.847074i	0.938731	−	0.344650i	$-0.112003\pi$
$948$	0.873325	−	1.47660i	0.0283643	−	0.0479579i
$949$	44.9250	+	7.92149i	1.45833	+	0.257143i
$950$		0			0
$951$	0.313423	−	3.19549i	0.0101634	−	0.103621i
$952$	−6.23165	+	8.89972i	−0.201969	+	0.288442i
$953$	10.0312	−	37.4368i	0.324942	−	1.21270i	−0.589429	−	0.807820i	$-0.700647\pi$
$953$	10.0312	−	37.4368i	0.324942	−	1.21270i	0.914371	−	0.404878i	$-0.132686\pi$
$954$	−0.177820	−	1.14913i	−0.00575714	−	0.0372044i
$955$		0			0
$956$	10.4679	−	28.7604i	0.338557	−	0.930178i
$957$	−13.2655	+	15.4761i	−0.428812	+	0.500272i
$958$	−6.67210	+	0.583733i	−0.215566	+	0.0188596i
$959$	21.9691	+	18.4343i	0.709420	+	0.595274i
$960$		0			0
$961$	−21.5428	−	7.84095i	−0.694930	−	0.252934i
$962$	0.640290	+	2.38959i	0.0206438	+	0.0770436i
$963$	5.75867	+	23.4515i	0.185571	+	0.755715i
$964$	32.6511	−	18.8511i	1.05162	−	0.607154i
$965$		0			0
$966$	0.888601	+	1.95908i	0.0285903	+	0.0630322i
$967$	−30.4117	−	14.1812i	−0.977973	−	0.456036i	−0.133158	−	0.991095i	$-0.542512\pi$
$967$	−30.4117	−	14.1812i	−0.977973	−	0.456036i	−0.844815	+	0.535058i	$0.820290\pi$
$968$	−4.17382	+	2.92254i	−0.134152	+	0.0939340i
$969$	−2.19416	+	7.85765i	−0.0704867	+	0.252424i
$970$		0			0
$971$		−	3.53962i		−	0.113592i	−0.998386	−	0.0567959i	$-0.981912\pi$
$971$		−	3.53962i		−	0.113592i	0.998386	−	0.0567959i	$-0.0180884\pi$
$972$	−20.9909	+	22.5028i	−0.673284	+	0.721779i
$973$	30.8682	−	30.8682i	0.989589	−	0.989589i
$974$	−2.93893	+	2.46605i	−0.0941694	+	0.0790175i
$975$		0			0
$976$	−8.07991	+	45.8234i	−0.258632	+	1.46677i
$977$	−19.3025	+	41.3945i	−0.617543	+	1.32433i	0.310045	+	0.950722i	$0.399656\pi$
$977$	−19.3025	+	41.3945i	−0.617543	+	1.32433i	−0.927588	+	0.373604i	$0.878122\pi$
$978$	1.41417	−	3.76197i	0.0452201	−	0.120295i
$979$	−58.7374	+	10.3570i	−1.87726	+	0.331011i
$980$		0			0
$981$	31.2050	+	18.9011i	0.996298	+	0.603466i
$982$	−2.46224	+	0.659756i	−0.0785733	+	0.0210536i
$983$	13.7607	+	29.5099i	0.438898	+	0.941220i	0.993994	+	0.109434i	$0.0349038\pi$
$983$	13.7607	+	29.5099i	0.438898	+	0.941220i	−0.555096	+	0.831786i	$0.687318\pi$
$984$	−2.14963	+	4.48626i	−0.0685278	+	0.143017i
$985$		0			0
$986$	−1.63979	+	1.95422i	−0.0522215	+	0.0622352i
$987$	−21.0536	−	18.0463i	−0.670144	−	0.574420i
$988$	−6.79230	+	3.16730i	−0.216092	+	0.100765i
$989$	−9.16026	+	15.8660i	−0.291279	+	0.504511i
$990$		0			0
$991$	22.7542	+	39.4115i	0.722812	+	1.25195i	0.959868	+	0.280451i	$0.0904839\pi$
$991$	22.7542	+	39.4115i	0.722812	+	1.25195i	−0.237057	+	0.971496i	$0.576183\pi$
$992$	−11.4152	−	7.99298i	−0.362432	−	0.253777i
$993$	−25.7776	+	21.1726i	−0.818028	+	0.671892i
$994$	−1.03320	−	2.83869i	−0.0327710	−	0.0900377i
$995$		0			0
$996$	7.61395	+	29.6583i	0.241257	+	0.939759i
$997$	−8.98411	−	0.786008i	−0.284530	−	0.0248931i	−0.0560024	−	0.998431i	$-0.517835\pi$
$997$	−8.98411	−	0.786008i	−0.284530	−	0.0248931i	−0.228527	+	0.973538i	$0.573391\pi$
$998$	−0.0619968	−	0.0619968i	−0.00196248	−	0.00196248i
$999$	−16.4473	+	3.85602i	−0.520368	+	0.121999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.32.10		192
5.2	odd	4		135.2.q.a.113.10	yes	192
5.3	odd	4	inner	675.2.ba.b.518.7		192
5.4	even	2		135.2.q.a.32.7	✓	192
15.2	even	4		405.2.r.a.368.7		192
15.14	odd	2		405.2.r.a.287.10		192
27.11	odd	18	inner	675.2.ba.b.632.7		192
135.38	even	36	inner	675.2.ba.b.443.10		192
135.92	even	36		135.2.q.a.38.7	yes	192
135.97	odd	36		405.2.r.a.278.10		192
135.119	odd	18		135.2.q.a.92.10	yes	192
135.124	even	18		405.2.r.a.197.7		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.7	✓	192	5.4	even	2
135.2.q.a.38.7	yes	192	135.92	even	36
135.2.q.a.92.10	yes	192	135.119	odd	18
135.2.q.a.113.10	yes	192	5.2	odd	4
405.2.r.a.197.7		192	135.124	even	18
405.2.r.a.278.10		192	135.97	odd	36
405.2.r.a.287.10		192	15.14	odd	2
405.2.r.a.368.7		192	15.2	even	4
675.2.ba.b.32.10		192	1.1	even	1	trivial
675.2.ba.b.443.10		192	135.38	even	36	inner
675.2.ba.b.518.7		192	5.3	odd	4	inner
675.2.ba.b.632.7		192	27.11	odd	18	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0140240 - 0.160295i) q^{2} +(-0.850222 - 1.50901i) q^{3} +(1.94412 + 0.342800i) q^{4} +(-0.253811 + 0.115124i) q^{6} +(-1.66092 + 2.37204i) q^{7} +(0.165506 - 0.617675i) q^{8} +(-1.55424 + 2.56599i) q^{9} +(-1.48958 + 4.09258i) q^{11} +(-1.13564 - 3.22516i) q^{12} +(4.71104 - 0.412163i) q^{13} +(0.356933 + 0.299503i) q^{14} +(3.61342 + 1.31518i) q^{16} +(1.51857 + 5.66739i) q^{17} +(0.389520 + 0.285124i) q^{18} +(-0.695229 + 0.401391i) q^{19} +(4.99158 + 0.489589i) q^{21} +(0.635132 + 0.296167i) q^{22} +(-2.18347 + 1.52888i) q^{23} +(-1.07280 + 0.275411i) q^{24} -0.760939i q^{26} +(5.19357 + 0.163709i) q^{27} +(-4.04215 + 4.04215i) q^{28} +(-2.06994 + 1.73689i) q^{29} +(1.27517 - 7.23183i) q^{31} +(0.801990 - 1.71987i) q^{32} +(7.44223 - 1.23181i) q^{33} +(0.929752 - 0.163940i) q^{34} +(-3.90126 + 4.45580i) q^{36} +(-3.14033 + 0.841448i) q^{37} +(0.0545912 + 0.117071i) q^{38} +(-4.62739 - 6.75860i) q^{39} +(2.88706 - 3.44066i) q^{41} +(0.148481 - 0.793261i) q^{42} +(6.22917 - 2.90471i) q^{43} +(-4.29885 + 7.44583i) q^{44} +(0.214452 + 0.371442i) q^{46} +(-4.52886 - 3.17114i) q^{47} +(-1.08759 - 6.57090i) q^{48} +(-0.473765 - 1.30166i) q^{49} +(7.26104 - 7.11008i) q^{51} +(9.30011 + 0.813654i) q^{52} +(-1.70331 - 1.70331i) q^{53} +(0.0990765 - 0.830210i) q^{54} +(1.19026 + 1.41849i) q^{56} +(1.19680 + 0.707839i) q^{57} +(0.249386 + 0.356161i) q^{58} +(4.31439 - 1.57031i) q^{59} +(2.10123 + 11.9167i) q^{61} +(-1.14135 - 0.305823i) q^{62} +(-3.50516 - 7.94862i) q^{63} +(6.39585 + 3.69265i) q^{64} +(-0.0930836 - 1.21023i) q^{66} +(0.582021 + 6.65253i) q^{67} +(1.00950 + 11.5386i) q^{68} +(4.16355 + 1.99500i) q^{69} +(-5.61473 - 3.24167i) q^{71} +(1.32772 + 1.38470i) q^{72} +(9.31768 + 2.49666i) q^{73} +(0.0908402 + 0.515180i) q^{74} +(-1.48920 + 0.542026i) q^{76} +(-7.23368 - 10.3308i) q^{77} +(-1.14827 + 0.646967i) q^{78} +(0.322504 + 0.384345i) q^{79} +(-4.16865 - 7.97636i) q^{81} +(-0.511034 - 0.511034i) q^{82} +(-8.92110 - 0.780495i) q^{83} +(9.53639 + 2.66293i) q^{84} +(-0.378253 - 1.03924i) q^{86} +(4.38090 + 1.64683i) q^{87} +(2.28135 + 1.59742i) q^{88} +(6.84734 + 11.8599i) q^{89} +(-6.84699 + 11.8593i) q^{91} +(-4.76903 + 2.22384i) q^{92} +(-11.9971 + 4.22442i) q^{93} +(-0.571832 + 0.681483i) q^{94} +(-3.27718 + 0.252061i) q^{96} +(-3.08067 - 6.60652i) q^{97} +(-0.215294 + 0.0576878i) q^{98} +(-8.18637 - 10.1831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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