LMFDB - Embedded newform 361.2.e.f.99.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(28,361)] 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("361.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,3,-3,-9,3,3,0,6,-15,0,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			99.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	361.99
Dual form			361.2.e.f.62.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26604 + 0.460802i) q^{2} +(-0.500000 - 2.83564i) q^{3} +(-0.141559 - 0.118782i) q^{4} +(0.673648 - 0.565258i) q^{5} +(0.673648 - 3.82045i) q^{6} +(-0.173648 + 0.300767i) q^{7} +(-1.47178 - 2.54920i) q^{8} +(-4.97178 + 1.80958i) q^{9} +(1.11334 - 0.405223i) q^{10} +(1.11334 + 1.92836i) q^{11} +(-0.266044 + 0.460802i) q^{12} +(0.446967 - 2.53487i) q^{13} +(-0.358441 + 0.300767i) q^{14} +(-1.93969 - 1.62760i) q^{15} +(-0.624485 - 3.54163i) q^{16} +(-0.439693 - 0.160035i) q^{17} -7.12836 q^{18} -0.162504 q^{20} +(0.939693 + 0.342020i) q^{21} +(0.520945 + 2.95442i) q^{22} +(-2.06418 - 1.73205i) q^{23} +(-6.49273 + 5.44804i) q^{24} +(-0.733956 + 4.16247i) q^{25} +(1.73396 - 3.00330i) q^{26} +(3.29813 + 5.71253i) q^{27} +(0.0603074 - 0.0219501i) q^{28} +(6.46451 - 2.35289i) q^{29} +(-1.70574 - 2.95442i) q^{30} +(3.55303 - 6.15403i) q^{31} +(-0.180922 + 1.02606i) q^{32} +(4.91147 - 4.12122i) q^{33} +(-0.482926 - 0.405223i) q^{34} +(0.0530334 + 0.300767i) q^{35} +(0.918748 + 0.334397i) q^{36} +4.94356 q^{37} -7.41147 q^{39} +(-2.43242 - 0.885328i) q^{40} +(0.429892 + 2.43804i) q^{41} +(1.03209 + 0.866025i) q^{42} +(2.98886 - 2.50795i) q^{43} +(0.0714517 - 0.405223i) q^{44} +(-2.32635 + 4.02936i) q^{45} +(-1.81521 - 3.14403i) q^{46} +(6.85117 - 2.49362i) q^{47} +(-9.73055 + 3.54163i) q^{48} +(3.43969 + 5.95772i) q^{49} +(-2.84730 + 4.93166i) q^{50} +(-0.233956 + 1.32683i) q^{51} +(-0.364370 + 0.305743i) q^{52} +(-2.17365 - 1.82391i) q^{53} +(1.54323 + 8.75211i) q^{54} +(1.84002 + 0.669713i) q^{55} +1.02229 q^{56} +9.26857 q^{58} +(5.92514 + 2.15658i) q^{59} +(0.0812519 + 0.460802i) q^{60} +(6.99273 + 5.86759i) q^{61} +(7.33409 - 6.15403i) q^{62} +(0.319078 - 1.80958i) q^{63} +(-4.29813 + 7.44459i) q^{64} +(-1.13176 - 1.96026i) q^{65} +(8.11721 - 2.95442i) q^{66} +(-7.21213 + 2.62500i) q^{67} +(0.0432332 + 0.0748822i) q^{68} +(-3.87939 + 6.71929i) q^{69} +(-0.0714517 + 0.405223i) q^{70} +(-7.12836 + 5.98140i) q^{71} +(11.9304 + 10.0108i) q^{72} +(0.241230 + 1.36808i) q^{73} +(6.25877 + 2.27801i) q^{74} +12.1702 q^{75} -0.773318 q^{77} +(-9.38326 - 3.41523i) q^{78} +(-2.05690 - 11.6653i) q^{79} +(-2.42262 - 2.03282i) q^{80} +(2.39053 - 2.00589i) q^{81} +(-0.579193 + 3.28476i) q^{82} +(7.41534 - 12.8438i) q^{83} +(-0.0923963 - 0.160035i) q^{84} +(-0.386659 + 0.140732i) q^{85} +(4.93969 - 1.79790i) q^{86} +(-9.90420 - 17.1546i) q^{87} +(3.27719 - 5.67626i) q^{88} +(-1.78699 + 10.1345i) q^{89} +(-4.80200 + 4.02936i) q^{90} +(0.684793 + 0.574609i) q^{91} +(0.0864665 + 0.490376i) q^{92} +(-19.2271 - 6.99811i) q^{93} +9.82295 q^{94} +3.00000 q^{96} +(-8.88326 - 3.23324i) q^{97} +(1.60947 + 9.12776i) q^{98} +(-9.02481 - 7.57272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9} + 3 q^{12} + 15 q^{13} + 6 q^{14} - 6 q^{15} + 9 q^{16} + 3 q^{17} - 6 q^{18} - 6 q^{20} + 6 q^{23} - 21 q^{24} - 9 q^{25} + 15 q^{26}+ \cdots - 27 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^3 - 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9 + 3 * q^12 + 15 * q^13 + 6 * q^14 - 6 * q^15 + 9 * q^16 + 3 * q^17 - 6 * q^18 - 6 * q^20 + 6 * q^23 - 21 * q^24 - 9 * q^25 + 15 * q^26 + 6 * q^27 + 6 * q^28 + 6 * q^29 + 9 * q^31 - 18 * q^32 + 9 * q^33 + 18 * q^34 - 12 * q^35 + 3 * q^36 - 24 * q^39 + 9 * q^40 - 6 * q^41 - 3 * q^42 + 24 * q^43 - 15 * q^45 - 18 * q^46 + 15 * q^47 - 21 * q^48 + 15 * q^49 - 15 * q^50 - 6 * q^51 - 21 * q^52 - 12 * q^53 - 6 * q^54 - 9 * q^55 - 6 * q^56 + 36 * q^58 - 6 * q^59 + 3 * q^60 + 24 * q^61 - 3 * q^62 - 15 * q^63 - 12 * q^64 - 12 * q^65 + 18 * q^66 + 6 * q^67 - 15 * q^68 - 12 * q^69 - 6 * q^71 - 3 * q^72 + 24 * q^73 + 15 * q^74 + 30 * q^75 - 18 * q^77 - 21 * q^78 + 24 * q^79 + 12 * q^80 - 3 * q^81 + 45 * q^82 + 3 * q^84 - 9 * q^85 + 24 * q^86 - 21 * q^87 + 9 * q^88 - 3 * q^89 + 9 * q^90 - 3 * q^91 - 30 * q^92 - 36 * q^93 + 18 * q^94 + 18 * q^96 - 18 * q^97 + 27 * q^98 - 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	1.26604	+	0.460802i	0.895229	+	0.325837i	0.748339	−	0.663316i	$-0.230852\pi$
$2$	1.26604	+	0.460802i	0.895229	+	0.325837i	0.146889	+	0.989153i	$0.453074\pi$
$3$	−0.500000	−	2.83564i	−0.288675	−	1.63716i	−0.691854	−	0.722037i	$-0.743206\pi$
$3$	−0.500000	−	2.83564i	−0.288675	−	1.63716i	0.403179	−	0.915121i	$-0.367905\pi$
$4$	−0.141559	−	0.118782i	−0.0707796	−	0.0593912i
$5$	0.673648	−	0.565258i	0.301265	−	0.252791i	−0.479606	−	0.877484i	$-0.659220\pi$
$5$	0.673648	−	0.565258i	0.301265	−	0.252791i	0.780870	+	0.624693i	$0.214776\pi$
$6$	0.673648	−	3.82045i	0.275016	−	1.55969i
$7$	−0.173648	+	0.300767i	−0.0656328	+	0.113679i	−0.896975	−	0.442082i	$-0.854240\pi$
$7$	−0.173648	+	0.300767i	−0.0656328	+	0.113679i	0.831342	+	0.555762i	$0.187573\pi$
$8$	−1.47178	−	2.54920i	−0.520353	−	0.901278i
$9$	−4.97178	+	1.80958i	−1.65726	+	0.603193i
$10$	1.11334	−	0.405223i	0.352069	−	0.128143i
$11$	1.11334	+	1.92836i	0.335685	+	0.581423i	0.983616	−	0.180276i	$-0.0576989\pi$
$11$	1.11334	+	1.92836i	0.335685	+	0.581423i	−0.647931	+	0.761699i	$0.724366\pi$
$12$	−0.266044	+	0.460802i	−0.0768004	+	0.133022i
$13$	0.446967	−	2.53487i	0.123966	−	0.703047i	−0.857950	−	0.513733i	$-0.828262\pi$
$13$	0.446967	−	2.53487i	0.123966	−	0.703047i	0.981916	−	0.189315i	$-0.0606266\pi$
$14$	−0.358441	+	0.300767i	−0.0957973	+	0.0803835i
$15$	−1.93969	−	1.62760i	−0.500826	−	0.420243i
$16$	−0.624485	−	3.54163i	−0.156121	−	0.885408i
$17$	−0.439693	−	0.160035i	−0.106641	−	0.0388142i	0.288149	−	0.957586i	$-0.406960\pi$
$17$	−0.439693	−	0.160035i	−0.106641	−	0.0388142i	−0.394790	+	0.918772i	$0.629183\pi$
$18$	−7.12836			−1.68017
$19$		0			0
$19$		0			0
$20$	−0.162504			−0.0363370
$21$	0.939693	+	0.342020i	0.205058	+	0.0746349i
$22$	0.520945	+	2.95442i	0.111066	+	0.629885i
$23$	−2.06418	−	1.73205i	−0.430411	−	0.361158i	0.401696	−	0.915773i	$-0.368421\pi$
$23$	−2.06418	−	1.73205i	−0.430411	−	0.361158i	−0.832107	+	0.554616i	$0.812865\pi$
$24$	−6.49273	+	5.44804i	−1.32532	+	1.11208i
$25$	−0.733956	+	4.16247i	−0.146791	+	0.832494i
$26$	1.73396	−	3.00330i	0.340057	−	0.588995i
$27$	3.29813	+	5.71253i	0.634726	+	1.09938i
$28$	0.0603074	−	0.0219501i	0.0113970	−	0.00414818i
$29$	6.46451	−	2.35289i	1.20043	−	0.436920i	0.337055	−	0.941485i	$-0.390569\pi$
$29$	6.46451	−	2.35289i	1.20043	−	0.436920i	0.863374	+	0.504565i	$0.168347\pi$
$30$	−1.70574	−	2.95442i	−0.311424	−	0.539401i
$31$	3.55303	−	6.15403i	0.638144	−	1.10530i	−0.347696	−	0.937607i	$-0.613036\pi$
$31$	3.55303	−	6.15403i	0.638144	−	1.10530i	0.985840	−	0.167690i	$-0.0536307\pi$
$32$	−0.180922	+	1.02606i	−0.0319828	+	0.181384i
$33$	4.91147	−	4.12122i	0.854978	−	0.717412i
$34$	−0.482926	−	0.405223i	−0.0828211	−	0.0694952i
$35$	0.0530334	+	0.300767i	0.00896428	+	0.0508390i
$36$	0.918748	+	0.334397i	0.153125	+	0.0557328i
$37$	4.94356			0.812717			0.406358	−	0.913714i	$-0.366798\pi$
$37$	4.94356			0.812717			0.406358	+	0.913714i	$0.366798\pi$
$38$		0			0
$39$	−7.41147			−1.18679
$40$	−2.43242	−	0.885328i	−0.384599	−	0.139983i
$41$	0.429892	+	2.43804i	0.0671379	+	0.380758i	0.999800	+	0.0200065i	$0.00636868\pi$
$41$	0.429892	+	2.43804i	0.0671379	+	0.380758i	−0.932662	+	0.360752i	$0.882520\pi$
$42$	1.03209	+	0.866025i	0.159255	+	0.133631i
$43$	2.98886	−	2.50795i	0.455796	−	0.382458i	−0.385785	−	0.922589i	$-0.626069\pi$
$43$	2.98886	−	2.50795i	0.455796	−	0.382458i	0.841581	+	0.540130i	$0.181625\pi$
$44$	0.0714517	−	0.405223i	0.0107718	−	0.0610897i
$45$	−2.32635	+	4.02936i	−0.346792	+	0.600661i
$46$	−1.81521	−	3.14403i	−0.267638	−	0.463562i
$47$	6.85117	−	2.49362i	0.999345	−	0.363732i	0.210013	−	0.977699i	$-0.432649\pi$
$47$	6.85117	−	2.49362i	0.999345	−	0.363732i	0.789332	+	0.613967i	$0.210427\pi$
$48$	−9.73055	+	3.54163i	−1.40448	+	0.511190i
$49$	3.43969	+	5.95772i	0.491385	+	0.851103i
$50$	−2.84730	+	4.93166i	−0.402669	+	0.697442i
$51$	−0.233956	+	1.32683i	−0.0327603	+	0.185793i
$52$	−0.364370	+	0.305743i	−0.0505291	+	0.0423989i
$53$	−2.17365	−	1.82391i	−0.298574	−	0.250533i	0.481177	−	0.876624i	$-0.340210\pi$
$53$	−2.17365	−	1.82391i	−0.298574	−	0.250533i	−0.779750	+	0.626091i	$0.784654\pi$
$54$	1.54323	+	8.75211i	0.210007	+	1.19101i
$55$	1.84002	+	0.669713i	0.248109	+	0.0903041i
$56$	1.02229			0.136609
$57$		0			0
$58$	9.26857			1.21702
$59$	5.92514	+	2.15658i	0.771388	+	0.280762i	0.697577	−	0.716510i	$-0.254262\pi$
$59$	5.92514	+	2.15658i	0.771388	+	0.280762i	0.0738112	+	0.997272i	$0.476484\pi$
$60$	0.0812519	+	0.460802i	0.0104896	+	0.0594893i
$61$	6.99273	+	5.86759i	0.895327	+	0.751268i	0.969271	−	0.245994i	$-0.0791143\pi$
$61$	6.99273	+	5.86759i	0.895327	+	0.751268i	−0.0739445	+	0.997262i	$0.523559\pi$
$62$	7.33409	−	6.15403i	0.931431	−	0.781563i
$63$	0.319078	−	1.80958i	0.0402000	−	0.227986i
$64$	−4.29813	+	7.44459i	−0.537267	+	0.930573i
$65$	−1.13176	−	1.96026i	−0.140377	−	0.243141i
$66$	8.11721	−	2.95442i	0.999160	−	0.363664i
$67$	−7.21213	+	2.62500i	−0.881102	+	0.320695i	−0.742655	−	0.669675i	$-0.766434\pi$
$67$	−7.21213	+	2.62500i	−0.881102	+	0.320695i	−0.138448	+	0.990370i	$0.544211\pi$
$68$	0.0432332	+	0.0748822i	0.00524280	+	0.00908080i
$69$	−3.87939	+	6.71929i	−0.467023	+	0.808908i
$70$	−0.0714517	+	0.405223i	−0.00854012	+	0.0484334i
$71$	−7.12836	+	5.98140i	−0.845980	+	0.709862i	−0.958901	−	0.283742i	$-0.908424\pi$
$71$	−7.12836	+	5.98140i	−0.845980	+	0.709862i	0.112920	+	0.993604i	$0.463979\pi$
$72$	11.9304	+	10.0108i	1.40601	+	1.17978i
$73$	0.241230	+	1.36808i	0.0282338	+	0.160122i	0.995665	−	0.0930125i	$-0.0296497\pi$
$73$	0.241230	+	1.36808i	0.0282338	+	0.160122i	−0.967431	+	0.253134i	$0.918539\pi$
$74$	6.25877	+	2.27801i	0.727567	+	0.264813i
$75$	12.1702			1.40530
$76$		0			0
$77$	−0.773318			−0.0881278
$78$	−9.38326	−	3.41523i	−1.06244	−	0.386698i
$79$	−2.05690	−	11.6653i	−0.231420	−	1.31245i	−0.850024	−	0.526744i	$-0.823413\pi$
$79$	−2.05690	−	11.6653i	−0.231420	−	1.31245i	0.618604	−	0.785703i	$-0.287698\pi$
$80$	−2.42262	−	2.03282i	−0.270857	−	0.227276i
$81$	2.39053	−	2.00589i	0.265614	−	0.222877i
$82$	−0.579193	+	3.28476i	−0.0639611	+	0.362742i
$83$	7.41534	−	12.8438i	0.813940	−	1.40979i	−0.0961469	−	0.995367i	$-0.530652\pi$
$83$	7.41534	−	12.8438i	0.813940	−	1.40979i	0.910087	−	0.414418i	$-0.136015\pi$
$84$	−0.0923963	−	0.160035i	−0.0100813	−	0.0174613i
$85$	−0.386659	+	0.140732i	−0.0419391	+	0.0152646i
$86$	4.93969	−	1.79790i	0.532661	−	0.193873i
$87$	−9.90420	−	17.1546i	−1.06184	−	1.83916i
$88$	3.27719	−	5.67626i	0.349349	−	0.605091i
$89$	−1.78699	+	10.1345i	−0.189420	+	1.07426i	0.730723	+	0.682674i	$0.239183\pi$
$89$	−1.78699	+	10.1345i	−0.189420	+	1.07426i	−0.920143	+	0.391582i	$0.871928\pi$
$90$	−4.80200	+	4.02936i	−0.506176	+	0.424732i
$91$	0.684793	+	0.574609i	0.0717858	+	0.0602354i
$92$	0.0864665	+	0.490376i	0.00901475	+	0.0511252i
$93$	−19.2271	−	6.99811i	−1.99376	−	0.725670i
$94$	9.82295			1.01316
$95$		0			0
$96$	3.00000			0.306186
$97$	−8.88326	−	3.23324i	−0.901958	−	0.328286i	−0.150921	−	0.988546i	$-0.548224\pi$
$97$	−8.88326	−	3.23324i	−0.901958	−	0.328286i	−0.751037	+	0.660260i	$0.770446\pi$
$98$	1.60947	+	9.12776i	0.162581	+	0.922043i
$99$	−9.02481	−	7.57272i	−0.907028	−	0.761087i
$100$	0.598326	−	0.502055i	0.0598326	−	0.0502055i
$101$	−1.60607	+	9.10846i	−0.159810	+	0.906325i	0.794446	+	0.607334i	$0.207761\pi$
$101$	−1.60607	+	9.10846i	−0.159810	+	0.906325i	−0.954256	+	0.298991i	$0.903350\pi$
$102$	−0.907604	+	1.57202i	−0.0898662	+	0.155653i
$103$	2.75490	+	4.77163i	0.271448	+	0.470162i	0.969233	−	0.246145i	$-0.0791640\pi$
$103$	2.75490	+	4.77163i	0.271448	+	0.470162i	−0.697785	+	0.716308i	$0.745831\pi$
$104$	−7.11974	+	2.59137i	−0.698148	+	0.254105i
$105$	0.826352	−	0.300767i	0.0806437	−	0.0293519i
$106$	−1.91147	−	3.31077i	−0.185659	−	0.321570i
$107$	−5.11721	+	8.86327i	−0.494699	+	0.856845i	−0.999981	−	0.00610974i	$-0.998055\pi$
$107$	−5.11721	+	8.86327i	−0.494699	+	0.856845i	0.505282	+	0.862954i	$0.331389\pi$
$108$	0.211667	−	1.20042i	0.0203677	−	0.115511i
$109$	−1.39646	+	1.17177i	−0.133757	+	0.112235i	−0.707212	−	0.707002i	$-0.750047\pi$
$109$	−1.39646	+	1.17177i	−0.133757	+	0.112235i	0.573455	+	0.819237i	$0.305603\pi$
$110$	2.02094	+	1.69577i	0.192690	+	0.161686i
$111$	−2.47178	−	14.0182i	−0.234611	−	1.33055i
$112$	1.17365	+	0.427173i	0.110899	+	0.0403641i
$113$	−17.6878			−1.66393			−0.831963	−	0.554830i	$-0.812783\pi$
$113$	−17.6878			−1.66393			−0.831963	+	0.554830i	$0.812783\pi$
$114$		0			0
$115$	−2.36959			−0.220965
$116$	−1.19459	−	0.434796i	−0.110915	−	0.0403698i
$117$	2.36484	+	13.4117i	0.218629	+	1.23991i
$118$	6.50774	+	5.46064i	0.599086	+	0.502693i
$119$	0.124485	−	0.104455i	0.0114115	−	0.00957541i
$120$	−1.29426	+	7.34013i	−0.118150	+	0.670059i
$121$	3.02094	−	5.23243i	0.274631	−	0.475675i
$122$	6.14930	+	10.6509i	0.556731	+	0.964287i
$123$	6.69846	−	2.43804i	0.603980	−	0.219831i
$124$	−1.23396	+	0.449123i	−0.110812	+	0.0403324i
$125$	4.05690	+	7.02676i	0.362861	+	0.628493i
$126$	1.23783	−	2.14398i	0.110274	−	0.191001i
$127$	2.01501	−	11.4277i	0.178804	−	1.01405i	−0.754858	−	0.655889i	$-0.772294\pi$
$127$	2.01501	−	11.4277i	0.178804	−	1.01405i	0.933661	−	0.358157i	$-0.116595\pi$
$128$	−7.27584	+	6.10516i	−0.643100	+	0.539625i
$129$	−8.60607	−	7.22135i	−0.757722	−	0.635804i
$130$	−0.529563	−	3.00330i	−0.0464457	−	0.263407i
$131$	−1.73396	−	0.631108i	−0.151496	−	0.0551402i	0.265159	−	0.964205i	$-0.414576\pi$
$131$	−1.73396	−	0.631108i	−0.151496	−	0.0551402i	−0.416655	+	0.909065i	$0.636798\pi$
$132$	−1.18479			−0.103123
$133$		0			0
$134$	−10.3405			−0.893282
$135$	5.45084	+	1.98394i	0.469133	+	0.170751i
$136$	0.239170	+	1.35640i	0.0205087	+	0.116310i
$137$	0.195937	+	0.164411i	0.0167400	+	0.0140465i	0.651119	−	0.758975i	$-0.274300\pi$
$137$	0.195937	+	0.164411i	0.0167400	+	0.0140465i	−0.634379	+	0.773022i	$0.718744\pi$
$138$	−8.00774	+	6.71929i	−0.681664	+	0.571984i
$139$	0.740352	−	4.19875i	0.0627959	−	0.356133i	−0.937178	−	0.348852i	$-0.886571\pi$
$139$	0.740352	−	4.19875i	0.0627959	−	0.356133i	0.999973	−	0.00728048i	$-0.00231747\pi$
$140$	0.0282185	−	0.0488759i	0.00238490	−	0.00413076i
$141$	−10.4966	−	18.1806i	−0.883973	−	1.53109i
$142$	−11.7811	+	4.28795i	−0.988645	+	0.359837i
$143$	5.38578	−	1.96026i	0.450382	−	0.163926i
$144$	9.51367	+	16.4782i	0.792806	+	1.37318i
$145$	3.02481	−	5.23913i	0.251197	−	0.435086i
$146$	−0.325008	+	1.84321i	−0.0268978	+	0.152545i
$147$	15.1741	−	12.7326i	1.25154	−	1.05017i
$148$	−0.699807	−	0.587208i	−0.0575238	−	0.0482682i
$149$	2.87551	+	16.3079i	0.235571	+	1.33599i	0.841407	+	0.540402i	$0.181728\pi$
$149$	2.87551	+	16.3079i	0.235571	+	1.33599i	−0.605836	+	0.795590i	$0.707161\pi$
$150$	15.4081	+	5.60808i	1.25806	+	0.457898i
$151$	−4.36184			−0.354962			−0.177481	−	0.984124i	$-0.556795\pi$
$151$	−4.36184			−0.354962			−0.177481	+	0.984124i	$0.556795\pi$
$152$		0			0
$153$	2.47565			0.200145
$154$	−0.979055	−	0.356347i	−0.0788945	−	0.0287153i
$155$	−1.08512	−	6.15403i	−0.0871591	−	0.494304i
$156$	1.04916	+	0.880352i	0.0840003	+	0.0704846i
$157$	−7.36824	+	6.18269i	−0.588050	+	0.493432i	−0.887579	−	0.460655i	$-0.847615\pi$
$157$	−7.36824	+	6.18269i	−0.588050	+	0.493432i	0.299530	+	0.954087i	$0.403170\pi$
$158$	2.77126	−	15.7166i	0.220470	−	1.25034i
$159$	−4.08512	+	7.07564i	−0.323971	+	0.561135i
$160$	0.458111	+	0.793471i	0.0362168	+	0.0627294i
$161$	0.879385	−	0.320070i	0.0693053	−	0.0252251i
$162$	3.95084	−	1.43799i	0.310407	−	0.112979i
$163$	−4.17752	−	7.23567i	−0.327209	−	0.566742i	0.654748	−	0.755847i	$-0.272775\pi$
$163$	−4.17752	−	7.23567i	−0.327209	−	0.566742i	−0.981957	+	0.189105i	$0.939441\pi$
$164$	0.228741	−	0.396191i	0.0178617	−	0.0309373i
$165$	0.979055	−	5.55250i	0.0762194	−	0.432261i
$166$	15.3066	−	12.8438i	1.18802	−	0.996869i
$167$	3.09105	+	2.59370i	0.239193	+	0.200707i	0.754502	−	0.656298i	$-0.227878\pi$
$167$	3.09105	+	2.59370i	0.239193	+	0.200707i	−0.515309	+	0.857004i	$0.672323\pi$
$168$	−0.511144	−	2.89884i	−0.0394356	−	0.223651i
$169$	5.99020	+	2.18025i	0.460785	+	0.167712i
$170$	−0.554378			−0.0425188
$171$		0			0
$172$	−0.721000			−0.0549758
$173$	18.9290	+	6.88960i	1.43915	+	0.523806i	0.939538	−	0.342445i	$-0.111255\pi$
$173$	18.9290	+	6.88960i	1.43915	+	0.523806i	0.499608	+	0.866251i	$0.333477\pi$
$174$	−4.63429	−	26.2823i	−0.351324	−	1.99246i
$175$	−1.12449	−	0.943555i	−0.0850031	−	0.0713261i
$176$	6.13429	−	5.14728i	0.462389	−	0.387991i
$177$	3.15270	−	17.8799i	0.236972	−	1.34393i
$178$	−6.93242	+	12.0073i	−0.519607	+	0.899985i
$179$	5.75624	+	9.97011i	0.430242	+	0.745201i	0.996894	−	0.0787564i	$-0.0250949\pi$
$179$	5.75624	+	9.97011i	0.430242	+	0.745201i	−0.566652	+	0.823957i	$0.691762\pi$
$180$	0.807934	−	0.294064i	0.0602198	−	0.0219182i
$181$	−8.02229	+	2.91987i	−0.596292	+	0.217033i	−0.622495	−	0.782624i	$-0.713881\pi$
$181$	−8.02229	+	2.91987i	−0.596292	+	0.217033i	0.0262026	+	0.999657i	$0.491659\pi$
$182$	0.602196	+	1.04303i	0.0446378	+	0.0773149i
$183$	13.1420	−	22.7627i	0.971487	−	1.68266i
$184$	−1.37733	+	7.81120i	−0.101538	+	0.575850i
$185$	3.33022	−	2.79439i	0.244843	−	0.205448i
$186$	−21.1177	−	17.7198i	−1.54842	−	1.29928i
$187$	−0.180922	−	1.02606i	−0.0132303	−	0.0750330i
$188$	−1.26604	−	0.460802i	−0.0923358	−	0.0336075i
$189$	−2.29086			−0.166635
$190$		0			0
$191$	18.3354			1.32671			0.663353	−	0.748307i	$-0.269133\pi$
$191$	18.3354			1.32671			0.663353	+	0.748307i	$0.269133\pi$
$192$	23.2592	+	8.46567i	1.67859	+	0.610957i
$193$	0.0516892	+	0.293144i	0.00372067	+	0.0211010i	0.986612	−	0.163088i	$-0.0521454\pi$
$193$	0.0516892	+	0.293144i	0.00372067	+	0.0211010i	−0.982891	+	0.184189i	$0.941034\pi$
$194$	−9.75671	−	8.18685i	−0.700491	−	0.587782i
$195$	−4.99273	+	4.18939i	−0.357537	+	0.300009i
$196$	0.220752	−	1.25195i	0.0157680	−	0.0894247i
$197$	−6.57057	+	11.3806i	−0.468134	+	0.810832i	−0.999337	−	0.0364128i	$-0.988407\pi$
$197$	−6.57057	+	11.3806i	−0.468134	+	0.810832i	0.531203	+	0.847245i	$0.321740\pi$
$198$	−7.93629	−	13.7461i	−0.564008	−	0.976890i
$199$	0.241230	−	0.0878004i	0.0171003	−	0.00622400i	−0.333456	−	0.942766i	$-0.608215\pi$
$199$	0.241230	−	0.0878004i	0.0171003	−	0.00622400i	0.350556	+	0.936542i	$0.385993\pi$
$200$	11.6912	−	4.25524i	0.826692	−	0.300891i
$201$	11.0496	+	19.1385i	0.779381	+	1.34993i
$202$	−6.23055	+	10.7916i	−0.438380	+	0.759297i
$203$	−0.414878	+	2.35289i	−0.0291187	+	0.165140i
$204$	0.190722	−	0.160035i	0.0133532	−	0.0112047i
$205$	1.66772	+	1.39938i	0.116479	+	0.0977371i
$206$	1.28905	+	7.31056i	0.0898123	+	0.509351i
$207$	13.3969	+	4.87608i	0.931151	+	0.338911i
$208$	−9.25671			−0.641837
$209$		0			0
$210$	1.18479			0.0817585
$211$	−2.30066	−	0.837372i	−0.158384	−	0.0576470i	0.261611	−	0.965173i	$-0.415746\pi$
$211$	−2.30066	−	0.837372i	−0.158384	−	0.0576470i	−0.419995	+	0.907526i	$0.637968\pi$
$212$	0.0910521	+	0.516382i	0.00625348	+	0.0354653i
$213$	20.5253	+	17.2228i	1.40637	+	1.18008i
$214$	−10.5628	+	8.86327i	−0.722060	+	0.605881i
$215$	0.595800	−	3.37895i	0.0406332	−	0.230442i
$216$	9.70826	−	16.8152i	0.660564	−	1.14413i
$217$	1.23396	+	2.13727i	0.0837664	+	0.145088i
$218$	−2.30793	+	0.840019i	−0.156313	+	0.0568933i
$219$	3.75877	−	1.36808i	0.253994	−	0.0924463i
$220$	−0.180922	−	0.313366i	−0.0121978	−	0.0211272i
$221$	−0.602196	+	1.04303i	−0.0405081	+	0.0701621i
$222$	3.33022	−	18.8866i	0.223510	−	1.26759i
$223$	−6.51889	+	5.46999i	−0.436537	+	0.366298i	−0.834412	−	0.551142i	$-0.814192\pi$
$223$	−6.51889	+	5.46999i	−0.436537	+	0.366298i	0.397875	+	0.917440i	$0.369748\pi$
$224$	−0.277189	−	0.232589i	−0.0185205	−	0.0155405i
$225$	−3.88326	−	22.0230i	−0.258884	−	1.46820i
$226$	−22.3935	−	8.15058i	−1.48959	−	0.542168i
$227$	−14.1506			−0.939211			−0.469606	−	0.882876i	$-0.655604\pi$
$227$	−14.1506			−0.939211			−0.469606	+	0.882876i	$0.655604\pi$
$228$		0			0
$229$	−20.5330			−1.35686			−0.678430	−	0.734665i	$-0.737339\pi$
$229$	−20.5330			−1.35686			−0.678430	+	0.734665i	$0.737339\pi$
$230$	−3.00000	−	1.09191i	−0.197814	−	0.0719985i
$231$	0.386659	+	2.19285i	0.0254403	+	0.144279i
$232$	−15.5123	−	13.0164i	−1.01843	−	0.854568i
$233$	13.5214	−	11.3458i	0.885817	−	0.743289i	−0.0815496	−	0.996669i	$-0.525987\pi$
$233$	13.5214	−	11.3458i	0.885817	−	0.743289i	0.967367	+	0.253380i	$0.0815425\pi$
$234$	−3.18614	+	18.0695i	−0.208284	+	1.18124i
$235$	3.20574	−	5.55250i	0.209119	−	0.362205i
$236$	−0.582596	−	1.00909i	−0.0379238	−	0.0656859i
$237$	−32.0501	+	11.6653i	−2.08188	+	0.757741i
$238$	0.205737	−	0.0748822i	0.0133360	−	0.00485389i
$239$	−1.17617	−	2.03719i	−0.0760804	−	0.131775i	0.825475	−	0.564438i	$-0.190907\pi$
$239$	−1.17617	−	2.03719i	−0.0760804	−	0.131775i	−0.901556	+	0.432663i	$0.857574\pi$
$240$	−4.55303	+	7.88609i	−0.293897	+	0.509045i
$241$	2.39646	−	13.5910i	0.154370	−	0.875473i	−0.804990	−	0.593288i	$-0.797830\pi$
$241$	2.39646	−	13.5910i	0.154370	−	0.875473i	0.959360	−	0.282185i	$-0.0910593\pi$
$242$	6.23577	−	5.23243i	0.400850	−	0.336353i
$243$	8.27584	+	6.94426i	0.530896	+	0.445474i
$244$	−0.292919	−	1.66122i	−0.0187522	−	0.106349i
$245$	5.68479	+	2.06910i	0.363188	+	0.132190i
$246$	9.60401			0.612329
$247$		0			0
$248$	−20.9172			−1.32824
$249$	−40.1279	−	14.6054i	−2.54301	−	0.925578i
$250$	1.89827	+	10.7656i	0.120057	+	0.680878i
$251$	−3.19072	−	2.67733i	−0.201397	−	0.168992i	0.536512	−	0.843893i	$-0.319742\pi$
$251$	−3.19072	−	2.67733i	−0.201397	−	0.168992i	−0.737908	+	0.674901i	$0.764186\pi$
$252$	−0.260115	+	0.218262i	−0.0163857	+	0.0137492i
$253$	1.04189	−	5.90885i	0.0655030	−	0.371486i
$254$	7.81702	−	13.5395i	0.490483	−	0.849542i
$255$	0.592396	+	1.02606i	0.0370973	+	0.0642544i
$256$	4.13088	−	1.50352i	0.258180	−	0.0939699i
$257$	−0.627011	+	0.228213i	−0.0391119	+	0.0142356i	−0.361502	−	0.932371i	$-0.617736\pi$
$257$	−0.627011	+	0.228213i	−0.0391119	+	0.0142356i	0.322390	+	0.946607i	$0.395514\pi$
$258$	−7.56805	−	13.1082i	−0.471166	−	0.816084i
$259$	−0.858441	+	1.48686i	−0.0533409	+	0.0923892i
$260$	−0.0726338	+	0.411927i	−0.00450456	+	0.0255466i
$261$	−27.8824	+	23.3961i	−1.72588	+	1.44818i
$262$	−1.90445	−	1.59802i	−0.117657	−	0.0987261i
$263$	1.97952	+	11.2264i	0.122063	+	0.692251i	0.983009	+	0.183556i	$0.0587609\pi$
$263$	1.97952	+	11.2264i	0.122063	+	0.692251i	−0.860947	+	0.508695i	$0.830128\pi$
$264$	−17.7344	−	6.45480i	−1.09148	−	0.397266i
$265$	−2.49525			−0.153282
$266$		0			0
$267$	29.6313			1.81341
$268$	1.33275	+	0.485081i	0.0814106	+	0.0296310i
$269$	3.36706	+	19.0955i	0.205293	+	1.16428i	0.896978	+	0.442076i	$0.145758\pi$
$269$	3.36706	+	19.0955i	0.205293	+	1.16428i	−0.691684	+	0.722200i	$0.743131\pi$
$270$	5.98680	+	5.02352i	0.364345	+	0.305722i
$271$	−10.2606	+	8.60965i	−0.623286	+	0.522999i	−0.898835	−	0.438288i	$-0.855585\pi$
$271$	−10.2606	+	8.60965i	−0.623286	+	0.522999i	0.275549	+	0.961287i	$0.411141\pi$
$272$	−0.292204	+	1.65717i	−0.0177174	+	0.100481i
$273$	1.28699	−	2.22913i	0.0778921	−	0.134913i
$274$	0.172304	+	0.298439i	0.0104093	+	0.0180294i
$275$	−8.84389	+	3.21891i	−0.533307	+	0.194108i
$276$	1.34730	−	0.490376i	0.0810977	−	0.0295172i
$277$	−8.87346	−	15.3693i	−0.533154	−	0.923450i	−0.999250	−	0.0387161i	$-0.987673\pi$
$277$	−8.87346	−	15.3693i	−0.533154	−	0.923450i	0.466096	−	0.884734i	$-0.345660\pi$
$278$	2.87211	−	4.97464i	0.172258	−	0.298359i
$279$	−6.52869	+	37.0260i	−0.390862	+	2.21669i
$280$	0.688663	−	0.577857i	0.0411555	−	0.0345335i
$281$	14.0025	+	11.7495i	0.835321	+	0.700917i	0.956506	−	0.291713i	$-0.0942251\pi$
$281$	14.0025	+	11.7495i	0.835321	+	0.700917i	−0.121185	+	0.992630i	$0.538670\pi$
$282$	−4.91147	−	27.8544i	−0.292474	−	1.65870i
$283$	−7.22416	−	2.62938i	−0.429431	−	0.156300i	0.118256	−	0.992983i	$-0.462270\pi$
$283$	−7.22416	−	2.62938i	−0.429431	−	0.156300i	−0.547688	+	0.836683i	$0.684492\pi$
$284$	1.71957			0.102038
$285$		0			0
$286$	7.72193			0.456608
$287$	−0.807934	−	0.294064i	−0.0476908	−	0.0173580i
$288$	−0.957234	−	5.42874i	−0.0564055	−	0.319892i
$289$	−12.8550	−	10.7867i	−0.756179	−	0.634509i
$290$	6.24376	−	5.23913i	0.366646	−	0.307652i
$291$	−4.72668	+	26.8063i	−0.277083	+	1.57142i
$292$	0.128356	−	0.222318i	0.00751144	−	0.0130102i
$293$	5.25150	+	9.09586i	0.306796	+	0.531386i	0.977660	−	0.210195i	$-0.0674098\pi$
$293$	5.25150	+	9.09586i	0.306796	+	0.531386i	−0.670864	+	0.741581i	$0.734076\pi$
$294$	25.0783	−	9.12776i	1.46260	−	0.532342i
$295$	5.21048	−	1.89646i	0.303366	−	0.110416i
$296$	−7.27584	−	12.6021i	−0.422900	−	0.732484i
$297$	−7.34389	+	12.7200i	−0.426136	+	0.738089i
$298$	−3.87417	+	21.9715i	−0.224425	+	1.27278i
$299$	−5.31315	+	4.45826i	−0.307267	+	0.257828i
$300$	−1.72281	−	1.44561i	−0.0994666	−	0.0834623i
$301$	0.235300	+	1.33445i	0.0135625	+	0.0769165i
$302$	−5.52229	−	2.00995i	−0.317772	−	0.115660i
$303$	26.6313			1.52993
$304$		0			0
$305$	8.02734			0.459644
$306$	3.13429	+	1.14079i	0.179175	+	0.0652144i
$307$	−2.03091	−	11.5178i	−0.115910	−	0.657358i	−0.986296	−	0.164988i	$-0.947242\pi$
$307$	−2.03091	−	11.5178i	−0.115910	−	0.657358i	0.870386	−	0.492371i	$-0.163870\pi$
$308$	0.109470	+	0.0918566i	0.00623766	+	0.00523401i
$309$	12.1532	−	10.1977i	0.691370	−	0.580128i
$310$	1.46198	−	8.29131i	0.0830350	−	0.470915i
$311$	−7.98293	+	13.8268i	−0.452670	+	0.784048i	−0.998551	−	0.0538151i	$-0.982862\pi$
$311$	−7.98293	+	13.8268i	−0.452670	+	0.784048i	0.545881	+	0.837863i	$0.316195\pi$
$312$	10.9081	+	18.8933i	0.617548	+	1.06962i
$313$	25.0228	−	9.10754i	1.41437	−	0.514788i	0.481961	−	0.876193i	$-0.339925\pi$
$313$	25.0228	−	9.10754i	1.41437	−	0.514788i	0.932409	+	0.361404i	$0.117703\pi$
$314$	−12.1775	+	4.43225i	−0.687217	+	0.250127i
$315$	−0.807934	−	1.39938i	−0.0455219	−	0.0788462i
$316$	−1.09446	+	1.89565i	−0.0615679	+	0.106639i
$317$	5.12819	−	29.0834i	0.288028	−	1.63349i	−0.406236	−	0.913768i	$-0.633159\pi$
$317$	5.12819	−	29.0834i	0.288028	−	1.63349i	0.694264	−	0.719720i	$-0.255730\pi$
$318$	−8.43242	+	7.07564i	−0.472867	+	0.396782i
$319$	11.7344	+	9.84635i	0.657002	+	0.551290i
$320$	1.31268	+	7.44459i	0.0733811	+	0.416165i
$321$	27.6917	+	10.0789i	1.54560	+	0.562551i
$322$	1.26083			0.0702633
$323$		0			0
$324$	−0.576666			−0.0320370
$325$	10.2233	+	3.72097i	0.567085	+	0.206402i
$326$	−1.95471	−	11.0857i	−0.108261	−	0.613980i
$327$	4.02094	+	3.37397i	0.222359	+	0.186581i
$328$	5.58235	−	4.68415i	0.308234	−	0.258639i
$329$	−0.439693	+	2.49362i	−0.0242410	+	0.137478i
$330$	3.79813	−	6.57856i	0.209080	−	0.362138i
$331$	−13.8327	−	23.9590i	−0.760317	−	1.31691i	−0.942687	−	0.333677i	$-0.891710\pi$
$331$	−13.8327	−	23.9590i	−0.760317	−	1.31691i	0.182371	−	0.983230i	$-0.441623\pi$
$332$	−2.57532	+	0.937341i	−0.141339	+	0.0514432i
$333$	−24.5783	+	8.94578i	−1.34688	+	0.490225i
$334$	2.71823	+	4.70810i	0.148735	+	0.257616i
$335$	−3.37464	+	5.84504i	−0.184376	+	0.319349i
$336$	0.624485	−	3.54163i	0.0340685	−	0.193212i
$337$	13.6814	−	11.4800i	0.745273	−	0.625358i	−0.188975	−	0.981982i	$-0.560517\pi$
$337$	13.6814	−	11.4800i	0.745273	−	0.625358i	0.934248	+	0.356624i	$0.116072\pi$
$338$	6.57919	+	5.52060i	0.357861	+	0.300281i
$339$	8.84389	+	50.1562i	0.480334	+	2.72411i
$340$	0.0714517	+	0.0260063i	0.00387501	+	0.00141039i
$341$	15.8229			0.856861
$342$		0			0
$343$	−4.82026			−0.260270
$344$	−10.7922	−	3.92804i	−0.581877	−	0.211786i
$345$	1.18479	+	6.71929i	0.0637871	+	0.361755i
$346$	20.7902	+	17.4451i	1.11769	+	0.937853i
$347$	−4.44356	+	3.72859i	−0.238543	+	0.200161i	−0.754220	−	0.656622i	$-0.771985\pi$
$347$	−4.44356	+	3.72859i	−0.238543	+	0.200161i	0.515677	+	0.856783i	$0.327540\pi$
$348$	−0.635630	+	3.60483i	−0.0340733	+	0.193239i
$349$	−2.68614	+	4.65253i	−0.143786	+	0.249044i	−0.928919	−	0.370282i	$-0.879261\pi$
$349$	−2.68614	+	4.65253i	−0.143786	+	0.249044i	0.785134	+	0.619326i	$0.212594\pi$
$350$	−0.988856	−	1.71275i	−0.0528566	−	0.0915502i
$351$	15.9547	−	5.80704i	0.851599	−	0.309957i
$352$	−2.18004	+	0.793471i	−0.116197	+	0.0422922i
$353$	12.6172	+	21.8537i	0.671546	+	1.16315i	0.977466	+	0.211095i	$0.0677029\pi$
$353$	12.6172	+	21.8537i	0.671546	+	1.16315i	−0.305919	+	0.952057i	$0.598964\pi$
$354$	12.2306	−	21.1839i	0.650047	−	1.12591i
$355$	−1.42097	+	8.05872i	−0.0754172	+	0.427712i
$356$	1.45677	−	1.22237i	0.0772085	−	0.0647856i
$357$	−0.358441	−	0.300767i	−0.0189707	−	0.0159183i
$358$	2.69341	+	15.2751i	0.142351	+	0.807314i
$359$	−6.28359	−	2.28704i	−0.331635	−	0.120705i	0.170836	−	0.985300i	$-0.445353\pi$
$359$	−6.28359	−	2.28704i	−0.331635	−	0.120705i	−0.502471	+	0.864594i	$0.667575\pi$
$360$	13.6955			0.721818
$361$		0			0
$362$	−11.5021			−0.604535
$363$	−16.3478	−	5.95010i	−0.858035	−	0.312299i
$364$	−0.0286853	−	0.162683i	−0.00150352	−	0.00852688i
$365$	0.935822	+	0.785248i	0.0489832	+	0.0411018i
$366$	27.1275	−	22.7627i	1.41798	−	1.18982i
$367$	1.40983	−	7.99552i	0.0735923	−	0.417363i	−0.925648	−	0.378386i	$-0.876479\pi$
$367$	1.40983	−	7.99552i	0.0735923	−	0.417363i	0.999240	−	0.0389764i	$-0.0124097\pi$
$368$	−4.84524	+	8.39220i	−0.252575	+	0.437473i
$369$	−6.54916	−	11.3435i	−0.340936	−	0.590518i
$370$	5.50387	−	2.00324i	0.286133	−	0.104144i
$371$	0.926022	−	0.337044i	0.0480767	−	0.0174985i
$372$	1.89053	+	3.27449i	0.0980194	+	0.169775i
$373$	−17.4488	+	30.2222i	−0.903463	+	1.56484i	−0.0804968	+	0.996755i	$0.525651\pi$
$373$	−17.4488	+	30.2222i	−0.903463	+	1.56484i	−0.822967	+	0.568090i	$0.807683\pi$
$374$	0.243756	−	1.38241i	0.0126043	−	0.0714826i
$375$	17.8969	−	15.0173i	0.924193	−	0.775490i
$376$	−16.4402	−	13.7949i	−0.847836	−	0.711419i
$377$	−3.07486	−	17.4384i	−0.158363	−	0.898122i
$378$	−2.90033	−	1.05563i	−0.149177	−	0.0542959i
$379$	1.70140			0.0873950			0.0436975	−	0.999045i	$-0.486086\pi$
$379$	1.70140			0.0873950			0.0436975	+	0.999045i	$0.486086\pi$
$380$		0			0
$381$	−33.4124			−1.71177
$382$	23.2135	+	8.44901i	1.18770	+	0.432289i
$383$	0.509962	+	2.89214i	0.0260579	+	0.147781i	0.995061	−	0.0992680i	$-0.0316501\pi$
$383$	0.509962	+	2.89214i	0.0260579	+	0.147781i	−0.969003	+	0.247049i	$0.920539\pi$
$384$	20.9500	+	17.5791i	1.06910	+	0.897080i
$385$	−0.520945	+	0.437124i	−0.0265498	+	0.0222779i
$386$	−0.0696407	+	0.394952i	−0.00354462	+	0.0201025i
$387$	−10.3216	+	17.8775i	−0.524677	+	0.908767i
$388$	0.873455	+	1.51287i	0.0443430	+	0.0768043i
$389$	23.0856	−	8.40247i	1.17049	−	0.426022i	0.317654	−	0.948207i	$-0.397105\pi$
$389$	23.0856	−	8.40247i	1.17049	−	0.426022i	0.852832	+	0.522185i	$0.174883\pi$
$390$	−8.25150	+	3.00330i	−0.417831	+	0.152078i
$391$	0.630415	+	1.09191i	0.0318815	+	0.0552203i
$392$	10.1250	−	17.5369i	0.511387	−	0.885749i
$393$	−0.922618	+	5.23243i	−0.0465399	+	0.263941i
$394$	−13.5628	+	11.3806i	−0.683286	+	0.573345i
$395$	−7.97952	−	6.69561i	−0.401493	−	0.336893i
$396$	0.378041	+	2.14398i	0.0189973	+	0.107739i
$397$	29.9158	+	10.8885i	1.50143	+	0.546476i	0.956431	−	0.291959i	$-0.0943071\pi$
$397$	29.9158	+	10.8885i	1.50143	+	0.546476i	0.545001	+	0.838436i	$0.316529\pi$
$398$	0.345866			0.0173367
$399$		0			0
$400$	15.2003			0.760014
$401$	0.0812519	+	0.0295733i	0.00405753	+	0.00147682i	0.344048	−	0.938952i	$-0.388202\pi$
$401$	0.0812519	+	0.0295733i	0.00405753	+	0.00147682i	−0.339991	+	0.940429i	$0.610424\pi$
$402$	5.17024	+	29.3219i	0.257868	+	1.46244i
$403$	−14.0116	−	11.7571i	−0.697968	−	0.585665i
$404$	1.30928	−	1.09861i	0.0651390	−	0.0546581i
$405$	0.476529	−	2.70253i	0.0236789	−	0.134290i
$406$	−1.60947	+	2.78768i	−0.0798767	+	0.138350i
$407$	5.50387	+	9.53298i	0.272817	+	0.472532i
$408$	3.72668	−	1.35640i	0.184498	−	0.0671519i
$409$	−18.7995	+	6.84245i	−0.929574	+	0.338337i	−0.762041	−	0.647529i	$-0.775802\pi$
$409$	−18.7995	+	6.84245i	−0.929574	+	0.338337i	−0.167534	+	0.985866i	$0.553580\pi$
$410$	1.46657	+	2.54017i	0.0724286	+	0.125450i
$411$	0.368241	−	0.637812i	0.0181640	−	0.0314609i
$412$	0.176803	−	1.00270i	0.00871048	−	0.0493996i
$413$	−1.67752	+	1.40761i	−0.0825453	+	0.0692637i
$414$	14.7142	+	12.3467i	0.723163	+	0.606806i
$415$	−2.26470	−	12.8438i	−0.111170	−	0.630475i
$416$	2.52007	+	0.917229i	0.123556	+	0.0449709i
$417$	−12.2763			−0.601174
$418$		0			0
$419$	25.4097			1.24135			0.620673	−	0.784070i	$-0.286859\pi$
$419$	25.4097			1.24135			0.620673	+	0.784070i	$0.286859\pi$
$420$	−0.152704	−	0.0555796i	−0.00745117	−	0.00271201i
$421$	0.758770	+	4.30320i	0.0369802	+	0.209725i	0.997699	−	0.0677984i	$-0.0215975\pi$
$421$	0.758770	+	4.30320i	0.0369802	+	0.209725i	−0.960719	+	0.277524i	$0.910486\pi$
$422$	−2.52687	−	2.12030i	−0.123006	−	0.103215i
$423$	−29.5501	+	24.7955i	−1.43677	+	1.20560i
$424$	−1.45037	+	8.22546i	−0.0704362	+	0.399464i
$425$	0.988856	−	1.71275i	0.0479665	−	0.0830805i
$426$	18.0496	+	31.2629i	0.874507	+	1.51469i
$427$	−2.97906	+	1.08429i	−0.144167	+	0.0524724i
$428$	1.77719	−	0.646844i	0.0859037	−	0.0312664i
$429$	−8.25150	−	14.2920i	−0.398386	−	0.690025i
$430$	2.31134	−	4.00335i	0.111463	−	0.193059i
$431$	−6.65183	+	37.7244i	−0.320407	+	1.81712i	0.219751	+	0.975556i	$0.429476\pi$
$431$	−6.65183	+	37.7244i	−0.320407	+	1.81712i	−0.540158	+	0.841564i	$0.681636\pi$
$432$	18.1721	−	15.2482i	0.874303	−	0.733628i
$433$	−13.8892	−	11.6544i	−0.667472	−	0.560075i	0.244844	−	0.969562i	$-0.421263\pi$
$433$	−13.8892	−	11.6544i	−0.667472	−	0.560075i	−0.912316	+	0.409487i	$0.865708\pi$
$434$	0.577382	+	3.27449i	0.0277152	+	0.157181i
$435$	−16.3687	−	5.95772i	−0.784819	−	0.285651i
$436$	0.336867			0.0161330
$437$		0			0
$438$	5.38919			0.257505
$439$	5.72328	+	2.08310i	0.273157	+	0.0994211i	0.474967	−	0.880004i	$-0.342460\pi$
$439$	5.72328	+	2.08310i	0.273157	+	0.0994211i	−0.201810	+	0.979425i	$0.564682\pi$
$440$	−1.00088	−	5.67626i	−0.0477150	−	0.270605i
$441$	−27.8824	−	23.3961i	−1.32773	−	1.11410i
$442$	−1.24304	+	1.04303i	−0.0591254	+	0.0496121i
$443$	−5.19088	+	29.4390i	−0.246626	+	1.39869i	0.570059	+	0.821604i	$0.306920\pi$
$443$	−5.19088	+	29.4390i	−0.246626	+	1.39869i	−0.816685	+	0.577084i	$0.804191\pi$
$444$	−1.31521	+	2.27801i	−0.0624170	+	0.108109i
$445$	4.52481	+	7.83721i	0.214497	+	0.371519i
$446$	−10.7738	+	3.92134i	−0.510154	+	0.185681i
$447$	44.8055	−	16.3079i	2.11923	−	0.771335i
$448$	−1.49273	−	2.58548i	−0.0705247	−	0.122152i
$449$	5.62495	−	9.74270i	0.265458	−	0.459787i	−0.702226	−	0.711955i	$-0.747810\pi$
$449$	5.62495	−	9.74270i	0.265458	−	0.459787i	0.967683	+	0.252168i	$0.0811435\pi$
$450$	5.23190	−	29.6716i	0.246634	−	1.39873i
$451$	−4.22281	+	3.54336i	−0.198844	+	0.166850i
$452$	2.50387	+	2.10100i	0.117772	+	0.0988226i
$453$	2.18092	+	12.3686i	0.102469	+	0.581129i
$454$	−17.9153	−	6.52065i	−0.840809	−	0.306029i
$455$	0.786112			0.0368535
$456$		0			0
$457$	−23.3901			−1.09414			−0.547072	−	0.837086i	$-0.684258\pi$
$457$	−23.3901			−1.09414			−0.547072	+	0.837086i	$0.684258\pi$
$458$	−25.9957	−	9.46167i	−1.21470	−	0.442115i
$459$	−0.535959	−	3.03958i	−0.0250164	−	0.141875i
$460$	0.335437	+	0.281465i	0.0156398	+	0.0131234i
$461$	−28.0553	+	23.5412i	−1.30667	+	1.09642i	−0.317714	+	0.948187i	$0.602915\pi$
$461$	−28.0553	+	23.5412i	−1.30667	+	1.09642i	−0.988952	+	0.148237i	$0.952640\pi$
$462$	−0.520945	+	2.95442i	−0.0242365	+	0.137452i
$463$	21.4932	−	37.2273i	0.998873	−	1.73010i	0.458340	−	0.888777i	$-0.348444\pi$
$463$	21.4932	−	37.2273i	0.998873	−	1.73010i	0.540534	−	0.841322i	$-0.318222\pi$
$464$	−12.3701	−	21.4256i	−0.574265	−	0.994657i
$465$	−16.9081	+	6.15403i	−0.784093	+	0.285387i
$466$	22.3469	−	8.13360i	1.03520	−	0.376782i
$467$	−12.7981	−	22.1670i	−0.592227	−	1.02577i	−0.993932	−	0.109998i	$-0.964916\pi$
$467$	−12.7981	−	22.1670i	−0.592227	−	1.02577i	0.401705	−	0.915769i	$-0.368418\pi$
$468$	1.25830	−	2.17945i	0.0581651	−	0.100745i
$469$	0.462859	−	2.62500i	0.0213728	−	0.121211i
$470$	6.61721	−	5.55250i	0.305229	−	0.256118i
$471$	21.2160	+	17.8023i	0.977582	+	0.820289i
$472$	−3.22297	−	18.2784i	−0.148349	−	0.841331i
$473$	8.16385	+	2.97140i	0.375374	+	0.136625i
$474$	−45.9522			−2.11066
$475$		0			0
$476$	−0.0300295			−0.00137640
$477$	14.1074	+	5.13468i	0.645934	+	0.235101i
$478$	−0.550345	−	3.12116i	−0.0251722	−	0.142759i
$479$	29.2447	+	24.5392i	1.33622	+	1.12123i	0.982579	+	0.185845i	$0.0595023\pi$
$479$	29.2447	+	24.5392i	1.33622	+	1.12123i	0.353645	+	0.935380i	$0.384942\pi$
$480$	2.02094	−	1.69577i	0.0922431	−	0.0774011i
$481$	2.20961	−	12.5313i	0.100749	−	0.571378i
$482$	9.29679	−	16.1025i	0.423457	−	0.733449i
$483$	−1.34730	−	2.33359i	−0.0613041	−	0.106182i
$484$	−1.04916	+	0.381864i	−0.0476892	+	0.0173575i
$485$	−7.81180	+	2.84326i	−0.354716	+	0.129106i
$486$	7.27766	+	12.6053i	0.330121	+	0.571787i
$487$	−3.88191	+	6.72367i	−0.175906	+	0.304678i	−0.940475	−	0.339864i	$-0.889619\pi$
$487$	−3.88191	+	6.72367i	−0.175906	+	0.304678i	0.764568	+	0.644543i	$0.222952\pi$
$488$	4.66591	−	26.4617i	0.211216	−	1.19786i
$489$	−18.4290	+	15.4638i	−0.833389	+	0.699296i
$490$	6.24376	+	5.23913i	0.282064	+	0.236680i
$491$	−6.37686	−	36.1650i	−0.287784	−	1.63210i	−0.695169	−	0.718846i	$-0.744671\pi$
$491$	−6.37686	−	36.1650i	−0.287784	−	1.63210i	0.407386	−	0.913256i	$-0.366440\pi$
$492$	−1.23783	−	0.450532i	−0.0558055	−	0.0203115i
$493$	−3.21894			−0.144974
$494$		0			0
$495$	−10.3601			−0.465651
$496$	−24.0141	−	8.74043i	−1.07827	−	0.392457i
$497$	−0.561185	−	3.18264i	−0.0251726	−	0.142761i
$498$	−44.0736	−	36.9821i	−1.97498	−	1.65721i
$499$	3.77379	−	3.16658i	0.168938	−	0.141756i	−0.554399	−	0.832251i	$-0.687052\pi$
$499$	3.77379	−	3.16658i	0.168938	−	0.141756i	0.723337	+	0.690495i	$0.242607\pi$
$500$	0.260363	−	1.47659i	0.0116438	−	0.0660352i
$501$	5.80928	−	10.0620i	0.259539	−	0.449535i
$502$	−2.80587	−	4.85992i	−0.125232	−	0.216909i
$503$	−30.9624	+	11.2694i	−1.38055	+	0.502478i	−0.922344	−	0.386369i	$-0.873729\pi$
$503$	−30.9624	+	11.2694i	−1.38055	+	0.502478i	−0.458203	+	0.888847i	$0.651507\pi$
$504$	−5.08260	+	1.84991i	−0.226397	+	0.0824017i
$505$	4.06670	+	7.04374i	0.180966	+	0.313442i
$506$	4.04189	−	7.00076i	0.179684	−	0.311222i
$507$	3.18732	−	18.0762i	0.141554	−	0.802791i
$508$	−1.64266	+	1.37835i	−0.0728810	+	0.0611544i
$509$	−28.2939	−	23.7414i	−1.25410	−	1.05232i	−0.996284	−	0.0861240i	$-0.972552\pi$
$509$	−28.2939	−	23.7414i	−1.25410	−	1.05232i	−0.257819	−	0.966193i	$-0.583004\pi$
$510$	0.277189	+	1.57202i	0.0122741	+	0.0696100i
$511$	−0.453363	−	0.165011i	−0.0200556	−	0.00729964i
$512$	24.9186			1.10126
$513$		0			0
$514$	−0.898986			−0.0396526
$515$	4.55303	+	1.65717i	0.200631	+	0.0730236i
$516$	0.360500	+	2.04450i	0.0158701	+	0.0900040i
$517$	12.4363	+	10.4353i	0.546947	+	0.458943i
$518$	−1.77197	+	1.48686i	−0.0778561	+	0.0653290i
$519$	10.0719	−	57.1207i	0.442108	−	2.50732i
$520$	−3.33140	+	5.77016i	−0.146092	+	0.253038i
$521$	−4.64590	−	8.04693i	−0.203540	−	0.352542i	0.746126	−	0.665804i	$-0.231912\pi$
$521$	−4.64590	−	8.04693i	−0.203540	−	0.352542i	−0.949667	+	0.313262i	$0.898578\pi$
$522$	−46.0813	+	16.7722i	−2.01692	+	0.734100i
$523$	26.7015	−	9.71854i	1.16757	−	0.424962i	0.315776	−	0.948834i	$-0.397735\pi$
$523$	26.7015	−	9.71854i	1.16757	−	0.424962i	0.851797	+	0.523872i	$0.175513\pi$
$524$	0.170493	+	0.295303i	0.00744802	+	0.0129004i
$525$	−2.11334	+	3.66041i	−0.0922338	+	0.159754i
$526$	−2.66700	+	15.1253i	−0.116287	+	0.659496i
$527$	−2.54710	+	2.13727i	−0.110954	+	0.0931011i
$528$	−17.6630	−	14.8210i	−0.768682	−	0.645001i
$529$	−2.73308	−	15.5001i	−0.118829	−	0.673916i
$530$	−3.15910	−	1.14982i	−0.137223	−	0.0499449i
$531$	−33.3610			−1.44775
$532$		0			0
$533$	6.37227			0.276014
$534$	37.5146	+	13.6542i	1.62342	+	0.590875i
$535$	1.56283	+	8.86327i	0.0675672	+	0.383193i
$536$	17.3063	+	14.5217i	0.747520	+	0.627244i
$537$	25.3935	−	21.3077i	1.09581	−	0.919495i
$538$	−4.53643	+	25.7274i	−0.195579	+	1.10918i
$539$	−7.65910	+	13.2660i	−0.329901	+	0.571405i
$540$	−0.535959	−	0.928309i	−0.0230640	−	0.0399480i
$541$	−14.0817	+	5.12533i	−0.605420	+	0.220355i	−0.626498	−	0.779423i	$-0.715512\pi$
$541$	−14.0817	+	5.12533i	−0.605420	+	0.220355i	0.0210779	+	0.999778i	$0.493290\pi$
$542$	−16.9577	+	6.17210i	−0.728396	+	0.265114i
$543$	12.2909	+	21.2884i	0.527451	+	0.913572i
$544$	0.243756	−	0.422197i	0.0104509	−	0.0181016i
$545$	−0.278371	+	1.57872i	−0.0119241	+	0.0676249i
$546$	2.65657	−	2.22913i	0.113691	−	0.0953980i
$547$	−2.97771	−	2.49860i	−0.127318	−	0.106832i	0.576905	−	0.816811i	$-0.304260\pi$
$547$	−2.97771	−	2.49860i	−0.127318	−	0.106832i	−0.704223	+	0.709979i	$0.748705\pi$
$548$	−0.00820761	−	0.0465477i	−0.000350612	−	0.00198842i
$549$	−45.3842	−	16.5185i	−1.93695	−	0.704992i
$550$	−12.6800			−0.540679
$551$		0			0
$552$	22.8384			0.972068
$553$	3.86571	+	1.40701i	0.164387	+	0.0598319i
$554$	−4.15199	−	23.5471i	−0.176401	−	1.00042i
$555$	−9.58899	−	8.04612i	−0.407030	−	0.341539i
$556$	−0.603541	+	0.506431i	−0.0255958	+	0.0214774i
$557$	2.29292	−	13.0038i	0.0971541	−	0.550988i	−0.896912	−	0.442209i	$-0.854195\pi$
$557$	2.29292	−	13.0038i	0.0971541	−	0.550988i	0.994066	−	0.108779i	$-0.0346940\pi$
$558$	−25.3273	+	43.8681i	−1.07219	+	1.85709i
$559$	−5.02141	−	8.69734i	−0.212383	−	0.367858i
$560$	1.03209	−	0.375650i	0.0436137	−	0.0158741i
$561$	−2.81908	+	1.02606i	−0.119022	+	0.0433203i
$562$	12.3136	+	21.3278i	0.519418	+	0.899659i
$563$	−5.35638	+	9.27752i	−0.225745	+	0.391001i	−0.956543	−	0.291593i	$-0.905815\pi$
$563$	−5.35638	+	9.27752i	−0.225745	+	0.391001i	0.730798	+	0.682594i	$0.239148\pi$
$564$	−0.673648	+	3.82045i	−0.0283657	+	0.160870i
$565$	−11.9153	+	9.99816i	−0.501282	+	0.420626i
$566$	−7.93448	−	6.65782i	−0.333511	−	0.279849i
$567$	0.188196	+	1.06731i	0.00790349	+	0.0448229i
$568$	25.7392	+	9.36829i	1.07999	+	0.393085i
$569$	−13.4706			−0.564717			−0.282358	−	0.959309i	$-0.591117\pi$
$569$	−13.4706			−0.564717			−0.282358	+	0.959309i	$0.591117\pi$
$570$		0			0
$571$	12.6655			0.530035			0.265017	−	0.964244i	$-0.414622\pi$
$571$	12.6655			0.530035			0.265017	+	0.964244i	$0.414622\pi$
$572$	−0.995252	−	0.362242i	−0.0416136	−	0.0151461i
$573$	−9.16772	−	51.9927i	−0.382987	−	2.17203i
$574$	−0.887374	−	0.744596i	−0.0370383	−	0.0310788i
$575$	8.72462	−	7.32083i	0.363842	−	0.305300i
$576$	7.89780	−	44.7907i	0.329075	−	1.86628i
$577$	5.27719	−	9.14036i	0.219692	−	0.380518i	−0.735022	−	0.678044i	$-0.762828\pi$
$577$	5.27719	−	9.14036i	0.219692	−	0.380518i	0.954714	+	0.297526i	$0.0961613\pi$
$578$	−11.3045	−	19.5800i	−0.470206	−	0.814421i
$579$	0.805407	−	0.293144i	0.0334716	−	0.0121827i
$580$	−1.05051	+	0.382353i	−0.0436199	+	0.0158764i
$581$	2.57532	+	4.46059i	0.106842	+	0.185056i
$582$	−18.3366	+	31.7600i	−0.760077	+	1.31649i
$583$	1.09714	−	6.22221i	0.0454391	−	0.257698i
$584$	3.13247	−	2.62846i	0.129623	−	0.108766i
$585$	9.17412	+	7.69800i	0.379303	+	0.318273i
$586$	2.45723	+	13.9357i	0.101507	+	0.575677i
$587$	17.9996	+	6.55131i	0.742923	+	0.270402i	0.685624	−	0.727955i	$-0.259529\pi$
$587$	17.9996	+	6.55131i	0.742923	+	0.270402i	0.0572981	+	0.998357i	$0.481751\pi$
$588$	−3.66044			−0.150954
$589$		0			0
$590$	7.47060			0.307560
$591$	35.5565	+	12.9415i	1.46260	+	0.532342i
$592$	−3.08718	−	17.5083i	−0.126882	−	0.719586i
$593$	−6.66044	−	5.58878i	−0.273512	−	0.229504i	0.495706	−	0.868490i	$-0.334909\pi$
$593$	−6.66044	−	5.58878i	−0.273512	−	0.229504i	−0.769218	+	0.638987i	$0.779354\pi$
$594$	−15.1591	+	12.7200i	−0.621985	+	0.521908i
$595$	0.0248149	−	0.140732i	0.00101731	−	0.00576947i
$596$	1.53003	−	2.65009i	0.0626724	−	0.108552i
$597$	−0.369585	−	0.640140i	−0.0151261	−	0.0261992i
$598$	−8.78106	+	3.19604i	−0.359084	+	0.130696i
$599$	−18.6356	+	6.78281i	−0.761431	+	0.277138i	−0.693408	−	0.720545i	$-0.743891\pi$
$599$	−18.6356	+	6.78281i	−0.761431	+	0.277138i	−0.0680235	+	0.997684i	$0.521669\pi$
$600$	−17.9119	−	31.0244i	−0.731252	−	1.26657i
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	−0.283718	−	0.958908i	$-0.591568\pi$
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	0.972298	−	0.233747i	$-0.0750986\pi$
$602$	−0.317018	+	1.79790i	−0.0129207	+	0.0732770i
$603$	31.1070	−	26.1019i	1.26677	−	1.06295i
$604$	0.617460	+	0.518110i	0.0251241	+	0.0210816i
$605$	−0.922618	−	5.23243i	−0.0375098	−	0.212729i
$606$	33.7165	+	12.2718i	1.36964	+	0.498507i
$607$	35.2850			1.43217			0.716087	−	0.698011i	$-0.245932\pi$
$607$	35.2850			1.43217			0.716087	+	0.698011i	$0.245932\pi$
$608$		0			0
$609$	6.87939			0.278767
$610$	10.1630	+	3.69902i	0.411487	+	0.149769i
$611$	−3.25877	−	18.4814i	−0.131836	−	0.747678i
$612$	−0.350452	−	0.294064i	−0.0141662	−	0.0118868i
$613$	14.1361	−	11.8616i	0.570952	−	0.479085i	−0.311010	−	0.950407i	$-0.600667\pi$
$613$	14.1361	−	11.8616i	0.570952	−	0.479085i	0.881962	+	0.471321i	$0.156223\pi$
$614$	2.73623	−	15.5180i	0.110425	−	0.626254i
$615$	3.13429	−	5.42874i	0.126387	−	0.218908i
$616$	1.13816	+	1.97134i	0.0458576	+	0.0794277i
$617$	33.5333	−	12.2051i	1.35000	−	0.491360i	0.437053	−	0.899436i	$-0.356022\pi$
$617$	33.5333	−	12.2051i	1.35000	−	0.491360i	0.912948	+	0.408076i	$0.133800\pi$
$618$	20.0856	−	7.31056i	0.807961	−	0.294074i
$619$	−1.82976	−	3.16923i	−0.0735441	−	0.127382i	0.826908	−	0.562337i	$-0.190098\pi$
$619$	−1.82976	−	3.16923i	−0.0735441	−	0.127382i	−0.900452	+	0.434955i	$0.856764\pi$
$620$	−0.577382	+	1.00005i	−0.0231882	+	0.0401631i
$621$	3.08647	−	17.5042i	0.123856	−	0.702420i
$622$	−16.4782	+	13.8268i	−0.660715	+	0.554406i
$623$	−2.73783	−	2.29731i	−0.109689	−	0.0920397i
$624$	4.62836	+	26.2487i	0.185283	+	1.05079i
$625$	−13.1540	−	4.78768i	−0.526162	−	0.191507i
$626$	35.8767			1.43392
$627$		0			0
$628$	1.77744			0.0709275
$629$	−2.17365	−	0.791143i	−0.0866690	−	0.0315449i
$630$	−0.378041	−	2.14398i	−0.0150615	−	0.0854181i
$631$	−0.608126	−	0.510278i	−0.0242091	−	0.0203139i	0.630603	−	0.776106i	$-0.282808\pi$
$631$	−0.608126	−	0.510278i	−0.0242091	−	0.0203139i	−0.654812	+	0.755792i	$0.727252\pi$
$632$	−26.7098	+	22.4122i	−1.06246	+	0.891510i
$633$	−1.22416	+	6.94253i	−0.0486558	+	0.275941i
$634$	19.8942	−	34.4578i	0.790101	−	1.36850i
$635$	−5.10220	−	8.83726i	−0.202474	−	0.350696i
$636$	1.41875	−	0.516382i	0.0562570	−	0.0204759i
$637$	16.6395	−	6.05628i	0.659281	−	0.239959i
$638$	10.3191	+	17.8732i	0.408536	+	0.707605i
$639$	24.6168	−	42.6375i	0.973826	−	1.68672i
$640$	−1.45037	+	8.22546i	−0.0573309	+	0.325140i
$641$	22.5082	−	18.8866i	0.889021	−	0.745977i	−0.0789927	−	0.996875i	$-0.525170\pi$
$641$	22.5082	−	18.8866i	0.889021	−	0.745977i	0.968013	+	0.250898i	$0.0807259\pi$
$642$	30.4145	+	25.5208i	1.20036	+	1.00722i
$643$	3.85740	+	21.8764i	0.152121	+	0.862721i	0.961371	+	0.275257i	$0.0887628\pi$
$643$	3.85740	+	21.8764i	0.152121	+	0.862721i	−0.809250	+	0.587465i	$0.800126\pi$
$644$	−0.162504	−	0.0591466i	−0.00640355	−	0.00233070i
$645$	−9.87939			−0.389000
$646$		0			0
$647$	11.2591			0.442640			0.221320	−	0.975201i	$-0.428963\pi$
$647$	11.2591			0.442640			0.221320	+	0.975201i	$0.428963\pi$
$648$	−8.63176	−	3.14170i	−0.339088	−	0.123418i
$649$	2.43804	+	13.8268i	0.0957016	+	0.542751i
$650$	11.2285	+	9.42182i	0.440418	+	0.369554i
$651$	5.44356	−	4.56769i	0.213350	−	0.179022i
$652$	−0.268104	+	1.52049i	−0.0104998	+	0.0595471i
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$	3.53596	+	6.12446i	0.138267	+	0.239485i
$655$	−1.52481	+	0.554987i	−0.0595794	+	0.0216851i
$656$	8.36618	−	3.04504i	0.326645	−	0.118889i
$657$	−3.67499	−	6.36527i	−0.143375	−	0.248333i
$658$	−1.70574	+	2.95442i	−0.0664966	+	0.115175i
$659$	4.86665	−	27.6001i	0.189578	−	1.07515i	−0.730354	−	0.683069i	$-0.760645\pi$
$659$	4.86665	−	27.6001i	0.189578	−	1.07515i	0.919931	−	0.392079i	$-0.128244\pi$
$660$	−0.798133	+	0.669713i	−0.0310673	+	0.0260686i
$661$	8.70826	+	7.30710i	0.338712	+	0.284213i	0.796239	−	0.604983i	$-0.206820\pi$
$661$	8.70826	+	7.30710i	0.338712	+	0.284213i	−0.457526	+	0.889196i	$0.651264\pi$
$662$	−6.47250	−	36.7074i	−0.251561	−	1.42667i
$663$	3.25877	+	1.18610i	0.126560	+	0.0460641i
$664$	−43.6551			−1.69415
$665$		0			0
$666$	−35.2395			−1.36550
$667$	−17.4192	−	6.34008i	−0.674475	−	0.245489i
$668$	−0.129481	−	0.734325i	−0.00500978	−	0.0284119i
$669$	18.7704	+	15.7502i	0.725705	+	0.608939i
$670$	−6.96585	+	5.84504i	−0.269114	+	0.225814i
$671$	−3.52956	+	20.0171i	−0.136257	+	0.772753i
$672$	−0.520945	+	0.902302i	−0.0200959	+	0.0348071i
$673$	8.28359	+	14.3476i	0.319309	+	0.553059i	0.980344	−	0.197296i	$-0.0632160\pi$
$673$	8.28359	+	14.3476i	0.319309	+	0.553059i	−0.661035	+	0.750355i	$0.729883\pi$
$674$	22.6113	−	8.22983i	0.870954	−	0.317001i
$675$	−26.1989	+	9.53563i	−1.00840	+	0.367027i
$676$	−0.588993	−	1.02017i	−0.0226536	−	0.0392371i
$677$	4.52481	−	7.83721i	0.173903	−	0.301208i	−0.765878	−	0.642986i	$-0.777695\pi$
$677$	4.52481	−	7.83721i	0.173903	−	0.301208i	0.939781	+	0.341777i	$0.111029\pi$
$678$	−11.9153	+	67.5753i	−0.457606	+	2.59521i
$679$	2.51501	−	2.11035i	0.0965174	−	0.0809877i
$680$	0.927833	+	0.778544i	0.0355808	+	0.0298558i
$681$	7.07532	+	40.1261i	0.271127	+	1.53764i
$682$	20.0326	+	7.29125i	0.767086	+	0.279197i
$683$	8.73143			0.334099			0.167049	−	0.985949i	$-0.446576\pi$
$683$	8.73143			0.334099			0.167049	+	0.985949i	$0.446576\pi$
$684$		0			0
$685$	0.224927			0.00859402
$686$	−6.10266	−	2.22119i	−0.233001	−	0.0848053i
$687$	10.2665	+	58.2243i	0.391692	+	2.22139i
$688$	−10.7487	−	9.01925i	−0.409791	−	0.343856i
$689$	−5.59492	+	4.69470i	−0.213150	+	0.178854i
$690$	−1.59627	+	9.05288i	−0.0607688	+	0.344637i
$691$	−17.3601	+	30.0686i	−0.660409	+	1.14386i	0.320099	+	0.947384i	$0.396284\pi$
$691$	−17.3601	+	30.0686i	−0.660409	+	1.14386i	−0.980508	+	0.196478i	$0.937050\pi$
$692$	−1.86122	−	3.22372i	−0.0707528	−	0.122547i
$693$	3.84477	−	1.39938i	0.146051	−	0.0531581i
$694$	−7.34389	+	2.67296i	−0.278770	+	0.101464i
$695$	−1.87464	−	3.24697i	−0.0711091	−	0.123164i
$696$	−29.1536	+	50.4956i	−1.10507	+	1.91403i
$697$	0.201151	−	1.14079i	0.00761915	−	0.0432104i
$698$	−5.54466	+	4.65253i	−0.209869	+	0.176101i
$699$	−38.9334	−	32.6690i	−1.47259	−	1.23565i
$700$	0.0471036	+	0.267138i	0.00178035	+	0.0100969i
$701$	−37.0381	−	13.4808i	−1.39891	−	0.509161i	−0.471055	−	0.882104i	$-0.656126\pi$
$701$	−37.0381	−	13.4808i	−1.39891	−	0.509161i	−0.927854	+	0.372943i	$0.878349\pi$
$702$	22.8753			0.863371
$703$		0			0
$704$	−19.1411			−0.721409
$705$	−17.3478	−	6.31407i	−0.653355	−	0.237802i
$706$	5.90373	+	33.4817i	0.222190	+	1.26010i
$707$	−2.46064	−	2.06472i	−0.0925418	−	0.0776518i
$708$	−2.57011	+	2.15658i	−0.0965906	+	0.0810491i
$709$	−7.14068	+	40.4968i	−0.268174	+	1.52089i	0.491668	+	0.870783i	$0.336387\pi$
$709$	−7.14068	+	40.4968i	−0.268174	+	1.52089i	−0.759842	+	0.650107i	$0.774724\pi$
$710$	−5.51249	+	9.54791i	−0.206880	+	0.358327i
$711$	31.3357	+	54.2751i	1.17518	+	2.03548i
$712$	28.4650	−	10.3604i	1.06677	−	0.388273i
$713$	−17.9932	+	6.54899i	−0.673850	+	0.245261i
$714$	−0.315207	−	0.545955i	−0.0117963	−	0.0204319i
$715$	2.52007	−	4.36488i	0.0942452	−	0.163237i
$716$	0.369423	−	2.09510i	0.0138060	−	0.0782976i
$717$	−5.18866	+	4.35381i	−0.193774	+	0.162596i
$718$	−6.90143	−	5.79098i	−0.257559	−	0.216118i
$719$	−7.36190	−	41.7514i	−0.274553	−	1.55706i	−0.740379	−	0.672189i	$-0.765354\pi$
$719$	−7.36190	−	41.7514i	−0.274553	−	1.55706i	0.465827	−	0.884876i	$-0.345757\pi$
$720$	15.7233	+	5.72281i	0.585972	+	0.213276i
$721$	−1.91353			−0.0712637
$722$		0			0
$723$	−39.7374			−1.47785
$724$	1.48246	+	0.539571i	0.0550952	+	0.0200530i
$725$	5.04916	+	28.6352i	0.187521	+	1.06349i
$726$	−17.9552	−	15.0662i	−0.666379	−	0.559158i
$727$	39.5710	−	33.2040i	1.46761	−	1.23147i	0.549288	−	0.835633i	$-0.314899\pi$
$727$	39.5710	−	33.2040i	1.46761	−	1.23147i	0.918321	−	0.395837i	$-0.129545\pi$
$728$	0.456929	−	2.59137i	0.0169349	−	0.0960427i
$729$	20.2344	−	35.0470i	0.749423	−	1.29804i
$730$	0.822948	+	1.42539i	0.0304587	+	0.0527560i
$731$	−1.71554	+	0.624404i	−0.0634514	+	0.0230944i
$732$	−4.56418	+	1.66122i	−0.168697	+	0.0614006i
$733$	11.4581	+	19.8460i	0.423215	+	0.733030i	0.996252	−	0.0864997i	$-0.0275682\pi$
$733$	11.4581	+	19.8460i	0.423215	+	0.733030i	−0.573037	+	0.819530i	$0.694235\pi$
$734$	5.46926	−	9.47303i	0.201874	−	0.349656i
$735$	3.02481	−	17.1546i	0.111572	−	0.632756i
$736$	2.15064	−	1.80460i	0.0792738	−	0.0665186i
$737$	−13.0915	−	10.9851i	−0.482232	−	0.404641i
$738$	−3.06443	−	17.3792i	−0.112803	−	0.639738i
$739$	−26.4304	−	9.61986i	−0.972256	−	0.353872i	−0.193432	−	0.981114i	$-0.561962\pi$
$739$	−26.4304	−	9.61986i	−0.972256	−	0.353872i	−0.778825	+	0.627241i	$0.784184\pi$
$740$	−0.803348			−0.0295317
$741$		0			0
$742$	1.32770			0.0487413
$743$	−5.76264	−	2.09743i	−0.211411	−	0.0769472i	0.234144	−	0.972202i	$-0.424771\pi$
$743$	−5.76264	−	2.09743i	−0.211411	−	0.0769472i	−0.445555	+	0.895255i	$0.646994\pi$
$744$	10.4586	+	59.3135i	0.383430	+	2.17454i
$745$	11.1552	+	9.36035i	0.408696	+	0.342937i
$746$	−36.0174	+	30.2222i	−1.31869	+	1.10651i
$747$	−13.6257	+	77.2750i	−0.498537	+	2.82734i
$748$	−0.0962667	+	0.166739i	−0.00351986	+	0.00609657i
$749$	−1.77719	−	3.07818i	−0.0649371	−	0.112474i
$750$	29.5783	−	10.7656i	1.08005	−	0.393105i
$751$	−5.30066	+	1.92928i	−0.193424	+	0.0704005i	−0.436916	−	0.899502i	$-0.643929\pi$
$751$	−5.30066	+	1.92928i	−0.193424	+	0.0704005i	0.243492	+	0.969903i	$0.421707\pi$
$752$	−13.1099	−	22.7071i	−0.478070	−	0.828042i
$753$	−5.99660	+	10.3864i	−0.218528	+	0.378502i
$754$	4.14274	−	23.4947i	0.150870	−	0.855625i
$755$	−2.93835	+	2.46557i	−0.106937	+	0.0897312i
$756$	0.324292	+	0.272114i	0.0117944	+	0.00989668i
$757$	2.72487	+	15.4535i	0.0990371	+	0.561667i	0.993435	+	0.114396i	$0.0364932\pi$
$757$	2.72487	+	15.4535i	0.0990371	+	0.561667i	−0.894398	+	0.447272i	$0.852396\pi$
$758$	2.15405	+	0.784009i	0.0782385	+	0.0284765i
$759$	−17.2763			−0.627090
$760$		0			0
$761$	4.86484			0.176350			0.0881751	−	0.996105i	$-0.471896\pi$
$761$	4.86484			0.176350			0.0881751	+	0.996105i	$0.471896\pi$
$762$	−42.3016	−	15.3965i	−1.53243	−	0.557757i
$763$	−0.109937	−	0.623485i	−0.00398000	−	0.0225717i
$764$	−2.59555	−	2.17793i	−0.0939038	−	0.0787946i
$765$	1.66772	−	1.39938i	0.0602965	−	0.0505948i
$766$	−0.687070	+	3.89657i	−0.0248249	+	0.140789i
$767$	8.11499	−	14.0556i	0.293015	−	0.507517i
$768$	−6.32888	−	10.9619i	−0.228374	−	0.395555i
$769$	−21.1732	+	7.70643i	−0.763526	+	0.277901i	−0.694286	−	0.719699i	$-0.744280\pi$
$769$	−21.1732	+	7.70643i	−0.763526	+	0.277901i	−0.0692404	+	0.997600i	$0.522058\pi$
$770$	−0.860967	+	0.313366i	−0.0310271	+	0.0112929i
$771$	0.960637	+	1.66387i	0.0345965	+	0.0599229i
$772$	0.0275033	−	0.0476371i	0.000989864	−	0.00171450i
$773$	−4.58987	+	26.0304i	−0.165086	+	0.936250i	0.783889	+	0.620900i	$0.213233\pi$
$773$	−4.58987	+	26.0304i	−0.165086	+	0.936250i	−0.948976	+	0.315350i	$0.897878\pi$
$774$	−21.3056	+	17.8775i	−0.765815	+	0.642595i
$775$	23.0082	+	19.3062i	0.826479	+	0.693498i
$776$	4.83203	+	27.4038i	0.173460	+	0.983740i
$777$	4.64543	+	1.69080i	0.166654	+	0.0606570i
$778$	33.0993			1.18667
$779$		0			0
$780$	1.20439			0.0431242
$781$	−19.4706	−	7.08672i	−0.696713	−	0.253583i
$782$	0.294978	+	1.67290i	0.0105484	+	0.0598229i
$783$	34.7618	+	29.1686i	1.24228	+	1.04240i
$784$	18.9520	−	15.9026i	0.676858	−	0.567951i
$785$	−1.46879	+	8.32991i	−0.0524233	+	0.297307i
$786$	−3.57919	+	6.19934i	−0.127666	+	0.221123i
$787$	7.77884	+	13.4733i	0.277286	+	0.480273i	0.970709	−	0.240257i	$-0.0772318\pi$
$787$	7.77884	+	13.4733i	0.277286	+	0.480273i	−0.693424	+	0.720530i	$0.743899\pi$
$788$	2.28194	−	0.830557i	0.0812906	−	0.0295874i
$789$	30.8444	−	11.2264i	1.09809	−	0.399671i
$790$	−7.01707	−	12.1539i	−0.249656	−	0.432417i
$791$	3.07145	−	5.31991i	0.109208	−	0.189154i
$792$	−6.02182	+	34.1514i	−0.213976	+	1.21352i
$793$	17.9991	−	15.1031i	0.639168	−	0.536325i
$794$	32.8573	+	27.5706i	1.16606	+	0.978443i
$795$	1.24763	+	7.07564i	0.0442487	+	0.250947i
$796$	−0.0445774	−	0.0162249i	−0.00158000	−	0.000575075i
$797$	33.4935			1.18640			0.593200	−	0.805055i	$-0.297864\pi$
$797$	33.4935			1.18640			0.593200	+	0.805055i	$0.297864\pi$
$798$		0			0
$799$	−3.41147			−0.120689
$800$	−4.13816	−	1.50617i	−0.146306	−	0.0532510i
$801$	−9.45471	−	53.6203i	−0.334066	−	1.89458i
$802$	0.0892411	+	0.0748822i	0.00315121	+	0.00264418i
$803$	−2.36959	+	1.98832i	−0.0836208	+	0.0701662i
$804$	0.709141	−	4.02174i	0.0250095	−	0.141836i
$805$	0.411474	−	0.712694i	0.0145026	−	0.0251192i
$806$	−12.3216	−	21.3416i	−0.434010	−	0.751727i
$807$	52.4646	−	19.0955i	1.84684	−	0.672195i
$808$	25.5831	−	9.31147i	0.900009	−	0.327576i
$809$	−20.5581	−	35.6076i	−0.722784	−	1.25190i	−0.959880	−	0.280412i	$-0.909529\pi$
$809$	−20.5581	−	35.6076i	−0.722784	−	1.25190i	0.237096	−	0.971486i	$-0.423804\pi$
$810$	1.84864	−	3.20194i	0.0649546	−	0.112505i
$811$	2.89780	−	16.4343i	0.101756	−	0.577085i	−0.890711	−	0.454570i	$-0.849793\pi$
$811$	2.89780	−	16.4343i	0.101756	−	0.577085i	0.992467	−	0.122515i	$-0.0390959\pi$
$812$	0.338211	−	0.283793i	0.0118689	−	0.00995918i
$813$	29.5442	+	24.7905i	1.03616	+	0.869441i
$814$	2.57532	+	14.6054i	0.0902650	+	0.511918i
$815$	−6.90420	−	2.51292i	−0.241844	−	0.0880239i
$816$	4.84524			0.169617
$817$		0			0
$818$	−26.9540			−0.942424
$819$	−4.44444	−	1.61764i	−0.155301	−	0.0565251i
$820$	−0.0698592	−	0.396191i	−0.00243959	−	0.0138356i
$821$	−24.0462	−	20.1772i	−0.839219	−	0.704188i	0.118169	−	0.992994i	$-0.462298\pi$
$821$	−24.0462	−	20.1772i	−0.839219	−	0.704188i	−0.957388	+	0.288805i	$0.906742\pi$
$822$	0.760115	−	0.637812i	0.0265120	−	0.0222462i
$823$	8.04442	−	45.6221i	0.280411	−	1.59029i	−0.440822	−	0.897595i	$-0.645313\pi$
$823$	8.04442	−	45.6221i	0.280411	−	1.59029i	0.721232	−	0.692693i	$-0.243576\pi$
$824$	8.10922	−	14.0456i	0.282498	−	0.489301i
$825$	13.5496	+	23.4686i	0.471738	+	0.817073i
$826$	−2.77244	+	1.00909i	−0.0964656	+	0.0351106i
$827$	−38.3007	+	13.9403i	−1.33185	+	0.484752i	−0.907235	−	0.420623i	$-0.861811\pi$
$827$	−38.3007	+	13.9403i	−1.33185	+	0.484752i	−0.424611	+	0.905376i	$0.639589\pi$
$828$	−1.31727	−	2.28157i	−0.0457782	−	0.0792901i
$829$	17.7417	−	30.7295i	0.616195	−	1.06728i	−0.373979	−	0.927437i	$-0.622007\pi$
$829$	17.7417	−	30.7295i	0.616195	−	1.06728i	0.990174	−	0.139843i	$-0.0446598\pi$
$830$	3.05122	−	17.3043i	0.105909	−	0.600642i
$831$	−39.1450	+	32.8466i	−1.35793	+	1.13943i
$832$	16.9500	+	14.2227i	0.587634	+	0.493084i
$833$	−0.558963	−	3.17004i	−0.0193669	−	0.109835i
$834$	−15.5424	−	5.65695i	−0.538188	−	0.195884i
$835$	3.54839			0.122797
$836$		0			0
$837$	46.8735			1.62019
$838$	32.1698	+	11.7089i	1.11129	+	0.404476i
$839$	−6.63382	−	37.6223i	−0.229025	−	1.29886i	−0.854839	−	0.518893i	$-0.826344\pi$
$839$	−6.63382	−	37.6223i	−0.229025	−	1.29886i	0.625815	−	0.779972i	$-0.284767\pi$
$840$	−1.98293	−	1.66387i	−0.0684174	−	0.0574091i
$841$	14.0385	−	11.7797i	0.484086	−	0.406196i
$842$	−1.02229	+	5.79769i	−0.0352304	+	0.199802i
$843$	26.3161	−	45.5809i	0.906376	−	1.56989i
$844$	0.226215	+	0.391815i	0.00778663	+	0.0134868i
$845$	5.26769	−	1.91728i	0.181214	−	0.0659566i
$846$	−48.8376	+	17.7754i	−1.67907	+	0.611131i
$847$	1.04916	+	1.81720i	0.0360497	+	0.0624399i
$848$	−5.10220	+	8.83726i	−0.175210	+	0.303473i
$849$	−3.84389	+	21.7998i	−0.131922	+	0.748167i
$850$	2.04117	−	1.71275i	0.0700117	−	0.0587468i
$851$	−10.2044	−	8.56250i	−0.349802	−	0.293519i
$852$	−0.859785	−	4.87608i	−0.0294557	−	0.167052i
$853$	24.0577	+	8.75628i	0.823719	+	0.299809i	0.719278	−	0.694722i	$-0.244473\pi$
$853$	24.0577	+	8.75628i	0.823719	+	0.299809i	0.104441	+	0.994531i	$0.466695\pi$
$854$	−4.27126			−0.146159
$855$		0			0
$856$	30.1257			1.02967
$857$	19.8148	+	7.21200i	0.676861	+	0.246357i	0.657499	−	0.753455i	$-0.271614\pi$
$857$	19.8148	+	7.21200i	0.676861	+	0.246357i	0.0193616	+	0.999813i	$0.493837\pi$
$858$	−3.86097	−	21.8966i	−0.131811	−	0.747539i
$859$	−14.9893	−	12.5775i	−0.511429	−	0.429140i	0.350203	−	0.936674i	$-0.386113\pi$
$859$	−14.9893	−	12.5775i	−0.511429	−	0.429140i	−0.861632	+	0.507534i	$0.830557\pi$
$860$	−0.485700	+	0.407551i	−0.0165622	+	0.0138974i
$861$	−0.429892	+	2.43804i	−0.0146507	+	0.0830882i
$862$	−25.8050	+	44.6956i	−0.878922	+	1.52234i
$863$	−2.47447	−	4.28591i	−0.0842319	−	0.145894i	0.820832	−	0.571170i	$-0.193510\pi$
$863$	−2.47447	−	4.28591i	−0.0842319	−	0.145894i	−0.905064	+	0.425276i	$0.860177\pi$
$864$	−6.45811	+	2.35056i	−0.219709	+	0.0799677i
$865$	16.6459	−	6.05861i	0.565977	−	0.205999i
$866$	−12.2139	−	21.1552i	−0.415047	−	0.718882i
$867$	−24.1596	+	41.8456i	−0.820502	+	1.42115i
$868$	0.0791925	−	0.449123i	0.00268797	−	0.0152442i
$869$	20.2049	−	16.9539i	0.685403	−	0.575121i
$870$	−17.9782	−	15.0855i	−0.609517	−	0.511446i
$871$	3.43047	+	19.4551i	0.116237	+	0.659212i
$872$	5.04236	+	1.83527i	0.170756	+	0.0621500i
$873$	50.0164			1.69280
$874$		0			0
$875$	−2.81790			−0.0952623
$876$	−0.694593	−	0.252811i	−0.0234681	−	0.00854169i
$877$	0.211829	+	1.20134i	0.00715296	+	0.0405664i	0.988175	−	0.153328i	$-0.0489991\pi$
$877$	0.211829	+	1.20134i	0.00715296	+	0.0405664i	−0.981022	+	0.193895i	$0.937888\pi$
$878$	6.28603	+	5.27460i	0.212143	+	0.178009i
$879$	23.1668	−	19.4393i	0.781398	−	0.655671i
$880$	1.22281	−	6.93491i	0.0412210	−	0.233776i
$881$	−23.2515	+	40.2728i	−0.783363	+	1.35682i	0.146609	+	0.989194i	$0.453164\pi$
$881$	−23.2515	+	40.2728i	−0.783363	+	1.35682i	−0.929972	+	0.367630i	$0.880169\pi$
$882$	−24.5194	−	42.4688i	−0.825610	−	1.43000i
$883$	−12.1454	+	4.42057i	−0.408726	+	0.148764i	−0.538197	−	0.842819i	$-0.680894\pi$
$883$	−12.1454	+	4.42057i	−0.408726	+	0.148764i	0.129471	+	0.991583i	$0.458672\pi$
$884$	0.209141	−	0.0761210i	0.00703416	−	0.00256023i
$885$	−7.98293	−	13.8268i	−0.268343	−	0.464784i
$886$	−20.1374	+	34.8791i	−0.676531	+	1.17179i
$887$	−4.03286	+	22.8715i	−0.135410	+	0.767949i	0.839163	+	0.543880i	$0.183045\pi$
$887$	−4.03286	+	22.8715i	−0.135410	+	0.767949i	−0.974573	+	0.224069i	$0.928066\pi$
$888$	−32.0972	+	26.9327i	−1.07711	+	0.903804i
$889$	3.08718	+	2.59045i	0.103541	+	0.0868810i
$890$	2.11721	+	12.0073i	0.0709691	+	0.402486i
$891$	6.52956	+	2.37657i	0.218749	+	0.0796180i
$892$	1.57255			0.0526528
$893$		0			0
$894$	64.2404			2.14852
$895$	9.51337	+	3.46258i	0.317997	+	0.115741i
$896$	−0.572796	−	3.24849i	−0.0191358	−	0.108524i
$897$	15.2986	+	12.8370i	0.510805	+	0.428617i
$898$	11.6109	−	9.74270i	0.387461	−	0.325118i
$899$	8.48886	−	48.1427i	0.283119	−	1.60565i
$900$	−2.06624	+	3.57883i	−0.0688746	+	0.119294i
$901$	0.663848	+	1.14982i	0.0221160	+	0.0383060i
$902$	−6.97906	+	2.54017i	−0.232377	+	0.0845784i
$903$	3.66637	−	1.33445i	0.122009	−	0.0444078i
$904$	26.0326	+	45.0897i	0.865830	+	1.49966i
$905$	−3.75372	+	6.50163i	−0.124778	+	0.216122i
$906$	−2.93835	+	16.6642i	−0.0976201	+	0.553631i
$907$	−30.6393	+	25.7095i	−1.01736	+	0.853669i	−0.989294	−	0.145937i	$-0.953380\pi$
$907$	−30.6393	+	25.7095i	−1.01736	+	0.853669i	−0.0280687	+	0.999606i	$0.508936\pi$
$908$	2.00316	+	1.68085i	0.0664770	+	0.0557809i
$909$	−8.49747	−	48.1916i	−0.281843	−	1.59841i
$910$	0.995252	+	0.362242i	0.0329923	+	0.0120082i
$911$	−18.7997			−0.622863			−0.311431	−	0.950269i	$-0.600808\pi$
$911$	−18.7997			−0.622863			−0.311431	+	0.950269i	$0.600808\pi$
$912$		0			0
$913$	33.0232			1.09291
$914$	−29.6129	−	10.7782i	−0.979509	−	0.356512i
$915$	−4.01367	−	22.7627i	−0.132688	−	0.752510i
$916$	2.90664	+	2.43896i	0.0960381	+	0.0805855i
$917$	0.490915	−	0.411927i	0.0162114	−	0.0136030i
$918$	0.722096	−	4.09521i	0.0238327	−	0.135162i
$919$	−19.9158	+	34.4952i	−0.656962	+	1.13789i	0.324436	+	0.945908i	$0.394825\pi$
$919$	−19.9158	+	34.4952i	−0.656962	+	1.13789i	−0.981398	+	0.191984i	$0.938508\pi$
$920$	3.48751	+	6.04055i	0.114980	+	0.199151i
$921$	−31.6450	+	11.5178i	−1.04274	+	0.379526i
$922$	−46.3671	+	16.8762i	−1.52702	+	0.555790i
$923$	11.9760	+	20.7430i	0.394193	+	0.682763i
$924$	0.205737	−	0.356347i	0.00676825	−	0.0117230i
$925$	−3.62836	+	20.5774i	−0.119300	+	0.676582i
$926$	44.3658	−	37.2273i	1.45795	−	1.22337i
$927$	−22.3314	−	18.7383i	−0.733460	−	0.615446i
$928$	1.24463	+	7.05866i	0.0408571	+	0.231712i
$929$	−25.3285	−	9.21881i	−0.831000	−	0.302459i	−0.108731	−	0.994071i	$-0.534679\pi$
$929$	−25.3285	−	9.21881i	−0.831000	−	0.302459i	−0.722269	+	0.691612i	$0.756901\pi$
$930$	−24.2422			−0.794932
$931$		0			0
$932$	−3.26176			−0.106843
$933$	43.1994	+	15.7233i	1.41428	+	0.514758i
$934$	−5.98839	−	33.9618i	−0.195946	−	1.11127i
$935$	−0.701867	−	0.588936i	−0.0229535	−	0.0192603i
$936$	30.7085	−	25.7675i	1.00374	−	0.842236i
$937$	0.455585	−	2.58375i	0.0148833	−	0.0844074i	−0.976461	−	0.215692i	$-0.930799\pi$
$937$	0.455585	−	2.58375i	0.0148833	−	0.0844074i	0.991345	+	0.131285i	$0.0419103\pi$
$938$	1.79561	−	3.11008i	0.0586287	−	0.101548i
$939$	−38.3371	−	66.4018i	−1.25108	−	2.16694i
$940$	−1.11334	+	0.405223i	−0.0363132	+	0.0132169i
$941$	17.5437	−	6.38538i	0.571908	−	0.208158i	−0.0398455	−	0.999206i	$-0.512687\pi$
$941$	17.5437	−	6.38538i	0.571908	−	0.208158i	0.611754	+	0.791048i	$0.290464\pi$
$942$	18.6570	+	32.3149i	0.607879	+	1.05288i
$943$	3.33544	−	5.77715i	0.108617	−	0.188130i
$944$	3.93763	−	22.3314i	0.128159	−	0.726826i
$945$	−1.54323	+	1.29493i	−0.0502014	+	0.0421240i
$946$	8.96657	+	7.52384i	0.291528	+	0.244621i
$947$	1.45858	+	8.27201i	0.0473974	+	0.268804i	0.999292	−	0.0376214i	$-0.0119781\pi$
$947$	1.45858	+	8.27201i	0.0473974	+	0.268804i	−0.951895	+	0.306425i	$0.900867\pi$
$948$	5.92262	+	2.15566i	0.192358	+	0.0700125i
$949$	3.57573			0.116073
$950$		0			0
$951$	−85.0343			−2.75742
$952$	−0.449493	−	0.163602i	−0.0145681	−	0.00530237i
$953$	5.85070	+	33.1810i	0.189523	+	1.07484i	0.920005	+	0.391906i	$0.128184\pi$
$953$	5.85070	+	33.1810i	0.189523	+	1.07484i	−0.730483	+	0.682931i	$0.760705\pi$
$954$	15.4945	+	13.0015i	0.501654	+	0.420938i
$955$	12.3516	−	10.3643i	0.399689	−	0.335379i
$956$	−0.0754843	+	0.428092i	−0.00244134	+	0.0138455i
$957$	22.0535	−	38.1978i	0.712888	−	1.23476i
$958$	25.7173	+	44.5438i	0.830890	+	1.43914i
$959$	−0.0834734	+	0.0303818i	−0.00269550	+	0.000981081i
$960$	20.4538	−	7.44459i	0.660145	−	0.240273i
$961$	−9.74809	−	16.8842i	−0.314455	−	0.544651i
$962$	8.57192	−	14.8470i	0.276370	−	0.478686i
$963$	9.40286	−	53.3262i	0.303003	−	1.71841i
$964$	−1.95361	+	1.63927i	−0.0629216	+	0.0527975i
$965$	0.200522	+	0.168258i	0.00645505	+	0.00541643i
$966$	−0.630415	−	3.57526i	−0.0202833	−	0.115032i
$967$	−11.0351	−	4.01644i	−0.354864	−	0.129160i	0.158436	−	0.987369i	$-0.449355\pi$
$967$	−11.0351	−	4.01644i	−0.354864	−	0.129160i	−0.513300	+	0.858209i	$0.671577\pi$
$968$	−17.7847			−0.571621
$969$		0			0
$970$	−11.2003			−0.359619
$971$	−12.0368	−	4.38105i	−0.386280	−	0.140595i	0.141578	−	0.989927i	$-0.454783\pi$
$971$	−12.0368	−	4.38105i	−0.386280	−	0.140595i	−0.527858	+	0.849333i	$0.677005\pi$
$972$	−0.346667	−	1.96605i	−0.0111194	−	0.0630610i
$973$	1.13429	+	0.951778i	0.0363635	+	0.0305126i
$974$	−8.01296	+	6.72367i	−0.256752	+	0.215440i
$975$	5.43969	−	30.8500i	0.174210	−	0.987992i
$976$	16.4140	−	28.4299i	0.525399	−	0.910018i
$977$	−7.26382	−	12.5813i	−0.232390	−	0.402512i	0.726121	−	0.687567i	$-0.241321\pi$
$977$	−7.26382	−	12.5813i	−0.232390	−	0.402512i	−0.958511	+	0.285055i	$0.907988\pi$
$978$	−30.4577	+	11.0857i	−0.973930	+	0.354481i
$979$	−21.5326	+	7.83721i	−0.688183	+	0.250478i
$980$	−0.558963	−	0.968153i	−0.0178554	−	0.0309265i
$981$	4.82248	−	8.35278i	0.153970	−	0.266684i
$982$	8.59152	−	48.7249i	0.274166	−	1.55487i
$983$	−28.3821	+	23.8154i	−0.905249	+	0.759594i	−0.971209	−	0.238228i	$-0.923433\pi$
$983$	−28.3821	+	23.8154i	−0.905249	+	0.759594i	0.0659599	+	0.997822i	$0.478989\pi$
$984$	−16.0737	−	13.4875i	−0.512412	−	0.429965i
$985$	2.00670	+	11.3806i	0.0639388	+	0.362615i
$986$	−4.07532	−	1.48330i	−0.129785	−	0.0472378i
$987$	7.29086			0.232071
$988$		0			0
$989$	−10.5134			−0.334307
$990$	−13.1163	−	4.77396i	−0.416864	−	0.151726i
$991$	0.595856	+	3.37927i	0.0189280	+	0.107346i	0.992808	−	0.119717i	$-0.0381988\pi$
$991$	0.595856	+	3.37927i	0.0189280	+	0.107346i	−0.973880	+	0.227063i	$0.927088\pi$
$992$	5.67159	+	4.75903i	0.180073	+	0.151099i
$993$	−61.0228	+	51.2042i	−1.93650	+	1.62492i
$994$	0.756082	−	4.28795i	0.0239815	−	0.136006i
$995$	0.112874	−	0.195503i	0.00357835	−	0.00619788i
$996$	3.94562	+	6.83402i	0.125022	+	0.216544i
$997$	−12.0055	+	4.36965i	−0.380219	+	0.138388i	−0.525057	−	0.851067i	$-0.675956\pi$
$997$	−12.0055	+	4.36965i	−0.380219	+	0.138388i	0.144838	+	0.989455i	$0.453734\pi$
$998$	6.23695	−	2.27006i	0.197427	−	0.0718576i
$999$	16.3045	+	28.2403i	0.515852	+	0.893483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.f.99.1		6
19.2	odd	18		361.2.e.a.54.1		6
19.3	odd	18		361.2.e.h.245.1		6
19.4	even	9		361.2.c.i.292.2		6
19.5	even	9	inner	361.2.e.f.62.1		6
19.6	even	9		361.2.c.i.68.2		6
19.7	even	3		361.2.e.g.234.1		6
19.8	odd	6		361.2.e.h.28.1		6
19.9	even	9		361.2.a.g.1.2		3
19.10	odd	18		361.2.a.h.1.2		3
19.11	even	3		19.2.e.a.9.1	✓	6
19.12	odd	6		361.2.e.a.234.1		6
19.13	odd	18		361.2.c.h.68.2		6
19.14	odd	18		361.2.e.b.62.1		6
19.15	odd	18		361.2.c.h.292.2		6
19.16	even	9		19.2.e.a.17.1	yes	6
19.17	even	9		361.2.e.g.54.1		6
19.18	odd	2		361.2.e.b.99.1		6
57.11	odd	6		171.2.u.c.28.1		6
57.29	even	18		3249.2.a.s.1.2		3
57.35	odd	18		171.2.u.c.55.1		6
57.47	odd	18		3249.2.a.z.1.2		3
76.11	odd	6		304.2.u.b.161.1		6
76.35	odd	18		304.2.u.b.17.1		6
76.47	odd	18		5776.2.a.br.1.3		3
76.67	even	18		5776.2.a.bi.1.1		3
95.9	even	18		9025.2.a.bd.1.2		3
95.29	odd	18		9025.2.a.x.1.2		3
95.49	even	6		475.2.l.a.351.1		6
95.54	even	18		475.2.l.a.226.1		6
95.68	odd	12		475.2.u.a.199.1		12
95.73	odd	36		475.2.u.a.74.2		12
95.87	odd	12		475.2.u.a.199.2		12
95.92	odd	36		475.2.u.a.74.1		12
133.11	even	3		931.2.v.b.275.1		6
133.16	even	9		931.2.v.b.606.1		6
133.30	even	3		931.2.x.a.655.1		6
133.54	odd	18		931.2.v.a.606.1		6
133.68	odd	6		931.2.x.b.655.1		6
133.73	odd	18		931.2.x.b.226.1		6
133.87	odd	6		931.2.v.a.275.1		6
133.111	odd	18		931.2.w.a.834.1		6
133.125	odd	6		931.2.w.a.883.1		6
133.130	even	9		931.2.x.a.226.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	19.11	even	3
19.2.e.a.17.1	yes	6	19.16	even	9
171.2.u.c.28.1		6	57.11	odd	6
171.2.u.c.55.1		6	57.35	odd	18
304.2.u.b.17.1		6	76.35	odd	18
304.2.u.b.161.1		6	76.11	odd	6
361.2.a.g.1.2		3	19.9	even	9
361.2.a.h.1.2		3	19.10	odd	18
361.2.c.h.68.2		6	19.13	odd	18
361.2.c.h.292.2		6	19.15	odd	18
361.2.c.i.68.2		6	19.6	even	9
361.2.c.i.292.2		6	19.4	even	9
361.2.e.a.54.1		6	19.2	odd	18
361.2.e.a.234.1		6	19.12	odd	6
361.2.e.b.62.1		6	19.14	odd	18
361.2.e.b.99.1		6	19.18	odd	2
361.2.e.f.62.1		6	19.5	even	9	inner
361.2.e.f.99.1		6	1.1	even	1	trivial
361.2.e.g.54.1		6	19.17	even	9
361.2.e.g.234.1		6	19.7	even	3
361.2.e.h.28.1		6	19.8	odd	6
361.2.e.h.245.1		6	19.3	odd	18
475.2.l.a.226.1		6	95.54	even	18
475.2.l.a.351.1		6	95.49	even	6
475.2.u.a.74.1		12	95.92	odd	36
475.2.u.a.74.2		12	95.73	odd	36
475.2.u.a.199.1		12	95.68	odd	12
475.2.u.a.199.2		12	95.87	odd	12
931.2.v.a.275.1		6	133.87	odd	6
931.2.v.a.606.1		6	133.54	odd	18
931.2.v.b.275.1		6	133.11	even	3
931.2.v.b.606.1		6	133.16	even	9
931.2.w.a.834.1		6	133.111	odd	18
931.2.w.a.883.1		6	133.125	odd	6
931.2.x.a.226.1		6	133.130	even	9
931.2.x.a.655.1		6	133.30	even	3
931.2.x.b.226.1		6	133.73	odd	18
931.2.x.b.655.1		6	133.68	odd	6
3249.2.a.s.1.2		3	57.29	even	18
3249.2.a.z.1.2		3	57.47	odd	18
5776.2.a.bi.1.1		3	76.67	even	18
5776.2.a.br.1.3		3	76.47	odd	18
9025.2.a.x.1.2		3	95.29	odd	18
9025.2.a.bd.1.2		3	95.9	even	18

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26604 + 0.460802i) q^{2} +(-0.500000 - 2.83564i) q^{3} +(-0.141559 - 0.118782i) q^{4} +(0.673648 - 0.565258i) q^{5} +(0.673648 - 3.82045i) q^{6} +(-0.173648 + 0.300767i) q^{7} +(-1.47178 - 2.54920i) q^{8} +(-4.97178 + 1.80958i) q^{9} +(1.11334 - 0.405223i) q^{10} +(1.11334 + 1.92836i) q^{11} +(-0.266044 + 0.460802i) q^{12} +(0.446967 - 2.53487i) q^{13} +(-0.358441 + 0.300767i) q^{14} +(-1.93969 - 1.62760i) q^{15} +(-0.624485 - 3.54163i) q^{16} +(-0.439693 - 0.160035i) q^{17} -7.12836 q^{18} -0.162504 q^{20} +(0.939693 + 0.342020i) q^{21} +(0.520945 + 2.95442i) q^{22} +(-2.06418 - 1.73205i) q^{23} +(-6.49273 + 5.44804i) q^{24} +(-0.733956 + 4.16247i) q^{25} +(1.73396 - 3.00330i) q^{26} +(3.29813 + 5.71253i) q^{27} +(0.0603074 - 0.0219501i) q^{28} +(6.46451 - 2.35289i) q^{29} +(-1.70574 - 2.95442i) q^{30} +(3.55303 - 6.15403i) q^{31} +(-0.180922 + 1.02606i) q^{32} +(4.91147 - 4.12122i) q^{33} +(-0.482926 - 0.405223i) q^{34} +(0.0530334 + 0.300767i) q^{35} +(0.918748 + 0.334397i) q^{36} +4.94356 q^{37} -7.41147 q^{39} +(-2.43242 - 0.885328i) q^{40} +(0.429892 + 2.43804i) q^{41} +(1.03209 + 0.866025i) q^{42} +(2.98886 - 2.50795i) q^{43} +(0.0714517 - 0.405223i) q^{44} +(-2.32635 + 4.02936i) q^{45} +(-1.81521 - 3.14403i) q^{46} +(6.85117 - 2.49362i) q^{47} +(-9.73055 + 3.54163i) q^{48} +(3.43969 + 5.95772i) q^{49} +(-2.84730 + 4.93166i) q^{50} +(-0.233956 + 1.32683i) q^{51} +(-0.364370 + 0.305743i) q^{52} +(-2.17365 - 1.82391i) q^{53} +(1.54323 + 8.75211i) q^{54} +(1.84002 + 0.669713i) q^{55} +1.02229 q^{56} +9.26857 q^{58} +(5.92514 + 2.15658i) q^{59} +(0.0812519 + 0.460802i) q^{60} +(6.99273 + 5.86759i) q^{61} +(7.33409 - 6.15403i) q^{62} +(0.319078 - 1.80958i) q^{63} +(-4.29813 + 7.44459i) q^{64} +(-1.13176 - 1.96026i) q^{65} +(8.11721 - 2.95442i) q^{66} +(-7.21213 + 2.62500i) q^{67} +(0.0432332 + 0.0748822i) q^{68} +(-3.87939 + 6.71929i) q^{69} +(-0.0714517 + 0.405223i) q^{70} +(-7.12836 + 5.98140i) q^{71} +(11.9304 + 10.0108i) q^{72} +(0.241230 + 1.36808i) q^{73} +(6.25877 + 2.27801i) q^{74} +12.1702 q^{75} -0.773318 q^{77} +(-9.38326 - 3.41523i) q^{78} +(-2.05690 - 11.6653i) q^{79} +(-2.42262 - 2.03282i) q^{80} +(2.39053 - 2.00589i) q^{81} +(-0.579193 + 3.28476i) q^{82} +(7.41534 - 12.8438i) q^{83} +(-0.0923963 - 0.160035i) q^{84} +(-0.386659 + 0.140732i) q^{85} +(4.93969 - 1.79790i) q^{86} +(-9.90420 - 17.1546i) q^{87} +(3.27719 - 5.67626i) q^{88} +(-1.78699 + 10.1345i) q^{89} +(-4.80200 + 4.02936i) q^{90} +(0.684793 + 0.574609i) q^{91} +(0.0864665 + 0.490376i) q^{92} +(-19.2271 - 6.99811i) q^{93} +9.82295 q^{94} +3.00000 q^{96} +(-8.88326 - 3.23324i) q^{97} +(1.60947 + 9.12776i) q^{98} +(-9.02481 - 7.57272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9} + 3 q^{12} + 15 q^{13} + 6 q^{14} - 6 q^{15} + 9 q^{16} + 3 q^{17} - 6 q^{18} - 6 q^{20} + 6 q^{23} - 21 q^{24} - 9 q^{25} + 15 q^{26}+ \cdots - 27 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 - 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9 + 3 * q^12 + 15 * q^13 + 6 * q^14 - 6 * q^15 + 9 * q^16 + 3 * q^17 - 6 * q^18 - 6 * q^20 + 6 * q^23 - 21 * q^24 - 9 * q^25 + 15 * q^26 + 6 * q^27 + 6 * q^28 + 6 * q^29 + 9 * q^31 - 18 * q^32 + 9 * q^33 + 18 * q^34 - 12 * q^35 + 3 * q^36 - 24 * q^39 + 9 * q^40 - 6 * q^41 - 3 * q^42 + 24 * q^43 - 15 * q^45 - 18 * q^46 + 15 * q^47 - 21 * q^48 + 15 * q^49 - 15 * q^50 - 6 * q^51 - 21 * q^52 - 12 * q^53 - 6 * q^54 - 9 * q^55 - 6 * q^56 + 36 * q^58 - 6 * q^59 + 3 * q^60 + 24 * q^61 - 3 * q^62 - 15 * q^63 - 12 * q^64 - 12 * q^65 + 18 * q^66 + 6 * q^67 - 15 * q^68 - 12 * q^69 - 6 * q^71 - 3 * q^72 + 24 * q^73 + 15 * q^74 + 30 * q^75 - 18 * q^77 - 21 * q^78 + 24 * q^79 + 12 * q^80 - 3 * q^81 + 45 * q^82 + 3 * q^84 - 9 * q^85 + 24 * q^86 - 21 * q^87 + 9 * q^88 - 3 * q^89 + 9 * q^90 - 3 * q^91 - 30 * q^92 - 36 * q^93 + 18 * q^94 + 18 * q^96 - 18 * q^97 + 27 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more