LMFDB - Embedded newform 950.2.u.g.99.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.3
Character	$\chi$	$=$	950.99
Dual form			950.2.u.g.499.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342020 + 0.939693i) q^{2} +(3.13139 - 0.552148i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.552148 + 3.13139i) q^{6} +(2.89781 + 1.67305i) q^{7} +(0.866025 - 0.500000i) q^{8} +(6.68164 - 2.43192i) q^{9} +O(q^{10})$	\(q+(-0.342020 + 0.939693i) q^{2} +(3.13139 - 0.552148i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.552148 + 3.13139i) q^{6} +(2.89781 + 1.67305i) q^{7} +(0.866025 - 0.500000i) q^{8} +(6.68164 - 2.43192i) q^{9} +(-3.09216 - 5.35578i) q^{11} +(-2.75370 - 1.58985i) q^{12} +(0.727397 + 0.128260i) q^{13} +(-2.56327 + 2.15083i) q^{14} +(0.173648 + 0.984808i) q^{16} +(0.296919 - 0.815778i) q^{17} +7.11045i q^{18} +(2.59916 - 3.49919i) q^{19} +(9.99794 + 3.63895i) q^{21} +(6.09037 - 1.07390i) q^{22} +(-0.735009 + 0.875950i) q^{23} +(2.43579 - 2.04387i) q^{24} +(-0.369309 + 0.639662i) q^{26} +(11.3189 - 6.53498i) q^{27} +(-1.14444 - 3.14431i) q^{28} +(-7.32010 + 2.66430i) q^{29} +(-3.23887 + 5.60988i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(-12.6399 - 15.0637i) q^{33} +(0.665029 + 0.558025i) q^{34} +(-6.68164 - 2.43192i) q^{36} +1.68113i q^{37} +(2.39920 + 3.63921i) q^{38} +2.34858 q^{39} +(1.68282 + 9.54373i) q^{41} +(-6.83899 + 8.15040i) q^{42} +(-1.19449 - 1.42354i) q^{43} +(-1.07390 + 6.09037i) q^{44} +(-0.571736 - 0.990275i) q^{46} +(-0.113446 - 0.311691i) q^{47} +(1.08752 + 2.98793i) q^{48} +(2.09821 + 3.63420i) q^{49} +(0.479338 - 2.71846i) q^{51} +(-0.474775 - 0.565815i) q^{52} +(-4.56693 + 5.44265i) q^{53} +(2.26958 + 12.8714i) q^{54} +3.34610 q^{56} +(6.20691 - 12.3925i) q^{57} -7.78988i q^{58} +(4.56719 + 1.66232i) q^{59} +(5.53664 + 4.64579i) q^{61} +(-4.16381 - 4.96223i) q^{62} +(23.4308 + 4.13149i) q^{63} +(0.500000 - 0.866025i) q^{64} +(18.4784 - 6.72557i) q^{66} +(-1.00039 - 2.74854i) q^{67} +(-0.751825 + 0.434067i) q^{68} +(-1.81794 + 3.14877i) q^{69} +(-5.27849 + 4.42918i) q^{71} +(4.57051 - 5.44692i) q^{72} +(7.69790 - 1.35735i) q^{73} +(-1.57975 - 0.574982i) q^{74} +(-4.24031 + 1.00983i) q^{76} -20.6934i q^{77} +(-0.803262 + 2.20694i) q^{78} +(0.399207 + 2.26401i) q^{79} +(15.4949 - 13.0018i) q^{81} +(-9.54373 - 1.68282i) q^{82} +(-9.91318 - 5.72338i) q^{83} +(-5.31979 - 9.21415i) q^{84} +(1.74623 - 0.635576i) q^{86} +(-21.4510 + 12.3847i) q^{87} +(-5.35578 - 3.09216i) q^{88} +(-0.404290 + 2.29284i) q^{89} +(1.89328 + 1.58865i) q^{91} +(1.12610 - 0.198562i) q^{92} +(-7.04466 + 19.3550i) q^{93} +0.331695 q^{94} -3.17969 q^{96} +(-2.34081 + 6.43131i) q^{97} +(-4.13266 + 0.728700i) q^{98} +(-33.6855 - 28.2655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{9}+O(q^{10}) $ 36 * q + 36 * q^9	$ 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) $ 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$3$	3.13139	−	0.552148i	1.80791	−	0.318783i	0.835047	−	0.550178i	$-0.185440\pi$
$3$	3.13139	−	0.552148i	1.80791	−	0.318783i	0.972860	+	0.231396i	$0.0743292\pi$
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.552148	+	3.13139i	−0.225413	+	1.27838i
$7$	2.89781	+	1.67305i	1.09527	+	0.632354i	0.934975	−	0.354715i	$-0.115422\pi$
$7$	2.89781	+	1.67305i	1.09527	+	0.632354i	0.160295	+	0.987069i	$0.448755\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	6.68164	−	2.43192i	2.22721	−	0.810639i
$10$		0			0
$11$	−3.09216	−	5.35578i	−0.932322	−	1.61483i	−0.779341	−	0.626600i	$-0.784446\pi$
$11$	−3.09216	−	5.35578i	−0.932322	−	1.61483i	−0.152981	−	0.988229i	$-0.548887\pi$
$12$	−2.75370	−	1.58985i	−0.794923	−	0.458949i
$13$	0.727397	+	0.128260i	0.201744	+	0.0355729i	0.273607	−	0.961842i	$-0.411783\pi$
$13$	0.727397	+	0.128260i	0.201744	+	0.0355729i	−0.0718630	+	0.997415i	$0.522894\pi$
$14$	−2.56327	+	2.15083i	−0.685061	+	0.574835i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	0.296919	−	0.815778i	0.0720134	−	0.197855i	−0.898464	−	0.439047i	$-0.855316\pi$
$17$	0.296919	−	0.815778i	0.0720134	−	0.197855i	0.970477	+	0.241192i	$0.0775383\pi$
$18$			7.11045i			1.67595i
$19$	2.59916	−	3.49919i	0.596289	−	0.802770i
$19$	2.59916	−	3.49919i	0.596289	−	0.802770i
$20$		0			0
$21$	9.99794	+	3.63895i	2.18173	+	0.794085i
$22$	6.09037	−	1.07390i	1.29847	−	0.228956i
$23$	−0.735009	+	0.875950i	−0.153260	+	0.182648i	−0.837211	−	0.546879i	$-0.815816\pi$
$23$	−0.735009	+	0.875950i	−0.153260	+	0.182648i	0.683951	+	0.729528i	$0.260260\pi$
$24$	2.43579	−	2.04387i	0.497203	−	0.417203i
$25$		0			0
$26$	−0.369309	+	0.639662i	−0.0724275	+	0.125448i
$27$	11.3189	−	6.53498i	2.17833	−	1.25766i
$28$	−1.14444	−	3.14431i	−0.216278	−	0.594219i
$29$	−7.32010	+	2.66430i	−1.35931	+	0.494748i	−0.915840	−	0.401543i	$-0.868474\pi$
$29$	−7.32010	+	2.66430i	−1.35931	+	0.494748i	−0.443468	+	0.896290i	$0.646252\pi$
$30$		0			0
$31$	−3.23887	+	5.60988i	−0.581718	+	1.00756i	0.413558	+	0.910478i	$0.364286\pi$
$31$	−3.23887	+	5.60988i	−0.581718	+	1.00756i	−0.995276	+	0.0970869i	$0.969048\pi$
$32$	−0.984808	−	0.173648i	−0.174091	−	0.0306970i
$33$	−12.6399	−	15.0637i	−2.20033	−	2.62225i
$34$	0.665029	+	0.558025i	0.114051	+	0.0957005i
$35$		0			0
$36$	−6.68164	−	2.43192i	−1.11361	−	0.405319i
$37$			1.68113i			0.276377i	0.990406	+	0.138188i	$0.0441279\pi$
$37$			1.68113i			0.276377i	−0.990406	+	0.138188i	$0.955872\pi$
$38$	2.39920	+	3.63921i	0.389202	+	0.590357i
$39$	2.34858			0.376074
$40$		0			0
$41$	1.68282	+	9.54373i	0.262812	+	1.49048i	0.775194	+	0.631723i	$0.217652\pi$
$41$	1.68282	+	9.54373i	0.262812	+	1.49048i	−0.512383	+	0.858757i	$0.671237\pi$
$42$	−6.83899	+	8.15040i	−1.05528	+	1.25763i
$43$	−1.19449	−	1.42354i	−0.182158	−	0.217088i	0.667236	−	0.744846i	$-0.267477\pi$
$43$	−1.19449	−	1.42354i	−0.182158	−	0.217088i	−0.849395	+	0.527758i	$0.823033\pi$
$44$	−1.07390	+	6.09037i	−0.161896	+	0.918158i
$45$		0			0
$46$	−0.571736	−	0.990275i	−0.0842978	−	0.146008i
$47$	−0.113446	−	0.311691i	−0.0165479	−	0.0454649i	0.931144	−	0.364652i	$-0.118812\pi$
$47$	−0.113446	−	0.311691i	−0.0165479	−	0.0454649i	−0.947692	+	0.319188i	$0.896590\pi$
$48$	1.08752	+	2.98793i	0.156970	+	0.431271i
$49$	2.09821	+	3.63420i	0.299744	+	0.519172i
$50$		0			0
$51$	0.479338	−	2.71846i	0.0671207	−	0.380661i
$52$	−0.474775	−	0.565815i	−0.0658394	−	0.0784644i
$53$	−4.56693	+	5.44265i	−0.627316	+	0.747606i	−0.982310	−	0.187263i	$-0.940038\pi$
$53$	−4.56693	+	5.44265i	−0.627316	+	0.747606i	0.354994	+	0.934868i	$0.384483\pi$
$54$	2.26958	+	12.8714i	0.308850	+	1.75158i
$55$		0			0
$56$	3.34610			0.447142
$57$	6.20691	−	12.3925i	0.822125	−	1.64142i
$58$		−	7.78988i		−	1.02286i
$59$	4.56719	+	1.66232i	0.594597	+	0.216416i	0.621750	−	0.783216i	$-0.286422\pi$
$59$	4.56719	+	1.66232i	0.594597	+	0.216416i	−0.0271531	+	0.999631i	$0.508644\pi$
$60$		0			0
$61$	5.53664	+	4.64579i	0.708894	+	0.594833i	0.924289	−	0.381694i	$-0.124659\pi$
$61$	5.53664	+	4.64579i	0.708894	+	0.594833i	−0.215394	+	0.976527i	$0.569104\pi$
$62$	−4.16381	−	4.96223i	−0.528804	−	0.630204i
$63$	23.4308	+	4.13149i	2.95201	+	0.520519i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	18.4784	−	6.72557i	2.27453	−	0.827861i
$67$	−1.00039	−	2.74854i	−0.122217	−	0.335787i	0.863464	−	0.504410i	$-0.168290\pi$
$67$	−1.00039	−	2.74854i	−0.122217	−	0.335787i	−0.985681	+	0.168623i	$0.946068\pi$
$68$	−0.751825	+	0.434067i	−0.0911722	+	0.0526383i
$69$	−1.81794	+	3.14877i	−0.218855	+	0.379068i
$70$		0			0
$71$	−5.27849	+	4.42918i	−0.626442	+	0.525647i	−0.899821	−	0.436259i	$-0.856303\pi$
$71$	−5.27849	+	4.42918i	−0.626442	+	0.525647i	0.273379	+	0.961906i	$0.411859\pi$
$72$	4.57051	−	5.44692i	0.538640	−	0.641926i
$73$	7.69790	−	1.35735i	0.900972	−	0.158866i	0.296070	−	0.955166i	$-0.404324\pi$
$73$	7.69790	−	1.35735i	0.900972	−	0.158866i	0.604901	+	0.796301i	$0.293213\pi$
$74$	−1.57975	−	0.574982i	−0.183642	−	0.0668403i
$75$		0			0
$76$	−4.24031	+	1.00983i	−0.486397	+	0.115835i
$77$		−	20.6934i		−	2.35823i
$78$	−0.803262	+	2.20694i	−0.0909515	+	0.249887i
$79$	0.399207	+	2.26401i	0.0449143	+	0.254721i	0.998995	−	0.0448292i	$-0.0142744\pi$
$79$	0.399207	+	2.26401i	0.0449143	+	0.254721i	−0.954080	+	0.299551i	$0.903163\pi$
$80$		0			0
$81$	15.4949	−	13.0018i	1.72165	−	1.44464i
$82$	−9.54373	−	1.68282i	−1.05393	−	0.185836i
$83$	−9.91318	−	5.72338i	−1.08811	−	0.628223i	−0.155040	−	0.987908i	$-0.549551\pi$
$83$	−9.91318	−	5.72338i	−1.08811	−	0.628223i	−0.933074	+	0.359686i	$0.882884\pi$
$84$	−5.31979	−	9.21415i	−0.580437	−	1.00535i
$85$		0			0
$86$	1.74623	−	0.635576i	0.188301	−	0.0685359i
$87$	−21.4510	+	12.3847i	−2.29978	+	1.32778i
$88$	−5.35578	−	3.09216i	−0.570928	−	0.329626i
$89$	−0.404290	+	2.29284i	−0.0428546	+	0.243041i	−0.998709	−	0.0508007i	$-0.983823\pi$
$89$	−0.404290	+	2.29284i	−0.0428546	+	0.243041i	0.955854	+	0.293841i	$0.0949338\pi$
$90$		0			0
$91$	1.89328	+	1.58865i	0.198469	+	0.166535i
$92$	1.12610	−	0.198562i	0.117404	−	0.0207015i
$93$	−7.04466	+	19.3550i	−0.730497	+	2.00702i
$94$	0.331695			0.0342117
$95$		0			0
$96$	−3.17969			−0.324526
$97$	−2.34081	+	6.43131i	−0.237673	+	0.653000i	0.762311	+	0.647211i	$0.224065\pi$
$97$	−2.34081	+	6.43131i	−0.237673	+	0.653000i	−0.999983	+	0.00578901i	$0.998157\pi$
$98$	−4.13266	+	0.728700i	−0.417462	+	0.0736098i
$99$	−33.6855	−	28.2655i	−3.38552	−	2.84079i
$100$		0			0
$101$	1.76892	−	10.0321i	0.176015	−	0.998228i	−0.760952	−	0.648809i	$-0.775268\pi$
$101$	1.76892	−	10.0321i	0.176015	−	0.998228i	0.936966	−	0.349420i	$-0.113621\pi$
$102$	2.39057	+	1.38020i	0.236702	+	0.136660i
$103$	−1.79310	+	1.03525i	−0.176680	+	0.102006i	−0.585732	−	0.810505i	$-0.699193\pi$
$103$	−1.79310	+	1.03525i	−0.176680	+	0.102006i	0.409052	+	0.912511i	$0.365859\pi$
$104$	0.694074	−	0.252622i	0.0680596	−	0.0247717i
$105$		0			0
$106$	−3.55244	−	6.15300i	−0.345043	−	0.597632i
$107$	12.6761	+	7.31857i	1.22545	+	0.707513i	0.966075	−	0.258264i	$-0.0831503\pi$
$107$	12.6761	+	7.31857i	1.22545	+	0.707513i	0.259374	+	0.965777i	$0.416484\pi$
$108$	−12.8714	−	2.26958i	−1.23855	−	0.218390i
$109$	6.66091	−	5.58917i	0.637999	−	0.535345i	−0.265404	−	0.964137i	$-0.585505\pi$
$109$	6.66091	−	5.58917i	0.637999	−	0.535345i	0.903403	+	0.428792i	$0.141061\pi$
$110$		0			0
$111$	0.928235	+	5.26428i	0.0881041	+	0.499663i
$112$	−1.14444	+	3.14431i	−0.108139	+	0.297109i
$113$		−	10.8308i		−	1.01888i	−0.860507	−	0.509439i	$-0.829853\pi$
$113$		−	10.8308i		−	1.01888i	0.860507	−	0.509439i	$-0.170147\pi$
$114$	9.52221	+	10.0711i	0.891836	+	0.943240i
$115$		0			0
$116$	7.32010	+	2.66430i	0.679654	+	0.247374i
$117$	5.17212	−	0.911985i	0.478163	−	0.0843130i
$118$	−3.12414	+	3.72320i	−0.287600	+	0.342749i
$119$	2.22526	−	1.86721i	0.203989	−	0.171167i
$120$		0			0
$121$	−13.6229	+	23.5956i	−1.23845	+	2.14506i
$122$	−6.25926	+	3.61379i	−0.566687	+	0.327177i
$123$	10.5391	+	28.9559i	0.950279	+	2.61087i
$124$	6.08708	−	2.21552i	0.546636	−	0.198959i
$125$		0			0
$126$	−11.8962	+	20.6047i	−1.05979	+	1.83562i
$127$	−11.0540	−	1.94911i	−0.980880	−	0.172956i	−0.339857	−	0.940477i	$-0.610379\pi$
$127$	−11.0540	−	1.94911i	−0.980880	−	0.172956i	−0.641023	+	0.767522i	$0.721490\pi$
$128$	0.642788	+	0.766044i	0.0568149	+	0.0677094i
$129$	−4.52642	−	3.79812i	−0.398529	−	0.334406i
$130$		0			0
$131$	−14.2703	−	5.19396i	−1.24680	−	0.453798i	−0.367481	−	0.930031i	$-0.619780\pi$
$131$	−14.2703	−	5.19396i	−1.24680	−	0.453798i	−0.879319	+	0.476233i	$0.842002\pi$
$132$			19.6643i			1.71155i
$133$	13.3862	−	5.79147i	1.16073	−	0.502184i
$134$	2.92493			0.252676
$135$		0			0
$136$	−0.150750	−	0.854944i	−0.0129267	−	0.0733109i
$137$	5.49600	−	6.54988i	0.469555	−	0.559594i	−0.478341	−	0.878174i	$-0.658762\pi$
$137$	5.49600	−	6.54988i	0.469555	−	0.559594i	0.947896	+	0.318580i	$0.103206\pi$
$138$	−2.33710	−	2.78525i	−0.198948	−	0.237096i
$139$	−1.52883	+	8.67044i	−0.129674	+	0.735417i	0.848748	+	0.528798i	$0.177357\pi$
$139$	−1.52883	+	8.67044i	−0.129674	+	0.735417i	−0.978421	+	0.206619i	$0.933754\pi$
$140$		0			0
$141$	−0.527344	−	0.913387i	−0.0444104	−	0.0769210i
$142$	−2.35672	−	6.47503i	−0.197771	−	0.543372i
$143$	−1.56230	−	4.29238i	−0.130646	−	0.358947i
$144$	3.55522	+	6.15783i	0.296269	+	0.513152i
$145$		0			0
$146$	−1.35735	+	7.69790i	−0.112335	+	0.637083i
$147$	8.57692	+	10.2216i	0.707413	+	0.843061i
$148$	1.08061	−	1.28782i	0.0888258	−	0.105858i
$149$	−0.132240	−	0.749969i	−0.0108335	−	0.0614398i	0.978912	−	0.204284i	$-0.0654865\pi$
$149$	−0.132240	−	0.749969i	−0.0108335	−	0.0614398i	−0.989745	+	0.142844i	$0.954375\pi$
$150$		0			0
$151$	−6.08784			−0.495421			−0.247711	−	0.968834i	$-0.579678\pi$
$151$	−6.08784			−0.495421			−0.247711	+	0.968834i	$0.579678\pi$
$152$	0.501343	−	4.32997i	0.0406643	−	0.351207i
$153$		−	6.17282i		−	0.499043i
$154$	19.4454	+	7.07756i	1.56696	+	0.570326i
$155$		0			0
$156$	−1.79912	−	1.50964i	−0.144045	−	0.120868i
$157$	15.6683	+	18.6728i	1.25047	+	1.49025i	0.803034	+	0.595933i	$0.203218\pi$
$157$	15.6683	+	18.6728i	1.25047	+	1.49025i	0.447434	+	0.894317i	$0.352338\pi$
$158$	−2.26401	−	0.399207i	−0.180115	−	0.0317592i
$159$	−11.2957	+	19.5647i	−0.895804	+	1.55158i
$160$		0			0
$161$	−3.59543	+	1.30863i	−0.283360	+	0.103134i
$162$	6.91809	+	19.0073i	0.543536	+	1.49335i
$163$	3.73250	−	2.15496i	0.292352	−	0.168789i	−0.346650	−	0.937994i	$-0.612681\pi$
$163$	3.73250	−	2.15496i	0.292352	−	0.168789i	0.639002	+	0.769205i	$0.279348\pi$
$164$	4.84548	−	8.39261i	0.378368	−	0.655353i
$165$		0			0
$166$	8.76873	−	7.35783i	0.680585	−	0.571079i
$167$	−3.34993	+	3.99229i	−0.259225	+	0.308933i	−0.879922	−	0.475118i	$-0.842405\pi$
$167$	−3.34993	+	3.99229i	−0.259225	+	0.308933i	0.620697	+	0.784051i	$0.286850\pi$
$168$	10.4779	−	1.84754i	0.808391	−	0.142541i
$169$	−11.7033	−	4.25967i	−0.900258	−	0.327667i
$170$		0			0
$171$	8.85690	−	29.7013i	0.677304	−	2.27131i
$172$			1.85830i			0.141694i
$173$	−2.40637	+	6.61144i	−0.182953	+	0.502658i	−0.996935	−	0.0782309i	$-0.975073\pi$
$173$	−2.40637	+	6.61144i	−0.182953	+	0.502658i	0.813983	+	0.580889i	$0.197295\pi$
$174$	−4.30117	−	24.3931i	−0.326071	−	1.84924i
$175$		0			0
$176$	4.73747	−	3.97521i	0.357100	−	0.299642i
$177$	15.2195	+	2.68360i	1.14397	+	0.201712i
$178$	−2.01629	−	1.16411i	−0.151127	−	0.0872534i
$179$	1.59972	+	2.77080i	0.119569	+	0.207099i	0.919597	−	0.392863i	$-0.128515\pi$
$179$	1.59972	+	2.77080i	0.119569	+	0.207099i	−0.800028	+	0.599963i	$0.795182\pi$
$180$		0			0
$181$	4.44963	−	1.61953i	0.330738	−	0.120379i	−0.171313	−	0.985217i	$-0.554801\pi$
$181$	4.44963	−	1.61953i	0.330738	−	0.120379i	0.502052	+	0.864838i	$0.332579\pi$
$182$	−2.14038	+	1.23575i	−0.158655	+	0.0915997i
$183$	19.9025	+	11.4907i	1.47124	+	0.849419i
$184$	−0.198562	+	1.12610i	−0.0146382	+	0.0830172i
$185$		0			0
$186$	−15.7784	−	13.2396i	−1.15693	−	0.970777i
$187$	−5.28725	+	0.932285i	−0.386642	+	0.0681754i
$188$	−0.113446	+	0.311691i	−0.00827393	+	0.0227324i
$189$	43.7335			3.18114
$190$		0			0
$191$	−18.4307			−1.33360			−0.666800	−	0.745237i	$-0.732336\pi$
$191$	−18.4307			−1.33360			−0.666800	+	0.745237i	$0.732336\pi$
$192$	1.08752	−	2.98793i	0.0784849	−	0.215636i
$193$	−13.3437	+	2.35285i	−0.960501	+	0.169362i	−0.631851	−	0.775090i	$-0.717705\pi$
$193$	−13.3437	+	2.35285i	−0.960501	+	0.169362i	−0.328649	+	0.944452i	$0.606593\pi$
$194$	−5.24285	−	4.39927i	−0.376415	−	0.315849i
$195$		0			0
$196$	0.728700	−	4.13266i	0.0520500	−	0.295190i
$197$	−7.09361	−	4.09550i	−0.505399	−	0.291792i	0.225541	−	0.974234i	$-0.427585\pi$
$197$	−7.09361	−	4.09550i	−0.505399	−	0.291792i	−0.730940	+	0.682441i	$0.760918\pi$
$198$	38.0820	−	21.9867i	2.70637	−	1.56252i
$199$	5.58408	−	2.03244i	0.395845	−	0.144076i	−0.136425	−	0.990650i	$-0.543561\pi$
$199$	5.58408	−	2.03244i	0.395845	−	0.144076i	0.532270	+	0.846575i	$0.321339\pi$
$200$		0			0
$201$	−4.65019	−	8.05437i	−0.327999	−	0.568112i
$202$	8.82205	+	5.09342i	0.620718	+	0.358371i
$203$	−25.6698	−	4.52627i	−1.80166	−	0.317682i
$204$	−2.11459	+	1.77435i	−0.148051	+	0.124229i
$205$		0			0
$206$	−0.359538	−	2.03904i	−0.0250502	−	0.142067i
$207$	−2.78083	+	7.64026i	−0.193281	+	0.531035i
$208$			0.738619i			0.0512140i
$209$	−26.7779	−	3.10047i	−1.85227	−	0.214464i
$210$		0			0
$211$	1.63846	+	0.596352i	0.112796	+	0.0410545i	0.397802	−	0.917471i	$-0.369773\pi$
$211$	1.63846	+	0.596352i	0.112796	+	0.0410545i	−0.285005	+	0.958526i	$0.591995\pi$
$212$	6.99694	−	1.23375i	0.480552	−	0.0847342i
$213$	−14.0834	+	16.7840i	−0.964981	+	1.15002i
$214$	−11.2127	+	9.40858i	−0.766485	+	0.643157i
$215$		0			0
$216$	6.53498	−	11.3189i	0.444649	−	0.770155i
$217$	−18.7713	+	10.8376i	−1.27428	+	0.735703i
$218$	2.97393	+	8.17082i	0.201420	+	0.553397i
$219$	23.3557	−	8.50076i	1.57823	−	0.574428i
$220$		0			0
$221$	0.320610	−	0.555312i	0.0215665	−	0.0373543i
$222$	−5.26428	−	0.928235i	−0.353315	−	0.0622990i
$223$	−16.9959	−	20.2549i	−1.13813	−	1.35637i	−0.925281	−	0.379283i	$-0.876171\pi$
$223$	−16.9959	−	20.2549i	−1.13813	−	1.35637i	−0.212848	−	0.977085i	$-0.568274\pi$
$224$	−2.56327	−	2.15083i	−0.171265	−	0.143709i
$225$		0			0
$226$	10.1777	+	3.70436i	0.677007	+	0.246411i
$227$		−	27.4472i		−	1.82174i	−0.412697	−	0.910869i	$-0.635413\pi$
$227$		−	27.4472i		−	1.82174i	0.412697	−	0.910869i	$-0.364587\pi$
$228$	−12.7205	+	5.50345i	−0.842434	+	0.364475i
$229$	11.5722			0.764711			0.382355	−	0.924015i	$-0.375113\pi$
$229$	11.5722			0.764711			0.382355	+	0.924015i	$0.375113\pi$
$230$		0			0
$231$	−11.4258	−	64.7990i	−0.751764	−	4.26346i
$232$	−5.00724	+	5.96740i	−0.328741	+	0.391779i
$233$	−8.26488	−	9.84970i	−0.541450	−	0.645275i	0.424062	−	0.905633i	$-0.360604\pi$
$233$	−8.26488	−	9.84970i	−0.541450	−	0.645275i	−0.965512	+	0.260358i	$0.916159\pi$
$234$	−0.911985	+	5.17212i	−0.0596183	+	0.338112i
$235$		0			0
$236$	−2.43015	−	4.20914i	−0.158189	−	0.273992i
$237$	2.50014	+	6.86908i	0.162402	+	0.446195i
$238$	0.993522	+	2.72968i	0.0644005	+	0.176939i
$239$	−5.65708	−	9.79836i	−0.365926	−	0.633803i	0.622998	−	0.782223i	$-0.285914\pi$
$239$	−5.65708	−	9.79836i	−0.365926	−	0.633803i	−0.988924	+	0.148420i	$0.952581\pi$
$240$		0			0
$241$	−4.13196	+	23.4335i	−0.266163	+	1.50948i	0.499541	+	0.866290i	$0.333502\pi$
$241$	−4.13196	+	23.4335i	−0.266163	+	1.50948i	−0.765704	+	0.643193i	$0.777609\pi$
$242$	−17.5133	−	20.8715i	−1.12580	−	1.34167i
$243$	16.1379	−	19.2325i	1.03525	−	1.23376i
$244$	−1.25506	−	7.11777i	−0.0803467	−	0.455669i
$245$		0			0
$246$	−30.8143			−1.96465
$247$	2.33943	−	2.21194i	0.148854	−	0.140742i
$248$			6.47773i			0.411337i
$249$	−34.2022	−	12.4486i	−2.16747	−	0.788896i
$250$		0			0
$251$	19.9736	+	16.7599i	1.26072	+	1.05787i	0.995604	+	0.0936578i	$0.0298560\pi$
$251$	19.9736	+	16.7599i	1.26072	+	1.05787i	0.265120	+	0.964215i	$0.414588\pi$
$252$	−15.2934	−	18.2260i	−0.963394	−	1.14813i
$253$	6.96417	+	1.22797i	0.437833	+	0.0772018i
$254$	5.61224	−	9.72069i	0.352143	−	0.609930i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	3.47247	+	9.54054i	0.216607	+	0.595122i	0.999639	−	0.0268585i	$-0.00855035\pi$
$257$	3.47247	+	9.54054i	0.216607	+	0.595122i	−0.783032	+	0.621981i	$0.786328\pi$
$258$	5.11719	−	2.95441i	0.318582	−	0.183934i
$259$	−2.81263	+	4.87161i	−0.174768	+	0.302707i
$260$		0			0
$261$	−42.4309	+	35.6037i	−2.62641	+	2.20382i
$262$	9.76144	−	11.6332i	0.603064	−	0.718704i
$263$	16.8663	−	2.97399i	1.04002	−	0.183384i	0.372545	−	0.928014i	$-0.378485\pi$
$263$	16.8663	−	2.97399i	1.04002	−	0.183384i	0.667477	+	0.744630i	$0.267374\pi$
$264$	−18.4784	−	6.72557i	−1.13726	−	0.413930i
$265$		0			0
$266$	0.863848	+	14.5597i	0.0529659	+	0.892714i
$267$			7.40300i			0.453056i
$268$	−1.00039	+	2.74854i	−0.0611083	+	0.167894i
$269$	−3.96080	−	22.4628i	−0.241495	−	1.36958i	−0.828495	−	0.559997i	$-0.810802\pi$
$269$	−3.96080	−	22.4628i	−0.241495	−	1.36958i	0.587000	−	0.809587i	$-0.300309\pi$
$270$		0			0
$271$	13.6282	−	11.4354i	0.827852	−	0.694650i	−0.126945	−	0.991910i	$-0.540517\pi$
$271$	13.6282	−	11.4354i	0.827852	−	0.694650i	0.954797	+	0.297260i	$0.0960727\pi$
$272$	0.854944	+	0.150750i	0.0518386	+	0.00914054i
$273$	6.80574	+	3.92930i	0.411902	+	0.237812i
$274$	4.27513	+	7.40475i	0.258270	+	0.447337i
$275$		0			0
$276$	3.41662	−	1.24355i	0.205656	−	0.0748527i
$277$	−18.0765	+	10.4365i	−1.08611	+	0.627066i	−0.932538	−	0.361071i	$-0.882411\pi$
$277$	−18.0765	+	10.4365i	−1.08611	+	0.627066i	−0.153572	+	0.988137i	$0.549078\pi$
$278$	−7.62466	−	4.40210i	−0.457296	−	0.264020i
$279$	−7.99817	+	45.3598i	−0.478838	+	2.71562i
$280$		0			0
$281$	−20.8354	−	17.4830i	−1.24294	−	1.04295i	−0.997289	−	0.0735907i	$-0.976554\pi$
$281$	−20.8354	−	17.4830i	−1.24294	−	1.04295i	−0.245650	−	0.969359i	$-0.579001\pi$
$282$	1.03867	−	0.183145i	0.0618516	−	0.0109061i
$283$	6.73563	−	18.5060i	0.400392	−	1.10007i	−0.561700	−	0.827341i	$-0.689852\pi$
$283$	6.73563	−	18.5060i	0.400392	−	1.10007i	0.962092	−	0.272726i	$-0.0879254\pi$
$284$	6.89058			0.408881
$285$		0			0
$286$	4.56786			0.270103
$287$	−11.0907	+	30.4714i	−0.654662	+	1.79867i
$288$	−7.00242	+	1.23472i	−0.412622	+	0.0727564i
$289$	12.4454	+	10.4429i	0.732084	+	0.614291i
$290$		0			0
$291$	−3.77893	+	21.4314i	−0.221525	+	1.25633i
$292$	−6.76942	−	3.90833i	−0.396151	−	0.228718i
$293$	12.7973	−	7.38854i	0.747628	−	0.431643i	−0.0772085	−	0.997015i	$-0.524601\pi$
$293$	12.7973	−	7.38854i	0.747628	−	0.431643i	0.824836	+	0.565372i	$0.191267\pi$
$294$	−12.5386	+	4.56368i	−0.731267	+	0.266159i
$295$		0			0
$296$	0.840567	+	1.45590i	0.0488570	+	0.0846227i
$297$	−69.9999	−	40.4145i	−4.06181	−	2.34508i
$298$	0.749969	+	0.132240i	0.0434445	+	0.00766044i
$299$	−0.646993	+	0.542892i	−0.0374166	+	0.0313962i
$300$		0			0
$301$	−1.07976	−	6.12360i	−0.0622361	−	0.352958i
$302$	2.08216	−	5.72070i	0.119815	−	0.329189i
$303$		−	32.3910i		−	1.86081i
$304$	3.89737	+	1.95205i	0.223530	+	0.111958i
$305$		0			0
$306$	5.80055	+	2.11123i	0.331595	+	0.120691i
$307$	4.17455	−	0.736086i	0.238254	−	0.0420106i	−0.0532459	−	0.998581i	$-0.516957\pi$
$307$	4.17455	−	0.736086i	0.238254	−	0.0420106i	0.291500	+	0.956571i	$0.405846\pi$
$308$	−13.3015	+	15.8521i	−0.757921	+	0.903255i
$309$	−5.04328	+	4.23182i	−0.286902	+	0.240740i
$310$		0			0
$311$	3.49343	−	6.05079i	0.198094	−	0.343109i	−0.749816	−	0.661646i	$-0.769858\pi$
$311$	3.49343	−	6.05079i	0.198094	−	0.343109i	0.947910	+	0.318537i	$0.103192\pi$
$312$	2.03393	−	1.17429i	0.115149	−	0.0664811i
$313$	−2.60608	−	7.16016i	−0.147305	−	0.404716i	0.843993	−	0.536354i	$-0.180199\pi$
$313$	−2.60608	−	7.16016i	−0.147305	−	0.404716i	−0.991298	+	0.131638i	$0.957976\pi$
$314$	−22.9056	+	8.33694i	−1.29264	+	0.470481i
$315$		0			0
$316$	1.14947	−	1.99094i	0.0646627	−	0.111999i
$317$	13.5297	+	2.38566i	0.759905	+	0.133992i	0.540156	−	0.841565i	$-0.318365\pi$
$317$	13.5297	+	2.38566i	0.759905	+	0.133992i	0.219749	+	0.975557i	$0.429476\pi$
$318$	−14.5214	−	17.3060i	−0.814321	−	0.970470i
$319$	36.9043	+	30.9664i	2.06625	+	1.73379i
$320$		0			0
$321$	43.7348	+	15.9182i	2.44104	+	0.888466i
$322$		−	3.82618i		−	0.213224i
$323$	−2.08283	−	3.15932i	−0.115892	−	0.175789i
$324$	−20.2271			−1.12373
$325$		0			0
$326$	0.748409	+	4.24444i	0.0414506	+	0.235078i
$327$	17.7718	−	21.1796i	0.982785	−	1.17124i
$328$	6.22923	+	7.42370i	0.343952	+	0.409905i
$329$	0.192730	−	1.09302i	0.0106255	−	0.0602604i
$330$		0			0
$331$	3.32212	+	5.75409i	0.182600	+	0.316273i	0.942765	−	0.333457i	$-0.108215\pi$
$331$	3.32212	+	5.75409i	0.182600	+	0.316273i	−0.760165	+	0.649730i	$0.774882\pi$
$332$	3.91502	+	10.7564i	0.214865	+	0.590336i
$333$	4.08838	+	11.2327i	0.224042	+	0.615550i
$334$	−2.60578	−	4.51335i	−0.142582	−	0.246959i
$335$		0			0
$336$	−1.84754	+	10.4779i	−0.100792	+	0.571619i
$337$	−11.8323	−	14.1012i	−0.644545	−	0.768139i	0.340536	−	0.940232i	$-0.389392\pi$
$337$	−11.8323	−	14.1012i	−0.644545	−	0.768139i	−0.985081	+	0.172093i	$0.944947\pi$
$338$	8.00556	−	9.54066i	0.435445	−	0.518943i
$339$	−5.98022	−	33.9155i	−0.324801	−	1.84204i
$340$		0			0
$341$	40.0604			2.16939
$342$	24.8808	+	18.4812i	1.34540	+	0.999349i
$343$		−	9.38108i		−	0.506531i
$344$	−1.74623	−	0.635576i	−0.0941504	−	0.0342680i
$345$		0			0
$346$	−5.38969	−	4.52249i	−0.289752	−	0.243131i
$347$	4.76787	+	5.68212i	0.255952	+	0.305032i	0.878684	−	0.477403i	$-0.158422\pi$
$347$	4.76787	+	5.68212i	0.255952	+	0.305032i	−0.622732	+	0.782435i	$0.713977\pi$
$348$	24.3931	+	4.30117i	1.30761	+	0.230567i
$349$	9.57581	−	16.5858i	0.512581	−	0.887817i	−0.487312	−	0.873228i	$-0.662023\pi$
$349$	9.57581	−	16.5858i	0.512581	−	0.887817i	0.999894	−	0.0145891i	$-0.00464403\pi$
$350$		0			0
$351$	9.07153	−	3.30177i	0.484202	−	0.176235i
$352$	2.11516	+	5.81136i	0.112739	+	0.309747i
$353$	1.38857	−	0.801691i	0.0739061	−	0.0426697i	−0.462592	−	0.886572i	$-0.653080\pi$
$353$	1.38857	−	0.801691i	0.0739061	−	0.0426697i	0.536498	+	0.843902i	$0.319747\pi$
$354$	−7.72713	+	13.3838i	−0.410692	+	0.711340i
$355$		0			0
$356$	1.78351	−	1.49655i	0.0945261	−	0.0793168i
$357$	5.93716	−	7.07563i	0.314228	−	0.374482i
$358$	−3.15084	+	0.555577i	−0.166527	+	0.0293632i
$359$	−20.2961	−	7.38717i	−1.07119	−	0.389880i	−0.254566	−	0.967055i	$-0.581933\pi$
$359$	−20.2961	−	7.38717i	−1.07119	−	0.389880i	−0.816620	+	0.577175i	$0.804155\pi$
$360$		0			0
$361$	−5.48872	−	18.1899i	−0.288880	−	0.957365i
$362$			4.73520i			0.248876i
$363$	−29.6304	+	81.4089i	−1.55519	+	4.27286i
$364$	−0.429171	−	2.43395i	−0.0224947	−	0.127574i
$365$		0			0
$366$	−17.6048	+	14.7722i	−0.920219	+	0.772155i
$367$	19.4420	+	3.42815i	1.01486	+	0.178948i	0.656255	−	0.754540i	$-0.272140\pi$
$367$	19.4420	+	3.42815i	1.01486	+	0.178948i	0.358610	+	0.933488i	$0.383251\pi$
$368$	−0.990275	−	0.571736i	−0.0516217	−	0.0298038i
$369$	34.4535	+	59.6753i	1.79358	+	3.10657i
$370$		0			0
$371$	−22.3399	+	8.13107i	−1.15983	+	0.422144i
$372$	17.8377	−	10.2986i	0.924842	−	0.533958i
$373$	−20.0572	−	11.5800i	−1.03852	−	0.599592i	−0.119109	−	0.992881i	$-0.538004\pi$
$373$	−20.0572	−	11.5800i	−1.03852	−	0.599592i	−0.919415	+	0.393289i	$0.871337\pi$
$374$	0.932285	−	5.28725i	0.0482073	−	0.273397i
$375$		0			0
$376$	−0.254093	−	0.213209i	−0.0131039	−	0.0109954i
$377$	−5.66634	+	0.999129i	−0.291831	+	0.0514578i
$378$	−14.9577	+	41.0960i	−0.769343	+	2.11375i
$379$	3.52957			0.181302			0.0906508	−	0.995883i	$-0.471105\pi$
$379$	3.52957			0.181302			0.0906508	+	0.995883i	$0.471105\pi$
$380$		0			0
$381$	−35.6904			−1.82847
$382$	6.30368	−	17.3192i	0.322524	−	0.886128i
$383$	36.1246	−	6.36973i	1.84588	−	0.325478i	0.862362	−	0.506293i	$-0.168985\pi$
$383$	36.1246	−	6.36973i	1.84588	−	0.325478i	0.983517	+	0.180815i	$0.0578734\pi$
$384$	2.43579	+	2.04387i	0.124301	+	0.104301i
$385$		0			0
$386$	2.35285	−	13.3437i	0.119757	−	0.679176i
$387$	−11.4431	−	6.60667i	−0.581685	−	0.335836i
$388$	5.92713	−	3.42203i	0.300904	−	0.173727i
$389$	−23.1021	+	8.40847i	−1.17132	+	0.426327i	−0.853129	−	0.521699i	$-0.825298\pi$
$389$	−23.1021	+	8.40847i	−1.17132	+	0.426327i	−0.318193	+	0.948026i	$0.603076\pi$
$390$		0			0
$391$	0.496343	+	0.859691i	0.0251011	+	0.0434764i
$392$	3.63420	+	2.09821i	0.183555	+	0.105976i
$393$	−47.5536	−	8.38498i	−2.39876	−	0.422966i
$394$	6.27467	−	5.26507i	0.316113	−	0.265251i
$395$		0			0
$396$	7.63589	+	43.3053i	0.383718	+	2.17617i
$397$	6.96208	−	19.1282i	0.349417	−	0.960015i	−0.633137	−	0.774039i	$-0.718233\pi$
$397$	6.96208	−	19.1282i	0.349417	−	0.960015i	0.982554	−	0.185976i	$-0.0595446\pi$
$398$			5.94246i			0.297868i
$399$	38.7197	−	25.5265i	1.93841	−	1.27792i
$400$		0			0
$401$	−18.9313	−	6.89045i	−0.945386	−	0.344092i	−0.177096	−	0.984194i	$-0.556670\pi$
$401$	−18.9313	−	6.89045i	−0.945386	−	0.344092i	−0.768291	+	0.640101i	$0.778892\pi$
$402$	9.15910	−	1.61500i	0.456814	−	0.0805487i
$403$	−3.07547	+	3.66520i	−0.153200	+	0.182576i
$404$	−7.80356	+	6.54797i	−0.388242	+	0.325774i
$405$		0			0
$406$	13.0329	−	22.5736i	0.646811	−	1.12031i
$407$	9.00379	−	5.19834i	0.446301	−	0.257672i
$408$	−0.944111	−	2.59392i	−0.0467405	−	0.128418i
$409$	12.1073	−	4.40670i	0.598668	−	0.217897i	−0.0248698	−	0.999691i	$-0.507917\pi$
$409$	12.1073	−	4.40670i	0.598668	−	0.217897i	0.623537	+	0.781794i	$0.285695\pi$
$410$		0			0
$411$	13.5936	−	23.5448i	0.670523	−	1.16138i
$412$	2.03904	+	0.359538i	0.100456	+	0.0177132i
$413$	10.4537	+	12.4582i	0.514393	+	0.613030i
$414$	−6.22840	−	5.22625i	−0.306109	−	0.256856i
$415$		0			0
$416$	−0.694074	−	0.252622i	−0.0340298	−	0.0123858i
$417$			27.9946i			1.37090i
$418$	12.0721	−	24.1026i	0.590465	−	1.17890i
$419$	−20.0166			−0.977876			−0.488938	−	0.872319i	$-0.662616\pi$
$419$	−20.0166			−0.977876			−0.488938	+	0.872319i	$0.662616\pi$
$420$		0			0
$421$	1.16311	+	6.59634i	0.0566867	+	0.321486i	0.999944	−	0.0105764i	$-0.00336662\pi$
$421$	1.16311	+	6.59634i	0.0566867	+	0.321486i	−0.943257	+	0.332062i	$0.892256\pi$
$422$	−1.12077	+	1.33569i	−0.0545585	+	0.0650202i
$423$	−1.51601	−	1.80672i	−0.0737112	−	0.0878455i
$424$	−1.23375	+	6.99694i	−0.0599161	+	0.339801i
$425$		0			0
$426$	−10.9550	−	18.9746i	−0.530770	−	0.919321i
$427$	8.27149	+	22.7257i	0.400285	+	1.09978i
$428$	−5.00620	−	13.7544i	−0.241984	−	0.664845i
$429$	−7.26219	−	12.5785i	−0.350622	−	0.607295i
$430$		0			0
$431$	−4.86528	+	27.5924i	−0.234352	+	1.32908i	0.609621	+	0.792693i	$0.291321\pi$
$431$	−4.86528	+	27.5924i	−0.234352	+	1.32908i	−0.843974	+	0.536385i	$0.819790\pi$
$432$	8.40121	+	10.0122i	0.404203	+	0.481711i
$433$	−14.5384	+	17.3262i	−0.698673	+	0.832646i	−0.992376	−	0.123251i	$-0.960668\pi$
$433$	−14.5384	+	17.3262i	−0.698673	+	0.832646i	0.293702	+	0.955897i	$0.405113\pi$
$434$	−3.76386	−	21.3459i	−0.180671	−	1.02464i
$435$		0			0
$436$	−8.69520			−0.416425
$437$	1.15471	+	4.84868i	0.0552373	+	0.231944i
$438$			24.8546i			1.18760i
$439$	−3.88563	−	1.41425i	−0.185451	−	0.0674986i	0.247626	−	0.968856i	$-0.420350\pi$
$439$	−3.88563	−	1.41425i	−0.185451	−	0.0674986i	−0.433076	+	0.901357i	$0.642572\pi$
$440$		0			0
$441$	22.8575	+	19.1798i	1.08845	+	0.913322i
$442$	0.412168	+	0.491202i	0.0196048	+	0.0233641i
$443$	28.5001	+	5.02534i	1.35408	+	0.238761i	0.803144	−	0.595786i	$-0.203159\pi$
$443$	28.5001	+	5.02534i	1.35408	+	0.238761i	0.550937	+	0.834547i	$0.314270\pi$
$444$	2.67274	−	4.62933i	0.126843	−	0.219698i
$445$		0			0
$446$	24.8463	−	9.04332i	1.17651	−	0.428214i
$447$	−0.828187	−	2.27543i	−0.0391719	−	0.107624i
$448$	2.89781	−	1.67305i	0.136909	−	0.0790443i
$449$	−2.78070	+	4.81632i	−0.131229	+	0.227296i	−0.924151	−	0.382028i	$-0.875226\pi$
$449$	−2.78070	+	4.81632i	−0.131229	+	0.227296i	0.792921	+	0.609324i	$0.208559\pi$
$450$		0			0
$451$	45.9106	−	38.5236i	2.16185	−	1.81400i
$452$	−6.96192	+	8.29690i	−0.327461	+	0.390253i
$453$	−19.0634	+	3.36139i	−0.895676	+	0.157932i
$454$	25.7920	+	9.38751i	1.21048	+	0.440578i
$455$		0			0
$456$	−0.820886	−	13.8356i	−0.0384415	−	0.647913i
$457$		−	3.44090i		−	0.160959i	−0.996756	−	0.0804793i	$-0.974355\pi$
$457$		−	3.44090i		−	0.160959i	0.996756	−	0.0804793i	$-0.0256451\pi$
$458$	−3.95792	+	10.8743i	−0.184941	+	0.508122i
$459$	−1.97029	−	11.1741i	−0.0919654	−	0.521562i
$460$		0			0
$461$	−3.88985	+	3.26397i	−0.181169	+	0.152018i	−0.728862	−	0.684661i	$-0.759950\pi$
$461$	−3.88985	+	3.26397i	−0.181169	+	0.152018i	0.547693	+	0.836679i	$0.315506\pi$
$462$	64.7990	+	11.4258i	3.01472	+	0.531577i
$463$	−4.44107	−	2.56405i	−0.206394	−	0.119162i	0.393240	−	0.919436i	$-0.371354\pi$
$463$	−4.44107	−	2.56405i	−0.206394	−	0.119162i	−0.599634	+	0.800274i	$0.704687\pi$
$464$	−3.89494	−	6.74624i	−0.180818	−	0.313186i
$465$		0			0
$466$	12.0824	−	4.39765i	0.559708	−	0.203717i
$467$	25.6535	−	14.8110i	1.18710	−	0.685373i	0.229454	−	0.973320i	$-0.426306\pi$
$467$	25.6535	−	14.8110i	1.18710	−	0.685373i	0.957646	+	0.287947i	$0.0929727\pi$
$468$	−4.54829	−	2.62595i	−0.210245	−	0.121385i
$469$	1.69952	−	9.63844i	0.0784764	−	0.445062i
$470$		0			0
$471$	59.3737	+	49.8205i	2.73580	+	2.29561i
$472$	4.78646	−	0.843982i	0.220315	−	0.0388474i
$473$	−3.93061	+	10.7993i	−0.180729	+	0.496550i
$474$	−7.30992			−0.335756
$475$		0			0
$476$	−2.90486			−0.133144
$477$	−17.2785	+	47.4722i	−0.791127	+	2.17360i
$478$	11.1423	−	1.96468i	0.509636	−	0.0898626i
$479$	28.8677	+	24.2229i	1.31900	+	1.10677i	0.986516	+	0.163664i	$0.0523314\pi$
$479$	28.8677	+	24.2229i	1.31900	+	1.10677i	0.332485	+	0.943109i	$0.392113\pi$
$480$		0			0
$481$	−0.215622	+	1.22285i	−0.00983151	+	0.0557573i
$482$	−20.6071	−	11.8975i	−0.938626	−	0.541916i
$483$	−10.5361	+	6.08303i	−0.479410	+	0.276788i
$484$	25.6027	−	9.31863i	1.16376	−	0.423574i
$485$		0			0
$486$	12.5531	+	21.7426i	0.569420	+	0.986264i
$487$	15.3757	+	8.87714i	0.696738	+	0.402262i	0.806131	−	0.591737i	$-0.201558\pi$
$487$	15.3757	+	8.87714i	0.696738	+	0.402262i	−0.109393	+	0.993999i	$0.534891\pi$
$488$	7.11777	+	1.25506i	0.322206	+	0.0568137i
$489$	10.4980	−	8.80890i	0.474738	−	0.398352i
$490$		0			0
$491$	−3.87201	−	21.9592i	−0.174741	−	0.991006i	−0.938442	−	0.345436i	$-0.887731\pi$
$491$	−3.87201	−	21.9592i	−0.174741	−	0.991006i	0.763701	−	0.645570i	$-0.223380\pi$
$492$	10.5391	−	28.9559i	0.475139	−	1.30543i
$493$			6.76266i			0.304575i
$494$	1.27841	+	2.95487i	0.0575183	+	0.132946i
$495$		0			0
$496$	−6.08708	−	2.21552i	−0.273318	−	0.0994796i
$497$	−22.7063	+	4.00374i	−1.01852	+	0.179592i
$498$	23.3957	−	27.8819i	1.04838	−	1.24942i
$499$	14.4603	−	12.1337i	0.647334	−	0.543177i	−0.258927	−	0.965897i	$-0.583369\pi$
$499$	14.4603	−	12.1337i	0.647334	−	0.543177i	0.906261	+	0.422719i	$0.138924\pi$
$500$		0			0
$501$	−8.28559	+	14.3511i	−0.370173	+	0.641158i
$502$	−22.5805	+	13.0369i	−1.00782	+	0.581864i
$503$	13.9751	+	38.3963i	0.623119	+	1.71201i	0.699221	+	0.714905i	$0.253530\pi$
$503$	13.9751	+	38.3963i	0.623119	+	1.71201i	−0.0761023	+	0.997100i	$0.524248\pi$
$504$	22.3575	−	8.13745i	0.995880	−	0.362471i
$505$		0			0
$506$	−3.53580	+	6.12418i	−0.157185	+	0.272253i
$507$	−38.9997	−	6.87669i	−1.73204	−	0.305405i
$508$	7.21496	+	8.59845i	0.320112	+	0.381495i
$509$	10.1977	+	8.55692i	0.452007	+	0.379279i	0.840180	−	0.542308i	$-0.182449\pi$
$509$	10.1977	+	8.55692i	0.452007	+	0.379279i	−0.388173	+	0.921586i	$0.626894\pi$
$510$		0			0
$511$	24.5780	+	8.94566i	1.08727	+	0.395733i
$512$		−	1.00000i		−	0.0441942i
$513$	6.55254	−	56.5926i	0.289302	−	2.49862i
$514$	−10.1528			−0.447822
$515$		0			0
$516$	1.02606	+	5.81905i	0.0451696	+	0.256170i
$517$	−1.31856	+	1.57139i	−0.0579900	+	0.0691098i
$518$	−3.61584	−	4.30919i	−0.158871	−	0.189335i
$519$	−3.88477	+	22.0316i	−0.170523	+	0.967082i
$520$		0			0
$521$	13.8343	+	23.9617i	0.606091	+	1.04978i	0.991878	+	0.127193i	$0.0405968\pi$
$521$	13.8343	+	23.9617i	0.606091	+	1.04978i	−0.385787	+	0.922588i	$0.626070\pi$
$522$	−18.9443	−	52.0492i	−0.829172	−	2.27813i
$523$	−0.367514	−	1.00974i	−0.0160703	−	0.0441527i	0.931398	−	0.364002i	$-0.118590\pi$
$523$	−0.367514	−	1.00974i	−0.0160703	−	0.0441527i	−0.947468	+	0.319849i	$0.896368\pi$
$524$	7.59305	+	13.1516i	0.331704	+	0.574528i
$525$		0			0
$526$	−2.97399	+	16.8663i	−0.129672	+	0.735407i
$527$	3.61474	+	4.30788i	0.157460	+	0.187654i
$528$	12.6399	−	15.0637i	0.550083	−	0.655563i
$529$	3.76686	+	21.3629i	0.163776	+	0.928822i
$530$		0			0
$531$	34.5589			1.49973
$532$	−13.9771	−	4.16797i	−0.605985	−	0.180704i
$533$			7.15792i			0.310044i
$534$	−6.95655	−	2.53198i	−0.301039	−	0.109569i
$535$		0			0
$536$	−2.24063	−	1.88011i	−0.0967804	−	0.0812084i
$537$	6.53924	+	7.79316i	0.282189	+	0.336300i
$538$	22.4628	+	3.96080i	0.968442	+	0.170762i
$539$	12.9760	−	22.4751i	0.558916	−	0.968071i
$540$		0			0
$541$	−14.5180	+	5.28411i	−0.624177	+	0.227182i	−0.634695	−	0.772763i	$-0.718874\pi$
$541$	−14.5180	+	5.28411i	−0.624177	+	0.227182i	0.0105181	+	0.999945i	$0.496652\pi$
$542$	6.08464	+	16.7174i	0.261358	+	0.718074i
$543$	13.0393	−	7.52824i	0.559569	−	0.323068i
$544$	−0.434067	+	0.751825i	−0.0186104	+	0.0322342i
$545$		0			0
$546$	−6.02003	+	5.05141i	−0.257634	+	0.216180i
$547$	21.5990	−	25.7407i	0.923508	−	1.10059i	−0.0711601	−	0.997465i	$-0.522670\pi$
$547$	21.5990	−	25.7407i	0.923508	−	1.10059i	0.994668	−	0.103129i	$-0.0328854\pi$
$548$	−8.42037	+	1.48474i	−0.359700	+	0.0634248i
$549$	48.2920	+	17.5769i	2.06105	+	0.750162i
$550$		0			0
$551$	−9.70322	+	32.5394i	−0.413371	+	1.38622i
$552$			3.63589i			0.154754i
$553$	−2.63099	+	7.22858i	−0.111881	+	0.307391i
$554$	−3.62454	−	20.5558i	−0.153992	−	0.873333i
$555$		0			0
$556$	6.74440	−	5.65923i	0.286026	−	0.240005i
$557$	−14.0324	−	2.47429i	−0.594571	−	0.104839i	−0.131739	−	0.991285i	$-0.542056\pi$
$557$	−14.0324	−	2.47429i	−0.594571	−	0.104839i	−0.462833	+	0.886446i	$0.653167\pi$
$558$	−39.8888	−	23.0298i	−1.68863	−	0.974929i
$559$	−0.686287	−	1.18868i	−0.0290269	−	0.0502760i
$560$		0			0
$561$	−16.0417	+	5.83869i	−0.677280	+	0.246510i
$562$	23.5548	−	13.5994i	0.993599	−	0.573655i
$563$	12.7930	+	7.38607i	0.539163	+	0.311286i	0.744740	−	0.667355i	$-0.232574\pi$
$563$	12.7930	+	7.38607i	0.539163	+	0.311286i	−0.205577	+	0.978641i	$0.565907\pi$
$564$	−0.183145	+	1.03867i	−0.00771178	+	0.0437357i
$565$		0			0
$566$	15.0862	+	12.6588i	0.634122	+	0.532091i
$567$	66.6539	−	11.7529i	2.79920	−	0.493574i
$568$	−2.35672	+	6.47503i	−0.0988857	+	0.271686i
$569$	−19.4550			−0.815598			−0.407799	−	0.913072i	$-0.633704\pi$
$569$	−19.4550			−0.815598			−0.407799	+	0.913072i	$0.633704\pi$
$570$		0			0
$571$	−39.3956			−1.64866			−0.824328	−	0.566112i	$-0.808447\pi$
$571$	−39.3956			−1.64866			−0.824328	+	0.566112i	$0.808447\pi$
$572$	−1.56230	+	4.29238i	−0.0653230	+	0.179473i
$573$	−57.7137	+	10.1765i	−2.41102	+	0.425129i
$574$	−24.8405	−	20.8436i	−1.03682	−	0.869997i
$575$		0			0
$576$	1.23472	−	7.00242i	0.0514465	−	0.291768i
$577$	13.7657	+	7.94763i	0.573073	+	0.330864i	0.758376	−	0.651818i	$-0.225993\pi$
$577$	13.7657	+	7.94763i	0.573073	+	0.330864i	−0.185303	+	0.982682i	$0.559327\pi$
$578$	−14.0697	+	8.12317i	−0.585224	+	0.337879i
$579$	−40.4852	+	14.7354i	−1.68251	+	0.612382i
$580$		0			0
$581$	−19.1510	−	33.1706i	−0.794519	−	1.37615i
$582$	−18.8464	−	10.8810i	−0.781210	−	0.451032i
$583$	43.2713	+	7.62990i	1.79212	+	0.315998i
$584$	5.98791	−	5.02445i	0.247781	−	0.207913i
$585$		0			0
$586$	2.56601	+	14.5526i	0.106001	+	0.601161i
$587$	−4.40009	+	12.0891i	−0.181611	+	0.498973i	−0.996774	−	0.0802592i	$-0.974425\pi$
$587$	−4.40009	+	12.0891i	−0.181611	+	0.498973i	0.815163	+	0.579232i	$0.196647\pi$
$588$		−	13.3433i		−	0.550269i
$589$	11.2117	+	25.9144i	0.461971	+	1.06778i
$590$		0			0
$591$	−24.4742	−	8.90787i	−1.00673	−	0.366421i
$592$	−1.65559	+	0.291926i	−0.0680445	+	0.0119981i
$593$	1.39986	−	1.66829i	0.0574855	−	0.0685086i	−0.736535	−	0.676399i	$-0.763540\pi$
$593$	1.39986	−	1.66829i	0.0574855	−	0.0685086i	0.794021	+	0.607890i	$0.207984\pi$
$594$	61.9185	−	51.9558i	2.54055	−	2.13177i
$595$		0			0
$596$	−0.380769	+	0.659512i	−0.0155969	+	0.0270146i
$597$	16.3637	−	9.44759i	0.669722	−	0.386664i
$598$	−0.288867	−	0.793654i	−0.0118126	−	0.0324549i
$599$	3.32108	−	1.20877i	0.135696	−	0.0493891i	−0.273280	−	0.961935i	$-0.588108\pi$
$599$	3.32108	−	1.20877i	0.135696	−	0.0493891i	0.408975	+	0.912545i	$0.365886\pi$
$600$		0			0
$601$	−11.2019	+	19.4022i	−0.456935	+	0.791434i	−0.998797	−	0.0490333i	$-0.984386\pi$
$601$	−11.2019	+	19.4022i	−0.456935	+	0.791434i	0.541863	+	0.840467i	$0.317719\pi$
$602$	6.12360	+	1.07976i	0.249579	+	0.0440076i
$603$	−13.3684	−	15.9319i	−0.544405	−	0.648796i
$604$	4.66356	+	3.91319i	0.189757	+	0.159225i
$605$		0			0
$606$	30.4376	+	11.0784i	1.23644	+	0.450028i
$607$		−	12.5717i		−	0.510269i	−0.966906	−	0.255134i	$-0.917880\pi$
$607$		−	12.5717i		−	0.510269i	0.966906	−	0.255134i	$-0.0821197\pi$
$608$	−3.16730	+	2.99469i	−0.128451	+	0.121451i
$609$	−82.8812			−3.35851
$610$		0			0
$611$	−0.0425431	−	0.241274i	−0.00172111	−	0.00976090i
$612$	−3.96781	+	4.72865i	−0.160389	+	0.191144i
$613$	30.1404	+	35.9199i	1.21736	+	1.45079i	0.854901	+	0.518791i	$0.173618\pi$
$613$	30.1404	+	35.9199i	1.21736	+	1.45079i	0.362458	+	0.932000i	$0.381938\pi$
$614$	−0.736086	+	4.17455i	−0.0297060	+	0.168471i
$615$		0			0
$616$	−10.3467	−	17.9210i	−0.416880	−	0.722058i
$617$	−0.180720	−	0.496525i	−0.00727553	−	0.0199893i	0.936002	−	0.351995i	$-0.114497\pi$
$617$	−0.180720	−	0.496525i	−0.00727553	−	0.0199893i	−0.943277	+	0.332006i	$0.892275\pi$
$618$	−2.25170	−	6.18650i	−0.0905768	−	0.248858i
$619$	10.9317	+	18.9343i	0.439383	+	0.761034i	0.997642	−	0.0686330i	$-0.0218637\pi$
$619$	10.9317	+	18.9343i	0.439383	+	0.761034i	−0.558259	+	0.829667i	$0.688530\pi$
$620$		0			0
$621$	−2.59520	+	14.7181i	−0.104142	+	0.590616i
$622$	4.49106	+	5.35224i	0.180075	+	0.214605i
$623$	−5.00760	+	5.96783i	−0.200625	+	0.239096i
$624$	0.407827	+	2.31290i	0.0163261	+	0.0925901i
$625$		0			0
$626$	7.61968			0.304544
$627$	−85.5640	+	5.07663i	−3.41710	+	0.202741i
$628$		−	24.3756i		−	0.972692i
$629$	1.37143	+	0.499161i	0.0546826	+	0.0199028i
$630$		0			0
$631$	23.0776	+	19.3644i	0.918705	+	0.770885i	0.973755	−	0.227598i	$-0.0730873\pi$
$631$	23.0776	+	19.3644i	0.918705	+	0.770885i	−0.0550497	+	0.998484i	$0.517532\pi$
$632$	1.47773	+	1.76109i	0.0587810	+	0.0700524i
$633$	5.45993	+	0.962734i	0.217013	+	0.0382652i
$634$	−6.86922	+	11.8978i	−0.272812	+	0.472524i
$635$		0			0
$636$	21.2289	−	7.72669i	0.841781	−	0.306383i
$637$	1.06011	+	2.91263i	0.0420031	+	0.115402i
$638$	−41.7209	+	24.0876i	−1.65175	+	0.953637i
$639$	−24.4976	+	42.4310i	−0.969109	+	1.67855i
$640$		0			0
$641$	24.6653	−	20.6967i	0.974223	−	0.817470i	−0.00898505	−	0.999960i	$-0.502860\pi$
$641$	24.6653	−	20.6967i	0.974223	−	0.817470i	0.983208	+	0.182490i	$0.0584156\pi$
$642$	−29.9164	+	35.6530i	−1.18071	+	1.40711i
$643$	−25.2027	+	4.44391i	−0.993896	+	0.175251i	−0.646866	−	0.762604i	$-0.723921\pi$
$643$	−25.2027	+	4.44391i	−0.993896	+	0.175251i	−0.347030	+	0.937854i	$0.612810\pi$
$644$	3.59543	+	1.30863i	0.141680	+	0.0515672i
$645$		0			0
$646$	3.68115	−	0.876666i	0.144833	−	0.0344920i
$647$		−	18.8860i		−	0.742483i	−0.928536	−	0.371242i	$-0.878932\pi$
$647$		−	18.8860i		−	0.742483i	0.928536	−	0.371242i	$-0.121068\pi$
$648$	6.91809	−	19.0073i	0.271768	−	0.746677i
$649$	−5.21946	−	29.6010i	−0.204882	−	1.16194i
$650$		0			0
$651$	−52.7961	+	44.3012i	−2.06924	+	1.73630i
$652$	−4.24444	−	0.748409i	−0.166225	−	0.0293100i
$653$	21.5038	+	12.4152i	0.841510	+	0.485846i	0.857777	−	0.514022i	$-0.171845\pi$
$653$	21.5038	+	12.4152i	0.841510	+	0.485846i	−0.0162674	+	0.999868i	$0.505178\pi$
$654$	13.8240	+	23.9439i	0.540562	+	0.936282i
$655$		0			0
$656$	−9.10652	+	3.31450i	−0.355550	+	0.129410i
$657$	48.1336	−	27.7900i	1.87787	−	1.08419i
$658$	0.961190	+	0.554943i	0.0374711	+	0.0216339i
$659$	−5.44946	+	30.9054i	−0.212281	+	1.20391i	0.673282	+	0.739386i	$0.264884\pi$
$659$	−5.44946	+	30.9054i	−0.212281	+	1.20391i	−0.885563	+	0.464519i	$0.846227\pi$
$660$		0			0
$661$	−14.2738	−	11.9771i	−0.555186	−	0.465857i	0.321506	−	0.946907i	$-0.395811\pi$
$661$	−14.2738	−	11.9771i	−0.555186	−	0.465857i	−0.876693	+	0.481051i	$0.840255\pi$
$662$	−6.54331	+	1.15376i	−0.254313	+	0.0448422i
$663$	0.697338	−	1.91592i	0.0270824	−	0.0744082i
$664$	−11.4468			−0.444220
$665$		0			0
$666$	−11.9536			−0.463193
$667$	3.04655	−	8.37032i	0.117963	−	0.324100i
$668$	5.13239	−	0.904979i	0.198578	−	0.0350147i
$669$	−64.4044	−	54.0417i	−2.49002	−	2.08937i
$670$		0			0
$671$	7.76167	−	44.0186i	0.299636	−	1.69932i
$672$	−9.21415	−	5.31979i	−0.355444	−	0.205215i
$673$	12.6234	−	7.28810i	0.486594	−	0.280935i	−0.236566	−	0.971615i	$-0.576022\pi$
$673$	12.6234	−	7.28810i	0.486594	−	0.280935i	0.723161	+	0.690680i	$0.242689\pi$
$674$	17.2976	−	6.29582i	0.666280	−	0.242506i
$675$		0			0
$676$	6.22722	+	10.7859i	0.239509	+	0.414841i
$677$	−2.11001	−	1.21821i	−0.0810941	−	0.0468197i	0.458905	−	0.888486i	$-0.348242\pi$
$677$	−2.11001	−	1.21821i	−0.0810941	−	0.0468197i	−0.539999	+	0.841666i	$0.681575\pi$
$678$	33.9155	+	5.98022i	1.30252	+	0.229669i
$679$	−17.5431	+	14.7204i	−0.673244	+	0.564918i
$680$		0			0
$681$	−15.1549	−	85.9479i	−0.580738	−	3.29353i
$682$	−13.7015	+	37.6445i	−0.524656	+	1.44148i
$683$		−	15.0962i		−	0.577639i	−0.957384	−	0.288820i	$-0.906737\pi$
$683$		−	15.0962i		−	0.577639i	0.957384	−	0.288820i	$-0.0932628\pi$
$684$	−25.8764	+	17.0594i	−0.989409	+	0.652282i
$685$		0			0
$686$	8.81533	+	3.20852i	0.336571	+	0.122502i
$687$	36.2370	−	6.38955i	1.38253	−	0.243777i
$688$	1.19449	−	1.42354i	0.0455396	−	0.0542720i
$689$	−4.02004	+	3.37322i	−0.153151	+	0.128509i
$690$		0			0
$691$	6.12019	−	10.6005i	0.232823	−	0.403261i	−0.725815	−	0.687890i	$-0.758537\pi$
$691$	6.12019	−	10.6005i	0.232823	−	0.403261i	0.958638	+	0.284629i	$0.0918704\pi$
$692$	6.09314	−	3.51787i	0.231626	−	0.133729i
$693$	−50.3246	−	138.266i	−1.91167	−	5.25228i
$694$	−6.97015	+	2.53693i	−0.264583	+	0.0963005i
$695$		0			0
$696$	−12.3847	+	21.4510i	−0.469442	+	0.813097i
$697$	8.28523	+	1.46091i	0.313825	+	0.0553359i
$698$	12.3104	+	14.6710i	0.465956	+	0.555305i
$699$	−31.3190	−	26.2798i	−1.18459	−	0.993992i
$700$		0			0
$701$	−41.9967	−	15.2856i	−1.58620	−	0.577328i	−0.609656	−	0.792666i	$-0.708692\pi$
$701$	−41.9967	−	15.2856i	−1.58620	−	0.577328i	−0.976539	+	0.215339i	$0.930914\pi$
$702$			9.65372i			0.364356i
$703$	5.88261	+	4.36954i	0.221867	+	0.164800i
$704$	−6.18432			−0.233080
$705$		0			0
$706$	0.278424	+	1.57902i	0.0104786	+	0.0594273i
$707$	21.9102	−	26.1115i	0.824017	−	0.982026i
$708$	−9.93381	−	11.8386i	−0.373335	−	0.444924i
$709$	2.78707	−	15.8063i	0.104671	−	0.593617i	−0.886681	−	0.462382i	$-0.846995\pi$
$709$	2.78707	−	15.8063i	0.104671	−	0.593617i	0.991351	−	0.131235i	$-0.0418941\pi$
$710$		0			0
$711$	8.17325	+	14.1565i	0.306521	+	0.530910i
$712$	0.796295	+	2.18780i	0.0298424	+	0.0819914i
$713$	−2.53338	−	6.96040i	−0.0948758	−	0.260669i
$714$	4.61829	+	7.99911i	0.172835	+	0.299359i
$715$		0			0
$716$	0.555577	−	3.15084i	0.0207629	−	0.117752i
$717$	−23.1247	−	27.5589i	−0.863606	−	1.02921i
$718$	13.8833	−	16.5455i	0.518122	−	0.617474i
$719$	0.265213	+	1.50410i	0.00989079	+	0.0560934i	0.989354	−	0.145531i	$-0.0464891\pi$
$719$	0.265213	+	1.50410i	0.00989079	+	0.0560934i	−0.979463	+	0.201624i	$0.935378\pi$
$720$		0			0
$721$	−6.92809			−0.258016
$722$	18.9702	+	1.06362i	0.705998	+	0.0395838i
$723$			75.6608i			2.81385i
$724$	−4.44963	−	1.61953i	−0.165369	−	0.0601894i
$725$		0			0
$726$	−66.3651	−	55.6869i	−2.46304	−	2.06674i
$727$	−24.4052	−	29.0850i	−0.905139	−	1.07870i	−0.996559	−	0.0828900i	$-0.973585\pi$
$727$	−24.4052	−	29.0850i	−0.905139	−	1.07870i	0.0914199	−	0.995812i	$-0.470859\pi$
$728$	2.43395	+	0.429171i	0.0902081	+	0.0159061i
$729$	9.57428	−	16.5831i	0.354603	−	0.614190i
$730$		0			0
$731$	−1.51596	+	0.551764i	−0.0560698	+	0.0204077i
$732$	−7.86012	−	21.5955i	−0.290519	−	0.798193i
$733$	27.7319	−	16.0110i	1.02430	−	0.591381i	0.108955	−	0.994047i	$-0.465250\pi$
$733$	27.7319	−	16.0110i	1.02430	−	0.591381i	0.915347	+	0.402666i	$0.131916\pi$
$734$	−9.87097	+	17.0970i	−0.364344	+	0.631062i
$735$		0			0
$736$	0.875950	−	0.735009i	0.0322879	−	0.0270928i
$737$	−11.6272	+	13.8568i	−0.428294	+	0.510421i
$738$	−67.8602	+	11.9656i	−2.49797	+	0.440459i
$739$	−36.3892	−	13.2446i	−1.33860	−	0.487210i	−0.429228	−	0.903196i	$-0.641214\pi$
$739$	−36.3892	−	13.2446i	−1.33860	−	0.487210i	−0.909371	+	0.415986i	$0.863436\pi$
$740$		0			0
$741$	6.10434	−	8.21814i	0.224249	−	0.301901i
$742$		−	23.7737i		−	0.872758i
$743$	10.6802	−	29.3436i	0.391819	−	1.07651i	−0.574351	−	0.818609i	$-0.694746\pi$
$743$	10.6802	−	29.3436i	0.391819	−	1.07651i	0.966170	−	0.257905i	$-0.0830321\pi$
$744$	3.57667	+	20.2843i	0.131127	+	0.743658i
$745$		0			0
$746$	17.7417	−	14.8870i	0.649568	−	0.545052i
$747$	−80.1551	−	14.1335i	−2.93272	−	0.517118i
$748$	4.64953	+	2.68441i	0.170004	+	0.0981517i
$749$	24.4887	+	42.4157i	0.894798	+	1.54984i
$750$		0			0
$751$	32.3847	−	11.7871i	1.18173	−	0.430116i	0.324920	−	0.945741i	$-0.394663\pi$
$751$	32.3847	−	11.7871i	1.18173	−	0.430116i	0.856814	+	0.515625i	$0.172440\pi$
$752$	0.287256	−	0.165847i	0.0104752	−	0.00604784i
$753$	71.7991	+	41.4532i	2.61650	+	1.51064i
$754$	0.999129	−	5.66634i	0.0363861	−	0.206356i
$755$		0			0
$756$	−33.5018	−	28.1113i	−1.21845	−	1.02240i
$757$	2.66191	−	0.469366i	0.0967487	−	0.0170594i	−0.125064	−	0.992149i	$-0.539914\pi$
$757$	2.66191	−	0.469366i	0.0967487	−	0.0170594i	0.221813	+	0.975089i	$0.428803\pi$
$758$	−1.20718	+	3.31671i	−0.0438468	+	0.120468i
$759$	22.4855			0.816173
$760$		0			0
$761$	9.19327			0.333256			0.166628	−	0.986020i	$-0.446712\pi$
$761$	9.19327			0.333256			0.166628	+	0.986020i	$0.446712\pi$
$762$	12.2068	−	33.5380i	0.442207	−	1.21495i
$763$	28.6530	−	5.05230i	1.03731	−	0.182906i
$764$	14.1187	+	11.8470i	0.510798	+	0.428611i
$765$		0			0
$766$	−6.36973	+	36.1246i	−0.230148	+	1.30523i
$767$	3.10895	+	1.79495i	0.112258	+	0.0648120i
$768$	−2.75370	+	1.58985i	−0.0993654	+	0.0573686i
$769$	0.0570740	−	0.0207732i	0.00205814	−	0.000749102i	−0.340991	−	0.940067i	$-0.610763\pi$
$769$	0.0570740	−	0.0207732i	0.00205814	−	0.000749102i	0.343049	+	0.939318i	$0.388540\pi$
$770$		0			0
$771$	16.1414	+	27.9578i	0.581320	+	1.00688i
$772$	11.7343	+	6.77477i	0.422325	+	0.243829i
$773$	−9.75016	−	1.71922i	−0.350689	−	0.0618359i	−0.00447097	−	0.999990i	$-0.501423\pi$
$773$	−9.75016	−	1.71922i	−0.350689	−	0.0618359i	−0.346218	+	0.938154i	$0.612534\pi$
$774$	10.1220	−	8.49337i	0.363828	−	0.305288i
$775$		0			0
$776$	1.18846	+	6.74008i	0.0426632	+	0.241955i
$777$	−6.11757	+	16.8079i	−0.219466	+	0.602979i
$778$		−	24.5847i		−	0.881405i
$779$	37.7693	+	18.9172i	1.35322	+	0.677779i
$780$		0			0
$781$	40.0437	+	14.5747i	1.43288	+	0.521524i
$782$	−0.977604	+	0.172378i	−0.0349591	+	0.00616423i
$783$	−65.4445	+	77.9937i	−2.33879	+	2.78727i
$784$	−3.21464	+	2.69741i	−0.114809	+	0.0963359i
$785$		0			0
$786$	24.1436	−	41.8179i	0.861173	−	1.49160i
$787$	9.68415	−	5.59115i	0.345203	−	0.199303i	−0.317368	−	0.948303i	$-0.602799\pi$
$787$	9.68415	−	5.59115i	0.345203	−	0.199303i	0.662570	+	0.749000i	$0.269466\pi$
$788$	2.80149	+	7.69702i	0.0997988	+	0.274195i
$789$	51.1729	−	18.6254i	1.82180	−	0.663082i
$790$		0			0
$791$	18.1205	−	31.3857i	0.644293	−	1.11595i
$792$	−43.3053	−	7.63589i	−1.53879	−	0.271329i
$793$	3.43147	+	4.08947i	0.121855	+	0.145221i
$794$	15.5934	+	13.0844i	0.553390	+	0.464349i
$795$		0			0
$796$	−5.58408	−	2.03244i	−0.197923	−	0.0720379i
$797$			16.8348i			0.596320i	0.954516	+	0.298160i	$0.0963729\pi$
$797$			16.8348i			0.596320i	−0.954516	+	0.298160i	$0.903627\pi$
$798$	10.7442	+	45.1152i	0.380339	+	1.59706i
$799$	−0.287955			−0.0101871
$800$		0			0
$801$	2.87468	+	16.3031i	0.101572	+	0.576043i
$802$	12.9498	−	15.4330i	0.457273	−	0.544957i
$803$	−31.0728	−	37.0312i	−1.09654	−	1.30680i
$804$	−1.61500	+	9.15910i	−0.0569565	+	0.323016i
$805$		0			0
$806$	−2.39229	−	4.14356i	−0.0842647	−	0.145951i
$807$	−24.8056	−	68.1529i	−0.873199	−	2.39910i
$808$	−3.48410	−	9.57249i	−0.122570	−	0.336759i
$809$	13.1217	+	22.7275i	0.461335	+	0.799056i	0.999028	−	0.0440848i	$-0.0140372\pi$
$809$	13.1217	+	22.7275i	0.461335	+	0.799056i	−0.537692	+	0.843141i	$0.680704\pi$
$810$		0			0
$811$	7.65768	−	43.4288i	0.268897	−	1.52499i	−0.488805	−	0.872393i	$-0.662567\pi$
$811$	7.65768	−	43.4288i	0.268897	−	1.52499i	0.757703	−	0.652600i	$-0.226322\pi$
$812$	16.7548	+	19.9675i	0.587977	+	0.700723i
$813$	36.3610	−	43.3334i	1.27524	−	1.51977i
$814$	1.80536	+	10.2387i	0.0632780	+	0.358867i
$815$		0			0
$816$	2.76040			0.0966332
$817$	−8.08592	+	0.479748i	−0.282891	+	0.0167843i
$818$			12.8843i			0.450490i
$819$	16.5136	+	6.01047i	0.577033	+	0.210023i
$820$		0			0
$821$	−35.5474	−	29.8278i	−1.24061	−	1.04100i	−0.997476	−	0.0710073i	$-0.977379\pi$
$821$	−35.5474	−	29.8278i	−1.24061	−	1.04100i	−0.243138	−	0.969992i	$-0.578177\pi$
$822$	17.4756	+	20.8266i	0.609532	+	0.726412i
$823$	−30.8035	−	5.43149i	−1.07374	−	0.189330i	−0.391296	−	0.920265i	$-0.627973\pi$
$823$	−30.8035	−	5.43149i	−1.07374	−	0.189330i	−0.682447	+	0.730935i	$0.739084\pi$
$824$	−1.03525	+	1.79310i	−0.0360646	+	0.0624656i
$825$		0			0
$826$	−15.2823	+	5.56230i	−0.531739	+	0.193537i
$827$	6.74267	+	18.5253i	0.234466	+	0.644189i	1.00000		0.000793747i	$0.000252658\pi$
$827$	6.74267	+	18.5253i	0.234466	+	0.644189i	−0.765534	+	0.643395i	$0.777525\pi$
$828$	7.04130	−	4.06530i	0.244702	−	0.141279i
$829$	−27.3133	+	47.3081i	−0.948632	+	1.64308i	−0.200320	+	0.979730i	$0.564198\pi$
$829$	−27.3133	+	47.3081i	−0.948632	+	1.64308i	−0.748311	+	0.663348i	$0.769135\pi$
$830$		0			0
$831$	−50.8420	+	42.6615i	−1.76369	+	1.47991i
$832$	0.474775	−	0.565815i	0.0164599	−	0.0196161i
$833$	3.58770	−	0.632609i	0.124307	−	0.0219186i
$834$	−26.3064	−	9.57473i	−0.910915	−	0.331546i
$835$		0			0
$836$	18.5202	+	19.5876i	0.640533	+	0.677452i
$837$			84.6638i			2.92641i
$838$	6.84609	−	18.8095i	0.236494	−	0.649762i
$839$	−6.63032	−	37.6024i	−0.228904	−	1.29818i	−0.855079	−	0.518497i	$-0.826492\pi$
$839$	−6.63032	−	37.6024i	−0.228904	−	1.29818i	0.626175	−	0.779682i	$-0.284619\pi$
$840$		0			0
$841$	24.2700	−	20.3650i	0.836898	−	0.702241i
$842$	−6.59634	−	1.16311i	−0.227325	−	0.0400835i
$843$	−74.8970	−	43.2418i	−2.57959	−	1.48933i
$844$	−0.871808	−	1.51002i	−0.0300089	−	0.0519769i
$845$		0			0
$846$	2.21627	−	0.806655i	0.0761968	−	0.0277334i
$847$	−78.9534	+	45.5838i	−2.71287	+	1.56628i
$848$	−6.15300	−	3.55244i	−0.211295	−	0.121991i
$849$	10.8738	−	61.6685i	0.373189	−	2.11646i
$850$		0			0
$851$	−1.47259	−	1.23565i	−0.0504797	−	0.0423575i
$852$	21.5771	−	3.80462i	0.739219	−	0.130344i
$853$	11.3882	−	31.2888i	0.389925	−	1.07131i	−0.577111	−	0.816666i	$-0.695820\pi$
$853$	11.3882	−	31.2888i	0.389925	−	1.07131i	0.967035	−	0.254643i	$-0.0819579\pi$
$854$	−24.1842			−0.827567
$855$		0			0
$856$	14.6371			0.500287
$857$	−13.8112	+	37.9460i	−0.471782	+	1.29621i	0.444537	+	0.895761i	$0.353368\pi$
$857$	−13.8112	+	37.9460i	−0.471782	+	1.29621i	−0.916319	+	0.400450i	$0.868854\pi$
$858$	14.3037	−	2.52213i	0.488321	−	0.0861042i
$859$	5.94441	+	4.98795i	0.202821	+	0.170187i	0.738541	−	0.674209i	$-0.235515\pi$
$859$	5.94441	+	4.98795i	0.202821	+	0.170187i	−0.535720	+	0.844396i	$0.679960\pi$
$860$		0			0
$861$	−17.9045	+	101.541i	−0.610183	+	3.46052i
$862$	−24.2643	−	14.0090i	−0.826446	−	0.477149i
$863$	40.1932	−	23.2056i	1.36819	−	0.789926i	0.377495	−	0.926011i	$-0.376785\pi$
$863$	40.1932	−	23.2056i	1.36819	−	0.789926i	0.990697	+	0.136085i	$0.0434521\pi$
$864$	−12.2818	+	4.47019i	−0.417834	+	0.152079i
$865$		0			0
$866$	−11.3089	−	19.5876i	−0.384292	−	0.665614i
$867$	44.7375	+	25.8292i	1.51936	+	0.877205i
$868$	21.3459	+	3.76386i	0.724526	+	0.127754i
$869$	10.8912	−	9.13876i	0.369457	−	0.310011i
$870$		0			0
$871$	−0.375151	−	2.12759i	−0.0127115	−	0.0720906i
$872$	2.97393	−	8.17082i	0.100710	−	0.276699i
$873$			48.6643i			1.64704i
$874$	−4.95120	−	0.573271i	−0.167477	−	0.0193912i
$875$		0			0
$876$	−23.3557	−	8.50076i	−0.789115	−	0.287214i
$877$	26.6390	−	4.69718i	0.899536	−	0.158612i	0.295288	−	0.955408i	$-0.404585\pi$
$877$	26.6390	−	4.69718i	0.899536	−	0.158612i	0.604248	+	0.796796i	$0.293473\pi$
$878$	2.65793	−	3.16759i	0.0897006	−	0.106901i
$879$	35.9938	−	30.2024i	1.21404	−	1.01870i
$880$		0			0
$881$	−10.1018	+	17.4968i	−0.340338	+	0.589482i	−0.984495	−	0.175410i	$-0.943875\pi$
$881$	−10.1018	+	17.4968i	−0.340338	+	0.589482i	0.644158	+	0.764893i	$0.277208\pi$
$882$	−25.8408	+	14.9192i	−0.870106	+	0.502356i
$883$	−5.14304	−	14.1304i	−0.173077	−	0.475525i	0.822577	−	0.568654i	$-0.192535\pi$
$883$	−5.14304	−	14.1304i	−0.173077	−	0.475525i	−0.995654	+	0.0931285i	$0.970313\pi$
$884$	−0.602549	+	0.219310i	−0.0202659	+	0.00737619i
$885$		0			0
$886$	−14.4699	+	25.0626i	−0.486125	+	0.841994i
$887$	28.7442	+	5.06838i	0.965137	+	0.170180i	0.633940	−	0.773382i	$-0.281437\pi$
$887$	28.7442	+	5.06838i	0.965137	+	0.170180i	0.331197	+	0.943562i	$0.392548\pi$
$888$	3.43601	+	4.09488i	0.115305	+	0.137415i
$889$	−28.7713	−	24.1420i	−0.964959	−	0.809697i
$890$		0			0
$891$	−117.547	−	42.7837i	−3.93798	−	1.43331i
$892$			26.4409i			0.885307i
$893$	−1.38553	−	0.413165i	−0.0463651	−	0.0138260i
$894$	2.42146			0.0809857
$895$		0			0
$896$	0.581045	+	3.29527i	0.0194114	+	0.110087i
$897$	−1.72623	+	2.05724i	−0.0576371	+	0.0686892i
$898$	−3.57480	−	4.26028i	−0.119293	−	0.142167i
$899$	8.76243	−	49.6942i	0.292243	−	1.65739i
$900$		0			0
$901$	3.08399	+	5.34162i	0.102743	+	0.177955i
$902$	20.4980	+	56.3177i	0.682507	+	1.87517i
$903$	−6.76226	−	18.5792i	−0.225034	−	0.618276i
$904$	−5.41542	−	9.37977i	−0.180114	−	0.311967i
$905$		0			0
$906$	3.36139	−	19.0634i	0.111675	−	0.633338i
$907$	33.7769	+	40.2537i	1.12154	+	1.33660i	0.935200	+	0.354119i	$0.115219\pi$
$907$	33.7769	+	40.2537i	1.12154	+	1.33660i	0.186343	+	0.982485i	$0.440336\pi$
$908$	−17.6427	+	21.0258i	−0.585495	+	0.697766i
$909$	−12.5778	−	71.3325i	−0.417181	−	2.36595i
$910$		0			0
$911$	−28.5338			−0.945366			−0.472683	−	0.881233i	$-0.656714\pi$
$911$	−28.5338			−0.945366			−0.472683	+	0.881233i	$0.656714\pi$
$912$	13.2820	+	3.96068i	0.439811	+	0.131151i
$913$			70.7905i			2.34282i
$914$	3.23339	+	1.17686i	0.106951	+	0.0389270i
$915$		0			0
$916$	−8.86480	−	7.43845i	−0.292901	−	0.245773i
$917$	−32.6628	−	38.9260i	−1.07862	−	1.28545i
$918$	11.1741	+	1.97029i	0.368800	+	0.0650294i
$919$	13.5016	−	23.3855i	0.445378	−	0.771418i	−0.552700	−	0.833380i	$-0.686403\pi$
$919$	13.5016	−	23.3855i	0.445378	−	0.771418i	0.998078	+	0.0619624i	$0.0197359\pi$
$920$		0			0
$921$	12.6657	−	4.60994i	0.417349	−	0.151903i
$922$	−1.73672	−	4.77161i	−0.0571960	−	0.157145i
$923$	−4.40765	+	2.54476i	−0.145079	+	0.0837617i
$924$	−32.8993	+	56.9833i	−1.08231	+	1.87461i
$925$		0			0
$926$	3.92835	−	3.29628i	0.129094	−	0.108323i
$927$	−9.46322	+	11.2778i	−0.310813	+	0.370412i
$928$	7.67154	−	1.35270i	0.251831	−	0.0444045i
$929$	−10.4901	−	3.81810i	−0.344170	−	0.125268i	0.164151	−	0.986435i	$-0.447512\pi$
$929$	−10.4901	−	3.81810i	−0.344170	−	0.125268i	−0.508321	+	0.861168i	$0.669734\pi$
$930$		0			0
$931$	18.1704	+	2.10384i	0.595510	+	0.0689507i
$932$			12.8579i			0.421173i
$933$	7.59834	−	20.8763i	0.248758	−	0.683458i
$934$	5.14382	+	29.1720i	0.168311	+	0.954538i
$935$		0			0
$936$	4.02320	−	3.37586i	0.131502	−	0.110344i
$937$	13.4691	+	2.37497i	0.440017	+	0.0775869i	0.389268	−	0.921125i	$-0.372728\pi$
$937$	13.4691	+	2.37497i	0.440017	+	0.0775869i	0.0507491	+	0.998711i	$0.483839\pi$
$938$	8.47591	+	4.89357i	0.276748	+	0.159781i
$939$	−12.1141	−	20.9823i	−0.395330	−	0.684731i
$940$		0			0
$941$	3.22980	−	1.17555i	0.105288	−	0.0383218i	−0.288839	−	0.957378i	$-0.593269\pi$
$941$	3.22980	−	1.17555i	0.105288	−	0.0383218i	0.394127	+	0.919056i	$0.371047\pi$
$942$	−67.1229	+	38.7534i	−2.18698	+	1.26266i
$943$	−9.59672	−	5.54067i	−0.312512	−	0.180429i
$944$	−0.843982	+	4.78646i	−0.0274693	+	0.155786i
$945$		0			0
$946$	−8.80363	−	7.38712i	−0.286231	−	0.240176i
$947$	−40.2580	+	7.09857i	−1.30821	+	0.230673i	−0.783917	−	0.620866i	$-0.786781\pi$
$947$	−40.2580	+	7.09857i	−1.30821	+	0.230673i	−0.524292	+	0.851538i	$0.675670\pi$
$948$	2.50014	−	6.86908i	0.0812008	−	0.223097i
$949$	5.77353			0.187417
$950$		0			0
$951$	43.6840			1.41655
$952$	0.993522	−	2.72968i	0.0322002	−	0.0884694i
$953$	−42.9380	+	7.57113i	−1.39090	+	0.245253i	−0.818398	−	0.574652i	$-0.805138\pi$
$953$	−42.9380	+	7.57113i	−1.39090	+	0.245253i	−0.572500	+	0.819905i	$0.694026\pi$
$954$	−38.6997	−	32.4729i	−1.25295	−	1.05135i
$955$		0			0
$956$	−1.96468	+	11.1423i	−0.0635424	+	0.360367i
$957$	132.660	+	76.5911i	4.28828	+	2.47584i
$958$	−32.6354	+	18.8421i	−1.05440	+	0.608760i
$959$	26.8847	−	9.78522i	0.868152	−	0.315981i
$960$		0			0
$961$	−5.48052	−	9.49254i	−0.176791	−	0.306211i
$962$	−1.07536	−	0.620858i	−0.0346709	−	0.0200173i
$963$	102.496	+	18.0727i	3.30287	+	0.582386i
$964$	18.2280	−	15.2951i	0.587085	−	0.492623i
$965$		0			0
$966$	−2.11262	−	11.9812i	−0.0679723	−	0.385490i
$967$	7.88890	−	21.6746i	0.253690	−	0.697008i	−0.745833	−	0.666133i	$-0.767948\pi$
$967$	7.88890	−	21.6746i	0.253690	−	0.697008i	0.999523	−	0.0308750i	$-0.00982937\pi$
$968$			27.2459i			0.875715i
$969$	−8.26654	−	8.74301i	−0.265560	−	0.280866i
$970$		0			0
$971$	30.8948	+	11.2448i	0.991462	+	0.360863i	0.786286	−	0.617862i	$-0.212001\pi$
$971$	30.8948	+	11.2448i	0.991462	+	0.360863i	0.205176	+	0.978725i	$0.434223\pi$
$972$	−24.7248	+	4.35964i	−0.793047	+	0.139836i
$973$	−18.9364	+	22.5675i	−0.607072	+	0.723480i
$974$	−13.6006	+	11.4122i	−0.435790	+	0.365672i
$975$		0			0
$976$	−3.61379	+	6.25926i	−0.115675	+	0.200354i
$977$	48.7663	−	28.1552i	1.56017	−	0.900765i	0.562932	−	0.826503i	$-0.309673\pi$
$977$	48.7663	−	28.1552i	1.56017	−	0.900765i	0.997239	−	0.0742618i	$-0.0236601\pi$
$978$	4.68712	+	12.8777i	0.149877	+	0.411785i
$979$	13.5301	−	4.92455i	0.432424	−	0.157389i
$980$		0			0
$981$	30.9134	−	53.5436i	0.986988	−	1.70951i
$982$	21.9592	+	3.87201i	0.700747	+	0.123561i
$983$	22.1804	+	26.4336i	0.707445	+	0.843100i	0.993347	−	0.115159i	$-0.0367377\pi$
$983$	22.1804	+	26.4336i	0.707445	+	0.843100i	−0.285902	+	0.958259i	$0.592293\pi$
$984$	23.6051	+	19.8070i	0.752503	+	0.631425i
$985$		0			0
$986$	−6.35482	−	2.31296i	−0.202379	−	0.0736598i
$987$		−	3.52910i		−	0.112332i
$988$	−3.21391	+	0.190686i	−0.102248	+	0.00606652i
$989$	2.12491			0.0675683
$990$		0			0
$991$	7.27532	+	41.2604i	0.231108	+	1.31068i	0.850657	+	0.525721i	$0.176205\pi$
$991$	7.27532	+	41.2604i	0.231108	+	1.31068i	−0.619549	+	0.784958i	$0.712684\pi$
$992$	4.16381	−	4.96223i	0.132201	−	0.157551i
$993$	13.5800	+	16.1840i	0.430947	+	0.513583i
$994$	4.00374	−	22.7063i	0.126991	−	0.720201i
$995$		0			0
$996$	18.1986	+	31.5209i	0.576644	+	0.998777i
$997$	11.2266	+	30.8447i	0.355549	+	0.976862i	0.980555	+	0.196243i	$0.0628740\pi$
$997$	11.2266	+	30.8447i	0.355549	+	0.976862i	−0.625007	+	0.780619i	$0.714904\pi$
$998$	6.45619	+	17.7382i	0.204367	+	0.561494i
$999$	10.9862	+	19.0286i	0.347587	+	0.602039i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.g.99.3		36
5.2	odd	4		950.2.l.i.251.1		18
5.3	odd	4		190.2.k.d.61.3	✓	18
5.4	even	2	inner	950.2.u.g.99.4		36
19.5	even	9	inner	950.2.u.g.499.4		36
95.24	even	18	inner	950.2.u.g.499.3		36
95.28	odd	36		3610.2.a.bi.1.8		9
95.43	odd	36		190.2.k.d.81.3	yes	18
95.48	even	36		3610.2.a.bj.1.2		9
95.62	odd	36		950.2.l.i.651.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.61.3	✓	18	5.3	odd	4
190.2.k.d.81.3	yes	18	95.43	odd	36
950.2.l.i.251.1		18	5.2	odd	4
950.2.l.i.651.1		18	95.62	odd	36
950.2.u.g.99.3		36	1.1	even	1	trivial
950.2.u.g.99.4		36	5.4	even	2	inner
950.2.u.g.499.3		36	95.24	even	18	inner
950.2.u.g.499.4		36	19.5	even	9	inner
3610.2.a.bi.1.8		9	95.28	odd	36
3610.2.a.bj.1.2		9	95.48	even	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.342020 + 0.939693i) q^{2} +(3.13139 - 0.552148i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.552148 + 3.13139i) q^{6} +(2.89781 + 1.67305i) q^{7} +(0.866025 - 0.500000i) q^{8} +(6.68164 - 2.43192i) q^{9} +O(q^{10})\)	\(q+(-0.342020 + 0.939693i) q^{2} +(3.13139 - 0.552148i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.552148 + 3.13139i) q^{6} +(2.89781 + 1.67305i) q^{7} +(0.866025 - 0.500000i) q^{8} +(6.68164 - 2.43192i) q^{9} +(-3.09216 - 5.35578i) q^{11} +(-2.75370 - 1.58985i) q^{12} +(0.727397 + 0.128260i) q^{13} +(-2.56327 + 2.15083i) q^{14} +(0.173648 + 0.984808i) q^{16} +(0.296919 - 0.815778i) q^{17} +7.11045i q^{18} +(2.59916 - 3.49919i) q^{19} +(9.99794 + 3.63895i) q^{21} +(6.09037 - 1.07390i) q^{22} +(-0.735009 + 0.875950i) q^{23} +(2.43579 - 2.04387i) q^{24} +(-0.369309 + 0.639662i) q^{26} +(11.3189 - 6.53498i) q^{27} +(-1.14444 - 3.14431i) q^{28} +(-7.32010 + 2.66430i) q^{29} +(-3.23887 + 5.60988i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(-12.6399 - 15.0637i) q^{33} +(0.665029 + 0.558025i) q^{34} +(-6.68164 - 2.43192i) q^{36} +1.68113i q^{37} +(2.39920 + 3.63921i) q^{38} +2.34858 q^{39} +(1.68282 + 9.54373i) q^{41} +(-6.83899 + 8.15040i) q^{42} +(-1.19449 - 1.42354i) q^{43} +(-1.07390 + 6.09037i) q^{44} +(-0.571736 - 0.990275i) q^{46} +(-0.113446 - 0.311691i) q^{47} +(1.08752 + 2.98793i) q^{48} +(2.09821 + 3.63420i) q^{49} +(0.479338 - 2.71846i) q^{51} +(-0.474775 - 0.565815i) q^{52} +(-4.56693 + 5.44265i) q^{53} +(2.26958 + 12.8714i) q^{54} +3.34610 q^{56} +(6.20691 - 12.3925i) q^{57} -7.78988i q^{58} +(4.56719 + 1.66232i) q^{59} +(5.53664 + 4.64579i) q^{61} +(-4.16381 - 4.96223i) q^{62} +(23.4308 + 4.13149i) q^{63} +(0.500000 - 0.866025i) q^{64} +(18.4784 - 6.72557i) q^{66} +(-1.00039 - 2.74854i) q^{67} +(-0.751825 + 0.434067i) q^{68} +(-1.81794 + 3.14877i) q^{69} +(-5.27849 + 4.42918i) q^{71} +(4.57051 - 5.44692i) q^{72} +(7.69790 - 1.35735i) q^{73} +(-1.57975 - 0.574982i) q^{74} +(-4.24031 + 1.00983i) q^{76} -20.6934i q^{77} +(-0.803262 + 2.20694i) q^{78} +(0.399207 + 2.26401i) q^{79} +(15.4949 - 13.0018i) q^{81} +(-9.54373 - 1.68282i) q^{82} +(-9.91318 - 5.72338i) q^{83} +(-5.31979 - 9.21415i) q^{84} +(1.74623 - 0.635576i) q^{86} +(-21.4510 + 12.3847i) q^{87} +(-5.35578 - 3.09216i) q^{88} +(-0.404290 + 2.29284i) q^{89} +(1.89328 + 1.58865i) q^{91} +(1.12610 - 0.198562i) q^{92} +(-7.04466 + 19.3550i) q^{93} +0.331695 q^{94} -3.17969 q^{96} +(-2.34081 + 6.43131i) q^{97} +(-4.13266 + 0.728700i) q^{98} +(-33.6855 - 28.2655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{9}+O(q^{10}) \) 36 * q + 36 * q^9	\( 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) \) 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Introduction

L-functions

Modular forms

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