LMFDB - Embedded newform 950.2.u.g.99.4

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			99.4
Character	$\chi$	$=$	950.99
Dual form			950.2.u.g.499.4

$q$-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	−0.972860	−	0.231396i	$-0.925671\pi$
$3$	−3.13139	+	0.552148i	−1.80791	+	0.318783i	−0.835047	+	0.550178i	$0.814560\pi$
$4$	−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	−0.160295	−	0.987069i	$-0.551245\pi$
$7$	−2.89781	−	1.67305i	−1.09527	−	0.632354i	−0.934975	+	0.354715i	$0.884578\pi$
$8$	−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	0.0718630	−	0.997415i	$-0.477106\pi$
$13$	−0.727397	−	0.128260i	−0.201744	−	0.0355729i	−0.273607	+	0.961842i	$0.588217\pi$
$14$	−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	−0.970477	−	0.241192i	$-0.922462\pi$
$17$	−0.296919	+	0.815778i	−0.0720134	+	0.197855i	0.898464	+	0.439047i	$0.144684\pi$
$18$		−	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	−0.683951	−	0.729528i	$-0.739740\pi$
$23$	0.735009	−	0.875950i	0.153260	−	0.182648i	0.837211	+	0.546879i	$0.184184\pi$
$24$	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	$-0.955872\pi$
$37$		−	1.68113i		−	0.276377i	0.990406	−	0.138188i	$-0.0441279\pi$
$38$	−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	0.849395	−	0.527758i	$-0.176967\pi$
$43$	1.19449	+	1.42354i	0.182158	+	0.217088i	−0.667236	+	0.744846i	$0.732523\pi$
$44$	−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	0.947692	−	0.319188i	$-0.103410\pi$
$47$	0.113446	+	0.311691i	0.0165479	+	0.0454649i	−0.931144	+	0.364652i	$0.881188\pi$
$48$	−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	−0.354994	−	0.934868i	$-0.615517\pi$
$53$	4.56693	−	5.44265i	0.627316	−	0.747606i	0.982310	+	0.187263i	$0.0599616\pi$
$54$	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	0.985681	−	0.168623i	$-0.0539321\pi$
$67$	1.00039	+	2.74854i	0.122217	+	0.335787i	−0.863464	+	0.504410i	$0.831710\pi$
$68$	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	−0.604901	−	0.796301i	$-0.706787\pi$
$73$	−7.69790	+	1.35735i	−0.900972	+	0.158866i	−0.296070	+	0.955166i	$0.595676\pi$
$74$	−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	0.933074	−	0.359686i	$-0.117116\pi$
$83$	9.91318	+	5.72338i	1.08811	+	0.628223i	0.155040	+	0.987908i	$0.450449\pi$
$84$	−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	$-0.775935\pi$
$97$	2.34081	−	6.43131i	0.237673	−	0.653000i	0.999983	−	0.00578901i	$-0.00184271\pi$
$98$	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	−0.409052	−	0.912511i	$-0.634141\pi$
$103$	1.79310	−	1.03525i	0.176680	−	0.102006i	0.585732	+	0.810505i	$0.300807\pi$
$104$	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	−0.259374	−	0.965777i	$-0.583516\pi$
$107$	−12.6761	−	7.31857i	−1.22545	−	0.707513i	−0.966075	+	0.258264i	$0.916850\pi$
$108$	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	$0.170147\pi$
$113$			10.8308i			1.01888i	−0.860507	+	0.509439i	$0.829853\pi$
$114$	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	0.641023	−	0.767522i	$-0.278510\pi$
$127$	11.0540	+	1.94911i	0.980880	+	0.172956i	0.339857	+	0.940477i	$0.389621\pi$
$128$	−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	−0.947896	−	0.318580i	$-0.896794\pi$
$137$	−5.49600	+	6.54988i	−0.469555	+	0.559594i	0.478341	+	0.878174i	$0.341238\pi$
$138$	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	$-0.796782\pi$
$157$	−15.6683	−	18.6728i	−1.25047	−	1.49025i	−0.447434	−	0.894317i	$-0.647662\pi$
$158$	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	−0.639002	−	0.769205i	$-0.720652\pi$
$163$	−3.73250	+	2.15496i	−0.292352	+	0.168789i	0.346650	+	0.937994i	$0.387319\pi$
$164$	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	−0.620697	−	0.784051i	$-0.713150\pi$
$167$	3.34993	−	3.99229i	0.259225	−	0.308933i	0.879922	+	0.475118i	$0.157595\pi$
$168$	−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	−0.813983	−	0.580889i	$-0.802705\pi$
$173$	2.40637	−	6.61144i	0.182953	−	0.502658i	0.996935	+	0.0782309i	$0.0249271\pi$
$174$	−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	0.328649	−	0.944452i	$-0.393407\pi$
$193$	13.3437	−	2.35285i	0.960501	−	0.169362i	0.631851	+	0.775090i	$0.282295\pi$
$194$	−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	0.730940	−	0.682441i	$-0.239082\pi$
$197$	7.09361	+	4.09550i	0.505399	+	0.291792i	−0.225541	+	0.974234i	$0.572415\pi$
$198$	−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	$0.123829\pi$
$223$	16.9959	+	20.2549i	1.13813	+	1.35637i	0.212848	+	0.977085i	$0.431726\pi$
$224$	−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	$0.364587\pi$
$227$			27.4472i			1.82174i	−0.412697	+	0.910869i	$0.635413\pi$
$228$	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	0.965512	−	0.260358i	$-0.0838406\pi$
$233$	8.26488	+	9.84970i	0.541450	+	0.645275i	−0.424062	+	0.905633i	$0.639396\pi$
$234$	−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	0.783032	−	0.621981i	$-0.213672\pi$
$257$	−3.47247	−	9.54054i	−0.216607	−	0.595122i	−0.999639	+	0.0268585i	$0.991450\pi$
$258$	−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	−0.667477	−	0.744630i	$-0.732626\pi$
$263$	−16.8663	+	2.97399i	−1.04002	+	0.183384i	−0.372545	+	0.928014i	$0.621515\pi$
$264$	−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	0.153572	−	0.988137i	$-0.450922\pi$
$277$	18.0765	−	10.4365i	1.08611	−	0.627066i	0.932538	+	0.361071i	$0.117589\pi$
$278$	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	$0.310148\pi$
$283$	−6.73563	+	18.5060i	−0.400392	+	1.10007i	−0.962092	+	0.272726i	$0.912075\pi$
$284$	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	−0.824836	−	0.565372i	$-0.808733\pi$
$293$	−12.7973	+	7.38854i	−0.747628	+	0.431643i	0.0772085	+	0.997015i	$0.475399\pi$
$294$	−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	−0.291500	−	0.956571i	$-0.594154\pi$
$307$	−4.17455	+	0.736086i	−0.238254	+	0.0420106i	0.0532459	+	0.998581i	$0.483043\pi$
$308$	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	0.991298	−	0.131638i	$-0.0420235\pi$
$313$	2.60608	+	7.16016i	0.147305	+	0.404716i	−0.843993	+	0.536354i	$0.819801\pi$
$314$	−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	−0.219749	−	0.975557i	$-0.570524\pi$
$317$	−13.5297	−	2.38566i	−0.759905	−	0.133992i	−0.540156	+	0.841565i	$0.681635\pi$
$318$	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	0.985081	−	0.172093i	$-0.0550528\pi$
$337$	11.8323	+	14.1012i	0.644545	+	0.768139i	−0.340536	+	0.940232i	$0.610608\pi$
$338$	−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	0.622732	−	0.782435i	$-0.286023\pi$
$347$	−4.76787	−	5.68212i	−0.255952	−	0.305032i	−0.878684	+	0.477403i	$0.841578\pi$
$348$	−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	−0.536498	−	0.843902i	$-0.680253\pi$
$353$	−1.38857	+	0.801691i	−0.0739061	+	0.0426697i	0.462592	+	0.886572i	$0.346920\pi$
$354$	−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	−0.358610	−	0.933488i	$-0.616749\pi$
$367$	−19.4420	−	3.42815i	−1.01486	−	0.178948i	−0.656255	+	0.754540i	$0.727860\pi$
$368$	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	0.919415	−	0.393289i	$-0.128663\pi$
$373$	20.0572	+	11.5800i	1.03852	+	0.599592i	0.119109	+	0.992881i	$0.461996\pi$
$374$	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	−0.983517	−	0.180815i	$-0.942127\pi$
$383$	−36.1246	+	6.36973i	−1.84588	+	0.325478i	−0.862362	+	0.506293i	$0.831015\pi$
$384$	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	$0.281767\pi$
$397$	−6.96208	+	19.1282i	−0.349417	+	0.960015i	−0.982554	+	0.185976i	$0.940455\pi$
$398$		−	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	−0.293702	−	0.955897i	$-0.594887\pi$
$433$	14.5384	−	17.3262i	0.698673	−	0.832646i	0.992376	+	0.123251i	$0.0393319\pi$
$434$	−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	−0.550937	−	0.834547i	$-0.685730\pi$
$443$	−28.5001	−	5.02534i	−1.35408	−	0.238761i	−0.803144	+	0.595786i	$0.796841\pi$
$444$	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	$0.0256451\pi$
$457$			3.44090i			0.160959i	−0.996756	+	0.0804793i	$0.974355\pi$
$458$	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	0.599634	−	0.800274i	$-0.295313\pi$
$463$	4.44107	+	2.56405i	0.206394	+	0.119162i	−0.393240	+	0.919436i	$0.628646\pi$
$464$	−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	−0.957646	−	0.287947i	$-0.907027\pi$
$467$	−25.6535	+	14.8110i	−1.18710	+	0.685373i	−0.229454	+	0.973320i	$0.573694\pi$
$468$	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	0.109393	−	0.993999i	$-0.465109\pi$
$487$	−15.3757	−	8.87714i	−0.696738	−	0.402262i	−0.806131	+	0.591737i	$0.798442\pi$
$488$	−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	$-0.746470\pi$
$503$	−13.9751	−	38.3963i	−0.623119	−	1.71201i	0.0761023	−	0.997100i	$-0.475752\pi$
$504$	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	0.947468	−	0.319849i	$-0.103632\pi$
$523$	0.367514	+	1.00974i	0.0160703	+	0.0441527i	−0.931398	+	0.364002i	$0.881410\pi$
$524$	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	$0.477330\pi$
$547$	−21.5990	+	25.7407i	−0.923508	+	1.10059i	−0.994668	+	0.103129i	$0.967115\pi$
$548$	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	0.462833	−	0.886446i	$-0.346833\pi$
$557$	14.0324	+	2.47429i	0.594571	+	0.104839i	0.131739	+	0.991285i	$0.457944\pi$
$558$	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	0.205577	−	0.978641i	$-0.434093\pi$
$563$	−12.7930	−	7.38607i	−0.539163	−	0.311286i	−0.744740	+	0.667355i	$0.767426\pi$
$564$	−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	0.185303	−	0.982682i	$-0.440673\pi$
$577$	−13.7657	−	7.94763i	−0.573073	−	0.330864i	−0.758376	+	0.651818i	$0.774007\pi$
$578$	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	−0.815163	−	0.579232i	$-0.803353\pi$
$587$	4.40009	−	12.0891i	0.181611	−	0.498973i	0.996774	+	0.0802592i	$0.0255748\pi$
$588$			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	−0.794021	−	0.607890i	$-0.792016\pi$
$593$	−1.39986	+	1.66829i	−0.0574855	+	0.0685086i	0.736535	+	0.676399i	$0.236460\pi$
$594$	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	$0.0821197\pi$
$607$			12.5717i			0.510269i	−0.966906	+	0.255134i	$0.917880\pi$
$608$	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	$-0.826382\pi$
$613$	−30.1404	−	35.9199i	−1.21736	−	1.45079i	−0.362458	−	0.932000i	$-0.618062\pi$
$614$	−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	0.943277	−	0.332006i	$-0.107725\pi$
$617$	0.180720	+	0.496525i	0.00727553	+	0.0199893i	−0.936002	+	0.351995i	$0.885503\pi$
$618$	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	0.347030	−	0.937854i	$-0.387190\pi$
$643$	25.2027	−	4.44391i	0.993896	−	0.175251i	0.646866	+	0.762604i	$0.276079\pi$
$644$	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	$0.121068\pi$
$647$			18.8860i			0.742483i	−0.928536	+	0.371242i	$0.878932\pi$
$648$	−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	0.0162674	−	0.999868i	$-0.494822\pi$
$653$	−21.5038	−	12.4152i	−0.841510	−	0.485846i	−0.857777	+	0.514022i	$0.828155\pi$
$654$	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	−0.723161	−	0.690680i	$-0.757311\pi$
$673$	−12.6234	+	7.28810i	−0.486594	+	0.280935i	0.236566	+	0.971615i	$0.423978\pi$
$674$	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	0.539999	−	0.841666i	$-0.318425\pi$
$677$	2.11001	+	1.21821i	0.0810941	+	0.0468197i	−0.458905	+	0.888486i	$0.651758\pi$
$678$	−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	$0.0932628\pi$
$683$			15.0962i			0.577639i	−0.957384	+	0.288820i	$0.906737\pi$
$684$	−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	$0.0264150\pi$
$727$	24.4052	+	29.0850i	0.905139	+	1.07870i	−0.0914199	+	0.995812i	$0.529141\pi$
$728$	−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	−0.915347	−	0.402666i	$-0.868084\pi$
$733$	−27.7319	+	16.0110i	−1.02430	+	0.591381i	−0.108955	+	0.994047i	$0.534750\pi$
$734$	−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	$0.305254\pi$
$743$	−10.6802	+	29.3436i	−0.391819	+	1.07651i	−0.966170	+	0.257905i	$0.916968\pi$
$744$	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	−0.221813	−	0.975089i	$-0.571197\pi$
$757$	−2.66191	+	0.469366i	−0.0967487	+	0.0170594i	0.125064	+	0.992149i	$0.460086\pi$
$758$	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	0.346218	−	0.938154i	$-0.387466\pi$
$773$	9.75016	+	1.71922i	0.350689	+	0.0618359i	0.00447097	+	0.999990i	$0.498577\pi$
$774$	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	−0.662570	−	0.749000i	$-0.730534\pi$
$787$	−9.68415	+	5.59115i	−0.345203	+	0.199303i	0.317368	+	0.948303i	$0.397201\pi$
$788$	−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	$-0.903627\pi$
$797$		−	16.8348i		−	0.596320i	0.954516	−	0.298160i	$-0.0963729\pi$
$798$	−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	0.682447	−	0.730935i	$-0.260916\pi$
$823$	30.8035	+	5.43149i	1.07374	+	0.189330i	0.391296	+	0.920265i	$0.372027\pi$
$824$	−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	$-0.999747\pi$
$827$	−6.74267	−	18.5253i	−0.234466	−	0.644189i	0.765534	−	0.643395i	$-0.222475\pi$
$828$	−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	$0.304180\pi$
$853$	−11.3882	+	31.2888i	−0.389925	+	1.07131i	−0.967035	+	0.254643i	$0.918042\pi$
$854$	−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	$-0.646632\pi$
$857$	13.8112	−	37.9460i	0.471782	−	1.29621i	0.916319	−	0.400450i	$-0.131146\pi$
$858$	−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	−0.990697	−	0.136085i	$-0.956548\pi$
$863$	−40.1932	+	23.2056i	−1.36819	+	0.789926i	−0.377495	+	0.926011i	$0.623215\pi$
$864$	−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	−0.604248	−	0.796796i	$-0.706527\pi$
$877$	−26.6390	+	4.69718i	−0.899536	+	0.158612i	−0.295288	+	0.955408i	$0.595415\pi$
$878$	−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	0.995654	−	0.0931285i	$-0.0296867\pi$
$883$	5.14304	+	14.1304i	0.173077	+	0.475525i	−0.822577	+	0.568654i	$0.807465\pi$
$884$	−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	−0.331197	−	0.943562i	$-0.607452\pi$
$887$	−28.7442	−	5.06838i	−0.965137	−	0.170180i	−0.633940	+	0.773382i	$0.718563\pi$
$888$	−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	$-0.884781\pi$
$907$	−33.7769	−	40.2537i	−1.12154	−	1.33660i	−0.186343	−	0.982485i	$-0.559664\pi$
$908$	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	−0.0507491	−	0.998711i	$-0.516161\pi$
$937$	−13.4691	−	2.37497i	−0.440017	−	0.0775869i	−0.389268	+	0.921125i	$0.627272\pi$
$938$	−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	0.524292	−	0.851538i	$-0.324330\pi$
$947$	40.2580	−	7.09857i	1.30821	−	0.230673i	0.783917	+	0.620866i	$0.213219\pi$
$948$	−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	0.572500	−	0.819905i	$-0.305974\pi$
$953$	42.9380	−	7.57113i	1.39090	−	0.245253i	0.818398	+	0.574652i	$0.194862\pi$
$954$	−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	$0.232052\pi$
$967$	−7.88890	+	21.6746i	−0.253690	+	0.697008i	−0.999523	+	0.0308750i	$0.990171\pi$
$968$		−	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	$0.690327\pi$
$977$	−48.7663	+	28.1552i	−1.56017	+	0.900765i	−0.997239	+	0.0742618i	$0.976340\pi$
$978$	−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	0.285902	−	0.958259i	$-0.407707\pi$
$983$	−22.1804	−	26.4336i	−0.707445	−	0.843100i	−0.993347	+	0.115159i	$0.963262\pi$
$984$	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	$-0.937126\pi$
$997$	−11.2266	−	30.8447i	−0.355549	−	0.976862i	0.625007	−	0.780619i	$-0.285096\pi$
$998$	−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.99.4		36
5.2	odd	4		190.2.k.d.61.3	✓	18
5.3	odd	4		950.2.l.i.251.1		18
5.4	even	2	inner	950.2.u.g.99.3		36
19.5	even	9	inner	950.2.u.g.499.3		36
95.24	even	18	inner	950.2.u.g.499.4		36
95.43	odd	36		950.2.l.i.651.1		18
95.47	odd	36		3610.2.a.bi.1.8		9
95.62	odd	36		190.2.k.d.81.3	yes	18
95.67	even	36		3610.2.a.bj.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.61.3	✓	18	5.2	odd	4
190.2.k.d.81.3	yes	18	95.62	odd	36
950.2.l.i.251.1		18	5.3	odd	4
950.2.l.i.651.1		18	95.43	odd	36
950.2.u.g.99.3		36	5.4	even	2	inner
950.2.u.g.99.4		36	1.1	even	1	trivial
950.2.u.g.499.3		36	19.5	even	9	inner
950.2.u.g.499.4		36	95.24	even	18	inner
3610.2.a.bi.1.8		9	95.47	odd	36
3610.2.a.bj.1.2		9	95.67	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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