LMFDB - Embedded newform 132.2.j.a.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [132,2,Mod(7,132)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(132, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

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

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

chi := DirichletCharacter("132.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	132.j (of order $10$, degree $4$, 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:	$1.05402530668$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	132.19
Dual form			132.2.j.a.7.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.140058 - 1.40726i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.96077 - 0.394195i) q^{4} +(-0.213696 - 0.155259i) q^{5} +(-0.301665 - 1.38167i) q^{6} +(1.03321 - 3.17989i) q^{7} +(-0.829356 + 2.70410i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.140058 - 1.40726i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.96077 - 0.394195i) q^{4} +(-0.213696 - 0.155259i) q^{5} +(-0.301665 - 1.38167i) q^{6} +(1.03321 - 3.17989i) q^{7} +(-0.829356 + 2.70410i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-0.248420 + 0.278981i) q^{10} +(-1.85745 - 2.74771i) q^{11} +(-1.98661 + 0.231009i) q^{12} +(3.89823 + 5.36545i) q^{13} +(-4.33023 - 1.89936i) q^{14} +(-0.251215 - 0.0816246i) q^{15} +(3.68922 + 1.54585i) q^{16} +(-2.74676 + 3.78059i) q^{17} +(-0.713858 - 1.22082i) q^{18} +(1.27559 + 3.92586i) q^{19} +(0.357806 + 0.388665i) q^{20} -3.34353i q^{21} +(-4.12689 + 2.22908i) q^{22} +0.765361i q^{23} +(0.0468496 + 2.82804i) q^{24} +(-1.52352 - 4.68893i) q^{25} +(8.09657 - 4.73436i) q^{26} +(0.587785 - 0.809017i) q^{27} +(-3.27938 + 5.82774i) q^{28} +(3.67765 + 1.19494i) q^{29} +(-0.150052 + 0.342092i) q^{30} +(2.37677 + 3.27135i) q^{31} +(2.69212 - 4.97519i) q^{32} +(-2.61562 - 2.03924i) q^{33} +(4.93558 + 4.39491i) q^{34} +(-0.714499 + 0.519114i) q^{35} +(-1.81800 + 0.833600i) q^{36} +(0.274094 - 0.843576i) q^{37} +(5.70337 - 1.24524i) q^{38} +(5.36545 + 3.89823i) q^{39} +(0.597067 - 0.449091i) q^{40} +(-5.66025 + 1.83913i) q^{41} +(-4.70523 - 0.468287i) q^{42} -2.10908 q^{43} +(2.55889 + 6.11981i) q^{44} -0.264143 q^{45} +(1.07706 + 0.107195i) q^{46} +(-4.91501 + 1.59698i) q^{47} +(3.98635 + 0.330158i) q^{48} +(-3.38106 - 2.45648i) q^{49} +(-6.81192 + 1.48728i) q^{50} +(-1.44406 + 4.44436i) q^{51} +(-5.52849 - 12.0571i) q^{52} +(4.59637 - 3.33946i) q^{53} +(-1.05617 - 0.940476i) q^{54} +(-0.0296780 + 0.875559i) q^{55} +(7.74185 + 5.43116i) q^{56} +(2.42632 + 3.33954i) q^{57} +(2.19667 - 5.00805i) q^{58} +(-9.46770 - 3.07624i) q^{59} +(0.460397 + 0.259074i) q^{60} +(1.87298 - 2.57794i) q^{61} +(4.93652 - 2.88656i) q^{62} +(-1.03321 - 3.17989i) q^{63} +(-6.62434 - 4.48532i) q^{64} -1.75181i q^{65} +(-3.23608 + 3.39526i) q^{66} -5.99397i q^{67} +(6.87605 - 6.33011i) q^{68} +(0.236510 + 0.727902i) q^{69} +(0.630458 + 1.07819i) q^{70} +(2.69549 - 3.71003i) q^{71} +(0.918469 + 2.67515i) q^{72} +(-14.3347 - 4.65764i) q^{73} +(-1.14874 - 0.503872i) q^{74} +(-2.89792 - 3.98864i) q^{75} +(-0.953581 - 8.20054i) q^{76} +(-10.6565 + 3.06752i) q^{77} +(6.23730 - 7.00462i) q^{78} +(-11.6701 + 8.47885i) q^{79} +(-0.548364 - 0.903127i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.79537 + 8.22304i) q^{82} +(0.496492 + 0.360722i) q^{83} +(-1.31800 + 6.55589i) q^{84} +(1.17394 - 0.381437i) q^{85} +(-0.295392 + 2.96802i) q^{86} +3.86691 q^{87} +(8.97056 - 2.74390i) q^{88} +2.78024 q^{89} +(-0.0369952 + 0.371718i) q^{90} +(21.0892 - 6.85231i) q^{91} +(0.301701 - 1.50070i) q^{92} +(3.27135 + 2.37677i) q^{93} +(1.55899 + 7.14037i) q^{94} +(0.336938 - 1.03699i) q^{95} +(1.02294 - 5.56360i) q^{96} +(8.14034 - 5.91430i) q^{97} +(-3.93046 + 4.41398i) q^{98} +(-3.11777 - 1.13116i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} + 12 q^{9}+O(q^{10}) $ 48 * q - 4 * q^4 + 12 * q^9	$ 48 q - 4 q^{4} + 12 q^{9} + 8 q^{12} - 14 q^{14} - 24 q^{16} - 10 q^{18} - 22 q^{20} - 26 q^{22} - 30 q^{24} - 20 q^{25} - 38 q^{26} - 10 q^{28} - 20 q^{30} - 4 q^{33} + 4 q^{36} - 48 q^{37} + 58 q^{38} + 70 q^{40} - 40 q^{41} + 12 q^{42} + 34 q^{44} + 70 q^{46} - 16 q^{48} - 28 q^{49} + 70 q^{50} + 30 q^{52} - 64 q^{53} + 60 q^{56} - 54 q^{58} - 12 q^{60} - 40 q^{64} - 8 q^{66} + 4 q^{70} + 10 q^{72} + 20 q^{73} + 50 q^{74} - 8 q^{77} + 40 q^{78} + 58 q^{80} - 12 q^{81} + 62 q^{82} + 60 q^{84} + 40 q^{85} + 8 q^{86} + 8 q^{88} + 48 q^{89} + 20 q^{90} + 42 q^{92} + 24 q^{93} - 10 q^{94} + 50 q^{96} + 48 q^{97}+O(q^{100}) $ 48 * q - 4 * q^4 + 12 * q^9 + 8 * q^12 - 14 * q^14 - 24 * q^16 - 10 * q^18 - 22 * q^20 - 26 * q^22 - 30 * q^24 - 20 * q^25 - 38 * q^26 - 10 * q^28 - 20 * q^30 - 4 * q^33 + 4 * q^36 - 48 * q^37 + 58 * q^38 + 70 * q^40 - 40 * q^41 + 12 * q^42 + 34 * q^44 + 70 * q^46 - 16 * q^48 - 28 * q^49 + 70 * q^50 + 30 * q^52 - 64 * q^53 + 60 * q^56 - 54 * q^58 - 12 * q^60 - 40 * q^64 - 8 * q^66 + 4 * q^70 + 10 * q^72 + 20 * q^73 + 50 * q^74 - 8 * q^77 + 40 * q^78 + 58 * q^80 - 12 * q^81 + 62 * q^82 + 60 * q^84 + 40 * q^85 + 8 * q^86 + 8 * q^88 + 48 * q^89 + 20 * q^90 + 42 * q^92 + 24 * q^93 - 10 * q^94 + 50 * q^96 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.140058	−	1.40726i	0.0990356	−	0.995084i
$2$	0.140058	−	1.40726i	0.0990356	−	0.995084i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$	−1.96077	−	0.394195i	−0.980384	−	0.197097i
$5$	−0.213696	−	0.155259i	−0.0955677	−	0.0694340i	0.538975	−	0.842322i	$-0.318812\pi$
$5$	−0.213696	−	0.155259i	−0.0955677	−	0.0694340i	−0.634543	+	0.772888i	$0.718812\pi$
$6$	−0.301665	−	1.38167i	−0.123154	−	0.564062i
$7$	1.03321	−	3.17989i	0.390516	−	1.20189i	−0.541883	−	0.840454i	$-0.682288\pi$
$7$	1.03321	−	3.17989i	0.390516	−	1.20189i	0.932399	−	0.361431i	$-0.117712\pi$
$8$	−0.829356	+	2.70410i	−0.293221	+	0.956045i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	−0.248420	+	0.278981i	−0.0785573	+	0.0882214i
$11$	−1.85745	−	2.74771i	−0.560041	−	0.828465i
$11$	−1.85745	−	2.74771i	−0.560041	−	0.828465i
$12$	−1.98661	+	0.231009i	−0.573486	+	0.0666865i
$13$	3.89823	+	5.36545i	1.08117	+	1.48811i	0.858221	+	0.513280i	$0.171570\pi$
$13$	3.89823	+	5.36545i	1.08117	+	1.48811i	0.222953	+	0.974829i	$0.428430\pi$
$14$	−4.33023	−	1.89936i	−1.15730	−	0.507626i
$15$	−0.251215	−	0.0816246i	−0.0648633	−	0.0210754i
$16$	3.68922	+	1.54585i	0.922305	+	0.386462i
$17$	−2.74676	+	3.78059i	−0.666188	+	0.916929i	−0.999666	−	0.0258289i	$-0.991777\pi$
$17$	−2.74676	+	3.78059i	−0.666188	+	0.916929i	0.333479	+	0.942758i	$0.391777\pi$
$18$	−0.713858	−	1.22082i	−0.168258	−	0.287750i
$19$	1.27559	+	3.92586i	0.292640	+	0.900655i	0.984004	+	0.178147i	$0.0570104\pi$
$19$	1.27559	+	3.92586i	0.292640	+	0.900655i	−0.691363	+	0.722507i	$0.742990\pi$
$20$	0.357806	+	0.388665i	0.0800078	+	0.0869081i
$21$		−	3.34353i		−	0.729619i
$22$	−4.12689	+	2.22908i	−0.879856	+	0.475240i
$23$			0.765361i			0.159589i	0.996811	+	0.0797944i	$0.0254264\pi$
$23$			0.765361i			0.159589i	−0.996811	+	0.0797944i	$0.974574\pi$
$24$	0.0468496	+	2.82804i	0.00956314	+	0.577271i
$25$	−1.52352	−	4.68893i	−0.304705	−	0.937785i
$26$	8.09657	−	4.73436i	1.58787	−	0.928483i
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	−3.27938	+	5.82774i	−0.619744	+	1.10134i
$29$	3.67765	+	1.19494i	0.682922	+	0.221895i	0.629874	−	0.776697i	$-0.283106\pi$
$29$	3.67765	+	1.19494i	0.682922	+	0.221895i	0.0530476	+	0.998592i	$0.483106\pi$
$30$	−0.150052	+	0.342092i	−0.0273955	+	0.0624572i
$31$	2.37677	+	3.27135i	0.426881	+	0.587551i	0.967234	−	0.253887i	$-0.0817092\pi$
$31$	2.37677	+	3.27135i	0.426881	+	0.587551i	−0.540353	+	0.841439i	$0.681709\pi$
$32$	2.69212	−	4.97519i	0.475904	−	0.879497i
$33$	−2.61562	−	2.03924i	−0.455322	−	0.354986i
$34$	4.93558	+	4.39491i	0.846445	+	0.753721i
$35$	−0.714499	+	0.519114i	−0.120772	+	0.0877463i
$36$	−1.81800	+	0.833600i	−0.302999	+	0.138933i
$37$	0.274094	−	0.843576i	0.0450608	−	0.138683i	−0.925995	−	0.377536i	$-0.876771\pi$
$37$	0.274094	−	0.843576i	0.0450608	−	0.138683i	0.971056	+	0.238853i	$0.0767714\pi$
$38$	5.70337	−	1.24524i	0.925209	−	0.202005i
$39$	5.36545	+	3.89823i	0.859160	+	0.624216i
$40$	0.597067	−	0.449091i	0.0944045	−	0.0710074i
$41$	−5.66025	+	1.83913i	−0.883983	+	0.287223i	−0.715610	−	0.698500i	$-0.753851\pi$
$41$	−5.66025	+	1.83913i	−0.883983	+	0.287223i	−0.168373	+	0.985723i	$0.553851\pi$
$42$	−4.70523	−	0.468287i	−0.726032	−	0.0722583i
$43$	−2.10908			−0.321631			−0.160816	−	0.986984i	$-0.551412\pi$
$43$	−2.10908			−0.321631			−0.160816	+	0.986984i	$0.551412\pi$
$44$	2.55889	+	6.11981i	0.385767	+	0.922596i
$45$	−0.264143			−0.0393761
$46$	1.07706	+	0.107195i	0.158804	+	0.0158050i
$47$	−4.91501	+	1.59698i	−0.716928	+	0.232944i	−0.644691	−	0.764444i	$-0.723014\pi$
$47$	−4.91501	+	1.59698i	−0.716928	+	0.232944i	−0.0722371	+	0.997387i	$0.523014\pi$
$48$	3.98635	+	0.330158i	0.575380	+	0.0476543i
$49$	−3.38106	−	2.45648i	−0.483008	−	0.350926i
$50$	−6.81192	+	1.48728i	−0.963352	+	0.210333i
$51$	−1.44406	+	4.44436i	−0.202209	+	0.622334i
$52$	−5.52849	−	12.0571i	−0.766663	−	1.67201i
$53$	4.59637	−	3.33946i	0.631360	−	0.458710i	−0.225511	−	0.974241i	$-0.572405\pi$
$53$	4.59637	−	3.33946i	0.631360	−	0.458710i	0.856871	+	0.515531i	$0.172405\pi$
$54$	−1.05617	−	0.940476i	−0.143727	−	0.127983i
$55$	−0.0296780	+	0.875559i	−0.00400178	+	0.118060i
$56$	7.74185	+	5.43116i	1.03455	+	0.725769i
$57$	2.42632	+	3.33954i	0.321374	+	0.442333i
$58$	2.19667	−	5.00805i	0.288437	−	0.657589i
$59$	−9.46770	−	3.07624i	−1.23259	−	0.400493i	−0.380938	−	0.924601i	$-0.624399\pi$
$59$	−9.46770	−	3.07624i	−1.23259	−	0.400493i	−0.851652	+	0.524108i	$0.824399\pi$
$60$	0.460397	+	0.259074i	0.0594371	+	0.0334464i
$61$	1.87298	−	2.57794i	0.239811	−	0.330071i	−0.672100	−	0.740461i	$-0.734607\pi$
$61$	1.87298	−	2.57794i	0.239811	−	0.330071i	0.911910	+	0.410390i	$0.134607\pi$
$62$	4.93652	−	2.88656i	0.626939	−	0.366594i
$63$	−1.03321	−	3.17989i	−0.130172	−	0.400628i
$64$	−6.62434	−	4.48532i	−0.828042	−	0.560666i
$65$		−	1.75181i		−	0.217285i
$66$	−3.23608	+	3.39526i	−0.398334	+	0.417927i
$67$		−	5.99397i		−	0.732280i	−0.930560	−	0.366140i	$-0.880679\pi$
$67$		−	5.99397i		−	0.732280i	0.930560	−	0.366140i	$-0.119321\pi$
$68$	6.87605	−	6.33011i	0.833844	−	0.767638i
$69$	0.236510	+	0.727902i	0.0284724	+	0.0876291i
$70$	0.630458	+	1.07819i	0.0753542	+	0.128869i
$71$	2.69549	−	3.71003i	0.319896	−	0.440299i	−0.618539	−	0.785754i	$-0.712275\pi$
$71$	2.69549	−	3.71003i	0.319896	−	0.440299i	0.938435	+	0.345455i	$0.112275\pi$
$72$	0.918469	+	2.67515i	0.108243	+	0.315269i
$73$	−14.3347	−	4.65764i	−1.67775	−	0.545135i	−0.693280	−	0.720669i	$-0.743835\pi$
$73$	−14.3347	−	4.65764i	−1.67775	−	0.545135i	−0.984473	+	0.175534i	$0.943835\pi$
$74$	−1.14874	−	0.503872i	−0.133539	−	0.0585739i
$75$	−2.89792	−	3.98864i	−0.334622	−	0.460568i
$76$	−0.953581	−	8.20054i	−0.109383	−	0.940666i
$77$	−10.6565	+	3.06752i	−1.21442	+	0.349576i
$78$	6.23730	−	7.00462i	0.706235	−	0.793117i
$79$	−11.6701	+	8.47885i	−1.31299	+	0.953945i	−0.313002	+	0.949753i	$0.601335\pi$
$79$	−11.6701	+	8.47885i	−1.31299	+	0.953945i	−0.999991	+	0.00419263i	$0.998665\pi$
$80$	−0.548364	−	0.903127i	−0.0613090	−	0.100973i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	1.79537	+	8.22304i	0.198266	+	0.908083i
$83$	0.496492	+	0.360722i	0.0544971	+	0.0395944i	0.614700	−	0.788761i	$-0.289277\pi$
$83$	0.496492	+	0.360722i	0.0544971	+	0.0395944i	−0.560203	+	0.828355i	$0.689277\pi$
$84$	−1.31800	+	6.55589i	−0.143806	+	0.715307i
$85$	1.17394	−	0.381437i	0.127332	−	0.0413727i
$86$	−0.295392	+	2.96802i	−0.0318529	+	0.320050i
$87$	3.86691			0.414576
$88$	8.97056	−	2.74390i	0.956265	−	0.292501i
$89$	2.78024			0.294705			0.147353	−	0.989084i	$-0.452925\pi$
$89$	2.78024			0.294705			0.147353	+	0.989084i	$0.452925\pi$
$90$	−0.0369952	+	0.371718i	−0.00389963	+	0.0391825i
$91$	21.0892	−	6.85231i	2.21075	−	0.718317i
$92$	0.301701	−	1.50070i	0.0314546	−	0.156458i
$93$	3.27135	+	2.37677i	0.339223	+	0.246460i
$94$	1.55899	+	7.14037i	0.160797	+	0.736473i
$95$	0.336938	−	1.03699i	0.0345691	−	0.106393i
$96$	1.02294	−	5.56360i	0.104403	−	0.567832i
$97$	8.14034	−	5.91430i	0.826526	−	0.600506i	−0.0920484	−	0.995755i	$-0.529341\pi$
$97$	8.14034	−	5.91430i	0.826526	−	0.600506i	0.918574	+	0.395248i	$0.129341\pi$
$98$	−3.93046	+	4.41398i	−0.397036	+	0.445880i
$99$	−3.11777	−	1.13116i	−0.313347	−	0.113686i
$100$	1.13893	+	9.79446i	0.113893	+	0.979446i
$101$	11.6323	+	16.0105i	1.15746	+	1.59310i	0.720198	+	0.693769i	$0.244051\pi$
$101$	11.6323	+	16.0105i	1.15746	+	1.59310i	0.437260	+	0.899335i	$0.355949\pi$
$102$	6.05212	+	2.65463i	0.599249	+	0.262848i
$103$	−6.38362	−	2.07416i	−0.628997	−	0.204373i	−0.0228662	−	0.999739i	$-0.507279\pi$
$103$	−6.38362	−	2.07416i	−0.628997	−	0.204373i	−0.606131	+	0.795365i	$0.707279\pi$
$104$	−17.7418	+	6.09134i	−1.73972	+	0.597305i
$105$	−0.519114	+	0.714499i	−0.0506604	+	0.0697280i
$106$	−4.05573	−	6.93601i	−0.393928	−	0.673685i
$107$	3.77667	+	11.6234i	0.365104	+	1.12368i	0.949916	+	0.312506i	$0.101168\pi$
$107$	3.77667	+	11.6234i	0.365104	+	1.12368i	−0.584811	+	0.811169i	$0.698832\pi$
$108$	−1.47142	+	1.35459i	−0.141588	+	0.130346i
$109$		−	2.09407i		−	0.200576i	−0.994958	−	0.100288i	$-0.968024\pi$
$109$		−	2.09407i		−	0.200576i	0.994958	−	0.100288i	$-0.0319764\pi$
$110$	1.22798	+	0.164393i	0.117084	+	0.0156743i
$111$		−	0.886988i		−	0.0841892i
$112$	8.72737	−	10.1341i	0.824659	−	0.957585i
$113$	−3.72590	−	11.4671i	−0.350503	−	1.07874i	−0.958571	−	0.284853i	$-0.908055\pi$
$113$	−3.72590	−	11.4671i	−0.350503	−	1.07874i	0.608068	−	0.793885i	$-0.291945\pi$
$114$	5.03943	−	2.94673i	0.471986	−	0.275987i
$115$	0.118829	−	0.163555i	0.0110809	−	0.0152515i
$116$	−6.73997	−	3.79271i	−0.625791	−	0.352144i
$117$	6.30747	+	2.04942i	0.583126	+	0.189469i
$118$	−5.65510	+	12.8927i	−0.520594	+	1.18687i
$119$	9.18389	+	12.6405i	0.841886	+	1.15876i
$120$	0.429067	−	0.611614i	0.0391683	−	0.0558325i
$121$	−4.09979	+	10.2074i	−0.372708	+	0.927949i
$122$	−3.36550	−	2.99683i	−0.304698	−	0.271320i
$123$	−4.81490	+	3.49823i	−0.434145	+	0.315425i
$124$	−3.37075	−	7.35126i	−0.302702	−	0.660163i
$125$	−0.810551	+	2.49462i	−0.0724979	+	0.223125i
$126$	−4.61964	+	1.00863i	−0.411551	+	0.0898557i
$127$	−1.89867	−	1.37946i	−0.168480	−	0.122408i	0.500350	−	0.865823i	$-0.333205\pi$
$127$	−1.89867	−	1.37946i	−0.168480	−	0.122408i	−0.668830	+	0.743415i	$0.733205\pi$
$128$	−7.23981	+	8.69397i	−0.639915	+	0.768446i
$129$	−2.00585	+	0.651741i	−0.176605	+	0.0573826i
$130$	−2.46526	−	0.245354i	−0.216217	−	0.0215190i
$131$	13.7656			1.20271			0.601353	−	0.798983i	$-0.294628\pi$
$131$	13.7656			1.20271			0.601353	+	0.798983i	$0.294628\pi$
$132$	4.32477	+	5.02955i	0.376423	+	0.437766i
$133$	13.8018			1.19676
$134$	−8.43508	−	0.839501i	−0.728680	−	0.0725218i
$135$	−0.251215	+	0.0816246i	−0.0216211	+	0.00702512i
$136$	−7.94507	−	10.5630i	−0.681284	−	0.905768i
$137$	−4.81224	−	3.49630i	−0.411138	−	0.298709i	0.362925	−	0.931819i	$-0.381778\pi$
$137$	−4.81224	−	3.49630i	−0.411138	−	0.298709i	−0.774062	+	0.633110i	$0.781778\pi$
$138$	1.05747	−	0.230883i	0.0900180	−	0.0196540i
$139$	−2.33565	+	7.18840i	−0.198107	+	0.609712i	0.801819	+	0.597567i	$0.203866\pi$
$139$	−2.33565	+	7.18840i	−0.198107	+	0.609712i	−0.999926	+	0.0121448i	$0.996134\pi$
$140$	1.60560	−	0.736210i	0.135698	−	0.0622211i
$141$	−4.18096	+	3.03764i	−0.352100	+	0.255816i
$142$	−4.84345	−	4.31288i	−0.406453	−	0.361929i
$143$	7.50194	−	20.6772i	0.627344	−	1.72912i
$144$	3.89327	−	0.917851i	0.324439	−	0.0764876i
$145$	−0.600373	−	0.826342i	−0.0498582	−	0.0686240i
$146$	−8.56220	+	19.5204i	−0.708612	+	1.61552i
$147$	−3.97467	−	1.29145i	−0.327826	−	0.106517i
$148$	−0.869969	+	1.54601i	−0.0715110	+	0.127081i
$149$	10.4316	−	14.3578i	0.854588	−	1.17624i	−0.128245	−	0.991743i	$-0.540934\pi$
$149$	10.4316	−	14.3578i	0.854588	−	1.17624i	0.982833	−	0.184497i	$-0.0590656\pi$
$150$	−6.01893	+	3.51949i	−0.491444	+	0.287365i
$151$	−4.19328	−	12.9056i	−0.341245	−	1.05024i	−0.963564	−	0.267479i	$-0.913809\pi$
$151$	−4.19328	−	12.9056i	−0.341245	−	1.05024i	0.622319	−	0.782764i	$-0.286191\pi$
$152$	−11.6739	+	0.193390i	−0.946875	+	0.0156860i
$153$			4.67307i			0.377795i
$154$	2.82427	+	15.4262i	0.227586	+	1.24308i
$155$		−	1.06809i		−	0.0857910i
$156$	−8.98375	−	9.75856i	−0.719275	−	0.781310i
$157$	4.46673	+	13.7472i	0.356484	+	1.09714i	0.955144	+	0.296141i	$0.0957000\pi$
$157$	4.46673	+	13.7472i	0.356484	+	1.09714i	−0.598660	+	0.801003i	$0.704300\pi$
$158$	10.2975	+	17.6105i	0.819222	+	1.40101i
$159$	3.33946	−	4.59637i	0.264836	−	0.364516i
$160$	−1.34774	+	0.645202i	−0.106548	+	0.0510077i
$161$	2.43376	+	0.790778i	0.191807	+	0.0623220i
$162$	−1.29510	−	0.568070i	−0.101753	−	0.0446318i
$163$	3.68738	+	5.07524i	0.288818	+	0.397523i	0.928630	−	0.371008i	$-0.120988\pi$
$163$	3.68738	+	5.07524i	0.288818	+	0.397523i	−0.639812	+	0.768531i	$0.720988\pi$
$164$	11.8234	−	1.37486i	0.923254	−	0.107358i
$165$	0.242337	+	0.841877i	0.0188659	+	0.0655401i
$166$	0.577168	−	0.648172i	0.0447969	−	0.0503079i
$167$	1.90114	−	1.38126i	0.147115	−	0.106885i	−0.511793	−	0.859109i	$-0.671019\pi$
$167$	1.90114	−	1.38126i	0.147115	−	0.106885i	0.658908	+	0.752223i	$0.271019\pi$
$168$	9.04126	+	2.77298i	0.697548	+	0.213940i
$169$	−9.57467	+	29.4678i	−0.736513	+	2.26675i
$170$	−0.372362	−	1.70547i	−0.0285589	−	0.130803i
$171$	3.33954	+	2.42632i	0.255381	+	0.185545i
$172$	4.13541	+	0.831388i	0.315322	+	0.0633927i
$173$	15.5257	−	5.04461i	1.18040	−	0.383534i	0.347883	−	0.937538i	$-0.386901\pi$
$173$	15.5257	−	5.04461i	1.18040	−	0.383534i	0.832514	+	0.554004i	$0.186901\pi$
$174$	0.541589	−	5.44175i	0.0410578	−	0.412538i
$175$	−16.4844			−1.24610
$176$	−2.60499	−	13.0082i	−0.196358	−	0.980532i
$177$	−9.95493			−0.748259
$178$	0.389394	−	3.91253i	0.0291863	−	0.293256i
$179$	−23.3391	+	7.58332i	−1.74444	+	0.566804i	−0.995408	−	0.0957267i	$-0.969483\pi$
$179$	−23.3391	+	7.58332i	−1.74444	+	0.566804i	−0.749035	+	0.662530i	$0.769483\pi$
$180$	0.517922	+	0.104124i	0.0386037	+	0.00776092i
$181$	−10.6410	−	7.73114i	−0.790939	−	0.574651i	0.117303	−	0.993096i	$-0.462575\pi$
$181$	−10.6410	−	7.73114i	−0.790939	−	0.574651i	−0.908242	+	0.418445i	$0.862575\pi$
$182$	−6.68928	−	30.6378i	−0.495842	−	2.27102i
$183$	0.984684	−	3.03055i	0.0727899	−	0.224024i
$184$	−2.06961	−	0.634756i	−0.152574	−	0.0467949i
$185$	−0.189546	+	0.137713i	−0.0139357	+	0.0101249i
$186$	3.80292	−	4.27075i	0.278843	−	0.313147i
$187$	15.4899	+	0.525047i	1.13274	+	0.0383952i
$188$	10.2667	−	1.19384i	0.748777	−	0.0870698i
$189$	−1.96528	−	2.70498i	−0.142953	−	0.196758i
$190$	−1.41212	−	0.619397i	−0.102446	−	0.0449358i
$191$	10.5402	+	3.42473i	0.762665	+	0.247805i	0.664422	−	0.747358i	$-0.268678\pi$
$191$	10.5402	+	3.42473i	0.762665	+	0.247805i	0.0982428	+	0.995162i	$0.468678\pi$
$192$	−7.68616	−	2.21876i	−0.554701	−	0.160125i
$193$	8.15394	−	11.2229i	0.586933	−	0.807844i	−0.407501	−	0.913205i	$-0.633600\pi$
$193$	8.15394	−	11.2229i	0.586933	−	0.807844i	0.994434	+	0.105361i	$0.0335997\pi$
$194$	−7.18285	−	12.2839i	−0.515699	−	0.881934i
$195$	−0.541339	−	1.66607i	−0.0387661	−	0.119310i
$196$	5.66114	+	6.14939i	0.404367	+	0.439242i
$197$		−	6.04339i		−	0.430574i	−0.976551	−	0.215287i	$-0.930931\pi$
$197$		−	6.04339i		−	0.430574i	0.976551	−	0.215287i	$-0.0690686\pi$
$198$	−2.02851	+	4.22908i	−0.144160	+	0.300548i
$199$		−	17.1475i		−	1.21556i	−0.794107	−	0.607778i	$-0.792061\pi$
$199$		−	17.1475i		−	1.21556i	0.794107	−	0.607778i	$-0.207939\pi$
$200$	13.9429	−	0.230979i	0.985910	−	0.0163327i
$201$	−1.85224	−	5.70061i	−0.130647	−	0.402090i
$202$	24.1601	−	14.1273i	1.69990	−	0.993994i
$203$	7.59955	−	10.4599i	0.533384	−	0.734140i
$204$	4.58341	−	8.14511i	0.320903	−	0.570272i
$205$	1.49511	+	0.485792i	0.104423	+	0.0339292i
$206$	−3.81297	+	8.69292i	−0.265662	+	0.605664i
$207$	0.449868	+	0.619190i	0.0312680	+	0.0430367i
$208$	6.08725	+	25.8204i	0.422075	+	1.79032i
$209$	8.41778	−	10.7970i	0.582270	−	0.746846i
$210$	0.932781	+	0.830600i	0.0643680	+	0.0573169i
$211$	−10.3629	+	7.52909i	−0.713411	+	0.518324i	−0.884272	−	0.466972i	$-0.845345\pi$
$211$	−10.3629	+	7.52909i	−0.713411	+	0.518324i	0.170861	+	0.985295i	$0.445345\pi$
$212$	−10.3288	+	4.73604i	−0.709386	+	0.325272i
$213$	1.41710	−	4.36140i	0.0970983	−	0.298838i
$214$	16.8861	−	3.68682i	1.15431	−	0.252025i
$215$	0.450701	+	0.327453i	0.0307376	+	0.0223321i
$216$	1.70018	+	2.26039i	0.115683	+	0.153800i
$217$	12.8582	−	4.17789i	0.872873	−	0.283614i
$218$	−2.94691	−	0.293290i	−0.199590	−	0.0198641i
$219$	−15.0724			−1.01850
$220$	0.403333	−	1.70507i	0.0271927	−	0.114956i
$221$	−30.9921			−2.08476
$222$	−1.24822	−	0.124229i	−0.0837753	−	0.00833773i
$223$	1.94261	−	0.631192i	0.130087	−	0.0422677i	−0.243250	−	0.969964i	$-0.578214\pi$
$223$	1.94261	−	0.631192i	0.130087	−	0.0422677i	0.373337	+	0.927696i	$0.378214\pi$
$224$	−13.0390	−	13.7010i	−0.871207	−	0.915440i
$225$	−3.98864	−	2.89792i	−0.265909	−	0.193194i
$226$	−16.6591	+	3.63726i	−1.10815	+	0.241947i
$227$	5.65067	−	17.3910i	0.375048	−	1.15428i	−0.568398	−	0.822754i	$-0.692436\pi$
$227$	5.65067	−	17.3910i	0.375048	−	1.15428i	0.943446	−	0.331526i	$-0.107564\pi$
$228$	−3.44101	−	7.50450i	−0.227887	−	0.496998i
$229$	−10.0961	+	7.33523i	−0.667168	+	0.484726i	−0.869076	−	0.494679i	$-0.835286\pi$
$229$	−10.0961	+	7.33523i	−0.667168	+	0.484726i	0.201908	+	0.979404i	$0.435286\pi$
$230$	−0.213521	−	0.190131i	−0.0140792	−	0.0125369i
$231$	−9.18705	+	6.21044i	−0.604464	+	0.408617i
$232$	−6.28132	+	8.95370i	−0.412389	+	0.587839i
$233$	−7.79576	−	10.7299i	−0.510717	−	0.702942i	0.473323	−	0.880889i	$-0.343054\pi$
$233$	−7.79576	−	10.7299i	−0.510717	−	0.702942i	−0.984040	+	0.177947i	$0.943054\pi$
$234$	3.76748	−	8.58922i	0.246288	−	0.561495i
$235$	1.29826	+	0.421831i	0.0846894	+	0.0275172i
$236$	17.3513	+	9.76392i	1.12948	+	0.635577i
$237$	−8.47885	+	11.6701i	−0.550761	+	0.758057i
$238$	19.0748	−	11.1537i	1.23644	−	0.722989i
$239$	6.21895	+	19.1400i	0.402271	+	1.23806i	0.923153	+	0.384433i	$0.125603\pi$
$239$	6.21895	+	19.1400i	0.402271	+	1.23806i	−0.520882	+	0.853629i	$0.674397\pi$
$240$	−0.800607	−	0.689471i	−0.0516789	−	0.0445052i
$241$			10.0285i			0.645994i	0.946400	+	0.322997i	$0.104690\pi$
$241$			10.0285i			0.645994i	−0.946400	+	0.322997i	$0.895310\pi$
$242$	13.7903	+	7.19910i	0.886476	+	0.462776i
$243$		−	1.00000i		−	0.0641500i
$244$	−4.68869	+	4.31641i	−0.300163	+	0.276330i
$245$	0.341127	+	1.04988i	0.0217938	+	0.0670744i
$246$	4.24856	+	7.26577i	0.270878	+	0.463249i
$247$	−16.0915	+	22.1480i	−1.02388	+	1.40925i
$248$	−10.8172	+	3.71393i	−0.686896	+	0.235835i
$249$	0.583661	+	0.189643i	0.0369880	+	0.0120181i
$250$	3.39706	+	1.49005i	0.214849	+	0.0942388i
$251$	7.39146	+	10.1735i	0.466545	+	0.642144i	0.975850	−	0.218442i	$-0.0700975\pi$
$251$	7.39146	+	10.1735i	0.466545	+	0.642144i	−0.509305	+	0.860586i	$0.670098\pi$
$252$	0.772386	+	6.64231i	0.0486557	+	0.418426i
$253$	2.10299	−	1.42162i	0.132214	−	0.0893763i
$254$	−2.20719	+	2.47872i	−0.138491	+	0.155529i
$255$	0.998616	−	0.725537i	0.0625358	−	0.0454349i
$256$	11.2207	+	11.4060i	0.701294	+	0.712873i
$257$	0.311817	−	0.959673i	0.0194506	−	0.0598628i	−0.940860	−	0.338795i	$-0.889981\pi$
$257$	0.311817	−	0.959673i	0.0194506	−	0.0598628i	0.960311	+	0.278933i	$0.0899806\pi$
$258$	0.636235	+	2.91404i	0.0396102	+	0.181420i
$259$	−2.39928	−	1.74318i	−0.149084	−	0.108316i
$260$	−0.690555	+	3.43489i	−0.0428264	+	0.213023i
$261$	3.67765	−	1.19494i	0.227641	−	0.0739649i
$262$	1.92798	−	19.3718i	0.119111	−	1.19679i
$263$	−14.7299			−0.908282			−0.454141	−	0.890930i	$-0.650054\pi$
$263$	−14.7299			−0.908282			−0.454141	+	0.890930i	$0.650054\pi$
$264$	7.68360	−	5.38166i	0.472893	−	0.331218i
$265$	−1.50071			−0.0921877
$266$	1.93304	−	19.4227i	0.118522	−	1.19088i
$267$	2.64417	−	0.859142i	0.161820	−	0.0525787i
$268$	−2.36279	+	11.7528i	−0.144331	+	0.717916i
$269$	9.60330	+	6.97720i	0.585523	+	0.425408i	0.840711	−	0.541484i	$-0.182137\pi$
$269$	9.60330	+	6.97720i	0.585523	+	0.425408i	−0.255188	+	0.966892i	$0.582137\pi$
$270$	0.0796826	+	0.364957i	0.00484933	+	0.0222106i
$271$	−4.35634	+	13.4074i	−0.264629	+	0.814443i	0.727150	+	0.686478i	$0.240844\pi$
$271$	−4.35634	+	13.4074i	−0.264629	+	0.814443i	−0.991779	+	0.127965i	$0.959156\pi$
$272$	−15.9776	+	9.70136i	−0.968787	+	0.588232i
$273$	17.9396	−	13.0339i	1.08575	−	0.788845i
$274$	−5.59420	+	6.28240i	−0.337958	+	0.379534i
$275$	−10.0539	+	12.8956i	−0.606275	+	0.777636i
$276$	−0.176805	−	1.52048i	−0.0106424	−	0.0915220i
$277$	−12.0276	−	16.5545i	−0.722665	−	0.994664i	−0.999431	−	0.0337262i	$-0.989263\pi$
$277$	−12.0276	−	16.5545i	−0.722665	−	0.994664i	0.276766	−	0.960937i	$-0.410737\pi$
$278$	9.78883	+	4.29366i	0.587095	+	0.257517i
$279$	3.84570	+	1.24954i	0.230236	+	0.0748082i
$280$	−0.811164	−	2.36261i	−0.0484763	−	0.141193i
$281$	−7.74854	+	10.6650i	−0.462239	+	0.636218i	−0.974971	−	0.222331i	$-0.928633\pi$
$281$	−7.74854	+	10.6650i	−0.462239	+	0.636218i	0.512732	+	0.858549i	$0.328633\pi$
$282$	3.68918	+	6.30914i	0.219688	+	0.375704i
$283$	−1.28277	−	3.94797i	−0.0762529	−	0.234682i	0.905664	−	0.423997i	$-0.139373\pi$
$283$	−1.28277	−	3.94797i	−0.0762529	−	0.234682i	−0.981916	+	0.189315i	$0.939373\pi$
$284$	−6.74771	+	6.21195i	−0.400403	+	0.368611i
$285$		−	1.09035i		−	0.0645870i
$286$	−28.0476	−	13.4532i	−1.65849	−	0.795504i
$287$			19.8992i			1.17461i
$288$	−0.746374	−	5.60740i	−0.0439805	−	0.330419i
$289$	−1.49490	−	4.60083i	−0.0879353	−	0.270637i
$290$	−1.24697	+	0.729146i	−0.0732243	+	0.0428169i
$291$	5.91430	−	8.14034i	0.346702	−	0.477195i
$292$	26.2711	+	14.7832i	1.53740	+	0.865123i
$293$	−7.59864	−	2.46895i	−0.443917	−	0.144237i	0.0785249	−	0.996912i	$-0.474979\pi$
$293$	−7.59864	−	2.46895i	−0.443917	−	0.144237i	−0.522442	+	0.852675i	$0.674979\pi$
$294$	−2.37409	+	5.41253i	−0.138460	+	0.315665i
$295$	1.54559	+	2.12733i	0.0899880	+	0.123858i
$296$	2.05379	+	1.44080i	0.119374	+	0.0837450i
$297$	−3.31472	−	0.112356i	−0.192340	−	0.00651955i
$298$	−18.7442	−	16.6909i	−1.08582	−	0.966876i
$299$	−4.10651	+	2.98355i	−0.237486	+	0.172543i
$300$	4.10984	+	8.96314i	0.237282	+	0.517487i
$301$	−2.17912	+	6.70663i	−0.125602	+	0.386564i
$302$	−18.7488	+	4.09352i	−1.07887	+	0.235556i
$303$	16.0105	+	11.6323i	0.919779	+	0.668259i
$304$	−1.36286	+	16.4552i	−0.0781654	+	0.943773i
$305$	−0.800496	+	0.260097i	−0.0458363	+	0.0148931i
$306$	6.57623	+	0.654499i	0.375938	+	0.0374152i
$307$	28.2669			1.61328			0.806639	−	0.591044i	$-0.201284\pi$
$307$	28.2669			1.61328			0.806639	+	0.591044i	$0.201284\pi$
$308$	22.1042	−	1.81394i	1.25950	−	0.103359i
$309$	−6.71214			−0.381840
$310$	−1.50308	−	0.149594i	−0.0853692	−	0.00849636i
$311$	12.2480	−	3.97962i	0.694522	−	0.225664i	0.0595796	−	0.998224i	$-0.481024\pi$
$311$	12.2480	−	3.97962i	0.694522	−	0.225664i	0.634942	+	0.772560i	$0.281024\pi$
$312$	−14.9911	+	11.2757i	−0.848703	+	0.638362i
$313$	−7.79540	−	5.66369i	−0.440622	−	0.320131i	0.345260	−	0.938507i	$-0.387791\pi$
$313$	−7.79540	−	5.66369i	−0.440622	−	0.320131i	−0.785882	+	0.618376i	$0.787791\pi$
$314$	19.9715	−	4.36046i	1.12706	−	0.246075i
$315$	−0.272915	+	0.839945i	−0.0153770	+	0.0473255i
$316$	26.2247	−	12.0247i	1.47526	−	0.676445i
$317$	−5.37930	+	3.90829i	−0.302132	+	0.219512i	−0.728513	−	0.685032i	$-0.759788\pi$
$317$	−5.37930	+	3.90829i	−0.302132	+	0.219512i	0.426381	+	0.904544i	$0.359788\pi$
$318$	−6.00058	−	5.34325i	−0.336496	−	0.299634i
$319$	−3.54769	−	12.3246i	−0.198632	−	0.690047i
$320$	0.719206	+	1.98698i	0.0402049	+	0.111076i
$321$	7.18365	+	9.88744i	0.400952	+	0.551863i
$322$	1.45370	−	3.31419i	0.0810114	−	0.184692i
$323$	−18.3458	−	5.96092i	−1.02079	−	0.331675i
$324$	−0.980812	+	1.74299i	−0.0544896	+	0.0968327i
$325$	19.2192	−	26.4529i	1.06609	−	1.46734i
$326$	7.65863	−	4.47827i	0.424172	−	0.248029i
$327$	−0.647104	−	1.99158i	−0.0357849	−	0.110135i
$328$	−0.278827	−	16.8312i	−0.0153957	−	0.929347i
$329$			17.2792i			0.952633i
$330$	1.21868	−	0.223121i	0.0670863	−	0.0122824i
$331$		−	4.25037i		−	0.233621i	−0.993154	−	0.116811i	$-0.962733\pi$
$331$		−	4.25037i		−	0.233621i	0.993154	−	0.116811i	$-0.0372671\pi$
$332$	−0.831310	−	0.903007i	−0.0456241	−	0.0495590i
$333$	−0.274094	−	0.843576i	−0.0150203	−	0.0462277i
$334$	−1.67753	−	2.86886i	−0.0917901	−	0.156977i
$335$	−0.930619	+	1.28089i	−0.0508451	+	0.0699823i
$336$	5.16860	−	12.3350i	0.281970	−	0.672931i
$337$	18.7683	+	6.09818i	1.02237	+	0.332189i	0.771770	−	0.635901i	$-0.219372\pi$
$337$	18.7683	+	6.09818i	1.02237	+	0.332189i	0.250602	+	0.968090i	$0.419372\pi$
$338$	40.1279	+	17.6012i	2.18267	+	0.957382i
$339$	−7.08708	−	9.75454i	−0.384918	−	0.529794i
$340$	−2.45219	+	0.285148i	−0.132989	+	0.0154643i
$341$	4.57397	−	12.6070i	0.247695	−	0.682709i
$342$	3.88219	−	4.35978i	0.209925	−	0.235750i
$343$	7.63014	−	5.54362i	0.411989	−	0.299328i
$344$	1.74917	−	5.70316i	0.0943092	−	0.307494i
$345$	0.0624723	−	0.192270i	0.00336339	−	0.0103515i
$346$	−4.92459	−	22.5552i	−0.264747	−	1.21258i
$347$	−7.87165	−	5.71909i	−0.422572	−	0.307017i	0.356100	−	0.934448i	$-0.384106\pi$
$347$	−7.87165	−	5.71909i	−0.422572	−	0.307017i	−0.778672	+	0.627431i	$0.784106\pi$
$348$	−7.58210	−	1.52431i	−0.406443	−	0.0817119i
$349$	−18.2493	+	5.92957i	−0.976865	+	0.317403i	−0.753584	−	0.657352i	$-0.771677\pi$
$349$	−18.2493	+	5.92957i	−0.976865	+	0.317403i	−0.223281	+	0.974754i	$0.571677\pi$
$350$	−2.30876	+	23.1978i	−0.123409	+	1.23998i
$351$	6.63206			0.353993
$352$	−18.6708	+	1.84400i	−0.995158	+	0.0982854i
$353$	−2.30703			−0.122791			−0.0613955	−	0.998114i	$-0.519555\pi$
$353$	−2.30703			−0.122791			−0.0613955	+	0.998114i	$0.519555\pi$
$354$	−1.39426	+	14.0092i	−0.0741042	+	0.744580i
$355$	−1.15203	+	0.374318i	−0.0611435	+	0.0198667i
$356$	−5.45141	−	1.09596i	−0.288924	−	0.0580857i
$357$	12.6405	+	9.18389i	0.669009	+	0.486063i
$358$	7.40290	+	33.9062i	0.391255	+	1.79200i
$359$	5.45434	−	16.7867i	0.287869	−	0.885971i	−0.697655	−	0.716434i	$-0.745773\pi$
$359$	5.45434	−	16.7867i	0.287869	−	0.885971i	0.985524	−	0.169536i	$-0.0542270\pi$
$360$	0.219068	−	0.714269i	0.0115459	−	0.0376453i
$361$	1.58605	−	1.15233i	0.0834765	−	0.0606492i
$362$	−12.3701	+	13.8919i	−0.650157	+	0.730140i
$363$	−0.744857	+	10.9748i	−0.0390948	+	0.576025i
$364$	−44.0522	+	5.12251i	−2.30896	+	0.268493i
$365$	2.34013	+	3.22092i	0.122488	+	0.168590i
$366$	−4.12686	−	1.81016i	−0.215714	−	0.0946185i
$367$	5.96243	+	1.93731i	0.311236	+	0.101127i	0.460470	−	0.887675i	$-0.347681\pi$
$367$	5.96243	+	1.93731i	0.311236	+	0.101127i	−0.149234	+	0.988802i	$0.547681\pi$
$368$	−1.18313	+	2.82359i	−0.0616751	+	0.147190i
$369$	−3.49823	+	4.81490i	−0.182111	+	0.250654i
$370$	0.167251	+	0.286028i	0.00869496	+	0.0148699i
$371$	−5.87010	−	18.0663i	−0.304760	−	0.937956i
$372$	−5.47744	−	5.94985i	−0.283992	−	0.308485i
$373$			0.0244567i			0.00126632i	1.00000		0.000633161i	$0.000201541\pi$
$373$			0.0244567i			0.00126632i	−1.00000		0.000633161i	$0.999798\pi$
$374$	2.90836	−	21.7248i	0.150388	−	1.12336i
$375$			2.62300i			0.135451i
$376$	−0.242116	−	14.6152i	−0.0124862	−	0.753719i
$377$	7.92492	+	24.3904i	0.408154	+	1.25617i
$378$	−4.08186	+	2.38681i	−0.209948	+	0.122764i
$379$	18.8371	−	25.9270i	0.967596	−	1.33178i	0.0243438	−	0.999704i	$-0.492250\pi$
$379$	18.8371	−	25.9270i	0.967596	−	1.33178i	0.943252	−	0.332078i	$-0.107750\pi$
$380$	−1.06943	+	1.90047i	−0.0548607	+	0.0974922i
$381$	−2.23202	−	0.725227i	−0.114350	−	0.0371545i
$382$	6.29573	−	14.3532i	0.322117	−	0.734374i
$383$	−20.7395	−	28.5454i	−1.05974	−	1.45860i	−0.880052	−	0.474878i	$-0.842492\pi$
$383$	−20.7395	−	28.5454i	−1.05974	−	1.45860i	−0.179685	−	0.983724i	$-0.557508\pi$
$384$	−4.19888	+	10.5057i	−0.214273	+	0.536116i
$385$	2.75352	+	0.999008i	0.140332	+	0.0509142i
$386$	−14.6516	−	13.0466i	−0.745745	−	0.664053i
$387$	−1.70628	+	1.23968i	−0.0867350	+	0.0630167i
$388$	−18.2927	+	8.38769i	−0.928671	+	0.425820i
$389$	2.94817	−	9.07354i	0.149478	−	0.460047i	−0.848081	−	0.529866i	$-0.822242\pi$
$389$	2.94817	−	9.07354i	0.149478	−	0.460047i	0.997560	+	0.0698193i	$0.0222423\pi$
$390$	−2.42042	+	0.528460i	−0.122563	+	0.0267596i
$391$	−2.89352	−	2.10226i	−0.146332	−	0.106316i
$392$	9.44668	−	7.10543i	0.477130	−	0.358879i
$393$	13.0919	−	4.25381i	0.660397	−	0.214576i
$394$	−8.50462	−	0.846422i	−0.428457	−	0.0426421i
$395$	3.81028			0.191716
$396$	5.66732	+	3.44695i	0.284794	+	0.173216i
$397$	−8.04088			−0.403560			−0.201780	−	0.979431i	$-0.564673\pi$
$397$	−8.04088			−0.403560			−0.201780	+	0.979431i	$0.564673\pi$
$398$	−24.1310	−	2.40164i	−1.20958	−	0.120383i
$399$	13.1263	−	4.26498i	0.657135	−	0.213516i
$400$	1.62776	−	19.6536i	0.0813878	−	0.982681i
$401$	30.1047	+	21.8724i	1.50336	+	1.09225i	0.969020	+	0.246983i	$0.0794390\pi$
$401$	30.1047	+	21.8724i	1.50336	+	1.09225i	0.534338	+	0.845271i	$0.320561\pi$
$402$	−8.28166	+	1.80817i	−0.413052	+	0.0901834i
$403$	−8.28705	+	25.5049i	−0.412807	+	1.27049i
$404$	−16.4970	−	35.9783i	−0.820756	−	1.78999i
$405$	−0.213696	+	0.155259i	−0.0106186	+	0.00771489i
$406$	−13.6554	−	12.1595i	−0.677707	−	0.603468i
$407$	−2.82702	+	0.813766i	−0.140130	+	0.0403369i
$408$	−10.8204	−	7.59083i	−0.535687	−	0.375802i
$409$	−6.07530	−	8.36194i	−0.300404	−	0.413471i	0.631954	−	0.775006i	$-0.282253\pi$
$409$	−6.07530	−	8.36194i	−0.300404	−	0.413471i	−0.932359	+	0.361534i	$0.882253\pi$
$410$	0.893038	−	2.03598i	0.0441040	−	0.100550i
$411$	−5.65713	−	1.83811i	−0.279046	−	0.0906674i
$412$	11.6992	+	6.58335i	0.576377	+	0.324338i
$413$	−19.5642	+	26.9279i	−0.962693	+	1.32503i
$414$	0.934369	−	0.546359i	0.0459218	−	0.0268521i
$415$	−0.0500928	−	0.154170i	−0.00245896	−	0.00756790i
$416$	37.1886	−	4.95000i	1.82332	−	0.242694i
$417$			7.55833i			0.370133i
$418$	−14.0153	−	13.3582i	−0.685509	−	0.653372i
$419$		−	2.33902i		−	0.114269i	−0.998366	−	0.0571343i	$-0.981804\pi$
$419$		−	2.33902i		−	0.114269i	0.998366	−	0.0571343i	$-0.0181963\pi$
$420$	1.29951	−	1.19634i	0.0634098	−	0.0583752i
$421$	4.01513	+	12.3573i	0.195686	+	0.602258i	0.999968	+	0.00801103i	$0.00255002\pi$
$421$	4.01513	+	12.3573i	0.195686	+	0.602258i	−0.804282	+	0.594247i	$0.797450\pi$
$422$	9.14399	+	15.6378i	0.445122	+	0.761237i
$423$	−3.03764	+	4.18096i	−0.147695	+	0.203285i
$424$	5.21821	+	15.1987i	0.253419	+	0.738112i
$425$	21.9117	+	7.11954i	1.06287	+	0.345348i
$426$	−5.93915	−	2.60508i	−0.287753	−	0.126217i
$427$	−6.26237	−	8.61942i	−0.303057	−	0.417123i
$428$	−2.82329	−	24.2795i	−0.136469	−	1.17359i
$429$	0.745151	−	21.9834i	0.0359763	−	1.06137i
$430$	0.523937	−	0.588392i	0.0252665	−	0.0283748i
$431$	22.6258	−	16.4386i	1.08985	−	0.791821i	0.110474	−	0.993879i	$-0.464763\pi$
$431$	22.6258	−	16.4386i	1.08985	−	0.791821i	0.979374	+	0.202058i	$0.0647630\pi$
$432$	3.41909	−	2.07601i	0.164501	−	0.0998823i
$433$	9.68478	−	29.8067i	0.465421	−	1.43242i	−0.393032	−	0.919525i	$-0.628574\pi$
$433$	9.68478	−	29.8067i	0.465421	−	1.43242i	0.858453	−	0.512893i	$-0.171426\pi$
$434$	−4.07849	−	18.6800i	−0.195774	−	0.896670i
$435$	−0.826342	−	0.600373i	−0.0396201	−	0.0287857i
$436$	−0.825472	+	4.10599i	−0.0395330	+	0.196641i
$437$	−3.00470	+	0.976287i	−0.143734	+	0.0467021i
$438$	−2.11101	+	21.2108i	−0.100868	+	1.01349i
$439$	1.92512			0.0918811			0.0459405	−	0.998944i	$-0.485372\pi$
$439$	1.92512			0.0918811			0.0459405	+	0.998944i	$0.485372\pi$
$440$	−2.34299	−	0.806402i	−0.111698	−	0.0384437i
$441$	−4.17922			−0.199010
$442$	−4.34068	+	43.6140i	−0.206465	+	2.07451i
$443$	−25.8441	+	8.39727i	−1.22789	+	0.398966i	−0.849950	−	0.526863i	$-0.823368\pi$
$443$	−25.8441	+	8.39727i	−1.22789	+	0.398966i	−0.377942	+	0.925829i	$0.623368\pi$
$444$	−0.349646	+	1.73918i	−0.0165935	+	0.0825377i
$445$	−0.594127	−	0.431658i	−0.0281643	−	0.0204626i
$446$	−0.616175	−	2.82216i	−0.0291767	−	0.133633i
$447$	5.48420	−	16.8786i	0.259394	−	0.798333i
$448$	−21.1072	+	16.4304i	−0.997220	+	0.776263i
$449$	8.13130	−	5.90774i	0.383740	−	0.278803i	−0.379146	−	0.925337i	$-0.623782\pi$
$449$	8.13130	−	5.90774i	0.383740	−	0.278803i	0.762885	+	0.646534i	$0.223782\pi$
$450$	−4.63676	+	5.20718i	−0.218579	+	0.245469i
$451$	15.5670	+	12.1366i	0.733021	+	0.571492i
$452$	2.78534	+	23.9531i	0.131011	+	1.12666i
$453$	−7.97610	−	10.9782i	−0.374750	−	0.515799i
$454$	−23.6822	−	10.3877i	−1.11146	−	0.487519i
$455$	−5.57057	−	1.80999i	−0.261152	−	0.0848535i
$456$	−11.0427	+	3.79134i	−0.517123	+	0.177546i
$457$	5.80668	−	7.99221i	0.271625	−	0.373860i	−0.651312	−	0.758810i	$-0.725781\pi$
$457$	5.80668	−	7.99221i	0.271625	−	0.373860i	0.922937	+	0.384950i	$0.125781\pi$
$458$	8.90856	+	15.2352i	0.416270	+	0.711893i
$459$	1.44406	+	4.44436i	0.0674029	+	0.207445i
$460$	−0.297469	+	0.273850i	−0.0138696	+	0.0127683i
$461$			23.0867i			1.07526i	0.843182	+	0.537628i	$0.180679\pi$
$461$			23.0867i			1.07526i	−0.843182	+	0.537628i	$0.819321\pi$
$462$	7.45299	+	13.7984i	0.346744	+	0.641960i
$463$		−	5.87663i		−	0.273110i	−0.990632	−	0.136555i	$-0.956397\pi$
$463$		−	5.87663i		−	0.273110i	0.990632	−	0.136555i	$-0.0436031\pi$
$464$	11.7205	+	10.0935i	0.544108	+	0.468578i
$465$	−0.330058	−	1.01581i	−0.0153061	−	0.0471072i
$466$	−16.1917	+	9.46786i	−0.750065	+	0.438590i
$467$	2.22211	−	3.05847i	0.102827	−	0.141529i	−0.754503	−	0.656297i	$-0.772122\pi$
$467$	2.22211	−	3.05847i	0.102827	−	0.141529i	0.857330	+	0.514768i	$0.172122\pi$
$468$	−11.5596	−	6.50481i	−0.534343	−	0.300685i
$469$	−19.0602	−	6.19302i	−0.880117	−	0.285967i
$470$	0.775458	−	1.76792i	0.0357692	−	0.0815478i
$471$	8.49623	+	11.6941i	0.391485	+	0.538833i
$472$	16.1706	−	23.0503i	0.744311	−	1.06098i
$473$	3.91750	+	5.79513i	0.180127	+	0.266460i
$474$	15.2354	+	13.5664i	0.699785	+	0.623128i
$475$	16.4647	−	11.9623i	0.755452	−	0.548868i
$476$	−13.0246	−	28.4054i	−0.596984	−	1.30196i
$477$	1.75566	−	5.40336i	0.0803860	−	0.247403i
$478$	27.8059	−	6.07099i	1.27181	−	0.277681i
$479$	17.5590	+	12.7573i	0.802290	+	0.582898i	0.911585	−	0.411112i	$-0.134859\pi$
$479$	17.5590	+	12.7573i	0.802290	+	0.582898i	−0.109295	+	0.994009i	$0.534859\pi$
$480$	−1.08240	+	1.03010i	−0.0494044	+	0.0470173i
$481$	5.59465	−	1.81781i	0.255094	−	0.0828851i
$482$	14.1128	+	1.40457i	0.642818	+	0.0639764i
$483$	2.55901			0.116439
$484$	12.0624	−	18.3983i	0.548293	−	0.836286i
$485$	−2.65781			−0.120685
$486$	−1.40726	−	0.140058i	−0.0638347	−	0.00635314i
$487$	−7.27475	+	2.36371i	−0.329651	+	0.107110i	−0.469166	−	0.883110i	$-0.655445\pi$
$487$	−7.27475	+	2.36371i	−0.329651	+	0.107110i	0.139516	+	0.990220i	$0.455445\pi$
$488$	5.41764	+	7.20276i	0.245245	+	0.326053i
$489$	5.07524	+	3.68738i	0.229510	+	0.166749i
$490$	1.52523	−	0.333011i	0.0689030	−	0.0150439i
$491$	−7.07668	+	21.7798i	−0.319366	+	0.982908i	0.654553	+	0.756016i	$0.272857\pi$
$491$	−7.07668	+	21.7798i	−0.319366	+	0.982908i	−0.973920	+	0.226893i	$0.927143\pi$
$492$	10.8199	−	4.96121i	0.487798	−	0.223668i
$493$	−14.6192	+	10.6215i	−0.658416	+	0.478367i
$494$	28.9143	+	25.7469i	1.30092	+	1.15841i
$495$	0.490631	+	0.725787i	0.0220522	+	0.0326217i
$496$	3.71143	+	15.7429i	0.166648	+	0.706875i
$497$	−9.01247	−	12.4046i	−0.404264	−	0.556422i
$498$	0.348623	−	0.794803i	0.0156222	−	0.0356160i
$499$	36.2914	+	11.7918i	1.62462	+	0.527873i	0.973027	−	0.230692i	$-0.0740989\pi$
$499$	36.2914	+	11.7918i	1.62462	+	0.527873i	0.651598	+	0.758564i	$0.274099\pi$
$500$	2.57267	−	4.57185i	0.115053	−	0.204459i
$501$	1.38126	−	1.90114i	0.0617102	−	0.0849368i
$502$	15.3520	−	8.97684i	0.685192	−	0.400656i
$503$	0.902960	+	2.77903i	0.0402610	+	0.123911i	0.969167	−	0.246405i	$-0.0792494\pi$
$503$	0.902960	+	2.77903i	0.0402610	+	0.123911i	−0.928906	+	0.370316i	$0.879249\pi$
$504$	9.45564	−	0.156643i	0.421188	−	0.00697744i
$505$		−	5.22740i		−	0.232616i
$506$	−1.70605	−	3.15856i	−0.0758430	−	0.140415i
$507$			30.9843i			1.37606i
$508$	3.17907	+	3.45325i	0.141048	+	0.153213i
$509$	−9.59462	−	29.5292i	−0.425274	−	1.30886i	−0.902732	−	0.430204i	$-0.858442\pi$
$509$	−9.59462	−	29.5292i	−0.425274	−	1.30886i	0.477457	−	0.878655i	$-0.341558\pi$
$510$	−0.881157	−	1.50693i	−0.0390183	−	0.0667280i
$511$	−29.6215	+	40.7705i	−1.31038	+	1.80358i
$512$	17.6227	−	14.1930i	0.778821	−	0.627246i
$513$	3.92586	+	1.27559i	0.173331	+	0.0563187i
$514$	−1.30684	−	0.573217i	−0.0576422	−	0.0252835i
$515$	1.04212	+	1.43436i	0.0459213	+	0.0632053i
$516$	4.18992	−	0.487215i	0.184451	−	0.0214485i
$517$	13.5174	+	10.5387i	0.594495	+	0.463491i
$518$	−2.78915	+	3.13227i	−0.122548	+	0.137624i
$519$	13.2069	−	9.59541i	0.579721	−	0.421192i
$520$	4.73708	+	1.45287i	0.207735	+	0.0637128i
$521$	0.962822	−	2.96326i	0.0421820	−	0.129823i	−0.927748	−	0.373208i	$-0.878258\pi$
$521$	0.962822	−	2.96326i	0.0421820	−	0.129823i	0.969930	+	0.243385i	$0.0782578\pi$
$522$	−1.16651	−	5.34277i	−0.0510568	−	0.233847i
$523$	−31.4971	−	22.8840i	−1.37727	−	1.00065i	−0.997129	−	0.0757180i	$-0.975875\pi$
$523$	−31.4971	−	22.8840i	−1.37727	−	1.00065i	−0.380142	−	0.924928i	$-0.624125\pi$
$524$	−26.9912	−	5.42633i	−1.17911	−	0.237050i
$525$	−15.6776	+	5.09396i	−0.684226	+	0.222318i
$526$	−2.06303	+	20.7288i	−0.0899523	+	0.903817i
$527$	−18.8961			−0.823126
$528$	−6.49725	−	11.5666i	−0.282757	−	0.503371i
$529$	22.4142			0.974531
$530$	−0.210185	+	2.11189i	−0.00912986	+	0.0917345i
$531$	−9.46770	+	3.07624i	−0.410863	+	0.133498i
$532$	−27.0621	−	5.44059i	−1.17329	−	0.235879i
$533$	−31.9327	−	23.2005i	−1.38316	−	1.00492i
$534$	−0.838702	−	3.84137i	−0.0362942	−	0.166232i
$535$	0.997579	−	3.07023i	0.0431291	−	0.132738i
$536$	16.2083	+	4.97113i	0.700093	+	0.214720i
$537$	−19.8534	+	14.4243i	−0.856737	+	0.622456i
$538$	11.1638	−	12.5371i	0.481304	−	0.540514i
$539$	−0.469560	+	13.8529i	−0.0202254	+	0.596689i
$540$	0.524749	−	0.0610193i	0.0225816	−	0.00262585i
$541$	−3.61016	−	4.96896i	−0.155213	−	0.213632i	0.724328	−	0.689456i	$-0.242150\pi$
$541$	−3.61016	−	4.96896i	−0.155213	−	0.213632i	−0.879541	+	0.475823i	$0.842150\pi$
$542$	18.2576	+	8.00831i	0.784231	+	0.343986i
$543$	−12.5092	−	4.06450i	−0.536823	−	0.174424i
$544$	11.4146	+	23.8435i	0.489395	+	1.02228i
$545$	−0.325124	+	0.447494i	−0.0139268	+	0.0191686i
$546$	−15.8295	−	27.0712i	−0.677439	−	1.15854i
$547$	7.06160	+	21.7334i	0.301932	+	0.929252i	0.980804	+	0.194996i	$0.0624692\pi$
$547$	7.06160	+	21.7334i	0.301932	+	0.929252i	−0.678872	+	0.734257i	$0.737531\pi$
$548$	8.05747	+	8.75239i	0.344198	+	0.373884i
$549$		−	3.18650i		−	0.135997i
$550$	16.7394	+	15.9546i	0.713770	+	0.680308i
$551$			15.9622i			0.680012i
$552$	−2.16447	+	0.0358569i	−0.0921260	+	0.00152617i
$553$	14.9041	+	45.8702i	0.633788	+	1.95060i
$554$	−24.9811	+	14.6073i	−1.06134	+	0.620606i
$555$	−0.137713	+	0.189546i	−0.00584559	+	0.00804577i
$556$	7.41330	−	13.1741i	0.314394	−	0.558705i
$557$	−17.3847	−	5.64864i	−0.736615	−	0.239341i	−0.0834032	−	0.996516i	$-0.526579\pi$
$557$	−17.3847	−	5.64864i	−0.736615	−	0.239341i	−0.653212	+	0.757175i	$0.726579\pi$
$558$	2.29705	−	5.23689i	0.0972420	−	0.221695i
$559$	−8.22167	−	11.3162i	−0.347739	−	0.478622i
$560$	−3.43842	+	0.810618i	−0.145300	+	0.0342549i
$561$	14.8940	−	4.28730i	0.628827	−	0.181010i
$562$	13.9231	+	12.3979i	0.587312	+	0.522975i
$563$	13.4244	−	9.75341i	0.565772	−	0.411057i	−0.267795	−	0.963476i	$-0.586295\pi$
$563$	13.4244	−	9.75341i	0.565772	−	0.411057i	0.833567	+	0.552419i	$0.186295\pi$
$564$	9.39531	−	4.30800i	0.395614	−	0.181400i
$565$	−0.984169	+	3.02896i	−0.0414043	+	0.127429i
$566$	−5.73548	+	1.25225i	−0.241080	+	0.0526361i
$567$	−2.70498	−	1.96528i	−0.113598	−	0.0825340i
$568$	7.79677	+	10.3658i	0.327145	+	0.434940i
$569$	−39.2099	+	12.7401i	−1.64376	+	0.534091i	−0.977375	−	0.211513i	$-0.932161\pi$
$569$	−39.2099	+	12.7401i	−1.64376	+	0.534091i	−0.666389	+	0.745604i	$0.732161\pi$
$570$	−1.53441	−	0.152712i	−0.0642695	−	0.00639641i
$571$	−8.89753			−0.372350			−0.186175	−	0.982517i	$-0.559609\pi$
$571$	−8.89753			−0.372350			−0.186175	+	0.982517i	$0.559609\pi$
$572$	−22.8604	+	37.5860i	−0.955842	+	1.57155i
$573$	11.0827			0.462985
$574$	28.0033	+	2.78703i	1.16884	+	0.116328i
$575$	3.58872	−	1.16605i	0.149660	−	0.0486275i
$576$	−7.99561	+	0.264985i	−0.333150	+	0.0110410i
$577$	−16.3150	−	11.8536i	−0.679204	−	0.493470i	0.193890	−	0.981023i	$-0.437890\pi$
$577$	−16.3150	−	11.8536i	−0.679204	−	0.493470i	−0.873093	+	0.487553i	$0.837890\pi$
$578$	−6.68394	+	1.45933i	−0.278015	+	0.0607003i
$579$	4.28678	−	13.1933i	0.178152	−	0.548297i
$580$	0.851451	+	1.85693i	0.0353546	+	0.0771048i
$581$	1.66004	−	1.20609i	0.0688699	−	0.0500369i
$582$	−10.6272	−	9.46308i	−0.440513	−	0.392257i
$583$	−17.7134	−	6.42661i	−0.733612	−	0.266163i
$584$	24.4833	−	34.8997i	1.01313	−	1.44416i
$585$	−1.02969	−	1.41725i	−0.0425724	−	0.0585959i
$586$	−4.53870	+	10.3475i	−0.187492	+	0.427450i
$587$	−0.526749	−	0.171151i	−0.0217413	−	0.00706417i	0.298126	−	0.954526i	$-0.403638\pi$
$587$	−0.526749	−	0.171151i	−0.0217413	−	0.00706417i	−0.319867	+	0.947462i	$0.603638\pi$
$588$	7.28433	+	4.09903i	0.300401	+	0.169041i
$589$	−9.81107	+	13.5038i	−0.404258	+	0.556414i
$590$	3.21018	−	1.87711i	0.132161	−	0.0772793i
$591$	−1.86751	−	5.74760i	−0.0768191	−	0.236425i
$592$	2.31524	−	2.68843i	0.0951556	−	0.110494i
$593$		−	34.6597i		−	1.42330i	−0.702533	−	0.711651i	$-0.747948\pi$
$593$		−	34.6597i		−	1.42330i	0.702533	−	0.711651i	$-0.252052\pi$
$594$	−0.622366	+	4.64894i	−0.0255360	+	0.190748i
$595$		−	4.12712i		−	0.169195i
$596$	−26.1137	+	24.0403i	−1.06966	+	0.984729i
$597$	−5.29887	−	16.3083i	−0.216868	−	0.667453i
$598$	3.62349	+	6.19680i	0.148176	+	0.253406i
$599$	−19.4341	+	26.7488i	−0.794057	+	1.09293i	0.199535	+	0.979891i	$0.436057\pi$
$599$	−19.4341	+	26.7488i	−0.794057	+	1.09293i	−0.993591	+	0.113034i	$0.963943\pi$
$600$	13.1891	−	4.52826i	0.538442	−	0.184865i
$601$	−10.1517	−	3.29847i	−0.414095	−	0.134548i	0.0945579	−	0.995519i	$-0.469856\pi$
$601$	−10.1517	−	3.29847i	−0.414095	−	0.134548i	−0.508653	+	0.860972i	$0.669856\pi$
$602$	9.13278	+	4.00590i	0.372224	+	0.163268i
$603$	−3.52317	−	4.84923i	−0.143475	−	0.197476i
$604$	3.13473	+	26.9579i	0.127550	+	1.09690i
$605$	2.46091	−	1.54476i	0.100050	−	0.0628033i
$606$	18.6121	−	20.9018i	0.756064	−	0.849076i
$607$	−6.00393	+	4.36211i	−0.243692	+	0.177053i	−0.702927	−	0.711262i	$-0.748124\pi$
$607$	−6.00393	+	4.36211i	−0.243692	+	0.177053i	0.459235	+	0.888315i	$0.348124\pi$
$608$	22.9659	+	4.22258i	0.931392	+	0.171248i
$609$	3.99532	−	12.2963i	0.161899	−	0.498273i
$610$	0.253909	+	1.16294i	0.0102805	+	0.0470859i
$611$	−27.7284	−	20.1458i	−1.12177	−	0.815014i
$612$	1.84210	−	9.16281i	0.0744625	−	0.370385i
$613$	8.38874	−	2.72567i	0.338818	−	0.110089i	−0.134666	−	0.990891i	$-0.542996\pi$
$613$	8.38874	−	2.72567i	0.338818	−	0.110089i	0.473484	+	0.880802i	$0.342996\pi$
$614$	3.95899	−	39.7789i	0.159772	−	1.60535i
$615$	1.57206			0.0633914
$616$	0.543169	−	31.3604i	0.0218849	−	1.26355i
$617$	30.1412			1.21344			0.606719	−	0.794917i	$-0.292485\pi$
$617$	30.1412			1.21344			0.606719	+	0.794917i	$0.292485\pi$
$618$	−0.940085	+	9.44573i	−0.0378158	+	0.379963i
$619$	7.17057	−	2.32986i	0.288210	−	0.0936450i	−0.161344	−	0.986898i	$-0.551583\pi$
$619$	7.17057	−	2.32986i	0.288210	−	0.0936450i	0.449554	+	0.893253i	$0.351583\pi$
$620$	−0.421035	+	2.09427i	−0.0169092	+	0.0841081i
$621$	0.619190	+	0.449868i	0.0248472	+	0.0180526i
$622$	−3.88494	−	17.7935i	−0.155772	−	0.713456i
$623$	2.87257	−	8.84087i	0.115087	−	0.354202i
$624$	13.7683	+	22.6756i	0.551172	+	0.907751i
$625$	−19.3827	+	14.0823i	−0.775307	+	0.563293i
$626$	−9.06209	+	10.1769i	−0.362194	+	0.406752i
$627$	4.66932	−	12.8698i	0.186475	−	0.513971i
$628$	−3.33915	−	28.7158i	−0.133247	−	1.14588i
$629$	2.43635	+	3.35334i	0.0971435	+	0.133707i
$630$	1.14380	+	0.501703i	0.0455700	+	0.0199883i
$631$	39.5316	+	12.8446i	1.57373	+	0.511336i	0.960431	−	0.278516i	$-0.0898427\pi$
$631$	39.5316	+	12.8446i	1.57373	+	0.511336i	0.613297	+	0.789852i	$0.289843\pi$
$632$	−13.2490	−	38.5892i	−0.527016	−	1.53500i
$633$	−7.52909	+	10.3629i	−0.299254	+	0.411888i
$634$	4.74658	+	8.11747i	0.188511	+	0.322386i
$635$	0.191563	+	0.589571i	0.00760196	+	0.0233964i
$636$	−8.35977	+	7.69602i	−0.331486	+	0.305167i
$637$		−	27.7169i		−	1.09818i
$638$	−17.8409	+	3.26636i	−0.706326	+	0.129317i
$639$		−	4.58584i		−	0.181413i
$640$	2.89694	−	0.733819i	0.114511	−	0.0290067i
$641$	−8.25277	−	25.3994i	−0.325965	−	1.00322i	−0.971003	−	0.239066i	$-0.923159\pi$
$641$	−8.25277	−	25.3994i	−0.325965	−	1.00322i	0.645039	−	0.764150i	$-0.276841\pi$
$642$	14.9203	−	8.72446i	0.588859	−	0.344327i
$643$	−9.57732	+	13.1820i	−0.377693	+	0.519849i	−0.954971	−	0.296698i	$-0.904115\pi$
$643$	−9.57732	+	13.1820i	−0.377693	+	0.519849i	0.577279	+	0.816547i	$0.304115\pi$
$644$	−4.46032	−	2.50991i	−0.175761	−	0.0989043i
$645$	0.529831	+	0.172152i	0.0208621	+	0.00677850i
$646$	−10.9580	+	24.9825i	−0.431139	+	0.982924i
$647$	2.85269	+	3.92639i	0.112151	+	0.154362i	0.861402	−	0.507923i	$-0.169587\pi$
$647$	2.85269	+	3.92639i	0.112151	+	0.154362i	−0.749252	+	0.662285i	$0.769587\pi$
$648$	2.31547	+	1.62438i	0.0909602	+	0.0638116i
$649$	9.13314	+	31.7284i	0.358507	+	1.24545i
$650$	−34.5344	−	30.7513i	−1.35455	−	1.20617i
$651$	10.9379	−	7.94682i	0.428688	−	0.311460i
$652$	−5.22945	−	11.4049i	−0.204801	−	0.446651i
$653$	1.84727	−	5.68532i	0.0722893	−	0.222484i	−0.908384	−	0.418138i	$-0.862683\pi$
$653$	1.84727	−	5.68532i	0.0722893	−	0.222484i	0.980673	+	0.195654i	$0.0626830\pi$
$654$	−2.89330	+	0.631708i	−0.113137	+	0.0247017i
$655$	−2.94165	−	2.13724i	−0.114940	−	0.0835087i
$656$	−23.7249	−	1.96495i	−0.926303	−	0.0767185i
$657$	−14.3347	+	4.65764i	−0.559251	+	0.181712i
$658$	24.3164	+	2.42008i	0.947950	+	0.0943446i
$659$	38.6071			1.50392			0.751959	−	0.659209i	$-0.229109\pi$
$659$	38.6071			1.50392			0.751959	+	0.659209i	$0.229109\pi$
$660$	−0.143303	−	1.74625i	−0.00557807	−	0.0679728i
$661$	38.4608			1.49595			0.747975	−	0.663727i	$-0.231026\pi$
$661$	38.4608			1.49595			0.747975	+	0.663727i	$0.231026\pi$
$662$	−5.98138	−	0.595296i	−0.232473	−	0.0231368i
$663$	−29.4753	+	9.57709i	−1.14472	+	0.371943i
$664$	−1.38720	+	1.04340i	−0.0538337	+	0.0404917i
$665$	−2.94938	−	2.14285i	−0.114372	−	0.0830962i
$666$	−1.22552	+	0.267573i	−0.0474880	+	0.0103683i
$667$	−0.914560	+	2.81473i	−0.0354119	+	0.108987i
$668$	−4.27219	+	1.95891i	−0.165296	+	0.0757926i
$669$	1.65248	−	1.20060i	0.0638886	−	0.0464178i
$670$	1.67220	+	1.48902i	0.0646028	+	0.0575259i
$671$	−10.5624	−	0.358023i	−0.407756	−	0.0138213i
$672$	−16.6347	−	9.00119i	−0.641698	−	0.347228i
$673$	4.48381	+	6.17144i	0.172838	+	0.237891i	0.886644	−	0.462452i	$-0.153030\pi$
$673$	4.48381	+	6.17144i	0.172838	+	0.237891i	−0.713806	+	0.700343i	$0.753030\pi$
$674$	11.2104	−	25.5577i	0.431807	−	0.984447i
$675$	−4.68893	−	1.52352i	−0.180477	−	0.0586405i
$676$	30.3898	−	54.0052i	1.16884	−	2.07712i
$677$	−4.43491	+	6.10413i	−0.170448	+	0.234601i	−0.885692	−	0.464274i	$-0.846315\pi$
$677$	−4.43491	+	6.10413i	−0.170448	+	0.234601i	0.715244	+	0.698875i	$0.246315\pi$
$678$	−14.7198	+	8.60718i	−0.565310	+	0.330557i
$679$	−10.3962	−	31.9961i	−0.398968	−	1.22790i
$680$	0.0578292	+	3.49081i	0.00221765	+	0.133866i
$681$		−	18.2860i		−	0.700720i
$682$	−17.1008	−	8.20249i	−0.654822	−	0.314089i
$683$			10.7849i			0.412674i	0.978481	+	0.206337i	$0.0661543\pi$
$683$			10.7849i			0.412674i	−0.978481	+	0.206337i	$0.933846\pi$
$684$	−5.59162	−	6.07387i	−0.213801	−	0.232240i
$685$	0.485524	+	1.49429i	0.0185509	+	0.0570939i
$686$	−6.73267	−	11.5140i	−0.257054	−	0.439608i
$687$	−7.33523	+	10.0961i	−0.279857	+	0.385190i
$688$	−7.78085	−	3.26032i	−0.296642	−	0.124298i
$689$	35.8354	+	11.6436i	1.36522	+	0.443587i
$690$	−0.261824	−	0.114844i	−0.00996748	−	0.00437202i
$691$	−16.0497	−	22.0905i	−0.610558	−	0.840361i	0.386065	−	0.922471i	$-0.373834\pi$
$691$	−16.0497	−	22.0905i	−0.610558	−	0.840361i	−0.996623	+	0.0821106i	$0.973834\pi$
$692$	−32.4308	+	3.77115i	−1.23284	+	0.143358i
$693$	−6.81827	+	8.74543i	−0.259005	+	0.332211i
$694$	−9.15074	+	10.2765i	−0.347357	+	0.390089i
$695$	1.61518	−	1.17350i	0.0612674	−	0.0445134i
$696$	−3.20704	+	10.4565i	−0.121563	+	0.396353i
$697$	8.59437	−	26.4508i	0.325535	−	1.00189i
$698$	5.78850	+	26.5121i	0.219098	+	1.00350i
$699$	−10.7299	−	7.79576i	−0.405844	−	0.294863i
$700$	32.3221	+	6.49806i	1.22166	+	0.245604i
$701$	9.15601	−	2.97497i	0.345818	−	0.112363i	−0.130958	−	0.991388i	$-0.541805\pi$
$701$	9.15601	−	2.97497i	0.345818	−	0.112363i	0.476776	+	0.879025i	$0.341805\pi$
$702$	0.928870	−	9.33305i	0.0350580	−	0.352253i
$703$	3.66140			0.138092
$704$	−0.0200024	+	26.5330i	−0.000753867	+	1.00000i
$705$	1.36507			0.0514117
$706$	−0.323117	+	3.24660i	−0.0121607	+	0.122187i
$707$	62.9302	−	20.4473i	2.36673	−	0.768999i
$708$	19.5193	+	3.92418i	0.733581	+	0.147480i
$709$	14.5854	+	10.5969i	0.547765	+	0.397974i	0.826961	−	0.562260i	$-0.190068\pi$
$709$	14.5854	+	10.5969i	0.547765	+	0.397974i	−0.279196	+	0.960234i	$0.590068\pi$
$710$	0.365412	+	1.67363i	0.0137137	+	0.0628104i
$711$	−4.45760	+	13.7191i	−0.167173	+	0.514505i
$712$	−2.30581	+	7.51806i	−0.0864139	+	0.281751i
$713$	−2.50376	+	1.81909i	−0.0937666	+	0.0681254i
$714$	14.6945	−	16.5023i	0.549929	−	0.617582i
$715$	−4.81346	+	3.25390i	−0.180013	+	0.121689i
$716$	48.7518	−	5.66899i	1.82194	−	0.211860i
$717$	11.8292	+	16.2814i	0.441768	+	0.608041i
$718$	−22.8594	−	10.0268i	−0.853106	−	0.374197i
$719$	45.6978	+	14.8481i	1.70424	+	0.553741i	0.989358	−	0.145504i	$-0.0464803\pi$
$719$	45.6978	+	14.8481i	1.70424	+	0.553741i	0.714882	+	0.699245i	$0.246480\pi$
$720$	−0.974481	−	0.408325i	−0.0363167	−	0.0152174i
$721$	−13.1912	+	18.1562i	−0.491267	+	0.676171i
$722$	−1.39950	−	2.39338i	−0.0520839	−	0.0890725i
$723$	3.09899	+	9.53770i	0.115253	+	0.354711i
$724$	17.8169	+	19.3536i	0.662162	+	0.719271i
$725$		−	19.0647i		−	0.708046i
$726$	15.3400	+	2.58530i	0.569322	+	0.0959497i
$727$		−	27.0238i		−	1.00226i	−0.865373	−	0.501128i	$-0.832919\pi$
$727$		−	27.0238i		−	1.00226i	0.865373	−	0.501128i	$-0.167081\pi$
$728$	1.03887	+	62.7104i	0.0385030	+	2.32420i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	4.86042	−	2.84206i	0.179892	−	0.105189i
$731$	5.79313	−	7.97356i	0.214267	−	0.294913i
$732$	−3.12536	+	5.55404i	−0.115517	+	0.205283i
$733$	−32.7676	−	10.6468i	−1.21030	−	0.393250i	−0.366759	−	0.930316i	$-0.619532\pi$
$733$	−32.7676	−	10.6468i	−1.21030	−	0.393250i	−0.843540	+	0.537066i	$0.819532\pi$
$734$	3.56139	−	8.11936i	0.131453	−	0.299691i
$735$	0.648862	+	0.893082i	0.0239336	+	0.0329418i
$736$	3.80782	+	2.06044i	0.140358	+	0.0759489i
$737$	−16.4697	+	11.1335i	−0.606668	+	0.410107i
$738$	6.28587	+	5.59728i	0.231386	+	0.206039i
$739$	−23.8296	+	17.3132i	−0.876585	+	0.636876i	−0.932346	−	0.361568i	$-0.882242\pi$
$739$	−23.8296	+	17.3132i	−0.876585	+	0.636876i	0.0557608	+	0.998444i	$0.482242\pi$
$740$	0.425941	−	0.195305i	0.0156579	−	0.00717957i
$741$	−8.45980	+	26.0366i	−0.310778	+	0.956478i
$742$	−26.2462	+	5.73044i	−0.963527	+	0.210371i
$743$	35.7350	+	25.9630i	1.31099	+	0.952491i	0.999998	+	0.00207936i	$0.000661883\pi$
$743$	35.7350	+	25.9630i	1.31099	+	0.952491i	0.310994	+	0.950412i	$0.399338\pi$
$744$	−9.14015	+	6.87487i	−0.335094	+	0.252045i
$745$	−4.45837	+	1.44861i	−0.163342	+	0.0530731i
$746$	0.0344170	+	0.00342535i	0.00126010	+	0.000125411i
$747$	0.613698			0.0224540
$748$	−30.1652	−	7.13555i	−1.10295	−	0.260901i
$749$	40.8632			1.49311
$750$	3.69124	+	0.367370i	0.134785	+	0.0134145i
$751$	−11.6991	+	3.80126i	−0.426905	+	0.138710i	−0.514586	−	0.857439i	$-0.672054\pi$
$751$	−11.6991	+	3.80126i	−0.426905	+	0.138710i	0.0876808	+	0.996149i	$0.472054\pi$
$752$	−20.6012	−	1.70624i	−0.751250	−	0.0622202i
$753$	10.1735	+	7.39146i	0.370742	+	0.269360i
$754$	35.4336	−	7.73637i	1.29042	−	0.281742i
$755$	−1.10762	+	3.40892i	−0.0403106	+	0.124063i
$756$	2.78717	+	6.07853i	0.101368	+	0.221074i
$757$	−9.30726	+	6.76212i	−0.338278	+	0.245773i	−0.743935	−	0.668252i	$-0.767043\pi$
$757$	−9.30726	+	6.76212i	−0.338278	+	0.245773i	0.405657	+	0.914025i	$0.367043\pi$
$758$	−33.8478	−	30.1400i	−1.22941	−	1.09473i
$759$	1.56076	−	2.00190i	0.0566519	−	0.0726643i
$760$	2.52468	+	1.77115i	0.0915798	+	0.0642462i
$761$	−7.53101	−	10.3655i	−0.272999	−	0.375751i	0.650400	−	0.759591i	$-0.274601\pi$
$761$	−7.53101	−	10.3655i	−0.272999	−	0.375751i	−0.923399	+	0.383841i	$0.874601\pi$
$762$	−1.33319	+	3.03946i	−0.0482965	+	0.110108i
$763$	−6.65892	−	2.16361i	−0.241069	−	0.0783280i
$764$	−19.3169	−	10.8700i	−0.698862	−	0.393263i
$765$	0.725537	−	0.998616i	0.0262319	−	0.0361050i
$766$	−43.0756	+	25.1878i	−1.55638	+	0.910073i
$767$	−20.4018	−	62.7904i	−0.736668	−	2.26723i
$768$	14.1962	+	7.38033i	0.512260	+	0.266315i
$769$			6.41973i			0.231501i	0.993278	+	0.115751i	$0.0369274\pi$
$769$			6.41973i			0.231501i	−0.993278	+	0.115751i	$0.963073\pi$
$770$	1.79152	−	3.73500i	0.0645618	−	0.134600i
$771$		−	1.00906i		−	0.0363404i
$772$	−20.4120	+	18.7913i	−0.734644	+	0.676314i
$773$	8.70055	+	26.7775i	0.312937	+	0.963121i	0.976595	+	0.215085i	$0.0690028\pi$
$773$	8.70055	+	26.7775i	0.312937	+	0.963121i	−0.663658	+	0.748036i	$0.730997\pi$
$774$	1.50558	+	2.57481i	0.0541170	+	0.0925495i
$775$	11.7180	−	16.1285i	0.420924	−	0.579352i
$776$	9.24164	+	26.9174i	0.331756	+	0.966277i
$777$	−2.82052	−	0.916444i	−0.101186	−	0.0328772i
$778$	−12.3559	−	5.41966i	−0.442981	−	0.194304i
$779$	−14.4403	−	19.8754i	−0.517378	−	0.712110i
$780$	0.404684	+	3.48017i	0.0144900	+	0.124610i
$781$	−15.2008	−	0.515247i	−0.543927	−	0.0184370i
$782$	−3.36369	+	3.77750i	−0.120285	+	0.135083i
$783$	3.12839	−	2.27291i	0.111800	−	0.0812272i
$784$	−8.67612	−	14.2891i	−0.309861	−	0.510326i
$785$	1.17985	−	3.63122i	0.0421108	−	0.129604i
$786$	−4.15260	−	19.0195i	−0.148118	−	0.678401i
$787$	−10.3223	−	7.49956i	−0.367949	−	0.267330i	0.388411	−	0.921486i	$-0.373024\pi$
$787$	−10.3223	−	7.49956i	−0.367949	−	0.267330i	−0.756360	+	0.654156i	$0.773024\pi$
$788$	−2.38227	+	11.8497i	−0.0848650	+	0.422127i
$789$	−14.0089	+	4.55178i	−0.498731	+	0.162048i
$790$	0.533658	−	5.36206i	0.0189867	−	0.190773i
$791$	−40.3139			−1.43340
$792$	5.64452	−	7.49263i	0.200569	−	0.266239i
$793$	21.1331			0.750459
$794$	−1.12619	+	11.3156i	−0.0399669	+	0.401576i
$795$	−1.42726	+	0.463744i	−0.0506196	+	0.0164473i
$796$	−6.75946	+	33.6223i	−0.239583	+	1.19171i
$797$	32.4990	+	23.6119i	1.15117	+	0.836376i	0.988636	−	0.150327i	$-0.0480325\pi$
$797$	32.4990	+	23.6119i	1.15117	+	0.836376i	0.162536	+	0.986703i	$0.448033\pi$
$798$	−4.16351	−	19.0694i	−0.147387	−	0.675050i
$799$	7.46282	−	22.9682i	0.264015	−	0.812556i
$800$	−27.4298	−	5.04332i	−0.969790	−	0.178308i
$801$	2.24926	−	1.63419i	0.0794738	−	0.0577411i
$802$	34.9965	−	39.3018i	1.23577	−	1.38780i
$803$	13.8282	+	48.0389i	0.487986	+	1.69526i
$804$	1.38466	+	11.9077i	0.0488332	+	0.419952i
$805$	−0.397310	−	0.546850i	−0.0140033	−	0.0192739i
$806$	34.7314	+	15.2342i	1.22336	+	0.536602i
$807$	11.2894	+	3.66813i	0.397404	+	0.129124i
$808$	−52.9413	+	18.1766i	−1.86247	+	0.639449i
$809$	11.8866	−	16.3605i	0.417910	−	0.575204i	−0.547215	−	0.836992i	$-0.684312\pi$
$809$	11.8866	−	16.3605i	0.417910	−	0.575204i	0.965125	+	0.261788i	$0.0843121\pi$
$810$	0.188560	+	0.322471i	0.00662534	+	0.0113305i
$811$	8.62836	+	26.5554i	0.302983	+	0.932485i	0.980422	+	0.196907i	$0.0630896\pi$
$811$	8.62836	+	26.5554i	0.302983	+	0.932485i	−0.677439	+	0.735579i	$0.736910\pi$
$812$	−19.0242	+	17.5137i	−0.667618	+	0.614611i
$813$			14.0974i			0.494417i
$814$	0.749236	+	4.09232i	0.0262607	+	0.143436i
$815$		−	1.65706i		−	0.0580441i
$816$	−12.1978	+	14.1639i	−0.427007	+	0.495836i
$817$	−2.69032	−	8.27995i	−0.0941223	−	0.289679i
$818$	−12.6183	+	7.37839i	−0.441189	+	0.257979i
$819$	13.0339	−	17.9396i	0.455440	−	0.626859i
$820$	−2.74007	−	1.54189i	−0.0956876	−	0.0538452i
$821$	−25.0864	−	8.15107i	−0.875522	−	0.284474i	−0.163425	−	0.986556i	$-0.552254\pi$
$821$	−25.0864	−	8.15107i	−0.875522	−	0.284474i	−0.712097	+	0.702081i	$0.752254\pi$
$822$	−3.37903	+	7.70362i	−0.117857	+	0.268695i
$823$	25.1235	+	34.5796i	0.875752	+	1.20537i	0.977579	+	0.210567i	$0.0675309\pi$
$823$	25.1235	+	34.5796i	0.875752	+	1.20537i	−0.101828	+	0.994802i	$0.532469\pi$
$824$	10.9030	−	15.5417i	0.379826	−	0.541422i
$825$	−5.57689	+	15.3713i	−0.194162	+	0.535160i
$826$	35.1544	+	31.3034i	1.22318	+	1.08919i
$827$	−10.1906	+	7.40391i	−0.354362	+	0.257459i	−0.750697	−	0.660647i	$-0.770282\pi$
$827$	−10.1906	+	7.40391i	−0.354362	+	0.257459i	0.396334	+	0.918106i	$0.370282\pi$
$828$	−0.638005	−	1.39142i	−0.0221722	−	0.0483553i
$829$	−3.42053	+	10.5273i	−0.118800	+	0.365628i	−0.992721	−	0.120440i	$-0.961569\pi$
$829$	−3.42053	+	10.5273i	−0.118800	+	0.365628i	0.873921	+	0.486068i	$0.161569\pi$
$830$	−0.223973	+	0.0489010i	−0.00777422	+	0.00169738i
$831$	−16.5545	−	12.0276i	−0.574269	−	0.417231i
$832$	−1.75740	−	53.0274i	−0.0609268	−	1.83839i
$833$	18.5739	−	6.03504i	0.643549	−	0.209102i
$834$	10.6365	+	1.05860i	0.368313	+	0.0366564i
$835$	−0.620720			−0.0214809
$836$	−20.7614	+	17.8522i	−0.718050	+	0.617432i
$837$	4.04361			0.139768
$838$	−3.29161	−	0.327598i	−0.113707	−	0.0113167i
$839$	−0.759442	+	0.246758i	−0.0262189	+	0.00851902i	−0.322097	−	0.946707i	$-0.604388\pi$
$839$	−0.759442	+	0.246758i	−0.0262189	+	0.00851902i	0.295878	+	0.955226i	$0.404388\pi$
$840$	−1.50155	−	1.99631i	−0.0518084	−	0.0688793i
$841$	−11.3643	−	8.25664i	−0.391872	−	0.284712i
$842$	17.9523	−	3.91961i	0.618678	−	0.135079i
$843$	−4.07365	+	12.5374i	−0.140304	+	0.431811i
$844$	23.2872	−	10.6778i	0.801577	−	0.367545i
$845$	6.62121	−	4.81059i	0.227777	−	0.165489i
$846$	5.45825	+	4.86033i	0.187659	+	0.167102i
$847$	28.2226	+	23.5833i	0.969740	+	0.810331i
$848$	22.1193	−	5.21470i	0.759581	−	0.179074i
$849$	−2.43998	−	3.35834i	−0.0837398	−	0.115258i
$850$	13.0879	−	29.8383i	0.448913	−	1.02345i
$851$	0.645640	+	0.209781i	0.0221323	+	0.00719121i
$852$	−4.49785	+	7.99307i	−0.154094	+	0.273838i
$853$	9.71467	−	13.3711i	0.332624	−	0.457818i	−0.609645	−	0.792675i	$-0.708688\pi$
$853$	9.71467	−	13.3711i	0.332624	−	0.457818i	0.942269	+	0.334857i	$0.108688\pi$
$854$	−13.0069	+	7.60558i	−0.445086	+	0.260258i
$855$	−0.336938	−	1.03699i	−0.0115230	−	0.0354642i
$856$	−34.5630	+	0.572575i	−1.18134	+	0.0195702i
$857$			4.04192i			0.138069i	0.997614	+	0.0690347i	$0.0219919\pi$
$857$			4.04192i			0.138069i	−0.997614	+	0.0690347i	$0.978008\pi$
$858$	−30.8321	−	4.12757i	−1.05259	−	0.140913i
$859$			13.5474i			0.462231i	0.972926	+	0.231115i	$0.0742375\pi$
$859$			13.5474i			0.462231i	−0.972926	+	0.231115i	$0.925762\pi$
$860$	−0.754640	−	0.819724i	−0.0257330	−	0.0279524i
$861$	6.14919	+	18.9252i	0.209564	+	0.644971i
$862$	−19.9645	−	34.1428i	−0.679994	−	1.16291i
$863$	9.44467	−	12.9995i	0.321500	−	0.442507i	−0.617424	−	0.786630i	$-0.711824\pi$
$863$	9.44467	−	12.9995i	0.321500	−	0.442507i	0.938925	+	0.344123i	$0.111824\pi$
$864$	−2.44263	−	5.10231i	−0.0830998	−	0.173584i
$865$	−4.10100	−	1.33250i	−0.139438	−	0.0453062i
$866$	−40.5894	−	17.8037i	−1.37928	−	0.604993i
$867$	−2.84347	−	3.91370i	−0.0965692	−	0.132916i
$868$	−26.8589	+	3.12323i	−0.911650	+	0.106009i
$869$	44.9740	+	16.3171i	1.52564	+	0.553520i
$870$	−0.960616	+	1.07879i	−0.0325679	+	0.0365745i
$871$	32.1604	−	23.3659i	1.08971	−	0.791723i
$872$	5.66258	+	1.73673i	0.191759	+	0.0588131i
$873$	3.10933	−	9.56954i	0.105235	−	0.323880i
$874$	0.953060	+	4.36514i	0.0322377	+	0.147653i
$875$	7.09514	+	5.15492i	0.239860	+	0.174268i
$876$	29.5535	+	5.94147i	0.998521	+	0.200744i
$877$	−8.88213	+	2.88598i	−0.299928	+	0.0974526i	−0.455115	−	0.890432i	$-0.650402\pi$
$877$	−8.88213	+	2.88598i	−0.299928	+	0.0974526i	0.155187	+	0.987885i	$0.450402\pi$
$878$	0.269628	−	2.70915i	0.00909950	−	0.0914294i
$879$	−7.98968			−0.269485
$880$	−1.46297	+	3.18425i	−0.0493168	+	0.107341i
$881$	−27.4351			−0.924312			−0.462156	−	0.886799i	$-0.652924\pi$
$881$	−27.4351			−0.924312			−0.462156	+	0.886799i	$0.652924\pi$
$882$	−0.585331	+	5.88125i	−0.0197091	+	0.198032i
$883$	−24.6985	+	8.02501i	−0.831169	+	0.270063i	−0.693538	−	0.720420i	$-0.743949\pi$
$883$	−24.6985	+	8.02501i	−0.831169	+	0.270063i	−0.137631	+	0.990484i	$0.543949\pi$
$884$	60.7683	+	12.2169i	2.04386	+	0.410900i
$885$	2.12733	+	1.54559i	0.0715094	+	0.0519546i
$886$	8.19748	+	37.5455i	0.275400	+	1.26137i
$887$	−6.60250	+	20.3204i	−0.221690	+	0.682292i	0.776920	+	0.629599i	$0.216781\pi$
$887$	−6.60250	+	20.3204i	−0.221690	+	0.682292i	−0.998611	+	0.0526937i	$0.983219\pi$
$888$	2.39851	+	0.735629i	0.0804886	+	0.0246861i
$889$	−6.34826	+	4.61228i	−0.212914	+	0.154691i
$890$	−0.690668	+	0.775634i	−0.0231512	+	0.0259993i
$891$	−3.18721	+	0.917448i	−0.106775	+	0.0307357i
$892$	−4.05782	+	0.471854i	−0.135866	+	0.0157988i
$893$	−12.5391	−	17.2586i	−0.419604	−	0.577536i
$894$	−22.9846	−	10.0817i	−0.768719	−	0.337182i
$895$	6.16484	+	2.00308i	0.206068	+	0.0669555i
$896$	20.1656	+	32.0045i	0.673687	+	1.06919i
$897$	−2.98355	+	4.10651i	−0.0996179	+	0.137112i
$898$	−7.17488	−	12.2703i	−0.239429	−	0.409465i
$899$	4.83187	+	14.8710i	0.161152	+	0.495974i
$900$	6.67845	+	7.25444i	0.222615	+	0.241815i
$901$			26.5497i			0.884499i
$902$	19.2597	−	20.2070i	0.641277	−	0.672820i
$903$			7.05177i			0.234668i
$904$	34.0984	−	0.564878i	1.13410	−	0.0187876i
$905$	1.07361	+	3.30422i	0.0356879	+	0.109836i
$906$	−16.5662	+	9.68688i	−0.550377	+	0.321825i
$907$	11.6618	−	16.0511i	0.387223	−	0.532967i	−0.570257	−	0.821467i	$-0.693156\pi$
$907$	11.6618	−	16.0511i	0.387223	−	0.532967i	0.957480	+	0.288499i	$0.0931563\pi$
$908$	−17.9351	+	31.8722i	−0.595197	+	1.05772i
$909$	18.8215	+	6.11547i	0.624269	+	0.202837i
$910$	−3.32732	+	7.58574i	−0.110300	+	0.251465i
$911$	−6.00261	−	8.26188i	−0.198875	−	0.273728i	0.697918	−	0.716177i	$-0.254110\pi$
$911$	−6.00261	−	8.26188i	−0.198875	−	0.273728i	−0.896794	+	0.442449i	$0.854110\pi$
$912$	3.78879	+	16.0710i	0.125459	+	0.532165i
$913$	0.0689525	−	2.03424i	0.00228200	−	0.0673234i
$914$	−10.4339	−	9.29088i	−0.345121	−	0.307315i
$915$	−0.680943	+	0.494734i	−0.0225113	+	0.0163554i
$916$	22.6876	−	10.4029i	0.749619	−	0.343720i
$917$	14.2227	−	43.7731i	0.469676	−	1.44552i
$918$	6.45662	−	1.40970i	0.213100	−	0.0465271i
$919$	−24.3478	−	17.6897i	−0.803159	−	0.583529i	0.108680	−	0.994077i	$-0.465338\pi$
$919$	−24.3478	−	17.6897i	−0.803159	−	0.583529i	−0.911839	+	0.410548i	$0.865338\pi$
$920$	0.343716	+	0.456971i	0.0113320	+	0.0150659i
$921$	26.8834	−	8.73496i	0.885840	−	0.287827i
$922$	32.4890	+	3.23347i	1.06997	+	0.106489i
$923$	30.4136			1.00108
$924$	20.4618	−	8.55573i	0.673144	−	0.281463i
$925$	−4.37305			−0.143785
$926$	−8.26996	−	0.823067i	−0.271768	−	0.0270476i
$927$	−6.38362	+	2.07416i	−0.209666	+	0.0681245i
$928$	15.8457	−	15.0801i	0.520161	−	0.495027i
$929$	13.9833	+	10.1594i	0.458776	+	0.333321i	0.793051	−	0.609155i	$-0.208491\pi$
$929$	13.9833	+	10.1594i	0.458776	+	0.333321i	−0.334275	+	0.942476i	$0.608491\pi$
$930$	−1.47574	+	0.322205i	−0.0483915	+	0.0105655i
$931$	5.33097	−	16.4070i	0.174716	−	0.537719i
$932$	11.0560	+	24.1120i	0.362151	+	0.789814i
$933$	10.4188	−	7.56969i	0.341096	−	0.247821i
$934$	−3.99285	−	3.55545i	−0.130650	−	0.116338i
$935$	−3.22862	−	2.51715i	−0.105587	−	0.0823197i
$936$	−10.7730	+	15.3563i	−0.352126	+	0.501938i
$937$	−4.26015	−	5.86359i	−0.139173	−	0.191555i	0.733741	−	0.679429i	$-0.237773\pi$
$937$	−4.26015	−	5.86359i	−0.139173	−	0.191555i	−0.872914	+	0.487874i	$0.837773\pi$
$938$	−11.3847	+	25.9553i	−0.371724	+	0.847469i
$939$	−9.16404	−	2.97758i	−0.299057	−	0.0971696i
$940$	−2.37931	−	1.33888i	−0.0776045	−	0.0436695i
$941$	−22.6672	+	31.1987i	−0.738930	+	1.01705i	0.259750	+	0.965676i	$0.416360\pi$
$941$	−22.6672	+	31.1987i	−0.738930	+	1.01705i	−0.998680	+	0.0513733i	$0.983640\pi$
$942$	17.6465	−	10.3186i	0.574955	−	0.336197i
$943$	−1.40760	−	4.33214i	−0.0458377	−	0.141074i
$944$	−30.1730	−	25.9846i	−0.982049	−	0.845726i
$945$			0.883170i			0.0287295i
$946$	8.70393	−	4.70129i	0.282989	−	0.152852i
$947$		−	25.4572i		−	0.827247i	−0.910448	−	0.413624i	$-0.864263\pi$
$947$		−	25.4572i		−	0.827247i	0.910448	−	0.413624i	$-0.135737\pi$
$948$	21.2254	−	19.5401i	0.689368	−	0.634633i
$949$	−30.8897	−	95.0689i	−1.00272	−	3.08607i
$950$	−14.5281	−	24.8455i	−0.471353	−	0.806095i
$951$	−3.90829	+	5.37930i	−0.126735	+	0.174436i
$952$	−41.7980	+	14.3507i	−1.35468	+	0.465108i
$953$	−28.3146	−	9.19996i	−0.917198	−	0.298016i	−0.187881	−	0.982192i	$-0.560162\pi$
$953$	−28.3146	−	9.19996i	−0.917198	−	0.298016i	−0.729317	+	0.684176i	$0.760162\pi$
$954$	−7.35804	−	3.22745i	−0.238225	−	0.104493i
$955$	−1.72068	−	2.36832i	−0.0556800	−	0.0766370i
$956$	−4.64904	−	39.9805i	−0.150361	−	1.29306i
$957$	−7.18257	−	10.6251i	−0.232180	−	0.343461i
$958$	20.4122	−	22.9233i	0.659488	−	0.740618i
$959$	−16.0899	+	11.6900i	−0.519570	+	0.377490i
$960$	1.29802	+	1.66749i	0.0418933	+	0.0538179i
$961$	4.52686	−	13.9323i	0.146028	−	0.449428i
$962$	−1.77456	−	8.12773i	−0.0572142	−	0.262049i
$963$	9.88744	+	7.18365i	0.318618	+	0.231490i
$964$	3.95320	−	19.6636i	0.127324	−	0.633322i
$965$	−3.48493	+	1.13232i	−0.112184	+	0.0364507i
$966$	0.358409	−	3.60120i	0.0115316	−	0.115867i
$967$	−27.0950			−0.871316			−0.435658	−	0.900112i	$-0.643484\pi$
$967$	−27.0950			−0.871316			−0.435658	+	0.900112i	$0.643484\pi$
$968$	−24.2018	−	19.5518i	−0.777874	−	0.628420i
$969$	−19.2900			−0.619683
$970$	−0.372246	+	3.74023i	−0.0119521	+	0.120091i
$971$	0.248827	−	0.0808487i	0.00798523	−	0.00259456i	−0.305022	−	0.952345i	$-0.598664\pi$
$971$	0.248827	−	0.0808487i	0.00798523	−	0.00259456i	0.313007	+	0.949751i	$0.398664\pi$
$972$	−0.394195	+	1.96077i	−0.0126438	+	0.0628917i
$973$	20.4451	+	14.8542i	0.655440	+	0.476205i
$974$	2.30747	+	10.5685i	0.0739363	+	0.338638i
$975$	10.1041	−	31.0973i	0.323591	−	0.995909i
$976$	10.8949	−	6.61523i	0.348739	−	0.211748i
$977$	−41.1035	+	29.8634i	−1.31502	+	0.955416i	−0.315037	+	0.949079i	$0.602017\pi$
$977$	−41.1035	+	29.8634i	−1.31502	+	0.955416i	−0.999980	+	0.00633607i	$0.997983\pi$
$978$	5.89992	−	6.62574i	0.188659	−	0.211868i
$979$	−5.16415	−	7.63929i	−0.165047	−	0.244153i
$980$	−0.255013	−	2.19304i	−0.00814609	−	0.0700542i
$981$	−1.23086	−	1.69414i	−0.0392985	−	0.0540897i
$982$	29.6587	+	13.0092i	0.946448	+	0.415139i
$983$	−9.50959	−	3.08985i	−0.303309	−	0.0985510i	0.153409	−	0.988163i	$-0.450975\pi$
$983$	−9.50959	−	3.08985i	−0.303309	−	0.0985510i	−0.456717	+	0.889612i	$0.650975\pi$
$984$	−5.46631	−	15.9213i	−0.174259	−	0.507551i
$985$	−0.938291	+	1.29145i	−0.0298964	+	0.0411489i
$986$	12.8997	+	22.0607i	0.410809	+	0.702554i
$987$	5.33957	+	16.4335i	0.169960	+	0.523084i
$988$	40.2823	−	37.0840i	1.28155	−	1.17980i
$989$		−	1.61421i		−	0.0513287i
$990$	1.09009	−	0.588794i	0.0346453	−	0.0187131i
$991$			55.4443i			1.76125i	0.473816	+	0.880624i	$0.342876\pi$
$991$			55.4443i			1.76125i	−0.473816	+	0.880624i	$0.657124\pi$
$992$	22.6741	−	3.01804i	0.719904	−	0.0958230i
$993$	−1.31344	−	4.04234i	−0.0416807	−	0.128280i
$994$	−18.7188	+	10.9455i	−0.593723	+	0.347171i
$995$	−2.66231	+	3.66435i	−0.0844009	+	0.116168i
$996$	−1.06967	−	0.601922i	−0.0338937	−	0.0190726i
$997$	53.9438	+	17.5274i	1.70842	+	0.555098i	0.990069	−	0.140585i	$-0.0448983\pi$
$997$	53.9438	+	17.5274i	1.70842	+	0.555098i	0.718349	+	0.695683i	$0.244898\pi$
$998$	21.6770	−	49.4199i	0.686173	−	1.56436i
$999$	−0.521359	−	0.717589i	−0.0164951	−	0.0227035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.j.a.19.8	yes	48
3.2	odd	2		396.2.r.b.19.5		48
4.3	odd	2	inner	132.2.j.a.19.1	yes	48
11.7	odd	10	inner	132.2.j.a.7.1	✓	48
12.11	even	2		396.2.r.b.19.12		48
33.29	even	10		396.2.r.b.271.12		48
44.7	even	10	inner	132.2.j.a.7.8	yes	48
132.95	odd	10		396.2.r.b.271.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.7.1	✓	48	11.7	odd	10	inner
132.2.j.a.7.8	yes	48	44.7	even	10	inner
132.2.j.a.19.1	yes	48	4.3	odd	2	inner
132.2.j.a.19.8	yes	48	1.1	even	1	trivial
396.2.r.b.19.5		48	3.2	odd	2
396.2.r.b.19.12		48	12.11	even	2
396.2.r.b.271.5		48	132.95	odd	10
396.2.r.b.271.12		48	33.29	even	10

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:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.140058 - 1.40726i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.96077 - 0.394195i) q^{4} +(-0.213696 - 0.155259i) q^{5} +(-0.301665 - 1.38167i) q^{6} +(1.03321 - 3.17989i) q^{7} +(-0.829356 + 2.70410i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.140058 - 1.40726i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.96077 - 0.394195i) q^{4} +(-0.213696 - 0.155259i) q^{5} +(-0.301665 - 1.38167i) q^{6} +(1.03321 - 3.17989i) q^{7} +(-0.829356 + 2.70410i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-0.248420 + 0.278981i) q^{10} +(-1.85745 - 2.74771i) q^{11} +(-1.98661 + 0.231009i) q^{12} +(3.89823 + 5.36545i) q^{13} +(-4.33023 - 1.89936i) q^{14} +(-0.251215 - 0.0816246i) q^{15} +(3.68922 + 1.54585i) q^{16} +(-2.74676 + 3.78059i) q^{17} +(-0.713858 - 1.22082i) q^{18} +(1.27559 + 3.92586i) q^{19} +(0.357806 + 0.388665i) q^{20} -3.34353i q^{21} +(-4.12689 + 2.22908i) q^{22} +0.765361i q^{23} +(0.0468496 + 2.82804i) q^{24} +(-1.52352 - 4.68893i) q^{25} +(8.09657 - 4.73436i) q^{26} +(0.587785 - 0.809017i) q^{27} +(-3.27938 + 5.82774i) q^{28} +(3.67765 + 1.19494i) q^{29} +(-0.150052 + 0.342092i) q^{30} +(2.37677 + 3.27135i) q^{31} +(2.69212 - 4.97519i) q^{32} +(-2.61562 - 2.03924i) q^{33} +(4.93558 + 4.39491i) q^{34} +(-0.714499 + 0.519114i) q^{35} +(-1.81800 + 0.833600i) q^{36} +(0.274094 - 0.843576i) q^{37} +(5.70337 - 1.24524i) q^{38} +(5.36545 + 3.89823i) q^{39} +(0.597067 - 0.449091i) q^{40} +(-5.66025 + 1.83913i) q^{41} +(-4.70523 - 0.468287i) q^{42} -2.10908 q^{43} +(2.55889 + 6.11981i) q^{44} -0.264143 q^{45} +(1.07706 + 0.107195i) q^{46} +(-4.91501 + 1.59698i) q^{47} +(3.98635 + 0.330158i) q^{48} +(-3.38106 - 2.45648i) q^{49} +(-6.81192 + 1.48728i) q^{50} +(-1.44406 + 4.44436i) q^{51} +(-5.52849 - 12.0571i) q^{52} +(4.59637 - 3.33946i) q^{53} +(-1.05617 - 0.940476i) q^{54} +(-0.0296780 + 0.875559i) q^{55} +(7.74185 + 5.43116i) q^{56} +(2.42632 + 3.33954i) q^{57} +(2.19667 - 5.00805i) q^{58} +(-9.46770 - 3.07624i) q^{59} +(0.460397 + 0.259074i) q^{60} +(1.87298 - 2.57794i) q^{61} +(4.93652 - 2.88656i) q^{62} +(-1.03321 - 3.17989i) q^{63} +(-6.62434 - 4.48532i) q^{64} -1.75181i q^{65} +(-3.23608 + 3.39526i) q^{66} -5.99397i q^{67} +(6.87605 - 6.33011i) q^{68} +(0.236510 + 0.727902i) q^{69} +(0.630458 + 1.07819i) q^{70} +(2.69549 - 3.71003i) q^{71} +(0.918469 + 2.67515i) q^{72} +(-14.3347 - 4.65764i) q^{73} +(-1.14874 - 0.503872i) q^{74} +(-2.89792 - 3.98864i) q^{75} +(-0.953581 - 8.20054i) q^{76} +(-10.6565 + 3.06752i) q^{77} +(6.23730 - 7.00462i) q^{78} +(-11.6701 + 8.47885i) q^{79} +(-0.548364 - 0.903127i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.79537 + 8.22304i) q^{82} +(0.496492 + 0.360722i) q^{83} +(-1.31800 + 6.55589i) q^{84} +(1.17394 - 0.381437i) q^{85} +(-0.295392 + 2.96802i) q^{86} +3.86691 q^{87} +(8.97056 - 2.74390i) q^{88} +2.78024 q^{89} +(-0.0369952 + 0.371718i) q^{90} +(21.0892 - 6.85231i) q^{91} +(0.301701 - 1.50070i) q^{92} +(3.27135 + 2.37677i) q^{93} +(1.55899 + 7.14037i) q^{94} +(0.336938 - 1.03699i) q^{95} +(1.02294 - 5.56360i) q^{96} +(8.14034 - 5.91430i) q^{97} +(-3.93046 + 4.41398i) q^{98} +(-3.11777 - 1.13116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} + 12 q^{9}+O(q^{10}) \) 48 * q - 4 * q^4 + 12 * q^9	\( 48 q - 4 q^{4} + 12 q^{9} + 8 q^{12} - 14 q^{14} - 24 q^{16} - 10 q^{18} - 22 q^{20} - 26 q^{22} - 30 q^{24} - 20 q^{25} - 38 q^{26} - 10 q^{28} - 20 q^{30} - 4 q^{33} + 4 q^{36} - 48 q^{37} + 58 q^{38} + 70 q^{40} - 40 q^{41} + 12 q^{42} + 34 q^{44} + 70 q^{46} - 16 q^{48} - 28 q^{49} + 70 q^{50} + 30 q^{52} - 64 q^{53} + 60 q^{56} - 54 q^{58} - 12 q^{60} - 40 q^{64} - 8 q^{66} + 4 q^{70} + 10 q^{72} + 20 q^{73} + 50 q^{74} - 8 q^{77} + 40 q^{78} + 58 q^{80} - 12 q^{81} + 62 q^{82} + 60 q^{84} + 40 q^{85} + 8 q^{86} + 8 q^{88} + 48 q^{89} + 20 q^{90} + 42 q^{92} + 24 q^{93} - 10 q^{94} + 50 q^{96} + 48 q^{97}+O(q^{100}) \) 48 * q - 4 * q^4 + 12 * q^9 + 8 * q^12 - 14 * q^14 - 24 * q^16 - 10 * q^18 - 22 * q^20 - 26 * q^22 - 30 * q^24 - 20 * q^25 - 38 * q^26 - 10 * q^28 - 20 * q^30 - 4 * q^33 + 4 * q^36 - 48 * q^37 + 58 * q^38 + 70 * q^40 - 40 * q^41 + 12 * q^42 + 34 * q^44 + 70 * q^46 - 16 * q^48 - 28 * q^49 + 70 * q^50 + 30 * q^52 - 64 * q^53 + 60 * q^56 - 54 * q^58 - 12 * q^60 - 40 * q^64 - 8 * q^66 + 4 * q^70 + 10 * q^72 + 20 * q^73 + 50 * q^74 - 8 * q^77 + 40 * q^78 + 58 * q^80 - 12 * q^81 + 62 * q^82 + 60 * q^84 + 40 * q^85 + 8 * q^86 + 8 * q^88 + 48 * q^89 + 20 * q^90 + 42 * q^92 + 24 * q^93 - 10 * q^94 + 50 * q^96 + 48 * q^97

Introduction

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