LMFDB - Embedded newform 132.2.j.a.7.11

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			7.11
Character	$\chi$	$=$	132.7
Dual form			132.2.j.a.19.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16623 + 0.799941i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.720190 + 1.86583i) q^{4} +(-1.53251 + 1.11343i) q^{5} +(0.861957 + 1.12117i) q^{6} +(-1.07196 - 3.29914i) q^{7} +(-0.652646 + 2.75210i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.16623 + 0.799941i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.720190 + 1.86583i) q^{4} +(-1.53251 + 1.11343i) q^{5} +(0.861957 + 1.12117i) q^{6} +(-1.07196 - 3.29914i) q^{7} +(-0.652646 + 2.75210i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-2.67794 + 0.0726042i) q^{10} +(-0.210969 - 3.30991i) q^{11} +(0.108368 + 1.99706i) q^{12} +(1.06787 - 1.46980i) q^{13} +(1.38897 - 4.70507i) q^{14} +(-1.80157 + 0.585367i) q^{15} +(-2.96265 + 2.68751i) q^{16} +(1.74921 + 2.40759i) q^{17} +(0.473308 + 1.33266i) q^{18} +(1.34636 - 4.14366i) q^{19} +(-3.18118 - 2.05752i) q^{20} -3.46892i q^{21} +(2.40169 - 4.02888i) q^{22} +3.82341i q^{23} +(-1.47115 + 2.41572i) q^{24} +(-0.436233 + 1.34259i) q^{25} +(2.42114 - 0.859894i) q^{26} +(0.587785 + 0.809017i) q^{27} +(5.38363 - 4.37610i) q^{28} +(-8.48417 + 2.75668i) q^{29} +(-2.56931 - 0.758479i) q^{30} +(-1.65449 + 2.27721i) q^{31} +(-5.60498 + 0.764309i) q^{32} +(0.822174 - 3.21310i) q^{33} +(0.114062 + 4.20707i) q^{34} +(5.31616 + 3.86242i) q^{35} +(-0.514062 + 1.93281i) q^{36} +(-3.51620 - 10.8218i) q^{37} +(4.88484 - 3.75546i) q^{38} +(1.46980 - 1.06787i) q^{39} +(-2.06409 - 4.94430i) q^{40} +(7.37845 + 2.39740i) q^{41} +(2.77493 - 4.04557i) q^{42} -2.35165 q^{43} +(6.02379 - 2.77740i) q^{44} -1.89429 q^{45} +(-3.05850 + 4.45898i) q^{46} +(-2.66757 - 0.866745i) q^{47} +(-3.64813 + 1.64046i) q^{48} +(-4.07214 + 2.95858i) q^{49} +(-1.58274 + 1.21681i) q^{50} +(0.919617 + 2.83029i) q^{51} +(3.51148 + 0.933936i) q^{52} +(5.05557 + 3.67309i) q^{53} +(0.0383280 + 1.41369i) q^{54} +(4.00867 + 4.83757i) q^{55} +(9.77918 - 0.796961i) q^{56} +(2.56092 - 3.52481i) q^{57} +(-12.0997 - 3.57191i) q^{58} +(-7.68642 + 2.49747i) q^{59} +(-2.38967 - 2.93986i) q^{60} +(4.57345 + 6.29481i) q^{61} +(-3.75115 + 1.33226i) q^{62} +(1.07196 - 3.29914i) q^{63} +(-7.14811 - 3.59229i) q^{64} +3.44150i q^{65} +(3.52914 - 3.08953i) q^{66} +15.0787i q^{67} +(-3.23238 + 4.99766i) q^{68} +(-1.18150 + 3.63628i) q^{69} +(3.11017 + 8.75708i) q^{70} +(-3.24129 - 4.46126i) q^{71} +(-2.14565 + 1.84288i) q^{72} +(11.1487 - 3.62244i) q^{73} +(4.55606 - 15.4334i) q^{74} +(-0.829764 + 1.14207i) q^{75} +(8.70100 - 0.472149i) q^{76} +(-10.6937 + 4.24410i) q^{77} +(2.56837 - 0.0696334i) q^{78} +(4.34223 + 3.15482i) q^{79} +(1.54793 - 7.41735i) q^{80} +(0.309017 + 0.951057i) q^{81} +(6.68720 + 8.69825i) q^{82} +(6.10662 - 4.43672i) q^{83} +(6.47243 - 2.49829i) q^{84} +(-5.36138 - 1.74202i) q^{85} +(-2.74257 - 1.88118i) q^{86} -8.92079 q^{87} +(9.24689 + 1.57959i) q^{88} -5.20905 q^{89} +(-2.20918 - 1.51532i) q^{90} +(-5.99381 - 1.94751i) q^{91} +(-7.13384 + 2.75358i) q^{92} +(-2.27721 + 1.65449i) q^{93} +(-2.41765 - 3.14472i) q^{94} +(2.55038 + 7.84928i) q^{95} +(-5.56684 - 1.00513i) q^{96} +(6.72491 + 4.88593i) q^{97} +(-7.11574 + 0.192922i) q^{98} +(1.77484 - 2.80178i) 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 $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

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 $

$2$	1.16623	+	0.799941i	0.824650	+	0.565643i
$2$	1.16623	+	0.799941i	0.824650	+	0.565643i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	0.720190	+	1.86583i	0.360095	+	0.932916i
$5$	−1.53251	+	1.11343i	−0.685359	+	0.497943i	−0.875131	−	0.483886i	$-0.839225\pi$
$5$	−1.53251	+	1.11343i	−0.685359	+	0.497943i	0.189772	+	0.981828i	$0.439225\pi$
$6$	0.861957	+	1.12117i	0.351892	+	0.457717i
$7$	−1.07196	−	3.29914i	−0.405162	−	1.24696i	−0.920760	−	0.390129i	$-0.872430\pi$
$7$	−1.07196	−	3.29914i	−0.405162	−	1.24696i	0.515599	−	0.856830i	$-0.327570\pi$
$8$	−0.652646	+	2.75210i	−0.230745	+	0.973014i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−2.67794	+	0.0726042i	−0.846839	+	0.0229595i
$11$	−0.210969	−	3.30991i	−0.0636096	−	0.997975i
$11$	−0.210969	−	3.30991i	−0.0636096	−	0.997975i
$12$	0.108368	+	1.99706i	0.0312832	+	0.576502i
$13$	1.06787	−	1.46980i	0.296175	−	0.407650i	−0.634833	−	0.772650i	$-0.718931\pi$
$13$	1.06787	−	1.46980i	0.296175	−	0.407650i	0.931008	+	0.365000i	$0.118931\pi$
$14$	1.38897	−	4.70507i	0.371218	−	1.25748i
$15$	−1.80157	+	0.585367i	−0.465164	+	0.151141i
$16$	−2.96265	+	2.68751i	−0.740663	+	0.671877i
$17$	1.74921	+	2.40759i	0.424247	+	0.583926i	0.966621	−	0.256212i	$-0.0824744\pi$
$17$	1.74921	+	2.40759i	0.424247	+	0.583926i	−0.542374	+	0.840137i	$0.682474\pi$
$18$	0.473308	+	1.33266i	0.111560	+	0.314111i
$19$	1.34636	−	4.14366i	0.308875	−	0.950621i	−0.669327	−	0.742968i	$-0.733418\pi$
$19$	1.34636	−	4.14366i	0.308875	−	0.950621i	0.978203	−	0.207653i	$-0.0665825\pi$
$20$	−3.18118	−	2.05752i	−0.711333	−	0.460076i
$21$		−	3.46892i		−	0.756981i
$22$	2.40169	−	4.02888i	0.512042	−	0.858960i
$23$			3.82341i			0.797236i	0.917117	+	0.398618i	$0.130510\pi$
$23$			3.82341i			0.797236i	−0.917117	+	0.398618i	$0.869490\pi$
$24$	−1.47115	+	2.41572i	−0.300297	+	0.493108i
$25$	−0.436233	+	1.34259i	−0.0872466	+	0.268517i
$26$	2.42114	−	0.859894i	0.474825	−	0.168639i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	5.38363	−	4.37610i	1.01741	−	0.827005i
$29$	−8.48417	+	2.75668i	−1.57547	+	0.511902i	−0.960885	−	0.276948i	$-0.910677\pi$
$29$	−8.48417	+	2.75668i	−1.57547	+	0.511902i	−0.614587	+	0.788849i	$0.710677\pi$
$30$	−2.56931	−	0.758479i	−0.469090	−	0.138479i
$31$	−1.65449	+	2.27721i	−0.297155	+	0.408999i	−0.931322	−	0.364197i	$-0.881343\pi$
$31$	−1.65449	+	2.27721i	−0.297155	+	0.408999i	0.634167	+	0.773196i	$0.281343\pi$
$32$	−5.60498	+	0.764309i	−0.990830	+	0.135112i
$33$	0.822174	−	3.21310i	0.143122	−	0.559329i
$34$	0.114062	+	4.20707i	0.0195615	+	0.721507i
$35$	5.31616	+	3.86242i	0.898595	+	0.652868i
$36$	−0.514062	+	1.93281i	−0.0856770	+	0.322134i
$37$	−3.51620	−	10.8218i	−0.578060	−	1.77909i	−0.625513	−	0.780213i	$-0.715110\pi$
$37$	−3.51620	−	10.8218i	−0.578060	−	1.77909i	0.0474530	−	0.998873i	$-0.484890\pi$
$38$	4.88484	−	3.75546i	0.792426	−	0.609216i
$39$	1.46980	−	1.06787i	0.235357	−	0.170997i
$40$	−2.06409	−	4.94430i	−0.326362	−	0.781762i
$41$	7.37845	+	2.39740i	1.15232	+	0.374412i	0.822017	−	0.569463i	$-0.192849\pi$
$41$	7.37845	+	2.39740i	1.15232	+	0.374412i	0.330304	+	0.943875i	$0.392849\pi$
$42$	2.77493	−	4.04557i	0.428182	−	0.624245i
$43$	−2.35165			−0.358623			−0.179312	−	0.983792i	$-0.557387\pi$
$43$	−2.35165			−0.358623			−0.179312	+	0.983792i	$0.557387\pi$
$44$	6.02379	−	2.77740i	0.908121	−	0.418708i
$45$	−1.89429			−0.282384
$46$	−3.05850	+	4.45898i	−0.450951	+	0.657441i
$47$	−2.66757	−	0.866745i	−0.389104	−	0.126428i	0.107930	−	0.994158i	$-0.465578\pi$
$47$	−2.66757	−	0.866745i	−0.389104	−	0.126428i	−0.497034	+	0.867731i	$0.665578\pi$
$48$	−3.64813	+	1.64046i	−0.526563	+	0.236780i
$49$	−4.07214	+	2.95858i	−0.581734	+	0.422654i
$50$	−1.58274	+	1.21681i	−0.223833	+	0.172082i
$51$	0.919617	+	2.83029i	0.128772	+	0.396320i
$52$	3.51148	+	0.933936i	0.486954	+	0.129514i
$53$	5.05557	+	3.67309i	0.694437	+	0.504538i	0.878116	−	0.478449i	$-0.158801\pi$
$53$	5.05557	+	3.67309i	0.694437	+	0.504538i	−0.183679	+	0.982986i	$0.558801\pi$
$54$	0.0383280	+	1.41369i	0.00521578	+	0.192379i
$55$	4.00867	+	4.83757i	0.540530	+	0.652297i
$56$	9.77918	−	0.796961i	1.30680	−	0.106498i
$57$	2.56092	−	3.52481i	0.339202	−	0.466872i
$58$	−12.0997	−	3.57191i	−1.58877	−	0.469015i
$59$	−7.68642	+	2.49747i	−1.00069	+	0.325143i	−0.763140	−	0.646233i	$-0.776343\pi$
$59$	−7.68642	+	2.49747i	−1.00069	+	0.325143i	−0.237547	+	0.971376i	$0.576343\pi$
$60$	−2.38967	−	2.93986i	−0.308505	−	0.379534i
$61$	4.57345	+	6.29481i	0.585570	+	0.805968i	0.994292	−	0.106691i	$-0.0340255\pi$
$61$	4.57345	+	6.29481i	0.585570	+	0.805968i	−0.408722	+	0.912659i	$0.634025\pi$
$62$	−3.75115	+	1.33226i	−0.476396	+	0.169197i
$63$	1.07196	−	3.29914i	0.135054	−	0.415653i
$64$	−7.14811	−	3.59229i	−0.893513	−	0.449036i
$65$			3.44150i			0.426865i
$66$	3.52914	−	3.08953i	0.434407	−	0.380295i
$67$			15.0787i			1.84216i	0.389377	+	0.921079i	$0.372690\pi$
$67$			15.0787i			1.84216i	−0.389377	+	0.921079i	$0.627310\pi$
$68$	−3.23238	+	4.99766i	−0.391984	+	0.606055i
$69$	−1.18150	+	3.63628i	−0.142236	+	0.437757i
$70$	3.11017	+	8.75708i	0.371736	+	1.04667i
$71$	−3.24129	−	4.46126i	−0.384671	−	0.529454i	0.572144	−	0.820153i	$-0.306112\pi$
$71$	−3.24129	−	4.46126i	−0.384671	−	0.529454i	−0.956814	+	0.290700i	$0.906112\pi$
$72$	−2.14565	+	1.84288i	−0.252867	+	0.217186i
$73$	11.1487	−	3.62244i	1.30486	−	0.423974i	0.427589	−	0.903973i	$-0.359363\pi$
$73$	11.1487	−	3.62244i	1.30486	−	0.423974i	0.877269	+	0.479999i	$0.159363\pi$
$74$	4.55606	−	15.4334i	0.529631	−	1.79410i
$75$	−0.829764	+	1.14207i	−0.0958129	+	0.131875i
$76$	8.70100	−	0.472149i	0.998073	−	0.0541593i
$77$	−10.6937	+	4.24410i	−1.21866	+	0.483660i
$78$	2.56837	−	0.0696334i	0.290810	−	0.00788443i
$79$	4.34223	+	3.15482i	0.488539	+	0.354945i	0.804622	−	0.593787i	$-0.202368\pi$
$79$	4.34223	+	3.15482i	0.488539	+	0.354945i	−0.316083	+	0.948732i	$0.602368\pi$
$80$	1.54793	−	7.41735i	0.173064	−	0.829285i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	6.68720	+	8.69825i	0.738478	+	0.960561i
$83$	6.10662	−	4.43672i	0.670288	−	0.486993i	−0.199833	−	0.979830i	$-0.564040\pi$
$83$	6.10662	−	4.43672i	0.670288	−	0.486993i	0.870122	+	0.492837i	$0.164040\pi$
$84$	6.47243	−	2.49829i	0.706200	−	0.272585i
$85$	−5.36138	−	1.74202i	−0.581523	−	0.188948i
$86$	−2.74257	−	1.88118i	−0.295738	−	0.202853i
$87$	−8.92079			−0.956409
$88$	9.24689	+	1.57959i	0.985721	+	0.168385i
$89$	−5.20905			−0.552158			−0.276079	−	0.961135i	$-0.589035\pi$
$89$	−5.20905			−0.552158			−0.276079	+	0.961135i	$0.589035\pi$
$90$	−2.20918	−	1.51532i	−0.232868	−	0.159728i
$91$	−5.99381	−	1.94751i	−0.628322	−	0.204154i
$92$	−7.13384	+	2.75358i	−0.743754	+	0.287081i
$93$	−2.27721	+	1.65449i	−0.236136	+	0.171563i
$94$	−2.41765	−	3.14472i	−0.249362	−	0.324353i
$95$	2.55038	+	7.84928i	0.261664	+	0.805319i
$96$	−5.56684	−	1.00513i	−0.568163	−	0.102586i
$97$	6.72491	+	4.88593i	0.682811	+	0.496091i	0.874289	−	0.485406i	$-0.161328\pi$
$97$	6.72491	+	4.88593i	0.682811	+	0.496091i	−0.191478	+	0.981497i	$0.561328\pi$
$98$	−7.11574	+	0.192922i	−0.718799	+	0.0194880i
$99$	1.77484	−	2.80178i	0.178378	−	0.281589i
$100$	−2.81921	+	0.152981i	−0.281921	+	0.0152981i
$101$	7.18085	−	9.88359i	0.714521	−	0.983454i	−0.285167	−	0.958478i	$-0.592049\pi$
$101$	7.18085	−	9.88359i	0.714521	−	0.983454i	0.999688	−	0.0249764i	$-0.00795105\pi$
$102$	−1.19158	+	4.03641i	−0.117984	+	0.399664i
$103$	13.0192	−	4.23019i	1.28282	−	0.416813i	0.413246	−	0.910619i	$-0.364395\pi$
$103$	13.0192	−	4.23019i	1.28282	−	0.416813i	0.869572	+	0.493806i	$0.164395\pi$
$104$	3.34810	+	3.89816i	0.328308	+	0.382246i
$105$	3.86242	+	5.31616i	0.376933	+	0.518804i
$106$	2.95772	+	8.32783i	0.287279	+	0.808870i
$107$	1.16180	−	3.57564i	0.112315	−	0.345670i	−0.879062	−	0.476707i	$-0.841830\pi$
$107$	1.16180	−	3.57564i	0.112315	−	0.345670i	0.991378	+	0.131036i	$0.0418304\pi$
$108$	−1.08617	+	1.67935i	−0.104517	+	0.161596i
$109$			1.43350i			0.137305i	0.997641	+	0.0686524i	$0.0218699\pi$
$109$			1.43350i			0.137305i	−0.997641	+	0.0686524i	$0.978130\pi$
$110$	0.805276	+	8.84842i	0.0767801	+	0.843664i
$111$		−	11.3787i		−	1.08002i
$112$	12.0423	+	6.89332i	1.13789	+	0.651358i
$113$	3.77854	−	11.6292i	0.355455	−	1.09398i	−0.600290	−	0.799783i	$-0.704948\pi$
$113$	3.77854	−	11.6292i	0.355455	−	1.09398i	0.955745	−	0.294196i	$-0.0950520\pi$
$114$	5.80626	−	2.06215i	0.543806	−	0.193138i
$115$	−4.25711	−	5.85941i	−0.396978	−	0.546393i
$116$	−11.2537	−	13.8447i	−1.04488	−	1.28545i
$117$	1.72786	−	0.561415i	0.159740	−	0.0519028i
$118$	−10.9620	−	3.23605i	−1.00913	−	0.297903i
$119$	6.06789	−	8.35174i	0.556243	−	0.765603i
$120$	−0.435199	−	5.34015i	−0.0397280	−	0.487486i
$121$	−10.9110	+	1.39658i	−0.991908	+	0.126962i
$122$	0.298223	+	10.9997i	0.0269999	+	0.995866i
$123$	6.27649	+	4.56013i	0.565932	+	0.411173i
$124$	−5.44044	−	1.44697i	−0.488566	−	0.129942i
$125$	−3.75318	−	11.5511i	−0.335695	−	1.03316i
$126$	3.88927	−	2.99006i	0.346484	−	0.266376i
$127$	−4.15959	+	3.02212i	−0.369104	+	0.268170i	−0.756839	−	0.653601i	$-0.773258\pi$
$127$	−4.15959	+	3.02212i	−0.369104	+	0.268170i	0.387735	+	0.921771i	$0.373258\pi$
$128$	−5.46273	−	9.90750i	−0.482841	−	0.875708i
$129$	−2.23655	−	0.726699i	−0.196917	−	0.0639823i
$130$	−2.75299	+	4.01358i	−0.241453	+	0.352014i
$131$	−3.48536			−0.304517			−0.152259	−	0.988341i	$-0.548655\pi$
$131$	−3.48536			−0.304517			−0.152259	+	0.988341i	$0.548655\pi$
$132$	6.58723	−	0.780007i	0.573345	−	0.0678909i
$133$	−15.1138			−1.31053
$134$	−12.0621	+	17.5853i	−1.04200	+	1.51913i
$135$	−1.80157	−	0.585367i	−0.155055	−	0.0503803i
$136$	−7.76754	+	3.24271i	−0.666061	+	0.278060i
$137$	−2.73135	+	1.98444i	−0.233355	+	0.169542i	−0.698318	−	0.715788i	$-0.746068\pi$
$137$	−2.73135	+	1.98444i	−0.233355	+	0.169542i	0.464963	+	0.885330i	$0.346068\pi$
$138$	−4.28671	+	3.29561i	−0.364909	+	0.280541i
$139$	−7.02174	−	21.6107i	−0.595577	−	1.83300i	−0.551835	−	0.833953i	$-0.686072\pi$
$139$	−7.02174	−	21.6107i	−0.595577	−	1.83300i	−0.0437412	−	0.999043i	$-0.513928\pi$
$140$	−3.37797	+	12.7007i	−0.285491	+	1.07341i
$141$	−2.26917	−	1.64865i	−0.191098	−	0.138841i
$142$	−0.211357	−	7.79570i	−0.0177367	−	0.654201i
$143$	−5.09020	−	3.22448i	−0.425664	−	0.269645i
$144$	−3.97651	+	0.432836i	−0.331376	+	0.0360697i
$145$	9.93271	−	13.6712i	0.824866	−	1.13533i
$146$	15.8997	+	4.69371i	1.31587	+	0.388454i
$147$	−4.78708	+	1.55542i	−0.394832	+	0.128289i
$148$	17.6592	−	14.3544i	1.45158	−	1.17992i
$149$	−8.22015	−	11.3141i	−0.673421	−	0.926884i	0.326411	−	0.945228i	$-0.394161\pi$
$149$	−8.22015	−	11.3141i	−0.673421	−	0.926884i	−0.999832	+	0.0183440i	$0.994161\pi$
$150$	−1.88129	+	0.668159i	−0.153606	+	0.0545549i
$151$	−2.51556	+	7.74210i	−0.204713	+	0.630043i	0.795012	+	0.606594i	$0.207465\pi$
$151$	−2.51556	+	7.74210i	−0.204713	+	0.630043i	−0.999725	+	0.0234490i	$0.992535\pi$
$152$	10.5251	+	6.40965i	0.853696	+	0.519891i
$153$			2.97594i			0.240591i
$154$	−15.8664	−	3.60474i	−1.27855	−	0.290478i
$155$		−	5.33201i		−	0.428277i
$156$	3.05101	+	1.97333i	0.244276	+	0.157993i
$157$	−5.73392	+	17.6472i	−0.457617	+	1.40840i	0.410419	+	0.911897i	$0.365382\pi$
$157$	−5.73392	+	17.6472i	−0.457617	+	1.40840i	−0.868036	+	0.496502i	$0.834618\pi$
$158$	2.54038	+	7.15277i	0.202102	+	0.569044i
$159$	3.67309	+	5.05557i	0.291295	+	0.400933i
$160$	7.73868	−	7.41209i	0.611797	−	0.585977i
$161$	12.6140	−	4.09853i	0.994121	−	0.323009i
$162$	−0.400403	+	1.35635i	−0.0314587	+	0.106565i
$163$	0.374651	−	0.515663i	0.0293450	−	0.0403899i	−0.794092	−	0.607797i	$-0.792053\pi$
$163$	0.374651	−	0.515663i	0.0293450	−	0.0403899i	0.823437	+	0.567407i	$0.192053\pi$
$164$	0.840738	+	15.4935i	0.0656506	+	1.20984i
$165$	2.31759	+	5.83955i	0.180424	+	0.454608i
$166$	10.6708	−	0.289307i	0.828218	−	0.0224546i
$167$	−7.36364	−	5.35000i	−0.569816	−	0.413995i	0.265223	−	0.964187i	$-0.414555\pi$
$167$	−7.36364	−	5.35000i	−0.569816	−	0.413995i	−0.835038	+	0.550192i	$0.814555\pi$
$168$	9.54683	+	2.26398i	0.736554	+	0.174670i
$169$	2.99726	+	9.22460i	0.230558	+	0.709585i
$170$	−4.85910	−	6.32038i	−0.372676	−	0.484751i
$171$	3.52481	−	2.56092i	0.269549	−	0.195839i
$172$	−1.69363	−	4.38778i	−0.129138	−	0.334565i
$173$	15.6017	+	5.06931i	1.18618	+	0.385412i	0.834658	−	0.550769i	$-0.185665\pi$
$173$	15.6017	+	5.06931i	1.18618	+	0.385412i	0.351519	+	0.936181i	$0.385665\pi$
$174$	−10.4037	−	7.13610i	−0.788703	−	0.540986i
$175$	4.89701			0.370179
$176$	9.52043	+	9.23912i	0.717629	+	0.696425i
$177$	−8.08198			−0.607479
$178$	−6.07496	−	4.16693i	−0.455337	−	0.312325i
$179$	0.513988	+	0.167005i	0.0384172	+	0.0124825i	0.328163	−	0.944621i	$-0.393571\pi$
$179$	0.513988	+	0.167005i	0.0384172	+	0.0124825i	−0.289745	+	0.957104i	$0.593571\pi$
$180$	−1.36425	−	3.53442i	−0.101685	−	0.263440i
$181$	4.07479	−	2.96051i	0.302877	−	0.220053i	−0.425957	−	0.904743i	$-0.640063\pi$
$181$	4.07479	−	2.96051i	0.302877	−	0.220053i	0.728834	+	0.684690i	$0.240063\pi$
$182$	−5.43228	−	7.06593i	−0.402667	−	0.523762i
$183$	2.40440	+	7.40000i	0.177739	+	0.547023i
$184$	−10.5224	−	2.49533i	−0.775722	−	0.183958i
$185$	17.4379	+	12.6694i	1.28206	+	0.931473i
$186$	−3.97925	+	0.107885i	−0.291772	+	0.00791052i
$187$	7.59986	−	6.29767i	0.555757	−	0.460531i
$188$	−0.303956	−	5.60145i	−0.0221683	−	0.408528i
$189$	2.03898	−	2.80642i	0.148314	−	0.204137i
$190$	−3.30462	+	11.1942i	−0.239742	+	0.812115i
$191$	−2.78876	+	0.906124i	−0.201788	+	0.0655648i	−0.408167	−	0.912907i	$-0.633832\pi$
$191$	−2.78876	+	0.906124i	−0.201788	+	0.0655648i	0.206379	+	0.978472i	$0.433832\pi$
$192$	−5.68818	−	5.62536i	−0.410509	−	0.405975i
$193$	6.51760	+	8.97070i	0.469147	+	0.645725i	0.976374	−	0.216087i	$-0.0693295\pi$
$193$	6.51760	+	8.97070i	0.469147	+	0.645725i	−0.507227	+	0.861812i	$0.669329\pi$
$194$	3.93434	+	11.0777i	0.282469	+	0.795329i
$195$	−1.06348	+	3.27306i	−0.0761574	+	0.234388i
$196$	−8.45293	−	5.46718i	−0.603780	−	0.390513i
$197$		−	5.97699i		−	0.425843i	−0.977069	−	0.212921i	$-0.931702\pi$
$197$		−	5.97699i		−	0.425843i	0.977069	−	0.212921i	$-0.0682978\pi$
$198$	4.31113	−	1.84775i	0.306378	−	0.131314i
$199$			2.73310i			0.193745i	0.995297	+	0.0968723i	$0.0308838\pi$
$199$			2.73310i			0.193745i	−0.995297	+	0.0968723i	$0.969116\pi$
$200$	−3.41023	−	2.07679i	−0.241140	−	0.146851i
$201$	−4.65958	+	14.3407i	−0.328661	+	1.01152i
$202$	16.2808	−	5.78230i	1.14551	−	0.406841i
$203$	18.1893	+	25.0355i	1.27664	+	1.75715i
$204$	−4.61854	+	3.75420i	−0.323363	+	0.262846i
$205$	−13.9769	+	4.54137i	−0.976189	+	0.317183i
$206$	18.5673	+	5.48119i	1.29364	+	0.381893i
$207$	−2.24734	+	3.09320i	−0.156201	+	0.214993i
$208$	0.786366	+	7.22444i	0.0545247	+	0.500925i
$209$	−13.9992	−	3.58213i	−0.968343	−	0.247781i
$210$	0.251859	+	9.28958i	0.0173799	+	0.641042i
$211$	−20.5281	−	14.9146i	−1.41321	−	1.02676i	−0.992845	−	0.119408i	$-0.961900\pi$
$211$	−20.5281	−	14.9146i	−1.41321	−	1.02676i	−0.420370	−	0.907353i	$-0.638100\pi$
$212$	−3.21239	+	12.0782i	−0.220628	+	0.829532i
$213$	−1.70405	−	5.24452i	−0.116759	−	0.359349i
$214$	4.21522	−	3.24066i	0.288147	−	0.221527i
$215$	3.60392	−	2.61840i	0.245786	−	0.178574i
$216$	−2.61011	+	1.08964i	−0.177596	+	0.0741408i
$217$	9.28638	+	3.01733i	0.630401	+	0.204830i
$218$	−1.14672	+	1.67180i	−0.0776655	+	0.113228i
$219$	11.7225			0.792130
$220$	−6.13907	+	10.9635i	−0.413896	+	0.739158i
$221$	5.40662			0.363689
$222$	9.10226	−	13.2702i	0.610904	−	0.890635i
$223$	19.2234	+	6.24606i	1.28729	+	0.418267i	0.871143	−	0.491029i	$-0.163379\pi$
$223$	19.2234	+	6.24606i	1.28729	+	0.418267i	0.416150	+	0.909296i	$0.363379\pi$
$224$	8.52986	+	17.6723i	0.569926	+	1.18078i
$225$	−1.14207	+	0.829764i	−0.0761382	+	0.0553176i
$226$	13.7093	−	10.5397i	0.911928	−	0.701089i
$227$	1.06125	+	3.26618i	0.0704373	+	0.216784i	0.980078	−	0.198612i	$-0.0636432\pi$
$227$	1.06125	+	3.26618i	0.0704373	+	0.216784i	−0.909641	+	0.415395i	$0.863643\pi$
$228$	8.42105	+	2.23972i	0.557697	+	0.148329i
$229$	−4.73582	−	3.44077i	−0.312952	−	0.227373i	0.420210	−	0.907427i	$-0.361956\pi$
$229$	−4.73582	−	3.44077i	−0.312952	−	0.227373i	−0.733162	+	0.680054i	$0.761956\pi$
$230$	−0.277596	−	10.2389i	−0.0183041	−	0.675131i
$231$	−11.4818	+	0.731836i	−0.755448	+	0.0481513i
$232$	−2.04949	−	25.1484i	−0.134555	−	1.65108i
$233$	−5.80493	+	7.98980i	−0.380294	+	0.523429i	−0.955662	−	0.294465i	$-0.904859\pi$
$233$	−5.80493	+	7.98980i	−0.380294	+	0.523429i	0.575369	+	0.817894i	$0.304859\pi$
$234$	2.46418	+	0.727444i	0.161088	+	0.0475545i
$235$	5.05313	−	1.64186i	0.329630	−	0.107103i
$236$	−10.1955	−	12.5429i	−0.663673	−	0.816474i
$237$	3.15482	+	4.34223i	0.204927	+	0.282058i
$238$	13.7575	−	4.88611i	0.891764	−	0.316719i
$239$	−6.05813	+	18.6450i	−0.391868	+	1.20605i	0.539506	+	0.841982i	$0.318611\pi$
$239$	−6.05813	+	18.6450i	−0.391868	+	1.20605i	−0.931374	+	0.364064i	$0.881389\pi$
$240$	3.76426	−	6.57598i	0.242982	−	0.424478i
$241$		−	12.1924i		−	0.785384i	−0.919670	−	0.392692i	$-0.871544\pi$
$241$		−	12.1924i		−	0.785384i	0.919670	−	0.392692i	$-0.128456\pi$
$242$	−13.8419	−	7.09941i	−0.889792	−	0.456367i
$243$			1.00000i			0.0641500i
$244$	−8.45130	+	13.0667i	−0.541039	+	0.836513i
$245$	2.94641	−	9.06811i	0.188239	−	0.579340i
$246$	3.67200	+	10.3390i	0.234118	+	0.659190i
$247$	−4.65262	−	6.40379i	−0.296039	−	0.407463i
$248$	−5.18731	−	6.03953i	−0.329395	−	0.383511i
$249$	7.17876	−	2.33252i	0.454935	−	0.147817i
$250$	4.86312	−	16.4736i	0.307571	−	1.04188i
$251$	−13.7792	+	18.9654i	−0.869733	+	1.19708i	0.109427	+	0.993995i	$0.465098\pi$
$251$	−13.7792	+	18.9654i	−0.869733	+	1.19708i	−0.979160	+	0.203090i	$0.934902\pi$
$252$	6.92766	−	0.375921i	0.436401	−	0.0236808i
$253$	12.6551	−	0.806622i	0.795622	−	0.0507119i
$254$	−7.26857	+	0.197065i	−0.456070	+	0.0123650i
$255$	−4.56066	−	3.31351i	−0.285600	−	0.207500i
$256$	1.55461	−	15.9243i	0.0971632	−	0.995268i
$257$	−4.56819	−	14.0594i	−0.284956	−	0.877004i	−0.986412	−	0.164291i	$-0.947466\pi$
$257$	−4.56819	−	14.0594i	−0.284956	−	0.877004i	0.701456	−	0.712713i	$-0.252534\pi$
$258$	−2.02702	−	2.63661i	−0.126197	−	0.164148i
$259$	−31.9333	+	23.2009i	−1.98424	+	1.44164i
$260$	−6.42125	+	2.47853i	−0.398229	+	0.153712i
$261$	−8.48417	−	2.75668i	−0.525157	−	0.170634i
$262$	−4.06474	−	2.78808i	−0.251120	−	0.172248i
$263$	10.3241			0.636611			0.318306	−	0.947988i	$-0.396886\pi$
$263$	10.3241			0.636611			0.318306	+	0.947988i	$0.396886\pi$
$264$	8.30619	+	4.35972i	0.511211	+	0.268322i
$265$	−11.8375			−0.727169
$266$	−17.6261	−	12.0901i	−1.08073	−	0.741292i
$267$	−4.95410	−	1.60968i	−0.303186	−	0.0985111i
$268$	−28.1343	+	10.8595i	−1.71858	+	0.663352i
$269$	−4.14874	+	3.01423i	−0.252953	+	0.183781i	−0.707034	−	0.707179i	$-0.749967\pi$
$269$	−4.14874	+	3.01423i	−0.252953	+	0.183781i	0.454082	+	0.890960i	$0.349967\pi$
$270$	−1.63279	−	2.12382i	−0.0993686	−	0.129252i
$271$	3.21618	+	9.89839i	0.195369	+	0.601284i	0.999972	+	0.00747111i	$0.00237815\pi$
$271$	3.21618	+	9.89839i	0.195369	+	0.601284i	−0.804603	+	0.593813i	$0.797622\pi$
$272$	−11.6527	−	2.43182i	−0.706550	−	0.147451i
$273$	−5.09864	−	3.70438i	−0.308584	−	0.224199i
$274$	−4.77282	+	0.129401i	−0.288337	+	0.00781737i
$275$	4.53587	+	1.16065i	0.273523	+	0.0699896i
$276$	−7.63559	+	0.414336i	−0.459608	+	0.0249401i
$277$	10.9032	−	15.0070i	0.655110	−	0.901681i	−0.344197	−	0.938897i	$-0.611849\pi$
$277$	10.9032	−	15.0070i	0.655110	−	0.901681i	0.999307	+	0.0372160i	$0.0118490\pi$
$278$	9.09830	−	30.8201i	0.545680	−	1.84846i
$279$	−2.67702	+	0.869817i	−0.160269	+	0.0520746i
$280$	−14.0993	+	12.1098i	−0.842596	+	0.723700i
$281$	−7.89816	−	10.8709i	−0.471165	−	0.648503i	0.505612	−	0.862761i	$-0.331267\pi$
$281$	−7.89816	−	10.8709i	−0.471165	−	0.648503i	−0.976777	+	0.214258i	$0.931267\pi$
$282$	−1.32755	−	3.73790i	−0.0790547	−	0.222589i
$283$	−0.130142	+	0.400534i	−0.00773611	+	0.0238093i	−0.954850	−	0.297088i	$-0.903984\pi$
$283$	−0.130142	+	0.400534i	−0.00773611	+	0.0238093i	0.947114	+	0.320897i	$0.103984\pi$
$284$	5.98961	−	9.26066i	0.355418	−	0.549519i
$285$			8.25322i			0.488878i
$286$	−3.35696	−	7.83235i	−0.198501	−	0.463137i
$287$		−	26.9125i		−	1.58859i
$288$	−4.98378	−	2.67619i	−0.293672	−	0.157696i
$289$	2.51656	−	7.74519i	0.148033	−	0.455599i
$290$	22.5200	−	7.99820i	1.32242	−	0.469671i
$291$	4.88593	+	6.72491i	0.286419	+	0.394221i
$292$	14.7881	+	18.1928i	0.865405	+	1.06465i
$293$	−17.0553	+	5.54161i	−0.996382	+	0.323744i	−0.761419	−	0.648260i	$-0.775497\pi$
$293$	−17.0553	+	5.54161i	−0.996382	+	0.323744i	−0.234963	+	0.972004i	$0.575497\pi$
$294$	−6.82709	−	2.01541i	−0.398164	−	0.117541i
$295$	8.99875	−	12.3857i	0.523928	−	0.721124i
$296$	32.0774	−	2.61417i	1.86446	−	0.151945i
$297$	2.55377	−	2.11619i	0.148185	−	0.122794i
$298$	−0.536015	−	19.7704i	−0.0310505	−	1.14527i
$299$	5.61966	+	4.08292i	0.324993	+	0.236122i
$300$	−2.72850	−	0.725691i	−0.157530	−	0.0418978i
$301$	2.52087	+	7.75843i	0.145300	+	0.447188i
$302$	−9.12695	+	7.01678i	−0.525197	+	0.403770i
$303$	9.88359	−	7.18085i	0.567798	−	0.412529i
$304$	7.14733	+	15.8946i	0.409927	+	0.911616i
$305$	−14.0177	−	4.55463i	−0.802652	−	0.260797i
$306$	−2.38058	+	3.47064i	−0.136088	+	0.198403i
$307$	9.77664			0.557983			0.278991	−	0.960294i	$-0.410000\pi$
$307$	9.77664			0.557983			0.278991	+	0.960294i	$0.410000\pi$
$308$	−15.6203	−	16.8961i	−0.890048	−	0.962745i
$309$	13.6892			0.778750
$310$	4.26529	−	6.21836i	0.242252	−	0.353179i
$311$	−10.8311	−	3.51925i	−0.614178	−	0.199558i	−0.0146241	−	0.999893i	$-0.504655\pi$
$311$	−10.8311	−	3.51925i	−0.614178	−	0.199558i	−0.599554	+	0.800335i	$0.704655\pi$
$312$	1.97964	+	4.74199i	0.112075	+	0.268462i
$313$	−10.8009	+	7.84731i	−0.610503	+	0.443556i	−0.849591	−	0.527442i	$-0.823151\pi$
$313$	−10.8009	+	7.84731i	−0.610503	+	0.443556i	0.239089	+	0.970998i	$0.423151\pi$
$314$	−20.8038	+	15.9939i	−1.17403	+	0.902588i
$315$	2.03059	+	6.24952i	0.114411	+	0.352121i
$316$	−2.75912	+	10.3739i	−0.155213	+	0.583580i
$317$	9.51230	+	6.91109i	0.534264	+	0.388165i	0.821950	−	0.569559i	$-0.192886\pi$
$317$	9.51230	+	6.91109i	0.534264	+	0.388165i	−0.287686	+	0.957725i	$0.592886\pi$
$318$	0.239513	+	8.83422i	0.0134312	+	0.495399i
$319$	10.9142	+	27.5003i	0.611080	+	1.53972i
$320$	14.9543	−	2.45372i	0.835972	−	0.137167i
$321$	2.20987	−	3.04162i	0.123343	−	0.169767i
$322$	17.9894	+	5.31060i	1.00251	+	0.295948i
$323$	12.3313	−	4.00668i	0.686131	−	0.222938i
$324$	−1.55196	+	1.26152i	−0.0862200	+	0.0700842i
$325$	1.50750	+	2.07489i	0.0836209	+	0.115094i
$326$	0.849430	−	0.301684i	0.0470456	−	0.0167087i
$327$	−0.442977	+	1.36334i	−0.0244967	+	0.0753931i
$328$	−11.4134	+	18.7416i	−0.630200	+	1.03483i
$329$			9.72980i			0.536421i
$330$	−1.96845	+	8.66419i	−0.108360	+	0.476948i
$331$		−	0.109341i		−	0.00600991i	−0.999995	−	0.00300496i	$-0.999043\pi$
$331$		−	0.109341i		−	0.00600991i	0.999995	−	0.00300496i	$-0.000956508\pi$
$332$	12.6761	+	8.19864i	0.695691	+	0.449959i
$333$	3.51620	−	10.8218i	0.192687	−	0.593029i
$334$	−4.30803	−	12.1298i	−0.235725	−	0.663714i
$335$	−16.7891	−	23.1083i	−0.917288	−	1.26254i
$336$	9.32276	+	10.2772i	0.508598	+	0.560668i
$337$	−19.3456	+	6.28577i	−1.05382	+	0.342408i	−0.784167	−	0.620549i	$-0.786910\pi$
$337$	−19.3456	+	6.28577i	−1.05382	+	0.342408i	−0.269655	+	0.962957i	$0.586910\pi$
$338$	−3.88364	+	13.1556i	−0.211242	+	0.715573i
$339$	7.18721	−	9.89235i	0.390356	−	0.537279i
$340$	−0.610902	−	11.2580i	−0.0331308	−	0.610551i
$341$	7.88640	+	4.99579i	0.427073	+	0.270537i
$342$	6.15933	−	0.166991i	0.333058	−	0.00902986i
$343$	−5.51899	−	4.00978i	−0.297998	−	0.216508i
$344$	1.53479	−	6.47197i	0.0827505	−	0.348945i
$345$	−2.23810	−	6.88815i	−0.120495	−	0.370846i
$346$	14.1401	+	18.3924i	0.760175	+	0.988783i
$347$	−0.0735503	+	0.0534374i	−0.00394839	+	0.00286867i	−0.589758	−	0.807580i	$-0.700777\pi$
$347$	−0.0735503	+	0.0534374i	−0.00394839	+	0.00286867i	0.585809	+	0.810449i	$0.300777\pi$
$348$	−6.42467	−	16.6447i	−0.344398	−	0.892249i
$349$	3.99941	+	1.29949i	0.214083	+	0.0695599i	0.414095	−	0.910234i	$-0.364098\pi$
$349$	3.99941	+	1.29949i	0.214083	+	0.0695599i	−0.200012	+	0.979793i	$0.564098\pi$
$350$	5.71105	+	3.91732i	0.305268	+	0.209389i
$351$	1.81678			0.0969724
$352$	3.71227	+	18.3907i	0.197865	+	0.980229i
$353$	22.5015			1.19764			0.598818	−	0.800885i	$-0.295637\pi$
$353$	22.5015			1.19764			0.598818	+	0.800885i	$0.295637\pi$
$354$	−9.42546	−	6.46511i	−0.500958	−	0.343616i
$355$	9.93463	+	3.22796i	0.527275	+	0.171322i
$356$	−3.75151	−	9.71921i	−0.198829	−	0.515117i
$357$	8.35174	−	6.06789i	0.442021	−	0.321147i
$358$	0.465835	+	0.605926i	0.0246201	+	0.0320242i
$359$	0.804066	+	2.47466i	0.0424370	+	0.130608i	0.970030	−	0.242984i	$-0.0781262\pi$
$359$	0.804066	+	2.47466i	0.0424370	+	0.130608i	−0.927593	+	0.373591i	$0.878126\pi$
$360$	1.23630	−	5.21327i	0.0651586	−	0.274763i
$361$	0.0140835	+	0.0102322i	0.000741236	+	0.000538539i
$362$	7.12038	−	0.193047i	0.374239	−	0.0101463i
$363$	−10.8085	−	2.04346i	−0.567301	−	0.107254i
$364$	−0.682965	−	12.5860i	−0.0357971	−	0.659686i
$365$	−13.0522	+	17.9648i	−0.683182	+	0.940319i
$366$	−3.11547	+	10.5535i	−0.162848	+	0.551640i
$367$	14.6886	−	4.77262i	0.766739	−	0.249129i	0.100571	−	0.994930i	$-0.467933\pi$
$367$	14.6886	−	4.77262i	0.766739	−	0.249129i	0.666169	+	0.745801i	$0.267933\pi$
$368$	−10.2754	−	11.3274i	−0.535644	−	0.590483i
$369$	4.56013	+	6.27649i	0.237391	+	0.326741i
$370$	10.2019	+	28.7248i	0.530371	+	1.49333i
$371$	6.69869	−	20.6165i	0.347779	−	1.07035i
$372$	−4.72702	−	3.05734i	−0.245085	−	0.158516i
$373$		−	5.55960i		−	0.287865i	−0.989587	−	0.143933i	$-0.954025\pi$
$373$		−	5.55960i		−	0.287865i	0.989587	−	0.143933i	$-0.0459749\pi$
$374$	13.9010	−	1.26510i	0.718801	−	0.0654166i
$375$		−	12.1456i		−	0.627194i
$376$	4.12634	−	6.77573i	0.212800	−	0.349432i
$377$	−5.00826	+	15.4139i	−0.257939	+	0.793854i
$378$	4.62289	−	1.64187i	0.237776	−	0.0844486i
$379$	−15.1814	−	20.8954i	−0.779818	−	1.07333i	−0.995302	−	0.0968197i	$-0.969133\pi$
$379$	−15.1814	−	20.8954i	−0.779818	−	1.07333i	0.215484	−	0.976507i	$-0.430867\pi$
$380$	−12.8087	+	10.4116i	−0.657071	+	0.534102i
$381$	−4.88990	+	1.58882i	−0.250517	+	0.0813979i
$382$	−3.97719	−	1.17409i	−0.203491	−	0.0600719i
$383$	−0.0646313	+	0.0889574i	−0.00330251	+	0.00454551i	−0.810665	−	0.585510i	$-0.800894\pi$
$383$	−0.0646313	+	0.0889574i	−0.00330251	+	0.00454551i	0.807363	+	0.590056i	$0.200894\pi$
$384$	−2.13377	−	11.1107i	−0.108889	−	0.566989i
$385$	11.6627	−	18.4109i	0.594386	−	0.938304i
$386$	0.424996	+	15.6756i	0.0216317	+	0.797867i
$387$	−1.90252	−	1.38226i	−0.0967107	−	0.0702644i
$388$	−4.27311	+	16.0664i	−0.216934	+	0.815645i
$389$	6.06738	+	18.6735i	0.307628	+	0.946782i	0.978683	+	0.205375i	$0.0658413\pi$
$389$	6.06738	+	18.6735i	0.307628	+	0.946782i	−0.671055	+	0.741407i	$0.734159\pi$
$390$	−3.85851	+	2.96642i	−0.195383	+	0.150210i
$391$	−9.20520	+	6.68797i	−0.465527	+	0.338225i
$392$	−5.48465	−	13.1378i	−0.277017	−	0.663561i
$393$	−3.31477	−	1.07704i	−0.167208	−	0.0543292i
$394$	4.78123	−	6.97055i	0.240875	−	0.351171i
$395$	−10.1672			−0.511567
$396$	6.50586	+	1.29373i	0.326932	+	0.0650126i
$397$	30.2146			1.51643			0.758215	−	0.652005i	$-0.226072\pi$
$397$	30.2146			1.51643			0.758215	+	0.652005i	$0.226072\pi$
$398$	−2.18632	+	3.18743i	−0.109590	+	0.159771i
$399$	−14.3740	−	4.67041i	−0.719602	−	0.233813i
$400$	−2.31581	−	5.15000i	−0.115790	−	0.257500i
$401$	−0.155811	+	0.113203i	−0.00778083	+	0.00565310i	−0.591669	−	0.806181i	$-0.701531\pi$
$401$	−0.155811	+	0.113203i	−0.00778083	+	0.00565310i	0.583888	+	0.811834i	$0.301531\pi$
$402$	−16.9059	+	12.9972i	−0.843187	+	0.648241i
$403$	1.58026	+	4.86355i	0.0787185	+	0.242271i
$404$	23.6127	+	6.28019i	1.17478	+	0.312451i
$405$	−1.53251	−	1.11343i	−0.0761510	−	0.0553270i
$406$	1.18608	+	43.7475i	0.0588642	+	2.17115i
$407$	−35.0772	+	13.9214i	−1.73871	+	0.690057i
$408$	−8.38942	+	0.683701i	−0.415338	+	0.0338483i
$409$	−18.2103	+	25.0644i	−0.900443	+	1.23935i	0.0698831	+	0.997555i	$0.477737\pi$
$409$	−18.2103	+	25.0644i	−0.900443	+	1.23935i	−0.970326	+	0.241799i	$0.922263\pi$
$410$	−19.9331	−	5.88440i	−0.984427	−	0.290610i
$411$	−3.21089	+	1.04328i	−0.158382	+	0.0514614i
$412$	17.2691	+	21.2451i	0.850788	+	1.04667i
$413$	16.4790	+	22.6814i	0.810880	+	1.11608i
$414$	−5.09530	+	1.80965i	−0.250420	+	0.0889394i
$415$	−4.41846	+	13.5986i	−0.216894	+	0.667530i
$416$	−4.86203	+	9.05441i	−0.238381	+	0.443929i
$417$		−	22.7228i		−	1.11274i
$418$	−13.4608	−	15.3761i	−0.658388	−	0.752070i
$419$		−	28.8010i		−	1.40702i	−0.710686	−	0.703510i	$-0.751615\pi$
$419$		−	28.8010i		−	1.40702i	0.710686	−	0.703510i	$-0.248385\pi$
$420$	−7.13738	+	11.0353i	−0.348269	+	0.538466i
$421$	−0.977355	+	3.00799i	−0.0476334	+	0.146601i	−0.972044	−	0.234798i	$-0.924557\pi$
$421$	−0.977355	+	3.00799i	−0.0476334	+	0.146601i	0.924411	+	0.381398i	$0.124557\pi$
$422$	−12.0098	−	33.8151i	−0.584627	−	1.64609i
$423$	−1.64865	−	2.26917i	−0.0801599	−	0.110331i
$424$	−13.4082	+	11.5162i	−0.651160	+	0.559277i
$425$	−3.99546	+	1.29820i	−0.193808	+	0.0629721i
$426$	2.20799	−	7.47946i	0.106978	−	0.362381i
$427$	15.8650	−	21.8362i	0.767759	−	1.05673i
$428$	7.50826	−	0.407427i	0.362925	−	0.0196937i
$429$	−3.84465	−	4.63963i	−0.185621	−	0.224003i
$430$	6.29758	−	0.170740i	0.303696	−	0.00823379i
$431$	2.16293	+	1.57146i	0.104185	+	0.0756947i	0.638658	−	0.769491i	$-0.279490\pi$
$431$	2.16293	+	1.57146i	0.104185	+	0.0756947i	−0.534473	+	0.845185i	$0.679490\pi$
$432$	−3.91564	−	0.817159i	−0.188391	−	0.0393156i
$433$	−6.48467	−	19.9578i	−0.311634	−	0.959110i	−0.977118	−	0.212698i	$-0.931775\pi$
$433$	−6.48467	−	19.9578i	−0.311634	−	0.959110i	0.665484	−	0.746412i	$-0.268225\pi$
$434$	8.41638	+	10.9475i	0.403999	+	0.525495i
$435$	13.6712	−	9.93271i	0.655484	−	0.476237i
$436$	−2.67468	+	1.03240i	−0.128094	+	0.0494428i
$437$	15.8429	+	5.14767i	0.757869	+	0.246247i
$438$	13.6711	+	9.37727i	0.653230	+	0.448063i
$439$	−9.75312			−0.465491			−0.232746	−	0.972538i	$-0.574771\pi$
$439$	−9.75312			−0.465491			−0.232746	+	0.972538i	$0.574771\pi$
$440$	−15.9297	+	7.87506i	−0.759419	+	0.375429i
$441$	−5.03344			−0.239688
$442$	6.30537	+	4.32498i	0.299916	+	0.205718i
$443$	19.6000	+	6.36841i	0.931222	+	0.302572i	0.735062	−	0.678000i	$-0.237153\pi$
$443$	19.6000	+	6.36841i	0.931222	+	0.302572i	0.196160	+	0.980572i	$0.437153\pi$
$444$	21.2307	−	8.19481i	1.00756	−	0.388909i
$445$	7.98292	−	5.79993i	0.378427	−	0.274943i
$446$	17.4224	+	22.6619i	0.824976	+	1.07307i
$447$	−4.32159	−	13.3005i	−0.204404	−	0.629091i
$448$	−4.18902	+	27.4334i	−0.197913	+	1.29611i
$449$	−32.3068	−	23.4722i	−1.52465	−	1.10772i	−0.959121	−	0.282995i	$-0.908672\pi$
$449$	−32.3068	−	23.4722i	−1.52465	−	1.10772i	−0.565529	−	0.824728i	$-0.691328\pi$
$450$	−1.99568	+	0.0541069i	−0.0940774	+	0.00255062i
$451$	6.37856	−	24.9278i	0.300355	−	1.17380i
$452$	24.4193	−	1.32508i	1.14859	−	0.0623267i
$453$	−4.78488	+	6.58582i	−0.224813	+	0.309429i
$454$	−1.37509	+	4.65805i	−0.0645362	+	0.218613i
$455$	11.3540	−	3.68913i	0.532283	−	0.172949i
$456$	8.02925	+	9.34836i	0.376004	+	0.437777i
$457$	−19.8109	−	27.2674i	−0.926716	−	1.27552i	−0.961127	−	0.276107i	$-0.910955\pi$
$457$	−19.8109	−	27.2674i	−0.926716	−	1.27552i	0.0344108	−	0.999408i	$-0.489045\pi$
$458$	−2.77065	−	7.80111i	−0.129464	−	0.364522i
$459$	−0.919617	+	2.83029i	−0.0429240	+	0.132107i
$460$	7.86675	−	12.1629i	0.366789	−	0.567100i
$461$			18.4692i			0.860196i	0.902782	+	0.430098i	$0.141521\pi$
$461$			18.4692i			0.860196i	−0.902782	+	0.430098i	$0.858479\pi$
$462$	−13.9759	−	8.33129i	−0.650217	−	0.387606i
$463$			21.9821i			1.02159i	0.859701	+	0.510797i	$0.170650\pi$
$463$			21.9821i			1.02159i	−0.859701	+	0.510797i	$0.829350\pi$
$464$	17.7271	−	30.9683i	0.822959	−	1.43767i
$465$	1.64768	−	5.07104i	0.0764094	−	0.235164i
$466$	−13.1613	+	4.67435i	−0.609683	+	0.216535i
$467$	21.5485	+	29.6590i	0.997147	+	1.37245i	0.927060	+	0.374914i	$0.122328\pi$
$467$	21.5485	+	29.6590i	0.997147	+	1.37245i	0.0700868	+	0.997541i	$0.477672\pi$
$468$	2.29189	+	2.81956i	0.105943	+	0.130334i
$469$	49.7468	−	16.1637i	2.29709	−	0.746371i
$470$	7.20651	+	2.12741i	0.332412	+	0.0981303i
$471$	−10.9066	+	15.0116i	−0.502548	+	0.691698i
$472$	−1.85678	−	22.7838i	−0.0854651	−	1.04871i
$473$	0.496125	+	7.78374i	0.0228119	+	0.357897i
$474$	0.205718	+	7.58771i	0.00944893	+	0.348515i
$475$	4.97590	+	3.61520i	0.228310	+	0.165877i
$476$	19.9530	+	5.30682i	0.914543	+	0.243238i
$477$	1.93106	+	5.94318i	0.0884171	+	0.272120i
$478$	−21.9801	+	16.8982i	−1.00535	+	0.772908i
$479$	19.1217	−	13.8928i	0.873695	−	0.634776i	−0.0578810	−	0.998323i	$-0.518434\pi$
$479$	19.1217	−	13.8928i	0.873695	−	0.634776i	0.931576	+	0.363547i	$0.118434\pi$
$480$	9.65039	−	4.65793i	0.440478	−	0.212604i
$481$	−19.6607	−	6.38816i	−0.896452	−	0.291275i
$482$	9.75322	−	14.2192i	0.444247	−	0.647667i
$483$	13.2631			0.603493
$484$	−10.4638	−	19.3523i	−0.475626	−	0.879648i
$485$	−15.7462			−0.714996
$486$	−0.799941	+	1.16623i	−0.0362860	+	0.0529013i
$487$	35.0909	+	11.4017i	1.59012	+	0.516661i	0.964638	−	0.263577i	$-0.0849023\pi$
$487$	35.0909	+	11.4017i	1.59012	+	0.516661i	0.625482	+	0.780238i	$0.284902\pi$
$488$	−20.3088	+	8.47831i	−0.919336	+	0.383795i
$489$	0.515663	−	0.374651i	0.0233191	−	0.0169423i
$490$	10.6901	−	8.21856i	0.482931	−	0.371277i
$491$	−5.75631	−	17.7161i	−0.259779	−	0.799517i	−0.992850	−	0.119365i	$-0.961914\pi$
$491$	−5.75631	−	17.7161i	−0.259779	−	0.799517i	0.733072	−	0.680151i	$-0.238086\pi$
$492$	−3.98818	+	14.9950i	−0.179801	+	0.676028i
$493$	−21.4776	−	15.6044i	−0.967302	−	0.702786i
$494$	−0.303386	−	11.1901i	−0.0136500	−	0.503467i
$495$	0.399636	+	6.26991i	0.0179623	+	0.281812i
$496$	−1.21834	−	11.1930i	−0.0547051	−	0.502582i
$497$	−11.2438	+	15.4758i	−0.504353	+	0.694183i
$498$	10.2380	+	3.02232i	0.458774	+	0.135434i
$499$	−32.6136	+	10.5968i	−1.45998	+	0.474377i	−0.928065	−	0.372418i	$-0.878529\pi$
$499$	−32.6136	+	10.5968i	−1.45998	+	0.474377i	−0.531919	+	0.846795i	$0.678529\pi$
$500$	18.8494	−	15.3218i	0.842972	−	0.685212i
$501$	−5.35000	−	7.36364i	−0.239020	−	0.328983i
$502$	−31.2409	+	11.0955i	−1.39435	+	0.495217i
$503$	1.01615	−	3.12740i	0.0453080	−	0.139444i	−0.925843	−	0.377907i	$-0.876644\pi$
$503$	1.01615	−	3.12740i	0.0453080	−	0.139444i	0.971151	+	0.238464i	$0.0766438\pi$
$504$	8.37996	+	5.10330i	0.373273	+	0.227319i
$505$			23.1421i			1.02981i
$506$	15.4041	+	9.18265i	0.684794	+	0.408219i
$507$			9.69932i			0.430762i
$508$	−8.63447	−	5.58460i	−0.383093	−	0.247776i
$509$	10.4865	−	32.2741i	0.464806	−	1.43052i	−0.394421	−	0.918930i	$-0.629055\pi$
$509$	10.4865	−	32.2741i	0.464806	−	1.43052i	0.859227	−	0.511595i	$-0.170945\pi$
$510$	−2.66817	−	7.51258i	−0.118149	−	0.332663i
$511$	−23.9019	−	32.8981i	−1.05736	−	1.45533i
$512$	14.5515	−	17.3278i	0.643093	−	0.765788i
$513$	4.14366	−	1.34636i	0.182947	−	0.0594431i
$514$	5.91915	−	20.0508i	0.261083	−	0.884404i
$515$	−15.2420	+	20.9788i	−0.671642	+	0.924436i
$516$	−0.254844	−	4.69639i	−0.0112189	−	0.206747i
$517$	−2.30607	+	9.01225i	−0.101421	+	0.396358i
$518$	−55.8010	+	1.51287i	−2.45176	+	0.0664719i
$519$	13.2716	+	9.64239i	0.582559	+	0.423254i
$520$	−9.47134	−	2.24608i	−0.415346	−	0.0984970i
$521$	6.93119	+	21.3320i	0.303661	+	0.934572i	0.980174	+	0.198141i	$0.0634904\pi$
$521$	6.93119	+	21.3320i	0.303661	+	0.934572i	−0.676513	+	0.736431i	$0.736510\pi$
$522$	−7.68933	−	10.0018i	−0.336553	−	0.437765i
$523$	−21.7656	+	15.8137i	−0.951744	+	0.691483i	−0.951219	−	0.308517i	$-0.900167\pi$
$523$	−21.7656	+	15.8137i	−0.951744	+	0.691483i	−0.000525638		1.00000i	$0.500167\pi$
$524$	−2.51012	−	6.50309i	−0.109655	−	0.284089i
$525$	4.65733	+	1.51326i	0.203263	+	0.0660441i
$526$	12.0403	+	8.25867i	0.524982	+	0.360095i
$527$	−8.37664			−0.364892
$528$	6.19942	+	11.7289i	0.269795	+	0.510435i
$529$	8.38153			0.364414
$530$	−13.8052	−	9.46926i	−0.599660	−	0.411319i
$531$	−7.68642	−	2.49747i	−0.333562	−	0.108381i
$532$	−10.8848	−	28.1997i	−0.471915	−	1.22261i
$533$	11.4030	−	8.28475i	0.493918	−	0.358852i
$534$	−4.48997	−	5.84025i	−0.194300	−	0.252732i
$535$	2.20078	+	6.77329i	0.0951478	+	0.292835i
$536$	−41.4981	−	9.84105i	−1.79245	−	0.425069i
$537$	0.437224	+	0.317662i	0.0188676	+	0.0137081i
$538$	−7.24959	+	0.196551i	−0.312552	+	0.00847390i
$539$	10.6517	+	12.8542i	0.458802	+	0.553671i
$540$	−0.205280	−	3.78301i	−0.00883386	−	0.162795i
$541$	−8.91106	+	12.2650i	−0.383116	+	0.527315i	−0.956407	−	0.292038i	$-0.905667\pi$
$541$	−8.91106	+	12.2650i	−0.383116	+	0.527315i	0.573290	+	0.819352i	$0.305667\pi$
$542$	−4.16731	+	14.1166i	−0.179001	+	0.606358i
$543$	4.79020	−	1.55643i	0.205567	−	0.0667929i
$544$	−11.6445	−	12.1575i	−0.499252	−	0.521250i
$545$	−1.59611	−	2.19686i	−0.0683699	−	0.0941031i
$546$	−2.98291	−	8.39877i	−0.127657	−	0.359434i
$547$	2.14142	−	6.59062i	0.0915606	−	0.281795i	−0.894781	−	0.446504i	$-0.852669\pi$
$547$	2.14142	−	6.59062i	0.0915606	−	0.281795i	0.986342	+	0.164710i	$0.0526687\pi$
$548$	−5.66973	−	3.66706i	−0.242199	−	0.156649i
$549$			7.78082i			0.332077i
$550$	4.36143	+	4.98201i	0.185972	+	0.212434i
$551$			38.8670i			1.65579i
$552$	−9.23630	−	5.62480i	−0.393123	−	0.239408i
$553$	5.75351	−	17.7075i	0.244664	−	0.752998i
$554$	24.7203	−	8.77968i	1.05027	−	0.373013i
$555$	12.6694	+	17.4379i	0.537786	+	0.740199i
$556$	35.2649	−	28.6652i	1.49557	−	1.21568i
$557$	−0.278322	+	0.0904324i	−0.0117929	+	0.00383174i	−0.314908	−	0.949122i	$-0.601973\pi$
$557$	−0.278322	+	0.0904324i	−0.0117929	+	0.00383174i	0.303115	+	0.952954i	$0.401973\pi$
$558$	−3.81783	−	1.12705i	−0.161621	−	0.0477118i
$559$	−2.51127	+	3.45646i	−0.106215	+	0.146193i
$560$	−26.1302	+	2.84422i	−1.10420	+	0.120190i
$561$	9.17399	−	3.64095i	0.387326	−	0.153721i
$562$	−0.515019	−	18.9960i	−0.0217248	−	0.801299i
$563$	−15.4345	−	11.2138i	−0.650486	−	0.472606i	0.212951	−	0.977063i	$-0.431693\pi$
$563$	−15.4345	−	11.2138i	−0.650486	−	0.472606i	−0.863437	+	0.504457i	$0.831693\pi$
$564$	1.44186	−	5.42122i	0.0607134	−	0.228275i
$565$	7.15764	+	22.0290i	0.301124	+	0.926765i
$566$	−0.472179	+	0.363010i	−0.0198472	+	0.0152585i
$567$	2.80642	−	2.03898i	0.117859	−	0.0856292i
$568$	14.3932	−	6.00874i	0.603927	−	0.252121i
$569$	−29.4110	−	9.55621i	−1.23297	−	0.400617i	−0.381183	−	0.924500i	$-0.624483\pi$
$569$	−29.4110	−	9.55621i	−1.23297	−	0.400617i	−0.851791	+	0.523882i	$0.824483\pi$
$570$	−6.60208	+	9.62516i	−0.276531	+	0.403154i
$571$	14.7169			0.615883			0.307942	−	0.951405i	$-0.400360\pi$
$571$	14.7169			0.615883			0.307942	+	0.951405i	$0.400360\pi$
$572$	2.35043	−	11.8197i	0.0982763	−	0.494207i
$573$	−2.93228			−0.122498
$574$	21.5284	−	31.3862i	0.898578	−	1.31003i
$575$	−5.13326	−	1.66790i	−0.214072	−	0.0695561i
$576$	−3.67144	−	7.10778i	−0.152977	−	0.296157i
$577$	5.09251	−	3.69993i	0.212004	−	0.154030i	−0.476716	−	0.879057i	$-0.658173\pi$
$577$	5.09251	−	3.69993i	0.212004	−	0.154030i	0.688720	+	0.725027i	$0.258173\pi$
$578$	9.13058	−	7.01958i	0.379782	−	0.291976i
$579$	3.42650	+	10.5457i	0.142401	+	0.438264i
$580$	32.6616	+	8.68689i	1.35620	+	0.360703i
$581$	−21.1834	−	15.3906i	−0.878835	−	0.638511i
$582$	0.318600	+	11.7513i	0.0132064	+	0.487105i
$583$	11.0910	−	17.5084i	0.459343	−	0.725124i
$584$	2.69315	+	33.0465i	0.111443	+	1.36748i
$585$	−2.02286	+	2.78423i	−0.0836350	+	0.115114i
$586$	−24.3234	−	7.18044i	−1.00479	−	0.296621i
$587$	−40.0307	+	13.0068i	−1.65224	+	0.536847i	−0.979225	−	0.202778i	$-0.935003\pi$
$587$	−40.0307	+	13.0068i	−1.65224	+	0.536847i	−0.673020	+	0.739624i	$0.735003\pi$
$588$	−6.34976	−	7.81169i	−0.261860	−	0.322149i
$589$	7.20845	+	9.92158i	0.297019	+	0.408811i
$590$	20.4025	−	7.24614i	0.839956	−	0.298319i
$591$	1.84699	−	5.68445i	0.0759750	−	0.233827i
$592$	39.5009	+	22.6113i	1.62348	+	0.929318i
$593$		−	19.2298i		−	0.789675i	−0.918751	−	0.394837i	$-0.870801\pi$
$593$		−	19.2298i		−	0.789675i	0.918751	−	0.394837i	$-0.129199\pi$
$594$	4.67111	−	0.425108i	0.191658	−	0.0174424i
$595$			19.5553i			0.801690i
$596$	15.1901	−	23.4857i	0.622209	−	0.962011i
$597$	−0.844575	+	2.59934i	−0.0345662	+	0.106384i
$598$	3.28773	+	9.25703i	0.134445	+	0.378548i
$599$	9.14751	+	12.5905i	0.373757	+	0.514433i	0.953917	−	0.300070i	$-0.0970100\pi$
$599$	9.14751	+	12.5905i	0.373757	+	0.514433i	−0.580160	+	0.814502i	$0.697010\pi$
$600$	−2.60156	−	3.02896i	−0.106208	−	0.123657i
$601$	−4.94174	+	1.60567i	−0.201578	+	0.0654966i	−0.408066	−	0.912953i	$-0.633797\pi$
$601$	−4.94174	+	1.60567i	−0.201578	+	0.0654966i	0.206488	+	0.978449i	$0.433797\pi$
$602$	−3.26637	+	11.0647i	−0.133127	+	0.450962i
$603$	−8.86304	+	12.1989i	−0.360931	+	0.496779i
$604$	−16.2571	+	0.882174i	−0.661494	+	0.0358951i
$605$	15.1662	−	14.2889i	0.616593	−	0.580927i
$606$	17.2708	−	0.468245i	0.701579	−	0.0190212i
$607$	−4.32559	−	3.14273i	−0.175570	−	0.127559i	0.496529	−	0.868020i	$-0.334607\pi$
$607$	−4.32559	−	3.14273i	−0.175570	−	0.127559i	−0.672100	+	0.740460i	$0.734607\pi$
$608$	−4.37927	+	24.2542i	−0.177603	+	0.983637i
$609$	9.56270	+	29.4310i	0.387500	+	1.19260i
$610$	−12.7045	−	16.5251i	−0.514389	−	0.669081i
$611$	−4.12257	+	2.99522i	−0.166781	+	0.121174i
$612$	−5.55261	+	2.14324i	−0.224451	+	0.0866355i
$613$	−20.2178	−	6.56916i	−0.816590	−	0.265326i	−0.129203	−	0.991618i	$-0.541242\pi$
$613$	−20.2178	−	6.56916i	−0.816590	−	0.265326i	−0.687386	+	0.726292i	$0.741242\pi$
$614$	11.4018	+	7.82073i	0.460140	+	0.315619i
$615$	−14.6962			−0.592607
$616$	−4.70097	−	32.2001i	−0.189408	−	1.29738i
$617$	5.45994			0.219809			0.109905	−	0.993942i	$-0.464945\pi$
$617$	5.45994			0.219809			0.109905	+	0.993942i	$0.464945\pi$
$618$	15.9647	+	10.9505i	0.642196	+	0.440495i
$619$	−6.31236	−	2.05101i	−0.253715	−	0.0824371i	0.179398	−	0.983777i	$-0.442585\pi$
$619$	−6.31236	−	2.05101i	−0.253715	−	0.0824371i	−0.433113	+	0.901339i	$0.642585\pi$
$620$	9.94863	−	3.84006i	0.399547	−	0.154221i
$621$	−3.09320	+	2.24734i	−0.124126	+	0.0901828i
$622$	−9.81642	−	12.7685i	−0.393603	−	0.511971i
$623$	5.58387	+	17.1854i	0.223713	+	0.688519i
$624$	−1.48459	+	7.11385i	−0.0594314	+	0.284782i
$625$	12.9028	+	9.37445i	0.516113	+	0.374978i
$626$	−18.8737	+	0.511704i	−0.754346	+	0.0204518i
$627$	−12.2071	−	7.73279i	−0.487503	−	0.308818i
$628$	−37.0562	+	2.01081i	−1.47870	+	0.0802400i
$629$	19.9037	−	27.3952i	0.793614	−	1.09232i
$630$	−2.63111	+	8.91274i	−0.104826	+	0.355092i
$631$	19.5656	−	6.35725i	0.778894	−	0.253078i	0.107526	−	0.994202i	$-0.465707\pi$
$631$	19.5656	−	6.35725i	0.778894	−	0.253078i	0.671368	+	0.741124i	$0.265707\pi$
$632$	−11.5163	+	9.89128i	−0.458094	+	0.393454i
$633$	−14.9146	−	20.5281i	−0.592801	−	0.815920i
$634$	5.56508	+	15.6692i	0.221017	+	0.622303i
$635$	3.00969	−	9.26286i	0.119436	−	0.367585i
$636$	−6.78752	+	10.4943i	−0.269143	+	0.416128i
$637$			9.14464i			0.362324i
$638$	−9.27005	+	40.8024i	−0.367005	+	1.61538i
$639$		−	5.51442i		−	0.218147i
$640$	19.4030	+	9.10096i	0.766972	+	0.359747i
$641$	−6.24661	+	19.2251i	−0.246726	+	0.759346i	0.748621	+	0.662998i	$0.230716\pi$
$641$	−6.24661	+	19.2251i	−0.246726	+	0.759346i	−0.995348	+	0.0963480i	$0.969284\pi$
$642$	5.01034	−	1.77947i	0.197742	−	0.0702302i
$643$	12.0086	+	16.5284i	0.473573	+	0.651817i	0.977254	−	0.212072i	$-0.0680213\pi$
$643$	12.0086	+	16.5284i	0.473573	+	0.651817i	−0.503681	+	0.863890i	$0.668021\pi$
$644$	16.7316	+	20.5838i	0.659319	+	0.811117i
$645$	4.23667	−	1.37658i	0.166819	−	0.0542026i
$646$	17.5862	+	5.19158i	0.691921	+	0.204260i
$647$	8.24593	−	11.3496i	0.324181	−	0.446197i	−0.615557	−	0.788092i	$-0.711069\pi$
$647$	8.24593	−	11.3496i	0.324181	−	0.446197i	0.939738	+	0.341896i	$0.111069\pi$
$648$	−2.81908	+	0.229743i	−0.110744	+	0.00902515i
$649$	9.88799	+	24.9145i	0.388138	+	0.977978i
$650$	0.0983001	+	3.62571i	0.00385565	+	0.142212i
$651$	7.89947	+	5.73930i	0.309605	+	0.224941i
$652$	1.23196	+	0.327660i	0.0482473	+	0.0128322i
$653$	13.1470	+	40.4622i	0.514480	+	1.58341i	0.784226	+	0.620476i	$0.213060\pi$
$653$	13.1470	+	40.4622i	0.514480	+	1.58341i	−0.269745	+	0.962932i	$0.586940\pi$
$654$	−1.60721	+	1.23562i	−0.0628468	+	0.0483165i
$655$	5.34135	−	3.88072i	0.208704	−	0.151632i
$656$	−28.3028	+	12.7270i	−1.10504	+	0.496905i
$657$	11.1487	+	3.62244i	0.434953	+	0.141325i
$658$	−7.78326	+	11.3472i	−0.303423	+	0.442360i
$659$	35.3651			1.37763			0.688815	−	0.724937i	$-0.258131\pi$
$659$	35.3651			1.37763			0.688815	+	0.724937i	$0.258131\pi$
$660$	−9.22651	+	8.52981i	−0.359141	+	0.332022i
$661$	−6.75994			−0.262931			−0.131466	−	0.991321i	$-0.541968\pi$
$661$	−6.75994			−0.262931			−0.131466	+	0.991321i	$0.541968\pi$
$662$	0.0874661	−	0.127517i	0.00339947	−	0.00495607i
$663$	5.14200	+	1.67074i	0.199699	+	0.0648861i
$664$	8.22483	+	19.7016i	0.319185	+	0.764571i
$665$	23.1620	−	16.8282i	0.898183	−	0.652569i
$666$	12.7575	−	9.80792i	0.494342	−	0.380049i
$667$	−10.5399	−	32.4385i	−0.408107	−	1.25602i
$668$	4.67897	−	17.5923i	0.181035	−	0.680667i
$669$	16.3524	+	11.8807i	0.632220	+	0.459335i
$670$	−1.09478	−	40.3799i	−0.0422950	−	1.56001i
$671$	19.8704	−	16.4657i	0.767088	−	0.635652i
$672$	2.65133	+	19.4433i	0.102277	+	0.750040i
$673$	−21.9062	+	30.1512i	−0.844420	+	1.16224i	0.140645	+	0.990060i	$0.455083\pi$
$673$	−21.9062	+	30.1512i	−0.844420	+	1.16224i	−0.985065	+	0.172184i	$0.944917\pi$
$674$	−27.5897	−	8.14468i	−1.06272	−	0.313721i
$675$	−1.34259	+	0.436233i	−0.0516762	+	0.0167906i
$676$	−15.0530	+	12.2358i	−0.578960	+	0.470609i
$677$	−20.6777	−	28.4604i	−0.794709	−	1.09382i	−0.993506	−	0.113782i	$-0.963703\pi$
$677$	−20.6777	−	28.4604i	−0.794709	−	1.09382i	0.198797	−	0.980041i	$-0.436297\pi$
$678$	16.2952	−	5.78742i	0.625815	−	0.222265i
$679$	8.91058	−	27.4240i	0.341957	−	1.05243i
$680$	8.29328	−	13.6181i	0.318033	−	0.522231i
$681$			3.43426i			0.131601i
$682$	5.20103	+	12.1349i	0.199158	+	0.464669i
$683$			6.86049i			0.262509i	0.991349	+	0.131255i	$0.0419005\pi$
$683$			6.86049i			0.262509i	−0.991349	+	0.131255i	$0.958099\pi$
$684$	7.31678	+	4.73234i	0.279764	+	0.180946i
$685$	1.97628	−	6.08235i	0.0755096	−	0.232395i
$686$	−3.22883	−	9.09120i	−0.123277	−	0.347104i
$687$	−3.44077	−	4.73582i	−0.131274	−	0.180683i
$688$	6.96712	−	6.32007i	0.265619	−	0.240950i
$689$	10.7974	−	3.50830i	0.411350	−	0.133656i
$690$	2.89998	−	9.82352i	0.110400	−	0.373975i
$691$	−17.7244	+	24.3956i	−0.674270	+	0.928053i	−0.999848	−	0.0174625i	$-0.994441\pi$
$691$	−17.7244	+	24.3956i	−0.674270	+	0.928053i	0.325578	+	0.945515i	$0.394441\pi$
$692$	1.77774	+	32.7610i	0.0675795	+	1.24539i
$693$	−11.1460	−	2.85206i	−0.423402	−	0.108341i
$694$	−0.128523	+	0.00348452i	−0.00487868	+	0.000132271i
$695$	34.8230	+	25.3004i	1.32091	+	0.959698i
$696$	5.82211	−	24.5509i	0.220687	−	0.930600i
$697$	7.13454	+	21.9578i	0.270240	+	0.831713i
$698$	3.62472	+	4.71479i	0.137198	+	0.178457i
$699$	−7.98980	+	5.80493i	−0.302202	+	0.219563i
$700$	3.52678	+	9.13699i	0.133300	+	0.345346i
$701$	2.65130	+	0.861459i	0.100138	+	0.0325369i	0.358658	−	0.933469i	$-0.383235\pi$
$701$	2.65130	+	0.861459i	0.100138	+	0.0325369i	−0.258519	+	0.966006i	$0.583235\pi$
$702$	2.11878	+	1.45331i	0.0799683	+	0.0548518i
$703$	−49.5758			−1.86979
$704$	−10.3821	+	24.4174i	−0.391291	+	0.920267i
$705$	5.31318			0.200106
$706$	26.2420	+	17.9999i	0.987630	+	0.677435i
$707$	−40.3050	−	13.0959i	−1.51582	−	0.492521i
$708$	−5.82057	−	15.0796i	−0.218750	−	0.566727i
$709$	19.9662	−	14.5063i	0.749846	−	0.544795i	−0.145933	−	0.989294i	$-0.546618\pi$
$709$	19.9662	−	14.5063i	0.749846	−	0.544795i	0.895779	+	0.444499i	$0.146618\pi$
$710$	9.00390	+	11.7117i	0.337910	+	0.439531i
$711$	1.65859	+	5.10460i	0.0622018	+	0.191437i
$712$	3.39966	−	14.3358i	0.127408	−	0.537258i
$713$	−8.70671	−	6.32579i	−0.326069	−	0.236903i
$714$	14.5940	−	0.395672i	0.546167	−	0.0148077i
$715$	11.3910	−	0.726049i	0.426001	−	0.0271527i
$716$	0.0585663	+	1.07929i	0.00218873	+	0.0403349i
$717$	−11.5233	+	15.8604i	−0.430344	+	0.592317i
$718$	−1.04185	+	3.52923i	−0.0388817	+	0.131710i
$719$	−17.1274	+	5.56504i	−0.638745	+	0.207541i	−0.610445	−	0.792059i	$-0.709009\pi$
$719$	−17.1274	+	5.56504i	−0.638745	+	0.207541i	−0.0283002	+	0.999599i	$0.509009\pi$
$720$	5.61211	−	5.09091i	0.209151	−	0.189727i
$721$	−27.9120	−	38.4176i	−1.03950	−	1.43075i
$722$	0.00823940	+	0.0231991i	0.000306639	+	0.000863381i
$723$	3.76767	−	11.5957i	0.140121	−	0.431248i
$724$	8.45843	+	5.47074i	0.314355	+	0.203318i
$725$		−	12.5933i		−	0.467703i
$726$	−10.9706	−	11.0293i	−0.407157	−	0.409337i
$727$			3.09840i			0.114913i	0.998348	+	0.0574566i	$0.0182991\pi$
$727$			3.09840i			0.114913i	−0.998348	+	0.0574566i	$0.981701\pi$
$728$	9.27156	−	15.2245i	0.343627	−	0.564258i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−29.5926	+	10.5101i	−1.09527	+	0.388997i
$731$	−4.11354	−	5.66180i	−0.152145	−	0.209409i
$732$	−12.0755	+	9.81562i	−0.446324	+	0.362796i
$733$	−5.56847	+	1.80931i	−0.205676	+	0.0668283i	−0.410043	−	0.912066i	$-0.634486\pi$
$733$	−5.56847	+	1.80931i	−0.205676	+	0.0668283i	0.204367	+	0.978894i	$0.434486\pi$
$734$	20.9481	+	6.18404i	0.773210	+	0.228257i
$735$	5.60440	−	7.71379i	0.206721	−	0.284528i
$736$	−2.92227	−	21.4301i	−0.107716	−	0.789926i
$737$	49.9091	−	3.18114i	1.83843	−	0.117179i
$738$	0.297355	+	10.9677i	0.0109458	+	0.403726i
$739$	3.46213	+	2.51539i	0.127357	+	0.0925300i	0.649640	−	0.760242i	$-0.274920\pi$
$739$	3.46213	+	2.51539i	0.127357	+	0.0925300i	−0.522283	+	0.852772i	$0.674920\pi$
$740$	−11.0803	+	41.6606i	−0.407321	+	1.53147i
$741$	−2.44603	−	7.52810i	−0.0898571	−	0.276552i
$742$	24.3042	−	18.6850i	0.892234	−	0.685948i
$743$	34.1318	−	24.7982i	1.25217	−	0.909757i	0.253827	−	0.967250i	$-0.418310\pi$
$743$	34.1318	−	24.7982i	1.25217	−	0.909757i	0.998346	+	0.0574923i	$0.0183105\pi$
$744$	−3.06711	−	7.34690i	−0.112446	−	0.269351i
$745$	25.1949	+	8.18632i	0.923070	+	0.299924i
$746$	4.44735	−	6.48378i	0.162829	−	0.237388i
$747$	7.54819			0.276174
$748$	17.2237	+	9.64454i	0.629762	+	0.352639i
$749$	−13.0420			−0.476543
$750$	9.71572	−	14.1645i	0.354768	−	0.517215i
$751$	−10.4683	−	3.40134i	−0.381992	−	0.124117i	0.111725	−	0.993739i	$-0.464362\pi$
$751$	−10.4683	−	3.40134i	−0.381992	−	0.124117i	−0.493718	+	0.869622i	$0.664362\pi$
$752$	10.2325	−	4.60124i	0.373139	−	0.167790i
$753$	−18.9654	+	13.7792i	−0.691137	+	0.502140i
$754$	−18.1710	+	13.9698i	−0.661747	+	0.508750i
$755$	−4.76519	−	14.6658i	−0.173423	−	0.533742i
$756$	6.70476	+	1.78324i	0.243850	+	0.0648559i
$757$	−17.6019	−	12.7886i	−0.639753	−	0.464808i	0.220012	−	0.975497i	$-0.429390\pi$
$757$	−17.6019	−	12.7886i	−0.639753	−	0.464808i	−0.859765	+	0.510689i	$0.829390\pi$
$758$	−0.989943	−	36.5132i	−0.0359564	−	1.32622i
$759$	12.2850	+	3.14351i	0.445918	+	0.114102i
$760$	−23.2665	+	1.89612i	−0.843964	+	0.0687794i
$761$	4.47259	−	6.15599i	0.162131	−	0.223154i	−0.720220	−	0.693745i	$-0.755959\pi$
$761$	4.47259	−	6.15599i	0.162131	−	0.223154i	0.882351	+	0.470591i	$0.155959\pi$
$762$	−6.97371	−	2.05869i	−0.252631	−	0.0745785i
$763$	4.72934	−	1.53665i	0.171213	−	0.0556306i
$764$	−3.69911	−	4.55078i	−0.133829	−	0.164641i
$765$	−3.31351	−	4.56066i	−0.119800	−	0.164891i
$766$	−0.146536	+	0.0520437i	−0.00529455	+	0.00188041i
$767$	−4.53735	+	13.9645i	−0.163834	+	0.504229i
$768$	6.39940	−	14.6645i	0.230919	−	0.529160i
$769$		−	12.9034i		−	0.465307i	−0.972560	−	0.232653i	$-0.925259\pi$
$769$		−	12.9034i		−	0.465307i	0.972560	−	0.232653i	$-0.0747408\pi$
$770$	28.3290	−	12.1418i	1.02091	−	0.437562i
$771$		−	14.7830i		−	0.532396i
$772$	−12.0439	+	18.6214i	−0.433470	+	0.670197i
$773$	−7.73840	+	23.8163i	−0.278331	+	0.856614i	0.709988	+	0.704214i	$0.248700\pi$
$773$	−7.73840	+	23.8163i	−0.278331	+	0.856614i	−0.988319	+	0.152401i	$0.951300\pi$
$774$	−1.11305	−	3.13395i	−0.0400079	−	0.112647i
$775$	−2.33561	−	3.21469i	−0.0838976	−	0.115475i
$776$	−17.8356	+	15.3188i	−0.640259	+	0.549914i
$777$	−37.5399	+	12.1974i	−1.34674	+	0.437581i
$778$	−7.86170	+	26.6311i	−0.281855	+	0.954772i
$779$	19.8681	−	27.3460i	0.711847	−	0.979773i
$780$	−6.87288	+	0.372949i	−0.246089	+	0.0133537i
$781$	−14.0825	+	11.6696i	−0.503913	+	0.417570i
$782$	−16.0854	+	0.436106i	−0.575211	+	0.0155951i
$783$	−7.21707	−	5.24351i	−0.257917	−	0.187388i
$784$	4.11312	−	19.7091i	0.146897	−	0.703898i
$785$	−10.8617	−	33.4288i	−0.387670	−	1.19313i
$786$	−3.00423	−	3.90769i	−0.107157	−	0.139383i
$787$	3.63457	−	2.64067i	0.129558	−	0.0941296i	−0.521119	−	0.853484i	$-0.674485\pi$
$787$	3.63457	−	2.64067i	0.129558	−	0.0941296i	0.650677	+	0.759355i	$0.274485\pi$
$788$	11.1520	−	4.30457i	0.397275	−	0.153344i
$789$	9.81880	+	3.19032i	0.349559	+	0.113578i
$790$	−11.8573	−	8.13315i	−0.421864	−	0.289364i
$791$	−42.4167			−1.50816
$792$	6.55243	+	6.71310i	0.232830	+	0.238540i
$793$	14.1360			0.501984
$794$	35.2373	+	24.1699i	1.25052	+	0.857758i
$795$	−11.2581	−	3.65798i	−0.399283	−	0.129735i
$796$	−5.09951	+	1.96835i	−0.180747	+	0.0697665i
$797$	3.79132	−	2.75456i	0.134296	−	0.0975714i	−0.518609	−	0.855011i	$-0.673550\pi$
$797$	3.79132	−	2.75456i	0.134296	−	0.0975714i	0.652905	+	0.757440i	$0.273550\pi$
$798$	−13.0274	−	16.9452i	−0.461165	−	0.599852i
$799$	−2.57938	−	7.93852i	−0.0912520	−	0.280845i
$800$	1.41893	−	7.85859i	0.0501666	−	0.277843i
$801$	−4.21421	−	3.06180i	−0.148902	−	0.108183i
$802$	−0.272268	+	0.00738171i	−0.00961410	+	0.000260657i
$803$	−14.3420	−	36.1370i	−0.506117	−	1.27525i
$804$	−30.1131	+	1.63405i	−1.06201	+	0.0576286i
$805$	−14.7676	+	20.3259i	−0.520490	+	0.716393i
$806$	−2.04760	+	6.93614i	−0.0721236	+	0.244315i
$807$	−4.87713	+	1.58468i	−0.171683	+	0.0557832i
$808$	22.5141	+	26.2129i	0.792043	+	0.922167i
$809$	5.40400	+	7.43797i	0.189995	+	0.261505i	0.893378	−	0.449305i	$-0.148328\pi$
$809$	5.40400	+	7.43797i	0.189995	+	0.261505i	−0.703384	+	0.710810i	$0.748328\pi$
$810$	−0.896580	−	2.52444i	−0.0315026	−	0.0886997i
$811$	−0.540273	+	1.66279i	−0.0189716	+	0.0583884i	−0.960094	−	0.279677i	$-0.909773\pi$
$811$	−0.540273	+	1.66279i	−0.0189716	+	0.0583884i	0.941123	+	0.338066i	$0.109773\pi$
$812$	−33.6122	+	51.9685i	−1.17956	+	1.82374i
$813$			10.4078i			0.365017i
$814$	−52.0444	−	11.8242i	−1.82416	−	0.414437i
$815$			1.20741i			0.0422937i
$816$	−10.3309	−	5.91368i	−0.361655	−	0.207020i
$817$	−3.16616	+	9.74443i	−0.110770	+	0.340914i
$818$	−41.2875	+	14.6637i	−1.44358	+	0.512703i
$819$	−3.70438	−	5.09864i	−0.129441	−	0.178161i
$820$	−18.5395	−	22.8079i	−0.647426	−	0.796486i
$821$	21.3086	−	6.92358i	0.743675	−	0.241635i	0.0874178	−	0.996172i	$-0.472138\pi$
$821$	21.3086	−	6.92358i	0.743675	−	0.241635i	0.656258	+	0.754537i	$0.272138\pi$
$822$	−4.57921	−	1.35182i	−0.159718	−	0.0471500i
$823$	16.2633	−	22.3844i	0.566901	−	0.780273i	−0.425282	−	0.905061i	$-0.639825\pi$
$823$	16.2633	−	22.3844i	0.566901	−	0.780273i	0.992183	+	0.124788i	$0.0398251\pi$
$824$	3.14499	+	38.5909i	0.109561	+	1.34438i
$825$	3.95521	+	2.50550i	0.137703	+	0.0872304i
$826$	1.07456	+	39.6340i	0.0373886	+	1.37904i
$827$	5.02913	+	3.65387i	0.174880	+	0.127058i	0.671782	−	0.740749i	$-0.265529\pi$
$827$	5.02913	+	3.65387i	0.174880	+	0.127058i	−0.496902	+	0.867807i	$0.665529\pi$
$828$	−7.38991	−	1.96547i	−0.256817	−	0.0683048i
$829$	−5.92631	−	18.2393i	−0.205829	−	0.633477i	−0.999678	−	0.0253622i	$-0.991926\pi$
$829$	−5.92631	−	18.2393i	−0.205829	−	0.633477i	0.793849	−	0.608115i	$-0.208074\pi$
$830$	−16.0310	+	12.3246i	−0.556445	+	0.427794i
$831$	15.0070	−	10.9032i	0.520586	−	0.378228i
$832$	−12.9132	+	6.67020i	−0.447686	+	0.231247i
$833$	−14.2461	−	4.62883i	−0.493598	−	0.160380i
$834$	18.1769	−	26.5001i	0.629415	−	0.917623i
$835$	17.2417			0.596674
$836$	−3.39841	−	28.6999i	−0.117537	−	0.992607i
$837$	−2.81479			−0.0972932
$838$	23.0391	−	33.5886i	0.795871	−	1.16030i
$839$	−39.6524	−	12.8838i	−1.36895	−	0.444800i	−0.469931	−	0.882703i	$-0.655721\pi$
$839$	−39.6524	−	12.8838i	−1.36895	−	0.444800i	−0.899022	+	0.437904i	$0.855721\pi$
$840$	−17.1514	+	7.16019i	−0.591779	+	0.247050i
$841$	40.9205	−	29.7305i	1.41105	−	1.02519i
$842$	−3.54604	+	2.72619i	−0.122204	+	0.0939506i
$843$	−4.15231	−	12.7795i	−0.143013	−	0.440149i
$844$	13.0439	−	49.0433i	0.448989	−	1.68814i
$845$	−14.8643	−	10.7996i	−0.511348	−	0.371516i
$846$	−0.107504	−	3.96519i	−0.00369607	−	0.136326i
$847$	16.3036	+	34.4998i	0.560199	+	1.18543i
$848$	−24.8494	+	2.70481i	−0.853331	+	0.0928834i
$849$	−0.247544	+	0.340715i	−0.00849568	+	0.0116933i
$850$	−5.69812	−	1.68213i	−0.195444	−	0.0576964i
$851$	41.3760	−	13.4439i	1.41835	−	0.460851i
$852$	8.55815	−	6.95652i	0.293198	−	0.238327i
$853$	14.8390	+	20.4241i	0.508078	+	0.699309i	0.983594	−	0.180398i	$-0.0577385\pi$
$853$	14.8390	+	20.4241i	0.508078	+	0.699309i	−0.475516	+	0.879707i	$0.657738\pi$
$854$	35.9699	−	12.7751i	1.23086	−	0.437154i
$855$	−2.55038	+	7.84928i	−0.0872213	+	0.268440i
$856$	9.08228	+	5.53101i	0.310426	+	0.189046i
$857$		−	20.1558i		−	0.688510i	−0.938876	−	0.344255i	$-0.888132\pi$
$857$		−	20.1558i		−	0.688510i	0.938876	−	0.344255i	$-0.111868\pi$
$858$	−0.772326	−	8.48637i	−0.0263668	−	0.289720i
$859$		−	2.64305i		−	0.0901798i	−0.998983	−	0.0450899i	$-0.985643\pi$
$859$		−	2.64305i		−	0.0901798i	0.998983	−	0.0450899i	$-0.0143574\pi$
$860$	7.48101	+	4.83856i	0.255100	+	0.164994i
$861$	8.31642	−	25.5953i	0.283423	−	0.872285i
$862$	1.26540	+	3.56291i	0.0430998	+	0.121353i
$863$	−18.9266	−	26.0502i	−0.644267	−	0.886758i	0.354567	−	0.935031i	$-0.384628\pi$
$863$	−18.9266	−	26.0502i	−0.644267	−	0.886758i	−0.998834	+	0.0482726i	$0.984628\pi$
$864$	−3.91287	−	4.08528i	−0.133118	−	0.138984i
$865$	−29.5541	+	9.60272i	−1.00487	+	0.326502i
$866$	8.40240	−	28.4627i	0.285525	−	0.967203i
$867$	4.78679	−	6.58845i	0.162568	−	0.223755i
$868$	1.05814	+	19.4999i	0.0359155	+	0.661869i
$869$	9.52608	−	15.0380i	0.323150	−	0.510128i
$870$	23.8893	−	0.647687i	0.809925	−	0.0219586i
$871$	22.1627	+	16.1022i	0.750955	+	0.545601i
$872$	−3.94515	−	0.935570i	−0.133600	−	0.0316824i
$873$	2.56869	+	7.90561i	0.0869369	+	0.267564i
$874$	14.3587	+	18.6768i	0.485689	+	0.631751i
$875$	−34.0855	+	24.7646i	−1.15230	+	0.837196i
$876$	8.44240	+	21.8721i	0.285242	+	0.738990i
$877$	−32.3463	−	10.5100i	−1.09226	−	0.354896i	−0.293139	−	0.956070i	$-0.594700\pi$
$877$	−32.3463	−	10.5100i	−1.09226	−	0.354896i	−0.799118	+	0.601174i	$0.794700\pi$
$878$	−11.3744	−	7.80192i	−0.383867	−	0.263302i
$879$	−17.9330			−0.604866
$880$	−24.8773	−	3.55868i	−0.838614	−	0.119963i
$881$	−4.53963			−0.152944			−0.0764719	−	0.997072i	$-0.524366\pi$
$881$	−4.53963			−0.152944			−0.0764719	+	0.997072i	$0.524366\pi$
$882$	−5.87015	−	4.02645i	−0.197658	−	0.135578i
$883$	2.08769	+	0.678332i	0.0702564	+	0.0228277i	0.343934	−	0.938994i	$-0.388240\pi$
$883$	2.08769	+	0.678332i	0.0702564	+	0.0228277i	−0.273678	+	0.961821i	$0.588240\pi$
$884$	3.89380	+	10.0878i	0.130963	+	0.339291i
$885$	12.3857	−	8.99875i	0.416341	−	0.302490i
$886$	17.7637	+	23.1058i	0.596784	+	0.776256i
$887$	6.21007	+	19.1126i	0.208514	+	0.641739i	0.999551	+	0.0299709i	$0.00954145\pi$
$887$	6.21007	+	19.1126i	0.208514	+	0.641739i	−0.791037	+	0.611768i	$0.790459\pi$
$888$	31.3153	+	7.42624i	1.05087	+	0.249208i
$889$	14.4293	+	10.4835i	0.483944	+	0.351606i
$890$	13.9495	−	0.378199i	0.467589	−	0.0126773i
$891$	3.08272	−	1.22346i	0.103275	−	0.0409875i
$892$	2.19041	+	40.3659i	0.0733403	+	1.35155i
$893$	−7.18299	+	9.88654i	−0.240370	+	0.330840i
$894$	5.59962	−	18.9684i	0.187279	−	0.634400i
$895$	−0.973640	+	0.316355i	−0.0325452	+	0.0105746i
$896$	−26.8305	+	28.6427i	−0.896343	+	0.956887i
$897$	4.08292	+	5.61966i	0.136325	+	0.187635i
$898$	−18.9008	−	53.2176i	−0.630727	−	1.77589i
$899$	7.75945	−	23.8811i	0.258792	−	0.796480i
$900$	−2.37071	−	1.53333i	−0.0790237	−	0.0511109i
$901$			18.5968i			0.619548i
$902$	27.3796	−	23.9691i	0.911642	−	0.798083i
$903$			8.15769i			0.271471i
$904$	29.5386	+	17.9886i	0.982438	+	0.598293i
$905$	−2.94833	+	9.07401i	−0.0980057	+	0.301630i
$906$	−10.8485	+	3.85297i	−0.360419	+	0.128006i
$907$	25.2363	+	34.7347i	0.837957	+	1.15335i	0.986389	+	0.164426i	$0.0525771\pi$
$907$	25.2363	+	34.7347i	0.837957	+	1.15335i	−0.148433	+	0.988922i	$0.547423\pi$
$908$	−5.32984	+	4.33237i	−0.176877	+	0.143775i
$909$	11.6189	−	3.77520i	0.385373	−	0.125215i
$910$	16.1925	+	4.78013i	0.536775	+	0.158460i
$911$	13.7521	−	18.9282i	0.455628	−	0.627118i	−0.517967	−	0.855401i	$-0.673311\pi$
$911$	13.7521	−	18.9282i	0.455628	−	0.627118i	0.973595	+	0.228283i	$0.0733111\pi$
$912$	1.88582	+	17.3253i	0.0624458	+	0.573697i
$913$	−15.9734	−	19.2763i	−0.528643	−	0.637953i
$914$	−1.29182	−	47.6477i	−0.0427296	−	1.57604i
$915$	−11.9242	−	8.66342i	−0.394201	−	0.286404i
$916$	3.00921	−	11.3143i	0.0994272	−	0.373833i
$917$	3.73615	+	11.4987i	0.123379	+	0.379721i
$918$	−3.33655	+	2.56513i	−0.110123	+	0.0846620i
$919$	13.0131	−	9.45455i	0.429261	−	0.311877i	−0.352092	−	0.935965i	$-0.614530\pi$
$919$	13.0131	−	9.45455i	0.429261	−	0.311877i	0.781354	+	0.624089i	$0.214530\pi$
$920$	18.9041	−	7.89188i	0.623249	−	0.260188i
$921$	9.29814	+	3.02115i	0.306384	+	0.0995502i
$922$	−14.7743	+	21.5394i	−0.486564	+	0.709361i
$923$	−10.0185			−0.329762
$924$	−9.63458	−	20.8961i	−0.316954	−	0.687431i
$925$	16.0630			0.528150
$926$	−17.5844	+	25.6362i	−0.577858	+	0.842457i
$927$	13.0192	+	4.23019i	0.427606	+	0.138938i
$928$	45.4467	−	21.9357i	1.49186	−	0.720073i
$929$	−5.33225	+	3.87411i	−0.174945	+	0.127105i	−0.671812	−	0.740722i	$-0.734484\pi$
$929$	−5.33225	+	3.87411i	−0.174945	+	0.127105i	0.496867	+	0.867827i	$0.334484\pi$
$930$	5.97811	−	4.59596i	0.196030	−	0.150707i
$931$	6.77680	+	20.8569i	0.222101	+	0.683556i
$932$	−19.0883	−	5.07684i	−0.625257	−	0.166297i
$933$	−9.21352	−	6.69401i	−0.301637	−	0.219152i
$934$	1.40513	+	51.8268i	0.0459771	+	1.69582i
$935$	−4.63483	+	18.1132i	−0.151575	+	0.592364i
$936$	0.417391	+	5.12164i	0.0136429	+	0.167406i
$937$	6.99890	−	9.63316i	0.228644	−	0.314702i	−0.679245	−	0.733911i	$-0.737693\pi$
$937$	6.99890	−	9.63316i	0.228644	−	0.314702i	0.907889	+	0.419210i	$0.137693\pi$
$938$	70.9463	+	20.9439i	2.31648	+	0.683841i
$939$	−12.6972	+	4.12558i	−0.414358	+	0.134633i
$940$	6.70266	+	8.24584i	0.218617	+	0.268950i
$941$	−6.88516	−	9.47660i	−0.224450	−	0.308928i	0.681909	−	0.731437i	$-0.261150\pi$
$941$	−6.88516	−	9.47660i	−0.224450	−	0.308928i	−0.906359	+	0.422508i	$0.861150\pi$
$942$	−24.7280	+	8.78239i	−0.805680	+	0.286146i
$943$	−9.16626	+	28.2109i	−0.298495	+	0.918672i
$944$	16.0602	−	28.0564i	0.522716	−	0.913160i
$945$			6.57114i			0.213759i
$946$	−5.64793	+	9.47451i	−0.183630	+	0.308043i
$947$			34.4025i			1.11793i	0.829191	+	0.558966i	$0.188802\pi$
$947$			34.4025i			1.11793i	−0.829191	+	0.558966i	$0.811198\pi$
$948$	−5.82980	+	9.01359i	−0.189343	+	0.292748i
$949$	6.58116	−	20.2547i	0.213634	−	0.657496i
$950$	2.91110	+	8.19658i	0.0944486	+	0.265932i
$951$	6.91109	+	9.51230i	0.224107	+	0.308457i
$952$	19.0246	+	22.1502i	0.616592	+	0.717891i
$953$	19.7117	−	6.40471i	0.638523	−	0.207469i	0.0281762	−	0.999603i	$-0.491030\pi$
$953$	19.7117	−	6.40471i	0.638523	−	0.207469i	0.610347	+	0.792134i	$0.291030\pi$
$954$	−2.50213	+	8.47586i	−0.0810096	+	0.274416i
$955$	3.26490	−	4.49375i	0.105650	−	0.145414i
$956$	−39.1514	+	2.12451i	−1.26625	+	0.0687114i
$957$	1.88201	+	29.5270i	0.0608368	+	0.954472i
$958$	33.4138	−	0.905912i	1.07955	−	0.0292687i
$959$	9.47485	+	6.88388i	0.305959	+	0.222292i
$960$	14.9806	+	2.28751i	0.483498	+	0.0738292i
$961$	7.13118	+	21.9475i	0.230038	+	0.707984i
$962$	−17.8188	−	23.1775i	−0.574501	−	0.747272i
$963$	3.04162	−	2.20987i	0.0980149	−	0.0712120i
$964$	22.7490	−	8.78087i	0.732697	−	0.282813i
$965$	−19.9766	−	6.49078i	−0.643068	−	0.208946i
$966$	15.4679	+	10.6097i	0.497670	+	0.341362i
$967$	−55.9913			−1.80056			−0.900280	−	0.435312i	$-0.856638\pi$
$967$	−55.9913			−1.80056			−0.900280	+	0.435312i	$0.856638\pi$
$968$	3.27749	−	30.9396i	0.105342	−	0.994436i
$969$	12.9659			0.416524
$970$	−18.3637	−	12.5960i	−0.589621	−	0.404433i
$971$	48.0716	+	15.6194i	1.54269	+	0.501251i	0.952118	−	0.305732i	$-0.0989010\pi$
$971$	48.0716	+	15.6194i	1.54269	+	0.501251i	0.590575	+	0.806983i	$0.298901\pi$
$972$	−1.86583	+	0.720190i	−0.0598466	+	0.0231001i
$973$	−63.7698	+	46.3315i	−2.04437	+	1.48532i
$974$	31.8034	+	41.3677i	1.01905	+	1.32551i
$975$	0.792538	+	2.43918i	0.0253815	+	0.0781163i
$976$	−30.4669	−	6.35816i	−0.975221	−	0.203520i
$977$	17.4903	+	12.7074i	0.559563	+	0.406546i	0.831299	−	0.555826i	$-0.187598\pi$
$977$	17.4903	+	12.7074i	0.559563	+	0.406546i	−0.271736	+	0.962372i	$0.587598\pi$
$978$	0.901081	−	0.0244301i	0.0288134	−	0.000781188i
$979$	1.09895	+	17.2415i	0.0351225	+	0.551040i
$980$	19.0415	−	1.03327i	0.608260	−	0.0330065i
$981$	−0.842592	+	1.15973i	−0.0269019	+	0.0370273i
$982$	7.45864	−	25.2658i	0.238015	−	0.806264i
$983$	−1.27749	+	0.415082i	−0.0407456	+	0.0132391i	−0.329319	−	0.944219i	$-0.606819\pi$
$983$	−1.27749	+	0.415082i	−0.0407456	+	0.0132391i	0.288573	+	0.957458i	$0.406819\pi$
$984$	−16.6463	+	14.2974i	−0.530664	+	0.455783i
$985$	6.65498	+	9.15979i	0.212045	+	0.291855i
$986$	−12.5653	−	35.3791i	−0.400159	−	1.12670i
$987$	−3.00667	+	9.25359i	−0.0957034	+	0.294545i
$988$	8.59761	−	13.2930i	0.273527	−	0.422905i
$989$		−	8.99132i		−	0.285907i
$990$	−4.54949	+	7.63185i	−0.144592	+	0.242556i
$991$			18.7949i			0.597039i	0.954404	+	0.298520i	$0.0964928\pi$
$991$			18.7949i			0.597039i	−0.954404	+	0.298520i	$0.903507\pi$
$992$	7.53289	−	14.0283i	0.239170	−	0.445398i
$993$	0.0337881	−	0.103989i	0.00107223	−	0.00330000i
$994$	−25.4926	+	9.05395i	−0.808575	+	0.287174i
$995$	−3.04313	−	4.18851i	−0.0964737	−	0.132785i
$996$	9.52216	+	11.7145i	0.301721	+	0.371188i
$997$	−14.1935	+	4.61173i	−0.449511	+	0.146055i	−0.525020	−	0.851090i	$-0.675942\pi$
$997$	−14.1935	+	4.61173i	−0.449511	+	0.146055i	0.0755083	+	0.997145i	$0.475942\pi$
$998$	−46.5118	−	13.7306i	−1.47230	−	0.434635i
$999$	6.68822	−	9.20554i	0.211606	−	0.291250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.j.a.7.11	yes	48
3.2	odd	2		396.2.r.b.271.2		48
4.3	odd	2	inner	132.2.j.a.7.3	✓	48
11.8	odd	10	inner	132.2.j.a.19.3	yes	48
12.11	even	2		396.2.r.b.271.10		48
33.8	even	10		396.2.r.b.19.10		48
44.19	even	10	inner	132.2.j.a.19.11	yes	48
132.107	odd	10		396.2.r.b.19.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.7.3	✓	48	4.3	odd	2	inner
132.2.j.a.7.11	yes	48	1.1	even	1	trivial
132.2.j.a.19.3	yes	48	11.8	odd	10	inner
132.2.j.a.19.11	yes	48	44.19	even	10	inner
396.2.r.b.19.2		48	132.107	odd	10
396.2.r.b.19.10		48	33.8	even	10
396.2.r.b.271.2		48	3.2	odd	2
396.2.r.b.271.10		48	12.11	even	2

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)

\(f(q)\)	\(=\)	\(q+(1.16623 + 0.799941i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.720190 + 1.86583i) q^{4} +(-1.53251 + 1.11343i) q^{5} +(0.861957 + 1.12117i) q^{6} +(-1.07196 - 3.29914i) q^{7} +(-0.652646 + 2.75210i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.16623 + 0.799941i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.720190 + 1.86583i) q^{4} +(-1.53251 + 1.11343i) q^{5} +(0.861957 + 1.12117i) q^{6} +(-1.07196 - 3.29914i) q^{7} +(-0.652646 + 2.75210i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-2.67794 + 0.0726042i) q^{10} +(-0.210969 - 3.30991i) q^{11} +(0.108368 + 1.99706i) q^{12} +(1.06787 - 1.46980i) q^{13} +(1.38897 - 4.70507i) q^{14} +(-1.80157 + 0.585367i) q^{15} +(-2.96265 + 2.68751i) q^{16} +(1.74921 + 2.40759i) q^{17} +(0.473308 + 1.33266i) q^{18} +(1.34636 - 4.14366i) q^{19} +(-3.18118 - 2.05752i) q^{20} -3.46892i q^{21} +(2.40169 - 4.02888i) q^{22} +3.82341i q^{23} +(-1.47115 + 2.41572i) q^{24} +(-0.436233 + 1.34259i) q^{25} +(2.42114 - 0.859894i) q^{26} +(0.587785 + 0.809017i) q^{27} +(5.38363 - 4.37610i) q^{28} +(-8.48417 + 2.75668i) q^{29} +(-2.56931 - 0.758479i) q^{30} +(-1.65449 + 2.27721i) q^{31} +(-5.60498 + 0.764309i) q^{32} +(0.822174 - 3.21310i) q^{33} +(0.114062 + 4.20707i) q^{34} +(5.31616 + 3.86242i) q^{35} +(-0.514062 + 1.93281i) q^{36} +(-3.51620 - 10.8218i) q^{37} +(4.88484 - 3.75546i) q^{38} +(1.46980 - 1.06787i) q^{39} +(-2.06409 - 4.94430i) q^{40} +(7.37845 + 2.39740i) q^{41} +(2.77493 - 4.04557i) q^{42} -2.35165 q^{43} +(6.02379 - 2.77740i) q^{44} -1.89429 q^{45} +(-3.05850 + 4.45898i) q^{46} +(-2.66757 - 0.866745i) q^{47} +(-3.64813 + 1.64046i) q^{48} +(-4.07214 + 2.95858i) q^{49} +(-1.58274 + 1.21681i) q^{50} +(0.919617 + 2.83029i) q^{51} +(3.51148 + 0.933936i) q^{52} +(5.05557 + 3.67309i) q^{53} +(0.0383280 + 1.41369i) q^{54} +(4.00867 + 4.83757i) q^{55} +(9.77918 - 0.796961i) q^{56} +(2.56092 - 3.52481i) q^{57} +(-12.0997 - 3.57191i) q^{58} +(-7.68642 + 2.49747i) q^{59} +(-2.38967 - 2.93986i) q^{60} +(4.57345 + 6.29481i) q^{61} +(-3.75115 + 1.33226i) q^{62} +(1.07196 - 3.29914i) q^{63} +(-7.14811 - 3.59229i) q^{64} +3.44150i q^{65} +(3.52914 - 3.08953i) q^{66} +15.0787i q^{67} +(-3.23238 + 4.99766i) q^{68} +(-1.18150 + 3.63628i) q^{69} +(3.11017 + 8.75708i) q^{70} +(-3.24129 - 4.46126i) q^{71} +(-2.14565 + 1.84288i) q^{72} +(11.1487 - 3.62244i) q^{73} +(4.55606 - 15.4334i) q^{74} +(-0.829764 + 1.14207i) q^{75} +(8.70100 - 0.472149i) q^{76} +(-10.6937 + 4.24410i) q^{77} +(2.56837 - 0.0696334i) q^{78} +(4.34223 + 3.15482i) q^{79} +(1.54793 - 7.41735i) q^{80} +(0.309017 + 0.951057i) q^{81} +(6.68720 + 8.69825i) q^{82} +(6.10662 - 4.43672i) q^{83} +(6.47243 - 2.49829i) q^{84} +(-5.36138 - 1.74202i) q^{85} +(-2.74257 - 1.88118i) q^{86} -8.92079 q^{87} +(9.24689 + 1.57959i) q^{88} -5.20905 q^{89} +(-2.20918 - 1.51532i) q^{90} +(-5.99381 - 1.94751i) q^{91} +(-7.13384 + 2.75358i) q^{92} +(-2.27721 + 1.65449i) q^{93} +(-2.41765 - 3.14472i) q^{94} +(2.55038 + 7.84928i) q^{95} +(-5.56684 - 1.00513i) q^{96} +(6.72491 + 4.88593i) q^{97} +(-7.11574 + 0.192922i) q^{98} +(1.77484 - 2.80178i) 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

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