LMFDB - Embedded newform 133.2.i.c.122.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(12,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("133.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.i (of order $6$, degree $2$, 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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			122.1
Root			$-0.895644 - 1.09445i$ of defining polynomial
Character	$\chi$	$=$	133.122
Dual form			133.2.i.c.12.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18890i q^{2} +(1.39564 + 2.41733i) q^{3} -2.79129 q^{4} +3.92095i q^{5} +(5.29129 - 3.05493i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.73205i q^{8} +(-2.39564 + 4.14938i) q^{9} +O(q^{10})$	\(q-2.18890i q^{2} +(1.39564 + 2.41733i) q^{3} -2.79129 q^{4} +3.92095i q^{5} +(5.29129 - 3.05493i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.73205i q^{8} +(-2.39564 + 4.14938i) q^{9} +8.58258 q^{10} +(1.50000 - 2.59808i) q^{11} +(-3.89564 - 6.74745i) q^{12} +(-0.395644 - 0.685275i) q^{13} +(-5.68693 - 1.09445i) q^{14} +(-9.47822 + 5.47225i) q^{15} -1.79129 q^{16} +(0.791288 - 0.456850i) q^{17} +(9.08258 + 5.24383i) q^{18} +(-4.00000 - 1.73205i) q^{19} -10.9445i q^{20} +(6.97822 - 2.41733i) q^{21} +(-5.68693 - 3.28335i) q^{22} +(0.791288 - 1.37055i) q^{23} +(-4.18693 + 2.41733i) q^{24} -10.3739 q^{25} +(-1.50000 + 0.866025i) q^{26} -5.00000 q^{27} +(-1.39564 + 7.25198i) q^{28} +(6.08258 - 3.51178i) q^{29} +(11.9782 + 20.7469i) q^{30} +7.38505i q^{32} +8.37386 q^{33} +(-1.00000 - 1.73205i) q^{34} +(10.1869 + 1.96048i) q^{35} +(6.68693 - 11.5821i) q^{36} +(-1.81307 + 1.04678i) q^{37} +(-3.79129 + 8.75560i) q^{38} +(1.10436 - 1.91280i) q^{39} -6.79129 q^{40} +(-4.18693 + 7.25198i) q^{41} +(-5.29129 - 15.2746i) q^{42} +(1.10436 - 1.91280i) q^{43} +(-4.18693 + 7.25198i) q^{44} +(-16.2695 - 9.39320i) q^{45} +(-3.00000 - 1.73205i) q^{46} +(0.708712 + 0.409175i) q^{47} +(-2.50000 - 4.33013i) q^{48} +(-6.50000 - 2.59808i) q^{49} +22.7074i q^{50} +(2.20871 + 1.27520i) q^{51} +(1.10436 + 1.91280i) q^{52} -3.92095i q^{53} +10.9445i q^{54} +(10.1869 + 5.88143i) q^{55} +(4.50000 + 0.866025i) q^{56} +(-1.39564 - 12.0866i) q^{57} +(-7.68693 - 13.3142i) q^{58} +(2.60436 + 4.51088i) q^{59} +(26.4564 - 15.2746i) q^{60} +(-5.68693 - 3.28335i) q^{61} +(9.58258 + 8.29875i) q^{63} +12.5826 q^{64} +(2.68693 - 1.55130i) q^{65} -18.3296i q^{66} +3.46410i q^{67} +(-2.20871 + 1.27520i) q^{68} +4.41742 q^{69} +(4.29129 - 22.2982i) q^{70} +(6.08258 + 3.51178i) q^{71} +(-7.18693 - 4.14938i) q^{72} +(-8.37386 + 4.83465i) q^{73} +(2.29129 + 3.96863i) q^{74} +(-14.4782 - 25.0770i) q^{75} +(11.1652 + 4.83465i) q^{76} +(-6.00000 - 5.19615i) q^{77} +(-4.18693 - 2.41733i) q^{78} -6.92820i q^{79} -7.02355i q^{80} +(0.208712 + 0.361500i) q^{81} +(15.8739 + 9.16478i) q^{82} +4.93000i q^{83} +(-19.4782 + 6.74745i) q^{84} +(1.79129 + 3.10260i) q^{85} +(-4.18693 - 2.41733i) q^{86} +(16.9782 + 9.80238i) q^{87} +(4.50000 + 2.59808i) q^{88} +(-5.68693 + 9.85005i) q^{89} +(-20.5608 + 35.6123i) q^{90} +(-1.97822 + 0.685275i) q^{91} +(-2.20871 + 3.82560i) q^{92} +(0.895644 - 1.55130i) q^{94} +(6.79129 - 15.6838i) q^{95} +(-17.8521 + 10.3069i) q^{96} +(1.00000 - 1.73205i) q^{97} +(-5.68693 + 14.2279i) q^{98} +(7.18693 + 12.4481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 2 q^{4} + 12 q^{6} + 2 q^{7} - 5 q^{9}+O(q^{10}) $ 4 * q + q^3 - 2 * q^4 + 12 * q^6 + 2 * q^7 - 5 * q^9	$ 4 q + q^{3} - 2 q^{4} + 12 q^{6} + 2 q^{7} - 5 q^{9} + 16 q^{10} + 6 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} + 2 q^{16} - 6 q^{17} + 18 q^{18} - 16 q^{19} + 5 q^{21} - 9 q^{22} - 6 q^{23} - 3 q^{24} - 14 q^{25} - 6 q^{26} - 20 q^{27} - q^{28} + 6 q^{29} + 25 q^{30} + 6 q^{33} - 4 q^{34} + 27 q^{35} + 13 q^{36} - 21 q^{37} - 6 q^{38} + 9 q^{39} - 18 q^{40} - 3 q^{41} - 12 q^{42} + 9 q^{43} - 3 q^{44} - 33 q^{45} - 12 q^{46} + 12 q^{47} - 10 q^{48} - 26 q^{49} + 18 q^{51} + 9 q^{52} + 27 q^{55} + 18 q^{56} - q^{57} - 17 q^{58} + 15 q^{59} + 60 q^{60} - 9 q^{61} + 20 q^{63} + 32 q^{64} - 3 q^{65} - 18 q^{68} + 36 q^{69} + 8 q^{70} + 6 q^{71} - 15 q^{72} - 6 q^{73} - 35 q^{75} + 8 q^{76} - 24 q^{77} - 3 q^{78} + 10 q^{81} + 36 q^{82} - 55 q^{84} - 2 q^{85} - 3 q^{86} + 45 q^{87} + 18 q^{88} - 9 q^{89} - 41 q^{90} + 15 q^{91} - 18 q^{92} - q^{94} + 18 q^{95} - 21 q^{96} + 4 q^{97} - 9 q^{98} + 15 q^{99}+O(q^{100}) $ 4 * q + q^3 - 2 * q^4 + 12 * q^6 + 2 * q^7 - 5 * q^9 + 16 * q^10 + 6 * q^11 - 11 * q^12 + 3 * q^13 - 9 * q^14 - 15 * q^15 + 2 * q^16 - 6 * q^17 + 18 * q^18 - 16 * q^19 + 5 * q^21 - 9 * q^22 - 6 * q^23 - 3 * q^24 - 14 * q^25 - 6 * q^26 - 20 * q^27 - q^28 + 6 * q^29 + 25 * q^30 + 6 * q^33 - 4 * q^34 + 27 * q^35 + 13 * q^36 - 21 * q^37 - 6 * q^38 + 9 * q^39 - 18 * q^40 - 3 * q^41 - 12 * q^42 + 9 * q^43 - 3 * q^44 - 33 * q^45 - 12 * q^46 + 12 * q^47 - 10 * q^48 - 26 * q^49 + 18 * q^51 + 9 * q^52 + 27 * q^55 + 18 * q^56 - q^57 - 17 * q^58 + 15 * q^59 + 60 * q^60 - 9 * q^61 + 20 * q^63 + 32 * q^64 - 3 * q^65 - 18 * q^68 + 36 * q^69 + 8 * q^70 + 6 * q^71 - 15 * q^72 - 6 * q^73 - 35 * q^75 + 8 * q^76 - 24 * q^77 - 3 * q^78 + 10 * q^81 + 36 * q^82 - 55 * q^84 - 2 * q^85 - 3 * q^86 + 45 * q^87 + 18 * q^88 - 9 * q^89 - 41 * q^90 + 15 * q^91 - 18 * q^92 - q^94 + 18 * q^95 - 21 * q^96 + 4 * q^97 - 9 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	2.18890i		−	1.54779i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$		−	2.18890i		−	1.54779i	0.633316	−	0.773893i	$-0.281693\pi$
$3$	1.39564	+	2.41733i	0.805775	+	1.39564i	0.915766	+	0.401711i	$0.131584\pi$
$3$	1.39564	+	2.41733i	0.805775	+	1.39564i	−0.109991	+	0.993933i	$0.535082\pi$
$4$	−2.79129			−1.39564
$5$			3.92095i			1.75350i	0.480944	+	0.876751i	$0.340294\pi$
$5$			3.92095i			1.75350i	−0.480944	+	0.876751i	$0.659706\pi$
$6$	5.29129	−	3.05493i	2.16016	−	1.24717i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$			1.73205i			0.612372i
$9$	−2.39564	+	4.14938i	−0.798548	+	1.38313i
$10$	8.58258			2.71405
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	−3.89564	−	6.74745i	−1.12458	−	1.94782i
$13$	−0.395644	−	0.685275i	−0.109732	−	0.190061i	0.805930	−	0.592011i	$-0.201666\pi$
$13$	−0.395644	−	0.685275i	−0.109732	−	0.190061i	−0.915662	+	0.401950i	$0.868333\pi$
$14$	−5.68693	−	1.09445i	−1.51990	−	0.292504i
$15$	−9.47822	+	5.47225i	−2.44727	+	1.41293i
$16$	−1.79129			−0.447822
$17$	0.791288	−	0.456850i	0.191915	−	0.110802i	−0.400963	−	0.916094i	$-0.631325\pi$
$17$	0.791288	−	0.456850i	0.191915	−	0.110802i	0.592879	+	0.805292i	$0.297991\pi$
$18$	9.08258	+	5.24383i	2.14078	+	1.23598i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$20$		−	10.9445i		−	2.44727i
$21$	6.97822	−	2.41733i	1.52277	−	0.527504i
$22$	−5.68693	−	3.28335i	−1.21246	−	0.700013i
$23$	0.791288	−	1.37055i	0.164995	−	0.285780i	−0.771659	−	0.636037i	$-0.780573\pi$
$23$	0.791288	−	1.37055i	0.164995	−	0.285780i	0.936653	+	0.350257i	$0.113906\pi$
$24$	−4.18693	+	2.41733i	−0.854654	+	0.493435i
$25$	−10.3739			−2.07477
$26$	−1.50000	+	0.866025i	−0.294174	+	0.169842i
$27$	−5.00000			−0.962250
$28$	−1.39564	+	7.25198i	−0.263752	+	1.37050i
$29$	6.08258	−	3.51178i	1.12951	−	0.652121i	0.185695	−	0.982607i	$-0.440546\pi$
$29$	6.08258	−	3.51178i	1.12951	−	0.652121i	0.943811	+	0.330487i	$0.107213\pi$
$30$	11.9782	+	20.7469i	2.18691	+	3.78785i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$			7.38505i			1.30551i
$33$	8.37386			1.45770
$34$	−1.00000	−	1.73205i	−0.171499	−	0.297044i
$35$	10.1869	+	1.96048i	1.72191	+	0.331381i
$36$	6.68693	−	11.5821i	1.11449	−	1.93035i
$37$	−1.81307	+	1.04678i	−0.298067	+	0.172089i	−0.641574	−	0.767061i	$-0.721718\pi$
$37$	−1.81307	+	1.04678i	−0.298067	+	0.172089i	0.343507	+	0.939150i	$0.388385\pi$
$38$	−3.79129	+	8.75560i	−0.615028	+	1.42035i
$39$	1.10436	−	1.91280i	0.176838	−	0.306293i
$40$	−6.79129			−1.07380
$41$	−4.18693	+	7.25198i	−0.653889	+	1.13257i	0.328282	+	0.944580i	$0.393530\pi$
$41$	−4.18693	+	7.25198i	−0.653889	+	1.13257i	−0.982171	+	0.187989i	$0.939803\pi$
$42$	−5.29129	−	15.2746i	−0.816463	−	2.35693i
$43$	1.10436	−	1.91280i	0.168413	−	0.291699i	−0.769449	−	0.638708i	$-0.779469\pi$
$43$	1.10436	−	1.91280i	0.168413	−	0.291699i	0.937862	+	0.347009i	$0.112803\pi$
$44$	−4.18693	+	7.25198i	−0.631204	+	1.09328i
$45$	−16.2695	−	9.39320i	−2.42531	−	1.40026i
$46$	−3.00000	−	1.73205i	−0.442326	−	0.255377i
$47$	0.708712	+	0.409175i	0.103376	+	0.0596843i	0.550797	−	0.834639i	$-0.314324\pi$
$47$	0.708712	+	0.409175i	0.103376	+	0.0596843i	−0.447421	+	0.894324i	$0.647657\pi$
$48$	−2.50000	−	4.33013i	−0.360844	−	0.625000i
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$			22.7074i			3.21131i
$51$	2.20871	+	1.27520i	0.309282	+	0.178564i
$52$	1.10436	+	1.91280i	0.153147	+	0.265258i
$53$		−	3.92095i		−	0.538584i	−0.963059	−	0.269292i	$-0.913210\pi$
$53$		−	3.92095i		−	0.538584i	0.963059	−	0.269292i	$-0.0867897\pi$
$54$			10.9445i			1.48936i
$55$	10.1869	+	5.88143i	1.37361	+	0.793052i
$56$	4.50000	+	0.866025i	0.601338	+	0.115728i
$57$	−1.39564	−	12.0866i	−0.184858	−	1.60091i
$58$	−7.68693	−	13.3142i	−1.00934	−	1.74823i
$59$	2.60436	+	4.51088i	0.339058	+	0.587266i	0.984256	−	0.176750i	$-0.0565583\pi$
$59$	2.60436	+	4.51088i	0.339058	+	0.587266i	−0.645198	+	0.764016i	$0.723225\pi$
$60$	26.4564	−	15.2746i	3.41551	−	1.97195i
$61$	−5.68693	−	3.28335i	−0.728137	−	0.420390i	0.0896032	−	0.995978i	$-0.471440\pi$
$61$	−5.68693	−	3.28335i	−0.728137	−	0.420390i	−0.817740	+	0.575587i	$0.804773\pi$
$62$		0			0
$63$	9.58258	+	8.29875i	1.20729	+	1.04554i
$64$	12.5826			1.57282
$65$	2.68693	−	1.55130i	0.333273	−	0.192415i
$66$		−	18.3296i		−	2.25621i
$67$			3.46410i			0.423207i	0.977356	+	0.211604i	$0.0678686\pi$
$67$			3.46410i			0.423207i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−2.20871	+	1.27520i	−0.267846	+	0.154641i
$69$	4.41742			0.531795
$70$	4.29129	−	22.2982i	0.512907	−	2.66514i
$71$	6.08258	+	3.51178i	0.721869	+	0.416771i	0.815440	−	0.578841i	$-0.196495\pi$
$71$	6.08258	+	3.51178i	0.721869	+	0.416771i	−0.0935712	+	0.995613i	$0.529828\pi$
$72$	−7.18693	−	4.14938i	−0.846988	−	0.489009i
$73$	−8.37386	+	4.83465i	−0.980087	+	0.565853i	−0.902296	−	0.431116i	$-0.858120\pi$
$73$	−8.37386	+	4.83465i	−0.980087	+	0.565853i	−0.0777903	+	0.996970i	$0.524786\pi$
$74$	2.29129	+	3.96863i	0.266357	+	0.461344i
$75$	−14.4782	−	25.0770i	−1.67180	−	2.89564i
$76$	11.1652	+	4.83465i	1.28073	+	0.554573i
$77$	−6.00000	−	5.19615i	−0.683763	−	0.592157i
$78$	−4.18693	−	2.41733i	−0.474077	−	0.273708i
$79$		−	6.92820i		−	0.779484i	−0.920924	−	0.389742i	$-0.872564\pi$
$79$		−	6.92820i		−	0.779484i	0.920924	−	0.389742i	$-0.127436\pi$
$80$		−	7.02355i		−	0.785257i
$81$	0.208712	+	0.361500i	0.0231902	+	0.0401667i
$82$	15.8739	+	9.16478i	1.75297	+	1.01208i
$83$			4.93000i			0.541138i	0.962701	+	0.270569i	$0.0872118\pi$
$83$			4.93000i			0.541138i	−0.962701	+	0.270569i	$0.912788\pi$
$84$	−19.4782	+	6.74745i	−2.12525	+	0.736208i
$85$	1.79129	+	3.10260i	0.194292	+	0.336524i
$86$	−4.18693	−	2.41733i	−0.451488	−	0.260667i
$87$	16.9782	+	9.80238i	1.82026	+	1.05093i
$88$	4.50000	+	2.59808i	0.479702	+	0.276956i
$89$	−5.68693	+	9.85005i	−0.602814	+	1.04410i	0.389579	+	0.920993i	$0.372620\pi$
$89$	−5.68693	+	9.85005i	−0.602814	+	1.04410i	−0.992393	+	0.123111i	$0.960713\pi$
$90$	−20.5608	+	35.6123i	−2.16730	+	3.75387i
$91$	−1.97822	+	0.685275i	−0.207374	+	0.0718364i
$92$	−2.20871	+	3.82560i	−0.230274	+	0.398847i
$93$		0			0
$94$	0.895644	−	1.55130i	0.0923786	−	0.160004i
$95$	6.79129	−	15.6838i	0.696771	−	1.60912i
$96$	−17.8521	+	10.3069i	−1.82202	+	1.05194i
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	−5.68693	+	14.2279i	−0.574467	+	1.43723i
$99$	7.18693	+	12.4481i	0.722314	+	1.25108i
$100$	28.9564			2.89564
$101$		−	19.1479i		−	1.90529i	−0.304088	−	0.952644i	$-0.598352\pi$
$101$		−	19.1479i		−	1.90529i	0.304088	−	0.952644i	$-0.401648\pi$
$102$	2.79129	−	4.83465i	0.276379	−	0.478702i
$103$	5.18693	+	8.98403i	0.511084	+	0.885223i	0.999917	+	0.0128458i	$0.00408907\pi$
$103$	5.18693	+	8.98403i	0.511084	+	0.885223i	−0.488834	+	0.872377i	$0.662578\pi$
$104$	1.18693	−	0.685275i	0.116388	−	0.0671968i
$105$	9.47822	+	27.3613i	0.924980	+	2.67019i
$106$	−8.58258			−0.833613
$107$	−12.7913	+	7.38505i	−1.23658	+	0.713940i	−0.968394	−	0.249427i	$-0.919758\pi$
$107$	−12.7913	+	7.38505i	−1.23658	+	0.713940i	−0.268187	+	0.963367i	$0.586424\pi$
$108$	13.9564			1.34296
$109$	−4.81307	+	2.77883i	−0.461008	+	0.266163i	−0.712468	−	0.701704i	$-0.752423\pi$
$109$	−4.81307	+	2.77883i	−0.461008	+	0.266163i	0.251460	+	0.967868i	$0.419089\pi$
$110$	12.8739	−	22.2982i	1.22747	−	2.12605i
$111$	−5.06080	−	2.92185i	−0.480349	−	0.277330i
$112$	−0.895644	+	4.65390i	−0.0846304	+	0.439752i
$113$			13.2288i			1.24446i	0.782836	+	0.622228i	$0.213772\pi$
$113$			13.2288i			1.24446i	−0.782836	+	0.622228i	$0.786228\pi$
$114$	−26.4564	+	3.05493i	−2.47787	+	0.286120i
$115$	5.37386	+	3.10260i	0.501115	+	0.289319i
$116$	−16.9782	+	9.80238i	−1.57639	+	0.910128i
$117$	3.79129			0.350505
$118$	9.87386	−	5.70068i	0.908963	−	0.524790i
$119$	−0.791288	−	2.28425i	−0.0725372	−	0.209397i
$120$	−9.47822	−	16.4168i	−0.865239	−	1.49864i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−7.18693	+	12.4481i	−0.650674	+	1.12700i
$123$	−23.3739			−2.10755
$124$		0			0
$125$		−	21.0707i		−	1.88462i
$126$	18.1652	−	20.9753i	1.61828	−	1.86863i
$127$	3.31307	−	1.91280i	0.293987	−	0.169734i	−0.345751	−	0.938326i	$-0.612376\pi$
$127$	3.31307	−	1.91280i	0.293987	−	0.169734i	0.639739	+	0.768593i	$0.279043\pi$
$128$		−	12.7719i		−	1.12889i
$129$	6.16515			0.542811
$130$	−3.39564	−	5.88143i	−0.297818	−	0.515835i
$131$		−	14.0471i		−	1.22730i	−0.789578	−	0.613651i	$-0.789700\pi$
$131$		−	14.0471i		−	1.22730i	0.789578	−	0.613651i	$-0.210300\pi$
$132$	−23.3739			−2.03443
$133$	−6.50000	+	9.52628i	−0.563621	+	0.826033i
$134$	7.58258			0.655035
$135$		−	19.6048i		−	1.68731i
$136$	0.791288	+	1.37055i	0.0678524	+	0.117524i
$137$	12.9564			1.10694			0.553472	−	0.832868i	$-0.313303\pi$
$137$	12.9564			1.10694			0.553472	+	0.832868i	$0.313303\pi$
$138$		−	9.66930i		−	0.823106i
$139$	18.2477	−	10.5353i	1.54775	−	0.893595i	0.549439	−	0.835534i	$-0.314841\pi$
$139$	18.2477	−	10.5353i	1.54775	−	0.893595i	0.998313	−	0.0580612i	$-0.0184919\pi$
$140$	−28.4347	−	5.47225i	−2.40317	−	0.462490i
$141$			2.28425i			0.192369i
$142$	7.68693	−	13.3142i	0.645073	−	1.11730i
$143$	−2.37386			−0.198512
$144$	4.29129	−	7.43273i	0.357607	−	0.619394i
$145$	13.7695	+	23.8495i	1.14350	+	1.98059i
$146$	10.5826	+	18.3296i	0.875820	+	1.51697i
$147$	−2.79129	−	19.3386i	−0.230222	−	1.59502i
$148$	5.06080	−	2.92185i	0.415995	−	0.240175i
$149$	15.7913			1.29367			0.646836	−	0.762629i	$-0.276092\pi$
$149$	15.7913			1.29367			0.646836	+	0.762629i	$0.276092\pi$
$150$	−54.8911	+	31.6914i	−4.48184	+	2.58759i
$151$	−5.06080	−	2.92185i	−0.411842	−	0.237777i	0.279739	−	0.960076i	$-0.409752\pi$
$151$	−5.06080	−	2.92185i	−0.411842	−	0.237777i	−0.691581	+	0.722299i	$0.743085\pi$
$152$	3.00000	−	6.92820i	0.243332	−	0.561951i
$153$			4.37780i			0.353924i
$154$	−11.3739	+	13.1334i	−0.916532	+	1.05832i
$155$		0			0
$156$	−3.08258	+	5.33918i	−0.246804	+	0.427476i
$157$	−3.31307	+	1.91280i	−0.264412	+	0.152658i	−0.626345	−	0.779546i	$-0.715450\pi$
$157$	−3.31307	+	1.91280i	−0.264412	+	0.152658i	0.361934	+	0.932204i	$0.382117\pi$
$158$	−15.1652			−1.20647
$159$	9.47822	−	5.47225i	0.751672	−	0.433978i
$160$	−28.9564			−2.28921
$161$	−3.16515	−	2.74110i	−0.249449	−	0.216029i
$162$	0.791288	−	0.456850i	0.0621694	−	0.0358935i
$163$	3.00000	+	5.19615i	0.234978	+	0.406994i	0.959266	−	0.282503i	$-0.0911648\pi$
$163$	3.00000	+	5.19615i	0.234978	+	0.406994i	−0.724288	+	0.689497i	$0.757831\pi$
$164$	11.6869	−	20.2424i	0.912596	−	1.58066i
$165$			32.8335i			2.55609i
$166$	10.7913			0.837566
$167$	11.0608	+	19.1579i	0.855910	+	1.48248i	0.875798	+	0.482677i	$0.160336\pi$
$167$	11.0608	+	19.1579i	0.855910	+	1.48248i	−0.0198882	+	0.999802i	$0.506331\pi$
$168$	4.18693	+	12.0866i	0.323029	+	0.932504i
$169$	6.18693	−	10.7161i	0.475918	−	0.824314i
$170$	6.79129	−	3.92095i	0.520868	−	0.300723i
$171$	16.7695	−	12.4481i	1.28240	−	0.951932i
$172$	−3.08258	+	5.33918i	−0.235044	+	0.407108i
$173$	−7.74773			−0.589049			−0.294524	−	0.955644i	$-0.595161\pi$
$173$	−7.74773			−0.589049			−0.294524	+	0.955644i	$0.595161\pi$
$174$	21.4564	−	37.1636i	1.62661	−	2.81737i
$175$	−5.18693	+	26.9521i	−0.392095	+	2.03739i
$176$	−2.68693	+	4.65390i	−0.202535	+	0.350801i
$177$	−7.26951	+	12.5912i	−0.546410	+	0.946409i
$178$	21.5608	+	12.4481i	1.61605	+	0.933027i
$179$	−8.20871	−	4.73930i	−0.613548	−	0.354232i	0.160805	−	0.986986i	$-0.448591\pi$
$179$	−8.20871	−	4.73930i	−0.613548	−	0.354232i	−0.774353	+	0.632754i	$0.781924\pi$
$180$	45.4129	+	26.2191i	3.38488	+	1.95426i
$181$	−7.87386	−	13.6379i	−0.585260	−	1.01370i	−0.994843	−	0.101427i	$-0.967659\pi$
$181$	−7.87386	−	13.6379i	−0.585260	−	1.01370i	0.409583	−	0.912273i	$-0.365674\pi$
$182$	1.50000	+	4.33013i	0.111187	+	0.320970i
$183$		−	18.3296i		−	1.35496i
$184$	2.37386	+	1.37055i	0.175004	+	0.101038i
$185$	−4.10436	−	7.10895i	−0.301758	−	0.522661i
$186$		0			0
$187$		−	2.74110i		−	0.200449i
$188$	−1.97822	−	1.14213i	−0.144276	−	0.0832981i
$189$	−2.50000	+	12.9904i	−0.181848	+	0.944911i
$190$	−34.3303	−	14.8655i	−2.49058	−	1.07845i
$191$	5.76951	+	9.99308i	0.417467	+	0.723074i	0.995684	−	0.0928091i	$-0.0295846\pi$
$191$	5.76951	+	9.99308i	0.417467	+	0.723074i	−0.578217	+	0.815883i	$0.696251\pi$
$192$	17.5608	+	30.4162i	1.26734	+	2.19510i
$193$	−6.24773	+	3.60713i	−0.449721	+	0.259647i	−0.707712	−	0.706501i	$-0.750273\pi$
$193$	−6.24773	+	3.60713i	−0.449721	+	0.259647i	0.257991	+	0.966147i	$0.416939\pi$
$194$	−3.79129	−	2.18890i	−0.272199	−	0.157154i
$195$	7.50000	+	4.33013i	0.537086	+	0.310087i
$196$	18.1434	+	7.25198i	1.29596	+	0.517998i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	27.2477	−	15.7315i	1.93641	−	1.11799i
$199$		−	25.5438i		−	1.81075i	−0.424610	−	0.905376i	$-0.639589\pi$
$199$		−	25.5438i		−	1.81075i	0.424610	−	0.905376i	$-0.360411\pi$
$200$		−	17.9681i		−	1.27053i
$201$	−8.37386	+	4.83465i	−0.590647	+	0.341010i
$202$	−41.9129			−2.94898
$203$	−6.08258	−	17.5589i	−0.426913	−	1.23239i
$204$	−6.16515	−	3.55945i	−0.431647	−	0.249211i
$205$	−28.4347	−	16.4168i	−1.98596	−	1.14660i
$206$	19.6652	−	11.3537i	1.37014	−	0.791048i
$207$	3.79129	+	6.56670i	0.263513	+	0.456417i
$208$	0.708712	+	1.22753i	0.0491403	+	0.0851136i
$209$	−10.5000	+	7.79423i	−0.726300	+	0.539138i
$210$	59.8911	−	20.7469i	4.13288	−	1.43167i
$211$	15.2477	+	8.80328i	1.04970	+	0.606043i	0.922564	−	0.385843i	$-0.126089\pi$
$211$	15.2477	+	8.80328i	1.04970	+	0.606043i	0.127132	+	0.991886i	$0.459423\pi$
$212$			10.9445i			0.751672i
$213$			19.6048i			1.34330i
$214$	16.1652	+	27.9989i	1.10503	+	1.91396i
$215$	7.50000	+	4.33013i	0.511496	+	0.295312i
$216$		−	8.66025i		−	0.589256i
$217$		0			0
$218$	6.08258	+	10.5353i	0.411964	+	0.713543i
$219$	−23.3739	−	13.4949i	−1.57946	−	0.911901i
$220$	−28.4347	−	16.4168i	−1.91706	−	1.10682i
$221$	−0.626136	−	0.361500i	−0.0421185	−	0.0243171i
$222$	−6.39564	+	11.0776i	−0.429248	+	0.743479i
$223$	2.20871	−	3.82560i	0.147906	−	0.256181i	−0.782547	−	0.622591i	$-0.786080\pi$
$223$	2.20871	−	3.82560i	0.147906	−	0.256181i	0.930453	+	0.366410i	$0.119413\pi$
$224$	19.1869	+	3.69253i	1.28198	+	0.246717i
$225$	24.8521	−	43.0451i	1.65681	−	2.86967i
$226$	28.9564			1.92615
$227$	−2.76951	+	4.79693i	−0.183819	+	0.318383i	−0.943178	−	0.332288i	$-0.892179\pi$
$227$	−2.76951	+	4.79693i	−0.183819	+	0.318383i	0.759359	+	0.650672i	$0.225513\pi$
$228$	3.89564	+	33.7373i	0.257995	+	2.23431i
$229$	6.00000	−	3.46410i	0.396491	−	0.228914i	−0.288478	−	0.957487i	$-0.593149\pi$
$229$	6.00000	−	3.46410i	0.396491	−	0.228914i	0.684969	+	0.728572i	$0.259816\pi$
$230$	6.79129	−	11.7629i	0.447804	−	0.775620i
$231$	4.18693	−	21.7559i	0.275480	−	1.43144i
$232$	6.08258	+	10.5353i	0.399341	+	0.691678i
$233$	−22.5826			−1.47943			−0.739717	−	0.672918i	$-0.765041\pi$
$233$	−22.5826			−1.47943			−0.739717	+	0.672918i	$0.765041\pi$
$234$		−	8.29875i		−	0.542507i
$235$	−1.60436	+	2.77883i	−0.104657	+	0.181271i
$236$	−7.26951	−	12.5912i	−0.473205	−	0.819614i
$237$	16.7477	−	9.66930i	1.08788	−	0.628089i
$238$	−5.00000	+	1.73205i	−0.324102	+	0.112272i
$239$	−17.5390			−1.13450			−0.567252	−	0.823544i	$-0.691994\pi$
$239$	−17.5390			−1.13450			−0.567252	+	0.823544i	$0.691994\pi$
$240$	16.9782	−	9.80238i	1.09594	−	0.632741i
$241$	−6.37386			−0.410577			−0.205288	−	0.978702i	$-0.565813\pi$
$241$	−6.37386			−0.410577			−0.205288	+	0.978702i	$0.565813\pi$
$242$	3.79129	−	2.18890i	0.243713	−	0.140708i
$243$	−8.08258	+	13.9994i	−0.518497	+	0.898064i
$244$	15.8739	+	9.16478i	1.01622	+	0.586715i
$245$	10.1869	−	25.4862i	0.650819	−	1.62825i
$246$			51.1631i			3.26204i
$247$	0.395644	+	3.42638i	0.0251742	+	0.218015i
$248$		0			0
$249$	−11.9174	+	6.88053i	−0.755236	+	0.436036i
$250$	−46.1216			−2.91699
$251$	−3.70871	+	2.14123i	−0.234092	+	0.135153i	−0.612458	−	0.790503i	$-0.709819\pi$
$251$	−3.70871	+	2.14123i	−0.234092	+	0.135153i	0.378366	+	0.925656i	$0.376486\pi$
$252$	−26.7477	−	23.1642i	−1.68495	−	1.45921i
$253$	−2.37386	−	4.11165i	−0.149244	−	0.258497i
$254$	−4.18693	−	7.25198i	−0.262711	−	0.455030i
$255$	−5.00000	+	8.66025i	−0.313112	+	0.542326i
$256$	−2.79129			−0.174455
$257$	−3.87386	+	6.70973i	−0.241645	+	0.418541i	−0.961183	−	0.275912i	$-0.911020\pi$
$257$	−3.87386	+	6.70973i	−0.241645	+	0.418541i	0.719538	+	0.694453i	$0.244354\pi$
$258$		−	13.4949i		−	0.840156i
$259$	1.81307	+	5.23388i	0.112659	+	0.325217i
$260$	−7.50000	+	4.33013i	−0.465130	+	0.268543i
$261$			33.6519i			2.08300i
$262$	−30.7477			−1.89960
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$			14.5040i			0.892657i
$265$	15.3739			0.944409
$266$	20.8521	+	14.2279i	1.27852	+	0.872366i
$267$	−31.7477			−1.94293
$268$		−	9.66930i		−	0.590647i
$269$	0.791288	+	1.37055i	0.0482457	+	0.0835640i	0.889140	−	0.457636i	$-0.151304\pi$
$269$	0.791288	+	1.37055i	0.0482457	+	0.0835640i	−0.840894	+	0.541200i	$0.817970\pi$
$270$	−42.9129			−2.61159
$271$		−	5.55765i		−	0.337603i	−0.985650	−	0.168802i	$-0.946010\pi$
$271$		−	5.55765i		−	0.337603i	0.985650	−	0.168802i	$-0.0539897\pi$
$272$	−1.41742	+	0.818350i	−0.0859440	+	0.0496198i
$273$	−4.41742	−	3.82560i	−0.267355	−	0.231536i
$274$		−	28.3604i		−	1.71331i
$275$	−15.5608	+	26.9521i	−0.938351	+	1.62527i
$276$	−12.3303			−0.742197
$277$	4.26951	−	7.39500i	0.256530	−	0.444323i	−0.708780	−	0.705430i	$-0.750754\pi$
$277$	4.26951	−	7.39500i	0.256530	−	0.444323i	0.965310	+	0.261107i	$0.0840875\pi$
$278$	−23.0608	−	39.9425i	−1.38309	−	2.39559i
$279$		0			0
$280$	−3.39564	+	17.6443i	−0.202929	+	1.05445i
$281$	12.4782	−	7.20430i	0.744388	−	0.429773i	−0.0792745	−	0.996853i	$-0.525260\pi$
$281$	12.4782	−	7.20430i	0.744388	−	0.429773i	0.823663	+	0.567080i	$0.191927\pi$
$282$	5.00000			0.297746
$283$	5.37386	−	3.10260i	0.319443	−	0.184431i	−0.331701	−	0.943384i	$-0.607623\pi$
$283$	5.37386	−	3.10260i	0.319443	−	0.184431i	0.651144	+	0.758954i	$0.274289\pi$
$284$	−16.9782	−	9.80238i	−1.00747	−	0.581664i
$285$	47.3911	−	5.47225i	2.80721	−	0.324148i
$286$			5.19615i			0.307255i
$287$	16.7477	+	14.5040i	0.988587	+	0.856142i
$288$	−30.6434	−	17.6920i	−1.80568	−	1.04251i
$289$	−8.08258	+	13.9994i	−0.475446	+	0.823496i
$290$	52.2042	−	30.1401i	3.06553	−	1.76989i
$291$	5.58258			0.327256
$292$	23.3739	−	13.4949i	1.36785	−	0.789730i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$	−42.3303	+	6.10985i	−2.46875	+	0.356334i
$295$	−17.6869	+	10.2116i	−1.02977	+	0.594540i
$296$	−1.81307	−	3.14033i	−0.105382	−	0.182528i
$297$	−7.50000	+	12.9904i	−0.435194	+	0.753778i
$298$		−	34.5656i		−	2.00233i
$299$	−1.25227			−0.0724208
$300$	40.4129	+	69.9972i	2.33324	+	4.04129i
$301$	−4.41742	−	3.82560i	−0.254616	−	0.220504i
$302$	−6.39564	+	11.0776i	−0.368028	+	0.637443i
$303$	46.2867	−	26.7237i	2.65910	−	1.53523i
$304$	7.16515	+	3.10260i	0.410950	+	0.177946i
$305$	12.8739	−	22.2982i	0.737155	−	1.27679i
$306$	9.58258			0.547799
$307$	−12.3956	+	21.4699i	−0.707457	+	1.22535i	0.258341	+	0.966054i	$0.416824\pi$
$307$	−12.3956	+	21.4699i	−0.707457	+	1.22535i	−0.965798	+	0.259297i	$0.916509\pi$
$308$	16.7477	+	14.5040i	0.954290	+	0.826440i
$309$	−14.4782	+	25.0770i	−0.823637	+	1.42658i
$310$		0			0
$311$	4.73049	+	2.73115i	0.268242	+	0.154869i	0.628088	−	0.778142i	$-0.283838\pi$
$311$	4.73049	+	2.73115i	0.268242	+	0.154869i	−0.359847	+	0.933011i	$0.617171\pi$
$312$	3.31307	+	1.91280i	0.187566	+	0.108291i
$313$	−7.50000	−	4.33013i	−0.423925	−	0.244753i	0.272830	−	0.962062i	$-0.412040\pi$
$313$	−7.50000	−	4.33013i	−0.423925	−	0.244753i	−0.696755	+	0.717309i	$0.745374\pi$
$314$	4.18693	+	7.25198i	0.236282	+	0.409253i
$315$	−32.5390	+	37.5728i	−1.83337	+	2.11699i
$316$			19.3386i			1.08788i
$317$	17.2913	+	9.98313i	0.971175	+	0.560708i	0.899594	−	0.436726i	$-0.143862\pi$
$317$	17.2913	+	9.98313i	0.971175	+	0.560708i	0.0715811	+	0.997435i	$0.477196\pi$
$318$	−11.9782	−	20.7469i	−0.671705	−	1.16343i
$319$		−	21.0707i		−	1.17973i
$320$			49.3357i			2.75795i
$321$	−35.7042	−	20.6138i	−1.99281	−	1.15055i
$322$	−6.00000	+	6.92820i	−0.334367	+	0.386094i
$323$	−3.95644	+	0.456850i	−0.220142	+	0.0254198i
$324$	−0.582576	−	1.00905i	−0.0323653	−	0.0560584i
$325$	4.10436	+	7.10895i	0.227669	+	0.394334i
$326$	11.3739	−	6.56670i	0.629940	−	0.363696i
$327$	−13.4347	−	7.75650i	−0.742938	−	0.428936i
$328$	−12.5608	−	7.25198i	−0.693554	−	0.400424i
$329$	1.41742	−	1.63670i	0.0781451	−	0.0902342i
$330$	71.8693			3.95628
$331$	8.68693	−	5.01540i	0.477477	−	0.275671i	−0.241887	−	0.970304i	$-0.577766\pi$
$331$	8.68693	−	5.01540i	0.477477	−	0.275671i	0.719364	+	0.694633i	$0.244433\pi$
$332$		−	13.7611i		−	0.755236i
$333$		−	10.0308i		−	0.549685i
$334$	41.9347	−	24.2110i	2.29456	−	1.32477i
$335$	−13.5826			−0.742095
$336$	−12.5000	+	4.33013i	−0.681931	+	0.236228i
$337$	−15.8739	−	9.16478i	−0.864704	−	0.499237i	0.000880414	−	1.00000i	$-0.499720\pi$
$337$	−15.8739	−	9.16478i	−0.864704	−	0.499237i	−0.865585	+	0.500762i	$0.833053\pi$
$338$	−23.4564	−	13.5426i	−1.27586	−	0.736619i
$339$	−31.9782	+	18.4626i	−1.73682	+	1.00275i
$340$	−5.00000	−	8.66025i	−0.271163	−	0.469668i
$341$		0			0
$342$	−27.2477	−	36.7068i	−1.47339	−	1.98488i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	3.31307	+	1.91280i	0.178629	+	0.103131i
$345$			17.3205i			0.932505i
$346$			16.9590i			0.911722i
$347$	14.1434	+	24.4970i	0.759256	+	1.31507i	0.943231	+	0.332139i	$0.107770\pi$
$347$	14.1434	+	24.4970i	0.759256	+	1.31507i	−0.183975	+	0.982931i	$0.558896\pi$
$348$	−47.3911	−	27.3613i	−2.54043	−	1.46672i
$349$			23.4503i			1.25526i	0.778510	+	0.627632i	$0.215976\pi$
$349$			23.4503i			1.25526i	−0.778510	+	0.627632i	$0.784024\pi$
$350$	58.9955	+	11.3537i	3.15344	+	0.606880i
$351$	1.97822	+	3.42638i	0.105590	+	0.182886i
$352$	19.1869	+	11.0776i	1.02267	+	0.590437i
$353$	−16.2695	−	9.39320i	−0.865939	−	0.499950i	5.79298e−5	−	1.00000i	$-0.499982\pi$
$353$	−16.2695	−	9.39320i	−0.865939	−	0.499950i	−0.865996	+	0.500050i	$0.833315\pi$
$354$	27.5608	+	15.9122i	1.46484	+	0.845726i
$355$	−13.7695	+	23.8495i	−0.730810	+	1.26580i
$356$	15.8739	−	27.4943i	0.841313	−	1.45720i
$357$	4.41742	−	5.10080i	0.233795	−	0.269963i
$358$	−10.3739	+	17.9681i	−0.548276	+	0.949641i
$359$	−14.3739			−0.758624			−0.379312	−	0.925269i	$-0.623839\pi$
$359$	−14.3739			−0.758624			−0.379312	+	0.925269i	$0.623839\pi$
$360$	16.2695	−	28.1796i	0.857478	−	1.48520i
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$	−29.8521	+	17.2351i	−1.56899	+	0.905857i
$363$	−2.79129	+	4.83465i	−0.146505	+	0.253753i
$364$	5.52178	−	1.91280i	0.289420	−	0.100258i
$365$	−18.9564	−	32.8335i	−0.992225	−	1.71858i
$366$	−40.1216			−2.09719
$367$			6.20520i			0.323909i	0.986798	+	0.161954i	$0.0517798\pi$
$367$			6.20520i			0.323909i	−0.986798	+	0.161954i	$0.948220\pi$
$368$	−1.41742	+	2.45505i	−0.0738883	+	0.127978i
$369$	−20.0608	−	34.7463i	−1.04432	−	1.80882i
$370$	−15.5608	+	8.98403i	−0.808967	+	0.467057i
$371$	−10.1869	−	1.96048i	−0.528879	−	0.101783i
$372$		0			0
$373$	29.3085	−	16.9213i	1.51754	−	0.876151i	0.517750	−	0.855532i	$-0.326770\pi$
$373$	29.3085	−	16.9213i	1.51754	−	0.876151i	0.999787	−	0.0206191i	$-0.00656373\pi$
$374$	−6.00000			−0.310253
$375$	50.9347	−	29.4071i	2.63025	−	1.51858i
$376$	−0.708712	+	1.22753i	−0.0365490	+	0.0633048i
$377$	−4.81307	−	2.77883i	−0.247886	−	0.143117i
$378$	28.4347	+	5.47225i	1.46252	+	0.281462i
$379$		−	34.2795i		−	1.76082i	−0.474213	−	0.880410i	$-0.657267\pi$
$379$		−	34.2795i		−	1.76082i	0.474213	−	0.880410i	$-0.342733\pi$
$380$	−18.9564	+	43.7780i	−0.972445	+	2.24577i
$381$	9.24773	+	5.33918i	0.473775	+	0.273534i
$382$	21.8739	−	12.6289i	1.11916	−	0.646150i
$383$	28.9129			1.47738			0.738690	−	0.674046i	$-0.235445\pi$
$383$	28.9129			1.47738			0.738690	+	0.674046i	$0.235445\pi$
$384$	30.8739	−	17.8250i	1.57553	−	0.909630i
$385$	20.3739	−	23.5257i	1.03835	−	1.19898i
$386$	7.89564	+	13.6757i	0.401878	+	0.696073i
$387$	5.29129	+	9.16478i	0.268971	+	0.465872i
$388$	−2.79129	+	4.83465i	−0.141706	+	0.245442i
$389$	11.0436			0.559931			0.279965	−	0.960010i	$-0.409677\pi$
$389$	11.0436			0.559931			0.279965	+	0.960010i	$0.409677\pi$
$390$	9.47822	−	16.4168i	0.479948	−	0.831295i
$391$		−	1.44600i		−	0.0731274i
$392$	4.50000	−	11.2583i	0.227284	−	0.568632i
$393$	33.9564	−	19.6048i	1.71288	−	0.988929i
$394$			26.2668i			1.32330i
$395$	27.1652			1.36683
$396$	−20.0608	−	34.7463i	−1.00809	−	1.74607i
$397$		−	11.4014i		−	0.572218i	−0.958197	−	0.286109i	$-0.907638\pi$
$397$		−	11.4014i		−	0.572218i	0.958197	−	0.286109i	$-0.0923619\pi$
$398$	−55.9129			−2.80266
$399$	−32.0998	−	2.41733i	−1.60700	−	0.121018i
$400$	18.5826			0.929129
$401$		−	30.1878i		−	1.50751i	−0.657158	−	0.753753i	$-0.728242\pi$
$401$		−	30.1878i		−	1.50751i	0.657158	−	0.753753i	$-0.271758\pi$
$402$	10.5826	+	18.3296i	0.527811	+	0.914195i
$403$		0			0
$404$			53.4473i			2.65910i
$405$	−1.41742	+	0.818350i	−0.0704324	+	0.0406642i
$406$	−38.4347	+	13.3142i	−1.90748	+	0.660770i
$407$			6.28065i			0.311320i
$408$	−2.20871	+	3.82560i	−0.109348	+	0.189396i
$409$	−33.1652			−1.63991			−0.819956	−	0.572427i	$-0.806002\pi$
$409$	−33.1652			−1.63991			−0.819956	+	0.572427i	$0.806002\pi$
$410$	−35.9347	+	62.2407i	−1.77469	+	3.07385i
$411$	18.0826	+	31.3199i	0.891948	+	1.54490i
$412$	−14.4782	−	25.0770i	−0.713291	−	1.23546i
$413$	13.0218	−	4.51088i	0.640760	−	0.221966i
$414$	14.3739	−	8.29875i	0.706437	−	0.407862i
$415$	−19.3303			−0.948887
$416$	5.06080	−	2.92185i	0.248126	−	0.143256i
$417$	50.9347	+	29.4071i	2.49428	+	1.44007i
$418$	17.0608	+	22.9835i	0.834471	+	1.12416i
$419$		−	35.3085i		−	1.72493i	−0.506115	−	0.862466i	$-0.668919\pi$
$419$		−	35.3085i		−	1.72493i	0.506115	−	0.862466i	$-0.331081\pi$
$420$	−26.4564	−	76.3732i	−1.29094	−	3.72663i
$421$	20.6869	+	11.9436i	1.00822	+	0.582096i	0.910670	−	0.413135i	$-0.135566\pi$
$421$	20.6869	+	11.9436i	1.00822	+	0.582096i	0.0975495	+	0.995231i	$0.468900\pi$
$422$	19.2695	−	33.3758i	0.938025	−	1.62471i
$423$	−3.39564	+	1.96048i	−0.165102	+	0.0953216i
$424$	6.79129			0.329814
$425$	−8.20871	+	4.73930i	−0.398181	+	0.229890i
$426$	42.9129			2.07914
$427$	−11.3739	+	13.1334i	−0.550420	+	0.635570i
$428$	35.7042	−	20.6138i	1.72583	−	0.996406i
$429$	−3.31307	−	5.73840i	−0.159956	−	0.277053i
$430$	9.47822	−	16.4168i	0.457080	−	0.791686i
$431$		−	23.4304i		−	1.12860i	−0.825570	−	0.564300i	$-0.809146\pi$
$431$		−	23.4304i		−	1.12860i	0.825570	−	0.564300i	$-0.190854\pi$
$432$	8.95644			0.430917
$433$	11.3131	+	19.5948i	0.543671	+	0.941666i	0.998689	+	0.0511841i	$0.0162995\pi$
$433$	11.3131	+	19.5948i	0.543671	+	0.941666i	−0.455018	+	0.890482i	$0.650367\pi$
$434$		0			0
$435$	−38.4347	+	66.5708i	−1.84280	+	3.19182i
$436$	13.4347	−	7.75650i	0.643403	−	0.371469i
$437$	−5.53901	+	4.11165i	−0.264967	+	0.196687i
$438$	−29.5390	+	51.1631i	−1.41143	+	2.44467i
$439$	15.1652			0.723793			0.361897	−	0.932218i	$-0.382129\pi$
$439$	15.1652			0.723793			0.361897	+	0.932218i	$0.382129\pi$
$440$	−10.1869	+	17.6443i	−0.485643	+	0.841158i
$441$	26.3521	−	20.7469i	1.25486	−	0.987947i
$442$	−0.791288	+	1.37055i	−0.0376377	+	0.0651905i
$443$	7.66515	−	13.2764i	0.364182	−	0.630782i	−0.624462	−	0.781055i	$-0.714682\pi$
$443$	7.66515	−	13.2764i	0.364182	−	0.630782i	0.988645	+	0.150273i	$0.0480152\pi$
$444$	14.1261	+	8.15573i	0.670397	+	0.387054i
$445$	−38.6216	−	22.2982i	−1.83084	−	1.05704i
$446$	−8.37386	−	4.83465i	−0.396514	−	0.228927i
$447$	22.0390	+	38.1727i	1.04241	+	1.80551i
$448$	6.29129	−	32.6905i	0.297235	−	1.54448i
$449$			0.552200i			0.0260600i	0.999915	+	0.0130300i	$0.00414769\pi$
$449$			0.552200i			0.0260600i	−0.999915	+	0.0130300i	$0.995852\pi$
$450$	−94.2214	−	54.3988i	−4.44164	−	2.56438i
$451$	12.5608	+	21.7559i	0.591465	+	1.02445i
$452$		−	36.9253i		−	1.73682i
$453$		−	16.3115i		−	0.766379i
$454$	10.5000	+	6.06218i	0.492789	+	0.284512i
$455$	−2.68693	−	7.75650i	−0.125965	−	0.363631i
$456$	20.9347	−	2.41733i	0.980355	−	0.113202i
$457$	−13.0390	−	22.5842i	−0.609939	−	1.05645i	−0.991250	−	0.131999i	$-0.957860\pi$
$457$	−13.0390	−	22.5842i	−0.609939	−	1.05645i	0.381310	−	0.924447i	$-0.375473\pi$
$458$	−7.58258	−	13.1334i	−0.354310	−	0.613684i
$459$	−3.95644	+	2.28425i	−0.184671	+	0.106620i
$460$	−15.0000	−	8.66025i	−0.699379	−	0.403786i
$461$	−13.6652	−	7.88958i	−0.636450	−	0.367454i	0.146796	−	0.989167i	$-0.453104\pi$
$461$	−13.6652	−	7.88958i	−0.636450	−	0.367454i	−0.783246	+	0.621712i	$0.786437\pi$
$462$	−47.6216	−	9.16478i	−2.21556	−	0.426384i
$463$	−19.0000			−0.883005			−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000			−0.883005			−0.441502	+	0.897260i	$0.645554\pi$
$464$	−10.8956	+	6.29060i	−0.505818	+	0.292034i
$465$		0			0
$466$			49.4310i			2.28985i
$467$	−1.73049	+	0.999100i	−0.0800776	+	0.0462328i	−0.539504	−	0.841983i	$-0.681388\pi$
$467$	−1.73049	+	0.999100i	−0.0800776	+	0.0462328i	0.459427	+	0.888216i	$0.348055\pi$
$468$	−10.5826			−0.489180
$469$	9.00000	+	1.73205i	0.415581	+	0.0799787i
$470$	6.08258	+	3.51178i	0.280568	+	0.161986i
$471$	−9.24773	−	5.33918i	−0.426113	−	0.246016i
$472$	−7.81307	+	4.51088i	−0.359626	+	0.207630i
$473$	−3.31307	−	5.73840i	−0.152335	−	0.263852i
$474$	−21.1652	−	36.6591i	−0.972148	−	1.68381i
$475$	41.4955	+	17.9681i	1.90394	+	0.824431i
$476$	2.20871	+	6.37600i	0.101236	+	0.292244i
$477$	16.2695	+	9.39320i	0.744930	+	0.430085i
$478$			38.3912i			1.75597i
$479$			20.9753i			0.958386i	0.877709	+	0.479193i	$0.159071\pi$
$479$			20.9753i			0.958386i	−0.877709	+	0.479193i	$0.840929\pi$
$480$	−40.4129	−	69.9972i	−1.84459	−	3.19492i
$481$	1.43466	+	0.828301i	0.0654148	+	0.0377673i
$482$			13.9518i			0.635485i
$483$	2.20871	−	11.4768i	0.100500	−	0.522213i
$484$	−2.79129	−	4.83465i	−0.126877	−	0.219757i
$485$	6.79129	+	3.92095i	0.308376	+	0.178041i
$486$	30.6434	+	17.6920i	1.39001	+	0.802524i
$487$	1.81307	+	1.04678i	0.0821580	+	0.0474339i	0.540516	−	0.841334i	$-0.318229\pi$
$487$	1.81307	+	1.04678i	0.0821580	+	0.0474339i	−0.458358	+	0.888768i	$0.651562\pi$
$488$	5.68693	−	9.85005i	0.257435	−	0.445891i
$489$	−8.37386	+	14.5040i	−0.378679	+	0.655892i
$490$	−55.7867	−	22.2982i	−2.52019	−	1.00733i
$491$	13.0390	−	22.5842i	0.588443	−	1.01921i	−0.405994	−	0.913876i	$-0.633075\pi$
$491$	13.0390	−	22.5842i	0.588443	−	1.01921i	0.994437	−	0.105337i	$-0.0335920\pi$
$492$	65.2432			2.94139
$493$	3.20871	−	5.55765i	0.144513	−	0.250304i
$494$	7.50000	−	0.866025i	0.337441	−	0.0389643i
$495$	−48.8085	+	28.1796i	−2.19378	+	1.26658i
$496$		0			0
$497$	12.1652	−	14.0471i	0.545682	−	0.630099i
$498$	15.0608	+	26.0861i	0.674890	+	1.16894i
$499$	9.74773			0.436368			0.218184	−	0.975908i	$-0.429987\pi$
$499$	9.74773			0.436368			0.218184	+	0.975908i	$0.429987\pi$
$500$			58.8143i			2.63025i
$501$	−30.8739	+	53.4751i	−1.37934	+	2.38909i
$502$	4.68693	+	8.11800i	0.209188	+	0.362324i
$503$	19.5826	−	11.3060i	0.873144	−	0.504110i	0.00475218	−	0.999989i	$-0.498487\pi$
$503$	19.5826	−	11.3060i	0.873144	−	0.504110i	0.868392	+	0.495879i	$0.165154\pi$
$504$	−14.3739	+	16.5975i	−0.640263	+	0.739312i
$505$	75.0780			3.34093
$506$	−9.00000	+	5.19615i	−0.400099	+	0.230997i
$507$	34.5390			1.53393
$508$	−9.24773	+	5.33918i	−0.410302	+	0.236888i
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	−0.982988	−	0.183669i	$-0.941202\pi$
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	0.650556	+	0.759458i	$0.274536\pi$
$510$	18.9564	+	10.9445i	0.839405	+	0.484631i
$511$	8.37386	+	24.1733i	0.370438	+	1.06936i
$512$		−	19.4340i		−	0.858868i
$513$	20.0000	+	8.66025i	0.883022	+	0.382360i
$514$	14.6869	+	8.47950i	0.647813	+	0.374015i
$515$	−35.2259	+	20.3377i	−1.55224	+	0.896187i
$516$	−17.2087			−0.757571
$517$	2.12614	−	1.22753i	0.0935074	−	0.0539865i
$518$	11.4564	−	3.96863i	0.503367	−	0.174371i
$519$	−10.8131	−	18.7288i	−0.474641	−	0.822102i
$520$	2.68693	+	4.65390i	0.117830	+	0.204087i
$521$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$521$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$522$	73.6606			3.22404
$523$	16.7477	−	29.0079i	0.732327	−	1.26843i	−0.223559	−	0.974690i	$-0.571768\pi$
$523$	16.7477	−	29.0079i	0.732327	−	1.26843i	0.955886	−	0.293737i	$-0.0948990\pi$
$524$			39.2095i			1.71288i
$525$	−72.3911	+	25.0770i	−3.15941	+	1.09445i
$526$	−22.7477	+	13.1334i	−0.991848	+	0.572644i
$527$		0			0
$528$	−15.0000			−0.652791
$529$	10.2477	+	17.7496i	0.445553	+	0.771721i
$530$		−	33.6519i		−	1.46174i
$531$	−24.9564			−1.08302
$532$	18.1434	−	26.5906i	0.786615	−	1.15285i
$533$	6.62614			0.287010
$534$			69.4926i			3.00724i
$535$	−28.9564	−	50.1540i	−1.25190	−	2.16835i
$536$	−6.00000			−0.259161
$537$		−	26.4575i		−	1.14173i
$538$	3.00000	−	1.73205i	0.129339	−	0.0746740i
$539$	−16.5000	+	12.9904i	−0.710705	+	0.559535i
$540$			54.7225i			2.35488i
$541$	−11.8739	+	20.5661i	−0.510497	+	0.884207i	0.489429	+	0.872043i	$0.337205\pi$
$541$	−11.8739	+	20.5661i	−0.510497	+	0.884207i	−0.999926	+	0.0121639i	$0.996128\pi$
$542$	−12.1652			−0.522538
$543$	21.9782	−	38.0674i	0.943176	−	1.63363i
$544$	3.37386	+	5.84370i	0.144653	+	0.250547i
$545$	−10.8956	−	18.8718i	−0.466718	−	0.808379i
$546$	−8.37386	+	9.66930i	−0.358368	+	0.413808i
$547$	23.9347	−	13.8187i	1.02337	−	0.590844i	0.108293	−	0.994119i	$-0.465461\pi$
$547$	23.9347	−	13.8187i	1.02337	−	0.590844i	0.915079	+	0.403275i	$0.132128\pi$
$548$	−36.1652			−1.54490
$549$	27.2477	−	15.7315i	1.16290	−	0.671403i
$550$	58.9955	+	34.0610i	2.51557	+	1.45237i
$551$	−30.4129	+	3.51178i	−1.29563	+	0.149607i
$552$			7.65120i			0.325657i
$553$	−18.0000	−	3.46410i	−0.765438	−	0.147309i
$554$	−16.1869	−	9.34553i	−0.687717	−	0.397053i
$555$	11.4564	−	19.8431i	0.486299	−	0.842294i
$556$	−50.9347	+	29.4071i	−2.16011	+	1.24714i
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$		0			0
$559$	−1.74773			−0.0739210
$560$	−18.2477	−	3.51178i	−0.771107	−	0.148400i
$561$	6.62614	−	3.82560i	0.279756	−	0.161517i
$562$	−15.7695	−	27.3136i	−0.665197	−	1.15215i
$563$	−7.35208	+	12.7342i	−0.309853	+	0.536682i	−0.978330	−	0.207051i	$-0.933613\pi$
$563$	−7.35208	+	12.7342i	−0.309853	+	0.536682i	0.668477	+	0.743733i	$0.266947\pi$
$564$		−	6.37600i		−	0.268478i
$565$	−51.8693			−2.18216
$566$	−6.79129	−	11.7629i	−0.285459	−	0.494430i
$567$	1.04356	−	0.361500i	0.0438254	−	0.0151816i
$568$	−6.08258	+	10.5353i	−0.255219	+	0.442053i
$569$	−13.2695	+	7.66115i	−0.556287	+	0.321172i	−0.751654	−	0.659558i	$-0.770744\pi$
$569$	−13.2695	+	7.66115i	−0.556287	+	0.321172i	0.195367	+	0.980730i	$0.437410\pi$
$570$	−11.9782	−	103.734i	−0.501712	−	4.34496i
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$	6.62614			0.277053
$573$	−16.1044	+	27.8936i	−0.672769	+	1.16527i
$574$	31.7477	−	36.6591i	1.32512	−	1.53012i
$575$	−8.20871	+	14.2179i	−0.342327	+	0.592928i
$576$	−30.1434	+	52.2099i	−1.25597	+	2.17541i
$577$	−21.8085	−	12.5912i	−0.907901	−	0.524177i	−0.0281456	−	0.999604i	$-0.508960\pi$
$577$	−21.8085	−	12.5912i	−0.907901	−	0.524177i	−0.879755	+	0.475427i	$0.842294\pi$
$578$	30.6434	+	17.6920i	1.27460	+	0.735888i
$579$	−17.4392	−	10.0685i	−0.724749	−	0.418434i
$580$	−38.4347	−	66.5708i	−1.59591	−	2.76420i
$581$	12.8085	+	2.46500i	0.531387	+	0.102265i
$582$		−	12.2197i		−	0.506523i
$583$	−10.1869	−	5.88143i	−0.421900	−	0.243584i
$584$	−8.37386	−	14.5040i	−0.346513	−	0.600178i
$585$			14.8655i			0.614611i
$586$		−	45.9669i		−	1.89888i
$587$	8.76951	+	5.06308i	0.361956	+	0.208976i	0.669939	−	0.742417i	$-0.266320\pi$
$587$	8.76951	+	5.06308i	0.361956	+	0.208976i	−0.307982	+	0.951392i	$0.599654\pi$
$588$	7.79129	+	53.9796i	0.321307	+	2.22608i
$589$		0			0
$590$	22.3521	+	38.7149i	0.920221	+	1.59387i
$591$	−16.7477	−	29.0079i	−0.688909	−	1.19323i
$592$	3.24773	−	1.87508i	0.133481	−	0.0770652i
$593$	33.1652	+	19.1479i	1.36193	+	0.786310i	0.989881	−	0.141903i	$-0.0453220\pi$
$593$	33.1652	+	19.1479i	1.36193	+	0.786310i	0.372049	+	0.928213i	$0.378655\pi$
$594$	28.4347	+	16.4168i	1.16669	+	0.673588i
$595$	8.95644	−	3.10260i	0.367178	−	0.127194i
$596$	−44.0780			−1.80551
$597$	61.7477	−	35.6501i	2.52717	−	1.45906i
$598$			2.74110i			0.112092i
$599$			7.09900i			0.290057i	0.989427	+	0.145029i	$0.0463274\pi$
$599$			7.09900i			0.290057i	−0.989427	+	0.145029i	$0.953673\pi$
$600$	43.4347	−	25.0770i	1.77321	−	1.02376i
$601$	34.4955			1.40710			0.703549	−	0.710646i	$-0.251597\pi$
$601$	34.4955			1.40710			0.703549	+	0.710646i	$0.251597\pi$
$602$	−8.37386	+	9.66930i	−0.341293	+	0.394091i
$603$	−14.3739	−	8.29875i	−0.585349	−	0.337951i
$604$	14.1261	+	8.15573i	0.574784	+	0.331852i
$605$	−6.79129	+	3.92095i	−0.276105	+	0.159409i
$606$	−58.4955	−	101.317i	−2.37622	−	4.11573i
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	0.688274	−	0.725450i	$-0.258368\pi$
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	−0.972396	+	0.233338i	$0.925035\pi$
$608$	12.7913	−	29.5402i	0.518755	−	1.19801i
$609$	33.9564	−	39.2095i	1.37598	−	1.58885i
$610$	−48.8085	−	28.1796i	−1.97620	−	1.14096i
$611$		−	0.647551i		−	0.0261971i
$612$		−	12.2197i		−	0.493952i
$613$	−4.18693	−	7.25198i	−0.169109	−	0.292905i	0.768998	−	0.639251i	$-0.220756\pi$
$613$	−4.18693	−	7.25198i	−0.169109	−	0.292905i	−0.938107	+	0.346346i	$0.887422\pi$
$614$	46.9955	+	27.1328i	1.89658	+	1.09499i
$615$		−	91.6478i		−	3.69560i
$616$	9.00000	−	10.3923i	0.362620	−	0.418718i
$617$	13.4174	+	23.2397i	0.540165	+	0.935594i	0.998894	+	0.0470172i	$0.0149716\pi$
$617$	13.4174	+	23.2397i	0.540165	+	0.935594i	−0.458729	+	0.888576i	$0.651695\pi$
$618$	54.8911	+	31.6914i	2.20804	+	1.27481i
$619$	7.50000	+	4.33013i	0.301450	+	0.174042i	0.643094	−	0.765787i	$-0.277650\pi$
$619$	7.50000	+	4.33013i	0.301450	+	0.174042i	−0.341644	+	0.939829i	$0.610984\pi$
$620$		0			0
$621$	−3.95644	+	6.85275i	−0.158766	+	0.274992i
$622$	5.97822	−	10.3546i	0.239705	−	0.415181i
$623$	22.7477	+	19.7001i	0.911368	+	0.789268i
$624$	−1.97822	+	3.42638i	−0.0791922	+	0.137165i
$625$	30.7477			1.22991
$626$	−9.47822	+	16.4168i	−0.378826	+	0.656146i
$627$	−33.4955	−	14.5040i	−1.33768	−	0.579232i
$628$	9.24773	−	5.33918i	0.369024	−	0.213056i
$629$	−0.956439	+	1.65660i	−0.0381357	+	0.0660530i
$630$	82.2432	+	71.2247i	3.27665	+	2.83766i
$631$	−12.6434	−	21.8990i	−0.503325	−	0.871784i	−0.999993	−	0.00384324i	$-0.998777\pi$
$631$	−12.6434	−	21.8990i	−0.503325	−	0.871784i	0.496668	−	0.867941i	$-0.334557\pi$
$632$	12.0000			0.477334
$633$			49.1450i			1.95334i
$634$	21.8521	−	37.8489i	0.867857	−	1.50317i
$635$	7.50000	+	12.9904i	0.297628	+	0.515508i
$636$	−26.4564	+	15.2746i	−1.04907	+	0.605679i
$637$	0.791288	+	5.48220i	0.0313520	+	0.217213i
$638$	−46.1216			−1.82597
$639$	−29.1434	+	16.8259i	−1.15289	+	0.665624i
$640$	50.0780			1.97951
$641$	−12.1652	+	7.02355i	−0.480495	+	0.277414i	−0.720623	−	0.693328i	$-0.756144\pi$
$641$	−12.1652	+	7.02355i	−0.480495	+	0.277414i	0.240128	+	0.970741i	$0.422811\pi$
$642$	−45.1216	+	78.1529i	−1.78081	+	3.08445i
$643$	−18.2477	−	10.5353i	−0.719620	−	0.415473i	0.0949927	−	0.995478i	$-0.469717\pi$
$643$	−18.2477	−	10.5353i	−0.719620	−	0.415473i	−0.814613	+	0.580005i	$0.803051\pi$
$644$	8.83485	+	7.65120i	0.348142	+	0.301500i
$645$			24.1733i			0.951821i
$646$	1.00000	+	8.66025i	0.0393445	+	0.340733i
$647$	10.2695	+	5.92910i	0.403736	+	0.233097i	0.688095	−	0.725621i	$-0.258447\pi$
$647$	10.2695	+	5.92910i	0.403736	+	0.233097i	−0.284359	+	0.958718i	$0.591781\pi$
$648$	−0.626136	+	0.361500i	−0.0245970	+	0.0142011i
$649$	15.6261			0.613380
$650$	15.5608	−	8.98403i	0.610345	−	0.352383i
$651$		0			0
$652$	−8.37386	−	14.5040i	−0.327946	−	0.568019i
$653$	−7.50000	−	12.9904i	−0.293498	−	0.508353i	0.681137	−	0.732156i	$-0.261486\pi$
$653$	−7.50000	−	12.9904i	−0.293498	−	0.508353i	−0.974634	+	0.223803i	$0.928153\pi$
$654$	−16.9782	+	29.4071i	−0.663901	+	1.14991i
$655$	55.0780			2.15208
$656$	7.50000	−	12.9904i	0.292826	−	0.507189i
$657$		−	46.3284i		−	1.80744i
$658$	−3.58258	−	3.10260i	−0.139663	−	0.120952i
$659$	−34.5826	+	19.9663i	−1.34715	+	0.777775i	−0.987844	−	0.155446i	$-0.950318\pi$
$659$	−34.5826	+	19.9663i	−1.34715	+	0.777775i	−0.359302	+	0.933222i	$0.616985\pi$
$660$		−	91.6478i		−	3.56739i
$661$	24.4955			0.952763			0.476381	−	0.879239i	$-0.341948\pi$
$661$	24.4955			0.952763			0.476381	+	0.879239i	$0.341948\pi$
$662$	−10.9782	−	19.0148i	−0.426681	−	0.739033i
$663$		−	2.01810i		−	0.0783766i
$664$	−8.53901			−0.331378
$665$	−37.3521	−	25.4862i	−1.44845	−	0.988312i
$666$	−21.9564			−0.850795
$667$		−	11.1153i		−	0.430386i
$668$	−30.8739	−	53.4751i	−1.19455	−	2.06901i
$669$	12.3303			0.476717
$670$			29.7309i			1.14861i
$671$	−17.0608	+	9.85005i	−0.658625	+	0.380257i
$672$	17.8521	+	51.5345i	0.688659	+	1.98799i
$673$			35.9361i			1.38524i	0.721305	+	0.692618i	$0.243543\pi$
$673$			35.9361i			1.38524i	−0.721305	+	0.692618i	$0.756457\pi$
$674$	−20.0608	+	34.7463i	−0.772713	+	1.33838i
$675$	51.8693			1.99645
$676$	−17.2695	+	29.9117i	−0.664212	+	1.15045i
$677$	−19.6652	−	34.0610i	−0.755793	−	1.30907i	−0.944979	−	0.327131i	$-0.893918\pi$
$677$	−19.6652	−	34.0610i	−0.755793	−	1.30907i	0.189186	−	0.981941i	$-0.439415\pi$
$678$	40.4129	+	69.9972i	1.55205	+	2.68822i
$679$	−4.00000	−	3.46410i	−0.153506	−	0.132940i
$680$	−5.37386	+	3.10260i	−0.206078	+	0.118979i
$681$	−15.4610			−0.592466
$682$		0			0
$683$	−40.7650	−	23.5357i	−1.55983	−	0.900567i	−0.997273	−	0.0738075i	$-0.976485\pi$
$683$	−40.7650	−	23.5357i	−1.55983	−	0.900567i	−0.562555	−	0.826760i	$-0.690182\pi$
$684$	−46.8085	+	34.7463i	−1.78977	+	1.32856i
$685$			50.8016i			1.94103i
$686$	34.1216	+	21.8890i	1.30277	+	0.835726i
$687$	16.7477	+	9.66930i	0.638966	+	0.368907i
$688$	−1.97822	+	3.42638i	−0.0754189	+	0.130629i
$689$	−2.68693	+	1.55130i	−0.102364	+	0.0590999i
$690$	37.9129			1.44332
$691$	37.5000	−	21.6506i	1.42657	−	0.823629i	0.429719	−	0.902963i	$-0.358613\pi$
$691$	37.5000	−	21.6506i	1.42657	−	0.823629i	0.996848	+	0.0793336i	$0.0252792\pi$
$692$	21.6261			0.822102
$693$	35.9347	−	12.4481i	1.36504	−	0.472865i
$694$	53.6216	−	30.9584i	2.03545	−	1.17517i
$695$	41.3085	+	71.5485i	1.56692	+	2.71399i
$696$	−16.9782	+	29.4071i	−0.643558	+	1.11467i
$697$			7.65120i			0.289810i
$698$	51.3303			1.94288
$699$	−31.5172	−	54.5895i	−1.19209	−	2.06476i
$700$	14.4782	−	75.2310i	0.547225	−	2.84347i
$701$	−16.7477	+	29.0079i	−0.632553	+	1.09561i	0.354475	+	0.935065i	$0.384660\pi$
$701$	−16.7477	+	29.0079i	−0.632553	+	1.09561i	−0.987028	+	0.160548i	$0.948674\pi$
$702$	7.50000	−	4.33013i	0.283069	−	0.163430i
$703$	9.06534	−	1.04678i	0.341906	−	0.0394799i
$704$	18.8739	−	32.6905i	0.711335	−	1.23207i
$705$	−8.95644			−0.337319
$706$	−20.5608	+	35.6123i	−0.773816	+	1.34029i
$707$	−49.7477	−	9.57395i	−1.87096	−	0.360066i
$708$	20.2913	−	35.1455i	0.762593	−	1.32085i
$709$	11.2913	−	19.5571i	0.424053	−	0.734482i	−0.572278	−	0.820059i	$-0.693940\pi$
$709$	11.2913	−	19.5571i	0.424053	−	0.734482i	0.996331	+	0.0855778i	$0.0272736\pi$
$710$	52.2042	+	30.1401i	1.95919	+	1.13114i
$711$	28.7477	+	16.5975i	1.07812	+	0.622455i
$712$	−17.0608	−	9.85005i	−0.639380	−	0.369146i
$713$		0			0
$714$	−11.1652	−	9.66930i	−0.417845	−	0.361865i
$715$		−	9.30780i		−	0.348092i
$716$	22.9129	+	13.2288i	0.856294	+	0.494382i
$717$	−24.4782	−	42.3975i	−0.914156	−	1.58336i
$718$			31.4630i			1.17419i
$719$			10.2016i			0.380456i	0.981740	+	0.190228i	$0.0609227\pi$
$719$			10.2016i			0.380456i	−0.981740	+	0.190228i	$0.939077\pi$
$720$	29.1434	+	16.8259i	1.08611	+	0.627066i
$721$	25.9347	−	8.98403i	0.965857	−	0.334583i
$722$	30.3303	−	28.4557i	1.12878	−	1.05901i
$723$	−8.89564	−	15.4077i	−0.330833	−	0.573019i
$724$	21.9782	+	38.0674i	0.816814	+	1.41476i
$725$	−63.0998	+	36.4307i	−2.34347	+	1.35300i
$726$	10.5826	+	6.10985i	0.392756	+	0.226758i
$727$	−11.7523	−	6.78518i	−0.435868	−	0.251648i	0.265976	−	0.963980i	$-0.414306\pi$
$727$	−11.7523	−	6.78518i	−0.435868	−	0.251648i	−0.701843	+	0.712331i	$0.747639\pi$
$728$	−1.18693	−	3.42638i	−0.0439906	−	0.126990i
$729$	−43.8693			−1.62479
$730$	−71.8693	+	41.4938i	−2.66000	+	1.53575i
$731$		−	2.01810i		−	0.0746422i
$732$			51.1631i			1.89104i
$733$	−23.3085	+	13.4572i	−0.860920	+	0.497052i	−0.864320	−	0.502942i	$-0.832251\pi$
$733$	−23.3085	+	13.4572i	−0.860920	+	0.497052i	0.00340032	+	0.999994i	$0.498918\pi$
$734$	13.5826			0.501342
$735$	75.8258	−	10.9445i	2.79688	−	0.403694i
$736$	10.1216	+	5.84370i	0.373087	+	0.215402i
$737$	9.00000	+	5.19615i	0.331519	+	0.191403i
$738$	−76.0562	+	43.9111i	−2.79967	+	1.61639i
$739$	0.873864	+	1.51358i	0.0321456	+	0.0556778i	0.881651	−	0.471903i	$-0.156433\pi$
$739$	0.873864	+	1.51358i	0.0321456	+	0.0556778i	−0.849505	+	0.527580i	$0.823099\pi$
$740$	11.4564	+	19.8431i	0.421147	+	0.729448i
$741$	−7.73049	+	5.73840i	−0.283987	+	0.210805i
$742$	−4.29129	+	22.2982i	−0.157538	+	0.818592i
$743$	26.6044	+	15.3600i	0.976019	+	0.563505i	0.901066	−	0.433682i	$-0.142786\pi$
$743$	26.6044	+	15.3600i	0.976019	+	0.563505i	0.0749532	+	0.997187i	$0.476119\pi$
$744$		0			0
$745$			61.9169i			2.26846i
$746$	−37.0390	−	64.1535i	−1.35609	−	2.34882i
$747$	−20.4564	−	11.8105i	−0.748462	−	0.432125i
$748$			7.65120i			0.279756i
$749$	12.7913	+	36.9253i	0.467383	+	1.34922i
$750$	−64.3693	−	111.491i	−2.35044	−	4.07107i
$751$	−14.6869	−	8.47950i	−0.535934	−	0.309421i	0.207496	−	0.978236i	$-0.433469\pi$
$751$	−14.6869	−	8.47950i	−0.535934	−	0.309421i	−0.743429	+	0.668814i	$0.766802\pi$
$752$	−1.26951	−	0.732950i	−0.0462942	−	0.0267280i
$753$	−10.3521	−	5.97678i	−0.377251	−	0.217806i
$754$	−6.08258	+	10.5353i	−0.221514	+	0.383674i
$755$	11.4564	−	19.8431i	0.416943	−	0.722166i
$756$	6.97822	−	36.2599i	0.253795	−	1.31876i
$757$	−27.1216	+	46.9760i	−0.985751	+	1.70737i	−0.347200	+	0.937791i	$0.612868\pi$
$757$	−27.1216	+	46.9760i	−0.985751	+	1.70737i	−0.638551	+	0.769580i	$0.720466\pi$
$758$	−75.0345			−2.72537
$759$	6.62614	−	11.4768i	0.240514	−	0.416582i
$760$	27.1652	+	11.7629i	0.985384	+	0.426684i
$761$	−1.73049	+	0.999100i	−0.0627303	+	0.0362174i	−0.531037	−	0.847349i	$-0.678198\pi$
$761$	−1.73049	+	0.999100i	−0.0627303	+	0.0362174i	0.468307	+	0.883566i	$0.344864\pi$
$762$	11.6869	−	20.2424i	0.423373	−	0.733303i
$763$	4.81307	+	13.8941i	0.174245	+	0.503001i
$764$	−16.1044	−	27.8936i	−0.582635	−	1.00915i
$765$	−17.1652			−0.620607
$766$		−	63.2874i		−	2.28667i
$767$	2.06080	−	3.56940i	0.0744110	−	0.128884i
$768$	−3.89564	−	6.74745i	−0.140572	−	0.243478i
$769$	−18.3131	+	10.5731i	−0.660386	+	0.381274i	−0.792424	−	0.609971i	$-0.791181\pi$
$769$	−18.3131	+	10.5731i	−0.660386	+	0.381274i	0.132038	+	0.991245i	$0.457848\pi$
$770$	−51.4955	−	44.5964i	−1.85577	−	1.60714i
$771$	−21.6261			−0.778846
$772$	17.4392	−	10.0685i	0.627651	−	0.362374i
$773$	33.6606			1.21069			0.605344	−	0.795964i	$-0.293036\pi$
$773$	33.6606			1.21069			0.605344	+	0.795964i	$0.293036\pi$
$774$	20.0608	−	11.5821i	0.721070	−	0.416310i
$775$		0			0
$776$	3.00000	+	1.73205i	0.107694	+	0.0621770i
$777$	−10.1216	+	11.6874i	−0.363110	+	0.419283i
$778$		−	24.1733i		−	0.866653i
$779$	29.3085	−	21.7559i	1.05009	−	0.779487i
$780$	−20.9347	−	12.0866i	−0.749581	−	0.432771i
$781$	18.2477	−	10.5353i	0.652955	−	0.376984i
$782$	−3.16515			−0.113186
$783$	−30.4129	+	17.5589i	−1.08687	+	0.627503i
$784$	11.6434	+	4.65390i	0.415835	+	0.166211i
$785$	−7.50000	−	12.9904i	−0.267686	−	0.463647i
$786$	−42.9129	−	74.3273i	−1.53065	−	2.65117i
$787$	8.20871	−	14.2179i	0.292609	−	0.506814i	−0.681817	−	0.731523i	$-0.738810\pi$
$787$	8.20871	−	14.2179i	0.292609	−	0.506814i	0.974426	+	0.224709i	$0.0721432\pi$
$788$	33.4955			1.19323
$789$	16.7477	−	29.0079i	0.596235	−	1.03271i
$790$		−	59.4618i		−	2.11556i
$791$	34.3693	+	6.61438i	1.22203	+	0.235180i
$792$	−21.5608	+	12.4481i	−0.766130	+	0.442325i
$793$			5.19615i			0.184521i
$794$	−24.9564			−0.885671
$795$	21.4564	+	37.1636i	0.760981	+	1.31806i
$796$			71.3001i			2.52717i
$797$	6.49545			0.230081			0.115040	−	0.993361i	$-0.463300\pi$
$797$	6.49545			0.230081			0.115040	+	0.993361i	$0.463300\pi$
$798$	−5.29129	+	70.2633i	−0.187310	+	2.48729i
$799$	0.747727			0.0264527
$800$		−	76.6115i		−	2.70863i
$801$	−27.2477	−	47.1944i	−0.962751	−	1.66753i
$802$	−66.0780			−2.33330
$803$			29.0079i			1.02367i
$804$	23.3739	−	13.4949i	0.824333	−	0.475929i
$805$	10.7477	−	12.4104i	0.378808	−	0.437409i
$806$		0			0
$807$	−2.20871	+	3.82560i	−0.0777504	+	0.134668i
$808$	33.1652			1.16675
$809$	7.03901	−	12.1919i	0.247479	−	0.428645i	−0.715347	−	0.698769i	$-0.753731\pi$
$809$	7.03901	−	12.1919i	0.247479	−	0.428645i	0.962826	+	0.270124i	$0.0870647\pi$
$810$	1.79129	+	3.10260i	0.0629394	+	0.109014i
$811$	−13.0608	−	22.6220i	−0.458627	−	0.794364i	0.540262	−	0.841497i	$-0.318325\pi$
$811$	−13.0608	−	22.6220i	−0.458627	−	0.794364i	−0.998889	+	0.0471323i	$0.984992\pi$
$812$	16.9782	+	49.0119i	0.595819	+	1.71998i
$813$	13.4347	−	7.75650i	0.471174	−	0.272032i
$814$	13.7477			0.481858
$815$	−20.3739	+	11.7629i	−0.713665	+	0.412035i
$816$	−3.95644	−	2.28425i	−0.138503	−	0.0799648i
$817$	−7.73049	+	5.73840i	−0.270456	+	0.200761i
$818$			72.5952i			2.53823i
$819$	1.89564	−	9.85005i	0.0662392	−	0.344189i
$820$	79.3693	+	45.8239i	2.77170	+	1.60024i
$821$	19.9782	−	34.6033i	0.697245	−	1.20766i	−0.272173	−	0.962248i	$-0.587742\pi$
$821$	19.9782	−	34.6033i	0.697245	−	1.20766i	0.969418	−	0.245415i	$-0.0789242\pi$
$822$	68.5562	−	39.5810i	2.39117	−	1.38054i
$823$	−34.5826			−1.20547			−0.602736	−	0.797940i	$-0.705923\pi$
$823$	−34.5826			−1.20547			−0.602736	+	0.797940i	$0.705923\pi$
$824$	−15.5608	+	8.98403i	−0.542086	+	0.312973i
$825$	−86.8693			−3.02440
$826$	−9.87386	−	28.5034i	−0.343556	−	0.991760i
$827$	−23.7042	+	13.6856i	−0.824275	+	0.475895i	−0.851888	−	0.523723i	$-0.824543\pi$
$827$	−23.7042	+	13.6856i	−0.824275	+	0.475895i	0.0276137	+	0.999619i	$0.491209\pi$
$828$	−10.5826	−	18.3296i	−0.367770	−	0.636996i
$829$	−20.8739	+	36.1546i	−0.724979	+	1.25570i	0.234003	+	0.972236i	$0.424817\pi$
$829$	−20.8739	+	36.1546i	−0.724979	+	1.25570i	−0.958983	+	0.283465i	$0.908516\pi$
$830$			42.3121i			1.46868i
$831$	23.8348			0.826822
$832$	−4.97822	−	8.62253i	−0.172589	−	0.298932i
$833$	−6.33030	+	0.913701i	−0.219332	+	0.0316578i
$834$	64.3693	−	111.491i	2.22893	−	3.86062i
$835$	−75.1170	+	43.3688i	−2.59953	+	1.50084i
$836$	29.3085	−	21.7559i	1.01366	−	0.752445i
$837$		0			0
$838$	−77.2867			−2.66983
$839$	−21.0826	+	36.5161i	−0.727851	+	1.26068i	0.229938	+	0.973205i	$0.426148\pi$
$839$	−21.0826	+	36.5161i	−0.727851	+	1.26068i	−0.957790	+	0.287470i	$0.907186\pi$
$840$	−47.3911	+	16.4168i	−1.63515	+	0.566432i
$841$	10.1652	−	17.6066i	0.350522	−	0.607123i
$842$	26.1434	−	45.2816i	0.900960	−	1.56051i
$843$	34.8303	+	20.1093i	1.19962	+	0.692601i
$844$	−42.5608	−	24.5725i	−1.46500	−	0.845820i
$845$	42.0172	+	24.2587i	1.44544	+	0.834523i
$846$	4.29129	+	7.43273i	0.147538	+	0.255542i
$847$	5.00000	−	1.73205i	0.171802	−	0.0595140i
$848$			7.02355i			0.241190i
$849$	15.0000	+	8.66025i	0.514799	+	0.297219i
$850$	10.3739	+	17.9681i	0.355821	+	0.616299i
$851$			3.31320i			0.113575i
$852$		−	54.7225i		−	1.87476i
$853$	12.8739	+	7.43273i	0.440793	+	0.254492i	0.703934	−	0.710266i	$-0.251425\pi$
$853$	12.8739	+	7.43273i	0.440793	+	0.254492i	−0.263141	+	0.964757i	$0.584758\pi$
$854$	28.7477	+	24.8963i	0.983727	+	0.851933i
$855$	48.8085	+	65.7524i	1.66922	+	2.24869i
$856$	−12.7913	−	22.1552i	−0.437197	−	0.757248i
$857$	14.0608	+	24.3540i	0.480308	+	0.831917i	0.999745	−	0.0225915i	$-0.00719169\pi$
$857$	14.0608	+	24.3540i	0.480308	+	0.831917i	−0.519437	+	0.854509i	$0.673858\pi$
$858$	−12.5608	+	7.25198i	−0.428818	+	0.247578i
$859$	1.18693	+	0.685275i	0.0404976	+	0.0233813i	0.520112	−	0.854098i	$-0.325890\pi$
$859$	1.18693	+	0.685275i	0.0404976	+	0.0233813i	−0.479615	+	0.877479i	$0.659223\pi$
$860$	−20.9347	−	12.0866i	−0.713866	−	0.412151i
$861$	−11.6869	+	60.7271i	−0.398290	+	2.06957i
$862$	−51.2867			−1.74683
$863$	−16.0390	+	9.26013i	−0.545974	+	0.315218i	−0.747497	−	0.664265i	$-0.768744\pi$
$863$	−16.0390	+	9.26013i	−0.545974	+	0.315218i	0.201522	+	0.979484i	$0.435411\pi$
$864$		−	36.9253i		−	1.25622i
$865$		−	30.3785i		−	1.03290i
$866$	42.8911	−	24.7632i	1.45750	−	0.841487i
$867$	−45.1216			−1.53241
$868$		0			0
$869$	−18.0000	−	10.3923i	−0.610608	−	0.352535i
$870$	145.717	+	84.1297i	4.94026	+	2.85226i
$871$	2.37386	−	1.37055i	0.0804353	−	0.0464393i
$872$	−4.81307	−	8.33648i	−0.162991	−	0.282309i
$873$	4.79129	+	8.29875i	0.162161	+	0.280870i
$874$	9.00000	+	12.1244i	0.304430	+	0.410112i
$875$	−54.7432	−	10.5353i	−1.85066	−	0.356159i
$876$	65.2432	+	37.6682i	2.20436	+	1.27269i
$877$			4.75920i			0.160707i	0.996766	+	0.0803534i	$0.0256049\pi$
$877$			4.75920i			0.160707i	−0.996766	+	0.0803534i	$0.974395\pi$
$878$		−	33.1950i		−	1.12028i
$879$	29.3085	+	50.7638i	0.988552	+	1.71222i
$880$	−18.2477	−	10.5353i	−0.615131	−	0.355146i
$881$			4.93000i			0.166096i	0.996546	+	0.0830480i	$0.0264655\pi$
$881$			4.93000i			0.166096i	−0.996546	+	0.0830480i	$0.973535\pi$
$882$	−45.4129	−	57.6821i	−1.52913	−	1.94226i
$883$	−20.5000	−	35.5070i	−0.689880	−	1.19491i	−0.971876	−	0.235492i	$-0.924330\pi$
$883$	−20.5000	−	35.5070i	−0.689880	−	1.19491i	0.281996	−	0.959415i	$-0.409003\pi$
$884$	1.74773	+	1.00905i	0.0587824	+	0.0339380i
$885$	−49.3693	−	28.5034i	−1.65953	−	0.958131i
$886$	−29.0608	−	16.7783i	−0.976317	−	0.563677i
$887$	5.29129	−	9.16478i	0.177664	−	0.307723i	−0.763416	−	0.645907i	$-0.776479\pi$
$887$	5.29129	−	9.16478i	0.177664	−	0.307723i	0.941080	+	0.338184i	$0.109813\pi$
$888$	5.06080	−	8.76555i	0.169829	−	0.294153i
$889$	−3.31307	−	9.56400i	−0.111117	−	0.320766i
$890$	−48.8085	+	84.5388i	−1.63607	+	2.83375i
$891$	1.25227			0.0419527
$892$	−6.16515	+	10.6784i	−0.206425	+	0.357538i
$893$	−2.12614	−	2.86423i	−0.0711484	−	0.0958477i
$894$	83.5562	−	48.2412i	2.79454	−	1.61343i
$895$	18.5826	−	32.1860i	0.621147	−	1.07586i
$896$	−33.1824	−	6.38595i	−1.10855	−	0.213340i
$897$	−1.74773	−	3.02715i	−0.0583549	−	0.101074i
$898$	1.20871			0.0403352
$899$		0			0
$900$	−69.3693	+	120.151i	−2.31231	+	4.00504i
$901$	−1.79129	−	3.10260i	−0.0596765	−	0.103363i
$902$	47.6216	−	27.4943i	1.58563	−	0.915461i
$903$	3.08258	−	16.0175i	0.102582	−	0.533030i
$904$	−22.9129			−0.762071
$905$	53.4737	−	30.8730i	1.77753	−	1.02625i
$906$	−35.7042			−1.18619
$907$	−19.9955	+	11.5444i	−0.663938	+	0.383325i	−0.793776	−	0.608210i	$-0.791888\pi$
$907$	−19.9955	+	11.5444i	−0.663938	+	0.383325i	0.129838	+	0.991535i	$0.458554\pi$
$908$	7.73049	−	13.3896i	0.256545	−	0.444350i
$909$	79.4519	+	45.8716i	2.63525	+	1.52146i
$910$	−16.9782	+	5.88143i	−0.562822	+	0.194967i
$911$			4.73930i			0.157020i	0.996913	+	0.0785100i	$0.0250163\pi$
$911$			4.73930i			0.157020i	−0.996913	+	0.0785100i	$0.974984\pi$
$912$	2.50000	+	21.6506i	0.0827833	+	0.716924i
$913$	12.8085	+	7.39500i	0.423900	+	0.244739i
$914$	−49.4347	+	28.5411i	−1.63515	+	0.944056i
$915$	71.8693			2.37593
$916$	−16.7477	+	9.66930i	−0.553360	+	0.319483i
$917$	−36.4955	−	7.02355i	−1.20519	−	0.231938i
$918$	5.00000	+	8.66025i	0.165025	+	0.285831i
$919$	−11.0000	−	19.0526i	−0.362857	−	0.628486i	0.625573	−	0.780165i	$-0.284865\pi$
$919$	−11.0000	−	19.0526i	−0.362857	−	0.628486i	−0.988430	+	0.151680i	$0.951532\pi$
$920$	−5.37386	+	9.30780i	−0.177171	+	0.306869i
$921$	−69.1996			−2.28021
$922$	−17.2695	+	29.9117i	−0.568741	+	0.985088i
$923$		−	5.55765i		−	0.182932i
$924$	−11.6869	+	60.7271i	−0.384472	+	1.99777i
$925$	18.8085	−	10.8591i	0.618420	−	0.357045i
$926$			41.5891i			1.36670i
$927$	−49.7042			−1.63250
$928$	25.9347	+	44.9201i	0.851347	+	1.47458i
$929$			9.21245i			0.302251i	0.988515	+	0.151125i	$0.0482897\pi$
$929$			9.21245i			0.302251i	−0.988515	+	0.151125i	$0.951710\pi$
$930$		0			0
$931$	21.5000	+	21.6506i	0.704634	+	0.709571i
$932$	63.0345			2.06476
$933$			15.2469i			0.499160i
$934$	2.18693	+	3.78788i	0.0715586	+	0.123943i
$935$	10.7477			0.351488
$936$			6.56670i			0.214639i
$937$	30.5608	−	17.6443i	0.998378	−	0.576414i	0.0906098	−	0.995886i	$-0.471118\pi$
$937$	30.5608	−	17.6443i	0.998378	−	0.576414i	0.907768	+	0.419473i	$0.137785\pi$
$938$	3.79129	−	19.7001i	0.123790	−	0.643231i
$939$		−	24.1733i		−	0.788865i
$940$	4.47822	−	7.75650i	0.146063	−	0.252989i
$941$	9.79129			0.319187			0.159593	−	0.987183i	$-0.448982\pi$
$941$	9.79129			0.319187			0.159593	+	0.987183i	$0.448982\pi$
$942$	−11.6869	+	20.2424i	−0.380781	+	0.659532i
$943$	6.62614	+	11.4768i	0.215777	+	0.373736i
$944$	−4.66515	−	8.08028i	−0.151838	−	0.262991i
$945$	−50.9347	−	9.80238i	−1.65690	−	0.318871i
$946$	−12.5608	+	7.25198i	−0.408387	+	0.235782i
$947$	54.1652			1.76013			0.880065	−	0.474852i	$-0.157499\pi$
$947$	54.1652			1.76013			0.880065	+	0.474852i	$0.157499\pi$
$948$	−46.7477	+	26.9898i	−1.51830	+	0.876588i
$949$	6.62614	+	3.82560i	0.215093	+	0.124184i
$950$	39.3303	−	90.8294i	1.27604	−	2.94690i
$951$			55.7316i			1.80722i
$952$	3.95644	−	1.37055i	0.128229	−	0.0444198i
$953$	14.3911	+	8.30870i	0.466173	+	0.269145i	0.714636	−	0.699496i	$-0.246592\pi$
$953$	14.3911	+	8.30870i	0.466173	+	0.269145i	−0.248463	+	0.968641i	$0.579925\pi$
$954$	20.5608	−	35.6123i	0.665680	−	1.15299i
$955$	−39.1824	+	22.6220i	−1.26791	+	0.732029i
$956$	48.9564			1.58336
$957$	50.9347	−	29.4071i	1.64648	−	0.950598i
$958$	45.9129			1.48338
$959$	6.47822	−	33.6618i	0.209193	−	1.08700i
$960$	−119.260	+	68.8550i	−3.84911	+	2.22229i
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	1.81307	−	3.14033i	0.0584557	−	0.101248i
$963$		−	70.7678i		−	2.28046i
$964$	17.7913			0.573019
$965$	−14.1434	−	24.4970i	−0.455291	−	0.788588i
$966$	−25.1216	−	4.83465i	−0.808274	−	0.155552i
$967$	−15.7913	+	27.3513i	−0.507814	+	0.879559i	0.492146	+	0.870513i	$0.336213\pi$
$967$	−15.7913	+	27.3513i	−0.507814	+	0.879559i	−0.999959	+	0.00904597i	$0.997121\pi$
$968$	−3.00000	+	1.73205i	−0.0964237	+	0.0556702i
$969$	−6.62614	−	8.92640i	−0.212862	−	0.286757i
$970$	8.58258	−	14.8655i	0.275570	−	0.477301i
$971$	34.4519			1.10561			0.552807	−	0.833309i	$-0.313557\pi$
$971$	34.4519			1.10561			0.552807	+	0.833309i	$0.313557\pi$
$972$	22.5608	−	39.0764i	0.723638	−	1.25338i
$973$	−18.2477	−	52.6767i	−0.584995	−	1.68874i
$974$	2.29129	−	3.96863i	0.0734176	−	0.127163i
$975$	−11.4564	+	19.8431i	−0.366900	+	0.635489i
$976$	10.1869	+	5.88143i	0.326076	+	0.188260i
$977$	25.5826	+	14.7701i	0.818459	+	0.472538i	0.849885	−	0.526969i	$-0.176671\pi$
$977$	25.5826	+	14.7701i	0.818459	+	0.472538i	−0.0314257	+	0.999506i	$0.510005\pi$
$978$	31.7477	+	18.3296i	1.01518	+	0.586115i
$979$	17.0608	+	29.5502i	0.545265	+	0.944427i
$980$	−28.4347	+	71.1393i	−0.908312	+	2.27246i
$981$		−	26.6283i		−	0.850177i
$982$	−49.4347	−	28.5411i	−1.57752	−	0.910784i
$983$	−0.643371	−	1.11435i	−0.0205203	−	0.0355423i	0.855583	−	0.517666i	$-0.173199\pi$
$983$	−0.643371	−	1.11435i	−0.0205203	−	0.0355423i	−0.876103	+	0.482124i	$0.839866\pi$
$984$		−	40.4847i		−	1.29061i
$985$		−	47.0514i		−	1.49918i
$986$	−12.1652	−	7.02355i	−0.387417	−	0.223676i
$987$	5.93466	+	1.14213i	0.188902	+	0.0363543i
$988$	−1.10436	−	9.56400i	−0.0351342	−	0.304272i
$989$	−1.74773	−	3.02715i	−0.0555745	−	0.0962578i
$990$	61.6824	+	106.837i	1.96039	+	3.39550i
$991$	37.1869	−	21.4699i	1.18128	−	0.682013i	0.224971	−	0.974365i	$-0.427771\pi$
$991$	37.1869	−	21.4699i	1.18128	−	0.682013i	0.956311	+	0.292352i	$0.0944379\pi$
$992$		0			0
$993$	24.2477	+	13.9994i	0.769478	+	0.444259i
$994$	−30.7477	−	26.6283i	−0.975259	−	0.844599i
$995$	100.156			3.17516
$996$	33.2650	−	19.2055i	1.05404	−	0.608551i
$997$			26.2668i			0.831878i	0.909392	+	0.415939i	$0.136547\pi$
$997$			26.2668i			0.831878i	−0.909392	+	0.415939i	$0.863453\pi$
$998$		−	21.3368i		−	0.675405i
$999$	9.06534	−	5.23388i	0.286815	−	0.165593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.i.c.122.1	yes	4
7.2	even	3		931.2.s.c.901.1		4
7.3	odd	6		931.2.p.e.293.2		4
7.4	even	3		931.2.p.f.293.2		4
7.5	odd	6		133.2.s.c.103.1	yes	4
7.6	odd	2		931.2.i.d.521.1		4
19.12	odd	6		133.2.s.c.31.1	yes	4
133.12	even	6	inner	133.2.i.c.12.2	✓	4
133.31	even	6		931.2.p.f.734.2		4
133.69	even	6		931.2.s.c.31.1		4
133.88	odd	6		931.2.p.e.734.2		4
133.107	odd	6		931.2.i.d.411.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.i.c.12.2	✓	4	133.12	even	6	inner
133.2.i.c.122.1	yes	4	1.1	even	1	trivial
133.2.s.c.31.1	yes	4	19.12	odd	6
133.2.s.c.103.1	yes	4	7.5	odd	6
931.2.i.d.411.2		4	133.107	odd	6
931.2.i.d.521.1		4	7.6	odd	2
931.2.p.e.293.2		4	7.3	odd	6
931.2.p.e.734.2		4	133.88	odd	6
931.2.p.f.293.2		4	7.4	even	3
931.2.p.f.734.2		4	133.31	even	6
931.2.s.c.31.1		4	133.69	even	6
931.2.s.c.901.1		4	7.2	even	3

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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.18890i q^{2} +(1.39564 + 2.41733i) q^{3} -2.79129 q^{4} +3.92095i q^{5} +(5.29129 - 3.05493i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.73205i q^{8} +(-2.39564 + 4.14938i) q^{9} +O(q^{10})\)	\(q-2.18890i q^{2} +(1.39564 + 2.41733i) q^{3} -2.79129 q^{4} +3.92095i q^{5} +(5.29129 - 3.05493i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.73205i q^{8} +(-2.39564 + 4.14938i) q^{9} +8.58258 q^{10} +(1.50000 - 2.59808i) q^{11} +(-3.89564 - 6.74745i) q^{12} +(-0.395644 - 0.685275i) q^{13} +(-5.68693 - 1.09445i) q^{14} +(-9.47822 + 5.47225i) q^{15} -1.79129 q^{16} +(0.791288 - 0.456850i) q^{17} +(9.08258 + 5.24383i) q^{18} +(-4.00000 - 1.73205i) q^{19} -10.9445i q^{20} +(6.97822 - 2.41733i) q^{21} +(-5.68693 - 3.28335i) q^{22} +(0.791288 - 1.37055i) q^{23} +(-4.18693 + 2.41733i) q^{24} -10.3739 q^{25} +(-1.50000 + 0.866025i) q^{26} -5.00000 q^{27} +(-1.39564 + 7.25198i) q^{28} +(6.08258 - 3.51178i) q^{29} +(11.9782 + 20.7469i) q^{30} +7.38505i q^{32} +8.37386 q^{33} +(-1.00000 - 1.73205i) q^{34} +(10.1869 + 1.96048i) q^{35} +(6.68693 - 11.5821i) q^{36} +(-1.81307 + 1.04678i) q^{37} +(-3.79129 + 8.75560i) q^{38} +(1.10436 - 1.91280i) q^{39} -6.79129 q^{40} +(-4.18693 + 7.25198i) q^{41} +(-5.29129 - 15.2746i) q^{42} +(1.10436 - 1.91280i) q^{43} +(-4.18693 + 7.25198i) q^{44} +(-16.2695 - 9.39320i) q^{45} +(-3.00000 - 1.73205i) q^{46} +(0.708712 + 0.409175i) q^{47} +(-2.50000 - 4.33013i) q^{48} +(-6.50000 - 2.59808i) q^{49} +22.7074i q^{50} +(2.20871 + 1.27520i) q^{51} +(1.10436 + 1.91280i) q^{52} -3.92095i q^{53} +10.9445i q^{54} +(10.1869 + 5.88143i) q^{55} +(4.50000 + 0.866025i) q^{56} +(-1.39564 - 12.0866i) q^{57} +(-7.68693 - 13.3142i) q^{58} +(2.60436 + 4.51088i) q^{59} +(26.4564 - 15.2746i) q^{60} +(-5.68693 - 3.28335i) q^{61} +(9.58258 + 8.29875i) q^{63} +12.5826 q^{64} +(2.68693 - 1.55130i) q^{65} -18.3296i q^{66} +3.46410i q^{67} +(-2.20871 + 1.27520i) q^{68} +4.41742 q^{69} +(4.29129 - 22.2982i) q^{70} +(6.08258 + 3.51178i) q^{71} +(-7.18693 - 4.14938i) q^{72} +(-8.37386 + 4.83465i) q^{73} +(2.29129 + 3.96863i) q^{74} +(-14.4782 - 25.0770i) q^{75} +(11.1652 + 4.83465i) q^{76} +(-6.00000 - 5.19615i) q^{77} +(-4.18693 - 2.41733i) q^{78} -6.92820i q^{79} -7.02355i q^{80} +(0.208712 + 0.361500i) q^{81} +(15.8739 + 9.16478i) q^{82} +4.93000i q^{83} +(-19.4782 + 6.74745i) q^{84} +(1.79129 + 3.10260i) q^{85} +(-4.18693 - 2.41733i) q^{86} +(16.9782 + 9.80238i) q^{87} +(4.50000 + 2.59808i) q^{88} +(-5.68693 + 9.85005i) q^{89} +(-20.5608 + 35.6123i) q^{90} +(-1.97822 + 0.685275i) q^{91} +(-2.20871 + 3.82560i) q^{92} +(0.895644 - 1.55130i) q^{94} +(6.79129 - 15.6838i) q^{95} +(-17.8521 + 10.3069i) q^{96} +(1.00000 - 1.73205i) q^{97} +(-5.68693 + 14.2279i) q^{98} +(7.18693 + 12.4481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 2 q^{4} + 12 q^{6} + 2 q^{7} - 5 q^{9}+O(q^{10}) \) 4 * q + q^3 - 2 * q^4 + 12 * q^6 + 2 * q^7 - 5 * q^9	\( 4 q + q^{3} - 2 q^{4} + 12 q^{6} + 2 q^{7} - 5 q^{9} + 16 q^{10} + 6 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} + 2 q^{16} - 6 q^{17} + 18 q^{18} - 16 q^{19} + 5 q^{21} - 9 q^{22} - 6 q^{23} - 3 q^{24} - 14 q^{25} - 6 q^{26} - 20 q^{27} - q^{28} + 6 q^{29} + 25 q^{30} + 6 q^{33} - 4 q^{34} + 27 q^{35} + 13 q^{36} - 21 q^{37} - 6 q^{38} + 9 q^{39} - 18 q^{40} - 3 q^{41} - 12 q^{42} + 9 q^{43} - 3 q^{44} - 33 q^{45} - 12 q^{46} + 12 q^{47} - 10 q^{48} - 26 q^{49} + 18 q^{51} + 9 q^{52} + 27 q^{55} + 18 q^{56} - q^{57} - 17 q^{58} + 15 q^{59} + 60 q^{60} - 9 q^{61} + 20 q^{63} + 32 q^{64} - 3 q^{65} - 18 q^{68} + 36 q^{69} + 8 q^{70} + 6 q^{71} - 15 q^{72} - 6 q^{73} - 35 q^{75} + 8 q^{76} - 24 q^{77} - 3 q^{78} + 10 q^{81} + 36 q^{82} - 55 q^{84} - 2 q^{85} - 3 q^{86} + 45 q^{87} + 18 q^{88} - 9 q^{89} - 41 q^{90} + 15 q^{91} - 18 q^{92} - q^{94} + 18 q^{95} - 21 q^{96} + 4 q^{97} - 9 q^{98} + 15 q^{99}+O(q^{100}) \) 4 * q + q^3 - 2 * q^4 + 12 * q^6 + 2 * q^7 - 5 * q^9 + 16 * q^10 + 6 * q^11 - 11 * q^12 + 3 * q^13 - 9 * q^14 - 15 * q^15 + 2 * q^16 - 6 * q^17 + 18 * q^18 - 16 * q^19 + 5 * q^21 - 9 * q^22 - 6 * q^23 - 3 * q^24 - 14 * q^25 - 6 * q^26 - 20 * q^27 - q^28 + 6 * q^29 + 25 * q^30 + 6 * q^33 - 4 * q^34 + 27 * q^35 + 13 * q^36 - 21 * q^37 - 6 * q^38 + 9 * q^39 - 18 * q^40 - 3 * q^41 - 12 * q^42 + 9 * q^43 - 3 * q^44 - 33 * q^45 - 12 * q^46 + 12 * q^47 - 10 * q^48 - 26 * q^49 + 18 * q^51 + 9 * q^52 + 27 * q^55 + 18 * q^56 - q^57 - 17 * q^58 + 15 * q^59 + 60 * q^60 - 9 * q^61 + 20 * q^63 + 32 * q^64 - 3 * q^65 - 18 * q^68 + 36 * q^69 + 8 * q^70 + 6 * q^71 - 15 * q^72 - 6 * q^73 - 35 * q^75 + 8 * q^76 - 24 * q^77 - 3 * q^78 + 10 * q^81 + 36 * q^82 - 55 * q^84 - 2 * q^85 - 3 * q^86 + 45 * q^87 + 18 * q^88 - 9 * q^89 - 41 * q^90 + 15 * q^91 - 18 * q^92 - q^94 + 18 * q^95 - 21 * q^96 + 4 * q^97 - 9 * q^98 + 15 * q^99

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