LMFDB - Embedded newform 961.2.g.k.732.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			732.2
Root			$-2.52368i$ of defining polynomial
Character	$\chi$	$=$	961.732
Dual form			961.2.g.k.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.284315 - 0.206567i) q^{2} +(-2.64315 - 1.17681i) q^{3} +(-0.579869 - 1.78465i) q^{4} +(-1.48661 + 2.57489i) q^{5} +(0.508398 + 0.880572i) q^{6} +(-0.724084 + 0.804176i) q^{7} +(-0.420982 + 1.29565i) q^{8} +(3.59399 + 3.99153i) q^{9} +O(q^{10})$	\(q+(-0.284315 - 0.206567i) q^{2} +(-2.64315 - 1.17681i) q^{3} +(-0.579869 - 1.78465i) q^{4} +(-1.48661 + 2.57489i) q^{5} +(0.508398 + 0.880572i) q^{6} +(-0.724084 + 0.804176i) q^{7} +(-0.420982 + 1.29565i) q^{8} +(3.59399 + 3.99153i) q^{9} +(0.954554 - 0.424995i) q^{10} +(2.37824 + 0.505510i) q^{11} +(-0.567511 + 5.39951i) q^{12} +(-0.300378 - 2.85791i) q^{13} +(0.371984 - 0.0790676i) q^{14} +(6.95951 - 5.05638i) q^{15} +(-2.64890 + 1.92454i) q^{16} +(1.78489 - 0.379390i) q^{17} +(-0.197307 - 1.87725i) q^{18} +(-0.221420 + 2.10667i) q^{19} +(5.45733 + 1.15999i) q^{20} +(2.86023 - 1.27345i) q^{21} +(-0.571747 - 0.634989i) q^{22} +(-0.136652 + 0.420572i) q^{23} +(2.63745 - 2.92919i) q^{24} +(-1.92005 - 3.32562i) q^{25} +(-0.504947 + 0.874594i) q^{26} +(-2.11998 - 6.52462i) q^{27} +(1.85505 + 0.825921i) q^{28} +(2.55579 + 1.85689i) q^{29} -3.02317 q^{30} +3.87532 q^{32} +(-5.69116 - 4.13487i) q^{33} +(-0.585840 - 0.260833i) q^{34} +(-0.994234 - 3.05994i) q^{35} +(5.03946 - 8.72860i) q^{36} +(-1.57338 - 2.72517i) q^{37} +(0.498121 - 0.553219i) q^{38} +(-2.56926 + 7.90738i) q^{39} +(-2.71032 - 3.01011i) q^{40} +(-6.34570 + 2.82529i) q^{41} +(-1.07626 - 0.228766i) q^{42} +(0.879333 - 8.36630i) q^{43} +(-0.476906 - 4.53746i) q^{44} +(-15.6207 + 3.32027i) q^{45} +(0.125728 - 0.0913471i) q^{46} +(6.44144 - 4.67998i) q^{47} +(9.26627 - 1.96961i) q^{48} +(0.609297 + 5.79707i) q^{49} +(-0.141065 + 1.34214i) q^{50} +(-5.16421 - 1.09769i) q^{51} +(-4.92620 + 2.19328i) q^{52} +(-3.33026 - 3.69863i) q^{53} +(-0.745029 + 2.29296i) q^{54} +(-4.83716 + 5.37221i) q^{55} +(-0.737104 - 1.27670i) q^{56} +(3.06439 - 5.30768i) q^{57} +(-0.343078 - 1.05588i) q^{58} +(-10.9753 - 4.88651i) q^{59} +(-13.0595 - 9.48827i) q^{60} -14.4351 q^{61} -5.81225 q^{63} +(4.19600 + 3.04857i) q^{64} +(7.80536 + 3.47517i) q^{65} +(0.763955 + 2.35121i) q^{66} +(3.21879 - 5.57511i) q^{67} +(-1.71208 - 2.96541i) q^{68} +(0.856125 - 0.950823i) q^{69} +(-0.349406 + 1.07536i) q^{70} +(1.12272 + 1.24690i) q^{71} +(-6.68463 + 2.97619i) q^{72} +(-14.0464 - 2.98565i) q^{73} +(-0.115595 + 1.09981i) q^{74} +(1.16137 + 11.0497i) q^{75} +(3.88807 - 0.826435i) q^{76} +(-2.12856 + 1.54649i) q^{77} +(2.36388 - 1.71746i) q^{78} +(3.37230 - 0.716805i) q^{79} +(-1.01759 - 9.68169i) q^{80} +(-0.390488 + 3.71525i) q^{81} +(2.38779 + 0.507540i) q^{82} +(11.7424 - 5.22804i) q^{83} +(-3.93123 - 4.36607i) q^{84} +(-1.67655 + 5.15991i) q^{85} +(-1.97821 + 2.19702i) q^{86} +(-4.57015 - 7.91573i) q^{87} +(-1.65616 + 2.86855i) q^{88} +(0.698188 + 2.14880i) q^{89} +(5.12704 + 2.28271i) q^{90} +(2.51576 + 1.82781i) q^{91} +0.829816 q^{92} -2.79812 q^{94} +(-5.09528 - 3.70194i) q^{95} +(-10.2431 - 4.56051i) q^{96} +(1.05463 + 3.24582i) q^{97} +(1.02425 - 1.77405i) q^{98} +(6.52961 + 11.3096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9	\( 16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} - 21 q^{14} + 14 q^{15} - 2 q^{16} + 9 q^{17} + 12 q^{18} - 29 q^{19} - 8 q^{20} - 6 q^{21} - 21 q^{22} + q^{23} - 5 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} + 45 q^{28} - 14 q^{29} - 22 q^{30} - 42 q^{32} - 13 q^{33} - 17 q^{34} - 9 q^{35} + q^{36} - 8 q^{37} + 23 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} - 51 q^{42} - 37 q^{43} - 6 q^{44} - 70 q^{45} + 34 q^{46} + 14 q^{47} + 4 q^{48} - 43 q^{49} + 3 q^{50} + 33 q^{51} - 46 q^{52} - 9 q^{53} - 46 q^{54} + 8 q^{55} - 30 q^{56} - 17 q^{57} - 15 q^{58} - 11 q^{59} - 75 q^{60} - 60 q^{61} - 46 q^{63} + 23 q^{64} + 18 q^{65} - 30 q^{66} + 13 q^{67} + 30 q^{68} - 37 q^{69} + 12 q^{70} + 31 q^{71} - 38 q^{72} - 13 q^{73} + 43 q^{74} - 17 q^{75} - 12 q^{76} + 18 q^{77} - 15 q^{78} - 12 q^{79} + 6 q^{80} - 22 q^{81} - q^{82} + 44 q^{83} + 23 q^{84} + 37 q^{85} + 19 q^{86} + 15 q^{87} - 17 q^{88} + q^{89} + 7 q^{90} + 8 q^{91} - 64 q^{92} + 44 q^{94} - 22 q^{95} + 8 q^{96} + 3 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 - 21 * q^14 + 14 * q^15 - 2 * q^16 + 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 - 6 * q^21 - 21 * q^22 + q^23 - 5 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 45 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 - 17 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 51 * q^42 - 37 * q^43 - 6 * q^44 - 70 * q^45 + 34 * q^46 + 14 * q^47 + 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 - 46 * q^52 - 9 * q^53 - 46 * q^54 + 8 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 - 11 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 + 18 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 - 13 * q^73 + 43 * q^74 - 17 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 - 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 + 44 * q^83 + 23 * q^84 + 37 * q^85 + 19 * q^86 + 15 * q^87 - 17 * q^88 + q^89 + 7 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

Coefficient data

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

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

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

$2$	−0.284315	−	0.206567i	−0.201041	−	0.146065i	0.482710	−	0.875780i	$-0.339653\pi$
$2$	−0.284315	−	0.206567i	−0.201041	−	0.146065i	−0.683751	+	0.729715i	$0.739653\pi$
$3$	−2.64315	−	1.17681i	−1.52603	−	0.679430i	−0.539343	−	0.842086i	$-0.681327\pi$
$3$	−2.64315	−	1.17681i	−1.52603	−	0.679430i	−0.986683	+	0.162656i	$0.947994\pi$
$4$	−0.579869	−	1.78465i	−0.289934	−	0.892327i
$5$	−1.48661	+	2.57489i	−0.664834	+	1.15153i	0.314496	+	0.949259i	$0.398165\pi$
$5$	−1.48661	+	2.57489i	−0.664834	+	1.15153i	−0.979330	+	0.202268i	$0.935169\pi$
$6$	0.508398	+	0.880572i	0.207553	+	0.359492i
$7$	−0.724084	+	0.804176i	−0.273678	+	0.303950i	−0.864278	−	0.503014i	$-0.832224\pi$
$7$	−0.724084	+	0.804176i	−0.273678	+	0.303950i	0.590600	+	0.806964i	$0.298891\pi$
$8$	−0.420982	+	1.29565i	−0.148840	+	0.458081i
$9$	3.59399	+	3.99153i	1.19800	+	1.33051i
$10$	0.954554	−	0.424995i	0.301856	−	0.134395i
$11$	2.37824	+	0.505510i	0.717066	+	0.152417i	0.551974	−	0.833861i	$-0.313875\pi$
$11$	2.37824	+	0.505510i	0.717066	+	0.152417i	0.165092	+	0.986278i	$0.447208\pi$
$12$	−0.567511	+	5.39951i	−0.163826	+	1.55870i
$13$	−0.300378	−	2.85791i	−0.0833100	−	0.792642i	−0.953797	−	0.300451i	$-0.902863\pi$
$13$	−0.300378	−	2.85791i	−0.0833100	−	0.792642i	0.870487	−	0.492191i	$-0.163804\pi$
$14$	0.371984	−	0.0790676i	0.0994169	−	0.0211317i
$15$	6.95951	−	5.05638i	1.79694	−	1.30555i
$16$	−2.64890	+	1.92454i	−0.662226	+	0.481135i
$17$	1.78489	−	0.379390i	0.432899	−	0.0920156i	0.0136923	−	0.999906i	$-0.495641\pi$
$17$	1.78489	−	0.379390i	0.432899	−	0.0920156i	0.419207	+	0.907891i	$0.362308\pi$
$18$	−0.197307	−	1.87725i	−0.0465057	−	0.442473i
$19$	−0.221420	+	2.10667i	−0.0507972	+	0.483303i	0.939318	+	0.343047i	$0.111459\pi$
$19$	−0.221420	+	2.10667i	−0.0507972	+	0.483303i	−0.990115	+	0.140256i	$0.955208\pi$
$20$	5.45733	+	1.15999i	1.22030	+	0.259382i
$21$	2.86023	−	1.27345i	0.624152	−	0.277890i
$22$	−0.571747	−	0.634989i	−0.121897	−	0.135380i
$23$	−0.136652	+	0.420572i	−0.0284939	+	0.0876953i	−0.964292	−	0.264841i	$-0.914681\pi$
$23$	−0.136652	+	0.420572i	−0.0284939	+	0.0876953i	0.935798	+	0.352536i	$0.114681\pi$
$24$	2.63745	−	2.92919i	0.538367	−	0.597917i
$25$	−1.92005	−	3.32562i	−0.384010	−	0.665124i
$26$	−0.504947	+	0.874594i	−0.0990283	+	0.171522i
$27$	−2.11998	−	6.52462i	−0.407990	−	1.25566i
$28$	1.85505	+	0.825921i	0.350571	+	0.156084i
$29$	2.55579	+	1.85689i	0.474599	+	0.344816i	0.799231	−	0.601024i	$-0.205240\pi$
$29$	2.55579	+	1.85689i	0.474599	+	0.344816i	−0.324632	+	0.945840i	$0.605240\pi$
$30$	−3.02317			−0.551953
$31$		0			0
$31$		0			0
$32$	3.87532			0.685067
$33$	−5.69116	−	4.13487i	−0.990704	−	0.719789i
$34$	−0.585840	−	0.260833i	−0.100471	−	0.0447324i
$35$	−0.994234	−	3.05994i	−0.168056	−	0.517224i
$36$	5.03946	−	8.72860i	0.839910	−	1.45477i
$37$	−1.57338	−	2.72517i	−0.258661	−	0.448015i	0.707222	−	0.706991i	$-0.249948\pi$
$37$	−1.57338	−	2.72517i	−0.258661	−	0.448015i	−0.965884	+	0.258977i	$0.916615\pi$
$38$	0.498121	−	0.553219i	0.0808059	−	0.0897440i
$39$	−2.56926	+	7.90738i	−0.411412	+	1.26619i
$40$	−2.71032	−	3.01011i	−0.428539	−	0.475941i
$41$	−6.34570	+	2.82529i	−0.991032	+	0.441236i	−0.837221	−	0.546864i	$-0.815821\pi$
$41$	−6.34570	+	2.82529i	−0.991032	+	0.441236i	−0.153811	+	0.988100i	$0.549155\pi$
$42$	−1.07626	−	0.228766i	−0.166070	−	0.0352993i
$43$	0.879333	−	8.36630i	0.134097	−	1.27585i	−0.695924	−	0.718116i	$-0.745005\pi$
$43$	0.879333	−	8.36630i	0.134097	−	1.27585i	0.830021	−	0.557732i	$-0.188328\pi$
$44$	−0.476906	−	4.53746i	−0.0718963	−	0.684048i
$45$	−15.6207	+	3.32027i	−2.32859	+	0.494957i
$46$	0.125728	−	0.0913471i	0.0185377	−	0.0134684i
$47$	6.44144	−	4.67998i	0.939580	−	0.682645i	−0.00873953	−	0.999962i	$-0.502782\pi$
$47$	6.44144	−	4.67998i	0.939580	−	0.682645i	0.948320	+	0.317317i	$0.102782\pi$
$48$	9.26627	−	1.96961i	1.33747	−	0.284288i
$49$	0.609297	+	5.79707i	0.0870424	+	0.828153i
$50$	−0.141065	+	1.34214i	−0.0199496	+	0.189807i
$51$	−5.16421	−	1.09769i	−0.723134	−	0.153707i
$52$	−4.92620	+	2.19328i	−0.683141	+	0.304154i
$53$	−3.33026	−	3.69863i	−0.457447	−	0.508046i	0.469658	−	0.882848i	$-0.344377\pi$
$53$	−3.33026	−	3.69863i	−0.457447	−	0.508046i	−0.927105	+	0.374802i	$0.877711\pi$
$54$	−0.745029	+	2.29296i	−0.101386	+	0.312033i
$55$	−4.83716	+	5.37221i	−0.652243	+	0.724389i
$56$	−0.737104	−	1.27670i	−0.0984997	−	0.170606i
$57$	3.06439	−	5.30768i	0.405889	−	0.703020i
$58$	−0.343078	−	1.05588i	−0.0450483	−	0.138644i
$59$	−10.9753	−	4.88651i	−1.42886	−	0.636169i	−0.460940	−	0.887431i	$-0.652488\pi$
$59$	−10.9753	−	4.88651i	−1.42886	−	0.636169i	−0.967919	+	0.251262i	$0.919154\pi$
$60$	−13.0595	−	9.48827i	−1.68597	−	1.22493i
$61$	−14.4351			−1.84823			−0.924115	−	0.382115i	$-0.875196\pi$
$61$	−14.4351			−1.84823			−0.924115	+	0.382115i	$0.875196\pi$
$62$		0			0
$63$	−5.81225			−0.732274
$64$	4.19600	+	3.04857i	0.524499	+	0.381071i
$65$	7.80536	+	3.47517i	0.968136	+	0.431042i
$66$	0.763955	+	2.35121i	0.0940363	+	0.289414i
$67$	3.21879	−	5.57511i	0.393238	−	0.681108i	−0.599636	−	0.800273i	$-0.704688\pi$
$67$	3.21879	−	5.57511i	0.393238	−	0.681108i	0.992875	+	0.119164i	$0.0380215\pi$
$68$	−1.71208	−	2.96541i	−0.207620	−	0.359609i
$69$	0.856125	−	0.950823i	0.103065	−	0.114466i
$70$	−0.349406	+	1.07536i	−0.0417620	+	0.128530i
$71$	1.12272	+	1.24690i	0.133242	+	0.147980i	0.806073	−	0.591816i	$-0.201589\pi$
$71$	1.12272	+	1.24690i	0.133242	+	0.147980i	−0.672831	+	0.739796i	$0.734922\pi$
$72$	−6.68463	+	2.97619i	−0.787792	+	0.350747i
$73$	−14.0464	−	2.98565i	−1.64400	−	0.349443i	−0.709309	−	0.704898i	$-0.750993\pi$
$73$	−14.0464	−	2.98565i	−1.64400	−	0.349443i	−0.934694	+	0.355455i	$0.884326\pi$
$74$	−0.115595	+	1.09981i	−0.0134376	+	0.127851i
$75$	1.16137	+	11.0497i	0.134103	+	1.27590i
$76$	3.88807	−	0.826435i	0.445992	−	0.0947985i
$77$	−2.12856	+	1.54649i	−0.242572	+	0.176239i
$78$	2.36388	−	1.71746i	0.267657	−	0.194464i
$79$	3.37230	−	0.716805i	0.379414	−	0.0806469i	−0.0142570	−	0.999898i	$-0.504538\pi$
$79$	3.37230	−	0.716805i	0.379414	−	0.0806469i	0.393671	+	0.919251i	$0.371205\pi$
$80$	−1.01759	−	9.68169i	−0.113770	−	1.08245i
$81$	−0.390488	+	3.71525i	−0.0433876	+	0.412805i
$82$	2.38779	+	0.507540i	0.263687	+	0.0560484i
$83$	11.7424	−	5.22804i	1.28889	−	0.573851i	0.356161	−	0.934425i	$-0.384086\pi$
$83$	11.7424	−	5.22804i	1.28889	−	0.573851i	0.932731	+	0.360573i	$0.117419\pi$
$84$	−3.93123	−	4.36607i	−0.428932	−	0.476378i
$85$	−1.67655	+	5.15991i	−0.181848	+	0.559670i
$86$	−1.97821	+	2.19702i	−0.213315	+	0.236911i
$87$	−4.57015	−	7.91573i	−0.489972	−	0.848656i
$88$	−1.65616	+	2.86855i	−0.176547	+	0.305789i
$89$	0.698188	+	2.14880i	0.0740078	+	0.227773i	0.981217	−	0.192907i	$-0.0617916\pi$
$89$	0.698188	+	2.14880i	0.0740078	+	0.227773i	−0.907209	+	0.420680i	$0.861792\pi$
$90$	5.12704	+	2.28271i	0.540438	+	0.240618i
$91$	2.51576	+	1.82781i	0.263724	+	0.191606i
$92$	0.829816			0.0865143
$93$		0			0
$94$	−2.79812			−0.288604
$95$	−5.09528	−	3.70194i	−0.522765	−	0.379811i
$96$	−10.2431	−	4.56051i	−1.04543	−	0.465455i
$97$	1.05463	+	3.24582i	0.107082	+	0.329563i	0.990213	−	0.139562i	$-0.0445693\pi$
$97$	1.05463	+	3.24582i	0.107082	+	0.329563i	−0.883132	+	0.469125i	$0.844569\pi$
$98$	1.02425	−	1.77405i	0.103465	−	0.179207i
$99$	6.52961	+	11.3096i	0.656251	+	1.13666i
$100$	−4.82170	+	5.35504i	−0.482170	+	0.535504i
$101$	5.47495	−	16.8502i	0.544778	−	1.67665i	−0.176741	−	0.984257i	$-0.556555\pi$
$101$	5.47495	−	16.8502i	0.544778	−	1.67665i	0.721518	−	0.692395i	$-0.243445\pi$
$102$	1.24152	+	1.37884i	0.122928	+	0.136526i
$103$	7.37583	−	3.28393i	0.726762	−	0.323575i	−0.00979397	−	0.999952i	$-0.503118\pi$
$103$	7.37583	−	3.28393i	0.726762	−	0.323575i	0.736556	+	0.676377i	$0.236451\pi$
$104$	3.82930	+	0.813944i	0.375494	+	0.0798137i
$105$	−0.973045	+	9.25791i	−0.0949595	+	0.903479i
$106$	0.182829	+	1.73950i	0.0177579	+	0.168955i
$107$	11.8857	−	2.52638i	1.14903	−	0.244234i	0.406245	−	0.913764i	$-0.366838\pi$
$107$	11.8857	−	2.52638i	1.14903	−	0.244234i	0.742785	+	0.669530i	$0.233505\pi$
$108$	−10.4149	+	7.56685i	−1.00217	+	0.728121i
$109$	0.511381	−	0.371540i	0.0489815	−	0.0355871i	−0.563025	−	0.826440i	$-0.690363\pi$
$109$	0.511381	−	0.371540i	0.0489815	−	0.0355871i	0.612007	+	0.790853i	$0.290363\pi$
$110$	2.48500	−	0.528202i	0.236935	−	0.0503621i
$111$	0.951676	+	9.05459i	0.0903291	+	0.859424i
$112$	0.370357	−	3.52371i	0.0349955	−	0.332960i
$113$	11.0534	+	2.34947i	1.03982	+	0.221020i	0.696019	−	0.718024i	$-0.254953\pi$
$113$	11.0534	+	2.34947i	1.03982	+	0.221020i	0.343798	+	0.939044i	$0.388286\pi$
$114$	−1.96764	+	0.876051i	−0.184287	+	0.0820497i
$115$	−0.879779	−	0.977093i	−0.0820398	−	0.0911144i
$116$	1.83188	−	5.63796i	0.170086	−	0.523472i
$117$	10.3279	−	11.4703i	0.954813	−	1.06043i
$118$	2.11104	+	3.65643i	0.194337	+	0.336602i
$119$	−0.987313	+	1.71008i	−0.0905068	+	0.156762i
$120$	3.62146	+	11.1457i	0.330593	+	1.01746i
$121$	−4.64852	−	2.06965i	−0.422593	−	0.188150i
$122$	4.10412	+	2.98182i	0.371570	+	0.269961i
$123$	20.0975			1.81213
$124$		0			0
$125$	−3.44866			−0.308458
$126$	1.65251	+	1.20062i	0.147217	+	0.106960i
$127$	0.107621	+	0.0479161i	0.00954985	+	0.00425186i	0.411506	−	0.911407i	$-0.365003\pi$
$127$	0.107621	+	0.0479161i	0.00954985	+	0.00425186i	−0.401956	+	0.915659i	$0.631670\pi$
$128$	−2.95833	−	9.10481i	−0.261482	−	0.804759i
$129$	−12.1697	+	21.0786i	−1.07149	+	1.85587i
$130$	−1.50132	−	2.60037i	−0.131675	−	0.228068i
$131$	3.87022	−	4.29831i	0.338143	−	0.375545i	−0.549960	−	0.835191i	$-0.685357\pi$
$131$	3.87022	−	4.29831i	0.338143	−	0.375545i	0.888102	+	0.459646i	$0.152024\pi$
$132$	−4.07918	+	12.5544i	−0.355047	+	1.09272i
$133$	−1.53381	−	1.70347i	−0.132998	−	0.147709i
$134$	−2.06678	+	0.920192i	−0.178543	+	0.0794924i
$135$	19.9518	+	4.24089i	1.71718	+	0.364997i
$136$	−0.259850	+	2.47231i	−0.0222820	+	0.211999i
$137$	−1.23400	−	11.7408i	−0.105428	−	1.00308i	−0.911510	−	0.411277i	$-0.865083\pi$
$137$	−1.23400	−	11.7408i	−0.105428	−	1.00308i	0.806083	−	0.591803i	$-0.201584\pi$
$138$	−0.439818	+	0.0934861i	−0.0374398	+	0.00795807i
$139$	12.4767	−	9.06482i	1.05826	−	0.768868i	0.0844915	−	0.996424i	$-0.473073\pi$
$139$	12.4767	−	9.06482i	1.05826	−	0.768868i	0.973765	+	0.227556i	$0.0730734\pi$
$140$	−4.88440	+	3.54873i	−0.412807	+	0.299922i
$141$	−22.5331	+	4.78957i	−1.89763	+	0.403354i
$142$	−0.0616362	−	0.586429i	−0.00517240	−	0.0492121i
$143$	0.730331	−	6.94864i	0.0610734	−	0.581074i
$144$	−17.2020	−	3.65640i	−1.43350	−	0.304700i
$145$	−8.58078	+	3.82041i	−0.712595	+	0.317268i
$146$	3.37685	+	3.75038i	0.279470	+	0.310383i
$147$	5.21157	−	16.0396i	0.429843	−	1.32292i
$148$	−3.95112	+	4.38817i	−0.324780	+	0.360705i
$149$	5.97511	+	10.3492i	0.489500	+	0.847840i	0.999927	−	0.0120817i	$-0.00384583\pi$
$149$	5.97511	+	10.3492i	0.489500	+	0.847840i	−0.510427	+	0.859921i	$0.670512\pi$
$150$	1.95230	−	3.38148i	0.159404	−	0.276097i
$151$	−1.33561	−	4.11059i	−0.108691	−	0.334515i	0.881888	−	0.471458i	$-0.156272\pi$
$151$	−1.33561	−	4.11059i	−0.108691	−	0.334515i	−0.990579	+	0.136943i	$0.956272\pi$
$152$	−2.63629	−	1.17375i	−0.213831	−	0.0952039i
$153$	7.92923	+	5.76092i	0.641040	+	0.465743i
$154$	0.924636			0.0745093
$155$		0			0
$156$	15.6018			1.24914
$157$	7.04204	+	5.11634i	0.562016	+	0.408328i	0.832196	−	0.554481i	$-0.187083\pi$
$157$	7.04204	+	5.11634i	0.562016	+	0.408328i	−0.270180	+	0.962810i	$0.587083\pi$
$158$	−1.10686	−	0.492808i	−0.0880574	−	0.0392057i
$159$	4.44982	+	13.6951i	0.352893	+	1.08609i
$160$	−5.76111	+	9.97854i	−0.455456	+	0.788873i
$161$	−0.239267	−	0.414422i	−0.0188568	−	0.0326610i
$162$	0.878469	−	0.975638i	0.0690190	−	0.0766534i
$163$	0.966575	−	2.97481i	0.0757080	−	0.233005i	−0.906040	−	0.423192i	$-0.860909\pi$
$163$	0.966575	−	2.97481i	0.0757080	−	0.233005i	0.981748	+	0.190187i	$0.0609095\pi$
$164$	8.72184	+	9.68658i	0.681061	+	0.756395i
$165$	19.1074	−	8.50717i	1.48751	−	0.662282i
$166$	−4.41847	−	0.939174i	−0.342939	−	0.0728940i
$167$	1.39597	−	13.2818i	0.108023	−	1.02777i	−0.797454	−	0.603380i	$-0.793820\pi$
$167$	1.39597	−	13.2818i	0.108023	−	1.02777i	0.905477	−	0.424395i	$-0.139513\pi$
$168$	0.445847	+	4.24195i	0.0343978	+	0.327274i
$169$	4.63850	−	0.985943i	0.356807	−	0.0758417i
$170$	1.54253	−	1.12072i	0.118307	−	0.0859551i
$171$	−9.20462	+	6.68755i	−0.703895	+	0.511410i
$172$	−15.4408	+	3.28205i	−1.17735	+	0.250254i
$173$	−1.99072	−	18.9404i	−0.151351	−	1.44001i	−0.761726	−	0.647900i	$-0.775648\pi$
$173$	−1.99072	−	18.9404i	−0.151351	−	1.44001i	0.610374	−	0.792113i	$-0.291019\pi$
$174$	−0.335766	+	3.19460i	−0.0254544	+	0.242182i
$175$	4.06466	+	0.863970i	0.307259	+	0.0653100i
$176$	−7.27260	+	3.23797i	−0.548193	+	0.244071i
$177$	23.2589	+	25.8316i	1.74824	+	1.94162i
$178$	0.245366	−	0.755159i	0.0183910	−	0.0566016i
$179$	−0.0530821	+	0.0589537i	−0.00396754	+	0.00440640i	−0.745125	−	0.666924i	$-0.767610\pi$
$179$	−0.0530821	+	0.0589537i	−0.00396754	+	0.00440640i	0.741158	+	0.671331i	$0.234277\pi$
$180$	14.9835	+	25.9521i	1.11680	+	1.93436i
$181$	−1.08143	+	1.87308i	−0.0803817	+	0.139225i	−0.903414	−	0.428769i	$-0.858947\pi$
$181$	−1.08143	+	1.87308i	−0.0803817	+	0.139225i	0.823032	+	0.567995i	$0.192281\pi$
$182$	−0.337704	−	1.03935i	−0.0250323	−	0.0770415i
$183$	38.1543	+	16.9874i	2.82045	+	1.25574i
$184$	−0.487386	−	0.354107i	−0.0359306	−	0.0261051i
$185$	9.35601			0.687868
$186$		0			0
$187$	4.43668			0.324442
$188$	−12.0873	−	8.78195i	−0.881559	−	0.640490i
$189$	6.78199	+	3.01954i	0.493317	+	0.219639i
$190$	0.683966	+	2.10503i	0.0496201	+	0.152715i
$191$	2.67085	−	4.62604i	0.193256	−	0.334729i	−0.753072	−	0.657939i	$-0.771429\pi$
$191$	2.67085	−	4.62604i	0.193256	−	0.334729i	0.946327	+	0.323210i	$0.104762\pi$
$192$	−7.50308	−	12.9957i	−0.541488	−	0.937885i
$193$	−1.42771	+	1.58563i	−0.102769	+	0.114136i	−0.792335	−	0.610087i	$-0.791135\pi$
$193$	−1.42771	+	1.58563i	−0.102769	+	0.114136i	0.689566	+	0.724223i	$0.257801\pi$
$194$	0.370632	−	1.14069i	0.0266098	−	0.0818966i
$195$	−16.5412	−	18.3708i	−1.18454	−	1.31556i
$196$	9.99245	−	4.44893i	0.713746	−	0.317780i
$197$	5.74733	+	1.22163i	0.409480	+	0.0870377i	0.408046	−	0.912961i	$-0.366210\pi$
$197$	5.74733	+	1.22163i	0.409480	+	0.0870377i	0.00143405	+	0.999999i	$0.499544\pi$
$198$	0.479727	−	4.56429i	0.0340927	−	0.324370i
$199$	−0.724169	−	6.89001i	−0.0513350	−	0.488420i	−0.989740	−	0.142882i	$-0.954363\pi$
$199$	−0.724169	−	6.89001i	−0.0513350	−	0.488420i	0.938405	−	0.345538i	$-0.112304\pi$
$200$	5.11714	−	1.08768i	0.361837	−	0.0769108i
$201$	−15.0686	+	10.9480i	−1.06286	+	0.772211i
$202$	−5.03729	+	3.65981i	−0.354423	+	0.257503i
$203$	−3.34388	+	0.710763i	−0.234694	+	0.0498858i
$204$	1.03557	+	9.85283i	0.0725047	+	0.689836i
$205$	2.15880	−	20.5396i	0.150777	−	1.43455i
$206$	−2.77541	−	0.589931i	−0.193372	−	0.0411025i
$207$	−2.16985	+	0.966082i	−0.150815	+	0.0671473i
$208$	6.29584	+	6.99224i	0.436538	+	0.484824i
$209$	−1.59153	+	4.89823i	−0.110089	+	0.338818i
$210$	2.18903	−	2.43116i	0.151057	−	0.167766i
$211$	−8.35437	−	14.4702i	−0.575139	−	0.996170i	−0.996027	−	0.0890568i	$-0.971615\pi$
$211$	−8.35437	−	14.4702i	−0.575139	−	0.996170i	0.420888	−	0.907113i	$-0.361719\pi$
$212$	−4.66966	+	8.08808i	−0.320713	+	0.555492i
$213$	−1.50015	−	4.61698i	−0.102788	−	0.316350i
$214$	−3.90114	−	1.73690i	−0.266676	−	0.118732i
$215$	20.2351	+	14.7016i	1.38002	+	1.00264i
$216$	9.34610			0.635921
$217$		0			0
$218$	−0.222141			−0.0150453
$219$	33.6132	+	24.4214i	2.27137	+	1.65024i
$220$	12.3925	+	5.51747i	0.835499	+	0.371988i
$221$	−1.62040	−	4.98709i	−0.109000	−	0.335468i
$222$	1.59980	−	2.77094i	0.107372	−	0.185973i
$223$	3.13078	+	5.42267i	0.209653	+	0.363129i	0.951605	−	0.307323i	$-0.0994333\pi$
$223$	3.13078	+	5.42267i	0.209653	+	0.363129i	−0.741952	+	0.670453i	$0.766100\pi$
$224$	−2.80606	+	3.11644i	−0.187488	+	0.208226i
$225$	6.37369	−	19.6162i	0.424912	−	1.30775i
$226$	−2.65732	−	2.95126i	−0.176763	−	0.196315i
$227$	−7.16906	+	3.19187i	−0.475827	+	0.211852i	−0.630615	−	0.776096i	$-0.717197\pi$
$227$	−7.16906	+	3.19187i	−0.475827	+	0.211852i	0.154788	+	0.987948i	$0.450531\pi$
$228$	−11.2493	−	2.39112i	−0.745004	−	0.158356i
$229$	−1.33514	+	12.7030i	−0.0882286	+	0.839439i	0.857501	+	0.514483i	$0.172016\pi$
$229$	−1.33514	+	12.7030i	−0.0882286	+	0.839439i	−0.945729	+	0.324956i	$0.894651\pi$
$230$	0.0482991	+	0.459535i	0.00318475	+	0.0303009i
$231$	7.44604	−	1.58271i	0.489914	−	0.104134i
$232$	−3.48183	+	2.52969i	−0.228593	+	0.166083i
$233$	−10.2887	+	7.47514i	−0.674032	+	0.489713i	−0.871373	−	0.490622i	$-0.836770\pi$
$233$	−10.2887	+	7.47514i	−0.674032	+	0.489713i	0.197340	+	0.980335i	$0.436770\pi$
$234$	−5.30575	+	1.12777i	−0.346848	+	0.0737248i
$235$	2.47450	+	23.5433i	0.161419	+	1.53580i
$236$	−2.35650	+	22.4206i	−0.153395	+	1.45946i
$237$	−9.75706	−	2.07393i	−0.633789	−	0.134716i
$238$	0.633953	−	0.282254i	0.0410930	−	0.0182958i
$239$	−17.0124	−	18.8942i	−1.10044	−	1.22216i	−0.973120	−	0.230301i	$-0.926029\pi$
$239$	−17.0124	−	18.8942i	−1.10044	−	1.22216i	−0.127320	−	0.991862i	$-0.540638\pi$
$240$	−8.70385	+	26.7877i	−0.561831	+	1.72914i
$241$	1.57980	−	1.75455i	0.101764	−	0.113021i	−0.690111	−	0.723703i	$-0.742438\pi$
$241$	1.57980	−	1.75455i	0.101764	−	0.113021i	0.791875	+	0.610683i	$0.209105\pi$
$242$	0.894121	+	1.54866i	0.0574763	+	0.0995519i
$243$	−4.88634	+	8.46339i	−0.313459	+	0.542927i
$244$	8.37048	+	25.7617i	0.535865	+	1.64922i
$245$	−15.8326	−	7.04914i	−1.01151	−	0.450353i
$246$	−5.71401	−	4.15147i	−0.364312	−	0.264688i
$247$	6.08718			0.387318
$248$		0			0
$249$	−37.1893			−2.35677
$250$	0.980506	+	0.712379i	0.0620126	+	0.0450548i
$251$	2.15289	+	0.958530i	0.135889	+	0.0605019i	0.473555	−	0.880764i	$-0.342971\pi$
$251$	2.15289	+	0.958530i	0.135889	+	0.0605019i	−0.337665	+	0.941266i	$0.609637\pi$
$252$	3.37034	+	10.3728i	0.212312	+	0.653428i
$253$	−0.537595	+	0.931142i	−0.0337983	+	0.0585404i
$254$	−0.0207005	−	0.0358542i	−0.00129886	−	0.00224970i
$255$	10.5036	−	11.6654i	0.657762	−	0.730518i
$256$	2.16580	−	6.66565i	0.135363	−	0.416603i
$257$	−17.4068	−	19.3322i	−1.08580	−	1.20591i	−0.977311	−	0.211811i	$-0.932064\pi$
$257$	−17.4068	−	19.3322i	−1.08580	−	1.20591i	−0.108494	−	0.994097i	$-0.534603\pi$
$258$	7.81418	−	3.47909i	0.486489	−	0.216599i
$259$	3.33077	+	0.707977i	0.206964	+	0.0439915i
$260$	1.67589	−	15.9450i	0.103934	−	0.988867i
$261$	1.77366	+	16.8752i	0.109786	+	1.04455i
$262$	−1.98825	+	0.422616i	−0.122834	+	0.0261093i
$263$	−18.5552	+	13.4812i	−1.14417	+	0.831285i	−0.987694	−	0.156398i	$-0.950012\pi$
$263$	−18.5552	+	13.4812i	−1.14417	+	0.831285i	−0.156471	+	0.987683i	$0.550012\pi$
$264$	7.75322	−	5.63304i	0.477178	−	0.346690i
$265$	14.4744	−	3.07663i	0.889155	−	0.188996i
$266$	0.0842047	+	0.801154i	0.00516292	+	0.0491219i
$267$	0.683309	−	6.50125i	0.0418178	−	0.397870i
$268$	−11.8161	−	2.51159i	−0.721784	−	0.153420i
$269$	−15.5735	+	6.93377i	−0.949534	+	0.422760i	−0.822263	−	0.569108i	$-0.807288\pi$
$269$	−15.5735	+	6.93377i	−0.949534	+	0.422760i	−0.127271	+	0.991868i	$0.540622\pi$
$270$	−4.79657	−	5.32713i	−0.291910	−	0.324199i
$271$	2.23929	−	6.89184i	0.136027	−	0.418649i	−0.859721	−	0.510764i	$-0.829363\pi$
$271$	2.23929	−	6.89184i	0.136027	−	0.418649i	0.995748	+	0.0921146i	$0.0293626\pi$
$272$	−3.99785	+	4.44006i	−0.242405	+	0.269218i
$273$	−4.49857	−	7.79175i	−0.272266	−	0.471578i
$274$	−2.07440	+	3.59297i	−0.125319	+	0.217059i
$275$	−2.88520	−	8.87972i	−0.173984	−	0.535467i
$276$	−2.19333	−	0.976534i	−0.132023	−	0.0587804i
$277$	−12.2188	−	8.87748i	−0.734157	−	0.533396i	0.156719	−	0.987643i	$-0.449908\pi$
$277$	−12.2188	−	8.87748i	−0.734157	−	0.533396i	−0.890876	+	0.454247i	$0.849908\pi$
$278$	−5.41979			−0.325058
$279$		0			0
$280$	4.38316			0.261944
$281$	2.01209	+	1.46187i	0.120031	+	0.0872078i	0.646181	−	0.763184i	$-0.276365\pi$
$281$	2.01209	+	1.46187i	0.120031	+	0.0872078i	−0.526150	+	0.850392i	$0.676365\pi$
$282$	7.39587	+	3.29285i	0.440418	+	0.196087i
$283$	−1.46052	−	4.49503i	−0.0868192	−	0.267202i	0.898216	−	0.439554i	$-0.144863\pi$
$283$	−1.46052	−	4.49503i	−0.0868192	−	0.267202i	−0.985035	+	0.172352i	$0.944863\pi$
$284$	1.57426	−	2.72670i	0.0934153	−	0.161800i
$285$	9.11114	+	15.7810i	0.539697	+	0.934783i
$286$	−1.64300	+	1.82474i	−0.0971527	+	0.107899i
$287$	2.32279	−	7.14881i	0.137110	−	0.421981i
$288$	13.9279	+	15.4685i	0.820708	+	0.911489i
$289$	−12.4884	+	5.56018i	−0.734611	+	0.327070i
$290$	3.22881	+	0.686306i	0.189602	+	0.0403013i
$291$	1.03216	−	9.82031i	0.0605061	−	0.575677i
$292$	2.81671	+	26.7992i	0.164835	+	1.56830i
$293$	10.3184	−	2.19324i	0.602806	−	0.128130i	0.103608	−	0.994618i	$-0.466961\pi$
$293$	10.3184	−	2.19324i	0.602806	−	0.128130i	0.499198	+	0.866488i	$0.333628\pi$
$294$	−4.79497	+	3.48375i	−0.279648	+	0.203177i
$295$	28.8982	−	20.9958i	1.68252	−	1.22242i
$296$	4.19322	−	0.891297i	0.243726	−	0.0518056i
$297$	−1.74355	−	16.5888i	−0.101171	−	0.962579i
$298$	0.438988	−	4.17669i	0.0254299	−	0.241949i
$299$	1.24300	+	0.264209i	0.0718848	+	0.0152796i
$300$	19.0464	−	8.47998i	1.09964	−	0.489592i
$301$	6.09127	+	6.76504i	0.351095	+	0.389930i
$302$	−0.469377	+	1.44459i	−0.0270096	+	0.0831271i
$303$	−34.3005	+	38.0946i	−1.97051	+	2.18848i
$304$	−3.46785	−	6.00650i	−0.198895	−	0.344496i
$305$	21.4595	−	37.1689i	1.22877	−	2.12829i
$306$	−1.06438	−	3.27583i	−0.0608467	−	0.187267i
$307$	2.41953	+	1.07724i	0.138090	+	0.0614815i	0.474618	−	0.880192i	$-0.342586\pi$
$307$	2.41953	+	1.07724i	0.138090	+	0.0614815i	−0.336528	+	0.941673i	$0.609253\pi$
$308$	3.99424	+	2.90198i	0.227593	+	0.165356i
$309$	−23.3600			−1.32890
$310$		0			0
$311$	5.51283			0.312604			0.156302	−	0.987709i	$-0.450043\pi$
$311$	5.51283			0.312604			0.156302	+	0.987709i	$0.450043\pi$
$312$	−9.16358	−	6.65773i	−0.518786	−	0.376920i
$313$	−24.3692	−	10.8499i	−1.37743	−	0.613272i	−0.421491	−	0.906833i	$-0.638493\pi$
$313$	−24.3692	−	10.8499i	−1.37743	−	0.613272i	−0.955940	+	0.293561i	$0.905160\pi$
$314$	−0.945290	−	2.90930i	−0.0533458	−	0.164181i
$315$	8.64057	−	14.9659i	0.486841	−	0.843234i
$316$	−3.23474	−	5.60274i	−0.181969	−	0.315179i
$317$	7.18662	−	7.98155i	0.403641	−	0.448288i	−0.506716	−	0.862113i	$-0.669141\pi$
$317$	7.18662	−	7.98155i	0.403641	−	0.448288i	0.910357	+	0.413825i	$0.135807\pi$
$318$	1.56381	−	4.81291i	0.0876941	−	0.269895i
$319$	5.13961	+	5.70812i	0.287763	+	0.319593i
$320$	−14.0876	+	6.27219i	−0.787519	+	0.350626i
$321$	−34.3887	−	7.30954i	−1.91939	−	0.407979i
$322$	−0.0175788	+	0.167251i	−0.000979626	+	0.00932052i
$323$	0.404039	+	3.84418i	0.0224813	+	0.213896i
$324$	6.85686	−	1.45747i	0.380937	−	0.0809706i
$325$	−8.92758	+	6.48627i	−0.495213	+	0.359793i
$326$	−0.889309	+	0.646121i	−0.0492543	+	0.0357853i
$327$	−1.78889	+	0.380241i	−0.0989259	+	0.0210274i
$328$	−0.989157	−	9.41120i	−0.0546171	−	0.519647i
$329$	−0.900611	+	8.56874i	−0.0496523	+	0.472410i
$330$	−7.18982	−	1.52824i	−0.395787	−	0.0841271i
$331$	17.9490	−	7.99140i	0.986565	−	0.439247i	0.150938	−	0.988543i	$-0.451771\pi$
$331$	17.9490	−	7.99140i	0.986565	−	0.439247i	0.835628	+	0.549296i	$0.185104\pi$
$332$	−16.1393	−	17.9245i	−0.885757	−	0.983733i
$333$	5.22289	−	16.0744i	0.286213	−	0.880872i
$334$	−3.14047	+	3.48784i	−0.171839	+	0.190846i
$335$	9.57021	+	16.5761i	0.522876	+	0.905649i
$336$	−5.12565	+	8.87788i	−0.279627	+	0.484328i
$337$	5.92655	+	18.2401i	0.322840	+	0.993599i	0.972406	+	0.233294i	$0.0749505\pi$
$337$	5.92655	+	18.2401i	0.322840	+	0.993599i	−0.649566	+	0.760305i	$0.725050\pi$
$338$	−1.52246	−	0.677841i	−0.0828107	−	0.0368697i
$339$	−26.4510	−	19.2178i	−1.43662	−	1.04376i
$340$	10.1808			0.552133
$341$		0			0
$342$	3.99844			0.216211
$343$	−11.2313	−	8.15999i	−0.606431	−	0.440598i
$344$	10.4696	+	4.66137i	0.564483	+	0.251324i
$345$	1.17554	+	3.61794i	0.0632889	+	0.194783i
$346$	−3.34647	+	5.79626i	−0.179907	+	0.311609i
$347$	−5.32998	−	9.23180i	−0.286128	−	0.495589i	0.686754	−	0.726890i	$-0.259035\pi$
$347$	−5.32998	−	9.23180i	−0.286128	−	0.495589i	−0.972882	+	0.231301i	$0.925702\pi$
$348$	−11.4767	+	12.7462i	−0.615218	+	0.683269i
$349$	−5.77910	+	17.7862i	−0.309348	+	0.952075i	0.668671	+	0.743559i	$0.266864\pi$
$349$	−5.77910	+	17.7862i	−0.309348	+	0.952075i	−0.978019	+	0.208517i	$0.933136\pi$
$350$	−0.977176	−	1.08526i	−0.0522322	−	0.0580098i
$351$	−18.0100	+	8.01857i	−0.961302	+	0.427999i
$352$	9.21644	+	1.95901i	0.491238	+	0.104416i
$353$	1.32356	−	12.5929i	0.0704463	−	0.670251i	−0.901134	−	0.433541i	$-0.857264\pi$
$353$	1.32356	−	12.5929i	0.0704463	−	0.670251i	0.971580	−	0.236711i	$-0.0760693\pi$
$354$	−1.27689	−	12.1488i	−0.0678660	−	0.645702i
$355$	−4.87969	+	1.03721i	−0.258987	+	0.0550494i
$356$	3.43001	−	2.49205i	0.181790	−	0.132078i
$357$	4.62205	−	3.35812i	0.244625	−	0.177730i
$358$	0.0272699	−	0.00579640i	0.00144126	−	0.000306349i
$359$	2.37051	+	22.5539i	0.125111	+	1.19035i	0.859325	+	0.511431i	$0.170884\pi$
$359$	2.37051	+	22.5539i	0.125111	+	1.19035i	−0.734214	+	0.678918i	$0.762449\pi$
$360$	2.27411	−	21.6367i	0.119856	−	1.14035i
$361$	14.1958	+	3.01741i	0.747146	+	0.158811i
$362$	0.694383	−	0.309159i	0.0364959	−	0.0162490i
$363$	9.85117	+	10.9408i	0.517052	+	0.574245i
$364$	1.80319	−	5.54965i	0.0945129	−	0.290881i
$365$	28.5692	−	31.7294i	1.49538	−	1.66079i
$366$	−7.33880	−	12.7112i	−0.383605	−	0.664424i
$367$	−4.35984	+	7.55147i	−0.227582	+	0.394183i	−0.957091	−	0.289788i	$-0.906415\pi$
$367$	−4.35984	+	7.55147i	−0.227582	+	0.394183i	0.729509	+	0.683971i	$0.239749\pi$
$368$	−0.447430	−	1.37705i	−0.0233239	−	0.0717836i
$369$	−34.0836	−	15.1750i	−1.77432	−	0.789980i
$370$	−2.66005	−	1.93264i	−0.138290	−	0.100473i
$371$	5.38574			0.279614
$372$		0			0
$373$	25.4134			1.31586			0.657928	−	0.753081i	$-0.271433\pi$
$373$	25.4134			1.31586			0.657928	+	0.753081i	$0.271433\pi$
$374$	−1.26141	−	0.916471i	−0.0652262	−	0.0473896i
$375$	9.11535	+	4.05841i	0.470714	+	0.209576i
$376$	3.35188	+	10.3160i	0.172860	+	0.532009i
$377$	4.53913	−	7.86200i	0.233777	−	0.404914i
$378$	−1.30448	−	2.25943i	−0.0670954	−	0.116213i
$379$	14.7864	−	16.4219i	0.759525	−	0.843538i	−0.232100	−	0.972692i	$-0.574560\pi$
$379$	14.7864	−	16.4219i	0.759525	−	0.843538i	0.991624	+	0.129154i	$0.0412263\pi$
$380$	−3.65208	+	11.2399i	−0.187348	+	0.576597i
$381$	−0.228072	−	0.253299i	−0.0116845	−	0.0129769i
$382$	−1.71495	+	0.763544i	−0.0877444	+	0.0390663i
$383$	26.0604	+	5.53931i	1.33163	+	0.283046i	0.818123	−	0.575043i	$-0.195015\pi$
$383$	26.0604	+	5.53931i	1.33163	+	0.283046i	0.513502	+	0.858088i	$0.328348\pi$
$384$	−2.89528	+	27.5468i	−0.147749	+	1.40574i
$385$	−0.817696	−	7.77986i	−0.0416737	−	0.396498i
$386$	0.733457	−	0.155901i	0.0373320	−	0.00793516i
$387$	36.5547	−	26.5585i	1.85818	−	1.35005i
$388$	5.18112	−	3.76430i	0.263032	−	0.191104i
$389$	12.6720	−	2.69351i	0.642494	−	0.136566i	0.124868	−	0.992173i	$-0.460149\pi$
$389$	12.6720	−	2.69351i	0.642494	−	0.136566i	0.517626	+	0.855607i	$0.326816\pi$
$390$	0.908095	+	8.63995i	0.0459832	+	0.437501i
$391$	−0.0843482	+	0.802519i	−0.00426567	+	0.0405851i
$392$	−7.76747	−	1.65103i	−0.392317	−	0.0833895i
$393$	−15.2879	+	6.80660i	−0.771171	+	0.343348i
$394$	−1.38170	−	1.53454i	−0.0696092	−	0.0773088i
$395$	−3.16762	+	9.74894i	−0.159380	+	0.490522i
$396$	16.3974	−	18.2112i	0.824002	−	0.915147i
$397$	1.46363	+	2.53508i	0.0734574	+	0.127232i	0.900414	−	0.435033i	$-0.143263\pi$
$397$	1.46363	+	2.53508i	0.0734574	+	0.127232i	−0.826957	+	0.562265i	$0.809930\pi$
$398$	−1.21736	+	2.10852i	−0.0610205	+	0.105691i
$399$	2.04944	+	6.30752i	0.102600	+	0.315771i
$400$	11.4863	+	5.11404i	0.574316	+	0.255702i
$401$	9.93025	+	7.21475i	0.495893	+	0.360287i	0.807446	−	0.589942i	$-0.200849\pi$
$401$	9.93025	+	7.21475i	0.495893	+	0.360287i	−0.311553	+	0.950229i	$0.600849\pi$
$402$	6.54572			0.326471
$403$		0			0
$404$	−33.2464			−1.65407
$405$	−8.98586	−	6.52861i	−0.446511	−	0.324409i
$406$	1.09753	+	0.488654i	0.0544697	+	0.0242515i
$407$	−2.36426	−	7.27645i	−0.117192	−	0.360680i
$408$	3.59625	−	6.22889i	0.178041	−	0.308376i
$409$	8.59861	+	14.8932i	0.425174	+	0.736423i	0.996437	−	0.0843442i	$-0.0268795\pi$
$409$	8.59861	+	14.8932i	0.425174	+	0.736423i	−0.571263	+	0.820767i	$0.693546\pi$
$410$	−4.85658	+	5.39378i	−0.239850	+	0.266380i
$411$	−10.5549	+	32.4848i	−0.520637	+	1.60236i
$412$	−10.1377	−	11.2590i	−0.499448	−	0.554693i
$413$	11.8766	−	5.28782i	0.584411	−	0.260196i
$414$	0.816482	+	0.173549i	0.0401279	+	0.00852945i
$415$	−3.99474	+	38.0074i	−0.196094	+	1.86571i
$416$	−1.16406	−	11.0753i	−0.0570729	−	0.543012i
$417$	−43.6453	+	9.27709i	−2.13732	+	0.454301i
$418$	1.46431	−	1.06388i	0.0716217	−	0.0520362i
$419$	−18.7251	+	13.6046i	−0.914782	+	0.664628i	−0.942220	−	0.334996i	$-0.891265\pi$
$419$	−18.7251	+	13.6046i	−0.914782	+	0.664628i	0.0274378	+	0.999624i	$0.491265\pi$
$420$	17.0864	−	3.63182i	0.833731	−	0.177215i
$421$	−3.05037	−	29.0224i	−0.148666	−	1.41446i	−0.773545	−	0.633742i	$-0.781518\pi$
$421$	−3.05037	−	29.0224i	−0.148666	−	1.41446i	0.624878	−	0.780722i	$-0.285149\pi$
$422$	−0.613791	+	5.83983i	−0.0298789	+	0.284278i
$423$	41.8308	+	8.89140i	2.03388	+	0.432315i
$424$	6.19411	−	2.75779i	0.300813	−	0.133930i
$425$	−4.68878	−	5.20742i	−0.227439	−	0.252597i
$426$	−0.527201	+	1.62256i	−0.0255430	+	0.0786132i
$427$	10.4522	−	11.6084i	0.505819	−	0.561769i
$428$	−11.4008	−	19.7468i	−0.551080	−	0.954498i
$429$	−10.1076	+	17.5069i	−0.487999	+	0.845239i
$430$	−2.71626	−	8.35979i	−0.130990	−	0.403145i
$431$	27.7281	+	12.3454i	1.33562	+	0.594655i	0.945353	−	0.326048i	$-0.105717\pi$
$431$	27.7281	+	12.3454i	1.33562	+	0.594655i	0.390264	+	0.920703i	$0.372384\pi$
$432$	18.1725	+	13.2031i	0.874326	+	0.635235i
$433$	−13.8400			−0.665107			−0.332553	−	0.943084i	$-0.607910\pi$
$433$	−13.8400			−0.665107			−0.332553	+	0.943084i	$0.607910\pi$
$434$		0			0
$435$	27.1762			1.30300
$436$	−0.959605	−	0.697194i	−0.0459567	−	0.0333895i
$437$	−0.855749	−	0.381004i	−0.0409360	−	0.0182259i
$438$	−4.51207	−	13.8867i	−0.215595	−	0.663534i
$439$	−6.46006	+	11.1892i	−0.308322	+	0.534029i	−0.977995	−	0.208626i	$-0.933101\pi$
$439$	−6.46006	+	11.1892i	−0.308322	+	0.534029i	0.669674	+	0.742656i	$0.266434\pi$
$440$	−4.92414	−	8.52887i	−0.234749	−	0.406598i
$441$	−20.9494	+	23.2667i	−0.997590	+	1.10794i
$442$	−0.569463	+	1.75263i	−0.0270866	+	0.0833639i
$443$	15.8974	+	17.6558i	0.755307	+	0.838854i	0.991124	−	0.132944i	$-0.0424430\pi$
$443$	15.8974	+	17.6558i	0.755307	+	0.838854i	−0.235816	+	0.971798i	$0.575776\pi$
$444$	15.6075	−	6.94889i	0.740697	−	0.329780i
$445$	−6.57087	−	1.39668i	−0.311489	−	0.0662091i
$446$	0.230017	−	2.18846i	0.0108916	−	0.103627i
$447$	−3.61412	−	34.3861i	−0.170942	−	1.62641i
$448$	−5.48984	+	1.16690i	−0.259370	+	0.0551309i
$449$	15.7054	−	11.4106i	0.741181	−	0.538500i	−0.151900	−	0.988396i	$-0.548539\pi$
$449$	15.7054	−	11.4106i	0.741181	−	0.538500i	0.893081	+	0.449896i	$0.148539\pi$
$450$	−5.86419	+	4.26058i	−0.276440	+	0.200846i
$451$	−16.5198	+	3.51139i	−0.777888	+	0.165345i
$452$	−2.21653	−	21.0889i	−0.104257	−	0.991937i
$453$	−1.30715	+	12.4367i	−0.0614152	+	0.584326i
$454$	2.69761	+	0.573394i	0.126605	+	0.0269107i
$455$	−8.44638	+	3.76057i	−0.395972	+	0.176298i
$456$	5.58684	+	6.20482i	0.261628	+	0.290567i
$457$	7.52208	−	23.1506i	0.351868	−	1.08294i	−0.605935	−	0.795514i	$-0.707201\pi$
$457$	7.52208	−	23.1506i	0.351868	−	1.08294i	0.957803	−	0.287424i	$-0.0927990\pi$
$458$	3.00362	−	3.33586i	0.140350	−	0.155874i
$459$	−6.25931	−	10.8414i	−0.292159	−	0.506035i
$460$	−1.23362	+	2.13669i	−0.0575177	+	0.0996235i
$461$	−11.8487	−	36.4665i	−0.551848	−	1.69841i	−0.704126	−	0.710075i	$-0.748661\pi$
$461$	−11.8487	−	36.4665i	−0.551848	−	1.69841i	0.152279	−	0.988338i	$-0.451339\pi$
$462$	−2.44395	−	1.08812i	−0.113703	−	0.0506239i
$463$	5.33489	+	3.87603i	0.247934	+	0.180134i	0.704810	−	0.709396i	$-0.251032\pi$
$463$	5.33489	+	3.87603i	0.247934	+	0.180134i	−0.456877	+	0.889530i	$0.651032\pi$
$464$	−10.3437			−0.480195
$465$		0			0
$466$	4.46933			0.207038
$467$	−31.0674	−	22.5718i	−1.43763	−	1.04450i	−0.988532	−	0.151014i	$-0.951746\pi$
$467$	−31.0674	−	22.5718i	−1.43763	−	1.04450i	−0.449096	−	0.893484i	$-0.648254\pi$
$468$	−26.4593	−	11.7804i	−1.22308	−	0.544551i
$469$	2.15270	+	6.62532i	0.0994024	+	0.305929i
$470$	4.15973	−	7.20487i	0.191874	−	0.332336i
$471$	−12.5922	−	21.8104i	−0.580220	−	1.00497i
$472$	10.9516	−	12.1630i	0.504088	−	0.559846i
$473$	6.32051	−	19.4525i	0.290617	−	0.894429i
$474$	2.34567	+	2.60513i	0.107740	+	0.119658i
$475$	7.43112	−	3.30855i	0.340963	−	0.151807i
$476$	3.62440	+	0.770391i	0.166124	+	0.0353108i
$477$	2.79427	−	26.5857i	0.127941	−	1.21728i
$478$	0.933965	+	8.88609i	0.0427186	+	0.406440i
$479$	−7.36071	+	1.56457i	−0.336319	+	0.0714869i	−0.372976	−	0.927841i	$-0.621663\pi$
$479$	−7.36071	+	1.56457i	−0.336319	+	0.0714869i	0.0366565	+	0.999328i	$0.488329\pi$
$480$	26.9703	−	19.5951i	1.23102	−	0.894389i
$481$	−7.31567	+	5.31515i	−0.333566	+	0.242350i
$482$	−0.811594	+	0.172510i	−0.0369671	+	0.00785760i
$483$	0.144723	+	1.37695i	0.00658514	+	0.0626534i
$484$	−0.998083	+	9.49612i	−0.0453674	+	0.431642i
$485$	−9.92548	−	2.10973i	−0.450693	−	0.0957977i
$486$	3.13751	−	1.39691i	0.142321	−	0.0633652i
$487$	16.7498	+	18.6026i	0.759008	+	0.842964i	0.991564	−	0.129619i	$-0.0413755\pi$
$487$	16.7498	+	18.6026i	0.759008	+	0.842964i	−0.232556	+	0.972583i	$0.574709\pi$
$488$	6.07693	−	18.7029i	0.275090	−	0.846639i
$489$	−6.05559	+	6.72541i	−0.273843	+	0.304134i
$490$	3.04533	+	5.27467i	0.137574	+	0.238285i
$491$	19.8550	−	34.3899i	0.896044	−	1.55199i	0.0635377	−	0.997979i	$-0.479762\pi$
$491$	19.8550	−	34.3899i	0.896044	−	1.55199i	0.832507	−	0.554015i	$-0.186905\pi$
$492$	−11.6539	−	35.8670i	−0.525399	−	1.61701i
$493$	5.26630	+	2.34471i	0.237182	+	0.105600i
$494$	−1.73068	−	1.25741i	−0.0778668	−	0.0565735i
$495$	−38.8281			−1.74519
$496$		0			0
$497$	−1.81567			−0.0814440
$498$	10.5735	+	7.68207i	0.473808	+	0.344242i
$499$	−21.6091	−	9.62098i	−0.967355	−	0.430694i	−0.138626	−	0.990345i	$-0.544269\pi$
$499$	−21.6091	−	9.62098i	−0.967355	−	0.430694i	−0.828729	+	0.559651i	$0.810935\pi$
$500$	1.99977	+	6.15467i	0.0894325	+	0.275245i
$501$	−19.3199	+	33.4630i	−0.863148	+	1.49502i
$502$	−0.414099	−	0.717241i	−0.0184822	−	0.0320120i
$503$	−13.5074	+	15.0014i	−0.602263	+	0.668881i	−0.964768	−	0.263101i	$-0.915255\pi$
$503$	−13.5074	+	15.0014i	−0.602263	+	0.668881i	0.362505	+	0.931982i	$0.381922\pi$
$504$	2.44685	−	7.53063i	0.108991	−	0.335441i
$505$	35.2482	+	39.1471i	1.56852	+	1.74202i
$506$	0.345189	−	0.153688i	0.0153455	−	0.00683227i
$507$	−13.4205	−	2.85262i	−0.596026	−	0.126689i
$508$	0.0231073	−	0.219852i	0.00102522	−	0.00975434i
$509$	−1.23751	−	11.7742i	−0.0548518	−	0.521880i	−0.987105	−	0.160074i	$-0.948827\pi$
$509$	−1.23751	−	11.7742i	−0.0548518	−	0.521880i	0.932253	−	0.361806i	$-0.117840\pi$
$510$	−5.39603	+	1.14696i	−0.238940	+	0.0507883i
$511$	12.5717	−	9.13389i	0.556140	−	0.404060i
$512$	−17.4827	+	12.7019i	−0.772633	+	0.561351i
$513$	14.2146	−	3.02141i	0.627591	−	0.133399i
$514$	0.955617	+	9.09209i	0.0421504	+	0.401035i
$515$	−2.50925	+	23.8739i	−0.110571	+	1.05201i
$516$	44.6748	+	9.49593i	1.96670	+	0.418035i
$517$	17.6851	−	7.87389i	0.777788	−	0.346293i
$518$	−0.800743	−	0.889315i	−0.0351826	−	0.0390742i
$519$	−17.0275	+	52.4051i	−0.747422	+	2.30033i
$520$	−7.78852	+	8.65002i	−0.341549	+	0.379329i
$521$	16.3742	+	28.3610i	0.717368	+	1.24252i	0.962039	+	0.272911i	$0.0879865\pi$
$521$	16.3742	+	28.3610i	0.717368	+	1.24252i	−0.244672	+	0.969606i	$0.578680\pi$
$522$	2.98158	−	5.16425i	0.130500	−	0.226033i
$523$	−9.11682	−	28.0587i	−0.398651	−	1.22692i	−0.926082	−	0.377323i	$-0.876845\pi$
$523$	−9.11682	−	28.0587i	−0.398651	−	1.22692i	0.527431	−	0.849598i	$-0.323155\pi$
$524$	−9.91522	−	4.41454i	−0.433148	−	0.192850i
$525$	−9.72679	−	7.06693i	−0.424512	−	0.308426i
$526$	8.06030			0.351446
$527$		0			0
$528$	23.0331			1.00239
$529$	18.4492	+	13.4041i	0.802138	+	0.582788i
$530$	−4.75081	−	2.11520i	−0.206362	−	0.0918784i
$531$	−19.9404	−	61.3703i	−0.865340	−	2.66324i
$532$	−2.15069	+	3.72510i	−0.0932441	+	0.161504i
$533$	9.98053	+	17.2868i	0.432305	+	0.748774i
$534$	−1.53722	+	1.70725i	−0.0665219	+	0.0738801i
$535$	−11.1643	+	34.3600i	−0.482673	+	1.48551i
$536$	5.86834	+	6.51745i	0.253474	+	0.281511i
$537$	0.209681	−	0.0933561i	0.00904842	−	0.00402861i
$538$	5.86007	+	1.24560i	0.252645	+	0.0537014i
$539$	−1.48143	+	14.0948i	−0.0638095	+	0.607107i
$540$	−4.00092	−	38.0662i	−0.172172	−	1.63811i
$541$	−12.9759	+	2.75812i	−0.557879	+	0.118581i	−0.478218	−	0.878241i	$-0.658717\pi$
$541$	−12.9759	+	2.75812i	−0.557879	+	0.118581i	−0.0796610	+	0.996822i	$0.525384\pi$
$542$	−2.06029	+	1.49689i	−0.0884970	+	0.0642968i
$543$	5.06264	−	3.67822i	0.217258	−	0.157848i
$544$	6.91702	−	1.47026i	0.296565	−	0.0630368i
$545$	0.196449	+	1.86909i	0.00841496	+	0.0800630i
$546$	−0.330507	+	3.14456i	−0.0141444	+	0.134575i
$547$	−36.9386	−	7.85155i	−1.57938	−	0.335708i	−0.667003	−	0.745055i	$-0.732423\pi$
$547$	−36.9386	−	7.85155i	−1.57938	−	0.335708i	−0.912379	+	0.409347i	$0.865756\pi$
$548$	−20.2376	+	9.01036i	−0.864508	+	0.384904i
$549$	−51.8798	−	57.6183i	−2.21417	−	2.45909i
$550$	−1.01395	+	3.12062i	−0.0432351	+	0.133064i
$551$	−4.47776	+	4.97306i	−0.190759	+	0.211860i
$552$	0.871520	+	1.50952i	0.0370944	+	0.0642493i
$553$	−1.86539	+	3.23095i	−0.0793245	+	0.137394i
$554$	1.64019	+	5.04800i	0.0696852	+	0.214469i
$555$	−24.7294	−	11.0102i	−1.04970	−	0.467358i
$556$	−23.4124	−	17.0101i	−0.992907	−	0.721389i
$557$	−11.3637			−0.481496			−0.240748	−	0.970588i	$-0.577393\pi$
$557$	−11.3637			−0.481496			−0.240748	+	0.970588i	$0.577393\pi$
$558$		0			0
$559$	−24.1743			−1.02246
$560$	8.52261	+	6.19204i	0.360146	+	0.261661i
$561$	−11.7268	−	5.22112i	−0.495107	−	0.220436i
$562$	−0.270094	−	0.831262i	−0.0113932	−	0.0350647i
$563$	10.0933	−	17.4821i	0.425381	−	0.736781i	−0.571075	−	0.820898i	$-0.693474\pi$
$563$	10.0933	−	17.4821i	0.425381	−	0.736781i	0.996456	+	0.0841167i	$0.0268068\pi$
$564$	21.6140	+	37.4365i	0.910113	+	1.57636i
$565$	−22.4818	+	24.9686i	−0.945816	+	1.05044i
$566$	−0.513276	+	1.57970i	−0.0215746	+	0.0663998i
$567$	−2.70497	−	3.00417i	−0.113598	−	0.126163i
$568$	−2.08819	+	0.929724i	−0.0876187	+	0.0390103i
$569$	30.3125	+	6.44311i	1.27076	+	0.270109i	0.793457	−	0.608627i	$-0.208279\pi$
$569$	30.3125	+	6.44311i	1.27076	+	0.270109i	0.477308	+	0.878736i	$0.341613\pi$
$570$	0.669390	−	6.36882i	0.0280377	−	0.266761i
$571$	1.08706	+	10.3427i	0.0454922	+	0.432830i	0.993436	+	0.114391i	$0.0364918\pi$
$571$	1.08706	+	10.3427i	0.0454922	+	0.432830i	−0.947944	+	0.318438i	$0.896842\pi$
$572$	−12.8244	+	2.72591i	−0.536215	+	0.113976i
$573$	−12.5034	+	9.08427i	−0.522338	+	0.379501i
$574$	−2.13711	+	1.55270i	−0.0892012	+	0.0648085i
$575$	1.66104	−	0.353065i	0.0692702	−	0.0147238i
$576$	2.91191	+	27.7050i	0.121330	+	1.15437i
$577$	−0.565902	+	5.38420i	−0.0235588	+	0.224147i	0.976407	+	0.215936i	$0.0692803\pi$
$577$	−0.565902	+	5.38420i	−0.0235588	+	0.224147i	−0.999966	+	0.00821097i	$0.997386\pi$
$578$	4.69918	+	0.998842i	0.195460	+	0.0415463i
$579$	5.63963	−	2.51093i	0.234375	−	0.104351i
$580$	11.7938	+	13.0984i	0.489712	+	0.543881i
$581$	−4.29819	+	13.2285i	−0.178319	+	0.548809i
$582$	−2.32201	+	2.57885i	−0.0962503	+	0.106897i
$583$	−6.05046	−	10.4797i	−0.250585	−	0.434025i
$584$	9.78162	−	16.9423i	0.404766	−	0.701076i
$585$	14.1811	+	43.6451i	0.586318	+	1.80450i
$586$	−3.38672	−	1.50786i	−0.139904	−	0.0622893i
$587$	10.1635	+	7.38424i	0.419494	+	0.304780i	0.777434	−	0.628964i	$-0.216521\pi$
$587$	10.1635	+	7.38424i	0.419494	+	0.304780i	−0.357940	+	0.933744i	$0.616521\pi$
$588$	−31.6471			−1.30510
$589$		0			0
$590$	−12.5532			−0.516809
$591$	−13.7535	−	9.99247i	−0.565741	−	0.411035i
$592$	9.41241	+	4.19068i	0.386848	+	0.172236i
$593$	8.36510	+	25.7451i	0.343513	+	1.05723i	0.962375	+	0.271726i	$0.0875943\pi$
$593$	8.36510	+	25.7451i	0.343513	+	1.05723i	−0.618861	+	0.785500i	$0.712406\pi$
$594$	−2.93098	+	5.07660i	−0.120259	+	0.208295i
$595$	−2.93551	−	5.08445i	−0.120344	−	0.208442i
$596$	15.0050	−	16.6647i	0.614627	−	0.682612i
$597$	−6.19413	+	19.0636i	−0.253509	+	0.780220i
$598$	−0.298828	−	0.331882i	−0.0122200	−	0.0135717i
$599$	−13.1140	+	5.83874i	−0.535824	+	0.238564i	−0.656765	−	0.754095i	$-0.728076\pi$
$599$	−13.1140	+	5.83874i	−0.535824	+	0.238564i	0.120941	+	0.992660i	$0.461409\pi$
$600$	−14.8054	−	3.14698i	−0.604427	−	0.128475i
$601$	−0.0669000	+	0.636511i	−0.00272891	+	0.0259638i	−0.995802	−	0.0915377i	$-0.970822\pi$
$601$	−0.0669000	+	0.636511i	−0.00272891	+	0.0259638i	0.993073	+	0.117501i	$0.0374885\pi$
$602$	−0.334405	−	3.18165i	−0.0136293	−	0.129675i
$603$	33.8216	−	7.18900i	1.37732	−	0.292759i
$604$	−6.56150	+	4.76721i	−0.266984	+	0.193975i
$605$	12.2397	−	8.89266i	0.497614	−	0.361538i
$606$	17.6212	−	3.74551i	0.715813	−	0.152151i
$607$	0.681298	+	6.48211i	0.0276530	+	0.263101i	0.999610	+	0.0279405i	$0.00889489\pi$
$607$	0.681298	+	6.48211i	0.0276530	+	0.263101i	−0.971957	+	0.235160i	$0.924438\pi$
$608$	−0.858073	+	8.16402i	−0.0347995	+	0.331095i
$609$	9.67482	+	2.05645i	0.392043	+	0.0833314i
$610$	−13.7791	+	6.13486i	−0.557900	+	0.248393i
$611$	−15.3098	−	17.0033i	−0.619369	−	0.687879i
$612$	5.68333	−	17.4915i	0.229735	−	0.707052i
$613$	6.98929	−	7.76239i	0.282295	−	0.313520i	−0.585276	−	0.810834i	$-0.699014\pi$
$613$	6.98929	−	7.76239i	0.282295	−	0.313520i	0.867570	+	0.497314i	$0.165680\pi$
$614$	−0.465385	−	0.806070i	−0.0187814	−	0.0325303i
$615$	−29.8772	+	51.7489i	−1.20477	+	2.08672i
$616$	−1.10762	−	3.40892i	−0.0446274	−	0.137349i
$617$	19.8270	+	8.82755i	0.798205	+	0.355384i	0.764972	−	0.644064i	$-0.222753\pi$
$617$	19.8270	+	8.82755i	0.798205	+	0.355384i	0.0332333	+	0.999448i	$0.489420\pi$
$618$	6.64159	+	4.82540i	0.267164	+	0.194106i
$619$	28.5478			1.14743			0.573716	−	0.819054i	$-0.305501\pi$
$619$	28.5478			1.14743			0.573716	+	0.819054i	$0.305501\pi$
$620$		0			0
$621$	3.03377			0.121741
$622$	−1.56738	−	1.13877i	−0.0628462	−	0.0456604i
$623$	−2.23356	−	0.994446i	−0.0894858	−	0.0398416i
$624$	−8.41235	−	25.8906i	−0.336764	−	1.03645i
$625$	14.7271	−	25.5080i	0.589083	−	1.02032i
$626$	4.68731	+	8.11866i	0.187343	+	0.324487i
$627$	9.97095	−	11.0739i	0.398201	−	0.442247i
$628$	5.04743	−	15.5344i	0.201414	−	0.619890i
$629$	−3.84220	−	4.26720i	−0.153199	−	0.170144i
$630$	−5.54810	+	2.47018i	−0.221042	+	0.0984141i
$631$	−26.6452	−	5.66362i	−1.06073	−	0.225465i	−0.355669	−	0.934612i	$-0.615747\pi$
$631$	−26.6452	−	5.66362i	−1.06073	−	0.225465i	−0.705061	+	0.709147i	$0.749080\pi$
$632$	−0.490951	+	4.67109i	−0.0195290	+	0.185806i
$633$	5.05325	+	48.0784i	0.200849	+	1.91095i
$634$	−3.69199	+	0.784756i	−0.146627	+	0.0311666i
$635$	−0.283370	+	0.205880i	−0.0112452	+	0.00817012i
$636$	21.8607	−	15.8828i	0.866835	−	0.629792i
$637$	16.3845	−	3.48263i	0.649177	−	0.137987i
$638$	−0.282160	−	2.68458i	−0.0111708	−	0.106283i
$639$	−0.942021	+	8.96273i	−0.0372658	+	0.354560i
$640$	27.8418	+	5.91796i	1.10054	+	0.233928i
$641$	37.6455	−	16.7608i	1.48691	−	0.662013i	0.507086	−	0.861895i	$-0.330722\pi$
$641$	37.6455	−	16.7608i	1.48691	−	0.662013i	0.979820	+	0.199882i	$0.0640558\pi$
$642$	8.26731	+	9.18177i	0.326285	+	0.362376i
$643$	−9.52156	+	29.3044i	−0.375494	+	1.15565i	0.567651	+	0.823269i	$0.307852\pi$
$643$	−9.52156	+	29.3044i	−0.375494	+	1.15565i	−0.943145	+	0.332382i	$0.892148\pi$
$644$	−0.600856	+	0.667318i	−0.0236770	+	0.0262960i
$645$	−36.1834	−	62.6715i	−1.42472	−	2.46769i
$646$	0.679205	−	1.17642i	0.0267230	−	0.0462855i
$647$	2.75525	+	8.47978i	0.108320	+	0.333375i	0.990495	−	0.137547i	$-0.0439217\pi$
$647$	2.75525	+	8.47978i	0.108320	+	0.333375i	−0.882175	+	0.470921i	$0.843922\pi$
$648$	−4.64927	−	2.06999i	−0.182641	−	0.0813168i
$649$	−23.6317	−	17.1694i	−0.927623	−	0.673958i
$650$	3.87809			0.152111
$651$		0			0
$652$	−5.86949			−0.229867
$653$	−31.7469	−	23.0655i	−1.24235	−	0.902623i	−0.244601	−	0.969624i	$-0.578657\pi$
$653$	−31.7469	−	23.0655i	−1.24235	−	0.902623i	−0.997753	+	0.0670010i	$0.978657\pi$
$654$	0.587153	+	0.261418i	0.0229595	+	0.0102222i
$655$	5.31417	+	16.3553i	0.207642	+	0.639056i
$656$	11.3718	−	19.6965i	0.443993	−	0.769018i
$657$	−38.5652	−	66.7969i	−1.50457	−	2.60600i
$658$	2.02608	−	2.25018i	0.0789846	−	0.0877213i
$659$	10.1832	−	31.3407i	0.396681	−	1.22086i	−0.530963	−	0.847395i	$-0.678170\pi$
$659$	10.1832	−	31.3407i	0.396681	−	1.22086i	0.927644	−	0.373465i	$-0.121830\pi$
$660$	−26.2621	−	29.1671i	−1.02225	−	1.13533i
$661$	−0.155006	+	0.0690131i	−0.00602903	+	0.00268430i	−0.409749	−	0.912198i	$-0.634384\pi$
$661$	−0.155006	+	0.0690131i	−0.00602903	+	0.00268430i	0.403720	+	0.914883i	$0.367717\pi$
$662$	−6.75392	−	1.43559i	−0.262499	−	0.0557958i
$663$	−1.58587	+	15.0886i	−0.0615901	+	0.585991i
$664$	1.83038	+	17.4149i	0.0710325	+	0.675829i
$665$	6.66642	−	1.41699i	0.258513	−	0.0549486i
$666$	−4.80539	+	3.49132i	−0.186205	+	0.135286i
$667$	−1.13021	+	0.821147i	−0.0437620	+	0.0317950i
$668$	−24.5128	+	5.21036i	−0.948430	+	0.201595i
$669$	−1.89369	−	18.0173i	−0.0732144	−	0.696589i
$670$	0.703118	−	6.68972i	0.0271638	−	0.258446i
$671$	−34.3302	−	7.29711i	−1.32530	−	0.281702i
$672$	11.0843	−	4.93504i	0.427586	−	0.190373i
$673$	−9.76017	−	10.8398i	−0.376227	−	0.417842i	0.525060	−	0.851065i	$-0.324043\pi$
$673$	−9.76017	−	10.8398i	−0.376227	−	0.417842i	−0.901287	+	0.433223i	$0.857376\pi$
$674$	2.08278	−	6.41015i	0.0802258	−	0.246910i
$675$	−17.6280	+	19.5778i	−0.678501	+	0.753551i
$676$	−4.44929	−	7.70639i	−0.171126	−	0.296400i
$677$	−7.88341	+	13.6545i	−0.302984	+	0.524784i	−0.976810	−	0.214106i	$-0.931316\pi$
$677$	−7.88341	+	13.6545i	−0.302984	+	0.524784i	0.673826	+	0.738890i	$0.264650\pi$
$678$	3.55065	+	10.9278i	0.136362	+	0.419679i
$679$	−3.37386	−	1.50214i	−0.129477	−	0.0576467i
$680$	−5.97963	−	4.34445i	−0.229308	−	0.166602i
$681$	22.7051			0.870063
$682$		0			0
$683$	20.5935			0.787988			0.393994	−	0.919113i	$-0.371093\pi$
$683$	20.5935			0.787988			0.393994	+	0.919113i	$0.371093\pi$
$684$	17.2724	+	12.5492i	0.660428	+	0.479829i
$685$	32.0657	+	14.2766i	1.22517	+	0.545479i
$686$	1.50763	+	4.64001i	0.0575616	+	0.177156i
$687$	18.4780	−	32.0048i	0.704979	−	1.22106i
$688$	13.7720	+	23.8538i	0.525053	+	0.909418i
$689$	−9.57002	+	10.6286i	−0.364589	+	0.404917i
$690$	0.413123	−	1.27146i	0.0157273	−	0.0484037i
$691$	−3.98247	−	4.42298i	−0.151500	−	0.168258i	0.662617	−	0.748958i	$-0.269446\pi$
$691$	−3.98247	−	4.42298i	−0.151500	−	0.168258i	−0.814118	+	0.580700i	$0.802779\pi$
$692$	−32.6477	+	14.5357i	−1.24108	+	0.552564i
$693$	−13.8229	−	2.93815i	−0.525089	−	0.111611i
$694$	−0.391590	+	3.72573i	−0.0148646	+	0.141427i
$695$	4.79296	+	45.6020i	0.181807	+	1.72978i
$696$	12.1800	−	2.58893i	0.461680	−	0.0981332i
$697$	−10.2545	+	7.45032i	−0.388417	+	0.282201i
$698$	5.31713	−	3.86312i	0.201256	−	0.146221i
$699$	35.9913	−	7.65019i	1.36132	−	0.289357i
$700$	−0.815083	−	7.75500i	−0.0308072	−	0.293111i
$701$	2.78364	−	26.4845i	0.105136	−	1.00031i	−0.807037	−	0.590502i	$-0.798930\pi$
$701$	2.78364	−	26.4845i	0.105136	−	1.00031i	0.912173	−	0.409805i	$-0.134403\pi$
$702$	6.77688	+	1.44047i	0.255777	+	0.0543670i
$703$	6.08940	−	2.71118i	0.229666	−	0.102254i
$704$	8.43800	+	9.37135i	0.318019	+	0.353196i
$705$	21.1655	−	65.1407i	0.797138	−	2.45334i
$706$	−2.97758	+	3.30694i	−0.112063	+	0.124458i
$707$	9.58617	+	16.6037i	0.360525	+	0.624448i
$708$	32.6133	−	56.4879i	1.22568	−	2.12295i
$709$	−0.816662	−	2.51343i	−0.0306704	−	0.0943938i	0.934550	−	0.355833i	$-0.115803\pi$
$709$	−0.816662	−	2.51343i	−0.0306704	−	0.0943938i	−0.965220	+	0.261439i	$0.915803\pi$
$710$	1.60162	+	0.713088i	0.0601078	+	0.0267617i
$711$	14.9812	+	10.8845i	0.561839	+	0.408200i
$712$	−3.07802			−0.115354
$713$		0			0
$714$	−2.00779			−0.0751398
$715$	16.8063	+	12.2105i	0.628519	+	0.456646i
$716$	0.135992	+	0.0605478i	0.00508228	+	0.00226278i
$717$	22.7315	+	69.9605i	0.848925	+	2.61272i
$718$	3.98491	−	6.90207i	0.148716	−	0.257583i
$719$	−2.59912	−	4.50181i	−0.0969308	−	0.167889i	0.813482	−	0.581590i	$-0.197569\pi$
$719$	−2.59912	−	4.50181i	−0.0969308	−	0.167889i	−0.910413	+	0.413701i	$0.864236\pi$
$720$	34.9876	−	38.8577i	1.30391	−	1.44814i
$721$	−2.69986	+	8.30930i	−0.100548	+	0.309455i
$722$	−3.41277	−	3.79027i	−0.127010	−	0.141059i
$723$	−6.24044	+	2.77842i	−0.232084	+	0.103331i
$724$	3.96989	+	0.843826i	0.147540	+	0.0313606i
$725$	1.26807	−	12.0649i	0.0470951	−	0.448080i
$726$	−0.540821	−	5.14556i	−0.0200717	−	0.190970i
$727$	−23.6775	+	5.03280i	−0.878149	+	0.186656i	−0.624862	−	0.780735i	$-0.714845\pi$
$727$	−23.6775	+	5.03280i	−0.878149	+	0.186656i	−0.253286	+	0.967391i	$0.581512\pi$
$728$	−3.42729	+	2.49007i	−0.127024	+	0.0922882i
$729$	31.9419	−	23.2071i	1.18303	−	0.859524i
$730$	−14.6769	+	3.11967i	−0.543216	+	0.115464i
$731$	−1.60458	−	15.2665i	−0.0593474	−	0.564653i
$732$	8.19210	−	77.9426i	0.302789	−	2.88084i
$733$	−39.4807	−	8.39189i	−1.45825	−	0.309961i	−0.590533	−	0.807013i	$-0.701083\pi$
$733$	−39.4807	−	8.39189i	−1.45825	−	0.309961i	−0.867721	+	0.497052i	$0.834416\pi$
$734$	2.79945	−	1.24640i	0.103330	−	0.0460053i
$735$	33.5526	+	37.2639i	1.23761	+	1.37450i
$736$	−0.529571	+	1.62985i	−0.0195202	+	0.0600771i
$737$	10.4733	−	11.6318i	0.385790	−	0.428464i
$738$	6.55583	+	11.3550i	0.241324	+	0.417985i
$739$	−3.04893	+	5.28089i	−0.112157	+	0.194261i	−0.916640	−	0.399715i	$-0.869109\pi$
$739$	−3.04893	+	5.28089i	−0.112157	+	0.194261i	0.804483	+	0.593976i	$0.202442\pi$
$740$	−5.42526	−	16.6972i	−0.199437	−	0.613803i
$741$	−16.0894	−	7.16344i	−0.591057	−	0.263156i
$742$	−1.53125	−	1.11251i	−0.0562138	−	0.0408417i
$743$	16.2263			0.595284			0.297642	−	0.954678i	$-0.403800\pi$
$743$	16.2263			0.595284			0.297642	+	0.954678i	$0.403800\pi$
$744$		0			0
$745$	−35.5308			−1.30175
$746$	−7.22540	−	5.24956i	−0.264541	−	0.192200i
$747$	63.0698	+	28.0805i	2.30760	+	1.02741i
$748$	−2.57269	−	7.91793i	−0.0940670	−	0.289508i
$749$	−6.57456	+	11.3875i	−0.240229	+	0.416089i
$750$	−1.75329	−	3.03680i	−0.0640213	−	0.110888i
$751$	24.3861	−	27.0835i	0.889862	−	0.988291i	−0.110123	−	0.993918i	$-0.535124\pi$
$751$	24.3861	−	27.0835i	0.889862	−	0.988291i	0.999984	+	0.00562661i	$0.00179101\pi$
$752$	−8.05593	+	24.7936i	−0.293770	+	0.904130i
$753$	−4.56243	−	5.06709i	−0.166264	−	0.184655i
$754$	−2.91457	+	1.29765i	−0.106142	+	0.0472576i
$755$	12.5699	+	2.67181i	0.457464	+	0.0972370i
$756$	1.45616	−	13.8544i	0.0529600	−	0.503881i
$757$	−4.55349	−	43.3236i	−0.165499	−	1.57462i	−0.690381	−	0.723446i	$-0.742557\pi$
$757$	−4.55349	−	43.3236i	−0.165499	−	1.57462i	0.524881	−	0.851175i	$-0.324110\pi$
$758$	−7.59621	+	1.61462i	−0.275907	+	0.0586458i
$759$	2.51672	−	1.82851i	0.0913512	−	0.0663705i
$760$	6.94144	−	5.04325i	0.251792	−	0.182938i
$761$	−3.22718	+	0.685959i	−0.116985	+	0.0248660i	−0.266032	−	0.963964i	$-0.585713\pi$
$761$	−3.22718	+	0.685959i	−0.116985	+	0.0248660i	0.149047	+	0.988830i	$0.452379\pi$
$762$	0.0125209	+	0.119129i	0.000453586	+	0.00431558i
$763$	−0.0714990	+	0.680267i	−0.00258844	+	0.0246273i
$764$	−9.80462	−	2.08404i	−0.354719	−	0.0753978i
$765$	−26.6215	+	11.8526i	−0.962501	+	0.428533i
$766$	−6.26513	−	6.95813i	−0.226368	−	0.251407i
$767$	−10.6685	+	32.8342i	−0.385216	+	1.18557i
$768$	−13.5687	+	15.0696i	−0.489620	+	0.543778i
$769$	22.8568	+	39.5891i	0.824237	+	1.42762i	0.902501	+	0.430688i	$0.141729\pi$
$769$	22.8568	+	39.5891i	0.824237	+	1.42762i	−0.0782634	+	0.996933i	$0.524938\pi$
$770$	−1.37458	+	2.38084i	−0.0495363	+	0.0857995i
$771$	23.2585	+	71.5823i	0.837635	+	2.57798i
$772$	3.65768	+	1.62851i	0.131643	+	0.0586112i
$773$	−24.2710	−	17.6339i	−0.872969	−	0.634249i	0.0584131	−	0.998292i	$-0.481396\pi$
$773$	−24.2710	−	17.6339i	−0.872969	−	0.634249i	−0.931382	+	0.364044i	$0.881396\pi$
$774$	−15.8791			−0.570764
$775$		0			0
$776$	−4.64943			−0.166905
$777$	−7.97058	−	5.79097i	−0.285943	−	0.207750i
$778$	−4.15921	−	1.85180i	−0.149115	−	0.0663903i
$779$	−4.54689	−	13.9939i	−0.162909	−	0.501383i
$780$	−23.1938	+	40.1729i	−0.830472	+	1.43842i
$781$	2.03977	+	3.53298i	0.0729886	+	0.126420i
$782$	0.189755	−	0.210745i	0.00678564	−	0.00753621i
$783$	6.69730	−	20.6122i	0.239342	−	0.736619i
$784$	−12.7707	−	14.1833i	−0.456095	−	0.506545i
$785$	−23.6428	+	10.5265i	−0.843848	+	0.375706i
$786$	5.75259	+	1.22275i	0.205188	+	0.0436141i
$787$	4.51897	−	42.9951i	0.161084	−	1.53261i	−0.553374	−	0.832933i	$-0.686660\pi$
$787$	4.51897	−	42.9951i	0.161084	−	1.53261i	0.714458	−	0.699679i	$-0.246673\pi$
$788$	−1.15251	−	10.9654i	−0.0410564	−	0.390625i
$789$	64.9091	−	13.7969i	2.31083	−	0.491181i
$790$	2.91441	−	2.11744i	0.103690	−	0.0753352i
$791$	−9.89298	+	7.18767i	−0.351754	+	0.255564i
$792$	−17.4022	+	3.69894i	−0.618359	+	0.131436i
$793$	4.33600	+	41.2543i	0.153976	+	1.46498i
$794$	0.107532	−	1.02310i	0.00381616	−	0.0363084i
$795$	−41.8786	−	8.90158i	−1.48528	−	0.315707i
$796$	−11.8764	+	5.28769i	−0.420946	+	0.187417i
$797$	15.2721	+	16.9613i	0.540964	+	0.600802i	0.950205	−	0.311625i	$-0.100873\pi$
$797$	15.2721	+	16.9613i	0.540964	+	0.600802i	−0.409241	+	0.912426i	$0.634206\pi$
$798$	0.720239	−	2.21667i	0.0254962	−	0.0784691i
$799$	9.72172	−	10.7971i	0.343930	−	0.381972i
$800$	−7.44080	−	12.8878i	−0.263072	−	0.455654i
$801$	−6.06773	+	10.5096i	−0.214393	+	0.371339i
$802$	−1.33299	−	4.10252i	−0.0470695	−	0.144865i
$803$	−31.8963	−	14.2012i	−1.12560	−	0.501148i
$804$	28.2762	+	20.5438i	0.997223	+	0.724525i
$805$	1.42279			0.0501467
$806$		0			0
$807$	49.3229			1.73625
$808$	19.5270	+	14.1872i	0.686959	+	0.499105i
$809$	−19.4023	−	8.63844i	−0.682147	−	0.303711i	0.0362519	−	0.999343i	$-0.488458\pi$
$809$	−19.4023	−	8.63844i	−0.682147	−	0.303711i	−0.718399	+	0.695631i	$0.755125\pi$
$810$	1.20622	+	3.71236i	0.0423822	+	0.130439i
$811$	−1.06157	+	1.83869i	−0.0372767	+	0.0645652i	−0.884062	−	0.467370i	$-0.845202\pi$
$811$	−1.06157	+	1.83869i	−0.0372767	+	0.0645652i	0.846785	+	0.531935i	$0.178535\pi$
$812$	3.20748	+	5.55551i	0.112560	+	0.194960i
$813$	−14.0292	+	15.5810i	−0.492024	+	0.546448i
$814$	−0.830879	+	2.55718i	−0.0291223	+	0.0896292i
$815$	6.22290	+	6.91123i	0.217979	+	0.242090i
$816$	15.7920	−	7.03106i	0.552832	−	0.246136i
$817$	17.4303	+	3.70493i	0.609810	+	0.129619i
$818$	0.631735	−	6.01056i	0.0220881	−	0.210154i
$819$	1.74587	+	16.6109i	0.0610058	+	0.580431i
$820$	−37.9079	+	8.05758i	−1.32380	+	0.281383i
$821$	−33.8104	+	24.5647i	−1.17999	+	0.857313i	−0.992171	−	0.124891i	$-0.960142\pi$
$821$	−33.8104	+	24.5647i	−1.17999	+	0.857313i	−0.187819	+	0.982204i	$0.560142\pi$
$822$	9.71121	−	7.05561i	0.338717	−	0.246093i
$823$	−15.9423	+	3.38865i	−0.555715	+	0.118121i	−0.477204	−	0.878792i	$-0.658350\pi$
$823$	−15.9423	+	3.38865i	−0.555715	+	0.118121i	−0.0785108	+	0.996913i	$0.525016\pi$
$824$	1.14973	+	10.9390i	0.0400528	+	0.381077i
$825$	−2.82371	+	26.8658i	−0.0983089	+	0.935347i
$826$	−4.46899	−	0.949913i	−0.155496	−	0.0330517i
$827$	−28.4017	+	12.6452i	−0.987623	+	0.439718i	−0.836006	−	0.548721i	$-0.815115\pi$
$827$	−28.4017	+	12.6452i	−0.987623	+	0.439718i	−0.151618	+	0.988439i	$0.548448\pi$
$828$	2.98235	+	3.31224i	0.103644	+	0.115108i
$829$	−8.66756	+	26.6760i	−0.301037	+	0.926496i	0.680090	+	0.733129i	$0.261941\pi$
$829$	−8.66756	+	26.6760i	−0.301037	+	0.926496i	−0.981126	+	0.193367i	$0.938059\pi$
$830$	8.98683	−	9.98089i	0.311937	−	0.346442i
$831$	21.8491	+	37.8437i	0.757936	+	1.31278i
$832$	7.45215	−	12.9075i	0.258357	−	0.447487i
$833$	3.28688	+	10.1160i	0.113884	+	0.350498i
$834$	14.3253	+	6.37805i	0.496046	+	0.220854i
$835$	32.1239	+	23.3394i	1.11169	+	0.807692i
$836$	9.66453			0.334255
$837$		0			0
$838$	8.13409			0.280987
$839$	18.6621	+	13.5588i	0.644287	+	0.468102i	0.861320	−	0.508062i	$-0.169638\pi$
$839$	18.6621	+	13.5588i	0.644287	+	0.468102i	−0.217034	+	0.976164i	$0.569638\pi$
$840$	−11.5854	−	5.15814i	−0.399733	−	0.177973i
$841$	−5.87746	−	18.0890i	−0.202671	−	0.623757i
$842$	−5.12779	+	8.88160i	−0.176715	+	0.306080i
$843$	−3.59793	−	6.23179i	−0.123919	−	0.214634i
$844$	−20.9798	+	23.3005i	−0.722156	+	0.802035i
$845$	−4.35696	+	13.4093i	−0.149884	+	0.461296i
$846$	−10.0564	−	11.1688i	−0.345747	−	0.383991i
$847$	5.03028	−	2.23963i	0.172843	−	0.0769545i
$848$	15.9397	+	3.38809i	0.547372	+	0.116347i
$849$	−1.42940	+	13.5998i	−0.0490568	+	0.466745i
$850$	0.257410	+	2.44909i	0.00882909	+	0.0840032i
$851$	1.36113	−	0.289318i	0.0466591	−	0.00991769i
$852$	−7.36982	+	5.35449i	−0.252486	+	0.183442i
$853$	−24.2874	+	17.6458i	−0.831585	+	0.604182i	−0.920007	−	0.391901i	$-0.871818\pi$
$853$	−24.2874	+	17.6458i	−0.831585	+	0.604182i	0.0884221	+	0.996083i	$0.471818\pi$
$854$	−5.36964	+	1.14135i	−0.183745	+	0.0390562i
$855$	−3.53599	−	33.6427i	−0.120928	−	1.15056i
$856$	−1.73035	+	16.4632i	−0.0591422	+	0.562701i
$857$	53.3945	+	11.3494i	1.82392	+	0.387687i	0.987141	−	0.159851i	$-0.0511015\pi$
$857$	53.3945	+	11.3494i	1.82392	+	0.387687i	0.836781	+	0.547538i	$0.184435\pi$
$858$	6.49007	−	2.88957i	0.221567	−	0.0986482i
$859$	6.24728	+	6.93830i	0.213154	+	0.236732i	0.840235	−	0.542223i	$-0.182417\pi$
$859$	6.24728	+	6.93830i	0.213154	+	0.236732i	−0.627081	+	0.778954i	$0.715750\pi$
$860$	14.5036	−	44.6376i	0.494570	−	1.52213i
$861$	−14.5523	+	16.1619i	−0.495940	+	0.550797i
$862$	−5.33338	−	9.23768i	−0.181656	−	0.314637i
$863$	−6.65836	+	11.5326i	−0.226653	+	0.392575i	−0.956814	−	0.290700i	$-0.906112\pi$
$863$	−6.65836	+	11.5326i	−0.226653	+	0.392575i	0.730161	+	0.683275i	$0.239445\pi$
$864$	−8.21560	−	25.2850i	−0.279500	−	0.860214i
$865$	51.7289	+	23.0312i	1.75884	+	0.783085i
$866$	3.93491	+	2.85888i	0.133714	+	0.0971487i
$867$	39.5520			1.34326
$868$		0			0
$869$	8.38250			0.284357
$870$	−7.72660	−	5.61370i	−0.261956	−	0.190322i
$871$	−16.9000	−	7.52438i	−0.572636	−	0.254954i
$872$	0.266104	+	0.818983i	0.00901141	+	0.0277343i
$873$	−9.16547	+	15.8751i	−0.310204	+	0.537290i
$874$	0.164599	+	0.285094i	0.00556766	+	0.00964346i
$875$	2.49712	−	2.77333i	0.0844181	−	0.0937558i
$876$	24.0925	−	74.1490i	0.814010	−	2.50526i
$877$	−28.4822	−	31.6327i	−0.961777	−	1.06816i	−0.997630	−	0.0688047i	$-0.978081\pi$
$877$	−28.4822	−	31.6327i	−0.961777	−	1.06816i	0.0358529	−	0.999357i	$-0.488585\pi$
$878$	4.14800	−	1.84681i	0.139988	−	0.0623268i
$879$	−29.8541	−	6.34568i	−1.00695	−	0.214034i
$880$	2.47413	−	23.5398i	0.0834029	−	0.793526i
$881$	0.603457	+	5.74151i	0.0203310	+	0.193436i	0.999973	−	0.00731486i	$-0.00232841\pi$
$881$	0.603457	+	5.74151i	0.0203310	+	0.193436i	−0.979642	+	0.200751i	$0.935662\pi$
$882$	10.7623	−	2.28761i	0.362387	−	0.0770277i
$883$	−22.0029	+	15.9860i	−0.740457	+	0.537973i	−0.892854	−	0.450346i	$-0.851301\pi$
$883$	−22.0029	+	15.9860i	−0.740457	+	0.537973i	0.152397	+	0.988319i	$0.451301\pi$
$884$	−7.96061	+	5.78372i	−0.267744	+	0.194528i
$885$	−101.091	+	21.4875i	−3.39812	+	0.722293i
$886$	−0.872753	−	8.30369i	−0.0293207	−	0.278968i
$887$	0.770551	−	7.33131i	0.0258726	−	0.246161i	−0.973940	−	0.226805i	$-0.927172\pi$
$887$	0.770551	−	7.33131i	0.0258726	−	0.246161i	0.999813	−	0.0193557i	$-0.00616149\pi$
$888$	−12.1322	−	2.57878i	−0.407131	−	0.0865383i
$889$	−0.116460	+	0.0518512i	−0.00390594	+	0.00173903i
$890$	1.57969	+	1.75442i	0.0529513	+	0.0588084i
$891$	−2.80677	+	8.63835i	−0.0940304	+	0.289396i
$892$	7.86215	−	8.73180i	0.263244	−	0.292362i
$893$	8.43290	+	14.6062i	0.282196	+	0.488778i
$894$	−6.07548	+	10.5230i	−0.203194	+	0.351943i
$895$	−0.0728867	−	0.224322i	−0.00243633	−	0.00749826i
$896$	9.46395	+	4.21362i	0.316168	+	0.140767i
$897$	−2.97453	−	2.16112i	−0.0993166	−	0.0721578i
$898$	−6.82232			−0.227664
$899$		0			0
$900$	−38.7040			−1.29013
$901$	−7.34737	−	5.33818i	−0.244776	−	0.177841i
$902$	5.42217	+	2.41410i	0.180538	+	0.0803809i
$903$	−8.13900	−	25.0493i	−0.270849	−	0.833588i
$904$	−7.69738	+	13.3322i	−0.256011	+	0.443424i
$905$	−3.21533	−	5.56911i	−0.106881	−	0.185123i
$906$	2.94065	−	3.26592i	0.0976964	−	0.108503i
$907$	5.09354	−	15.6763i	0.169128	−	0.520523i	−0.830189	−	0.557482i	$-0.811767\pi$
$907$	5.09354	−	15.6763i	0.169128	−	0.520523i	0.999317	+	0.0369599i	$0.0117674\pi$
$908$	9.85350	+	10.9434i	0.327000	+	0.363170i
$909$	86.9349	−	38.7059i	2.88345	−	1.28379i
$910$	3.17824	+	0.675556i	0.105358	+	0.0223945i
$911$	−4.68361	+	44.5616i	−0.155175	+	1.47639i	0.588852	+	0.808241i	$0.299580\pi$
$911$	−4.68361	+	44.5616i	−0.155175	+	1.47639i	−0.744027	+	0.668150i	$0.767087\pi$
$912$	2.09757	+	19.9571i	0.0694576	+	0.660845i
$913$	30.5690	−	6.49763i	1.01169	−	0.215040i
$914$	−6.92078	+	5.02824i	−0.228919	+	0.166319i
$915$	−100.461	+	72.9895i	−3.32115	+	2.41296i
$916$	23.4447	−	4.98332i	0.774634	−	0.164654i
$917$	0.654240	+	6.22468i	0.0216049	+	0.205557i
$918$	−0.459867	+	4.37535i	−0.0151779	+	0.144408i
$919$	10.1305	+	2.15330i	0.334174	+	0.0710309i	0.371943	−	0.928256i	$-0.378692\pi$
$919$	10.1305	+	2.15330i	0.334174	+	0.0710309i	−0.0377687	+	0.999287i	$0.512025\pi$
$920$	1.63634	−	0.728546i	0.0539486	−	0.0240195i
$921$	−5.12747	−	5.69464i	−0.168956	−	0.187645i
$922$	−4.16401	+	12.8155i	−0.137134	+	0.422056i
$923$	3.22630	−	3.58317i	0.106195	−	0.117941i
$924$	−7.14231	−	12.3708i	−0.234965	−	0.406971i
$925$	−6.04191	+	10.4649i	−0.198657	+	0.344084i
$926$	−0.716131	−	2.20402i	−0.0235335	−	0.0724287i
$927$	39.6166	+	17.6384i	1.30118	+	0.579322i
$928$	9.90452	+	7.19606i	0.325132	+	0.236222i
$929$	44.0624			1.44564			0.722820	−	0.691037i	$-0.242846\pi$
$929$	44.0624			1.44564			0.722820	+	0.691037i	$0.242846\pi$
$930$		0			0
$931$	−12.3474			−0.404671
$932$	19.3066	+	14.0271i	0.632409	+	0.459472i
$933$	−14.5713	−	6.48754i	−0.477042	−	0.212393i
$934$	4.17034	+	12.8350i	0.136458	+	0.419974i
$935$	−6.59563	+	11.4240i	−0.215700	+	0.373604i
$936$	10.5136	+	18.2101i	0.343648	+	0.595216i
$937$	−23.1298	+	25.6882i	−0.755617	+	0.839198i	−0.991161	−	0.132666i	$-0.957646\pi$
$937$	−23.1298	+	25.6882i	−0.755617	+	0.839198i	0.235543	+	0.971864i	$0.424313\pi$
$938$	0.756528	−	2.32835i	0.0247015	−	0.0760235i
$939$	51.6434	+	57.3558i	1.68532	+	1.87174i
$940$	40.5818	−	18.0682i	1.32363	−	0.589319i
$941$	21.6651	+	4.60505i	0.706261	+	0.150120i	0.547020	−	0.837119i	$-0.315762\pi$
$941$	21.6651	+	4.60505i	0.706261	+	0.150120i	0.159241	+	0.987240i	$0.449095\pi$
$942$	−0.925144	+	8.80216i	−0.0301428	+	0.286790i
$943$	−0.321084	−	3.05491i	−0.0104559	−	0.0994815i
$944$	38.4767	−	8.17848i	1.25231	−	0.266187i
$945$	−17.8572	+	12.9740i	−0.580894	+	0.422044i
$946$	−5.81526	+	4.22504i	−0.189071	+	0.137368i
$947$	27.4689	−	5.83869i	0.892619	−	0.189732i	0.261302	−	0.965257i	$-0.415848\pi$
$947$	27.4689	−	5.83869i	0.892619	−	0.189732i	0.631317	+	0.775525i	$0.282515\pi$
$948$	1.95658	+	18.6156i	0.0635466	+	0.604606i
$949$	−4.31348	+	41.0401i	−0.140022	+	1.33222i
$950$	−2.79621	−	0.594354i	−0.0907212	−	0.0192834i
$951$	−28.3881	+	12.6392i	−0.920547	+	0.409854i
$952$	−1.80002	−	1.99912i	−0.0583389	−	0.0647919i
$953$	2.36916	−	7.29152i	0.0767446	−	0.236196i	−0.905323	−	0.424723i	$-0.860371\pi$
$953$	2.36916	−	7.29152i	0.0767446	−	0.236196i	0.982068	+	0.188527i	$0.0603715\pi$
$954$	−6.28618	+	6.98151i	−0.203523	+	0.226035i
$955$	7.94104	+	13.7543i	0.256966	+	0.445078i
$956$	−23.8546	+	41.3173i	−0.771512	+	1.33630i
$957$	−6.86743	−	21.1358i	−0.221992	−	0.683222i
$958$	2.41595	+	1.07565i	0.0780557	+	0.0347526i
$959$	10.3352	+	7.50893i	0.333740	+	0.242476i
$960$	44.6168			1.44000
$961$		0			0
$962$	3.17789			0.102459
$963$	52.8011	+	38.3622i	1.70149	+	1.23621i
$964$	−4.04734	−	1.80199i	−0.130356	−	0.0580383i
$965$	−1.96038	−	6.03342i	−0.0631067	−	0.194223i
$966$	0.243285	−	0.421383i	0.00782758	−	0.0135578i
$967$	0.925182	+	1.60246i	0.0297518	+	0.0515317i	0.880518	−	0.474013i	$-0.157195\pi$
$967$	0.925182	+	1.60246i	0.0297518	+	0.0515317i	−0.850766	+	0.525545i	$0.823862\pi$
$968$	4.63849	−	5.15156i	0.149087	−	0.165578i
$969$	3.45592	−	10.6362i	0.111020	−	0.341685i
$970$	2.38616	+	2.65010i	0.0766150	+	0.0850896i
$971$	45.1031	−	20.0812i	1.44743	−	0.644436i	0.475499	−	0.879716i	$-0.342268\pi$
$971$	45.1031	−	20.0812i	1.44743	−	0.644436i	0.971928	+	0.235280i	$0.0756009\pi$
$972$	17.9376	+	3.81276i	0.575350	+	0.122294i
$973$	−1.74443	+	16.5971i	−0.0559238	+	0.532079i
$974$	−0.919552	−	8.74896i	−0.0294644	−	0.280335i
$975$	31.2301	−	6.63816i	1.00016	−	0.212591i
$976$	38.2373	−	27.7810i	1.22395	−	0.889248i
$977$	28.8192	−	20.9383i	0.922007	−	0.669877i	−0.0220160	−	0.999758i	$-0.507008\pi$
$977$	28.8192	−	20.9383i	0.922007	−	0.669877i	0.944023	+	0.329881i	$0.107008\pi$
$978$	3.11094	−	0.661251i	0.0994769	−	0.0211445i
$979$	0.574217	+	5.46331i	0.0183520	+	0.174608i
$980$	−3.39942	+	32.3433i	−0.108590	+	1.03317i
$981$	3.32092	+	0.705883i	0.106029	+	0.0225371i
$982$	−12.7489	+	5.67617i	−0.406833	+	0.181134i
$983$	−4.27146	−	4.74393i	−0.136238	−	0.151308i	0.671165	−	0.741308i	$-0.265794\pi$
$983$	−4.27146	−	4.74393i	−0.136238	−	0.151308i	−0.807403	+	0.590000i	$0.799128\pi$
$984$	−8.46068	+	26.0393i	−0.269717	+	0.830103i
$985$	−11.6896	+	12.9827i	−0.372463	+	0.413662i
$986$	−1.01295	−	1.75448i	−0.0322588	−	0.0558739i
$987$	12.4642	−	21.5887i	0.396740	−	0.687175i
$988$	−3.52977	−	10.8635i	−0.112297	−	0.345614i
$989$	3.39847	+	1.51310i	0.108065	+	0.0481136i
$990$	11.0394	+	8.02059i	0.350855	+	0.254911i
$991$	−44.2919			−1.40698			−0.703489	−	0.710706i	$-0.748376\pi$
$991$	−44.2919			−1.40698			−0.703489	+	0.710706i	$0.748376\pi$
$992$		0			0
$993$	−56.8463			−1.80396
$994$	0.516222	+	0.375058i	0.0163736	+	0.0118961i
$995$	18.8176	+	8.37813i	0.596558	+	0.265605i
$996$	21.5649	+	66.3699i	0.683310	+	2.10301i
$997$	−2.66158	+	4.60999i	−0.0842931	+	0.146000i	−0.905090	−	0.425221i	$-0.860197\pi$
$997$	−2.66158	+	4.60999i	−0.0842931	+	0.146000i	0.820797	+	0.571220i	$0.193530\pi$
$998$	4.15641	+	7.19911i	0.131569	+	0.227884i
$999$	−14.4452	+	16.0430i	−0.457025	+	0.507577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.k.732.2		16
31.2	even	5		961.2.g.s.448.1		16
31.3	odd	30		961.2.d.n.388.3		16
31.4	even	5		961.2.c.j.521.4		16
31.5	even	3		31.2.g.a.10.2	✓	16
31.6	odd	6		961.2.d.n.374.3		16
31.7	even	15		961.2.a.i.1.4		8
31.8	even	5		961.2.g.t.844.1		16
31.9	even	15		961.2.g.s.547.1		16
31.10	even	15		961.2.g.t.846.1		16
31.11	odd	30		961.2.c.i.439.4		16
31.12	odd	30		961.2.d.q.628.2		16
31.13	odd	30		961.2.g.j.235.2		16
31.14	even	15		961.2.d.p.531.2		16
31.15	odd	10		961.2.g.l.338.2		16
31.16	even	5		31.2.g.a.28.2	yes	16
31.17	odd	30		961.2.d.q.531.2		16
31.18	even	15	inner	961.2.g.k.235.2		16
31.19	even	15		961.2.d.p.628.2		16
31.20	even	15		961.2.c.j.439.4		16
31.21	odd	30		961.2.g.n.846.1		16
31.22	odd	30		961.2.g.m.547.1		16
31.23	odd	10		961.2.g.n.844.1		16
31.24	odd	30		961.2.a.j.1.4		8
31.25	even	3		961.2.d.o.374.3		16
31.26	odd	6		961.2.g.l.816.2		16
31.27	odd	10		961.2.c.i.521.4		16
31.28	even	15		961.2.d.o.388.3		16
31.29	odd	10		961.2.g.m.448.1		16
31.30	odd	2		961.2.g.j.732.2		16
93.5	odd	6		279.2.y.c.10.1		16
93.38	odd	30		8649.2.a.bf.1.5		8
93.47	odd	10		279.2.y.c.28.1		16
93.86	even	30		8649.2.a.be.1.5		8
124.47	odd	10		496.2.bg.c.369.1		16
124.67	odd	6		496.2.bg.c.289.1		16
155.47	odd	20		775.2.ck.a.524.2		32
155.67	odd	12		775.2.ck.a.599.3		32
155.78	odd	20		775.2.ck.a.524.3		32
155.98	odd	12		775.2.ck.a.599.2		32
155.109	even	10		775.2.bl.a.276.1		16
155.129	even	6		775.2.bl.a.351.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.2	✓	16	31.5	even	3
31.2.g.a.28.2	yes	16	31.16	even	5
279.2.y.c.10.1		16	93.5	odd	6
279.2.y.c.28.1		16	93.47	odd	10
496.2.bg.c.289.1		16	124.67	odd	6
496.2.bg.c.369.1		16	124.47	odd	10
775.2.bl.a.276.1		16	155.109	even	10
775.2.bl.a.351.1		16	155.129	even	6
775.2.ck.a.524.2		32	155.47	odd	20
775.2.ck.a.524.3		32	155.78	odd	20
775.2.ck.a.599.2		32	155.98	odd	12
775.2.ck.a.599.3		32	155.67	odd	12
961.2.a.i.1.4		8	31.7	even	15
961.2.a.j.1.4		8	31.24	odd	30
961.2.c.i.439.4		16	31.11	odd	30
961.2.c.i.521.4		16	31.27	odd	10
961.2.c.j.439.4		16	31.20	even	15
961.2.c.j.521.4		16	31.4	even	5
961.2.d.n.374.3		16	31.6	odd	6
961.2.d.n.388.3		16	31.3	odd	30
961.2.d.o.374.3		16	31.25	even	3
961.2.d.o.388.3		16	31.28	even	15
961.2.d.p.531.2		16	31.14	even	15
961.2.d.p.628.2		16	31.19	even	15
961.2.d.q.531.2		16	31.17	odd	30
961.2.d.q.628.2		16	31.12	odd	30
961.2.g.j.235.2		16	31.13	odd	30
961.2.g.j.732.2		16	31.30	odd	2
961.2.g.k.235.2		16	31.18	even	15	inner
961.2.g.k.732.2		16	1.1	even	1	trivial
961.2.g.l.338.2		16	31.15	odd	10
961.2.g.l.816.2		16	31.26	odd	6
961.2.g.m.448.1		16	31.29	odd	10
961.2.g.m.547.1		16	31.22	odd	30
961.2.g.n.844.1		16	31.23	odd	10
961.2.g.n.846.1		16	31.21	odd	30
961.2.g.s.448.1		16	31.2	even	5
961.2.g.s.547.1		16	31.9	even	15
961.2.g.t.844.1		16	31.8	even	5
961.2.g.t.846.1		16	31.10	even	15
8649.2.a.be.1.5		8	93.86	even	30
8649.2.a.bf.1.5		8	93.38	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.284315 - 0.206567i) q^{2} +(-2.64315 - 1.17681i) q^{3} +(-0.579869 - 1.78465i) q^{4} +(-1.48661 + 2.57489i) q^{5} +(0.508398 + 0.880572i) q^{6} +(-0.724084 + 0.804176i) q^{7} +(-0.420982 + 1.29565i) q^{8} +(3.59399 + 3.99153i) q^{9} +O(q^{10})\)	\(q+(-0.284315 - 0.206567i) q^{2} +(-2.64315 - 1.17681i) q^{3} +(-0.579869 - 1.78465i) q^{4} +(-1.48661 + 2.57489i) q^{5} +(0.508398 + 0.880572i) q^{6} +(-0.724084 + 0.804176i) q^{7} +(-0.420982 + 1.29565i) q^{8} +(3.59399 + 3.99153i) q^{9} +(0.954554 - 0.424995i) q^{10} +(2.37824 + 0.505510i) q^{11} +(-0.567511 + 5.39951i) q^{12} +(-0.300378 - 2.85791i) q^{13} +(0.371984 - 0.0790676i) q^{14} +(6.95951 - 5.05638i) q^{15} +(-2.64890 + 1.92454i) q^{16} +(1.78489 - 0.379390i) q^{17} +(-0.197307 - 1.87725i) q^{18} +(-0.221420 + 2.10667i) q^{19} +(5.45733 + 1.15999i) q^{20} +(2.86023 - 1.27345i) q^{21} +(-0.571747 - 0.634989i) q^{22} +(-0.136652 + 0.420572i) q^{23} +(2.63745 - 2.92919i) q^{24} +(-1.92005 - 3.32562i) q^{25} +(-0.504947 + 0.874594i) q^{26} +(-2.11998 - 6.52462i) q^{27} +(1.85505 + 0.825921i) q^{28} +(2.55579 + 1.85689i) q^{29} -3.02317 q^{30} +3.87532 q^{32} +(-5.69116 - 4.13487i) q^{33} +(-0.585840 - 0.260833i) q^{34} +(-0.994234 - 3.05994i) q^{35} +(5.03946 - 8.72860i) q^{36} +(-1.57338 - 2.72517i) q^{37} +(0.498121 - 0.553219i) q^{38} +(-2.56926 + 7.90738i) q^{39} +(-2.71032 - 3.01011i) q^{40} +(-6.34570 + 2.82529i) q^{41} +(-1.07626 - 0.228766i) q^{42} +(0.879333 - 8.36630i) q^{43} +(-0.476906 - 4.53746i) q^{44} +(-15.6207 + 3.32027i) q^{45} +(0.125728 - 0.0913471i) q^{46} +(6.44144 - 4.67998i) q^{47} +(9.26627 - 1.96961i) q^{48} +(0.609297 + 5.79707i) q^{49} +(-0.141065 + 1.34214i) q^{50} +(-5.16421 - 1.09769i) q^{51} +(-4.92620 + 2.19328i) q^{52} +(-3.33026 - 3.69863i) q^{53} +(-0.745029 + 2.29296i) q^{54} +(-4.83716 + 5.37221i) q^{55} +(-0.737104 - 1.27670i) q^{56} +(3.06439 - 5.30768i) q^{57} +(-0.343078 - 1.05588i) q^{58} +(-10.9753 - 4.88651i) q^{59} +(-13.0595 - 9.48827i) q^{60} -14.4351 q^{61} -5.81225 q^{63} +(4.19600 + 3.04857i) q^{64} +(7.80536 + 3.47517i) q^{65} +(0.763955 + 2.35121i) q^{66} +(3.21879 - 5.57511i) q^{67} +(-1.71208 - 2.96541i) q^{68} +(0.856125 - 0.950823i) q^{69} +(-0.349406 + 1.07536i) q^{70} +(1.12272 + 1.24690i) q^{71} +(-6.68463 + 2.97619i) q^{72} +(-14.0464 - 2.98565i) q^{73} +(-0.115595 + 1.09981i) q^{74} +(1.16137 + 11.0497i) q^{75} +(3.88807 - 0.826435i) q^{76} +(-2.12856 + 1.54649i) q^{77} +(2.36388 - 1.71746i) q^{78} +(3.37230 - 0.716805i) q^{79} +(-1.01759 - 9.68169i) q^{80} +(-0.390488 + 3.71525i) q^{81} +(2.38779 + 0.507540i) q^{82} +(11.7424 - 5.22804i) q^{83} +(-3.93123 - 4.36607i) q^{84} +(-1.67655 + 5.15991i) q^{85} +(-1.97821 + 2.19702i) q^{86} +(-4.57015 - 7.91573i) q^{87} +(-1.65616 + 2.86855i) q^{88} +(0.698188 + 2.14880i) q^{89} +(5.12704 + 2.28271i) q^{90} +(2.51576 + 1.82781i) q^{91} +0.829816 q^{92} -2.79812 q^{94} +(-5.09528 - 3.70194i) q^{95} +(-10.2431 - 4.56051i) q^{96} +(1.05463 + 3.24582i) q^{97} +(1.02425 - 1.77405i) q^{98} +(6.52961 + 11.3096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9	\( 16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} - 21 q^{14} + 14 q^{15} - 2 q^{16} + 9 q^{17} + 12 q^{18} - 29 q^{19} - 8 q^{20} - 6 q^{21} - 21 q^{22} + q^{23} - 5 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} + 45 q^{28} - 14 q^{29} - 22 q^{30} - 42 q^{32} - 13 q^{33} - 17 q^{34} - 9 q^{35} + q^{36} - 8 q^{37} + 23 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} - 51 q^{42} - 37 q^{43} - 6 q^{44} - 70 q^{45} + 34 q^{46} + 14 q^{47} + 4 q^{48} - 43 q^{49} + 3 q^{50} + 33 q^{51} - 46 q^{52} - 9 q^{53} - 46 q^{54} + 8 q^{55} - 30 q^{56} - 17 q^{57} - 15 q^{58} - 11 q^{59} - 75 q^{60} - 60 q^{61} - 46 q^{63} + 23 q^{64} + 18 q^{65} - 30 q^{66} + 13 q^{67} + 30 q^{68} - 37 q^{69} + 12 q^{70} + 31 q^{71} - 38 q^{72} - 13 q^{73} + 43 q^{74} - 17 q^{75} - 12 q^{76} + 18 q^{77} - 15 q^{78} - 12 q^{79} + 6 q^{80} - 22 q^{81} - q^{82} + 44 q^{83} + 23 q^{84} + 37 q^{85} + 19 q^{86} + 15 q^{87} - 17 q^{88} + q^{89} + 7 q^{90} + 8 q^{91} - 64 q^{92} + 44 q^{94} - 22 q^{95} + 8 q^{96} + 3 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 - 21 * q^14 + 14 * q^15 - 2 * q^16 + 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 - 6 * q^21 - 21 * q^22 + q^23 - 5 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 45 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 - 17 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 51 * q^42 - 37 * q^43 - 6 * q^44 - 70 * q^45 + 34 * q^46 + 14 * q^47 + 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 - 46 * q^52 - 9 * q^53 - 46 * q^54 + 8 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 - 11 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 + 18 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 - 13 * q^73 + 43 * q^74 - 17 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 - 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 + 44 * q^83 + 23 * q^84 + 37 * q^85 + 19 * q^86 + 15 * q^87 - 17 * q^88 + q^89 + 7 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

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