LMFDB - Embedded newform 403.2.bk.a.9.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(9,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 2]))

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

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

chi := DirichletCharacter("403.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bk (of order $15$, degree $8$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$35$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.12
Character	$\chi$	$=$	403.9
Dual form			403.2.bk.a.224.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.718707 - 0.798205i) q^{2} +(-0.717726 + 0.797115i) q^{3} +(0.0884655 - 0.841693i) q^{4} +(1.01665 + 1.76088i) q^{5} +1.15210 q^{6} +(-3.07573 - 2.23465i) q^{7} +(-2.47334 + 1.79699i) q^{8} +(0.193323 + 1.83935i) q^{9} +O(q^{10})$	\(q+(-0.718707 - 0.798205i) q^{2} +(-0.717726 + 0.797115i) q^{3} +(0.0884655 - 0.841693i) q^{4} +(1.01665 + 1.76088i) q^{5} +1.15210 q^{6} +(-3.07573 - 2.23465i) q^{7} +(-2.47334 + 1.79699i) q^{8} +(0.193323 + 1.83935i) q^{9} +(0.674874 - 2.07705i) q^{10} +(4.07613 + 2.96148i) q^{11} +(0.607432 + 0.674622i) q^{12} +(-2.49899 - 2.59905i) q^{13} +(0.426840 + 4.06111i) q^{14} +(-2.13330 - 0.453447i) q^{15} +(1.55630 + 0.330802i) q^{16} +(-3.17763 + 2.30868i) q^{17} +(1.32923 - 1.47626i) q^{18} +(-1.21694 + 3.74536i) q^{19} +(1.57206 - 0.699926i) q^{20} +(3.98880 - 0.847845i) q^{21} +(-0.565674 - 5.38202i) q^{22} +(0.954659 + 9.08297i) q^{23} +(0.342774 - 3.26128i) q^{24} +(0.432864 - 0.749742i) q^{25} +(-0.278530 + 3.86266i) q^{26} +(-4.20824 - 3.05746i) q^{27} +(-2.15298 + 2.39113i) q^{28} +(-3.37135 - 3.74427i) q^{29} +(1.17127 + 2.02870i) q^{30} +(2.64095 + 4.90157i) q^{31} +(2.20274 + 3.81526i) q^{32} +(-5.28619 + 1.12361i) q^{33} +(4.12658 + 0.877133i) q^{34} +(0.808024 - 7.68783i) q^{35} +1.56527 q^{36} +(3.19609 + 5.53579i) q^{37} +(3.86419 - 1.72045i) q^{38} +(3.86533 - 0.126581i) q^{39} +(-5.67879 - 2.52836i) q^{40} +(1.28049 - 3.94095i) q^{41} +(-3.54353 - 2.57453i) q^{42} +(-2.78592 + 8.57418i) q^{43} +(2.85326 - 3.16886i) q^{44} +(-3.04233 + 2.21038i) q^{45} +(6.56395 - 7.29001i) q^{46} +(2.45575 + 7.55803i) q^{47} +(-1.38068 + 1.00313i) q^{48} +(2.30333 + 7.08891i) q^{49} +(-0.909550 + 0.193331i) q^{50} +(0.440380 - 4.18994i) q^{51} +(-2.40867 + 1.87346i) q^{52} +(-3.39572 - 1.51187i) q^{53} +(0.584007 + 5.55646i) q^{54} +(-1.07084 + 10.1884i) q^{55} +11.6229 q^{56} +(-2.11205 - 3.65818i) q^{57} +(-0.565677 + 5.38206i) q^{58} +(0.0770209 + 0.237046i) q^{59} +(-0.570386 + 1.75547i) q^{60} +(-1.08425 - 1.87798i) q^{61} +(2.01439 - 5.63081i) q^{62} +(3.51568 - 6.08933i) q^{63} +(2.44557 - 7.52668i) q^{64} +(2.03603 - 7.04274i) q^{65} +(4.69609 + 3.41191i) q^{66} -4.44609 q^{67} +(1.66209 + 2.87883i) q^{68} +(-7.92536 - 5.75811i) q^{69} +(-6.71720 + 4.88033i) q^{70} +(-0.906711 - 8.62678i) q^{71} +(-3.78343 - 4.20193i) q^{72} +(1.16742 - 11.1073i) q^{73} +(2.12164 - 6.52975i) q^{74} +(0.286953 + 0.883152i) q^{75} +(3.04479 + 1.35563i) q^{76} +(-5.91919 - 18.2174i) q^{77} +(-2.87908 - 2.99435i) q^{78} +(-1.10445 - 10.5082i) q^{79} +(0.999702 + 3.07677i) q^{80} +(0.0303275 - 0.00644632i) q^{81} +(-4.06599 + 1.81029i) q^{82} +(4.27872 - 0.909471i) q^{83} +(-0.360754 - 3.43235i) q^{84} +(-7.29584 - 3.24832i) q^{85} +(8.84621 - 3.93859i) q^{86} +5.40432 q^{87} -15.4034 q^{88} +(-11.3989 + 5.07514i) q^{89} +(3.95088 + 0.839785i) q^{90} +(1.87826 + 13.5783i) q^{91} +7.72953 q^{92} +(-5.80259 - 1.41285i) q^{93} +(4.26789 - 7.39220i) q^{94} +(-7.83233 + 1.66481i) q^{95} +(-4.62216 - 0.982471i) q^{96} +(1.16050 - 11.0415i) q^{97} +(4.00299 - 6.93338i) q^{98} +(-4.65918 + 8.06993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9}+O(q^{10}) $ 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9} - 9 q^{10} - 6 q^{11} - 50 q^{12} - 6 q^{13} - 21 q^{15} + 23 q^{16} + 3 q^{17} - 15 q^{18} - 9 q^{19} + 60 q^{20} - 34 q^{21} + 41 q^{22} - 12 q^{23} - 89 q^{24} - 112 q^{25} + 39 q^{26} + 48 q^{27} + 66 q^{28} - 11 q^{29} + 24 q^{30} - 22 q^{31} + q^{32} - 37 q^{33} - 49 q^{34} + 41 q^{35} + 134 q^{36} + 17 q^{37} - 23 q^{38} + 10 q^{39} + 31 q^{40} + q^{41} - 71 q^{42} - 7 q^{43} - 42 q^{44} - 13 q^{45} + 21 q^{46} - 20 q^{47} - 3 q^{48} - 69 q^{49} - 42 q^{50} - 71 q^{51} - 140 q^{52} - 8 q^{53} - 149 q^{54} + 5 q^{55} - 126 q^{56} + 21 q^{57} + 79 q^{58} + 77 q^{59} + 2 q^{60} + 53 q^{61} + 72 q^{62} + 17 q^{63} - 91 q^{64} - 25 q^{65} - 62 q^{66} - 14 q^{67} + 83 q^{68} - 31 q^{69} + 134 q^{70} + 32 q^{71} - 70 q^{72} - 31 q^{73} + 51 q^{74} + 79 q^{75} + 98 q^{76} - 80 q^{77} - 141 q^{78} - 142 q^{79} + 6 q^{80} + 66 q^{81} - 48 q^{82} + 94 q^{83} + 130 q^{84} + 90 q^{85} - 34 q^{86} + 22 q^{87} - 122 q^{88} - 15 q^{89} + 43 q^{90} + 56 q^{91} - 294 q^{92} - 52 q^{93} - 57 q^{94} + 94 q^{95} + 24 q^{96} + 46 q^{97} + 73 q^{98} + 12 q^{99}+O(q^{100}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9 - 9 * q^10 - 6 * q^11 - 50 * q^12 - 6 * q^13 - 21 * q^15 + 23 * q^16 + 3 * q^17 - 15 * q^18 - 9 * q^19 + 60 * q^20 - 34 * q^21 + 41 * q^22 - 12 * q^23 - 89 * q^24 - 112 * q^25 + 39 * q^26 + 48 * q^27 + 66 * q^28 - 11 * q^29 + 24 * q^30 - 22 * q^31 + q^32 - 37 * q^33 - 49 * q^34 + 41 * q^35 + 134 * q^36 + 17 * q^37 - 23 * q^38 + 10 * q^39 + 31 * q^40 + q^41 - 71 * q^42 - 7 * q^43 - 42 * q^44 - 13 * q^45 + 21 * q^46 - 20 * q^47 - 3 * q^48 - 69 * q^49 - 42 * q^50 - 71 * q^51 - 140 * q^52 - 8 * q^53 - 149 * q^54 + 5 * q^55 - 126 * q^56 + 21 * q^57 + 79 * q^58 + 77 * q^59 + 2 * q^60 + 53 * q^61 + 72 * q^62 + 17 * q^63 - 91 * q^64 - 25 * q^65 - 62 * q^66 - 14 * q^67 + 83 * q^68 - 31 * q^69 + 134 * q^70 + 32 * q^71 - 70 * q^72 - 31 * q^73 + 51 * q^74 + 79 * q^75 + 98 * q^76 - 80 * q^77 - 141 * q^78 - 142 * q^79 + 6 * q^80 + 66 * q^81 - 48 * q^82 + 94 * q^83 + 130 * q^84 + 90 * q^85 - 34 * q^86 + 22 * q^87 - 122 * q^88 - 15 * q^89 + 43 * q^90 + 56 * q^91 - 294 * q^92 - 52 * q^93 - 57 * q^94 + 94 * q^95 + 24 * q^96 + 46 * q^97 + 73 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	−0.718707	−	0.798205i	−0.508203	−	0.564416i	0.433374	−	0.901214i	$-0.357323\pi$
$2$	−0.718707	−	0.798205i	−0.508203	−	0.564416i	−0.941577	+	0.336798i	$0.890656\pi$
$3$	−0.717726	+	0.797115i	−0.414379	+	0.460215i	−0.913812	−	0.406138i	$-0.866875\pi$
$3$	−0.717726	+	0.797115i	−0.414379	+	0.460215i	0.499433	+	0.866353i	$0.333542\pi$
$4$	0.0884655	−	0.841693i	0.0442328	−	0.420847i
$5$	1.01665	+	1.76088i	0.454658	+	0.787490i	0.998668	−	0.0515880i	$-0.0164283\pi$
$5$	1.01665	+	1.76088i	0.454658	+	0.787490i	−0.544011	+	0.839078i	$0.683095\pi$
$6$	1.15210			0.470341
$7$	−3.07573	−	2.23465i	−1.16251	−	0.844617i	−0.172421	−	0.985023i	$-0.555159\pi$
$7$	−3.07573	−	2.23465i	−1.16251	−	0.844617i	−0.990094	+	0.140407i	$0.955159\pi$
$8$	−2.47334	+	1.79699i	−0.874458	+	0.635331i
$9$	0.193323	+	1.83935i	0.0644410	+	0.613115i
$10$	0.674874	−	2.07705i	0.213414	−	0.656821i
$11$	4.07613	+	2.96148i	1.22900	+	0.892920i	0.996815	−	0.0797514i	$-0.0254127\pi$
$11$	4.07613	+	2.96148i	1.22900	+	0.892920i	0.232185	+	0.972672i	$0.425413\pi$
$12$	0.607432	+	0.674622i	0.175351	+	0.194747i
$13$	−2.49899	−	2.59905i	−0.693095	−	0.720846i
$13$	−2.49899	−	2.59905i	−0.693095	−	0.720846i
$14$	0.426840	+	4.06111i	0.114078	+	1.08538i
$15$	−2.13330	−	0.453447i	−0.550815	−	0.117079i
$16$	1.55630	+	0.330802i	0.389075	+	0.0827004i
$17$	−3.17763	+	2.30868i	−0.770688	+	0.559938i	−0.902170	−	0.431381i	$-0.858026\pi$
$17$	−3.17763	+	2.30868i	−0.770688	+	0.559938i	0.131482	+	0.991319i	$0.458026\pi$
$18$	1.32923	−	1.47626i	0.313303	−	0.347958i
$19$	−1.21694	+	3.74536i	−0.279185	+	0.859244i	0.708896	+	0.705313i	$0.249193\pi$
$19$	−1.21694	+	3.74536i	−0.279185	+	0.859244i	−0.988082	+	0.153931i	$0.950807\pi$
$20$	1.57206	−	0.699926i	0.351523	−	0.156508i
$21$	3.98880	−	0.847845i	0.870427	−	0.185015i
$22$	−0.565674	−	5.38202i	−0.120602	−	1.14745i
$23$	0.954659	+	9.08297i	0.199060	+	1.89393i	0.403390	+	0.915028i	$0.367832\pi$
$23$	0.954659	+	9.08297i	0.199060	+	1.89393i	−0.204329	+	0.978902i	$0.565501\pi$
$24$	0.342774	−	3.26128i	0.0699685	−	0.665706i
$25$	0.432864	−	0.749742i	0.0865728	−	0.149948i
$26$	−0.278530	+	3.86266i	−0.0546242	+	0.757530i
$27$	−4.20824	−	3.05746i	−0.809876	−	0.588409i
$28$	−2.15298	+	2.39113i	−0.406875	+	0.451881i
$29$	−3.37135	−	3.74427i	−0.626044	−	0.695293i	0.343793	−	0.939045i	$-0.388288\pi$
$29$	−3.37135	−	3.74427i	−0.626044	−	0.695293i	−0.969837	+	0.243753i	$0.921621\pi$
$30$	1.17127	+	2.02870i	0.213844	+	0.370389i
$31$	2.64095	+	4.90157i	0.474328	+	0.880348i
$31$	2.64095	+	4.90157i	0.474328	+	0.880348i
$32$	2.20274	+	3.81526i	0.389393	+	0.674449i
$33$	−5.28619	+	1.12361i	−0.920207	+	0.195596i
$34$	4.12658	+	0.877133i	0.707703	+	0.150427i
$35$	0.808024	−	7.68783i	0.136581	−	1.29948i
$36$	1.56527			0.260878
$37$	3.19609	+	5.53579i	0.525434	+	0.910078i	0.999561	+	0.0296220i	$0.00943036\pi$
$37$	3.19609	+	5.53579i	0.525434	+	0.910078i	−0.474127	+	0.880456i	$0.657236\pi$
$38$	3.86419	−	1.72045i	0.626854	−	0.279093i
$39$	3.86533	−	0.126581i	0.618948	−	0.0202692i
$40$	−5.67879	−	2.52836i	−0.897895	−	0.399769i
$41$	1.28049	−	3.94095i	0.199979	−	0.615473i	−0.799903	−	0.600129i	$-0.795116\pi$
$41$	1.28049	−	3.94095i	0.199979	−	0.615473i	0.999882	−	0.0153437i	$-0.00488426\pi$
$42$	−3.54353	−	2.57453i	−0.546779	−	0.397258i
$43$	−2.78592	+	8.57418i	−0.424849	+	1.30755i	0.478290	+	0.878202i	$0.341257\pi$
$43$	−2.78592	+	8.57418i	−0.424849	+	1.30755i	−0.903139	+	0.429348i	$0.858743\pi$
$44$	2.85326	−	3.16886i	0.430144	−	0.477724i
$45$	−3.04233	+	2.21038i	−0.453524	+	0.329504i
$46$	6.56395	−	7.29001i	0.967802	−	1.07485i
$47$	2.45575	+	7.55803i	0.358208	+	1.10245i	0.954126	+	0.299406i	$0.0967885\pi$
$47$	2.45575	+	7.55803i	0.358208	+	1.10245i	−0.595918	+	0.803046i	$0.703212\pi$
$48$	−1.38068	+	1.00313i	−0.199284	+	0.144789i
$49$	2.30333	+	7.08891i	0.329047	+	1.01270i
$50$	−0.909550	+	0.193331i	−0.128630	+	0.0273411i
$51$	0.440380	−	4.18994i	0.0616655	−	0.586708i
$52$	−2.40867	+	1.87346i	−0.334023	+	0.259802i
$53$	−3.39572	−	1.51187i	−0.466437	−	0.207671i	0.160041	−	0.987110i	$-0.448838\pi$
$53$	−3.39572	−	1.51187i	−0.466437	−	0.207671i	−0.626478	+	0.779439i	$0.715504\pi$
$54$	0.584007	+	5.55646i	0.0794733	+	0.756138i
$55$	−1.07084	+	10.1884i	−0.144392	+	1.37380i
$56$	11.6229			1.55318
$57$	−2.11205	−	3.65818i	−0.279748	−	0.484538i
$58$	−0.565677	+	5.38206i	−0.0742771	+	0.706699i
$59$	0.0770209	+	0.237046i	0.0100273	+	0.0308608i	0.955945	−	0.293546i	$-0.0948354\pi$
$59$	0.0770209	+	0.237046i	0.0100273	+	0.0308608i	−0.945918	+	0.324407i	$0.894835\pi$
$60$	−0.570386	+	1.75547i	−0.0736365	+	0.226630i
$61$	−1.08425	−	1.87798i	−0.138824	−	0.240451i	0.788228	−	0.615384i	$-0.210999\pi$
$61$	−1.08425	−	1.87798i	−0.138824	−	0.240451i	−0.927052	+	0.374933i	$0.877666\pi$
$62$	2.01439	−	5.63081i	0.255828	−	0.715113i
$63$	3.51568	−	6.08933i	0.442933	−	0.767183i
$64$	2.44557	−	7.52668i	0.305696	−	0.940835i
$65$	2.03603	−	7.04274i	0.252538	−	0.873544i
$66$	4.69609	+	3.41191i	0.578049	+	0.419977i
$67$	−4.44609			−0.543176			−0.271588	−	0.962414i	$-0.587549\pi$
$67$	−4.44609			−0.543176			−0.271588	+	0.962414i	$0.587549\pi$
$68$	1.66209	+	2.87883i	0.201558	+	0.349109i
$69$	−7.92536	−	5.75811i	−0.954101	−	0.693195i
$70$	−6.71720	+	4.88033i	−0.802859	+	0.583311i
$71$	−0.906711	−	8.62678i	−0.107607	−	1.02381i	−0.906462	−	0.422287i	$-0.861227\pi$
$71$	−0.906711	−	8.62678i	−0.107607	−	1.02381i	0.798855	−	0.601523i	$-0.205439\pi$
$72$	−3.78343	−	4.20193i	−0.445882	−	0.495202i
$73$	1.16742	−	11.1073i	0.136637	−	1.30001i	−0.684388	−	0.729118i	$-0.739931\pi$
$73$	1.16742	−	11.1073i	0.136637	−	1.30001i	0.821025	−	0.570893i	$-0.193403\pi$
$74$	2.12164	−	6.52975i	0.246636	−	0.759068i
$75$	0.286953	+	0.883152i	0.0331345	+	0.101978i
$76$	3.04479	+	1.35563i	0.349261	+	0.155501i
$77$	−5.91919	−	18.2174i	−0.674555	−	2.07607i
$78$	−2.87908	−	2.99435i	−0.325991	−	0.339043i
$79$	−1.10445	−	10.5082i	−0.124261	−	1.18226i	−0.861904	−	0.507072i	$-0.830728\pi$
$79$	−1.10445	−	10.5082i	−0.124261	−	1.18226i	0.737643	−	0.675191i	$-0.235939\pi$
$80$	0.999702	+	3.07677i	0.111770	+	0.343993i
$81$	0.0303275	−	0.00644632i	0.00336973	−	0.000716258i
$82$	−4.06599	+	1.81029i	−0.449013	+	0.199913i
$83$	4.27872	−	0.909471i	0.469651	−	0.0998274i	0.0329940	−	0.999456i	$-0.489496\pi$
$83$	4.27872	−	0.909471i	0.469651	−	0.0998274i	0.436657	+	0.899628i	$0.356162\pi$
$84$	−0.360754	−	3.43235i	−0.0393615	−	0.374500i
$85$	−7.29584	−	3.24832i	−0.791345	−	0.352329i
$86$	8.84621	−	3.93859i	0.953912	−	0.424709i
$87$	5.40432			0.579404
$88$	−15.4034			−1.64201
$89$	−11.3989	+	5.07514i	−1.20829	+	0.537963i	−0.909239	−	0.416275i	$-0.863335\pi$
$89$	−11.3989	+	5.07514i	−1.20829	+	0.537963i	−0.299047	+	0.954238i	$0.596669\pi$
$90$	3.95088	+	0.839785i	0.416459	+	0.0885211i
$91$	1.87826	+	13.5783i	0.196895	+	1.42339i
$92$	7.72953			0.805859
$93$	−5.80259	−	1.41285i	−0.601701	−	0.146505i
$94$	4.26789	−	7.39220i	0.440199	−	0.762447i
$95$	−7.83233	+	1.66481i	−0.803580	+	0.170806i
$96$	−4.62216	−	0.982471i	−0.471748	−	0.100273i
$97$	1.16050	−	11.0415i	0.117831	−	1.12109i	−0.762585	−	0.646888i	$-0.776070\pi$
$97$	1.16050	−	11.0415i	0.117831	−	1.12109i	0.880416	−	0.474202i	$-0.157263\pi$
$98$	4.00299	−	6.93338i	0.404363	−	0.700377i
$99$	−4.65918	+	8.06993i	−0.468265	+	0.811059i
$100$	−0.592759	−	0.430665i	−0.0592759	−	0.0430665i
$101$	−0.668156	−	6.35708i	−0.0664840	−	0.632553i	−0.976133	−	0.217175i	$-0.930316\pi$
$101$	−0.668156	−	6.35708i	−0.0664840	−	0.632553i	0.909649	−	0.415378i	$-0.136351\pi$
$102$	−3.66093	+	2.65982i	−0.362486	+	0.263362i
$103$	2.57371	−	0.547058i	0.253595	−	0.0539032i	−0.0793600	−	0.996846i	$-0.525288\pi$
$103$	2.57371	−	0.547058i	0.253595	−	0.0539032i	0.332955	+	0.942943i	$0.391954\pi$
$104$	10.8513	+	1.93767i	1.06406	+	0.190004i
$105$	5.54815	+	6.16184i	0.541444	+	0.601334i
$106$	1.23374	+	3.79707i	0.119832	+	0.368804i
$107$	−7.16451	−	3.18984i	−0.692619	−	0.308374i	0.0300693	−	0.999548i	$-0.490427\pi$
$107$	−7.16451	−	3.18984i	−0.692619	−	0.308374i	−0.722689	+	0.691174i	$0.757094\pi$
$108$	−2.94573	+	3.27156i	−0.283453	+	0.314806i
$109$	3.73711	+	11.5017i	0.357951	+	1.10166i	0.954279	+	0.298918i	$0.0966257\pi$
$109$	3.73711	+	11.5017i	0.357951	+	1.10166i	−0.596328	+	0.802741i	$0.703374\pi$
$110$	8.90202	−	6.46769i	0.848774	−	0.616671i
$111$	−6.70658	−	1.42553i	−0.636560	−	0.135305i
$112$	−4.04753	−	4.49523i	−0.382455	−	0.424760i
$113$	−8.94112	+	3.98084i	−0.841110	+	0.374486i	−0.781629	−	0.623743i	$-0.785611\pi$
$113$	−8.94112	+	3.98084i	−0.841110	+	0.374486i	−0.0594808	+	0.998229i	$0.518944\pi$
$114$	−1.40203	+	4.31501i	−0.131312	+	0.404138i
$115$	−15.0235	+	10.9152i	−1.40095	+	1.01785i
$116$	−3.44977	+	2.50641i	−0.320303	+	0.232714i
$117$	4.29743	−	5.09896i	0.397298	−	0.471399i
$118$	0.133856	−	0.231845i	0.0123224	−	0.0213431i
$119$	14.9326			1.36887
$120$	6.09121	−	2.71198i	0.556049	−	0.247569i
$121$	4.44527	+	13.6811i	0.404116	+	1.24374i
$122$	−0.719753	+	2.21517i	−0.0651634	+	0.200552i
$123$	2.22235	+	3.84922i	0.200383	+	0.347073i
$124$	4.35925	−	1.78925i	0.391472	−	0.160679i
$125$	11.9267			1.06676
$126$	−7.38727	+	1.57021i	−0.658111	+	0.139886i
$127$	2.07872	−	2.30865i	0.184457	−	0.204860i	−0.643824	−	0.765174i	$-0.722653\pi$
$127$	2.07872	−	2.30865i	0.184457	−	0.204860i	0.828280	+	0.560314i	$0.189320\pi$
$128$	0.283733	−	0.126326i	0.0250787	−	0.0111657i
$129$	−4.83508	−	8.37461i	−0.425705	−	0.737343i
$130$	−7.08485	+	3.43650i	−0.621383	+	0.301401i
$131$	0.789255	−	0.351399i	0.0689576	−	0.0307019i	−0.371968	−	0.928246i	$-0.621317\pi$
$131$	0.789255	−	0.351399i	0.0689576	−	0.0307019i	0.440926	+	0.897544i	$0.354650\pi$
$132$	0.478093	+	4.54875i	0.0416126	+	0.395918i
$133$	12.1125	−	8.80026i	1.05029	−	0.763080i
$134$	3.19544	+	3.54889i	0.276044	+	0.306577i
$135$	1.10555	−	10.5186i	0.0951502	−	0.905294i
$136$	3.71068	−	11.4203i	0.318188	−	0.979283i
$137$	6.42366	+	1.36539i	0.548810	+	0.116653i	0.473968	−	0.880542i	$-0.342821\pi$
$137$	6.42366	+	1.36539i	0.548810	+	0.116653i	0.0748424	+	0.997195i	$0.476155\pi$
$138$	1.09986	+	10.4645i	0.0936262	+	0.890794i
$139$	−13.8916	+	15.4282i	−1.17827	+	1.30860i	−0.236776	+	0.971564i	$0.576091\pi$
$139$	−13.8916	+	15.4282i	−1.17827	+	1.30860i	−0.941492	+	0.337035i	$0.890576\pi$
$140$	−6.39931	−	1.36022i	−0.540841	−	0.114959i
$141$	−7.78718	−	3.46707i	−0.655798	−	0.291980i
$142$	−6.23428	+	6.92387i	−0.523169	+	0.581038i
$143$	−2.48918	−	17.9948i	−0.208156	−	1.50480i
$144$	−0.307590	+	2.92652i	−0.0256325	+	0.243877i
$145$	3.16574	−	9.74315i	0.262900	−	0.809124i
$146$	−9.70493	+	7.05105i	−0.803186	+	0.583549i
$147$	−7.30384	−	3.25188i	−0.602411	−	0.268210i
$148$	4.94218	−	2.20040i	0.406245	−	0.180872i
$149$	11.1505			0.913484			0.456742	−	0.889599i	$-0.349016\pi$
$149$	11.1505			0.913484			0.456742	+	0.889599i	$0.349016\pi$
$150$	0.498701	−	0.863775i	0.0407187	−	0.0705269i
$151$	16.3558	+	11.8832i	1.33101	+	0.967037i	0.999724	+	0.0235076i	$0.00748339\pi$
$151$	16.3558	+	11.8832i	1.33101	+	0.967037i	0.331289	+	0.943529i	$0.392517\pi$
$152$	−3.72045	−	11.4504i	−0.301768	−	0.928748i
$153$	−4.86077	−	5.39843i	−0.392970	−	0.436438i
$154$	−10.2871	+	17.8177i	−0.828955	+	1.43579i
$155$	−5.94618	+	9.63355i	−0.477609	+	0.773786i
$156$	0.235406	−	3.26462i	0.0188476	−	0.261379i
$157$	4.41399	−	13.5849i	0.352275	−	1.08419i	−0.605298	−	0.795999i	$-0.706946\pi$
$157$	4.41399	−	13.5849i	0.352275	−	1.08419i	0.957573	−	0.288191i	$-0.0930538\pi$
$158$	−7.59390	+	8.43389i	−0.604139	+	0.670964i
$159$	3.64233	−	1.62167i	0.288855	−	0.128607i
$160$	−4.47881	+	7.75753i	−0.354081	+	0.613287i
$161$	17.3610	−	30.0701i	1.36823	−	2.36985i
$162$	−0.0269421	−	0.0195746i	−0.00211677	−	0.00153792i
$163$	−1.84347	−	0.820765i	−0.144392	−	0.0642873i	0.333269	−	0.942832i	$-0.391848\pi$
$163$	−1.84347	−	0.820765i	−0.144392	−	0.0642873i	−0.477660	+	0.878545i	$0.658515\pi$
$164$	−3.20379	−	1.42642i	−0.250174	−	0.111385i
$165$	−7.35273	−	8.16603i	−0.572409	−	0.635725i
$166$	−3.80109	−	2.76165i	−0.295022	−	0.214346i
$167$	11.1450	−	2.36895i	0.862428	−	0.183315i	0.244596	−	0.969625i	$-0.421345\pi$
$167$	11.1450	−	2.36895i	0.862428	−	0.183315i	0.617832	+	0.786310i	$0.288011\pi$
$168$	−8.34208	+	9.26482i	−0.643606	+	0.714797i
$169$	−0.510088	+	12.9900i	−0.0392375	+	0.999230i
$170$	2.65075	+	8.15816i	0.203303	+	0.625702i
$171$	−7.12427	−	1.51431i	−0.544807	−	0.115802i
$172$	6.97037	+	3.10341i	0.531486	+	0.236633i
$173$	0.337282	+	0.0716916i	0.0256431	+	0.00545061i	0.220715	−	0.975338i	$-0.429161\pi$
$173$	0.337282	+	0.0716916i	0.0256431	+	0.00545061i	−0.195072	+	0.980789i	$0.562494\pi$
$174$	−3.88412	−	4.31375i	−0.294454	−	0.327025i
$175$	−3.00678	+	1.33870i	−0.227291	+	0.101196i
$176$	5.36402	+	5.95734i	0.404328	+	0.449052i
$177$	−0.244233	−	0.108740i	−0.0183577	−	0.00817336i
$178$	12.2435	+	5.45116i	0.917689	+	0.408581i
$179$	−1.74944	+	16.6448i	−0.130759	+	1.24409i	0.710594	+	0.703602i	$0.248426\pi$
$179$	−1.74944	+	16.6448i	−0.130759	+	1.24409i	−0.841353	+	0.540486i	$0.818240\pi$
$180$	1.59132	+	2.75625i	0.118610	+	0.205439i
$181$	3.43128	+	5.94316i	0.255045	+	0.441751i	0.964908	−	0.262589i	$-0.0845763\pi$
$181$	3.43128	+	5.94316i	0.255045	+	0.441751i	−0.709863	+	0.704340i	$0.751243\pi$
$182$	9.48836	−	11.2581i	0.703324	−	0.834503i
$183$	2.27516	+	0.483601i	0.168185	+	0.0357488i
$184$	−18.6832	−	20.7498i	−1.37734	−	1.52969i
$185$	−6.49858	+	11.2559i	−0.477785	+	0.827548i
$186$	3.04262	+	5.64708i	0.223096	+	0.414064i
$187$	−19.7895			−1.44715
$188$	6.57879	−	1.39836i	0.479807	−	0.101986i
$189$	6.11104	+	18.8078i	0.444512	+	1.36807i
$190$	6.95801	+	5.05529i	0.504787	+	0.366749i
$191$	5.38148	−	9.32100i	0.389390	−	0.674444i	−0.602977	−	0.797758i	$-0.706019\pi$
$191$	5.38148	−	9.32100i	0.389390	−	0.674444i	0.992368	+	0.123315i	$0.0393524\pi$
$192$	4.24439	+	7.35149i	0.306312	+	0.530548i
$193$	−1.02941	+	9.79413i	−0.0740982	+	0.704997i	0.892907	+	0.450241i	$0.148662\pi$
$193$	−1.02941	+	9.79413i	−0.0740982	+	0.704997i	−0.967005	+	0.254756i	$0.918005\pi$
$194$	−9.64741	+	7.00925i	−0.692644	+	0.503235i
$195$	4.15256	+	6.67770i	0.297371	+	0.478200i
$196$	6.17046	−	1.31157i	0.440747	−	0.0936836i
$197$	19.0686	+	13.8541i	1.35858	+	0.987065i	0.998534	+	0.0541301i	$0.0172386\pi$
$197$	19.0686	+	13.8541i	1.35858	+	0.987065i	0.360045	+	0.932935i	$0.382761\pi$
$198$	9.79004	−	2.08094i	0.695748	−	0.147886i
$199$	5.68895	+	1.20922i	0.403279	+	0.0857196i	0.405086	−	0.914279i	$-0.367242\pi$
$199$	5.68895	+	1.20922i	0.403279	+	0.0857196i	−0.00180655	+	0.999998i	$0.500575\pi$
$200$	0.276657	+	2.63222i	0.0195626	+	0.186126i
$201$	3.19107	−	3.54405i	0.225081	−	0.249978i
$202$	−4.59404	+	5.10220i	−0.323236	+	0.358990i
$203$	2.00225	+	19.0501i	0.140530	+	1.33706i
$204$	−3.48768	−	0.741330i	−0.244187	−	0.0519035i
$205$	8.24136	−	1.75175i	0.575601	−	0.122348i
$206$	−2.28640	−	1.66117i	−0.159301	−	0.115739i
$207$	−16.5222	+	3.51189i	−1.14837	+	0.244094i
$208$	−3.02941	−	4.87157i	−0.210052	−	0.337782i
$209$	−16.0522	+	11.6626i	−1.11036	+	0.806720i
$210$	0.930921	−	8.85712i	0.0642396	−	0.611199i
$211$	−9.72685	−	16.8474i	−0.669624	−	1.15982i	−0.978009	−	0.208561i	$-0.933122\pi$
$211$	−9.72685	−	16.8474i	−0.669624	−	1.15982i	0.308386	−	0.951261i	$-0.400211\pi$
$212$	−1.57293	+	2.72440i	−0.108030	+	0.187113i
$213$	7.52731	+	5.46891i	0.515763	+	0.374723i
$214$	2.60303	+	8.01131i	0.177940	+	0.547642i
$215$	−17.9304	+	3.81123i	−1.22284	+	0.259923i
$216$	15.9026			1.08204
$217$	2.83045	−	20.9775i	0.192144	−	1.42404i
$218$	6.49479	−	11.2493i	0.439883	−	0.761899i
$219$	8.01590	+	8.90256i	0.541665	+	0.601579i
$220$	8.48074	+	1.80264i	0.571771	+	0.121534i
$221$	13.9412	+	2.48943i	0.937789	+	0.167457i
$222$	3.68220	+	6.37776i	0.247133	+	0.428047i
$223$	−6.88209	−	11.9201i	−0.460859	−	0.798231i	0.538145	−	0.842852i	$-0.319125\pi$
$223$	−6.88209	−	11.9201i	−0.460859	−	0.798231i	−0.999004	+	0.0446215i	$0.985792\pi$
$224$	1.75072	−	16.6570i	0.116975	−	1.11294i
$225$	1.46272	+	0.651244i	0.0975145	+	0.0434162i
$226$	9.60358	+	4.27579i	0.638820	+	0.284421i
$227$	12.4696	+	13.8489i	0.827638	+	0.919186i	0.997804	−	0.0662299i	$-0.0210971\pi$
$227$	12.4696	+	13.8489i	0.827638	+	0.919186i	−0.170166	+	0.985415i	$0.554430\pi$
$228$	−3.26591	+	1.45408i	−0.216290	+	0.0962986i
$229$	1.75793	+	1.95238i	0.116167	+	0.129017i	0.798423	−	0.602096i	$-0.205668\pi$
$229$	1.75793	+	1.95238i	0.116167	+	0.129017i	−0.682256	+	0.731113i	$0.739001\pi$
$230$	19.5101	+	4.14699i	1.28645	+	0.273444i
$231$	18.7697	+	8.35682i	1.23496	+	0.549839i
$232$	15.0669	+	3.20257i	0.989190	+	0.210259i
$233$	1.22383	+	3.76655i	0.0801756	+	0.246755i	0.983108	−	0.183028i	$-0.0585900\pi$
$233$	1.22383	+	3.76655i	0.0801756	+	0.246755i	−0.902932	+	0.429783i	$0.858590\pi$
$234$	−7.15861	+	0.234429i	−0.467973	+	0.0153251i
$235$	−10.8122	+	12.0081i	−0.705308	+	0.783324i
$236$	0.206334	−	0.0438576i	0.0134312	−	0.00285489i
$237$	9.16893	+	6.66162i	0.595586	+	0.432719i
$238$	−10.7322	−	11.9193i	−0.695663	−	0.772612i
$239$	−3.34031	−	1.48720i	−0.216067	−	0.0961991i	0.295849	−	0.955235i	$-0.404397\pi$
$239$	−3.34031	−	1.48720i	−0.216067	−	0.0961991i	−0.511916	+	0.859036i	$0.671064\pi$
$240$	−3.17005	−	1.41140i	−0.204626	−	0.0911053i
$241$	6.16894	+	4.48200i	0.397376	+	0.288711i	0.768472	−	0.639884i	$-0.221018\pi$
$241$	6.16894	+	4.48200i	0.397376	+	0.288711i	−0.371095	+	0.928595i	$0.621018\pi$
$242$	7.72551	−	13.3810i	0.496614	−	0.860162i
$243$	7.78587	−	13.4855i	0.499464	−	0.865097i
$244$	−1.67660	+	0.746471i	−0.107333	+	0.0477879i
$245$	−10.1411	+	11.2628i	−0.647889	+	0.719554i
$246$	1.47525	−	4.54035i	0.0940585	−	0.289482i
$247$	12.7755	−	6.19673i	0.812885	−	0.394289i
$248$	−15.3400	−	7.37751i	−0.974092	−	0.468472i
$249$	−2.34600	+	4.06339i	−0.148672	+	0.257507i
$250$	−8.57182	−	9.51998i	−0.542130	−	0.602096i
$251$	5.66096	+	17.4227i	0.357317	+	1.09971i	0.954654	+	0.297718i	$0.0962255\pi$
$251$	5.66096	+	17.4227i	0.357317	+	1.09971i	−0.597337	+	0.801990i	$0.703775\pi$
$252$	−4.81433	−	3.49782i	−0.303274	−	0.220342i
$253$	−23.0077	+	39.8506i	−1.44648	+	2.50538i
$254$	−3.33677			−0.209368
$255$	7.82569	−	3.48422i	0.490064	−	0.218191i
$256$	−14.7644	−	6.57353i	−0.922774	−	0.410846i
$257$	0.375142	−	0.272556i	0.0234007	−	0.0170016i	−0.576023	−	0.817433i	$-0.695396\pi$
$257$	0.375142	−	0.272556i	0.0234007	−	0.0170016i	0.599424	+	0.800432i	$0.295396\pi$
$258$	−3.20965	+	9.87828i	−0.199824	+	0.614995i
$259$	2.54023	−	24.1687i	0.157842	−	1.50177i
$260$	−5.74770	−	2.33675i	−0.356457	−	0.144919i
$261$	6.23524	−	6.92493i	0.385952	−	0.428643i
$262$	−0.847732	−	0.377435i	−0.0523730	−	0.0233180i
$263$	6.95860	+	1.47910i	0.429086	+	0.0912050i	0.417392	−	0.908727i	$-0.362944\pi$
$263$	6.95860	+	1.47910i	0.429086	+	0.0912050i	0.0116940	+	0.999932i	$0.496278\pi$
$264$	11.0554	−	12.2783i	0.680414	−	0.755676i
$265$	−0.790015	−	7.51649i	−0.0485302	−	0.461734i
$266$	−15.7298	−	3.34347i	−0.964454	−	0.205001i
$267$	4.13585	−	12.7288i	0.253110	−	0.778992i
$268$	−0.393326	+	3.74224i	−0.0240262	+	0.228594i
$269$	−7.12742	−	7.91580i	−0.434567	−	0.482635i	0.485589	−	0.874187i	$-0.338605\pi$
$269$	−7.12742	−	7.91580i	−0.434567	−	0.482635i	−0.920156	+	0.391552i	$0.871938\pi$
$270$	−9.19053	+	6.67731i	−0.559318	+	0.406368i
$271$	−0.186613	−	1.77551i	−0.0113360	−	0.107854i	0.987391	−	0.158302i	$-0.0506019\pi$
$271$	−0.186613	−	1.77551i	−0.0113360	−	0.107854i	−0.998727	+	0.0504475i	$0.983935\pi$
$272$	−5.70906	+	2.54184i	−0.346162	+	0.154121i
$273$	−12.1716	−	8.24831i	−0.736656	−	0.499211i
$274$	−3.52687	−	6.10871i	−0.213066	−	0.369041i
$275$	3.98476	−	1.77413i	0.240290	−	0.106984i
$276$	−5.54768	+	6.16133i	−0.333931	+	0.370868i
$277$	3.80896	−	0.809620i	0.228858	−	0.0486454i	−0.0920549	−	0.995754i	$-0.529344\pi$
$277$	3.80896	−	0.809620i	0.228858	−	0.0486454i	0.320913	+	0.947109i	$0.396010\pi$
$278$	22.2988			1.33739
$279$	−8.50513	+	5.80520i	−0.509189	+	0.347548i
$280$	11.8164	+	20.4666i	0.706166	+	1.22311i
$281$	−6.07640	+	18.7012i	−0.362488	+	1.11562i	0.589051	+	0.808096i	$0.299502\pi$
$281$	−6.07640	+	18.7012i	−0.362488	+	1.11562i	−0.951539	+	0.307527i	$0.900498\pi$
$282$	2.82926	+	8.70757i	0.168480	+	0.518528i
$283$	−4.87972	+	2.17259i	−0.290069	+	0.129147i	−0.546613	−	0.837386i	$-0.684083\pi$
$283$	−4.87972	+	2.17259i	−0.290069	+	0.129147i	0.256544	+	0.966533i	$0.417416\pi$
$284$	−7.34131			−0.435627
$285$	4.29442	−	7.43815i	0.254379	−	0.440598i
$286$	−12.5745	+	14.9198i	−0.743547	+	0.882229i
$287$	−12.7451	+	9.25984i	−0.752318	+	0.546591i
$288$	−6.59174	+	4.78918i	−0.388422	+	0.282205i
$289$	−0.485981	+	1.49569i	−0.0285871	+	0.0879821i
$290$	−10.0523	+	4.47556i	−0.590289	+	0.262814i
$291$	7.96839	+	8.84980i	0.467115	+	0.518784i
$292$	−9.24565	−	1.96522i	−0.541061	−	0.115006i
$293$	0.206162	−	0.149785i	0.0120441	−	0.00875055i	−0.581747	−	0.813370i	$-0.697631\pi$
$293$	0.206162	−	0.149785i	0.0120441	−	0.00875055i	0.593791	+	0.804619i	$0.297631\pi$
$294$	2.65365	+	8.16711i	0.154764	+	0.476315i
$295$	−0.339107	+	0.376617i	−0.0197436	+	0.0219275i
$296$	−17.8528	−	7.94856i	−1.03767	−	0.462001i
$297$	−8.09870	−	24.9252i	−0.469934	−	1.44631i
$298$	−8.01394	−	8.90038i	−0.464235	−	0.515585i
$299$	21.2214	−	25.1795i	1.22726	−	1.45617i
$300$	0.768728	−	0.163398i	0.0443825	−	0.00943380i
$301$	27.7290	−	20.1463i	1.59827	−	1.16121i
$302$	−2.26980	−	21.5957i	−0.130613	−	1.24270i
$303$	5.54688	+	4.03004i	0.318660	+	0.231520i
$304$	−3.13290	+	5.42633i	−0.179684	+	0.311222i
$305$	2.20460	−	3.81848i	0.126235	−	0.218645i
$306$	−0.815586	+	7.75978i	−0.0466240	+	0.443597i
$307$	−31.8855	−	6.77746i	−1.81980	−	0.386810i	−0.833599	−	0.552370i	$-0.813724\pi$
$307$	−31.8855	−	6.77746i	−1.81980	−	0.386810i	−0.986200	+	0.165560i	$0.947057\pi$
$308$	−15.8571	+	3.37053i	−0.903543	+	0.192054i
$309$	−1.41115	+	2.44418i	−0.0802773	+	0.139044i
$310$	11.9631	−	2.17743i	0.679459	−	0.123670i
$311$	−33.3708			−1.89228			−0.946141	−	0.323755i	$-0.895055\pi$
$311$	−33.3708			−1.89228			−0.946141	+	0.323755i	$0.895055\pi$
$312$	−9.33281	+	7.25902i	−0.528366	+	0.410961i
$313$	6.85107	+	1.45624i	0.387245	+	0.0823115i	0.397420	−	0.917637i	$-0.369906\pi$
$313$	6.85107	+	1.45624i	0.387245	+	0.0823115i	−0.0101750	+	0.999948i	$0.503239\pi$
$314$	−14.0159	+	6.24026i	−0.790961	+	0.352158i
$315$	14.2968			0.805533
$316$	−8.94237			−0.503048
$317$	−11.7841	+	5.24660i	−0.661859	+	0.294678i	−0.710041	−	0.704160i	$-0.751324\pi$
$317$	−11.7841	+	5.24660i	−0.661859	+	0.294678i	0.0481826	+	0.998839i	$0.484657\pi$
$318$	−3.91219	−	1.74182i	−0.219385	−	0.0976764i
$319$	−2.65349	−	25.2463i	−0.148567	−	1.41352i
$320$	15.7399	−	3.34561i	0.879885	−	0.187025i
$321$	7.68483	−	3.42151i	0.428925	−	0.190970i
$322$	−36.4795	+	7.75396i	−2.03292	+	0.432111i
$323$	−4.77986	−	14.7109i	−0.265958	−	0.818536i
$324$	−0.00274288	−	0.0260968i	−0.000152382	−	0.00144982i
$325$	−3.03034	+	0.748565i	−0.168093	+	0.0415229i
$326$	0.669775	+	2.06136i	0.0370954	+	0.114168i
$327$	−11.8504	−	5.27612i	−0.655327	−	0.291770i
$328$	3.91474	+	12.0483i	0.216155	+	0.665258i
$329$	9.33629	−	28.7341i	0.514726	−	1.58416i
$330$	−1.23371	+	11.7380i	−0.0679135	+	0.646154i
$331$	18.2522	+	20.2712i	1.00323	+	1.11420i	0.993452	+	0.114251i	$0.0364468\pi$
$331$	18.2522	+	20.2712i	1.00323	+	1.11420i	0.00978123	+	0.999952i	$0.496886\pi$
$332$	−0.386976	−	3.68183i	−0.0212380	−	0.202067i
$333$	−9.56435	+	6.94891i	−0.524123	+	0.380798i
$334$	−9.90092	−	7.19344i	−0.541754	−	0.393607i
$335$	−4.52010	−	7.82904i	−0.246959	−	0.427746i
$336$	6.48823			0.353962
$337$	4.55041	+	3.30606i	0.247877	+	0.180093i	0.704785	−	0.709421i	$-0.251043\pi$
$337$	4.55041	+	3.30606i	0.247877	+	0.180093i	−0.456909	+	0.889514i	$0.651043\pi$
$338$	10.7353	−	8.92884i	0.583922	−	0.485665i
$339$	3.24408	−	9.98426i	0.176194	−	0.542271i
$340$	−3.37951	+	5.85349i	−0.183280	+	0.317450i
$341$	−3.75108	+	27.8006i	−0.203132	+	1.50548i
$342$	3.91153	+	6.77497i	0.211511	+	0.366349i
$343$	0.533047	−	1.64055i	0.0287819	−	0.0885814i
$344$	−8.51716	−	26.2131i	−0.459214	−	1.41332i
$345$	2.08207	−	19.8096i	0.112095	−	1.06651i
$346$	−0.185183	−	0.320746i	−0.00995548	−	0.0172434i
$347$	23.2982			1.25071			0.625355	−	0.780340i	$-0.284954\pi$
$347$	23.2982			1.25071			0.625355	+	0.780340i	$0.284954\pi$
$348$	0.478096	−	4.54878i	0.0256286	−	0.243840i
$349$	−1.47247	−	14.0096i	−0.0788194	−	0.749917i	−0.960539	−	0.278144i	$-0.910281\pi$
$349$	−1.47247	−	14.0096i	−0.0788194	−	0.749917i	0.881720	−	0.471773i	$-0.156386\pi$
$350$	3.22955	+	1.43789i	0.172627	+	0.0768584i
$351$	2.56986	+	18.5780i	0.137169	+	0.991619i
$352$	−2.32016	+	22.0749i	−0.123665	+	1.17659i
$353$	3.10898	−	0.660833i	0.165474	−	0.0351726i	−0.124430	−	0.992228i	$-0.539710\pi$
$353$	3.10898	−	0.660833i	0.165474	−	0.0351726i	0.289904	+	0.957056i	$0.406377\pi$
$354$	0.0887355	+	0.273100i	0.00471624	+	0.0145151i
$355$	14.2689	−	10.3670i	0.757316	−	0.550222i
$356$	3.26329	+	10.0434i	0.172954	+	0.532298i
$357$	−10.7175	+	11.9030i	−0.567231	+	0.629974i
$358$	14.5433	−	10.5663i	0.768636	−	0.558447i
$359$	3.01296	−	3.34623i	0.159018	−	0.176607i	−0.658371	−	0.752694i	$-0.728754\pi$
$359$	3.01296	−	3.34623i	0.159018	−	0.176607i	0.817389	+	0.576086i	$0.195421\pi$
$360$	3.55269	−	10.9340i	0.187243	−	0.576275i
$361$	2.82455	+	2.05216i	0.148661	+	0.108008i
$362$	2.27777	−	7.01025i	0.119717	−	0.368451i
$363$	−14.0959	−	6.27592i	−0.739845	−	0.329400i
$364$	11.5949	−	0.379708i	0.607740	−	0.0199021i
$365$	20.7455	−	9.23649i	1.08587	−	0.483460i
$366$	−1.24916	−	2.16361i	−0.0652948	−	0.113094i
$367$	31.0413			1.62034			0.810170	−	0.586194i	$-0.199375\pi$
$367$	31.0413			1.62034			0.810170	+	0.586194i	$0.199375\pi$
$368$	−1.51893	+	14.4516i	−0.0791796	+	0.753343i
$369$	7.49632	+	1.59339i	0.390243	+	0.0829487i
$370$	13.6551	−	2.90247i	0.709893	−	0.150892i
$371$	7.06580	+	12.2383i	0.366838	+	0.635382i
$372$	−1.70251	+	4.75901i	−0.0882712	+	0.246743i
$373$	−8.89332	−	15.4037i	−0.460478	−	0.797572i	0.538506	−	0.842621i	$-0.318989\pi$
$373$	−8.89332	−	15.4037i	−0.460478	−	0.797572i	−0.998985	+	0.0450494i	$0.985655\pi$
$374$	14.2229	+	15.7961i	0.735448	+	0.816797i
$375$	−8.56012	+	9.50698i	−0.442043	+	0.490938i
$376$	−19.6556	−	14.2806i	−1.01366	−	0.736466i
$377$	−1.30654	+	18.1192i	−0.0672904	+	0.933186i
$378$	10.6205	−	18.3952i	0.546258	−	0.946146i
$379$	−1.64097	+	15.6128i	−0.0842909	+	0.801975i	0.867955	+	0.496643i	$0.165434\pi$
$379$	−1.64097	+	15.6128i	−0.0842909	+	0.801975i	−0.952246	+	0.305332i	$0.901233\pi$
$380$	0.708371	+	6.73970i	0.0363387	+	0.345739i
$381$	0.348311	+	3.31396i	0.0178445	+	0.169779i
$382$	−11.3078	+	2.40354i	−0.578556	+	0.122976i
$383$	33.0574	−	14.7181i	1.68916	−	0.752061i	0.689544	−	0.724244i	$-0.257811\pi$
$383$	33.0574	−	14.7181i	1.68916	−	0.752061i	0.999613	−	0.0278167i	$-0.00885548\pi$
$384$	−0.102946	+	0.316835i	−0.00525344	+	0.0161684i
$385$	26.0610	−	28.9436i	1.32819	−	1.47510i
$386$	8.55757	−	6.21744i	0.435569	−	0.316459i
$387$	−16.3095	−	3.46668i	−0.829056	−	0.176221i
$388$	−9.19085	−	1.95358i	−0.466595	−	0.0991778i
$389$	−0.0633082	−	0.602338i	−0.00320985	−	0.0305397i	0.992800	−	0.119786i	$-0.0382208\pi$
$389$	−0.0633082	−	0.602338i	−0.00320985	−	0.0305397i	−0.996010	+	0.0892463i	$0.971554\pi$
$390$	2.34570	−	8.11391i	0.118779	−	0.410864i
$391$	−24.0032	−	26.6583i	−1.21390	−	1.34817i
$392$	−18.4356	−	13.3942i	−0.931138	−	0.676511i
$393$	−0.286363	+	0.881336i	−0.0144451	+	0.0444575i
$394$	−2.64628	−	25.1777i	−0.133318	−	1.26843i
$395$	17.3808	−	12.6279i	0.874524	−	0.635379i
$396$	6.38023	+	4.63551i	0.320619	+	0.232943i
$397$	25.3295			1.27125			0.635625	−	0.771998i	$-0.280742\pi$
$397$	25.3295			1.27125			0.635625	+	0.771998i	$0.280742\pi$
$398$	−3.12348	−	5.41003i	−0.156566	−	0.271180i
$399$	−1.67865	+	15.9713i	−0.0840375	+	0.799563i
$400$	0.921682	−	1.02363i	0.0460841	−	0.0511816i
$401$	4.24361	+	4.71300i	0.211916	+	0.235356i	0.839726	−	0.543010i	$-0.182715\pi$
$401$	4.24361	+	4.71300i	0.211916	+	0.235356i	−0.627811	+	0.778366i	$0.716049\pi$
$402$	−5.12232			−0.255478
$403$	6.13972	−	19.1129i	0.305841	−	0.952083i
$404$	−5.40982			−0.269149
$405$	0.0421836	+	0.0468496i	0.00209612	+	0.00232798i
$406$	13.7669	−	15.2897i	0.683238	−	0.758813i
$407$	−3.36646	+	32.0298i	−0.166869	+	1.58766i
$408$	6.44005	+	11.1545i	0.318830	+	0.552230i
$409$	−20.5911			−1.01817			−0.509083	−	0.860718i	$-0.670015\pi$
$409$	−20.5911			−1.01817			−0.509083	+	0.860718i	$0.670015\pi$
$410$	−7.32138	−	5.31929i	−0.361577	−	0.262701i
$411$	−5.69880	+	4.14042i	−0.281101	+	0.204232i
$412$	−0.232771	−	2.21467i	−0.0114678	−	0.109109i
$413$	0.292819	−	0.901203i	0.0144087	−	0.0443453i
$414$	14.6778	+	10.6640i	0.721375	+	0.524109i
$415$	5.95141	+	6.60971i	0.292143	+	0.324458i
$416$	4.41141	−	15.2593i	0.216287	−	0.748150i
$417$	−2.32768	−	22.1464i	−0.113987	−	1.08451i
$418$	20.8460	+	4.43096i	1.01961	+	0.216725i
$419$	−33.9986	−	7.22662i	−1.66094	−	0.353044i	−0.720619	−	0.693332i	$-0.756142\pi$
$419$	−33.9986	−	7.22662i	−1.66094	−	0.353044i	−0.940321	+	0.340288i	$0.889476\pi$
$420$	5.67720	−	4.12473i	0.277019	−	0.201266i
$421$	20.6935	−	22.9824i	1.00854	−	1.12010i	0.0157915	−	0.999875i	$-0.494973\pi$
$421$	20.6935	−	22.9824i	1.00854	−	1.12010i	0.992747	−	0.120220i	$-0.0383601\pi$
$422$	−6.45692	+	19.8724i	−0.314318	+	0.967371i
$423$	−13.4271	+	5.97812i	−0.652846	+	0.290666i
$424$	11.1156	−	2.36269i	0.539820	−	0.114742i
$425$	0.355436	+	3.38175i	0.0172412	+	0.164039i
$426$	−1.04462	−	9.93888i	−0.0506119	−	0.481540i
$427$	−0.861757	+	8.19907i	−0.0417033	+	0.396781i
$428$	−3.31868	+	5.74813i	−0.160415	+	0.277846i
$429$	16.1305	+	10.9311i	0.778786	+	0.527761i
$430$	15.9288	+	11.5730i	0.768157	+	0.558099i
$431$	−19.0839	+	21.1948i	−0.919239	+	1.02092i	0.0804693	+	0.996757i	$0.474358\pi$
$431$	−19.0839	+	21.1948i	−0.919239	+	1.02092i	−0.999708	+	0.0241610i	$0.992309\pi$
$432$	−5.53786	−	6.15042i	−0.266441	−	0.295912i
$433$	−17.4632	−	30.2471i	−0.839227	−	1.45358i	−0.890542	−	0.454901i	$-0.849675\pi$
$433$	−17.4632	−	30.2471i	−0.839227	−	1.45358i	0.0513156	−	0.998682i	$-0.483659\pi$
$434$	−18.7786	+	12.8174i	−0.901401	+	0.615253i
$435$	5.49428	+	9.51637i	0.263430	+	0.456275i
$436$	10.0115	−	2.12800i	0.479462	−	0.101913i
$437$	−35.1808	−	7.47790i	−1.68292	−	0.357716i
$438$	1.34498	−	12.7967i	0.0642658	−	0.611448i
$439$	0.0328534			0.00156801			0.000784003	−	1.00000i	$-0.499750\pi$
$439$	0.0328534			0.00156801			0.000784003		1.00000i	$0.499750\pi$
$440$	−15.6598	−	27.1236i	−0.746551	−	1.29306i
$441$	−12.5937	+	5.60707i	−0.599699	+	0.267003i
$442$	−8.03259	−	12.9171i	−0.382071	−	0.614405i
$443$	35.4089	+	15.7651i	1.68233	+	0.749021i	0.999836	+	0.0181284i	$0.00577075\pi$
$443$	35.4089	+	15.7651i	1.68233	+	0.749021i	0.682493	+	0.730892i	$0.260896\pi$
$444$	−1.79316	+	5.51877i	−0.0850995	+	0.261909i
$445$	−20.5254	−	14.9126i	−0.972997	−	0.706924i
$446$	−4.56850	+	14.0604i	−0.216325	+	0.665779i
$447$	−8.00300	+	8.88823i	−0.378529	+	0.420399i
$448$	−24.3414	+	17.6850i	−1.15002	+	0.835539i
$449$	13.5790	−	15.0810i	0.640833	−	0.711717i	−0.331986	−	0.943284i	$-0.607719\pi$
$449$	13.5790	−	15.0810i	0.640833	−	0.711717i	0.972819	+	0.231567i	$0.0743853\pi$
$450$	−0.531439	−	1.63560i	−0.0250523	−	0.0771030i
$451$	16.8905	−	12.2717i	0.795343	−	0.577850i
$452$	2.55967	+	7.87785i	0.120397	+	0.370543i
$453$	−21.2112	+	4.50858i	−0.996589	+	0.211831i
$454$	2.09227	−	19.9066i	0.0981952	−	0.934265i
$455$	−22.0003	+	17.1117i	−1.03139	+	0.802210i
$456$	11.7975	+	5.25260i	0.552470	+	0.245975i
$457$	1.79109	+	17.0411i	0.0837837	+	0.797149i	0.953052	+	0.302808i	$0.0979240\pi$
$457$	1.79109	+	17.0411i	0.0837837	+	0.797149i	−0.869268	+	0.494341i	$0.835409\pi$
$458$	0.294962	−	2.80638i	0.0137827	−	0.131133i
$459$	20.4309			0.953634
$460$	7.85819	+	13.6108i	0.366390	+	0.634606i
$461$	−0.334690	+	3.18436i	−0.0155881	+	0.148310i	−0.999547	−	0.0300823i	$-0.990423\pi$
$461$	−0.334690	+	3.18436i	−0.0155881	+	0.148310i	0.983959	+	0.178393i	$0.0570897\pi$
$462$	−6.81948	−	20.9882i	−0.317271	−	0.976459i
$463$	2.78153	−	8.56066i	0.129269	−	0.397848i	−0.865386	−	0.501106i	$-0.832927\pi$
$463$	2.78153	−	8.56066i	0.129269	−	0.397848i	0.994655	+	0.103258i	$0.0329268\pi$
$464$	−4.00822	−	6.94245i	−0.186077	−	0.322295i
$465$	−3.41132	−	11.6540i	−0.158196	−	0.540443i
$466$	2.12691	−	3.68391i	0.0985271	−	0.170654i
$467$	−8.27715	+	25.4744i	−0.383021	+	1.17882i	0.554885	+	0.831927i	$0.312762\pi$
$467$	−8.27715	+	25.4744i	−0.383021	+	1.17882i	−0.937906	+	0.346890i	$0.887238\pi$
$468$	−3.91159	−	4.06820i	−0.180813	−	0.188053i
$469$	13.6750	+	9.93543i	0.631451	+	0.458776i
$470$	17.3557			0.800560
$471$	7.66066	+	13.2687i	0.352985	+	0.611388i
$472$	−0.616467	−	0.447890i	−0.0283752	−	0.0206158i
$473$	−36.7480	+	26.6990i	−1.68968	+	1.22762i
$474$	−1.27244	−	12.1064i	−0.0584450	−	0.556067i
$475$	2.28128	+	2.53362i	0.104672	+	0.116251i
$476$	1.32102	−	12.5687i	0.0605488	−	0.576084i
$477$	2.12438	−	6.53817i	0.0972687	−	0.299362i
$478$	1.21361	+	3.73511i	0.0555093	+	0.170840i
$479$	9.80306	+	4.36460i	0.447913	+	0.199424i	0.618282	−	0.785957i	$-0.287829\pi$
$479$	9.80306	+	4.36460i	0.447913	+	0.199424i	−0.170369	+	0.985380i	$0.554496\pi$
$480$	−2.96909	−	9.13791i	−0.135520	−	0.417087i
$481$	6.40078	−	22.1407i	0.291850	−	1.00953i
$482$	−0.856108	−	8.14532i	−0.0389946	−	0.371009i
$483$	11.5089	+	35.4207i	0.523673	+	1.61170i
$484$	11.9086	−	2.53125i	0.541299	−	0.115057i
$485$	20.6225	−	9.18174i	0.936421	−	0.416921i
$486$	−16.3600	+	3.47742i	−0.742104	+	0.157739i
$487$	2.97725	+	28.3266i	0.134912	+	1.28360i	0.827170	+	0.561952i	$0.189949\pi$
$487$	2.97725	+	28.3266i	0.134912	+	1.28360i	−0.692258	+	0.721650i	$0.743384\pi$
$488$	6.05643	+	2.69649i	0.274162	+	0.122065i
$489$	1.97735	−	0.880373i	0.0894189	−	0.0398118i
$490$	16.2785			0.735387
$491$	22.6209			1.02087			0.510433	−	0.859918i	$-0.329485\pi$
$491$	22.6209			1.02087			0.510433	+	0.859918i	$0.329485\pi$
$492$	3.43647	−	1.53001i	0.154928	−	0.0689783i
$493$	19.3572	+	4.11451i	0.871806	+	0.185308i
$494$	−14.1281	−	5.74382i	−0.635653	−	0.258427i
$495$	−18.9469			−0.851601
$496$	2.48865	+	8.50194i	0.111744	+	0.381749i
$497$	−16.4890	+	28.5598i	−0.739632	+	1.28108i
$498$	4.92950	−	1.04780i	0.220896	−	0.0469529i
$499$	19.8480	+	4.21882i	0.888517	+	0.188860i	0.629489	−	0.777010i	$-0.283264\pi$
$499$	19.8480	+	4.21882i	0.888517	+	0.188860i	0.259028	+	0.965870i	$0.416598\pi$
$500$	1.05510	−	10.0386i	0.0471857	−	0.448942i
$501$	−6.11075	+	10.5841i	−0.273008	+	0.472864i
$502$	9.83828	−	17.0404i	0.439104	−	0.760550i
$503$	11.2854	+	8.19930i	0.503190	+	0.365589i	0.810234	−	0.586106i	$-0.199340\pi$
$503$	11.2854	+	8.19930i	0.503190	+	0.365589i	−0.307044	+	0.951695i	$0.599340\pi$
$504$	2.24698	+	21.3786i	0.100088	+	0.952278i
$505$	10.5148	−	7.63944i	0.467902	−	0.339951i
$506$	48.3447	−	10.2760i	2.14919	−	0.456824i
$507$	−9.98842	−	9.72985i	−0.443601	−	0.432118i
$508$	−1.75928	−	1.95388i	−0.0780555	−	0.0866895i
$509$	−3.02616	−	9.31355i	−0.134132	−	0.412816i	0.861322	−	0.508060i	$-0.169637\pi$
$509$	−3.02616	−	9.31355i	−0.134132	−	0.412816i	−0.995454	+	0.0952435i	$0.969637\pi$
$510$	−8.40550	−	3.74237i	−0.372202	−	0.165715i
$511$	−28.4115	+	31.5542i	−1.25685	+	1.39588i
$512$	5.17229	+	15.9187i	0.228585	+	0.703513i
$513$	16.5725	−	12.0406i	0.731693	−	0.531606i
$514$	−0.487173	−	0.103552i	−0.0214883	−	0.00456747i
$515$	3.57985	+	3.97583i	0.157747	+	0.175196i
$516$	−7.47659	+	3.32879i	−0.329138	+	0.146542i
$517$	−12.3730	+	38.0802i	−0.544164	+	1.67476i
$518$	−21.1173	+	15.3426i	−0.927839	+	0.674115i
$519$	−0.299223	+	0.217398i	−0.0131344	+	0.00954271i
$520$	7.61992	+	21.0778i	0.334156	+	0.924322i
$521$	4.37715	−	7.58144i	0.191766	−	0.332149i	−0.754069	−	0.656795i	$-0.771912\pi$
$521$	4.37715	−	7.58144i	0.191766	−	0.332149i	0.945836	+	0.324646i	$0.105245\pi$
$522$	−10.0088			−0.438074
$523$	25.0761	−	11.1646i	1.09650	−	0.488194i	0.222902	−	0.974841i	$-0.428447\pi$
$523$	25.0761	−	11.1646i	1.09650	−	0.488194i	0.873599	+	0.486647i	$0.161780\pi$
$524$	−0.225948	−	0.695397i	−0.00987060	−	0.0303786i
$525$	1.09094	−	3.35757i	0.0476126	−	0.146536i
$526$	−3.82057	−	6.61743i	−0.166585	−	0.288534i
$527$	−19.7081	−	9.47827i	−0.858499	−	0.412880i
$528$	−8.59858			−0.374205
$529$	−59.0916	+	12.5603i	−2.56920	+	0.546100i
$530$	−5.43191	+	6.03275i	−0.235947	+	0.262046i
$531$	−0.421120	+	0.187495i	−0.0182750	+	0.00813657i
$532$	−6.33558	−	10.9735i	−0.274682	−	0.475764i
$533$	−13.4427	+	6.52034i	−0.582266	+	0.282427i
$534$	−13.1327	+	5.84704i	−0.568306	+	0.253026i
$535$	−1.66683	−	15.8588i	−0.0720632	−	0.685635i
$536$	10.9967	−	7.98956i	0.474985	−	0.345097i
$537$	−12.0122	−	13.3409i	−0.518364	−	0.575702i
$538$	−1.19591	+	11.3783i	−0.0515592	+	0.490553i
$539$	−11.6050	+	35.7166i	−0.499864	+	1.53842i
$540$	−8.75560	−	1.86106i	−0.376781	−	0.0800873i
$541$	−0.249646	−	2.37522i	−0.0107331	−	0.102119i	0.987844	−	0.155450i	$-0.0496828\pi$
$541$	−0.249646	−	2.37522i	−0.0107331	−	0.102119i	−0.998577	+	0.0533312i	$0.983016\pi$
$542$	−1.28310	+	1.42503i	−0.0551138	+	0.0612101i
$543$	−7.20010	−	1.53043i	−0.308986	−	0.0656770i
$544$	−15.8077	−	7.03804i	−0.677750	−	0.301754i
$545$	−16.4537	+	18.2737i	−0.704801	+	0.782760i
$546$	2.16394	+	15.6435i	0.0926080	+	0.669481i
$547$	−1.34806	+	12.8259i	−0.0576389	+	0.548398i	0.927156	+	0.374676i	$0.122246\pi$
$547$	−1.34806	+	12.8259i	−0.0576389	+	0.548398i	−0.984795	+	0.173722i	$0.944421\pi$
$548$	1.71751	−	5.28596i	0.0733685	−	0.225805i
$549$	3.24464	−	2.35737i	0.138478	−	0.100610i
$550$	−4.27999	−	1.90557i	−0.182499	−	0.0812539i
$551$	18.1264	−	8.07038i	0.772209	−	0.343810i
$552$	29.9493			1.27473
$553$	−20.0851	+	34.7884i	−0.854104	+	1.47935i
$554$	−3.38377	−	2.45845i	−0.143763	−	0.104450i
$555$	−4.30803	−	13.2588i	−0.182866	−	0.562803i
$556$	11.7568	+	13.0573i	0.498601	+	0.553753i
$557$	8.34908	−	14.4610i	0.353762	−	0.612734i	−0.633143	−	0.774035i	$-0.718236\pi$
$557$	8.34908	−	14.4610i	0.353762	−	0.612734i	0.986905	+	0.161301i	$0.0515690\pi$
$558$	10.7464	+	2.61660i	0.454933	+	0.110769i
$559$	29.2467	−	14.1861i	1.23700	−	0.600006i
$560$	3.80067	−	11.6973i	0.160608	−	0.494300i
$561$	14.2035	−	15.7745i	0.599671	−	0.666002i
$562$	19.2946	−	8.59050i	0.813893	−	0.362368i
$563$	19.4205	−	33.6372i	0.818475	−	1.41764i	−0.0883301	−	0.996091i	$-0.528153\pi$
$563$	19.4205	−	33.6372i	0.818475	−	1.41764i	0.906805	−	0.421550i	$-0.138514\pi$
$564$	−3.60711	+	6.24769i	−0.151887	+	0.263075i
$565$	−16.0998	−	11.6972i	−0.677322	−	0.492103i
$566$	5.24126	+	2.33356i	0.220306	+	0.0980868i
$567$	−0.107684	−	0.0479442i	−0.00452232	−	0.00201347i
$568$	17.7448	+	19.7076i	0.744555	+	0.826913i
$569$	−22.0338	−	16.0085i	−0.923707	−	0.671112i	0.0207371	−	0.999785i	$-0.493399\pi$
$569$	−22.0338	−	16.0085i	−0.923707	−	0.671112i	−0.944444	+	0.328673i	$0.893399\pi$
$570$	−9.02360	+	1.91802i	−0.377957	+	0.0803372i
$571$	−7.24268	+	8.04381i	−0.303097	+	0.336623i	−0.875382	−	0.483431i	$-0.839390\pi$
$571$	−7.24268	+	8.04381i	−0.303097	+	0.336623i	0.572286	+	0.820054i	$0.306057\pi$
$572$	−15.3663	+	0.503212i	−0.642496	+	0.0210403i
$573$	3.56748	+	10.9796i	0.149034	+	0.458678i
$574$	16.5512	+	3.51807i	0.690834	+	0.146841i
$575$	7.22312	+	3.21594i	0.301225	+	0.134114i
$576$	14.3169	+	3.04316i	0.596540	+	0.126798i
$577$	−25.7116	−	28.5556i	−1.07039	−	1.18879i	−0.981244	−	0.192768i	$-0.938254\pi$
$577$	−25.7116	−	28.5556i	−1.07039	−	1.18879i	−0.0891437	−	0.996019i	$-0.528413\pi$
$578$	1.54315	−	0.687054i	0.0641865	−	0.0285777i
$579$	−7.06822	−	7.85006i	−0.293745	−	0.326237i
$580$	−7.92068	−	3.52651i	−0.328888	−	0.146430i
$581$	−15.1925	−	6.76415i	−0.630292	−	0.280624i
$582$	1.33701	−	12.7208i	0.0554209	−	0.527295i
$583$	−9.36400	−	16.2189i	−0.387817	−	0.671719i
$584$	17.0722	+	29.5700i	0.706453	+	1.22361i
$585$	13.3476	+	2.38343i	0.551857	+	0.0985428i
$586$	−0.267729	−	0.0569076i	−0.0110598	−	0.00235083i
$587$	−8.34045	−	9.26300i	−0.344247	−	0.382325i	0.546014	−	0.837776i	$-0.316145\pi$
$587$	−8.34045	−	9.26300i	−0.344247	−	0.382325i	−0.890261	+	0.455451i	$0.849478\pi$
$588$	−3.38322	+	5.85991i	−0.139522	+	0.241659i
$589$	−21.5720	+	3.92637i	−0.888860	+	0.161783i
$590$	0.544336			0.0224099
$591$	−24.7293	+	5.25638i	−1.01723	+	0.216219i
$592$	3.14282	+	9.67262i	0.129169	+	0.397542i
$593$	11.2639	+	8.18369i	0.462552	+	0.336064i	0.794532	−	0.607223i	$-0.207716\pi$
$593$	11.2639	+	8.18369i	0.462552	+	0.336064i	−0.331979	+	0.943287i	$0.607716\pi$
$594$	−14.0749	+	24.3784i	−0.577498	+	1.00026i
$595$	15.1812	+	26.2945i	0.622367	+	1.07797i
$596$	0.986434	−	9.38529i	0.0404059	−	0.384437i
$597$	−5.04700	+	3.66686i	−0.206560	+	0.150075i
$598$	−35.3503	+	1.15765i	−1.44558	+	0.0473396i
$599$	6.68268	−	1.42045i	0.273047	−	0.0580379i	−0.0693531	−	0.997592i	$-0.522094\pi$
$599$	6.68268	−	1.42045i	0.273047	−	0.0580379i	0.342400	+	0.939554i	$0.388760\pi$
$600$	−2.29674	−	1.66868i	−0.0937642	−	0.0681237i
$601$	−3.06640	+	0.651783i	−0.125081	+	0.0265868i	−0.270027	−	0.962853i	$-0.587033\pi$
$601$	−3.06640	+	0.651783i	−0.125081	+	0.0265868i	0.144946	+	0.989440i	$0.453699\pi$
$602$	−36.0099	−	7.65413i	−1.46765	−	0.311959i
$603$	−0.859531	−	8.17789i	−0.0350028	−	0.333030i
$604$	11.4489	−	12.7153i	0.465848	−	0.517377i
$605$	−19.5716	+	21.7365i	−0.795699	+	0.883713i
$606$	−0.769780	−	7.32397i	−0.0312702	−	0.297516i
$607$	−5.21783	−	1.10908i	−0.211785	−	0.0450163i	0.100797	−	0.994907i	$-0.467861\pi$
$607$	−5.21783	−	1.10908i	−0.211785	−	0.0450163i	−0.312582	+	0.949891i	$0.601194\pi$
$608$	−16.9701	+	3.60711i	−0.688229	+	0.146288i
$609$	−16.6222	−	12.0767i	−0.673566	−	0.489374i
$610$	−4.63239	+	0.984645i	−0.187560	+	0.0398671i
$611$	13.5068	−	25.2701i	0.546425	−	1.02232i
$612$	−4.97383	+	3.61370i	−0.201055	+	0.146075i
$613$	−3.25808	+	30.9985i	−0.131592	+	1.25202i	0.706982	+	0.707232i	$0.250056\pi$
$613$	−3.25808	+	30.9985i	−0.131592	+	1.25202i	−0.838574	+	0.544787i	$0.816611\pi$
$614$	17.5065	+	30.3221i	0.706505	+	1.22370i
$615$	−4.51868	+	7.82659i	−0.182211	+	0.315599i
$616$	47.3766	+	34.4211i	1.90886	+	1.38687i
$617$	−13.2751	−	40.8567i	−0.534437	−	1.64483i	−0.744862	−	0.667219i	$-0.767485\pi$
$617$	−13.2751	−	40.8567i	−0.534437	−	1.64483i	0.210425	−	0.977610i	$-0.432515\pi$
$618$	2.96516	−	0.630263i	0.119276	−	0.0253529i
$619$	12.2401			0.491971			0.245985	−	0.969274i	$-0.420889\pi$
$619$	12.2401			0.491971			0.245985	+	0.969274i	$0.420889\pi$
$620$	7.58246	+	5.85710i	0.304519	+	0.235227i
$621$	23.7534	−	41.1421i	0.953192	−	1.65098i
$622$	23.9838	+	26.6367i	0.961662	+	1.06803i
$623$	46.4011	+	9.86287i	1.85902	+	0.395147i
$624$	6.05748	+	1.08166i	0.242493	+	0.0433010i
$625$	9.96094	+	17.2529i	0.398438	+	0.690114i
$626$	−3.76153	−	6.51516i	−0.150341	−	0.260398i
$627$	2.22464	−	21.1660i	0.0888436	−	0.845290i
$628$	−11.0438	−	4.91701i	−0.440695	−	0.196210i
$629$	−22.9364	−	10.2119i	−0.914533	−	0.407176i
$630$	−10.2752	−	11.4118i	−0.409374	−	0.454656i
$631$	−11.5352	+	5.13580i	−0.459209	+	0.204453i	−0.623285	−	0.781995i	$-0.714202\pi$
$631$	−11.5352	+	5.13580i	−0.459209	+	0.204453i	0.164076	+	0.986448i	$0.447536\pi$
$632$	21.6148	+	24.0056i	0.859789	+	0.954892i
$633$	20.4105	+	4.33839i	0.811245	+	0.172436i
$634$	12.6571	+	5.63533i	0.502680	+	0.223807i
$635$	6.17859	+	1.31330i	0.245190	+	0.0521167i
$636$	−1.04273	−	3.20918i	−0.0413468	−	0.127252i
$637$	12.6684	−	23.7016i	0.501941	−	0.939091i
$638$	−18.2446	+	20.2627i	−0.722313	+	0.802209i
$639$	15.6923	−	3.33551i	0.620779	−	0.131951i
$640$	0.510900	+	0.371191i	0.0201951	+	0.0146726i
$641$	28.9470	+	32.1490i	1.14334	+	1.26981i	0.957884	+	0.287155i	$0.0927094\pi$
$641$	28.9470	+	32.1490i	1.14334	+	1.26981i	0.185455	+	0.982653i	$0.440624\pi$
$642$	−8.25420	−	3.67501i	−0.325767	−	0.145041i
$643$	−7.63081	−	3.39745i	−0.300930	−	0.133983i	0.250717	−	0.968060i	$-0.419334\pi$
$643$	−7.63081	−	3.39745i	−0.300930	−	0.133983i	−0.551647	+	0.834078i	$0.686000\pi$
$644$	−23.7739	−	17.2728i	−0.936823	−	0.680642i
$645$	9.83113	−	17.0280i	0.387100	−	0.670478i
$646$	−8.30699	+	14.3881i	−0.326834	+	0.566093i
$647$	11.9017	−	5.29898i	0.467904	−	0.208324i	−0.159221	−	0.987243i	$-0.550898\pi$
$647$	11.9017	−	5.29898i	0.467904	−	0.208324i	0.627125	+	0.778919i	$0.284232\pi$
$648$	−0.0634264	+	0.0704421i	−0.00249162	+	0.00276723i
$649$	−0.388060	+	1.19433i	−0.0152327	+	0.0468814i
$650$	2.77543	+	1.88083i	0.108861	+	0.0737723i
$651$	14.6900	+	17.3123i	0.575745	+	0.678521i
$652$	−0.853916	+	1.47903i	−0.0334419	+	0.0579231i
$653$	−23.7405	−	26.3665i	−0.929038	−	1.03180i	−0.999412	−	0.0342804i	$-0.989086\pi$
$653$	−23.7405	−	26.3665i	−0.929038	−	1.03180i	0.0703744	−	0.997521i	$-0.477581\pi$
$654$	4.30551	+	13.2510i	0.168359	+	0.518156i
$655$	1.42117	+	1.03254i	0.0555295	+	0.0403446i
$656$	3.29650	−	5.70971i	0.128707	−	0.222927i
$657$	20.6558			0.805861
$658$	−29.6458	+	13.1992i	−1.15571	+	0.514557i
$659$	23.1613	+	10.3121i	0.902237	+	0.401702i	0.804804	−	0.593541i	$-0.202270\pi$
$659$	23.1613	+	10.3121i	0.902237	+	0.401702i	0.0974324	+	0.995242i	$0.468937\pi$
$660$	−7.52375	+	5.46633i	−0.292862	+	0.212777i
$661$	−1.37050	+	4.21796i	−0.0533062	+	0.164059i	−0.974165	−	0.225836i	$-0.927489\pi$
$661$	−1.37050	+	4.21796i	−0.0533062	+	0.164059i	0.920859	+	0.389895i	$0.127489\pi$
$662$	3.06253	−	29.1380i	0.119029	−	1.13248i
$663$	−11.9903	+	9.32605i	−0.465666	+	0.362194i
$664$	−8.94843	+	9.93823i	−0.347266	+	0.385678i
$665$	27.8104	+	12.3820i	1.07844	+	0.480152i
$666$	12.4206	+	2.64008i	0.481289	+	0.102301i
$667$	30.7906	−	34.1964i	1.19222	−	1.32409i
$668$	−1.00798	−	9.59026i	−0.0389998	−	0.371058i
$669$	14.4412	+	3.06956i	0.558328	+	0.118676i
$670$	−3.00055	+	9.23475i	−0.115921	+	0.356769i
$671$	1.14205	−	10.8659i	0.0440884	−	0.419473i
$672$	12.0210	+	13.3507i	0.463721	+	0.515015i
$673$	10.0972	−	7.33603i	0.389218	−	0.282783i	−0.375917	−	0.926653i	$-0.622672\pi$
$673$	10.0972	−	7.33603i	0.389218	−	0.282783i	0.765135	+	0.643870i	$0.222672\pi$
$674$	−0.631492	−	6.00825i	−0.0243242	−	0.231429i
$675$	−4.11390	+	1.83163i	−0.158344	+	0.0704994i
$676$	10.8885	+	1.57850i	0.418787	+	0.0607117i
$677$	−6.70691	−	11.6167i	−0.257768	−	0.446466i	0.707876	−	0.706337i	$-0.249654\pi$
$677$	−6.70691	−	11.6167i	−0.257768	−	0.446466i	−0.965644	+	0.259870i	$0.916320\pi$
$678$	−10.3010	+	4.58632i	−0.395609	+	0.176136i
$679$	−28.2431	+	31.3672i	−1.08387	+	1.20376i
$680$	23.8823	−	5.07633i	0.915843	−	0.194668i
$681$	−19.9890			−0.765979
$682$	24.8865	−	16.9863i	0.952952	−	0.650440i
$683$	−8.32351	−	14.4167i	−0.318490	−	0.551641i	0.661683	−	0.749784i	$-0.269842\pi$
$683$	−8.32351	−	14.4167i	−0.318490	−	0.551641i	−0.980173	+	0.198142i	$0.936509\pi$
$684$	−1.90484	+	5.86249i	−0.0728333	+	0.224158i
$685$	4.12629	+	12.6994i	0.157658	+	0.485220i
$686$	−1.69260	+	0.753595i	−0.0646238	+	0.0287724i
$687$	−2.81798			−0.107513
$688$	−7.17208	+	12.4224i	−0.273433	+	0.473600i
$689$	4.55644	+	12.6038i	0.173587	+	0.480166i
$690$	−17.3085	+	12.5754i	−0.658923	+	0.478736i
$691$	−10.9329	+	7.94322i	−0.415907	+	0.302174i	−0.775989	−	0.630747i	$-0.782749\pi$
$691$	−10.9329	+	7.94322i	−0.415907	+	0.302174i	0.360082	+	0.932921i	$0.382749\pi$
$692$	0.0901801	−	0.277546i	0.00342813	−	0.0105507i
$693$	32.3638	−	14.4093i	1.22940	−	0.547364i
$694$	−16.7445	−	18.5967i	−0.635614	−	0.705921i
$695$	−41.2900	−	8.77645i	−1.56622	−	0.332910i
$696$	−13.3667	+	9.71149i	−0.506664	+	0.368113i
$697$	5.02947	+	15.4791i	0.190505	+	0.586314i
$698$	−10.1243	+	11.2441i	−0.383209	+	0.425597i
$699$	−3.88075	−	1.72782i	−0.146783	−	0.0653522i
$700$	0.860781	+	2.64921i	0.0325345	+	0.100131i
$701$	25.3570	+	28.1618i	0.957720	+	1.06366i	0.997920	+	0.0644638i	$0.0205337\pi$
$701$	25.3570	+	28.1618i	0.957720	+	1.06366i	−0.0402004	+	0.999192i	$0.512800\pi$
$702$	12.9821	−	15.4034i	0.489976	−	0.581364i
$703$	−24.6230	+	5.23378i	−0.928673	+	0.197396i
$704$	32.2586	−	23.4372i	1.21579	−	0.883324i
$705$	−1.81169	−	17.2371i	−0.0682322	−	0.649186i
$706$	−2.76192	−	2.00665i	−0.103946	−	0.0755214i
$707$	−12.1508	+	21.0457i	−0.456976	+	0.791506i
$708$	−0.113131	+	0.195949i	−0.00425174	+	0.00736423i
$709$	0.717975	−	6.83108i	0.0269641	−	0.256547i	−0.972733	−	0.231929i	$-0.925496\pi$
$709$	0.717975	−	6.83108i	0.0269641	−	0.256547i	0.999697	−	0.0246179i	$-0.00783693\pi$
$710$	−18.5302	−	3.93871i	−0.695424	−	0.147817i
$711$	19.1147	−	4.06295i	0.716856	−	0.152372i
$712$	19.0735	−	33.0363i	0.714810	−	1.23809i
$713$	−41.9996	+	28.6670i	−1.57290	+	1.07359i
$714$	17.2038			0.643835
$715$	29.1560	−	22.6775i	1.09037	−	0.848089i
$716$	13.8550	+	2.94498i	0.517787	+	0.110059i
$717$	3.58290	−	1.59521i	0.133806	−	0.0595742i
$718$	−4.83641			−0.180493
$719$	−35.3987			−1.32015			−0.660075	−	0.751200i	$-0.729475\pi$
$719$	−35.3987			−1.32015			−0.660075	+	0.751200i	$0.729475\pi$
$720$	−5.46597	+	2.43361i	−0.203705	+	0.0906952i
$721$	−9.13849	−	4.06872i	−0.340335	−	0.151527i
$722$	−0.391983	−	3.72947i	−0.0145881	−	0.138797i
$723$	−8.00028	+	1.70051i	−0.297534	+	0.0632427i
$724$	5.30586	−	2.36232i	0.197191	−	0.0877950i
$725$	−4.26657	+	0.906888i	−0.158456	+	0.0336810i
$726$	5.12138	+	15.7620i	0.190072	+	0.584982i
$727$	1.71833	+	16.3488i	0.0637293	+	0.606343i	0.979050	+	0.203618i	$0.0652702\pi$
$727$	1.71833	+	16.3488i	0.0637293	+	0.606343i	−0.915321	+	0.402725i	$0.868063\pi$
$728$	−29.0456	−	30.2086i	−1.07650	−	1.11960i
$729$	5.19014	+	15.9736i	0.192227	+	0.591615i
$730$	−22.2825	−	9.92082i	−0.824714	−	0.367186i
$731$	−10.9424	−	33.6774i	−0.404721	−	1.24560i
$732$	0.608317	−	1.87221i	0.0224840	−	0.0691987i
$733$	−0.810480	+	7.71121i	−0.0299358	+	0.284820i	0.969305	+	0.245861i	$0.0790707\pi$
$733$	−0.810480	+	7.71121i	−0.0299358	+	0.284820i	−0.999241	+	0.0389587i	$0.987596\pi$
$734$	−22.3096	−	24.7773i	−0.823461	−	0.914546i
$735$	−1.69924	−	16.1672i	−0.0626775	−	0.596336i
$736$	−32.5510	+	23.6497i	−1.19985	+	0.871739i
$737$	−18.1228	−	13.1670i	−0.667563	−	0.485013i
$738$	−4.11580	−	7.12878i	−0.151505	−	0.262414i
$739$	−40.5830			−1.49287			−0.746435	−	0.665458i	$-0.768236\pi$
$739$	−40.5830			−1.49287			−0.746435	+	0.665458i	$0.768236\pi$
$740$	8.89909	+	6.46557i	0.327137	+	0.237679i
$741$	−4.22979	+	14.6311i	−0.155385	+	0.537487i
$742$	4.69045	−	14.4357i	0.172192	−	0.529952i
$743$	−18.7162	+	32.4174i	−0.686631	+	1.18928i	0.286290	+	0.958143i	$0.407578\pi$
$743$	−18.7162	+	32.4174i	−0.686631	+	1.18928i	−0.972921	+	0.231137i	$0.925755\pi$
$744$	16.8906	−	6.93273i	0.619241	−	0.254166i
$745$	11.3361	+	19.6347i	0.415322	+	0.719360i
$746$	−5.90360	+	18.1694i	−0.216146	+	0.665230i
$747$	2.50001	+	7.69423i	0.0914704	+	0.281517i
$748$	−1.75069	+	16.6567i	−0.0640116	+	0.609030i
$749$	14.9079	+	25.8212i	0.544722	+	0.943487i
$750$	13.7407			0.501741
$751$	1.24911	−	11.8845i	0.0455806	−	0.433670i	−0.947806	−	0.318849i	$-0.896704\pi$
$751$	1.24911	−	11.8845i	0.0455806	−	0.433670i	0.993386	−	0.114821i	$-0.0366296\pi$
$752$	1.32168	+	12.5749i	0.0481966	+	0.458560i
$753$	−17.9509	−	7.99225i	−0.654167	−	0.291254i
$754$	15.4018	−	11.9795i	0.560902	−	0.436268i
$755$	−4.29682	+	40.8815i	−0.156377	+	1.48783i
$756$	16.3710	−	3.47977i	0.595409	−	0.126558i
$757$	12.2019	+	37.5537i	0.443487	+	1.36491i	0.884134	+	0.467233i	$0.154749\pi$
$757$	12.2019	+	37.5537i	0.443487	+	1.36491i	−0.440647	+	0.897680i	$0.645251\pi$
$758$	13.6416	−	9.91118i	0.495484	−	0.359990i
$759$	−15.2523	−	46.9416i	−0.553622	−	1.70387i
$760$	16.3804	−	18.1922i	0.594178	−	0.659902i
$761$	−14.6309	+	10.6300i	−0.530371	+	0.385337i	−0.820497	−	0.571651i	$-0.806303\pi$
$761$	−14.6309	+	10.6300i	−0.530371	+	0.385337i	0.290125	+	0.956989i	$0.406303\pi$
$762$	2.39489	−	2.65979i	0.0867576	−	0.0963540i
$763$	14.2078	−	43.7271i	0.514356	−	1.58303i
$764$	−7.36934	−	5.35414i	−0.266613	−	0.193706i
$765$	4.56432	−	14.0475i	0.165023	−	0.507890i
$766$	−35.5067	−	15.8086i	−1.28291	−	0.571188i
$767$	0.423619	−	0.792557i	0.0152960	−	0.0286176i
$768$	15.8366	−	7.05093i	0.571456	−	0.254428i
$769$	−17.1304	−	29.6707i	−0.617737	−	1.06995i	−0.989898	−	0.141784i	$-0.954716\pi$
$769$	−17.1304	−	29.6707i	−0.617737	−	1.06995i	0.372160	−	0.928168i	$-0.378617\pi$
$770$	−41.8332			−1.50756
$771$	−0.0519900	+	0.494652i	−0.00187237	+	0.0178145i
$772$	8.15259	+	1.73289i	0.293418	+	0.0623679i
$773$	41.5867	−	8.83952i	1.49577	−	0.317935i	0.613882	−	0.789398i	$-0.289607\pi$
$773$	41.5867	−	8.83952i	1.49577	−	0.317935i	0.881886	+	0.471462i	$0.156274\pi$
$774$	8.95460	+	15.5098i	0.321866	+	0.557489i
$775$	4.81808	+	0.141685i	0.173071	+	0.00508948i
$776$	16.9710	+	29.3947i	0.609224	+	1.05521i
$777$	17.4420	+	19.3714i	0.625730	+	0.694944i
$778$	−0.435289	+	0.483437i	−0.0156059	+	0.0173321i
$779$	13.2020	+	9.59181i	0.473011	+	0.343662i
$780$	5.98793	−	2.90444i	0.214402	−	0.103996i
$781$	21.8522	−	37.8491i	0.781932	−	1.35435i
$782$	−4.02749	+	38.3190i	−0.144023	+	1.37029i
$783$	2.73949	+	26.0645i	0.0979015	+	0.931471i
$784$	1.23964	+	11.7944i	0.0442730	+	0.421229i
$785$	28.4088	−	6.03847i	1.01395	−	0.215522i
$786$	0.909298	−	0.404845i	0.0324336	−	0.0144404i
$787$	−5.42220	+	16.6878i	−0.193281	+	0.594857i	0.806712	+	0.590945i	$0.201245\pi$
$787$	−5.42220	+	16.6878i	−0.193281	+	0.594857i	−0.999992	+	0.00391148i	$0.998755\pi$
$788$	13.3478	−	14.8243i	0.475497	−	0.528092i
$789$	−6.17338	+	4.48522i	−0.219778	+	0.159678i
$790$	−22.5714	−	4.79770i	−0.803054	−	0.170694i
$791$	36.3962	+	7.73626i	1.29410	+	0.275070i
$792$	−2.97783	−	28.3322i	−0.105813	−	1.00674i
$793$	−2.17142	+	7.51108i	−0.0771094	+	0.266726i
$794$	−18.2045	−	20.2181i	−0.646053	−	0.717514i
$795$	6.55852	+	4.76505i	0.232607	+	0.168999i
$796$	1.52107	−	4.68138i	0.0539129	−	0.165927i
$797$	3.51831	+	33.4745i	0.124625	+	1.18573i	0.860803	+	0.508939i	$0.169962\pi$
$797$	3.51831	+	33.4745i	0.124625	+	1.18573i	−0.736178	+	0.676788i	$0.763371\pi$
$798$	13.9548	−	10.1387i	0.493994	−	0.358908i
$799$	−25.2525	−	18.3470i	−0.893371	−	0.649072i
$800$	3.81395			0.134843
$801$	−11.5386	−	19.9854i	−0.407697	−	0.706151i
$802$	0.712032	−	6.77454i	0.0251427	−	0.239217i
$803$	37.6526	−	41.8175i	1.32873	−	1.47571i
$804$	−2.70070	−	2.99943i	−0.0952463	−	0.105782i
$805$	70.5997			2.48831
$806$	−19.6687	+	8.83584i	−0.692800	+	0.311229i
$807$	11.4253			0.402191
$808$	13.0762	+	14.5226i	0.460018	+	0.510902i
$809$	−2.88988	+	3.20953i	−0.101603	+	0.112841i	−0.791801	−	0.610779i	$-0.790856\pi$
$809$	−2.88988	+	3.20953i	−0.101603	+	0.112841i	0.690199	+	0.723620i	$0.257523\pi$
$810$	0.00707796	−	0.0673423i	0.000248694	−	0.00236617i
$811$	−3.73999	−	6.47785i	−0.131329	−	0.227468i	0.792860	−	0.609403i	$-0.208591\pi$
$811$	−3.73999	−	6.47785i	−0.131329	−	0.227468i	−0.924189	+	0.381935i	$0.875258\pi$
$812$	16.2115			0.568911
$813$	1.54922	+	1.12558i	0.0543336	+	0.0394757i
$814$	27.9858	−	20.3329i	0.980902	−	0.712667i
$815$	−0.428884	−	4.08056i	−0.0150232	−	0.142936i
$816$	2.07140	−	6.37512i	0.0725136	−	0.223174i
$817$	−28.7231	−	20.8685i	−1.00489	−	0.730098i
$818$	14.7990	+	16.4359i	0.517434	+	0.574669i
$819$	−24.6121	+	6.07977i	−0.860016	+	0.212444i
$820$	−0.745364	−	7.09166i	−0.0260292	−	0.247652i
$821$	−26.8528	−	5.70775i	−0.937170	−	0.199202i	−0.286083	−	0.958205i	$-0.592353\pi$
$821$	−26.8528	−	5.70775i	−0.937170	−	0.199202i	−0.651087	+	0.759003i	$0.725687\pi$
$822$	7.40067	+	1.57306i	0.258128	+	0.0548668i
$823$	5.25780	−	3.82001i	0.183275	−	0.133157i	−0.492365	−	0.870389i	$-0.663867\pi$
$823$	5.25780	−	3.82001i	0.183275	−	0.133157i	0.675640	+	0.737232i	$0.263867\pi$
$824$	−5.38259	+	5.97797i	−0.187511	+	0.208253i
$825$	−1.44578	+	4.44965i	−0.0503355	+	0.154917i
$826$	−0.929795	+	0.413972i	−0.0323517	+	0.0144039i
$827$	−20.3625	+	4.32819i	−0.708074	+	0.150506i	−0.547852	−	0.836575i	$-0.684554\pi$
$827$	−20.3625	+	4.32819i	−0.708074	+	0.150506i	−0.160222	+	0.987081i	$0.551221\pi$
$828$	1.49430	+	14.2173i	0.0519304	+	0.494084i
$829$	5.50693	+	52.3949i	0.191264	+	1.81975i	0.497129	+	0.867677i	$0.334388\pi$
$829$	5.50693	+	52.3949i	0.191264	+	1.81975i	−0.305866	+	0.952075i	$0.598946\pi$
$830$	0.998584	−	9.50090i	0.0346614	−	0.329781i
$831$	−2.08843	+	3.61727i	−0.0724469	+	0.125482i
$832$	−25.6736	+	12.4530i	−0.890074	+	0.431729i
$833$	−23.6852	−	17.2083i	−0.820642	−	0.596232i
$834$	−16.0044	+	17.7747i	−0.554188	+	0.615488i
$835$	15.5020	+	17.2167i	0.536468	+	0.595808i
$836$	8.39628	+	14.5428i	0.290391	+	0.502973i
$837$	3.87265	−	28.7016i	0.133858	−	0.992071i
$838$	18.6667	+	32.3317i	0.644830	+	1.11688i
$839$	37.5724	−	7.98625i	1.29714	−	0.275716i	0.492935	−	0.870066i	$-0.335924\pi$
$839$	37.5724	−	7.98625i	1.29714	−	0.275716i	0.804207	+	0.594350i	$0.202591\pi$
$840$	−24.7952	−	5.27038i	−0.855516	−	0.181845i
$841$	0.377813	−	3.59465i	0.0130280	−	0.123953i
$842$	−33.2172			−1.14474
$843$	−10.5459	−	18.2660i	−0.363219	−	0.629113i
$844$	−15.0408	+	6.69661i	−0.517726	+	0.230507i
$845$	−23.3924	+	12.3080i	−0.804723	+	0.423408i
$846$	14.4219	+	6.42104i	0.495835	+	0.220760i
$847$	16.9001	−	52.0131i	0.580693	−	1.78719i
$848$	−4.78462	−	3.47623i	−0.164305	−	0.119374i
$849$	1.77049	−	5.44902i	0.0607632	−	0.187010i
$850$	2.44387	−	2.71419i	0.0838241	−	0.0930961i
$851$	−47.2303	+	34.3148i	−1.61903	+	1.17630i
$852$	5.26905	−	5.85187i	0.180515	−	0.200482i
$853$	−7.52084	−	23.1468i	−0.257509	−	0.792530i	−0.993325	−	0.115349i	$-0.963201\pi$
$853$	−7.52084	−	23.1468i	−0.257509	−	0.792530i	0.735816	−	0.677181i	$-0.236799\pi$
$854$	7.16389	−	5.20487i	0.245143	−	0.178107i
$855$	−4.57634	−	14.0845i	−0.156507	−	0.481680i
$856$	23.4524	−	4.98496i	0.801586	−	0.170382i
$857$	−1.60500	+	15.2705i	−0.0548257	+	0.521631i	0.932300	+	0.361686i	$0.117799\pi$
$857$	−1.60500	+	15.2705i	−0.0548257	+	0.521631i	−0.987126	+	0.159946i	$0.948868\pi$
$858$	−2.86778	−	20.7317i	−0.0979043	−	0.707768i
$859$	−21.4562	−	9.55290i	−0.732075	−	0.325941i	0.00662246	−	0.999978i	$-0.497892\pi$
$859$	−21.4562	−	9.55290i	−0.732075	−	0.325941i	−0.738697	+	0.674037i	$0.764559\pi$
$860$	1.62166	+	15.4291i	0.0552981	+	0.526127i
$861$	1.76631	−	16.8053i	0.0601957	−	0.572724i
$862$	30.6335			1.04338
$863$	−23.4400	−	40.5993i	−0.797907	−	1.38202i	−0.920977	−	0.389618i	$-0.872607\pi$
$863$	−23.4400	−	40.5993i	−0.797907	−	1.38202i	0.123069	−	0.992398i	$-0.460726\pi$
$864$	2.39536	−	22.7903i	0.0814917	−	0.775342i
$865$	0.216656	+	0.666799i	0.00736653	+	0.0226718i
$866$	−11.5925	+	35.6780i	−0.393929	+	1.21239i
$867$	−0.843440	−	1.46088i	−0.0286447	−	0.0496141i
$868$	−17.4062	−	4.23815i	−0.590805	−	0.143852i
$869$	26.6179	−	46.1035i	0.902950	−	1.56396i
$870$	3.64724	−	11.2250i	0.123653	−	0.380564i
$871$	11.1107	+	11.5556i	0.376473	+	0.391546i
$872$	−29.9115	−	21.7320i	−1.01293	−	0.735937i
$873$	20.5334			0.694950
$874$	19.3158	+	33.4559i	0.653365	+	1.13166i
$875$	−36.6833	−	26.6520i	−1.24012	−	0.901003i
$876$	8.20236	−	5.95936i	0.277132	−	0.201348i
$877$	3.55508	+	33.8243i	0.120046	+	1.14216i	0.874234	+	0.485505i	$0.161364\pi$
$877$	3.55508	+	33.8243i	0.120046	+	1.14216i	−0.754187	+	0.656659i	$0.771969\pi$
$878$	−0.0236120	−	0.0262237i	−0.000796865	−	0.000885008i
$879$	−0.0285715	+	0.271840i	−0.000963692	+	0.00916892i
$880$	−5.03687	+	15.5019i	−0.169793	+	0.522569i
$881$	5.27786	+	16.2436i	0.177816	+	0.547260i	0.999751	−	0.0223208i	$-0.00710553\pi$
$881$	5.27786	+	16.2436i	0.177816	+	0.547260i	−0.821935	+	0.569581i	$0.807106\pi$
$882$	13.5267	+	6.02250i	0.455469	+	0.202788i
$883$	10.2573	+	31.5686i	0.345185	+	1.06237i	0.961485	+	0.274858i	$0.0886307\pi$
$883$	10.2573	+	31.5686i	0.345185	+	1.06237i	−0.616300	+	0.787511i	$0.711369\pi$
$884$	3.32865	−	11.5140i	0.111955	−	0.387258i
$885$	−0.0568209	−	0.540615i	−0.00191001	−	0.0181726i
$886$	−12.8649	−	39.5940i	−0.432204	−	1.33019i
$887$	−17.2212	+	3.66048i	−0.578232	+	0.122907i	−0.487738	−	0.872990i	$-0.662178\pi$
$887$	−17.2212	+	3.66048i	−0.578232	+	0.122907i	−0.0904938	+	0.995897i	$0.528845\pi$
$888$	19.1493	−	8.52582i	0.642609	−	0.286108i
$889$	−11.5526	+	2.45558i	−0.387462	+	0.0823575i
$890$	2.84846	+	27.1012i	0.0954804	+	0.908436i
$891$	0.142710	+	0.0635384i	0.00478095	+	0.00212862i
$892$	−10.6419	+	4.73809i	−0.356318	+	0.158643i
$893$	−31.2960			−1.04728
$894$	12.8464			0.429649
$895$	−31.0880	+	13.8413i	−1.03916	+	0.462663i
$896$	−1.15498	−	0.245498i	−0.0385851	−	0.00820151i
$897$	4.83980	+	34.9878i	0.161596	+	1.16821i
$898$	−21.7971			−0.727378
$899$	9.44923	−	26.4133i	0.315150	−	0.880934i
$900$	0.677547	−	1.17355i	0.0225849	−	0.0391182i
$901$	14.2808	−	3.03547i	0.475761	−	0.101126i
$902$	−21.9346	−	4.66235i	−0.730343	−	0.155239i
$903$	−3.84289	+	36.5627i	−0.127883	+	1.21673i
$904$	14.9609	−	25.9131i	0.497593	−	0.861855i
$905$	−6.97680	+	12.0842i	−0.231917	+	0.401691i
$906$	18.8434	+	13.6905i	0.626030	+	0.454837i
$907$	−2.70617	−	25.7475i	−0.0898570	−	0.854933i	−0.942896	−	0.333086i	$-0.891910\pi$
$907$	−2.70617	−	25.7475i	−0.0898570	−	0.854933i	0.853039	−	0.521847i	$-0.174757\pi$
$908$	12.7597	−	9.27045i	0.423445	−	0.307651i
$909$	11.5637	−	2.45794i	0.383544	−	0.0815247i
$910$	29.4704	+	5.26241i	0.976935	+	0.174447i
$911$	−26.8131	−	29.7790i	−0.888357	−	0.986621i	0.111617	−	0.993751i	$-0.464397\pi$
$911$	−26.8131	−	29.7790i	−0.888357	−	0.986621i	−0.999975	+	0.00713060i	$0.997730\pi$
$912$	−2.07685	−	6.39190i	−0.0687715	−	0.211657i
$913$	20.1340	+	8.96424i	0.666338	+	0.296673i
$914$	12.3150	−	13.6772i	0.407345	−	0.452402i
$915$	1.46147	+	4.49794i	0.0483147	+	0.148697i
$916$	1.79882	−	1.30692i	0.0594347	−	0.0431818i
$917$	−3.21279	−	0.682899i	−0.106096	−	0.0225513i
$918$	−14.6838	−	16.3081i	−0.484639	−	0.538246i
$919$	47.3614	−	21.0867i	1.56231	−	0.695585i	0.570263	−	0.821462i	$-0.306841\pi$
$919$	47.3614	−	21.0867i	1.56231	−	0.695585i	0.992046	+	0.125877i	$0.0401745\pi$
$920$	17.5437	−	53.9940i	0.578399	−	1.78013i
$921$	28.2874	−	20.5520i	0.932103	−	0.677212i
$922$	2.78232	−	2.02147i	0.0916307	−	0.0665736i
$923$	−20.1555	+	23.9148i	−0.663428	+	0.787166i
$924$	8.69435	−	15.0591i	0.286023	−	0.495407i
$925$	5.53389			0.181953
$926$	−8.83226	+	3.93238i	−0.290246	+	0.129226i
$927$	1.50379	+	4.62817i	0.0493908	+	0.152009i
$928$	6.85913	−	21.1102i	0.225162	−	0.692977i
$929$	0.256424	+	0.444140i	0.00841300	+	0.0145717i	0.870201	−	0.492696i	$-0.163989\pi$
$929$	0.256424	+	0.444140i	0.00841300	+	0.0145717i	−0.861788	+	0.507268i	$0.830655\pi$
$930$	−6.85057	+	11.0988i	−0.224639	+	0.363943i
$931$	−29.3535			−0.962024
$932$	3.27855	−	0.696877i	0.107392	−	0.0228270i
$933$	23.9511	−	26.6003i	0.784122	−	0.870856i
$934$	26.2827	−	11.7018i	0.859995	−	0.382894i
$935$	−20.1190	−	34.8470i	−0.657960	−	1.13962i
$936$	−1.46624	+	20.3339i	−0.0479256	+	0.664634i
$937$	4.77631	−	2.12655i	0.156035	−	0.0694714i	−0.327233	−	0.944944i	$-0.606116\pi$
$937$	4.77631	−	2.12655i	0.156035	−	0.0694714i	0.483268	+	0.875472i	$0.339450\pi$
$938$	−1.89777	−	18.0561i	−0.0619644	−	0.589552i
$939$	−6.07798	+	4.41591i	−0.198347	+	0.144108i
$940$	9.15065	+	10.1628i	0.298461	+	0.331475i
$941$	1.71614	−	16.3279i	0.0559444	−	0.532276i	−0.930279	−	0.366854i	$-0.880435\pi$
$941$	1.71614	−	16.3279i	0.0559444	−	0.532276i	0.986223	−	0.165422i	$-0.0528985\pi$
$942$	5.08534	−	15.6511i	0.165689	−	0.509939i
$943$	37.0180	+	7.86841i	1.20547	+	0.256231i
$944$	0.0414524	+	0.394393i	0.00134916	+	0.0128364i
$945$	−26.9056	+	29.8817i	−0.875240	+	0.972052i
$946$	47.7224	+	10.1437i	1.55159	+	0.329800i
$947$	−10.3793	−	4.62118i	−0.337284	−	0.150168i	0.231104	−	0.972929i	$-0.425766\pi$
$947$	−10.3793	−	4.62118i	−0.337284	−	0.150168i	−0.568388	+	0.822761i	$0.692433\pi$
$948$	6.41817	−	7.12810i	0.208452	−	0.231510i
$949$	−31.7858	+	24.7228i	−1.03181	+	0.802537i
$950$	0.382775	−	3.64186i	0.0124189	−	0.118158i
$951$	4.27558	−	13.1589i	0.138645	−	0.426706i
$952$	−36.9334	+	26.8337i	−1.19702	+	0.869684i
$953$	−10.6596	−	4.74595i	−0.345298	−	0.153736i	0.226758	−	0.973951i	$-0.427187\pi$
$953$	−10.6596	−	4.74595i	−0.345298	−	0.153736i	−0.572056	+	0.820215i	$0.693854\pi$
$954$	−6.74561	+	3.00334i	−0.218397	+	0.0972367i
$955$	21.8842			0.708157
$956$	−1.54727	+	2.67995i	−0.0500423	+	0.0866758i
$957$	22.0287	+	16.0048i	0.712087	+	0.517361i
$958$	−3.56168	−	10.9617i	−0.115073	−	0.354157i
$959$	−16.7062	−	18.5542i	−0.539473	−	0.599145i
$960$	−8.63007	+	14.9477i	−0.278534	+	0.482436i
$961$	−17.0508	+	25.8896i	−0.550026	+	0.835147i
$962$	−22.2731	+	10.8035i	−0.718113	+	0.348320i
$963$	4.48216	−	13.7947i	0.144436	−	0.444527i
$964$	4.31821	−	4.79585i	0.139080	−	0.154464i
$965$	−18.2929	+	8.14450i	−0.588868	+	0.262181i
$966$	20.0015	−	34.6436i	0.643537	−	1.11464i
$967$	−8.65290	+	14.9873i	−0.278258	+	0.481958i	−0.970952	−	0.239274i	$-0.923090\pi$
$967$	−8.65290	+	14.9873i	−0.278258	+	0.481958i	0.692694	+	0.721232i	$0.256424\pi$
$968$	−35.5795	−	25.8500i	−1.14357	−	0.830851i
$969$	15.1569	+	6.74829i	0.486910	+	0.216786i
$970$	−22.1505	−	9.86202i	−0.711208	−	0.316650i
$971$	16.3860	+	18.1985i	0.525851	+	0.584017i	0.946296	−	0.323301i	$-0.104793\pi$
$971$	16.3860	+	18.1985i	0.525851	+	0.584017i	−0.420445	+	0.907318i	$0.638126\pi$
$972$	−10.6619	−	7.74632i	−0.341980	−	0.248463i
$973$	77.2031	−	16.4100i	2.47502	−	0.526081i
$974$	20.4707	−	22.7350i	0.655923	−	0.728476i
$975$	1.57826	−	2.95279i	0.0505447	−	0.0945651i
$976$	−1.06618	−	3.28137i	−0.0341277	−	0.105034i
$977$	9.45068	+	2.00880i	0.302354	+	0.0642673i	0.356590	−	0.934261i	$-0.383939\pi$
$977$	9.45068	+	2.00880i	0.302354	+	0.0642673i	−0.0542365	+	0.998528i	$0.517273\pi$
$978$	−2.12385	−	0.945600i	−0.0679133	−	0.0302370i
$979$	−61.4935	−	13.0708i	−1.96534	−	0.417746i
$980$	8.58269	+	9.53204i	0.274164	+	0.304490i
$981$	−20.4330	+	9.09738i	−0.652377	+	0.290457i
$982$	−16.2578	−	18.0561i	−0.518806	−	0.576193i
$983$	4.36511	+	1.94347i	0.139225	+	0.0619871i	0.475167	−	0.879896i	$-0.342388\pi$
$983$	4.36511	+	1.94347i	0.139225	+	0.0619871i	−0.335941	+	0.941883i	$0.609054\pi$
$984$	−12.4136	−	5.52690i	−0.395732	−	0.176191i
$985$	−5.00950	+	47.6622i	−0.159616	+	1.51864i
$986$	−10.6280	−	18.4082i	−0.338463	−	0.586235i
$987$	16.2035	+	28.0653i	0.515764	+	0.893330i
$988$	−4.08556	−	11.3012i	−0.129979	−	0.359540i
$989$	−80.5386	−	17.1190i	−2.56098	−	0.544353i
$990$	13.6173	+	15.1235i	0.432786	+	0.480657i
$991$	12.6377	−	21.8892i	0.401451	−	0.695334i	−0.592450	−	0.805607i	$-0.701839\pi$
$991$	12.6377	−	21.8892i	0.401451	−	0.695334i	0.993901	+	0.110273i	$0.0351726\pi$
$992$	−12.8834	+	20.8728i	−0.409050	+	0.662711i
$993$	−29.2585			−0.928492
$994$	34.6473	−	7.36451i	1.09895	−	0.233588i
$995$	3.65435	+	11.2469i	0.115851	+	0.356551i
$996$	3.21258	+	2.33408i	0.101795	+	0.0739581i
$997$	−30.7647	+	53.2861i	−0.974329	+	1.68759i	−0.292198	+	0.956358i	$0.594387\pi$
$997$	−30.7647	+	53.2861i	−0.974329	+	1.68759i	−0.682131	+	0.731230i	$0.738947\pi$
$998$	−10.8974	−	18.8748i	−0.344951	−	0.597473i
$999$	3.47557	−	33.0678i	0.109962	−	1.04622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bk.a.9.12	yes	280
13.3	even	3		403.2.bj.a.133.24	yes	280
31.7	even	15		403.2.bj.a.100.24	✓	280
403.224	even	15	inner	403.2.bk.a.224.12	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bj.a.100.24	✓	280	31.7	even	15
403.2.bj.a.133.24	yes	280	13.3	even	3
403.2.bk.a.9.12	yes	280	1.1	even	1	trivial
403.2.bk.a.224.12	yes	280	403.224	even	15	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bk (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.718707 - 0.798205i) q^{2} +(-0.717726 + 0.797115i) q^{3} +(0.0884655 - 0.841693i) q^{4} +(1.01665 + 1.76088i) q^{5} +1.15210 q^{6} +(-3.07573 - 2.23465i) q^{7} +(-2.47334 + 1.79699i) q^{8} +(0.193323 + 1.83935i) q^{9} +O(q^{10})\)	\(q+(-0.718707 - 0.798205i) q^{2} +(-0.717726 + 0.797115i) q^{3} +(0.0884655 - 0.841693i) q^{4} +(1.01665 + 1.76088i) q^{5} +1.15210 q^{6} +(-3.07573 - 2.23465i) q^{7} +(-2.47334 + 1.79699i) q^{8} +(0.193323 + 1.83935i) q^{9} +(0.674874 - 2.07705i) q^{10} +(4.07613 + 2.96148i) q^{11} +(0.607432 + 0.674622i) q^{12} +(-2.49899 - 2.59905i) q^{13} +(0.426840 + 4.06111i) q^{14} +(-2.13330 - 0.453447i) q^{15} +(1.55630 + 0.330802i) q^{16} +(-3.17763 + 2.30868i) q^{17} +(1.32923 - 1.47626i) q^{18} +(-1.21694 + 3.74536i) q^{19} +(1.57206 - 0.699926i) q^{20} +(3.98880 - 0.847845i) q^{21} +(-0.565674 - 5.38202i) q^{22} +(0.954659 + 9.08297i) q^{23} +(0.342774 - 3.26128i) q^{24} +(0.432864 - 0.749742i) q^{25} +(-0.278530 + 3.86266i) q^{26} +(-4.20824 - 3.05746i) q^{27} +(-2.15298 + 2.39113i) q^{28} +(-3.37135 - 3.74427i) q^{29} +(1.17127 + 2.02870i) q^{30} +(2.64095 + 4.90157i) q^{31} +(2.20274 + 3.81526i) q^{32} +(-5.28619 + 1.12361i) q^{33} +(4.12658 + 0.877133i) q^{34} +(0.808024 - 7.68783i) q^{35} +1.56527 q^{36} +(3.19609 + 5.53579i) q^{37} +(3.86419 - 1.72045i) q^{38} +(3.86533 - 0.126581i) q^{39} +(-5.67879 - 2.52836i) q^{40} +(1.28049 - 3.94095i) q^{41} +(-3.54353 - 2.57453i) q^{42} +(-2.78592 + 8.57418i) q^{43} +(2.85326 - 3.16886i) q^{44} +(-3.04233 + 2.21038i) q^{45} +(6.56395 - 7.29001i) q^{46} +(2.45575 + 7.55803i) q^{47} +(-1.38068 + 1.00313i) q^{48} +(2.30333 + 7.08891i) q^{49} +(-0.909550 + 0.193331i) q^{50} +(0.440380 - 4.18994i) q^{51} +(-2.40867 + 1.87346i) q^{52} +(-3.39572 - 1.51187i) q^{53} +(0.584007 + 5.55646i) q^{54} +(-1.07084 + 10.1884i) q^{55} +11.6229 q^{56} +(-2.11205 - 3.65818i) q^{57} +(-0.565677 + 5.38206i) q^{58} +(0.0770209 + 0.237046i) q^{59} +(-0.570386 + 1.75547i) q^{60} +(-1.08425 - 1.87798i) q^{61} +(2.01439 - 5.63081i) q^{62} +(3.51568 - 6.08933i) q^{63} +(2.44557 - 7.52668i) q^{64} +(2.03603 - 7.04274i) q^{65} +(4.69609 + 3.41191i) q^{66} -4.44609 q^{67} +(1.66209 + 2.87883i) q^{68} +(-7.92536 - 5.75811i) q^{69} +(-6.71720 + 4.88033i) q^{70} +(-0.906711 - 8.62678i) q^{71} +(-3.78343 - 4.20193i) q^{72} +(1.16742 - 11.1073i) q^{73} +(2.12164 - 6.52975i) q^{74} +(0.286953 + 0.883152i) q^{75} +(3.04479 + 1.35563i) q^{76} +(-5.91919 - 18.2174i) q^{77} +(-2.87908 - 2.99435i) q^{78} +(-1.10445 - 10.5082i) q^{79} +(0.999702 + 3.07677i) q^{80} +(0.0303275 - 0.00644632i) q^{81} +(-4.06599 + 1.81029i) q^{82} +(4.27872 - 0.909471i) q^{83} +(-0.360754 - 3.43235i) q^{84} +(-7.29584 - 3.24832i) q^{85} +(8.84621 - 3.93859i) q^{86} +5.40432 q^{87} -15.4034 q^{88} +(-11.3989 + 5.07514i) q^{89} +(3.95088 + 0.839785i) q^{90} +(1.87826 + 13.5783i) q^{91} +7.72953 q^{92} +(-5.80259 - 1.41285i) q^{93} +(4.26789 - 7.39220i) q^{94} +(-7.83233 + 1.66481i) q^{95} +(-4.62216 - 0.982471i) q^{96} +(1.16050 - 11.0415i) q^{97} +(4.00299 - 6.93338i) q^{98} +(-4.65918 + 8.06993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9}+O(q^{10}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9} - 9 q^{10} - 6 q^{11} - 50 q^{12} - 6 q^{13} - 21 q^{15} + 23 q^{16} + 3 q^{17} - 15 q^{18} - 9 q^{19} + 60 q^{20} - 34 q^{21} + 41 q^{22} - 12 q^{23} - 89 q^{24} - 112 q^{25} + 39 q^{26} + 48 q^{27} + 66 q^{28} - 11 q^{29} + 24 q^{30} - 22 q^{31} + q^{32} - 37 q^{33} - 49 q^{34} + 41 q^{35} + 134 q^{36} + 17 q^{37} - 23 q^{38} + 10 q^{39} + 31 q^{40} + q^{41} - 71 q^{42} - 7 q^{43} - 42 q^{44} - 13 q^{45} + 21 q^{46} - 20 q^{47} - 3 q^{48} - 69 q^{49} - 42 q^{50} - 71 q^{51} - 140 q^{52} - 8 q^{53} - 149 q^{54} + 5 q^{55} - 126 q^{56} + 21 q^{57} + 79 q^{58} + 77 q^{59} + 2 q^{60} + 53 q^{61} + 72 q^{62} + 17 q^{63} - 91 q^{64} - 25 q^{65} - 62 q^{66} - 14 q^{67} + 83 q^{68} - 31 q^{69} + 134 q^{70} + 32 q^{71} - 70 q^{72} - 31 q^{73} + 51 q^{74} + 79 q^{75} + 98 q^{76} - 80 q^{77} - 141 q^{78} - 142 q^{79} + 6 q^{80} + 66 q^{81} - 48 q^{82} + 94 q^{83} + 130 q^{84} + 90 q^{85} - 34 q^{86} + 22 q^{87} - 122 q^{88} - 15 q^{89} + 43 q^{90} + 56 q^{91} - 294 q^{92} - 52 q^{93} - 57 q^{94} + 94 q^{95} + 24 q^{96} + 46 q^{97} + 73 q^{98} + 12 q^{99}+O(q^{100}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9 - 9 * q^10 - 6 * q^11 - 50 * q^12 - 6 * q^13 - 21 * q^15 + 23 * q^16 + 3 * q^17 - 15 * q^18 - 9 * q^19 + 60 * q^20 - 34 * q^21 + 41 * q^22 - 12 * q^23 - 89 * q^24 - 112 * q^25 + 39 * q^26 + 48 * q^27 + 66 * q^28 - 11 * q^29 + 24 * q^30 - 22 * q^31 + q^32 - 37 * q^33 - 49 * q^34 + 41 * q^35 + 134 * q^36 + 17 * q^37 - 23 * q^38 + 10 * q^39 + 31 * q^40 + q^41 - 71 * q^42 - 7 * q^43 - 42 * q^44 - 13 * q^45 + 21 * q^46 - 20 * q^47 - 3 * q^48 - 69 * q^49 - 42 * q^50 - 71 * q^51 - 140 * q^52 - 8 * q^53 - 149 * q^54 + 5 * q^55 - 126 * q^56 + 21 * q^57 + 79 * q^58 + 77 * q^59 + 2 * q^60 + 53 * q^61 + 72 * q^62 + 17 * q^63 - 91 * q^64 - 25 * q^65 - 62 * q^66 - 14 * q^67 + 83 * q^68 - 31 * q^69 + 134 * q^70 + 32 * q^71 - 70 * q^72 - 31 * q^73 + 51 * q^74 + 79 * q^75 + 98 * q^76 - 80 * q^77 - 141 * q^78 - 142 * q^79 + 6 * q^80 + 66 * q^81 - 48 * q^82 + 94 * q^83 + 130 * q^84 + 90 * q^85 - 34 * q^86 + 22 * q^87 - 122 * q^88 - 15 * q^89 + 43 * q^90 + 56 * q^91 - 294 * q^92 - 52 * q^93 - 57 * q^94 + 94 * q^95 + 24 * q^96 + 46 * q^97 + 73 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

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