LMFDB - Embedded newform 861.2.bw.a.824.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(236,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 25, 21]))

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

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

chi := DirichletCharacter("861.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.bw (of order $30$, 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:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$864$
Relative dimension:	$108$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			824.17
Character	$\chi$	$=$	861.824
Dual form			861.2.bw.a.605.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.10072 + 0.220794i) q^{2} +(-1.58756 + 0.692569i) q^{3} +(2.40798 - 0.511831i) q^{4} +(1.58817 + 1.76385i) q^{5} +(3.18210 - 1.80542i) q^{6} +(-0.338439 - 2.62402i) q^{7} +(-0.927655 + 0.301413i) q^{8} +(2.04070 - 2.19899i) q^{9} +O(q^{10})$	\(q+(-2.10072 + 0.220794i) q^{2} +(-1.58756 + 0.692569i) q^{3} +(2.40798 - 0.511831i) q^{4} +(1.58817 + 1.76385i) q^{5} +(3.18210 - 1.80542i) q^{6} +(-0.338439 - 2.62402i) q^{7} +(-0.927655 + 0.301413i) q^{8} +(2.04070 - 2.19899i) q^{9} +(-3.72575 - 3.35468i) q^{10} +(2.61402 - 2.90317i) q^{11} +(-3.46833 + 2.48025i) q^{12} +(2.12311 - 1.54253i) q^{13} +(1.29033 + 5.43759i) q^{14} +(-3.74291 - 1.70029i) q^{15} +(-2.61569 + 1.16458i) q^{16} +(-3.84529 - 3.46231i) q^{17} +(-3.80140 + 5.07004i) q^{18} +(0.472784 - 0.210497i) q^{19} +(4.72707 + 3.43442i) q^{20} +(2.35460 + 3.93139i) q^{21} +(-4.85032 + 6.67590i) q^{22} +(-6.67084 + 0.701133i) q^{23} +(1.26396 - 1.12098i) q^{24} +(-0.0662131 + 0.629975i) q^{25} +(-4.11947 + 3.70919i) q^{26} +(-1.71678 + 4.90435i) q^{27} +(-2.15801 - 6.14534i) q^{28} +(-0.169272 + 0.520964i) q^{29} +(8.23821 + 2.74542i) q^{30} +(-1.44495 - 1.30104i) q^{31} +(6.92712 - 3.99938i) q^{32} +(-2.13928 + 6.41934i) q^{33} +(8.84233 + 6.42433i) q^{34} +(4.09086 - 4.76435i) q^{35} +(3.78843 - 6.33961i) q^{36} +(1.48113 + 1.64496i) q^{37} +(-0.946711 + 0.546584i) q^{38} +(-2.30226 + 3.91926i) q^{39} +(-2.00492 - 1.15754i) q^{40} +(-5.76396 - 2.78869i) q^{41} +(-5.81439 - 7.73887i) q^{42} +(-6.12990 + 4.45363i) q^{43} +(4.80857 - 8.32869i) q^{44} +(7.11966 + 0.107094i) q^{45} +(13.8588 - 2.94577i) q^{46} +(-10.5659 + 1.11052i) q^{47} +(3.34601 - 3.66038i) q^{48} +(-6.77092 + 1.77614i) q^{49} -1.33802i q^{50} +(8.50252 + 2.83350i) q^{51} +(4.32288 - 4.80104i) q^{52} +(-4.29602 + 0.913146i) q^{53} +(2.52361 - 10.6817i) q^{54} +9.27226 q^{55} +(1.10487 + 2.33217i) q^{56} +(-0.604790 + 0.661613i) q^{57} +(0.240566 - 1.13177i) q^{58} +(3.13256 + 1.39471i) q^{59} +(-9.88309 - 2.17852i) q^{60} +(5.57771 + 12.5277i) q^{61} +(3.32270 + 2.41408i) q^{62} +(-6.46084 - 4.61059i) q^{63} +(-9.03610 + 6.56511i) q^{64} +(6.09265 + 1.29503i) q^{65} +(3.07666 - 13.9576i) q^{66} +(-2.86747 - 13.4904i) q^{67} +(-11.0315 - 6.36903i) q^{68} +(10.1048 - 5.73311i) q^{69} +(-7.54180 + 10.9118i) q^{70} +(-4.75666 - 14.6395i) q^{71} +(-1.23026 + 2.65500i) q^{72} +(3.33086 - 1.92307i) q^{73} +(-3.47464 - 3.12858i) q^{74} +(-0.331184 - 1.04598i) q^{75} +(1.03071 - 0.748858i) q^{76} +(-8.50264 - 5.87669i) q^{77} +(3.97104 - 8.74158i) q^{78} +(-11.1101 - 6.41445i) q^{79} +(-6.20830 - 2.76411i) q^{80} +(-0.671119 - 8.97494i) q^{81} +(12.7242 + 4.58560i) q^{82} -11.8609 q^{83} +(7.68204 + 8.26153i) q^{84} -12.2812i q^{85} +(11.8939 - 10.7093i) q^{86} +(-0.0920750 - 0.944295i) q^{87} +(-1.54986 + 3.48104i) q^{88} +(-1.28077 - 2.87665i) q^{89} +(-14.9800 + 1.34701i) q^{90} +(-4.76616 - 5.04902i) q^{91} +(-15.7044 + 5.10265i) q^{92} +(3.19501 + 1.06475i) q^{93} +(21.9508 - 4.66578i) q^{94} +(1.12215 + 0.499613i) q^{95} +(-8.22738 + 11.1468i) q^{96} +(-1.18877 + 3.65867i) q^{97} +(13.8316 - 5.22615i) q^{98} +(-1.04961 - 11.6727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9}+O(q^{10}) $ 864 * q - 110 * q^4 - 20 * q^7 - 12 * q^9	$ 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9} - 18 q^{10} - 15 q^{12} - 50 q^{15} + 82 q^{16} - 15 q^{18} - 30 q^{19} - 14 q^{21} + 30 q^{24} + 78 q^{25} + 15 q^{30} - 18 q^{31} + 36 q^{33} + 16 q^{36} - 10 q^{37} - 2 q^{39} - 144 q^{40} - 24 q^{42} - 8 q^{43} + 69 q^{45} - 12 q^{46} + 52 q^{49} - 18 q^{51} - 30 q^{52} + 15 q^{54} - 38 q^{57} - 10 q^{58} - 126 q^{61} + 65 q^{63} - 16 q^{64} - 70 q^{67} - 260 q^{70} - 33 q^{72} - 48 q^{73} + 60 q^{75} - 2 q^{78} + 68 q^{81} - 150 q^{82} + 115 q^{84} - 138 q^{87} + 30 q^{88} + 64 q^{91} - 15 q^{93} + 60 q^{94} - 30 q^{99}+O(q^{100}) $ 864 * q - 110 * q^4 - 20 * q^7 - 12 * q^9 - 18 * q^10 - 15 * q^12 - 50 * q^15 + 82 * q^16 - 15 * q^18 - 30 * q^19 - 14 * q^21 + 30 * q^24 + 78 * q^25 + 15 * q^30 - 18 * q^31 + 36 * q^33 + 16 * q^36 - 10 * q^37 - 2 * q^39 - 144 * q^40 - 24 * q^42 - 8 * q^43 + 69 * q^45 - 12 * q^46 + 52 * q^49 - 18 * q^51 - 30 * q^52 + 15 * q^54 - 38 * q^57 - 10 * q^58 - 126 * q^61 + 65 * q^63 - 16 * q^64 - 70 * q^67 - 260 * q^70 - 33 * q^72 - 48 * q^73 + 60 * q^75 - 2 * q^78 + 68 * q^81 - 150 * q^82 + 115 * q^84 - 138 * q^87 + 30 * q^88 + 64 * q^91 - 15 * q^93 + 60 * q^94 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.10072	+	0.220794i	−1.48543	+	0.156125i	−0.812232	−	0.583335i	$-0.801748\pi$
$2$	−2.10072	+	0.220794i	−1.48543	+	0.156125i	−0.673201	+	0.739460i	$0.735081\pi$
$3$	−1.58756	+	0.692569i	−0.916578	+	0.399855i
$3$	−1.58756	+	0.692569i	−0.916578	+	0.399855i
$4$	2.40798	−	0.511831i	1.20399	−	0.255915i
$5$	1.58817	+	1.76385i	0.710253	+	0.788816i	0.984973	−	0.172709i	$-0.0552519\pi$
$5$	1.58817	+	1.76385i	0.710253	+	0.788816i	−0.274720	+	0.961524i	$0.588585\pi$
$6$	3.18210	−	1.80542i	1.29909	−	0.737059i
$7$	−0.338439	−	2.62402i	−0.127918	−	0.991785i
$7$	−0.338439	−	2.62402i	−0.127918	−	0.991785i
$8$	−0.927655	+	0.301413i	−0.327976	+	0.106566i
$9$	2.04070	−	2.19899i	0.680232	−	0.732997i
$10$	−3.72575	−	3.35468i	−1.17819	−	1.06084i
$11$	2.61402	−	2.90317i	0.788158	−	0.875338i	−0.206513	−	0.978444i	$-0.566212\pi$
$11$	2.61402	−	2.90317i	0.788158	−	0.875338i	0.994670	+	0.103106i	$0.0328782\pi$
$12$	−3.46833	+	2.48025i	−1.00122	+	0.715987i
$13$	2.12311	−	1.54253i	0.588844	−	0.427821i	−0.253057	−	0.967451i	$-0.581436\pi$
$13$	2.12311	−	1.54253i	0.588844	−	0.427821i	0.841902	+	0.539631i	$0.181436\pi$
$14$	1.29033	+	5.43759i	0.344856	+	1.45326i
$15$	−3.74291	−	1.70029i	−0.966414	−	0.439013i
$16$	−2.61569	+	1.16458i	−0.653922	+	0.291145i
$17$	−3.84529	−	3.46231i	−0.932619	−	0.839734i	0.0546967	−	0.998503i	$-0.482581\pi$
$17$	−3.84529	−	3.46231i	−0.932619	−	0.839734i	−0.987316	+	0.158769i	$0.949247\pi$
$18$	−3.80140	+	5.07004i	−0.896000	+	1.19502i
$19$	0.472784	−	0.210497i	0.108464	−	0.0482914i	−0.351787	−	0.936080i	$-0.614426\pi$
$19$	0.472784	−	0.210497i	0.108464	−	0.0482914i	0.460251	+	0.887789i	$0.347759\pi$
$20$	4.72707	+	3.43442i	1.05701	+	0.767960i
$21$	2.35460	+	3.93139i	0.513817	+	0.857900i
$22$	−4.85032	+	6.67590i	−1.03409	+	1.42331i
$23$	−6.67084	+	0.701133i	−1.39097	+	0.146196i	−0.770201	−	0.637801i	$-0.779844\pi$
$23$	−6.67084	+	0.701133i	−1.39097	+	0.146196i	−0.620765	+	0.783997i	$0.713178\pi$
$24$	1.26396	−	1.12098i	0.258005	−	0.228819i
$25$	−0.0662131	+	0.629975i	−0.0132426	+	0.125995i
$26$	−4.11947	+	3.70919i	−0.807895	+	0.727432i
$27$	−1.71678	+	4.90435i	−0.330394	+	0.943843i
$28$	−2.15801	−	6.14534i	−0.407825	−	1.16136i
$29$	−0.169272	+	0.520964i	−0.0314330	+	0.0967407i	−0.965542	−	0.260247i	$-0.916196\pi$
$29$	−0.169272	+	0.520964i	−0.0314330	+	0.0967407i	0.934109	+	0.356987i	$0.116196\pi$
$30$	8.23821	+	2.74542i	1.50408	+	0.501243i
$31$	−1.44495	−	1.30104i	−0.259521	−	0.233674i	0.529091	−	0.848565i	$-0.322533\pi$
$31$	−1.44495	−	1.30104i	−0.259521	−	0.233674i	−0.788612	+	0.614892i	$0.789200\pi$
$32$	6.92712	−	3.99938i	1.22455	−	0.706997i
$33$	−2.13928	+	6.41934i	−0.372400	+	1.11746i
$34$	8.84233	+	6.42433i	1.51645	+	1.10176i
$35$	4.09086	−	4.76435i	0.691481	−	0.805322i
$36$	3.78843	−	6.33961i	0.631406	−	1.05660i
$37$	1.48113	+	1.64496i	0.243497	+	0.270431i	0.852488	−	0.522746i	$-0.175092\pi$
$37$	1.48113	+	1.64496i	0.243497	+	0.270431i	−0.608992	+	0.793177i	$0.708426\pi$
$38$	−0.946711	+	0.546584i	−0.153577	+	0.0886676i
$39$	−2.30226	+	3.91926i	−0.368656	+	0.627583i
$40$	−2.00492	−	1.15754i	−0.317006	−	0.183024i
$41$	−5.76396	−	2.78869i	−0.900179	−	0.435520i
$41$	−5.76396	−	2.78869i	−0.900179	−	0.435520i
$42$	−5.81439	−	7.73887i	−0.897180	−	1.19413i
$43$	−6.12990	+	4.45363i	−0.934801	+	0.679172i	−0.947163	−	0.320751i	$-0.896065\pi$
$43$	−6.12990	+	4.45363i	−0.934801	+	0.679172i	0.0123629	+	0.999924i	$0.496065\pi$
$44$	4.80857	−	8.32869i	0.724920	−	1.25560i
$45$	7.11966	+	0.107094i	1.06134	+	0.0159646i
$46$	13.8588	−	2.94577i	2.04336	−	0.434330i
$47$	−10.5659	+	1.11052i	−1.54119	+	0.161986i	−0.836675	−	0.547700i	$-0.815503\pi$
$47$	−10.5659	+	1.11052i	−1.54119	+	0.161986i	−0.704518	+	0.709686i	$0.748837\pi$
$48$	3.34601	−	3.66038i	0.482955	−	0.528331i
$49$	−6.77092	+	1.77614i	−0.967274	+	0.253734i
$50$		−	1.33802i		−	0.189225i
$51$	8.50252	+	2.83350i	1.19059	+	0.396770i
$52$	4.32288	−	4.80104i	0.599476	−	0.665785i
$53$	−4.29602	+	0.913146i	−0.590103	+	0.125430i	−0.493279	−	0.869871i	$-0.664202\pi$
$53$	−4.29602	+	0.913146i	−0.590103	+	0.125430i	−0.0968242	+	0.995301i	$0.530868\pi$
$54$	2.52361	−	10.6817i	0.343420	−	1.45360i
$55$	9.27226			1.25027
$56$	1.10487	+	2.33217i	0.147644	+	0.311650i
$57$	−0.604790	+	0.661613i	−0.0801064	+	0.0876328i
$58$	0.240566	−	1.13177i	0.0315879	−	0.148609i
$59$	3.13256	+	1.39471i	0.407825	+	0.181575i	0.600387	−	0.799709i	$-0.295013\pi$
$59$	3.13256	+	1.39471i	0.407825	+	0.181575i	−0.192562	+	0.981285i	$0.561680\pi$
$60$	−9.88309	−	2.17852i	−1.27590	−	0.281246i
$61$	5.57771	+	12.5277i	0.714153	+	1.60401i	0.794513	+	0.607248i	$0.207726\pi$
$61$	5.57771	+	12.5277i	0.714153	+	1.60401i	−0.0803598	+	0.996766i	$0.525607\pi$
$62$	3.32270	+	2.41408i	0.421983	+	0.306589i
$63$	−6.46084	−	4.61059i	−0.813989	−	0.580880i
$64$	−9.03610	+	6.56511i	−1.12951	+	0.820639i
$65$	6.09265	+	1.29503i	0.755700	+	0.160629i
$66$	3.07666	−	13.9576i	0.378711	−	1.71806i
$67$	−2.86747	−	13.4904i	−0.350317	−	1.64811i	−0.702135	−	0.712044i	$-0.747770\pi$
$67$	−2.86747	−	13.4904i	−0.350317	−	1.64811i	0.351818	−	0.936068i	$-0.385564\pi$
$68$	−11.0315	−	6.36903i	−1.33776	−	0.772358i
$69$	10.1048	−	5.73311i	1.21647	−	0.690185i
$70$	−7.54180	+	10.9118i	−0.901418	+	1.30421i
$71$	−4.75666	−	14.6395i	−0.564511	−	1.73739i	−0.669399	−	0.742903i	$-0.733448\pi$
$71$	−4.75666	−	14.6395i	−0.564511	−	1.73739i	0.104887	−	0.994484i	$-0.466552\pi$
$72$	−1.23026	+	2.65500i	−0.144987	+	0.312895i
$73$	3.33086	−	1.92307i	0.389848	−	0.225079i	−0.292246	−	0.956343i	$-0.594403\pi$
$73$	3.33086	−	1.92307i	0.389848	−	0.225079i	0.682094	+	0.731264i	$0.261069\pi$
$74$	−3.47464	−	3.12858i	−0.403919	−	0.363690i
$75$	−0.331184	−	1.04598i	−0.0382418	−	0.120779i
$76$	1.03071	−	0.748858i	0.118231	−	0.0858999i
$77$	−8.50264	−	5.87669i	−0.968966	−	0.669711i
$78$	3.97104	−	8.74158i	0.449632	−	0.989789i
$79$	−11.1101	−	6.41445i	−1.24999	−	0.721682i	−0.278882	−	0.960325i	$-0.589964\pi$
$79$	−11.1101	−	6.41445i	−1.24999	−	0.721682i	−0.971107	+	0.238644i	$0.923297\pi$
$80$	−6.20830	−	2.76411i	−0.694109	−	0.309037i
$81$	−0.671119	−	8.97494i	−0.0745687	−	0.997216i
$82$	12.7242	+	4.58560i	1.40515	+	0.506395i
$83$	−11.8609			−1.30190			−0.650949	−	0.759121i	$-0.725629\pi$
$83$	−11.8609			−1.30190			−0.650949	+	0.759121i	$0.725629\pi$
$84$	7.68204	+	8.26153i	0.838179	+	0.901407i
$85$		−	12.2812i		−	1.33209i
$86$	11.8939	−	10.7093i	1.28255	−	1.15481i
$87$	−0.0920750	−	0.944295i	−0.00987147	−	0.101239i
$88$	−1.54986	+	3.48104i	−0.165215	+	0.371080i
$89$	−1.28077	−	2.87665i	−0.135761	−	0.304925i	0.832853	−	0.553495i	$-0.186706\pi$
$89$	−1.28077	−	2.87665i	−0.135761	−	0.304925i	−0.968614	+	0.248570i	$0.920039\pi$
$90$	−14.9800	+	1.34701i	−1.57904	+	0.141987i
$91$	−4.76616	−	5.04902i	−0.499630	−	0.529281i
$92$	−15.7044	+	5.10265i	−1.63729	+	0.531988i
$93$	3.19501	+	1.06475i	0.331307	+	0.110410i
$94$	21.9508	−	4.66578i	2.26405	−	0.481238i
$95$	1.12215	+	0.499613i	0.115130	+	0.0512592i
$96$	−8.22738	+	11.1468i	−0.839704	+	1.13766i
$97$	−1.18877	+	3.65867i	−0.120702	+	0.371482i	−0.993094	−	0.117326i	$-0.962568\pi$
$97$	−1.18877	+	3.65867i	−0.120702	+	0.371482i	0.872392	+	0.488807i	$0.162568\pi$
$98$	13.8316	−	5.22615i	1.39721	−	0.527921i
$99$	−1.04961	−	11.6727i	−0.105490	−	1.17315i
$100$	0.163001	+	1.55085i	0.0163001	+	0.155085i
$101$	11.2744	+	1.18499i	1.12184	+	0.117911i	0.647238	−	0.762288i	$-0.275924\pi$
$101$	11.2744	+	1.18499i	1.12184	+	0.117911i	0.474606	+	0.880198i	$0.342591\pi$
$102$	−18.4870	−	4.07508i	−1.83049	−	0.403493i
$103$	1.42322	+	3.19660i	0.140234	+	0.314970i	0.969986	−	0.243162i	$-0.0781848\pi$
$103$	1.42322	+	3.19660i	0.140234	+	0.314970i	−0.829752	+	0.558132i	$0.811518\pi$
$104$	−1.50457	+	2.07087i	−0.147536	+	0.203065i
$105$	−3.19485	+	10.3969i	−0.311785	+	1.01463i
$106$	8.82310	−	2.86680i	0.856976	−	0.278448i
$107$	0.858446	+	1.92810i	0.0829891	+	0.186397i	0.950274	−	0.311416i	$-0.100803\pi$
$107$	0.858446	+	1.92810i	0.0829891	+	0.186397i	−0.867285	+	0.497813i	$0.834137\pi$
$108$	−1.62375	+	12.6883i	−0.156246	+	1.22093i
$109$	−8.25874	+	4.76818i	−0.791043	+	0.456709i	−0.840330	−	0.542076i	$-0.817639\pi$
$109$	−8.25874	+	4.76818i	−0.791043	+	0.456709i	0.0492863	+	0.998785i	$0.484305\pi$
$110$	−19.4784	+	2.04726i	−1.85719	+	0.195199i
$111$	−3.49064	−	1.58569i	−0.331317	−	0.150507i
$112$	3.94112	+	6.46946i	0.372401	+	0.611307i
$113$	8.95115	−	2.90841i	0.842054	−	0.273600i	0.143940	−	0.989586i	$-0.454023\pi$
$113$	8.95115	−	2.90841i	0.842054	−	0.273600i	0.698114	+	0.715987i	$0.254023\pi$
$114$	1.12441	−	1.52340i	0.105311	−	0.142679i
$115$	−11.8311	−	10.6528i	−1.10326	−	0.993379i
$116$	−0.140956	+	1.34111i	−0.0130874	+	0.124519i
$117$	0.940614	−	7.81653i	0.0869598	−	0.722638i
$118$	−6.88857	−	2.23823i	−0.634145	−	0.206046i
$119$	−7.78377	+	11.2619i	−0.713537	+	1.03237i
$120$	3.98462	+	0.449122i	0.363744	+	0.0409990i
$121$	−0.445447	−	4.23815i	−0.0404952	−	0.385286i
$122$	−14.4833	−	25.0857i	−1.31125	−	2.27116i
$123$	11.0820	+	0.435275i	0.999230	+	0.0392474i
$124$	−4.14532	−	2.39330i	−0.372261	−	0.214925i
$125$	8.38462	−	6.09179i	0.749944	−	0.544866i
$126$	14.5904	+	8.25905i	1.29982	+	0.735774i
$127$	2.14263	−	6.59433i	0.190127	−	0.585152i	−0.809872	−	0.586607i	$-0.800463\pi$
$127$	2.14263	−	6.59433i	0.190127	−	0.585152i	0.999999	+	0.00145529i	$0.000463233\pi$
$128$	5.64431	−	5.08216i	0.498891	−	0.449204i
$129$	6.64713	−	11.3158i	0.585248	−	0.996299i
$130$	−13.0849	−	1.37528i	−1.14762	−	0.120620i
$131$	18.2258	+	3.87400i	1.59239	+	0.338473i	0.916969	−	0.398958i	$-0.130628\pi$
$131$	18.2258	+	3.87400i	1.59239	+	0.338473i	0.675423	+	0.737431i	$0.263961\pi$
$132$	−1.86570	+	16.5526i	−0.162389	+	1.44072i
$133$	−0.712357	−	1.16935i	−0.0617692	−	0.101396i
$134$	9.00235	+	27.7064i	0.777684	+	2.39347i
$135$	−11.3771	+	4.76084i	−0.979181	+	0.409748i
$136$	4.61069	+	2.05281i	0.395363	+	0.176027i
$137$	−9.54682	−	16.5356i	−0.815640	−	1.41273i	−0.908867	−	0.417085i	$-0.863052\pi$
$137$	−9.54682	−	16.5356i	−0.815640	−	1.41273i	0.0932274	−	0.995645i	$-0.470282\pi$
$138$	−19.9615	+	14.2747i	−1.69923	+	1.21515i
$139$	−4.53559	+	6.24271i	−0.384704	+	0.529499i	−0.956823	−	0.290671i	$-0.906121\pi$
$139$	−4.53559	+	6.24271i	−0.384704	+	0.529499i	0.572119	+	0.820171i	$0.306121\pi$
$140$	7.41215	−	13.5663i	0.626441	−	1.14656i
$141$	16.0049	−	9.08062i	1.34785	−	0.764726i
$142$	13.2247	+	29.7032i	1.10979	+	2.49264i
$143$	1.07164	−	10.1959i	0.0896148	−	0.852628i
$144$	−2.77692	+	8.12842i	−0.231410	+	0.677368i
$145$	−1.18773	+	0.528813i	−0.0986359	+	0.0439155i
$146$	−6.57260	+	4.77528i	−0.543952	+	0.395205i
$147$	9.51914	−	7.50906i	0.785126	−	0.619336i
$148$	4.40848	+	3.20295i	0.362374	+	0.263280i
$149$	14.1065	+	15.6668i	1.15565	+	1.28347i	0.952573	+	0.304311i	$0.0984263\pi$
$149$	14.1065	+	15.6668i	1.15565	+	1.28347i	0.203073	+	0.979164i	$0.434907\pi$
$150$	0.926672	+	2.12419i	0.0756624	+	0.173439i
$151$	−5.28777	+	11.8765i	−0.430313	+	0.966498i	0.560108	+	0.828419i	$0.310759\pi$
$151$	−5.28777	+	11.8765i	−0.430313	+	0.966498i	−0.990421	+	0.138079i	$0.955907\pi$
$152$	−0.375134	+	0.337772i	−0.0304274	+	0.0273970i
$153$	−15.4607	+	1.39022i	−1.24992	+	0.112393i
$154$	19.1592	+	10.4679i	1.54389	+	0.843531i
$155$		−	4.61495i		−	0.370682i
$156$	−3.53778	+	10.6158i	−0.283249	+	0.849948i
$157$	−0.316654	+	3.01276i	−0.0252718	+	0.240445i	0.974593	+	0.223984i	$0.0719064\pi$
$157$	−0.316654	+	3.01276i	−0.0252718	+	0.240445i	−0.999865	+	0.0164605i	$0.994760\pi$
$158$	24.7556	+	11.0219i	1.96945	+	0.876855i
$159$	6.18777	−	4.42496i	0.490722	−	0.350922i
$160$	18.0558	+	5.86667i	1.42743	+	0.463801i
$161$	4.09746	+	17.2671i	0.322925	+	1.36084i
$162$	3.39145	+	18.7057i	0.266457	+	1.46966i
$163$	6.39416	−	11.0750i	0.500829	−	0.867461i	−0.499171	−	0.866504i	$-0.666362\pi$
$163$	6.39416	−	11.0750i	0.500829	−	0.867461i	1.00000		0.000957403i	$-0.000304751\pi$
$164$	−15.3068	−	3.76492i	−1.19526	−	0.293991i
$165$	−14.7203	+	6.42168i	−1.14597	+	0.499927i
$166$	24.9163	−	2.61881i	1.93388	−	0.203259i
$167$			5.52225i			0.427324i	0.976908	+	0.213662i	$0.0685392\pi$
$167$			5.52225i			0.427324i	−0.976908	+	0.213662i	$0.931461\pi$
$168$	−3.36924	−	2.93727i	−0.259942	−	0.226615i
$169$	−1.88903	+	5.81382i	−0.145310	+	0.447217i
$170$	2.71163	+	25.7994i	0.207973	+	1.97873i
$171$	0.501928	−	1.46921i	0.0383834	−	0.112353i
$172$	−12.4811	+	13.8617i	−0.951678	+	1.05695i
$173$	−6.20539	+	10.7481i	−0.471787	+	0.817160i	−0.999479	−	0.0322763i	$-0.989724\pi$
$173$	−6.20539	+	10.7481i	−0.471787	+	0.817160i	0.527692	+	0.849436i	$0.323058\pi$
$174$	0.401919	+	1.96337i	0.0304694	+	0.148843i
$175$	1.67547	−	0.0394641i	0.126654	−	0.00298320i
$176$	−3.45650	+	10.6380i	−0.260543	+	0.801870i
$177$	−5.93906	−	0.0446651i	−0.446407	−	0.00335724i
$178$	3.32568	+	5.76026i	0.249271	+	0.431749i
$179$	13.0215	−	2.76781i	0.973273	−	0.206876i	0.306282	−	0.951941i	$-0.400915\pi$
$179$	13.0215	−	2.76781i	0.973273	−	0.206876i	0.666992	+	0.745065i	$0.267582\pi$
$180$	17.1988	−	3.38618i	1.28192	−	0.252391i
$181$	−4.57906	−	14.0929i	−0.340359	−	1.04752i	−0.964022	−	0.265823i	$-0.914356\pi$
$181$	−4.57906	−	14.0929i	−0.340359	−	1.04752i	0.623663	−	0.781693i	$-0.285644\pi$
$182$	11.1272	+	9.55423i	0.824800	+	0.708207i
$183$	−17.5313	−	16.0256i	−1.29595	−	1.18465i
$184$	5.97691	−	2.66109i	0.440623	−	0.196178i
$185$	−0.549167	+	5.22498i	−0.0403756	+	0.384148i
$186$	−6.94691	−	1.53130i	−0.509372	−	0.112281i
$187$	−20.1033	+	2.11295i	−1.47010	+	0.154514i
$188$	−24.8740	+	8.08205i	−1.81412	+	0.589444i
$189$	13.4501	+	2.84502i	0.978353	+	0.206945i
$190$	−2.46763	−	0.801781i	−0.179021	−	0.0581673i
$191$	6.35192	−	11.0018i	0.459609	−	0.796066i	−0.539331	−	0.842094i	$-0.681323\pi$
$191$	6.35192	−	11.0018i	0.459609	−	0.796066i	0.998940	+	0.0460278i	$0.0146563\pi$
$192$	9.79857	−	16.6806i	0.707151	−	1.20382i
$193$	−2.59990	−	12.2315i	−0.187145	−	0.880446i	−0.967058	−	0.254558i	$-0.918070\pi$
$193$	−2.59990	−	12.2315i	−0.187145	−	0.880446i	0.779913	−	0.625888i	$-0.215263\pi$
$194$	1.68947	−	7.94832i	0.121297	−	0.570656i
$195$	−10.5693	+	2.16364i	−0.756887	+	0.154941i
$196$	−15.3951	+	7.74246i	−1.09965	+	0.553033i
$197$	−12.3769	+	4.02150i	−0.881817	+	0.286520i	−0.714712	−	0.699419i	$-0.753442\pi$
$197$	−12.3769	+	4.02150i	−0.881817	+	0.286520i	−0.167106	+	0.985939i	$0.553442\pi$
$198$	4.78220	+	24.2893i	0.339856	+	1.72617i
$199$	9.11007	+	4.05606i	0.645796	+	0.287527i	0.703380	−	0.710814i	$-0.251673\pi$
$199$	9.11007	+	4.05606i	0.645796	+	0.287527i	−0.0575845	+	0.998341i	$0.518340\pi$
$200$	−0.128460	−	0.604357i	−0.00908350	−	0.0427345i
$201$	13.8953	+	19.4309i	0.980099	+	1.37055i
$202$	−23.9460			−1.68483
$203$	1.42431	+	0.267857i	0.0999668	+	0.0187999i
$204$	21.9241	+	2.47115i	1.53500	+	0.173015i
$205$	−4.23535	−	14.5957i	−0.295809	−	1.01940i
$206$	−3.69557	−	6.40091i	−0.257483	−	0.445973i
$207$	−12.0714	+	16.0999i	−0.839018	+	1.11902i
$208$	−3.75699	+	6.50730i	−0.260500	+	0.451200i
$209$	0.624761	−	1.92282i	0.0432156	−	0.133004i
$210$	4.41590	−	22.5463i	0.304726	−	1.55585i
$211$	2.53552	+	3.48984i	0.174552	+	0.240251i	0.887325	−	0.461144i	$-0.152561\pi$
$211$	2.53552	+	3.48984i	0.174552	+	0.240251i	−0.712773	+	0.701395i	$0.752561\pi$
$212$	−9.87732	+	4.39767i	−0.678377	+	0.302033i
$213$	17.6903	+	19.9468i	1.21212	+	1.36673i
$214$	−2.22907	−	3.86086i	−0.152376	−	0.263923i
$215$	−17.5909	−	3.73905i	−1.19969	−	0.255001i
$216$	0.114338	−	5.06701i	0.00777969	−	0.344766i
$217$	−2.92492	+	4.23190i	−0.198557	+	0.287280i
$218$	16.2965	−	11.8401i	1.10374	−	0.801913i
$219$	−3.95608	+	5.35985i	−0.267327	+	0.362185i
$220$	22.3274	−	4.74583i	1.50531	−	0.319964i
$221$	−13.5047	−	1.41940i	−0.908423	−	0.0954791i
$222$	7.68297	+	2.56038i	0.515647	+	0.171842i
$223$	3.98503	+	5.48492i	0.266857	+	0.367298i	0.921326	−	0.388792i	$-0.127107\pi$
$223$	3.98503	+	5.48492i	0.266857	+	0.367298i	−0.654468	+	0.756089i	$0.727107\pi$
$224$	−12.8388	−	16.8233i	−0.857831	−	1.12406i
$225$	1.25019	+	1.43119i	0.0833459	+	0.0954127i
$226$	−18.1617	+	8.08611i	−1.20810	+	0.537880i
$227$	−3.35178	−	0.352286i	−0.222465	−	0.0233820i	−0.00735999	−	0.999973i	$-0.502343\pi$
$227$	−3.35178	−	0.352286i	−0.222465	−	0.0233820i	−0.215105	+	0.976591i	$0.569009\pi$
$228$	−1.11769	+	1.90270i	−0.0740205	+	0.126009i
$229$	23.7354	+	5.04512i	1.56848	+	0.333391i	0.908498	−	0.417890i	$-0.137230\pi$
$229$	23.7354	+	5.04512i	1.56848	+	0.333391i	0.659982	+	0.751281i	$0.270564\pi$
$230$	27.2060	+	19.7663i	1.79391	+	1.30335i
$231$	17.5685	+	3.44094i	1.15592	+	0.226397i
$232$		−	0.534296i		−	0.0350783i
$233$	0.991837	+	9.43670i	0.0649774	+	0.618219i	0.977753	+	0.209758i	$0.0672676\pi$
$233$	0.991837	+	9.43670i	0.0649774	+	0.618219i	−0.912776	+	0.408461i	$0.866066\pi$
$234$	−0.250119	+	16.6280i	−0.0163508	+	1.08701i
$235$	−18.7392	−	16.8729i	−1.22241	−	1.10067i
$236$	8.25698	+	1.75508i	0.537484	+	0.114246i
$237$	22.0805	+	2.48878i	1.43428	+	0.161663i
$238$	13.8649	−	25.3767i	0.898731	−	1.64492i
$239$	−18.6848	−	13.5753i	−1.20862	−	0.878112i	−0.213513	−	0.976940i	$-0.568491\pi$
$239$	−18.6848	−	13.5753i	−1.20862	−	0.878112i	−0.995104	+	0.0988284i	$0.968491\pi$
$240$	11.7704	+	0.0885201i	0.759776	+	0.00571395i
$241$	−2.75216	−	12.9479i	−0.177282	−	0.834048i	−0.973437	−	0.228955i	$-0.926469\pi$
$241$	−2.75216	−	12.9479i	−0.177282	−	0.834048i	0.796155	−	0.605093i	$-0.206864\pi$
$242$	1.87152	+	8.80480i	0.120306	+	0.565994i
$243$	7.28121	+	13.7835i	0.467090	+	0.884210i
$244$	19.8431	+	27.3117i	1.27032	+	1.74845i
$245$	−13.8862	−	9.12204i	−0.887158	−	0.582785i
$246$	−23.3763	+	1.53245i	−1.49042	+	0.0977056i
$247$	0.679075	−	1.17619i	0.0432085	−	0.0748393i
$248$	1.73257	+	0.771389i	0.110018	+	0.0489832i
$249$	18.8298	−	8.21446i	1.19329	−	0.520571i
$250$	−16.2687	+	14.6484i	−1.02892	+	0.926447i
$251$	6.88059	−	21.1763i	0.434299	−	1.33663i	−0.459504	−	0.888175i	$-0.651973\pi$
$251$	6.88059	−	21.1763i	0.434299	−	1.33663i	0.893803	−	0.448459i	$-0.148027\pi$
$252$	−17.9174	−	7.79534i	−1.12869	−	0.491060i
$253$	−15.4022	+	21.1993i	−0.968329	+	1.33279i
$254$	−3.04507	+	14.3259i	−0.191064	+	0.898888i
$255$	8.50561	+	19.4972i	0.532642	+	1.22096i
$256$	4.21236	−	4.67830i	0.263272	−	0.292394i
$257$	0.0212842	−	0.100134i	0.00132767	−	0.00624621i	−0.977479	−	0.211034i	$-0.932317\pi$
$257$	0.0212842	−	0.100134i	0.00132767	−	0.00624621i	0.978806	+	0.204788i	$0.0656503\pi$
$258$	−11.4653	+	25.2389i	−0.713798	+	1.57131i
$259$	3.81514	−	4.44324i	0.237061	−	0.276089i
$260$	15.3338			0.950961
$261$	0.800164	+	1.43536i	0.0495289	+	0.0888464i
$262$	−39.1426	−	4.11405i	−2.41824	−	0.254167i
$263$	8.99637	−	9.99148i	0.554740	−	0.616101i	−0.398921	−	0.916985i	$-0.630615\pi$
$263$	8.99637	−	9.99148i	0.554740	−	0.616101i	0.953661	+	0.300884i	$0.0972818\pi$
$264$	0.0496339	−	6.59974i	0.00305475	−	0.406186i
$265$	−8.43347	−	6.12727i	−0.518064	−	0.376395i
$266$	1.75465	+	2.29920i	0.107584	+	0.140973i
$267$	4.02558	+	3.67984i	0.246361	+	0.225203i
$268$	−13.8096	−	31.0168i	−0.843555	−	1.89466i
$269$	−1.40622	−	0.626087i	−0.0857384	−	0.0381732i	0.363419	−	0.931626i	$-0.381609\pi$
$269$	−1.40622	−	0.626087i	−0.0857384	−	0.0381732i	−0.449158	+	0.893452i	$0.648276\pi$
$270$	22.8488	−	12.5132i	1.39054	−	0.761528i
$271$	−5.85147	−	13.1426i	−0.355451	−	0.798357i	−0.999445	−	0.0333255i	$-0.989390\pi$
$271$	−5.85147	−	13.1426i	−0.355451	−	0.798357i	0.643993	−	0.765031i	$-0.277276\pi$
$272$	14.0902	+	4.57818i	0.854344	+	0.277593i
$273$	11.0634	+	4.71473i	0.669585	+	0.285348i
$274$	23.7062	+	32.6287i	1.43214	+	1.97117i
$275$	1.65584	+	1.83900i	0.0998509	+	0.110896i
$276$	21.3977	−	18.9771i	1.28799	−	1.14229i
$277$	−2.14379	+	2.38092i	−0.128808	+	0.143055i	−0.804098	−	0.594496i	$-0.797351\pi$
$277$	−2.14379	+	2.38092i	−0.128808	+	0.143055i	0.675291	+	0.737552i	$0.264018\pi$
$278$	8.14965	−	14.1156i	0.488783	−	0.846598i
$279$	−5.80968	+	0.522407i	−0.347817	+	0.0312757i
$280$	−2.35887	+	5.65271i	−0.140969	+	0.337814i
$281$	20.4884	−	14.8857i	1.22224	−	0.888007i	0.225953	−	0.974138i	$-0.427450\pi$
$281$	20.4884	−	14.8857i	1.22224	−	0.888007i	0.996284	+	0.0861312i	$0.0274504\pi$
$282$	−31.6168	+	22.6096i	−1.88275	+	1.34638i
$283$	−3.32779	−	15.6560i	−0.197817	−	0.930654i	−0.959282	−	0.282449i	$-0.908853\pi$
$283$	−3.32779	−	15.6560i	−0.197817	−	0.930654i	0.761466	−	0.648205i	$-0.224480\pi$
$284$	−18.9469	−	32.8169i	−1.12429	−	1.94733i
$285$	−2.12749	−	0.0160000i	−0.126022	−	0.000947757i
$286$			21.6554i			1.28051i
$287$	−5.36682	+	16.0685i	−0.316793	+	0.948495i
$288$	5.34156	−	23.3942i	0.314755	−	1.37852i
$289$	1.02164	+	9.72030i	0.0600967	+	0.571782i
$290$	2.37834	−	1.37313i	0.139661	−	0.0806331i
$291$	−0.646632	−	6.63167i	−0.0379062	−	0.388755i
$292$	7.03635	−	6.33555i	0.411771	−	0.370760i
$293$	−6.94504	−	9.55902i	−0.405733	−	0.558444i	0.556438	−	0.830889i	$-0.312168\pi$
$293$	−6.94504	−	9.55902i	−0.405733	−	0.558444i	−0.962171	+	0.272445i	$0.912168\pi$
$294$	−18.3391	+	17.8762i	−1.06956	+	1.04256i
$295$	2.51500	+	7.74039i	0.146429	+	0.450663i
$296$	−1.86980	−	1.07953i	−0.108680	−	0.0627462i
$297$	9.75046	+	17.8042i	0.565779	+	1.03310i
$298$	−33.0928	−	29.7969i	−1.91702	−	1.72609i
$299$	−13.0814	+	11.7785i	−0.756517	+	0.681171i
$300$	−1.33285	−	2.34919i	−0.0769521	−	0.135630i
$301$	13.7610	+	14.5777i	0.793171	+	0.840243i
$302$	8.48585	−	26.1168i	0.488306	−	1.50285i
$303$	−18.7195	+	5.92706i	−1.07541	+	0.340501i
$304$	−0.991515	+	1.10119i	−0.0568673	+	0.0631575i
$305$	−13.2386	+	29.7345i	−0.758042	+	1.70259i
$306$	32.1715	−	6.33410i	1.83912	−	0.362096i
$307$	3.34668	−	4.60631i	0.191005	−	0.262896i	−0.702764	−	0.711423i	$-0.748051\pi$
$307$	3.34668	−	4.60631i	0.191005	−	0.262896i	0.893769	+	0.448527i	$0.148051\pi$
$308$	−23.4820	−	9.79902i	−1.33801	−	0.558351i
$309$	−4.47331	−	4.08912i	−0.254478	−	0.232622i
$310$	1.01896	+	9.69471i	0.0578728	+	0.550623i
$311$	10.7131	+	9.64609i	0.607482	+	0.546980i	0.914429	−	0.404747i	$-0.132641\pi$
$311$	10.7131	+	9.64609i	0.607482	+	0.546980i	−0.306946	+	0.951727i	$0.599307\pi$
$312$	0.954383	−	4.32965i	0.0540313	−	0.245118i
$313$	7.46453	+	8.29020i	0.421920	+	0.468590i	0.916205	−	0.400710i	$-0.131237\pi$
$313$	7.46453	+	8.29020i	0.421920	+	0.468590i	−0.494285	+	0.869300i	$0.664570\pi$
$314$		−	6.39889i		−	0.361110i
$315$	−2.12855	−	18.7183i	−0.119930	−	1.05466i
$316$	−30.0361	−	9.75931i	−1.68966	−	0.549004i
$317$	−5.42176	−	1.15243i	−0.304517	−	0.0647270i	0.0531191	−	0.998588i	$-0.483084\pi$
$317$	−5.42176	−	1.15243i	−0.304517	−	0.0647270i	−0.357636	+	0.933861i	$0.616417\pi$
$318$	−12.0218	+	10.6618i	−0.674147	+	0.597886i
$319$	1.06997	+	1.85324i	0.0599066	+	0.103761i
$320$	−25.9307	−	5.51175i	−1.44957	−	0.308116i
$321$	−2.69818	−	2.46644i	−0.150598	−	0.137663i
$322$	−12.4201	−	35.3686i	−0.692144	−	1.97102i
$323$	−2.54680	−	0.827505i	−0.141708	−	0.0460436i
$324$	−6.20969	−	21.2679i	−0.344983	−	1.18155i
$325$	0.831177	+	1.43964i	0.0461054	+	0.0798569i
$326$	−10.9870	+	24.6773i	−0.608515	+	1.36675i
$327$	9.80895	−	13.2895i	0.542436	−	0.734912i
$328$	6.18751	+	0.849608i	0.341648	+	0.0469118i
$329$	6.48993	+	27.3492i	0.357801	+	1.50781i
$330$	29.5053	−	16.7403i	1.62421	−	0.921523i
$331$	−27.8854	−	16.0996i	−1.53272	−	0.884916i	−0.999235	−	0.0391063i	$-0.987549\pi$
$331$	−27.8854	−	16.0996i	−1.53272	−	0.884916i	−0.533485	−	0.845810i	$-0.679118\pi$
$332$	−28.5607	+	6.07076i	−1.56747	+	0.333176i
$333$	6.63980	+	0.0998759i	0.363859	+	0.00547317i
$334$	−1.21928	−	11.6007i	−0.0667161	−	0.634762i
$335$	19.2409	−	26.4828i	1.05124	−	1.44691i
$336$	−10.7373	−	7.54117i	−0.585769	−	0.411404i
$337$	6.95676			0.378959			0.189479	−	0.981885i	$-0.439320\pi$
$337$	6.95676			0.378959			0.189479	+	0.981885i	$0.439320\pi$
$338$	2.68465	−	12.6303i	0.146026	−	0.686997i
$339$	−12.1962	+	10.8166i	−0.662408	+	0.587475i
$340$	−6.28592	−	29.5729i	−0.340902	−	1.60382i
$341$	−7.55427	+	0.793986i	−0.409087	+	0.0429968i
$342$	−0.730016	+	3.19722i	−0.0394748	+	0.172886i
$343$	6.95216	+	17.1659i	0.375381	+	0.926870i
$344$	4.34405	−	5.97907i	0.234215	−	0.322370i
$345$	26.1605	+	8.71809i	1.40843	+	0.469366i
$346$	10.6627	−	23.9488i	0.573229	−	1.28749i
$347$	−0.307124	+	2.92209i	−0.0164873	+	0.156866i	−0.999668	−	0.0257698i	$-0.991796\pi$
$347$	−0.307124	+	2.92209i	−0.0164873	+	0.156866i	0.983181	+	0.182636i	$0.0584630\pi$
$348$	−0.705034	−	2.22671i	−0.0377938	−	0.119364i
$349$	3.76638	−	5.18398i	0.201610	−	0.277492i	−0.696226	−	0.717823i	$-0.745139\pi$
$349$	3.76638	−	5.18398i	0.201610	−	0.277492i	0.897836	+	0.440331i	$0.145139\pi$
$350$	−3.51099	+	0.452838i	−0.187670	+	0.0242052i
$351$	3.92021	+	13.0607i	0.209245	+	0.697126i
$352$	6.49680	−	30.5651i	0.346281	−	1.62912i
$353$	−0.407345	+	3.87563i	−0.0216808	+	0.206279i	−1.00000		0.000825286i	$-0.999737\pi$
$353$	−0.407345	+	3.87563i	−0.0216808	+	0.206279i	0.978319	+	0.207104i	$0.0664040\pi$
$354$	12.4862	−	1.21748i	0.663632	−	0.0647085i
$355$	18.2674	−	31.6401i	0.969532	−	1.67928i
$356$	−4.55642	−	6.27137i	−0.241490	−	0.332382i
$357$	4.55757	−	23.2697i	0.241212	−	1.23156i
$358$	−26.7434	+	8.68946i	−1.41343	+	0.459252i
$359$	1.29749	−	6.10421i	0.0684789	−	0.322168i	−0.930553	−	0.366157i	$-0.880673\pi$
$359$	1.29749	−	6.10421i	0.0684789	−	0.322168i	0.999032	+	0.0439890i	$0.0140067\pi$
$360$	−6.63687	+	2.04661i	−0.349794	+	0.107866i
$361$	−12.5343	+	13.9207i	−0.659698	+	0.732669i
$362$	12.7309	+	28.5942i	0.669124	+	1.50288i
$363$	3.64238	+	6.41981i	0.191176	+	0.336953i
$364$	−14.0610	−	9.71844i	−0.736999	−	0.509385i
$365$	8.68199	+	2.82095i	0.454436	+	0.147655i
$366$	40.3667	+	29.7945i	2.11000	+	1.55738i
$367$	0.669956	−	1.50475i	0.0349714	−	0.0785471i	−0.895215	−	0.445634i	$-0.852978\pi$
$367$	0.669956	−	1.50475i	0.0349714	−	0.0785471i	0.930187	+	0.367087i	$0.119645\pi$
$368$	16.6323	−	9.60266i	0.867019	−	0.500573i
$369$	−17.8948	+	6.98402i	−0.931565	+	0.363574i
$370$		−	11.0975i		−	0.576930i
$371$	3.85005	+	10.9638i	0.199885	+	0.569211i
$372$	8.23847	+	0.928590i	0.427145	+	0.0481452i
$373$	1.49286	+	1.65799i	0.0772973	+	0.0858474i	0.780553	−	0.625090i	$-0.214938\pi$
$373$	1.49286	+	1.65799i	0.0772973	+	0.0858474i	−0.703256	+	0.710937i	$0.748271\pi$
$374$	41.7649	−	8.87741i	2.15961	−	0.459040i
$375$	−9.09211	+	15.4780i	−0.469515	+	0.799281i
$376$	9.46677	−	4.21488i	0.488212	−	0.217366i
$377$	0.444221	+	1.36717i	0.0228785	+	0.0704129i
$378$	−28.8831	−	3.00688i	−1.48559	−	0.154657i
$379$	1.09397	+	3.36691i	0.0561937	+	0.172946i	0.975214	−	0.221264i	$-0.0710182\pi$
$379$	1.09397	+	3.36691i	0.0561937	+	0.172946i	−0.919020	+	0.394210i	$0.871018\pi$
$380$	2.95782	+	0.628705i	0.151733	+	0.0322519i
$381$	1.16548	+	11.9528i	0.0597092	+	0.612361i
$382$	−10.9145	+	24.5143i	−0.558432	+	1.25426i
$383$	7.09790	+	4.09798i	0.362686	+	0.209397i	0.670258	−	0.742128i	$-0.266183\pi$
$383$	7.09790	+	4.09798i	0.362686	+	0.209397i	−0.307572	+	0.951525i	$0.599517\pi$
$384$	−5.44094	+	11.9773i	−0.277657	+	0.611215i
$385$	−3.13809	−	24.3306i	−0.159932	−	1.24000i
$386$	8.16231	+	25.1210i	0.415451	+	1.27863i
$387$	−2.71577	+	22.5681i	−0.138050	+	1.14720i
$388$	−0.989918	+	9.41844i	−0.0502555	+	0.478149i
$389$	−19.7413	−	2.07489i	−1.00092	−	0.105201i	−0.410132	−	0.912026i	$-0.634517\pi$
$389$	−19.7413	−	2.07489i	−1.00092	−	0.105201i	−0.590791	+	0.806825i	$0.701184\pi$
$390$	21.7255	−	6.87885i	1.10011	−	0.348324i
$391$	28.0788	+	20.4005i	1.42001	+	1.03170i
$392$	5.74573	−	3.68849i	0.290203	−	0.186297i
$393$	−31.6175	+	6.47238i	−1.59489	+	0.326488i
$394$	25.1125	−	11.1808i	1.26515	−	0.563280i
$395$	−6.33075	−	29.7838i	−0.318535	−	1.49859i
$396$	−8.50188	−	27.5703i	−0.427235	−	1.38546i
$397$	−0.922727	−	8.77916i	−0.0463103	−	0.440613i	−0.992969	−	0.118375i	$-0.962231\pi$
$397$	−0.922727	−	8.77916i	−0.0463103	−	0.440613i	0.946659	−	0.322238i	$-0.104435\pi$
$398$	−20.0333	−	6.50920i	−1.00418	−	0.326277i
$399$	1.94077	+	1.36306i	0.0971599	+	0.0682385i
$400$	−0.560463	−	1.72493i	−0.0280232	−	0.0862464i
$401$	1.53920	+	0.888660i	0.0768642	+	0.0443776i	0.537940	−	0.842983i	$-0.319203\pi$
$401$	1.53920	+	0.888660i	0.0768642	+	0.0443776i	−0.461075	+	0.887361i	$0.652536\pi$
$402$	−33.4803	−	37.7508i	−1.66985	−	1.88284i
$403$	−5.07468	−	0.533370i	−0.252788	−	0.0265691i
$404$	27.7550	−	2.91717i	1.38086	−	0.145134i
$405$	14.7646	−	15.4375i	0.733657	−	0.767096i
$406$	−3.05121	−	0.248213i	−0.151429	−	0.0123186i
$407$	8.64732			0.428632
$408$	−8.74146	−	0.0657408i	−0.432767	−	0.00325465i
$409$	25.5162	−	14.7318i	1.26169	−	0.728440i	0.288292	−	0.957542i	$-0.406913\pi$
$409$	25.5162	−	14.7318i	1.26169	−	0.728440i	0.973402	+	0.229103i	$0.0735792\pi$
$410$	12.1199	+	29.7262i	0.598560	+	1.46807i
$411$	26.6082	+	19.6394i	1.31249	+	0.968740i
$412$	5.06319	+	6.96888i	0.249445	+	0.343332i
$413$	2.59955	−	8.69191i	0.127915	−	0.427701i
$414$	21.8038	−	36.4867i	1.07160	−	1.79322i
$415$	−18.8371	−	20.9207i	−0.924677	−	1.02696i
$416$	8.53788	−	19.1764i	0.418604	−	0.940200i
$417$	2.87702	−	13.0519i	0.140888	−	0.639154i
$418$	−0.887900	+	4.17724i	−0.0434286	+	0.204316i
$419$	−26.8445			−1.31144			−0.655720	−	0.755004i	$-0.727635\pi$
$419$	−26.8445			−1.31144			−0.655720	+	0.755004i	$0.727635\pi$
$420$	−2.37166	+	26.6707i	−0.115725	+	1.30140i
$421$	−21.8918	+	7.11306i	−1.06694	+	0.346669i	−0.789295	−	0.614015i	$-0.789554\pi$
$421$	−21.8918	+	7.11306i	−1.06694	+	0.346669i	−0.277644	+	0.960684i	$0.589554\pi$
$422$	−6.09695	−	6.77135i	−0.296795	−	0.329624i
$423$	−19.1197	+	25.5005i	−0.929633	+	1.23988i
$424$	3.70999	−	2.14196i	0.180173	−	0.104023i
$425$	2.43578	−	2.19319i	0.118153	−	0.106385i
$426$	−41.5666	−	37.9966i	−2.01391	−	1.84094i
$427$	30.9853	−	18.8759i	1.49948	−	0.913468i
$428$	3.05398	+	4.20344i	0.147620	+	0.203181i
$429$	5.36011	+	16.9289i	0.258788	+	0.817333i
$430$	37.7790	+	3.97073i	1.82187	+	0.191486i
$431$	8.34687	+	0.877291i	0.402054	+	0.0422576i	0.303398	−	0.952864i	$-0.401879\pi$
$431$	8.34687	+	0.877291i	0.402054	+	0.0422576i	0.0986565	+	0.995122i	$0.468546\pi$
$432$	−1.22096	−	14.8276i	−0.0587434	−	0.713392i
$433$	9.49752	+	13.0722i	0.456422	+	0.628211i	0.973762	−	0.227569i	$-0.0730778\pi$
$433$	9.49752	+	13.0722i	0.456422	+	0.628211i	−0.517340	+	0.855780i	$0.673078\pi$
$434$	5.21006	−	9.53584i	0.250091	−	0.457735i
$435$	1.51936	−	1.66211i	0.0728477	−	0.0796921i
$436$	−17.4463	+	15.7087i	−0.835528	+	0.752313i
$437$	−3.00628	+	1.73568i	−0.143810	+	0.0830287i
$438$	7.12720	−	12.1330i	0.340551	−	0.579738i
$439$	−23.0475	−	25.5969i	−1.10000	−	1.22167i	−0.973253	−	0.229736i	$-0.926214\pi$
$439$	−23.0475	−	25.5969i	−1.10000	−	1.22167i	−0.126745	−	0.991935i	$-0.540453\pi$
$440$	−8.60146	+	2.79478i	−0.410058	+	0.133236i
$441$	−9.91167	+	18.5137i	−0.471984	+	0.881607i
$442$	28.6829			1.36431
$443$	4.73963	−	22.2982i	0.225187	−	1.05942i	−0.709709	−	0.704495i	$-0.751173\pi$
$443$	4.73963	−	22.2982i	0.225187	−	1.05942i	0.934895	−	0.354924i	$-0.115493\pi$
$444$	−9.21698	−	2.03169i	−0.437419	−	0.0964200i
$445$	3.03989	−	6.82770i	0.144105	−	0.323664i
$446$	−9.58247	−	10.6424i	−0.453743	−	0.503933i
$447$	−33.2452	−	15.1023i	−1.57244	−	0.714315i
$448$	20.2851	+	21.4890i	0.958382	+	1.01526i
$449$	−8.59559	−	11.8308i	−0.405651	−	0.558331i	0.556500	−	0.830848i	$-0.312144\pi$
$449$	−8.59559	−	11.8308i	−0.405651	−	0.558331i	−0.962151	+	0.272517i	$0.912144\pi$
$450$	−2.94229	−	2.73049i	−0.138701	−	0.128717i
$451$	−23.1631	+	9.44403i	−1.09071	+	0.444702i
$452$	20.0655	−	11.5848i	0.943804	−	0.544905i
$453$	0.169340	−	22.5169i	0.00795627	−	1.05793i
$454$	7.11892			0.334108
$455$	1.33620	−	16.4255i	0.0626418	−	0.770039i
$456$	0.361618	−	0.796040i	0.0169343	−	0.0372780i
$457$	−17.2826	+	1.81648i	−0.808447	+	0.0849712i	−0.499728	−	0.866182i	$-0.666567\pi$
$457$	−17.2826	+	1.81648i	−0.808447	+	0.0849712i	−0.308719	+	0.951153i	$0.599900\pi$
$458$	−50.9754	−	5.35773i	−2.38192	−	0.250350i
$459$	23.5819	−	12.9146i	1.10071	−	0.602803i
$460$	−33.9415	−	19.5962i	−1.58253	−	0.913675i
$461$	−6.94697	−	21.3806i	−0.323552	−	0.995792i	−0.972090	−	0.234609i	$-0.924619\pi$
$461$	−6.94697	−	21.3806i	−0.323552	−	0.995792i	0.648537	−	0.761183i	$-0.275381\pi$
$462$	−37.6662	−	3.34942i	−1.75239	−	0.155829i
$463$	21.9343	+	7.12688i	1.01937	+	0.331214i	0.770581	−	0.637342i	$-0.219966\pi$
$463$	21.9343	+	7.12688i	1.01937	+	0.331214i	0.248792	+	0.968557i	$0.419966\pi$
$464$	−0.163943	−	1.55981i	−0.00761085	−	0.0724124i
$465$	3.19617	+	7.32651i	0.148219	+	0.339759i
$466$	−4.16714	−	19.6049i	−0.193039	−	0.908178i
$467$	1.97051	−	0.877327i	0.0911842	−	0.0405978i	−0.360638	−	0.932706i	$-0.617441\pi$
$467$	1.97051	−	0.877327i	0.0911842	−	0.0405978i	0.451822	+	0.892108i	$0.350774\pi$
$468$	−1.73577	−	19.3034i	−0.0802359	−	0.892302i
$469$	−34.4285	+	12.0900i	−1.58976	+	0.558262i
$470$	43.0913	+	31.3077i	1.98765	+	1.44412i
$471$	−1.58384	−	5.00225i	−0.0729795	−	0.230492i
$472$	−3.32632	−	0.349610i	−0.153106	−	0.0160921i
$473$	−3.09406	+	29.4380i	−0.142265	+	1.35356i
$474$	−46.9344	−	0.352974i	−2.15577	−	0.0162126i
$475$	0.101304	+	0.311780i	0.00464812	+	0.0143055i
$476$	−12.9789	+	31.1023i	−0.594889	+	1.42557i
$477$	−6.75886	+	11.3104i	−0.309467	+	0.517865i
$478$	42.2488	+	24.3924i	1.93242	+	1.11568i
$479$	−12.8586	+	28.8809i	−0.587525	+	1.31960i	0.338081	+	0.941117i	$0.390222\pi$
$479$	−12.8586	+	28.8809i	−0.587525	+	1.31960i	−0.925607	+	0.378487i	$0.876445\pi$
$480$	−32.7277	+	3.19116i	−1.49381	+	0.145656i
$481$	5.68201	+	1.20775i	0.259077	+	0.0550686i
$482$	8.64035	+	26.5923i	0.393557	+	1.21124i
$483$	−18.4636	−	24.5748i	−0.840124	−	1.11819i
$484$	−3.24184	−	9.97736i	−0.147356	−	0.453516i
$485$	−8.34131	+	3.71379i	−0.378759	+	0.168635i
$486$	−18.3391	−	27.3475i	−0.831878	−	1.24051i
$487$	29.5368	−	6.27825i	1.33844	−	0.284494i	0.517586	−	0.855631i	$-0.326831\pi$
$487$	29.5368	−	6.27825i	1.33844	−	0.284494i	0.820855	+	0.571137i	$0.193497\pi$
$488$	−8.95023	−	9.94023i	−0.405158	−	0.449973i
$489$	−2.48090	+	22.0106i	−0.112190	+	0.995355i
$490$	31.1852	+	16.0968i	1.40880	+	0.727181i
$491$			31.4654i			1.42001i	0.704195	+	0.710007i	$0.251308\pi$
$491$			31.4654i			1.42001i	−0.704195	+	0.710007i	$0.748692\pi$
$492$	26.9079	−	4.62398i	1.21310	−	0.208465i
$493$	2.45464	−	1.41719i	0.110551	−	0.0638269i
$494$	−1.16685	+	2.62078i	−0.0524990	+	0.117915i
$495$	18.9219	−	20.3896i	0.850474	−	0.916445i
$496$	5.29470	+	1.72035i	0.237739	+	0.0772462i
$497$	−36.8044	+	17.4361i	−1.65090	+	0.782117i
$498$	−37.7425	+	21.4138i	−1.69128	+	0.959576i
$499$	−8.75009	−	19.6530i	−0.391708	−	0.879791i	−0.996515	−	0.0834182i	$-0.973416\pi$
$499$	−8.75009	−	19.6530i	−0.391708	−	0.879791i	0.604807	−	0.796372i	$-0.293250\pi$
$500$	17.0720	−	18.9604i	0.763483	−	0.847934i
$501$	−3.82454	−	8.76690i	−0.170868	−	0.391676i
$502$	−9.77858	+	46.0046i	−0.436439	+	2.05329i
$503$	24.2742	−	7.88715i	1.08233	−	0.351671i	0.287053	−	0.957915i	$-0.407324\pi$
$503$	24.2742	−	7.88715i	1.08233	−	0.351671i	0.795279	+	0.606244i	$0.207324\pi$
$504$	7.38312	+	2.32966i	0.328871	+	0.103771i
$505$	15.8156	+	21.7683i	0.703783	+	0.968675i
$506$	27.6750	−	47.9346i	1.23031	−	2.13095i
$507$	−1.02753	−	10.5381i	−0.0456343	−	0.468012i
$508$	1.78421	−	16.9756i	0.0791616	−	0.753172i
$509$	6.46697	−	30.4247i	0.286643	−	1.34855i	−0.565286	−	0.824895i	$-0.691234\pi$
$509$	6.46697	−	30.4247i	0.286643	−	1.34855i	0.851930	−	0.523656i	$-0.175432\pi$
$510$	−22.1728	−	39.0802i	−0.981827	−	1.73050i
$511$	−6.17347	−	8.08939i	−0.273098	−	0.357854i
$512$	−16.7447	+	23.0471i	−0.740018	+	1.01855i
$513$	0.220688	+	2.68008i	0.00974361	+	0.118328i
$514$	−0.0226030	+	0.215054i	−0.000996977	+	0.00948561i
$515$	−3.37799	+	7.58709i	−0.148852	+	0.334327i
$516$	10.2144	−	30.6503i	0.449662	−	1.34931i
$517$	−24.3954	+	33.5774i	−1.07291	+	1.47673i
$518$	−7.03350	+	10.1764i	−0.309034	+	0.447123i
$519$	2.40767	−	21.3609i	0.105685	−	0.937638i
$520$	−6.04222	+	0.635063i	−0.264969	+	0.0278493i
$521$	4.24823	+	19.9864i	0.186118	+	0.875619i	0.967757	+	0.251887i	$0.0810510\pi$
$521$	4.24823	+	19.9864i	0.186118	+	0.875619i	−0.781638	+	0.623732i	$0.785616\pi$
$522$	−1.99784	−	2.83861i	−0.0874430	−	0.124243i
$523$	6.80446	−	32.0125i	0.297538	−	1.39981i	−0.534538	−	0.845145i	$-0.679514\pi$
$523$	6.80446	−	32.0125i	0.297538	−	1.39981i	0.832076	−	0.554662i	$-0.187152\pi$
$524$	45.8700			2.00384
$525$	−2.63258	+	1.22303i	−0.114895	+	0.0533775i
$526$	−16.6928	+	22.9756i	−0.727840	+	1.00179i
$527$	1.05165	+	10.0057i	0.0458104	+	0.435857i
$528$	−1.88016	−	19.2823i	−0.0818233	−	0.839156i
$529$	21.5111	−	4.57233i	0.935265	−	0.198797i
$530$	19.0692	+	11.0096i	0.828314	+	0.478227i
$531$	9.45955	−	4.04230i	0.410510	−	0.175421i
$532$	−2.31385	−	2.45117i	−0.100318	−	0.106272i
$533$	−16.5391	+	2.97038i	−0.716390	+	0.128661i
$534$	−9.26910	−	6.84149i	−0.401113	−	0.296060i
$535$	−2.03751	+	4.57633i	−0.0880893	+	0.197852i
$536$	6.72620	+	11.6501i	0.290528	+	0.503209i
$537$	−18.7555	+	13.4124i	−0.809361	+	0.578786i
$538$	3.09230	+	1.00475i	0.133319	+	0.0433178i
$539$	−12.5429	+	24.3000i	−0.540261	+	1.04667i
$540$	−24.9589	+	17.2871i	−1.07406	+	0.743919i
$541$	11.2509	+	2.39145i	0.483713	+	0.102816i	0.443312	−	0.896367i	$-0.353803\pi$
$541$	11.2509	+	2.39145i	0.483713	+	0.102816i	0.0404008	+	0.999184i	$0.487137\pi$
$542$	15.1941	+	26.3170i	0.652643	+	1.13041i
$543$	17.0298	+	19.2020i	0.730820	+	0.824037i
$544$	−40.4839	−	8.60511i	−1.73573	−	0.368941i
$545$	−21.5266	−	6.99443i	−0.922100	−	0.299609i
$546$	−24.2820	−	7.46158i	−1.03917	−	0.319326i
$547$		−	3.52767i		−	0.150832i	−0.997152	−	0.0754161i	$-0.975972\pi$
$547$		−	3.52767i		−	0.150832i	0.997152	−	0.0754161i	$-0.0240285\pi$
$548$	−31.4519	−	34.9309i	−1.34356	−	1.49217i
$549$	38.9308	+	13.3000i	1.66153	+	0.567630i
$550$	−3.88450	−	3.49762i	−0.165635	−	0.149139i
$551$	0.0296326	+	0.281935i	0.00126239	+	0.0120108i
$552$	−7.64571	+	8.36406i	−0.325423	+	0.355998i
$553$	−13.0715	+	31.3241i	−0.555857	+	1.33204i
$554$	3.97780	−	5.47497i	0.169000	−	0.232609i
$555$	−2.74682	−	8.67531i	−0.116596	−	0.368246i
$556$	−7.72638	+	17.3537i	−0.327672	+	0.735963i
$557$	7.88077	−	8.75248i	0.333919	−	0.370854i	−0.552680	−	0.833394i	$-0.686395\pi$
$557$	7.88077	−	8.75248i	0.333919	−	0.370854i	0.886599	+	0.462539i	$0.153062\pi$
$558$	12.0892	−	2.38018i	0.511775	−	0.100761i
$559$	−6.14458	+	18.9111i	−0.259888	+	0.799854i
$560$	−5.15195	+	17.2262i	−0.217709	+	0.727938i
$561$	30.4519	−	17.2774i	1.28568	−	0.729451i
$562$	−39.7537	+	35.7944i	−1.67691	+	1.50990i
$563$	24.9328	+	22.4496i	1.05079	+	0.946136i	0.998621	−	0.0525019i	$-0.0167195\pi$
$563$	24.9328	+	22.4496i	1.05079	+	0.946136i	0.0521701	+	0.998638i	$0.483386\pi$
$564$	33.8916	−	30.0577i	1.42709	−	1.26566i
$565$	19.3460	+	11.1694i	0.813891	+	0.469900i
$566$	10.4475	+	32.1542i	0.439142	+	1.35154i
$567$	−23.3233	+	4.79850i	−0.979485	+	0.201518i
$568$	8.82508	+	12.1467i	0.370292	+	0.509663i
$569$	17.0399	−	15.3428i	0.714349	−	0.643203i	−0.229603	−	0.973284i	$-0.573743\pi$
$569$	17.0399	−	15.3428i	0.714349	−	0.643203i	0.943953	+	0.330081i	$0.107076\pi$
$570$	4.47280	−	0.436127i	0.187345	−	0.0182674i
$571$	6.40475	−	3.69779i	0.268031	−	0.154748i	−0.359962	−	0.932967i	$-0.617210\pi$
$571$	6.40475	−	3.69779i	0.268031	−	0.154748i	0.627992	+	0.778220i	$0.283877\pi$
$572$	−2.63812	−	25.1001i	−0.110306	−	1.04949i
$573$	−2.46452	+	21.8652i	−0.102957	+	0.913434i
$574$	7.72634	−	34.9404i	0.322491	−	1.45838i
$575$		−	4.24889i		−	0.177191i
$576$	−4.00332	+	33.2677i	−0.166805	+	1.38615i
$577$	−6.82004	−	11.8127i	−0.283922	−	0.491767i	0.688425	−	0.725307i	$-0.258302\pi$
$577$	−6.82004	−	11.8127i	−0.283922	−	0.491767i	−0.972347	+	0.233540i	$0.924969\pi$
$578$	−4.29238	−	20.1940i	−0.178539	−	0.839961i
$579$	12.5987	+	17.6177i	0.523583	+	0.732167i
$580$	−2.58937	+	1.88129i	−0.107518	+	0.0781162i
$581$	4.01418	+	31.1231i	0.166536	+	1.29120i
$582$	2.82263	+	13.7885i	0.117002	+	0.571552i
$583$	−8.57887	+	14.8590i	−0.355300	+	0.615398i
$584$	−2.51025	+	2.78792i	−0.103875	+	0.115365i
$585$	15.2810	−	10.7549i	0.631792	−	0.444661i
$586$	16.7002	+	18.5474i	0.689877	+	0.766186i
$587$	26.6851	+	36.7289i	1.10141	+	1.51596i	0.833499	+	0.552521i	$0.186334\pi$
$587$	26.6851	+	36.7289i	1.10141	+	1.51596i	0.267914	+	0.963443i	$0.413666\pi$
$588$	19.0785	−	22.9538i	0.786784	−	0.946599i
$589$	−0.957016	−	0.310953i	−0.0394331	−	0.0128126i
$590$	−6.99235	−	15.7051i	−0.287871	−	0.646568i
$591$	16.8639	−	14.9562i	0.693688	−	0.615217i
$592$	−5.78987	−	2.57782i	−0.237962	−	0.105948i
$593$	−4.82866	−	10.8453i	−0.198289	−	0.445365i	0.786845	−	0.617150i	$-0.211713\pi$
$593$	−4.82866	−	10.8453i	−0.198289	−	0.445365i	−0.985134	+	0.171786i	$0.945046\pi$
$594$	−24.4140	−	35.2487i	−1.00172	−	1.44627i
$595$	−32.2262	+	4.15645i	−1.32114	+	0.170398i
$596$	41.9868	+	30.5052i	1.71984	+	1.24954i
$597$	−17.2719	−	0.129895i	−0.706891	−	0.00531623i
$598$	24.8797	−	27.6317i	1.01741	−	1.12994i
$599$	−28.9366	−	3.04136i	−1.18232	−	0.124267i	−0.507101	−	0.861887i	$-0.669283\pi$
$599$	−28.9366	−	3.04136i	−1.18232	−	0.124267i	−0.675216	+	0.737620i	$0.735950\pi$
$600$	0.622497	+	0.870486i	0.0254134	+	0.0355375i
$601$	6.36225			0.259522			0.129761	−	0.991545i	$-0.458579\pi$
$601$	6.36225			0.259522			0.129761	+	0.991545i	$0.458579\pi$
$602$	−32.1267	−	27.5852i	−1.30938	−	1.12429i
$603$	−35.5168	−	21.2242i	−1.44636	−	0.864317i
$604$	−6.65405	+	31.3048i	−0.270749	+	1.27378i
$605$	6.76799	−	7.51661i	0.275158	−	0.305594i
$606$	38.0157	−	16.5842i	1.54428	−	0.673689i
$607$	−3.33428	+	15.6865i	−0.135334	+	0.636697i	0.857226	+	0.514941i	$0.172186\pi$
$607$	−3.33428	+	15.6865i	−0.135334	+	0.636697i	−0.992560	+	0.121757i	$0.961147\pi$
$608$	2.43318	−	3.34898i	0.0986784	−	0.135819i
$609$	−2.44668	+	0.561192i	−0.0991446	+	0.0227407i
$610$	21.2454	−	65.3868i	0.860203	−	2.64743i
$611$	−20.7195	+	18.6559i	−0.838222	+	0.754738i
$612$	−36.5173	+	11.2609i	−1.47612	+	0.455193i
$613$	22.9496	+	10.2178i	0.926926	+	0.412694i	0.813971	−	0.580906i	$-0.197302\pi$
$613$	22.9496	+	10.2178i	0.926926	+	0.412694i	0.112955	+	0.993600i	$0.463968\pi$
$614$	−6.01339	+	10.4155i	−0.242680	+	0.420335i
$615$	16.8324	+	20.2382i	0.678747	+	0.816083i
$616$	9.65883	+	2.88873i	0.389166	+	0.116390i
$617$	−23.6047	−	32.4891i	−0.950290	−	1.30796i	−0.951398	−	0.307963i	$-0.900353\pi$
$617$	−23.6047	−	32.4891i	−0.950290	−	1.30796i	0.00110793	−	0.999999i	$-0.499647\pi$
$618$	10.3000	+	7.60240i	0.414327	+	0.305813i
$619$	−0.277863	−	1.30724i	−0.0111683	−	0.0525425i	0.972211	−	0.234108i	$-0.0752169\pi$
$619$	−0.277863	−	1.30724i	−0.0111683	−	0.0525425i	−0.983379	+	0.181565i	$0.941884\pi$
$620$	−2.36207	−	11.1127i	−0.0948632	−	0.446296i
$621$	8.01373	−	33.9198i	0.321580	−	1.36116i
$622$	−24.6350	−	17.8983i	−0.987772	−	0.717658i
$623$	−7.11492	+	4.33433i	−0.285053	+	0.173651i
$624$	1.45770	−	12.9327i	0.0583545	−	0.517723i
$625$	27.1592	+	5.77287i	1.08637	+	0.230915i
$626$	−17.5113	−	15.7673i	−0.699893	−	0.630186i
$627$	0.339837	+	3.48528i	0.0135718	+	0.139189i
$628$	0.779530	+	7.41674i	0.0311066	+	0.295960i
$629$		−	11.4535i		−	0.456681i
$630$	8.60440	+	38.8520i	0.342808	+	1.54790i
$631$	−34.3348	−	24.9457i	−1.36685	−	0.993072i	−0.997976	−	0.0635909i	$-0.979745\pi$
$631$	−34.3348	−	24.9457i	−1.36685	−	0.993072i	−0.368870	−	0.929481i	$-0.620255\pi$
$632$	12.2398	+	2.60165i	0.486873	+	0.103488i
$633$	−6.44225	−	3.78431i	−0.256056	−	0.150413i
$634$	11.6441	+	1.22384i	0.462444	+	0.0486049i
$635$	15.0342	−	6.69367i	0.596616	−	0.265630i
$636$	12.6352	−	13.8223i	0.501017	−	0.548090i
$637$	−11.6357	+	14.2153i	−0.461021	+	0.563230i
$638$	−2.65688	−	3.65689i	−0.105187	−	0.144778i
$639$	−41.8990	−	19.4149i	−1.65750	−	0.768041i
$640$	17.9283	+	1.88434i	0.708678	+	0.0744851i
$641$	34.9605	−	7.43108i	1.38086	−	0.293510i	0.543153	−	0.839634i	$-0.317231\pi$
$641$	34.9605	−	7.43108i	1.38086	−	0.293510i	0.837704	+	0.546124i	$0.183897\pi$
$642$	6.21269	+	4.58556i	0.245195	+	0.180978i
$643$	36.0587	−	26.1982i	1.42202	−	1.03316i	0.430582	−	0.902551i	$-0.358308\pi$
$643$	36.0587	−	26.1982i	1.42202	−	1.03316i	0.991435	−	0.130604i	$-0.0416917\pi$
$644$	18.7044	+	39.4815i	0.737057	+	1.55579i
$645$	30.5161	−	6.24691i	1.20157	−	0.245972i
$646$	5.53282	+	1.17604i	0.217686	+	0.0462705i
$647$	21.9432	+	38.0067i	0.862675	+	1.49420i	0.869337	+	0.494220i	$0.164546\pi$
$647$	21.9432	+	38.0067i	0.862675	+	1.49420i	−0.00666154	+	0.999978i	$0.502120\pi$
$648$	3.32774	+	8.12337i	0.130726	+	0.319116i
$649$	12.2376	−	5.44855i	0.480370	−	0.213874i
$650$	−2.06394	−	2.84076i	−0.0809542	−	0.111424i
$651$	1.71261	−	8.74410i	0.0671224	−	0.342708i
$652$	9.72844	−	29.9411i	0.380995	−	1.17258i
$653$	15.5911	−	27.0047i	0.610129	−	1.05677i	−0.381090	−	0.924538i	$-0.624451\pi$
$653$	15.5911	−	27.0047i	0.610129	−	1.05677i	0.991218	−	0.132236i	$-0.0422156\pi$
$654$	−17.6716	+	30.0833i	−0.691014	+	1.17635i
$655$	22.1125	+	38.3000i	0.864008	+	1.49651i
$656$	18.3244	+	0.581756i	0.715446	+	0.0227138i
$657$	2.56846	−	11.2489i	0.100205	−	0.438863i
$658$	−19.6721	−	56.0201i	−0.766897	−	2.18389i
$659$	−3.09258			−0.120470			−0.0602350	−	0.998184i	$-0.519185\pi$
$659$	−3.09258			−0.120470			−0.0602350	+	0.998184i	$0.519185\pi$
$660$	−32.1592	+	22.9975i	−1.25180	+	0.895178i
$661$	1.00654	+	4.73540i	0.0391499	+	0.184186i	0.993378	−	0.114895i	$-0.0366533\pi$
$661$	1.00654	+	4.73540i	0.0391499	+	0.184186i	−0.954228	+	0.299081i	$0.903320\pi$
$662$	62.1341	+	27.6639i	2.41491	+	1.07519i
$663$	22.4225	−	7.09954i	0.870819	−	0.275723i
$664$	11.0028	−	3.57502i	0.426991	−	0.138738i
$665$	0.931212	−	3.11362i	0.0361109	−	0.120741i
$666$	−13.9704	+	1.25622i	−0.541343	+	0.0486776i
$667$	0.763918	−	3.59395i	0.0295790	−	0.139158i
$668$	2.82646	+	13.2974i	0.109359	+	0.514493i
$669$	−10.1252	−	5.94774i	−0.391461	−	0.229953i
$670$	−34.5725	+	59.8813i	−1.33565	+	2.31342i
$671$	50.9504	+	16.5548i	1.96692	+	0.639091i
$672$	32.0338	+	17.8163i	1.23573	+	0.687278i
$673$	5.24093	−	1.70288i	0.202023	−	0.0656413i	−0.206258	−	0.978498i	$-0.566128\pi$
$673$	5.24093	−	1.70288i	0.202023	−	0.0656413i	0.408281	+	0.912856i	$0.366128\pi$
$674$	−14.6142	+	1.53601i	−0.562918	+	0.0591651i
$675$	−2.97595	−	1.40626i	−0.114544	−	0.0541269i
$676$	−1.57303	+	14.9664i	−0.0605012	+	0.575631i
$677$	−12.6759	+	5.64366i	−0.487173	+	0.216903i	−0.635598	−	0.772020i	$-0.719246\pi$
$677$	−12.6759	+	5.64366i	−0.487173	+	0.216903i	0.148425	+	0.988924i	$0.452580\pi$
$678$	23.2326	−	25.4154i	0.892243	−	0.976073i
$679$	10.0027	+	1.88113i	0.383870	+	0.0721910i
$680$	3.70173	+	11.3928i	0.141955	+	0.436892i
$681$	5.56513	−	1.76206i	0.213256	−	0.0675223i
$682$	15.6941	−	3.33588i	0.600958	−	0.127738i
$683$	16.5674	+	28.6955i	0.633932	+	1.09800i	0.986740	+	0.162307i	$0.0518936\pi$
$683$	16.5674	+	28.6955i	0.633932	+	1.09800i	−0.352808	+	0.935696i	$0.614773\pi$
$684$	0.456643	−	3.79472i	0.0174602	−	0.145095i
$685$	14.0042	−	43.1005i	0.535073	−	1.64678i
$686$	−18.3947	−	34.5257i	−0.702312	−	1.31820i
$687$	−41.1755	+	8.42898i	−1.57094	+	0.321586i
$688$	10.8473	−	18.7881i	0.413549	−	0.716288i
$689$	−7.71235	+	8.56544i	−0.293817	+	0.326317i
$690$	−56.8807	−	12.5382i	−2.16541	−	0.477320i
$691$	0.0104461	+	0.0993877i	0.000397387	+	0.00378089i	0.994719	−	0.102638i	$-0.0327283\pi$
$691$	0.0104461	+	0.0993877i	0.000397387	+	0.00378089i	−0.994321	+	0.106419i	$0.966062\pi$
$692$	−9.44125	+	29.0572i	−0.358902	+	1.10459i
$693$	−30.2741	+	6.70469i	−1.15002	+	0.254690i
$694$		−	6.20631i		−	0.235588i
$695$	−18.2145	+	1.91442i	−0.690914	+	0.0726180i
$696$	0.370037	+	0.848227i	0.0140262	+	0.0321520i
$697$	12.5088	+	30.6799i	0.473803	+	1.16209i
$698$	−6.76751	+	11.7217i	−0.256154	+	0.443672i
$699$	−8.11017	−	14.2944i	−0.306755	−	0.540664i
$700$	4.01430	−	0.952588i	0.151726	−	0.0360044i
$701$	19.6979	+	6.40023i	0.743979	+	0.241734i	0.656389	−	0.754423i	$-0.272083\pi$
$701$	19.6979	+	6.40023i	0.743979	+	0.241734i	0.0875907	+	0.996157i	$0.472083\pi$
$702$	−11.1190	−	26.5712i	−0.419658	−	1.00287i
$703$	1.04652	+	0.465939i	0.0394701	+	0.0175732i
$704$	−4.56096	+	43.3947i	−0.171898	+	1.63550i
$705$	41.4353	+	13.8085i	1.56054	+	0.520059i
$706$		−	8.23155i		−	0.309799i
$707$	−0.706271	−	29.9852i	−0.0265621	−	1.12771i
$708$	−14.3240	+	2.93224i	−0.538328	+	0.110200i
$709$	−1.44119	+	1.29765i	−0.0541250	+	0.0487343i	−0.695749	−	0.718285i	$-0.744928\pi$
$709$	−1.44119	+	1.29765i	−0.0541250	+	0.0487343i	0.641624	+	0.767019i	$0.278261\pi$
$710$	−31.3887	+	70.5002i	−1.17800	+	2.64583i
$711$	−36.7777	+	11.3412i	−1.37927	+	0.425327i
$712$	2.05517	+	2.28250i	0.0770209	+	0.0855404i
$713$	10.5512	+	7.66593i	0.395147	+	0.287091i
$714$	−4.43636	+	49.8894i	−0.166027	+	1.86706i
$715$	19.6860	−	14.3027i	0.736215	−	0.534892i
$716$	29.9388	−	13.3296i	1.11887	−	0.498151i
$717$	39.0650	+	8.61108i	1.45891	+	0.321587i
$718$	−1.37789	+	13.1097i	−0.0514223	+	0.489250i
$719$	8.75198	+	19.6573i	0.326394	+	0.733093i	0.999982	−	0.00601432i	$-0.00191443\pi$
$719$	8.75198	+	19.6573i	0.326394	+	0.733093i	−0.673588	+	0.739107i	$0.735248\pi$
$720$	−18.7475	+	8.01128i	−0.698679	+	0.298563i
$721$	7.90625	−	4.81640i	0.294444	−	0.179372i
$722$	23.2574	−	32.0110i	0.865549	−	1.19133i
$723$	13.3365	+	18.6495i	0.495991	+	0.693583i
$724$	−18.2394	−	31.5916i	−0.677863	−	1.17409i
$725$	−0.316987	−	0.141132i	−0.0117726	−	0.00524150i
$726$	−9.06908	−	12.6820i	−0.336585	−	0.470673i
$727$	2.70266	+	8.31795i	0.100236	+	0.308496i	0.988583	−	0.150678i	$-0.0481456\pi$
$727$	2.70266	+	8.31795i	0.100236	+	0.308496i	−0.888347	+	0.459173i	$0.848146\pi$
$728$	5.94320	+	3.24716i	0.220270	+	0.120348i
$729$	−21.1054	−	16.8393i	−0.781680	−	0.623680i
$730$	−18.8613	−	4.00909i	−0.698087	−	0.148383i
$731$	38.9911	+	4.09813i	1.44214	+	0.151575i
$732$	−50.4173	−	29.6162i	−1.86348	−	1.09465i
$733$	−2.53477	+	2.28231i	−0.0936237	+	0.0842992i	−0.714614	−	0.699519i	$-0.753397\pi$
$733$	−2.53477	+	2.28231i	−0.0936237	+	0.0842992i	0.620990	+	0.783819i	$0.286731\pi$
$734$	−1.07515	+	3.30897i	−0.0396845	+	0.122136i
$735$	28.3629	+	4.86461i	1.04618	+	0.179434i
$736$	−43.4056	+	31.5360i	−1.59995	+	1.16243i
$737$	−46.6604	−	26.9394i	−1.71876	−	0.992326i
$738$	36.0499	−	18.6225i	1.32701	−	0.685505i
$739$	11.3765	+	19.7047i	0.418492	+	0.724849i	0.995788	−	0.0916859i	$-0.0292256\pi$
$739$	11.3765	+	19.7047i	0.418492	+	0.724849i	−0.577296	+	0.816535i	$0.695892\pi$
$740$	1.35192	+	12.8627i	0.0496977	+	0.472842i
$741$	−0.263478	+	2.33758i	−0.00967911	+	0.0858732i
$742$	−10.5086	−	22.1817i	−0.385783	−	0.814317i
$743$	−30.8807	−	10.0337i	−1.13290	−	0.368102i	−0.318224	−	0.948015i	$-0.603087\pi$
$743$	−30.8807	−	10.0337i	−1.13290	−	0.368102i	−0.814678	+	0.579913i	$0.803087\pi$
$744$	−3.28480	−	0.0247036i	−0.120426	−	0.000905676i
$745$	−5.23032	+	49.7632i	−0.191624	+	1.82318i
$746$	−3.50215	−	3.15335i	−0.128223	−	0.115452i
$747$	−24.2044	+	26.0819i	−0.885593	+	0.954287i
$748$	−47.3269	+	15.3774i	−1.73044	+	0.562255i
$749$	4.76884	−	2.90512i	0.174249	−	0.106151i
$750$	15.6825	−	34.5224i	0.572645	−	1.26058i
$751$	44.9342	−	4.72278i	1.63967	−	0.172337i	0.760665	−	0.649145i	$-0.224873\pi$
$751$	44.9342	−	4.72278i	1.63967	−	0.172337i	0.879007	+	0.476808i	$0.158206\pi$
$752$	26.3438	−	15.2096i	0.960658	−	0.554636i
$753$	3.74268	+	38.3839i	0.136391	+	1.39879i
$754$	−1.23505	−	2.77396i	−0.0449777	−	0.101022i
$755$	−29.3463	+	9.53518i	−1.06802	+	0.347021i
$756$	33.8437	−	0.0334485i	1.23088	−	0.00121651i
$757$	−27.3692	+	37.6705i	−0.994752	+	1.36916i	−0.0662611	+	0.997802i	$0.521107\pi$
$757$	−27.3692	+	37.6705i	−0.994752	+	1.36916i	−0.928491	+	0.371356i	$0.878893\pi$
$758$	−3.04153	−	6.83138i	−0.110473	−	0.248127i
$759$	9.76995	−	44.3223i	0.354627	−	1.60880i
$760$	−1.19156	−	0.125238i	−0.0432223	−	0.00454285i
$761$	1.12089	+	10.6645i	0.0406321	+	0.386588i	0.995873	+	0.0907591i	$0.0289293\pi$
$761$	1.12089	+	10.6645i	0.0406321	+	0.386588i	−0.955241	+	0.295829i	$0.904404\pi$
$762$	−5.08746	−	24.8522i	−0.184299	−	0.900299i
$763$	15.3069	+	20.0573i	0.554146	+	0.726124i
$764$	9.66418	−	29.7433i	0.349638	−	1.07607i
$765$	−27.0063	−	25.0623i	−0.976416	−	0.906129i
$766$	−15.8155	−	7.04152i	−0.571438	−	0.254420i
$767$	8.80214	−	1.87095i	0.317827	−	0.0675562i
$768$	−3.44733	+	10.3444i	−0.124395	+	0.373273i
$769$	38.5592	−	12.5286i	1.39048	−	0.451794i	0.484379	−	0.874858i	$-0.339045\pi$
$769$	38.5592	−	12.5286i	1.39048	−	0.451794i	0.906100	+	0.423064i	$0.139045\pi$
$770$	11.9643	+	50.4188i	0.431164	+	1.81697i
$771$	0.0355600	+	0.173710i	0.00128066	+	0.00625602i
$772$	−12.5210	−	28.1226i	−0.450640	−	1.01215i
$773$	19.2737	−	43.2895i	0.693228	−	1.55701i	−0.131394	−	0.991330i	$-0.541945\pi$
$773$	19.2737	−	43.2895i	0.693228	−	1.55701i	0.824622	−	0.565685i	$-0.191388\pi$
$774$	0.722149	−	48.0089i	0.0259571	−	1.72564i
$775$	0.915298	−	0.824138i	0.0328785	−	0.0296039i
$776$		−	3.75230i		−	0.134700i
$777$	−2.97952	+	9.69616i	−0.106890	+	0.347848i
$778$	41.9290			1.50323
$779$	−3.31212	−	0.105152i	−0.118669	−	0.00376747i
$780$	−24.3433	+	10.6197i	−0.871630	+	0.380246i
$781$	−54.9349	−	24.4586i	−1.96572	−	0.875197i
$782$	−63.4901	−	36.6560i	−2.27040	−	1.31082i
$783$	−2.26439	−	1.72455i	−0.0809228	−	0.0616303i
$784$	15.6421	−	12.5311i	0.558648	−	0.447539i
$785$	−5.81695	+	4.22626i	−0.207616	+	0.150842i
$786$	64.9904	−	20.5776i	2.31813	−	0.733980i
$787$	8.16804	+	7.35454i	0.291159	+	0.262161i	0.801746	−	0.597666i	$-0.203905\pi$
$787$	8.16804	+	7.35454i	0.291159	+	0.262161i	−0.510586	+	0.859827i	$0.670572\pi$
$788$	−27.7449	+	16.0185i	−0.988372	+	0.570637i
$789$	−7.36249	+	22.0927i	−0.262112	+	0.786521i
$790$	19.8752	+	61.1697i	0.707129	+	2.17632i
$791$	−10.6611	−	22.5037i	−0.379066	−	0.800138i
$792$	4.49198	+	10.5119i	0.159616	+	0.373523i
$793$	31.1665	+	17.9940i	1.10675	+	0.638985i
$794$	3.87678	+	18.2388i	0.137582	+	0.647271i
$795$	17.6322	+	3.88666i	0.625350	+	0.137846i
$796$	24.0128	+	5.10409i	0.851113	+	0.180910i
$797$	−24.9683	+	18.1405i	−0.884422	+	0.642570i	−0.934418	−	0.356179i	$-0.884079\pi$
$797$	−24.9683	+	18.1405i	−0.884422	+	0.642570i	0.0499957	+	0.998749i	$0.484079\pi$
$798$	−4.37796	−	2.43490i	−0.154978	−	0.0861946i
$799$	44.4738	+	32.3121i	1.57337	+	1.14312i
$800$	2.06084	+	4.62873i	0.0728618	+	0.163650i
$801$	−8.93939	−	3.05398i	−0.315858	−	0.107907i
$802$	−3.42965	−	1.52698i	−0.121105	−	0.0539195i
$803$	3.12395	−	14.6970i	0.110242	−	0.518646i
$804$	43.4049	+	39.6770i	1.53077	+	1.39930i
$805$	−23.9490	+	34.6504i	−0.844092	+	1.22127i
$806$	10.7782			0.379647
$807$	2.66606	+	0.0200503i	0.0938498	+	0.000705804i
$808$	−10.8159	+	2.29900i	−0.380503	+	0.0808784i
$809$	−5.46565	+	6.07021i	−0.192162	+	0.213417i	−0.831525	−	0.555488i	$-0.812532\pi$
$809$	−5.46565	+	6.07021i	−0.192162	+	0.213417i	0.639363	+	0.768905i	$0.279198\pi$
$810$	−27.6077	+	35.6898i	−0.970035	+	1.25401i
$811$			27.6300i			0.970219i	0.874453	+	0.485109i	$0.161220\pi$
$811$			27.6300i			0.970219i	−0.874453	+	0.485109i	$0.838780\pi$
$812$	3.56679	−	0.0840122i	0.125170	−	0.00294825i
$813$	18.3917	+	16.8121i	0.645026	+	0.589628i
$814$	−18.1656	+	1.90928i	−0.636704	+	0.0669203i
$815$	29.6896	−	6.31072i	1.03998	−	0.221055i
$816$	−25.5398	+	2.49029i	−0.894070	+	0.0871777i
$817$	−1.96064	+	3.39593i	−0.0685942	+	0.118809i
$818$	−50.3497	+	36.5812i	−1.76043	+	1.27903i
$819$	−20.8290	+	0.177233i	−0.727825	+	0.00619304i
$820$	−17.6691	−	32.9782i	−0.617032	−	1.15165i
$821$	−28.3230	−	16.3523i	−0.988479	−	0.570699i	−0.0836598	−	0.996494i	$-0.526661\pi$
$821$	−28.3230	−	16.3523i	−0.988479	−	0.570699i	−0.904819	+	0.425796i	$0.859994\pi$
$822$	−60.2326	−	35.3819i	−2.10085	−	1.23409i
$823$	22.4711	−	12.9737i	0.783294	−	0.452235i	−0.0543022	−	0.998525i	$-0.517293\pi$
$823$	22.4711	−	12.9737i	0.783294	−	0.452235i	0.837597	+	0.546289i	$0.183960\pi$
$824$	−2.28375	−	2.53636i	−0.0795583	−	0.0883584i
$825$	−3.90238	−	1.77274i	−0.135863	−	0.0617187i
$826$	−3.54180	+	18.8332i	−0.123235	+	0.655292i
$827$	−9.19718	−	6.68214i	−0.319817	−	0.232361i	0.416280	−	0.909236i	$-0.363334\pi$
$827$	−9.19718	−	6.68214i	−0.319817	−	0.232361i	−0.736098	+	0.676876i	$0.763334\pi$
$828$	−20.8271	+	44.9467i	−0.723793	+	1.56201i
$829$	−41.2335	+	23.8062i	−1.43210	+	0.826822i	−0.997281	−	0.0736972i	$-0.976520\pi$
$829$	−41.2335	+	23.8062i	−1.43210	+	0.826822i	−0.434817	+	0.900519i	$0.643187\pi$
$830$	44.1906	+	39.7894i	1.53388	+	1.38111i
$831$	1.75444	−	5.26457i	0.0608609	−	0.182626i
$832$	−9.05775	+	27.8769i	−0.314021	+	0.966458i
$833$	32.1857	+	16.6133i	1.11517	+	0.575616i
$834$	−3.16203	+	28.0536i	−0.109492	+	0.971416i
$835$	−9.74039	+	8.77029i	−0.337080	+	0.303508i
$836$	0.520252	−	4.94987i	0.0179933	−	0.171195i
$837$	8.86142	−	4.85296i	0.306295	−	0.167743i
$838$	56.3928	−	5.92712i	1.94806	−	0.204749i
$839$	30.7925	−	42.3823i	1.06308	−	1.46320i	0.186183	−	0.982515i	$-0.440388\pi$
$839$	30.7925	−	42.3823i	1.06308	−	1.46320i	0.876894	−	0.480684i	$-0.159612\pi$
$840$	−0.170047	−	10.6077i	−0.00586719	−	0.366000i
$841$	23.2187	+	16.8694i	0.800646	+	0.581704i
$842$	44.4179	−	19.7761i	1.53074	−	0.681530i
$843$	−22.2172	+	37.8216i	−0.765202	+	1.30265i
$844$	7.89168	+	7.10570i	0.271643	+	0.244588i
$845$	−13.2548	+	5.90141i	−0.455978	+	0.203015i
$846$	34.5348	−	57.7909i	1.18733	−	1.98689i
$847$	−10.9702	+	2.60321i	−0.376941	+	0.0894475i
$848$	10.1736	−	7.39155i	0.349363	−	0.253827i
$849$	16.1260	+	22.5502i	0.553441	+	0.773920i
$850$	−4.63264	+	5.14507i	−0.158898	+	0.176475i
$851$	−11.0337	−	9.93482i	−0.378232	−	0.340561i
$852$	52.8073	+	38.9768i	1.80915	+	1.33532i
$853$	41.3135	−	13.4236i	1.41455	−	0.459615i	0.500683	−	0.865631i	$-0.333082\pi$
$853$	41.3135	−	13.4236i	1.41455	−	0.459615i	0.913866	+	0.406016i	$0.133082\pi$
$854$	−60.9237	+	46.4943i	−2.08477	+	1.59100i
$855$	3.38861	−	1.44804i	0.115888	−	0.0495218i
$856$	−1.37750	−	1.52987i	−0.0470819	−	0.0522897i
$857$	2.70483	−	0.574929i	0.0923951	−	0.0196392i	−0.161482	−	0.986876i	$-0.551627\pi$
$857$	2.70483	−	0.574929i	0.0923951	−	0.0196392i	0.253877	+	0.967236i	$0.418294\pi$
$858$	−14.9979	−	34.3793i	−0.512019	−	1.17369i
$859$	−44.8544	+	4.71438i	−1.53041	+	0.160853i	−0.831972	−	0.554817i	$-0.812788\pi$
$859$	−44.8544	+	4.71438i	−1.53041	+	0.160853i	−0.698439	+	0.715670i	$0.746122\pi$
$860$	−44.2721			−1.50967
$861$	−2.60841	−	29.2266i	−0.0888944	−	0.996041i
$862$	−17.7281			−0.603822
$863$	4.99964	−	0.525483i	0.170190	−	0.0178877i	−0.0190503	−	0.999819i	$-0.506064\pi$
$863$	4.99964	−	0.525483i	0.170190	−	0.0178877i	0.189240	+	0.981931i	$0.439398\pi$
$864$	7.72204	+	40.8391i	0.262709	+	1.38937i
$865$	−28.8132	+	6.12443i	−0.979677	+	0.208237i
$866$	−22.8379	−	25.3641i	−0.776064	−	0.861906i
$867$	−8.35390	−	14.7240i	−0.283713	−	0.500053i
$868$	−4.87712	+	11.6874i	−0.165540	+	0.396695i
$869$	−47.6644	+	15.4871i	−1.61690	+	0.525364i
$870$	−2.82476	+	3.82709i	−0.0957684	+	0.129751i
$871$	−26.8972	−	24.2184i	−0.911378	−	0.820609i
$872$	6.22407	−	6.91253i	0.210773	−	0.234088i
$873$	5.61946	+	10.0803i	0.190190	+	0.341168i
$874$	5.93213	−	4.30994i	0.200657	−	0.145786i
$875$	−18.8226	−	19.9397i	−0.636321	−	0.674084i
$876$	−6.78282	+	14.9312i	−0.229170	+	0.504480i
$877$	−8.87487	+	3.95135i	−0.299683	+	0.133427i	−0.551070	−	0.834459i	$-0.685780\pi$
$877$	−8.87487	+	3.95135i	−0.299683	+	0.133427i	0.251387	+	0.967887i	$0.419113\pi$
$878$	54.0680	+	48.6830i	1.82471	+	1.64297i
$879$	17.6460	+	10.3656i	0.595183	+	0.349623i
$880$	−24.2533	+	10.7983i	−0.817579	+	0.364010i
$881$	24.0782	+	17.4939i	0.811216	+	0.589383i	0.914183	−	0.405302i	$-0.132834\pi$
$881$	24.0782	+	17.4939i	0.811216	+	0.589383i	−0.102967	+	0.994685i	$0.532834\pi$
$882$	16.7339	−	41.0806i	0.563460	−	1.38326i
$883$	−26.0379	+	35.8380i	−0.876243	+	1.20605i	0.101204	+	0.994866i	$0.467731\pi$
$883$	−26.0379	+	35.8380i	−0.876243	+	1.20605i	−0.977447	+	0.211180i	$0.932269\pi$
$884$	−33.2454	+	3.49424i	−1.11816	+	0.117524i
$885$	−9.35348	−	10.5465i	−0.314414	−	0.354517i
$886$	−5.03331	+	47.8887i	−0.169097	+	1.60885i
$887$	15.4747	−	13.9335i	0.519591	−	0.467842i	−0.367115	−	0.930176i	$-0.619654\pi$
$887$	15.4747	−	13.9335i	0.519591	−	0.467842i	0.886706	+	0.462334i	$0.152988\pi$
$888$	3.71606	+	0.418852i	0.124703	+	0.0140557i
$889$	−18.0288	−	3.39051i	−0.604666	−	0.113714i
$890$	−4.87843	+	15.0143i	−0.163526	+	0.503280i
$891$	−27.8101	−	21.5123i	−0.931672	−	0.720690i
$892$	12.4032	+	11.1679i	0.415290	+	0.373929i
$893$	−4.76162	+	2.74912i	−0.159342	+	0.0919960i
$894$	73.1733	+	24.3853i	2.44728	+	0.815568i
$895$	25.5624	+	18.5722i	0.854457	+	0.620799i
$896$	−15.2459	−	13.0908i	−0.509331	−	0.437332i
$897$	12.6101	−	27.7589i	0.421037	−	0.926843i
$898$	20.6691	+	22.9554i	0.689737	+	0.766030i
$899$	0.922385	−	0.532539i	0.0307633	−	0.0177612i
$900$	3.74295	+	2.80638i	0.124765	+	0.0935462i
$901$	19.6810	+	11.3628i	0.655670	+	0.378551i
$902$	46.5741	−	24.9535i	1.55075	−	0.830862i
$903$	−31.9425	−	13.6125i	−1.06298	−	0.452995i
$904$	−7.42695	+	5.39600i	−0.247017	+	0.179468i
$905$	17.5853	−	30.4587i	0.584557	−	1.01248i
$906$	4.61586	+	47.3390i	0.153352	+	1.57273i
$907$	−29.3440	+	6.23726i	−0.974352	+	0.207105i	−0.667465	−	0.744641i	$-0.732621\pi$
$907$	−29.3440	+	6.23726i	−0.974352	+	0.207105i	−0.306887	+	0.951746i	$0.599287\pi$
$908$	−8.25131	+	0.867247i	−0.273829	+	0.0287806i
$909$	25.6134	−	22.3741i	0.849543	−	0.742102i
$910$	0.819687	+	34.8004i	0.0271724	+	1.15362i
$911$		−	27.3092i		−	0.904793i	−0.891817	−	0.452396i	$-0.850569\pi$
$911$		−	27.3092i		−	0.904793i	0.891817	−	0.452396i	$-0.149431\pi$
$912$	0.811441	−	2.43490i	0.0268695	−	0.0806275i
$913$	−31.0046	+	34.4340i	−1.02610	+	1.13960i
$914$	35.9049	−	7.63181i	1.18763	−	0.252438i
$915$	0.423964	−	56.3739i	0.0140158	−	1.86366i
$916$	59.7365			1.97375
$917$	3.99714	−	49.1358i	0.131997	−	1.62261i
$918$	−46.6875	+	32.3368i	−1.54092	+	1.06727i
$919$	−7.90369	+	37.1839i	−0.260719	+	1.22659i	0.631641	+	0.775261i	$0.282382\pi$
$919$	−7.90369	+	37.1839i	−0.260719	+	1.22659i	−0.892360	+	0.451324i	$0.850952\pi$
$920$	14.1861	+	6.31607i	0.467702	+	0.208235i
$921$	−2.12287	+	9.63060i	−0.0699509	+	0.317339i
$922$	19.3143	+	43.3807i	0.636084	+	1.42867i
$923$	−32.6807	−	23.7439i	−1.07570	−	0.781541i
$924$	44.0656	−	0.706397i	1.44965	−	0.0232387i
$925$	−1.13436	+	0.824159i	−0.0372974	+	0.0270982i
$926$	−47.6514	−	10.1286i	−1.56592	−	0.332847i
$927$	9.93364	+	3.39364i	0.326264	+	0.111462i
$928$	0.910968	+	4.28577i	0.0299040	+	0.140687i
$929$	−5.92668	−	3.42177i	−0.194448	−	0.112265i	0.399615	−	0.916683i	$-0.369144\pi$
$929$	−5.92668	−	3.42177i	−0.194448	−	0.112265i	−0.594063	+	0.804418i	$0.702477\pi$
$930$	−8.33191	−	14.6852i	−0.273214	−	0.481548i
$931$	−2.82731	+	2.26499i	−0.0926614	+	0.0742320i
$932$	7.21831	+	22.2157i	0.236444	+	0.727699i
$933$	−23.6882	−	7.89421i	−0.775518	−	0.258445i
$934$	−3.94577	+	2.27809i	−0.129110	+	0.0745415i
$935$	−35.6545	−	32.1035i	−1.16603	−	1.04990i
$936$	1.48344	+	7.53456i	0.0484878	+	0.246275i
$937$	−16.8055	+	12.2099i	−0.549013	+	0.398881i	−0.827421	−	0.561582i	$-0.810193\pi$
$937$	−16.8055	+	12.2099i	−0.549013	+	0.398881i	0.278409	+	0.960463i	$0.410193\pi$
$938$	69.6552	−	32.9992i	2.27432	−	1.07746i
$939$	−17.5919	−	7.99149i	−0.574091	−	0.260793i
$940$	−53.7597	−	31.0382i	−1.75345	−	1.01235i
$941$	−11.3703	−	5.06238i	−0.370661	−	0.165029i	0.212949	−	0.977063i	$-0.431693\pi$
$941$	−11.3703	−	5.06238i	−0.370661	−	0.165029i	−0.583609	+	0.812035i	$0.698360\pi$
$942$	4.43167	+	10.1586i	0.144392	+	0.330986i
$943$	40.4057	+	14.5616i	1.31579	+	0.474191i
$944$	−9.81804			−0.319550
$945$	16.3430	+	28.2423i	0.531636	+	0.918723i
$946$		−	62.5241i		−	2.03283i
$947$	8.15134	−	7.33950i	0.264883	−	0.238502i	−0.525977	−	0.850499i	$-0.676300\pi$
$947$	8.15134	−	7.33950i	0.264883	−	0.238502i	0.790860	+	0.611997i	$0.209634\pi$
$948$	54.4431	−	5.30856i	1.76823	−	0.172414i
$949$	4.10539	−	9.22085i	0.133266	−	0.299321i
$950$	−0.281650	−	0.632595i	−0.00913792	−	0.0205241i
$951$	9.40552	−	1.92539i	0.304995	−	0.0624351i
$952$	3.82617	−	12.7933i	0.124007	−	0.414632i
$953$	25.2226	−	8.19532i	0.817040	−	0.265473i	0.129464	−	0.991584i	$-0.458674\pi$
$953$	25.2226	−	8.19532i	0.817040	−	0.265473i	0.687577	+	0.726112i	$0.258674\pi$
$954$	11.7012	−	25.2522i	0.378841	−	0.817570i
$955$	29.4935	−	6.26904i	0.954388	−	0.202861i
$956$	−51.9407	−	23.1255i	−1.67988	−	0.747932i
$957$	−2.98213	−	2.20110i	−0.0963986	−	0.0711514i
$958$	20.6356	−	63.5099i	0.666706	−	2.05191i
$959$	−40.1586	+	30.6473i	−1.29679	+	0.989653i
$960$	44.9839	−	9.20860i	1.45185	−	0.297206i
$961$	−2.84520	−	27.0703i	−0.0917807	−	0.873235i
$962$	−12.2030	−	1.28258i	−0.393440	−	0.0413522i
$963$	5.99170	+	2.04695i	0.193080	+	0.0659622i
$964$	−13.2543	−	29.7696i	−0.426892	−	0.958814i
$965$	17.4455	−	24.0116i	0.561590	−	0.772962i
$966$	44.2129	+	47.5481i	1.42253	+	1.52983i
$967$	7.31377	−	2.37639i	0.235195	−	0.0764195i	−0.189048	−	0.981968i	$-0.560540\pi$
$967$	7.31377	−	2.37639i	0.235195	−	0.0764195i	0.424243	+	0.905548i	$0.360540\pi$
$968$	1.69066	+	3.79727i	0.0543397	+	0.122049i
$969$	4.61630	−	0.450120i	0.148297	−	0.0144599i
$970$	16.7028	−	9.64335i	0.536294	−	0.309629i
$971$	44.3520	−	4.66159i	1.42332	−	0.149597i	0.638646	−	0.769501i	$-0.279495\pi$
$971$	44.3520	−	4.66159i	1.42332	−	0.149597i	0.784678	+	0.619903i	$0.212828\pi$
$972$	24.5878	+	29.4635i	0.788653	+	0.945042i
$973$	17.9160	+	9.78869i	0.574360	+	0.313811i
$974$	−60.6624	+	19.7104i	−1.94375	+	0.631562i
$975$	−2.31660	−	1.70987i	−0.0741904	−	0.0547597i
$976$	−29.1791	−	26.2730i	−0.934000	−	0.840977i
$977$	2.83355	−	26.9594i	0.0906533	−	0.862508i	−0.850828	−	0.525444i	$-0.823899\pi$
$977$	2.83355	−	26.9594i	0.0906533	−	0.862508i	0.941482	−	0.337064i	$-0.109434\pi$
$978$	0.351857	−	46.7859i	0.0112511	−	1.49605i
$979$	−11.6994	−	3.80135i	−0.373913	−	0.121492i
$980$	−38.1066	−	14.8582i	−1.21727	−	0.474629i
$981$	−6.36838	+	27.8913i	−0.203327	+	0.890501i
$982$	−6.94739	−	66.1000i	−0.221700	−	2.10933i
$983$	−2.57532	−	4.46059i	−0.0821401	−	0.142271i	0.822029	−	0.569446i	$-0.192842\pi$
$983$	−2.57532	−	4.46059i	−0.0821401	−	0.142271i	−0.904169	+	0.427175i	$0.859509\pi$
$984$	−10.4115	+	2.93648i	−0.331905	+	0.0936115i
$985$	−26.7500	−	15.4441i	−0.852324	−	0.492090i
$986$	−4.84360	+	3.51908i	−0.154252	+	0.112070i
$987$	−29.2444	−	38.9238i	−0.930858	−	1.23896i
$988$	1.03318	−	3.17981i	0.0328700	−	0.101163i
$989$	37.7690	−	34.0073i	1.20098	−	1.08137i
$990$	−35.2476	+	47.0107i	−1.12024	+	1.49410i
$991$	−53.6950	−	5.64357i	−1.70568	−	0.179274i	−0.799067	−	0.601242i	$-0.794673\pi$
$991$	−53.6950	−	5.64357i	−1.70568	−	0.179274i	−0.906611	+	0.421968i	$0.861339\pi$
$992$	−15.2127	−	3.23356i	−0.483004	−	0.102666i
$993$	55.4199	+	6.24659i	1.75870	+	0.198229i
$994$	73.4659	−	44.7546i	2.33020	−	1.41953i
$995$	7.31410	+	22.5105i	0.231873	+	0.713630i
$996$	41.1374	−	29.4179i	1.30349	−	0.932142i
$997$	24.5555	+	10.9328i	0.777681	+	0.346246i	0.756894	−	0.653538i	$-0.226716\pi$
$997$	24.5555	+	10.9328i	0.777681	+	0.346246i	0.0207873	+	0.999784i	$0.493383\pi$
$998$	22.7208	+	39.3535i	0.719213	+	1.24571i
$999$	−10.6103	+	4.43996i	−0.335694	+	0.140474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.bw.a.824.17	yes	864
3.2	odd	2	inner	861.2.bw.a.824.92	yes	864
7.3	odd	6	inner	861.2.bw.a.332.92	yes	864
21.17	even	6	inner	861.2.bw.a.332.17	yes	864
41.31	even	10	inner	861.2.bw.a.236.17	✓	864
123.113	odd	10	inner	861.2.bw.a.236.92	yes	864
287.31	odd	30	inner	861.2.bw.a.605.92	yes	864
861.605	even	30	inner	861.2.bw.a.605.17	yes	864

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.bw.a.236.17	✓	864	41.31	even	10	inner
861.2.bw.a.236.92	yes	864	123.113	odd	10	inner
861.2.bw.a.332.17	yes	864	21.17	even	6	inner
861.2.bw.a.332.92	yes	864	7.3	odd	6	inner
861.2.bw.a.605.17	yes	864	861.605	even	30	inner
861.2.bw.a.605.92	yes	864	287.31	odd	30	inner
861.2.bw.a.824.17	yes	864	1.1	even	1	trivial
861.2.bw.a.824.92	yes	864	3.2	odd	2	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:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.bw (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10072 + 0.220794i) q^{2} +(-1.58756 + 0.692569i) q^{3} +(2.40798 - 0.511831i) q^{4} +(1.58817 + 1.76385i) q^{5} +(3.18210 - 1.80542i) q^{6} +(-0.338439 - 2.62402i) q^{7} +(-0.927655 + 0.301413i) q^{8} +(2.04070 - 2.19899i) q^{9} +O(q^{10})\)	\(q+(-2.10072 + 0.220794i) q^{2} +(-1.58756 + 0.692569i) q^{3} +(2.40798 - 0.511831i) q^{4} +(1.58817 + 1.76385i) q^{5} +(3.18210 - 1.80542i) q^{6} +(-0.338439 - 2.62402i) q^{7} +(-0.927655 + 0.301413i) q^{8} +(2.04070 - 2.19899i) q^{9} +(-3.72575 - 3.35468i) q^{10} +(2.61402 - 2.90317i) q^{11} +(-3.46833 + 2.48025i) q^{12} +(2.12311 - 1.54253i) q^{13} +(1.29033 + 5.43759i) q^{14} +(-3.74291 - 1.70029i) q^{15} +(-2.61569 + 1.16458i) q^{16} +(-3.84529 - 3.46231i) q^{17} +(-3.80140 + 5.07004i) q^{18} +(0.472784 - 0.210497i) q^{19} +(4.72707 + 3.43442i) q^{20} +(2.35460 + 3.93139i) q^{21} +(-4.85032 + 6.67590i) q^{22} +(-6.67084 + 0.701133i) q^{23} +(1.26396 - 1.12098i) q^{24} +(-0.0662131 + 0.629975i) q^{25} +(-4.11947 + 3.70919i) q^{26} +(-1.71678 + 4.90435i) q^{27} +(-2.15801 - 6.14534i) q^{28} +(-0.169272 + 0.520964i) q^{29} +(8.23821 + 2.74542i) q^{30} +(-1.44495 - 1.30104i) q^{31} +(6.92712 - 3.99938i) q^{32} +(-2.13928 + 6.41934i) q^{33} +(8.84233 + 6.42433i) q^{34} +(4.09086 - 4.76435i) q^{35} +(3.78843 - 6.33961i) q^{36} +(1.48113 + 1.64496i) q^{37} +(-0.946711 + 0.546584i) q^{38} +(-2.30226 + 3.91926i) q^{39} +(-2.00492 - 1.15754i) q^{40} +(-5.76396 - 2.78869i) q^{41} +(-5.81439 - 7.73887i) q^{42} +(-6.12990 + 4.45363i) q^{43} +(4.80857 - 8.32869i) q^{44} +(7.11966 + 0.107094i) q^{45} +(13.8588 - 2.94577i) q^{46} +(-10.5659 + 1.11052i) q^{47} +(3.34601 - 3.66038i) q^{48} +(-6.77092 + 1.77614i) q^{49} -1.33802i q^{50} +(8.50252 + 2.83350i) q^{51} +(4.32288 - 4.80104i) q^{52} +(-4.29602 + 0.913146i) q^{53} +(2.52361 - 10.6817i) q^{54} +9.27226 q^{55} +(1.10487 + 2.33217i) q^{56} +(-0.604790 + 0.661613i) q^{57} +(0.240566 - 1.13177i) q^{58} +(3.13256 + 1.39471i) q^{59} +(-9.88309 - 2.17852i) q^{60} +(5.57771 + 12.5277i) q^{61} +(3.32270 + 2.41408i) q^{62} +(-6.46084 - 4.61059i) q^{63} +(-9.03610 + 6.56511i) q^{64} +(6.09265 + 1.29503i) q^{65} +(3.07666 - 13.9576i) q^{66} +(-2.86747 - 13.4904i) q^{67} +(-11.0315 - 6.36903i) q^{68} +(10.1048 - 5.73311i) q^{69} +(-7.54180 + 10.9118i) q^{70} +(-4.75666 - 14.6395i) q^{71} +(-1.23026 + 2.65500i) q^{72} +(3.33086 - 1.92307i) q^{73} +(-3.47464 - 3.12858i) q^{74} +(-0.331184 - 1.04598i) q^{75} +(1.03071 - 0.748858i) q^{76} +(-8.50264 - 5.87669i) q^{77} +(3.97104 - 8.74158i) q^{78} +(-11.1101 - 6.41445i) q^{79} +(-6.20830 - 2.76411i) q^{80} +(-0.671119 - 8.97494i) q^{81} +(12.7242 + 4.58560i) q^{82} -11.8609 q^{83} +(7.68204 + 8.26153i) q^{84} -12.2812i q^{85} +(11.8939 - 10.7093i) q^{86} +(-0.0920750 - 0.944295i) q^{87} +(-1.54986 + 3.48104i) q^{88} +(-1.28077 - 2.87665i) q^{89} +(-14.9800 + 1.34701i) q^{90} +(-4.76616 - 5.04902i) q^{91} +(-15.7044 + 5.10265i) q^{92} +(3.19501 + 1.06475i) q^{93} +(21.9508 - 4.66578i) q^{94} +(1.12215 + 0.499613i) q^{95} +(-8.22738 + 11.1468i) q^{96} +(-1.18877 + 3.65867i) q^{97} +(13.8316 - 5.22615i) q^{98} +(-1.04961 - 11.6727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9}+O(q^{10}) \) 864 * q - 110 * q^4 - 20 * q^7 - 12 * q^9	\( 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9} - 18 q^{10} - 15 q^{12} - 50 q^{15} + 82 q^{16} - 15 q^{18} - 30 q^{19} - 14 q^{21} + 30 q^{24} + 78 q^{25} + 15 q^{30} - 18 q^{31} + 36 q^{33} + 16 q^{36} - 10 q^{37} - 2 q^{39} - 144 q^{40} - 24 q^{42} - 8 q^{43} + 69 q^{45} - 12 q^{46} + 52 q^{49} - 18 q^{51} - 30 q^{52} + 15 q^{54} - 38 q^{57} - 10 q^{58} - 126 q^{61} + 65 q^{63} - 16 q^{64} - 70 q^{67} - 260 q^{70} - 33 q^{72} - 48 q^{73} + 60 q^{75} - 2 q^{78} + 68 q^{81} - 150 q^{82} + 115 q^{84} - 138 q^{87} + 30 q^{88} + 64 q^{91} - 15 q^{93} + 60 q^{94} - 30 q^{99}+O(q^{100}) \) 864 * q - 110 * q^4 - 20 * q^7 - 12 * q^9 - 18 * q^10 - 15 * q^12 - 50 * q^15 + 82 * q^16 - 15 * q^18 - 30 * q^19 - 14 * q^21 + 30 * q^24 + 78 * q^25 + 15 * q^30 - 18 * q^31 + 36 * q^33 + 16 * q^36 - 10 * q^37 - 2 * q^39 - 144 * q^40 - 24 * q^42 - 8 * q^43 + 69 * q^45 - 12 * q^46 + 52 * q^49 - 18 * q^51 - 30 * q^52 + 15 * q^54 - 38 * q^57 - 10 * q^58 - 126 * q^61 + 65 * q^63 - 16 * q^64 - 70 * q^67 - 260 * q^70 - 33 * q^72 - 48 * q^73 + 60 * q^75 - 2 * q^78 + 68 * q^81 - 150 * q^82 + 115 * q^84 - 138 * q^87 + 30 * q^88 + 64 * q^91 - 15 * q^93 + 60 * q^94 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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