LMFDB - Embedded newform 403.2.f.c.94.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.6
Character	$\chi$	$=$	403.94
Dual form			403.2.f.c.373.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.748359 - 1.29620i) q^{2} +(0.472887 + 0.819064i) q^{3} +(-0.120081 + 0.207987i) q^{4} +2.74524 q^{5} +(0.707778 - 1.22591i) q^{6} +(1.47907 - 2.56182i) q^{7} -2.63398 q^{8} +(1.05276 - 1.82343i) q^{9} +O(q^{10})$	\(q+(-0.748359 - 1.29620i) q^{2} +(0.472887 + 0.819064i) q^{3} +(-0.120081 + 0.207987i) q^{4} +2.74524 q^{5} +(0.707778 - 1.22591i) q^{6} +(1.47907 - 2.56182i) q^{7} -2.63398 q^{8} +(1.05276 - 1.82343i) q^{9} +(-2.05442 - 3.55837i) q^{10} +(2.37329 + 4.11066i) q^{11} -0.227139 q^{12} +(-3.20546 + 1.65077i) q^{13} -4.42750 q^{14} +(1.29819 + 2.24853i) q^{15} +(2.21132 + 3.83012i) q^{16} +(0.709910 - 1.22960i) q^{17} -3.15136 q^{18} +(0.240029 - 0.415742i) q^{19} +(-0.329652 + 0.570973i) q^{20} +2.79773 q^{21} +(3.55214 - 6.15249i) q^{22} +(-2.25007 - 3.89724i) q^{23} +(-1.24557 - 2.15740i) q^{24} +2.53635 q^{25} +(4.53855 + 2.91953i) q^{26} +4.82866 q^{27} +(0.355217 + 0.615253i) q^{28} +(3.21588 + 5.57006i) q^{29} +(1.94302 - 3.36541i) q^{30} +1.00000 q^{31} +(0.675746 - 1.17043i) q^{32} +(-2.24459 + 3.88775i) q^{33} -2.12507 q^{34} +(4.06040 - 7.03282i) q^{35} +(0.252832 + 0.437918i) q^{36} +(-5.43090 - 9.40660i) q^{37} -0.718510 q^{38} +(-2.86791 - 1.84485i) q^{39} -7.23091 q^{40} +(-4.05986 - 7.03188i) q^{41} +(-2.09371 - 3.62641i) q^{42} +(-3.27466 + 5.67187i) q^{43} -1.13995 q^{44} +(2.89007 - 5.00575i) q^{45} +(-3.36772 + 5.83306i) q^{46} +1.57090 q^{47} +(-2.09141 + 3.62243i) q^{48} +(-0.875296 - 1.51606i) q^{49} +(-1.89810 - 3.28760i) q^{50} +1.34283 q^{51} +(0.0415771 - 0.864918i) q^{52} +3.30954 q^{53} +(-3.61357 - 6.25888i) q^{54} +(6.51525 + 11.2847i) q^{55} +(-3.89584 + 6.74779i) q^{56} +0.454026 q^{57} +(4.81326 - 8.33681i) q^{58} +(-1.08009 + 1.87076i) q^{59} -0.623552 q^{60} +(-7.31732 + 12.6740i) q^{61} +(-0.748359 - 1.29620i) q^{62} +(-3.11420 - 5.39395i) q^{63} +6.82249 q^{64} +(-8.79975 + 4.53176i) q^{65} +6.71905 q^{66} +(-0.00292275 - 0.00506235i) q^{67} +(0.170493 + 0.295303i) q^{68} +(2.12806 - 3.68590i) q^{69} -12.1545 q^{70} +(2.21442 - 3.83549i) q^{71} +(-2.77294 + 4.80287i) q^{72} -5.00325 q^{73} +(-8.12853 + 14.0790i) q^{74} +(1.19940 + 2.07743i) q^{75} +(0.0576459 + 0.0998455i) q^{76} +14.0410 q^{77} +(-0.245062 + 5.09797i) q^{78} -1.66321 q^{79} +(6.07061 + 10.5146i) q^{80} +(-0.874858 - 1.51530i) q^{81} +(-6.07646 + 10.5247i) q^{82} +17.6993 q^{83} +(-0.335955 + 0.581891i) q^{84} +(1.94887 - 3.37555i) q^{85} +9.80247 q^{86} +(-3.04149 + 5.26802i) q^{87} +(-6.25119 - 10.8274i) q^{88} +(3.82299 + 6.62161i) q^{89} -8.65123 q^{90} +(-0.512115 + 10.6534i) q^{91} +1.08076 q^{92} +(0.472887 + 0.819064i) q^{93} +(-1.17560 - 2.03620i) q^{94} +(0.658937 - 1.14131i) q^{95} +1.27821 q^{96} +(-5.33293 + 9.23691i) q^{97} +(-1.31007 + 2.26911i) q^{98} +9.99398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.748359	−	1.29620i	−0.529169	−	0.916548i	−0.999421	−	0.0340161i	$-0.989170\pi$
$2$	−0.748359	−	1.29620i	−0.529169	−	0.916548i	0.470252	−	0.882532i	$-0.344163\pi$
$3$	0.472887	+	0.819064i	0.273021	+	0.472887i	0.969634	−	0.244561i	$-0.0786437\pi$
$3$	0.472887	+	0.819064i	0.273021	+	0.472887i	−0.696613	+	0.717447i	$0.745310\pi$
$4$	−0.120081	+	0.207987i	−0.0600406	+	0.103993i
$5$	2.74524			1.22771			0.613854	−	0.789419i	$-0.289618\pi$
$5$	2.74524			1.22771			0.613854	+	0.789419i	$0.289618\pi$
$6$	0.707778	−	1.22591i	0.288949	−	0.500475i
$7$	1.47907	−	2.56182i	0.559036	−	0.968279i	−0.438541	−	0.898711i	$-0.644505\pi$
$7$	1.47907	−	2.56182i	0.559036	−	0.968279i	0.997577	−	0.0695676i	$-0.0221619\pi$
$8$	−2.63398			−0.931252
$9$	1.05276	−	1.82343i	0.350919	−	0.607809i
$10$	−2.05442	−	3.55837i	−0.649666	−	1.12525i
$11$	2.37329	+	4.11066i	0.715574	+	1.23941i	0.962738	+	0.270436i	$0.0871679\pi$
$11$	2.37329	+	4.11066i	0.715574	+	1.23941i	−0.247164	+	0.968974i	$0.579499\pi$
$12$	−0.227139			−0.0655694
$13$	−3.20546	+	1.65077i	−0.889034	+	0.457841i
$13$	−3.20546	+	1.65077i	−0.889034	+	0.457841i
$14$	−4.42750			−1.18330
$15$	1.29819	+	2.24853i	0.335191	+	0.580568i
$16$	2.21132	+	3.83012i	0.552831	+	0.957531i
$17$	0.709910	−	1.22960i	0.172178	−	0.298222i	−0.767003	−	0.641644i	$-0.778253\pi$
$17$	0.709910	−	1.22960i	0.172178	−	0.298222i	0.939181	+	0.343422i	$0.111586\pi$
$18$	−3.15136			−0.742782
$19$	0.240029	−	0.415742i	0.0550664	−	0.0953778i	−0.837178	−	0.546930i	$-0.815796\pi$
$19$	0.240029	−	0.415742i	0.0550664	−	0.0953778i	0.892245	+	0.451552i	$0.149130\pi$
$20$	−0.329652	+	0.570973i	−0.0737123	+	0.127673i
$21$	2.79773			0.610515
$22$	3.55214	−	6.15249i	0.757319	−	1.31172i
$23$	−2.25007	−	3.89724i	−0.469172	−	0.812630i	0.530207	−	0.847868i	$-0.322114\pi$
$23$	−2.25007	−	3.89724i	−0.469172	−	0.812630i	−0.999379	+	0.0352383i	$0.988781\pi$
$24$	−1.24557	−	2.15740i	−0.254252	−	0.440377i
$25$	2.53635			0.507269
$26$	4.53855	+	2.91953i	0.890083	+	0.572567i
$27$	4.82866			0.929276
$28$	0.355217	+	0.615253i	0.0671296	+	0.116272i
$29$	3.21588	+	5.57006i	0.597173	+	1.03433i	0.993236	+	0.116111i	$0.0370429\pi$
$29$	3.21588	+	5.57006i	0.597173	+	1.03433i	−0.396063	+	0.918223i	$0.629624\pi$
$30$	1.94302	−	3.36541i	0.354745	−	0.614437i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.675746	−	1.17043i	0.119456	−	0.206904i
$33$	−2.24459	+	3.88775i	−0.390734	+	0.676771i
$34$	−2.12507			−0.364446
$35$	4.06040	−	7.03282i	0.686333	−	1.18876i
$36$	0.252832	+	0.437918i	0.0421387	+	0.0729864i
$37$	−5.43090	−	9.40660i	−0.892835	−	1.54644i	−0.836461	−	0.548026i	$-0.815379\pi$
$37$	−5.43090	−	9.40660i	−0.892835	−	1.54644i	−0.0563742	−	0.998410i	$-0.517954\pi$
$38$	−0.718510			−0.116558
$39$	−2.86791	−	1.84485i	−0.459232	−	0.295412i
$40$	−7.23091			−1.14331
$41$	−4.05986	−	7.03188i	−0.634043	−	1.09819i	−0.986717	−	0.162448i	$-0.948061\pi$
$41$	−4.05986	−	7.03188i	−0.634043	−	1.09819i	0.352674	−	0.935746i	$-0.385272\pi$
$42$	−2.09371	−	3.62641i	−0.323066	−	0.559567i
$43$	−3.27466	+	5.67187i	−0.499380	+	0.864952i	−1.00000		0.000715498i	$-0.999772\pi$
$43$	−3.27466	+	5.67187i	−0.499380	+	0.864952i	0.500620	+	0.865667i	$0.333106\pi$
$44$	−1.13995			−0.171854
$45$	2.89007	−	5.00575i	0.430826	−	0.746212i
$46$	−3.36772	+	5.83306i	−0.496543	+	0.860038i
$47$	1.57090			0.229140			0.114570	−	0.993415i	$-0.463451\pi$
$47$	1.57090			0.229140			0.114570	+	0.993415i	$0.463451\pi$
$48$	−2.09141	+	3.62243i	−0.301869	+	0.522853i
$49$	−0.875296	−	1.51606i	−0.125042	−	0.216580i
$50$	−1.89810	−	3.28760i	−0.268431	−	0.464937i
$51$	1.34283			0.188033
$52$	0.0415771	−	0.864918i	0.00576570	−	0.119943i
$53$	3.30954			0.454600			0.227300	−	0.973825i	$-0.427010\pi$
$53$	3.30954			0.454600			0.227300	+	0.973825i	$0.427010\pi$
$54$	−3.61357	−	6.25888i	−0.491744	−	0.851726i
$55$	6.51525	+	11.2847i	0.878516	+	1.52163i
$56$	−3.89584	+	6.74779i	−0.520603	+	0.901712i
$57$	0.454026			0.0601372
$58$	4.81326	−	8.33681i	0.632012	−	1.09468i
$59$	−1.08009	+	1.87076i	−0.140615	+	0.243553i	−0.927728	−	0.373256i	$-0.878241\pi$
$59$	−1.08009	+	1.87076i	−0.140615	+	0.243553i	0.787113	+	0.616809i	$0.211575\pi$
$60$	−0.623552			−0.0805002
$61$	−7.31732	+	12.6740i	−0.936887	+	1.62274i	−0.165652	+	0.986184i	$0.552973\pi$
$61$	−7.31732	+	12.6740i	−0.936887	+	1.62274i	−0.771234	+	0.636551i	$0.780360\pi$
$62$	−0.748359	−	1.29620i	−0.0950416	−	0.164617i
$63$	−3.11420	−	5.39395i	−0.392352	−	0.679574i
$64$	6.82249			0.852811
$65$	−8.79975	+	4.53176i	−1.09148	+	0.562096i
$66$	6.71905			0.827057
$67$	−0.00292275	−	0.00506235i	−0.000357071	−	0.000618465i	0.865847	−	0.500309i	$-0.166780\pi$
$67$	−0.00292275	−	0.00506235i	−0.000357071	−	0.000618465i	−0.866204	+	0.499691i	$0.833447\pi$
$68$	0.170493	+	0.295303i	0.0206754	+	0.0358108i
$69$	2.12806	−	3.68590i	0.256188	−	0.443731i
$70$	−12.1545			−1.45275
$71$	2.21442	−	3.83549i	0.262803	−	0.455189i	−0.704183	−	0.710019i	$-0.748686\pi$
$71$	2.21442	−	3.83549i	0.262803	−	0.455189i	0.966986	+	0.254830i	$0.0820197\pi$
$72$	−2.77294	+	4.80287i	−0.326794	+	0.566023i
$73$	−5.00325			−0.585586			−0.292793	−	0.956176i	$-0.594585\pi$
$73$	−5.00325			−0.585586			−0.292793	+	0.956176i	$0.594585\pi$
$74$	−8.12853	+	14.0790i	−0.944922	+	1.63665i
$75$	1.19940	+	2.07743i	0.138495	+	0.239881i
$76$	0.0576459	+	0.0998455i	0.00661243	+	0.0114531i
$77$	14.0410			1.60013
$78$	−0.245062	+	5.09797i	−0.0277478	+	0.577232i
$79$	−1.66321			−0.187125			−0.0935627	−	0.995613i	$-0.529826\pi$
$79$	−1.66321			−0.187125			−0.0935627	+	0.995613i	$0.529826\pi$
$80$	6.07061	+	10.5146i	0.678715	+	1.17557i
$81$	−0.874858	−	1.51530i	−0.0972064	−	0.168366i
$82$	−6.07646	+	10.5247i	−0.671032	+	1.16226i
$83$	17.6993			1.94275			0.971375	−	0.237551i	$-0.0763446\pi$
$83$	17.6993			1.94275			0.971375	+	0.237551i	$0.0763446\pi$
$84$	−0.335955	+	0.581891i	−0.0366557	+	0.0634895i
$85$	1.94887	−	3.37555i	0.211385	−	0.366129i
$86$	9.80247			1.05703
$87$	−3.04149	+	5.26802i	−0.326082	+	0.564791i
$88$	−6.25119	−	10.8274i	−0.666379	−	1.15420i
$89$	3.82299	+	6.62161i	0.405236	+	0.701889i	0.994349	−	0.106161i	$-0.0338560\pi$
$89$	3.82299	+	6.62161i	0.405236	+	0.701889i	−0.589113	+	0.808051i	$0.700523\pi$
$90$	−8.65123			−0.911920
$91$	−0.512115	+	10.6534i	−0.0536843	+	1.11678i
$92$	1.08076			0.112677
$93$	0.472887	+	0.819064i	0.0490361	+	0.0849330i
$94$	−1.17560	−	2.03620i	−0.121254	−	0.210018i
$95$	0.658937	−	1.14131i	0.0676055	−	0.117096i
$96$	1.27821			0.130456
$97$	−5.33293	+	9.23691i	−0.541477	+	0.937866i	0.457342	+	0.889291i	$0.348801\pi$
$97$	−5.33293	+	9.23691i	−0.541477	+	0.937866i	−0.998820	+	0.0485752i	$0.984532\pi$
$98$	−1.31007	+	2.26911i	−0.132337	+	0.229215i
$99$	9.99398			1.00443
$100$	−0.304567	+	0.527526i	−0.0304567	+	0.0527526i
$101$	1.29739	+	2.24714i	0.129095	+	0.223599i	0.923326	−	0.384017i	$-0.125460\pi$
$101$	1.29739	+	2.24714i	0.129095	+	0.223599i	−0.794231	+	0.607615i	$0.792126\pi$
$102$	−1.00492	−	1.74057i	−0.0995016	−	0.172342i
$103$	−9.17690			−0.904227			−0.452114	−	0.891960i	$-0.649330\pi$
$103$	−9.17690			−0.904227			−0.452114	+	0.891960i	$0.649330\pi$
$104$	8.44311	−	4.34809i	0.827915	−	0.426366i
$105$	7.68045			0.749535
$106$	−2.47672	−	4.28981i	−0.240560	−	0.416663i
$107$	5.52077	+	9.56226i	0.533713	+	0.924418i	0.999224	+	0.0393763i	$0.0125371\pi$
$107$	5.52077	+	9.56226i	0.533713	+	0.924418i	−0.465511	+	0.885042i	$0.654130\pi$
$108$	−0.579831	+	1.00430i	−0.0557942	+	0.0966385i
$109$	−13.7182			−1.31396			−0.656982	−	0.753906i	$-0.728167\pi$
$109$	−13.7182			−1.31396			−0.656982	+	0.753906i	$0.728167\pi$
$110$	9.75148	−	16.8901i	0.929768	−	1.61040i
$111$	5.13641	−	8.89652i	0.487526	−	0.844420i
$112$	13.0828			1.23621
$113$	−7.76439	+	13.4483i	−0.730412	+	1.26511i	0.226295	+	0.974059i	$0.427339\pi$
$113$	−7.76439	+	13.4483i	−0.730412	+	1.26511i	−0.956707	+	0.291052i	$0.905995\pi$
$114$	−0.339774	−	0.588506i	−0.0318228	−	0.0551187i
$115$	−6.17699	−	10.6989i	−0.576007	−	0.997673i
$116$	−1.54466			−0.143418
$117$	−0.364508	+	7.58277i	−0.0336987	+	0.701028i
$118$	3.23317			0.297637
$119$	−2.10001	−	3.63733i	−0.192508	−	0.333433i
$120$	−3.41940	−	5.92258i	−0.312147	−	0.540655i
$121$	−5.76500	+	9.98527i	−0.524091	+	0.907752i
$122$	21.9039			1.98309
$123$	3.83971	−	6.65056i	0.346215	−	0.599661i
$124$	−0.120081	+	0.207987i	−0.0107836	+	0.0186777i
$125$	−6.76332			−0.604930
$126$	−4.66108	+	8.07322i	−0.415242	+	0.719220i
$127$	3.86303	+	6.69096i	0.342788	+	0.593727i	0.984949	−	0.172843i	$-0.0552953\pi$
$127$	3.86303	+	6.69096i	0.342788	+	0.593727i	−0.642161	+	0.766570i	$0.721962\pi$
$128$	−6.45716	−	11.1841i	−0.570738	−	0.988547i
$129$	−6.19417			−0.545366
$130$	12.4594	+	8.01482i	1.09276	+	0.702946i
$131$	7.46605			0.652311			0.326156	−	0.945316i	$-0.394247\pi$
$131$	7.46605			0.652311			0.326156	+	0.945316i	$0.394247\pi$
$132$	−0.539067	−	0.933691i	−0.0469197	−	0.0812674i
$133$	−0.710039	−	1.22982i	−0.0615682	−	0.106639i
$134$	−0.00437453	+	0.00757691i	−0.000377902	+	0.000654545i
$135$	13.2558			1.14088
$136$	−1.86989	+	3.23874i	−0.160341	+	0.277720i
$137$	2.64163	−	4.57544i	0.225690	−	0.390906i	−0.730836	−	0.682553i	$-0.760870\pi$
$137$	2.64163	−	4.57544i	0.225690	−	0.390906i	0.956526	+	0.291646i	$0.0942030\pi$
$138$	−6.37020			−0.542268
$139$	−5.23414	+	9.06580i	−0.443954	+	0.768952i	−0.997979	−	0.0635489i	$-0.979758\pi$
$139$	−5.23414	+	9.06580i	−0.443954	+	0.768952i	0.554024	+	0.832500i	$0.313091\pi$
$140$	0.975155	+	1.68902i	0.0824157	+	0.142748i
$141$	0.742860	+	1.28667i	0.0625601	+	0.108357i
$142$	−6.62872			−0.556270
$143$	−14.3932	−	9.25878i	−1.20362	−	0.774258i
$144$	9.31193			0.775995
$145$	8.82835	+	15.2912i	0.733155	+	1.26986i
$146$	3.74423	+	6.48519i	0.309874	+	0.536718i
$147$	0.827832	−	1.43385i	0.0682784	−	0.118262i
$148$	2.60860			0.214425
$149$	−7.22617	+	12.5161i	−0.591991	+	1.02536i	0.401974	+	0.915651i	$0.368324\pi$
$149$	−7.22617	+	12.5161i	−0.591991	+	1.02536i	−0.993964	+	0.109706i	$0.965009\pi$
$150$	1.79517	−	3.10933i	0.146575	−	0.253875i
$151$	−17.4528			−1.42029			−0.710144	−	0.704056i	$-0.751370\pi$
$151$	−17.4528			−1.42029			−0.710144	+	0.704056i	$0.751370\pi$
$152$	−0.632231	+	1.09506i	−0.0512807	+	0.0888208i
$153$	−1.49472	−	2.58894i	−0.120841	−	0.209303i
$154$	−10.5077	−	18.1999i	−0.846737	−	1.46659i
$155$	2.74524			0.220503
$156$	0.728085	−	0.374954i	0.0582935	−	0.0300204i
$157$	3.18649			0.254309			0.127155	−	0.991883i	$-0.459416\pi$
$157$	3.18649			0.254309			0.127155	+	0.991883i	$0.459416\pi$
$158$	1.24468	+	2.15584i	0.0990210	+	0.171509i
$159$	1.56504	+	2.71072i	0.124116	+	0.214974i
$160$	1.85509	−	3.21310i	0.146657	−	0.254018i
$161$	−13.3120			−1.04914
$162$	−1.30941	+	2.26797i	−0.102877	+	0.178189i
$163$	7.28655	−	12.6207i	0.570726	−	0.988527i	−0.425765	−	0.904834i	$-0.639995\pi$
$163$	7.28655	−	12.6207i	0.570726	−	0.988527i	0.996492	−	0.0836933i	$-0.0266716\pi$
$164$	1.95005			0.152273
$165$	−6.16195	+	10.6728i	−0.479707	+	0.830877i
$166$	−13.2454	−	22.9417i	−1.02804	−	1.78062i
$167$	2.62760	+	4.55114i	0.203330	+	0.352177i	0.949599	−	0.313466i	$-0.101490\pi$
$167$	2.62760	+	4.55114i	0.203330	+	0.352177i	−0.746270	+	0.665644i	$0.768157\pi$
$168$	−7.36917			−0.568544
$169$	7.54992	−	10.5829i	0.580763	−	0.814073i
$170$	−5.83382			−0.447434
$171$	−0.505384	−	0.875350i	−0.0386476	−	0.0669397i
$172$	−0.786448	−	1.36217i	−0.0599661	−	0.103864i
$173$	−0.653283	+	1.13152i	−0.0496682	+	0.0860278i	−0.889791	−	0.456369i	$-0.849150\pi$
$173$	−0.653283	+	1.13152i	−0.0496682	+	0.0860278i	0.840122	+	0.542397i	$0.182483\pi$
$174$	9.10451			0.690211
$175$	3.75143	−	6.49767i	0.283582	−	0.491178i
$176$	−10.4962	+	18.1800i	−0.791182	+	1.37037i
$177$	−2.04304			−0.153564
$178$	5.72193	−	9.91068i	0.428877	−	0.742837i
$179$	2.20926	+	3.82654i	0.165128	+	0.286009i	0.936701	−	0.350131i	$-0.113863\pi$
$179$	2.20926	+	3.82654i	0.165128	+	0.286009i	−0.771573	+	0.636141i	$0.780530\pi$
$180$	0.694085	+	1.20219i	0.0517341	+	0.0896060i
$181$	1.61357			0.119936			0.0599680	−	0.998200i	$-0.480900\pi$
$181$	1.61357			0.119936			0.0599680	+	0.998200i	$0.480900\pi$
$182$	14.1922	−	7.30878i	1.05199	−	0.541763i
$183$	−13.8411			−1.02316
$184$	5.92664	+	10.2652i	0.436918	+	0.756764i
$185$	−14.9091	−	25.8234i	−1.09614	−	1.89857i
$186$	0.707778	−	1.22591i	0.0518968	−	0.0898879i
$187$	6.73928			0.492825
$188$	−0.188636	+	0.326727i	−0.0137577	+	0.0238290i
$189$	7.14193	−	12.3702i	0.519499	−	0.899798i
$190$	−1.97248			−0.143099
$191$	6.07295	−	10.5187i	0.439423	−	0.761104i	−0.558222	−	0.829692i	$-0.688516\pi$
$191$	6.07295	−	10.5187i	0.439423	−	0.761104i	0.997645	+	0.0685882i	$0.0218495\pi$
$192$	3.22627	+	5.58806i	0.232836	+	0.403283i
$193$	−10.4686	−	18.1321i	−0.753545	−	1.30518i	−0.946095	−	0.323891i	$-0.895009\pi$
$193$	−10.4686	−	18.1321i	−0.753545	−	1.30518i	0.192550	−	0.981287i	$-0.438324\pi$
$194$	15.9638			1.14613
$195$	−7.87309	−	5.06455i	−0.563804	−	0.362680i
$196$	0.420426			0.0300304
$197$	−5.84095	−	10.1168i	−0.416151	−	0.720794i	0.579398	−	0.815045i	$-0.303288\pi$
$197$	−5.84095	−	10.1168i	−0.416151	−	0.720794i	−0.995548	+	0.0942508i	$0.969954\pi$
$198$	−7.47908	−	12.9541i	−0.531515	−	0.920611i
$199$	6.44889	−	11.1698i	0.457150	−	0.791806i	−0.541659	−	0.840598i	$-0.682204\pi$
$199$	6.44889	−	11.1698i	0.457150	−	0.791806i	0.998809	+	0.0487917i	$0.0155371\pi$
$200$	−6.68068			−0.472396
$201$	0.00276426	−	0.00478784i	0.000194976	−	0.000337708i
$202$	1.94182	−	3.36333i	0.136626	−	0.236643i
$203$	19.0260			1.33537
$204$	−0.161248	+	0.279290i	−0.0112896	+	0.0195542i
$205$	−11.1453	−	19.3042i	−0.778420	−	1.34826i
$206$	6.86761	+	11.8951i	0.478489	+	0.828768i
$207$	−9.47510			−0.658565
$208$	−13.4110	−	8.62692i	−0.929882	−	0.598169i
$209$	2.27863			0.157616
$210$	−5.74773	−	9.95536i	−0.396631	−	0.686985i
$211$	8.18882	+	14.1834i	0.563741	+	0.976429i	0.997166	+	0.0752387i	$0.0239719\pi$
$211$	8.18882	+	14.1834i	0.563741	+	0.976429i	−0.433424	+	0.901190i	$0.642695\pi$
$212$	−0.397413	+	0.688339i	−0.0272944	+	0.0472754i
$213$	4.18868			0.287004
$214$	8.26303	−	14.3120i	0.564849	−	0.978348i
$215$	−8.98972	+	15.5706i	−0.613094	+	1.06191i
$216$	−12.7186			−0.865390
$217$	1.47907	−	2.56182i	0.100406	−	0.173908i
$218$	10.2661	+	17.7815i	0.695310	+	1.20431i
$219$	−2.36597	−	4.09798i	−0.159878	−	0.276916i
$220$	−3.12943			−0.210986
$221$	−0.245800	+	5.11333i	−0.0165343	+	0.343960i
$222$	−15.3755			−1.03194
$223$	7.93435	+	13.7427i	0.531323	+	0.920279i	0.999332	+	0.0365549i	$0.0116384\pi$
$223$	7.93435	+	13.7427i	0.531323	+	0.920279i	−0.468008	+	0.883724i	$0.655028\pi$
$224$	−1.99895	−	3.46229i	−0.133561	−	0.231334i
$225$	2.67015	−	4.62484i	0.178010	−	0.308323i
$226$	23.2422			1.54605
$227$	1.08557	−	1.88026i	0.0720517	−	0.124797i	−0.827749	−	0.561099i	$-0.810379\pi$
$227$	1.08557	−	1.88026i	0.0720517	−	0.124797i	0.899800	+	0.436302i	$0.143712\pi$
$228$	−0.0545199	+	0.0944313i	−0.00361067	+	0.00625387i
$229$	3.93913			0.260305			0.130152	−	0.991494i	$-0.458453\pi$
$229$	3.93913			0.260305			0.130152	+	0.991494i	$0.458453\pi$
$230$	−9.24520	+	16.0132i	−0.609610	+	1.05588i
$231$	6.63982	+	11.5005i	0.436868	+	0.756678i
$232$	−8.47055	−	14.6714i	−0.556119	−	0.963226i
$233$	−24.0046			−1.57259			−0.786296	−	0.617850i	$-0.788004\pi$
$233$	−24.0046			−1.57259			−0.786296	+	0.617850i	$0.788004\pi$
$234$	10.1015	−	5.20216i	0.660358	−	0.340076i
$235$	4.31251			0.281317
$236$	−0.259396	−	0.449287i	−0.0168852	−	0.0292461i
$237$	−0.786509	−	1.36227i	−0.0510892	−	0.0884892i
$238$	−3.14312	+	5.44405i	−0.203738	+	0.352885i
$239$	−6.93380			−0.448511			−0.224255	−	0.974530i	$-0.571995\pi$
$239$	−6.93380			−0.448511			−0.224255	+	0.974530i	$0.571995\pi$
$240$	−5.74143	+	9.94445i	−0.370608	+	0.641911i
$241$	11.2275	−	19.4466i	0.723228	−	1.25267i	−0.236471	−	0.971639i	$-0.575991\pi$
$241$	11.2275	−	19.4466i	0.723228	−	1.25267i	0.959699	−	0.281030i	$-0.0906760\pi$
$242$	17.2571			1.10933
$243$	8.07041	−	13.9784i	0.517717	−	0.896712i
$244$	−1.75734	−	3.04381i	−0.112502	−	0.194860i
$245$	−2.40290	−	4.16194i	−0.153516	−	0.265897i
$246$	−11.4939			−0.732825
$247$	−0.0831079	+	1.72888i	−0.00528803	+	0.110006i
$248$	−2.63398			−0.167258
$249$	8.36977	+	14.4969i	0.530412	+	0.918701i
$250$	5.06139	+	8.76659i	0.320110	+	0.554448i
$251$	0.668720	−	1.15826i	0.0422092	−	0.0731085i	−0.844149	−	0.536109i	$-0.819894\pi$
$251$	0.668720	−	1.15826i	0.0422092	−	0.0731085i	0.886358	+	0.463000i	$0.153227\pi$
$252$	1.49583			0.0942282
$253$	10.6801	−	18.4985i	0.671454	−	1.16299i
$254$	5.78186	−	10.0145i	0.362786	−	0.628364i
$255$	3.68639			0.230850
$256$	−2.84205	+	4.92258i	−0.177628	+	0.307661i
$257$	−15.3959	−	26.6665i	−0.960369	−	1.66341i	−0.721573	−	0.692338i	$-0.756581\pi$
$257$	−15.3959	−	26.6665i	−0.960369	−	1.66341i	−0.238796	−	0.971070i	$-0.576753\pi$
$258$	4.63546	+	8.02885i	0.288591	+	0.499854i
$259$	−32.1308			−1.99651
$260$	0.114139	−	2.37441i	0.00707860	−	0.147255i
$261$	13.5421			0.838237
$262$	−5.58728	−	9.67745i	−0.345183	−	0.597875i
$263$	10.6671	+	18.4760i	0.657765	+	1.13928i	0.981193	+	0.193029i	$0.0618312\pi$
$263$	10.6671	+	18.4760i	0.657765	+	1.13928i	−0.323428	+	0.946253i	$0.604835\pi$
$264$	5.91222	−	10.2403i	0.363872	−	0.630244i
$265$	9.08548			0.558116
$266$	−1.06273	+	1.84070i	−0.0651600	+	0.112860i
$267$	−3.61568	+	6.26254i	−0.221276	+	0.383262i
$268$	0.00140387			8.57549e−5
$269$	1.63816	−	2.83737i	0.0998801	−	0.172997i	−0.811755	−	0.583998i	$-0.801487\pi$
$269$	1.63816	−	2.83737i	0.0998801	−	0.172997i	0.911635	+	0.411001i	$0.134821\pi$
$270$	−9.92012	−	17.1821i	−0.603719	−	1.04567i
$271$	−9.85685	−	17.0726i	−0.598761	−	1.03708i	−0.993004	−	0.118078i	$-0.962327\pi$
$271$	−9.85685	−	17.0726i	−0.598761	−	1.03708i	0.394243	−	0.919006i	$-0.371007\pi$
$272$	6.27936			0.380742
$273$	−8.96801	+	4.61841i	−0.542769	+	0.279519i
$274$	−7.90755			−0.477713
$275$	6.01948	+	10.4260i	0.362988	+	0.628714i
$276$	0.511079	+	0.885215i	0.0307633	+	0.0532837i
$277$	−4.50051	+	7.79512i	−0.270410	+	0.468363i	−0.968967	−	0.247191i	$-0.920492\pi$
$277$	−4.50051	+	7.79512i	−0.270410	+	0.468363i	0.698557	+	0.715554i	$0.253826\pi$
$278$	15.6681			0.939708
$279$	1.05276	−	1.82343i	0.0630268	−	0.109166i
$280$	−10.6950	+	18.5243i	−0.639150	+	1.10704i
$281$	27.9641			1.66820			0.834099	−	0.551615i	$-0.185988\pi$
$281$	27.9641			1.66820			0.834099	+	0.551615i	$0.185988\pi$
$282$	1.11185	−	1.92578i	0.0662098	−	0.114679i
$283$	−13.5316	−	23.4375i	−0.804373	−	1.39321i	−0.916714	−	0.399545i	$-0.869168\pi$
$283$	−13.5316	−	23.4375i	−0.804373	−	1.39321i	0.112341	−	0.993670i	$-0.464165\pi$
$284$	0.531820	+	0.921139i	0.0315577	+	0.0546595i
$285$	1.24641			0.0738310
$286$	−1.22990	+	25.5853i	−0.0727254	+	1.51289i
$287$	−24.0192			−1.41781
$288$	−1.42279	−	2.46435i	−0.0838388	−	0.145213i
$289$	7.49206	+	12.9766i	0.440709	+	0.763331i
$290$	13.2135	−	22.8865i	0.775926	−	1.34394i
$291$	−10.0875			−0.591339
$292$	0.600796	−	1.04061i	0.0351589	−	0.0608970i
$293$	−9.59424	+	16.6177i	−0.560501	+	0.970817i	0.436951	+	0.899485i	$0.356058\pi$
$293$	−9.59424	+	16.6177i	−0.560501	+	0.970817i	−0.997453	+	0.0713316i	$0.977275\pi$
$294$	−2.47806			−0.144523
$295$	−2.96510	+	5.13570i	−0.172635	+	0.299012i
$296$	14.3049	+	24.7768i	0.831455	+	1.44012i
$297$	11.4598	+	19.8490i	0.664965	+	1.15175i
$298$	21.6311			1.25305
$299$	13.6459	+	8.77808i	0.789165	+	0.507650i
$300$	−0.576103			−0.0332614
$301$	9.68689	+	16.7782i	0.558343	+	0.967078i
$302$	13.0610	+	22.6222i	0.751573	+	1.30176i
$303$	−1.22703	+	2.12528i	−0.0704912	+	0.122094i
$304$	2.12313			0.121770
$305$	−20.0878	+	34.7931i	−1.15022	+	1.99225i
$306$	−2.23718	+	3.87490i	−0.127891	+	0.221514i
$307$	29.0178			1.65613			0.828067	−	0.560630i	$-0.189441\pi$
$307$	29.0178			1.65613			0.828067	+	0.560630i	$0.189441\pi$
$308$	−1.68606	+	2.92035i	−0.0960724	+	0.166402i
$309$	−4.33964	−	7.51647i	−0.246873	−	0.427597i
$310$	−2.05442	−	3.55837i	−0.116683	−	0.202102i
$311$	18.0910			1.02585			0.512924	−	0.858434i	$-0.328562\pi$
$311$	18.0910			1.02585			0.512924	+	0.858434i	$0.328562\pi$
$312$	7.55400	+	4.85929i	0.427661	+	0.275103i
$313$	34.6278			1.95728			0.978640	−	0.205581i	$-0.0659084\pi$
$313$	34.6278			1.95728			0.978640	+	0.205581i	$0.0659084\pi$
$314$	−2.38463	−	4.13031i	−0.134573	−	0.233087i
$315$	−8.54923	−	14.8077i	−0.481694	−	0.834319i
$316$	0.199720	−	0.345925i	0.0112351	−	0.0194598i
$317$	8.08041			0.453841			0.226920	−	0.973913i	$-0.427134\pi$
$317$	8.08041			0.453841			0.226920	+	0.973913i	$0.427134\pi$
$318$	2.34242	−	4.05719i	0.131356	−	0.227516i
$319$	−15.2644	+	26.4387i	−0.854643	+	1.48028i
$320$	18.7294			1.04700
$321$	−5.22140	+	9.04373i	−0.291430	+	0.504772i
$322$	9.96219	+	17.2550i	0.555171	+	0.961584i
$323$	−0.340797	−	0.590279i	−0.0189625	−	0.0328440i
$324$	0.420216			0.0233453
$325$	−8.13015	+	4.18692i	−0.450980	+	0.232249i
$326$	−21.8118			−1.20804
$327$	−6.48716	−	11.2361i	−0.358741	−	0.621357i
$328$	10.6936	+	18.5218i	0.590454	+	1.02270i
$329$	2.32348	−	4.02438i	0.128097	−	0.221871i
$330$	18.4454			1.01539
$331$	−6.70301	+	11.6100i	−0.368431	+	0.638141i	−0.989320	−	0.145757i	$-0.953438\pi$
$331$	−6.70301	+	11.6100i	−0.368431	+	0.638141i	0.620890	+	0.783898i	$0.286771\pi$
$332$	−2.12535	+	3.68122i	−0.116644	+	0.202033i
$333$	−22.8697			−1.25325
$334$	3.93277	−	6.81176i	0.215192	−	0.372723i
$335$	−0.00802365	−	0.0138974i	−0.000438379	−	0.000759294i
$336$	6.18669	+	10.7157i	0.337512	+	0.584587i
$337$	−15.9263			−0.867560			−0.433780	−	0.901019i	$-0.642821\pi$
$337$	−15.9263			−0.867560			−0.433780	+	0.901019i	$0.642821\pi$
$338$	−19.3676	−	1.86633i	−1.05346	−	0.101515i
$339$	−14.6867			−0.797673
$340$	0.468046	+	0.810679i	0.0253833	+	0.0439652i
$341$	2.37329	+	4.11066i	0.128521	+	0.222605i
$342$	−0.756416	+	1.31015i	−0.0409023	+	0.0708449i
$343$	15.5285			0.838459
$344$	8.62537	−	14.9396i	0.465049	−	0.805489i
$345$	5.84203	−	10.1187i	0.314524	−	0.544772i
$346$	1.95556			0.105132
$347$	0.520857	−	0.902151i	0.0279611	−	0.0484300i	−0.851706	−	0.524020i	$-0.824432\pi$
$347$	0.520857	−	0.902151i	0.0279611	−	0.0484300i	0.879667	+	0.475589i	$0.157765\pi$
$348$	−0.730451	−	1.26518i	−0.0391563	−	0.0678207i
$349$	−15.2203	−	26.3623i	−0.814723	−	1.41114i	−0.909526	−	0.415646i	$-0.863555\pi$
$349$	−15.2203	−	26.3623i	−0.814723	−	1.41114i	0.0948031	−	0.995496i	$-0.469778\pi$
$350$	−11.2297			−0.600251
$351$	−15.4781	+	7.97100i	−0.826158	+	0.425461i
$352$	6.41496			0.341919
$353$	−14.9735	−	25.9348i	−0.796957	−	1.38037i	−0.921589	−	0.388167i	$-0.873108\pi$
$353$	−14.9735	−	25.9348i	−0.796957	−	1.38037i	0.124632	−	0.992203i	$-0.460225\pi$
$354$	1.52892	+	2.64817i	0.0812613	+	0.140749i
$355$	6.07911	−	10.5293i	0.322646	−	0.558839i
$356$	−1.83627			−0.0973224
$357$	1.98614	−	3.44009i	0.105117	−	0.182069i
$358$	3.30663	−	5.72725i	0.174761	−	0.302695i
$359$	22.5067			1.18786			0.593929	−	0.804517i	$-0.297576\pi$
$359$	22.5067			1.18786			0.593929	+	0.804517i	$0.297576\pi$
$360$	−7.61238	+	13.1850i	−0.401208	+	0.694912i
$361$	9.38477	+	16.2549i	0.493935	+	0.855521i
$362$	−1.20753	−	2.09151i	−0.0634665	−	0.109927i
$363$	−10.9048			−0.572352
$364$	−2.15427	−	1.38579i	−0.112915	−	0.0726350i
$365$	−13.7351			−0.718929
$366$	10.3581	+	17.9407i	0.541425	+	0.937776i
$367$	−14.5666	−	25.2302i	−0.760372	−	1.31700i	−0.942659	−	0.333758i	$-0.891683\pi$
$367$	−14.5666	−	25.2302i	−0.760372	−	1.31700i	0.182286	−	0.983246i	$-0.441650\pi$
$368$	9.95127	−	17.2361i	0.518746	−	0.898494i
$369$	−17.0961			−0.889990
$370$	−22.3148	+	38.6503i	−1.16009	+	2.00933i
$371$	4.89504	−	8.47845i	0.254138	−	0.440179i
$372$	−0.227139			−0.0117766
$373$	−3.81385	+	6.60579i	−0.197474	+	0.342035i	−0.947709	−	0.319137i	$-0.896607\pi$
$373$	−3.81385	+	6.60579i	−0.197474	+	0.342035i	0.750235	+	0.661171i	$0.229940\pi$
$374$	−5.04340	−	8.73542i	−0.260788	−	0.451698i
$375$	−3.19829	−	5.53960i	−0.165159	−	0.286063i
$376$	−4.13773			−0.213387
$377$	−19.5032	−	12.5459i	−1.00447	−	0.646148i
$378$	−21.3789			−1.09961
$379$	5.12018	+	8.86841i	0.263006	+	0.455540i	0.967039	−	0.254627i	$-0.0819528\pi$
$379$	5.12018	+	8.86841i	0.263006	+	0.455540i	−0.704033	+	0.710167i	$0.748619\pi$
$380$	0.158252	+	0.274100i	0.00811814	+	0.0140610i
$381$	−3.65355	+	6.32814i	−0.187177	+	0.324200i
$382$	−18.1790			−0.930118
$383$	5.10899	−	8.84903i	0.261057	−	0.452164i	−0.705466	−	0.708744i	$-0.749262\pi$
$383$	5.10899	−	8.84903i	0.261057	−	0.452164i	0.966523	+	0.256580i	$0.0825956\pi$
$384$	6.10702	−	10.5777i	0.311647	−	0.539789i
$385$	38.5460			1.96449
$386$	−15.6685	+	27.1386i	−0.797506	+	1.38132i
$387$	6.89483	+	11.9422i	0.350484	+	0.607056i
$388$	−1.28077	−	2.21836i	−0.0650212	−	0.112620i
$389$	−8.78602			−0.445469			−0.222734	−	0.974879i	$-0.571498\pi$
$389$	−8.78602			−0.445469			−0.222734	+	0.974879i	$0.571498\pi$
$390$	−0.672754	+	13.9952i	−0.0340662	+	0.708673i
$391$	−6.38939			−0.323125
$392$	2.30551	+	3.99326i	0.116446	+	0.201690i
$393$	3.53060	+	6.11517i	0.178095	+	0.308470i
$394$	−8.74225	+	15.1420i	−0.440428	+	0.762844i
$395$	−4.56590			−0.229736
$396$	−1.20009	+	2.07861i	−0.0603067	+	0.104454i
$397$	4.19021	−	7.25765i	0.210300	−	0.364251i	−0.741508	−	0.670944i	$-0.765889\pi$
$397$	4.19021	−	7.25765i	0.210300	−	0.364251i	0.951809	+	0.306693i	$0.0992225\pi$
$398$	−19.3043			−0.967638
$399$	0.671536	−	1.16313i	0.0336189	−	0.0582296i
$400$	5.60868	+	9.71452i	0.280434	+	0.485726i
$401$	8.28905	+	14.3570i	0.413935	+	0.716957i	0.995316	−	0.0966747i	$-0.0308207\pi$
$401$	8.28905	+	14.3570i	0.413935	+	0.716957i	−0.581381	+	0.813632i	$0.697487\pi$
$402$	−0.00827463			−0.000412701
$403$	−3.20546	+	1.65077i	−0.159675	+	0.0822307i
$404$	−0.623166			−0.0310037
$405$	−2.40170	−	4.15986i	−0.119341	−	0.206705i
$406$	−14.2383	−	24.6614i	−0.706634	−	1.22393i
$407$	25.7782	−	44.6492i	1.27778	−	2.21318i
$408$	−3.53698			−0.175107
$409$	9.94933	−	17.2327i	0.491962	−	0.852104i	−0.507995	−	0.861360i	$-0.669613\pi$
$409$	9.94933	−	17.2327i	0.491962	−	0.852104i	0.999957	+	0.00925620i	$0.00294638\pi$
$410$	−16.6813	+	28.8929i	−0.823832	+	1.42692i
$411$	4.99677			0.246473
$412$	1.10197	−	1.90867i	0.0542903	−	0.0940335i
$413$	3.19505	+	5.53398i	0.157218	+	0.272310i
$414$	7.09077	+	12.2816i	0.348492	+	0.603607i
$415$	48.5888			2.38513
$416$	−0.233971	+	4.86725i	−0.0114714	+	0.238637i
$417$	−9.90063			−0.484836
$418$	−1.70523	−	2.95355i	−0.0834057	−	0.144463i
$419$	−7.22541	−	12.5148i	−0.352984	−	0.611387i	0.633787	−	0.773508i	$-0.281500\pi$
$419$	−7.22541	−	12.5148i	−0.352984	−	0.611387i	−0.986771	+	0.162121i	$0.948166\pi$
$420$	−0.922276	+	1.59743i	−0.0450025	+	0.0779466i
$421$	−30.4796			−1.48548			−0.742741	−	0.669579i	$-0.766475\pi$
$421$	−30.4796			−1.48548			−0.742741	+	0.669579i	$0.766475\pi$
$422$	12.2563	−	21.2286i	0.596629	−	1.03339i
$423$	1.65378	−	2.86443i	0.0804094	−	0.139273i
$424$	−8.71725			−0.423347
$425$	1.80058	−	3.11869i	0.0873408	−	0.151279i
$426$	−3.13463	−	5.42935i	−0.151874	−	0.263053i
$427$	21.6457	+	37.4914i	1.04751	+	1.81433i
$428$	−2.65176			−0.128178
$429$	0.777172	−	16.1673i	0.0375222	−	0.780566i
$430$	26.9101			1.29772
$431$	−17.0866	−	29.5948i	−0.823031	−	1.42553i	−0.903415	−	0.428768i	$-0.858948\pi$
$431$	−17.0866	−	29.5948i	−0.823031	−	1.42553i	0.0803833	−	0.996764i	$-0.474386\pi$
$432$	10.6777	+	18.4944i	0.513732	+	0.889811i
$433$	−16.0293	+	27.7636i	−0.770319	+	1.33423i	0.167069	+	0.985945i	$0.446570\pi$
$433$	−16.0293	+	27.7636i	−0.770319	+	1.33423i	−0.937388	+	0.348286i	$0.886764\pi$
$434$	−4.42750			−0.212527
$435$	−8.34963	+	14.4620i	−0.400334	+	0.693399i
$436$	1.64730	−	2.85320i	0.0788912	−	0.136644i
$437$	−2.16033			−0.103342
$438$	−3.54119	+	6.13352i	−0.169205	+	0.293071i
$439$	−7.94562	−	13.7622i	−0.379224	−	0.656835i	0.611726	−	0.791070i	$-0.290476\pi$
$439$	−7.94562	−	13.7622i	−0.379224	−	0.656835i	−0.990949	+	0.134235i	$0.957142\pi$
$440$	−17.1610	−	29.7238i	−0.818120	−	1.41703i
$441$	−3.68589			−0.175519
$442$	6.81181	−	3.50800i	0.324005	−	0.166858i
$443$	29.7007			1.41112			0.705562	−	0.708648i	$-0.250695\pi$
$443$	29.7007			1.41112			0.705562	+	0.708648i	$0.250695\pi$
$444$	1.23357	+	2.13661i	0.0585427	+	0.101399i
$445$	10.4950	+	18.1779i	0.497512	+	0.861716i
$446$	11.8755	−	20.5689i	0.562320	−	0.973967i
$447$	−13.6686			−0.646504
$448$	10.0909	−	17.4780i	0.476752	−	0.825759i
$449$	−5.30452	+	9.18770i	−0.250336	+	0.433594i	−0.963618	−	0.267282i	$-0.913874\pi$
$449$	−5.30452	+	9.18770i	−0.250336	+	0.433594i	0.713282	+	0.700877i	$0.247208\pi$
$450$	−7.99293			−0.376790
$451$	19.2704	−	33.3773i	0.907409	−	1.57168i
$452$	−1.86471	−	3.22978i	−0.0877087	−	0.151916i
$453$	−8.25320	−	14.2950i	−0.387769	−	0.671636i
$454$	−3.24958			−0.152510
$455$	−1.40588	+	29.2462i	−0.0659087	+	1.37108i
$456$	−1.19589			−0.0560029
$457$	−17.3695	−	30.0849i	−0.812513	−	1.40731i	−0.911100	−	0.412185i	$-0.864766\pi$
$457$	−17.3695	−	30.0849i	−0.812513	−	1.40731i	0.0985875	−	0.995128i	$-0.468568\pi$
$458$	−2.94788	−	5.10588i	−0.137745	−	0.238582i
$459$	3.42791	−	5.93732i	0.160001	−	0.277130i
$460$	2.96696			0.138335
$461$	−13.2859	+	23.0119i	−0.618788	+	1.07177i	0.370920	+	0.928665i	$0.379043\pi$
$461$	−13.2859	+	23.0119i	−0.618788	+	1.07177i	−0.989707	+	0.143107i	$0.954291\pi$
$462$	9.93794	−	17.2130i	0.462355	−	0.800822i
$463$	3.89482			0.181007			0.0905037	−	0.995896i	$-0.471152\pi$
$463$	3.89482			0.181007			0.0905037	+	0.995896i	$0.471152\pi$
$464$	−14.2227	+	24.6344i	−0.660272	+	1.14362i
$465$	1.29819	+	2.24853i	0.0602020	+	0.104273i
$466$	17.9640	+	31.1146i	0.832168	+	1.44136i
$467$	−24.3185			−1.12533			−0.562663	−	0.826686i	$-0.690223\pi$
$467$	−24.3185			−1.12533			−0.562663	+	0.826686i	$0.690223\pi$
$468$	−1.53334	−	0.986361i	−0.0708789	−	0.0455945i
$469$	−0.0172918			−0.000798461
$470$	−3.22730	−	5.58985i	−0.148864	−	0.257841i
$471$	1.50685	+	2.60994i	0.0694319	+	0.120260i
$472$	2.84493	−	4.92756i	0.130948	−	0.226809i
$473$	−31.0868			−1.42937
$474$	−1.17718	+	2.03894i	−0.0540697	+	0.0936515i
$475$	0.608796	−	1.05447i	0.0279335	−	0.0483822i
$476$	1.00869			0.0462331
$477$	3.48414	−	6.03470i	0.159528	−	0.276310i
$478$	5.18897	+	8.98756i	0.237338	+	0.411082i
$479$	−9.52527	−	16.4983i	−0.435221	−	0.753825i	0.562093	−	0.827074i	$-0.309996\pi$
$479$	−9.52527	−	16.4983i	−0.435221	−	0.753825i	−0.997314	+	0.0732496i	$0.976663\pi$
$480$	3.50898			0.160162
$481$	32.9367	+	21.1873i	1.50178	+	0.966058i
$482$	−33.6089			−1.53084
$483$	−6.29509	−	10.9034i	−0.286437	−	0.496123i
$484$	−1.38454	−	2.39809i	−0.0629334	−	0.109004i
$485$	−14.6402	+	25.3575i	−0.664776	+	1.15143i
$486$	−24.1582			−1.09584
$487$	6.56183	−	11.3654i	0.297345	−	0.515017i	−0.678183	−	0.734893i	$-0.737232\pi$
$487$	6.56183	−	11.3654i	0.297345	−	0.515017i	0.975528	+	0.219877i	$0.0705655\pi$
$488$	19.2737	−	33.3830i	0.872478	−	1.51118i
$489$	13.7828			0.623282
$490$	−3.59646	+	6.22925i	−0.162471	+	0.281409i
$491$	20.7333	+	35.9111i	0.935679	+	1.62064i	0.773419	+	0.633895i	$0.218545\pi$
$491$	20.7333	+	35.9111i	0.935679	+	1.62064i	0.162260	+	0.986748i	$0.448122\pi$
$492$	0.922152	+	1.59721i	0.0415738	+	0.0720080i
$493$	9.13193			0.411281
$494$	2.30316	−	1.18610i	0.103624	−	0.0533649i
$495$	27.4359			1.23315
$496$	2.21132	+	3.83012i	0.0992913	+	0.171978i
$497$	−6.55056	−	11.3459i	−0.293833	−	0.508933i
$498$	12.5272	−	21.6977i	0.561356	−	0.972297i
$499$	−14.2101			−0.636130			−0.318065	−	0.948069i	$-0.603033\pi$
$499$	−14.2101			−0.636130			−0.318065	+	0.948069i	$0.603033\pi$
$500$	0.812147	−	1.40668i	0.0363203	−	0.0629087i
$501$	−2.48512	+	4.30435i	−0.111027	+	0.192304i
$502$	−2.00177			−0.0893433
$503$	11.4105	−	19.7635i	0.508769	−	0.881213i	−0.491180	−	0.871058i	$-0.663434\pi$
$503$	11.4105	−	19.7635i	0.508769	−	0.881213i	0.999948	−	0.0101548i	$-0.00323243\pi$
$504$	8.20274	+	14.2076i	0.365379	+	0.632855i
$505$	3.56164	+	6.16893i	0.158491	+	0.274514i
$506$	−31.9703			−1.42125
$507$	12.2384	+	1.17933i	0.543525	+	0.0523761i
$508$	−1.85551			−0.0823248
$509$	−6.46268	−	11.1937i	−0.286453	−	0.496151i	0.686507	−	0.727123i	$-0.259143\pi$
$509$	−6.46268	−	11.1937i	−0.286453	−	0.496151i	−0.972961	+	0.230971i	$0.925810\pi$
$510$	−2.75874	−	4.77827i	−0.122159	−	0.211586i
$511$	−7.40016	+	12.8175i	−0.327364	+	0.567011i
$512$	−17.3211			−0.765494
$513$	1.15902	−	2.00748i	0.0511719	−	0.0886323i
$514$	−23.0433	+	39.9121i	−1.01640	+	1.76045i
$515$	−25.1928			−1.11013
$516$	0.743802	−	1.28830i	0.0327441	−	0.0567144i
$517$	3.72821	+	6.45744i	0.163966	+	0.283998i
$518$	24.0453	+	41.6477i	1.05649	+	1.82990i
$519$	−1.23572			−0.0542419
$520$	23.1784	−	11.9366i	1.01644	−	0.523453i
$521$	7.82428			0.342788			0.171394	−	0.985203i	$-0.445173\pi$
$521$	7.82428			0.342788			0.171394	+	0.985203i	$0.445173\pi$
$522$	−10.1344	−	17.5532i	−0.443569	−	0.768285i
$523$	−10.0802	−	17.4594i	−0.440776	−	0.763447i	0.556971	−	0.830532i	$-0.311963\pi$
$523$	−10.0802	−	17.4594i	−0.440776	−	0.763447i	−0.997747	+	0.0670851i	$0.978630\pi$
$524$	−0.896531	+	1.55284i	−0.0391651	+	0.0678360i
$525$	7.09602			0.309695
$526$	15.9657	−	27.6534i	0.696138	−	1.20575i
$527$	0.709910	−	1.22960i	0.0309241	−	0.0535622i
$528$	−19.8541			−0.864039
$529$	1.37436	−	2.38047i	0.0597549	−	0.103499i
$530$	−6.79920	−	11.7766i	−0.295338	−	0.511541i
$531$	2.27413	+	3.93892i	0.0986890	+	0.170934i
$532$	0.341049			0.0147863
$533$	24.6217	+	15.8385i	1.06648	+	0.686041i
$534$	10.8233			0.468370
$535$	15.1558	+	26.2507i	0.655244	+	1.13492i
$536$	0.00769846	+	0.0133341i	0.000332523	+	0.000575947i
$537$	−2.08946	+	3.61904i	−0.0901667	+	0.156173i
$538$	−4.90371			−0.211414
$539$	4.15466	−	7.19608i	0.178954	−	0.309957i
$540$	−1.59178	+	2.75704i	−0.0684991	+	0.118644i
$541$	18.6027			0.799793			0.399897	−	0.916560i	$-0.369046\pi$
$541$	18.6027			0.799793			0.399897	+	0.916560i	$0.369046\pi$
$542$	−14.7529	+	25.5528i	−0.633692	+	1.09759i
$543$	0.763038	+	1.32162i	0.0327451	+	0.0567162i
$544$	−0.959437	−	1.66179i	−0.0411355	−	0.0712488i
$545$	−37.6597			−1.61317
$546$	12.6976	+	8.16806i	0.543409	+	0.349561i
$547$	−23.4233			−1.00151			−0.500754	−	0.865590i	$-0.666944\pi$
$547$	−23.4233			−1.00151			−0.500754	+	0.865590i	$0.666944\pi$
$548$	0.634420	+	1.09885i	0.0271011	+	0.0469405i
$549$	15.4067	+	26.6852i	0.657542	+	1.13890i
$550$	9.00946	−	15.6048i	0.384165	−	0.665393i
$551$	3.08761			0.131537
$552$	−5.60526	+	9.70860i	−0.238576	+	0.413225i
$553$	−2.46000	+	4.26084i	−0.104610	+	0.181190i
$554$	13.4720			0.572370
$555$	14.1007	−	24.4231i	0.598540	−	1.03670i
$556$	−1.25704	−	2.17726i	−0.0533105	−	0.0923366i
$557$	−19.7412	−	34.1928i	−0.836462	−	1.44880i	−0.892834	−	0.450386i	$-0.851286\pi$
$557$	−19.7412	−	34.1928i	−0.836462	−	1.44880i	0.0563716	−	0.998410i	$-0.482047\pi$
$558$	−3.15136			−0.133408
$559$	1.13382	−	23.5866i	0.0479555	−	0.997609i
$560$	35.9155			1.51770
$561$	3.18692	+	5.51990i	0.134552	+	0.233051i
$562$	−20.9272	−	36.2469i	−0.882759	−	1.52898i
$563$	−9.42323	+	16.3215i	−0.397142	+	0.687870i	−0.993372	−	0.114944i	$-0.963331\pi$
$563$	−9.42323	+	16.3215i	−0.397142	+	0.687870i	0.596230	+	0.802813i	$0.296665\pi$
$564$	−0.356814			−0.0150246
$565$	−21.3151	+	36.9189i	−0.896734	+	1.55319i
$566$	−20.2530	+	35.0793i	−0.851299	+	1.47449i
$567$	−5.17590			−0.217368
$568$	−5.83274	+	10.1026i	−0.244736	+	0.423895i
$569$	0.406337	+	0.703796i	0.0170345	+	0.0295047i	0.874417	−	0.485175i	$-0.161244\pi$
$569$	0.406337	+	0.703796i	0.0170345	+	0.0295047i	−0.857382	+	0.514680i	$0.827911\pi$
$570$	−0.932762	−	1.61559i	−0.0390691	−	0.0676697i
$571$	10.2971			0.430921			0.215460	−	0.976513i	$-0.430875\pi$
$571$	10.2971			0.430921			0.215460	+	0.976513i	$0.430875\pi$
$572$	3.65406	−	1.88179i	0.152784	−	0.0786817i
$573$	11.4873			0.479888
$574$	17.9750	+	31.1336i	0.750262	+	1.29949i
$575$	−5.70696	−	9.88474i	−0.237997	−	0.412222i
$576$	7.18242	−	12.4403i	0.299267	−	0.518346i
$577$	27.4976			1.14474			0.572370	−	0.819996i	$-0.306024\pi$
$577$	27.4976			1.14474			0.572370	+	0.819996i	$0.306024\pi$
$578$	11.2135	−	19.4223i	0.466420	−	0.807863i
$579$	9.90091	−	17.1489i	0.411468	−	0.712683i
$580$	−4.24047			−0.176076
$581$	26.1785	−	45.3425i	1.08607	−	1.88112i
$582$	7.54906	+	13.0754i	0.312919	+	0.541991i
$583$	7.85449	+	13.6044i	0.325300	+	0.563436i
$584$	13.1785			0.545329
$585$	−1.00066	+	20.8165i	−0.0413723	+	0.860658i
$586$	28.7197			1.18640
$587$	−10.2313	−	17.7212i	−0.422293	−	0.731433i	0.573871	−	0.818946i	$-0.305441\pi$
$587$	−10.2313	−	17.7212i	−0.422293	−	0.731433i	−0.996163	+	0.0875135i	$0.972108\pi$
$588$	0.198814	+	0.344356i	0.00819895	+	0.0142010i
$589$	0.240029	−	0.415742i	0.00989021	−	0.0171304i
$590$	8.87582			0.365412
$591$	5.52422	−	9.56823i	0.227236	−	0.393584i
$592$	24.0190	−	41.6021i	0.987174	−	1.70984i
$593$	30.0395			1.23357			0.616786	−	0.787131i	$-0.288434\pi$
$593$	30.0395			1.23357			0.616786	+	0.787131i	$0.288434\pi$
$594$	17.1521	−	29.7083i	0.703759	−	1.21895i
$595$	−5.76504	−	9.98534i	−0.236343	−	0.409359i
$596$	−1.73545	−	3.00589i	−0.0710869	−	0.123126i
$597$	12.1984			0.499247
$598$	1.16604	−	24.2570i	0.0476831	−	0.991941i
$599$	0.498188			0.0203554			0.0101777	−	0.999948i	$-0.496760\pi$
$599$	0.498188			0.0203554			0.0101777	+	0.999948i	$0.496760\pi$
$600$	−3.15921	−	5.47191i	−0.128974	−	0.223390i
$601$	4.56310	+	7.90352i	0.186133	+	0.322391i	0.943958	−	0.330067i	$-0.107071\pi$
$601$	4.56310	+	7.90352i	0.186133	+	0.322391i	−0.757825	+	0.652458i	$0.773738\pi$
$602$	14.4985	−	25.1122i	0.590916	−	1.02350i
$603$	−0.0123078			−0.000501211
$604$	2.09575	−	3.62995i	0.0852749	−	0.147700i
$605$	−15.8263	+	27.4120i	−0.643431	+	1.11446i
$606$	3.67304			0.149207
$607$	1.48234	−	2.56748i	0.0601662	−	0.104211i	−0.834373	−	0.551200i	$-0.814170\pi$
$607$	1.48234	−	2.56748i	0.0601662	−	0.104211i	0.894540	+	0.446989i	$0.147504\pi$
$608$	−0.324397	−	0.561872i	−0.0131560	−	0.0227869i
$609$	8.99716	+	15.5835i	0.364583	+	0.631477i
$610$	60.1315			2.43465
$611$	−5.03546	+	2.59320i	−0.203713	+	0.104910i
$612$	0.717952			0.0290215
$613$	−7.68955	−	13.3187i	−0.310578	−	0.537937i	0.667910	−	0.744242i	$-0.267189\pi$
$613$	−7.68955	−	13.3187i	−0.310578	−	0.537937i	−0.978488	+	0.206305i	$0.933856\pi$
$614$	−21.7157	−	37.6127i	−0.876375	−	1.51793i
$615$	10.5409	−	18.2574i	0.425051	−	0.736209i
$616$	−36.9838			−1.49012
$617$	−8.49293	+	14.7102i	−0.341912	+	0.592210i	−0.984788	−	0.173761i	$-0.944408\pi$
$617$	−8.49293	+	14.7102i	−0.341912	+	0.592210i	0.642875	+	0.765971i	$0.277741\pi$
$618$	−6.49521	+	11.2500i	−0.261276	+	0.452543i
$619$	−2.69320			−0.108249			−0.0541244	−	0.998534i	$-0.517237\pi$
$619$	−2.69320			−0.108249			−0.0541244	+	0.998534i	$0.517237\pi$
$620$	−0.329652	+	0.570973i	−0.0132391	+	0.0229308i
$621$	−10.8648	−	18.8184i	−0.435990	−	0.755158i
$622$	−13.5386	−	23.4495i	−0.542847	−	0.940239i
$623$	22.6179			0.906166
$624$	0.724133	−	15.0640i	0.0289885	−	0.603042i
$625$	−31.2487			−1.24995
$626$	−25.9140	−	44.8844i	−1.03573	−	1.79394i
$627$	1.07753	+	1.86634i	0.0430326	+	0.0745346i
$628$	−0.382637	+	0.662746i	−0.0152689	+	0.0264465i
$629$	−15.4218			−0.614908
$630$	−12.7958	+	22.1629i	−0.509796	+	0.882992i
$631$	−6.18780	+	10.7176i	−0.246333	+	0.426661i	−0.962505	−	0.271262i	$-0.912559\pi$
$631$	−6.18780	+	10.7176i	−0.246333	+	0.426661i	0.716173	+	0.697923i	$0.245892\pi$
$632$	4.38085			0.174261
$633$	−7.74477	+	13.4143i	−0.307827	+	0.533172i
$634$	−6.04704	−	10.4738i	−0.240159	−	0.415967i
$635$	10.6049	+	18.3683i	0.420844	+	0.728924i
$636$	−0.751726			−0.0298079
$637$	5.30838	+	3.41474i	0.210326	+	0.135297i
$638$	45.6930			1.80900
$639$	−4.66249	−	8.07566i	−0.184445	−	0.319468i
$640$	−17.7265	−	30.7031i	−0.700700	−	1.21365i
$641$	2.42205	−	4.19511i	0.0956652	−	0.165697i	−0.814221	−	0.580555i	$-0.802836\pi$
$641$	2.42205	−	4.19511i	0.0956652	−	0.165697i	0.909886	+	0.414858i	$0.136169\pi$
$642$	15.6299			0.616864
$643$	−23.8091	+	41.2385i	−0.938938	+	1.62629i	−0.171482	+	0.985187i	$0.554856\pi$
$643$	−23.8091	+	41.2385i	−0.938938	+	1.62629i	−0.767456	+	0.641101i	$0.778478\pi$
$644$	1.59853	−	2.76873i	0.0629907	−	0.109103i
$645$	−17.0045			−0.669551
$646$	−0.510077	+	0.883480i	−0.0200687	+	0.0347601i
$647$	7.97266	+	13.8091i	0.313438	+	0.542890i	0.979104	−	0.203359i	$-0.0651860\pi$
$647$	7.97266	+	13.8091i	0.313438	+	0.542890i	−0.665666	+	0.746249i	$0.731853\pi$
$648$	2.30436	+	3.99126i	0.0905237	+	0.156792i
$649$	−10.2534			−0.402482
$650$	11.5113	+	7.40494i	0.451512	+	0.290446i
$651$	2.79773			0.109652
$652$	1.74995	+	3.03101i	0.0685334	+	0.118703i
$653$	−8.19020	−	14.1858i	−0.320507	−	0.555135i	0.660086	−	0.751190i	$-0.270520\pi$
$653$	−8.19020	−	14.1858i	−0.320507	−	0.555135i	−0.980593	+	0.196056i	$0.937187\pi$
$654$	−9.70944	+	16.8172i	−0.379669	+	0.657606i
$655$	20.4961			0.800849
$656$	17.9553	−	31.0995i	0.701037	−	1.21423i
$657$	−5.26720	+	9.12306i	−0.205493	+	0.355925i
$658$	−6.95517			−0.271141
$659$	22.2210	−	38.4879i	0.865608	−	1.49928i	−0.000834033	−	1.00000i	$-0.500265\pi$
$659$	22.2210	−	38.4879i	0.865608	−	1.49928i	0.866442	−	0.499278i	$-0.166401\pi$
$660$	−1.47987	−	2.56321i	−0.0576038	−	0.0997727i
$661$	0.490132	+	0.848934i	0.0190639	+	0.0330197i	0.875400	−	0.483399i	$-0.160598\pi$
$661$	0.490132	+	0.848934i	0.0190639	+	0.0330197i	−0.856336	+	0.516419i	$0.827265\pi$
$662$	20.0650			0.779849
$663$	−4.30438	+	2.21670i	−0.167168	+	0.0860895i
$664$	−46.6196			−1.80919
$665$	−1.94923	−	3.37616i	−0.0755878	−	0.130922i
$666$	17.1147	+	29.6436i	0.663182	+	1.14866i
$667$	14.4719	−	25.0661i	0.560354	−	0.970562i
$668$	−1.26210			−0.0488321
$669$	−7.50410	+	12.9975i	−0.290125	+	0.502512i
$670$	−0.0120091	+	0.0208004i	−0.000463953	+	0.000803591i
$671$	−69.4645			−2.68165
$672$	1.89056	−	3.27454i	0.0729298	−	0.126318i
$673$	−8.11761	−	14.0601i	−0.312911	−	0.541977i	0.666080	−	0.745880i	$-0.267971\pi$
$673$	−8.11761	−	14.0601i	−0.312911	−	0.541977i	−0.978991	+	0.203903i	$0.934637\pi$
$674$	11.9186	+	20.6436i	0.459086	+	0.795161i
$675$	12.2472			0.471393
$676$	1.29451	+	2.84109i	0.0497887	+	0.109273i
$677$	16.4582			0.632539			0.316270	−	0.948669i	$-0.397570\pi$
$677$	16.4582			0.632539			0.316270	+	0.948669i	$0.397570\pi$
$678$	10.9909	+	19.0368i	0.422104	+	0.731106i
$679$	15.7756	+	27.3241i	0.605410	+	1.04860i
$680$	−5.13329	+	8.89112i	−0.196853	+	0.340959i
$681$	2.05340			0.0786866
$682$	3.55214	−	6.15249i	0.136019	−	0.235591i
$683$	−15.5315	+	26.9014i	−0.594298	+	1.02935i	0.399348	+	0.916800i	$0.369237\pi$
$683$	−15.5315	+	26.9014i	−0.594298	+	1.02935i	−0.993646	+	0.112555i	$0.964097\pi$
$684$	0.242748			0.00928170
$685$	7.25192	−	12.5607i	0.277082	−	0.479919i
$686$	−11.6209	−	20.1279i	−0.443687	−	0.768489i
$687$	1.86276	+	3.22640i	0.0710688	+	0.123095i
$688$	−28.9653			−1.10429
$689$	−10.6086	+	5.46328i	−0.404155	+	0.208135i
$690$	−17.4877			−0.665747
$691$	−10.7550	−	18.6282i	−0.409140	−	0.708651i	0.585654	−	0.810561i	$-0.300838\pi$
$691$	−10.7550	−	18.6282i	−0.409140	−	0.708651i	−0.994794	+	0.101910i	$0.967505\pi$
$692$	−0.156894	−	0.271748i	−0.00596421	−	0.0103303i
$693$	14.7818	−	25.6028i	0.561514	−	0.972570i
$694$	−1.55915			−0.0591846
$695$	−14.3690	+	24.8878i	−0.545047	+	0.944049i
$696$	8.01123	−	13.8759i	0.303665	−	0.525963i
$697$	−11.5285			−0.436674
$698$	−22.7805	+	39.4569i	−0.862253	+	1.49347i
$699$	−11.3515	−	19.6613i	−0.429351	−	0.743658i
$700$	0.900953	+	1.56050i	0.0340528	+	0.0589812i
$701$	21.2727			0.803460			0.401730	−	0.915758i	$-0.368409\pi$
$701$	21.2727			0.803460			0.401730	+	0.915758i	$0.368409\pi$
$702$	21.9151	+	14.0974i	0.827133	+	0.532073i
$703$	−5.21429			−0.196661
$704$	16.1917	+	28.0449i	0.610249	+	1.05698i
$705$	2.03933	+	3.53222i	0.0768056	+	0.133031i
$706$	−22.4110	+	38.8171i	−0.843450	+	1.46090i
$707$	7.67570			0.288674
$708$	0.245330	−	0.424924i	0.00922006	−	0.0159696i
$709$	11.5106	−	19.9370i	0.432290	−	0.748748i	−0.564780	−	0.825241i	$-0.691039\pi$
$709$	11.5106	−	19.9370i	0.432290	−	0.748748i	0.997070	+	0.0764933i	$0.0243724\pi$
$710$	−18.1974			−0.682937
$711$	−1.75095	+	3.03274i	−0.0656658	+	0.113736i
$712$	−10.0697	−	17.4412i	−0.377377	−	0.653636i
$713$	−2.25007	−	3.89724i	−0.0842658	−	0.145953i
$714$	−5.94537			−0.222500
$715$	−39.5129	−	25.4176i	−1.47770	−	0.950564i
$716$	−1.06116			−0.0396574
$717$	−3.27891	−	5.67923i	−0.122453	−	0.212095i
$718$	−16.8431	−	29.1731i	−0.628578	−	1.08873i
$719$	−2.23942	+	3.87879i	−0.0835164	+	0.144655i	−0.904758	−	0.425926i	$-0.859948\pi$
$719$	−2.23942	+	3.87879i	−0.0835164	+	0.144655i	0.821242	+	0.570580i	$0.193282\pi$
$720$	25.5635			0.952695
$721$	−13.5733	+	23.5096i	−0.505495	+	0.875544i
$722$	14.0463	−	24.3290i	0.522751	−	0.905431i
$723$	21.2374			0.789827
$724$	−0.193760	+	0.335602i	−0.00720103	+	0.0124725i
$725$	8.15658	+	14.1276i	0.302928	+	0.524686i
$726$	8.16068	+	14.1347i	0.302871	+	0.524588i
$727$	5.49552			0.203817			0.101909	−	0.994794i	$-0.467505\pi$
$727$	5.49552			0.203817			0.101909	+	0.994794i	$0.467505\pi$
$728$	1.34890	−	28.0609i	0.0499936	−	1.04001i
$729$	10.0164			0.370978
$730$	10.2788	+	17.8034i	0.380435	+	0.658934i
$731$	4.64942	+	8.05303i	0.171965	+	0.297852i
$732$	1.66205	−	2.87875i	0.0614311	−	0.106402i
$733$	−21.4598			−0.792634			−0.396317	−	0.918114i	$-0.629712\pi$
$733$	−21.4598			−0.792634			−0.396317	+	0.918114i	$0.629712\pi$
$734$	−21.8021	+	37.7624i	−0.804732	+	1.39384i
$735$	2.27260	−	3.93625i	0.0838260	−	0.145191i
$736$	−6.08191			−0.224182
$737$	0.0138731	−	0.0240288i	0.000511021	−	0.000885114i
$738$	12.7940	+	22.1599i	0.470955	+	0.815719i
$739$	22.1428	+	38.3525i	0.814536	+	1.41082i	0.909661	+	0.415352i	$0.136342\pi$
$739$	22.1428	+	38.3525i	0.814536	+	1.41082i	−0.0951245	+	0.995465i	$0.530325\pi$
$740$	7.16122			0.263252
$741$	−1.45536	+	0.749492i	−0.0534640	+	0.0275333i
$742$	−14.6530			−0.537928
$743$	5.57841	+	9.66209i	0.204652	+	0.354468i	0.950022	−	0.312184i	$-0.101060\pi$
$743$	5.57841	+	9.66209i	0.204652	+	0.354468i	−0.745370	+	0.666651i	$0.767727\pi$
$744$	−1.24557	−	2.15740i	−0.0456650	−	0.0790941i
$745$	−19.8376	+	34.3597i	−0.726792	+	1.25884i
$746$	11.4165			0.417988
$747$	18.6330	−	32.2734i	0.681747	−	1.18082i
$748$	−0.809260	+	1.40168i	−0.0295895	+	0.0512505i
$749$	32.6624			1.19346
$750$	−4.78693	+	8.29121i	−0.174794	+	0.302752i
$751$	−17.5905	−	30.4676i	−0.641886	−	1.11178i	−0.985011	−	0.172489i	$-0.944819\pi$
$751$	−17.5905	−	30.4676i	−0.641886	−	1.11178i	0.343126	−	0.939290i	$-0.388514\pi$
$752$	3.47378	+	6.01676i	0.126676	+	0.219408i
$753$	1.26491			0.0460961
$754$	−1.66655	+	34.6689i	−0.0606921	+	1.26257i
$755$	−47.9121			−1.74370
$756$	1.71522	+	2.97085i	0.0623820	+	0.108049i
$757$	−10.9844	−	19.0255i	−0.399233	−	0.691492i	0.594398	−	0.804171i	$-0.297390\pi$
$757$	−10.9844	−	19.0255i	−0.399233	−	0.691492i	−0.993631	+	0.112679i	$0.964057\pi$
$758$	7.66346	−	13.2735i	0.278349	−	0.482115i
$759$	20.2020			0.733286
$760$	−1.73563	+	3.00619i	−0.0629578	+	0.109046i
$761$	−19.0892	+	33.0634i	−0.691982	+	1.19855i	0.279205	+	0.960232i	$0.409929\pi$
$761$	−19.0892	+	33.0634i	−0.691982	+	1.19855i	−0.971187	+	0.238317i	$0.923404\pi$
$762$	10.9367			0.396194
$763$	−20.2902	+	35.1436i	−0.734554	+	1.27228i
$764$	1.45849	+	2.52618i	0.0527664	+	0.0913942i
$765$	−4.10337	−	7.10725i	−0.148358	−	0.256963i
$766$	−15.2934			−0.552574
$767$	0.373971	−	7.77963i	0.0135033	−	0.280906i
$768$	−5.37588			−0.193985
$769$	11.8433	+	20.5132i	0.427080	+	0.739724i	0.996612	−	0.0822448i	$-0.0262089\pi$
$769$	11.8433	+	20.5132i	0.427080	+	0.739724i	−0.569532	+	0.821969i	$0.692876\pi$
$770$	−28.8463	−	49.9632i	−1.03955	−	1.80055i
$771$	14.5610	−	25.2204i	0.524403	−	0.908292i
$772$	5.02831			0.180973
$773$	18.1614	−	31.4564i	0.653219	−	1.13141i	−0.329119	−	0.944289i	$-0.606752\pi$
$773$	18.1614	−	31.4564i	0.653219	−	1.13141i	0.982337	−	0.187119i	$-0.0599151\pi$
$774$	10.3196	−	17.8741i	0.370930	−	0.642470i
$775$	2.53635			0.0911082
$776$	14.0468	−	24.3298i	0.504252	−	0.873390i
$777$	−15.1942	−	26.3171i	−0.545089	−	0.944122i
$778$	6.57509	+	11.3884i	0.235729	+	0.408294i
$779$	−3.89793			−0.139658
$780$	1.99877	−	1.02934i	0.0715674	−	0.0368563i
$781$	21.0218			0.752220
$782$	4.78155	+	8.28189i	0.170988	+	0.296160i
$783$	15.5284	+	26.8959i	0.554939	+	0.961182i
$784$	3.87112	−	6.70498i	0.138254	−	0.239464i
$785$	8.74767			0.312218
$786$	5.28430	−	9.15268i	0.188485	−	0.326465i
$787$	−0.301254	+	0.521788i	−0.0107386	+	0.0185997i	−0.871345	−	0.490671i	$-0.836752\pi$
$787$	−0.301254	+	0.521788i	−0.0107386	+	0.0185997i	0.860606	+	0.509271i	$0.170085\pi$
$788$	2.80555			0.0999437
$789$	−10.0887	+	17.4742i	−0.359168	+	0.622097i
$790$	3.41693	+	5.91830i	0.121569	+	0.210564i
$791$	22.9681	+	39.7820i	0.816653	+	1.41449i
$792$	−26.3239			−0.935380
$793$	2.53356	−	52.7051i	0.0899693	−	1.87161i
$794$	−12.5431			−0.445138
$795$	4.29640	+	7.44159i	0.152378	+	0.263926i
$796$	1.54878	+	2.68256i	0.0548950	+	0.0950810i
$797$	−3.79217	+	6.56822i	−0.134325	+	0.232658i	−0.925340	−	0.379139i	$-0.876220\pi$
$797$	−3.79217	+	6.56822i	−0.134325	+	0.232658i	0.791014	+	0.611798i	$0.209553\pi$
$798$	−2.01020			−0.0711603
$799$	1.11520	−	1.93158i	0.0394529	−	0.0683345i
$800$	1.71393	−	2.96861i	0.0605964	−	0.104956i
$801$	16.0987			0.568819
$802$	12.4064	−	21.4884i	0.438084	−	0.758783i
$803$	−11.8742	−	20.5666i	−0.419030	−	0.725781i
$804$	0.000663871		0.00114986i	2.34129e−5		4.05524e-5i
$805$	−36.5448			−1.28803
$806$	4.53855	+	2.91953i	0.159864	+	0.102836i
$807$	3.09865			0.109078
$808$	−3.41729	−	5.91891i	−0.120220	−	0.208227i
$809$	11.2238	+	19.4402i	0.394609	+	0.683482i	0.993051	−	0.117684i	$-0.0375469\pi$
$809$	11.2238	+	19.4402i	0.394609	+	0.683482i	−0.598443	+	0.801166i	$0.704214\pi$
$810$	−3.59466	+	6.22613i	−0.126303	+	0.218764i
$811$	4.43260			0.155650			0.0778248	−	0.996967i	$-0.475203\pi$
$811$	4.43260			0.155650			0.0778248	+	0.996967i	$0.475203\pi$
$812$	−2.28467	+	3.95716i	−0.0801761	+	0.138869i
$813$	9.32235	−	16.1468i	0.326949	−	0.566292i
$814$	−77.1654			−2.70465
$815$	20.0033	−	34.6468i	0.700686	−	1.21362i
$816$	2.96943	+	5.14320i	0.103951	+	0.180048i
$817$	1.57202	+	2.72282i	0.0549981	+	0.0952596i
$818$	−29.7827			−1.04133
$819$	18.8866	+	12.1493i	0.659951	+	0.424529i
$820$	5.35335			0.186947
$821$	0.00327410	+	0.00567090i	0.000114267	+	0.000197916i	0.866083	−	0.499901i	$-0.166630\pi$
$821$	0.00327410	+	0.00567090i	0.000114267	+	0.000197916i	−0.865968	+	0.500099i	$0.833297\pi$
$822$	−3.73938	−	6.47679i	−0.130426	−	0.225904i
$823$	18.1296	−	31.4014i	0.631958	−	1.09458i	−0.355192	−	0.934793i	$-0.615585\pi$
$823$	18.1296	−	31.4014i	0.631958	−	1.09458i	0.987151	−	0.159791i	$-0.0510820\pi$
$824$	24.1718			0.842064
$825$	−5.69307	+	9.86068i	−0.198207	+	0.343305i
$826$	4.78208	−	8.28281i	0.166390	−	0.288196i
$827$	−52.1904			−1.81484			−0.907419	−	0.420227i	$-0.861950\pi$
$827$	−52.1904			−1.81484			−0.907419	+	0.420227i	$0.861950\pi$
$828$	1.13778	−	1.97069i	0.0395406	−	0.0684863i
$829$	−23.2400	−	40.2528i	−0.807158	−	1.39804i	−0.914824	−	0.403852i	$-0.867671\pi$
$829$	−23.2400	−	40.2528i	−0.807158	−	1.39804i	0.107666	−	0.994187i	$-0.465662\pi$
$830$	−36.3619	−	62.9806i	−1.26214	−	2.18609i
$831$	−8.51294			−0.295310
$832$	−21.8692	+	11.2624i	−0.758178	+	0.390452i
$833$	−2.48552			−0.0861183
$834$	7.40922	+	12.8332i	0.256560	+	0.444376i
$835$	7.21339	+	12.4940i	0.249630	+	0.432371i
$836$	−0.273621	+	0.473925i	−0.00946336	+	0.0163910i
$837$	4.82866			0.166903
$838$	−10.8144	+	18.7311i	−0.373577	+	0.647054i
$839$	−9.13705	+	15.8258i	−0.315446	+	0.546368i	−0.979532	−	0.201288i	$-0.935487\pi$
$839$	−9.13705	+	15.8258i	−0.315446	+	0.546368i	0.664086	+	0.747656i	$0.268821\pi$
$840$	−20.2301			−0.698006
$841$	−6.18372	+	10.7105i	−0.213232	+	0.369328i
$842$	22.8096	+	39.5074i	0.786072	+	1.36152i
$843$	13.2239	+	22.9044i	0.455454	+	0.788869i
$844$	−3.93329			−0.135389
$845$	20.7263	−	29.0527i	0.713008	−	0.999444i
$846$	−4.95048			−0.170201
$847$	17.0537	+	29.5378i	0.585971	+	1.01493i
$848$	7.31846	+	12.6759i	0.251317	+	0.435294i
$849$	12.7979	−	22.1666i	0.439222	−	0.760755i
$850$	−5.38991			−0.184872
$851$	−24.4398	+	42.3310i	−0.837787	+	1.45109i
$852$	−0.502981	+	0.871189i	−0.0172319	+	0.0298465i
$853$	33.1308			1.13438			0.567188	−	0.823588i	$-0.308031\pi$
$853$	33.1308			1.13438			0.567188	+	0.823588i	$0.308031\pi$
$854$	32.3974	−	56.1140i	1.10862	−	1.92018i
$855$	−1.38740	−	2.40305i	−0.0474481	−	0.0821824i
$856$	−14.5416	−	25.1868i	−0.497022	−	0.860867i
$857$	−35.7268			−1.22040			−0.610201	−	0.792246i	$-0.708912\pi$
$857$	−35.7268			−1.22040			−0.610201	+	0.792246i	$0.708912\pi$
$858$	−21.5376	+	11.0916i	−0.735282	+	0.378661i
$859$	17.9856			0.613661			0.306830	−	0.951764i	$-0.400732\pi$
$859$	17.9856			0.613661			0.306830	+	0.951764i	$0.400732\pi$
$860$	−2.15899	−	3.73948i	−0.0736210	−	0.127515i
$861$	−11.3584	−	19.6733i	−0.387093	−	0.670464i
$862$	−25.5738	+	44.2951i	−0.871046	+	1.50870i
$863$	5.58804			0.190219			0.0951096	−	0.995467i	$-0.469680\pi$
$863$	5.58804			0.190219			0.0951096	+	0.995467i	$0.469680\pi$
$864$	3.26295	−	5.65159i	0.111008	−	0.192271i
$865$	−1.79342	+	3.10629i	−0.0609781	+	0.105617i
$866$	47.9826			1.63052
$867$	−7.08579	+	12.2730i	−0.240646	+	0.416811i
$868$	0.355217	+	0.615253i	0.0120568	+	0.0208831i
$869$	−3.94727	−	6.83687i	−0.133902	−	0.231925i
$870$	24.9941			0.847378
$871$	0.0177255	+	0.0114024i	0.000600606	+	0.000386354i
$872$	36.1334			1.22363
$873$	11.2285	+	19.4484i	0.380029	+	0.658229i
$874$	1.61670	+	2.80021i	0.0546857	+	0.0947184i
$875$	−10.0034	+	17.3264i	−0.338178	+	0.585741i
$876$	1.13643			0.0383966
$877$	−1.11606	+	1.93308i	−0.0376868	+	0.0652755i	−0.884254	−	0.467007i	$-0.845332\pi$
$877$	−1.11606	+	1.93308i	−0.0376868	+	0.0652755i	0.846567	+	0.532283i	$0.178666\pi$
$878$	−11.8923	+	20.5981i	−0.401347	+	0.695154i
$879$	−18.1480			−0.612115
$880$	−28.8146	+	49.9084i	−0.971341	+	1.68241i
$881$	12.5104	+	21.6687i	0.421486	+	0.730035i	0.996085	−	0.0883997i	$-0.0281753\pi$
$881$	12.5104	+	21.6687i	0.421486	+	0.730035i	−0.574599	+	0.818435i	$0.694842\pi$
$882$	2.75837	+	4.77763i	0.0928791	+	0.160871i
$883$	9.99436			0.336337			0.168168	−	0.985758i	$-0.446215\pi$
$883$	9.99436			0.336337			0.168168	+	0.985758i	$0.446215\pi$
$884$	−1.03399	−	0.665137i	−0.0347768	−	0.0223710i
$885$	−5.60862			−0.188532
$886$	−22.2268	−	38.4979i	−0.746724	−	1.29336i
$887$	14.7999	+	25.6342i	0.496932	+	0.860712i	0.999994	−	0.00353865i	$-0.00112639\pi$
$887$	14.7999	+	25.6342i	0.496932	+	0.860712i	−0.503061	+	0.864251i	$0.667793\pi$
$888$	−13.5292	+	23.4332i	−0.454010	+	0.786368i
$889$	22.8548			0.766524
$890$	15.7081	−	27.2072i	0.526536	−	0.911987i
$891$	4.15258	−	7.19248i	0.139117	−	0.240957i
$892$	−3.81106			−0.127604
$893$	0.377062	−	0.653091i	0.0126179	−	0.0218548i
$894$	10.2290	+	17.7172i	0.342110	+	0.592552i
$895$	6.06494	+	10.5048i	0.202729	+	0.351136i
$896$	−38.2024			−1.27625
$897$	−0.736822	+	15.3279i	−0.0246018	+	0.511785i
$898$	15.8787			0.529880
$899$	3.21588	+	5.57006i	0.107255	+	0.185772i
$900$	0.641270	+	1.11071i	0.0213757	+	0.0370237i
$901$	2.34947	−	4.06941i	0.0782723	−	0.135572i
$902$	−57.6847			−1.92069
$903$	−9.16161	+	15.8684i	−0.304879	+	0.528066i
$904$	20.4512	−	35.4226i	0.680198	−	1.17814i
$905$	4.42965			0.147247
$906$	−12.3527	+	21.3955i	−0.410391	+	0.710818i
$907$	22.6583	+	39.2454i	0.752357	+	1.30312i	0.946677	+	0.322183i	$0.104417\pi$
$907$	22.6583	+	39.2454i	0.752357	+	1.30312i	−0.194320	+	0.980938i	$0.562250\pi$
$908$	0.260712	+	0.451567i	0.00865204	+	0.0149858i
$909$	5.46332			0.181207
$910$	38.9609	−	20.0644i	1.29154	−	0.665127i
$911$	−42.7200			−1.41538			−0.707688	−	0.706525i	$-0.750262\pi$
$911$	−42.7200			−1.41538			−0.707688	+	0.706525i	$0.750262\pi$
$912$	1.00400	+	1.73898i	0.0332457	+	0.0575832i
$913$	42.0055	+	72.7557i	1.39018	+	2.40786i
$914$	−25.9973	+	45.0286i	−0.859914	+	1.48941i
$915$	−37.9970			−1.25614
$916$	−0.473015	+	0.819285i	−0.0156288	+	0.0270699i
$917$	11.0428	−	19.1267i	0.364665	−	0.631619i
$918$	−10.2612			−0.338671
$919$	14.0035	−	24.2548i	0.461933	−	0.800092i	−0.537124	−	0.843503i	$-0.680489\pi$
$919$	14.0035	−	24.2548i	0.461933	−	0.800092i	0.999057	+	0.0434113i	$0.0138226\pi$
$920$	16.2701	+	28.1806i	0.536408	+	0.929085i
$921$	13.7221	+	23.7674i	0.452160	+	0.783164i
$922$	39.7706			1.30977
$923$	−0.766724	+	15.9500i	−0.0252370	+	0.525000i
$924$	−3.18927			−0.104919
$925$	−13.7747	−	23.8584i	−0.452908	−	0.784459i
$926$	−2.91472	−	5.04844i	−0.0957836	−	0.165902i
$927$	−9.66104	+	16.7334i	−0.317310	+	0.549597i
$928$	8.69246			0.285344
$929$	0.705321	−	1.22165i	0.0231408	−	0.0400811i	−0.854223	−	0.519907i	$-0.825967\pi$
$929$	0.705321	−	1.22165i	0.0231408	−	0.0400811i	0.877364	+	0.479826i	$0.159300\pi$
$930$	1.94302	−	3.36541i	0.0637142	−	0.110356i
$931$	−0.840385			−0.0275425
$932$	2.88250	−	4.99263i	0.0944193	−	0.163539i
$933$	8.55501	+	14.8177i	0.280078	+	0.485110i
$934$	18.1990	+	31.5215i	0.595489	+	1.03142i
$935$	18.5009			0.605046
$936$	0.960106	−	19.9729i	0.0313820	−	0.652834i
$937$	−35.3123			−1.15360			−0.576801	−	0.816885i	$-0.695699\pi$
$937$	−35.3123			−1.15360			−0.576801	+	0.816885i	$0.695699\pi$
$938$	0.0129405	+	0.0224136i	0.000422521	+	0.000731828i
$939$	16.3750	+	28.3624i	0.534379	+	0.925572i
$940$	−0.517851	+	0.896944i	−0.0168904	+	0.0292551i
$941$	−2.06540			−0.0673303			−0.0336651	−	0.999433i	$-0.510718\pi$
$941$	−2.06540			−0.0673303			−0.0336651	+	0.999433i	$0.510718\pi$
$942$	2.25533	−	3.90634i	0.0734825	−	0.127275i
$943$	−18.2699	+	31.6444i	−0.594951	+	1.03048i
$944$	−9.55368			−0.310946
$945$	19.6063	−	33.9591i	0.637793	−	1.10469i
$946$	23.2641	+	40.2946i	0.756381	+	1.31009i
$947$	−3.69011	−	6.39146i	−0.119912	−	0.207694i	0.799820	−	0.600239i	$-0.204928\pi$
$947$	−3.69011	−	6.39146i	−0.119912	−	0.207694i	−0.919733	+	0.392545i	$0.871595\pi$
$948$	0.377779			0.0122697
$949$	16.0377	−	8.25921i	0.520606	−	0.268105i
$950$	−1.82239			−0.0591262
$951$	3.82112	+	6.61837i	0.123908	+	0.214615i
$952$	5.53139	+	9.58064i	0.179273	+	0.310510i
$953$	−9.90255	+	17.1517i	−0.320775	+	0.555599i	−0.980648	−	0.195778i	$-0.937277\pi$
$953$	−9.90255	+	17.1517i	−0.320775	+	0.555599i	0.659873	+	0.751377i	$0.270610\pi$
$954$	−10.4295			−0.337669
$955$	16.6717	−	28.8763i	0.539484	−	0.934414i
$956$	0.832619	−	1.44214i	0.0269288	−	0.0466421i
$957$	−28.8734			−0.933343
$958$	−14.2566	+	24.6932i	−0.460611	+	0.797802i
$959$	−7.81432	−	13.5348i	−0.252338	−	0.437061i
$960$	8.85688	+	15.3406i	0.285855	+	0.495115i
$961$	1.00000			0.0322581
$962$	2.81443	−	58.5480i	0.0907410	−	1.88766i
$963$	23.2481			0.749159
$964$	2.69643	+	4.67035i	0.0868461	+	0.150422i
$965$	−28.7388	−	49.7770i	−0.925134	−	1.60238i
$966$	−9.42197	+	16.3193i	−0.303147	+	0.525066i
$967$	44.0600			1.41687			0.708436	−	0.705775i	$-0.249401\pi$
$967$	44.0600			1.41687			0.708436	+	0.705775i	$0.249401\pi$
$968$	15.1849	−	26.3010i	0.488061	−	0.845346i
$969$	0.322317	−	0.558270i	0.0103543	−	0.0179342i
$970$	43.8244			1.40712
$971$	5.72615	−	9.91799i	0.183761	−	0.318283i	−0.759397	−	0.650627i	$-0.774506\pi$
$971$	5.72615	−	9.91799i	0.183761	−	0.318283i	0.943158	+	0.332344i	$0.107839\pi$
$972$	1.93821	+	3.35707i	0.0621680	+	0.107678i
$973$	15.4833	+	26.8179i	0.496373	+	0.859743i
$974$	−19.6424			−0.629384
$975$	−7.27400	−	4.67917i	−0.232954	−	0.149854i
$976$	−64.7238			−2.07176
$977$	22.8429	+	39.5651i	0.730810	+	1.26580i	0.956537	+	0.291610i	$0.0941908\pi$
$977$	22.8429	+	39.5651i	0.730810	+	1.26580i	−0.225727	+	0.974190i	$0.572476\pi$
$978$	−10.3145	−	17.8653i	−0.329822	−	0.571268i
$979$	−18.1461	+	31.4300i	−0.579952	+	1.00451i
$980$	1.15417			0.0368686
$981$	−14.4419	+	25.0141i	−0.461095	+	0.798640i
$982$	31.0318	−	53.7487i	0.990265	−	1.71519i
$983$	−61.7562			−1.96972			−0.984859	−	0.173358i	$-0.944538\pi$
$983$	−61.7562			−1.96972			−0.984859	+	0.173358i	$0.944538\pi$
$984$	−10.1137	+	17.5174i	−0.322413	+	0.558436i
$985$	−16.0348	−	27.7731i	−0.510912	−	0.884925i
$986$	−6.83395	−	11.8368i	−0.217637	−	0.376959i
$987$	4.39497			0.139893
$988$	−0.349603	−	0.224891i	−0.0111224	−	0.00715473i
$989$	29.4728			0.937181
$990$	−20.5319	−	35.5622i	−0.652546	−	1.13024i
$991$	14.3812	+	24.9090i	0.456834	+	0.791259i	0.998792	−	0.0491465i	$-0.0156501\pi$
$991$	14.3812	+	24.9090i	0.456834	+	0.791259i	−0.541958	+	0.840406i	$0.682317\pi$
$992$	0.675746	−	1.17043i	0.0214550	−	0.0371611i
$993$	−12.6791			−0.402358
$994$	−9.80434	+	16.9816i	−0.310975	+	0.538624i
$995$	17.7038	−	30.6638i	0.561247	−	0.972108i
$996$	−4.02020			−0.127385
$997$	−3.92925	+	6.80566i	−0.124441	+	0.215537i	−0.921514	−	0.388345i	$-0.873047\pi$
$997$	−3.92925	+	6.80566i	−0.124441	+	0.215537i	0.797074	+	0.603882i	$0.206380\pi$
$998$	10.6342	+	18.4190i	0.336621	+	0.583044i
$999$	−26.2240	−	45.4213i	−0.829690	−	1.43707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.c.94.6	✓	36
13.3	even	3		5239.2.a.p.1.13		18
13.9	even	3	inner	403.2.f.c.373.6	yes	36
13.10	even	6		5239.2.a.o.1.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.c.94.6	✓	36	1.1	even	1	trivial
403.2.f.c.373.6	yes	36	13.9	even	3	inner
5239.2.a.o.1.6		18	13.10	even	6
5239.2.a.p.1.13		18	13.3	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.748359 - 1.29620i) q^{2} +(0.472887 + 0.819064i) q^{3} +(-0.120081 + 0.207987i) q^{4} +2.74524 q^{5} +(0.707778 - 1.22591i) q^{6} +(1.47907 - 2.56182i) q^{7} -2.63398 q^{8} +(1.05276 - 1.82343i) q^{9} +O(q^{10})\)	\(q+(-0.748359 - 1.29620i) q^{2} +(0.472887 + 0.819064i) q^{3} +(-0.120081 + 0.207987i) q^{4} +2.74524 q^{5} +(0.707778 - 1.22591i) q^{6} +(1.47907 - 2.56182i) q^{7} -2.63398 q^{8} +(1.05276 - 1.82343i) q^{9} +(-2.05442 - 3.55837i) q^{10} +(2.37329 + 4.11066i) q^{11} -0.227139 q^{12} +(-3.20546 + 1.65077i) q^{13} -4.42750 q^{14} +(1.29819 + 2.24853i) q^{15} +(2.21132 + 3.83012i) q^{16} +(0.709910 - 1.22960i) q^{17} -3.15136 q^{18} +(0.240029 - 0.415742i) q^{19} +(-0.329652 + 0.570973i) q^{20} +2.79773 q^{21} +(3.55214 - 6.15249i) q^{22} +(-2.25007 - 3.89724i) q^{23} +(-1.24557 - 2.15740i) q^{24} +2.53635 q^{25} +(4.53855 + 2.91953i) q^{26} +4.82866 q^{27} +(0.355217 + 0.615253i) q^{28} +(3.21588 + 5.57006i) q^{29} +(1.94302 - 3.36541i) q^{30} +1.00000 q^{31} +(0.675746 - 1.17043i) q^{32} +(-2.24459 + 3.88775i) q^{33} -2.12507 q^{34} +(4.06040 - 7.03282i) q^{35} +(0.252832 + 0.437918i) q^{36} +(-5.43090 - 9.40660i) q^{37} -0.718510 q^{38} +(-2.86791 - 1.84485i) q^{39} -7.23091 q^{40} +(-4.05986 - 7.03188i) q^{41} +(-2.09371 - 3.62641i) q^{42} +(-3.27466 + 5.67187i) q^{43} -1.13995 q^{44} +(2.89007 - 5.00575i) q^{45} +(-3.36772 + 5.83306i) q^{46} +1.57090 q^{47} +(-2.09141 + 3.62243i) q^{48} +(-0.875296 - 1.51606i) q^{49} +(-1.89810 - 3.28760i) q^{50} +1.34283 q^{51} +(0.0415771 - 0.864918i) q^{52} +3.30954 q^{53} +(-3.61357 - 6.25888i) q^{54} +(6.51525 + 11.2847i) q^{55} +(-3.89584 + 6.74779i) q^{56} +0.454026 q^{57} +(4.81326 - 8.33681i) q^{58} +(-1.08009 + 1.87076i) q^{59} -0.623552 q^{60} +(-7.31732 + 12.6740i) q^{61} +(-0.748359 - 1.29620i) q^{62} +(-3.11420 - 5.39395i) q^{63} +6.82249 q^{64} +(-8.79975 + 4.53176i) q^{65} +6.71905 q^{66} +(-0.00292275 - 0.00506235i) q^{67} +(0.170493 + 0.295303i) q^{68} +(2.12806 - 3.68590i) q^{69} -12.1545 q^{70} +(2.21442 - 3.83549i) q^{71} +(-2.77294 + 4.80287i) q^{72} -5.00325 q^{73} +(-8.12853 + 14.0790i) q^{74} +(1.19940 + 2.07743i) q^{75} +(0.0576459 + 0.0998455i) q^{76} +14.0410 q^{77} +(-0.245062 + 5.09797i) q^{78} -1.66321 q^{79} +(6.07061 + 10.5146i) q^{80} +(-0.874858 - 1.51530i) q^{81} +(-6.07646 + 10.5247i) q^{82} +17.6993 q^{83} +(-0.335955 + 0.581891i) q^{84} +(1.94887 - 3.37555i) q^{85} +9.80247 q^{86} +(-3.04149 + 5.26802i) q^{87} +(-6.25119 - 10.8274i) q^{88} +(3.82299 + 6.62161i) q^{89} -8.65123 q^{90} +(-0.512115 + 10.6534i) q^{91} +1.08076 q^{92} +(0.472887 + 0.819064i) q^{93} +(-1.17560 - 2.03620i) q^{94} +(0.658937 - 1.14131i) q^{95} +1.27821 q^{96} +(-5.33293 + 9.23691i) q^{97} +(-1.31007 + 2.26911i) q^{98} +9.99398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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