LMFDB - Embedded newform 403.2.h.b.118.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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([0, 2]))

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.3
Character	$\chi$	$=$	403.118
Dual form			403.2.h.b.222.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.85162 q^{2} +(0.240159 + 0.415967i) q^{3} +1.42848 q^{4} +(0.854909 - 1.48075i) q^{5} +(-0.444682 - 0.770212i) q^{6} +(-0.531962 - 0.921385i) q^{7} +1.05824 q^{8} +(1.38465 - 2.39828i) q^{9} +O(q^{10})$	\(q-1.85162 q^{2} +(0.240159 + 0.415967i) q^{3} +1.42848 q^{4} +(0.854909 - 1.48075i) q^{5} +(-0.444682 - 0.770212i) q^{6} +(-0.531962 - 0.921385i) q^{7} +1.05824 q^{8} +(1.38465 - 2.39828i) q^{9} +(-1.58296 + 2.74177i) q^{10} +(-1.35310 + 2.34363i) q^{11} +(0.343062 + 0.594201i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(0.984989 + 1.70605i) q^{14} +0.821256 q^{15} -4.81641 q^{16} +(-2.30153 - 3.98636i) q^{17} +(-2.56383 + 4.44069i) q^{18} +(-2.35112 - 4.07226i) q^{19} +(1.22122 - 2.11522i) q^{20} +(0.255511 - 0.442558i) q^{21} +(2.50541 - 4.33950i) q^{22} +0.635348 q^{23} +(0.254145 + 0.440192i) q^{24} +(1.03826 + 1.79832i) q^{25} +(0.925808 - 1.60355i) q^{26} +2.77110 q^{27} +(-0.759897 - 1.31618i) q^{28} +8.27995 q^{29} -1.52065 q^{30} +(-3.77960 - 4.08835i) q^{31} +6.80166 q^{32} -1.29983 q^{33} +(4.26154 + 7.38121i) q^{34} -1.81912 q^{35} +(1.97794 - 3.42589i) q^{36} +(-5.38526 - 9.32754i) q^{37} +(4.35337 + 7.54025i) q^{38} -0.480318 q^{39} +(0.904695 - 1.56698i) q^{40} +(2.87333 - 4.97675i) q^{41} +(-0.473108 + 0.819446i) q^{42} +(-3.63911 - 6.30313i) q^{43} +(-1.93287 + 3.34783i) q^{44} +(-2.36750 - 4.10062i) q^{45} -1.17642 q^{46} +1.75655 q^{47} +(-1.15670 - 2.00347i) q^{48} +(2.93403 - 5.08189i) q^{49} +(-1.92246 - 3.32980i) q^{50} +(1.10546 - 1.91472i) q^{51} +(-0.714240 + 1.23710i) q^{52} +(-0.713902 + 1.23651i) q^{53} -5.13100 q^{54} +(2.31355 + 4.00718i) q^{55} +(-0.562941 - 0.975042i) q^{56} +(1.12928 - 1.95598i) q^{57} -15.3313 q^{58} +(-1.20360 - 2.08470i) q^{59} +1.17315 q^{60} +11.0363 q^{61} +(6.99837 + 7.57005i) q^{62} -2.94632 q^{63} -2.96125 q^{64} +(0.854909 + 1.48075i) q^{65} +2.40679 q^{66} +(-2.39741 + 4.15244i) q^{67} +(-3.28768 - 5.69444i) q^{68} +(0.152585 + 0.264284i) q^{69} +3.36830 q^{70} +(-6.06136 + 10.4986i) q^{71} +(1.46528 - 2.53795i) q^{72} +(-3.91127 + 6.77452i) q^{73} +(9.97143 + 17.2710i) q^{74} +(-0.498695 + 0.863766i) q^{75} +(-3.35852 - 5.81713i) q^{76} +2.87918 q^{77} +0.889364 q^{78} +(-3.09572 - 5.36195i) q^{79} +(-4.11759 + 7.13187i) q^{80} +(-3.48844 - 6.04215i) q^{81} +(-5.32029 + 9.21502i) q^{82} +(4.24548 - 7.35339i) q^{83} +(0.364992 - 0.632185i) q^{84} -7.87038 q^{85} +(6.73824 + 11.6710i) q^{86} +(1.98850 + 3.44419i) q^{87} +(-1.43189 + 2.48011i) q^{88} +7.00404 q^{89} +(4.38369 + 7.59277i) q^{90} +1.06392 q^{91} +0.907582 q^{92} +(0.792916 - 2.55405i) q^{93} -3.25245 q^{94} -8.03997 q^{95} +(1.63348 + 2.82927i) q^{96} -9.12762 q^{97} +(-5.43270 + 9.40971i) q^{98} +(3.74712 + 6.49021i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.85162			−1.30929			−0.654645	−	0.755937i	$-0.727182\pi$
$2$	−1.85162			−1.30929			−0.654645	+	0.755937i	$0.727182\pi$
$3$	0.240159	+	0.415967i	0.138656	+	0.240159i	0.926988	−	0.375091i	$-0.122388\pi$
$3$	0.240159	+	0.415967i	0.138656	+	0.240159i	−0.788332	+	0.615250i	$0.789055\pi$
$4$	1.42848			0.714240
$5$	0.854909	−	1.48075i	0.382327	−	0.662210i	−0.609067	−	0.793118i	$-0.708456\pi$
$5$	0.854909	−	1.48075i	0.382327	−	0.662210i	0.991394	+	0.130909i	$0.0417895\pi$
$6$	−0.444682	−	0.770212i	−0.181541	−	0.314438i
$7$	−0.531962	−	0.921385i	−0.201063	−	0.348251i	0.747808	−	0.663915i	$-0.231106\pi$
$7$	−0.531962	−	0.921385i	−0.201063	−	0.348251i	−0.948871	+	0.315664i	$0.897773\pi$
$8$	1.05824			0.374143
$9$	1.38465	−	2.39828i	0.461549	−	0.799427i
$10$	−1.58296	+	2.74177i	−0.500577	+	0.867024i
$11$	−1.35310	+	2.34363i	−0.407974	+	0.706631i	−0.994663	−	0.103181i	$-0.967098\pi$
$11$	−1.35310	+	2.34363i	−0.407974	+	0.706631i	0.586689	+	0.809813i	$0.300431\pi$
$12$	0.343062	+	0.594201i	0.0990335	+	0.171531i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	0.984989	+	1.70605i	0.263249	+	0.455961i
$15$	0.821256			0.212047
$16$	−4.81641			−1.20410
$17$	−2.30153	−	3.98636i	−0.558202	−	0.966834i	−0.997647	−	0.0685648i	$-0.978158\pi$
$17$	−2.30153	−	3.98636i	−0.558202	−	0.966834i	0.439445	−	0.898270i	$-0.355175\pi$
$18$	−2.56383	+	4.44069i	−0.604302	+	1.04668i
$19$	−2.35112	−	4.07226i	−0.539383	−	0.934239i	−0.998937	−	0.0460895i	$-0.985324\pi$
$19$	−2.35112	−	4.07226i	−0.539383	−	0.934239i	0.459554	−	0.888150i	$-0.348009\pi$
$20$	1.22122	−	2.11522i	0.273073	−	0.472977i
$21$	0.255511	−	0.442558i	0.0557570	−	0.0965740i
$22$	2.50541	−	4.33950i	0.534156	−	0.925185i
$23$	0.635348			0.132479			0.0662396	−	0.997804i	$-0.478900\pi$
$23$	0.635348			0.132479			0.0662396	+	0.997804i	$0.478900\pi$
$24$	0.254145	+	0.440192i	0.0518771	+	0.0898537i
$25$	1.03826	+	1.79832i	0.207652	+	0.359664i
$26$	0.925808	−	1.60355i	0.181566	−	0.314481i
$27$	2.77110			0.533298
$28$	−0.759897	−	1.31618i	−0.143607	−	0.248735i
$29$	8.27995			1.53755			0.768774	−	0.639520i	$-0.220867\pi$
$29$	8.27995			1.53755			0.768774	+	0.639520i	$0.220867\pi$
$30$	−1.52065			−0.277632
$31$	−3.77960	−	4.08835i	−0.678836	−	0.734289i
$31$	−3.77960	−	4.08835i	−0.678836	−	0.734289i
$32$	6.80166			1.20237
$33$	−1.29983			−0.226272
$34$	4.26154	+	7.38121i	0.730848	+	1.26587i
$35$	−1.81912			−0.307487
$36$	1.97794	−	3.42589i	0.329657	−	0.570982i
$37$	−5.38526	−	9.32754i	−0.885331	−	1.53344i	−0.845333	−	0.534239i	$-0.820598\pi$
$37$	−5.38526	−	9.32754i	−0.885331	−	1.53344i	−0.0399978	−	0.999200i	$-0.512735\pi$
$38$	4.35337	+	7.54025i	0.706209	+	1.22319i
$39$	−0.480318			−0.0769124
$40$	0.904695	−	1.56698i	0.143045	−	0.247761i
$41$	2.87333	−	4.97675i	0.448738	−	0.777237i	−0.549566	−	0.835450i	$-0.685207\pi$
$41$	2.87333	−	4.97675i	0.448738	−	0.777237i	0.998304	+	0.0582131i	$0.0185403\pi$
$42$	−0.473108	+	0.819446i	−0.0730021	+	0.126443i
$43$	−3.63911	−	6.30313i	−0.554959	−	0.961218i	−0.997907	−	0.0646703i	$-0.979400\pi$
$43$	−3.63911	−	6.30313i	−0.554959	−	0.961218i	0.442947	−	0.896548i	$-0.353933\pi$
$44$	−1.93287	+	3.34783i	−0.291391	+	0.504704i
$45$	−2.36750	−	4.10062i	−0.352925	−	0.611285i
$46$	−1.17642			−0.173454
$47$	1.75655			0.256219			0.128109	−	0.991760i	$-0.459109\pi$
$47$	1.75655			0.256219			0.128109	+	0.991760i	$0.459109\pi$
$48$	−1.15670	−	2.00347i	−0.166956	−	0.289176i
$49$	2.93403	−	5.08189i	0.419148	−	0.725985i
$50$	−1.92246	−	3.32980i	−0.271877	−	0.470905i
$51$	1.10546	−	1.91472i	0.154796	−	0.268114i
$52$	−0.714240	+	1.23710i	−0.0990472	+	0.171555i
$53$	−0.713902	+	1.23651i	−0.0980620	+	0.169848i	−0.910882	−	0.412666i	$-0.864598\pi$
$53$	−0.713902	+	1.23651i	−0.0980620	+	0.169848i	0.812820	+	0.582514i	$0.197931\pi$
$54$	−5.13100			−0.698241
$55$	2.31355	+	4.00718i	0.311959	+	0.540329i
$56$	−0.562941	−	0.975042i	−0.0752262	−	0.130296i
$57$	1.12928	−	1.95598i	0.149577	−	0.259075i
$58$	−15.3313			−2.01310
$59$	−1.20360	−	2.08470i	−0.156695	−	0.271404i	0.776980	−	0.629526i	$-0.216751\pi$
$59$	−1.20360	−	2.08470i	−0.156695	−	0.271404i	−0.933675	+	0.358121i	$0.883417\pi$
$60$	1.17315			0.151453
$61$	11.0363			1.41305			0.706526	−	0.707687i	$-0.250261\pi$
$61$	11.0363			1.41305			0.706526	+	0.707687i	$0.250261\pi$
$62$	6.99837	+	7.57005i	0.888794	+	0.961398i
$63$	−2.94632			−0.371201
$64$	−2.96125			−0.370156
$65$	0.854909	+	1.48075i	0.106038	+	0.183664i
$66$	2.40679			0.296255
$67$	−2.39741	+	4.15244i	−0.292891	+	0.507302i	−0.974492	−	0.224422i	$-0.927951\pi$
$67$	−2.39741	+	4.15244i	−0.292891	+	0.507302i	0.681601	+	0.731724i	$0.261284\pi$
$68$	−3.28768	−	5.69444i	−0.398690	−	0.690552i
$69$	0.152585	+	0.264284i	0.0183690	+	0.0318161i
$70$	3.36830			0.402589
$71$	−6.06136	+	10.4986i	−0.719351	+	1.24595i	0.241906	+	0.970300i	$0.422228\pi$
$71$	−6.06136	+	10.4986i	−0.719351	+	1.24595i	−0.961257	+	0.275653i	$0.911106\pi$
$72$	1.46528	−	2.53795i	0.172685	−	0.299100i
$73$	−3.91127	+	6.77452i	−0.457780	+	0.792898i	−0.998843	−	0.0480837i	$-0.984689\pi$
$73$	−3.91127	+	6.77452i	−0.457780	+	0.792898i	0.541063	+	0.840982i	$0.318022\pi$
$74$	9.97143	+	17.2710i	1.15916	+	2.00772i
$75$	−0.498695	+	0.863766i	−0.0575844	+	0.0997391i
$76$	−3.35852	−	5.81713i	−0.385249	−	0.667271i
$77$	2.87918			0.328113
$78$	0.889364			0.100701
$79$	−3.09572	−	5.36195i	−0.348296	−	0.603266i	0.637651	−	0.770325i	$-0.279906\pi$
$79$	−3.09572	−	5.36195i	−0.348296	−	0.603266i	−0.985947	+	0.167059i	$0.946573\pi$
$80$	−4.11759	+	7.13187i	−0.460360	+	0.797368i
$81$	−3.48844	−	6.04215i	−0.387604	−	0.671350i
$82$	−5.32029	+	9.21502i	−0.587528	+	1.01763i
$83$	4.24548	−	7.35339i	0.466002	−	0.807139i	−0.533244	−	0.845961i	$-0.679027\pi$
$83$	4.24548	−	7.35339i	0.466002	−	0.807139i	0.999246	+	0.0388224i	$0.0123607\pi$
$84$	0.364992	−	0.632185i	0.0398239	−	0.0689770i
$85$	−7.87038			−0.853663
$86$	6.73824	+	11.6710i	0.726603	+	1.25851i
$87$	1.98850	+	3.44419i	0.213190	+	0.369256i
$88$	−1.43189	+	2.48011i	−0.152641	+	0.264381i
$89$	7.00404			0.742426			0.371213	−	0.928548i	$-0.378942\pi$
$89$	7.00404			0.742426			0.371213	+	0.928548i	$0.378942\pi$
$90$	4.38369	+	7.59277i	0.462082	+	0.800349i
$91$	1.06392			0.111529
$92$	0.907582			0.0946220
$93$	0.792916	−	2.55405i	0.0822215	−	0.264842i
$94$	−3.25245			−0.335464
$95$	−8.03997			−0.824883
$96$	1.63348	+	2.82927i	0.166716	+	0.288761i
$97$	−9.12762			−0.926769			−0.463385	−	0.886157i	$-0.653365\pi$
$97$	−9.12762			−0.926769			−0.463385	+	0.886157i	$0.653365\pi$
$98$	−5.43270	+	9.40971i	−0.548786	+	0.950525i
$99$	3.74712	+	6.49021i	0.376600	+	0.652290i
$100$	1.48313	+	2.56886i	0.148313	+	0.256886i
$101$	14.0711			1.40013			0.700064	−	0.714080i	$-0.253155\pi$
$101$	14.0711			1.40013			0.700064	+	0.714080i	$0.253155\pi$
$102$	−2.04689	+	3.54533i	−0.202673	+	0.351040i
$103$	−5.70879	+	9.88791i	−0.562504	+	0.974285i	0.434774	+	0.900540i	$0.356828\pi$
$103$	−5.70879	+	9.88791i	−0.562504	+	0.974285i	−0.997277	+	0.0737450i	$0.976505\pi$
$104$	−0.529118	+	0.916459i	−0.0518843	+	0.0898662i
$105$	−0.436877	−	0.756693i	−0.0426348	−	0.0738457i
$106$	1.32187	−	2.28955i	0.128392	−	0.222381i
$107$	9.50665	+	16.4660i	0.919043	+	1.59183i	0.800872	+	0.598836i	$0.204370\pi$
$107$	9.50665	+	16.4660i	0.919043	+	1.59183i	0.118171	+	0.992993i	$0.462297\pi$
$108$	3.95845			0.380902
$109$	−12.3913			−1.18687			−0.593436	−	0.804881i	$-0.702229\pi$
$109$	−12.3913			−1.18687			−0.593436	+	0.804881i	$0.702229\pi$
$110$	−4.28380	−	7.41976i	−0.408445	−	0.707447i
$111$	2.58664	−	4.48019i	0.245513	−	0.425240i
$112$	2.56214	+	4.43776i	0.242100	+	0.419329i
$113$	−8.32725	+	14.4232i	−0.783361	+	1.35682i	0.146612	+	0.989194i	$0.453163\pi$
$113$	−8.32725	+	14.4232i	−0.783361	+	1.35682i	−0.929973	+	0.367628i	$0.880170\pi$
$114$	−2.09100	+	3.62172i	−0.195840	+	0.339205i
$115$	0.543165	−	0.940789i	0.0506504	−	0.0877291i
$116$	11.8277			1.09818
$117$	1.38465	+	2.39828i	0.128011	+	0.221721i
$118$	2.22860	+	3.86006i	0.205160	+	0.355347i
$119$	−2.44865	+	4.24118i	−0.224467	+	0.388789i
$120$	0.869083			0.0793360
$121$	1.83826	+	3.18396i	0.167115	+	0.289451i
$122$	−20.4350			−1.85009
$123$	2.76022			0.248881
$124$	−5.39908	−	5.84013i	−0.484852	−	0.524459i
$125$	12.0996			1.08222
$126$	5.45545			0.486010
$127$	−4.96085	−	8.59244i	−0.440204	−	0.762456i	0.557500	−	0.830177i	$-0.311761\pi$
$127$	−4.96085	−	8.59244i	−0.440204	−	0.762456i	−0.997704	+	0.0677208i	$0.978427\pi$
$128$	−8.12023			−0.717734
$129$	1.74793	−	3.02750i	0.153897	−	0.266557i
$130$	−1.58296	−	2.74177i	−0.138835	−	0.240469i
$131$	9.78575	+	16.9494i	0.854985	+	1.48088i	0.876659	+	0.481113i	$0.159767\pi$
$131$	9.78575	+	16.9494i	0.854985	+	1.48088i	−0.0216736	+	0.999765i	$0.506899\pi$
$132$	−1.85678			−0.161612
$133$	−2.50141	+	4.33257i	−0.216900	+	0.375681i
$134$	4.43909	−	7.68873i	0.383479	−	0.664205i
$135$	2.36903	−	4.10329i	0.203894	−	0.353155i
$136$	−2.43556	−	4.21851i	−0.208847	−	0.361734i
$137$	6.48511	−	11.2325i	0.554060	−	0.959660i	−0.443916	−	0.896068i	$-0.646411\pi$
$137$	6.48511	−	11.2325i	0.554060	−	0.959660i	0.997976	−	0.0635918i	$-0.0202556\pi$
$138$	−0.282528	−	0.489353i	−0.0240504	−	0.0416565i
$139$	15.0973			1.28054			0.640270	−	0.768150i	$-0.278823\pi$
$139$	15.0973			1.28054			0.640270	+	0.768150i	$0.278823\pi$
$140$	−2.59857			−0.219619
$141$	0.421850	+	0.730666i	0.0355262	+	0.0615332i
$142$	11.2233	−	19.4393i	0.941839	−	1.63131i
$143$	−1.35310	−	2.34363i	−0.113152	−	0.195984i
$144$	−6.66902	+	11.5511i	−0.555752	+	0.962591i
$145$	7.07861	−	12.2605i	0.587846	−	1.01818i
$146$	7.24217	−	12.5438i	0.599367	−	1.03813i
$147$	2.81854			0.232469
$148$	−7.69273	−	13.3242i	−0.632339	−	1.09524i
$149$	−6.98591	−	12.1000i	−0.572308	−	0.991267i	−0.996328	−	0.0856144i	$-0.972715\pi$
$149$	−6.98591	−	12.1000i	−0.572308	−	0.991267i	0.424020	−	0.905653i	$-0.360619\pi$
$150$	0.923392	−	1.59936i	0.0753946	−	0.130587i
$151$	20.0585			1.63233			0.816167	−	0.577816i	$-0.196095\pi$
$151$	20.0585			1.63233			0.816167	+	0.577816i	$0.196095\pi$
$152$	−2.48804	−	4.30941i	−0.201806	−	0.349539i
$153$	−12.7472			−1.03055
$154$	−5.33114			−0.429595
$155$	−9.28502	+	2.10146i	−0.745791	+	0.168793i
$156$	−0.686124			−0.0549339
$157$	−7.66309			−0.611582			−0.305791	−	0.952099i	$-0.598921\pi$
$157$	−7.66309			−0.611582			−0.305791	+	0.952099i	$0.598921\pi$
$158$	5.73209	+	9.92826i	0.456020	+	0.789850i
$159$	−0.685800			−0.0543875
$160$	5.81480	−	10.0715i	0.459700	−	0.796224i
$161$	−0.337981	−	0.585400i	−0.0266366	−	0.0461360i
$162$	6.45925	+	11.1877i	0.507486	+	0.878992i
$163$	−10.1777			−0.797176			−0.398588	−	0.917130i	$-0.630500\pi$
$163$	−10.1777			−0.797176			−0.398588	+	0.917130i	$0.630500\pi$
$164$	4.10449	−	7.10918i	0.320507	−	0.555134i
$165$	−1.11124	+	1.92472i	−0.0865098	+	0.149839i
$166$	−7.86099	+	13.6156i	−0.610131	+	1.05678i
$167$	−1.30887	−	2.26703i	−0.101284	−	0.175428i	0.810930	−	0.585143i	$-0.198962\pi$
$167$	−1.30887	−	2.26703i	−0.101284	−	0.175428i	−0.912214	+	0.409715i	$0.865628\pi$
$168$	0.270391	−	0.468330i	0.0208611	−	0.0361325i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	14.5729			1.11769
$171$	−13.0219			−0.995808
$172$	−5.19840	−	9.00389i	−0.396374	−	0.686540i
$173$	−0.582073	+	1.00818i	−0.0442542	+	0.0766506i	−0.887304	−	0.461185i	$-0.847424\pi$
$173$	−0.582073	+	1.00818i	−0.0442542	+	0.0766506i	0.843050	+	0.537835i	$0.180758\pi$
$174$	−3.68195	−	6.37732i	−0.279128	−	0.483463i
$175$	1.10463	−	1.91328i	0.0835022	−	0.144630i
$176$	6.51706	−	11.2879i	0.491242	−	0.850856i
$177$	0.578111	−	1.00132i	0.0434535	−	0.0752636i
$178$	−12.9688			−0.972051
$179$	−7.76515	−	13.4496i	−0.580394	−	1.00527i	−0.995432	−	0.0954683i	$-0.969565\pi$
$179$	−7.76515	−	13.4496i	−0.580394	−	1.00527i	0.415038	−	0.909804i	$-0.363768\pi$
$180$	−3.38192	−	5.85766i	−0.252073	−	0.436604i
$181$	2.78262	−	4.81964i	0.206830	−	0.358241i	−0.743884	−	0.668309i	$-0.767018\pi$
$181$	2.78262	−	4.81964i	0.206830	−	0.358241i	0.950714	+	0.310068i	$0.100352\pi$
$182$	−1.96998			−0.146024
$183$	2.65046	+	4.59073i	0.195928	+	0.339357i
$184$	0.672348			0.0495662
$185$	−18.4156			−1.35394
$186$	−1.46818	+	4.72911i	−0.107652	+	0.346755i
$187$	12.4567			0.910928
$188$	2.50919			0.183002
$189$	−1.47412	−	2.55325i	−0.107226	−	0.185721i
$190$	14.8869			1.08001
$191$	−3.43734	+	5.95365i	−0.248717	+	0.430791i	−0.963170	−	0.268893i	$-0.913342\pi$
$191$	−3.43734	+	5.95365i	−0.248717	+	0.430791i	0.714453	+	0.699684i	$0.246676\pi$
$192$	−0.711170	−	1.23178i	−0.0513242	−	0.0888962i
$193$	11.7763	+	20.3971i	0.847675	+	1.46822i	0.883278	+	0.468849i	$0.155331\pi$
$193$	11.7763	+	20.3971i	0.847675	+	1.46822i	−0.0356036	+	0.999366i	$0.511335\pi$
$194$	16.9008			1.21341
$195$	−0.410628	+	0.711229i	−0.0294057	+	0.0509321i
$196$	4.19121	−	7.25938i	0.299372	−	0.518527i
$197$	2.73347	−	4.73452i	0.194752	−	0.337320i	−0.752067	−	0.659086i	$-0.770943\pi$
$197$	2.73347	−	4.73452i	0.194752	−	0.337320i	0.946819	+	0.321766i	$0.104276\pi$
$198$	−6.93823	−	12.0174i	−0.493079	−	0.854037i
$199$	0.434015	−	0.751736i	0.0307665	−	0.0532891i	−0.850232	−	0.526408i	$-0.823539\pi$
$199$	0.434015	−	0.751736i	0.0307665	−	0.0532891i	0.880999	+	0.473119i	$0.156872\pi$
$200$	1.09872	+	1.90305i	0.0776916	+	0.134566i
$201$	−2.30304			−0.162444
$202$	−26.0543			−1.83317
$203$	−4.40462	−	7.62902i	−0.309144	−	0.535452i
$204$	1.57913	−	2.73514i	0.110561	−	0.191498i
$205$	−4.91286	−	8.50933i	−0.343129	−	0.594317i
$206$	10.5705	−	18.3086i	0.736480	−	1.27562i
$207$	0.879733	−	1.52374i	0.0611457	−	0.105907i
$208$	2.40820	−	4.17113i	0.166979	−	0.289216i
$209$	12.7252			0.880217
$210$	0.808928	+	1.40110i	0.0558213	+	0.0966854i
$211$	−3.48542	−	6.03692i	−0.239946	−	0.415599i	0.720753	−	0.693192i	$-0.243796\pi$
$211$	−3.48542	−	6.03692i	−0.239946	−	0.415599i	−0.960699	+	0.277594i	$0.910463\pi$
$212$	−1.01979	+	1.76634i	−0.0700398	+	0.121312i
$213$	−5.82276			−0.398969
$214$	−17.6027	−	30.4887i	−1.20329	−	2.08417i
$215$	−12.4444			−0.848704
$216$	2.93247			0.199529
$217$	−1.75634	+	5.65731i	−0.119228	+	0.384044i
$218$	22.9439			1.55396
$219$	−3.75731			−0.253895
$220$	3.30486	+	5.72418i	0.222813	+	0.385924i
$221$	4.60305			0.309635
$222$	−4.78946	+	8.29558i	−0.321447	+	0.556763i
$223$	3.62959	+	6.28663i	0.243055	+	0.420984i	0.961583	−	0.274514i	$-0.0885170\pi$
$223$	3.62959	+	6.28663i	0.243055	+	0.420984i	−0.718528	+	0.695498i	$0.755184\pi$
$224$	−3.61822	−	6.26695i	−0.241753	−	0.418728i
$225$	5.75050			0.383367
$226$	15.4189	−	26.7062i	1.02565	−	1.77647i
$227$	1.56075	−	2.70329i	0.103590	−	0.179424i	−0.809571	−	0.587022i	$-0.800300\pi$
$227$	1.56075	−	2.70329i	0.103590	−	0.179424i	0.913161	+	0.407598i	$0.133634\pi$
$228$	1.61316	−	2.79407i	0.106834	−	0.185042i
$229$	12.3556	+	21.4005i	0.816481	+	1.41419i	0.908260	+	0.418407i	$0.137411\pi$
$229$	12.3556	+	21.4005i	0.816481	+	1.41419i	−0.0917786	+	0.995779i	$0.529255\pi$
$230$	−1.00573	+	1.74198i	−0.0663160	+	0.114863i
$231$	0.691461	+	1.19765i	0.0454948	+	0.0787993i
$232$	8.76214			0.575263
$233$	−15.0588			−0.986534			−0.493267	−	0.869878i	$-0.664197\pi$
$233$	−15.0588			−0.986534			−0.493267	+	0.869878i	$0.664197\pi$
$234$	−2.56383	−	4.44069i	−0.167603	−	0.290297i
$235$	1.50169	−	2.60100i	0.0979593	−	0.169670i
$236$	−1.71932	−	2.97795i	−0.111918	−	0.193848i
$237$	1.48693	−	2.57544i	0.0965865	−	0.167293i
$238$	4.53395	−	7.85304i	0.293893	−	0.509037i
$239$	−9.36069	+	16.2132i	−0.605493	+	1.04874i	0.386480	+	0.922298i	$0.373691\pi$
$239$	−9.36069	+	16.2132i	−0.605493	+	1.04874i	−0.991973	+	0.126447i	$0.959643\pi$
$240$	−3.95550			−0.255327
$241$	3.71497	+	6.43452i	0.239302	+	0.414484i	0.960514	−	0.278231i	$-0.0897480\pi$
$241$	3.71497	+	6.43452i	0.239302	+	0.414484i	−0.721212	+	0.692714i	$0.756415\pi$
$242$	−3.40375	−	5.89547i	−0.218801	−	0.378975i
$243$	5.83220	−	10.1017i	0.374136	−	0.648022i
$244$	15.7651			1.00926
$245$	−5.01666	−	8.68912i	−0.320503	−	0.555127i
$246$	−5.11086			−0.325857
$247$	4.70224			0.299196
$248$	−3.99971	−	4.32644i	−0.253982	−	0.274729i
$249$	4.07836			0.258455
$250$	−22.4037			−1.41694
$251$	12.3850	+	21.4514i	0.781732	+	1.35400i	0.930932	+	0.365193i	$0.118997\pi$
$251$	12.3850	+	21.4514i	0.781732	+	1.35400i	−0.149199	+	0.988807i	$0.547670\pi$
$252$	−4.20876			−0.265127
$253$	−0.859687	+	1.48902i	−0.0540481	+	0.0936140i
$254$	9.18559	+	15.9099i	0.576355	+	0.998276i
$255$	−1.89014	−	3.27382i	−0.118365	−	0.205015i
$256$	20.9580			1.30988
$257$	−7.26926	+	12.5907i	−0.453444	+	0.785388i	−0.998597	−	0.0529481i	$-0.983138\pi$
$257$	−7.26926	+	12.5907i	−0.453444	+	0.785388i	0.545153	+	0.838337i	$0.316472\pi$
$258$	−3.23650	+	5.60577i	−0.201495	+	0.349000i
$259$	−5.72951	+	9.92379i	−0.356014	+	0.616635i
$260$	1.22122	+	2.11522i	0.0757369	+	0.131180i
$261$	11.4648	−	19.8576i	0.709654	−	1.22916i
$262$	−18.1195	−	31.3838i	−1.11942	−	1.93890i
$263$	18.1161			1.11708			0.558542	−	0.829476i	$-0.311361\pi$
$263$	18.1161			1.11708			0.558542	+	0.829476i	$0.311361\pi$
$264$	−1.37553			−0.0846580
$265$	1.22064	+	2.11422i	0.0749835	+	0.129875i
$266$	4.63165	−	8.02225i	0.283985	−	0.491876i
$267$	1.68208	+	2.91345i	0.102942	+	0.178300i
$268$	−3.42466	+	5.93168i	−0.209194	+	0.362335i
$269$	9.37251	−	16.2337i	0.571452	−	0.989783i	−0.424965	−	0.905210i	$-0.639714\pi$
$269$	9.37251	−	16.2337i	0.571452	−	0.989783i	0.996417	−	0.0845739i	$-0.0269529\pi$
$270$	−4.38654	+	7.59771i	−0.266956	+	0.462382i
$271$	1.64819			0.100121			0.0500603	−	0.998746i	$-0.484059\pi$
$271$	1.64819			0.100121			0.0500603	+	0.998746i	$0.484059\pi$
$272$	11.0851	+	19.1999i	0.672132	+	1.16417i
$273$	0.255511	+	0.442558i	0.0154642	+	0.0267848i
$274$	−12.0079	+	20.7983i	−0.725425	+	1.25647i
$275$	−5.61947			−0.338867
$276$	0.217964	+	0.377525i	0.0131199	+	0.0227243i
$277$	−3.48177			−0.209199			−0.104600	−	0.994514i	$-0.533356\pi$
$277$	−3.48177			−0.209199			−0.104600	+	0.994514i	$0.533356\pi$
$278$	−27.9545			−1.67660
$279$	−15.0384	+	3.40362i	−0.900327	+	0.203769i
$280$	−1.92505			−0.115044
$281$	14.8454			0.885601			0.442800	−	0.896620i	$-0.353985\pi$
$281$	14.8454			0.885601			0.442800	+	0.896620i	$0.353985\pi$
$282$	−0.781104	−	1.35291i	−0.0465141	−	0.0805648i
$283$	11.2319			0.667664			0.333832	−	0.942633i	$-0.391658\pi$
$283$	11.2319			0.667664			0.333832	+	0.942633i	$0.391658\pi$
$284$	−8.65853	+	14.9970i	−0.513789	+	0.889909i
$285$	−1.93087	−	3.34436i	−0.114375	−	0.198103i
$286$	2.50541	+	4.33950i	0.148148	+	0.256600i
$287$	−6.11400			−0.360898
$288$	9.41790	−	16.3123i	0.554955	−	0.961210i
$289$	−2.09405	+	3.62700i	−0.123179	+	0.213353i
$290$	−13.1069	+	22.7017i	−0.769661	+	1.33309i
$291$	−2.19208	−	3.79679i	−0.128502	−	0.222572i
$292$	−5.58718	+	9.67727i	−0.326965	+	0.566319i
$293$	−5.76767	−	9.98989i	−0.336951	−	0.583616i	0.646907	−	0.762569i	$-0.276062\pi$
$293$	−5.76767	−	9.98989i	−0.336951	−	0.583616i	−0.983858	+	0.178953i	$0.942729\pi$
$294$	−5.21885			−0.304369
$295$	−4.11587			−0.239635
$296$	−5.69887	−	9.87074i	−0.331240	−	0.573725i
$297$	−3.74956	+	6.49443i	−0.217571	+	0.376845i
$298$	12.9352	+	22.4045i	0.749318	+	1.29786i
$299$	−0.317674	+	0.550228i	−0.0183716	+	0.0318205i
$300$	−0.712376	+	1.23387i	−0.0411291	+	0.0712376i
$301$	−3.87174	+	6.70605i	−0.223163	+	0.386530i
$302$	−37.1405			−2.13720
$303$	3.37930	+	5.85313i	0.194136	+	0.336253i
$304$	11.3239	+	19.6136i	0.649472	+	1.12492i
$305$	9.43502	−	16.3419i	0.540248	−	0.935736i
$306$	23.6029			1.34929
$307$	14.2772	+	24.7288i	0.814842	+	1.41135i	0.909441	+	0.415833i	$0.136510\pi$
$307$	14.2772	+	24.7288i	0.814842	+	1.41135i	−0.0945991	+	0.995515i	$0.530157\pi$
$308$	4.11285			0.234352
$309$	−5.48407			−0.311978
$310$	17.1923	−	3.89110i	0.976457	−	0.221000i
$311$	−9.85332			−0.558730			−0.279365	−	0.960185i	$-0.590124\pi$
$311$	−9.85332			−0.558730			−0.279365	+	0.960185i	$0.590124\pi$
$312$	−0.508290			−0.0287762
$313$	−0.00983697	−	0.0170381i	−0.000556019	−	0.000963053i	0.865747	−	0.500481i	$-0.166844\pi$
$313$	−0.00983697	−	0.0170381i	−0.000556019	−	0.000963053i	−0.866303	+	0.499518i	$0.833510\pi$
$314$	14.1891			0.800737
$315$	−2.51883	+	4.36275i	−0.141920	+	0.245813i
$316$	−4.42218	−	7.65943i	−0.248767	−	0.430877i
$317$	−2.50984	−	4.34717i	−0.140967	−	0.244161i	0.786894	−	0.617088i	$-0.211688\pi$
$317$	−2.50984	−	4.34717i	−0.140967	−	0.244161i	−0.927861	+	0.372926i	$0.878354\pi$
$318$	1.26984			0.0712090
$319$	−11.2036	+	19.4052i	−0.627280	+	1.08648i
$320$	−2.53160	+	4.38485i	−0.141520	+	0.245121i
$321$	−4.56622	+	7.90892i	−0.254861	+	0.441433i
$322$	0.625811	+	1.08394i	0.0348751	+	0.0604054i
$323$	−10.8223	+	18.7448i	−0.602170	+	1.04299i
$324$	−4.98316	−	8.63109i	−0.276842	−	0.479505i
$325$	−2.07652			−0.115185
$326$	18.8451			1.04373
$327$	−2.97588	−	5.15438i	−0.164567	−	0.285038i
$328$	3.04066	−	5.26657i	0.167892	−	0.290798i
$329$	−0.934415	−	1.61845i	−0.0515160	−	0.0892283i
$330$	2.05759	−	3.56384i	0.113266	−	0.196183i
$331$	0.399168	−	0.691380i	0.0219403	−	0.0380017i	−0.854847	−	0.518880i	$-0.826349\pi$
$331$	0.399168	−	0.691380i	0.0219403	−	0.0380017i	0.876787	+	0.480879i	$0.159682\pi$
$332$	6.06458	−	10.5042i	0.332837	−	0.576491i
$333$	−29.8267			−1.63450
$334$	2.42353	+	4.19768i	0.132610	+	0.229687i
$335$	4.09914	+	7.09992i	0.223960	+	0.387910i
$336$	−1.23064	+	2.13154i	−0.0671371	+	0.116285i
$337$	22.3424			1.21707			0.608535	−	0.793527i	$-0.291758\pi$
$337$	22.3424			1.21707			0.608535	+	0.793527i	$0.291758\pi$
$338$	0.925808	+	1.60355i	0.0503573	+	0.0872214i
$339$	−7.99945			−0.434470
$340$	−11.2427			−0.609720
$341$	14.6958	−	3.32606i	0.795820	−	0.180116i
$342$	24.1115			1.30380
$343$	−13.6906			−0.739225
$344$	−3.85104	−	6.67020i	−0.207634	−	0.359633i
$345$	0.521784			0.0280919
$346$	1.07778	−	1.86676i	0.0579416	−	0.100358i
$347$	3.46154	+	5.99556i	0.185825	+	0.321858i	0.943854	−	0.330362i	$-0.107171\pi$
$347$	3.46154	+	5.99556i	0.185825	+	0.321858i	−0.758029	+	0.652221i	$0.773838\pi$
$348$	2.84054	+	4.91996i	0.152269	+	0.263737i
$349$	1.31962			0.0706374			0.0353187	−	0.999376i	$-0.488755\pi$
$349$	1.31962			0.0706374			0.0353187	+	0.999376i	$0.488755\pi$
$350$	−2.04535	+	3.54265i	−0.109329	+	0.189363i
$351$	−1.38555	+	2.39984i	−0.0739551	+	0.128094i
$352$	−9.20330	+	15.9406i	−0.490537	+	0.849636i
$353$	6.18537	+	10.7134i	0.329214	+	0.570216i	0.982356	−	0.187020i	$-0.0598828\pi$
$353$	6.18537	+	10.7134i	0.329214	+	0.570216i	−0.653142	+	0.757235i	$0.726550\pi$
$354$	−1.07044	+	1.85405i	−0.0568932	+	0.0985419i
$355$	10.3638	+	17.9507i	0.550055	+	0.952723i
$356$	10.0051			0.530270
$357$	−2.35226			−0.124495
$358$	14.3781	+	24.9035i	0.759904	+	1.31619i
$359$	6.59418	−	11.4214i	0.348027	−	0.602801i	−0.637872	−	0.770143i	$-0.720185\pi$
$359$	6.59418	−	11.4214i	0.348027	−	0.602801i	0.985899	+	0.167342i	$0.0535183\pi$
$360$	−2.50537	−	4.33942i	−0.132044	−	0.228708i
$361$	−1.55551	+	2.69422i	−0.0818688	+	0.141801i
$362$	−5.15234	+	8.92411i	−0.270801	+	0.469041i
$363$	−0.882949	+	1.52931i	−0.0463428	+	0.0802681i
$364$	1.51979			0.0796588
$365$	6.68757	+	11.5832i	0.350043	+	0.606293i
$366$	−4.90764	−	8.50028i	−0.256526	−	0.444317i
$367$	8.08565	−	14.0048i	0.422067	−	0.731042i	−0.574074	−	0.818803i	$-0.694638\pi$
$367$	8.08565	−	14.0048i	0.422067	−	0.731042i	0.996142	+	0.0877611i	$0.0279712\pi$
$368$	−3.06009			−0.159518
$369$	−7.95708	−	13.7821i	−0.414229	−	0.717466i
$370$	34.0987			1.77271
$371$	1.51907			0.0788664
$372$	1.13266	−	3.64840i	0.0587259	−	0.189161i
$373$	−29.8424			−1.54518			−0.772589	−	0.634906i	$-0.781039\pi$
$373$	−29.8424			−1.54518			−0.772589	+	0.634906i	$0.781039\pi$
$374$	−23.0651			−1.19267
$375$	2.90582	+	5.03303i	0.150056	+	0.259904i
$376$	1.85884			0.0958623
$377$	−4.13998	+	7.17065i	−0.213220	+	0.369307i
$378$	2.72950	+	4.72763i	0.140390	+	0.243163i
$379$	17.3471	+	30.0460i	0.891058	+	1.54336i	0.838609	+	0.544735i	$0.183370\pi$
$379$	17.3471	+	30.0460i	0.891058	+	1.54336i	0.0524497	+	0.998624i	$0.483297\pi$
$380$	−11.4849			−0.589164
$381$	2.38278	−	4.12710i	0.122074	−	0.211438i
$382$	6.36463	−	11.0239i	0.325643	−	0.564030i
$383$	−4.34955	+	7.53364i	−0.222252	+	0.384951i	−0.955491	−	0.295019i	$-0.904674\pi$
$383$	−4.34955	+	7.53364i	−0.222252	+	0.384951i	0.733240	+	0.679970i	$0.238007\pi$
$384$	−1.95015	−	3.37775i	−0.0995179	−	0.172370i
$385$	2.46144	−	4.26334i	0.125447	−	0.217280i
$386$	−21.8051	−	37.7676i	−1.10985	−	1.92232i
$387$	−20.1556			−1.02456
$388$	−13.0386			−0.661936
$389$	−15.9065	−	27.5509i	−0.806491	−	1.39688i	−0.915280	−	0.402819i	$-0.868030\pi$
$389$	−15.9065	−	27.5509i	−0.806491	−	1.39688i	0.108789	−	0.994065i	$-0.465303\pi$
$390$	0.760325	−	1.31692i	0.0385006	−	0.0666849i
$391$	−1.46227	−	2.53273i	−0.0739502	−	0.128086i
$392$	3.10490	−	5.37784i	0.156821	−	0.271622i
$393$	−4.70027	+	8.14111i	−0.237097	+	0.410665i
$394$	−5.06134	+	8.76650i	−0.254987	+	0.441650i
$395$	−10.5862			−0.532652
$396$	5.35269	+	9.27113i	0.268983	+	0.465892i
$397$	−9.46830	−	16.3996i	−0.475201	−	0.823072i	0.524396	−	0.851475i	$-0.324291\pi$
$397$	−9.46830	−	16.3996i	−0.475201	−	0.823072i	−0.999597	+	0.0284030i	$0.990958\pi$
$398$	−0.803628	+	1.39193i	−0.0402823	+	0.0697709i
$399$	−2.40294			−0.120298
$400$	−5.00069	−	8.66144i	−0.250034	−	0.433072i
$401$	−9.39135			−0.468982			−0.234491	−	0.972118i	$-0.575342\pi$
$401$	−9.39135			−0.468982			−0.234491	+	0.972118i	$0.575342\pi$
$402$	4.26435			0.212686
$403$	5.43042	−	1.22906i	0.270508	−	0.0612236i
$404$	20.1003			1.00003
$405$	−11.9292			−0.592766
$406$	8.15566	+	14.1260i	0.404759	+	0.701063i
$407$	29.1471			1.44477
$408$	1.16984	−	2.02623i	0.0579158	−	0.100313i
$409$	1.42983	+	2.47653i	0.0707003	+	0.122457i	0.899208	−	0.437521i	$-0.144143\pi$
$409$	1.42983	+	2.47653i	0.0707003	+	0.122457i	−0.828508	+	0.559977i	$0.810810\pi$
$410$	9.09673	+	15.7560i	0.449256	+	0.778134i
$411$	6.22983			0.307295
$412$	−8.15489	+	14.1247i	−0.401762	+	0.695873i
$413$	−1.28054	+	2.21796i	−0.0630112	+	0.109139i
$414$	−1.62893	+	2.82139i	−0.0800574	+	0.138664i
$415$	−7.25900	−	12.5730i	−0.356330	−	0.617182i
$416$	−3.40083	+	5.89041i	−0.166739	+	0.288801i
$417$	3.62576	+	6.28000i	0.177554	+	0.307533i
$418$	−23.5621			−1.15246
$419$	−14.6691			−0.716635			−0.358317	−	0.933600i	$-0.616649\pi$
$419$	−14.6691			−0.716635			−0.358317	+	0.933600i	$0.616649\pi$
$420$	−0.624070	−	1.08092i	−0.0304515	−	0.0527435i
$421$	1.66838	−	2.88972i	0.0813118	−	0.140836i	−0.822502	−	0.568762i	$-0.807422\pi$
$421$	1.66838	−	2.88972i	0.0813118	−	0.140836i	0.903814	+	0.427926i	$0.140756\pi$
$422$	6.45365	+	11.1781i	0.314159	+	0.544139i
$423$	2.43220	−	4.21269i	0.118257	−	0.204828i
$424$	−0.755477	+	1.30852i	−0.0366892	+	0.0635476i
$425$	4.77917	−	8.27777i	0.231824	−	0.401531i
$426$	10.7815			0.522366
$427$	−5.87088	−	10.1687i	−0.284112	−	0.492096i
$428$	13.5801	+	23.5214i	0.656417	+	1.13695i
$429$	0.649916	−	1.12569i	0.0313783	−	0.0543487i
$430$	23.0423			1.11120
$431$	9.98926	+	17.3019i	0.481166	+	0.833404i	0.999766	−	0.0216129i	$-0.00688014\pi$
$431$	9.98926	+	17.3019i	0.481166	+	0.833404i	−0.518601	+	0.855017i	$0.673547\pi$
$432$	−13.3467			−0.642144
$433$	18.1053			0.870087			0.435044	−	0.900409i	$-0.356733\pi$
$433$	18.1053			0.870087			0.435044	+	0.900409i	$0.356733\pi$
$434$	3.25207	−	10.4752i	0.156104	−	0.502824i
$435$	6.79996			0.326033
$436$	−17.7007			−0.847711
$437$	−1.49378	−	2.58730i	−0.0714571	−	0.123767i
$438$	6.95709			0.332423
$439$	5.34110	−	9.25105i	0.254917	−	0.441528i	−0.709956	−	0.704246i	$-0.751285\pi$
$439$	5.34110	−	9.25105i	0.254917	−	0.441528i	0.964873	+	0.262717i	$0.0846187\pi$
$440$	2.44828	+	4.24055i	0.116717	+	0.202160i
$441$	−8.12520	−	14.0733i	−0.386914	−	0.670155i
$442$	−8.52308			−0.405402
$443$	8.27714	−	14.3364i	0.393259	−	0.681144i	−0.599619	−	0.800286i	$-0.704681\pi$
$443$	8.27714	−	14.3364i	0.393259	−	0.681144i	0.992877	+	0.119142i	$0.0380143\pi$
$444$	3.69496	−	6.39985i	0.175355	−	0.303724i
$445$	5.98781	−	10.3712i	0.283850	−	0.491642i
$446$	−6.72060	−	11.6404i	−0.318230	−	0.551190i
$447$	3.35546	−	5.81183i	0.158708	−	0.274890i
$448$	1.57527	+	2.72845i	0.0744245	+	0.128907i
$449$	32.4331			1.53061			0.765305	−	0.643667i	$-0.222588\pi$
$449$	32.4331			1.53061			0.765305	+	0.643667i	$0.222588\pi$
$450$	−10.6477			−0.501938
$451$	7.77577	+	13.4680i	0.366147	+	0.634185i
$452$	−11.8953	+	20.6033i	−0.559508	+	0.969096i
$453$	4.81722	+	8.34366i	0.226333	+	0.392019i
$454$	−2.88990	+	5.00546i	−0.135630	+	0.234918i
$455$	0.909558	−	1.57540i	0.0426407	−	0.0738559i
$456$	1.19505	−	2.06988i	0.0559633	−	0.0969312i
$457$	5.20588			0.243521			0.121760	−	0.992560i	$-0.461146\pi$
$457$	5.20588			0.243521			0.121760	+	0.992560i	$0.461146\pi$
$458$	−22.8778	−	39.6255i	−1.06901	−	1.85158i
$459$	−6.37775	−	11.0466i	−0.297688	−	0.515610i
$460$	0.775900	−	1.34390i	0.0361765	−	0.0626596i
$461$	11.7156			0.545649			0.272824	−	0.962064i	$-0.412042\pi$
$461$	11.7156			0.545649			0.272824	+	0.962064i	$0.412042\pi$
$462$	−1.28032	−	2.21758i	−0.0595659	−	0.103171i
$463$	−15.7560			−0.732245			−0.366123	−	0.930567i	$-0.619315\pi$
$463$	−15.7560			−0.732245			−0.366123	+	0.930567i	$0.619315\pi$
$464$	−39.8796			−1.85136
$465$	−3.10402	−	3.35758i	−0.143946	−	0.155704i
$466$	27.8831			1.29166
$467$	−8.65616			−0.400559			−0.200280	−	0.979739i	$-0.564185\pi$
$467$	−8.65616			−0.400559			−0.200280	+	0.979739i	$0.564185\pi$
$468$	1.97794	+	3.42589i	0.0914303	+	0.158362i
$469$	5.10133			0.235558
$470$	−2.78055	+	4.81605i	−0.128257	+	0.222148i
$471$	−1.84036	−	3.18760i	−0.0847993	−	0.146877i
$472$	−1.27369	−	2.20610i	−0.0586265	−	0.101544i
$473$	19.6963			0.905636
$474$	−2.75322	+	4.76872i	−0.126460	+	0.219035i
$475$	4.88215	−	8.45613i	0.224008	−	0.387994i
$476$	−3.49784	+	6.05844i	−0.160323	+	0.277688i
$477$	1.97701	+	3.42427i	0.0905209	+	0.156787i
$478$	17.3324	−	30.0206i	0.792766	−	1.37311i
$479$	−15.2885	−	26.4804i	−0.698549	−	1.20992i	−0.968970	−	0.247180i	$-0.920496\pi$
$479$	−15.2885	−	26.4804i	−0.698549	−	1.20992i	0.270421	−	0.962742i	$-0.412837\pi$
$480$	5.58590			0.254960
$481$	10.7705			0.491093
$482$	−6.87869	−	11.9142i	−0.313316	−	0.542679i
$483$	0.162338	−	0.281178i	0.00738665	−	0.0127941i
$484$	2.62592	+	4.54822i	0.119360	+	0.206737i
$485$	−7.80328	+	13.5157i	−0.354329	+	0.613716i
$486$	−10.7990	+	18.7044i	−0.489852	+	0.848449i
$487$	−13.0319	+	22.5720i	−0.590534	+	1.02283i	0.403627	+	0.914924i	$0.367750\pi$
$487$	−13.0319	+	22.5720i	−0.590534	+	1.02283i	−0.994161	+	0.107911i	$0.965584\pi$
$488$	11.6790			0.528683
$489$	−2.44426	−	4.23357i	−0.110533	−	0.191449i
$490$	9.28893	+	16.0889i	0.419631	+	0.726822i
$491$	14.5108	−	25.1335i	0.654865	−	1.13426i	−0.327062	−	0.945003i	$-0.606059\pi$
$491$	14.5108	−	25.1335i	0.654865	−	1.13426i	0.981928	−	0.189257i	$-0.0606081\pi$
$492$	3.94292			0.177760
$493$	−19.0565	−	33.0069i	−0.858263	−	1.48656i
$494$	−8.70673			−0.391734
$495$	12.8138			0.575937
$496$	18.2041	+	19.6912i	0.817388	+	0.884159i
$497$	12.8977			0.578539
$498$	−7.55155			−0.338393
$499$	9.69877	+	16.7988i	0.434177	+	0.752016i	0.997228	−	0.0744057i	$-0.0237060\pi$
$499$	9.69877	+	16.7988i	0.434177	+	0.752016i	−0.563051	+	0.826422i	$0.690373\pi$
$500$	17.2840			0.772963
$501$	0.628675	−	1.08890i	0.0280871	−	0.0486483i
$502$	−22.9322	−	39.7197i	−1.02351	−	1.77278i
$503$	3.74310	+	6.48324i	0.166897	+	0.289073i	0.937327	−	0.348450i	$-0.113292\pi$
$503$	3.74310	+	6.48324i	0.166897	+	0.289073i	−0.770431	+	0.637524i	$0.779959\pi$
$504$	−3.11790			−0.138882
$505$	12.0295	−	20.8357i	0.535307	−	0.927178i
$506$	1.59181	−	2.75710i	0.0707646	−	0.122568i
$507$	0.240159	−	0.415967i	0.0106658	−	0.0184738i
$508$	−7.08647	−	12.2741i	−0.314411	−	0.544577i
$509$	−1.25885	+	2.18038i	−0.0557973	+	0.0966438i	−0.892575	−	0.450899i	$-0.851103\pi$
$509$	−1.25885	+	2.18038i	−0.0557973	+	0.0966438i	0.836778	+	0.547543i	$0.184437\pi$
$510$	3.49982	+	6.06186i	0.154975	+	0.268424i
$511$	8.32259			0.368170
$512$	−22.5658			−0.997275
$513$	−6.51517	−	11.2846i	−0.287652	−	0.498228i
$514$	13.4599	−	23.3132i	0.593690	−	1.02830i
$515$	9.76099	+	16.9065i	0.430121	+	0.744991i
$516$	2.49688	−	4.32473i	0.109919	−	0.190386i
$517$	−2.37678	+	4.11670i	−0.104530	+	0.181052i
$518$	10.6088	−	18.3750i	0.466126	−	0.807353i
$519$	−0.559160			−0.0245444
$520$	0.904695	+	1.56698i	0.0396735	+	0.0687165i
$521$	−16.1216	−	27.9234i	−0.706299	−	1.22335i	−0.966221	−	0.257716i	$-0.917030\pi$
$521$	−16.1216	−	27.9234i	−0.706299	−	1.22335i	0.259922	−	0.965630i	$-0.416303\pi$
$522$	−21.2284	+	36.7687i	−0.929143	+	1.60932i
$523$	−32.9410			−1.44041			−0.720204	−	0.693763i	$-0.755952\pi$
$523$	−32.9410			−1.44041			−0.720204	+	0.693763i	$0.755952\pi$
$524$	13.9787	+	24.2119i	0.610664	+	1.05770i
$525$	1.06115			0.0463123
$526$	−33.5440			−1.46259
$527$	−7.59879	+	24.4763i	−0.331008	+	1.06620i
$528$	6.26052			0.272454
$529$	−22.5963			−0.982449
$530$	−2.26016	−	3.91471i	−0.0981751	−	0.170044i
$531$	−6.66625			−0.289290
$532$	−3.57321	+	6.18899i	−0.154918	+	0.268327i
$533$	2.87333	+	4.97675i	0.124458	+	0.215567i
$534$	−3.11457	−	5.39459i	−0.134781	−	0.233447i
$535$	32.5093			1.40550
$536$	−2.53703	+	4.39426i	−0.109583	+	0.189803i
$537$	3.72974	−	6.46010i	0.160950	−	0.278774i
$538$	−17.3543	+	30.0585i	−0.748196	+	1.29591i
$539$	7.94006	+	13.7526i	0.342003	+	0.592366i
$540$	3.38412	−	5.86146i	0.145629	−	0.252237i
$541$	−5.10494	−	8.84202i	−0.219479	−	0.380148i	0.735170	−	0.677883i	$-0.237102\pi$
$541$	−5.10494	−	8.84202i	−0.219479	−	0.380148i	−0.954649	+	0.297734i	$0.903769\pi$
$542$	−3.05182			−0.131087
$543$	2.67308			0.114713
$544$	−15.6542	−	27.1139i	−0.671168	−	1.16250i
$545$	−10.5934	+	18.3484i	−0.453773	+	0.785958i
$546$	−0.473108	−	0.819446i	−0.0202471	−	0.0350691i
$547$	−15.0649	+	26.0932i	−0.644128	+	1.11566i	0.340374	+	0.940290i	$0.389446\pi$
$547$	−15.0649	+	26.0932i	−0.644128	+	1.11566i	−0.984502	+	0.175373i	$0.943887\pi$
$548$	9.26384	−	16.0454i	0.395732	−	0.685428i
$549$	15.2814	−	26.4681i	0.652193	−	1.12963i
$550$	10.4051			0.443675
$551$	−19.4671	−	33.7181i	−0.829328	−	1.43644i
$552$	0.161470	+	0.279675i	0.00687264	+	0.0119038i
$553$	−3.29361	+	5.70470i	−0.140059	+	0.242589i
$554$	6.44690			0.273902
$555$	−4.42268	−	7.66030i	−0.187732	−	0.325162i
$556$	21.5662			0.914612
$557$	23.4342			0.992938			0.496469	−	0.868055i	$-0.334630\pi$
$557$	23.4342			0.992938			0.496469	+	0.868055i	$0.334630\pi$
$558$	27.8454	−	6.30219i	1.17879	−	0.266793i
$559$	7.27823			0.307836
$560$	8.76160			0.370245
$561$	2.99160	+	5.18160i	0.126305	+	0.218767i
$562$	−27.4879			−1.15951
$563$	4.71443	−	8.16564i	0.198690	−	0.344141i	−0.749414	−	0.662102i	$-0.769665\pi$
$563$	4.71443	−	8.16564i	0.198690	−	0.344141i	0.948104	+	0.317961i	$0.102998\pi$
$564$	0.602604	+	1.04374i	0.0253742	+	0.0439494i
$565$	14.2381	+	24.6611i	0.599000	+	1.03750i
$566$	−20.7971			−0.874166
$567$	−3.71143	+	6.42839i	−0.155866	+	0.269967i
$568$	−6.41435	+	11.1100i	−0.269140	+	0.466164i
$569$	−20.1124	+	34.8356i	−0.843154	+	1.46039i	0.0440609	+	0.999029i	$0.485970\pi$
$569$	−20.1124	+	34.8356i	−0.843154	+	1.46039i	−0.887215	+	0.461357i	$0.847363\pi$
$570$	3.57523	+	6.19248i	0.149750	+	0.259374i
$571$	15.8757	−	27.4975i	0.664377	−	1.15073i	−0.315077	−	0.949066i	$-0.602030\pi$
$571$	15.8757	−	27.4975i	0.664377	−	1.15073i	0.979454	−	0.201668i	$-0.0646362\pi$
$572$	−1.93287	−	3.34783i	−0.0808174	−	0.139980i
$573$	−3.30203			−0.137944
$574$	11.3208			0.472520
$575$	0.659657	+	1.14256i	0.0275096	+	0.0476480i
$576$	−4.10028	+	7.10189i	−0.170845	+	0.295912i
$577$	1.41944	+	2.45855i	0.0590922	+	0.102351i	0.894058	−	0.447951i	$-0.147846\pi$
$577$	1.41944	+	2.45855i	0.0590922	+	0.102351i	−0.834966	+	0.550302i	$0.814513\pi$
$578$	3.87737	−	6.71580i	0.161277	−	0.279341i
$579$	−5.65635	+	9.79709i	−0.235070	+	0.407153i
$580$	10.1116	−	17.5139i	0.419863	−	0.727225i
$581$	−9.03373			−0.374782
$582$	4.05889	+	7.03020i	0.168246	+	0.291411i
$583$	−1.93196	−	3.34625i	−0.0800135	−	0.138587i
$584$	−4.13905	+	7.16904i	−0.171275	+	0.296657i
$585$	4.73499			0.195768
$586$	10.6795	+	18.4974i	0.441166	+	0.764122i
$587$	38.1659			1.57528			0.787638	−	0.616139i	$-0.211304\pi$
$587$	38.1659			1.57528			0.787638	+	0.616139i	$0.211304\pi$
$588$	4.02622			0.166039
$589$	−7.76252	+	25.0037i	−0.319849	+	1.03026i
$590$	7.62102			0.313752
$591$	2.62587			0.108014
$592$	25.9376	+	44.9252i	1.06603	+	1.84642i
$593$	−26.5339			−1.08962			−0.544809	−	0.838560i	$-0.683398\pi$
$593$	−26.5339			−1.08962			−0.544809	+	0.838560i	$0.683398\pi$
$594$	6.94274	−	12.0252i	0.284864	−	0.493399i
$595$	4.18674	+	7.25165i	0.171640	+	0.297289i
$596$	−9.97924	−	17.2845i	−0.408765	−	0.708003i
$597$	0.416930			0.0170638
$598$	0.588210	−	1.01881i	0.0240537	−	0.0416622i
$599$	1.75114	−	3.03307i	0.0715497	−	0.123928i	−0.828031	−	0.560682i	$-0.810539\pi$
$599$	1.75114	−	3.03307i	0.0715497	−	0.123928i	0.899581	+	0.436755i	$0.143872\pi$
$600$	−0.527737	+	0.914068i	−0.0215448	+	0.0373167i
$601$	13.8045	+	23.9101i	0.563097	+	0.975312i	0.997224	+	0.0744603i	$0.0237234\pi$
$601$	13.8045	+	23.9101i	0.563097	+	0.975312i	−0.434127	+	0.900851i	$0.642943\pi$
$602$	7.16897	−	12.4170i	0.292185	−	0.506080i
$603$	6.63915	+	11.4993i	0.270367	+	0.468289i
$604$	28.6531			1.16588
$605$	6.28618			0.255570
$606$	−6.25717	−	10.8377i	−0.254180	−	0.440253i
$607$	21.4814	−	37.2070i	0.871905	−	1.51018i	0.0118816	−	0.999929i	$-0.496218\pi$
$607$	21.4814	−	37.2070i	0.871905	−	1.51018i	0.860023	−	0.510254i	$-0.170449\pi$
$608$	−15.9915	−	27.6981i	−0.648541	−	1.12331i
$609$	2.11562	−	3.66436i	0.0857291	−	0.148487i
$610$	−17.4700	+	30.2590i	−0.707341	+	1.22515i
$611$	−0.878273	+	1.52121i	−0.0355311	+	0.0615417i
$612$	−18.2091			−0.736060
$613$	−14.9720	−	25.9323i	−0.604715	−	1.04740i	−0.992096	−	0.125477i	$-0.959954\pi$
$613$	−14.9720	−	25.9323i	−0.604715	−	1.04740i	0.387382	−	0.921919i	$-0.373380\pi$
$614$	−26.4359	−	45.7883i	−1.06686	−	1.84786i
$615$	2.35974	−	4.08718i	0.0951537	−	0.164811i
$616$	3.04685			0.122761
$617$	−4.74917	−	8.22581i	−0.191194	−	0.331159i	0.754452	−	0.656355i	$-0.227903\pi$
$617$	−4.74917	−	8.22581i	−0.191194	−	0.331159i	−0.945646	+	0.325197i	$0.894569\pi$
$618$	10.1544			0.408469
$619$	−33.9443			−1.36434			−0.682169	−	0.731195i	$-0.738963\pi$
$619$	−33.9443			−1.36434			−0.682169	+	0.731195i	$0.738963\pi$
$620$	−13.2635	+	3.00190i	−0.532674	+	0.120559i
$621$	1.76061			0.0706509
$622$	18.2446			0.731540
$623$	−3.72588	−	6.45341i	−0.149274	−	0.258550i
$624$	2.31341			0.0926103
$625$	5.15272	−	8.92478i	0.206109	−	0.356991i
$626$	0.0182143	+	0.0315481i	0.000727990	+	0.00126092i
$627$	3.05606	+	5.29325i	0.122047	+	0.211392i
$628$	−10.9466			−0.436816
$629$	−24.7886	+	42.9352i	−0.988388	+	1.71194i
$630$	4.66391	−	8.07813i	0.185815	−	0.321840i
$631$	−1.72256	+	2.98356i	−0.0685740	+	0.118774i	−0.898274	−	0.439436i	$-0.855178\pi$
$631$	−1.72256	+	2.98356i	−0.0685740	+	0.118774i	0.829700	+	0.558210i	$0.188512\pi$
$632$	−3.27600	−	5.67420i	−0.130312	−	0.225708i
$633$	1.67411	−	2.89964i	0.0665398	−	0.115250i
$634$	4.64726	+	8.04929i	0.184566	+	0.319678i
$635$	−16.9643			−0.673208
$636$	−0.979651			−0.0388457
$637$	2.93403	+	5.08189i	0.116251	+	0.201352i
$638$	20.7447	−	35.9309i	0.821291	−	1.42252i
$639$	16.7857	+	29.0737i	0.664032	+	1.15014i
$640$	−6.94206	+	12.0240i	−0.274409	+	0.475290i
$641$	1.30889	−	2.26706i	0.0516980	−	0.0895436i	−0.839018	−	0.544103i	$-0.816870\pi$
$641$	1.30889	−	2.26706i	0.0516980	−	0.0895436i	0.890716	+	0.454560i	$0.150203\pi$
$642$	8.45487	−	14.6443i	0.333687	−	0.577963i
$643$	−11.1280			−0.438844			−0.219422	−	0.975630i	$-0.570417\pi$
$643$	−11.1280			−0.438844			−0.219422	+	0.975630i	$0.570417\pi$
$644$	−0.482799	−	0.836232i	−0.0190249	−	0.0329522i
$645$	−2.98864	−	5.17648i	−0.117678	−	0.203824i
$646$	20.0388	−	34.7082i	0.788415	−	1.36557i
$647$	−23.1745			−0.911085			−0.455543	−	0.890214i	$-0.650555\pi$
$647$	−23.1745			−0.911085			−0.455543	+	0.890214i	$0.650555\pi$
$648$	−3.69159	−	6.39402i	−0.145019	−	0.251181i
$649$	6.51435			0.255711
$650$	3.84492			0.150810
$651$	−2.77506	+	0.628074i	−0.108763	+	0.0246162i
$652$	−14.5386			−0.569375
$653$	33.1778			1.29835			0.649173	−	0.760641i	$-0.275115\pi$
$653$	33.1778			1.29835			0.649173	+	0.760641i	$0.275115\pi$
$654$	5.51019	+	9.54393i	0.215466	+	0.373197i
$655$	33.4637			1.30754
$656$	−13.8391	+	23.9700i	−0.540326	+	0.935872i
$657$	10.8315	+	18.7607i	0.422576	+	0.731923i
$658$	1.73018	+	2.99676i	0.0674494	+	0.116826i
$659$	−21.2100			−0.826226			−0.413113	−	0.910680i	$-0.635559\pi$
$659$	−21.2100			−0.826226			−0.413113	+	0.910680i	$0.635559\pi$
$660$	−1.58738	+	2.74943i	−0.0617888	+	0.107021i
$661$	−3.39838	+	5.88617i	−0.132182	+	0.228945i	−0.924517	−	0.381140i	$-0.875532\pi$
$661$	−3.39838	+	5.88617i	−0.132182	+	0.228945i	0.792336	+	0.610085i	$0.208865\pi$
$662$	−0.739106	+	1.28017i	−0.0287262	+	0.0497552i
$663$	1.10546	+	1.91472i	0.0429327	+	0.0743616i
$664$	4.49272	−	7.78162i	0.174351	−	0.301985i
$665$	4.27696	+	7.40790i	0.165853	+	0.287266i
$666$	55.2277			2.14003
$667$	5.26065			0.203693
$668$	−1.86970	−	3.23841i	−0.0723408	−	0.125298i
$669$	−1.74336	+	3.01958i	−0.0674021	+	0.116744i
$670$	−7.59003	−	13.1463i	−0.293229	−	0.507887i
$671$	−14.9332	+	25.8650i	−0.576488	+	0.998507i
$672$	1.73790	−	3.01013i	0.0670408	−	0.116118i
$673$	11.2521	−	19.4891i	0.433735	−	0.751251i	−0.563456	−	0.826146i	$-0.690529\pi$
$673$	11.2521	−	19.4891i	0.433735	−	0.751251i	0.997191	+	0.0748945i	$0.0238620\pi$
$674$	−41.3696			−1.59350
$675$	2.87712	+	4.98332i	0.110740	+	0.191808i
$676$	−0.714240	−	1.23710i	−0.0274708	−	0.0475808i
$677$	−0.775354	+	1.34295i	−0.0297993	+	0.0516138i	−0.880540	−	0.473971i	$-0.842820\pi$
$677$	−0.775354	+	1.34295i	−0.0297993	+	0.0516138i	0.850741	+	0.525585i	$0.176153\pi$
$678$	14.8119			0.568848
$679$	4.85555	+	8.41005i	0.186339	+	0.322748i
$680$	−8.32872			−0.319392
$681$	1.49931			0.0574537
$682$	−27.2109	+	6.15859i	−1.04196	+	0.235824i
$683$	2.76304			0.105725			0.0528625	−	0.998602i	$-0.483166\pi$
$683$	2.76304			0.105725			0.0528625	+	0.998602i	$0.483166\pi$
$684$	−18.6015			−0.711246
$685$	−11.0884	−	19.2056i	−0.423664	−	0.733808i
$686$	25.3498			0.967860
$687$	−5.93461	+	10.2791i	−0.226420	+	0.392170i
$688$	17.5274	+	30.3584i	0.668227	+	1.15740i
$689$	−0.713902	−	1.23651i	−0.0271975	−	0.0471075i
$690$	−0.966143			−0.0367804
$691$	2.06460	−	3.57600i	0.0785412	−	0.136037i	−0.824080	−	0.566474i	$-0.808307\pi$
$691$	2.06460	−	3.57600i	0.0785412	−	0.136037i	0.902621	+	0.430437i	$0.141640\pi$
$692$	−0.831480	+	1.44017i	−0.0316081	+	0.0547469i
$693$	3.98665	−	6.90508i	0.151440	−	0.262302i
$694$	−6.40944	−	11.1015i	−0.243299	−	0.421406i
$695$	12.9068	−	22.3553i	0.489585	−	0.847985i
$696$	2.10431	+	3.64477i	0.0797635	+	0.138155i
$697$	−26.4521			−1.00195
$698$	−2.44342			−0.0924848
$699$	−3.61650	−	6.26397i	−0.136789	−	0.236925i
$700$	1.57794	−	2.73308i	0.0596406	−	0.103301i
$701$	−9.18635	−	15.9112i	−0.346964	−	0.600959i	0.638745	−	0.769419i	$-0.279454\pi$
$701$	−9.18635	−	15.9112i	−0.346964	−	0.600959i	−0.985709	+	0.168460i	$0.946121\pi$
$702$	2.56550	−	4.44358i	0.0968286	−	0.167712i
$703$	−25.3228	+	43.8603i	−0.955066	+	1.65422i
$704$	4.00685	−	6.94007i	0.151014	−	0.261564i
$705$	1.44257			0.0543305
$706$	−11.4529	−	19.8371i	−0.431037	−	0.746578i
$707$	−7.48529	−	12.9649i	−0.281513	−	0.487596i
$708$	0.825819	−	1.43036i	0.0310362	−	0.0537563i
$709$	−28.7385			−1.07930			−0.539649	−	0.841890i	$-0.681443\pi$
$709$	−28.7385			−1.07930			−0.539649	+	0.841890i	$0.681443\pi$
$710$	−19.1898	−	33.2377i	−0.720181	−	1.24739i
$711$	−17.1459			−0.643023
$712$	7.41192			0.277773
$713$	−2.40136	−	2.59753i	−0.0899318	−	0.0972781i
$714$	4.35548			0.163000
$715$	−4.62710			−0.173044
$716$	−11.0924	−	19.2125i	−0.414541	−	0.718006i
$717$	−8.99222			−0.335821
$718$	−12.2099	+	21.1481i	−0.455669	+	0.789241i
$719$	14.5606	+	25.2197i	0.543019	+	0.940537i	0.998729	+	0.0504085i	$0.0160523\pi$
$719$	14.5606	+	25.2197i	0.543019	+	0.940537i	−0.455709	+	0.890129i	$0.650614\pi$
$720$	11.4028	+	19.7503i	0.424958	+	0.736049i
$721$	12.1474			0.452394
$722$	2.88020	−	4.98866i	0.107190	−	0.185659i
$723$	−1.78437	+	3.09061i	−0.0663613	+	0.114941i
$724$	3.97491	−	6.88475i	0.147727	−	0.255870i
$725$	8.59675	+	14.8900i	0.319275	+	0.553001i
$726$	1.63488	−	2.83170i	0.0606762	−	0.105094i
$727$	−11.7725	−	20.3906i	−0.436620	−	0.756247i	0.560807	−	0.827947i	$-0.310491\pi$
$727$	−11.7725	−	20.3906i	−0.436620	−	0.756247i	−0.997426	+	0.0716995i	$0.977158\pi$
$728$	1.12588			0.0417280
$729$	−15.3280			−0.567704
$730$	−12.3828	−	21.4476i	−0.458308	−	0.793813i
$731$	−16.7510	+	29.0136i	−0.619559	+	1.07311i
$732$	3.78613	+	6.55777i	0.139939	+	0.242382i
$733$	16.1044	−	27.8936i	0.594829	−	1.03027i	−0.398742	−	0.917063i	$-0.630553\pi$
$733$	16.1044	−	27.8936i	0.594829	−	1.03027i	0.993571	−	0.113211i	$-0.0361136\pi$
$734$	−14.9715	+	25.9314i	−0.552609	+	0.957146i
$735$	2.40959	−	4.17354i	0.0888792	−	0.153943i
$736$	4.32142			0.159290
$737$	−6.48786	−	11.2373i	−0.238984	−	0.413932i
$738$	14.7335	+	25.5191i	0.542346	+	0.939371i
$739$	24.6445	−	42.6854i	0.906561	−	1.57021i	0.0877528	−	0.996142i	$-0.472031\pi$
$739$	24.6445	−	42.6854i	0.906561	−	1.57021i	0.818808	−	0.574067i	$-0.194635\pi$
$740$	−26.3064			−0.967041
$741$	1.12928	+	1.95598i	0.0414853	+	0.0718546i
$742$	−2.81274			−0.103259
$743$	18.3395			0.672811			0.336406	−	0.941717i	$-0.390789\pi$
$743$	18.3395			0.672811			0.336406	+	0.941717i	$0.390789\pi$
$744$	0.839092	−	2.70278i	0.0307626	−	0.0990888i
$745$	−23.8893			−0.875236
$746$	55.2566			2.02309
$747$	−11.7570	−	20.3637i	−0.430165	−	0.745068i
$748$	17.7942			0.650621
$749$	10.1144	−	17.5186i	0.369570	−	0.640115i
$750$	−5.38046	−	9.31923i	−0.196467	−	0.340290i
$751$	−11.2367	−	19.4625i	−0.410031	−	0.710195i	0.584861	−	0.811133i	$-0.301149\pi$
$751$	−11.2367	−	19.4625i	−0.410031	−	0.710195i	−0.994893	+	0.100938i	$0.967816\pi$
$752$	−8.46024			−0.308513
$753$	−5.94872	+	10.3035i	−0.216783	+	0.375480i
$754$	7.66564	−	13.2773i	0.279166	−	0.483530i
$755$	17.1482	−	29.7015i	0.624085	−	1.08095i
$756$	−2.10575	−	3.64726i	−0.0765852	−	0.132650i
$757$	13.6772	−	23.6896i	0.497107	−	0.861015i	−0.502887	−	0.864352i	$-0.667729\pi$
$757$	13.6772	−	23.6896i	0.497107	−	0.861015i	0.999994	+	0.00333715i	$0.00106225\pi$
$758$	−32.1201	−	55.6336i	−1.16665	−	2.02070i
$759$	−0.825846			−0.0299763
$760$	−8.50818			−0.308624
$761$	1.27170	+	2.20264i	0.0460989	+	0.0798457i	0.888154	−	0.459546i	$-0.151988\pi$
$761$	1.27170	+	2.20264i	0.0460989	+	0.0798457i	−0.842055	+	0.539391i	$0.818654\pi$
$762$	−4.41200	+	7.64181i	−0.159830	+	0.276834i
$763$	6.59170	+	11.4172i	0.238636	+	0.413329i
$764$	−4.91017	+	8.50467i	−0.177644	+	0.307688i
$765$	−10.8977	+	18.8754i	−0.394007	+	0.682441i
$766$	8.05369	−	13.9494i	0.290992	−	0.504012i
$767$	2.40720			0.0869190
$768$	5.03326	+	8.71786i	0.181622	+	0.314579i
$769$	3.84841	+	6.66565i	0.138777	+	0.240369i	0.927034	−	0.374977i	$-0.122349\pi$
$769$	3.84841	+	6.66565i	0.138777	+	0.240369i	−0.788257	+	0.615346i	$0.789016\pi$
$770$	−4.55764	+	7.89406i	−0.164246	+	0.284482i
$771$	−6.98311			−0.251491
$772$	16.8222	+	29.1368i	0.605443	+	1.04866i
$773$	36.0890			1.29803			0.649015	−	0.760775i	$-0.275181\pi$
$773$	36.0890			1.29803			0.649015	+	0.760775i	$0.275181\pi$
$774$	37.3203			1.34145
$775$	3.42795	−	11.0417i	0.123136	−	0.396630i
$776$	−9.65917			−0.346744
$777$	−5.50397			−0.197454
$778$	29.4527	+	51.0136i	1.05593	+	1.82893i
$779$	−27.0221			−0.968167
$780$	−0.586574	+	1.01598i	−0.0210027	+	0.0363778i
$781$	−16.4032	−	28.4112i	−0.586953	−	1.01663i
$782$	2.70756	+	4.68964i	0.0968223	+	0.167701i
$783$	22.9445			0.819971
$784$	−14.1315	+	24.4765i	−0.504696	+	0.874159i
$785$	−6.55125	+	11.3471i	−0.233824	+	0.404995i
$786$	8.70310	−	15.0742i	0.310429	−	0.537679i
$787$	−21.3902	−	37.0489i	−0.762477	−	1.32065i	−0.941570	−	0.336817i	$-0.890650\pi$
$787$	−21.3902	−	37.0489i	−0.762477	−	1.32065i	0.179093	−	0.983832i	$-0.442684\pi$
$788$	3.90471	−	6.76316i	0.139100	−	0.240928i
$789$	4.35074	+	7.53570i	0.154890	+	0.268278i
$790$	19.6016			0.697395
$791$	17.7191			0.630019
$792$	3.96534	+	6.86817i	0.140902	+	0.244050i
$793$	−5.51814	+	9.55770i	−0.195955	+	0.339404i
$794$	17.5317	+	30.3657i	0.622175	+	1.07764i
$795$	−0.586297	+	1.01550i	−0.0207938	+	0.0360159i
$796$	0.619981	−	1.07384i	0.0219747	−	0.0380612i
$797$	−4.11022	+	7.11910i	−0.145591	+	0.252172i	−0.929593	−	0.368587i	$-0.879842\pi$
$797$	−4.11022	+	7.11910i	−0.145591	+	0.252172i	0.784002	+	0.620758i	$0.213175\pi$
$798$	4.44933			0.157504
$799$	−4.04274	−	7.00223i	−0.143022	−	0.247721i
$800$	7.06190	+	12.2316i	0.249676	+	0.432451i
$801$	9.69812	−	16.7976i	0.342666	−	0.593515i
$802$	17.3892			0.614033
$803$	−10.5847	−	18.3332i	−0.373525	−	0.646963i
$804$	−3.28985			−0.116024
$805$	−1.15577			−0.0407356
$806$	−10.0550	+	2.27574i	−0.354174	+	0.0801595i
$807$	9.00356			0.316940
$808$	14.8906			0.523848
$809$	7.40995	+	12.8344i	0.260520	+	0.451234i	0.966380	−	0.257117i	$-0.0827727\pi$
$809$	7.40995	+	12.8344i	0.260520	+	0.451234i	−0.705860	+	0.708351i	$0.749439\pi$
$810$	22.0883			0.776103
$811$	4.81082	−	8.33258i	0.168931	−	0.292597i	−0.769113	−	0.639112i	$-0.779302\pi$
$811$	4.81082	−	8.33258i	0.168931	−	0.292597i	0.938044	+	0.346516i	$0.112635\pi$
$812$	−6.29191	−	10.8979i	−0.220803	−	0.382442i
$813$	0.395828	+	0.685595i	0.0138823	+	0.0240449i
$814$	−53.9692			−1.89162
$815$	−8.70097	+	15.0705i	−0.304782	+	0.527898i
$816$	−5.32436	+	9.22207i	−0.186390	+	0.322837i
$817$	−17.1120	+	29.6388i	−0.598672	+	1.03693i
$818$	−2.64749	−	4.58558i	−0.0925672	−	0.160331i
$819$	1.47316	−	2.55159i	0.0514763	−	0.0891596i
$820$	−7.01793	−	12.1554i	−0.245077	−	0.424485i
$821$	13.0944			0.456997			0.228498	−	0.973544i	$-0.426618\pi$
$821$	13.0944			0.456997			0.228498	+	0.973544i	$0.426618\pi$
$822$	−11.5352			−0.402338
$823$	−6.77408	−	11.7330i	−0.236130	−	0.408988i	0.723471	−	0.690355i	$-0.242546\pi$
$823$	−6.77408	−	11.7330i	−0.236130	−	0.408988i	−0.959600	+	0.281367i	$0.909212\pi$
$824$	−6.04124	+	10.4637i	−0.210457	+	0.364522i
$825$	−1.34957	−	2.33752i	−0.0469858	−	0.0813819i
$826$	2.37107	−	4.10681i	0.0824999	−	0.142894i
$827$	17.2586	−	29.8927i	0.600139	−	1.03947i	−0.392660	−	0.919684i	$-0.628445\pi$
$827$	17.2586	−	29.8927i	0.600139	−	1.03947i	0.992799	−	0.119788i	$-0.0382215\pi$
$828$	1.25668	−	2.17664i	0.0436727	−	0.0756433i
$829$	41.1238			1.42829			0.714145	−	0.699998i	$-0.246816\pi$
$829$	41.1238			1.42829			0.714145	+	0.699998i	$0.246816\pi$
$830$	13.4409	+	23.2803i	0.466539	+	0.808070i
$831$	−0.836178	−	1.44830i	−0.0290067	−	0.0502411i
$832$	1.48062	−	2.56451i	0.0513314	−	0.0889085i
$833$	−27.0110			−0.935876
$834$	−6.71351	−	11.6281i	−0.232470	−	0.402650i
$835$	−4.47587			−0.154894
$836$	18.1776			0.628686
$837$	−10.4736	−	11.3292i	−0.362022	−	0.391595i
$838$	27.1616			0.938282
$839$	27.1183			0.936229			0.468115	−	0.883668i	$-0.344933\pi$
$839$	27.1183			0.936229			0.468115	+	0.883668i	$0.344933\pi$
$840$	−0.462319	−	0.800760i	−0.0159515	−	0.0276288i
$841$	39.5576			1.36406
$842$	−3.08920	+	5.35064i	−0.106461	+	0.184395i
$843$	3.56525	+	6.17519i	0.122794	+	0.212685i
$844$	−4.97885	−	8.62361i	−0.171379	−	0.296837i
$845$	−1.70982			−0.0588195
$846$	−4.50349	+	7.80028i	−0.154833	+	0.268179i
$847$	1.95577	−	3.38749i	0.0672010	−	0.116396i
$848$	3.43844	−	5.95556i	0.118077	−	0.204515i
$849$	2.69743	+	4.67209i	0.0925756	+	0.160346i
$850$	−8.84919	+	15.3272i	−0.303525	+	0.525720i
$851$	−3.42152	−	5.92624i	−0.117288	−	0.203149i
$852$	−8.31770			−0.284960
$853$	48.9624			1.67644			0.838220	−	0.545333i	$-0.183597\pi$
$853$	48.9624			1.67644			0.838220	+	0.545333i	$0.183597\pi$
$854$	10.8706	+	18.8285i	0.371985	+	0.644297i
$855$	−11.1325	+	19.2821i	−0.380724	+	0.659434i
$856$	10.0603	+	17.4249i	0.343853	+	0.595571i
$857$	−21.6538	+	37.5055i	−0.739681	+	1.28117i	0.212958	+	0.977061i	$0.431690\pi$
$857$	−21.6538	+	37.5055i	−0.739681	+	1.28117i	−0.952639	+	0.304104i	$0.901643\pi$
$858$	−1.20340	+	2.08434i	−0.0410832	+	0.0711582i
$859$	−22.0294	+	38.1561i	−0.751635	+	1.30187i	0.195395	+	0.980725i	$0.437401\pi$
$859$	−22.0294	+	38.1561i	−0.751635	+	1.30187i	−0.947030	+	0.321145i	$0.895932\pi$
$860$	−17.7766			−0.606178
$861$	−1.46833	−	2.54322i	−0.0500406	−	0.0866728i
$862$	−18.4963	−	32.0365i	−0.629986	−	1.09117i
$863$	−11.8798	+	20.5764i	−0.404393	+	0.700429i	−0.994251	−	0.107078i	$-0.965850\pi$
$863$	−11.8798	+	20.5764i	−0.404393	+	0.700429i	0.589858	+	0.807507i	$0.299184\pi$
$864$	18.8480			0.641223
$865$	0.995240	+	1.72381i	0.0338392	+	0.0586111i
$866$	−33.5241			−1.13920
$867$	−2.01162			−0.0683181
$868$	−2.50890	+	8.08136i	−0.0851575	+	0.274299i
$869$	16.7552			0.568383
$870$	−12.5909			−0.426872
$871$	−2.39741	−	4.15244i	−0.0812333	−	0.140700i
$872$	−13.1129			−0.444060
$873$	−12.6385	+	21.8906i	−0.427750	+	0.740884i
$874$	2.76590	+	4.79068i	0.0935581	+	0.162047i
$875$	−6.43651	−	11.1484i	−0.217594	−	0.376883i
$876$	−5.36724			−0.181342
$877$	18.9034	−	32.7416i	0.638321	−	1.10560i	−0.347480	−	0.937687i	$-0.612962\pi$
$877$	18.9034	−	32.7416i	0.638321	−	1.10560i	0.985801	−	0.167917i	$-0.0537042\pi$
$878$	−9.88966	+	17.1294i	−0.333760	+	0.578089i
$879$	2.77031	−	4.79832i	0.0934403	−	0.161843i
$880$	−11.1430	−	19.3002i	−0.375630	−	0.650610i
$881$	−24.0028	+	41.5740i	−0.808674	+	1.40066i	0.105109	+	0.994461i	$0.466481\pi$
$881$	−24.0028	+	41.5740i	−0.808674	+	1.40066i	−0.913783	+	0.406203i	$0.866852\pi$
$882$	15.0448	+	26.0583i	0.506583	+	0.877428i
$883$	−19.6568			−0.661504			−0.330752	−	0.943718i	$-0.607302\pi$
$883$	−19.6568			−0.661504			−0.330752	+	0.943718i	$0.607302\pi$
$884$	6.57537			0.221154
$885$	−0.988464	−	1.71207i	−0.0332269	−	0.0575506i
$886$	−15.3261	+	26.5455i	−0.514890	+	0.891815i
$887$	6.73761	+	11.6699i	0.226227	+	0.391836i	0.956687	−	0.291119i	$-0.0940276\pi$
$887$	6.73761	+	11.6699i	0.226227	+	0.391836i	−0.730460	+	0.682955i	$0.760694\pi$
$888$	2.73727	−	4.74109i	0.0918568	−	0.159101i
$889$	−5.27796	+	9.14170i	−0.177017	+	0.306603i
$890$	−11.0871	+	19.2035i	−0.371641	+	0.643702i
$891$	18.8808			0.632530
$892$	5.18479	+	8.98033i	0.173600	+	0.300684i
$893$	−4.12985	−	7.15310i	−0.138200	−	0.239369i
$894$	−6.21302	+	10.7613i	−0.207794	+	0.359911i
$895$	−26.5540			−0.887601
$896$	4.31965	+	7.48186i	0.144309	+	0.249951i
$897$	−0.305169			−0.0101893
$898$	−60.0536			−2.00401
$899$	−31.2949	−	33.8514i	−1.04374	−	1.12901i
$900$	8.21447			0.273816
$901$	6.57226			0.218954
$902$	−14.3977	−	24.9376i	−0.479392	−	0.830332i
$903$	−3.71933			−0.123772
$904$	−8.81219	+	15.2632i	−0.293089	+	0.507645i
$905$	−4.75777	−	8.24070i	−0.158154	−	0.273930i
$906$	−8.91963	−	15.4493i	−0.296335	−	0.513267i
$907$	31.6085			1.04954			0.524772	−	0.851243i	$-0.324151\pi$
$907$	31.6085			1.04954			0.524772	+	0.851243i	$0.324151\pi$
$908$	2.22950	−	3.86160i	0.0739884	−	0.128152i
$909$	19.4835	−	33.7465i	0.646228	−	1.11930i
$910$	−1.68415	+	2.91704i	−0.0558291	+	0.0966988i
$911$	8.40001	+	14.5492i	0.278305	+	0.482038i	0.970964	−	0.239227i	$-0.0768941\pi$
$911$	8.40001	+	14.5492i	0.278305	+	0.482038i	−0.692659	+	0.721265i	$0.743561\pi$
$912$	−5.43909	+	9.42078i	−0.180106	+	0.311953i
$913$	11.4891	+	19.8997i	0.380233	+	0.658583i
$914$	−9.63929			−0.318840
$915$	9.06362			0.299634
$916$	17.6497	+	30.5702i	0.583163	+	1.01007i
$917$	10.4113	−	18.0329i	0.343811	−	0.595498i
$918$	11.8091	+	20.4540i	0.389760	+	0.675083i
$919$	4.85972	−	8.41729i	0.160307	−	0.277661i	−0.774671	−	0.632364i	$-0.782085\pi$
$919$	4.85972	−	8.41729i	0.160307	−	0.277661i	0.934979	+	0.354703i	$0.115418\pi$
$920$	0.574797	−	0.995577i	0.0189505	−	0.0328232i
$921$	−6.85759	+	11.8777i	−0.225965	+	0.391383i
$922$	−21.6927			−0.714412
$923$	−6.06136	−	10.4986i	−0.199512	−	0.345565i
$924$	0.987738	+	1.71081i	0.0324942	+	0.0562816i
$925$	11.1826	−	19.3688i	0.367682	−	0.636844i
$926$	29.1741			0.958721
$927$	15.8093	+	27.3825i	0.519246	+	0.899361i
$928$	56.3174			1.84871
$929$	−4.06830			−0.133477			−0.0667383	−	0.997771i	$-0.521259\pi$
$929$	−4.06830			−0.133477			−0.0667383	+	0.997771i	$0.521259\pi$
$930$	5.74745	+	6.21695i	0.188466	+	0.203862i
$931$	−27.5930			−0.904325
$932$	−21.5112			−0.704622
$933$	−2.36636	−	4.09866i	−0.0774712	−	0.134184i
$934$	16.0279			0.524448
$935$	10.6494	−	18.4453i	0.348272	−	0.603225i
$936$	1.46528	+	2.53795i	0.0478943	+	0.0829553i
$937$	19.6049	+	33.9567i	0.640464	+	1.10932i	0.985329	+	0.170665i	$0.0545915\pi$
$937$	19.6049	+	33.9567i	0.640464	+	1.10932i	−0.344865	+	0.938652i	$0.612075\pi$
$938$	−9.44570			−0.308413
$939$	0.00472487	−	0.00818372i	0.000154190	−	0.000267066i
$940$	2.14513	−	3.71547i	0.0699664	−	0.121185i
$941$	−18.8899	+	32.7183i	−0.615793	+	1.06658i	0.374452	+	0.927246i	$0.377831\pi$
$941$	−18.8899	+	32.7183i	−0.615793	+	1.06658i	−0.990245	+	0.139338i	$0.955502\pi$
$942$	3.40764	+	5.90221i	0.111027	+	0.192304i
$943$	1.82556	−	3.16197i	0.0594485	−	0.102968i
$944$	5.79703	+	10.0407i	0.188677	+	0.326798i
$945$	−5.04094			−0.163982
$946$	−36.4699			−1.18574
$947$	1.53501	+	2.65872i	0.0498813	+	0.0863969i	0.889888	−	0.456179i	$-0.150782\pi$
$947$	1.53501	+	2.65872i	0.0498813	+	0.0863969i	−0.840007	+	0.542576i	$0.817449\pi$
$948$	2.12405	−	3.67896i	0.0689859	−	0.119487i
$949$	−3.91127	−	6.77452i	−0.126965	−	0.219910i
$950$	−9.03986	+	15.6575i	−0.293292	+	0.507996i
$951$	1.20552	−	2.08802i	0.0390917	−	0.0677088i
$952$	−2.59125	+	4.48817i	−0.0839828	+	0.145462i
$953$	36.0680			1.16836			0.584178	−	0.811625i	$-0.301417\pi$
$953$	36.0680			1.16836			0.584178	+	0.811625i	$0.301417\pi$
$954$	−3.66065	−	6.34044i	−0.118518	−	0.205279i
$955$	5.87723	+	10.1797i	0.190183	+	0.329406i
$956$	−13.3716	+	23.1602i	−0.432467	+	0.749055i
$957$	−10.7626			−0.347904
$958$	28.3084	+	49.0316i	0.914603	+	1.58414i
$959$	−13.7993			−0.445603
$960$	−2.43194			−0.0784906
$961$	−2.42922	+	30.9047i	−0.0783620	+	0.996925i
$962$	−19.9429			−0.642984
$963$	52.6535			1.69673
$964$	5.30676	+	9.19158i	0.170919	+	0.296041i
$965$	40.2706			1.29636
$966$	−0.300588	+	0.520634i	−0.00967126	+	0.0167511i
$967$	−6.49904	−	11.2567i	−0.208995	−	0.361990i	0.742403	−	0.669953i	$-0.233686\pi$
$967$	−6.49904	−	11.2567i	−0.208995	−	0.361990i	−0.951398	+	0.307963i	$0.900353\pi$
$968$	1.94531	+	3.36938i	0.0625247	+	0.108296i
$969$	−10.3963			−0.333977
$970$	14.4487	−	25.0259i	0.463919	−	0.803532i
$971$	−23.5675	+	40.8200i	−0.756316	+	1.30998i	0.188402	+	0.982092i	$0.439669\pi$
$971$	−23.5675	+	40.8200i	−0.756316	+	1.30998i	−0.944718	+	0.327885i	$0.893664\pi$
$972$	8.33118	−	14.4300i	0.267223	−	0.462843i
$973$	−8.03120	−	13.9105i	−0.257469	−	0.445949i
$974$	24.1302	−	41.7947i	0.773180	−	1.33919i
$975$	−0.498695	−	0.863766i	−0.0159710	−	0.0276626i
$976$	−53.1552			−1.70146
$977$	−8.40957			−0.269046			−0.134523	−	0.990910i	$-0.542950\pi$
$977$	−8.40957			−0.269046			−0.134523	+	0.990910i	$0.542950\pi$
$978$	4.52582	+	7.83895i	0.144720	+	0.250662i
$979$	−9.47713	+	16.4149i	−0.302891	+	0.524622i
$980$	−7.16620	−	12.4122i	−0.228916	−	0.396494i
$981$	−17.1576	+	29.7178i	−0.547800	+	0.948817i
$982$	−26.8685	+	46.5376i	−0.857409	+	1.48508i
$983$	15.7290	−	27.2433i	0.501676	−	0.868928i	−0.498322	−	0.866992i	$-0.666050\pi$
$983$	15.7290	−	27.2433i	0.501676	−	0.868928i	0.999998	−	0.00193600i	$-0.000616248\pi$
$984$	2.92096			0.0931169
$985$	−4.67374	−	8.09516i	−0.148918	−	0.257933i
$986$	35.2854	+	61.1161i	1.12372	+	1.94633i
$987$	0.448816	−	0.777373i	0.0142860	−	0.0247440i
$988$	6.71705			0.213698
$989$	−2.31210	−	4.00468i	−0.0735206	−	0.127341i
$990$	−23.7262			−0.754069
$991$	−36.5934			−1.16243			−0.581214	−	0.813751i	$-0.697422\pi$
$991$	−36.5934			−1.16243			−0.581214	+	0.813751i	$0.697422\pi$
$992$	−25.7076	−	27.8076i	−0.816216	−	0.882891i
$993$	0.383455			0.0121686
$994$	−23.8815			−0.757475
$995$	−0.742086	−	1.28533i	−0.0235257	−	0.0407477i
$996$	5.82585			0.184599
$997$	9.78905	−	16.9551i	0.310022	−	0.536975i	−0.668344	−	0.743852i	$-0.732997\pi$
$997$	9.78905	−	16.9551i	0.310022	−	0.536975i	0.978367	+	0.206877i	$0.0663301\pi$
$998$	−17.9584	−	31.1049i	−0.568463	−	0.984607i
$999$	−14.9231	−	25.8475i	−0.472145	−	0.817779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.118.3	✓	34
31.5	even	3	inner	403.2.h.b.222.3	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.3	✓	34	1.1	even	1	trivial
403.2.h.b.222.3	yes	34	31.5	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.85162 q^{2} +(0.240159 + 0.415967i) q^{3} +1.42848 q^{4} +(0.854909 - 1.48075i) q^{5} +(-0.444682 - 0.770212i) q^{6} +(-0.531962 - 0.921385i) q^{7} +1.05824 q^{8} +(1.38465 - 2.39828i) q^{9} +O(q^{10})\)	\(q-1.85162 q^{2} +(0.240159 + 0.415967i) q^{3} +1.42848 q^{4} +(0.854909 - 1.48075i) q^{5} +(-0.444682 - 0.770212i) q^{6} +(-0.531962 - 0.921385i) q^{7} +1.05824 q^{8} +(1.38465 - 2.39828i) q^{9} +(-1.58296 + 2.74177i) q^{10} +(-1.35310 + 2.34363i) q^{11} +(0.343062 + 0.594201i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(0.984989 + 1.70605i) q^{14} +0.821256 q^{15} -4.81641 q^{16} +(-2.30153 - 3.98636i) q^{17} +(-2.56383 + 4.44069i) q^{18} +(-2.35112 - 4.07226i) q^{19} +(1.22122 - 2.11522i) q^{20} +(0.255511 - 0.442558i) q^{21} +(2.50541 - 4.33950i) q^{22} +0.635348 q^{23} +(0.254145 + 0.440192i) q^{24} +(1.03826 + 1.79832i) q^{25} +(0.925808 - 1.60355i) q^{26} +2.77110 q^{27} +(-0.759897 - 1.31618i) q^{28} +8.27995 q^{29} -1.52065 q^{30} +(-3.77960 - 4.08835i) q^{31} +6.80166 q^{32} -1.29983 q^{33} +(4.26154 + 7.38121i) q^{34} -1.81912 q^{35} +(1.97794 - 3.42589i) q^{36} +(-5.38526 - 9.32754i) q^{37} +(4.35337 + 7.54025i) q^{38} -0.480318 q^{39} +(0.904695 - 1.56698i) q^{40} +(2.87333 - 4.97675i) q^{41} +(-0.473108 + 0.819446i) q^{42} +(-3.63911 - 6.30313i) q^{43} +(-1.93287 + 3.34783i) q^{44} +(-2.36750 - 4.10062i) q^{45} -1.17642 q^{46} +1.75655 q^{47} +(-1.15670 - 2.00347i) q^{48} +(2.93403 - 5.08189i) q^{49} +(-1.92246 - 3.32980i) q^{50} +(1.10546 - 1.91472i) q^{51} +(-0.714240 + 1.23710i) q^{52} +(-0.713902 + 1.23651i) q^{53} -5.13100 q^{54} +(2.31355 + 4.00718i) q^{55} +(-0.562941 - 0.975042i) q^{56} +(1.12928 - 1.95598i) q^{57} -15.3313 q^{58} +(-1.20360 - 2.08470i) q^{59} +1.17315 q^{60} +11.0363 q^{61} +(6.99837 + 7.57005i) q^{62} -2.94632 q^{63} -2.96125 q^{64} +(0.854909 + 1.48075i) q^{65} +2.40679 q^{66} +(-2.39741 + 4.15244i) q^{67} +(-3.28768 - 5.69444i) q^{68} +(0.152585 + 0.264284i) q^{69} +3.36830 q^{70} +(-6.06136 + 10.4986i) q^{71} +(1.46528 - 2.53795i) q^{72} +(-3.91127 + 6.77452i) q^{73} +(9.97143 + 17.2710i) q^{74} +(-0.498695 + 0.863766i) q^{75} +(-3.35852 - 5.81713i) q^{76} +2.87918 q^{77} +0.889364 q^{78} +(-3.09572 - 5.36195i) q^{79} +(-4.11759 + 7.13187i) q^{80} +(-3.48844 - 6.04215i) q^{81} +(-5.32029 + 9.21502i) q^{82} +(4.24548 - 7.35339i) q^{83} +(0.364992 - 0.632185i) q^{84} -7.87038 q^{85} +(6.73824 + 11.6710i) q^{86} +(1.98850 + 3.44419i) q^{87} +(-1.43189 + 2.48011i) q^{88} +7.00404 q^{89} +(4.38369 + 7.59277i) q^{90} +1.06392 q^{91} +0.907582 q^{92} +(0.792916 - 2.55405i) q^{93} -3.25245 q^{94} -8.03997 q^{95} +(1.63348 + 2.82927i) q^{96} -9.12762 q^{97} +(-5.43270 + 9.40971i) q^{98} +(3.74712 + 6.49021i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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