LMFDB - Embedded newform 403.2.bi.b.14.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(14,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("403.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$17$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			14.17
Character	$\chi$	$=$	403.14
Dual form			403.2.bi.b.144.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.849257 - 2.61374i) q^{2} +(-2.02850 + 2.25288i) q^{3} +(-4.49238 - 3.26391i) q^{4} +(1.75209 - 3.03471i) q^{5} +(4.16574 + 7.21527i) q^{6} +(0.0345203 - 0.328439i) q^{7} +(-7.89944 + 5.73928i) q^{8} +(-0.647064 - 6.15640i) q^{9} +O(q^{10})$	\(q+(0.849257 - 2.61374i) q^{2} +(-2.02850 + 2.25288i) q^{3} +(-4.49238 - 3.26391i) q^{4} +(1.75209 - 3.03471i) q^{5} +(4.16574 + 7.21527i) q^{6} +(0.0345203 - 0.328439i) q^{7} +(-7.89944 + 5.73928i) q^{8} +(-0.647064 - 6.15640i) q^{9} +(-6.44398 - 7.15676i) q^{10} +(-2.31186 + 1.02931i) q^{11} +(16.4660 - 3.49996i) q^{12} +(-0.978148 - 0.207912i) q^{13} +(-0.829139 - 0.369156i) q^{14} +(3.28272 + 10.1032i) q^{15} +(4.86048 + 14.9590i) q^{16} +(-1.11549 - 0.496646i) q^{17} +(-16.6408 - 3.53711i) q^{18} +(-4.99851 + 1.06247i) q^{19} +(-17.7761 + 7.91442i) q^{20} +(0.669910 + 0.744010i) q^{21} +(0.726982 + 6.91677i) q^{22} +(-2.31565 + 1.68242i) q^{23} +(3.09413 - 29.4387i) q^{24} +(-3.63964 - 6.30404i) q^{25} +(-1.37413 + 2.38006i) q^{26} +(7.82448 + 5.68482i) q^{27} +(-1.22707 + 1.36280i) q^{28} +(-1.30877 + 4.02797i) q^{29} +29.1950 q^{30} +(3.04134 - 4.66372i) q^{31} +23.6983 q^{32} +(2.37072 - 7.29632i) q^{33} +(-2.24544 + 2.49381i) q^{34} +(-0.936234 - 0.680214i) q^{35} +(-17.1871 + 29.7689i) q^{36} +(-2.00908 - 3.47983i) q^{37} +(-1.46800 + 13.9671i) q^{38} +(2.45258 - 1.78190i) q^{39} +(3.57651 + 34.0282i) q^{40} +(-5.49696 - 6.10499i) q^{41} +(2.51358 - 1.11912i) q^{42} +(9.33786 - 1.98482i) q^{43} +(13.7454 + 2.92167i) q^{44} +(-19.8166 - 8.82292i) q^{45} +(2.43083 + 7.48133i) q^{46} +(-1.81187 - 5.57636i) q^{47} +(-43.5604 - 19.3943i) q^{48} +(6.74035 + 1.43271i) q^{49} +(-19.5681 + 4.15933i) q^{50} +(3.38165 - 1.50561i) q^{51} +(3.71561 + 4.12660i) q^{52} +(-1.28904 - 12.2644i) q^{53} +(21.5037 - 15.6233i) q^{54} +(-0.926943 + 8.81928i) q^{55} +(1.61231 + 2.79261i) q^{56} +(7.74588 - 13.4163i) q^{57} +(9.41660 + 6.84156i) q^{58} +(-1.70255 + 1.89087i) q^{59} +(18.2286 - 56.1018i) q^{60} +1.91789 q^{61} +(-9.60688 - 11.9100i) q^{62} -2.04434 q^{63} +(10.4050 - 32.0233i) q^{64} +(-2.34475 + 2.60411i) q^{65} +(-17.0574 - 12.3929i) q^{66} +(-2.33605 + 4.04616i) q^{67} +(3.39018 + 5.87197i) q^{68} +(0.907017 - 8.62969i) q^{69} +(-2.57301 + 1.86940i) q^{70} +(-1.47856 - 14.0676i) q^{71} +(40.4447 + 44.9184i) q^{72} +(-1.99628 + 0.888800i) q^{73} +(-10.8016 + 2.29596i) q^{74} +(21.5853 + 4.58809i) q^{75} +(25.9230 + 11.5417i) q^{76} +(0.258259 + 0.794839i) q^{77} +(-2.57457 - 7.92370i) q^{78} +(-9.14591 - 4.07202i) q^{79} +(53.9122 + 11.4594i) q^{80} +(-10.5141 + 2.23485i) q^{81} +(-20.6252 + 9.18293i) q^{82} +(0.305047 + 0.338789i) q^{83} +(-0.581111 - 5.52891i) q^{84} +(-3.46161 + 2.51501i) q^{85} +(2.74242 - 26.0924i) q^{86} +(-6.41970 - 11.1192i) q^{87} +(12.3550 - 21.3994i) q^{88} +(0.372588 + 0.270701i) q^{89} +(-39.8902 + 44.3026i) q^{90} +(-0.102052 + 0.314085i) q^{91} +15.8941 q^{92} +(4.33743 + 16.3122i) q^{93} -16.1139 q^{94} +(-5.53356 + 17.0305i) q^{95} +(-48.0721 + 53.3895i) q^{96} +(8.40753 + 6.10843i) q^{97} +(9.46902 - 16.4008i) q^{98} +(7.83276 + 13.5667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9	\( 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9} + 7 q^{10} + 5 q^{11} + 28 q^{12} + 17 q^{13} - 3 q^{14} + 17 q^{15} - 78 q^{16} - 12 q^{17} + 34 q^{18} - 23 q^{19} + 8 q^{20} - 38 q^{21} + 8 q^{22} + 9 q^{23} + 46 q^{24} - 69 q^{25} - 12 q^{26} - 58 q^{27} + 7 q^{28} + 18 q^{29} + 60 q^{30} + 14 q^{31} + 212 q^{32} - 41 q^{33} - 30 q^{35} - 106 q^{36} + 6 q^{37} - 62 q^{38} + 6 q^{39} + 39 q^{40} - 5 q^{41} + 37 q^{42} + q^{43} - 88 q^{44} - 168 q^{45} + 6 q^{46} - 81 q^{47} - 101 q^{48} + 117 q^{49} - 20 q^{50} + 35 q^{51} + 7 q^{52} + 25 q^{53} + 57 q^{54} + 19 q^{55} - 63 q^{56} - 20 q^{57} - 44 q^{58} + 9 q^{59} + 113 q^{60} + 8 q^{61} + 57 q^{62} + 112 q^{63} - 146 q^{64} - 5 q^{65} + 70 q^{66} - 99 q^{67} - 56 q^{68} - 65 q^{69} + 169 q^{70} - q^{71} - 43 q^{72} + 50 q^{73} - 26 q^{74} - 18 q^{75} - 94 q^{76} + 114 q^{77} - 17 q^{79} + 217 q^{80} + 54 q^{81} - 25 q^{82} - 53 q^{83} - 22 q^{84} + 2 q^{85} - 54 q^{86} - 28 q^{87} + 70 q^{88} - 101 q^{89} + 165 q^{90} - 4 q^{91} + 64 q^{92} + 61 q^{93} - 90 q^{94} - 33 q^{95} - 217 q^{96} + 73 q^{97} + 33 q^{98} - 15 q^{99}+O(q^{100}) \) 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9 + 7 * q^10 + 5 * q^11 + 28 * q^12 + 17 * q^13 - 3 * q^14 + 17 * q^15 - 78 * q^16 - 12 * q^17 + 34 * q^18 - 23 * q^19 + 8 * q^20 - 38 * q^21 + 8 * q^22 + 9 * q^23 + 46 * q^24 - 69 * q^25 - 12 * q^26 - 58 * q^27 + 7 * q^28 + 18 * q^29 + 60 * q^30 + 14 * q^31 + 212 * q^32 - 41 * q^33 - 30 * q^35 - 106 * q^36 + 6 * q^37 - 62 * q^38 + 6 * q^39 + 39 * q^40 - 5 * q^41 + 37 * q^42 + q^43 - 88 * q^44 - 168 * q^45 + 6 * q^46 - 81 * q^47 - 101 * q^48 + 117 * q^49 - 20 * q^50 + 35 * q^51 + 7 * q^52 + 25 * q^53 + 57 * q^54 + 19 * q^55 - 63 * q^56 - 20 * q^57 - 44 * q^58 + 9 * q^59 + 113 * q^60 + 8 * q^61 + 57 * q^62 + 112 * q^63 - 146 * q^64 - 5 * q^65 + 70 * q^66 - 99 * q^67 - 56 * q^68 - 65 * q^69 + 169 * q^70 - q^71 - 43 * q^72 + 50 * q^73 - 26 * q^74 - 18 * q^75 - 94 * q^76 + 114 * q^77 - 17 * q^79 + 217 * q^80 + 54 * q^81 - 25 * q^82 - 53 * q^83 - 22 * q^84 + 2 * q^85 - 54 * q^86 - 28 * q^87 + 70 * q^88 - 101 * q^89 + 165 * q^90 - 4 * q^91 + 64 * q^92 + 61 * q^93 - 90 * q^94 - 33 * q^95 - 217 * q^96 + 73 * q^97 + 33 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{11}{15}\right)$

Coefficient data

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

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

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

$2$	0.849257	−	2.61374i	0.600515	−	1.84820i	0.0754209	−	0.997152i	$-0.475970\pi$
$2$	0.849257	−	2.61374i	0.600515	−	1.84820i	0.525094	−	0.851044i	$-0.324030\pi$
$3$	−2.02850	+	2.25288i	−1.17116	+	1.30070i	−0.225985	+	0.974131i	$0.572560\pi$
$3$	−2.02850	+	2.25288i	−1.17116	+	1.30070i	−0.945172	+	0.326572i	$0.894107\pi$
$4$	−4.49238	−	3.26391i	−2.24619	−	1.63195i
$5$	1.75209	−	3.03471i	0.783558	−	1.35716i	−0.146298	−	0.989241i	$-0.546736\pi$
$5$	1.75209	−	3.03471i	0.783558	−	1.35716i	0.929856	−	0.367923i	$-0.119931\pi$
$6$	4.16574	+	7.21527i	1.70065	+	2.94562i
$7$	0.0345203	−	0.328439i	0.0130475	−	0.124138i	−0.986059	−	0.166394i	$-0.946788\pi$
$7$	0.0345203	−	0.328439i	0.0130475	−	0.124138i	0.999107	+	0.0422555i	$0.0134544\pi$
$8$	−7.89944	+	5.73928i	−2.79287	+	2.02914i
$9$	−0.647064	−	6.15640i	−0.215688	−	2.05213i
$10$	−6.44398	−	7.15676i	−2.03776	−	2.26317i
$11$	−2.31186	+	1.02931i	−0.697053	+	0.310348i	−0.724500	−	0.689275i	$-0.757929\pi$
$11$	−2.31186	+	1.02931i	−0.697053	+	0.310348i	0.0274463	+	0.999623i	$0.491262\pi$
$12$	16.4660	−	3.49996i	4.75333	−	1.01035i
$13$	−0.978148	−	0.207912i	−0.271289	−	0.0576643i
$13$	−0.978148	−	0.207912i	−0.271289	−	0.0576643i
$14$	−0.829139	−	0.369156i	−0.221597	−	0.0986612i
$15$	3.28272	+	10.1032i	0.847595	+	2.60863i
$16$	4.86048	+	14.9590i	1.21512	+	3.73975i
$17$	−1.11549	−	0.496646i	−0.270545	−	0.120454i	0.266980	−	0.963702i	$-0.413974\pi$
$17$	−1.11549	−	0.496646i	−0.270545	−	0.120454i	−0.537525	+	0.843248i	$0.680641\pi$
$18$	−16.6408	−	3.53711i	−3.92227	−	0.833704i
$19$	−4.99851	+	1.06247i	−1.14674	+	0.243746i	−0.741814	−	0.670605i	$-0.766034\pi$
$19$	−4.99851	+	1.06247i	−1.14674	+	0.243746i	−0.404921	+	0.914351i	$0.632701\pi$
$20$	−17.7761	+	7.91442i	−3.97485	+	1.76972i
$21$	0.669910	+	0.744010i	0.146186	+	0.162356i
$22$	0.726982	+	6.91677i	0.154993	+	1.47466i
$23$	−2.31565	+	1.68242i	−0.482847	+	0.350809i	−0.802427	−	0.596751i	$-0.796458\pi$
$23$	−2.31565	+	1.68242i	−0.482847	+	0.350809i	0.319580	+	0.947559i	$0.396458\pi$
$24$	3.09413	−	29.4387i	0.631586	−	6.00914i
$25$	−3.63964	−	6.30404i	−0.727928	−	1.26081i
$26$	−1.37413	+	2.38006i	−0.269488	+	0.466768i
$27$	7.82448	+	5.68482i	1.50582	+	1.09404i
$28$	−1.22707	+	1.36280i	−0.231895	+	0.257546i
$29$	−1.30877	+	4.02797i	−0.243032	+	0.747975i	0.752922	+	0.658110i	$0.228644\pi$
$29$	−1.30877	+	4.02797i	−0.243032	+	0.747975i	−0.995954	+	0.0898653i	$0.971356\pi$
$30$	29.1950			5.33025
$31$	3.04134	−	4.66372i	0.546241	−	0.837628i
$31$	3.04134	−	4.66372i	0.546241	−	0.837628i
$32$	23.6983			4.18931
$33$	2.37072	−	7.29632i	0.412689	−	1.27013i
$34$	−2.24544	+	2.49381i	−0.385090	+	0.427686i
$35$	−0.936234	−	0.680214i	−0.158252	−	0.114977i
$36$	−17.1871	+	29.7689i	−2.86451	+	4.96148i
$37$	−2.00908	−	3.47983i	−0.330291	−	0.572081i	0.652278	−	0.757980i	$-0.273814\pi$
$37$	−2.00908	−	3.47983i	−0.330291	−	0.572081i	−0.982569	+	0.185899i	$0.940480\pi$
$38$	−1.46800	+	13.9671i	−0.238142	+	2.26577i
$39$	2.45258	−	1.78190i	0.392727	−	0.285333i
$40$	3.57651	+	34.0282i	0.565496	+	5.38034i
$41$	−5.49696	−	6.10499i	−0.858480	−	0.953439i	0.140850	−	0.990031i	$-0.455016\pi$
$41$	−5.49696	−	6.10499i	−0.858480	−	0.953439i	−0.999330	+	0.0365920i	$0.988350\pi$
$42$	2.51358	−	1.11912i	0.387854	−	0.172684i
$43$	9.33786	−	1.98482i	1.42401	−	0.302683i	0.569447	−	0.822028i	$-0.307158\pi$
$43$	9.33786	−	1.98482i	1.42401	−	0.302683i	0.854564	+	0.519345i	$0.173824\pi$
$44$	13.7454	+	2.92167i	2.07219	+	0.440458i
$45$	−19.8166	−	8.82292i	−2.95408	−	1.31524i
$46$	2.43083	+	7.48133i	0.358406	+	1.10306i
$47$	−1.81187	−	5.57636i	−0.264288	−	0.813395i	−0.991857	−	0.127360i	$-0.959350\pi$
$47$	−1.81187	−	5.57636i	−0.264288	−	0.813395i	0.727568	−	0.686035i	$-0.240650\pi$
$48$	−43.5604	−	19.3943i	−6.28740	−	2.79933i
$49$	6.74035	+	1.43271i	0.962908	+	0.204672i
$50$	−19.5681	+	4.15933i	−2.76735	+	0.588219i
$51$	3.38165	−	1.50561i	0.473526	−	0.210827i
$52$	3.71561	+	4.12660i	0.515262	+	0.572257i
$53$	−1.28904	−	12.2644i	−0.177064	−	1.68465i	−0.617269	−	0.786752i	$-0.711761\pi$
$53$	−1.28904	−	12.2644i	−0.177064	−	1.68465i	0.440205	−	0.897897i	$-0.354906\pi$
$54$	21.5037	−	15.6233i	2.92628	−	2.12606i
$55$	−0.926943	+	8.81928i	−0.124989	+	1.18919i
$56$	1.61231	+	2.79261i	0.215454	+	0.373178i
$57$	7.74588	−	13.4163i	1.02597	−	1.77703i
$58$	9.41660	+	6.84156i	1.23646	+	0.898341i
$59$	−1.70255	+	1.89087i	−0.221653	+	0.246171i	−0.843707	−	0.536803i	$-0.819632\pi$
$59$	−1.70255	+	1.89087i	−0.221653	+	0.246171i	0.622054	+	0.782974i	$0.286298\pi$
$60$	18.2286	−	56.1018i	2.35330	−	7.24272i
$61$	1.91789			0.245561			0.122781	−	0.992434i	$-0.460819\pi$
$61$	1.91789			0.245561			0.122781	+	0.992434i	$0.460819\pi$
$62$	−9.60688	−	11.9100i	−1.22007	−	1.51257i
$63$	−2.04434			−0.257563
$64$	10.4050	−	32.0233i	1.30062	−	4.00291i
$65$	−2.34475	+	2.60411i	−0.290831	+	0.323000i
$66$	−17.0574	−	12.3929i	−2.09961	−	1.52546i
$67$	−2.33605	+	4.04616i	−0.285394	+	0.494318i	−0.972705	−	0.232046i	$-0.925458\pi$
$67$	−2.33605	+	4.04616i	−0.285394	+	0.494318i	0.687310	+	0.726364i	$0.258791\pi$
$68$	3.39018	+	5.87197i	0.411120	+	0.712081i
$69$	0.907017	−	8.62969i	0.109192	−	1.03889i
$70$	−2.57301	+	1.86940i	−0.307533	+	0.223436i
$71$	−1.47856	−	14.0676i	−0.175473	−	1.66952i	−0.628340	−	0.777939i	$-0.716265\pi$
$71$	−1.47856	−	14.0676i	−0.175473	−	1.66952i	0.452867	−	0.891578i	$-0.350401\pi$
$72$	40.4447	+	44.9184i	4.76646	+	5.29369i
$73$	−1.99628	+	0.888800i	−0.233647	+	0.104026i	−0.520221	−	0.854032i	$-0.674150\pi$
$73$	−1.99628	+	0.888800i	−0.233647	+	0.104026i	0.286574	+	0.958058i	$0.407484\pi$
$74$	−10.8016	+	2.29596i	−1.25566	+	0.266899i
$75$	21.5853	+	4.58809i	2.49245	+	0.529787i
$76$	25.9230	+	11.5417i	2.97357	+	1.32392i
$77$	0.258259	+	0.794839i	0.0294313	+	0.0905803i
$78$	−2.57457	−	7.92370i	−0.291512	−	0.897182i
$79$	−9.14591	−	4.07202i	−1.02899	−	0.458138i	−0.178399	−	0.983958i	$-0.557092\pi$
$79$	−9.14591	−	4.07202i	−1.02899	−	0.458138i	−0.850596	+	0.525820i	$0.823758\pi$
$80$	53.9122	+	11.4594i	6.02757	+	1.28120i
$81$	−10.5141	+	2.23485i	−1.16824	+	0.248316i
$82$	−20.6252	+	9.18293i	−2.27767	+	1.01409i
$83$	0.305047	+	0.338789i	0.0334832	+	0.0371869i	0.759654	−	0.650328i	$-0.225368\pi$
$83$	0.305047	+	0.338789i	0.0334832	+	0.0371869i	−0.726171	+	0.687515i	$0.758702\pi$
$84$	−0.581111	−	5.52891i	−0.0634045	−	0.603253i
$85$	−3.46161	+	2.51501i	−0.375464	+	0.272791i
$86$	2.74242	−	26.0924i	0.295723	−	2.81362i
$87$	−6.41970	−	11.1192i	−0.688264	−	1.19211i
$88$	12.3550	−	21.3994i	1.31704	−	2.28118i
$89$	0.372588	+	0.270701i	0.0394943	+	0.0286943i	0.607357	−	0.794429i	$-0.292230\pi$
$89$	0.372588	+	0.270701i	0.0394943	+	0.0286943i	−0.567863	+	0.823123i	$0.692230\pi$
$90$	−39.8902	+	44.3026i	−4.20480	+	4.66990i
$91$	−0.102052	+	0.314085i	−0.0106980	+	0.0329250i
$92$	15.8941			1.65707
$93$	4.33743	+	16.3122i	0.449770	+	1.69149i
$94$	−16.1139			−1.66202
$95$	−5.53356	+	17.0305i	−0.567731	+	1.74730i
$96$	−48.0721	+	53.3895i	−4.90634	+	5.44904i
$97$	8.40753	+	6.10843i	0.853656	+	0.620217i	0.926152	−	0.377152i	$-0.123096\pi$
$97$	8.40753	+	6.10843i	0.853656	+	0.620217i	−0.0724960	+	0.997369i	$0.523096\pi$
$98$	9.46902	−	16.4008i	0.956515	−	1.65673i
$99$	7.83276	+	13.5667i	0.787222	+	1.36351i
$100$	−4.22515	+	40.1996i	−0.422515	+	4.01996i
$101$	−5.53427	+	4.02088i	−0.550680	+	0.400093i	−0.828036	−	0.560674i	$-0.810542\pi$
$101$	−5.53427	+	4.02088i	−0.550680	+	0.400093i	0.277356	+	0.960767i	$0.410542\pi$
$102$	−1.06338	−	10.1174i	−0.105291	−	1.00177i
$103$	0.872684	+	0.969214i	0.0859881	+	0.0954995i	0.784603	−	0.619998i	$-0.212867\pi$
$103$	0.872684	+	0.969214i	0.0859881	+	0.0954995i	−0.698615	+	0.715498i	$0.746200\pi$
$104$	8.92008	−	3.97148i	0.874686	−	0.389435i
$105$	3.43160	−	0.729409i	0.334890	−	0.0711830i
$106$	−33.1508	−	7.04642i	−3.21989	−	0.684409i
$107$	7.42372	+	3.30525i	0.717678	+	0.319531i	0.732884	−	0.680354i	$-0.238174\pi$
$107$	7.42372	+	3.30525i	0.717678	+	0.319531i	−0.0152061	+	0.999884i	$0.504840\pi$
$108$	−16.5959	−	51.0768i	−1.59694	−	4.91487i
$109$	−0.233170	−	0.717622i	−0.0223336	−	0.0687357i	0.939269	−	0.343183i	$-0.111505\pi$
$109$	−0.233170	−	0.717622i	−0.0223336	−	0.0687357i	−0.961602	+	0.274447i	$0.911505\pi$
$110$	22.2641	+	9.91262i	2.12280	+	0.945132i
$111$	11.9151	+	2.53263i	1.13093	+	0.240387i
$112$	5.08091	−	1.07998i	0.480101	−	0.102049i
$113$	13.8348	−	6.15964i	1.30147	−	0.579450i	0.365261	−	0.930905i	$-0.380980\pi$
$113$	13.8348	−	6.15964i	1.30147	−	0.579450i	0.936205	+	0.351455i	$0.114313\pi$
$114$	−28.4884	−	31.6396i	−2.66819	−	2.96332i
$115$	1.04842	+	9.97508i	0.0977660	+	0.930181i
$116$	19.0264	−	13.8235i	1.76656	−	1.28348i
$117$	−0.647064	+	6.15640i	−0.0598211	+	0.569159i
$118$	3.49636	+	6.05587i	0.321866	+	0.557488i
$119$	−0.201625	+	0.349225i	−0.0184829	+	0.0320134i
$120$	−83.9166	−	60.9690i	−7.66050	−	5.56568i
$121$	−3.07519	+	3.41535i	−0.279563	+	0.310486i
$122$	1.62878	−	5.01288i	0.147463	−	0.453845i
$123$	24.9044			2.24556
$124$	−28.8848	+	11.0245i	−2.59393	+	0.990033i
$125$	−7.98700			−0.714379
$126$	−1.73617	+	5.34338i	−0.154670	+	0.476026i
$127$	5.81645	−	6.45982i	0.516126	−	0.573216i	−0.427590	−	0.903973i	$-0.640637\pi$
$127$	5.81645	−	6.45982i	0.516126	−	0.573216i	0.943716	+	0.330757i	$0.107304\pi$
$128$	−36.5195	−	26.5330i	−3.22790	−	2.34520i
$129$	−14.4703	+	25.0633i	−1.27404	+	2.20670i
$130$	4.81519	+	8.34015i	0.422320	+	0.731479i
$131$	−0.458057	+	4.35812i	−0.0400206	+	0.380771i	0.956118	+	0.292981i	$0.0946472\pi$
$131$	−0.458057	+	4.35812i	−0.0400206	+	0.380771i	−0.996139	+	0.0877902i	$0.972020\pi$
$132$	−34.4647	+	25.0401i	−2.99977	+	2.17946i
$133$	0.176405	+	1.67838i	0.0152963	+	0.145534i
$134$	8.59173	+	9.54208i	0.742212	+	0.824310i
$135$	30.9610	−	13.7847i	2.66470	−	1.18640i
$136$	11.6621	−	2.47886i	1.00002	−	0.212560i
$137$	2.75125	+	0.584796i	0.235055	+	0.0499625i	0.323933	−	0.946080i	$-0.394995\pi$
$137$	2.75125	+	0.584796i	0.235055	+	0.0499625i	−0.0888780	+	0.996043i	$0.528328\pi$
$138$	−21.7855	−	9.69953i	−1.85450	−	0.825679i
$139$	0.0231913	+	0.0713756i	0.00196706	+	0.00605400i	0.952035	−	0.305988i	$-0.0989869\pi$
$139$	0.0231913	+	0.0713756i	0.00196706	+	0.00605400i	−0.950068	+	0.312042i	$0.898987\pi$
$140$	1.98577	+	6.11157i	0.167828	+	0.516522i
$141$	16.2383	+	7.22974i	1.36751	+	0.608854i
$142$	−38.0248	−	8.08241i	−3.19097	−	0.678261i
$143$	2.47535	−	0.526152i	0.206999	−	0.0439990i
$144$	88.9486	−	39.6025i	7.41238	−	3.30021i
$145$	9.93063	+	11.0291i	0.824694	+	0.915916i
$146$	0.627743	+	5.97258i	0.0519524	+	0.494294i
$147$	−16.9006	+	12.2790i	−1.39393	+	1.01275i
$148$	−2.33229	+	22.1902i	−0.191713	+	1.82402i
$149$	−10.4719	−	18.1379i	−0.857894	−	1.48592i	−0.873934	−	0.486044i	$-0.838439\pi$
$149$	−10.4719	−	18.1379i	−0.857894	−	1.48592i	0.0160406	−	0.999871i	$-0.494894\pi$
$150$	30.3235	−	52.5219i	2.47591	−	4.28840i
$151$	−4.72742	−	3.43467i	−0.384712	−	0.279509i	0.378573	−	0.925571i	$-0.376415\pi$
$151$	−4.72742	−	3.43467i	−0.384712	−	0.279509i	−0.763285	+	0.646062i	$0.776415\pi$
$152$	33.3876	−	37.0807i	2.70809	−	3.00764i
$153$	−2.33576	+	7.18874i	−0.188835	+	0.581175i
$154$	2.29683			0.185084
$155$	−8.82431	−	17.4008i	−0.708786	−	1.39767i
$156$	−16.8339			−1.34779
$157$	3.28486	−	10.1098i	0.262160	−	0.806847i	−0.730174	−	0.683262i	$-0.760561\pi$
$157$	3.28486	−	10.1098i	0.262160	−	0.806847i	0.992334	−	0.123585i	$-0.0394392\pi$
$158$	−18.4104	+	20.4469i	−1.46466	+	1.62667i
$159$	30.2452	+	21.9744i	2.39860	+	1.74268i
$160$	41.5216	−	71.9175i	3.28257	−	5.68558i
$161$	0.472635	+	0.818628i	0.0372489	+	0.0645169i
$162$	−3.08788	+	29.3792i	−0.242606	+	2.30825i
$163$	11.2817	−	8.19662i	0.883650	−	0.642009i	−0.0505649	−	0.998721i	$-0.516102\pi$
$163$	11.2817	−	8.19662i	0.883650	−	0.642009i	0.934214	+	0.356712i	$0.116102\pi$
$164$	4.76832	+	45.3675i	0.372343	+	3.54261i
$165$	−17.9885	−	19.9782i	−1.40040	−	1.55530i
$166$	1.14457	−	0.509596i	0.0888359	−	0.0395523i
$167$	−22.6207	+	4.80818i	−1.75044	+	0.372068i	−0.968058	−	0.250727i	$-0.919330\pi$
$167$	−22.6207	+	4.80818i	−1.75044	+	0.372068i	−0.782385	+	0.622795i	$0.785997\pi$
$168$	−9.56200	−	2.03247i	−0.737724	−	0.156808i
$169$	0.913545	+	0.406737i	0.0702727	+	0.0312874i
$170$	3.63379	+	11.1836i	0.278699	+	0.857746i
$171$	9.77531	+	30.0853i	0.747537	+	2.30068i
$172$	−48.4276	−	21.5613i	−3.69257	−	1.64404i
$173$	2.28428	+	0.485538i	0.173670	+	0.0369148i	0.293926	−	0.955828i	$-0.405038\pi$
$173$	2.28428	+	0.485538i	0.173670	+	0.0369148i	−0.120256	+	0.992743i	$0.538371\pi$
$174$	−34.5148	+	7.33635i	−2.61656	+	0.556168i
$175$	−2.19613	+	0.977782i	−0.166012	+	0.0739134i
$176$	−26.6342	−	29.5803i	−2.00763	−	2.22970i
$177$	−0.806286	−	7.67130i	−0.0606041	−	0.576610i
$178$	1.02397	−	0.743956i	0.0767496	−	0.0557618i
$179$	−1.23714	+	11.7706i	−0.0924684	+	0.879778i	0.845714	+	0.533637i	$0.179175\pi$
$179$	−1.23714	+	11.7706i	−0.0924684	+	0.879778i	−0.938182	+	0.346141i	$0.887492\pi$
$180$	60.2266	+	104.315i	4.48902	+	7.77522i
$181$	−9.64767	+	16.7102i	−0.717105	+	1.24206i	0.245036	+	0.969514i	$0.421200\pi$
$181$	−9.64767	+	16.7102i	−0.717105	+	1.24206i	−0.962142	+	0.272549i	$0.912133\pi$
$182$	0.734268	+	0.533477i	0.0544276	+	0.0395440i
$183$	−3.89046	+	4.32079i	−0.287591	+	0.319402i
$184$	8.63648	−	26.5803i	0.636690	−	1.95953i
$185$	−14.0804			−1.03521
$186$	46.3194	+	2.51628i	3.39630	+	0.184503i
$187$	3.09005			0.225967
$188$	−10.0611	+	30.9649i	−0.733782	+	2.25835i
$189$	2.13722	−	2.37362i	0.155460	−	0.172656i
$190$	39.8141	+	28.9266i	2.88842	+	2.09856i
$191$	−3.87799	+	6.71688i	−0.280601	+	0.486016i	−0.971533	−	0.236904i	$-0.923867\pi$
$191$	−3.87799	+	6.71688i	−0.280601	+	0.486016i	0.690932	+	0.722920i	$0.257201\pi$
$192$	51.0381	+	88.4006i	3.68336	+	6.37977i
$193$	1.25899	−	11.9785i	0.0906243	−	0.862233i	−0.850909	−	0.525313i	$-0.823948\pi$
$193$	1.25899	−	11.9785i	0.0906243	−	0.862233i	0.941533	−	0.336920i	$-0.109385\pi$
$194$	23.1060	−	16.7875i	1.65892	−	1.20527i
$195$	−1.11042	−	10.5649i	−0.0795186	−	0.756569i
$196$	−25.6040	−	28.4362i	−1.82886	−	2.03115i
$197$	7.65266	−	3.40718i	0.545229	−	0.242752i	−0.115590	−	0.993297i	$-0.536876\pi$
$197$	7.65266	−	3.40718i	0.545229	−	0.242752i	0.660819	+	0.750545i	$0.270209\pi$
$198$	42.1120	−	8.95118i	2.99277	−	0.636133i
$199$	2.21248	+	0.470276i	0.156838	+	0.0333370i	0.285662	−	0.958331i	$-0.407787\pi$
$199$	2.21248	+	0.470276i	0.156838	+	0.0333370i	−0.128823	+	0.991668i	$0.541120\pi$
$200$	64.9318	+	28.9095i	4.59137	+	2.04421i
$201$	−4.37684	−	13.4705i	−0.308718	−	0.950137i
$202$	5.80954	+	17.8799i	0.408758	+	1.25803i
$203$	1.27776	+	0.568897i	0.0896814	+	0.0399287i
$204$	−20.1059	−	4.27363i	−1.40769	−	0.299214i
$205$	−28.1580	+	5.98517i	−1.96664	+	0.418023i
$206$	3.27441	−	1.45786i	0.228139	−	0.101574i
$207$	11.8560	+	13.1674i	0.824050	+	0.915201i
$208$	−1.64411	−	15.6427i	−0.113999	−	1.08462i
$209$	10.4623	−	7.60128i	0.723690	−	0.525792i
$210$	1.00782	−	9.58877i	0.0695462	−	0.661688i
$211$	8.19725	+	14.1981i	0.564322	+	0.977435i	0.997112	+	0.0759401i	$0.0241958\pi$
$211$	8.19725	+	14.1981i	0.564322	+	0.977435i	−0.432790	+	0.901495i	$0.642471\pi$
$212$	−34.2391	+	59.3039i	−2.35155	+	4.07301i
$213$	34.6919	+	25.2052i	2.37705	+	1.72703i
$214$	14.9437	−	16.5967i	1.02153	−	1.13453i
$215$	10.3374	−	31.8153i	0.705006	−	2.16978i
$216$	−94.4358			−6.42554
$217$	−1.42676	−	1.15989i	−0.0968547	−	0.0787384i
$218$	−2.07370			−0.140449
$219$	2.04710	−	6.30032i	0.138330	−	0.425736i
$220$	32.9495	−	36.5941i	2.22145	−	2.46718i
$221$	0.987851	+	0.717716i	0.0664501	+	0.0482788i
$222$	16.7386	−	28.9921i	1.12342	−	1.94583i
$223$	−7.16644	−	12.4126i	−0.479900	−	0.831212i	0.519834	−	0.854267i	$-0.325994\pi$
$223$	−7.16644	−	12.4126i	−0.479900	−	0.831212i	−0.999734	+	0.0230554i	$0.992661\pi$
$224$	0.818074	−	7.78345i	0.0546599	−	0.520054i
$225$	−36.4551	+	26.4862i	−2.43034	+	1.76575i
$226$	−4.35044	−	41.3917i	−0.289387	−	2.75333i
$227$	−10.2860	−	11.4238i	−0.682706	−	0.758222i	0.297818	−	0.954623i	$-0.403741\pi$
$227$	−10.2860	−	11.4238i	−0.682706	−	0.758222i	−0.980524	+	0.196401i	$0.937075\pi$
$228$	−78.5869	+	34.9892i	−5.20455	+	2.31721i
$229$	−1.42892	+	0.303727i	−0.0944259	+	0.0200708i	−0.254882	−	0.966972i	$-0.582037\pi$
$229$	−1.42892	+	0.303727i	−0.0944259	+	0.0200708i	0.160456	+	0.987043i	$0.448703\pi$
$230$	26.9627	+	5.73109i	1.77787	+	0.377897i
$231$	−2.31456	−	1.03051i	−0.152287	−	0.0678024i
$232$	−12.7791	−	39.3301i	−0.838990	−	2.58215i
$233$	5.33770	+	16.4278i	0.349684	+	1.07622i	0.959028	+	0.283312i	$0.0914331\pi$
$233$	5.33770	+	16.4278i	0.349684	+	1.07622i	−0.609344	+	0.792906i	$0.708567\pi$
$234$	15.5417	+	6.91962i	1.01599	+	0.452350i
$235$	−20.0972	−	4.27179i	−1.31100	−	0.278661i
$236$	13.8202	−	2.93757i	0.899616	−	0.191219i
$237$	27.7263	−	12.3445i	1.80102	−	0.801864i
$238$	0.741553	+	0.823578i	0.0480677	+	0.0533846i
$239$	−0.906114	−	8.62110i	−0.0586117	−	0.557653i	−0.983942	−	0.178490i	$-0.942879\pi$
$239$	−0.906114	−	8.62110i	−0.0586117	−	0.557653i	0.925330	−	0.379163i	$-0.123788\pi$
$240$	−135.178	+	98.2125i	−8.72569	+	6.33959i
$241$	−1.80520	+	17.1753i	−0.116283	+	1.10636i	0.768337	+	0.640045i	$0.221084\pi$
$241$	−1.80520	+	17.1753i	−0.116283	+	1.10636i	−0.884620	+	0.466312i	$0.845582\pi$
$242$	6.31522	+	10.9383i	0.405958	+	0.703139i
$243$	1.78571	−	3.09294i	0.114553	−	0.198412i
$244$	−8.61591	−	6.25983i	−0.551577	−	0.400744i
$245$	16.1576	−	17.9448i	1.03227	−	1.14645i
$246$	21.1502	−	65.0938i	1.34849	−	4.15023i
$247$	5.11018			0.325153
$248$	2.74147	+	54.2959i	0.174083	+	3.44779i
$249$	−1.38204			−0.0875833
$250$	−6.78301	+	20.8760i	−0.428995	+	1.32031i
$251$	0.161121	−	0.178943i	0.0101699	−	0.0112948i	−0.738038	−	0.674759i	$-0.764248\pi$
$251$	0.161121	−	0.178943i	0.0101699	−	0.0112948i	0.748208	+	0.663464i	$0.230914\pi$
$252$	9.18396	+	6.67254i	0.578535	+	0.420330i
$253$	3.62174	−	6.27305i	0.227697	−	0.394383i
$254$	−11.9447	−	20.6887i	−0.749474	−	1.29813i
$255$	1.35588	−	12.9003i	0.0849082	−	0.807848i
$256$	−45.8835	+	33.3363i	−2.86772	+	2.08352i
$257$	−0.937887	−	8.92340i	−0.0585038	−	0.556626i	−0.984038	−	0.177961i	$-0.943050\pi$
$257$	−0.937887	−	8.92340i	−0.0585038	−	0.556626i	0.925534	−	0.378665i	$-0.123617\pi$
$258$	53.2201	+	59.1069i	3.31334	+	3.67984i
$259$	−1.21227	+	0.539736i	−0.0753267	+	0.0335376i
$260$	19.0331	−	4.04562i	1.18038	−	0.250898i
$261$	25.6446	+	5.45093i	1.58736	+	0.337404i
$262$	11.0020	+	4.89841i	0.679706	+	0.302625i
$263$	−8.45578	−	26.0242i	−0.521406	−	1.60472i	−0.771315	−	0.636453i	$-0.780401\pi$
$263$	−8.45578	−	26.0242i	−0.521406	−	1.60472i	0.249910	−	0.968269i	$-0.419599\pi$
$264$	23.1483	+	71.2430i	1.42468	+	4.38471i
$265$	−39.4775	−	17.5765i	−2.42508	−	1.07972i
$266$	4.53667	+	0.964299i	0.278161	+	0.0591250i
$267$	−1.36566	+	0.290279i	−0.0835768	+	0.0177648i
$268$	23.7008	−	10.5523i	1.44775	−	0.644582i
$269$	17.0370	+	18.9215i	1.03877	+	1.15367i	0.987921	+	0.154961i	$0.0495251\pi$
$269$	17.0370	+	18.9215i	1.03877	+	1.15367i	0.0508460	+	0.998707i	$0.483808\pi$
$270$	−9.73589	−	92.6308i	−0.592507	−	5.63733i
$271$	−3.37918	+	2.45512i	−0.205270	+	0.149138i	−0.685671	−	0.727911i	$-0.740491\pi$
$271$	−3.37918	+	2.45512i	−0.205270	+	0.149138i	0.480401	+	0.877049i	$0.340491\pi$
$272$	2.00754	−	19.1005i	0.121725	−	1.15814i
$273$	−0.500582	−	0.867034i	−0.0302966	−	0.0524753i
$274$	3.86502	−	6.69441i	0.233494	−	0.404424i
$275$	14.9032	+	10.8278i	0.898694	+	0.652939i
$276$	−32.2412	+	35.8075i	−1.94069	+	2.15536i
$277$	−1.39072	+	4.28019i	−0.0835601	+	0.257171i	−0.984104	−	0.177594i	$-0.943169\pi$
$277$	−1.39072	+	4.28019i	−0.0835601	+	0.257171i	0.900544	+	0.434765i	$0.143169\pi$
$278$	0.206253			0.0123702
$279$	−30.6796	−	15.7060i	−1.83674	−	0.940293i
$280$	11.2997			0.675284
$281$	−1.40474	+	4.32335i	−0.0837999	+	0.257910i	−0.984173	−	0.177208i	$-0.943293\pi$
$281$	−1.40474	+	4.32335i	−0.0837999	+	0.257910i	0.900373	+	0.435118i	$0.143293\pi$
$282$	32.6871	−	36.3027i	1.94649	−	2.16180i
$283$	−10.0878	−	7.32924i	−0.599660	−	0.435678i	0.246098	−	0.969245i	$-0.420851\pi$
$283$	−10.0878	−	7.32924i	−0.599660	−	0.435678i	−0.845758	+	0.533566i	$0.820851\pi$
$284$	−39.2731	+	68.0230i	−2.33043	+	4.03642i
$285$	−27.1430	−	47.0130i	−1.60781	−	2.78481i
$286$	0.726982	−	6.91677i	0.0429873	−	0.408997i
$287$	−2.19487	+	1.59467i	−0.129559	+	0.0941303i
$288$	−15.3343	−	145.896i	−0.903583	−	8.59702i
$289$	−10.3776	−	11.5255i	−0.610445	−	0.677968i
$290$	37.2609	−	16.5896i	2.18803	−	0.974175i
$291$	−30.8163	+	6.55020i	−1.80648	+	0.383980i
$292$	11.8690	+	2.52284i	0.694581	+	0.147638i
$293$	−0.517306	−	0.230320i	−0.0302214	−	0.0134554i	0.391570	−	0.920148i	$-0.371932\pi$
$293$	−0.517306	−	0.230320i	−0.0302214	−	0.0134554i	−0.421792	+	0.906693i	$0.638599\pi$
$294$	17.7412	+	54.6017i	1.03469	+	3.18444i
$295$	2.75523	+	8.47973i	0.160416	+	0.493709i
$296$	35.8424	+	15.9581i	2.08330	+	0.927543i
$297$	−23.9406	−	5.08873i	−1.38917	−	0.295278i
$298$	−56.3012	+	11.9672i	−3.26144	+	0.693241i
$299$	2.61484	−	1.16420i	0.151220	−	0.0673276i
$300$	−81.9943	−	91.0639i	−4.73394	−	5.25758i
$301$	−0.329548	−	3.13544i	−0.0189948	−	0.180724i
$302$	−12.9921	+	9.43934i	−0.747613	+	0.543173i
$303$	2.16772	−	20.6244i	0.124532	−	1.18484i
$304$	−40.1885	−	69.6086i	−2.30497	−	3.99233i
$305$	3.36032	−	5.82025i	0.192411	−	0.333266i
$306$	16.8059	+	12.2102i	0.960727	+	0.698009i
$307$	4.40765	−	4.89519i	0.251558	−	0.279383i	−0.604119	−	0.796894i	$-0.706475\pi$
$307$	4.40765	−	4.89519i	0.251558	−	0.279383i	0.855677	+	0.517511i	$0.173141\pi$
$308$	1.43408	−	4.41365i	0.0817145	−	0.251491i
$309$	−3.95377			−0.224922
$310$	−52.9754	+	8.28672i	−3.00880	+	0.470654i
$311$	30.3986			1.72375			0.861874	−	0.507122i	$-0.169291\pi$
$311$	30.3986			1.72375			0.861874	+	0.507122i	$0.169291\pi$
$312$	−9.14716	+	28.1521i	−0.517856	+	1.59380i
$313$	7.48446	−	8.31233i	0.423047	−	0.469841i	−0.493513	−	0.869738i	$-0.664288\pi$
$313$	7.48446	−	8.31233i	0.423047	−	0.469841i	0.916560	+	0.399897i	$0.130954\pi$
$314$	−23.6346	−	17.1716i	−1.33378	−	0.969048i
$315$	−3.58187	+	6.20397i	−0.201815	+	0.349554i
$316$	27.7962	+	48.1445i	1.56366	+	2.70834i
$317$	0.547113	−	5.20543i	0.0307289	−	0.292366i	−0.968355	−	0.249576i	$-0.919709\pi$
$317$	0.547113	−	5.20543i	0.0307289	−	0.292366i	0.999084	−	0.0427900i	$-0.0136246\pi$
$318$	83.1213	−	60.3912i	4.66121	−	3.38657i
$319$	−1.12033	−	10.6592i	−0.0627265	−	0.596803i
$320$	−78.9509	−	87.6838i	−4.41349	−	4.90168i
$321$	−22.5054	+	10.0200i	−1.25613	+	0.559264i
$322$	2.54107	−	0.540122i	0.141608	−	0.0300998i
$323$	6.10343	+	1.29732i	0.339604	+	0.0721851i
$324$	54.5278	+	24.2773i	3.02932	+	1.34874i
$325$	2.24942	+	6.92300i	0.124775	+	0.384019i
$326$	−11.8428	−	36.4485i	−0.655913	−	2.01869i
$327$	2.08970	+	0.930396i	0.115561	+	0.0514510i
$328$	78.4611	+	16.6774i	4.33229	+	0.920857i
$329$	−1.89404	+	0.402591i	−0.104422	+	0.0221955i
$330$	−67.4948	+	30.0506i	−3.71547	+	1.65423i
$331$	23.8187	+	26.4533i	1.30919	+	1.45401i	0.808645	+	0.588297i	$0.200201\pi$
$331$	23.8187	+	26.4533i	1.30919	+	1.45401i	0.500548	+	0.865709i	$0.333132\pi$
$332$	−0.264612	−	2.51762i	−0.0145225	−	0.138172i
$333$	−20.1232	+	14.6204i	−1.10275	+	0.801193i
$334$	−6.64344	+	63.2081i	−0.363513	+	3.45859i
$335$	8.18595	+	14.1785i	0.447246	+	0.774654i
$336$	−7.87358	+	13.6374i	−0.429539	+	0.743983i
$337$	18.8339	+	13.6836i	1.02595	+	0.745395i	0.967494	−	0.252895i	$-0.0813826\pi$
$337$	18.8339	+	13.6836i	1.02595	+	0.745395i	0.0584548	+	0.998290i	$0.481383\pi$
$338$	1.83894	−	2.04235i	0.100025	−	0.111089i
$339$	−14.1870	+	43.6630i	−0.770530	+	2.37145i
$340$	23.7596			1.28855
$341$	−2.23077	+	13.9124i	−0.120803	+	0.753396i
$342$	86.9370			4.70102
$343$	1.41760	−	4.36293i	0.0765433	−	0.235576i
$344$	−62.3725	+	69.2716i	−3.36290	+	3.73488i
$345$	−24.5994	−	17.8725i	−1.32439	−	0.962224i
$346$	3.20901	−	5.55817i	0.172517	−	0.298809i
$347$	−3.53936	−	6.13035i	−0.190003	−	0.329094i	0.755248	−	0.655439i	$-0.227516\pi$
$347$	−3.53936	−	6.13035i	−0.190003	−	0.329094i	−0.945251	+	0.326345i	$0.894183\pi$
$348$	−7.45244	+	70.9052i	−0.399493	+	3.80092i
$349$	−13.7998	+	10.0261i	−0.738684	+	0.536685i	−0.892299	−	0.451446i	$-0.850909\pi$
$349$	−13.7998	+	10.0261i	−0.738684	+	0.536685i	0.153615	+	0.988131i	$0.450909\pi$
$350$	0.690590	+	6.57052i	0.0369136	+	0.351209i
$351$	−6.47156	−	7.18739i	−0.345426	−	0.383635i
$352$	−54.7873	+	24.3929i	−2.92017	+	1.30014i
$353$	11.5969	−	2.46500i	0.617243	−	0.131199i	0.111330	−	0.993784i	$-0.464489\pi$
$353$	11.5969	−	2.46500i	0.617243	−	0.131199i	0.505913	+	0.862585i	$0.331156\pi$
$354$	−20.7355	−	4.40748i	−1.10208	−	0.234255i
$355$	−45.2816	−	20.1607i	−2.40330	−	1.07002i
$356$	−0.790266	−	2.43219i	−0.0418840	−	0.128906i
$357$	−0.377765	−	1.16264i	−0.0199934	−	0.0615335i
$358$	29.7147	+	13.2299i	1.57047	+	0.699220i
$359$	3.08295	+	0.655301i	0.162712	+	0.0345854i	0.288547	−	0.957466i	$-0.406828\pi$
$359$	3.08295	+	0.655301i	0.162712	+	0.0345854i	−0.125835	+	0.992051i	$0.540161\pi$
$360$	207.177	−	44.0369i	10.9192	−	2.32095i
$361$	6.49886	−	2.89348i	0.342045	−	0.152288i
$362$	35.4830	+	39.4078i	1.86494	+	2.07123i
$363$	−1.45634	−	13.8561i	−0.0764378	−	0.727257i
$364$	1.48360	−	1.07790i	0.0777619	−	0.0564973i
$365$	−0.800409	+	7.61538i	−0.0418953	+	0.398607i
$366$	7.98944	+	13.8381i	0.417615	+	0.723330i
$367$	−5.46865	+	9.47197i	−0.285461	+	0.494433i	−0.972721	−	0.231979i	$-0.925480\pi$
$367$	−5.46865	+	9.47197i	−0.285461	+	0.494433i	0.687260	+	0.726412i	$0.258813\pi$
$368$	−36.4225	−	26.4625i	−1.89865	−	1.37945i
$369$	−34.0279	+	37.7918i	−1.77142	+	1.96736i
$370$	−11.9579	+	36.8025i	−0.621659	+	1.91327i
$371$	−4.07262			−0.211440
$372$	33.7560	−	87.4374i	1.75017	−	4.53342i
$373$	−24.8870			−1.28860			−0.644301	−	0.764772i	$-0.722851\pi$
$373$	−24.8870			−1.28860			−0.644301	+	0.764772i	$0.722851\pi$
$374$	2.62425	−	8.07661i	0.135697	−	0.417632i
$375$	16.2017	−	17.9938i	0.836650	−	0.929194i
$376$	46.3170	+	33.6513i	2.38862	+	1.73543i
$377$	2.11763	−	3.66784i	0.109063	−	0.188903i
$378$	−4.38900	−	7.60196i	−0.225746	−	0.391003i
$379$	−3.38035	+	32.1619i	−0.173637	+	1.65205i	0.467039	+	0.884236i	$0.345321\pi$
$379$	−3.38035	+	32.1619i	−0.173637	+	1.65205i	−0.640677	+	0.767811i	$0.721346\pi$
$380$	80.4450	−	58.4467i	4.12674	−	2.99825i
$381$	2.75452	+	26.2075i	0.141119	+	1.34265i
$382$	14.2628	+	15.8404i	0.729747	+	0.810467i
$383$	−22.2290	+	9.89701i	−1.13585	+	0.505714i	−0.886513	−	0.462703i	$-0.846880\pi$
$383$	−22.2290	+	9.89701i	−1.13585	+	0.505714i	−0.249338	+	0.968417i	$0.580213\pi$
$384$	133.856	−	28.4519i	6.83079	−	1.45193i
$385$	2.86460	+	0.608889i	0.145993	+	0.0310318i
$386$	−30.2396	−	13.4635i	−1.53915	−	0.685275i
$387$	−18.2616	−	56.2033i	−0.928287	−	2.85698i
$388$	−17.8325	−	54.8828i	−0.905309	−	2.78625i
$389$	24.7782	+	11.0320i	1.25630	+	0.559342i	0.923480	−	0.383647i	$-0.125332\pi$
$389$	24.7782	+	11.0320i	1.25630	+	0.559342i	0.332823	+	0.942989i	$0.391999\pi$
$390$	−28.5570	−	6.06998i	−1.44604	−	0.307365i
$391$	3.41864	−	0.726655i	0.172888	−	0.0367485i
$392$	−61.4677	+	27.3672i	−3.10459	+	1.38225i
$393$	−8.88916	−	9.87242i	−0.448399	−	0.497998i
$394$	−2.40643	−	22.8957i	−0.121234	−	1.15347i
$395$	−28.3818	+	20.6206i	−1.42805	+	1.03754i
$396$	9.09282	−	86.5124i	0.456931	−	4.34741i
$397$	8.95318	+	15.5074i	0.449347	+	0.778292i	0.998344	−	0.0575325i	$-0.0183233\pi$
$397$	8.95318	+	15.5074i	0.449347	+	0.778292i	−0.548996	+	0.835825i	$0.684990\pi$
$398$	3.10814	−	5.38346i	0.155797	−	0.269849i
$399$	−4.13903	−	3.00718i	−0.207211	−	0.150548i
$400$	76.6118	−	85.0860i	3.83059	−	4.25430i
$401$	8.20482	−	25.2518i	0.409729	−	1.26102i	−0.507152	−	0.861857i	$-0.669302\pi$
$401$	8.20482	−	25.2518i	0.409729	−	1.26102i	0.916881	−	0.399160i	$-0.130698\pi$
$402$	−38.9255			−1.94143
$403$	−3.94452	+	3.92947i	−0.196491	+	0.195741i
$404$	37.9859			1.88987
$405$	−11.6396	+	35.8229i	−0.578375	+	1.78006i
$406$	2.57210	−	2.85661i	0.127651	−	0.141771i
$407$	8.22655	+	5.97694i	0.407775	+	0.296266i
$408$	−18.0721	+	31.3017i	−0.894700	+	1.54967i
$409$	5.42971	+	9.40453i	0.268482	+	0.465024i	0.968470	−	0.249130i	$-0.0801447\pi$
$409$	5.42971	+	9.40453i	0.268482	+	0.465024i	−0.699988	+	0.714155i	$0.746811\pi$
$410$	−8.26969	+	78.6808i	−0.408411	+	3.88577i
$411$	−6.89839	+	5.01197i	−0.340273	+	0.247222i
$412$	−0.757007	−	7.20244i	−0.0372951	−	0.354839i
$413$	0.562265	+	0.624458i	0.0276672	+	0.0307276i
$414$	44.4851	−	19.8061i	2.18632	−	0.973414i
$415$	1.56260	−	0.332140i	0.0767048	−	0.0163041i
$416$	−23.1804	−	4.92716i	−1.13651	−	0.241574i
$417$	−0.207844	−	0.0925383i	−0.0101782	−	0.00453162i
$418$	−10.9826	−	33.8011i	−0.537179	−	1.65327i
$419$	−1.25662	−	3.86746i	−0.0613897	−	0.188938i	0.915658	−	0.401958i	$-0.131670\pi$
$419$	−1.25662	−	3.86746i	−0.0613897	−	0.188938i	−0.977048	+	0.213020i	$0.931670\pi$
$420$	−17.7968	−	7.92364i	−0.868394	−	0.386634i
$421$	2.96574	+	0.630388i	0.144541	+	0.0307232i	0.279614	−	0.960112i	$-0.409793\pi$
$421$	2.96574	+	0.630388i	0.144541	+	0.0307232i	−0.135073	+	0.990836i	$0.543127\pi$
$422$	44.0717	−	9.36772i	2.14538	−	0.456014i
$423$	−33.1579	+	14.7628i	−1.61219	+	0.717794i
$424$	80.5718	+	89.4840i	3.91291	+	4.34573i
$425$	0.929088	+	8.83968i	0.0450674	+	0.428787i
$426$	95.3422	−	69.2701i	4.61934	−	3.35615i
$427$	0.0662063	−	0.629911i	0.00320395	−	0.0304835i
$428$	−22.5622	−	39.0788i	−1.09058	−	1.88895i
$429$	−3.83590	+	6.64397i	−0.185199	+	0.320774i
$430$	−74.3779	−	54.0387i	−3.58682	−	2.60598i
$431$	26.6623	−	29.6114i	1.28428	−	1.42633i	0.433192	−	0.901302i	$-0.357387\pi$
$431$	26.6623	−	29.6114i	1.28428	−	1.42633i	0.851083	−	0.525031i	$-0.175946\pi$
$432$	−47.0086	+	144.677i	−2.26170	+	6.96080i
$433$	7.22719			0.347317			0.173658	−	0.984806i	$-0.444441\pi$
$433$	7.22719			0.347317			0.173658	+	0.984806i	$0.444441\pi$
$434$	−4.24334	+	2.74414i	−0.203687	+	0.131723i
$435$	−44.9916			−2.15718
$436$	−1.29477	+	3.98488i	−0.0620080	+	0.190841i
$437$	9.78729	−	10.8699i	0.468189	−	0.519977i
$438$	−14.7289	−	10.7012i	−0.703774	−	0.511322i
$439$	5.26197	−	9.11399i	0.251140	−	0.434987i	−0.712700	−	0.701469i	$-0.752528\pi$
$439$	5.26197	−	9.11399i	0.251140	−	0.434987i	0.963840	+	0.266482i	$0.0858612\pi$
$440$	−43.2940	−	74.9874i	−2.06396	−	3.57488i
$441$	4.45887	−	42.4234i	0.212327	−	2.02016i
$442$	2.71486	−	1.97246i	0.129133	−	0.0938206i
$443$	−1.79891	−	17.1155i	−0.0854689	−	0.813182i	−0.950345	−	0.311197i	$-0.899270\pi$
$443$	−1.79891	−	17.1155i	−0.0854689	−	0.813182i	0.864876	−	0.501985i	$-0.167397\pi$
$444$	−45.2609	−	50.2673i	−2.14799	−	2.38558i
$445$	1.47431	−	0.656404i	0.0698889	−	0.0311165i
$446$	−38.5296	+	8.18972i	−1.82443	+	0.387795i
$447$	62.1049	+	13.2008i	2.93746	+	0.624377i
$448$	−10.1585	−	4.52286i	−0.479945	−	0.213685i
$449$	2.60483	+	8.01686i	0.122930	+	0.378339i	0.993518	−	0.113673i	$-0.0362616\pi$
$449$	2.60483	+	8.01686i	0.122930	+	0.378339i	−0.870588	+	0.492012i	$0.836262\pi$
$450$	38.2683	+	117.778i	1.80399	+	5.55210i
$451$	18.9921	+	8.45584i	0.894305	+	0.398170i
$452$	−82.2556	−	17.4840i	−3.86898	−	0.822377i
$453$	17.3275	−	3.68307i	0.814117	−	0.173046i
$454$	−38.5942	+	17.1833i	−1.81132	+	0.806450i
$455$	0.774351	+	0.860004i	0.0363021	+	0.0403176i
$456$	15.8115	+	150.437i	0.740443	+	7.04485i
$457$	10.5875	−	7.69229i	0.495264	−	0.359830i	−0.311941	−	0.950101i	$-0.600979\pi$
$457$	10.5875	−	7.69229i	0.495264	−	0.359830i	0.807205	+	0.590271i	$0.200979\pi$
$458$	−0.419658	+	3.99278i	−0.0196093	+	0.186570i
$459$	−5.90476	−	10.2273i	−0.275610	−	0.477371i
$460$	27.8478	−	48.2338i	1.29841	−	2.24891i
$461$	−16.5083	−	11.9940i	−0.768870	−	0.558617i	0.132748	−	0.991150i	$-0.457620\pi$
$461$	−16.5083	−	11.9940i	−0.768870	−	0.558617i	−0.901618	+	0.432533i	$0.857620\pi$
$462$	−4.65914	+	5.17449i	−0.216763	+	0.240739i
$463$	10.8810	−	33.4884i	0.505684	−	1.55634i	−0.293933	−	0.955826i	$-0.594964\pi$
$463$	10.8810	−	33.4884i	0.505684	−	1.55634i	0.799617	−	0.600510i	$-0.205036\pi$
$464$	−66.6156			−3.09255
$465$	57.1022	+	15.4175i	2.64805	+	0.714971i
$466$	47.4710			2.19905
$467$	3.76285	−	11.5809i	0.174124	−	0.535898i	−0.825468	−	0.564448i	$-0.809089\pi$
$467$	3.76285	−	11.5809i	0.174124	−	0.535898i	0.999592	+	0.0285499i	$0.00908896\pi$
$468$	23.0008	−	25.5450i	1.06321	−	1.18082i
$469$	1.24828	+	0.906926i	0.0576401	+	0.0418780i
$470$	−28.2330	+	48.9010i	−1.30229	+	2.25564i
$471$	16.1127	+	27.9081i	0.742436	+	1.28594i
$472$	2.59694	−	24.7083i	0.119534	−	1.13729i
$473$	−19.5449	+	14.2002i	−0.898675	+	0.652925i
$474$	−8.71872	−	82.9531i	−0.400464	−	3.81016i
$475$	24.8906	+	27.6438i	1.14206	+	1.26838i
$476$	2.04561	−	0.910766i	0.0937606	−	0.0417449i
$477$	−74.6707	+	15.8717i	−3.41893	+	0.726717i
$478$	−23.3029	−	4.95318i	−1.06585	−	0.226553i
$479$	−31.4494	−	14.0022i	−1.43696	−	0.639775i	−0.467269	−	0.884115i	$-0.654762\pi$
$479$	−31.4494	−	14.0022i	−1.43696	−	0.639775i	−0.969689	+	0.244341i	$0.921429\pi$
$480$	77.7949	+	239.428i	3.55084	+	10.9284i
$481$	1.24168	+	3.82150i	0.0566158	+	0.174246i
$482$	43.3587	+	19.3046i	1.97494	+	0.879298i
$483$	−2.80302	−	0.595799i	−0.127542	−	0.0271098i
$484$	24.9623	−	5.30591i	1.13465	−	0.241178i
$485$	33.2681	−	14.8119i	1.51062	−	0.672573i
$486$	−6.56762	−	7.29408i	−0.297913	−	0.330866i
$487$	−0.680174	−	6.47143i	−0.0308216	−	0.293248i	−0.999065	−	0.0432380i	$-0.986233\pi$
$487$	−0.680174	−	6.47143i	−0.0308216	−	0.293248i	0.968243	−	0.250010i	$-0.0804340\pi$
$488$	−15.1503	+	11.0073i	−0.685821	+	0.498278i
$489$	−4.41892	+	42.0432i	−0.199830	+	1.90126i
$490$	−33.1811	−	57.4714i	−1.49897	−	2.59629i
$491$	4.63459	−	8.02734i	0.209156	−	0.362269i	−0.742293	−	0.670076i	$-0.766262\pi$
$491$	4.63459	−	8.02734i	0.209156	−	0.362269i	0.951449	+	0.307807i	$0.0995950\pi$
$492$	−111.880	−	81.2858i	−5.04395	−	3.66464i
$493$	3.46038	−	3.84315i	0.155848	−	0.173087i
$494$	4.33985	−	13.3567i	0.195259	−	0.600946i
$495$	54.8948			2.46734
$496$	84.5469	+	22.8276i	3.79627	+	1.02499i
$497$	−4.67139			−0.209540
$498$	−1.17371	+	3.61230i	−0.0525951	+	0.161871i
$499$	5.89468	−	6.54670i	0.263882	−	0.293071i	−0.596614	−	0.802529i	$-0.703487\pi$
$499$	5.89468	−	6.54670i	0.263882	−	0.293071i	0.860495	+	0.509458i	$0.170154\pi$
$500$	35.8807	+	26.0688i	1.60463	+	1.16583i
$501$	35.0539	−	60.7152i	1.56609	−	2.71256i
$502$	−0.330877	−	0.573097i	−0.0147678	−	0.0255786i
$503$	1.08118	−	10.2867i	0.0482075	−	0.458664i	−0.943616	−	0.331043i	$-0.892599\pi$
$503$	1.08118	−	10.2867i	0.0482075	−	0.458664i	0.991823	−	0.127620i	$-0.0407339\pi$
$504$	16.1491	−	11.7330i	0.719340	−	0.522631i
$505$	2.50567	+	23.8398i	0.111501	+	1.06086i
$506$	−13.3203	−	14.7937i	−0.592161	−	0.657662i
$507$	−2.76946	+	1.23304i	−0.122996	+	0.0547614i
$508$	−47.2140	+	10.0356i	−2.09478	+	0.445260i
$509$	−15.1170	−	3.21322i	−0.670050	−	0.142424i	−0.139689	−	0.990195i	$-0.544610\pi$
$509$	−15.1170	−	3.21322i	−0.670050	−	0.142424i	−0.530361	+	0.847772i	$0.677944\pi$
$510$	−32.5666	−	14.4996i	−1.44207	−	0.642052i
$511$	0.223005	+	0.686337i	0.00986514	+	0.0303618i
$512$	20.2673	+	62.3764i	0.895697	+	2.75667i
$513$	−45.1507	−	20.1024i	−1.99345	−	0.887541i
$514$	−24.1200	−	5.12686i	−1.06389	−	0.226136i
$515$	4.47030	−	0.950192i	0.196985	−	0.0418705i
$516$	146.811	−	65.3643i	6.46298	−	2.87750i
$517$	9.92859	+	11.0268i	0.436659	+	0.484959i
$518$	0.381206	+	3.62693i	0.0167492	+	0.159358i
$519$	−5.72752	+	4.16129i	−0.251410	+	0.182660i
$520$	3.57651	−	34.0282i	0.156840	−	1.49224i
$521$	20.5056	+	35.5167i	0.898365	+	1.55601i	0.829583	+	0.558383i	$0.188578\pi$
$521$	20.5056	+	35.5167i	0.898365	+	1.55601i	0.0687819	+	0.997632i	$0.478089\pi$
$522$	36.0262	−	62.3992i	1.57682	−	2.73114i
$523$	23.8024	+	17.2935i	1.04081	+	0.756190i	0.970443	−	0.241332i	$-0.0775841\pi$
$523$	23.8024	+	17.2935i	1.04081	+	0.756190i	0.0703633	+	0.997521i	$0.477584\pi$
$524$	16.2823	−	18.0833i	0.711295	−	0.789973i
$525$	2.25204	−	6.93107i	0.0982871	−	0.302497i
$526$	−75.2018			−3.27895
$527$	−5.70879	+	3.69184i	−0.248679	+	0.160819i
$528$	120.668			5.25142
$529$	−4.57568	+	14.0825i	−0.198943	+	0.612283i
$530$	−79.4671	+	88.2571i	−3.45183	+	3.83364i
$531$	12.7426	+	9.25807i	0.552983	+	0.401766i
$532$	4.68560	−	8.11570i	0.203147	−	0.351860i
$533$	4.10754	+	7.11446i	0.177917	+	0.308162i
$534$	−0.401077	+	3.81599i	−0.0173563	+	0.165134i
$535$	23.0375	−	16.7377i	0.995998	−	0.723635i
$536$	−4.76855	−	45.3697i	−0.205970	−	1.95967i
$537$	−24.0083	−	26.6639i	−1.03603	−	1.15063i
$538$	63.9249	−	28.4612i	2.75600	−	1.22705i
$539$	−17.0575	+	3.62568i	−0.734718	+	0.156169i
$540$	−184.081	−	39.1275i	−7.92157	−	1.68378i
$541$	−15.0850	−	6.71628i	−0.648555	−	0.288756i	0.0559719	−	0.998432i	$-0.482174\pi$
$541$	−15.0850	−	6.71628i	−0.648555	−	0.288756i	−0.704527	+	0.709677i	$0.748841\pi$
$542$	3.54726	+	10.9173i	0.152368	+	0.468940i
$543$	−18.0759	−	55.6319i	−0.775711	−	2.38739i
$544$	−26.4351	−	11.7697i	−1.13340	−	0.504621i
$545$	−2.58631	−	0.549737i	−0.110785	−	0.0235481i
$546$	−2.69133	+	0.572059i	−0.115178	+	0.0244819i
$547$	−36.1116	+	16.0779i	−1.54402	+	0.687443i	−0.989474	−	0.144708i	$-0.953776\pi$
$547$	−36.1116	+	16.0779i	−1.54402	+	0.687443i	−0.554548	+	0.832152i	$0.687109\pi$
$548$	−10.4509	−	11.6069i	−0.446442	−	0.495824i
$549$	−1.24100	−	11.8073i	−0.0529645	−	0.503924i
$550$	40.9576	−	29.7575i	1.74644	−	1.26886i
$551$	2.26230	−	21.5243i	0.0963772	−	0.916968i
$552$	42.3633	+	73.3753i	1.80310	+	3.12306i
$553$	−1.65313	+	2.86331i	−0.0702983	+	0.121760i
$554$	10.0062	+	7.26995i	0.425124	+	0.308871i
$555$	28.5621	−	31.7214i	1.21239	−	1.34650i
$556$	0.128779	−	0.396341i	0.00546144	−	0.0168086i
$557$	30.9427			1.31109			0.655543	−	0.755158i	$-0.272440\pi$
$557$	30.9427			1.31109			0.655543	+	0.755158i	$0.272440\pi$
$558$	−67.1063	+	66.8503i	−2.84084	+	2.83000i
$559$	−9.54648			−0.403773
$560$	5.62478	−	17.3113i	0.237690	−	0.731536i
$561$	−6.26819	+	6.96153i	−0.264643	+	0.293916i
$562$	10.1071	+	7.34327i	0.426344	+	0.309757i
$563$	−10.4785	+	18.1492i	−0.441614	+	0.764898i	−0.997809	−	0.0661533i	$-0.978927\pi$
$563$	−10.4785	+	18.1492i	−0.441614	+	0.764898i	0.556195	+	0.831052i	$0.312261\pi$
$564$	−49.3513	−	85.4790i	−2.07807	−	3.59931i
$565$	5.54706	−	52.7767i	0.233367	−	2.22033i
$566$	−27.7239	+	20.1426i	−1.16532	+	0.846657i
$567$	0.371060	+	3.53040i	0.0155830	+	0.148263i
$568$	92.4177	+	102.640i	3.87776	+	4.30669i
$569$	−7.27673	+	3.23981i	−0.305056	+	0.135820i	−0.553556	−	0.832812i	$-0.686729\pi$
$569$	−7.27673	+	3.23981i	−0.305056	+	0.135820i	0.248499	+	0.968632i	$0.420063\pi$
$570$	−145.931	+	31.0186i	−6.11239	+	1.29923i
$571$	−7.20657	−	1.53180i	−0.301585	−	0.0641040i	0.0546335	−	0.998506i	$-0.482601\pi$
$571$	−7.20657	−	1.53180i	−0.301585	−	0.0641040i	−0.356219	+	0.934403i	$0.615934\pi$
$572$	−12.8375	−	5.71564i	−0.536764	−	0.238983i
$573$	−7.26581	−	22.3619i	−0.303534	−	0.934180i
$574$	2.30404	+	7.09112i	0.0961690	+	0.295978i
$575$	19.0342	+	8.47456i	0.793780	+	0.353414i
$576$	−203.881	−	43.3362i	−8.49504	−	1.80568i
$577$	13.4210	−	2.85272i	0.558723	−	0.118760i	0.0801095	−	0.996786i	$-0.474473\pi$
$577$	13.4210	−	2.85272i	0.558723	−	0.118760i	0.478613	+	0.878026i	$0.341140\pi$
$578$	−38.9378	+	17.3362i	−1.61960	+	0.721092i
$579$	24.4323	+	27.1348i	1.01537	+	1.12769i
$580$	−8.61430	−	81.9596i	−0.357689	−	3.40319i
$581$	0.121802	−	0.0884942i	0.00505319	−	0.00367136i
$582$	−9.05039	+	86.1087i	−0.375151	+	3.56932i
$583$	15.6040	+	27.0269i	0.646251	+	1.11934i
$584$	10.6684	−	18.4782i	0.441462	−	0.764634i
$585$	17.5492	+	12.7502i	0.725569	+	0.527157i
$586$	−1.04132	+	1.15651i	−0.0430166	+	0.0477748i
$587$	−3.86338	+	11.8903i	−0.159459	+	0.490764i	−0.998585	−	0.0531723i	$-0.983067\pi$
$587$	−3.86338	+	11.8903i	−0.159459	+	0.490764i	0.839126	+	0.543936i	$0.183067\pi$
$588$	116.001			4.78381
$589$	−10.2471	+	26.5429i	−0.422226	+	1.09368i
$590$	24.5037			1.00880
$591$	−7.84747	+	24.1520i	−0.322802	+	0.993482i
$592$	42.2898	−	46.9676i	1.73810	−	1.93035i
$593$	−19.0839	−	13.8653i	−0.783682	−	0.569378i	0.122400	−	0.992481i	$-0.460941\pi$
$593$	−19.0839	−	13.8653i	−0.783682	−	0.569378i	−0.906082	+	0.423103i	$0.860941\pi$
$594$	−33.6323	+	58.2529i	−1.37995	+	2.39015i
$595$	0.706530	+	1.22375i	0.0289649	+	0.0501687i
$596$	−12.1566	+	115.662i	−0.497952	+	4.73769i
$597$	−5.54750	+	4.03049i	−0.227044	+	0.164957i
$598$	−0.822256	−	7.82324i	−0.0336245	−	0.319916i
$599$	2.77776	+	3.08502i	0.113496	+	0.126050i	0.797216	−	0.603695i	$-0.206305\pi$
$599$	2.77776	+	3.08502i	0.113496	+	0.126050i	−0.683719	+	0.729745i	$0.739639\pi$
$600$	−196.844	+	87.6406i	−8.03612	+	3.57791i
$601$	23.2923	−	4.95092i	0.950111	−	0.201952i	0.293311	−	0.956017i	$-0.405243\pi$
$601$	23.2923	−	4.95092i	0.950111	−	0.201952i	0.656800	+	0.754065i	$0.271909\pi$
$602$	−8.47510	−	1.80144i	−0.345419	−	0.0734211i
$603$	26.4214	+	11.7636i	1.07596	+	0.479049i
$604$	10.0269	+	30.8597i	0.407990	+	1.25566i
$605$	4.97657	+	15.3163i	0.202327	+	0.622697i
$606$	−52.0661	−	23.1813i	−2.11504	−	0.941676i
$607$	21.8819	+	4.65114i	0.888159	+	0.188784i	0.629329	−	0.777139i	$-0.283330\pi$
$607$	21.8819	+	4.65114i	0.888159	+	0.188784i	0.258830	+	0.965923i	$0.416663\pi$
$608$	−118.456	+	25.1786i	−4.80403	+	1.02113i
$609$	−3.87361	+	1.72464i	−0.156966	+	0.0698859i
$610$	−12.3589	−	13.7259i	−0.500396	−	0.555746i
$611$	0.612885	+	5.83121i	0.0247947	+	0.235905i
$612$	33.9565	−	24.6709i	1.37261	−	0.997260i
$613$	−1.86211	+	17.7168i	−0.0752098	+	0.715573i	0.890330	+	0.455316i	$0.150474\pi$
$613$	−1.86211	+	17.7168i	−0.0752098	+	0.715573i	−0.965539	+	0.260257i	$0.916193\pi$
$614$	−9.05155	−	15.6777i	−0.365291	−	0.632702i
$615$	43.6348	−	75.5777i	1.75952	−	3.04759i
$616$	−6.60190	−	4.79656i	−0.265998	−	0.193259i
$617$	27.2581	−	30.2732i	1.09737	−	1.21875i	0.123335	−	0.992365i	$-0.460641\pi$
$617$	27.2581	−	30.2732i	1.09737	−	1.21875i	0.974037	−	0.226389i	$-0.0726922\pi$
$618$	−3.35776	+	10.3341i	−0.135069	+	0.415700i
$619$	−0.442962			−0.0178041			−0.00890207	−	0.999960i	$-0.502834\pi$
$619$	−0.442962			−0.0178041			−0.00890207	+	0.999960i	$0.502834\pi$
$620$	−17.1525	+	106.973i	−0.688862	+	4.29614i
$621$	−27.6830			−1.11088
$622$	25.8163	−	79.4543i	1.03514	−	3.18583i
$623$	0.101771	−	0.113028i	0.00407736	−	0.00452837i
$624$	38.5762	+	28.0272i	1.54428	+	1.12199i
$625$	4.20425	−	7.28198i	0.168170	−	0.291279i
$626$	−15.3701	−	26.6218i	−0.614312	−	1.06402i
$627$	−4.09796	+	38.9895i	−0.163657	+	1.55709i
$628$	−47.7542	+	34.6955i	−1.90560	+	1.38450i
$629$	0.512857	+	4.87951i	0.0204490	+	0.194559i
$630$	13.1737	+	14.6308i	0.524852	+	0.582907i
$631$	−32.0234	+	14.2577i	−1.27483	+	0.567592i	−0.928783	−	0.370625i	$-0.879144\pi$
$631$	−32.0234	+	14.2577i	−1.27483	+	0.567592i	−0.346049	+	0.938216i	$0.612477\pi$
$632$	95.6180	−	20.3242i	3.80348	−	0.808455i
$633$	−48.6147	−	10.3334i	−1.93226	−	0.410715i
$634$	−13.1410	−	5.85076i	−0.521897	−	0.232363i
$635$	−9.41273	−	28.9694i	−0.373533	−	1.14962i
$636$	−64.1505	−	197.435i	−2.54373	−	7.82880i
$637$	−6.29518	−	2.80280i	−0.249424	−	0.111051i
$638$	−28.8120	−	6.12417i	−1.14068	−	0.242458i
$639$	−85.6490	+	18.2053i	−3.38822	+	0.720189i
$640$	−144.505	+	64.3379i	−5.71207	+	2.54318i
$641$	−26.0179	−	28.8958i	−1.02764	−	1.14131i	−0.989863	−	0.142028i	$-0.954638\pi$
$641$	−26.0179	−	28.8958i	−1.02764	−	1.14131i	−0.0377810	−	0.999286i	$-0.512029\pi$
$642$	7.07697	+	67.3329i	0.279306	+	2.65742i
$643$	10.2275	−	7.43075i	0.403335	−	0.293040i	−0.367563	−	0.929999i	$-0.619808\pi$
$643$	10.2275	−	7.43075i	0.403335	−	0.293040i	0.770898	+	0.636959i	$0.219808\pi$
$644$	0.548668	−	5.22023i	0.0216206	−	0.205706i
$645$	50.7066	+	87.8264i	1.99657	+	3.45816i
$646$	8.57425	−	14.8510i	0.337350	−	0.584306i
$647$	−32.6545	−	23.7249i	−1.28378	−	0.932721i	−0.284120	−	0.958789i	$-0.591701\pi$
$647$	−32.6545	−	23.7249i	−1.28378	−	0.932721i	−0.999660	+	0.0260676i	$0.991701\pi$
$648$	70.2293	−	77.9975i	2.75887	−	3.06403i
$649$	1.98977	−	6.12390i	0.0781055	−	0.240384i
$650$	20.0053			0.784672
$651$	5.50728	−	0.861480i	0.215847	−	0.0337640i
$652$	−77.4347			−3.03258
$653$	11.3550	−	34.9472i	0.444357	−	1.36759i	−0.438830	−	0.898570i	$-0.644607\pi$
$653$	11.3550	−	34.9472i	0.444357	−	1.36759i	0.883187	−	0.469021i	$-0.155393\pi$
$654$	4.20651	−	4.67181i	0.164488	−	0.182682i
$655$	12.4231	+	9.02589i	0.485410	+	0.352671i
$656$	64.6067	−	111.902i	2.52247	−	4.36905i
$657$	6.76353	+	11.7148i	0.263870	+	0.457037i
$658$	−0.556258	+	5.29244i	−0.0216852	+	0.206321i
$659$	−14.6678	+	10.6568i	−0.571376	+	0.415129i	−0.835605	−	0.549331i	$-0.814883\pi$
$659$	−14.6678	+	10.6568i	−0.571376	+	0.415129i	0.264229	+	0.964460i	$0.414883\pi$
$660$	15.6041	+	148.463i	0.607387	+	5.77890i
$661$	16.7445	+	18.5966i	0.651285	+	0.723325i	0.974845	−	0.222882i	$-0.0715466\pi$
$661$	16.7445	+	18.5966i	0.651285	+	0.723325i	−0.323561	+	0.946207i	$0.604880\pi$
$662$	89.3704	−	39.7902i	3.47348	−	1.54649i
$663$	−3.62079	+	0.769623i	−0.140620	+	0.0298897i
$664$	−4.35410	−	0.925494i	−0.168972	−	0.0359161i
$665$	5.40248	+	2.40534i	0.209499	+	0.0932750i
$666$	21.1242	+	65.0135i	0.818545	+	2.51922i
$667$	−3.74608	−	11.5293i	−0.145049	−	0.446415i
$668$	117.314	+	52.2317i	4.53903	+	2.02091i
$669$	42.5014	+	9.03395i	1.64320	+	0.349273i
$670$	44.0109	−	9.35481i	1.70029	−	0.361408i
$671$	−4.43391	+	1.97410i	−0.171169	+	0.0762094i
$672$	15.8757	+	17.6318i	0.612420	+	0.680161i
$673$	1.13818	+	10.8290i	0.0438735	+	0.417428i	0.994311	+	0.106514i	$0.0339687\pi$
$673$	1.13818	+	10.8290i	0.0438735	+	0.417428i	−0.950438	+	0.310915i	$0.899365\pi$
$674$	51.7604	−	37.6061i	1.99373	−	1.44853i
$675$	7.35904	−	70.0165i	0.283249	−	2.69494i
$676$	−2.77645	−	4.80895i	−0.106786	−	0.184959i
$677$	2.12277	−	3.67675i	0.0815847	−	0.141309i	−0.822346	−	0.568988i	$-0.807335\pi$
$677$	2.12277	−	3.67675i	0.0815847	−	0.141309i	0.903931	+	0.427679i	$0.140669\pi$
$678$	102.075	+	74.1621i	3.92018	+	2.84818i
$679$	2.29648	−	2.55050i	0.0881307	−	0.0978791i
$680$	12.9105	−	39.7343i	0.495093	−	1.52374i
$681$	46.6016			1.78578
$682$	34.4688	+	17.6458i	1.31988	+	0.675693i
$683$	46.7426			1.78856			0.894278	−	0.447511i	$-0.147689\pi$
$683$	46.7426			1.78856			0.894278	+	0.447511i	$0.147689\pi$
$684$	54.2813	−	167.061i	2.07550	−	6.38772i
$685$	6.59512	−	7.32462i	0.251986	−	0.279859i
$686$	−10.1997	−	7.41050i	−0.389425	−	0.282934i
$687$	2.21432	−	3.83531i	0.0844814	−	0.146326i
$688$	75.0775	+	130.038i	2.86230	+	4.95765i
$689$	−1.28904	+	12.2644i	−0.0491087	+	0.467238i
$690$	−67.6054	+	49.1182i	−2.57369	+	1.86990i
$691$	3.02241	+	28.7563i	0.114978	+	1.09394i	0.888089	+	0.459671i	$0.152033\pi$
$691$	3.02241	+	28.7563i	0.114978	+	1.09394i	−0.773111	+	0.634270i	$0.781301\pi$
$692$	−8.67710	−	9.63689i	−0.329854	−	0.366340i
$693$	4.72623	−	2.10426i	0.179535	−	0.0799341i
$694$	−19.0290	+	4.04474i	−0.722330	+	0.153536i
$695$	0.257237	+	0.0546775i	0.00975757	+	0.00207404i
$696$	114.529	+	50.9914i	4.34119	+	1.93282i
$697$	3.09976	+	9.54007i	0.117412	+	0.361356i
$698$	14.4861	+	44.5838i	0.548308	+	1.68752i
$699$	−47.8373	−	21.2986i	−1.80937	−	0.805586i
$700$	13.0573	+	2.77541i	0.493518	+	0.104901i
$701$	3.65787	−	0.777505i	0.138156	−	0.0293659i	−0.138315	−	0.990388i	$-0.544169\pi$
$701$	3.65787	−	0.777505i	0.138156	−	0.0293659i	0.276471	+	0.961022i	$0.410835\pi$
$702$	−24.2820	+	10.8111i	−0.916466	+	0.408037i
$703$	13.7396	+	15.2594i	0.518200	+	0.575519i
$704$	8.90690	+	84.7435i	0.335691	+	3.19389i
$705$	50.3911	−	36.6112i	1.89784	−	1.37886i
$706$	3.40589	−	32.4048i	0.128182	−	1.21957i
$707$	1.12957	+	1.95647i	0.0424819	+	0.0735807i
$708$	−21.4163	+	37.0941i	−0.804872	+	1.39408i
$709$	−25.3006	−	18.3820i	−0.950184	−	0.690349i	0.000666222	−	1.00000i	$-0.499788\pi$
$709$	−25.3006	−	18.3820i	−0.950184	−	0.690349i	−0.950850	+	0.309651i	$0.899788\pi$
$710$	−91.1506	+	101.233i	−3.42082	+	3.79921i
$711$	−19.1510	+	58.9407i	−0.718219	+	2.21045i
$712$	−4.49687			−0.168527
$713$	0.803637	+	15.9164i	0.0300964	+	0.596072i
$714$	−3.35967			−0.125732
$715$	2.74032	−	8.43383i	0.102482	−	0.315407i
$716$	43.9760	−	48.8403i	1.64346	−	1.82525i
$717$	21.2604	+	15.4466i	0.793984	+	0.576863i
$718$	4.33100	−	7.50151i	0.161632	−	0.279954i
$719$	−21.7294	−	37.6364i	−0.810368	−	1.40360i	−0.912606	−	0.408839i	$-0.865934\pi$
$719$	−21.7294	−	37.6364i	−0.810368	−	1.40360i	0.102238	−	0.994760i	$-0.467400\pi$
$720$	35.6640	−	339.320i	1.32912	−	12.6457i
$721$	0.348453	−	0.253166i	0.0129771	−	0.00942839i
$722$	−2.04361	−	19.4437i	−0.0760554	−	0.723619i
$723$	−35.0321	−	38.9070i	−1.30286	−	1.44697i
$724$	97.8818	−	43.5798i	3.63775	−	1.61963i
$725$	30.1559	−	6.40983i	1.11996	−	0.238055i
$726$	−37.4531	−	7.96090i	−1.39002	−	0.295457i
$727$	−22.0895	−	9.83487i	−0.819254	−	0.364755i	−0.0460707	−	0.998938i	$-0.514670\pi$
$727$	−22.0895	−	9.83487i	−0.819254	−	0.364755i	−0.773183	+	0.634183i	$0.781337\pi$
$728$	−0.996464	−	3.06680i	−0.0369314	−	0.113663i
$729$	−6.61918	−	20.3717i	−0.245155	−	0.754509i
$730$	19.2249	+	8.55948i	0.711546	+	0.316800i
$731$	−11.4020	−	2.42357i	−0.421719	−	0.0896391i
$732$	31.5801	−	6.71255i	1.16723	−	0.248103i
$733$	−28.2193	+	12.5640i	−1.04230	+	0.464063i	−0.855211	−	0.518280i	$-0.826573\pi$
$733$	−28.2193	+	12.5640i	−1.04230	+	0.464063i	−0.187091	+	0.982343i	$0.559906\pi$
$734$	20.1130	+	22.3378i	0.742385	+	0.824502i
$735$	7.65181	+	72.8021i	0.282241	+	2.68535i
$736$	−54.8770	+	39.8705i	−2.02279	+	1.46965i
$737$	1.23589	−	11.7587i	0.0455246	−	0.433137i
$738$	69.8796	+	121.035i	2.57230	+	4.45536i
$739$	−2.05597	+	3.56104i	−0.0756300	+	0.130995i	−0.901360	−	0.433070i	$-0.857430\pi$
$739$	−2.05597	+	3.56104i	−0.0756300	+	0.130995i	0.825730	+	0.564065i	$0.190763\pi$
$740$	63.2545	+	45.9571i	2.32528	+	1.68942i
$741$	−10.3660	+	11.5126i	−0.380805	+	0.422927i
$742$	−3.45870	+	10.6448i	−0.126973	+	0.390782i
$743$	−5.54208			−0.203319			−0.101660	−	0.994819i	$-0.532415\pi$
$743$	−5.54208			−0.203319			−0.101660	+	0.994819i	$0.532415\pi$
$744$	−127.883	−	103.963i	−4.68843	−	3.81148i
$745$	−73.3910			−2.68884
$746$	−21.1355	+	65.0483i	−0.773825	+	2.38159i
$747$	1.88834	−	2.09721i	0.0690906	−	0.0767328i
$748$	−13.8817	−	10.0857i	−0.507566	−	0.368768i
$749$	1.34184	−	2.32414i	0.0490299	−	0.0849222i
$750$	−33.2717	−	57.6283i	−1.21491	−	2.10429i
$751$	2.03896	−	19.3994i	0.0744028	−	0.707895i	−0.892204	−	0.451632i	$-0.850842\pi$
$751$	2.03896	−	19.3994i	0.0744028	−	0.707895i	0.966607	−	0.256263i	$-0.0824913\pi$
$752$	74.6102	−	54.2075i	2.72076	−	1.97674i
$753$	0.0763028	+	0.725972i	0.00278063	+	0.0264559i
$754$	−7.78838	−	8.64987i	−0.283636	−	0.315010i
$755$	−18.7061	+	8.32848i	−0.680784	+	0.303105i
$756$	−17.3485	+	3.68754i	−0.630959	+	0.134115i
$757$	2.08951	+	0.444138i	0.0759444	+	0.0161425i	0.245727	−	0.969339i	$-0.420973\pi$
$757$	2.08951	+	0.444138i	0.0759444	+	0.0161425i	−0.169783	+	0.985482i	$0.554307\pi$
$758$	81.1922	+	36.1491i	2.94904	+	1.31300i
$759$	6.78571	+	20.8843i	0.246306	+	0.758051i
$760$	−54.0310	−	166.290i	−1.95991	−	6.03199i
$761$	−45.5494	−	20.2799i	−1.65116	−	0.735145i	−0.651441	−	0.758699i	$-0.725835\pi$
$761$	−45.5494	−	20.2799i	−1.65116	−	0.735145i	−0.999723	+	0.0235537i	$0.992502\pi$
$762$	70.8391	+	15.0573i	2.56623	+	0.545469i
$763$	−0.243744	+	0.0518094i	−0.00882414	+	0.00187563i
$764$	39.3447	−	17.5174i	1.42344	−	0.633757i
$765$	17.7233	+	19.6837i	0.640786	+	0.711665i
$766$	6.99008	+	66.5061i	0.252562	+	2.40296i
$767$	2.05848	−	1.49557i	0.0743275	−	0.0540021i
$768$	17.9721	−	170.993i	0.648512	−	6.17018i
$769$	−16.2350	−	28.1198i	−0.585449	−	1.01403i	−0.994819	−	0.101659i	$-0.967585\pi$
$769$	−16.2350	−	28.1198i	−0.585449	−	1.01403i	0.409370	−	0.912368i	$-0.365748\pi$
$770$	4.02426	−	6.97022i	0.145024	−	0.251189i
$771$	22.0059	+	15.9882i	0.792522	+	0.575801i
$772$	−44.7527	+	49.7029i	−1.61068	+	1.78885i
$773$	−1.26084	+	3.88048i	−0.0453494	+	0.139571i	−0.971167	−	0.238398i	$-0.923378\pi$
$773$	−1.26084	+	3.88048i	−0.0453494	+	0.139571i	0.925818	+	0.377970i	$0.123378\pi$
$774$	−162.410			−5.83770
$775$	−40.4696	−	2.19850i	−1.45371	−	0.0789724i
$776$	−101.473			−3.64266
$777$	1.24313	−	3.82595i	0.0445970	−	0.137255i
$778$	49.8777	−	55.3948i	1.78820	−	1.98600i
$779$	33.9629	+	24.6755i	1.21685	+	0.884091i
$780$	−29.4945	+	51.0859i	−1.05607	+	1.82917i
$781$	17.8981	+	31.0005i	0.640446	+	1.10928i
$782$	1.00402	−	9.55258i	0.0359035	−	0.341599i
$783$	−33.1387	+	24.0767i	−1.18428	+	0.860430i
$784$	11.3295	+	107.793i	0.404624	+	3.84974i
$785$	−24.9248	−	27.6818i	−0.889605	−	0.988006i
$786$	−33.3532	+	14.8498i	−1.18967	+	0.529674i
$787$	26.6437	−	5.66330i	0.949746	−	0.201875i	0.293107	−	0.956080i	$-0.405311\pi$
$787$	26.6437	−	5.66330i	0.949746	−	0.201875i	0.656639	+	0.754205i	$0.271977\pi$
$788$	−45.4994	−	9.67120i	−1.62085	−	0.344522i
$789$	75.7821	+	33.7404i	2.69791	+	1.20119i
$790$	29.7935	+	91.6951i	1.06001	+	3.26236i
$791$	−1.54548	−	4.75651i	−0.0549511	−	0.169122i
$792$	−139.738	−	62.2152i	−4.96536	−	2.21072i
$793$	−1.87598	−	0.398752i	−0.0666181	−	0.0141601i
$794$	48.1358	−	10.2316i	1.70828	−	0.363105i
$795$	119.678	−	53.2841i	4.24455	−	1.88979i
$796$	−8.40436	−	9.33398i	−0.297885	−	0.330834i
$797$	1.06114	+	10.0961i	0.0375874	+	0.357620i	0.997109	+	0.0759851i	$0.0242102\pi$
$797$	1.06114	+	10.0961i	0.0375874	+	0.357620i	−0.959522	+	0.281635i	$0.909123\pi$
$798$	−11.3751	+	8.26450i	−0.402675	+	0.292560i
$799$	−0.748364	+	7.12021i	−0.0264752	+	0.251895i
$800$	−86.2533	−	149.395i	−3.04951	−	5.28191i
$801$	1.42546	−	2.46896i	0.0503660	−	0.0872366i
$802$	−59.0339	−	42.8906i	−2.08456	−	1.51452i
$803$	3.70028	−	4.10957i	0.130580	−	0.145024i
$804$	−24.3041	+	74.8003i	−0.857140	+	2.63800i
$805$	3.31240			0.116747
$806$	6.92072	+	13.6471i	0.243772	+	0.480699i
$807$	−77.1877			−2.71714
$808$	20.6407	−	63.5255i	0.726136	−	2.23482i
$809$	−9.20077	+	10.2185i	−0.323482	+	0.359263i	−0.882849	−	0.469657i	$-0.844378\pi$
$809$	−9.20077	+	10.2185i	−0.323482	+	0.359263i	0.559367	+	0.828920i	$0.311044\pi$
$810$	83.7470	+	60.8458i	2.94257	+	2.13790i
$811$	−12.0825	+	20.9275i	−0.424274	+	0.734865i	−0.996352	−	0.0853345i	$-0.972804\pi$
$811$	−12.0825	+	20.9275i	−0.424274	+	0.734865i	0.572078	+	0.820199i	$0.306137\pi$
$812$	−3.88338	−	6.72620i	−0.136280	−	0.236043i
$813$	1.32359	−	12.5931i	0.0464203	−	0.441660i
$814$	22.6086	−	16.4261i	0.792433	−	0.575736i
$815$	−5.10784	−	48.5978i	−0.178920	−	1.70231i
$816$	38.9589	+	43.2682i	1.36383	+	1.51469i
$817$	−44.5666	+	19.8423i	−1.55919	+	0.694195i
$818$	29.1923	−	6.20501i	1.02068	−	0.216953i
$819$	1.99967	+	0.425042i	0.0698740	+	0.0148522i
$820$	146.032	+	65.0175i	5.09965	+	2.27051i
$821$	−13.7224	−	42.2332i	−0.478915	−	1.47395i	−0.840605	−	0.541649i	$-0.817800\pi$
$821$	−13.7224	−	42.2332i	−0.478915	−	1.47395i	0.361690	−	0.932298i	$-0.382200\pi$
$822$	7.24151	+	22.2871i	0.252577	+	0.777351i
$823$	33.8099	+	15.0531i	1.17854	+	0.524720i	0.900079	−	0.435728i	$-0.143509\pi$
$823$	33.8099	+	15.0531i	1.17854	+	0.524720i	0.278461	+	0.960447i	$0.410176\pi$
$824$	−12.4563	−	2.64767i	−0.433936	−	0.0922359i
$825$	−54.6248	+	11.6109i	−1.90179	+	0.404238i
$826$	2.10968	−	0.939290i	0.0734052	−	0.0326821i
$827$	29.4897	+	32.7516i	1.02546	+	1.13889i	0.990221	+	0.139506i	$0.0445516\pi$
$827$	29.4897	+	32.7516i	1.02546	+	1.13889i	0.0352359	+	0.999379i	$0.488782\pi$
$828$	−10.2845	−	97.8502i	−0.357410	−	3.40053i
$829$	13.8839	−	10.0873i	0.482209	−	0.350345i	−0.319971	−	0.947427i	$-0.603673\pi$
$829$	13.8839	−	10.0873i	0.482209	−	0.350345i	0.802180	+	0.597082i	$0.203673\pi$
$830$	0.458916	−	4.36630i	0.0159292	−	0.151556i
$831$	−6.82168	−	11.8155i	−0.236641	−	0.409875i
$832$	−16.8356	+	29.1602i	−0.583671	+	1.01095i
$833$	−6.80722	−	4.94573i	−0.235856	−	0.171360i
$834$	−0.418385	+	0.464663i	−0.0144875	+	0.0160900i
$835$	−25.0421	+	77.0716i	−0.866617	+	2.66717i
$836$	−71.8104			−2.48361
$837$	50.3093	−	19.2017i	1.73894	−	0.663707i
$838$	−11.1758			−0.386060
$839$	−4.90689	+	15.1019i	−0.169405	+	0.521374i	−0.999334	−	0.0364947i	$-0.988381\pi$
$839$	−4.90689	+	15.1019i	−0.169405	+	0.521374i	0.829929	+	0.557869i	$0.188381\pi$
$840$	−22.9214	+	25.4568i	−0.790864	+	0.878344i
$841$	8.94984	+	6.50244i	0.308615	+	0.224222i
$842$	4.16635	−	7.21633i	0.143582	−	0.248691i
$843$	−6.89048	−	11.9347i	−0.237321	−	0.411051i
$844$	9.51595	−	90.5382i	0.327553	−	3.11645i
$845$	2.83494	−	2.05971i	0.0975249	−	0.0708560i
$846$	10.4267	+	99.2037i	0.358478	+	3.41069i
$847$	1.01558	+	1.12791i	0.0348957	+	0.0387556i
$848$	177.198	−	78.8938i	6.08502	−	2.70922i
$849$	36.9752	−	7.85931i	1.26898	−	0.269731i
$850$	23.8937	+	5.07876i	0.819547	+	0.174200i
$851$	10.5069	+	4.67796i	0.360171	+	0.160359i
$852$	−73.5821	−	226.462i	−2.52088	−	7.75848i
$853$	−9.37960	−	28.8674i	−0.321151	−	0.988402i	−0.973148	−	0.230180i	$-0.926068\pi$
$853$	−9.37960	−	28.8674i	−0.321151	−	0.988402i	0.651997	−	0.758222i	$-0.273932\pi$
$854$	−1.59020	−	0.708003i	−0.0544155	−	0.0242274i
$855$	108.427	+	23.0470i	3.70814	+	0.788189i
$856$	−77.6130	+	16.4972i	−2.65276	+	0.563861i
$857$	31.7843	−	14.1513i	1.08573	−	0.483399i	0.215733	−	0.976452i	$-0.430786\pi$
$857$	31.7843	−	14.1513i	1.08573	−	0.483399i	0.869999	+	0.493054i	$0.164119\pi$
$858$	14.1080	+	15.6685i	0.481639	+	0.534914i
$859$	1.88126	+	17.8990i	0.0641876	+	0.610705i	0.978579	+	0.205873i	$0.0660033\pi$
$859$	1.88126	+	17.8990i	0.0641876	+	0.610705i	−0.914391	+	0.404832i	$0.867330\pi$
$860$	−150.282	+	109.186i	−5.12457	+	3.72322i
$861$	0.859709	−	8.17959i	0.0292988	−	0.278760i
$862$	−54.7536	−	94.8360i	−1.86491	−	3.23013i
$863$	−16.0167	+	27.7417i	−0.545214	+	0.944338i	0.453379	+	0.891318i	$0.350218\pi$
$863$	−16.0167	+	27.7417i	−0.545214	+	0.944338i	−0.998593	+	0.0530207i	$0.983115\pi$
$864$	185.427	+	134.721i	6.30836	+	4.58329i
$865$	5.47572	−	6.08141i	0.186180	−	0.206774i
$866$	6.13774	−	18.8900i	0.208569	−	0.641909i
$867$	47.0165			1.59676
$868$	2.62378	+	9.86747i	0.0890568	+	0.334924i
$869$	25.3355			0.859447
$870$	−38.2094	+	117.596i	−1.29542	+	3.98689i
$871$	3.12625	−	3.47205i	0.105929	−	0.117646i
$872$	5.96054	+	4.33059i	0.201850	+	0.146652i
$873$	32.1657	−	55.7127i	1.08864	−	1.88559i
$874$	−20.0992	−	34.8128i	−0.679864	−	1.17756i
$875$	−0.275714	+	2.62324i	−0.00932083	+	0.0886818i
$876$	−29.7600	+	21.6219i	−1.00550	+	0.730536i
$877$	−2.17225	−	20.6676i	−0.0733517	−	0.697895i	−0.967970	−	0.251065i	$-0.919219\pi$
$877$	−2.17225	−	20.6676i	−0.0733517	−	0.697895i	0.894619	−	0.446831i	$-0.147447\pi$
$878$	−19.3529	−	21.4936i	−0.653128	−	0.725372i
$879$	1.56824	−	0.698226i	0.0528955	−	0.0235506i
$880$	−136.433	+	28.9997i	−4.59916	+	0.977581i
$881$	−37.6284	−	7.99816i	−1.26773	−	0.269465i	−0.475518	−	0.879706i	$-0.657739\pi$
$881$	−37.6284	−	7.99816i	−1.26773	−	0.269465i	−0.792216	+	0.610241i	$0.791073\pi$
$882$	−107.097	−	47.6827i	−3.60615	−	1.60556i
$883$	−15.9146	−	48.9801i	−0.535569	−	1.64831i	−0.742417	−	0.669938i	$-0.766321\pi$
$883$	−15.9146	−	48.9801i	−0.535569	−	1.64831i	0.206848	−	0.978373i	$-0.433679\pi$
$884$	−2.09525	−	6.44851i	−0.0704708	−	0.216887i
$885$	−24.6928	−	10.9940i	−0.830041	−	0.369558i
$886$	−46.2633	−	9.83356i	−1.55425	−	0.330365i
$887$	−52.9407	+	11.2529i	−1.77757	+	0.377835i	−0.975606	−	0.219530i	$-0.929548\pi$
$887$	−52.9407	+	11.2529i	−1.77757	+	0.377835i	−0.801969	+	0.597365i	$0.796214\pi$
$888$	−108.658	+	48.3777i	−3.64633	+	1.62345i
$889$	−1.92087	−	2.13334i	−0.0644240	−	0.0715500i
$890$	−0.463606	−	4.41092i	−0.0155401	−	0.147854i
$891$	22.0069	−	15.9889i	0.737258	−	0.535649i
$892$	−8.31931	+	79.1530i	−0.278551	+	2.65024i
$893$	14.9813	+	25.9484i	0.501331	+	0.868330i
$894$	87.2466	−	151.115i	2.91796	−	5.05406i
$895$	33.5528	+	24.3776i	1.12155	+	0.814852i
$896$	−9.97513	+	11.0785i	−0.333246	+	0.370107i
$897$	−2.68141	+	8.25253i	−0.0895296	+	0.275544i
$898$	23.1662			0.773066
$899$	14.8049	+	18.3541i	0.493771	+	0.612145i
$900$	250.219			8.34063
$901$	−4.65318	+	14.3210i	−0.155020	+	0.477102i
$902$	38.2306	−	42.4594i	1.27294	−	1.41374i
$903$	7.73226	+	5.61782i	0.257313	+	0.186949i
$904$	−73.9351	+	128.059i	−2.45904	+	4.25919i
$905$	33.8072	+	58.5557i	1.12379	+	1.94646i
$906$	5.08888	−	48.4175i	0.169067	−	1.60856i
$907$	25.4206	−	18.4691i	0.844076	−	0.613257i	−0.0794303	−	0.996840i	$-0.525310\pi$
$907$	25.4206	−	18.4691i	0.844076	−	0.613257i	0.923506	+	0.383583i	$0.125310\pi$
$908$	8.92256	+	84.8925i	0.296106	+	2.81726i
$909$	28.3352	+	31.4694i	0.939819	+	1.04377i
$910$	2.90545	−	1.29359i	0.0963148	−	0.0428821i
$911$	−37.0545	+	7.87617i	−1.22767	+	0.260949i	−0.775710	−	0.631089i	$-0.782608\pi$
$911$	−37.0545	+	7.87617i	−1.22767	+	0.260949i	−0.451960	+	0.892038i	$0.649275\pi$
$912$	238.343	+	50.6613i	7.89231	+	1.67756i
$913$	−1.05395	−	0.469247i	−0.0348805	−	0.0155298i
$914$	−11.1141	−	34.2058i	−0.367623	−	1.13143i
$915$	6.29591	+	19.3768i	0.208136	+	0.640578i
$916$	7.41061	+	3.29942i	0.244853	+	0.109016i
$917$	1.41557	+	0.300888i	0.0467461	+	0.00993619i
$918$	−31.7463	+	6.74788i	−1.04778	+	0.222713i
$919$	9.42066	−	4.19435i	0.310759	−	0.138359i	−0.245431	−	0.969414i	$-0.578929\pi$
$919$	9.42066	−	4.19435i	0.310759	−	0.138359i	0.556190	+	0.831055i	$0.312263\pi$
$920$	−65.5317	−	72.7804i	−2.16052	−	2.39950i
$921$	2.08735	+	19.8598i	0.0687806	+	0.654404i
$922$	−45.3691	+	32.9626i	−1.49415	+	1.08556i
$923$	−1.47856	+	14.0676i	−0.0486675	+	0.463041i
$924$	7.03440	+	12.1839i	0.231415	+	0.400822i
$925$	−14.6247	+	25.3307i	−0.480856	+	0.832868i
$926$	−78.2892	−	56.8804i	−2.57274	−	1.86921i
$927$	5.40218	−	5.99973i	0.177431	−	0.197057i
$928$	−31.0155	+	95.4560i	−1.01814	+	3.13350i
$929$	−41.1708			−1.35077			−0.675385	−	0.737465i	$-0.736022\pi$
$929$	−41.1708			−1.35077			−0.675385	+	0.737465i	$0.736022\pi$
$930$	88.7919	−	136.157i	2.91160	−	4.46477i
$931$	−35.2139			−1.15409
$932$	29.6397	−	91.2216i	0.970880	−	2.98806i
$933$	−61.6638	+	68.4846i	−2.01878	+	2.24208i
$934$	−27.0738	−	19.6703i	−0.885881	−	0.643630i
$935$	5.41405	−	9.37742i	0.177058	−	0.306674i
$936$	−30.2219	−	52.3458i	−0.987832	−	1.71098i
$937$	−2.66263	+	25.3332i	−0.0869844	+	0.827601i	0.860855	+	0.508851i	$0.169930\pi$
$937$	−2.66263	+	25.3332i	−0.0869844	+	0.827601i	−0.947839	+	0.318750i	$0.896737\pi$
$938$	3.43058	−	2.49246i	0.112012	−	0.0813818i
$939$	3.54445	+	33.7232i	0.115669	+	1.10052i
$940$	76.3415	+	84.7859i	2.48999	+	2.76541i
$941$	−34.8734	+	15.5267i	−1.13684	+	0.506154i	−0.886833	−	0.462089i	$-0.847100\pi$
$941$	−34.8734	+	15.5267i	−1.13684	+	0.506154i	−0.250008	+	0.968244i	$0.580433\pi$
$942$	86.6285	−	18.4135i	2.82251	−	0.599943i
$943$	23.0002	+	4.88884i	0.748989	+	0.159203i
$944$	−36.5608	−	16.2779i	−1.18995	−	0.529801i
$945$	−3.45866	−	10.6446i	−0.112510	−	0.346270i
$946$	20.5170	+	63.1449i	0.667066	+	2.05302i
$947$	36.9021	+	16.4299i	1.19916	+	0.533900i	0.906455	−	0.422303i	$-0.138778\pi$
$947$	36.9021	+	16.4299i	1.19916	+	0.533900i	0.292704	+	0.956203i	$0.405445\pi$
$948$	−164.849	−	35.0397i	−5.35404	−	1.13804i
$949$	2.13745	−	0.454328i	0.0693845	−	0.0147481i
$950$	93.3923	−	41.5809i	3.03005	−	1.34906i
$951$	10.6174	+	11.7918i	0.344293	+	0.382376i
$952$	−0.411574	−	3.91586i	−0.0133392	−	0.126914i
$953$	18.2588	−	13.2658i	0.591462	−	0.429722i	−0.251376	−	0.967889i	$-0.580883\pi$
$953$	18.2588	−	13.2658i	0.591462	−	0.429722i	0.842838	+	0.538167i	$0.180883\pi$
$954$	−21.9299	+	208.649i	−0.710007	+	6.75527i
$955$	13.5892	+	23.5371i	0.439735	+	0.761644i
$956$	−24.0679	+	41.6868i	−0.778411	+	1.34825i
$957$	26.2866	+	19.0983i	0.849725	+	0.617362i
$958$	−63.3066	+	70.3091i	−2.04534	+	2.27159i
$959$	0.287044	−	0.883430i	0.00926912	−	0.0285274i
$960$	357.694			11.5445
$961$	−12.5005	−	28.3679i	−0.403241	−	0.915094i
$962$	11.0429			0.356039
$963$	15.5448	−	47.8421i	0.500925	−	1.54169i
$964$	64.1682	−	71.2660i	2.06672	−	2.29532i
$965$	−34.1454	−	24.8081i	−1.09918	−	0.798602i
$966$	−3.93775	+	6.82038i	−0.126695	+	0.219442i
$967$	12.6307	+	21.8769i	0.406174	+	0.703515i	0.994457	−	0.105140i	$-0.0335292\pi$
$967$	12.6307	+	21.8769i	0.406174	+	0.703515i	−0.588283	+	0.808655i	$0.700196\pi$
$968$	4.69067	−	44.6288i	0.150764	−	1.43442i
$969$	−15.3036	+	11.1187i	−0.491621	+	0.357184i
$970$	−10.4614	−	99.5333i	−0.335894	−	3.19582i
$971$	11.8825	+	13.1968i	0.381327	+	0.423507i	0.903001	−	0.429638i	$-0.141359\pi$
$971$	11.8825	+	13.1968i	0.381327	+	0.423507i	−0.521674	+	0.853145i	$0.674692\pi$
$972$	−18.1171	+	8.06627i	−0.581108	+	0.258726i
$973$	0.0242431	−	0.00515303i	0.000777198	−	0.000165199i
$974$	−17.4923	−	3.71810i	−0.560489	−	0.119136i
$975$	−20.1597	−	8.97567i	−0.645626	−	0.287451i
$976$	9.32188	+	28.6898i	0.298386	+	0.918338i
$977$	−5.28071	−	16.2523i	−0.168945	−	0.519958i	0.830361	−	0.557226i	$-0.188134\pi$
$977$	−5.28071	−	16.2523i	−0.168945	−	0.519958i	−0.999305	+	0.0372680i	$0.988134\pi$
$978$	106.137	+	47.2554i	3.39390	+	1.51106i
$979$	−1.14001	−	0.242316i	−0.0364348	−	0.00774447i
$980$	−131.156	+	27.8781i	−4.18963	+	0.890533i
$981$	−4.26709	+	1.89983i	−0.136238	+	0.0606570i
$982$	−17.0455	−	18.9309i	−0.543942	−	0.604109i
$983$	−2.94429	−	28.0131i	−0.0939083	−	0.893478i	−0.935491	−	0.353350i	$-0.885042\pi$
$983$	−2.94429	−	28.0131i	−0.0939083	−	0.893478i	0.841583	−	0.540128i	$-0.181624\pi$
$984$	−196.731	+	142.933i	−6.27156	+	4.55655i
$985$	3.06834	−	29.1933i	0.0977654	−	0.930175i
$986$	−7.10625	−	12.3084i	−0.226309	−	0.391979i
$987$	2.93508	−	5.08371i	0.0934246	−	0.161816i
$988$	−22.9569	−	16.6791i	−0.730355	−	0.530634i
$989$	−18.2839	+	20.3064i	−0.581395	+	0.645705i
$990$	46.6198	−	143.481i	1.48167	−	4.56012i
$991$	−27.4468			−0.871877			−0.435939	−	0.899976i	$-0.643584\pi$
$991$	−27.4468			−0.871877			−0.435939	+	0.899976i	$0.643584\pi$
$992$	72.0747	−	110.522i	2.28837	−	3.50908i
$993$	−107.913			−3.42450
$994$	−3.96721	+	12.2098i	−0.125832	+	0.387272i
$995$	5.30361	−	5.89026i	0.168136	−	0.186734i
$996$	6.20866	+	4.51085i	0.196729	+	0.142932i
$997$	7.60308	−	13.1689i	0.240792	−	0.417064i	−0.720148	−	0.693820i	$-0.755926\pi$
$997$	7.60308	−	13.1689i	0.240792	−	0.417064i	0.960940	+	0.276757i	$0.0892596\pi$
$998$	−12.1053	−	20.9670i	−0.383187	−	0.663699i
$999$	4.06219	−	38.6492i	0.128522	−	1.22281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bi.b.14.17	✓	136
31.20	even	15	inner	403.2.bi.b.144.17	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bi.b.14.17	✓	136	1.1	even	1	trivial
403.2.bi.b.144.17	yes	136	31.20	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.849257 - 2.61374i) q^{2} +(-2.02850 + 2.25288i) q^{3} +(-4.49238 - 3.26391i) q^{4} +(1.75209 - 3.03471i) q^{5} +(4.16574 + 7.21527i) q^{6} +(0.0345203 - 0.328439i) q^{7} +(-7.89944 + 5.73928i) q^{8} +(-0.647064 - 6.15640i) q^{9} +O(q^{10})\)	\(q+(0.849257 - 2.61374i) q^{2} +(-2.02850 + 2.25288i) q^{3} +(-4.49238 - 3.26391i) q^{4} +(1.75209 - 3.03471i) q^{5} +(4.16574 + 7.21527i) q^{6} +(0.0345203 - 0.328439i) q^{7} +(-7.89944 + 5.73928i) q^{8} +(-0.647064 - 6.15640i) q^{9} +(-6.44398 - 7.15676i) q^{10} +(-2.31186 + 1.02931i) q^{11} +(16.4660 - 3.49996i) q^{12} +(-0.978148 - 0.207912i) q^{13} +(-0.829139 - 0.369156i) q^{14} +(3.28272 + 10.1032i) q^{15} +(4.86048 + 14.9590i) q^{16} +(-1.11549 - 0.496646i) q^{17} +(-16.6408 - 3.53711i) q^{18} +(-4.99851 + 1.06247i) q^{19} +(-17.7761 + 7.91442i) q^{20} +(0.669910 + 0.744010i) q^{21} +(0.726982 + 6.91677i) q^{22} +(-2.31565 + 1.68242i) q^{23} +(3.09413 - 29.4387i) q^{24} +(-3.63964 - 6.30404i) q^{25} +(-1.37413 + 2.38006i) q^{26} +(7.82448 + 5.68482i) q^{27} +(-1.22707 + 1.36280i) q^{28} +(-1.30877 + 4.02797i) q^{29} +29.1950 q^{30} +(3.04134 - 4.66372i) q^{31} +23.6983 q^{32} +(2.37072 - 7.29632i) q^{33} +(-2.24544 + 2.49381i) q^{34} +(-0.936234 - 0.680214i) q^{35} +(-17.1871 + 29.7689i) q^{36} +(-2.00908 - 3.47983i) q^{37} +(-1.46800 + 13.9671i) q^{38} +(2.45258 - 1.78190i) q^{39} +(3.57651 + 34.0282i) q^{40} +(-5.49696 - 6.10499i) q^{41} +(2.51358 - 1.11912i) q^{42} +(9.33786 - 1.98482i) q^{43} +(13.7454 + 2.92167i) q^{44} +(-19.8166 - 8.82292i) q^{45} +(2.43083 + 7.48133i) q^{46} +(-1.81187 - 5.57636i) q^{47} +(-43.5604 - 19.3943i) q^{48} +(6.74035 + 1.43271i) q^{49} +(-19.5681 + 4.15933i) q^{50} +(3.38165 - 1.50561i) q^{51} +(3.71561 + 4.12660i) q^{52} +(-1.28904 - 12.2644i) q^{53} +(21.5037 - 15.6233i) q^{54} +(-0.926943 + 8.81928i) q^{55} +(1.61231 + 2.79261i) q^{56} +(7.74588 - 13.4163i) q^{57} +(9.41660 + 6.84156i) q^{58} +(-1.70255 + 1.89087i) q^{59} +(18.2286 - 56.1018i) q^{60} +1.91789 q^{61} +(-9.60688 - 11.9100i) q^{62} -2.04434 q^{63} +(10.4050 - 32.0233i) q^{64} +(-2.34475 + 2.60411i) q^{65} +(-17.0574 - 12.3929i) q^{66} +(-2.33605 + 4.04616i) q^{67} +(3.39018 + 5.87197i) q^{68} +(0.907017 - 8.62969i) q^{69} +(-2.57301 + 1.86940i) q^{70} +(-1.47856 - 14.0676i) q^{71} +(40.4447 + 44.9184i) q^{72} +(-1.99628 + 0.888800i) q^{73} +(-10.8016 + 2.29596i) q^{74} +(21.5853 + 4.58809i) q^{75} +(25.9230 + 11.5417i) q^{76} +(0.258259 + 0.794839i) q^{77} +(-2.57457 - 7.92370i) q^{78} +(-9.14591 - 4.07202i) q^{79} +(53.9122 + 11.4594i) q^{80} +(-10.5141 + 2.23485i) q^{81} +(-20.6252 + 9.18293i) q^{82} +(0.305047 + 0.338789i) q^{83} +(-0.581111 - 5.52891i) q^{84} +(-3.46161 + 2.51501i) q^{85} +(2.74242 - 26.0924i) q^{86} +(-6.41970 - 11.1192i) q^{87} +(12.3550 - 21.3994i) q^{88} +(0.372588 + 0.270701i) q^{89} +(-39.8902 + 44.3026i) q^{90} +(-0.102052 + 0.314085i) q^{91} +15.8941 q^{92} +(4.33743 + 16.3122i) q^{93} -16.1139 q^{94} +(-5.53356 + 17.0305i) q^{95} +(-48.0721 + 53.3895i) q^{96} +(8.40753 + 6.10843i) q^{97} +(9.46902 - 16.4008i) q^{98} +(7.83276 + 13.5667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9	\( 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9} + 7 q^{10} + 5 q^{11} + 28 q^{12} + 17 q^{13} - 3 q^{14} + 17 q^{15} - 78 q^{16} - 12 q^{17} + 34 q^{18} - 23 q^{19} + 8 q^{20} - 38 q^{21} + 8 q^{22} + 9 q^{23} + 46 q^{24} - 69 q^{25} - 12 q^{26} - 58 q^{27} + 7 q^{28} + 18 q^{29} + 60 q^{30} + 14 q^{31} + 212 q^{32} - 41 q^{33} - 30 q^{35} - 106 q^{36} + 6 q^{37} - 62 q^{38} + 6 q^{39} + 39 q^{40} - 5 q^{41} + 37 q^{42} + q^{43} - 88 q^{44} - 168 q^{45} + 6 q^{46} - 81 q^{47} - 101 q^{48} + 117 q^{49} - 20 q^{50} + 35 q^{51} + 7 q^{52} + 25 q^{53} + 57 q^{54} + 19 q^{55} - 63 q^{56} - 20 q^{57} - 44 q^{58} + 9 q^{59} + 113 q^{60} + 8 q^{61} + 57 q^{62} + 112 q^{63} - 146 q^{64} - 5 q^{65} + 70 q^{66} - 99 q^{67} - 56 q^{68} - 65 q^{69} + 169 q^{70} - q^{71} - 43 q^{72} + 50 q^{73} - 26 q^{74} - 18 q^{75} - 94 q^{76} + 114 q^{77} - 17 q^{79} + 217 q^{80} + 54 q^{81} - 25 q^{82} - 53 q^{83} - 22 q^{84} + 2 q^{85} - 54 q^{86} - 28 q^{87} + 70 q^{88} - 101 q^{89} + 165 q^{90} - 4 q^{91} + 64 q^{92} + 61 q^{93} - 90 q^{94} - 33 q^{95} - 217 q^{96} + 73 q^{97} + 33 q^{98} - 15 q^{99}+O(q^{100}) \) 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9 + 7 * q^10 + 5 * q^11 + 28 * q^12 + 17 * q^13 - 3 * q^14 + 17 * q^15 - 78 * q^16 - 12 * q^17 + 34 * q^18 - 23 * q^19 + 8 * q^20 - 38 * q^21 + 8 * q^22 + 9 * q^23 + 46 * q^24 - 69 * q^25 - 12 * q^26 - 58 * q^27 + 7 * q^28 + 18 * q^29 + 60 * q^30 + 14 * q^31 + 212 * q^32 - 41 * q^33 - 30 * q^35 - 106 * q^36 + 6 * q^37 - 62 * q^38 + 6 * q^39 + 39 * q^40 - 5 * q^41 + 37 * q^42 + q^43 - 88 * q^44 - 168 * q^45 + 6 * q^46 - 81 * q^47 - 101 * q^48 + 117 * q^49 - 20 * q^50 + 35 * q^51 + 7 * q^52 + 25 * q^53 + 57 * q^54 + 19 * q^55 - 63 * q^56 - 20 * q^57 - 44 * q^58 + 9 * q^59 + 113 * q^60 + 8 * q^61 + 57 * q^62 + 112 * q^63 - 146 * q^64 - 5 * q^65 + 70 * q^66 - 99 * q^67 - 56 * q^68 - 65 * q^69 + 169 * q^70 - q^71 - 43 * q^72 + 50 * q^73 - 26 * q^74 - 18 * q^75 - 94 * q^76 + 114 * q^77 - 17 * q^79 + 217 * q^80 + 54 * q^81 - 25 * q^82 - 53 * q^83 - 22 * q^84 + 2 * q^85 - 54 * q^86 - 28 * q^87 + 70 * q^88 - 101 * q^89 + 165 * q^90 - 4 * q^91 + 64 * q^92 + 61 * q^93 - 90 * q^94 - 33 * q^95 - 217 * q^96 + 73 * q^97 + 33 * q^98 - 15 * q^99

Introduction

L-functions

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