LMFDB - Embedded newform 231.2.y.b.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	231.16
Dual form			231.2.y.b.130.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.17404 - 0.462106i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(2.68580 + 1.19580i) q^{4} +(-0.640870 - 0.711758i) q^{5} +(0.686823 - 2.11382i) q^{6} +(-1.08656 + 2.41234i) q^{7} +(-1.69019 - 1.22800i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-2.17404 - 0.462106i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(2.68580 + 1.19580i) q^{4} +(-0.640870 - 0.711758i) q^{5} +(0.686823 - 2.11382i) q^{6} +(-1.08656 + 2.41234i) q^{7} +(-1.69019 - 1.22800i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(1.06437 + 1.84354i) q^{10} +(-0.329590 - 3.30021i) q^{11} +(-1.46999 + 2.54609i) q^{12} +(0.742167 + 2.28416i) q^{13} +(3.47697 - 4.74241i) q^{14} +(0.774848 - 0.562960i) q^{15} +(-0.827382 - 0.918900i) q^{16} +(-5.34821 + 1.13680i) q^{17} +(2.03045 + 0.904015i) q^{18} +(-3.37720 + 1.50363i) q^{19} +(-0.870131 - 2.67799i) q^{20} +(-2.28555 - 1.33276i) q^{21} +(-0.808505 + 7.32708i) q^{22} +(-3.32561 + 5.76013i) q^{23} +(1.39794 - 1.55257i) q^{24} +(0.426757 - 4.06032i) q^{25} +(-0.557977 - 5.30879i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-5.80294 + 5.17977i) q^{28} +(-7.45926 + 5.41947i) q^{29} +(-1.94469 + 0.865834i) q^{30} +(-3.63006 + 4.03159i) q^{31} +(3.46332 + 5.99864i) q^{32} +(3.31658 + 0.0171815i) q^{33} +12.1525 q^{34} +(2.41335 - 0.772632i) q^{35} +(-2.37849 - 1.72807i) q^{36} +(-0.358198 - 3.40803i) q^{37} +(8.03699 - 1.70831i) q^{38} +(-2.34922 + 0.499342i) q^{39} +(0.209157 + 1.98999i) q^{40} +(-1.02137 - 0.742071i) q^{41} +(4.35299 + 3.95364i) q^{42} +1.31321 q^{43} +(3.06116 - 9.25782i) q^{44} +(0.478883 + 0.829449i) q^{45} +(9.89178 - 10.9859i) q^{46} +(1.82511 - 0.812591i) q^{47} +(1.00035 - 0.726798i) q^{48} +(-4.63879 - 5.24229i) q^{49} +(-2.80408 + 8.63008i) q^{50} +(-0.571529 - 5.43774i) q^{51} +(-0.738070 + 7.02226i) q^{52} +(5.52267 - 6.13354i) q^{53} +(-1.11130 + 1.92483i) q^{54} +(-2.13773 + 2.34959i) q^{55} +(4.79883 - 2.74303i) q^{56} +(-1.14238 - 3.51587i) q^{57} +(18.7211 - 8.33516i) q^{58} +(11.0391 + 4.91494i) q^{59} +(2.75427 - 0.585439i) q^{60} +(-4.12004 - 4.57577i) q^{61} +(9.75490 - 7.08735i) q^{62} +(1.56437 - 2.13372i) q^{63} +(-3.99317 - 12.2897i) q^{64} +(1.15013 - 1.99209i) q^{65} +(-7.20242 - 1.56996i) q^{66} +(2.01630 + 3.49234i) q^{67} +(-15.7236 - 3.34215i) q^{68} +(-5.38095 - 3.90949i) q^{69} +(-5.60374 + 0.564508i) q^{70} +(-0.210187 + 0.646890i) q^{71} +(1.39794 + 1.55257i) q^{72} +(1.18848 + 0.529147i) q^{73} +(-0.796133 + 7.57470i) q^{74} +(3.99347 + 0.848838i) q^{75} -10.8685 q^{76} +(8.31935 + 2.79078i) q^{77} +5.33804 q^{78} +(7.42557 + 1.57835i) q^{79} +(-0.123791 + 1.17779i) q^{80} +(0.913545 + 0.406737i) q^{81} +(1.87759 + 2.08527i) q^{82} +(-3.49888 + 10.7684i) q^{83} +(-4.54482 - 6.31259i) q^{84} +(4.23663 + 3.07809i) q^{85} +(-2.85496 - 0.606841i) q^{86} +(-4.61008 - 7.98489i) q^{87} +(-3.49557 + 5.98271i) q^{88} +(-1.96745 + 3.40772i) q^{89} +(-0.657815 - 2.02455i) q^{90} +(-6.31657 - 0.691504i) q^{91} +(-15.8199 + 11.4938i) q^{92} +(-3.63006 - 4.03159i) q^{93} +(-4.34336 + 0.923209i) q^{94} +(3.23456 + 1.44012i) q^{95} +(-6.32780 + 2.81732i) q^{96} +(2.37225 + 7.30103i) q^{97} +(7.66240 + 13.5405i) q^{98} +(-0.363764 + 3.29662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−2.17404	−	0.462106i	−1.53728	−	0.326758i	−0.640051	−	0.768332i	$-0.721087\pi$
$2$	−2.17404	−	0.462106i	−1.53728	−	0.326758i	−0.897225	+	0.441574i	$0.854420\pi$
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$4$	2.68580	+	1.19580i	1.34290	+	0.597898i
$5$	−0.640870	−	0.711758i	−0.286606	−	0.318308i	0.582599	−	0.812759i	$-0.302036\pi$
$5$	−0.640870	−	0.711758i	−0.286606	−	0.318308i	−0.869205	+	0.494451i	$0.835369\pi$
$6$	0.686823	−	2.11382i	0.280394	−	0.862965i
$7$	−1.08656	+	2.41234i	−0.410680	+	0.911780i
$7$	−1.08656	+	2.41234i	−0.410680	+	0.911780i
$8$	−1.69019	−	1.22800i	−0.597573	−	0.434162i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	1.06437	+	1.84354i	0.336582	+	0.582978i
$11$	−0.329590	−	3.30021i	−0.0993750	−	0.995050i
$11$	−0.329590	−	3.30021i	−0.0993750	−	0.995050i
$12$	−1.46999	+	2.54609i	−0.424349	+	0.734993i
$13$	0.742167	+	2.28416i	0.205840	+	0.633511i	0.999678	+	0.0253810i	$0.00807990\pi$
$13$	0.742167	+	2.28416i	0.205840	+	0.633511i	−0.793838	+	0.608130i	$0.791920\pi$
$14$	3.47697	−	4.74241i	0.929260	−	1.26746i
$15$	0.774848	−	0.562960i	0.200065	−	0.145356i
$16$	−0.827382	−	0.918900i	−0.206845	−	0.229725i
$17$	−5.34821	+	1.13680i	−1.29713	+	0.275714i	−0.804202	−	0.594356i	$-0.797407\pi$
$17$	−5.34821	+	1.13680i	−1.29713	+	0.275714i	−0.492929	+	0.870070i	$0.664074\pi$
$18$	2.03045	+	0.904015i	0.478582	+	0.213078i
$19$	−3.37720	+	1.50363i	−0.774783	+	0.344956i	−0.755747	−	0.654863i	$-0.772726\pi$
$19$	−3.37720	+	1.50363i	−0.774783	+	0.344956i	−0.0190354	+	0.999819i	$0.506060\pi$
$20$	−0.870131	−	2.67799i	−0.194567	−	0.598817i
$21$	−2.28555	−	1.33276i	−0.498748	−	0.290833i
$22$	−0.808505	+	7.32708i	−0.172374	+	1.56214i
$23$	−3.32561	+	5.76013i	−0.693438	+	1.20107i	0.277267	+	0.960793i	$0.410571\pi$
$23$	−3.32561	+	5.76013i	−0.693438	+	1.20107i	−0.970704	+	0.240277i	$0.922762\pi$
$24$	1.39794	−	1.55257i	0.285354	−	0.316917i
$25$	0.426757	−	4.06032i	0.0853514	−	0.812064i
$26$	−0.557977	−	5.30879i	−0.109428	−	1.04114i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−5.80294	+	5.17977i	−1.09665	+	0.978884i
$29$	−7.45926	+	5.41947i	−1.38515	+	1.00637i	−0.388773	+	0.921334i	$0.627101\pi$
$29$	−7.45926	+	5.41947i	−1.38515	+	1.00637i	−0.996378	+	0.0850373i	$0.972899\pi$
$30$	−1.94469	+	0.865834i	−0.355051	+	0.158079i
$31$	−3.63006	+	4.03159i	−0.651978	+	0.724095i	−0.974977	−	0.222304i	$-0.928642\pi$
$31$	−3.63006	+	4.03159i	−0.651978	+	0.724095i	0.322999	+	0.946399i	$0.395309\pi$
$32$	3.46332	+	5.99864i	0.612234	+	1.06042i
$33$	3.31658	+	0.0171815i	0.577343	+	0.00299091i
$34$	12.1525			2.08414
$35$	2.41335	−	0.772632i	0.407930	−	0.130599i
$36$	−2.37849	−	1.72807i	−0.396415	−	0.288012i
$37$	−0.358198	−	3.40803i	−0.0588874	−	0.560276i	−0.983695	−	0.179842i	$-0.942441\pi$
$37$	−0.358198	−	3.40803i	−0.0588874	−	0.560276i	0.924808	−	0.380434i	$-0.124225\pi$
$38$	8.03699	−	1.70831i	1.30377	−	0.277125i
$39$	−2.34922	+	0.499342i	−0.376176	+	0.0799587i
$40$	0.209157	+	1.98999i	0.0330706	+	0.314645i
$41$	−1.02137	−	0.742071i	−0.159512	−	0.115892i	0.505166	−	0.863022i	$-0.331431\pi$
$41$	−1.02137	−	0.742071i	−0.159512	−	0.115892i	−0.664678	+	0.747130i	$0.731431\pi$
$42$	4.35299	+	3.95364i	0.671681	+	0.610060i
$43$	1.31321			0.200263			0.100131	−	0.994974i	$-0.468074\pi$
$43$	1.31321			0.200263			0.100131	+	0.994974i	$0.468074\pi$
$44$	3.06116	−	9.25782i	0.461487	−	1.39567i
$45$	0.478883	+	0.829449i	0.0713876	+	0.123647i
$46$	9.89178	−	10.9859i	1.45846	−	1.61979i
$47$	1.82511	−	0.812591i	0.266220	−	0.118529i	−0.269286	−	0.963060i	$-0.586788\pi$
$47$	1.82511	−	0.812591i	0.266220	−	0.118529i	0.535506	+	0.844532i	$0.320121\pi$
$48$	1.00035	−	0.726798i	0.144388	−	0.104904i
$49$	−4.63879	−	5.24229i	−0.662684	−	0.748899i
$50$	−2.80408	+	8.63008i	−0.396557	+	1.22048i
$51$	−0.571529	−	5.43774i	−0.0800301	−	0.761435i
$52$	−0.738070	+	7.02226i	−0.102352	+	0.973813i
$53$	5.52267	−	6.13354i	0.758597	−	0.842507i	−0.232919	−	0.972496i	$-0.574828\pi$
$53$	5.52267	−	6.13354i	0.758597	−	0.842507i	0.991515	+	0.129989i	$0.0414943\pi$
$54$	−1.11130	+	1.92483i	−0.151229	+	0.261937i
$55$	−2.13773	+	2.34959i	−0.288251	+	0.316819i
$56$	4.79883	−	2.74303i	0.641271	−	0.366553i
$57$	−1.14238	−	3.51587i	−0.151311	−	0.465688i
$58$	18.7211	−	8.33516i	2.45820	−	1.09446i
$59$	11.0391	+	4.91494i	1.43717	+	0.639871i	0.969736	−	0.244156i	$-0.0785109\pi$
$59$	11.0391	+	4.91494i	1.43717	+	0.639871i	0.467437	+	0.884027i	$0.345178\pi$
$60$	2.75427	−	0.585439i	0.355575	−	0.0755798i
$61$	−4.12004	−	4.57577i	−0.527517	−	0.585867i	0.419216	−	0.907887i	$-0.362305\pi$
$61$	−4.12004	−	4.57577i	−0.527517	−	0.585867i	−0.946733	+	0.322019i	$0.895638\pi$
$62$	9.75490	−	7.08735i	1.23887	−	0.900094i
$63$	1.56437	−	2.13372i	0.197092	−	0.268823i
$64$	−3.99317	−	12.2897i	−0.499146	−	1.53621i
$65$	1.15013	−	1.99209i	0.142657	−	0.247088i
$66$	−7.20242	−	1.56996i	−0.886557	−	0.193249i
$67$	2.01630	+	3.49234i	0.246331	+	0.426657i	0.962505	−	0.271264i	$-0.0874418\pi$
$67$	2.01630	+	3.49234i	0.246331	+	0.426657i	−0.716174	+	0.697921i	$0.754108\pi$
$68$	−15.7236	−	3.34215i	−1.90677	−	0.405295i
$69$	−5.38095	−	3.90949i	−0.647790	−	0.470647i
$70$	−5.60374	+	0.564508i	−0.669775	+	0.0674716i
$71$	−0.210187	+	0.646890i	−0.0249447	+	0.0767718i	−0.962754	−	0.270379i	$-0.912851\pi$
$71$	−0.210187	+	0.646890i	−0.0249447	+	0.0767718i	0.937809	+	0.347151i	$0.112851\pi$
$72$	1.39794	+	1.55257i	0.164749	+	0.182972i
$73$	1.18848	+	0.529147i	0.139102	+	0.0619320i	0.475107	−	0.879928i	$-0.342409\pi$
$73$	1.18848	+	0.529147i	0.139102	+	0.0619320i	−0.336005	+	0.941860i	$0.609076\pi$
$74$	−0.796133	+	7.57470i	−0.0925486	+	0.880541i
$75$	3.99347	+	0.848838i	0.461126	+	0.0980154i
$76$	−10.8685			−1.24670
$77$	8.31935	+	2.79078i	0.948078	+	0.318039i
$78$	5.33804			0.604414
$79$	7.42557	+	1.57835i	0.835442	+	0.177579i	0.605720	−	0.795678i	$-0.292885\pi$
$79$	7.42557	+	1.57835i	0.835442	+	0.177579i	0.229722	+	0.973256i	$0.426218\pi$
$80$	−0.123791	+	1.17779i	−0.0138402	+	0.131681i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	1.87759	+	2.08527i	0.207345	+	0.230280i
$83$	−3.49888	+	10.7684i	−0.384052	+	1.18199i	0.553114	+	0.833105i	$0.313439\pi$
$83$	−3.49888	+	10.7684i	−0.384052	+	1.18199i	−0.937166	+	0.348884i	$0.886561\pi$
$84$	−4.54482	−	6.31259i	−0.495880	−	0.688760i
$85$	4.23663	+	3.07809i	0.459527	+	0.333866i
$86$	−2.85496	−	0.606841i	−0.307859	−	0.0654374i
$87$	−4.61008	−	7.98489i	−0.494252	−	0.856070i
$88$	−3.49557	+	5.98271i	−0.372629	+	0.637759i
$89$	−1.96745	+	3.40772i	−0.208549	+	0.361217i	−0.951258	−	0.308397i	$-0.900207\pi$
$89$	−1.96745	+	3.40772i	−0.208549	+	0.361217i	0.742709	+	0.669615i	$0.233541\pi$
$90$	−0.657815	−	2.02455i	−0.0693398	−	0.213406i
$91$	−6.31657	−	0.691504i	−0.662156	−	0.0724894i
$92$	−15.8199	+	11.4938i	−1.64933	+	1.19831i
$93$	−3.63006	−	4.03159i	−0.376420	−	0.418056i
$94$	−4.34336	+	0.923209i	−0.447983	+	0.0952217i
$95$	3.23456	+	1.44012i	0.331859	+	0.147753i
$96$	−6.32780	+	2.81732i	−0.645828	+	0.287541i
$97$	2.37225	+	7.30103i	0.240865	+	0.741307i	0.996289	+	0.0860707i	$0.0274311\pi$
$97$	2.37225	+	7.30103i	0.240865	+	0.741307i	−0.755424	+	0.655237i	$0.772569\pi$
$98$	7.66240	+	13.5405i	0.774019	+	1.36780i
$99$	−0.363764	+	3.29662i	−0.0365597	+	0.331322i
$100$	6.00149	−	10.3949i	0.600149	−	1.03949i
$101$	2.20916	−	2.45352i	0.219820	−	0.244135i	−0.623141	−	0.782110i	$-0.714144\pi$
$101$	2.20916	−	2.45352i	0.219820	−	0.244135i	0.842961	+	0.537975i	$0.180810\pi$
$102$	−1.27028	+	12.0859i	−0.125777	+	1.19669i
$103$	1.78680	+	17.0003i	0.176059	+	1.67509i	0.624309	+	0.781178i	$0.285381\pi$
$103$	1.78680	+	17.0003i	0.176059	+	1.67509i	−0.448250	+	0.893908i	$0.647953\pi$
$104$	1.55053	−	4.77203i	0.152042	−	0.467936i
$105$	0.516136	+	2.48089i	0.0503697	+	0.242110i
$106$	−14.8408	+	10.7825i	−1.44147	+	1.04729i
$107$	−3.02435	+	1.34653i	−0.292375	+	0.130174i	−0.547683	−	0.836686i	$-0.684490\pi$
$107$	−3.02435	+	1.34653i	−0.292375	+	0.130174i	0.255308	+	0.966860i	$0.417823\pi$
$108$	1.96723	−	2.18483i	0.189296	−	0.210235i
$109$	−1.43675	−	2.48853i	−0.137616	−	0.238358i	0.788978	−	0.614422i	$-0.210611\pi$
$109$	−1.43675	−	2.48853i	−0.137616	−	0.238358i	−0.926594	+	0.376064i	$0.877277\pi$
$110$	5.73325	−	4.12024i	0.546644	−	0.392850i
$111$	3.42680			0.325257
$112$	3.11570	−	0.997490i	0.294406	−	0.0942539i
$113$	−7.56843	−	5.49879i	−0.711978	−	0.517282i	0.171833	−	0.985126i	$-0.445031\pi$
$113$	−7.56843	−	5.49879i	−0.711978	−	0.517282i	−0.883811	+	0.467844i	$0.845031\pi$
$114$	0.858862	+	8.17153i	0.0804398	+	0.765334i
$115$	6.23110	−	1.32446i	0.581053	−	0.123507i
$116$	−26.5147	+	5.63587i	−2.46183	+	0.523277i
$117$	−0.251046	−	2.38855i	−0.0232092	−	0.220821i
$118$	−21.7283	−	15.7865i	−2.00025	−	1.45327i
$119$	3.06879	−	14.1369i	0.281316	−	1.29593i
$120$	−2.00095			−0.182661
$121$	−10.7827	+	2.17543i	−0.980249	+	0.197766i
$122$	6.84263	+	11.8518i	0.619503	+	1.07301i
$123$	0.844769	−	0.938211i	0.0761702	−	0.0845956i
$124$	−14.5706	+	6.48723i	−1.30848	+	0.582571i
$125$	−7.03770	+	5.11319i	−0.629471	+	0.457338i
$126$	−4.38699	+	3.91588i	−0.390824	+	0.348854i
$127$	5.76089	−	17.7302i	0.511196	−	1.57330i	−0.278902	−	0.960319i	$-0.589971\pi$
$127$	5.76089	−	17.7302i	0.511196	−	1.57330i	0.790098	−	0.612980i	$-0.210029\pi$
$128$	1.55409	+	14.7862i	0.137363	+	1.30693i
$129$	−0.137268	+	1.30602i	−0.0120858	+	0.114988i
$130$	−3.42099	+	3.79939i	−0.300040	+	0.333229i
$131$	8.37499	−	14.5059i	0.731726	−	1.26739i	−0.224418	−	0.974493i	$-0.572048\pi$
$131$	8.37499	−	14.5059i	0.731726	−	1.26739i	0.956145	−	0.292895i	$-0.0946185\pi$
$132$	8.88712	+	4.01210i	0.773525	+	0.349208i
$133$	0.0422599	−	9.78074i	0.00366439	−	0.848097i
$134$	−2.76969	−	8.52421i	−0.239264	−	0.736380i
$135$	−0.874962	+	0.389558i	−0.0753047	+	0.0335278i
$136$	10.4355	+	4.64617i	0.894834	+	0.398406i
$137$	−6.31035	+	1.34131i	−0.539129	+	0.114595i	−0.469425	−	0.882972i	$-0.655539\pi$
$137$	−6.31035	+	1.34131i	−0.539129	+	0.114595i	−0.0697041	+	0.997568i	$0.522206\pi$
$138$	9.89178	+	10.9859i	0.842045	+	0.935185i
$139$	6.92036	−	5.02794i	0.586977	−	0.426464i	−0.254255	−	0.967137i	$-0.581830\pi$
$139$	6.92036	−	5.02794i	0.586977	−	0.426464i	0.841233	+	0.540673i	$0.181830\pi$
$140$	7.40567	+	0.810734i	0.625894	+	0.0685195i
$141$	0.617364	+	1.90005i	0.0519914	+	0.160013i
$142$	0.755887	−	1.30923i	0.0634326	−	0.109868i
$143$	7.29358	−	3.20214i	0.609919	−	0.267776i
$144$	0.618251	+	1.07084i	0.0515209	+	0.0892369i
$145$	8.63777	+	1.83602i	0.717328	+	0.152473i
$146$	−2.33928	−	1.69959i	−0.193601	−	0.140659i
$147$	5.69846	−	4.06541i	0.470001	−	0.335309i
$148$	3.11325	−	9.58161i	0.255908	−	0.787604i
$149$	14.5569	+	16.1671i	1.19255	+	1.32446i	0.933493	+	0.358596i	$0.116744\pi$
$149$	14.5569	+	16.1671i	1.19255	+	1.32446i	0.259055	+	0.965863i	$0.416589\pi$
$150$	−8.28969	−	3.69081i	−0.676851	−	0.301353i
$151$	0.490074	−	4.66274i	0.0398817	−	0.379449i	−0.956317	−	0.292333i	$-0.905568\pi$
$151$	0.490074	−	4.66274i	0.0398817	−	0.379449i	0.996198	−	0.0871155i	$-0.0277649\pi$
$152$	7.55456	+	1.60577i	0.612755	+	0.130245i
$153$	5.46769			0.442036
$154$	−16.7969	−	9.91168i	−1.35353	−	0.798706i
$155$	5.19591			0.417346
$156$	−6.90664	−	1.46805i	−0.552974	−	0.117538i
$157$	−2.04594	+	19.4658i	−0.163284	+	1.55354i	0.539408	+	0.842045i	$0.318648\pi$
$157$	−2.04594	+	19.4658i	−0.163284	+	1.55354i	−0.702691	+	0.711495i	$0.748018\pi$
$158$	−15.4141	−	6.86280i	−1.22628	−	0.545975i
$159$	5.52267	+	6.13354i	0.437976	+	0.486422i
$160$	2.05005	−	6.30940i	0.162070	−	0.498801i
$161$	−10.2819	−	14.2812i	−0.810330	−	1.12552i
$162$	−1.79813	−	1.30641i	−0.141274	−	0.102642i
$163$	−23.5288	−	5.00120i	−1.84292	−	0.391724i	−0.851706	−	0.524019i	$-0.824432\pi$
$163$	−23.5288	−	5.00120i	−1.84292	−	0.391724i	−0.991210	+	0.132295i	$0.957765\pi$
$164$	−1.85584	−	3.21441i	−0.144917	−	0.251003i
$165$	−2.11327	−	2.37161i	−0.164518	−	0.184630i
$166$	12.5828	−	21.7941i	0.976618	−	1.69155i
$167$	5.45292	+	16.7824i	0.421960	+	1.29866i	0.905875	+	0.423544i	$0.139214\pi$
$167$	5.45292	+	16.7824i	0.421960	+	1.29866i	−0.483915	+	0.875115i	$0.660786\pi$
$168$	2.22639	+	5.05927i	0.171770	+	0.390331i
$169$	5.85067	−	4.25076i	0.450051	−	0.326981i
$170$	−7.78818	−	8.64965i	−0.597326	−	0.663398i
$171$	3.61602	−	0.768609i	0.276524	−	0.0587770i
$172$	3.52702	+	1.57033i	0.268933	+	0.119736i
$173$	−9.92700	+	4.41979i	−0.754736	+	0.336030i	−0.747781	−	0.663946i	$-0.768881\pi$
$173$	−9.92700	+	4.41979i	−0.754736	+	0.336030i	−0.00695525	+	0.999976i	$0.502214\pi$
$174$	6.33261	+	19.4898i	0.480074	+	1.47752i
$175$	9.33119	+	5.44125i	0.705371	+	0.411320i
$176$	−2.75987	+	3.03339i	−0.208033	+	0.228650i
$177$	−6.04192	+	10.4649i	−0.454138	+	0.786591i
$178$	5.85202	−	6.49933i	0.438628	−	0.487145i
$179$	0.173894	−	1.65449i	0.0129975	−	0.123663i	−0.986099	−	0.166158i	$-0.946864\pi$
$179$	0.173894	−	1.65449i	0.0129975	−	0.123663i	0.999097	+	0.0424949i	$0.0135306\pi$
$180$	0.294332	+	2.80038i	0.0219382	+	0.208728i
$181$	2.04085	−	6.28110i	0.151695	−	0.466870i	−0.846116	−	0.532999i	$-0.821065\pi$
$181$	2.04085	−	6.28110i	0.151695	−	0.466870i	0.997811	+	0.0661290i	$0.0210649\pi$
$182$	13.4129	+	4.42228i	0.994230	+	0.327801i
$183$	4.98136	−	3.61917i	0.368233	−	0.267537i
$184$	12.6943	−	5.65188i	0.935838	−	0.416662i
$185$	−2.19613	+	2.43905i	−0.161463	+	0.179323i
$186$	6.02886	+	10.4423i	0.442057	+	0.765666i
$187$	5.51438	+	17.2755i	0.403251	+	1.26331i
$188$	5.87357			0.428374
$189$	1.95851	+	1.77883i	0.142461	+	0.129391i
$190$	−6.36657	−	4.62558i	−0.461880	−	0.335575i
$191$	−0.836182	−	7.95574i	−0.0605040	−	0.575657i	−0.982212	−	0.187773i	$-0.939873\pi$
$191$	−0.836182	−	7.95574i	−0.0605040	−	0.575657i	0.921708	−	0.387884i	$-0.126794\pi$
$192$	12.6398	−	2.68667i	0.912199	−	0.193894i
$193$	−19.0720	+	4.05388i	−1.37283	+	0.291805i	−0.834537	−	0.550952i	$-0.814265\pi$
$193$	−19.0720	+	4.05388i	−1.37283	+	0.291805i	−0.538295	+	0.842756i	$0.680932\pi$
$194$	−1.78351	−	16.9689i	−0.128048	−	1.21830i
$195$	1.86096	+	1.35206i	0.133266	+	0.0968232i
$196$	−6.19014	−	19.6268i	−0.442153	−	1.40191i
$197$	11.6139			0.827457			0.413729	−	0.910400i	$-0.364226\pi$
$197$	11.6139			0.827457			0.413729	+	0.910400i	$0.364226\pi$
$198$	2.31422	−	6.99886i	0.164465	−	0.497388i
$199$	3.89671	+	6.74930i	0.276231	+	0.478445i	0.970445	−	0.241323i	$-0.0775813\pi$
$199$	3.89671	+	6.74930i	0.276231	+	0.478445i	−0.694214	+	0.719768i	$0.744248\pi$
$200$	−5.70735	+	6.33866i	−0.403571	+	0.448211i
$201$	−3.68397	+	1.64021i	−0.259847	+	0.115691i
$202$	−5.93659	+	4.31318i	−0.417697	+	0.303475i
$203$	−4.96871	−	23.8829i	−0.348735	−	1.67625i
$204$	4.96741	−	15.2881i	0.347788	−	1.07038i
$205$	0.126392	+	1.20254i	0.00882762	+	0.0839892i
$206$	3.97135	−	37.7849i	0.276697	−	2.63260i
$207$	4.45054	−	4.94282i	0.309334	−	0.343550i
$208$	1.48486	−	2.57185i	0.102956	−	0.178325i
$209$	6.07537	+	10.6499i	0.420242	+	0.736668i
$210$	0.0243345	−	5.63205i	0.00167924	−	0.388648i
$211$	5.70841	+	17.5687i	0.392983	+	1.20948i	0.930521	+	0.366239i	$0.119355\pi$
$211$	5.70841	+	17.5687i	0.392983	+	1.20948i	−0.537538	+	0.843240i	$0.680645\pi$
$212$	22.1672	−	9.86949i	1.52245	−	0.677839i
$213$	−0.621376	−	0.276654i	−0.0425760	−	0.0189560i
$214$	7.19728	−	1.52983i	0.491996	−	0.104577i
$215$	−0.841596	−	0.934687i	−0.0573964	−	0.0637452i
$216$	−1.69019	+	1.22800i	−0.115003	+	0.0835545i
$217$	−5.78130	−	13.1375i	−0.392461	−	0.891831i
$218$	1.97359	+	6.07409i	0.133668	+	0.411389i
$219$	−0.650479	+	1.12666i	−0.0439553	+	0.0761328i
$220$	−8.55113	+	3.75425i	−0.576517	+	0.253112i
$221$	−6.56588	−	11.3724i	−0.441669	−	0.764993i
$222$	−7.44999	−	1.58354i	−0.500010	−	0.106280i
$223$	12.5191	+	9.09563i	0.838338	+	0.609088i	0.921906	−	0.387414i	$-0.126632\pi$
$223$	12.5191	+	9.09563i	0.838338	+	0.609088i	−0.0835679	+	0.996502i	$0.526632\pi$
$224$	−18.2339	+	1.83684i	−1.21830	+	0.122729i
$225$	−1.26162	+	3.88287i	−0.0841080	+	0.258858i
$226$	13.9130	+	15.4520i	0.925480	+	1.02785i
$227$	7.11011	+	3.16562i	0.471914	+	0.210110i	0.628892	−	0.777492i	$-0.283509\pi$
$227$	7.11011	+	3.16562i	0.471914	+	0.210110i	−0.156978	+	0.987602i	$0.550175\pi$
$228$	1.13607	−	10.8090i	0.0752380	−	0.715842i
$229$	22.7719	+	4.84031i	1.50481	+	0.319857i	0.885258	−	0.465101i	$-0.153982\pi$
$229$	22.7719	+	4.84031i	1.50481	+	0.319857i	0.619549	+	0.784958i	$0.287315\pi$
$230$	−14.1587			−0.933596
$231$	−3.64510	+	7.98206i	−0.239830	+	0.525181i
$232$	19.2627			1.26466
$233$	−16.3317	−	3.47140i	−1.06992	−	0.227419i	−0.360900	−	0.932604i	$-0.617530\pi$
$233$	−16.3317	−	3.47140i	−1.06992	−	0.227419i	−0.709023	+	0.705185i	$0.750864\pi$
$234$	−0.557977	+	5.30879i	−0.0364761	+	0.347047i
$235$	−1.74803	−	0.778271i	−0.114029	−	0.0507688i
$236$	23.7716	+	26.4011i	1.54740	+	1.71856i
$237$	−2.34589	+	7.21991i	−0.152382	+	0.468984i
$238$	−13.2044	+	29.3160i	−0.855914	+	1.90028i
$239$	−10.8982	−	7.91803i	−0.704948	−	0.512175i	0.176592	−	0.984284i	$-0.443493\pi$
$239$	−10.8982	−	7.91803i	−0.704948	−	0.512175i	−0.881540	+	0.472109i	$0.843493\pi$
$240$	−1.15840	−	0.246225i	−0.0747744	−	0.0158938i
$241$	−12.1898	−	21.1134i	−0.785215	−	1.36003i	−0.928871	−	0.370405i	$-0.879219\pi$
$241$	−12.1898	−	21.1134i	−0.785215	−	1.36003i	0.143655	−	0.989628i	$-0.454114\pi$
$242$	24.4473	+	0.253305i	1.57153	+	0.0162831i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−5.59392	−	17.2163i	−0.358114	−	1.10216i
$245$	−0.758387	+	6.66132i	−0.0484515	+	0.425576i
$246$	−2.27011	+	1.64933i	−0.144737	+	0.105158i
$247$	−5.94096	−	6.59811i	−0.378014	−	0.419827i
$248$	11.0863	−	2.35646i	0.703978	−	0.149635i
$249$	−10.3437	−	4.60532i	−0.655506	−	0.291850i
$250$	17.6631	−	7.86410i	1.11711	−	0.497369i
$251$	7.58726	+	23.3512i	0.478904	+	1.47391i	0.840620	+	0.541625i	$0.182191\pi$
$251$	7.58726	+	23.3512i	0.478904	+	1.47391i	−0.361716	+	0.932288i	$0.617809\pi$
$252$	6.75307	−	3.86008i	0.425403	−	0.243162i
$253$	20.1057	+	9.07673i	1.26403	+	0.570649i
$254$	−20.7176	+	35.8839i	−1.29994	+	2.25156i
$255$	−3.50408	+	3.89167i	−0.219434	+	0.243706i
$256$	0.752657	−	7.16105i	0.0470410	−	0.447566i
$257$	−2.37848	−	22.6297i	−0.148366	−	1.41160i	−0.774838	−	0.632160i	$-0.782168\pi$
$257$	−2.37848	−	22.6297i	−0.148366	−	1.41160i	0.626472	−	0.779444i	$-0.284498\pi$
$258$	0.901942	−	2.77589i	0.0561525	−	0.172820i
$259$	8.61053	+	2.83892i	0.535032	+	0.176402i
$260$	5.47116	−	3.97503i	0.339307	−	0.246521i
$261$	8.42303	−	3.75018i	0.521373	−	0.232130i
$262$	−24.9108	+	27.6662i	−1.53899	+	1.70923i
$263$	−4.30680	−	7.45960i	−0.265569	−	0.459979i	0.702144	−	0.712035i	$-0.252226\pi$
$263$	−4.30680	−	7.45960i	−0.265569	−	0.459979i	−0.967713	+	0.252056i	$0.918893\pi$
$264$	−5.58455	−	4.10178i	−0.343706	−	0.252447i
$265$	−7.90491			−0.485595
$266$	−4.61161	+	21.2441i	−0.282756	+	1.30256i
$267$	−3.18339	−	2.31287i	−0.194821	−	0.141545i
$268$	1.23926	+	11.7908i	0.0757001	+	0.720238i
$269$	−21.6497	+	4.60179i	−1.32001	+	0.280576i	−0.813452	−	0.581633i	$-0.802414\pi$
$269$	−21.6497	+	4.60179i	−1.32001	+	0.280576i	−0.506554	+	0.862208i	$0.669081\pi$
$270$	2.08222	−	0.442589i	0.126720	−	0.0269351i
$271$	2.18673	+	20.8053i	0.132834	+	1.26383i	0.834372	+	0.551202i	$0.185831\pi$
$271$	2.18673	+	20.8053i	0.132834	+	1.26383i	−0.701538	+	0.712632i	$0.747503\pi$
$272$	5.46961	+	3.97390i	0.331644	+	0.240953i
$273$	1.34798	−	6.20969i	0.0815833	−	0.375827i
$274$	14.3387			0.866235
$275$	−13.5406	−	0.0701466i	−0.816526	−	0.00423000i
$276$	−9.77721	−	16.9346i	−0.588519	−	1.01934i
$277$	−8.34317	+	9.26603i	−0.501293	+	0.556742i	−0.939685	−	0.342042i	$-0.888882\pi$
$277$	−8.34317	+	9.26603i	−0.501293	+	0.556742i	0.438392	+	0.898784i	$0.355548\pi$
$278$	−17.3686	+	7.73298i	−1.04170	+	0.463793i
$279$	4.38895	−	3.18876i	0.262759	−	0.190906i
$280$	−5.02780	−	1.65768i	−0.300469	−	0.0990655i
$281$	6.96613	−	21.4396i	0.415565	−	1.27898i	−0.496180	−	0.868220i	$-0.665264\pi$
$281$	6.96613	−	21.4396i	0.415565	−	1.27898i	0.911745	−	0.410757i	$-0.134736\pi$
$282$	−0.464147	−	4.41606i	−0.0276396	−	0.262973i
$283$	−0.573884	+	5.46014i	−0.0341138	+	0.324571i	0.964135	+	0.265413i	$0.0855083\pi$
$283$	−0.573884	+	5.46014i	−0.0341138	+	0.324571i	−0.998249	+	0.0591583i	$0.981158\pi$
$284$	−1.33807	+	1.48608i	−0.0793998	+	0.0881824i
$285$	−1.77034	+	3.06631i	−0.104866	+	0.181633i
$286$	−17.3362	+	3.59116i	−1.02511	+	0.212350i
$287$	2.89991	−	1.65760i	0.171176	−	0.0978450i
$288$	−2.14045	−	6.58762i	−0.126127	−	0.388179i
$289$	11.7807	−	5.24512i	0.692985	−	0.308537i
$290$	−17.9304	−	7.98313i	−1.05291	−	0.468785i
$291$	−7.50900	+	1.59609i	−0.440186	+	0.0935643i
$292$	2.55928	+	2.84237i	0.149770	+	0.166337i
$293$	10.4718	−	7.60820i	0.611768	−	0.444476i	−0.238268	−	0.971199i	$-0.576580\pi$
$293$	10.4718	−	7.60820i	0.611768	−	0.444476i	0.850036	+	0.526724i	$0.176580\pi$
$294$	−14.2673	+	6.20505i	−0.832086	+	0.361886i
$295$	−3.57640	−	11.0070i	−0.208226	−	0.640854i
$296$	−3.57962	+	6.20008i	−0.208061	+	0.360372i
$297$	−3.24053	−	0.706362i	−0.188035	−	0.0409873i
$298$	−24.1763	−	41.8746i	−1.40050	−	2.42573i
$299$	−15.6252	−	3.32124i	−0.903628	−	0.192072i
$300$	9.71062	+	7.05518i	0.560643	+	0.407331i
$301$	−1.42688	+	3.16791i	−0.0822438	+	0.182595i
$302$	−3.22012	+	9.91051i	−0.185297	+	0.570285i
$303$	2.20916	+	2.45352i	0.126913	+	0.140951i
$304$	4.17592	+	1.85924i	0.239505	+	0.106635i
$305$	−0.616431	+	5.86495i	−0.0352967	+	0.335826i
$306$	−11.8870	−	2.52665i	−0.679532	−	0.144439i
$307$	−23.5062			−1.34157			−0.670785	−	0.741652i	$-0.734043\pi$
$307$	−23.5062			−1.34157			−0.670785	+	0.741652i	$0.734043\pi$
$308$	19.0069	+	17.4437i	1.08302	+	0.993948i
$309$	−17.0939			−0.972438
$310$	−11.2961	−	2.40106i	−0.641575	−	0.136371i
$311$	2.36402	−	22.4922i	0.134052	−	1.27542i	−0.696127	−	0.717918i	$-0.745095\pi$
$311$	2.36402	−	22.4922i	0.134052	−	1.27542i	0.830179	−	0.557497i	$-0.188238\pi$
$312$	4.58382	+	2.04085i	0.259508	+	0.115540i
$313$	−19.9249	−	22.1288i	−1.12622	−	1.25079i	−0.964536	−	0.263951i	$-0.914974\pi$
$313$	−19.9249	−	22.1288i	−1.12622	−	1.25079i	−0.161683	−	0.986843i	$-0.551692\pi$
$314$	13.4432	−	41.3739i	0.758643	−	2.33486i
$315$	−2.52125	+	0.253985i	−0.142056	+	0.0143104i
$316$	18.0562	+	13.1186i	1.01574	+	0.737979i
$317$	24.9915	+	5.31212i	1.40366	+	0.298358i	0.846653	−	0.532146i	$-0.178614\pi$
$317$	24.9915	+	5.31212i	1.40366	+	0.298358i	0.557012	+	0.830504i	$0.311948\pi$
$318$	−9.17213	−	15.8866i	−0.514348	−	0.890876i
$319$	20.3439	+	22.8309i	1.13904	+	1.27829i
$320$	−6.18820	+	10.7183i	−0.345931	+	0.599170i
$321$	−1.02302	−	3.14853i	−0.0570994	−	0.175734i
$322$	15.7539	+	35.7992i	0.877928	+	1.99501i
$323$	16.3526	−	11.8809i	0.909886	−	0.661071i
$324$	1.96723	+	2.18483i	0.109290	+	0.121379i
$325$	9.59113	−	2.03866i	0.532020	−	0.113084i
$326$	48.8413	+	21.7456i	2.70507	+	1.20438i
$327$	2.62508	−	1.16876i	0.145167	−	0.0646327i
$328$	0.815056	+	2.50848i	0.0450039	+	0.138508i
$329$	−0.0228381	+	5.28571i	−0.00125911	+	0.291411i
$330$	3.49838	+	6.13253i	0.192580	+	0.337585i
$331$	−7.41531	+	12.8437i	−0.407582	+	0.705954i	−0.994618	−	0.103607i	$-0.966961\pi$
$331$	−7.41531	+	12.8437i	−0.407582	+	0.705954i	0.587036	+	0.809561i	$0.300295\pi$
$332$	−22.2741	+	24.7379i	−1.22245	+	1.35767i
$333$	−0.358198	+	3.40803i	−0.0196291	+	0.186759i
$334$	−4.09962	−	39.0053i	−0.224321	−	2.13428i
$335$	1.19351	−	3.67325i	0.0652086	−	0.200691i
$336$	0.666346	+	3.20290i	0.0363522	+	0.174732i
$337$	−2.35158	+	1.70852i	−0.128099	+	0.0930691i	−0.649990	−	0.759943i	$-0.725227\pi$
$337$	−2.35158	+	1.70852i	−0.128099	+	0.0930691i	0.521891	+	0.853012i	$0.325227\pi$
$338$	−14.6839	+	6.53768i	−0.798697	+	0.355603i
$339$	6.25978	−	6.95219i	0.339985	−	0.377591i
$340$	7.69797	+	13.3333i	0.417481	+	0.723098i
$341$	14.5015	+	10.6512i	0.785301	+	0.576794i
$342$	−8.21654			−0.444300
$343$	17.6865	−	5.49429i	0.954982	−	0.296664i
$344$	−2.21957	−	1.61261i	−0.119671	−	0.0869464i
$345$	0.665879	+	6.33541i	0.0358497	+	0.341087i
$346$	23.6241	−	5.02145i	1.27004	−	0.269955i
$347$	6.44985	−	1.37096i	0.346246	−	0.0735969i	−0.0315062	−	0.999504i	$-0.510030\pi$
$347$	6.44985	−	1.37096i	0.346246	−	0.0735969i	0.377752	+	0.925907i	$0.376697\pi$
$348$	−2.83346	−	26.9585i	−0.151889	−	1.44513i
$349$	−19.6775	−	14.2965i	−1.05331	−	0.765275i	−0.0804719	−	0.996757i	$-0.525643\pi$
$349$	−19.6775	−	14.2965i	−1.05331	−	0.765275i	−0.972839	+	0.231481i	$0.925643\pi$
$350$	−17.7719	−	16.1415i	−0.949948	−	0.862798i
$351$	2.40170			0.128193
$352$	18.6553	−	13.4068i	0.994331	−	0.714583i
$353$	13.3844	+	23.1824i	0.712379	+	1.23388i	0.963962	+	0.266041i	$0.0857157\pi$
$353$	13.3844	+	23.1824i	0.712379	+	1.23388i	−0.251583	+	0.967836i	$0.580951\pi$
$354$	17.9712	−	19.9591i	0.955161	−	1.06081i
$355$	0.595132	−	0.264970i	0.0315863	−	0.0140631i
$356$	−9.35909	+	6.79978i	−0.496031	+	0.360388i
$357$	13.7387	+	4.52969i	0.727128	+	0.239737i
$358$	−1.14260	+	3.51657i	−0.0603885	+	0.185857i
$359$	0.484344	+	4.60823i	0.0255627	+	0.243213i	0.999840	+	0.0178624i	$0.00568609\pi$
$359$	0.484344	+	4.60823i	0.0255627	+	0.243213i	−0.974278	+	0.225351i	$0.927647\pi$
$360$	0.209157	−	1.98999i	0.0110235	−	0.104882i
$361$	−3.56889	+	3.96366i	−0.187837	+	0.208614i
$362$	−7.33941	+	12.7122i	−0.385751	+	0.668140i
$363$	−1.03641	−	10.9511i	−0.0543973	−	0.574782i
$364$	−16.1381	−	9.41057i	−0.845869	−	0.493248i
$365$	−0.385039	−	1.18503i	−0.0201539	−	0.0620272i
$366$	−12.5021	+	5.56630i	−0.653496	+	0.290955i
$367$	−27.4381	−	12.2162i	−1.43226	−	0.637682i	−0.463591	−	0.886049i	$-0.653439\pi$
$367$	−27.4381	−	12.2162i	−1.43226	−	0.637682i	−0.968666	+	0.248367i	$0.920106\pi$
$368$	8.04453	−	1.70992i	0.419350	−	0.0891356i
$369$	0.844769	+	0.938211i	0.0439769	+	0.0488413i
$370$	5.90157	−	4.28774i	0.306808	−	0.222909i
$371$	8.79551	+	19.9870i	0.456640	+	1.03767i
$372$	−4.92866	−	15.1688i	−0.255539	−	0.786468i
$373$	10.8062	−	18.7168i	0.559521	−	0.969119i	−0.438015	−	0.898968i	$-0.644318\pi$
$373$	10.8062	−	18.7168i	0.559521	−	0.969119i	0.997536	−	0.0701517i	$-0.0223483\pi$
$374$	−4.00534	−	40.1058i	−0.207111	−	2.07382i
$375$	−4.34954	−	7.53362i	−0.224609	−	0.389035i
$376$	−4.08264	−	0.867792i	−0.210546	−	0.0447529i
$377$	−17.9149	−	13.0160i	−0.922666	−	0.670356i
$378$	−3.43586	−	4.77228i	−0.176722	−	0.245460i
$379$	−7.23832	+	22.2773i	−0.371807	+	1.14431i	0.573800	+	0.818996i	$0.305469\pi$
$379$	−7.23832	+	22.2773i	−0.371807	+	1.14431i	−0.945607	+	0.325310i	$0.894531\pi$
$380$	6.96530	+	7.73575i	0.357312	+	0.396836i
$381$	17.0309	+	7.58264i	0.872519	+	0.388470i
$382$	−1.85850	+	17.6825i	−0.0950892	+	0.904714i
$383$	−9.70060	−	2.06193i	−0.495677	−	0.105359i	−0.0467116	−	0.998908i	$-0.514874\pi$
$383$	−9.70060	−	2.06193i	−0.495677	−	0.105359i	−0.448966	+	0.893549i	$0.648208\pi$
$384$	−14.8676			−0.758710
$385$	−3.34526	−	7.70989i	−0.170490	−	0.392932i
$386$	43.3365			2.20577
$387$	−1.28451	−	0.273032i	−0.0652954	−	0.0138790i
$388$	−2.35915	+	22.4458i	−0.119768	+	1.13951i
$389$	−1.86897	−	0.832119i	−0.0947605	−	0.0421901i	0.358809	−	0.933411i	$-0.383183\pi$
$389$	−1.86897	−	0.832119i	−0.0947605	−	0.0421901i	−0.453569	+	0.891221i	$0.649850\pi$
$390$	−3.42099	−	3.79939i	−0.173228	−	0.192390i
$391$	11.2380	−	34.5869i	0.568328	−	1.74913i
$392$	1.40292	+	14.5569i	0.0708582	+	0.735234i
$393$	13.5510	+	9.84539i	0.683559	+	0.496634i
$394$	−25.2491	−	5.36686i	−1.27203	−	0.270378i
$395$	−3.63542	−	6.29673i	−0.182918	−	0.316823i
$396$	−4.91907	+	8.41906i	−0.247193	+	0.423074i
$397$	−9.17228	+	15.8868i	−0.460343	+	0.797338i	−0.998978	−	0.0452014i	$-0.985607\pi$
$397$	−9.17228	+	15.8868i	−0.460343	+	0.797338i	0.538635	+	0.842540i	$0.318940\pi$
$398$	−5.35270	−	16.4739i	−0.268307	−	0.825763i
$399$	9.72274	+	1.06439i	0.486746	+	0.0532863i
$400$	−4.08412	+	2.96729i	−0.204206	+	0.148364i
$401$	−2.29363	−	2.54733i	−0.114538	−	0.127208i	0.683149	−	0.730279i	$-0.260610\pi$
$401$	−2.29363	−	2.54733i	−0.114538	−	0.127208i	−0.797687	+	0.603071i	$0.793943\pi$
$402$	8.76703	−	1.86349i	0.437260	−	0.0929424i
$403$	−11.9029	−	5.29951i	−0.592925	−	0.263987i
$404$	8.86728	−	3.94797i	0.441164	−	0.196419i
$405$	−0.295966	−	0.910889i	−0.0147067	−	0.0452624i
$406$	−0.234262	+	54.2183i	−0.0116262	+	2.69081i
$407$	−11.1291	+	2.30538i	−0.551651	+	0.114273i
$408$	−5.71152	+	9.89265i	−0.282762	+	0.489759i
$409$	−8.56195	+	9.50901i	−0.423361	+	0.470190i	−0.916659	−	0.399670i	$-0.869125\pi$
$409$	−8.56195	+	9.50901i	−0.423361	+	0.470190i	0.493298	+	0.869861i	$0.335791\pi$
$410$	0.280920	−	2.67278i	0.0138737	−	0.131999i
$411$	−0.674347	−	6.41598i	−0.0332631	−	0.316477i
$412$	−15.5298	+	47.7960i	−0.765101	+	2.35474i
$413$	−23.8512	+	21.2898i	−1.17364	+	1.04760i
$414$	−11.9597	+	8.68925i	−0.587789	+	0.427053i
$415$	9.90685	−	4.41081i	0.486308	−	0.216518i
$416$	−11.1315	+	12.3628i	−0.545765	+	0.606134i
$417$	4.27702	+	7.40801i	0.209446	+	0.362772i
$418$	−8.28670	−	25.9607i	−0.405316	−	1.26978i
$419$	−1.99577			−0.0974999			−0.0487499	−	0.998811i	$-0.515524\pi$
$419$	−1.99577			−0.0974999			−0.0487499	+	0.998811i	$0.515524\pi$
$420$	−1.58040	+	7.28036i	−0.0771154	+	0.355245i
$421$	11.2720	+	8.18959i	0.549364	+	0.399136i	0.827551	−	0.561391i	$-0.189734\pi$
$421$	11.2720	+	8.18959i	0.549364	+	0.399136i	−0.278187	+	0.960527i	$0.589734\pi$
$422$	−4.29171	−	40.8328i	−0.208917	−	1.98771i
$423$	−1.95417	+	0.415372i	−0.0950152	+	0.0201961i
$424$	−16.8663	+	3.58505i	−0.819101	+	0.174105i
$425$	2.33337	+	22.2006i	0.113185	+	1.07689i
$426$	1.22305	+	0.888598i	0.0592570	+	0.0430527i
$427$	15.5150	−	4.96711i	0.750823	−	0.240375i
$428$	−9.73297			−0.470461
$429$	2.42221	+	7.58834i	0.116945	+	0.366368i
$430$	1.39774	+	2.42095i	0.0674048	+	0.116749i
$431$	6.76199	−	7.50995i	0.325713	−	0.361741i	−0.557941	−	0.829880i	$-0.688409\pi$
$431$	6.76199	−	7.50995i	0.325713	−	0.361741i	0.883655	+	0.468139i	$0.155075\pi$
$432$	−1.12960	+	0.502931i	−0.0543480	+	0.0241973i
$433$	7.68228	−	5.58150i	0.369187	−	0.268230i	−0.387687	−	0.921791i	$-0.626726\pi$
$433$	7.68228	−	5.58150i	0.369187	−	0.268230i	0.756874	+	0.653561i	$0.226726\pi$
$434$	6.49785	+	31.2330i	0.311907	+	1.49923i
$435$	−2.72885	+	8.39854i	−0.130838	+	0.402679i
$436$	−0.883061	−	8.40176i	−0.0422909	−	0.402371i
$437$	2.57017	−	24.4536i	0.122948	−	1.16977i
$438$	1.93480	−	2.14881i	0.0924484	−	0.102674i
$439$	−5.40325	+	9.35871i	−0.257883	+	0.446667i	−0.965675	−	0.259755i	$-0.916358\pi$
$439$	−5.40325	+	9.35871i	−0.257883	+	0.446667i	0.707791	+	0.706421i	$0.249692\pi$
$440$	6.49845	−	1.34614i	0.309801	−	0.0641748i
$441$	3.44748	+	6.09220i	0.164166	+	0.290105i
$442$	9.01920	+	27.7582i	0.428999	+	1.32032i
$443$	−5.26208	+	2.34283i	−0.250009	+	0.111311i	−0.527915	−	0.849297i	$-0.677026\pi$
$443$	−5.26208	+	2.34283i	−0.250009	+	0.111311i	0.277906	+	0.960608i	$0.410359\pi$
$444$	9.20370	+	4.09775i	0.436788	+	0.194471i
$445$	3.68635	−	0.783557i	0.174750	−	0.0371442i
$446$	−23.0137	−	25.5593i	−1.08973	−	1.21027i
$447$	−17.6001	+	12.7872i	−0.832457	+	0.604815i
$448$	33.9858	+	3.72059i	1.60568	+	0.175781i
$449$	−0.763407	−	2.34953i	−0.0360274	−	0.110881i	0.931426	−	0.363932i	$-0.118566\pi$
$449$	−0.763407	−	2.34953i	−0.0360274	−	0.110881i	−0.967453	+	0.253051i	$0.918566\pi$
$450$	4.53710	−	7.85849i	0.213881	−	0.370453i
$451$	−2.11235	+	3.61532i	−0.0994669	+	0.170239i
$452$	−13.7519	−	23.8189i	−0.646833	−	1.12035i
$453$	4.58597	+	0.974779i	0.215468	+	0.0457991i
$454$	−13.9948	−	10.1678i	−0.656807	−	0.477198i
$455$	3.55592	+	4.93903i	0.166704	+	0.231546i
$456$	−2.38664	+	7.34532i	−0.111765	+	0.343976i
$457$	6.84743	+	7.60484i	0.320309	+	0.355740i	0.881699	−	0.471812i	$-0.156400\pi$
$457$	6.84743	+	7.60484i	0.320309	+	0.355740i	−0.561390	+	0.827551i	$0.689733\pi$
$458$	−47.2701	−	21.0460i	−2.20879	−	0.983415i
$459$	−0.571529	+	5.43774i	−0.0266767	+	0.253812i
$460$	18.3193	+	3.89388i	0.854141	+	0.181553i
$461$	−31.5828			−1.47096			−0.735478	−	0.677549i	$-0.763042\pi$
$461$	−31.5828			−1.47096			−0.735478	+	0.677549i	$0.763042\pi$
$462$	11.6131	−	15.6689i	0.540292	−	0.728981i
$463$	−11.1523			−0.518293			−0.259147	−	0.965838i	$-0.583441\pi$
$463$	−11.1523			−0.518293			−0.259147	+	0.965838i	$0.583441\pi$
$464$	11.1516	+	2.37035i	0.517701	+	0.110041i
$465$	−0.543121	+	5.16745i	−0.0251866	+	0.239635i
$466$	33.9015	+	15.0939i	1.57046	+	0.699212i
$467$	8.55080	+	9.49662i	0.395684	+	0.439451i	0.907761	−	0.419488i	$-0.137790\pi$
$467$	8.55080	+	9.49662i	0.395684	+	0.439451i	−0.512077	+	0.858939i	$0.671124\pi$
$468$	2.18195	−	6.71536i	0.100861	−	0.310417i
$469$	−10.6155	+	1.06939i	−0.490180	+	0.0493797i
$470$	3.44063	+	2.49976i	0.158704	+	0.115305i
$471$	−19.1453	−	4.06946i	−0.882169	−	0.187511i
$472$	−12.6227	−	21.8632i	−0.581008	−	1.00633i
$473$	−0.432820	−	4.33386i	−0.0199011	−	0.199271i
$474$	8.43642	−	14.6123i	0.387497	−	0.671165i
$475$	4.66396	+	14.3542i	0.213997	+	0.658616i
$476$	25.1470	−	34.2992i	1.15261	−	1.57210i
$477$	−6.67722	+	4.85128i	−0.305729	+	0.222125i
$478$	20.0342	+	22.2502i	0.916342	+	1.01770i
$479$	−2.10359	+	0.447132i	−0.0961156	+	0.0204300i	−0.255718	−	0.966751i	$-0.582312\pi$
$479$	−2.10359	+	0.447132i	−0.0961156	+	0.0204300i	0.159603	+	0.987181i	$0.448979\pi$
$480$	6.06054	+	2.69833i	0.276625	+	0.123161i
$481$	7.51862	−	3.34751i	0.342820	−	0.152633i
$482$	16.7445	+	51.5342i	0.762690	+	2.34732i
$483$	15.2777	−	8.73281i	0.695161	−	0.397357i
$484$	−31.5616	−	7.05118i	−1.43462	−	0.320508i
$485$	3.67627	−	6.36748i	0.166931	−	0.289132i
$486$	1.48721	−	1.65172i	0.0674614	−	0.0749234i
$487$	1.78899	−	17.0211i	0.0810670	−	0.771301i	−0.876171	−	0.482000i	$-0.839910\pi$
$487$	1.78899	−	17.0211i	0.0810670	−	0.771301i	0.957238	−	0.289301i	$-0.0934229\pi$
$488$	1.34463	+	12.7933i	0.0608686	+	0.579126i
$489$	7.43323	−	22.8771i	0.336142	−	1.03454i
$490$	4.72699	−	14.1315i	0.213544	−	0.638396i
$491$	4.24319	−	3.08286i	0.191492	−	0.139127i	−0.487908	−	0.872895i	$-0.662240\pi$
$491$	4.24319	−	3.08286i	0.191492	−	0.139127i	0.679401	+	0.733768i	$0.262240\pi$
$492$	3.39079	−	1.50968i	0.152868	−	0.0680614i
$493$	33.7329	−	37.4641i	1.51925	−	1.68730i
$494$	9.86684	+	17.0899i	0.443930	+	0.768910i
$495$	2.57952	−	1.85379i	0.115941	−	0.0833216i
$496$	6.70807			0.301201
$497$	−1.33214	−	1.20993i	−0.0597546	−	0.0542726i
$498$	20.3595	+	14.7920i	0.912329	+	0.662846i
$499$	3.63938	+	34.6264i	0.162921	+	1.55009i	0.704660	+	0.709545i	$0.251100\pi$
$499$	3.63938	+	34.6264i	0.162921	+	1.55009i	−0.541739	+	0.840547i	$0.682234\pi$
$500$	−25.0162	+	5.31735i	−1.11876	+	0.237799i
$501$	−17.2604	+	3.66882i	−0.771139	+	0.163911i
$502$	−5.70426	−	54.2724i	−0.254594	−	2.42230i
$503$	2.76700	+	2.01034i	0.123374	+	0.0896366i	0.647761	−	0.761843i	$-0.275705\pi$
$503$	2.76700	+	2.01034i	0.123374	+	0.0896366i	−0.524387	+	0.851480i	$0.675705\pi$
$504$	−5.26427	+	1.68536i	−0.234489	+	0.0750717i
$505$	−3.16210			−0.140712
$506$	−39.5161	−	29.0241i	−1.75671	−	1.29028i
$507$	3.61591	+	6.26294i	0.160588	+	0.278147i
$508$	36.6743	−	40.7309i	1.62716	−	1.80714i
$509$	−15.1016	+	6.72368i	−0.669368	+	0.298022i	−0.713142	−	0.701020i	$-0.752729\pi$
$509$	−15.1016	+	6.72368i	−0.669368	+	0.298022i	0.0437740	+	0.999041i	$0.486062\pi$
$510$	9.41635	−	6.84138i	0.416963	−	0.302941i
$511$	−2.56784	+	2.29208i	−0.113595	+	0.101396i
$512$	4.24323	−	13.0593i	0.187526	−	0.577146i
$513$	0.386421	+	3.67655i	0.0170609	+	0.162324i
$514$	−5.28643	+	50.2970i	−0.233174	+	2.21850i
$515$	10.9550	−	12.1667i	0.482734	−	0.536130i
$516$	−1.93040	+	3.34355i	−0.0849811	+	0.147192i
$517$	−3.28326	−	5.75542i	−0.144397	−	0.253123i
$518$	−17.4077	−	10.1509i	−0.764851	−	0.446004i
$519$	−3.35792	−	10.3346i	−0.147396	−	0.453639i
$520$	−4.39022	+	1.95465i	−0.192524	+	0.0857172i
$521$	22.4552	+	9.99770i	0.983781	+	0.438007i	0.834632	−	0.550807i	$-0.185680\pi$
$521$	22.4552	+	9.99770i	0.983781	+	0.438007i	0.149148	+	0.988815i	$0.452347\pi$
$522$	−20.0450	+	4.26069i	−0.877344	+	0.186485i
$523$	5.51014	+	6.11963i	0.240942	+	0.267593i	0.851472	−	0.524400i	$-0.175710\pi$
$523$	5.51014	+	6.11963i	0.240942	+	0.267593i	−0.610530	+	0.791993i	$0.709044\pi$
$524$	39.8396	−	28.9452i	1.74040	−	1.26448i
$525$	−6.38682	+	8.71130i	−0.278744	+	0.380192i
$526$	5.91602	+	18.2076i	0.257951	+	0.793891i
$527$	14.8312	−	25.6884i	0.646058	−	1.11900i
$528$	−2.72829	−	3.06182i	−0.118734	−	0.133249i
$529$	−10.6194	−	18.3933i	−0.461712	−	0.799709i
$530$	17.1856	+	3.65290i	0.746493	+	0.158672i
$531$	−9.77603	−	7.10270i	−0.424244	−	0.308231i
$532$	11.8093	−	26.2186i	0.511996	−	1.13672i
$533$	0.936976	−	2.88372i	0.0405849	−	0.124908i
$534$	5.85202	+	6.49933i	0.253242	+	0.281253i
$535$	2.89662	+	1.28966i	0.125232	+	0.0557567i
$536$	0.880640	−	8.37873i	0.0380378	−	0.361906i
$537$	1.62725	+	0.345884i	0.0702212	+	0.0149260i
$538$	49.1937			2.12089
$539$	−15.7718	+	17.0368i	−0.679338	+	0.733826i
$540$	−2.81580			−0.121173
$541$	37.5940	+	7.99086i	1.61629	+	0.343554i	0.925279	−	0.379287i	$-0.123831\pi$
$541$	37.5940	+	7.99086i	1.61629	+	0.343554i	0.691015	+	0.722841i	$0.257164\pi$
$542$	4.86024	−	46.2420i	0.208765	−	1.98627i
$543$	6.03336	+	2.68622i	0.258916	+	0.115277i
$544$	−25.3418	−	28.1449i	−1.08652	−	1.20670i
$545$	−0.850460	+	2.61745i	−0.0364297	+	0.112119i
$546$	−5.80008	+	12.8772i	−0.248221	+	0.551092i
$547$	−13.9610	−	10.1432i	−0.596928	−	0.433693i	0.247859	−	0.968796i	$-0.420273\pi$
$547$	−13.9610	−	10.1432i	−0.596928	−	0.433693i	−0.844787	+	0.535103i	$0.820273\pi$
$548$	−18.5523	−	3.94340i	−0.792513	−	0.168454i
$549$	3.07865	+	5.33238i	0.131394	+	0.227581i
$550$	29.4052	+	6.40967i	1.25384	+	0.273309i
$551$	17.0426	−	29.5186i	0.726038	−	1.25753i
$552$	4.29400	+	13.2156i	0.182765	+	0.562492i
$553$	−11.8758	+	16.1981i	−0.505012	+	0.688811i
$554$	22.4202	−	16.2893i	0.952545	−	0.692064i
$555$	−2.19613	−	2.43905i	−0.0932207	−	0.103532i
$556$	24.5991	−	5.22870i	1.04323	−	0.221746i
$557$	12.4020	+	5.52174i	0.525491	+	0.233964i	0.652296	−	0.757964i	$-0.273806\pi$
$557$	12.4020	+	5.52174i	0.525491	+	0.233964i	−0.126805	+	0.991928i	$0.540472\pi$
$558$	−11.0153	+	4.90432i	−0.466314	+	0.207616i
$559$	0.974621	+	2.99957i	0.0412221	+	0.126868i
$560$	−2.70673	−	1.57836i	−0.114380	−	0.0666980i
$561$	−17.7573	+	3.67839i	−0.749713	+	0.155302i
$562$	−25.0520	+	43.3913i	−1.05675	+	1.83035i
$563$	−15.0653	+	16.7317i	−0.634927	+	0.705157i	−0.971644	−	0.236448i	$-0.924017\pi$
$563$	−15.0653	+	16.7317i	−0.634927	+	0.705157i	0.336718	+	0.941606i	$0.390683\pi$
$564$	−0.613955	+	5.84139i	−0.0258522	+	0.245967i
$565$	0.936573	+	8.91090i	0.0394019	+	0.374884i
$566$	3.77080	−	11.6053i	0.158499	−	0.487809i
$567$	−1.97381	+	1.76184i	−0.0828921	+	0.0739904i
$568$	1.14963	−	0.835259i	0.0482376	−	0.0350467i
$569$	1.82212	−	0.811262i	0.0763874	−	0.0340099i	−0.368187	−	0.929752i	$-0.620021\pi$
$569$	1.82212	−	0.811262i	0.0763874	−	0.0340099i	0.444575	+	0.895742i	$0.353355\pi$
$570$	5.26573	−	5.84819i	0.220557	−	0.244954i
$571$	−13.1020	−	22.6933i	−0.548300	−	0.949684i	−0.998391	−	0.0567012i	$-0.981942\pi$
$571$	−13.1020	−	22.6933i	−0.548300	−	0.949684i	0.450091	−	0.892983i	$-0.351392\pi$
$572$	23.4182	+	0.121318i	0.979163	+	0.00507254i
$573$	7.99956			0.334186
$574$	−7.07049	+	2.26362i	−0.295117	+	0.0944815i
$575$	21.9687	+	15.9612i	0.916160	+	0.665629i
$576$	1.35074	+	12.8514i	0.0562806	+	0.535474i
$577$	−11.3929	+	2.42163i	−0.474291	+	0.100814i	−0.438854	−	0.898558i	$-0.644615\pi$
$577$	−11.3929	+	2.42163i	−0.474291	+	0.100814i	−0.0354365	+	0.999372i	$0.511282\pi$
$578$	−28.0356	+	5.95914i	−1.16613	+	0.247868i
$579$	−2.03810	−	19.3913i	−0.0847007	−	0.805874i
$580$	21.0038	+	15.2602i	0.872137	+	0.633644i
$581$	−22.1754	−	20.1410i	−0.919992	−	0.835590i
$582$	17.0624			0.707259
$583$	−22.0622	−	16.2044i	−0.913722	−	0.671117i
$584$	−1.35897	−	2.35381i	−0.0562347	−	0.0974014i
$585$	−1.53918	+	1.70943i	−0.0636372	+	0.0706763i
$586$	−26.2818	+	11.7014i	−1.08569	+	0.483381i
$587$	−3.00543	+	2.18357i	−0.124047	+	0.0901257i	−0.648079	−	0.761573i	$-0.724427\pi$
$587$	−3.00543	+	2.18357i	−0.124047	+	0.0901257i	0.524032	+	0.851699i	$0.324427\pi$
$588$	20.1663	−	4.10467i	0.831645	−	0.169274i
$589$	6.19743	−	19.0737i	0.255361	−	0.785919i
$590$	2.68881	+	25.5824i	0.110697	+	1.05321i
$591$	−1.21398	+	11.5503i	−0.0499367	+	0.475116i
$592$	−2.83527	+	3.14889i	−0.116529	+	0.129418i
$593$	−3.85284	+	6.67332i	−0.158217	+	0.274040i	−0.934226	−	0.356682i	$-0.883908\pi$
$593$	−3.85284	+	6.67332i	−0.158217	+	0.274040i	0.776009	+	0.630722i	$0.217241\pi$
$594$	6.71862	+	3.03312i	0.275668	+	0.124451i
$595$	−12.0287	+	6.87568i	−0.493131	+	0.281875i
$596$	19.7644	+	60.8286i	0.809582	+	2.49164i
$597$	−7.11965	+	3.16987i	−0.291388	+	0.129734i
$598$	32.4349	+	14.4410i	1.32636	+	0.590535i
$599$	−14.0988	+	2.99679i	−0.576061	+	0.122446i	−0.486724	−	0.873556i	$-0.661808\pi$
$599$	−14.0988	+	2.99679i	−0.576061	+	0.122446i	−0.0893374	+	0.996001i	$0.528475\pi$
$600$	−5.70735	−	6.33866i	−0.233002	−	0.258775i
$601$	25.3097	−	18.3886i	1.03240	−	0.750085i	0.0636148	−	0.997975i	$-0.479737\pi$
$601$	25.3097	−	18.3886i	1.03240	−	0.750085i	0.968788	+	0.247890i	$0.0797371\pi$
$602$	4.56599	−	6.22778i	0.186096	−	0.253825i
$603$	−1.24614	−	3.83524i	−0.0507469	−	0.156183i
$604$	6.89193	−	11.9372i	0.280428	−	0.485716i
$605$	8.45871	+	6.28054i	0.343896	+	0.255340i
$606$	−3.66901	−	6.35492i	−0.149043	−	0.258151i
$607$	−41.6331	−	8.84940i	−1.68984	−	0.359186i	−0.740163	−	0.672427i	$-0.765252\pi$
$607$	−41.6331	−	8.84940i	−1.68984	−	0.359186i	−0.949674	+	0.313241i	$0.898585\pi$
$608$	−20.7160	−	15.0511i	−0.840146	−	0.610402i
$609$	24.2714	−	2.44505i	0.983527	−	0.0990783i
$610$	4.05037	−	12.4657i	0.163995	−	0.504723i
$611$	3.21062	+	3.56575i	0.129888	+	0.144255i
$612$	14.6851	+	6.53824i	0.593611	+	0.264293i
$613$	−1.99980	+	19.0268i	−0.0807711	+	0.768486i	0.876910	+	0.480655i	$0.159601\pi$
$613$	−1.99980	+	19.0268i	−0.0807711	+	0.768486i	−0.957681	+	0.287831i	$0.907066\pi$
$614$	51.1034	+	10.8624i	2.06236	+	0.438369i
$615$	−1.20917			−0.0487583
$616$	−10.6342	−	14.9331i	−0.428465	−	0.601671i
$617$	5.09296			0.205035			0.102517	−	0.994731i	$-0.467310\pi$
$617$	5.09296			0.205035			0.102517	+	0.994731i	$0.467310\pi$
$618$	37.1628	+	7.89919i	1.49491	+	0.317752i
$619$	3.41226	−	32.4655i	0.137150	−	1.30490i	−0.682014	−	0.731340i	$-0.738895\pi$
$619$	3.41226	−	32.4655i	0.137150	−	1.30490i	0.819164	−	0.573559i	$-0.194438\pi$
$620$	13.9552	+	6.21325i	0.560453	+	0.249530i
$621$	4.45054	+	4.94282i	0.178594	+	0.198349i
$622$	−15.5332	+	47.8064i	−0.622826	+	1.91686i
$623$	−6.08283	−	8.44883i	−0.243704	−	0.338495i
$624$	2.40255	+	1.74555i	0.0961788	+	0.0698780i
$625$	−11.8177	−	2.51194i	−0.472710	−	0.100478i
$626$	33.0915	+	57.3162i	1.32260	+	2.29082i
$627$	−11.2266	+	4.92887i	−0.448347	+	0.196840i
$628$	−28.7721	+	49.8347i	−1.14813	+	1.98862i
$629$	5.78995	+	17.8196i	0.230861	+	0.710516i
$630$	5.59865	+	0.612910i	0.223056	+	0.0244189i
$631$	17.8326	−	12.9562i	0.709906	−	0.515777i	−0.173238	−	0.984880i	$-0.555423\pi$
$631$	17.8326	−	12.9562i	0.709906	−	0.515777i	0.883143	+	0.469103i	$0.155423\pi$
$632$	−10.6124	−	11.7863i	−0.422139	−	0.468833i
$633$	−18.0691	+	3.84071i	−0.718184	+	0.152655i
$634$	−51.8778	−	23.0975i	−2.06033	−	0.917318i
$635$	−16.3116	+	7.26238i	−0.647305	+	0.288199i
$636$	7.49832	+	23.0774i	0.297328	+	0.915080i
$637$	8.53146	−	14.4864i	0.338029	−	0.573971i
$638$	−33.6780	−	59.0363i	−1.33333	−	2.33727i
$639$	0.340090	−	0.589054i	0.0134538	−	0.0233026i
$640$	9.52821	−	10.5821i	0.376636	−	0.418296i
$641$	0.496748	−	4.72624i	0.0196204	−	0.186675i	−0.980322	−	0.197405i	$-0.936749\pi$
$641$	0.496748	−	4.72624i	0.0196204	−	0.186675i	0.999942	+	0.0107295i	$0.00341537\pi$
$642$	0.769128	+	7.31777i	0.0303551	+	0.288809i
$643$	−15.3067	+	47.1092i	−0.603637	+	1.85780i	−0.0977382	+	0.995212i	$0.531161\pi$
$643$	−15.3067	+	47.1092i	−0.603637	+	1.85780i	−0.505899	+	0.862593i	$0.668839\pi$
$644$	−10.5378	−	50.6516i	−0.415247	−	1.99595i
$645$	1.01754	−	0.739285i	0.0400655	−	0.0291093i
$646$	−41.0415	+	18.2728i	−1.61476	+	0.718935i
$647$	−21.0898	+	23.4226i	−0.829127	+	0.920839i	−0.997897	−	0.0648164i	$-0.979354\pi$
$647$	−21.0898	+	23.4226i	−0.829127	+	0.920839i	0.168770	+	0.985655i	$0.446020\pi$
$648$	−1.04460	−	1.80929i	−0.0410356	−	0.0710757i
$649$	12.5819	−	38.0513i	0.493884	−	1.49365i
$650$	−21.7935			−0.854813
$651$	13.6698	−	4.37639i	0.535763	−	0.171524i
$652$	−57.2132	−	41.5678i	−2.24064	−	1.62792i
$653$	4.16688	+	39.6452i	0.163063	+	1.55144i	0.703893	+	0.710306i	$0.251443\pi$
$653$	4.16688	+	39.6452i	0.163063	+	1.55144i	−0.540830	+	0.841132i	$0.681890\pi$
$654$	−6.24711	+	1.32786i	−0.244281	+	0.0519236i
$655$	−15.6920	+	3.33543i	−0.613136	+	0.130326i
$656$	0.163176	+	1.55252i	0.00637095	+	0.0606156i
$657$	−1.05250	−	0.764684i	−0.0410618	−	0.0298332i
$658$	2.49221	−	11.4808i	0.0971564	−	0.447567i
$659$	−23.2122			−0.904218			−0.452109	−	0.891963i	$-0.649328\pi$
$659$	−23.2122			−0.904218			−0.452109	+	0.891963i	$0.649328\pi$
$660$	−2.83985	−	8.89672i	−0.110541	−	0.346304i
$661$	0.545742	+	0.945253i	0.0212269	+	0.0367661i	0.876444	−	0.481504i	$-0.159909\pi$
$661$	0.545742	+	0.945253i	0.0212269	+	0.0367661i	−0.855217	+	0.518270i	$0.826576\pi$
$662$	22.0563	−	24.4960i	0.857243	−	0.952064i
$663$	11.9965	−	5.34117i	0.465904	−	0.207434i
$664$	19.1374	−	13.9041i	0.742674	−	0.539584i
$665$	−6.98860	+	6.23810i	−0.271006	+	0.241903i
$666$	2.35360	−	7.24365i	0.0912003	−	0.280686i
$667$	−6.41024	−	60.9894i	−0.248206	−	2.36152i
$668$	−5.42282	+	51.5947i	−0.209815	+	1.99626i
$669$	−10.3544	+	11.4997i	−0.400324	+	0.444605i
$670$	−4.29217	+	7.43426i	−0.165821	+	0.287210i
$671$	−13.7431	+	15.1051i	−0.530545	+	0.583127i
$672$	0.0791815	−	18.3260i	0.00305449	−	0.706940i
$673$	−6.85827	−	21.1076i	−0.264367	−	0.813637i	−0.991839	−	0.127500i	$-0.959305\pi$
$673$	−6.85827	−	21.1076i	−0.264367	−	0.813637i	0.727472	−	0.686137i	$-0.240695\pi$
$674$	5.90194	−	2.62771i	0.227334	−	0.101216i
$675$	−3.72972	−	1.66058i	−0.143557	−	0.0639157i
$676$	20.7968	−	4.42049i	0.799875	−	0.170019i
$677$	9.66936	+	10.7389i	0.371624	+	0.412730i	0.899729	−	0.436449i	$-0.143764\pi$
$677$	9.66936	+	10.7389i	0.371624	+	0.412730i	−0.528105	+	0.849179i	$0.677097\pi$
$678$	−16.8216	+	12.2216i	−0.646031	+	0.469369i
$679$	−20.1902	−	2.21031i	−0.774827	−	0.0848240i
$680$	−3.38083	−	10.4051i	−0.129649	−	0.399018i
$681$	−3.89149	+	6.74026i	−0.149122	+	0.258287i
$682$	−26.6048	−	29.8573i	−1.01875	−	1.14329i
$683$	1.68966	+	2.92658i	0.0646531	+	0.111982i	0.896540	−	0.442963i	$-0.146073\pi$
$683$	1.68966	+	2.92658i	0.0646531	+	0.111982i	−0.831887	+	0.554945i	$0.812739\pi$
$684$	10.6310	+	2.25969i	0.406487	+	0.0864014i
$685$	4.99880	+	3.63184i	0.190994	+	0.138765i
$686$	−40.9901	+	3.77174i	−1.56501	+	0.144006i
$687$	−7.19410	+	22.1412i	−0.274472	+	0.844738i
$688$	−1.08653	−	1.20671i	−0.0414234	−	0.0460053i
$689$	18.1087	+	8.06251i	0.689887	+	0.307157i
$690$	1.47999	−	14.0811i	0.0563421	−	0.536059i
$691$	19.7088	+	4.18923i	0.749757	+	0.159366i	0.566915	−	0.823777i	$-0.308137\pi$
$691$	19.7088	+	4.18923i	0.749757	+	0.159366i	0.182842	+	0.983142i	$0.441470\pi$
$692$	−31.9471			−1.21445
$693$	−7.55731	−	4.45949i	−0.287079	−	0.169402i
$694$	−14.6557			−0.556324
$695$	−8.01373	−	1.70337i	−0.303978	−	0.0646125i
$696$	−2.01350	+	19.1571i	−0.0763214	+	0.726150i
$697$	6.30610	+	2.80766i	0.238861	+	0.106348i
$698$	36.1730	+	40.1742i	1.36917	+	1.52062i
$699$	5.15951	−	15.8793i	0.195151	−	0.600612i
$700$	18.5551	+	25.7723i	0.701316	+	0.974101i
$701$	6.56605	+	4.77052i	0.247996	+	0.180180i	0.704838	−	0.709368i	$-0.251020\pi$
$701$	6.56605	+	4.77052i	0.247996	+	0.180180i	−0.456842	+	0.889548i	$0.651020\pi$
$702$	−5.22139	−	1.10984i	−0.197069	−	0.0418882i
$703$	6.33411	+	10.9710i	0.238895	+	0.413779i
$704$	−39.2425	+	17.2289i	−1.47901	+	0.649337i
$705$	0.956726	−	1.65710i	0.0360324	−	0.0624099i
$706$	−18.3854	−	56.5845i	−0.691944	−	2.12958i
$707$	3.51836	+	7.99515i	0.132321	+	0.300689i
$708$	−28.7413	+	20.8818i	−1.08016	+	0.784784i
$709$	29.1799	+	32.4075i	1.09587	+	1.21709i	0.974477	+	0.224486i	$0.0720702\pi$
$709$	29.1799	+	32.4075i	1.09587	+	1.21709i	0.121395	+	0.992604i	$0.461263\pi$
$710$	−1.41628	+	0.301040i	−0.0531521	+	0.0112978i
$711$	−6.93515	−	3.08773i	−0.260088	−	0.115799i
$712$	7.51002	−	3.34367i	0.281450	−	0.125310i
$713$	−11.1503	−	34.3171i	−0.417582	−	1.28519i
$714$	−27.7752	−	16.1964i	−1.03946	−	0.606136i
$715$	−6.95338	−	3.13911i	−0.260042	−	0.117396i
$716$	2.44548	−	4.23570i	0.0913920	−	0.158296i
$717$	9.01383	−	10.0109i	0.336628	−	0.373863i
$718$	1.07651	−	10.2423i	0.0401749	−	0.382238i
$719$	4.14269	+	39.4150i	0.154496	+	1.46993i	0.747247	+	0.664547i	$0.231375\pi$
$719$	4.14269	+	39.4150i	0.154496	+	1.46993i	−0.592750	+	0.805386i	$0.701958\pi$
$720$	0.365962	−	1.12632i	0.0136386	−	0.0419753i
$721$	−42.9519	−	14.1614i	−1.59961	−	0.527398i
$722$	9.59053	−	6.96793i	0.356923	−	0.259320i
$723$	22.2719	−	9.91609i	0.828301	−	0.368783i
$724$	12.9922	−	14.4293i	0.482852	−	0.536262i
$725$	18.8215	+	32.5998i	0.699013	+	1.21073i
$726$	−2.80736	+	24.2869i	−0.104191	+	0.901373i
$727$	−2.84843			−0.105642			−0.0528212	−	0.998604i	$-0.516821\pi$
$727$	−2.84843			−0.105642			−0.0528212	+	0.998604i	$0.516821\pi$
$728$	9.82704	+	8.92549i	0.364214	+	0.330801i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	0.289480	+	2.75422i	0.0107141	+	0.101938i
$731$	−7.02332	+	1.49285i	−0.259767	+	0.0552151i
$732$	17.7067	−	3.76368i	0.654460	−	0.139110i
$733$	−0.480787	−	4.57438i	−0.0177583	−	0.168959i	0.982048	−	0.188630i	$-0.0604047\pi$
$733$	−0.480787	−	4.57438i	−0.0177583	−	0.168959i	−0.999806	+	0.0196714i	$0.993738\pi$
$734$	54.0062	+	39.2378i	1.99341	+	1.44829i
$735$	−6.54556	−	1.45053i	−0.241437	−	0.0535036i
$736$	−46.0706			−1.69818
$737$	10.8609	−	7.80526i	0.400066	−	0.287510i
$738$	−1.40300	−	2.43008i	−0.0516453	−	0.0894523i
$739$	−20.6426	+	22.9259i	−0.759350	+	0.843344i	−0.991604	−	0.129311i	$-0.958723\pi$
$739$	−20.6426	+	22.9259i	−0.759350	+	0.843344i	0.232254	+	0.972655i	$0.425390\pi$
$740$	−8.81498	+	3.92468i	−0.324045	+	0.144274i
$741$	7.18296	−	5.21873i	0.263873	−	0.191715i
$742$	−9.88565	−	47.5169i	−0.362913	−	1.74440i
$743$	−12.8381	+	39.5116i	−0.470984	+	1.44954i	0.380315	+	0.924857i	$0.375816\pi$
$743$	−12.8381	+	39.5116i	−0.470984	+	1.44954i	−0.851299	+	0.524682i	$0.824184\pi$
$744$	1.18472	+	11.2718i	0.0434339	+	0.413246i
$745$	2.17797	−	20.7220i	0.0797946	−	0.759195i
$746$	−32.1421	+	35.6974i	−1.17681	+	1.30698i
$747$	5.66130	−	9.80566i	0.207136	−	0.358770i
$748$	−5.84746	+	52.9926i	−0.213804	+	1.93760i
$749$	0.0378446	−	8.75884i	0.00138281	−	0.320041i
$750$	5.97473	+	18.3883i	0.218166	+	0.671446i
$751$	3.48737	−	1.55268i	0.127256	−	0.0566580i	−0.342121	−	0.939656i	$-0.611145\pi$
$751$	3.48737	−	1.55268i	0.127256	−	0.0566580i	0.469377	+	0.882998i	$0.344479\pi$
$752$	−2.25675	−	1.00477i	−0.0822953	−	0.0366402i
$753$	−24.0163	+	5.10483i	−0.875204	+	0.186030i
$754$	32.9330	+	36.5758i	1.19935	+	1.33201i
$755$	−3.63282	+	2.63940i	−0.132212	+	0.0960575i
$756$	3.13304	+	7.11956i	0.113948	+	0.258936i
$757$	4.90075	+	15.0830i	0.178121	+	0.548199i	0.999762	−	0.0218052i	$-0.00694137\pi$
$757$	4.90075	+	15.0830i	0.178121	+	0.548199i	−0.821641	+	0.570005i	$0.806941\pi$
$758$	26.0308	−	45.0867i	0.945482	−	1.63762i
$759$	−11.1286	+	19.0468i	−0.403943	+	0.691355i
$760$	−3.69857	−	6.40611i	−0.134161	−	0.232374i
$761$	−8.68591	−	1.84625i	−0.314864	−	0.0669264i	0.0477690	−	0.998858i	$-0.484789\pi$
$761$	−8.68591	−	1.84625i	−0.314864	−	0.0669264i	−0.362633	+	0.931932i	$0.618122\pi$
$762$	−33.5218	−	24.3550i	−1.21437	−	0.882288i
$763$	7.56431	−	0.762011i	0.273846	−	0.0275867i
$764$	7.26762	−	22.3674i	0.262933	−	0.809225i
$765$	−3.50408	−	3.89167i	−0.126690	−	0.140704i
$766$	20.1366	+	8.96540i	0.727566	+	0.323933i
$767$	−3.03360	+	28.8628i	−0.109537	+	1.04218i
$768$	7.04315	+	1.49707i	0.254148	+	0.0540207i
$769$	13.5853			0.489900			0.244950	−	0.969536i	$-0.421228\pi$
$769$	13.5853			0.489900			0.244950	+	0.969536i	$0.421228\pi$
$770$	3.70993	+	18.3074i	0.133697	+	0.659754i
$771$	22.7544			0.819479
$772$	−56.0712	−	11.9183i	−2.01805	−	0.428949i
$773$	1.86491	−	17.7434i	0.0670762	−	0.638187i	−0.908403	−	0.418096i	$-0.862698\pi$
$773$	1.86491	−	17.7434i	0.0670762	−	0.638187i	0.975479	−	0.220092i	$-0.0706356\pi$
$774$	2.66641	+	1.18716i	0.0958420	+	0.0426716i
$775$	14.8204	+	16.4597i	0.532364	+	0.591250i
$776$	4.95608	−	15.2532i	0.177913	−	0.547560i
$777$	−3.72341	+	8.26661i	−0.133577	+	0.296563i
$778$	3.67868	+	2.67272i	0.131887	+	0.0958216i
$779$	4.56518	+	0.970359i	0.163565	+	0.0347667i
$780$	3.38136	+	5.85669i	0.121072	+	0.209703i
$781$	2.20415	+	0.480454i	0.0788706	+	0.0171920i
$782$	−40.4145	+	70.0000i	−1.44522	+	2.50320i
$783$	2.84919	+	8.76889i	0.101822	+	0.313375i
$784$	−0.979099	+	8.59996i	−0.0349678	+	0.307141i
$785$	15.1661	−	11.0188i	0.541302	−	0.393279i
$786$	−24.9108	−	27.6662i	−0.888539	−	0.986822i
$787$	−7.66868	+	1.63003i	−0.273359	+	0.0581042i	−0.342551	−	0.939499i	$-0.611291\pi$
$787$	−7.66868	+	1.63003i	−0.273359	+	0.0581042i	0.0691925	+	0.997603i	$0.477958\pi$
$788$	31.1926	+	13.8879i	1.11119	+	0.494735i
$789$	7.86892	−	3.50347i	0.280141	−	0.124727i
$790$	4.99378	+	15.3693i	0.177671	+	0.546814i
$791$	21.4885	−	12.2829i	0.764042	−	0.436729i
$792$	4.66306	−	5.12521i	0.165695	−	0.182116i
$793$	7.39401	−	12.8068i	0.262569	−	0.454783i
$794$	27.2823	−	30.3000i	0.968211	−	1.07531i
$795$	0.826288	−	7.86161i	0.0293054	−	0.278822i
$796$	2.39500	+	22.7869i	0.0848887	+	0.807662i
$797$	6.96695	−	21.4421i	0.246782	−	0.759517i	−0.748556	−	0.663071i	$-0.769253\pi$
$797$	6.96695	−	21.4421i	0.246782	−	0.759517i	0.995338	−	0.0964456i	$-0.0307474\pi$
$798$	−20.6457	−	6.80696i	−0.730851	−	0.240964i
$799$	−8.83731	+	6.42068i	−0.312642	+	0.227147i
$800$	25.8344	−	11.5022i	0.913384	−	0.406665i
$801$	2.63296	−	2.92419i	0.0930309	−	0.103321i
$802$	3.80929	+	6.59789i	0.134511	+	0.232980i
$803$	1.35458	−	4.09665i	0.0478022	−	0.144567i
$804$	−11.8558			−0.418120
$805$	−3.57539	+	16.4707i	−0.126016	+	0.580514i
$806$	23.4284	+	17.0217i	0.825229	+	0.599564i
$807$	−2.31357	−	22.0121i	−0.0814414	−	0.774863i
$808$	−6.74682	+	1.43408i	−0.237352	+	0.0504508i
$809$	−30.2609	+	6.43216i	−1.06392	+	0.226143i	−0.706436	−	0.707777i	$-0.749698\pi$
$809$	−30.2609	+	6.43216i	−1.06392	+	0.226143i	−0.357482	+	0.933920i	$0.616365\pi$
$810$	0.222513	+	2.11707i	0.00781832	+	0.0743863i
$811$	−42.6940	−	31.0190i	−1.49919	−	1.08923i	−0.970702	−	0.240286i	$-0.922759\pi$
$811$	−42.6940	−	31.0190i	−1.49919	−	1.08923i	−0.528489	−	0.848940i	$-0.677241\pi$
$812$	15.2141	−	70.0861i	0.533909	−	2.45954i
$813$	−20.9199			−0.733694
$814$	25.2605	+	0.130862i	0.885379	+	0.00458669i
$815$	11.5192	+	19.9519i	0.403502	+	0.698885i
$816$	−4.52387	+	5.02426i	−0.158367	+	0.175884i
$817$	−4.43497	+	1.97458i	−0.155160	+	0.0690817i
$818$	23.0082	−	16.7164i	0.804462	−	0.584476i
$819$	6.03477	+	1.98968i	0.210872	+	0.0695251i
$820$	−1.09853	+	3.38093i	−0.0383623	+	0.118067i
$821$	4.98384	+	47.4181i	0.173937	+	1.65490i	0.638692	+	0.769463i	$0.279476\pi$
$821$	4.98384	+	47.4181i	0.173937	+	1.65490i	−0.464755	+	0.885439i	$0.653858\pi$
$822$	−1.49881	+	14.2602i	−0.0522769	+	0.497381i
$823$	−6.46422	+	7.17924i	−0.225329	+	0.250253i	−0.845199	−	0.534451i	$-0.820518\pi$
$823$	−6.46422	+	7.17924i	−0.225329	+	0.250253i	0.619871	+	0.784704i	$0.287185\pi$
$824$	17.8562	−	30.9279i	0.622051	−	1.07742i
$825$	1.48514	−	13.4590i	0.0517058	−	0.468584i
$826$	61.6914	−	35.2630i	2.14652	−	1.22696i
$827$	−11.4548	−	35.2543i	−0.398323	−	1.22591i	−0.926344	−	0.376680i	$-0.877066\pi$
$827$	−11.4548	−	35.2543i	−0.398323	−	1.22591i	0.528021	−	0.849231i	$-0.322934\pi$
$828$	17.8638	−	7.95350i	0.620812	−	0.276403i
$829$	−22.1193	−	9.84814i	−0.768234	−	0.342040i	−0.0150821	−	0.999886i	$-0.504801\pi$
$829$	−22.1193	−	9.84814i	−0.768234	−	0.342040i	−0.753152	+	0.657846i	$0.771468\pi$
$830$	−23.5761	+	5.01126i	−0.818339	+	0.173943i
$831$	−8.34317	−	9.26603i	−0.289421	−	0.321435i
$832$	25.1080	−	18.2420i	0.870464	−	0.632429i
$833$	30.7686	+	22.7635i	1.06607	+	0.788709i
$834$	−5.87511	−	18.0817i	−0.203438	−	0.626119i
$835$	8.45038	−	14.6365i	0.292437	−	0.506516i
$836$	3.58215	+	35.8683i	0.123891	+	1.24053i
$837$	2.71252	+	4.69822i	0.0937584	+	0.162394i
$838$	4.33888	+	0.922258i	0.149884	+	0.0318589i
$839$	1.95127	+	1.41768i	0.0673653	+	0.0489438i	0.620958	−	0.783844i	$-0.286744\pi$
$839$	1.95127	+	1.41768i	0.0673653	+	0.0489438i	−0.553593	+	0.832787i	$0.686744\pi$
$840$	2.17415	−	4.82698i	0.0750153	−	0.166547i
$841$	17.3085	−	53.2699i	0.596843	−	1.83689i
$842$	−20.7213	−	23.0133i	−0.714103	−	0.793091i
$843$	20.5940	+	9.16902i	0.709293	+	0.315798i
$844$	−5.67690	+	54.0121i	−0.195407	+	1.85917i
$845$	−6.77503	−	1.44008i	−0.233068	−	0.0495402i
$846$	4.44039			0.152664
$847$	6.46819	−	28.3754i	0.222250	−	0.974990i
$848$	−10.2055			−0.350457
$849$	−5.37024	−	1.14148i	−0.184306	−	0.0391755i
$850$	5.18617	−	49.3431i	0.177884	−	1.69245i
$851$	20.8219	+	9.27051i	0.713766	+	0.317789i
$852$	−1.33807	−	1.48608i	−0.0458415	−	0.0509121i
$853$	13.3395	−	41.0549i	0.456737	−	1.40569i	−0.412346	−	0.911027i	$-0.635291\pi$
$853$	13.3395	−	41.0549i	0.456737	−	1.40569i	0.869083	−	0.494666i	$-0.164709\pi$
$854$	−36.0255	+	3.62912i	−1.23277	+	0.124186i
$855$	−2.86446	−	2.08115i	−0.0979626	−	0.0711740i
$856$	6.76526	+	1.43800i	0.231232	+	0.0491498i
$857$	6.06159	+	10.4990i	0.207060	+	0.358638i	0.950787	−	0.309845i	$-0.100277\pi$
$857$	6.06159	+	10.4990i	0.207060	+	0.358638i	−0.743727	+	0.668483i	$0.766944\pi$
$858$	−1.75936	−	17.6166i	−0.0600636	−	0.601422i
$859$	−17.5570	+	30.4096i	−0.599036	+	1.03756i	0.393928	+	0.919141i	$0.371116\pi$
$859$	−17.5570	+	30.4096i	−0.599036	+	1.03756i	−0.992964	+	0.118419i	$0.962217\pi$
$860$	−1.14266	−	3.51676i	−0.0389645	−	0.119921i
$861$	1.34540	+	3.05729i	0.0458509	+	0.104192i
$862$	−18.1712	+	13.2021i	−0.618913	+	0.449667i
$863$	17.3029	+	19.2168i	0.588998	+	0.654148i	0.961797	−	0.273764i	$-0.0882686\pi$
$863$	17.3029	+	19.2168i	0.588998	+	0.654148i	−0.372799	+	0.927912i	$0.621602\pi$
$864$	6.77527	−	1.44013i	0.230499	−	0.0489942i
$865$	9.50774	+	4.23312i	0.323273	+	0.143930i
$866$	−19.2808	+	8.58437i	−0.655188	+	0.291709i
$867$	3.98497	+	12.2645i	0.135337	+	0.416523i
$868$	0.182326	−	42.1979i	0.00618853	−	1.43229i
$869$	2.76150	−	25.0261i	0.0936776	−	0.848954i
$870$	9.81363	−	16.9977i	0.332713	−	0.576276i
$871$	−6.48061	+	7.19745i	−0.219587	+	0.243876i
$872$	−0.627516	+	5.97042i	−0.0212504	+	0.202184i
$873$	−0.802440	−	7.63470i	−0.0271585	−	0.258396i
$874$	−16.8878	+	51.9753i	−0.571238	+	1.75809i
$875$	−4.68790	−	22.5331i	−0.158480	−	0.761758i
$876$	−3.09431	+	2.24815i	−0.104547	+	0.0759579i
$877$	45.0891	−	20.0750i	1.52255	−	0.677884i	0.536436	−	0.843941i	$-0.319770\pi$
$877$	45.0891	−	20.0750i	1.52255	−	0.677884i	0.986116	+	0.166057i	$0.0531037\pi$
$878$	16.0716	−	17.8493i	0.542389	−	0.602385i
$879$	6.47192	+	11.2097i	0.218292	+	0.378093i
$880$	3.92776	+	0.0203477i	0.132405	+	0.000685920i
$881$	15.9623			0.537782			0.268891	−	0.963171i	$-0.413343\pi$
$881$	15.9623			0.537782			0.268891	+	0.963171i	$0.413343\pi$
$882$	−4.67972	−	14.8378i	−0.157574	−	0.499613i
$883$	40.7930	+	29.6379i	1.37279	+	0.997394i	0.997513	+	0.0704827i	$0.0224540\pi$
$883$	40.7930	+	29.6379i	1.37279	+	0.997394i	0.375282	+	0.926911i	$0.377546\pi$
$884$	−4.03553	−	38.3955i	−0.135730	−	1.29138i
$885$	11.3206	−	2.40626i	0.380537	−	0.0808856i
$886$	12.5226	−	2.66176i	0.420704	−	0.0894234i
$887$	−4.16521	−	39.6293i	−0.139854	−	1.33062i	−0.809140	−	0.587616i	$-0.800066\pi$
$887$	−4.16521	−	39.6293i	−0.139854	−	1.33062i	0.669286	−	0.743005i	$-0.266600\pi$
$888$	−5.79194	−	4.20809i	−0.194365	−	0.141214i
$889$	36.5117	+	33.1621i	1.22456	+	1.11222i
$890$	−8.37634			−0.280775
$891$	1.04122	−	3.14895i	0.0348822	−	0.105494i
$892$	22.7472	+	39.3993i	0.761632	+	1.31918i
$893$	−4.94192	+	5.48856i	−0.165375	+	0.183668i
$894$	44.1723	−	19.6668i	1.47734	−	0.657756i
$895$	−1.28904	+	0.936545i	−0.0430880	+	0.0313053i
$896$	−37.3579	−	12.3170i	−1.24804	−	0.411483i
$897$	4.93632	−	15.1924i	0.164819	−	0.507260i
$898$	0.573946	+	5.46073i	0.0191528	+	0.182227i
$899$	5.22848	−	49.7457i	0.174380	−	1.65911i
$900$	−8.03157	+	8.91996i	−0.267719	+	0.297332i
$901$	−22.5638	+	39.0816i	−0.751708	+	1.30200i
$902$	6.26300	−	6.88371i	0.208535	−	0.229202i
$903$	−3.00141	−	1.75020i	−0.0998806	−	0.0582429i
$904$	6.03960	+	18.5880i	0.200874	+	0.618227i
$905$	−5.77854	+	2.57277i	−0.192085	+	0.0855218i
$906$	−9.51962	−	4.23841i	−0.316268	−	0.140812i
$907$	14.5991	−	3.10313i	0.484754	−	0.103038i	0.0409492	−	0.999161i	$-0.486962\pi$
$907$	14.5991	−	3.10313i	0.484754	−	0.103038i	0.443804	+	0.896124i	$0.353628\pi$
$908$	15.3109	+	17.0045i	0.508110	+	0.564313i
$909$	−2.67100	+	1.94060i	−0.0885916	+	0.0643656i
$910$	−5.44833	−	12.3808i	−0.180610	−	0.410421i
$911$	−4.38632	−	13.4997i	−0.145325	−	0.447265i	0.851727	−	0.523985i	$-0.175555\pi$
$911$	−4.38632	−	13.4997i	−0.145325	−	0.447265i	−0.997053	+	0.0767201i	$0.975555\pi$
$912$	−2.28555	+	3.95870i	−0.0756823	+	0.131086i
$913$	36.6913	+	7.99786i	1.21430	+	0.264690i
$914$	−11.3723	−	19.6974i	−0.376163	−	0.651533i
$915$	−5.76838	−	1.22611i	−0.190697	−	0.0405339i
$916$	55.3726	+	40.2306i	1.82956	+	1.32926i
$917$	25.8933	+	35.9648i	0.855073	+	1.18766i
$918$	3.75533	−	11.5577i	0.123944	−	0.381462i
$919$	15.2583	+	16.9461i	0.503325	+	0.558999i	0.940244	−	0.340502i	$-0.110597\pi$
$919$	15.2583	+	16.9461i	0.503325	+	0.558999i	−0.436919	+	0.899501i	$0.643930\pi$
$920$	−12.1582	−	5.41317i	−0.400843	−	0.178467i
$921$	2.45707	−	23.3774i	0.0809632	−	0.770313i
$922$	68.6620	+	14.5946i	2.26126	+	0.480646i
$923$	−1.63359			−0.0537703
$924$	−19.3349	+	17.0794i	−0.636072	+	0.561871i
$925$	−13.9905			−0.460006
$926$	24.2456	+	5.15356i	0.796759	+	0.169356i
$927$	1.78680	−	17.0003i	0.0586862	−	0.558362i
$928$	−58.3433	−	25.9761i	−1.91521	−	0.852708i
$929$	−18.4951	−	20.5409i	−0.606806	−	0.673926i	0.358957	−	0.933354i	$-0.383133\pi$
$929$	−18.4951	−	20.5409i	−0.606806	−	0.673926i	−0.965762	+	0.259428i	$0.916466\pi$
$930$	3.56867	−	10.9832i	0.117021	−	0.360155i
$931$	23.5486	+	10.7293i	0.771773	+	0.351638i
$932$	−39.7125	−	28.8528i	−1.30083	−	0.945106i
$933$	22.1219	+	4.70215i	0.724238	+	0.153941i
$934$	−14.2013	−	24.5974i	−0.464681	−	0.804850i
$935$	8.76199	−	14.9963i	0.286548	−	0.490430i
$936$	−2.50881	+	4.34538i	−0.0820029	+	0.142033i
$937$	−6.89512	−	21.2210i	−0.225254	−	0.693259i	−0.998266	−	0.0588682i	$-0.981251\pi$
$937$	−6.89512	−	21.2210i	−0.225254	−	0.693259i	0.773012	−	0.634391i	$-0.218749\pi$
$938$	23.5727	+	2.58062i	0.769677	+	0.0842602i
$939$	24.0903	−	17.5026i	0.786157	−	0.571176i
$940$	−3.76419	−	4.18056i	−0.122774	−	0.136355i
$941$	32.7960	−	6.97101i	1.06912	−	0.227248i	0.360443	−	0.932781i	$-0.382626\pi$
$941$	32.7960	−	6.97101i	1.06912	−	0.227248i	0.708677	+	0.705533i	$0.249292\pi$
$942$	39.7421	+	17.6943i	1.29487	+	0.576512i
$943$	7.67111	−	3.41540i	0.249806	−	0.111221i
$944$	−4.61724	−	14.2104i	−0.150278	−	0.462509i
$945$	0.0109486	−	2.53398i	0.000356160	−	0.0824305i
$946$	−1.06174	+	9.62198i	−0.0345200	+	0.312838i
$947$	29.5345	−	51.1552i	0.959741	−	1.66232i	0.236615	−	0.971603i	$-0.423962\pi$
$947$	29.5345	−	51.1552i	0.959741	−	1.66232i	0.723126	−	0.690717i	$-0.242705\pi$
$948$	−14.9341	+	16.5860i	−0.485038	+	0.538689i
$949$	−0.326601	+	3.10740i	−0.0106019	+	0.100870i
$950$	−3.50646	−	33.3618i	−0.113765	−	1.08240i
$951$	−7.89534	+	24.2994i	−0.256024	+	0.787961i
$952$	−22.5469	+	20.1256i	−0.730749	+	0.652274i
$953$	−48.1693	+	34.9970i	−1.56036	+	1.13366i	−0.624638	+	0.780914i	$0.714754\pi$
$953$	−48.1693	+	34.9970i	−1.56036	+	1.13366i	−0.935717	+	0.352751i	$0.885246\pi$
$954$	16.7583	−	7.46128i	0.542571	−	0.241568i
$955$	−5.12668	+	5.69375i	−0.165895	+	0.184246i
$956$	−19.8021	−	34.2983i	−0.640447	−	1.10929i
$957$	−24.8324	+	17.8460i	−0.802716	+	0.576878i
$958$	4.77991			0.154432
$959$	3.62086	−	16.6801i	0.116924	−	0.538629i
$960$	−10.0127	−	7.27467i	−0.323159	−	0.234789i
$961$	0.164001	+	1.56037i	0.00529037	+	0.0503345i
$962$	−17.8927	+	3.80320i	−0.576882	+	0.122620i
$963$	3.23822	−	0.688305i	0.104350	−	0.0221803i
$964$	−7.49213	−	71.2828i	−0.241305	−	2.29587i
$965$	15.1081	+	10.9766i	0.486345	+	0.353351i
$966$	−37.2498	+	11.9255i	−1.19849	+	0.383697i
$967$	−20.4020			−0.656084			−0.328042	−	0.944663i	$-0.606389\pi$
$967$	−20.4020			−0.656084			−0.328042	+	0.944663i	$0.606389\pi$
$968$	20.8963	+	9.56427i	0.671633	+	0.307407i
$969$	10.1065	+	17.5050i	0.324667	+	0.562340i
$970$	−10.9348	+	12.1443i	−0.351095	+	0.389930i
$971$	47.8100	−	21.2864i	1.53430	−	0.683113i	0.546301	−	0.837589i	$-0.316036\pi$
$971$	47.8100	−	21.2864i	1.53430	−	0.683113i	0.987997	+	0.154476i	$0.0493689\pi$
$972$	−2.37849	+	1.72807i	−0.0762901	+	0.0554280i
$973$	4.60973	+	22.1574i	0.147781	+	0.710334i
$974$	−11.7549	+	36.1779i	−0.376651	+	1.15921i
$975$	1.02494	+	9.75168i	0.0328245	+	0.312304i
$976$	−0.795830	+	7.57181i	−0.0254739	+	0.242368i
$977$	28.8182	−	32.0059i	0.921977	−	1.02396i	−0.0776587	−	0.996980i	$-0.524744\pi$
$977$	28.8182	−	32.0059i	0.921977	−	1.02396i	0.999636	−	0.0269795i	$-0.00858890\pi$
$978$	−26.7318	+	46.3008i	−0.854787	+	1.48053i
$979$	11.8946	+	5.36983i	0.380154	+	0.171621i
$980$	−10.0025	+	16.9841i	−0.319517	+	0.542537i
$981$	0.887963	+	2.73287i	0.0283505	+	0.0872538i
$982$	−10.6494	+	4.74144i	−0.339837	+	0.151305i
$983$	−40.1636	−	17.8820i	−1.28102	−	0.570346i	−0.350490	−	0.936566i	$-0.613985\pi$
$983$	−40.1636	−	17.8820i	−1.28102	−	0.570346i	−0.930528	+	0.366220i	$0.880652\pi$
$984$	−2.57994	+	0.548383i	−0.0822454	+	0.0174818i
$985$	−7.44301	−	8.26630i	−0.237154	−	0.263386i
$986$	−90.6488	+	65.8602i	−2.88685	+	2.09742i
$987$	−5.25437	−	0.575221i	−0.167248	−	0.0183095i
$988$	−8.06625	−	24.8254i	−0.256622	−	0.789800i
$989$	−4.36722	+	7.56425i	−0.138870	+	0.240529i
$990$	−6.46461	+	2.83820i	−0.205459	+	0.0902038i
$991$	4.40261	+	7.62554i	0.139853	+	0.242233i	0.927441	−	0.373969i	$-0.122004\pi$
$991$	4.40261	+	7.62554i	0.139853	+	0.242233i	−0.787588	+	0.616203i	$0.788670\pi$
$992$	−36.7561	−	7.81275i	−1.16701	−	0.248055i
$993$	−11.9982	−	8.71722i	−0.380752	−	0.276633i
$994$	2.33701	+	3.24601i	0.0741253	+	0.102957i
$995$	2.30659	−	7.09894i	0.0731237	−	0.225052i
$996$	−22.2741	−	24.7379i	−0.705783	−	0.783851i
$997$	−34.2593	−	15.2532i	−1.08500	−	0.483075i	−0.215249	−	0.976559i	$-0.569056\pi$
$997$	−34.2593	−	15.2532i	−1.08500	−	0.483075i	−0.869755	+	0.493484i	$0.835723\pi$
$998$	8.08891	−	76.9609i	0.256050	−	2.43615i
$999$	−3.35192	−	0.712472i	−0.106050	−	0.0225416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.b.16.2	✓	64
3.2	odd	2		693.2.by.c.478.7		64
7.4	even	3	inner	231.2.y.b.214.7	yes	64
11.9	even	5	inner	231.2.y.b.163.7	yes	64
21.11	odd	6		693.2.by.c.676.2		64
33.20	odd	10		693.2.by.c.163.2		64
77.53	even	15	inner	231.2.y.b.130.2	yes	64
231.53	odd	30		693.2.by.c.361.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.16.2	✓	64	1.1	even	1	trivial
231.2.y.b.130.2	yes	64	77.53	even	15	inner
231.2.y.b.163.7	yes	64	11.9	even	5	inner
231.2.y.b.214.7	yes	64	7.4	even	3	inner
693.2.by.c.163.2		64	33.20	odd	10
693.2.by.c.361.7		64	231.53	odd	30
693.2.by.c.478.7		64	3.2	odd	2
693.2.by.c.676.2		64	21.11	odd	6

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.17404 - 0.462106i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(2.68580 + 1.19580i) q^{4} +(-0.640870 - 0.711758i) q^{5} +(0.686823 - 2.11382i) q^{6} +(-1.08656 + 2.41234i) q^{7} +(-1.69019 - 1.22800i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-2.17404 - 0.462106i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(2.68580 + 1.19580i) q^{4} +(-0.640870 - 0.711758i) q^{5} +(0.686823 - 2.11382i) q^{6} +(-1.08656 + 2.41234i) q^{7} +(-1.69019 - 1.22800i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(1.06437 + 1.84354i) q^{10} +(-0.329590 - 3.30021i) q^{11} +(-1.46999 + 2.54609i) q^{12} +(0.742167 + 2.28416i) q^{13} +(3.47697 - 4.74241i) q^{14} +(0.774848 - 0.562960i) q^{15} +(-0.827382 - 0.918900i) q^{16} +(-5.34821 + 1.13680i) q^{17} +(2.03045 + 0.904015i) q^{18} +(-3.37720 + 1.50363i) q^{19} +(-0.870131 - 2.67799i) q^{20} +(-2.28555 - 1.33276i) q^{21} +(-0.808505 + 7.32708i) q^{22} +(-3.32561 + 5.76013i) q^{23} +(1.39794 - 1.55257i) q^{24} +(0.426757 - 4.06032i) q^{25} +(-0.557977 - 5.30879i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-5.80294 + 5.17977i) q^{28} +(-7.45926 + 5.41947i) q^{29} +(-1.94469 + 0.865834i) q^{30} +(-3.63006 + 4.03159i) q^{31} +(3.46332 + 5.99864i) q^{32} +(3.31658 + 0.0171815i) q^{33} +12.1525 q^{34} +(2.41335 - 0.772632i) q^{35} +(-2.37849 - 1.72807i) q^{36} +(-0.358198 - 3.40803i) q^{37} +(8.03699 - 1.70831i) q^{38} +(-2.34922 + 0.499342i) q^{39} +(0.209157 + 1.98999i) q^{40} +(-1.02137 - 0.742071i) q^{41} +(4.35299 + 3.95364i) q^{42} +1.31321 q^{43} +(3.06116 - 9.25782i) q^{44} +(0.478883 + 0.829449i) q^{45} +(9.89178 - 10.9859i) q^{46} +(1.82511 - 0.812591i) q^{47} +(1.00035 - 0.726798i) q^{48} +(-4.63879 - 5.24229i) q^{49} +(-2.80408 + 8.63008i) q^{50} +(-0.571529 - 5.43774i) q^{51} +(-0.738070 + 7.02226i) q^{52} +(5.52267 - 6.13354i) q^{53} +(-1.11130 + 1.92483i) q^{54} +(-2.13773 + 2.34959i) q^{55} +(4.79883 - 2.74303i) q^{56} +(-1.14238 - 3.51587i) q^{57} +(18.7211 - 8.33516i) q^{58} +(11.0391 + 4.91494i) q^{59} +(2.75427 - 0.585439i) q^{60} +(-4.12004 - 4.57577i) q^{61} +(9.75490 - 7.08735i) q^{62} +(1.56437 - 2.13372i) q^{63} +(-3.99317 - 12.2897i) q^{64} +(1.15013 - 1.99209i) q^{65} +(-7.20242 - 1.56996i) q^{66} +(2.01630 + 3.49234i) q^{67} +(-15.7236 - 3.34215i) q^{68} +(-5.38095 - 3.90949i) q^{69} +(-5.60374 + 0.564508i) q^{70} +(-0.210187 + 0.646890i) q^{71} +(1.39794 + 1.55257i) q^{72} +(1.18848 + 0.529147i) q^{73} +(-0.796133 + 7.57470i) q^{74} +(3.99347 + 0.848838i) q^{75} -10.8685 q^{76} +(8.31935 + 2.79078i) q^{77} +5.33804 q^{78} +(7.42557 + 1.57835i) q^{79} +(-0.123791 + 1.17779i) q^{80} +(0.913545 + 0.406737i) q^{81} +(1.87759 + 2.08527i) q^{82} +(-3.49888 + 10.7684i) q^{83} +(-4.54482 - 6.31259i) q^{84} +(4.23663 + 3.07809i) q^{85} +(-2.85496 - 0.606841i) q^{86} +(-4.61008 - 7.98489i) q^{87} +(-3.49557 + 5.98271i) q^{88} +(-1.96745 + 3.40772i) q^{89} +(-0.657815 - 2.02455i) q^{90} +(-6.31657 - 0.691504i) q^{91} +(-15.8199 + 11.4938i) q^{92} +(-3.63006 - 4.03159i) q^{93} +(-4.34336 + 0.923209i) q^{94} +(3.23456 + 1.44012i) q^{95} +(-6.32780 + 2.81732i) q^{96} +(2.37225 + 7.30103i) q^{97} +(7.66240 + 13.5405i) q^{98} +(-0.363764 + 3.29662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Introduction

L-functions

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