LMFDB - Embedded newform 483.2.q.a.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.1
Root			$-0.841254 - 0.540641i$ of defining polynomial
Character	$\chi$	$=$	483.85
Dual form			483.2.q.a.358.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64589 - 1.89945i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.614354 - 4.27292i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.357685 - 2.48775i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-4.89867 - 3.14818i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(1.64589 - 1.89945i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.614354 - 4.27292i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.357685 - 2.48775i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-4.89867 - 3.14818i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-2.41153 - 0.708089i) q^{10} +(0.0756100 + 0.0872586i) q^{11} +(-2.82694 - 3.26247i) q^{12} +(1.24690 + 0.366124i) q^{13} +(-1.04408 + 2.28621i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(-5.75848 + 1.69084i) q^{16} +(-0.556939 + 3.87359i) q^{17} +(-1.04408 - 2.28621i) q^{18} +(0.195368 + 1.35881i) q^{19} +(-3.63158 + 2.33387i) q^{20} +(-0.654861 + 0.755750i) q^{21} +0.290189 q^{22} +(4.67421 + 1.07322i) q^{23} -5.82306 q^{24} +(2.61944 - 3.02300i) q^{25} +(2.74769 - 1.76584i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(1.79329 + 3.92676i) q^{28} +(0.291772 - 2.02932i) q^{29} +(-2.41153 + 0.708089i) q^{30} +(-4.96496 - 3.19079i) q^{31} +(-1.42815 + 3.12721i) q^{32} +(0.110783 + 0.0325288i) q^{33} +(6.44105 + 7.43337i) q^{34} +(0.654861 + 0.755750i) q^{35} +(-4.14200 - 1.21620i) q^{36} +(0.215215 - 0.471255i) q^{37} +(2.90255 + 1.86536i) q^{38} +(1.24690 - 0.366124i) q^{39} +(-0.828708 + 5.76379i) q^{40} +(3.90875 + 8.55897i) q^{41} +(0.357685 + 2.48775i) q^{42} +(-5.54386 + 3.56282i) q^{43} +(0.326398 - 0.376684i) q^{44} -1.00000 q^{45} +(9.73174 - 7.11204i) q^{46} +5.90055 q^{47} +(-3.93020 + 4.53569i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-1.43074 - 9.95102i) q^{50} +(1.62570 + 3.55978i) q^{51} +(0.798379 - 5.55285i) q^{52} +(-4.20482 + 1.23465i) q^{53} +(-2.11435 - 1.35881i) q^{54} +(0.0479637 - 0.105026i) q^{55} +(5.58718 + 1.64055i) q^{56} +(0.898983 + 1.03748i) q^{57} +(-3.37437 - 3.89423i) q^{58} +(3.46155 + 1.01640i) q^{59} +(-1.79329 + 3.92676i) q^{60} +(4.23338 + 2.72063i) q^{61} +(-14.2325 + 4.17904i) q^{62} +(-0.142315 + 0.989821i) q^{63} +(-1.39688 - 3.05874i) q^{64} +(-0.184944 - 1.28632i) q^{65} +(0.244123 - 0.156888i) q^{66} +(9.18262 - 10.5973i) q^{67} +16.8937 q^{68} +(4.51242 - 1.62422i) q^{69} +2.51334 q^{70} +(-6.24539 + 7.20756i) q^{71} +(-4.89867 + 3.14818i) q^{72} +(-0.0848998 - 0.590491i) q^{73} +(-0.540908 - 1.18442i) q^{74} +(0.569259 - 3.95929i) q^{75} +(5.68608 - 1.66958i) q^{76} +(-0.0971309 - 0.0624222i) q^{77} +(1.35682 - 2.97103i) q^{78} +(-9.06631 - 2.66211i) q^{79} +(3.93020 + 4.53569i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(22.6907 + 6.66260i) q^{82} +(-5.33741 + 11.6873i) q^{83} +(3.63158 + 2.33387i) q^{84} +(3.75491 - 1.10254i) q^{85} +(-2.35715 + 16.3943i) q^{86} +(-0.851677 - 1.86491i) q^{87} +(-0.0956823 - 0.665485i) q^{88} +(-4.28379 + 2.75302i) q^{89} +(-1.64589 + 1.89945i) q^{90} -1.29954 q^{91} +(1.71417 - 20.6319i) q^{92} -5.90186 q^{93} +(9.71162 - 11.2078i) q^{94} +(1.15486 - 0.742184i) q^{95} +(0.489262 + 3.40289i) q^{96} +(3.21109 + 7.03130i) q^{97} +(0.357685 - 2.48775i) q^{98} +(0.110783 - 0.0325288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - q^{3} + 8 q^{4} + q^{5} + 4 q^{6} - q^{7} - 7 q^{8} - q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - q^3 + 8 * q^4 + q^5 + 4 * q^6 - q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} - q^{3} + 8 q^{4} + q^{5} + 4 q^{6} - q^{7} - 7 q^{8} - q^{9} - 4 q^{10} - q^{11} - 3 q^{12} + 15 q^{13} - 7 q^{14} + q^{15} - 10 q^{16} - 24 q^{17} - 7 q^{18} + 5 q^{19} - 8 q^{20} - q^{21} + 26 q^{22} + 21 q^{23} - 18 q^{24} + 4 q^{25} + 6 q^{26} - q^{27} - 3 q^{28} - 22 q^{29} - 4 q^{30} - 8 q^{31} + 10 q^{32} - q^{33} + 8 q^{34} + q^{35} - 14 q^{36} - 2 q^{37} + 2 q^{38} + 15 q^{39} - 4 q^{40} + 7 q^{41} + 4 q^{42} + q^{43} + 19 q^{44} - 10 q^{45} + 15 q^{46} - 6 q^{47} + q^{48} - q^{49} - 16 q^{50} + 20 q^{51} - 21 q^{52} - q^{53} - 7 q^{54} + 12 q^{55} + 4 q^{56} - 6 q^{57} + 22 q^{58} + 10 q^{59} + 3 q^{60} + 5 q^{61} - 34 q^{62} - q^{63} + 13 q^{64} - 4 q^{65} - 7 q^{66} + 29 q^{67} - 28 q^{68} - q^{69} - 4 q^{70} + 22 q^{71} - 7 q^{72} - 33 q^{73} - 36 q^{74} + 4 q^{75} + 26 q^{76} - q^{77} + 28 q^{78} + 27 q^{79} - q^{80} - q^{81} + 38 q^{82} + 25 q^{83} + 8 q^{84} + 2 q^{85} + 18 q^{86} - 7 q^{88} - 38 q^{89} - 4 q^{90} - 18 q^{91} + 41 q^{92} - 30 q^{93} - 42 q^{94} + 6 q^{95} - 23 q^{96} - q^{97} + 4 q^{98} - q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - q^3 + 8 * q^4 + q^5 + 4 * q^6 - q^7 - 7 * q^8 - q^9 - 4 * q^10 - q^11 - 3 * q^12 + 15 * q^13 - 7 * q^14 + q^15 - 10 * q^16 - 24 * q^17 - 7 * q^18 + 5 * q^19 - 8 * q^20 - q^21 + 26 * q^22 + 21 * q^23 - 18 * q^24 + 4 * q^25 + 6 * q^26 - q^27 - 3 * q^28 - 22 * q^29 - 4 * q^30 - 8 * q^31 + 10 * q^32 - q^33 + 8 * q^34 + q^35 - 14 * q^36 - 2 * q^37 + 2 * q^38 + 15 * q^39 - 4 * q^40 + 7 * q^41 + 4 * q^42 + q^43 + 19 * q^44 - 10 * q^45 + 15 * q^46 - 6 * q^47 + q^48 - q^49 - 16 * q^50 + 20 * q^51 - 21 * q^52 - q^53 - 7 * q^54 + 12 * q^55 + 4 * q^56 - 6 * q^57 + 22 * q^58 + 10 * q^59 + 3 * q^60 + 5 * q^61 - 34 * q^62 - q^63 + 13 * q^64 - 4 * q^65 - 7 * q^66 + 29 * q^67 - 28 * q^68 - q^69 - 4 * q^70 + 22 * q^71 - 7 * q^72 - 33 * q^73 - 36 * q^74 + 4 * q^75 + 26 * q^76 - q^77 + 28 * q^78 + 27 * q^79 - q^80 - q^81 + 38 * q^82 + 25 * q^83 + 8 * q^84 + 2 * q^85 + 18 * q^86 - 7 * q^88 - 38 * q^89 - 4 * q^90 - 18 * q^91 + 41 * q^92 - 30 * q^93 - 42 * q^94 + 6 * q^95 - 23 * q^96 - q^97 + 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

Coefficient data

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

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

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

$2$	1.64589	−	1.89945i	1.16382	−	1.34312i	0.235257	−	0.971933i	$-0.424407\pi$
$2$	1.64589	−	1.89945i	1.16382	−	1.34312i	0.928560	−	0.371183i	$-0.121048\pi$
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	−0.614354	−	4.27292i	−0.307177	−	2.13646i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i	0.793710	−	0.608296i	$-0.208147\pi$
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i	−0.979489	+	0.201497i	$0.935420\pi$
$6$	0.357685	−	2.48775i	0.146024	−	1.01562i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$8$	−4.89867	−	3.14818i	−1.73194	−	1.11305i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−2.41153	−	0.708089i	−0.762593	−	0.223917i
$11$	0.0756100	+	0.0872586i	0.0227973	+	0.0263095i	0.767034	−	0.641607i	$-0.221732\pi$
$11$	0.0756100	+	0.0872586i	0.0227973	+	0.0263095i	−0.744236	+	0.667916i	$0.767186\pi$
$12$	−2.82694	−	3.26247i	−0.816069	−	0.941793i
$13$	1.24690	+	0.366124i	0.345828	+	0.101544i	0.450034	−	0.893011i	$-0.351412\pi$
$13$	1.24690	+	0.366124i	0.345828	+	0.101544i	−0.104206	+	0.994556i	$0.533230\pi$
$14$	−1.04408	+	2.28621i	−0.279042	+	0.611016i
$15$	−0.841254	−	0.540641i	−0.217211	−	0.139593i
$16$	−5.75848	+	1.69084i	−1.43962	+	0.422710i
$17$	−0.556939	+	3.87359i	−0.135077	+	0.939484i	0.803718	+	0.595010i	$0.202852\pi$
$17$	−0.556939	+	3.87359i	−0.135077	+	0.939484i	−0.938796	+	0.344474i	$0.888057\pi$
$18$	−1.04408	−	2.28621i	−0.246092	−	0.538865i
$19$	0.195368	+	1.35881i	0.0448204	+	0.311733i	0.999883	+	0.0153272i	$0.00487899\pi$
$19$	0.195368	+	1.35881i	0.0448204	+	0.311733i	−0.955062	+	0.296406i	$0.904212\pi$
$20$	−3.63158	+	2.33387i	−0.812045	+	0.521870i
$21$	−0.654861	+	0.755750i	−0.142902	+	0.164918i
$22$	0.290189			0.0618685
$23$	4.67421	+	1.07322i	0.974639	+	0.223782i
$23$	4.67421	+	1.07322i	0.974639	+	0.223782i
$24$	−5.82306			−1.18863
$25$	2.61944	−	3.02300i	0.523889	−	0.604600i
$26$	2.74769	−	1.76584i	0.538867	−	0.346309i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	1.79329	+	3.92676i	0.338900	+	0.742087i
$29$	0.291772	−	2.02932i	0.0541806	−	0.376834i	−0.944633	−	0.328130i	$-0.893582\pi$
$29$	0.291772	−	2.02932i	0.0541806	−	0.376834i	0.998813	−	0.0487046i	$-0.0155093\pi$
$30$	−2.41153	+	0.708089i	−0.440283	+	0.129279i
$31$	−4.96496	−	3.19079i	−0.891733	−	0.573082i	0.0125945	−	0.999921i	$-0.495991\pi$
$31$	−4.96496	−	3.19079i	−0.891733	−	0.573082i	−0.904328	+	0.426838i	$0.859627\pi$
$32$	−1.42815	+	3.12721i	−0.252463	+	0.552817i
$33$	0.110783	+	0.0325288i	0.0192848	+	0.00566253i
$34$	6.44105	+	7.43337i	1.10463	+	1.27481i
$35$	0.654861	+	0.755750i	0.110692	+	0.127745i
$36$	−4.14200	−	1.21620i	−0.690333	−	0.202700i
$37$	0.215215	−	0.471255i	0.0353811	−	0.0774738i	−0.891116	−	0.453775i	$-0.850077\pi$
$37$	0.215215	−	0.471255i	0.0353811	−	0.0774738i	0.926497	+	0.376301i	$0.122804\pi$
$38$	2.90255	+	1.86536i	0.470856	+	0.302601i
$39$	1.24690	−	0.366124i	0.199664	−	0.0586267i
$40$	−0.828708	+	5.76379i	−0.131030	+	0.911335i
$41$	3.90875	+	8.55897i	0.610444	+	1.33669i	0.922270	+	0.386547i	$0.126332\pi$
$41$	3.90875	+	8.55897i	0.610444	+	1.33669i	−0.311826	+	0.950139i	$0.600940\pi$
$42$	0.357685	+	2.48775i	0.0551920	+	0.383869i
$43$	−5.54386	+	3.56282i	−0.845431	+	0.543325i	−0.890147	−	0.455674i	$-0.849398\pi$
$43$	−5.54386	+	3.56282i	−0.845431	+	0.543325i	0.0447157	+	0.999000i	$0.485762\pi$
$44$	0.326398	−	0.376684i	0.0492064	−	0.0567872i
$45$	−1.00000			−0.149071
$46$	9.73174	−	7.11204i	1.43487	−	1.04861i
$47$	5.90055			0.860683			0.430342	−	0.902666i	$-0.358393\pi$
$47$	5.90055			0.860683			0.430342	+	0.902666i	$0.358393\pi$
$48$	−3.93020	+	4.53569i	−0.567276	+	0.654671i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	−1.43074	−	9.95102i	−0.202337	−	1.40729i
$51$	1.62570	+	3.55978i	0.227643	+	0.498469i
$52$	0.798379	−	5.55285i	0.110715	−	0.770042i
$53$	−4.20482	+	1.23465i	−0.577576	+	0.169592i	−0.557457	−	0.830206i	$-0.688223\pi$
$53$	−4.20482	+	1.23465i	−0.577576	+	0.169592i	−0.0201194	+	0.999798i	$0.506405\pi$
$54$	−2.11435	−	1.35881i	−0.287727	−	0.184911i
$55$	0.0479637	−	0.105026i	0.00646742	−	0.0141617i
$56$	5.58718	+	1.64055i	0.746619	+	0.219227i
$57$	0.898983	+	1.03748i	0.119073	+	0.137418i
$58$	−3.37437	−	3.89423i	−0.443076	−	0.511337i
$59$	3.46155	+	1.01640i	0.450655	+	0.132324i	0.499181	−	0.866498i	$-0.333634\pi$
$59$	3.46155	+	1.01640i	0.450655	+	0.132324i	−0.0485262	+	0.998822i	$0.515452\pi$
$60$	−1.79329	+	3.92676i	−0.231513	+	0.506942i
$61$	4.23338	+	2.72063i	0.542029	+	0.348341i	0.782832	−	0.622233i	$-0.213774\pi$
$61$	4.23338	+	2.72063i	0.542029	+	0.348341i	−0.240803	+	0.970574i	$0.577411\pi$
$62$	−14.2325	+	4.17904i	−1.80753	+	0.530739i
$63$	−0.142315	+	0.989821i	−0.0179300	+	0.124706i
$64$	−1.39688	−	3.05874i	−0.174610	−	0.382342i
$65$	−0.184944	−	1.28632i	−0.0229395	−	0.159548i
$66$	0.244123	−	0.156888i	0.0300494	−	0.0193116i
$67$	9.18262	−	10.5973i	1.12184	−	1.29467i	0.170897	−	0.985289i	$-0.445334\pi$
$67$	9.18262	−	10.5973i	1.12184	−	1.29467i	0.950939	−	0.309378i	$-0.100121\pi$
$68$	16.8937			2.04867
$69$	4.51242	−	1.62422i	0.543231	−	0.195533i
$70$	2.51334			0.300401
$71$	−6.24539	+	7.20756i	−0.741191	+	0.855381i	−0.993684	−	0.112218i	$-0.964204\pi$
$71$	−6.24539	+	7.20756i	−0.741191	+	0.855381i	0.252492	+	0.967599i	$0.418750\pi$
$72$	−4.89867	+	3.14818i	−0.577314	+	0.371017i
$73$	−0.0848998	−	0.590491i	−0.00993677	−	0.0691117i	0.984250	−	0.176784i	$-0.0565694\pi$
$73$	−0.0848998	−	0.590491i	−0.00993677	−	0.0691117i	−0.994186	+	0.107672i	$0.965660\pi$
$74$	−0.540908	−	1.18442i	−0.0628792	−	0.137686i
$75$	0.569259	−	3.95929i	0.0657324	−	0.457179i
$76$	5.68608	−	1.66958i	0.652238	−	0.191514i
$77$	−0.0971309	−	0.0624222i	−0.0110691	−	0.00711367i
$78$	1.35682	−	2.97103i	0.153630	−	0.336403i
$79$	−9.06631	−	2.66211i	−1.02004	−	0.299511i	−0.271385	−	0.962471i	$-0.587482\pi$
$79$	−9.06631	−	2.66211i	−1.02004	−	0.299511i	−0.748655	+	0.662960i	$0.769300\pi$
$80$	3.93020	+	4.53569i	0.439410	+	0.507106i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	22.6907	+	6.66260i	2.50577	+	0.735761i
$83$	−5.33741	+	11.6873i	−0.585857	+	1.28285i	0.352056	+	0.935979i	$0.385483\pi$
$83$	−5.33741	+	11.6873i	−0.585857	+	1.28285i	−0.937913	+	0.346869i	$0.887245\pi$
$84$	3.63158	+	2.33387i	0.396237	+	0.254646i
$85$	3.75491	−	1.10254i	0.407277	−	0.119587i
$86$	−2.35715	+	16.3943i	−0.254177	+	1.76784i
$87$	−0.851677	−	1.86491i	−0.0913094	−	0.199940i
$88$	−0.0956823	−	0.665485i	−0.0101998	−	0.0709410i
$89$	−4.28379	+	2.75302i	−0.454080	+	0.291820i	−0.747619	−	0.664127i	$-0.768803\pi$
$89$	−4.28379	+	2.75302i	−0.454080	+	0.291820i	0.293539	+	0.955947i	$0.405167\pi$
$90$	−1.64589	+	1.89945i	−0.173492	+	0.200220i
$91$	−1.29954			−0.136229
$92$	1.71417	−	20.6319i	0.178714	−	2.15102i
$93$	−5.90186			−0.611994
$94$	9.71162	−	11.2078i	1.00168	−	1.15600i
$95$	1.15486	−	0.742184i	0.118486	−	0.0761465i
$96$	0.489262	+	3.40289i	0.0499351	+	0.347306i
$97$	3.21109	+	7.03130i	0.326037	+	0.713921i	0.999684	−	0.0251321i	$-0.00800064\pi$
$97$	3.21109	+	7.03130i	0.326037	+	0.713921i	−0.673647	+	0.739053i	$0.735273\pi$
$98$	0.357685	−	2.48775i	0.0361317	−	0.251301i
$99$	0.110783	−	0.0325288i	0.0111341	−	0.00326926i
$100$	−14.5263	−	9.33549i	−1.45263	−	0.933549i
$101$	−3.42316	+	7.49569i	−0.340618	+	0.745849i	−0.999982	−	0.00597482i	$-0.998098\pi$
$101$	−3.42316	+	7.49569i	−0.340618	+	0.745849i	0.659365	+	0.751823i	$0.270825\pi$
$102$	9.43734	+	2.77105i	0.934436	+	0.274375i
$103$	4.73006	+	5.45879i	0.466067	+	0.537870i	0.939313	−	0.343060i	$-0.111463\pi$
$103$	4.73006	+	5.45879i	0.466067	+	0.537870i	−0.473246	+	0.880930i	$0.656918\pi$
$104$	−4.95554	−	5.71900i	−0.485930	−	0.560794i
$105$	0.959493	+	0.281733i	0.0936369	+	0.0274943i
$106$	−4.57550	+	10.0189i	−0.444412	+	0.973126i
$107$	−5.16323	−	3.31821i	−0.499149	−	0.320783i	0.266727	−	0.963772i	$-0.414058\pi$
$107$	−5.16323	−	3.31821i	−0.499149	−	0.320783i	−0.765876	+	0.642989i	$0.777694\pi$
$108$	−4.14200	+	1.21620i	−0.398564	+	0.117029i
$109$	0.827474	−	5.75521i	0.0792576	−	0.551249i	−0.911043	−	0.412310i	$-0.864722\pi$
$109$	0.827474	−	5.75521i	0.0792576	−	0.551249i	0.990301	−	0.138938i	$-0.0443690\pi$
$110$	−0.120549	−	0.263965i	−0.0114939	−	0.0251681i
$111$	−0.0737293	−	0.512799i	−0.00699808	−	0.0486727i
$112$	5.04885	−	3.24470i	0.477072	−	0.306595i
$113$	−5.34625	+	6.16991i	−0.502933	+	0.580416i	−0.949275	−	0.314447i	$-0.898181\pi$
$113$	−5.34625	+	6.16991i	−0.502933	+	0.580416i	0.446342	+	0.894862i	$0.352727\pi$
$114$	3.45027			0.323148
$115$	−0.965501	−	4.69764i	−0.0900334	−	0.438057i
$116$	−8.85036			−0.821736
$117$	0.851020	−	0.982129i	0.0786768	−	0.0907979i
$118$	7.62792	−	4.90216i	0.702207	−	0.451281i
$119$	−0.556939	−	3.87359i	−0.0510545	−	0.355092i
$120$	2.41899	+	5.29684i	0.220822	+	0.483533i
$121$	1.56357	−	10.8748i	0.142142	−	0.988622i
$122$	12.1354	−	3.56327i	1.09869	−	0.322603i
$123$	7.91558	+	5.08703i	0.713724	+	0.458682i
$124$	−10.5837	+	23.1752i	−0.950449	+	2.08119i
$125$	−8.63544	−	2.53559i	−0.772377	−	0.226790i
$126$	1.64589	+	1.89945i	0.146627	+	0.169217i
$127$	1.70873	+	1.97198i	0.151625	+	0.174985i	0.826481	−	0.562965i	$-0.190340\pi$
$127$	1.70873	+	1.97198i	0.151625	+	0.174985i	−0.674856	+	0.737950i	$0.735794\pi$
$128$	−14.7063	−	4.31815i	−1.29986	−	0.381674i
$129$	−2.73758	+	5.99447i	−0.241031	+	0.527784i
$130$	−2.74769	−	1.76584i	−0.240989	−	0.154874i
$131$	−17.0443	+	5.00465i	−1.48917	+	0.437259i	−0.922275	−	0.386534i	$-0.873672\pi$
$131$	−17.0443	+	5.00465i	−1.48917	+	0.437259i	−0.566891	+	0.823793i	$0.691854\pi$
$132$	0.0709331	−	0.493351i	0.00617393	−	0.0429407i
$133$	−0.570276	−	1.24873i	−0.0494492	−	0.108279i
$134$	−5.01555	−	34.8839i	−0.433278	−	3.01351i
$135$	−0.841254	+	0.540641i	−0.0724036	+	0.0465310i
$136$	14.9230	−	17.2221i	1.27964	−	1.47678i
$137$	17.5508			1.49946			0.749732	−	0.661742i	$-0.230183\pi$
$137$	17.5508			1.49946			0.749732	+	0.661742i	$0.230183\pi$
$138$	4.34180	−	11.2444i	0.369599	−	0.957187i
$139$	−3.89067			−0.330002			−0.165001	−	0.986293i	$-0.552763\pi$
$139$	−3.89067			−0.330002			−0.165001	+	0.986293i	$0.552763\pi$
$140$	2.82694	−	3.26247i	0.238920	−	0.275729i
$141$	4.96386	−	3.19008i	0.418032	−	0.268653i
$142$	3.41123	+	23.7257i	0.286264	+	1.99101i
$143$	0.0623309	+	0.136486i	0.00521237	+	0.0114135i
$144$	−0.854114	+	5.94049i	−0.0711762	+	0.495041i
$145$	−1.96714	+	0.577603i	−0.163362	+	0.0479674i
$146$	−1.26135	−	0.810618i	−0.104390	−	0.0670872i
$147$	0.415415	−	0.909632i	0.0342629	−	0.0750252i
$148$	−2.14585	−	0.630080i	−0.176388	−	0.0517922i
$149$	9.95176	+	11.4849i	0.815280	+	0.940883i	0.999114	−	0.0420740i	$-0.0133965\pi$
$149$	9.95176	+	11.4849i	0.815280	+	0.940883i	−0.183835	+	0.982957i	$0.558851\pi$
$150$	−6.58354	−	7.59781i	−0.537544	−	0.620359i
$151$	−2.75686	−	0.809486i	−0.224350	−	0.0658750i	0.167626	−	0.985851i	$-0.446390\pi$
$151$	−2.75686	−	0.809486i	−0.224350	−	0.0658750i	−0.391975	+	0.919976i	$0.628208\pi$
$152$	3.32075	−	7.27143i	0.269348	−	0.589791i
$153$	3.29218	+	2.11576i	0.266157	+	0.171049i
$154$	−0.278434	+	0.0817557i	−0.0224369	+	0.00658806i
$155$	−0.839922	+	5.84179i	−0.0674642	+	0.469224i
$156$	−2.33046	−	5.10299i	−0.186586	−	0.408566i
$157$	0.0117213	+	0.0815234i	0.000935461	+	0.00650628i	0.990284	−	0.139061i	$-0.0444084\pi$
$157$	0.0117213	+	0.0815234i	0.000935461	+	0.00650628i	−0.989348	+	0.145567i	$0.953499\pi$
$158$	−19.9787	+	12.8395i	−1.58942	+	1.02146i
$159$	−2.86982	+	3.31195i	−0.227591	+	0.262655i
$160$	3.43788			0.271788
$161$	−4.78723	+	0.287130i	−0.377286	+	0.0226290i
$162$	−2.51334			−0.197466
$163$	−0.152551	+	0.176054i	−0.0119487	+	0.0137896i	−0.761692	−	0.647939i	$-0.775631\pi$
$163$	−0.152551	+	0.176054i	−0.0119487	+	0.0137896i	0.749744	+	0.661728i	$0.230177\pi$
$164$	34.1705	−	21.9600i	2.66826	−	1.71479i
$165$	−0.0164316	−	0.114284i	−0.00127920	−	0.00889704i
$166$	13.4147	+	29.3741i	1.04118	+	2.27987i
$167$	3.59886	−	25.0306i	0.278488	−	1.93693i	−0.0652710	−	0.997868i	$-0.520791\pi$
$167$	3.59886	−	25.0306i	0.278488	−	1.93693i	0.343759	−	0.939058i	$-0.388300\pi$
$168$	5.58718	−	1.64055i	0.431061	−	0.126571i
$169$	−9.51558	−	6.11529i	−0.731967	−	0.470407i
$170$	4.08592	−	8.94692i	0.313376	−	0.686198i
$171$	1.31718	+	0.386758i	0.100727	+	0.0295762i
$172$	18.6296	+	21.4997i	1.42049	+	1.63933i
$173$	−0.859268	−	0.991648i	−0.0653289	−	0.0753936i	0.722144	−	0.691742i	$-0.243157\pi$
$173$	−0.859268	−	0.991648i	−0.0653289	−	0.0753936i	−0.787473	+	0.616349i	$0.788611\pi$
$174$	−4.94408	−	1.45171i	−0.374810	−	0.110054i
$175$	−1.66166	+	3.63853i	−0.125610	+	0.275047i
$176$	−0.582939	−	0.374632i	−0.0439407	−	0.0282390i
$177$	3.46155	−	1.01640i	0.260186	−	0.0763974i
$178$	−1.82138	+	12.6680i	−0.136519	+	0.949507i
$179$	−1.39145	−	3.04684i	−0.104002	−	0.227732i	0.850476	−	0.526013i	$-0.176314\pi$
$179$	−1.39145	−	3.04684i	−0.104002	−	0.227732i	−0.954478	+	0.298282i	$0.903587\pi$
$180$	0.614354	+	4.27292i	0.0457912	+	0.318485i
$181$	12.1814	−	7.82850i	0.905435	−	0.581888i	−0.00296228	−	0.999996i	$-0.500943\pi$
$181$	12.1814	−	7.82850i	0.905435	−	0.581888i	0.908397	+	0.418108i	$0.137307\pi$
$182$	−2.13890	+	2.46842i	−0.158546	+	0.182972i
$183$	5.03223			0.371993
$184$	−19.5187	−	19.9726i	−1.43894	−	1.47240i
$185$	−0.518072			−0.0380894
$186$	−9.71379	+	11.2103i	−0.712250	+	0.821980i
$187$	−0.380115	+	0.244285i	−0.0277967	+	0.0178639i
$188$	−3.62502	−	25.2126i	−0.264382	−	1.83882i
$189$	0.415415	+	0.909632i	0.0302170	+	0.0661660i
$190$	0.491025	−	3.41515i	0.0356227	−	0.247761i
$191$	9.03520	−	2.65297i	0.653764	−	0.191962i	0.0620032	−	0.998076i	$-0.480251\pi$
$191$	9.03520	−	2.65297i	0.653764	−	0.191962i	0.591761	+	0.806113i	$0.298433\pi$
$192$	−2.82881	−	1.81796i	−0.204151	−	0.131200i
$193$	−6.01797	+	13.1775i	−0.433183	+	0.948538i	0.559617	+	0.828752i	$0.310948\pi$
$193$	−6.01797	+	13.1775i	−0.433183	+	0.948538i	−0.992800	+	0.119787i	$0.961779\pi$
$194$	18.6407	+	5.47341i	1.33833	+	0.392968i
$195$	−0.851020	−	0.982129i	−0.0609428	−	0.0703317i
$196$	−2.82694	−	3.26247i	−0.201925	−	0.233033i
$197$	−21.6347	−	6.35252i	−1.54141	−	0.452599i	−0.602890	−	0.797825i	$-0.705984\pi$
$197$	−21.6347	−	6.35252i	−1.54141	−	0.452599i	−0.938520	+	0.345226i	$0.887802\pi$
$198$	0.120549	−	0.263965i	0.00856704	−	0.0187592i
$199$	0.286448	+	0.184089i	0.0203057	+	0.0130497i	0.550754	−	0.834667i	$-0.314340\pi$
$199$	0.286448	+	0.184089i	0.0203057	+	0.0130497i	−0.530449	+	0.847717i	$0.677976\pi$
$200$	−22.3487	+	6.56218i	−1.58029	+	0.464016i
$201$	1.99557	−	13.8795i	0.140757	−	0.978986i
$202$	8.60357	+	18.8392i	0.605345	+	1.32552i
$203$	0.291772	+	2.02932i	0.0204783	+	0.142430i
$204$	14.2119	−	9.13344i	0.995033	−	0.639469i
$205$	6.16176	−	7.11105i	0.430356	−	0.496657i
$206$	18.1539			1.26484
$207$	2.91797	−	3.80598i	0.202813	−	0.264534i
$208$	−7.79931			−0.540785
$209$	−0.103796	+	0.119787i	−0.00717974	+	0.00828587i
$210$	2.11435	−	1.35881i	0.145904	−	0.0937670i
$211$	3.31980	+	23.0897i	0.228545	+	1.58956i	0.704246	+	0.709956i	$0.251285\pi$
$211$	3.31980	+	23.0897i	0.228545	+	1.58956i	−0.475701	+	0.879607i	$0.657806\pi$
$212$	7.85880	+	17.2084i	0.539744	+	1.18188i
$213$	−1.35725	+	9.43990i	−0.0929974	+	0.646811i
$214$	−14.8009	+	4.34593i	−1.01177	+	0.297082i
$215$	5.54386	+	3.56282i	0.378088	+	0.242983i
$216$	−2.41899	+	5.29684i	−0.164591	+	0.360404i
$217$	5.66279	+	1.66275i	0.384415	+	0.112875i
$218$	−9.56982	−	11.0442i	−0.648150	−	0.748005i
$219$	−0.390666	−	0.450852i	−0.0263987	−	0.0304658i
$220$	−0.478234	−	0.140422i	−0.0322425	−	0.00946726i
$221$	−2.11266	+	4.62608i	−0.142113	+	0.311184i
$222$	−1.09539	−	0.703963i	−0.0735176	−	0.0472469i
$223$	−8.47992	+	2.48993i	−0.567858	+	0.166738i	−0.553044	−	0.833152i	$-0.686534\pi$
$223$	−8.47992	+	2.48993i	−0.567858	+	0.166738i	−0.0148139	+	0.999890i	$0.504716\pi$
$224$	0.489262	−	3.40289i	0.0326902	−	0.227365i
$225$	−1.66166	−	3.63853i	−0.110777	−	0.242569i
$226$	2.92013	+	20.3099i	0.194244	+	1.35100i
$227$	−22.5419	+	14.4868i	−1.49616	+	0.961522i	−0.500771	+	0.865580i	$0.666950\pi$
$227$	−22.5419	+	14.4868i	−1.49616	+	0.961522i	−0.995387	+	0.0959424i	$0.969414\pi$
$228$	3.88079	−	4.47867i	0.257011	−	0.296607i
$229$	−6.98558			−0.461620			−0.230810	−	0.972999i	$-0.574138\pi$
$229$	−6.98558			−0.461620			−0.230810	+	0.972999i	$0.574138\pi$
$230$	−10.5121	−	5.89785i	−0.693144	−	0.388893i
$231$	−0.115460			−0.00759669
$232$	−7.81795	+	9.02239i	−0.513274	+	0.592349i
$233$	−4.69994	+	3.02047i	−0.307904	+	0.197878i	−0.685462	−	0.728108i	$-0.740400\pi$
$233$	−4.69994	+	3.02047i	−0.307904	+	0.197878i	0.377559	+	0.925986i	$0.376764\pi$
$234$	−0.464827	−	3.23294i	−0.0303867	−	0.211344i
$235$	−2.45118	−	5.36733i	−0.159897	−	0.350126i
$236$	2.21639	−	15.4154i	0.144275	−	1.00345i
$237$	−9.06631	+	2.66211i	−0.588920	+	0.172923i
$238$	−8.27437	−	5.31761i	−0.536348	−	0.344690i
$239$	−6.86114	+	15.0238i	−0.443811	+	0.971810i	0.547073	+	0.837085i	$0.315742\pi$
$239$	−6.86114	+	15.0238i	−0.443811	+	0.971810i	−0.990883	+	0.134724i	$0.956985\pi$
$240$	5.75848	+	1.69084i	0.371708	+	0.109143i
$241$	−13.7443	−	15.8618i	−0.885350	−	1.02175i	−0.999600	−	0.0282959i	$-0.990992\pi$
$241$	−13.7443	−	15.8618i	−0.885350	−	1.02175i	0.114250	−	0.993452i	$-0.463554\pi$
$242$	−18.0828	−	20.8687i	−1.16241	−	1.34149i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	9.02425	−	19.7604i	0.577719	−	1.26503i
$245$	−0.841254	−	0.540641i	−0.0537457	−	0.0345403i
$246$	22.6907	−	6.66260i	1.44671	−	0.424792i
$247$	−0.253889	+	1.76584i	−0.0161546	+	0.112357i
$248$	14.2765	+	31.2612i	0.906560	+	1.98509i
$249$	1.82852	+	12.7176i	0.115877	+	0.805946i
$250$	−19.0292	+	12.2293i	−1.20351	+	0.773450i
$251$	−13.1677	+	15.1963i	−0.831138	+	0.959184i	−0.999648	−	0.0265155i	$-0.991559\pi$
$251$	−13.1677	+	15.1963i	−0.831138	+	0.959184i	0.168510	+	0.985700i	$0.446104\pi$
$252$	4.31686			0.271937
$253$	0.259769	+	0.489011i	0.0163316	+	0.0307439i
$254$	6.55804			0.411488
$255$	2.56275	−	2.95757i	0.160486	−	0.185210i
$256$	−26.7494	+	17.1908i	−1.67184	+	1.07442i
$257$	0.844801	+	5.87572i	0.0526973	+	0.366518i	0.999058	+	0.0434043i	$0.0138204\pi$
$257$	0.844801	+	5.87572i	0.0526973	+	0.366518i	−0.946360	+	0.323113i	$0.895271\pi$
$258$	6.88047	+	15.0661i	0.428360	+	0.937977i
$259$	−0.0737293	+	0.512799i	−0.00458132	+	0.0318638i
$260$	−5.38271	+	1.58051i	−0.333821	+	0.0980188i
$261$	−1.72472	−	1.10841i	−0.106758	−	0.0686090i
$262$	−18.5468	+	40.6119i	−1.14583	+	2.50901i
$263$	−5.93759	−	1.74343i	−0.366127	−	0.107505i	0.0934936	−	0.995620i	$-0.470197\pi$
$263$	−5.93759	−	1.74343i	−0.366127	−	0.107505i	−0.459621	+	0.888115i	$0.652015\pi$
$264$	−0.440282	−	0.508112i	−0.0270975	−	0.0312721i
$265$	2.86982	+	3.31195i	0.176292	+	0.203451i
$266$	−3.31051	−	0.972054i	−0.202981	−	0.0596005i
$267$	−2.11535	+	4.63198i	−0.129458	+	0.283472i
$268$	−50.9229	−	32.7261i	−3.11061	−	1.99907i
$269$	19.4189	−	5.70192i	1.18399	−	0.347652i	0.370282	−	0.928920i	$-0.379261\pi$
$269$	19.4189	−	5.70192i	1.18399	−	0.347652i	0.813713	+	0.581268i	$0.197443\pi$
$270$	−0.357685	+	2.48775i	−0.0217680	+	0.151400i
$271$	−12.4234	−	27.2034i	−0.754665	−	1.65249i	−0.757796	−	0.652492i	$-0.773724\pi$
$271$	−12.4234	−	27.2034i	−0.754665	−	1.65249i	0.00313049	−	0.999995i	$-0.499004\pi$
$272$	−3.34251	−	23.2477i	−0.202670	−	1.40960i
$273$	−1.09325	+	0.702586i	−0.0661662	+	0.0425224i
$274$	28.8866	−	33.3369i	1.74510	−	2.01395i
$275$	0.461839			0.0278499
$276$	−9.71238	−	18.2834i	−0.584616	−	1.10053i
$277$	16.2919			0.978884			0.489442	−	0.872036i	$-0.337201\pi$
$277$	16.2919			0.978884			0.489442	+	0.872036i	$0.337201\pi$
$278$	−6.40360	+	7.39014i	−0.384062	+	0.443231i
$279$	−4.96496	+	3.19079i	−0.297244	+	0.191027i
$280$	−0.828708	−	5.76379i	−0.0495248	−	0.344452i
$281$	11.0973	+	24.2997i	0.662010	+	1.44960i	0.880637	+	0.473792i	$0.157115\pi$
$281$	11.0973	+	24.2997i	0.662010	+	1.44960i	−0.218627	+	0.975809i	$0.570158\pi$
$282$	2.11054	−	14.6791i	0.125681	−	0.874128i
$283$	−17.6139	+	5.17191i	−1.04704	+	0.307438i	−0.759620	−	0.650367i	$-0.774615\pi$
$283$	−17.6139	+	5.17191i	−1.04704	+	0.307438i	−0.287419	+	0.957805i	$0.592797\pi$
$284$	34.6343	+	22.2581i	2.05516	+	1.32077i
$285$	0.570276	−	1.24873i	0.0337802	−	0.0739684i
$286$	0.361838	+	0.106245i	0.0213959	+	0.00628240i
$287$	−6.16176	−	7.11105i	−0.363717	−	0.419752i
$288$	2.25133	+	2.59818i	0.132661	+	0.153099i
$289$	1.61684	+	0.474746i	0.0951079	+	0.0279262i
$290$	−2.14055	+	4.68715i	−0.125698	+	0.275239i
$291$	6.50275	+	4.17906i	0.381198	+	0.244981i
$292$	−2.47096	+	0.725541i	−0.144602	+	0.0424591i
$293$	0.923102	−	6.42031i	0.0539282	−	0.375079i	−0.944929	−	0.327276i	$-0.893869\pi$
$293$	0.923102	−	6.42031i	0.0539282	−	0.375079i	0.998857	−	0.0478023i	$-0.0152217\pi$
$294$	−1.04408	−	2.28621i	−0.0608919	−	0.133335i
$295$	−0.513427	−	3.57096i	−0.0298929	−	0.207909i
$296$	−2.53786	+	1.63099i	−0.147510	+	0.0947991i
$297$	0.0756100	−	0.0872586i	0.00438734	−	0.00506326i
$298$	38.1946			2.21255
$299$	5.43535	+	3.04954i	0.314334	+	0.176359i
$300$	−17.2675			−0.996937
$301$	4.31553	−	4.98039i	0.248743	−	0.287065i
$302$	−6.07505	+	3.90420i	−0.349580	+	0.224661i
$303$	1.17272	+	8.15647i	0.0673712	+	0.468577i
$304$	−3.42256	−	7.49435i	−0.196297	−	0.429831i
$305$	0.716162	−	4.98101i	0.0410073	−	0.285212i
$306$	9.43734	−	2.77105i	0.539497	−	0.158411i
$307$	−22.8714	−	14.6985i	−1.30534	−	0.838890i	−0.311555	−	0.950228i	$-0.600850\pi$
$307$	−22.8714	−	14.6985i	−1.30534	−	0.838890i	−0.993783	+	0.111338i	$0.964486\pi$
$308$	−0.207053	+	0.453382i	−0.0117979	+	0.0258338i
$309$	6.93043	+	2.03496i	0.394258	+	0.115765i
$310$	9.71379	+	11.2103i	0.551706	+	0.636703i
$311$	11.2629	+	12.9981i	0.638662	+	0.737055i	0.979138	−	0.203198i	$-0.0651335\pi$
$311$	11.2629	+	12.9981i	0.638662	+	0.737055i	−0.340476	+	0.940253i	$0.610588\pi$
$312$	−7.26079	−	2.13196i	−0.411061	−	0.120698i
$313$	13.2713	−	29.0602i	0.750140	−	1.64258i	−0.0159725	−	0.999872i	$-0.505084\pi$
$313$	13.2713	−	29.0602i	0.750140	−	1.64258i	0.766113	−	0.642706i	$-0.222188\pi$
$314$	0.174142	+	0.111914i	0.00982739	+	0.00631568i
$315$	0.959493	−	0.281733i	0.0540613	−	0.0158738i
$316$	−5.80507	+	40.3751i	−0.326561	+	2.27128i
$317$	−2.06777	−	4.52779i	−0.116138	−	0.254306i	0.842632	−	0.538490i	$-0.181005\pi$
$317$	−2.06777	−	4.52779i	−0.116138	−	0.254306i	−0.958770	+	0.284183i	$0.908278\pi$
$318$	1.56750	+	10.9022i	0.0879008	+	0.611364i
$319$	0.199136	−	0.127977i	0.0111495	−	0.00716534i
$320$	−2.20204	+	2.54129i	−0.123098	+	0.142062i
$321$	−6.13755			−0.342565
$322$	−7.33384	+	9.56570i	−0.408699	+	0.533076i
$323$	−5.37230			−0.298923
$324$	−2.82694	+	3.26247i	−0.157052	+	0.181248i
$325$	4.37298	−	2.81034i	0.242569	−	0.155890i
$326$	0.0833235	+	0.579528i	0.00461486	+	0.0320971i
$327$	−2.41538	−	5.28895i	−0.133571	−	0.292480i
$328$	7.79753	−	54.2330i	0.430547	−	2.99452i
$329$	−5.66153	+	1.66238i	−0.312130	+	0.0916497i
$330$	−0.244123	−	0.156888i	−0.0134385	−	0.00863641i
$331$	0.997212	−	2.18359i	0.0548117	−	0.120021i	−0.880244	−	0.474520i	$-0.842621\pi$
$331$	0.997212	−	2.18359i	0.0548117	−	0.120021i	0.935056	+	0.354500i	$0.115349\pi$
$332$	53.2180	+	15.6262i	2.92072	+	0.857600i
$333$	−0.339265	−	0.391533i	−0.0185916	−	0.0214559i
$334$	−41.6211	−	48.0334i	−2.27741	−	2.62827i
$335$	−13.4543	−	3.95052i	−0.735084	−	0.215840i
$336$	2.49315	−	5.45923i	0.136012	−	0.297825i
$337$	24.9667	+	16.0451i	1.36002	+	0.874034i	0.998302	−	0.0582517i	$-0.0185526\pi$
$337$	24.9667	+	16.0451i	1.36002	+	0.874034i	0.361722	+	0.932286i	$0.382189\pi$
$338$	−27.2773	+	8.00933i	−1.48369	+	0.435650i
$339$	−1.16185	+	8.08086i	−0.0631031	+	0.438892i
$340$	−7.01791	−	15.3671i	−0.380599	−	0.833397i
$341$	−0.0969772	−	0.674491i	−0.00525161	−	0.0365257i
$342$	2.90255	−	1.86536i	0.156952	−	0.100867i
$343$	−0.654861	+	0.755750i	−0.0353592	+	0.0408066i
$344$	38.3740			2.06898
$345$	−3.35197	−	3.42992i	−0.180464	−	0.184660i
$346$	−3.29784			−0.177293
$347$	17.6929	−	20.4187i	0.949803	−	1.09613i	−0.0454656	−	0.998966i	$-0.514477\pi$
$347$	17.6929	−	20.4187i	0.949803	−	1.09613i	0.995268	−	0.0971648i	$-0.0309774\pi$
$348$	−7.44540	+	4.78487i	−0.399115	+	0.256496i
$349$	0.543634	+	3.78105i	0.0291000	+	0.202395i	0.999185	−	0.0403715i	$-0.0128541\pi$
$349$	0.543634	+	3.78105i	0.0291000	+	0.202395i	−0.970085	+	0.242767i	$0.921945\pi$
$350$	4.17631	+	9.14485i	0.223233	+	0.488813i
$351$	0.184944	−	1.28632i	0.00987159	−	0.0686584i
$352$	−0.380858	+	0.111830i	−0.0202998	+	0.00596056i
$353$	2.68833	+	1.72768i	0.143085	+	0.0919552i	0.610225	−	0.792228i	$-0.291079\pi$
$353$	2.68833	+	1.72768i	0.143085	+	0.0919552i	−0.467140	+	0.884184i	$0.654715\pi$
$354$	3.76670	−	8.24793i	0.200198	−	0.438372i
$355$	9.15066	+	2.68688i	0.485667	+	0.142605i
$356$	14.3952	+	16.6130i	0.762945	+	0.880485i
$357$	−2.56275	−	2.95757i	−0.135635	−	0.156531i
$358$	−8.07749	−	2.37177i	−0.426909	−	0.125352i
$359$	6.39592	−	14.0051i	0.337564	−	0.739161i	−0.662386	−	0.749162i	$-0.730456\pi$
$359$	6.39592	−	14.0051i	0.337564	−	0.739161i	0.999950	+	0.0100011i	$0.00318349\pi$
$360$	4.89867	+	3.14818i	0.258183	+	0.165924i
$361$	16.4222	−	4.82198i	0.864324	−	0.253789i
$362$	5.17930	−	36.0228i	0.272218	−	1.89332i
$363$	−4.56403	−	9.99383i	−0.239549	−	0.524540i
$364$	0.798379	+	5.55285i	0.0418464	+	0.291048i
$365$	−0.501861	+	0.322526i	−0.0262686	+	0.0168818i
$366$	8.28248	−	9.55849i	0.432932	−	0.499630i
$367$	−21.7502			−1.13535			−0.567675	−	0.823253i	$-0.692157\pi$
$367$	−21.7502			−1.13535			−0.567675	+	0.823253i	$0.692157\pi$
$368$	−28.7309	+	1.72323i	−1.49770	+	0.0898298i
$369$	9.40926			0.489827
$370$	−0.852687	+	0.984054i	−0.0443291	+	0.0511585i
$371$	3.68665	−	2.36927i	0.191402	−	0.123006i
$372$	3.62583	+	25.2182i	0.187991	+	1.30750i
$373$	−11.6573	−	25.5259i	−0.603591	−	1.32168i	−0.926872	−	0.375377i	$-0.877513\pi$
$373$	−11.6573	−	25.5259i	−0.603591	−	1.32168i	0.323281	−	0.946303i	$-0.395214\pi$
$374$	−0.161618	+	1.12407i	−0.00835704	+	0.0581245i
$375$	−8.63544	+	2.53559i	−0.445932	+	0.130937i
$376$	−28.9048	−	18.5760i	−1.49065	−	0.957984i
$377$	1.10679	−	2.42353i	0.0570026	−	0.124818i
$378$	2.41153	+	0.708089i	0.124036	+	0.0364202i
$379$	−23.6643	−	27.3101i	−1.21555	−	1.40282i	−0.889164	−	0.457589i	$-0.848713\pi$
$379$	−23.6643	−	27.3101i	−1.21555	−	1.40282i	−0.326390	−	0.945235i	$-0.605832\pi$
$380$	−3.88079	−	4.47867i	−0.199080	−	0.229751i
$381$	2.50360	+	0.735124i	0.128263	+	0.0376615i
$382$	9.83171	−	21.5284i	0.503034	−	1.10149i
$383$	1.52038	+	0.977088i	0.0776877	+	0.0499269i	0.578908	−	0.815393i	$-0.303479\pi$
$383$	1.52038	+	0.977088i	0.0776877	+	0.0499269i	−0.501220	+	0.865320i	$0.667115\pi$
$384$	−14.7063	+	4.31815i	−0.750476	+	0.220360i
$385$	−0.0164316	+	0.114284i	−0.000837433	+	0.00582448i
$386$	15.1252	+	33.1195i	0.769852	+	1.68574i
$387$	0.937855	+	6.52292i	0.0476738	+	0.331579i
$388$	28.0715	−	18.0404i	1.42511	−	0.915865i
$389$	18.2139	−	21.0200i	0.923483	−	1.06576i	−0.0741676	−	0.997246i	$-0.523630\pi$
$389$	18.2139	−	21.0200i	0.923483	−	1.06576i	0.997650	−	0.0685102i	$-0.0218246\pi$
$390$	−3.26619			−0.165390
$391$	−6.76046	+	17.5083i	−0.341891	+	0.885431i
$392$	−5.82306			−0.294109
$393$	−11.6328	+	13.4250i	−0.586799	+	0.677203i
$394$	−47.6746	+	30.6386i	−2.40181	+	1.54355i
$395$	1.34474	+	9.35289i	0.0676613	+	0.470595i
$396$	−0.207053	−	0.453382i	−0.0104048	−	0.0227833i
$397$	4.92752	−	34.2717i	0.247305	−	1.72005i	−0.366355	−	0.930475i	$-0.619394\pi$
$397$	4.92752	−	34.2717i	0.247305	−	1.72005i	0.613660	−	0.789570i	$-0.289697\pi$
$398$	0.821128	−	0.241105i	0.0411594	−	0.0120855i
$399$	−1.15486	−	0.742184i	−0.0578154	−	0.0371557i
$400$	−9.97259	+	21.8369i	−0.498629	+	1.09185i
$401$	5.43767	+	1.59664i	0.271544	+	0.0797326i	0.414670	−	0.909972i	$-0.363897\pi$
$401$	5.43767	+	1.59664i	0.271544	+	0.0797326i	−0.143125	+	0.989705i	$0.545715\pi$
$402$	−23.0790	−	26.6346i	−1.15108	−	1.32841i
$403$	−5.02260	−	5.79639i	−0.250194	−	0.288739i
$404$	34.1315	+	10.0219i	1.69811	+	0.498609i
$405$	−0.415415	+	0.909632i	−0.0206421	+	0.0452000i
$406$	4.33481	+	2.78582i	0.215133	+	0.138258i
$407$	0.0573934	−	0.0168522i	0.00284489	−	0.000835334i
$408$	3.24309	−	22.5562i	0.160557	−	1.11670i
$409$	15.0654	+	32.9887i	0.744937	+	1.63118i	0.775258	+	0.631645i	$0.217620\pi$
$409$	15.0654	+	32.9887i	0.744937	+	1.63118i	−0.0303208	+	0.999540i	$0.509653\pi$
$410$	−3.36555	−	23.4079i	−0.166213	−	1.15604i
$411$	14.7646	−	9.48866i	0.728286	−	0.468041i
$412$	20.4190	−	23.5648i	1.00597	−	1.16096i
$413$	−3.60768			−0.177522
$414$	−2.42663	−	11.8067i	−0.119262	−	0.580270i
$415$	12.8484			0.630702
$416$	−2.92571	+	3.37644i	−0.143445	+	0.165544i
$417$	−3.27304	+	2.10345i	−0.160281	+	0.103007i
$418$	0.0566936	+	0.394313i	0.00277297	+	0.0192865i
$419$	−2.11037	−	4.62106i	−0.103098	−	0.225753i	0.851052	−	0.525081i	$-0.175965\pi$
$419$	−2.11037	−	4.62106i	−0.103098	−	0.225753i	−0.954150	+	0.299328i	$0.903238\pi$
$420$	0.614354	−	4.27292i	0.0299774	−	0.208497i
$421$	0.473773	−	0.139112i	0.0230903	−	0.00677992i	−0.270167	−	0.962813i	$-0.587079\pi$
$421$	0.473773	−	0.139112i	0.0230903	−	0.00677992i	0.293257	+	0.956034i	$0.405261\pi$
$422$	49.3219	+	31.6973i	2.40095	+	1.54300i
$423$	2.45118	−	5.36733i	0.119180	−	0.260968i
$424$	24.4849	+	7.18942i	1.18909	+	0.349149i
$425$	10.2510	+	11.8303i	0.497246	+	0.573853i
$426$	15.6968	+	18.1150i	0.760511	+	0.877677i
$427$	−4.82839	−	1.41774i	−0.233662	−	0.0686094i
$428$	−11.0064	+	24.1007i	−0.532015	+	1.16495i
$429$	0.126226	+	0.0811204i	0.00609424	+	0.00391653i
$430$	15.8920	−	4.66631i	0.766379	−	0.225029i
$431$	5.03667	−	35.0308i	0.242608	−	1.68737i	−0.396324	−	0.918111i	$-0.629714\pi$
$431$	5.03667	−	35.0308i	0.242608	−	1.68737i	0.638931	−	0.769264i	$-0.279377\pi$
$432$	2.49315	+	5.45923i	0.119952	+	0.262657i
$433$	−1.92348	−	13.3781i	−0.0924365	−	0.642910i	−0.982388	−	0.186854i	$-0.940171\pi$
$433$	−1.92348	−	13.3781i	−0.0924365	−	0.642910i	0.889951	−	0.456056i	$-0.150738\pi$
$434$	12.4786	−	8.01952i	0.598993	−	0.384949i
$435$	−1.34258	+	1.54943i	−0.0643720	+	0.0742893i
$436$	−25.0999			−1.20207
$437$	−0.545114	+	6.56104i	−0.0260763	+	0.313857i
$438$	−1.49936			−0.0716424
$439$	10.5248	−	12.1463i	0.502323	−	0.579712i	−0.446793	−	0.894637i	$-0.647434\pi$
$439$	10.5248	−	12.1463i	0.502323	−	0.579712i	0.949116	+	0.314925i	$0.101979\pi$
$440$	−0.565599	+	0.363488i	−0.0269639	+	0.0173286i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	5.30983	+	11.6269i	0.252563	+	0.553036i
$443$	4.37434	−	30.4242i	0.207831	−	1.44550i	−0.572384	−	0.819986i	$-0.693981\pi$
$443$	4.37434	−	30.4242i	0.207831	−	1.44550i	0.780215	−	0.625512i	$-0.215110\pi$
$444$	−2.14585	+	0.630080i	−0.101838	+	0.0299023i
$445$	4.28379	+	2.75302i	0.203071	+	0.130506i
$446$	−9.22748	+	20.2054i	−0.436934	+	0.956751i
$447$	14.5812	+	4.28142i	0.689666	+	0.202504i
$448$	2.20204	+	2.54129i	0.104037	+	0.120065i
$449$	22.4282	+	25.8836i	1.05845	+	1.22152i	0.974344	+	0.225065i	$0.0722593\pi$
$449$	22.4282	+	25.8836i	1.05845	+	1.22152i	0.0841102	+	0.996456i	$0.473195\pi$
$450$	−9.64612	−	2.83236i	−0.454722	−	0.133519i
$451$	−0.451303	+	0.988216i	−0.0212510	+	0.0465333i
$452$	29.6480	+	19.0536i	1.39453	+	0.896207i
$453$	−2.75686	+	0.809486i	−0.129528	+	0.0380330i
$454$	−9.58439	+	66.6609i	−0.449818	+	3.12855i
$455$	0.539850	+	1.18211i	0.0253085	+	0.0554180i
$456$	−1.13764	−	7.91245i	−0.0532748	−	0.370534i
$457$	−17.3188	+	11.1301i	−0.810140	+	0.520645i	−0.878910	−	0.476987i	$-0.841729\pi$
$457$	−17.3188	+	11.1301i	−0.810140	+	0.520645i	0.0687706	+	0.997633i	$0.478092\pi$
$458$	−11.4975	+	13.2688i	−0.537241	+	0.620009i
$459$	3.91343			0.182663
$460$	−19.4795	+	7.01152i	−0.908236	+	0.326914i
$461$	33.8255			1.57541			0.787705	−	0.616052i	$-0.211269\pi$
$461$	33.8255			1.57541			0.787705	+	0.616052i	$0.211269\pi$
$462$	−0.190033	+	0.219310i	−0.00884116	+	0.0102032i
$463$	−6.12832	+	3.93843i	−0.284807	+	0.183035i	−0.675242	−	0.737596i	$-0.735961\pi$
$463$	−6.12832	+	3.93843i	−0.284807	+	0.183035i	0.390435	+	0.920630i	$0.372325\pi$
$464$	1.75109	+	12.1791i	0.0812924	+	0.565401i
$465$	2.45172	+	5.36852i	0.113696	+	0.248959i
$466$	−1.99833	+	13.8987i	−0.0925708	+	0.643844i
$467$	−0.527255	+	0.154816i	−0.0243984	+	0.00716403i	−0.293909	−	0.955833i	$-0.594956\pi$
$467$	−0.527255	+	0.154816i	−0.0243984	+	0.00716403i	0.269511	+	0.962997i	$0.413138\pi$
$468$	−4.71939	−	3.03297i	−0.218154	−	0.140199i
$469$	−5.82505	+	12.7551i	−0.268976	+	0.588975i
$470$	−14.2293	−	4.17811i	−0.656350	−	0.192722i
$471$	0.0539355	+	0.0622448i	0.00248522	+	0.00286809i
$472$	−13.7571	−	15.8766i	−0.633224	−	0.730779i
$473$	−0.730058	−	0.214365i	−0.0335681	−	0.00985649i
$474$	−9.86556	+	21.6026i	−0.453140	+	0.992239i
$475$	4.61944	+	2.96874i	0.211955	+	0.136215i
$476$	−16.2094	+	4.75951i	−0.742957	+	0.218152i
$477$	−0.623671	+	4.33773i	−0.0285559	+	0.198611i
$478$	17.2444	+	37.7599i	0.788739	+	1.72710i
$479$	−3.29006	−	22.8829i	−0.150327	−	1.04554i	−0.915672	−	0.401925i	$-0.868341\pi$
$479$	−3.29006	−	22.8829i	−0.150327	−	1.04554i	0.765346	−	0.643619i	$-0.222568\pi$
$480$	2.89213	−	1.85866i	0.132007	−	0.0848358i
$481$	0.440889	−	0.508814i	0.0201028	−	0.0231999i
$482$	−52.7503			−2.40271
$483$	−3.87204	+	2.82972i	−0.176184	+	0.128757i
$484$	−47.4279			−2.15582
$485$	5.06196	−	5.84182i	0.229852	−	0.265263i
$486$	−2.11435	+	1.35881i	−0.0959090	+	0.0616370i
$487$	3.04693	+	21.1919i	0.138070	+	0.960296i	0.934601	+	0.355698i	$0.115757\pi$
$487$	3.04693	+	21.1919i	0.138070	+	0.960296i	−0.796531	+	0.604598i	$0.793334\pi$
$488$	−12.1729	−	26.6549i	−0.551041	−	1.20661i
$489$	−0.0331526	+	0.230581i	−0.00149921	+	0.0104272i
$490$	−2.41153	+	0.708089i	−0.108942	+	0.0319882i
$491$	7.79191	+	5.00755i	0.351644	+	0.225988i	0.704523	−	0.709681i	$-0.251161\pi$
$491$	7.79191	+	5.00755i	0.351644	+	0.225988i	−0.352879	+	0.935669i	$0.614797\pi$
$492$	16.8735	−	36.9479i	0.760718	−	1.66574i
$493$	7.69824	+	2.26041i	0.346712	+	0.101804i
$494$	2.93625	+	3.38861i	0.132108	+	0.152461i
$495$	−0.0756100	−	0.0872586i	−0.00339842	−	0.00392198i
$496$	33.9857	+	9.97911i	1.52600	+	0.448075i
$497$	3.96180	−	8.67514i	0.177711	−	0.389133i
$498$	27.1660	+	17.4585i	1.21734	+	0.782336i
$499$	15.7085	−	4.61243i	0.703209	−	0.206481i	0.0894699	−	0.995990i	$-0.471483\pi$
$499$	15.7085	−	4.61243i	0.703209	−	0.206481i	0.613739	+	0.789509i	$0.289665\pi$
$500$	−5.52918	+	38.4563i	−0.247273	+	1.71982i
$501$	−10.5050	−	23.0028i	−0.469329	−	1.02769i
$502$	7.19220	+	50.0229i	0.321004	+	2.23263i
$503$	−21.5535	+	13.8516i	−0.961023	+	0.617612i	−0.924281	−	0.381713i	$-0.875334\pi$
$503$	−21.5535	+	13.8516i	−0.961023	+	0.617612i	−0.0367419	+	0.999325i	$0.511698\pi$
$504$	3.81329	−	4.40077i	0.169858	−	0.196026i
$505$	8.24035			0.366691
$506$	1.35640	+	0.311436i	0.0602995	+	0.0138450i
$507$	−11.3112			−0.502347
$508$	7.37634	−	8.51275i	0.327272	−	0.377692i
$509$	−9.81467	+	6.30751i	−0.435028	+	0.279575i	−0.739770	−	0.672859i	$-0.765066\pi$
$509$	−9.81467	+	6.30751i	−0.435028	+	0.279575i	0.304743	+	0.952435i	$0.401430\pi$
$510$	−1.39977	−	9.73565i	−0.0619831	−	0.431102i
$511$	0.247821	+	0.542653i	0.0109630	+	0.0240056i
$512$	−7.01077	+	48.7610i	−0.309835	+	2.15495i
$513$	1.31718	−	0.386758i	0.0581548	−	0.0170758i
$514$	12.5511	+	8.06611i	0.553606	+	0.355781i
$515$	3.00055	−	6.57028i	0.132220	−	0.289521i
$516$	27.2958	+	8.01476i	1.20163	+	0.352830i
$517$	0.446140	+	0.514874i	0.0196212	+	0.0226441i
$518$	0.852687	+	0.984054i	0.0374649	+	0.0432368i
$519$	−1.25899	−	0.369672i	−0.0552634	−	0.0162268i
$520$	−3.14358	+	6.88347i	−0.137855	+	0.301860i
$521$	13.6161	+	8.75056i	0.596534	+	0.383369i	0.803786	−	0.594918i	$-0.202816\pi$
$521$	13.6161	+	8.75056i	0.596534	+	0.383369i	−0.207252	+	0.978288i	$0.566452\pi$
$522$	−4.94408	+	1.45171i	−0.216396	+	0.0635397i
$523$	1.77195	−	12.3242i	0.0774821	−	0.538900i	−0.913700	−	0.406390i	$-0.866787\pi$
$523$	1.77195	−	12.3242i	0.0774821	−	0.538900i	0.991182	−	0.132510i	$-0.0423036\pi$
$524$	31.8557	+	69.7543i	1.39162	+	3.04723i
$525$	0.569259	+	3.95929i	0.0248445	+	0.172797i
$526$	−13.0842	+	8.40868i	−0.570497	+	0.366636i
$527$	15.1250	−	17.4552i	0.658855	−	0.760359i
$528$	−0.692941			−0.0301564
$529$	20.6964	+	10.0329i	0.899844	+	0.436213i
$530$	11.0143			0.478430
$531$	2.36253	−	2.72650i	0.102525	−	0.118320i
$532$	−4.98538	+	3.20391i	−0.216143	+	0.138907i
$533$	1.74019	+	12.1033i	0.0753760	+	0.524251i
$534$	5.31660	+	11.6417i	0.230072	+	0.503787i
$535$	−0.873464	+	6.07508i	−0.0377631	+	0.262648i
$536$	−78.3449	+	23.0041i	−3.38398	+	0.993627i
$537$	−2.81781	−	1.81089i	−0.121597	−	0.0781458i
$538$	21.1308	−	46.2701i	0.911015	−	1.99485i
$539$	0.110783	+	0.0325288i	0.00477175	+	0.00140111i
$540$	2.82694	+	3.26247i	0.121652	+	0.140394i
$541$	16.9697	+	19.5841i	0.729585	+	0.841986i	0.992425	−	0.122853i	$-0.0392045\pi$
$541$	16.9697	+	19.5841i	0.729585	+	0.841986i	−0.262840	+	0.964840i	$0.584659\pi$
$542$	−72.1190	−	21.1760i	−3.09777	−	0.909589i
$543$	6.01523	−	13.1715i	0.258138	−	0.565243i
$544$	−11.3181	−	7.27373i	−0.485261	−	0.311859i
$545$	−5.57887	+	1.63810i	−0.238972	+	0.0701686i
$546$	−0.464827	+	3.23294i	−0.0198928	+	0.138357i
$547$	13.5986	+	29.7768i	0.581434	+	1.27316i	0.940482	+	0.339844i	$0.110374\pi$
$547$	13.5986	+	29.7768i	0.581434	+	1.27316i	−0.359048	+	0.933319i	$0.616898\pi$
$548$	−10.7824	−	74.9931i	−0.460600	−	3.20355i
$549$	4.23338	−	2.72063i	0.180676	−	0.116114i
$550$	0.760134	−	0.877241i	0.0324122	−	0.0374057i
$551$	2.81446			0.119900
$552$	−27.2182	−	6.24942i	−1.15848	−	0.265993i
$553$	9.44906			0.401815
$554$	26.8146	−	30.9456i	1.13924	−	1.31475i
$555$	−0.435830	+	0.280091i	−0.0184999	+	0.0118892i
$556$	2.39025	+	16.6245i	0.101369	+	0.705037i
$557$	−8.11340	−	17.7659i	−0.343776	−	0.752764i	0.656223	−	0.754567i	$-0.272153\pi$
$557$	−8.11340	−	17.7659i	−0.343776	−	0.752764i	−0.999998	+	0.00180364i	$0.999426\pi$
$558$	−2.11101	+	14.6824i	−0.0893661	+	0.621555i
$559$	−8.21709	+	2.41275i	−0.347546	+	0.102049i
$560$	−5.04885	−	3.24470i	−0.213353	−	0.137114i
$561$	−0.187702	+	0.411011i	−0.00792480	+	0.0173529i
$562$	64.4211	+	18.9157i	2.71744	+	0.797913i
$563$	−2.96396	−	3.42059i	−0.124916	−	0.144161i	0.689846	−	0.723956i	$-0.257678\pi$
$563$	−2.96396	−	3.42059i	−0.124916	−	0.144161i	−0.814762	+	0.579795i	$0.803133\pi$
$564$	−16.6805	−	19.2503i	−0.702376	−	0.810586i
$565$	7.83326	+	2.30005i	0.329548	+	0.0967639i
$566$	−19.1667	+	41.9692i	−0.805636	+	1.76410i
$567$	0.841254	+	0.540641i	0.0353293	+	0.0227048i
$568$	53.2848	−	15.6458i	2.23578	−	0.656485i
$569$	1.07776	−	7.49601i	0.0451822	−	0.314249i	−0.954680	−	0.297635i	$-0.903802\pi$
$569$	1.07776	−	7.49601i	0.0451822	−	0.314249i	0.999862	−	0.0166142i	$-0.00528872\pi$
$570$	−1.43330	−	3.13848i	−0.0600341	−	0.131456i
$571$	−0.313113	−	2.17775i	−0.0131034	−	0.0911360i	0.982220	−	0.187732i	$-0.0601136\pi$
$571$	−0.313113	−	2.17775i	−0.0131034	−	0.0911360i	−0.995324	+	0.0965959i	$0.969205\pi$
$572$	0.544899	−	0.350186i	0.0227834	−	0.0146420i
$573$	6.16659	−	7.11662i	0.257613	−	0.297301i
$574$	−23.6487			−0.987076
$575$	15.4882	−	11.3189i	0.645901	−	0.472030i
$576$	−3.36261			−0.140109
$577$	11.9916	−	13.8391i	0.499218	−	0.576128i	−0.449087	−	0.893488i	$-0.648251\pi$
$577$	11.9916	−	13.8391i	0.499218	−	0.576128i	0.948305	+	0.317360i	$0.102796\pi$
$578$	3.56288	−	2.28973i	0.148196	−	0.0952400i
$579$	2.06166	+	14.3392i	0.0856799	+	0.595916i
$580$	3.67657	+	8.05057i	0.152661	+	0.334282i
$581$	1.82852	−	12.7176i	0.0758596	−	0.527615i
$582$	18.6407	−	5.47341i	0.772683	−	0.226880i
$583$	−0.425660	−	0.273555i	−0.0176290	−	0.0113295i
$584$	−1.44308	+	3.15990i	−0.0597150	+	0.130758i
$585$	−1.24690	−	0.366124i	−0.0515531	−	0.0151373i
$586$	−10.6758	−	12.3205i	−0.441012	−	0.508955i
$587$	−0.573496	−	0.661849i	−0.0236707	−	0.0273174i	0.743791	−	0.668412i	$-0.233026\pi$
$587$	−0.573496	−	0.661849i	−0.0236707	−	0.0273174i	−0.767461	+	0.641095i	$0.778480\pi$
$588$	−4.14200	−	1.21620i	−0.170813	−	0.0501553i
$589$	3.36569	−	7.36983i	0.138681	−	0.303668i
$590$	−7.62792	−	4.90216i	−0.314036	−	0.201819i
$591$	−21.6347	+	6.35252i	−0.889933	+	0.261308i
$592$	−0.442493	+	3.07760i	−0.0181863	+	0.126489i
$593$	−3.49519	−	7.65341i	−0.143530	−	0.314288i	0.824190	−	0.566313i	$-0.191631\pi$
$593$	−3.49519	−	7.65341i	−0.143530	−	0.314288i	−0.967721	+	0.252025i	$0.918903\pi$
$594$	−0.0412982	−	0.287235i	−0.00169449	−	0.0117854i
$595$	−3.29218	+	2.11576i	−0.134966	+	0.0867376i
$596$	42.9604	−	49.5789i	1.75973	−	2.03083i
$597$	0.340501			0.0139358
$598$	14.7384	−	5.30500i	0.602699	−	0.216938i
$599$	2.53861			0.103725			0.0518624	−	0.998654i	$-0.483484\pi$
$599$	2.53861			0.103725			0.0518624	+	0.998654i	$0.483484\pi$
$600$	−15.2532	+	17.6031i	−0.622708	+	0.718643i
$601$	3.68531	−	2.36840i	0.150327	−	0.0966091i	−0.463315	−	0.886194i	$-0.653340\pi$
$601$	3.68531	−	2.36840i	0.150327	−	0.0966091i	0.613642	+	0.789584i	$0.289704\pi$
$602$	−2.35715	−	16.3943i	−0.0960701	−	0.668182i
$603$	−5.82505	−	12.7551i	−0.237215	−	0.519427i
$604$	−1.76519	+	12.2771i	−0.0718244	+	0.499550i
$605$	−10.5416	+	3.09530i	−0.428578	+	0.125842i
$606$	17.4230	+	11.1971i	0.707762	+	0.454851i
$607$	19.4977	−	42.6940i	0.791388	−	1.73290i	0.118752	−	0.992924i	$-0.462111\pi$
$607$	19.4977	−	42.6940i	0.791388	−	1.73290i	0.672636	−	0.739974i	$-0.265162\pi$
$608$	−4.52830	−	1.32963i	−0.183647	−	0.0539236i
$609$	1.34258	+	1.54943i	0.0544043	+	0.0627859i
$610$	−8.28248	−	9.55849i	−0.335348	−	0.387012i
$611$	7.35740	+	2.16033i	0.297649	+	0.0873976i
$612$	7.01791	−	15.3671i	0.283682	−	0.621177i
$613$	3.16751	+	2.03563i	0.127934	+	0.0822184i	0.603043	−	0.797709i	$-0.293955\pi$
$613$	3.16751	+	2.03563i	0.127934	+	0.0822184i	−0.475108	+	0.879927i	$0.657591\pi$
$614$	−65.5628	+	19.2510i	−2.64590	+	0.776907i
$615$	1.33908	−	9.31349i	0.0539968	−	0.375556i
$616$	0.279295	+	0.611572i	0.0112531	+	0.0246409i
$617$	−4.68821	−	32.6072i	−0.188740	−	1.31272i	−0.835275	−	0.549832i	$-0.814692\pi$
$617$	−4.68821	−	32.6072i	−0.188740	−	1.31272i	0.646535	−	0.762884i	$-0.276217\pi$
$618$	15.2720	−	9.81472i	0.614330	−	0.394806i
$619$	−25.7293	+	29.6932i	−1.03415	+	1.19347i	−0.0533230	+	0.998577i	$0.516981\pi$
$619$	−25.7293	+	29.6932i	−1.03415	+	1.19347i	−0.980825	+	0.194893i	$0.937564\pi$
$620$	25.4775			1.02320
$621$	0.397086	−	4.77936i	0.0159345	−	0.191789i
$622$	43.2268			1.73324
$623$	3.33465	−	3.84839i	0.133600	−	0.154182i
$624$	−6.56120	+	4.21663i	−0.262658	+	0.168800i
$625$	−1.56546	−	10.8880i	−0.0626185	−	0.435521i
$626$	−33.3553	−	73.0380i	−1.33315	−	2.91919i
$627$	−0.0225571	+	0.156888i	−0.000900844	+	0.00626551i
$628$	0.341142	−	0.100168i	0.0136131	−	0.00399716i
$629$	1.70559	+	1.09611i	0.0680063	+	0.0437050i
$630$	1.04408	−	2.28621i	0.0415971	−	0.0910849i
$631$	−25.5725	−	7.50877i	−1.01803	−	0.298920i	−0.270193	−	0.962806i	$-0.587088\pi$
$631$	−25.5725	−	7.50877i	−1.01803	−	0.298920i	−0.747833	+	0.663887i	$0.768906\pi$
$632$	36.0320	+	41.5832i	1.43328	+	1.65409i
$633$	15.2760	+	17.6295i	0.607168	+	0.700710i
$634$	−12.0037	−	3.52459i	−0.476726	−	0.139979i
$635$	1.08394	−	2.37350i	0.0430149	−	0.0941895i
$636$	15.9148	+	10.2278i	0.631062	+	0.405559i
$637$	1.24690	−	0.366124i	0.0494041	−	0.0145063i
$638$	0.0846689	−	0.588885i	0.00335208	−	0.0233142i
$639$	3.96180	+	8.67514i	0.156726	+	0.343183i
$640$	2.18128	+	15.1711i	0.0862226	+	0.599691i
$641$	−23.7071	+	15.2356i	−0.936375	+	0.601772i	−0.917365	−	0.398047i	$-0.869688\pi$
$641$	−23.7071	+	15.2356i	−0.936375	+	0.601772i	−0.0190105	+	0.999819i	$0.506052\pi$
$642$	−10.1017	+	11.6580i	−0.398682	+	0.460104i
$643$	−42.1359			−1.66168			−0.830839	−	0.556513i	$-0.812139\pi$
$643$	−42.1359			−1.66168			−0.830839	+	0.556513i	$0.812139\pi$
$644$	4.16794	+	20.2791i	0.164240	+	0.799107i
$645$	6.59000			0.259481
$646$	−8.84218	+	10.2044i	−0.347891	+	0.401488i
$647$	31.2107	−	20.0579i	1.22702	−	0.788557i	0.243594	−	0.969877i	$-0.421674\pi$
$647$	31.2107	−	20.0579i	1.22702	−	0.788557i	0.983424	+	0.181321i	$0.0580372\pi$
$648$	0.828708	+	5.76379i	0.0325547	+	0.226423i
$649$	0.173038	+	0.378900i	0.00679233	+	0.0148731i
$650$	1.85931	−	12.9318i	0.0729281	−	0.507226i
$651$	5.66279	−	1.66275i	0.221942	−	0.0651682i
$652$	0.845984	+	0.543681i	0.0331313	+	0.0212922i
$653$	19.4981	−	42.6949i	0.763019	−	1.67078i	0.0215731	−	0.999767i	$-0.493133\pi$
$653$	19.4981	−	42.6949i	0.763019	−	1.67078i	0.741446	−	0.671012i	$-0.234140\pi$
$654$	−14.0216	−	4.11710i	−0.548287	−	0.160992i
$655$	11.6328	+	13.4250i	0.454533	+	0.524559i
$656$	−36.9803	−	42.6775i	−1.44384	−	1.66628i
$657$	−0.572398	−	0.168071i	−0.0223314	−	0.00655708i
$658$	−6.16063	+	13.4899i	−0.240166	+	0.525891i
$659$	29.7006	+	19.0874i	1.15697	+	0.743539i	0.971015	−	0.239019i	$-0.0768258\pi$
$659$	29.7006	+	19.0874i	1.15697	+	0.743539i	0.185955	+	0.982558i	$0.440462\pi$
$660$	−0.478234	+	0.140422i	−0.0186152	+	0.00546593i
$661$	−0.434692	+	3.02335i	−0.0169076	+	0.117595i	−0.996527	−	0.0832662i	$-0.973465\pi$
$661$	−0.434692	+	3.02335i	−0.0169076	+	0.117595i	0.979620	+	0.200861i	$0.0643739\pi$
$662$	−2.50633	−	5.48810i	−0.0974112	−	0.213301i
$663$	0.723766	+	5.03390i	0.0281087	+	0.195501i
$664$	62.9400	−	40.4491i	2.44254	−	1.56973i
$665$	−0.898983	+	1.03748i	−0.0348611	+	0.0402318i
$666$	−1.30209			−0.0504549
$667$	3.54170	−	9.17230i	0.137135	−	0.355153i
$668$	−109.165			−4.22371
$669$	−5.78761	+	6.67925i	−0.223762	+	0.258235i
$670$	−29.6480	+	19.0536i	−1.14540	+	0.736105i
$671$	0.0826878	+	0.575106i	0.00319213	+	0.0222017i
$672$	−1.42815	−	3.12721i	−0.0550920	−	0.120635i
$673$	−5.92268	+	41.1931i	−0.228302	+	1.58788i	0.476956	+	0.878927i	$0.341740\pi$
$673$	−5.92268	+	41.1931i	−0.228302	+	1.58788i	−0.705258	+	0.708951i	$0.749169\pi$
$674$	71.5694	−	21.0147i	2.75675	−	0.809454i
$675$	−3.36501	−	2.16256i	−0.129519	−	0.0832371i
$676$	−20.2842	+	44.4163i	−0.780163	+	1.70832i
$677$	26.9914	+	7.92539i	1.03736	+	0.304597i	0.755701	−	0.654916i	$-0.227296\pi$
$677$	26.9914	+	7.92539i	1.03736	+	0.304597i	0.281662	+	0.959514i	$0.409114\pi$
$678$	13.4369	+	15.5071i	0.516042	+	0.595545i
$679$	−5.06196	−	5.84182i	−0.194260	−	0.224188i
$680$	−21.8650	−	6.42015i	−0.838486	−	0.246202i
$681$	−11.1313	+	24.3741i	−0.426552	+	0.934019i
$682$	−1.44078	−	0.925932i	−0.0551702	−	0.0354558i
$683$	−2.95583	+	0.867909i	−0.113102	+	0.0332096i	−0.337794	−	0.941220i	$-0.609681\pi$
$683$	−2.95583	+	0.867909i	−0.113102	+	0.0332096i	0.224692	+	0.974430i	$0.427862\pi$
$684$	0.843376	−	5.86581i	0.0322473	−	0.224285i
$685$	−7.29085	−	15.9647i	−0.278569	−	0.609981i
$686$	0.357685	+	2.48775i	0.0136565	+	0.0949829i
$687$	−5.87664	+	3.77669i	−0.224208	+	0.144090i
$688$	25.9000	−	29.8902i	0.987429	−	1.13955i
$689$	−5.69503			−0.216963
$690$	−12.0319	+	0.721655i	−0.458047	+	0.0274729i
$691$	−36.8765			−1.40285			−0.701424	−	0.712744i	$-0.747452\pi$
$691$	−36.8765			−1.40285			−0.701424	+	0.712744i	$0.747452\pi$
$692$	−3.70934	+	4.28081i	−0.141008	+	0.162732i
$693$	−0.0971309	+	0.0624222i	−0.00368970	+	0.00237122i
$694$	−9.66385	−	67.2135i	−0.366835	−	2.55139i
$695$	1.61624	+	3.53908i	0.0613076	+	0.134245i
$696$	−1.69900	+	11.8168i	−0.0644005	+	0.447916i
$697$	−35.3309	+	10.3741i	−1.33825	+	0.392947i
$698$	8.07670	+	5.19058i	0.305707	+	0.196466i
$699$	−2.32086	+	5.08196i	−0.0877828	+	0.192218i
$700$	16.5680	+	4.86480i	0.626212	+	0.183872i
$701$	−20.7757	−	23.9764i	−0.784686	−	0.905576i	0.212753	−	0.977106i	$-0.431757\pi$
$701$	−20.7757	−	23.9764i	−0.784686	−	0.905576i	−0.997438	+	0.0715304i	$0.977212\pi$
$702$	−2.13890	−	2.46842i	−0.0807276	−	0.0931646i
$703$	0.682393	+	0.200369i	0.0257369	+	0.00755705i
$704$	0.161283	−	0.353161i	0.00607858	−	0.0133102i
$705$	−4.96386	−	3.19008i	−0.186950	−	0.120145i
$706$	7.70633	−	2.26278i	0.290031	−	0.0851609i
$707$	1.17272	−	8.15647i	0.0441048	−	0.306756i
$708$	−6.46962	−	14.1665i	−0.243143	−	0.532409i
$709$	3.96744	+	27.5941i	0.149000	+	1.03632i	0.917861	+	0.396902i	$0.129915\pi$
$709$	3.96744	+	27.5941i	0.149000	+	1.03632i	−0.768861	+	0.639416i	$0.779176\pi$
$710$	20.1645	−	12.9590i	0.756762	−	0.486341i
$711$	−6.18782	+	7.14113i	−0.232061	+	0.267813i
$712$	29.6519			1.11125
$713$	−19.7828	−	20.2429i	−0.740873	−	0.758102i
$714$	−9.83576			−0.368094
$715$	0.0982585	−	0.113396i	0.00367466	−	0.00424078i
$716$	−12.1641	+	7.81738i	−0.454593	+	0.292149i
$717$	2.35052	+	16.3482i	0.0877819	+	0.610537i
$718$	−16.0751	−	35.1996i	−0.599917	−	1.31364i
$719$	−4.25422	+	29.5887i	−0.158656	+	1.10347i	0.742458	+	0.669892i	$0.233660\pi$
$719$	−4.25422	+	29.5887i	−0.158656	+	1.10347i	−0.901114	+	0.433582i	$0.857249\pi$
$720$	5.75848	−	1.69084i	0.214606	−	0.0630139i
$721$	−6.07638	−	3.90505i	−0.226296	−	0.145432i
$722$	17.8699	−	39.1296i	0.665048	−	1.45625i
$723$	−20.1380	−	5.91305i	−0.748940	−	0.219909i
$724$	−40.9343	−	47.2407i	−1.52131	−	1.75569i
$725$	−5.37034	−	6.19770i	−0.199449	−	0.230177i
$726$	−26.4947	−	7.77954i	−0.983310	−	0.288726i
$727$	15.1324	−	33.1352i	0.561228	−	1.22892i	−0.390110	−	0.920768i	$-0.627563\pi$
$727$	15.1324	−	33.1352i	0.561228	−	1.22892i	0.951338	−	0.308149i	$-0.0997097\pi$
$728$	6.36603	+	4.09120i	0.235941	+	0.151630i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−0.213382	+	1.48410i	−0.00789761	+	0.0549291i
$731$	−10.7133	−	23.4589i	−0.396247	−	0.867660i
$732$	−3.09157	−	21.5024i	−0.114268	−	0.794750i
$733$	−4.64785	+	2.98699i	−0.171672	+	0.110327i	−0.623655	−	0.781700i	$-0.714353\pi$
$733$	−4.64785	+	2.98699i	−0.171672	+	0.110327i	0.451983	+	0.892026i	$0.350717\pi$
$734$	−35.7983	+	41.3134i	−1.32134	+	1.52491i
$735$	−1.00000			−0.0368856
$736$	−10.0316	+	13.0845i	−0.369771	+	0.482301i
$737$	1.61900			0.0596368
$738$	15.4866	−	17.8725i	0.570069	−	0.657894i
$739$	−25.1392	+	16.1560i	−0.924762	+	0.594308i	−0.914036	−	0.405634i	$-0.867051\pi$
$739$	−25.1392	+	16.1560i	−0.924762	+	0.594308i	−0.0107264	+	0.999942i	$0.503414\pi$
$740$	0.318279	+	2.21368i	0.0117002	+	0.0813766i
$741$	0.741098	+	1.62278i	0.0272249	+	0.0596142i
$742$	1.56750	−	10.9022i	0.0575446	−	0.400231i
$743$	−36.7756	+	10.7983i	−1.34916	+	0.396151i	−0.874931	−	0.484248i	$-0.839093\pi$
$743$	−36.7756	+	10.7983i	−1.34916	+	0.396151i	−0.474234	+	0.880399i	$0.657275\pi$
$744$	28.9113	+	18.5801i	1.05994	+	0.681181i
$745$	6.31296	−	13.8235i	0.231289	−	0.506452i
$746$	−67.6718	−	19.8702i	−2.47764	−	0.727501i
$747$	8.41390	+	9.71016i	0.307849	+	0.355276i
$748$	1.27734	+	1.47412i	0.0467040	+	0.0538993i
$749$	5.88893	+	1.72915i	0.215177	+	0.0631817i
$750$	−9.39670	+	20.5759i	−0.343119	+	0.751326i
$751$	−5.12622	−	3.29442i	−0.187059	−	0.120215i	0.443760	−	0.896146i	$-0.353644\pi$
$751$	−5.12622	−	3.29442i	−0.187059	−	0.120215i	−0.630818	+	0.775931i	$0.717281\pi$
$752$	−33.9782	+	9.97689i	−1.23906	+	0.363820i
$753$	−2.86162	+	19.9030i	−0.104283	+	0.725305i
$754$	−2.78174	−	6.09116i	−0.101305	−	0.221827i
$755$	0.408905	+	2.84400i	0.0148816	+	0.103504i
$756$	3.63158	−	2.33387i	0.132079	−	0.0848821i
$757$	18.3350	−	21.1597i	0.666395	−	0.769061i	−0.317413	−	0.948287i	$-0.602814\pi$
$757$	18.3350	−	21.1597i	0.666395	−	0.769061i	0.983808	+	0.179227i	$0.0573595\pi$
$758$	−90.8230			−3.29884
$759$	0.482911	+	0.270940i	0.0175286	+	0.00983451i
$760$	−7.99381			−0.289966
$761$	−4.02529	+	4.64544i	−0.145917	+	0.168397i	−0.824003	−	0.566585i	$-0.808264\pi$
$761$	−4.02529	+	4.64544i	−0.145917	+	0.168397i	0.678086	+	0.734982i	$0.262810\pi$
$762$	5.51698	−	3.54555i	0.199859	−	0.128442i
$763$	0.827474	+	5.75521i	0.0299566	+	0.208353i
$764$	−16.8868	−	36.9769i	−0.610942	−	1.33778i
$765$	0.556939	−	3.87359i	0.0201362	−	0.140050i
$766$	4.35830	−	1.27971i	0.157472	−	0.0462379i
$767$	3.94408	+	2.53471i	0.142413	+	0.0915230i
$768$	−13.2090	+	28.9236i	−0.476637	+	1.04369i
$769$	44.3543	+	13.0236i	1.59946	+	0.469643i	0.955395	−	0.295331i	$-0.0954299\pi$
$769$	44.3543	+	13.0236i	1.59946	+	0.469643i	0.644061	+	0.764974i	$0.277248\pi$
$770$	0.190033	+	0.219310i	0.00684833	+	0.00790340i
$771$	3.88735	+	4.48624i	0.139999	+	0.161568i
$772$	60.0037	+	17.6187i	2.15958	+	0.634110i
$773$	4.33722	−	9.49720i	0.155999	−	0.341590i	−0.815454	−	0.578822i	$-0.803513\pi$
$773$	4.33722	−	9.49720i	0.155999	−	0.341590i	0.971453	+	0.237231i	$0.0762399\pi$
$774$	13.9336	+	8.95457i	0.500833	+	0.321866i
$775$	−22.6512	+	6.65099i	−0.813654	+	0.238910i
$776$	6.40577	−	44.5531i	0.229954	−	1.59936i
$777$	0.215215	+	0.471255i	0.00772079	+	0.0169062i
$778$	−9.94845	−	69.1930i	−0.356669	−	2.48069i
$779$	−10.8664	+	6.98340i	−0.389329	+	0.250206i
$780$	−3.67374	+	4.23972i	−0.131541	+	0.151806i
$781$	−1.10114			−0.0394018
$782$	22.1292	+	41.6578i	0.791338	+	1.48968i
$783$	−2.05018			−0.0732676
$784$	−3.93020	+	4.53569i	−0.140364	+	0.161989i
$785$	0.0692871	−	0.0445281i	0.00247296	−	0.00158928i
$786$	6.35386	+	44.1921i	0.226635	+	1.57628i
$787$	−11.5014	−	25.1846i	−0.409982	−	0.897736i	−0.996160	−	0.0875531i	$-0.972095\pi$
$787$	−11.5014	−	25.1846i	−0.409982	−	0.897736i	0.586178	−	0.810182i	$-0.300632\pi$
$788$	−13.8525	+	96.3462i	−0.493474	+	3.43219i
$789$	−5.93759	+	1.74343i	−0.211384	+	0.0620679i
$790$	19.9787	+	12.8395i	0.710809	+	0.456809i
$791$	3.39143	−	7.42619i	0.120585	−	0.264045i
$792$	−0.645095	−	0.189417i	−0.0229224	−	0.00673063i
$793$	4.28253	+	4.94230i	0.152077	+	0.175506i
$794$	−56.9873	−	65.7668i	−2.02240	−	2.33398i
$795$	4.20482	+	1.23465i	0.149130	+	0.0437884i
$796$	0.610617	−	1.33706i	0.0216427	−	0.0473910i
$797$	7.43814	+	4.78021i	0.263473	+	0.169324i	0.665707	−	0.746213i	$-0.268130\pi$
$797$	7.43814	+	4.78021i	0.263473	+	0.169324i	−0.402235	+	0.915537i	$0.631766\pi$
$798$	−3.31051	+	0.972054i	−0.117191	+	0.0344103i
$799$	−3.28624	+	22.8563i	−0.116259	+	0.808598i
$800$	5.71259	+	12.5088i	0.201971	+	0.442254i
$801$	0.724688	+	5.04031i	0.0256056	+	0.178091i
$802$	11.9825	−	7.70071i	0.423118	−	0.271922i
$803$	0.0451062	−	0.0520553i	0.00159176	−	0.00183699i
$804$	−60.5321			−2.13480
$805$	2.24987	+	4.23534i	0.0792975	+	0.149276i
$806$	−19.2766			−0.678989
$807$	13.2536	−	15.2954i	0.466548	−	0.538425i
$808$	40.3667	−	25.9421i	1.42010	−	0.912641i
$809$	3.99829	+	27.8087i	0.140573	+	0.977703i	0.930967	+	0.365105i	$0.118967\pi$
$809$	3.99829	+	27.8087i	0.140573	+	0.977703i	−0.790394	+	0.612599i	$0.790124\pi$
$810$	1.04408	+	2.28621i	0.0366852	+	0.0803293i
$811$	5.12069	−	35.6152i	0.179812	−	1.25062i	−0.677385	−	0.735629i	$-0.736887\pi$
$811$	5.12069	−	35.6152i	0.179812	−	1.25062i	0.857197	−	0.514989i	$-0.172204\pi$
$812$	8.49186	−	2.49344i	0.298006	−	0.0875024i
$813$	−25.1584	−	16.1684i	−0.882345	−	0.567049i
$814$	0.0624530	−	0.136753i	0.00218898	−	0.00479319i
$815$	0.223516	+	0.0656302i	0.00782942	+	0.00229893i
$816$	−15.3806	−	17.7501i	−0.538427	−	0.621378i
$817$	−5.92430	−	6.83701i	−0.207265	−	0.239197i
$818$	87.4564	+	25.6795i	3.05784	+	0.897863i
$819$	−0.539850	+	1.18211i	−0.0188639	+	0.0413061i
$820$	−34.1705	−	21.9600i	−1.19328	−	0.766877i
$821$	−26.2119	+	7.69651i	−0.914802	+	0.268610i	−0.705061	−	0.709147i	$-0.749080\pi$
$821$	−26.2119	+	7.69651i	−0.914802	+	0.268610i	−0.209741	+	0.977757i	$0.567262\pi$
$822$	6.27765	−	43.6620i	0.218958	−	1.52289i
$823$	13.6863	+	29.9688i	0.477074	+	1.04465i	0.983258	+	0.182221i	$0.0583286\pi$
$823$	13.6863	+	29.9688i	0.477074	+	1.04465i	−0.506184	+	0.862426i	$0.668944\pi$
$824$	−5.98576	−	41.6319i	−0.208524	−	1.45032i
$825$	0.388524	−	0.249689i	0.0135267	−	0.00869305i
$826$	−5.93783	+	6.85262i	−0.206604	+	0.238433i
$827$	−6.26818			−0.217966			−0.108983	−	0.994044i	$-0.534759\pi$
$827$	−6.26818			−0.217966			−0.108983	+	0.994044i	$0.534759\pi$
$828$	−18.0553	−	10.1300i	−0.627465	−	0.352043i
$829$	−9.77224			−0.339404			−0.169702	−	0.985495i	$-0.554280\pi$
$829$	−9.77224			−0.339404			−0.169702	+	0.985495i	$0.554280\pi$
$830$	21.1470	−	24.4049i	0.734022	−	0.847107i
$831$	13.7056	−	8.80805i	0.475442	−	0.305548i
$832$	−0.621895	−	4.32537i	−0.0215603	−	0.149955i
$833$	1.62570	+	3.55978i	0.0563270	+	0.123339i
$834$	−1.39163	+	9.67903i	−0.0481884	+	0.335157i
$835$	−24.2636	+	7.12445i	−0.839678	+	0.246552i
$836$	0.575610	+	0.369922i	0.0199079	+	0.0127940i
$837$	−2.45172	+	5.36852i	−0.0847439	+	0.185563i
$838$	−12.2509	−	3.59719i	−0.423200	−	0.124263i
$839$	15.0019	+	17.3131i	0.517924	+	0.597716i	0.953110	−	0.302624i	$-0.0978628\pi$
$839$	15.0019	+	17.3131i	0.517924	+	0.597716i	−0.435186	+	0.900341i	$0.643317\pi$
$840$	−3.81329	−	4.40077i	−0.131571	−	0.151841i
$841$	23.7923	+	6.98605i	0.820424	+	0.240898i
$842$	0.515539	−	1.12887i	0.0177666	−	0.0389035i
$843$	22.4731	+	14.4426i	0.774014	+	0.497429i
$844$	96.6211	−	28.3705i	3.32584	−	0.976554i
$845$	−1.60975	+	11.1961i	−0.0553771	+	0.385156i
$846$	−6.16063	−	13.4899i	−0.211807	−	0.463792i
$847$	1.56357	+	10.8748i	0.0537248	+	0.373664i
$848$	22.1258	−	14.2194i	0.759802	−	0.488295i
$849$	−12.0216	+	13.8737i	−0.412581	+	0.476144i
$850$	39.3430			1.34946
$851$	1.51172	−	1.97177i	0.0518210	−	0.0675914i
$852$	41.1698			1.41045
$853$	7.52600	−	8.68547i	0.257685	−	0.297385i	−0.612135	−	0.790753i	$-0.709689\pi$
$853$	7.52600	−	8.68547i	0.257685	−	0.297385i	0.869820	+	0.493369i	$0.164235\pi$
$854$	−10.6399	+	6.83786i	−0.364091	+	0.233987i
$855$	−0.195368	−	1.35881i	−0.00668144	−	0.0464704i
$856$	14.8466	+	32.5096i	0.507448	+	1.11116i
$857$	0.576295	−	4.00822i	0.0196859	−	0.136918i	−0.977608	−	0.210433i	$-0.932513\pi$
$857$	0.576295	−	4.00822i	0.0196859	−	0.136918i	0.997294	+	0.0735150i	$0.0234217\pi$
$858$	0.361838	−	0.106245i	0.0123529	−	0.00362715i
$859$	42.8840	+	27.5599i	1.46318	+	0.940330i	0.998494	+	0.0548562i	$0.0174700\pi$
$859$	42.8840	+	27.5599i	1.46318	+	0.940330i	0.464688	+	0.885474i	$0.346166\pi$
$860$	11.8178	−	25.8773i	0.402983	−	0.882410i
$861$	−9.02812	−	2.65090i	−0.307678	−	0.0903423i
$862$	−58.2496	−	67.2236i	−1.98399	−	2.28965i
$863$	24.4701	+	28.2400i	0.832971	+	0.961300i	0.999695	−	0.0247036i	$-0.00786421\pi$
$863$	24.4701	+	28.2400i	0.832971	+	0.961300i	−0.166724	+	0.986004i	$0.553319\pi$
$864$	3.29862	+	0.968563i	0.112221	+	0.0329512i
$865$	−0.545082	+	1.19356i	−0.0185333	+	0.0405823i
$866$	−28.5769	−	18.3652i	−0.971082	−	0.624076i
$867$	1.61684	−	0.474746i	0.0549106	−	0.0161232i
$868$	3.62583	−	25.2182i	0.123069	−	0.855962i
$869$	−0.453212	−	0.992396i	−0.0153742	−	0.0336647i
$870$	0.733320	+	5.10035i	0.0248619	+	0.172918i
$871$	15.3298	−	9.85184i	0.519429	−	0.333817i
$872$	−22.1720	+	25.5878i	−0.750838	+	0.866513i
$873$	7.72983			0.261615
$874$	11.5652	+	11.8341i	0.391199	+	0.400296i
$875$	9.00000			0.304256
$876$	−1.68645	+	1.94627i	−0.0569799	+	0.0657583i
$877$	−31.8890	+	20.4938i	−1.07681	+	0.692027i	−0.953819	−	0.300381i	$-0.902886\pi$
$877$	−31.8890	+	20.4938i	−1.07681	+	0.692027i	−0.122995	+	0.992407i	$0.539250\pi$
$878$	−5.74867	−	39.9829i	−0.194008	−	1.34936i
$879$	−2.69452	−	5.90018i	−0.0908839	−	0.199008i
$880$	−0.0986158	+	0.685888i	−0.00332434	+	0.0231213i
$881$	8.58129	−	2.51969i	0.289111	−	0.0848906i	−0.133961	−	0.990987i	$-0.542770\pi$
$881$	8.58129	−	2.51969i	0.289111	−	0.0848906i	0.423072	+	0.906096i	$0.360952\pi$
$882$	−2.11435	−	1.35881i	−0.0711940	−	0.0457536i
$883$	0.637485	−	1.39590i	0.0214531	−	0.0469757i	−0.898602	−	0.438764i	$-0.855416\pi$
$883$	0.637485	−	1.39590i	0.0214531	−	0.0469757i	0.920055	+	0.391789i	$0.128144\pi$
$884$	21.0648	+	6.18519i	0.708487	+	0.208031i
$885$	−2.36253	−	2.72650i	−0.0794156	−	0.0916504i
$886$	−50.5897	−	58.3836i	−1.69959	−	1.96144i
$887$	−34.3034	−	10.0724i	−1.15180	−	0.338198i	−0.350556	−	0.936542i	$-0.614007\pi$
$887$	−34.3034	−	10.0724i	−1.15180	−	0.338198i	−0.801239	+	0.598344i	$0.795826\pi$
$888$	−1.25321	+	2.74414i	−0.0420549	+	0.0920875i
$889$	−2.19508	−	1.41069i	−0.0736206	−	0.0473131i
$890$	12.2799	−	3.60569i	0.411622	−	0.120863i
$891$	0.0164316	−	0.114284i	0.000550480	−	0.00382867i
$892$	15.8490	+	34.7044i	0.530662	+	1.16199i
$893$	1.15278	+	8.01774i	0.0385762	+	0.268303i
$894$	32.1313	−	20.6495i	1.07463	−	0.690624i
$895$	−2.19348	+	2.53141i	−0.0733198	+	0.0846156i
$896$	15.3271			0.512043
$897$	6.22121	−	0.373138i	0.207720	−	0.0124587i
$898$	86.0790			2.87249
$899$	−7.92375	+	9.14449i	−0.264272	+	0.304986i
$900$	−14.5263	+	9.33549i	−0.484210	+	0.311183i
$901$	−2.44069	−	16.9754i	−0.0813112	−	0.565532i
$902$	1.13428	+	2.48372i	0.0377673	+	0.0826988i
$903$	0.937855	−	6.52292i	0.0312099	−	0.217069i
$904$	45.6135	−	13.3933i	1.51708	−	0.445456i
$905$	−12.1814	−	7.82850i	−0.404923	−	0.260228i
$906$	−2.99989	+	6.56884i	−0.0996646	+	0.218235i
$907$	28.7411	+	8.43916i	0.954334	+	0.280218i	0.721590	−	0.692320i	$-0.243411\pi$
$907$	28.7411	+	8.43916i	0.954334	+	0.280218i	0.232744	+	0.972538i	$0.425230\pi$
$908$	75.7497	+	87.4198i	2.51384	+	2.90113i
$909$	5.39628	+	6.22764i	0.178983	+	0.206558i
$910$	3.13389	+	0.920192i	0.103887	+	0.0305041i
$911$	−6.01182	+	13.1641i	−0.199181	+	0.436145i	−0.982696	−	0.185228i	$-0.940698\pi$
$911$	−6.01182	+	13.1641i	−0.199181	+	0.436145i	0.783515	+	0.621373i	$0.213425\pi$
$912$	−6.93099	−	4.45428i	−0.229508	−	0.147496i
$913$	−1.42338	+	0.417942i	−0.0471070	+	0.0138319i
$914$	−7.36363	+	51.2152i	−0.243567	+	1.69405i
$915$	−2.09047	−	4.57748i	−0.0691087	−	0.151327i
$916$	4.29161	+	29.8488i	0.141799	+	0.986233i
$917$	14.9439	−	9.60386i	0.493491	−	0.317147i
$918$	6.44105	−	7.43337i	0.212586	−	0.245338i
$919$	−54.7339			−1.80551			−0.902753	−	0.430159i	$-0.858457\pi$
$919$	−54.7339			−1.80551			−0.902753	+	0.430159i	$0.858457\pi$
$920$	−10.0594	+	26.0517i	−0.331647	+	0.858901i
$921$	−27.1872			−0.895850
$922$	55.6729	−	64.2500i	1.83349	−	2.11596i
$923$	−10.4263	+	6.70054i	−0.343184	+	0.220551i
$924$	0.0709331	+	0.493351i	0.00233353	+	0.0162300i
$925$	−0.860859	−	1.88502i	−0.0283049	−	0.0619791i
$926$	−2.60565	+	18.1227i	−0.0856269	+	0.595548i
$927$	6.93043	−	2.03496i	0.227625	−	0.0668367i
$928$	5.92940	+	3.81059i	0.194642	+	0.125089i
$929$	−15.4216	+	33.7685i	−0.505965	+	1.10791i	0.468520	+	0.883453i	$0.344788\pi$
$929$	−15.4216	+	33.7685i	−0.505965	+	1.10791i	−0.974484	+	0.224455i	$0.927940\pi$
$930$	14.2325	+	4.17904i	0.466702	+	0.137036i
$931$	0.898983	+	1.03748i	0.0294630	+	0.0340021i
$932$	15.7937	+	18.2269i	0.517339	+	0.597041i
$933$	16.5023	+	4.84551i	0.540261	+	0.158635i
$934$	−0.573735	+	1.25631i	−0.0187732	+	0.0411076i
$935$	0.380115	+	0.244285i	0.0124311	+	0.00798897i
$936$	−7.26079	+	2.13196i	−0.237326	+	0.0696853i
$937$	−4.67933	+	32.5454i	−0.152867	+	1.06321i	0.758516	+	0.651654i	$0.225925\pi$
$937$	−4.67933	+	32.5454i	−0.152867	+	1.06321i	−0.911383	+	0.411559i	$0.864984\pi$
$938$	14.6403	+	32.0578i	0.478023	+	1.04673i
$939$	−4.54656	−	31.6220i	−0.148371	−	1.03195i
$940$	−21.4283	+	13.7711i	−0.698914	+	0.449164i
$941$	−2.93300	+	3.38486i	−0.0956129	+	0.110343i	−0.801540	−	0.597942i	$-0.795985\pi$
$941$	−2.93300	+	3.38486i	−0.0956129	+	0.110343i	0.705927	+	0.708285i	$0.250531\pi$
$942$	0.207003			0.00674452
$943$	9.08465	+	44.2013i	0.295837	+	1.43939i
$944$	−21.6518			−0.704706
$945$	0.654861	−	0.755750i	0.0213026	−	0.0245845i
$946$	−1.60877	+	1.03389i	−0.0523056	+	0.0336147i
$947$	0.593050	+	4.12475i	0.0192715	+	0.134036i	0.997186	−	0.0749700i	$-0.0238861\pi$
$947$	0.593050	+	4.12475i	0.0192715	+	0.134036i	−0.977914	+	0.209006i	$0.932977\pi$
$948$	16.9449	+	37.1042i	0.550345	+	1.20509i
$949$	0.110331	−	0.767368i	0.00358149	−	0.0249098i
$950$	13.2421	−	3.88822i	0.429629	−	0.126150i
$951$	−4.18743	−	2.69110i	−0.135787	−	0.0872649i
$952$	−9.46652	+	20.7288i	−0.306812	+	0.671824i
$953$	−14.2636	−	4.18816i	−0.462042	−	0.135668i	0.0424231	−	0.999100i	$-0.486492\pi$
$953$	−14.2636	−	4.18816i	−0.462042	−	0.135668i	−0.504466	+	0.863432i	$0.668310\pi$
$954$	7.21282	+	8.32404i	0.233524	+	0.269501i
$955$	−6.16659	−	7.11662i	−0.199546	−	0.230288i
$956$	68.4108	+	20.0872i	2.21256	+	0.649667i
$957$	0.0983344	−	0.215322i	0.00317870	−	0.00696038i
$958$	−48.8800	−	31.4133i	−1.57924	−	1.01492i
$959$	−16.8398	+	4.94462i	−0.543787	+	0.159670i
$960$	−0.478549	+	3.32838i	−0.0154451	+	0.107423i
$961$	1.59185	+	3.48567i	0.0513501	+	0.112441i
$962$	−0.240814	−	1.67490i	−0.00776415	−	0.0540009i
$963$	−5.16323	+	3.31821i	−0.166383	+	0.106928i
$964$	−59.3324	+	68.4732i	−1.91097	+	2.20537i
$965$	14.4866			0.466342
$966$	−0.998011	+	12.0122i	−0.0321105	+	0.386485i
$967$	−14.1305			−0.454405			−0.227203	−	0.973848i	$-0.572958\pi$
$967$	−14.1305			−0.454405			−0.227203	+	0.973848i	$0.572958\pi$
$968$	−41.8954	+	48.3498i	−1.34657	+	1.55402i
$969$	−4.51946	+	2.90448i	−0.145186	+	0.0933054i
$970$	−2.76485	−	19.2299i	−0.0887739	−	0.617436i
$971$	−11.2959	−	24.7346i	−0.362503	−	0.793770i	−0.999733	−	0.0230971i	$-0.992647\pi$
$971$	−11.2959	−	24.7346i	−0.362503	−	0.793770i	0.637230	−	0.770673i	$-0.280080\pi$
$972$	−0.614354	+	4.27292i	−0.0197054	+	0.137054i
$973$	3.73307	−	1.09613i	0.119677	−	0.0351403i
$974$	45.2679	+	29.0919i	1.45048	+	0.932165i
$975$	2.15940	−	4.72842i	0.0691561	−	0.151431i
$976$	−28.9780	−	8.50871i	−0.927563	−	0.272357i
$977$	−21.3710	−	24.6635i	−0.683720	−	0.789055i	0.302737	−	0.953074i	$-0.402100\pi$
$977$	−21.3710	−	24.6635i	−0.683720	−	0.789055i	−0.986457	+	0.164019i	$0.947554\pi$
$978$	0.383413	+	0.442482i	0.0122602	+	0.0141490i
$979$	−0.564122	−	0.165641i	−0.0180294	−	0.00529391i
$980$	−1.79329	+	3.92676i	−0.0572845	+	0.125436i
$981$	−4.89138	−	3.14350i	−0.156170	−	0.100364i
$982$	22.3362	−	6.55850i	0.712777	−	0.209290i
$983$	−4.18829	+	29.1302i	−0.133586	+	0.929109i	0.807241	+	0.590222i	$0.200960\pi$
$983$	−4.18829	+	29.1302i	−0.133586	+	0.929109i	−0.940827	+	0.338887i	$0.889949\pi$
$984$	−22.7609	−	49.8394i	−0.725590	−	1.58882i
$985$	3.20892	+	22.3186i	0.102245	+	0.711128i
$986$	16.9640	−	10.9021i	0.540243	−	0.347193i
$987$	−3.86404	+	4.45934i	−0.122994	+	0.141942i
$988$	7.70126			0.245010
$989$	−29.7368	+	10.7036i	−0.945576	+	0.340354i
$990$	−0.290189			−0.00922282
$991$	−21.4830	+	24.7927i	−0.682429	+	0.787565i	−0.986267	−	0.165159i	$-0.947186\pi$
$991$	−21.4830	+	24.7927i	−0.682429	+	0.787565i	0.303838	+	0.952724i	$0.401732\pi$
$992$	17.0690	−	10.9695i	0.541940	−	0.348284i
$993$	−0.341629	−	2.37609i	−0.0108413	−	0.0754028i
$994$	−9.95735	−	21.8035i	−0.315828	−	0.691566i
$995$	0.0484583	−	0.337035i	0.00153623	−	0.0106847i
$996$	53.2180	−	15.6262i	1.68628	−	0.495136i
$997$	−17.1774	−	11.0392i	−0.544012	−	0.349616i	0.239594	−	0.970873i	$-0.422986\pi$
$997$	−17.1774	−	11.0392i	−0.544012	−	0.349616i	−0.783606	+	0.621258i	$0.786622\pi$
$998$	17.0933	−	37.4291i	0.541079	−	1.18480i
$999$	−0.497086	−	0.145958i	−0.0157271	−	0.00461790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.a.85.1	✓	10
23.13	even	11	inner	483.2.q.a.358.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.a.85.1	✓	10	1.1	even	1	trivial
483.2.q.a.358.1	yes	10	23.13	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64589 - 1.89945i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.614354 - 4.27292i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.357685 - 2.48775i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-4.89867 - 3.14818i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(1.64589 - 1.89945i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.614354 - 4.27292i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.357685 - 2.48775i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-4.89867 - 3.14818i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-2.41153 - 0.708089i) q^{10} +(0.0756100 + 0.0872586i) q^{11} +(-2.82694 - 3.26247i) q^{12} +(1.24690 + 0.366124i) q^{13} +(-1.04408 + 2.28621i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(-5.75848 + 1.69084i) q^{16} +(-0.556939 + 3.87359i) q^{17} +(-1.04408 - 2.28621i) q^{18} +(0.195368 + 1.35881i) q^{19} +(-3.63158 + 2.33387i) q^{20} +(-0.654861 + 0.755750i) q^{21} +0.290189 q^{22} +(4.67421 + 1.07322i) q^{23} -5.82306 q^{24} +(2.61944 - 3.02300i) q^{25} +(2.74769 - 1.76584i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(1.79329 + 3.92676i) q^{28} +(0.291772 - 2.02932i) q^{29} +(-2.41153 + 0.708089i) q^{30} +(-4.96496 - 3.19079i) q^{31} +(-1.42815 + 3.12721i) q^{32} +(0.110783 + 0.0325288i) q^{33} +(6.44105 + 7.43337i) q^{34} +(0.654861 + 0.755750i) q^{35} +(-4.14200 - 1.21620i) q^{36} +(0.215215 - 0.471255i) q^{37} +(2.90255 + 1.86536i) q^{38} +(1.24690 - 0.366124i) q^{39} +(-0.828708 + 5.76379i) q^{40} +(3.90875 + 8.55897i) q^{41} +(0.357685 + 2.48775i) q^{42} +(-5.54386 + 3.56282i) q^{43} +(0.326398 - 0.376684i) q^{44} -1.00000 q^{45} +(9.73174 - 7.11204i) q^{46} +5.90055 q^{47} +(-3.93020 + 4.53569i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-1.43074 - 9.95102i) q^{50} +(1.62570 + 3.55978i) q^{51} +(0.798379 - 5.55285i) q^{52} +(-4.20482 + 1.23465i) q^{53} +(-2.11435 - 1.35881i) q^{54} +(0.0479637 - 0.105026i) q^{55} +(5.58718 + 1.64055i) q^{56} +(0.898983 + 1.03748i) q^{57} +(-3.37437 - 3.89423i) q^{58} +(3.46155 + 1.01640i) q^{59} +(-1.79329 + 3.92676i) q^{60} +(4.23338 + 2.72063i) q^{61} +(-14.2325 + 4.17904i) q^{62} +(-0.142315 + 0.989821i) q^{63} +(-1.39688 - 3.05874i) q^{64} +(-0.184944 - 1.28632i) q^{65} +(0.244123 - 0.156888i) q^{66} +(9.18262 - 10.5973i) q^{67} +16.8937 q^{68} +(4.51242 - 1.62422i) q^{69} +2.51334 q^{70} +(-6.24539 + 7.20756i) q^{71} +(-4.89867 + 3.14818i) q^{72} +(-0.0848998 - 0.590491i) q^{73} +(-0.540908 - 1.18442i) q^{74} +(0.569259 - 3.95929i) q^{75} +(5.68608 - 1.66958i) q^{76} +(-0.0971309 - 0.0624222i) q^{77} +(1.35682 - 2.97103i) q^{78} +(-9.06631 - 2.66211i) q^{79} +(3.93020 + 4.53569i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(22.6907 + 6.66260i) q^{82} +(-5.33741 + 11.6873i) q^{83} +(3.63158 + 2.33387i) q^{84} +(3.75491 - 1.10254i) q^{85} +(-2.35715 + 16.3943i) q^{86} +(-0.851677 - 1.86491i) q^{87} +(-0.0956823 - 0.665485i) q^{88} +(-4.28379 + 2.75302i) q^{89} +(-1.64589 + 1.89945i) q^{90} -1.29954 q^{91} +(1.71417 - 20.6319i) q^{92} -5.90186 q^{93} +(9.71162 - 11.2078i) q^{94} +(1.15486 - 0.742184i) q^{95} +(0.489262 + 3.40289i) q^{96} +(3.21109 + 7.03130i) q^{97} +(0.357685 - 2.48775i) q^{98} +(0.110783 - 0.0325288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - q^{3} + 8 q^{4} + q^{5} + 4 q^{6} - q^{7} - 7 q^{8} - q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - q^3 + 8 * q^4 + q^5 + 4 * q^6 - q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} - q^{3} + 8 q^{4} + q^{5} + 4 q^{6} - q^{7} - 7 q^{8} - q^{9} - 4 q^{10} - q^{11} - 3 q^{12} + 15 q^{13} - 7 q^{14} + q^{15} - 10 q^{16} - 24 q^{17} - 7 q^{18} + 5 q^{19} - 8 q^{20} - q^{21} + 26 q^{22} + 21 q^{23} - 18 q^{24} + 4 q^{25} + 6 q^{26} - q^{27} - 3 q^{28} - 22 q^{29} - 4 q^{30} - 8 q^{31} + 10 q^{32} - q^{33} + 8 q^{34} + q^{35} - 14 q^{36} - 2 q^{37} + 2 q^{38} + 15 q^{39} - 4 q^{40} + 7 q^{41} + 4 q^{42} + q^{43} + 19 q^{44} - 10 q^{45} + 15 q^{46} - 6 q^{47} + q^{48} - q^{49} - 16 q^{50} + 20 q^{51} - 21 q^{52} - q^{53} - 7 q^{54} + 12 q^{55} + 4 q^{56} - 6 q^{57} + 22 q^{58} + 10 q^{59} + 3 q^{60} + 5 q^{61} - 34 q^{62} - q^{63} + 13 q^{64} - 4 q^{65} - 7 q^{66} + 29 q^{67} - 28 q^{68} - q^{69} - 4 q^{70} + 22 q^{71} - 7 q^{72} - 33 q^{73} - 36 q^{74} + 4 q^{75} + 26 q^{76} - q^{77} + 28 q^{78} + 27 q^{79} - q^{80} - q^{81} + 38 q^{82} + 25 q^{83} + 8 q^{84} + 2 q^{85} + 18 q^{86} - 7 q^{88} - 38 q^{89} - 4 q^{90} - 18 q^{91} + 41 q^{92} - 30 q^{93} - 42 q^{94} + 6 q^{95} - 23 q^{96} - q^{97} + 4 q^{98} - q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - q^3 + 8 * q^4 + q^5 + 4 * q^6 - q^7 - 7 * q^8 - q^9 - 4 * q^10 - q^11 - 3 * q^12 + 15 * q^13 - 7 * q^14 + q^15 - 10 * q^16 - 24 * q^17 - 7 * q^18 + 5 * q^19 - 8 * q^20 - q^21 + 26 * q^22 + 21 * q^23 - 18 * q^24 + 4 * q^25 + 6 * q^26 - q^27 - 3 * q^28 - 22 * q^29 - 4 * q^30 - 8 * q^31 + 10 * q^32 - q^33 + 8 * q^34 + q^35 - 14 * q^36 - 2 * q^37 + 2 * q^38 + 15 * q^39 - 4 * q^40 + 7 * q^41 + 4 * q^42 + q^43 + 19 * q^44 - 10 * q^45 + 15 * q^46 - 6 * q^47 + q^48 - q^49 - 16 * q^50 + 20 * q^51 - 21 * q^52 - q^53 - 7 * q^54 + 12 * q^55 + 4 * q^56 - 6 * q^57 + 22 * q^58 + 10 * q^59 + 3 * q^60 + 5 * q^61 - 34 * q^62 - q^63 + 13 * q^64 - 4 * q^65 - 7 * q^66 + 29 * q^67 - 28 * q^68 - q^69 - 4 * q^70 + 22 * q^71 - 7 * q^72 - 33 * q^73 - 36 * q^74 + 4 * q^75 + 26 * q^76 - q^77 + 28 * q^78 + 27 * q^79 - q^80 - q^81 + 38 * q^82 + 25 * q^83 + 8 * q^84 + 2 * q^85 + 18 * q^86 - 7 * q^88 - 38 * q^89 - 4 * q^90 - 18 * q^91 + 41 * q^92 - 30 * q^93 - 42 * q^94 + 6 * q^95 - 23 * q^96 - q^97 + 4 * q^98 - q^99

Introduction

L-functions

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