LMFDB - Embedded newform 69.2.e.c.52.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (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:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
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			52.2
Root			$2.55199 - 0.749331i$ of defining polynomial
Character	$\chi$	$=$	69.52
Dual form			69.2.e.c.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.236364 + 0.517565i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(1.09772 + 1.26683i) q^{4} +(2.27341 - 1.46103i) q^{5} +(0.372604 - 0.430008i) q^{6} +(-0.481879 + 3.35154i) q^{7} +(-2.00700 + 0.589308i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.236364 + 0.517565i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(1.09772 + 1.26683i) q^{4} +(2.27341 - 1.46103i) q^{5} +(0.372604 - 0.430008i) q^{6} +(-0.481879 + 3.35154i) q^{7} +(-2.00700 + 0.589308i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.218827 + 1.52197i) q^{10} +(-1.86448 - 4.08263i) q^{11} +(-0.696343 - 1.52478i) q^{12} +(-0.891052 - 6.19740i) q^{13} +(-1.62074 - 1.04159i) q^{14} +(-2.59294 + 0.761356i) q^{15} +(-0.307736 + 2.14035i) q^{16} +(-2.00981 + 2.31944i) q^{17} +(-0.478659 + 0.307615i) q^{18} +(-0.686559 - 0.792332i) q^{19} +(4.34644 + 1.27623i) q^{20} +(1.40660 - 3.08002i) q^{21} +2.55372 q^{22} +(-3.18128 + 3.58879i) q^{23} +2.09173 q^{24} +(0.956704 - 2.09489i) q^{25} +(3.41817 + 1.00367i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-4.77480 + 3.06858i) q^{28} +(1.45248 - 1.67625i) q^{29} +(0.218827 - 1.52197i) q^{30} +(6.22433 - 1.82763i) q^{31} +(-4.55438 - 2.92692i) q^{32} +(0.638741 + 4.44254i) q^{33} +(-0.725416 - 1.58844i) q^{34} +(3.80120 + 8.32347i) q^{35} +(0.238557 + 1.65920i) q^{36} +(0.235181 + 0.151142i) q^{37} +(0.572361 - 0.168060i) q^{38} +(-0.891052 + 6.19740i) q^{39} +(-3.70173 + 4.27203i) q^{40} +(1.19434 - 0.767558i) q^{41} +(1.26164 + 1.45601i) q^{42} +(-1.76507 - 0.518271i) q^{43} +(3.12534 - 6.84355i) q^{44} +2.70241 q^{45} +(-1.10549 - 2.49478i) q^{46} +4.74565 q^{47} +(0.898277 - 1.96695i) q^{48} +(-4.28417 - 1.25794i) q^{49} +(0.858110 + 0.990312i) q^{50} +(2.58186 - 1.65926i) q^{51} +(6.87295 - 7.93180i) q^{52} +(-0.768306 + 5.34369i) q^{53} +(0.545935 - 0.160301i) q^{54} +(-10.2036 - 6.55744i) q^{55} +(-1.00796 - 7.01051i) q^{56} +(0.435523 + 0.953663i) q^{57} +(0.524255 + 1.14796i) q^{58} +(1.54995 + 10.7801i) q^{59} +(-3.81082 - 2.44907i) q^{60} +(-4.49474 + 1.31978i) q^{61} +(-0.525291 + 3.65348i) q^{62} +(-2.21736 + 2.55897i) q^{63} +(-1.04683 + 0.672754i) q^{64} +(-11.0803 - 12.7874i) q^{65} +(-2.45028 - 0.719467i) q^{66} +(-0.0835538 + 0.182957i) q^{67} -5.14454 q^{68} +(4.06350 - 2.54715i) q^{69} -5.20640 q^{70} +(-1.25365 + 2.74512i) q^{71} +(-2.00700 - 0.589308i) q^{72} +(7.91764 + 9.13745i) q^{73} +(-0.133814 + 0.0859970i) q^{74} +(-1.50815 + 1.74050i) q^{75} +(0.250104 - 1.73951i) q^{76} +(14.5816 - 4.28153i) q^{77} +(-2.99695 - 1.92602i) q^{78} +(-1.10543 - 7.68843i) q^{79} +(2.42751 + 5.31551i) q^{80} +(0.415415 + 0.909632i) q^{81} +(0.114961 + 0.799573i) q^{82} +(-12.4179 - 7.98047i) q^{83} +(5.44591 - 1.59906i) q^{84} +(-1.18034 + 8.20944i) q^{85} +(0.685438 - 0.791037i) q^{86} +(-1.86590 + 1.19914i) q^{87} +(6.14793 + 7.09509i) q^{88} +(0.838282 + 0.246142i) q^{89} +(-0.638752 + 1.39867i) q^{90} +21.2002 q^{91} +(-8.03854 - 0.0906751i) q^{92} -6.48711 q^{93} +(-1.12170 + 2.45618i) q^{94} +(-2.71845 - 0.798210i) q^{95} +(3.54529 + 4.09148i) q^{96} +(9.73536 - 6.25653i) q^{97} +(1.66369 - 1.92000i) q^{98} +(0.638741 - 4.44254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.236364	+	0.517565i	−0.167135	+	0.365974i	−0.974604	−	0.223936i	$-0.928109\pi$
$2$	−0.236364	+	0.517565i	−0.167135	+	0.365974i	0.807469	+	0.589910i	$0.200837\pi$
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	1.09772	+	1.26683i	0.548858	+	0.633416i
$5$	2.27341	−	1.46103i	1.01670	−	0.653393i	0.0775811	−	0.996986i	$-0.475280\pi$
$5$	2.27341	−	1.46103i	1.01670	−	0.653393i	0.939119	+	0.343593i	$0.111644\pi$
$6$	0.372604	−	0.430008i	0.152115	−	0.175550i
$7$	−0.481879	+	3.35154i	−0.182133	+	1.26676i	0.669574	+	0.742745i	$0.266477\pi$
$7$	−0.481879	+	3.35154i	−0.182133	+	1.26676i	−0.851707	+	0.524018i	$0.824432\pi$
$8$	−2.00700	+	0.589308i	−0.709581	+	0.208352i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	0.218827	+	1.52197i	0.0691990	+	0.481290i
$11$	−1.86448	−	4.08263i	−0.562161	−	1.23096i	−0.950867	−	0.309599i	$-0.899805\pi$
$11$	−1.86448	−	4.08263i	−0.562161	−	1.23096i	0.388707	−	0.921362i	$-0.372922\pi$
$12$	−0.696343	−	1.52478i	−0.201017	−	0.440166i
$13$	−0.891052	−	6.19740i	−0.247133	−	1.71885i	−0.614621	−	0.788822i	$-0.710691\pi$
$13$	−0.891052	−	6.19740i	−0.247133	−	1.71885i	0.367488	−	0.930028i	$-0.380218\pi$
$14$	−1.62074	−	1.04159i	−0.433161	−	0.278376i
$15$	−2.59294	+	0.761356i	−0.669495	+	0.196581i
$16$	−0.307736	+	2.14035i	−0.0769340	+	0.535088i
$17$	−2.00981	+	2.31944i	−0.487450	+	0.562548i	−0.945183	−	0.326542i	$-0.894116\pi$
$17$	−2.00981	+	2.31944i	−0.487450	+	0.562548i	0.457732	+	0.889090i	$0.348662\pi$
$18$	−0.478659	+	0.307615i	−0.112821	+	0.0725056i
$19$	−0.686559	−	0.792332i	−0.157507	−	0.181773i	0.671511	−	0.740995i	$-0.265646\pi$
$19$	−0.686559	−	0.792332i	−0.157507	−	0.181773i	−0.829018	+	0.559221i	$0.811100\pi$
$20$	4.34644	+	1.27623i	0.971894	+	0.285374i
$21$	1.40660	−	3.08002i	0.306945	−	0.672115i
$22$	2.55372			0.544455
$23$	−3.18128	+	3.58879i	−0.663343	+	0.748315i
$23$	−3.18128	+	3.58879i	−0.663343	+	0.748315i
$24$	2.09173			0.426972
$25$	0.956704	−	2.09489i	0.191341	−	0.418978i
$26$	3.41817	+	1.00367i	0.670358	+	0.196835i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	−4.77480	+	3.06858i	−0.902353	+	0.579907i
$29$	1.45248	−	1.67625i	0.269719	−	0.311272i	−0.604691	−	0.796460i	$-0.706703\pi$
$29$	1.45248	−	1.67625i	0.269719	−	0.311272i	0.874410	+	0.485188i	$0.161249\pi$
$30$	0.218827	−	1.52197i	0.0399521	−	0.277873i
$31$	6.22433	−	1.82763i	1.11792	−	0.328252i	0.329973	−	0.943990i	$-0.392960\pi$
$31$	6.22433	−	1.82763i	1.11792	−	0.328252i	0.787951	+	0.615739i	$0.211142\pi$
$32$	−4.55438	−	2.92692i	−0.805108	−	0.517412i
$33$	0.638741	+	4.44254i	0.111191	+	0.773347i
$34$	−0.725416	−	1.58844i	−0.124408	−	0.272415i
$35$	3.80120	+	8.32347i	0.642520	+	1.40692i
$36$	0.238557	+	1.65920i	0.0397594	+	0.276533i
$37$	0.235181	+	0.151142i	0.0386635	+	0.0248475i	0.559830	−	0.828608i	$-0.310867\pi$
$37$	0.235181	+	0.151142i	0.0386635	+	0.0248475i	−0.521166	+	0.853455i	$0.674503\pi$
$38$	0.572361	−	0.168060i	0.0928492	−	0.0272630i
$39$	−0.891052	+	6.19740i	−0.142683	+	0.992379i
$40$	−3.70173	+	4.27203i	−0.585295	+	0.675467i
$41$	1.19434	−	0.767558i	0.186525	−	0.119872i	−0.444046	−	0.896004i	$-0.646457\pi$
$41$	1.19434	−	0.767558i	0.186525	−	0.119872i	0.630571	+	0.776132i	$0.282821\pi$
$42$	1.26164	+	1.45601i	0.194675	+	0.224667i
$43$	−1.76507	−	0.518271i	−0.269171	−	0.0790356i	0.144362	−	0.989525i	$-0.453887\pi$
$43$	−1.76507	−	0.518271i	−0.269171	−	0.0790356i	−0.413533	+	0.910489i	$0.635705\pi$
$44$	3.12534	−	6.84355i	0.471163	−	1.03170i
$45$	2.70241			0.402851
$46$	−1.10549	−	2.49478i	−0.162996	−	0.367835i
$47$	4.74565			0.692225			0.346112	−	0.938193i	$-0.387502\pi$
$47$	4.74565			0.692225			0.346112	+	0.938193i	$0.387502\pi$
$48$	0.898277	−	1.96695i	0.129655	−	0.283905i
$49$	−4.28417	−	1.25794i	−0.612024	−	0.179706i
$50$	0.858110	+	0.990312i	0.121355	+	0.140051i
$51$	2.58186	−	1.65926i	0.361533	−	0.232343i
$52$	6.87295	−	7.93180i	0.953106	−	1.09994i
$53$	−0.768306	+	5.34369i	−0.105535	+	0.734012i	0.866500	+	0.499177i	$0.166364\pi$
$53$	−0.768306	+	5.34369i	−0.105535	+	0.734012i	−0.972035	+	0.234835i	$0.924545\pi$
$54$	0.545935	−	0.160301i	0.0742923	−	0.0218142i
$55$	−10.2036	−	6.55744i	−1.37585	−	0.884205i
$56$	−1.00796	−	7.01051i	−0.134694	−	0.936819i
$57$	0.435523	+	0.953663i	0.0576864	+	0.126316i
$58$	0.524255	+	1.14796i	0.0688380	+	0.150734i
$59$	1.54995	+	10.7801i	0.201786	+	1.40346i	0.798980	+	0.601358i	$0.205373\pi$
$59$	1.54995	+	10.7801i	0.201786	+	1.40346i	−0.597193	+	0.802097i	$0.703717\pi$
$60$	−3.81082	−	2.44907i	−0.491975	−	0.316173i
$61$	−4.49474	+	1.31978i	−0.575493	+	0.168980i	−0.556512	−	0.830840i	$-0.687861\pi$
$61$	−4.49474	+	1.31978i	−0.575493	+	0.168980i	−0.0189815	+	0.999820i	$0.506042\pi$
$62$	−0.525291	+	3.65348i	−0.0667121	+	0.463993i
$63$	−2.21736	+	2.55897i	−0.279361	+	0.322400i
$64$	−1.04683	+	0.672754i	−0.130853	+	0.0840943i
$65$	−11.0803	−	12.7874i	−1.37435	−	1.58608i
$66$	−2.45028	−	0.719467i	−0.301608	−	0.0885602i
$67$	−0.0835538	+	0.182957i	−0.0102077	+	0.0223518i	−0.914667	−	0.404208i	$-0.867547\pi$
$67$	−0.0835538	+	0.182957i	−0.0102077	+	0.0223518i	0.904459	+	0.426560i	$0.140275\pi$
$68$	−5.14454			−0.623868
$69$	4.06350	−	2.54715i	0.489188	−	0.306641i
$70$	−5.20640			−0.622284
$71$	−1.25365	+	2.74512i	−0.148781	+	0.325786i	−0.969319	−	0.245807i	$-0.920947\pi$
$71$	−1.25365	+	2.74512i	−0.148781	+	0.325786i	0.820537	+	0.571593i	$0.193674\pi$
$72$	−2.00700	−	0.589308i	−0.236527	−	0.0694506i
$73$	7.91764	+	9.13745i	0.926690	+	1.06946i	0.997407	+	0.0719611i	$0.0229257\pi$
$73$	7.91764	+	9.13745i	0.926690	+	1.06946i	−0.0707172	+	0.997496i	$0.522529\pi$
$74$	−0.133814	+	0.0859970i	−0.0155556	+	0.00999695i
$75$	−1.50815	+	1.74050i	−0.174146	+	0.200975i
$76$	0.250104	−	1.73951i	0.0286889	−	0.199535i
$77$	14.5816	−	4.28153i	1.66172	−	0.487926i
$78$	−2.99695	−	1.92602i	−0.339337	−	0.218079i
$79$	−1.10543	−	7.68843i	−0.124371	−	0.865016i	−0.952513	−	0.304498i	$-0.901511\pi$
$79$	−1.10543	−	7.68843i	−0.124371	−	0.865016i	0.828142	−	0.560518i	$-0.189398\pi$
$80$	2.42751	+	5.31551i	0.271404	+	0.594292i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	0.114961	+	0.799573i	0.0126954	+	0.0882981i
$83$	−12.4179	−	7.98047i	−1.36304	−	0.875971i	−0.364562	−	0.931179i	$-0.618781\pi$
$83$	−12.4179	−	7.98047i	−1.36304	−	0.875971i	−0.998475	+	0.0552086i	$0.982418\pi$
$84$	5.44591	−	1.59906i	0.594198	−	0.174472i
$85$	−1.18034	+	8.20944i	−0.128026	+	0.890439i
$86$	0.685438	−	0.791037i	0.0739127	−	0.0852997i
$87$	−1.86590	+	1.19914i	−0.200045	+	0.128561i
$88$	6.14793	+	7.09509i	0.655371	+	0.756339i
$89$	0.838282	+	0.246142i	0.0888577	+	0.0260910i	0.325859	−	0.945418i	$-0.394346\pi$
$89$	0.838282	+	0.246142i	0.0888577	+	0.0260910i	−0.237002	+	0.971509i	$0.576165\pi$
$90$	−0.638752	+	1.39867i	−0.0673303	+	0.147433i
$91$	21.2002			2.22239
$92$	−8.03854	−	0.0906751i	−0.838076	−	0.00945354i
$93$	−6.48711			−0.672682
$94$	−1.12170	+	2.45618i	−0.115695	+	0.253336i
$95$	−2.71845	−	0.798210i	−0.278907	−	0.0818946i
$96$	3.54529	+	4.09148i	0.361839	+	0.417585i
$97$	9.73536	−	6.25653i	0.988476	−	0.635255i	0.0567390	−	0.998389i	$-0.481930\pi$
$97$	9.73536	−	6.25653i	0.988476	−	0.635255i	0.931737	+	0.363134i	$0.118293\pi$
$98$	1.66369	−	1.92000i	0.168058	−	0.193949i
$99$	0.638741	−	4.44254i	0.0641959	−	0.446492i
$100$	3.70406	−	1.08761i	0.370406	−	0.108761i
$101$	7.93886	+	5.10200i	0.789947	+	0.507668i	0.872321	−	0.488934i	$-0.162614\pi$
$101$	7.93886	+	5.10200i	0.789947	+	0.507668i	−0.0823744	+	0.996601i	$0.526250\pi$
$102$	0.248516	+	1.72847i	0.0246068	+	0.171144i
$103$	1.66695	+	3.65011i	0.164250	+	0.359656i	0.973804	−	0.227388i	$-0.0730186\pi$
$103$	1.66695	+	3.65011i	0.164250	+	0.359656i	−0.809555	+	0.587044i	$0.800291\pi$
$104$	5.44052	+	11.9131i	0.533487	+	1.16817i
$105$	−1.30223	−	9.05723i	−0.127085	−	0.883895i
$106$	−2.58410	−	1.66070i	−0.250990	−	0.161302i
$107$	−3.52529	+	1.03512i	−0.340803	+	0.100069i	−0.447655	−	0.894206i	$-0.647741\pi$
$107$	−3.52529	+	1.03512i	−0.340803	+	0.100069i	0.106853	+	0.994275i	$0.465923\pi$
$108$	0.238557	−	1.65920i	0.0229551	−	0.159656i
$109$	−8.78273	+	10.1358i	−0.841233	+	0.970835i	−0.999864	−	0.0165033i	$-0.994747\pi$
$109$	−8.78273	+	10.1358i	−0.841233	+	0.970835i	0.158631	+	0.987338i	$0.449292\pi$
$110$	5.80566	−	3.73107i	0.553548	−	0.355744i
$111$	−0.183073	−	0.211278i	−0.0173765	−	0.0200536i
$112$	−7.02518	−	2.06278i	−0.663817	−	0.194914i
$113$	0.288666	−	0.632091i	0.0271554	−	0.0594621i	−0.895568	−	0.444924i	$-0.853231\pi$
$113$	0.288666	−	0.632091i	0.0271554	−	0.0594621i	0.922724	+	0.385462i	$0.125958\pi$
$114$	−0.596524			−0.0558696
$115$	−1.98902	+	12.8068i	−0.185477	+	1.19424i
$116$	3.71794			0.345202
$117$	2.60097	−	5.69533i	0.240460	−	0.526533i
$118$	−5.94578	−	1.74584i	−0.547353	−	0.160717i
$119$	−6.80522	−	7.85365i	−0.623834	−	0.719943i
$120$	4.75535	−	3.05608i	0.434102	−	0.278981i
$121$	−5.98816	+	6.91070i	−0.544378	+	0.628246i
$122$	0.379326	−	2.63827i	0.0343425	−	0.238858i
$123$	−1.36221	+	0.399981i	−0.122826	+	0.0360651i
$124$	9.14785	+	5.87897i	0.821501	+	0.527947i
$125$	1.03724	+	7.21419i	0.0927739	+	0.645257i
$126$	−0.800329	−	1.75248i	−0.0712990	−	0.156123i
$127$	−4.54632	−	9.95505i	−0.403421	−	0.883368i	−0.996912	−	0.0785275i	$-0.974978\pi$
$127$	−4.54632	−	9.95505i	−0.403421	−	0.883368i	0.593491	−	0.804840i	$-0.297749\pi$
$128$	−1.64169	−	11.4182i	−0.145106	−	1.00924i
$129$	1.54756	+	0.994555i	0.136255	+	0.0875657i
$130$	9.23729	−	2.71231i	0.810164	−	0.237886i
$131$	0.503437	−	3.50148i	0.0439855	−	0.305926i	−0.955938	−	0.293568i	$-0.905157\pi$
$131$	0.503437	−	3.50148i	0.0439855	−	0.305926i	0.999924	−	0.0123577i	$-0.00393369\pi$
$132$	−4.92680	+	5.68583i	−0.428823	+	0.494888i
$133$	2.98637	−	1.91922i	0.258951	−	0.166418i
$134$	−0.0749432	−	0.0864890i	−0.00647410	−	0.00747152i
$135$	−2.59294	−	0.761356i	−0.223165	−	0.0655271i
$136$	2.66682	−	5.83951i	0.228678	−	0.500734i
$137$	12.7925			1.09294			0.546469	−	0.837479i	$-0.315972\pi$
$137$	12.7925			1.09294			0.546469	+	0.837479i	$0.315972\pi$
$138$	0.357851	+	2.70518i	0.0304623	+	0.230280i
$139$	8.21741			0.696992			0.348496	−	0.937310i	$-0.386693\pi$
$139$	8.21741			0.696992			0.348496	+	0.937310i	$0.386693\pi$
$140$	−6.37179	+	13.9523i	−0.538515	+	1.17918i
$141$	−4.55342	−	1.33701i	−0.383467	−	0.112596i
$142$	−1.12446	−	1.29769i	−0.0943625	−	0.108900i
$143$	−23.6404	+	15.1928i	−1.97691	+	1.27048i
$144$	−1.41605	+	1.63420i	−0.118004	+	0.136184i
$145$	0.853026	−	5.93293i	0.0708399	−	0.492703i
$146$	−6.60067	+	1.93813i	−0.546275	+	0.160401i
$147$	3.75622	+	2.41398i	0.309808	+	0.199102i
$148$	0.0666909	+	0.463846i	0.00548196	+	0.0381279i
$149$	−7.73403	−	16.9352i	−0.633597	−	1.38738i	−0.905205	−	0.424975i	$-0.860283\pi$
$149$	−7.73403	−	16.9352i	−0.633597	−	1.38738i	0.271608	−	0.962408i	$-0.412445\pi$
$150$	−0.544348	−	1.19196i	−0.0444458	−	0.0973227i
$151$	0.778374	+	5.41371i	0.0633432	+	0.440562i	0.996670	+	0.0815349i	$0.0259822\pi$
$151$	0.778374	+	5.41371i	0.0633432	+	0.440562i	−0.933327	+	0.359027i	$0.883109\pi$
$152$	1.84485	+	1.18561i	0.149637	+	0.0961659i
$153$	−2.94474	+	0.864655i	−0.238068	+	0.0699032i
$154$	−1.23058	+	8.55890i	−0.0991633	+	0.689696i
$155$	11.4802	−	13.2489i	0.922115	−	1.06418i
$156$	−8.82919	+	5.67418i	−0.706901	+	0.454298i
$157$	−10.7637	−	12.4219i	−0.859033	−	0.991377i	−0.999999	−	0.00136270i	$-0.999566\pi$
$157$	−10.7637	−	12.4219i	−0.859033	−	0.991377i	0.140966	−	0.990014i	$-0.454979\pi$
$158$	4.24055	+	1.24514i	0.337360	+	0.0990577i
$159$	2.24267	−	4.91077i	0.177856	−	0.389450i
$160$	−14.6303			−1.15663
$161$	−10.4950	−	12.3916i	−0.827121	−	0.976592i
$162$	−0.568983			−0.0447035
$163$	4.16078	−	9.11084i	0.325898	−	0.713616i	−0.673782	−	0.738930i	$-0.735331\pi$
$163$	4.16078	−	9.11084i	0.325898	−	0.713616i	0.999680	+	0.0253139i	$0.00805853\pi$
$164$	2.28342	+	0.670472i	0.178305	+	0.0523551i
$165$	7.94282	+	9.16650i	0.618347	+	0.713611i
$166$	7.06554	−	4.54075i	0.548393	−	0.352430i
$167$	4.84536	−	5.59184i	0.374945	−	0.432709i	−0.536646	−	0.843807i	$-0.680309\pi$
$167$	4.84536	−	5.59184i	0.374945	−	0.432709i	0.911591	+	0.411098i	$0.134855\pi$
$168$	−1.00796	+	7.01051i	−0.0777657	+	0.540873i
$169$	−25.1404	+	7.38190i	−1.93388	+	0.567838i
$170$	−3.96993	−	2.55132i	−0.304480	−	0.195677i
$171$	−0.149204	−	1.03773i	−0.0114099	−	0.0793575i
$172$	−1.28098	−	2.80496i	−0.0976740	−	0.213876i
$173$	2.33259	+	5.10767i	0.177344	+	0.388329i	0.977340	−	0.211677i	$-0.0678923\pi$
$173$	2.33259	+	5.10767i	0.177344	+	0.388329i	−0.799996	+	0.600005i	$0.795165\pi$
$174$	−0.179602	−	1.24916i	−0.0136156	−	0.0946983i
$175$	6.56009	+	4.21591i	0.495896	+	0.318693i
$176$	9.31204	−	2.73426i	0.701921	−	0.206103i
$177$	1.54995	−	10.7801i	0.116501	−	0.810285i
$178$	−0.325534	+	0.375686i	−0.0243998	+	0.0281589i
$179$	18.1247	−	11.6480i	1.35470	−	0.870614i	0.356726	−	0.934209i	$-0.383893\pi$
$179$	18.1247	−	11.6480i	1.35470	−	0.870614i	0.997976	+	0.0635946i	$0.0202565\pi$
$180$	2.96648	+	3.42350i	0.221108	+	0.255172i
$181$	−9.84568	−	2.89095i	−0.731824	−	0.214883i	−0.105471	−	0.994422i	$-0.533635\pi$
$181$	−9.84568	−	2.89095i	−0.731824	−	0.214883i	−0.626353	+	0.779540i	$0.715453\pi$
$182$	−5.01097	+	10.9725i	−0.371438	+	0.813335i
$183$	4.68450			0.346288
$184$	4.26992	−	9.07745i	0.314783	−	0.669199i
$185$	0.755486			0.0555444
$186$	1.53332	−	3.35750i	0.112428	−	0.246184i
$187$	13.2167	+	3.88077i	0.966499	+	0.283790i
$188$	5.20938	+	6.01194i	0.379933	+	0.438466i
$189$	2.84849	−	1.83061i	0.207197	−	0.133157i
$190$	1.05567	−	1.21831i	0.0765863	−	0.0883853i
$191$	−1.20256	+	8.36400i	−0.0870143	+	0.605198i	0.898926	+	0.438100i	$0.144349\pi$
$191$	−1.20256	+	8.36400i	−0.0870143	+	0.605198i	−0.985940	+	0.167097i	$0.946561\pi$
$192$	1.19396	−	0.350578i	0.0861666	−	0.0253008i
$193$	0.329863	+	0.211990i	0.0237440	+	0.0152594i	0.552459	−	0.833540i	$-0.313690\pi$
$193$	0.329863	+	0.211990i	0.0237440	+	0.0152594i	−0.528715	+	0.848799i	$0.677326\pi$
$194$	0.937075	+	6.51750i	0.0672780	+	0.467929i
$195$	7.02888	+	15.3911i	0.503348	+	1.10218i
$196$	−3.10919	−	6.80819i	−0.222085	−	0.486299i
$197$	3.21162	+	22.3373i	0.228818	+	1.59146i	0.703099	+	0.711092i	$0.251799\pi$
$197$	3.21162	+	22.3373i	0.228818	+	1.59146i	−0.474281	+	0.880373i	$0.657292\pi$
$198$	2.14833	+	1.38065i	0.152675	+	0.0981183i
$199$	−12.8230	+	3.76518i	−0.908999	+	0.266906i	−0.702620	−	0.711566i	$-0.747986\pi$
$199$	−12.8230	+	3.76518i	−0.908999	+	0.266906i	−0.206380	+	0.978472i	$0.566168\pi$
$200$	−0.685568	+	4.76823i	−0.0484770	+	0.337165i
$201$	0.131714	−	0.152006i	0.00929042	−	0.0107217i
$202$	−4.51708	+	2.90295i	−0.317820	+	0.204251i
$203$	4.91810	+	5.67580i	0.345183	+	0.398363i
$204$	4.93615	+	1.44939i	0.345600	+	0.101477i
$205$	1.59381	−	3.48995i	0.111316	−	0.243749i
$206$	−2.28318			−0.159076
$207$	−4.61651	+	1.29915i	−0.320870	+	0.0902974i
$208$	13.5388			0.938749
$209$	−1.95473	+	4.28025i	−0.135211	+	0.296071i
$210$	4.99550	+	1.46681i	0.344722	+	0.101220i
$211$	0.366068	+	0.422465i	0.0252011	+	0.0290837i	0.768210	−	0.640198i	$-0.221148\pi$
$211$	0.366068	+	0.422465i	0.0252011	+	0.0290837i	−0.743009	+	0.669281i	$0.766602\pi$
$212$	−7.61293	+	4.89254i	−0.522858	+	0.336021i
$213$	1.97626	−	2.28073i	0.135411	−	0.156273i
$214$	0.297510	−	2.06923i	0.0203374	−	0.141450i
$215$	−4.76994	+	1.40058i	−0.325307	+	0.0955188i
$216$	1.75967	+	1.13087i	0.119731	+	0.0769462i
$217$	3.12600	+	21.7418i	0.212207	+	1.47593i
$218$	−3.17002	−	6.94137i	−0.214701	−	0.470129i
$219$	−5.02261	−	10.9980i	−0.339396	−	0.743174i
$220$	−2.89346	−	20.1244i	−0.195077	−	1.35679i
$221$	16.1654	+	10.3889i	1.08740	+	0.698830i
$222$	0.152622	−	0.0448138i	0.0102433	−	0.00300770i
$223$	4.22619	−	29.3938i	0.283007	−	1.96836i	0.0359582	−	0.999353i	$-0.488552\pi$
$223$	4.22619	−	29.3938i	0.283007	−	1.96836i	0.247049	−	0.969003i	$-0.420539\pi$
$224$	12.0044	−	13.8538i	0.802075	−	0.925644i
$225$	1.93741	−	1.24510i	0.129161	−	0.0830066i
$226$	0.258918	+	0.298807i	0.0172229	+	0.0198763i
$227$	23.6710	+	6.95043i	1.57110	+	0.461316i	0.947321	−	0.320285i	$-0.103779\pi$
$227$	23.6710	+	6.95043i	1.57110	+	0.461316i	0.623778	+	0.781602i	$0.285597\pi$
$228$	−0.730049	+	1.59859i	−0.0483487	+	0.105869i
$229$	−28.4810			−1.88207			−0.941037	−	0.338302i	$-0.890147\pi$
$229$	−28.4810			−1.88207			−0.941037	+	0.338302i	$0.890147\pi$
$230$	−6.15819	−	4.05650i	−0.406059	−	0.267478i
$231$	−15.1972			−0.999899
$232$	−1.92730	+	4.22019i	−0.126533	+	0.277069i
$233$	14.4529	+	4.24374i	0.946839	+	0.278017i	0.718470	−	0.695558i	$-0.244843\pi$
$233$	14.4529	+	4.24374i	0.946839	+	0.278017i	0.228369	+	0.973575i	$0.426661\pi$
$234$	2.33293	+	2.69234i	0.152508	+	0.176004i
$235$	10.7888	−	6.93355i	0.703785	−	0.452295i
$236$	−11.9552	+	13.7971i	−0.778219	+	0.898112i
$237$	−1.10543	+	7.68843i	−0.0718054	+	0.499417i
$238$	5.67328	−	1.66583i	0.367744	−	0.107979i
$239$	−22.6822	−	14.5770i	−1.46719	−	0.942907i	−0.998217	−	0.0596958i	$-0.980987\pi$
$239$	−22.6822	−	14.5770i	−1.46719	−	0.942907i	−0.468975	−	0.883211i	$-0.655377\pi$
$240$	−0.831628	−	5.78410i	−0.0536814	−	0.373362i
$241$	8.76904	+	19.2015i	0.564864	+	1.23688i	0.949487	+	0.313806i	$0.101604\pi$
$241$	8.76904	+	19.2015i	0.564864	+	1.23688i	−0.384624	+	0.923074i	$0.625669\pi$
$242$	−2.16135	−	4.73270i	−0.138937	−	0.304229i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	−6.60589	−	4.24535i	−0.422899	−	0.271780i
$245$	−11.5776	+	3.39948i	−0.739664	+	0.217185i
$246$	0.114961	−	0.799573i	0.00732967	−	0.0509789i
$247$	−4.29864	+	4.96089i	−0.273516	+	0.315654i
$248$	−11.4152	+	7.33610i	−0.724865	+	0.465843i
$249$	9.66649	+	11.1557i	0.612589	+	0.706965i
$250$	−3.97898	−	1.16833i	−0.251653	−	0.0738919i
$251$	−0.966692	+	2.11676i	−0.0610170	+	0.133609i	−0.937684	−	0.347489i	$-0.887034\pi$
$251$	−0.966692	+	2.11676i	−0.0610170	+	0.133609i	0.876667	+	0.481098i	$0.159762\pi$
$252$	−5.67582			−0.357543
$253$	20.5832	+	6.29679i	1.29405	+	0.395876i
$254$	6.22697			0.390715
$255$	3.44539	−	7.54436i	0.215759	−	0.472446i
$256$	3.90978	+	1.14801i	0.244361	+	0.0717509i
$257$	−17.4817	−	20.1749i	−1.09048	−	1.25848i	−0.963826	−	0.266531i	$-0.914123\pi$
$257$	−17.4817	−	20.1749i	−1.09048	−	1.25848i	−0.126651	−	0.991947i	$-0.540423\pi$
$258$	−0.880534	+	0.565885i	−0.0548196	+	0.0352304i
$259$	−0.619886	+	0.715387i	−0.0385179	+	0.0444520i
$260$	4.03641	−	28.0738i	0.250327	−	1.74107i
$261$	2.12815	−	0.624882i	0.131729	−	0.0386792i
$262$	1.69325	+	1.08819i	0.104609	+	0.0672283i
$263$	−1.42355	−	9.90102i	−0.0877800	−	0.610523i	−0.985464	−	0.169884i	$-0.945661\pi$
$263$	−1.42355	−	9.90102i	−0.0877800	−	0.610523i	0.897684	−	0.440639i	$-0.145248\pi$
$264$	−3.89998	−	8.53976i	−0.240027	−	0.525586i
$265$	6.06062	+	13.2709i	0.372301	+	0.815225i
$266$	0.287452	+	1.99927i	0.0176248	+	0.122583i
$267$	−0.734979	−	0.472343i	−0.0449800	−	0.0289069i
$268$	−0.323495	+	0.0949866i	−0.0197606	+	0.00580223i
$269$	2.49684	−	17.3659i	0.152235	−	1.05882i	−0.760228	−	0.649657i	$-0.774913\pi$
$269$	2.49684	−	17.3659i	0.152235	−	1.05882i	0.912463	−	0.409160i	$-0.134178\pi$
$270$	1.00693	−	1.16206i	0.0612797	−	0.0707206i
$271$	0.958576	−	0.616040i	0.0582294	−	0.0374217i	−0.511202	−	0.859460i	$-0.670800\pi$
$271$	0.958576	−	0.616040i	0.0582294	−	0.0374217i	0.569432	+	0.822039i	$0.307163\pi$
$272$	−4.34593	−	5.01547i	−0.263511	−	0.304108i
$273$	−20.3415	−	5.97280i	−1.23112	−	0.361490i
$274$	−3.02369	+	6.62096i	−0.182668	+	0.399987i
$275$	−10.3364			−0.623309
$276$	7.68738	+	2.35172i	0.462726	+	0.141557i
$277$	−21.3674			−1.28384			−0.641920	−	0.766772i	$-0.721862\pi$
$277$	−21.3674			−1.28384			−0.641920	+	0.766772i	$0.721862\pi$
$278$	−1.94230	+	4.25304i	−0.116491	+	0.255080i
$279$	6.22433	+	1.82763i	0.372641	+	0.109417i
$280$	−12.5341	−	14.4651i	−0.749055	−	0.864455i
$281$	−10.4177	+	6.69502i	−0.621465	+	0.399391i	−0.813141	−	0.582067i	$-0.802244\pi$
$281$	−10.4177	+	6.69502i	−0.621465	+	0.399391i	0.191676	+	0.981458i	$0.438608\pi$
$282$	1.76825	−	2.04067i	0.105298	−	0.121520i
$283$	1.01281	−	7.04422i	0.0602051	−	0.418735i	−0.937323	−	0.348462i	$-0.886704\pi$
$283$	1.01281	−	7.04422i	0.0602051	−	0.418735i	0.997528	−	0.0702729i	$-0.0223870\pi$
$284$	−4.85376	+	1.42519i	−0.288018	+	0.0845697i
$285$	2.38345	+	1.53175i	0.141184	+	0.0907332i
$286$	−2.27550	−	15.8264i	−0.134553	−	0.935837i
$287$	1.99697	+	4.37276i	0.117878	+	0.258116i
$288$	−2.24897	−	4.92457i	−0.132522	−	0.290183i
$289$	1.07887	+	7.50369i	0.0634628	+	0.441393i
$290$	2.86905	+	1.84383i	0.168476	+	0.108273i
$291$	−11.1037	+	3.26033i	−0.650909	+	0.191124i
$292$	−2.88429	+	20.0606i	−0.168790	+	1.17396i
$293$	11.7773	−	13.5917i	0.688038	−	0.794038i	−0.299046	−	0.954239i	$-0.596669\pi$
$293$	11.7773	−	13.5917i	0.688038	−	0.794038i	0.987085	+	0.160200i	$0.0512140\pi$
$294$	−2.13723	+	1.37351i	−0.124646	+	0.0801048i
$295$	19.2738	+	22.2432i	1.12216	+	1.29505i
$296$	−0.561077	−	0.164747i	−0.0326119	−	0.00957573i
$297$	−1.86448	+	4.08263i	−0.108188	+	0.236898i
$298$	10.5931			0.613641
$299$	25.0759	+	16.5179i	1.45018	+	0.955255i
$300$	−3.86044			−0.222882
$301$	2.58756	−	5.66596i	0.149144	−	0.326580i
$302$	−2.98593	−	0.876747i	−0.171821	−	0.0504511i
$303$	−6.17989	−	7.13197i	−0.355025	−	0.409721i
$304$	1.90715	−	1.22565i	0.109382	−	0.0702958i
$305$	−8.29016	+	9.56736i	−0.474693	+	0.547825i
$306$	0.248516	−	1.72847i	0.0142067	−	0.0988100i
$307$	−1.75668	+	0.515809i	−0.100259	+	0.0294388i	−0.331477	−	0.943463i	$-0.607547\pi$
$307$	−1.75668	+	0.515809i	−0.100259	+	0.0294388i	0.231218	+	0.972902i	$0.425729\pi$
$308$	21.4304	+	13.7725i	1.22111	+	0.784760i
$309$	−0.571072	−	3.97189i	−0.0324871	−	0.225953i
$310$	4.14365	+	9.07333i	0.235344	+	0.515330i
$311$	−3.84938	−	8.42896i	−0.218278	−	0.477963i	0.768539	−	0.639803i	$-0.220984\pi$
$311$	−3.84938	−	8.42896i	−0.218278	−	0.477963i	−0.986817	+	0.161841i	$0.948257\pi$
$312$	−1.86384	−	12.9633i	−0.105519	−	0.733901i
$313$	11.7077	+	7.52409i	0.661759	+	0.425287i	0.827946	−	0.560808i	$-0.189509\pi$
$313$	11.7077	+	7.52409i	0.661759	+	0.425287i	−0.166187	+	0.986094i	$0.553146\pi$
$314$	8.97329	−	2.63479i	0.506392	−	0.148690i
$315$	−1.30223	+	9.05723i	−0.0733725	+	0.510317i
$316$	8.52650	−	9.84011i	0.479653	−	0.553549i
$317$	−22.7584	+	14.6259i	−1.27824	+	0.821473i	−0.990669	−	0.136287i	$-0.956483\pi$
$317$	−22.7584	+	14.6259i	−1.27824	+	0.821473i	−0.287568	+	0.957760i	$0.592847\pi$
$318$	2.01156	+	2.32146i	0.112802	+	0.130181i
$319$	−9.55163	−	2.80461i	−0.534789	−	0.157028i
$320$	−1.39695	+	3.05889i	−0.0780918	+	0.170997i
$321$	3.67412			0.205069
$322$	8.89407	−	2.50292i	0.495647	−	0.139482i
$323$	3.21762			0.179033
$324$	−0.696343	+	1.52478i	−0.0386857	+	0.0847099i
$325$	−13.8353	−	4.06242i	−0.767447	−	0.225343i
$326$	3.73199	+	4.30695i	0.206696	+	0.238540i
$327$	11.2826	−	7.25086i	0.623927	−	0.400973i
$328$	−1.94472	+	2.24432i	−0.107379	+	0.123922i
$329$	−2.28683	+	15.9053i	−0.126077	+	0.876885i
$330$	−6.62165	+	1.94429i	−0.364510	+	0.107030i
$331$	13.8155	+	8.87867i	0.759367	+	0.488016i	0.862128	−	0.506690i	$-0.169131\pi$
$331$	13.8155	+	8.87867i	0.759367	+	0.488016i	−0.102761	+	0.994706i	$0.532768\pi$
$332$	−3.52136	−	24.4916i	−0.193260	−	1.34415i
$333$	0.116134	+	0.254297i	0.00636408	+	0.0139354i
$334$	1.74887	+	3.82949i	0.0956940	+	0.209541i
$335$	0.0773544	+	0.538012i	0.00422632	+	0.0293947i
$336$	6.15946	+	3.95845i	0.336026	+	0.215951i
$337$	15.9032	−	4.66961i	0.866305	−	0.254370i	0.181762	−	0.983343i	$-0.441820\pi$
$337$	15.9032	−	4.66961i	0.866305	−	0.254370i	0.684543	+	0.728972i	$0.260002\pi$
$338$	2.12168	−	14.7566i	0.115404	−	0.802654i
$339$	−0.455054	+	0.525160i	−0.0247151	+	0.0285228i
$340$	−11.6957	+	7.51634i	−0.634286	+	0.407631i
$341$	−19.0667	−	22.0041i	−1.03252	−	1.19159i
$342$	0.572361	+	0.168060i	0.0309497	+	0.00908766i
$343$	−3.56568	+	7.80775i	−0.192529	+	0.421579i
$344$	3.84791			0.207466
$345$	5.51653	−	11.7276i	0.297000	−	0.631394i
$346$	−3.19489			−0.171758
$347$	−0.0775703	+	0.169855i	−0.00416419	+	0.00911830i	−0.911703	−	0.410851i	$-0.865232\pi$
$347$	−0.0775703	+	0.169855i	−0.00416419	+	0.00911830i	0.907538	+	0.419969i	$0.137959\pi$
$348$	−3.56734	−	1.04746i	−0.191229	−	0.0561500i
$349$	−6.88632	−	7.94723i	−0.368616	−	0.425406i	0.540892	−	0.841092i	$-0.318087\pi$
$349$	−6.88632	−	7.94723i	−0.368616	−	0.425406i	−0.909508	+	0.415686i	$0.863541\pi$
$350$	−3.73258	+	2.39878i	−0.199515	+	0.128220i
$351$	−4.10017	+	4.73185i	−0.218851	+	0.252567i
$352$	−3.45802	+	24.0510i	−0.184313	+	1.28192i
$353$	19.8284	−	5.82213i	1.05536	−	0.309881i	0.292377	−	0.956303i	$-0.405554\pi$
$353$	19.8284	−	5.82213i	1.05536	−	0.309881i	0.762980	+	0.646422i	$0.223736\pi$
$354$	5.21307	+	3.35024i	0.277072	+	0.178063i
$355$	1.16064	+	8.07241i	0.0616002	+	0.428439i
$356$	0.608375	+	1.33216i	0.0322438	+	0.0706041i
$357$	4.31694	+	9.45277i	0.228477	+	0.500294i
$358$	1.74459	+	12.1339i	0.0922043	+	0.641295i
$359$	13.1887	+	8.47588i	0.696074	+	0.447340i	0.840241	−	0.542214i	$-0.182414\pi$
$359$	13.1887	+	8.47588i	0.696074	+	0.447340i	−0.144166	+	0.989553i	$0.546050\pi$
$360$	−5.42373	+	1.59255i	−0.285855	+	0.0839347i
$361$	2.54756	−	17.7186i	0.134082	−	0.932560i
$362$	3.82342	−	4.41246i	0.200954	−	0.231914i
$363$	7.69256	−	4.94371i	0.403755	−	0.259478i
$364$	23.2718	+	26.8571i	1.21978	+	1.40770i
$365$	31.3502	+	9.20524i	1.64094	+	0.481824i
$366$	−1.10725	+	2.42453i	−0.0578767	+	0.126732i
$367$	5.44563			0.284259			0.142130	−	0.989848i	$-0.454605\pi$
$367$	5.44563			0.284259			0.142130	+	0.989848i	$0.454605\pi$
$368$	−6.70228	−	7.91347i	−0.349381	−	0.412518i
$369$	1.41972			0.0739076
$370$	−0.178570	+	0.391013i	−0.00928339	+	0.0203278i
$371$	−17.5394	−	5.15002i	−0.910598	−	0.267376i
$372$	−7.12100	−	8.21807i	−0.369207	−	0.426087i
$373$	−3.38805	+	2.17737i	−0.175427	+	0.112740i	−0.625407	−	0.780298i	$-0.715067\pi$
$373$	−3.38805	+	2.17737i	−0.175427	+	0.112740i	0.449981	+	0.893038i	$0.351431\pi$
$374$	−5.13249	+	5.92321i	−0.265395	+	0.306282i
$375$	1.03724	−	7.21419i	0.0535630	−	0.372539i
$376$	−9.52451	+	2.79665i	−0.491189	+	0.144226i
$377$	−11.6826	−	7.50798i	−0.601687	−	0.386681i
$378$	0.274181	+	1.90697i	0.0141023	+	0.0980839i
$379$	−4.63145	−	10.1415i	−0.237902	−	0.520932i	0.752593	−	0.658486i	$-0.228803\pi$
$379$	−4.63145	−	10.1415i	−0.237902	−	0.520932i	−0.990494	+	0.137555i	$0.956076\pi$
$380$	−1.97289	−	4.32003i	−0.101207	−	0.221613i
$381$	1.55750	+	10.8326i	0.0797931	+	0.554973i
$382$	−4.04467	−	2.59935i	−0.206943	−	0.132994i
$383$	14.4041	−	4.22944i	0.736017	−	0.216114i	0.107822	−	0.994170i	$-0.465612\pi$
$383$	14.4041	−	4.22944i	0.736017	−	0.216114i	0.628195	+	0.778056i	$0.283794\pi$
$384$	−1.64169	+	11.4182i	−0.0837772	+	0.582683i
$385$	26.8944	−	31.0378i	1.37067	−	1.58183i
$386$	−0.187686	+	0.120619i	−0.00955297	+	0.00613932i
$387$	−1.20467	−	1.39027i	−0.0612370	−	0.0706712i
$388$	18.6126	+	5.46516i	0.944913	+	0.277452i
$389$	−13.7756	+	30.1644i	−0.698452	+	1.52940i	0.143387	+	0.989667i	$0.454201\pi$
$389$	−13.7756	+	30.1644i	−0.698452	+	1.52940i	−0.841838	+	0.539730i	$0.818526\pi$
$390$	−9.62726			−0.487495
$391$	−1.93023	−	14.5916i	−0.0976159	−	0.737929i
$392$	9.33963			0.471723
$393$	−1.46953	+	3.21781i	−0.0741278	+	0.162317i
$394$	−12.3201	−	3.61751i	−0.620677	−	0.182247i
$395$	−13.7461	−	15.8639i	−0.691643	−	0.798199i
$396$	6.32911	−	4.06747i	0.318050	−	0.204398i
$397$	4.36833	−	5.04133i	0.219240	−	0.253017i	−0.635466	−	0.772129i	$-0.719192\pi$
$397$	4.36833	−	5.04133i	0.219240	−	0.253017i	0.854706	+	0.519112i	$0.173737\pi$
$398$	1.08217	−	7.52669i	0.0542445	−	0.377279i
$399$	−3.40611	+	1.00012i	−0.170519	+	0.0500688i
$400$	4.18939	+	2.69236i	0.209469	+	0.134618i
$401$	0.886108	+	6.16302i	0.0442501	+	0.307766i	0.999912	+	0.0132987i	$0.00423322\pi$
$401$	0.886108	+	6.16302i	0.0442501	+	0.307766i	−0.955661	+	0.294468i	$0.904858\pi$
$402$	0.0475407	+	0.104100i	0.00237111	+	0.00519201i
$403$	−16.8728	−	36.9462i	−0.840492	−	1.84042i
$404$	2.25125	+	15.6578i	0.112004	+	0.779002i
$405$	2.27341	+	1.46103i	0.112967	+	0.0725993i
$406$	−4.10005	+	1.20388i	−0.203482	+	0.0597478i
$407$	0.178567	−	1.24196i	0.00885122	−	0.0615616i
$408$	−4.20397	+	4.85164i	−0.208128	+	0.240192i
$409$	−1.64881	+	1.05962i	−0.0815282	+	0.0523950i	−0.580770	−	0.814068i	$-0.697248\pi$
$409$	−1.64881	+	1.05962i	−0.0815282	+	0.0523950i	0.499242	+	0.866463i	$0.333612\pi$
$410$	1.42956	+	1.64980i	0.0706008	+	0.0814776i
$411$	−12.2743	−	3.60407i	−0.605448	−	0.177776i
$412$	−2.79424	+	6.11853i	−0.137662	+	0.301439i
$413$	−36.8770			−1.81460
$414$	0.418781	−	2.69642i	0.0205820	−	0.132522i
$415$	−39.8906			−1.95815
$416$	−14.0811	+	30.8334i	−0.690384	+	1.51173i
$417$	−7.88455	−	2.31511i	−0.386108	−	0.113372i
$418$	−1.75328	−	2.02339i	−0.0857558	−	0.0989675i
$419$	6.95250	−	4.46810i	0.339652	−	0.218281i	−0.359684	−	0.933074i	$-0.617116\pi$
$419$	6.95250	−	4.46810i	0.339652	−	0.218281i	0.699336	+	0.714793i	$0.253479\pi$
$420$	10.0445	−	11.5920i	0.490122	−	0.565631i
$421$	0.252051	−	1.75305i	0.0122842	−	0.0854385i	−0.982757	−	0.184901i	$-0.940803\pi$
$421$	0.252051	−	1.75305i	0.0122842	−	0.0854385i	0.995041	+	0.0994630i	$0.0317125\pi$
$422$	−0.305178	+	0.0896084i	−0.0148558	+	0.00436207i
$423$	3.99230	+	2.56569i	0.194112	+	0.124748i
$424$	−1.60709	−	11.1775i	−0.0780470	−	0.542829i
$425$	2.93618	+	6.42935i	0.142426	+	0.311869i
$426$	0.713307	+	1.56193i	0.0345599	+	0.0756755i
$427$	−2.25736	−	15.7003i	−0.109241	−	0.759790i
$428$	−5.18109	−	3.32968i	−0.250437	−	0.160946i
$429$	26.9631	−	7.91707i	1.30179	−	0.382240i
$430$	0.402550	−	2.79980i	0.0194127	−	0.135018i
$431$	−17.5221	+	20.2215i	−0.844008	+	0.974037i	−0.999906	−	0.0137365i	$-0.995627\pi$
$431$	−17.5221	+	20.2215i	−0.844008	+	0.974037i	0.155898	+	0.987773i	$0.450173\pi$
$432$	1.81909	−	1.16906i	0.0875212	−	0.0562465i
$433$	−16.0940	−	18.5735i	−0.773428	−	0.892583i	0.223189	−	0.974775i	$-0.428353\pi$
$433$	−16.0940	−	18.5735i	−0.773428	−	0.892583i	−0.996617	+	0.0821919i	$0.973808\pi$
$434$	−11.9917	−	3.52107i	−0.575618	−	0.169017i
$435$	−2.48997	+	5.45228i	−0.119385	+	0.261417i
$436$	−22.4813			−1.07666
$437$	5.02765	+	0.0567122i	0.240505	+	0.00271291i
$438$	6.87933			0.328707
$439$	2.32447	−	5.08987i	0.110941	−	0.242926i	−0.846016	−	0.533158i	$-0.821005\pi$
$439$	2.32447	−	5.08987i	0.110941	−	0.242926i	0.956956	+	0.290232i	$0.0937324\pi$
$440$	24.3429	+	7.14772i	1.16050	+	0.340754i
$441$	−2.92397	−	3.37445i	−0.139237	−	0.160688i
$442$	−9.19781	+	5.91108i	−0.437495	+	0.281161i
$443$	−8.19690	+	9.45973i	−0.389447	+	0.449445i	−0.916289	−	0.400518i	$-0.868830\pi$
$443$	−8.19690	+	9.45973i	−0.389447	+	0.449445i	0.526842	+	0.849963i	$0.323376\pi$
$444$	0.0666909	−	0.463846i	0.00316501	−	0.0220131i
$445$	2.26538	−	0.665175i	0.107389	−	0.0315323i
$446$	14.2143	+	9.13497i	0.673066	+	0.432553i
$447$	2.64956	+	18.4281i	0.125320	+	0.871620i
$448$	−1.75032	−	3.83267i	−0.0826948	−	0.181076i
$449$	−3.38548	−	7.41317i	−0.159771	−	0.349849i	0.812769	−	0.582586i	$-0.197959\pi$
$449$	−3.38548	−	7.41317i	−0.159771	−	0.349849i	−0.972540	+	0.232737i	$0.925232\pi$
$450$	0.186485	+	1.29703i	0.00879100	+	0.0611427i
$451$	−5.36049	−	3.44497i	−0.252415	−	0.162218i
$452$	1.11763	−	0.328165i	0.0525687	−	0.0154356i
$453$	0.778374	−	5.41371i	0.0365712	−	0.254358i
$454$	−9.19227	+	10.6084i	−0.431414	+	0.497879i
$455$	48.1968	−	30.9742i	2.25950	−	1.45209i
$456$	−1.43609	−	1.65734i	−0.0672513	−	0.0776121i
$457$	17.3676	+	5.09960i	0.812424	+	0.238549i	0.661451	−	0.749989i	$-0.269941\pi$
$457$	17.3676	+	5.09960i	0.812424	+	0.238549i	0.150973	+	0.988538i	$0.451759\pi$
$458$	6.73187	−	14.7407i	0.314560	−	0.688790i
$459$	3.06906			0.143252
$460$	−18.4074	+	11.5384i	−0.858249	+	0.537982i
$461$	13.1011			0.610180			0.305090	−	0.952324i	$-0.401313\pi$
$461$	13.1011			0.610180			0.305090	+	0.952324i	$0.401313\pi$
$462$	3.59206	−	7.86551i	0.167118	−	0.365937i
$463$	18.6776	+	5.48425i	0.868023	+	0.254875i	0.685274	−	0.728285i	$-0.259682\pi$
$463$	18.6776	+	5.48425i	0.868023	+	0.254875i	0.182749	+	0.983160i	$0.441501\pi$
$464$	3.14079	+	3.62466i	0.145807	+	0.168271i
$465$	−14.7479	+	9.47787i	−0.683915	+	0.439526i
$466$	−5.61255	+	6.47723i	−0.259996	+	0.300052i
$467$	0.170185	−	1.18366i	0.00787520	−	0.0547732i	−0.985505	−	0.169647i	$-0.945737\pi$
$467$	0.170185	−	1.18366i	0.00787520	−	0.0547732i	0.993380	+	0.114874i	$0.0366463\pi$
$468$	10.0701	−	2.95686i	0.465493	−	0.136681i
$469$	−0.572926	−	0.368197i	−0.0264553	−	0.0170018i
$470$	1.03847	+	7.22275i	0.0479013	+	0.333161i
$471$	6.82799	+	14.9512i	0.314617	+	0.688916i
$472$	−9.46357	−	20.7223i	−0.435596	−	0.953822i
$473$	1.17502	+	8.17244i	0.0540274	+	0.375769i
$474$	−3.71798	−	2.38940i	−0.170772	−	0.109749i
$475$	−2.31668	+	0.680239i	−0.106297	+	0.0312115i
$476$	2.47905	−	17.2421i	0.113627	−	0.790293i
$477$	−3.53535	+	4.08002i	−0.161873	+	0.186811i
$478$	12.9058	−	8.29405i	0.590297	−	0.379361i
$479$	11.4506	+	13.2147i	0.523192	+	0.603796i	0.954427	−	0.298444i	$-0.0964675\pi$
$479$	11.4506	+	13.2147i	0.523192	+	0.603796i	−0.431235	+	0.902240i	$0.641922\pi$
$480$	14.0377	+	4.12183i	0.640729	+	0.188135i
$481$	0.727128	−	1.59219i	0.0331542	−	0.0725975i
$482$	−12.0107			−0.547073
$483$	6.57877	+	14.8464i	0.299344	+	0.675535i
$484$	−15.3280			−0.696727
$485$	12.9915	−	28.4473i	0.589912	−	1.29173i
$486$	0.545935	+	0.160301i	0.0247641	+	0.00727140i
$487$	14.7431	+	17.0144i	0.668073	+	0.770997i	0.984074	−	0.177762i	$-0.0568856\pi$
$487$	14.7431	+	17.0144i	0.668073	+	0.770997i	−0.316001	+	0.948759i	$0.602340\pi$
$488$	8.24319	−	5.29758i	0.373152	−	0.239810i
$489$	−6.55906	+	7.56956i	−0.296611	+	0.342307i
$490$	0.977068	−	6.79565i	0.0441394	−	0.306996i
$491$	−28.2419	+	8.29258i	−1.27454	+	0.374239i	−0.847887	−	0.530176i	$-0.822126\pi$
$491$	−28.2419	+	8.29258i	−1.27454	+	0.374239i	−0.426653	+	0.904415i	$0.640307\pi$
$492$	−2.00203	−	1.28663i	−0.0902585	−	0.0580056i
$493$	0.968762	+	6.73789i	0.0436309	+	0.303459i
$494$	−1.55154	−	3.39740i	−0.0698071	−	0.152856i
$495$	−5.03857	−	11.0329i	−0.226467	−	0.495894i
$496$	1.99632	+	13.8847i	0.0896373	+	0.623441i
$497$	−8.59627	−	5.52449i	−0.385595	−	0.247807i
$498$	−8.05862	+	2.36622i	−0.361115	+	0.106033i
$499$	1.84778	−	12.8516i	0.0827180	−	0.575317i	−0.905741	−	0.423831i	$-0.860685\pi$
$499$	1.84778	−	12.8516i	0.0827180	−	0.575317i	0.988459	−	0.151486i	$-0.0484058\pi$
$500$	−8.00057	+	9.23315i	−0.357796	+	0.412919i
$501$	−6.22449	+	4.00024i	−0.278090	+	0.178717i
$502$	−0.867069	−	1.00065i	−0.0386992	−	0.0446613i
$503$	0.705392	+	0.207122i	0.0314519	+	0.00923510i	0.297421	−	0.954747i	$-0.403874\pi$
$503$	0.705392	+	0.207122i	0.0314519	+	0.00923510i	−0.265969	+	0.963982i	$0.585692\pi$
$504$	2.94222	−	6.44256i	0.131057	−	0.286974i
$505$	25.5025			1.13485
$506$	−8.12411	+	9.16478i	−0.361161	+	0.407424i
$507$	26.2018			1.16366
$508$	7.62081	−	16.6872i	0.338119	−	0.740377i
$509$	−2.65234	−	0.778796i	−0.117563	−	0.0345195i	0.222422	−	0.974950i	$-0.428604\pi$
$509$	−2.65234	−	0.778796i	−0.117563	−	0.0345195i	−0.339985	+	0.940431i	$0.610422\pi$
$510$	3.09033	+	3.56643i	0.136842	+	0.157924i
$511$	−34.4399	+	22.1332i	−1.52353	+	0.979114i
$512$	13.5901	−	15.6839i	0.600605	−	0.693136i
$513$	−0.149204	+	1.03773i	−0.00658750	+	0.0458171i
$514$	14.5739	−	4.27928i	0.642826	−	0.188751i
$515$	9.12259	+	5.86273i	0.401989	+	0.258343i
$516$	0.438845	+	3.05224i	0.0193191	+	0.134367i
$517$	−8.84816	−	19.3748i	−0.389142	−	0.852101i
$518$	−0.223740	−	0.489923i	−0.00983059	−	0.0215260i
$519$	−0.799111	−	5.55794i	−0.0350771	−	0.243966i
$520$	29.7739	+	19.1345i	1.30567	+	0.839104i
$521$	15.7236	−	4.61686i	0.688862	−	0.202268i	0.0814765	−	0.996675i	$-0.474036\pi$
$521$	15.7236	−	4.61686i	0.688862	−	0.202268i	0.607386	+	0.794407i	$0.292218\pi$
$522$	−0.179602	+	1.24916i	−0.00786095	+	0.0546741i
$523$	−16.2792	+	18.7872i	−0.711839	+	0.821506i	−0.990301	−	0.138941i	$-0.955630\pi$
$523$	−16.2792	+	18.7872i	−0.711839	+	0.821506i	0.278462	+	0.960447i	$0.410176\pi$
$524$	4.98842	−	3.20586i	0.217920	−	0.140049i
$525$	−5.10660	−	5.89333i	−0.222870	−	0.257206i
$526$	5.46090	+	1.60346i	0.238106	+	0.0699143i
$527$	−8.27064	+	18.1102i	−0.360275	+	0.788892i
$528$	−9.70517			−0.422363
$529$	−2.75887	−	22.8339i	−0.119951	−	0.992780i
$530$	−8.30107			−0.360575
$531$	−4.52428	+	9.90680i	−0.196337	+	0.429919i
$532$	5.70952	+	1.67647i	0.247539	+	0.0726840i
$533$	−5.82109	−	6.71790i	−0.252139	−	0.290984i
$534$	0.418190	−	0.268755i	0.0180969	−	0.0116302i
$535$	−6.50209	+	7.50381i	−0.281110	+	0.324418i
$536$	0.0598742	−	0.416434i	0.00258617	−	0.0179872i
$537$	−20.6721	+	6.06989i	−0.892068	+	0.261935i
$538$	8.39781	+	5.39695i	0.362055	+	0.232679i
$539$	2.85200	+	19.8361i	0.122844	+	0.854401i
$540$	−1.88180	−	4.12057i	−0.0809799	−	0.177321i
$541$	15.9154	+	34.8498i	0.684255	+	1.49831i	0.858070	+	0.513532i	$0.171663\pi$
$541$	15.9154	+	34.8498i	0.684255	+	1.49831i	−0.173815	+	0.984778i	$0.555609\pi$
$542$	0.0922675	+	0.641735i	0.00396323	+	0.0275649i
$543$	8.63238	+	5.54770i	0.370451	+	0.238074i
$544$	15.9423	−	4.68107i	0.683519	−	0.200699i
$545$	−5.15800	+	35.8747i	−0.220945	+	1.53670i
$546$	7.89930	−	9.11628i	0.338059	−	0.390141i
$547$	−15.8646	+	10.1956i	−0.678323	+	0.435932i	−0.833917	−	0.551889i	$-0.813907\pi$
$547$	−15.8646	+	10.1956i	−0.678323	+	0.435932i	0.155594	+	0.987821i	$0.450271\pi$
$548$	14.0426	+	16.2060i	0.599868	+	0.692285i
$549$	−4.49474	−	1.31978i	−0.191831	−	0.0563267i
$550$	2.44316	−	5.34976i	0.104176	−	0.228115i
$551$	−2.32536			−0.0990637
$552$	−6.65438	+	7.50678i	−0.283229	+	0.319510i
$553$	26.3008			1.11842
$554$	5.05047	−	11.0590i	0.214574	−	0.469851i
$555$	−0.724883	−	0.212845i	−0.0307696	−	0.00903477i
$556$	9.02038	+	10.4101i	0.382549	+	0.441486i
$557$	19.1542	−	12.3096i	0.811588	−	0.521576i	−0.0677904	−	0.997700i	$-0.521595\pi$
$557$	19.1542	−	12.3096i	0.811588	−	0.521576i	0.879378	+	0.476124i	$0.157959\pi$
$558$	−2.41712	+	2.78951i	−0.102325	+	0.118089i
$559$	−1.63917	+	11.4007i	−0.0693294	+	0.482196i
$560$	−18.9849	+	5.57447i	−0.802259	+	0.235564i
$561$	−11.5880	−	7.44714i	−0.489245	−	0.314418i
$562$	−1.00275	−	6.97427i	−0.0422984	−	0.294192i
$563$	−7.56278	−	16.5602i	−0.318733	−	0.697928i	0.680666	−	0.732594i	$-0.261691\pi$
$563$	−7.56278	−	16.5602i	−0.318733	−	0.697928i	−0.999399	+	0.0346659i	$0.988963\pi$
$564$	−3.30460	−	7.23607i	−0.139149	−	0.304694i
$565$	−0.267248	−	1.85875i	−0.0112432	−	0.0781983i
$566$	3.40645	+	2.18919i	0.143184	+	0.0920186i
$567$	−3.24885	+	0.953948i	−0.136439	+	0.0400620i
$568$	0.898361	−	6.24824i	0.0376944	−	0.262170i
$569$	20.6338	−	23.8127i	0.865013	−	0.998279i	−0.134959	−	0.990851i	$-0.543090\pi$
$569$	20.6338	−	23.8127i	0.865013	−	0.998279i	0.999972	−	0.00742738i	$-0.00236423\pi$
$570$	−1.35614	+	0.871541i	−0.0568026	+	0.0365048i
$571$	−3.16999	−	3.65836i	−0.132660	−	0.153098i	0.685533	−	0.728042i	$-0.259569\pi$
$571$	−3.16999	−	3.65836i	−0.132660	−	0.153098i	−0.818193	+	0.574944i	$0.805024\pi$
$572$	−45.1971	−	13.2711i	−1.88979	−	0.554891i
$573$	3.51026	−	7.68640i	0.146643	−	0.321104i
$574$	−2.73520			−0.114165
$575$	4.47458	+	10.0978i	0.186603	+	0.421109i
$576$	−1.24436			−0.0518485
$577$	10.4429	−	22.8667i	0.434743	−	0.951954i	−0.557791	−	0.829982i	$-0.688351\pi$
$577$	10.4429	−	22.8667i	0.434743	−	0.951954i	0.992534	−	0.121972i	$-0.0389218\pi$
$578$	−4.13865	−	1.21522i	−0.172145	−	0.0505464i
$579$	−0.256776	−	0.296336i	−0.0106713	−	0.0123153i
$580$	8.45240	−	5.43203i	0.350967	−	0.225553i
$581$	32.7308	−	37.7733i	1.35790	−	1.56710i
$582$	0.937075	−	6.51750i	0.0388430	−	0.270159i
$583$	23.2488	−	6.82646i	0.962867	−	0.282723i
$584$	−21.2755	−	13.6729i	−0.880385	−	0.565789i
$585$	−2.40799	−	16.7479i	−0.0995580	−	0.692441i
$586$	4.25088	+	9.30812i	0.175602	+	0.384515i
$587$	12.9330	+	28.3194i	0.533804	+	1.16887i	0.963944	+	0.266106i	$0.0857370\pi$
$587$	12.9330	+	28.3194i	0.533804	+	1.16887i	−0.430140	+	0.902762i	$0.641536\pi$
$588$	1.06516	+	7.40837i	0.0439266	+	0.305516i
$589$	−5.72146	−	3.67696i	−0.235749	−	0.151507i
$590$	−16.0679	+	4.71796i	−0.661505	+	0.194235i
$591$	3.21162	−	22.3373i	0.132108	−	0.918833i
$592$	−0.395870	+	0.456858i	−0.0162702	+	0.0187768i
$593$	−21.7689	+	13.9900i	−0.893941	+	0.574501i	−0.904988	−	0.425438i	$-0.860120\pi$
$593$	−21.7689	+	13.9900i	−0.893941	+	0.574501i	0.0110463	+	0.999939i	$0.496484\pi$
$594$	−1.67233	−	1.92997i	−0.0686166	−	0.0791878i
$595$	−26.9455	−	7.91191i	−1.10466	−	0.324357i
$596$	12.9642	−	28.3877i	0.531036	−	1.16281i
$597$	13.3644			0.546967
$598$	−14.4761	+	9.07416i	−0.591972	+	0.371070i
$599$	−43.7707			−1.78842			−0.894210	−	0.447647i	$-0.852262\pi$
$599$	−43.7707			−1.78842			−0.894210	+	0.447647i	$0.852262\pi$
$600$	2.00116	−	4.38194i	0.0816971	−	0.178892i
$601$	−12.5602	−	3.68802i	−0.512342	−	0.150437i	0.0153345	−	0.999882i	$-0.495119\pi$
$601$	−12.5602	−	3.68802i	−0.512342	−	0.150437i	−0.527677	+	0.849445i	$0.676937\pi$
$602$	2.32090	+	2.67846i	0.0945927	+	0.109166i
$603$	−0.169204	+	0.108741i	−0.00689053	+	0.00442827i
$604$	−6.00383	+	6.92879i	−0.244292	+	0.281928i
$605$	−3.51678	+	24.4597i	−0.142977	+	0.994430i
$606$	5.15196	−	1.51275i	0.209284	−	0.0614513i
$607$	10.2332	+	6.57650i	0.415354	+	0.266932i	0.731585	−	0.681750i	$-0.238781\pi$
$607$	10.2332	+	6.57650i	0.415354	+	0.266932i	−0.316231	+	0.948682i	$0.602417\pi$
$608$	0.807758	+	5.61808i	0.0327589	+	0.227843i
$609$	−3.11983	−	6.83148i	−0.126422	−	0.276825i
$610$	−2.99223	−	6.55207i	−0.121152	−	0.265286i
$611$	−4.22862	−	29.4107i	−0.171072	−	1.18983i
$612$	−4.32787	−	2.78135i	−0.174944	−	0.112429i
$613$	−40.9582	+	12.0264i	−1.65429	+	0.485742i	−0.969925	−	0.243402i	$-0.921736\pi$
$613$	−40.9582	+	12.0264i	−1.65429	+	0.485742i	−0.684360	+	0.729144i	$0.739918\pi$
$614$	0.148252	−	1.03112i	0.00598297	−	0.0416125i
$615$	−2.51248	+	2.89955i	−0.101313	+	0.116921i
$616$	−26.7420	+	17.1861i	−1.07747	+	0.692446i
$617$	−0.260539	−	0.300678i	−0.0104889	−	0.0121048i	0.750481	−	0.660892i	$-0.229822\pi$
$617$	−0.260539	−	0.300678i	−0.0104889	−	0.0121048i	−0.760970	+	0.648787i	$0.775276\pi$
$618$	2.19069	+	0.643245i	0.0881226	+	0.0258751i
$619$	−12.4831	+	27.3343i	−0.501740	+	1.09866i	0.474160	+	0.880439i	$0.342752\pi$
$619$	−12.4831	+	27.3343i	−0.501740	+	1.09866i	−0.975900	+	0.218219i	$0.929975\pi$
$620$	29.3862			1.18018
$621$	4.79553	+	0.0540938i	0.192438	+	0.00217071i
$622$	5.27239			0.211403
$623$	−1.22890	+	2.69092i	−0.0492350	+	0.107810i
$624$	−12.9904	−	3.81433i	−0.520033	−	0.152695i
$625$	20.4390	+	23.5878i	0.817559	+	0.943514i
$626$	−6.66148	+	4.28108i	−0.266246	+	0.171106i
$627$	3.08143	−	3.55616i	0.123061	−	0.142019i
$628$	3.92105	−	27.2715i	0.156467	−	1.08825i
$629$	−0.823234	+	0.241723i	−0.0328245	+	0.00963814i
$630$	−4.37990	−	2.81479i	−0.174499	−	0.112144i
$631$	3.43513	+	23.8919i	0.136750	+	0.951120i	0.936470	+	0.350747i	$0.114072\pi$
$631$	3.43513	+	23.8919i	0.136750	+	0.951120i	−0.799720	+	0.600373i	$0.795019\pi$
$632$	6.74945	+	14.7792i	0.268479	+	0.587886i
$633$	−0.232217	−	0.508485i	−0.00922981	−	0.0202105i
$634$	−2.19060	−	15.2360i	−0.0869999	−	0.605098i
$635$	−24.8803	−	15.9896i	−0.987344	−	0.634528i
$636$	8.68294	−	2.54954i	0.344301	−	0.101096i
$637$	−3.97858	+	27.6716i	−0.157637	+	1.09639i
$638$	3.70923	−	4.28068i	0.146850	−	0.169474i
$639$	−2.53877	+	1.63157i	−0.100432	+	0.0645437i
$640$	−20.4146	−	23.5597i	−0.806958	−	0.931279i
$641$	−31.6282	−	9.28689i	−1.24924	−	0.366810i	−0.410761	−	0.911743i	$-0.634737\pi$
$641$	−31.6282	−	9.28689i	−1.24924	−	0.366810i	−0.838479	+	0.544933i	$0.816555\pi$
$642$	−0.868429	+	1.90159i	−0.0342742	+	0.0750499i
$643$	7.50786			0.296081			0.148040	−	0.988981i	$-0.452703\pi$
$643$	7.50786			0.296081			0.148040	+	0.988981i	$0.452703\pi$
$644$	4.17751	−	26.8978i	0.164617	−	1.05992i
$645$	4.97131			0.195745
$646$	−0.760529	+	1.66533i	−0.0299226	+	0.0655214i
$647$	−13.2481	−	3.88998i	−0.520835	−	0.152931i	0.0107395	−	0.999942i	$-0.496581\pi$
$647$	−13.2481	−	3.88998i	−0.520835	−	0.152931i	−0.531575	+	0.847011i	$0.678400\pi$
$648$	−1.36979	−	1.58082i	−0.0538104	−	0.0621006i
$649$	41.1215	−	26.4272i	1.61416	−	1.03736i
$650$	5.37274	−	6.20048i	0.210736	−	0.243203i
$651$	3.12600	−	21.7418i	0.122518	−	0.852129i
$652$	16.1093	−	4.73011i	0.630888	−	0.185245i
$653$	20.0883	+	12.9100i	0.786116	+	0.505206i	0.871058	−	0.491180i	$-0.163434\pi$
$653$	20.0883	+	12.9100i	0.786116	+	0.505206i	−0.0849423	+	0.996386i	$0.527071\pi$
$654$	1.08600	+	7.55329i	0.0424660	+	0.295357i
$655$	−3.97126	−	8.69584i	−0.155170	−	0.339775i
$656$	1.27530	+	2.79252i	0.0497922	+	0.109030i
$657$	1.72067	+	11.9675i	0.0671297	+	0.466897i
$658$	−7.69147	−	4.94301i	−0.299845	−	0.192699i
$659$	−19.8085	+	5.81631i	−0.771631	+	0.226571i	−0.643768	−	0.765220i	$-0.722630\pi$
$659$	−19.8085	+	5.81631i	−0.771631	+	0.226571i	−0.127863	+	0.991792i	$0.540812\pi$
$660$	−2.89346	+	20.1244i	−0.112628	+	0.783342i
$661$	30.0235	−	34.6490i	1.16778	−	1.34769i	0.241703	−	0.970350i	$-0.422294\pi$
$661$	30.0235	−	34.6490i	1.16778	−	1.34769i	0.926076	−	0.377338i	$-0.123161\pi$
$662$	−7.86076	+	5.05181i	−0.305517	+	0.196344i
$663$	−12.5837	−	14.5223i	−0.488710	−	0.564001i
$664$	29.6256	+	8.69885i	1.14969	+	0.337581i
$665$	3.98520	−	8.72636i	0.154539	−	0.338394i
$666$	−0.159065			−0.00616364
$667$	1.39497	+	10.5453i	0.0540134	+	0.408315i
$668$	12.4027			0.479877
$669$	−12.3362	+	27.0125i	−0.476945	+	1.04436i
$670$	−0.296740	−	0.0871307i	−0.0114641	−	0.00336615i
$671$	13.7685	+	15.8897i	0.531527	+	0.613415i
$672$	−15.4212	+	9.91057i	−0.594884	+	0.382309i
$673$	−22.7553	+	26.2610i	−0.877153	+	1.01229i	0.122650	+	0.992450i	$0.460861\pi$
$673$	−22.7553	+	26.2610i	−0.877153	+	1.01229i	−0.999803	+	0.0198386i	$0.993685\pi$
$674$	−1.34213	+	9.33469i	−0.0516967	+	0.359559i
$675$	−2.20972	+	0.648832i	−0.0850521	+	0.0249736i
$676$	−36.9487	−	23.7455i	−1.42110	−	0.913288i
$677$	−4.44431	−	30.9109i	−0.170809	−	1.18800i	−0.877181	−	0.480161i	$-0.840578\pi$
$677$	−4.44431	−	30.9109i	−0.170809	−	1.18800i	0.706372	−	0.707841i	$-0.250331\pi$
$678$	−0.164246	−	0.359649i	−0.00630783	−	0.0138122i
$679$	16.2778	+	35.6433i	0.624683	+	1.36787i
$680$	−2.46895	−	17.1719i	−0.0946798	−	0.658513i
$681$	−20.7540	−	13.3378i	−0.795295	−	0.511105i
$682$	15.8952	−	4.66726i	0.608659	−	0.178719i
$683$	−3.56583	+	24.8009i	−0.136443	+	0.948980i	0.800459	+	0.599387i	$0.204589\pi$
$683$	−3.56583	+	24.8009i	−0.136443	+	0.948980i	−0.936902	+	0.349592i	$0.886320\pi$
$684$	1.15085	−	1.32815i	0.0440039	−	0.0507832i
$685$	29.0826	−	18.6903i	1.11119	−	0.714119i
$686$	−3.19822	−	3.69094i	−0.122109	−	0.140921i
$687$	27.3273	+	8.02401i	1.04260	+	0.306135i
$688$	1.65246	−	3.61838i	0.0629994	−	0.137949i
$689$	33.8016			1.28774
$690$	4.76589	+	5.62715i	0.181434	+	0.214222i
$691$	47.0943			1.79155			0.895775	−	0.444507i	$-0.146621\pi$
$691$	47.0943			1.79155			0.895775	+	0.444507i	$0.146621\pi$
$692$	−3.91003	+	8.56177i	−0.148637	+	0.325470i
$693$	14.5816	+	4.28153i	0.553908	+	0.162642i
$694$	−0.0695763	−	0.0802953i	−0.00264108	−	0.00304797i
$695$	18.6815	−	12.0059i	0.708631	−	0.455410i
$696$	3.03819	−	3.50626i	0.115162	−	0.132904i
$697$	−0.620095	+	4.31286i	−0.0234878	+	0.163361i
$698$	5.74089	−	1.68568i	0.217296	−	0.0638038i
$699$	−12.6718	−	8.14369i	−0.479292	−	0.308023i
$700$	1.86026	+	12.9384i	0.0703113	+	0.489026i
$701$	10.6225	+	23.2601i	0.401207	+	0.878522i	0.997146	+	0.0754920i	$0.0240527\pi$
$701$	10.6225	+	23.2601i	0.401207	+	0.878522i	−0.595939	+	0.803030i	$0.703220\pi$
$702$	−1.47991	−	3.24054i	−0.0558554	−	0.122306i
$703$	−0.0417114	−	0.290109i	−0.00157317	−	0.0109417i
$704$	4.69839	+	3.01947i	0.177077	+	0.113801i
$705$	−12.3052	+	3.61313i	−0.463441	+	0.136078i
$706$	−1.67338	+	11.6386i	−0.0629784	+	0.438025i
$707$	−20.9251	+	24.1489i	−0.786970	+	0.908212i
$708$	15.3580	−	9.87001i	0.577190	−	0.370938i
$709$	13.9512	+	16.1005i	0.523947	+	0.604667i	0.954615	−	0.297843i	$-0.0962674\pi$
$709$	13.9512	+	16.1005i	0.523947	+	0.604667i	−0.430668	+	0.902511i	$0.641722\pi$
$710$	−4.45233	−	1.30732i	−0.167093	−	0.0490629i
$711$	3.22673	−	7.06556i	0.121012	−	0.264979i
$712$	−1.82748			−0.0684878
$713$	−13.2424	+	28.1521i	−0.495931	+	1.05430i
$714$	−5.91279			−0.221281
$715$	−31.5472	+	69.0787i	−1.17980	+	2.58340i
$716$	34.6518	+	10.1747i	1.29500	+	0.380246i
$717$	17.6566	+	20.3768i	0.659399	+	0.760987i
$718$	−7.50415	+	4.82263i	−0.280053	+	0.179979i
$719$	11.0585	−	12.7622i	0.412412	−	0.475949i	−0.511098	−	0.859522i	$-0.670761\pi$
$719$	11.0585	−	12.7622i	0.412412	−	0.475949i	0.923510	+	0.383573i	$0.125307\pi$
$720$	−0.831628	+	5.78410i	−0.0309930	+	0.215561i
$721$	−13.0368	+	3.82794i	−0.485515	+	0.142560i
$722$	8.56839	+	5.50657i	0.318883	+	0.204933i
$723$	−3.00414	−	20.8943i	−0.111725	−	0.777066i
$724$	−7.14541	−	15.6463i	−0.265557	−	0.581489i
$725$	−2.12197	−	4.64646i	−0.0788079	−	0.172565i
$726$	0.740446	+	5.14992i	0.0274805	+	0.191131i
$727$	−39.3725	−	25.3032i	−1.46024	−	0.938442i	−0.998681	−	0.0513351i	$-0.983652\pi$
$727$	−39.3725	−	25.3032i	−1.46024	−	0.938442i	−0.461563	−	0.887107i	$-0.652711\pi$
$728$	−42.5488	+	12.4935i	−1.57696	+	0.463038i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−12.1744	+	14.0500i	−0.450593	+	0.520012i
$731$	4.74955	−	3.05235i	0.175669	−	0.112895i
$732$	5.14225	+	5.93447i	0.190063	+	0.219344i
$733$	1.17020	+	0.343601i	0.0432223	+	0.0126912i	0.303272	−	0.952904i	$-0.401921\pi$
$733$	1.17020	+	0.343601i	0.0432223	+	0.0126912i	−0.260050	+	0.965595i	$0.583739\pi$
$734$	−1.28715	+	2.81846i	−0.0475096	+	0.104031i
$735$	12.0663			0.445074
$736$	24.9929	−	7.03336i	0.921250	−	0.259253i
$737$	0.902732			0.0332526
$738$	−0.335570	+	0.734797i	−0.0123525	+	0.0270482i
$739$	27.8695	+	8.18321i	1.02519	+	0.301024i	0.750756	−	0.660580i	$-0.229690\pi$
$739$	27.8695	+	8.18321i	1.02519	+	0.301024i	0.274439	+	0.961604i	$0.411508\pi$
$740$	0.829309	+	0.957074i	0.0304860	+	0.0351827i
$741$	5.52216	−	3.54888i	0.202862	−	0.130371i
$742$	6.81114	−	7.86047i	0.250045	−	0.288567i
$743$	3.79826	−	26.4174i	0.139344	−	0.969162i	−0.793420	−	0.608675i	$-0.791701\pi$
$743$	3.79826	−	26.4174i	0.139344	−	0.969162i	0.932764	−	0.360487i	$-0.117390\pi$
$744$	13.0196	−	3.82290i	0.477322	−	0.140154i
$745$	−42.3255	−	27.2009i	−1.55068	−	0.996565i
$746$	−0.326116	−	2.26819i	−0.0119400	−	0.0830442i
$747$	−6.13200	−	13.4272i	−0.224358	−	0.491276i
$748$	9.59188	+	21.0033i	0.350714	+	0.767956i
$749$	−1.77048	−	12.3140i	−0.0646919	−	0.449942i
$750$	3.48864	+	2.24201i	0.127387	+	0.0818668i
$751$	−1.31007	+	0.384670i	−0.0478050	+	0.0140368i	−0.305548	−	0.952177i	$-0.598840\pi$
$751$	−1.31007	+	0.384670i	−0.0478050	+	0.0140368i	0.257743	+	0.966214i	$0.417021\pi$
$752$	−1.46041	+	10.1574i	−0.0532556	+	0.370401i
$753$	1.52389	−	1.75867i	0.0555338	−	0.0640894i
$754$	6.64722	−	4.27191i	0.242077	−	0.155574i
$755$	9.67917	+	11.1704i	0.352261	+	0.406531i
$756$	5.44591	+	1.59906i	0.198066	+	0.0581574i
$757$	21.6745	−	47.4605i	0.787773	−	1.72498i	0.104855	−	0.994488i	$-0.466562\pi$
$757$	21.6745	−	47.4605i	0.787773	−	1.72498i	0.682918	−	0.730495i	$-0.260711\pi$
$758$	6.34357			0.230409
$759$	−17.9754	−	11.8407i	−0.652465	−	0.429789i
$760$	5.92632			0.214970
$761$	9.05143	−	19.8199i	0.328114	−	0.718470i	−0.671635	−	0.740883i	$-0.734407\pi$
$761$	9.05143	−	19.8199i	0.328114	−	0.718470i	0.999749	+	0.0224126i	$0.00713475\pi$
$762$	−5.97473	−	1.75434i	−0.216442	−	0.0635530i
$763$	−29.7384	−	34.3199i	−1.07660	−	1.24246i
$764$	−11.9158	+	7.65785i	−0.431100	+	0.277051i
$765$	−5.43132	+	6.26808i	−0.196370	+	0.226623i
$766$	−1.21561	+	8.45476i	−0.0439218	+	0.305483i
$767$	65.4278	−	19.2113i	2.36246	−	0.693681i
$768$	−3.42797	−	2.20302i	−0.123696	−	0.0794948i
$769$	−5.35823	−	37.2673i	−0.193223	−	1.34389i	−0.823409	−	0.567449i	$-0.807931\pi$
$769$	−5.35823	−	37.2673i	−0.193223	−	1.34389i	0.630186	−	0.776444i	$-0.282979\pi$
$770$	9.70721	+	21.2558i	0.349823	+	0.766007i
$771$	11.0896	+	24.2829i	0.399383	+	0.874526i
$772$	0.0935400	+	0.650585i	0.00336658	+	0.0234151i
$773$	1.53486	+	0.986395i	0.0552051	+	0.0354782i	0.567952	−	0.823061i	$-0.307736\pi$
$773$	1.53486	+	0.986395i	0.0552051	+	0.0354782i	−0.512747	+	0.858540i	$0.671372\pi$
$774$	1.00429	−	0.294887i	0.0360986	−	0.0105995i
$775$	2.12616	−	14.7878i	0.0763740	−	0.531193i
$776$	−15.8518	+	18.2940i	−0.569047	+	0.656715i
$777$	0.796324	−	0.511767i	0.0285680	−	0.0183595i
$778$	−12.3560	−	14.2596i	−0.442983	−	0.511230i
$779$	−1.42815	−	0.419342i	−0.0511687	−	0.0150245i
$780$	−11.7822	+	25.7995i	−0.421871	+	0.923769i
$781$	13.5447			0.484668
$782$	8.00833	+	2.44991i	0.286377	+	0.0876085i
$783$	−2.21800			−0.0792648
$784$	4.01084	−	8.78251i	0.143244	−	0.313661i
$785$	−42.6190	−	12.5141i	−1.52114	−	0.446646i
$786$	−1.31808	−	1.52115i	−0.0470145	−	0.0542576i
$787$	−24.2453	+	15.5815i	−0.864250	+	0.555420i	−0.895989	−	0.444076i	$-0.853532\pi$
$787$	−24.2453	+	15.5815i	−0.864250	+	0.555420i	0.0317386	+	0.999496i	$0.489896\pi$
$788$	−24.7721	+	28.5886i	−0.882471	+	1.01843i
$789$	−1.42355	+	9.90102i	−0.0506798	+	0.352486i
$790$	11.4597	−	3.36487i	0.407717	−	0.119717i
$791$	1.97938	+	1.27207i	0.0703785	+	0.0452295i
$792$	1.33607	+	9.29259i	0.0474753	+	0.330198i
$793$	12.1842	+	26.6798i	0.432675	+	0.947426i
$794$	1.57670	+	3.45248i	0.0559549	+	0.122524i
$795$	−2.07628	−	14.4408i	−0.0736379	−	0.512163i
$796$	−18.8459	−	12.1115i	−0.667974	−	0.429281i
$797$	0.861256	−	0.252887i	0.0305072	−	0.00895773i	−0.266443	−	0.963851i	$-0.585849\pi$
$797$	0.861256	−	0.252887i	0.0305072	−	0.00895773i	0.296951	+	0.954893i	$0.404030\pi$
$798$	0.287452	−	1.99927i	0.0101757	−	0.0707736i
$799$	−9.53786	+	11.0073i	−0.337425	+	0.389409i
$800$	−10.4888	+	6.74072i	−0.370834	+	0.238320i
$801$	0.572133	+	0.660277i	0.0202153	+	0.0233297i
$802$	−3.39920	−	0.998096i	−0.120030	−	0.0352440i
$803$	22.5426	−	49.3614i	0.795511	−	1.74193i
$804$	0.337152			0.0118904
$805$	−41.9639	−	12.8376i	−1.47903	−	0.452465i
$806$	23.1102			0.814021
$807$	−7.28824	+	15.9590i	−0.256558	+	0.561784i
$808$	−18.9399	−	5.56127i	−0.666304	−	0.195645i
$809$	24.6586	+	28.4575i	0.866949	+	1.00051i	0.999956	+	0.00939782i	$0.00299146\pi$
$809$	24.6586	+	28.4575i	0.866949	+	1.00051i	−0.133006	+	0.991115i	$0.542463\pi$
$810$	−1.29353	+	0.831302i	−0.0454500	+	0.0292090i
$811$	13.4067	−	15.4722i	0.470775	−	0.543303i	−0.469852	−	0.882745i	$-0.655693\pi$
$811$	13.4067	−	15.4722i	0.470775	−	0.543303i	0.940627	+	0.339442i	$0.110238\pi$
$812$	−1.79160	+	12.4608i	−0.0628727	+	0.437289i
$813$	−1.09331	+	0.321023i	−0.0383439	+	0.0112588i
$814$	0.600587	+	0.385974i	0.0210506	+	0.0135284i
$815$	−3.85207	−	26.7917i	−0.134932	−	0.938473i
$816$	2.75687	+	6.03670i	0.0965098	+	0.211327i
$817$	0.801182	+	1.75434i	0.0280298	+	0.0613767i
$818$	−0.158705	−	1.10382i	−0.00554901	−	0.0385942i
$819$	17.8348	+	11.4617i	0.623197	+	0.400505i
$820$	6.17073	−	1.81189i	0.215491	−	0.0632739i
$821$	2.30296	−	16.0174i	0.0803739	−	0.559013i	−0.909351	−	0.416029i	$-0.863421\pi$
$821$	2.30296	−	16.0174i	0.0803739	−	0.559013i	0.989725	−	0.142983i	$-0.0456695\pi$
$822$	4.76655	−	5.50089i	0.166252	−	0.191866i
$823$	−15.0421	+	9.66699i	−0.524336	+	0.336970i	−0.775885	−	0.630874i	$-0.782696\pi$
$823$	−15.0421	+	9.66699i	−0.524336	+	0.336970i	0.251549	+	0.967844i	$0.419060\pi$
$824$	−5.49660	−	6.34342i	−0.191483	−	0.220984i
$825$	9.91772	+	2.91210i	0.345291	+	0.101386i
$826$	8.71639	−	19.0862i	0.303282	−	0.664095i
$827$	−8.08676			−0.281204			−0.140602	−	0.990066i	$-0.544904\pi$
$827$	−8.08676			−0.281204			−0.140602	+	0.990066i	$0.544904\pi$
$828$	−6.71343	−	4.42225i	−0.233308	−	0.153684i
$829$	−37.2365			−1.29328			−0.646639	−	0.762796i	$-0.723826\pi$
$829$	−37.2365			−1.29328			−0.646639	+	0.762796i	$0.723826\pi$
$830$	9.42870	−	20.6460i	0.327275	−	0.716632i
$831$	20.5018	+	6.01988i	0.711200	+	0.208827i
$832$	5.10211	+	5.88814i	0.176884	+	0.204135i
$833$	11.5281	−	7.40865i	0.399425	−	0.256695i
$834$	3.06184	−	3.53355i	0.106023	−	0.122357i
$835$	2.84563	−	19.7918i	0.0984769	−	0.684922i
$836$	−7.56809	+	2.22219i	−0.261748	+	0.0768562i
$837$	−5.45730	−	3.50720i	−0.188632	−	0.121226i
$838$	0.669211	+	4.65446i	0.0231175	+	0.160786i
$839$	−14.4379	−	31.6145i	−0.498451	−	1.09145i	−0.976970	−	0.213377i	$-0.931554\pi$
$839$	−14.4379	−	31.6145i	−0.498451	−	1.09145i	0.478519	−	0.878077i	$-0.341174\pi$
$840$	7.95107	+	17.4104i	0.274338	+	0.600717i
$841$	3.42701	+	23.8354i	0.118173	+	0.821910i
$842$	0.847742	+	0.544810i	0.0292151	+	0.0187754i
$843$	11.8819	−	3.48883i	0.409233	−	0.120162i
$844$	−0.133353	+	0.927493i	−0.00459021	+	0.0319256i
$845$	−46.3693	+	53.5131i	−1.59515	+	1.84090i
$846$	−2.27155	+	1.45984i	−0.0780974	+	0.0501902i
$847$	−20.2759	−	23.3997i	−0.696689	−	0.804022i
$848$	−11.2009	−	3.28889i	−0.384642	−	0.112941i
$849$	−2.95637	+	6.47354i	−0.101462	+	0.222171i
$850$	−4.02161			−0.137940
$851$	−1.29059	+	0.363192i	−0.0442410	+	0.0124501i
$852$	5.05867			0.173307
$853$	−11.7305	+	25.6863i	−0.401646	+	0.879482i	0.595455	+	0.803389i	$0.296972\pi$
$853$	−11.7305	+	25.6863i	−0.401646	+	0.879482i	−0.997101	+	0.0760933i	$0.975755\pi$
$854$	8.65948	+	2.54265i	0.296321	+	0.0870078i
$855$	−1.85536	−	2.14120i	−0.0634521	−	0.0732276i
$856$	6.46525	−	4.15496i	0.220978	−	0.142014i
$857$	4.86922	−	5.61938i	0.166330	−	0.191954i	−0.666466	−	0.745536i	$-0.732194\pi$
$857$	4.86922	−	5.61938i	0.166330	−	0.191954i	0.832795	+	0.553581i	$0.186739\pi$
$858$	−2.27550	+	15.8264i	−0.0776843	+	0.540306i
$859$	−39.2382	+	11.5214i	−1.33879	+	0.393104i	−0.871237	−	0.490862i	$-0.836682\pi$
$859$	−39.2382	+	11.5214i	−1.33879	+	0.393104i	−0.467551	+	0.883966i	$0.654864\pi$
$860$	−7.01034	−	4.50527i	−0.239051	−	0.153628i
$861$	−0.684133	−	4.75825i	−0.0233152	−	0.162161i
$862$	−6.32437	−	13.8484i	−0.215409	−	0.471680i
$863$	−8.82000	−	19.3131i	−0.300236	−	0.657426i	0.698044	−	0.716055i	$-0.254054\pi$
$863$	−8.82000	−	19.3131i	−0.300236	−	0.657426i	−0.998280	+	0.0586297i	$0.981327\pi$
$864$	0.770464	+	5.35870i	0.0262117	+	0.182307i
$865$	12.7654	+	8.20383i	0.434037	+	0.278939i
$866$	13.4170	−	3.93959i	0.455928	−	0.133873i
$867$	1.07887	−	7.50369i	0.0366403	−	0.254839i
$868$	−24.1118	+	27.8264i	−0.818406	+	0.944491i
$869$	−29.3280	+	18.8480i	−0.994884	+	0.639373i
$870$	−2.23337	−	2.57744i	−0.0757182	−	0.0873835i
$871$	1.20831	+	0.354792i	0.0409421	+	0.0120217i
$872$	11.6538	−	25.5183i	0.394648	−	0.864158i
$873$	11.5724			0.391668
$874$	−1.21771	+	2.58873i	−0.0411896	+	0.0875651i
$875$	−24.6785			−0.834285
$876$	8.41919	−	18.4355i	0.284458	−	0.622876i
$877$	−17.9522	−	5.27124i	−0.606203	−	0.177997i	−0.0357955	−	0.999359i	$-0.511396\pi$
$877$	−17.9522	−	5.27124i	−0.606203	−	0.177997i	−0.570407	+	0.821362i	$0.693215\pi$
$878$	2.08492	+	2.40612i	0.0703626	+	0.0812028i
$879$	−15.1295	+	9.72313i	−0.510305	+	0.327953i
$880$	17.1752	−	19.8213i	0.578977	−	0.668175i
$881$	−5.10803	+	35.5271i	−0.172094	+	1.19694i	0.702357	+	0.711825i	$0.252131\pi$
$881$	−5.10803	+	35.5271i	−0.172094	+	1.19694i	−0.874451	+	0.485114i	$0.838778\pi$
$882$	2.43762	−	0.715749i	0.0820788	−	0.0241005i
$883$	5.34188	+	3.43302i	0.179769	+	0.115530i	0.627430	−	0.778673i	$-0.284107\pi$
$883$	5.34188	+	3.43302i	0.179769	+	0.115530i	−0.447662	+	0.894203i	$0.647743\pi$
$884$	4.58406	+	31.8828i	0.154179	+	1.07234i
$885$	−12.2265	−	26.7722i	−0.410988	−	0.899938i
$886$	−2.95857	−	6.47837i	−0.0993951	−	0.217645i
$887$	−2.27527	−	15.8248i	−0.0763960	−	0.531346i	−0.991699	−	0.128580i	$-0.958958\pi$
$887$	−2.27527	−	15.8248i	−0.0763960	−	0.531346i	0.915303	−	0.402766i	$-0.131951\pi$
$888$	0.491935	+	0.316147i	0.0165082	+	0.0106092i
$889$	35.5555	−	10.4400i	1.19249	−	0.350148i
$890$	−0.191183	+	1.32970i	−0.00640845	+	0.0445718i
$891$	2.93916	−	3.39197i	0.0984657	−	0.113635i
$892$	41.8762	−	26.9122i	1.40212	−	0.901087i
$893$	−3.25817	−	3.76013i	−0.109031	−	0.125828i
$894$	−10.1640	−	2.98442i	−0.339935	−	0.0998139i
$895$	24.1867	−	52.9615i	0.808472	−	1.77031i
$896$	39.0597			1.30489
$897$	−19.4065	−	22.9135i	−0.647965	−	0.765059i
$898$	4.63700			0.154739
$899$	5.97715	−	13.0881i	0.199349	−	0.436514i
$900$	3.70406	+	1.08761i	0.123469	+	0.0362537i
$901$	−10.8502	−	12.5218i	−0.361473	−	0.417163i
$902$	3.05002	−	1.96013i	0.101555	−	0.0652652i
$903$	−4.07903	+	4.70745i	−0.135742	+	0.156654i
$904$	−0.206856	+	1.43872i	−0.00687994	+	0.0478511i
$905$	−26.6070	+	7.81253i	−0.884448	+	0.259697i
$906$	2.61797	+	1.68246i	0.0869761	+	0.0558961i
$907$	3.33936	+	23.2257i	0.110881	+	0.771198i	0.967066	+	0.254527i	$0.0819197\pi$
$907$	3.33936	+	23.2257i	0.110881	+	0.771198i	−0.856184	+	0.516671i	$0.827171\pi$
$908$	17.1790	+	37.6168i	0.570105	+	1.24836i
$909$	3.92025	+	8.58415i	0.130026	+	0.284718i
$910$	4.63917	+	32.2662i	0.153787	+	1.06961i
$911$	23.3996	+	15.0380i	0.775263	+	0.498231i	0.867458	−	0.497510i	$-0.165752\pi$
$911$	23.3996	+	15.0380i	0.775263	+	0.498231i	−0.0921956	+	0.995741i	$0.529389\pi$
$912$	−2.17520	+	0.638696i	−0.0720280	+	0.0211493i
$913$	−9.42854	+	65.5770i	−0.312039	+	2.17028i
$914$	−6.74446	+	7.78352i	−0.223087	+	0.257456i
$915$	10.6498	−	6.84420i	0.352071	−	0.226262i
$916$	−31.2640	−	36.0806i	−1.03299	−	1.19214i
$917$	11.4928	+	3.37458i	0.379525	+	0.111438i
$918$	−0.725416	+	1.58844i	−0.0239423	+	0.0524263i
$919$	38.7863			1.27944			0.639720	−	0.768608i	$-0.279050\pi$
$919$	38.7863			1.27944			0.639720	+	0.768608i	$0.279050\pi$
$920$	−3.55516	−	26.8753i	−0.117210	−	0.886051i
$921$	1.83085			0.0603285
$922$	−3.09663	+	6.78068i	−0.101982	+	0.223310i
$923$	18.1297	+	5.32336i	0.596746	+	0.175220i
$924$	−16.6822	−	19.2522i	−0.548803	−	0.633352i
$925$	0.541624	−	0.348080i	0.0178085	−	0.0114448i
$926$	−7.25317	+	8.37060i	−0.238354	+	0.275075i
$927$	−0.571072	+	3.97189i	−0.0187565	+	0.130454i
$928$	−11.5214	+	3.38299i	−0.378208	+	0.111052i
$929$	−27.2494	−	17.5121i	−0.894023	−	0.574554i	0.0109891	−	0.999940i	$-0.496502\pi$
$929$	−27.2494	−	17.5121i	−0.894023	−	0.574554i	−0.905012	+	0.425386i	$0.860138\pi$
$930$	−1.41955	−	9.87320i	−0.0465489	−	0.323755i
$931$	1.94462	+	4.25813i	0.0637325	+	0.139555i
$932$	10.4890	+	22.9678i	0.343580	+	0.752335i
$933$	1.31874	+	9.17202i	0.0431735	+	0.300279i
$934$	0.572395	+	0.367856i	0.0187293	+	0.0120366i
$935$	35.7169	−	10.4874i	1.16807	−	0.342975i
$936$	−1.86384	+	12.9633i	−0.0609215	+	0.423718i
$937$	0.936770	−	1.08109i	0.0306029	−	0.0353177i	−0.740242	−	0.672341i	$-0.765289\pi$
$937$	0.936770	−	1.08109i	0.0306029	−	0.0353177i	0.770845	+	0.637023i	$0.219834\pi$
$938$	0.325985	−	0.209498i	0.0106438	−	0.00684035i
$939$	−9.11369	−	10.5178i	−0.297414	−	0.343234i
$940$	20.6267	+	6.05655i	0.672769	+	0.197543i
$941$	−0.263641	+	0.577294i	−0.00859446	+	0.0188192i	−0.913881	−	0.405983i	$-0.866929\pi$
$941$	−0.263641	+	0.577294i	−0.00859446	+	0.0188192i	0.905286	+	0.424802i	$0.139656\pi$
$942$	−9.35211			−0.304708
$943$	−1.04494	+	6.72807i	−0.0340279	+	0.219096i
$944$	−23.5503			−0.766496
$945$	3.80120	−	8.32347i	0.123653	−	0.270762i
$946$	−4.50750	−	1.32352i	−0.146551	−	0.0430314i
$947$	21.7906	+	25.1476i	0.708098	+	0.817188i	0.989823	−	0.142307i	$-0.0454520\pi$
$947$	21.7906	+	25.1476i	0.708098	+	0.817188i	−0.281725	+	0.959495i	$0.590907\pi$
$948$	−10.9534	+	7.03932i	−0.355750	+	0.228627i
$949$	49.5734	−	57.2108i	1.60922	−	1.85714i
$950$	0.195512	−	1.35982i	0.00634325	−	0.0441183i
$951$	25.9571	−	7.62169i	0.841716	−	0.247150i
$952$	18.2863	+	11.7519i	0.592662	+	0.380881i
$953$	5.69080	+	39.5804i	0.184343	+	1.28214i	0.846346	+	0.532634i	$0.178798\pi$
$953$	5.69080	+	39.5804i	0.184343	+	1.28214i	−0.662003	+	0.749502i	$0.730293\pi$
$954$	−1.27604	−	2.79414i	−0.0413134	−	0.0904637i
$955$	9.48615	+	20.7718i	0.306965	+	0.672159i
$956$	−6.43206	−	44.7360i	−0.208028	−	1.44686i
$957$	8.37457	+	5.38201i	0.270712	+	0.173976i
$958$	−9.54599	+	2.80295i	−0.308417	+	0.0905594i
$959$	−6.16444	+	42.8746i	−0.199060	+	1.38449i
$960$	2.20215	−	2.54142i	0.0710742	−	0.0820240i
$961$	9.32324	−	5.99169i	0.300750	−	0.193280i
$962$	0.652193	+	0.752671i	0.0210276	+	0.0242671i
$963$	−3.52529	−	1.03512i	−0.113601	−	0.0333562i
$964$	−14.6992	+	32.1867i	−0.473429	+	1.03666i
$965$	1.05964			0.0341109
$966$	−9.23896	−	0.104216i	−0.297259	−	0.00335309i
$967$	50.8204			1.63427			0.817136	−	0.576444i	$-0.195560\pi$
$967$	50.8204			1.63427			0.817136	+	0.576444i	$0.195560\pi$
$968$	7.94569	−	17.3986i	0.255384	−	0.559213i
$969$	−3.08728	−	0.906509i	−0.0991779	−	0.0291212i
$970$	11.6526	+	13.4478i	0.374143	+	0.431784i
$971$	36.1031	−	23.2020i	1.15860	−	0.744589i	0.187269	−	0.982309i	$-0.440036\pi$
$971$	36.1031	−	23.2020i	1.15860	−	0.744589i	0.971334	+	0.237720i	$0.0763999\pi$
$972$	1.09772	−	1.26683i	0.0352093	−	0.0406337i
$973$	−3.95980	+	27.5410i	−0.126945	+	0.882923i
$974$	−12.2908	+	3.60891i	−0.393823	+	0.115637i
$975$	12.1304	+	7.79573i	0.388484	+	0.249663i
$976$	−1.44159	−	10.0265i	−0.0461442	−	0.320940i
$977$	4.38860	+	9.60970i	0.140404	+	0.307442i	0.966751	−	0.255719i	$-0.0823123\pi$
$977$	4.38860	+	9.60970i	0.140404	+	0.307442i	−0.826347	+	0.563161i	$0.809585\pi$
$978$	−2.36741	−	5.18391i	−0.0757015	−	0.165763i
$979$	−0.558050	−	3.88132i	−0.0178354	−	0.124048i
$980$	−17.0155	−	10.9352i	−0.543539	−	0.349311i
$981$	−12.8683	+	3.77848i	−0.410854	+	0.120638i
$982$	2.38343	−	16.5771i	0.0760582	−	0.528996i
$983$	−31.0101	+	35.7876i	−0.989068	+	1.14145i	0.000877467		1.00000i	$0.499721\pi$
$983$	−31.0101	+	35.7876i	−0.989068	+	1.14145i	−0.989946	+	0.141446i	$0.954825\pi$
$984$	2.49824	−	1.60552i	0.0796410	−	0.0511822i
$985$	39.9368	+	46.0895i	1.27249	+	1.46853i
$986$	−3.71627	−	1.09120i	−0.118350	−	0.0347508i
$987$	6.67522	−	14.6167i	0.212475	−	0.465255i
$988$	−11.0033			−0.350062
$989$	7.47516	−	4.68570i	0.237696	−	0.148997i
$990$	6.90120			0.219334
$991$	10.0139	−	21.9274i	0.318102	−	0.696546i	−0.681268	−	0.732034i	$-0.738571\pi$
$991$	10.0139	−	21.9274i	0.318102	−	0.696546i	0.999370	+	0.0354879i	$0.0112985\pi$
$992$	−33.6973	−	9.89442i	−1.06989	−	0.314148i
$993$	−10.7544	−	12.4113i	−0.341282	−	0.393860i
$994$	4.89113	−	3.14334i	0.155137	−	0.0997006i
$995$	−23.6509	+	27.2946i	−0.749785	+	0.865298i
$996$	−3.52136	+	24.4916i	−0.111579	+	0.776047i
$997$	−27.1075	+	7.95949i	−0.858504	+	0.252079i	−0.681219	−	0.732080i	$-0.738550\pi$
$997$	−27.1075	+	7.95949i	−0.858504	+	0.252079i	−0.177285	+	0.984160i	$0.556732\pi$
$998$	6.21479	+	3.99400i	0.196726	+	0.126428i
$999$	−0.0397856	−	0.276715i	−0.00125876	−	0.00875487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.c.52.2	yes	20
3.2	odd	2		207.2.i.d.190.1		20
23.2	even	11		1587.2.a.u.1.6		10
23.4	even	11	inner	69.2.e.c.4.2	✓	20
23.21	odd	22		1587.2.a.t.1.6		10
69.2	odd	22		4761.2.a.bt.1.5		10
69.44	even	22		4761.2.a.bu.1.5		10
69.50	odd	22		207.2.i.d.73.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.4.2	✓	20	23.4	even	11	inner
69.2.e.c.52.2	yes	20	1.1	even	1	trivial
207.2.i.d.73.1		20	69.50	odd	22
207.2.i.d.190.1		20	3.2	odd	2
1587.2.a.t.1.6		10	23.21	odd	22
1587.2.a.u.1.6		10	23.2	even	11
4761.2.a.bt.1.5		10	69.2	odd	22
4761.2.a.bu.1.5		10	69.44	even	22

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.236364 + 0.517565i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(1.09772 + 1.26683i) q^{4} +(2.27341 - 1.46103i) q^{5} +(0.372604 - 0.430008i) q^{6} +(-0.481879 + 3.35154i) q^{7} +(-2.00700 + 0.589308i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.236364 + 0.517565i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(1.09772 + 1.26683i) q^{4} +(2.27341 - 1.46103i) q^{5} +(0.372604 - 0.430008i) q^{6} +(-0.481879 + 3.35154i) q^{7} +(-2.00700 + 0.589308i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.218827 + 1.52197i) q^{10} +(-1.86448 - 4.08263i) q^{11} +(-0.696343 - 1.52478i) q^{12} +(-0.891052 - 6.19740i) q^{13} +(-1.62074 - 1.04159i) q^{14} +(-2.59294 + 0.761356i) q^{15} +(-0.307736 + 2.14035i) q^{16} +(-2.00981 + 2.31944i) q^{17} +(-0.478659 + 0.307615i) q^{18} +(-0.686559 - 0.792332i) q^{19} +(4.34644 + 1.27623i) q^{20} +(1.40660 - 3.08002i) q^{21} +2.55372 q^{22} +(-3.18128 + 3.58879i) q^{23} +2.09173 q^{24} +(0.956704 - 2.09489i) q^{25} +(3.41817 + 1.00367i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-4.77480 + 3.06858i) q^{28} +(1.45248 - 1.67625i) q^{29} +(0.218827 - 1.52197i) q^{30} +(6.22433 - 1.82763i) q^{31} +(-4.55438 - 2.92692i) q^{32} +(0.638741 + 4.44254i) q^{33} +(-0.725416 - 1.58844i) q^{34} +(3.80120 + 8.32347i) q^{35} +(0.238557 + 1.65920i) q^{36} +(0.235181 + 0.151142i) q^{37} +(0.572361 - 0.168060i) q^{38} +(-0.891052 + 6.19740i) q^{39} +(-3.70173 + 4.27203i) q^{40} +(1.19434 - 0.767558i) q^{41} +(1.26164 + 1.45601i) q^{42} +(-1.76507 - 0.518271i) q^{43} +(3.12534 - 6.84355i) q^{44} +2.70241 q^{45} +(-1.10549 - 2.49478i) q^{46} +4.74565 q^{47} +(0.898277 - 1.96695i) q^{48} +(-4.28417 - 1.25794i) q^{49} +(0.858110 + 0.990312i) q^{50} +(2.58186 - 1.65926i) q^{51} +(6.87295 - 7.93180i) q^{52} +(-0.768306 + 5.34369i) q^{53} +(0.545935 - 0.160301i) q^{54} +(-10.2036 - 6.55744i) q^{55} +(-1.00796 - 7.01051i) q^{56} +(0.435523 + 0.953663i) q^{57} +(0.524255 + 1.14796i) q^{58} +(1.54995 + 10.7801i) q^{59} +(-3.81082 - 2.44907i) q^{60} +(-4.49474 + 1.31978i) q^{61} +(-0.525291 + 3.65348i) q^{62} +(-2.21736 + 2.55897i) q^{63} +(-1.04683 + 0.672754i) q^{64} +(-11.0803 - 12.7874i) q^{65} +(-2.45028 - 0.719467i) q^{66} +(-0.0835538 + 0.182957i) q^{67} -5.14454 q^{68} +(4.06350 - 2.54715i) q^{69} -5.20640 q^{70} +(-1.25365 + 2.74512i) q^{71} +(-2.00700 - 0.589308i) q^{72} +(7.91764 + 9.13745i) q^{73} +(-0.133814 + 0.0859970i) q^{74} +(-1.50815 + 1.74050i) q^{75} +(0.250104 - 1.73951i) q^{76} +(14.5816 - 4.28153i) q^{77} +(-2.99695 - 1.92602i) q^{78} +(-1.10543 - 7.68843i) q^{79} +(2.42751 + 5.31551i) q^{80} +(0.415415 + 0.909632i) q^{81} +(0.114961 + 0.799573i) q^{82} +(-12.4179 - 7.98047i) q^{83} +(5.44591 - 1.59906i) q^{84} +(-1.18034 + 8.20944i) q^{85} +(0.685438 - 0.791037i) q^{86} +(-1.86590 + 1.19914i) q^{87} +(6.14793 + 7.09509i) q^{88} +(0.838282 + 0.246142i) q^{89} +(-0.638752 + 1.39867i) q^{90} +21.2002 q^{91} +(-8.03854 - 0.0906751i) q^{92} -6.48711 q^{93} +(-1.12170 + 2.45618i) q^{94} +(-2.71845 - 0.798210i) q^{95} +(3.54529 + 4.09148i) q^{96} +(9.73536 - 6.25653i) q^{97} +(1.66369 - 1.92000i) q^{98} +(0.638741 - 4.44254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

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