LMFDB - Embedded newform 69.2.e.c.13.2

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			13.2
Root			$1.76796 - 1.13620i$ of defining polynomial
Character	$\chi$	$=$	69.13
Dual form			69.2.e.c.16.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.460828 + 0.531824i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.214155 - 1.48948i) q^{4} +(-0.700489 + 1.53386i) q^{5} +(0.100148 + 0.696541i) q^{6} +(-3.11747 - 0.915371i) q^{7} +(2.07482 - 1.33341i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(0.460828 + 0.531824i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.214155 - 1.48948i) q^{4} +(-0.700489 + 1.53386i) q^{5} +(0.100148 + 0.696541i) q^{6} +(-3.11747 - 0.915371i) q^{7} +(2.07482 - 1.33341i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-1.13855 + 0.334308i) q^{10} +(-1.33800 + 1.54413i) q^{11} +(0.985435 - 1.13725i) q^{12} +(-0.227131 + 0.0666916i) q^{13} +(-0.949800 - 2.07977i) q^{14} +(-1.41856 + 0.911650i) q^{15} +(-1.22242 - 0.358935i) q^{16} +(-0.427674 - 2.97454i) q^{17} +(-0.292329 + 0.640112i) q^{18} +(0.682288 - 4.74542i) q^{19} +(2.13464 + 1.37185i) q^{20} +(-2.12769 - 2.45549i) q^{21} -1.43779 q^{22} +(-0.779295 + 4.73209i) q^{23} +2.46634 q^{24} +(1.41227 + 1.62985i) q^{25} +(-0.140136 - 0.0900602i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-2.03105 + 4.44738i) q^{28} +(1.01178 + 7.03706i) q^{29} +(-1.13855 - 0.334308i) q^{30} +(5.64145 - 3.62554i) q^{31} +(-2.42155 - 5.30245i) q^{32} +(-1.96042 + 0.575630i) q^{33} +(1.38485 - 1.59820i) q^{34} +(3.58780 - 4.14054i) q^{35} +(1.44385 - 0.423951i) q^{36} +(4.77286 + 10.4511i) q^{37} +(2.83815 - 1.82397i) q^{38} +(-0.227131 - 0.0666916i) q^{39} +(0.591865 + 4.11651i) q^{40} +(3.40729 - 7.46093i) q^{41} +(0.325387 - 2.26312i) q^{42} +(2.42547 + 1.55876i) q^{43} +(2.01342 + 2.32361i) q^{44} -1.68624 q^{45} +(-2.87576 + 1.76623i) q^{46} -13.2857 q^{47} +(-0.834310 - 0.962845i) q^{48} +(2.99192 + 1.92279i) q^{49} +(-0.215978 + 1.50216i) q^{50} +(1.24837 - 2.73356i) q^{51} +(0.0506948 + 0.352590i) q^{52} +(-0.510122 - 0.149785i) q^{53} +(-0.591994 + 0.380451i) q^{54} +(-1.43123 - 3.13395i) q^{55} +(-7.68874 + 2.25762i) q^{56} +(3.13954 - 3.62323i) q^{57} +(-3.27622 + 3.78096i) q^{58} +(3.30904 - 0.971623i) q^{59} +(1.05410 + 2.30815i) q^{60} +(4.08228 - 2.62352i) q^{61} +(4.52789 + 1.32951i) q^{62} +(-0.462392 - 3.21601i) q^{63} +(0.645553 - 1.41356i) q^{64} +(0.0568072 - 0.395103i) q^{65} +(-1.20955 - 0.777330i) q^{66} +(-9.77557 - 11.2816i) q^{67} -4.52211 q^{68} +(-3.21395 + 3.55957i) q^{69} +3.85540 q^{70} +(-8.80741 - 10.1643i) q^{71} +(2.07482 + 1.33341i) q^{72} +(-0.632363 + 4.39818i) q^{73} +(-3.35868 + 7.35449i) q^{74} +(0.306915 + 2.13464i) q^{75} +(-6.92211 - 2.03251i) q^{76} +(5.58462 - 3.58902i) q^{77} +(-0.0692000 - 0.151527i) q^{78} +(-2.00690 + 0.589280i) q^{79} +(1.40685 - 1.62359i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(5.53808 - 1.62613i) q^{82} +(2.67666 + 5.86108i) q^{83} +(-4.11307 + 2.64331i) q^{84} +(4.86210 + 1.42764i) q^{85} +(0.288742 + 2.00824i) q^{86} +(-2.95336 + 6.46696i) q^{87} +(-0.717150 + 4.98789i) q^{88} +(2.11082 + 1.35654i) q^{89} +(-0.777067 - 0.896783i) q^{90} +0.769120 q^{91} +(6.88149 + 2.17415i) q^{92} +6.70601 q^{93} +(-6.12245 - 7.06568i) q^{94} +(6.80086 + 4.37065i) q^{95} +(0.829585 - 5.76989i) q^{96} +(0.753920 - 1.65086i) q^{97} +(0.356175 + 2.47725i) q^{98} +(-1.96042 - 0.575630i) 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 $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	0.460828	+	0.531824i	0.325855	+	0.376056i	0.894913	−	0.446241i	$-0.147238\pi$
$2$	0.460828	+	0.531824i	0.325855	+	0.376056i	−0.569058	+	0.822297i	$0.692692\pi$
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$4$	0.214155	−	1.48948i	0.107078	−	0.744742i
$5$	−0.700489	+	1.53386i	−0.313268	+	0.685962i	−0.999127	−	0.0417726i	$-0.986699\pi$
$5$	−0.700489	+	1.53386i	−0.313268	+	0.685962i	0.685859	+	0.727735i	$0.259427\pi$
$6$	0.100148	+	0.696541i	0.0408851	+	0.284362i
$7$	−3.11747	−	0.915371i	−1.17829	−	0.345978i	−0.366777	−	0.930309i	$-0.619539\pi$
$7$	−3.11747	−	0.915371i	−1.17829	−	0.345978i	−0.811515	+	0.584331i	$0.801357\pi$
$8$	2.07482	−	1.33341i	0.733559	−	0.471430i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	−1.13855	+	0.334308i	−0.360040	+	0.105717i
$11$	−1.33800	+	1.54413i	−0.403422	+	0.465573i	−0.920716	−	0.390234i	$-0.872394\pi$
$11$	−1.33800	+	1.54413i	−0.403422	+	0.465573i	0.517294	+	0.855808i	$0.326939\pi$
$12$	0.985435	−	1.13725i	0.284471	−	0.328296i
$13$	−0.227131	+	0.0666916i	−0.0629947	+	0.0184969i	−0.313078	−	0.949727i	$-0.601360\pi$
$13$	−0.227131	+	0.0666916i	−0.0629947	+	0.0184969i	0.250083	+	0.968224i	$0.419542\pi$
$14$	−0.949800	−	2.07977i	−0.253845	−	0.555843i
$15$	−1.41856	+	0.911650i	−0.366269	+	0.235387i
$16$	−1.22242	−	0.358935i	−0.305605	−	0.0897336i
$17$	−0.427674	−	2.97454i	−0.103726	−	0.721431i	−0.973617	−	0.228187i	$-0.926720\pi$
$17$	−0.427674	−	2.97454i	−0.103726	−	0.721431i	0.869891	−	0.493244i	$-0.164189\pi$
$18$	−0.292329	+	0.640112i	−0.0689027	+	0.150876i
$19$	0.682288	−	4.74542i	0.156528	−	1.08867i	−0.748443	−	0.663199i	$-0.769198\pi$
$19$	0.682288	−	4.74542i	0.156528	−	1.08867i	0.904970	−	0.425474i	$-0.139893\pi$
$20$	2.13464	+	1.37185i	0.477321	+	0.306755i
$21$	−2.12769	−	2.45549i	−0.464301	−	0.535832i
$22$	−1.43779			−0.306539
$23$	−0.779295	+	4.73209i	−0.162494	+	0.986710i
$23$	−0.779295	+	4.73209i	−0.162494	+	0.986710i
$24$	2.46634			0.503440
$25$	1.41227	+	1.62985i	0.282454	+	0.325969i
$26$	−0.140136	−	0.0900602i	−0.0274830	−	0.0176623i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	−2.03105	+	4.44738i	−0.383833	+	0.840477i
$29$	1.01178	+	7.03706i	0.187882	+	1.30675i	0.837479	+	0.546470i	$0.184029\pi$
$29$	1.01178	+	7.03706i	0.187882	+	1.30675i	−0.649597	+	0.760279i	$0.725062\pi$
$30$	−1.13855	−	0.334308i	−0.207869	−	0.0610360i
$31$	5.64145	−	3.62554i	1.01323	−	0.651166i	0.0750062	−	0.997183i	$-0.476102\pi$
$31$	5.64145	−	3.62554i	1.01323	−	0.651166i	0.938228	+	0.346017i	$0.112466\pi$
$32$	−2.42155	−	5.30245i	−0.428073	−	0.937349i
$33$	−1.96042	+	0.575630i	−0.341265	+	0.100204i
$34$	1.38485	−	1.59820i	0.237499	−	0.274089i
$35$	3.58780	−	4.14054i	0.606449	−	0.699880i
$36$	1.44385	−	0.423951i	0.240641	−	0.0706586i
$37$	4.77286	+	10.4511i	0.784653	+	1.71815i	0.691358	+	0.722513i	$0.257013\pi$
$37$	4.77286	+	10.4511i	0.784653	+	1.71815i	0.0932958	+	0.995638i	$0.470260\pi$
$38$	2.83815	−	1.82397i	0.460408	−	0.295886i
$39$	−0.227131	−	0.0666916i	−0.0363700	−	0.0106792i
$40$	0.591865	+	4.11651i	0.0935821	+	0.650878i
$41$	3.40729	−	7.46093i	0.532130	−	1.16520i	−0.432510	−	0.901629i	$-0.642372\pi$
$41$	3.40729	−	7.46093i	0.532130	−	1.16520i	0.964640	−	0.263573i	$-0.0849008\pi$
$42$	0.325387	−	2.26312i	0.0502083	−	0.349207i
$43$	2.42547	+	1.55876i	0.369881	+	0.237708i	0.712355	−	0.701819i	$-0.247629\pi$
$43$	2.42547	+	1.55876i	0.369881	+	0.237708i	−0.342474	+	0.939527i	$0.611265\pi$
$44$	2.01342	+	2.32361i	0.303535	+	0.350298i
$45$	−1.68624			−0.251370
$46$	−2.87576	+	1.76623i	−0.424008	+	0.260417i
$47$	−13.2857			−1.93793			−0.968963	−	0.247206i	$-0.920487\pi$
$47$	−13.2857			−1.93793			−0.968963	+	0.247206i	$0.920487\pi$
$48$	−0.834310	−	0.962845i	−0.120422	−	0.138975i
$49$	2.99192	+	1.92279i	0.427417	+	0.274684i
$50$	−0.215978	+	1.50216i	−0.0305439	+	0.212437i
$51$	1.24837	−	2.73356i	0.174807	−	0.382775i
$52$	0.0506948	+	0.352590i	0.00703010	+	0.0488954i
$53$	−0.510122	−	0.149785i	−0.0700706	−	0.0205746i	0.246509	−	0.969140i	$-0.420716\pi$
$53$	−0.510122	−	0.149785i	−0.0700706	−	0.0205746i	−0.316580	+	0.948566i	$0.602535\pi$
$54$	−0.591994	+	0.380451i	−0.0805601	+	0.0517728i
$55$	−1.43123	−	3.13395i	−0.192986	−	0.422581i
$56$	−7.68874	+	2.25762i	−1.02745	+	0.301687i
$57$	3.13954	−	3.62323i	0.415843	−	0.479908i
$58$	−3.27622	+	3.78096i	−0.430189	+	0.496465i
$59$	3.30904	−	0.971623i	0.430801	−	0.126495i	−0.0591410	−	0.998250i	$-0.518836\pi$
$59$	3.30904	−	0.971623i	0.430801	−	0.126495i	0.489942	+	0.871755i	$0.337018\pi$
$60$	1.05410	+	2.30815i	0.136083	+	0.297981i
$61$	4.08228	−	2.62352i	0.522683	−	0.335908i	−0.252550	−	0.967584i	$-0.581269\pi$
$61$	4.08228	−	2.62352i	0.522683	−	0.335908i	0.775232	+	0.631676i	$0.217633\pi$
$62$	4.52789	+	1.32951i	0.575042	+	0.168848i
$63$	−0.462392	−	3.21601i	−0.0582559	−	0.405179i
$64$	0.645553	−	1.41356i	0.0806941	−	0.176696i
$65$	0.0568072	−	0.395103i	0.00704607	−	0.0490065i
$66$	−1.20955	−	0.777330i	−0.148885	−	0.0956827i
$67$	−9.77557	−	11.2816i	−1.19428	−	1.37827i	−0.907383	−	0.420305i	$-0.861923\pi$
$67$	−9.77557	−	11.2816i	−1.19428	−	1.37827i	−0.286893	−	0.957963i	$-0.592623\pi$
$68$	−4.52211			−0.548387
$69$	−3.21395	+	3.55957i	−0.386914	+	0.428522i
$70$	3.85540			0.460808
$71$	−8.80741	−	10.1643i	−1.04525	−	1.20628i	−0.978013	−	0.208543i	$-0.933128\pi$
$71$	−8.80741	−	10.1643i	−1.04525	−	1.20628i	−0.0672342	−	0.997737i	$-0.521417\pi$
$72$	2.07482	+	1.33341i	0.244520	+	0.157143i
$73$	−0.632363	+	4.39818i	−0.0740124	+	0.514768i	0.918766	+	0.394803i	$0.129187\pi$
$73$	−0.632363	+	4.39818i	−0.0740124	+	0.514768i	−0.992778	+	0.119965i	$0.961722\pi$
$74$	−3.35868	+	7.35449i	−0.390439	+	0.854942i
$75$	0.306915	+	2.13464i	0.0354395	+	0.246487i
$76$	−6.92211	−	2.03251i	−0.794020	−	0.233145i
$77$	5.58462	−	3.58902i	0.636426	−	0.409006i
$78$	−0.0692000	−	0.151527i	−0.00783536	−	0.0171570i
$79$	−2.00690	+	0.589280i	−0.225794	+	0.0662992i	−0.392673	−	0.919678i	$-0.628449\pi$
$79$	−2.00690	+	0.589280i	−0.225794	+	0.0662992i	0.166878	+	0.985977i	$0.446631\pi$
$80$	1.40685	−	1.62359i	0.157290	−	0.181523i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	5.53808	−	1.62613i	0.611579	−	0.179576i
$83$	2.67666	+	5.86108i	0.293802	+	0.643337i	0.997759	−	0.0669055i	$-0.0213126\pi$
$83$	2.67666	+	5.86108i	0.293802	+	0.643337i	−0.703957	+	0.710242i	$0.748585\pi$
$84$	−4.11307	+	2.64331i	−0.448773	+	0.288409i
$85$	4.86210	+	1.42764i	0.527368	+	0.154849i
$86$	0.288742	+	2.00824i	0.0311358	+	0.216555i
$87$	−2.95336	+	6.46696i	−0.316633	+	0.693331i
$88$	−0.717150	+	4.98789i	−0.0764485	+	0.531711i
$89$	2.11082	+	1.35654i	0.223746	+	0.143793i	0.647712	−	0.761885i	$-0.275726\pi$
$89$	2.11082	+	1.35654i	0.223746	+	0.143793i	−0.423966	+	0.905678i	$0.639362\pi$
$90$	−0.777067	−	0.896783i	−0.0819100	−	0.0945292i
$91$	0.769120			0.0806257
$92$	6.88149	+	2.17415i	0.717444	+	0.226671i
$93$	6.70601			0.695380
$94$	−6.12245	−	7.06568i	−0.631482	−	0.728769i
$95$	6.80086	+	4.37065i	0.697754	+	0.448419i
$96$	0.829585	−	5.76989i	0.0846691	−	0.588887i
$97$	0.753920	−	1.65086i	0.0765490	−	0.167619i	−0.867488	−	0.497458i	$-0.834267\pi$
$97$	0.753920	−	1.65086i	0.0765490	−	0.167619i	0.944037	+	0.329839i	$0.106994\pi$
$98$	0.356175	+	2.47725i	0.0359791	+	0.250240i
$99$	−1.96042	−	0.575630i	−0.197029	−	0.0578530i
$100$	2.73007	−	1.75451i	0.273007	−	0.175451i
$101$	−0.996737	−	2.18255i	−0.0991791	−	0.217172i	0.853538	−	0.521030i	$-0.174452\pi$
$101$	−0.996737	−	2.18255i	−0.0991791	−	0.217172i	−0.952717	+	0.303859i	$0.901725\pi$
$102$	2.02906	−	0.595785i	0.200907	−	0.0589915i
$103$	−2.69154	+	3.10620i	−0.265205	+	0.306063i	−0.872696	−	0.488263i	$-0.837631\pi$
$103$	−2.69154	+	3.10620i	−0.265205	+	0.306063i	0.607491	+	0.794326i	$0.292176\pi$
$104$	−0.382328	+	0.441230i	−0.0374904	+	0.0432662i
$105$	5.25680	−	1.54353i	0.513011	−	0.150634i
$106$	−0.155419	−	0.340320i	−0.0150956	−	0.0330548i
$107$	11.3204	−	7.27515i	1.09438	−	0.703315i	0.136545	−	0.990634i	$-0.456400\pi$
$107$	11.3204	−	7.27515i	1.09438	−	0.703315i	0.957835	+	0.287319i	$0.0927638\pi$
$108$	1.44385	+	0.423951i	0.138934	+	0.0407947i
$109$	−2.25241	−	15.6658i	−0.215741	−	1.50051i	−0.753518	−	0.657427i	$-0.771645\pi$
$109$	−2.25241	−	15.6658i	−0.215741	−	1.50051i	0.537777	−	0.843087i	$-0.319264\pi$
$110$	1.00716	−	2.20537i	0.0960289	−	0.210274i
$111$	−1.63511	+	11.3724i	−0.155198	+	1.07942i
$112$	3.48229	+	2.23793i	0.329046	+	0.211465i
$113$	8.47022	+	9.77515i	0.796811	+	0.919569i	0.998202	−	0.0599420i	$-0.0190916\pi$
$113$	8.47022	+	9.77515i	0.796811	+	0.919569i	−0.201391	+	0.979511i	$0.564546\pi$
$114$	3.37371			0.315977
$115$	−6.71247	−	4.51011i	−0.625941	−	0.420570i
$116$	10.6983			0.993309
$117$	−0.155018	−	0.178901i	−0.0143314	−	0.0165394i
$118$	2.04163	+	1.31208i	0.187948	+	0.120787i
$119$	−1.38955	+	9.66450i	−0.127379	+	0.885943i
$120$	−1.72765	+	3.78302i	−0.157712	+	0.345341i
$121$	0.971358	+	6.75594i	0.0883053	+	0.614177i
$122$	3.27648	+	0.962062i	0.296639	+	0.0871010i
$123$	6.90008	−	4.43441i	0.622159	−	0.399838i
$124$	−4.19204	−	9.17928i	−0.376456	−	0.824324i
$125$	−11.5789	+	3.39987i	−1.03565	+	0.304094i
$126$	1.49727	−	1.72794i	0.133387	−	0.153937i
$127$	−3.48534	+	4.02229i	−0.309274	+	0.356921i	−0.889014	−	0.457881i	$-0.848609\pi$
$127$	−3.48534	+	4.02229i	−0.309274	+	0.356921i	0.579740	+	0.814802i	$0.303154\pi$
$128$	−10.1369	+	2.97647i	−0.895987	+	0.263086i
$129$	1.19771	+	2.62262i	0.105453	+	0.230909i
$130$	0.236304	−	0.151863i	0.0207252	−	0.0133193i
$131$	−4.35715	−	1.27937i	−0.380686	−	0.111779i	0.0857904	−	0.996313i	$-0.472658\pi$
$131$	−4.35715	−	1.27937i	−0.380686	−	0.111779i	−0.466476	+	0.884534i	$0.654477\pi$
$132$	0.437558	+	3.04328i	0.0380845	+	0.264884i
$133$	−6.47083	+	14.1691i	−0.561092	+	1.22862i
$134$	1.49497	−	10.3978i	0.129146	−	0.898230i
$135$	−1.41856	−	0.911650i	−0.122090	−	0.0784624i
$136$	−4.85361	−	5.60136i	−0.416194	−	0.480313i
$137$	−16.4974			−1.40947			−0.704734	−	0.709471i	$-0.748934\pi$
$137$	−16.4974			−1.40947			−0.704734	+	0.709471i	$0.748934\pi$
$138$	−3.37414	−	0.0689037i	−0.287226	−	0.00586547i
$139$	3.46582			0.293967			0.146984	−	0.989139i	$-0.453044\pi$
$139$	3.46582			0.293967			0.146984	+	0.989139i	$0.453044\pi$
$140$	−5.39893	−	6.23069i	−0.456292	−	0.526590i
$141$	−11.1767	−	7.18282i	−0.941247	−	0.604902i
$142$	1.34691	−	9.36799i	0.113030	−	0.786144i
$143$	0.200920	−	0.439953i	0.0168018	−	0.0367907i
$144$	−0.181313	−	1.26106i	−0.0151094	−	0.105088i
$145$	−11.5026	−	3.37746i	−0.955238	−	0.280483i
$146$	−2.63047	+	1.69050i	−0.217699	+	0.139907i
$147$	1.47742	+	3.23511i	0.121856	+	0.266827i
$148$	16.5889	−	4.87094i	1.36360	−	0.400389i
$149$	−2.00991	+	2.31956i	−0.164658	+	0.190026i	−0.832082	−	0.554652i	$-0.812851\pi$
$149$	−2.00991	+	2.31956i	−0.164658	+	0.190026i	0.667424	+	0.744678i	$0.267397\pi$
$150$	−0.993820	+	1.14693i	−0.0811450	+	0.0936464i
$151$	−1.81890	+	0.534078i	−0.148020	+	0.0434627i	−0.354903	−	0.934903i	$-0.615486\pi$
$151$	−1.81890	+	0.534078i	−0.148020	+	0.0434627i	0.206883	+	0.978366i	$0.433668\pi$
$152$	−4.91194	−	10.7557i	−0.398411	−	0.872399i
$153$	2.52807	−	1.62469i	0.204382	−	0.131349i
$154$	4.48228	+	1.31611i	0.361192	+	0.106056i
$155$	1.60929	+	11.1928i	0.129261	+	0.899030i
$156$	−0.147977	+	0.324025i	−0.0118477	+	0.0259428i
$157$	−0.307090	+	2.13586i	−0.0245085	+	0.170460i	−0.998399	−	0.0565561i	$-0.981988\pi$
$157$	−0.307090	+	2.13586i	−0.0245085	+	0.170460i	0.973891	+	0.227016i	$0.0728971\pi$
$158$	−1.23823	−	0.795763i	−0.0985084	−	0.0633075i
$159$	−0.348162	−	0.401800i	−0.0276110	−	0.0318648i
$160$	9.82947			0.777088
$161$	6.76105	−	14.0388i	0.532845	−	1.10641i
$162$	−0.703704			−0.0552882
$163$	7.92140	+	9.14179i	0.620452	+	0.716040i	0.975793	−	0.218697i	$-0.0701806\pi$
$163$	7.92140	+	9.14179i	0.620452	+	0.716040i	−0.355341	+	0.934737i	$0.615635\pi$
$164$	−10.3832	−	6.67291i	−0.810795	−	0.521067i
$165$	0.490316	−	3.41022i	0.0381711	−	0.265486i
$166$	−1.88358	+	4.12446i	−0.146194	+	0.320120i
$167$	1.87408	+	13.0345i	0.145021	+	1.00864i	0.924219	+	0.381864i	$0.124718\pi$
$167$	1.87408	+	13.0345i	0.145021	+	1.00864i	−0.779198	+	0.626778i	$0.784373\pi$
$168$	−7.68874	−	2.25762i	−0.593199	−	0.174179i
$169$	−10.8892	+	6.99804i	−0.837627	+	0.538310i
$170$	1.48134	+	3.24368i	0.113613	+	0.248779i
$171$	4.60002	−	1.35069i	0.351772	−	0.103290i
$172$	2.84117	−	3.27889i	0.216637	−	0.250013i
$173$	11.5528	−	13.3327i	0.878346	−	1.01367i	−0.121432	−	0.992600i	$-0.538749\pi$
$173$	11.5528	−	13.3327i	0.878346	−	1.01367i	0.999778	−	0.0210657i	$-0.00670590\pi$
$174$	−4.80028	+	1.40949i	−0.363908	+	0.106853i
$175$	−2.91079	−	6.37374i	−0.220035	−	0.481809i
$176$	2.18984	−	1.40732i	0.165065	−	0.106081i
$177$	3.30904	+	0.971623i	0.248723	+	0.0730317i
$178$	0.251283	+	1.74771i	0.0188345	+	0.130997i
$179$	4.47341	−	9.79541i	0.334359	−	0.732143i	−0.665540	−	0.746362i	$-0.731799\pi$
$179$	4.47341	−	9.79541i	0.334359	−	0.732143i	0.999899	+	0.0142186i	$0.00452608\pi$
$180$	−0.361117	+	2.51163i	−0.0269161	+	0.187206i
$181$	−1.20016	−	0.771298i	−0.0892074	−	0.0573301i	0.495277	−	0.868735i	$-0.335067\pi$
$181$	−1.20016	−	0.771298i	−0.0892074	−	0.0573301i	−0.584484	+	0.811405i	$0.698703\pi$
$182$	0.354432	+	0.409037i	0.0262723	+	0.0303198i
$183$	4.85262			0.358716
$184$	4.69290	+	10.8574i	0.345965	+	0.800415i
$185$	−19.3738			−1.42439
$186$	3.09032	+	3.56642i	0.226593	+	0.261502i
$187$	5.16531	+	3.31954i	0.377725	+	0.242749i
$188$	−2.84522	+	19.7889i	−0.207509	+	1.44325i
$189$	1.34972	−	2.95546i	0.0981774	−	0.214978i
$190$	0.809613	+	5.63098i	0.0587355	+	0.408514i
$191$	13.3309	+	3.91430i	0.964590	+	0.283229i	0.725849	−	0.687854i	$-0.241447\pi$
$191$	13.3309	+	3.91430i	0.964590	+	0.283229i	0.238741	+	0.971083i	$0.423265\pi$
$192$	1.30730	−	0.840153i	0.0943466	−	0.0606329i
$193$	3.36305	+	7.36404i	0.242077	+	0.530075i	0.991203	−	0.132353i	$-0.0422532\pi$
$193$	3.36305	+	7.36404i	0.242077	+	0.530075i	−0.749125	+	0.662428i	$0.769526\pi$
$194$	1.22539	−	0.359808i	0.0879780	−	0.0258327i
$195$	0.261398	−	0.301669i	0.0187191	−	0.0216030i
$196$	3.50470	−	4.04464i	0.250336	−	0.288903i
$197$	−1.70543	+	0.500760i	−0.121507	+	0.0356777i	−0.341921	−	0.939729i	$-0.611077\pi$
$197$	−1.70543	+	0.500760i	−0.121507	+	0.0356777i	0.220414	+	0.975406i	$0.429259\pi$
$198$	−0.597281	−	1.30786i	−0.0424469	−	0.0929458i
$199$	5.53721	−	3.55855i	0.392522	−	0.252259i	−0.329461	−	0.944169i	$-0.606867\pi$
$199$	5.53721	−	3.55855i	0.392522	−	0.252259i	0.721983	+	0.691910i	$0.243231\pi$
$200$	5.10345	+	1.49851i	0.360868	+	0.105960i
$201$	−2.12443	−	14.7758i	−0.149846	−	1.04220i
$202$	0.701408	−	1.53587i	0.0493509	−	0.108063i
$203$	3.28734	−	22.8639i	0.230726	−	1.60473i
$204$	−3.80424	−	2.44484i	−0.266350	−	0.171173i
$205$	9.05724	+	10.4526i	0.632585	+	0.730042i
$206$	−2.89229			−0.201515
$207$	−4.62819	+	1.25691i	−0.321682	+	0.0873613i
$208$	0.301587			0.0209113
$209$	6.41466	+	7.40291i	0.443711	+	0.512070i
$210$	3.24337	+	2.08439i	0.223814	+	0.143836i
$211$	−1.94389	+	13.5201i	−0.133823	+	0.930760i	0.806683	+	0.590984i	$0.201260\pi$
$211$	−1.94389	+	13.5201i	−0.133823	+	0.930760i	−0.940506	+	0.339776i	$0.889649\pi$
$212$	−0.332348	+	0.727741i	−0.0228258	+	0.0499814i
$213$	−1.91403	−	13.3124i	−0.131147	−	0.912150i
$214$	9.08584	+	2.66784i	0.621095	+	0.182370i
$215$	−4.08993	+	2.62844i	−0.278931	+	0.179258i
$216$	1.02456	+	2.24346i	0.0697122	+	0.152648i
$217$	−20.9057	+	6.13848i	−1.41917	+	0.416707i
$218$	7.29349	−	8.41714i	0.493978	−	0.570081i
$219$	−2.90981	+	3.35810i	−0.196627	+	0.226920i
$220$	−4.97447	+	1.46064i	−0.335379	+	0.0984761i
$221$	0.295514	+	0.647086i	0.0198785	+	0.0435277i
$222$	−6.80164	+	4.37115i	−0.456496	+	0.293372i
$223$	−10.9392	−	3.21204i	−0.732542	−	0.215094i	−0.105874	−	0.994380i	$-0.533764\pi$
$223$	−10.9392	−	3.21204i	−0.732542	−	0.215094i	−0.626669	+	0.779286i	$0.715582\pi$
$224$	2.69539	+	18.7468i	0.180093	+	1.25257i
$225$	−0.895882	+	1.96171i	−0.0597255	+	0.130781i
$226$	−1.29535	+	9.00933i	−0.0861651	+	0.599292i
$227$	−1.33704	−	0.859266i	−0.0887427	−	0.0570315i	0.495517	−	0.868598i	$-0.334979\pi$
$227$	−1.33704	−	0.859266i	−0.0887427	−	0.0570315i	−0.584260	+	0.811567i	$0.698615\pi$
$228$	−4.72439	−	5.45224i	−0.312880	−	0.361083i
$229$	26.2296			1.73330			0.866650	−	0.498916i	$-0.166268\pi$
$229$	26.2296			1.73330			0.866650	+	0.498916i	$0.166268\pi$
$230$	−0.694711	−	5.64824i	−0.0458079	−	0.372434i
$231$	6.63845			0.436778
$232$	11.4825	+	13.2515i	0.753863	+	0.870005i
$233$	−8.36970	−	5.37888i	−0.548317	−	0.352382i	0.236967	−	0.971518i	$-0.423847\pi$
$233$	−8.36970	−	5.37888i	−0.548317	−	0.352382i	−0.785284	+	0.619136i	$0.787483\pi$
$234$	0.0237069	−	0.164885i	0.00154977	−	0.0107789i
$235$	9.30653	−	20.3785i	0.607091	−	1.32934i
$236$	−0.738567	−	5.13685i	−0.0480766	−	0.334380i
$237$	−2.00690	−	0.589280i	−0.130362	−	0.0382779i
$238$	−5.78015	+	3.71468i	−0.374672	+	0.240787i
$239$	4.79659	+	10.5031i	0.310266	+	0.679387i	0.998957	−	0.0456678i	$-0.0145416\pi$
$239$	4.79659	+	10.5031i	0.310266	+	0.679387i	−0.688691	+	0.725055i	$0.741814\pi$
$240$	2.06129	−	0.605250i	0.133056	−	0.0390687i
$241$	3.59998	−	4.15459i	0.231895	−	0.267621i	−0.627862	−	0.778325i	$-0.716070\pi$
$241$	3.59998	−	4.15459i	0.231895	−	0.267621i	0.859757	+	0.510704i	$0.170615\pi$
$242$	−3.14534	+	3.62992i	−0.202190	+	0.233340i
$243$	−0.959493	+	0.281733i	−0.0615515	+	0.0180732i
$244$	−3.03345	−	6.64233i	−0.194197	−	0.425232i
$245$	−5.04510	+	3.24229i	−0.322319	+	0.207142i
$246$	5.53808	+	1.62613i	0.353095	+	0.103678i
$247$	0.161511	+	1.12333i	0.0102767	+	0.0714760i
$248$	6.87068	−	15.0447i	0.436288	−	0.955338i
$249$	−0.916984	+	6.37777i	−0.0581115	+	0.404175i
$250$	−7.14402	−	4.59118i	−0.451828	−	0.290372i
$251$	13.4416	+	15.5124i	0.848425	+	0.979135i	0.999957	−	0.00931785i	$-0.00296601\pi$
$251$	13.4416	+	15.5124i	0.848425	+	0.979135i	−0.151532	+	0.988452i	$0.548421\pi$
$252$	−4.88921			−0.307991
$253$	−6.26428	−	7.53487i	−0.393832	−	0.473713i
$254$	−3.74529			−0.235001
$255$	3.31842	+	3.82966i	0.207807	+	0.239822i
$256$	−8.86896	−	5.69973i	−0.554310	−	0.356233i
$257$	2.47969	−	17.2466i	0.154679	−	1.07581i	−0.753566	−	0.657373i	$-0.771668\pi$
$257$	2.47969	−	17.2466i	0.154679	−	1.07581i	0.908244	−	0.418441i	$-0.137423\pi$
$258$	−0.842834	+	1.84555i	−0.0524725	+	0.114899i
$259$	−5.31260	−	36.9499i	−0.330109	−	2.29596i
$260$	−0.576334	−	0.169227i	−0.0357427	−	0.0104950i
$261$	−5.98083	+	3.84364i	−0.370204	+	0.237916i
$262$	−1.32749	−	2.90681i	−0.0820129	−	0.179583i
$263$	18.4511	−	5.41773i	1.13774	−	0.334072i	0.341997	−	0.939701i	$-0.388897\pi$
$263$	18.4511	−	5.41773i	1.13774	−	0.334072i	0.795747	+	0.605630i	$0.207079\pi$
$264$	−3.29996	+	3.80836i	−0.203099	+	0.234388i
$265$	0.587084	−	0.677531i	0.0360643	−	0.0416204i
$266$	−10.5174	+	3.08820i	−0.644865	+	0.189349i
$267$	1.04233	+	2.28239i	0.0637896	+	0.139680i
$268$	−18.8973	+	12.1445i	−1.15433	+	0.741846i
$269$	−23.0209	−	6.75956i	−1.40361	−	0.412138i	−0.509689	−	0.860359i	$-0.670240\pi$
$269$	−23.0209	−	6.75956i	−1.40361	−	0.412138i	−0.893923	+	0.448221i	$0.852058\pi$
$270$	−0.168873	−	1.17454i	−0.0102773	−	0.0714800i
$271$	−9.38523	+	20.5508i	−0.570112	+	1.24837i	0.376626	+	0.926365i	$0.377084\pi$
$271$	−9.38523	+	20.5508i	−0.570112	+	1.24837i	−0.946738	+	0.322005i	$0.895643\pi$
$272$	−0.544868	+	3.78964i	−0.0330374	+	0.229780i
$273$	0.647025	+	0.415818i	0.0391597	+	0.0251664i
$274$	−7.60247	−	8.77372i	−0.459282	−	0.530040i
$275$	−4.40631			−0.265711
$276$	4.61364	+	5.54942i	0.277708	+	0.334036i
$277$	2.08852			0.125487			0.0627435	−	0.998030i	$-0.480015\pi$
$277$	2.08852			0.125487			0.0627435	+	0.998030i	$0.480015\pi$
$278$	1.59715	+	1.84321i	0.0957907	+	0.110548i
$279$	5.64145	+	3.62554i	0.337745	+	0.217055i
$280$	1.92302	−	13.3749i	0.114922	−	0.799302i
$281$	8.14441	−	17.8338i	0.485855	−	1.06387i	−0.494958	−	0.868917i	$-0.664816\pi$
$281$	8.14441	−	17.8338i	0.485855	−	1.06387i	0.980812	−	0.194956i	$-0.0624563\pi$
$282$	−1.33054	−	9.25407i	−0.0792322	−	0.551072i
$283$	−4.82108	−	1.41560i	−0.286583	−	0.0841484i	0.135282	−	0.990807i	$-0.456806\pi$
$283$	−4.82108	−	1.41560i	−0.286583	−	0.0841484i	−0.421865	+	0.906659i	$0.638624\pi$
$284$	−17.0257	+	10.9418i	−1.01029	+	0.649274i
$285$	3.35830	+	7.35365i	0.198928	+	0.435593i
$286$	0.326567	−	0.0958888i	0.0193103	−	0.00567002i
$287$	−17.4516	+	20.1403i	−1.03014	+	1.18884i
$288$	3.81733	−	4.40543i	0.224938	−	0.259593i
$289$	7.64642	−	2.24519i	0.449789	−	0.132070i
$290$	−3.50450	−	7.67378i	−0.205791	−	0.450620i
$291$	1.52676	−	0.981188i	0.0895001	−	0.0575182i
$292$	6.41559	+	1.88379i	0.375444	+	0.110240i
$293$	−0.420981	−	2.92798i	−0.0245940	−	0.171055i	0.973822	−	0.227310i	$-0.0729930\pi$
$293$	−0.420981	−	2.92798i	−0.0245940	−	0.171055i	−0.998416	+	0.0562552i	$0.982084\pi$
$294$	−1.03967	+	2.27656i	−0.0606348	+	0.132772i
$295$	−0.827619	+	5.75621i	−0.0481858	+	0.335140i
$296$	23.8384	+	15.3200i	1.38558	+	0.890457i
$297$	−1.33800	−	1.54413i	−0.0776385	−	0.0895996i
$298$	−2.15982			−0.125115
$299$	−0.138589	−	1.12678i	−0.00801481	−	0.0651631i
$300$	3.24525			0.187364
$301$	−6.13449	−	7.07958i	−0.353586	−	0.408060i
$302$	−1.12224	−	0.721218i	−0.0645775	−	0.0415014i
$303$	0.341467	−	2.37495i	0.0196168	−	0.136438i
$304$	−2.53734	+	5.55599i	−0.145526	+	0.318658i
$305$	1.16452	+	8.09939i	0.0666800	+	0.463770i
$306$	2.02906	+	0.595785i	0.115993	+	0.0340588i
$307$	19.9296	−	12.8079i	1.13744	−	0.730988i	0.170340	−	0.985385i	$-0.445513\pi$
$307$	19.9296	−	12.8079i	1.13744	−	0.730988i	0.967100	+	0.254397i	$0.0818770\pi$
$308$	−4.14981	−	9.08681i	−0.236457	−	0.517769i
$309$	−3.94360	+	1.15795i	−0.224344	+	0.0658733i
$310$	−5.21101	+	6.01383i	−0.295966	+	0.341563i
$311$	−17.1662	+	19.8109i	−0.973409	+	1.12337i	0.0189294	+	0.999821i	$0.493974\pi$
$311$	−17.1662	+	19.8109i	−0.973409	+	1.12337i	−0.992338	+	0.123553i	$0.960571\pi$
$312$	−0.560182	+	0.164484i	−0.0317141	+	0.00931209i
$313$	−2.75232	−	6.02675i	−0.155570	−	0.340652i	0.815758	−	0.578393i	$-0.196320\pi$
$313$	−2.75232	−	6.02675i	−0.155570	−	0.340652i	−0.971328	+	0.237742i	$0.923593\pi$
$314$	−1.27742	+	0.820947i	−0.0720889	+	0.0463287i
$315$	5.25680	+	1.54353i	0.296187	+	0.0869683i
$316$	0.447934	+	3.11545i	0.0251983	+	0.175258i
$317$	4.61225	−	10.0994i	0.259050	−	0.567240i	−0.734761	−	0.678326i	$-0.762706\pi$
$317$	4.61225	−	10.0994i	0.259050	−	0.567240i	0.993811	+	0.111086i	$0.0354330\pi$
$318$	0.0532442	−	0.370321i	0.00298579	−	0.0207666i
$319$	−12.2199	−	7.85326i	−0.684183	−	0.439698i
$320$	1.71600	+	1.98037i	0.0959275	+	0.110706i
$321$	13.4565			0.751070
$322$	10.5819	−	2.87379i	0.589703	−	0.160150i
$323$	−14.4072			−0.801639
$324$	0.985435	+	1.13725i	0.0547464	+	0.0631807i
$325$	−0.429467	−	0.276002i	−0.0238225	−	0.0153098i
$326$	−1.21142	+	8.42559i	−0.0670942	+	0.466650i
$327$	6.57474	−	14.3967i	0.363584	−	0.796138i
$328$	−2.87893	−	20.0234i	−0.158962	−	1.10561i
$329$	41.4179	+	12.1614i	2.28344	+	0.670479i
$330$	2.03959	−	1.31077i	0.112276	−	0.0721552i
$331$	9.32901	+	20.4277i	0.512769	+	1.12281i	0.972105	+	0.234545i	$0.0753599\pi$
$331$	9.32901	+	20.4277i	0.512769	+	1.12281i	−0.459337	+	0.888262i	$0.651913\pi$
$332$	9.30320	−	2.73167i	0.510580	−	0.149920i
$333$	−7.52394	+	8.68309i	−0.412310	+	0.475831i
$334$	−6.06844	+	7.00336i	−0.332050	+	0.383207i
$335$	24.1521	−	7.09169i	1.31957	−	0.387460i
$336$	1.71957	+	3.76534i	0.0938104	+	0.205416i
$337$	−29.3824	+	18.8830i	−1.60056	+	1.02862i	−0.633615	+	0.773648i	$0.718430\pi$
$337$	−29.3824	+	18.8830i	−1.60056	+	1.02862i	−0.966949	+	0.254972i	$0.917934\pi$
$338$	−8.73975	−	2.56622i	−0.475380	−	0.139584i
$339$	1.84075	+	12.8027i	0.0999760	+	0.695349i
$340$	3.16769	−	6.93628i	0.171792	−	0.376173i
$341$	−1.94994	+	13.5621i	−0.105595	+	0.734430i
$342$	2.83815	+	1.82397i	0.153469	+	0.0986288i
$343$	7.32670	+	8.45547i	0.395605	+	0.456552i
$344$	7.11087			0.383393
$345$	−3.20854	−	7.42318i	−0.172742	−	0.399651i
$346$	12.4145			0.667409
$347$	6.72501	+	7.76108i	0.361018	+	0.416637i	0.906980	−	0.421173i	$-0.138381\pi$
$347$	6.72501	+	7.76108i	0.361018	+	0.416637i	−0.545963	+	0.837809i	$0.683836\pi$
$348$	8.99995	+	5.78392i	0.482448	+	0.310050i
$349$	4.30303	−	29.9282i	0.230336	−	1.60202i	−0.466319	−	0.884616i	$-0.654420\pi$
$349$	4.30303	−	29.9282i	0.230336	−	1.60202i	0.696655	−	0.717406i	$-0.254671\pi$
$350$	2.04833	−	4.48523i	0.109488	−	0.239745i
$351$	−0.0336887	−	0.234310i	−0.00179817	−	0.0125065i
$352$	11.4277	+	3.35548i	0.609099	+	0.178848i
$353$	−2.65533	+	1.70648i	−0.141329	+	0.0908266i	−0.609395	−	0.792867i	$-0.708587\pi$
$353$	−2.65533	+	1.70648i	−0.141329	+	0.0908266i	0.468066	+	0.883694i	$0.344951\pi$
$354$	1.00817	+	2.20758i	0.0535835	+	0.117332i
$355$	21.7601	−	6.38934i	1.15491	−	0.339111i
$356$	2.47259	−	2.85352i	0.131047	−	0.151236i
$357$	−6.39398	+	7.37905i	−0.338405	+	0.390541i
$358$	7.27091	−	2.13493i	0.384280	−	0.112835i
$359$	−9.08412	−	19.8915i	−0.479442	−	1.04983i	−0.982617	−	0.185646i	$-0.940562\pi$
$359$	−9.08412	−	19.8915i	−0.479442	−	1.04983i	0.503175	−	0.864184i	$-0.332165\pi$
$360$	−3.49864	+	2.24844i	−0.184395	+	0.118503i
$361$	−3.82312	−	1.12257i	−0.201217	−	0.0590826i
$362$	−0.142874	−	0.993711i	−0.00750930	−	0.0522283i
$363$	−2.83538	+	6.20862i	−0.148819	+	0.325868i
$364$	0.164711	−	1.14559i	0.00863322	−	0.0600453i
$365$	−6.30322	−	4.05083i	−0.329925	−	0.212030i
$366$	2.23622	+	2.58074i	0.116889	+	0.134897i
$367$	−8.13884			−0.424844			−0.212422	−	0.977178i	$-0.568135\pi$
$367$	−8.13884			−0.424844			−0.212422	+	0.977178i	$0.568135\pi$
$368$	2.65114	−	5.50488i	0.138200	−	0.286962i
$369$	8.20214			0.426987
$370$	−8.92801	−	10.3035i	−0.464145	−	0.535652i
$371$	1.45318	+	0.933901i	0.0754453	+	0.0484857i
$372$	1.43613	−	9.98849i	0.0744597	−	0.517879i
$373$	1.83693	−	4.02231i	0.0951124	−	0.208267i	−0.856096	−	0.516818i	$-0.827117\pi$
$373$	1.83693	−	4.02231i	0.0951124	−	0.208267i	0.951208	+	0.308550i	$0.0998438\pi$
$374$	0.614907	+	4.27677i	0.0317961	+	0.221147i
$375$	−11.5789	−	3.39987i	−0.597932	−	0.175569i
$376$	−27.5655	+	17.7153i	−1.42158	+	0.913596i
$377$	−0.699118	−	1.53086i	−0.0360064	−	0.0788430i
$378$	2.19377	−	0.644150i	0.112836	−	0.0331315i
$379$	−6.90798	+	7.97223i	−0.354839	+	0.409506i	−0.904904	−	0.425616i	$-0.860057\pi$
$379$	−6.90798	+	7.97223i	−0.354839	+	0.409506i	0.550065	+	0.835122i	$0.314603\pi$
$380$	7.96645	−	9.19378i	0.408670	−	0.471631i
$381$	−5.10667	+	1.49945i	−0.261623	+	0.0768193i
$382$	4.06153	+	8.89351i	0.207806	+	0.455032i
$383$	−4.54448	+	2.92056i	−0.232212	+	0.149234i	−0.651573	−	0.758586i	$-0.725891\pi$
$383$	−4.54448	+	2.92056i	−0.232212	+	0.149234i	0.419361	+	0.907820i	$0.362254\pi$
$384$	−10.1369	−	2.97647i	−0.517298	−	0.151893i
$385$	1.59308	+	11.0801i	0.0811906	+	0.564693i
$386$	−2.36659	+	5.18211i	−0.120456	+	0.263762i
$387$	−0.410317	+	2.85382i	−0.0208576	+	0.145068i
$388$	−2.29747	−	1.47649i	−0.116636	−	0.0749575i
$389$	−1.04941	−	1.21108i	−0.0532070	−	0.0614042i	0.728522	−	0.685022i	$-0.240208\pi$
$389$	−1.04941	−	1.21108i	−0.0532070	−	0.0614042i	−0.781729	+	0.623618i	$0.785662\pi$
$390$	0.280895			0.0142237
$391$	14.4091	+	0.294249i	0.728698	+	0.0148808i
$392$	8.77156			0.443030
$393$	−2.97378	−	3.43193i	−0.150008	−	0.173118i
$394$	−1.05223	−	0.676225i	−0.0530104	−	0.0340677i
$395$	0.501943	−	3.49109i	0.0252555	−	0.175656i
$396$	−1.27723	+	2.79673i	−0.0641830	+	0.140541i
$397$	0.992549	+	6.90333i	0.0498146	+	0.346468i	0.999452	+	0.0331158i	$0.0105430\pi$
$397$	0.992549	+	6.90333i	0.0498146	+	0.346468i	−0.949637	+	0.313352i	$0.898548\pi$
$398$	4.44422	+	1.30494i	0.222769	+	0.0654108i
$399$	−13.1040	+	8.42145i	−0.656022	+	0.421600i
$400$	−1.14138	−	2.49927i	−0.0570688	−	0.124963i
$401$	0.916430	−	0.269088i	0.0457643	−	0.0134376i	−0.258770	−	0.965939i	$-0.583317\pi$
$401$	0.916430	−	0.269088i	0.0457643	−	0.0134376i	0.304535	+	0.952501i	$0.401499\pi$
$402$	6.87911	−	7.93891i	0.343099	−	0.395957i
$403$	−1.03955	+	1.19971i	−0.0517839	+	0.0597618i
$404$	−3.46433	+	1.01722i	−0.172357	+	0.0506085i
$405$	−0.700489	−	1.53386i	−0.0348076	−	0.0762180i
$406$	13.6745	−	8.78806i	0.678654	−	0.436144i
$407$	−22.5240	−	6.61363i	−1.11647	−	0.327826i
$408$	−1.05479	−	7.33623i	−0.0522199	−	0.363197i
$409$	6.47056	−	14.1686i	0.319949	−	0.700590i	−0.679504	−	0.733672i	$-0.737805\pi$
$409$	6.47056	−	14.1686i	0.319949	−	0.700590i	0.999453	+	0.0330820i	$0.0105323\pi$
$410$	−1.38512	+	9.63371i	−0.0684061	+	0.475775i
$411$	−13.8785	−	8.91917i	−0.684576	−	0.439950i
$412$	4.05023	+	4.67421i	0.199540	+	0.230282i
$413$	−11.2052			−0.551373
$414$	−2.80126	−	1.88216i	−0.137674	−	0.0925033i
$415$	−10.8650			−0.533344
$416$	0.903636	+	1.04285i	0.0443044	+	0.0511300i
$417$	2.91564	+	1.87377i	0.142779	+	0.0917587i
$418$	−0.980990	+	6.82294i	−0.0479818	+	0.333721i
$419$	−12.6482	+	27.6957i	−0.617905	+	1.35302i	0.299128	+	0.954213i	$0.403304\pi$
$419$	−12.6482	+	27.6957i	−0.617905	+	1.35302i	−0.917033	+	0.398811i	$0.869423\pi$
$420$	−1.17330	−	8.16047i	−0.0572511	−	0.398190i
$421$	23.2692	+	6.83246i	1.13407	+	0.332993i	0.794307	−	0.607517i	$-0.207834\pi$
$421$	23.2692	+	6.83246i	1.13407	+	0.332993i	0.339765	+	0.940510i	$0.389652\pi$
$422$	−8.08610	+	5.19662i	−0.393625	+	0.252968i
$423$	−5.51910	−	12.0851i	−0.268348	−	0.587600i
$424$	−1.25813	+	0.369422i	−0.0611004	+	0.0179407i
$425$	4.24404	−	4.89789i	0.205866	−	0.237583i
$426$	6.19781	−	7.15266i	0.300285	−	0.346547i
$427$	−15.1279	+	4.44194i	−0.732089	+	0.214961i
$428$	−8.41190	−	18.4195i	−0.406605	−	0.890340i
$429$	0.406881	−	0.261487i	0.0196444	−	0.0126247i
$430$	−3.28262	−	0.963865i	−0.158302	−	0.0464817i
$431$	−1.38617	−	9.64102i	−0.0667694	−	0.464392i	−0.995586	−	0.0938521i	$-0.970082\pi$
$431$	−1.38617	−	9.64102i	−0.0667694	−	0.464392i	0.928817	−	0.370539i	$-0.120827\pi$
$432$	0.529249	−	1.15889i	0.0254635	−	0.0557573i
$433$	0.888425	−	6.17913i	0.0426950	−	0.296950i	−0.957275	−	0.289180i	$-0.906617\pi$
$433$	0.888425	−	6.17913i	0.0426950	−	0.296950i	0.999970	−	0.00777039i	$-0.00247342\pi$
$434$	−12.8986	−	8.28940i	−0.619150	−	0.397904i
$435$	−7.85060	−	9.06007i	−0.376407	−	0.434397i
$436$	−23.8164			−1.14060
$437$	21.9241	+	6.92673i	1.04877	+	0.331351i
$438$	−3.12684			−0.149406
$439$	10.9508	+	12.6379i	0.522655	+	0.603176i	0.954294	−	0.298871i	$-0.0966099\pi$
$439$	10.9508	+	12.6379i	0.522655	+	0.603176i	−0.431639	+	0.902047i	$0.642064\pi$
$440$	−7.14836	−	4.59397i	−0.340785	−	0.219009i
$441$	−0.506143	+	3.52030i	−0.0241021	+	0.167634i
$442$	−0.207955	+	0.455357i	−0.00989140	+	0.0216591i
$443$	−4.32524	−	30.0827i	−0.205498	−	1.42927i	−0.787615	−	0.616168i	$-0.788684\pi$
$443$	−4.32524	−	30.0827i	−0.205498	−	1.42927i	0.582117	−	0.813105i	$-0.302225\pi$
$444$	16.5889	+	4.87094i	0.787274	+	0.231164i
$445$	−3.55934	+	2.28745i	−0.168729	+	0.108436i
$446$	−3.33285	−	7.29792i	−0.157815	−	0.345567i
$447$	−2.94489	+	0.864698i	−0.139289	+	0.0408988i
$448$	−3.30643	+	3.81582i	−0.156214	+	0.180280i
$449$	−11.2761	+	13.0133i	−0.532153	+	0.614137i	−0.956632	−	0.291301i	$-0.905912\pi$
$449$	−11.2761	+	13.0133i	−0.532153	+	0.614137i	0.424478	+	0.905438i	$0.360457\pi$
$450$	−1.45613	+	0.427559i	−0.0686427	+	0.0201553i
$451$	6.96171	+	15.2440i	0.327814	+	0.717813i
$452$	16.3739	−	10.5228i	0.770162	−	0.494953i
$453$	−1.81890	−	0.534078i	−0.0854595	−	0.0250932i
$454$	−0.159169	−	1.10705i	−0.00747018	−	0.0519562i
$455$	−0.538760	+	1.17972i	−0.0252575	+	0.0553062i
$456$	1.68276	−	11.7038i	0.0788023	−	0.548082i
$457$	−9.70917	−	6.23971i	−0.454176	−	0.291881i	0.293483	−	0.955964i	$-0.405186\pi$
$457$	−9.70917	−	6.23971i	−0.454176	−	0.291881i	−0.747659	+	0.664083i	$0.768822\pi$
$458$	12.0873	+	13.9495i	0.564804	+	0.651819i
$459$	3.00512			0.140267
$460$	−8.15524	+	9.03225i	−0.380240	+	0.421131i
$461$	−36.3205			−1.69162			−0.845808	−	0.533488i	$-0.820881\pi$
$461$	−36.3205			−1.69162			−0.845808	+	0.533488i	$0.820881\pi$
$462$	3.05918	+	3.53049i	0.142326	+	0.164253i
$463$	−12.4043	−	7.97178i	−0.576478	−	0.370480i	0.219677	−	0.975573i	$-0.429500\pi$
$463$	−12.4043	−	7.97178i	−0.576478	−	0.370480i	−0.796155	+	0.605093i	$0.793136\pi$
$464$	1.28903	−	8.96539i	0.0598417	−	0.416208i
$465$	−4.69749	+	10.2861i	−0.217841	+	0.477005i
$466$	−0.996376	−	6.92995i	−0.0461562	−	0.321024i
$467$	7.78126	+	2.28478i	0.360074	+	0.105727i	0.456765	−	0.889587i	$-0.349008\pi$
$467$	7.78126	+	2.28478i	0.360074	+	0.105727i	−0.0966917	+	0.995314i	$0.530826\pi$
$468$	−0.299668	+	0.192585i	−0.0138521	+	0.00890223i
$469$	20.1482	+	44.1183i	0.930356	+	2.03719i
$470$	15.1265	−	4.44153i	0.697732	−	0.204872i
$471$	−1.41307	+	1.63077i	−0.0651110	+	0.0751421i
$472$	5.57010	−	6.42824i	0.256385	−	0.295884i
$473$	−5.65221	+	1.65964i	−0.259889	+	0.0763102i
$474$	−0.611445	−	1.33888i	−0.0280846	−	0.0614966i
$475$	8.69788	−	5.58979i	0.399086	−	0.256477i
$476$	14.0975	+	4.13941i	0.646160	+	0.189730i
$477$	−0.0756628	−	0.526246i	−0.00346436	−	0.0240952i
$478$	−3.37538	+	7.39105i	−0.154386	+	0.338059i
$479$	4.40254	−	30.6204i	0.201157	−	1.39908i	−0.599700	−	0.800225i	$-0.704714\pi$
$479$	4.40254	−	30.6204i	0.201157	−	1.39908i	0.800858	−	0.598855i	$-0.204377\pi$
$480$	8.26907	+	5.31421i	0.377430	+	0.242559i
$481$	−1.78106	−	2.05546i	−0.0812095	−	0.0937208i
$482$	3.86848			0.176205
$483$	13.2777	−	8.15489i	0.604156	−	0.371060i
$484$	10.2709			0.466859
$485$	2.00406	+	2.31281i	0.0909999	+	0.105019i
$486$	−0.591994	−	0.380451i	−0.0268534	−	0.0172576i
$487$	−2.25517	+	15.6850i	−0.102191	+	0.710757i	0.872729	+	0.488205i	$0.162348\pi$
$487$	−2.25517	+	15.6850i	−0.102191	+	0.710757i	−0.974921	+	0.222553i	$0.928561\pi$
$488$	4.97178	−	10.8867i	0.225062	−	0.492816i
$489$	1.72149	+	11.9732i	0.0778483	+	0.541447i
$490$	−4.04925	−	1.18897i	−0.182926	−	0.0537120i
$491$	0.632340	−	0.406380i	0.0285371	−	0.0183397i	−0.526294	−	0.850302i	$-0.676419\pi$
$491$	0.632340	−	0.406380i	0.0285371	−	0.0183397i	0.554832	+	0.831963i	$0.312783\pi$
$492$	−5.12730	−	11.2272i	−0.231156	−	0.506162i
$493$	20.4993	−	6.01913i	0.923241	−	0.271088i
$494$	−0.522987	+	0.603559i	−0.0235303	+	0.0271554i
$495$	2.25619	−	2.60378i	0.101408	−	0.117031i
$496$	−8.19755	+	2.40702i	−0.368081	+	0.108078i
$497$	18.1527	+	39.7489i	0.814261	+	1.78298i
$498$	−3.81442	+	2.45138i	−0.170928	+	0.109849i
$499$	29.6761	+	8.71370i	1.32849	+	0.390079i	0.867548	−	0.497354i	$-0.165695\pi$
$499$	29.6761	+	8.71370i	1.32849	+	0.390079i	0.460938	+	0.887432i	$0.347513\pi$
$500$	2.58437	+	17.9747i	0.115577	+	0.803853i
$501$	−5.47042	+	11.9785i	−0.244400	+	0.535162i
$502$	−2.05561	+	14.2971i	−0.0917465	+	0.638111i
$503$	−23.5817	−	15.1550i	−1.05145	−	0.675729i	−0.103661	−	0.994613i	$-0.533056\pi$
$503$	−23.5817	−	15.1550i	−1.05145	−	0.675729i	−0.947794	+	0.318884i	$0.896692\pi$
$504$	−5.24762	−	6.05608i	−0.233748	−	0.269759i
$505$	4.04593			0.180041
$506$	1.12047	−	6.80377i	0.0498108	−	0.302465i
$507$	−12.9440			−0.574862
$508$	5.24474	+	6.05275i	0.232698	+	0.268547i
$509$	18.7265	+	12.0348i	0.830038	+	0.533433i	0.885290	−	0.465040i	$-0.153960\pi$
$509$	18.7265	+	12.0348i	0.830038	+	0.533433i	−0.0552522	+	0.998472i	$0.517596\pi$
$510$	−0.507484	+	3.52963i	−0.0224718	+	0.156294i
$511$	5.99733	−	13.1323i	0.265306	−	0.580940i
$512$	1.95127	+	13.5714i	0.0862348	+	0.599776i
$513$	4.60002	+	1.35069i	0.203096	+	0.0596343i
$514$	10.3149	−	6.62896i	0.454969	−	0.292391i
$515$	−2.87908	−	6.30430i	−0.126867	−	0.277801i
$516$	4.16285	−	1.22232i	0.183259	−	0.0538097i
$517$	17.7763	−	20.5150i	0.781801	−	0.902247i
$518$	17.2027	−	19.8529i	0.755841	−	0.872288i
$519$	16.9271	−	4.97023i	0.743016	−	0.218169i
$520$	−0.408968	−	0.895514i	−0.0179344	−	0.0392709i
$521$	−10.2196	+	6.56776i	−0.447730	+	0.287739i	−0.745012	−	0.667051i	$-0.767556\pi$
$521$	−10.2196	+	6.56776i	−0.447730	+	0.287739i	0.297282	+	0.954790i	$0.403920\pi$
$522$	−4.80028	−	1.40949i	−0.210102	−	0.0616916i
$523$	−2.87440	−	19.9919i	−0.125689	−	0.874183i	−0.950931	−	0.309404i	$-0.899870\pi$
$523$	−2.87440	−	19.9919i	−0.125689	−	0.874183i	0.825242	−	0.564779i	$-0.191039\pi$
$524$	−2.83871	+	6.21591i	−0.124010	+	0.271543i
$525$	0.997192	−	6.93562i	0.0435210	−	0.302695i
$526$	11.3841	+	7.31609i	0.496369	+	0.318997i
$527$	−13.1970	−	15.2302i	−0.574870	−	0.663436i
$528$	2.60306			0.113284
$529$	−21.7854	−	7.37539i	−0.947191	−	0.320669i
$530$	0.630872			0.0274033
$531$	2.25845	+	2.60639i	0.0980082	+	0.113108i
$532$	19.7189	+	12.6726i	0.854925	+	0.549427i
$533$	−0.276320	+	1.92184i	−0.0119687	+	0.0832443i
$534$	−0.733493	+	1.60612i	−0.0317413	+	0.0695038i
$535$	3.22926	+	22.4600i	0.139613	+	0.971030i
$536$	−35.3255	−	10.3725i	−1.52583	−	0.448024i
$537$	9.05907	−	5.82191i	0.390928	−	0.251234i
$538$	−7.01381	−	15.3581i	−0.302387	−	0.662134i
$539$	−6.97223	+	2.04723i	−0.300315	+	0.0881805i
$540$	−1.66168	+	1.91768i	−0.0715073	+	0.0825238i
$541$	12.4594	−	14.3789i	0.535670	−	0.618196i	−0.421814	−	0.906682i	$-0.638606\pi$
$541$	12.4594	−	14.3789i	0.535670	−	0.618196i	0.957484	+	0.288486i	$0.0931519\pi$
$542$	−15.2544	+	4.47909i	−0.655231	+	0.192393i
$543$	−0.592646	−	1.29771i	−0.0254329	−	0.0556902i
$544$	−14.7367	+	9.47070i	−0.631830	+	0.406053i
$545$	25.6069	+	7.51888i	1.09688	+	0.322073i
$546$	0.0770255	+	0.535724i	0.00329639	+	0.0229269i
$547$	−0.147373	+	0.322702i	−0.00630122	+	0.0137977i	−0.912756	−	0.408504i	$-0.866051\pi$
$547$	−0.147373	+	0.322702i	−0.00630122	+	0.0137977i	0.906455	+	0.422302i	$0.138778\pi$
$548$	−3.53301	+	24.5726i	−0.150923	+	1.04969i
$549$	4.08228	+	2.62352i	0.174228	+	0.111969i
$550$	−2.03055	−	2.34338i	−0.0865830	−	0.0999222i
$551$	34.0841			1.45203
$552$	−1.92201	+	11.6710i	−0.0818061	+	0.496749i
$553$	6.79587			0.288990
$554$	0.962449	+	1.11073i	0.0408905	+	0.0471902i
$555$	−16.2983	−	10.4743i	−0.691825	−	0.444609i
$556$	0.742225	−	5.16229i	0.0314774	−	0.218930i
$557$	−4.30127	+	9.41847i	−0.182251	+	0.399073i	−0.978602	−	0.205760i	$-0.934033\pi$
$557$	−4.30127	+	9.41847i	−0.182251	+	0.399073i	0.796352	+	0.604834i	$0.206760\pi$
$558$	0.671590	+	4.67101i	0.0284307	+	0.197740i
$559$	−0.654855	−	0.192283i	−0.0276974	−	0.00813270i
$560$	−5.87198	+	3.77369i	−0.248136	+	0.159468i
$561$	2.55065	+	5.58515i	0.107689	+	0.235805i
$562$	13.2376	−	3.88691i	0.558394	−	0.163959i
$563$	−9.43294	+	10.8862i	−0.397551	+	0.458799i	−0.918868	−	0.394565i	$-0.870895\pi$
$563$	−9.43294	+	10.8862i	−0.397551	+	0.458799i	0.521317	+	0.853363i	$0.325441\pi$
$564$	−13.0922	+	15.1093i	−0.551283	+	0.636214i
$565$	−20.9270	+	6.14472i	−0.880405	+	0.258510i
$566$	−1.46884	−	3.21631i	−0.0617399	−	0.135192i
$567$	2.73330	−	1.75658i	0.114788	−	0.0737696i
$568$	−31.8269	−	9.34522i	−1.33543	−	0.392117i
$569$	−2.69816	−	18.7661i	−0.113113	−	0.786716i	−0.964860	−	0.262764i	$-0.915366\pi$
$569$	−2.69816	−	18.7661i	−0.113113	−	0.786716i	0.851748	−	0.523952i	$-0.175543\pi$
$570$	−2.36325	+	5.17479i	−0.0989856	+	0.216748i
$571$	−0.955235	+	6.64381i	−0.0399754	+	0.278035i	−0.999998	−	0.00188690i	$-0.999399\pi$
$571$	−0.955235	+	6.64381i	−0.0399754	+	0.278035i	0.960023	+	0.279922i	$0.0903085\pi$
$572$	−0.612275	−	0.393485i	−0.0256005	−	0.0164524i
$573$	9.09843	+	10.5001i	0.380092	+	0.438650i
$574$	−18.7533			−0.782747
$575$	−8.81315	+	5.41286i	−0.367534	+	0.225732i
$576$	1.55400			0.0647498
$577$	−8.20449	−	9.46849i	−0.341557	−	0.394178i	0.558819	−	0.829289i	$-0.311255\pi$
$577$	−8.20449	−	9.46849i	−0.341557	−	0.394178i	−0.900377	+	0.435111i	$0.856709\pi$
$578$	4.71773	+	3.03190i	0.196232	+	0.126110i
$579$	−1.15213	+	8.01323i	−0.0478808	+	0.333018i
$580$	−7.49402	+	16.4096i	−0.311172	+	0.681372i
$581$	−2.97935	−	20.7219i	−0.123604	−	0.859687i
$582$	1.22539	+	0.359808i	0.0507941	+	0.0149145i
$583$	0.913830	−	0.587283i	0.0378470	−	0.0243228i
$584$	4.55252	+	9.96862i	0.188384	+	0.412504i
$585$	0.382997	−	0.112458i	0.0158350	−	0.00464957i
$586$	1.36317	−	1.57319i	0.0563122	−	0.0649877i
$587$	4.51105	−	5.20603i	0.186191	−	0.214876i	−0.654978	−	0.755648i	$-0.727322\pi$
$587$	4.51105	−	5.20603i	0.186191	−	0.214876i	0.841169	+	0.540772i	$0.181868\pi$
$588$	5.13504	−	1.50778i	0.211766	−	0.0621800i
$589$	−13.3556	−	29.2447i	−0.550308	−	1.20501i
$590$	−3.44268	+	2.21248i	−0.141733	+	0.0910863i
$591$	−1.70543	−	0.500760i	−0.0701521	−	0.0205985i
$592$	−2.08317	−	14.4888i	−0.0856178	−	0.595485i
$593$	−13.5898	+	29.7575i	−0.558067	+	1.22200i	0.394845	+	0.918748i	$0.370798\pi$
$593$	−13.5898	+	29.7575i	−0.558067	+	1.22200i	−0.952912	+	0.303248i	$0.901929\pi$
$594$	0.204619	−	1.42316i	0.00839564	−	0.0583929i
$595$	−13.8506	−	8.90124i	−0.567819	−	0.364915i
$596$	3.02451	+	3.49047i	0.123889	+	0.142975i
$597$	6.58209			0.269387
$598$	0.535381	−	0.592955i	0.0218934	−	0.0242477i
$599$	26.8624			1.09757			0.548784	−	0.835964i	$-0.315091\pi$
$599$	26.8624			1.09757			0.548784	+	0.835964i	$0.315091\pi$
$600$	3.48314	+	4.01976i	0.142199	+	0.164106i
$601$	−25.9428	−	16.6724i	−1.05823	−	0.680083i	−0.108800	−	0.994064i	$-0.534701\pi$
$601$	−25.9428	−	16.6724i	−1.05823	−	0.680083i	−0.949429	+	0.313981i	$0.898337\pi$
$602$	0.938145	−	6.52494i	0.0382359	−	0.265937i
$603$	6.20119	−	13.5787i	0.252532	−	0.552968i
$604$	0.405973	+	2.82360i	0.0165188	+	0.114891i
$605$	−11.0431	−	3.24254i	−0.448965	−	0.131828i
$606$	1.42042	−	0.912846i	0.0577004	−	0.0370818i
$607$	−14.9460	−	32.7272i	−0.606640	−	1.32836i	−0.924849	−	0.380335i	$-0.875809\pi$
$607$	−14.9460	−	32.7272i	−0.606640	−	1.32836i	0.318209	−	0.948021i	$-0.396919\pi$
$608$	−26.8145	+	7.87346i	−1.08747	+	0.319311i
$609$	15.1267	−	17.4571i	0.612964	−	0.707398i
$610$	−3.77081	+	4.35174i	−0.152676	+	0.176197i
$611$	3.01760	−	0.886048i	0.122079	−	0.0358457i
$612$	−1.87855	−	4.11346i	−0.0759360	−	0.166277i
$613$	17.5091	−	11.2524i	0.707187	−	0.454481i	−0.136972	−	0.990575i	$-0.543737\pi$
$613$	17.5091	−	11.2524i	0.707187	−	0.454481i	0.844158	+	0.536094i	$0.180101\pi$
$614$	15.9957	+	4.69675i	0.645533	+	0.189546i
$615$	1.96833	+	13.6900i	0.0793705	+	0.552034i
$616$	6.80146	−	14.8931i	0.274039	−	0.600061i
$617$	2.59278	−	18.0332i	0.104382	−	0.725990i	−0.868668	−	0.495394i	$-0.835024\pi$
$617$	2.59278	−	18.0332i	0.104382	−	0.725990i	0.973050	−	0.230595i	$-0.0740674\pi$
$618$	−2.43315	−	1.56369i	−0.0978756	−	0.0629008i
$619$	13.8159	+	15.9444i	0.555310	+	0.640862i	0.962112	−	0.272655i	$-0.0879017\pi$
$619$	13.8159	+	15.9444i	0.555310	+	0.640862i	−0.406802	+	0.913516i	$0.633356\pi$
$620$	17.0162			0.683386
$621$	−4.57302	−	1.44481i	−0.183509	−	0.0579782i
$622$	−18.4466			−0.739642
$623$	−5.33866	−	6.16114i	−0.213889	−	0.246841i
$624$	0.253711	+	0.163050i	0.0101566	+	0.00652723i
$625$	1.36140	−	9.46875i	0.0544561	−	0.378750i
$626$	1.93682	−	4.24105i	0.0774109	−	0.169506i
$627$	1.39404	+	9.69575i	0.0556725	+	0.387211i
$628$	3.11557	+	0.914812i	0.124325	+	0.0365050i
$629$	29.0460	−	18.6667i	1.15814	−	0.744291i
$630$	1.60159	+	3.50700i	0.0638089	+	0.139722i
$631$	−28.2607	+	8.29809i	−1.12504	+	0.330342i	−0.790757	−	0.612131i	$-0.790313\pi$
$631$	−28.2607	+	8.29809i	−1.12504	+	0.330342i	−0.334284	+	0.942472i	$0.608494\pi$
$632$	−3.37821	+	3.89867i	−0.134378	+	0.155081i
$633$	−8.94481	+	10.3229i	−0.355524	+	0.410297i
$634$	7.49657	−	2.20119i	0.297727	−	0.0874205i
$635$	−3.72818	−	8.16358i	−0.147948	−	0.323962i
$636$	−0.673035	+	0.432533i	−0.0266876	+	0.0171511i
$637$	−0.807791	−	0.237189i	−0.0320059	−	0.00939777i
$638$	−1.45473	−	10.1178i	−0.0575931	−	0.400569i
$639$	5.58704	−	12.2339i	0.221020	−	0.483966i
$640$	2.53533	−	17.6336i	0.100218	−	0.697030i
$641$	33.4698	+	21.5097i	1.32198	+	0.849584i	0.995420	−	0.0955936i	$-0.0304749\pi$
$641$	33.4698	+	21.5097i	1.32198	+	0.849584i	0.326558	+	0.945177i	$0.394111\pi$
$642$	6.20115	+	7.15651i	0.244740	+	0.282445i
$643$	−33.1070			−1.30561			−0.652806	−	0.757525i	$-0.726408\pi$
$643$	−33.1070			−1.30561			−0.652806	+	0.757525i	$0.726408\pi$
$644$	−19.4626	−	13.0770i	−0.766936	−	0.515304i
$645$	−4.86171			−0.191430
$646$	−6.63925	−	7.66211i	−0.261218	−	0.301462i
$647$	26.5632	+	17.0711i	1.04431	+	0.671134i	0.946048	−	0.324027i	$-0.105037\pi$
$647$	26.5632	+	17.0711i	1.04431	+	0.671134i	0.0982575	+	0.995161i	$0.468673\pi$
$648$	−0.350997	+	2.44124i	−0.0137885	+	0.0959009i
$649$	−2.92718	+	6.40963i	−0.114902	+	0.251600i
$650$	−0.0511261	−	0.355590i	−0.00200533	−	0.0139474i
$651$	−20.9057	−	6.13848i	−0.819361	−	0.240586i
$652$	15.3130	−	9.84104i	0.599702	−	0.385405i
$653$	5.87583	+	12.8663i	0.229939	+	0.503496i	0.989071	−	0.147441i	$-0.0471035\pi$
$653$	5.87583	+	12.8663i	0.229939	+	0.503496i	−0.759132	+	0.650937i	$0.774376\pi$
$654$	10.6863	−	3.13779i	0.417868	−	0.122697i
$655$	5.01451	−	5.78706i	0.195933	−	0.226119i
$656$	−6.84313	+	7.89739i	−0.267179	+	0.308341i
$657$	−4.26342	+	1.25185i	−0.166332	+	0.0488394i
$658$	12.6188	+	27.6313i	0.491932	+	1.07718i
$659$	−4.37949	+	2.81453i	−0.170601	+	0.109638i	−0.623155	−	0.782099i	$-0.714149\pi$
$659$	−4.37949	+	2.81453i	−0.170601	+	0.109638i	0.452554	+	0.891737i	$0.350513\pi$
$660$	−4.97447	−	1.46064i	−0.193631	−	0.0568552i
$661$	1.49548	+	10.4013i	0.0581673	+	0.404563i	0.998015	+	0.0629700i	$0.0200572\pi$
$661$	1.49548	+	10.4013i	0.0581673	+	0.404563i	−0.939848	+	0.341593i	$0.889034\pi$
$662$	−6.56486	+	14.3750i	−0.255151	+	0.558702i
$663$	−0.101239	+	0.704131i	−0.00393179	+	0.0273462i
$664$	13.3688	+	8.59160i	0.518810	+	0.333419i
$665$	−17.2007	−	19.8507i	−0.667015	−	0.769776i
$666$	−8.08512			−0.313292
$667$	−34.0885	−	0.696124i	−1.31991	−	0.0269540i
$668$	19.8161			0.766706
$669$	−7.46607	−	8.61631i	−0.288655	−	0.333126i
$670$	14.9015	+	9.57660i	0.575695	+	0.369976i
$671$	−1.41102	+	9.81385i	−0.0544718	+	0.378860i
$672$	−7.86779	+	17.2281i	−0.303507	+	0.664587i
$673$	3.94517	+	27.4393i	0.152075	+	1.05771i	0.912734	+	0.408554i	$0.133967\pi$
$673$	3.94517	+	27.4393i	0.152075	+	1.05771i	−0.760659	+	0.649152i	$0.775124\pi$
$674$	−23.5827	−	6.92450i	−0.908370	−	0.266722i
$675$	−1.81424	+	1.16594i	−0.0698302	+	0.0448772i
$676$	8.09149	+	17.7179i	0.311211	+	0.681457i
$677$	−26.6582	+	7.82754i	−1.02456	+	0.300837i	−0.750496	−	0.660876i	$-0.770185\pi$
$677$	−26.6582	+	7.82754i	−1.02456	+	0.300837i	−0.274061	+	0.961712i	$0.588367\pi$
$678$	−5.96053	+	6.87881i	−0.228913	+	0.264179i
$679$	−3.86147	+	4.45637i	−0.148189	+	0.171020i
$680$	11.9916	−	3.52105i	0.459857	−	0.135026i
$681$	−0.660238	−	1.44572i	−0.0253004	−	0.0554001i
$682$	−8.11124	+	5.21278i	−0.310596	+	0.199608i
$683$	10.3732	+	3.04585i	0.396921	+	0.116546i	0.474100	−	0.880471i	$-0.342773\pi$
$683$	10.3732	+	3.04585i	0.396921	+	0.116546i	−0.0771798	+	0.997017i	$0.524592\pi$
$684$	−1.02671	−	7.14091i	−0.0392572	−	0.273040i
$685$	11.5563	−	25.3047i	0.441542	−	0.966842i
$686$	−1.12047	+	7.79303i	−0.0427797	+	0.297539i
$687$	22.0657	+	14.1808i	0.841860	+	0.541031i
$688$	−2.40545	−	2.77604i	−0.0917070	−	0.105836i
$689$	0.125854			0.00479464
$690$	2.46924	−	5.12719i	0.0940023	−	0.195189i
$691$	6.10633			0.232296			0.116148	−	0.993232i	$-0.462945\pi$
$691$	6.10633			0.232296			0.116148	+	0.993232i	$0.462945\pi$
$692$	−17.3847	−	20.0630i	−0.660868	−	0.762682i
$693$	5.58462	+	3.58902i	0.212142	+	0.136335i
$694$	−1.02845	+	7.15305i	−0.0390395	+	0.271526i
$695$	−2.42777	+	5.31608i	−0.0920907	+	0.201650i
$696$	2.49539	+	17.3558i	0.0945874	+	0.657870i
$697$	−23.6500	−	6.94427i	−0.895809	−	0.263033i
$698$	17.8995	−	11.5033i	0.677507	−	0.435407i
$699$	−4.13300	−	9.05000i	−0.156324	−	0.342303i
$700$	−10.1169	+	2.97060i	−0.382385	+	0.112278i
$701$	12.3067	−	14.2027i	0.464819	−	0.536430i	−0.474144	−	0.880447i	$-0.657242\pi$
$701$	12.3067	−	14.2027i	0.464819	−	0.536430i	0.938963	+	0.344017i	$0.111788\pi$
$702$	0.109087	−	0.125893i	0.00411722	−	0.00475153i
$703$	52.8513	−	15.5186i	1.99333	−	0.585293i
$704$	1.31898	+	2.88817i	0.0497110	+	0.108852i
$705$	18.8466	−	12.1120i	0.709803	−	0.456163i
$706$	−2.13120	−	0.625776i	−0.0802086	−	0.0235514i
$707$	1.10945	+	7.71641i	0.0417253	+	0.290206i
$708$	2.15587	−	4.72069i	0.0810224	−	0.177414i
$709$	−2.12480	+	14.7783i	−0.0797985	+	0.555011i	0.910226	+	0.414113i	$0.135908\pi$
$709$	−2.12480	+	14.7783i	−0.0797985	+	0.555011i	−0.990024	+	0.140898i	$0.955001\pi$
$710$	13.4257	+	8.62815i	0.503856	+	0.323809i
$711$	−1.36973	−	1.58075i	−0.0513687	−	0.0592827i
$712$	6.18838			0.231919
$713$	12.7600	+	29.5212i	0.477867	+	1.10558i
$714$	−6.87088			−0.257136
$715$	0.534083	+	0.616365i	0.0199736	+	0.0230507i
$716$	−13.6321	−	8.76082i	−0.509455	−	0.327407i
$717$	−1.64324	+	11.4290i	−0.0613679	+	0.426823i
$718$	6.39253	−	13.9977i	0.238567	−	0.522389i
$719$	−2.17016	−	15.0938i	−0.0809333	−	0.562904i	−0.989430	−	0.145012i	$-0.953678\pi$
$719$	−2.17016	−	15.0938i	−0.0809333	−	0.562904i	0.908497	−	0.417892i	$-0.137231\pi$
$720$	2.06129	+	0.605250i	0.0768198	+	0.0225563i
$721$	11.2341	−	7.21972i	0.418380	−	0.268876i
$722$	−1.16479	−	2.55054i	−0.0433491	−	0.0949213i
$723$	5.27463	−	1.54877i	0.196166	−	0.0575995i
$724$	−1.40586	+	1.62245i	−0.0522483	+	0.0602977i
$725$	−10.0404	+	11.5873i	−0.372892	+	0.430340i
$726$	−4.60851	+	1.35318i	−0.171038	+	0.0502213i
$727$	−9.70715	−	21.2557i	−0.360018	−	0.788330i	−0.999804	−	0.0197768i	$-0.993704\pi$
$727$	−9.70715	−	21.2557i	−0.360018	−	0.788330i	0.639786	−	0.768553i	$-0.279023\pi$
$728$	1.59579	−	1.02555i	0.0591437	−	0.0380094i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−0.750370	−	5.21894i	−0.0277724	−	0.193162i
$731$	3.59927	−	7.88130i	0.133124	−	0.291500i
$732$	1.03921	−	7.22789i	0.0384105	−	0.267151i
$733$	45.1623	+	29.0240i	1.66811	+	1.07203i	0.904637	+	0.426182i	$0.140142\pi$
$733$	45.1623	+	29.0240i	1.66811	+	1.07203i	0.763469	+	0.645845i	$0.223495\pi$
$734$	−3.75061	−	4.32843i	−0.138437	−	0.159765i
$735$	−5.99712			−0.221207
$736$	26.9788	−	7.32681i	0.994451	−	0.270070i
$737$	30.5000			1.12348
$738$	3.77978	+	4.36210i	0.139136	+	0.160571i
$739$	−7.10502	−	4.56612i	−0.261362	−	0.167967i	0.403397	−	0.915025i	$-0.367829\pi$
$739$	−7.10502	−	4.56612i	−0.261362	−	0.167967i	−0.664759	+	0.747058i	$0.731466\pi$
$740$	−4.14902	+	28.8570i	−0.152521	+	1.06081i
$741$	−0.471448	+	1.03233i	−0.0173191	+	0.0379235i
$742$	0.172994	+	1.20320i	0.00635083	+	0.0441710i
$743$	−10.3844	−	3.04914i	−0.380968	−	0.111862i	0.0856409	−	0.996326i	$-0.472706\pi$
$743$	−10.3844	−	3.04914i	−0.380968	−	0.111862i	−0.466609	+	0.884464i	$0.654524\pi$
$744$	13.9137	−	8.94182i	0.510103	−	0.327823i
$745$	−2.14995	−	4.70774i	−0.0787682	−	0.172478i
$746$	2.98567	−	0.876671i	0.109313	−	0.0320972i
$747$	−4.21950	+	4.86956i	−0.154383	+	0.178168i
$748$	6.05058	−	6.98274i	0.221231	−	0.255314i
$749$	−41.9503	+	12.3177i	−1.53283	+	0.450080i
$750$	−3.52775	−	7.72470i	−0.128815	−	0.282066i
$751$	12.6562	−	8.13365i	0.461832	−	0.296801i	−0.288959	−	0.957342i	$-0.593309\pi$
$751$	12.6562	−	8.13365i	0.461832	−	0.296801i	0.750791	+	0.660540i	$0.229673\pi$
$752$	16.2408	+	4.76871i	0.592239	+	0.173897i
$753$	2.92113	+	20.3169i	0.106452	+	0.740390i
$754$	0.491972	−	1.07727i	0.0179166	−	0.0392318i
$755$	0.454922	−	3.16405i	0.0165563	−	0.115152i
$756$	−4.11307	−	2.64331i	−0.149591	−	0.0961362i
$757$	−2.37325	−	2.73887i	−0.0862572	−	0.0995461i	0.710980	−	0.703212i	$-0.248252\pi$
$757$	−2.37325	−	2.73887i	−0.0862572	−	0.0995461i	−0.797237	+	0.603666i	$0.793706\pi$
$758$	−7.42321			−0.269623
$759$	−1.19619	−	9.72546i	−0.0434191	−	0.353012i
$760$	19.9384			0.723242
$761$	0.554520	+	0.639950i	0.0201013	+	0.0231982i	0.765711	−	0.643185i	$-0.222387\pi$
$761$	0.554520	+	0.639950i	0.0201013	+	0.0231982i	−0.745610	+	0.666383i	$0.767842\pi$
$762$	−3.15074	−	2.02486i	−0.114139	−	0.0733529i
$763$	−7.31824	+	50.8995i	−0.264938	+	1.84269i
$764$	8.68518	−	19.0179i	0.314219	−	0.688043i
$765$	0.721161	+	5.01578i	0.0260736	+	0.181346i
$766$	−3.64745	−	1.07099i	−0.131788	−	0.0386963i
$767$	−0.686786	+	0.441371i	−0.0247984	+	0.0159370i
$768$	−4.37953	−	9.58984i	−0.158033	−	0.346044i
$769$	−38.4180	+	11.2806i	−1.38539	+	0.406787i	−0.887642	−	0.460535i	$-0.847658\pi$
$769$	−38.4180	+	11.2806i	−1.38539	+	0.406787i	−0.497748	+	0.867322i	$0.665840\pi$
$770$	−5.15852	+	5.95325i	−0.185900	+	0.214540i
$771$	11.4103	−	13.1681i	0.410931	−	0.474239i
$772$	11.6888	−	3.43215i	0.420690	−	0.123526i
$773$	16.2066	+	35.4876i	0.582913	+	1.27640i	0.939631	+	0.342189i	$0.111168\pi$
$773$	16.2066	+	35.4876i	0.582913	+	1.27640i	−0.356719	+	0.934212i	$0.616104\pi$
$774$	−1.70682	+	1.09690i	−0.0613502	+	0.0394274i
$775$	13.8763	+	4.07445i	0.498452	+	0.146359i
$776$	−0.637011	−	4.43051i	−0.0228674	−	0.159046i
$777$	15.5074	−	33.9565i	0.556325	−	1.21818i
$778$	0.160485	−	1.11620i	0.00575367	−	0.0400177i
$779$	−33.0805	−	21.2595i	−1.18523	−	0.761702i
$780$	−0.393352	−	0.453952i	−0.0140843	−	0.0162541i
$781$	27.4793			0.983287
$782$	6.48362	+	7.79869i	0.231854	+	0.278880i
$783$	−7.10942			−0.254070
$784$	−2.96722	−	3.42436i	−0.105972	−	0.122299i
$785$	−3.06099	−	1.96718i	−0.109252	−	0.0702117i
$786$	0.454779	−	3.16306i	0.0162214	−	0.112823i
$787$	−16.1795	+	35.4281i	−0.576735	+	1.26287i	0.366398	+	0.930458i	$0.380591\pi$
$787$	−16.1795	+	35.4281i	−0.576735	+	1.26287i	−0.943133	+	0.332416i	$0.892136\pi$
$788$	0.380646	+	2.64745i	0.0135600	+	0.0943116i
$789$	18.4511	+	5.41773i	0.656876	+	0.192876i
$790$	2.08795	−	1.34185i	0.0742861	−	0.0477408i
$791$	−17.4577	−	38.2271i	−0.620726	−	1.35920i
$792$	−4.83506	+	1.41970i	−0.171806	+	0.0504469i
$793$	−0.752245	+	0.868136i	−0.0267130	+	0.0308284i
$794$	−3.21396	+	3.70911i	−0.114059	+	0.131631i
$795$	0.860188	−	0.252574i	0.0305077	−	0.00895787i
$796$	−4.11458	−	9.00966i	−0.145837	−	0.319339i
$797$	18.7123	−	12.0257i	0.662823	−	0.425971i	−0.165508	−	0.986208i	$-0.552927\pi$
$797$	18.7123	−	12.0257i	0.662823	−	0.425971i	0.828332	+	0.560238i	$0.189290\pi$
$798$	−10.5174	−	3.08820i	−0.372313	−	0.109321i
$799$	5.68197	+	39.5189i	0.201014	+	1.39808i
$800$	5.22229	−	11.4352i	0.184636	−	0.404296i
$801$	−0.357087	+	2.48359i	−0.0126170	+	0.0877534i
$802$	0.565424	+	0.363376i	0.0199658	+	0.0128313i
$803$	−5.94527	−	6.86121i	−0.209804	−	0.242127i
$804$	−22.4632			−0.792217
$805$	16.7975	+	20.2045i	0.592033	+	0.712115i
$806$	−1.11709			−0.0393478
$807$	−15.7120	−	18.1326i	−0.553087	−	0.638297i
$808$	−4.97827	−	3.19934i	−0.175135	−	0.112552i
$809$	7.67660	−	53.3919i	0.269895	−	1.87716i	−0.179401	−	0.983776i	$-0.557416\pi$
$809$	7.67660	−	53.3919i	0.269895	−	1.87716i	0.449296	−	0.893383i	$-0.351675\pi$
$810$	0.492937	−	1.07938i	0.0173200	−	0.0379256i
$811$	7.03044	+	48.8978i	0.246872	+	1.71703i	0.616078	+	0.787685i	$0.288720\pi$
$811$	7.03044	+	48.8978i	0.246872	+	1.71703i	−0.369206	+	0.929347i	$0.620370\pi$
$812$	−33.3515	−	9.79288i	−1.17041	−	0.343663i
$813$	−19.0059	+	12.2144i	−0.666568	+	0.428377i
$814$	−6.86239	−	15.0265i	−0.240527	−	0.526680i
$815$	−19.5711	+	5.74658i	−0.685544	+	0.201294i
$816$	−2.50720	+	2.89347i	−0.0877697	+	0.101292i
$817$	9.05183	−	10.4464i	0.316683	−	0.365472i
$818$	10.5170	−	3.08807i	0.367718	−	0.107972i
$819$	0.319504	+	0.699616i	0.0111644	+	0.0244466i
$820$	17.5086	−	11.2521i	0.611428	−	0.392941i
$821$	−16.8019	−	4.93349i	−0.586391	−	0.172180i	−0.0249388	−	0.999689i	$-0.507939\pi$
$821$	−16.8019	−	4.93349i	−0.586391	−	0.172180i	−0.561453	+	0.827509i	$0.689757\pi$
$822$	−1.65217	−	11.4911i	−0.0576262	−	0.400799i
$823$	−5.65453	+	12.3817i	−0.197105	+	0.431599i	−0.982216	−	0.187756i	$-0.939879\pi$
$823$	−5.65453	+	12.3817i	−0.197105	+	0.431599i	0.785111	+	0.619355i	$0.212606\pi$
$824$	−1.44263	+	10.0337i	−0.0502564	+	0.349541i
$825$	−3.70683	−	2.38223i	−0.129055	−	0.0829387i
$826$	−5.16369	−	5.95921i	−0.179668	−	0.207347i
$827$	−22.5564			−0.784365			−0.392182	−	0.919888i	$-0.628280\pi$
$827$	−22.5564			−0.784365			−0.392182	+	0.919888i	$0.628280\pi$
$828$	0.880996	+	7.16279i	0.0306167	+	0.248924i
$829$	−49.2936			−1.71204			−0.856019	−	0.516944i	$-0.827070\pi$
$829$	−49.2936			−1.71204			−0.856019	+	0.516944i	$0.827070\pi$
$830$	−5.00691	−	5.77829i	−0.173793	−	0.200567i
$831$	1.75697	+	1.12914i	0.0609488	+	0.0391694i
$832$	−0.0523521	+	0.364117i	−0.00181498	+	0.0126235i
$833$	4.43985	−	9.72191i	0.153832	−	0.336844i
$834$	0.347094	+	2.41409i	0.0120189	+	0.0835931i
$835$	−21.3059	−	6.25597i	−0.737320	−	0.216497i
$836$	12.4002	−	7.96915i	0.428871	−	0.275619i
$837$	2.78578	+	6.10000i	0.0962905	+	0.210847i
$838$	−20.5579	+	6.03634i	−0.710161	+	0.208522i
$839$	3.73033	−	4.30503i	0.128785	−	0.148626i	−0.687694	−	0.726000i	$-0.741377\pi$
$839$	3.73033	−	4.30503i	0.128785	−	0.148626i	0.816480	+	0.577374i	$0.195923\pi$
$840$	8.84875	−	10.2120i	0.305311	−	0.352347i
$841$	−20.6712	+	6.06961i	−0.712800	+	0.209297i
$842$	7.08944	+	15.5237i	0.244318	+	0.534982i
$843$	16.4932	−	10.5995i	0.568055	−	0.365067i
$844$	19.7216	+	5.79079i	0.678847	+	0.199327i
$845$	−3.10625	−	21.6045i	−0.106858	−	0.743216i
$846$	3.88381	−	8.50436i	0.133528	−	0.292386i
$847$	3.15602	−	21.9506i	0.108442	−	0.754231i
$848$	0.569819	+	0.366201i	0.0195677	+	0.0125754i
$849$	−3.29042	−	3.79735i	−0.112927	−	0.130325i
$850$	4.56059			0.156427
$851$	−53.1751	+	14.4411i	−1.82282	+	0.495035i
$852$	−20.2385			−0.693360
$853$	−23.2854	−	26.8727i	−0.797275	−	0.920105i	0.200953	−	0.979601i	$-0.435596\pi$
$853$	−23.2854	−	26.8727i	−0.797275	−	0.920105i	−0.998229	+	0.0594960i	$0.981051\pi$
$854$	−9.33368	−	5.99839i	−0.319392	−	0.205261i
$855$	−1.15050	+	8.00192i	−0.0393463	+	0.273660i
$856$	13.7870	−	30.1892i	0.471229	−	1.03185i
$857$	3.63010	+	25.2479i	0.124002	+	0.862451i	0.952950	+	0.303126i	$0.0980304\pi$
$857$	3.63010	+	25.2479i	0.124002	+	0.862451i	−0.828949	+	0.559325i	$0.811060\pi$
$858$	0.326567	+	0.0958888i	0.0111488	+	0.00327359i
$859$	−28.7873	+	18.5005i	−0.982209	+	0.631227i	−0.930058	−	0.367412i	$-0.880244\pi$
$859$	−28.7873	+	18.5005i	−0.982209	+	0.631227i	−0.0521507	+	0.998639i	$0.516608\pi$
$860$	3.03914	+	6.65478i	0.103634	+	0.226926i
$861$	−25.5699	+	7.50800i	−0.871420	+	0.255872i
$862$	4.48854	−	5.18005i	0.152880	−	0.176433i
$863$	18.4346	−	21.2747i	0.627522	−	0.724199i	−0.349595	−	0.936901i	$-0.613681\pi$
$863$	18.4346	−	21.2747i	0.627522	−	0.724199i	0.977117	+	0.212702i	$0.0682263\pi$
$864$	5.59310	−	1.64228i	0.190281	−	0.0558716i
$865$	12.3578	+	27.0598i	0.420178	+	0.920061i
$866$	3.69562	−	2.37503i	0.125582	−	0.0807069i
$867$	7.64642	+	2.24519i	0.259686	+	0.0762507i
$868$	4.66609	+	32.4534i	0.158377	+	1.10154i
$869$	1.77531	−	3.88738i	0.0602232	−	0.131870i
$870$	1.20059	−	8.35027i	0.0407037	−	0.283101i
$871$	2.97272	+	1.91045i	0.100727	+	0.0647332i
$872$	−25.5622	−	29.5004i	−0.865647	−	0.999009i
$873$	1.81486			0.0614237
$874$	6.41942	+	14.8518i	0.217140	+	0.502369i
$875$	39.2090			1.32551
$876$	4.37869	+	5.05327i	0.147942	+	0.170734i
$877$	−12.5229	−	8.04799i	−0.422869	−	0.271761i	0.311852	−	0.950131i	$-0.399051\pi$
$877$	−12.5229	−	8.04799i	−0.422869	−	0.271761i	−0.734721	+	0.678369i	$0.762687\pi$
$878$	−1.67471	+	11.6478i	−0.0565186	+	0.393095i
$879$	1.22884	−	2.69078i	0.0414476	−	0.0907577i
$880$	0.624675	+	4.34471i	0.0210578	+	0.146460i
$881$	−25.0561	−	7.35715i	−0.844163	−	0.247869i	−0.169073	−	0.985604i	$-0.554077\pi$
$881$	−25.0561	−	7.35715i	−0.844163	−	0.247869i	−0.675090	+	0.737735i	$0.735895\pi$
$882$	−2.10543	+	1.35308i	−0.0708934	+	0.0455604i
$883$	−14.3890	−	31.5074i	−0.484227	−	1.06031i	−0.981279	−	0.192589i	$-0.938311\pi$
$883$	−14.3890	−	31.5074i	−0.484227	−	1.06031i	0.497052	−	0.867721i	$-0.334416\pi$
$884$	1.02711	−	0.301587i	0.0345455	−	0.0101435i
$885$	−3.80828	+	4.39499i	−0.128014	+	0.147736i
$886$	14.0055	−	16.1632i	0.470525	−	0.543014i
$887$	52.5394	−	15.4270i	1.76410	−	0.517987i	0.771164	−	0.636636i	$-0.219675\pi$
$887$	52.5394	−	15.4270i	1.76410	−	0.517987i	0.992936	+	0.118650i	$0.0378565\pi$
$888$	11.7715	+	25.7760i	0.395026	+	0.864986i
$889$	14.5473	−	9.34899i	0.487901	−	0.313555i
$890$	−2.85677	−	0.838822i	−0.0957590	−	0.0281174i
$891$	−0.290775	−	2.02238i	−0.00974132	−	0.0677524i
$892$	−7.12696	+	15.6059i	−0.238628	+	0.522523i
$893$	−9.06471	+	63.0465i	−0.303339	+	2.10977i
$894$	−1.81696	−	1.16769i	−0.0607681	−	0.0390533i
$895$	11.8912	+	13.7232i	0.397479	+	0.458715i
$896$	34.3261			1.14676
$897$	0.492593	−	1.02283i	0.0164472	−	0.0341513i
$898$	−12.1172			−0.404355
$899$	31.2210	+	36.0310i	1.04128	+	1.20170i
$900$	2.73007	+	1.75451i	0.0910025	+	0.0584837i
$901$	−0.227376	+	1.58143i	−0.00757499	+	0.0526852i
$902$	−4.89899	+	10.7273i	−0.163118	+	0.357179i
$903$	−1.33315	−	9.27228i	−0.0443645	−	0.308562i
$904$	30.6084	+	8.98744i	1.01802	+	0.298918i
$905$	2.02376	−	1.30059i	0.0672722	−	0.0432332i
$906$	−0.554166	−	1.21345i	−0.0184109	−	0.0403143i
$907$	9.75887	−	2.86546i	0.324038	−	0.0951461i	−0.115668	−	0.993288i	$-0.536901\pi$
$907$	9.75887	−	2.86546i	0.324038	−	0.0951461i	0.439706	+	0.898142i	$0.355083\pi$
$908$	−1.56620	+	1.80749i	−0.0519761	+	0.0599836i
$909$	1.57126	−	1.81333i	0.0521153	−	0.0601443i
$910$	−0.875680	+	0.257123i	−0.0290285	+	0.00852354i
$911$	12.8358	+	28.1066i	0.425271	+	0.931213i	0.994071	+	0.108737i	$0.0346806\pi$
$911$	12.8358	+	28.1066i	0.425271	+	0.931213i	−0.568800	+	0.822476i	$0.692592\pi$
$912$	−5.13834	+	3.30221i	−0.170147	+	0.109347i
$913$	−12.6317	−	3.70899i	−0.418047	−	0.122750i
$914$	−1.15583	−	8.03900i	−0.0382316	−	0.265907i
$915$	−3.39921	+	7.44322i	−0.112374	+	0.246065i
$916$	5.61721	−	39.0686i	0.185598	−	1.29086i
$917$	12.4122	+	7.97681i	0.409886	+	0.263417i
$918$	1.38485	+	1.59820i	0.0457067	+	0.0527484i
$919$	1.12747			0.0371917			0.0185959	−	0.999827i	$-0.494080\pi$
$919$	1.12747			0.0371917			0.0185959	+	0.999827i	$0.494080\pi$
$920$	−19.9410	−	0.407216i	−0.657434	−	0.0134255i
$921$	23.6903			0.780622
$922$	−16.7375	−	19.3161i	−0.551221	−	0.636143i
$923$	2.67831	+	1.72124i	0.0881575	+	0.0566554i
$924$	1.42166	−	9.88786i	0.0467692	−	0.325287i
$925$	−10.2931	+	22.5388i	−0.338436	+	0.741071i
$926$	−1.47668	−	10.2705i	−0.0485268	−	0.337511i
$927$	−3.94360	−	1.15795i	−0.129525	−	0.0380320i
$928$	34.8636	−	22.4055i	1.14445	−	0.735495i
$929$	4.61059	+	10.0958i	0.151269	+	0.331232i	0.970062	−	0.242856i	$-0.0780841\pi$
$929$	4.61059	+	10.0958i	0.151269	+	0.331232i	−0.818794	+	0.574088i	$0.805357\pi$
$930$	−7.63511	+	2.24187i	−0.250365	+	0.0735138i
$931$	11.1658	−	12.8860i	0.365944	−	0.422322i
$932$	−9.80417	+	11.3146i	−0.321146	+	0.370623i
$933$	−25.1518	+	7.38522i	−0.823431	+	0.241781i
$934$	2.37072	+	5.19115i	0.0775723	+	0.169860i
$935$	−8.70994	+	5.59754i	−0.284846	+	0.183059i
$936$	−0.560182	−	0.164484i	−0.0183101	−	0.00537634i
$937$	−5.05507	−	35.1588i	−0.165142	−	1.14859i	−0.888755	−	0.458382i	$-0.848429\pi$
$937$	−5.05507	−	35.1588i	−0.165142	−	1.14859i	0.723613	−	0.690206i	$-0.242480\pi$
$938$	−14.1783	+	31.0462i	−0.462939	+	1.01370i
$939$	0.942904	−	6.55804i	0.0307705	−	0.214014i
$940$	−28.3603	−	18.2261i	−0.925012	−	0.594469i
$941$	−37.5077	−	43.2862i	−1.22272	−	1.41109i	−0.882217	−	0.470844i	$-0.843950\pi$
$941$	−37.5077	−	43.2862i	−1.22272	−	1.41109i	−0.340499	−	0.940245i	$-0.610596\pi$
$942$	−1.51847			−0.0494744
$943$	32.6505	+	21.9379i	1.06325	+	0.714396i
$944$	−4.39379			−0.143006
$945$	3.58780	+	4.14054i	0.116711	+	0.134692i
$946$	−3.48733	−	2.24117i	−0.113383	−	0.0728668i
$947$	3.46314	−	24.0867i	0.112537	−	0.782712i	−0.852900	−	0.522075i	$-0.825158\pi$
$947$	3.46314	−	24.0867i	0.112537	−	0.782712i	0.965437	−	0.260637i	$-0.0839327\pi$
$948$	−1.30751	+	2.86305i	−0.0424660	+	0.0929877i
$949$	−0.149693	−	1.04113i	−0.00485923	−	0.0337967i
$950$	6.98101	+	2.04981i	0.226494	+	0.0665046i
$951$	9.34023	−	6.00260i	0.302878	−	0.194648i
$952$	10.0036	+	21.9049i	0.324220	+	0.709942i
$953$	47.7219	−	14.0124i	1.54586	−	0.453906i	0.606002	−	0.795463i	$-0.292772\pi$
$953$	47.7219	−	14.0124i	1.54586	−	0.453906i	0.939861	+	0.341557i	$0.110954\pi$
$954$	0.245003	−	0.282748i	0.00793226	−	0.00915431i
$955$	−15.3421	+	17.7058i	−0.496460	+	0.572945i
$956$	16.6714	−	4.89516i	0.539191	−	0.158321i
$957$	−6.03425	−	13.2132i	−0.195060	−	0.427121i
$958$	18.3135	−	11.7693i	0.591681	−	0.380250i
$959$	51.4301	+	15.1012i	1.66077	+	0.487645i
$960$	0.372923	+	2.59374i	0.0120360	+	0.0837125i
$961$	5.80356	−	12.7080i	0.187212	−	0.409936i
$962$	0.272377	−	1.89443i	0.00878180	−	0.0610787i
$963$	11.3204	+	7.27515i	0.364793	+	0.234438i
$964$	−5.41725	−	6.25183i	−0.174478	−	0.201358i
$965$	−13.6512			−0.439447
$966$	10.4557	+	3.30340i	0.336407	+	0.106285i
$967$	46.0629			1.48128			0.740641	−	0.671901i	$-0.234522\pi$
$967$	46.0629			1.48128			0.740641	+	0.671901i	$0.234522\pi$
$968$	11.0238	+	12.7221i	0.354318	+	0.408905i
$969$	−12.1201	−	7.78913i	−0.389355	−	0.250223i
$970$	−0.306481	+	2.13162i	−0.00984050	+	0.0684422i
$971$	−10.3764	+	22.7210i	−0.332993	+	0.729153i	−0.999872	−	0.0160132i	$-0.994903\pi$
$971$	−10.3764	+	22.7210i	−0.332993	+	0.729153i	0.666879	+	0.745166i	$0.267630\pi$
$972$	0.214155	+	1.48948i	0.00686904	+	0.0477752i
$973$	−10.8046	−	3.17251i	−0.346379	−	0.101706i
$974$	−9.38093	+	6.02876i	−0.300584	+	0.193174i
$975$	−0.212073	−	0.464375i	−0.00679176	−	0.0148719i
$976$	−5.93193	+	1.74177i	−0.189876	+	0.0557528i
$977$	15.7122	−	18.1328i	0.502678	−	0.580121i	−0.446531	−	0.894768i	$-0.647341\pi$
$977$	15.7122	−	18.1328i	0.502678	−	0.580121i	0.949209	+	0.314647i	$0.101886\pi$
$978$	−5.57432	+	6.43311i	−0.178247	+	0.205708i
$979$	−4.91894	+	1.44433i	−0.157210	+	0.0461611i
$980$	3.74890	+	8.20894i	0.119754	+	0.262225i
$981$	13.3145	−	8.55668i	0.425098	−	0.273194i
$982$	0.507523	+	0.149022i	0.0161957	+	0.00475549i
$983$	−0.868902	−	6.04334i	−0.0277137	−	0.192753i	0.971261	−	0.238015i	$-0.0764967\pi$
$983$	−0.868902	−	6.04334i	−0.0277137	−	0.192753i	−0.998975	+	0.0452623i	$0.985588\pi$
$984$	8.40355	−	18.4012i	0.267895	−	0.586609i
$985$	0.426542	−	2.96667i	0.0135908	−	0.0945258i
$986$	12.6478	+	8.12822i	0.402787	+	0.258855i
$987$	28.2680	+	32.6230i	0.899780	+	1.03840i
$988$	1.70778			0.0543316
$989$	−9.26634	+	10.2628i	−0.294652	+	0.326339i
$990$	2.42447			0.0770546
$991$	10.5406	+	12.1645i	0.334833	+	0.386418i	0.898052	−	0.439890i	$-0.144983\pi$
$991$	10.5406	+	12.1645i	0.334833	+	0.386418i	−0.563219	+	0.826308i	$0.690437\pi$
$992$	−32.8853	−	21.1341i	−1.04411	−	0.671008i
$993$	−3.19598	+	22.2285i	−0.101421	+	0.705400i
$994$	−12.7741	+	27.9715i	−0.405171	+	0.887201i
$995$	1.57955	+	10.9860i	0.0500751	+	0.348280i
$996$	9.30320	+	2.73167i	0.294783	+	0.0865562i
$997$	14.2420	−	9.15281i	0.451050	−	0.289872i	−0.295326	−	0.955397i	$-0.595428\pi$
$997$	14.2420	−	9.15281i	0.451050	−	0.289872i	0.746376	+	0.665524i	$0.231792\pi$
$998$	9.04144	+	19.7980i	0.286202	+	0.626694i
$999$	−11.0240	+	3.23693i	−0.348783	+	0.102412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.c.13.2	✓	20
3.2	odd	2		207.2.i.d.82.1		20
23.4	even	11		1587.2.a.u.1.5		10
23.16	even	11	inner	69.2.e.c.16.2	yes	20
23.19	odd	22		1587.2.a.t.1.5		10
69.50	odd	22		4761.2.a.bt.1.6		10
69.62	odd	22		207.2.i.d.154.1		20
69.65	even	22		4761.2.a.bu.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.13.2	✓	20	1.1	even	1	trivial
69.2.e.c.16.2	yes	20	23.16	even	11	inner
207.2.i.d.82.1		20	3.2	odd	2
207.2.i.d.154.1		20	69.62	odd	22
1587.2.a.t.1.5		10	23.19	odd	22
1587.2.a.u.1.5		10	23.4	even	11
4761.2.a.bt.1.6		10	69.50	odd	22
4761.2.a.bu.1.6		10	69.65	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)

\(f(q)\)	\(=\)	\(q+(0.460828 + 0.531824i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.214155 - 1.48948i) q^{4} +(-0.700489 + 1.53386i) q^{5} +(0.100148 + 0.696541i) q^{6} +(-3.11747 - 0.915371i) q^{7} +(2.07482 - 1.33341i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.460828 + 0.531824i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.214155 - 1.48948i) q^{4} +(-0.700489 + 1.53386i) q^{5} +(0.100148 + 0.696541i) q^{6} +(-3.11747 - 0.915371i) q^{7} +(2.07482 - 1.33341i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-1.13855 + 0.334308i) q^{10} +(-1.33800 + 1.54413i) q^{11} +(0.985435 - 1.13725i) q^{12} +(-0.227131 + 0.0666916i) q^{13} +(-0.949800 - 2.07977i) q^{14} +(-1.41856 + 0.911650i) q^{15} +(-1.22242 - 0.358935i) q^{16} +(-0.427674 - 2.97454i) q^{17} +(-0.292329 + 0.640112i) q^{18} +(0.682288 - 4.74542i) q^{19} +(2.13464 + 1.37185i) q^{20} +(-2.12769 - 2.45549i) q^{21} -1.43779 q^{22} +(-0.779295 + 4.73209i) q^{23} +2.46634 q^{24} +(1.41227 + 1.62985i) q^{25} +(-0.140136 - 0.0900602i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-2.03105 + 4.44738i) q^{28} +(1.01178 + 7.03706i) q^{29} +(-1.13855 - 0.334308i) q^{30} +(5.64145 - 3.62554i) q^{31} +(-2.42155 - 5.30245i) q^{32} +(-1.96042 + 0.575630i) q^{33} +(1.38485 - 1.59820i) q^{34} +(3.58780 - 4.14054i) q^{35} +(1.44385 - 0.423951i) q^{36} +(4.77286 + 10.4511i) q^{37} +(2.83815 - 1.82397i) q^{38} +(-0.227131 - 0.0666916i) q^{39} +(0.591865 + 4.11651i) q^{40} +(3.40729 - 7.46093i) q^{41} +(0.325387 - 2.26312i) q^{42} +(2.42547 + 1.55876i) q^{43} +(2.01342 + 2.32361i) q^{44} -1.68624 q^{45} +(-2.87576 + 1.76623i) q^{46} -13.2857 q^{47} +(-0.834310 - 0.962845i) q^{48} +(2.99192 + 1.92279i) q^{49} +(-0.215978 + 1.50216i) q^{50} +(1.24837 - 2.73356i) q^{51} +(0.0506948 + 0.352590i) q^{52} +(-0.510122 - 0.149785i) q^{53} +(-0.591994 + 0.380451i) q^{54} +(-1.43123 - 3.13395i) q^{55} +(-7.68874 + 2.25762i) q^{56} +(3.13954 - 3.62323i) q^{57} +(-3.27622 + 3.78096i) q^{58} +(3.30904 - 0.971623i) q^{59} +(1.05410 + 2.30815i) q^{60} +(4.08228 - 2.62352i) q^{61} +(4.52789 + 1.32951i) q^{62} +(-0.462392 - 3.21601i) q^{63} +(0.645553 - 1.41356i) q^{64} +(0.0568072 - 0.395103i) q^{65} +(-1.20955 - 0.777330i) q^{66} +(-9.77557 - 11.2816i) q^{67} -4.52211 q^{68} +(-3.21395 + 3.55957i) q^{69} +3.85540 q^{70} +(-8.80741 - 10.1643i) q^{71} +(2.07482 + 1.33341i) q^{72} +(-0.632363 + 4.39818i) q^{73} +(-3.35868 + 7.35449i) q^{74} +(0.306915 + 2.13464i) q^{75} +(-6.92211 - 2.03251i) q^{76} +(5.58462 - 3.58902i) q^{77} +(-0.0692000 - 0.151527i) q^{78} +(-2.00690 + 0.589280i) q^{79} +(1.40685 - 1.62359i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(5.53808 - 1.62613i) q^{82} +(2.67666 + 5.86108i) q^{83} +(-4.11307 + 2.64331i) q^{84} +(4.86210 + 1.42764i) q^{85} +(0.288742 + 2.00824i) q^{86} +(-2.95336 + 6.46696i) q^{87} +(-0.717150 + 4.98789i) q^{88} +(2.11082 + 1.35654i) q^{89} +(-0.777067 - 0.896783i) q^{90} +0.769120 q^{91} +(6.88149 + 2.17415i) q^{92} +6.70601 q^{93} +(-6.12245 - 7.06568i) q^{94} +(6.80086 + 4.37065i) q^{95} +(0.829585 - 5.76989i) q^{96} +(0.753920 - 1.65086i) q^{97} +(0.356175 + 2.47725i) q^{98} +(-1.96042 - 0.575630i) 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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