LMFDB - Embedded newform 65.2.o.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(2,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("65.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.o (of order $12$, degree $4$, 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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
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} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.2
Root			$-1.83163i$ of defining polynomial
Character	$\chi$	$=$	65.33
Dual form			65.2.o.a.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.915816 + 1.58624i) q^{2} +(1.91432 - 0.512942i) q^{3} +(-0.677439 - 1.17336i) q^{4} +(1.45480 - 1.69810i) q^{5} +(-0.939520 + 3.50634i) q^{6} +(-3.06478 + 1.76945i) q^{7} -1.18163 q^{8} +(0.803451 - 0.463873i) q^{9} +O(q^{10})$	\(q+(-0.915816 + 1.58624i) q^{2} +(1.91432 - 0.512942i) q^{3} +(-0.677439 - 1.17336i) q^{4} +(1.45480 - 1.69810i) q^{5} +(-0.939520 + 3.50634i) q^{6} +(-3.06478 + 1.76945i) q^{7} -1.18163 q^{8} +(0.803451 - 0.463873i) q^{9} +(1.36126 + 3.86282i) q^{10} +(-1.00269 - 3.74209i) q^{11} +(-1.89870 - 1.89870i) q^{12} +(0.573112 + 3.55971i) q^{13} -6.48197i q^{14} +(1.91394 - 3.99694i) q^{15} +(2.43703 - 4.22106i) q^{16} +(0.524334 - 1.95684i) q^{17} +1.69929i q^{18} +(-0.518968 - 0.139057i) q^{19} +(-2.97802 - 0.556646i) q^{20} +(-4.95936 + 4.95936i) q^{21} +(6.85414 + 1.83656i) q^{22} +(0.0788026 + 0.294095i) q^{23} +(-2.26202 + 0.606106i) q^{24} +(-0.767094 - 4.94081i) q^{25} +(-6.17142 - 2.35095i) q^{26} +(-2.90402 + 2.90402i) q^{27} +(4.15240 + 2.39739i) q^{28} +(1.71273 + 0.988843i) q^{29} +(4.58730 + 6.69643i) q^{30} +(4.13563 + 4.13563i) q^{31} +(3.28212 + 5.68479i) q^{32} +(-3.83895 - 6.64926i) q^{33} +(2.62382 + 2.62382i) q^{34} +(-1.45395 + 7.77851i) q^{35} +(-1.08858 - 0.628491i) q^{36} +(4.69189 + 2.70887i) q^{37} +(0.695857 - 0.695857i) q^{38} +(2.92305 + 6.52047i) q^{39} +(-1.71904 + 2.00652i) q^{40} +(0.649884 - 0.174136i) q^{41} +(-3.32487 - 12.4086i) q^{42} +(-8.51164 - 2.28069i) q^{43} +(-3.71155 + 3.71155i) q^{44} +(0.381161 - 2.03919i) q^{45} +(-0.538675 - 0.144337i) q^{46} -9.75201i q^{47} +(2.50011 - 9.33053i) q^{48} +(2.76192 - 4.78379i) q^{49} +(8.53982 + 3.30807i) q^{50} -4.01498i q^{51} +(3.78857 - 3.08395i) q^{52} +(3.16254 + 3.16254i) q^{53} +(-1.94693 - 7.26602i) q^{54} +(-7.81317 - 3.74134i) q^{55} +(3.62143 - 2.09083i) q^{56} -1.06480 q^{57} +(-3.13709 + 1.81120i) q^{58} +(-3.14703 + 11.7449i) q^{59} +(-5.98642 + 0.461950i) q^{60} +(1.44316 + 2.49963i) q^{61} +(-10.3476 + 2.77263i) q^{62} +(-1.64160 + 2.84334i) q^{63} -2.27514 q^{64} +(6.87851 + 4.20548i) q^{65} +14.0631 q^{66} +(-1.14494 + 1.98310i) q^{67} +(-2.65128 + 0.710408i) q^{68} +(0.301707 + 0.522573i) q^{69} +(-11.0070 - 9.43000i) q^{70} +(-1.19607 + 4.46378i) q^{71} +(-0.949380 + 0.548125i) q^{72} +14.7546 q^{73} +(-8.59382 + 4.96165i) q^{74} +(-4.00281 - 9.06483i) q^{75} +(0.188405 + 0.703137i) q^{76} +(9.69449 + 9.69449i) q^{77} +(-13.0200 - 1.33490i) q^{78} -1.59718i q^{79} +(-3.62239 - 10.2791i) q^{80} +(-5.46126 + 9.45918i) q^{81} +(-0.318953 + 1.19035i) q^{82} -7.57341i q^{83} +(9.17877 + 2.45944i) q^{84} +(-2.56011 - 3.73719i) q^{85} +(11.4128 - 11.4128i) q^{86} +(3.78593 + 1.01444i) q^{87} +(1.18481 + 4.42176i) q^{88} +(-4.54423 + 1.21762i) q^{89} +(2.88556 + 2.47213i) q^{90} +(-8.05520 - 9.89564i) q^{91} +(0.291695 - 0.291695i) q^{92} +(10.0383 + 5.79560i) q^{93} +(15.4690 + 8.93105i) q^{94} +(-0.991129 + 0.678959i) q^{95} +(9.19900 + 9.19900i) q^{96} +(-8.91268 - 15.4372i) q^{97} +(5.05883 + 8.76215i) q^{98} +(-2.54147 - 2.54147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	−0.915816	+	1.58624i	−0.647580	+	1.12164i	0.336119	+	0.941819i	$0.390885\pi$
$2$	−0.915816	+	1.58624i	−0.647580	+	1.12164i	−0.983699	+	0.179822i	$0.942448\pi$
$3$	1.91432	−	0.512942i	1.10524	−	0.296147i	0.340341	−	0.940302i	$-0.389458\pi$
$3$	1.91432	−	0.512942i	1.10524	−	0.296147i	0.764895	+	0.644155i	$0.222791\pi$
$4$	−0.677439	−	1.17336i	−0.338719	−	0.586679i
$5$	1.45480	−	1.69810i	0.650608	−	0.759414i
$5$	1.45480	−	1.69810i	0.650608	−	0.759414i
$6$	−0.939520	+	3.50634i	−0.383558	+	1.43146i
$7$	−3.06478	+	1.76945i	−1.15838	+	0.668790i	−0.950915	−	0.309453i	$-0.899854\pi$
$7$	−3.06478	+	1.76945i	−1.15838	+	0.668790i	−0.207464	+	0.978243i	$0.566521\pi$
$8$	−1.18163			−0.417769
$9$	0.803451	−	0.463873i	0.267817	−	0.154624i
$10$	1.36126	+	3.86282i	0.430469	+	1.22153i
$11$	−1.00269	−	3.74209i	−0.302323	−	1.12828i	−0.935226	−	0.354053i	$-0.884803\pi$
$11$	−1.00269	−	3.74209i	−0.302323	−	1.12828i	0.632903	−	0.774231i	$-0.281863\pi$
$12$	−1.89870	−	1.89870i	−0.548108	−	0.548108i
$13$	0.573112	+	3.55971i	0.158953	+	0.987286i
$13$	0.573112	+	3.55971i	0.158953	+	0.987286i
$14$		−	6.48197i		−	1.73238i
$15$	1.91394	−	3.99694i	0.494177	−	1.03201i
$16$	2.43703	−	4.22106i	0.609258	−	1.05527i
$17$	0.524334	−	1.95684i	0.127170	−	0.474603i	−0.872738	−	0.488189i	$-0.837658\pi$
$17$	0.524334	−	1.95684i	0.127170	−	0.474603i	0.999908	+	0.0135853i	$0.00432448\pi$
$18$			1.69929i			0.400526i
$19$	−0.518968	−	0.139057i	−0.119059	−	0.0319019i	0.198797	−	0.980041i	$-0.436296\pi$
$19$	−0.518968	−	0.139057i	−0.119059	−	0.0319019i	−0.317857	+	0.948139i	$0.602963\pi$
$20$	−2.97802	−	0.556646i	−0.665906	−	0.124470i
$21$	−4.95936	+	4.95936i	−1.08222	+	1.08222i
$22$	6.85414	+	1.83656i	1.46131	+	0.391556i
$23$	0.0788026	+	0.294095i	0.0164315	+	0.0613231i	0.973655	−	0.228027i	$-0.0732275\pi$
$23$	0.0788026	+	0.294095i	0.0164315	+	0.0613231i	−0.957223	+	0.289350i	$0.906561\pi$
$24$	−2.26202	+	0.606106i	−0.461733	+	0.123721i
$25$	−0.767094	−	4.94081i	−0.153419	−	0.988161i
$26$	−6.17142	−	2.35095i	−1.21032	−	0.461059i
$27$	−2.90402	+	2.90402i	−0.558879	+	0.558879i
$28$	4.15240	+	2.39739i	0.784730	+	0.453064i
$29$	1.71273	+	0.988843i	0.318045	+	0.183624i	0.650521	−	0.759488i	$-0.274551\pi$
$29$	1.71273	+	0.988843i	0.318045	+	0.183624i	−0.332476	+	0.943112i	$0.607884\pi$
$30$	4.58730	+	6.69643i	0.837522	+	1.22260i
$31$	4.13563	+	4.13563i	0.742781	+	0.742781i	0.973112	−	0.230331i	$-0.0739810\pi$
$31$	4.13563	+	4.13563i	0.742781	+	0.742781i	−0.230331	+	0.973112i	$0.573981\pi$
$32$	3.28212	+	5.68479i	0.580202	+	1.00494i
$33$	−3.83895	−	6.64926i	−0.668276	−	1.15749i
$34$	2.62382	+	2.62382i	0.449982	+	0.449982i
$35$	−1.45395	+	7.77851i	−0.245762	+	1.31481i
$36$	−1.08858	−	0.628491i	−0.181430	−	0.104748i
$37$	4.69189	+	2.70887i	0.771342	+	0.445335i	0.833353	−	0.552741i	$-0.186418\pi$
$37$	4.69189	+	2.70887i	0.771342	+	0.445335i	−0.0620109	+	0.998075i	$0.519751\pi$
$38$	0.695857	−	0.695857i	0.112883	−	0.112883i
$39$	2.92305	+	6.52047i	0.468062	+	1.04411i
$40$	−1.71904	+	2.00652i	−0.271803	+	0.317259i
$41$	0.649884	−	0.174136i	0.101495	−	0.0271955i	−0.207714	−	0.978190i	$-0.566602\pi$
$41$	0.649884	−	0.174136i	0.101495	−	0.0271955i	0.309209	+	0.950994i	$0.399936\pi$
$42$	−3.32487	−	12.4086i	−0.513039	−	1.91469i
$43$	−8.51164	−	2.28069i	−1.29801	−	0.347802i	−0.457314	−	0.889305i	$-0.651189\pi$
$43$	−8.51164	−	2.28069i	−1.29801	−	0.347802i	−0.840698	+	0.541504i	$0.817855\pi$
$44$	−3.71155	+	3.71155i	−0.559538	+	0.559538i
$45$	0.381161	−	2.03919i	0.0568201	−	0.303984i
$46$	−0.538675	−	0.144337i	−0.0794232	−	0.0212814i
$47$		−	9.75201i		−	1.42248i	−0.702951	−	0.711238i	$-0.748135\pi$
$47$		−	9.75201i		−	1.42248i	0.702951	−	0.711238i	$-0.251865\pi$
$48$	2.50011	−	9.33053i	0.360860	−	1.34675i
$49$	2.76192	−	4.78379i	0.394561	−	0.683399i
$50$	8.53982	+	3.30807i	1.20771	+	0.467832i
$51$		−	4.01498i		−	0.562209i
$52$	3.78857	−	3.08395i	0.525380	−	0.427667i
$53$	3.16254	+	3.16254i	0.434409	+	0.434409i	0.890125	−	0.455716i	$-0.150617\pi$
$53$	3.16254	+	3.16254i	0.434409	+	0.434409i	−0.455716	+	0.890125i	$0.650617\pi$
$54$	−1.94693	−	7.26602i	−0.264943	−	0.988781i
$55$	−7.81317	−	3.74134i	−1.05353	−	0.504482i
$56$	3.62143	−	2.09083i	0.483934	−	0.279399i
$57$	−1.06480			−0.141036
$58$	−3.13709	+	1.81120i	−0.411919	+	0.237822i
$59$	−3.14703	+	11.7449i	−0.409708	+	1.52905i	0.385495	+	0.922710i	$0.374031\pi$
$59$	−3.14703	+	11.7449i	−0.409708	+	1.52905i	−0.795203	+	0.606343i	$0.792636\pi$
$60$	−5.98642	+	0.461950i	−0.772844	+	0.0596374i
$61$	1.44316	+	2.49963i	0.184778	+	0.320044i	0.943502	−	0.331368i	$-0.107510\pi$
$61$	1.44316	+	2.49963i	0.184778	+	0.320044i	−0.758724	+	0.651412i	$0.774177\pi$
$62$	−10.3476	+	2.77263i	−1.31414	+	0.352124i
$63$	−1.64160	+	2.84334i	−0.206822	+	0.358227i
$64$	−2.27514			−0.284392
$65$	6.87851	+	4.20548i	0.853175	+	0.521625i
$66$	14.0631			1.73105
$67$	−1.14494	+	1.98310i	−0.139877	+	0.242274i	−0.927450	−	0.373947i	$-0.878004\pi$
$67$	−1.14494	+	1.98310i	−0.139877	+	0.242274i	0.787573	+	0.616222i	$0.211337\pi$
$68$	−2.65128	+	0.710408i	−0.321515	+	0.0861496i
$69$	0.301707	+	0.522573i	0.0363213	+	0.0629104i
$70$	−11.0070	−	9.43000i	−1.31559	−	1.12710i
$71$	−1.19607	+	4.46378i	−0.141947	+	0.529753i	0.857925	+	0.513774i	$0.171753\pi$
$71$	−1.19607	+	4.46378i	−0.141947	+	0.529753i	−0.999872	+	0.0159789i	$0.994914\pi$
$72$	−0.949380	+	0.548125i	−0.111886	+	0.0645972i
$73$	14.7546			1.72690			0.863449	−	0.504436i	$-0.168299\pi$
$73$	14.7546			1.72690			0.863449	+	0.504436i	$0.168299\pi$
$74$	−8.59382	+	4.96165i	−0.999011	+	0.576780i
$75$	−4.00281	−	9.06483i	−0.462205	−	1.04672i
$76$	0.188405	+	0.703137i	0.0216115	+	0.0806554i
$77$	9.69449	+	9.69449i	1.10479	+	1.10479i
$78$	−13.0200	−	1.33490i	−1.47422	−	0.151147i
$79$		−	1.59718i		−	0.179696i	−0.995955	−	0.0898482i	$-0.971362\pi$
$79$		−	1.59718i		−	0.179696i	0.995955	−	0.0898482i	$-0.0286382\pi$
$80$	−3.62239	−	10.2791i	−0.404995	−	1.14924i
$81$	−5.46126	+	9.45918i	−0.606807	+	1.05102i
$82$	−0.318953	+	1.19035i	−0.0352225	+	0.131452i
$83$		−	7.57341i		−	0.831290i	−0.909527	−	0.415645i	$-0.863556\pi$
$83$		−	7.57341i		−	0.831290i	0.909527	−	0.415645i	$-0.136444\pi$
$84$	9.17877	+	2.45944i	1.00149	+	0.268347i
$85$	−2.56011	−	3.73719i	−0.277683	−	0.405355i
$86$	11.4128	−	11.4128i	1.23068	−	1.23068i
$87$	3.78593	+	1.01444i	0.405895	+	0.108759i
$88$	1.18481	+	4.42176i	0.126301	+	0.471361i
$89$	−4.54423	+	1.21762i	−0.481687	+	0.129068i	−0.491488	−	0.870884i	$-0.663547\pi$
$89$	−4.54423	+	1.21762i	−0.481687	+	0.129068i	0.00980081	+	0.999952i	$0.496880\pi$
$90$	2.88556	+	2.47213i	0.304165	+	0.260586i
$91$	−8.05520	−	9.89564i	−0.844415	−	1.03735i
$92$	0.291695	−	0.291695i	0.0304113	−	0.0304113i
$93$	10.0383	+	5.79560i	1.04092	+	0.600976i
$94$	15.4690	+	8.93105i	1.59551	+	0.921167i
$95$	−0.991129	+	0.678959i	−0.101688	+	0.0696597i
$96$	9.19900	+	9.19900i	0.938869	+	0.938869i
$97$	−8.91268	−	15.4372i	−0.904945	−	1.56741i	−0.820991	−	0.570942i	$-0.806578\pi$
$97$	−8.91268	−	15.4372i	−0.904945	−	1.56741i	−0.0839547	−	0.996470i	$-0.526755\pi$
$98$	5.05883	+	8.76215i	0.511019	+	0.885111i
$99$	−2.54147	−	2.54147i	−0.255427	−	0.255427i
$100$	−5.27768	+	4.24717i	−0.527768	+	0.424717i
$101$	−3.94379	−	2.27695i	−0.392421	−	0.226565i	0.290787	−	0.956788i	$-0.406083\pi$
$101$	−3.94379	−	2.27695i	−0.392421	−	0.226565i	−0.683209	+	0.730223i	$0.739416\pi$
$102$	6.36872	+	3.67698i	0.630597	+	0.364075i
$103$	−9.79285	+	9.79285i	−0.964918	+	0.964918i	−0.999405	−	0.0344872i	$-0.989020\pi$
$103$	−9.79285	+	9.79285i	−0.964918	+	0.964918i	0.0344872	+	0.999405i	$0.489020\pi$
$104$	−0.677205	−	4.20625i	−0.0664055	−	0.412457i
$105$	1.20660	+	15.6364i	0.117752	+	1.52596i
$106$	−7.91286	+	2.12024i	−0.768565	+	0.205936i
$107$	−1.82991	−	6.82933i	−0.176904	−	0.660216i	−0.996219	−	0.0868725i	$-0.972313\pi$
$107$	−1.82991	−	6.82933i	−0.176904	−	0.660216i	0.819315	−	0.573344i	$-0.194354\pi$
$108$	5.37475	+	1.44016i	0.517186	+	0.138580i
$109$	9.89281	−	9.89281i	0.947560	−	0.947560i	−0.0511324	−	0.998692i	$-0.516283\pi$
$109$	9.89281	−	9.89281i	0.947560	−	0.947560i	0.998692	+	0.0511324i	$0.0162830\pi$
$110$	13.0901	−	8.96719i	1.24809	−	0.854988i
$111$	10.3713	+	2.77898i	0.984399	+	0.263769i
$112$			17.2488i			1.62986i
$113$	0.593341	−	2.21438i	0.0558168	−	0.208311i	−0.932385	−	0.361466i	$-0.882277\pi$
$113$	0.593341	−	2.21438i	0.0558168	−	0.208311i	0.988202	+	0.153154i	$0.0489432\pi$
$114$	0.975161	−	1.68903i	0.0913322	−	0.158192i
$115$	0.614046	+	0.294036i	0.0572601	+	0.0274190i
$116$		−	2.67952i		−	0.248787i
$117$	2.11172	+	2.59420i	0.195229	+	0.239834i
$118$	−15.7481	−	15.7481i	−1.44973	−	1.44973i
$119$	1.85557	+	6.92507i	0.170099	+	0.634820i
$120$	−2.26156	+	4.72290i	−0.206452	+	0.431140i
$121$	−3.47160	+	2.00433i	−0.315600	+	0.182212i
$122$	−5.28668			−0.478633
$123$	1.15477	−	0.666705i	0.104122	−	0.0601148i
$124$	2.05094	−	7.65421i	0.184180	−	0.687368i
$125$	−9.50596	−	5.88530i	−0.850239	−	0.526397i
$126$	−3.00681	−	5.20795i	−0.267868	−	0.463961i
$127$	−1.24225	+	0.332860i	−0.110232	+	0.0295366i	−0.313513	−	0.949584i	$-0.601506\pi$
$127$	−1.24225	+	0.332860i	−0.110232	+	0.0295366i	0.203281	+	0.979120i	$0.434839\pi$
$128$	−4.48062	+	7.76067i	−0.396035	+	0.685953i
$129$	−17.4639			−1.53761
$130$	−12.9704	+	7.05953i	−1.13758	+	0.619162i
$131$	−5.59439			−0.488785			−0.244392	−	0.969676i	$-0.578588\pi$
$131$	−5.59439			−0.488785			−0.244392	+	0.969676i	$0.578588\pi$
$132$	−5.20131	+	9.00893i	−0.452716	+	0.784127i
$133$	1.83658	−	0.492109i	0.159251	−	0.0426713i
$134$	−2.09712	−	3.63231i	−0.181163	−	0.313784i
$135$	0.706541	+	9.15610i	0.0608094	+	0.788032i
$136$	−0.619567	+	2.31226i	−0.0531274	+	0.198274i
$137$	12.3757	−	7.14509i	1.05732	−	0.610446i	0.132633	−	0.991165i	$-0.457657\pi$
$137$	12.3757	−	7.14509i	1.05732	−	0.610446i	0.924691	+	0.380719i	$0.124324\pi$
$138$	−1.10523			−0.0940838
$139$	15.0832	−	8.70830i	1.27934	−	0.738629i	0.302615	−	0.953113i	$-0.402140\pi$
$139$	15.0832	−	8.70830i	1.27934	−	0.738629i	0.976727	+	0.214484i	$0.0688071\pi$
$140$	10.1119	−	3.56347i	0.854615	−	0.301168i
$141$	−5.00221	−	18.6685i	−0.421262	−	1.57217i
$142$	−5.98525	−	5.98525i	−0.502271	−	0.502271i
$143$	12.7461	−	5.71393i	1.06588	−	0.477823i
$144$		−	4.52189i		−	0.376824i
$145$	4.17084	−	1.46981i	0.346369	−	0.122061i
$146$	−13.5125	+	23.4044i	−1.11830	+	1.93696i
$147$	2.83341	−	10.5744i	0.233696	−	0.872165i
$148$		−	7.34036i		−	0.603374i
$149$	−12.6828	−	3.39833i	−1.03901	−	0.278402i	−0.301308	−	0.953527i	$-0.597423\pi$
$149$	−12.6828	−	3.39833i	−1.03901	−	0.278402i	−0.737704	+	0.675124i	$0.764090\pi$
$150$	18.0448	+	1.95230i	1.47335	+	0.159404i
$151$	0.765191	−	0.765191i	0.0622704	−	0.0622704i	−0.675286	−	0.737556i	$-0.735980\pi$
$151$	0.765191	−	0.765191i	0.0622704	−	0.0622704i	0.737556	+	0.675286i	$0.235980\pi$
$152$	0.613227	+	0.164314i	0.0497392	+	0.0133276i
$153$	−0.486448	−	1.81545i	−0.0393270	−	0.146770i
$154$	−24.2562	+	6.49942i	−1.95462	+	0.523738i
$155$	13.0392	−	1.00619i	1.04734	−	0.0808190i
$156$	5.67066	−	7.84700i	0.454016	−	0.628263i
$157$	3.03481	−	3.03481i	0.242204	−	0.242204i	−0.575557	−	0.817762i	$-0.695215\pi$
$157$	3.03481	−	3.03481i	0.242204	−	0.242204i	0.817762	+	0.575557i	$0.195215\pi$
$158$	2.53350	+	1.46272i	0.201555	+	0.116368i
$159$	7.67633	+	4.43193i	0.608773	+	0.351475i
$160$	14.4282	+	2.69689i	1.14065	+	0.213208i
$161$	−0.761901	−	0.761901i	−0.0600462	−	0.0600462i
$162$	−10.0030	−	17.3257i	−0.785912	−	1.36124i
$163$	−1.13179	−	1.96032i	−0.0886486	−	0.153544i	0.818292	−	0.574803i	$-0.194921\pi$
$163$	−1.13179	−	1.96032i	−0.0886486	−	0.153544i	−0.906940	+	0.421260i	$0.861588\pi$
$164$	−0.644580	−	0.644580i	−0.0503333	−	0.0503333i
$165$	−16.8760	−	3.15444i	−1.31380	−	0.245573i
$166$	12.0133	+	6.93585i	0.932409	+	0.538327i
$167$	−0.536563	−	0.309785i	−0.0415205	−	0.0239719i	0.479096	−	0.877762i	$-0.340965\pi$
$167$	−0.536563	−	0.309785i	−0.0415205	−	0.0239719i	−0.520617	+	0.853791i	$0.674298\pi$
$168$	5.86012	−	5.86012i	0.452118	−	0.452118i
$169$	−12.3431	+	4.08023i	−0.949468	+	0.313864i
$170$	8.27267	−	0.638370i	0.634485	−	0.0489608i
$171$	−0.481470	+	0.129009i	−0.0368189	+	0.00986560i
$172$	3.09005	+	11.5322i	0.235614	+	0.879324i
$173$	−6.39606	−	1.71382i	−0.486283	−	0.130299i	0.00734343	−	0.999973i	$-0.497662\pi$
$173$	−6.39606	−	1.71382i	−0.486283	−	0.130299i	−0.493627	+	0.869674i	$0.664329\pi$
$174$	−5.07636	+	5.07636i	−0.384838	+	0.384838i
$175$	11.0935	+	13.7852i	0.838590	+	1.04206i
$176$	−18.2392	−	4.88718i	−1.37483	−	0.368385i
$177$			24.0977i			1.81130i
$178$	2.23024	−	8.32336i	0.167163	−	0.623862i
$179$	1.09512	−	1.89680i	0.0818528	−	0.141773i	−0.822193	−	0.569209i	$-0.807250\pi$
$179$	1.09512	−	1.89680i	0.0818528	−	0.141773i	0.904046	+	0.427436i	$0.140583\pi$
$180$	−2.65091	+	0.934185i	−0.197587	+	0.0696300i
$181$			9.59255i			0.713009i	0.934294	+	0.356504i	$0.116031\pi$
$181$			9.59255i			0.713009i	−0.934294	+	0.356504i	$0.883969\pi$
$182$	23.0739	−	3.71490i	1.71035	−	0.275367i
$183$	4.04484	+	4.04484i	0.299003	+	0.299003i
$184$	−0.0931154	−	0.347511i	−0.00686456	−	0.0256189i
$185$	11.4257	−	4.02644i	0.840035	−	0.296030i
$186$	−18.3864	+	10.6154i	−1.34816	+	0.778359i
$187$	−7.84842			−0.573933
$188$	−11.4426	+	6.60639i	−0.834537	+	0.481820i
$189$	3.76166	−	14.0387i	0.273621	−	1.02117i
$190$	−0.169300	−	2.19397i	−0.0122823	−	0.159167i
$191$	−1.86557	−	3.23126i	−0.134988	−	0.233806i	0.790605	−	0.612326i	$-0.209766\pi$
$191$	−1.86557	−	3.23126i	−0.134988	−	0.233806i	−0.925593	+	0.378521i	$0.876433\pi$
$192$	−4.35536	+	1.16701i	−0.314321	+	0.0842220i
$193$	−0.142043	+	0.246025i	−0.0102245	+	0.0177093i	−0.871092	−	0.491119i	$-0.836588\pi$
$193$	−0.142043	+	0.246025i	−0.0102245	+	0.0177093i	0.860868	+	0.508829i	$0.169921\pi$
$194$	32.6495			2.34410
$195$	15.3249	+	4.52237i	1.09744	+	0.323854i
$196$	−7.48414			−0.534581
$197$	−12.9246	+	22.3860i	−0.920838	+	1.59494i	−0.122716	+	0.992442i	$0.539160\pi$
$197$	−12.9246	+	22.3860i	−0.920838	+	1.59494i	−0.798122	+	0.602496i	$0.794173\pi$
$198$	6.35890	−	1.70386i	0.451907	−	0.121088i
$199$	2.87625	+	4.98181i	0.203892	+	0.353151i	0.949779	−	0.312921i	$-0.101308\pi$
$199$	2.87625	+	4.98181i	0.203892	+	0.353151i	−0.745887	+	0.666072i	$0.767974\pi$
$200$	0.906420	+	5.83819i	0.0640936	+	0.412823i
$201$	−1.17458	+	4.38359i	−0.0828484	+	0.309194i
$202$	7.22357	−	4.17053i	0.508248	−	0.293437i
$203$	−6.99884			−0.491223
$204$	−4.71101	+	2.71990i	−0.329836	+	0.190431i
$205$	0.649753	−	1.35690i	0.0453807	−	0.0947702i
$206$	−6.56536	−	24.5023i	−0.457430	−	1.70715i
$207$	0.199737	+	0.199737i	0.0138827	+	0.0138827i
$208$	16.4225	+	6.25598i	1.13869	+	0.433774i
$209$			2.08146i			0.143977i
$210$	−25.9081	−	12.4061i	−1.78783	−	0.856102i
$211$	1.61372	−	2.79504i	0.111093	−	0.192418i	−0.805118	−	0.593114i	$-0.797898\pi$
$211$	1.61372	−	2.79504i	0.111093	−	0.192418i	0.916211	+	0.400696i	$0.131232\pi$
$212$	1.56837	−	5.85322i	0.107716	−	0.402001i
$213$			9.15863i			0.627539i
$214$	12.5088	+	3.35173i	0.855085	+	0.229119i
$215$	−16.2556	+	11.1357i	−1.10862	+	0.759447i
$216$	3.43147	−	3.43147i	0.233482	−	0.233482i
$217$	−19.9926	−	5.35700i	−1.35719	−	0.363657i
$218$	6.63238	+	24.7524i	0.449201	+	1.67644i
$219$	28.2451	−	7.56826i	1.90863	−	0.511416i
$220$	0.903013	+	11.7022i	0.0608811	+	0.788961i
$221$	7.26628	+	0.744987i	0.488783	+	0.0501133i
$222$	−13.9063	+	13.9063i	−0.933331	+	0.933331i
$223$	6.42178	+	3.70762i	0.430034	+	0.248280i	0.699361	−	0.714768i	$-0.253468\pi$
$223$	6.42178	+	3.70762i	0.430034	+	0.248280i	−0.269327	+	0.963049i	$0.586801\pi$
$224$	−20.1179	−	11.6151i	−1.34419	−	0.776067i
$225$	−2.90823	−	3.61386i	−0.193882	−	0.240924i
$226$	2.96914	+	2.96914i	0.197504	+	0.197504i
$227$	1.95115	+	3.37949i	0.129502	+	0.224305i	0.923484	−	0.383637i	$-0.125329\pi$
$227$	1.95115	+	3.37949i	0.129502	+	0.224305i	−0.793981	+	0.607942i	$0.791995\pi$
$228$	0.721337	+	1.24939i	0.0477717	+	0.0827430i
$229$	−12.3946	−	12.3946i	−0.819060	−	0.819060i	0.166912	−	0.985972i	$-0.446621\pi$
$229$	−12.3946	−	12.3946i	−0.819060	−	0.819060i	−0.985972	+	0.166912i	$0.946621\pi$
$230$	−1.02877	+	0.704741i	−0.0678348	+	0.0464693i
$231$	23.5311	+	13.5857i	1.54823	+	0.893872i
$232$	−2.02381	−	1.16844i	−0.132869	−	0.0767121i
$233$	−2.88962	+	2.88962i	−0.189305	+	0.189305i	−0.795396	−	0.606090i	$-0.792737\pi$
$233$	−2.88962	+	2.88962i	−0.189305	+	0.189305i	0.606090	+	0.795396i	$0.292737\pi$
$234$	−6.04898	+	0.973883i	−0.395434	+	0.0636647i
$235$	−16.5599	−	14.1873i	−1.08025	−	0.925474i
$236$	15.9129	−	4.26384i	1.03584	−	0.277552i
$237$	−0.819258	−	3.05751i	−0.0532165	−	0.198607i
$238$	−12.6842	−	3.39872i	−0.822193	−	0.220306i
$239$	8.97299	−	8.97299i	0.580415	−	0.580415i	−0.354602	−	0.935017i	$-0.615384\pi$
$239$	8.97299	−	8.97299i	0.580415	−	0.580415i	0.935017	+	0.354602i	$0.115384\pi$
$240$	−12.2070	−	17.8195i	−0.787960	−	1.15025i
$241$	16.9497	+	4.54165i	1.09183	+	0.292554i	0.759432	−	0.650587i	$-0.225477\pi$
$241$	16.9497	+	4.54165i	1.09183	+	0.292554i	0.332394	+	0.943141i	$0.392144\pi$
$242$		−	7.34239i		−	0.471986i
$243$	−2.41378	+	9.00835i	−0.154844	+	0.577886i
$244$	1.95530	−	3.38669i	0.125176	−	0.216810i
$245$	−4.10531	−	11.6495i	−0.262278	−	0.744260i
$246$			2.44232i			0.155716i
$247$	0.197576	−	1.92707i	0.0125715	−	0.122617i
$248$	−4.88677	−	4.88677i	−0.310311	−	0.310311i
$249$	−3.88472	−	14.4980i	−0.246184	−	0.918771i
$250$	18.0412	−	9.68888i	1.14103	−	0.612779i
$251$	18.8524	−	10.8845i	1.18996	−	0.687021i	0.231659	−	0.972797i	$-0.425585\pi$
$251$	18.8524	−	10.8845i	1.18996	−	0.687021i	0.958296	+	0.285776i	$0.0922513\pi$
$252$	4.44834			0.280219
$253$	1.02152	−	0.589774i	0.0642223	−	0.0370787i
$254$	0.609678	−	2.27535i	0.0382546	−	0.142768i
$255$	−6.81784	−	5.84100i	−0.426950	−	0.365778i
$256$	−10.4820	−	18.1554i	−0.655125	−	1.13471i
$257$	12.3766	−	3.31629i	0.772029	−	0.206864i	0.148761	−	0.988873i	$-0.452471\pi$
$257$	12.3766	−	3.31629i	0.772029	−	0.206864i	0.623268	+	0.782009i	$0.285805\pi$
$258$	15.9937	−	27.7019i	0.995725	−	1.72465i
$259$	−19.1728			−1.19134
$260$	0.274759	−	10.9199i	0.0170398	−	0.677224i
$261$	1.83479			0.113571
$262$	5.12344	−	8.87405i	0.316527	−	0.548241i
$263$	−15.9426	+	4.27179i	−0.983060	+	0.263410i	−0.714333	−	0.699806i	$-0.753270\pi$
$263$	−15.9426	+	4.27179i	−0.983060	+	0.263410i	−0.268727	+	0.963216i	$0.586603\pi$
$264$	4.53621	+	7.85695i	0.279185	+	0.483562i
$265$	9.97120	−	0.769439i	0.612526	−	0.0472663i
$266$	−0.901363	+	3.36393i	−0.0552661	+	0.206256i
$267$	−8.07456	+	4.66185i	−0.494155	+	0.285301i
$268$	3.10252			0.189516
$269$	−27.9787	+	16.1535i	−1.70589	+	0.984895i	−0.766370	+	0.642400i	$0.777939\pi$
$269$	−27.9787	+	16.1535i	−1.70589	+	0.984895i	−0.939519	+	0.342495i	$0.888728\pi$
$270$	−15.1708	−	7.26456i	−0.923268	−	0.442107i
$271$	4.52218	+	16.8770i	0.274703	+	1.02521i	0.956040	+	0.293236i	$0.0947321\pi$
$271$	4.52218	+	16.8770i	0.274703	+	1.02521i	−0.681337	+	0.731970i	$0.738601\pi$
$272$	−6.98212	−	6.98212i	−0.423353	−	0.423353i
$273$	−20.4962	−	14.8116i	−1.24048	−	0.896440i
$274$			26.1743i			1.58125i
$275$	−17.7198	+	7.82464i	−1.06854	+	0.471844i
$276$	0.408777	−	0.708022i	0.0246055	−	0.0426179i
$277$	−0.795705	+	2.96961i	−0.0478093	+	0.178427i	−0.985702	−	0.168499i	$-0.946108\pi$
$277$	−0.795705	+	2.96961i	−0.0478093	+	0.178427i	0.937892	+	0.346926i	$0.112775\pi$
$278$			31.9008i			1.91328i
$279$	5.24118	+	1.40437i	0.313781	+	0.0840775i
$280$	1.71802	−	9.19131i	0.102671	−	0.549286i
$281$	−18.6757	+	18.6757i	−1.11410	+	1.11410i	−0.121508	+	0.992590i	$0.538773\pi$
$281$	−18.6757	+	18.6757i	−1.11410	+	1.11410i	−0.992590	+	0.121508i	$0.961227\pi$
$282$	34.1938	+	9.16221i	2.03621	+	0.545602i
$283$	−3.97005	−	14.8164i	−0.235995	−	0.880745i	−0.977698	−	0.210016i	$-0.932648\pi$
$283$	−3.97005	−	14.8164i	−0.235995	−	0.880745i	0.741703	−	0.670728i	$-0.234018\pi$
$284$	6.04787	−	1.62052i	0.358875	−	0.0961603i
$285$	−1.54907	+	1.80814i	−0.0917593	+	0.107105i
$286$	−2.60944	+	25.4513i	−0.154299	+	1.50497i
$287$	−1.68363	+	1.68363i	−0.0993814	+	0.0993814i
$288$	5.27404	+	3.04497i	0.310776	+	0.179427i
$289$	11.1681	+	6.44793i	0.656949	+	0.379290i
$290$	−1.48825	+	7.96202i	−0.0873929	+	0.467546i
$291$	−24.9801	−	24.9801i	−1.46436	−	1.46436i
$292$	−9.99535	−	17.3125i	−0.584934	−	1.01314i
$293$	5.18835	+	8.98649i	0.303107	+	0.524996i	0.976838	−	0.213980i	$-0.0686428\pi$
$293$	5.18835	+	8.98649i	0.303107	+	0.524996i	−0.673731	+	0.738976i	$0.735309\pi$
$294$	14.1787	+	14.1787i	0.826919	+	0.826919i
$295$	15.3657	+	22.4305i	0.894624	+	1.30595i
$296$	−5.54407	−	3.20087i	−0.322243	−	0.186047i
$297$	13.7790	+	7.95528i	0.799536	+	0.461612i
$298$	17.0057	−	17.0057i	0.985111	−	0.985111i
$299$	−1.00173	+	0.449064i	−0.0579316	+	0.0259701i
$300$	−7.92463	+	10.8376i	−0.457529	+	0.625709i
$301$	30.1219	−	8.07113i	1.73620	−	0.465212i
$302$	0.513002	+	1.91455i	0.0295200	+	0.110170i
$303$	−8.71763	−	2.33588i	−0.500814	−	0.134193i
$304$	−1.85171	+	1.85171i	−0.106203	+	0.106203i
$305$	6.34413	+	1.18583i	0.363264	+	0.0679006i
$306$	3.32524	+	0.890994i	0.190091	+	0.0509347i
$307$		−	2.13935i		−	0.122099i	−0.998135	−	0.0610496i	$-0.980555\pi$
$307$		−	2.13935i		−	0.122099i	0.998135	−	0.0610496i	$-0.0194448\pi$
$308$	4.80768	−	17.9425i	0.273943	−	1.02237i
$309$	−13.7235	+	23.7698i	−0.780704	+	1.35222i
$310$	−10.3455	+	21.6049i	−0.587585	+	1.22707i
$311$		−	3.82084i		−	0.216660i	−0.994115	−	0.108330i	$-0.965450\pi$
$311$		−	3.82084i		−	0.216660i	0.994115	−	0.108330i	$-0.0345503\pi$
$312$	−3.45395	−	7.70477i	−0.195542	−	0.436196i
$313$	3.04531	+	3.04531i	0.172131	+	0.172131i	0.787915	−	0.615784i	$-0.211161\pi$
$313$	3.04531	+	3.04531i	0.172131	+	0.172131i	−0.615784	+	0.787915i	$0.711161\pi$
$314$	2.03461	+	7.59327i	0.114820	+	0.428513i
$315$	2.44007	+	6.92410i	0.137482	+	0.390129i
$316$	−1.87406	+	1.08199i	−0.105424	+	0.0608666i
$317$	−23.1127			−1.29814			−0.649068	−	0.760730i	$-0.724841\pi$
$317$	−23.1127			−1.29814			−0.649068	+	0.760730i	$0.724841\pi$
$318$	−14.0602	+	8.11767i	−0.788458	+	0.455216i
$319$	1.98301	−	7.40069i	0.111027	−	0.414359i
$320$	−3.30988	+	3.86342i	−0.185028	+	0.215972i
$321$	−7.00609	−	12.1349i	−0.391042	−	0.677305i
$322$	1.90632	−	0.510796i	0.106235	−	0.0284656i
$323$	−0.544224	+	0.942624i	−0.0302814	+	0.0524490i
$324$	14.7987			0.822149
$325$	17.1482	−	5.56227i	0.951212	−	0.308539i
$326$	4.14604			0.229628
$327$	13.8636	−	24.0125i	0.766660	−	1.32789i
$328$	−0.767921	+	0.205764i	−0.0424013	+	0.0113614i
$329$	17.2557	+	29.8878i	0.951338	+	1.64777i
$330$	20.4590	−	23.8806i	1.12623	−	1.31458i
$331$	0.516858	−	1.92894i	0.0284091	−	0.106024i	−0.950265	−	0.311441i	$-0.899188\pi$
$331$	0.516858	−	1.92894i	0.0284091	−	0.106024i	0.978675	+	0.205417i	$0.0658550\pi$
$332$	−8.88632	+	5.13052i	−0.487700	+	0.281574i
$333$	5.02628			0.275438
$334$	0.982786	−	0.567412i	0.0537756	−	0.0310474i
$335$	1.70184	+	4.82925i	0.0929813	+	0.263850i
$336$	8.84765	+	33.0199i	0.482679	+	1.80138i
$337$	−6.12727	−	6.12727i	−0.333773	−	0.333773i	0.520244	−	0.854018i	$-0.325841\pi$
$337$	−6.12727	−	6.12727i	−0.333773	−	0.333773i	−0.854018	+	0.520244i	$0.825841\pi$
$338$	4.83178	−	23.3158i	0.262814	−	1.26821i
$339$		−	4.54338i		−	0.246763i
$340$	−2.65074	+	5.53564i	−0.143757	+	0.300212i
$341$	11.3292	−	19.6227i	0.613508	−	1.06263i
$342$	0.236298	−	0.881876i	0.0127775	−	0.0476864i
$343$		−	5.22396i		−	0.282067i
$344$	10.0576	+	2.69492i	0.542269	+	0.145301i
$345$	1.32631	+	0.247911i	0.0714059	+	0.0133471i
$346$	8.57614	−	8.57614i	0.461056	−	0.461056i
$347$	31.4009	+	8.41384i	1.68569	+	0.451679i	0.969271	−	0.245994i	$-0.0791144\pi$
$347$	31.4009	+	8.41384i	1.68569	+	0.451679i	0.716417	+	0.697673i	$0.245781\pi$
$348$	−1.37444	−	5.12947i	−0.0736776	−	0.274969i
$349$	−6.57321	+	1.76129i	−0.351856	+	0.0942795i	−0.430418	−	0.902630i	$-0.641634\pi$
$349$	−6.57321	+	1.76129i	−0.351856	+	0.0942795i	0.0785620	+	0.996909i	$0.474967\pi$
$350$	−32.0262	+	4.97228i	−1.71187	+	0.265780i
$351$	−12.0018	−	8.67315i	−0.640609	−	0.462938i
$352$	17.9821	−	17.9821i	0.958448	−	0.958448i
$353$	−23.6652	−	13.6631i	−1.25957	−	0.727213i	−0.286579	−	0.958057i	$-0.592518\pi$
$353$	−23.6652	−	13.6631i	−1.25957	−	0.727213i	−0.972991	+	0.230843i	$0.925852\pi$
$354$	−38.2248	−	22.0691i	−2.03163	−	1.17296i
$355$	5.83991	+	8.52496i	0.309950	+	0.452458i
$356$	4.50714	+	4.50714i	0.238878	+	0.238878i
$357$	7.10431	+	12.3050i	0.376000	+	0.651251i
$358$	2.00585	+	3.47423i	0.106012	+	0.183619i
$359$	−3.89871	−	3.89871i	−0.205766	−	0.205766i	0.596699	−	0.802465i	$-0.296479\pi$
$359$	−3.89871	−	3.89871i	−0.205766	−	0.205766i	−0.802465	+	0.596699i	$0.796479\pi$
$360$	−0.450390	+	2.40956i	−0.0237376	+	0.126995i
$361$	−16.2045	−	9.35567i	−0.852868	−	0.492404i
$362$	−15.2161	−	8.78501i	−0.799740	−	0.461730i
$363$	−5.61766	+	5.61766i	−0.294851	+	0.294851i
$364$	−6.15423	+	16.1553i	−0.322569	+	0.846769i
$365$	21.4651	−	25.0548i	1.12353	−	1.31143i
$366$	−10.1204	+	2.71176i	−0.529003	+	0.141746i
$367$	4.67826	+	17.4595i	0.244203	+	0.911378i	0.973782	+	0.227482i	$0.0730493\pi$
$367$	4.67826	+	17.4595i	0.244203	+	0.911378i	−0.729579	+	0.683896i	$0.760284\pi$
$368$	1.43344	+	0.384089i	0.0747232	+	0.0200220i
$369$	0.441373	−	0.441373i	0.0229770	−	0.0229770i
$370$	−4.07695	+	21.8114i	−0.211950	+	1.13392i
$371$	−15.2885	−	4.09653i	−0.793738	−	0.212681i
$372$		−	15.7046i		−	0.814248i
$373$	4.01536	−	14.9855i	0.207907	−	0.775921i	−0.780636	−	0.624986i	$-0.785105\pi$
$373$	4.01536	−	14.9855i	0.207907	−	0.775921i	0.988544	−	0.150936i	$-0.0482286\pi$
$374$	7.18771	−	12.4495i	0.371668	−	0.643747i
$375$	−21.2163	−	6.39037i	−1.09561	−	0.329997i
$376$			11.5232i			0.594266i
$377$	−2.53841	+	6.66353i	−0.130735	+	0.343189i
$378$	18.8238	+	18.8238i	0.968191	+	0.968191i
$379$	5.53029	+	20.6393i	0.284072	+	1.06017i	0.949515	+	0.313722i	$0.101576\pi$
$379$	5.53029	+	20.6393i	0.284072	+	1.06017i	−0.665443	+	0.746449i	$0.731757\pi$
$380$	1.46809	+	0.702996i	0.0753115	+	0.0360629i
$381$	−2.20733	+	1.27440i	−0.113085	+	0.0652897i
$382$	6.83407			0.349661
$383$	16.8072	−	9.70362i	0.858806	−	0.495832i	−0.00480620	−	0.999988i	$-0.501530\pi$
$383$	16.8072	−	9.70362i	0.858806	−	0.495832i	0.863612	+	0.504157i	$0.168197\pi$
$384$	−4.59660	+	17.1547i	−0.234569	+	0.875424i
$385$	30.5658	−	2.35865i	1.55778	−	0.120208i
$386$	−0.260170	−	0.450628i	−0.0132423	−	0.0229364i
$387$	−7.89664	+	2.11590i	−0.401409	+	0.107557i
$388$	−12.0756	+	20.9155i	−0.613045	+	1.06182i
$389$	14.8591			0.753387			0.376693	−	0.926338i	$-0.377061\pi$
$389$	14.8591			0.753387			0.376693	+	0.926338i	$0.377061\pi$
$390$	−21.2083	+	20.1673i	−1.07393	+	1.02121i
$391$	0.616816			0.0311937
$392$	−3.26357	+	5.65266i	−0.164835	+	0.285503i
$393$	−10.7095	+	2.86960i	−0.540222	+	0.144752i
$394$	−23.6731	−	41.0030i	−1.19263	−	2.06570i
$395$	−2.71217	−	2.32358i	−0.136464	−	0.116912i
$396$	−1.26036	+	4.70374i	−0.0633357	+	0.236372i
$397$	−4.57070	+	2.63889i	−0.229397	+	0.132442i	−0.610294	−	0.792175i	$-0.708949\pi$
$397$	−4.57070	+	2.63889i	−0.229397	+	0.132442i	0.380897	+	0.924617i	$0.375615\pi$
$398$	−10.5365			−0.528145
$399$	3.26338	−	1.88411i	0.163373	−	0.0943236i
$400$	−22.7249	−	8.80295i	−1.13624	−	0.440147i
$401$	7.21557	+	26.9289i	0.360328	+	1.34476i	0.873645	+	0.486564i	$0.161750\pi$
$401$	7.21557	+	26.9289i	0.360328	+	1.34476i	−0.513317	+	0.858199i	$0.671583\pi$
$402$	−5.87772	−	5.87772i	−0.293154	−	0.293154i
$403$	−12.3515	+	17.0918i	−0.615270	+	0.851404i
$404$			6.16996i			0.306967i
$405$	8.11759	+	23.0350i	0.403366	+	1.14462i
$406$	6.40965	−	11.1018i	0.318106	−	0.550975i
$407$	5.43231	−	20.2737i	0.269270	−	1.00493i
$408$			4.74421i			0.234873i
$409$	−2.54532	−	0.682016i	−0.125858	−	0.0337235i	0.195340	−	0.980736i	$-0.437419\pi$
$409$	−2.54532	−	0.682016i	−0.125858	−	0.0337235i	−0.321198	+	0.947012i	$0.604086\pi$
$410$	1.55732	+	2.27334i	0.0769105	+	0.112272i
$411$	20.0260	−	20.0260i	0.987810	−	0.987810i
$412$	18.1246	+	4.85646i	0.892933	+	0.239261i
$413$	−11.1370	−	41.5640i	−0.548018	−	2.04523i
$414$	−0.499753	+	0.133908i	−0.0245615	+	0.00658124i
$415$	−12.8604	−	11.0178i	−0.631293	−	0.540844i
$416$	−18.3552	+	14.9414i	−0.899938	+	0.732563i
$417$	24.4073	−	24.4073i	1.19523	−	1.19523i
$418$	−3.30169	−	1.90623i	−0.161491	−	0.0932368i
$419$	−17.0348	−	9.83506i	−0.832205	−	0.480474i	0.0224018	−	0.999749i	$-0.492869\pi$
$419$	−17.0348	−	9.83506i	−0.832205	−	0.480474i	−0.854607	+	0.519275i	$0.826202\pi$
$420$	17.5297	−	12.0085i	0.855361	−	0.585953i
$421$	10.4427	+	10.4427i	0.508948	+	0.508948i	0.914203	−	0.405256i	$-0.132817\pi$
$421$	10.4427	+	10.4427i	0.508948	+	0.508948i	−0.405256	+	0.914203i	$0.632817\pi$
$422$	2.95573	+	5.11948i	0.143883	+	0.249212i
$423$	−4.52369	−	7.83526i	−0.219949	−	0.380964i
$424$	−3.73695	−	3.73695i	−0.181482	−	0.181482i
$425$	−10.0706	−	1.08955i	−0.488495	−	0.0528509i
$426$	−14.5278	−	8.38762i	−0.703874	−	0.406382i
$427$	−8.84594	−	5.10721i	−0.428085	−	0.247155i
$428$	−6.77359	+	6.77359i	−0.327414	+	0.327414i
$429$	21.4693	−	17.4763i	1.03655	−	0.843765i
$430$	−2.77671	−	35.9835i	−0.133905	−	1.73528i
$431$	16.5486	−	4.43419i	0.797119	−	0.213587i	0.162800	−	0.986659i	$-0.447947\pi$
$431$	16.5486	−	4.43419i	0.797119	−	0.213587i	0.634319	+	0.773072i	$0.281281\pi$
$432$	5.18086	+	19.3352i	0.249264	+	0.930267i
$433$	10.8538	+	2.90826i	0.521599	+	0.139762i	0.510006	−	0.860171i	$-0.329643\pi$
$433$	10.8538	+	2.90826i	0.521599	+	0.139762i	0.0115927	+	0.999933i	$0.496310\pi$
$434$	26.8070	−	26.8070i	1.28678	−	1.28678i
$435$	7.23040	−	4.95309i	0.346671	−	0.237482i
$436$	−18.3096	−	4.90604i	−0.876870	−	0.234957i
$437$		−	0.163584i		−	0.00782528i
$438$	−13.8623	+	51.7347i	−0.662365	+	2.47198i
$439$	−2.12218	+	3.67572i	−0.101286	+	0.175432i	−0.912215	−	0.409712i	$-0.865629\pi$
$439$	−2.12218	+	3.67572i	−0.101286	+	0.175432i	0.810929	+	0.585145i	$0.198962\pi$
$440$	9.23226	+	4.42087i	0.440131	+	0.210757i
$441$		−	5.12473i		−	0.244035i
$442$	−7.83631	+	10.8438i	−0.372735	+	0.515787i
$443$	15.1569	+	15.1569i	0.720126	+	0.720126i	0.968631	−	0.248505i	$-0.0799392\pi$
$443$	15.1569	+	15.1569i	0.720126	+	0.720126i	−0.248505	+	0.968631i	$0.579939\pi$
$444$	−3.76518	−	14.0518i	−0.178687	−	0.666870i
$445$	−4.54331	+	9.48796i	−0.215374	+	0.449773i
$446$	−11.7623	+	6.79099i	−0.556963	+	0.321563i
$447$	−26.0221			−1.23080
$448$	6.97281	−	4.02575i	0.329434	−	0.190199i
$449$	3.76524	−	14.0521i	0.177693	−	0.663158i	−0.818385	−	0.574671i	$-0.805130\pi$
$449$	3.76524	−	14.0521i	0.177693	−	0.663158i	0.996077	−	0.0884873i	$-0.0282033\pi$
$450$	8.39586	−	1.30351i	0.395785	−	0.0614483i
$451$	−1.30327	−	2.25732i	−0.0613684	−	0.106293i
$452$	−3.00021	+	0.803904i	−0.141118	+	0.0378124i
$453$	1.07233	−	1.85732i	0.0503822	−	0.0872646i
$454$	−7.14758			−0.335453
$455$	−28.5225	−	0.717664i	−1.33716	−	0.0336446i
$456$	1.25820			0.0589205
$457$	−15.1476	+	26.2365i	−0.708576	+	1.22729i	0.256809	+	0.966462i	$0.417329\pi$
$457$	−15.1476	+	26.2365i	−0.708576	+	1.22729i	−0.965385	+	0.260828i	$0.916004\pi$
$458$	31.0121	−	8.30966i	1.44910	−	0.388285i
$459$	4.16003	+	7.20538i	0.194173	+	0.336318i
$460$	−0.0709688	−	0.919687i	−0.00330894	−	0.0428806i
$461$	1.79565	−	6.70146i	0.0836318	−	0.312118i	−0.911420	−	0.411478i	$-0.865013\pi$
$461$	1.79565	−	6.70146i	0.0836318	−	0.312118i	0.995052	+	0.0993596i	$0.0316794\pi$
$462$	−43.1003	+	24.8840i	−2.00521	+	1.15771i
$463$	31.4463			1.46143			0.730717	−	0.682680i	$-0.239186\pi$
$463$	31.4463			1.46143			0.730717	+	0.682680i	$0.239186\pi$
$464$	8.34794	−	4.81968i	0.387543	−	0.223748i
$465$	24.4452	−	8.61454i	1.13362	−	0.399490i
$466$	−1.93727	−	7.22999i	−0.0897423	−	0.334923i
$467$	3.69622	+	3.69622i	0.171041	+	0.171041i	0.787436	−	0.616396i	$-0.211408\pi$
$467$	3.69622	+	3.69622i	0.171041	+	0.171041i	−0.616396	+	0.787436i	$0.711408\pi$
$468$	1.61337	−	4.23522i	0.0745780	−	0.195773i
$469$		−	8.10369i		−	0.374194i
$470$	37.6702	−	13.2751i	1.73760	−	0.612332i
$471$	4.25293	−	7.36630i	0.195965	−	0.339421i
$472$	3.71862	−	13.8781i	0.171163	−	0.638790i
$473$			34.1382i			1.56968i
$474$	5.60024	+	1.50058i	0.257227	+	0.0689239i
$475$	−0.288956	+	2.67079i	−0.0132582	+	0.122544i
$476$	6.86855	−	6.86855i	0.314820	−	0.314820i
$477$	4.00797	+	1.07393i	0.183512	+	0.0491720i
$478$	6.01571	+	22.4509i	0.275152	+	1.02688i
$479$	18.6940	−	5.00904i	0.854150	−	0.228869i	0.194928	−	0.980818i	$-0.437553\pi$
$479$	18.6940	−	5.00904i	0.854150	−	0.228869i	0.659222	+	0.751949i	$0.270886\pi$
$480$	29.0036	−	2.23810i	1.32383	−	0.102155i
$481$	−6.95380	+	18.2543i	−0.317066	+	0.832323i
$482$	−22.7270	+	22.7270i	−1.03518	+	1.03518i
$483$	−1.84934	−	1.06771i	−0.0841477	−	0.0485827i
$484$	4.70359	+	2.71562i	0.213800	+	0.123437i
$485$	−39.1801	−	7.32348i	−1.77908	−	0.332542i
$486$	−12.0788	−	12.0788i	−0.547907	−	0.547907i
$487$	11.6813	+	20.2327i	0.529332	+	0.916830i	0.999415	+	0.0342077i	$0.0108908\pi$
$487$	11.6813	+	20.2327i	0.529332	+	0.916830i	−0.470083	+	0.882622i	$0.655776\pi$
$488$	−1.70528	−	2.95363i	−0.0771943	−	0.133704i
$489$	−3.17214	−	3.17214i	−0.143449	−	0.143449i
$490$	22.2386	+	4.15680i	1.00464	+	0.187785i
$491$	18.4624	+	10.6593i	0.833198	+	0.481047i	0.854946	−	0.518716i	$-0.173590\pi$
$491$	18.4624	+	10.6593i	0.833198	+	0.481047i	−0.0217482	+	0.999763i	$0.506923\pi$
$492$	−1.56457	−	0.903303i	−0.0705362	−	0.0407241i
$493$	2.83305	−	2.83305i	0.127594	−	0.127594i
$494$	2.87585	+	2.07824i	0.129391	+	0.0935046i
$495$	−8.01301	+	0.618334i	−0.360158	+	0.0277920i
$496$	27.5354	−	7.37809i	1.23638	−	0.331286i
$497$	−4.23276	−	15.7969i	−0.189865	−	0.708587i
$498$	26.5549	+	7.11538i	1.18996	+	0.318848i
$499$	−23.0389	+	23.0389i	−1.03136	+	1.03136i	−0.0318687	+	0.999492i	$0.510146\pi$
$499$	−23.0389	+	23.0389i	−1.03136	+	1.03136i	−0.999492	+	0.0318687i	$0.989854\pi$
$500$	−0.465858	+	15.1408i	−0.0208338	+	0.677118i
$501$	−1.18606	−	0.317803i	−0.0529891	−	0.0141984i
$502$			39.8727i			1.77960i
$503$	0.169996	−	0.634433i	0.00757973	−	0.0282879i	−0.962032	−	0.272935i	$-0.912006\pi$
$503$	0.169996	−	0.634433i	0.00757973	−	0.0282879i	0.969612	+	0.244647i	$0.0786722\pi$
$504$	1.93976	−	3.35977i	0.0864039	−	0.149656i
$505$	−9.60392	+	3.38444i	−0.427369	+	0.150606i
$506$			2.16050i			0.0960458i
$507$	−21.5357	+	14.1422i	−0.956436	+	0.628075i
$508$	1.23211	+	1.23211i	0.0546662	+	0.0546662i
$509$	−8.29035	−	30.9400i	−0.367463	−	1.37139i	−0.864050	−	0.503405i	$-0.832080\pi$
$509$	−8.29035	−	30.9400i	−0.367463	−	1.37139i	0.496587	−	0.867987i	$-0.334586\pi$
$510$	15.5091	−	5.46544i	0.686755	−	0.242014i
$511$	−45.2197	+	26.1076i	−2.00040	+	1.15493i
$512$	20.4758			0.904912
$513$	1.91092	−	1.10327i	0.0843690	−	0.0487105i
$514$	−6.07422	+	22.6693i	−0.267923	+	0.999901i
$515$	2.38258	+	30.8759i	0.104989	+	1.36056i
$516$	11.8307	+	20.4914i	0.520818	+	0.902084i
$517$	−36.4929	+	9.77825i	−1.60496	+	0.430047i
$518$	17.5588	−	30.4127i	0.771489	−	1.33626i
$519$	−13.1232			−0.576046
$520$	−8.12784	−	4.96931i	−0.356430	−	0.217919i
$521$	−23.4746			−1.02844			−0.514220	−	0.857658i	$-0.671919\pi$
$521$	−23.4746			−1.02844			−0.514220	+	0.857658i	$0.671919\pi$
$522$	−1.68033	+	2.91042i	−0.0735461	+	0.127386i
$523$	−23.9001	+	6.40400i	−1.04508	+	0.280027i	−0.740216	−	0.672370i	$-0.765277\pi$
$523$	−23.9001	+	6.40400i	−1.04508	+	0.280027i	−0.304861	+	0.952397i	$0.598610\pi$
$524$	3.78986	+	6.56423i	0.165561	+	0.286760i
$525$	28.3075	+	20.6989i	1.23544	+	0.903376i
$526$	7.82436	−	29.2009i	0.341158	−	1.27322i
$527$	10.2612	−	5.92431i	0.446985	−	0.258067i
$528$	−37.4226			−1.62861
$529$	19.8383	−	11.4536i	0.862535	−	0.497985i
$530$	−7.91127	+	16.5214i	−0.343643	+	0.717643i
$531$	2.91964	+	10.8963i	0.126702	+	0.472857i
$532$	−1.82159	−	1.82159i	−0.0789759	−	0.0789759i
$533$	0.992330	+	2.21360i	0.0429826	+	0.0958817i
$534$		−	17.0776i		−	0.739019i
$535$	−14.2591	−	6.82795i	−0.616473	−	0.295198i
$536$	1.35290	−	2.34329i	0.0584363	−	0.101215i
$537$	1.12346	−	4.19281i	0.0484809	−	0.180933i
$538$		−	59.1745i		−	2.55119i
$539$	−20.6708	−	5.53871i	−0.890353	−	0.238569i
$540$	10.2647	−	7.03172i	0.441724	−	0.302597i
$541$	−27.6908	+	27.6908i	−1.19052	+	1.19052i	−0.213597	+	0.976922i	$0.568518\pi$
$541$	−27.6908	+	27.6908i	−1.19052	+	1.19052i	−0.976922	+	0.213597i	$0.931482\pi$
$542$	−30.9125	−	8.28297i	−1.32780	−	0.355784i
$543$	4.92042	+	18.3632i	0.211155	+	0.788042i
$544$	12.8452	−	3.44185i	0.550731	−	0.147568i
$545$	−2.40690	−	31.1911i	−0.103100	−	1.33608i
$546$	42.2655	−	18.9471i	1.80880	−	0.810861i
$547$	6.53914	−	6.53914i	0.279593	−	0.279593i	−0.553353	−	0.832947i	$-0.686652\pi$
$547$	6.53914	−	6.53914i	0.279593	−	0.279593i	0.832947	+	0.553353i	$0.186652\pi$
$548$	−16.7675	−	9.68071i	−0.716272	−	0.413540i
$549$	2.31902	+	1.33889i	0.0989733	+	0.0571422i
$550$	3.81632	−	35.2738i	0.162729	−	1.50408i
$551$	−0.751344	−	0.751344i	−0.0320083	−	0.0320083i
$552$	−0.356506	−	0.617486i	−0.0151739	−	0.0262820i
$553$	2.82613	+	4.89500i	0.120179	+	0.208156i
$554$	−3.98180	−	3.98180i	−0.169170	−	0.169170i
$555$	19.8072	−	13.5686i	0.840768	−	0.575956i
$556$	−20.4359	−	11.7987i	−0.866676	−	0.500375i
$557$	14.0717	+	8.12429i	0.596237	+	0.344237i	0.767560	−	0.640978i	$-0.221471\pi$
$557$	14.0717	+	8.12429i	0.596237	+	0.344237i	−0.171323	+	0.985215i	$0.554804\pi$
$558$	−7.02763	+	7.02763i	−0.297503	+	0.297503i
$559$	3.24046	−	31.6061i	0.137057	−	1.33679i
$560$	29.2903	+	25.0937i	1.23774	+	1.06040i
$561$	−15.0244	+	4.02578i	−0.634332	+	0.169969i
$562$	−12.5206	−	46.7277i	−0.528151	−	1.97109i
$563$	31.4174	+	8.41827i	1.32409	+	0.354788i	0.850507	−	0.525964i	$-0.176295\pi$
$563$	31.4174	+	8.41827i	1.32409	+	0.354788i	0.473579	+	0.880751i	$0.342962\pi$
$564$	−18.5161	+	18.5161i	−0.779670	+	0.779670i
$565$	−2.89704	−	4.22904i	−0.121879	−	0.177917i
$566$	27.1382	+	7.27167i	1.14071	+	0.305651i
$567$		−	38.6538i		−	1.62331i
$568$	1.41331	−	5.27453i	0.0593010	−	0.221314i
$569$	−16.4164	+	28.4341i	−0.688212	+	1.19202i	0.284203	+	0.958764i	$0.408271\pi$
$569$	−16.4164	+	28.4341i	−0.688212	+	1.19202i	−0.972416	+	0.233255i	$0.925062\pi$
$570$	−1.44947	−	4.11313i	−0.0607118	−	0.172280i
$571$		−	31.7967i		−	1.33065i	−0.746554	−	0.665325i	$-0.768293\pi$
$571$		−	31.7967i		−	1.33065i	0.746554	−	0.665325i	$-0.231707\pi$
$572$	−15.3392	−	11.0849i	−0.641364	−	0.463484i
$573$	−5.22875	−	5.22875i	−0.218434	−	0.218434i
$574$	−1.12874	−	4.21253i	−0.0471129	−	0.175828i
$575$	1.39262	−	0.614947i	0.0580762	−	0.0256451i
$576$	−1.82796	+	1.05538i	−0.0761652	+	0.0439740i
$577$	39.9389			1.66268			0.831338	−	0.555767i	$-0.187575\pi$
$577$	39.9389			1.66268			0.831338	+	0.555767i	$0.187575\pi$
$578$	−20.4559	+	11.8102i	−0.850854	+	0.491241i
$579$	−0.145719	+	0.543832i	−0.00605589	+	0.0226009i
$580$	−4.55010	−	3.89818i	−0.188933	−	0.161863i
$581$	13.4008	+	23.2109i	0.555959	+	0.962949i
$582$	62.5017	−	16.7473i	2.59078	−	0.694197i
$583$	8.66348	−	15.0056i	0.358805	−	0.621468i
$584$	−17.4345			−0.721444
$585$	7.47736	+	0.188140i	0.309151	+	0.00777864i
$586$	−19.0063			−0.785143
$587$	9.32773	−	16.1561i	0.384997	−	0.666834i	−0.606772	−	0.794876i	$-0.707536\pi$
$587$	9.32773	−	16.1561i	0.384997	−	0.666834i	0.991769	+	0.128042i	$0.0408692\pi$
$588$	−14.3271	+	3.83892i	−0.590838	+	0.158315i
$589$	−1.57117	−	2.72135i	−0.0647389	−	0.112131i
$590$	−49.6522	+	3.83147i	−2.04415	+	0.157739i
$591$	−13.2591	+	49.4837i	−0.545407	+	2.03549i
$592$	22.8686	−	13.2032i	0.939893	−	0.542647i
$593$	8.65172			0.355284			0.177642	−	0.984095i	$-0.443153\pi$
$593$	8.65172			0.355284			0.177642	+	0.984095i	$0.443153\pi$
$594$	−25.2380	+	14.5712i	−1.03553	+	0.597862i
$595$	14.4590	+	6.92367i	0.592759	+	0.283843i
$596$	4.60433	+	17.1836i	0.188601	+	0.703867i
$597$	8.06145	+	8.06145i	0.329933	+	0.329933i
$598$	0.205079	−	2.00025i	0.00838628	−	0.0817962i
$599$			35.1779i			1.43733i	0.695356	+	0.718666i	$0.255247\pi$
$599$			35.1779i			1.43733i	−0.695356	+	0.718666i	$0.744753\pi$
$600$	4.72983	+	10.7113i	0.193095	+	0.437285i
$601$	20.0384	−	34.7076i	0.817385	−	1.41575i	−0.0902170	−	0.995922i	$-0.528756\pi$
$601$	20.0384	−	34.7076i	0.817385	−	1.41575i	0.907602	−	0.419831i	$-0.137911\pi$
$602$	−14.7834	+	55.1722i	−0.602524	+	2.24865i
$603$			2.12443i			0.0865136i
$604$	−1.41621	−	0.379473i	−0.0576249	−	0.0154405i
$605$	−1.64694	+	8.81103i	−0.0669577	+	0.358219i
$606$	11.6890	−	11.6890i	0.474834	−	0.474834i
$607$	−41.5934	−	11.1449i	−1.68822	−	0.452358i	−0.718292	−	0.695742i	$-0.755076\pi$
$607$	−41.5934	−	11.1449i	−1.68822	−	0.452358i	−0.969930	+	0.243384i	$0.921742\pi$
$608$	−0.912802	−	3.40662i	−0.0370190	−	0.138157i
$609$	−13.3981	+	3.59000i	−0.542917	+	0.145474i
$610$	−7.69108	+	8.97731i	−0.311403	+	0.363481i
$611$	34.7143	−	5.58899i	1.40439	−	0.226106i
$612$	−1.80063	+	1.80063i	−0.0727863	+	0.0727863i
$613$	17.5625	+	10.1397i	0.709344	+	0.409540i	0.810818	−	0.585298i	$-0.199022\pi$
$613$	17.5625	+	10.1397i	0.709344	+	0.409540i	−0.101474	+	0.994838i	$0.532356\pi$
$614$	3.39352	+	1.95925i	0.136952	+	0.0790690i
$615$	0.547826	−	2.93084i	0.0220905	−	0.118183i
$616$	−11.4553	−	11.4553i	−0.461546	−	0.461546i
$617$	−4.33527	−	7.50891i	−0.174531	−	0.302297i	0.765468	−	0.643474i	$-0.222508\pi$
$617$	−4.33527	−	7.50891i	−0.174531	−	0.302297i	−0.939999	+	0.341177i	$0.889174\pi$
$618$	−25.1365	−	43.5376i	−1.01114	−	1.75134i
$619$	−21.3034	−	21.3034i	−0.856257	−	0.856257i	0.134638	−	0.990895i	$-0.457013\pi$
$619$	−21.3034	−	21.3034i	−0.856257	−	0.856257i	−0.990895	+	0.134638i	$0.957013\pi$
$620$	−10.0139	−	14.6181i	−0.402168	−	0.587076i
$621$	−1.08290	−	0.625215i	−0.0434554	−	0.0250890i
$622$	6.06077	+	3.49919i	0.243015	+	0.140305i
$623$	11.7725	−	11.7725i	0.471657	−	0.471657i
$624$	34.6468	+	3.55222i	1.38698	+	0.142203i
$625$	−23.8231	+	7.58013i	−0.952925	+	0.303205i
$626$	−7.61954	+	2.04165i	−0.304538	+	0.0816007i
$627$	1.06767	+	3.98458i	0.0426385	+	0.159129i
$628$	−5.61682	−	1.50502i	−0.224136	−	0.0600569i
$629$	7.76093	−	7.76093i	0.309449	−	0.309449i
$630$	−13.2179	−	2.47067i	−0.526615	−	0.0984340i
$631$	−27.4324	−	7.35050i	−1.09207	−	0.292619i	−0.332537	−	0.943090i	$-0.607905\pi$
$631$	−27.4324	−	7.35050i	−1.09207	−	0.292619i	−0.759531	+	0.650472i	$0.774571\pi$
$632$			1.88727i			0.0750715i
$633$	1.65548	−	6.17835i	0.0657996	−	0.245567i
$634$	21.1670	−	36.6622i	0.840647	−	1.45604i
$635$	−1.24200	+	2.59371i	−0.0492873	+	0.102928i
$636$		−	12.0094i		−	0.476206i
$637$	18.6118	+	7.09000i	0.737427	+	0.280916i
$638$	9.92320	+	9.92320i	0.392863	+	0.392863i
$639$	1.10965	+	4.14125i	0.0438969	+	0.163825i
$640$	6.65997	+	18.8988i	0.263259	+	0.747041i
$641$	14.1756	−	8.18429i	0.559903	−	0.323260i	−0.193204	−	0.981159i	$-0.561888\pi$
$641$	14.1756	−	8.18429i	0.559903	−	0.323260i	0.753107	+	0.657899i	$0.228554\pi$
$642$	25.6652			1.01292
$643$	−35.5518	+	20.5258i	−1.40203	+	0.809460i	−0.994600	−	0.103779i	$-0.966907\pi$
$643$	−35.5518	+	20.5258i	−1.40203	+	0.809460i	−0.407425	+	0.913239i	$0.633573\pi$
$644$	−0.377841	+	1.41012i	−0.0148890	+	0.0555666i
$645$	−25.4065	+	29.6555i	−1.00038	+	1.16768i
$646$	−0.996819	−	1.72654i	−0.0392193	−	0.0679298i
$647$	2.73861	−	0.733807i	0.107666	−	0.0288489i	−0.204584	−	0.978849i	$-0.565584\pi$
$647$	2.73861	−	0.733807i	0.107666	−	0.0288489i	0.312250	+	0.950000i	$0.398917\pi$
$648$	6.45318	−	11.1772i	0.253505	−	0.439083i
$649$	47.1059			1.84907
$650$	−6.88151	+	32.2952i	−0.269915	+	1.26672i
$651$	−41.0201			−1.60771
$652$	−1.53344	+	2.65599i	−0.0600540	+	0.104017i
$653$	−1.21283	+	0.324978i	−0.0474619	+	0.0127174i	−0.282472	−	0.959276i	$-0.591154\pi$
$653$	−1.21283	+	0.324978i	−0.0474619	+	0.0127174i	0.235010	+	0.971993i	$0.424488\pi$
$654$	25.3930	+	43.9820i	0.992947	+	1.71983i
$655$	−8.13874	+	9.49985i	−0.318007	+	0.371190i
$656$	0.848749	−	3.16758i	0.0331381	−	0.123673i
$657$	11.8546	−	6.84427i	0.462493	−	0.267020i
$658$	−63.2122			−2.46427
$659$	8.09916	−	4.67605i	0.315498	−	0.182153i	−0.333886	−	0.942613i	$-0.608360\pi$
$659$	8.09916	−	4.67605i	0.315498	−	0.182153i	0.649384	+	0.760460i	$0.275027\pi$
$660$	7.73119	+	21.9386i	0.300936	+	0.853958i
$661$	−6.64415	−	24.7963i	−0.258427	−	0.964464i	−0.966152	−	0.257975i	$-0.916945\pi$
$661$	−6.64415	−	24.7963i	−0.258427	−	0.964464i	0.707724	−	0.706489i	$-0.249722\pi$
$662$	2.58641	+	2.58641i	0.100524	+	0.100524i
$663$	14.2922	−	2.30103i	0.555061	−	0.0893647i
$664$			8.94896i			0.347287i
$665$	1.83621	−	3.83462i	0.0712051	−	0.148700i
$666$	−4.60315	+	7.97288i	−0.178368	+	0.308943i
$667$	−0.155847	+	0.581628i	−0.00603441	+	0.0225207i
$668$			0.839440i			0.0324789i
$669$	14.1952	+	3.80358i	0.548817	+	0.147055i
$670$	−9.21892	−	1.72318i	−0.356158	−	0.0665724i
$671$	7.90679	−	7.90679i	0.305238	−	0.305238i
$672$	−44.4701	−	11.9157i	−1.71547	−	0.459660i
$673$	10.6983	+	39.9267i	0.412390	+	1.53906i	0.790007	+	0.613098i	$0.210077\pi$
$673$	10.6983	+	39.9267i	0.412390	+	1.53906i	−0.377617	+	0.925962i	$0.623256\pi$
$674$	15.3308	−	4.10787i	0.590519	−	0.158229i
$675$	16.5759	+	12.1205i	0.638005	+	0.466520i
$676$	13.1493	+	11.7188i	0.505740	+	0.450721i
$677$	15.5322	−	15.5322i	0.596950	−	0.596950i	−0.342549	−	0.939500i	$-0.611290\pi$
$677$	15.5322	−	15.5322i	0.596950	−	0.596950i	0.939500	+	0.342549i	$0.111290\pi$
$678$	7.20690	+	4.16090i	0.276779	+	0.159799i
$679$	54.6308	+	31.5411i	2.09654	+	1.21044i
$680$	3.02510	+	4.41597i	0.116007	+	0.169345i
$681$	5.46862	+	5.46862i	0.209558	+	0.209558i
$682$	20.7508	+	35.9415i	0.794591	+	1.37627i
$683$	3.32652	+	5.76170i	0.127286	+	0.220465i	0.922624	−	0.385700i	$-0.126040\pi$
$683$	3.32652	+	5.76170i	0.127286	+	0.220465i	−0.795338	+	0.606166i	$0.792707\pi$
$684$	0.477541	+	0.477541i	0.0182592	+	0.0182592i
$685$	5.87106	−	31.4098i	0.224322	−	1.20011i
$686$	8.28646	+	4.78419i	0.316378	+	0.182661i
$687$	−30.0851	−	17.3696i	−1.14782	−	0.662692i
$688$	−30.3701	+	30.3701i	−1.15785	+	1.15785i
$689$	−9.44525	+	13.0702i	−0.359835	+	0.497936i
$690$	−1.60790	+	1.87680i	−0.0612117	+	0.0714485i
$691$	−36.3445	+	9.73848i	−1.38261	+	0.370469i	−0.872069	−	0.489384i	$-0.837222\pi$
$691$	−36.3445	+	9.73848i	−1.38261	+	0.370469i	−0.510542	+	0.859853i	$0.670555\pi$
$692$	2.32201	+	8.66588i	0.0882698	+	0.329427i
$693$	12.2861	+	3.29204i	0.466709	+	0.125054i
$694$	−42.1038	+	42.1038i	−1.59824	+	1.59824i
$695$	7.15555	−	38.2817i	0.271425	−	1.45211i
$696$	−4.47356	−	1.19869i	−0.169570	−	0.0454361i
$697$		−	1.36302i		−	0.0516282i
$698$	3.22603	−	12.0397i	0.122107	−	0.455710i
$699$	−4.04946	+	7.01387i	−0.153165	+	0.265289i
$700$	8.65976	−	22.3552i	0.327308	−	0.844949i
$701$			40.3398i			1.52361i	0.647804	+	0.761807i	$0.275688\pi$
$701$			40.3398i			1.52361i	−0.647804	+	0.761807i	$0.724312\pi$
$702$	24.7491	−	11.0947i	0.934096	−	0.418744i
$703$	−2.05825	−	2.05825i	−0.0776285	−	0.0776285i
$704$	2.28126	+	8.51379i	0.0859783	+	0.320875i
$705$	−38.9782	−	18.6647i	−1.46801	−	0.702955i
$706$	43.3459	−	25.0258i	1.63134	−	0.941857i
$707$	16.1158			0.606097
$708$	28.2753	−	16.3247i	1.06265	−	0.613521i
$709$	−11.5415	+	43.0733i	−0.433449	+	1.61765i	0.311304	+	0.950311i	$0.399234\pi$
$709$	−11.5415	+	43.0733i	−0.433449	+	1.61765i	−0.744752	+	0.667341i	$0.767432\pi$
$710$	−18.8709	+	1.45620i	−0.708213	+	0.0546501i
$711$	−0.740887	−	1.28325i	−0.0277854	−	0.0481258i
$712$	5.36959	−	1.43878i	0.201234	−	0.0539204i
$713$	−0.890371	+	1.54217i	−0.0333447	+	0.0577546i
$714$	−26.0250			−0.973960
$715$	8.84027	−	29.9568i	0.330607	−	1.12032i
$716$	−2.96749			−0.110900
$717$	12.5746	−	21.7798i	0.469607	−	0.813383i
$718$	9.75479	−	2.61379i	0.364045	−	0.0975457i
$719$	−13.7825	−	23.8720i	−0.514001	−	0.890276i	−0.999868	−	0.0162430i	$-0.994829\pi$
$719$	−13.7825	−	23.8720i	−0.514001	−	0.890276i	0.485867	−	0.874033i	$-0.338504\pi$
$720$	−7.67863	−	6.57846i	−0.286166	−	0.245165i
$721$	12.6850	−	47.3409i	0.472413	−	1.76307i
$722$	29.6807	−	17.1361i	1.10460	−	0.637741i
$723$	34.7768			1.29336
$724$	11.2555	−	6.49836i	0.418307	−	0.241510i
$725$	3.57186	−	9.22079i	0.132656	−	0.342451i
$726$	−3.76622	−	14.0557i	−0.139777	−	0.521656i
$727$	29.4624	+	29.4624i	1.09270	+	1.09270i	0.995240	+	0.0974593i	$0.0310716\pi$
$727$	29.4624	+	29.4624i	1.09270	+	1.09270i	0.0974593	+	0.995240i	$0.468928\pi$
$728$	9.51825	+	11.6930i	0.352770	+	0.433370i
$729$		−	14.2845i		−	0.529057i
$730$	20.0849	+	56.9944i	0.743377	+	2.10946i
$731$	−8.92588	+	15.4601i	−0.330135	+	0.571811i
$732$	2.00591	−	7.48617i	0.0741407	−	0.276697i
$733$		−	23.3958i		−	0.864144i	−0.901839	−	0.432072i	$-0.857783\pi$
$733$		−	23.3958i		−	0.864144i	0.901839	−	0.432072i	$-0.142217\pi$
$734$	−31.9794	−	8.56885i	−1.18038	−	0.316282i
$735$	−13.8344	−	20.1951i	−0.510290	−	0.744909i
$736$	−1.41323	+	1.41323i	−0.0520924	+	0.0520924i
$737$	8.56897	+	2.29605i	0.315642	+	0.0845761i
$738$	0.295907	+	1.10434i	0.0108925	+	0.0406513i
$739$	−15.5120	+	4.15644i	−0.570620	+	0.152897i	−0.532581	−	0.846379i	$-0.678778\pi$
$739$	−15.5120	+	4.15644i	−0.570620	+	0.152897i	−0.0380389	+	0.999276i	$0.512111\pi$
$740$	−12.4647	−	10.6788i	−0.458210	−	0.392560i
$741$	−0.610250	−	3.79038i	−0.0224181	−	0.139243i
$742$	20.4995	−	20.4995i	0.752561	−	0.752561i
$743$	−45.2759	−	26.1400i	−1.66101	−	0.958985i	−0.972234	−	0.234011i	$-0.924815\pi$
$743$	−45.2759	−	26.1400i	−1.66101	−	0.958985i	−0.688777	−	0.724973i	$-0.741852\pi$
$744$	−11.8615	−	6.84824i	−0.434864	−	0.251069i
$745$	−24.2216	+	16.5927i	−0.887412	+	0.607909i
$746$	20.0933	+	20.0933i	0.735669	+	0.735669i
$747$	−3.51310	−	6.08487i	−0.128538	−	0.222634i
$748$	5.31682	+	9.20901i	0.194402	+	0.336715i
$749$	17.6925	+	17.6925i	0.646468	+	0.646468i
$750$	29.5669	−	27.8017i	1.07963	−	1.01518i
$751$	23.7599	+	13.7178i	0.867010	+	0.500569i	0.866354	−	0.499431i	$-0.166458\pi$
$751$	23.7599	+	13.7178i	0.867010	+	0.500569i	0.000656703		1.00000i	$0.499791\pi$
$752$	−41.1638	−	23.7659i	−1.50109	−	0.866655i
$753$	30.5066	−	30.5066i	1.11172	−	1.11172i
$754$	−8.24524	−	10.1291i	−0.300274	−	0.368880i
$755$	−0.186169	−	2.41257i	−0.00677539	−	0.0878026i
$756$	−19.0207	+	5.09659i	−0.691777	+	0.185361i
$757$	0.622824	+	2.32441i	0.0226369	+	0.0844821i	0.976320	−	0.216330i	$-0.0694088\pi$
$757$	0.622824	+	2.32441i	0.0226369	+	0.0844821i	−0.953683	+	0.300813i	$0.902742\pi$
$758$	−37.8037	−	10.1295i	−1.37309	−	0.367919i
$759$	1.65300	−	1.65300i	0.0600000	−	0.0600000i
$760$	1.17115	−	0.802277i	0.0424819	−	0.0291016i
$761$	2.35997	+	0.632352i	0.0855488	+	0.0229227i	0.301340	−	0.953517i	$-0.402566\pi$
$761$	2.35997	+	0.632352i	0.0855488	+	0.0229227i	−0.215791	+	0.976440i	$0.569233\pi$
$762$		−	4.66848i		−	0.169121i
$763$	−12.8144	+	47.8242i	−0.463914	+	1.73135i
$764$	−2.52761	+	4.37796i	−0.0914459	+	0.158389i
$765$	−3.79050	−	1.81508i	−0.137046	−	0.0656245i
$766$			35.5469i			1.28436i
$767$	−43.6120	−	4.47139i	−1.57474	−	0.161452i
$768$	−29.3786	−	29.3786i	−1.06011	−	1.06011i
$769$	−3.50862	−	13.0944i	−0.126524	−	0.472195i	0.873365	−	0.487066i	$-0.161933\pi$
$769$	−3.50862	−	13.0944i	−0.126524	−	0.472195i	−0.999889	+	0.0148712i	$0.995266\pi$
$770$	−24.2513	+	50.6448i	−0.873955	+	1.82511i
$771$	21.9917	−	12.6969i	0.792011	−	0.457268i
$772$	0.384901			0.0138529
$773$	19.4375	−	11.2222i	0.699118	−	0.403636i	−0.107901	−	0.994162i	$-0.534413\pi$
$773$	19.4375	−	11.2222i	0.699118	−	0.403636i	0.807019	+	0.590525i	$0.201079\pi$
$774$	3.87555	−	14.4637i	0.139304	−	0.519888i
$775$	17.2609	−	23.6058i	0.620031	−	0.847944i
$776$	10.5315	+	18.2410i	0.378058	+	0.654815i
$777$	−36.7030	+	9.83454i	−1.31671	+	0.352812i
$778$	−13.6082	+	23.5701i	−0.487878	+	0.845030i
$779$	−0.361484			−0.0129515
$780$	−5.07530	−	21.0452i	−0.181725	−	0.753539i
$781$	17.9032			0.640626
$782$	−0.564890	+	0.978419i	−0.0202004	+	0.0349882i
$783$	−7.84541	+	2.10217i	−0.280372	+	0.0751255i
$784$	−13.4618	−	23.3165i	−0.480778	−	0.832732i
$785$	−0.738363	−	9.56847i	−0.0263533	−	0.341513i
$786$	5.25605	−	19.6158i	0.187477	−	0.699674i
$787$	11.6877	−	6.74791i	0.416622	−	0.240537i	−0.277009	−	0.960867i	$-0.589343\pi$
$787$	11.6877	−	6.74791i	0.416622	−	0.240537i	0.693631	+	0.720330i	$0.256010\pi$
$788$	35.0224			1.24762
$789$	−28.3280	+	16.3552i	−1.00850	+	0.582260i
$790$	6.16960	−	2.17418i	0.219504	−	0.0773538i
$791$	2.09978	+	7.83647i	0.0746594	+	0.278633i
$792$	3.00307	+	3.00307i	0.106709	+	0.106709i
$793$	−8.07086	+	6.56980i	−0.286605	+	0.233300i
$794$		−	9.66696i		−	0.343068i
$795$	18.6934	−	6.58760i	0.662987	−	0.233638i
$796$	3.89696	−	6.74974i	0.138124	−	0.239238i
$797$	−1.62398	+	6.06076i	−0.0575242	+	0.214683i	−0.988705	−	0.149874i	$-0.952113\pi$
$797$	−1.62398	+	6.06076i	−0.0575242	+	0.214683i	0.931181	+	0.364558i	$0.118780\pi$
$798$			6.90201i			0.244328i
$799$	−19.0831	−	5.11330i	−0.675112	−	0.180896i
$800$	25.5698	−	20.5771i	0.904028	−	0.727510i
$801$	−3.08625	+	3.08625i	−0.109047	+	0.109047i
$802$	−49.3238	−	13.2163i	−1.74168	−	0.466683i
$803$	−14.7943	−	55.2132i	−0.522081	−	1.94843i
$804$	5.93922	−	1.59141i	0.209460	−	0.0561247i
$805$	−2.40220	+	0.185369i	−0.0846664	+	0.00653339i
$806$	−15.8001	−	35.2454i	−0.556534	−	1.24146i
$807$	−45.2744	+	45.2744i	−1.59374	+	1.59374i
$808$	4.66009	+	2.69050i	0.163941	+	0.0946516i
$809$	18.6872	+	10.7890i	0.657006	+	0.379322i	0.791135	−	0.611641i	$-0.209490\pi$
$809$	18.6872	+	10.7890i	0.657006	+	0.379322i	−0.134130	+	0.990964i	$0.542824\pi$
$810$	−43.9733	−	8.21941i	−1.54506	−	0.288801i
$811$	22.5473	+	22.5473i	0.791743	+	0.791743i	0.981777	−	0.190035i	$-0.0608601\pi$
$811$	22.5473	+	22.5473i	0.791743	+	0.791743i	−0.190035	+	0.981777i	$0.560860\pi$
$812$	4.74129	+	8.21215i	0.166387	+	0.288190i
$813$	17.3138	+	29.9885i	0.607223	+	1.05174i
$814$	27.1839	+	27.1839i	0.952795	+	0.952795i
$815$	−4.97535	−	0.929983i	−0.174279	−	0.0325759i
$816$	−16.9475	−	9.78462i	−0.593280	−	0.342530i
$817$	4.10012	+	2.36721i	0.143445	+	0.0828180i
$818$	3.41289	−	3.41289i	0.119329	−	0.119329i
$819$	−11.0623	−	4.21408i	−0.386547	−	0.147252i
$820$	−2.03230	+	0.156825i	−0.0709710	+	0.00547656i
$821$	−17.3216	+	4.64130i	−0.604526	+	0.161982i	−0.548084	−	0.836423i	$-0.684642\pi$
$821$	−17.3216	+	4.64130i	−0.604526	+	0.161982i	−0.0564427	+	0.998406i	$0.517976\pi$
$822$	13.4259	+	50.1062i	0.468282	+	1.74765i
$823$	1.11284	+	0.298185i	0.0387913	+	0.0103941i	0.278162	−	0.960534i	$-0.410275\pi$
$823$	1.11284	+	0.298185i	0.0387913	+	0.0103941i	−0.239371	+	0.970928i	$0.576941\pi$
$824$	11.5715	−	11.5715i	0.403112	−	0.403112i
$825$	−29.9079	+	24.0681i	−1.04126	+	0.837944i
$826$	76.1300	+	20.3990i	2.64890	+	0.709771i
$827$			4.45029i			0.154752i	0.997002	+	0.0773759i	$0.0246542\pi$
$827$			4.45029i			0.154752i	−0.997002	+	0.0773759i	$0.975346\pi$
$828$	0.0990534	−	0.369672i	0.00344234	−	0.0128470i
$829$	14.5637	−	25.2251i	0.505819	−	0.876103i	−0.494159	−	0.869372i	$-0.664524\pi$
$829$	14.5637	−	25.2251i	0.505819	−	0.876103i	0.999977	−	0.00673181i	$-0.00214282\pi$
$830$	29.2547	−	10.3094i	1.01545	−	0.357845i
$831$			6.09295i			0.211362i
$832$	−1.30391	−	8.09884i	−0.0452050	−	0.280777i
$833$	−7.91294	−	7.91294i	−0.274167	−	0.274167i
$834$	16.3633	+	61.0685i	0.566613	+	2.11463i
$835$	−1.30664	+	0.460462i	−0.0452181	+	0.0159349i
$836$	2.44229	−	1.41006i	0.0844685	−	0.0487679i
$837$	−24.0199			−0.830249
$838$	31.2015	−	18.0142i	1.07784	−	0.622291i
$839$	8.36719	−	31.2268i	0.288867	−	1.07807i	−0.657099	−	0.753804i	$-0.728217\pi$
$839$	8.36719	−	31.2268i	0.288867	−	1.07807i	0.945967	−	0.324264i	$-0.105117\pi$
$840$	−1.42575	−	18.4764i	−0.0491931	−	0.637496i
$841$	−12.5444	−	21.7275i	−0.432565	−	0.749224i
$842$	−26.1283	+	7.00106i	−0.900441	+	0.241273i
$843$	−26.1718	+	45.3309i	−0.901405	+	1.56128i
$844$	−4.37277			−0.150517
$845$	−11.0281	+	26.8957i	−0.379379	+	0.925241i
$846$	16.5715			0.569739
$847$	7.09313	−	12.2857i	0.243723	−	0.422140i
$848$	21.0565	−	5.64207i	0.723083	−	0.193750i
$849$	−15.1999	−	26.3270i	−0.521660	−	0.903541i
$850$	10.9511	−	14.9765i	0.375619	−	0.513691i
$851$	−0.426931	+	1.59333i	−0.0146350	+	0.0546186i
$852$	10.7464	−	6.20441i	0.368164	−	0.212560i
$853$	9.24230			0.316450			0.158225	−	0.987403i	$-0.449423\pi$
$853$	9.24230			0.316450			0.158225	+	0.987403i	$0.449423\pi$
$854$	16.2025	−	9.35453i	0.554439	−	0.320105i
$855$	−0.481373	+	1.00527i	−0.0164626	+	0.0343794i
$856$	2.16228	+	8.06972i	0.0739051	+	0.275817i
$857$	−37.7913	−	37.7913i	−1.29093	−	1.29093i	−0.934214	−	0.356713i	$-0.883897\pi$
$857$	−37.7913	−	37.7913i	−1.29093	−	1.29093i	−0.356713	−	0.934214i	$-0.616103\pi$
$858$	8.05973	+	50.0606i	0.275155	+	1.70904i
$859$		−	6.16263i		−	0.210266i	−0.994458	−	0.105133i	$-0.966473\pi$
$859$		−	6.16263i		−	0.210266i	0.994458	−	0.105133i	$-0.0335269\pi$
$860$	24.0783	+	11.5299i	0.821063	+	0.393166i
$861$	−2.35941	+	4.08661i	−0.0804083	+	0.139271i
$862$	−8.12181	+	30.3110i	−0.276630	+	1.03240i
$863$		−	33.7740i		−	1.14968i	−0.818266	−	0.574840i	$-0.805064\pi$
$863$		−	33.7740i		−	1.14968i	0.818266	−	0.574840i	$-0.194936\pi$
$864$	−26.0401	−	6.97742i	−0.885902	−	0.237377i
$865$	−12.2152	+	8.36789i	−0.415331	+	0.284517i
$866$	−14.5532	+	14.5532i	−0.494539	+	0.494539i
$867$	24.6868	+	6.61482i	0.838409	+	0.224651i
$868$	7.25808	+	27.0875i	0.246355	+	0.919410i
$869$	−5.97678	+	1.60147i	−0.202748	+	0.0543263i
$870$	1.23507	+	16.0053i	0.0418727	+	0.542630i
$871$	−7.71545	−	2.93913i	−0.261428	−	0.0995886i
$872$	−11.6896	+	11.6896i	−0.395861	+	0.395861i
$873$	−14.3218	−	8.26870i	−0.484720	−	0.279853i
$874$	0.259484	+	0.149813i	0.00877716	+	0.00506750i
$875$	39.5474	+	1.21681i	1.33695	+	0.0411357i
$876$	−28.0146	−	28.0146i	−0.946527	−	0.946527i
$877$	−11.3486	−	19.6563i	−0.383214	−	0.663747i	0.608305	−	0.793703i	$-0.291850\pi$
$877$	−11.3486	−	19.6563i	−0.383214	−	0.663747i	−0.991520	+	0.129956i	$0.958516\pi$
$878$	−3.88705	−	6.73256i	−0.131181	−	0.227213i
$879$	14.5417	+	14.5417i	0.490480	+	0.490480i
$880$	−34.8334	+	23.8621i	−1.17423	+	0.804392i
$881$	−6.78312	−	3.91623i	−0.228529	−	0.131941i	0.381364	−	0.924425i	$-0.375454\pi$
$881$	−6.78312	−	3.91623i	−0.228529	−	0.131941i	−0.609893	+	0.792484i	$0.708788\pi$
$882$	8.12905	+	4.69331i	0.273719	+	0.158032i
$883$	18.9296	−	18.9296i	0.637032	−	0.637032i	−0.312790	−	0.949822i	$-0.601264\pi$
$883$	18.9296	−	18.9296i	0.637032	−	0.637032i	0.949822	+	0.312790i	$0.101264\pi$
$884$	−4.04832	−	9.03064i	−0.136160	−	0.303733i
$885$	40.9204	+	35.0575i	1.37552	+	1.17844i
$886$	−37.9234	+	10.1615i	−1.27406	+	0.341384i
$887$	9.19729	+	34.3248i	0.308815	+	1.15251i	0.929612	+	0.368541i	$0.120143\pi$
$887$	9.19729	+	34.3248i	0.308815	+	1.15251i	−0.620797	+	0.783972i	$0.713191\pi$
$888$	−12.2550	−	3.28372i	−0.411251	−	0.110194i
$889$	3.21825	−	3.21825i	0.107937	−	0.107937i
$890$	−10.8893	−	15.8960i	−0.365012	−	0.532836i
$891$	40.8731	+	10.9519i	1.36930	+	0.366903i
$892$		−	10.0467i		−	0.336389i
$893$	−1.35608	+	5.06098i	−0.0453796	+	0.169359i
$894$	23.8314	−	41.2772i	0.797042	−	1.38052i
$895$	−1.62777	−	4.61908i	−0.0544104	−	0.154399i
$896$		−	31.7130i		−	1.05946i
$897$	−1.68730	+	1.37348i	−0.0563372	+	0.0458593i
$898$	18.8417	+	18.8417i	0.628755	+	0.628755i
$899$	2.99371	+	11.1727i	0.0998459	+	0.372630i
$900$	−2.27021	+	5.86056i	−0.0756736	+	0.195352i
$901$	7.84682	−	4.53036i	0.261415	−	0.150928i
$902$	4.77421			0.158964
$903$	53.5230	−	30.9015i	1.78113	−	1.02834i
$904$	−0.701108	+	2.61657i	−0.0233185	+	0.0870258i
$905$	16.2891	+	13.9553i	0.541469	+	0.463889i
$906$	1.96411	+	3.40193i	0.0652530	+	0.113022i
$907$	44.9172	−	12.0355i	1.49145	−	0.399633i	0.581225	−	0.813743i	$-0.302574\pi$
$907$	44.9172	−	12.0355i	1.49145	−	0.399633i	0.910227	+	0.414109i	$0.135907\pi$
$908$	2.64357	−	4.57880i	0.0877300	−	0.151953i
$909$	−4.22485			−0.140130
$910$	27.2598	−	44.5863i	0.903653	−	1.47802i
$911$	17.7325			0.587504			0.293752	−	0.955882i	$-0.405096\pi$
$911$	17.7325			0.587504			0.293752	+	0.955882i	$0.405096\pi$
$912$	−2.59495	+	4.49459i	−0.0859274	+	0.148831i
$913$	−28.3404	+	7.59379i	−0.937931	+	0.251318i
$914$	−27.7449	−	48.0556i	−0.917720	−	1.58954i
$915$	12.7530	−	0.984100i	0.421601	−	0.0325333i
$916$	−6.14674	+	22.9399i	−0.203094	+	0.757957i
$917$	17.1456	−	9.89902i	0.566198	−	0.326894i
$918$	−15.2393			−0.502971
$919$	42.2580	−	24.3977i	1.39396	−	0.804806i	0.400213	−	0.916422i	$-0.368936\pi$
$919$	42.2580	−	24.3977i	1.39396	−	0.804806i	0.993751	+	0.111617i	$0.0356029\pi$
$920$	−0.725574	−	0.347441i	−0.0239215	−	0.0114548i
$921$	−1.09736	−	4.09541i	−0.0361593	−	0.134948i
$922$	8.98564	+	8.98564i	0.295926	+	0.295926i
$923$	−16.5752	−	1.69940i	−0.545581	−	0.0559365i
$924$		−	36.8139i		−	1.21109i
$925$	9.78485	−	25.2597i	0.321724	−	0.830533i
$926$	−28.7990	+	49.8814i	−0.946395	+	1.63920i
$927$	−3.32544	+	12.4107i	−0.109222	+	0.407621i
$928$			12.9820i			0.426155i
$929$	10.0330	+	2.68833i	0.329171	+	0.0882012i	0.419620	−	0.907700i	$-0.362163\pi$
$929$	10.0330	+	2.68833i	0.329171	+	0.0882012i	−0.0904485	+	0.995901i	$0.528830\pi$
$930$	−8.72260	+	46.6653i	−0.286025	+	1.53022i
$931$	−2.09857	+	2.09857i	−0.0687778	+	0.0687778i
$932$	5.34810	+	1.43302i	0.175183	+	0.0469401i
$933$	−1.95987	−	7.31433i	−0.0641632	−	0.239460i
$934$	−9.24814	+	2.47803i	−0.302608	+	0.0810837i
$935$	−11.4179	+	13.3274i	−0.373406	+	0.435853i
$936$	−2.49527	−	3.06538i	−0.0815604	−	0.100195i
$937$	5.31856	−	5.31856i	0.173750	−	0.173750i	−0.614875	−	0.788625i	$-0.710794\pi$
$937$	5.31856	−	5.31856i	0.173750	−	0.173750i	0.788625	+	0.614875i	$0.210794\pi$
$938$	12.8544	+	7.42149i	0.419711	+	0.242320i
$939$	7.39178	+	4.26764i	0.241221	+	0.139269i
$940$	−5.42842	+	29.0417i	−0.177055	+	0.947235i
$941$	−38.9093	−	38.9093i	−1.26841	−	1.26841i	−0.946911	−	0.321497i	$-0.895814\pi$
$941$	−38.9093	−	38.9093i	−1.26841	−	1.26841i	−0.321497	−	0.946911i	$-0.604186\pi$
$942$	7.78981	+	13.4923i	0.253806	+	0.439604i
$943$	0.102425	+	0.177406i	0.00333542	+	0.00577712i
$944$	41.9064	+	41.9064i	1.36394	+	1.36394i
$945$	−18.3667	−	26.8113i	−0.597468	−	0.872170i
$946$	−54.1514	−	31.2643i	−1.76061	−	1.01649i
$947$	29.2298	+	16.8759i	0.949842	+	0.548392i	0.893032	−	0.449993i	$-0.148574\pi$
$947$	29.2298	+	16.8759i	0.949842	+	0.548392i	0.0568101	+	0.998385i	$0.481907\pi$
$948$	−3.03256	+	3.03256i	−0.0984930	+	0.0984930i
$949$	8.45606	+	52.5222i	0.274495	+	1.70494i
$950$	−3.97188	−	2.90431i	−0.128865	−	0.0942281i
$951$	−44.2451	+	11.8554i	−1.43475	+	0.384439i
$952$	−2.19259	−	8.18285i	−0.0710622	−	0.265208i
$953$	4.26581	+	1.14302i	0.138183	+	0.0370260i	0.327248	−	0.944939i	$-0.393879\pi$
$953$	4.26581	+	1.14302i	0.138183	+	0.0370260i	−0.189065	+	0.981965i	$0.560546\pi$
$954$	−5.37407	+	5.37407i	−0.173992	+	0.173992i
$955$	−8.20103	−	1.53292i	−0.265379	−	0.0496042i
$956$	−16.6072	−	4.44988i	−0.537115	−	0.143919i
$957$		−	15.1845i		−	0.490845i
$958$	−9.17471	+	34.2405i	−0.296422	+	1.10626i
$959$	−25.2858	+	43.7963i	−0.816520	+	1.41425i
$960$	−4.35448	+	9.09361i	−0.140540	+	0.293495i
$961$			3.20686i			0.103447i
$962$	−22.5872	−	27.7479i	−0.728242	−	0.894630i
$963$	−4.63819	−	4.63819i	−0.149463	−	0.149463i
$964$	−6.15338	−	22.9647i	−0.198187	−	0.739645i
$965$	0.211132	+	0.599122i	0.00679657	+	0.0192864i
$966$	3.38730	−	1.95566i	0.108985	−	0.0629223i
$967$	16.2803			0.523540			0.261770	−	0.965130i	$-0.415694\pi$
$967$	16.2803			0.523540			0.261770	+	0.965130i	$0.415694\pi$
$968$	4.10214	−	2.36837i	0.131848	−	0.0761223i
$969$	−0.558310	+	2.08364i	−0.0179355	+	0.0669363i
$970$	47.4986	−	55.4421i	1.52509	−	1.78014i
$971$	−6.40146	−	11.0877i	−0.205433	−	0.355820i	0.744838	−	0.667245i	$-0.232527\pi$
$971$	−6.40146	−	11.0877i	−0.205433	−	0.355820i	−0.950270	+	0.311426i	$0.899193\pi$
$972$	12.2052	−	3.27038i	0.391482	−	0.104897i
$973$	−30.8179	+	53.3781i	−0.987975	+	1.71122i
$974$	−42.7918			−1.37114
$975$	29.9741	−	19.4440i	0.959940	−	0.622707i
$976$	14.0681			0.450309
$977$	8.02436	−	13.8986i	0.256722	−	0.444655i	−0.708640	−	0.705570i	$-0.750691\pi$
$977$	8.02436	−	13.8986i	0.256722	−	0.444655i	0.965362	+	0.260915i	$0.0840242\pi$
$978$	7.93687	−	2.12668i	0.253793	−	0.0680037i
$979$	9.11292	+	15.7840i	0.291250	+	0.504460i
$980$	−10.8879	+	12.7088i	−0.347803	+	0.405968i
$981$	3.35939	−	12.5374i	0.107257	−	0.400288i
$982$	−33.8164	+	19.5239i	−1.07912	+	0.623033i
$983$	−34.3036			−1.09411			−0.547057	−	0.837096i	$-0.684252\pi$
$983$	−34.3036			−1.09411			−0.547057	+	0.837096i	$0.684252\pi$
$984$	−1.36450	+	0.787797i	−0.0434988	+	0.0251141i
$985$	19.2110	+	54.5145i	0.612114	+	1.73698i
$986$	1.89934	+	7.08844i	0.0604874	+	0.225742i
$987$	48.3637	+	48.3637i	1.53943	+	1.53943i
$988$	−2.39499	+	1.07364i	−0.0761947	+	0.0341572i
$989$		−	2.68296i		−	0.0853131i
$990$	6.35762	−	13.2768i	0.202058	−	0.421966i
$991$	−11.1772	+	19.3596i	−0.355057	+	0.614977i	−0.987128	−	0.159934i	$-0.948872\pi$
$991$	−11.1772	+	19.3596i	−0.355057	+	0.614977i	0.632071	+	0.774911i	$0.282205\pi$
$992$	−9.93658	+	37.0838i	−0.315487	+	1.17741i
$993$		−	3.95773i		−	0.125595i
$994$	28.9341	+	7.75287i	0.917734	+	0.245906i
$995$	12.6440	+	2.36339i	0.400842	+	0.0749246i
$996$	−14.3796	+	14.3796i	−0.455637	+	0.455637i
$997$	−11.4991	−	3.08118i	−0.364181	−	0.0975820i	0.0720881	−	0.997398i	$-0.477034\pi$
$997$	−11.4991	−	3.08118i	−0.364181	−	0.0975820i	−0.436269	+	0.899816i	$0.643700\pi$
$998$	−15.4458	−	57.6445i	−0.488928	−	1.82471i
$999$	−21.4920	+	5.75875i	−0.679975	+	0.182199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.o.a.33.2	yes	20
3.2	odd	2		585.2.cf.a.163.4		20
5.2	odd	4		65.2.t.a.7.2	yes	20
5.3	odd	4		325.2.x.b.7.4		20
5.4	even	2		325.2.s.b.293.4		20
13.2	odd	12		65.2.t.a.28.2	yes	20
13.3	even	3		845.2.o.e.258.2		20
13.4	even	6		845.2.k.d.268.3		20
13.5	odd	4		845.2.t.f.188.4		20
13.6	odd	12		845.2.f.e.408.3		20
13.7	odd	12		845.2.f.d.408.8		20
13.8	odd	4		845.2.t.e.188.2		20
13.9	even	3		845.2.k.e.268.8		20
13.10	even	6		845.2.o.f.258.4		20
13.11	odd	12		845.2.t.g.418.4		20
13.12	even	2		845.2.o.g.488.4		20
15.2	even	4		585.2.dp.a.397.4		20
39.2	even	12		585.2.dp.a.28.4		20
65.2	even	12	inner	65.2.o.a.2.2	✓	20
65.7	even	12		845.2.k.d.577.3		20
65.12	odd	4		845.2.t.g.657.4		20
65.17	odd	12		845.2.f.d.437.3		20
65.22	odd	12		845.2.f.e.437.8		20
65.28	even	12		325.2.s.b.132.4		20
65.32	even	12		845.2.k.e.577.8		20
65.37	even	12		845.2.o.g.587.4		20
65.42	odd	12		845.2.t.f.427.4		20
65.47	even	4		845.2.o.f.357.4		20
65.54	odd	12		325.2.x.b.93.4		20
65.57	even	4		845.2.o.e.357.2		20
65.62	odd	12		845.2.t.e.427.2		20
195.2	odd	12		585.2.cf.a.262.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.2	✓	20	65.2	even	12	inner
65.2.o.a.33.2	yes	20	1.1	even	1	trivial
65.2.t.a.7.2	yes	20	5.2	odd	4
65.2.t.a.28.2	yes	20	13.2	odd	12
325.2.s.b.132.4		20	65.28	even	12
325.2.s.b.293.4		20	5.4	even	2
325.2.x.b.7.4		20	5.3	odd	4
325.2.x.b.93.4		20	65.54	odd	12
585.2.cf.a.163.4		20	3.2	odd	2
585.2.cf.a.262.4		20	195.2	odd	12
585.2.dp.a.28.4		20	39.2	even	12
585.2.dp.a.397.4		20	15.2	even	4
845.2.f.d.408.8		20	13.7	odd	12
845.2.f.d.437.3		20	65.17	odd	12
845.2.f.e.408.3		20	13.6	odd	12
845.2.f.e.437.8		20	65.22	odd	12
845.2.k.d.268.3		20	13.4	even	6
845.2.k.d.577.3		20	65.7	even	12
845.2.k.e.268.8		20	13.9	even	3
845.2.k.e.577.8		20	65.32	even	12
845.2.o.e.258.2		20	13.3	even	3
845.2.o.e.357.2		20	65.57	even	4
845.2.o.f.258.4		20	13.10	even	6
845.2.o.f.357.4		20	65.47	even	4
845.2.o.g.488.4		20	13.12	even	2
845.2.o.g.587.4		20	65.37	even	12
845.2.t.e.188.2		20	13.8	odd	4
845.2.t.e.427.2		20	65.62	odd	12
845.2.t.f.188.4		20	13.5	odd	4
845.2.t.f.427.4		20	65.42	odd	12
845.2.t.g.418.4		20	13.11	odd	12
845.2.t.g.657.4		20	65.12	odd	4

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.915816 + 1.58624i) q^{2} +(1.91432 - 0.512942i) q^{3} +(-0.677439 - 1.17336i) q^{4} +(1.45480 - 1.69810i) q^{5} +(-0.939520 + 3.50634i) q^{6} +(-3.06478 + 1.76945i) q^{7} -1.18163 q^{8} +(0.803451 - 0.463873i) q^{9} +O(q^{10})\)	\(q+(-0.915816 + 1.58624i) q^{2} +(1.91432 - 0.512942i) q^{3} +(-0.677439 - 1.17336i) q^{4} +(1.45480 - 1.69810i) q^{5} +(-0.939520 + 3.50634i) q^{6} +(-3.06478 + 1.76945i) q^{7} -1.18163 q^{8} +(0.803451 - 0.463873i) q^{9} +(1.36126 + 3.86282i) q^{10} +(-1.00269 - 3.74209i) q^{11} +(-1.89870 - 1.89870i) q^{12} +(0.573112 + 3.55971i) q^{13} -6.48197i q^{14} +(1.91394 - 3.99694i) q^{15} +(2.43703 - 4.22106i) q^{16} +(0.524334 - 1.95684i) q^{17} +1.69929i q^{18} +(-0.518968 - 0.139057i) q^{19} +(-2.97802 - 0.556646i) q^{20} +(-4.95936 + 4.95936i) q^{21} +(6.85414 + 1.83656i) q^{22} +(0.0788026 + 0.294095i) q^{23} +(-2.26202 + 0.606106i) q^{24} +(-0.767094 - 4.94081i) q^{25} +(-6.17142 - 2.35095i) q^{26} +(-2.90402 + 2.90402i) q^{27} +(4.15240 + 2.39739i) q^{28} +(1.71273 + 0.988843i) q^{29} +(4.58730 + 6.69643i) q^{30} +(4.13563 + 4.13563i) q^{31} +(3.28212 + 5.68479i) q^{32} +(-3.83895 - 6.64926i) q^{33} +(2.62382 + 2.62382i) q^{34} +(-1.45395 + 7.77851i) q^{35} +(-1.08858 - 0.628491i) q^{36} +(4.69189 + 2.70887i) q^{37} +(0.695857 - 0.695857i) q^{38} +(2.92305 + 6.52047i) q^{39} +(-1.71904 + 2.00652i) q^{40} +(0.649884 - 0.174136i) q^{41} +(-3.32487 - 12.4086i) q^{42} +(-8.51164 - 2.28069i) q^{43} +(-3.71155 + 3.71155i) q^{44} +(0.381161 - 2.03919i) q^{45} +(-0.538675 - 0.144337i) q^{46} -9.75201i q^{47} +(2.50011 - 9.33053i) q^{48} +(2.76192 - 4.78379i) q^{49} +(8.53982 + 3.30807i) q^{50} -4.01498i q^{51} +(3.78857 - 3.08395i) q^{52} +(3.16254 + 3.16254i) q^{53} +(-1.94693 - 7.26602i) q^{54} +(-7.81317 - 3.74134i) q^{55} +(3.62143 - 2.09083i) q^{56} -1.06480 q^{57} +(-3.13709 + 1.81120i) q^{58} +(-3.14703 + 11.7449i) q^{59} +(-5.98642 + 0.461950i) q^{60} +(1.44316 + 2.49963i) q^{61} +(-10.3476 + 2.77263i) q^{62} +(-1.64160 + 2.84334i) q^{63} -2.27514 q^{64} +(6.87851 + 4.20548i) q^{65} +14.0631 q^{66} +(-1.14494 + 1.98310i) q^{67} +(-2.65128 + 0.710408i) q^{68} +(0.301707 + 0.522573i) q^{69} +(-11.0070 - 9.43000i) q^{70} +(-1.19607 + 4.46378i) q^{71} +(-0.949380 + 0.548125i) q^{72} +14.7546 q^{73} +(-8.59382 + 4.96165i) q^{74} +(-4.00281 - 9.06483i) q^{75} +(0.188405 + 0.703137i) q^{76} +(9.69449 + 9.69449i) q^{77} +(-13.0200 - 1.33490i) q^{78} -1.59718i q^{79} +(-3.62239 - 10.2791i) q^{80} +(-5.46126 + 9.45918i) q^{81} +(-0.318953 + 1.19035i) q^{82} -7.57341i q^{83} +(9.17877 + 2.45944i) q^{84} +(-2.56011 - 3.73719i) q^{85} +(11.4128 - 11.4128i) q^{86} +(3.78593 + 1.01444i) q^{87} +(1.18481 + 4.42176i) q^{88} +(-4.54423 + 1.21762i) q^{89} +(2.88556 + 2.47213i) q^{90} +(-8.05520 - 9.89564i) q^{91} +(0.291695 - 0.291695i) q^{92} +(10.0383 + 5.79560i) q^{93} +(15.4690 + 8.93105i) q^{94} +(-0.991129 + 0.678959i) q^{95} +(9.19900 + 9.19900i) q^{96} +(-8.91268 - 15.4372i) q^{97} +(5.05883 + 8.76215i) q^{98} +(-2.54147 - 2.54147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Introduction

L-functions

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