LMFDB - Embedded newform 65.2.o.a.2.2

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

$q$-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} +(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} - 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}+ \cdots - 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

Character values

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

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{12}\right)$

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	−0.983699	−	0.179822i	$-0.942448\pi$
$2$	−0.915816	−	1.58624i	−0.647580	−	1.12164i	0.336119	−	0.941819i	$-0.390885\pi$
$3$	1.91432	+	0.512942i	1.10524	+	0.296147i	0.764895	−	0.644155i	$-0.222791\pi$
$3$	1.91432	+	0.512942i	1.10524	+	0.296147i	0.340341	+	0.940302i	$0.389458\pi$
$4$	−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	−0.207464	−	0.978243i	$-0.566521\pi$
$7$	−3.06478	−	1.76945i	−1.15838	−	0.668790i	−0.950915	+	0.309453i	$0.899854\pi$
$8$	−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	0.632903	+	0.774231i	$0.281863\pi$
$11$	−1.00269	+	3.74209i	−0.302323	+	1.12828i	−0.935226	+	0.354053i	$0.884803\pi$
$12$	−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	0.999908	−	0.0135853i	$-0.00432448\pi$
$17$	0.524334	+	1.95684i	0.127170	+	0.474603i	−0.872738	+	0.488189i	$0.837658\pi$
$18$		−	1.69929i		−	0.400526i
$19$	−0.518968	+	0.139057i	−0.119059	+	0.0319019i	−0.317857	−	0.948139i	$-0.602963\pi$
$19$	−0.518968	+	0.139057i	−0.119059	+	0.0319019i	0.198797	+	0.980041i	$0.436296\pi$
$20$	−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	−0.957223	−	0.289350i	$-0.906561\pi$
$23$	0.0788026	−	0.294095i	0.0164315	−	0.0613231i	0.973655	+	0.228027i	$0.0732275\pi$
$24$	−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	−0.332476	−	0.943112i	$-0.607884\pi$
$29$	1.71273	−	0.988843i	0.318045	−	0.183624i	0.650521	+	0.759488i	$0.274551\pi$
$30$	4.58730	−	6.69643i	0.837522	−	1.22260i
$31$	4.13563	−	4.13563i	0.742781	−	0.742781i	−0.230331	−	0.973112i	$-0.573981\pi$
$31$	4.13563	−	4.13563i	0.742781	−	0.742781i	0.973112	+	0.230331i	$0.0739810\pi$
$32$	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	−0.0620109	−	0.998075i	$-0.519751\pi$
$37$	4.69189	−	2.70887i	0.771342	−	0.445335i	0.833353	+	0.552741i	$0.186418\pi$
$38$	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	0.309209	−	0.950994i	$-0.399936\pi$
$41$	0.649884	+	0.174136i	0.101495	+	0.0271955i	−0.207714	+	0.978190i	$0.566602\pi$
$42$	−3.32487	+	12.4086i	−0.513039	+	1.91469i
$43$	−8.51164	+	2.28069i	−1.29801	+	0.347802i	−0.840698	−	0.541504i	$-0.817855\pi$
$43$	−8.51164	+	2.28069i	−1.29801	+	0.347802i	−0.457314	+	0.889305i	$0.651189\pi$
$44$	−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	$0.251865\pi$
$47$			9.75201i			1.42248i	−0.702951	+	0.711238i	$0.748135\pi$
$48$	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	−0.455716	−	0.890125i	$-0.650617\pi$
$53$	3.16254	−	3.16254i	0.434409	−	0.434409i	0.890125	+	0.455716i	$0.150617\pi$
$54$	−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	−0.795203	−	0.606343i	$-0.792636\pi$
$59$	−3.14703	−	11.7449i	−0.409708	−	1.52905i	0.385495	−	0.922710i	$-0.374031\pi$
$60$	−5.98642	−	0.461950i	−0.772844	−	0.0596374i
$61$	1.44316	−	2.49963i	0.184778	−	0.320044i	−0.758724	−	0.651412i	$-0.774177\pi$
$61$	1.44316	−	2.49963i	0.184778	−	0.320044i	0.943502	+	0.331368i	$0.107510\pi$
$62$	−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	0.787573	−	0.616222i	$-0.211337\pi$
$67$	−1.14494	−	1.98310i	−0.139877	−	0.242274i	−0.927450	+	0.373947i	$0.878004\pi$
$68$	−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	−0.999872	−	0.0159789i	$-0.994914\pi$
$71$	−1.19607	−	4.46378i	−0.141947	−	0.529753i	0.857925	−	0.513774i	$-0.171753\pi$
$72$	−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	$0.0286382\pi$
$79$			1.59718i			0.179696i	−0.995955	+	0.0898482i	$0.971362\pi$
$80$	−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	$0.136444\pi$
$83$			7.57341i			0.831290i	−0.909527	+	0.415645i	$0.863556\pi$
$84$	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	0.00980081	−	0.999952i	$-0.496880\pi$
$89$	−4.54423	−	1.21762i	−0.481687	−	0.129068i	−0.491488	+	0.870884i	$0.663547\pi$
$90$	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	−0.0839547	+	0.996470i	$0.526755\pi$
$97$	−8.91268	+	15.4372i	−0.904945	+	1.56741i	−0.820991	+	0.570942i	$0.806578\pi$
$98$	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	−0.683209	−	0.730223i	$-0.739416\pi$
$101$	−3.94379	+	2.27695i	−0.392421	+	0.226565i	0.290787	+	0.956788i	$0.406083\pi$
$102$	6.36872	−	3.67698i	0.630597	−	0.364075i
$103$	−9.79285	−	9.79285i	−0.964918	−	0.964918i	0.0344872	−	0.999405i	$-0.489020\pi$
$103$	−9.79285	−	9.79285i	−0.964918	−	0.964918i	−0.999405	+	0.0344872i	$0.989020\pi$
$104$	−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	0.819315	+	0.573344i	$0.194354\pi$
$107$	−1.82991	+	6.82933i	−0.176904	+	0.660216i	−0.996219	+	0.0868725i	$0.972313\pi$
$108$	5.37475	−	1.44016i	0.517186	−	0.138580i
$109$	9.89281	+	9.89281i	0.947560	+	0.947560i	0.998692	−	0.0511324i	$-0.0162830\pi$
$109$	9.89281	+	9.89281i	0.947560	+	0.947560i	−0.0511324	+	0.998692i	$0.516283\pi$
$110$	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	0.988202	−	0.153154i	$-0.0489432\pi$
$113$	0.593341	+	2.21438i	0.0558168	+	0.208311i	−0.932385	+	0.361466i	$0.882277\pi$
$114$	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	0.203281	−	0.979120i	$-0.434839\pi$
$127$	−1.24225	−	0.332860i	−0.110232	−	0.0295366i	−0.313513	+	0.949584i	$0.601506\pi$
$128$	−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	0.924691	−	0.380719i	$-0.124324\pi$
$137$	12.3757	+	7.14509i	1.05732	+	0.610446i	0.132633	+	0.991165i	$0.457657\pi$
$138$	−1.10523			−0.0940838
$139$	15.0832	+	8.70830i	1.27934	+	0.738629i	0.976727	−	0.214484i	$-0.0688071\pi$
$139$	15.0832	+	8.70830i	1.27934	+	0.738629i	0.302615	+	0.953113i	$0.402140\pi$
$140$	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	−0.737704	−	0.675124i	$-0.764090\pi$
$149$	−12.6828	+	3.39833i	−1.03901	+	0.278402i	−0.301308	+	0.953527i	$0.597423\pi$
$150$	18.0448	−	1.95230i	1.47335	−	0.159404i
$151$	0.765191	+	0.765191i	0.0622704	+	0.0622704i	0.737556	−	0.675286i	$-0.235980\pi$
$151$	0.765191	+	0.765191i	0.0622704	+	0.0622704i	−0.675286	+	0.737556i	$0.735980\pi$
$152$	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	0.817762	−	0.575557i	$-0.195215\pi$
$157$	3.03481	+	3.03481i	0.242204	+	0.242204i	−0.575557	+	0.817762i	$0.695215\pi$
$158$	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	−0.906940	−	0.421260i	$-0.861588\pi$
$163$	−1.13179	+	1.96032i	−0.0886486	+	0.153544i	0.818292	+	0.574803i	$0.194921\pi$
$164$	−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	−0.520617	−	0.853791i	$-0.674298\pi$
$167$	−0.536563	+	0.309785i	−0.0415205	+	0.0239719i	0.479096	+	0.877762i	$0.340965\pi$
$168$	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	−0.493627	−	0.869674i	$-0.664329\pi$
$173$	−6.39606	+	1.71382i	−0.486283	+	0.130299i	0.00734343	+	0.999973i	$0.497662\pi$
$174$	−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	0.904046	−	0.427436i	$-0.140583\pi$
$179$	1.09512	+	1.89680i	0.0818528	+	0.141773i	−0.822193	+	0.569209i	$0.807250\pi$
$180$	−2.65091	−	0.934185i	−0.197587	−	0.0696300i
$181$		−	9.59255i		−	0.713009i	−0.934294	−	0.356504i	$-0.883969\pi$
$181$		−	9.59255i		−	0.713009i	0.934294	−	0.356504i	$-0.116031\pi$
$182$	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	−0.925593	−	0.378521i	$-0.876433\pi$
$191$	−1.86557	+	3.23126i	−0.134988	+	0.233806i	0.790605	+	0.612326i	$0.209766\pi$
$192$	−4.35536	−	1.16701i	−0.314321	−	0.0842220i
$193$	−0.142043	−	0.246025i	−0.0102245	−	0.0177093i	0.860868	−	0.508829i	$-0.169921\pi$
$193$	−0.142043	−	0.246025i	−0.0102245	−	0.0177093i	−0.871092	+	0.491119i	$0.836588\pi$
$194$	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	−0.798122	−	0.602496i	$-0.794173\pi$
$197$	−12.9246	−	22.3860i	−0.920838	−	1.59494i	−0.122716	−	0.992442i	$-0.539160\pi$
$198$	6.35890	+	1.70386i	0.451907	+	0.121088i
$199$	2.87625	−	4.98181i	0.203892	−	0.353151i	−0.745887	−	0.666072i	$-0.767974\pi$
$199$	2.87625	−	4.98181i	0.203892	−	0.353151i	0.949779	+	0.312921i	$0.101308\pi$
$200$	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	0.916211	−	0.400696i	$-0.131232\pi$
$211$	1.61372	+	2.79504i	0.111093	+	0.192418i	−0.805118	+	0.593114i	$0.797898\pi$
$212$	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	−0.269327	−	0.963049i	$-0.586801\pi$
$223$	6.42178	−	3.70762i	0.430034	−	0.248280i	0.699361	+	0.714768i	$0.253468\pi$
$224$	−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	−0.793981	−	0.607942i	$-0.791995\pi$
$227$	1.95115	−	3.37949i	0.129502	−	0.224305i	0.923484	+	0.383637i	$0.125329\pi$
$228$	0.721337	−	1.24939i	0.0477717	−	0.0827430i
$229$	−12.3946	+	12.3946i	−0.819060	+	0.819060i	−0.985972	−	0.166912i	$-0.946621\pi$
$229$	−12.3946	+	12.3946i	−0.819060	+	0.819060i	0.166912	+	0.985972i	$0.446621\pi$
$230$	−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	0.606090	−	0.795396i	$-0.292737\pi$
$233$	−2.88962	−	2.88962i	−0.189305	−	0.189305i	−0.795396	+	0.606090i	$0.792737\pi$
$234$	−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	0.935017	−	0.354602i	$-0.115384\pi$
$239$	8.97299	+	8.97299i	0.580415	+	0.580415i	−0.354602	+	0.935017i	$0.615384\pi$
$240$	−12.2070	+	17.8195i	−0.787960	+	1.15025i
$241$	16.9497	−	4.54165i	1.09183	−	0.292554i	0.332394	−	0.943141i	$-0.392144\pi$
$241$	16.9497	−	4.54165i	1.09183	−	0.292554i	0.759432	+	0.650587i	$0.225477\pi$
$242$			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	0.958296	−	0.285776i	$-0.0922513\pi$
$251$	18.8524	+	10.8845i	1.18996	+	0.687021i	0.231659	+	0.972797i	$0.425585\pi$
$252$	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	0.623268	−	0.782009i	$-0.285805\pi$
$257$	12.3766	+	3.31629i	0.772029	+	0.206864i	0.148761	+	0.988873i	$0.452471\pi$
$258$	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	−0.268727	−	0.963216i	$-0.586603\pi$
$263$	−15.9426	−	4.27179i	−0.983060	−	0.263410i	−0.714333	+	0.699806i	$0.753270\pi$
$264$	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	−0.939519	−	0.342495i	$-0.888728\pi$
$269$	−27.9787	−	16.1535i	−1.70589	−	0.984895i	−0.766370	−	0.642400i	$-0.777939\pi$
$270$	−15.1708	+	7.26456i	−0.923268	+	0.442107i
$271$	4.52218	−	16.8770i	0.274703	−	1.02521i	−0.681337	−	0.731970i	$-0.738601\pi$
$271$	4.52218	−	16.8770i	0.274703	−	1.02521i	0.956040	−	0.293236i	$-0.0947321\pi$
$272$	−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	0.937892	−	0.346926i	$-0.112775\pi$
$277$	−0.795705	−	2.96961i	−0.0478093	−	0.178427i	−0.985702	+	0.168499i	$0.946108\pi$
$278$		−	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	−0.992590	−	0.121508i	$-0.961227\pi$
$281$	−18.6757	−	18.6757i	−1.11410	−	1.11410i	−0.121508	−	0.992590i	$-0.538773\pi$
$282$	34.1938	−	9.16221i	2.03621	−	0.545602i
$283$	−3.97005	+	14.8164i	−0.235995	+	0.880745i	0.741703	+	0.670728i	$0.234018\pi$
$283$	−3.97005	+	14.8164i	−0.235995	+	0.880745i	−0.977698	+	0.210016i	$0.932648\pi$
$284$	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	−0.673731	−	0.738976i	$-0.735309\pi$
$293$	5.18835	−	8.98649i	0.303107	−	0.524996i	0.976838	+	0.213980i	$0.0686428\pi$
$294$	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	$0.0194448\pi$
$307$			2.13935i			0.122099i	−0.998135	+	0.0610496i	$0.980555\pi$
$308$	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	$0.0345503\pi$
$311$			3.82084i			0.216660i	−0.994115	+	0.108330i	$0.965450\pi$
$312$	−3.45395	+	7.70477i	−0.195542	+	0.436196i
$313$	3.04531	−	3.04531i	0.172131	−	0.172131i	−0.615784	−	0.787915i	$-0.711161\pi$
$313$	3.04531	−	3.04531i	0.172131	−	0.172131i	0.787915	+	0.615784i	$0.211161\pi$
$314$	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	0.978675	−	0.205417i	$-0.0658550\pi$
$331$	0.516858	+	1.92894i	0.0284091	+	0.106024i	−0.950265	+	0.311441i	$0.899188\pi$
$332$	−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	−0.854018	−	0.520244i	$-0.825841\pi$
$337$	−6.12727	+	6.12727i	−0.333773	+	0.333773i	0.520244	+	0.854018i	$0.325841\pi$
$338$	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	0.716417	−	0.697673i	$-0.245781\pi$
$347$	31.4009	−	8.41384i	1.68569	−	0.451679i	0.969271	+	0.245994i	$0.0791144\pi$
$348$	−1.37444	+	5.12947i	−0.0736776	+	0.274969i
$349$	−6.57321	−	1.76129i	−0.351856	−	0.0942795i	0.0785620	−	0.996909i	$-0.474967\pi$
$349$	−6.57321	−	1.76129i	−0.351856	−	0.0942795i	−0.430418	+	0.902630i	$0.641634\pi$
$350$	−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	−0.972991	−	0.230843i	$-0.925852\pi$
$353$	−23.6652	+	13.6631i	−1.25957	+	0.727213i	−0.286579	+	0.958057i	$0.592518\pi$
$354$	−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	−0.802465	−	0.596699i	$-0.796479\pi$
$359$	−3.89871	+	3.89871i	−0.205766	+	0.205766i	0.596699	+	0.802465i	$0.296479\pi$
$360$	−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	−0.729579	−	0.683896i	$-0.760284\pi$
$367$	4.67826	−	17.4595i	0.244203	−	0.911378i	0.973782	−	0.227482i	$-0.0730493\pi$
$368$	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	0.988544	+	0.150936i	$0.0482286\pi$
$373$	4.01536	+	14.9855i	0.207907	+	0.775921i	−0.780636	+	0.624986i	$0.785105\pi$
$374$	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	−0.665443	−	0.746449i	$-0.731757\pi$
$379$	5.53029	−	20.6393i	0.284072	−	1.06017i	0.949515	−	0.313722i	$-0.101576\pi$
$380$	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	0.863612	−	0.504157i	$-0.168197\pi$
$383$	16.8072	+	9.70362i	0.858806	+	0.495832i	−0.00480620	+	0.999988i	$0.501530\pi$
$384$	−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	0.380897	−	0.924617i	$-0.375615\pi$
$397$	−4.57070	−	2.63889i	−0.229397	−	0.132442i	−0.610294	+	0.792175i	$0.708949\pi$
$398$	−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	−0.513317	−	0.858199i	$-0.671583\pi$
$401$	7.21557	−	26.9289i	0.360328	−	1.34476i	0.873645	−	0.486564i	$-0.161750\pi$
$402$	−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	−0.321198	−	0.947012i	$-0.604086\pi$
$409$	−2.54532	+	0.682016i	−0.125858	+	0.0337235i	0.195340	+	0.980736i	$0.437419\pi$
$410$	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	−0.854607	−	0.519275i	$-0.826202\pi$
$419$	−17.0348	+	9.83506i	−0.832205	+	0.480474i	0.0224018	+	0.999749i	$0.492869\pi$
$420$	17.5297	+	12.0085i	0.855361	+	0.585953i
$421$	10.4427	−	10.4427i	0.508948	−	0.508948i	−0.405256	−	0.914203i	$-0.632817\pi$
$421$	10.4427	−	10.4427i	0.508948	−	0.508948i	0.914203	+	0.405256i	$0.132817\pi$
$422$	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	0.634319	−	0.773072i	$-0.281281\pi$
$431$	16.5486	+	4.43419i	0.797119	+	0.213587i	0.162800	+	0.986659i	$0.447947\pi$
$432$	5.18086	−	19.3352i	0.249264	−	0.930267i
$433$	10.8538	−	2.90826i	0.521599	−	0.139762i	0.0115927	−	0.999933i	$-0.496310\pi$
$433$	10.8538	−	2.90826i	0.521599	−	0.139762i	0.510006	+	0.860171i	$0.329643\pi$
$434$	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	0.810929	−	0.585145i	$-0.198962\pi$
$439$	−2.12218	−	3.67572i	−0.101286	−	0.175432i	−0.912215	+	0.409712i	$0.865629\pi$
$440$	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	−0.248505	−	0.968631i	$-0.579939\pi$
$443$	15.1569	−	15.1569i	0.720126	−	0.720126i	0.968631	+	0.248505i	$0.0799392\pi$
$444$	−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	0.996077	+	0.0884873i	$0.0282033\pi$
$449$	3.76524	+	14.0521i	0.177693	+	0.663158i	−0.818385	+	0.574671i	$0.805130\pi$
$450$	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	−0.965385	−	0.260828i	$-0.916004\pi$
$457$	−15.1476	−	26.2365i	−0.708576	−	1.22729i	0.256809	−	0.966462i	$-0.417329\pi$
$458$	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	0.995052	−	0.0993596i	$-0.0316794\pi$
$461$	1.79565	+	6.70146i	0.0836318	+	0.312118i	−0.911420	+	0.411478i	$0.865013\pi$
$462$	−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	−0.616396	−	0.787436i	$-0.711408\pi$
$467$	3.69622	−	3.69622i	0.171041	−	0.171041i	0.787436	+	0.616396i	$0.211408\pi$
$468$	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	0.659222	−	0.751949i	$-0.270886\pi$
$479$	18.6940	+	5.00904i	0.854150	+	0.228869i	0.194928	+	0.980818i	$0.437553\pi$
$480$	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	−0.470083	−	0.882622i	$-0.655776\pi$
$487$	11.6813	−	20.2327i	0.529332	−	0.916830i	0.999415	−	0.0342077i	$-0.0108908\pi$
$488$	−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	−0.0217482	−	0.999763i	$-0.506923\pi$
$491$	18.4624	−	10.6593i	0.833198	−	0.481047i	0.854946	+	0.518716i	$0.173590\pi$
$492$	−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	−0.999492	−	0.0318687i	$-0.989854\pi$
$499$	−23.0389	−	23.0389i	−1.03136	−	1.03136i	−0.0318687	−	0.999492i	$-0.510146\pi$
$500$	−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	0.969612	−	0.244647i	$-0.0786722\pi$
$503$	0.169996	+	0.634433i	0.00757973	+	0.0282879i	−0.962032	+	0.272935i	$0.912006\pi$
$504$	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	0.496587	+	0.867987i	$0.334586\pi$
$509$	−8.29035	+	30.9400i	−0.367463	+	1.37139i	−0.864050	+	0.503405i	$0.832080\pi$
$510$	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	−0.304861	−	0.952397i	$-0.598610\pi$
$523$	−23.9001	−	6.40400i	−1.04508	−	0.280027i	−0.740216	+	0.672370i	$0.765277\pi$
$524$	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	−0.976922	−	0.213597i	$-0.931482\pi$
$541$	−27.6908	−	27.6908i	−1.19052	−	1.19052i	−0.213597	−	0.976922i	$-0.568518\pi$
$542$	−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	0.832947	−	0.553353i	$-0.186652\pi$
$547$	6.53914	+	6.53914i	0.279593	+	0.279593i	−0.553353	+	0.832947i	$0.686652\pi$
$548$	−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	−0.171323	−	0.985215i	$-0.554804\pi$
$557$	14.0717	−	8.12429i	0.596237	−	0.344237i	0.767560	+	0.640978i	$0.221471\pi$
$558$	−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	0.473579	−	0.880751i	$-0.342962\pi$
$563$	31.4174	−	8.41827i	1.32409	−	0.354788i	0.850507	+	0.525964i	$0.176295\pi$
$564$	−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	−0.972416	−	0.233255i	$-0.925062\pi$
$569$	−16.4164	−	28.4341i	−0.688212	−	1.19202i	0.284203	−	0.958764i	$-0.408271\pi$
$570$	−1.44947	+	4.11313i	−0.0607118	+	0.172280i
$571$			31.7967i			1.33065i	0.746554	+	0.665325i	$0.231707\pi$
$571$			31.7967i			1.33065i	−0.746554	+	0.665325i	$0.768293\pi$
$572$	−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	0.991769	−	0.128042i	$-0.0408692\pi$
$587$	9.32773	+	16.1561i	0.384997	+	0.666834i	−0.606772	+	0.794876i	$0.707536\pi$
$588$	−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	$-0.744753\pi$
$599$		−	35.1779i		−	1.43733i	0.695356	−	0.718666i	$-0.255247\pi$
$600$	4.72983	−	10.7113i	0.193095	−	0.437285i
$601$	20.0384	+	34.7076i	0.817385	+	1.41575i	0.907602	+	0.419831i	$0.137911\pi$
$601$	20.0384	+	34.7076i	0.817385	+	1.41575i	−0.0902170	+	0.995922i	$0.528756\pi$
$602$	−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	−0.969930	−	0.243384i	$-0.921742\pi$
$607$	−41.5934	+	11.1449i	−1.68822	+	0.452358i	−0.718292	+	0.695742i	$0.755076\pi$
$608$	−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	−0.101474	−	0.994838i	$-0.532356\pi$
$613$	17.5625	−	10.1397i	0.709344	−	0.409540i	0.810818	+	0.585298i	$0.199022\pi$
$614$	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	−0.939999	−	0.341177i	$-0.889174\pi$
$617$	−4.33527	+	7.50891i	−0.174531	+	0.302297i	0.765468	+	0.643474i	$0.222508\pi$
$618$	−25.1365	+	43.5376i	−1.01114	+	1.75134i
$619$	−21.3034	+	21.3034i	−0.856257	+	0.856257i	−0.990895	−	0.134638i	$-0.957013\pi$
$619$	−21.3034	+	21.3034i	−0.856257	+	0.856257i	0.134638	+	0.990895i	$0.457013\pi$
$620$	−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	−0.759531	−	0.650472i	$-0.774571\pi$
$631$	−27.4324	+	7.35050i	−1.09207	+	0.292619i	−0.332537	+	0.943090i	$0.607905\pi$
$632$		−	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	0.753107	−	0.657899i	$-0.228554\pi$
$641$	14.1756	+	8.18429i	0.559903	+	0.323260i	−0.193204	+	0.981159i	$0.561888\pi$
$642$	25.6652			1.01292
$643$	−35.5518	−	20.5258i	−1.40203	−	0.809460i	−0.407425	−	0.913239i	$-0.633573\pi$
$643$	−35.5518	−	20.5258i	−1.40203	−	0.809460i	−0.994600	+	0.103779i	$0.966907\pi$
$644$	−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	0.312250	−	0.950000i	$-0.398917\pi$
$647$	2.73861	+	0.733807i	0.107666	+	0.0288489i	−0.204584	+	0.978849i	$0.565584\pi$
$648$	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	0.235010	−	0.971993i	$-0.424488\pi$
$653$	−1.21283	−	0.324978i	−0.0474619	−	0.0127174i	−0.282472	+	0.959276i	$0.591154\pi$
$654$	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	0.649384	−	0.760460i	$-0.275027\pi$
$659$	8.09916	+	4.67605i	0.315498	+	0.182153i	−0.333886	+	0.942613i	$0.608360\pi$
$660$	7.73119	−	21.9386i	0.300936	−	0.853958i
$661$	−6.64415	+	24.7963i	−0.258427	+	0.964464i	0.707724	+	0.706489i	$0.249722\pi$
$661$	−6.64415	+	24.7963i	−0.258427	+	0.964464i	−0.966152	+	0.257975i	$0.916945\pi$
$662$	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	−0.377617	−	0.925962i	$-0.623256\pi$
$673$	10.6983	−	39.9267i	0.412390	−	1.53906i	0.790007	−	0.613098i	$-0.210077\pi$
$674$	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	0.939500	−	0.342549i	$-0.111290\pi$
$677$	15.5322	+	15.5322i	0.596950	+	0.596950i	−0.342549	+	0.939500i	$0.611290\pi$
$678$	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	−0.795338	−	0.606166i	$-0.792707\pi$
$683$	3.32652	−	5.76170i	0.127286	−	0.220465i	0.922624	+	0.385700i	$0.126040\pi$
$684$	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	−0.510542	−	0.859853i	$-0.670555\pi$
$691$	−36.3445	−	9.73848i	−1.38261	−	0.370469i	−0.872069	+	0.489384i	$0.837222\pi$
$692$	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	$-0.724312\pi$
$701$		−	40.3398i		−	1.52361i	0.647804	−	0.761807i	$-0.275688\pi$
$702$	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	−0.744752	−	0.667341i	$-0.767432\pi$
$709$	−11.5415	−	43.0733i	−0.433449	−	1.61765i	0.311304	−	0.950311i	$-0.399234\pi$
$710$	−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	0.485867	+	0.874033i	$0.338504\pi$
$719$	−13.7825	+	23.8720i	−0.514001	+	0.890276i	−0.999868	+	0.0162430i	$0.994829\pi$
$720$	−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	0.0974593	−	0.995240i	$-0.468928\pi$
$727$	29.4624	−	29.4624i	1.09270	−	1.09270i	0.995240	−	0.0974593i	$-0.0310716\pi$
$728$	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	$0.142217\pi$
$733$			23.3958i			0.864144i	−0.901839	+	0.432072i	$0.857783\pi$
$734$	−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	−0.0380389	−	0.999276i	$-0.512111\pi$
$739$	−15.5120	−	4.15644i	−0.570620	−	0.152897i	−0.532581	+	0.846379i	$0.678778\pi$
$740$	−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	−0.688777	+	0.724973i	$0.741852\pi$
$743$	−45.2759	+	26.1400i	−1.66101	+	0.958985i	−0.972234	+	0.234011i	$0.924815\pi$
$744$	−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	0.000656703	−	1.00000i	$-0.499791\pi$
$751$	23.7599	−	13.7178i	0.867010	−	0.500569i	0.866354	+	0.499431i	$0.166458\pi$
$752$	−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	−0.953683	−	0.300813i	$-0.902742\pi$
$757$	0.622824	−	2.32441i	0.0226369	−	0.0844821i	0.976320	+	0.216330i	$0.0694088\pi$
$758$	−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	−0.215791	−	0.976440i	$-0.569233\pi$
$761$	2.35997	−	0.632352i	0.0855488	−	0.0229227i	0.301340	+	0.953517i	$0.402566\pi$
$762$			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

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21}+ \cdots - 60 q^{99}+O(q^{100}) \) 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

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