LMFDB - Embedded newform 45.2.e.b.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,2,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("45.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	45.e (of order $3$, degree $2$, 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:	$0.359326809096$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.3
Root			$1.71903 + 0.211943i$ of defining polynomial
Character	$\chi$	$=$	45.16
Dual form			45.2.e.b.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04307 - 1.80664i) q^{2} +(-1.04307 + 1.38276i) q^{3} +(-1.17597 - 2.03684i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.41016 + 3.32675i) q^{6} +(-2.04307 + 3.53869i) q^{7} -0.734191 q^{8} +(-0.824030 - 2.88461i) q^{9} +O(q^{10})$	\(q+(1.04307 - 1.80664i) q^{2} +(-1.04307 + 1.38276i) q^{3} +(-1.17597 - 2.03684i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.41016 + 3.32675i) q^{6} +(-2.04307 + 3.53869i) q^{7} -0.734191 q^{8} +(-0.824030 - 2.88461i) q^{9} -2.08613 q^{10} +(0.675970 - 1.17081i) q^{11} +(4.04307 + 0.498476i) q^{12} +(-0.324030 - 0.561237i) q^{13} +(4.26210 + 7.38217i) q^{14} +(1.71903 + 0.211943i) q^{15} +(1.58613 - 2.74726i) q^{16} -1.35194 q^{17} +(-6.07097 - 1.52011i) q^{18} +0.648061 q^{19} +(-1.17597 + 2.03684i) q^{20} +(-2.76210 - 6.51615i) q^{21} +(-1.41016 - 2.44247i) q^{22} +(-2.39500 - 4.14827i) q^{23} +(0.765809 - 1.01521i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.35194 q^{26} +(4.84823 + 1.86940i) q^{27} +9.61033 q^{28} +(-1.93807 + 3.35683i) q^{29} +(2.17597 - 2.88461i) q^{30} +(3.84823 + 6.66533i) q^{31} +(-4.04307 - 7.00279i) q^{32} +(0.913870 + 2.15594i) q^{33} +(-1.41016 + 2.44247i) q^{34} +4.08613 q^{35} +(-4.90645 + 5.07063i) q^{36} +7.52420 q^{37} +(0.675970 - 1.17081i) q^{38} +(1.11404 + 0.137352i) q^{39} +(0.367095 + 0.635828i) q^{40} +(0.0898394 + 0.155606i) q^{41} +(-14.6534 - 1.80664i) q^{42} +(0.410161 - 0.710419i) q^{43} -3.17968 q^{44} +(-2.08613 + 2.15594i) q^{45} -9.99258 q^{46} +(-5.45323 + 9.44526i) q^{47} +(2.14435 + 5.05880i) q^{48} +(-4.84823 - 8.39738i) q^{49} +(1.04307 + 1.80664i) q^{50} +(1.41016 - 1.86940i) q^{51} +(-0.762100 + 1.32000i) q^{52} +4.17226 q^{53} +(8.43436 - 6.80911i) q^{54} -1.35194 q^{55} +(1.50000 - 2.59808i) q^{56} +(-0.675970 + 0.896110i) q^{57} +(4.04307 + 7.00279i) q^{58} +(-2.08613 - 3.61328i) q^{59} +(-1.58984 - 3.75064i) q^{60} +(1.91016 - 3.30850i) q^{61} +16.0558 q^{62} +(11.8913 + 2.97746i) q^{63} -10.5242 q^{64} +(-0.324030 + 0.561237i) q^{65} +(4.84823 + 0.597746i) q^{66} +(-4.07097 - 7.05113i) q^{67} +(1.58984 + 2.75368i) q^{68} +(8.23419 + 1.01521i) q^{69} +(4.26210 - 7.38217i) q^{70} -6.11644 q^{71} +(0.604996 + 2.11785i) q^{72} -12.3445 q^{73} +(7.84823 - 13.5935i) q^{74} +(-0.675970 - 1.59470i) q^{75} +(-0.762100 - 1.32000i) q^{76} +(2.76210 + 4.78410i) q^{77} +(1.41016 - 1.86940i) q^{78} +(-5.17226 + 8.95862i) q^{79} -3.17226 q^{80} +(-7.64195 + 4.75401i) q^{81} +0.374833 q^{82} +(6.12920 - 10.6161i) q^{83} +(-10.0242 + 13.2887i) q^{84} +(0.675970 + 1.17081i) q^{85} +(-0.855648 - 1.48203i) q^{86} +(-2.62015 - 6.18127i) q^{87} +(-0.496291 + 0.859601i) q^{88} -3.00000 q^{89} +(1.71903 + 6.01767i) q^{90} +2.64806 q^{91} +(-5.63290 + 9.75648i) q^{92} +(-13.2305 - 1.63121i) q^{93} +(11.3761 + 19.7041i) q^{94} +(-0.324030 - 0.561237i) q^{95} +(13.9003 + 1.71380i) q^{96} +(6.79001 - 11.7606i) q^{97} -20.2281 q^{98} +(-3.93436 - 0.985122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + q^{3} - 5 q^{4} - 3 q^{5} - 4 q^{6} - 5 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) $ 6 * q - q^2 + q^3 - 5 * q^4 - 3 * q^5 - 4 * q^6 - 5 * q^7 + 6 * q^8 - 7 * q^9	\( 6 q - q^{2} + q^{3} - 5 q^{4} - 3 q^{5} - 4 q^{6} - 5 q^{7} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 2 q^{11} + 17 q^{12} - 4 q^{13} + 9 q^{14} + q^{15} - 5 q^{16} - 4 q^{17} - 23 q^{18} + 8 q^{19} - 5 q^{20} + 4 q^{22} - 3 q^{23} + 15 q^{24} - 3 q^{25} - 4 q^{26} - 2 q^{27} + 10 q^{28} + 7 q^{29} + 11 q^{30} - 8 q^{31} - 17 q^{32} + 20 q^{33} + 4 q^{34} + 10 q^{35} + 10 q^{36} + 12 q^{37} + 2 q^{38} - 14 q^{39} - 3 q^{40} + 13 q^{41} - 33 q^{42} - 10 q^{43} - 44 q^{44} + 2 q^{45} - 6 q^{46} - 13 q^{47} - 10 q^{48} + 2 q^{49} - q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 5 q^{54} - 4 q^{55} + 9 q^{56} - 2 q^{57} + 17 q^{58} + 2 q^{59} - 22 q^{60} - q^{61} + 84 q^{62} + 33 q^{63} - 30 q^{64} - 4 q^{65} - 2 q^{66} - 11 q^{67} + 22 q^{68} + 39 q^{69} + 9 q^{70} - 20 q^{71} + 15 q^{72} - 16 q^{73} + 16 q^{74} - 2 q^{75} + 12 q^{76} - 4 q^{78} - 2 q^{79} + 10 q^{80} - 19 q^{81} - 58 q^{82} + 15 q^{83} - 27 q^{84} + 2 q^{85} - 28 q^{86} - 26 q^{87} + 24 q^{88} - 18 q^{89} + q^{90} + 20 q^{91} - 39 q^{92} - 42 q^{93} + 31 q^{94} - 4 q^{95} + 13 q^{96} + 18 q^{97} - 80 q^{98} + 22 q^{99}+O(q^{100}) \) 6 * q - q^2 + q^3 - 5 * q^4 - 3 * q^5 - 4 * q^6 - 5 * q^7 + 6 * q^8 - 7 * q^9 + 2 * q^10 + 2 * q^11 + 17 * q^12 - 4 * q^13 + 9 * q^14 + q^15 - 5 * q^16 - 4 * q^17 - 23 * q^18 + 8 * q^19 - 5 * q^20 + 4 * q^22 - 3 * q^23 + 15 * q^24 - 3 * q^25 - 4 * q^26 - 2 * q^27 + 10 * q^28 + 7 * q^29 + 11 * q^30 - 8 * q^31 - 17 * q^32 + 20 * q^33 + 4 * q^34 + 10 * q^35 + 10 * q^36 + 12 * q^37 + 2 * q^38 - 14 * q^39 - 3 * q^40 + 13 * q^41 - 33 * q^42 - 10 * q^43 - 44 * q^44 + 2 * q^45 - 6 * q^46 - 13 * q^47 - 10 * q^48 + 2 * q^49 - q^50 - 4 * q^51 + 12 * q^52 - 4 * q^53 + 5 * q^54 - 4 * q^55 + 9 * q^56 - 2 * q^57 + 17 * q^58 + 2 * q^59 - 22 * q^60 - q^61 + 84 * q^62 + 33 * q^63 - 30 * q^64 - 4 * q^65 - 2 * q^66 - 11 * q^67 + 22 * q^68 + 39 * q^69 + 9 * q^70 - 20 * q^71 + 15 * q^72 - 16 * q^73 + 16 * q^74 - 2 * q^75 + 12 * q^76 - 4 * q^78 - 2 * q^79 + 10 * q^80 - 19 * q^81 - 58 * q^82 + 15 * q^83 - 27 * q^84 + 2 * q^85 - 28 * q^86 - 26 * q^87 + 24 * q^88 - 18 * q^89 + q^90 + 20 * q^91 - 39 * q^92 - 42 * q^93 + 31 * q^94 - 4 * q^95 + 13 * q^96 + 18 * q^97 - 80 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.04307	−	1.80664i	0.737558	−	1.27749i	−0.216033	−	0.976386i	$-0.569312\pi$
$2$	1.04307	−	1.80664i	0.737558	−	1.27749i	0.953592	−	0.301103i	$-0.0973547\pi$
$3$	−1.04307	+	1.38276i	−0.602214	+	0.798335i
$3$	−1.04307	+	1.38276i	−0.602214	+	0.798335i
$4$	−1.17597	−	2.03684i	−0.587985	−	1.01842i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.41016	+	3.32675i	0.575696	+	1.35814i
$7$	−2.04307	+	3.53869i	−0.772206	+	1.33750i	0.164145	+	0.986436i	$0.447513\pi$
$7$	−2.04307	+	3.53869i	−0.772206	+	1.33750i	−0.936351	+	0.351064i	$0.885820\pi$
$8$	−0.734191			−0.259576
$9$	−0.824030	−	2.88461i	−0.274677	−	0.961537i
$10$	−2.08613			−0.659692
$11$	0.675970	−	1.17081i	0.203813	−	0.353014i	−0.745941	−	0.666012i	$-0.768000\pi$
$11$	0.675970	−	1.17081i	0.203813	−	0.353014i	0.949754	+	0.312998i	$0.101333\pi$
$12$	4.04307	+	0.498476i	1.16713	+	0.143898i
$13$	−0.324030	−	0.561237i	−0.0898699	−	0.155659i	0.817586	−	0.575806i	$-0.195312\pi$
$13$	−0.324030	−	0.561237i	−0.0898699	−	0.155659i	−0.907456	+	0.420147i	$0.861978\pi$
$14$	4.26210	+	7.38217i	1.13909	+	1.97297i
$15$	1.71903	+	0.211943i	0.443853	+	0.0547234i
$16$	1.58613	−	2.74726i	0.396533	−	0.686815i
$17$	−1.35194			−0.327893			−0.163947	−	0.986469i	$-0.552423\pi$
$17$	−1.35194			−0.327893			−0.163947	+	0.986469i	$0.552423\pi$
$18$	−6.07097	−	1.52011i	−1.43094	−	0.358293i
$19$	0.648061			0.148675			0.0743377	−	0.997233i	$-0.476316\pi$
$19$	0.648061			0.148675			0.0743377	+	0.997233i	$0.476316\pi$
$20$	−1.17597	+	2.03684i	−0.262955	+	0.455451i
$21$	−2.76210	−	6.51615i	−0.602740	−	1.42194i
$22$	−1.41016	−	2.44247i	−0.300647	−	0.520736i
$23$	−2.39500	−	4.14827i	−0.499393	−	0.864974i	0.500607	−	0.865675i	$-0.333110\pi$
$23$	−2.39500	−	4.14827i	−0.499393	−	0.864974i	−1.00000		0.000700856i	$0.999777\pi$
$24$	0.765809	−	1.01521i	0.156320	−	0.207228i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.35194			−0.265137
$27$	4.84823	+	1.86940i	0.933042	+	0.359767i
$28$	9.61033			1.81618
$29$	−1.93807	+	3.35683i	−0.359890	+	0.623349i	−0.987942	−	0.154823i	$-0.950519\pi$
$29$	−1.93807	+	3.35683i	−0.359890	+	0.623349i	0.628052	+	0.778172i	$0.283853\pi$
$30$	2.17597	−	2.88461i	0.397276	−	0.526655i
$31$	3.84823	+	6.66533i	0.691163	+	1.19713i	0.971457	+	0.237215i	$0.0762345\pi$
$31$	3.84823	+	6.66533i	0.691163	+	1.19713i	−0.280295	+	0.959914i	$0.590432\pi$
$32$	−4.04307	−	7.00279i	−0.714720	−	1.23793i
$33$	0.913870	+	2.15594i	0.159084	+	0.375300i
$34$	−1.41016	+	2.44247i	−0.241841	+	0.418880i
$35$	4.08613			0.690682
$36$	−4.90645	+	5.07063i	−0.817742	+	0.845105i
$37$	7.52420			1.23697			0.618485	−	0.785796i	$-0.287747\pi$
$37$	7.52420			1.23697			0.618485	+	0.785796i	$0.287747\pi$
$38$	0.675970	−	1.17081i	0.109657	−	0.189931i
$39$	1.11404	+	0.137352i	0.178389	+	0.0219939i
$40$	0.367095	+	0.635828i	0.0580429	+	0.100533i
$41$	0.0898394	+	0.155606i	0.0140306	+	0.0243016i	0.872955	−	0.487800i	$-0.162200\pi$
$41$	0.0898394	+	0.155606i	0.0140306	+	0.0243016i	−0.858925	+	0.512102i	$0.828867\pi$
$42$	−14.6534	−	1.80664i	−2.26107	−	0.278771i
$43$	0.410161	−	0.710419i	0.0625489	−	0.108338i	−0.833055	−	0.553190i	$-0.813410\pi$
$43$	0.410161	−	0.710419i	0.0625489	−	0.108338i	0.895604	+	0.444852i	$0.146744\pi$
$44$	−3.17968			−0.479355
$45$	−2.08613	+	2.15594i	−0.310982	+	0.321388i
$46$	−9.99258			−1.47333
$47$	−5.45323	+	9.44526i	−0.795435	+	1.37773i	0.127128	+	0.991886i	$0.459424\pi$
$47$	−5.45323	+	9.44526i	−0.795435	+	1.37773i	−0.922563	+	0.385847i	$0.873909\pi$
$48$	2.14435	+	5.05880i	0.309510	+	0.730175i
$49$	−4.84823	−	8.39738i	−0.692604	−	1.19963i
$50$	1.04307	+	1.80664i	0.147512	+	0.255498i
$51$	1.41016	−	1.86940i	0.197462	−	0.261769i
$52$	−0.762100	+	1.32000i	−0.105684	+	0.183050i
$53$	4.17226			0.573104			0.286552	−	0.958065i	$-0.407491\pi$
$53$	4.17226			0.573104			0.286552	+	0.958065i	$0.407491\pi$
$54$	8.43436	−	6.80911i	1.14777	−	0.926602i
$55$	−1.35194			−0.182295
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	−0.675970	+	0.896110i	−0.0895344	+	0.118693i
$58$	4.04307	+	7.00279i	0.530880	+	0.919512i
$59$	−2.08613	−	3.61328i	−0.271591	−	0.470409i	0.697678	−	0.716411i	$-0.254216\pi$
$59$	−2.08613	−	3.61328i	−0.271591	−	0.470409i	−0.969269	+	0.246002i	$0.920883\pi$
$60$	−1.58984	−	3.75064i	−0.205247	−	0.484205i
$61$	1.91016	−	3.30850i	0.244571	−	0.423609i	−0.717440	−	0.696620i	$-0.754686\pi$
$61$	1.91016	−	3.30850i	0.244571	−	0.423609i	0.962011	+	0.273011i	$0.0880195\pi$
$62$	16.0558			2.03909
$63$	11.8913	+	2.97746i	1.49816	+	0.375124i
$64$	−10.5242			−1.31552
$65$	−0.324030	+	0.561237i	−0.0401910	+	0.0696129i
$66$	4.84823	+	0.597746i	0.596776	+	0.0735775i
$67$	−4.07097	−	7.05113i	−0.497349	−	0.861433i	0.502647	−	0.864492i	$-0.332360\pi$
$67$	−4.07097	−	7.05113i	−0.497349	−	0.861433i	−0.999995	+	0.00305885i	$0.999026\pi$
$68$	1.58984	+	2.75368i	0.192796	+	0.333933i
$69$	8.23419	+	1.01521i	0.991280	+	0.122217i
$70$	4.26210	−	7.38217i	0.509418	−	0.882338i
$71$	−6.11644			−0.725888			−0.362944	−	0.931811i	$-0.618228\pi$
$71$	−6.11644			−0.725888			−0.362944	+	0.931811i	$0.618228\pi$
$72$	0.604996	+	2.11785i	0.0712994	+	0.249592i
$73$	−12.3445			−1.44482			−0.722408	−	0.691467i	$-0.756965\pi$
$73$	−12.3445			−1.44482			−0.722408	+	0.691467i	$0.756965\pi$
$74$	7.84823	−	13.5935i	0.912338	−	1.58022i
$75$	−0.675970	−	1.59470i	−0.0780542	−	0.184140i
$76$	−0.762100	−	1.32000i	−0.0874188	−	0.151414i
$77$	2.76210	+	4.78410i	0.314770	+	0.545198i
$78$	1.41016	−	1.86940i	0.159669	−	0.211668i
$79$	−5.17226	+	8.95862i	−0.581925	+	1.00792i	0.413326	+	0.910583i	$0.364367\pi$
$79$	−5.17226	+	8.95862i	−0.581925	+	1.00792i	−0.995251	+	0.0973403i	$0.968966\pi$
$80$	−3.17226			−0.354669
$81$	−7.64195	+	4.75401i	−0.849105	+	0.528224i
$82$	0.374833			0.0413934
$83$	6.12920	−	10.6161i	0.672767	−	1.16527i	−0.304350	−	0.952560i	$-0.598439\pi$
$83$	6.12920	−	10.6161i	0.672767	−	1.16527i	0.977116	−	0.212706i	$-0.0682275\pi$
$84$	−10.0242	+	13.2887i	−1.09373	+	1.44992i
$85$	0.675970	+	1.17081i	0.0733192	+	0.126993i
$86$	−0.855648	−	1.48203i	−0.0922669	−	0.159811i
$87$	−2.62015	−	6.18127i	−0.280910	−	0.662702i
$88$	−0.496291	+	0.859601i	−0.0529048	+	0.0916338i
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$	1.71903	+	6.01767i	0.181202	+	0.634318i
$91$	2.64806			0.277592
$92$	−5.63290	+	9.75648i	−0.587271	+	1.01718i
$93$	−13.2305	−	1.63121i	−1.37194	−	0.169148i
$94$	11.3761	+	19.7041i	1.17336	+	2.03232i
$95$	−0.324030	−	0.561237i	−0.0332448	−	0.0575817i
$96$	13.9003	+	1.71380i	1.41870	+	0.174914i
$97$	6.79001	−	11.7606i	0.689421	−	1.19411i	−0.282605	−	0.959237i	$-0.591198\pi$
$97$	6.79001	−	11.7606i	0.689421	−	1.19411i	0.972025	−	0.234876i	$-0.0754683\pi$
$98$	−20.2281			−2.04334
$99$	−3.93436	−	0.985122i	−0.395418	−	0.0990085i
$100$	2.35194			0.235194
$101$	0.734191	−	1.27166i	0.0730547	−	0.126535i	−0.827184	−	0.561931i	$-0.810059\pi$
$101$	0.734191	−	1.27166i	0.0730547	−	0.126535i	0.900239	+	0.435397i	$0.143392\pi$
$102$	−1.90645	−	4.49756i	−0.188767	−	0.445325i
$103$	−3.76210	−	6.51615i	−0.370691	−	0.642055i	0.618981	−	0.785406i	$-0.287546\pi$
$103$	−3.76210	−	6.51615i	−0.370691	−	0.642055i	−0.989672	+	0.143351i	$0.954212\pi$
$104$	0.237900	+	0.412055i	0.0233280	+	0.0404053i
$105$	−4.26210	+	5.65012i	−0.415938	+	0.551396i
$106$	4.35194	−	7.53778i	0.422698	−	0.732134i
$107$	1.20999			0.116974			0.0584871	−	0.998288i	$-0.481372\pi$
$107$	1.20999			0.116974			0.0584871	+	0.998288i	$0.481372\pi$
$108$	−1.89370	−	12.0734i	−0.182221	−	1.16177i
$109$	14.1042			1.35094			0.675469	−	0.737388i	$-0.263941\pi$
$109$	14.1042			1.35094			0.675469	+	0.737388i	$0.263941\pi$
$110$	−1.41016	+	2.44247i	−0.134454	+	0.232880i
$111$	−7.84823	+	10.4041i	−0.744921	+	0.987517i
$112$	6.48113	+	11.2257i	0.612410	+	1.06072i
$113$	5.96227	+	10.3270i	0.560883	+	0.971478i	0.997420	+	0.0717915i	$0.0228716\pi$
$113$	5.96227	+	10.3270i	0.560883	+	0.971478i	−0.436537	+	0.899687i	$0.643795\pi$
$114$	0.913870	+	2.15594i	0.0855917	+	0.201922i
$115$	−2.39500	+	4.14827i	−0.223335	+	0.386828i
$116$	9.11644			0.846440
$117$	−1.35194	+	1.39718i	−0.124987	+	0.129169i
$118$	−8.70388			−0.801257
$119$	2.76210	−	4.78410i	0.253201	−	0.438557i
$120$	−1.26210	−	0.155606i	−0.115213	−	0.0142049i
$121$	4.58613	+	7.94341i	0.416921	+	0.722128i
$122$	−3.98484	−	6.90195i	−0.360771	−	0.624873i
$123$	−0.308874	−	0.0380816i	−0.0278502	−	0.00343370i
$124$	9.05080	−	15.6765i	0.812786	−	1.40779i
$125$	1.00000			0.0894427
$126$	17.7826	−	18.3776i	1.58420	−	1.63721i
$127$	−7.07871			−0.628134			−0.314067	−	0.949401i	$-0.601692\pi$
$127$	−7.07871			−0.628134			−0.314067	+	0.949401i	$0.601692\pi$
$128$	−2.89130	+	5.00787i	−0.255557	+	0.442637i
$129$	0.554512	+	1.30817i	0.0488221	+	0.115178i
$130$	0.675970	+	1.17081i	0.0592865	+	0.102687i
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	0.966803	−	0.255524i	$-0.0822479\pi$
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	−0.704692	+	0.709514i	$0.748915\pi$
$132$	3.31661	−	4.39672i	0.288674	−	0.382685i
$133$	−1.32403	+	2.29329i	−0.114808	+	0.198853i
$134$	−16.9852			−1.46729
$135$	−0.805165	−	5.13339i	−0.0692976	−	0.441812i
$136$	0.992582			0.0851132
$137$	3.73419	−	6.46781i	0.319033	−	0.552582i	−0.661253	−	0.750163i	$-0.729975\pi$
$137$	3.73419	−	6.46781i	0.319033	−	0.552582i	0.980287	+	0.197581i	$0.0633084\pi$
$138$	10.4229	−	13.8173i	0.887257	−	1.17621i
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	0.645021	−	0.764165i	$-0.276849\pi$
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	−0.984297	+	0.176522i	$0.943515\pi$
$140$	−4.80516	−	8.32279i	−0.406111	−	0.703404i
$141$	−7.37243	−	17.3925i	−0.620871	−	1.46471i
$142$	−6.37985	+	11.0502i	−0.535385	+	0.927314i
$143$	−0.876139			−0.0732664
$144$	−9.23179	−	2.31154i	−0.769316	−	0.192629i
$145$	3.87614			0.321896
$146$	−12.8761	+	22.3021i	−1.06564	+	1.84574i
$147$	16.6686	+	2.05509i	1.37480	+	0.169501i
$148$	−8.84823	−	15.3256i	−0.727320	−	1.25976i
$149$	5.29241	+	9.16673i	0.433571	+	0.750968i	0.997178	−	0.0750759i	$-0.0239199\pi$
$149$	5.29241	+	9.16673i	0.433571	+	0.750968i	−0.563607	+	0.826043i	$0.690587\pi$
$150$	−3.58613	−	0.442140i	−0.292806	−	0.0361006i
$151$	−8.84823	+	15.3256i	−0.720059	+	1.24718i	0.240917	+	0.970546i	$0.422552\pi$
$151$	−8.84823	+	15.3256i	−0.720059	+	1.24718i	−0.960976	+	0.276633i	$0.910781\pi$
$152$	−0.475800			−0.0385925
$153$	1.11404	+	3.89982i	0.0900647	+	0.315282i
$154$	11.5242			0.928646
$155$	3.84823	−	6.66533i	0.309097	−	0.535372i
$156$	−1.03031	−	2.43064i	−0.0824910	−	0.194607i
$157$	1.26581	+	2.19245i	0.101023	+	0.174976i	0.912106	−	0.409954i	$-0.134455\pi$
$157$	1.26581	+	2.19245i	0.101023	+	0.174976i	−0.811084	+	0.584930i	$0.801122\pi$
$158$	10.7900	+	18.6888i	0.858407	+	1.48680i
$159$	−4.35194	+	5.76922i	−0.345131	+	0.457529i
$160$	−4.04307	+	7.00279i	−0.319632	+	0.553619i
$161$	19.5726			1.54254
$162$	0.617748	+	18.7650i	0.0485349	+	1.47432i
$163$	8.47580			0.663876			0.331938	−	0.943301i	$-0.392298\pi$
$163$	8.47580			0.663876			0.331938	+	0.943301i	$0.392298\pi$
$164$	0.211297	−	0.365977i	0.0164995	−	0.0285780i
$165$	1.41016	−	1.86940i	0.109781	−	0.145533i
$166$	−12.7863	−	22.1465i	−0.992409	−	1.71890i
$167$	−6.36710	−	11.0281i	−0.492701	−	0.853383i	0.507264	−	0.861791i	$-0.330657\pi$
$167$	−6.36710	−	11.0281i	−0.492701	−	0.853383i	−0.999965	+	0.00840816i	$0.997324\pi$
$168$	2.02791	+	4.78410i	0.156457	+	0.369101i
$169$	6.29001	−	10.8946i	0.483847	−	0.838047i
$170$	2.82032			0.216309
$171$	−0.534022	−	1.86940i	−0.0408377	−	0.142957i
$172$	−1.92935			−0.147111
$173$	−11.5242	+	19.9605i	−0.876169	+	1.51757i	−0.0206561	+	0.999787i	$0.506576\pi$
$173$	−11.5242	+	19.9605i	−0.876169	+	1.51757i	−0.855513	+	0.517782i	$0.826758\pi$
$174$	−13.9003	−	1.71380i	−1.05378	−	0.129923i
$175$	−2.04307	−	3.53869i	−0.154441	−	0.267500i
$176$	−2.14435	−	3.71413i	−0.161637	−	0.279963i
$177$	7.17226	+	0.884280i	0.539100	+	0.0664666i
$178$	−3.12920	+	5.41993i	−0.234543	+	0.406241i
$179$	2.22808			0.166534			0.0832672	−	0.996527i	$-0.473465\pi$
$179$	2.22808			0.166534			0.0832672	+	0.996527i	$0.473465\pi$
$180$	6.84452	+	1.71380i	0.510160	+	0.127739i
$181$	0.468382			0.0348146			0.0174073	−	0.999848i	$-0.494459\pi$
$181$	0.468382			0.0348146			0.0174073	+	0.999848i	$0.494459\pi$
$182$	2.76210	−	4.78410i	0.204740	−	0.354621i
$183$	2.58242	+	6.09226i	0.190898	+	0.450353i
$184$	1.75839	+	3.04562i	0.129630	+	0.224526i
$185$	−3.76210	−	6.51615i	−0.276595	−	0.479077i
$186$	−16.7473	+	22.2013i	−1.22797	+	1.62788i
$187$	−0.913870	+	1.58287i	−0.0668288	+	0.115751i
$188$	25.6513			1.87081
$189$	−16.5205	+	13.3371i	−1.20169	+	0.970130i
$190$	−1.35194			−0.0980800
$191$	10.1140	−	17.5180i	0.731826	−	1.26756i	−0.224276	−	0.974526i	$-0.572002\pi$
$191$	10.1140	−	17.5180i	0.731826	−	1.26756i	0.956102	−	0.293034i	$-0.0946650\pi$
$192$	10.9774	−	14.5524i	0.792227	−	1.05023i
$193$	9.96467	+	17.2593i	0.717273	+	1.24235i	0.962076	+	0.272780i	$0.0879432\pi$
$193$	9.96467	+	17.2593i	0.717273	+	1.24235i	−0.244804	+	0.969573i	$0.578723\pi$
$194$	−14.1648	−	24.5342i	−1.01698	−	1.76145i
$195$	−0.438069	−	1.03346i	−0.0313708	−	0.0740077i
$196$	−11.4027	+	19.7501i	−0.814482	+	1.41072i
$197$	−15.5800			−1.11003			−0.555015	−	0.831840i	$-0.687288\pi$
$197$	−15.5800			−1.11003			−0.555015	+	0.831840i	$0.687288\pi$
$198$	−5.88356	+	6.08043i	−0.418126	+	0.432118i
$199$	3.58482			0.254121			0.127061	−	0.991895i	$-0.459446\pi$
$199$	3.58482			0.254121			0.127061	+	0.991895i	$0.459446\pi$
$200$	0.367095	−	0.635828i	0.0259576	−	0.0449598i
$201$	13.9963	+	1.72563i	0.987222	+	0.121716i
$202$	−1.53162	−	2.65284i	−0.107764	−	0.186653i
$203$	−7.91920	−	13.7165i	−0.555819	−	0.962707i
$204$	−5.46598	−	0.673910i	−0.382695	−	0.0471831i
$205$	0.0898394	−	0.155606i	0.00627466	−	0.0108680i
$206$	−15.6965			−1.09362
$207$	−9.99258	+	10.3270i	−0.694532	+	0.717773i
$208$	−2.05582			−0.142545
$209$	0.438069	−	0.758758i	0.0303019	−	0.0524844i
$210$	5.76210	+	13.5935i	0.397623	+	0.938043i
$211$	−7.49629	−	12.9840i	−0.516066	−	0.893852i	−0.999826	−	0.0186518i	$-0.994063\pi$
$211$	−7.49629	−	12.9840i	−0.516066	−	0.893852i	0.483760	−	0.875201i	$-0.339271\pi$
$212$	−4.90645	−	8.49822i	−0.336976	−	0.583660i
$213$	6.37985	−	8.45755i	0.437140	−	0.579502i
$214$	1.26210	−	2.18602i	0.0862754	−	0.149433i
$215$	−0.820321			−0.0559454
$216$	−3.55953	−	1.37250i	−0.242195	−	0.0933867i
$217$	−31.4487			−2.13488
$218$	14.7116	−	25.4813i	0.996396	−	1.72581i
$219$	12.8761	−	17.0695i	0.870089	−	1.15345i
$220$	1.58984	+	2.75368i	0.107187	+	0.185653i
$221$	0.438069	+	0.758758i	0.0294677	+	0.0510396i
$222$	10.6103	+	25.0311i	0.712119	+	1.67998i
$223$	13.4155	−	23.2363i	0.898368	−	1.55602i	0.0687878	−	0.997631i	$-0.478087\pi$
$223$	13.4155	−	23.2363i	0.898368	−	1.55602i	0.829580	−	0.558388i	$-0.188580\pi$
$224$	33.0410			2.20764
$225$	2.91016	+	0.728674i	0.194011	+	0.0485782i
$226$	24.8761			1.65474
$227$	−0.675970	+	1.17081i	−0.0448657	+	0.0777096i	−0.887586	−	0.460642i	$-0.847619\pi$
$227$	−0.675970	+	1.17081i	−0.0448657	+	0.0777096i	0.842721	+	0.538351i	$0.180953\pi$
$228$	2.62015	+	0.323043i	0.173524	+	0.0213940i
$229$	4.11775	+	7.13215i	0.272108	+	0.471306i	0.969402	−	0.245480i	$-0.0789457\pi$
$229$	4.11775	+	7.13215i	0.272108	+	0.471306i	−0.697293	+	0.716786i	$0.745612\pi$
$230$	4.99629	+	8.65383i	0.329446	+	0.570617i
$231$	−9.49629	−	1.17081i	−0.624810	−	0.0770339i
$232$	1.42291	−	2.46456i	0.0934188	−	0.161806i
$233$	8.58744			0.562582			0.281291	−	0.959623i	$-0.409237\pi$
$233$	8.58744			0.562582			0.281291	+	0.959623i	$0.409237\pi$
$234$	1.11404	+	3.89982i	0.0728270	+	0.254939i
$235$	10.9065			0.711458
$236$	−4.90645	+	8.49822i	−0.319383	+	0.553187i
$237$	−6.99258	−	16.4964i	−0.454217	−	1.07156i
$238$	−5.76210	−	9.98025i	−0.373501	−	0.646923i
$239$	11.9623	+	20.7193i	0.773775	+	1.34022i	0.935480	+	0.353378i	$0.114967\pi$
$239$	11.9623	+	20.7193i	0.773775	+	1.34022i	−0.161706	+	0.986839i	$0.551700\pi$
$240$	3.30887	−	4.38646i	0.213587	−	0.283145i
$241$	3.12015	−	5.40426i	0.200987	−	0.348119i	−0.747860	−	0.663857i	$-0.768919\pi$
$241$	3.12015	−	5.40426i	0.200987	−	0.348119i	0.948847	+	0.315737i	$0.102252\pi$
$242$	19.1345			1.23001
$243$	1.39741	−	15.5257i	0.0896438	−	0.995974i
$244$	−8.98516			−0.575216
$245$	−4.84823	+	8.39738i	−0.309742	+	0.536489i
$246$	−0.390976	+	0.518303i	−0.0249277	+	0.0330458i
$247$	−0.209991	−	0.363716i	−0.0133614	−	0.0231427i
$248$	−2.82534	−	4.89363i	−0.179409	−	0.310746i
$249$	8.28630	+	19.5484i	0.525123	+	1.23883i
$250$	1.04307	−	1.80664i	0.0659692	−	0.114262i
$251$	−28.5726			−1.80349			−0.901743	−	0.432272i	$-0.857712\pi$
$251$	−28.5726			−1.80349			−0.901743	+	0.432272i	$0.857712\pi$
$252$	−7.91920	−	27.7221i	−0.498863	−	1.74633i
$253$	−6.47580			−0.407130
$254$	−7.38356	+	12.7887i	−0.463286	+	0.802434i
$255$	−2.32403	−	0.286534i	−0.145536	−	0.0179434i
$256$	−4.49258	−	7.78138i	−0.280786	−	0.486336i
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$	2.94178	+	0.362697i	0.183147	+	0.0225805i
$259$	−15.3724	+	26.6258i	−0.955196	+	1.65445i
$260$	1.52420			0.0945268
$261$	11.2802	+	2.82444i	0.698226	+	0.174828i
$262$	12.5168			0.773289
$263$	−15.9344	+	27.5991i	−0.982555	+	1.70183i	−0.330220	+	0.943904i	$0.607123\pi$
$263$	−15.9344	+	27.5991i	−0.982555	+	1.70183i	−0.652335	+	0.757931i	$0.726211\pi$
$264$	−0.670955	−	1.58287i	−0.0412944	−	0.0974188i
$265$	−2.08613	−	3.61328i	−0.128150	−	0.221962i
$266$	2.76210	+	4.78410i	0.169355	+	0.293332i
$267$	3.12920	−	4.14827i	0.191504	−	0.253870i
$268$	−9.57468	+	16.5838i	−0.584867	+	1.01302i
$269$	−31.4971			−1.92041			−0.960207	−	0.279289i	$-0.909901\pi$
$269$	−31.4971			−1.92041			−0.960207	+	0.279289i	$0.909901\pi$
$270$	−10.1140	−	3.89982i	−0.615521	−	0.237335i
$271$	−3.24030			−0.196834			−0.0984172	−	0.995145i	$-0.531378\pi$
$271$	−3.24030			−0.196834			−0.0984172	+	0.995145i	$0.531378\pi$
$272$	−2.14435	+	3.71413i	−0.130020	+	0.225202i
$273$	−2.76210	+	3.66162i	−0.167170	+	0.221612i
$274$	−7.79001	−	13.4927i	−0.470612	−	0.815123i
$275$	0.675970	+	1.17081i	0.0407625	+	0.0706027i
$276$	−7.61534	−	17.9656i	−0.458390	−	1.08140i
$277$	2.79241	−	4.83660i	0.167780	−	0.290603i	−0.769859	−	0.638214i	$-0.779674\pi$
$277$	2.79241	−	4.83660i	0.167780	−	0.290603i	0.937639	+	0.347611i	$0.113007\pi$
$278$	−16.6890			−1.00094
$279$	16.0558	−	16.5931i	0.961237	−	0.993402i
$280$	−3.00000			−0.179284
$281$	12.0521	−	20.8749i	0.718969	−	1.24529i	−0.242440	−	0.970166i	$-0.577948\pi$
$281$	12.0521	−	20.8749i	0.718969	−	1.24529i	0.961409	−	0.275124i	$-0.0887188\pi$
$282$	−39.1120	−	4.82218i	−2.32908	−	0.287157i
$283$	5.27114	+	9.12989i	0.313337	+	0.542715i	0.979083	−	0.203463i	$-0.0652197\pi$
$283$	5.27114	+	9.12989i	0.313337	+	0.542715i	−0.665746	+	0.746179i	$0.731886\pi$
$284$	7.19275	+	12.4582i	0.426811	+	0.739259i
$285$	1.11404	+	0.137352i	0.0659900	+	0.00813602i
$286$	−0.913870	+	1.58287i	−0.0540383	+	0.0935970i
$287$	−0.734191			−0.0433379
$288$	−16.8687	+	17.4332i	−0.993999	+	1.02726i
$289$	−15.1723			−0.892486
$290$	4.04307	−	7.00279i	0.237417	−	0.411218i
$291$	9.17968	+	21.6560i	0.538122	+	1.26950i
$292$	14.5168	+	25.1438i	0.849530	+	1.47143i
$293$	−9.49629	−	16.4481i	−0.554779	−	0.960906i	−0.997921	−	0.0644541i	$-0.979469\pi$
$293$	−9.49629	−	16.4481i	−0.554779	−	0.960906i	0.443141	−	0.896452i	$-0.353864\pi$
$294$	21.0992	−	27.9705i	1.23053	−	1.63127i
$295$	−2.08613	+	3.61328i	−0.121459	+	0.210373i
$296$	−5.52420			−0.321088
$297$	5.46598	−	4.41271i	0.317168	−	0.256052i
$298$	22.0813			1.27914
$299$	−1.55211	+	2.68833i	−0.0897607	+	0.155470i
$300$	−2.45323	+	3.25216i	−0.141637	+	0.187763i
$301$	1.67597	+	2.90286i	0.0966013	+	0.167318i
$302$	18.4586	+	31.9712i	1.06217	+	1.83973i
$303$	0.992582	+	2.34163i	0.0570223	+	0.134523i
$304$	1.02791	−	1.78039i	0.0589546	−	0.102112i
$305$	−3.82032			−0.218751
$306$	8.20759	+	2.05509i	0.469197	+	0.117482i
$307$	29.4791			1.68246			0.841229	−	0.540679i	$-0.181833\pi$
$307$	29.4791			1.68246			0.841229	+	0.540679i	$0.181833\pi$
$308$	6.49629	−	11.2519i	0.370161	−	0.641137i
$309$	12.9344	+	1.59470i	0.735810	+	0.0907193i
$310$	−8.02791	−	13.9047i	−0.455955	−	0.789736i
$311$	4.70628	+	8.15152i	0.266869	+	0.462230i	0.968052	−	0.250751i	$-0.0806776\pi$
$311$	4.70628	+	8.15152i	0.266869	+	0.462230i	−0.701183	+	0.712982i	$0.747344\pi$
$312$	−0.817917	−	0.100842i	−0.0463055	−	0.00570908i
$313$	−5.81050	+	10.0641i	−0.328429	+	0.568855i	−0.982200	−	0.187837i	$-0.939852\pi$
$313$	−5.81050	+	10.0641i	−0.328429	+	0.568855i	0.653771	+	0.756692i	$0.273186\pi$
$314$	5.28128			0.298040
$315$	−3.36710	−	11.7869i	−0.189714	−	0.664116i
$316$	24.3297			1.36865
$317$	4.58984	−	7.94984i	0.257791	−	0.446507i	−0.707859	−	0.706354i	$-0.750339\pi$
$317$	4.58984	−	7.94984i	0.257791	−	0.446507i	0.965650	+	0.259847i	$0.0836720\pi$
$318$	5.88356	+	13.8801i	0.329934	+	0.778355i
$319$	2.62015	+	4.53824i	0.146700	+	0.254092i
$320$	5.26210	+	9.11422i	0.294160	+	0.509501i
$321$	−1.26210	+	1.67312i	−0.0704435	+	0.0933846i
$322$	20.4155	−	35.3607i	1.13771	−	1.97057i
$323$	−0.876139			−0.0487497
$324$	18.6699	+	9.97484i	1.03721	+	0.554158i
$325$	0.648061			0.0359479
$326$	8.84081	−	15.3127i	0.489647	−	0.848094i
$327$	−14.7116	+	19.5027i	−0.813554	+	1.07850i
$328$	−0.0659593	−	0.114245i	−0.00364199	−	0.00630812i
$329$	−22.2826	−	38.5946i	−1.22848	−	2.12779i
$330$	−1.90645	−	4.49756i	−0.104947	−	0.247583i
$331$	3.61033	−	6.25327i	0.198442	−	0.343711i	−0.749582	−	0.661912i	$-0.769745\pi$
$331$	3.61033	−	6.25327i	0.198442	−	0.343711i	0.948023	+	0.318201i	$0.103079\pi$
$332$	−28.8310			−1.58231
$333$	−6.20017	−	21.7044i	−0.339767	−	1.18939i
$334$	−26.5652			−1.45358
$335$	−4.07097	+	7.05113i	−0.222421	+	0.385245i
$336$	−22.2826	−	2.74726i	−1.21561	−	0.149875i
$337$	−1.14195	−	1.97791i	−0.0622059	−	0.107744i	0.833245	−	0.552904i	$-0.186480\pi$
$337$	−1.14195	−	1.97791i	−0.0622059	−	0.107744i	−0.895451	+	0.445160i	$0.853147\pi$
$338$	−13.1218	−	22.7276i	−0.713731	−	1.23622i
$339$	−20.4987	−	2.52732i	−1.11334	−	0.137265i
$340$	1.58984	−	2.75368i	0.0862211	−	0.149339i
$341$	10.4051			0.563470
$342$	−3.93436	−	0.985122i	−0.212746	−	0.0532693i
$343$	11.0181			0.594921
$344$	−0.301136	+	0.521583i	−0.0162362	+	0.0281219i
$345$	−3.23790	−	7.63862i	−0.174323	−	0.411250i
$346$	24.0410	+	41.6402i	1.29245	+	2.23859i
$347$	0.354343	+	0.613740i	0.0190221	+	0.0329473i	0.875380	−	0.483436i	$-0.160611\pi$
$347$	0.354343	+	0.613740i	0.0190221	+	0.0329473i	−0.856358	+	0.516383i	$0.827278\pi$
$348$	−9.50904	+	12.6058i	−0.509738	+	0.675743i
$349$	10.6723	−	18.4849i	0.571273	−	0.989474i	−0.425163	−	0.905117i	$-0.639783\pi$
$349$	10.6723	−	18.4849i	0.571273	−	0.989474i	0.996436	−	0.0843569i	$-0.0268836\pi$
$350$	−8.52420			−0.455638
$351$	−0.521796	−	3.32675i	−0.0278514	−	0.177569i
$352$	−10.9320			−0.582675
$353$	5.04840	−	8.74408i	0.268699	−	0.465401i	−0.699827	−	0.714312i	$-0.746740\pi$
$353$	5.04840	−	8.74408i	0.268699	−	0.465401i	0.968526	+	0.248912i	$0.0800729\pi$
$354$	9.07871	−	12.0353i	0.482528	−	0.639671i
$355$	3.05822	+	5.29699i	0.162314	+	0.281135i
$356$	3.52791	+	6.11052i	0.186979	+	0.323857i
$357$	3.73419	+	8.80944i	0.197634	+	0.466245i
$358$	2.32403	−	4.02534i	0.122829	−	0.212746i
$359$	30.5578			1.61278			0.806388	−	0.591386i	$-0.201419\pi$
$359$	30.5578			1.61278			0.806388	+	0.591386i	$0.201419\pi$
$360$	1.53162	−	1.58287i	0.0807234	−	0.0834245i
$361$	−18.5800			−0.977896
$362$	0.488553	−	0.846198i	0.0256778	−	0.0444752i
$363$	−15.7674	−	1.94399i	−0.827576	−	0.102033i
$364$	−3.11404	−	5.39367i	−0.163220	−	0.282705i
$365$	6.17226	+	10.6907i	0.323071	+	0.559575i
$366$	13.7002	+	1.68912i	0.716119	+	0.0882916i
$367$	3.58984	−	6.21778i	0.187388	−	0.324566i	−0.756991	−	0.653426i	$-0.773331\pi$
$367$	3.58984	−	6.21778i	0.187388	−	0.324566i	0.944379	+	0.328860i	$0.106664\pi$
$368$	−15.1952			−0.792102
$369$	0.374833	−	0.387376i	0.0195130	−	0.0201660i
$370$	−15.6965			−0.816020
$371$	−8.52420	+	14.7643i	−0.442554	+	0.766527i
$372$	12.2361	+	28.8666i	0.634414	+	1.49666i
$373$	10.9623	+	18.9872i	0.567605	+	0.983120i	0.996802	+	0.0799096i	$0.0254632\pi$
$373$	10.9623	+	18.9872i	0.567605	+	0.983120i	−0.429197	+	0.903211i	$0.641204\pi$
$374$	1.90645	+	3.30207i	0.0985803	+	0.170746i
$375$	−1.04307	+	1.38276i	−0.0538637	+	0.0714052i
$376$	4.00371	−	6.93463i	0.206476	−	0.357626i
$377$	2.51197			0.129373
$378$	6.86339	+	43.7581i	0.353014	+	2.25067i
$379$	−17.3929			−0.893414			−0.446707	−	0.894680i	$-0.647403\pi$
$379$	−17.3929			−0.893414			−0.446707	+	0.894680i	$0.647403\pi$
$380$	−0.762100	+	1.32000i	−0.0390949	+	0.0677143i
$381$	7.38356	−	9.78813i	0.378271	−	0.501461i
$382$	−21.0992	−	36.5449i	−1.07953	−	1.86980i
$383$	−0.237900	−	0.412055i	−0.0121561	−	0.0210550i	0.859883	−	0.510491i	$-0.170536\pi$
$383$	−0.237900	−	0.412055i	−0.0121561	−	0.0210550i	−0.872039	+	0.489436i	$0.837203\pi$
$384$	−3.90886	−	9.22149i	−0.199473	−	0.470582i
$385$	2.76210	−	4.78410i	0.140770	−	0.243820i
$386$	41.5752			2.11612
$387$	−2.38727	−	0.597746i	−0.121352	−	0.0303852i
$388$	−31.9394			−1.62148
$389$	2.79372	−	4.83886i	0.141647	−	0.245340i	−0.786470	−	0.617629i	$-0.788094\pi$
$389$	2.79372	−	4.83886i	0.141647	−	0.245340i	0.928117	+	0.372289i	$0.121427\pi$
$390$	−2.32403	−	0.286534i	−0.117682	−	0.0145092i
$391$	3.23790	+	5.60821i	0.163748	+	0.283619i
$392$	3.55953	+	6.16528i	0.179783	+	0.311394i
$393$	−10.3142	−	1.27166i	−0.520283	−	0.0641466i
$394$	−16.2510	+	28.1475i	−0.818712	+	1.41805i
$395$	10.3445			0.520489
$396$	2.62015	+	9.17213i	0.131668	+	0.460917i
$397$	3.75228			0.188321			0.0941607	−	0.995557i	$-0.469983\pi$
$397$	3.75228			0.188321			0.0941607	+	0.995557i	$0.469983\pi$
$398$	3.73921	−	6.47649i	0.187429	−	0.324637i
$399$	−1.79001	−	4.22286i	−0.0896125	−	0.211407i
$400$	1.58613	+	2.74726i	0.0793065	+	0.137363i
$401$	−11.7826	−	20.4080i	−0.588394	−	1.01913i	−0.994443	−	0.105278i	$-0.966427\pi$
$401$	−11.7826	−	20.4080i	−0.588394	−	1.01913i	0.406048	−	0.913852i	$-0.366906\pi$
$402$	17.7166	−	23.4863i	0.883625	−	1.17139i
$403$	2.49389	−	4.31954i	0.124229	−	0.215172i
$404$	−3.45355			−0.171820
$405$	7.93807	+	4.24111i	0.394446	+	0.210743i
$406$	−33.0410			−1.63980
$407$	5.08613	−	8.80944i	0.252110	−	0.436668i
$408$	−1.03533	+	1.37250i	−0.0512563	+	0.0679488i
$409$	−0.524200	−	0.907940i	−0.0259200	−	0.0448948i	0.852774	−	0.522279i	$-0.174918\pi$
$409$	−0.524200	−	0.907940i	−0.0259200	−	0.0448948i	−0.878694	+	0.477385i	$0.841585\pi$
$410$	−0.187417	−	0.324615i	−0.00925585	−	0.0160316i
$411$	5.04840	+	11.9098i	0.249019	+	0.587468i
$412$	−8.84823	+	15.3256i	−0.435921	+	0.755037i
$413$	17.0484			0.838897
$414$	8.23419	+	28.8247i	0.404688	+	1.41666i
$415$	−12.2584			−0.601741
$416$	−2.62015	+	4.53824i	−0.128464	+	0.222505i
$417$	13.7523	+	1.69554i	0.673452	+	0.0830310i
$418$	−0.913870	−	1.58287i	−0.0446988	−	0.0774207i
$419$	12.9599	+	22.4471i	0.633131	+	1.09661i	0.986908	+	0.161285i	$0.0515638\pi$
$419$	12.9599	+	22.4471i	0.633131	+	1.09661i	−0.353777	+	0.935330i	$0.615103\pi$
$420$	16.5205	+	2.03684i	0.806117	+	0.0993876i
$421$	−3.82032	+	6.61699i	−0.186191	+	0.322492i	−0.943977	−	0.330011i	$-0.892948\pi$
$421$	−3.82032	+	6.61699i	−0.186191	+	0.322492i	0.757786	+	0.652503i	$0.226281\pi$
$422$	−31.2765			−1.52252
$423$	31.7395	+	7.94724i	1.54323	+	0.386408i
$424$	−3.06324			−0.148764
$425$	0.675970	−	1.17081i	0.0327893	−	0.0567928i
$426$	−8.62517	−	20.3479i	−0.417891	−	0.985858i
$427$	7.80516	+	13.5189i	0.377718	+	0.654227i
$428$	−1.42291	−	2.46456i	−0.0687791	−	0.119129i
$429$	0.913870	−	1.21149i	0.0441220	−	0.0584911i
$430$	−0.855648	+	1.48203i	−0.0412630	+	0.0714697i
$431$	7.98516			0.384632			0.192316	−	0.981333i	$-0.438400\pi$
$431$	7.98516			0.384632			0.192316	+	0.981333i	$0.438400\pi$
$432$	12.8257	−	10.3542i	0.617075	−	0.498168i
$433$	−12.5120			−0.601287			−0.300644	−	0.953737i	$-0.597201\pi$
$433$	−12.5120			−0.601287			−0.300644	+	0.953737i	$0.597201\pi$
$434$	−32.8031	+	56.8166i	−1.57460	+	2.72728i
$435$	−4.04307	+	5.35976i	−0.193850	+	0.256981i
$436$	−16.5861	−	28.7280i	−0.794332	−	1.37582i
$437$	−1.55211	−	2.68833i	−0.0742474	−	0.128600i
$438$	−17.4078	−	41.0671i	−0.831775	−	1.96226i
$439$	4.38225	−	7.59028i	0.209153	−	0.362264i	−0.742295	−	0.670074i	$-0.766263\pi$
$439$	4.38225	−	7.59028i	0.209153	−	0.362264i	0.951448	+	0.307809i	$0.0995958\pi$
$440$	0.992582			0.0473195
$441$	−20.2281	+	20.9049i	−0.963242	+	0.995474i
$442$	1.82774			0.0869367
$443$	−1.83548	+	3.17914i	−0.0872062	+	0.151046i	−0.906329	−	0.422572i	$-0.861127\pi$
$443$	−1.83548	+	3.17914i	−0.0872062	+	0.151046i	0.819123	+	0.573618i	$0.194461\pi$
$444$	30.4208	+	3.75064i	1.44371	+	0.177997i
$445$	1.50000	+	2.59808i	0.0711068	+	0.123161i
$446$	−27.9865	−	48.4740i	−1.32520	−	2.29531i
$447$	−18.1957	−	2.24338i	−0.860626	−	0.106108i
$448$	21.5016	−	37.2419i	1.01586	−	1.75951i
$449$	28.1723			1.32953			0.664766	−	0.747052i	$-0.268531\pi$
$449$	28.1723			1.32953			0.664766	+	0.747052i	$0.268531\pi$
$450$	4.35194	−	4.49756i	0.205152	−	0.212017i
$451$	0.242915			0.0114384
$452$	14.0229	−	24.2884i	0.659581	−	1.14243i
$453$	−11.9623	−	28.2205i	−0.562036	−	1.32592i
$454$	1.41016	+	2.44247i	0.0661821	+	0.114631i
$455$	−1.32403	−	2.29329i	−0.0620715	−	0.107511i
$456$	0.496291	−	0.657916i	0.0232409	−	0.0308097i
$457$	−17.6308	+	30.5375i	−0.824735	+	1.42848i	0.0773867	+	0.997001i	$0.475342\pi$
$457$	−17.6308	+	30.5375i	−0.824735	+	1.42848i	−0.902122	+	0.431482i	$0.857991\pi$
$458$	17.1803			0.802784
$459$	−6.55451	−	2.52732i	−0.305938	−	0.117965i
$460$	11.2658			0.525271
$461$	−17.3384	+	30.0310i	−0.807530	+	1.39868i	0.107039	+	0.994255i	$0.465863\pi$
$461$	−17.3384	+	30.0310i	−0.807530	+	1.39868i	−0.914570	+	0.404428i	$0.867470\pi$
$462$	−12.0205	+	15.9352i	−0.559244	+	0.741371i
$463$	−3.72437	−	6.45080i	−0.173086	−	0.299794i	0.766411	−	0.642350i	$-0.222041\pi$
$463$	−3.72437	−	6.45080i	−0.173086	−	0.299794i	−0.939497	+	0.342556i	$0.888707\pi$
$464$	6.14806	+	10.6488i	0.285417	+	0.494356i
$465$	5.20257	+	12.2735i	0.241264	+	0.569172i
$466$	8.95725	−	15.5144i	0.414937	−	0.718692i
$467$	29.9655			1.38664			0.693319	−	0.720630i	$-0.256148\pi$
$467$	29.9655			1.38664			0.693319	+	0.720630i	$0.256148\pi$
$468$	4.43567	+	1.11064i	0.205039	+	0.0513395i
$469$	33.2691			1.53622
$470$	11.3761	−	19.7041i	0.524742	−	0.908880i
$471$	−4.35194	−	0.536558i	−0.200527	−	0.0247233i
$472$	1.53162	+	2.65284i	0.0704984	+	0.122107i
$473$	−0.554512	−	0.960443i	−0.0254965	−	0.0441612i
$474$	−37.0968	−	4.57373i	−1.70391	−	0.210078i
$475$	−0.324030	+	0.561237i	−0.0148675	+	0.0257513i
$476$	−12.9926			−0.595514
$477$	−3.43807	−	12.0353i	−0.157418	−	0.551061i
$478$	49.9097			2.28282
$479$	3.99258	−	6.91535i	0.182426	−	0.315971i	−0.760280	−	0.649595i	$-0.774938\pi$
$479$	3.99258	−	6.91535i	0.182426	−	0.315971i	0.942706	+	0.333625i	$0.108272\pi$
$480$	−5.46598	−	12.8949i	−0.249487	−	0.588571i
$481$	−2.43807	−	4.22286i	−0.111166	−	0.192546i
$482$	−6.50904	−	11.2740i	−0.296479	−	0.513516i
$483$	−20.4155	+	27.0641i	−0.928937	+	1.23146i
$484$	10.7863	−	18.6824i	0.490286	−	0.849201i
$485$	−13.5800			−0.616637
$486$	−26.5918	−	18.7189i	−1.20623	−	0.849108i
$487$	−11.9442			−0.541243			−0.270621	−	0.962686i	$-0.587229\pi$
$487$	−11.9442			−0.541243			−0.270621	+	0.962686i	$0.587229\pi$
$488$	−1.40242	+	2.42907i	−0.0634847	+	0.109959i
$489$	−8.84081	+	11.7200i	−0.399795	+	0.529995i
$490$	10.1140	+	17.5180i	0.456906	+	0.791384i
$491$	4.61033	+	7.98533i	0.208061	+	0.360373i	0.951104	−	0.308872i	$-0.0999513\pi$
$491$	4.61033	+	7.98533i	0.208061	+	0.360373i	−0.743042	+	0.669244i	$0.766618\pi$
$492$	0.285660	+	0.673910i	0.0128786	+	0.0303822i
$493$	2.62015	−	4.53824i	0.118006	−	0.204392i
$494$	−0.876139			−0.0394193
$495$	1.11404	+	3.89982i	0.0500723	+	0.175284i
$496$	24.4152			1.09627
$497$	12.4963	−	21.6442i	0.560535	−	0.970876i
$498$	43.9602	+	5.41993i	1.96990	+	0.242873i
$499$	−15.0861	−	26.1299i	−0.675348	−	1.16974i	−0.976367	−	0.216119i	$-0.930660\pi$
$499$	−15.0861	−	26.1299i	−0.675348	−	1.16974i	0.301019	−	0.953618i	$-0.402673\pi$
$500$	−1.17597	−	2.03684i	−0.0525910	−	0.0910902i
$501$	21.8905	+	2.69892i	0.977996	+	0.120579i
$502$	−29.8031	+	51.6204i	−1.33018	+	2.30393i
$503$	−10.5981			−0.472546			−0.236273	−	0.971687i	$-0.575926\pi$
$503$	−10.5981			−0.472546			−0.236273	+	0.971687i	$0.575926\pi$
$504$	−8.73048	−	2.18602i	−0.388887	−	0.0973731i
$505$	−1.46838			−0.0653421
$506$	−6.75468	+	11.6995i	−0.300282	+	0.520104i
$507$	8.50371	+	20.0613i	0.377663	+	0.890955i
$508$	8.32435	+	14.4182i	0.369333	+	0.639704i
$509$	−14.3761	−	24.9002i	−0.637211	−	1.10368i	−0.986042	−	0.166496i	$-0.946755\pi$
$509$	−14.3761	−	24.9002i	−0.637211	−	1.10368i	0.348831	−	0.937186i	$-0.386579\pi$
$510$	−2.94178	+	3.89982i	−0.130264	+	0.172687i
$511$	25.2207	−	43.6835i	1.11570	−	1.93244i
$512$	−30.3094			−1.33950
$513$	3.14195	+	1.21149i	0.138720	+	0.0534884i
$514$	37.5503			1.65627
$515$	−3.76210	+	6.51615i	−0.165778	+	0.287136i
$516$	2.01243	−	2.66781i	0.0885924	−	0.117444i
$517$	7.37243	+	12.7694i	0.324239	+	0.561599i
$518$	32.0689	+	55.5449i	1.40903	+	2.44050i
$519$	−15.5800	−	36.7553i	−0.683887	−	1.61338i
$520$	0.237900	−	0.412055i	0.0104326	−	0.0180698i
$521$	−36.0942			−1.58132			−0.790658	−	0.612259i	$-0.790261\pi$
$521$	−36.0942			−1.58132			−0.790658	+	0.612259i	$0.790261\pi$
$522$	16.8687	−	17.4332i	0.738324	−	0.763030i
$523$	11.1297			0.486669			0.243334	−	0.969942i	$-0.421759\pi$
$523$	11.1297			0.486669			0.243334	+	0.969942i	$0.421759\pi$
$524$	7.05582	−	12.2210i	0.308235	−	0.533878i
$525$	7.02420	+	0.866025i	0.306561	+	0.0377964i
$526$	33.2411	+	57.5754i	1.44938	+	2.51041i
$527$	−5.20257	−	9.01112i	−0.226628	−	0.392531i
$528$	7.37243	+	0.908959i	0.320844	+	0.0395574i
$529$	0.0279088	−	0.0483395i	0.00121343	−	0.00210172i
$530$	−8.70388			−0.378072
$531$	−8.70388	+	8.99513i	−0.377716	+	0.390355i
$532$	6.22808			0.270021
$533$	0.0582214	−	0.100842i	0.00252185	−	0.00436797i
$534$	−4.23048	−	9.98025i	−0.183071	−	0.431888i
$535$	−0.604996	−	1.04788i	−0.0261562	−	0.0453039i
$536$	2.98887	+	5.17688i	0.129100	+	0.223607i
$537$	−2.32403	+	3.08089i	−0.100289	+	0.132950i
$538$	−32.8536	+	56.9040i	−1.41642	+	2.45331i
$539$	−13.1090			−0.564646
$540$	−9.50904	+	7.67670i	−0.409204	+	0.330353i
$541$	−34.7374			−1.49348			−0.746740	−	0.665116i	$-0.768382\pi$
$541$	−34.7374			−1.49348			−0.746740	+	0.665116i	$0.768382\pi$
$542$	−3.37985	+	5.85407i	−0.145177	+	0.251454i
$543$	−0.488553	+	0.647658i	−0.0209658	+	0.0277937i
$544$	5.46598	+	9.46735i	0.234352	+	0.405909i
$545$	−7.05211	−	12.2146i	−0.302079	−	0.523216i
$546$	3.73419	+	8.80944i	0.159809	+	0.377009i
$547$	1.35727	−	2.35087i	0.0580328	−	0.100516i	−0.835549	−	0.549415i	$-0.814851\pi$
$547$	1.35727	−	2.35087i	0.0580328	−	0.100516i	0.893582	+	0.448899i	$0.148184\pi$
$548$	−17.5652			−0.750347
$549$	−11.1177	−	2.78377i	−0.474494	−	0.118808i
$550$	2.82032			0.120259
$551$	−1.25599	+	2.17543i	−0.0535068	+	0.0926766i
$552$	−6.04547	−	0.745356i	−0.257312	−	0.0317245i
$553$	−21.1345	−	36.6061i	−0.898732	−	1.55665i
$554$	−5.82534	−	10.0898i	−0.247495	−	0.428674i
$555$	12.9344	+	1.59470i	0.549033	+	0.0676912i
$556$	−9.40776	+	16.2947i	−0.398978	+	0.691050i
$557$	−8.93676			−0.378663			−0.189331	−	0.981913i	$-0.560632\pi$
$557$	−8.93676			−0.378663			−0.189331	+	0.981913i	$0.560632\pi$
$558$	−13.2305	−	46.3148i	−0.560091	−	1.96066i
$559$	−0.531618			−0.0224850
$560$	6.48113	−	11.2257i	0.273878	−	0.474370i
$561$	−1.23550	−	2.91469i	−0.0521627	−	0.123059i
$562$	−25.1423	−	43.5477i	−1.06056	−	1.83695i
$563$	4.68130	+	8.10826i	0.197293	+	0.341722i	0.947650	−	0.319311i	$-0.103451\pi$
$563$	4.68130	+	8.10826i	0.197293	+	0.341722i	−0.750357	+	0.661033i	$0.770118\pi$
$564$	−26.7560	+	35.4695i	−1.12663	+	1.49354i
$565$	5.96227	−	10.3270i	0.250835	−	0.434458i
$566$	21.9926			0.924417
$567$	−1.20999	−	36.7553i	−0.0508149	−	1.54358i
$568$	4.49064			0.188423
$569$	−17.9368	+	31.0674i	−0.751948	+	1.30241i	0.194929	+	0.980817i	$0.437552\pi$
$569$	−17.9368	+	31.0674i	−0.751948	+	1.30241i	−0.946877	+	0.321595i	$0.895781\pi$
$570$	1.41016	−	1.86940i	0.0590651	−	0.0783007i
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	1.03031	+	1.78455i	0.0430795	+	0.0746159i
$573$	13.6736	+	32.2577i	0.571221	+	1.34758i
$574$	−0.765809	+	1.32642i	−0.0319643	+	0.0553637i
$575$	4.79001			0.199757
$576$	8.67226	+	30.3582i	0.361344	+	1.26493i
$577$	1.35675			0.0564821			0.0282411	−	0.999601i	$-0.491009\pi$
$577$	1.35675			0.0564821			0.0282411	+	0.999601i	$0.491009\pi$
$578$	−15.8257	+	27.4108i	−0.658260	+	1.14014i
$579$	−34.2592	−	4.22388i	−1.42377	−	0.175538i
$580$	−4.55822	−	7.89507i	−0.189270	−	0.327825i
$581$	25.0447	+	43.3787i	1.03903	+	1.79965i
$582$	48.6997	+	6.00427i	2.01867	+	0.248885i
$583$	2.82032	−	4.88494i	0.116806	−	0.202314i
$584$	9.06324			0.375039
$585$	1.88596	+	0.472225i	0.0779749	+	0.0195241i
$586$	−39.6210			−1.63673
$587$	−14.3950	+	24.9329i	−0.594145	+	1.02909i	0.399521	+	0.916724i	$0.369176\pi$
$587$	−14.3950	+	24.9329i	−0.594145	+	1.02909i	−0.993667	+	0.112366i	$0.964157\pi$
$588$	−15.4158	−	36.3679i	−0.635737	−	1.49979i
$589$	2.49389	+	4.31954i	0.102759	+	0.177984i
$590$	4.35194	+	7.53778i	0.179167	+	0.310325i
$591$	16.2510	−	21.5434i	0.668476	−	0.886176i
$592$	11.9344	−	20.6709i	0.490499	−	0.849570i
$593$	30.9171			1.26961			0.634807	−	0.772671i	$-0.281080\pi$
$593$	30.9171			1.26961			0.634807	+	0.772671i	$0.281080\pi$
$594$	−2.27082	−	14.4778i	−0.0931730	−	0.594032i
$595$	−5.52420			−0.226470
$596$	12.4474	−	21.5596i	0.509867	−	0.883115i
$597$	−3.73921	+	4.95694i	−0.153035	+	0.202874i
$598$	3.23790	+	5.60821i	0.132408	+	0.229337i
$599$	−0.696460	−	1.20630i	−0.0284566	−	0.0492882i	0.851446	−	0.524442i	$-0.175726\pi$
$599$	−0.696460	−	1.20630i	−0.0284566	−	0.0492882i	−0.879903	+	0.475153i	$0.842393\pi$
$600$	0.496291	+	1.17081i	0.0202610	+	0.0477983i
$601$	−4.41256	+	7.64279i	−0.179992	+	0.311756i	−0.941878	−	0.335956i	$-0.890941\pi$
$601$	−4.41256	+	7.64279i	−0.179992	+	0.311756i	0.761885	+	0.647712i	$0.224274\pi$
$602$	6.99258			0.284996
$603$	−16.9852	+	17.5535i	−0.691689	+	0.714835i
$604$	41.6210			1.69353
$605$	4.58613	−	7.94341i	0.186453	−	0.322946i
$606$	5.26581	+	0.649230i	0.213909	+	0.0263732i
$607$	1.07839	+	1.86783i	0.0437706	+	0.0758129i	0.887081	−	0.461614i	$-0.152730\pi$
$607$	1.07839	+	1.86783i	0.0437706	+	0.0758129i	−0.843310	+	0.537427i	$0.819396\pi$
$608$	−2.62015	−	4.53824i	−0.106261	−	0.184050i
$609$	27.2268	+	3.35683i	1.10328	+	0.136026i
$610$	−3.98484	+	6.90195i	−0.161342	+	0.279452i
$611$	7.06804			0.285942
$612$	6.63322	−	6.85518i	0.268132	−	0.277104i
$613$	−9.57521			−0.386739			−0.193370	−	0.981126i	$-0.561942\pi$
$613$	−9.57521			−0.386739			−0.193370	+	0.981126i	$0.561942\pi$
$614$	30.7486	−	53.2581i	1.24091	−	2.14932i
$615$	0.121457	+	0.286534i	0.00489764	+	0.0115542i
$616$	−2.02791	−	3.51244i	−0.0817068	−	0.141520i
$617$	18.8384	+	32.6291i	0.758406	+	1.31360i	0.943663	+	0.330907i	$0.107355\pi$
$617$	18.8384	+	32.6291i	0.758406	+	1.31360i	−0.185258	+	0.982690i	$0.559312\pi$
$618$	16.3724	−	21.7044i	0.658596	−	0.873078i
$619$	−8.55211	+	14.8127i	−0.343738	+	0.595372i	−0.985124	−	0.171847i	$-0.945027\pi$
$619$	−8.55211	+	14.8127i	−0.343738	+	0.595372i	0.641385	+	0.767219i	$0.278360\pi$
$620$	−18.1016			−0.726978
$621$	−3.85675	−	24.5890i	−0.154766	−	0.986722i
$622$	19.6358			0.787325
$623$	6.12920	−	10.6161i	0.245561	−	0.425324i
$624$	2.14435	−	2.84269i	0.0858428	−	0.113799i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	12.1215	+	20.9950i	0.484471	+	0.839128i
$627$	0.592243	+	1.39718i	0.0236519	+	0.0557979i
$628$	2.97711	−	5.15650i	0.118799	−	0.205767i
$629$	−10.1723			−0.405595
$630$	−24.8068	−	6.21136i	−0.988326	−	0.247466i
$631$	33.1090			1.31805			0.659025	−	0.752121i	$-0.270969\pi$
$631$	33.1090			1.31805			0.659025	+	0.752121i	$0.270969\pi$
$632$	3.79743	−	6.57734i	0.151054	−	0.261632i
$633$	25.7728	+	3.17757i	1.02438	+	0.126297i
$634$	−9.57500	−	16.5844i	−0.380272	−	0.658650i
$635$	3.53936	+	6.13034i	0.140455	+	0.243275i
$636$	16.8687	+	2.07977i	0.668888	+	0.0824684i
$637$	−3.14195	+	5.44201i	−0.124489	+	0.215620i
$638$	10.9320			0.432800
$639$	5.04013	+	17.6436i	0.199385	+	0.697968i
$640$	5.78259			0.228577
$641$	11.5763	−	20.0508i	0.457237	−	0.791957i	−0.541577	−	0.840651i	$-0.682173\pi$
$641$	11.5763	−	20.0508i	0.457237	−	0.791957i	0.998814	+	0.0486939i	$0.0155059\pi$
$642$	1.70628	+	4.02534i	0.0673416	+	0.158867i
$643$	−21.5319	−	37.2944i	−0.849137	−	1.47075i	−0.881980	−	0.471287i	$-0.843789\pi$
$643$	−21.5319	−	37.2944i	−0.849137	−	1.47075i	0.0328430	−	0.999461i	$-0.489544\pi$
$644$	−23.0168	−	39.8662i	−0.906988	−	1.57095i
$645$	0.855648	−	1.13430i	0.0336911	−	0.0446632i
$646$	−0.913870	+	1.58287i	−0.0359557	+	0.0622771i
$647$	−20.6439			−0.811595			−0.405798	−	0.913963i	$-0.633006\pi$
$647$	−20.6439			−0.811595			−0.405798	+	0.913963i	$0.633006\pi$
$648$	5.61065	−	3.49035i	0.220407	−	0.137114i
$649$	−5.64064			−0.221415
$650$	0.675970	−	1.17081i	0.0265137	−	0.0459231i
$651$	32.8031	−	43.4859i	1.28565	−	1.70435i
$652$	−9.96728	−	17.2638i	−0.390349	−	0.676104i
$653$	−3.41758	−	5.91942i	−0.133740	−	0.231645i	0.791375	−	0.611331i	$-0.209365\pi$
$653$	−3.41758	−	5.91942i	−0.133740	−	0.231645i	−0.925116	+	0.379686i	$0.876032\pi$
$654$	19.8892	+	46.9212i	0.777730	+	1.83476i
$655$	3.00000	−	5.19615i	0.117220	−	0.203030i
$656$	0.569988			0.0222543
$657$	10.1723	+	35.6091i	0.396858	+	1.38924i
$658$	−92.9688			−3.62430
$659$	13.4307	−	23.2626i	0.523184	−	0.906181i	−0.476452	−	0.879200i	$-0.658077\pi$
$659$	13.4307	−	23.2626i	0.523184	−	0.906181i	0.999636	−	0.0269806i	$-0.00858924\pi$
$660$	−5.46598	−	0.673910i	−0.212763	−	0.0262319i
$661$	1.06063	+	1.83706i	0.0412535	+	0.0714532i	0.885915	−	0.463848i	$-0.153532\pi$
$661$	1.06063	+	1.83706i	0.0412535	+	0.0714532i	−0.844661	+	0.535301i	$0.820198\pi$
$662$	−7.53162	−	13.0451i	−0.292725	−	0.507014i
$663$	−1.50611	−	0.185691i	−0.0584926	−	0.00721165i
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$	2.64806			0.102687
$666$	−45.6792	−	11.4376i	−1.77003	−	0.443198i
$667$	18.5667			0.718907
$668$	−14.9750	+	25.9375i	−0.579401	+	1.00355i
$669$	18.1369	+	42.7874i	0.701214	+	1.65425i
$670$	8.49258	+	14.7096i	0.328097	+	0.568281i
$671$	−2.58242	−	4.47288i	−0.0996933	−	0.172674i
$672$	−34.4639	+	45.6876i	−1.32947	+	1.76244i
$673$	−17.4102	+	30.1553i	−0.671112	+	1.16240i	0.306477	+	0.951878i	$0.400850\pi$
$673$	−17.4102	+	30.1553i	−0.671112	+	1.16240i	−0.977589	+	0.210523i	$0.932483\pi$
$674$	−4.76450			−0.183522
$675$	−4.04307	+	3.26399i	−0.155618	+	0.125631i
$676$	−29.5874			−1.13798
$677$	12.3421	−	21.3772i	0.474346	−	0.821592i	−0.525222	−	0.850965i	$-0.676018\pi$
$677$	12.3421	−	21.3772i	0.474346	−	0.821592i	0.999569	+	0.0293735i	$0.00935121\pi$
$678$	−25.9474	+	34.3976i	−0.996505	+	1.32103i
$679$	27.7449	+	48.0555i	1.06475	+	1.84420i
$680$	−0.496291	−	0.859601i	−0.0190319	−	0.0329642i
$681$	−0.913870	−	2.15594i	−0.0350196	−	0.0826157i
$682$	10.8532	−	18.7984i	0.415592	−	0.719827i
$683$	−38.4610			−1.47167			−0.735834	−	0.677162i	$-0.763210\pi$
$683$	−38.4610			−1.47167			−0.735834	+	0.677162i	$0.763210\pi$
$684$	−3.17968	+	3.28608i	−0.121578	+	0.125646i
$685$	−7.46838			−0.285352
$686$	11.4926	−	19.9057i	0.438789	−	0.760005i
$687$	−14.1571	−	1.74545i	−0.540127	−	0.0665932i
$688$	−1.30114	−	2.25363i	−0.0496054	−	0.0859190i
$689$	−1.35194	−	2.34163i	−0.0515048	−	0.0892089i
$690$	−17.1776	−	2.11785i	−0.653940	−	0.0806253i
$691$	−0.240304	+	0.416219i	−0.00914159	+	0.0158337i	−0.870560	−	0.492062i	$-0.836243\pi$
$691$	−0.240304	+	0.416219i	−0.00914159	+	0.0158337i	0.861418	+	0.507896i	$0.169577\pi$
$692$	54.2084			2.06070
$693$	11.5242	−	11.9098i	0.437768	−	0.452417i
$694$	1.47841			0.0561197
$695$	−4.00000	+	6.92820i	−0.151729	+	0.262802i
$696$	1.92369	+	4.53824i	0.0729174	+	0.172021i
$697$	−0.121457	−	0.210370i	−0.00460053	−	0.00796835i
$698$	−22.2637	−	38.5619i	−0.842694	−	1.45959i
$699$	−8.95725	+	11.8743i	−0.338794	+	0.449128i
$700$	−4.80516	+	8.32279i	−0.181618	+	0.314572i
$701$	−18.1797			−0.686637			−0.343318	−	0.939219i	$-0.611551\pi$
$701$	−18.1797			−0.686637			−0.343318	+	0.939219i	$0.611551\pi$
$702$	−6.55451	−	2.52732i	−0.247384	−	0.0953875i
$703$	4.87614			0.183907
$704$	−7.11404	+	12.3219i	−0.268120	+	0.464398i
$705$	−11.3761	+	15.0810i	−0.428450	+	0.567982i
$706$	−10.5316	−	18.2413i	−0.396363	−	0.686520i
$707$	3.00000	+	5.19615i	0.112827	+	0.195421i
$708$	−6.63322	−	15.6486i	−0.249292	−	0.588111i
$709$	−3.59355	+	6.22421i	−0.134959	+	0.233755i	−0.925582	−	0.378548i	$-0.876423\pi$
$709$	−3.59355	+	6.22421i	−0.134959	+	0.233755i	0.790623	+	0.612303i	$0.209757\pi$
$710$	12.7597			0.478863
$711$	30.1042	+	7.53778i	1.12900	+	0.282689i
$712$	2.20257			0.0825449
$713$	18.4331	−	31.9270i	0.690323	−	1.19568i
$714$	19.8105	+	2.44247i	0.741389	+	0.0914071i
$715$	0.438069	+	0.758758i	0.0163829	+	0.0283760i
$716$	−2.62015	−	4.53824i	−0.0979197	−	0.169602i
$717$	−41.1271	−	5.07063i	−1.53592	−	0.189366i
$718$	31.8737	−	55.2069i	1.18952	−	2.06030i
$719$	12.5168			0.466797			0.233399	−	0.972381i	$-0.425015\pi$
$719$	12.5168			0.466797			0.233399	+	0.972381i	$0.425015\pi$
$720$	2.61404	+	9.15073i	0.0974195	+	0.341028i
$721$	30.7449			1.14500
$722$	−19.3802	+	33.5674i	−0.721255	+	1.24925i
$723$	4.21826	+	9.95141i	0.156879	+	0.370097i
$724$	−0.550803	−	0.954019i	−0.0204704	−	0.0354558i
$725$	−1.93807	−	3.35683i	−0.0719781	−	0.124670i
$726$	−19.9586	+	26.4584i	−0.740732	+	0.981963i
$727$	−4.21292	+	7.29699i	−0.156249	+	0.270631i	−0.933513	−	0.358544i	$-0.883273\pi$
$727$	−4.21292	+	7.29699i	−0.156249	+	0.270631i	0.777264	+	0.629174i	$0.216607\pi$
$728$	−1.94418			−0.0720562
$729$	20.0107	+	18.1266i	0.741136	+	0.671355i
$730$	25.7523			0.953135
$731$	−0.554512	+	0.960443i	−0.0205094	+	0.0355233i
$732$	9.37211	−	12.4243i	0.346403	−	0.459215i
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$	−7.48887	−	12.9711i	−0.276419	−	0.478772i
$735$	−6.55451	−	15.4629i	−0.241767	−	0.570359i
$736$	−19.3663	+	33.5434i	−0.713852	+	1.23643i
$737$	−11.0074			−0.405463
$738$	−0.308874	−	1.08125i	−0.0113698	−	0.0398013i
$739$	−1.81290			−0.0666887			−0.0333444	−	0.999444i	$-0.510616\pi$
$739$	−1.81290			−0.0666887			−0.0333444	+	0.999444i	$0.510616\pi$
$740$	−8.84823	+	15.3256i	−0.325267	+	0.563380i
$741$	0.721965	+	0.0890123i	0.0265220	+	0.00326995i
$742$	17.7826	+	30.8003i	0.652819	+	1.13072i
$743$	−10.0686	−	17.4393i	−0.369380	−	0.639785i	0.620089	−	0.784532i	$-0.287097\pi$
$743$	−10.0686	−	17.4393i	−0.369380	−	0.639785i	−0.989469	+	0.144747i	$0.953763\pi$
$744$	9.71370	+	1.19762i	0.356122	+	0.0439068i
$745$	5.29241	−	9.16673i	0.193899	−	0.335843i
$746$	45.7374			1.67457
$747$	−35.6739	−	8.93237i	−1.30524	−	0.326818i
$748$	4.29873			0.157177
$749$	−2.47209	+	4.28179i	−0.0903282	+	0.156453i
$750$	1.41016	+	3.32675i	0.0514918	+	0.121476i
$751$	−6.10662	−	10.5770i	−0.222834	−	0.385959i	0.732834	−	0.680408i	$-0.238197\pi$
$751$	−6.10662	−	10.5770i	−0.222834	−	0.385959i	−0.955667	+	0.294449i	$0.904864\pi$
$752$	17.2991	+	29.9628i	0.630832	+	1.09263i
$753$	29.8031	−	39.5089i	1.08608	−	1.43979i
$754$	2.62015	−	4.53824i	0.0954203	−	0.165273i
$755$	17.6965			0.644040
$756$	46.5931	+	17.9656i	1.69457	+	0.653402i
$757$	52.9533			1.92462			0.962310	−	0.271955i	$-0.0876701\pi$
$757$	52.9533			1.92462			0.962310	+	0.271955i	$0.0876701\pi$
$758$	−18.1419	+	31.4228i	−0.658945	+	1.14133i
$759$	6.75468	−	8.95445i	0.245179	−	0.325026i
$760$	0.237900	+	0.412055i	0.00862955	+	0.0149468i
$761$	9.22677	+	15.9812i	0.334470	+	0.579319i	0.983383	−	0.181543i	$-0.0581093\pi$
$761$	9.22677	+	15.9812i	0.334470	+	0.579319i	−0.648913	+	0.760863i	$0.724776\pi$
$762$	−9.98212	−	23.5491i	−0.361614	−	0.853094i
$763$	−28.8158	+	49.9105i	−1.04320	+	1.80688i
$764$	−47.5752			−1.72121
$765$	2.82032	−	2.91469i	0.101969	−	0.105381i
$766$	−0.992582			−0.0358634
$767$	−1.35194	+	2.34163i	−0.0488157	+	0.0845513i
$768$	15.4458	+	1.90434i	0.557353	+	0.0687169i
$769$	2.22677	+	3.85688i	0.0802995	+	0.139083i	0.903379	−	0.428844i	$-0.141079\pi$

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04307 - 1.80664i) q^{2} +(-1.04307 + 1.38276i) q^{3} +(-1.17597 - 2.03684i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.41016 + 3.32675i) q^{6} +(-2.04307 + 3.53869i) q^{7} -0.734191 q^{8} +(-0.824030 - 2.88461i) q^{9} +O(q^{10})\)	\(q+(1.04307 - 1.80664i) q^{2} +(-1.04307 + 1.38276i) q^{3} +(-1.17597 - 2.03684i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.41016 + 3.32675i) q^{6} +(-2.04307 + 3.53869i) q^{7} -0.734191 q^{8} +(-0.824030 - 2.88461i) q^{9} -2.08613 q^{10} +(0.675970 - 1.17081i) q^{11} +(4.04307 + 0.498476i) q^{12} +(-0.324030 - 0.561237i) q^{13} +(4.26210 + 7.38217i) q^{14} +(1.71903 + 0.211943i) q^{15} +(1.58613 - 2.74726i) q^{16} -1.35194 q^{17} +(-6.07097 - 1.52011i) q^{18} +0.648061 q^{19} +(-1.17597 + 2.03684i) q^{20} +(-2.76210 - 6.51615i) q^{21} +(-1.41016 - 2.44247i) q^{22} +(-2.39500 - 4.14827i) q^{23} +(0.765809 - 1.01521i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.35194 q^{26} +(4.84823 + 1.86940i) q^{27} +9.61033 q^{28} +(-1.93807 + 3.35683i) q^{29} +(2.17597 - 2.88461i) q^{30} +(3.84823 + 6.66533i) q^{31} +(-4.04307 - 7.00279i) q^{32} +(0.913870 + 2.15594i) q^{33} +(-1.41016 + 2.44247i) q^{34} +4.08613 q^{35} +(-4.90645 + 5.07063i) q^{36} +7.52420 q^{37} +(0.675970 - 1.17081i) q^{38} +(1.11404 + 0.137352i) q^{39} +(0.367095 + 0.635828i) q^{40} +(0.0898394 + 0.155606i) q^{41} +(-14.6534 - 1.80664i) q^{42} +(0.410161 - 0.710419i) q^{43} -3.17968 q^{44} +(-2.08613 + 2.15594i) q^{45} -9.99258 q^{46} +(-5.45323 + 9.44526i) q^{47} +(2.14435 + 5.05880i) q^{48} +(-4.84823 - 8.39738i) q^{49} +(1.04307 + 1.80664i) q^{50} +(1.41016 - 1.86940i) q^{51} +(-0.762100 + 1.32000i) q^{52} +4.17226 q^{53} +(8.43436 - 6.80911i) q^{54} -1.35194 q^{55} +(1.50000 - 2.59808i) q^{56} +(-0.675970 + 0.896110i) q^{57} +(4.04307 + 7.00279i) q^{58} +(-2.08613 - 3.61328i) q^{59} +(-1.58984 - 3.75064i) q^{60} +(1.91016 - 3.30850i) q^{61} +16.0558 q^{62} +(11.8913 + 2.97746i) q^{63} -10.5242 q^{64} +(-0.324030 + 0.561237i) q^{65} +(4.84823 + 0.597746i) q^{66} +(-4.07097 - 7.05113i) q^{67} +(1.58984 + 2.75368i) q^{68} +(8.23419 + 1.01521i) q^{69} +(4.26210 - 7.38217i) q^{70} -6.11644 q^{71} +(0.604996 + 2.11785i) q^{72} -12.3445 q^{73} +(7.84823 - 13.5935i) q^{74} +(-0.675970 - 1.59470i) q^{75} +(-0.762100 - 1.32000i) q^{76} +(2.76210 + 4.78410i) q^{77} +(1.41016 - 1.86940i) q^{78} +(-5.17226 + 8.95862i) q^{79} -3.17226 q^{80} +(-7.64195 + 4.75401i) q^{81} +0.374833 q^{82} +(6.12920 - 10.6161i) q^{83} +(-10.0242 + 13.2887i) q^{84} +(0.675970 + 1.17081i) q^{85} +(-0.855648 - 1.48203i) q^{86} +(-2.62015 - 6.18127i) q^{87} +(-0.496291 + 0.859601i) q^{88} -3.00000 q^{89} +(1.71903 + 6.01767i) q^{90} +2.64806 q^{91} +(-5.63290 + 9.75648i) q^{92} +(-13.2305 - 1.63121i) q^{93} +(11.3761 + 19.7041i) q^{94} +(-0.324030 - 0.561237i) q^{95} +(13.9003 + 1.71380i) q^{96} +(6.79001 - 11.7606i) q^{97} -20.2281 q^{98} +(-3.93436 - 0.985122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + q^{3} - 5 q^{4} - 3 q^{5} - 4 q^{6} - 5 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 6 * q - q^2 + q^3 - 5 * q^4 - 3 * q^5 - 4 * q^6 - 5 * q^7 + 6 * q^8 - 7 * q^9	\( 6 q - q^{2} + q^{3} - 5 q^{4} - 3 q^{5} - 4 q^{6} - 5 q^{7} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 2 q^{11} + 17 q^{12} - 4 q^{13} + 9 q^{14} + q^{15} - 5 q^{16} - 4 q^{17} - 23 q^{18} + 8 q^{19} - 5 q^{20} + 4 q^{22} - 3 q^{23} + 15 q^{24} - 3 q^{25} - 4 q^{26} - 2 q^{27} + 10 q^{28} + 7 q^{29} + 11 q^{30} - 8 q^{31} - 17 q^{32} + 20 q^{33} + 4 q^{34} + 10 q^{35} + 10 q^{36} + 12 q^{37} + 2 q^{38} - 14 q^{39} - 3 q^{40} + 13 q^{41} - 33 q^{42} - 10 q^{43} - 44 q^{44} + 2 q^{45} - 6 q^{46} - 13 q^{47} - 10 q^{48} + 2 q^{49} - q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 5 q^{54} - 4 q^{55} + 9 q^{56} - 2 q^{57} + 17 q^{58} + 2 q^{59} - 22 q^{60} - q^{61} + 84 q^{62} + 33 q^{63} - 30 q^{64} - 4 q^{65} - 2 q^{66} - 11 q^{67} + 22 q^{68} + 39 q^{69} + 9 q^{70} - 20 q^{71} + 15 q^{72} - 16 q^{73} + 16 q^{74} - 2 q^{75} + 12 q^{76} - 4 q^{78} - 2 q^{79} + 10 q^{80} - 19 q^{81} - 58 q^{82} + 15 q^{83} - 27 q^{84} + 2 q^{85} - 28 q^{86} - 26 q^{87} + 24 q^{88} - 18 q^{89} + q^{90} + 20 q^{91} - 39 q^{92} - 42 q^{93} + 31 q^{94} - 4 q^{95} + 13 q^{96} + 18 q^{97} - 80 q^{98} + 22 q^{99}+O(q^{100}) \) 6 * q - q^2 + q^3 - 5 * q^4 - 3 * q^5 - 4 * q^6 - 5 * q^7 + 6 * q^8 - 7 * q^9 + 2 * q^10 + 2 * q^11 + 17 * q^12 - 4 * q^13 + 9 * q^14 + q^15 - 5 * q^16 - 4 * q^17 - 23 * q^18 + 8 * q^19 - 5 * q^20 + 4 * q^22 - 3 * q^23 + 15 * q^24 - 3 * q^25 - 4 * q^26 - 2 * q^27 + 10 * q^28 + 7 * q^29 + 11 * q^30 - 8 * q^31 - 17 * q^32 + 20 * q^33 + 4 * q^34 + 10 * q^35 + 10 * q^36 + 12 * q^37 + 2 * q^38 - 14 * q^39 - 3 * q^40 + 13 * q^41 - 33 * q^42 - 10 * q^43 - 44 * q^44 + 2 * q^45 - 6 * q^46 - 13 * q^47 - 10 * q^48 + 2 * q^49 - q^50 - 4 * q^51 + 12 * q^52 - 4 * q^53 + 5 * q^54 - 4 * q^55 + 9 * q^56 - 2 * q^57 + 17 * q^58 + 2 * q^59 - 22 * q^60 - q^61 + 84 * q^62 + 33 * q^63 - 30 * q^64 - 4 * q^65 - 2 * q^66 - 11 * q^67 + 22 * q^68 + 39 * q^69 + 9 * q^70 - 20 * q^71 + 15 * q^72 - 16 * q^73 + 16 * q^74 - 2 * q^75 + 12 * q^76 - 4 * q^78 - 2 * q^79 + 10 * q^80 - 19 * q^81 - 58 * q^82 + 15 * q^83 - 27 * q^84 + 2 * q^85 - 28 * q^86 - 26 * q^87 + 24 * q^88 - 18 * q^89 + q^90 + 20 * q^91 - 39 * q^92 - 42 * q^93 + 31 * q^94 - 4 * q^95 + 13 * q^96 + 18 * q^97 - 80 * q^98 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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