LMFDB - Embedded newform 507.2.s.a.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(5,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([26, 3]))

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

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

chi := DirichletCharacter("507.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.s (of order $52$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$1392$
Relative dimension:	$58$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			5.9
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.392585 + 2.14227i) q^{2} +(-1.02029 - 1.39965i) q^{3} +(-2.56516 - 0.972837i) q^{4} +(-1.56541 - 0.0946898i) q^{5} +(3.39897 - 1.63625i) q^{6} +(2.97174 + 1.79648i) q^{7} +(0.837658 - 1.38566i) q^{8} +(-0.918027 + 2.85609i) q^{9} +(0.817408 - 3.31635i) q^{10} +(-0.554218 - 3.02427i) q^{11} +(1.25557 + 4.58289i) q^{12} +(2.28578 + 2.78840i) q^{13} +(-5.01520 + 5.66099i) q^{14} +(1.46463 + 2.28763i) q^{15} +(-1.46739 - 1.30000i) q^{16} +(-5.53037 + 1.36311i) q^{17} +(-5.75810 - 3.08792i) q^{18} +(-2.10882 + 2.10882i) q^{19} +(3.92341 + 1.76578i) q^{20} +(-0.517590 - 5.99231i) q^{21} +6.69638 q^{22} -1.33384 q^{23} +(-2.79408 + 0.241341i) q^{24} +(-2.52200 - 0.306227i) q^{25} +(-6.87088 + 3.80207i) q^{26} +(4.93417 - 1.62911i) q^{27} +(-5.87531 - 7.49928i) q^{28} +(-4.60112 + 3.17593i) q^{29} +(-5.47572 + 2.23955i) q^{30} +(-5.46079 - 4.27826i) q^{31} +(5.91019 - 4.63034i) q^{32} +(-3.66745 + 3.86134i) q^{33} +(-0.749014 - 12.3827i) q^{34} +(-4.48188 - 3.09362i) q^{35} +(5.13339 - 6.43323i) q^{36} +(-2.83240 + 3.61529i) q^{37} +(-3.68978 - 5.34556i) q^{38} +(1.57063 - 6.04426i) q^{39} +(-1.44248 + 2.08980i) q^{40} +(-0.429594 - 1.37862i) q^{41} +(13.0403 + 1.24368i) q^{42} +(-2.61145 - 0.317087i) q^{43} +(-1.52046 + 8.29691i) q^{44} +(1.70753 - 4.38401i) q^{45} +(0.523645 - 2.85744i) q^{46} +(-4.32493 - 1.94649i) q^{47} +(-0.322375 + 3.38021i) q^{48} +(2.35083 + 4.47914i) q^{49} +(1.64612 - 5.28259i) q^{50} +(7.55045 + 6.34981i) q^{51} +(-3.15073 - 9.37640i) q^{52} +(2.18691 + 8.87264i) q^{53} +(1.55292 + 11.2099i) q^{54} +(0.581211 + 4.78670i) q^{55} +(4.97860 - 2.61297i) q^{56} +(5.10322 + 0.800005i) q^{57} +(-4.99736 - 11.1037i) q^{58} +(-0.756881 + 12.5127i) q^{59} +(-1.53153 - 7.29299i) q^{60} +(-0.299979 - 0.0739381i) q^{61} +(11.3090 - 10.0189i) q^{62} +(-7.85904 + 6.83833i) q^{63} +(5.77707 + 11.0073i) q^{64} +(-3.31415 - 4.58143i) q^{65} +(-6.83223 - 9.37257i) q^{66} +(2.03855 + 0.917476i) q^{67} +(15.5124 + 1.88354i) q^{68} +(1.36090 + 1.86690i) q^{69} +(8.38688 - 8.38688i) q^{70} +(-2.86374 - 9.19007i) q^{71} +(3.18856 + 3.66449i) q^{72} +(9.12208 - 1.67168i) q^{73} +(-6.63297 - 7.48707i) q^{74} +(2.14456 + 3.84236i) q^{75} +(7.46102 - 3.35793i) q^{76} +(3.78605 - 9.98299i) q^{77} +(12.3318 + 5.73760i) q^{78} +(4.76583 + 12.5665i) q^{79} +(2.17398 + 2.17398i) q^{80} +(-7.31445 - 5.24393i) q^{81} +(3.12202 - 0.379082i) q^{82} +(8.11695 + 2.52934i) q^{83} +(-4.50184 + 15.8748i) q^{84} +(8.78637 - 1.61016i) q^{85} +(1.70450 - 5.46994i) q^{86} +(9.13965 + 3.19959i) q^{87} +(-4.65484 - 1.76535i) q^{88} +(-4.02598 + 4.02598i) q^{89} +(8.72139 + 5.37909i) q^{90} +(1.78344 + 12.3928i) q^{91} +(3.42151 + 1.29761i) q^{92} +(-0.416476 + 12.0082i) q^{93} +(5.86782 - 8.50100i) q^{94} +(3.50086 - 3.10149i) q^{95} +(-12.5109 - 3.54791i) q^{96} +(-18.8657 + 1.14117i) q^{97} +(-10.5184 + 3.27768i) q^{98} +(9.14637 + 1.19347i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100}) $ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{52}\right)$

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 $

$2$	−0.392585	+	2.14227i	−0.277600	+	1.51481i	0.488770	+	0.872413i	$0.337446\pi$
$2$	−0.392585	+	2.14227i	−0.277600	+	1.51481i	−0.766369	+	0.642400i	$0.777939\pi$
$3$	−1.02029	−	1.39965i	−0.589063	−	0.808087i
$3$	−1.02029	−	1.39965i	−0.589063	−	0.808087i
$4$	−2.56516	−	0.972837i	−1.28258	−	0.486419i
$5$	−1.56541	−	0.0946898i	−0.700072	−	0.0423466i	−0.293492	−	0.955962i	$-0.594817\pi$
$5$	−1.56541	−	0.0946898i	−0.700072	−	0.0423466i	−0.406580	+	0.913615i	$0.633279\pi$
$6$	3.39897	−	1.63625i	1.38762	−	0.667996i
$7$	2.97174	+	1.79648i	1.12321	+	0.679005i	0.951960	−	0.306222i	$-0.0990650\pi$
$7$	2.97174	+	1.79648i	1.12321	+	0.679005i	0.171252	+	0.985227i	$0.445219\pi$
$8$	0.837658	−	1.38566i	0.296157	−	0.489903i
$9$	−0.918027	+	2.85609i	−0.306009	+	0.952029i
$10$	0.817408	−	3.31635i	0.258487	−	1.04872i
$11$	−0.554218	−	3.02427i	−0.167103	−	0.911852i	−0.955125	−	0.296204i	$-0.904279\pi$
$11$	−0.554218	−	3.02427i	−0.167103	−	0.911852i	0.788021	−	0.615648i	$-0.211106\pi$
$12$	1.25557	+	4.58289i	0.362452	+	1.32297i
$13$	2.28578	+	2.78840i	0.633962	+	0.773364i
$13$	2.28578	+	2.78840i	0.633962	+	0.773364i
$14$	−5.01520	+	5.66099i	−1.34037	+	1.51296i
$15$	1.46463	+	2.28763i	0.378167	+	0.590664i
$16$	−1.46739	−	1.30000i	−0.366848	−	0.324999i
$17$	−5.53037	+	1.36311i	−1.34131	+	0.330604i	−0.843709	−	0.536801i	$-0.819633\pi$
$17$	−5.53037	+	1.36311i	−1.34131	+	0.330604i	−0.497603	+	0.867405i	$0.665787\pi$
$18$	−5.75810	−	3.08792i	−1.35720	−	0.727829i
$19$	−2.10882	+	2.10882i	−0.483798	+	0.483798i	−0.906342	−	0.422545i	$-0.861137\pi$
$19$	−2.10882	+	2.10882i	−0.483798	+	0.483798i	0.422545	+	0.906342i	$0.361137\pi$
$20$	3.92341	+	1.76578i	0.877301	+	0.394841i
$21$	−0.517590	−	5.99231i	−0.112947	−	1.30763i
$22$	6.69638			1.42767
$23$	−1.33384			−0.278124			−0.139062	−	0.990284i	$-0.544409\pi$
$23$	−1.33384			−0.278124			−0.139062	+	0.990284i	$0.544409\pi$
$24$	−2.79408	+	0.241341i	−0.570339	+	0.0492635i
$25$	−2.52200	−	0.306227i	−0.504401	−	0.0612454i
$26$	−6.87088	+	3.80207i	−1.34749	+	0.745648i
$27$	4.93417	−	1.62911i	0.949581	−	0.313523i
$28$	−5.87531	−	7.49928i	−1.11033	−	1.41723i
$29$	−4.60112	+	3.17593i	−0.854407	+	0.589755i	−0.912739	−	0.408542i	$-0.866037\pi$
$29$	−4.60112	+	3.17593i	−0.854407	+	0.589755i	0.0583320	+	0.998297i	$0.481422\pi$
$30$	−5.47572	+	2.23955i	−0.999725	+	0.408884i
$31$	−5.46079	−	4.27826i	−0.980787	−	0.768397i	−0.00796868	−	0.999968i	$-0.502537\pi$
$31$	−5.46079	−	4.27826i	−0.980787	−	0.768397i	−0.972818	+	0.231571i	$0.925613\pi$
$32$	5.91019	−	4.63034i	1.04478	−	0.818536i
$33$	−3.66745	+	3.86134i	−0.638422	+	0.672172i
$34$	−0.749014	−	12.3827i	−0.128455	−	2.12361i
$35$	−4.48188	−	3.09362i	−0.757576	−	0.522917i
$36$	5.13339	−	6.43323i	0.855566	−	1.07220i
$37$	−2.83240	+	3.61529i	−0.465644	+	0.594350i	−0.961756	−	0.273908i	$-0.911684\pi$
$37$	−2.83240	+	3.61529i	−0.465644	+	0.594350i	0.496112	+	0.868258i	$0.334760\pi$
$38$	−3.68978	−	5.34556i	−0.598561	−	0.867165i
$39$	1.57063	−	6.04426i	0.251502	−	0.967857i
$40$	−1.44248	+	2.08980i	−0.228077	+	0.330426i
$41$	−0.429594	−	1.37862i	−0.0670913	−	0.215304i	0.915087	−	0.403258i	$-0.132122\pi$
$41$	−0.429594	−	1.37862i	−0.0670913	−	0.215304i	−0.982178	+	0.187954i	$0.939814\pi$
$42$	13.0403	+	1.24368i	2.01217	+	0.191903i
$43$	−2.61145	−	0.317087i	−0.398242	−	0.0483553i	−0.0810340	−	0.996711i	$-0.525822\pi$
$43$	−2.61145	−	0.317087i	−0.398242	−	0.0483553i	−0.317208	+	0.948356i	$0.602745\pi$
$44$	−1.52046	+	8.29691i	−0.229219	+	1.25081i
$45$	1.70753	−	4.38401i	0.254544	−	0.653530i
$46$	0.523645	−	2.85744i	0.0772072	−	0.421306i
$47$	−4.32493	−	1.94649i	−0.630856	−	0.283925i	0.0696503	−	0.997571i	$-0.477812\pi$
$47$	−4.32493	−	1.94649i	−0.630856	−	0.283925i	−0.700506	+	0.713646i	$0.747042\pi$
$48$	−0.322375	+	3.38021i	−0.0465308	+	0.487891i
$49$	2.35083	+	4.47914i	0.335834	+	0.639877i
$50$	1.64612	−	5.28259i	0.232797	−	0.747071i
$51$	7.55045	+	6.34981i	1.05727	+	0.889151i
$52$	−3.15073	−	9.37640i	−0.436928	−	1.30027i
$53$	2.18691	+	8.87264i	0.300395	+	1.21875i	0.906101	+	0.423062i	$0.139045\pi$
$53$	2.18691	+	8.87264i	0.300395	+	1.21875i	−0.605706	+	0.795689i	$0.707109\pi$
$54$	1.55292	+	11.2099i	0.211325	+	1.52547i
$55$	0.581211	+	4.78670i	0.0783704	+	0.645439i
$56$	4.97860	−	2.61297i	0.665294	−	0.349173i
$57$	5.10322	+	0.800005i	0.675938	+	0.105963i
$58$	−4.99736	−	11.1037i	−0.656185	−	1.45798i
$59$	−0.756881	+	12.5127i	−0.0985376	+	1.62902i	0.527730	+	0.849412i	$0.323043\pi$
$59$	−0.756881	+	12.5127i	−0.0985376	+	1.62902i	−0.626268	+	0.779608i	$0.715418\pi$
$60$	−1.53153	−	7.29299i	−0.197720	−	0.941522i
$61$	−0.299979	−	0.0739381i	−0.0384083	−	0.00946681i	0.220065	−	0.975485i	$-0.429373\pi$
$61$	−0.299979	−	0.0739381i	−0.0384083	−	0.00946681i	−0.258473	+	0.966018i	$0.583219\pi$
$62$	11.3090	−	10.0189i	1.43624	−	1.27240i
$63$	−7.85904	+	6.83833i	−0.990145	+	0.861548i
$64$	5.77707	+	11.0073i	0.722134	+	1.37591i
$65$	−3.31415	−	4.58143i	−0.411070	−	0.568257i
$66$	−6.83223	−	9.37257i	−0.840990	−	1.15368i
$67$	2.03855	+	0.917476i	0.249048	+	0.112088i	0.531092	−	0.847314i	$-0.321782\pi$
$67$	2.03855	+	0.917476i	0.249048	+	0.112088i	−0.282044	+	0.959401i	$0.591012\pi$
$68$	15.5124	+	1.88354i	1.88115	+	0.228413i
$69$	1.36090	+	1.86690i	0.163833	+	0.224749i
$70$	8.38688	−	8.38688i	1.00242	−	1.00242i
$71$	−2.86374	−	9.19007i	−0.339864	−	1.09066i	−0.953581	−	0.301135i	$-0.902634\pi$
$71$	−2.86374	−	9.19007i	−0.339864	−	1.09066i	0.613718	−	0.789525i	$-0.289673\pi$
$72$	3.18856	+	3.66449i	0.375775	+	0.431865i
$73$	9.12208	−	1.67168i	1.06766	−	0.195656i	0.382431	−	0.923984i	$-0.375087\pi$
$73$	9.12208	−	1.67168i	1.06766	−	0.195656i	0.685228	+	0.728328i	$0.259702\pi$
$74$	−6.63297	−	7.48707i	−0.771067	−	0.870355i
$75$	2.14456	+	3.84236i	0.247632	+	0.443677i
$76$	7.46102	−	3.35793i	0.855837	−	0.385181i
$77$	3.78605	−	9.98299i	0.431460	−	1.13767i
$78$	12.3318	+	5.73760i	1.39631	+	0.649655i
$79$	4.76583	+	12.5665i	0.536198	+	1.41384i	0.880080	+	0.474825i	$0.157489\pi$
$79$	4.76583	+	12.5665i	0.536198	+	1.41384i	−0.343882	+	0.939013i	$0.611742\pi$
$80$	2.17398	+	2.17398i	0.243058	+	0.243058i
$81$	−7.31445	−	5.24393i	−0.812717	−	0.582659i
$82$	3.12202	−	0.379082i	0.344769	−	0.0418626i
$83$	8.11695	+	2.52934i	0.890951	+	0.277632i	0.708607	−	0.705603i	$-0.249324\pi$
$83$	8.11695	+	2.52934i	0.890951	+	0.277632i	0.182344	+	0.983235i	$0.441632\pi$
$84$	−4.50184	+	15.8748i	−0.491191	+	1.73208i
$85$	8.78637	−	1.61016i	0.953016	−	0.174647i
$86$	1.70450	−	5.46994i	0.183801	−	0.589839i
$87$	9.13965	+	3.19959i	0.979873	+	0.343033i
$88$	−4.65484	−	1.76535i	−0.496208	−	0.188187i
$89$	−4.02598	+	4.02598i	−0.426753	+	0.426753i	−0.887521	−	0.460768i	$-0.847574\pi$
$89$	−4.02598	+	4.02598i	−0.426753	+	0.426753i	0.460768	+	0.887521i	$0.347574\pi$
$90$	8.72139	+	5.37909i	0.919315	+	0.567006i
$91$	1.78344	+	12.3928i	0.186955	+	1.29912i
$92$	3.42151	+	1.29761i	0.356717	+	0.135285i
$93$	−0.416476	+	12.0082i	−0.0431865	+	1.24520i
$94$	5.86782	−	8.50100i	0.605219	−	0.876811i
$95$	3.50086	−	3.10149i	0.359180	−	0.318206i
$96$	−12.5109	−	3.54791i	−1.27689	−	0.362107i
$97$	−18.8657	+	1.14117i	−1.91552	+	0.115868i	−0.974768	−	0.223221i	$-0.928343\pi$
$97$	−18.8657	+	1.14117i	−1.91552	+	0.115868i	−0.940754	+	0.339088i	$0.889881\pi$
$98$	−10.5184	+	3.27768i	−1.06252	+	0.331095i
$99$	9.14637	+	1.19347i	0.919244	+	0.119948i
$100$	6.17144	+	3.23902i	0.617144	+	0.323902i
$101$	0.135461	−	1.11562i	0.0134789	−	0.111009i	−0.984417	−	0.175852i	$-0.943732\pi$
$101$	0.135461	−	1.11562i	0.0134789	−	0.111009i	0.997895	+	0.0648438i	$0.0206549\pi$
$102$	−16.5672	+	13.6823i	−1.64040	+	1.35474i
$103$	7.70221	−	14.6753i	0.758921	−	1.44600i	−0.131715	−	0.991288i	$-0.542048\pi$
$103$	7.70221	−	14.6753i	0.758921	−	1.44600i	0.890636	−	0.454716i	$-0.150259\pi$
$104$	5.77847	−	0.831577i	0.566626	−	0.0815428i
$105$	0.242830	+	9.42943i	0.0236978	+	0.920218i
$106$	−19.8661	+	1.20168i	−1.92957	+	0.116717i
$107$	6.56229	+	7.40730i	0.634401	+	0.716091i	0.974522	−	0.224291i	$-0.0720066\pi$
$107$	6.56229	+	7.40730i	0.634401	+	0.716091i	−0.340121	+	0.940382i	$0.610468\pi$
$108$	−14.2418	−	0.621202i	−1.37042	−	0.0597752i
$109$	−7.59042	−	9.68846i	−0.727030	−	0.927986i	0.272384	−	0.962188i	$-0.412188\pi$
$109$	−7.59042	−	9.68846i	−0.727030	−	0.927986i	−0.999415	+	0.0342027i	$0.989111\pi$
$110$	−10.4826	−	0.634079i	−0.999474	−	0.0604571i
$111$	7.95000	+	0.275726i	0.754580	+	0.0261707i
$112$	−2.02529	−	6.49940i	−0.191372	−	0.614135i
$113$	0.638677	+	1.21690i	0.0600816	+	0.114476i	0.913645	−	0.406513i	$-0.133255\pi$
$113$	0.638677	+	1.21690i	0.0600816	+	0.114476i	−0.853563	+	0.520989i	$0.825563\pi$
$114$	−3.71727	+	10.6184i	−0.348155	+	0.994504i
$115$	2.08800	+	0.126301i	0.194707	+	0.0117776i
$116$	14.8923	−	3.67062i	1.38271	−	0.340808i
$117$	−10.0623	+	3.96856i	−0.930263	+	0.366893i
$118$	−26.5085	−	6.53376i	−2.44031	−	0.601482i
$119$	−18.8836	−	5.88438i	−1.73106	−	0.539420i
$120$	4.39673	−	0.113226i	0.401365	−	0.0103361i
$121$	1.44612	−	0.548441i	0.131465	−	0.0498582i
$122$	0.276163	−	0.613608i	0.0250026	−	0.0555535i
$123$	−1.49127	+	2.00786i	−0.134463	+	0.181043i
$124$	9.84576	+	16.2869i	0.884175	+	1.46260i
$125$	11.6319	+	2.13162i	1.04039	+	0.190658i
$126$	−11.5642	−	19.5208i	−1.03022	−	1.73905i
$127$	−20.2678	+	7.68657i	−1.79848	+	0.682073i	−0.802087	+	0.597208i	$0.796277\pi$
$127$	−20.2678	+	7.68657i	−1.79848	+	0.682073i	−0.996392	+	0.0848656i	$0.972954\pi$
$128$	−11.5124	+	3.58742i	−1.01757	+	0.317086i
$129$	2.22062	+	3.97863i	0.195514	+	0.350299i
$130$	11.1158	−	5.30120i	0.974916	−	0.464946i
$131$	7.29177	−	5.03315i	0.637085	−	0.439748i	−0.205245	−	0.978711i	$-0.565799\pi$
$131$	7.29177	−	5.03315i	0.637085	−	0.439748i	0.842330	+	0.538963i	$0.181184\pi$
$132$	13.1641	−	6.33711i	1.14578	−	0.551575i
$133$	−10.0553	+	2.47842i	−0.871908	+	0.214906i
$134$	−2.76578	+	4.00693i	−0.238927	+	0.346146i
$135$	−7.87825	+	2.08301i	−0.678052	+	0.179277i
$136$	−2.74375	+	8.80501i	−0.235275	+	0.755024i
$137$	−1.78890	−	2.28336i	−0.152836	−	0.195081i	0.704699	−	0.709507i	$-0.251082\pi$
$137$	−1.78890	−	2.28336i	−0.152836	−	0.195081i	−0.857535	+	0.514426i	$0.828005\pi$
$138$	−4.53368	+	2.18249i	−0.385932	+	0.185786i
$139$	8.18581	+	7.25200i	0.694311	+	0.615106i	0.934644	−	0.355584i	$-0.115718\pi$
$139$	8.18581	+	7.25200i	0.694311	+	0.615106i	−0.240333	+	0.970691i	$0.577257\pi$
$140$	8.48715	+	12.2958i	0.717295	+	1.03918i
$141$	1.68827	+	8.03936i	0.142178	+	0.677036i
$142$	20.8119	−	2.52702i	1.74649	−	0.212063i
$143$	7.16607	−	8.45821i	0.599257	−	0.707311i
$144$	5.06001	−	2.99757i	0.421668	−	0.249797i
$145$	7.50337	−	4.53594i	0.623121	−	0.376690i
$146$			20.1982i			1.67162i
$147$	3.87069	−	7.86035i	0.319249	−	0.648311i
$148$	10.7827	−	6.51834i	0.886328	−	0.535804i
$149$	−1.87398	+	4.16382i	−0.153523	+	0.341113i	−0.972569	−	0.232614i	$-0.925272\pi$
$149$	−1.87398	+	4.16382i	−0.153523	+	0.341113i	0.819047	+	0.573727i	$0.194503\pi$
$150$	−9.07329	+	3.08577i	−0.740831	+	0.251952i
$151$	3.53109	−	1.58921i	0.287356	−	0.129328i	−0.261609	−	0.965174i	$-0.584253\pi$
$151$	3.53109	−	1.58921i	0.287356	−	0.129328i	0.548964	+	0.835846i	$0.315022\pi$
$152$	1.15563	+	4.68858i	0.0937340	+	0.380294i
$153$	1.18386	−	17.0466i	0.0957095	−	1.37814i
$154$	19.8999	+	12.0299i	1.60358	+	0.969398i
$155$	8.14326	+	7.21430i	0.654083	+	0.579467i
$156$	−9.90900	+	13.9765i	−0.793355	+	1.11902i
$157$	17.3514	−	15.3720i	1.38479	−	1.22682i	0.440482	−	0.897762i	$-0.354808\pi$
$157$	17.3514	−	15.3720i	1.38479	−	1.22682i	0.944310	−	0.329057i	$-0.106731\pi$
$158$	−28.7917	+	5.27628i	−2.29055	+	0.419759i
$159$	10.1873	−	12.1135i	0.807905	−	0.960667i
$160$	−9.69031	+	6.68874i	−0.766086	+	0.528791i
$161$	−3.96382	−	2.39621i	−0.312393	−	0.188848i
$162$	14.1055	−	13.6108i	1.10823	−	1.06937i
$163$	−14.1663	+	18.0820i	−1.10959	+	1.41629i	−0.211007	+	0.977484i	$0.567674\pi$
$163$	−14.1663	+	18.0820i	−1.10959	+	1.41629i	−0.898583	+	0.438803i	$0.855403\pi$
$164$	−0.239191	+	3.95429i	−0.0186777	+	0.308779i
$165$	6.10669	−	5.69730i	0.475405	−	0.443534i
$166$	−8.60513	+	16.3957i	−0.667888	+	1.27255i
$167$	2.10381	+	0.385538i	0.162798	+	0.0298338i	0.261036	−	0.965329i	$-0.415936\pi$
$167$	2.10381	+	0.385538i	0.162798	+	0.0298338i	−0.0982377	+	0.995163i	$0.531321\pi$
$168$	−8.73684	−	4.30231i	−0.674062	−	0.331930i
$169$	−2.55040	+	12.7474i	−0.196185	+	0.980567i
$170$			19.4549i			1.49212i
$171$	−4.08703	−	7.95894i	−0.312543	−	0.608636i
$172$	6.39031	+	3.35389i	0.487256	+	0.255732i
$173$	6.00060	−	15.8223i	0.456217	−	1.20295i	−0.487772	−	0.872971i	$-0.662190\pi$
$173$	6.00060	−	15.8223i	0.456217	−	1.20295i	0.943990	−	0.329975i	$-0.107040\pi$
$174$	−10.4425	+	18.3235i	−0.791643	+	1.38910i
$175$	−6.94461	−	5.44076i	−0.524963	−	0.411282i
$176$	−3.11829	+	5.15828i	−0.235050	+	0.388820i
$177$	18.2857	−	11.7072i	1.37443	−	0.879969i
$178$	−7.04419	−	10.2053i	−0.527985	−	0.764918i
$179$	14.6614	+	3.61371i	1.09584	+	0.270101i	0.745490	−	0.666517i	$-0.232215\pi$
$179$	14.6614	+	3.61371i	1.09584	+	0.270101i	0.350353	+	0.936618i	$0.386062\pi$
$180$	−8.64502	+	9.58455i	−0.644362	+	0.714390i
$181$	−1.03867	−	1.17242i	−0.0772039	−	0.0871452i	0.708639	−	0.705571i	$-0.249309\pi$
$181$	−1.03867	−	1.17242i	−0.0772039	−	0.0871452i	−0.785843	+	0.618426i	$0.787771\pi$
$182$	−27.2488	−	1.04462i	−2.01982	−	0.0774323i
$183$	0.202577	+	0.495303i	0.0149749	+	0.0366138i
$184$	−1.11730	+	1.84824i	−0.0823684	+	0.136254i
$185$	4.77620	−	5.39121i	0.351153	−	0.396370i
$186$	−25.5614	−	5.60646i	−1.87425	−	0.411085i
$187$	7.18746	+	15.9699i	0.525599	+	1.16783i
$188$	9.20052	+	9.20052i	0.671017	+	0.671017i
$189$	17.5897	+	4.02282i	1.27946	+	0.292617i
$190$	5.26984	+	8.71738i	0.382314	+	0.632425i
$191$			21.1862i			1.53298i	0.642256	+	0.766490i	$0.277999\pi$
$191$			21.1862i			1.53298i	−0.642256	+	0.766490i	$0.722001\pi$
$192$	9.51206	−	19.3165i	0.686474	−	1.39405i
$193$	−0.237398	−	0.392704i	−0.0170883	−	0.0282674i	0.847120	−	0.531401i	$-0.178334\pi$
$193$	−0.237398	−	0.392704i	−0.0170883	−	0.0282674i	−0.864209	+	0.503134i	$0.832180\pi$
$194$	4.96172	−	40.8634i	0.356231	−	2.93382i
$195$	−3.03101	+	9.31302i	−0.217055	+	0.666919i
$196$	−1.67279	−	13.7767i	−0.119485	−	0.984050i
$197$	10.6365	−	8.33318i	0.757821	−	0.593714i	−0.161662	−	0.986846i	$-0.551685\pi$
$197$	10.6365	−	8.33318i	0.757821	−	0.593714i	0.919482	+	0.393132i	$0.128608\pi$
$198$	−6.14746	+	19.1254i	−0.436881	+	1.35919i
$199$	−1.22980	+	1.38816i	−0.0871784	+	0.0984041i	−0.790481	−	0.612486i	$-0.790169\pi$
$199$	−1.22980	+	1.38816i	−0.0871784	+	0.0984041i	0.703303	+	0.710891i	$0.251708\pi$
$200$	−2.53690	+	3.23812i	−0.179386	+	0.228969i
$201$	−0.795761	−	3.78934i	−0.0561287	−	0.267279i
$202$	2.33678	+	0.728171i	0.164416	+	0.0512339i
$203$	−19.3788	+	1.17220i	−1.36013	+	0.0822725i
$204$	−13.1908	−	23.6336i	−0.923540	−	1.65468i
$205$	0.541949	+	2.19878i	0.0378514	+	0.153569i
$206$	28.4147	+	22.2615i	1.97975	+	1.55103i
$207$	1.22450	−	3.80955i	0.0851086	−	0.264782i
$208$	0.270777	−	7.06320i	0.0187750	−	0.489745i
$209$	7.54641	+	5.20891i	0.521996	+	0.360308i
$210$	−20.2957	−	3.18165i	−1.40054	−	0.219555i
$211$	6.81702	+	17.9750i	0.469303	+	1.23745i	0.935675	+	0.352862i	$0.114792\pi$
$211$	6.81702	+	17.9750i	0.469303	+	1.23745i	−0.466372	+	0.884589i	$0.654439\pi$
$212$	3.02186	−	24.8873i	0.207542	−	1.70926i
$213$	−9.94102	+	13.3847i	−0.681148	+	0.917107i
$214$	−18.4447	+	11.1502i	−1.26085	+	0.762212i
$215$	4.05796	+	0.743649i	0.276750	+	0.0507164i
$216$	1.87575	−	8.20169i	0.127629	−	0.558055i
$217$	−8.54225	−	22.5241i	−0.579885	−	1.52903i
$218$	23.7352	−	12.4572i	1.60755	−	0.843706i
$219$	−11.6469	−	11.0621i	−0.787025	−	0.747508i
$220$	3.16578	−	12.8441i	0.213437	−	0.865948i
$221$	−16.4421	−	12.3051i	−1.10602	−	0.827733i
$222$	−3.71173	+	16.9228i	−0.249115	+	1.13578i
$223$	0.545120	−	9.01190i	0.0365039	−	0.603482i	−0.933224	−	0.359294i	$-0.883017\pi$
$223$	0.545120	−	9.01190i	0.0365039	−	0.603482i	0.969728	−	0.244187i	$-0.0785211\pi$
$224$	25.8818	−	3.14263i	1.72930	−	0.209975i
$225$	3.18988	−	6.92194i	0.212659	−	0.461463i
$226$	−2.85765	+	0.890481i	−0.190088	+	0.0592339i
$227$	26.1372	−	11.7634i	1.73478	−	0.780763i	0.740739	−	0.671793i	$-0.234476\pi$
$227$	26.1372	−	11.7634i	1.73478	−	0.780763i	0.994045	−	0.108969i	$-0.0347550\pi$
$228$	−12.3123	−	7.01674i	−0.815402	−	0.464695i
$229$	−0.380127	+	0.297810i	−0.0251195	+	0.0196799i	−0.629200	−	0.777243i	$-0.716617\pi$
$229$	−0.380127	+	0.297810i	−0.0251195	+	0.0196799i	0.604081	+	0.796923i	$0.293540\pi$
$230$	−1.09029	+	4.42348i	−0.0718915	+	0.291675i
$231$	−17.8355	+	4.88638i	−1.17349	+	0.321500i
$232$	0.546572	+	9.03591i	0.0358842	+	0.593237i
$233$	−0.0158242	+	0.00830517i	−0.00103668	+	0.000544089i	−0.465241	−	0.885184i	$-0.654032\pi$
$233$	−0.0158242	+	0.00830517i	−0.00103668	+	0.000544089i	0.464205	+	0.885728i	$0.346340\pi$
$234$	−4.55139	−	23.1142i	−0.297534	−	1.51102i
$235$	6.58597	+	3.45659i	0.429621	+	0.225483i
$236$	14.1144	−	31.3609i	0.918768	−	2.04142i
$237$	12.7261	−	19.4919i	0.826650	−	1.26613i
$238$	20.0194	−	38.1437i	1.29766	−	2.47249i
$239$	−7.22312	−	7.22312i	−0.467225	−	0.467225i	0.433790	−	0.901014i	$-0.357176\pi$
$239$	−7.22312	−	7.22312i	−0.467225	−	0.467225i	−0.901014	+	0.433790i	$0.857176\pi$
$240$	0.824720	−	5.26088i	0.0532354	−	0.339588i
$241$	0.169972	+	2.80998i	0.0109489	+	0.181007i	0.999539	+	0.0303735i	$0.00966967\pi$
$241$	0.169972	+	2.80998i	0.0109489	+	0.181007i	−0.988590	+	0.150633i	$0.951869\pi$
$242$	0.607182	+	3.31329i	0.0390311	+	0.212986i
$243$	0.123189	+	15.5880i	0.00790256	+	0.999969i
$244$	0.697564	+	0.481494i	0.0446570	+	0.0308245i
$245$	−3.25589	−	7.23429i	−0.208011	−	0.462182i
$246$	−3.71594	−	3.98295i	−0.236919	−	0.253944i
$247$	−10.7006	−	1.05994i	−0.680861	−	0.0674426i
$248$	−10.5025	+	3.98306i	−0.666907	+	0.252924i
$249$	−4.74143	−	13.9415i	−0.300476	−	0.883509i
$250$	−9.13301	+	24.0818i	−0.577622	+	1.52307i
$251$	−1.13103	−	9.31487i	−0.0713900	−	0.587949i	−0.983877	−	0.178845i	$-0.942764\pi$
$251$	−1.13103	−	9.31487i	−0.0713900	−	0.587949i	0.912487	−	0.409105i	$-0.134159\pi$
$252$	26.8123	−	9.89584i	1.68901	−	0.623379i
$253$	0.739237	+	4.03389i	0.0464754	+	0.253608i
$254$	−8.50986	−	46.4368i	−0.533956	−	2.91370i
$255$	−11.2183	−	10.6550i	−0.702516	−	0.667242i
$256$	−0.168774	−	1.38998i	−0.0105484	−	0.0868735i
$257$	−6.00922	+	15.8450i	−0.374845	+	0.988385i	0.606321	+	0.795220i	$0.292645\pi$
$257$	−6.00922	+	15.8450i	−0.374845	+	0.988385i	−0.981166	+	0.193165i	$0.938125\pi$
$258$	−9.39507	+	3.19521i	−0.584911	+	0.198925i
$259$	−14.9119	+	5.65536i	−0.926583	+	0.351407i
$260$	4.04434	+	14.9762i	0.250819	+	0.928787i
$261$	−4.84676	−	16.0568i	−0.300007	−	0.993890i
$262$	7.91971	+	17.5969i	0.489281	+	1.08714i
$263$	−9.48253	−	6.54531i	−0.584718	−	0.403601i	0.238654	−	0.971105i	$-0.423294\pi$
$263$	−9.48253	−	6.54531i	−0.584718	−	0.403601i	−0.823371	+	0.567503i	$0.807909\pi$
$264$	2.27841	+	8.31630i	0.140227	+	0.511833i
$265$	−2.58326	−	14.0964i	−0.158688	−	0.865934i
$266$	−1.36186	−	22.5142i	−0.0835010	−	1.38044i
$267$	9.74261	+	1.52730i	0.596238	+	0.0934691i
$268$	−4.33665	−	4.33665i	−0.264903	−	0.264903i
$269$	−10.8721	+	20.7150i	−0.662882	+	1.26302i	0.289229	+	0.957260i	$0.406601\pi$
$269$	−10.8721	+	20.7150i	−0.662882	+	1.26302i	−0.952110	+	0.305755i	$0.901091\pi$
$270$	−1.36949	−	17.6951i	−0.0833446	−	1.07689i
$271$	3.62810	−	8.06132i	0.220392	−	0.489690i	−0.768219	−	0.640187i	$-0.778857\pi$
$271$	3.62810	−	8.06132i	0.220392	−	0.489690i	0.988610	+	0.150497i	$0.0480875\pi$
$272$	9.88728	+	5.18925i	0.599504	+	0.314644i
$273$	15.5259	−	15.1404i	0.939670	−	0.916337i
$274$	5.59388	−	2.93589i	0.337939	−	0.177364i
$275$	0.471628	+	7.79694i	0.0284403	+	0.470173i
$276$	−1.67473	−	6.11284i	−0.100807	−	0.367949i
$277$	−2.44937	+	9.93749i	−0.147168	+	0.597086i	0.850321	+	0.526265i	$0.176408\pi$
$277$	−2.44937	+	9.93749i	−0.147168	+	0.597086i	−0.997489	+	0.0708208i	$0.977438\pi$
$278$	−18.7494	+	14.6892i	−1.12451	+	0.880999i
$279$	17.2322	−	11.6689i	1.03167	−	0.698600i
$280$	−8.04097	+	3.61895i	−0.480540	+	0.216273i
$281$	−18.5859	+	5.79161i	−1.10874	+	0.345499i	−0.796582	−	0.604530i	$-0.793361\pi$
$281$	−18.5859	+	5.79161i	−1.10874	+	0.345499i	−0.312162	+	0.950029i	$0.601053\pi$
$282$	−17.8853	+	0.460587i	−1.06505	+	0.0274276i
$283$	−6.20775	+	0.753758i	−0.369013	+	0.0448062i	−0.302943	−	0.953009i	$-0.597969\pi$
$283$	−6.20775	+	0.753758i	−0.369013	+	0.0448062i	−0.0660699	+	0.997815i	$0.521046\pi$
$284$	−1.59448	+	26.3600i	−0.0946152	+	1.56418i
$285$	−7.91287	−	1.73556i	−0.468718	−	0.102806i
$286$	15.3065	+	18.6722i	0.905090	+	1.10411i
$287$	1.20001	−	4.86864i	0.0708345	−	0.287387i
$288$	7.79893	+	21.1308i	0.459556	+	1.24514i
$289$	13.6742	−	7.17677i	0.804364	−	0.422163i
$290$	6.77150	+	17.8550i	0.397636	+	1.04848i
$291$	20.8457	+	25.2410i	1.22199	+	1.47966i
$292$	−25.0259	−	4.58616i	−1.46453	−	0.268385i
$293$	6.69350	−	4.04636i	0.391039	−	0.236391i	−0.308136	−	0.951342i	$-0.599705\pi$
$293$	6.69350	−	4.04636i	0.391039	−	0.236391i	0.699174	+	0.714951i	$0.253551\pi$
$294$	15.3194	+	11.3779i	0.893446	+	0.663574i
$295$	2.36966	−	19.5159i	0.137967	−	1.13626i
$296$	2.63697	+	6.95311i	0.153271	+	0.404141i
$297$	−7.66149	−	14.0194i	−0.444565	−	0.813486i
$298$	−8.18432	−	5.64923i	−0.474105	−	0.327251i
$299$	−3.04886	−	3.71928i	−0.176320	−	0.215091i
$300$	−1.76315	−	11.9426i	−0.101796	−	0.689505i
$301$	−7.19090	−	5.63371i	−0.414477	−	0.324722i
$302$	2.01827	+	8.18844i	0.116138	+	0.471192i
$303$	−1.69969	+	0.948658i	−0.0976445	+	0.0544990i
$304$	5.83594	−	0.353010i	0.334714	−	0.0202465i
$305$	0.462588	+	0.144148i	0.0264877	+	0.00825391i
$306$	36.0536	+	9.22839i	2.06105	+	0.527552i
$307$	−16.6658	+	21.2723i	−0.951169	+	1.21408i	0.0255763	+	0.999673i	$0.491858\pi$
$307$	−16.6658	+	21.2723i	−0.951169	+	1.21408i	−0.976745	+	0.214404i	$0.931219\pi$
$308$	−19.4236	+	21.9248i	−1.10676	+	1.24928i
$309$	−28.3988	+	4.19268i	−1.61555	+	0.238513i
$310$	−18.6519	+	14.6128i	−1.05936	+	0.829953i
$311$	3.31346	+	27.2888i	0.187889	+	1.54740i	0.715922	+	0.698180i	$0.246007\pi$
$311$	3.31346	+	27.2888i	0.187889	+	1.54740i	−0.528033	+	0.849224i	$0.677070\pi$
$312$	−7.05962	−	7.23938i	−0.399672	−	0.409849i
$313$	3.78222	−	31.1494i	0.213784	−	1.76067i	−0.351891	−	0.936041i	$-0.614461\pi$
$313$	3.78222	−	31.1494i	0.213784	−	1.76067i	0.565675	−	0.824628i	$-0.308616\pi$
$314$	26.1190	+	43.2062i	1.47398	+	2.43827i
$315$	12.9501	−	9.96061i	0.729657	−	0.561217i
$316$		−	36.8714i		−	2.07418i
$317$	−5.38985	−	8.91590i	−0.302724	−	0.500767i	0.666972	−	0.745083i	$-0.267590\pi$
$317$	−5.38985	−	8.91590i	−0.302724	−	0.500767i	−0.969696	+	0.244317i	$0.921436\pi$
$318$	21.9511	+	26.5795i	1.23096	+	1.49051i
$319$	12.1549	+	12.1549i	0.680543	+	0.680543i
$320$	−8.00120	−	17.7779i	−0.447281	−	0.993817i
$321$	3.67218	−	16.7425i	0.204961	−	0.934474i
$322$	6.68946	−	7.55084i	0.372789	−	0.420792i
$323$	8.78802	−	14.5372i	0.488978	−	0.808869i
$324$	13.6613	+	20.5673i	0.758959	+	1.14263i
$325$	−4.91087	−	7.73234i	−0.272406	−	0.428913i
$326$	−33.1749	−	37.4467i	−1.83739	−	2.07398i
$327$	−5.81602	+	20.5089i	−0.321626	+	1.13415i
$328$	−2.27014	−	0.559539i	−0.125347	−	0.0308954i
$329$	−9.35573	−	13.5541i	−0.515798	−	0.747263i
$330$	9.80775	+	15.3189i	0.539899	+	0.843275i
$331$	−2.01507	+	3.33333i	−0.110758	+	0.183217i	−0.906243	−	0.422757i	$-0.861062\pi$
$331$	−2.01507	+	3.33333i	−0.110758	+	0.183217i	0.795485	+	0.605974i	$0.207216\pi$
$332$	−18.3606	−	14.3846i	−1.00767	−	0.789460i
$333$	−7.72536	−	11.4085i	−0.423347	−	0.625183i
$334$	−1.65185	+	4.35558i	−0.0903854	+	0.238327i
$335$	−3.10429	−	1.62925i	−0.169605	−	0.0890157i
$336$	−7.03048	+	9.46595i	−0.383544	+	0.516410i
$337$		−	21.3522i		−	1.16313i	−0.813501	−	0.581563i	$-0.802441\pi$
$337$		−	21.3522i		−	1.16313i	0.813501	−	0.581563i	$-0.197559\pi$
$338$	−26.3070	−	10.4681i	−1.43091	−	0.569388i
$339$	1.05159	−	2.13551i	0.0571147	−	0.115985i
$340$	−24.1049	−	4.41738i	−1.30727	−	0.239566i
$341$	−9.91214	+	18.8860i	−0.536772	+	1.02273i
$342$	18.6547	−	5.63094i	1.00873	−	0.304487i
$343$	0.407054	−	6.72940i	0.0219788	−	0.363354i
$344$	−2.62687	+	3.35296i	−0.141632	+	0.180779i
$345$	−1.95358	−	3.05133i	−0.105177	−	0.164278i
$346$	31.5398	+	19.0665i	1.69559	+	1.02502i
$347$	2.06849	−	1.42778i	0.111042	−	0.0766471i	−0.511249	−	0.859432i	$-0.670817\pi$
$347$	2.06849	−	1.42778i	0.111042	−	0.0766471i	0.622292	+	0.782785i	$0.286202\pi$
$348$	−20.3320	−	17.0989i	−1.08991	−	0.916595i
$349$	−7.51667	+	1.37748i	−0.402358	+	0.0737349i	−0.377624	−	0.925959i	$-0.623259\pi$
$349$	−7.51667	+	1.37748i	−0.402358	+	0.0737349i	−0.0247347	+	0.999694i	$0.507874\pi$
$350$	14.3819	−	12.7413i	0.768746	−	0.681049i
$351$	15.8211	+	10.0347i	0.844465	+	0.535610i
$352$	−17.2789	−	15.3078i	−0.920970	−	0.815908i
$353$	6.15756	+	3.72237i	0.327734	+	0.198122i	0.671632	−	0.740885i	$-0.265594\pi$
$353$	6.15756	+	3.72237i	0.327734	+	0.198122i	−0.343898	+	0.939007i	$0.611747\pi$
$354$	17.9013	+	43.7689i	0.951445	+	2.32629i
$355$	3.61272	+	14.6574i	0.191743	+	0.777933i
$356$	14.2439	−	6.41067i	0.754926	−	0.339765i
$357$	11.0307	+	32.4342i	0.583805	+	1.71660i
$358$	−13.4974	+	29.9899i	−0.713358	+	1.58502i
$359$	−8.18601	+	4.94862i	−0.432041	+	0.261178i	−0.716605	−	0.697479i	$-0.754305\pi$
$359$	−8.18601	+	4.94862i	−0.432041	+	0.261178i	0.284564	+	0.958657i	$0.408151\pi$
$360$	−4.64441	−	6.03835i	−0.244782	−	0.318249i
$361$			10.1057i			0.531880i
$362$	2.91940	−	1.76484i	0.153441	−	0.0927580i
$363$	−2.24308	−	1.46449i	−0.117731	−	0.0768658i
$364$	7.48135	−	33.5244i	0.392129	−	1.75716i
$365$	−14.4381	+	1.75310i	−0.755724	+	0.0917615i
$366$	−1.14060	+	0.239526i	−0.0596201	+	0.0125202i
$367$	17.6985	+	25.6408i	0.923856	+	1.33844i	0.940937	+	0.338583i	$0.109947\pi$
$367$	17.6985	+	25.6408i	0.923856	+	1.33844i	−0.0170805	+	0.999854i	$0.505437\pi$
$368$	1.95726	+	1.73399i	0.102029	+	0.0903902i
$369$	4.33182	+	0.0386495i	0.225506	+	0.00201201i
$370$	9.67436	+	12.3484i	0.502946	+	0.641963i
$371$	−9.44059	+	30.2959i	−0.490131	+	1.57289i
$372$	12.7504	−	30.3979i	0.661076	−	1.57606i
$373$	−7.31885	+	10.6032i	−0.378956	+	0.549012i	−0.965332	−	0.261027i	$-0.915939\pi$
$373$	−7.31885	+	10.6032i	−0.378956	+	0.549012i	0.586376	+	0.810039i	$0.300554\pi$
$374$	−37.0335	+	9.12793i	−1.91496	+	0.471994i
$375$	−8.88434	−	18.4554i	−0.458786	−	0.953033i
$376$	−6.31998	+	4.36237i	−0.325928	+	0.224972i
$377$	−19.3729	−	5.57032i	−0.997757	−	0.286886i
$378$	−15.5234	+	36.1026i	−0.798440	+	1.85692i
$379$	29.2795	−	9.12386i	1.50399	−	0.468661i	0.568697	−	0.822547i	$-0.307448\pi$
$379$	29.2795	−	9.12386i	1.50399	−	0.468661i	0.935289	+	0.353886i	$0.115140\pi$
$380$	−11.9975	+	4.55005i	−0.615459	+	0.233413i
$381$	31.4375	+	20.5253i	1.61059	+	1.05154i
$382$	−45.3866	−	8.31740i	−2.32218	−	0.425555i
$383$	8.70162	+	14.3942i	0.444632	+	0.735511i	0.995050	−	0.0993780i	$-0.0316853\pi$
$383$	8.70162	+	14.3942i	0.444632	+	0.735511i	−0.550418	+	0.834890i	$0.685531\pi$
$384$	16.7671	+	12.4532i	0.855644	+	0.635498i
$385$	−6.87200	+	15.2690i	−0.350230	+	0.778178i
$386$	0.934476	−	0.354400i	0.0475636	−	0.0180385i
$387$	3.30301	−	7.16742i	0.167901	−	0.364341i
$388$	49.5037	+	15.4260i	2.51317	+	0.783136i
$389$	−30.2926	−	7.46647i	−1.53590	−	0.378565i	−0.621511	−	0.783406i	$-0.713481\pi$
$389$	−30.2926	−	7.46647i	−1.53590	−	0.378565i	−0.914387	+	0.404841i	$0.867327\pi$
$390$	−18.7611	−	10.1494i	−0.950004	−	0.513934i
$391$	7.37662	−	1.81817i	0.373052	−	0.0919490i
$392$	8.17574	+	0.494541i	0.412937	+	0.0249781i
$393$	−14.4843	−	5.07066i	−0.730638	−	0.255781i
$394$	13.6762	+	26.0578i	0.688996	+	1.31277i
$395$	−6.27056	−	20.1229i	−0.315506	−	1.01249i
$396$	−22.3008	−	11.9594i	−1.12066	−	0.600981i
$397$	11.6889	+	0.707048i	0.586649	+	0.0354857i	0.351037	−	0.936362i	$-0.385829\pi$
$397$	11.6889	+	0.707048i	0.586649	+	0.0354857i	0.235612	+	0.971847i	$0.424291\pi$
$398$	−2.49101	−	3.17954i	−0.124863	−	0.159376i
$399$	13.7282	+	11.5452i	0.687272	+	0.577985i
$400$	3.30268	+	3.72796i	0.165134	+	0.186398i
$401$	19.6992	−	1.19158i	0.983730	−	0.0595047i	0.439326	−	0.898328i	$-0.355217\pi$
$401$	19.6992	−	1.19158i	0.983730	−	0.0595047i	0.544404	+	0.838823i	$0.316756\pi$
$402$	8.43018	−	0.217097i	0.420459	−	0.0108278i
$403$	−0.552666	−	25.0060i	−0.0275302	−	1.24564i
$404$	−1.43280	+	2.72997i	−0.0712844	+	0.135821i
$405$	10.9536	+	8.90150i	0.544287	+	0.442319i
$406$	5.09667	−	41.9748i	0.252943	−	2.08318i
$407$	12.5034	+	6.56229i	0.619770	+	0.325280i
$408$	15.1233	−	5.14336i	0.748717	−	0.254634i
$409$	−12.4167	+	3.86919i	−0.613964	+	0.191319i	−0.588686	−	0.808362i	$-0.700355\pi$
$409$	−12.4167	+	3.86919i	−0.613964	+	0.191319i	−0.0252776	+	0.999680i	$0.508047\pi$
$410$	−4.92313	+	0.297794i	−0.243136	+	0.0147070i
$411$	−1.37071	+	4.83352i	−0.0676122	+	0.238420i
$412$	−34.0341	+	30.1516i	−1.67674	+	1.48546i
$413$	−24.7281	+	35.8249i	−1.21679	+	1.76283i
$414$	7.68037	+	4.11878i	0.377470	+	0.202427i
$415$	−12.4668	−	4.72805i	−0.611973	−	0.232091i
$416$	26.4207	+	5.89606i	1.29538	+	0.289078i
$417$	1.79836	−	18.8564i	0.0880660	−	0.923401i
$418$	−14.1215	+	14.1215i	−0.690705	+	0.690705i
$419$	20.8867	+	7.92126i	1.02038	+	0.386979i	0.807354	−	0.590068i	$-0.200899\pi$
$419$	20.8867	+	7.92126i	1.02038	+	0.386979i	0.213026	+	0.977047i	$0.431668\pi$
$420$	8.55040	−	24.4242i	0.417217	−	1.19178i
$421$	−6.08986	+	19.5431i	−0.296802	+	0.952470i	0.679060	+	0.734082i	$0.262387\pi$
$421$	−6.08986	+	19.5431i	−0.296802	+	0.952470i	−0.975862	+	0.218388i	$0.929920\pi$
$422$	−41.1836	+	7.54717i	−2.00479	+	0.367391i
$423$	9.52976	−	10.5654i	0.463353	−	0.513709i
$424$	14.1263	+	4.40193i	0.686034	+	0.213777i
$425$	14.3650	−	1.74423i	0.696807	−	0.0846077i
$426$	−24.7710	−	26.5510i	−1.20016	−	1.28640i
$427$	−0.758630	−	0.758630i	−0.0367127	−	0.0367127i
$428$	−9.62724	−	25.3850i	−0.465350	−	1.22703i
$429$	−19.1500	−	1.40017i	−0.924569	−	0.0676008i
$430$	−3.18619	+	8.40129i	−0.153652	+	0.405146i
$431$	−33.3207	+	14.9964i	−1.60500	+	0.722353i	−0.997412	−	0.0718980i	$-0.977094\pi$
$431$	−33.3207	+	14.9964i	−1.60500	+	0.722353i	−0.607590	+	0.794251i	$0.707864\pi$
$432$	−9.35821	−	4.02385i	−0.450247	−	0.193598i
$433$	−2.07968	−	2.34748i	−0.0999432	−	0.112813i	0.696411	−	0.717643i	$-0.254779\pi$
$433$	−2.07968	−	2.34748i	−0.0999432	−	0.112813i	−0.796354	+	0.604831i	$0.793241\pi$
$434$	51.6061	−	9.45718i	2.47717	−	0.453959i
$435$	−14.0043	−	5.87411i	−0.671456	−	0.281642i
$436$	10.0454	+	32.2367i	0.481085	+	1.54386i
$437$	2.81283	−	2.81283i	0.134556	−	0.134556i
$438$	28.2704	−	20.6080i	1.35081	−	0.984688i
$439$	−15.1326	−	1.83742i	−0.722237	−	0.0876955i	−0.248840	−	0.968545i	$-0.580049\pi$
$439$	−15.1326	−	1.83742i	−0.722237	−	0.0876955i	−0.473397	+	0.880849i	$0.656972\pi$
$440$	7.11957	+	3.20426i	0.339412	+	0.152757i
$441$	−14.9509	+	2.60221i	−0.711950	+	0.123915i
$442$	32.8159	−	30.3927i	1.56089	−	1.44563i
$443$	8.00627	+	15.2547i	0.380389	+	0.724772i	0.998099	−	0.0616350i	$-0.0196315\pi$
$443$	8.00627	+	15.2547i	0.380389	+	0.724772i	−0.617709	+	0.786407i	$0.711939\pi$
$444$	−20.1248	−	8.44133i	−0.955080	−	0.400608i
$445$	6.68353	−	5.92109i	0.316830	−	0.280687i
$446$	19.0919	+	4.70573i	0.904028	+	0.222823i
$447$	7.73988	−	1.62538i	0.366084	−	0.0768776i
$448$	−2.60642	+	43.0892i	−0.123142	+	2.03577i
$449$	−6.86443	−	15.2521i	−0.323952	−	0.719793i	0.675900	−	0.736994i	$-0.263755\pi$
$449$	−6.86443	−	15.2521i	−0.323952	−	0.719793i	−0.999852	+	0.0172010i	$0.994524\pi$
$450$	13.5764	+	9.55103i	0.639995	+	0.450240i
$451$	−3.93122	+	2.06326i	−0.185114	+	0.0971552i
$452$	−0.454466	−	3.74286i	−0.0213763	−	0.176049i
$453$	−5.82706	−	3.32082i	−0.273779	−	0.156026i
$454$	14.9393	+	60.6109i	0.701134	+	2.84461i
$455$	−1.61834	−	19.5686i	−0.0758689	−	0.917391i
$456$	5.38328	−	6.40117i	0.252095	−	0.299762i
$457$	−1.07301	+	3.44340i	−0.0501932	+	0.161076i	−0.976414	−	0.215905i	$-0.930730\pi$
$457$	−1.07301	+	3.44340i	−0.0501932	+	0.161076i	0.926221	+	0.376980i	$0.123038\pi$
$458$	−0.488758	−	0.931250i	−0.0228381	−	0.0435145i
$459$	−25.0671	+	15.7354i	−1.17003	+	0.734467i
$460$	−5.23319	−	2.35527i	−0.243999	−	0.109815i
$461$	4.70831	−	25.6924i	0.219288	−	1.19661i	−0.671084	−	0.741381i	$-0.734171\pi$
$461$	4.70831	−	25.6924i	0.219288	−	1.19661i	0.890372	−	0.455233i	$-0.150444\pi$
$462$	−3.46598	−	40.1268i	−0.161252	−	1.86687i
$463$	1.66258	−	9.07240i	0.0772666	−	0.421630i	−0.922130	−	0.386881i	$-0.873552\pi$
$463$	1.66258	−	9.07240i	0.0772666	−	0.421630i	0.999396	−	0.0347487i	$-0.0110631\pi$
$464$	10.8804	+	1.32111i	0.505108	+	0.0613312i
$465$	1.78901	−	18.7584i	0.0829634	−	0.869898i
$466$	−0.0115796	−	0.0371601i	−0.000536413	−	0.00172141i
$467$	−10.2135	+	14.7969i	−0.472627	+	0.684718i	−0.984707	−	0.174220i	$-0.944260\pi$
$467$	−10.2135	+	14.7969i	−0.472627	+	0.684718i	0.512080	+	0.858938i	$0.328875\pi$
$468$	29.6723	−	0.390975i	1.37160	−	0.0180728i
$469$	4.40981	+	6.38871i	0.203626	+	0.295003i
$470$	−9.99049	+	12.7519i	−0.460827	+	0.588202i
$471$	−39.2188	−	8.60199i	−1.80711	−	0.396359i
$472$	16.7043	+	11.5302i	0.768879	+	0.530719i
$473$	0.488354	+	8.07346i	0.0224546	+	0.371218i
$474$	36.7608	+	34.9150i	1.68848	+	1.60370i
$475$	5.96425	−	4.67269i	0.273658	−	0.214398i
$476$	42.7150	+	33.4651i	1.95784	+	1.53387i
$477$	−27.3487	−	1.89933i	−1.25221	−	0.0869642i
$478$	18.3096	−	12.6382i	0.837460	−	0.578057i
$479$	−10.8080	−	13.7954i	−0.493831	−	0.630328i	0.474423	−	0.880297i	$-0.342657\pi$
$479$	−10.8080	−	13.7954i	−0.493831	−	0.630328i	−0.968254	+	0.249969i	$0.919580\pi$
$480$	19.2488	+	6.73859i	0.878582	+	0.307573i
$481$	−16.5551	+	0.365890i	−0.754850	+	0.0166831i
$482$	−6.08646	−	0.739030i	−0.277231	−	0.0336619i
$483$	0.690381	+	7.99277i	0.0314134	+	0.363684i
$484$	−4.24307			−0.192867
$485$	29.6406			1.34591
$486$	−33.4420	−	5.85571i	−1.51696	−	0.265620i
$487$	10.5573	+	4.75146i	0.478398	+	0.215309i	0.635241	−	0.772314i	$-0.280901\pi$
$487$	10.5573	+	4.75146i	0.478398	+	0.215309i	−0.156843	+	0.987624i	$0.550132\pi$
$488$	−0.353732	+	0.353732i	−0.0160127	+	0.0160127i
$489$	39.7621	+	1.37905i	1.79810	+	0.0623627i
$490$	16.7760	−	4.13491i	0.757863	−	0.186796i
$491$	−8.01397	−	7.09976i	−0.361666	−	0.320408i	0.462647	−	0.886543i	$-0.346900\pi$
$491$	−8.01397	−	7.09976i	−0.361666	−	0.320408i	−0.824313	+	0.566135i	$0.808438\pi$
$492$	5.77866	−	3.69973i	0.260522	−	0.166797i
$493$	21.1168	−	23.8359i	0.951052	−	1.07352i
$494$	6.47157	−	22.5074i	0.291170	−	1.01266i
$495$	−14.2048	−	2.73433i	−0.638458	−	0.122899i
$496$	2.45141	+	13.3769i	0.110071	+	0.600640i
$497$	7.99947	−	32.4551i	0.358825	−	1.45581i
$498$	31.7279	−	4.68418i	1.42176	−	0.209903i
$499$	−0.206725	+	0.341964i	−0.00925426	+	0.0153084i	−0.860374	−	0.509663i	$-0.829770\pi$
$499$	−0.206725	+	0.341964i	−0.00925426	+	0.0153084i	0.851120	+	0.524971i	$0.175924\pi$
$500$	−27.7639	−	16.7839i	−1.24164	−	0.750598i
$501$	−1.60688	−	3.33796i	−0.0717900	−	0.149129i
$502$	20.3990	+	1.23391i	0.910451	+	0.0550722i
$503$	6.49229	+	2.46220i	0.289477	+	0.109784i	0.495069	−	0.868854i	$-0.335143\pi$
$503$	6.49229	+	2.46220i	0.289477	+	0.109784i	−0.205592	+	0.978638i	$0.565912\pi$
$504$	2.89238	+	16.6181i	0.128837	+	0.740229i
$505$	−0.317690	+	1.73358i	−0.0141370	+	0.0771433i
$506$	−8.93188			−0.397071
$507$	20.4440	−	9.43632i	0.907949	−	0.419081i
$508$	59.4680			2.63847
$509$	−6.58036	+	35.9078i	−0.291669	+	1.59159i	0.432284	+	0.901738i	$0.357708\pi$
$509$	−6.58036	+	35.9078i	−0.291669	+	1.59159i	−0.723953	+	0.689850i	$0.757677\pi$
$510$	27.2300	−	19.8496i	1.20576	−	0.878954i
$511$	30.1116	+	11.4198i	1.33206	+	0.505183i
$512$	−21.0289	−	1.27202i	−0.929356	−	0.0562157i
$513$	−6.96978	+	13.8408i	−0.307723	+	0.611087i
$514$	−31.5852	−	19.0939i	−1.39316	−	0.842196i
$515$	−13.4467	+	22.2436i	−0.592533	+	0.980169i
$516$	−1.82568	−	12.3661i	−0.0803712	−	0.544388i
$517$	−3.48977	+	14.1585i	−0.153480	+	0.622692i
$518$	−6.26108	−	34.1656i	−0.275096	−	1.50115i
$519$	−28.2680	+	7.74455i	−1.24083	+	0.339948i
$520$	−9.12441	+	0.754595i	−0.400132	+	0.0330912i
$521$	23.3928	−	26.4050i	1.02486	−	1.15683i	0.0373432	−	0.999302i	$-0.488111\pi$
$521$	23.3928	−	26.4050i	1.02486	−	1.15683i	0.987515	−	0.157524i	$-0.0503510\pi$
$522$	36.3007	−	4.07940i	1.58884	−	0.178551i
$523$	−26.3053	−	23.3044i	−1.15025	−	1.01903i	−0.999536	−	0.0304541i	$-0.990305\pi$
$523$	−26.3053	−	23.3044i	−1.15025	−	1.01903i	−0.150713	−	0.988578i	$-0.548157\pi$
$524$	−23.6010	+	5.81712i	−1.03101	+	0.254122i
$525$	−0.529642	+	15.2711i	−0.0231155	+	0.666487i
$526$	17.7445	−	17.7445i	0.773698	−	0.773698i
$527$	36.0320	+	16.2167i	1.56958	+	0.706409i
$528$	10.4013	−	0.898422i	0.452660	−	0.0390988i
$529$	−21.2209			−0.922647
$530$	31.2124			1.35578
$531$	−35.0426	−	13.6488i	−1.52072	−	0.592306i
$532$	28.2047	+	3.42467i	1.22283	+	0.148478i
$533$	2.86218	−	4.34910i	0.123975	−	0.188380i
$534$	−7.09669	+	20.2717i	−0.307104	+	0.877242i
$535$	−9.57128	−	12.2168i	−0.413802	−	0.528180i
$536$	2.97891	−	2.05619i	0.128669	−	0.0888140i
$537$	−9.90091	−	24.2078i	−0.427256	−	1.04464i
$538$	−40.1089	−	31.4233i	−1.72922	−	1.35475i
$539$	12.2433	−	9.59199i	0.527355	−	0.413156i
$540$	22.2354	+	2.32099i	0.956859	+	0.0998794i
$541$	1.05385	+	17.4223i	0.0453087	+	0.749043i	0.947905	+	0.318554i	$0.103197\pi$
$541$	1.05385	+	17.4223i	0.0453087	+	0.749043i	−0.902596	+	0.430489i	$0.858341\pi$
$542$	15.8452	+	10.9371i	0.680608	+	0.469790i
$543$	−0.581229	+	2.64998i	−0.0249429	+	0.113722i
$544$	−26.3739	+	33.6638i	−1.13077	+	1.44332i
$545$	10.9647	+	15.8851i	0.469677	+	0.680444i
$546$	26.3395	+	39.2045i	1.12723	+	1.67780i
$547$	−15.7291	+	22.7875i	−0.672526	+	0.974323i	0.327044	+	0.945009i	$0.393947\pi$
$547$	−15.7291	+	22.7875i	−0.672526	+	0.974323i	−0.999570	+	0.0293135i	$0.990668\pi$
$548$	2.36748	+	7.59751i	0.101134	+	0.324549i
$549$	0.486562	−	0.788888i	0.0207660	−	0.0336689i
$550$	−16.8883	−	2.05061i	−0.720120	−	0.0874384i
$551$	3.00549	−	16.4004i	0.128038	−	0.698682i
$552$	3.72685	−	0.321909i	0.158625	−	0.0137014i
$553$	−8.41258	+	45.9060i	−0.357739	+	1.95212i
$554$	−20.3272	−	9.14852i	−0.863619	−	0.388683i
$555$	−12.4189	−	1.18441i	−0.527152	−	0.0502753i
$556$	−13.9429	−	26.5660i	−0.591311	−	1.12665i
$557$	11.3129	−	36.3045i	0.479344	−	1.53827i	−0.325946	−	0.945388i	$-0.605683\pi$
$557$	11.3129	−	36.3045i	0.479344	−	1.53827i	0.805290	−	0.592881i	$-0.202010\pi$
$558$	18.2329	+	41.4971i	0.771859	+	1.75671i
$559$	−5.08503	−	8.00656i	−0.215074	−	0.338642i
$560$	2.55499	+	10.3660i	0.107968	+	0.438043i
$561$	15.0189	−	26.3538i	0.634100	−	1.11266i
$562$	−5.11062	−	42.0898i	−0.215579	−	1.77545i
$563$	−17.4739	+	9.17102i	−0.736438	+	0.386512i	−0.790853	−	0.612006i	$-0.790363\pi$
$563$	−17.4739	+	9.17102i	−0.736438	+	0.386512i	0.0544153	+	0.998518i	$0.482671\pi$
$564$	3.49031	−	22.2647i	0.146969	−	0.937511i
$565$	−0.884562	−	1.96542i	−0.0372138	−	0.0826857i
$566$	0.822321	−	13.5946i	0.0345647	−	0.571423i
$567$	−12.3160	−	28.7238i	−0.517225	−	1.20629i
$568$	−15.1331	−	3.72998i	−0.634971	−	0.156506i
$569$	−8.52225	+	7.55005i	−0.357271	+	0.316515i	−0.822597	−	0.568625i	$-0.807476\pi$
$569$	−8.52225	+	7.55005i	−0.357271	+	0.316515i	0.465326	+	0.885139i	$0.345937\pi$
$570$	6.82451	−	16.2702i	0.285847	−	0.681482i
$571$	9.82240	+	18.7150i	0.411055	+	0.783200i	0.999682	−	0.0252049i	$-0.00802381\pi$
$571$	9.82240	+	18.7150i	0.411055	+	0.783200i	−0.588627	+	0.808404i	$0.700331\pi$
$572$	−26.6106	+	14.7252i	−1.11264	+	0.615694i
$573$	29.6532	−	21.6160i	1.23878	−	0.903022i
$574$	9.95883	+	4.48211i	0.415674	+	0.187080i
$575$	3.36394	+	0.408457i	0.140286	+	0.0170338i
$576$	−36.7413	+	6.39482i	−1.53089	+	0.266451i
$577$	10.0983	−	10.0983i	0.420396	−	0.420396i	−0.464944	−	0.885340i	$-0.653926\pi$
$577$	10.0983	−	10.0983i	0.420396	−	0.420396i	0.885340	+	0.464944i	$0.153926\pi$
$578$	10.0063	+	32.1113i	0.416206	+	1.33565i
$579$	−0.307433	+	0.732944i	−0.0127765	+	0.0304601i
$580$	−23.6601	+	4.33587i	−0.982431	+	0.180037i
$581$	19.5776	+	22.0985i	0.812214	+	0.916800i
$582$	−62.2568	+	34.7478i	−2.58063	+	1.44034i
$583$	25.6213	−	11.5312i	1.06112	−	0.477573i
$584$	5.32481	−	14.0404i	0.220342	−	0.580994i
$585$	16.1275	−	5.25962i	0.666788	−	0.217458i
$586$	6.04063	+	15.9278i	0.249536	+	0.657973i
$587$	−16.8746	−	16.8746i	−0.696488	−	0.696488i	0.267164	−	0.963651i	$-0.413914\pi$
$587$	−16.8746	−	16.8746i	−0.696488	−	0.696488i	−0.963651	+	0.267164i	$0.913914\pi$
$588$	−17.5758	+	16.3975i	−0.724814	+	0.676222i
$589$	20.5379	−	2.49376i	0.846251	−	0.102753i
$590$	40.8780	+	12.7381i	1.68292	+	0.524419i
$591$	−22.5158	−	6.38514i	−0.926177	−	0.262650i
$592$	8.85612	−	1.62294i	0.363984	−	0.0667026i
$593$	12.6440	−	40.5760i	0.519226	−	1.66626i	−0.206638	−	0.978417i	$-0.566252\pi$
$593$	12.6440	−	40.5760i	0.519226	−	1.66626i	0.725864	−	0.687838i	$-0.241440\pi$
$594$	33.0411	−	10.9092i	1.35569	−	0.447608i
$595$	29.0034	+	10.9995i	1.18902	+	0.450937i
$596$	8.85778	−	8.85778i	0.362829	−	0.362829i
$597$	3.19769	+	0.304968i	0.130873	+	0.0124815i
$598$	9.16463	−	5.07135i	0.374770	−	0.207383i
$599$	−14.5059	−	5.50135i	−0.592694	−	0.224779i	0.0399762	−	0.999201i	$-0.487272\pi$
$599$	−14.5059	−	5.50135i	−0.592694	−	0.224779i	−0.632670	+	0.774422i	$0.718041\pi$
$600$	7.12059	+	0.246960i	0.290697	+	0.0100821i
$601$	−23.6099	+	34.2048i	−0.963066	+	1.39524i	−0.0449248	+	0.998990i	$0.514305\pi$
$601$	−23.6099	+	34.2048i	−0.963066	+	1.39524i	−0.918142	+	0.396252i	$0.870311\pi$
$602$	14.8920	−	13.1931i	0.606951	−	0.537712i
$603$	−4.49183	+	4.98000i	−0.182922	+	0.202801i
$604$	−10.6039	+	0.641415i	−0.431465	+	0.0260988i
$605$	−2.31570	+	0.721601i	−0.0941466	+	0.0293373i
$606$	−1.36501	−	4.01362i	−0.0554496	−	0.163042i
$607$	0.718443	+	0.377068i	0.0291607	+	0.0153047i	0.479241	−	0.877684i	$-0.340912\pi$
$607$	0.718443	+	0.377068i	0.0291607	+	0.0153047i	−0.450080	+	0.892988i	$0.648604\pi$
$608$	−2.69898	+	22.2281i	−0.109458	+	0.901470i
$609$	21.4126	+	25.9275i	0.867684	+	1.05064i
$610$	−0.490410	+	0.934398i	−0.0198561	+	0.0378327i
$611$	−4.45824	−	16.5089i	−0.180361	−	0.667879i
$612$	−19.6204	+	42.5756i	−0.793106	+	1.72101i
$613$	−36.0501	+	2.18063i	−1.45605	+	0.0880747i	−0.769331	−	0.638850i	$-0.779410\pi$
$613$	−36.0501	+	2.18063i	−1.45605	+	0.0880747i	−0.686717	+	0.726925i	$0.740949\pi$
$614$	−39.0283	−	44.0539i	−1.57506	−	1.77787i
$615$	2.52457	−	3.00192i	0.101800	−	0.121049i
$616$	−10.6616	−	13.6085i	−0.429567	−	0.548302i
$617$	−7.06348	−	0.427262i	−0.284365	−	0.0172009i	−0.0824196	−	0.996598i	$-0.526265\pi$
$617$	−7.06348	−	0.427262i	−0.284365	−	0.0172009i	−0.201945	+	0.979397i	$0.564726\pi$
$618$	2.16709	−	62.4838i	0.0871733	−	2.51347i
$619$	−13.7327	−	44.0698i	−0.551964	−	1.77132i	−0.632496	−	0.774563i	$-0.717970\pi$
$619$	−13.7327	−	44.0698i	−0.551964	−	1.77132i	0.0805323	−	0.996752i	$-0.474338\pi$
$620$	−13.8704	−	26.4279i	−0.557050	−	1.06137i
$621$	−6.58137	+	2.17297i	−0.264101	+	0.0871984i
$622$	−59.7607	−	3.61486i	−2.39619	−	0.144943i
$623$	−19.1968	+	4.73158i	−0.769102	+	0.189567i
$624$	−10.1623	+	6.82750i	−0.406816	+	0.273319i
$625$	−5.67329	−	1.39834i	−0.226931	−	0.0559336i
$626$	65.2456	+	20.3313i	2.60774	+	0.812604i
$627$	−0.408867	−	15.8769i	−0.0163286	−	0.634062i
$628$	−59.4636	+	22.5516i	−2.37285	+	0.899905i
$629$	10.7362	−	23.8548i	0.428079	−	0.951153i
$630$	16.2543	+	31.6530i	0.647586	+	1.26109i
$631$	−10.2996	−	17.0377i	−0.410022	−	0.678260i	0.580707	−	0.814113i	$-0.302776\pi$
$631$	−10.2996	−	17.0377i	−0.410022	−	0.678260i	−0.990729	+	0.135853i	$0.956623\pi$
$632$	21.4049	+	3.92260i	0.851442	+	0.156033i
$633$	18.2034	−	27.8811i	0.723519	−	1.10817i
$634$	21.2162	−	8.04625i	0.842604	−	0.319558i
$635$	32.4553	−	10.1135i	1.28795	−	0.401341i
$636$	−37.9166	+	21.1626i	−1.50349	+	0.839152i
$637$	−7.11616	+	16.7934i	−0.281953	+	0.665380i
$638$	−30.8109	+	21.2672i	−1.21981	+	0.841977i
$639$	28.8766	+	0.257644i	1.14234	+	0.0101922i
$640$	18.3614	−	4.52567i	0.725797	−	0.178893i
$641$	1.31814	−	1.90966i	0.0520635	−	0.0754270i	−0.796088	−	0.605181i	$-0.793101\pi$
$641$	1.31814	−	1.90966i	0.0520635	−	0.0754270i	0.848151	+	0.529754i	$0.177716\pi$
$642$	34.4252	+	14.4397i	1.35866	+	0.569888i
$643$	0.667121	−	2.14087i	0.0263087	−	0.0844275i	−0.940633	−	0.339426i	$-0.889767\pi$
$643$	0.667121	−	2.14087i	0.0263087	−	0.0844275i	0.966941	+	0.254998i	$0.0820749\pi$
$644$	7.83670	+	10.0028i	0.308809	+	0.394166i
$645$	−3.09944	−	6.43845i	−0.122040	−	0.253514i
$646$	27.6925	+	24.5334i	1.08955	+	0.965253i
$647$	25.3848	+	36.7763i	0.997980	+	1.44582i	0.892310	+	0.451423i	$0.149083\pi$
$647$	25.3848	+	36.7763i	0.997980	+	1.44582i	0.105670	+	0.994401i	$0.466301\pi$
$648$	−13.3933	+	5.74269i	−0.526138	+	0.225594i
$649$	38.2614	−	4.64577i	1.50189	−	0.182363i
$650$	18.4927	−	7.48480i	0.725343	−	0.293578i
$651$	−22.8102	+	34.9371i	−0.894002	+	1.36929i
$652$	53.9296	−	32.6016i	2.11205	−	1.27678i
$653$		−	3.04055i		−	0.118986i	−0.998229	−	0.0594929i	$-0.981052\pi$
$653$		−	3.04055i		−	0.118986i	0.998229	−	0.0594929i	$-0.0189484\pi$
$654$	−41.6524	−	20.5110i	−1.62874	−	0.802042i
$655$	−11.8912	+	7.18848i	−0.464627	+	0.280877i
$656$	−1.16181	+	2.58144i	−0.0453612	+	0.100788i
$657$	−3.59985	+	27.5881i	−0.140443	+	1.07631i
$658$	32.7095	−	14.7213i	1.27515	−	0.573898i
$659$	−6.58044	−	26.6979i	−0.256338	−	1.04000i	−0.948124	−	0.317900i	$-0.897022\pi$
$659$	−6.58044	−	26.6979i	−0.256338	−	1.04000i	0.691787	−	0.722102i	$-0.256824\pi$
$660$	−21.2072	+	8.67367i	−0.825489	+	0.337622i
$661$	18.3173	+	11.0732i	0.712462	+	0.430698i	0.826617	−	0.562765i	$-0.190262\pi$
$661$	18.3173	+	11.0732i	0.712462	+	0.430698i	−0.114155	+	0.993463i	$0.536416\pi$
$662$	−6.34981	−	5.62544i	−0.246792	−	0.218639i
$663$	−0.447146	+	35.5680i	−0.0173657	+	1.38135i
$664$	10.3040	−	9.12857i	0.399874	−	0.354257i
$665$	15.9754	−	2.92760i	0.619499	−	0.113527i
$666$	27.4730	−	12.0710i	1.06456	−	0.467741i
$667$	6.13715	−	4.23617i	0.237631	−	0.164025i
$668$	−5.02156	−	3.03564i	−0.194290	−	0.117452i
$669$	−13.1697	+	8.43175i	−0.509169	+	0.325990i
$670$	4.70900	−	6.01059i	0.181924	−	0.232209i
$671$	−0.0573552	+	0.948195i	−0.00221417	+	0.0366047i
$672$	−30.8055	−	33.0191i	−1.18835	−	1.27374i
$673$	7.16531	−	13.6524i	0.276202	−	0.526260i	−0.707354	−	0.706859i	$-0.750111\pi$
$673$	7.16531	−	13.6524i	0.276202	−	0.526260i	0.983557	+	0.180599i	$0.0578038\pi$
$674$	45.7421	+	8.38254i	1.76192	+	0.322883i
$675$	−12.9429	+	2.59766i	−0.498171	+	0.0999839i
$676$	18.9433	−	30.2179i	0.728589	−	1.16223i
$677$			4.66991i			0.179479i	0.995965	+	0.0897397i	$0.0286035\pi$
$677$			4.66991i			0.179479i	−0.995965	+	0.0897397i	$0.971396\pi$
$678$	4.16199	+	3.09116i	0.159840	+	0.118715i
$679$	−58.1140	−	30.5006i	−2.23021	−	1.17051i
$680$	5.12884	−	13.5236i	0.196682	−	0.518608i
$681$	−43.1320	−	24.5808i	−1.65282	−	0.941937i
$682$	−36.5675	−	28.6488i	−1.40024	−	1.09702i
$683$	5.85274	−	9.68162i	0.223949	−	0.370457i	−0.723521	−	0.690303i	$-0.757477\pi$
$683$	5.85274	−	9.68162i	0.223949	−	0.370457i	0.947470	+	0.319846i	$0.103631\pi$
$684$	2.74112	+	24.3920i	0.104809	+	0.932651i
$685$	2.58415	+	3.74379i	0.0987354	+	0.143043i
$686$	14.2564	+	3.51388i	0.544311	+	0.134161i
$687$	0.804668	+	0.228192i	0.0307000	+	0.00870605i
$688$	3.41981	+	3.86017i	0.130379	+	0.147167i
$689$	−19.7417	+	26.3789i	−0.752100	+	1.00496i
$690$	7.30372	−	2.98720i	0.278048	−	0.113721i
$691$	5.00254	−	8.27522i	0.190306	−	0.314804i	−0.746029	−	0.665914i	$-0.768042\pi$
$691$	5.00254	−	8.27522i	0.190306	−	0.314804i	0.936334	+	0.351110i	$0.114196\pi$
$692$	−30.7850	+	34.7491i	−1.17027	+	1.32096i
$693$	25.0366	+	19.9779i	0.951061	+	0.758899i
$694$	2.24662	+	4.99179i	0.0852806	+	0.189486i
$695$	−12.1275	−	12.1275i	−0.460021	−	0.460021i
$696$	12.0894	−	9.98424i	0.458249	−	0.378451i
$697$	4.25503	+	7.03867i	0.161171	+	0.266609i
$698$		−	16.6435i		−	0.629966i
$699$	0.0277695	+	0.0136746i	0.00105034	+	0.000517221i
$700$	12.5211	+	20.7124i	0.473252	+	0.782855i
$701$	−1.35288	+	11.1419i	−0.0510975	+	0.420826i	0.944605	+	0.328211i	$0.106446\pi$
$701$	−1.35288	+	11.1419i	−0.0510975	+	0.420826i	−0.995702	+	0.0926149i	$0.970477\pi$
$702$	−27.7080	+	29.9535i	−1.04577	+	1.13052i
$703$	−1.65098	−	13.5971i	−0.0622679	−	0.512823i
$704$	30.0873	−	23.5719i	1.13396	−	0.888399i
$705$	−1.88158	−	12.7448i	−0.0708645	−	0.479995i
$706$	−10.3917	+	11.7298i	−0.391097	+	0.441457i
$707$	2.40675	−	3.07199i	0.0905151	−	0.115534i
$708$	−58.2949	+	12.2419i	−2.19086	+	0.460080i
$709$	−40.2313	−	12.5366i	−1.51092	−	0.470821i	−0.573553	−	0.819168i	$-0.694435\pi$
$709$	−40.2313	−	12.5366i	−1.51092	−	0.470821i	−0.937366	+	0.348347i	$0.886743\pi$
$710$	−32.8184	+	1.98515i	−1.23165	+	0.0745012i
$711$	−40.2661	+	2.07527i	−1.51010	+	0.0778285i
$712$	2.20623	+	8.95102i	0.0826819	+	0.335454i
$713$	7.28380	+	5.70650i	0.272781	+	0.213710i
$714$	−73.8132	+	10.8975i	−2.76239	+	0.407828i
$715$	−12.0187	+	12.5620i	−0.449475	+	0.469792i
$716$	−34.0933	−	23.5329i	−1.27412	−	0.879465i
$717$	−2.74016	+	17.4795i	−0.102333	+	0.652783i
$718$	−7.38756	−	19.4794i	−0.275701	−	0.726965i
$719$	−5.29795	+	43.6325i	−0.197580	+	1.62722i	0.469990	+	0.882672i	$0.344258\pi$
$719$	−5.29795	+	43.6325i	−0.197580	+	1.62722i	−0.667570	+	0.744547i	$0.732665\pi$
$720$	−8.20483	+	4.21329i	−0.305776	+	0.157020i
$721$	49.2529	−	29.7744i	1.83427	−	1.10886i
$722$	−21.6492	−	3.96736i	−0.805698	−	0.147650i
$723$	3.75956	−	3.10489i	0.139819	−	0.115472i
$724$	1.52379	+	4.01790i	0.0566312	+	0.149324i
$725$	12.5766	−	6.60071i	0.467084	−	0.245144i
$726$	4.01793	−	4.23034i	0.149119	−	0.157003i
$727$	−2.30254	+	9.34177i	−0.0853964	+	0.346467i	−0.998061	−	0.0622423i	$-0.980175\pi$
$727$	−2.30254	+	9.34177i	−0.0853964	+	0.346467i	0.912665	+	0.408709i	$0.134021\pi$
$728$	18.6660	+	7.90967i	0.691809	+	0.293152i
$729$	21.6920	−	16.0766i	0.803407	−	0.595431i
$730$	1.91257	−	31.6185i	0.0707873	−	1.17025i
$731$	14.8745	−	1.80609i	0.550153	−	0.0668007i
$732$	−0.0377942	−	1.46761i	−0.00139692	−	0.0542443i
$733$	16.2257	−	5.05613i	0.599310	−	0.186752i	0.0171855	−	0.999852i	$-0.494529\pi$
$733$	16.2257	−	5.05613i	0.599310	−	0.186752i	0.582124	+	0.813100i	$0.302222\pi$
$734$	−61.8776	+	27.8488i	−2.28394	+	1.02792i
$735$	−6.80351	+	11.9382i	−0.250951	+	0.440345i
$736$	−7.88323	+	6.17612i	−0.290580	+	0.227655i
$737$	1.64490	−	6.67360i	0.0605905	−	0.245825i
$738$	−1.78341	+	9.26476i	−0.0656482	+	0.341040i
$739$	0.281333	+	4.65099i	0.0103490	+	0.171089i	0.999678	+	0.0253884i	$0.00808224\pi$
$739$	0.281333	+	4.65099i	0.0103490	+	0.171089i	−0.989329	+	0.145701i	$0.953456\pi$
$740$	−17.4965	+	9.18286i	−0.643183	+	0.337569i
$741$	9.43411	+	16.0585i	0.346571	+	0.589923i
$742$	−61.1958	−	32.1180i	−2.24657	−	1.17909i
$743$	−12.4746	+	27.7173i	−0.457647	+	1.01685i	0.528187	+	0.849128i	$0.322872\pi$
$743$	−12.4746	+	27.7173i	−0.457647	+	1.01685i	−0.985834	+	0.167722i	$0.946359\pi$
$744$	16.2904	+	10.6359i	0.597235	+	0.389930i
$745$	3.32782	−	6.34063i	0.121922	−	0.232303i
$746$	−19.8416	−	19.8416i	−0.726453	−	0.726453i
$747$	−14.6756	+	20.8607i	−0.536952	+	0.763253i
$748$	−2.90090	−	47.9576i	−0.106067	−	1.75350i
$749$	6.19437	+	33.8016i	0.226337	+	1.23508i
$750$	43.0243	−	11.7873i	1.57103	−	0.430413i
$751$	21.2957	+	14.6994i	0.777093	+	0.536388i	0.889315	−	0.457295i	$-0.151182\pi$
$751$	21.2957	+	14.6994i	0.777093	+	0.536388i	−0.112223	+	0.993683i	$0.535797\pi$
$752$	3.81594	+	8.47867i	0.139153	+	0.309185i
$753$	−11.8836	+	11.0869i	−0.433061	+	0.404029i
$754$	19.5387	−	39.3152i	0.711556	−	1.43178i
$755$	−5.67808	+	2.15341i	−0.206646	+	0.0783706i
$756$	−41.2069	−	27.4311i	−1.49868	−	0.997660i
$757$	−14.1563	+	37.3270i	−0.514518	+	1.35667i	0.386258	+	0.922391i	$0.373767\pi$
$757$	−14.1563	+	37.3270i	−0.514518	+	1.35667i	−0.900777	+	0.434283i	$0.857002\pi$
$758$	8.05106	+	66.3064i	0.292428	+	2.40836i
$759$	4.89178	−	5.15039i	0.177561	−	0.186947i
$760$	−1.36507	−	7.44897i	−0.0495165	−	0.270203i
$761$	2.83623	+	15.4768i	0.102813	+	0.561033i	0.994178	+	0.107747i	$0.0343638\pi$
$761$	2.83623	+	15.4768i	0.102813	+	0.561033i	−0.891365	+	0.453286i	$0.850252\pi$
$762$	−56.3126	+	59.2897i	−2.03999	+	2.14784i
$763$	−5.15164	−	42.4276i	−0.186502	−	1.53598i
$764$	20.6107	−	54.3460i	0.745670	−	1.96617i
$765$	−3.46737	+	26.5728i	−0.125363	+	0.960741i
$766$	−34.2525	+	12.9902i	−1.23759	+	0.469357i
$767$	−36.6206	+	26.4909i	−1.32230	+	0.956531i
$768$	−1.77328	+	1.65440i	−0.0639877	+	0.0596980i
$769$	11.1301	+	24.7300i	0.401360	+	0.891785i	0.996130	+	0.0878897i	$0.0280123\pi$
$769$	11.1301	+	24.7300i	0.401360	+	0.891785i	−0.594770	+	0.80

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.s (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.392585 + 2.14227i) q^{2} +(-1.02029 - 1.39965i) q^{3} +(-2.56516 - 0.972837i) q^{4} +(-1.56541 - 0.0946898i) q^{5} +(3.39897 - 1.63625i) q^{6} +(2.97174 + 1.79648i) q^{7} +(0.837658 - 1.38566i) q^{8} +(-0.918027 + 2.85609i) q^{9} +(0.817408 - 3.31635i) q^{10} +(-0.554218 - 3.02427i) q^{11} +(1.25557 + 4.58289i) q^{12} +(2.28578 + 2.78840i) q^{13} +(-5.01520 + 5.66099i) q^{14} +(1.46463 + 2.28763i) q^{15} +(-1.46739 - 1.30000i) q^{16} +(-5.53037 + 1.36311i) q^{17} +(-5.75810 - 3.08792i) q^{18} +(-2.10882 + 2.10882i) q^{19} +(3.92341 + 1.76578i) q^{20} +(-0.517590 - 5.99231i) q^{21} +6.69638 q^{22} -1.33384 q^{23} +(-2.79408 + 0.241341i) q^{24} +(-2.52200 - 0.306227i) q^{25} +(-6.87088 + 3.80207i) q^{26} +(4.93417 - 1.62911i) q^{27} +(-5.87531 - 7.49928i) q^{28} +(-4.60112 + 3.17593i) q^{29} +(-5.47572 + 2.23955i) q^{30} +(-5.46079 - 4.27826i) q^{31} +(5.91019 - 4.63034i) q^{32} +(-3.66745 + 3.86134i) q^{33} +(-0.749014 - 12.3827i) q^{34} +(-4.48188 - 3.09362i) q^{35} +(5.13339 - 6.43323i) q^{36} +(-2.83240 + 3.61529i) q^{37} +(-3.68978 - 5.34556i) q^{38} +(1.57063 - 6.04426i) q^{39} +(-1.44248 + 2.08980i) q^{40} +(-0.429594 - 1.37862i) q^{41} +(13.0403 + 1.24368i) q^{42} +(-2.61145 - 0.317087i) q^{43} +(-1.52046 + 8.29691i) q^{44} +(1.70753 - 4.38401i) q^{45} +(0.523645 - 2.85744i) q^{46} +(-4.32493 - 1.94649i) q^{47} +(-0.322375 + 3.38021i) q^{48} +(2.35083 + 4.47914i) q^{49} +(1.64612 - 5.28259i) q^{50} +(7.55045 + 6.34981i) q^{51} +(-3.15073 - 9.37640i) q^{52} +(2.18691 + 8.87264i) q^{53} +(1.55292 + 11.2099i) q^{54} +(0.581211 + 4.78670i) q^{55} +(4.97860 - 2.61297i) q^{56} +(5.10322 + 0.800005i) q^{57} +(-4.99736 - 11.1037i) q^{58} +(-0.756881 + 12.5127i) q^{59} +(-1.53153 - 7.29299i) q^{60} +(-0.299979 - 0.0739381i) q^{61} +(11.3090 - 10.0189i) q^{62} +(-7.85904 + 6.83833i) q^{63} +(5.77707 + 11.0073i) q^{64} +(-3.31415 - 4.58143i) q^{65} +(-6.83223 - 9.37257i) q^{66} +(2.03855 + 0.917476i) q^{67} +(15.5124 + 1.88354i) q^{68} +(1.36090 + 1.86690i) q^{69} +(8.38688 - 8.38688i) q^{70} +(-2.86374 - 9.19007i) q^{71} +(3.18856 + 3.66449i) q^{72} +(9.12208 - 1.67168i) q^{73} +(-6.63297 - 7.48707i) q^{74} +(2.14456 + 3.84236i) q^{75} +(7.46102 - 3.35793i) q^{76} +(3.78605 - 9.98299i) q^{77} +(12.3318 + 5.73760i) q^{78} +(4.76583 + 12.5665i) q^{79} +(2.17398 + 2.17398i) q^{80} +(-7.31445 - 5.24393i) q^{81} +(3.12202 - 0.379082i) q^{82} +(8.11695 + 2.52934i) q^{83} +(-4.50184 + 15.8748i) q^{84} +(8.78637 - 1.61016i) q^{85} +(1.70450 - 5.46994i) q^{86} +(9.13965 + 3.19959i) q^{87} +(-4.65484 - 1.76535i) q^{88} +(-4.02598 + 4.02598i) q^{89} +(8.72139 + 5.37909i) q^{90} +(1.78344 + 12.3928i) q^{91} +(3.42151 + 1.29761i) q^{92} +(-0.416476 + 12.0082i) q^{93} +(5.86782 - 8.50100i) q^{94} +(3.50086 - 3.10149i) q^{95} +(-12.5109 - 3.54791i) q^{96} +(-18.8657 + 1.14117i) q^{97} +(-10.5184 + 3.27768i) q^{98} +(9.14637 + 1.19347i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100}) \) 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Introduction

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