LMFDB - Embedded newform 115.4.g.a.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$110$
Relative dimension:	$11$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			16.6
Character	$\chi$	$=$	115.16
Dual form			115.4.g.a.36.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0310213 - 0.0358005i) q^{2} +(1.55482 - 0.999222i) q^{3} +(1.13820 + 7.91635i) q^{4} +(2.07708 + 4.54816i) q^{5} +(0.0124599 - 0.0866606i) q^{6} +(-22.1880 + 6.51498i) q^{7} +(0.637525 + 0.409713i) q^{8} +(-9.79718 + 21.4528i) q^{9} +O(q^{10})$	\(q+(0.0310213 - 0.0358005i) q^{2} +(1.55482 - 0.999222i) q^{3} +(1.13820 + 7.91635i) q^{4} +(2.07708 + 4.54816i) q^{5} +(0.0124599 - 0.0866606i) q^{6} +(-22.1880 + 6.51498i) q^{7} +(0.637525 + 0.409713i) q^{8} +(-9.79718 + 21.4528i) q^{9} +(0.227260 + 0.0667296i) q^{10} +(-19.5776 - 22.5937i) q^{11} +(9.67989 + 11.1712i) q^{12} +(12.9817 + 3.81176i) q^{13} +(-0.455061 + 0.996445i) q^{14} +(7.77410 + 4.99611i) q^{15} +(-61.3559 + 18.0157i) q^{16} +(4.45101 - 30.9575i) q^{17} +(0.464101 + 1.01624i) q^{18} +(15.7696 + 109.680i) q^{19} +(-33.6407 + 21.6196i) q^{20} +(-27.9884 + 32.3004i) q^{21} -1.41619 q^{22} +(87.1572 + 67.6064i) q^{23} +1.40063 q^{24} +(-16.3715 + 18.8937i) q^{25} +(0.539171 - 0.346504i) q^{26} +(13.3051 + 92.5388i) q^{27} +(-76.8292 - 168.233i) q^{28} +(-3.64066 + 25.3214i) q^{29} +(0.420026 - 0.123331i) q^{30} +(191.522 + 123.084i) q^{31} +(-3.77687 + 8.27020i) q^{32} +(-53.0158 - 15.5668i) q^{33} +(-0.970217 - 1.11969i) q^{34} +(-75.7173 - 87.3824i) q^{35} +(-180.979 - 53.1403i) q^{36} +(107.010 - 234.319i) q^{37} +(4.41579 + 2.83786i) q^{38} +(23.9929 - 7.04496i) q^{39} +(-0.539251 + 3.75057i) q^{40} +(-104.122 - 227.995i) q^{41} +(0.288132 + 2.00400i) q^{42} +(-160.659 + 103.249i) q^{43} +(156.577 - 180.699i) q^{44} -117.920 q^{45} +(5.12408 - 1.02303i) q^{46} +324.003 q^{47} +(-77.3957 + 89.3194i) q^{48} +(161.312 - 103.669i) q^{49} +(0.168539 + 1.17222i) q^{50} +(-24.0129 - 52.5809i) q^{51} +(-15.3995 + 107.106i) q^{52} +(416.321 - 122.243i) q^{53} +(3.72568 + 2.39435i) q^{54} +(62.0958 - 135.971i) q^{55} +(-16.8147 - 4.93723i) q^{56} +(134.113 + 154.775i) q^{57} +(0.793580 + 0.915840i) q^{58} +(449.227 + 131.905i) q^{59} +(-30.7025 + 67.2291i) q^{60} +(-487.551 - 313.330i) q^{61} +(10.3478 - 3.03837i) q^{62} +(77.6150 - 539.824i) q^{63} +(-212.335 - 464.948i) q^{64} +(9.62739 + 66.9600i) q^{65} +(-2.20192 + 1.41509i) q^{66} +(556.128 - 641.806i) q^{67} +250.136 q^{68} +(203.068 + 18.0264i) q^{69} -5.47719 q^{70} +(-586.557 + 676.923i) q^{71} +(-15.0355 + 9.66270i) q^{72} +(102.152 + 710.485i) q^{73} +(-5.06915 - 11.0999i) q^{74} +(-6.57572 + 45.7352i) q^{75} +(-850.316 + 249.675i) q^{76} +(581.585 + 373.762i) q^{77} +(0.492079 - 1.07750i) q^{78} +(-396.873 - 116.533i) q^{79} +(-209.379 - 241.636i) q^{80} +(-303.842 - 350.652i) q^{81} +(-11.3923 - 3.34509i) q^{82} +(-418.469 + 916.320i) q^{83} +(-287.557 - 184.802i) q^{84} +(150.045 - 44.0571i) q^{85} +(-1.28748 + 8.95461i) q^{86} +(19.6411 + 43.0080i) q^{87} +(-3.22426 - 22.4252i) q^{88} +(311.469 - 200.169i) q^{89} +(-3.65805 + 4.22161i) q^{90} -312.870 q^{91} +(-435.994 + 766.916i) q^{92} +420.771 q^{93} +(10.0510 - 11.5995i) q^{94} +(-466.087 + 299.536i) q^{95} +(2.39141 + 16.6326i) q^{96} +(41.7989 + 91.5267i) q^{97} +(1.29271 - 8.99100i) q^{98} +(676.505 - 198.640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9}+O(q^{10}) $ 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9} - 10 q^{10} + 2 q^{11} - 57 q^{12} + 34 q^{13} - 154 q^{14} + 30 q^{15} + 16 q^{16} + 252 q^{17} - 33 q^{18} - 160 q^{19} - 200 q^{20} - 684 q^{21} - 704 q^{22} + 127 q^{23} - 3090 q^{24} - 275 q^{25} - 567 q^{26} + 384 q^{27} - 188 q^{28} + 340 q^{29} - 15 q^{30} + 582 q^{31} - 1364 q^{32} + 1760 q^{33} + 1819 q^{34} + 665 q^{35} + 2794 q^{36} + 312 q^{37} + 3123 q^{38} - 1560 q^{39} - 1205 q^{40} + 1324 q^{41} + 1454 q^{42} - 1740 q^{43} - 369 q^{44} + 3730 q^{45} - 4322 q^{46} - 2858 q^{47} - 2686 q^{48} + 2015 q^{49} - 325 q^{50} - 1426 q^{51} + 1717 q^{52} + 882 q^{53} + 2541 q^{54} + 450 q^{55} + 7755 q^{56} + 3688 q^{57} + 6622 q^{58} + 2605 q^{59} + 1530 q^{60} - 104 q^{61} - 9360 q^{62} - 7618 q^{63} + 3483 q^{64} + 170 q^{65} - 1766 q^{66} - 166 q^{67} - 5018 q^{68} - 1194 q^{69} - 770 q^{70} - 1222 q^{71} + 3303 q^{72} - 922 q^{73} + 1245 q^{74} + 150 q^{75} + 1360 q^{76} - 3093 q^{77} - 1600 q^{78} + 2448 q^{79} + 2115 q^{80} - 1371 q^{81} + 6609 q^{82} + 6704 q^{83} + 3894 q^{84} - 720 q^{85} - 5074 q^{86} - 6324 q^{87} + 1918 q^{88} - 5380 q^{89} - 165 q^{90} + 7828 q^{91} - 16225 q^{92} - 24948 q^{93} - 16490 q^{94} + 685 q^{95} + 675 q^{96} - 4400 q^{97} + 8790 q^{98} - 3626 q^{99}+O(q^{100}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9 - 10 * q^10 + 2 * q^11 - 57 * q^12 + 34 * q^13 - 154 * q^14 + 30 * q^15 + 16 * q^16 + 252 * q^17 - 33 * q^18 - 160 * q^19 - 200 * q^20 - 684 * q^21 - 704 * q^22 + 127 * q^23 - 3090 * q^24 - 275 * q^25 - 567 * q^26 + 384 * q^27 - 188 * q^28 + 340 * q^29 - 15 * q^30 + 582 * q^31 - 1364 * q^32 + 1760 * q^33 + 1819 * q^34 + 665 * q^35 + 2794 * q^36 + 312 * q^37 + 3123 * q^38 - 1560 * q^39 - 1205 * q^40 + 1324 * q^41 + 1454 * q^42 - 1740 * q^43 - 369 * q^44 + 3730 * q^45 - 4322 * q^46 - 2858 * q^47 - 2686 * q^48 + 2015 * q^49 - 325 * q^50 - 1426 * q^51 + 1717 * q^52 + 882 * q^53 + 2541 * q^54 + 450 * q^55 + 7755 * q^56 + 3688 * q^57 + 6622 * q^58 + 2605 * q^59 + 1530 * q^60 - 104 * q^61 - 9360 * q^62 - 7618 * q^63 + 3483 * q^64 + 170 * q^65 - 1766 * q^66 - 166 * q^67 - 5018 * q^68 - 1194 * q^69 - 770 * q^70 - 1222 * q^71 + 3303 * q^72 - 922 * q^73 + 1245 * q^74 + 150 * q^75 + 1360 * q^76 - 3093 * q^77 - 1600 * q^78 + 2448 * q^79 + 2115 * q^80 - 1371 * q^81 + 6609 * q^82 + 6704 * q^83 + 3894 * q^84 - 720 * q^85 - 5074 * q^86 - 6324 * q^87 + 1918 * q^88 - 5380 * q^89 - 165 * q^90 + 7828 * q^91 - 16225 * q^92 - 24948 * q^93 - 16490 * q^94 + 685 * q^95 + 675 * q^96 - 4400 * q^97 + 8790 * q^98 - 3626 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.0310213	−	0.0358005i	0.0109677	−	0.0126574i	−0.750239	−	0.661166i	$-0.770062\pi$
$2$	0.0310213	−	0.0358005i	0.0109677	−	0.0126574i	0.761207	+	0.648509i	$0.224607\pi$
$3$	1.55482	−	0.999222i	0.299225	−	0.192300i	−0.382410	−	0.923993i	$-0.624906\pi$
$3$	1.55482	−	0.999222i	0.299225	−	0.192300i	0.681635	+	0.731693i	$0.261269\pi$
$4$	1.13820	+	7.91635i	0.142275	+	0.989544i
$5$	2.07708	+	4.54816i	0.185779	+	0.406800i
$5$	2.07708	+	4.54816i	0.185779	+	0.406800i
$6$	0.0124599	−	0.0866606i	0.000847789	−	0.00589650i
$7$	−22.1880	+	6.51498i	−1.19804	+	0.351776i	−0.819103	−	0.573647i	$-0.805528\pi$
$7$	−22.1880	+	6.51498i	−1.19804	+	0.351776i	−0.378936	+	0.925423i	$0.623710\pi$
$8$	0.637525	+	0.409713i	0.0281749	+	0.0181069i
$9$	−9.79718	+	21.4528i	−0.362859	+	0.794550i
$10$	0.227260	+	0.0667296i	0.00718660	+	0.00211017i
$11$	−19.5776	−	22.5937i	−0.536624	−	0.619297i	0.421090	−	0.907019i	$-0.361648\pi$
$11$	−19.5776	−	22.5937i	−0.536624	−	0.619297i	−0.957714	+	0.287722i	$0.907102\pi$
$12$	9.67989	+	11.1712i	0.232862	+	0.268737i
$13$	12.9817	+	3.81176i	0.276959	+	0.0813224i	0.417262	−	0.908786i	$-0.362990\pi$
$13$	12.9817	+	3.81176i	0.276959	+	0.0813224i	−0.140303	+	0.990109i	$0.544808\pi$
$14$	−0.455061	+	0.996445i	−0.00868716	+	0.0190222i
$15$	7.77410	+	4.99611i	0.133818	+	0.0859994i
$16$	−61.3559	+	18.0157i	−0.958686	+	0.281496i
$17$	4.45101	−	30.9575i	0.0635017	−	0.441664i	−0.933122	−	0.359560i	$-0.882927\pi$
$17$	4.45101	−	30.9575i	0.0635017	−	0.441664i	0.996624	−	0.0821043i	$-0.0261641\pi$
$18$	0.464101	+	1.01624i	0.00607721	+	0.0133072i
$19$	15.7696	+	109.680i	0.190410	+	1.32433i	0.830924	+	0.556385i	$0.187812\pi$
$19$	15.7696	+	109.680i	0.190410	+	1.32433i	−0.640514	+	0.767946i	$0.721279\pi$
$20$	−33.6407	+	21.6196i	−0.376114	+	0.241714i
$21$	−27.9884	+	32.3004i	−0.290837	+	0.335644i
$22$	−1.41619			−0.0137242
$23$	87.1572	+	67.6064i	0.790153	+	0.612909i
$23$	87.1572	+	67.6064i	0.790153	+	0.612909i
$24$	1.40063			0.0119126
$25$	−16.3715	+	18.8937i	−0.130972	+	0.151150i
$26$	0.539171	−	0.346504i	0.00406693	−	0.00261366i
$27$	13.3051	+	92.5388i	0.0948357	+	0.659597i
$28$	−76.8292	−	168.233i	−0.518549	−	1.13546i
$29$	−3.64066	+	25.3214i	−0.0233122	+	0.162140i	−0.998152	−	0.0607667i	$-0.980645\pi$
$29$	−3.64066	+	25.3214i	−0.0233122	+	0.162140i	0.974840	+	0.222907i	$0.0715545\pi$
$30$	0.420026	−	0.123331i	0.00255620	−	0.000750568i
$31$	191.522	+	123.084i	1.10963	+	0.713114i	0.961212	−	0.275811i	$-0.0889464\pi$
$31$	191.522	+	123.084i	1.10963	+	0.713114i	0.148415	+	0.988925i	$0.452583\pi$
$32$	−3.77687	+	8.27020i	−0.0208645	+	0.0456868i
$33$	−53.0158	−	15.5668i	−0.279662	−	0.0821163i
$34$	−0.970217	−	1.11969i	−0.00489385	−	0.00564780i
$35$	−75.7173	−	87.3824i	−0.365673	−	0.422009i
$36$	−180.979	−	53.1403i	−0.837867	−	0.246020i
$37$	107.010	−	234.319i	0.475468	−	1.04113i	−0.508217	−	0.861229i	$-0.669695\pi$
$37$	107.010	−	234.319i	0.475468	−	1.04113i	0.983685	−	0.179900i	$-0.0575774\pi$
$38$	4.41579	+	2.83786i	0.0188509	+	0.0121148i
$39$	23.9929	−	7.04496i	0.0985114	−	0.0289256i
$40$	−0.539251	+	3.75057i	−0.00213158	+	0.0148254i
$41$	−104.122	−	227.995i	−0.396612	−	0.868458i	−0.997603	−	0.0692026i	$-0.977955\pi$
$41$	−104.122	−	227.995i	−0.396612	−	0.868458i	0.600991	−	0.799256i	$-0.294773\pi$
$42$	0.288132	+	2.00400i	0.00105856	+	0.00736247i
$43$	−160.659	+	103.249i	−0.569774	+	0.366172i	−0.793584	−	0.608461i	$-0.791787\pi$
$43$	−160.659	+	103.249i	−0.569774	+	0.366172i	0.223809	+	0.974633i	$0.428151\pi$
$44$	156.577	−	180.699i	0.536473	−	0.619123i
$45$	−117.920			−0.390634
$46$	5.12408	−	1.02303i	0.0164240	−	0.00327908i
$47$	324.003			1.00555			0.502773	−	0.864418i	$-0.332313\pi$
$47$	324.003			1.00555			0.502773	+	0.864418i	$0.332313\pi$
$48$	−77.3957	+	89.3194i	−0.232731	+	0.268586i
$49$	161.312	−	103.669i	0.470297	−	0.302242i
$50$	0.168539	+	1.17222i	0.000476702	+	0.00331553i
$51$	−24.0129	−	52.5809i	−0.0659309	−	0.144368i
$52$	−15.3995	+	107.106i	−0.0410678	+	0.285633i
$53$	416.321	−	122.243i	1.07898	−	0.316818i	0.306511	−	0.951867i	$-0.400838\pi$
$53$	416.321	−	122.243i	1.07898	−	0.316818i	0.772472	+	0.635049i	$0.219020\pi$
$54$	3.72568	+	2.39435i	0.00938890	+	0.00603388i
$55$	62.0958	−	135.971i	0.152236	−	0.333351i
$56$	−16.8147	−	4.93723i	−0.0401242	−	0.0117815i
$57$	134.113	+	154.775i	0.311645	+	0.359657i
$58$	0.793580	+	0.915840i	0.00179659	+	0.00207337i
$59$	449.227	+	131.905i	0.991261	+	0.291061i	0.736865	−	0.676040i	$-0.236305\pi$
$59$	449.227	+	131.905i	0.991261	+	0.291061i	0.254396	+	0.967100i	$0.418123\pi$
$60$	−30.7025	+	67.2291i	−0.0660612	+	0.144654i
$61$	−487.551	−	313.330i	−1.02335	−	0.657669i	−0.0825372	−	0.996588i	$-0.526302\pi$
$61$	−487.551	−	313.330i	−1.02335	−	0.657669i	−0.940816	+	0.338919i	$0.889939\pi$
$62$	10.3478	−	3.03837i	0.0211962	−	0.00622377i
$63$	77.6150	−	539.824i	0.155215	−	1.07955i
$64$	−212.335	−	464.948i	−0.414716	−	0.908101i
$65$	9.62739	+	66.9600i	0.0183712	+	0.127775i
$66$	−2.20192	+	1.41509i	−0.00410663	+	0.00263917i
$67$	556.128	−	641.806i	1.01406	−	1.17029i	0.0287346	−	0.999587i	$-0.490852\pi$
$67$	556.128	−	641.806i	1.01406	−	1.17029i	0.985323	−	0.170698i	$-0.0546023\pi$
$68$	250.136			0.446081
$69$	203.068	+	18.0264i	0.354297	+	0.0314511i
$70$	−5.47719			−0.00935213
$71$	−586.557	+	676.923i	−0.980444	+	1.13149i	0.0108650	+	0.999941i	$0.496542\pi$
$71$	−586.557	+	676.923i	−0.980444	+	1.13149i	−0.991309	+	0.131552i	$0.958004\pi$
$72$	−15.0355	+	9.66270i	−0.0246103	+	0.0158161i
$73$	102.152	+	710.485i	0.163781	+	1.13912i	0.891425	+	0.453168i	$0.149706\pi$
$73$	102.152	+	710.485i	0.163781	+	1.13912i	−0.727644	+	0.685955i	$0.759385\pi$
$74$	−5.06915	−	11.0999i	−0.00796319	−	0.0174370i
$75$	−6.57572	+	45.7352i	−0.0101240	+	0.0704139i
$76$	−850.316	+	249.675i	−1.28339	+	0.376838i
$77$	581.585	+	373.762i	0.860750	+	0.553170i
$78$	0.492079	−	1.07750i	0.000714321	−	0.00156414i
$79$	−396.873	−	116.533i	−0.565212	−	0.165961i	−0.0133710	−	0.999911i	$-0.504256\pi$
$79$	−396.873	−	116.533i	−0.565212	−	0.165961i	−0.551841	+	0.833949i	$0.686074\pi$
$80$	−209.379	−	241.636i	−0.292616	−	0.337697i
$81$	−303.842	−	350.652i	−0.416793	−	0.481005i
$82$	−11.3923	−	3.34509i	−0.0153423	−	0.00450492i
$83$	−418.469	+	916.320i	−0.553409	+	1.21180i	0.401762	+	0.915744i	$0.368398\pi$
$83$	−418.469	+	916.320i	−0.553409	+	1.21180i	−0.955171	+	0.296053i	$0.904329\pi$
$84$	−287.557	−	184.802i	−0.373513	−	0.240042i
$85$	150.045	−	44.0571i	0.191466	−	0.0562195i
$86$	−1.28748	+	8.95461i	−0.00161433	+	0.0112279i
$87$	19.6411	+	43.0080i	0.0242040	+	0.0529994i
$88$	−3.22426	−	22.4252i	−0.00390577	−	0.0271652i
$89$	311.469	−	200.169i	0.370963	−	0.238403i	−0.341855	−	0.939753i	$-0.611055\pi$
$89$	311.469	−	200.169i	0.370963	−	0.238403i	0.712817	+	0.701350i	$0.247419\pi$
$90$	−3.65805	+	4.22161i	−0.00428436	+	0.00494441i
$91$	−312.870			−0.360415
$92$	−435.994	+	766.916i	−0.494082	+	0.869093i
$93$	420.771			0.469161
$94$	10.0510	−	11.5995i	0.0110285	−	0.0127276i
$95$	−466.087	+	299.536i	−0.503363	+	0.323492i
$96$	2.39141	+	16.6326i	0.00254242	+	0.0176829i
$97$	41.7989	+	91.5267i	0.0437529	+	0.0958055i	0.930246	−	0.366936i	$-0.119593\pi$
$97$	41.7989	+	91.5267i	0.0437529	+	0.0958055i	−0.886493	+	0.462741i	$0.846866\pi$
$98$	1.29271	−	8.99100i	0.00133248	−	0.00926764i
$99$	676.505	−	198.640i	0.686781	−	0.201657i
$100$	−168.204	−	108.098i	−0.168204	−	0.108098i
$101$	−272.952	+	597.681i	−0.268908	+	0.588826i	−0.995123	−	0.0986413i	$-0.968550\pi$
$101$	−272.952	+	597.681i	−0.268908	+	0.588826i	0.726215	+	0.687468i	$0.241278\pi$
$102$	−2.62733	−	0.771455i	−0.00255044	−	0.000748876i
$103$	−306.183	−	353.354i	−0.292904	−	0.338030i	0.590156	−	0.807289i	$-0.299066\pi$
$103$	−306.183	−	353.354i	−0.292904	−	0.338030i	−0.883060	+	0.469260i	$0.844521\pi$
$104$	6.71441	+	7.74884i	0.00633079	+	0.00730612i
$105$	−205.041	−	60.2055i	−0.190571	−	0.0559568i
$106$	8.53847	−	18.6966i	0.00782386	−	0.0171319i
$107$	1626.47	+	1045.27i	1.46950	+	0.944393i	0.998045	+	0.0625060i	$0.0199092\pi$
$107$	1626.47	+	1045.27i	1.46950	+	0.944393i	0.471460	+	0.881887i	$0.343727\pi$
$108$	−717.426	+	210.655i	−0.639207	+	0.187688i
$109$	−229.012	+	1592.81i	−0.201242	+	1.39967i	0.599363	+	0.800477i	$0.295420\pi$
$109$	−229.012	+	1592.81i	−0.201242	+	1.39967i	−0.800605	+	0.599192i	$0.795489\pi$
$110$	−2.94153	−	6.44106i	−0.00254967	−	0.00558301i
$111$	−67.7555	−	471.250i	−0.0579376	−	0.402965i
$112$	1243.99	−	799.465i	1.04952	−	0.674485i
$113$	396.307	−	457.363i	0.329924	−	0.380753i	−0.566416	−	0.824119i	$-0.691670\pi$
$113$	396.307	−	457.363i	0.329924	−	0.380753i	0.896341	+	0.443366i	$0.146216\pi$
$114$	9.70141			0.00797035
$115$	−126.453	+	536.828i	−0.102537	+	0.435300i
$116$	−204.597			−0.163761
$117$	−208.957	+	241.149i	−0.165112	+	0.190549i
$118$	18.6579	−	11.9907i	0.0145559	−	0.00935452i
$119$	102.928	+	715.882i	0.0792893	+	0.551469i
$120$	2.90922	+	6.37029i	0.00221312	+	0.00484605i
$121$	62.2260	−	432.792i	0.0467513	−	0.325163i
$122$	−26.3419	+	7.73467i	−0.0195482	+	0.00573987i
$123$	−389.708	−	250.450i	−0.285681	−	0.183596i
$124$	−756.385	+	1656.25i	−0.547786	+	1.19948i
$125$	−119.937	−	35.2166i	−0.0858197	−	0.0251989i
$126$	−16.9183	−	19.5247i	−0.0119619	−	0.0138048i
$127$	−372.163	−	429.499i	−0.260032	−	0.300093i	0.610689	−	0.791871i	$-0.290893\pi$
$127$	−372.163	−	429.499i	−0.260032	−	0.300093i	−0.870721	+	0.491778i	$0.836347\pi$
$128$	−93.0205	−	27.3133i	−0.0642338	−	0.0188607i
$129$	−146.627	+	321.068i	−0.100076	+	0.219136i
$130$	2.69586	+	1.73252i	0.00181879	+	0.00116886i
$131$	−472.999	+	138.885i	−0.315467	+	0.0926294i	−0.435633	−	0.900124i	$-0.643475\pi$
$131$	−472.999	+	138.885i	−0.315467	+	0.0926294i	0.120166	+	0.992754i	$0.461657\pi$
$132$	62.8900	−	437.410i	0.0414687	−	0.288421i
$133$	−1064.46	−	2330.84i	−0.693987	−	1.51962i
$134$	−5.72516	−	39.8194i	−0.00369088	−	0.0256707i
$135$	−393.246	+	252.724i	−0.250705	+	0.161118i
$136$	15.5213	−	17.9125i	0.00978633	−	0.0112940i
$137$	−646.157			−0.402956			−0.201478	−	0.979493i	$-0.564574\pi$
$137$	−646.157			−0.402956			−0.201478	+	0.979493i	$0.564574\pi$
$138$	6.94478	−	6.71072i	0.00428391	−	0.00413952i
$139$	1443.41			0.880783			0.440392	−	0.897806i	$-0.354840\pi$
$139$	1443.41			0.880783			0.440392	+	0.897806i	$0.354840\pi$
$140$	605.569	−	698.863i	0.365571	−	0.421891i
$141$	503.766	−	323.751i	0.300885	−	0.193367i
$142$	6.03842	+	41.9981i	0.00356854	+	0.0248197i
$143$	−168.028	−	367.929i	−0.0982599	−	0.215159i
$144$	214.627	−	1492.76i	0.124205	−	0.863866i
$145$	−122.728	+	36.0361i	−0.0702895	+	0.0206389i
$146$	28.6046	+	18.3831i	0.0162146	+	0.0104205i
$147$	147.223	−	322.373i	0.0826037	−	0.180877i
$148$	1976.75	+	580.425i	1.09789	+	0.322369i
$149$	−334.894	−	386.488i	−0.184131	−	0.212499i	0.656178	−	0.754606i	$-0.272172\pi$
$149$	−334.894	−	386.488i	−0.184131	−	0.212499i	−0.840309	+	0.542107i	$0.817627\pi$
$150$	1.43335	+	1.65418i	0.000780219	+	0.000900421i
$151$	540.088	+	158.584i	0.291071	+	0.0854661i	0.424008	−	0.905658i	$-0.360623\pi$
$151$	540.088	+	158.584i	0.291071	+	0.0854661i	−0.132937	+	0.991124i	$0.542441\pi$
$152$	−34.8837	+	76.3847i	−0.0186148	+	0.0407606i
$153$	620.518	+	398.783i	0.327882	+	0.210717i
$154$	31.4224	−	9.22645i	0.0164421	−	0.00482785i
$155$	−161.999	+	1126.73i	−0.0839490	+	0.583878i
$156$	83.0791	+	181.918i	0.0426388	+	0.0933660i
$157$	−148.164	−	1030.50i	−0.0753169	−	0.523841i	−0.992197	−	0.124678i	$-0.960210\pi$
$157$	−148.164	−	1030.50i	−0.0753169	−	0.523841i	0.916880	−	0.399162i	$-0.130699\pi$
$158$	−16.4835	+	10.5933i	−0.00829971	+	0.00533390i
$159$	525.156	−	606.063i	0.261935	−	0.302289i
$160$	−45.4590			−0.0224616
$161$	−2374.30	−	932.223i	−1.16224	−	0.456332i
$162$	−21.9791			−0.0106595
$163$	935.164	−	1079.24i	0.449372	−	0.518603i	−0.485187	−	0.874410i	$-0.661249\pi$
$163$	935.164	−	1079.24i	0.449372	−	0.518603i	0.934559	+	0.355807i	$0.115794\pi$
$164$	1686.37	−	1083.77i	0.802950	−	0.516024i
$165$	−39.3173	−	273.458i	−0.0185506	−	0.129022i
$166$	19.8233	+	43.4069i	0.00926857	+	0.0202953i
$167$	70.2849	−	488.842i	0.0325677	−	0.226513i	−0.967037	−	0.254637i	$-0.918044\pi$
$167$	70.2849	−	488.842i	0.0325677	−	0.226513i	0.999604	+	0.0281235i	$0.00895315\pi$
$168$	−31.0772	+	9.12509i	−0.0142718	+	0.00419057i
$169$	−1694.24	−	1088.82i	−0.771161	−	0.495595i
$170$	3.07732	−	6.73838i	0.00138835	−	0.00304006i
$171$	−2507.44	−	736.252i	−1.12134	−	0.329255i
$172$	−1000.22	−	1154.32i	−0.443407	−	0.511719i
$173$	2008.30	+	2317.71i	0.882593	+	1.01857i	0.999676	+	0.0254443i	$0.00810005\pi$
$173$	2008.30	+	2317.71i	0.882593	+	1.01857i	−0.117083	+	0.993122i	$0.537354\pi$
$174$	2.14900	+	0.631004i	0.000936296	+	0.000274921i
$175$	240.159	−	525.874i	0.103739	−	0.227156i
$176$	1608.24	+	1033.55i	0.688783	+	0.442654i
$177$	830.270	−	243.789i	0.352581	−	0.103527i
$178$	2.49603	−	17.3603i	0.00105104	−	0.00731015i
$179$	1518.58	+	3325.23i	0.634102	+	1.38849i	0.904805	+	0.425826i	$0.140016\pi$
$179$	1518.58	+	3325.23i	0.634102	+	1.38849i	−0.270703	+	0.962663i	$0.587256\pi$
$180$	−134.217	−	933.500i	−0.0555775	−	0.386550i
$181$	2146.70	−	1379.60i	0.881562	−	0.566546i	−0.0197065	−	0.999806i	$-0.506273\pi$
$181$	2146.70	−	1379.60i	0.881562	−	0.566546i	0.901269	+	0.433260i	$0.142637\pi$
$182$	−9.70566	+	11.2009i	−0.00395292	+	0.00456191i
$183$	−1071.14			−0.432683
$184$	27.8657	+	78.8102i	0.0111646	+	0.0315759i
$185$	1287.99			0.511863
$186$	13.0529	−	15.0638i	0.00514561	−	0.00593835i
$187$	−786.585	+	505.507i	−0.307598	+	0.197681i
$188$	368.780	+	2564.92i	0.143064	+	0.995032i
$189$	−898.102	−	1966.57i	−0.345647	−	0.756861i
$190$	−3.73510	+	25.9782i	−0.00142617	+	0.00991923i
$191$	3408.11	−	1000.71i	1.29111	−	0.379104i	0.437125	−	0.899401i	$-0.355997\pi$
$191$	3408.11	−	1000.71i	1.29111	−	0.379104i	0.853986	+	0.520297i	$0.174179\pi$
$192$	−794.728	−	510.741i	−0.298722	−	0.191977i
$193$	500.784	−	1096.56i	0.186773	−	0.408976i	−0.792963	−	0.609270i	$-0.791463\pi$
$193$	500.784	−	1096.56i	0.186773	−	0.408976i	0.979736	+	0.200294i	$0.0641898\pi$
$194$	4.57336	+	1.34286i	0.00169252	+	0.000496968i
$195$	81.8768	+	94.4908i	0.0300683	+	0.0347007i
$196$	1004.28	+	1159.01i	0.365993	+	0.422379i
$197$	71.9305	+	21.1207i	0.0260144	+	0.00763852i	0.294714	−	0.955586i	$-0.404776\pi$
$197$	71.9305	+	21.1207i	0.0260144	+	0.00763852i	−0.268699	+	0.963224i	$0.586594\pi$
$198$	13.8747	−	30.3813i	0.00497995	−	0.0109046i
$199$	−4017.19	−	2581.69i	−1.43101	−	0.919654i	−0.999849	−	0.0173779i	$-0.994468\pi$
$199$	−4017.19	−	2581.69i	−1.43101	−	0.919654i	−0.431160	−	0.902276i	$-0.641895\pi$
$200$	−18.1783	+	5.33762i	−0.00642698	+	0.00188713i
$201$	223.372	−	1553.59i	0.0783854	−	0.545183i
$202$	12.9300	+	28.3127i	0.00450371	+	0.00986174i
$203$	−84.1893	−	585.549i	−0.0291080	−	0.202451i
$204$	388.917	−	249.942i	0.133479	−	0.0857815i
$205$	820.688	−	947.124i	0.279606	−	0.322683i
$206$	−22.1485			−0.00749106
$207$	−2304.24	+	1207.42i	−0.773701	+	0.405417i
$208$	−865.173			−0.288408
$209$	2169.35	−	2503.56i	0.717976	−	0.828588i
$210$	−8.51604	+	5.47293i	−0.00279839	+	0.00179842i
$211$	618.292	+	4300.32i	0.201730	+	1.40306i	0.799149	+	0.601133i	$0.205284\pi$
$211$	618.292	+	4300.32i	0.201730	+	1.40306i	−0.597419	+	0.801929i	$0.703807\pi$
$212$	1441.57	+	3156.61i	0.467017	+	1.02263i
$213$	−235.594	+	1638.59i	−0.0757871	+	0.527111i
$214$	87.8765	−	25.8029i	0.0280706	−	0.00824228i
$215$	−803.296	−	516.247i	−0.254811	−	0.163757i
$216$	−29.4320	+	64.4471i	−0.00927127	+	0.0203012i
$217$	−5051.39	−	1483.22i	−1.58023	−	0.463998i
$218$	49.9193	+	57.6100i	0.0155090	+	0.0178983i
$219$	868.761	+	1002.60i	0.268061	+	0.309359i
$220$	1147.07	+	336.810i	0.351525	+	0.103217i
$221$	175.784	−	384.913i	0.0535046	−	0.117159i
$222$	−18.9729	−	12.1931i	−0.00573592	−	0.00368625i
$223$	−5416.61	+	1590.46i	−1.62656	+	0.477601i	−0.962771	−	0.270318i	$-0.912871\pi$
$223$	−5416.61	+	1590.46i	−1.62656	+	0.477601i	−0.663790	+	0.747919i	$0.731053\pi$
$224$	29.9210	−	208.105i	0.00892492	−	0.0620742i
$225$	−244.930	−	536.321i	−0.0725717	−	0.158910i
$226$	−4.07986	−	28.3760i	−0.00120083	−	0.00835197i
$227$	−2155.55	+	1385.29i	−0.630259	+	0.405043i	−0.816405	−	0.577479i	$-0.804036\pi$
$227$	−2155.55	+	1385.29i	−0.630259	+	0.405043i	0.186147	+	0.982522i	$0.440400\pi$
$228$	−1072.61	+	1237.85i	−0.311558	+	0.359557i
$229$	−4456.59			−1.28602			−0.643012	−	0.765856i	$-0.722316\pi$
$229$	−4456.59			−1.28602			−0.643012	+	0.765856i	$0.722316\pi$
$230$	15.2960	+	21.1802i	0.00438517	+	0.00607209i
$231$	1277.73			0.363933
$232$	−12.6955	+	14.6514i	−0.00359267	+	0.00414617i
$233$	1216.79	−	781.981i	0.342121	−	0.219868i	−0.358285	−	0.933612i	$-0.616638\pi$
$233$	1216.79	−	781.981i	0.342121	−	0.219868i	0.700407	+	0.713744i	$0.253002\pi$
$234$	2.15114	+	14.9615i	0.000600960	+	0.00417977i
$235$	672.978	+	1473.62i	0.186810	+	0.409056i
$236$	−532.896	+	3706.37i	−0.146986	+	1.02231i
$237$	−733.509	+	215.378i	−0.201040	+	0.0590307i
$238$	28.8219	+	18.5227i	0.00784978	+	0.00504475i
$239$	−2827.04	+	6190.36i	−0.765130	+	1.67540i	−0.0280396	+	0.999607i	$0.508926\pi$
$239$	−2827.04	+	6190.36i	−0.765130	+	1.67540i	−0.737090	+	0.675794i	$0.763801\pi$
$240$	−566.995	−	166.485i	−0.152497	−	0.0447773i
$241$	4079.37	+	4707.84i	1.09035	+	1.25833i	0.963872	+	0.266366i	$0.0858230\pi$
$241$	4079.37	+	4707.84i	1.09035	+	1.25833i	0.126481	+	0.991969i	$0.459632\pi$
$242$	−13.5638	−	15.6535i	−0.00360296	−	0.00415803i
$243$	−3244.79	−	952.757i	−0.856599	−	0.251520i
$244$	1925.50	−	4216.26i	0.505195	−	1.10622i
$245$	806.560	+	518.345i	0.210323	+	0.135167i
$246$	−21.0555	+	6.18245i	−0.00545711	+	0.00160235i
$247$	−213.358	+	1483.94i	−0.0549621	+	0.382270i
$248$	71.6713	+	156.938i	0.0183513	+	0.0401838i
$249$	264.963	+	1842.86i	0.0674351	+	0.469021i
$250$	−4.98136	+	3.20133i	−0.00126020	+	0.000809879i
$251$	2420.83	−	2793.79i	0.608771	−	0.702560i	−0.364763	−	0.931100i	$-0.618850\pi$
$251$	2420.83	−	2793.79i	0.608771	−	0.702560i	0.973534	+	0.228541i	$0.0733954\pi$
$252$	4361.78			1.09034
$253$	−178.845	−	3292.78i	−0.0444423	−	0.818241i
$254$	−26.9212			−0.00665035
$255$	189.270	−	218.429i	0.0464805	−	0.0536413i
$256$	3436.11	−	2208.26i	0.838895	−	0.539125i
$257$	−451.305	−	3138.89i	−0.109539	−	0.761863i	−0.968355	−	0.249578i	$-0.919708\pi$
$257$	−451.305	−	3138.89i	−0.109539	−	0.761863i	0.858815	−	0.512285i	$-0.171201\pi$
$258$	6.94585	+	15.2093i	0.00167608	+	0.00367011i
$259$	−847.750	+	5896.23i	−0.203385	+	1.41457i
$260$	−519.121	+	152.428i	−0.123825	+	0.0363583i
$261$	−507.547	−	326.181i	−0.120369	−	0.0773566i
$262$	−9.70090	+	21.2420i	−0.00228750	+	0.00500892i
$263$	−3873.05	−	1137.23i	−0.908069	−	0.266633i	−0.205841	−	0.978585i	$-0.565993\pi$
$263$	−3873.05	−	1137.23i	−0.908069	−	0.266633i	−0.702228	+	0.711952i	$0.747811\pi$
$264$	−27.4210	−	31.6455i	−0.00639259	−	0.00737744i
$265$	1420.71	+	1639.59i	0.329334	+	0.380072i
$266$	−116.466	−	34.1975i	−0.0268458	−	0.00788265i
$267$	284.265	−	622.454i	0.0651564	−	0.142673i
$268$	5713.75	+	3672.00i	1.30232	+	0.836953i
$269$	3457.44	−	1015.20i	0.783658	−	0.230103i	0.134659	−	0.990892i	$-0.457006\pi$
$269$	3457.44	−	1015.20i	0.783658	−	0.230103i	0.648999	+	0.760789i	$0.275188\pi$
$270$	−3.15137	+	21.9182i	−0.000710318	+	0.00494037i
$271$	−757.486	−	1658.66i	−0.169793	−	0.371796i	0.805537	−	0.592545i	$-0.201877\pi$
$271$	−757.486	−	1658.66i	−0.169793	−	0.371796i	−0.975331	+	0.220750i	$0.929150\pi$
$272$	284.625	+	1979.61i	0.0634483	+	0.441293i
$273$	−486.457	+	312.627i	−0.107845	+	0.0693079i
$274$	−20.0446	+	23.1328i	−0.00441949	+	0.00510037i
$275$	747.395			0.163889
$276$	88.4278	+	1628.07i	0.0192852	+	0.355067i
$277$	−6886.99			−1.49386			−0.746930	−	0.664903i	$-0.768473\pi$
$277$	−6886.99			−1.49386			−0.746930	+	0.664903i	$0.768473\pi$
$278$	44.7766	−	51.6750i	0.00966016	−	0.0111484i
$279$	−4516.88	+	2902.82i	−0.969243	+	0.622894i
$280$	−12.4700	−	86.7308i	−0.00266152	−	0.0185113i
$281$	−695.102	−	1522.06i	−0.147567	−	0.323127i	0.821386	−	0.570373i	$-0.193201\pi$
$281$	−695.102	−	1522.06i	−0.147567	−	0.323127i	−0.968953	+	0.247247i	$0.920474\pi$
$282$	4.03705	−	28.0783i	0.000852491	−	0.00592921i
$283$	1452.16	−	426.394i	0.305025	−	0.0895635i	−0.125638	−	0.992076i	$-0.540098\pi$
$283$	1452.16	−	426.394i	0.305025	−	0.0895635i	0.430663	+	0.902513i	$0.358280\pi$
$284$	−6026.38	−	3872.92i	−1.25915	−	0.809209i
$285$	−425.379	+	931.449i	−0.0884114	+	0.193594i
$286$	−18.3845	−	5.39817i	−0.00380104	−	0.00111609i
$287$	3795.63	+	4380.39i	0.780659	+	0.900928i
$288$	−140.417	−	162.049i	−0.0287296	−	0.0331557i
$289$	3775.44	+	1108.57i	0.768458	+	0.225640i
$290$	−2.51706	+	5.51160i	−0.000509679	+	0.00111604i
$291$	156.445	+	100.541i	0.0315154	+	0.0202537i
$292$	−5508.18	+	1617.35i	−1.10391	+	0.324137i
$293$	1283.48	−	8926.82i	0.255911	−	1.77990i	−0.305331	−	0.952246i	$-0.598767\pi$
$293$	1283.48	−	8926.82i	0.255911	−	1.77990i	0.561241	−	0.827652i	$-0.310324\pi$
$294$	−6.97408	−	15.2711i	−0.00138346	−	0.00302935i
$295$	333.154	+	2317.13i	0.0657524	+	0.457318i
$296$	164.225	−	105.541i	0.0322479	−	0.0207244i
$297$	1830.32	−	2112.30i	0.357595	−	0.412687i
$298$	−24.2253			−0.00470918
$299$	873.745	+	1209.87i	0.168997	+	0.234008i
$300$	−369.540			−0.0711180
$301$	2892.04	−	3337.59i	0.553801	−	0.639121i
$302$	22.4316	−	14.4159i	0.00427416	−	0.00274683i
$303$	172.825	+	1202.03i	0.0327675	+	0.227903i
$304$	−2943.52	−	6445.41i	−0.555337	−	1.21602i
$305$	412.395	−	2868.27i	0.0774219	−	0.538481i
$306$	33.5259	−	9.84410i	0.00626324	−	0.00183905i
$307$	−3460.78	−	2224.11i	−0.643379	−	0.413474i	0.177863	−	0.984055i	$-0.443082\pi$
$307$	−3460.78	−	2224.11i	−0.643379	−	0.413474i	−0.821241	+	0.570581i	$0.806718\pi$
$308$	−2296.87	+	5029.44i	−0.424923	+	0.930452i
$309$	−829.140	−	243.457i	−0.152648	−	0.0448214i
$310$	35.3121	+	40.7523i	0.00646965	+	0.00746637i
$311$	3450.01	+	3981.52i	0.629042	+	0.725953i	0.977398	−	0.211409i	$-0.0678053\pi$
$311$	3450.01	+	3981.52i	0.629042	+	0.725953i	−0.348356	+	0.937362i	$0.613260\pi$
$312$	18.1825	+	5.33887i	0.00329930	+	0.000968762i
$313$	1966.35	−	4305.70i	0.355094	−	0.777548i	−0.644819	−	0.764336i	$-0.723067\pi$
$313$	1966.35	−	4305.70i	0.355094	−	0.777548i	0.999913	−	0.0132121i	$-0.00420568\pi$
$314$	−41.4887	−	26.6632i	−0.00745651	−	0.00479201i
$315$	2616.42	−	768.250i	0.467995	−	0.137416i
$316$	470.791	−	3274.43i	0.0838104	−	0.582914i
$317$	−4060.19	−	8890.57i	−0.719378	−	1.57522i	−0.814774	−	0.579778i	$-0.803139\pi$
$317$	−4060.19	−	8890.57i	−0.719378	−	1.57522i	0.0953965	−	0.995439i	$-0.469588\pi$
$318$	−5.40631	−	37.6017i	−0.000953368	−	0.00663082i
$319$	643.380	−	413.475i	0.112923	−	0.0725710i
$320$	1673.62	−	1931.46i	0.292370	−	0.337413i
$321$	3573.33			0.621320
$322$	−107.028	+	56.0823i	−0.0185231	+	0.00970603i
$323$	3465.60			0.597001
$324$	2430.05	−	2804.43i	0.416676	−	0.480870i
$325$	−284.548	+	182.868i	−0.0485658	+	0.0312113i
$326$	−9.62720	−	66.9587i	−0.00163559	−	0.0113758i
$327$	1235.50	+	2705.37i	0.208940	+	0.457515i
$328$	27.0321	−	188.012i	0.00455060	−	0.0316501i
$329$	−7188.97	+	2110.87i	−1.20468	+	0.353727i
$330$	−11.0096	−	7.07544i	−0.00183654	−	0.00118027i
$331$	1020.32	−	2234.18i	0.169431	−	0.371002i	−0.805801	−	0.592186i	$-0.798265\pi$
$331$	1020.32	−	2234.18i	0.169431	−	0.371002i	0.975232	+	0.221184i	$0.0709922\pi$
$332$	−7730.21	−	2269.79i	−1.27786	−	0.375214i
$333$	3978.41	+	4591.33i	0.654701	+	0.755565i
$334$	−15.3205	−	17.6808i	−0.00250988	−	0.00289655i
$335$	4074.16	+	1196.28i	0.664463	+	0.195104i
$336$	1135.34	−	2486.05i	0.184339	−	0.403646i
$337$	6808.43	+	4375.51i	1.10053	+	0.707268i	0.959210	−	0.282696i	$-0.0912287\pi$
$337$	6808.43	+	4375.51i	1.10053	+	0.707268i	0.141321	+	0.989964i	$0.454865\pi$
$338$	−91.5380	+	26.8780i	−0.0147308	+	0.00432535i
$339$	159.179	−	1107.12i	0.0255028	−	0.177376i
$340$	519.552	+	1137.66i	0.0828725	+	0.181466i
$341$	−968.619	−	6736.89i	−0.153823	−	1.06986i
$342$	−104.142	+	66.9283i	−0.0164660	+	0.0105821i
$343$	2290.42	−	2643.28i	0.360557	−	0.416105i
$344$	−144.727			−0.0226836
$345$	339.799	+	961.026i	0.0530266	+	0.149971i
$346$	145.275			0.0225724
$347$	4667.76	−	5386.89i	0.722129	−	0.833381i	−0.269433	−	0.963019i	$-0.586836\pi$
$347$	4667.76	−	5386.89i	0.722129	−	0.833381i	0.991561	+	0.129638i	$0.0413816\pi$
$348$	−318.111	+	204.438i	−0.0490016	+	0.0314914i
$349$	1434.55	+	9977.52i	0.220028	+	1.53033i	0.737924	+	0.674884i	$0.235806\pi$
$349$	1434.55	+	9977.52i	0.220028	+	1.53033i	−0.517896	+	0.855444i	$0.673285\pi$
$350$	−11.3765	−	24.9111i	−0.00173743	−	0.00380444i
$351$	−180.014	+	1252.02i	−0.0273744	+	0.190393i
$352$	260.797	−	76.5768i	0.0394901	−	0.0115953i
$353$	1567.18	+	1007.17i	0.236297	+	0.151859i	0.653431	−	0.756986i	$-0.273329\pi$
$353$	1567.18	+	1007.17i	0.236297	+	0.151859i	−0.417134	+	0.908845i	$0.636965\pi$
$354$	17.0283	−	37.2868i	0.00255662	−	0.00559822i
$355$	−4297.08	−	1261.74i	−0.642437	−	0.188637i
$356$	1939.12	+	2237.87i	0.288689	+	0.333165i
$357$	875.361	+	1010.22i	0.129773	+	0.149766i
$358$	166.153	+	48.7871i	0.0245293	+	0.00720245i
$359$	1561.28	−	3418.72i	0.229529	−	0.502599i	−0.759466	−	0.650547i	$-0.774540\pi$
$359$	1561.28	−	3418.72i	0.229529	−	0.502599i	0.988995	+	0.147948i	$0.0472669\pi$
$360$	−75.1773	−	48.3135i	−0.0110061	−	0.00707318i
$361$	−5199.84	+	1526.81i	−0.758105	+	0.222600i
$362$	17.2031	−	119.650i	0.00249771	−	0.0173720i
$363$	−335.705	−	735.091i	−0.0485397	−	0.106287i
$364$	−356.109	−	2476.79i	−0.0512780	−	0.356646i
$365$	−3019.22	+	1940.34i	−0.432968	+	0.278252i
$366$	−33.2282	+	38.3474i	−0.00474553	+	0.00547664i
$367$	3648.70			0.518967			0.259483	−	0.965748i	$-0.416448\pi$
$367$	3648.70			0.518967			0.259483	+	0.965748i	$0.416448\pi$
$368$	−6565.58	−	2577.85i	−0.930040	−	0.365163i
$369$	5911.23			0.833947
$370$	39.9550	−	46.1106i	0.00561396	−	0.00647885i
$371$	−8440.92	+	5424.65i	−1.18121	+	0.759120i
$372$	478.922	+	3330.97i	0.0667498	+	0.464255i
$373$	−4131.20	−	9046.07i	−0.573473	−	1.25573i	−0.944927	−	0.327280i	$-0.893868\pi$
$373$	−4131.20	−	9046.07i	−0.573473	−	1.25573i	0.371454	−	0.928451i	$-0.378859\pi$
$374$	−6.30348	+	43.8416i	−0.000871511	+	0.00606149i
$375$	−221.669	+	65.0879i	−0.0305252	+	0.00896300i
$376$	206.560	+	132.748i	0.0283312	+	0.0182073i
$377$	−143.781	+	314.836i	−0.0196422	+	0.0430103i
$378$	−98.2645	−	28.8531i	−0.0133708	−	0.00392603i
$379$	6383.48	+	7366.92i	0.865164	+	0.998452i	0.999971	+	0.00758061i	$0.00241301\pi$
$379$	6383.48	+	7366.92i	0.865164	+	0.998452i	−0.134807	+	0.990872i	$0.543042\pi$
$380$	−2901.73	−	3348.78i	−0.391726	−	0.452075i
$381$	−1007.81	−	295.920i	−0.135516	−	0.0397912i
$382$	69.8981	−	153.055i	0.00936203	−	0.0205000i
$383$	4155.13	+	2670.34i	0.554354	+	0.356261i	0.787630	−	0.616149i	$-0.211308\pi$
$383$	4155.13	+	2670.34i	0.554354	+	0.356261i	−0.233276	+	0.972411i	$0.574944\pi$
$384$	−171.922	+	50.4809i	−0.0228473	+	0.00670857i
$385$	−491.933	+	3421.47i	−0.0651201	+	0.452920i
$386$	−23.7226	−	51.9452i	−0.00312810	−	0.00684958i
$387$	−640.985	−	4458.15i	−0.0841940	−	0.585582i
$388$	−676.982	+	435.070i	−0.0885788	+	0.0569261i
$389$	8604.92	−	9930.60i	1.12156	−	1.29435i	0.170494	−	0.985359i	$-0.445464\pi$
$389$	8604.92	−	9930.60i	1.12156	−	1.29435i	0.951065	−	0.308990i	$-0.0999908\pi$
$390$	5.92275			0.000769000
$391$	2480.86	−	2397.25i	0.320876	−	0.310062i
$392$	145.315			0.0187232
$393$	−596.652	+	688.573i	−0.0765829	+	0.0883814i
$394$	2.98751	−	1.91996i	0.000382002	−	0.000245498i
$395$	−294.327	−	2047.09i	−0.0374917	−	0.260760i
$396$	2342.50	+	5129.36i	0.297260	+	0.650909i
$397$	−293.308	+	2040.00i	−0.0370799	+	0.257896i	−0.999926	−	0.0121539i	$-0.996131\pi$
$397$	−293.308	+	2040.00i	−0.0370799	+	0.257896i	0.962846	+	0.270050i	$0.0870403\pi$
$398$	−217.044	+	63.7299i	−0.0273353	+	0.00802636i
$399$	−3984.07	−	2560.40i	−0.499882	−	0.321254i
$400$	664.105	−	1454.19i	0.0830131	−	0.181773i
$401$	−968.456	−	284.364i	−0.120604	−	0.0354127i	0.220873	−	0.975302i	$-0.429109\pi$
$401$	−968.456	−	284.364i	−0.120604	−	0.0354127i	−0.341478	+	0.939890i	$0.610927\pi$
$402$	−48.6900	−	56.1912i	−0.00604088	−	0.00697155i
$403$	2017.11	+	2327.87i	0.249329	+	0.287741i
$404$	−5042.12	−	1480.50i	−0.620928	−	0.182321i
$405$	963.721	−	2110.25i	0.118241	−	0.258912i
$406$	−23.5746	−	15.1505i	−0.00288175	−	0.00185199i
$407$	−7389.13	+	2169.64i	−0.899915	+	0.264239i
$408$	6.23423	−	43.3600i	0.000756471	−	0.00526137i
$409$	2177.83	+	4768.78i	0.263293	+	0.576531i	0.994394	−	0.105738i	$-0.0337205\pi$
$409$	2177.83	+	4768.78i	0.263293	+	0.576531i	−0.731101	+	0.682269i	$0.760993\pi$
$410$	−8.44871	−	58.7621i	−0.00101769	−	0.00707818i
$411$	−1004.66	+	645.655i	−0.120575	+	0.0774885i
$412$	2448.78	−	2826.04i	0.292822	−	0.337935i
$413$	−10826.8			−1.28996
$414$	−28.2546	+	119.949i	−0.00335420	+	0.0142395i
$415$	−5036.76			−0.595771
$416$	−80.5541	+	92.9644i	−0.00949396	+	0.0109566i
$417$	2244.25	−	1442.29i	0.263553	−	0.169375i
$418$	−22.3327	−	155.328i	−0.00261323	−	0.0181754i
$419$	−1713.01	−	3750.96i	−0.199727	−	0.437342i	0.783093	−	0.621904i	$-0.213641\pi$
$419$	−1713.01	−	3750.96i	−0.199727	−	0.437342i	−0.982821	+	0.184562i	$0.940913\pi$
$420$	243.230	−	1691.70i	0.0282582	−	0.196540i
$421$	4625.90	−	1358.29i	0.535517	−	0.157242i	−0.00278155	−	0.999996i	$-0.500885\pi$
$421$	4625.90	−	1358.29i	0.535517	−	0.157242i	0.538299	+	0.842754i	$0.319067\pi$
$422$	173.134	+	111.266i	0.0199716	+	0.0128350i
$423$	−3174.32	+	6950.78i	−0.364871	+	0.798956i
$424$	315.500	+	92.6390i	0.0361368	+	0.0106107i
$425$	512.033	+	590.917i	0.0584405	+	0.0674440i
$426$	51.3541	+	59.2658i	0.00584064	+	0.00674046i
$427$	12859.1	+	3775.78i	1.45737	+	0.427922i
$428$	−6423.48	+	14065.4i	−0.725445	+	1.58850i
$429$	−628.896	−	404.167i	−0.0707771	−	0.0454857i
$430$	−43.4012	+	12.7437i	−0.00486742	+	0.00142920i
$431$	−875.498	+	6089.22i	−0.0978451	+	0.680528i	0.880576	+	0.473906i	$0.157156\pi$
$431$	−875.498	+	6089.22i	−0.0978451	+	0.680528i	−0.978421	+	0.206622i	$0.933753\pi$
$432$	−2483.50	−	5438.10i	−0.276591	−	0.605650i
$433$	−651.176	−	4529.03i	−0.0722714	−	0.502659i	−0.993518	−	0.113679i	$-0.963737\pi$
$433$	−651.176	−	4529.03i	−0.0722714	−	0.502659i	0.921246	−	0.388980i	$-0.127173\pi$
$434$	−209.801	+	134.831i	−0.0232045	+	0.0149126i
$435$	−154.811	+	178.662i	−0.0170635	+	0.0196924i
$436$	−12869.9			−1.41367
$437$	−6040.63	+	10625.5i	−0.661242	+	1.16313i
$438$	62.8438			0.00685569
$439$	1107.11	−	1277.68i	0.120364	−	0.138907i	−0.692370	−	0.721543i	$-0.743433\pi$
$439$	1107.11	−	1277.68i	0.120364	−	0.138907i	0.812733	+	0.582636i	$0.197979\pi$
$440$	95.2966	−	61.2434i	0.0103252	−	0.00663560i
$441$	643.590	+	4476.27i	0.0694946	+	0.483346i
$442$	−8.32704	−	18.2337i	−0.000896102	−	0.00196219i
$443$	−1425.32	+	9913.35i	−0.152865	+	1.06320i	0.758522	+	0.651648i	$0.225922\pi$
$443$	−1425.32	+	9913.35i	−0.152865	+	1.06320i	−0.911387	+	0.411551i	$0.864987\pi$
$444$	3653.46	−	1072.75i	0.390508	−	0.114664i
$445$	1557.35	+	1000.85i	0.165900	+	0.106617i
$446$	−111.091	+	243.256i	−0.0117944	+	0.0258262i
$447$	−906.887	−	266.286i	−0.0959603	−	0.0281765i
$448$	7740.41	+	8932.90i	0.816294	+	0.942054i
$449$	1291.51	+	1490.49i	0.135747	+	0.156660i	0.819553	−	0.573004i	$-0.194222\pi$
$449$	1291.51	+	1490.49i	0.135747	+	0.156660i	−0.683806	+	0.729664i	$0.739676\pi$
$450$	−26.7986	−	7.86878i	−0.00280733	−	0.000824307i
$451$	−3112.80	+	6816.08i	−0.325002	+	0.711656i
$452$	4071.72	+	2616.74i	0.423712	+	0.272303i
$453$	998.200	−	293.098i	0.103531	−	0.0303994i
$454$	−17.2740	+	120.143i	−0.00178570	+	0.0124198i
$455$	−649.855	−	1422.99i	−0.0669576	−	0.146617i
$456$	22.0874	+	153.621i	0.00226828	+	0.0157762i
$457$	−965.456	+	620.461i	−0.0988231	+	0.0635097i	−0.589119	−	0.808046i	$-0.700525\pi$
$457$	−965.456	+	620.461i	−0.0988231	+	0.0635097i	0.490296	+	0.871556i	$0.336889\pi$
$458$	−138.249	+	159.548i	−0.0141047	+	0.0162777i
$459$	2923.99			0.297342
$460$	−4393.65	−	390.027i	−0.445337	−	0.0395328i
$461$	−5230.90			−0.528476			−0.264238	−	0.964458i	$-0.585120\pi$
$461$	−5230.90			−0.528476			−0.264238	+	0.964458i	$0.585120\pi$
$462$	39.6369	−	45.7434i	0.00399151	−	0.00460644i
$463$	14096.0	−	9058.96i	1.41490	−	0.909300i	0.414898	−	0.909868i	$-0.363817\pi$
$463$	14096.0	−	9058.96i	1.41490	−	0.909300i	1.00000		0.000568262i	$0.000180883\pi$
$464$	−232.806	−	1619.20i	−0.0232926	−	0.162004i
$465$	873.973	+	1913.73i	0.0871603	+	0.190854i
$466$	9.75099	−	67.8197i	0.000969326	−	0.00674181i
$467$	9090.33	−	2669.16i	0.900751	−	0.264484i	0.201608	−	0.979466i	$-0.435383\pi$
$467$	9090.33	−	2669.16i	0.900751	−	0.264484i	0.699143	+	0.714982i	$0.253565\pi$
$468$	−2146.85	−	1379.70i	−0.212048	−	0.136275i
$469$	−8158.01	+	17863.6i	−0.803203	+	1.75877i
$470$	73.6329	+	21.6206i	0.00722645	+	0.00212188i
$471$	−1260.07	−	1454.20i	−0.123272	−	0.142263i
$472$	232.351	+	268.147i	0.0226585	+	0.0261493i
$473$	5478.10	+	1608.52i	0.532523	+	0.156363i
$474$	−15.0438	+	32.9413i	−0.00145777	+	0.00319207i
$475$	−2330.44	−	1497.68i	−0.225111	−	0.144670i
$476$	−5550.02	+	1629.63i	−0.534422	+	0.156920i
$477$	−1456.32	+	10128.9i	−0.139791	+	0.972266i
$478$	133.919	+	293.243i	0.0128145	+	0.0280598i
$479$	−1140.53	−	7932.56i	−0.108794	−	0.756676i	−0.969059	−	0.246830i	$-0.920611\pi$
$479$	−1140.53	−	7932.56i	−0.108794	−	0.756676i	0.860265	−	0.509847i	$-0.170298\pi$
$480$	−70.6806	+	45.4237i	−0.00672107	+	0.00431937i
$481$	2282.33	−	2633.95i	0.216352	−	0.249684i
$482$	295.091			0.0278859
$483$	−4623.10	+	923.011i	−0.435525	+	0.0869533i
$484$	3496.95			0.328414
$485$	−329.459	+	380.216i	−0.0308453	+	0.0355973i
$486$	−134.767	+	86.6094i	−0.0125785	+	0.00808371i
$487$	2580.90	+	17950.6i	0.240148	+	1.67026i	0.651395	+	0.758739i	$0.274184\pi$
$487$	2580.90	+	17950.6i	0.240148	+	1.67026i	−0.411247	+	0.911524i	$0.634907\pi$
$488$	−182.451	−	399.512i	−0.0169245	−	0.0370595i
$489$	375.614	−	2612.45i	0.0347359	−	0.241594i
$490$	43.5776	−	12.7955i	0.00401762	−	0.00117968i
$491$	−15319.8	−	9845.41i	−1.40809	−	0.904923i	−0.408120	−	0.912928i	$-0.633816\pi$
$491$	−15319.8	−	9845.41i	−1.40809	−	0.904923i	−0.999968	+	0.00800502i	$0.997452\pi$
$492$	1539.09	−	3370.13i	0.141031	−	0.308815i
$493$	767.681	+	225.412i	0.0701311	+	0.0205923i
$494$	46.5071	+	53.6720i	0.00423573	+	0.00488830i
$495$	2308.60	+	2664.26i	0.209624	+	0.241919i
$496$	−13968.5	−	4101.51i	−1.26452	−	0.371297i
$497$	8604.39	−	18841.0i	0.776578	−	1.70047i
$498$	74.1947	+	47.6820i	0.00667619	+	0.00429053i
$499$	−4153.41	+	1219.55i	−0.372609	+	0.109408i	−0.462675	−	0.886528i	$-0.653110\pi$
$499$	−4153.41	+	1219.55i	−0.372609	+	0.109408i	0.0900660	+	0.995936i	$0.471292\pi$
$500$	142.275	−	989.544i	0.0127255	−	0.0885075i
$501$	−379.182	−	830.292i	−0.0338135	−	0.0740413i
$502$	−24.9217	−	173.334i	−0.00221576	−	0.0154109i
$503$	15098.8	−	9703.44i	1.33842	−	0.860149i	0.341599	−	0.939846i	$-0.389032\pi$
$503$	15098.8	−	9703.44i	1.33842	−	0.860149i	0.996819	+	0.0796966i	$0.0253951\pi$
$504$	270.654	−	312.352i	0.0239204	−	0.0276056i
$505$	−3285.29			−0.289492
$506$	−123.431	−	95.7435i	−0.0108442	−	0.00841169i
$507$	−3722.21			−0.326054
$508$	2976.47	−	3435.02i	0.259959	−	0.300009i
$509$	7386.29	−	4746.88i	0.643205	−	0.413363i	−0.177972	−	0.984035i	$-0.556954\pi$
$509$	7386.29	−	4746.88i	0.643205	−	0.413363i	0.821178	+	0.570672i	$0.193317\pi$
$510$	−1.94847	−	13.5519i	−0.000169176	−	0.00117664i
$511$	−6895.35	−	15098.7i	−0.596932	−	1.30710i
$512$	137.913	−	959.204i	0.0119042	−	0.0827953i
$513$	−9939.84	+	2918.60i	−0.855467	+	0.251188i
$514$	−126.374	−	81.2157i	−0.0108446	−	0.00696940i
$515$	971.147	−	2126.51i	0.0830948	−	0.181952i
$516$	−2708.58	−	795.311i	−0.231083	−	0.0678520i
$517$	−6343.19	−	7320.43i	−0.539600	−	0.622732i
$518$	184.790	+	213.259i	0.0156741	+	0.0180889i
$519$	5438.46	+	1596.87i	0.459965	+	0.135058i
$520$	−21.2966	+	46.6331i	−0.00179600	+	0.00393269i
$521$	1934.66	+	1243.33i	0.162685	+	0.104552i	0.619450	−	0.785036i	$-0.287356\pi$
$521$	1934.66	+	1243.33i	0.162685	+	0.104552i	−0.456765	+	0.889587i	$0.650992\pi$
$522$	−27.4222	+	8.05189i	−0.00229931	+	0.000675138i
$523$	364.261	−	2533.49i	0.0304551	−	0.211820i	−0.968911	−	0.247408i	$-0.920421\pi$
$523$	364.261	−	2533.49i	0.0304551	−	0.211820i	0.999367	+	0.0355879i	$0.0113304\pi$
$524$	−1637.83	−	3586.35i	−0.136544	−	0.298989i
$525$	−152.062	−	1057.61i	−0.0126410	−	0.0879199i
$526$	−160.860	+	103.379i	−0.0133343	+	0.00856944i
$527$	4662.84	−	5381.20i	0.385420	−	0.444799i
$528$	3533.28			0.291224
$529$	3025.74	+	11784.8i	0.248685	+	0.968585i
$530$	102.770			0.00842275
$531$	−7230.90	+	8344.90i	−0.590950	+	0.681992i
$532$	17240.2	−	11079.6i	1.40499	−	0.902934i
$533$	−482.611	−	3356.64i	−0.0392199	−	0.272781i
$534$	−13.4659	−	29.4862i	−0.00109125	−	0.00238950i
$535$	−1375.75	+	9568.56i	−0.111176	+	0.773243i
$536$	617.502	−	181.315i	0.0497612	−	0.0146112i
$537$	5683.77	+	3652.74i	0.456746	+	0.293533i
$538$	70.9099	−	155.271i	0.00568242	−	0.0124428i
$539$	−5500.37	−	1615.05i	−0.439550	−	0.129064i
$540$	−2448.24	−	2825.42i	−0.195103	−	0.225161i
$541$	1002.28	+	1156.69i	0.0796513	+	0.0919225i	0.794176	−	0.607687i	$-0.207903\pi$
$541$	1002.28	+	1156.69i	0.0796513	+	0.0919225i	−0.714525	+	0.699610i	$0.753357\pi$
$542$	−82.8793	−	24.3355i	−0.00656821	−	0.00192860i
$543$	1959.20	−	4290.06i	0.154839	−	0.339050i
$544$	239.214	+	153.733i	0.0188533	+	0.0121163i
$545$	−7720.05	+	2266.81i	−0.606772	+	0.178164i
$546$	−3.89834	+	27.1135i	−0.000305556	+	0.00212519i
$547$	4678.70	+	10244.9i	0.365716	+	0.800807i	0.999625	+	0.0273986i	$0.00872232\pi$
$547$	4678.70	+	10244.9i	0.365716	+	0.800807i	−0.633908	+	0.773408i	$0.718550\pi$
$548$	−735.456	−	5115.21i	−0.0573305	−	0.398742i
$549$	11498.4	−	7389.60i	0.893883	−	0.574464i
$550$	23.1852	−	26.7571i	0.00179749	−	0.00207441i
$551$	−2834.66			−0.219166
$552$	122.075	+	94.6916i	0.00941279	+	0.00730135i
$553$	9565.03			0.735527
$554$	−213.644	+	246.558i	−0.0163842	+	0.0189084i
$555$	2002.59	−	1286.98i	0.153162	−	0.0984314i
$556$	1642.89	+	11426.6i	0.125313	+	0.871573i
$557$	856.796	+	1876.12i	0.0651770	+	0.142718i	0.939417	−	0.342776i	$-0.111367\pi$
$557$	856.796	+	1876.12i	0.0651770	+	0.142718i	−0.874240	+	0.485494i	$0.838640\pi$
$558$	−36.1971	+	251.756i	−0.00274614	+	0.0190998i
$559$	−2479.18	+	727.954i	−0.187582	+	0.0550790i
$560$	6219.96	+	3997.32i	0.469359	+	0.301639i
$561$	−717.884	+	1571.95i	−0.0540269	+	0.118302i
$562$	−76.0536	−	22.3313i	−0.00570841	−	0.00167614i
$563$	−13282.6	−	15328.9i	−0.994306	−	1.14749i	−0.989062	−	0.147504i	$-0.952876\pi$
$563$	−13282.6	−	15328.9i	−0.994306	−	1.14749i	−0.00524416	−	0.999986i	$-0.501669\pi$
$564$	3136.31	+	3619.50i	0.234153	+	0.270227i
$565$	2903.32	+	852.492i	0.216183	+	0.0634772i
$566$	29.7829	−	65.2155i	0.00221178	−	0.00484313i
$567$	9026.14	+	5800.75i	0.668540	+	0.429645i
$568$	−651.289	+	191.236i	−0.0481118	+	0.0141269i
$569$	879.548	−	6117.39i	0.0648024	−	0.450711i	−0.931425	−	0.363933i	$-0.881434\pi$
$569$	879.548	−	6117.39i	0.0648024	−	0.450711i	0.996228	−	0.0867781i	$-0.0276571\pi$
$570$	20.1506	+	44.1236i	0.00148073	+	0.00324234i
$571$	−716.071	−	4980.38i	−0.0524810	−	0.365013i	−0.999091	−	0.0426319i	$-0.986426\pi$
$571$	−716.071	−	4980.38i	−0.0524810	−	0.365013i	0.946610	−	0.322381i	$-0.104483\pi$
$572$	2721.41	−	1748.94i	0.198930	−	0.127844i
$573$	4299.06	−	4961.38i	0.313431	−	0.361719i
$574$	274.566			0.0199654
$575$	−2704.23	+	539.905i	−0.196129	+	0.0391576i
$576$	12054.7			0.872015
$577$	16465.7	−	19002.5i	1.18800	−	1.37103i	0.275836	−	0.961205i	$-0.411045\pi$
$577$	16465.7	−	19002.5i	1.18800	−	1.37103i	0.912165	−	0.409822i	$-0.134409\pi$
$578$	156.806	−	100.773i	0.0112842	−	0.00725193i
$579$	−317.082	−	2205.35i	−0.0227590	−	0.158292i
$580$	−424.963	−	930.539i	−0.0304235	−	0.0666181i
$581$	3315.19	−	23057.6i	0.236725	−	1.64646i
$582$	8.45257	−	2.48190i	0.000602011	−	0.000176766i
$583$	−10912.5	−	7013.02i	−0.775212	−	0.498199i
$584$	−225.970	+	494.805i	−0.0160115	+	0.0350602i
$585$	−1530.80	−	449.484i	−0.108190	−	0.0317673i
$586$	−279.769	−	322.871i	−0.0197221	−	0.0227605i
$587$	−7716.66	−	8905.50i	−0.542590	−	0.626183i	0.416550	−	0.909113i	$-0.363239\pi$
$587$	−7716.66	−	8905.50i	−0.542590	−	0.626183i	−0.959141	+	0.282930i	$0.908694\pi$
$588$	2719.59	+	798.543i	0.190738	+	0.0560057i
$589$	−10479.6	+	22947.1i	−0.733115	+	1.60530i
$590$	93.2895	+	59.9535i	0.00650960	+	0.00418347i
$591$	132.943	−	39.0357i	0.00925306	−	0.00271694i
$592$	−2344.26	+	16304.7i	−0.162751	+	1.13196i
$593$	−5715.17	−	12514.5i	−0.395774	−	0.866623i	−0.997681	−	0.0680577i	$-0.978320\pi$
$593$	−5715.17	−	12514.5i	−0.395774	−	0.866623i	0.601908	−	0.798566i	$-0.294407\pi$
$594$	−18.8425	−	131.053i	−0.00130154	−	0.00905244i
$595$	−3042.16	+	1955.08i	−0.209607	+	0.134706i
$596$	2678.40	−	3091.04i	0.184080	−	0.212439i
$597$	−8825.68			−0.605044
$598$	70.4185	+	6.25110i	0.00481543	+	0.000427469i
$599$	23169.5			1.58043			0.790216	−	0.612828i	$-0.209968\pi$
$599$	23169.5			1.58043			0.790216	+	0.612828i	$0.209968\pi$
$600$	−22.9305	+	26.4632i	−0.00156022	+	0.00180059i
$601$	13497.5	−	8674.32i	0.916098	−	0.588740i	0.00457487	−	0.999990i	$-0.498544\pi$
$601$	13497.5	−	8674.32i	0.916098	−	0.588740i	0.911523	+	0.411249i	$0.134907\pi$
$602$	−29.7726	−	207.073i	−0.00201568	−	0.0140194i
$603$	8320.08	+	18218.4i	0.561890	+	1.23037i
$604$	−640.679	+	4456.02i	−0.0431604	+	0.300187i
$605$	2097.65	−	615.927i	0.140962	−	0.0413900i
$606$	48.3944	+	31.1012i	0.00324404	+	0.00208482i
$607$	6891.91	−	15091.2i	0.460847	−	1.00911i	−0.526447	−	0.850208i	$-0.676476\pi$
$607$	6891.91	−	15091.2i	0.460847	−	1.00911i	0.987294	−	0.158905i	$-0.0507965\pi$
$608$	−966.634	−	283.829i	−0.0644773	−	0.0189322i
$609$	−715.993	−	826.300i	−0.0476412	−	0.0549809i
$610$	−89.8925	−	103.741i	−0.00596663	−	0.00688585i
$611$	4206.09	+	1235.02i	0.278495	+	0.0817735i
$612$	−2450.63	+	5366.14i	−0.161864	+	0.354433i
$613$	−15615.6	−	10035.5i	−1.02888	−	0.661224i	−0.0866711	−	0.996237i	$-0.527623\pi$
$613$	−15615.6	−	10035.5i	−1.02888	−	0.661224i	−0.942214	+	0.335013i	$0.891259\pi$
$614$	−186.982	+	54.9030i	−0.0122899	+	0.00360864i
$615$	329.634	−	2292.66i	0.0216132	−	0.150323i
$616$	217.640	+	476.565i	0.0142353	+	0.0311710i
$617$	3574.17	+	24858.9i	0.233210	+	1.62201i	0.684071	+	0.729416i	$0.260208\pi$
$617$	3574.17	+	24858.9i	0.233210	+	1.62201i	−0.450861	+	0.892594i	$0.648883\pi$
$618$	−34.4369	+	22.1313i	−0.00224151	+	0.00144053i
$619$	−12075.9	+	13936.3i	−0.784120	+	0.904923i	−0.997400	−	0.0720683i	$-0.977040\pi$
$619$	−12075.9	+	13936.3i	−0.784120	+	0.904923i	0.213280	+	0.976991i	$0.431585\pi$
$620$	−9103.97			−0.589717
$621$	−5096.59	+	8964.93i	−0.329338	+	0.579308i
$622$	249.564			0.0160878
$623$	−5606.78	+	6470.57i	−0.360563	+	0.416112i
$624$	−1345.19	+	864.500i	−0.0862991	+	0.0554610i
$625$	−88.9468	−	618.638i	−0.00569259	−	0.0395929i
$626$	−93.1476	−	203.965i	−0.00594716	−	0.0130225i
$627$	871.332	−	6060.25i	0.0554986	−	0.386002i
$628$	7989.18	−	2345.83i	0.507648	−	0.149059i
$629$	−6777.61	−	4355.71i	−0.429636	−	0.276110i
$630$	53.6610	−	117.501i	0.00339350	−	0.00743073i
$631$	−28160.5	−	8268.68i	−1.77663	−	0.521666i	−0.781828	−	0.623494i	$-0.785713\pi$
$631$	−28160.5	−	8268.68i	−1.77663	−	0.521666i	−0.994802	+	0.101828i	$0.967531\pi$
$632$	−205.272	−	236.896i	−0.0129197	−	0.0149102i
$633$	5258.31	+	6068.41i	0.330172	+	0.381039i
$634$	−444.239	−	130.440i	−0.0278281	−	0.00817106i
$635$	1180.42	−	2584.76i	0.0737693	−	0.161532i
$636$	5395.54	+	3467.50i	0.336395	+	0.216188i
$637$	2489.26	−	730.912i	0.154832	−	0.0454628i
$638$	5.15587	−	35.8599i	0.000319942	−	0.00222524i
$639$	−8775.32	−	19215.3i	−0.543265	−	1.18958i
$640$	−68.9854	−	479.804i	−0.00426076	−	0.0296342i
$641$	380.411	−	244.475i	0.0234405	−	0.0150643i	−0.528868	−	0.848704i	$-0.677383\pi$
$641$	380.411	−	244.475i	0.0234405	−	0.0150643i	0.552309	+	0.833640i	$0.313747\pi$
$642$	110.849	−	127.927i	0.00681445	−	0.00786429i
$643$	−6359.80			−0.390056			−0.195028	−	0.980798i	$-0.562480\pi$
$643$	−6359.80			−0.390056			−0.195028	+	0.980798i	$0.562480\pi$
$644$	4677.38	−	19856.8i	0.286203	−	1.21501i
$645$	−1764.83			−0.107736
$646$	107.508	−	124.070i	0.00654772	−	0.00755648i
$647$	−7368.52	+	4735.46i	−0.447738	+	0.287744i	−0.745015	−	0.667048i	$-0.767558\pi$
$647$	−7368.52	+	4735.46i	−0.447738	+	0.287744i	0.297277	+	0.954791i	$0.403921\pi$
$648$	−50.0403	−	348.038i	−0.00303359	−	0.0210991i
$649$	−5814.55	−	12732.1i	−0.351681	−	0.770075i
$650$	−2.28029	+	15.8598i	−0.000137600	+	0.000957032i
$651$	−9336.07	+	2741.32i	−0.562073	+	0.165039i
$652$	9608.02	+	6174.70i	0.577115	+	0.370889i
$653$	−10929.7	+	23932.6i	−0.654993	+	1.43423i	0.232122	+	0.972687i	$0.425433\pi$
$653$	−10929.7	+	23932.6i	−0.654993	+	1.43423i	−0.887115	+	0.461548i	$0.847294\pi$
$654$	135.181	+	39.6926i	0.00808254	+	0.00237325i
$655$	−1614.13	−	1862.80i	−0.0962888	−	0.111123i
$656$	10496.0	+	12113.0i	0.624693	+	0.720934i
$657$	−16242.7	−	4769.29i	−0.964519	−	0.283208i
$658$	−147.441	+	322.851i	−0.00873534	+	0.0191277i
$659$	12933.9	+	8312.09i	0.764540	+	0.491340i	0.863870	−	0.503715i	$-0.168034\pi$
$659$	12933.9	+	8312.09i	0.764540	+	0.491340i	−0.0993303	+	0.995055i	$0.531670\pi$
$660$	2120.04	−	622.499i	0.125034	−	0.0367132i
$661$	−2278.31	+	15846.0i	−0.134064	+	0.932433i	0.806117	+	0.591756i	$0.201565\pi$
$661$	−2278.31	+	15846.0i	−0.134064	+	0.932433i	−0.940180	+	0.340677i	$0.889344\pi$
$662$	−48.3333	−	105.835i	−0.00283765	−	0.00621359i
$663$	−111.301	−	774.118i	−0.00651974	−	0.0453458i
$664$	−642.212	+	412.725i	−0.0375342	+	0.0241217i
$665$	8390.07	−	9682.65i	0.489252	−	0.564627i
$666$	287.787			0.0167440
$667$	−2029.20	+	1960.81i	−0.117797	+	0.113827i
$668$	3949.84			0.228779
$669$	−6832.63	+	7885.28i	−0.394865	+	0.455699i
$670$	169.213	−	108.747i	0.00975713	−	0.00627053i
$671$	2465.77	+	17149.8i	0.141863	+	0.986680i
$672$	−161.422	−	353.464i	−0.00926633	−	0.0202904i
$673$	−2082.99	+	14487.5i	−0.119307	+	0.829798i	0.839015	+	0.544108i	$0.183132\pi$
$673$	−2082.99	+	14487.5i	−0.119307	+	0.829798i	−0.958322	+	0.285690i	$0.907777\pi$
$674$	367.852	−	108.011i	0.0210225	−	0.00617275i
$675$	−1966.23	−	1263.62i	−0.112119	−	0.0720544i
$676$	6691.11	−	14651.5i	0.380696	−	0.833608i
$677$	−6514.39	−	1912.80i	−0.369820	−	0.108589i	0.0915413	−	0.995801i	$-0.470821\pi$
$677$	−6514.39	−	1912.80i	−0.369820	−	0.108589i	−0.461361	+	0.887212i	$0.652639\pi$
$678$	−34.6974	−	40.0429i	−0.00196541	−	0.00226820i
$679$	−1523.73	−	1758.48i	−0.0861198	−	0.0993875i
$680$	113.708	+	33.3877i	0.00641250	+	0.00188288i
$681$	−1967.28	+	4307.74i	−0.110699	+	0.242398i
$682$	−271.232	−	174.310i	−0.0152288	−	0.00978693i
$683$	8397.01	−	2465.59i	0.470429	−	0.138130i	−0.0379216	−	0.999281i	$-0.512074\pi$
$683$	8397.01	−	2465.59i	0.470429	−	0.138130i	0.508350	+	0.861150i	$0.330256\pi$
$684$	2974.46	−	20687.8i	0.166274	−	1.15646i
$685$	−1342.12	−	2938.83i	−0.0748608	−	0.163922i
$686$	−23.5791	−	163.996i	−0.00131232	−	0.00912742i
$687$	−6929.19	+	4453.12i	−0.384811	+	0.247303i
$688$	7997.27	−	9229.34i	0.443159	−	0.511432i
$689$	5870.50			0.324598
$690$	44.9463	+	17.6473i	0.00247982	+	0.000973654i
$691$	11795.1			0.649361			0.324680	−	0.945824i	$-0.394743\pi$
$691$	11795.1			0.649361			0.324680	+	0.945824i	$0.394743\pi$
$692$	−16061.9	+	18536.5i	−0.882345	+	1.01828i
$693$	−13716.1	+	8814.83i	−0.751852	+	0.483186i
$694$	−48.0531	−	334.217i	−0.00262834	−	0.0182805i
$695$	2998.08	+	6564.88i	0.163631	+	0.358302i
$696$	−5.09923	+	35.4659i	−0.000277709	+	0.00193151i
$697$	−7521.59	+	2208.54i	−0.408752	+	0.120021i
$698$	401.702	+	258.158i	0.0217832	+	0.0139992i
$699$	1110.51	−	2431.68i	0.0600907	−	0.131580i
$700$	4436.35	+	1302.63i	0.239541	+	0.0703355i
$701$	11373.3	+	13125.5i	0.612789	+	0.707196i	0.974321	−	0.225164i	$-0.0722917\pi$
$701$	11373.3	+	13125.5i	0.612789	+	0.707196i	−0.361532	+	0.932360i	$0.617746\pi$
$702$	39.2388	+	45.2840i	0.00210965	+	0.00243467i
$703$	27387.6	+	8041.71i	1.46933	+	0.431435i
$704$	−6347.91	+	13900.0i	−0.339838	+	0.744141i
$705$	2518.83	+	1618.75i	0.134560	+	0.0864763i
$706$	84.6733	−	24.8623i	0.00451377	−	0.00132536i
$707$	2162.37	−	15039.6i	0.115027	−	0.800032i
$708$	2874.93	+	6295.23i	0.152608	+	0.334165i
$709$	−133.764	−	930.346i	−0.00708547	−	0.0492805i	0.985972	−	0.166911i	$-0.0533793\pi$
$709$	−133.764	−	930.346i	−0.00708547	−	0.0492805i	−0.993057	+	0.117630i	$0.962470\pi$
$710$	−178.472	+	114.697i	−0.00943370	+	0.00606267i
$711$	6388.20	−	7372.37i	0.336956	−	0.388868i
$712$	280.581			0.0147686
$713$	8371.29	+	23675.8i	0.439701	+	1.24357i
$714$	63.3213			0.00331896
$715$	1324.39	−	1528.43i	0.0692721	−	0.0799442i
$716$	−24595.3	+	15806.4i	−1.28375	+	0.825018i
$717$	1790.00	+	12449.7i	0.0932341	+	0.648457i
$718$	−73.9590	−	161.948i	−0.00384419	−	0.00841759i
$719$	169.270	−	1177.30i	0.00877982	−	0.0610650i	−0.984961	−	0.172780i	$-0.944725\pi$
$719$	169.270	−	1177.30i	0.00877982	−	0.0610650i	0.993740	+	0.111715i	$0.0356343\pi$
$720$	7235.11	−	2124.42i	0.374495	−	0.109962i
$721$	9095.69	+	5845.45i	0.469821	+	0.301936i
$722$	−106.645	+	233.521i	−0.00549713	+	0.0120370i
$723$	11046.9	+	3243.65i	0.568240	+	0.166850i
$724$	13364.8	+	15423.8i	0.686046	+	0.791739i
$725$	−418.812	−	483.335i	−0.0214542	−	0.0247595i
$726$	−36.7306	−	10.7851i	−0.00187769	−	0.000551339i
$727$	11164.2	−	24446.1i	0.569540	−	1.24712i	−0.377501	−	0.926009i	$-0.623217\pi$
$727$	11164.2	−	24446.1i	0.569540	−	1.24712i	0.947042	−	0.321110i	$-0.104056\pi$
$728$	−199.463	−	128.187i	−0.0101546	−	0.00652600i
$729$	6022.92	−	1768.49i	0.305996	−	0.0898485i
$730$	−24.1952	+	168.281i	−0.00122672	+	0.00853202i
$731$	2481.24	+	5433.16i	0.125543	+	0.274901i
$732$	−1219.17	−	8479.52i	−0.0615599	−	0.428159i
$733$	−23540.0	+	15128.2i	−1.18618	+	0.762310i	−0.976512	−	0.215463i	$-0.930874\pi$
$733$	−23540.0	+	15128.2i	−1.18618	+	0.762310i	−0.209666	+	0.977773i	$0.567238\pi$
$734$	113.188	−	130.626i	0.00569187	−	0.00656877i
$735$	1772.00			0.0889267
$736$	−888.300	+	465.466i	−0.0444880	+	0.0233116i
$737$	−25388.4			−1.26892
$738$	183.374	−	211.625i	0.00914648	−	0.0105556i
$739$	−14550.1	+	9350.76i	−0.724267	+	0.465458i	−0.850119	−	0.526591i	$-0.823470\pi$
$739$	−14550.1	+	9350.76i	−0.724267	+	0.465458i	0.125852	+	0.992049i	$0.459834\pi$
$740$	1465.99	+	10196.2i	0.0728253	+	0.506511i
$741$	1151.05	+	2520.45i	0.0570646	+	0.124954i
$742$	−67.6432	+	470.469i	−0.00334671	+	0.0232769i
$743$	−5594.41	+	1642.67i	−0.276230	+	0.0811085i	−0.416914	−	0.908946i	$-0.636888\pi$
$743$	−5594.41	+	1642.67i	−0.276230	+	0.0811085i	0.140683	+	0.990055i	$0.455070\pi$
$744$	268.252	+	172.395i	0.0132186	+	0.00849505i
$745$	1062.21	−	2325.91i	0.0522367	−	0.114382i
$746$	−452.009	−	132.722i	−0.0221840	−	0.00651380i
$747$	−15557.8	−	17954.7i	−0.762024	−	0.879422i
$748$	−4897.06	−	5651.51i	−0.239377	−	0.276256i
$749$	−42898.1	−	12596.0i	−2.09274	−	0.614484i
$750$	−4.54629	+	9.95498i	−0.000221343	+	0.000484673i
$751$	−20545.9	−	13204.0i	−0.998308	−	0.641574i	−0.0639664	−	0.997952i	$-0.520375\pi$
$751$	−20545.9	−	13204.0i	−0.998308	−	0.641574i	−0.934342	+	0.356378i	$0.884011\pi$
$752$	−19879.5	+	5837.14i	−0.964003	+	0.283057i
$753$	972.342	−	6762.79i	0.0470573	−	0.327291i
$754$	6.81102	+	14.9141i	0.000328969	+	0.000720342i
$755$	400.537	+	2785.80i	0.0193073	+	0.134285i
$756$	14545.8	−	9348.04i	0.699771	−	0.449715i
$757$	−16340.9	+	18858.4i	−0.784569	+	0.905441i	−0.997430	−	0.0716415i	$-0.977176\pi$
$757$	−16340.9	+	18858.4i	−0.784569	+	0.905441i	0.212861	+	0.977082i	$0.431722\pi$
$758$	461.764			0.0221267
$759$	−3568.29	−	4940.97i	−0.170646	−	0.236292i
$760$	−419.866			−0.0200397
$761$	11911.7	−	13746.9i	0.567411	−	0.654827i	−0.397439	−	0.917628i	$-0.630101\pi$
$761$	11911.7	−	13746.9i	0.567411	−	0.654827i	0.964850	+	0.262802i	$0.0846465\pi$
$762$	−41.8577	+	26.9003i	−0.00198995	+	0.00127887i
$763$	−5295.84	−	36833.4i	−0.251274	−	1.74765i
$764$

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0310213 - 0.0358005i) q^{2} +(1.55482 - 0.999222i) q^{3} +(1.13820 + 7.91635i) q^{4} +(2.07708 + 4.54816i) q^{5} +(0.0124599 - 0.0866606i) q^{6} +(-22.1880 + 6.51498i) q^{7} +(0.637525 + 0.409713i) q^{8} +(-9.79718 + 21.4528i) q^{9} +O(q^{10})\)	\(q+(0.0310213 - 0.0358005i) q^{2} +(1.55482 - 0.999222i) q^{3} +(1.13820 + 7.91635i) q^{4} +(2.07708 + 4.54816i) q^{5} +(0.0124599 - 0.0866606i) q^{6} +(-22.1880 + 6.51498i) q^{7} +(0.637525 + 0.409713i) q^{8} +(-9.79718 + 21.4528i) q^{9} +(0.227260 + 0.0667296i) q^{10} +(-19.5776 - 22.5937i) q^{11} +(9.67989 + 11.1712i) q^{12} +(12.9817 + 3.81176i) q^{13} +(-0.455061 + 0.996445i) q^{14} +(7.77410 + 4.99611i) q^{15} +(-61.3559 + 18.0157i) q^{16} +(4.45101 - 30.9575i) q^{17} +(0.464101 + 1.01624i) q^{18} +(15.7696 + 109.680i) q^{19} +(-33.6407 + 21.6196i) q^{20} +(-27.9884 + 32.3004i) q^{21} -1.41619 q^{22} +(87.1572 + 67.6064i) q^{23} +1.40063 q^{24} +(-16.3715 + 18.8937i) q^{25} +(0.539171 - 0.346504i) q^{26} +(13.3051 + 92.5388i) q^{27} +(-76.8292 - 168.233i) q^{28} +(-3.64066 + 25.3214i) q^{29} +(0.420026 - 0.123331i) q^{30} +(191.522 + 123.084i) q^{31} +(-3.77687 + 8.27020i) q^{32} +(-53.0158 - 15.5668i) q^{33} +(-0.970217 - 1.11969i) q^{34} +(-75.7173 - 87.3824i) q^{35} +(-180.979 - 53.1403i) q^{36} +(107.010 - 234.319i) q^{37} +(4.41579 + 2.83786i) q^{38} +(23.9929 - 7.04496i) q^{39} +(-0.539251 + 3.75057i) q^{40} +(-104.122 - 227.995i) q^{41} +(0.288132 + 2.00400i) q^{42} +(-160.659 + 103.249i) q^{43} +(156.577 - 180.699i) q^{44} -117.920 q^{45} +(5.12408 - 1.02303i) q^{46} +324.003 q^{47} +(-77.3957 + 89.3194i) q^{48} +(161.312 - 103.669i) q^{49} +(0.168539 + 1.17222i) q^{50} +(-24.0129 - 52.5809i) q^{51} +(-15.3995 + 107.106i) q^{52} +(416.321 - 122.243i) q^{53} +(3.72568 + 2.39435i) q^{54} +(62.0958 - 135.971i) q^{55} +(-16.8147 - 4.93723i) q^{56} +(134.113 + 154.775i) q^{57} +(0.793580 + 0.915840i) q^{58} +(449.227 + 131.905i) q^{59} +(-30.7025 + 67.2291i) q^{60} +(-487.551 - 313.330i) q^{61} +(10.3478 - 3.03837i) q^{62} +(77.6150 - 539.824i) q^{63} +(-212.335 - 464.948i) q^{64} +(9.62739 + 66.9600i) q^{65} +(-2.20192 + 1.41509i) q^{66} +(556.128 - 641.806i) q^{67} +250.136 q^{68} +(203.068 + 18.0264i) q^{69} -5.47719 q^{70} +(-586.557 + 676.923i) q^{71} +(-15.0355 + 9.66270i) q^{72} +(102.152 + 710.485i) q^{73} +(-5.06915 - 11.0999i) q^{74} +(-6.57572 + 45.7352i) q^{75} +(-850.316 + 249.675i) q^{76} +(581.585 + 373.762i) q^{77} +(0.492079 - 1.07750i) q^{78} +(-396.873 - 116.533i) q^{79} +(-209.379 - 241.636i) q^{80} +(-303.842 - 350.652i) q^{81} +(-11.3923 - 3.34509i) q^{82} +(-418.469 + 916.320i) q^{83} +(-287.557 - 184.802i) q^{84} +(150.045 - 44.0571i) q^{85} +(-1.28748 + 8.95461i) q^{86} +(19.6411 + 43.0080i) q^{87} +(-3.22426 - 22.4252i) q^{88} +(311.469 - 200.169i) q^{89} +(-3.65805 + 4.22161i) q^{90} -312.870 q^{91} +(-435.994 + 766.916i) q^{92} +420.771 q^{93} +(10.0510 - 11.5995i) q^{94} +(-466.087 + 299.536i) q^{95} +(2.39141 + 16.6326i) q^{96} +(41.7989 + 91.5267i) q^{97} +(1.29271 - 8.99100i) q^{98} +(676.505 - 198.640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9}+O(q^{10}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9} - 10 q^{10} + 2 q^{11} - 57 q^{12} + 34 q^{13} - 154 q^{14} + 30 q^{15} + 16 q^{16} + 252 q^{17} - 33 q^{18} - 160 q^{19} - 200 q^{20} - 684 q^{21} - 704 q^{22} + 127 q^{23} - 3090 q^{24} - 275 q^{25} - 567 q^{26} + 384 q^{27} - 188 q^{28} + 340 q^{29} - 15 q^{30} + 582 q^{31} - 1364 q^{32} + 1760 q^{33} + 1819 q^{34} + 665 q^{35} + 2794 q^{36} + 312 q^{37} + 3123 q^{38} - 1560 q^{39} - 1205 q^{40} + 1324 q^{41} + 1454 q^{42} - 1740 q^{43} - 369 q^{44} + 3730 q^{45} - 4322 q^{46} - 2858 q^{47} - 2686 q^{48} + 2015 q^{49} - 325 q^{50} - 1426 q^{51} + 1717 q^{52} + 882 q^{53} + 2541 q^{54} + 450 q^{55} + 7755 q^{56} + 3688 q^{57} + 6622 q^{58} + 2605 q^{59} + 1530 q^{60} - 104 q^{61} - 9360 q^{62} - 7618 q^{63} + 3483 q^{64} + 170 q^{65} - 1766 q^{66} - 166 q^{67} - 5018 q^{68} - 1194 q^{69} - 770 q^{70} - 1222 q^{71} + 3303 q^{72} - 922 q^{73} + 1245 q^{74} + 150 q^{75} + 1360 q^{76} - 3093 q^{77} - 1600 q^{78} + 2448 q^{79} + 2115 q^{80} - 1371 q^{81} + 6609 q^{82} + 6704 q^{83} + 3894 q^{84} - 720 q^{85} - 5074 q^{86} - 6324 q^{87} + 1918 q^{88} - 5380 q^{89} - 165 q^{90} + 7828 q^{91} - 16225 q^{92} - 24948 q^{93} - 16490 q^{94} + 685 q^{95} + 675 q^{96} - 4400 q^{97} + 8790 q^{98} - 3626 q^{99}+O(q^{100}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9 - 10 * q^10 + 2 * q^11 - 57 * q^12 + 34 * q^13 - 154 * q^14 + 30 * q^15 + 16 * q^16 + 252 * q^17 - 33 * q^18 - 160 * q^19 - 200 * q^20 - 684 * q^21 - 704 * q^22 + 127 * q^23 - 3090 * q^24 - 275 * q^25 - 567 * q^26 + 384 * q^27 - 188 * q^28 + 340 * q^29 - 15 * q^30 + 582 * q^31 - 1364 * q^32 + 1760 * q^33 + 1819 * q^34 + 665 * q^35 + 2794 * q^36 + 312 * q^37 + 3123 * q^38 - 1560 * q^39 - 1205 * q^40 + 1324 * q^41 + 1454 * q^42 - 1740 * q^43 - 369 * q^44 + 3730 * q^45 - 4322 * q^46 - 2858 * q^47 - 2686 * q^48 + 2015 * q^49 - 325 * q^50 - 1426 * q^51 + 1717 * q^52 + 882 * q^53 + 2541 * q^54 + 450 * q^55 + 7755 * q^56 + 3688 * q^57 + 6622 * q^58 + 2605 * q^59 + 1530 * q^60 - 104 * q^61 - 9360 * q^62 - 7618 * q^63 + 3483 * q^64 + 170 * q^65 - 1766 * q^66 - 166 * q^67 - 5018 * q^68 - 1194 * q^69 - 770 * q^70 - 1222 * q^71 + 3303 * q^72 - 922 * q^73 + 1245 * q^74 + 150 * q^75 + 1360 * q^76 - 3093 * q^77 - 1600 * q^78 + 2448 * q^79 + 2115 * q^80 - 1371 * q^81 + 6609 * q^82 + 6704 * q^83 + 3894 * q^84 - 720 * q^85 - 5074 * q^86 - 6324 * q^87 + 1918 * q^88 - 5380 * q^89 - 165 * q^90 + 7828 * q^91 - 16225 * q^92 - 24948 * q^93 - 16490 * q^94 + 685 * q^95 + 675 * q^96 - 4400 * q^97 + 8790 * q^98 - 3626 * q^99

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