LMFDB - Embedded newform 115.4.g.a.36.8

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			36.8
Character	$\chi$	$=$	115.36
Dual form			115.4.g.a.16.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.784981 + 0.905916i) q^{2} +(6.23621 + 4.00777i) q^{3} +(0.934030 - 6.49632i) q^{4} +(2.07708 - 4.54816i) q^{5} +(1.26460 + 8.79550i) q^{6} +(8.12768 + 2.38650i) q^{7} +(14.6856 - 9.43786i) q^{8} +(11.6119 + 25.4265i) q^{9} +O(q^{10})$	\(q+(0.784981 + 0.905916i) q^{2} +(6.23621 + 4.00777i) q^{3} +(0.934030 - 6.49632i) q^{4} +(2.07708 - 4.54816i) q^{5} +(1.26460 + 8.79550i) q^{6} +(8.12768 + 2.38650i) q^{7} +(14.6856 - 9.43786i) q^{8} +(11.6119 + 25.4265i) q^{9} +(5.75072 - 1.68856i) q^{10} +(13.9544 - 16.1043i) q^{11} +(31.8605 - 36.7690i) q^{12} +(-12.7635 + 3.74769i) q^{13} +(4.21810 + 9.23635i) q^{14} +(31.1810 - 20.0388i) q^{15} +(-30.3003 - 8.89698i) q^{16} +(3.21473 + 22.3589i) q^{17} +(-13.9192 + 30.4787i) q^{18} +(-16.8267 + 117.032i) q^{19} +(-27.6062 - 17.7415i) q^{20} +(41.1213 + 47.4566i) q^{21} +25.5431 q^{22} +(-109.364 - 14.3672i) q^{23} +129.407 q^{24} +(-16.3715 - 18.8937i) q^{25} +(-13.4142 - 8.62077i) q^{26} +(-1.00488 + 6.98911i) q^{27} +(23.0950 - 50.5709i) q^{28} +(39.3749 + 273.859i) q^{29} +(42.6300 + 12.5173i) q^{30} +(53.4229 - 34.3328i) q^{31} +(-73.7398 - 161.468i) q^{32} +(151.565 - 44.5035i) q^{33} +(-17.7318 + 20.4636i) q^{34} +(27.7360 - 32.0090i) q^{35} +(176.024 - 51.6855i) q^{36} +(-81.0712 - 177.521i) q^{37} +(-119.230 + 76.6246i) q^{38} +(-94.6156 - 27.7816i) q^{39} +(-12.4218 - 86.3956i) q^{40} +(11.4634 - 25.1013i) q^{41} +(-10.7122 + 74.5050i) q^{42} +(24.8094 + 15.9440i) q^{43} +(-91.5847 - 105.694i) q^{44} +139.763 q^{45} +(-72.8335 - 110.353i) q^{46} -313.776 q^{47} +(-153.302 - 176.920i) q^{48} +(-228.186 - 146.646i) q^{49} +(4.26482 - 29.6624i) q^{50} +(-69.5617 + 152.319i) q^{51} +(12.4247 + 86.4160i) q^{52} +(22.8416 + 6.70690i) q^{53} +(-7.12036 + 4.57598i) q^{54} +(-44.2604 - 96.9168i) q^{55} +(141.883 - 41.6607i) q^{56} +(-573.974 + 662.401i) q^{57} +(-217.184 + 250.644i) q^{58} +(-630.788 + 185.216i) q^{59} +(-101.055 - 221.279i) q^{60} +(379.558 - 243.927i) q^{61} +(73.0386 + 21.4461i) q^{62} +(33.6973 + 234.370i) q^{63} +(-16.5571 + 36.2550i) q^{64} +(-9.46558 + 65.8345i) q^{65} +(159.292 + 102.371i) q^{66} +(187.329 + 216.189i) q^{67} +148.253 q^{68} +(-624.439 - 527.904i) q^{69} +50.7697 q^{70} +(-462.390 - 533.626i) q^{71} +(410.499 + 263.812i) q^{72} +(112.766 - 784.304i) q^{73} +(97.1799 - 212.794i) q^{74} +(-26.3745 - 183.439i) q^{75} +(744.563 + 218.623i) q^{76} +(151.850 - 97.5881i) q^{77} +(-49.1036 - 107.522i) q^{78} +(254.724 - 74.7937i) q^{79} +(-103.401 + 119.331i) q^{80} +(459.958 - 530.819i) q^{81} +(31.7382 - 9.31918i) q^{82} +(167.064 + 365.818i) q^{83} +(346.702 - 222.812i) q^{84} +(108.369 + 31.8201i) q^{85} +(5.03094 + 34.9910i) q^{86} +(-852.011 + 1865.64i) q^{87} +(52.9393 - 368.201i) q^{88} +(1269.69 + 815.981i) q^{89} +(109.711 + 126.613i) q^{90} -112.681 q^{91} +(-195.484 + 697.047i) q^{92} +470.754 q^{93} +(-246.308 - 284.255i) q^{94} +(497.332 + 319.616i) q^{95} +(187.268 - 1302.48i) q^{96} +(-136.810 + 299.571i) q^{97} +(-46.2725 - 321.832i) q^{98} +(571.513 + 167.811i) 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 $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.784981	+	0.905916i	0.277533	+	0.320290i	0.877353	−	0.479845i	$-0.159307\pi$
$2$	0.784981	+	0.905916i	0.277533	+	0.320290i	−0.599821	+	0.800134i	$0.704762\pi$
$3$	6.23621	+	4.00777i	1.20016	+	0.771295i	0.978984	−	0.203939i	$-0.0653743\pi$
$3$	6.23621	+	4.00777i	1.20016	+	0.771295i	0.221175	+	0.975234i	$0.429011\pi$
$4$	0.934030	−	6.49632i	0.116754	−	0.812040i
$5$	2.07708	−	4.54816i	0.185779	−	0.406800i
$5$	2.07708	−	4.54816i	0.185779	−	0.406800i
$6$	1.26460	+	8.79550i	0.0860453	+	0.598458i
$7$	8.12768	+	2.38650i	0.438853	+	0.128859i	0.493693	−	0.869636i	$-0.335647\pi$
$7$	8.12768	+	2.38650i	0.438853	+	0.128859i	−0.0548398	+	0.998495i	$0.517465\pi$
$8$	14.6856	−	9.43786i	0.649018	−	0.417098i
$9$	11.6119	+	25.4265i	0.430070	+	0.941722i
$10$	5.75072	−	1.68856i	0.181854	−	0.0533970i
$11$	13.9544	−	16.1043i	0.382493	−	0.441420i	−0.531557	−	0.847023i	$-0.678393\pi$
$11$	13.9544	−	16.1043i	0.382493	−	0.441420i	0.914050	+	0.405602i	$0.132938\pi$
$12$	31.8605	−	36.7690i	0.766446	−	0.884525i
$13$	−12.7635	+	3.74769i	−0.272304	+	0.0799556i	−0.415034	−	0.909806i	$-0.636230\pi$
$13$	−12.7635	+	3.74769i	−0.272304	+	0.0799556i	0.142730	+	0.989762i	$0.454412\pi$
$14$	4.21810	+	9.23635i	0.0805239	+	0.176323i
$15$	31.1810	−	20.0388i	0.536727	−	0.344934i
$16$	−30.3003	−	8.89698i	−0.473443	−	0.139015i
$17$	3.21473	+	22.3589i	0.0458639	+	0.318991i	0.999819	+	0.0190402i	$0.00606104\pi$
$17$	3.21473	+	22.3589i	0.0458639	+	0.318991i	−0.953955	+	0.299950i	$0.903030\pi$
$18$	−13.9192	+	30.4787i	−0.182265	+	0.399106i
$19$	−16.8267	+	117.032i	−0.203174	+	1.41311i	0.591613	+	0.806222i	$0.298491\pi$
$19$	−16.8267	+	117.032i	−0.203174	+	1.41311i	−0.794788	+	0.606888i	$0.792418\pi$
$20$	−27.6062	−	17.7415i	−0.308647	−	0.198356i
$21$	41.1213	+	47.4566i	0.427305	+	0.493137i
$22$	25.5431			0.247537
$23$	−109.364	−	14.3672i	−0.991481	−	0.130251i
$23$	−109.364	−	14.3672i	−0.991481	−	0.130251i
$24$	129.407			1.10063
$25$	−16.3715	−	18.8937i	−0.130972	−	0.151150i
$26$	−13.4142	−	8.62077i	−0.101182	−	0.0650258i
$27$	−1.00488	+	6.98911i	−0.00716258	+	0.0498169i
$28$	23.0950	−	50.5709i	0.155876	−	0.341322i
$29$	39.3749	+	273.859i	0.252129	+	1.75360i	0.585382	+	0.810758i	$0.300945\pi$
$29$	39.3749	+	273.859i	0.252129	+	1.75360i	−0.333253	+	0.942837i	$0.608146\pi$
$30$	42.6300	+	12.5173i	0.259438	+	0.0761779i
$31$	53.4229	−	34.3328i	0.309517	−	0.198915i	−0.376655	−	0.926354i	$-0.622926\pi$
$31$	53.4229	−	34.3328i	0.309517	−	0.198915i	0.686173	+	0.727439i	$0.259289\pi$
$32$	−73.7398	−	161.468i	−0.407359	−	0.891991i
$33$	151.565	−	44.5035i	0.799518	−	0.234760i
$34$	−17.7318	+	20.4636i	−0.0894407	+	0.103220i
$35$	27.7360	−	32.0090i	0.133950	−	0.154586i
$36$	176.024	−	51.6855i	0.814928	−	0.239285i
$37$	−81.0712	−	177.521i	−0.360217	−	0.788765i	−0.999799	−	0.0200421i	$-0.993620\pi$
$37$	−81.0712	−	177.521i	−0.360217	−	0.788765i	0.639582	−	0.768723i	$-0.279107\pi$
$38$	−119.230	+	76.6246i	−0.508992	+	0.327109i
$39$	−94.6156	−	27.7816i	−0.388477	−	0.114067i
$40$	−12.4218	−	86.3956i	−0.0491015	−	0.341508i
$41$	11.4634	−	25.1013i	0.0436654	−	0.0956138i	−0.886542	−	0.462648i	$-0.846899\pi$
$41$	11.4634	−	25.1013i	0.0436654	−	0.0956138i	0.930208	+	0.367034i	$0.119627\pi$
$42$	−10.7122	+	74.5050i	−0.0393554	+	0.273723i
$43$	24.8094	+	15.9440i	0.0879859	+	0.0565451i	0.583894	−	0.811830i	$-0.301528\pi$
$43$	24.8094	+	15.9440i	0.0879859	+	0.0565451i	−0.495908	+	0.868375i	$0.665165\pi$
$44$	−91.5847	−	105.694i	−0.313793	−	0.362137i
$45$	139.763			0.462991
$46$	−72.8335	−	110.353i	−0.233450	−	0.353710i
$47$	−313.776			−0.973808			−0.486904	−	0.873456i	$-0.661874\pi$
$47$	−313.776			−0.973808			−0.486904	+	0.873456i	$0.661874\pi$
$48$	−153.302	−	176.920i	−0.460985	−	0.532005i
$49$	−228.186	−	146.646i	−0.665266	−	0.427540i
$50$	4.26482	−	29.6624i	0.0120627	−	0.0838981i
$51$	−69.5617	+	152.319i	−0.190992	+	0.418214i
$52$	12.4247	+	86.4160i	0.0331347	+	0.230457i
$53$	22.8416	+	6.70690i	0.0591988	+	0.0173823i	0.311198	−	0.950345i	$-0.399270\pi$
$53$	22.8416	+	6.70690i	0.0591988	+	0.0173823i	−0.251999	+	0.967727i	$0.581088\pi$
$54$	−7.12036	+	4.57598i	−0.0179437	+	0.0115317i
$55$	−44.2604	−	96.9168i	−0.108510	−	0.237605i
$56$	141.883	−	41.6607i	0.338570	−	0.0994132i
$57$	−573.974	+	662.401i	−1.33377	+	1.53925i
$58$	−217.184	+	250.644i	−0.491684	+	0.567434i
$59$	−630.788	+	185.216i	−1.39189	+	0.408696i	−0.889892	−	0.456171i	$-0.849220\pi$
$59$	−630.788	+	185.216i	−1.39189	+	0.408696i	−0.502000	+	0.864868i	$0.667402\pi$
$60$	−101.055	−	221.279i	−0.217435	−	0.476116i
$61$	379.558	−	243.927i	0.796679	−	0.511995i	−0.0778513	−	0.996965i	$-0.524806\pi$
$61$	379.558	−	243.927i	0.796679	−	0.511995i	0.874531	+	0.484970i	$0.161170\pi$
$62$	73.0386	+	21.4461i	0.149611	+	0.0439299i
$63$	33.6973	+	234.370i	0.0673884	+	0.468696i
$64$	−16.5571	+	36.2550i	−0.0323381	+	0.0708106i
$65$	−9.46558	+	65.8345i	−0.0180625	+	0.125627i
$66$	159.292	+	102.371i	0.297083	+	0.190924i
$67$	187.329	+	216.189i	0.341580	+	0.394204i	0.900384	−	0.435095i	$-0.143285\pi$
$67$	187.329	+	216.189i	0.341580	+	0.394204i	−0.558805	+	0.829299i	$0.688740\pi$
$68$	148.253			0.264388
$69$	−624.439	−	527.904i	−1.08947	−	0.921047i
$70$	50.7697			0.0866877
$71$	−462.390	−	533.626i	−0.772895	−	0.891969i	0.223680	−	0.974663i	$-0.428193\pi$
$71$	−462.390	−	533.626i	−0.772895	−	0.891969i	−0.996575	+	0.0826938i	$0.973648\pi$
$72$	410.499	+	263.812i	0.671914	+	0.431813i
$73$	112.766	−	784.304i	0.180798	−	1.25748i	−0.674084	−	0.738655i	$-0.735461\pi$
$73$	112.766	−	784.304i	0.180798	−	1.25748i	0.854882	−	0.518823i	$-0.173630\pi$
$74$	97.1799	−	212.794i	0.152661	−	0.334282i
$75$	−26.3745	−	183.439i	−0.0406062	−	0.282422i
$76$	744.563	+	218.623i	1.12378	+	0.329972i
$77$	151.850	−	97.5881i	0.224739	−	0.144431i
$78$	−49.1036	−	107.522i	−0.0712806	−	0.156083i
$79$	254.724	−	74.7937i	0.362768	−	0.106518i	−0.0952686	−	0.995452i	$-0.530371\pi$
$79$	254.724	−	74.7937i	0.362768	−	0.106518i	0.458037	+	0.888933i	$0.348553\pi$
$80$	−103.401	+	119.331i	−0.144507	+	0.166770i
$81$	459.958	−	530.819i	0.630943	−	0.728147i
$82$	31.7382	−	9.31918i	0.0427427	−	0.0125504i
$83$	167.064	+	365.818i	0.220935	+	0.483780i	0.987348	−	0.158568i	$-0.0506877\pi$
$83$	167.064	+	365.818i	0.220935	+	0.483780i	−0.766413	+	0.642348i	$0.777960\pi$
$84$	346.702	−	222.812i	0.450336	−	0.289413i
$85$	108.369	+	31.8201i	0.138286	+	0.0406044i
$86$	5.03094	+	34.9910i	0.00630814	+	0.0438741i
$87$	−852.011	+	1865.64i	−1.04994	+	2.29906i
$88$	52.9393	−	368.201i	0.0641289	−	0.446027i
$89$	1269.69	+	815.981i	1.51221	+	0.971841i	0.993117	+	0.117125i	$0.0373679\pi$
$89$	1269.69	+	815.981i	1.51221	+	0.971841i	0.519097	+	0.854716i	$0.326268\pi$
$90$	109.711	+	126.613i	0.128495	+	0.148291i
$91$	−112.681			−0.129804
$92$	−195.484	+	697.047i	−0.221528	+	0.789915i
$93$	470.754			0.524892
$94$	−246.308	−	284.255i	−0.270263	−	0.311901i
$95$	497.332	+	319.616i	0.537107	+	0.345178i
$96$	187.268	−	1302.48i	0.199093	−	1.38472i
$97$	−136.810	+	299.571i	−0.143205	+	0.313576i	−0.967620	−	0.252410i	$-0.918777\pi$
$97$	−136.810	+	299.571i	−0.143205	+	0.313576i	0.824415	+	0.565985i	$0.191504\pi$
$98$	−46.2725	−	321.832i	−0.0476962	−	0.331734i
$99$	571.513	+	167.811i	0.580194	+	0.170360i
$100$	−138.031	+	88.7073i	−0.138031	+	0.0887073i
$101$	−164.274	−	359.711i	−0.161841	−	0.354382i	0.811287	−	0.584648i	$-0.198767\pi$
$101$	−164.274	−	359.711i	−0.161841	−	0.354382i	−0.973128	+	0.230267i	$0.926040\pi$
$102$	−192.593	+	56.5503i	−0.186956	+	0.0548953i
$103$	−268.101	+	309.405i	−0.256474	+	0.295986i	−0.869355	−	0.494189i	$-0.835465\pi$
$103$	−268.101	+	309.405i	−0.256474	+	0.295986i	0.612881	+	0.790175i	$0.290011\pi$
$104$	−152.069	+	175.497i	−0.143381	+	0.165470i
$105$	301.252	−	88.4556i	0.279992	−	0.0822132i
$106$	11.8543	+	25.9574i	0.0108622	+	0.0237849i
$107$	−1012.54	+	650.718i	−0.914819	+	0.587918i	−0.911150	−	0.412075i	$-0.864804\pi$
$107$	−1012.54	+	650.718i	−0.914819	+	0.587918i	−0.00366893	+	0.999993i	$0.501168\pi$
$108$	44.4649	+	13.0561i	0.0396170	+	0.0116326i
$109$	−1.22232	−	8.50145i	−0.00107411	−	0.00747056i	0.989277	−	0.146049i	$-0.0466558\pi$
$109$	−1.22232	−	8.50145i	−0.00107411	−	0.00747056i	−0.990351	+	0.138579i	$0.955747\pi$
$110$	53.0549	−	116.174i	0.0459872	−	0.100698i
$111$	205.887	−	1431.97i	0.176053	−	1.22448i
$112$	−225.039	−	144.624i	−0.189859	−	0.122015i
$113$	1321.55	+	1525.15i	1.10018	+	1.26968i	0.960136	+	0.279533i	$0.0901798\pi$
$113$	1321.55	+	1525.15i	1.10018	+	1.26968i	0.140047	+	0.990145i	$0.455275\pi$
$114$	−1050.64			−0.863169
$115$	−292.503	+	467.565i	−0.237183	+	0.379136i
$116$	1815.85			1.45343
$117$	−243.499	−	281.013i	−0.192406	−	0.222048i
$118$	−662.947	−	426.050i	−0.517197	−	0.332382i
$119$	−27.2314	+	189.398i	−0.0209773	+	0.145900i
$120$	268.788	−	588.564i	0.204474	−	0.447736i
$121$	124.800	+	868.000i	0.0937638	+	0.652141i
$122$	518.923	+	152.370i	0.385091	+	0.113073i
$123$	172.088	−	110.594i	0.126152	−	0.0810729i
$124$	−173.138	−	379.120i	−0.125389	−	0.274564i
$125$	−119.937	+	35.2166i	−0.0858197	+	0.0251989i
$126$	−185.868	+	214.503i	−0.131416	+	0.151662i
$127$	520.497	−	600.686i	0.363675	−	0.419703i	−0.544193	−	0.838960i	$-0.683164\pi$
$127$	520.497	−	600.686i	0.363675	−	0.419703i	0.907867	+	0.419257i	$0.137709\pi$
$128$	−1408.39	+	413.540i	−0.972540	+	0.285563i
$129$	90.8165	+	198.860i	0.0619841	+	0.135726i
$130$	−67.0709	+	43.1038i	−0.0452500	+	0.0290804i
$131$	825.673	+	242.439i	0.550682	+	0.161695i	0.545224	−	0.838290i	$-0.316445\pi$
$131$	825.673	+	242.439i	0.550682	+	0.161695i	0.00545784	+	0.999985i	$0.498263\pi$
$132$	−147.543	−	1026.18i	−0.0972875	−	0.676649i
$133$	−416.060	+	911.045i	−0.271256	+	0.593967i
$134$	−48.7995	+	339.408i	−0.0314600	+	0.218809i
$135$	29.7004	+	19.0873i	0.0189348	+	0.0121687i
$136$	258.231	+	298.014i	0.162817	+	0.187901i
$137$	406.045			0.253217			0.126609	−	0.991953i	$-0.459591\pi$
$137$	406.045			0.253217			0.126609	+	0.991953i	$0.459591\pi$
$138$	−11.9356	−	980.084i	−0.00736249	−	0.604567i
$139$	2230.31			1.36095			0.680475	−	0.732771i	$-0.261773\pi$
$139$	2230.31			1.36095			0.680475	+	0.732771i	$0.261773\pi$
$140$	−182.035	−	210.079i	−0.109891	−	0.126821i
$141$	−1956.77	−	1257.54i	−1.16872	−	0.751093i
$142$	120.454	−	837.773i	0.0711848	−	0.495101i
$143$	−117.753	+	257.843i	−0.0688602	+	0.150783i
$144$	−125.625	−	873.742i	−0.0726998	−	0.505638i
$145$	1327.34	+	389.741i	0.760202	+	0.223216i
$146$	799.033	−	513.507i	0.452934	−	0.291083i
$147$	−835.292	−	1829.04i	−0.468665	−	1.02623i
$148$	−1228.96	+	360.854i	−0.682565	+	0.200419i
$149$	−1494.18	+	1724.38i	−0.821532	+	0.948098i	−0.999353	−	0.0359648i	$-0.988550\pi$
$149$	−1494.18	+	1724.38i	−0.821532	+	0.948098i	0.177822	+	0.984063i	$0.443095\pi$
$150$	145.476	−	167.889i	0.0791874	−	0.0913871i
$151$	545.659	−	160.220i	0.294073	−	0.0863477i	−0.131368	−	0.991334i	$-0.541937\pi$
$151$	545.659	−	160.220i	0.294073	−	0.0863477i	0.425442	+	0.904986i	$0.360119\pi$
$152$	857.425	+	1877.50i	0.457542	+	1.00188i
$153$	−531.181	+	341.369i	−0.280676	+	0.180379i
$154$	207.606	+	60.9586i	0.108632	+	0.0318973i
$155$	−45.1878	−	314.288i	−0.0234166	−	0.162866i
$156$	−268.852	+	588.704i	−0.137983	+	0.302141i
$157$	486.111	−	3380.97i	0.247107	−	1.71867i	−0.367660	−	0.929960i	$-0.619841\pi$
$157$	486.111	−	3380.97i	0.247107	−	1.71867i	0.614767	−	0.788709i	$-0.289250\pi$
$158$	267.710	+	172.047i	0.134797	+	0.0866286i
$159$	115.565	+	133.369i	0.0576410	+	0.0665213i
$160$	−887.544			−0.438540
$161$	−854.591	−	377.771i	−0.418331	−	0.184922i
$162$	841.936			0.408325
$163$	−965.614	−	1114.38i	−0.464005	−	0.535490i	0.474730	−	0.880132i	$-0.342546\pi$
$163$	−965.614	−	1114.38i	−0.464005	−	0.535490i	−0.938734	+	0.344642i	$0.888000\pi$
$164$	−152.359	−	97.9152i	−0.0725441	−	0.0466213i
$165$	112.403	−	781.779i	0.0530336	−	0.368857i
$166$	−200.259	+	438.506i	−0.0936331	+	0.205028i
$167$	104.555	+	727.195i	0.0484473	+	0.336958i	0.999601	+	0.0282409i	$0.00899057\pi$
$167$	104.555	+	727.195i	0.0484473	+	0.336958i	−0.951154	+	0.308717i	$0.900100\pi$
$168$	1051.78	+	308.830i	0.483015	+	0.141826i
$169$	−1699.37	+	1092.12i	−0.773497	+	0.497096i
$170$	56.2415	+	123.152i	0.0253737	+	0.0555606i
$171$	−3171.12	+	931.123i	−1.41814	+	0.416402i
$172$	126.750	−	146.277i	0.0561896	−	0.0648462i
$173$	−145.016	+	167.358i	−0.0637306	+	0.0735490i	−0.786720	−	0.617310i	$-0.788222\pi$
$173$	−145.016	+	167.358i	−0.0637306	+	0.0735490i	0.722989	+	0.690860i	$0.242768\pi$
$174$	−2358.93	+	692.644i	−1.02776	+	0.301777i
$175$	−87.9725	−	192.633i	−0.0380005	−	0.0832096i
$176$	−566.104	+	363.813i	−0.242453	+	0.155815i
$177$	−4676.03	−	1373.01i	−1.98572	−	0.583059i
$178$	257.473	+	1790.76i	0.108418	+	0.754064i
$179$	−526.493	+	1152.86i	−0.219843	+	0.481389i	−0.987131	−	0.159914i	$-0.948878\pi$
$179$	−526.493	+	1152.86i	−0.219843	+	0.481389i	0.767288	+	0.641303i	$0.221606\pi$
$180$	130.542	−	907.942i	0.0540559	−	0.375967i
$181$	−1937.65	−	1245.25i	−0.795714	−	0.511374i	0.0785006	−	0.996914i	$-0.474987\pi$
$181$	−1937.65	−	1245.25i	−0.795714	−	0.511374i	−0.874215	+	0.485540i	$0.838623\pi$
$182$	−88.4526	−	102.080i	−0.0360250	−	0.0415750i
$183$	3344.61			1.35104
$184$	−1741.68	+	821.175i	−0.697816	+	0.329010i
$185$	−975.785			−0.387790
$186$	369.533	+	426.464i	0.145675	+	0.168117i
$187$	404.934	+	260.235i	0.158352	+	0.101766i
$188$	−293.076	+	2038.39i	−0.113696	+	0.790770i
$189$	−24.8469	+	54.4071i	−0.00956267	+	0.0209393i
$190$	100.851	+	701.433i	0.0385078	+	0.267828i
$191$	1832.71	+	538.132i	0.694295	+	0.203863i	0.609794	−	0.792560i	$-0.291252\pi$
$191$	1832.71	+	538.132i	0.694295	+	0.203863i	0.0845008	+	0.996423i	$0.473070\pi$
$192$	−248.555	+	159.737i	−0.0934267	+	0.0600417i
$193$	−2100.86	−	4600.25i	−0.783541	−	1.71571i	−0.694278	−	0.719706i	$-0.744276\pi$
$193$	−2100.86	−	4600.25i	−0.783541	−	1.71571i	−0.0892622	−	0.996008i	$-0.528451\pi$
$194$	−378.779	+	111.220i	−0.140179	+	0.0411603i
$195$	−322.879	+	372.622i	−0.118574	+	0.136841i
$196$	−1165.79	+	1345.40i	−0.424852	+	0.490305i
$197$	2866.29	−	841.619i	1.03662	−	0.304380i	0.281222	−	0.959643i	$-0.409260\pi$
$197$	2866.29	−	841.619i	1.03662	−	0.304380i	0.755401	+	0.655263i	$0.227442\pi$
$198$	296.604	+	649.471i	0.106458	+	0.233111i
$199$	2747.21	−	1765.52i	0.978615	−	0.628918i	0.0495256	−	0.998773i	$-0.484229\pi$
$199$	2747.21	−	1765.52i	0.978615	−	0.628918i	0.929089	+	0.369855i	$0.120593\pi$
$200$	−418.742	−	122.954i	−0.148048	−	0.0434707i
$201$	301.786	+	2098.97i	0.105902	+	0.736566i
$202$	196.915	−	431.185i	0.0685887	−	0.150188i
$203$	−333.537	+	2319.80i	−0.115319	+	0.802060i
$204$	924.540	+	594.165i	0.317307	+	0.203921i
$205$	−90.3545	−	104.275i	−0.0307836	−	0.0355261i
$206$	−490.749			−0.165981
$207$	−904.620	−	2947.59i	−0.303746	−	0.989717i
$208$	420.081			0.140035
$209$	1649.92	+	1904.10i	0.546062	+	0.630190i
$210$	316.611	+	203.473i	0.104039	+	0.0668618i
$211$	90.3106	−	628.124i	0.0294656	−	0.204938i	−0.969770	−	0.244019i	$-0.921534\pi$
$211$	90.3106	−	628.124i	0.0294656	−	0.204938i	0.999236	+	0.0390813i	$0.0124431\pi$
$212$	64.9049	−	142.122i	0.0210268	−	0.0460423i
$213$	−744.909	−	5180.96i	−0.239626	−	1.66664i
$214$	−1384.32	−	406.472i	−0.442196	−	0.129841i
$215$	124.047	−	79.7201i	0.0393485	−	0.0252877i
$216$	51.2049	+	112.123i	0.0161299	+	0.0353195i
$217$	516.139	−	151.552i	0.161465	−	0.0474103i
$218$	6.74210	−	7.78080i	0.00209465	−	0.00241735i
$219$	3846.54	−	4439.15i	1.18687	−	1.36972i
$220$	−670.943	+	197.007i	−0.205613	+	0.0603736i
$221$	−124.826	−	273.330i	−0.0379940	−	0.0831953i
$222$	1458.86	−	937.556i	0.441048	−	0.283444i
$223$	3312.40	+	972.607i	0.994684	+	0.292066i	0.738273	−	0.674502i	$-0.235642\pi$
$223$	3312.40	+	972.607i	0.994684	+	0.292066i	0.256411	+	0.966568i	$0.417460\pi$
$224$	−213.990	−	1488.34i	−0.0638296	−	0.443945i
$225$	290.297	−	635.663i	0.0860140	−	0.188344i
$226$	−344.266	+	2394.42i	−0.101328	+	0.704754i
$227$	3640.04	+	2339.31i	1.06431	+	0.683990i	0.950881	−	0.309556i	$-0.100180\pi$
$227$	3640.04	+	2339.31i	1.06431	+	0.683990i	0.113428	+	0.993546i	$0.463817\pi$
$228$	3767.06	+	4347.42i	1.09421	+	1.26278i
$229$	4308.30			1.24323			0.621617	−	0.783322i	$-0.286476\pi$
$229$	4308.30			1.24323			0.621617	+	0.783322i	$0.286476\pi$
$230$	−653.184	+	102.047i	−0.187259	+	0.0292555i
$231$	1338.08			0.381122
$232$	3162.88	+	3650.16i	0.895057	+	1.03295i
$233$	−3565.09	−	2291.14i	−1.00239	−	0.644196i	−0.0669767	−	0.997755i	$-0.521335\pi$
$233$	−3565.09	−	2291.14i	−1.00239	−	0.644196i	−0.935413	+	0.353558i	$0.884972\pi$
$234$	63.4320	−	441.179i	0.0177208	−	0.123251i
$235$	−651.737	+	1427.10i	−0.180913	+	0.396145i
$236$	614.048	+	4270.80i	0.169369	+	1.17799i
$237$	1888.27	+	554.445i	0.517536	+	0.151962i
$238$	−192.955	+	124.005i	−0.0525522	+	0.0337732i
$239$	−1828.57	−	4004.02i	−0.494898	−	1.08368i	−0.978094	−	0.208163i	$-0.933251\pi$
$239$	−1828.57	−	4004.02i	−0.494898	−	1.08368i	0.483196	−	0.875512i	$-0.339476\pi$
$240$	−1123.08	+	329.766i	−0.302061	+	0.0886931i
$241$	3189.56	−	3680.95i	0.852521	−	0.983861i	−0.147466	−	0.989067i	$-0.547112\pi$
$241$	3189.56	−	3680.95i	0.852521	−	0.983861i	0.999986	+	0.00520584i	$0.00165708\pi$
$242$	−688.370	+	794.421i	−0.182852	+	0.211022i
$243$	5178.72	−	1520.61i	1.36714	−	0.401428i
$244$	−1230.11	−	2693.57i	−0.322745	−	0.706713i
$245$	−1140.93	+	733.232i	−0.297516	+	0.191202i
$246$	235.275	+	69.0831i	0.0609781	+	0.0179048i
$247$	−223.834	−	1556.80i	−0.0576609	−	0.401040i
$248$	460.519	−	1008.40i	0.117915	−	0.258198i
$249$	−424.271	+	2950.87i	−0.107980	+	0.751019i
$250$	−126.051	−	81.0082i	−0.0318887	−	0.0204936i
$251$	3317.53	+	3828.63i	0.834264	+	0.962792i	0.999726	−	0.0234239i	$-0.00745675\pi$
$251$	3317.53	+	3828.63i	0.834264	+	0.962792i	−0.165461	+	0.986216i	$0.552911\pi$
$252$	1554.02			0.388468
$253$	−1757.49	+	1560.75i	−0.436730	+	0.387840i
$254$	952.752			0.235358
$255$	548.286	+	632.756i	0.134647	+	0.155391i
$256$	−1211.95	−	778.875i	−0.295887	−	0.190155i
$257$	773.531	−	5380.03i	0.187749	−	1.30582i	−0.650069	−	0.759875i	$-0.725260\pi$
$257$	773.531	−	5380.03i	0.187749	−	1.30582i	0.837818	−	0.545949i	$-0.183831\pi$
$258$	−108.862	+	238.374i	−0.0262691	+	0.0575213i
$259$	−235.266	−	1636.31i	−0.0564429	−	0.392569i
$260$	418.841	+	122.983i	0.0999055	+	0.0293349i
$261$	−6506.05	+	4181.18i	−1.54297	+	0.991604i
$262$	428.507	+	938.300i	0.101043	+	0.221253i
$263$	−2582.26	+	758.221i	−0.605434	+	0.177772i	−0.570061	−	0.821603i	$-0.693080\pi$
$263$	−2582.26	+	758.221i	−0.605434	+	0.177772i	−0.0353737	+	0.999374i	$0.511262\pi$
$264$	1805.80	−	2084.01i	0.420983	−	0.485840i
$265$	77.9478	−	89.9565i	0.0180690	−	0.0208528i
$266$	−1151.93	+	338.237i	−0.265524	+	0.0779648i
$267$	4647.80	+	10177.3i	1.06532	+	2.33273i
$268$	1579.40	−	1015.02i	0.359990	−	0.231351i
$269$	−2600.20	−	763.486i	−0.589356	−	0.173050i	−0.0265611	−	0.999647i	$-0.508456\pi$
$269$	−2600.20	−	763.486i	−0.589356	−	0.173050i	−0.562795	+	0.826597i	$0.690274\pi$
$270$	6.02276	+	41.8892i	0.00135753	+	0.00944184i
$271$	359.416	−	787.012i	0.0805645	−	0.176412i	−0.865063	−	0.501663i	$-0.832722\pi$
$271$	359.416	−	787.012i	0.0805645	−	0.176412i	0.945628	+	0.325252i	$0.105449\pi$
$272$	101.520	−	706.085i	0.0226306	−	0.157400i
$273$	−702.704	−	451.600i	−0.155786	−	0.100118i
$274$	318.737	+	367.843i	0.0702760	+	0.0811029i
$275$	−532.725			−0.116817
$276$	−4012.68	+	3563.48i	−0.875127	+	0.777160i
$277$	−5967.13			−1.29433			−0.647166	−	0.762349i	$-0.724046\pi$
$277$	−5967.13			−1.29433			−0.647166	+	0.762349i	$0.724046\pi$
$278$	1750.75	+	2020.47i	0.377708	+	0.435898i
$279$	1493.30	+	959.689i	0.320437	+	0.205932i
$280$	105.223	−	731.840i	0.0224581	−	0.156199i
$281$	−2228.31	+	4879.33i	−0.473061	+	1.03586i	0.511253	+	0.859430i	$0.329182\pi$
$281$	−2228.31	+	4879.33i	−0.473061	+	1.03586i	−0.984313	+	0.176428i	$0.943546\pi$
$282$	−396.802	−	2759.82i	−0.0837916	−	0.582783i
$283$	−6238.69	−	1831.85i	−1.31043	−	0.384777i	−0.449400	−	0.893331i	$-0.648362\pi$
$283$	−6238.69	−	1831.85i	−1.31043	−	0.384777i	−0.861030	+	0.508553i	$0.830180\pi$
$284$	−3898.49	+	2505.41i	−0.814553	+	0.523481i
$285$	1820.52	+	3986.38i	0.378380	+	0.828536i
$286$	−326.018	+	95.7276i	−0.0674052	+	0.0197919i
$287$	153.075	−	176.658i	0.0314834	−	0.0363338i
$288$	3249.30	−	3749.89i	0.664815	−	0.767237i
$289$	4224.40	−	1240.40i	0.859841	−	0.252472i
$290$	688.861	+	1508.40i	0.139487	+	0.305435i
$291$	−2053.78	+	1319.89i	−0.413728	+	0.265887i
$292$	−4989.76	−	1465.13i	−1.00001	−	0.293630i
$293$	−759.989	−	5285.84i	−0.151533	−	1.05393i	−0.913652	−	0.406496i	$-0.866750\pi$
$293$	−759.989	−	5285.84i	−0.151533	−	1.05393i	0.762120	−	0.647436i	$-0.224159\pi$
$294$	1001.26	−	2192.46i	0.198622	−	0.434922i
$295$	−467.802	+	3253.63i	−0.0923270	+	0.642149i
$296$	−2866.00	−	1841.86i	−0.562779	−	0.361676i
$297$	98.5320	+	113.712i	0.0192505	+	0.0222163i
$298$	−2735.05			−0.531668
$299$	1449.71	−	226.489i	0.280398	−	0.0438066i
$300$	−1216.31			−0.234079
$301$	163.592	+	188.795i	0.0313266	+	0.0361528i
$302$	573.477	+	368.552i	0.109271	+	0.0702244i
$303$	417.188	−	2901.60i	0.0790984	−	0.550141i
$304$	1551.09	−	3396.42i	0.292635	−	0.640782i
$305$	−321.049	−	2232.95i	−0.0602729	−	0.419207i
$306$	−726.218	−	213.237i	−0.135670	−	0.0398364i
$307$	−993.729	+	638.631i	−0.184740	+	0.118725i	−0.629742	−	0.776805i	$-0.716839\pi$
$307$	−993.729	+	638.631i	−0.184740	+	0.118725i	0.445002	+	0.895530i	$0.353203\pi$
$308$	−492.131	−	1077.62i	−0.0910447	−	0.199360i
$309$	−2911.96	+	855.028i	−0.536102	+	0.157414i
$310$	249.247	−	287.646i	0.0456654	−	0.0527007i
$311$	4031.68	−	4652.81i	0.735098	−	0.848348i	−0.257938	−	0.966162i	$-0.583043\pi$
$311$	4031.68	−	4652.81i	0.735098	−	0.848348i	0.993036	+	0.117813i	$0.0375884\pi$
$312$	−1651.68	+	484.978i	−0.299706	+	0.0880016i
$313$	−1608.00	−	3521.02i	−0.290381	−	0.635846i	0.707074	−	0.707139i	$-0.250015\pi$
$313$	−1608.00	−	3521.02i	−0.290381	−	0.635846i	−0.997455	+	0.0712935i	$0.977287\pi$
$314$	3444.47	−	2213.62i	0.619052	−	0.397841i
$315$	1135.94	+	333.544i	0.203185	+	0.0596605i
$316$	−247.964	−	1724.63i	−0.0441426	−	0.307018i
$317$	257.287	−	563.379i	0.0455857	−	0.0998187i	−0.885469	−	0.464699i	$-0.846163\pi$
$317$	257.287	−	563.379i	0.0455857	−	0.0998187i	0.931055	+	0.364880i	$0.118890\pi$
$318$	−30.1050	+	209.385i	−0.00530882	+	0.0369237i
$319$	4959.75	+	3187.44i	0.870510	+	0.559443i
$320$	130.503	+	150.609i	0.0227980	+	0.0263103i
$321$	−8922.32			−1.55139
$322$	−328.609	−	1070.73i	−0.0568717	−	0.185309i
$323$	−2670.81			−0.460087
$324$	−3018.76	−	3483.83i	−0.517620	−	0.597365i
$325$	279.765	+	179.794i	0.0477495	+	0.0306867i
$326$	251.545	−	1749.53i	0.0427355	−	0.297232i
$327$	26.4492	−	57.9156i	0.00447292	−	0.00979432i
$328$	−68.5560	−	476.818i	−0.0115408	−	0.0802678i
$329$	−2550.27	−	748.827i	−0.427359	−	0.125484i
$330$	796.460	−	511.854i	0.132860	−	0.0853837i
$331$	4339.14	+	9501.40i	0.720546	+	1.57778i	0.813137	+	0.582072i	$0.197758\pi$
$331$	4339.14	+	9501.40i	0.720546	+	1.57778i	−0.0925910	+	0.995704i	$0.529515\pi$
$332$	2532.51	−	743.613i	0.418644	−	0.122925i
$333$	3572.35	−	4122.71i	0.587879	−	0.678448i
$334$	−576.704	+	665.552i	−0.0944785	+	0.109034i
$335$	1372.36	−	402.960i	0.223820	−	0.0657196i
$336$	−823.771	−	1803.81i	−0.133751	−	0.292874i
$337$	7719.43	−	4960.97i	1.24779	−	0.801903i	0.261222	−	0.965279i	$-0.415874\pi$
$337$	7719.43	−	4960.97i	1.24779	−	0.801903i	0.986564	+	0.163375i	$0.0522381\pi$
$338$	−2323.34	−	682.196i	−0.373885	−	0.109783i
$339$	2129.01	+	14807.6i	0.341097	+	2.37238i
$340$	307.934	−	674.280i	0.0491178	−	0.107553i
$341$	192.581	−	1339.43i	0.0305832	−	0.212711i
$342$	−3332.78	−	2141.85i	−0.526948	−	0.338649i
$343$	−3407.34	−	3932.28i	−0.536382	−	0.619018i
$344$	514.818			0.0806893
$345$	−3698.00	+	1743.55i	−0.577083	+	0.272086i
$346$	−265.447			−0.0412443
$347$	4263.31	+	4920.13i	0.659558	+	0.761171i	0.982705	−	0.185178i	$-0.0592862\pi$
$347$	4263.31	+	4920.13i	0.659558	+	0.761171i	−0.323147	+	0.946349i	$0.604741\pi$
$348$	11324.0	+	7277.50i	1.74434	+	1.12102i
$349$	−565.948	+	3936.25i	−0.0868037	+	0.603733i	0.899266	+	0.437402i	$0.144101\pi$
$349$	−565.948	+	3936.25i	−0.0868037	+	0.603733i	−0.986070	+	0.166331i	$0.946808\pi$
$350$	105.452	−	230.909i	0.0161048	−	0.0352645i
$351$	−13.3673	−	92.9713i	−0.00203274	−	0.0141380i
$352$	−3629.32	−	1065.66i	−0.549555	−	0.161364i
$353$	−7928.47	+	5095.32i	−1.19544	+	0.768262i	−0.978161	−	0.207848i	$-0.933354\pi$
$353$	−7928.47	+	5095.32i	−1.19544	+	0.768262i	−0.217277	+	0.976110i	$0.569718\pi$
$354$	−2426.77	−	5313.88i	−0.364353	−	0.797823i
$355$	−3387.44	+	994.641i	−0.506441	+	0.148704i
$356$	6486.80	−	7486.17i	0.965730	−	1.11451i
$357$	−928.885	+	1071.99i	−0.137708	+	0.158924i
$358$	−1457.68	+	428.013i	−0.215198	+	0.0631877i
$359$	−957.723	−	2097.12i	−0.140799	−	0.308306i	0.826076	−	0.563559i	$-0.190568\pi$
$359$	−957.723	−	2097.12i	−0.140799	−	0.308306i	−0.966874	+	0.255253i	$0.917841\pi$
$360$	2052.50	−	1319.06i	0.300489	−	0.193113i
$361$	−6832.29	−	2006.14i	−0.996106	−	0.292483i
$362$	−392.924	−	2732.84i	−0.0570486	−	0.396782i
$363$	−2700.47	+	5913.20i	−0.390462	+	0.854993i
$364$	−105.248	+	732.013i	−0.0151551	+	0.105406i
$365$	−3332.92	−	2141.94i	−0.477953	−	0.307162i
$366$	2625.45	+	3029.93i	0.374958	+	0.432725i
$367$	−1772.26			−0.252075			−0.126037	−	0.992025i	$-0.540226\pi$
$367$	−1772.26			−0.252075			−0.126037	+	0.992025i	$0.540226\pi$
$368$	3185.95	+	1408.35i	0.451303	+	0.199497i
$369$	771.350			0.108821
$370$	−765.973	−	883.980i	−0.107624	−	0.124205i
$371$	169.643	+	109.023i	0.0237397	+	0.0152566i
$372$	439.699	−	3058.17i	0.0612831	−	0.426233i
$373$	−5718.48	+	12521.7i	−0.793812	+	1.73821i	−0.128410	+	0.991721i	$0.540987\pi$
$373$	−5718.48	+	12521.7i	−0.793812	+	1.73821i	−0.665403	+	0.746485i	$0.731740\pi$
$374$	82.1141	+	571.116i	0.0113530	+	0.0789618i
$375$	−889.090	−	261.060i	−0.122433	−	0.0359496i
$376$	−4607.99	+	2961.37i	−0.632018	+	0.406173i
$377$	−1528.90	−	3347.82i	−0.208865	−	0.457352i
$378$	−68.7926	+	20.1993i	−0.00936061	+	0.00274852i
$379$	8672.51	−	10008.6i	1.17540	−	1.35649i	0.254317	−	0.967121i	$-0.418149\pi$
$379$	8672.51	−	10008.6i	1.17540	−	1.35649i	0.921084	−	0.389364i	$-0.127305\pi$
$380$	2540.85	−	2932.30i	0.343007	−	0.395852i
$381$	5653.34	−	1659.97i	0.760182	−	0.223210i
$382$	951.140	+	2082.71i	0.127394	+	0.278954i
$383$	8091.92	−	5200.36i	1.07958	−	0.693802i	0.125117	−	0.992142i	$-0.460069\pi$
$383$	8091.92	−	5200.36i	1.07958	−	0.693802i	0.954460	+	0.298340i	$0.0964329\pi$
$384$	−10440.4	−	3065.57i	−1.38746	−	0.407394i
$385$	−128.442	−	893.336i	−0.0170027	−	0.118256i
$386$	2518.30	−	5514.31i	0.332068	−	0.727127i
$387$	−117.317	+	815.956i	−0.0154097	+	0.107177i
$388$	1818.33	+	1168.57i	0.237916	+	0.152899i
$389$	−2331.84	−	2691.09i	−0.303931	−	0.350755i	0.583154	−	0.812362i	$-0.301819\pi$
$389$	−2331.84	−	2691.09i	−0.303931	−	0.350755i	−0.887085	+	0.461607i	$0.847273\pi$
$390$	−591.018			−0.0767368
$391$	−30.3413	−	2491.46i	−0.00392436	−	0.322247i
$392$	−4735.08			−0.610096
$393$	4177.43	+	4821.01i	0.536192	+	0.618798i
$394$	3012.42	+	1935.96i	0.385186	+	0.247544i
$395$	188.907	−	1313.88i	0.0240631	−	0.167363i
$396$	1623.97	−	3555.99i	0.206079	−	0.451250i
$397$	−1626.84	−	11314.9i	−0.205665	−	1.43043i	−0.787094	−	0.616833i	$-0.788415\pi$
$397$	−1626.84	−	11314.9i	−0.205665	−	1.43043i	0.581429	−	0.813597i	$-0.302494\pi$
$398$	3755.92	+	1102.84i	0.473033	+	0.138895i
$399$	−6245.89	+	4013.99i	−0.783674	+	0.503637i
$400$	327.965	+	718.144i	0.0409957	+	0.0897680i
$401$	−10776.9	+	3164.38i	−1.34208	+	0.394069i	−0.872410	−	0.488776i	$-0.837444\pi$
$401$	−10776.9	+	3164.38i	−1.34208	+	0.394069i	−0.469666	+	0.882844i	$0.655626\pi$
$402$	−1664.59	+	1921.04i	−0.206523	+	0.238341i
$403$	−553.193	+	638.419i	−0.0683784	+	0.0789129i
$404$	−2490.23	+	731.198i	−0.306667	+	0.0900457i
$405$	−1458.89	−	3194.51i	−0.178994	−	0.391942i
$406$	−2363.37	+	1518.84i	−0.288896	+	0.185662i
$407$	−3990.15	−	1171.61i	−0.485957	−	0.142690i
$408$	416.009	+	2893.41i	0.0504792	+	0.351091i
$409$	−3922.72	+	8589.57i	−0.474245	+	1.03845i	0.509761	+	0.860316i	$0.329734\pi$
$409$	−3922.72	+	8589.57i	−0.474245	+	1.03845i	−0.984006	+	0.178136i	$0.942993\pi$
$410$	23.5375	−	163.707i	0.00283521	−	0.0197193i
$411$	2532.18	+	1627.33i	0.303901	+	0.195305i
$412$	1759.58	+	2030.66i	0.210408	+	0.242824i
$413$	−5568.86			−0.663501
$414$	1960.16	−	3133.31i	0.232697	−	0.371965i
$415$	2010.80			0.237847
$416$	1546.31	+	1784.53i	0.182245	+	0.210322i
$417$	13908.7	+	8938.55i	1.63336	+	1.04969i
$418$	−429.806	+	2989.37i	−0.0502931	+	0.349796i
$419$	−5561.99	+	12179.1i	−0.648499	+	1.42001i	0.244363	+	0.969684i	$0.421421\pi$
$419$	−5561.99	+	12179.1i	−0.648499	+	1.42001i	−0.892862	+	0.450330i	$0.851306\pi$
$420$	−293.257	−	2039.65i	−0.0340702	−	0.236964i
$421$	9709.55	+	2850.98i	1.12402	+	0.330043i	0.790356	−	0.612647i	$-0.209895\pi$
$421$	9709.55	+	2850.98i	1.12402	+	0.330043i	0.333668	+	0.942691i	$0.391714\pi$
$422$	639.920	−	411.252i	0.0738171	−	0.0474394i
$423$	−3643.54	−	7978.23i	−0.418806	−	0.917056i
$424$	398.741	−	117.081i	0.0456712	−	0.0134103i
$425$	369.814	−	426.788i	0.0422085	−	0.0487112i
$426$	4108.77	−	4741.78i	0.467302	−	0.539295i
$427$	3667.06	−	1076.75i	0.415600	−	0.122031i
$428$	3281.53	+	7185.55i	0.370605	+	0.811511i
$429$	−1767.71	+	1136.04i	−0.198941	+	0.127852i
$430$	169.594	+	49.7973i	0.0190199	+	0.00558474i
$431$	−1216.36	−	8460.00i	−0.135940	−	0.945484i	−0.937603	−	0.347708i	$-0.886960\pi$
$431$	−1216.36	−	8460.00i	−0.135940	−	0.945484i	0.801663	−	0.597777i	$-0.203949\pi$
$432$	92.6303	−	202.832i	0.0103164	−	0.0225897i
$433$	−1380.19	+	9599.41i	−0.153181	+	1.06540i	0.757662	+	0.652647i	$0.226342\pi$
$433$	−1380.19	+	9599.41i	−0.153181	+	1.06540i	−0.910843	+	0.412752i	$0.864567\pi$
$434$	542.453	+	348.613i	0.0599967	+	0.0385576i
$435$	6715.56	+	7750.17i	0.740199	+	0.854235i
$436$	−56.3698			−0.00619180
$437$	3521.68	−	12557.4i	0.385503	−	1.37461i
$438$	7040.95			0.768105
$439$	11211.0	+	12938.2i	1.21885	+	1.40662i	0.886027	+	0.463633i	$0.153454\pi$
$439$	11211.0	+	12938.2i	1.21885	+	1.40662i	0.332819	+	0.942991i	$0.392000\pi$
$440$	−1564.68	−	1005.56i	−0.169530	−	0.108950i
$441$	1079.03	−	7504.82i	0.116513	−	0.810368i
$442$	149.628	−	327.640i	0.0161020	−	0.0352585i
$443$	−544.307	−	3785.74i	−0.0583765	−	0.406018i	−0.997968	−	0.0637194i	$-0.979704\pi$
$443$	−544.307	−	3785.74i	−0.0583765	−	0.406018i	0.939591	−	0.342298i	$-0.111205\pi$
$444$	−9110.25	−	2675.01i	−0.973769	−	0.285924i
$445$	6348.46	−	4079.91i	0.676283	−	0.434620i
$446$	1719.07	+	3764.23i	0.182512	+	0.399645i
$447$	−16228.9	+	4765.25i	−1.71723	+	0.504225i
$448$	−221.093	+	255.155i	−0.0233163	+	0.0269084i
$449$	−2661.16	+	3071.14i	−0.279706	+	0.322798i	−0.878167	−	0.478354i	$-0.841234\pi$
$449$	−2661.16	+	3071.14i	−0.279706	+	0.322798i	0.598461	+	0.801152i	$0.295779\pi$
$450$	803.735	−	235.998i	0.0841965	−	0.0247223i
$451$	−244.273	−	534.884i	−0.0255042	−	0.0558464i
$452$	11142.2	−	7160.65i	1.15948	−	0.745152i
$453$	4044.97	+	1187.71i	0.419534	+	0.123186i
$454$	738.142	+	5133.89i	0.0763056	+	0.530717i
$455$	−234.047	+	512.492i	−0.0241150	+	0.0528044i
$456$	−2177.50	+	15144.8i	−0.223620	+	1.55531i
$457$	1257.05	+	807.856i	0.128670	+	0.0826913i	0.603393	−	0.797444i	$-0.293815\pi$
$457$	1257.05	+	807.856i	0.128670	+	0.0826913i	−0.474722	+	0.880136i	$0.657452\pi$
$458$	3381.93	+	3902.96i	0.345038	+	0.398195i
$459$	−159.500			−0.0162196
$460$	2764.25	+	2336.91i	0.280182	+	0.236867i
$461$	15716.4			1.58782			0.793912	−	0.608033i	$-0.208041\pi$
$461$	15716.4			1.58782			0.793912	+	0.608033i	$0.208041\pi$
$462$	1050.37	+	1212.19i	0.105774	+	0.122069i
$463$	5532.43	+	3555.47i	0.555321	+	0.356883i	0.788005	−	0.615669i	$-0.211114\pi$
$463$	5532.43	+	3555.47i	0.555321	+	0.356883i	−0.232684	+	0.972552i	$0.574751\pi$
$464$	1243.44	−	8648.32i	0.124408	−	0.865277i
$465$	977.792	−	2141.07i	0.0975140	−	0.213526i
$466$	−722.942	−	5028.17i	−0.0718662	−	0.499840i
$467$	−4854.59	−	1425.44i	−0.481035	−	0.141245i	0.0322198	−	0.999481i	$-0.489742\pi$
$467$	−4854.59	−	1425.44i	−0.481035	−	0.141245i	−0.513255	+	0.858236i	$0.671561\pi$
$468$	−2052.98	+	1319.37i	−0.202776	+	0.130316i
$469$	1006.61	+	2204.17i	0.0991066	+	0.217013i
$470$	−1804.44	+	529.831i	−0.177090	+	0.0519984i
$471$	16581.6	−	19136.2i	1.62217	−	1.87208i
$472$	−7515.45	+	8673.30i	−0.732896	+	0.845807i
$473$	602.968	−	177.047i	0.0586141	−	0.0172107i
$474$	979.972	+	2145.84i	0.0949612	+	0.207936i
$475$	2486.66	−	1598.08i	0.240202	−	0.154368i
$476$	1204.96	+	353.807i	0.116027	+	0.0340687i
$477$	94.7013	+	658.662i	0.00909030	+	0.0632244i
$478$	2191.91	−	4799.61i	0.209740	−	0.459266i
$479$	444.039	−	3088.36i	0.0423563	−	0.294595i	−0.957622	−	0.288028i	$-0.907001\pi$
$479$	444.039	−	3088.36i	0.0423563	−	0.294595i	0.999978	−	0.00656705i	$-0.00209037\pi$
$480$	−5534.91	−	3557.07i	−0.526318	−	0.338244i
$481$	1700.04	+	1961.96i	0.161155	+	0.185982i
$482$	5838.37			0.551723
$483$	−3815.39	−	5780.86i	−0.359434	−	0.544593i
$484$	5755.37			0.540512
$485$	1078.33	+	1244.46i	0.100958	+	0.116512i
$486$	5442.74	+	3497.84i	0.507999	+	0.326471i
$487$	−2820.72	+	19618.5i	−0.262462	+	1.82546i	0.251741	+	0.967795i	$0.418997\pi$
$487$	−2820.72	+	19618.5i	−0.262462	+	1.82546i	−0.514203	+	0.857669i	$0.671912\pi$
$488$	3271.89	−	7164.43i	0.303507	−	0.664587i
$489$	−1555.60	−	10819.5i	−0.143858	−	1.00056i
$490$	−1559.86	−	458.015i	−0.143810	−	0.0422265i
$491$	10667.2	−	6855.41i	0.980459	−	0.630103i	0.0508720	−	0.998705i	$-0.483800\pi$
$491$	10667.2	−	6855.41i	0.980459	−	0.630103i	0.929587	+	0.368602i	$0.120164\pi$
$492$	−557.721	−	1221.24i	−0.0511057	−	0.111906i
$493$	−5996.61	+	1760.76i	−0.547817	+	0.160853i
$494$	1234.63	−	1424.83i	0.112446	−	0.129770i
$495$	1950.31	−	2250.78i	0.177091	−	0.204373i
$496$	−1924.19	+	564.993i	−0.174191	+	0.0511471i
$497$	−2484.66	−	5440.64i	−0.224250	−	0.491038i
$498$	−3006.29	+	1932.02i	−0.270512	+	0.173847i
$499$	−4165.54	−	1223.11i	−0.373698	−	0.109728i	0.0894899	−	0.995988i	$-0.471476\pi$
$499$	−4165.54	−	1223.11i	−0.373698	−	0.109728i	−0.463188	+	0.886260i	$0.653295\pi$
$500$	116.754	+	812.040i	0.0104428	+	0.0726310i
$501$	−2262.40	+	4953.97i	−0.201750	+	0.441770i
$502$	−864.222	+	6010.80i	−0.0768369	+	0.534413i
$503$	−6392.77	−	4108.38i	−0.566679	−	0.364182i	0.225714	−	0.974194i	$-0.427529\pi$
$503$	−6392.77	−	4108.38i	−0.566679	−	0.364182i	−0.792393	+	0.610011i	$0.791165\pi$
$504$	2706.82	+	3123.83i	0.239229	+	0.276085i
$505$	−1977.23			−0.174229
$506$	−2793.51	−	366.983i	−0.245428	−	0.0322419i
$507$	−14974.6			−1.31173
$508$	−3416.09	−	3942.38i	−0.298355	−	0.344320i
$509$	−7802.81	−	5014.56i	−0.679476	−	0.436673i	0.154854	−	0.987937i	$-0.450509\pi$
$509$	−7802.81	−	5014.56i	−0.679476	−	0.436673i	−0.834331	+	0.551264i	$0.814146\pi$
$510$	−142.830	+	993.402i	−0.0124012	+	0.0862521i
$511$	2788.27	−	6105.46i	0.241381	−	0.528551i
$512$	1425.41	+	9913.91i	0.123036	+	0.855737i
$513$	−801.044	−	235.208i	−0.0689414	−	0.0202430i
$514$	5481.06	−	3522.46i	0.470349	−	0.302275i
$515$	850.358	+	1862.02i	0.0727597	+	0.159322i
$516$	1376.69	−	404.231i	0.117452	−	0.0344870i
$517$	−4378.57	+	5053.14i	−0.372474	+	0.429858i
$518$	1297.68	−	1497.60i	0.110071	−	0.127029i
$519$	−1575.08	+	462.486i	−0.133215	+	0.0391154i
$520$	482.329	+	1056.15i	0.0406760	+	0.0890681i
$521$	−12544.4	+	8061.78i	−1.05485	+	0.677914i	−0.948617	−	0.316427i	$-0.897517\pi$
$521$	−12544.4	+	8061.78i	−1.05485	+	0.677914i	−0.106238	+	0.994341i	$0.533880\pi$
$522$	−8894.92	−	2611.78i	−0.745824	−	0.218994i
$523$	−1327.71	−	9234.42i	−0.111007	−	0.772070i	−0.966944	−	0.254990i	$-0.917928\pi$
$523$	−1327.71	−	9234.42i	−0.111007	−	0.772070i	0.855937	−	0.517081i	$-0.172981\pi$
$524$	2346.17	−	5137.39i	0.195597	−	0.428297i
$525$	223.413	−	1553.87i	0.0185725	−	0.129174i
$526$	−2713.91	−	1744.13i	−0.224966	−	0.144577i
$527$	939.386	+	1084.11i	0.0776476	+	0.0896101i
$528$	−4988.42			−0.411161
$529$	11754.2	+	3142.53i	0.966069	+	0.258283i
$530$	142.681			0.0116937
$531$	−12034.0	−	13888.0i	−0.983490	−	1.13501i
$532$	5529.82	+	3553.80i	0.450655	+	0.289618i
$533$	−52.2406	+	363.341i	−0.00424539	+	0.0295273i
$534$	−5571.31	+	12199.5i	−0.451487	+	0.988619i
$535$	856.454	+	5956.77i	0.0692107	+	0.481371i
$536$	4791.39	+	1406.88i	0.386113	+	0.113373i
$537$	−7903.71	+	5079.40i	−0.635140	+	0.408180i
$538$	−1349.45	−	2954.88i	−0.108139	−	0.236792i
$539$	−5545.84	+	1628.41i	−0.443184	+	0.130131i
$540$	151.738	−	175.115i	0.0120922	−	0.0139551i
$541$	14314.5	−	16519.9i	1.13758	−	1.31284i	0.194259	−	0.980950i	$-0.437770\pi$
$541$	14314.5	−	16519.9i	1.13758	−	1.31284i	0.943320	−	0.331886i	$-0.107685\pi$
$542$	995.101	−	292.188i	0.0788621	−	0.0231560i
$543$	−7092.90	−	15531.3i	−0.560563	−	1.22746i
$544$	3373.19	−	2167.82i	0.265854	−	0.170854i
$545$	−41.2048	−	12.0988i	−0.00323857	−	0.000950930i
$546$	−142.497	−	991.088i	−0.0111691	−	0.0776825i
$547$	−9985.36	+	21864.9i	−0.780518	+	1.70910i	−0.0785252	+	0.996912i	$0.525021\pi$
$547$	−9985.36	+	21864.9i	−0.780518	+	1.70910i	−0.701993	+	0.712184i	$0.747706\pi$
$548$	379.258	−	2637.80i	0.0295640	−	0.205622i
$549$	10609.6	+	6818.38i	0.824785	+	0.530057i
$550$	−418.179	−	482.604i	−0.0324204	−	0.0374151i
$551$	−32712.9			−2.52925
$552$	−14152.5	−	1859.22i	−1.09125	−	0.143358i
$553$	2248.81			0.172928
$554$	−4684.08	−	5405.72i	−0.359219	−	0.414561i
$555$	−6085.20	−	3910.72i	−0.465410	−	0.299101i
$556$	2083.17	−	14488.8i	0.158896	−	1.10515i
$557$	−349.643	+	765.611i	−0.0265976	+	0.0582406i	−0.922465	−	0.386082i	$-0.873828\pi$
$557$	−349.643	+	765.611i	−0.0265976	+	0.0582406i	0.895867	+	0.444322i	$0.146556\pi$
$558$	302.818	+	2106.15i	0.0229737	+	0.159785i
$559$	−376.407	−	110.523i	−0.0284800	−	0.00836248i
$560$	−1125.19	+	723.118i	−0.0849073	+	0.0545666i
$561$	1482.29	+	3245.77i	0.111555	+	0.244272i
$562$	−6169.45	+	1811.51i	−0.463065	+	0.135968i
$563$	−4319.08	+	4984.49i	−0.323317	+	0.373128i	−0.894019	−	0.448030i	$-0.852126\pi$
$563$	−4319.08	+	4984.49i	−0.323317	+	0.373128i	0.570702	+	0.821158i	$0.306671\pi$
$564$	−9997.08	+	11537.2i	−0.746370	+	0.861357i
$565$	9681.56	−	2842.76i	0.720896	−	0.211674i
$566$	−3237.76	−	7089.70i	−0.240447	−	0.526506i
$567$	5005.19	−	3216.64i	0.370720	−	0.238247i
$568$	−11826.8	−	3472.65i	−0.873661	−	0.256530i
$569$	−713.173	−	4960.23i	−0.0525444	−	0.365454i	−0.999081	−	0.0428584i	$-0.986354\pi$
$569$	−713.173	−	4960.23i	−0.0525444	−	0.365454i	0.946537	−	0.322596i	$-0.104556\pi$
$570$	−2182.25	+	4778.47i	−0.160359	+	0.351137i
$571$	−3137.39	+	21821.0i	−0.229940	+	1.59926i	0.468412	+	0.883510i	$0.344826\pi$
$571$	−3137.39	+	21821.0i	−0.229940	+	1.59926i	−0.698352	+	0.715755i	$0.746083\pi$
$572$	1565.05	+	1005.80i	0.114402	+	0.0735217i
$573$	9272.46	+	10701.0i	0.676025	+	0.780175i
$574$	280.198			0.0203750
$575$	1519.01	+	2301.52i	0.110169	+	0.166922i
$576$	−1114.10			−0.0805915
$577$	10817.4	+	12484.0i	0.780479	+	0.900721i	0.997144	−	0.0755255i	$-0.0240634\pi$
$577$	10817.4	+	12484.0i	0.780479	+	0.900721i	−0.216665	+	0.976246i	$0.569518\pi$
$578$	4439.77	+	2853.27i	0.319498	+	0.205329i
$579$	5335.31	−	37107.9i	0.382949	−	2.66347i
$580$	3771.66	−	8258.77i	0.270016	−	0.591253i
$581$	484.813	+	3371.95i	0.0346186	+	0.240778i
$582$	−2807.89	−	824.470i	−0.199984	−	0.0587206i
$583$	426.751	−	274.256i	0.0303160	−	0.0194829i
$584$	−5746.12	−	12582.2i	−0.407151	−	0.891536i
$585$	−1783.86	+	523.787i	−0.126074	+	0.0370187i
$586$	4191.95	−	4837.77i	0.295508	−	0.341035i
$587$	−17670.9	+	20393.3i	−1.24252	+	1.43394i	−0.382277	+	0.924048i	$0.624860\pi$
$587$	−17670.9	+	20393.3i	−1.24252	+	1.43394i	−0.860239	+	0.509891i	$0.829686\pi$
$588$	−12662.2	+	3717.95i	−0.888060	+	0.260758i
$589$	3119.12	+	6829.92i	0.218202	+	0.477796i
$590$	−3314.73	+	2130.25i	−0.231297	+	0.148646i
$591$	21247.8	+	6238.92i	1.47888	+	0.434238i
$592$	877.082	+	6100.24i	0.0608916	+	0.423511i
$593$	1594.75	−	3492.01i	0.110436	−	0.241821i	−0.846342	−	0.532639i	$-0.821200\pi$
$593$	1594.75	−	3492.01i	0.110436	−	0.241821i	0.956778	+	0.290818i	$0.0939276\pi$
$594$	−25.6678	+	178.524i	−0.00177300	+	0.0123315i
$595$	804.852	+	517.247i	0.0554550	+	0.0356387i
$596$	9806.50	+	11317.3i	0.673976	+	0.777810i
$597$	24208.0			1.65958
$598$	1343.18	+	1135.53i	0.0918505	+	0.0776509i
$599$	−7910.73			−0.539606			−0.269803	−	0.962916i	$-0.586959\pi$
$599$	−7910.73			−0.539606			−0.269803	+	0.962916i	$0.586959\pi$
$600$	−2118.59	−	2444.99i	−0.144152	−	0.166360i
$601$	−22004.1	−	14141.2i	−1.49345	−	0.959784i	−0.995717	−	0.0924546i	$-0.970529\pi$
$601$	−22004.1	−	14141.2i	−1.49345	−	0.959784i	−0.497735	−	0.867329i	$-0.665835\pi$
$602$	−42.6161	+	296.401i	−0.00288522	+	0.0200671i
$603$	−3321.68	+	7273.47i	−0.224327	+	0.491208i
$604$	−531.178	−	3694.42i	−0.0357836	−	0.248881i
$605$	4207.02	+	1235.29i	0.282710	+	0.0830112i
$606$	2956.09	−	1899.77i	0.198157	−	0.127348i
$607$	−6073.56	−	13299.2i	−0.406126	−	0.889291i	−0.996612	−	0.0822437i	$-0.973791\pi$
$607$	−6073.56	−	13299.2i	−0.406126	−	0.889291i	0.590487	−	0.807047i	$-0.298936\pi$
$608$	20137.7	−	5912.98i	1.34325	−	0.394413i
$609$	−11377.2	+	13130.0i	−0.757026	+	0.873655i
$610$	1770.84	−	2043.66i	0.117540	−	0.135648i
$611$	4004.87	−	1175.94i	0.265172	−	0.0778614i
$612$	1721.50	+	3769.57i	0.113705	+	0.248980i
$613$	18395.8	−	11822.2i	1.21207	−	0.778949i	0.231065	−	0.972938i	$-0.425779\pi$
$613$	18395.8	−	11822.2i	1.21207	−	0.778949i	0.981004	+	0.193989i	$0.0621426\pi$
$614$	−1358.60	−	398.922i	−0.0892977	−	0.0262202i
$615$	−145.561	−	1012.40i	−0.00954404	−	0.0663802i
$616$	1308.98	−	2866.28i	0.0856177	−	0.187477i
$617$	2989.30	−	20791.0i	0.195048	−	1.35659i	−0.623353	−	0.781941i	$-0.714230\pi$
$617$	2989.30	−	20791.0i	0.195048	−	1.35659i	0.818401	−	0.574648i	$-0.194861\pi$
$618$	−3060.42	−	1966.81i	−0.199204	−	0.128021i
$619$	5231.54	+	6037.52i	0.339698	+	0.392033i	0.899736	−	0.436434i	$-0.143759\pi$
$619$	5231.54	+	6037.52i	0.339698	+	0.392033i	−0.560038	+	0.828467i	$0.689213\pi$
$620$	−2083.92			−0.134987
$621$	210.313	−	749.923i	0.0135903	−	0.0484595i
$622$	7379.84			0.475731
$623$	8372.30	+	9662.15i	0.538410	+	0.621358i
$624$	2619.71	+	1683.59i	0.168065	+	0.108009i
$625$	−88.9468	+	618.638i	−0.00569259	+	0.0395929i
$626$	1927.50	−	4220.64i	0.123065	−	0.269474i
$627$	2658.01	+	18486.9i	0.169299	+	1.17750i
$628$	−21509.8	−	6315.86i	−1.36678	−	0.401322i
$629$	3708.56	−	2383.35i	0.235088	−	0.151082i
$630$	589.532	+	1290.90i	0.0372818	+	0.0816358i
$631$	−3755.91	+	1102.83i	−0.236958	+	0.0695771i	−0.398055	−	0.917361i	$-0.630315\pi$
$631$	−3755.91	+	1102.83i	−0.236958	+	0.0695771i	0.161098	+	0.986938i	$0.448497\pi$
$632$	3034.88	−	3502.44i	0.191014	−	0.220442i
$633$	3080.57	−	3555.17i	0.193431	−	0.223231i
$634$	712.339	−	209.162i	0.0446224	−	0.0131023i
$635$	−1650.90	−	3614.98i	−0.103172	−	0.225915i
$636$	974.352	−	626.178i	0.0607477	−	0.0390402i
$637$	3462.03	+	1016.54i	0.215339	+	0.0632292i
$638$	1005.76	+	6995.19i	0.0624111	+	0.434079i
$639$	8199.03	−	17953.4i	0.507588	−	1.11146i
$640$	−1044.48	+	7264.53i	−0.0645105	+	0.448681i
$641$	10844.0	+	6969.03i	0.668195	+	0.429423i	0.830274	−	0.557355i	$-0.188184\pi$
$641$	10844.0	+	6969.03i	0.668195	+	0.429423i	−0.162079	+	0.986778i	$0.551820\pi$
$642$	−7003.85	−	8082.87i	−0.430560	−	0.496893i
$643$	−26674.9			−1.63601			−0.818007	−	0.575209i	$-0.804921\pi$
$643$	−26674.9			−1.63601			−0.818007	+	0.575209i	$0.804921\pi$
$644$	−3252.33	+	5198.85i	−0.199006	+	0.318111i
$645$	1093.08			0.0667288
$646$	−2096.54	−	2419.53i	−0.127689	−	0.147361i
$647$	−11487.0	−	7382.27i	−0.697993	−	0.448573i	0.142926	−	0.989733i	$-0.454349\pi$
$647$	−11487.0	−	7382.27i	−0.697993	−	0.448573i	−0.840919	+	0.541160i	$0.817985\pi$
$648$	1744.95	−	12136.4i	0.105784	−	0.735746i
$649$	−5819.52	+	12743.0i	−0.351982	+	0.770733i
$650$	56.7319	+	394.579i	0.00342340	+	0.0238102i
$651$	3826.14	+	1123.46i	0.230351	+	0.0676370i
$652$	−8141.27	+	5232.08i	−0.489013	+	0.314270i
$653$	−6101.42	−	13360.2i	−0.365646	−	0.800653i	−0.999627	−	0.0273046i	$-0.991308\pi$
$653$	−6101.42	−	13360.2i	−0.365646	−	0.800653i	0.633981	−	0.773349i	$-0.281420\pi$
$654$	73.2288	−	21.5019i	0.00437840	−	0.00128561i
$655$	2817.64	−	3251.73i	0.168083	−	0.193978i
$656$	−570.671	+	658.589i	−0.0339648	+	0.0391975i
$657$	21251.5	−	6240.01i	1.26195	−	0.370542i
$658$	−1323.54	−	2898.15i	−0.0784148	−	0.171704i
$659$	−19050.2	+	12242.8i	−1.12608	+	0.723690i	−0.964739	−	0.263208i	$-0.915219\pi$
$659$	−19050.2	+	12242.8i	−1.12608	+	0.723690i	−0.161344	+	0.986898i	$0.551583\pi$
$660$	−4973.70	−	1460.41i	−0.293335	−	0.0861308i
$661$	−2383.52	−	16577.8i	−0.140255	−	0.975493i	−0.931434	−	0.363909i	$-0.881442\pi$
$661$	−2383.52	−	16577.8i	−0.140255	−	0.975493i	0.791180	−	0.611584i	$-0.209467\pi$
$662$	−5201.32	+	11389.3i	−0.305370	+	0.668668i
$663$	317.004	−	2204.81i	0.0185693	−	0.129152i
$664$	5905.97	+	3795.53i	0.345175	+	0.221830i
$665$	3279.39	+	3784.62i	0.191232	+	0.220693i
$666$	6539.06			0.380456
$667$	−371.629	−	30516.1i	−0.0215735	−	1.77150i
$668$	4821.74			0.279280
$669$	16758.8	+	19340.7i	0.968510	+	1.11772i
$670$	1442.32	+	926.924i	0.0831668	+	0.0534481i
$671$	1368.25	−	9516.38i	0.0787193	−	0.547505i
$672$	4630.42	−	10139.2i	0.265807	−	0.582036i
$673$	195.281	+	1358.21i	0.0111850	+	0.0777935i	0.994649	−	0.103308i	$-0.0329428\pi$
$673$	195.281	+	1358.21i	0.0111850	+	0.0777935i	−0.983464	+	0.181102i	$0.942034\pi$
$674$	10553.8	+	3098.88i	0.603143	+	0.177099i
$675$	148.502	−	95.4364i	0.00846791	−	0.00544200i
$676$	5507.50	+	12059.7i	0.313353	+	0.686148i
$677$	−9789.22	+	2874.37i	−0.555731	+	0.163177i	−0.547526	−	0.836789i	$-0.684430\pi$
$677$	−9789.22	+	2874.37i	−0.555731	+	0.163177i	−0.00820575	+	0.999966i	$0.502612\pi$
$678$	−11743.2	+	13552.4i	−0.665184	+	0.767663i
$679$	−1826.87	+	2108.32i	−0.103253	+	0.119160i
$680$	1891.78	−	555.477i	0.106686	−	0.0313258i
$681$	13324.6	+	29176.9i	0.749782	+	1.64179i
$682$	1364.59	−	876.966i	0.0766169	−	0.0492387i
$683$	22525.6	+	6614.12i	1.26196	+	0.370545i	0.843224	−	0.537563i	$-0.180655\pi$
$683$	22525.6	+	6614.12i	1.26196	+	0.370545i	0.418736	+	0.908108i	$0.362473\pi$
$684$	3086.96	+	21470.3i	0.172563	+	1.20020i
$685$	843.386	−	1846.76i	0.0470425	−	0.103009i
$686$	887.619	−	6173.53i	0.0494016	−	0.343595i
$687$	26867.5	+	17266.7i	1.49208	+	0.958900i
$688$	−609.879	−	703.838i	−0.0337957	−	0.0390023i
$689$	−316.673			−0.0175099
$690$	−4482.37	−	1981.42i	−0.247306	−	0.109321i
$691$	−9341.27			−0.514267			−0.257134	−	0.966376i	$-0.582778\pi$
$691$	−9341.27			−0.514267			−0.257134	+	0.966376i	$0.582778\pi$
$692$	951.760	+	1098.39i	0.0522839	+	0.0603389i
$693$	4244.59	+	2727.83i	0.232668	+	0.149526i
$694$	−1110.60	+	7724.41i	−0.0607462	+	0.422499i
$695$	4632.51	−	10143.8i	0.252836	−	0.553634i
$696$	5095.40	+	35439.3i	0.277501	+	1.93006i
$697$	598.091	+	175.615i	0.0325026	+	0.00954362i
$698$	−4010.17	+	2577.18i	−0.217460	+	0.139753i
$699$	−13050.3	−	28576.1i	−0.706161	−	1.54628i
$700$	−1333.57	+	391.572i	−0.0720062	+	0.0211429i
$701$	−13514.6	+	15596.7i	−0.728159	+	0.840341i	−0.992263	−	0.124154i	$-0.960378\pi$
$701$	−13514.6	+	15596.7i	−0.728159	+	0.840341i	0.264104	+	0.964494i	$0.414924\pi$
$702$	73.7312	−	85.0903i	0.00396411	−	0.00457482i
$703$	22139.9	−	6500.86i	1.18780	−	0.348769i
$704$	352.816	+	772.559i	0.0188881	+	0.0413592i
$705$	−9783.87	+	6287.71i	−0.522669	+	0.335899i
$706$	−10839.6	−	3182.80i	−0.577839	−	0.169669i
$707$	−476.719	−	3315.65i	−0.0253591	−	0.176376i
$708$	−13287.0	+	29094.6i	−0.705307	+	1.54441i
$709$	3497.64	−	24326.6i	0.185270	−	1.28858i	−0.658786	−	0.752330i	$-0.728930\pi$
$709$	3497.64	−	24326.6i	0.185270	−	1.28858i	0.844057	−	0.536254i	$-0.180161\pi$
$710$	−3560.13	−	2287.96i	−0.188182	−	0.120937i
$711$	4859.57	+	5608.24i	0.256326	+	0.295816i
$712$	26347.3			1.38681
$713$	−6335.83	+	2987.25i	−0.332789	+	0.156905i
$714$	−1700.29			−0.0891201
$715$	928.131	+	1071.12i	0.0485456	+	0.0560246i
$716$	6997.57	+	4497.07i	0.365240	+	0.234725i
$717$	4643.81	−	32298.4i	0.241878	−	1.68230i
$718$	1148.02	−	2513.82i	0.0596710	−	0.130661i
$719$	−1812.61	−	12607.0i	−0.0940182	−	0.653911i	−0.981272	−	0.192629i	$-0.938299\pi$
$719$	−1812.61	−	12607.0i	−0.0940182	−	0.653911i	0.887253	−	0.461282i	$-0.152610\pi$
$720$	−4234.85	−	1243.47i	−0.219200	−	0.0643628i
$721$	−2917.43	+	1874.92i	−0.150695	+	0.0968457i
$722$	−3545.82	−	7764.26i	−0.182772	−	0.400216i
$723$	34643.1	−	10172.1i	1.78201	−	0.523245i
$724$	−9899.36	+	11424.5i	−0.508159	+	0.586447i
$725$	4529.58	−	5227.42i	0.232034	−	0.267781i
$726$	−7476.68	+	2195.35i	−0.382211	+	0.112227i
$727$	−6269.77	−	13728.9i	−0.319853	−	0.700380i	0.679596	−	0.733587i	$-0.262155\pi$
$727$	−6269.77	−	13728.9i	−0.319853	−	0.700380i	−0.999448	+	0.0332069i	$0.989428\pi$
$728$	−1654.79	+	1063.47i	−0.0842453	+	0.0541412i
$729$	20193.9	+	5929.46i	1.02596	+	0.301248i
$730$	−675.862	−	4700.72i	−0.0342668	−	0.238331i
$731$	−276.736	+	605.967i	−0.0140020	+	0.0306601i
$732$	3123.96	−	21727.6i	0.157739	−	1.09710i
$733$	−13313.5	−	8556.05i	−0.670865	−	0.431139i	0.160372	−	0.987057i	$-0.448731\pi$
$733$	−13313.5	−	8556.05i	−0.670865	−	0.431139i	−0.831237	+	0.555918i	$0.812367\pi$
$734$	−1391.19	−	1605.52i	−0.0699590	−	0.0807369i
$735$	−10053.7			−0.504540
$736$	5744.67	+	18718.3i	0.287706	+	0.937451i
$737$	6095.63			0.304661
$738$	605.495	+	698.779i	0.0302013	+	0.0348542i
$739$	10365.3	+	6661.39i	0.515960	+	0.331588i	0.772572	−	0.634927i	$-0.218970\pi$
$739$	10365.3	+	6661.39i	0.515960	+	0.331588i	−0.256612	+	0.966515i	$0.582606\pi$
$740$	−911.412	+	6339.01i	−0.0452759	+	0.314901i
$741$	4843.42	−	10605.6i	0.240118	−	0.525785i
$742$	34.4009	+	239.263i	0.00170202	+	0.0118378i
$743$	37964.7	+	11147.4i	1.87455	+	0.550417i	0.997552	+	0.0699215i	$0.0222749\pi$
$743$	37964.7	+	11147.4i	1.87455	+	0.550417i	0.876997	+	0.480496i	$0.159543\pi$
$744$	6913.31	−	4442.91i	0.340664	−	0.218932i
$745$	4739.22	+	10377.4i	0.233063	+	0.510336i
$746$	−15832.5	+	4648.85i	−0.777038	+	0.228159i
$747$	−7361.55	+	8495.68i	−0.360569	+	0.416119i
$748$	2068.79	−	2387.51i	0.101126	−	0.116706i
$749$	−9782.51	+	2872.40i	−0.477230	+	0.140127i
$750$	−461.420	−	1010.37i	−0.0224649	−	0.0491912i
$751$	−28742.9	+	18472.0i	−1.39660	+	0.897539i	−0.999793	−	0.0203641i	$-0.993517\pi$
$751$	−28742.9	+	18472.0i	−1.39660	+	0.897539i	−0.396805	+	0.917903i	$0.629881\pi$
$752$	9507.52	+	2791.66i	0.461042	+	0.135374i
$753$	5344.53	+	37172.0i	0.258653	+	1.79897i
$754$	1832.69	−	4013.03i	0.0885180	−	0.193827i
$755$	404.669	−	2814.53i	0.0195065	−	0.135671i
$756$	330.238	+	212.231i	0.0158871	+	0.0102100i
$757$	−14154.9	−	16335.7i	−0.679617	−	0.784320i	0.306232	−	0.951957i	$-0.400932\pi$
$757$	−14154.9	−	16335.7i	−0.679617	−	0.784320i	−0.985849	+	0.167637i	$0.946386\pi$
$758$	15874.7			0.760680
$759$	−17215.2	+	2689.53i	−0.823284	+	0.128622i
$760$	10320.1			0.492565
$761$	−16979.4	−	19595.2i	−0.808807	−	0.933413i	0.190023	−	0.981780i	$-0.439144\pi$
$761$	−16979.4	−	19595.2i	−0.808807	−	0.933413i	−0.998830	+	0.0483668i	$0.984598\pi$
$762$	5941.56	+	3818.41i	0.282467	+	0.181531i
$763$	10.3541	−	72.0141i	0.000491275	−	0.00341689i
$764$	5207.68	−	11403.2i	0.246607	−	0.539993i

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)

\(f(q)\)	\(=\)	\(q+(0.784981 + 0.905916i) q^{2} +(6.23621 + 4.00777i) q^{3} +(0.934030 - 6.49632i) q^{4} +(2.07708 - 4.54816i) q^{5} +(1.26460 + 8.79550i) q^{6} +(8.12768 + 2.38650i) q^{7} +(14.6856 - 9.43786i) q^{8} +(11.6119 + 25.4265i) q^{9} +O(q^{10})\)	\(q+(0.784981 + 0.905916i) q^{2} +(6.23621 + 4.00777i) q^{3} +(0.934030 - 6.49632i) q^{4} +(2.07708 - 4.54816i) q^{5} +(1.26460 + 8.79550i) q^{6} +(8.12768 + 2.38650i) q^{7} +(14.6856 - 9.43786i) q^{8} +(11.6119 + 25.4265i) q^{9} +(5.75072 - 1.68856i) q^{10} +(13.9544 - 16.1043i) q^{11} +(31.8605 - 36.7690i) q^{12} +(-12.7635 + 3.74769i) q^{13} +(4.21810 + 9.23635i) q^{14} +(31.1810 - 20.0388i) q^{15} +(-30.3003 - 8.89698i) q^{16} +(3.21473 + 22.3589i) q^{17} +(-13.9192 + 30.4787i) q^{18} +(-16.8267 + 117.032i) q^{19} +(-27.6062 - 17.7415i) q^{20} +(41.1213 + 47.4566i) q^{21} +25.5431 q^{22} +(-109.364 - 14.3672i) q^{23} +129.407 q^{24} +(-16.3715 - 18.8937i) q^{25} +(-13.4142 - 8.62077i) q^{26} +(-1.00488 + 6.98911i) q^{27} +(23.0950 - 50.5709i) q^{28} +(39.3749 + 273.859i) q^{29} +(42.6300 + 12.5173i) q^{30} +(53.4229 - 34.3328i) q^{31} +(-73.7398 - 161.468i) q^{32} +(151.565 - 44.5035i) q^{33} +(-17.7318 + 20.4636i) q^{34} +(27.7360 - 32.0090i) q^{35} +(176.024 - 51.6855i) q^{36} +(-81.0712 - 177.521i) q^{37} +(-119.230 + 76.6246i) q^{38} +(-94.6156 - 27.7816i) q^{39} +(-12.4218 - 86.3956i) q^{40} +(11.4634 - 25.1013i) q^{41} +(-10.7122 + 74.5050i) q^{42} +(24.8094 + 15.9440i) q^{43} +(-91.5847 - 105.694i) q^{44} +139.763 q^{45} +(-72.8335 - 110.353i) q^{46} -313.776 q^{47} +(-153.302 - 176.920i) q^{48} +(-228.186 - 146.646i) q^{49} +(4.26482 - 29.6624i) q^{50} +(-69.5617 + 152.319i) q^{51} +(12.4247 + 86.4160i) q^{52} +(22.8416 + 6.70690i) q^{53} +(-7.12036 + 4.57598i) q^{54} +(-44.2604 - 96.9168i) q^{55} +(141.883 - 41.6607i) q^{56} +(-573.974 + 662.401i) q^{57} +(-217.184 + 250.644i) q^{58} +(-630.788 + 185.216i) q^{59} +(-101.055 - 221.279i) q^{60} +(379.558 - 243.927i) q^{61} +(73.0386 + 21.4461i) q^{62} +(33.6973 + 234.370i) q^{63} +(-16.5571 + 36.2550i) q^{64} +(-9.46558 + 65.8345i) q^{65} +(159.292 + 102.371i) q^{66} +(187.329 + 216.189i) q^{67} +148.253 q^{68} +(-624.439 - 527.904i) q^{69} +50.7697 q^{70} +(-462.390 - 533.626i) q^{71} +(410.499 + 263.812i) q^{72} +(112.766 - 784.304i) q^{73} +(97.1799 - 212.794i) q^{74} +(-26.3745 - 183.439i) q^{75} +(744.563 + 218.623i) q^{76} +(151.850 - 97.5881i) q^{77} +(-49.1036 - 107.522i) q^{78} +(254.724 - 74.7937i) q^{79} +(-103.401 + 119.331i) q^{80} +(459.958 - 530.819i) q^{81} +(31.7382 - 9.31918i) q^{82} +(167.064 + 365.818i) q^{83} +(346.702 - 222.812i) q^{84} +(108.369 + 31.8201i) q^{85} +(5.03094 + 34.9910i) q^{86} +(-852.011 + 1865.64i) q^{87} +(52.9393 - 368.201i) q^{88} +(1269.69 + 815.981i) q^{89} +(109.711 + 126.613i) q^{90} -112.681 q^{91} +(-195.484 + 697.047i) q^{92} +470.754 q^{93} +(-246.308 - 284.255i) q^{94} +(497.332 + 319.616i) q^{95} +(187.268 - 1302.48i) q^{96} +(-136.810 + 299.571i) q^{97} +(-46.2725 - 321.832i) q^{98} +(571.513 + 167.811i) 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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