LMFDB - Embedded newform 115.4.g.a.16.1

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			16.1
Character	$\chi$	$=$	115.16
Dual form			115.4.g.a.36.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.13461 + 3.61754i) q^{2} +(-7.41459 + 4.76507i) q^{3} +(-2.12225 - 14.7606i) q^{4} +(2.07708 + 4.54816i) q^{5} +(6.00407 - 41.7592i) q^{6} +(30.1381 - 8.84935i) q^{7} +(27.8349 + 17.8884i) q^{8} +(21.0541 - 46.1020i) q^{9} +O(q^{10})$	\(q+(-3.13461 + 3.61754i) q^{2} +(-7.41459 + 4.76507i) q^{3} +(-2.12225 - 14.7606i) q^{4} +(2.07708 + 4.54816i) q^{5} +(6.00407 - 41.7592i) q^{6} +(30.1381 - 8.84935i) q^{7} +(27.8349 + 17.8884i) q^{8} +(21.0541 - 46.1020i) q^{9} +(-22.9640 - 6.74283i) q^{10} +(-10.6474 - 12.2878i) q^{11} +(86.0708 + 99.3310i) q^{12} +(9.76032 + 2.86589i) q^{13} +(-62.4585 + 136.765i) q^{14} +(-37.0729 - 23.8253i) q^{15} +(-37.4969 + 11.0101i) q^{16} +(6.29904 - 43.8108i) q^{17} +(100.779 + 220.676i) q^{18} +(-20.4034 - 141.909i) q^{19} +(62.7254 - 40.3112i) q^{20} +(-181.294 + 209.225i) q^{21} +77.8269 q^{22} +(21.8728 + 108.114i) q^{23} -291.623 q^{24} +(-16.3715 + 18.8937i) q^{25} +(-40.9623 + 26.3249i) q^{26} +(29.7049 + 206.602i) q^{27} +(-194.582 - 426.076i) q^{28} +(15.4948 - 107.769i) q^{29} +(202.398 - 59.4295i) q^{30} +(221.688 + 142.471i) q^{31} +(-32.2511 + 70.6200i) q^{32} +(137.498 + 40.3731i) q^{33} +(138.742 + 160.117i) q^{34} +(102.847 + 118.692i) q^{35} +(-725.174 - 212.930i) q^{36} +(168.893 - 369.824i) q^{37} +(577.317 + 371.019i) q^{38} +(-86.0249 + 25.2592i) q^{39} +(-23.5441 + 163.753i) q^{40} +(4.07059 + 8.91336i) q^{41} +(-188.591 - 1311.68i) q^{42} +(-101.393 + 65.1614i) q^{43} +(-158.778 + 183.240i) q^{44} +253.410 q^{45} +(-459.668 - 259.769i) q^{46} -253.723 q^{47} +(225.560 - 260.310i) q^{48} +(541.446 - 347.966i) q^{49} +(-17.0304 - 118.449i) q^{50} +(162.057 + 354.854i) q^{51} +(21.5883 - 150.150i) q^{52} +(187.836 - 55.1537i) q^{53} +(-840.505 - 540.160i) q^{54} +(33.7712 - 73.9487i) q^{55} +(997.191 + 292.802i) q^{56} +(827.488 + 954.972i) q^{57} +(341.287 + 393.867i) q^{58} +(540.807 + 158.795i) q^{59} +(-272.998 + 597.782i) q^{60} +(-600.889 - 386.168i) q^{61} +(-1210.30 + 355.376i) q^{62} +(226.557 - 1575.74i) q^{63} +(-284.251 - 622.422i) q^{64} +(7.23840 + 50.3442i) q^{65} +(-577.054 + 370.850i) q^{66} +(-443.032 + 511.286i) q^{67} -660.041 q^{68} +(-677.347 - 697.394i) q^{69} -751.761 q^{70} +(152.696 - 176.221i) q^{71} +(1410.73 - 906.619i) q^{72} +(11.2815 + 78.4646i) q^{73} +(808.438 + 1770.23i) q^{74} +(31.3581 - 218.101i) q^{75} +(-2051.36 + 602.333i) q^{76} +(-429.631 - 276.107i) q^{77} +(178.279 - 390.376i) q^{78} +(766.632 + 225.103i) q^{79} +(-127.959 - 147.673i) q^{80} +(-308.603 - 356.147i) q^{81} +(-45.0041 - 13.2144i) q^{82} +(-159.114 + 348.412i) q^{83} +(3473.03 + 2231.98i) q^{84} +(212.342 - 62.3492i) q^{85} +(82.1045 - 571.049i) q^{86} +(398.638 + 872.895i) q^{87} +(-76.5609 - 532.493i) q^{88} +(912.509 - 586.434i) q^{89} +(-794.342 + 916.720i) q^{90} +319.519 q^{91} +(1549.40 - 552.299i) q^{92} -2322.61 q^{93} +(795.325 - 917.854i) q^{94} +(603.045 - 387.553i) q^{95} +(-97.3805 - 677.296i) q^{96} +(117.830 + 258.011i) q^{97} +(-438.443 + 3049.44i) q^{98} +(-790.660 + 232.159i) 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 $

$2$	−3.13461	+	3.61754i	−1.10825	+	1.27899i	−0.151383	+	0.988475i	$0.548373\pi$
$2$	−3.13461	+	3.61754i	−1.10825	+	1.27899i	−0.956870	+	0.290517i	$0.906173\pi$
$3$	−7.41459	+	4.76507i	−1.42694	+	0.917038i	−0.427020	+	0.904242i	$0.640437\pi$
$3$	−7.41459	+	4.76507i	−1.42694	+	0.917038i	−0.999918	+	0.0127954i	$0.995927\pi$
$4$	−2.12225	−	14.7606i	−0.265281	−	1.84507i
$5$	2.07708	+	4.54816i	0.185779	+	0.406800i
$5$	2.07708	+	4.54816i	0.185779	+	0.406800i
$6$	6.00407	−	41.7592i	0.408525	−	2.84135i
$7$	30.1381	−	8.84935i	1.62731	−	0.477820i	0.664337	−	0.747433i	$-0.268714\pi$
$7$	30.1381	−	8.84935i	1.62731	−	0.477820i	0.962969	+	0.269613i	$0.0868957\pi$
$8$	27.8349	+	17.8884i	1.23014	+	0.790562i
$9$	21.0541	−	46.1020i	0.779780	−	1.70748i
$10$	−22.9640	−	6.74283i	−0.726184	−	0.213227i
$11$	−10.6474	−	12.2878i	−0.291846	−	0.336809i	0.590825	−	0.806800i	$-0.298803\pi$
$11$	−10.6474	−	12.2878i	−0.291846	−	0.336809i	−0.882671	+	0.469991i	$0.844257\pi$
$12$	86.0708	+	99.3310i	2.07054	+	2.38953i
$13$	9.76032	+	2.86589i	0.208233	+	0.0611427i	0.384185	−	0.923256i	$-0.374482\pi$
$13$	9.76032	+	2.86589i	0.208233	+	0.0611427i	−0.175953	+	0.984399i	$0.556301\pi$
$14$	−62.4585	+	136.765i	−1.19234	+	2.61086i
$15$	−37.0729	−	23.8253i	−0.638146	−	0.410112i
$16$	−37.4969	+	11.0101i	−0.585889	+	0.172032i
$17$	6.29904	−	43.8108i	0.0898671	−	0.625040i	−0.894256	−	0.447555i	$-0.852295\pi$
$17$	6.29904	−	43.8108i	0.0898671	−	0.625040i	0.984124	−	0.177485i	$-0.0567960\pi$
$18$	100.779	+	220.676i	1.31966	+	2.88965i
$19$	−20.4034	−	141.909i	−0.246361	−	1.71348i	−0.618905	−	0.785466i	$-0.712424\pi$
$19$	−20.4034	−	141.909i	−0.246361	−	1.71348i	0.372544	−	0.928015i	$-0.378486\pi$
$20$	62.7254	−	40.3112i	0.701292	−	0.450693i
$21$	−181.294	+	209.225i	−1.88389	+	2.17412i
$22$	77.8269			0.754216
$23$	21.8728	+	108.114i	0.198295	+	0.980142i
$23$	21.8728	+	108.114i	0.198295	+	0.980142i
$24$	−291.623			−2.48031
$25$	−16.3715	+	18.8937i	−0.130972	+	0.151150i
$26$	−40.9623	+	26.3249i	−0.308976	+	0.198567i
$27$	29.7049	+	206.602i	0.211730	+	1.47262i
$28$	−194.582	−	426.076i	−1.31331	−	2.87574i
$29$	15.4948	−	107.769i	0.0992178	−	0.690075i	−0.878128	−	0.478426i	$-0.841208\pi$
$29$	15.4948	−	107.769i	0.0992178	−	0.690075i	0.977346	−	0.211649i	$-0.0678833\pi$
$30$	202.398	−	59.4295i	1.23176	−	0.361677i
$31$	221.688	+	142.471i	1.28440	+	0.825434i	0.991424	−	0.130685i	$-0.0417177\pi$
$31$	221.688	+	142.471i	1.28440	+	0.825434i	0.292977	+	0.956119i	$0.405354\pi$
$32$	−32.2511	+	70.6200i	−0.178164	+	0.390124i
$33$	137.498	+	40.3731i	0.725313	+	0.212971i
$34$	138.742	+	160.117i	0.699825	+	0.807642i
$35$	102.847	+	118.692i	0.496697	+	0.573219i
$36$	−725.174	−	212.930i	−3.35729	−	0.985788i
$37$	168.893	−	369.824i	0.750429	−	1.64321i	−0.0151653	−	0.999885i	$-0.504827\pi$
$37$	168.893	−	369.824i	0.750429	−	1.64321i	0.765594	−	0.643324i	$-0.222445\pi$
$38$	577.317	+	371.019i	2.46456	+	1.58388i
$39$	−86.0249	+	25.2592i	−0.353206	+	0.103710i
$40$	−23.5441	+	163.753i	−0.0930663	+	0.647290i
$41$	4.07059	+	8.91336i	0.0155054	+	0.0339520i	0.917226	−	0.398367i	$-0.130423\pi$
$41$	4.07059	+	8.91336i	0.0155054	+	0.0339520i	−0.901721	+	0.432319i	$0.857696\pi$
$42$	−188.591	−	1311.68i	−0.692861	−	4.81895i
$43$	−101.393	+	65.1614i	−0.359589	+	0.231094i	−0.707943	−	0.706269i	$-0.750377\pi$
$43$	−101.393	+	65.1614i	−0.359589	+	0.231094i	0.348355	+	0.937363i	$0.386740\pi$
$44$	−158.778	+	183.240i	−0.544015	+	0.627827i
$45$	253.410			0.839469
$46$	−459.668	−	259.769i	−1.47336	−	0.832628i
$47$	−253.723			−0.787433			−0.393717	−	0.919232i	$-0.628811\pi$
$47$	−253.723			−0.787433			−0.393717	+	0.919232i	$0.628811\pi$
$48$	225.560	−	260.310i	0.678267	−	0.782762i
$49$	541.446	−	347.966i	1.57856	−	1.01448i
$50$	−17.0304	−	118.449i	−0.0481693	−	0.335025i
$51$	162.057	+	354.854i	0.444950	+	0.974305i
$52$	21.5883	−	150.150i	0.0575724	−	0.400425i
$53$	187.836	−	55.1537i	0.486817	−	0.142942i	−0.0291077	−	0.999576i	$-0.509267\pi$
$53$	187.836	−	55.1537i	0.486817	−	0.142942i	0.515925	+	0.856634i	$0.327448\pi$
$54$	−840.505	−	540.160i	−2.11812	−	1.36123i
$55$	33.7712	−	73.9487i	0.0827947	−	0.181295i
$56$	997.191	+	292.802i	2.37956	+	0.698702i
$57$	827.488	+	954.972i	1.92287	+	2.21911i
$58$	341.287	+	393.867i	0.772642	+	0.891676i
$59$	540.807	+	158.795i	1.19334	+	0.350396i	0.817303	−	0.576209i	$-0.195468\pi$
$59$	540.807	+	158.795i	1.19334	+	0.350396i	0.376037	+	0.926605i	$0.377287\pi$
$60$	−272.998	+	597.782i	−0.587398	+	1.28622i
$61$	−600.889	−	386.168i	−1.26124	−	0.810553i	−0.272790	−	0.962073i	$-0.587947\pi$
$61$	−600.889	−	386.168i	−1.26124	−	0.810553i	−0.988454	+	0.151521i	$0.951583\pi$
$62$	−1210.30	+	355.376i	−2.47917	+	0.727949i
$63$	226.557	−	1575.74i	0.453072	−	3.15119i
$64$	−284.251	−	622.422i	−0.555177	−	1.21567i
$65$	7.23840	+	50.3442i	0.0138125	+	0.0960681i
$66$	−577.054	+	370.850i	−1.07622	+	0.691644i
$67$	−443.032	+	511.286i	−0.807836	+	0.932292i	−0.998784	−	0.0493079i	$-0.984298\pi$
$67$	−443.032	+	511.286i	−0.807836	+	0.932292i	0.190948	+	0.981600i	$0.438844\pi$
$68$	−660.041			−1.17708
$69$	−677.347	−	697.394i	−1.18178	−	1.21676i
$70$	−751.761			−1.28361
$71$	152.696	−	176.221i	0.255235	−	0.294557i	−0.613642	−	0.789584i	$-0.710296\pi$
$71$	152.696	−	176.221i	0.255235	−	0.294557i	0.868878	+	0.495027i	$0.164842\pi$
$72$	1410.73	−	906.619i	2.30911	−	1.48397i
$73$	11.2815	+	78.4646i	0.0180877	+	0.125803i	0.996865	−	0.0791259i	$-0.0252129\pi$
$73$	11.2815	+	78.4646i	0.0180877	+	0.125803i	−0.978777	+	0.204928i	$0.934304\pi$
$74$	808.438	+	1770.23i	1.26999	+	2.78088i
$75$	31.3581	−	218.101i	0.0482790	−	0.335788i
$76$	−2051.36	+	602.333i	−3.09614	+	0.909109i
$77$	−429.631	−	276.107i	−0.635858	−	0.408641i
$78$	178.279	−	390.376i	0.258796	−	0.566685i
$79$	766.632	+	225.103i	1.09181	+	0.320584i	0.777593	−	0.628768i	$-0.216441\pi$
$79$	766.632	+	225.103i	1.09181	+	0.320584i	0.314215	+	0.949352i	$0.398259\pi$
$80$	−127.959	−	147.673i	−0.178829	−	0.206379i
$81$	−308.603	−	356.147i	−0.423324	−	0.488542i
$82$	−45.0041	−	13.2144i	−0.0606082	−	0.0177962i
$83$	−159.114	+	348.412i	−0.210423	+	0.460761i	−0.985186	−	0.171490i	$-0.945142\pi$
$83$	−159.114	+	348.412i	−0.210423	+	0.460761i	0.774763	+	0.632252i	$0.217869\pi$
$84$	3473.03	+	2231.98i	4.51117	+	2.89915i
$85$	212.342	−	62.3492i	0.270961	−	0.0795615i
$86$	82.1045	−	571.049i	0.102948	−	0.716021i
$87$	398.638	+	872.895i	0.491247	+	1.07568i
$88$	−76.5609	−	532.493i	−0.0927434	−	0.645044i
$89$	912.509	−	586.434i	1.08681	−	0.698448i	0.130687	−	0.991424i	$-0.458282\pi$
$89$	912.509	−	586.434i	1.08681	−	0.698448i	0.956120	+	0.292975i	$0.0946454\pi$
$90$	−794.342	+	916.720i	−0.930345	+	1.07368i
$91$	319.519			0.368074
$92$	1549.40	−	552.299i	1.75583	−	0.625883i
$93$	−2322.61			−2.58972
$94$	795.325	−	917.854i	0.872675	−	1.00712i
$95$	603.045	−	387.553i	0.651275	−	0.418549i
$96$	−97.3805	−	677.296i	−0.103530	−	0.720065i
$97$	117.830	+	258.011i	0.123338	+	0.270072i	0.961222	−	0.275776i	$-0.0889348\pi$
$97$	117.830	+	258.011i	0.123338	+	0.270072i	−0.837884	+	0.545848i	$0.816207\pi$
$98$	−438.443	+	3049.44i	−0.451933	+	3.14327i
$99$	−790.660	+	232.159i	−0.802670	+	0.235685i
$100$	313.627	+	201.556i	0.313627	+	0.201556i
$101$	385.906	−	845.017i	0.380189	−	0.832498i	−0.618711	−	0.785618i	$-0.712345\pi$
$101$	385.906	−	845.017i	0.380189	−	0.832498i	0.998901	−	0.0468798i	$-0.0149278\pi$
$102$	−1791.68	−	526.086i	−1.73925	−	0.510689i
$103$	640.238	+	738.874i	0.612471	+	0.706830i	0.974259	−	0.225431i	$-0.0723790\pi$
$103$	640.238	+	738.874i	0.612471	+	0.706830i	−0.361788	+	0.932260i	$0.617834\pi$
$104$	220.411	+	254.368i	0.207818	+	0.239835i
$105$	−1328.15	−	389.979i	−1.23442	−	0.362458i
$106$	−389.274	+	852.390i	−0.356694	+	0.781052i
$107$	−387.940	−	249.314i	−0.350500	−	0.225253i	0.353529	−	0.935423i	$-0.384981\pi$
$107$	−387.940	−	249.314i	−0.350500	−	0.225253i	−0.704030	+	0.710170i	$0.748618\pi$
$108$	2986.53	−	876.924i	2.66092	−	0.781316i
$109$	−105.889	+	736.478i	−0.0930493	+	0.647172i	0.888910	+	0.458081i	$0.151463\pi$
$109$	−105.889	+	736.478i	−0.0930493	+	0.647172i	−0.981960	+	0.189091i	$0.939446\pi$
$110$	161.652	+	353.969i	0.140118	+	0.306815i
$111$	509.965	+	3546.88i	0.436069	+	3.03293i
$112$	−1032.65	+	663.646i	−0.871220	+	0.559899i
$113$	277.397	−	320.133i	0.230932	−	0.266509i	−0.628443	−	0.777855i	$-0.716308\pi$
$113$	277.397	−	320.133i	0.230932	−	0.266509i	0.859375	+	0.511346i	$0.170853\pi$
$114$	−6048.50			−4.96925
$115$	−446.287	+	324.041i	−0.361883	+	0.262756i
$116$	−1623.61			−1.29956
$117$	337.618	−	389.631i	0.266776	−	0.307876i
$118$	−2269.67	+	1458.63i	−1.77068	+	1.13794i
$119$	−197.856	−	1376.12i	−0.152415	−	1.06007i
$120$	−605.724	−	1326.35i	−0.460790	−	1.00899i
$121$	151.799	−	1055.79i	0.114049	−	0.793229i
$122$	3280.53	−	963.250i	2.43447	−	0.714825i
$123$	−72.6545	−	46.6922i	−0.0532605	−	0.0342284i
$124$	1632.47	−	3574.61i	1.18226	−	2.58879i
$125$	−119.937	−	35.2166i	−0.0858197	−	0.0251989i
$126$	4990.13	+	5758.92i	3.52823	+	4.07179i
$127$	685.818	+	791.476i	0.479185	+	0.553009i	0.942943	−	0.332953i	$-0.108045\pi$
$127$	685.818	+	791.476i	0.479185	+	0.553009i	−0.463759	+	0.885962i	$0.653500\pi$
$128$	2546.72	+	747.785i	1.75860	+	0.516371i
$129$	441.290	−	966.290i	0.301189	−	0.659512i
$130$	−204.812	−	131.624i	−0.138178	−	0.0888017i
$131$	96.5026	−	28.3357i	0.0643623	−	0.0188985i	−0.249393	−	0.968402i	$-0.580231\pi$
$131$	96.5026	−	28.3357i	0.0643623	−	0.0188985i	0.313755	+	0.949504i	$0.398413\pi$
$132$	304.125	−	2115.23i	0.200535	−	1.39475i
$133$	−1870.72	−	4096.31i	−1.21964	−	2.67064i
$134$	−460.863	−	3205.37i	−0.297108	−	2.06643i
$135$	−877.961	+	564.231i	−0.559725	+	0.359713i
$136$	959.037	−	1106.79i	0.604682	−	0.697840i
$137$	248.105			0.154723			0.0773615	−	0.997003i	$-0.475350\pi$
$137$	248.105			0.154723			0.0773615	+	0.997003i	$0.475350\pi$
$138$	4646.07	−	264.267i	2.86594	−	0.163014i
$139$	−1099.46			−0.670899			−0.335449	−	0.942058i	$-0.608888\pi$
$139$	−1099.46			−0.670899			−0.335449	+	0.942058i	$0.608888\pi$
$140$	1533.70	−	1769.98i	0.925866	−	1.06851i
$141$	1881.25	−	1209.01i	1.12362	−	0.722106i
$142$	158.842	+	1104.77i	0.0938712	+	0.652888i
$143$	−68.7067	−	150.447i	−0.0401786	−	0.0879789i
$144$	−281.875	+	1960.49i	−0.163122	+	1.13454i
$145$	522.334	−	153.371i	0.299155	−	0.0878398i
$146$	−319.212	−	205.145i	−0.180946	−	0.116287i
$147$	−2356.52	+	5160.05i	−1.32219	+	2.89520i
$148$	−5817.26	−	1708.10i	−3.23092	−	0.948683i
$149$	441.774	+	509.835i	0.242896	+	0.280317i	0.864087	−	0.503342i	$-0.167896\pi$
$149$	441.774	+	509.835i	0.242896	+	0.280317i	−0.621191	+	0.783659i	$0.713351\pi$
$150$	690.692	+	797.101i	0.375965	+	0.433887i
$151$	911.999	+	267.787i	0.491506	+	0.144319i	0.518088	−	0.855327i	$-0.326644\pi$
$151$	911.999	+	267.787i	0.491506	+	0.144319i	−0.0265816	+	0.999647i	$0.508462\pi$
$152$	1970.59	−	4315.00i	1.05155	−	2.30258i
$153$	−1887.14	−	1212.79i	−0.997166	−	0.640840i
$154$	2345.56	−	688.718i	1.22734	−	0.360379i
$155$	−187.515	+	1304.20i	−0.0971715	+	0.675843i
$156$	555.407	+	1216.17i	0.285052	+	0.624178i
$157$	−341.567	−	2375.65i	−0.173631	−	1.20763i	−0.871134	−	0.491046i	$-0.836615\pi$
$157$	−341.567	−	2375.65i	−0.173631	−	1.20763i	0.697503	−	0.716582i	$-0.254294\pi$
$158$	−3217.41	+	2067.71i	−1.62002	+	1.04113i
$159$	−1129.92	+	1303.99i	−0.563574	+	0.650399i
$160$	−388.179			−0.191801
$161$	1615.94	+	3064.79i	0.791019	+	1.50024i
$162$	2255.73			1.09399
$163$	1980.69	−	2285.83i	0.951775	−	1.09841i	−0.0432784	−	0.999063i	$-0.513780\pi$
$163$	1980.69	−	2285.83i	0.951775	−	1.09841i	0.995053	−	0.0993436i	$-0.0316743\pi$
$164$	122.928	−	79.0007i	0.0585307	−	0.0376154i
$165$	101.971	+	709.221i	0.0481115	+	0.334623i
$166$	−761.631	−	1667.74i	−0.356109	−	0.779769i
$167$	591.866	−	4116.52i	0.274251	−	1.90746i	−0.127724	−	0.991810i	$-0.540767\pi$
$167$	591.866	−	4116.52i	0.274251	−	1.90746i	0.401975	−	0.915650i	$-0.368324\pi$
$168$	−8788.98	+	2580.68i	−4.03622	+	1.18514i
$169$	−1761.18	−	1131.84i	−0.801631	−	0.515177i
$170$	−440.059	+	963.596i	−0.198535	+	0.434732i
$171$	−6971.85	−	2047.12i	−3.11784	−	0.915481i
$172$	1177.00	+	1358.33i	0.521777	+	0.602162i
$173$	−1716.13	−	1980.52i	−0.754191	−	0.870382i	0.240777	−	0.970581i	$-0.422598\pi$
$173$	−1716.13	−	1980.52i	−0.754191	−	0.870382i	−0.994968	+	0.100198i	$0.968052\pi$
$174$	−4407.31	−	1294.10i	−1.92021	−	0.563825i
$175$	−326.210	+	714.299i	−0.140909	+	0.308548i
$176$	534.533	+	343.524i	0.228932	+	0.147125i
$177$	−4766.53	+	1399.58i	−2.02415	+	0.594343i
$178$	−738.917	+	5139.28i	−0.311147	+	2.16407i
$179$	1104.47	+	2418.45i	0.461184	+	1.00985i	0.987216	+	0.159387i	$0.0509518\pi$
$179$	1104.47	+	2418.45i	0.461184	+	1.00985i	−0.526032	+	0.850465i	$0.676321\pi$
$180$	−537.800	−	3740.48i	−0.222696	−	1.54888i
$181$	−870.717	+	559.576i	−0.357569	+	0.229795i	−0.707075	−	0.707139i	$-0.749986\pi$
$181$	−870.717	+	559.576i	−0.357569	+	0.229795i	0.349506	+	0.936934i	$0.386349\pi$
$182$	−1001.57	+	1155.87i	−0.407919	+	0.470764i
$183$	6295.46			2.54303
$184$	−1325.15	+	3400.60i	−0.530933	+	1.36248i
$185$	2032.82			0.807871
$186$	7280.49	−	8402.13i	2.87006	−	3.31223i
$187$	−605.404	+	389.070i	−0.236746	+	0.152148i
$188$	538.465	+	3745.11i	0.208891	+	1.45287i
$189$	2723.55	+	5963.74i	1.04820	+	2.29523i
$190$	−488.324	+	3396.37i	−0.186456	+	1.29683i
$191$	−187.434	+	55.0354i	−0.0710064	+	0.0208493i	−0.317043	−	0.948411i	$-0.602690\pi$
$191$	−187.434	+	55.0354i	−0.0710064	+	0.0208493i	0.246036	+	0.969261i	$0.420872\pi$
$192$	5073.49	+	3260.53i	1.90702	+	1.22557i
$193$	−914.472	+	2002.41i	−0.341063	+	0.746823i	−0.999985	−	0.00538728i	$-0.998285\pi$
$193$	−914.472	+	2002.41i	−0.341063	+	0.746823i	0.658923	+	0.752211i	$0.271012\pi$
$194$	−1302.71	−	382.511i	−0.482110	−	0.141560i
$195$	−293.563	−	338.790i	−0.107808	−	0.124417i
$196$	−6285.27	−	7253.59i	−2.29055	−	2.64344i
$197$	3373.12	+	990.439i	1.21992	+	0.358202i	0.827439	−	0.561556i	$-0.189797\pi$
$197$	3373.12	+	990.439i	1.21992	+	0.358202i	0.392486	+	0.919758i	$0.371615\pi$
$198$	1638.57	−	3587.97i	0.588122	−	1.28781i
$199$	711.863	+	457.486i	0.253581	+	0.162967i	0.661256	−	0.750161i	$-0.270024\pi$
$199$	711.863	+	457.486i	0.253581	+	0.162967i	−0.407675	+	0.913127i	$0.633660\pi$
$200$	−793.677	+	233.045i	−0.280607	+	0.0823937i
$201$	848.588	−	5902.06i	0.297785	−	2.07114i
$202$	1847.21	+	4044.83i	0.643413	+	1.40888i
$203$	−486.700	−	3385.07i	−0.168274	−	1.17037i
$204$	4893.93	−	3145.14i	1.67963	−	1.07943i
$205$	−32.0844	+	37.0274i	−0.0109311	+	0.0126152i
$206$	−4679.80			−1.58280
$207$	5444.77	+	1267.86i	1.82820	+	0.425711i
$208$	−397.535			−0.132520
$209$	−1526.50	+	1761.67i	−0.505216	+	0.583050i
$210$	5574.00	−	3582.19i	1.83163	−	1.17712i
$211$	673.131	+	4681.73i	0.219622	+	1.52750i	0.739437	+	0.673225i	$0.235092\pi$
$211$	673.131	+	4681.73i	0.219622	+	1.52750i	−0.519815	+	0.854279i	$0.673999\pi$
$212$	−1212.74	−	2655.52i	−0.392883	−	0.860293i
$213$	−292.476	+	2034.21i	−0.0940850	+	0.654376i
$214$	2117.94	−	621.884i	0.676540	−	0.198650i
$215$	−506.966	−	325.807i	−0.160813	−	0.103348i
$216$	−2868.95	+	6282.12i	−0.903737	+	1.97891i
$217$	7942.05	+	2332.00i	2.48452	+	0.729522i
$218$	−2332.31	−	2691.63i	−0.724606	−	0.836240i
$219$	−457.537	−	528.026i	−0.141176	−	0.162925i
$220$	−1163.20	−	341.545i	−0.356467	−	0.104668i
$221$	187.038	−	409.555i	0.0569299	−	0.124659i
$222$	−14429.5	−	9273.29i	−4.36237	−	2.80352i
$223$	5041.27	−	1480.25i	1.51385	−	0.444506i	0.583786	−	0.811907i	$-0.301571\pi$
$223$	5041.27	−	1480.25i	1.51385	−	0.444506i	0.930062	+	0.367401i	$0.119752\pi$
$224$	−347.046	+	2413.76i	−0.103518	+	0.719981i
$225$	526.351	+	1152.55i	0.155956	+	0.341496i
$226$	288.561	+	2006.98i	0.0849327	+	0.590720i
$227$	−4795.38	+	3081.80i	−1.40212	+	0.901085i	−0.999895	−	0.0144581i	$-0.995398\pi$
$227$	−4795.38	+	3081.80i	−1.40212	+	0.901085i	−0.402220	+	0.915543i	$0.631761\pi$
$228$	12339.8	−	14240.9i	3.58432	−	4.13652i
$229$	3746.82			1.08121			0.540605	−	0.841277i	$-0.318196\pi$
$229$	3746.82			1.08121			0.540605	+	0.841277i	$0.318196\pi$
$230$	226.707	−	2630.20i	0.0649940	−	0.754046i
$231$	4501.21			1.28207
$232$	2359.11	−	2722.55i	0.667599	−	0.770450i
$233$	−3435.45	+	2207.83i	−0.965939	+	0.620772i	−0.925636	−	0.378416i	$-0.876469\pi$
$233$	−3435.45	+	2207.83i	−0.965939	+	0.620772i	−0.0403037	+	0.999187i	$0.512833\pi$
$234$	351.205	+	2442.69i	0.0981155	+	0.682408i
$235$	−527.003	−	1153.97i	−0.146289	−	0.320328i
$236$	1196.18	−	8319.63i	0.329936	−	2.29475i
$237$	−6756.89	+	1984.00i	−1.85193	+	0.543776i
$238$	5598.36	+	3597.85i	1.52474	+	0.979889i
$239$	−1281.72	+	2806.57i	−0.346893	+	0.759589i	0.653105	+	0.757268i	$0.273466\pi$
$239$	−1281.72	+	2806.57i	−0.346893	+	0.759589i	−0.999997	+	0.00232110i	$0.999261\pi$
$240$	1652.44	+	485.200i	0.444435	+	0.130498i
$241$	−200.830	−	231.770i	−0.0536789	−	0.0619487i	0.728275	−	0.685285i	$-0.240322\pi$
$241$	−200.830	−	231.770i	−0.0536789	−	0.0619487i	−0.781954	+	0.623336i	$0.785777\pi$
$242$	3343.52	+	3858.62i	0.888138	+	1.02497i
$243$	−1422.11	−	417.569i	−0.375426	−	0.110235i
$244$	−4424.82	+	9689.01i	−1.16094	+	2.54211i
$245$	2707.23	+	1739.83i	0.705953	+	0.453689i
$246$	396.655	−	116.468i	0.102804	−	0.0301860i
$247$	207.551	−	1443.55i	0.0534663	−	0.371866i
$248$	3622.10	+	7931.30i	0.927434	+	2.03080i
$249$	−480.439	−	3341.52i	−0.122275	−	0.850444i
$250$	503.352	−	323.485i	0.127339	−	0.0818359i
$251$	−1871.46	+	2159.78i	−0.470619	+	0.543124i	−0.940584	−	0.339562i	$-0.889721\pi$
$251$	−1871.46	+	2159.78i	−0.470619	+	0.543124i	0.469964	+	0.882685i	$0.344267\pi$
$252$	−23739.7			−5.93436
$253$	1095.59	−	1419.90i	0.272249	−	0.352839i
$254$	−5012.96			−1.23835
$255$	−1277.33	+	1474.12i	−0.313684	+	0.362011i
$256$	−6083.06	+	3909.35i	−1.48512	+	0.954431i
$257$	−523.753	−	3642.78i	−0.127124	−	0.884166i	−0.949174	−	0.314751i	$-0.898079\pi$
$257$	−523.753	−	3642.78i	−0.127124	−	0.884166i	0.822050	−	0.569415i	$-0.192830\pi$
$258$	2112.32	+	4625.33i	0.509717	+	1.11613i
$259$	1817.42	−	12640.4i	0.436018	−	3.03257i
$260$	727.748	−	213.686i	0.173589	−	0.0509702i
$261$	−4642.12	−	2983.31i	−1.10092	−	0.707519i
$262$	−199.993	+	437.923i	−0.0471587	+	0.103263i
$263$	−3220.21	−	945.538i	−0.755005	−	0.221690i	−0.118492	−	0.992955i	$-0.537806\pi$
$263$	−3220.21	−	945.538i	−0.755005	−	0.221690i	−0.636514	+	0.771265i	$0.719624\pi$
$264$	3105.03	+	3583.40i	0.723869	+	0.835389i
$265$	640.998	+	739.751i	0.148589	+	0.171481i
$266$	20682.5	+	6072.94i	4.76740	+	1.39983i
$267$	−3971.48	+	8696.34i	−0.910303	+	1.99329i
$268$	8487.11	+	5454.34i	1.93445	+	1.24320i
$269$	−3482.74	+	1022.63i	−0.789392	+	0.231787i	−0.651488	−	0.758659i	$-0.725855\pi$
$269$	−3482.74	+	1022.63i	−0.789392	+	0.231787i	−0.137904	+	0.990446i	$0.544037\pi$
$270$	710.941	−	4944.70i	0.160246	−	1.11454i
$271$	−1224.48	−	2681.23i	−0.274471	−	0.601008i	0.721326	−	0.692596i	$-0.243533\pi$
$271$	−1224.48	−	2681.23i	−0.274471	−	0.601008i	−0.995797	+	0.0915880i	$0.970806\pi$
$272$	246.166	+	1712.12i	0.0548750	+	0.381664i
$273$	−2369.10	+	1522.53i	−0.525219	+	0.337537i
$274$	−777.713	+	897.529i	−0.171472	+	0.197889i
$275$	406.476			0.0891324
$276$	−8856.44	+	11478.1i	−1.93150	+	2.50326i
$277$	247.016			0.0535803			0.0267902	−	0.999641i	$-0.491471\pi$
$277$	247.016			0.0535803			0.0267902	+	0.999641i	$0.491471\pi$
$278$	3446.38	−	3977.34i	0.743526	−	0.858075i
$279$	11235.6	−	7220.69i	2.41096	−	1.54943i
$280$	739.532	+	5143.56i	0.157841	+	1.09781i
$281$	151.875	+	332.559i	0.0322423	+	0.0706008i	0.925068	−	0.379802i	$-0.124008\pi$
$281$	151.875	+	332.559i	0.0322423	+	0.0706008i	−0.892826	+	0.450402i	$0.851281\pi$
$282$	−1523.37	+	10595.3i	−0.321686	+	2.23738i
$283$	994.755	−	292.087i	0.208947	−	0.0613525i	−0.175584	−	0.984464i	$-0.556181\pi$
$283$	994.755	−	292.087i	0.208947	−	0.0613525i	0.384531	+	0.923112i	$0.374363\pi$
$284$	−2925.18	−	1879.90i	−0.611189	−	0.392787i
$285$	−2624.61	+	5747.10i	−0.545504	+	1.19449i
$286$	759.615	+	223.043i	0.157052	+	0.0461148i
$287$	201.558	+	232.610i	0.0414549	+	0.0478415i
$288$	2576.70	+	2973.67i	0.527200	+	0.608422i
$289$	2834.28	+	832.220i	0.576895	+	0.169392i
$290$	−1082.49	+	2370.32i	−0.219193	+	0.479965i
$291$	−2103.10	−	1351.58i	−0.423662	−	0.272271i
$292$	1134.24	−	333.043i	0.227317	−	0.0667462i
$293$	−736.636	+	5123.42i	−0.146876	+	1.02155i	0.774416	+	0.632676i	$0.218044\pi$
$293$	−736.636	+	5123.42i	−0.146876	+	1.02155i	−0.921293	+	0.388870i	$0.872865\pi$
$294$	−11279.9	−	24699.6i	−2.23761	−	4.89969i
$295$	401.070	+	2789.50i	0.0791566	+	0.550546i
$296$	11316.7	−	7272.79i	2.22219	−	1.42812i
$297$	2222.40	−	2564.78i	0.434197	−	0.501090i
$298$	−3229.14			−0.627715
$299$	−96.3568	+	1117.91i	−0.0186370	+	0.216222i
$300$	−3285.84			−0.632361
$301$	−2479.16	+	2861.11i	−0.474739	+	0.547879i
$302$	−3827.50	+	2459.78i	−0.729297	+	0.468691i
$303$	1165.23	+	8104.32i	0.220926	+	1.53657i
$304$	2327.49	+	5096.50i	0.439114	+	0.961526i
$305$	508.262	−	3535.04i	0.0954196	−	0.663658i
$306$	10302.8	−	3025.17i	1.92474	−	0.565155i
$307$	−2208.48	−	1419.30i	−0.410568	−	0.263856i	0.319013	−	0.947750i	$-0.396649\pi$
$307$	−2208.48	−	1419.30i	−0.410568	−	0.263856i	−0.729581	+	0.683894i	$0.760285\pi$
$308$	−3163.72	+	6927.58i	−0.585291	+	1.28161i
$309$	−8267.89	−	2427.67i	−1.52215	−	0.446943i
$310$	−4130.19	−	4766.50i	−0.756707	−	0.873286i
$311$	−4882.09	−	5634.23i	−0.890154	−	1.02729i	−0.999446	−	0.0332823i	$-0.989404\pi$
$311$	−4882.09	−	5634.23i	−0.890154	−	1.02729i	0.109292	−	0.994010i	$-0.465141\pi$
$312$	−2846.34	−	835.760i	−0.516481	−	0.151653i
$313$	−3355.55	+	7347.63i	−0.605964	+	1.32688i	0.319336	+	0.947642i	$0.396540\pi$
$313$	−3355.55	+	7347.63i	−0.605964	+	1.32688i	−0.925300	+	0.379235i	$0.876187\pi$
$314$	9664.68	+	6211.12i	1.73697	+	1.11629i
$315$	7637.30	−	2242.51i	1.36607	−	0.401115i
$316$	1695.67	−	11793.7i	0.301864	−	2.09951i
$317$	−3204.68	−	7017.28i	−0.567801	−	1.24331i	−0.947960	−	0.318389i	$-0.896858\pi$
$317$	−3204.68	−	7017.28i	−0.567801	−	1.24331i	0.380159	−	0.924921i	$-0.375869\pi$
$318$	−1175.39	−	8175.04i	−0.207273	−	1.44161i
$319$	−1489.22	+	957.061i	−0.261380	+	0.167978i
$320$	2240.47	−	2585.64i	0.391393	−	0.451692i
$321$	4064.41			0.706708
$322$	−16152.3	−	3761.20i	−2.79545	−	0.650942i
$323$	−6345.66			−1.09313
$324$	−4602.01	+	5311.00i	−0.789096	+	0.910665i
$325$	−213.939	+	137.490i	−0.0365144	+	0.0234664i
$326$	2060.40	+	14330.4i	0.350046	+	2.43463i
$327$	−2724.24	−	5965.25i	−0.460705	−	1.00880i
$328$	−46.1411	+	320.918i	−0.00776743	+	0.0540236i
$329$	−7646.75	+	2245.29i	−1.28140	+	0.376252i
$330$	−2885.27	−	1854.25i	−0.481300	−	0.309313i
$331$	2127.42	−	4658.40i	0.353274	−	0.773561i	−0.646668	−	0.762771i	$-0.723838\pi$
$331$	2127.42	−	4658.40i	0.353274	−	0.773561i	0.999942	−	0.0107897i	$-0.00343455\pi$
$332$	5480.45	+	1609.20i	0.905960	+	0.266014i
$333$	−13493.7	−	15572.6i	−2.22058	−	2.56268i
$334$	13036.4	+	15044.8i	2.13569	+	2.46471i
$335$	−3245.62	−	953.001i	−0.529335	−	0.155427i
$336$	4494.38	−	9841.33i	0.729728	−	1.59788i
$337$	1743.70	+	1120.61i	0.281855	+	0.181137i	0.673928	−	0.738797i	$-0.264606\pi$
$337$	1743.70	+	1120.61i	0.281855	+	0.181137i	−0.392073	+	0.919934i	$0.628242\pi$
$338$	9615.12	−	2823.25i	1.54732	−	0.454333i
$339$	−531.328	+	3695.47i	−0.0851261	+	0.592065i
$340$	−1370.95	−	3001.97i	−0.218678	−	0.478838i
$341$	−609.763	−	4240.99i	−0.0968343	−	0.673498i
$342$	29259.6	−	18804.0i	4.62625	−	2.97311i
$343$	6183.56	−	7136.21i	0.973414	−	1.12338i
$344$	−3987.90			−0.625038
$345$	1764.96	−	4529.22i	0.275427	−	0.706797i
$346$	12544.0			1.94905
$347$	3816.01	−	4403.91i	0.590358	−	0.681309i	−0.379441	−	0.925216i	$-0.623884\pi$
$347$	3816.01	−	4403.91i	0.590358	−	0.681309i	0.969799	+	0.243907i	$0.0784291\pi$
$348$	12038.4	−	7736.63i	1.85439	−	1.19174i
$349$	130.906	+	910.469i	0.0200780	+	0.139645i	0.997395	−	0.0721376i	$-0.0229821\pi$
$349$	130.906	+	910.469i	0.0200780	+	0.139645i	−0.977317	+	0.211783i	$0.932073\pi$
$350$	−1561.46	−	3419.13i	−0.238468	−	0.522172i
$351$	−302.170	+	2101.64i	−0.0459505	+	0.319593i
$352$	1211.15	−	355.626i	0.183394	−	0.0538492i
$353$	−48.5808	−	31.2210i	−0.00732492	−	0.00470744i	0.536973	−	0.843599i	$-0.319568\pi$
$353$	−48.5808	−	31.2210i	−0.00732492	−	0.00470744i	−0.544298	+	0.838892i	$0.683204\pi$
$354$	9878.19	−	21630.2i	1.48311	−	3.24755i
$355$	1118.64	+	328.463i	0.167243	+	0.0491071i
$356$	−10592.7	−	12224.6i	−1.57700	−	1.81995i
$357$	8024.31	+	9260.55i	1.18961	+	1.37289i
$358$	−12210.9	−	3585.45i	−1.80270	−	0.529321i
$359$	1876.07	−	4108.02i	0.275808	−	0.603936i	−0.720144	−	0.693825i	$-0.755924\pi$
$359$	1876.07	−	4108.02i	0.275808	−	0.603936i	0.995952	+	0.0898894i	$0.0286514\pi$
$360$	7053.63	+	4533.09i	1.03266	+	0.663653i
$361$	−13140.7	+	3858.45i	−1.91583	+	0.562538i
$362$	705.075	−	4903.91i	0.102370	−	0.711999i
$363$	3905.37	+	8551.56i	0.564679	+	1.23648i
$364$	−678.100	−	4716.29i	−0.0976432	−	0.679123i
$365$	−333.437	+	214.287i	−0.0478161	+	0.0307296i
$366$	−19733.8	+	22774.0i	−2.81832	+	3.25251i
$367$	−4426.13			−0.629542			−0.314771	−	0.949168i	$-0.601928\pi$
$367$	−4426.13			−0.629542			−0.314771	+	0.949168i	$0.601928\pi$
$368$	−2010.50	−	3813.11i	−0.284795	−	0.540141i
$369$	496.626			0.0700631
$370$	−6372.12	+	7353.81i	−0.895326	+	1.03326i
$371$	5172.96	−	3324.46i	0.723900	−	0.465222i
$372$	4929.17	+	34283.1i	0.687004	+	4.77821i
$373$	3833.97	+	8395.22i	0.532213	+	1.16538i	0.964605	+	0.263698i	$0.0849423\pi$
$373$	3833.97	+	8395.22i	0.532213	+	1.16538i	−0.432392	+	0.901686i	$0.642330\pi$
$374$	490.234	−	3409.66i	0.0677792	−	0.471415i
$375$	1057.09	−	310.390i	0.145568	−	0.0427425i
$376$	−7062.36	−	4538.70i	−0.968652	−	0.622515i
$377$	460.088	−	1007.45i	0.0628534	−	0.137630i
$378$	−30111.3	−	8841.48i	−4.09725	−	1.20306i
$379$	4060.23	+	4685.76i	0.550290	+	0.635069i	0.960951	−	0.276719i	$-0.0892472\pi$
$379$	4060.23	+	4685.76i	0.550290	+	0.635069i	−0.410660	+	0.911788i	$0.634702\pi$
$380$	−7000.33	−	8078.81i	−0.945024	−	1.09062i
$381$	−8856.49	−	2600.50i	−1.19090	−	0.349679i
$382$	388.439	−	850.562i	0.0520269	−	0.113923i
$383$	−6416.35	−	4123.54i	−0.856032	−	0.550138i	0.0374186	−	0.999300i	$-0.488087\pi$
$383$	−6416.35	−	4123.54i	−0.856032	−	0.550138i	−0.893451	+	0.449161i	$0.851723\pi$
$384$	−22446.2	+	6590.79i	−2.98294	+	0.875871i
$385$	363.404	−	2527.53i	0.0481059	−	0.334584i
$386$	−4377.29	−	9584.93i	−0.577197	−	1.26389i
$387$	869.332	+	6046.33i	0.114188	+	0.794192i
$388$	3558.33	−	2286.80i	0.465584	−	0.299213i
$389$	7136.62	−	8236.10i	0.930183	−	1.07349i	−0.0669451	−	0.997757i	$-0.521325\pi$
$389$	7136.62	−	8236.10i	0.930183	−	1.07349i	0.997128	−	0.0757319i	$-0.0241293\pi$
$390$	2145.79			0.278606
$391$	4874.32	−	277.250i	0.630448	−	0.0358597i
$392$	21295.6			2.74386
$393$	−580.505	+	669.939i	−0.0745105	+	0.0859897i
$394$	−14156.4	+	9097.76i	−1.81012	+	1.16330i
$395$	568.545	+	3954.32i	0.0724218	+	0.503705i
$396$	5104.78	+	11177.9i	0.647790	+	1.41846i
$397$	641.713	−	4463.21i	0.0811250	−	0.564237i	−0.908203	−	0.418530i	$-0.862545\pi$
$397$	641.713	−	4463.21i	0.0811250	−	0.564237i	0.989328	−	0.145707i	$-0.0465456\pi$
$398$	−3886.39	+	1141.15i	−0.489465	+	0.143720i
$399$	33389.8	+	21458.3i	4.18943	+	2.69238i
$400$	405.859	−	888.708i	0.0507324	−	0.111088i
$401$	10010.3	+	2939.29i	1.24661	+	0.366038i	0.837495	−	0.546445i	$-0.184019\pi$
$401$	10010.3	+	2939.29i	1.24661	+	0.366038i	0.409115	+	0.912483i	$0.365837\pi$
$402$	18690.9	+	21570.5i	2.31895	+	2.67621i
$403$	1755.45	+	2025.89i	0.216985	+	0.250414i
$404$	−13291.9	−	3902.86i	−1.63688	−	0.480631i
$405$	978.822	−	2143.32i	0.120094	−	0.262969i
$406$	13771.2	+	8850.23i	1.68339	+	1.08185i
$407$	−6342.58	+	1862.35i	−0.772457	+	0.226814i
$408$	−1836.95	+	12776.2i	−0.222898	+	1.55029i
$409$	−3858.52	−	8448.99i	−0.466483	−	1.02146i	−0.985962	−	0.166972i	$-0.946601\pi$
$409$	−3858.52	−	8448.99i	−0.466483	−	1.02146i	0.519478	−	0.854484i	$-0.326126\pi$
$410$	−33.3757	−	232.133i	−0.00402027	−	0.0279616i
$411$	−1839.60	+	1182.24i	−0.220780	+	0.141887i
$412$	9547.47	−	11018.4i	1.14167	−	1.31756i
$413$	17704.1			2.10935
$414$	−21653.8	+	15722.4i	−2.57059	+	1.86646i
$415$	−1915.13			−0.226530
$416$	−517.170	+	596.846i	−0.0609527	+	0.0703432i
$417$	8152.04	−	5239.00i	0.957331	−	0.615240i
$418$	−1587.93	−	11044.3i	−0.185810	−	1.29233i
$419$	3106.11	+	6801.43i	0.362156	+	0.793011i	0.999744	+	0.0226334i	$0.00720505\pi$
$419$	3106.11	+	6801.43i	0.362156	+	0.793011i	−0.637588	+	0.770378i	$0.720068\pi$
$420$	−2937.66	+	20431.9i	−0.341293	+	2.37375i
$421$	12118.1	−	3558.20i	1.40285	−	0.411914i	0.509189	−	0.860655i	$-0.329945\pi$
$421$	12118.1	−	3558.20i	1.40285	−	0.411914i	0.893662	+	0.448740i	$0.148127\pi$
$422$	−19046.3	−	12240.3i	−2.19706	−	1.41197i
$423$	−5341.91	+	11697.1i	−0.614025	+	1.34453i
$424$	6215.01	+	1824.89i	0.711857	+	0.209020i
$425$	724.625	+	836.261i	0.0827046	+	0.0954462i
$426$	−6442.04	−	7434.51i	−0.732671	−	0.845548i
$427$	−21527.0	−	6320.90i	−2.43973	−	0.716369i
$428$	−2856.71	+	6255.32i	−0.322627	+	0.706455i
$429$	1226.32	+	788.108i	0.138012	+	0.0886952i
$430$	2767.76	−	812.688i	0.310403	−	0.0911425i
$431$	−1553.13	+	10802.2i	−0.173576	+	1.20725i	0.697675	+	0.716414i	$0.254218\pi$
$431$	−1553.13	+	10802.2i	−0.173576	+	1.20725i	−0.871252	+	0.490837i	$0.836691\pi$
$432$	−3388.55	−	7419.89i	−0.377388	−	0.826365i
$433$	−269.874	−	1877.01i	−0.0299522	−	0.208322i	0.969350	−	0.245686i	$-0.0790131\pi$
$433$	−269.874	−	1877.01i	−0.0299522	−	0.208322i	−0.999302	+	0.0373635i	$0.988104\pi$
$434$	−33331.3	+	21420.8i	−3.68653	+	2.36919i
$435$	−3142.07	+	3626.14i	−0.346323	+	0.399678i
$436$	11095.6			1.21876
$437$	14896.0	−	5309.83i	1.63060	−	0.581244i
$438$	3344.35			0.364839
$439$	−4627.31	+	5340.20i	−0.503074	+	0.580578i	−0.949312	−	0.314336i	$-0.898218\pi$
$439$	−4627.31	+	5340.20i	−0.503074	+	0.580578i	0.446238	+	0.894914i	$0.352764\pi$
$440$	2262.84	−	1454.24i	0.245174	−	0.157564i
$441$	−4642.29	−	32287.8i	−0.501273	−	3.48643i
$442$	895.290	+	1960.41i	0.0963453	+	0.210967i
$443$	−348.639	+	2424.84i	−0.0373913	+	0.260062i	−0.999939	−	0.0110505i	$-0.996482\pi$
$443$	−348.639	+	2424.84i	−0.0373913	+	0.260062i	0.962548	+	0.271112i	$0.0873915\pi$
$444$	51271.8	−	15054.8i	5.48030	−	1.60916i
$445$	4562.55	+	2932.17i	0.486035	+	0.312356i
$446$	−10447.6	+	22877.0i	−1.10921	+	2.42883i
$447$	−5704.97	−	1675.13i	−0.603660	−	0.177251i
$448$	−14074.8	−	16243.2i	−1.48431	−	1.71299i
$449$	−8058.71	−	9300.24i	−0.847024	−	0.977518i	0.152918	−	0.988239i	$-0.451133\pi$
$449$	−8058.71	−	9300.24i	−0.847024	−	0.977518i	−0.999943	+	0.0107207i	$0.996587\pi$
$450$	−5819.30	−	1708.70i	−0.609610	−	0.178998i
$451$	66.1839	−	144.922i	0.00691015	−	0.0151311i
$452$	−5314.05	−	3415.13i	−0.552991	−	0.355386i
$453$	−8038.12	+	2360.21i	−0.833695	+	0.244795i
$454$	3883.12	−	27007.7i	0.401418	−	2.79193i
$455$	663.665	+	1453.22i	0.0683805	+	0.149732i
$456$	5950.11	+	41383.9i	0.611052	+	4.24996i
$457$	6206.78	−	3988.86i	0.635320	−	0.408295i	−0.182956	−	0.983121i	$-0.558567\pi$
$457$	6206.78	−	3988.86i	0.635320	−	0.408295i	0.818276	+	0.574826i	$0.194930\pi$
$458$	−11744.8	+	13554.3i	−1.19825	+	1.38286i
$459$	9238.52			0.939471
$460$	5730.17	+	5899.76i	0.580806	+	0.597996i
$461$	1619.39			0.163607			0.0818034	−	0.996648i	$-0.473932\pi$
$461$	1619.39			0.163607			0.0818034	+	0.996648i	$0.473932\pi$
$462$	−14109.6	+	16283.3i	−1.42086	+	1.63976i
$463$	6307.90	−	4053.84i	0.633159	−	0.406907i	−0.184319	−	0.982867i	$-0.559008\pi$
$463$	6307.90	−	4053.84i	0.633159	−	0.406907i	0.817478	+	0.575960i	$0.195371\pi$
$464$	605.536	+	4211.59i	0.0605847	+	0.421376i
$465$	−4824.24	−	10563.6i	−0.481115	−	1.05350i
$466$	2781.90	−	19348.6i	0.276543	−	1.92340i
$467$	7262.86	−	2132.57i	0.719668	−	0.211314i	0.0986641	−	0.995121i	$-0.468543\pi$
$467$	7262.86	−	2132.57i	0.719668	−	0.211314i	0.621004	+	0.783807i	$0.286725\pi$
$468$	−6467.70	−	4156.54i	−0.638824	−	0.410547i
$469$	−8827.61	+	19329.8i	−0.869128	+	1.90313i
$470$	5826.49	+	1710.81i	0.571822	+	0.167902i
$471$	13852.7	+	15986.9i	1.35520	+	1.56398i
$472$	12212.7	+	14094.2i	1.19096	+	1.37444i
$473$	1880.26	+	552.094i	0.182779	+	0.0536687i
$474$	14003.0	−	30662.4i	1.35692	−	2.97124i
$475$	3015.22	+	1937.77i	0.291259	+	0.187181i
$476$	−19892.4	+	5840.94i	−1.91548	+	0.562435i
$477$	1412.02	−	9820.83i	0.135539	−	0.942694i
$478$	−6135.17	−	13434.2i	−0.587063	−	1.28549i
$479$	300.525	+	2090.20i	0.0286667	+	0.199381i	0.999122	−	0.0419006i	$-0.0133413\pi$
$479$	300.525	+	2090.20i	0.0286667	+	0.199381i	−0.970455	+	0.241282i	$0.922432\pi$
$480$	2878.19	−	1849.70i	0.273689	−	0.175889i
$481$	2708.33	−	3125.58i	0.256734	−	0.296287i
$482$	1467.96			0.138722
$483$	−26585.5	−	15024.1i	−2.50451	−	1.41536i
$484$	−15906.2			−1.49382
$485$	−928.734	+	1071.82i	−0.0869518	+	0.100348i
$486$	5968.34	−	3835.62i	0.557056	−	0.357998i
$487$	−869.215	−	6045.53i	−0.0808787	−	0.562523i	−0.989459	−	0.144813i	$-0.953742\pi$
$487$	−869.215	−	6045.53i	−0.0808787	−	0.562523i	0.908580	−	0.417710i	$-0.137167\pi$
$488$	−9817.74	−	21497.9i	−0.910713	−	1.99418i
$489$	−3793.82	+	26386.6i	−0.350844	+	2.44017i
$490$	−14780.0	+	4339.81i	−1.36264	+	0.400107i
$491$	−7503.45	−	4822.18i	−0.689666	−	0.443222i	0.148301	−	0.988942i	$-0.452620\pi$
$491$	−7503.45	−	4822.18i	−0.689666	−	0.443222i	−0.837967	+	0.545721i	$0.816256\pi$
$492$	−535.013	+	1171.52i	−0.0490249	+	0.107350i
$493$	−4623.83	−	1357.68i	−0.422408	−	0.124030i
$494$	4571.50	+	5275.80i	0.416360	+	0.480505i
$495$	−2698.16	−	3113.84i	−0.244996	−	0.282741i
$496$	−9881.24	−	2901.39i	−0.894517	−	0.262654i
$497$	3042.54	−	6662.23i	0.274601	−	0.601292i
$498$	13594.1	+	8736.38i	1.22322	+	0.786118i
$499$	2893.77	−	849.687i	0.259605	−	0.0762269i	−0.149340	−	0.988786i	$-0.547715\pi$
$499$	2893.77	−	849.687i	0.259605	−	0.0762269i	0.408945	+	0.912559i	$0.365897\pi$
$500$	−265.281	+	1845.07i	−0.0237275	+	0.165028i
$501$	15227.0	+	33342.6i	1.35787	+	2.97333i
$502$	−1946.78	−	13540.1i	−0.173086	−	1.20384i
$503$	−9878.43	+	6348.48i	−0.875661	+	0.562753i	−0.899479	−	0.436963i	$-0.856054\pi$
$503$	−9878.43	+	6348.48i	−0.875661	+	0.562753i	0.0238187	+	0.999716i	$0.492418\pi$
$504$	34493.7	−	39807.8i	3.04855	−	3.51822i
$505$	4644.83			0.409291
$506$	1702.29	+	8414.15i	0.149557	+	0.739239i
$507$	18451.8			1.61631
$508$	10227.2	−	11802.8i	0.893223	−	1.03083i
$509$	3304.11	−	2123.42i	0.287725	−	0.184910i	−0.388814	−	0.921316i	$-0.627115\pi$
$509$	3304.11	−	2123.42i	0.287725	−	0.184910i	0.676539	+	0.736406i	$0.263479\pi$
$510$	−1328.74	−	9241.58i	−0.115368	−	0.802400i
$511$	1034.36	+	2264.94i	0.0895452	+	0.196077i
$512$	1903.94	−	13242.2i	0.164342	−	1.14303i
$513$	28712.6	−	8430.79i	2.47114	−	0.725591i
$514$	14819.7	+	9524.02i	1.27173	+	0.817289i
$515$	−2030.70	+	4446.60i	−0.173754	+	0.380467i
$516$	−15199.5	−	4462.99i	−1.29675	−	0.380760i
$517$	2701.49	+	3117.69i	0.229810	+	0.265214i
$518$	40030.2	+	46197.4i	3.39542	+	3.91852i
$519$	22161.7	+	6507.27i	1.87436	+	0.550361i
$520$	−699.096	+	1530.81i	−0.0589565	+	0.129097i
$521$	−7009.41	−	4504.67i	−0.589420	−	0.378797i	0.211670	−	0.977341i	$-0.432110\pi$
$521$	−7009.41	−	4504.67i	−0.589420	−	0.378797i	−0.801090	+	0.598544i	$0.795746\pi$
$522$	25343.5	−	7441.52i	2.12501	−	0.623959i
$523$	−527.561	+	3669.27i	−0.0441083	+	0.306780i	0.955810	+	0.293985i	$0.0949817\pi$
$523$	−527.561	+	3669.27i	−0.0441083	+	0.306780i	−0.999918	+	0.0127942i	$0.995927\pi$
$524$	−623.054	−	1364.30i	−0.0519432	−	0.113740i
$525$	−984.974	−	6850.65i	−0.0818815	−	0.569499i
$526$	13514.6	−	8685.32i	1.12028	−	0.719958i
$527$	7638.17	−	8814.92i	0.631355	−	0.728622i
$528$	−5600.26			−0.461591
$529$	−11210.2	+	4729.49i	−0.921358	+	0.388715i
$530$	−4685.36			−0.383998
$531$	18706.9	−	21589.0i	1.52884	−	1.76437i
$532$	−56493.8	+	36306.4i	−4.60398	+	2.95880i
$533$	14.1856	+	98.6631i	0.00115281	+	0.00801796i
$534$	−19010.2	−	41626.6i	−1.54055	−	3.37333i
$535$	328.139	−	2282.26i	0.0265172	−	0.184431i
$536$	−21477.8	+	6306.46i	−1.73079	+	0.508204i
$537$	−19713.3	−	12668.9i	−1.58415	−	1.01807i
$538$	7217.67	−	15804.5i	0.578393	−	1.26651i
$539$	−10040.7	−	2948.22i	−0.802382	−	0.235601i
$540$	10191.6	+	11761.8i	0.812182	+	0.937308i
$541$	725.683	+	837.483i	0.0576701	+	0.0665549i	0.783852	−	0.620948i	$-0.213252\pi$
$541$	725.683	+	837.483i	0.0576701	+	0.0665549i	−0.726182	+	0.687503i	$0.758707\pi$
$542$	13537.7	+	3975.03i	1.07287	+	0.315022i
$543$	3789.59	−	8298.05i	0.299497	−	0.655808i
$544$	2890.77	+	1857.78i	0.227832	+	0.146419i
$545$	−3569.56	+	1048.12i	−0.280556	+	0.0823787i
$546$	1918.41	−	13342.9i	0.150367	−	1.04583i
$547$	3747.09	+	8204.99i	0.292896	+	0.641353i	0.997681	−	0.0680685i	$-0.0216836\pi$
$547$	3747.09	+	8204.99i	0.292896	+	0.641353i	−0.704785	+	0.709421i	$0.748956\pi$
$548$	−526.541	−	3662.18i	−0.0410451	−	0.285475i
$549$	−30454.2	+	19571.7i	−2.36750	+	1.52150i
$550$	−1274.14	+	1470.44i	−0.0987812	+	0.114000i
$551$	−15609.5			−1.20687
$552$	−6378.61	−	31528.5i	−0.491833	−	2.43105i
$553$	25096.9			1.92989
$554$	−774.299	+	893.589i	−0.0593805	+	0.0685288i
$555$	−15072.6	+	9686.54i	−1.15278	+	0.740848i
$556$	2333.33	+	16228.7i	0.177977	+	1.23786i
$557$	−2840.61	−	6220.07i	−0.216087	−	0.473165i	0.770284	−	0.637701i	$-0.220115\pi$
$557$	−2840.61	−	6220.07i	−0.216087	−	0.473165i	−0.986371	+	0.164536i	$0.947387\pi$
$558$	−9098.19	+	63279.3i	−0.690246	+	4.80077i
$559$	−1176.38	+	345.415i	−0.0890078	+	0.0261351i
$560$	−5163.27	−	3318.23i	−0.389621	−	0.250394i
$561$	2634.88	−	5769.58i	0.198297	−	0.434210i
$562$	−1679.11	−	493.032i	−0.126030	−	0.0370059i
$563$	−4452.46	−	5138.41i	−0.333302	−	0.384651i	0.564217	−	0.825626i	$-0.309178\pi$
$563$	−4452.46	−	5138.41i	−0.333302	−	0.384651i	−0.897519	+	0.440976i	$0.854633\pi$
$564$	−21838.2	−	25202.6i	−1.63041	−	1.88160i
$565$	2032.19	+	596.704i	0.151318	+	0.0444310i
$566$	−2061.54	+	4514.14i	−0.153097	+	0.335236i
$567$	−12452.4	−	8002.67i	−0.922314	−	0.592735i
$568$	7402.59	−	2173.60i	0.546841	−	0.160567i
$569$	−3172.97	+	22068.5i	−0.233774	+	1.62594i	0.447762	+	0.894153i	$0.352221\pi$
$569$	−3172.97	+	22068.5i	−0.233774	+	1.62594i	−0.681536	+	0.731784i	$0.738688\pi$
$570$	−12563.2	−	27509.6i	−0.923183	−	2.02149i
$571$	−650.988	−	4527.72i	−0.0477111	−	0.331838i	−0.999672	−	0.0256177i	$-0.991845\pi$
$571$	−650.988	−	4527.72i	−0.0477111	−	0.331838i	0.951961	−	0.306220i	$-0.0990643\pi$
$572$	−2074.87	+	1333.44i	−0.151669	+	0.0974717i
$573$	1127.49	−	1301.20i	0.0822021	−	0.0948662i
$574$	−1473.28			−0.107132
$575$	−2400.76	−	1356.73i	−0.174120	−	0.0983991i
$576$	−34679.5			−2.50865
$577$	−13306.2	+	15356.2i	−0.960045	+	1.10795i	0.0340485	+	0.999420i	$0.489160\pi$
$577$	−13306.2	+	15356.2i	−0.960045	+	1.10795i	−0.994093	+	0.108530i	$0.965386\pi$
$578$	−11895.0	+	7644.43i	−0.855996	+	0.550115i
$579$	−2761.20	−	19204.6i	−0.198190	−	1.37844i
$580$	−3372.37	−	7384.46i	−0.241431	−	0.528660i
$581$	−1712.19	+	11908.6i	−0.122261	+	0.850344i
$582$	11481.8	−	3371.35i	0.817758	−	0.240115i
$583$	−2677.68	−	1720.84i	−0.190220	−	0.122247i
$584$	−1089.59	+	2385.86i	−0.0772044	+	0.169054i
$585$	2473.36	+	726.245i	0.174805	+	0.0513274i
$586$	−16225.1	−	18724.7i	−1.14377	−	1.31999i
$587$	2176.86	+	2512.23i	0.153064	+	0.176646i	0.827103	−	0.562050i	$-0.189987\pi$
$587$	2176.86	+	2512.23i	0.153064	+	0.176646i	−0.674039	+	0.738696i	$0.735442\pi$
$588$	81166.5	+	23832.6i	5.69260	+	1.67150i
$589$	15694.6	−	34366.4i	1.09794	−	2.40415i
$590$	−11348.3	−	7293.13i	−0.791870	−	0.508904i
$591$	−29729.8	+	8729.47i	−2.06924	+	0.607584i
$592$	−2261.17	+	15726.8i	−0.156982	+	1.09184i
$593$	6866.79	+	15036.2i	0.475523	+	1.04125i	0.983670	+	0.179980i	$0.0576033\pi$
$593$	6866.79	+	15036.2i	0.475523	+	1.04125i	−0.508147	+	0.861270i	$0.669669\pi$
$594$	2311.84	+	16079.2i	0.159690	+	1.11067i
$595$	5847.84	−	3758.18i	0.402921	−	0.258942i
$596$	6587.90	−	7602.85i	0.452770	−	0.522525i
$597$	−7458.12			−0.511291
$598$	−3742.04	−	3852.79i	−0.255892	−	0.263465i
$599$	6161.07			0.420258			0.210129	−	0.977674i	$-0.432612\pi$
$599$	6161.07			0.420258			0.210129	+	0.977674i	$0.432612\pi$
$600$	4774.32	−	5509.86i	0.324851	−	0.374898i
$601$	−8920.83	+	5733.07i	−0.605472	+	0.389113i	−0.807156	−	0.590338i	$-0.798995\pi$
$601$	−8920.83	+	5733.07i	−0.605472	+	0.389113i	0.201685	+	0.979450i	$0.435358\pi$
$602$	−2578.94	−	17936.9i	−0.174601	−	1.21438i
$603$	14243.7	+	31189.3i	0.961936	+	2.10635i
$604$	2017.20	−	14030.0i	0.135892	−	0.945150i
$605$	5117.19	−	1502.54i	0.343873	−	0.100970i
$606$	−32970.2	−	21188.7i	−2.21010	−	1.42035i
$607$	−4471.05	+	9790.23i	−0.298969	+	0.654651i	−0.998183	−	0.0602621i	$-0.980806\pi$
$607$	−4471.05	+	9790.23i	−0.298969	+	0.654651i	0.699214	+	0.714913i	$0.253534\pi$
$608$	10679.6	+	3135.82i	0.712362	+	0.209168i
$609$	19738.8	+	22779.7i	1.31339	+	1.51573i
$610$	11194.9	+	12919.6i	0.743064	+	0.857542i
$611$	−2476.42	−	727.143i	−0.163969	−	0.0481458i
$612$	−13896.5	+	30429.2i	−0.917867	+	2.00985i
$613$	−14821.7	−	9525.30i	−0.976576	−	0.627607i	−0.0480381	−	0.998846i	$-0.515297\pi$
$613$	−14821.7	−	9525.30i	−0.976576	−	0.627607i	−0.928538	+	0.371238i	$0.878933\pi$
$614$	12057.1	−	3540.28i	0.792483	−	0.232694i
$615$	61.4548	−	427.428i	0.00402943	−	0.0280253i
$616$	−7019.62	−	15370.8i	−0.459137	−	1.00537i
$617$	1552.49	+	10797.8i	0.101298	+	0.704543i	0.975663	+	0.219274i	$0.0703690\pi$
$617$	1552.49	+	10797.8i	0.101298	+	0.704543i	−0.874365	+	0.485268i	$0.838722\pi$
$618$	34698.8	−	22299.6i	2.25856	−	1.45149i
$619$	−15282.7	+	17637.2i	−0.992350	+	1.14523i	−0.00295367	+	0.999996i	$0.500940\pi$
$619$	−15282.7	+	17637.2i	−0.992350	+	1.14523i	−0.989397	+	0.145238i	$0.953605\pi$
$620$	19648.7			1.27276
$621$	−21686.8	+	7730.47i	−1.40139	+	0.499538i
$622$	35685.5			2.30041
$623$	22311.8	−	25749.1i	1.43483	−	1.65589i
$624$	2947.56	−	1894.28i	0.189098	−	0.121526i
$625$	−88.9468	−	618.638i	−0.00569259	−	0.0395929i
$626$	−16062.0	−	35170.8i	−1.02550	−	2.24554i
$627$	2923.87	−	20335.9i	0.186233	−	1.29528i
$628$	−34341.1	+	10083.5i	−2.18210	+	0.640723i
$629$	−15138.4	−	9728.88i	−0.959632	−	0.616718i
$630$	−15827.6	+	34657.6i	−1.00093	+	2.19174i
$631$	24965.7	+	7330.59i	1.57507	+	0.462482i	0.948472	−	0.316862i	$-0.102629\pi$
$631$	24965.7	+	7330.59i	1.57507	+	0.462482i	0.626597	+	0.779344i	$0.284447\pi$
$632$	17312.4	+	19979.5i	1.08963	+	1.25750i
$633$	−27299.7	−	31505.6i	−1.71417	−	1.97825i
$634$	35430.7	+	10403.4i	2.21945	+	0.651690i
$635$	−2175.26	+	4763.16i	−0.135941	+	0.297670i
$636$	21645.7	+	13910.8i	1.34954	+	0.867297i
$637$	6281.92	−	1844.54i	0.390736	−	0.114730i
$638$	1205.91	−	8387.31i	0.0748316	−	0.520465i
$639$	−4909.25	−	10749.8i	−0.303923	−	0.665499i
$640$	1888.69	+	13136.1i	0.116651	+	0.811329i
$641$	−62.5490	+	40.1978i	−0.00385419	+	0.00247694i	−0.542566	−	0.840013i	$-0.682547\pi$
$641$	−62.5490	+	40.1978i	−0.00385419	+	0.00247694i	0.538712	+	0.842490i	$0.318911\pi$
$642$	−12740.4	+	14703.2i	−0.783211	+	0.903874i
$643$	24.0567			0.00147543			0.000737716	−	1.00000i	$-0.499765\pi$
$643$	24.0567			0.00147543			0.000737716		1.00000i	$0.499765\pi$
$644$	41808.6	−	30356.5i	2.55821	−	1.85747i
$645$	5311.43			0.324244
$646$	19891.2	−	22955.7i	1.21147	−	1.39811i
$647$	−4040.50	+	2596.67i	−0.245515	+	0.157783i	−0.657611	−	0.753357i	$-0.728433\pi$
$647$	−4040.50	+	2596.67i	−0.245515	+	0.157783i	0.412096	+	0.911140i	$0.364797\pi$
$648$	−2219.03	−	15433.7i	−0.134525	−	0.935639i
$649$	−3806.95	−	8336.05i	−0.230255	−	0.504189i
$650$	173.240	−	1204.91i	0.0104539	−	0.0727083i
$651$	−69999.2	+	20553.6i	−4.21426	+	1.23742i
$652$	−37943.8	−	24385.0i	−2.27913	−	1.46471i
$653$	8003.65	−	17525.6i	0.479643	−	1.05027i	−0.502918	−	0.864334i	$-0.667740\pi$
$653$	8003.65	−	17525.6i	0.479643	−	1.05027i	0.982561	−	0.185939i	$-0.0595325\pi$
$654$	30118.9	+	8843.72i	1.80083	+	0.528772i
$655$	329.318	+	380.054i	0.0196451	+	0.0226716i
$656$	−250.771	−	289.405i	−0.0149253	−	0.0172247i
$657$	3854.89	+	1131.90i	0.228910	+	0.0672140i
$658$	15847.2	−	34700.5i	0.938887	−	2.05588i
$659$	−10560.0	−	6786.52i	−0.624219	−	0.401161i	0.189946	−	0.981795i	$-0.439169\pi$
$659$	−10560.0	−	6786.52i	−0.624219	−	0.401161i	−0.814165	+	0.580633i	$0.802805\pi$
$660$	10252.1	−	3010.29i	0.604641	−	0.177539i
$661$	−4726.62	+	32874.3i	−0.278130	+	1.93444i	0.0712538	+	0.997458i	$0.477300\pi$
$661$	−4726.62	+	32874.3i	−0.278130	+	1.93444i	−0.349384	+	0.936980i	$0.613609\pi$
$662$	10183.3	+	22298.3i	0.597862	+	1.30914i
$663$	564.751	+	3927.93i	0.0330816	+	0.230088i
$664$	−10661.5	+	6851.70i	−0.623110	+	0.400448i
$665$	14745.0	−	17016.7i	0.859832	−	0.992299i
$666$	98632.1			5.73861
$667$	11990.2	−	681.999i	0.696046	−	0.0395908i
$668$	−62018.3			−3.59216
$669$	−30325.4	+	34997.4i	−1.75254	+	2.02254i
$670$	13621.3	−	8753.87i	0.785428	−	0.504764i
$671$	1652.77	+	11495.3i	0.0950885	+	0.661355i
$672$	−8928.50	−	19550.7i	−0.512536	−	1.12230i
$673$	2297.91	−	15982.3i	0.131617	−	0.915414i	−0.811831	−	0.583893i	$-0.801529\pi$
$673$	2297.91	−	15982.3i	0.131617	−	0.915414i	0.943448	−	0.331522i	$-0.107562\pi$
$674$	−9519.65	+	2795.22i	−0.544040	+	0.159745i
$675$	−4389.81	−	2821.16i	−0.250317	−	0.160869i
$676$	−12969.0	+	28398.2i	−0.737881	+	1.61573i
$677$	−14521.6	−	4263.91i	−0.824385	−	0.242061i	−0.157782	−	0.987474i	$-0.550434\pi$
$677$	−14521.6	−	4263.91i	−0.824385	−	0.242061i	−0.666603	+	0.745413i	$0.732252\pi$
$678$	−11703.0	−	13506.0i	−0.662906	−	0.765034i
$679$	5834.39	+	6733.25i	0.329755	+	0.380557i
$680$	7025.84	+	2062.97i	0.396218	+	0.116340i
$681$	20870.7	−	45700.6i	1.17440	−	2.57159i
$682$	17253.3	+	11088.0i	0.968715	+	0.622556i
$683$	9029.93	−	2651.43i	0.505887	−	0.148542i	−0.0188232	−	0.999823i	$-0.505992\pi$
$683$	9029.93	−	2651.43i	0.505887	−	0.148542i	0.524710	+	0.851281i	$0.324174\pi$
$684$	−15420.7	+	107253.i	−0.862023	+	5.99550i
$685$	515.333	+	1128.42i	0.0287443	+	0.0629413i
$686$	6432.43	+	44738.5i	0.358005	+	2.48998i
$687$	−27781.1	+	17853.9i	−1.54282	+	0.991509i
$688$	3084.49	−	3559.69i	0.170923	−	0.197256i
$689$	1991.41			0.110111
$690$	10852.2	+	20582.2i	0.598746	+	1.13558i
$691$	4463.56			0.245734			0.122867	−	0.992423i	$-0.460791\pi$
$691$	4463.56			0.245734			0.122867	+	0.992423i	$0.460791\pi$
$692$	−25591.6	+	29534.3i	−1.40585	+	1.62243i
$693$	−21774.6	+	13993.7i	−1.19358	+	0.767064i
$694$	3969.59	+	27609.1i	0.217123	+	1.51013i
$695$	−2283.66	−	5000.52i	−0.124639	−	0.272922i
$696$	−4518.65	+	31427.9i	−0.246091	+	1.71160i
$697$	416.142	−	122.190i	0.0226148	−	0.00664030i
$698$	−3703.99	−	2380.41i	−0.200857	−	0.129083i
$699$	14952.0	−	32740.3i	0.809065	−	1.77161i
$700$	11235.8	+	3299.12i	0.606675	+	0.178136i
$701$	−3829.69	−	4419.69i	−0.206341	−	0.238131i	0.643141	−	0.765748i	$-0.277631\pi$
$701$	−3829.69	−	4419.69i	−0.206341	−	0.238131i	−0.849482	+	0.527617i	$0.823086\pi$
$702$	−6655.56	−	7680.93i	−0.357832	−	0.412960i
$703$	−55927.3	−	16421.7i	−3.00048	−	0.881021i
$704$	−4621.64	+	10120.0i	−0.247421	+	0.541777i
$705$	9406.27	+	6045.04i	0.502498	+	0.322936i
$706$	265.225	−	77.8772i	0.0141386	−	0.00415148i
$707$	4152.64	−	28882.3i	0.220900	−	1.53639i
$708$	30774.4	+	67386.5i	1.63358	+	3.57703i
$709$	−1093.45	−	7605.10i	−0.0579201	−	0.402843i	−0.998071	−	0.0620844i	$-0.980225\pi$
$709$	−1093.45	−	7605.10i	−0.0579201	−	0.402843i	0.940151	−	0.340759i	$-0.110684\pi$
$710$	−4694.74	+	3017.13i	−0.248155	+	0.159480i
$711$	26518.4	−	30603.9i	1.39876	−	1.61425i
$712$	35889.9			1.88909
$713$	−10554.1	+	27083.8i	−0.554353	+	1.42258i
$714$	−58653.5			−3.07430
$715$	541.547	−	624.978i	0.0283255	−	0.0326893i
$716$	33353.8	−	21435.2i	1.74091	−	1.11881i
$717$	−3870.08	−	26917.0i	−0.201577	−	1.40200i
$718$	8980.15	+	19663.8i	0.466764	+	1.02207i
$719$	4753.59	−	33061.9i	0.246563	−	1.71488i	−0.371227	−	0.928542i	$-0.621063\pi$
$719$	4753.59	−	33061.9i	0.246563	−	1.71488i	0.617790	−	0.786343i	$-0.288028\pi$
$720$	−9502.08	+	2790.06i	−0.491836	+	0.144416i
$721$	25834.1	+	16602.6i	1.33442	+	0.857577i
$722$	27232.8	−	59631.6i	1.40374	−	3.07376i
$723$	2593.47	+	761.513i	0.133406	+	0.0391715i
$724$	10107.6	+	11664.7i	0.518846	+	0.598780i
$725$	1782.48	+	2057.09i	0.0913100	+	0.105377i
$726$	−43177.4	−	12678.0i	−2.20725	−	0.648107i
$727$	−6929.72	+	15174.0i	−0.353520	+	0.774101i	0.646418	+	0.762984i	$0.276266\pi$
$727$	−6929.72	+	15174.0i	−0.353520	+	0.774101i	−0.999938	+	0.0111179i	$0.996461\pi$
$728$	8893.77	+	5715.68i	0.452782	+	0.290985i
$729$	24742.5	−	7265.04i	1.25705	−	0.369102i
$730$	270.005	−	1877.93i	0.0136895	−	0.0952126i
$731$	2216.09	+	4852.57i	0.112127	+	0.245525i
$732$	−13360.5	−	92924.6i	−0.674617	−	4.69207i
$733$	−17067.5	+	10968.6i	−0.860028	+	0.552707i	−0.894688	−	0.446693i	$-0.852602\pi$
$733$	−17067.5	+	10968.6i	−0.860028	+	0.552707i	0.0346592	+	0.999399i	$0.488965\pi$
$734$	13874.2	−	16011.7i	0.697692	−	0.805179i
$735$	−28363.4			−1.42340
$736$	−8340.41	−	1942.13i	−0.417706	−	0.0972661i
$737$	10999.7			0.549768
$738$	−1556.73	+	1796.56i	−0.0776477	+	0.0896102i
$739$	−18381.1	+	11812.8i	−0.914963	+	0.588011i	−0.911192	−	0.411982i	$-0.864837\pi$
$739$	−18381.1	+	11812.8i	−0.914963	+	0.588011i	−0.00377115	+	0.999993i	$0.501200\pi$
$740$	−4314.16	−	30005.7i	−0.214313	−	1.49058i
$741$	5339.71	+	11692.3i	0.264722	+	0.579660i
$742$	−4188.88	+	29134.3i	−0.207249	+	1.44145i
$743$	7359.06	−	2160.81i	0.363362	−	0.106693i	−0.0949551	−	0.995482i	$-0.530271\pi$
$743$	7359.06	−	2160.81i	0.363362	−	0.106693i	0.458317	+	0.888789i	$0.348453\pi$
$744$	−64649.6	−	41547.7i	−3.18571	−	2.04733i
$745$	−1401.21	+	3068.23i	−0.0689080	+	0.150887i
$746$	−42388.0	−	12446.3i	−2.08034	−	0.610844i
$747$	12712.5	+	14671.0i	0.622658	+	0.718585i
$748$	7027.72	+	8110.42i	0.343528	+	0.396452i
$749$	−13898.0	−	4080.83i	−0.678002	−	0.199079i
$750$	−2190.72	+	4797.01i	−0.106659	+	0.233550i
$751$	6981.55	+	4486.77i	0.339228	+	0.218009i	0.699152	−	0.714973i	$-0.253561\pi$
$751$	6981.55	+	4486.77i	0.339228	+	0.218009i	−0.359924	+	0.932982i	$0.617197\pi$
$752$	9513.83	−	2793.51i	0.461348	−	0.135464i
$753$	3584.61	−	24931.5i	0.173480	−	1.20658i
$754$	2202.30	+	4822.36i	0.106370	+	0.232918i
$755$	676.352	+	4704.13i	0.0326026	+	0.226756i
$756$	82248.2	−	52857.7i	3.95680	−	2.54288i
$757$	−5336.67	+	6158.84i	−0.256228	+	0.295703i	−0.869260	−	0.494355i	$-0.835404\pi$
$757$	−5336.67	+	6158.84i	−0.256228	+	0.295703i	0.613032	+	0.790058i	$0.289950\pi$
$758$	−29678.2			−1.42211
$759$	−1357.42	+	15748.5i	−0.0649161	+	0.753141i
$760$	23718.4			1.13205
$761$	14592.6	−	16840.8i	0.695115	−	0.802205i	−0.292969	−	0.956122i	$-0.594643\pi$
$761$	14592.6	−	16840.8i	0.695115	−	0.802205i	0.988084	+	0.153917i	$0.0491888\pi$
$762$	37169.1	−	23887.1i	1.76705	−	1.13562i
$763$	3326.04	+	23133.1i	0.157812	+	1.09761i
$764$	1210.14	+	2649.83i	0.0573052	+	0.125481i
$765$	1596.24	−	11102.1i

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)

\(f(q)\)	\(=\)	\(q+(-3.13461 + 3.61754i) q^{2} +(-7.41459 + 4.76507i) q^{3} +(-2.12225 - 14.7606i) q^{4} +(2.07708 + 4.54816i) q^{5} +(6.00407 - 41.7592i) q^{6} +(30.1381 - 8.84935i) q^{7} +(27.8349 + 17.8884i) q^{8} +(21.0541 - 46.1020i) q^{9} +O(q^{10})\)	\(q+(-3.13461 + 3.61754i) q^{2} +(-7.41459 + 4.76507i) q^{3} +(-2.12225 - 14.7606i) q^{4} +(2.07708 + 4.54816i) q^{5} +(6.00407 - 41.7592i) q^{6} +(30.1381 - 8.84935i) q^{7} +(27.8349 + 17.8884i) q^{8} +(21.0541 - 46.1020i) q^{9} +(-22.9640 - 6.74283i) q^{10} +(-10.6474 - 12.2878i) q^{11} +(86.0708 + 99.3310i) q^{12} +(9.76032 + 2.86589i) q^{13} +(-62.4585 + 136.765i) q^{14} +(-37.0729 - 23.8253i) q^{15} +(-37.4969 + 11.0101i) q^{16} +(6.29904 - 43.8108i) q^{17} +(100.779 + 220.676i) q^{18} +(-20.4034 - 141.909i) q^{19} +(62.7254 - 40.3112i) q^{20} +(-181.294 + 209.225i) q^{21} +77.8269 q^{22} +(21.8728 + 108.114i) q^{23} -291.623 q^{24} +(-16.3715 + 18.8937i) q^{25} +(-40.9623 + 26.3249i) q^{26} +(29.7049 + 206.602i) q^{27} +(-194.582 - 426.076i) q^{28} +(15.4948 - 107.769i) q^{29} +(202.398 - 59.4295i) q^{30} +(221.688 + 142.471i) q^{31} +(-32.2511 + 70.6200i) q^{32} +(137.498 + 40.3731i) q^{33} +(138.742 + 160.117i) q^{34} +(102.847 + 118.692i) q^{35} +(-725.174 - 212.930i) q^{36} +(168.893 - 369.824i) q^{37} +(577.317 + 371.019i) q^{38} +(-86.0249 + 25.2592i) q^{39} +(-23.5441 + 163.753i) q^{40} +(4.07059 + 8.91336i) q^{41} +(-188.591 - 1311.68i) q^{42} +(-101.393 + 65.1614i) q^{43} +(-158.778 + 183.240i) q^{44} +253.410 q^{45} +(-459.668 - 259.769i) q^{46} -253.723 q^{47} +(225.560 - 260.310i) q^{48} +(541.446 - 347.966i) q^{49} +(-17.0304 - 118.449i) q^{50} +(162.057 + 354.854i) q^{51} +(21.5883 - 150.150i) q^{52} +(187.836 - 55.1537i) q^{53} +(-840.505 - 540.160i) q^{54} +(33.7712 - 73.9487i) q^{55} +(997.191 + 292.802i) q^{56} +(827.488 + 954.972i) q^{57} +(341.287 + 393.867i) q^{58} +(540.807 + 158.795i) q^{59} +(-272.998 + 597.782i) q^{60} +(-600.889 - 386.168i) q^{61} +(-1210.30 + 355.376i) q^{62} +(226.557 - 1575.74i) q^{63} +(-284.251 - 622.422i) q^{64} +(7.23840 + 50.3442i) q^{65} +(-577.054 + 370.850i) q^{66} +(-443.032 + 511.286i) q^{67} -660.041 q^{68} +(-677.347 - 697.394i) q^{69} -751.761 q^{70} +(152.696 - 176.221i) q^{71} +(1410.73 - 906.619i) q^{72} +(11.2815 + 78.4646i) q^{73} +(808.438 + 1770.23i) q^{74} +(31.3581 - 218.101i) q^{75} +(-2051.36 + 602.333i) q^{76} +(-429.631 - 276.107i) q^{77} +(178.279 - 390.376i) q^{78} +(766.632 + 225.103i) q^{79} +(-127.959 - 147.673i) q^{80} +(-308.603 - 356.147i) q^{81} +(-45.0041 - 13.2144i) q^{82} +(-159.114 + 348.412i) q^{83} +(3473.03 + 2231.98i) q^{84} +(212.342 - 62.3492i) q^{85} +(82.1045 - 571.049i) q^{86} +(398.638 + 872.895i) q^{87} +(-76.5609 - 532.493i) q^{88} +(912.509 - 586.434i) q^{89} +(-794.342 + 916.720i) q^{90} +319.519 q^{91} +(1549.40 - 552.299i) q^{92} -2322.61 q^{93} +(795.325 - 917.854i) q^{94} +(603.045 - 387.553i) q^{95} +(-97.3805 - 677.296i) q^{96} +(117.830 + 258.011i) q^{97} +(-438.443 + 3049.44i) q^{98} +(-790.660 + 232.159i) 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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