LMFDB - Embedded newform 124.3.b.a.63.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,3,Mod(63,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("124.63");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	124.b (of order $2$, degree $1$, 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:	$3.37875527807$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			63.11
Character	$\chi$	$=$	124.63
Dual form			124.3.b.a.63.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.785439 - 1.83932i) q^{2} -0.629544i q^{3} +(-2.76617 + 2.88934i) q^{4} +8.36044 q^{5} +(-1.15793 + 0.494468i) q^{6} +10.6307i q^{7} +(7.48707 + 2.81846i) q^{8} +8.60367 q^{9} +O(q^{10})$	\(q+(-0.785439 - 1.83932i) q^{2} -0.629544i q^{3} +(-2.76617 + 2.88934i) q^{4} +8.36044 q^{5} +(-1.15793 + 0.494468i) q^{6} +10.6307i q^{7} +(7.48707 + 2.81846i) q^{8} +8.60367 q^{9} +(-6.56662 - 15.3775i) q^{10} -12.1759i q^{11} +(1.81897 + 1.74142i) q^{12} -14.9161 q^{13} +(19.5532 - 8.34977i) q^{14} -5.26326i q^{15} +(-0.696604 - 15.9848i) q^{16} +16.8744 q^{17} +(-6.75766 - 15.8249i) q^{18} +11.7174i q^{19} +(-23.1264 + 24.1562i) q^{20} +6.69249 q^{21} +(-22.3954 + 9.56344i) q^{22} -21.8685i q^{23} +(1.77434 - 4.71344i) q^{24} +44.8969 q^{25} +(11.7157 + 27.4354i) q^{26} -11.0823i q^{27} +(-30.7157 - 29.4063i) q^{28} -27.0914 q^{29} +(-9.68080 + 4.13397i) q^{30} +5.56776i q^{31} +(-28.8540 + 13.8364i) q^{32} -7.66527 q^{33} +(-13.2539 - 31.0374i) q^{34} +88.8773i q^{35} +(-23.7992 + 24.8590i) q^{36} -2.32174 q^{37} +(21.5520 - 9.20331i) q^{38} +9.39034i q^{39} +(62.5952 + 23.5636i) q^{40} +22.5468 q^{41} +(-5.25654 - 12.3096i) q^{42} +25.5496i q^{43} +(35.1804 + 33.6806i) q^{44} +71.9305 q^{45} +(-40.2231 + 17.1764i) q^{46} +38.3621i q^{47} +(-10.0631 + 0.438542i) q^{48} -64.0117 q^{49} +(-35.2638 - 82.5797i) q^{50} -10.6232i q^{51} +(41.2605 - 43.0977i) q^{52} -75.0089 q^{53} +(-20.3838 + 8.70446i) q^{54} -101.796i q^{55} +(-29.9622 + 79.5928i) q^{56} +7.37662 q^{57} +(21.2787 + 49.8297i) q^{58} -59.6920i q^{59} +(15.2074 + 14.5591i) q^{60} -74.5050 q^{61} +(10.2409 - 4.37314i) q^{62} +91.4631i q^{63} +(48.1126 + 42.2040i) q^{64} -124.705 q^{65} +(6.02060 + 14.0989i) q^{66} -75.8849i q^{67} +(-46.6776 + 48.7561i) q^{68} -13.7672 q^{69} +(163.473 - 69.8077i) q^{70} -76.7482i q^{71} +(64.4164 + 24.2491i) q^{72} +9.82790 q^{73} +(1.82358 + 4.27041i) q^{74} -28.2646i q^{75} +(-33.8556 - 32.4124i) q^{76} +129.438 q^{77} +(17.2718 - 7.37554i) q^{78} -68.2717i q^{79} +(-5.82391 - 133.640i) q^{80} +70.4563 q^{81} +(-17.7091 - 41.4707i) q^{82} +138.927i q^{83} +(-18.5126 + 19.3369i) q^{84} +141.078 q^{85} +(46.9937 - 20.0676i) q^{86} +17.0552i q^{87} +(34.3173 - 91.1620i) q^{88} -138.116 q^{89} +(-56.4970 - 132.303i) q^{90} -158.569i q^{91} +(63.1856 + 60.4920i) q^{92} +3.50515 q^{93} +(70.5600 - 30.1311i) q^{94} +97.9627i q^{95} +(8.71061 + 18.1649i) q^{96} +9.02529 q^{97} +(50.2773 + 117.738i) q^{98} -104.758i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9}+O(q^{10}) $ 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9	$ 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9} + q^{10} - 14 q^{12} + 12 q^{13} + 29 q^{14} + 50 q^{16} - 4 q^{17} - 34 q^{18} - 63 q^{20} - 16 q^{21} - 24 q^{22} - 20 q^{24} + 90 q^{25} + 38 q^{26} + 3 q^{28} - 4 q^{29} - 6 q^{30} + 118 q^{32} + 80 q^{33} + 4 q^{34} - 2 q^{36} + 76 q^{37} + 37 q^{38} - 180 q^{40} - 4 q^{41} - 38 q^{42} + 184 q^{44} - 20 q^{45} - 54 q^{46} - 172 q^{48} - 258 q^{49} - 31 q^{50} - 88 q^{52} - 132 q^{53} - 84 q^{54} - 28 q^{56} + 176 q^{57} + 164 q^{58} + 108 q^{60} - 100 q^{61} + 381 q^{64} - 104 q^{65} + 60 q^{66} + 214 q^{68} + 112 q^{69} + 45 q^{70} - 167 q^{72} - 132 q^{73} + 398 q^{74} - 317 q^{76} + 176 q^{77} - 188 q^{78} - 203 q^{80} + 158 q^{81} - 81 q^{82} + 176 q^{84} + 248 q^{85} - 78 q^{86} + 98 q^{88} - 20 q^{89} - 567 q^{90} - 260 q^{92} - 244 q^{94} - 90 q^{96} + 300 q^{97} - 371 q^{98}+O(q^{100}) $ 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9 + q^10 - 14 * q^12 + 12 * q^13 + 29 * q^14 + 50 * q^16 - 4 * q^17 - 34 * q^18 - 63 * q^20 - 16 * q^21 - 24 * q^22 - 20 * q^24 + 90 * q^25 + 38 * q^26 + 3 * q^28 - 4 * q^29 - 6 * q^30 + 118 * q^32 + 80 * q^33 + 4 * q^34 - 2 * q^36 + 76 * q^37 + 37 * q^38 - 180 * q^40 - 4 * q^41 - 38 * q^42 + 184 * q^44 - 20 * q^45 - 54 * q^46 - 172 * q^48 - 258 * q^49 - 31 * q^50 - 88 * q^52 - 132 * q^53 - 84 * q^54 - 28 * q^56 + 176 * q^57 + 164 * q^58 + 108 * q^60 - 100 * q^61 + 381 * q^64 - 104 * q^65 + 60 * q^66 + 214 * q^68 + 112 * q^69 + 45 * q^70 - 167 * q^72 - 132 * q^73 + 398 * q^74 - 317 * q^76 + 176 * q^77 - 188 * q^78 - 203 * q^80 + 158 * q^81 - 81 * q^82 + 176 * q^84 + 248 * q^85 - 78 * q^86 + 98 * q^88 - 20 * q^89 - 567 * q^90 - 260 * q^92 - 244 * q^94 - 90 * q^96 + 300 * q^97 - 371 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.785439	−	1.83932i	−0.392720	−	0.919658i
$2$	−0.785439	−	1.83932i	−0.392720	−	0.919658i
$3$		−	0.629544i		−	0.209848i	−0.994480	−	0.104924i	$-0.966540\pi$
$3$		−	0.629544i		−	0.209848i	0.994480	−	0.104924i	$-0.0334599\pi$
$4$	−2.76617	+	2.88934i	−0.691543	+	0.722336i
$5$	8.36044			1.67209			0.836044	−	0.548663i	$-0.184863\pi$
$5$	8.36044			1.67209			0.836044	+	0.548663i	$0.184863\pi$
$6$	−1.15793	+	0.494468i	−0.192988	+	0.0824114i
$7$			10.6307i			1.51867i	0.650699	+	0.759336i	$0.274476\pi$
$7$			10.6307i			1.51867i	−0.650699	+	0.759336i	$0.725524\pi$
$8$	7.48707	+	2.81846i	0.935884	+	0.352307i
$9$	8.60367			0.955964
$10$	−6.56662	−	15.3775i	−0.656662	−	1.53775i
$11$		−	12.1759i		−	1.10690i	−0.832882	−	0.553450i	$-0.813311\pi$
$11$		−	12.1759i		−	1.10690i	0.832882	−	0.553450i	$-0.186689\pi$
$12$	1.81897	+	1.74142i	0.151581	+	0.145119i
$13$	−14.9161			−1.14739			−0.573696	−	0.819068i	$-0.694491\pi$
$13$	−14.9161			−1.14739			−0.573696	+	0.819068i	$0.694491\pi$
$14$	19.5532	−	8.34977i	1.39666	−	0.596412i
$15$		−	5.26326i		−	0.350884i
$16$	−0.696604	−	15.9848i	−0.0435377	−	0.999052i
$17$	16.8744			0.992614			0.496307	−	0.868147i	$-0.334689\pi$
$17$	16.8744			0.992614			0.496307	+	0.868147i	$0.334689\pi$
$18$	−6.75766	−	15.8249i	−0.375426	−	0.879160i
$19$			11.7174i			0.616706i	0.951272	+	0.308353i	$0.0997778\pi$
$19$			11.7174i			0.616706i	−0.951272	+	0.308353i	$0.900222\pi$
$20$	−23.1264	+	24.1562i	−1.15632	+	1.20781i
$21$	6.69249			0.318690
$22$	−22.3954	+	9.56344i	−1.01797	+	0.434702i
$23$		−	21.8685i		−	0.950805i	−0.879768	−	0.475402i	$-0.842302\pi$
$23$		−	21.8685i		−	0.950805i	0.879768	−	0.475402i	$-0.157698\pi$
$24$	1.77434	−	4.71344i	0.0739310	−	0.196393i
$25$	44.8969			1.79588
$26$	11.7157	+	27.4354i	0.450604	+	1.05521i
$27$		−	11.0823i		−	0.410455i
$28$	−30.7157	−	29.4063i	−1.09699	−	1.05023i
$29$	−27.0914			−0.934187			−0.467093	−	0.884208i	$-0.654699\pi$
$29$	−27.0914			−0.934187			−0.467093	+	0.884208i	$0.654699\pi$
$30$	−9.68080	+	4.13397i	−0.322693	+	0.137799i
$31$			5.56776i			0.179605i
$31$			5.56776i			0.179605i
$32$	−28.8540	+	13.8364i	−0.901688	+	0.432387i
$33$	−7.66527			−0.232281
$34$	−13.2539	−	31.0374i	−0.389819	−	0.912866i
$35$			88.8773i			2.53935i
$36$	−23.7992	+	24.8590i	−0.661090	+	0.690527i
$37$	−2.32174			−0.0627496			−0.0313748	−	0.999508i	$-0.509989\pi$
$37$	−2.32174			−0.0627496			−0.0313748	+	0.999508i	$0.509989\pi$
$38$	21.5520	−	9.20331i	0.567159	−	0.242192i
$39$			9.39034i			0.240778i
$40$	62.5952	+	23.5636i	1.56488	+	0.589089i
$41$	22.5468			0.549921			0.274961	−	0.961455i	$-0.411335\pi$
$41$	22.5468			0.549921			0.274961	+	0.961455i	$0.411335\pi$
$42$	−5.25654	−	12.3096i	−0.125156	−	0.293086i
$43$			25.5496i			0.594176i	0.954850	+	0.297088i	$0.0960155\pi$
$43$			25.5496i			0.594176i	−0.954850	+	0.297088i	$0.903985\pi$
$44$	35.1804	+	33.6806i	0.799554	+	0.765469i
$45$	71.9305			1.59846
$46$	−40.2231	+	17.1764i	−0.874415	+	0.373400i
$47$			38.3621i			0.816215i	0.912934	+	0.408107i	$0.133811\pi$
$47$			38.3621i			0.816215i	−0.912934	+	0.408107i	$0.866189\pi$
$48$	−10.0631	+	0.438542i	−0.209649	+	0.00913630i
$49$	−64.0117			−1.30636
$50$	−35.2638	−	82.5797i	−0.705276	−	1.65159i
$51$		−	10.6232i		−	0.208298i
$52$	41.2605	−	43.0977i	0.793471	−	0.828803i
$53$	−75.0089			−1.41526			−0.707631	−	0.706582i	$-0.750236\pi$
$53$	−75.0089			−1.41526			−0.707631	+	0.706582i	$0.750236\pi$
$54$	−20.3838	+	8.70446i	−0.377478	+	0.161194i
$55$		−	101.796i		−	1.85084i
$56$	−29.9622	+	79.5928i	−0.535039	+	1.42130i
$57$	7.37662			0.129414
$58$	21.2787	+	49.8297i	0.366874	+	0.859133i
$59$		−	59.6920i		−	1.01173i	−0.862613	−	0.505865i	$-0.831174\pi$
$59$		−	59.6920i		−	1.01173i	0.862613	−	0.505865i	$-0.168826\pi$
$60$	15.2074	+	14.5591i	0.253456	+	0.242651i
$61$	−74.5050			−1.22139			−0.610697	−	0.791864i	$-0.709111\pi$
$61$	−74.5050			−1.22139			−0.610697	+	0.791864i	$0.709111\pi$
$62$	10.2409	−	4.37314i	0.165175	−	0.0705345i
$63$			91.4631i			1.45179i
$64$	48.1126	+	42.2040i	0.751759	+	0.659438i
$65$	−124.705			−1.91854
$66$	6.02060	+	14.0989i	0.0912212	+	0.213619i
$67$		−	75.8849i		−	1.13261i	−0.824196	−	0.566305i	$-0.808372\pi$
$67$		−	75.8849i		−	1.13261i	0.824196	−	0.566305i	$-0.191628\pi$
$68$	−46.6776	+	48.7561i	−0.686435	+	0.717001i
$69$	−13.7672			−0.199524
$70$	163.473	−	69.8077i	2.33534	−	0.997253i
$71$		−	76.7482i		−	1.08096i	−0.841357	−	0.540480i	$-0.818243\pi$
$71$		−	76.7482i		−	1.08096i	0.841357	−	0.540480i	$-0.181757\pi$
$72$	64.4164	+	24.2491i	0.894672	+	0.336793i
$73$	9.82790			0.134629			0.0673144	−	0.997732i	$-0.478557\pi$
$73$	9.82790			0.134629			0.0673144	+	0.997732i	$0.478557\pi$
$74$	1.82358	+	4.27041i	0.0246430	+	0.0577082i
$75$		−	28.2646i		−	0.376861i
$76$	−33.8556	−	32.4124i	−0.445469	−	0.426478i
$77$	129.438			1.68102
$78$	17.2718	−	7.37554i	0.221433	−	0.0945582i
$79$		−	68.2717i		−	0.864199i	−0.901826	−	0.432099i	$-0.857773\pi$
$79$		−	68.2717i		−	0.864199i	0.901826	−	0.432099i	$-0.142227\pi$
$80$	−5.82391	−	133.640i	−0.0727989	−	1.67050i
$81$	70.4563			0.869831
$82$	−17.7091	−	41.4707i	−0.215965	−	0.505740i
$83$			138.927i			1.67382i	0.547337	+	0.836912i	$0.315642\pi$
$83$			138.927i			1.67382i	−0.547337	+	0.836912i	$0.684358\pi$
$84$	−18.5126	+	19.3369i	−0.220388	+	0.230201i
$85$	141.078			1.65974
$86$	46.9937	−	20.0676i	0.546439	−	0.233345i
$87$			17.0552i			0.196037i
$88$	34.3173	−	91.1620i	0.389969	−	1.03593i
$89$	−138.116			−1.55187			−0.775935	−	0.630813i	$-0.782722\pi$
$89$	−138.116			−1.55187			−0.775935	+	0.630813i	$0.782722\pi$
$90$	−56.4970	−	132.303i	−0.627745	−	1.47003i
$91$		−	158.569i		−	1.74251i
$92$	63.1856	+	60.4920i	0.686800	+	0.657522i
$93$	3.50515			0.0376898
$94$	70.5600	−	30.1311i	0.750639	−	0.320544i
$95$			97.9627i			1.03119i
$96$	8.71061	+	18.1649i	0.0907355	+	0.189217i
$97$	9.02529			0.0930443			0.0465221	−	0.998917i	$-0.485186\pi$
$97$	9.02529			0.0930443			0.0465221	+	0.998917i	$0.485186\pi$
$98$	50.2773	+	117.738i	0.513034	+	1.20141i
$99$		−	104.758i		−	1.05816i
$100$	−124.193	+	129.723i	−1.24193	+	1.29723i
$101$	−125.339			−1.24098			−0.620488	−	0.784216i	$-0.713066\pi$
$101$	−125.339			−1.24098			−0.620488	+	0.784216i	$0.713066\pi$
$102$	−19.5394	+	8.34388i	−0.191563	+	0.0818027i
$103$			165.993i			1.61158i	0.592200	+	0.805791i	$0.298260\pi$
$103$			165.993i			1.61158i	−0.592200	+	0.805791i	$0.701740\pi$
$104$	−111.678	−	42.0404i	−1.07383	−	0.404235i
$105$	55.9521			0.532877
$106$	58.9150	+	137.965i	0.555802	+	1.30156i
$107$		−	61.8079i		−	0.577644i	−0.957383	−	0.288822i	$-0.906736\pi$
$107$		−	61.8079i		−	0.577644i	0.957383	−	0.288822i	$-0.0932635\pi$
$108$	32.0205	+	30.6555i	0.296486	+	0.283847i
$109$	−41.5653			−0.381333			−0.190667	−	0.981655i	$-0.561065\pi$
$109$	−41.5653			−0.381333			−0.190667	+	0.981655i	$0.561065\pi$
$110$	−187.235	+	79.9545i	−1.70214	+	0.726859i
$111$			1.46163i			0.0131679i
$112$	169.930	−	7.40538i	1.51723	−	0.0661195i
$113$	−37.8320			−0.334796			−0.167398	−	0.985889i	$-0.553536\pi$
$113$	−37.8320			−0.334796			−0.167398	+	0.985889i	$0.553536\pi$
$114$	−5.79389	−	13.5679i	−0.0508236	−	0.119017i
$115$		−	182.830i		−	1.58983i
$116$	74.9395	−	78.2764i	0.646030	−	0.674797i
$117$	−128.333			−1.09687
$118$	−109.793	+	46.8845i	−0.930445	+	0.397326i
$119$			179.387i			1.50745i
$120$	14.8343	−	39.4064i	0.123619	−	0.328387i
$121$	−27.2528			−0.225230
$122$	58.5192	+	137.038i	0.479665	+	1.12326i
$123$		−	14.1942i		−	0.115400i
$124$	−16.0872	−	15.4014i	−0.129735	−	0.124205i
$125$	166.347			1.33078
$126$	168.230	−	71.8387i	1.33516	−	0.570148i
$127$			153.236i			1.20658i	0.797520	+	0.603292i	$0.206145\pi$
$127$			153.236i			1.20658i	−0.797520	+	0.603292i	$0.793855\pi$
$128$	39.8371	−	121.643i	0.311227	−	0.950336i
$129$	16.0846			0.124687
$130$	97.9483	+	229.372i	0.753449	+	1.76440i
$131$		−	20.2581i		−	0.154642i	−0.997006	−	0.0773208i	$-0.975363\pi$
$131$		−	20.2581i		−	0.154642i	0.997006	−	0.0773208i	$-0.0246366\pi$
$132$	21.2034	−	22.1476i	0.160632	−	0.167785i
$133$	−124.564			−0.936573
$134$	−139.576	+	59.6030i	−1.04161	+	0.444798i
$135$		−	92.6527i		−	0.686316i
$136$	126.340	+	47.5599i	0.928972	+	0.349705i
$137$	196.067			1.43115			0.715574	−	0.698537i	$-0.246165\pi$
$137$	196.067			1.43115			0.715574	+	0.698537i	$0.246165\pi$
$138$	10.8133	+	25.3222i	0.0783571	+	0.183494i
$139$		−	181.793i		−	1.30787i	−0.756552	−	0.653933i	$-0.773118\pi$
$139$		−	181.793i		−	1.30787i	0.756552	−	0.653933i	$-0.226882\pi$
$140$	−256.797	−	245.850i	−1.83426	−	1.75607i
$141$	24.1506			0.171281
$142$	−141.164	+	60.2810i	−0.994114	+	0.424514i
$143$			181.617i			1.27005i
$144$	−5.99335	−	137.528i	−0.0416205	−	0.955057i
$145$	−226.496			−1.56204
$146$	−7.71922	−	18.0766i	−0.0528713	−	0.123812i
$147$			40.2982i			0.274137i
$148$	6.42232	−	6.70829i	0.0433940	−	0.0453263i
$149$	97.6607			0.655441			0.327720	−	0.944775i	$-0.393720\pi$
$149$	97.6607			0.655441			0.327720	+	0.944775i	$0.393720\pi$
$150$	−51.9875	+	22.2001i	−0.346583	+	0.148001i
$151$			187.414i			1.24115i	0.784147	+	0.620575i	$0.213101\pi$
$151$			187.414i			1.24115i	−0.784147	+	0.620575i	$0.786899\pi$
$152$	−33.0250	+	87.7291i	−0.217270	+	0.577165i
$153$	145.182			0.948903
$154$	−101.666	−	238.078i	−0.660169	−	1.54596i
$155$			46.5490i			0.300316i
$156$	−27.1319	−	25.9753i	−0.173922	−	0.166508i
$157$	−204.818			−1.30457			−0.652287	−	0.757972i	$-0.726190\pi$
$157$	−204.818			−1.30457			−0.652287	+	0.757972i	$0.726190\pi$
$158$	−125.573	+	53.6233i	−0.794768	+	0.339388i
$159$			47.2214i			0.296990i
$160$	−241.232	+	115.678i	−1.50770	+	0.722989i
$161$	232.478			1.44396
$162$	−55.3391	−	129.591i	−0.341600	−	0.799947i
$163$		−	36.6497i		−	0.224845i	−0.993661	−	0.112422i	$-0.964139\pi$
$163$		−	36.6497i		−	0.224845i	0.993661	−	0.112422i	$-0.0358609\pi$
$164$	−62.3682	+	65.1454i	−0.380294	+	0.397228i
$165$	−64.0850			−0.388394
$166$	255.531	−	109.119i	1.53935	−	0.657344i
$167$		−	195.790i		−	1.17240i	−0.810168	−	0.586198i	$-0.800624\pi$
$167$		−	195.790i		−	1.17240i	0.810168	−	0.586198i	$-0.199376\pi$
$168$	50.1072	+	18.8625i	0.298257	+	0.112277i
$169$	53.4902			0.316510
$170$	−110.808	−	259.487i	−0.651812	−	1.52639i
$171$			100.813i			0.589548i
$172$	−73.8215	−	70.6745i	−0.429195	−	0.410898i
$173$	153.208			0.885594			0.442797	−	0.896622i	$-0.353986\pi$
$173$	153.208			0.885594			0.442797	+	0.896622i	$0.353986\pi$
$174$	31.3700	−	13.3958i	0.180287	−	0.0769876i
$175$			477.286i			2.72735i
$176$	−194.630	+	8.48178i	−1.10585	+	0.0481919i
$177$	−37.5787			−0.212309
$178$	108.482	+	254.040i	0.609450	+	1.42719i
$179$			56.2746i			0.314383i	0.987568	+	0.157192i	$0.0502440\pi$
$179$			56.2746i			0.314383i	−0.987568	+	0.157192i	$0.949756\pi$
$180$	−198.972	+	207.832i	−1.10540	+	1.15462i
$181$	66.9235			0.369743			0.184872	−	0.982763i	$-0.440813\pi$
$181$	66.9235			0.369743			0.184872	+	0.982763i	$0.440813\pi$
$182$	−291.658	+	124.546i	−1.60252	+	0.684319i
$183$			46.9042i			0.256307i
$184$	61.6355	−	163.731i	0.334976	−	0.889843i
$185$	−19.4107			−0.104923
$186$	−2.75308	−	6.44708i	−0.0148015	−	0.0346617i
$187$		−	205.462i		−	1.09873i
$188$	−110.841	−	106.116i	−0.589581	−	0.564447i
$189$	117.812			0.623346
$190$	180.184	−	76.9437i	0.948339	−	0.404967i
$191$		−	224.265i		−	1.17416i	−0.809528	−	0.587082i	$-0.800277\pi$
$191$		−	224.265i		−	1.17416i	0.809528	−	0.587082i	$-0.199723\pi$
$192$	26.5693	−	30.2890i	0.138382	−	0.157755i
$193$	−94.4007			−0.489123			−0.244561	−	0.969634i	$-0.578644\pi$
$193$	−94.4007			−0.489123			−0.244561	+	0.969634i	$0.578644\pi$
$194$	−7.08882	−	16.6004i	−0.0365403	−	0.0855689i
$195$			78.5073i			0.402602i
$196$	177.067	−	184.952i	0.903405	−	0.943632i
$197$	282.940			1.43625			0.718123	−	0.695916i	$-0.245002\pi$
$197$	282.940			1.43625			0.718123	+	0.695916i	$0.245002\pi$
$198$	−192.682	+	82.2807i	−0.973143	+	0.415559i
$199$		−	215.758i		−	1.08421i	−0.840310	−	0.542106i	$-0.817627\pi$
$199$		−	215.758i		−	1.08421i	0.840310	−	0.542106i	$-0.182373\pi$
$200$	336.147	+	126.540i	1.68073	+	0.632701i
$201$	−47.7729			−0.237676
$202$	98.4459	+	230.537i	0.487356	+	1.14127i
$203$		−	288.001i		−	1.41872i
$204$	30.6941	+	29.3856i	0.150461	+	0.144047i
$205$	188.501			0.919517
$206$	305.314	−	130.377i	1.48211	−	0.632900i
$207$		−	188.150i		−	0.908935i
$208$	10.3906	+	238.431i	0.0499549	+	1.14630i
$209$	142.670			0.682632
$210$	−43.9470	−	102.914i	−0.209271	−	0.490065i
$211$		−	132.326i		−	0.627139i	−0.949565	−	0.313570i	$-0.898475\pi$
$211$		−	132.326i		−	0.627139i	0.949565	−	0.313570i	$-0.101525\pi$
$212$	207.487	−	216.727i	0.978715	−	1.02229i
$213$	−48.3163			−0.226837
$214$	−113.684	+	48.5463i	−0.531235	+	0.226852i
$215$			213.606i			0.993514i
$216$	31.2350	−	82.9739i	0.144606	−	0.384138i
$217$	−59.1892			−0.272761
$218$	32.6470	+	76.4518i	0.149757	+	0.350696i
$219$		−	6.18709i		−	0.0282515i
$220$	294.123	+	281.585i	1.33692	+	1.27993i
$221$	−251.701			−1.13892
$222$	2.68841	−	1.14802i	0.0121099	−	0.00517128i
$223$			281.714i			1.26329i	0.775258	+	0.631645i	$0.217620\pi$
$223$			281.714i			1.26329i	−0.775258	+	0.631645i	$0.782380\pi$
$224$	−147.090	−	306.738i	−0.656654	−	1.36937i
$225$	386.279			1.71679
$226$	29.7147	+	69.5849i	0.131481	+	0.307898i
$227$			217.333i			0.957416i	0.877974	+	0.478708i	$0.158895\pi$
$227$			217.333i			0.957416i	−0.877974	+	0.478708i	$0.841105\pi$
$228$	−20.4050	+	21.3136i	−0.0894956	+	0.0934806i
$229$	107.020			0.467338			0.233669	−	0.972316i	$-0.424927\pi$
$229$	107.020			0.467338			0.233669	+	0.972316i	$0.424927\pi$
$230$	−336.283	+	143.602i	−1.46210	+	0.624357i
$231$		−	81.4871i		−	0.352758i
$232$	−202.835	−	76.3561i	−0.874291	−	0.329121i
$233$	−296.570			−1.27283			−0.636417	−	0.771345i	$-0.719584\pi$
$233$	−296.570			−1.27283			−0.636417	+	0.771345i	$0.719584\pi$
$234$	100.798	+	236.046i	0.430761	+	1.00874i
$235$			320.724i			1.36478i
$236$	172.471	+	165.118i	0.730808	+	0.699654i
$237$	−42.9800			−0.181350
$238$	329.950	−	140.898i	1.38634	−	0.592007i
$239$		−	107.609i		−	0.450248i	−0.974330	−	0.225124i	$-0.927721\pi$
$239$		−	107.609i		−	0.450248i	0.974330	−	0.225124i	$-0.0722787\pi$
$240$	−84.1323	+	3.66641i	−0.350551	+	0.0152767i
$241$	58.5479			0.242937			0.121469	−	0.992595i	$-0.461240\pi$
$241$	58.5479			0.242937			0.121469	+	0.992595i	$0.461240\pi$
$242$	21.4054	+	50.1265i	0.0884522	+	0.207134i
$243$		−	144.096i		−	0.592987i
$244$	206.094	−	215.271i	0.844646	−	0.882256i
$245$	−535.166			−2.18435
$246$	−26.1076	+	11.1487i	−0.106128	+	0.0453198i
$247$		−	174.778i		−	0.707604i
$248$	−15.6925	+	41.6863i	−0.0632763	+	0.168090i
$249$	87.4609			0.351248
$250$	−130.655	−	305.965i	−0.522622	−	1.22386i
$251$			66.6417i			0.265505i	0.991149	+	0.132752i	$0.0423815\pi$
$251$			66.6417i			0.265505i	−0.991149	+	0.132752i	$0.957618\pi$
$252$	−264.268	−	253.002i	−1.04868	−	1.00398i
$253$	−266.269			−1.05245
$254$	281.850	−	120.358i	1.10965	−	0.473849i
$255$		−	88.8146i		−	0.348292i
$256$	−255.029	+	22.2702i	−0.996209	+	0.0869929i
$257$	384.382			1.49565			0.747826	−	0.663895i	$-0.231098\pi$
$257$	384.382			1.49565			0.747826	+	0.663895i	$0.231098\pi$
$258$	−12.6334	−	29.5846i	−0.0489669	−	0.114669i
$259$		−	24.6817i		−	0.0952960i
$260$	344.956	−	360.316i	1.32675	−	1.38583i
$261$	−233.086			−0.893049
$262$	−37.2610	+	15.9115i	−0.142217	+	0.0607308i
$263$		−	87.9027i		−	0.334231i	−0.985937	−	0.167115i	$-0.946555\pi$
$263$		−	87.9027i		−	0.334231i	0.985937	−	0.167115i	$-0.0534452\pi$
$264$	−57.3904	−	21.6042i	−0.217388	−	0.0818342i
$265$	−627.108			−2.36644
$266$	97.8377	+	229.113i	0.367811	+	0.861327i
$267$			86.9503i			0.325657i
$268$	219.258	+	209.911i	0.818125	+	0.783248i
$269$	370.468			1.37721			0.688603	−	0.725139i	$-0.258225\pi$
$269$	370.468			1.37721			0.688603	+	0.725139i	$0.258225\pi$
$270$	−170.418	+	72.7731i	−0.631177	+	0.269530i
$271$			88.3403i			0.325979i	0.986628	+	0.162989i	$0.0521137\pi$
$271$			88.3403i			0.325979i	−0.986628	+	0.162989i	$0.947886\pi$
$272$	−11.7548	−	269.735i	−0.0432162	−	0.991673i
$273$	−99.8258			−0.365662
$274$	−153.999	−	360.630i	−0.562040	−	1.31617i
$275$		−	546.661i		−	1.98786i
$276$	38.0824	−	39.7781i	0.137980	−	0.144124i
$277$	377.928			1.36436			0.682180	−	0.731184i	$-0.261032\pi$
$277$	377.928			1.36436			0.682180	+	0.731184i	$0.261032\pi$
$278$	−334.376	+	142.788i	−1.20279	+	0.513625i
$279$			47.9032i			0.171696i
$280$	−250.497	+	665.431i	−0.894632	+	2.37654i
$281$	−93.2034			−0.331685			−0.165842	−	0.986152i	$-0.553034\pi$
$281$	−93.2034			−0.331685			−0.165842	+	0.986152i	$0.553034\pi$
$282$	−18.9688	−	44.4206i	−0.0672654	−	0.157520i
$283$		−	367.952i		−	1.30018i	−0.759856	−	0.650091i	$-0.774731\pi$
$283$		−	367.952i		−	1.30018i	0.759856	−	0.650091i	$-0.225269\pi$
$284$	221.752	+	212.299i	0.780816	+	0.747530i
$285$	61.6718			0.216392
$286$	334.051	−	142.649i	1.16801	−	0.498774i
$287$			239.688i			0.835150i
$288$	−248.251	+	119.044i	−0.861981	+	0.413346i
$289$	−4.25313			−0.0147167
$290$	177.899	+	416.598i	0.613445	+	1.43655i
$291$		−	5.68182i		−	0.0195251i
$292$	−27.1856	+	28.3962i	−0.0931015	+	0.0972471i
$293$	369.227			1.26016			0.630081	−	0.776530i	$-0.283022\pi$
$293$	369.227			1.26016			0.630081	+	0.776530i	$0.283022\pi$
$294$	74.1211	−	31.6518i	0.252113	−	0.107659i
$295$		−	499.051i		−	1.69170i
$296$	−17.3830	−	6.54372i	−0.0587264	−	0.0221072i
$297$	−134.937			−0.454333
$298$	−76.7065	−	179.629i	−0.257405	−	0.602782i
$299$			326.193i			1.09095i
$300$	81.6660	+	78.1846i	0.272220	+	0.260615i
$301$	−271.610			−0.902358
$302$	344.713	−	147.202i	1.14143	−	0.487424i
$303$			78.9061i			0.260416i
$304$	187.301	−	8.16239i	0.616121	−	0.0268500i
$305$	−622.895			−2.04228
$306$	−114.032	−	267.036i	−0.372653	−	0.872667i
$307$		−	142.952i		−	0.465642i	−0.972520	−	0.232821i	$-0.925204\pi$
$307$		−	142.952i		−	0.465642i	0.972520	−	0.232821i	$-0.0747956\pi$
$308$	−358.049	+	373.992i	−1.16250	+	1.21426i
$309$	104.500			0.338187
$310$	85.6183	−	36.5614i	0.276188	−	0.117940i
$311$		−	89.7384i		−	0.288548i	−0.989538	−	0.144274i	$-0.953915\pi$
$311$		−	89.7384i		−	0.288548i	0.989538	−	0.144274i	$-0.0460846\pi$
$312$	−26.4663	+	70.3062i	−0.0848278	+	0.225340i
$313$	229.109			0.731976			0.365988	−	0.930619i	$-0.380731\pi$
$313$	229.109			0.731976			0.365988	+	0.930619i	$0.380731\pi$
$314$	160.872	+	376.725i	0.512332	+	1.19976i
$315$			764.671i			2.42753i
$316$	197.260	+	188.851i	0.624242	+	0.597630i
$317$	−254.125			−0.801657			−0.400828	−	0.916153i	$-0.631278\pi$
$317$	−254.125			−0.801657			−0.400828	+	0.916153i	$0.631278\pi$
$318$	86.8551	−	37.0895i	0.273129	−	0.116634i
$319$			329.863i			1.03405i
$320$	402.242	+	352.844i	1.25701	+	1.10264i
$321$	−38.9107			−0.121217
$322$	−182.597	−	427.600i	−0.567071	−	1.32795i
$323$			197.725i			0.612151i
$324$	−194.894	+	203.572i	−0.601525	+	0.628310i
$325$	−669.687			−2.06058
$326$	−67.4103	+	28.7861i	−0.206780	+	0.0883009i
$327$			26.1672i			0.0800220i
$328$	168.809	+	63.5472i	0.514663	+	0.193741i
$329$	−407.816			−1.23956
$330$	50.3349	+	117.873i	0.152530	+	0.357190i
$331$			426.714i			1.28917i	0.764534	+	0.644583i	$0.222969\pi$
$331$			426.714i			1.28917i	−0.764534	+	0.644583i	$0.777031\pi$
$332$	−401.409	−	384.297i	−1.20906	−	1.15752i
$333$	−19.9755			−0.0599864
$334$	−360.120	+	153.781i	−1.07820	+	0.460423i
$335$		−	634.431i		−	1.89382i
$336$	−4.66201	−	106.978i	−0.0138750	−	0.318388i
$337$	23.1141			0.0685877			0.0342939	−	0.999412i	$-0.489082\pi$
$337$	23.1141			0.0685877			0.0342939	+	0.999412i	$0.489082\pi$
$338$	−42.0133	−	98.3853i	−0.124300	−	0.291081i
$339$			23.8169i			0.0702562i
$340$	−390.245	+	407.622i	−1.14778	+	1.19889i
$341$	67.7926			0.198805
$342$	185.427	−	79.1823i	0.542183	−	0.231527i
$343$		−	159.585i		−	0.465263i
$344$	−72.0104	+	191.292i	−0.209333	+	0.556080i
$345$	−115.100			−0.333622
$346$	−120.335	−	281.797i	−0.347790	−	0.814443i
$347$			633.079i			1.82443i	0.409707	+	0.912217i	$0.365631\pi$
$347$			633.079i			1.82443i	−0.409707	+	0.912217i	$0.634369\pi$
$348$	−49.2784	−	47.1777i	−0.141605	−	0.135568i
$349$	−57.5039			−0.164768			−0.0823838	−	0.996601i	$-0.526253\pi$
$349$	−57.5039			−0.164768			−0.0823838	+	0.996601i	$0.526253\pi$
$350$	877.879	−	374.879i	2.50823	−	1.07108i
$351$			165.304i			0.470953i
$352$	168.471	+	351.324i	0.478610	+	0.998079i
$353$	−385.842			−1.09304			−0.546519	−	0.837447i	$-0.684047\pi$
$353$	−385.842			−1.09304			−0.546519	+	0.837447i	$0.684047\pi$
$354$	29.5158	+	69.1192i	0.0833780	+	0.195252i
$355$		−	641.648i		−	1.80746i
$356$	382.054	−	399.066i	1.07318	−	1.12097i
$357$	112.932			0.316336
$358$	103.507	−	44.2003i	0.289125	−	0.123464i
$359$			116.878i			0.325565i	0.986662	+	0.162783i	$0.0520469\pi$
$359$			116.878i			0.325565i	−0.986662	+	0.162783i	$0.947953\pi$
$360$	538.549	+	202.733i	1.49597	+	0.563148i
$361$	223.702			0.619674
$362$	−52.5644	−	123.094i	−0.145205	−	0.340037i
$363$			17.1568i			0.0472640i
$364$	458.159	+	438.628i	1.25868	+	1.20502i
$365$	82.1655			0.225111
$366$	86.2716	−	36.8404i	0.235715	−	0.100657i
$367$			277.861i			0.757115i	0.925578	+	0.378557i	$0.123580\pi$
$367$			277.861i			0.757115i	−0.925578	+	0.378557i	$0.876420\pi$
$368$	−349.564	+	15.2337i	−0.949903	+	0.0413959i
$369$	193.985			0.525705
$370$	15.2460	+	35.7025i	0.0412053	+	0.0964932i
$371$		−	797.397i		−	2.14932i
$372$	−9.69584	+	10.1276i	−0.0260641	+	0.0272247i
$373$	−247.997			−0.664872			−0.332436	−	0.943126i	$-0.607871\pi$
$373$	−247.997			−0.664872			−0.332436	+	0.943126i	$0.607871\pi$
$374$	−377.909	+	161.378i	−1.01045	+	0.431491i
$375$		−	104.723i		−	0.279261i
$376$	−108.122	+	287.220i	−0.287559	+	0.763883i
$377$	404.098			1.07188
$378$	−92.5345	−	216.694i	−0.244800	−	0.573265i
$379$		−	31.0847i		−	0.0820178i	−0.999159	−	0.0410089i	$-0.986943\pi$
$379$		−	31.0847i		−	0.0820178i	0.999159	−	0.0410089i	$-0.0130572\pi$
$380$	−283.048	−	270.981i	−0.744863	−	0.713109i
$381$	96.4689			0.253199
$382$	−412.495	+	176.147i	−1.07983	+	0.461117i
$383$			133.608i			0.348847i	0.984671	+	0.174423i	$0.0558061\pi$
$383$			133.608i			0.348847i	−0.984671	+	0.174423i	$0.944194\pi$
$384$	−76.5795	−	25.0792i	−0.199426	−	0.0653103i
$385$	1082.16			2.81081
$386$	74.1460	+	173.633i	0.192088	+	0.449826i
$387$			219.820i			0.568011i
$388$	−24.9655	+	26.0772i	−0.0643441	+	0.0672092i
$389$	375.119			0.964316			0.482158	−	0.876084i	$-0.339853\pi$
$389$	375.119			0.964316			0.482158	+	0.876084i	$0.339853\pi$
$390$	144.400	−	61.6627i	0.370256	−	0.158110i
$391$		−	369.019i		−	0.943782i
$392$	−479.261	−	180.415i	−1.22260	−	0.460241i
$393$	−12.7533			−0.0324512
$394$	−222.233	−	520.417i	−0.564042	−	1.32086i
$395$		−	570.781i		−	1.44502i
$396$	302.681	+	289.777i	0.764345	+	0.731761i
$397$	187.930			0.473376			0.236688	−	0.971586i	$-0.423938\pi$
$397$	187.930			0.473376			0.236688	+	0.971586i	$0.423938\pi$
$398$	−396.848	+	169.465i	−0.997105	+	0.425791i
$399$			78.4186i			0.196538i
$400$	−31.2754	−	717.670i	−0.0781884	−	1.79417i
$401$	−63.3984			−0.158101			−0.0790504	−	0.996871i	$-0.525189\pi$
$401$	−63.3984			−0.158101			−0.0790504	+	0.996871i	$0.525189\pi$
$402$	37.5227	+	87.8694i	0.0933400	+	0.218581i
$403$		−	83.0494i		−	0.206078i
$404$	346.708	−	362.146i	0.858188	−	0.896402i
$405$	589.046			1.45443
$406$	−529.724	+	226.207i	−1.30474	+	0.557160i
$407$			28.2693i			0.0694576i
$408$	29.9411	−	79.5367i	0.0733849	−	0.194943i
$409$	−114.716			−0.280478			−0.140239	−	0.990118i	$-0.544787\pi$
$409$	−114.716			−0.280478			−0.140239	+	0.990118i	$0.544787\pi$
$410$	−148.056	−	346.713i	−0.361112	−	0.845641i
$411$		−	123.433i		−	0.300323i
$412$	−479.611	−	459.165i	−1.16410	−	1.11448i
$413$	634.568			1.53648
$414$	−346.067	+	147.780i	−0.835910	+	0.356957i
$415$			1161.49i			2.79878i
$416$	430.390	−	206.385i	1.03459	−	0.496118i
$417$	−114.447			−0.274453
$418$	−112.059	−	262.416i	−0.268083	−	0.627788i
$419$		−	151.293i		−	0.361082i	−0.983568	−	0.180541i	$-0.942215\pi$
$419$		−	151.293i		−	0.361082i	0.983568	−	0.180541i	$-0.0577848\pi$
$420$	−154.773	+	161.665i	−0.368507	+	0.384916i
$421$	−182.819			−0.434250			−0.217125	−	0.976144i	$-0.569668\pi$
$421$	−182.819			−0.434250			−0.217125	+	0.976144i	$0.569668\pi$
$422$	−243.390	+	103.934i	−0.576754	+	0.246290i
$423$			330.055i			0.780272i
$424$	−561.598	−	211.410i	−1.32452	−	0.498608i
$425$	757.611			1.78261
$426$	37.9495	+	88.8690i	0.0890834	+	0.208613i
$427$		−	792.040i		−	1.85490i
$428$	178.584	+	170.971i	0.417253	+	0.399465i
$429$	114.336			0.266517
$430$	392.888	−	167.774i	0.913694	−	0.390173i
$431$		−	378.959i		−	0.879255i	−0.898180	−	0.439627i	$-0.855111\pi$
$431$		−	378.959i		−	0.879255i	0.898180	−	0.439627i	$-0.144889\pi$
$432$	−177.148	+	7.71996i	−0.410066	+	0.0178703i
$433$	−138.516			−0.319897			−0.159949	−	0.987125i	$-0.551133\pi$
$433$	−138.516			−0.319897			−0.159949	+	0.987125i	$0.551133\pi$
$434$	46.4895	+	108.868i	0.107119	+	0.250847i
$435$			142.589i			0.327791i
$436$	114.977	−	120.096i	0.263708	−	0.275451i
$437$	256.242			0.586367
$438$	−11.3800	+	4.85958i	−0.0259818	+	0.0110949i
$439$			661.758i			1.50742i	0.657206	+	0.753711i	$0.271738\pi$
$439$			661.758i			1.50742i	−0.657206	+	0.753711i	$0.728262\pi$
$440$	286.908	−	762.154i	0.652063	−	1.73217i
$441$	−550.736			−1.24884
$442$	197.696	+	462.958i	0.447276	+	1.04742i
$443$			816.155i			1.84234i	0.389166	+	0.921168i	$0.372763\pi$
$443$			816.155i			1.84234i	−0.389166	+	0.921168i	$0.627237\pi$
$444$	−4.22316	−	4.04313i	−0.00951162	−	0.00910615i
$445$	−1154.71			−2.59486
$446$	518.160	−	221.269i	1.16179	−	0.496119i
$447$		−	61.4817i		−	0.137543i
$448$	−448.658	+	511.470i	−1.00147	+	1.14167i
$449$	−549.495			−1.22382			−0.611909	−	0.790928i	$-0.709598\pi$
$449$	−549.495			−1.22382			−0.611909	+	0.790928i	$0.709598\pi$
$450$	−303.398	−	710.489i	−0.674219	−	1.57886i
$451$		−	274.528i		−	0.608709i
$452$	104.650	−	109.309i	0.231526	−	0.241835i
$453$	117.985			0.260453
$454$	399.745	−	170.702i	0.880496	−	0.375996i
$455$		−	1325.70i		−	2.91363i
$456$	55.2293	+	20.7907i	0.121117	+	0.0455937i
$457$	508.986			1.11375			0.556877	−	0.830595i	$-0.311999\pi$
$457$	508.986			1.11375			0.556877	+	0.830595i	$0.311999\pi$
$458$	−84.0580	−	196.844i	−0.183533	−	0.429791i
$459$		−	187.007i		−	0.407423i
$460$	528.259	+	505.740i	1.14839	+	1.09943i
$461$	271.921			0.589849			0.294925	−	0.955521i	$-0.404705\pi$
$461$	271.921			0.589849			0.294925	+	0.955521i	$0.404705\pi$
$462$	−149.881	+	64.0032i	−0.324417	+	0.138535i
$463$		−	444.837i		−	0.960771i	−0.877058	−	0.480385i	$-0.840497\pi$
$463$		−	444.837i		−	0.960771i	0.877058	−	0.480385i	$-0.159503\pi$
$464$	18.8720	+	433.052i	0.0406724	+	0.933301i
$465$	29.3046			0.0630206
$466$	232.938	+	545.487i	0.499867	+	1.17057i
$467$			573.025i			1.22703i	0.789681	+	0.613517i	$0.210246\pi$
$467$			573.025i			1.22703i	−0.789681	+	0.613517i	$0.789754\pi$
$468$	354.992	−	370.799i	0.758529	−	0.792305i
$469$	806.710			1.72006
$470$	589.913	−	251.909i	1.25513	−	0.535977i
$471$			128.942i			0.273762i
$472$	168.240	−	446.919i	0.356440	−	0.946861i
$473$	311.089			0.657694
$474$	33.7582	+	79.0539i	0.0712198	+	0.166780i
$475$			526.076i			1.10753i
$476$	−518.311	−	496.215i	−1.08889	−	1.04247i
$477$	−645.353			−1.35294
$478$	−197.927	+	84.5205i	−0.414074	+	0.176821i
$479$			922.787i			1.92649i	0.268630	+	0.963243i	$0.413429\pi$
$479$			922.787i			1.92649i	−0.268630	+	0.963243i	$0.586571\pi$
$480$	72.8245	+	151.866i	0.151718	+	0.316388i
$481$	34.6313			0.0719985
$482$	−45.9858	−	107.688i	−0.0954063	−	0.223419i
$483$		−	146.355i		−	0.303012i
$484$	75.3859	−	78.7427i	0.155756	−	0.162692i
$485$	75.4554			0.155578
$486$	−265.038	+	113.179i	−0.545345	+	0.232878i
$487$			477.401i			0.980290i	0.871641	+	0.490145i	$0.163056\pi$
$487$			477.401i			0.980290i	−0.871641	+	0.490145i	$0.836944\pi$
$488$	−557.825	−	209.989i	−1.14308	−	0.430306i
$489$	−23.0726			−0.0471831
$490$	420.341	+	984.340i	0.857838	+	2.00886i
$491$			53.5763i			0.109117i	0.998511	+	0.0545583i	$0.0173751\pi$
$491$			53.5763i			0.109117i	−0.998511	+	0.0545583i	$0.982625\pi$
$492$	41.0118	+	39.2635i	0.0833574	+	0.0798039i
$493$	−457.153			−0.927287
$494$	−321.472	+	137.278i	−0.650754	+	0.277890i
$495$		−	875.819i		−	1.76933i
$496$	88.9998	−	3.87852i	0.179435	−	0.00781961i
$497$	815.887			1.64162
$498$	−68.6952	−	160.868i	−0.137942	−	0.323029i
$499$		−	739.857i		−	1.48268i	−0.671129	−	0.741340i	$-0.734191\pi$
$499$		−	739.857i		−	1.48268i	0.671129	−	0.741340i	$-0.265809\pi$
$500$	−460.144	+	480.634i	−0.920288	+	0.961267i
$501$	−123.258			−0.246025
$502$	122.575	−	52.3430i	0.244174	−	0.104269i
$503$			399.559i			0.794351i	0.917743	+	0.397176i	$0.130010\pi$
$503$			399.559i			0.794351i	−0.917743	+	0.397176i	$0.869990\pi$
$504$	−257.785	+	684.791i	−0.511478	+	1.35871i
$505$	−1047.89			−2.07502
$506$	209.138	+	489.753i	0.413316	+	0.967891i
$507$		−	33.6744i		−	0.0664189i
$508$	−442.752	−	423.878i	−0.871559	−	0.834405i
$509$	−311.351			−0.611692			−0.305846	−	0.952081i	$-0.598939\pi$
$509$	−311.351			−0.611692			−0.305846	+	0.952081i	$0.598939\pi$
$510$	−163.358	+	69.7585i	−0.320310	+	0.136781i
$511$			104.477i			0.204457i
$512$	241.272	+	451.588i	0.471235	+	0.882008i
$513$	129.856			0.253130
$514$	−301.909	−	707.001i	−0.587372	−	1.37549i
$515$			1387.77i			2.69471i
$516$	−44.4926	+	46.4738i	−0.0862261	+	0.0900656i
$517$	467.094			0.903469
$518$	−45.3974	+	19.3860i	−0.0876398	+	0.0374246i
$519$		−	96.4509i		−	0.185840i
$520$	−933.677	−	351.476i	−1.79553	−	0.675916i
$521$	469.666			0.901470			0.450735	−	0.892658i	$-0.351162\pi$
$521$	469.666			0.901470			0.450735	+	0.892658i	$0.351162\pi$
$522$	183.075	+	428.719i	0.350718	+	0.821300i
$523$			665.018i			1.27154i	0.771877	+	0.635772i	$0.219318\pi$
$523$			665.018i			1.27154i	−0.771877	+	0.635772i	$0.780682\pi$
$524$	58.5325	+	56.0372i	0.111703	+	0.106941i
$525$	300.472			0.572328
$526$	−161.681	+	69.0422i	−0.307378	+	0.131259i
$527$			93.9529i			0.178279i
$528$	5.33965	+	122.528i	0.0101130	+	0.232061i
$529$	50.7683			0.0959704
$530$	492.555	+	1153.45i	0.929349	+	2.17632i
$531$		−	513.571i		−	0.967176i
$532$	344.566	−	359.909i	0.647680	−	0.676520i
$533$	−336.310			−0.630976
$534$	159.929	−	68.2942i	0.299493	−	0.127892i
$535$		−	516.741i		−	0.965871i
$536$	213.879	−	568.156i	0.399027	−	1.05999i
$537$	35.4273			0.0659727
$538$	−290.980	−	681.408i	−0.540855	−	1.26656i
$539$			779.401i			1.44601i
$540$	267.705	+	256.293i	0.495751	+	0.474617i
$541$	213.404			0.394462			0.197231	−	0.980357i	$-0.436805\pi$
$541$	213.404			0.394462			0.197231	+	0.980357i	$0.436805\pi$
$542$	162.486	−	69.3859i	0.299789	−	0.128018i
$543$		−	42.1313i		−	0.0775898i
$544$	−486.896	+	233.481i	−0.895029	+	0.429194i
$545$	−347.504			−0.637623
$546$	78.4071	+	183.611i	0.143603	+	0.336284i
$547$		−	687.760i		−	1.25733i	−0.777676	−	0.628666i	$-0.783601\pi$
$547$		−	687.760i		−	1.25733i	0.777676	−	0.628666i	$-0.216399\pi$
$548$	−542.355	+	566.505i	−0.989700	+	1.03377i
$549$	−641.017			−1.16761
$550$	−1005.48	+	429.369i	−1.82815	+	0.780671i
$551$		−	317.441i		−	0.576119i
$552$	−103.076	−	38.8022i	−0.186732	−	0.0702939i
$553$	725.776			1.31243
$554$	−296.839	−	695.129i	−0.535811	−	1.25475i
$555$			12.2199i			0.0220178i
$556$	525.263	+	502.871i	0.944718	+	0.904445i
$557$	194.315			0.348859			0.174430	−	0.984670i	$-0.444192\pi$
$557$	194.315			0.348859			0.174430	+	0.984670i	$0.444192\pi$
$558$	88.1092	−	37.6251i	0.157902	−	0.0674285i
$559$		−	381.100i		−	0.681753i
$560$	1420.69	−	61.9122i	2.53694	−	0.110558i
$561$	−129.347			−0.230565
$562$	73.2056	+	171.430i	0.130259	+	0.305036i
$563$		−	577.894i		−	1.02646i	−0.858252	−	0.513228i	$-0.828450\pi$
$563$		−	577.894i		−	1.02646i	0.858252	−	0.513228i	$-0.171550\pi$
$564$	−66.8047	+	69.7794i	−0.118448	+	0.123722i
$565$	−316.292			−0.559808
$566$	−676.779	+	289.004i	−1.19572	+	0.510607i
$567$			749.000i			1.32099i
$568$	216.312	−	574.619i	0.380830	−	1.01165i
$569$	233.761			0.410828			0.205414	−	0.978675i	$-0.434146\pi$
$569$	233.761			0.410828			0.205414	+	0.978675i	$0.434146\pi$
$570$	−48.4394	−	113.434i	−0.0849815	−	0.199007i
$571$			800.899i			1.40263i	0.712854	+	0.701313i	$0.247402\pi$
$571$			800.899i			1.40263i	−0.712854	+	0.701313i	$0.752598\pi$
$572$	−524.754	−	502.384i	−0.917402	−	0.878294i
$573$	−141.185			−0.246396
$574$	440.862	−	188.260i	0.768052	−	0.327980i
$575$		−	981.829i		−	1.70753i
$576$	413.945	+	363.110i	0.718654	+	0.630399i
$577$	310.346			0.537861			0.268931	−	0.963160i	$-0.413330\pi$
$577$	310.346			0.537861			0.268931	+	0.963160i	$0.413330\pi$
$578$	3.34057	+	7.82285i	0.00577954	+	0.0135343i
$579$			59.4293i			0.102641i
$580$	626.527	−	654.425i	1.08022	−	1.12832i
$581$	−1476.90			−2.54199
$582$	−10.4507	+	4.46272i	−0.0179565	+	0.00766791i
$583$			913.302i			1.56656i
$584$	73.5822	+	27.6995i	0.125997	+	0.0474307i
$585$	−1072.92			−1.83406
$586$	−290.006	−	679.126i	−0.494890	−	1.15892i
$587$		−	435.322i		−	0.741604i	−0.928712	−	0.370802i	$-0.879083\pi$
$587$		−	435.322i		−	0.741604i	0.928712	−	0.370802i	$-0.120917\pi$
$588$	−116.435	−	111.472i	−0.198019	−	0.189578i
$589$	−65.2398			−0.110764
$590$	−917.913	+	391.975i	−1.55579	+	0.664364i
$591$		−	178.123i		−	0.301393i
$592$	1.61733	+	37.1126i	0.00273198	+	0.0626901i
$593$	208.910			0.352293			0.176147	−	0.984364i	$-0.443637\pi$
$593$	208.910			0.352293			0.176147	+	0.984364i	$0.443637\pi$
$594$	105.985	+	248.192i	0.178425	+	0.417831i
$595$			1499.75i			2.52060i
$596$	−270.146	+	282.175i	−0.453265	+	0.473448i
$597$	−135.829			−0.227520
$598$	599.972	−	256.205i	1.00330	−	0.428436i
$599$		−	72.9649i		−	0.121811i	−0.998144	−	0.0609056i	$-0.980601\pi$
$599$		−	72.9649i		−	0.121811i	0.998144	−	0.0609056i	$-0.0193989\pi$
$600$	79.6625	−	211.619i	0.132771	−	0.352698i
$601$	169.555			0.282121			0.141061	−	0.990001i	$-0.454949\pi$
$601$	169.555			0.282121			0.141061	+	0.990001i	$0.454949\pi$
$602$	213.333	+	499.576i	0.354374	+	0.829861i
$603$		−	652.889i		−	1.08273i
$604$	−541.502	−	518.418i	−0.896527	−	0.858308i
$605$	−227.845			−0.376604
$606$	145.133	−	61.9760i	0.239494	−	0.102271i
$607$		−	727.323i		−	1.19823i	−0.800665	−	0.599113i	$-0.795520\pi$
$607$		−	727.323i		−	1.19823i	0.800665	−	0.599113i	$-0.204480\pi$
$608$	−162.127	−	338.094i	−0.266656	−	0.556076i
$609$	−181.309			−0.297716
$610$	489.246	+	1145.70i	0.802042	+	1.87820i
$611$		−	572.213i		−	0.936519i
$612$	−401.599	+	419.481i	−0.656207	+	0.685427i
$613$	−416.618			−0.679638			−0.339819	−	0.940491i	$-0.610366\pi$
$613$	−416.618			−0.679638			−0.339819	+	0.940491i	$0.610366\pi$
$614$	−262.934	+	112.280i	−0.428231	+	0.182867i
$615$		−	118.670i		−	0.192959i
$616$	969.115	+	364.817i	1.57324	+	0.592235i
$617$	104.272			0.168999			0.0844995	−	0.996424i	$-0.473071\pi$
$617$	104.272			0.168999			0.0844995	+	0.996424i	$0.473071\pi$
$618$	−82.0783	−	192.208i	−0.132813	−	0.311017i
$619$		−	248.510i		−	0.401469i	−0.979646	−	0.200735i	$-0.935667\pi$
$619$		−	248.510i		−	0.401469i	0.979646	−	0.200735i	$-0.0643329\pi$
$620$	−134.496	−	128.762i	−0.216929	−	0.207681i
$621$	−242.353			−0.390262
$622$	−165.057	+	70.4840i	−0.265365	+	0.113318i
$623$		−	1468.27i		−	2.35678i
$624$	150.103	−	6.54134i	0.240550	−	0.0104829i
$625$	268.311			0.429297
$626$	−179.951	−	421.403i	−0.287462	−	0.673168i
$627$		−	89.8171i		−	0.143249i
$628$	566.562	−	591.790i	0.902168	−	0.942340i
$629$	−39.1780			−0.0622862
$630$	1406.47	−	600.603i	2.23250	−	0.953338i
$631$		−	981.596i		−	1.55562i	−0.628500	−	0.777810i	$-0.716331\pi$
$631$		−	981.596i		−	1.55562i	0.628500	−	0.777810i	$-0.283669\pi$
$632$	192.421	−	511.155i	0.304464	−	0.808790i
$633$	−83.3052			−0.131604
$634$	199.600	+	467.417i	0.314826	+	0.737250i
$635$			1281.12i			2.01752i
$636$	−136.439	−	130.622i	−0.214526	−	0.205381i
$637$	954.806			1.49891
$638$	606.722	−	259.087i	0.950975	−	0.406093i
$639$		−	660.316i		−	1.03336i
$640$	333.055	−	1016.99i	0.520399	−	1.58904i
$641$	−1035.26			−1.61508			−0.807539	−	0.589814i	$-0.799201\pi$
$641$	−1035.26			−1.61508			−0.807539	+	0.589814i	$0.799201\pi$
$642$	30.5620	+	71.5692i	0.0476044	+	0.111478i
$643$			795.614i			1.23735i	0.785648	+	0.618673i	$0.212330\pi$
$643$			795.614i			1.23735i	−0.785648	+	0.618673i	$0.787670\pi$
$644$	−643.072	+	671.707i	−0.998560	+	1.04302i
$645$	134.474			0.208487
$646$	363.678	−	155.301i	0.562970	−	0.240404i
$647$			462.691i			0.715133i	0.933888	+	0.357567i	$0.116393\pi$
$647$			462.691i			0.715133i	−0.933888	+	0.357567i	$0.883607\pi$
$648$	527.512	+	198.578i	0.814061	+	0.306448i
$649$	−726.805			−1.11988
$650$	525.999	+	1231.77i	0.809229	+	1.89503i
$651$			37.2622i			0.0572384i
$652$	105.893	+	101.379i	0.162413	+	0.155490i
$653$	−1099.32			−1.68349			−0.841746	−	0.539874i	$-0.818472\pi$
$653$	−1099.32			−1.68349			−0.841746	+	0.539874i	$0.818472\pi$
$654$	48.1297	−	20.5527i	0.0735929	−	0.0314262i
$655$		−	169.366i		−	0.258574i
$656$	−15.7062	−	360.406i	−0.0239423	−	0.549400i
$657$	84.5560			0.128700
$658$	320.315	+	750.103i	0.486800	+	1.13997i
$659$		−	98.3808i		−	0.149288i	−0.997210	−	0.0746440i	$-0.976218\pi$
$659$		−	98.3808i		−	0.149288i	0.997210	−	0.0746440i	$-0.0237821\pi$
$660$	177.270	−	185.163i	0.268591	−	0.280551i
$661$	988.635			1.49567			0.747833	−	0.663887i	$-0.231094\pi$
$661$	988.635			1.49567			0.747833	+	0.663887i	$0.231094\pi$
$662$	784.862	−	335.158i	1.18559	−	0.506281i
$663$			158.457i			0.239000i
$664$	−391.561	+	1040.16i	−0.589701	+	1.56651i
$665$	−1041.41			−1.56603
$666$	15.6895	+	36.7412i	0.0235578	+	0.0551670i
$667$			592.449i			0.888229i
$668$	565.705	+	541.589i	0.846864	+	0.810762i
$669$	177.351			0.265099
$670$	−1166.92	+	498.307i	−1.74167	+	0.743742i
$671$			907.167i			1.35196i
$672$	−193.105	+	92.5998i	−0.287359	+	0.137797i
$673$	−511.058			−0.759372			−0.379686	−	0.925115i	$-0.623968\pi$
$673$	−511.058			−0.759372			−0.379686	+	0.925115i	$0.623968\pi$
$674$	−18.1547	−	42.5141i	−0.0269357	−	0.0630773i
$675$		−	497.560i		−	0.737126i
$676$	−147.963	+	154.551i	−0.218880	+	0.228626i
$677$	−67.8228			−0.100181			−0.0500907	−	0.998745i	$-0.515951\pi$
$677$	−67.8228			−0.100181			−0.0500907	+	0.998745i	$0.515951\pi$
$678$	43.8067	−	18.7067i	0.0646117	−	0.0275910i
$679$			95.9452i			0.141304i
$680$	1056.26	+	397.622i	1.55332	+	0.584738i
$681$	136.821			0.200912
$682$	−53.2470	−	124.692i	−0.0780747	−	0.182833i
$683$		−	261.546i		−	0.382936i	−0.981499	−	0.191468i	$-0.938675\pi$
$683$		−	261.546i		−	0.382936i	0.981499	−	0.191468i	$-0.0613249\pi$
$684$	−291.283	−	278.865i	−0.425852	−	0.407698i
$685$	1639.21			2.39300
$686$	−293.528	+	125.345i	−0.427883	+	0.182718i
$687$		−	67.3740i		−	0.0980698i
$688$	408.405	−	17.7979i	0.593613	−	0.0258691i
$689$	1118.84			1.62386
$690$	90.4038	+	211.705i	0.131020	+	0.306818i
$691$		−	160.712i		−	0.232579i	−0.993215	−	0.116290i	$-0.962900\pi$
$691$		−	160.712i		−	0.232579i	0.993215	−	0.116290i	$-0.0371001\pi$
$692$	−423.799	+	442.670i	−0.612426	+	0.639696i
$693$	1113.65			1.60699
$694$	1164.43	−	497.245i	1.67786	−	0.716491i
$695$		−	1519.87i		−	2.18687i
$696$	−48.0695	+	127.694i	−0.0690653	+	0.183468i
$697$	380.464			0.545860
$698$	45.1658	+	105.768i	0.0647075	+	0.151530i
$699$			186.704i			0.267102i
$700$	−1379.04	−	1320.25i	−1.97006	−	1.88608i
$701$	−376.378			−0.536916			−0.268458	−	0.963291i	$-0.586514\pi$
$701$	−376.378			−0.536916			−0.268458	+	0.963291i	$0.586514\pi$
$702$	304.047	−	129.837i	0.433116	−	0.184952i
$703$		−	27.2047i		−	0.0386981i
$704$	513.873	−	585.814i	0.729933	−	0.832123i
$705$	201.910			0.286397
$706$	303.056	+	709.686i	0.429257	+	1.00522i
$707$		−	1332.44i		−	1.88464i
$708$	103.949	−	108.578i	0.146821	−	0.153358i
$709$	1329.48			1.87515			0.937575	−	0.347783i	$-0.113065\pi$
$709$	1329.48			1.87515			0.937575	+	0.347783i	$0.113065\pi$
$710$	−1180.19	+	503.976i	−1.66225	+	0.709825i
$711$		−	587.388i		−	0.826143i
$712$	−1034.09	−	389.276i	−1.45237	−	0.546735i
$713$	121.759			0.170770
$714$	−88.7012	−	207.718i	−0.124231	−	0.290921i
$715$			1518.40i			2.12363i
$716$	−162.597	−	155.665i	−0.227090	−	0.217409i
$717$	−67.7447			−0.0944836
$718$	214.975	−	91.8005i	0.299409	−	0.127856i
$719$		−	33.7688i		−	0.0469664i	−0.999724	−	0.0234832i	$-0.992524\pi$
$719$		−	33.7688i		−	0.0469664i	0.999724	−	0.0234832i	$-0.00747561\pi$
$720$	−50.1070	−	1149.80i	−0.0695931	−	1.59694i
$721$	−1764.62			−2.44746
$722$	−175.705	−	411.459i	−0.243358	−	0.569888i
$723$		−	36.8585i		−	0.0509799i
$724$	−185.122	+	193.365i	−0.255693	+	0.267079i
$725$	−1216.32			−1.67768
$726$	31.5568	−	13.4756i	0.0434667	−	0.0185615i
$727$		−	1225.96i		−	1.68633i	−0.537656	−	0.843164i	$-0.680690\pi$
$727$		−	1225.96i		−	1.68633i	0.537656	−	0.843164i	$-0.319310\pi$
$728$	446.919	−	1187.21i	0.613900	−	1.63079i
$729$	543.392			0.745394
$730$	−64.5360	−	151.128i	−0.0884055	−	0.207025i
$731$			431.135i			0.589788i
$732$	−135.522	−	129.745i	−0.185140	−	0.177247i
$733$	−490.355			−0.668970			−0.334485	−	0.942401i	$-0.608562\pi$
$733$	−490.355			−0.668970			−0.334485	+	0.942401i	$0.608562\pi$
$734$	511.075	−	218.243i	0.696287	−	0.297334i
$735$			336.910i			0.458382i
$736$	302.581	+	630.994i	0.411116	+	0.857329i
$737$	−923.968			−1.25369
$738$	−152.364	−	356.800i	−0.206455	−	0.483469i
$739$			508.886i			0.688614i	0.938857	+	0.344307i	$0.111886\pi$
$739$			508.886i			0.688614i	−0.938857	+	0.344307i	$0.888114\pi$
$740$	53.6934	−	56.0843i	0.0725586	−	0.0757895i
$741$	−110.030			−0.148489
$742$	−1466.67	+	626.307i	−1.97664	+	0.844080i
$743$		−	632.353i		−	0.851080i	−0.904940	−	0.425540i	$-0.860084\pi$
$743$		−	632.353i		−	0.851080i	0.904940	−	0.425540i	$-0.139916\pi$
$744$	26.2433	+	9.87912i	0.0352733	+	0.0132784i
$745$	816.486			1.09595
$746$	194.787	+	456.146i	0.261108	+	0.611455i
$747$			1195.29i			1.60012i
$748$	593.649	+	568.342i	0.793649	+	0.759816i
$749$	657.061			0.877251
$750$	−192.618	+	82.2533i	−0.256824	+	0.109671i
$751$			552.460i			0.735633i	0.929898	+	0.367816i	$0.119895\pi$
$751$			552.460i			0.735633i	−0.929898	+	0.367816i	$0.880105\pi$
$752$	613.212	−	26.7232i	0.815441	−	0.0355361i
$753$	41.9539			0.0557156
$754$	−317.395	−	743.265i	−0.420948	−	0.985763i
$755$			1566.86i			2.07531i
$756$	−325.889	+	340.400i	−0.431070	+	0.450265i
$757$	−986.416			−1.30306			−0.651530	−	0.758623i	$-0.725872\pi$
$757$	−986.416			−1.30306			−0.651530	+	0.758623i	$0.725872\pi$
$758$	−57.1747	+	24.4152i	−0.0754283	+	0.0322100i
$759$			167.628i			0.220854i
$760$	−276.104	+	733.454i	−0.363295	+	0.965071i
$761$	952.905			1.25217			0.626087	−	0.779753i	$-0.284655\pi$
$761$	952.905			1.25217			0.626087	+	0.779753i	$0.284655\pi$
$762$	−75.7704	−	177.437i	−0.0994363	−	0.232857i
$763$		−	441.868i		−	0.579120i
$764$	647.979	+	620.356i	0.848140	+	0.811984i
$765$	1213.79			1.58665
$766$	245.748	−	104.941i	0.320820	−	0.136999i
$767$			890.372i			1.16085i
$768$	14.0200	+	160.552i	0.0182553	+	0.209052i
$769$	1510.32			1.96400			0.982000	−	0.188879i	$-0.0604854\pi$
$769$	1510.32			1.96400			0.982000	+	0.188879i	$0.0604854\pi$
$770$	−849.973	−	1990.44i	−1.10386	−	2.58499i
$771$		−	241.985i		−	0.313859i
$772$	261.128	−	272.756i	0.338249	−	0.353311i
$773$	212.813			0.275307			0.137654	−	0.990480i	$-0.456044\pi$
$773$	212.813			0.275307			0.137654	+	0.990480i	$0.456044\pi$
$774$	404.319	−	172.655i	0.522376	−	0.223069i
$775$			249.976i			0.322549i
$776$	67.5730	+	25.4374i	0.0870787	+	0.0327802i
$777$	−15.5382			−0.0199977
$778$	−294.633	−	689.963i	−0.378706	−	0.886841i
$779$			264.190i			0.339140i
$780$	−226.835	−	217.165i	−0.290814	−	0.278416i
$781$	−934.479			−1.19652
$782$	−678.743	+	289.842i	−0.867957	+	0.370642i
$783$			300.235i			0.383442i
$784$	44.5908	+	1023.22i	0.0568760	+	1.30512i
$785$	−1712.37			−2.18136
$786$	10.0170	+	23.4574i	0.0127442	+	0.0298440i
$787$			290.223i			0.368771i	0.982854	+	0.184386i	$0.0590296\pi$
$787$			290.223i			0.368771i	−0.982854	+	0.184386i	$0.940970\pi$
$788$	−782.661	+	817.512i	−0.993225	+	1.03745i
$789$	−55.3386			−0.0701376
$790$	−1049.85	+	448.314i	−1.32892	+	0.567486i
$791$		−	402.180i		−	0.508445i
$792$	295.255	−	784.328i	0.372797	−	0.990313i
$793$	1111.32			1.40142
$794$	−147.608	−	345.663i	−0.185904	−	0.435344i
$795$			394.792i			0.496593i
$796$	623.399	+	596.824i	0.783165	+	0.749779i
$797$	127.972			0.160567			0.0802836	−	0.996772i	$-0.474417\pi$
$797$	127.972			0.160567			0.0802836	+	0.996772i	$0.474417\pi$
$798$	144.237	−	61.5931i	0.180748	−	0.0771843i
$799$			647.339i			0.810187i
$800$	−1295.46	+	621.211i	−1.61932	+	0.776514i
$801$	−1188.31			−1.48353
$802$	49.7956	+	116.610i	0.0620893	+	0.145399i
$803$		−	119.664i		−	0.149021i
$804$	132.148	−	138.032i	0.164363	−	0.171682i
$805$	1943.61			2.41443
$806$	−152.754	+	65.2302i	−0.189521	+	0.0809308i
$807$		−	233.226i		−	0.289004i
$808$	−938.420	−	353.262i	−1.16141	−	0.437205i
$809$	−351.026			−0.433901			−0.216950	−	0.976183i	$-0.569611\pi$
$809$	−351.026			−0.433901			−0.216950	+	0.976183i	$0.569611\pi$
$810$	−462.659	−	1083.44i	−0.571185	−	1.33758i
$811$		−	140.417i		−	0.173141i	−0.996246	−	0.0865703i	$-0.972409\pi$
$811$		−	140.417i		−	0.173141i	0.996246	−	0.0865703i	$-0.0275907\pi$
$812$	832.133	+	796.659i	1.02479	+	0.981107i
$813$	55.6141			0.0684060
$814$	51.9961	−	22.2038i	0.0638773	−	0.0272774i
$815$		−	306.407i		−	0.375960i
$816$	−169.810	+	7.40016i	−0.208100	+	0.00906882i
$817$	−299.375			−0.366432
$818$	90.1022	+	210.998i	0.110149	+	0.257944i
$819$		−	1364.27i		−	1.66578i
$820$	−521.426	+	544.644i	−0.635885	+	0.664200i
$821$	−451.062			−0.549405			−0.274703	−	0.961529i	$-0.588579\pi$
$821$	−451.062			−0.549405			−0.274703	+	0.961529i	$0.588579\pi$
$822$	−227.032	+	96.9490i	−0.276195	+	0.117943i
$823$		−	1497.92i		−	1.82007i	−0.414526	−	0.910037i	$-0.636053\pi$
$823$		−	1497.92i		−	1.82007i	0.414526	−	0.910037i	$-0.363947\pi$
$824$	−467.845	+	1242.80i	−0.567772	+	1.50825i
$825$	−344.147			−0.417148
$826$	−498.414	−	1167.17i	−0.603407	−	1.41304i
$827$			537.933i			0.650464i	0.945634	+	0.325232i	$0.105442\pi$
$827$			537.933i			0.650464i	−0.945634	+	0.325232i	$0.894558\pi$
$828$	543.629	+	520.454i	0.656556	+	0.628567i
$829$	869.434			1.04877			0.524387	−	0.851480i	$-0.324294\pi$
$829$	869.434			1.04877			0.524387	+	0.851480i	$0.324294\pi$
$830$	2136.36	−	912.283i	2.57392	−	1.09914i
$831$		−	237.922i		−	0.286308i
$832$	−717.652	−	629.520i	−0.862563	−	0.756634i
$833$	−1080.16			−1.29671
$834$	89.8910	+	210.504i	0.107783	+	0.252403i
$835$		−	1636.89i		−	1.96035i
$836$	−394.650	+	412.223i	−0.472069	+	0.493090i
$837$	61.7035			0.0737199
$838$	−278.276	+	118.832i	−0.332072	+	0.141804i
$839$		−	1197.32i		−	1.42708i	−0.700614	−	0.713541i	$-0.747090\pi$
$839$		−	1197.32i		−	1.42708i	0.700614	−	0.713541i	$-0.252910\pi$
$840$	418.918	+	157.699i	0.498712	+	0.187737i
$841$	−107.055			−0.127295
$842$	143.593	+	336.262i	0.170538	+	0.399361i
$843$			58.6756i			0.0696033i
$844$	382.336	+	366.037i	0.453005	+	0.433694i
$845$	447.201			0.529232
$846$	607.076	−	259.238i	0.717584	−	0.306428i
$847$		−	289.716i		−	0.342050i
$848$	52.2515	+	1199.00i	0.0616173	+	1.41392i
$849$	−231.642			−0.272840
$850$	−595.057	−	1393.49i	−0.700067	−	1.63940i
$851$			50.7729i			0.0596626i
$852$	133.651	−	139.602i	0.156868	−	0.163853i
$853$	−305.889			−0.358604			−0.179302	−	0.983794i	$-0.557384\pi$
$853$	−305.889			−0.358604			−0.179302	+	0.983794i	$0.557384\pi$
$854$	−1456.81	+	622.100i	−1.70587	+	0.728454i
$855$			842.839i			0.985777i
$856$	174.203	−	462.760i	0.203508	−	0.540608i
$857$	140.140			0.163523			0.0817617	−	0.996652i	$-0.473945\pi$
$857$	140.140			0.163523			0.0817617	+	0.996652i	$0.473945\pi$
$858$	−89.8039	−	210.300i	−0.104667	−	0.245105i
$859$			43.2989i			0.0504062i	0.999682	+	0.0252031i	$0.00802324\pi$
$859$			43.2989i			0.0504062i	−0.999682	+	0.0252031i	$0.991977\pi$
$860$	−617.180	−	590.869i	−0.717651	−	0.687058i
$861$	150.894			0.175254
$862$	−697.025	+	297.649i	−0.808614	+	0.345301i
$863$			843.674i			0.977606i	0.872394	+	0.488803i	$0.162566\pi$
$863$			843.674i			0.977606i	−0.872394	+	0.488803i	$0.837434\pi$
$864$	153.339	+	319.768i	0.177475	+	0.370102i
$865$	1280.88			1.48079
$866$	108.796	+	254.774i	0.125630	+	0.294196i
$867$			2.67753i			0.00308827i
$868$	163.727	−	171.018i	0.188626	−	0.197025i
$869$	−831.270			−0.956583
$870$	262.267	−	111.995i	0.301456	−	0.128730i
$871$			1131.91i			1.29955i
$872$	−311.203	−	117.150i	−0.356884	−	0.134347i
$873$	77.6507			0.0889470
$874$	−201.263	−	471.311i	−0.230278	−	0.539257i
$875$			1768.39i			2.02101i
$876$	17.8766	+	17.1145i	0.0204071	+	0.0195371i
$877$	948.254			1.08125			0.540624	−	0.841264i	$-0.318188\pi$
$877$	948.254			1.08125			0.540624	+	0.841264i	$0.318188\pi$
$878$	1217.18	−	519.771i	1.38631	−	0.591994i
$879$		−	232.445i		−	0.264442i
$880$	−1627.19	+	70.9114i	−1.84908	+	0.0805812i
$881$	1198.60			1.36050			0.680248	−	0.732982i	$-0.261872\pi$
$881$	1198.60			1.36050			0.680248	+	0.732982i	$0.261872\pi$
$882$	432.570	+	1012.98i	0.490442	+	1.14850i
$883$			264.564i			0.299619i	0.988715	+	0.149809i	$0.0478660\pi$
$883$			264.564i			0.299619i	−0.988715	+	0.149809i	$0.952134\pi$
$884$	696.248	−	727.250i	0.787611	−	0.822681i
$885$	−314.175			−0.355000
$886$	1501.17	−	641.040i	1.69432	−	0.723521i
$887$			1273.77i			1.43605i	0.696020	+	0.718023i	$0.254953\pi$
$887$			1273.77i			1.43605i	−0.696020	+	0.718023i	$0.745047\pi$
$888$	−4.11956	+	10.9434i	−0.00463914	+	0.0123236i
$889$	−1629.01			−1.83241
$890$	906.958	+	2123.88i	1.01905	+	2.38639i
$891$		−	857.870i		−	0.962817i
$892$	−813.967	−	779.268i	−0.912519	−	0.873618i
$893$	−449.504			−0.503364
$894$	−113.084	+	48.2901i	−0.126492	+	0.0540158i
$895$			470.480i			0.525676i
$896$	1293.15	+	423.496i	1.44325	+	0.472652i
$897$	205.353			0.228933
$898$	431.595	+	1010.69i	0.480618	+	1.12549i
$899$		−	150.839i		−	0.167785i
$900$	−1068.51	+	1116.09i	−1.18724	+	1.24010i
$901$	−1265.73			−1.40481
$902$	−504.943	+	215.625i	−0.559804	+	0.239052i
$903$			170.990i			0.189358i
$904$	−283.251	−	106.628i	−0.313330	−	0.117951i
$905$	559.510			0.618243
$906$	−92.6701	−	217.012i	−0.102285	−	0.239527i
$907$		−	179.843i		−	0.198283i	−0.995073	−	0.0991415i	$-0.968390\pi$
$907$		−	179.843i		−	0.198283i	0.995073	−	0.0991415i	$-0.0316096\pi$
$908$	−627.951	−	601.181i	−0.691576	−	0.662094i
$909$	−1078.37			−1.18633
$910$	−2438.39	+	1041.26i	−2.67955	+	1.14424i
$911$			1371.11i			1.50506i	0.658560	+	0.752528i	$0.271166\pi$
$911$			1371.11i			1.50506i	−0.658560	+	0.752528i	$0.728834\pi$
$912$	−5.13858	−	117.914i	−0.00563441	−	0.129292i
$913$	1691.57			1.85276
$914$	−399.778	−	936.186i	−0.437393	−	1.02427i
$915$			392.139i			0.428568i
$916$	−296.036	+	309.218i	−0.323184	+	0.337575i
$917$	215.357			0.234850
$918$	−343.966	+	146.883i	−0.374690	+	0.160003i
$919$			1462.99i			1.59194i	0.605336	+	0.795970i	$0.293039\pi$
$919$			1462.99i			1.59194i	−0.605336	+	0.795970i	$0.706961\pi$
$920$	515.300	−	1368.86i	0.560108	−	1.48790i
$921$	−89.9945			−0.0977139
$922$	−213.577	−	500.148i	−0.231645	−	0.542460i
$923$			1144.78i			1.24029i
$924$	235.444	+	225.407i	0.254810	+	0.243947i
$925$	−104.239			−0.112691
$926$	−818.196	+	349.392i	−0.883581	+	0.377313i
$927$			1428.15i			1.54061i
$928$	781.696	−	374.847i	0.842345	−	0.403930i
$929$	−250.154			−0.269272			−0.134636	−	0.990895i	$-0.542987\pi$
$929$	−250.154			−0.269272			−0.134636	+	0.990895i	$0.542987\pi$
$930$	−23.0170	−	53.9004i	−0.0247494	−	0.0579574i
$931$		−	750.052i		−	0.805641i
$932$	820.365	−	856.894i	0.880219	−	0.919414i
$933$	−56.4942			−0.0605511
$934$	1053.97	−	450.076i	1.12845	−	0.481881i
$935$		−	1717.75i		−	1.83717i
$936$	−960.841	−	361.702i	−1.02654	−	0.386434i
$937$	248.352			0.265051			0.132525	−	0.991180i	$-0.457691\pi$
$937$	248.352			0.265051			0.132525	+	0.991180i	$0.457691\pi$
$938$	−633.621	−	1483.79i	−0.675503	−	1.58187i
$939$		−	144.234i		−	0.153604i
$940$	−926.682	−	887.177i	−0.985831	−	0.943805i
$941$	577.599			0.613814			0.306907	−	0.951740i	$-0.400706\pi$
$941$	577.599			0.613814			0.306907	+	0.951740i	$0.400706\pi$
$942$	237.165	−	101.276i	0.251768	−	0.107512i
$943$		−	493.064i		−	0.522868i
$944$	−954.167	+	41.5817i	−1.01077	+	0.0440484i
$945$	984.963			1.04229
$946$	−244.342	−	572.192i	−0.258289	−	0.604854i
$947$			366.321i			0.386823i	0.981118	+	0.193411i	$0.0619552\pi$
$947$			366.321i			0.386823i	−0.981118	+	0.193411i	$0.938045\pi$
$948$	118.890	−	124.184i	0.125411	−	0.130996i
$949$	−146.594			−0.154472
$950$	967.620	−	413.201i	1.01855	−	0.434948i
$951$			159.983i			0.168226i
$952$	−505.595	+	1343.08i	−0.531088	+	1.41080i
$953$	1580.76			1.65872			0.829358	−	0.558718i	$-0.188706\pi$
$953$	1580.76			1.65872			0.829358	+	0.558718i	$0.188706\pi$
$954$	506.885	+	1187.01i	0.531326	+	1.24424i
$955$		−	1874.95i		−	1.96330i
$956$	310.920	+	297.666i	0.325230	+	0.311366i
$957$	207.663			0.216994
$958$	1697.30	−	724.793i	1.77171	−	0.756569i
$959$			2084.33i			2.17344i
$960$	222.131	−	253.229i	0.231386	−	0.263780i
$961$	−31.0000			−0.0322581
$962$	−27.2007	−	63.6978i	−0.0282752	−	0.0662140i
$963$		−	531.775i		−	0.552206i
$964$	−161.953	+	169.165i	−0.168002	+	0.175482i
$965$	−789.231			−0.817856
$966$	−269.193	+	114.953i	−0.278667	+	0.118999i
$967$		−	1316.60i		−	1.36153i	−0.732504	−	0.680763i	$-0.761648\pi$
$967$		−	1316.60i		−	1.36153i	0.732504	−	0.680763i	$-0.238352\pi$
$968$	−204.044	−	76.8109i	−0.210789	−	0.0793501i
$969$	124.476			0.128459
$970$	−59.2656	−	138.786i	−0.0610986	−	0.143079i
$971$		−	281.894i		−	0.290313i	−0.989409	−	0.145156i	$-0.953631\pi$
$971$		−	281.894i		−	0.290313i	0.989409	−	0.145156i	$-0.0463685\pi$
$972$	416.342	+	398.594i	0.428336	+	0.410076i
$973$	1932.59			1.98622
$974$	878.092	−	374.970i	0.901532	−	0.384979i
$975$			421.597i			0.432407i
$976$	51.9005	+	1190.95i	0.0531767	+	1.22024i
$977$	1377.37			1.40979			0.704897	−	0.709310i	$-0.250993\pi$
$977$	1377.37			1.40979			0.704897	+	0.709310i	$0.250993\pi$
$978$	18.1221	+	42.4377i	0.0185297	+	0.0433924i
$979$			1681.69i			1.71777i
$980$	1480.36	−	1546.28i	1.51057	−	1.57784i
$981$	−357.615			−0.364541
$982$	98.5438	−	42.0809i	0.100350	−	0.0428523i
$983$		−	1824.35i		−	1.85590i	−0.372709	−	0.927948i	$-0.621571\pi$
$983$		−	1824.35i		−	1.85590i	0.372709	−	0.927948i	$-0.378429\pi$
$984$	40.0057	−	106.273i	0.0406562	−	0.108001i
$985$	2365.51			2.40153
$986$	359.066	+	840.848i	0.364164	+	0.852787i
$987$			256.738i			0.260119i
$988$	504.994	+	483.466i	0.511127	+	0.489338i
$989$	558.731			0.564945
$990$	−1610.91	+	687.903i	−1.62718	+	0.694851i
$991$		−	113.817i		−	0.114851i	−0.998350	−	0.0574255i	$-0.981711\pi$
$991$		−	113.817i		−	0.114851i	0.998350	−	0.0574255i	$-0.0182892\pi$
$992$	−77.0377	−	160.652i	−0.0776590	−	0.161948i
$993$	268.635			0.270529
$994$	−640.830	−	1500.67i	−0.644698	−	1.50973i
$995$		−	1803.83i		−	1.81290i
$996$	−241.932	+	252.704i	−0.242903	+	0.253719i
$997$	−1659.30			−1.66429			−0.832147	−	0.554555i	$-0.812888\pi$
$997$	−1659.30			−1.66429			−0.832147	+	0.554555i	$0.812888\pi$
$998$	−1360.83	+	581.113i	−1.36356	+	0.582278i
$999$			25.7301i			0.0257559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.3.b.a.63.11	✓	30
4.3	odd	2	inner	124.3.b.a.63.12	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.3.b.a.63.11	✓	30	1.1	even	1	trivial
124.3.b.a.63.12	yes	30	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	124.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.785439 - 1.83932i) q^{2} -0.629544i q^{3} +(-2.76617 + 2.88934i) q^{4} +8.36044 q^{5} +(-1.15793 + 0.494468i) q^{6} +10.6307i q^{7} +(7.48707 + 2.81846i) q^{8} +8.60367 q^{9} +O(q^{10})\)	\(q+(-0.785439 - 1.83932i) q^{2} -0.629544i q^{3} +(-2.76617 + 2.88934i) q^{4} +8.36044 q^{5} +(-1.15793 + 0.494468i) q^{6} +10.6307i q^{7} +(7.48707 + 2.81846i) q^{8} +8.60367 q^{9} +(-6.56662 - 15.3775i) q^{10} -12.1759i q^{11} +(1.81897 + 1.74142i) q^{12} -14.9161 q^{13} +(19.5532 - 8.34977i) q^{14} -5.26326i q^{15} +(-0.696604 - 15.9848i) q^{16} +16.8744 q^{17} +(-6.75766 - 15.8249i) q^{18} +11.7174i q^{19} +(-23.1264 + 24.1562i) q^{20} +6.69249 q^{21} +(-22.3954 + 9.56344i) q^{22} -21.8685i q^{23} +(1.77434 - 4.71344i) q^{24} +44.8969 q^{25} +(11.7157 + 27.4354i) q^{26} -11.0823i q^{27} +(-30.7157 - 29.4063i) q^{28} -27.0914 q^{29} +(-9.68080 + 4.13397i) q^{30} +5.56776i q^{31} +(-28.8540 + 13.8364i) q^{32} -7.66527 q^{33} +(-13.2539 - 31.0374i) q^{34} +88.8773i q^{35} +(-23.7992 + 24.8590i) q^{36} -2.32174 q^{37} +(21.5520 - 9.20331i) q^{38} +9.39034i q^{39} +(62.5952 + 23.5636i) q^{40} +22.5468 q^{41} +(-5.25654 - 12.3096i) q^{42} +25.5496i q^{43} +(35.1804 + 33.6806i) q^{44} +71.9305 q^{45} +(-40.2231 + 17.1764i) q^{46} +38.3621i q^{47} +(-10.0631 + 0.438542i) q^{48} -64.0117 q^{49} +(-35.2638 - 82.5797i) q^{50} -10.6232i q^{51} +(41.2605 - 43.0977i) q^{52} -75.0089 q^{53} +(-20.3838 + 8.70446i) q^{54} -101.796i q^{55} +(-29.9622 + 79.5928i) q^{56} +7.37662 q^{57} +(21.2787 + 49.8297i) q^{58} -59.6920i q^{59} +(15.2074 + 14.5591i) q^{60} -74.5050 q^{61} +(10.2409 - 4.37314i) q^{62} +91.4631i q^{63} +(48.1126 + 42.2040i) q^{64} -124.705 q^{65} +(6.02060 + 14.0989i) q^{66} -75.8849i q^{67} +(-46.6776 + 48.7561i) q^{68} -13.7672 q^{69} +(163.473 - 69.8077i) q^{70} -76.7482i q^{71} +(64.4164 + 24.2491i) q^{72} +9.82790 q^{73} +(1.82358 + 4.27041i) q^{74} -28.2646i q^{75} +(-33.8556 - 32.4124i) q^{76} +129.438 q^{77} +(17.2718 - 7.37554i) q^{78} -68.2717i q^{79} +(-5.82391 - 133.640i) q^{80} +70.4563 q^{81} +(-17.7091 - 41.4707i) q^{82} +138.927i q^{83} +(-18.5126 + 19.3369i) q^{84} +141.078 q^{85} +(46.9937 - 20.0676i) q^{86} +17.0552i q^{87} +(34.3173 - 91.1620i) q^{88} -138.116 q^{89} +(-56.4970 - 132.303i) q^{90} -158.569i q^{91} +(63.1856 + 60.4920i) q^{92} +3.50515 q^{93} +(70.5600 - 30.1311i) q^{94} +97.9627i q^{95} +(8.71061 + 18.1649i) q^{96} +9.02529 q^{97} +(50.2773 + 117.738i) q^{98} -104.758i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9}+O(q^{10}) \) 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9	\( 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9} + q^{10} - 14 q^{12} + 12 q^{13} + 29 q^{14} + 50 q^{16} - 4 q^{17} - 34 q^{18} - 63 q^{20} - 16 q^{21} - 24 q^{22} - 20 q^{24} + 90 q^{25} + 38 q^{26} + 3 q^{28} - 4 q^{29} - 6 q^{30} + 118 q^{32} + 80 q^{33} + 4 q^{34} - 2 q^{36} + 76 q^{37} + 37 q^{38} - 180 q^{40} - 4 q^{41} - 38 q^{42} + 184 q^{44} - 20 q^{45} - 54 q^{46} - 172 q^{48} - 258 q^{49} - 31 q^{50} - 88 q^{52} - 132 q^{53} - 84 q^{54} - 28 q^{56} + 176 q^{57} + 164 q^{58} + 108 q^{60} - 100 q^{61} + 381 q^{64} - 104 q^{65} + 60 q^{66} + 214 q^{68} + 112 q^{69} + 45 q^{70} - 167 q^{72} - 132 q^{73} + 398 q^{74} - 317 q^{76} + 176 q^{77} - 188 q^{78} - 203 q^{80} + 158 q^{81} - 81 q^{82} + 176 q^{84} + 248 q^{85} - 78 q^{86} + 98 q^{88} - 20 q^{89} - 567 q^{90} - 260 q^{92} - 244 q^{94} - 90 q^{96} + 300 q^{97} - 371 q^{98}+O(q^{100}) \) 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9 + q^10 - 14 * q^12 + 12 * q^13 + 29 * q^14 + 50 * q^16 - 4 * q^17 - 34 * q^18 - 63 * q^20 - 16 * q^21 - 24 * q^22 - 20 * q^24 + 90 * q^25 + 38 * q^26 + 3 * q^28 - 4 * q^29 - 6 * q^30 + 118 * q^32 + 80 * q^33 + 4 * q^34 - 2 * q^36 + 76 * q^37 + 37 * q^38 - 180 * q^40 - 4 * q^41 - 38 * q^42 + 184 * q^44 - 20 * q^45 - 54 * q^46 - 172 * q^48 - 258 * q^49 - 31 * q^50 - 88 * q^52 - 132 * q^53 - 84 * q^54 - 28 * q^56 + 176 * q^57 + 164 * q^58 + 108 * q^60 - 100 * q^61 + 381 * q^64 - 104 * q^65 + 60 * q^66 + 214 * q^68 + 112 * q^69 + 45 * q^70 - 167 * q^72 - 132 * q^73 + 398 * q^74 - 317 * q^76 + 176 * q^77 - 188 * q^78 - 203 * q^80 + 158 * q^81 - 81 * q^82 + 176 * q^84 + 248 * q^85 - 78 * q^86 + 98 * q^88 - 20 * q^89 - 567 * q^90 - 260 * q^92 - 244 * q^94 - 90 * q^96 + 300 * q^97 - 371 * q^98

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