LMFDB - Embedded newform 124.3.b.a.63.18

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			63.18
Character	$\chi$	$=$	124.63
Dual form			124.3.b.a.63.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.153814 + 1.99408i) q^{2} -2.07170i q^{3} +(-3.95268 + 0.613434i) q^{4} +1.93675 q^{5} +(4.13114 - 0.318657i) q^{6} +13.3450i q^{7} +(-1.83121 - 7.78760i) q^{8} +4.70804 q^{9} +O(q^{10})$	\(q+(0.153814 + 1.99408i) q^{2} -2.07170i q^{3} +(-3.95268 + 0.613434i) q^{4} +1.93675 q^{5} +(4.13114 - 0.318657i) q^{6} +13.3450i q^{7} +(-1.83121 - 7.78760i) q^{8} +4.70804 q^{9} +(0.297900 + 3.86204i) q^{10} +17.4823i q^{11} +(1.27085 + 8.18879i) q^{12} +7.73630 q^{13} +(-26.6109 + 2.05264i) q^{14} -4.01238i q^{15} +(15.2474 - 4.84942i) q^{16} -4.38255 q^{17} +(0.724163 + 9.38820i) q^{18} -11.1033i q^{19} +(-7.65537 + 1.18807i) q^{20} +27.6468 q^{21} +(-34.8611 + 2.68903i) q^{22} -16.8505i q^{23} +(-16.1336 + 3.79373i) q^{24} -21.2490 q^{25} +(1.18995 + 15.4268i) q^{26} -28.3990i q^{27} +(-8.18626 - 52.7484i) q^{28} -3.35081 q^{29} +(8.00099 - 0.617160i) q^{30} -5.56776i q^{31} +(12.0154 + 29.6586i) q^{32} +36.2182 q^{33} +(-0.674098 - 8.73915i) q^{34} +25.8459i q^{35} +(-18.6094 + 2.88807i) q^{36} +39.1911 q^{37} +(22.1408 - 1.70784i) q^{38} -16.0273i q^{39} +(-3.54661 - 15.0827i) q^{40} +25.8363 q^{41} +(4.25247 + 55.1299i) q^{42} +53.7953i q^{43} +(-10.7243 - 69.1021i) q^{44} +9.11832 q^{45} +(33.6011 - 2.59184i) q^{46} -61.1343i q^{47} +(-10.0466 - 31.5881i) q^{48} -129.088 q^{49} +(-3.26839 - 42.3721i) q^{50} +9.07935i q^{51} +(-30.5791 + 4.74571i) q^{52} +94.4405 q^{53} +(56.6298 - 4.36817i) q^{54} +33.8590i q^{55} +(103.925 - 24.4375i) q^{56} -23.0027 q^{57} +(-0.515402 - 6.68177i) q^{58} -79.1669i q^{59} +(2.46133 + 15.8597i) q^{60} -21.6877 q^{61} +(11.1025 - 0.856400i) q^{62} +62.8287i q^{63} +(-57.2933 + 28.5215i) q^{64} +14.9833 q^{65} +(5.57087 + 72.2219i) q^{66} -30.5676i q^{67} +(17.3228 - 2.68841i) q^{68} -34.9091 q^{69} +(-51.5388 + 3.97547i) q^{70} -28.6749i q^{71} +(-8.62143 - 36.6643i) q^{72} -107.189 q^{73} +(6.02813 + 78.1500i) q^{74} +44.0216i q^{75} +(6.81113 + 43.8878i) q^{76} -233.301 q^{77} +(31.9597 - 2.46523i) q^{78} +32.8423i q^{79} +(29.5305 - 9.39213i) q^{80} -16.4619 q^{81} +(3.97398 + 51.5195i) q^{82} +42.9357i q^{83} +(-109.279 + 16.9595i) q^{84} -8.48793 q^{85} +(-107.272 + 8.27447i) q^{86} +6.94188i q^{87} +(136.145 - 32.0139i) q^{88} +101.100 q^{89} +(1.40253 + 18.1826i) q^{90} +103.241i q^{91} +(10.3366 + 66.6045i) q^{92} -11.5348 q^{93} +(121.906 - 9.40331i) q^{94} -21.5043i q^{95} +(61.4438 - 24.8923i) q^{96} +101.743 q^{97} +(-19.8556 - 257.412i) q^{98} +82.3076i 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 $

$2$	0.153814	+	1.99408i	0.0769070	+	0.997038i
$2$	0.153814	+	1.99408i	0.0769070	+	0.997038i
$3$		−	2.07170i		−	0.690568i	−0.938498	−	0.345284i	$-0.887783\pi$
$3$		−	2.07170i		−	0.690568i	0.938498	−	0.345284i	$-0.112217\pi$
$4$	−3.95268	+	0.613434i	−0.988171	+	0.153358i
$5$	1.93675			0.387351			0.193675	−	0.981066i	$-0.437959\pi$
$5$	1.93675			0.387351			0.193675	+	0.981066i	$0.437959\pi$
$6$	4.13114	−	0.318657i	0.688523	−	0.0531095i
$7$			13.3450i			1.90642i	0.302301	+	0.953212i	$0.402245\pi$
$7$			13.3450i			1.90642i	−0.302301	+	0.953212i	$0.597755\pi$
$8$	−1.83121	−	7.78760i	−0.228902	−	0.973450i
$9$	4.70804			0.523116
$10$	0.297900	+	3.86204i	0.0297900	+	0.386204i
$11$			17.4823i			1.58930i	0.607066	+	0.794652i	$0.292347\pi$
$11$			17.4823i			1.58930i	−0.607066	+	0.794652i	$0.707653\pi$
$12$	1.27085	+	8.18879i	0.105904	+	0.682399i
$13$	7.73630			0.595100			0.297550	−	0.954706i	$-0.403831\pi$
$13$	7.73630			0.595100			0.297550	+	0.954706i	$0.403831\pi$
$14$	−26.6109	+	2.05264i	−1.90078	+	0.146617i
$15$		−	4.01238i		−	0.267492i
$16$	15.2474	−	4.84942i	0.952962	−	0.303089i
$17$	−4.38255			−0.257797			−0.128899	−	0.991658i	$-0.541144\pi$
$17$	−4.38255			−0.257797			−0.128899	+	0.991658i	$0.541144\pi$
$18$	0.724163	+	9.38820i	0.0402313	+	0.521567i
$19$		−	11.1033i		−	0.584384i	−0.956360	−	0.292192i	$-0.905615\pi$
$19$		−	11.1033i		−	0.584384i	0.956360	−	0.292192i	$-0.0943846\pi$
$20$	−7.65537	+	1.18807i	−0.382769	+	0.0594035i
$21$	27.6468			1.31652
$22$	−34.8611	+	2.68903i	−1.58460	+	0.122229i
$23$		−	16.8505i		−	0.732628i	−0.930491	−	0.366314i	$-0.880620\pi$
$23$		−	16.8505i		−	0.732628i	0.930491	−	0.366314i	$-0.119380\pi$
$24$	−16.1336	+	3.79373i	−0.672233	+	0.158072i
$25$	−21.2490			−0.849959
$26$	1.18995	+	15.4268i	0.0457674	+	0.593337i
$27$		−	28.3990i		−	1.05182i
$28$	−8.18626	−	52.7484i	−0.292366	−	1.88387i
$29$	−3.35081			−0.115545			−0.0577726	−	0.998330i	$-0.518400\pi$
$29$	−3.35081			−0.115545			−0.0577726	+	0.998330i	$0.518400\pi$
$30$	8.00099	−	0.617160i	0.266700	−	0.0205720i
$31$		−	5.56776i		−	0.179605i
$31$		−	5.56776i		−	0.179605i
$32$	12.0154	+	29.6586i	0.375481	+	0.926830i
$33$	36.2182			1.09752
$34$	−0.674098	−	8.73915i	−0.0198264	−	0.257034i
$35$			25.8459i			0.738455i
$36$	−18.6094	+	2.88807i	−0.516928	+	0.0802243i
$37$	39.1911			1.05922			0.529609	−	0.848242i	$-0.322339\pi$
$37$	39.1911			1.05922			0.529609	+	0.848242i	$0.322339\pi$
$38$	22.1408	−	1.70784i	0.582653	−	0.0449432i
$39$		−	16.0273i		−	0.410957i
$40$	−3.54661	−	15.0827i	−0.0886652	−	0.377066i
$41$	25.8363			0.630153			0.315077	−	0.949066i	$-0.397970\pi$
$41$	25.8363			0.630153			0.315077	+	0.949066i	$0.397970\pi$
$42$	4.25247	+	55.1299i	0.101249	+	1.31262i
$43$			53.7953i			1.25105i	0.780203	+	0.625527i	$0.215116\pi$
$43$			53.7953i			1.25105i	−0.780203	+	0.625527i	$0.784884\pi$
$44$	−10.7243	−	69.1021i	−0.243733	−	1.57050i
$45$	9.11832			0.202629
$46$	33.6011	−	2.59184i	0.730459	−	0.0563443i
$47$		−	61.1343i		−	1.30073i	−0.759622	−	0.650365i	$-0.774616\pi$
$47$		−	61.1343i		−	1.30073i	0.759622	−	0.650365i	$-0.225384\pi$
$48$	−10.0466	−	31.5881i	−0.209303	−	0.658085i
$49$	−129.088			−2.63446
$50$	−3.26839	−	42.3721i	−0.0653678	−	0.847442i
$51$			9.07935i			0.178027i
$52$	−30.5791	+	4.74571i	−0.588060	+	0.0912636i
$53$	94.4405			1.78190			0.890948	−	0.454105i	$-0.150041\pi$
$53$	94.4405			1.78190			0.890948	+	0.454105i	$0.150041\pi$
$54$	56.6298	−	4.36817i	1.04870	−	0.0808920i
$55$			33.8590i			0.615618i
$56$	103.925	−	24.4375i	1.85581	−	0.436384i
$57$	−23.0027			−0.403557
$58$	−0.515402	−	6.68177i	−0.00888623	−	0.115203i
$59$		−	79.1669i		−	1.34181i	−0.741542	−	0.670906i	$-0.765905\pi$
$59$		−	79.1669i		−	1.34181i	0.741542	−	0.670906i	$-0.234095\pi$
$60$	2.46133	+	15.8597i	0.0410222	+	0.264328i
$61$	−21.6877			−0.355536			−0.177768	−	0.984072i	$-0.556888\pi$
$61$	−21.6877			−0.355536			−0.177768	+	0.984072i	$0.556888\pi$
$62$	11.1025	−	0.856400i	0.179073	−	0.0138129i
$63$			62.8287i			0.997281i
$64$	−57.2933	+	28.5215i	−0.895208	+	0.445648i
$65$	14.9833			0.230512
$66$	5.57087	+	72.2219i	0.0844071	+	1.09427i
$67$		−	30.5676i		−	0.456233i	−0.973634	−	0.228117i	$-0.926743\pi$
$67$		−	30.5676i		−	0.456233i	0.973634	−	0.228117i	$-0.0732567\pi$
$68$	17.3228	−	2.68841i	0.254748	−	0.0395354i
$69$	−34.9091			−0.505930
$70$	−51.5388	+	3.97547i	−0.736268	+	0.0567924i
$71$		−	28.6749i		−	0.403872i	−0.979399	−	0.201936i	$-0.935277\pi$
$71$		−	28.6749i		−	0.403872i	0.979399	−	0.201936i	$-0.0647233\pi$
$72$	−8.62143	−	36.6643i	−0.119742	−	0.509227i
$73$	−107.189			−1.46834			−0.734169	−	0.678967i	$-0.762428\pi$
$73$	−107.189			−1.46834			−0.734169	+	0.678967i	$0.762428\pi$
$74$	6.02813	+	78.1500i	0.0814613	+	1.05608i
$75$			44.0216i			0.586955i
$76$	6.81113	+	43.8878i	0.0896202	+	0.577471i
$77$	−233.301			−3.02989
$78$	31.9597	−	2.46523i	0.409740	−	0.0316055i
$79$			32.8423i			0.415725i	0.978158	+	0.207863i	$0.0666507\pi$
$79$			32.8423i			0.415725i	−0.978158	+	0.207863i	$0.933349\pi$
$80$	29.5305	−	9.39213i	0.369131	−	0.117402i
$81$	−16.4619			−0.203234
$82$	3.97398	+	51.5195i	0.0484632	+	0.628287i
$83$			42.9357i			0.517298i	0.965971	+	0.258649i	$0.0832772\pi$
$83$			42.9357i			0.517298i	−0.965971	+	0.258649i	$0.916723\pi$
$84$	−109.279	+	16.9595i	−1.30094	+	0.201899i
$85$	−8.48793			−0.0998580
$86$	−107.272	+	8.27447i	−1.24735	+	0.0962148i
$87$			6.94188i			0.0797918i
$88$	136.145	−	32.0139i	1.54711	−	0.363794i
$89$	101.100			1.13596			0.567978	−	0.823043i	$-0.307726\pi$
$89$	101.100			1.13596			0.567978	+	0.823043i	$0.307726\pi$
$90$	1.40253	+	18.1826i	0.0155836	+	0.202029i
$91$			103.241i			1.13451i
$92$	10.3366	+	66.6045i	0.112355	+	0.723962i
$93$	−11.5348			−0.124030
$94$	121.906	−	9.40331i	1.29688	−	0.100035i
$95$		−	21.5043i		−	0.226361i
$96$	61.4438	−	24.8923i	0.640039	−	0.259295i
$97$	101.743			1.04890			0.524450	−	0.851441i	$-0.324271\pi$
$97$	101.743			1.04890			0.524450	+	0.851441i	$0.324271\pi$
$98$	−19.8556	−	257.412i	−0.202608	−	2.62665i
$99$			82.3076i			0.831390i
$100$	83.9905	−	13.0348i	0.839905	−	0.130348i
$101$	92.2930			0.913792			0.456896	−	0.889520i	$-0.348961\pi$
$101$	92.2930			0.913792			0.456896	+	0.889520i	$0.348961\pi$
$102$	−18.1049	+	1.39653i	−0.177499	+	0.0136915i
$103$		−	169.450i		−	1.64515i	−0.568657	−	0.822575i	$-0.692537\pi$
$103$		−	169.450i		−	1.64515i	0.568657	−	0.822575i	$-0.307463\pi$
$104$	−14.1668	−	60.2472i	−0.136219	−	0.579300i
$105$	53.5451			0.509953
$106$	14.5263	+	188.322i	0.137040	+	1.77662i
$107$			89.9518i			0.840671i	0.907369	+	0.420335i	$0.138088\pi$
$107$			89.9518i			0.840671i	−0.907369	+	0.420335i	$0.861912\pi$
$108$	17.4209	+	112.252i	0.161305	+	1.03937i
$109$	−112.203			−1.02938			−0.514690	−	0.857376i	$-0.672093\pi$
$109$	−112.203			−1.02938			−0.514690	+	0.857376i	$0.672093\pi$
$110$	−67.5174	+	5.20799i	−0.613795	+	0.0473453i
$111$		−	81.1923i		−	0.731462i
$112$	64.7154	+	203.476i	0.577816	+	1.81675i
$113$	12.3006			0.108855			0.0544275	−	0.998518i	$-0.482667\pi$
$113$	12.3006			0.108855			0.0544275	+	0.998518i	$0.482667\pi$
$114$	−3.53814	−	45.8692i	−0.0310363	−	0.402361i
$115$		−	32.6352i		−	0.283784i
$116$	13.2447	−	2.05550i	0.114178	−	0.0177198i
$117$	36.4228			0.311306
$118$	157.865	−	12.1770i	1.33784	−	0.103195i
$119$		−	58.4851i		−	0.491471i
$120$	−31.2468	+	7.34752i	−0.260390	+	0.0612293i
$121$	−184.632			−1.52589
$122$	−3.33587	−	43.2469i	−0.0273432	−	0.354483i
$123$		−	53.5251i		−	0.435163i
$124$	3.41546	+	22.0076i	0.0275440	+	0.177481i
$125$	−89.5729			−0.716583
$126$	−125.285	+	9.66394i	−0.994328	+	0.0766979i
$127$		−	90.7259i		−	0.714377i	−0.934032	−	0.357188i	$-0.883735\pi$
$127$		−	90.7259i		−	0.714377i	0.934032	−	0.357188i	$-0.116265\pi$
$128$	−65.6865	−	109.860i	−0.513176	−	0.858283i
$129$	111.448			0.863937
$130$	2.30464	+	29.8779i	0.0177280	+	0.229830i
$131$		−	138.491i		−	1.05719i	−0.848875	−	0.528593i	$-0.822720\pi$
$131$		−	138.491i		−	1.05719i	0.848875	−	0.528593i	$-0.177280\pi$
$132$	−143.159	+	22.2175i	−1.08454	+	0.168314i
$133$	148.173			1.11408
$134$	60.9542	−	4.70173i	0.454882	−	0.0350875i
$135$		−	55.0019i		−	0.407421i
$136$	8.02539	+	34.1296i	0.0590102	+	0.250953i
$137$	190.411			1.38986			0.694932	−	0.719076i	$-0.255435\pi$
$137$	190.411			1.38986			0.694932	+	0.719076i	$0.255435\pi$
$138$	−5.36952	−	69.6115i	−0.0389095	−	0.504431i
$139$			137.067i			0.986094i	0.870003	+	0.493047i	$0.164117\pi$
$139$			137.067i			0.986094i	−0.870003	+	0.493047i	$0.835883\pi$
$140$	−15.8548	−	102.161i	−0.113248	−	0.729720i
$141$	−126.652			−0.898242
$142$	57.1800	−	4.41061i	0.402676	−	0.0310606i
$143$			135.249i			0.945794i
$144$	71.7854	−	22.8313i	0.498510	−	0.158551i
$145$	−6.48969			−0.0447565
$146$	−16.4871	−	213.742i	−0.112925	−	1.46399i
$147$			267.433i			1.81927i
$148$	−154.910	+	24.0411i	−1.04669	+	0.162440i
$149$	−122.837			−0.824409			−0.412204	−	0.911091i	$-0.635241\pi$
$149$	−122.837			−0.824409			−0.412204	+	0.911091i	$0.635241\pi$
$150$	−87.7824	+	6.77114i	−0.585216	+	0.0451409i
$151$			96.2798i			0.637614i	0.947820	+	0.318807i	$0.103282\pi$
$151$			96.2798i			0.637614i	−0.947820	+	0.318807i	$0.896718\pi$
$152$	−86.4679	+	20.3325i	−0.568868	+	0.133766i
$153$	−20.6333			−0.134858
$154$	−35.8850	−	465.221i	−0.233020	−	3.02091i
$155$		−	10.7834i		−	0.0695702i
$156$	9.83170	+	63.3509i	0.0630237	+	0.406095i
$157$	154.120			0.981657			0.490828	−	0.871256i	$-0.336694\pi$
$157$	154.120			0.981657			0.490828	+	0.871256i	$0.336694\pi$
$158$	−65.4900	+	5.05161i	−0.414494	+	0.0319722i
$159$		−	195.653i		−	1.23052i
$160$	23.2708	+	57.4413i	0.145443	+	0.359008i
$161$	224.869			1.39670
$162$	−2.53208	−	32.8264i	−0.0156301	−	0.202632i
$163$			21.8065i			0.133782i	0.997760	+	0.0668911i	$0.0213080\pi$
$163$			21.8065i			0.133782i	−0.997760	+	0.0668911i	$0.978692\pi$
$164$	−102.123	+	15.8488i	−0.622699	+	0.0966393i
$165$	70.1458			0.425126
$166$	−85.6171	+	6.60412i	−0.515766	+	0.0397838i
$167$		−	72.4521i		−	0.433845i	−0.976189	−	0.216922i	$-0.930398\pi$
$167$		−	72.4521i		−	0.433845i	0.976189	−	0.216922i	$-0.0696018\pi$
$168$	−50.6272	−	215.302i	−0.301353	−	1.28156i
$169$	−109.150			−0.645856
$170$	−1.30556	−	16.9256i	−0.00767978	−	0.0995622i
$171$		−	52.2748i		−	0.305700i
$172$	−32.9999	−	212.636i	−0.191860	−	1.23625i
$173$	111.918			0.646924			0.323462	−	0.946241i	$-0.395153\pi$
$173$	111.918			0.646924			0.323462	+	0.946241i	$0.395153\pi$
$174$	−13.8426	+	1.06776i	−0.0795555	+	0.00613655i
$175$		−	283.567i		−	1.62038i
$176$	84.7792	+	266.560i	0.481700	+	1.51455i
$177$	−164.010			−0.926612
$178$	15.5506	+	201.601i	0.0873631	+	1.13259i
$179$			191.953i			1.07236i	0.844102	+	0.536182i	$0.180134\pi$
$179$			191.953i			1.07236i	−0.844102	+	0.536182i	$0.819866\pi$
$180$	−36.0418	+	5.59349i	−0.200232	+	0.0310749i
$181$	14.8253			0.0819079			0.0409539	−	0.999161i	$-0.486960\pi$
$181$	14.8253			0.0819079			0.0409539	+	0.999161i	$0.486960\pi$
$182$	−205.870	+	15.8799i	−1.13115	+	0.0872520i
$183$			44.9304i			0.245521i
$184$	−131.225	+	30.8568i	−0.713177	+	0.167700i
$185$	75.9034			0.410289
$186$	−1.77421	−	23.0012i	−0.00953875	−	0.123662i
$187$		−	76.6173i		−	0.409718i
$188$	37.5018	+	241.644i	0.199478	+	1.28534i
$189$	378.984			2.00521
$190$	42.8813	−	3.30767i	0.225691	−	0.0174088i
$191$		−	214.598i		−	1.12355i	−0.827291	−	0.561774i	$-0.810119\pi$
$191$		−	214.598i		−	1.12355i	0.827291	−	0.561774i	$-0.189881\pi$
$192$	59.0881	+	118.695i	0.307750	+	0.618202i
$193$	−149.849			−0.776421			−0.388210	−	0.921571i	$-0.626907\pi$
$193$	−149.849			−0.776421			−0.388210	+	0.921571i	$0.626907\pi$
$194$	15.6495	+	202.884i	0.0806677	+	1.04579i
$195$		−	31.0410i		−	0.159184i
$196$	510.245	−	79.1872i	2.60329	−	0.404016i
$197$	194.888			0.989277			0.494639	−	0.869099i	$-0.335300\pi$
$197$	194.888			0.989277			0.494639	+	0.869099i	$0.335300\pi$
$198$	−164.128	+	12.6601i	−0.828928	+	0.0639397i
$199$			189.208i			0.950793i	0.879772	+	0.475396i	$0.157695\pi$
$199$			189.208i			0.950793i	−0.879772	+	0.475396i	$0.842305\pi$
$200$	38.9114	+	165.479i	0.194557	+	0.827393i
$201$	−63.3270			−0.315060
$202$	14.1960	+	184.039i	0.0702770	+	0.911086i
$203$		−	44.7165i		−	0.220278i
$204$	−5.56958	−	35.8878i	−0.0273019	−	0.175921i
$205$	50.0385			0.244090
$206$	337.897	−	26.0639i	1.64028	−	0.126524i
$207$		−	79.3327i		−	0.383250i
$208$	117.958	−	37.5166i	0.567108	−	0.180368i
$209$	194.111			0.928763
$210$	8.23599	+	106.773i	0.0392190	+	0.508443i
$211$			329.195i			1.56016i	0.625677	+	0.780082i	$0.284823\pi$
$211$			329.195i			1.56016i	−0.625677	+	0.780082i	$0.715177\pi$
$212$	−373.293	+	57.9330i	−1.76082	+	0.273269i
$213$	−59.4059			−0.278901
$214$	−179.371	+	13.8358i	−0.838181	+	0.0646535i
$215$			104.188i			0.484596i
$216$	−221.160	+	52.0046i	−1.02389	+	0.240762i
$217$	74.3017			0.342404
$218$	−17.2583	−	223.740i	−0.0791666	−	1.02633i
$219$			222.063i			1.01399i
$220$	−20.7703	−	133.834i	−0.0944102	−	0.608336i
$221$	−33.9047			−0.153415
$222$	161.904	−	12.4885i	0.729295	−	0.0562545i
$223$		−	128.535i		−	0.576391i	−0.957572	−	0.288195i	$-0.906945\pi$
$223$		−	128.535i		−	0.576391i	0.957572	−	0.288195i	$-0.0930552\pi$
$224$	−395.793	+	160.345i	−1.76693	+	0.715825i
$225$	−100.041			−0.444627
$226$	1.89201	+	24.5284i	0.00837171	+	0.108533i
$227$			56.3655i			0.248306i	0.992263	+	0.124153i	$0.0396214\pi$
$227$			56.3655i			0.248306i	−0.992263	+	0.124153i	$0.960379\pi$
$228$	90.9225	−	14.1107i	0.398783	−	0.0618888i
$229$	−246.040			−1.07441			−0.537206	−	0.843451i	$-0.680520\pi$
$229$	−246.040			−1.07441			−0.537206	+	0.843451i	$0.680520\pi$
$230$	65.0770	−	5.01975i	0.282944	−	0.0218250i
$231$			483.331i			2.09234i
$232$	6.13604	+	26.0948i	0.0264485	+	0.112477i
$233$	−271.596			−1.16565			−0.582825	−	0.812598i	$-0.698053\pi$
$233$	−271.596			−1.16565			−0.582825	+	0.812598i	$0.698053\pi$
$234$	5.60234	+	72.6299i	0.0239416	+	0.310384i
$235$		−	118.402i		−	0.503839i
$236$	48.5637	+	312.922i	0.205778	+	1.32594i
$237$	68.0395			0.287086
$238$	116.624	−	8.99582i	0.490015	−	0.0377976i
$239$		−	183.369i		−	0.767234i	−0.923492	−	0.383617i	$-0.874678\pi$
$239$		−	183.369i		−	0.767234i	0.923492	−	0.383617i	$-0.125322\pi$
$240$	−19.4577	−	61.1784i	−0.0810738	−	0.254910i
$241$	−310.912			−1.29009			−0.645045	−	0.764145i	$-0.723161\pi$
$241$	−310.912			−1.29009			−0.645045	+	0.764145i	$0.723161\pi$
$242$	−28.3990	−	368.171i	−0.117351	−	1.52137i
$243$		−	221.487i		−	0.911468i
$244$	85.7245	−	13.3040i	0.351330	−	0.0545244i
$245$	−250.012			−1.02046
$246$	106.733	−	8.23291i	0.433875	−	0.0334671i
$247$		−	85.8983i		−	0.347767i
$248$	−43.3595	+	10.1958i	−0.174837	+	0.0411119i
$249$	88.9501			0.357229
$250$	−13.7776	−	178.615i	−0.0551103	−	0.714461i
$251$			138.057i			0.550029i	0.961440	+	0.275014i	$0.0886826\pi$
$251$			138.057i			0.550029i	−0.961440	+	0.275014i	$0.911317\pi$
$252$	−38.5413	−	248.342i	−0.152942	−	0.985484i
$253$	294.585			1.16437
$254$	180.914	−	13.9549i	0.712261	−	0.0549406i
$255$			17.5845i			0.0689587i
$256$	208.966	−	147.882i	0.816274	−	0.577664i
$257$	97.1018			0.377828			0.188914	−	0.981994i	$-0.439503\pi$
$257$	97.1018			0.377828			0.188914	+	0.981994i	$0.439503\pi$
$258$	17.1423	+	222.236i	0.0664428	+	0.861379i
$259$			523.004i			2.01932i
$260$	−59.2242	+	9.19127i	−0.227786	+	0.0353510i
$261$	−15.7758			−0.0604435
$262$	276.163	−	21.3019i	1.05406	−	0.0813051i
$263$		−	393.345i		−	1.49561i	−0.663920	−	0.747803i	$-0.731109\pi$
$263$		−	393.345i		−	1.49561i	0.663920	−	0.747803i	$-0.268891\pi$
$264$	−66.3233	−	282.053i	−0.251224	−	1.06838i
$265$	182.908			0.690219
$266$	22.7911	+	295.468i	0.0856808	+	1.11078i
$267$		−	209.450i		−	0.784455i
$268$	18.7512	+	120.824i	0.0699672	+	0.450836i
$269$	−471.266			−1.75192			−0.875959	−	0.482386i	$-0.839770\pi$
$269$	−471.266			−1.75192			−0.875959	+	0.482386i	$0.839770\pi$
$270$	109.678	−	8.46006i	0.406215	−	0.0313336i
$271$			88.1570i			0.325303i	0.986684	+	0.162651i	$0.0520046\pi$
$271$			88.1570i			0.325303i	−0.986684	+	0.162651i	$0.947995\pi$
$272$	−66.8225	+	21.2528i	−0.245671	+	0.0781354i
$273$	213.884			0.783458
$274$	29.2879	+	379.695i	0.106890	+	1.38575i
$275$		−	371.482i		−	1.35084i
$276$	137.985	−	21.4145i	0.499945	−	0.0775886i
$277$	−105.732			−0.381703			−0.190852	−	0.981619i	$-0.561125\pi$
$277$	−105.732			−0.381703			−0.190852	+	0.981619i	$0.561125\pi$
$278$	−273.322	+	21.0829i	−0.983174	+	0.0758376i
$279$		−	26.2133i		−	0.0939544i
$280$	201.278	−	47.3294i	0.718849	−	0.169034i
$281$	−366.809			−1.30537			−0.652685	−	0.757629i	$-0.726357\pi$
$281$	−366.809			−1.30537			−0.652685	+	0.757629i	$0.726357\pi$
$282$	−19.4809	−	252.554i	−0.0690811	−	0.895582i
$283$			160.628i			0.567590i	0.958885	+	0.283795i	$0.0915936\pi$
$283$			160.628i			0.567590i	−0.958885	+	0.283795i	$0.908406\pi$
$284$	17.5902	+	113.343i	0.0619372	+	0.399095i
$285$	−44.5506			−0.156318
$286$	−269.696	+	20.8031i	−0.942993	+	0.0727382i
$287$			344.784i			1.20134i
$288$	56.5689	+	139.634i	0.196420	+	0.484840i
$289$	−269.793			−0.933541
$290$	−0.998206	−	12.9409i	−0.00344209	−	0.0446239i
$291$		−	210.782i		−	0.724336i
$292$	423.683	−	65.7532i	1.45097	−	0.225182i
$293$	39.0705			0.133346			0.0666731	−	0.997775i	$-0.478762\pi$
$293$	39.0705			0.133346			0.0666731	+	0.997775i	$0.478762\pi$
$294$	−533.281	+	41.1349i	−1.81388	+	0.139915i
$295$		−	153.327i		−	0.519752i
$296$	−71.7671	−	305.204i	−0.242457	−	1.03109i
$297$	496.481			1.67165
$298$	−18.8940	−	244.946i	−0.0634028	−	0.821967i
$299$		−	130.360i		−	0.435987i
$300$	−27.0043	−	174.003i	−0.0900145	−	0.580011i
$301$	−717.897			−2.38504
$302$	−191.989	+	14.8092i	−0.635726	+	0.0490370i
$303$		−	191.204i		−	0.631035i
$304$	−53.8445	−	169.296i	−0.177120	−	0.556896i
$305$	−42.0037			−0.137717
$306$	−3.17368	−	41.1443i	−0.0103715	−	0.134458i
$307$		−	383.984i		−	1.25076i	−0.780319	−	0.625382i	$-0.784943\pi$
$307$		−	383.984i		−	1.25076i	0.780319	−	0.625382i	$-0.215057\pi$
$308$	922.166	−	143.115i	2.99405	−	0.464659i
$309$	−351.051			−1.13609
$310$	21.5029	−	1.65864i	0.0693642	−	0.00535044i
$311$			578.801i			1.86110i	0.366171	+	0.930548i	$0.380669\pi$
$311$			578.801i			1.86110i	−0.366171	+	0.930548i	$0.619331\pi$
$312$	−124.814	+	29.3494i	−0.400046	+	0.0940687i
$313$	110.309			0.352425			0.176213	−	0.984352i	$-0.443615\pi$
$313$	110.309			0.352425			0.176213	+	0.984352i	$0.443615\pi$
$314$	23.7058	+	307.327i	0.0754963	+	0.978750i
$315$			121.684i			0.386298i
$316$	−20.1466	−	129.815i	−0.0637550	−	0.410807i
$317$	−27.4885			−0.0867146			−0.0433573	−	0.999060i	$-0.513805\pi$
$317$	−27.4885			−0.0867146			−0.0433573	+	0.999060i	$0.513805\pi$
$318$	390.147	−	30.0941i	1.22688	−	0.0946357i
$319$		−	58.5800i		−	0.183636i
$320$	−110.963	+	55.2391i	−0.346760	+	0.172622i
$321$	186.353			0.580540
$322$	34.5880	+	448.406i	0.107416	+	1.39256i
$323$			48.6608i			0.150652i
$324$	65.0688	−	10.0983i	0.200830	−	0.0311676i
$325$	−164.388			−0.505811
$326$	−43.4838	+	3.35414i	−0.133386	+	0.0102888i
$327$			232.450i			0.710857i
$328$	−47.3117	−	201.202i	−0.144243	−	0.613422i
$329$	815.835			2.47974
$330$	10.7894	+	139.876i	0.0326952	+	0.423867i
$331$		−	76.0427i		−	0.229736i	−0.993381	−	0.114868i	$-0.963355\pi$
$331$		−	76.0427i		−	0.229736i	0.993381	−	0.114868i	$-0.0366445\pi$
$332$	−26.3382	−	169.711i	−0.0793320	−	0.511178i
$333$	184.513			0.554094
$334$	144.475	−	11.1441i	0.432560	−	0.0333657i
$335$		−	59.2019i		−	0.176722i
$336$	421.542	−	134.071i	1.25459	−	0.399021i
$337$	−401.730			−1.19208			−0.596039	−	0.802955i	$-0.703260\pi$
$337$	−401.730			−1.19208			−0.596039	+	0.802955i	$0.703260\pi$
$338$	−16.7888	−	217.653i	−0.0496709	−	0.643943i
$339$		−	25.4832i		−	0.0751717i
$340$	33.5501	−	5.20678i	0.0986767	−	0.0153141i
$341$	97.3375			0.285447
$342$	104.240	−	8.04059i	0.304795	−	0.0235105i
$343$		−	1068.78i		−	3.11597i
$344$	418.936	−	98.5106i	1.21784	−	0.286368i
$345$	−67.6104			−0.195972
$346$	17.2145	+	223.173i	0.0497530	+	0.645008i
$347$		−	245.422i		−	0.707269i	−0.935384	−	0.353635i	$-0.884946\pi$
$347$		−	245.422i		−	0.707269i	0.935384	−	0.353635i	$-0.115054\pi$
$348$	−4.25839	−	27.4391i	−0.0122367	−	0.0788479i
$349$	−56.1132			−0.160783			−0.0803915	−	0.996763i	$-0.525617\pi$
$349$	−56.1132			−0.160783			−0.0803915	+	0.996763i	$0.525617\pi$
$350$	565.455	−	43.6166i	1.61558	−	0.124619i
$351$		−	219.703i		−	0.625935i
$352$	−518.501	+	210.057i	−1.47301	+	0.596753i
$353$	−121.055			−0.342932			−0.171466	−	0.985190i	$-0.554850\pi$
$353$	−121.055			−0.342932			−0.171466	+	0.985190i	$0.554850\pi$
$354$	−25.2271	−	327.049i	−0.0712630	−	0.923868i
$355$		−	55.5363i		−	0.156440i
$356$	−399.617	+	62.0183i	−1.12252	+	0.174209i
$357$	−121.164			−0.339394
$358$	−382.769	+	29.5251i	−1.06919	+	0.0824724i
$359$			198.023i			0.551597i	0.961215	+	0.275799i	$0.0889423\pi$
$359$			198.023i			0.551597i	−0.961215	+	0.275799i	$0.911058\pi$
$360$	−16.6976	−	71.0098i	−0.0463822	−	0.197249i
$361$	237.717			0.658496
$362$	2.28034	+	29.5628i	0.00629929	+	0.0816653i
$363$			382.503i			1.05373i
$364$	−63.3313	−	408.078i	−0.173987	−	1.12109i
$365$	−207.598			−0.568762
$366$	−89.5947	+	6.91093i	−0.244794	+	0.0188823i
$367$			76.0125i			0.207118i	0.994623	+	0.103559i	$0.0330231\pi$
$367$			76.0125i			0.207118i	−0.994623	+	0.103559i	$0.966977\pi$
$368$	−81.7149	−	256.926i	−0.222051	−	0.698167i
$369$	121.638			0.329643
$370$	11.6750	+	151.357i	0.0315541	+	0.409074i
$371$			1260.31i			3.39705i
$372$	45.5932	−	7.07581i	0.122562	−	0.0190210i
$373$	428.596			1.14905			0.574526	−	0.818486i	$-0.305186\pi$
$373$	428.596			1.14905			0.574526	+	0.818486i	$0.305186\pi$
$374$	152.781	−	11.7848i	0.408505	−	0.0315102i
$375$			185.569i			0.494849i
$376$	−476.089	+	111.950i	−1.26619	+	0.297739i
$377$	−25.9229			−0.0687609
$378$	58.2931	+	755.723i	0.154214	+	1.99927i
$379$		−	716.619i		−	1.89081i	−0.325892	−	0.945407i	$-0.605665\pi$
$379$		−	716.619i		−	1.89081i	0.325892	−	0.945407i	$-0.394335\pi$
$380$	13.1915	+	84.9998i	0.0347144	+	0.223684i
$381$	−187.957			−0.493326
$382$	427.924	−	33.0081i	1.12022	−	0.0864087i
$383$		−	408.844i		−	1.06748i	−0.845649	−	0.533739i	$-0.820787\pi$
$383$		−	408.844i		−	1.06748i	0.845649	−	0.533739i	$-0.179213\pi$
$384$	−227.598	+	136.083i	−0.592703	+	0.354383i
$385$	−451.847			−1.17363
$386$	−23.0489	−	298.811i	−0.0597122	−	0.774121i
$387$			253.271i			0.654446i
$388$	−402.159	+	62.4128i	−1.03649	+	0.160858i
$389$	425.416			1.09361			0.546807	−	0.837259i	$-0.315843\pi$
$389$	425.416			1.09361			0.546807	+	0.837259i	$0.315843\pi$
$390$	61.8981	−	4.77454i	0.158713	−	0.0122424i
$391$			73.8480i			0.188870i
$392$	236.388	+	1005.29i	0.603031	+	2.56451i
$393$	−286.913			−0.730059
$394$	29.9764	+	388.621i	0.0760824	+	0.986347i
$395$			63.6074i			0.161031i
$396$	−50.4903	−	325.336i	−0.127501	−	0.821555i
$397$	412.873			1.03998			0.519991	−	0.854172i	$-0.325935\pi$
$397$	412.873			1.03998			0.519991	+	0.854172i	$0.325935\pi$
$398$	−377.295	+	29.1028i	−0.947977	+	0.0731226i
$399$		−	306.971i		−	0.769350i
$400$	−323.992	+	103.045i	−0.809979	+	0.257613i
$401$	−154.316			−0.384829			−0.192414	−	0.981314i	$-0.561632\pi$
$401$	−154.316			−0.384829			−0.192414	+	0.981314i	$0.561632\pi$
$402$	−9.74059	−	126.279i	−0.0242303	−	0.314127i
$403$		−	43.0739i		−	0.106883i
$404$	−364.805	+	56.6157i	−0.902982	+	0.140138i
$405$	−31.8827			−0.0787227
$406$	89.1681	−	6.87802i	0.219626	−	0.0169409i
$407$			685.151i			1.68342i
$408$	70.7063	−	16.6262i	0.173300	−	0.0407505i
$409$	611.123			1.49419			0.747094	−	0.664718i	$-0.231448\pi$
$409$	611.123			1.49419			0.747094	+	0.664718i	$0.231448\pi$
$410$	7.69662	+	99.7806i	0.0187723	+	0.243367i
$411$		−	394.476i		−	0.959795i
$412$	103.947	+	669.784i	0.252298	+	1.62569i
$413$	1056.48			2.55806
$414$	158.195	−	12.2025i	0.382115	−	0.0294746i
$415$			83.1559i			0.200376i
$416$	92.9545	+	229.448i	0.223448	+	0.551557i
$417$	283.962			0.680965
$418$	29.8571	+	387.073i	0.0714284	+	0.926012i
$419$			385.334i			0.919652i	0.888009	+	0.459826i	$0.152088\pi$
$419$			385.334i			0.919652i	−0.888009	+	0.459826i	$0.847912\pi$
$420$	−211.647	+	32.8464i	−0.503921	+	0.0782057i
$421$	−474.586			−1.12728			−0.563641	−	0.826020i	$-0.690600\pi$
$421$	−474.586			−1.12728			−0.563641	+	0.826020i	$0.690600\pi$
$422$	−656.439	+	50.6348i	−1.55554	+	0.119988i
$423$		−	287.823i		−	0.680432i
$424$	−172.941	−	735.465i	−0.407879	−	1.73459i
$425$	93.1248			0.219117
$426$	−9.13747	−	118.460i	−0.0214495	−	0.278075i
$427$		−	289.421i		−	0.677802i
$428$	−55.1795	−	355.551i	−0.128924	−	0.830726i
$429$	280.195			0.653135
$430$	−207.759	+	16.0256i	−0.483161	+	0.0372689i
$431$			218.221i			0.506313i	0.967425	+	0.253157i	$0.0814688\pi$
$431$			218.221i			0.506313i	−0.967425	+	0.253157i	$0.918531\pi$
$432$	−137.719	−	433.011i	−0.318793	−	1.00234i
$433$	−785.554			−1.81421			−0.907107	−	0.420901i	$-0.861714\pi$
$433$	−785.554			−1.81421			−0.907107	+	0.420901i	$0.861714\pi$
$434$	11.4286	+	148.163i	0.0263333	+	0.341390i
$435$			13.4447i			0.0309074i
$436$	443.501	−	68.8288i	1.01720	−	0.157864i
$437$	−187.095			−0.428136
$438$	−442.811	+	34.1564i	−1.01098	+	0.0779827i
$439$			492.511i			1.12189i	0.827852	+	0.560947i	$0.189563\pi$
$439$			492.511i			1.12189i	−0.827852	+	0.560947i	$0.810437\pi$
$440$	263.680	−	62.0030i	0.599273	−	0.140916i
$441$	−607.753			−1.37813
$442$	−5.21503	−	67.6086i	−0.0117987	−	0.152961i
$443$		−	575.436i		−	1.29895i	−0.760382	−	0.649476i	$-0.774988\pi$
$443$		−	575.436i		−	1.29895i	0.760382	−	0.649476i	$-0.225012\pi$
$444$	49.8061	+	320.927i	0.112176	+	0.722809i
$445$	195.806			0.440014
$446$	256.309	−	19.7705i	0.574684	−	0.0443285i
$447$			254.482i			0.569310i
$448$	−380.618	−	764.578i	−0.849595	−	1.70665i
$449$	32.4483			0.0722678			0.0361339	−	0.999347i	$-0.488496\pi$
$449$	32.4483			0.0722678			0.0361339	+	0.999347i	$0.488496\pi$
$450$	−15.3877	−	199.490i	−0.0341950	−	0.443310i
$451$			451.678i			1.00150i
$452$	−48.6204	+	7.54561i	−0.107567	+	0.0166938i
$453$	199.463			0.440316
$454$	−112.397	+	8.66981i	−0.247571	+	0.0190965i
$455$			199.952i			0.439455i
$456$	42.1229	+	179.136i	0.0923747	+	0.392842i
$457$	616.962			1.35003			0.675013	−	0.737806i	$-0.264138\pi$
$457$	616.962			1.35003			0.675013	+	0.737806i	$0.264138\pi$
$458$	−37.8444	−	490.623i	−0.0826298	−	1.07123i
$459$			124.460i			0.271155i
$460$	20.0195	+	128.997i	0.0435207	+	0.280427i
$461$	−304.939			−0.661473			−0.330737	−	0.943723i	$-0.607297\pi$
$461$	−304.939			−0.661473			−0.330737	+	0.943723i	$0.607297\pi$
$462$	−963.799	+	74.3431i	−2.08615	+	0.160916i
$463$			791.111i			1.70866i	0.519728	+	0.854332i	$0.326033\pi$
$463$			791.111i			1.70866i	−0.519728	+	0.854332i	$0.673967\pi$
$464$	−51.0911	+	16.2495i	−0.110110	+	0.0350204i
$465$	−22.3400			−0.0480430
$466$	−41.7753	−	541.584i	−0.0896467	−	1.16220i
$467$			349.265i			0.747891i	0.927451	+	0.373945i	$0.121995\pi$
$467$			349.265i			0.747891i	−0.927451	+	0.373945i	$0.878005\pi$
$468$	−143.968	+	22.3430i	−0.307624	+	0.0477415i
$469$	407.924			0.869774
$470$	236.103	−	18.2119i	0.502346	−	0.0387487i
$471$		−	319.291i		−	0.677901i
$472$	−616.520	+	144.971i	−1.30619	+	0.307143i
$473$	−940.467			−1.98830
$474$	10.4654	+	135.676i	0.0220790	+	0.286236i
$475$			235.934i			0.496702i
$476$	35.8767	+	231.173i	0.0753713	+	0.485657i
$477$	444.630			0.932139
$478$	365.652	−	28.2047i	0.764962	−	0.0590057i
$479$			116.117i			0.242416i	0.992627	+	0.121208i	$0.0386768\pi$
$479$			116.117i			0.242416i	−0.992627	+	0.121208i	$0.961323\pi$
$480$	119.001	−	48.2103i	0.247920	−	0.100438i
$481$	303.194			0.630340
$482$	−47.8226	−	619.982i	−0.0992170	−	1.28627i
$483$		−	465.862i		−	0.964517i
$484$	729.792	−	113.260i	1.50784	−	0.234007i
$485$	197.052			0.406292
$486$	441.662	−	34.0678i	0.908769	−	0.0700983i
$487$		−	80.7729i		−	0.165858i	−0.996555	−	0.0829290i	$-0.973573\pi$
$487$		−	80.7729i		−	0.165858i	0.996555	−	0.0829290i	$-0.0264275\pi$
$488$	39.7147	+	168.895i	0.0813826	+	0.346096i
$489$	45.1766			0.0923856
$490$	−38.4554	−	498.544i	−0.0784804	−	1.01744i
$491$		−	255.045i		−	0.519439i	−0.965684	−	0.259720i	$-0.916370\pi$
$491$		−	255.045i		−	0.519439i	0.965684	−	0.259720i	$-0.0836301\pi$
$492$	32.8341	+	211.568i	0.0667360	+	0.430016i
$493$	14.6851			0.0297872
$494$	171.288	−	13.2124i	0.346737	−	0.0267457i
$495$			159.410i			0.322040i
$496$	−27.0004	−	84.8939i	−0.0544363	−	0.171157i
$497$	382.666			0.769952
$498$	13.6818	+	177.373i	0.0274734	+	0.356171i
$499$			268.547i			0.538171i	0.963116	+	0.269086i	$0.0867214\pi$
$499$			268.547i			0.538171i	−0.963116	+	0.269086i	$0.913279\pi$
$500$	354.053	−	54.9471i	0.708106	−	0.109894i
$501$	−150.099			−0.299599
$502$	−275.297	+	21.2351i	−0.548400	+	0.0423011i
$503$			364.944i			0.725535i	0.931880	+	0.362767i	$0.118168\pi$
$503$			364.944i			0.725535i	−0.931880	+	0.362767i	$0.881832\pi$
$504$	489.285	−	115.053i	0.970803	−	0.228279i
$505$	178.749			0.353958
$506$	45.3114	+	587.426i	0.0895481	+	1.16092i
$507$			226.126i			0.446008i
$508$	55.6543	+	358.611i	0.109556	+	0.705926i
$509$	517.279			1.01627			0.508133	−	0.861279i	$-0.330336\pi$
$509$	517.279			1.01627			0.508133	+	0.861279i	$0.330336\pi$
$510$	−35.0648	+	2.70474i	−0.0687545	+	0.00530341i
$511$		−	1430.43i		−	2.79928i
$512$	327.030	+	393.948i	0.638731	+	0.769430i
$513$	−315.322			−0.614663
$514$	14.9356	+	193.628i	0.0290576	+	0.376709i
$515$		−	328.184i		−	0.637250i
$516$	−440.518	+	68.3659i	−0.853717	+	0.132492i
$517$	1068.77			2.06725
$518$	−1042.91	+	80.4453i	−2.01334	+	0.155300i
$519$		−	231.861i		−	0.446745i
$520$	−27.4376	−	116.684i	−0.0527646	−	0.224392i
$521$	−375.040			−0.719846			−0.359923	−	0.932982i	$-0.617197\pi$
$521$	−375.040			−0.719846			−0.359923	+	0.932982i	$0.617197\pi$
$522$	−2.42653	−	31.4581i	−0.00464853	−	0.0602645i
$523$			146.038i			0.279232i	0.990206	+	0.139616i	$0.0445868\pi$
$523$			146.038i			0.279232i	−0.990206	+	0.139616i	$0.955413\pi$
$524$	84.9554	+	547.413i	0.162129	+	1.04468i
$525$	−587.467			−1.11898
$526$	784.359	−	60.5019i	1.49118	−	0.115023i
$527$			24.4010i			0.0463018i
$528$	552.234	−	175.637i	1.04590	−	0.332647i
$529$	245.062			0.463256
$530$	28.1338	+	364.733i	0.0530827	+	0.688175i
$531$		−	372.721i		−	0.701923i
$532$	−585.681	+	90.8944i	−1.10090	+	0.170854i
$533$	199.877			0.375004
$534$	417.658	−	32.2163i	0.782132	−	0.0603301i
$535$			174.214i			0.325634i
$536$	−238.048	+	55.9758i	−0.444120	+	0.104432i
$537$	397.670			0.740540
$538$	−72.4873	−	939.740i	−0.134735	−	1.74673i
$539$		−	2256.77i		−	4.18695i
$540$	33.7400	+	217.405i	0.0624815	+	0.402602i
$541$	89.2223			0.164921			0.0824605	−	0.996594i	$-0.473722\pi$
$541$	89.2223			0.164921			0.0824605	+	0.996594i	$0.473722\pi$
$542$	−175.792	+	13.5598i	−0.324339	+	0.0250181i
$543$		−	30.7137i		−	0.0565629i
$544$	−52.6580	−	129.980i	−0.0967979	−	0.238934i
$545$	−217.309			−0.398731
$546$	32.8984	+	426.501i	0.0602535	+	0.781138i
$547$		−	357.418i		−	0.653415i	−0.945125	−	0.326708i	$-0.894061\pi$
$547$		−	357.418i		−	0.653415i	0.945125	−	0.326708i	$-0.105939\pi$
$548$	−752.635	+	116.805i	−1.37342	+	0.213147i
$549$	−102.106			−0.185986
$550$	740.763	−	57.1391i	1.34684	−	0.103889i
$551$			37.2050i			0.0675227i
$552$	63.9261	+	271.858i	0.115808	+	0.492497i
$553$	−438.279			−0.792549
$554$	−16.2630	−	210.837i	−0.0293557	−	0.380573i
$555$		−	157.249i		−	0.283332i
$556$	−84.0816	−	541.783i	−0.151226	−	0.974430i
$557$	314.408			0.564466			0.282233	−	0.959346i	$-0.408925\pi$
$557$	314.408			0.564466			0.282233	+	0.959346i	$0.408925\pi$
$558$	52.2713	−	4.03197i	0.0936761	−	0.00722575i
$559$			416.176i			0.744502i
$560$	125.338	+	394.083i	0.223817	+	0.703720i
$561$	−158.728			−0.282938
$562$	−56.4204	−	731.445i	−0.100392	−	1.30150i
$563$		−	267.424i		−	0.474997i	−0.971388	−	0.237499i	$-0.923672\pi$
$563$		−	267.424i		−	0.474997i	0.971388	−	0.237499i	$-0.0763275\pi$
$564$	500.616	−	77.6927i	0.887616	−	0.137753i
$565$	23.8232			0.0421650
$566$	−320.305	+	24.7069i	−0.565909	+	0.0436517i
$567$		−	219.684i		−	0.387450i
$568$	−223.309	+	52.5099i	−0.393149	+	0.0924469i
$569$	−514.341			−0.903939			−0.451970	−	0.892033i	$-0.649278\pi$
$569$	−514.341			−0.903939			−0.451970	+	0.892033i	$0.649278\pi$
$570$	−6.85251	−	88.8373i	−0.0120219	−	0.155855i
$571$			551.756i			0.966297i	0.875538	+	0.483149i	$0.160507\pi$
$571$			551.756i			0.966297i	−0.875538	+	0.483149i	$0.839493\pi$
$572$	−82.9661	−	534.595i	−0.145046	−	0.934606i
$573$	−444.583			−0.775886
$574$	−687.526	+	53.0327i	−1.19778	+	0.0923914i
$575$			358.055i			0.622704i
$576$	−269.739	+	134.280i	−0.468298	+	0.233126i
$577$	−735.931			−1.27544			−0.637722	−	0.770267i	$-0.720123\pi$
$577$	−735.931			−1.27544			−0.637722	+	0.770267i	$0.720123\pi$
$578$	−41.4980	−	537.988i	−0.0717958	−	0.930776i
$579$			310.443i			0.536171i
$580$	25.6517	−	3.98100i	0.0442271	−	0.00686379i
$581$	−572.976			−0.986189
$582$	420.315	−	32.4212i	0.722191	−	0.0557065i
$583$			1651.04i			2.83197i
$584$	196.285	+	834.742i	0.336105	+	1.42935i
$585$	70.5421			0.120585
$586$	6.00958	+	77.9095i	0.0102553	+	0.132951i
$587$		−	192.255i		−	0.327521i	−0.986500	−	0.163761i	$-0.947638\pi$
$587$		−	192.255i		−	0.327521i	0.986500	−	0.163761i	$-0.0523624\pi$
$588$	−164.052	−	1057.08i	−0.279001	−	1.79775i
$589$	−61.8205			−0.104958
$590$	305.745	−	23.5838i	0.518212	−	0.0399726i
$591$		−	403.749i		−	0.683163i
$592$	597.562	−	190.054i	1.00939	−	0.321037i
$593$	−132.440			−0.223338			−0.111669	−	0.993745i	$-0.535620\pi$
$593$	−132.440			−0.223338			−0.111669	+	0.993745i	$0.535620\pi$
$594$	76.3658	+	990.021i	0.128562	+	1.66670i
$595$		−	113.271i		−	0.190372i
$596$	485.535	−	75.3523i	0.814657	−	0.126430i
$597$	391.982			0.656587
$598$	259.948	−	20.0512i	0.434696	−	0.0335305i
$599$			6.53611i			0.0109117i	0.999985	+	0.00545585i	$0.00173666\pi$
$599$			6.53611i			0.0109117i	−0.999985	+	0.00545585i	$0.998263\pi$
$600$	342.822	−	80.6129i	0.571371	−	0.134355i
$601$	127.453			0.212069			0.106034	−	0.994362i	$-0.466185\pi$
$601$	127.453			0.212069			0.106034	+	0.994362i	$0.466185\pi$
$602$	−110.423	−	1431.54i	−0.183426	−	2.37798i
$603$		−	143.914i		−	0.238663i
$604$	−59.0613	−	380.563i	−0.0977836	−	0.630072i
$605$	−357.587			−0.591053
$606$	381.275	−	29.4098i	0.629166	−	0.0485311i
$607$		−	236.179i		−	0.389092i	−0.980893	−	0.194546i	$-0.937677\pi$
$607$		−	236.179i		−	0.389092i	0.980893	−	0.194546i	$-0.0623234\pi$
$608$	329.308	−	133.410i	0.541624	−	0.219425i
$609$	−92.6393			−0.152117
$610$	−6.46076	−	83.7585i	−0.0105914	−	0.137309i
$611$		−	472.953i		−	0.774064i
$612$	81.5567	−	12.6571i	0.133263	−	0.0206816i
$613$	−671.914			−1.09611			−0.548054	−	0.836443i	$-0.684631\pi$
$613$	−671.914			−1.09611			−0.548054	+	0.836443i	$0.684631\pi$
$614$	765.694	−	59.0622i	1.24706	−	0.0961925i
$615$		−	103.665i		−	0.168561i
$616$	427.224	+	1816.86i	0.693546	+	2.94944i
$617$	−1003.83			−1.62696			−0.813479	−	0.581595i	$-0.802429\pi$
$617$	−1003.83			−1.62696			−0.813479	+	0.581595i	$0.802429\pi$
$618$	−53.9966	−	700.023i	−0.0873731	−	1.13272i
$619$			249.447i			0.402983i	0.979490	+	0.201492i	$0.0645789\pi$
$619$			249.447i			0.402983i	−0.979490	+	0.201492i	$0.935421\pi$
$620$	6.61490	+	42.6233i	0.0106692	+	0.0687473i
$621$	−478.536			−0.770590
$622$	−1154.17	+	89.0277i	−1.85558	+	0.143131i
$623$			1349.18i			2.16562i
$624$	−77.7232	−	244.375i	−0.124556	−	0.391626i
$625$	357.744			0.572390
$626$	16.9671	+	219.965i	0.0271040	+	0.351381i
$627$		−	402.141i		−	0.641374i
$628$	−609.188	+	94.5425i	−0.970045	+	0.150545i
$629$	−171.757			−0.273063
$630$	−242.647	+	18.7167i	−0.385154	+	0.0297090i
$631$		−	892.655i		−	1.41467i	−0.706880	−	0.707334i	$-0.749898\pi$
$631$		−	892.655i		−	1.41467i	0.706880	−	0.707334i	$-0.250102\pi$
$632$	255.763	−	60.1412i	0.404688	−	0.0951601i
$633$	681.994			1.07740
$634$	−4.22812	−	54.8142i	−0.00666896	−	0.0864578i
$635$		−	175.714i		−	0.276714i
$636$	120.020	+	773.353i	0.188711	+	1.21596i
$637$	−998.666			−1.56776
$638$	116.813	−	9.01042i	0.183092	−	0.0141229i
$639$		−	135.003i		−	0.211272i
$640$	−127.219	−	212.772i	−0.198779	−	0.332457i
$641$	−254.186			−0.396546			−0.198273	−	0.980147i	$-0.563533\pi$
$641$	−254.186			−0.396546			−0.198273	+	0.980147i	$0.563533\pi$
$642$	28.6638	+	371.603i	0.0446476	+	0.578821i
$643$			884.980i			1.37633i	0.725554	+	0.688165i	$0.241584\pi$
$643$			884.980i			1.37633i	−0.725554	+	0.688165i	$0.758416\pi$
$644$	−888.835	+	137.942i	−1.38018	+	0.214196i
$645$	215.847			0.334647
$646$	−97.0333	+	7.48471i	−0.150206	+	0.0115862i
$647$			547.511i			0.846230i	0.906076	+	0.423115i	$0.139063\pi$
$647$			547.511i			0.846230i	−0.906076	+	0.423115i	$0.860937\pi$
$648$	30.1453	+	128.199i	0.0465205	+	0.197838i
$649$	1384.02			2.13255
$650$	−25.2853	−	327.803i	−0.0389004	−	0.504313i
$651$		−	153.931i		−	0.236453i
$652$	−13.3768	−	86.1941i	−0.0205166	−	0.132200i
$653$	−328.510			−0.503078			−0.251539	−	0.967847i	$-0.580937\pi$
$653$	−328.510			−0.503078			−0.251539	+	0.967847i	$0.580937\pi$
$654$	−463.524	+	35.7541i	−0.708752	+	0.0546699i
$655$		−	268.224i		−	0.409502i
$656$	393.936	−	125.291i	0.600512	−	0.190992i
$657$	−504.649			−0.768111
$658$	125.487	+	1626.84i	0.190710	+	2.47240i
$659$		−	186.296i		−	0.282694i	−0.989960	−	0.141347i	$-0.954857\pi$
$659$		−	186.296i		−	0.282694i	0.989960	−	0.141347i	$-0.0451434\pi$
$660$	−277.264	+	43.0298i	−0.420097	+	0.0651967i
$661$	−1078.45			−1.63155			−0.815775	−	0.578370i	$-0.803689\pi$
$661$	−1078.45			−1.63155			−0.815775	+	0.578370i	$0.803689\pi$
$662$	151.635	−	11.6964i	0.229056	−	0.0176683i
$663$			70.2406i			0.105944i
$664$	334.366	−	78.6244i	0.503563	−	0.118410i
$665$	286.975			0.431541
$666$	28.3807	+	367.933i	0.0426137	+	0.552453i
$667$			56.4627i			0.0846517i
$668$	44.4446	+	286.380i	0.0665338	+	0.428713i
$669$	−266.287			−0.398037
$670$	118.053	−	9.10609i	0.176199	−	0.0135912i
$671$		−	379.151i		−	0.565054i
$672$	332.187	+	819.965i	0.494326	+	1.22019i
$673$	661.374			0.982725			0.491362	−	0.870955i	$-0.336499\pi$
$673$	661.374			0.982725			0.491362	+	0.870955i	$0.336499\pi$
$674$	−61.7918	−	801.081i	−0.0916792	−	1.18855i
$675$			603.450i			0.894000i
$676$	431.434	−	66.9561i	0.638216	−	0.0990475i
$677$	13.7349			0.0202878			0.0101439	−	0.999949i	$-0.496771\pi$
$677$	13.7349			0.0202878			0.0101439	+	0.999949i	$0.496771\pi$
$678$	50.8155	−	3.91968i	0.0749491	−	0.00578123i
$679$			1357.76i			1.99965i
$680$	15.5432	+	66.1006i	0.0228576	+	0.0972067i
$681$	116.773			0.171472
$682$	14.9719	+	194.098i	0.0219529	+	0.284602i
$683$		−	763.496i		−	1.11786i	−0.829216	−	0.558929i	$-0.811213\pi$
$683$		−	763.496i		−	1.11786i	0.829216	−	0.558929i	$-0.188787\pi$
$684$	32.0671	+	206.626i	0.0468817	+	0.302084i
$685$	368.780			0.538365
$686$	2131.22	−	164.393i	3.10674	−	0.239640i
$687$			509.722i			0.741954i
$688$	260.876	+	820.238i	0.379180	+	1.19221i
$689$	730.620			1.06041
$690$	−10.3994	−	134.820i	−0.0150716	−	0.195392i
$691$		−	548.260i		−	0.793429i	−0.917942	−	0.396715i	$-0.870150\pi$
$691$		−	548.260i		−	0.793429i	0.917942	−	0.396715i	$-0.129850\pi$
$692$	−442.376	+	68.6542i	−0.639271	+	0.0992113i
$693$	−1098.39			−1.58498
$694$	489.391	−	37.7494i	0.705175	−	0.0543940i
$695$			265.465i			0.381964i
$696$	54.0606	−	12.7121i	0.0776733	−	0.0182645i
$697$	−113.229			−0.162452
$698$	−8.63100	−	111.894i	−0.0123653	−	0.160307i
$699$			562.667i			0.804960i
$700$	173.950	+	1120.85i	0.248500	+	1.60122i
$701$	−17.0735			−0.0243559			−0.0121780	−	0.999926i	$-0.503876\pi$
$701$	−17.0735			−0.0243559			−0.0121780	+	0.999926i	$0.503876\pi$
$702$	438.105	−	33.7934i	0.624081	−	0.0481388i
$703$		−	435.150i		−	0.618989i
$704$	−498.622	−	1001.62i	−0.708270	−	1.42276i
$705$	−245.294			−0.347935
$706$	−18.6200	−	241.393i	−0.0263739	−	0.341917i
$707$			1231.65i			1.74208i
$708$	648.281	−	100.610i	0.915651	−	0.142104i
$709$	898.082			1.26669			0.633344	−	0.773870i	$-0.281682\pi$
$709$	898.082			1.26669			0.633344	+	0.773870i	$0.281682\pi$
$710$	110.744	−	8.54226i	0.155977	−	0.0120313i
$711$			154.623i			0.217472i
$712$	−185.136	−	787.327i	−0.260022	−	1.10580i
$713$	−93.8194			−0.131584
$714$	−18.6367	−	241.610i	−0.0261018	−	0.338389i
$715$			261.943i			0.366354i
$716$	−117.751	−	758.730i	−0.164456	−	1.05968i
$717$	−379.886			−0.529827
$718$	−394.874	+	30.4588i	−0.549963	+	0.0424217i
$719$		−	1222.88i		−	1.70080i	−0.526133	−	0.850402i	$-0.676359\pi$
$719$		−	1222.88i		−	1.70080i	0.526133	−	0.850402i	$-0.323641\pi$
$720$	139.031	−	44.2186i	0.193098	−	0.0614147i
$721$	2261.31			3.13635
$722$	36.5642	+	474.026i	0.0506430	+	0.656546i
$723$			644.117i			0.890895i
$724$	−58.5998	+	9.09436i	−0.0809389	+	0.0125613i
$725$	71.2013			0.0982087
$726$	−762.740	+	58.8343i	−1.05061	+	0.0810390i
$727$			1002.04i			1.37832i	0.724608	+	0.689161i	$0.242021\pi$
$727$			1002.04i			1.37832i	−0.724608	+	0.689161i	$0.757979\pi$
$728$	803.997	−	189.056i	1.10439	−	0.259692i
$729$	−607.012			−0.832664
$730$	−31.9315	−	413.966i	−0.0437418	−	0.567077i
$731$		−	235.761i		−	0.322518i
$732$	−27.5619	−	177.596i	−0.0376528	−	0.242617i
$733$	934.722			1.27520			0.637600	−	0.770367i	$-0.279927\pi$
$733$	934.722			1.27520			0.637600	+	0.770367i	$0.279927\pi$
$734$	−151.575	+	11.6918i	−0.206505	+	0.0159289i
$735$			517.951i			0.704696i
$736$	499.760	−	202.465i	0.679022	−	0.275088i
$737$	534.393			0.725093
$738$	18.7097	+	242.556i	0.0253519	+	0.328667i
$739$		−	795.984i		−	1.07711i	−0.842590	−	0.538555i	$-0.818970\pi$
$739$		−	795.984i		−	1.07711i	0.842590	−	0.538555i	$-0.181030\pi$
$740$	−300.022	+	46.5617i	−0.405435	+	0.0629213i
$741$	−177.956			−0.240156
$742$	−2513.15	+	193.853i	−3.38699	+	0.261257i
$743$			497.265i			0.669266i	0.942348	+	0.334633i	$0.108612\pi$
$743$			497.265i			0.669266i	−0.942348	+	0.334633i	$0.891388\pi$
$744$	21.1226	+	89.8280i	0.0283906	+	0.120737i
$745$	−237.905			−0.319335
$746$	65.9241	+	854.654i	0.0883702	+	1.14565i
$747$			202.143i			0.270607i
$748$	46.9996	+	302.844i	0.0628337	+	0.404871i
$749$	−1200.40			−1.60268
$750$	−370.038	+	28.5430i	−0.493384	+	0.0380574i
$751$			282.573i			0.376263i	0.982144	+	0.188131i	$0.0602431\pi$
$751$			282.573i			0.376263i	−0.982144	+	0.188131i	$0.939757\pi$
$752$	−296.466	−	932.139i	−0.394236	−	1.23955i
$753$	286.014			0.379832
$754$	−3.98730	−	51.6922i	−0.00528820	−	0.0685573i
$755$			186.470i			0.246980i
$756$	−1498.00	+	232.482i	−1.98149	+	0.307515i
$757$	−816.967			−1.07922			−0.539608	−	0.841916i	$-0.681428\pi$
$757$	−816.967			−1.07922			−0.539608	+	0.841916i	$0.681428\pi$
$758$	1428.99	−	110.226i	1.88521	−	0.145417i
$759$		−	610.294i		−	0.804076i
$760$	−167.467	+	39.3790i	−0.220351	+	0.0518145i
$761$	−1349.11			−1.77281			−0.886404	−	0.462913i	$-0.846804\pi$
$761$	−1349.11			−1.77281			−0.886404	+	0.462913i	$0.846804\pi$
$762$	−28.9104	−	374.801i	−0.0379402	−	0.491865i
$763$		−	1497.34i		−	1.96244i
$764$	131.641	+	848.236i	0.172306	+	1.11026i
$765$	−39.9615			−0.0522373
$766$	815.266	−	62.8859i	1.06432	−	0.0820965i
$767$		−	612.459i		−	0.798512i
$768$	−306.368	−	432.916i	−0.398916	−	0.563693i
$769$	−301.487			−0.392051			−0.196025	−	0.980599i	$-0.562804\pi$
$769$	−301.487			−0.392051			−0.196025	+	0.980599i	$0.562804\pi$
$770$	−69.5005	−	901.018i	−0.0902603	−	1.17015i
$771$		−	201.166i		−	0.260916i
$772$	592.306	−	91.9226i	0.767236	−	0.119071i
$773$	1039.71			1.34503			0.672517	−	0.740082i	$-0.265213\pi$
$773$	1039.71			1.34503			0.672517	+	0.740082i	$0.265213\pi$
$774$	−505.041	+	38.9566i	−0.652508	+	0.0503315i
$775$			118.309i			0.152657i
$776$	−186.313	−	792.335i	−0.240095	−	1.02105i
$777$	1083.51			1.39448
$778$	65.4350	+	848.312i	0.0841066	+	1.09038i
$779$		−	286.868i		−	0.368251i
$780$	19.0416	+	122.695i	0.0244123	+	0.157301i
$781$	501.305			0.641875
$782$	−147.259	+	11.3589i	−0.188310	+	0.0145254i
$783$			95.1597i			0.121532i
$784$	−1968.26	+	626.003i	−2.51054	+	0.798474i
$785$	298.493			0.380246
$786$	−44.1313	−	572.127i	−0.0561467	−	0.727897i
$787$		−	1159.40i		−	1.47319i	−0.676336	−	0.736593i	$-0.736433\pi$
$787$		−	1159.40i		−	1.47319i	0.676336	−	0.736593i	$-0.263567\pi$
$788$	−770.329	+	119.551i	−0.977575	+	0.151714i
$789$	−814.893			−1.03282
$790$	−126.838	+	9.78372i	−0.160555	+	0.0123845i
$791$			164.151i			0.207524i
$792$	640.978	−	150.723i	0.809316	−	0.190306i
$793$	−167.782			−0.211579
$794$	63.5056	+	823.300i	0.0799819	+	1.03690i
$795$		−	378.931i		−	0.476643i
$796$	−116.066	−	747.878i	−0.145812	−	0.939545i
$797$	844.283			1.05933			0.529663	−	0.848208i	$-0.322318\pi$
$797$	844.283			1.05933			0.529663	+	0.848208i	$0.322318\pi$
$798$	612.123	−	47.2164i	0.767072	−	0.0591684i
$799$			267.924i			0.335324i
$800$	−255.315	−	630.214i	−0.319143	−	0.787768i
$801$	475.984			0.594237
$802$	−23.7360	−	307.719i	−0.0295960	−	0.383689i
$803$		−	1873.91i		−	2.33363i
$804$	250.312	−	38.8470i	0.311333	−	0.0483171i
$805$	435.516			0.541013
$806$	85.8926	−	6.62537i	0.106567	−	0.00822006i
$807$			976.323i			1.20982i
$808$	−169.008	−	718.741i	−0.209168	−	0.889530i
$809$	−1172.99			−1.44993			−0.724964	−	0.688786i	$-0.758144\pi$
$809$	−1172.99			−1.44993			−0.724964	+	0.688786i	$0.758144\pi$
$810$	−4.90401	−	63.5766i	−0.00605433	−	0.0784896i
$811$		−	530.048i		−	0.653574i	−0.945098	−	0.326787i	$-0.894034\pi$
$811$		−	530.048i		−	0.653574i	0.945098	−	0.326787i	$-0.105966\pi$
$812$	27.4306	+	176.750i	0.0337815	+	0.217672i
$813$	182.635			0.224644
$814$	−1366.24	+	105.386i	−1.67843	+	0.129467i
$815$			42.2338i			0.0518206i
$816$	44.0296	+	138.436i	0.0539578	+	0.169653i
$817$	597.305			0.731095
$818$	93.9993	+	1218.63i	0.114914	+	1.48976i
$819$			486.062i			0.593482i
$820$	−197.786	+	30.6953i	−0.241203	+	0.0374333i
$821$	676.140			0.823557			0.411778	−	0.911284i	$-0.364908\pi$
$821$	676.140			0.823557			0.411778	+	0.911284i	$0.364908\pi$
$822$	786.615	−	60.6759i	0.956952	−	0.0738150i
$823$			785.168i			0.954032i	0.878895	+	0.477016i	$0.158282\pi$
$823$			785.168i			0.954032i	−0.878895	+	0.477016i	$0.841718\pi$
$824$	−1319.61	+	310.300i	−1.60147	+	0.376577i
$825$	−769.600			−0.932849
$826$	162.501	+	2106.70i	0.196733	+	2.55049i
$827$			1042.76i			1.26090i	0.776231	+	0.630449i	$0.217129\pi$
$827$			1042.76i			1.26090i	−0.776231	+	0.630449i	$0.782871\pi$
$828$	48.6654	+	313.577i	0.0587746	+	0.378716i
$829$	−186.065			−0.224445			−0.112223	−	0.993683i	$-0.535797\pi$
$829$	−186.065			−0.224445			−0.112223	+	0.993683i	$0.535797\pi$
$830$	−165.819	+	12.7905i	−0.199782	+	0.0154103i
$831$			219.045i			0.263592i
$832$	−443.238	+	220.651i	−0.532738	+	0.265205i
$833$	565.736			0.679155
$834$	43.6774	+	566.243i	0.0523710	+	0.678948i
$835$		−	140.322i		−	0.168050i
$836$	−767.261	+	119.075i	−0.917776	+	0.142434i
$837$	−158.119			−0.188912
$838$	−768.385	+	59.2698i	−0.916928	+	0.0707277i
$839$		−	1109.13i		−	1.32197i	−0.750399	−	0.660985i	$-0.770139\pi$
$839$		−	1109.13i		−	1.32197i	0.750399	−	0.660985i	$-0.229861\pi$
$840$	−98.0525	−	416.988i	−0.116729	−	0.496414i
$841$	−829.772			−0.986649
$842$	−72.9980	−	946.361i	−0.0866959	−	1.12394i
$843$			759.919i			0.901447i
$844$	−201.939	−	1301.20i	−0.239264	−	1.54171i
$845$	−211.396			−0.250173
$846$	573.941	−	44.2712i	0.678417	−	0.0523300i
$847$		−	2463.91i		−	2.90899i
$848$	1439.97	−	457.982i	1.69808	−	0.540073i
$849$	332.774			0.391960
$850$	14.3239	+	185.698i	0.0168517	+	0.218468i
$851$		−	660.387i		−	0.776013i
$852$	234.813	−	36.4416i	0.275602	−	0.0427719i
$853$	1564.87			1.83455			0.917277	−	0.398249i	$-0.130382\pi$
$853$	1564.87			1.83455			0.917277	+	0.398249i	$0.130382\pi$
$854$	577.128	−	44.5171i	0.675794	−	0.0521277i
$855$		−	101.243i		−	0.118413i
$856$	700.508	−	164.721i	0.818351	−	0.192431i
$857$	−945.253			−1.10298			−0.551490	−	0.834182i	$-0.685940\pi$
$857$	−945.253			−1.10298			−0.551490	+	0.834182i	$0.685940\pi$
$858$	43.0979	+	558.730i	0.0502307	+	0.651201i
$859$			626.678i			0.729543i	0.931097	+	0.364772i	$0.118853\pi$
$859$			626.678i			0.729543i	−0.931097	+	0.364772i	$0.881147\pi$
$860$	−63.9126	−	411.823i	−0.0743170	−	0.478864i
$861$	714.291			0.829606
$862$	−435.149	+	33.5654i	−0.504813	+	0.0389390i
$863$		−	443.012i		−	0.513340i	−0.966499	−	0.256670i	$-0.917375\pi$
$863$		−	443.012i		−	0.513340i	0.966499	−	0.256670i	$-0.0826253\pi$
$864$	842.274	−	341.225i	0.974854	−	0.394936i
$865$	216.757			0.250587
$866$	−120.829	−	1566.46i	−0.139526	−	1.80884i
$867$			558.932i			0.644673i
$868$	−293.691	+	45.5792i	−0.338354	+	0.0525106i
$869$	−574.160			−0.660713
$870$	−26.8098	+	2.06799i	−0.0308159	+	0.00237700i
$871$		−	236.480i		−	0.271504i
$872$	205.467	+	873.788i	0.235627	+	1.00205i
$873$	479.012			0.548696
$874$	−28.7779	−	373.083i	−0.0329267	−	0.426868i
$875$		−	1195.35i		−	1.36611i
$876$	−136.221	−	877.745i	−0.155504	−	1.00199i
$877$	1404.15			1.60108			0.800542	−	0.599276i	$-0.204545\pi$
$877$	1404.15			1.60108			0.800542	+	0.599276i	$0.204545\pi$
$878$	−982.106	+	75.7552i	−1.11857	+	0.0862815i
$879$		−	80.9424i		−	0.0920846i
$880$	164.196	+	516.261i	0.186587	+	0.586661i
$881$	1183.20			1.34302			0.671511	−	0.740994i	$-0.265645\pi$
$881$	1183.20			1.34302			0.671511	+	0.740994i	$0.265645\pi$
$882$	−93.4810	−	1211.91i	−0.105988	−	1.37404i
$883$			1290.52i			1.46152i	0.682633	+	0.730761i	$0.260835\pi$
$883$			1290.52i			1.46152i	−0.682633	+	0.730761i	$0.739165\pi$
$884$	134.015	−	20.7983i	0.151600	−	0.0235275i
$885$	−317.648			−0.358924
$886$	1147.46	−	88.5101i	1.29511	−	0.0998985i
$887$		−	261.477i		−	0.294788i	−0.989078	−	0.147394i	$-0.952911\pi$
$887$		−	261.477i		−	0.294788i	0.989078	−	0.147394i	$-0.0470886\pi$
$888$	−632.292	+	148.680i	−0.712041	+	0.167433i
$889$	1210.73			1.36191
$890$	30.1177	+	390.452i	0.0338401	+	0.438711i
$891$		−	287.793i		−	0.323000i
$892$	78.8478	+	508.058i	0.0883944	+	0.569572i
$893$	−678.791			−0.760125
$894$	−507.456	+	39.1429i	−0.567624	+	0.0437840i
$895$			371.766i			0.415381i
$896$	1466.08	−	876.585i	1.63625	−	0.978332i
$897$	−270.068			−0.301079
$898$	4.99100	+	64.7043i	0.00555790	+	0.0720538i
$899$			18.6565i			0.0207525i
$900$	395.431	−	61.3686i	0.439368	−	0.0681874i
$901$	−413.891			−0.459368
$902$	−900.681	+	69.4745i	−0.998538	+	0.0770227i
$903$			1487.27i			1.64703i
$904$	−22.5250	−	95.7922i	−0.0249171	−	0.105965i
$905$	28.7130			0.0317271
$906$	30.6802	+	397.745i	0.0338634	+	0.439012i
$907$		−	324.616i		−	0.357901i	−0.983858	−	0.178950i	$-0.942730\pi$
$907$		−	324.616i		−	0.357901i	0.983858	−	0.178950i	$-0.0572701\pi$
$908$	−34.5765	−	222.795i	−0.0380799	−	0.245369i
$909$	434.519			0.478019
$910$	−398.719	+	30.7554i	−0.438153	+	0.0337971i
$911$			1283.61i			1.40902i	0.709696	+	0.704508i	$0.248832\pi$
$911$			1283.61i			1.40902i	−0.709696	+	0.704508i	$0.751168\pi$
$912$	−350.732	+	111.550i	−0.384574	+	0.122313i
$913$	−750.617			−0.822143
$914$	94.8974	+	1230.27i	0.103826	+	1.34603i
$915$			87.0192i			0.0951029i
$916$	972.519	−	150.929i	1.06170	−	0.164770i
$917$	1848.17			2.01545
$918$	−248.183	+	19.1437i	−0.270352	+	0.0208537i
$919$			4.77862i			0.00519981i	0.999997	+	0.00259990i	$0.000827576\pi$
$919$			4.77862i			0.00519981i	−0.999997	+	0.00259990i	$0.999172\pi$
$920$	−254.150	+	59.7619i	−0.276250	+	0.0649586i
$921$	−795.502			−0.863737
$922$	−46.9039	−	608.072i	−0.0508720	−	0.659514i
$923$		−	221.838i		−	0.240344i
$924$	−296.492	−	1910.45i	−0.320879	−	2.06759i
$925$	−832.770			−0.900292
$926$	−1577.54	+	121.684i	−1.70360	+	0.131408i
$927$		−	797.780i		−	0.860604i
$928$	−40.2612	−	99.3802i	−0.0433850	−	0.107091i
$929$	939.539			1.01134			0.505672	−	0.862726i	$-0.331244\pi$
$929$	939.539			1.01134			0.505672	+	0.862726i	$0.331244\pi$
$930$	−3.43620	−	44.5476i	−0.00369484	−	0.0479007i
$931$			1433.30i			1.53953i
$932$	1073.53	−	166.606i	1.15186	−	0.178762i
$933$	1199.10			1.28521
$934$	−696.461	+	53.7218i	−0.745675	+	0.0575180i
$935$		−	148.389i		−	0.158705i
$936$	−66.6979	−	283.646i	−0.0712585	−	0.303041i
$937$	508.334			0.542512			0.271256	−	0.962507i	$-0.412561\pi$
$937$	508.334			0.542512			0.271256	+	0.962507i	$0.412561\pi$
$938$	62.7444	+	813.432i	0.0668917	+	0.867198i
$939$		−	228.528i		−	0.243373i
$940$	72.6318	+	468.006i	0.0772679	+	0.497878i
$941$	271.168			0.288170			0.144085	−	0.989565i	$-0.453976\pi$
$941$	271.168			0.288170			0.144085	+	0.989565i	$0.453976\pi$
$942$	636.691	−	49.1115i	0.675893	−	0.0521353i
$943$		−	435.353i		−	0.461668i
$944$	−383.913	−	1207.09i	−0.406688	−	1.27870i
$945$	733.999			0.776718
$946$	−144.657	−	1875.36i	−0.152914	−	1.98241i
$947$			694.708i			0.733588i	0.930302	+	0.366794i	$0.119545\pi$
$947$			694.708i			0.733588i	−0.930302	+	0.366794i	$0.880455\pi$
$948$	−268.939	+	41.7377i	−0.283690	+	0.0440272i
$949$	−829.243			−0.873808
$950$	−470.470	+	36.2899i	−0.495231	+	0.0381999i
$951$			56.9481i			0.0598823i
$952$	−455.458	+	107.099i	−0.478422	+	0.112498i
$953$	−1489.75			−1.56322			−0.781611	−	0.623767i	$-0.785602\pi$
$953$	−1489.75			−1.56322			−0.781611	+	0.623767i	$0.785602\pi$
$954$	68.3904	+	886.627i	0.0716880	+	0.929378i
$955$		−	415.623i		−	0.435207i
$956$	112.485	+	724.799i	0.117662	+	0.758158i
$957$	−121.360			−0.126813
$958$	−231.547	+	17.8605i	−0.241698	+	0.0186435i
$959$			2541.03i			2.64967i
$960$	114.439	+	229.883i	0.119207	+	0.239461i
$961$	−31.0000			−0.0322581
$962$	46.6354	+	604.591i	0.0484776	+	0.628473i
$963$			423.497i			0.439768i
$964$	1228.94	−	190.724i	1.27483	−	0.197846i
$965$	−290.221			−0.300747
$966$	928.964	−	71.6561i	0.961660	−	0.0741781i
$967$		−	895.024i		−	0.925567i	−0.886471	−	0.462784i	$-0.846851\pi$
$967$		−	895.024i		−	0.925567i	0.886471	−	0.462784i	$-0.153149\pi$
$968$	338.101	+	1437.84i	0.349278	+	1.48537i
$969$	100.811			0.104036
$970$	30.3093	+	392.936i	0.0312467	+	0.405089i
$971$			451.132i			0.464606i	0.972644	+	0.232303i	$0.0746260\pi$
$971$			451.132i			0.464606i	−0.972644	+	0.232303i	$0.925374\pi$
$972$	135.868	+	875.467i	0.139781	+	0.900686i
$973$	−1829.16			−1.87991
$974$	161.067	−	12.4240i	0.165367	−	0.0127557i
$975$			340.564i			0.349297i
$976$	−330.681	+	105.173i	−0.338812	+	0.107759i
$977$	−100.236			−0.102596			−0.0512979	−	0.998683i	$-0.516336\pi$
$977$	−100.236			−0.102596			−0.0512979	+	0.998683i	$0.516336\pi$
$978$	6.94879	+	90.0856i	0.00710511	+	0.0921120i
$979$			1767.47i			1.80538i
$980$	988.219	−	153.366i	1.00839	−	0.156496i
$981$	−528.254			−0.538486
$982$	508.579	−	39.2295i	0.517901	−	0.0399485i
$983$			1034.11i			1.05199i	0.850488	+	0.525995i	$0.176307\pi$
$983$			1034.11i			1.05199i	−0.850488	+	0.525995i	$0.823693\pi$
$984$	−416.832	+	98.0158i	−0.423610	+	0.0996096i
$985$	377.449			0.383197
$986$	2.25878	+	29.2832i	0.00229085	+	0.0296990i
$987$		−	1690.17i		−	1.71243i
$988$	52.6930	+	339.529i	0.0533330	+	0.343653i
$989$	906.475			0.916557
$990$	−317.875	+	24.5194i	−0.321086	+	0.0247671i
$991$			1159.06i			1.16958i	0.811183	+	0.584792i	$0.198824\pi$
$991$			1159.06i			1.16958i	−0.811183	+	0.584792i	$0.801176\pi$
$992$	165.132	−	66.8988i	0.166464	−	0.0674383i
$993$	−157.538			−0.158648
$994$	58.8594	+	763.065i	0.0592147	+	0.767671i
$995$			366.449i			0.368290i
$996$	−351.591	+	54.5650i	−0.353003	+	0.0547841i
$997$	−254.324			−0.255090			−0.127545	−	0.991833i	$-0.540710\pi$
$997$	−254.324			−0.255090			−0.127545	+	0.991833i	$0.540710\pi$
$998$	−535.504	+	41.3064i	−0.536577	+	0.0413891i
$999$		−	1112.99i		−	1.11410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.3.b.a.63.18	yes	30
4.3	odd	2	inner	124.3.b.a.63.17	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.3.b.a.63.17	✓	30	4.3	odd	2	inner
124.3.b.a.63.18	yes	30	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.153814 + 1.99408i) q^{2} -2.07170i q^{3} +(-3.95268 + 0.613434i) q^{4} +1.93675 q^{5} +(4.13114 - 0.318657i) q^{6} +13.3450i q^{7} +(-1.83121 - 7.78760i) q^{8} +4.70804 q^{9} +O(q^{10})\)	\(q+(0.153814 + 1.99408i) q^{2} -2.07170i q^{3} +(-3.95268 + 0.613434i) q^{4} +1.93675 q^{5} +(4.13114 - 0.318657i) q^{6} +13.3450i q^{7} +(-1.83121 - 7.78760i) q^{8} +4.70804 q^{9} +(0.297900 + 3.86204i) q^{10} +17.4823i q^{11} +(1.27085 + 8.18879i) q^{12} +7.73630 q^{13} +(-26.6109 + 2.05264i) q^{14} -4.01238i q^{15} +(15.2474 - 4.84942i) q^{16} -4.38255 q^{17} +(0.724163 + 9.38820i) q^{18} -11.1033i q^{19} +(-7.65537 + 1.18807i) q^{20} +27.6468 q^{21} +(-34.8611 + 2.68903i) q^{22} -16.8505i q^{23} +(-16.1336 + 3.79373i) q^{24} -21.2490 q^{25} +(1.18995 + 15.4268i) q^{26} -28.3990i q^{27} +(-8.18626 - 52.7484i) q^{28} -3.35081 q^{29} +(8.00099 - 0.617160i) q^{30} -5.56776i q^{31} +(12.0154 + 29.6586i) q^{32} +36.2182 q^{33} +(-0.674098 - 8.73915i) q^{34} +25.8459i q^{35} +(-18.6094 + 2.88807i) q^{36} +39.1911 q^{37} +(22.1408 - 1.70784i) q^{38} -16.0273i q^{39} +(-3.54661 - 15.0827i) q^{40} +25.8363 q^{41} +(4.25247 + 55.1299i) q^{42} +53.7953i q^{43} +(-10.7243 - 69.1021i) q^{44} +9.11832 q^{45} +(33.6011 - 2.59184i) q^{46} -61.1343i q^{47} +(-10.0466 - 31.5881i) q^{48} -129.088 q^{49} +(-3.26839 - 42.3721i) q^{50} +9.07935i q^{51} +(-30.5791 + 4.74571i) q^{52} +94.4405 q^{53} +(56.6298 - 4.36817i) q^{54} +33.8590i q^{55} +(103.925 - 24.4375i) q^{56} -23.0027 q^{57} +(-0.515402 - 6.68177i) q^{58} -79.1669i q^{59} +(2.46133 + 15.8597i) q^{60} -21.6877 q^{61} +(11.1025 - 0.856400i) q^{62} +62.8287i q^{63} +(-57.2933 + 28.5215i) q^{64} +14.9833 q^{65} +(5.57087 + 72.2219i) q^{66} -30.5676i q^{67} +(17.3228 - 2.68841i) q^{68} -34.9091 q^{69} +(-51.5388 + 3.97547i) q^{70} -28.6749i q^{71} +(-8.62143 - 36.6643i) q^{72} -107.189 q^{73} +(6.02813 + 78.1500i) q^{74} +44.0216i q^{75} +(6.81113 + 43.8878i) q^{76} -233.301 q^{77} +(31.9597 - 2.46523i) q^{78} +32.8423i q^{79} +(29.5305 - 9.39213i) q^{80} -16.4619 q^{81} +(3.97398 + 51.5195i) q^{82} +42.9357i q^{83} +(-109.279 + 16.9595i) q^{84} -8.48793 q^{85} +(-107.272 + 8.27447i) q^{86} +6.94188i q^{87} +(136.145 - 32.0139i) q^{88} +101.100 q^{89} +(1.40253 + 18.1826i) q^{90} +103.241i q^{91} +(10.3366 + 66.6045i) q^{92} -11.5348 q^{93} +(121.906 - 9.40331i) q^{94} -21.5043i q^{95} +(61.4438 - 24.8923i) q^{96} +101.743 q^{97} +(-19.8556 - 257.412i) q^{98} +82.3076i 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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