LMFDB - Embedded newform 175.3.j.b.24.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,3,Mod(24,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("175.24");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	175.j (of order $6$, degree $2$, not 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:	$4.76840462631$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			24.12
Character	$\chi$	$=$	175.24
Dual form			175.3.j.b.124.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.08079 - 1.77870i) q^{2} +(-1.21658 + 2.10717i) q^{3} +(4.32752 - 7.49548i) q^{4} +8.65567i q^{6} +(4.46146 - 5.39402i) q^{7} -16.5598i q^{8} +(1.53989 + 2.66717i) q^{9} +O(q^{10})$	\(q+(3.08079 - 1.77870i) q^{2} +(-1.21658 + 2.10717i) q^{3} +(4.32752 - 7.49548i) q^{4} +8.65567i q^{6} +(4.46146 - 5.39402i) q^{7} -16.5598i q^{8} +(1.53989 + 2.66717i) q^{9} +(6.95056 - 12.0387i) q^{11} +(10.5295 + 18.2376i) q^{12} +0.702771 q^{13} +(4.15050 - 24.5534i) q^{14} +(-12.1447 - 21.0353i) q^{16} +(-13.6326 + 23.6124i) q^{17} +(9.48815 + 5.47799i) q^{18} +(-2.21652 + 1.27971i) q^{19} +(5.93841 + 15.9633i) q^{21} -49.4517i q^{22} +(-28.5402 + 16.4777i) q^{23} +(34.8942 + 20.1462i) q^{24} +(2.16509 - 1.25001i) q^{26} -29.3919 q^{27} +(-21.1237 - 56.7834i) q^{28} -3.39850 q^{29} +(20.7530 + 11.9818i) q^{31} +(-17.4660 - 10.0840i) q^{32} +(16.9118 + 29.2920i) q^{33} +96.9930i q^{34} +26.6556 q^{36} +(-20.6253 + 11.9080i) q^{37} +(-4.55242 + 7.88502i) q^{38} +(-0.854973 + 1.48086i) q^{39} -25.1015i q^{41} +(46.6888 + 38.6169i) q^{42} +25.1201i q^{43} +(-60.1573 - 104.196i) q^{44} +(-58.6176 + 101.529i) q^{46} +(-3.23167 - 5.59742i) q^{47} +59.0998 q^{48} +(-9.19081 - 48.1303i) q^{49} +(-33.1702 - 57.4524i) q^{51} +(3.04125 - 5.26760i) q^{52} +(-31.2139 - 18.0214i) q^{53} +(-90.5504 + 52.2793i) q^{54} +(-89.3236 - 73.8807i) q^{56} -6.22744i q^{57} +(-10.4701 + 6.04490i) q^{58} +(32.0135 + 18.4830i) q^{59} +(-30.3577 + 17.5270i) q^{61} +85.2476 q^{62} +(21.2569 + 3.59326i) q^{63} +25.4125 q^{64} +(104.203 + 60.1617i) q^{66} +(39.6006 + 22.8634i) q^{67} +(117.991 + 204.366i) q^{68} -80.1854i q^{69} +80.4090 q^{71} +(44.1676 - 25.5002i) q^{72} +(44.9121 - 77.7901i) q^{73} +(-42.3615 + 73.3722i) q^{74} +22.1518i q^{76} +(-33.9274 - 91.2017i) q^{77} +6.08295i q^{78} +(0.0415972 + 0.0720485i) q^{79} +(21.8985 - 37.9293i) q^{81} +(-44.6479 - 77.3324i) q^{82} +95.3085 q^{83} +(145.351 + 24.5701i) q^{84} +(44.6810 + 77.3898i) q^{86} +(4.13453 - 7.16122i) q^{87} +(-199.358 - 115.100i) q^{88} +(-104.811 + 60.5126i) q^{89} +(3.13538 - 3.79076i) q^{91} +285.230i q^{92} +(-50.4952 + 29.1534i) q^{93} +(-19.9122 - 11.4963i) q^{94} +(42.4973 - 24.5358i) q^{96} -0.362083 q^{97} +(-113.924 - 131.932i) q^{98} +42.8124 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{4} - 28 q^{9}+O(q^{10}) $ 24 * q + 20 * q^4 - 28 * q^9	$ 24 q + 20 q^{4} - 28 q^{9} - 28 q^{11} + 4 q^{14} - 44 q^{16} + 60 q^{19} - 168 q^{21} + 72 q^{24} + 132 q^{26} - 128 q^{29} + 264 q^{31} + 312 q^{36} + 48 q^{39} - 12 q^{44} - 428 q^{46} + 48 q^{49} - 264 q^{51} - 336 q^{54} - 920 q^{56} - 144 q^{59} + 144 q^{61} + 280 q^{64} + 1488 q^{66} - 16 q^{71} - 100 q^{74} + 24 q^{79} - 620 q^{81} + 552 q^{84} - 80 q^{86} - 408 q^{89} - 960 q^{91} + 84 q^{94} + 1080 q^{96} + 88 q^{99}+O(q^{100}) $ 24 * q + 20 * q^4 - 28 * q^9 - 28 * q^11 + 4 * q^14 - 44 * q^16 + 60 * q^19 - 168 * q^21 + 72 * q^24 + 132 * q^26 - 128 * q^29 + 264 * q^31 + 312 * q^36 + 48 * q^39 - 12 * q^44 - 428 * q^46 + 48 * q^49 - 264 * q^51 - 336 * q^54 - 920 * q^56 - 144 * q^59 + 144 * q^61 + 280 * q^64 + 1488 * q^66 - 16 * q^71 - 100 * q^74 + 24 * q^79 - 620 * q^81 + 552 * q^84 - 80 * q^86 - 408 * q^89 - 960 * q^91 + 84 * q^94 + 1080 * q^96 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	3.08079	−	1.77870i	1.54040	−	0.889348i	0.541582	−	0.840648i	$-0.317826\pi$
$2$	3.08079	−	1.77870i	1.54040	−	0.889348i	0.998813	−	0.0486998i	$-0.0155078\pi$
$3$	−1.21658	+	2.10717i	−0.405525	+	0.702390i	−0.994382	−	0.105847i	$-0.966245\pi$
$3$	−1.21658	+	2.10717i	−0.405525	+	0.702390i	0.588857	+	0.808237i	$0.299578\pi$
$4$	4.32752	−	7.49548i	1.08188	−	1.87387i
$5$		0			0
$5$		0			0
$6$			8.65567i			1.44261i
$7$	4.46146	−	5.39402i	0.637351	−	0.770574i
$7$	4.46146	−	5.39402i	0.637351	−	0.770574i
$8$		−	16.5598i		−	2.06997i
$9$	1.53989	+	2.66717i	0.171099	+	0.296352i
$10$		0			0
$11$	6.95056	−	12.0387i	0.631869	−	1.09443i	−0.355300	−	0.934752i	$-0.615621\pi$
$11$	6.95056	−	12.0387i	0.631869	−	1.09443i	0.987169	−	0.159677i	$-0.0510453\pi$
$12$	10.5295	+	18.2376i	0.877458	+	1.51980i
$13$	0.702771			0.0540593			0.0270296	−	0.999635i	$-0.491395\pi$
$13$	0.702771			0.0540593			0.0270296	+	0.999635i	$0.491395\pi$
$14$	4.15050	−	24.5534i	0.296464	−	1.75381i
$15$		0			0
$16$	−12.1447	−	21.0353i	−0.759045	−	1.31470i
$17$	−13.6326	+	23.6124i	−0.801918	+	1.38896i	0.116435	+	0.993198i	$0.462853\pi$
$17$	−13.6326	+	23.6124i	−0.801918	+	1.38896i	−0.918352	+	0.395764i	$0.870480\pi$
$18$	9.48815	+	5.47799i	0.527120	+	0.304333i
$19$	−2.21652	+	1.27971i	−0.116659	+	0.0673530i	−0.557194	−	0.830382i	$-0.688122\pi$
$19$	−2.21652	+	1.27971i	−0.116659	+	0.0673530i	0.440535	+	0.897735i	$0.354789\pi$
$20$		0			0
$21$	5.93841	+	15.9633i	0.282782	+	0.760156i
$22$		−	49.4517i		−	2.24781i
$23$	−28.5402	+	16.4777i	−1.24088	+	0.716422i	−0.969273	−	0.245987i	$-0.920888\pi$
$23$	−28.5402	+	16.4777i	−1.24088	+	0.716422i	−0.271605	+	0.962409i	$0.587555\pi$
$24$	34.8942	+	20.1462i	1.45393	+	0.839425i
$25$		0			0
$26$	2.16509	−	1.25001i	0.0832727	−	0.0480775i
$27$	−29.3919			−1.08859
$28$	−21.1237	−	56.7834i	−0.754418	−	2.02798i
$29$	−3.39850			−0.117190			−0.0585949	−	0.998282i	$-0.518662\pi$
$29$	−3.39850			−0.117190			−0.0585949	+	0.998282i	$0.518662\pi$
$30$		0			0
$31$	20.7530	+	11.9818i	0.669452	+	0.386508i	0.795869	−	0.605469i	$-0.207014\pi$
$31$	20.7530	+	11.9818i	0.669452	+	0.386508i	−0.126417	+	0.991977i	$0.540348\pi$
$32$	−17.4660	−	10.0840i	−0.545811	−	0.315124i
$33$	16.9118	+	29.2920i	0.512478	+	0.887637i
$34$			96.9930i			2.85273i
$35$		0			0
$36$	26.6556			0.740433
$37$	−20.6253	+	11.9080i	−0.557440	+	0.321838i	−0.752117	−	0.659029i	$-0.770967\pi$
$37$	−20.6253	+	11.9080i	−0.557440	+	0.321838i	0.194677	+	0.980867i	$0.437634\pi$
$38$	−4.55242	+	7.88502i	−0.119800	+	0.207500i
$39$	−0.854973	+	1.48086i	−0.0219224	+	0.0379707i
$40$		0			0
$41$		−	25.1015i		−	0.612231i	−0.951994	−	0.306116i	$-0.900971\pi$
$41$		−	25.1015i		−	0.612231i	0.951994	−	0.306116i	$-0.0990295\pi$
$42$	46.6888	+	38.6169i	1.11164	+	0.919450i
$43$			25.1201i			0.584189i	0.956390	+	0.292094i	$0.0943521\pi$
$43$			25.1201i			0.584189i	−0.956390	+	0.292094i	$0.905648\pi$
$44$	−60.1573	−	104.196i	−1.36721	−	2.36808i
$45$		0			0
$46$	−58.6176	+	101.529i	−1.27430	+	2.20715i
$47$	−3.23167	−	5.59742i	−0.0687590	−	0.119094i	0.829596	−	0.558364i	$-0.188571\pi$
$47$	−3.23167	−	5.59742i	−0.0687590	−	0.119094i	−0.898355	+	0.439270i	$0.855237\pi$
$48$	59.0998			1.23125
$49$	−9.19081	−	48.1303i	−0.187568	−	0.982252i
$50$		0			0
$51$	−33.1702	−	57.4524i	−0.650395	−	1.12652i
$52$	3.04125	−	5.26760i	0.0584856	−	0.101300i
$53$	−31.2139	−	18.0214i	−0.588942	−	0.340026i	0.175737	−	0.984437i	$-0.443769\pi$
$53$	−31.2139	−	18.0214i	−0.588942	−	0.340026i	−0.764679	+	0.644412i	$0.777102\pi$
$54$	−90.5504	+	52.2793i	−1.67686	+	0.968135i
$55$		0			0
$56$	−89.3236	−	73.8807i	−1.59506	−	1.31930i
$57$		−	6.22744i		−	0.109253i
$58$	−10.4701	+	6.04490i	−0.180518	+	0.104222i
$59$	32.0135	+	18.4830i	0.542602	+	0.313272i	0.746133	−	0.665797i	$-0.231908\pi$
$59$	32.0135	+	18.4830i	0.542602	+	0.313272i	−0.203531	+	0.979069i	$0.565242\pi$
$60$		0			0
$61$	−30.3577	+	17.5270i	−0.497667	+	0.287328i	−0.727750	−	0.685843i	$-0.759434\pi$
$61$	−30.3577	+	17.5270i	−0.497667	+	0.287328i	0.230083	+	0.973171i	$0.426100\pi$
$62$	85.2476			1.37496
$63$	21.2569	+	3.59326i	0.337411	+	0.0570359i
$64$	25.4125			0.397070
$65$		0			0
$66$	104.203	+	60.1617i	1.57884	+	0.911541i
$67$	39.6006	+	22.8634i	0.591053	+	0.341245i	0.765514	−	0.643419i	$-0.222485\pi$
$67$	39.6006	+	22.8634i	0.591053	+	0.341245i	−0.174461	+	0.984664i	$0.555818\pi$
$68$	117.991	+	204.366i	1.73516	+	3.00538i
$69$		−	80.1854i		−	1.16211i
$70$		0			0
$71$	80.4090			1.13252			0.566261	−	0.824226i	$-0.308389\pi$
$71$	80.4090			1.13252			0.566261	+	0.824226i	$0.308389\pi$
$72$	44.1676	−	25.5002i	0.613439	−	0.354169i
$73$	44.9121	−	77.7901i	0.615235	−	1.06562i	−0.375109	−	0.926981i	$-0.622395\pi$
$73$	44.9121	−	77.7901i	0.615235	−	1.06562i	0.990343	−	0.138637i	$-0.0442720\pi$
$74$	−42.3615	+	73.3722i	−0.572452	+	0.991517i
$75$		0			0
$76$			22.1518i			0.291471i
$77$	−33.9274	−	91.2017i	−0.440616	−	1.18444i
$78$			6.08295i			0.0779865i
$79$	0.0415972	+	0.0720485i	0.000526547	+	0.000912006i	0.866289	−	0.499544i	$-0.166499\pi$
$79$	0.0415972	+	0.0720485i	0.000526547	+	0.000912006i	−0.865762	+	0.500456i	$0.833166\pi$
$80$		0			0
$81$	21.8985	−	37.9293i	0.270352	−	0.468263i
$82$	−44.6479	−	77.3324i	−0.544487	−	0.943079i
$83$	95.3085			1.14830			0.574148	−	0.818752i	$-0.305334\pi$
$83$	95.3085			1.14830			0.574148	+	0.818752i	$0.305334\pi$
$84$	145.351	+	24.5701i	1.73037	+	0.292501i
$85$		0			0
$86$	44.6810	+	77.3898i	0.519547	+	0.899881i
$87$	4.13453	−	7.16122i	0.0475234	−	0.0823129i
$88$	−199.358	−	115.100i	−2.26544	−	1.30795i
$89$	−104.811	+	60.5126i	−1.17765	+	0.679917i	−0.955470	−	0.295089i	$-0.904651\pi$
$89$	−104.811	+	60.5126i	−1.17765	+	0.679917i	−0.222180	+	0.975006i	$0.571317\pi$
$90$		0			0
$91$	3.13538	−	3.79076i	0.0344547	−	0.0416567i
$92$			285.230i			3.10033i
$93$	−50.4952	+	29.1534i	−0.542959	+	0.313477i
$94$	−19.9122	−	11.4963i	−0.211832	−	0.122301i
$95$		0			0
$96$	42.4973	−	24.5358i	0.442680	−	0.255581i
$97$	−0.362083			−0.00373282			−0.00186641	−	0.999998i	$-0.500594\pi$
$97$	−0.362083			−0.00373282			−0.00186641	+	0.999998i	$0.500594\pi$
$98$	−113.924	−	131.932i	−1.16249	−	1.34624i
$99$	42.8124			0.432448
$100$		0			0
$101$	−139.134	−	80.3290i	−1.37756	−	0.795336i	−0.385697	−	0.922625i	$-0.626039\pi$
$101$	−139.134	−	80.3290i	−1.37756	−	0.795336i	−0.991866	+	0.127289i	$0.959372\pi$
$102$	−204.381	−	117.999i	−2.00373	−	1.15686i
$103$	−71.7266	−	124.234i	−0.696375	−	1.20616i	−0.969715	−	0.244239i	$-0.921462\pi$
$103$	−71.7266	−	124.234i	−0.696375	−	1.20616i	0.273340	−	0.961917i	$-0.411871\pi$
$104$		−	11.6377i		−	0.111901i
$105$		0			0
$106$	−128.218			−1.20960
$107$	−54.9609	+	31.7317i	−0.513653	+	0.296558i	−0.734334	−	0.678788i	$-0.762505\pi$
$107$	−54.9609	+	31.7317i	−0.513653	+	0.296558i	0.220681	+	0.975346i	$0.429172\pi$
$108$	−127.194	+	220.306i	−1.17772	+	2.03987i
$109$	28.3546	−	49.1115i	0.260134	−	0.450565i	−0.706144	−	0.708069i	$-0.749567\pi$
$109$	28.3546	−	49.1115i	0.260134	−	0.450565i	0.966277	+	0.257504i	$0.0829001\pi$
$110$		0			0
$111$		−	57.9480i		−	0.522054i
$112$	−167.648	−	28.3391i	−1.49685	−	0.253028i
$113$		−	53.1456i		−	0.470315i	−0.971957	−	0.235157i	$-0.924439\pi$
$113$		−	53.1456i		−	0.470315i	0.971957	−	0.235157i	$-0.0755606\pi$
$114$	−11.0767	−	19.1854i	−0.0971642	−	0.168293i
$115$		0			0
$116$	−14.7071	+	25.4734i	−0.126785	+	0.219598i
$117$	1.08219	+	1.87441i	0.00924948	+	0.0160206i
$118$	131.503			1.11443
$119$	66.5442	+	178.880i	0.559195	+	1.50319i
$120$		0			0
$121$	−36.1206	−	62.5627i	−0.298517	−	0.517047i
$122$	−62.3504	+	107.994i	−0.511069	+	0.885198i
$123$	52.8931	+	30.5379i	0.430025	+	0.248275i
$124$	179.618	−	103.702i	1.44853	−	0.836310i
$125$		0			0
$126$	71.8793	−	26.7394i	0.570471	−	0.212218i
$127$		−	39.1961i		−	0.308630i	−0.988022	−	0.154315i	$-0.950683\pi$
$127$		−	39.1961i		−	0.308630i	0.988022	−	0.154315i	$-0.0493171\pi$
$128$	148.154	−	85.5369i	1.15746	−	0.668257i
$129$	−52.9323	−	30.5605i	−0.410328	−	0.236903i
$130$		0			0
$131$	−46.8501	+	27.0489i	−0.357634	+	0.206480i	−0.668043	−	0.744123i	$-0.732868\pi$
$131$	−46.8501	+	27.0489i	−0.357634	+	0.206480i	0.310408	+	0.950603i	$0.399534\pi$
$132$	292.744			2.21775
$133$	−2.98614	+	17.6653i	−0.0224521	+	0.132822i
$134$	162.668			1.21394
$135$		0			0
$136$	391.015	+	225.753i	2.87511	+	1.65995i
$137$	71.5927	+	41.3341i	0.522574	+	0.301708i	0.737987	−	0.674815i	$-0.235776\pi$
$137$	71.5927	+	41.3341i	0.522574	+	0.301708i	−0.215413	+	0.976523i	$0.569110\pi$
$138$	−142.625	−	247.035i	−1.03352	−	1.79011i
$139$		−	98.5453i		−	0.708959i	−0.935064	−	0.354480i	$-0.884658\pi$
$139$		−	98.5453i		−	0.708959i	0.935064	−	0.354480i	$-0.115342\pi$
$140$		0			0
$141$	15.7263			0.111534
$142$	247.723	−	143.023i	1.74453	−	1.00721i
$143$	4.88465	−	8.46046i	0.0341584	−	0.0591641i
$144$	37.4030	−	64.7839i	0.259743	−	0.449889i
$145$		0			0
$146$		−	319.540i		−	2.18863i
$147$	112.600	+	39.1876i	0.765987	+	0.266582i
$148$			206.129i			1.39276i
$149$	37.5964	+	65.1189i	0.252325	+	0.437040i	0.964166	−	0.265301i	$-0.0854715\pi$
$149$	37.5964	+	65.1189i	0.252325	+	0.437040i	−0.711841	+	0.702341i	$0.752138\pi$
$150$		0			0
$151$	−77.4963	+	134.227i	−0.513220	+	0.888923i	0.486662	+	0.873590i	$0.338214\pi$
$151$	−77.4963	+	134.227i	−0.513220	+	0.888923i	−0.999882	+	0.0153332i	$0.995119\pi$
$152$	21.1916	+	36.7050i	0.139419	+	0.241480i
$153$	−83.9708			−0.548829
$154$	−266.743	−	220.627i	−1.73210	−	1.43264i
$155$		0			0
$156$	7.39982	+	12.8169i	0.0474347	+	0.0821594i
$157$	58.0108	−	100.478i	0.369495	−	0.639985i	−0.619991	−	0.784609i	$-0.712864\pi$
$157$	58.0108	−	100.478i	0.369495	−	0.639985i	0.989487	+	0.144624i	$0.0461973\pi$
$158$	0.256305	+	0.147978i	0.00162218	+	0.000936567i
$159$	75.9481	−	43.8487i	0.477661	−	0.275778i
$160$		0			0
$161$	−38.4499	+	227.461i	−0.238819	+	1.41280i
$162$		−	155.803i		−	0.961746i
$163$	164.709	−	95.0947i	1.01048	−	0.583403i	0.0991507	−	0.995072i	$-0.468387\pi$
$163$	164.709	−	95.0947i	1.01048	−	0.583403i	0.911333	+	0.411669i	$0.135054\pi$
$164$	−188.148	−	108.627i	−1.14724	−	0.662360i
$165$		0			0
$166$	293.626	−	169.525i	1.76883	−	1.02123i
$167$	−259.403			−1.55331			−0.776656	−	0.629925i	$-0.783086\pi$
$167$	−259.403			−1.55331			−0.776656	+	0.629925i	$0.783086\pi$
$168$	264.348	−	98.3387i	1.57350	−	0.585349i
$169$	−168.506			−0.997078
$170$		0			0
$171$	−6.82638	−	3.94121i	−0.0399204	−	0.0230480i
$172$	188.287	+	108.708i	1.09469	+	0.632021i
$173$	113.265	+	196.181i	0.654710	+	1.13399i	0.981966	+	0.189056i	$0.0605427\pi$
$173$	113.265	+	196.181i	0.654710	+	1.13399i	−0.327256	+	0.944936i	$0.606124\pi$
$174$		−	29.4163i		−	0.169059i
$175$		0			0
$176$	−337.650			−1.91847
$177$	−77.8938	+	44.9720i	−0.440078	+	0.254079i
$178$	−215.267	+	372.853i	−1.20936	+	2.09468i
$179$	93.5046	−	161.955i	0.522372	−	0.904775i	−0.477289	−	0.878746i	$-0.658381\pi$
$179$	93.5046	−	161.955i	0.522372	−	0.904775i	0.999661	−	0.0260288i	$-0.00828615\pi$
$180$		0			0
$181$		−	183.025i		−	1.01119i	−0.862771	−	0.505595i	$-0.831273\pi$
$181$		−	183.025i		−	1.01119i	0.862771	−	0.505595i	$-0.168727\pi$
$182$	2.91685	−	17.2554i	0.0160267	−	0.0948100i
$183$		−	85.2917i		−	0.466075i
$184$	272.867	+	472.619i	1.48297	+	2.56858i
$185$		0			0
$186$	−103.710	+	179.631i	−0.557581	+	0.965759i
$187$	189.508	+	328.238i	1.01341	+	1.75528i
$188$	−55.9404			−0.297555
$189$	−131.131	+	158.540i	−0.693814	+	0.838839i
$190$		0			0
$191$	98.7648	+	171.066i	0.517093	+	0.895631i	0.999803	+	0.0198511i	$0.00631922\pi$
$191$	98.7648	+	171.066i	0.517093	+	0.895631i	−0.482710	+	0.875780i	$0.660347\pi$
$192$	−30.9162	+	53.5484i	−0.161022	+	0.278898i
$193$	−73.3116	−	42.3264i	−0.379853	−	0.219308i	0.297902	−	0.954597i	$-0.403713\pi$
$193$	−73.3116	−	42.3264i	−0.379853	−	0.219308i	−0.677754	+	0.735289i	$0.737047\pi$
$194$	−1.11550	+	0.644036i	−0.00575002	+	0.00331977i
$195$		0			0
$196$	−400.533	−	139.395i	−2.04354	−	0.711200i
$197$		−	247.330i		−	1.25548i	−0.778421	−	0.627742i	$-0.783979\pi$
$197$		−	247.330i		−	1.25548i	0.778421	−	0.627742i	$-0.216021\pi$
$198$	131.896	−	76.1502i	0.666141	−	0.384597i
$199$	106.101	+	61.2572i	0.533169	+	0.307825i	0.742306	−	0.670061i	$-0.233732\pi$
$199$	106.101	+	61.2572i	0.533169	+	0.307825i	−0.209137	+	0.977886i	$0.567065\pi$
$200$		0			0
$201$	−96.3541	+	55.6301i	−0.479374	+	0.276767i
$202$	−571.523			−2.82932
$203$	−15.1623	+	18.3316i	−0.0746910	+	0.0903033i
$204$	−574.178			−2.81460
$205$		0			0
$206$	−441.949	−	255.160i	−2.14538	−	1.23864i
$207$	−87.8975	−	50.7477i	−0.424626	−	0.245158i
$208$	−8.53495	−	14.7830i	−0.0410334	−	0.0710719i
$209$			35.5787i			0.170233i
$210$		0			0
$211$	410.851			1.94716			0.973580	−	0.228348i	$-0.0733325\pi$
$211$	410.851			1.94716			0.973580	+	0.228348i	$0.0733325\pi$
$212$	−270.157	+	155.975i	−1.27433	+	0.735733i
$213$	−97.8237	+	169.436i	−0.459266	+	0.795472i
$214$	−112.882	+	195.517i	−0.527486	+	0.913632i
$215$		0			0
$216$			486.723i			2.25335i
$217$	157.218	−	58.4860i	0.724509	−	0.269521i
$218$		−	201.737i		−	0.925397i
$219$	109.278	+	189.275i	0.498986	+	0.864269i
$220$		0			0
$221$	−9.58059	+	16.5941i	−0.0433511	+	0.0750863i
$222$	−103.072	−	178.526i	−0.464288	−	0.804170i
$223$	−69.8903			−0.313409			−0.156705	−	0.987646i	$-0.550087\pi$
$223$	−69.8903			−0.313409			−0.156705	+	0.987646i	$0.550087\pi$
$224$	−132.317	+	49.2224i	−0.590700	+	0.219743i
$225$		0			0
$226$	−94.5298	−	163.730i	−0.418274	−	0.724471i
$227$	51.8101	−	89.7377i	0.228238	−	0.395320i	−0.729048	−	0.684463i	$-0.760037\pi$
$227$	51.8101	−	89.7377i	0.228238	−	0.395320i	0.957286	+	0.289142i	$0.0933701\pi$
$228$	−46.6776	−	26.9493i	−0.204726	−	0.118199i
$229$	262.717	−	151.680i	1.14724	−	0.662358i	0.199025	−	0.979994i	$-0.436222\pi$
$229$	262.717	−	151.680i	1.14724	−	0.662358i	0.948213	+	0.317636i	$0.102889\pi$
$230$		0			0
$231$	233.453	+	39.4628i	1.01062	+	0.170835i
$232$			56.2784i			0.242579i
$233$	−371.043	+	214.222i	−1.59246	+	0.919406i	−0.599574	+	0.800319i	$0.704663\pi$
$233$	−371.043	+	214.222i	−1.59246	+	0.919406i	−0.992884	+	0.119087i	$0.962003\pi$
$234$	6.66800	+	3.84977i	0.0284957	+	0.0164520i
$235$		0			0
$236$	277.078	−	159.971i	1.17406	−	0.677844i
$237$	−0.202425			−0.000854112
$238$	523.182	+	432.730i	2.19824	+	1.81819i
$239$	−109.615			−0.458641			−0.229320	−	0.973351i	$-0.573650\pi$
$239$	−109.615			−0.458641			−0.229320	+	0.973351i	$0.573650\pi$
$240$		0			0
$241$	247.622	+	142.965i	1.02748	+	0.593215i	0.916261	−	0.400581i	$-0.131192\pi$
$241$	247.622	+	142.965i	1.02748	+	0.593215i	0.111217	+	0.993796i	$0.464525\pi$
$242$	−222.560	−	128.495i	−0.919669	−	0.530971i
$243$	−78.9813	−	136.800i	−0.325026	−	0.562962i
$244$			303.394i			1.24342i
$245$		0			0
$246$	217.270			0.883212
$247$	−1.55770	+	0.899340i	−0.00630649	+	0.00364105i
$248$	198.415	−	343.665i	0.800060	−	1.38575i
$249$	−115.950	+	200.831i	−0.465663	+	0.806551i
$250$		0			0
$251$			101.215i			0.403248i	0.979463	+	0.201624i	$0.0646219\pi$
$251$			101.215i			0.403248i	−0.979463	+	0.201624i	$0.935378\pi$
$252$	118.923	−	143.781i	0.471915	−	0.570558i
$253$			458.117i			1.81074i
$254$	−69.7179	−	120.755i	−0.274480	−	0.475413i
$255$		0			0
$256$	253.463	−	439.011i	0.990091	−	1.71489i
$257$	253.214	+	438.580i	0.985269	+	1.70654i	0.640733	+	0.767763i	$0.278630\pi$
$257$	253.214	+	438.580i	0.985269	+	1.70654i	0.344536	+	0.938773i	$0.388036\pi$
$258$	−217.431			−0.842757
$259$	−27.7868	+	164.380i	−0.107285	+	0.634673i
$260$		0			0
$261$	−5.23332	−	9.06437i	−0.0200510	−	0.0347294i
$262$	−96.2236	+	166.664i	−0.367266	+	0.636123i
$263$	−47.2663	−	27.2892i	−0.179720	−	0.103761i	0.407441	−	0.913231i	$-0.366421\pi$
$263$	−47.2663	−	27.2892i	−0.179720	−	0.103761i	−0.587161	+	0.809470i	$0.699754\pi$
$264$	485.069	−	280.055i	1.83738	−	1.06081i
$265$		0			0
$266$	22.2215	+	59.7345i	0.0835395	+	0.224566i
$267$		−	294.472i		−	1.10289i
$268$	342.744	−	197.883i	1.27890	−	0.738371i
$269$	−423.694	−	244.620i	−1.57507	−	0.909368i	−0.995532	−	0.0944245i	$-0.969899\pi$
$269$	−423.694	−	244.620i	−1.57507	−	0.909368i	−0.579540	−	0.814944i	$-0.696768\pi$
$270$		0			0
$271$	−422.146	+	243.726i	−1.55773	+	0.899357i	−0.560259	+	0.828317i	$0.689298\pi$
$271$	−422.146	+	243.726i	−1.55773	+	0.899357i	−0.997473	+	0.0710401i	$0.977368\pi$
$272$	662.256			2.43477
$273$	4.17334	+	11.2185i	0.0152870	+	0.0410935i
$274$	294.083			1.07329
$275$		0			0
$276$	−601.028	−	347.004i	−2.17764	−	1.25726i
$277$	264.116	+	152.488i	0.953488	+	0.550497i	0.894163	−	0.447742i	$-0.147772\pi$
$277$	264.116	+	152.488i	0.953488	+	0.550497i	0.0593253	+	0.998239i	$0.481105\pi$
$278$	−175.282	−	303.598i	−0.630511	−	1.09208i
$279$			73.8023i			0.264524i
$280$		0			0
$281$	−110.177			−0.392089			−0.196044	−	0.980595i	$-0.562810\pi$
$281$	−110.177			−0.392089			−0.196044	+	0.980595i	$0.562810\pi$
$282$	48.4494	−	27.9723i	0.171806	−	0.0991925i
$283$	133.116	−	230.563i	0.470373	−	0.814710i	−0.529053	−	0.848589i	$-0.677453\pi$
$283$	133.116	−	230.563i	0.470373	−	0.814710i	0.999426	+	0.0338789i	$0.0107860\pi$
$284$	347.971	−	602.704i	1.22525	−	2.12220i
$285$		0			0
$286$		−	34.7532i		−	0.121515i
$287$	−135.398	−	111.989i	−0.471769	−	0.390206i
$288$		−	62.1128i		−	0.215669i
$289$	−227.196	−	393.514i	−0.786144	−	1.36164i
$290$		0			0
$291$	0.440502	−	0.762971i	0.00151375	−	0.00262189i
$292$	−388.716	−	673.276i	−1.33122	−	2.30574i
$293$	−8.79423			−0.0300145			−0.0150072	−	0.999887i	$-0.504777\pi$
$293$	−8.79423			−0.0300145			−0.0150072	+	0.999887i	$0.504777\pi$
$294$	416.600	−	79.5526i	1.41701	−	0.270587i
$295$		0			0
$296$	197.194	+	341.550i	0.666196	+	1.15388i
$297$	−204.290	+	353.841i	−0.687846	+	1.19138i
$298$	231.653	+	133.745i	0.777360	+	0.448809i
$299$	−20.0572	+	11.5800i	−0.0670810	+	0.0387292i
$300$		0			0
$301$	135.498	+	112.072i	0.450160	+	0.372333i
$302$			551.369i			1.82572i
$303$	338.534	−	195.452i	1.11727	−	0.645058i
$304$	53.8379	+	31.0833i	0.177098	+	0.102248i
$305$		0			0
$306$	−258.696	+	149.358i	−0.845413	+	0.488099i
$307$	447.196			1.45667			0.728333	−	0.685224i	$-0.240296\pi$
$307$	447.196			1.45667			0.728333	+	0.685224i	$0.240296\pi$
$308$	−830.421	−	140.374i	−2.69617	−	0.455761i
$309$	349.043			1.12959
$310$		0			0
$311$	−194.895	−	112.523i	−0.626671	−	0.361809i	0.152790	−	0.988259i	$-0.451174\pi$
$311$	−194.895	−	112.523i	−0.626671	−	0.361809i	−0.779462	+	0.626450i	$0.784507\pi$
$312$	24.5226	+	14.1582i	0.0785982	+	0.0453787i
$313$	168.049	+	291.069i	0.536898	+	0.929934i	0.999069	+	0.0431435i	$0.0137373\pi$
$313$	168.049	+	291.069i	0.536898	+	0.929934i	−0.462171	+	0.886791i	$0.652929\pi$
$314$		−	412.734i		−	1.31444i
$315$		0			0
$316$	0.720050			0.00227864
$317$	−71.3905	+	41.2173i	−0.225207	+	0.130023i	−0.608359	−	0.793662i	$-0.708172\pi$
$317$	−71.3905	+	41.2173i	−0.225207	+	0.130023i	0.383152	+	0.923685i	$0.374839\pi$
$318$	155.987	−	270.177i	0.490525	−	0.849614i
$319$	−23.6215	+	40.9136i	−0.0740486	+	0.128256i
$320$		0			0
$321$		−	154.416i		−	0.481046i
$322$	286.127	+	769.150i	0.888594	+	2.38866i
$323$		−	69.7829i		−	0.216046i
$324$	−189.532	−	328.279i	−0.584975	−	1.01321i
$325$		0			0
$326$	338.289	−	585.934i	1.03770	−	1.79734i
$327$	68.9909	+	119.496i	0.210981	+	0.365431i
$328$	−415.675			−1.26730
$329$	−44.6105	−	7.54095i	−0.135594	−	0.0229208i
$330$		0			0
$331$	47.3818	+	82.0677i	0.143147	+	0.247939i	0.928680	−	0.370881i	$-0.120944\pi$
$331$	47.3818	+	82.0677i	0.143147	+	0.247939i	−0.785533	+	0.618820i	$0.787611\pi$
$332$	412.449	−	714.383i	1.24232	−	2.15175i
$333$	−63.5213	−	36.6741i	−0.190755	−	0.110132i
$334$	−799.167	+	461.399i	−2.39271	+	1.38143i
$335$		0			0
$336$	263.671	−	318.785i	0.784736	−	0.948766i
$337$		−	362.615i		−	1.07601i	−0.842942	−	0.538005i	$-0.819178\pi$
$337$		−	362.615i		−	1.07601i	0.842942	−	0.538005i	$-0.180822\pi$
$338$	−519.132	+	299.721i	−1.53589	+	0.886749i
$339$	111.987	+	64.6556i	0.330345	+	0.190725i
$340$		0			0
$341$	288.490	−	166.560i	0.846012	−	0.488445i
$342$	−28.0409			−0.0819908
$343$	−300.620	−	165.156i	−0.876444	−	0.481504i
$344$	415.983			1.20925
$345$		0			0
$346$	697.891	+	402.927i	2.01703	+	1.16453i
$347$	−336.011	−	193.996i	−0.968330	−	0.559066i	−0.0696035	−	0.997575i	$-0.522173\pi$
$347$	−336.011	−	193.996i	−0.968330	−	0.559066i	−0.898727	+	0.438509i	$0.855507\pi$
$348$	−35.7845	−	61.9806i	−0.102829	−	0.178105i
$349$		−	445.741i		−	1.27719i	−0.769541	−	0.638597i	$-0.779515\pi$
$349$		−	445.741i		−	1.27719i	0.769541	−	0.638597i	$-0.220485\pi$
$350$		0			0
$351$	−20.6558			−0.0588484
$352$	−242.796	+	140.179i	−0.689762	+	0.398234i
$353$	143.028	−	247.732i	0.405179	−	0.701790i	−0.589163	−	0.808014i	$-0.700543\pi$
$353$	143.028	−	247.732i	0.405179	−	0.701790i	0.994342	+	0.106224i	$0.0338759\pi$
$354$	−159.983	+	277.099i	−0.451929	+	0.782764i
$355$		0			0
$356$			1047.48i			2.94235i
$357$	−457.886	−	77.4010i	−1.28260	−	0.216810i
$358$		−	665.265i		−	1.85828i
$359$	215.089	+	372.546i	0.599135	+	1.03773i	0.992949	+	0.118542i	$0.0378220\pi$
$359$	215.089	+	372.546i	0.599135	+	1.03773i	−0.393814	+	0.919190i	$0.628845\pi$
$360$		0			0
$361$	−177.225	+	306.962i	−0.490927	+	0.850311i
$362$	−325.546	−	563.863i	−0.899299	−	1.55763i
$363$	175.774			0.484225
$364$	−14.8451	−	39.9057i	−0.0407833	−	0.109631i
$365$		0			0
$366$	−151.708	−	262.766i	−0.414503	−	0.717940i
$367$	166.959	−	289.182i	0.454930	−	0.787961i	−0.543755	−	0.839244i	$-0.682998\pi$
$367$	166.959	−	289.182i	0.454930	−	0.787961i	0.998684	+	0.0512831i	$0.0163311\pi$
$368$	693.225	+	400.234i	1.88376	+	1.08759i
$369$	66.9499	−	38.6535i	0.181436	−	0.104752i
$370$		0			0
$371$	−236.467	+	87.9668i	−0.637377	+	0.237107i
$372$			504.647i			1.35658i
$373$	42.6786	−	24.6405i	0.114420	−	0.0660603i	−0.441698	−	0.897164i	$-0.645624\pi$
$373$	42.6786	−	24.6405i	0.114420	−	0.0660603i	0.556118	+	0.831104i	$0.312290\pi$
$374$	1167.67	+	674.155i	3.12212	+	1.80255i
$375$		0			0
$376$	−92.6919	+	53.5157i	−0.246521	+	0.142329i
$377$	−2.38837			−0.00633519
$378$	−121.991	+	721.672i	−0.322728	+	1.90918i
$379$	635.496			1.67677			0.838385	−	0.545078i	$-0.183500\pi$
$379$	635.496			1.67677			0.838385	+	0.545078i	$0.183500\pi$
$380$		0			0
$381$	82.5928	+	47.6850i	0.216779	+	0.125157i
$382$	608.547	+	351.345i	1.59306	+	0.919751i
$383$	48.7673	+	84.4675i	0.127330	+	0.220542i	0.922641	−	0.385659i	$-0.126026\pi$
$383$	48.7673	+	84.4675i	0.127330	+	0.220542i	−0.795311	+	0.606201i	$0.792693\pi$
$384$			416.248i			1.08398i
$385$		0			0
$386$	−301.143			−0.780164
$387$	−66.9995	+	38.6822i	−0.173125	+	0.0999540i
$388$	−1.56692	+	2.71399i	−0.00403846	+	0.00699481i
$389$	−335.431	+	580.983i	−0.862289	+	1.49353i	0.00742425	+	0.999972i	$0.497637\pi$
$389$	−335.431	+	580.983i	−0.862289	+	1.49353i	−0.869714	+	0.493557i	$0.835697\pi$
$390$		0			0
$391$		−	898.535i		−	2.29804i
$392$	−797.027	+	152.198i	−2.03323	+	0.388259i
$393$		−	131.628i		−	0.334932i
$394$	−439.926	−	761.973i	−1.11656	−	1.93394i
$395$		0			0
$396$	185.271	−	320.899i	0.467857	−	0.810351i
$397$	−278.676	−	482.681i	−0.701954	−	1.21582i	−0.967780	−	0.251799i	$-0.918978\pi$
$397$	−278.676	−	482.681i	−0.701954	−	1.21582i	0.265825	−	0.964021i	$-0.414356\pi$
$398$	435.832			1.09505
$399$	−33.5909	−	27.7834i	−0.0841877	−	0.0696327i
$400$		0			0
$401$	−297.504	−	515.293i	−0.741906	−	1.28502i	−0.951626	−	0.307258i	$-0.900589\pi$
$401$	−297.504	−	515.293i	−0.741906	−	1.28502i	0.209720	−	0.977762i	$-0.432745\pi$
$402$	−197.898	+	342.769i	−0.492284	+	0.852660i
$403$	14.5846	+	8.42042i	0.0361901	+	0.0208944i
$404$	−1204.21	+	695.250i	−2.98071	+	1.72092i
$405$		0			0
$406$	−14.1055	+	83.4448i	−0.0347426	+	0.205529i
$407$			331.070i			0.813439i
$408$	−951.398	+	549.290i	−2.33186	+	1.34630i
$409$	−394.822	−	227.951i	−0.965336	−	0.557337i	−0.0675247	−	0.997718i	$-0.521510\pi$
$409$	−394.822	−	227.951i	−0.965336	−	0.557337i	−0.897811	+	0.440381i	$0.854843\pi$
$410$		0			0
$411$	−174.196	+	100.572i	−0.423834	+	0.244701i
$412$	−1241.59			−3.01357
$413$	242.525	−	90.2203i	0.587227	−	0.218451i
$414$	−361.058			−0.872122
$415$		0			0
$416$	−12.2746	−	7.08672i	−0.0295061	−	0.0170354i
$417$	207.652	+	119.888i	0.497966	+	0.287501i
$418$	63.2837	+	109.611i	0.151396	+	0.262226i
$419$			120.662i			0.287977i	0.989579	+	0.143989i	$0.0459929\pi$
$419$			120.662i			0.287977i	−0.989579	+	0.143989i	$0.954007\pi$
$420$		0			0
$421$	−206.898			−0.491444			−0.245722	−	0.969340i	$-0.579025\pi$
$421$	−206.898			−0.491444			−0.245722	+	0.969340i	$0.579025\pi$
$422$	1265.74	−	730.778i	2.99939	−	1.73170i
$423$	9.95283	−	17.2388i	0.0235292	−	0.0407537i
$424$	−298.429	+	516.895i	−0.703843	+	1.21909i
$425$		0			0
$426$			695.994i			1.63379i
$427$	−40.8985	+	241.946i	−0.0957810	+	0.566618i
$428$			549.277i			1.28336i
$429$	11.8851	+	20.5856i	0.0277042	+	0.0479850i
$430$		0			0
$431$	134.929	−	233.704i	0.313060	−	0.542236i	−0.665963	−	0.745985i	$-0.731979\pi$
$431$	134.929	−	233.704i	0.313060	−	0.542236i	0.979023	+	0.203749i	$0.0653125\pi$
$432$	356.956	+	618.267i	0.826288	+	1.43117i
$433$	−8.67846			−0.0200426			−0.0100213	−	0.999950i	$-0.503190\pi$
$433$	−8.67846			−0.0200426			−0.0100213	+	0.999950i	$0.503190\pi$
$434$	380.328	−	459.827i	0.876332	−	1.05951i
$435$		0			0
$436$	−245.410	−	425.062i	−0.562866	−	0.974913i
$437$	42.1732	−	73.0462i	0.0965063	−	0.167154i
$438$	673.325	+	388.744i	1.53727	+	0.887544i
$439$	−3.11208	+	1.79676i	−0.00708901	+	0.00409284i	−0.503540	−	0.863972i	$-0.667969\pi$
$439$	−3.11208	+	1.79676i	−0.00708901	+	0.00409284i	0.496451	+	0.868065i	$0.334636\pi$
$440$		0			0
$441$	114.219	−	98.6288i	0.258999	−	0.223648i
$442$			68.1638i			0.154217i
$443$	−350.223	+	202.201i	−0.790571	+	0.456437i	−0.840164	−	0.542333i	$-0.817541\pi$
$443$	−350.223	+	202.201i	−0.790571	+	0.456437i	0.0495923	+	0.998770i	$0.484208\pi$
$444$	−434.348	−	250.771i	−0.978261	−	0.564799i
$445$		0			0
$446$	−215.317	+	124.314i	−0.482774	+	0.278730i
$447$	−182.955			−0.409296
$448$	113.377	−	137.075i	0.253073	−	0.305971i
$449$	−339.672			−0.756508			−0.378254	−	0.925702i	$-0.623475\pi$
$449$	−339.672			−0.756508			−0.378254	+	0.925702i	$0.623475\pi$
$450$		0			0
$451$	−302.190	−	174.469i	−0.670044	−	0.386850i
$452$	−398.352	−	229.988i	−0.881309	−	0.508824i
$453$	−188.560	−	326.596i	−0.416247	−	0.720962i
$454$		−	368.618i		−	0.811933i
$455$		0			0
$456$	−103.125			−0.226151
$457$	−551.033	+	318.139i	−1.20576	+	0.696147i	−0.961831	−	0.273646i	$-0.911770\pi$
$457$	−551.033	+	318.139i	−1.20576	+	0.696147i	−0.243931	+	0.969793i	$0.578437\pi$
$458$	539.585	−	934.589i	1.17813	−	2.04059i
$459$	400.688	−	694.012i	0.872959	−	1.51201i
$460$		0			0
$461$			483.724i			1.04929i	0.851321	+	0.524646i	$0.175802\pi$
$461$			483.724i			1.04929i	−0.851321	+	0.524646i	$0.824198\pi$
$462$	789.411	−	293.665i	1.70868	−	0.635638i
$463$		−	409.737i		−	0.884961i	−0.896778	−	0.442480i	$-0.854099\pi$
$463$		−	409.737i		−	0.884961i	0.896778	−	0.442480i	$-0.145901\pi$
$464$	41.2738	+	71.4884i	0.0889522	+	0.154070i
$465$		0			0
$466$	−762.070	+	1319.94i	−1.63534	+	2.83250i
$467$	183.303	+	317.491i	0.392512	+	0.679851i	0.992780	−	0.119948i	$-0.0382727\pi$
$467$	183.303	+	317.491i	0.392512	+	0.679851i	−0.600268	+	0.799799i	$0.704939\pi$
$468$	18.7328			0.0400273
$469$	300.002	−	111.602i	0.639663	−	0.237957i
$470$		0			0
$471$	141.149	+	244.477i	0.299679	+	0.519060i
$472$	306.075	−	530.137i	0.648463	−	1.12317i
$473$	302.414	+	174.599i	0.639353	+	0.369131i
$474$	−0.623628	+	0.360052i	−0.00131567	+	0.000759603i
$475$		0			0
$476$	1628.76	+	275.325i	3.42177	+	0.578415i
$477$		−	111.004i		−	0.232712i
$478$	−337.701	+	194.972i	−0.706488	+	0.407891i
$479$	73.5403	+	42.4585i	0.153529	+	0.0886399i	0.574796	−	0.818297i	$-0.305081\pi$
$479$	73.5403	+	42.4585i	0.153529	+	0.0886399i	−0.421267	+	0.906936i	$0.638415\pi$
$480$		0			0
$481$	−14.4948	+	8.36861i	−0.0301348	+	0.0173983i
$482$	1017.16			2.11030
$483$	−432.521	−	357.744i	−0.895490	−	0.740670i
$484$	−625.249			−1.29184
$485$		0			0
$486$	−486.650	−	280.968i	−1.00134	−	0.578122i
$487$	28.3585	+	16.3728i	0.0582311	+	0.0336197i	0.528833	−	0.848726i	$-0.322630\pi$
$487$	28.3585	+	16.3728i	0.0582311	+	0.0336197i	−0.470602	+	0.882346i	$0.655963\pi$
$488$	290.243	+	502.716i	0.594761	+	1.03016i
$489$			462.760i			0.946339i
$490$		0			0
$491$	522.932			1.06503			0.532517	−	0.846419i	$-0.321246\pi$
$491$	522.932			1.06503			0.532517	+	0.846419i	$0.321246\pi$
$492$	457.791	−	264.306i	0.930471	−	0.537207i
$493$	46.3304	−	80.2466i	0.0939765	−	0.162772i
$494$	−3.19930	+	5.54136i	−0.00647633	+	0.0112173i
$495$		0			0
$496$		−	582.060i		−	1.17351i
$497$	358.741	−	433.728i	0.721814	−	0.872692i
$498$			824.959i			1.65654i
$499$	−30.4582	−	52.7551i	−0.0610384	−	0.105722i	0.833891	−	0.551929i	$-0.186108\pi$
$499$	−30.4582	−	52.7551i	−0.0610384	−	0.105722i	−0.894930	+	0.446207i	$0.852775\pi$
$500$		0			0
$501$	315.583	−	546.606i	0.629907	−	1.09103i
$502$	180.031	+	311.823i	0.358628	+	0.621161i
$503$	523.122			1.04000			0.520002	−	0.854165i	$-0.325931\pi$
$503$	523.122			1.04000			0.520002	+	0.854165i	$0.325931\pi$
$504$	59.5035	−	352.009i	0.118063	−	0.698431i
$505$		0			0
$506$	814.850	+	1411.36i	1.61038	+	2.78925i
$507$	205.000	−	355.071i	0.404340	−	0.700337i
$508$	−293.793	−	169.622i	−0.578333	−	0.333901i
$509$	10.9283	−	6.30945i	0.0214701	−	0.0123958i	−0.489227	−	0.872157i	$-0.662721\pi$
$509$	10.9283	−	6.30945i	0.0214701	−	0.0123958i	0.510697	+	0.859761i	$0.329388\pi$
$510$		0			0
$511$	−219.227	−	589.314i	−0.429017	−	1.15326i
$512$		−	1119.04i		−	2.18563i
$513$	65.1477	−	37.6130i	0.126994	−	0.0733198i
$514$	1560.20	+	900.782i	3.03541	+	1.75249i
$515$		0			0
$516$	−458.131	+	264.502i	−0.887851	+	0.512601i
$517$	−89.8477			−0.173787
$518$	206.777	+	555.845i	0.399184	+	1.07306i
$519$	−551.181			−1.06201
$520$		0			0
$521$	−216.848	−	125.197i	−0.416215	−	0.240302i	0.277242	−	0.960800i	$-0.410580\pi$
$521$	−216.848	−	125.197i	−0.416215	−	0.240302i	−0.693456	+	0.720499i	$0.743913\pi$
$522$	−32.2455	−	18.6169i	−0.0617730	−	0.0356647i
$523$	175.033	+	303.166i	0.334671	+	0.579667i	0.983422	−	0.181334i	$-0.0580416\pi$
$523$	175.033	+	303.166i	0.334671	+	0.579667i	−0.648751	+	0.761001i	$0.724708\pi$
$524$			468.218i			0.893547i
$525$		0			0
$526$	−194.157			−0.369120
$527$	−565.835	+	326.685i	−1.07369	+	0.619895i
$528$	410.777	−	711.487i	0.777987	−	1.34751i
$529$	278.529	−	482.426i	0.526520	−	0.911959i
$530$		0			0
$531$			113.847i			0.214402i
$532$	119.487	+	98.8293i	0.224600	+	0.185769i
$533$		−	17.6406i		−	0.0330968i
$534$	−523.777	−	907.208i	−0.980855	−	1.69889i
$535$		0			0
$536$	378.612	−	655.776i	0.706367	−	1.22346i
$537$	227.511	+	394.060i	0.423670	+	0.733818i
$538$	−1740.42			−3.23498
$539$	−643.309	−	223.887i	−1.19352	−	0.415375i
$540$		0			0
$541$	−204.673	−	354.504i	−0.378324	−	0.655276i	0.612495	−	0.790475i	$-0.290166\pi$
$541$	−204.673	−	354.504i	−0.378324	−	0.655276i	−0.990819	+	0.135199i	$0.956833\pi$
$542$	−867.028	+	1501.74i	−1.59968	+	2.77073i
$543$	385.665	+	222.664i	0.710250	+	0.410063i
$544$	476.213	−	274.942i	0.875391	−	0.505407i
$545$		0			0
$546$	32.8115	+	27.1388i	0.0600944	+	0.0497048i
$547$			189.589i			0.346598i	0.984869	+	0.173299i	$0.0554427\pi$
$547$			189.589i			0.346598i	−0.984869	+	0.173299i	$0.944557\pi$
$548$	619.637	−	357.747i	1.13072	−	0.652824i
$549$	−93.4949	−	53.9793i	−0.170300	−	0.0983230i
$550$		0			0
$551$	7.53284	−	4.34908i	0.0136712	−	0.00789308i
$552$	−1327.85			−2.40553
$553$	0.574215	+	0.0970651i	0.00103836	+	0.000175525i
$554$	1084.92			1.95833
$555$		0			0
$556$	−738.644	−	426.456i	−1.32850	−	0.767008i
$557$	−106.866	−	61.6991i	−0.191860	−	0.110770i	0.400993	−	0.916081i	$-0.368665\pi$
$557$	−106.866	−	61.6991i	−0.191860	−	0.110770i	−0.592853	+	0.805311i	$0.701998\pi$
$558$	131.272	+	227.369i	0.235254	+	0.407472i
$559$			17.6537i			0.0315808i
$560$		0			0
$561$	−922.205			−1.64386
$562$	−339.432	+	195.971i	−0.603972	+	0.348703i
$563$	−215.617	+	373.460i	−0.382979	+	0.663339i	−0.991487	−	0.130209i	$-0.958435\pi$
$563$	−215.617	+	373.460i	−0.382979	+	0.663339i	0.608507	+	0.793548i	$0.291769\pi$
$564$	68.0557	−	117.876i	0.120666	−	0.209000i
$565$		0			0
$566$		−	947.088i		−	1.67330i
$567$	−106.892	−	287.341i	−0.188522	−	0.506773i
$568$		−	1331.55i		−	2.34429i
$569$	430.759	+	746.097i	0.757046	+	1.31124i	0.944351	+	0.328941i	$0.106692\pi$
$569$	430.759	+	746.097i	0.757046	+	1.31124i	−0.187304	+	0.982302i	$0.559975\pi$
$570$		0			0
$571$	−214.469	+	371.472i	−0.375603	+	0.650563i	−0.990417	−	0.138109i	$-0.955898\pi$
$571$	−214.469	+	371.472i	−0.375603	+	0.650563i	0.614814	+	0.788672i	$0.289231\pi$
$572$	−42.2768	−	73.2255i	−0.0739105	−	0.128017i
$573$	−480.619			−0.838777
$574$	−616.327	−	104.184i	−1.07374	−	0.181505i
$575$		0			0
$576$	39.1324	+	67.7792i	0.0679381	+	0.117672i
$577$	90.5781	−	156.886i	0.156981	−	0.271899i	−0.776798	−	0.629750i	$-0.783157\pi$
$577$	90.5781	−	156.886i	0.156981	−	0.271899i	0.933779	+	0.357851i	$0.116491\pi$
$578$	−1399.88	−	808.223i	−2.42194	−	1.39831i
$579$	178.378	−	102.987i	0.308080	−	0.177870i
$580$		0			0
$581$	425.215	−	514.096i	0.731867	−	0.884846i
$582$		−	3.13407i		−	0.00538501i
$583$	−433.908	+	250.517i	−0.744268	+	0.429703i
$584$	−1288.19	−	743.734i	−2.20580	−	1.27352i
$585$		0			0
$586$	−27.0932	+	15.6423i	−0.0462341	+	0.0266933i
$587$	−104.998			−0.178872			−0.0894359	−	0.995993i	$-0.528506\pi$
$587$	−104.998			−0.178872			−0.0894359	+	0.995993i	$0.528506\pi$
$588$	781.008	−	674.407i	1.32825	−	1.14695i
$589$	−61.3325			−0.104130
$590$		0			0
$591$	521.167	+	300.896i	0.881840	+	0.509130i
$592$	500.977	+	289.239i	0.846244	+	0.488579i
$593$	15.8984	+	27.5368i	0.0268101	+	0.0464365i	0.879119	−	0.476602i	$-0.158132\pi$
$593$	15.8984	+	27.5368i	0.0268101	+	0.0464365i	−0.852309	+	0.523039i	$0.824798\pi$
$594$			1453.48i			2.44694i
$595$		0			0
$596$	650.796			1.09194
$597$	−258.159	+	149.048i	−0.432427	+	0.249662i
$598$	−41.1947	+	71.3514i	−0.0688875	+	0.119317i
$599$	−58.9176	+	102.048i	−0.0983600	+	0.170365i	−0.911006	−	0.412393i	$-0.864693\pi$
$599$	−58.9176	+	102.048i	−0.0983600	+	0.170365i	0.812646	+	0.582758i	$0.198026\pi$
$600$		0			0
$601$			1044.07i			1.73722i	0.495494	+	0.868611i	$0.334987\pi$
$601$			1044.07i			1.73722i	−0.495494	+	0.868611i	$0.665013\pi$
$602$	616.784	+	104.261i	1.02456	+	0.173191i
$603$			140.828i			0.233546i
$604$	670.732	+	1161.74i	1.11048	+	1.92341i
$605$		0			0
$606$	695.301	−	1204.30i	1.14736	−	1.98729i
$607$	−145.373	−	251.794i	−0.239495	−	0.414817i	0.721075	−	0.692857i	$-0.243648\pi$
$607$	−145.373	−	251.794i	−0.239495	−	0.414817i	−0.960569	+	0.278040i	$0.910315\pi$
$608$	51.6181			0.0848982
$609$	−20.1817	−	54.2512i	−0.0331391	−	0.0890824i
$610$		0			0
$611$	−2.27112	−	3.93370i	−0.00371706	−	0.00643814i
$612$	−363.385	+	629.401i	−0.593766	+	1.02843i
$613$	−161.189	−	93.0624i	−0.262951	−	0.151815i	0.362729	−	0.931895i	$-0.381845\pi$
$613$	−161.189	−	93.0624i	−0.262951	−	0.151815i	−0.625680	+	0.780080i	$0.715178\pi$
$614$	1377.72	−	795.426i	2.24384	−	1.29548i
$615$		0			0
$616$	−1510.28	+	561.830i	−2.45175	+	0.912062i
$617$			386.307i			0.626105i	0.949736	+	0.313053i	$0.101352\pi$
$617$			386.307i			0.626105i	−0.949736	+	0.313053i	$0.898648\pi$
$618$	1075.33	−	620.842i	1.74001	−	1.00460i
$619$	−30.9861	−	17.8898i	−0.0500583	−	0.0289012i	0.474762	−	0.880114i	$-0.342534\pi$
$619$	−30.9861	−	17.8898i	−0.0500583	−	0.0289012i	−0.524820	+	0.851213i	$0.675867\pi$
$620$		0			0
$621$	838.851	−	484.311i	1.35081	−	0.779889i
$622$	−800.574			−1.28710
$623$	−141.203	+	835.326i	−0.226651	+	1.34081i
$624$	41.5336			0.0665603
$625$		0			0
$626$	1035.45	+	597.816i	1.65407	+	0.954978i
$627$	−74.9704	−	43.2842i	−0.119570	−	0.0690338i
$628$	−502.085	−	869.637i	−0.799498	−	1.38477i
$629$		−	649.349i		−	1.03235i
$630$		0			0
$631$	888.207			1.40762			0.703809	−	0.710389i	$-0.251481\pi$
$631$	888.207			1.40762			0.703809	+	0.710389i	$0.251481\pi$
$632$	1.19311	−	0.688840i	0.00188783	−	0.00108994i
$633$	−499.831	+	865.732i	−0.789622	+	1.36767i
$634$	−146.626	+	253.964i	−0.231272	+	0.400574i
$635$		0			0
$636$		−	759.023i		−	1.19343i
$637$	−6.45903	−	33.8246i	−0.0101398	−	0.0530998i
$638$			168.062i			0.263420i
$639$	123.821	+	214.464i	0.193773	+	0.335625i
$640$		0			0
$641$	−322.467	+	558.528i	−0.503068	+	0.871339i	0.496926	+	0.867793i	$0.334462\pi$
$641$	−322.467	+	558.528i	−0.503068	+	0.871339i	−0.999994	+	0.00354621i	$0.998871\pi$
$642$	−274.659	−	475.723i	−0.427817	−	0.741001i
$643$	466.160			0.724976			0.362488	−	0.931988i	$-0.381927\pi$
$643$	466.160			0.724976			0.362488	+	0.931988i	$0.381927\pi$
$644$	1538.53	+	1272.54i	2.38903	+	1.97600i
$645$		0			0
$646$	−124.123	−	214.987i	−0.192140	−	0.332797i
$647$	263.899	−	457.087i	0.407881	−	0.706471i	−0.586771	−	0.809753i	$-0.699601\pi$
$647$	263.899	−	457.087i	0.407881	−	0.706471i	0.994652	+	0.103282i	$0.0329345\pi$
$648$	−628.100	−	362.634i	−0.969290	−	0.559620i
$649$	445.024	−	256.935i	0.685707	−	0.395893i
$650$		0			0
$651$	−68.0281	+	402.438i	−0.104498	+	0.618185i
$652$		−	1646.10i		−	2.52469i
$653$	382.021	−	220.560i	0.585025	−	0.337764i	−0.178103	−	0.984012i	$-0.556996\pi$
$653$	382.021	−	220.560i	0.585025	−	0.337764i	0.763128	+	0.646248i	$0.223663\pi$
$654$	425.093	+	245.428i	0.649990	+	0.375272i
$655$		0			0
$656$	−528.016	+	304.850i	−0.804903	+	0.464711i
$657$	276.639			0.421064
$658$	−150.849	+	56.1164i	−0.229253	+	0.0852833i
$659$	−884.354			−1.34196			−0.670982	−	0.741474i	$-0.734127\pi$
$659$	−884.354			−1.34196			−0.670982	+	0.741474i	$0.734127\pi$
$660$		0			0
$661$	631.224	+	364.437i	0.954953	+	0.551342i	0.894616	−	0.446836i	$-0.147449\pi$
$661$	631.224	+	364.437i	0.954953	+	0.551342i	0.0603369	+	0.998178i	$0.480782\pi$
$662$	291.947	+	168.556i	0.441007	+	0.254616i
$663$	−23.3110	−	40.3759i	−0.0351599	−	0.0608987i
$664$		−	1578.29i		−	2.37694i
$665$		0			0
$666$	−260.928			−0.391784
$667$	96.9939	−	55.9995i	0.145418	−	0.0839572i
$668$	−1122.57	+	1944.35i	−1.68050	+	2.91070i
$669$	85.0268	−	147.271i	0.127095	−	0.220136i
$670$		0			0
$671$			487.290i			0.726215i
$672$	57.2532	−	338.697i	0.0851982	−	0.504013i
$673$		−	1042.57i		−	1.54914i	−0.632487	−	0.774571i	$-0.717966\pi$
$673$		−	1042.57i		−	1.54914i	0.632487	−	0.774571i	$-0.282034\pi$
$674$	−644.982	−	1117.14i	−0.956947	−	1.65748i
$675$		0			0
$676$	−729.213	+	1263.03i	−1.07872	+	1.86839i
$677$	−407.806	−	706.342i	−0.602373	−	1.04334i	−0.992461	−	0.122563i	$-0.960889\pi$
$677$	−407.806	−	706.342i	−0.602373	−	1.04334i	0.390088	−	0.920778i	$-0.372445\pi$
$678$	460.011			0.678482
$679$	−1.61542	+	1.95308i	−0.00237911	+	0.00287641i
$680$		0			0
$681$	126.062	+	218.345i	0.185113	+	0.320625i
$682$	592.518	−	1026.27i	0.868795	−	1.50480i
$683$	616.734	+	356.071i	0.902977	+	0.521334i	0.878165	−	0.478358i	$-0.158768\pi$
$683$	616.734	+	356.071i	0.902977	+	0.521334i	0.0248124	+	0.999692i	$0.492101\pi$
$684$	−59.0825	+	34.1113i	−0.0863780	+	0.0498703i
$685$		0			0
$686$	−1219.91	+	25.9007i	−1.77829	+	0.0377561i
$687$			738.121i			1.07441i
$688$	528.408	−	305.077i	0.768035	−	0.443425i
$689$	−21.9362	−	12.6649i	−0.0318378	−	0.0183815i
$690$		0			0
$691$	875.286	−	505.346i	1.26669	−	0.731326i	0.292333	−	0.956317i	$-0.405568\pi$
$691$	875.286	−	505.346i	1.26669	−	0.731326i	0.974361	+	0.224990i	$0.0722350\pi$
$692$	1960.62			2.83327
$693$	191.006	−	230.931i	0.275621	−	0.333233i
$694$	−1380.24			−1.98882
$695$		0			0
$696$	−118.588	−	68.4669i	−0.170385	−	0.0983720i
$697$	592.705	+	342.199i	0.850366	+	0.490959i
$698$	−792.837	−	1373.23i	−1.13587	−	1.96738i
$699$		−	1042.47i		−	1.49137i
$700$		0			0
$701$	60.6890			0.0865748			0.0432874	−	0.999063i	$-0.486217\pi$
$701$	60.6890			0.0865748			0.0432874	+	0.999063i	$0.486217\pi$
$702$	−63.6361	+	36.7403i	−0.0906498	+	0.0523367i
$703$	30.4775	−	52.7886i	0.0433535	−	0.0750905i
$704$	176.631	−	305.934i	0.250896	−	0.434565i
$705$		0			0
$706$		−	1017.61i		−	1.44138i
$707$	−1054.04	+	392.106i	−1.49086	+	0.554605i
$708$			778.468i			1.09953i
$709$	324.501	+	562.052i	0.457688	+	0.792740i	0.998838	−	0.0481865i	$-0.0153442\pi$
$709$	324.501	+	562.052i	0.457688	+	0.792740i	−0.541150	+	0.840926i	$0.682011\pi$
$710$		0			0
$711$	−0.128110	+	0.221893i	−0.000180183	+	0.000312086i
$712$	1002.07	+	1735.64i	1.40741	+	2.43770i
$713$	−789.727			−1.10761
$714$	−1548.33	+	575.984i	−2.16852	+	0.806701i
$715$		0			0
$716$	−809.285	−	1401.72i	−1.13029	−	1.95771i
$717$	133.355	−	230.978i	0.185990	−	0.322145i
$718$	1325.29	+	765.157i	1.84581	+	1.06568i
$719$	182.027	−	105.093i	0.253167	−	0.146166i	−0.368047	−	0.929807i	$-0.619973\pi$
$719$	182.027	−	105.093i	0.253167	−	0.146166i	0.621213	+	0.783641i	$0.286640\pi$
$720$		0			0
$721$	−990.126	−	167.371i	−1.37327	−	0.232137i
$722$			1260.92i			1.74642i
$723$	−602.502	+	347.855i	−0.833336	+	0.481127i
$724$	−1371.86	−	792.045i	−1.89484	−	1.09398i
$725$		0			0
$726$	541.522	−	312.648i	0.745898	−	0.430644i
$727$	743.893			1.02324			0.511618	−	0.859213i	$-0.329046\pi$
$727$	743.893			1.02324			0.511618	+	0.859213i	$0.329046\pi$
$728$	−62.7740	−	51.9212i	−0.0862280	−	0.0713203i
$729$	778.520			1.06793
$730$		0			0
$731$	−593.145	−	342.452i	−0.811416	−	0.468471i
$732$	−639.302	−	369.101i	−0.873363	−	0.504237i
$733$	177.002	+	306.576i	0.241476	+	0.418248i	0.961135	−	0.276079i	$-0.0890352\pi$
$733$	177.002	+	306.576i	0.241476	+	0.418248i	−0.719659	+	0.694328i	$0.755702\pi$
$734$		−	1187.88i		−	1.61836i
$735$		0			0
$736$	664.643			0.903047
$737$	550.492	−	317.827i	0.746937	−	0.431244i
$738$	137.506	−	238.167i	0.186322	−	0.322719i
$739$	−619.606	+	1073.19i	−0.838438	+	1.45222i	0.0527626	+	0.998607i	$0.483197\pi$
$739$	−619.606	+	1073.19i	−0.838438	+	1.45222i	−0.891200	+	0.453610i	$0.850136\pi$
$740$		0			0
$741$		−	4.37646i		−	0.00590615i
$742$	−572.039	+	691.610i	−0.770942	+	0.932089i
$743$			1060.01i			1.42666i	0.700830	+	0.713328i	$0.252813\pi$
$743$			1060.01i			1.42666i	−0.700830	+	0.713328i	$0.747187\pi$
$744$	482.773	+	836.188i	0.648889	+	1.12391i
$745$		0			0
$746$	87.6558	−	151.824i	0.117501	−	0.203518i
$747$	146.765	+	254.204i	0.196472	+	0.340299i
$748$	3280.40			4.38556
$749$	−74.0444	+	438.029i	−0.0988576	+	0.584819i
$750$		0			0
$751$	509.992	+	883.332i	0.679084	+	1.17621i	0.975257	+	0.221073i	$0.0709561\pi$
$751$	509.992	+	883.332i	0.679084	+	1.17621i	−0.296173	+	0.955134i	$0.595711\pi$
$752$	−78.4955	+	135.958i	−0.104382	+	0.180795i
$753$	−213.278	−	123.136i	−0.283237	−	0.163527i
$754$	−7.35806	+	4.24818i	−0.00975870	+	0.00563419i
$755$		0			0
$756$	620.866	+	1668.97i	0.821251	+	2.20764i
$757$			1023.43i			1.35196i	0.736921	+	0.675978i	$0.236279\pi$
$757$			1023.43i			1.35196i	−0.736921	+	0.675978i	$0.763721\pi$
$758$	1957.83	−	1130.35i	2.58289	−	1.49123i
$759$	−965.330	−	557.334i	−1.27184	−	0.734300i
$760$		0			0
$761$	−388.132	+	224.088i	−0.510028	+	0.294465i	−0.732845	−	0.680395i	$-0.761808\pi$
$761$	−388.132	+	224.088i	−0.510028	+	0.294465i	0.222817	+	0.974860i	$0.428475\pi$
$762$	339.268			0.445234
$763$	−138.406	−	372.054i	−0.181397	−	0.487620i
$764$	1709.62			2.23773
$765$		0			0
$766$	300.484	+	173.485i	0.392277	+	0.226481i
$767$	22.4982	+	12.9893i	0.0293327	+	0.0169352i
$768$	616.714	+	1068.18i	0.803014	+	1.39086i
$769$			1383.52i			1.79912i	0.436798	+	0.899560i	$0.356112\pi$
$769$			1383.52i			1.79912i	−0.436798	+	0.899560i	$0.643888\pi$
$770$		0			0
$771$	−1232.22			−1.59821
$772$	−634.514	+	366.337i	−0.821909	+	0.474529i
$773$	152.858	−	264.759i	0.197747	−	0.342508i	−0.750051	−	0.661381i	$-0.769971\pi$
$773$	152.858	−	264.759i	0.197747	−	0.342508i	0.947798	+	0.318873i	$0.103304\pi$
$774$	−137.608	+	238.343i	−0.177788	+	0.307937i
$775$		0			0
$776$			5.99601i			0.00772682i
$777$	−312.572	−	258.532i	−0.402281	−	0.332732i
$778$			2386.52i			3.06750i
$779$	32.1225	+	55.6379i	0.0412356	+	0.0714222i
$780$		0			0
$781$	558.888	−	968.022i	0.715606	−	1.23947i
$782$	−1598.22	−	2768.20i	−2.04376	−	3.53990i
$783$	99.8885			0.127571
$784$	−900.814	+	777.860i	−1.14900	+	0.992169i
$785$		0			0
$786$	−234.126	−	405.519i	−0.297871	−	0.515927i
$787$	−281.008	+	486.720i	−0.357062	+	0.618450i	−0.987469	−	0.157815i	$-0.949555\pi$
$787$	−281.008	+	486.720i	−0.357062	+	0.618450i	0.630406	+	0.776265i	$0.282888\pi$
$788$	−1853.86	−	1070.33i	−2.35261	−	1.35828i
$789$	115.006	−	66.3988i	0.145762	−	0.0841557i
$790$		0			0
$791$	−286.668	−	237.107i	−0.362412	−	0.299756i
$792$		−	708.963i		−	0.895155i
$793$	−21.3345	+	12.3175i	−0.0269035	+	0.0155327i
$794$	−1717.08	−	991.359i	−2.16257	−	1.24856i
$795$		0			0
$796$	918.304	−	530.183i	1.15365	−	0.666059i
$797$	1187.30			1.48971			0.744855	−	0.667226i	$-0.232518\pi$
$797$	1187.30			1.48971			0.744855	+	0.667226i	$0.232518\pi$
$798$	−152.905	−	25.8470i	−0.191610	−	0.0323897i
$799$	176.224			0.220556
$800$		0			0
$801$	−322.794	−	186.365i	−0.402989	−	0.232666i
$802$	−1833.10	−	1058.34i	−2.28566	−	1.31963i
$803$	−624.329	−	1081.37i	−0.777495	−	1.34666i
$804$			962.960i			1.19771i
$805$		0			0
$806$	59.9095			0.0743294
$807$	1030.91	−	595.197i	1.27746	−	0.737543i
$808$	−1330.23	+	2304.02i	−1.64632	+	2.85151i
$809$	−54.8294	+	94.9673i	−0.0677743	+	0.117389i	−0.897921	−	0.440156i	$-0.854923\pi$
$809$	−54.8294	+	94.9673i	−0.0677743	+	0.117389i	0.830147	+	0.557545i	$0.188256\pi$
$810$		0			0
$811$			343.153i			0.423123i	0.977365	+	0.211561i	$0.0678549\pi$
$811$			343.153i			0.423123i	−0.977365	+	0.211561i	$0.932145\pi$
$812$	71.7889	+	192.979i	0.0884100	+	0.237658i
$813$		−	1186.04i		−	1.45885i
$814$	588.872	+	1019.96i	0.723430	+	1.25302i
$815$		0			0
$816$	−805.684	+	1395.49i	−0.987358	+	1.71015i
$817$	−32.1464	−	55.6791i	−0.0393468	−	0.0681507i
$818$	−1621.82			−1.98267
$819$	14.9387	+	2.52524i	0.0182402	+	0.00308332i
$820$		0			0
$821$	236.282	+	409.252i	0.287797	+	0.498480i	0.973284	−	0.229606i	$-0.0737437\pi$
$821$	236.282	+	409.252i	0.287797	+	0.498480i	−0.685486	+	0.728086i	$0.740410\pi$
$822$	−357.774	+	619.682i	−0.435248	+	0.753872i
$823$	−1329.29	−	767.466i	−1.61518	−	0.932523i	−0.988144	−	0.153530i	$-0.950936\pi$
$823$	−1329.29	−	767.466i	−1.61518	−	0.932523i	−0.627033	−	0.778992i	$-0.715731\pi$
$824$	−2057.29	+	1187.78i	−2.49671	+	1.44147i
$825$		0			0
$826$	586.694	−	709.328i	0.710283	−	0.858750i
$827$		−	421.191i		−	0.509299i	−0.967033	−	0.254650i	$-0.918040\pi$
$827$		−	421.191i		−	0.509299i	0.967033	−	0.254650i	$-0.0819602\pi$
$828$	−760.756	+	439.222i	−0.918787	+	0.530462i
$829$	1175.23	+	678.517i	1.41764	+	0.818477i	0.996091	−	0.0883274i	$-0.0281522\pi$
$829$	1175.23	+	678.517i	1.41764	+	0.818477i	0.421552	+	0.906804i	$0.361485\pi$
$830$		0			0
$831$	−642.634	+	371.025i	−0.773327	+	0.446480i
$832$	17.8591			0.0214653
$833$	1261.77	+	439.125i	1.51472	+	0.527161i
$834$	852.976			1.02275
$835$		0			0
$836$	266.679	+	153.967i	0.318994	+	0.184172i
$837$	−609.971	−	352.167i	−0.728758	−	0.420749i
$838$	214.622	+	371.736i	0.256112	+	0.443599i
$839$		−	45.8593i		−	0.0546595i	−0.999626	−	0.0273297i	$-0.991300\pi$
$839$		−	45.8593i		−	0.0546595i	0.999626	−	0.0273297i	$-0.00870041\pi$
$840$		0			0
$841$	−829.450			−0.986267
$842$	−637.410	+	368.009i	−0.757019	+	0.437065i
$843$	134.039	−	232.162i	0.159002	−	0.275399i
$844$	1777.96	−	3079.52i	2.10659	−	3.64872i
$845$		0			0
$846$		−	70.8122i		−	0.0837024i
$847$	−498.614	−	84.2857i	−0.588683	−	0.0995108i
$848$			875.457i			1.03238i
$849$	323.890	+	560.994i	0.381496	+	0.660771i
$850$		0			0
$851$	392.433	−	679.715i	0.461144	−	0.798725i
$852$	846.667	+	1466.47i	0.993740	+	1.72121i
$853$	713.413			0.836358			0.418179	−	0.908365i	$-0.362668\pi$
$853$	713.413			0.836358			0.418179	+	0.908365i	$0.362668\pi$
$854$	304.348	+	818.130i	0.356380	+	0.957998i
$855$		0			0
$856$	525.469	+	910.139i	0.613866	+	1.06325i
$857$	−86.0417	+	149.029i	−0.100399	+	0.173896i	−0.911849	−	0.410526i	$-0.865345\pi$
$857$	−86.0417	+	149.029i	−0.100399	+	0.173896i	0.811450	+	0.584421i	$0.198678\pi$
$858$	73.2309	+	42.2799i	0.0853507	+	0.0492773i
$859$	−225.787	+	130.358i	−0.262849	+	0.151756i	−0.625633	−	0.780117i	$-0.715159\pi$
$859$	−225.787	+	130.358i	−0.262849	+	0.151756i	0.362785	+	0.931873i	$0.381826\pi$
$860$		0			0
$861$	400.702	−	149.063i	0.465391	−	0.173128i
$862$		−	959.990i		−	1.11368i
$863$	944.055	−	545.050i	1.09392	−	0.631576i	0.159304	−	0.987230i	$-0.449075\pi$
$863$	944.055	−	545.050i	1.09392	−	0.631576i	0.934618	+	0.355653i	$0.115742\pi$
$864$	513.358	+	296.387i	0.594164	+	0.343041i
$865$		0			0
$866$	−26.7365	+	15.4363i	−0.0308736	+	0.0178249i
$867$	1105.60			1.27520
$868$	241.985	−	1431.53i	0.278784	−	1.64922i
$869$	1.15650			0.00133083
$870$		0			0
$871$	27.8301	+	16.0677i	0.0319519	+	0.0184474i
$872$	−813.276	−	469.545i	−0.932655	−	0.538469i
$873$	−0.557568	−	0.965736i	−0.000638681	−	0.00110623i
$874$		−	300.053i		−	0.343310i
$875$		0			0
$876$	1891.61			2.15937
$877$	−563.884	+	325.559i	−0.642970	+	0.371219i	−0.785758	−	0.618535i	$-0.787727\pi$
$877$	−563.884	+	325.559i	−0.642970	+	0.371219i	0.142788	+	0.989753i	$0.454393\pi$
$878$	−6.39177	+	11.0709i	−0.00727992	+	0.0126092i
$879$	10.6988	−	18.5309i	0.0121716	−	0.0210819i
$880$		0			0
$881$			1649.45i			1.87225i	0.351671	+	0.936123i	$0.385613\pi$
$881$			1649.45i			1.87225i	−0.351671	+	0.936123i	$0.614387\pi$
$882$	176.454	−	507.015i	0.200061	−	0.574847i
$883$			1487.78i			1.68492i	0.538759	+	0.842460i	$0.318893\pi$
$883$			1487.78i			1.68492i	−0.538759	+	0.842460i	$0.681107\pi$
$884$	82.9203	+	143.622i	0.0938012	+	0.162469i
$885$		0			0
$886$	−719.310	+	1245.88i	−0.811862	+	1.40619i
$887$	76.9555	+	133.291i	0.0867592	+	0.150271i	0.906140	−	0.422979i	$-0.139016\pi$
$887$	76.9555	+	133.291i	0.0867592	+	0.150271i	−0.819380	+	0.573250i	$0.805682\pi$
$888$	−959.605			−1.08064
$889$	−211.424	−	174.872i	−0.237823	−	0.196706i
$890$		0			0
$891$	−304.413	−	527.259i	−0.341654	−	0.591761i
$892$	−302.451	+	523.861i	−0.339071	+	0.587288i
$893$	14.3261	+	8.27118i	0.0160427	+	0.00926224i
$894$	−563.648	+	325.422i	−0.630478	+	0.364007i
$895$		0			0
$896$	199.596	−	1180.77i	0.222764	−	1.31782i
$897$		−	56.3520i		−	0.0628227i
$898$	−1046.46	+	604.173i	−1.16532	+	0.672799i
$899$	−70.5291	−	40.7200i	−0.0784528	−	0.0452948i
$900$		0			0
$901$	851.053	−	491.356i	0.944565	−	0.545345i
$902$	−1241.31			−1.37618
$903$	−400.999	+	149.174i	−0.444074	+	0.165198i
$904$	−880.078			−0.973538
$905$		0			0
$906$	−1161.83	−	670.782i	−1.28237	−	0.740377i
$907$	−910.978	−	525.953i	−1.00439	−	0.579883i	−0.0948429	−	0.995492i	$-0.530235\pi$
$907$	−910.978	−	525.953i	−1.00439	−	0.579883i	−0.909543	+	0.415610i	$0.863568\pi$
$908$	−448.418	−	776.683i	−0.493852	−	0.855378i
$909$		−	494.791i		−	0.544324i
$910$		0			0
$911$	−1305.28			−1.43279			−0.716397	−	0.697693i	$-0.754210\pi$
$911$	−1305.28			−1.43279			−0.716397	+	0.697693i	$0.754210\pi$
$912$	−130.996	+	75.6305i	−0.143636	+	0.0829281i
$913$	662.447	−	1147.39i	0.725572	−	1.25673i
$914$	−1131.74	+	1960.24i	−1.23823	+	2.14468i
$915$		0			0
$916$		−	2625.59i		−	2.86636i
$917$	−63.1174	+	373.388i	−0.0688303	+	0.407184i
$918$		−	2850.81i		−	3.10546i
$919$	−854.848	−	1480.64i	−0.930194	−	1.61114i	−0.782988	−	0.622037i	$-0.786306\pi$
$919$	−854.848	−	1480.64i	−0.930194	−	1.61114i	−0.147205	−	0.989106i	$-0.547028\pi$
$920$		0			0
$921$	−544.048	+	942.319i	−0.590714	+	1.02315i
$922$	860.397	+	1490.25i	0.933185	+	1.61632i
$923$	56.5091			0.0612233
$924$	1306.06	−	1579.06i	1.41349	−	1.70894i
$925$		0			0
$926$	−728.797	−	1262.31i	−0.787038	−	1.36319i
$927$	220.902	−	382.614i	0.238298	−	0.412744i
$928$	59.3581	+	34.2704i	0.0639634	+	0.0369293i
$929$	703.298	−	406.049i	0.757048	−	0.437082i	−0.0711866	−	0.997463i	$-0.522679\pi$
$929$	703.298	−	406.049i	0.757048	−	0.437082i	0.828235	+	0.560381i	$0.189345\pi$
$930$		0			0
$931$	81.9643	+	94.9201i	0.0880390	+	0.101955i
$932$			3708.19i			3.97874i
$933$	474.208	−	273.784i	0.508262	−	0.293445i
$934$	1129.44	+	652.081i	1.20925	+	0.698160i
$935$		0			0
$936$	31.0397	−	17.9208i	0.0331621	−	0.0191461i
$937$	−996.727			−1.06374			−0.531871	−	0.846825i	$-0.678511\pi$
$937$	−996.727			−1.06374			−0.531871	+	0.846825i	$0.678511\pi$
$938$	725.737	−	877.434i	0.773706	−	0.935431i
$939$	−817.777			−0.870902
$940$		0			0
$941$	1330.08	+	767.920i	1.41347	+	0.816068i	0.995714	−	0.0924907i	$-0.0294828\pi$
$941$	1330.08	+	767.920i	1.41347	+	0.816068i	0.417757	+	0.908559i	$0.362816\pi$
$942$	869.701	+	502.122i	0.923249	+	0.533038i
$943$	413.615	+	716.402i	0.438616	+	0.759705i
$944$		−	897.884i		−	0.951149i
$945$		0			0
$946$	1242.23			1.31314
$947$	1035.53	−	597.863i	1.09348	−	0.631323i	0.158981	−	0.987282i	$-0.449179\pi$
$947$	1035.53	−	597.863i	1.09348	−	0.631323i	0.934502	+	0.355959i	$0.115846\pi$
$948$	−0.875995	+	1.51727i	−0.000924046	+	0.00160049i
$949$	31.5629	−	54.6686i	0.0332591	−	0.0576065i
$950$		0			0
$951$		−	200.576i		−	0.210911i
$952$	2962.21	−	1101.96i	3.11156	−	1.15752i
$953$		−	770.228i		−	0.808214i	−0.914712	−	0.404107i	$-0.867582\pi$
$953$		−	770.228i		−	0.808214i	0.914712	−	0.404107i	$-0.132418\pi$
$954$	−197.442	−	341.979i	−0.206962	−	0.358468i
$955$		0			0
$956$	−474.361	+	821.618i	−0.496194	+	0.859433i
$957$	−57.4746	−	99.5490i	−0.0600571	−	0.104022i
$958$	302.083			0.315327
$959$	542.364	−	201.762i	0.565552	−	0.210388i
$960$		0			0
$961$	−193.375	−	334.936i	−0.201223	−	0.348528i
$962$	−29.7704	+	51.5638i	−0.0309464	+	0.0536007i
$963$	−169.267	−	97.7265i	−0.175771	−	0.101481i
$964$	2143.18	−	1237.36i	2.22321	−	1.28357i
$965$		0			0
$966$	−1968.83	−	332.810i	−2.03812	−	0.344524i
$967$		−	628.771i		−	0.650229i	−0.945675	−	0.325114i	$-0.894597\pi$
$967$		−	628.771i		−	0.650229i	0.945675	−	0.325114i	$-0.105403\pi$
$968$	−1036.02	+	598.148i	−1.07027	+	0.617922i
$969$	147.044	+	84.8962i	0.151749	+	0.0876121i
$970$		0			0
$971$	−584.383	+	337.394i	−0.601837	+	0.347471i	−0.769764	−	0.638329i	$-0.779626\pi$
$971$	−584.383	+	337.394i	−0.601837	+	0.347471i	0.167927	+	0.985799i	$0.446293\pi$
$972$	−1367.17			−1.40656
$973$	−531.555	−	439.656i	−0.546305	−	0.451856i
$974$	116.489			0.119599
$975$		0			0
$976$	737.371	+	425.721i	0.755503	+	0.436190i
$977$	1000.26	+	577.502i	1.02381	+	0.591098i	0.915206	−	0.402987i	$-0.132028\pi$
$977$	1000.26	+	577.502i	1.02381	+	0.591098i	0.108605	+	0.994085i	$0.465361\pi$
$978$	823.108	+	1425.67i	0.841624	+	1.45774i
$979$			1682.39i			1.71847i
$980$		0			0
$981$	174.652			0.178034
$982$	1611.04	−	930.137i	1.64057	−	0.947186i
$983$	119.623	−	207.193i	0.121692	−	0.210776i	−0.798743	−	0.601672i	$-0.794501\pi$
$983$	119.623	−	207.193i	0.121692	−	0.210776i	0.920435	+	0.390896i	$0.127835\pi$
$984$	505.700	−	875.897i	0.513922	−	0.890140i
$985$		0			0
$986$		−	329.631i		−	0.334311i
$987$	70.1621	−	84.8278i	0.0710863	−	0.0859451i
$988$			15.5676i			0.0157567i
$989$	−413.922	−	716.933i	−0.418525	−	0.724907i
$990$		0			0
$991$	356.230	−	617.008i	0.359465	−	0.622612i	−0.628407	−	0.777885i	$-0.716293\pi$
$991$	356.230	−	617.008i	0.359465	−	0.622612i	0.987872	+	0.155273i	$0.0496259\pi$
$992$	−241.647	−	418.545i	−0.243596	−	0.421921i
$993$	−230.574			−0.232199
$994$	333.738	−	1974.32i	0.335753	−	1.98623i
$995$		0			0
$996$	1003.55	+	1738.20i	1.00758	+	1.74518i
$997$	697.807	−	1208.64i	0.699906	−	1.21227i	−0.268592	−	0.963254i	$-0.586558\pi$
$997$	697.807	−	1208.64i	0.699906	−	1.21227i	0.968499	−	0.249019i	$-0.0801083\pi$
$998$	−187.670	−	108.352i	−0.188047	−	0.108569i
$999$	606.217	−	349.999i	0.606824	−	0.350350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.3.j.b.24.12		24
5.2	odd	4		175.3.i.d.101.6		12
5.3	odd	4		35.3.h.a.31.1	yes	12
5.4	even	2	inner	175.3.j.b.24.1		24
7.5	odd	6	inner	175.3.j.b.124.1		24
15.8	even	4		315.3.w.c.136.6		12
20.3	even	4		560.3.bx.c.241.5		12
35.3	even	12		245.3.d.a.146.11		12
35.12	even	12		175.3.i.d.26.6		12
35.13	even	4		245.3.h.c.31.1		12
35.18	odd	12		245.3.d.a.146.12		12
35.19	odd	6	inner	175.3.j.b.124.12		24
35.23	odd	12		245.3.h.c.166.1		12
35.33	even	12		35.3.h.a.26.1	✓	12
105.68	odd	12		315.3.w.c.271.6		12
140.103	odd	12		560.3.bx.c.481.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.h.a.26.1	✓	12	35.33	even	12
35.3.h.a.31.1	yes	12	5.3	odd	4
175.3.i.d.26.6		12	35.12	even	12
175.3.i.d.101.6		12	5.2	odd	4
175.3.j.b.24.1		24	5.4	even	2	inner
175.3.j.b.24.12		24	1.1	even	1	trivial
175.3.j.b.124.1		24	7.5	odd	6	inner
175.3.j.b.124.12		24	35.19	odd	6	inner
245.3.d.a.146.11		12	35.3	even	12
245.3.d.a.146.12		12	35.18	odd	12
245.3.h.c.31.1		12	35.13	even	4
245.3.h.c.166.1		12	35.23	odd	12
315.3.w.c.136.6		12	15.8	even	4
315.3.w.c.271.6		12	105.68	odd	12
560.3.bx.c.241.5		12	20.3	even	4
560.3.bx.c.481.5		12	140.103	odd	12

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	175.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.08079 - 1.77870i) q^{2} +(-1.21658 + 2.10717i) q^{3} +(4.32752 - 7.49548i) q^{4} +8.65567i q^{6} +(4.46146 - 5.39402i) q^{7} -16.5598i q^{8} +(1.53989 + 2.66717i) q^{9} +O(q^{10})\)	\(q+(3.08079 - 1.77870i) q^{2} +(-1.21658 + 2.10717i) q^{3} +(4.32752 - 7.49548i) q^{4} +8.65567i q^{6} +(4.46146 - 5.39402i) q^{7} -16.5598i q^{8} +(1.53989 + 2.66717i) q^{9} +(6.95056 - 12.0387i) q^{11} +(10.5295 + 18.2376i) q^{12} +0.702771 q^{13} +(4.15050 - 24.5534i) q^{14} +(-12.1447 - 21.0353i) q^{16} +(-13.6326 + 23.6124i) q^{17} +(9.48815 + 5.47799i) q^{18} +(-2.21652 + 1.27971i) q^{19} +(5.93841 + 15.9633i) q^{21} -49.4517i q^{22} +(-28.5402 + 16.4777i) q^{23} +(34.8942 + 20.1462i) q^{24} +(2.16509 - 1.25001i) q^{26} -29.3919 q^{27} +(-21.1237 - 56.7834i) q^{28} -3.39850 q^{29} +(20.7530 + 11.9818i) q^{31} +(-17.4660 - 10.0840i) q^{32} +(16.9118 + 29.2920i) q^{33} +96.9930i q^{34} +26.6556 q^{36} +(-20.6253 + 11.9080i) q^{37} +(-4.55242 + 7.88502i) q^{38} +(-0.854973 + 1.48086i) q^{39} -25.1015i q^{41} +(46.6888 + 38.6169i) q^{42} +25.1201i q^{43} +(-60.1573 - 104.196i) q^{44} +(-58.6176 + 101.529i) q^{46} +(-3.23167 - 5.59742i) q^{47} +59.0998 q^{48} +(-9.19081 - 48.1303i) q^{49} +(-33.1702 - 57.4524i) q^{51} +(3.04125 - 5.26760i) q^{52} +(-31.2139 - 18.0214i) q^{53} +(-90.5504 + 52.2793i) q^{54} +(-89.3236 - 73.8807i) q^{56} -6.22744i q^{57} +(-10.4701 + 6.04490i) q^{58} +(32.0135 + 18.4830i) q^{59} +(-30.3577 + 17.5270i) q^{61} +85.2476 q^{62} +(21.2569 + 3.59326i) q^{63} +25.4125 q^{64} +(104.203 + 60.1617i) q^{66} +(39.6006 + 22.8634i) q^{67} +(117.991 + 204.366i) q^{68} -80.1854i q^{69} +80.4090 q^{71} +(44.1676 - 25.5002i) q^{72} +(44.9121 - 77.7901i) q^{73} +(-42.3615 + 73.3722i) q^{74} +22.1518i q^{76} +(-33.9274 - 91.2017i) q^{77} +6.08295i q^{78} +(0.0415972 + 0.0720485i) q^{79} +(21.8985 - 37.9293i) q^{81} +(-44.6479 - 77.3324i) q^{82} +95.3085 q^{83} +(145.351 + 24.5701i) q^{84} +(44.6810 + 77.3898i) q^{86} +(4.13453 - 7.16122i) q^{87} +(-199.358 - 115.100i) q^{88} +(-104.811 + 60.5126i) q^{89} +(3.13538 - 3.79076i) q^{91} +285.230i q^{92} +(-50.4952 + 29.1534i) q^{93} +(-19.9122 - 11.4963i) q^{94} +(42.4973 - 24.5358i) q^{96} -0.362083 q^{97} +(-113.924 - 131.932i) q^{98} +42.8124 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{4} - 28 q^{9}+O(q^{10}) \) 24 * q + 20 * q^4 - 28 * q^9	\( 24 q + 20 q^{4} - 28 q^{9} - 28 q^{11} + 4 q^{14} - 44 q^{16} + 60 q^{19} - 168 q^{21} + 72 q^{24} + 132 q^{26} - 128 q^{29} + 264 q^{31} + 312 q^{36} + 48 q^{39} - 12 q^{44} - 428 q^{46} + 48 q^{49} - 264 q^{51} - 336 q^{54} - 920 q^{56} - 144 q^{59} + 144 q^{61} + 280 q^{64} + 1488 q^{66} - 16 q^{71} - 100 q^{74} + 24 q^{79} - 620 q^{81} + 552 q^{84} - 80 q^{86} - 408 q^{89} - 960 q^{91} + 84 q^{94} + 1080 q^{96} + 88 q^{99}+O(q^{100}) \) 24 * q + 20 * q^4 - 28 * q^9 - 28 * q^11 + 4 * q^14 - 44 * q^16 + 60 * q^19 - 168 * q^21 + 72 * q^24 + 132 * q^26 - 128 * q^29 + 264 * q^31 + 312 * q^36 + 48 * q^39 - 12 * q^44 - 428 * q^46 + 48 * q^49 - 264 * q^51 - 336 * q^54 - 920 * q^56 - 144 * q^59 + 144 * q^61 + 280 * q^64 + 1488 * q^66 - 16 * q^71 - 100 * q^74 + 24 * q^79 - 620 * q^81 + 552 * q^84 - 80 * q^86 - 408 * q^89 - 960 * q^91 + 84 * q^94 + 1080 * q^96 + 88 * q^99

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