LMFDB - Embedded newform 288.3.u.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(19,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 0]))

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

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

chi := DirichletCharacter("288.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.u (of order $8$, degree $4$, 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:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	288.19
Dual form			288.3.u.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82416 + 0.820030i) q^{2} +(2.65510 - 2.99173i) q^{4} +(7.60625 - 3.15061i) q^{5} +(6.84161 + 6.84161i) q^{7} +(-2.39002 + 7.63465i) q^{8} +O(q^{10})$	\(q+(-1.82416 + 0.820030i) q^{2} +(2.65510 - 2.99173i) q^{4} +(7.60625 - 3.15061i) q^{5} +(6.84161 + 6.84161i) q^{7} +(-2.39002 + 7.63465i) q^{8} +(-11.2914 + 11.9846i) q^{10} +(2.23818 - 0.927086i) q^{11} +(1.40964 + 0.583890i) q^{13} +(-18.0905 - 6.86984i) q^{14} +(-1.90088 - 15.8867i) q^{16} -2.67812i q^{17} +(5.38908 - 13.0104i) q^{19} +(10.7696 - 31.1210i) q^{20} +(-3.32256 + 3.52653i) q^{22} +(-18.8388 + 18.8388i) q^{23} +(30.2510 - 30.2510i) q^{25} +(-3.05020 + 0.0908360i) q^{26} +(38.6334 - 2.30307i) q^{28} +(10.0298 - 24.2140i) q^{29} +47.5858i q^{31} +(16.4951 + 27.4210i) q^{32} +(2.19614 + 4.88532i) q^{34} +(73.5942 + 30.4837i) q^{35} +(-28.2682 + 11.7091i) q^{37} +(0.838382 + 28.1522i) q^{38} +(5.87475 + 65.6010i) q^{40} +(-6.93962 - 6.93962i) q^{41} +(8.48982 - 3.51660i) q^{43} +(3.16902 - 9.15755i) q^{44} +(18.9165 - 49.8132i) q^{46} +67.0112 q^{47} +44.6152i q^{49} +(-30.3759 + 79.9893i) q^{50} +(5.48956 - 2.66696i) q^{52} +(10.5006 + 25.3507i) q^{53} +(14.1033 - 14.1033i) q^{55} +(-68.5848 + 35.8817i) q^{56} +(1.56034 + 52.3950i) q^{58} +(-27.9364 - 67.4445i) q^{59} +(31.5752 - 76.2294i) q^{61} +(-39.0218 - 86.8040i) q^{62} +(-52.5757 - 36.4938i) q^{64} +12.5616 q^{65} +(90.1903 + 37.3580i) q^{67} +(-8.01222 - 7.11069i) q^{68} +(-159.245 + 4.74236i) q^{70} +(-1.98379 - 1.98379i) q^{71} +(-55.5273 - 55.5273i) q^{73} +(41.9639 - 44.5400i) q^{74} +(-24.6150 - 50.6666i) q^{76} +(21.6555 + 8.97002i) q^{77} +10.9856 q^{79} +(-64.5113 - 114.849i) q^{80} +(18.3496 + 6.96826i) q^{82} +(-34.1779 + 82.5128i) q^{83} +(-8.43772 - 20.3705i) q^{85} +(-12.6031 + 13.3767i) q^{86} +(1.72868 + 19.3035i) q^{88} +(16.1705 - 16.1705i) q^{89} +(5.64942 + 13.6389i) q^{91} +(6.34164 + 106.379i) q^{92} +(-122.239 + 54.9512i) q^{94} -115.939i q^{95} -62.6434 q^{97} +(-36.5858 - 81.3851i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

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 $

$2$	−1.82416	+	0.820030i	−0.912079	+	0.410015i
$2$	−1.82416	+	0.820030i	−0.912079	+	0.410015i
$3$		0			0
$3$		0			0
$4$	2.65510	−	2.99173i	0.663775	−	0.747932i
$5$	7.60625	−	3.15061i	1.52125	−	0.630122i	0.543408	−	0.839469i	$-0.317134\pi$
$5$	7.60625	−	3.15061i	1.52125	−	0.630122i	0.977842	+	0.209346i	$0.0671336\pi$
$6$		0			0
$7$	6.84161	+	6.84161i	0.977372	+	0.977372i	0.999750	−	0.0223772i	$-0.00712349\pi$
$7$	6.84161	+	6.84161i	0.977372	+	0.977372i	−0.0223772	+	0.999750i	$0.507123\pi$
$8$	−2.39002	+	7.63465i	−0.298752	+	0.954331i
$9$		0			0
$10$	−11.2914	+	11.9846i	−1.12914	+	1.19846i
$11$	2.23818	−	0.927086i	0.203471	−	0.0842806i	−0.278621	−	0.960401i	$-0.589877\pi$
$11$	2.23818	−	0.927086i	0.203471	−	0.0842806i	0.482092	+	0.876121i	$0.339877\pi$
$12$		0			0
$13$	1.40964	+	0.583890i	0.108433	+	0.0449146i	0.436241	−	0.899830i	$-0.356310\pi$
$13$	1.40964	+	0.583890i	0.108433	+	0.0449146i	−0.327807	+	0.944745i	$0.606310\pi$
$14$	−18.0905	−	6.86984i	−1.29218	−	0.490703i
$15$		0			0
$16$	−1.90088	−	15.8867i	−0.118805	−	0.992918i
$17$		−	2.67812i		−	0.157537i	−0.996893	−	0.0787683i	$-0.974901\pi$
$17$		−	2.67812i		−	0.157537i	0.996893	−	0.0787683i	$-0.0250987\pi$
$18$		0			0
$19$	5.38908	−	13.0104i	0.283636	−	0.684757i	−0.716279	−	0.697814i	$-0.754156\pi$
$19$	5.38908	−	13.0104i	0.283636	−	0.684757i	0.999915	+	0.0130566i	$0.00415616\pi$
$20$	10.7696	−	31.1210i	0.538479	−	1.55605i
$21$		0			0
$22$	−3.32256	+	3.52653i	−0.151026	+	0.160297i
$23$	−18.8388	+	18.8388i	−0.819076	+	0.819076i	−0.985974	−	0.166898i	$-0.946625\pi$
$23$	−18.8388	+	18.8388i	−0.819076	+	0.819076i	0.166898	+	0.985974i	$0.446625\pi$
$24$		0			0
$25$	30.2510	−	30.2510i	1.21004	−	1.21004i
$26$	−3.05020	+	0.0908360i	−0.117316	+	0.00349369i
$27$		0			0
$28$	38.6334	−	2.30307i	1.37976	−	0.0822525i
$29$	10.0298	−	24.2140i	0.345855	−	0.834967i	−0.651245	−	0.758867i	$-0.725753\pi$
$29$	10.0298	−	24.2140i	0.345855	−	0.834967i	0.997100	−	0.0761000i	$-0.0242468\pi$
$30$		0			0
$31$			47.5858i			1.53503i	0.641033	+	0.767513i	$0.278506\pi$
$31$			47.5858i			1.53503i	−0.641033	+	0.767513i	$0.721494\pi$
$32$	16.4951	+	27.4210i	0.515470	+	0.856907i
$33$		0			0
$34$	2.19614	+	4.88532i	0.0645924	+	0.143686i
$35$	73.5942	+	30.4837i	2.10269	+	0.870963i
$36$		0			0
$37$	−28.2682	+	11.7091i	−0.764006	+	0.316462i	−0.730442	−	0.682975i	$-0.760686\pi$
$37$	−28.2682	+	11.7091i	−0.764006	+	0.316462i	−0.0335642	+	0.999437i	$0.510686\pi$
$38$	0.838382	+	28.1522i	0.0220627	+	0.740848i
$39$		0			0
$40$	5.87475	+	65.6010i	0.146869	+	1.64003i
$41$	−6.93962	−	6.93962i	−0.169259	−	0.169259i	0.617395	−	0.786654i	$-0.288188\pi$
$41$	−6.93962	−	6.93962i	−0.169259	−	0.169259i	−0.786654	+	0.617395i	$0.788188\pi$
$42$		0			0
$43$	8.48982	−	3.51660i	0.197438	−	0.0817814i	−0.281774	−	0.959481i	$-0.590923\pi$
$43$	8.48982	−	3.51660i	0.197438	−	0.0817814i	0.479211	+	0.877700i	$0.340923\pi$
$44$	3.16902	−	9.15755i	0.0720231	−	0.208126i
$45$		0			0
$46$	18.9165	−	49.8132i	0.411228	−	1.08290i
$47$	67.0112			1.42577			0.712885	−	0.701281i	$-0.247388\pi$
$47$	67.0112			1.42577			0.712885	+	0.701281i	$0.247388\pi$
$48$		0			0
$49$			44.6152i			0.910513i
$50$	−30.3759	+	79.9893i	−0.607517	+	1.59979i
$51$		0			0
$52$	5.48956	−	2.66696i	0.105569	−	0.0512877i
$53$	10.5006	+	25.3507i	0.198124	+	0.478315i	0.991451	−	0.130482i	$-0.0416525\pi$
$53$	10.5006	+	25.3507i	0.198124	+	0.478315i	−0.793326	+	0.608797i	$0.791653\pi$
$54$		0			0
$55$	14.1033	−	14.1033i	0.256424	−	0.256424i
$56$	−68.5848	+	35.8817i	−1.22473	+	0.640745i
$57$		0			0
$58$	1.56034	+	52.3950i	0.0269024	+	0.903361i
$59$	−27.9364	−	67.4445i	−0.473499	−	1.14313i	−0.962606	−	0.270904i	$-0.912677\pi$
$59$	−27.9364	−	67.4445i	−0.473499	−	1.14313i	0.489107	−	0.872224i	$-0.337323\pi$
$60$		0			0
$61$	31.5752	−	76.2294i	0.517627	−	1.24966i	−0.421730	−	0.906721i	$-0.638577\pi$
$61$	31.5752	−	76.2294i	0.517627	−	1.24966i	0.939357	−	0.342941i	$-0.111423\pi$
$62$	−39.0218	−	86.8040i	−0.629384	−	1.40006i
$63$		0			0
$64$	−52.5757	−	36.4938i	−0.821495	−	0.570216i
$65$	12.5616			0.193256
$66$		0			0
$67$	90.1903	+	37.3580i	1.34612	+	0.557583i	0.935211	−	0.354092i	$-0.115210\pi$
$67$	90.1903	+	37.3580i	1.34612	+	0.557583i	0.410913	+	0.911674i	$0.365210\pi$
$68$	−8.01222	−	7.11069i	−0.117827	−	0.104569i
$69$		0			0
$70$	−159.245	+	4.74236i	−2.27493	+	0.0677481i
$71$	−1.98379	−	1.98379i	−0.0279407	−	0.0279407i	0.692998	−	0.720939i	$-0.256289\pi$
$71$	−1.98379	−	1.98379i	−0.0279407	−	0.0279407i	−0.720939	+	0.692998i	$0.756289\pi$
$72$		0			0
$73$	−55.5273	−	55.5273i	−0.760648	−	0.760648i	0.215792	−	0.976439i	$-0.430767\pi$
$73$	−55.5273	−	55.5273i	−0.760648	−	0.760648i	−0.976439	+	0.215792i	$0.930767\pi$
$74$	41.9639	−	44.5400i	0.567080	−	0.601892i
$75$		0			0
$76$	−24.6150	−	50.6666i	−0.323882	−	0.666665i
$77$	21.6555	+	8.97002i	0.281241	+	0.116494i
$78$		0			0
$79$	10.9856			0.139058			0.0695292	−	0.997580i	$-0.477850\pi$
$79$	10.9856			0.139058			0.0695292	+	0.997580i	$0.477850\pi$
$80$	−64.5113	−	114.849i	−0.806391	−	1.43561i
$81$		0			0
$82$	18.3496	+	6.96826i	0.223776	+	0.0849788i
$83$	−34.1779	+	82.5128i	−0.411782	+	0.994130i	0.572877	+	0.819641i	$0.305827\pi$
$83$	−34.1779	+	82.5128i	−0.411782	+	0.994130i	−0.984659	+	0.174489i	$0.944173\pi$
$84$		0			0
$85$	−8.43772	−	20.3705i	−0.0992674	−	0.239653i
$86$	−12.6031	+	13.3767i	−0.146547	+	0.155543i
$87$		0			0
$88$	1.72868	+	19.3035i	0.0196441	+	0.219358i
$89$	16.1705	−	16.1705i	0.181691	−	0.181691i	−0.610401	−	0.792093i	$-0.708992\pi$
$89$	16.1705	−	16.1705i	0.181691	−	0.181691i	0.792093	+	0.610401i	$0.208992\pi$
$90$		0			0
$91$	5.64942	+	13.6389i	0.0620816	+	0.149878i
$92$	6.34164	+	106.379i	0.0689308	+	1.15630i
$93$		0			0
$94$	−122.239	+	54.9512i	−1.30042	+	0.584587i
$95$		−	115.939i		−	1.22041i
$96$		0			0
$97$	−62.6434			−0.645808			−0.322904	−	0.946432i	$-0.604659\pi$
$97$	−62.6434			−0.645808			−0.322904	+	0.946432i	$0.604659\pi$
$98$	−36.5858	−	81.3851i	−0.373324	−	0.830460i
$99$		0			0
$100$	−10.1833	−	170.822i	−0.101833	−	1.70822i
$101$	−39.7340	+	16.4584i	−0.393406	+	0.162954i	−0.570612	−	0.821220i	$-0.693294\pi$
$101$	−39.7340	+	16.4584i	−0.393406	+	0.162954i	0.177206	+	0.984174i	$0.443294\pi$
$102$		0			0
$103$	−36.3254	−	36.3254i	−0.352674	−	0.352674i	0.508430	−	0.861104i	$-0.330226\pi$
$103$	−36.3254	−	36.3254i	−0.352674	−	0.352674i	−0.861104	+	0.508430i	$0.830226\pi$
$104$	−7.82684	+	9.36656i	−0.0752581	+	0.0900631i
$105$		0			0
$106$	−39.9431	−	37.6328i	−0.376821	−	0.355027i
$107$	−111.798	+	46.3084i	−1.04484	+	0.432789i	−0.838049	−	0.545596i	$-0.816304\pi$
$107$	−111.798	+	46.3084i	−1.04484	+	0.432789i	−0.206796	+	0.978384i	$0.566304\pi$
$108$		0			0
$109$	−55.7631	−	23.0978i	−0.511588	−	0.211907i	0.111929	−	0.993716i	$-0.464297\pi$
$109$	−55.7631	−	23.0978i	−0.511588	−	0.211907i	−0.623517	+	0.781809i	$0.714297\pi$
$110$	−14.1615	+	37.2918i	−0.128741	+	0.339016i
$111$		0			0
$112$	95.6854	−	121.695i	0.854334	−	1.08657i
$113$			80.7753i			0.714825i	0.933947	+	0.357413i	$0.116341\pi$
$113$			80.7753i			0.714825i	−0.933947	+	0.357413i	$0.883659\pi$
$114$		0			0
$115$	−83.9387	+	202.646i	−0.729901	+	1.76214i
$116$	−45.8118	−	94.2971i	−0.394929	−	0.812906i
$117$		0			0
$118$	106.267	+	100.121i	0.900568	+	0.848481i
$119$	18.3227	−	18.3227i	0.153972	−	0.153972i
$120$		0			0
$121$	−81.4099	+	81.4099i	−0.672809	+	0.672809i
$122$	4.91217	+	164.947i	0.0402637	+	1.35203i
$123$		0			0
$124$	142.364	+	126.345i	1.14810	+	1.01891i
$125$	56.0222	−	135.250i	0.448178	−	1.08200i
$126$		0			0
$127$		−	143.036i		−	1.12627i	−0.826365	−	0.563135i	$-0.809595\pi$
$127$		−	143.036i		−	1.12627i	0.826365	−	0.563135i	$-0.190405\pi$
$128$	125.832	+	23.4569i	0.983065	+	0.183257i
$129$		0			0
$130$	−22.9144	+	10.3009i	−0.176265	+	0.0792379i
$131$	56.1430	+	23.2552i	0.428573	+	0.177521i	0.586534	−	0.809925i	$-0.300492\pi$
$131$	56.1430	+	23.2552i	0.428573	+	0.177521i	−0.157961	+	0.987445i	$0.550492\pi$
$132$		0			0
$133$	125.882	−	52.1420i	0.946481	−	0.392045i
$134$	−195.156	+	5.81181i	−1.45639	+	0.0433717i
$135$		0			0
$136$	20.4465	+	6.40075i	0.150342	+	0.0470644i
$137$	−168.165	−	168.165i	−1.22748	−	1.22748i	−0.964915	−	0.262563i	$-0.915432\pi$
$137$	−168.165	−	168.165i	−1.22748	−	1.22748i	−0.262563	−	0.964915i	$-0.584568\pi$
$138$		0			0
$139$	−97.5768	+	40.4176i	−0.701991	+	0.290774i	−0.704986	−	0.709221i	$-0.749047\pi$
$139$	−97.5768	+	40.4176i	−0.701991	+	0.290774i	0.00299484	+	0.999996i	$0.499047\pi$
$140$	286.599	−	139.237i	2.04714	−	0.994547i
$141$		0			0
$142$	5.24551	+	1.99198i	0.0369402	+	0.0140280i
$143$	3.69634			0.0258485
$144$		0			0
$145$		−	215.778i		−	1.48812i
$146$	146.825	+	55.7565i	1.00565	+	0.381894i
$147$		0			0
$148$	−40.0246	+	115.660i	−0.270437	+	0.781484i
$149$	−44.3735	−	107.127i	−0.297809	−	0.718974i	−0.999976	−	0.00696156i	$-0.997784\pi$
$149$	−44.3735	−	107.127i	−0.297809	−	0.718974i	0.702167	−	0.712012i	$-0.252216\pi$
$150$		0			0
$151$	−128.078	+	128.078i	−0.848200	+	0.848200i	−0.989908	−	0.141708i	$-0.954741\pi$
$151$	−128.078	+	128.078i	−0.848200	+	0.848200i	0.141708	+	0.989908i	$0.454741\pi$
$152$	86.4498	+	72.2388i	0.568748	+	0.475255i
$153$		0			0
$154$	−46.8588	+	1.39547i	−0.304278	+	0.00906149i
$155$	149.924	+	361.950i	0.967254	+	2.33516i
$156$		0			0
$157$	20.1590	−	48.6682i	0.128401	−	0.309988i	−0.846585	−	0.532254i	$-0.821345\pi$
$157$	20.1590	−	48.6682i	0.128401	−	0.309988i	0.974986	+	0.222265i	$0.0713452\pi$
$158$	−20.0395	+	9.00854i	−0.126832	+	0.0570161i
$159$		0			0
$160$	211.859	+	156.602i	1.32412	+	0.978761i
$161$	−257.775			−1.60109
$162$		0			0
$163$	68.6749	+	28.4461i	0.421319	+	0.174516i	0.583262	−	0.812284i	$-0.301776\pi$
$163$	68.6749	+	28.4461i	0.421319	+	0.174516i	−0.161943	+	0.986800i	$0.551776\pi$
$164$	−39.1868	+	2.33606i	−0.238944	+	0.0142443i
$165$		0			0
$166$	−5.31707	−	178.543i	−0.0320306	−	1.07556i
$167$	−131.350	−	131.350i	−0.786527	−	0.786527i	0.194396	−	0.980923i	$-0.437725\pi$
$167$	−131.350	−	131.350i	−0.786527	−	0.786527i	−0.980923	+	0.194396i	$0.937725\pi$
$168$		0			0
$169$	−117.855	−	117.855i	−0.697366	−	0.697366i
$170$	32.0961	+	30.2398i	0.188801	+	0.177881i
$171$		0			0
$172$	12.0206	−	34.7362i	0.0698873	−	0.201954i
$173$	206.045	+	85.3465i	1.19101	+	0.493333i	0.888084	−	0.459681i	$-0.152036\pi$
$173$	206.045	+	85.3465i	1.19101	+	0.493333i	0.302926	+	0.953014i	$0.402036\pi$
$174$		0			0
$175$	413.931			2.36532
$176$	−18.9828	−	33.7950i	−0.107857	−	0.192017i
$177$		0			0
$178$	−16.2373	+	42.7579i	−0.0912207	+	0.240213i
$179$	−80.2014	+	193.623i	−0.448053	+	1.08169i	0.524998	+	0.851104i	$0.324066\pi$
$179$	−80.2014	+	193.623i	−0.448053	+	1.08169i	−0.973051	+	0.230591i	$0.925934\pi$
$180$		0			0
$181$	93.4345	+	225.571i	0.516213	+	1.24625i	0.940213	+	0.340586i	$0.110626\pi$
$181$	93.4345	+	225.571i	0.516213	+	1.24625i	−0.424000	+	0.905662i	$0.639374\pi$
$182$	−21.4898	−	20.2468i	−0.118076	−	0.111246i
$183$		0			0
$184$	−98.8023	−	188.852i	−0.536969	−	1.02637i
$185$	−178.124	+	178.124i	−0.962835	+	0.962835i
$186$		0			0
$187$	−2.48285	−	5.99413i	−0.0132773	−	0.0320542i
$188$	177.922	−	200.479i	0.946391	−	1.06638i
$189$		0			0
$190$	95.0736	+	211.491i	0.500388	+	1.11311i
$191$			20.1639i			0.105570i	0.998606	+	0.0527851i	$0.0168098\pi$
$191$			20.1639i			0.105570i	−0.998606	+	0.0527851i	$0.983190\pi$
$192$		0			0
$193$	115.896			0.600497			0.300248	−	0.953861i	$-0.402930\pi$
$193$	115.896			0.600497			0.300248	+	0.953861i	$0.402930\pi$
$194$	114.271	−	51.3694i	0.589028	−	0.264791i
$195$		0			0
$196$	133.476	+	118.458i	0.681002	+	0.604376i
$197$	177.705	−	73.6077i	0.902055	−	0.373643i	0.117045	−	0.993127i	$-0.462658\pi$
$197$	177.705	−	73.6077i	0.902055	−	0.373643i	0.785010	+	0.619483i	$0.212658\pi$
$198$		0			0
$199$	−22.1763	−	22.1763i	−0.111439	−	0.111439i	0.649189	−	0.760627i	$-0.275109\pi$
$199$	−22.1763	−	22.1763i	−0.111439	−	0.111439i	−0.760627	+	0.649189i	$0.775109\pi$
$200$	158.655	+	303.256i	0.793277	+	1.51628i
$201$		0			0
$202$	58.9847	−	62.6057i	0.292003	−	0.309929i
$203$	234.283	−	97.0431i	1.15410	−	0.478045i
$204$		0			0
$205$	−74.6485	−	30.9204i	−0.364139	−	0.150831i
$206$	96.0512	+	36.4753i	0.466268	+	0.177065i
$207$		0			0
$208$	6.59653	−	23.5043i	0.0317141	−	0.113002i
$209$		−	34.1158i		−	0.163233i
$210$		0			0
$211$	−116.936	+	282.308i	−0.554197	+	1.33795i	0.360103	+	0.932913i	$0.382742\pi$
$211$	−116.936	+	282.308i	−0.554197	+	1.33795i	−0.914300	+	0.405038i	$0.867258\pi$
$212$	103.722	+	35.8937i	0.489257	+	0.169310i
$213$		0			0
$214$	165.963	−	176.152i	0.775530	−	0.823139i
$215$	53.4962	−	53.4962i	0.248820	−	0.248820i
$216$		0			0
$217$	−325.563	+	325.563i	−1.50029	+	1.50029i
$218$	120.662	−	3.59334i	0.553493	−	0.0164832i
$219$		0			0
$220$	−4.74755	−	79.6389i	−0.0215798	−	0.361995i
$221$	1.56373	−	3.77518i	0.00707570	−	0.0170822i
$222$		0			0
$223$			12.1409i			0.0544434i	0.999629	+	0.0272217i	$0.00866601\pi$
$223$			12.1409i			0.0544434i	−0.999629	+	0.0272217i	$0.991334\pi$
$224$	−74.7512	+	300.457i	−0.333711	+	1.34132i
$225$		0			0
$226$	−66.2381	−	147.347i	−0.293089	−	0.651977i
$227$	−215.118	−	89.1048i	−0.947656	−	0.392532i	−0.145307	−	0.989387i	$-0.546417\pi$
$227$	−215.118	−	89.1048i	−0.947656	−	0.392532i	−0.802350	+	0.596854i	$0.796417\pi$
$228$		0			0
$229$	85.4872	−	35.4100i	0.373307	−	0.154629i	−0.188139	−	0.982142i	$-0.560245\pi$
$229$	85.4872	−	35.4100i	0.373307	−	0.154629i	0.561445	+	0.827514i	$0.310245\pi$
$230$	−13.0584	−	438.490i	−0.0567755	−	1.90648i
$231$		0			0
$232$	160.894	+	134.446i	0.693510	+	0.579508i
$233$	−33.1162	−	33.1162i	−0.142129	−	0.142129i	0.632462	−	0.774591i	$-0.282044\pi$
$233$	−33.1162	−	33.1162i	−0.142129	−	0.142129i	−0.774591	+	0.632462i	$0.782044\pi$
$234$		0			0
$235$	509.704	−	211.126i	2.16895	−	0.898410i
$236$	−275.950	−	95.4938i	−1.16928	−	0.404635i
$237$		0			0
$238$	−18.3983	+	48.4486i	−0.0773037	+	0.203565i
$239$	−332.992			−1.39327			−0.696636	−	0.717425i	$-0.745321\pi$
$239$	−332.992			−1.39327			−0.696636	+	0.717425i	$0.745321\pi$
$240$		0			0
$241$		−	218.867i		−	0.908160i	−0.890961	−	0.454080i	$-0.849968\pi$
$241$		−	218.867i		−	0.908160i	0.890961	−	0.454080i	$-0.150032\pi$
$242$	81.7459	−	215.263i	0.337793	−	0.889517i
$243$		0			0
$244$	−144.222	−	296.861i	−0.591074	−	1.21664i
$245$	140.565	+	339.354i	0.573735	+	1.38512i
$246$		0			0
$247$	15.1933	−	15.1933i	0.0615112	−	0.0615112i
$248$	−363.301	−	113.731i	−1.46492	−	0.458592i
$249$		0			0
$250$	8.71540	+	292.657i	0.0348616	+	1.17063i
$251$	−92.6681	−	223.721i	−0.369196	−	0.891318i	−0.993883	−	0.110442i	$-0.964773\pi$
$251$	−92.6681	−	223.721i	−0.369196	−	0.891318i	0.624687	−	0.780875i	$-0.285227\pi$
$252$		0			0
$253$	−24.6995	+	59.6298i	−0.0976263	+	0.235691i
$254$	117.294	+	260.921i	0.461788	+	1.02725i
$255$		0			0
$256$	−248.773	+	60.3972i	−0.971771	+	0.235927i
$257$	138.514			0.538966			0.269483	−	0.963005i	$-0.413147\pi$
$257$	138.514			0.538966			0.269483	+	0.963005i	$0.413147\pi$
$258$		0			0
$259$	−273.509	−	113.291i	−1.05602	−	0.437418i
$260$	33.3524	−	37.5810i	0.128279	−	0.144542i
$261$		0			0
$262$	−121.484	+	3.61782i	−0.463678	+	0.0138085i
$263$	−91.6940	−	91.6940i	−0.348647	−	0.348647i	0.510959	−	0.859605i	$-0.329290\pi$
$263$	−91.6940	−	91.6940i	−0.348647	−	0.348647i	−0.859605	+	0.510959i	$0.829290\pi$
$264$		0			0
$265$	159.740	+	159.740i	0.602793	+	0.602793i
$266$	−186.870	+	198.342i	−0.702521	+	0.745648i
$267$		0			0
$268$	351.230	−	170.636i	1.31056	−	0.636700i
$269$	−179.504	−	74.3530i	−0.667301	−	0.276405i	0.0232059	−	0.999731i	$-0.492613\pi$
$269$	−179.504	−	74.3530i	−0.667301	−	0.276405i	−0.690507	+	0.723325i	$0.742613\pi$
$270$		0			0
$271$	−454.375			−1.67666			−0.838331	−	0.545161i	$-0.816468\pi$
$271$	−454.375			−1.67666			−0.838331	+	0.545161i	$0.816468\pi$
$272$	−42.5465	+	5.09078i	−0.156421	+	0.0187161i
$273$		0			0
$274$	444.659	+	168.859i	1.62284	+	0.616272i
$275$	39.6620	−	95.7526i	0.144226	−	0.348191i
$276$		0			0
$277$	−12.5345	−	30.2610i	−0.0452510	−	0.109246i	0.899638	−	0.436637i	$-0.143830\pi$
$277$	−12.5345	−	30.2610i	−0.0452510	−	0.109246i	−0.944889	+	0.327391i	$0.893830\pi$
$278$	144.852	−	153.744i	0.521049	−	0.553036i
$279$		0			0
$280$	−408.624	+	489.009i	−1.45937	+	1.74646i
$281$	−312.777	+	312.777i	−1.11308	+	1.11308i	−0.120353	+	0.992731i	$0.538403\pi$
$281$	−312.777	+	312.777i	−1.11308	+	1.11308i	−0.992731	+	0.120353i	$0.961597\pi$
$282$		0			0
$283$	−74.2838	−	179.337i	−0.262487	−	0.633700i	0.736604	−	0.676324i	$-0.236428\pi$
$283$	−74.2838	−	179.337i	−0.262487	−	0.633700i	−0.999091	+	0.0426244i	$0.986428\pi$
$284$	−11.2021	+	0.667798i	−0.0394441	+	0.00235140i
$285$		0			0
$286$	−6.74271	+	3.03111i	−0.0235759	+	0.0105983i
$287$		−	94.9562i		−	0.330858i
$288$		0			0
$289$	281.828			0.975182
$290$	176.944	+	393.613i	0.610153	+	1.35729i
$291$		0			0
$292$	−313.553	+	18.6920i	−1.07381	+	0.0640137i
$293$	156.211	−	64.7046i	0.533143	−	0.220835i	−0.0998364	−	0.995004i	$-0.531832\pi$
$293$	156.211	−	64.7046i	0.533143	−	0.220835i	0.632979	+	0.774169i	$0.281832\pi$
$294$		0			0
$295$	−424.983	−	424.983i	−1.44062	−	1.44062i
$296$	−21.8332	−	243.803i	−0.0737609	−	0.823658i
$297$		0			0
$298$	168.792	+	159.029i	0.566415	+	0.533655i
$299$	−37.5555	+	15.5560i	−0.125604	+	0.0520268i
$300$		0			0
$301$	82.1432	+	34.0248i	0.272901	+	0.113039i
$302$	128.607	−	338.663i	0.425851	−	1.12140i
$303$		0			0
$304$	−216.936	−	60.8835i	−0.713605	−	0.200275i
$305$		−	679.301i		−	2.22722i
$306$		0			0
$307$	111.488	−	269.157i	0.363155	−	0.876733i	−0.631681	−	0.775229i	$-0.717635\pi$
$307$	111.488	−	269.157i	0.363155	−	0.876733i	0.994835	−	0.101504i	$-0.0323654\pi$
$308$	84.3335	−	40.9712i	0.273810	−	0.133023i
$309$		0			0
$310$	−570.295	−	537.311i	−1.83966	−	1.73326i
$311$	74.0508	−	74.0508i	0.238105	−	0.238105i	−0.577960	−	0.816065i	$-0.696151\pi$
$311$	74.0508	−	74.0508i	0.238105	−	0.238105i	0.816065	+	0.577960i	$0.196151\pi$
$312$		0			0
$313$	−119.709	+	119.709i	−0.382458	+	0.382458i	−0.871987	−	0.489529i	$-0.837169\pi$
$313$	−119.709	+	119.709i	−0.382458	+	0.382458i	0.489529	+	0.871987i	$0.337169\pi$
$314$	3.13615	+	105.309i	0.00998773	+	0.335380i
$315$		0			0
$316$	29.1679	−	32.8660i	0.0923036	−	0.104006i
$317$	−154.558	+	373.135i	−0.487563	+	1.17708i	0.468379	+	0.883528i	$0.344838\pi$
$317$	−154.558	+	373.135i	−0.487563	+	1.17708i	−0.955942	+	0.293554i	$0.905162\pi$
$318$		0			0
$319$		−	63.4940i		−	0.199041i
$320$	−514.881	−	111.936i	−1.60900	−	0.349799i
$321$		0			0
$322$	470.222	−	211.383i	1.46032	−	0.656469i
$323$	−34.8434	−	14.4326i	−0.107874	−	0.0446830i
$324$		0			0
$325$	60.3061	−	24.9796i	0.185557	−	0.0768604i
$326$	−148.601	+	4.42537i	−0.455830	+	0.0135748i
$327$		0			0
$328$	69.5673	−	36.3957i	0.212095	−	0.110963i
$329$	458.464	+	458.464i	1.39351	+	1.39351i
$330$		0			0
$331$	−376.019	+	155.752i	−1.13601	+	0.470551i	−0.869820	−	0.493370i	$-0.835765\pi$
$331$	−376.019	+	155.752i	−1.13601	+	0.470551i	−0.266190	+	0.963921i	$0.585765\pi$
$332$	156.110	+	321.331i	0.470211	+	0.967864i
$333$		0			0
$334$	347.314	+	131.892i	1.03986	+	0.394887i
$335$	803.711			2.39914
$336$		0			0
$337$			584.284i			1.73378i	0.498499	+	0.866890i	$0.333885\pi$
$337$			584.284i			1.73378i	−0.498499	+	0.866890i	$0.666115\pi$
$338$	311.630	+	118.341i	0.921984	+	0.350122i
$339$		0			0
$340$	−83.3459	−	28.8423i	−0.245135	−	0.0848302i
$341$	44.1162	+	106.506i	0.129373	+	0.312334i
$342$		0			0
$343$	29.9994	−	29.9994i	0.0874617	−	0.0874617i
$344$	6.55719	+	73.2215i	0.0190616	+	0.212853i
$345$		0			0
$346$	−445.845	+	13.2774i	−1.28857	+	0.0383740i
$347$	15.0226	+	36.2679i	0.0432929	+	0.104518i	0.944047	−	0.329812i	$-0.106985\pi$
$347$	15.0226	+	36.2679i	0.0432929	+	0.104518i	−0.900754	+	0.434330i	$0.856985\pi$
$348$		0			0
$349$	82.9090	−	200.160i	0.237562	−	0.573525i	−0.759468	−	0.650545i	$-0.774541\pi$
$349$	82.9090	−	200.160i	0.237562	−	0.573525i	0.997030	+	0.0770202i	$0.0245406\pi$
$350$	−755.075	+	339.436i	−2.15736	+	0.969817i
$351$		0			0
$352$	62.3406	+	46.0810i	0.177104	+	0.130912i
$353$	213.926			0.606022			0.303011	−	0.952987i	$-0.402008\pi$
$353$	213.926			0.606022			0.303011	+	0.952987i	$0.402008\pi$
$354$		0			0
$355$	−21.3394	−	8.83905i	−0.0601109	−	0.0248987i
$356$	−5.44344	−	91.3123i	−0.0152906	−	0.256495i
$357$		0			0
$358$	−12.4770	−	418.967i	−0.0348519	−	1.17030i
$359$	−235.583	−	235.583i	−0.656219	−	0.656219i	0.298264	−	0.954483i	$-0.403592\pi$
$359$	−235.583	−	235.583i	−0.656219	−	0.656219i	−0.954483	+	0.298264i	$0.903592\pi$
$360$		0			0
$361$	115.037	+	115.037i	0.318663	+	0.318663i
$362$	−355.414	−	334.858i	−0.981807	−	0.925021i
$363$		0			0
$364$	55.8037	+	19.3112i	0.153307	+	0.0530526i
$365$	−597.299	−	247.410i	−1.63644	−	0.677834i
$366$		0			0
$367$	266.252			0.725482			0.362741	−	0.931890i	$-0.381841\pi$
$367$	266.252			0.725482			0.362741	+	0.931890i	$0.381841\pi$
$368$	335.095	+	263.475i	0.910585	+	0.715965i
$369$		0			0
$370$	178.860	−	470.994i	0.483404	−	1.27296i
$371$	−101.598	+	245.280i	−0.273850	+	0.661133i
$372$		0			0
$373$	133.648	+	322.655i	0.358306	+	0.865028i	0.995539	+	0.0943560i	$0.0300792\pi$
$373$	133.648	+	322.655i	0.358306	+	0.865028i	−0.637232	+	0.770672i	$0.719921\pi$
$374$	9.44448	+	8.89823i	0.0252526	+	0.0237921i
$375$		0			0
$376$	−160.158	+	511.607i	−0.425952	+	1.36066i
$377$	28.2767	−	28.2767i	0.0750045	−	0.0750045i
$378$		0			0
$379$	1.26349	+	3.05034i	0.00333376	+	0.00804840i	0.925538	−	0.378656i	$-0.123614\pi$
$379$	1.26349	+	3.05034i	0.00333376	+	0.00804840i	−0.922204	+	0.386704i	$0.873614\pi$
$380$	−346.859	−	307.830i	−0.912786	−	0.810080i
$381$		0			0
$382$	−16.5350	−	36.7822i	−0.0432854	−	0.0962884i
$383$			310.584i			0.810923i	0.914112	+	0.405462i	$0.132889\pi$
$383$			310.584i			0.810923i	−0.914112	+	0.405462i	$0.867111\pi$
$384$		0			0
$385$	192.978			0.501243
$386$	−211.412	+	95.0381i	−0.547700	+	0.246213i
$387$		0			0
$388$	−166.324	+	187.412i	−0.428671	+	0.483020i
$389$	677.246	−	280.524i	1.74099	−	0.721142i	0.742296	−	0.670072i	$-0.233737\pi$
$389$	677.246	−	280.524i	1.74099	−	0.721142i	0.998695	−	0.0510705i	$-0.0162633\pi$
$390$		0			0
$391$	50.4525	+	50.4525i	0.129035	+	0.129035i
$392$	−340.621	−	106.631i	−0.868931	−	0.272018i
$393$		0			0
$394$	−263.801	+	279.995i	−0.669545	+	0.710648i
$395$	83.5594	−	34.6114i	0.211543	−	0.0876239i
$396$		0			0
$397$	−467.679	−	193.719i	−1.17803	−	0.487957i	−0.294192	−	0.955746i	$-0.595051\pi$
$397$	−467.679	−	193.719i	−1.17803	−	0.487957i	−0.883840	+	0.467789i	$0.845051\pi$
$398$	58.6383	+	22.2678i	0.147332	+	0.0559493i
$399$		0			0
$400$	−538.092	−	423.085i	−1.34523	−	1.05771i
$401$			447.783i			1.11667i	0.829617	+	0.558333i	$0.188559\pi$
$401$			447.783i			1.11667i	−0.829617	+	0.558333i	$0.811441\pi$
$402$		0			0
$403$	−27.7849	+	67.0786i	−0.0689451	+	0.166448i
$404$	−56.2588	+	162.572i	−0.139255	+	0.402406i
$405$		0			0
$406$	−347.790	+	369.141i	−0.856627	+	0.909214i
$407$	−52.4142	+	52.4142i	−0.128782	+	0.128782i
$408$		0			0
$409$	266.640	−	266.640i	0.651931	−	0.651931i	−0.301527	−	0.953458i	$-0.597496\pi$
$409$	266.640	−	266.640i	0.651931	−	0.651931i	0.953458	+	0.301527i	$0.0974962\pi$
$410$	161.526	−	4.81030i	0.393966	−	0.0117324i
$411$		0			0
$412$	−205.123	+	12.2281i	−0.497872	+	0.0296799i
$413$	270.299	−	652.559i	0.654477	−	1.58005i
$414$		0			0
$415$			735.294i			1.77179i
$416$	7.24114	+	48.2850i	0.0174066	+	0.116070i
$417$		0			0
$418$	27.9760	+	62.2326i	0.0669282	+	0.148882i
$419$	565.518	+	234.245i	1.34969	+	0.559058i	0.936205	−	0.351455i	$-0.114313\pi$
$419$	565.518	+	234.245i	1.34969	+	0.559058i	0.413481	+	0.910513i	$0.364313\pi$
$420$		0			0
$421$	−184.538	+	76.4382i	−0.438333	+	0.181564i	−0.590926	−	0.806726i	$-0.701238\pi$
$421$	−184.538	+	76.4382i	−0.438333	+	0.181564i	0.152593	+	0.988289i	$0.451238\pi$
$422$	−18.1917	−	610.864i	−0.0431084	−	1.44755i
$423$		0			0
$424$	−218.640	+	19.5798i	−0.515660	+	0.0461788i
$425$	−81.0159	−	81.0159i	−0.190626	−	0.190626i
$426$		0			0
$427$	737.557	−	305.506i	1.72730	−	0.715471i
$428$	−158.294	+	457.424i	−0.369845	+	1.06875i
$429$		0			0
$430$	−53.7170	+	141.454i	−0.124923	+	0.328963i
$431$	−329.019			−0.763385			−0.381692	−	0.924289i	$-0.624659\pi$
$431$	−329.019			−0.763385			−0.381692	+	0.924289i	$0.624659\pi$
$432$		0			0
$433$		−	403.449i		−	0.931753i	−0.884850	−	0.465877i	$-0.845739\pi$
$433$		−	403.449i		−	0.931753i	0.884850	−	0.465877i	$-0.154261\pi$
$434$	326.907	−	860.851i	0.753242	−	1.98353i
$435$		0			0
$436$	−217.159	+	105.501i	−0.498071	+	0.241975i
$437$	143.576	+	346.623i	0.328549	+	0.793188i
$438$		0			0
$439$	432.214	−	432.214i	0.984542	−	0.984542i	−0.0153402	−	0.999882i	$-0.504883\pi$
$439$	432.214	−	432.214i	0.984542	−	0.984542i	0.999882	+	0.0153402i	$0.00488314\pi$
$440$	73.9666	+	141.381i	0.168106	+	0.321320i
$441$		0			0
$442$	0.243270	+	8.16882i	0.000550385	+	0.0184815i
$443$	−138.144	−	333.509i	−0.311838	−	0.752843i	−0.999637	−	0.0269419i	$-0.991423\pi$
$443$	−138.144	−	333.509i	−0.311838	−	0.752843i	0.687799	−	0.725901i	$-0.258577\pi$
$444$		0			0
$445$	72.0501	−	173.944i	0.161910	−	0.390886i
$446$	−9.95589	−	22.1469i	−0.0223226	−	0.0496567i
$447$		0			0
$448$	−110.025	−	609.378i	−0.245592	−	1.36022i
$449$	320.009			0.712715			0.356358	−	0.934350i	$-0.384019\pi$
$449$	320.009			0.712715			0.356358	+	0.934350i	$0.384019\pi$
$450$		0			0
$451$	−21.9658	−	9.09852i	−0.0487046	−	0.0201741i
$452$	241.658	+	214.466i	0.534641	+	0.474483i
$453$		0			0
$454$	465.478	−	13.8621i	1.02528	−	0.0305332i
$455$	85.9419	+	85.9419i	0.188883	+	0.188883i
$456$		0			0
$457$	−148.390	−	148.390i	−0.324705	−	0.324705i	0.525864	−	0.850569i	$-0.323742\pi$
$457$	−148.390	−	148.390i	−0.324705	−	0.324705i	−0.850569	+	0.525864i	$0.823742\pi$
$458$	−126.905	+	134.695i	−0.277085	+	0.294095i
$459$		0			0
$460$	383.396	+	789.167i	0.833469	+	1.71558i
$461$	224.303	+	92.9092i	0.486557	+	0.201538i	0.612456	−	0.790505i	$-0.290182\pi$
$461$	224.303	+	92.9092i	0.486557	+	0.201538i	−0.125899	+	0.992043i	$0.540182\pi$
$462$		0			0
$463$	675.592			1.45916			0.729581	−	0.683894i	$-0.239715\pi$
$463$	675.592			1.45916			0.729581	+	0.683894i	$0.239715\pi$
$464$	−403.746	−	113.312i	−0.870143	−	0.244207i
$465$		0			0
$466$	87.5654	+	33.2529i	0.187909	+	0.0713581i
$467$	−190.920	+	460.923i	−0.408823	+	0.986987i	0.576625	+	0.817009i	$0.304369\pi$
$467$	−190.920	+	460.923i	−0.408823	+	0.986987i	−0.985448	+	0.169977i	$0.945631\pi$
$468$		0			0
$469$	361.458	+	872.636i	0.770698	+	1.86063i
$470$	−756.651	+	803.100i	−1.60989	+	1.70872i
$471$		0			0
$472$	581.684	−	52.0914i	1.23238	−	0.110363i
$473$	15.7416	−	15.7416i	0.0332803	−	0.0332803i
$474$		0			0
$475$	−230.552	−	556.603i	−0.485373	−	1.17179i
$476$	−6.16791	−	103.465i	−0.0129578	−	0.217363i
$477$		0			0
$478$	607.430	−	273.063i	1.27077	−	0.571262i
$479$		−	775.709i		−	1.61943i	−0.586821	−	0.809717i	$-0.699621\pi$
$479$		−	775.709i		−	1.61943i	0.586821	−	0.809717i	$-0.300379\pi$
$480$		0			0
$481$	−46.6847			−0.0970576
$482$	179.477	+	399.247i	0.372359	+	0.828314i
$483$		0			0
$484$	27.4048	+	459.708i	0.0566215	+	0.949810i
$485$	−476.481	+	197.365i	−0.982435	+	0.406938i
$486$		0			0
$487$	−422.101	−	422.101i	−0.866738	−	0.866738i	0.125372	−	0.992110i	$-0.459988\pi$
$487$	−422.101	−	422.101i	−0.866738	−	0.866738i	−0.992110	+	0.125372i	$0.959988\pi$
$488$	506.519	+	423.255i	1.03795	+	0.867326i
$489$		0			0
$490$	−534.693	−	503.768i	−1.09121	−	1.02810i
$491$	277.565	−	114.971i	0.565306	−	0.234157i	−0.0816809	−	0.996659i	$-0.526029\pi$
$491$	277.565	−	114.971i	0.565306	−	0.234157i	0.646987	+	0.762501i	$0.276029\pi$
$492$		0			0
$493$	−64.8482	−	26.8610i	−0.131538	−	0.0544848i
$494$	−15.2560	+	40.1739i	−0.0308826	+	0.0813236i
$495$		0			0
$496$	755.981	−	90.4548i	1.52415	−	0.182368i
$497$		−	27.1446i		−	0.0546170i
$498$		0			0
$499$	−328.498	+	793.063i	−0.658312	+	1.58930i	0.142099	+	0.989852i	$0.454615\pi$
$499$	−328.498	+	793.063i	−0.658312	+	1.58930i	−0.800410	+	0.599452i	$0.795385\pi$
$500$	−255.885	−	526.705i	−0.511771	−	1.05341i
$501$		0			0
$502$	352.499	+	332.111i	0.702189	+	0.661576i
$503$	115.459	−	115.459i	0.229540	−	0.229540i	−0.582960	−	0.812501i	$-0.698106\pi$
$503$	115.459	−	115.459i	0.229540	−	0.229540i	0.812501	+	0.582960i	$0.198106\pi$
$504$		0			0
$505$	−250.373	+	250.373i	−0.495788	+	0.495788i
$506$	−3.84250	−	129.028i	−0.00759388	−	0.254997i
$507$		0			0
$508$	−427.926	−	379.776i	−0.842374	−	0.747590i
$509$	97.7110	−	235.895i	0.191967	−	0.463449i	−0.798364	−	0.602175i	$-0.794301\pi$
$509$	97.7110	−	235.895i	0.191967	−	0.463449i	0.990331	+	0.138727i	$0.0443009\pi$
$510$		0			0
$511$		−	759.792i		−	1.48687i
$512$	404.274	−	314.176i	0.789598	−	0.613624i
$513$		0			0
$514$	−252.672	+	113.586i	−0.491579	+	0.220984i
$515$	−390.747	−	161.853i	−0.758733	−	0.314277i
$516$		0			0
$517$	149.983	−	62.1252i	0.290103	−	0.120165i
$518$	591.826	−	17.6248i	1.14252	−	0.0340246i
$519$		0			0
$520$	−30.0225	+	95.9037i	−0.0577356	+	0.184430i
$521$	−229.899	−	229.899i	−0.441264	−	0.441264i	0.451173	−	0.892437i	$-0.351006\pi$
$521$	−229.899	−	229.899i	−0.441264	−	0.441264i	−0.892437	+	0.451173i	$0.851006\pi$
$522$		0			0
$523$	−900.921	+	373.174i	−1.72260	+	0.713525i	−0.722856	+	0.690999i	$0.757171\pi$
$523$	−900.921	+	373.174i	−1.72260	+	0.713525i	−0.999746	+	0.0225265i	$0.992829\pi$
$524$	218.639	−	106.220i	0.417249	−	0.202709i
$525$		0			0
$526$	242.456	+	92.0725i	0.460943	+	0.175043i
$527$	127.441			0.241823
$528$		0			0
$529$		−	180.797i		−	0.341772i
$530$	−422.383	−	160.400i	−0.796950	−	0.302641i
$531$		0			0
$532$	178.235	−	515.047i	0.335027	−	0.968133i
$533$	−5.73035	−	13.8343i	−0.0107511	−	0.0259555i
$534$		0			0
$535$	−704.466	+	704.466i	−1.31676	+	1.31676i
$536$	−500.772	+	599.285i	−0.934276	+	1.11807i
$537$		0			0
$538$	388.415	−	11.5671i	0.721962	−	0.0215002i
$539$	41.3621	+	99.8569i	0.0767386	+	0.185263i
$540$		0			0
$541$	86.3781	−	208.535i	0.159664	−	0.385462i	−0.823721	−	0.566995i	$-0.808106\pi$
$541$	86.3781	−	208.535i	0.159664	−	0.385462i	0.983385	+	0.181533i	$0.0581058\pi$
$542$	828.852	−	372.602i	1.52925	−	0.687457i
$543$		0			0
$544$	73.4369	−	44.1758i	0.134994	−	0.0812055i
$545$	−496.920			−0.911780
$546$		0			0
$547$	497.491	+	206.067i	0.909489	+	0.376723i	0.787861	−	0.615853i	$-0.211188\pi$
$547$	497.491	+	206.067i	0.909489	+	0.376723i	0.121628	+	0.992576i	$0.461188\pi$
$548$	−949.596	+	56.6087i	−1.73284	+	0.103301i
$549$		0			0
$550$	6.17024	+	207.192i	0.0112186	+	0.376713i
$551$	−260.983	−	260.983i	−0.473653	−	0.473653i
$552$		0			0
$553$	75.1593	+	75.1593i	0.135912	+	0.135912i
$554$	47.6799	+	44.9222i	0.0860648	+	0.0810869i
$555$		0			0
$556$	−138.158	+	399.236i	−0.248485	+	0.718050i
$557$	527.914	+	218.669i	0.947782	+	0.392584i	0.802397	−	0.596791i	$-0.203558\pi$
$557$	527.914	+	218.669i	0.947782	+	0.392584i	0.145385	+	0.989375i	$0.453558\pi$
$558$		0			0
$559$	14.0209			0.0250820
$560$	344.392	−	1227.11i	0.614985	−	2.19127i
$561$		0			0
$562$	314.068	−	827.040i	0.558839	−	1.47160i
$563$	303.900	−	733.680i	0.539788	−	1.30316i	−0.385084	−	0.922882i	$-0.625827\pi$
$563$	303.900	−	733.680i	0.539788	−	1.30316i	0.924871	−	0.380281i	$-0.124173\pi$
$564$		0			0
$565$	254.491	+	614.397i	0.450427	+	1.08743i
$566$	282.567	+	266.224i	0.499235	+	0.470360i
$567$		0			0
$568$	19.8868	−	10.4042i	0.0350120	−	0.0183173i
$569$	143.631	−	143.631i	0.252426	−	0.252426i	−0.569538	−	0.821965i	$-0.692878\pi$
$569$	143.631	−	143.631i	0.252426	−	0.252426i	0.821965	+	0.569538i	$0.192878\pi$
$570$		0			0
$571$	−371.018	−	895.717i	−0.649769	−	1.56868i	−0.813109	−	0.582112i	$-0.802227\pi$
$571$	−371.018	−	895.717i	−0.649769	−	1.56868i	0.163339	−	0.986570i	$-0.447773\pi$
$572$	9.81416	−	11.0584i	0.0171576	−	0.0193329i
$573$		0			0
$574$	77.8670	+	173.215i	0.135657	+	0.301769i
$575$			1139.78i			1.98223i
$576$		0			0
$577$	706.702			1.22479			0.612393	−	0.790553i	$-0.290207\pi$
$577$	706.702			1.22479			0.612393	+	0.790553i	$0.290207\pi$
$578$	−514.098	+	231.107i	−0.889443	+	0.399839i
$579$		0			0
$580$	−645.549	−	572.912i	−1.11302	−	0.987780i
$581$	−798.352	+	330.688i	−1.37410	+	0.569171i
$582$		0			0
$583$	47.0045	+	47.0045i	0.0806253	+	0.0806253i
$584$	556.642	−	291.220i	0.953155	−	0.498665i
$585$		0			0
$586$	−231.893	+	246.129i	−0.395722	+	0.420015i
$587$	−293.599	+	121.613i	−0.500169	+	0.207177i	−0.618481	−	0.785800i	$-0.712252\pi$
$587$	−293.599	+	121.613i	−0.500169	+	0.207177i	0.118312	+	0.992976i	$0.462252\pi$
$588$		0			0
$589$	619.110	+	256.444i	1.05112	+	0.435389i
$590$	1123.74	+	426.737i	1.90464	+	0.723283i
$591$		0			0
$592$	239.753	+	426.831i	0.404988	+	0.720998i
$593$			674.627i			1.13765i	0.822458	+	0.568825i	$0.192602\pi$
$593$			674.627i			1.13765i	−0.822458	+	0.568825i	$0.807398\pi$
$594$		0			0
$595$	81.6391	−	197.094i	0.137209	−	0.331251i
$596$	−438.311	−	151.680i	−0.735422	−	0.254496i
$597$		0			0
$598$	55.7508	−	59.1733i	0.0932288	−	0.0989520i
$599$	−379.725	+	379.725i	−0.633932	+	0.633932i	−0.949052	−	0.315120i	$-0.897955\pi$
$599$	−379.725	+	379.725i	−0.633932	+	0.633932i	0.315120	+	0.949052i	$0.397955\pi$
$600$		0			0
$601$	−548.542	+	548.542i	−0.912715	+	0.912715i	−0.996485	−	0.0837700i	$-0.973304\pi$
$601$	−548.542	+	548.542i	−0.912715	+	0.912715i	0.0837700	+	0.996485i	$0.473304\pi$
$602$	−177.743	+	5.29326i	−0.295255	+	0.00879278i
$603$		0			0
$604$	43.1146	+	723.236i	0.0713818	+	1.19741i
$605$	−362.733	+	875.715i	−0.599559	+	1.44746i
$606$		0			0
$607$		−	1.05067i		−	0.00173092i	−1.00000		0.000865460i	$-0.999725\pi$
$607$		−	1.05067i		−	0.00173092i	1.00000		0.000865460i	$-0.000275484\pi$
$608$	445.652	−	66.8330i	0.732980	−	0.109923i
$609$		0			0
$610$	557.047	+	1239.15i	0.913192	+	2.03140i
$611$	94.4614	+	39.1272i	0.154601	+	0.0640379i
$612$		0			0
$613$	625.826	−	259.226i	1.02092	−	0.422881i	0.191495	−	0.981494i	$-0.438666\pi$
$613$	625.826	−	259.226i	1.02092	−	0.422881i	0.829428	+	0.558613i	$0.188666\pi$
$614$	17.3443	+	582.408i	0.0282481	+	0.948548i
$615$		0			0
$616$	−120.240	+	143.894i	−0.195195	+	0.233594i
$617$	−180.644	−	180.644i	−0.292779	−	0.292779i	0.545398	−	0.838177i	$-0.316378\pi$
$617$	−180.644	−	180.644i	−0.292779	−	0.292779i	−0.838177	+	0.545398i	$0.816378\pi$
$618$		0			0
$619$	555.651	−	230.158i	0.897658	−	0.371822i	0.114339	−	0.993442i	$-0.463525\pi$
$619$	555.651	−	230.158i	0.897658	−	0.371822i	0.783319	+	0.621620i	$0.213525\pi$
$620$	1480.92	+	512.480i	2.38858	+	0.826580i
$621$		0			0
$622$	−74.3564	+	195.804i	−0.119544	+	0.314798i
$623$	221.265			0.355160
$624$		0			0
$625$		−	135.712i		−	0.217139i
$626$	120.203	−	316.534i	0.192018	−	0.505645i
$627$		0			0
$628$	−92.0778	−	189.529i	−0.146621	−	0.301798i
$629$	31.3584	+	75.7058i	0.0498543	+	0.120359i
$630$		0			0
$631$	−267.583	+	267.583i	−0.424062	+	0.424062i	−0.886600	−	0.462537i	$-0.846939\pi$
$631$	−267.583	+	267.583i	−0.424062	+	0.424062i	0.462537	+	0.886600i	$0.346939\pi$
$632$	−26.2558	+	83.8713i	−0.0415440	+	0.132708i
$633$		0			0
$634$	−24.0446	−	807.399i	−0.0379252	−	1.27350i
$635$	−450.652	−	1087.97i	−0.709688	−	1.71334i
$636$		0			0
$637$	−26.0503	+	62.8911i	−0.0408954	+	0.0987301i
$638$	52.0670	+	115.823i	0.0816097	+	0.181541i
$639$		0			0
$640$	1031.02	−	218.030i	1.61096	−	0.340672i
$641$	834.869			1.30245			0.651224	−	0.758886i	$-0.274256\pi$
$641$	834.869			1.30245			0.651224	+	0.758886i	$0.274256\pi$
$642$		0			0
$643$	1006.71	+	416.995i	1.56565	+	0.648514i	0.986060	−	0.166393i	$-0.0532119\pi$
$643$	1006.71	+	416.995i	1.56565	+	0.648514i	0.579592	+	0.814907i	$0.303212\pi$
$644$	−684.418	+	771.192i	−1.06276	+	1.19750i
$645$		0			0
$646$	75.3951	−	2.24529i	0.116711	−	0.00347568i
$647$	857.194	+	857.194i	1.32488	+	1.32488i	0.909776	+	0.415099i	$0.136253\pi$
$647$	857.194	+	857.194i	1.32488	+	1.32488i	0.415099	+	0.909776i	$0.363747\pi$
$648$		0			0
$649$	−125.054	−	125.054i	−0.192687	−	0.192687i
$650$	−89.5239	+	95.0196i	−0.137729	+	0.146184i
$651$		0			0
$652$	267.442	−	129.930i	0.410187	−	0.199278i
$653$	105.248	+	43.5953i	0.161177	+	0.0667616i	0.461813	−	0.886977i	$-0.347199\pi$
$653$	105.248	+	43.5953i	0.161177	+	0.0667616i	−0.300636	+	0.953739i	$0.597199\pi$
$654$		0			0
$655$	500.306			0.763826
$656$	−97.0561	+	123.439i	−0.147951	+	0.188169i
$657$		0			0
$658$	−1212.27	−	460.357i	−1.84235	−	0.699630i
$659$	222.875	−	538.067i	0.338201	−	0.816490i	−0.659687	−	0.751540i	$-0.729311\pi$
$659$	222.875	−	538.067i	0.338201	−	0.816490i	0.997889	−	0.0649499i	$-0.0206888\pi$
$660$		0			0
$661$	−396.971	−	958.372i	−0.600561	−	1.44988i	−0.873005	−	0.487711i	$-0.837832\pi$
$661$	−396.971	−	958.372i	−0.600561	−	1.44988i	0.272445	−	0.962171i	$-0.412168\pi$
$662$	558.197	−	592.464i	0.843197	−	0.894960i
$663$		0			0
$664$	−548.270	−	458.143i	−0.825708	−	0.689974i
$665$	793.210	−	793.210i	1.19280	−	1.19280i
$666$		0			0
$667$	267.214	+	645.111i	0.400620	+	0.967183i
$668$	−741.711	+	44.2160i	−1.11035	+	0.0661916i
$669$		0			0
$670$	−1466.09	+	659.067i	−2.18820	+	0.983682i
$671$		−	199.888i		−	0.297896i
$672$		0			0
$673$	−908.805			−1.35038			−0.675190	−	0.737644i	$-0.735938\pi$
$673$	−908.805			−1.35038			−0.675190	+	0.737644i	$0.735938\pi$
$674$	−479.131	−	1065.83i	−0.710876	−	1.58134i
$675$		0			0
$676$	−665.507	+	39.6732i	−0.984477	+	0.0586881i
$677$	−963.142	+	398.947i	−1.42266	+	0.589286i	−0.955528	−	0.294900i	$-0.904713\pi$
$677$	−963.142	+	398.947i	−1.42266	+	0.589286i	−0.467134	+	0.884186i	$0.654713\pi$
$678$		0			0
$679$	−428.581	−	428.581i	−0.631195	−	0.631195i
$680$	175.688	−	15.7333i	0.258364	−	0.0231372i
$681$		0			0
$682$	−167.813	−	158.107i	−0.246060	−	0.231828i
$683$	−248.963	+	103.124i	−0.364515	+	0.150987i	−0.557420	−	0.830230i	$-0.688209\pi$
$683$	−248.963	+	103.124i	−0.364515	+	0.150987i	0.192906	+	0.981217i	$0.438209\pi$
$684$		0			0
$685$	−1808.92	−	749.280i	−2.64076	−	1.09384i
$686$	−30.1232	+	79.3239i	−0.0439113	+	0.115633i
$687$		0			0
$688$	−72.0052	−	128.190i	−0.104659	−	0.186323i
$689$			41.8664i			0.0607640i
$690$		0			0
$691$	−222.756	+	537.780i	−0.322367	+	0.778263i	0.676748	+	0.736214i	$0.263388\pi$
$691$	−222.756	+	537.780i	−0.322367	+	0.778263i	−0.999116	+	0.0420488i	$0.986612\pi$
$692$	802.403	−	389.826i	1.15954	−	0.563333i
$693$		0			0
$694$	−57.1444	−	53.8393i	−0.0823407	−	0.0775782i
$695$	−614.853	+	614.853i	−0.884681	+	0.884681i
$696$		0			0
$697$	−18.5851	+	18.5851i	−0.0266645	+	0.0266645i
$698$	12.8982	+	433.111i	0.0184788	+	0.620504i
$699$		0			0
$700$	1099.03	−	1238.37i	1.57004	−	1.76910i
$701$	236.347	−	570.592i	0.337157	−	0.813969i	−0.660829	−	0.750536i	$-0.729795\pi$
$701$	236.347	−	570.592i	0.337157	−	0.813969i	0.997986	−	0.0634324i	$-0.0202047\pi$
$702$		0			0
$703$			430.882i			0.612919i
$704$	−151.507	−	32.9378i	−0.215209	−	0.0467866i
$705$		0			0
$706$	−390.234	+	175.426i	−0.552740	+	0.248478i
$707$	−384.446	−	159.243i	−0.543771	−	0.225237i
$708$		0			0
$709$	−599.630	+	248.375i	−0.845740	+	0.350317i	−0.763114	−	0.646264i	$-0.776331\pi$
$709$	−599.630	+	248.375i	−0.845740	+	0.350317i	−0.0826257	+	0.996581i	$0.526331\pi$
$710$	46.1746	−	1.37509i	0.0650347	−	0.00193675i
$711$		0			0
$712$	84.8085	+	162.104i	0.119113	+	0.227674i
$713$	−896.458	−	896.458i	−1.25730	−	1.25730i
$714$		0			0
$715$	28.1153	−	11.6457i	0.0393221	−	0.0162877i
$716$	366.326	+	754.031i	0.511628	+	1.05312i
$717$		0			0
$718$	622.925	+	236.555i	0.867583	+	0.329464i
$719$	−96.4410			−0.134132			−0.0670661	−	0.997749i	$-0.521364\pi$
$719$	−96.4410			−0.134132			−0.0670661	+	0.997749i	$0.521364\pi$
$720$		0			0
$721$		−	497.048i		−	0.689388i
$722$	−304.181	−	115.512i	−0.421303	−	0.159989i
$723$		0			0
$724$	922.925	+	319.383i	1.27476	+	0.441137i
$725$	−429.088	−	1035.91i	−0.591846	−	1.42884i
$726$		0			0
$727$	−708.402	+	708.402i	−0.974418	+	0.974418i	−0.999681	−	0.0252626i	$-0.991958\pi$
$727$	−708.402	+	708.402i	−0.974418	+	0.974418i	0.0252626	+	0.999681i	$0.491958\pi$
$728$	−117.631	+	10.5341i	−0.161580	+	0.0144700i
$729$		0			0
$730$	1292.45	−	38.4896i	1.77048	−	0.0527255i
$731$	−9.41788	−	22.7368i	−0.0128836	−	0.0311037i
$732$		0			0
$733$	−149.531	+	361.000i	−0.203999	+	0.492497i	−0.992457	−	0.122591i	$-0.960880\pi$
$733$	−149.531	+	361.000i	−0.203999	+	0.492497i	0.788458	+	0.615088i	$0.210880\pi$
$734$	−485.686	+	218.335i	−0.661697	+	0.297459i
$735$		0			0
$736$	−827.324	−	205.832i	−1.12408	−	0.279663i
$737$	236.497			0.320891
$738$		0			0
$739$	−971.442	−	402.384i	−1.31454	−	0.544499i	−0.388331	−	0.921520i	$-0.626948\pi$
$739$	−971.442	−	402.384i	−1.31454	−	0.544499i	−0.926205	+	0.377021i	$0.876948\pi$
$740$	59.9615	+	1005.84i	0.0810291	+	1.35924i
$741$		0			0
$742$	−15.8057	−	530.744i	−0.0213015	−	0.715288i
$743$	−117.181	−	117.181i	−0.157714	−	0.157714i	0.623839	−	0.781553i	$-0.285572\pi$
$743$	−117.181	−	117.181i	−0.157714	−	0.157714i	−0.781553	+	0.623839i	$0.785572\pi$
$744$		0			0
$745$	−675.032	−	675.032i	−0.906083	−	0.906083i
$746$	−508.383	−	478.979i	−0.681478	−	0.642063i
$747$		0			0
$748$	−24.5250	−	8.48701i	−0.0327875	−	0.0113463i
$749$	−1081.70	−	448.056i	−1.44420	−	0.598206i
$750$		0			0
$751$	604.910			0.805473			0.402736	−	0.915316i	$-0.368059\pi$
$751$	604.910			0.805473			0.402736	+	0.915316i	$0.368059\pi$
$752$	−127.380	−	1064.59i	−0.169388	−	1.41567i
$753$		0			0
$754$	−28.3934	+	74.7689i	−0.0376570	+	0.0991629i
$755$	−570.670	+	1377.72i	−0.755855	+	1.82479i
$756$		0			0
$757$	−459.899	−	1110.29i	−0.607528	−	1.46670i	−0.865680	−	0.500598i	$-0.833113\pi$
$757$	−459.899	−	1110.29i	−0.607528	−	1.46670i	0.258152	−	0.966104i	$-0.416887\pi$
$758$	−4.80619	−	4.52820i	−0.00634061	−	0.00597388i
$759$		0			0
$760$	885.155	+	277.096i	1.16468	+	0.364601i
$761$	−202.753	+	202.753i	−0.266430	+	0.266430i	−0.827660	−	0.561230i	$-0.810328\pi$
$761$	−202.753	+	202.753i	−0.266430	+	0.266430i	0.561230	+	0.827660i	$0.310328\pi$
$762$		0			0
$763$	−223.483	−	539.535i	−0.292900	−	0.707124i
$764$	60.3250	+	53.5372i	0.0789594	+	0.0700749i
$765$		0			0
$766$	−254.688	−	566.553i	−0.332491	−	0.739626i
$767$		−	111.384i		−	0.145220i
$768$		0			0
$769$	954.072			1.24067			0.620333	−	0.784338i	$-0.286997\pi$
$769$	954.072			1.24067			0.620333	+	0.784338i	$0.286997\pi$
$770$	−352.023	+	158.248i	−0.457173	+	0.205517i
$771$		0			0
$772$	307.715	−	346.729i	0.398595	−	0.449131i
$773$	−244.204	+	101.153i	−0.315918	+	0.130857i	−0.535007	−	0.844847i	$-0.679691\pi$
$773$	−244.204	+	101.153i	−0.315918	+	0.130857i	0.219090	+	0.975705i	$0.429691\pi$
$774$		0			0
$775$	1439.52	+	1439.52i	1.85744	+	1.85744i
$776$	149.719	−	478.260i	0.192936	−	0.616314i
$777$		0			0
$778$	−1005.36	+	1067.08i	−1.29224	+	1.37157i
$779$	−127.685	+	52.8890i	−0.163909	+	0.0678934i
$780$		0			0
$781$	−6.27923	−	2.60094i	−0.00803999	−	0.00333027i
$782$	−133.406	−	50.6607i	−0.170596	−	0.0647835i
$783$		0			0
$784$	708.787	−	84.8079i	0.904065	−	0.108173i
$785$		−	433.696i		−	0.552479i
$786$		0			0
$787$	−19.8368	+	47.8903i	−0.0252056	+	0.0608518i	−0.935981	−	0.352050i	$-0.885485\pi$
$787$	−19.8368	+	47.8903i	−0.0252056	+	0.0608518i	0.910776	+	0.412902i	$0.135485\pi$
$788$	251.610	−	727.080i	0.319302	−	0.922691i
$789$		0			0
$790$	−124.043	+	131.658i	−0.157016	+	0.166656i
$791$	−552.633	+	552.633i	−0.698650	+	0.698650i
$792$		0			0
$793$	89.0192	−	89.0192i	0.112256	−	0.112256i
$794$	1011.98	−	30.1369i	1.27453	−	0.0379558i
$795$		0			0
$796$	−125.226	+	7.46515i	−0.157319	+	0.00937832i
$797$	−187.462	+	452.574i	−0.235210	+	0.567847i	−0.996775	−	0.0802411i	$-0.974431\pi$
$797$	−187.462	+	452.574i	−0.235210	+	0.567847i	0.761566	+	0.648088i	$0.224431\pi$
$798$		0			0
$799$		−	179.464i		−	0.224611i
$800$	1328.51	+	330.522i	1.66063	+	0.413152i
$801$		0			0
$802$	−367.195	−	816.826i	−0.457849	−	1.01849i
$803$	−175.759	−	72.8017i	−0.218878	−	0.0906622i
$804$		0			0
$805$	−1960.70	+	812.148i	−2.43565	+	1.00888i
$806$	−4.32251	−	145.146i	−0.00536291	−	0.180082i
$807$		0			0
$808$	−30.6889	−	342.691i	−0.0379813	−	0.424122i
$809$	772.357	+	772.357i	0.954706	+	0.954706i	0.999018	−	0.0443114i	$-0.0141094\pi$
$809$	772.357	+	772.357i	0.954706	+	0.954706i	−0.0443114	+	0.999018i	$0.514109\pi$
$810$		0			0
$811$	518.106	−	214.607i	0.638849	−	0.264620i	−0.0396587	−	0.999213i	$-0.512627\pi$
$811$	518.106	−	214.607i	0.638849	−	0.264620i	0.678508	+	0.734593i	$0.262627\pi$
$812$	331.718	−	958.570i	0.408520	−	1.18050i
$813$		0			0
$814$	52.6305	−	138.593i	0.0646566	−	0.170262i
$815$	611.981			0.750897
$816$		0			0
$817$		−	129.407i		−	0.158393i
$818$	−267.740	+	705.046i	−0.327311	+	0.861914i
$819$		0			0
$820$	−290.705	+	141.231i	−0.354518	+	0.172233i
$821$	−328.590	−	793.287i	−0.400232	−	0.966245i	−0.987609	−	0.156932i	$-0.949840\pi$
$821$	−328.590	−	793.287i	−0.400232	−	0.966245i	0.587378	−	0.809313i	$-0.300160\pi$
$822$		0			0
$823$	−370.318	+	370.318i	−0.449961	+	0.449961i	−0.895341	−	0.445381i	$-0.853068\pi$
$823$	−370.318	+	370.318i	−0.449961	+	0.449961i	0.445381	+	0.895341i	$0.353068\pi$
$824$	364.150	−	190.513i	0.441930	−	0.231206i
$825$		0			0
$826$	42.0505	+	1412.02i	0.0509086	+	1.70947i
$827$	55.6405	+	134.328i	0.0672799	+	0.162428i	0.953943	−	0.299988i	$-0.0969827\pi$
$827$	55.6405	+	134.328i	0.0672799	+	0.162428i	−0.886663	+	0.462416i	$0.846983\pi$
$828$		0			0
$829$	492.586	−	1189.21i	0.594193	−	1.43451i	−0.285226	−	0.958460i	$-0.592069\pi$
$829$	492.586	−	1189.21i	0.594193	−	1.43451i	0.879419	−	0.476048i	$-0.157931\pi$
$830$	−602.963	−	1341.29i	−0.726462	−	1.61601i
$831$		0			0
$832$	−52.8041	−	82.1414i	−0.0634665	−	0.0987277i
$833$	119.485			0.143439
$834$		0			0
$835$	−1412.91	−	585.248i	−1.69211	−	0.700896i
$836$	−102.065	−	90.5809i	−0.122088	−	0.108350i
$837$		0			0
$838$	−1223.68	+	36.4417i	−1.46024	+	0.0434865i
$839$	215.217	+	215.217i	0.256516	+	0.256516i	0.823636	−	0.567119i	$-0.191942\pi$
$839$	215.217	+	215.217i	0.256516	+	0.256516i	−0.567119	+	0.823636i	$0.691942\pi$
$840$		0			0
$841$	108.953	+	108.953i	0.129552	+	0.129552i
$842$	273.945	−	290.762i	0.325351	−	0.345323i
$843$		0			0
$844$	534.112	+	1099.39i	0.632834	+	1.30260i
$845$	−1267.75	−	525.119i	−1.50029	−	0.621442i
$846$		0			0
$847$	−1113.95			−1.31517
$848$	382.778	−	215.008i	0.451389	−	0.253547i
$849$		0			0
$850$	214.221	+	81.3503i	0.252025	+	0.0957062i
$851$	311.954	−	753.123i	0.366573	−	0.884986i
$852$		0			0
$853$	−68.6449	−	165.723i	−0.0804747	−	0.194283i	0.878521	−	0.477704i	$-0.158531\pi$
$853$	−68.6449	−	165.723i	−0.0804747	−	0.194283i	−0.958996	+	0.283421i	$0.908531\pi$
$854$	−1094.90	+	1162.11i	−1.28208	+	1.36078i
$855$		0			0
$856$	−86.3484	−	964.219i	−0.100874	−	1.12642i
$857$	−713.771	+	713.771i	−0.832871	+	0.832871i	−0.987909	−	0.155037i	$-0.950450\pi$
$857$	−713.771	+	713.771i	−0.832871	+	0.832871i	0.155037	+	0.987909i	$0.450450\pi$
$858$		0			0
$859$	343.845	+	830.116i	0.400285	+	0.966375i	0.987596	+	0.157013i	$0.0501866\pi$
$859$	343.845	+	830.116i	0.400285	+	0.966375i	−0.587311	+	0.809361i	$0.699813\pi$
$860$	−18.0083	−	302.084i	−0.0209399	−	0.351261i
$861$		0			0
$862$	600.182	−	269.805i	0.696267	−	0.312999i
$863$			1574.26i			1.82417i	0.410002	+	0.912085i	$0.365528\pi$
$863$			1574.26i			1.82417i	−0.410002	+	0.912085i	$0.634472\pi$
$864$		0			0
$865$	1836.12			2.12268
$866$	330.840	+	735.955i	0.382033	+	0.849832i
$867$		0			0
$868$	109.594	+	1838.40i	0.126260	+	2.11797i
$869$	24.5878	−	10.1846i	0.0282944	−	0.0117199i
$870$		0			0
$871$	105.322	+	105.322i	0.120921	+	0.120921i
$872$	309.618	−	370.527i	0.355067	−	0.424917i
$873$		0			0
$874$	−546.147	−	514.559i	−0.624882	−	0.588740i
$875$	1308.61	−	542.043i	1.49555	−	0.619477i
$876$		0			0
$877$	1227.56	+	508.470i	1.39972	+	0.579784i	0.949679	−	0.313224i	$-0.101409\pi$
$877$	1227.56	+	508.470i	1.39972	+	0.579784i	0.450042	+	0.893007i	$0.351409\pi$
$878$	−433.998	+	1142.85i	−0.494303	+	1.30166i
$879$		0			0
$880$	−250.863	−	197.246i	−0.285072	−	0.224143i
$881$		−	1187.59i		−	1.34800i	−0.738732	−	0.674000i	$-0.764575\pi$
$881$		−	1187.59i		−	1.34800i	0.738732	−	0.674000i	$-0.235425\pi$
$882$		0			0
$883$	544.271	−	1313.99i	0.616389	−	1.48809i	−0.239480	−	0.970901i	$-0.576977\pi$
$883$	544.271	−	1313.99i	0.616389	−	1.48809i	0.855869	−	0.517193i	$-0.173023\pi$
$884$	−7.14244	−	14.7017i	−0.00807969	−	0.0166309i
$885$		0			0
$886$	525.484	+	495.091i	0.593097	+	0.558794i
$887$	95.1081	−	95.1081i	0.107224	−	0.107224i	−0.651459	−	0.758684i	$-0.725843\pi$
$887$	95.1081	−	95.1081i	0.107224	−	0.107224i	0.758684	+	0.651459i	$0.225843\pi$
$888$		0			0
$889$	978.598	−	978.598i	1.10079	−	1.10079i
$890$	11.2089	+	376.385i	0.0125942	+	0.422904i
$891$		0			0
$892$	36.3222	+	32.2353i	0.0407200	+	0.0361382i
$893$	361.129	−	871.842i	0.404400	−	0.976307i
$894$		0			0
$895$			1725.43i			1.92786i
$896$	700.412	+	1021.38i	0.781710	+	1.13993i
$897$		0			0
$898$	−583.747	+	262.417i	−0.650052	+	0.292224i
$899$	1152.25	+	477.276i	1.28170	+	0.530896i
$900$		0			0
$901$	67.8922	−	28.1219i	0.0753521	−	0.0312119i
$902$	47.5301	−	1.41546i	0.0526941	−	0.00156925i
$903$		0			0
$904$	−616.691	−	193.054i	−0.682180	−	0.213555i
$905$	1421.37	+	1421.37i	1.57058	+	1.57058i
$906$		0			0
$907$	103.742	−	42.9713i	0.114379	−	0.0473774i	−0.324760	−	0.945796i	$-0.605284\pi$
$907$	103.742	−	42.9713i	0.114379	−	0.0473774i	0.439139	+	0.898419i	$0.355284\pi$
$908$	−837.737	+	406.992i	−0.922618	+	0.448230i
$909$		0			0
$910$	−227.246	−	86.2966i	−0.249721	−	0.0948314i
$911$	−134.755			−0.147920			−0.0739598	−	0.997261i	$-0.523564\pi$
$911$	−134.755			−0.147920			−0.0739598	+	0.997261i	$0.523564\pi$
$912$		0			0
$913$			216.365i			0.236982i
$914$	392.372	+	149.003i	0.429291	+	0.163023i
$915$		0			0
$916$	121.040	−	349.772i	0.132140	−	0.381847i
$917$	225.005	+	543.211i	0.245371	+	0.592379i
$918$		0			0
$919$	847.025	−	847.025i	0.921681	−	0.921681i	−0.0754671	−	0.997148i	$-0.524045\pi$
$919$	847.025	−	847.025i	0.921681	−	0.921681i	0.997148	+	0.0754671i	$0.0240448\pi$
$920$	−1346.51	−	1125.17i	−1.46360	−	1.22301i
$921$		0			0
$922$	−485.352	+	14.4539i	−0.526412	+	0.0156767i
$923$	−1.63811	−	3.95474i	−0.00177476	−	0.00428465i
$924$		0			0
$925$	−500.931	+	1209.35i	−0.541547	+	1.30741i
$926$	−1232.39	+	554.006i	−1.33087	+	0.598278i
$927$		0			0
$928$	829.416	−	124.385i	0.893767	−	0.134035i
$929$	1150.33			1.23824			0.619121	−	0.785295i	$-0.287489\pi$
$929$	1150.33			1.23824			0.619121	+	0.785295i	$0.287489\pi$
$930$		0			0
$931$	580.461	+	240.435i	0.623481	+	0.258254i
$932$	−187.001	+	11.1478i	−0.200645	+	0.0119612i
$933$		0			0
$934$	−29.7016	−	997.356i	−0.0318004	−	1.06783i
$935$	−37.7704	−	37.7704i	−0.0403961	−	0.0403961i
$936$		0			0
$937$	1191.07	+	1191.07i	1.27115	+	1.27115i	0.945484	+	0.325670i	$0.105590\pi$
$937$	1191.07	+	1191.07i	1.27115	+	1.27115i	0.325670	+	0.945484i	$0.394410\pi$
$938$	−1374.94	−	1295.42i	−1.46582	−	1.38104i
$939$		0			0
$940$	721.683	−	2085.46i	0.767748	−	2.21857i
$941$	741.098	+	306.973i	0.787564	+	0.326220i	0.739964	−	0.672647i	$-0.234843\pi$
$941$	741.098	+	306.973i	0.787564	+	0.326220i	0.0476005	+	0.998866i	$0.484843\pi$
$942$		0			0
$943$	261.467			0.277272
$944$	−1018.37	+	572.021i	−1.07878	+	0.605955i
$945$		0			0
$946$	−15.8066	+	41.6237i	−0.0167088	+	0.0439997i
$947$	75.9383	−	183.331i	0.0801883	−	0.193592i	−0.878701	−	0.477373i	$-0.841589\pi$
$947$	75.9383	−	183.331i	0.0801883	−	0.193592i	0.958889	+	0.283781i	$0.0915890\pi$
$948$		0			0
$949$	−45.8514	−	110.695i	−0.0483155	−	0.116644i
$950$	876.995	+	826.271i	0.923152	+	0.869759i
$951$		0			0
$952$	96.0956	+	183.678i	0.100941	+	0.192940i
$953$	240.916	−	240.916i	0.252798	−	0.252798i	−0.569319	−	0.822117i	$-0.692793\pi$
$953$	240.916	−	240.916i	0.252798	−	0.252798i	0.822117	+	0.569319i	$0.192793\pi$
$954$		0			0
$955$	63.5287	+	153.372i	0.0665222	+	0.160599i
$956$	−884.127	+	996.221i	−0.924819	+	1.04207i
$957$		0			0
$958$	636.105	+	1415.02i	0.663992	+	1.47705i
$959$		−	2301.03i		−	2.39941i
$960$		0			0
$961$	−1303.41			−1.35631
$962$	85.1603	−	38.2829i	0.0885242	−	0.0397951i
$963$		0			0
$964$	−654.789	−	581.113i	−0.679242	−	0.602814i
$965$	881.533	−	365.143i	0.913506	−	0.378386i
$966$		0			0
$967$	474.501	+	474.501i	0.490694	+	0.490694i	0.908525	−	0.417831i	$-0.137209\pi$
$967$	474.501	+	474.501i	0.490694	+	0.490694i	−0.417831	+	0.908525i	$0.637209\pi$
$968$	−426.965	−	816.107i	−0.441080	−	0.843086i
$969$		0			0
$970$	707.331	−	750.753i	0.729208	−	0.773973i
$971$	−486.579	+	201.548i	−0.501111	+	0.207567i	−0.618897	−	0.785472i	$-0.712420\pi$
$971$	−486.579	+	201.548i	−0.501111	+	0.207567i	0.117786	+	0.993039i	$0.462420\pi$
$972$		0			0
$973$	−944.103	−	391.060i	−0.970301	−	0.401912i
$974$	1116.11	+	423.843i	1.14591	+	0.435158i
$975$		0			0
$976$	−1271.05	−	356.723i	−1.30231	−	0.365495i
$977$		−	137.589i		−	0.140828i	−0.997518	−	0.0704140i	$-0.977568\pi$
$977$		−	137.589i		−	0.140828i	0.997518	−	0.0704140i	$-0.0224320\pi$
$978$		0			0
$979$	21.2012	−	51.1841i	0.0216559	−	0.0522821i
$980$	1388.47	+	480.487i	1.41681	+	0.490293i
$981$		0			0
$982$	−412.043	+	437.338i	−0.419596	+	0.445354i
$983$	602.812	−	602.812i	0.613237	−	0.613237i	−0.330551	−	0.943788i	$-0.607235\pi$
$983$	602.812	−	602.812i	0.613237	−	0.613237i	0.943788	+	0.330551i	$0.107235\pi$
$984$		0			0
$985$	1119.76	−	1119.76i	1.13681	−	1.13681i
$986$	140.320	−	4.17878i	0.142313	−	0.00423811i
$987$		0			0
$988$	−5.11447	−	85.7938i	−0.00517659	−	0.0868359i
$989$	−93.6893	+	226.186i	−0.0947313	+	0.228702i
$990$		0			0
$991$		−	82.2289i		−	0.0829757i	−0.999139	−	0.0414879i	$-0.986790\pi$
$991$		−	82.2289i		−	0.0829757i	0.999139	−	0.0414879i	$-0.0132098\pi$
$992$	−1304.85	+	784.931i	−1.31538	+	0.791261i
$993$		0			0
$994$	22.2594	+	49.5161i	0.0223938	+	0.0498150i
$995$	−238.547	−	98.8096i	−0.239746	−	0.0993061i
$996$		0			0
$997$	1201.68	−	497.750i	1.20529	−	0.499248i	0.312586	−	0.949889i	$-0.398805\pi$
$997$	1201.68	−	497.750i	1.20529	−	0.499248i	0.892705	+	0.450641i	$0.148805\pi$
$998$	−51.1045	−	1716.05i	−0.0512069	−	1.71949i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.a.19.1		28
3.2	odd	2		32.3.h.a.19.7	✓	28
12.11	even	2		128.3.h.a.111.4		28
24.5	odd	2		256.3.h.b.223.4		28
24.11	even	2		256.3.h.a.223.4		28
32.27	odd	8	inner	288.3.u.a.91.1		28
96.5	odd	8		128.3.h.a.15.4		28
96.11	even	8		256.3.h.b.31.4		28
96.53	odd	8		256.3.h.a.31.4		28
96.59	even	8		32.3.h.a.27.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.7	✓	28	3.2	odd	2
32.3.h.a.27.7	yes	28	96.59	even	8
128.3.h.a.15.4		28	96.5	odd	8
128.3.h.a.111.4		28	12.11	even	2
256.3.h.a.31.4		28	96.53	odd	8
256.3.h.a.223.4		28	24.11	even	2
256.3.h.b.31.4		28	96.11	even	8
256.3.h.b.223.4		28	24.5	odd	2
288.3.u.a.19.1		28	1.1	even	1	trivial
288.3.u.a.91.1		28	32.27	odd	8	inner

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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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.82416 + 0.820030i) q^{2} +(2.65510 - 2.99173i) q^{4} +(7.60625 - 3.15061i) q^{5} +(6.84161 + 6.84161i) q^{7} +(-2.39002 + 7.63465i) q^{8} +O(q^{10})\)	\(q+(-1.82416 + 0.820030i) q^{2} +(2.65510 - 2.99173i) q^{4} +(7.60625 - 3.15061i) q^{5} +(6.84161 + 6.84161i) q^{7} +(-2.39002 + 7.63465i) q^{8} +(-11.2914 + 11.9846i) q^{10} +(2.23818 - 0.927086i) q^{11} +(1.40964 + 0.583890i) q^{13} +(-18.0905 - 6.86984i) q^{14} +(-1.90088 - 15.8867i) q^{16} -2.67812i q^{17} +(5.38908 - 13.0104i) q^{19} +(10.7696 - 31.1210i) q^{20} +(-3.32256 + 3.52653i) q^{22} +(-18.8388 + 18.8388i) q^{23} +(30.2510 - 30.2510i) q^{25} +(-3.05020 + 0.0908360i) q^{26} +(38.6334 - 2.30307i) q^{28} +(10.0298 - 24.2140i) q^{29} +47.5858i q^{31} +(16.4951 + 27.4210i) q^{32} +(2.19614 + 4.88532i) q^{34} +(73.5942 + 30.4837i) q^{35} +(-28.2682 + 11.7091i) q^{37} +(0.838382 + 28.1522i) q^{38} +(5.87475 + 65.6010i) q^{40} +(-6.93962 - 6.93962i) q^{41} +(8.48982 - 3.51660i) q^{43} +(3.16902 - 9.15755i) q^{44} +(18.9165 - 49.8132i) q^{46} +67.0112 q^{47} +44.6152i q^{49} +(-30.3759 + 79.9893i) q^{50} +(5.48956 - 2.66696i) q^{52} +(10.5006 + 25.3507i) q^{53} +(14.1033 - 14.1033i) q^{55} +(-68.5848 + 35.8817i) q^{56} +(1.56034 + 52.3950i) q^{58} +(-27.9364 - 67.4445i) q^{59} +(31.5752 - 76.2294i) q^{61} +(-39.0218 - 86.8040i) q^{62} +(-52.5757 - 36.4938i) q^{64} +12.5616 q^{65} +(90.1903 + 37.3580i) q^{67} +(-8.01222 - 7.11069i) q^{68} +(-159.245 + 4.74236i) q^{70} +(-1.98379 - 1.98379i) q^{71} +(-55.5273 - 55.5273i) q^{73} +(41.9639 - 44.5400i) q^{74} +(-24.6150 - 50.6666i) q^{76} +(21.6555 + 8.97002i) q^{77} +10.9856 q^{79} +(-64.5113 - 114.849i) q^{80} +(18.3496 + 6.96826i) q^{82} +(-34.1779 + 82.5128i) q^{83} +(-8.43772 - 20.3705i) q^{85} +(-12.6031 + 13.3767i) q^{86} +(1.72868 + 19.3035i) q^{88} +(16.1705 - 16.1705i) q^{89} +(5.64942 + 13.6389i) q^{91} +(6.34164 + 106.379i) q^{92} +(-122.239 + 54.9512i) q^{94} -115.939i q^{95} -62.6434 q^{97} +(-36.5858 - 81.3851i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

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