LMFDB - Embedded newform 387.3.w.b.199.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,3,Mod(82,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("387.82");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	387.w (of order $14$, degree $6$, 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:	$10.5449862307$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			199.5
Character	$\chi$	$=$	387.199
Dual form			387.3.w.b.352.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.844666 - 0.192789i) q^{2} +(-2.92758 + 1.40985i) q^{4} +(-0.831553 + 0.663142i) q^{5} +0.302383i q^{7} +(-4.91050 + 3.91600i) q^{8} +O(q^{10})$	\(q+(0.844666 - 0.192789i) q^{2} +(-2.92758 + 1.40985i) q^{4} +(-0.831553 + 0.663142i) q^{5} +0.302383i q^{7} +(-4.91050 + 3.91600i) q^{8} +(-0.574538 + 0.720448i) q^{10} +(4.95809 + 2.38769i) q^{11} +(-12.6441 - 15.8552i) q^{13} +(0.0582962 + 0.255412i) q^{14} +(4.71103 - 5.90745i) q^{16} +(13.9269 - 17.4637i) q^{17} +(-11.5294 - 23.9411i) q^{19} +(1.49951 - 3.11377i) q^{20} +(4.64825 + 1.06093i) q^{22} +(-25.4900 - 12.2753i) q^{23} +(-5.31130 + 23.2703i) q^{25} +(-13.7368 - 10.9547i) q^{26} +(-0.426314 - 0.885251i) q^{28} +(-32.2996 + 7.37217i) q^{29} +(1.10365 + 4.83540i) q^{31} +(13.7408 - 28.5332i) q^{32} +(8.39672 - 17.4360i) q^{34} +(-0.200523 - 0.251447i) q^{35} -24.6655i q^{37} +(-14.3541 - 17.9995i) q^{38} +(1.48648 - 6.51272i) q^{40} +(-12.5719 - 55.0811i) q^{41} +(-16.1683 + 39.8445i) q^{43} -17.8815 q^{44} +(-23.8971 - 5.45436i) q^{46} +(11.2262 - 5.40625i) q^{47} +48.9086 q^{49} +20.6796i q^{50} +(59.3701 + 28.5911i) q^{52} +(-39.6570 + 49.7283i) q^{53} +(-5.70629 + 1.30242i) q^{55} +(-1.18413 - 1.48485i) q^{56} +(-25.8611 + 12.4540i) q^{58} +(51.6529 - 64.7707i) q^{59} +(-50.9949 - 11.6393i) q^{61} +(1.86443 + 3.87153i) q^{62} +(-0.619859 + 2.71578i) q^{64} +(21.0285 + 4.79961i) q^{65} +(-35.8982 + 17.2877i) q^{67} +(-16.1508 + 70.7613i) q^{68} +(-0.217851 - 0.173730i) q^{70} +(9.29195 + 19.2949i) q^{71} +(72.6272 - 57.9182i) q^{73} +(-4.75525 - 20.8341i) q^{74} +(67.5068 + 53.8349i) q^{76} +(-0.721996 + 1.49924i) q^{77} -79.2902 q^{79} +8.03643i q^{80} +(-21.2381 - 44.1014i) q^{82} +(-21.7886 + 95.4621i) q^{83} +23.7575i q^{85} +(-5.97524 + 36.7724i) q^{86} +(-33.6969 + 7.69109i) q^{88} +(29.9831 + 6.84344i) q^{89} +(4.79434 - 3.82336i) q^{91} +91.9305 q^{92} +(8.44011 - 6.73076i) q^{94} +(25.4637 + 12.2627i) q^{95} +(32.3163 + 15.5627i) q^{97} +(41.3114 - 9.42906i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 7 q^{2} + 5 q^{4} + 7 q^{5} - 21 q^{8}+O(q^{10}) $ 42 * q + 7 * q^2 + 5 * q^4 + 7 * q^5 - 21 * q^8	$ 42 q + 7 q^{2} + 5 q^{4} + 7 q^{5} - 21 q^{8} - 5 q^{10} + 24 q^{11} - 34 q^{13} - 69 q^{14} - 39 q^{16} - 22 q^{17} - 49 q^{19} - 133 q^{20} + 77 q^{22} - 42 q^{23} + 10 q^{25} - 49 q^{26} + 105 q^{28} - 63 q^{29} - 152 q^{31} - 343 q^{32} + 161 q^{34} - 58 q^{35} + 289 q^{38} - 101 q^{40} - 133 q^{41} - 79 q^{43} - 148 q^{44} - 504 q^{46} - 6 q^{47} - 302 q^{49} - 267 q^{52} + 394 q^{53} - 637 q^{55} - 355 q^{56} + 165 q^{58} + 46 q^{59} - 175 q^{61} + 91 q^{62} + 725 q^{64} - 161 q^{65} - 756 q^{67} + 586 q^{68} + 1526 q^{70} - 266 q^{71} - 252 q^{73} - 204 q^{74} + 994 q^{76} - 791 q^{77} - 178 q^{79} + 245 q^{82} - 238 q^{83} - 365 q^{86} - 119 q^{88} - 252 q^{89} - 224 q^{91} + 764 q^{92} + 133 q^{94} - 11 q^{95} - 491 q^{97} + 553 q^{98}+O(q^{100}) $ 42 * q + 7 * q^2 + 5 * q^4 + 7 * q^5 - 21 * q^8 - 5 * q^10 + 24 * q^11 - 34 * q^13 - 69 * q^14 - 39 * q^16 - 22 * q^17 - 49 * q^19 - 133 * q^20 + 77 * q^22 - 42 * q^23 + 10 * q^25 - 49 * q^26 + 105 * q^28 - 63 * q^29 - 152 * q^31 - 343 * q^32 + 161 * q^34 - 58 * q^35 + 289 * q^38 - 101 * q^40 - 133 * q^41 - 79 * q^43 - 148 * q^44 - 504 * q^46 - 6 * q^47 - 302 * q^49 - 267 * q^52 + 394 * q^53 - 637 * q^55 - 355 * q^56 + 165 * q^58 + 46 * q^59 - 175 * q^61 + 91 * q^62 + 725 * q^64 - 161 * q^65 - 756 * q^67 + 586 * q^68 + 1526 * q^70 - 266 * q^71 - 252 * q^73 - 204 * q^74 + 994 * q^76 - 791 * q^77 - 178 * q^79 + 245 * q^82 - 238 * q^83 - 365 * q^86 - 119 * q^88 - 252 * q^89 - 224 * q^91 + 764 * q^92 + 133 * q^94 - 11 * q^95 - 491 * q^97 + 553 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$1$

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 $

$2$	0.844666	−	0.192789i	0.422333	−	0.0963947i	−0.00607209	−	0.999982i	$-0.501933\pi$
$2$	0.844666	−	0.192789i	0.422333	−	0.0963947i	0.428405	+	0.903587i	$0.359076\pi$
$3$		0			0
$3$		0			0
$4$	−2.92758	+	1.40985i	−0.731896	+	0.352462i
$5$	−0.831553	+	0.663142i	−0.166311	+	0.132628i	−0.703109	−	0.711083i	$-0.748205\pi$
$5$	−0.831553	+	0.663142i	−0.166311	+	0.132628i	0.536798	+	0.843711i	$0.319634\pi$
$6$		0			0
$7$			0.302383i			0.0431975i	0.999767	+	0.0215988i	$0.00687564\pi$
$7$			0.302383i			0.0431975i	−0.999767	+	0.0215988i	$0.993124\pi$
$8$	−4.91050	+	3.91600i	−0.613813	+	0.489499i
$9$		0			0
$10$	−0.574538	+	0.720448i	−0.0574538	+	0.0720448i
$11$	4.95809	+	2.38769i	0.450735	+	0.217063i	0.645458	−	0.763796i	$-0.276667\pi$
$11$	4.95809	+	2.38769i	0.450735	+	0.217063i	−0.194723	+	0.980858i	$0.562381\pi$
$12$		0			0
$13$	−12.6441	−	15.8552i	−0.972623	−	1.21963i	−0.975582	−	0.219635i	$-0.929513\pi$
$13$	−12.6441	−	15.8552i	−0.972623	−	1.21963i	0.00295926	−	0.999996i	$-0.499058\pi$
$14$	0.0582962	+	0.255412i	0.00416402	+	0.0182437i
$15$		0			0
$16$	4.71103	−	5.90745i	0.294439	−	0.369215i
$17$	13.9269	−	17.4637i	0.819227	−	1.02728i	−0.179823	−	0.983699i	$-0.557552\pi$
$17$	13.9269	−	17.4637i	0.819227	−	1.02728i	0.999050	−	0.0435792i	$-0.0138761\pi$
$18$		0			0
$19$	−11.5294	−	23.9411i	−0.606813	−	1.26006i	−0.947462	−	0.319870i	$-0.896361\pi$
$19$	−11.5294	−	23.9411i	−0.606813	−	1.26006i	0.340649	−	0.940191i	$-0.389353\pi$
$20$	1.49951	−	3.11377i	0.0749756	−	0.155688i
$21$		0			0
$22$	4.64825	+	1.06093i	0.211284	+	0.0482242i
$23$	−25.4900	−	12.2753i	−1.10826	−	0.533711i	−0.212015	−	0.977266i	$-0.568003\pi$
$23$	−25.4900	−	12.2753i	−1.10826	−	0.533711i	−0.896247	+	0.443556i	$0.853717\pi$
$24$		0			0
$25$	−5.31130	+	23.2703i	−0.212452	+	0.930813i
$26$	−13.7368	−	10.9547i	−0.528337	−	0.421334i
$27$		0			0
$28$	−0.426314	−	0.885251i	−0.0152255	−	0.0316161i
$29$	−32.2996	+	7.37217i	−1.11378	+	0.254213i	−0.739535	−	0.673118i	$-0.764955\pi$
$29$	−32.2996	+	7.37217i	−1.11378	+	0.254213i	−0.374244	+	0.927330i	$0.622098\pi$
$30$		0			0
$31$	1.10365	+	4.83540i	0.0356016	+	0.155981i	0.989604	−	0.143817i	$-0.0459378\pi$
$31$	1.10365	+	4.83540i	0.0356016	+	0.155981i	−0.954003	+	0.299798i	$0.903081\pi$
$32$	13.7408	−	28.5332i	0.429401	−	0.891661i
$33$		0			0
$34$	8.39672	−	17.4360i	0.246962	−	0.512823i
$35$	−0.200523	−	0.251447i	−0.00572922	−	0.00718421i
$36$		0			0
$37$		−	24.6655i		−	0.666635i	−0.942815	−	0.333318i	$-0.891832\pi$
$37$		−	24.6655i		−	0.666635i	0.942815	−	0.333318i	$-0.108168\pi$
$38$	−14.3541	−	17.9995i	−0.377740	−	0.473671i
$39$		0			0
$40$	1.48648	−	6.51272i	0.0371621	−	0.162818i
$41$	−12.5719	−	55.0811i	−0.306632	−	1.34344i	−0.859910	−	0.510445i	$-0.829481\pi$
$41$	−12.5719	−	55.0811i	−0.306632	−	1.34344i	0.553279	−	0.832996i	$-0.313376\pi$
$42$		0			0
$43$	−16.1683	+	39.8445i	−0.376008	+	0.926616i
$43$	−16.1683	+	39.8445i	−0.376008	+	0.926616i
$44$	−17.8815			−0.406397
$45$		0			0
$46$	−23.8971	−	5.45436i	−0.519502	−	0.118573i
$47$	11.2262	−	5.40625i	0.238855	−	0.115027i	−0.310627	−	0.950532i	$-0.600539\pi$
$47$	11.2262	−	5.40625i	0.238855	−	0.115027i	0.549483	+	0.835505i	$0.314825\pi$
$48$		0			0
$49$	48.9086			0.998134
$50$			20.6796i			0.413592i
$51$		0			0
$52$	59.3701	+	28.5911i	1.14173	+	0.549829i
$53$	−39.6570	+	49.7283i	−0.748246	+	0.938271i	−0.999561	−	0.0296347i	$-0.990566\pi$
$53$	−39.6570	+	49.7283i	−0.748246	+	0.938271i	0.251315	+	0.967905i	$0.419137\pi$
$54$		0			0
$55$	−5.70629	+	1.30242i	−0.103751	+	0.0236804i
$56$	−1.18413	−	1.48485i	−0.0211452	−	0.0265152i
$57$		0			0
$58$	−25.8611	+	12.4540i	−0.445881	+	0.214725i
$59$	51.6529	−	64.7707i	0.875473	−	1.09781i	−0.119009	−	0.992893i	$-0.537972\pi$
$59$	51.6529	−	64.7707i	0.875473	−	1.09781i	0.994481	−	0.104915i	$-0.0334570\pi$
$60$		0			0
$61$	−50.9949	−	11.6393i	−0.835982	−	0.190807i	−0.216960	−	0.976181i	$-0.569614\pi$
$61$	−50.9949	−	11.6393i	−0.835982	−	0.190807i	−0.619023	+	0.785373i	$0.712471\pi$
$62$	1.86443	+	3.87153i	0.0300714	+	0.0624440i
$63$		0			0
$64$	−0.619859	+	2.71578i	−0.00968530	+	0.0424341i
$65$	21.0285	+	4.79961i	0.323515	+	0.0738402i
$66$		0			0
$67$	−35.8982	+	17.2877i	−0.535794	+	0.258025i	−0.682156	−	0.731206i	$-0.738958\pi$
$67$	−35.8982	+	17.2877i	−0.535794	+	0.258025i	0.146362	+	0.989231i	$0.453243\pi$
$68$	−16.1508	+	70.7613i	−0.237512	+	1.04061i
$69$		0			0
$70$	−0.217851	−	0.173730i	−0.00311216	−	0.00248186i
$71$	9.29195	+	19.2949i	0.130873	+	0.271760i	0.956100	−	0.293041i	$-0.0946673\pi$
$71$	9.29195	+	19.2949i	0.130873	+	0.271760i	−0.825227	+	0.564801i	$0.808953\pi$
$72$		0			0
$73$	72.6272	−	57.9182i	0.994893	−	0.793401i	0.0164387	−	0.999865i	$-0.494767\pi$
$73$	72.6272	−	57.9182i	0.994893	−	0.793401i	0.978454	+	0.206464i	$0.0661957\pi$
$74$	−4.75525	−	20.8341i	−0.0642601	−	0.281542i
$75$		0			0
$76$	67.5068	+	53.8349i	0.888248	+	0.708354i
$77$	−0.721996	+	1.49924i	−0.00937657	+	0.0194706i
$78$		0			0
$79$	−79.2902			−1.00367			−0.501837	−	0.864962i	$-0.667342\pi$
$79$	−79.2902			−1.00367			−0.501837	+	0.864962i	$0.667342\pi$
$80$			8.03643i			0.100455i
$81$		0			0
$82$	−21.2381	−	44.1014i	−0.259001	−	0.537822i
$83$	−21.7886	+	95.4621i	−0.262513	+	1.15015i	0.656002	+	0.754760i	$0.272246\pi$
$83$	−21.7886	+	95.4621i	−0.262513	+	1.15015i	−0.918515	+	0.395386i	$0.870611\pi$
$84$		0			0
$85$			23.7575i			0.279500i
$86$	−5.97524	+	36.7724i	−0.0694796	+	0.427586i
$87$		0			0
$88$	−33.6969	+	7.69109i	−0.382919	+	0.0873987i
$89$	29.9831	+	6.84344i	0.336889	+	0.0768926i	0.387619	−	0.921820i	$-0.373298\pi$
$89$	29.9831	+	6.84344i	0.336889	+	0.0768926i	−0.0507302	+	0.998712i	$0.516155\pi$
$90$		0			0
$91$	4.79434	−	3.82336i	0.0526850	−	0.0420149i
$92$	91.9305			0.999245
$93$		0			0
$94$	8.44011	−	6.73076i	0.0897884	−	0.0716039i
$95$	25.4637	+	12.2627i	0.268039	+	0.129081i
$96$		0			0
$97$	32.3163	+	15.5627i	0.333158	+	0.160440i	0.592982	−	0.805216i	$-0.297950\pi$
$97$	32.3163	+	15.5627i	0.333158	+	0.160440i	−0.259825	+	0.965656i	$0.583665\pi$
$98$	41.3114	−	9.42906i	0.421545	−	0.0962149i
$99$		0			0
$100$	−17.2584	−	75.6139i	−0.172584	−	0.756139i
$101$	−26.2844	+	12.6579i	−0.260242	+	0.125326i	−0.559456	−	0.828860i	$-0.688990\pi$
$101$	−26.2844	+	12.6579i	−0.260242	+	0.125326i	0.299214	+	0.954186i	$0.403276\pi$
$102$		0			0
$103$	−42.0813	+	52.7682i	−0.408556	+	0.512313i	−0.942955	−	0.332919i	$-0.891966\pi$
$103$	−42.0813	+	52.7682i	−0.408556	+	0.512313i	0.534399	+	0.845232i	$0.320538\pi$
$104$	124.178	+	28.3428i	1.19402	+	0.272527i
$105$		0			0
$106$	−23.9098	+	49.6493i	−0.225564	+	0.468390i
$107$	−3.06697	+	13.4373i	−0.0286633	+	0.125582i	−0.987235	−	0.159268i	$-0.949087\pi$
$107$	−3.06697	+	13.4373i	−0.0286633	+	0.125582i	0.958572	+	0.284850i	$0.0919438\pi$
$108$		0			0
$109$	90.7422	+	43.6991i	0.832497	+	0.400910i	0.801051	−	0.598596i	$-0.204274\pi$
$109$	90.7422	+	43.6991i	0.832497	+	0.400910i	0.0314461	+	0.999505i	$0.489989\pi$
$110$	−4.56881	+	2.20022i	−0.0415347	+	0.0200020i
$111$		0			0
$112$	1.78631	+	1.42453i	0.0159492	+	0.0127191i
$113$	−106.961	−	85.2984i	−0.946556	−	0.754853i	0.0229966	−	0.999736i	$-0.492679\pi$
$113$	−106.961	−	85.2984i	−0.946556	−	0.754853i	−0.969553	+	0.244882i	$0.921251\pi$
$114$		0			0
$115$	29.3366	−	6.69589i	0.255101	−	0.0582251i
$116$	84.1661	−	67.1202i	0.725570	−	0.578623i
$117$		0			0
$118$	31.1423	−	64.6677i	0.263918	−	0.548031i
$119$	5.28073	+	4.21124i	0.0443759	+	0.0353886i
$120$		0			0
$121$	−56.5607	−	70.9249i	−0.467444	−	0.586156i
$122$	−45.3176			−0.371456
$123$		0			0
$124$	−10.0482	−	12.6001i	−0.0810340	−	0.101613i
$125$	−22.5518	−	46.8293i	−0.180415	−	0.374635i
$126$		0			0
$127$	−18.7891	−	82.3203i	−0.147945	−	0.648192i	−0.993454	−	0.114230i	$-0.963560\pi$
$127$	−18.7891	−	82.3203i	−0.147945	−	0.648192i	0.845509	−	0.533961i	$-0.179297\pi$
$128$			129.091i			1.00852i
$129$		0			0
$130$	18.6874			0.143749
$131$	45.1831	−	10.3128i	0.344909	−	0.0787233i	−0.0465572	−	0.998916i	$-0.514825\pi$
$131$	45.1831	−	10.3128i	0.344909	−	0.0787233i	0.391467	+	0.920192i	$0.371968\pi$
$132$		0			0
$133$	7.23939	−	3.48631i	0.0544315	−	0.0262128i
$134$	−26.9891	+	21.5231i	−0.201411	+	0.160620i
$135$		0			0
$136$			140.293i			1.03157i
$137$	−114.791	+	91.5426i	−0.837889	+	0.668195i	−0.945365	−	0.326013i	$-0.894295\pi$
$137$	−114.791	+	91.5426i	−0.837889	+	0.668195i	0.107476	+	0.994208i	$0.465723\pi$
$138$		0			0
$139$	−17.1502	+	21.5057i	−0.123383	+	0.154717i	−0.839686	−	0.543072i	$-0.817261\pi$
$139$	−17.1502	+	21.5057i	−0.123383	+	0.154717i	0.716304	+	0.697789i	$0.245833\pi$
$140$	0.941549	+	0.453426i	0.00672535	+	0.00323876i
$141$		0			0
$142$	11.5685	+	14.5064i	0.0814680	+	0.102158i
$143$	−24.8333	−	108.802i	−0.173659	−	0.760850i
$144$		0			0
$145$	21.9700	−	27.5496i	0.151518	−	0.189997i
$146$	50.1797	−	62.9233i	0.343696	−	0.430982i
$147$		0			0
$148$	34.7747	+	72.2103i	0.234964	+	0.487908i
$149$	−43.8929	+	91.1445i	−0.294583	+	0.611708i	−0.994757	−	0.102264i	$-0.967391\pi$
$149$	−43.8929	+	91.1445i	−0.294583	+	0.611708i	0.700174	+	0.713972i	$0.253106\pi$
$150$		0			0
$151$	114.117	+	26.0465i	0.755742	+	0.172493i	0.582998	−	0.812474i	$-0.301880\pi$
$151$	114.117	+	26.0465i	0.755742	+	0.172493i	0.172744	+	0.984967i	$0.444737\pi$
$152$	150.369	+	72.4138i	0.989268	+	0.476406i
$153$		0			0
$154$	−0.320808	+	1.40555i	−0.00208317	+	0.00912695i
$155$	−4.12430	−	3.28902i	−0.0266084	−	0.0212195i
$156$		0			0
$157$	91.9503	+	190.937i	0.585670	+	1.21616i	0.957655	+	0.287918i	$0.0929631\pi$
$157$	91.9503	+	190.937i	0.585670	+	1.21616i	−0.371985	+	0.928239i	$0.621323\pi$
$158$	−66.9737	+	15.2863i	−0.423884	+	0.0967488i
$159$		0			0
$160$	7.49528	+	32.8390i	0.0468455	+	0.205244i
$161$	3.71185	−	7.70774i	0.0230550	−	0.0478742i
$162$		0			0
$163$	61.8614	−	128.457i	0.379518	−	0.788077i	−0.620475	−	0.784227i	$-0.713060\pi$
$163$	61.8614	−	128.457i	0.379518	−	0.788077i	0.999993	−	0.00385077i	$-0.00122574\pi$
$164$	114.461	+	143.530i	0.697935	+	0.875183i
$165$		0			0
$166$			84.8342i			0.511049i
$167$	51.3450	+	64.3846i	0.307455	+	0.385536i	0.911422	−	0.411473i	$-0.134986\pi$
$167$	51.3450	+	64.3846i	0.307455	+	0.385536i	−0.603967	+	0.797009i	$0.706414\pi$
$168$		0			0
$169$	−53.9080	+	236.186i	−0.318982	+	1.39755i
$170$	4.58019	+	20.0671i	0.0269423	+	0.118042i
$171$		0			0
$172$	−8.84061	−	139.443i	−0.0513989	−	0.810715i
$173$	−43.9904			−0.254280			−0.127140	−	0.991885i	$-0.540580\pi$
$173$	−43.9904			−0.254280			−0.127140	+	0.991885i	$0.540580\pi$
$174$		0			0
$175$	−7.03655	−	1.60605i	−0.0402088	−	0.00917740i
$176$	37.4628	−	18.0411i	0.212857	−	0.102507i
$177$		0			0
$178$	26.6450			0.149691
$179$		−	150.763i		−	0.842253i	−0.907002	−	0.421127i	$-0.861635\pi$
$179$		−	150.763i		−	0.842253i	0.907002	−	0.421127i	$-0.138365\pi$
$180$		0			0
$181$	−280.100	−	134.889i	−1.54752	−	0.745244i	−0.551479	−	0.834189i	$-0.685936\pi$
$181$	−280.100	−	134.889i	−1.54752	−	0.745244i	−0.996037	+	0.0889441i	$0.971651\pi$
$182$	3.31251	−	4.15376i	0.0182006	−	0.0228228i
$183$		0			0
$184$	173.239	−	39.5407i	0.941516	−	0.214895i
$185$	16.3567	+	20.5107i	0.0884147	+	0.110869i
$186$		0			0
$187$	110.748	−	53.3337i	0.592238	−	0.285207i
$188$	−25.2436	+	31.6545i	−0.134274	+	0.168375i
$189$		0			0
$190$	23.8724	+	5.44873i	0.125644	+	0.0286775i
$191$	−49.8976	−	103.613i	−0.261244	−	0.542479i	0.728549	−	0.684994i	$-0.240195\pi$
$191$	−49.8976	−	103.613i	−0.261244	−	0.542479i	−0.989793	+	0.142515i	$0.954481\pi$
$192$		0			0
$193$	0.381280	−	1.67050i	0.00197555	−	0.00865543i	−0.973931	−	0.226846i	$-0.927158\pi$
$193$	0.381280	−	1.67050i	0.00197555	−	0.00865543i	0.975906	+	0.218191i	$0.0700156\pi$
$194$	30.2968	+	6.91504i	0.156169	+	0.0356446i
$195$		0			0
$196$	−143.184	+	68.9537i	−0.730530	+	0.351805i
$197$	−79.5194	+	348.397i	−0.403652	+	1.76851i	0.208751	+	0.977969i	$0.433060\pi$
$197$	−79.5194	+	348.397i	−0.403652	+	1.76851i	−0.612403	+	0.790546i	$0.709797\pi$
$198$		0			0
$199$	−196.496	−	156.700i	−0.987415	−	0.787437i	−0.0102563	−	0.999947i	$-0.503265\pi$
$199$	−196.496	−	156.700i	−0.987415	−	0.787437i	−0.977159	+	0.212510i	$0.931836\pi$
$200$	−65.0453	−	135.068i	−0.325227	−	0.675340i
$201$		0			0
$202$	−19.7612	+	15.7591i	−0.0978280	+	0.0780152i
$203$	−2.22922	−	9.76684i	−0.0109814	−	0.0481125i
$204$		0			0
$205$	46.9808	+	37.4659i	0.229174	+	0.182760i
$206$	−25.3714	+	52.6843i	−0.123162	+	0.255749i
$207$		0			0
$208$	−153.230			−0.736685
$209$		−	146.231i		−	0.699670i
$210$		0			0
$211$	38.5677	+	80.0866i	0.182785	+	0.379557i	0.972147	−	0.234370i	$-0.0753029\pi$
$211$	38.5677	+	80.0866i	0.182785	+	0.379557i	−0.789362	+	0.613928i	$0.789589\pi$
$212$	45.9898	−	201.494i	0.216933	−	0.950445i
$213$		0			0
$214$			11.9413i			0.0558005i
$215$	−12.9777	−	43.8547i	−0.0603615	−	0.203975i
$216$		0			0
$217$	−1.46214	+	0.333724i	−0.00673798	+	0.00153790i
$218$	85.0716	+	19.4170i	0.390237	+	0.0890689i
$219$		0			0
$220$	14.8694	−	11.8580i	0.0675882	−	0.0538998i
$221$	−452.983			−2.04970
$222$		0			0
$223$	214.263	−	170.869i	0.960823	−	0.766231i	−0.0114851	−	0.999934i	$-0.503656\pi$
$223$	214.263	−	170.869i	0.960823	−	0.766231i	0.972308	+	0.233703i	$0.0750845\pi$
$224$	8.62794	+	4.15500i	0.0385176	+	0.0185491i
$225$		0			0
$226$	−106.791	−	51.4277i	−0.472526	−	0.227556i
$227$	253.278	−	57.8090i	1.11576	−	0.254665i	0.375392	−	0.926866i	$-0.377508\pi$
$227$	253.278	−	57.8090i	1.11576	−	0.254665i	0.740369	+	0.672201i	$0.234651\pi$
$228$		0			0
$229$	−12.5285	−	54.8910i	−0.0547097	−	0.239699i	0.940178	−	0.340682i	$-0.110658\pi$
$229$	−12.5285	−	54.8910i	−0.0547097	−	0.239699i	−0.994888	+	0.100984i	$0.967801\pi$
$230$	23.4887	−	11.3116i	0.102125	−	0.0491808i
$231$		0			0
$232$	129.738	−	162.686i	0.559215	−	0.701233i
$233$	72.7240	+	16.5988i	0.312120	+	0.0712393i	0.375712	−	0.926737i	$-0.377398\pi$
$233$	72.7240	+	16.5988i	0.312120	+	0.0712393i	−0.0635916	+	0.997976i	$0.520255\pi$
$234$		0			0
$235$	−5.75007	+	11.9401i	−0.0244684	+	0.0508091i
$236$	−59.9012	+	262.444i	−0.253819	+	1.11205i
$237$		0			0
$238$	5.27234	+	2.53902i	0.0221527	+	0.0106682i
$239$	395.505	−	190.465i	1.65483	−	0.796925i	0.655711	−	0.755012i	$-0.272369\pi$
$239$	395.505	−	190.465i	1.65483	−	0.796925i	0.999121	−	0.0419133i	$-0.0133453\pi$
$240$		0			0
$241$	−131.969	−	105.242i	−0.547590	−	0.436689i	0.310213	−	0.950667i	$-0.399600\pi$
$241$	−131.969	−	105.242i	−0.547590	−	0.436689i	−0.857803	+	0.513978i	$0.828171\pi$
$242$	−61.4485	−	49.0035i	−0.253919	−	0.202494i
$243$		0			0
$244$	165.701	−	37.8203i	0.679104	−	0.155001i
$245$	−40.6701	+	32.4333i	−0.166000	+	0.132381i
$246$		0			0
$247$	−233.812	+	485.516i	−0.946608	+	1.96565i
$248$	−24.3549	−	19.4224i	−0.0982051	−	0.0783160i
$249$		0			0
$250$	−28.0770	−	35.2074i	−0.112308	−	0.140830i
$251$	−3.56660			−0.0142096			−0.00710478	−	0.999975i	$-0.502262\pi$
$251$	−3.56660			−0.0142096			−0.00710478	+	0.999975i	$0.502262\pi$
$252$		0			0
$253$	−97.0720	−	121.724i	−0.383684	−	0.481124i
$254$	−31.7410	−	65.9108i	−0.124964	−	0.259491i
$255$		0			0
$256$	22.4080	+	98.1757i	0.0875311	+	0.383499i
$257$		−	433.357i		−	1.68621i	−0.537747	−	0.843106i	$-0.680724\pi$
$257$		−	433.357i		−	1.68621i	0.537747	−	0.843106i	$-0.319276\pi$
$258$		0			0
$259$	7.45843			0.0287970
$260$	−68.3293	+	15.5957i	−0.262805	+	0.0599836i
$261$		0			0
$262$	36.1765	−	17.4217i	0.138078	−	0.0664949i
$263$	−102.332	+	81.6071i	−0.389095	+	0.310293i	−0.798426	−	0.602093i	$-0.794334\pi$
$263$	−102.332	+	81.6071i	−0.389095	+	0.310293i	0.409331	+	0.912386i	$0.365762\pi$
$264$		0			0
$265$		−	67.6500i		−	0.255283i
$266$	5.44274	−	4.34044i	0.0204614	−	0.0163175i
$267$		0			0
$268$	80.7220	−	101.222i	0.301201	−	0.377695i
$269$	−329.810	−	158.828i	−1.22606	−	0.590440i	−0.295068	−	0.955476i	$-0.595342\pi$
$269$	−329.810	−	158.828i	−1.22606	−	0.590440i	−0.930993	+	0.365036i	$0.881057\pi$
$270$		0			0
$271$	13.6191	+	17.0779i	0.0502552	+	0.0630180i	0.806324	−	0.591474i	$-0.201454\pi$
$271$	13.6191	+	17.0779i	0.0502552	+	0.0630180i	−0.756069	+	0.654492i	$0.772882\pi$
$272$	−37.5562	−	164.544i	−0.138074	−	0.604942i
$273$		0			0
$274$	−79.3114	+	99.4534i	−0.289458	+	0.362969i
$275$	−81.8962	+	102.695i	−0.297804	+	0.373435i
$276$		0			0
$277$	−109.353	−	227.075i	−0.394778	−	0.819764i	−0.999724	−	0.0234977i	$-0.992520\pi$
$277$	−109.353	−	227.075i	−0.394778	−	0.819764i	0.604946	−	0.796266i	$-0.293195\pi$
$278$	−10.3401	+	21.4715i	−0.0371947	+	0.0772355i
$279$		0			0
$280$	1.96933	+	0.449487i	0.00703333	+	0.00160531i
$281$	−191.046	−	92.0031i	−0.679880	−	0.327413i	0.0618747	−	0.998084i	$-0.480292\pi$
$281$	−191.046	−	92.0031i	−0.679880	−	0.327413i	−0.741755	+	0.670671i	$0.766006\pi$
$282$		0			0
$283$	14.2648	−	62.4982i	0.0504057	−	0.220842i	−0.943452	−	0.331510i	$-0.892442\pi$
$283$	14.2648	−	62.4982i	0.0504057	−	0.220842i	0.993857	+	0.110668i	$0.0352991\pi$
$284$	−54.4059	−	43.3873i	−0.191570	−	0.152772i
$285$		0			0
$286$	−41.9516	−	87.1134i	−0.146684	−	0.304592i
$287$	16.6556	−	3.80153i	0.0580333	−	0.0132457i
$288$		0			0
$289$	−46.7159	−	204.676i	−0.161647	−	0.708220i
$290$	13.2461	−	27.5058i	0.0456761	−	0.0948474i
$291$		0			0
$292$	−130.966	+	271.954i	−0.448514	+	0.931349i
$293$	−130.578	−	163.739i	−0.445658	−	0.558837i	0.507367	−	0.861730i	$-0.330619\pi$
$293$	−130.578	−	163.739i	−0.445658	−	0.558837i	−0.953025	+	0.302893i	$0.902048\pi$
$294$		0			0
$295$			88.1134i			0.298690i
$296$	96.5900	+	121.120i	0.326318	+	0.409189i
$297$		0			0
$298$	−19.5031	+	85.4487i	−0.0654467	+	0.286741i
$299$	127.670	+	559.360i	0.426991	+	1.87077i
$300$		0			0
$301$	−12.0483	−	4.88903i	−0.0400276	−	0.0162426i
$302$	101.412			0.335802
$303$		0			0
$304$	−195.747	−	44.6779i	−0.643903	−	0.146967i
$305$	50.1235	−	24.1382i	0.164339	−	0.0791416i
$306$		0			0
$307$	−113.215			−0.368780			−0.184390	−	0.982853i	$-0.559031\pi$
$307$	−113.215			−0.368780			−0.184390	+	0.982853i	$0.559031\pi$
$308$		−	5.40705i		−	0.0175554i
$309$		0			0
$310$	−4.11774	−	1.98300i	−0.0132830	−	0.00639677i
$311$	27.5310	−	34.5228i	0.0885241	−	0.111006i	−0.735597	−	0.677420i	$-0.763098\pi$
$311$	27.5310	−	34.5228i	0.0885241	−	0.111006i	0.824121	+	0.566414i	$0.191670\pi$
$312$		0			0
$313$	−72.3142	+	16.5052i	−0.231036	+	0.0527324i	−0.336471	−	0.941694i	$-0.609234\pi$
$313$	−72.3142	+	16.5052i	−0.231036	+	0.0527324i	0.105435	+	0.994426i	$0.466376\pi$
$314$	114.478	+	143.551i	0.364579	+	0.457168i
$315$		0			0
$316$	232.129	−	111.787i	0.734584	−	0.353757i
$317$	203.262	−	254.882i	0.641204	−	0.804044i	−0.349949	−	0.936769i	$-0.613801\pi$
$317$	203.262	−	254.882i	0.641204	−	0.804044i	0.991153	+	0.132725i	$0.0423726\pi$
$318$		0			0
$319$	−177.747	−	40.5695i	−0.557199	−	0.127177i
$320$	−1.28550	−	2.66937i	−0.00401719	−	0.00834178i
$321$		0			0
$322$	1.64930	−	7.22607i	0.00512206	−	0.0224412i
$323$	−578.671	−	132.078i	−1.79155	−	0.408910i
$324$		0			0
$325$	436.112	−	210.021i	1.34188	−	0.646217i
$326$	27.4872	−	120.429i	0.0843165	−	0.369415i
$327$		0			0
$328$	277.432	+	221.244i	0.845828	+	0.674525i
$329$	1.63476	+	3.39461i	0.00496886	+	0.0103180i
$330$		0			0
$331$	196.452	−	156.665i	0.593511	−	0.473309i	−0.280076	−	0.959978i	$-0.590360\pi$
$331$	196.452	−	156.665i	0.593511	−	0.473309i	0.873587	+	0.486669i	$0.161788\pi$
$332$	−70.7993	−	310.192i	−0.213251	−	0.934313i
$333$		0			0
$334$	55.7820	+	44.4847i	0.167012	+	0.133188i
$335$	18.3871	−	38.1812i	0.0548869	−	0.113974i
$336$		0			0
$337$	513.631			1.52413			0.762064	−	0.647501i	$-0.224186\pi$
$337$	513.631			1.52413			0.762064	+	0.647501i	$0.224186\pi$
$338$			209.892i			0.620981i
$339$		0			0
$340$	−33.4945	−	69.5520i	−0.0985132	−	0.204565i
$341$	−6.07344	+	26.6095i	−0.0178107	+	0.0780337i
$342$		0			0
$343$			29.6059i			0.0863145i
$344$	−76.6362	−	258.972i	−0.222780	−	0.752825i
$345$		0			0
$346$	−37.1572	+	8.48088i	−0.107391	+	0.0245112i
$347$	50.4078	+	11.5053i	0.145267	+	0.0331563i	0.294536	−	0.955640i	$-0.404835\pi$
$347$	50.4078	+	11.5053i	0.145267	+	0.0331563i	−0.149269	+	0.988797i	$0.547692\pi$
$348$		0			0
$349$	−473.778	+	377.825i	−1.35753	+	1.08259i	−0.369349	+	0.929291i	$0.620419\pi$
$349$	−473.778	+	377.825i	−1.35753	+	1.08259i	−0.988179	+	0.153302i	$0.951009\pi$
$350$	−6.25316			−0.0178662
$351$		0			0
$352$	136.257	−	108.661i	0.387093	−	0.308696i
$353$	−282.421	−	136.007i	−0.800059	−	0.385288i	−0.0112581	−	0.999937i	$-0.503584\pi$
$353$	−282.421	−	136.007i	−0.800059	−	0.385288i	−0.788801	+	0.614648i	$0.789298\pi$
$354$		0			0
$355$	−20.5220	−	9.88289i	−0.0578085	−	0.0278391i
$356$	−97.4262	+	22.2369i	−0.273669	+	0.0624632i
$357$		0			0
$358$	−29.0656	−	127.345i	−0.0811888	−	0.355711i
$359$	277.969	−	133.863i	0.774286	−	0.372877i	−0.00464226	−	0.999989i	$-0.501478\pi$
$359$	277.969	−	133.863i	0.774286	−	0.372877i	0.778929	+	0.627113i	$0.215763\pi$
$360$		0			0
$361$	−215.170	+	269.815i	−0.596040	+	0.747410i
$362$	−262.596	−	59.9359i	−0.725405	−	0.165569i
$363$		0			0
$364$	−8.64546	+	17.9525i	−0.0237513	+	0.0493200i
$365$	−21.9854	+	96.3242i	−0.0602339	+	0.263902i
$366$		0			0
$367$	88.8360	+	42.7812i	0.242060	+	0.116570i	0.550981	−	0.834518i	$-0.314254\pi$
$367$	88.8360	+	42.7812i	0.242060	+	0.116570i	−0.308921	+	0.951088i	$0.599968\pi$
$368$	−192.600	+	92.7514i	−0.523370	+	0.252042i
$369$		0			0
$370$	17.7702	+	14.1713i	0.0480276	+	0.0383007i
$371$	−15.0370	−	11.9916i	−0.0405310	−	0.0323224i
$372$		0			0
$373$	195.815	−	44.6935i	0.524973	−	0.119822i	0.0481825	−	0.998839i	$-0.484657\pi$
$373$	195.815	−	44.6935i	0.524973	−	0.119822i	0.476791	+	0.879017i	$0.341800\pi$
$374$	83.2633	−	66.4003i	0.222629	−	0.177541i
$375$		0			0
$376$	−33.9554	+	70.5091i	−0.0903069	+	0.187524i
$377$	525.286	+	418.902i	1.39333	+	1.11115i
$378$		0			0
$379$	−115.127	−	144.365i	−0.303765	−	0.380909i	0.606397	−	0.795162i	$-0.292614\pi$
$379$	−115.127	−	144.365i	−0.303765	−	0.380909i	−0.910162	+	0.414253i	$0.864043\pi$
$380$	−91.8357			−0.241673
$381$		0			0
$382$	−62.1224	−	77.8990i	−0.162624	−	0.203924i
$383$	187.470	+	389.285i	0.489477	+	1.01641i	0.988696	+	0.149934i	$0.0479061\pi$
$383$	187.470	+	389.285i	0.489477	+	1.01641i	−0.499219	+	0.866476i	$0.666380\pi$
$384$		0			0
$385$	−0.393830	−	1.72548i	−0.00102294	−	0.00448177i
$386$		−	1.48452i		−	0.00384590i
$387$		0			0
$388$	−116.550			−0.300386
$389$	458.980	−	104.759i	1.17990	−	0.269304i	0.412792	−	0.910825i	$-0.364554\pi$
$389$	458.980	−	104.759i	1.17990	−	0.269304i	0.767105	+	0.641522i	$0.221697\pi$
$390$		0			0
$391$	−569.369	+	274.194i	−1.45619	+	0.701263i
$392$	−240.166	+	191.526i	−0.612667	+	0.488586i
$393$		0			0
$394$			309.610i			0.785812i
$395$	65.9340	−	52.5806i	0.166922	−	0.133115i
$396$		0			0
$397$	191.438	−	240.055i	0.482211	−	0.604674i	−0.479903	−	0.877322i	$-0.659328\pi$
$397$	191.438	−	240.055i	0.482211	−	0.604674i	0.962114	+	0.272648i	$0.0878995\pi$
$398$	−196.183	−	94.4769i	−0.492923	−	0.237379i
$399$		0			0
$400$	112.446	+	141.003i	0.281116	+	0.352509i
$401$	84.2379	+	369.070i	0.210070	+	0.920375i	0.964518	+	0.264016i	$0.0850471\pi$
$401$	84.2379	+	369.070i	0.210070	+	0.920375i	−0.754449	+	0.656359i	$0.772096\pi$
$402$		0			0
$403$	62.7116	−	78.6378i	0.155612	−	0.195131i
$404$	59.1041	−	74.1142i	0.146297	−	0.183451i
$405$		0			0
$406$	−3.76589	−	7.81995i	−0.00927559	−	0.0192610i
$407$	58.8935	−	122.294i	0.144702	−	0.300476i
$408$		0			0
$409$	380.868	+	86.9307i	0.931218	+	0.212544i	0.661113	−	0.750286i	$-0.270084\pi$
$409$	380.868	+	86.9307i	0.931218	+	0.212544i	0.270105	+	0.962831i	$0.412942\pi$
$410$	46.9061	+	22.5888i	0.114405	+	0.0550946i
$411$		0			0
$412$	48.8011	−	213.812i	0.118449	−	0.518960i
$413$	19.5855	+	15.6189i	0.0474226	+	0.0378183i
$414$		0			0
$415$	−45.1865	−	93.8308i	−0.108883	−	0.226098i
$416$	−626.139	+	142.912i	−1.50514	+	0.343539i
$417$		0			0
$418$	−28.1918	−	123.516i	−0.0674445	−	0.295494i
$419$	172.739	−	358.695i	0.412264	−	0.856075i	−0.586666	−	0.809829i	$-0.699560\pi$
$419$	172.739	−	358.695i	0.412264	−	0.856075i	0.998930	−	0.0462460i	$-0.0147258\pi$
$420$		0			0
$421$	−24.7654	+	51.4259i	−0.0588252	+	0.122152i	−0.928309	−	0.371810i	$-0.878737\pi$
$421$	−24.7654	+	51.4259i	−0.0588252	+	0.122152i	0.869484	+	0.493962i	$0.164452\pi$
$422$	48.0166	+	60.2110i	0.113784	+	0.142680i
$423$		0			0
$424$		−	399.488i		−	0.942188i
$425$	332.417	+	416.838i	0.782157	+	0.980794i
$426$		0			0
$427$	3.51951	−	15.4200i	0.00824241	−	0.0361124i
$428$	−9.96574	−	43.6628i	−0.0232844	−	0.102016i
$429$		0			0
$430$	−19.4166	−	34.5406i	−0.0451548	−	0.0803270i
$431$	841.359			1.95211			0.976055	−	0.217526i	$-0.0697986\pi$
$431$	841.359			1.95211			0.976055	+	0.217526i	$0.0697986\pi$
$432$		0			0
$433$	−814.672	−	185.944i	−1.88146	−	0.429431i	−0.882310	−	0.470668i	$-0.844013\pi$
$433$	−814.672	−	185.944i	−1.88146	−	0.429431i	−0.999149	+	0.0412373i	$0.986870\pi$
$434$	−1.17068	+	0.563771i	−0.00269743	+	0.00129901i
$435$		0			0
$436$	−327.265			−0.750607
$437$			751.788i			1.72034i
$438$		0			0
$439$	569.311	+	274.166i	1.29684	+	0.624523i	0.949662	−	0.313277i	$-0.101427\pi$
$439$	569.311	+	274.166i	1.29684	+	0.624523i	0.347174	+	0.937801i	$0.387141\pi$
$440$	22.9205	−	28.7413i	0.0520919	−	0.0653212i
$441$		0			0
$442$	−382.620	+	87.3304i	−0.865655	+	0.197580i
$443$	542.027	+	679.680i	1.22354	+	1.53427i	0.762657	+	0.646803i	$0.223895\pi$
$443$	542.027	+	679.680i	1.22354	+	1.53427i	0.460880	+	0.887463i	$0.347534\pi$
$444$		0			0
$445$	−29.4707	+	14.1923i	−0.0662263	+	0.0318929i
$446$	148.039	−	185.635i	0.331926	−	0.416223i
$447$		0			0
$448$	−0.821205	−	0.187435i	−0.00183305	−	0.000418381i
$449$	−206.682	−	429.180i	−0.460316	−	0.955857i	−0.993918	−	0.110121i	$-0.964876\pi$
$449$	−206.682	−	429.180i	−0.460316	−	0.955857i	0.533602	−	0.845736i	$-0.320838\pi$
$450$		0			0
$451$	69.1839	−	303.114i	0.153401	−	0.672094i
$452$	433.395	+	98.9195i	0.958838	+	0.218849i
$453$		0			0
$454$	202.790	−	97.6586i	0.446674	−	0.215107i
$455$	−1.45132	+	6.35865i	−0.00318972	+	0.0139751i
$456$		0			0
$457$	97.8225	+	78.0109i	0.214054	+	0.170702i	0.724647	−	0.689120i	$-0.242003\pi$
$457$	97.8225	+	78.0109i	0.214054	+	0.170702i	−0.510593	+	0.859822i	$0.670574\pi$
$458$	−21.1648	−	43.9492i	−0.0462114	−	0.0959589i
$459$		0			0
$460$	−76.4451	+	60.9630i	−0.166185	+	0.132528i
$461$	−121.760	−	533.467i	−0.264122	−	1.15720i	−0.916732	−	0.399502i	$-0.869183\pi$
$461$	−121.760	−	533.467i	−0.264122	−	1.15720i	0.652610	−	0.757694i	$-0.273674\pi$
$462$		0			0
$463$	606.923	+	484.005i	1.31085	+	1.04537i	0.995338	+	0.0964445i	$0.0307470\pi$
$463$	606.923	+	484.005i	1.31085	+	1.04537i	0.315510	+	0.948922i	$0.397824\pi$
$464$	−108.614	+	225.539i	−0.234081	+	0.486075i
$465$		0			0
$466$	64.6275			0.138686
$467$			331.656i			0.710184i	0.934831	+	0.355092i	$0.115550\pi$
$467$			331.656i			0.710184i	−0.934831	+	0.355092i	$0.884450\pi$
$468$		0			0
$469$	−5.22749	−	10.8550i	−0.0111460	−	0.0231450i
$470$	−2.55495	+	11.1940i	−0.00543607	+	0.0238170i
$471$		0			0
$472$			520.329i			1.10239i
$473$	−175.300	+	158.948i	−0.370614	+	0.336041i
$474$		0			0
$475$	618.354	−	141.135i	1.30180	−	0.297127i
$476$	−21.3970	−	4.88373i	−0.0449517	−	0.0102599i
$477$		0			0
$478$	297.350	−	237.129i	0.622071	−	0.496085i
$479$	164.469			0.343359			0.171679	−	0.985153i	$-0.445081\pi$
$479$	164.469			0.343359			0.171679	+	0.985153i	$0.445081\pi$
$480$		0			0
$481$	−391.077	+	311.873i	−0.813049	+	0.648385i
$482$	−131.759	−	63.4520i	−0.273360	−	0.131643i
$483$		0			0
$484$	265.580	+	127.896i	0.548718	+	0.264249i
$485$	−37.1930	+	8.48906i	−0.0766866	+	0.0175032i
$486$		0			0
$487$	−84.9004	−	371.973i	−0.174333	−	0.763805i	−0.984181	−	0.177165i	$-0.943308\pi$
$487$	−84.9004	−	371.973i	−0.174333	−	0.763805i	0.809848	−	0.586640i	$-0.199550\pi$
$488$	295.990	−	142.541i	0.606537	−	0.292093i
$489$		0			0
$490$	−28.0998	+	35.2361i	−0.0573466	+	0.0719103i
$491$	−17.3795	−	3.96677i	−0.0353962	−	0.00807895i	0.204786	−	0.978807i	$-0.434350\pi$
$491$	−17.3795	−	3.96677i	−0.0353962	−	0.00807895i	−0.240182	+	0.970728i	$0.577207\pi$
$492$		0			0
$493$	−321.086	+	666.743i	−0.651291	+	1.35242i
$494$	−103.891	+	455.175i	−0.210305	+	0.921407i
$495$		0			0
$496$	33.7642	+	16.2600i	0.0680730	+	0.0327822i
$497$	−5.83446	+	2.80973i	−0.0117394	+	0.00565337i
$498$		0			0
$499$	−89.5761	−	71.4346i	−0.179511	−	0.143155i	0.529612	−	0.848240i	$-0.322338\pi$
$499$	−89.5761	−	71.4346i	−0.179511	−	0.143155i	−0.709123	+	0.705085i	$0.750909\pi$
$500$	132.045	+	105.302i	0.264089	+	0.210604i
$501$		0			0
$502$	−3.01259	+	0.687603i	−0.00600117	+	0.00136973i
$503$	−398.644	+	317.908i	−0.792532	+	0.632023i	−0.933738	−	0.357957i	$-0.883473\pi$
$503$	−398.644	+	317.908i	−0.792532	+	0.632023i	0.141206	+	0.989980i	$0.454902\pi$
$504$		0			0
$505$	13.4629	−	27.9560i	0.0266592	−	0.0553585i
$506$	−105.461	−	84.1020i	−0.208420	−	0.166209i
$507$		0			0
$508$	171.066	+	214.510i	0.336744	+	0.422263i
$509$	279.653			0.549417			0.274709	−	0.961528i	$-0.411419\pi$
$509$	279.653			0.549417			0.274709	+	0.961528i	$0.411419\pi$
$510$		0			0
$511$	17.5135	+	21.9612i	0.0342730	+	0.0429769i
$512$	−186.188	−	386.623i	−0.363648	−	0.755122i
$513$		0			0
$514$	−83.5466	−	366.042i	−0.162542	−	0.712143i
$515$		−	71.7854i		−	0.139389i
$516$		0			0
$517$	68.5688			0.132628
$518$	6.29988	−	1.43791i	0.0121619	−	0.00277588i
$519$		0			0
$520$	−122.056	+	58.7789i	−0.234722	+	0.113036i
$521$	−127.595	+	101.754i	−0.244904	+	0.195305i	−0.738247	−	0.674530i	$-0.764346\pi$
$521$	−127.595	+	101.754i	−0.244904	+	0.195305i	0.493343	+	0.869835i	$0.335775\pi$
$522$		0			0
$523$			402.940i			0.770439i	0.922825	+	0.385220i	$0.125874\pi$
$523$			402.940i			0.770439i	−0.922825	+	0.385220i	$0.874126\pi$
$524$	−117.738	+	93.8929i	−0.224691	+	0.179185i
$525$		0			0
$526$	−70.7034	+	88.6592i	−0.134417	+	0.168554i
$527$	99.8145	+	48.0681i	0.189401	+	0.0912109i
$528$		0			0
$529$	169.231	+	212.209i	0.319907	+	0.401151i
$530$	−13.0422	−	57.1416i	−0.0246079	−	0.107814i
$531$		0			0
$532$	−16.2787	+	20.4129i	−0.0305991	+	0.0383701i
$533$	−714.361	+	895.780i	−1.34026	+	1.68064i
$534$		0			0
$535$	−6.36048	−	13.2077i	−0.0118887	−	0.0246872i
$536$	108.580	−	225.468i	0.202574	−	0.420650i
$537$		0			0
$538$	−309.200	−	70.5729i	−0.574721	−	0.131176i
$539$	242.493	+	116.778i	0.449894	+	0.216658i
$540$		0			0
$541$	−36.9797	+	162.019i	−0.0683544	+	0.299480i	−0.997537	−	0.0701405i	$-0.977655\pi$
$541$	−36.9797	+	162.019i	−0.0683544	+	0.299480i	0.929183	+	0.369621i	$0.120512\pi$
$542$	14.7961	+	11.7995i	0.0272990	+	0.0217702i
$543$		0			0
$544$	−306.929	−	637.344i	−0.564207	−	1.17159i
$545$	−104.436	+	23.8368i	−0.191625	+	0.0437372i
$546$		0			0
$547$	191.646	+	839.658i	0.350359	+	1.53502i	0.776353	+	0.630298i	$0.217067\pi$
$547$	191.646	+	839.658i	0.350359	+	1.53502i	−0.425994	+	0.904726i	$0.640076\pi$
$548$	206.998	−	429.837i	0.377734	−	0.784373i
$549$		0			0
$550$	−49.3765	+	102.531i	−0.0897754	+	0.186420i
$551$	548.895	+	688.292i	0.996179	+	1.24917i
$552$		0			0
$553$		−	23.9760i		−	0.0433562i
$554$	−136.145	−	170.720i	−0.245748	−	0.308159i
$555$		0			0
$556$	19.8889	−	87.1388i	0.0357713	−	0.156725i
$557$	−80.7033	−	353.584i	−0.144889	−	0.634801i	−0.994259	−	0.107002i	$-0.965875\pi$
$557$	−80.7033	−	353.584i	−0.144889	−	0.634801i	0.849370	−	0.527799i	$-0.176982\pi$
$558$		0			0
$559$	836.177	−	247.446i	1.49584	−	0.442658i
$560$	−2.43008			−0.00433943
$561$		0			0
$562$	−179.108	−	40.8801i	−0.318697	−	0.0727405i
$563$	296.194	−	142.640i	0.526100	−	0.253356i	−0.151929	−	0.988391i	$-0.548549\pi$
$563$	296.194	−	142.640i	0.526100	−	0.253356i	0.678029	+	0.735035i	$0.262834\pi$
$564$		0			0
$565$	145.509			0.257537
$566$		−	55.5402i		−	0.0981275i
$567$		0			0
$568$	−121.187	−	58.3606i	−0.213357	−	0.102748i
$569$	−79.5676	+	99.7746i	−0.139838	+	0.175351i	−0.846819	−	0.531882i	$-0.821485\pi$
$569$	−79.5676	+	99.7746i	−0.139838	+	0.175351i	0.706981	+	0.707232i	$0.250057\pi$
$570$		0			0
$571$	834.419	−	190.451i	1.46133	−	0.333539i	0.583344	−	0.812225i	$-0.301744\pi$
$571$	834.419	−	190.451i	1.46133	−	0.333539i	0.877986	+	0.478686i	$0.158887\pi$
$572$	226.095	+	283.515i	0.395271	+	0.495655i
$573$		0			0
$574$	13.3355	−	6.42204i	0.0232326	−	0.0111882i
$575$	421.036	−	527.963i	0.732237	−	0.918196i
$576$		0			0
$577$	378.607	+	86.4147i	0.656165	+	0.149765i	0.537625	−	0.843184i	$-0.319321\pi$
$577$	378.607	+	86.4147i	0.656165	+	0.149765i	0.118540	+	0.992949i	$0.462179\pi$
$578$	−78.9186	−	163.876i	−0.136537	−	0.283523i
$579$		0			0
$580$	−25.4784	+	111.628i	−0.0439282	+	0.192462i
$581$	−28.8661	−	6.58850i	−0.0496835	−	0.0113399i
$582$		0			0
$583$	−315.359	+	151.869i	−0.540924	+	0.260495i
$584$	−129.828	+	568.815i	−0.222309	+	0.973999i
$585$		0			0
$586$	−141.862	−	113.131i	−0.242085	−	0.193056i
$587$	−444.020	−	922.016i	−0.756422	−	1.57073i	−0.819742	−	0.572733i	$-0.805883\pi$
$587$	−444.020	−	922.016i	−0.756422	−	1.57073i	0.0633202	−	0.997993i	$-0.479831\pi$
$588$		0			0
$589$	103.041	−	82.1721i	0.174942	−	0.139511i
$590$	16.9873	+	74.4264i	0.0287921	+	0.126146i
$591$		0			0
$592$	−145.710	−	116.200i	−0.246132	−	0.196284i
$593$	4.55877	−	9.46638i	0.00768764	−	0.0159635i	−0.897090	−	0.441848i	$-0.854323\pi$
$593$	4.55877	−	9.46638i	0.00768764	−	0.0159635i	0.904777	+	0.425885i	$0.140037\pi$
$594$		0			0
$595$	−7.18386			−0.0120737
$596$		−	328.716i		−	0.551536i
$597$		0			0
$598$	215.677	+	447.859i	0.360665	+	0.748928i
$599$	118.588	−	519.569i	0.197977	−	0.867394i	−0.774162	−	0.632988i	$-0.781828\pi$
$599$	118.588	−	519.569i	0.197977	−	0.867394i	0.972139	−	0.234406i	$-0.0753146\pi$
$600$		0			0
$601$		−	56.8479i		−	0.0945888i	−0.998881	−	0.0472944i	$-0.984940\pi$
$601$		−	56.8479i		−	0.0945888i	0.998881	−	0.0472944i	$-0.0150599\pi$
$602$	−11.1193	−	1.80681i	−0.0184707	−	0.00300135i
$603$		0			0
$604$	−370.809	+	84.6346i	−0.613922	+	0.140124i
$605$	94.0665	+	21.4701i	0.155482	+	0.0354877i
$606$		0			0
$607$	−150.156	+	119.746i	−0.247374	+	0.197274i	−0.739325	−	0.673349i	$-0.764855\pi$
$607$	−150.156	+	119.746i	−0.247374	+	0.197274i	0.491951	+	0.870623i	$0.336284\pi$
$608$	−841.541			−1.38411
$609$		0			0
$610$	37.6840	−	30.0520i	0.0617770	−	0.0492655i
$611$	−227.662	−	109.636i	−0.372606	−	0.179437i
$612$		0			0
$613$	166.780	+	80.3172i	0.272072	+	0.131023i	0.564946	−	0.825128i	$-0.308897\pi$
$613$	166.780	+	80.3172i	0.272072	+	0.131023i	−0.292873	+	0.956151i	$0.594611\pi$
$614$	−95.6292	+	21.8267i	−0.155748	+	0.0355484i
$615$		0			0
$616$	−2.32565	−	10.1894i	−0.00377541	−	0.0165412i
$617$	−754.934	+	363.557i	−1.22356	+	0.589234i	−0.930300	−	0.366800i	$-0.880453\pi$
$617$	−754.934	+	363.557i	−1.22356	+	0.589234i	−0.293257	+	0.956034i	$0.594739\pi$
$618$		0			0
$619$	−173.375	+	217.405i	−0.280088	+	0.351220i	−0.901898	−	0.431949i	$-0.857826\pi$
$619$	−173.375	+	217.405i	−0.280088	+	0.351220i	0.621810	+	0.783168i	$0.286398\pi$
$620$	16.7112	+	3.81423i	0.0269536	+	0.00615199i
$621$		0			0
$622$	16.5989	−	34.4679i	0.0266863	−	0.0554146i
$623$	−2.06934	+	9.06637i	−0.00332157	+	0.0145528i
$624$		0			0
$625$	−487.818	−	234.921i	−0.780508	−	0.375873i
$626$	−57.8993	+	27.8828i	−0.0924909	+	0.0445413i
$627$		0			0
$628$	−538.384	−	429.347i	−0.857299	−	0.683673i
$629$	−430.752	−	343.513i	−0.684820	−	0.546126i
$630$		0			0
$631$	150.928	−	34.4484i	0.239189	−	0.0545933i	−0.101246	−	0.994861i	$-0.532283\pi$
$631$	150.928	−	34.4484i	0.239189	−	0.0545933i	0.340435	+	0.940268i	$0.389426\pi$
$632$	389.355	−	310.500i	0.616068	−	0.491297i
$633$		0			0
$634$	122.550	−	254.477i	0.193296	−	0.401383i
$635$	70.2141	+	55.9939i	0.110573	+	0.0881794i
$636$		0			0
$637$	−618.405	−	775.455i	−0.970808	−	1.21735i
$638$	−157.958			−0.247583
$639$		0			0
$640$	−85.6057	−	107.346i	−0.133759	−	0.167728i
$641$	−317.481	−	659.257i	−0.495291	−	1.02848i	−0.987443	−	0.157973i	$-0.949504\pi$
$641$	−317.481	−	659.257i	−0.495291	−	1.02848i	0.492153	−	0.870509i	$-0.336210\pi$
$642$		0			0
$643$	−271.265	−	1188.49i	−0.421873	−	1.84835i	−0.521399	−	0.853313i	$-0.674590\pi$
$643$	−271.265	−	1188.49i	−0.421873	−	1.84835i	0.0995261	−	0.995035i	$-0.468267\pi$
$644$			27.7982i			0.0431649i
$645$		0			0
$646$	−514.246			−0.796047
$647$	202.845	−	46.2981i	0.313517	−	0.0715582i	−0.0628673	−	0.998022i	$-0.520024\pi$
$647$	202.845	−	46.2981i	0.313517	−	0.0715582i	0.376384	+	0.926464i	$0.377167\pi$
$648$		0			0
$649$	410.752	−	197.808i	0.632899	−	0.304788i
$650$	327.879	−	261.475i	0.504430	−	0.402269i
$651$		0			0
$652$			463.283i			0.710556i
$653$	−594.755	+	474.302i	−0.910805	+	0.726342i	−0.962202	−	0.272336i	$-0.912204\pi$
$653$	−594.755	+	474.302i	−0.910805	+	0.726342i	0.0513977	+	0.998678i	$0.483632\pi$
$654$		0			0
$655$	−30.7334	+	38.5384i	−0.0469212	+	0.0588373i
$656$	−384.615	−	185.221i	−0.586303	−	0.282349i
$657$		0			0
$658$	2.03527	+	2.55214i	0.00309311	+	0.00387864i
$659$	−181.565	−	795.490i	−0.275516	−	1.20712i	−0.903396	−	0.428806i	$-0.858934\pi$
$659$	−181.565	−	795.490i	−0.275516	−	1.20712i	0.627880	−	0.778310i	$-0.283923\pi$
$660$		0			0
$661$	67.1647	−	84.2218i	0.101611	−	0.127416i	−0.728426	−	0.685124i	$-0.759748\pi$
$661$	67.1647	−	84.2218i	0.101611	−	0.127416i	0.830037	+	0.557709i	$0.188319\pi$
$662$	135.733	−	170.204i	0.205035	−	0.257105i
$663$		0			0
$664$	−266.836	−	554.091i	−0.401862	−	0.834475i
$665$	−3.70802	+	7.69979i	−0.00557597	+	0.0115786i
$666$		0			0
$667$	913.813	+	208.572i	1.37003	+	0.312702i
$668$	−241.089	−	116.102i	−0.360912	−	0.173806i
$669$		0			0
$670$	8.17002	−	35.7952i	0.0121941	−	0.0534257i
$671$	−225.046	−	179.468i	−0.335389	−	0.267464i
$672$		0			0
$673$	−16.9997	−	35.3002i	−0.0252596	−	0.0524520i	0.887957	−	0.459926i	$-0.152124\pi$
$673$	−16.9997	−	35.3002i	−0.0252596	−	0.0524520i	−0.913217	+	0.407474i	$0.866410\pi$
$674$	433.847	−	99.0227i	0.643690	−	0.146918i
$675$		0			0
$676$	−175.167	−	767.458i	−0.259123	−	1.13529i
$677$	160.174	−	332.604i	0.236594	−	0.491292i	−0.748538	−	0.663092i	$-0.769244\pi$
$677$	160.174	−	332.604i	0.236594	−	0.491292i	0.985132	+	0.171800i	$0.0549583\pi$
$678$		0			0
$679$	−4.70589	+	9.77189i	−0.00693062	+	0.0143916i
$680$	−93.0342	−	116.661i	−0.136815	−	0.171561i
$681$		0			0
$682$			23.6470i			0.0346731i
$683$	217.384	+	272.590i	0.318278	+	0.399108i	0.915074	−	0.403285i	$-0.132132\pi$
$683$	217.384	+	272.590i	0.318278	+	0.399108i	−0.596797	+	0.802392i	$0.703560\pi$
$684$		0			0
$685$	34.7490	−	152.245i	0.0507284	−	0.222256i
$686$	5.70770	+	25.0071i	0.00832026	+	0.0364534i
$687$		0			0
$688$	159.210	+	283.222i	0.231409	+	0.411660i
$689$	1289.88			1.87210
$690$		0			0
$691$	664.988	+	151.779i	0.962357	+	0.219652i	0.674708	−	0.738085i	$-0.264269\pi$
$691$	664.988	+	151.779i	0.962357	+	0.219652i	0.287648	+	0.957736i	$0.407127\pi$
$692$	128.785	−	62.0198i	0.186106	−	0.0896240i
$693$		0			0
$694$	44.7958			0.0645473
$695$		−	29.2561i		−	0.0420951i
$696$		0			0
$697$	−1137.01	−	547.554i	−1.63129	−	0.785587i
$698$	−327.343	+	410.475i	−0.468973	+	0.588073i
$699$		0			0
$700$	22.8644	−	5.21864i	0.0326634	−	0.00745520i
$701$	−141.292	−	177.175i	−0.201558	−	0.252746i	0.670772	−	0.741664i	$-0.265963\pi$
$701$	−141.292	−	177.175i	−0.201558	−	0.252746i	−0.872330	+	0.488918i	$0.837392\pi$
$702$		0			0
$703$	−590.521	+	284.380i	−0.840001	+	0.404523i
$704$	−9.55775	+	11.9850i	−0.0135763	+	0.0170242i
$705$		0			0
$706$	−264.772	−	60.4325i	−0.375031	−	0.0855984i
$707$	−3.82754	−	7.94796i	−0.00541377	−	0.0112418i
$708$		0			0
$709$	−200.265	+	877.417i	−0.282461	+	1.23754i	0.612167	+	0.790729i	$0.290298\pi$
$709$	−200.265	+	877.417i	−0.282461	+	1.23754i	−0.894627	+	0.446813i	$0.852559\pi$
$710$	−19.2396	−	4.39131i	−0.0270980	−	0.00618494i
$711$		0			0
$712$	−174.031	+	83.8089i	−0.244425	+	0.117709i
$713$	31.2242	−	136.802i	0.0437927	−	0.191868i
$714$		0			0
$715$	92.8010	+	74.0063i	0.129792	+	0.103505i
$716$	212.554	+	441.372i	0.296863	+	0.616442i
$717$		0			0
$718$	208.983	−	166.659i	0.291063	−	0.232115i
$719$	22.0183	+	96.4685i	0.0306235	+	0.134170i	0.987929	−	0.154908i	$-0.0495082\pi$
$719$	22.0183	+	96.4685i	0.0306235	+	0.134170i	−0.957305	+	0.289079i	$0.906651\pi$
$720$		0			0
$721$	−15.9562	−	12.7246i	−0.0221307	−	0.0176486i
$722$	−129.730	+	269.386i	−0.179681	+	0.373111i
$723$		0			0
$724$	1010.19			1.39529
$725$		−	790.778i		−	1.09073i
$726$		0			0
$727$	−363.195	−	754.182i	−0.499580	−	1.03739i	−0.986473	−	0.163927i	$-0.947584\pi$
$727$	−363.195	−	754.182i	−0.499580	−	1.03739i	0.486892	−	0.873462i	$-0.338130\pi$
$728$	−8.57036	+	37.5492i	−0.0117725	+	0.0515786i
$729$		0			0
$730$			85.6003i			0.117261i
$731$	470.660	+	837.268i	0.643857	+	1.14537i
$732$		0			0
$733$	−859.811	+	196.246i	−1.17300	+	0.267730i	−0.764253	−	0.644916i	$-0.776892\pi$
$733$	−859.811	+	196.246i	−1.17300	+	0.267730i	−0.408750	+	0.912646i	$0.634035\pi$
$734$	83.2845	+	19.0091i	0.113467	+	0.0258980i
$735$		0			0
$736$	−700.509	+	558.637i	−0.951778	+	0.759018i
$737$	−219.264			−0.297509
$738$		0			0
$739$	17.4864	−	13.9449i	0.0236622	−	0.0188700i	−0.611587	−	0.791177i	$-0.709469\pi$
$739$	17.4864	−	13.9449i	0.0236622	−	0.0188700i	0.635250	+	0.772307i	$0.280897\pi$
$740$	−76.8026	−	36.9862i	−0.103787	−	0.0499814i
$741$		0			0
$742$	−15.0131	−	7.22992i	−0.0202333	−	0.00974383i
$743$	−193.249	+	44.1079i	−0.260093	+	0.0593645i	−0.350579	−	0.936533i	$-0.614015\pi$
$743$	−193.249	+	44.1079i	−0.260093	+	0.0593645i	0.0904859	+	0.995898i	$0.471158\pi$
$744$		0			0
$745$	−23.9424	−	104.899i	−0.0321375	−	0.140804i
$746$	156.782	−	75.5021i	0.210163	−	0.101209i
$747$		0			0
$748$	−249.033	+	312.277i	−0.332932	+	0.417483i
$749$	−4.06321	−	0.927400i	−0.00542484	−	0.00123818i
$750$		0			0
$751$	462.332	−	960.042i	0.615622	−	1.27835i	−0.327169	−	0.944966i	$-0.606095\pi$
$751$	462.332	−	960.042i	0.615622	−	1.27835i	0.942791	−	0.333386i	$-0.108191\pi$
$752$	20.9498	−	91.7871i	0.0278588	−	0.122057i
$753$		0			0
$754$	524.451	+	252.562i	0.695559	+	0.334964i
$755$	−112.167	+	54.0167i	−0.148565	+	0.0715453i
$756$		0			0
$757$	−509.378	−	406.215i	−0.672890	−	0.536612i	0.226362	−	0.974043i	$-0.427317\pi$
$757$	−509.378	−	406.215i	−0.672890	−	0.536612i	−0.899252	+	0.437432i	$0.855888\pi$
$758$	−125.076	−	99.7446i	−0.165008	−	0.131589i
$759$		0			0
$760$	−173.060	+	39.4999i	−0.227711	+	0.0519735i
$761$	400.049	−	319.028i	0.525688	−	0.419222i	−0.324355	−	0.945935i	$-0.605147\pi$
$761$	400.049	−	319.028i	0.525688	−	0.419222i	0.850043	+	0.526713i	$0.176576\pi$
$762$		0			0
$763$	−13.2139	+	27.4389i	−0.0173183	+	0.0359618i
$764$	292.159	+	232.989i	0.382407	+	0.304959i
$765$		0			0
$766$	233.399	+	292.674i	0.304699	+	0.382080i
$767$	−1680.06			−2.19042
$768$		0			0
$769$	−211.105	−	264.718i	−0.274519	−	0.344236i	0.625391	−	0.780312i	$-0.284940\pi$
$769$	−211.105	−	264.718i	−0.274519	−	0.344236i	−0.899910	+	0.436075i	$0.856368\pi$
$770$	−0.665310	−	1.38153i	−0.000864039	−	0.00179419i
$771$		0			0
$772$	1.23892	+	5.42807i	0.00160482	+	0.00703118i
$773$		−	513.752i		−	0.664621i	−0.943170	−	0.332311i	$-0.892172\pi$
$773$		−	513.752i		−	0.664621i	0.943170	−	0.332311i	$-0.107828\pi$
$774$		0			0
$775$	−118.383			−0.152752
$776$	−219.633	+	50.1297i	−0.283032	+	0.0646002i
$777$		0			0
$778$	367.488	−	176.973i	0.472350	−	0.227472i
$779$	−1173.76	+	936.040i	−1.50675	+	1.20159i
$780$		0			0
$781$			117.852i			0.150899i
$782$	−428.065	+	341.370i	−0.547398	+	0.436535i
$783$		0			0
$784$	230.410	−	288.925i	0.293890	−	0.368526i
$785$	−203.080	−	97.7980i	−0.258700	−	0.124583i
$786$		0			0
$787$	−69.4862	−	87.1329i	−0.0882925	−	0.110715i	0.735723	−	0.677283i	$-0.236843\pi$
$787$	−69.4862	−	87.1329i	−0.0882925	−	0.110715i	−0.824015	+	0.566567i	$0.808271\pi$
$788$	−258.388	−	1132.07i	−0.327904	−	1.43664i
$789$		0			0
$790$	45.5552	−	57.1244i	0.0576648	−	0.0723094i
$791$	25.7928	−	32.3431i	0.0326078	−	0.0408889i
$792$		0			0
$793$	460.242	+	955.702i	0.580381	+	1.20517i
$794$	115.421	−	239.674i	0.145366	−	0.301856i
$795$		0			0
$796$	796.181	+	181.723i	1.00023	+	0.228295i
$797$	899.213	+	433.038i	1.12825	+	0.543335i	0.902431	−	0.430835i	$-0.141781\pi$
$797$	899.213	+	433.038i	1.12825	+	0.543335i	0.225816	+	0.974170i	$0.427495\pi$
$798$		0			0
$799$	61.9323	−	271.343i	0.0775123	−	0.339603i
$800$	590.994	+	471.302i	0.738743	+	0.589128i
$801$		0			0
$802$	142.306	+	295.501i	0.177439	+	0.368455i
$803$	498.382	−	113.753i	0.620651	−	0.141659i
$804$		0			0
$805$	2.02472	+	8.87088i	0.00251518	+	0.0110197i
$806$	37.8098	−	78.5128i	0.0469104	−	0.0974105i
$807$		0			0
$808$	79.5014	−	165.086i	0.0983929	−	0.204315i
$809$	−252.720	−	316.900i	−0.312385	−	0.391719i	0.600709	−	0.799468i	$-0.294885\pi$
$809$	−252.720	−	316.900i	−0.312385	−	0.391719i	−0.913094	+	0.407749i	$0.866314\pi$
$810$		0			0
$811$			1126.53i			1.38907i	0.719459	+	0.694534i	$0.244390\pi$
$811$			1126.53i			1.38907i	−0.719459	+	0.694534i	$0.755610\pi$
$812$	20.2960	+	25.4504i	0.0249951	+	0.0313428i
$813$		0			0
$814$	26.1684	−	114.651i	0.0321479	−	0.140849i
$815$	33.7438	+	147.841i	0.0414035	+	0.181400i
$816$		0			0
$817$	1140.34	−	72.2966i	1.39576	−	0.0884904i
$818$	338.466			0.413772
$819$		0			0
$820$	−190.361	−	43.4487i	−0.232148	−	0.0529863i
$821$	185.139	−	89.1581i	0.225504	−	0.108597i	−0.317721	−	0.948184i	$-0.602917\pi$
$821$	185.139	−	89.1581i	0.225504	−	0.108597i	0.543225	+	0.839587i	$0.317203\pi$
$822$		0			0
$823$	−806.160			−0.979538			−0.489769	−	0.871852i	$-0.662919\pi$
$823$	−806.160			−0.979538			−0.489769	+	0.871852i	$0.662919\pi$
$824$		−	423.909i		−	0.514452i
$825$		0			0
$826$	19.5544	+	9.41690i	0.0236736	+	0.0114006i
$827$	−405.969	+	509.069i	−0.490893	+	0.615561i	−0.964148	−	0.265365i	$-0.914508\pi$
$827$	−405.969	+	509.069i	−0.490893	+	0.615561i	0.473255	+	0.880926i	$0.343079\pi$
$828$		0			0
$829$	−616.946	+	140.814i	−0.744205	+	0.169860i	−0.577778	−	0.816194i	$-0.696080\pi$
$829$	−616.946	+	140.814i	−0.744205	+	0.169860i	−0.166427	+	0.986054i	$0.553223\pi$
$830$	−56.2571	−	70.5441i	−0.0677796	−	0.0849930i
$831$		0			0
$832$	50.8968	−	24.5106i	0.0611740	−	0.0294598i
$833$	681.143	−	854.126i	0.817698	−	1.02536i
$834$		0			0
$835$	−85.3922	−	19.4902i	−0.102266	−	0.0233416i
$836$	206.164	+	428.103i	0.246607	+	0.512085i
$837$		0			0
$838$	76.7537	−	336.280i	0.0915915	−	0.401289i
$839$	1442.32	+	329.199i	1.71909	+	0.392371i	0.964554	−	0.263887i	$-0.0850045\pi$
$839$	1442.32	+	329.199i	1.71909	+	0.392371i	0.754537	+	0.656258i	$0.227862\pi$
$840$		0			0
$841$	231.200	−	111.340i	0.274911	−	0.132390i
$842$	−11.0041	+	48.2122i	−0.0130690	+	0.0572592i
$843$		0			0
$844$	−225.820	−	180.086i	−0.267559	−	0.213372i
$845$	−111.798	−	232.150i	−0.132305	−	0.274734i
$846$		0			0
$847$	21.4465	−	17.1030i	0.0253205	−	0.0201924i
$848$	106.942	+	468.543i	0.126111	+	0.552528i
$849$		0			0
$850$	361.143	+	288.002i	0.424874	+	0.338826i
$851$	−302.778	+	628.724i	−0.355790	+	0.738806i
$852$		0			0
$853$	−1125.72			−1.31972			−0.659861	−	0.751388i	$-0.729385\pi$
$853$	−1125.72			−1.31972			−0.659861	+	0.751388i	$0.729385\pi$
$854$		−	13.7033i		−	0.0160460i
$855$		0			0
$856$	−37.5600	−	77.9941i	−0.0438785	−	0.0911146i
$857$	−234.106	+	1025.69i	−0.273170	+	1.19683i	0.633078	+	0.774088i	$0.281791\pi$
$857$	−234.106	+	1025.69i	−0.273170	+	1.19683i	−0.906248	+	0.422747i	$0.861066\pi$
$858$		0			0
$859$			459.916i			0.535409i	0.963501	+	0.267705i	$0.0862651\pi$
$859$			459.916i			0.535409i	−0.963501	+	0.267705i	$0.913735\pi$
$860$	99.8219	+	110.092i	0.116072	+	0.128014i
$861$		0			0
$862$	710.667	−	162.205i	0.824440	−	0.188173i
$863$	−1115.66	−	254.643i	−1.29277	−	0.295067i	−0.479804	−	0.877375i	$-0.659292\pi$
$863$	−1115.66	−	254.643i	−1.29277	−	0.295067i	−0.812968	+	0.582309i	$0.802150\pi$
$864$		0			0
$865$	36.5803	−	29.1718i	0.0422894	−	0.0337247i
$866$	−723.974			−0.835997
$867$		0			0
$868$	3.81004	−	3.03841i	0.00438945	−	0.00350047i
$869$	−393.128	−	189.320i	−0.452391	−	0.217860i
$870$		0			0
$871$	728.000	+	350.586i	0.835821	+	0.402510i
$872$	−616.715	+	140.761i	−0.707242	+	0.161423i
$873$		0			0
$874$	144.937	+	635.010i	0.165832	+	0.726556i
$875$	14.1604	−	6.81928i	0.0161833	−	0.00779347i
$876$		0			0
$877$	222.830	−	279.420i	0.254082	−	0.318609i	−0.638389	−	0.769714i	$-0.720399\pi$
$877$	222.830	−	279.420i	0.254082	−	0.318609i	0.892471	+	0.451105i	$0.148970\pi$
$878$	533.734	+	121.821i	0.607897	+	0.138749i
$879$		0			0
$880$	−19.1885	+	39.8453i	−0.0218051	+	0.0452788i
$881$	−194.664	+	852.879i	−0.220958	+	0.968080i	0.735801	+	0.677198i	$0.236806\pi$
$881$	−194.664	+	852.879i	−0.220958	+	0.968080i	−0.956759	+	0.290882i	$0.906051\pi$
$882$		0			0
$883$	−620.045	−	298.598i	−0.702203	−	0.338163i	0.0484814	−	0.998824i	$-0.484562\pi$
$883$	−620.045	−	298.598i	−0.702203	−	0.338163i	−0.750684	+	0.660661i	$0.770276\pi$
$884$	1326.15	−	638.639i	1.50017	−	0.722442i
$885$		0			0
$886$	588.866	+	469.605i	0.664635	+	0.530029i
$887$	−186.359	−	148.616i	−0.210100	−	0.167549i	0.512786	−	0.858516i	$-0.328613\pi$
$887$	−186.359	−	148.616i	−0.210100	−	0.167549i	−0.722886	+	0.690967i	$0.757185\pi$
$888$		0			0
$889$	24.8922	−	5.68149i	0.0280003	−	0.00639088i
$890$	−22.1568	+	17.6694i	−0.0248952	+	0.0198533i
$891$		0			0
$892$	−386.374	+	802.314i	−0.433155	+	0.899455i
$893$	−258.863	−	206.437i	−0.289881	−	0.231172i
$894$		0			0
$895$	99.9774	+	125.368i	0.111707	+	0.140076i
$896$	−39.0349			−0.0435658
$897$		0			0
$898$	−257.319	−	322.667i	−0.286546	−	0.359318i
$899$	−71.2948	−	148.045i	−0.0793046	−	0.164678i
$900$		0			0
$901$	316.144	+	1385.12i	0.350882	+	1.53731i
$902$		−	269.368i		−	0.298635i
$903$		0			0
$904$	859.260			0.950509
$905$	322.369	−	73.5786i	0.356209	−	0.0813023i
$906$		0			0
$907$	1085.69	−	522.841i	1.19701	−	0.576451i	0.274191	−	0.961675i	$-0.411590\pi$
$907$	1085.69	−	522.841i	1.19701	−	0.576451i	0.922823	+	0.385224i	$0.125876\pi$
$908$	−659.990	+	526.324i	−0.726861	+	0.579652i
$909$		0			0
$910$			5.65073i			0.00620960i
$911$	1242.13	−	990.563i	1.36348	−	1.08734i	0.376509	−	0.926413i	$-0.377124\pi$
$911$	1242.13	−	990.563i	1.36348	−	1.08734i	0.986967	−	0.160923i	$-0.0514470\pi$
$912$		0			0
$913$	−335.964	+	421.285i	−0.367978	+	0.461429i
$914$	97.6670	+	47.0340i	0.106857	+	0.0514595i
$915$		0			0
$916$	114.066	+	143.035i	0.124527	+	0.156151i
$917$	3.11840	+	13.6626i	0.00340065	+	0.0148992i
$918$		0			0
$919$	234.326	−	293.835i	0.254979	−	0.319734i	−0.637823	−	0.770183i	$-0.720165\pi$
$919$	234.326	−	293.835i	0.254979	−	0.319734i	0.892802	+	0.450449i	$0.148736\pi$
$920$	−117.836	+	147.762i	−0.128083	+	0.160611i
$921$		0			0
$922$	−205.694	−	427.127i	−0.223095	−	0.463262i
$923$	188.437	−	391.293i	0.204157	−	0.423936i
$924$		0			0
$925$	573.974	+	131.006i	0.620513	+	0.141628i
$926$	605.958	+	291.814i	0.654382	+	0.315134i
$927$		0			0
$928$	−233.472	+	1022.91i	−0.251587	+	1.10227i
$929$	420.046	+	334.975i	0.452148	+	0.360576i	0.822929	−	0.568144i	$-0.192338\pi$
$929$	420.046	+	334.975i	0.452148	+	0.360576i	−0.370781	+	0.928720i	$0.620910\pi$
$930$		0			0
$931$	−563.889	−	1170.93i	−0.605681	−	1.25771i
$932$	−236.307	+	53.9356i	−0.253548	+	0.0578708i
$933$		0			0
$934$	63.9398	+	280.139i	0.0684580	+	0.299934i
$935$	−56.7255	+	117.792i	−0.0606690	+	0.125980i
$936$		0			0
$937$	378.289	−	785.526i	0.403724	−	0.838342i	−0.595660	−	0.803237i	$-0.703109\pi$
$937$	378.289	−	785.526i	0.403724	−	0.838342i	0.999384	−	0.0351047i	$-0.0111765\pi$
$938$	−6.50821	−	8.16104i	−0.00693839	−	0.00870047i
$939$		0			0
$940$		−	43.0625i		−	0.0458111i
$941$	276.222	+	346.372i	0.293541	+	0.368089i	0.906631	−	0.421924i	$-0.138645\pi$
$941$	276.222	+	346.372i	0.293541	+	0.368089i	−0.613090	+	0.790013i	$0.710074\pi$
$942$		0			0
$943$	−355.681	+	1558.34i	−0.377181	+	1.65254i
$944$	−139.291	−	610.273i	−0.147554	−	0.646476i
$945$		0			0
$946$	−117.427	+	168.054i	−0.124130	+	0.177646i
$947$	−765.005			−0.807819			−0.403910	−	0.914799i	$-0.632349\pi$
$947$	−765.005			−0.807819			−0.403910	+	0.914799i	$0.632349\pi$
$948$		0			0
$949$	−1836.61	−	419.194i	−1.93531	−	0.441722i
$950$	495.093	−	238.424i	0.521151	−	0.250973i
$951$		0			0
$952$	−42.4222			−0.0445612
$953$		−	38.7778i		−	0.0406903i	−0.999793	−	0.0203451i	$-0.993523\pi$
$953$		−	38.7778i		−	0.0406903i	0.999793	−	0.0203451i	$-0.00647650\pi$
$954$		0			0
$955$	110.203	+	53.0709i	0.115396	+	0.0555716i
$956$	−889.346	+	1115.20i	−0.930279	+	1.16653i
$957$		0			0
$958$	138.921	−	31.7078i	0.145012	−	0.0330980i
$959$	−27.6809	−	34.7108i	−0.0288644	−	0.0361948i
$960$		0			0
$961$	843.668	−	406.289i	0.877906	−	0.422777i
$962$	−270.203	+	338.824i	−0.280876	+	0.352208i
$963$		0			0
$964$	534.726	+	122.048i	0.554695	+	0.126606i
$965$	0.790722	+	1.64195i	0.000819401	+	0.00170150i
$966$		0			0
$967$	−126.429	+	553.921i	−0.130743	+	0.572824i	0.866536	+	0.499114i	$0.166341\pi$
$967$	−126.429	+	553.921i	−0.130743	+	0.572824i	−0.997280	+	0.0737103i	$0.976516\pi$
$968$	555.483	+	126.785i	0.573846	+	0.130977i
$969$		0			0
$970$	−29.7790	+	14.3408i	−0.0307000	+	0.0147844i
$971$	−148.447	+	650.391i	−0.152881	+	0.669815i	0.839158	+	0.543887i	$0.183048\pi$
$971$	−148.447	+	650.391i	−0.152881	+	0.669815i	−0.992039	+	0.125928i	$0.959809\pi$
$972$		0			0
$973$	−6.50294	−	5.18592i	−0.00668340	−	0.00532983i
$974$	−143.425	−	297.825i	−0.147253	−	0.305775i
$975$		0			0
$976$	−308.997	+	246.417i	−0.316595	+	0.252476i
$977$	−39.7516	−	174.163i	−0.0406874	−	0.178263i	0.950501	−	0.310721i	$-0.100570\pi$
$977$	−39.7516	−	174.163i	−0.0406874	−	0.178263i	−0.991189	+	0.132458i	$0.957713\pi$
$978$		0			0
$979$	132.319	+	105.521i	0.135157	+	0.107784i
$980$	73.3389	−	152.290i	0.0748356	−	0.155398i
$981$		0			0
$982$	−15.4447			−0.0157278
$983$		−	448.952i		−	0.456716i	−0.973577	−	0.228358i	$-0.926664\pi$
$983$		−	448.952i		−	0.456716i	0.973577	−	0.228358i	$-0.0733356\pi$
$984$		0			0
$985$	−164.912	−	342.444i	−0.167424	−	0.347658i
$986$	−142.670	+	625.077i	−0.144695	+	0.633952i
$987$		0			0
$988$		−	1751.03i		−	1.77230i
$989$	901.236	−	817.165i	0.911260	−	0.826254i
$990$		0			0
$991$	−23.2361	+	5.30348i	−0.0234471	+	0.00535165i	−0.234228	−	0.972182i	$-0.575256\pi$
$991$	−23.2361	+	5.30348i	−0.0234471	+	0.00535165i	0.210781	+	0.977533i	$0.432399\pi$
$992$	153.134	+	34.9519i	0.154369	+	0.0352338i
$993$		0			0
$994$	−4.38648	+	3.49810i	−0.00441296	+	0.00351922i
$995$	267.311			0.268654
$996$		0			0
$997$	159.486	−	127.186i	0.159966	−	0.127569i	−0.540235	−	0.841514i	$-0.681665\pi$
$997$	159.486	−	127.186i	0.159966	−	0.127569i	0.700202	+	0.713945i	$0.253093\pi$
$998$	−89.4337	−	43.0690i	−0.0896130	−	0.0431553i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.3.w.b.199.5		42
3.2	odd	2		43.3.f.a.27.3	yes	42
43.8	odd	14	inner	387.3.w.b.352.5		42
129.8	even	14		43.3.f.a.8.3	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.3.f.a.8.3	✓	42	129.8	even	14
43.3.f.a.27.3	yes	42	3.2	odd	2
387.3.w.b.199.5		42	1.1	even	1	trivial
387.3.w.b.352.5		42	43.8	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	387.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.844666 - 0.192789i) q^{2} +(-2.92758 + 1.40985i) q^{4} +(-0.831553 + 0.663142i) q^{5} +0.302383i q^{7} +(-4.91050 + 3.91600i) q^{8} +O(q^{10})\)	\(q+(0.844666 - 0.192789i) q^{2} +(-2.92758 + 1.40985i) q^{4} +(-0.831553 + 0.663142i) q^{5} +0.302383i q^{7} +(-4.91050 + 3.91600i) q^{8} +(-0.574538 + 0.720448i) q^{10} +(4.95809 + 2.38769i) q^{11} +(-12.6441 - 15.8552i) q^{13} +(0.0582962 + 0.255412i) q^{14} +(4.71103 - 5.90745i) q^{16} +(13.9269 - 17.4637i) q^{17} +(-11.5294 - 23.9411i) q^{19} +(1.49951 - 3.11377i) q^{20} +(4.64825 + 1.06093i) q^{22} +(-25.4900 - 12.2753i) q^{23} +(-5.31130 + 23.2703i) q^{25} +(-13.7368 - 10.9547i) q^{26} +(-0.426314 - 0.885251i) q^{28} +(-32.2996 + 7.37217i) q^{29} +(1.10365 + 4.83540i) q^{31} +(13.7408 - 28.5332i) q^{32} +(8.39672 - 17.4360i) q^{34} +(-0.200523 - 0.251447i) q^{35} -24.6655i q^{37} +(-14.3541 - 17.9995i) q^{38} +(1.48648 - 6.51272i) q^{40} +(-12.5719 - 55.0811i) q^{41} +(-16.1683 + 39.8445i) q^{43} -17.8815 q^{44} +(-23.8971 - 5.45436i) q^{46} +(11.2262 - 5.40625i) q^{47} +48.9086 q^{49} +20.6796i q^{50} +(59.3701 + 28.5911i) q^{52} +(-39.6570 + 49.7283i) q^{53} +(-5.70629 + 1.30242i) q^{55} +(-1.18413 - 1.48485i) q^{56} +(-25.8611 + 12.4540i) q^{58} +(51.6529 - 64.7707i) q^{59} +(-50.9949 - 11.6393i) q^{61} +(1.86443 + 3.87153i) q^{62} +(-0.619859 + 2.71578i) q^{64} +(21.0285 + 4.79961i) q^{65} +(-35.8982 + 17.2877i) q^{67} +(-16.1508 + 70.7613i) q^{68} +(-0.217851 - 0.173730i) q^{70} +(9.29195 + 19.2949i) q^{71} +(72.6272 - 57.9182i) q^{73} +(-4.75525 - 20.8341i) q^{74} +(67.5068 + 53.8349i) q^{76} +(-0.721996 + 1.49924i) q^{77} -79.2902 q^{79} +8.03643i q^{80} +(-21.2381 - 44.1014i) q^{82} +(-21.7886 + 95.4621i) q^{83} +23.7575i q^{85} +(-5.97524 + 36.7724i) q^{86} +(-33.6969 + 7.69109i) q^{88} +(29.9831 + 6.84344i) q^{89} +(4.79434 - 3.82336i) q^{91} +91.9305 q^{92} +(8.44011 - 6.73076i) q^{94} +(25.4637 + 12.2627i) q^{95} +(32.3163 + 15.5627i) q^{97} +(41.3114 - 9.42906i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 7 q^{2} + 5 q^{4} + 7 q^{5} - 21 q^{8}+O(q^{10}) \) 42 * q + 7 * q^2 + 5 * q^4 + 7 * q^5 - 21 * q^8	\( 42 q + 7 q^{2} + 5 q^{4} + 7 q^{5} - 21 q^{8} - 5 q^{10} + 24 q^{11} - 34 q^{13} - 69 q^{14} - 39 q^{16} - 22 q^{17} - 49 q^{19} - 133 q^{20} + 77 q^{22} - 42 q^{23} + 10 q^{25} - 49 q^{26} + 105 q^{28} - 63 q^{29} - 152 q^{31} - 343 q^{32} + 161 q^{34} - 58 q^{35} + 289 q^{38} - 101 q^{40} - 133 q^{41} - 79 q^{43} - 148 q^{44} - 504 q^{46} - 6 q^{47} - 302 q^{49} - 267 q^{52} + 394 q^{53} - 637 q^{55} - 355 q^{56} + 165 q^{58} + 46 q^{59} - 175 q^{61} + 91 q^{62} + 725 q^{64} - 161 q^{65} - 756 q^{67} + 586 q^{68} + 1526 q^{70} - 266 q^{71} - 252 q^{73} - 204 q^{74} + 994 q^{76} - 791 q^{77} - 178 q^{79} + 245 q^{82} - 238 q^{83} - 365 q^{86} - 119 q^{88} - 252 q^{89} - 224 q^{91} + 764 q^{92} + 133 q^{94} - 11 q^{95} - 491 q^{97} + 553 q^{98}+O(q^{100}) \) 42 * q + 7 * q^2 + 5 * q^4 + 7 * q^5 - 21 * q^8 - 5 * q^10 + 24 * q^11 - 34 * q^13 - 69 * q^14 - 39 * q^16 - 22 * q^17 - 49 * q^19 - 133 * q^20 + 77 * q^22 - 42 * q^23 + 10 * q^25 - 49 * q^26 + 105 * q^28 - 63 * q^29 - 152 * q^31 - 343 * q^32 + 161 * q^34 - 58 * q^35 + 289 * q^38 - 101 * q^40 - 133 * q^41 - 79 * q^43 - 148 * q^44 - 504 * q^46 - 6 * q^47 - 302 * q^49 - 267 * q^52 + 394 * q^53 - 637 * q^55 - 355 * q^56 + 165 * q^58 + 46 * q^59 - 175 * q^61 + 91 * q^62 + 725 * q^64 - 161 * q^65 - 756 * q^67 + 586 * q^68 + 1526 * q^70 - 266 * q^71 - 252 * q^73 - 204 * q^74 + 994 * q^76 - 791 * q^77 - 178 * q^79 + 245 * q^82 - 238 * q^83 - 365 * q^86 - 119 * q^88 - 252 * q^89 - 224 * q^91 + 764 * q^92 + 133 * q^94 - 11 * q^95 - 491 * q^97 + 553 * q^98

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