LMFDB - Embedded newform 387.3.w.b.352.5

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			352.5
Character	$\chi$	$=$	387.352
Dual form			387.3.w.b.199.5

$q$-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 $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{13}{14}\right)$	$1$

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	0.428405	−	0.903587i	$-0.359076\pi$
$2$	0.844666	+	0.192789i	0.422333	+	0.0963947i	−0.00607209	+	0.999982i	$0.501933\pi$
$3$		0			0
$3$		0			0
$4$	−2.92758	−	1.40985i	−0.731896	−	0.352462i
$5$	−0.831553	−	0.663142i	−0.166311	−	0.132628i	0.536798	−	0.843711i	$-0.319634\pi$
$5$	−0.831553	−	0.663142i	−0.166311	−	0.132628i	−0.703109	+	0.711083i	$0.748205\pi$
$6$		0			0
$7$		−	0.302383i		−	0.0431975i	−0.999767	−	0.0215988i	$-0.993124\pi$
$7$		−	0.302383i		−	0.0431975i	0.999767	−	0.0215988i	$-0.00687564\pi$
$8$	−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	−0.194723	−	0.980858i	$-0.562381\pi$
$11$	4.95809	−	2.38769i	0.450735	−	0.217063i	0.645458	+	0.763796i	$0.276667\pi$
$12$		0			0
$13$	−12.6441	+	15.8552i	−0.972623	+	1.21963i	0.00295926	+	0.999996i	$0.499058\pi$
$13$	−12.6441	+	15.8552i	−0.972623	+	1.21963i	−0.975582	+	0.219635i	$0.929513\pi$
$14$	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	0.999050	+	0.0435792i	$0.0138761\pi$
$17$	13.9269	+	17.4637i	0.819227	+	1.02728i	−0.179823	+	0.983699i	$0.557552\pi$
$18$		0			0
$19$	−11.5294	+	23.9411i	−0.606813	+	1.26006i	0.340649	+	0.940191i	$0.389353\pi$
$19$	−11.5294	+	23.9411i	−0.606813	+	1.26006i	−0.947462	+	0.319870i	$0.896361\pi$
$20$	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	−0.896247	−	0.443556i	$-0.853717\pi$
$23$	−25.4900	+	12.2753i	−1.10826	+	0.533711i	−0.212015	+	0.977266i	$0.568003\pi$
$24$		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	−0.374244	−	0.927330i	$-0.622098\pi$
$29$	−32.2996	−	7.37217i	−1.11378	−	0.254213i	−0.739535	+	0.673118i	$0.764955\pi$
$30$		0			0
$31$	1.10365	−	4.83540i	0.0356016	−	0.155981i	−0.954003	−	0.299798i	$-0.903081\pi$
$31$	1.10365	−	4.83540i	0.0356016	−	0.155981i	0.989604	+	0.143817i	$0.0459378\pi$
$32$	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	$0.108168\pi$
$37$			24.6655i			0.666635i	−0.942815	+	0.333318i	$0.891832\pi$
$38$	−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	0.553279	+	0.832996i	$0.313376\pi$
$41$	−12.5719	+	55.0811i	−0.306632	+	1.34344i	−0.859910	+	0.510445i	$0.829481\pi$
$42$		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	0.549483	−	0.835505i	$-0.314825\pi$
$47$	11.2262	+	5.40625i	0.238855	+	0.115027i	−0.310627	+	0.950532i	$0.600539\pi$
$48$		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	0.251315	−	0.967905i	$-0.419137\pi$
$53$	−39.6570	−	49.7283i	−0.748246	−	0.938271i	−0.999561	+	0.0296347i	$0.990566\pi$
$54$		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	0.994481	+	0.104915i	$0.0334570\pi$
$59$	51.6529	+	64.7707i	0.875473	+	1.09781i	−0.119009	+	0.992893i	$0.537972\pi$
$60$		0			0
$61$	−50.9949	+	11.6393i	−0.835982	+	0.190807i	−0.619023	−	0.785373i	$-0.712471\pi$
$61$	−50.9949	+	11.6393i	−0.835982	+	0.190807i	−0.216960	+	0.976181i	$0.569614\pi$
$62$	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	0.146362	−	0.989231i	$-0.453243\pi$
$67$	−35.8982	−	17.2877i	−0.535794	−	0.258025i	−0.682156	+	0.731206i	$0.738958\pi$
$68$	−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	−0.825227	−	0.564801i	$-0.808953\pi$
$71$	9.29195	−	19.2949i	0.130873	−	0.271760i	0.956100	+	0.293041i	$0.0946673\pi$
$72$		0			0
$73$	72.6272	+	57.9182i	0.994893	+	0.793401i	0.978454	−	0.206464i	$-0.0661957\pi$
$73$	72.6272	+	57.9182i	0.994893	+	0.793401i	0.0164387	+	0.999865i	$0.494767\pi$
$74$	−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	−0.918515	−	0.395386i	$-0.870611\pi$
$83$	−21.7886	−	95.4621i	−0.262513	−	1.15015i	0.656002	−	0.754760i	$-0.272246\pi$
$84$		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	−0.0507302	−	0.998712i	$-0.516155\pi$
$89$	29.9831	−	6.84344i	0.336889	−	0.0768926i	0.387619	+	0.921820i	$0.373298\pi$
$90$		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	−0.259825	−	0.965656i	$-0.583665\pi$
$97$	32.3163	−	15.5627i	0.333158	−	0.160440i	0.592982	+	0.805216i	$0.297950\pi$
$98$	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	0.299214	−	0.954186i	$-0.403276\pi$
$101$	−26.2844	−	12.6579i	−0.260242	−	0.125326i	−0.559456	+	0.828860i	$0.688990\pi$
$102$		0			0
$103$	−42.0813	−	52.7682i	−0.408556	−	0.512313i	0.534399	−	0.845232i	$-0.320538\pi$
$103$	−42.0813	−	52.7682i	−0.408556	−	0.512313i	−0.942955	+	0.332919i	$0.891966\pi$
$104$	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	0.958572	−	0.284850i	$-0.0919438\pi$
$107$	−3.06697	−	13.4373i	−0.0286633	−	0.125582i	−0.987235	+	0.159268i	$0.949087\pi$
$108$		0			0
$109$	90.7422	−	43.6991i	0.832497	−	0.400910i	0.0314461	−	0.999505i	$-0.489989\pi$
$109$	90.7422	−	43.6991i	0.832497	−	0.400910i	0.801051	+	0.598596i	$0.204274\pi$
$110$	−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	−0.969553	−	0.244882i	$-0.921251\pi$
$113$	−106.961	+	85.2984i	−0.946556	+	0.754853i	0.0229966	+	0.999736i	$0.492679\pi$
$114$		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	0.845509	+	0.533961i	$0.179297\pi$
$127$	−18.7891	+	82.3203i	−0.147945	+	0.648192i	−0.993454	+	0.114230i	$0.963560\pi$
$128$		−	129.091i		−	1.00852i
$129$		0			0
$130$	18.6874			0.143749
$131$	45.1831	+	10.3128i	0.344909	+	0.0787233i	0.391467	−	0.920192i	$-0.371968\pi$
$131$	45.1831	+	10.3128i	0.344909	+	0.0787233i	−0.0465572	+	0.998916i	$0.514825\pi$
$132$		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	0.107476	−	0.994208i	$-0.465723\pi$
$137$	−114.791	−	91.5426i	−0.837889	−	0.668195i	−0.945365	+	0.326013i	$0.894295\pi$
$138$		0			0
$139$	−17.1502	−	21.5057i	−0.123383	−	0.154717i	0.716304	−	0.697789i	$-0.245833\pi$
$139$	−17.1502	−	21.5057i	−0.123383	−	0.154717i	−0.839686	+	0.543072i	$0.817261\pi$
$140$	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	0.700174	−	0.713972i	$-0.253106\pi$
$149$	−43.8929	−	91.1445i	−0.294583	−	0.611708i	−0.994757	+	0.102264i	$0.967391\pi$
$150$		0			0
$151$	114.117	−	26.0465i	0.755742	−	0.172493i	0.172744	−	0.984967i	$-0.444737\pi$
$151$	114.117	−	26.0465i	0.755742	−	0.172493i	0.582998	+	0.812474i	$0.301880\pi$
$152$	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	−0.371985	−	0.928239i	$-0.621323\pi$
$157$	91.9503	−	190.937i	0.585670	−	1.21616i	0.957655	−	0.287918i	$-0.0929631\pi$
$158$	−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	0.999993	+	0.00385077i	$0.00122574\pi$
$163$	61.8614	+	128.457i	0.379518	+	0.788077i	−0.620475	+	0.784227i	$0.713060\pi$
$164$	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	−0.603967	−	0.797009i	$-0.706414\pi$
$167$	51.3450	−	64.3846i	0.307455	−	0.385536i	0.911422	+	0.411473i	$0.134986\pi$
$168$		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	$0.138365\pi$
$179$			150.763i			0.842253i	−0.907002	+	0.421127i	$0.861635\pi$
$180$		0			0
$181$	−280.100	+	134.889i	−1.54752	+	0.745244i	−0.996037	−	0.0889441i	$-0.971651\pi$
$181$	−280.100	+	134.889i	−1.54752	+	0.745244i	−0.551479	+	0.834189i	$0.685936\pi$
$182$	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	−0.989793	−	0.142515i	$-0.954481\pi$
$191$	−49.8976	+	103.613i	−0.261244	+	0.542479i	0.728549	+	0.684994i	$0.240195\pi$
$192$		0			0
$193$	0.381280	+	1.67050i	0.00197555	+	0.00865543i	0.975906	−	0.218191i	$-0.0700156\pi$
$193$	0.381280	+	1.67050i	0.00197555	+	0.00865543i	−0.973931	+	0.226846i	$0.927158\pi$
$194$	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	−0.612403	−	0.790546i	$-0.709797\pi$
$197$	−79.5194	−	348.397i	−0.403652	−	1.76851i	0.208751	−	0.977969i	$-0.433060\pi$
$198$		0			0
$199$	−196.496	+	156.700i	−0.987415	+	0.787437i	−0.977159	−	0.212510i	$-0.931836\pi$
$199$	−196.496	+	156.700i	−0.987415	+	0.787437i	−0.0102563	+	0.999947i	$0.503265\pi$
$200$	−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	−0.789362	−	0.613928i	$-0.789589\pi$
$211$	38.5677	−	80.0866i	0.182785	−	0.379557i	0.972147	+	0.234370i	$0.0753029\pi$
$212$	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	0.972308	−	0.233703i	$-0.0750845\pi$
$223$	214.263	+	170.869i	0.960823	+	0.766231i	−0.0114851	+	0.999934i	$0.503656\pi$
$224$	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	0.740369	−	0.672201i	$-0.234651\pi$
$227$	253.278	+	57.8090i	1.11576	+	0.254665i	0.375392	+	0.926866i	$0.377508\pi$
$228$		0			0
$229$	−12.5285	+	54.8910i	−0.0547097	+	0.239699i	−0.994888	−	0.100984i	$-0.967801\pi$
$229$	−12.5285	+	54.8910i	−0.0547097	+	0.239699i	0.940178	+	0.340682i	$0.110658\pi$
$230$	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	−0.0635916	−	0.997976i	$-0.520255\pi$
$233$	72.7240	−	16.5988i	0.312120	−	0.0712393i	0.375712	+	0.926737i	$0.377398\pi$
$234$		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	0.999121	+	0.0419133i	$0.0133453\pi$
$239$	395.505	+	190.465i	1.65483	+	0.796925i	0.655711	+	0.755012i	$0.272369\pi$
$240$		0			0
$241$	−131.969	+	105.242i	−0.547590	+	0.436689i	−0.857803	−	0.513978i	$-0.828171\pi$
$241$	−131.969	+	105.242i	−0.547590	+	0.436689i	0.310213	+	0.950667i	$0.399600\pi$
$242$	−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	$0.319276\pi$
$257$			433.357i			1.68621i	−0.537747	+	0.843106i	$0.680724\pi$
$258$		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	0.409331	−	0.912386i	$-0.365762\pi$
$263$	−102.332	−	81.6071i	−0.389095	−	0.310293i	−0.798426	+	0.602093i	$0.794334\pi$
$264$		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	−0.930993	−	0.365036i	$-0.881057\pi$
$269$	−329.810	+	158.828i	−1.22606	+	0.590440i	−0.295068	+	0.955476i	$0.595342\pi$
$270$		0			0
$271$	13.6191	−	17.0779i	0.0502552	−	0.0630180i	−0.756069	−	0.654492i	$-0.772882\pi$
$271$	13.6191	−	17.0779i	0.0502552	−	0.0630180i	0.806324	+	0.591474i	$0.201454\pi$
$272$	−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	0.604946	+	0.796266i	$0.293195\pi$
$277$	−109.353	+	227.075i	−0.394778	+	0.819764i	−0.999724	+	0.0234977i	$0.992520\pi$
$278$	−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	−0.741755	−	0.670671i	$-0.766006\pi$
$281$	−191.046	+	92.0031i	−0.679880	+	0.327413i	0.0618747	+	0.998084i	$0.480292\pi$
$282$		0			0
$283$	14.2648	+	62.4982i	0.0504057	+	0.220842i	0.993857	−	0.110668i	$-0.0352991\pi$
$283$	14.2648	+	62.4982i	0.0504057	+	0.220842i	−0.943452	+	0.331510i	$0.892442\pi$
$284$	−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	−0.953025	−	0.302893i	$-0.902048\pi$
$293$	−130.578	+	163.739i	−0.445658	+	0.558837i	0.507367	+	0.861730i	$0.330619\pi$
$294$		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	0.824121	−	0.566414i	$-0.191670\pi$
$311$	27.5310	+	34.5228i	0.0885241	+	0.111006i	−0.735597	+	0.677420i	$0.763098\pi$
$312$		0			0
$313$	−72.3142	−	16.5052i	−0.231036	−	0.0527324i	0.105435	−	0.994426i	$-0.466376\pi$
$313$	−72.3142	−	16.5052i	−0.231036	−	0.0527324i	−0.336471	+	0.941694i	$0.609234\pi$
$314$	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	0.991153	−	0.132725i	$-0.0423726\pi$
$317$	203.262	+	254.882i	0.641204	+	0.804044i	−0.349949	+	0.936769i	$0.613801\pi$
$318$		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	0.873587	−	0.486669i	$-0.161788\pi$
$331$	196.452	+	156.665i	0.593511	+	0.473309i	−0.280076	+	0.959978i	$0.590360\pi$
$332$	−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	−0.149269	−	0.988797i	$-0.547692\pi$
$347$	50.4078	−	11.5053i	0.145267	−	0.0331563i	0.294536	+	0.955640i	$0.404835\pi$
$348$		0			0
$349$	−473.778	−	377.825i	−1.35753	−	1.08259i	−0.988179	−	0.153302i	$-0.951009\pi$
$349$	−473.778	−	377.825i	−1.35753	−	1.08259i	−0.369349	−	0.929291i	$-0.620419\pi$
$350$	−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	−0.788801	−	0.614648i	$-0.789298\pi$
$353$	−282.421	+	136.007i	−0.800059	+	0.385288i	−0.0112581	+	0.999937i	$0.503584\pi$
$354$		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	0.778929	−	0.627113i	$-0.215763\pi$
$359$	277.969	+	133.863i	0.774286	+	0.372877i	−0.00464226	+	0.999989i	$0.501478\pi$
$360$		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	−0.308921	−	0.951088i	$-0.599968\pi$
$367$	88.8360	−	42.7812i	0.242060	−	0.116570i	0.550981	+	0.834518i	$0.314254\pi$
$368$	−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	0.476791	−	0.879017i	$-0.341800\pi$
$373$	195.815	+	44.6935i	0.524973	+	0.119822i	0.0481825	+	0.998839i	$0.484657\pi$
$374$	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	−0.910162	−	0.414253i	$-0.864043\pi$
$379$	−115.127	+	144.365i	−0.303765	+	0.380909i	0.606397	+	0.795162i	$0.292614\pi$
$380$	−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	−0.499219	−	0.866476i	$-0.666380\pi$
$383$	187.470	−	389.285i	0.489477	−	1.01641i	0.988696	−	0.149934i	$-0.0479061\pi$
$384$		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	0.767105	−	0.641522i	$-0.221697\pi$
$389$	458.980	+	104.759i	1.17990	+	0.269304i	0.412792	+	0.910825i	$0.364554\pi$
$390$		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	0.962114	−	0.272648i	$-0.0878995\pi$
$397$	191.438	+	240.055i	0.482211	+	0.604674i	−0.479903	+	0.877322i	$0.659328\pi$
$398$	−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	−0.754449	−	0.656359i	$-0.772096\pi$
$401$	84.2379	−	369.070i	0.210070	−	0.920375i	0.964518	−	0.264016i	$-0.0850471\pi$
$402$		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	0.270105	−	0.962831i	$-0.412942\pi$
$409$	380.868	−	86.9307i	0.931218	−	0.212544i	0.661113	+	0.750286i	$0.270084\pi$
$410$	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	0.998930	+	0.0462460i	$0.0147258\pi$
$419$	172.739	+	358.695i	0.412264	+	0.856075i	−0.586666	+	0.809829i	$0.699560\pi$
$420$		0			0
$421$	−24.7654	−	51.4259i	−0.0588252	−	0.122152i	0.869484	−	0.493962i	$-0.164452\pi$
$421$	−24.7654	−	51.4259i	−0.0588252	−	0.122152i	−0.928309	+	0.371810i	$0.878737\pi$
$422$	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	−0.999149	−	0.0412373i	$-0.986870\pi$
$433$	−814.672	+	185.944i	−1.88146	+	0.429431i	−0.882310	+	0.470668i	$0.844013\pi$
$434$	−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	0.347174	−	0.937801i	$-0.387141\pi$
$439$	569.311	−	274.166i	1.29684	−	0.624523i	0.949662	+	0.313277i	$0.101427\pi$
$440$	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	0.460880	−	0.887463i	$-0.347534\pi$
$443$	542.027	−	679.680i	1.22354	−	1.53427i	0.762657	−	0.646803i	$-0.223895\pi$
$444$		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	0.533602	+	0.845736i	$0.320838\pi$
$449$	−206.682	+	429.180i	−0.460316	+	0.955857i	−0.993918	+	0.110121i	$0.964876\pi$
$450$		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	−0.510593	−	0.859822i	$-0.670574\pi$
$457$	97.8225	−	78.0109i	0.214054	−	0.170702i	0.724647	+	0.689120i	$0.242003\pi$
$458$	−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	0.652610	+	0.757694i	$0.273674\pi$
$461$	−121.760	+	533.467i	−0.264122	+	1.15720i	−0.916732	+	0.399502i	$0.869183\pi$
$462$		0			0
$463$	606.923	−	484.005i	1.31085	−	1.04537i	0.315510	−	0.948922i	$-0.397824\pi$
$463$	606.923	−	484.005i	1.31085	−	1.04537i	0.995338	−	0.0964445i	$-0.0307470\pi$
$464$	−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	$-0.884450\pi$
$467$		−	331.656i		−	0.710184i	0.934831	−	0.355092i	$-0.115550\pi$
$468$		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	0.809848	+	0.586640i	$0.199550\pi$
$487$	−84.9004	+	371.973i	−0.174333	+	0.763805i	−0.984181	+	0.177165i	$0.943308\pi$
$488$	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	−0.240182	−	0.970728i	$-0.577207\pi$
$491$	−17.3795	+	3.96677i	−0.0353962	+	0.00807895i	0.204786	+	0.978807i	$0.434350\pi$
$492$		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	−0.709123	−	0.705085i	$-0.750909\pi$
$499$	−89.5761	+	71.4346i	−0.179511	+	0.143155i	0.529612	+	0.848240i	$0.322338\pi$
$500$	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	0.141206	−	0.989980i	$-0.454902\pi$
$503$	−398.644	−	317.908i	−0.792532	−	0.632023i	−0.933738	+	0.357957i	$0.883473\pi$
$504$		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	0.493343	−	0.869835i	$-0.335775\pi$
$521$	−127.595	−	101.754i	−0.244904	−	0.195305i	−0.738247	+	0.674530i	$0.764346\pi$
$522$		0			0
$523$		−	402.940i		−	0.770439i	−0.922825	−	0.385220i	$-0.874126\pi$
$523$		−	402.940i		−	0.770439i	0.922825	−	0.385220i	$-0.125874\pi$
$524$	−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	0.929183	−	0.369621i	$-0.120512\pi$
$541$	−36.9797	−	162.019i	−0.0683544	−	0.299480i	−0.997537	+	0.0701405i	$0.977655\pi$
$542$	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	−0.425994	−	0.904726i	$-0.640076\pi$
$547$	191.646	−	839.658i	0.350359	−	1.53502i	0.776353	−	0.630298i	$-0.217067\pi$
$548$	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	0.849370	+	0.527799i	$0.176982\pi$
$557$	−80.7033	+	353.584i	−0.144889	+	0.634801i	−0.994259	+	0.107002i	$0.965875\pi$
$558$		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	0.678029	−	0.735035i	$-0.262834\pi$
$563$	296.194	+	142.640i	0.526100	+	0.253356i	−0.151929	+	0.988391i	$0.548549\pi$
$564$		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	0.706981	−	0.707232i	$-0.250057\pi$
$569$	−79.5676	−	99.7746i	−0.139838	−	0.175351i	−0.846819	+	0.531882i	$0.821485\pi$
$570$		0			0
$571$	834.419	+	190.451i	1.46133	+	0.333539i	0.877986	−	0.478686i	$-0.158887\pi$
$571$	834.419	+	190.451i	1.46133	+	0.333539i	0.583344	+	0.812225i	$0.301744\pi$
$572$	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	0.118540	−	0.992949i	$-0.462179\pi$
$577$	378.607	−	86.4147i	0.656165	−	0.149765i	0.537625	+	0.843184i	$0.319321\pi$
$578$	−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	0.0633202	+	0.997993i	$0.479831\pi$
$587$	−444.020	+	922.016i	−0.756422	+	1.57073i	−0.819742	+	0.572733i	$0.805883\pi$
$588$		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	0.904777	−	0.425885i	$-0.140037\pi$
$593$	4.55877	+	9.46638i	0.00768764	+	0.0159635i	−0.897090	+	0.441848i	$0.854323\pi$
$594$		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	0.972139	+	0.234406i	$0.0753146\pi$
$599$	118.588	+	519.569i	0.197977	+	0.867394i	−0.774162	+	0.632988i	$0.781828\pi$
$600$		0			0
$601$			56.8479i			0.0945888i	0.998881	+	0.0472944i	$0.0150599\pi$
$601$			56.8479i			0.0945888i	−0.998881	+	0.0472944i	$0.984940\pi$
$602$	−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	0.491951	−	0.870623i	$-0.336284\pi$
$607$	−150.156	−	119.746i	−0.247374	−	0.197274i	−0.739325	+	0.673349i	$0.764855\pi$
$608$	−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	−0.292873	−	0.956151i	$-0.594611\pi$
$613$	166.780	−	80.3172i	0.272072	−	0.131023i	0.564946	+	0.825128i	$0.308897\pi$
$614$	−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	−0.293257	−	0.956034i	$-0.594739\pi$
$617$	−754.934	−	363.557i	−1.22356	−	0.589234i	−0.930300	+	0.366800i	$0.880453\pi$
$618$		0			0
$619$	−173.375	−	217.405i	−0.280088	−	0.351220i	0.621810	−	0.783168i	$-0.286398\pi$
$619$	−173.375	−	217.405i	−0.280088	−	0.351220i	−0.901898	+	0.431949i	$0.857826\pi$
$620$	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	0.340435	−	0.940268i	$-0.389426\pi$
$631$	150.928	+	34.4484i	0.239189	+	0.0545933i	−0.101246	+	0.994861i	$0.532283\pi$
$632$	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	0.492153	+	0.870509i	$0.336210\pi$
$641$	−317.481	+	659.257i	−0.495291	+	1.02848i	−0.987443	+	0.157973i	$0.949504\pi$
$642$		0			0
$643$	−271.265	+	1188.49i	−0.421873	+	1.84835i	0.0995261	+	0.995035i	$0.468267\pi$
$643$	−271.265	+	1188.49i	−0.421873	+	1.84835i	−0.521399	+	0.853313i	$0.674590\pi$
$644$		−	27.7982i		−	0.0431649i
$645$		0			0
$646$	−514.246			−0.796047
$647$	202.845	+	46.2981i	0.313517	+	0.0715582i	0.376384	−	0.926464i	$-0.377167\pi$
$647$	202.845	+	46.2981i	0.313517	+	0.0715582i	−0.0628673	+	0.998022i	$0.520024\pi$
$648$		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	0.0513977	−	0.998678i	$-0.483632\pi$
$653$	−594.755	−	474.302i	−0.910805	−	0.726342i	−0.962202	+	0.272336i	$0.912204\pi$
$654$		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	0.627880	+	0.778310i	$0.283923\pi$
$659$	−181.565	+	795.490i	−0.275516	+	1.20712i	−0.903396	+	0.428806i	$0.858934\pi$
$660$		0			0
$661$	67.1647	+	84.2218i	0.101611	+	0.127416i	0.830037	−	0.557709i	$-0.188319\pi$
$661$	67.1647	+	84.2218i	0.101611	+	0.127416i	−0.728426	+	0.685124i	$0.759748\pi$
$662$	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	−0.913217	−	0.407474i	$-0.866410\pi$
$673$	−16.9997	+	35.3002i	−0.0252596	+	0.0524520i	0.887957	+	0.459926i	$0.152124\pi$
$674$	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	0.985132	−	0.171800i	$-0.0549583\pi$
$677$	160.174	+	332.604i	0.236594	+	0.491292i	−0.748538	+	0.663092i	$0.769244\pi$
$678$		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	−0.596797	−	0.802392i	$-0.703560\pi$
$683$	217.384	−	272.590i	0.318278	−	0.399108i	0.915074	+	0.403285i	$0.132132\pi$
$684$		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	0.287648	−	0.957736i	$-0.407127\pi$
$691$	664.988	−	151.779i	0.962357	−	0.219652i	0.674708	+	0.738085i	$0.264269\pi$
$692$	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	−0.872330	−	0.488918i	$-0.837392\pi$
$701$	−141.292	+	177.175i	−0.201558	+	0.252746i	0.670772	+	0.741664i	$0.265963\pi$
$702$		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	−0.894627	−	0.446813i	$-0.852559\pi$
$709$	−200.265	−	877.417i	−0.282461	−	1.23754i	0.612167	−	0.790729i	$-0.290298\pi$
$710$	−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	−0.957305	−	0.289079i	$-0.906651\pi$
$719$	22.0183	−	96.4685i	0.0306235	−	0.134170i	0.987929	+	0.154908i	$0.0495082\pi$
$720$		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	0.486892	+	0.873462i	$0.338130\pi$
$727$	−363.195	+	754.182i	−0.499580	+	1.03739i	−0.986473	+	0.163927i	$0.947584\pi$
$728$	−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	−0.408750	−	0.912646i	$-0.634035\pi$
$733$	−859.811	−	196.246i	−1.17300	−	0.267730i	−0.764253	+	0.644916i	$0.776892\pi$
$734$	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	0.635250	−	0.772307i	$-0.280897\pi$
$739$	17.4864	+	13.9449i	0.0236622	+	0.0188700i	−0.611587	+	0.791177i	$0.709469\pi$
$740$	−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	0.0904859	−	0.995898i	$-0.471158\pi$
$743$	−193.249	−	44.1079i	−0.260093	−	0.0593645i	−0.350579	+	0.936533i	$0.614015\pi$
$744$		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	0.942791	+	0.333386i	$0.108191\pi$
$751$	462.332	+	960.042i	0.615622	+	1.27835i	−0.327169	+	0.944966i	$0.606095\pi$
$752$	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	−0.899252	−	0.437432i	$-0.855888\pi$
$757$	−509.378	+	406.215i	−0.672890	+	0.536612i	0.226362	+	0.974043i	$0.427317\pi$
$758$	−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	0.850043	−	0.526713i	$-0.176576\pi$
$761$	400.049	+	319.028i	0.525688	+	0.419222i	−0.324355	+	0.945935i	$0.605147\pi$
$762$		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	−0.899910	−	0.436075i	$-0.856368\pi$
$769$	−211.105	+	264.718i	−0.274519	+	0.344236i	0.625391	+	0.780312i	$0.284940\pi$
$770$	−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	$0.107828\pi$
$773$			513.752i			0.664621i	−0.943170	+	0.332311i	$0.892172\pi$
$774$		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	−0.824015	−	0.566567i	$-0.808271\pi$
$787$	−69.4862	+	87.1329i	−0.0882925	+	0.110715i	0.735723	+	0.677283i	$0.236843\pi$
$788$	−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	0.225816	−	0.974170i	$-0.427495\pi$
$797$	899.213	−	433.038i	1.12825	−	0.543335i	0.902431	+	0.430835i	$0.141781\pi$
$798$		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	−0.913094	−	0.407749i	$-0.866314\pi$
$809$	−252.720	+	316.900i	−0.312385	+	0.391719i	0.600709	+	0.799468i	$0.294885\pi$
$810$		0			0
$811$		−	1126.53i		−	1.38907i	−0.719459	−	0.694534i	$-0.755610\pi$
$811$		−	1126.53i		−	1.38907i	0.719459	−	0.694534i	$-0.244390\pi$
$812$	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	0.543225	−	0.839587i	$-0.317203\pi$
$821$	185.139	+	89.1581i	0.225504	+	0.108597i	−0.317721	+	0.948184i	$0.602917\pi$
$822$		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	0.473255	−	0.880926i	$-0.343079\pi$
$827$	−405.969	−	509.069i	−0.490893	−	0.615561i	−0.964148	+	0.265365i	$0.914508\pi$
$828$		0			0
$829$	−616.946	−	140.814i	−0.744205	−	0.169860i	−0.166427	−	0.986054i	$-0.553223\pi$
$829$	−616.946	−	140.814i	−0.744205	−	0.169860i	−0.577778	+	0.816194i	$0.696080\pi$
$830$	−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	0.754537	−	0.656258i	$-0.227862\pi$
$839$	1442.32	−	329.199i	1.71909	−	0.392371i	0.964554	+	0.263887i	$0.0850045\pi$
$840$		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	−0.906248	−	0.422747i	$-0.861066\pi$
$857$	−234.106	−	1025.69i	−0.273170	−	1.19683i	0.633078	−	0.774088i	$-0.281791\pi$
$858$		0			0
$859$		−	459.916i		−	0.535409i	−0.963501	−	0.267705i	$-0.913735\pi$
$859$		−	459.916i		−	0.535409i	0.963501	−	0.267705i	$-0.0862651\pi$
$860$	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	−0.812968	−	0.582309i	$-0.802150\pi$
$863$	−1115.66	+	254.643i	−1.29277	+	0.295067i	−0.479804	+	0.877375i	$0.659292\pi$
$864$		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	0.892471	−	0.451105i	$-0.148970\pi$
$877$	222.830	+	279.420i	0.254082	+	0.318609i	−0.638389	+	0.769714i	$0.720399\pi$
$878$	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	−0.956759	−	0.290882i	$-0.906051\pi$
$881$	−194.664	−	852.879i	−0.220958	−	0.968080i	0.735801	−	0.677198i	$-0.236806\pi$
$882$		0			0
$883$	−620.045	+	298.598i	−0.702203	+	0.338163i	−0.750684	−	0.660661i	$-0.770276\pi$
$883$	−620.045	+	298.598i	−0.702203	+	0.338163i	0.0484814	+	0.998824i	$0.484562\pi$
$884$	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	−0.722886	−	0.690967i	$-0.757185\pi$
$887$	−186.359	+	148.616i	−0.210100	+	0.167549i	0.512786	+	0.858516i	$0.328613\pi$
$888$		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	0.922823	−	0.385224i	$-0.125876\pi$
$907$	1085.69	+	522.841i	1.19701	+	0.576451i	0.274191	+	0.961675i	$0.411590\pi$
$908$	−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	0.986967	+	0.160923i	$0.0514470\pi$
$911$	1242.13	+	990.563i	1.36348	+	1.08734i	0.376509	+	0.926413i	$0.377124\pi$
$912$		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	0.892802	−	0.450449i	$-0.148736\pi$
$919$	234.326	+	293.835i	0.254979	+	0.319734i	−0.637823	+	0.770183i	$0.720165\pi$
$920$	−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	−0.370781	−	0.928720i	$-0.620910\pi$
$929$	420.046	−	334.975i	0.452148	−	0.360576i	0.822929	+	0.568144i	$0.192338\pi$
$930$		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	0.999384	+	0.0351047i	$0.0111765\pi$
$937$	378.289	+	785.526i	0.403724	+	0.838342i	−0.595660	+	0.803237i	$0.703109\pi$
$938$	−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	−0.613090	−	0.790013i	$-0.710074\pi$
$941$	276.222	−	346.372i	0.293541	−	0.368089i	0.906631	+	0.421924i	$0.138645\pi$
$942$		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	$0.00647650\pi$
$953$			38.7778i			0.0406903i	−0.999793	+	0.0203451i	$0.993523\pi$
$954$		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	−0.997280	−	0.0737103i	$-0.976516\pi$
$967$	−126.429	−	553.921i	−0.130743	−	0.572824i	0.866536	−	0.499114i	$-0.166341\pi$
$968$	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	−0.992039	−	0.125928i	$-0.959809\pi$
$971$	−148.447	−	650.391i	−0.152881	−	0.669815i	0.839158	−	0.543887i	$-0.183048\pi$
$972$		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	−0.991189	−	0.132458i	$-0.957713\pi$
$977$	−39.7516	+	174.163i	−0.0406874	+	0.178263i	0.950501	+	0.310721i	$0.100570\pi$
$978$		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	$0.0733356\pi$
$983$			448.952i			0.456716i	−0.973577	+	0.228358i	$0.926664\pi$
$984$		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	0.210781	−	0.977533i	$-0.432399\pi$
$991$	−23.2361	−	5.30348i	−0.0234471	−	0.00535165i	−0.234228	+	0.972182i	$0.575256\pi$
$992$	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	0.700202	−	0.713945i	$-0.253093\pi$
$997$	159.486	+	127.186i	0.159966	+	0.127569i	−0.540235	+	0.841514i	$0.681665\pi$
$998$	−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.352.5		42
3.2	odd	2		43.3.f.a.8.3	✓	42
43.27	odd	14	inner	387.3.w.b.199.5		42
129.113	even	14		43.3.f.a.27.3	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.3.f.a.8.3	✓	42	3.2	odd	2
43.3.f.a.27.3	yes	42	129.113	even	14
387.3.w.b.199.5		42	43.27	odd	14	inner
387.3.w.b.352.5		42	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
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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