LMFDB - Embedded newform 162.5.f.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,5,Mod(17,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	162.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.7459340196$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	162.17
Dual form			162.5.f.a.143.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-41.7224 - 7.35678i) q^{5} +(19.0320 - 15.9698i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(-59.9146 + 103.775i) q^{10} +(18.0860 - 3.18905i) q^{11} +(-100.351 + 36.5247i) q^{13} +(-24.0341 - 66.0331i) q^{14} +(11.1135 + 63.0277i) q^{16} +(339.433 + 195.972i) q^{17} +(205.064 + 355.182i) q^{19} +(217.859 + 259.634i) q^{20} +(9.02000 - 51.1549i) q^{22} +(-218.656 + 260.583i) q^{23} +(1099.33 + 400.122i) q^{25} +302.051i q^{26} -198.756 q^{28} +(-485.587 + 1334.14i) q^{29} +(-923.152 - 774.616i) q^{31} +(178.269 + 31.4337i) q^{32} +(849.225 - 712.585i) q^{34} +(-911.547 + 526.282i) q^{35} +(755.062 - 1307.80i) q^{37} +(1142.40 - 201.435i) q^{38} +(900.820 - 327.872i) q^{40} +(207.264 + 569.453i) q^{41} +(337.617 + 1914.72i) q^{43} +(-127.237 - 73.4600i) q^{44} +(481.070 + 833.237i) q^{46} +(-2025.36 - 2413.73i) q^{47} +(-309.745 + 1756.65i) q^{49} +(2126.93 - 2534.78i) q^{50} +(802.807 + 292.198i) q^{52} +3309.93i q^{53} -778.052 q^{55} +(-192.273 + 528.265i) q^{56} +(3076.20 + 2581.24i) q^{58} +(4797.62 + 845.950i) q^{59} +(1691.36 - 1419.22i) q^{61} +(-2951.85 + 1704.25i) q^{62} +(256.000 - 443.405i) q^{64} +(4455.58 - 785.639i) q^{65} +(-3252.29 + 1183.74i) q^{67} +(-1072.42 - 2946.45i) q^{68} +(516.968 + 2931.87i) q^{70} +(-5743.28 - 3315.88i) q^{71} +(-2945.25 - 5101.32i) q^{73} +(-2745.52 - 3271.98i) q^{74} +(569.745 - 3231.18i) q^{76} +(293.285 - 349.523i) q^{77} +(-2340.08 - 851.720i) q^{79} -2711.42i q^{80} +1714.03 q^{82} +(-3787.29 + 10405.5i) q^{83} +(-12720.2 - 10673.6i) q^{85} +(5415.65 + 954.924i) q^{86} +(-318.332 + 267.112i) q^{88} +(-6082.16 + 3511.54i) q^{89} +(-1326.59 + 2297.72i) q^{91} +(2680.00 - 472.556i) q^{92} +(-8374.63 + 3048.11i) q^{94} +(-5942.78 - 16327.6i) q^{95} +(350.066 + 1985.32i) q^{97} +(4369.27 + 2522.60i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{5} - 720 q^{11} + 288 q^{14} - 288 q^{20} - 1008 q^{22} - 4716 q^{23} - 882 q^{25} + 6084 q^{29} + 3330 q^{31} + 288 q^{34} - 5346 q^{35} - 576 q^{38} + 13356 q^{41} + 1260 q^{43} - 16578 q^{47}+ \cdots - 82944 q^{98}+O(q^{100}) $ 72 * q + 18 * q^5 - 720 * q^11 + 288 * q^14 - 288 * q^20 - 1008 * q^22 - 4716 * q^23 - 882 * q^25 + 6084 * q^29 + 3330 * q^31 + 288 * q^34 - 5346 * q^35 - 576 * q^38 + 13356 * q^41 + 1260 * q^43 - 16578 * q^47 - 5904 * q^49 - 15552 * q^50 + 2304 * q^56 + 40104 * q^59 + 8352 * q^61 + 18432 * q^64 + 19674 * q^65 - 24192 * q^67 - 10224 * q^68 + 14400 * q^70 - 39528 * q^71 - 12222 * q^73 - 33120 * q^74 + 9792 * q^76 - 28206 * q^77 + 11304 * q^79 + 30078 * q^83 - 52200 * q^85 + 46224 * q^86 - 16128 * q^88 + 102222 * q^89 + 12078 * q^91 + 27504 * q^92 + 4032 * q^94 - 46728 * q^95 + 49680 * q^97 - 82944 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.967379	−	2.65785i	0.241845	−	0.664463i
$2$	0.967379	−	2.65785i	0.241845	−	0.664463i
$3$		0			0
$3$		0			0
$4$	−6.12836	−	5.14230i	−0.383022	−	0.321394i
$5$	−41.7224	−	7.35678i	−1.66889	−	0.294271i	−0.742226	−	0.670150i	$-0.766230\pi$
$5$	−41.7224	−	7.35678i	−1.66889	−	0.294271i	−0.926669	+	0.375879i	$0.877341\pi$
$6$		0			0
$7$	19.0320	−	15.9698i	0.388409	−	0.325914i	−0.427584	−	0.903976i	$-0.640635\pi$
$7$	19.0320	−	15.9698i	0.388409	−	0.325914i	0.815993	+	0.578062i	$0.196191\pi$
$8$	−19.5959	+	11.3137i	−0.306186	+	0.176777i
$9$		0			0
$10$	−59.9146	+	103.775i	−0.599146	+	1.03775i
$11$	18.0860	−	3.18905i	0.149471	−	0.0263558i	−0.0984119	−	0.995146i	$-0.531376\pi$
$11$	18.0860	−	3.18905i	0.149471	−	0.0263558i	0.247883	+	0.968790i	$0.420265\pi$
$12$		0			0
$13$	−100.351	+	36.5247i	−0.593792	+	0.216123i	−0.621397	−	0.783496i	$-0.713434\pi$
$13$	−100.351	+	36.5247i	−0.593792	+	0.216123i	0.0276042	+	0.999619i	$0.491212\pi$
$14$	−24.0341	−	66.0331i	−0.122623	−	0.336904i
$15$		0			0
$16$	11.1135	+	63.0277i	0.0434120	+	0.246202i
$17$	339.433	+	195.972i	1.17451	+	0.678104i	0.954738	−	0.297448i	$-0.0961353\pi$
$17$	339.433	+	195.972i	1.17451	+	0.678104i	0.219772	+	0.975551i	$0.429469\pi$
$18$		0			0
$19$	205.064	+	355.182i	0.568045	+	0.983883i	0.996759	+	0.0804431i	$0.0256335\pi$
$19$	205.064	+	355.182i	0.568045	+	0.983883i	−0.428714	+	0.903440i	$0.641033\pi$
$20$	217.859	+	259.634i	0.544647	+	0.649085i
$21$		0			0
$22$	9.02000	−	51.1549i	0.0186364	−	0.105692i
$23$	−218.656	+	260.583i	−0.413337	+	0.492596i	−0.932038	−	0.362359i	$-0.881971\pi$
$23$	−218.656	+	260.583i	−0.413337	+	0.492596i	0.518701	+	0.854956i	$0.326416\pi$
$24$		0			0
$25$	1099.33	+	400.122i	1.75892	+	0.640195i
$26$			302.051i			0.446821i
$27$		0			0
$28$	−198.756			−0.253516
$29$	−485.587	+	1334.14i	−0.577392	+	1.58637i	0.215167	+	0.976577i	$0.430970\pi$
$29$	−485.587	+	1334.14i	−0.577392	+	1.58637i	−0.792560	+	0.609795i	$0.791252\pi$
$30$		0			0
$31$	−923.152	−	774.616i	−0.960616	−	0.806052i	0.0204376	−	0.999791i	$-0.493494\pi$
$31$	−923.152	−	774.616i	−0.960616	−	0.806052i	−0.981053	+	0.193739i	$0.937939\pi$
$32$	178.269	+	31.4337i	0.174091	+	0.0306970i
$33$		0			0
$34$	849.225	−	712.585i	0.734624	−	0.616423i
$35$	−911.547	+	526.282i	−0.744120	+	0.429618i
$36$		0			0
$37$	755.062	−	1307.80i	0.551542	−	0.955299i	−0.446621	−	0.894723i	$-0.647373\pi$
$37$	755.062	−	1307.80i	0.551542	−	0.955299i	0.998164	−	0.0605763i	$-0.0192938\pi$
$38$	1142.40	−	201.435i	0.791133	−	0.139498i
$39$		0			0
$40$	900.820	−	327.872i	0.563013	−	0.204920i
$41$	207.264	+	569.453i	0.123298	+	0.338759i	0.985950	−	0.167039i	$-0.0534205\pi$
$41$	207.264	+	569.453i	0.123298	+	0.338759i	−0.862652	+	0.505798i	$0.831198\pi$
$42$		0			0
$43$	337.617	+	1914.72i	0.182594	+	1.03554i	0.929008	+	0.370061i	$0.120663\pi$
$43$	337.617	+	1914.72i	0.182594	+	1.03554i	−0.746413	+	0.665483i	$0.768226\pi$
$44$	−127.237	−	73.4600i	−0.0657213	−	0.0379442i
$45$		0			0
$46$	481.070	+	833.237i	0.227349	+	0.393779i
$47$	−2025.36	−	2413.73i	−0.916867	−	1.09268i	−0.995404	−	0.0957684i	$-0.969469\pi$
$47$	−2025.36	−	2413.73i	−0.916867	−	1.09268i	0.0785366	−	0.996911i	$-0.474975\pi$
$48$		0			0
$49$	−309.745	+	1756.65i	−0.129007	+	0.731632i
$50$	2126.93	−	2534.78i	0.850772	−	1.01391i
$51$		0			0
$52$	802.807	+	292.198i	0.296896	+	0.108061i
$53$			3309.93i			1.17833i	0.808013	+	0.589165i	$0.200543\pi$
$53$			3309.93i			1.17833i	−0.808013	+	0.589165i	$0.799457\pi$
$54$		0			0
$55$	−778.052			−0.257207
$56$	−192.273	+	528.265i	−0.0613115	+	0.168452i
$57$		0			0
$58$	3076.20	+	2581.24i	0.914446	+	0.767311i
$59$	4797.62	+	845.950i	1.37823	+	0.243019i	0.813168	−	0.582029i	$-0.197741\pi$
$59$	4797.62	+	845.950i	1.37823	+	0.243019i	0.565062	+	0.825048i	$0.308852\pi$
$60$		0			0
$61$	1691.36	−	1419.22i	0.454543	−	0.381407i	−0.386575	−	0.922258i	$-0.626342\pi$
$61$	1691.36	−	1419.22i	0.454543	−	0.381407i	0.841119	+	0.540851i	$0.181898\pi$
$62$	−2951.85	+	1704.25i	−0.767912	+	0.443354i
$63$		0			0
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	4455.58	−	785.639i	1.05458	−	0.185950i
$66$		0			0
$67$	−3252.29	+	1183.74i	−0.724503	+	0.263698i	−0.677836	−	0.735213i	$-0.737082\pi$
$67$	−3252.29	+	1183.74i	−0.724503	+	0.263698i	−0.0466669	+	0.998911i	$0.514860\pi$
$68$	−1072.42	−	2946.45i	−0.231925	−	0.637209i
$69$		0			0
$70$	516.968	+	2931.87i	0.105504	+	0.598341i
$71$	−5743.28	−	3315.88i	−1.13931	−	0.657783i	−0.193053	−	0.981188i	$-0.561839\pi$
$71$	−5743.28	−	3315.88i	−1.13931	−	0.657783i	−0.946260	+	0.323405i	$0.895172\pi$
$72$		0			0
$73$	−2945.25	−	5101.32i	−0.552684	−	0.957276i	−0.998080	−	0.0619425i	$-0.980270\pi$
$73$	−2945.25	−	5101.32i	−0.552684	−	0.957276i	0.445396	−	0.895334i	$-0.353063\pi$
$74$	−2745.52	−	3271.98i	−0.501374	−	0.597514i
$75$		0			0
$76$	569.745	−	3231.18i	0.0986400	−	0.559415i
$77$	293.285	−	349.523i	0.0494662	−	0.0589515i
$78$		0			0
$79$	−2340.08	−	851.720i	−0.374953	−	0.136472i	0.147668	−	0.989037i	$-0.452823\pi$
$79$	−2340.08	−	851.720i	−0.374953	−	0.136472i	−0.522621	+	0.852565i	$0.675046\pi$
$80$		−	2711.42i		−	0.423660i
$81$		0			0
$82$	1714.03			0.254912
$83$	−3787.29	+	10405.5i	−0.549759	+	1.51045i	0.284279	+	0.958742i	$0.408246\pi$
$83$	−3787.29	+	10405.5i	−0.549759	+	1.51045i	−0.834038	+	0.551708i	$0.813976\pi$
$84$		0			0
$85$	−12720.2	−	10673.6i	−1.76059	−	1.47731i
$86$	5415.65	+	954.924i	0.732240	+	0.129114i
$87$		0			0
$88$	−318.332	+	267.112i	−0.0411069	+	0.0344928i
$89$	−6082.16	+	3511.54i	−0.767852	+	0.443320i	−0.832108	−	0.554614i	$-0.812866\pi$
$89$	−6082.16	+	3511.54i	−0.767852	+	0.443320i	0.0642555	+	0.997933i	$0.479533\pi$
$90$		0			0
$91$	−1326.59	+	2297.72i	−0.160197	+	0.277469i
$92$	2680.00	−	472.556i	0.316635	−	0.0558313i
$93$		0			0
$94$	−8374.63	+	3048.11i	−0.947785	+	0.344965i
$95$	−5942.78	−	16327.6i	−0.658479	−	1.80916i
$96$		0			0
$97$	350.066	+	1985.32i	0.0372054	+	0.211002i	0.997743	−	0.0671476i	$-0.0213898\pi$
$97$	350.066	+	1985.32i	0.0372054	+	0.211002i	−0.960538	+	0.278150i	$0.910279\pi$
$98$	4369.27	+	2522.60i	0.454943	+	0.262662i
$99$		0			0
$100$	−4679.51	−	8105.15i	−0.467951	−	0.810515i
$101$	11176.5	+	13319.6i	1.09562	+	1.30571i	0.948563	+	0.316587i	$0.102537\pi$
$101$	11176.5	+	13319.6i	1.09562	+	1.30571i	0.147061	+	0.989127i	$0.453019\pi$
$102$		0			0
$103$	−2302.42	+	13057.7i	−0.217026	+	1.23081i	0.660331	+	0.750975i	$0.270416\pi$
$103$	−2302.42	+	13057.7i	−0.217026	+	1.23081i	−0.877357	+	0.479839i	$0.840695\pi$
$104$	1553.24	−	1851.08i	0.143606	−	0.171142i
$105$		0			0
$106$	8797.30	+	3201.96i	0.782957	+	0.284973i
$107$		−	10520.6i		−	0.918907i	−0.888202	−	0.459453i	$-0.848045\pi$
$107$		−	10520.6i		−	0.918907i	0.888202	−	0.459453i	$-0.151955\pi$
$108$		0			0
$109$	−10635.3			−0.895153			−0.447576	−	0.894246i	$-0.647713\pi$
$109$	−10635.3			−0.895153			−0.447576	+	0.894246i	$0.647713\pi$
$110$	−752.671	+	2067.95i	−0.0622042	+	0.170905i
$111$		0			0
$112$	1218.05	+	1022.06i	0.0971022	+	0.0814784i
$113$	−13895.7	−	2450.19i	−1.08824	−	0.191885i	−0.399382	−	0.916785i	$-0.630775\pi$
$113$	−13895.7	−	2450.19i	−1.08824	−	0.191885i	−0.688855	+	0.724899i	$0.741886\pi$
$114$		0			0
$115$	11039.9	−	9263.56i	0.834773	−	0.700458i
$116$	9836.39	−	5679.04i	0.731004	−	0.422045i
$117$		0			0
$118$	6889.53	−	11933.0i	0.494795	−	0.857010i
$119$	9589.73	−	1690.93i	0.677193	−	0.119407i
$120$		0			0
$121$	−13441.1	+	4892.16i	−0.918046	+	0.334141i
$122$	−2135.88	−	5868.29i	−0.143502	−	0.394269i
$123$		0			0
$124$	1674.09	+	9494.25i	0.108877	+	0.617472i
$125$	−19991.6	−	11542.1i	−1.27946	−	0.738697i
$126$		0			0
$127$	5562.96	+	9635.34i	0.344904	+	0.597392i	0.985336	−	0.170623i	$-0.0545780\pi$
$127$	5562.96	+	9635.34i	0.344904	+	0.597392i	−0.640432	+	0.768015i	$0.721245\pi$
$128$	−930.856	−	1109.35i	−0.0568149	−	0.0677094i
$129$		0			0
$130$	2222.12	−	12602.3i	0.131487	−	0.745698i
$131$	1203.03	−	1433.72i	0.0701026	−	0.0835450i	−0.729853	−	0.683604i	$-0.760412\pi$
$131$	1203.03	−	1433.72i	0.0701026	−	0.0835450i	0.799956	+	0.600059i	$0.204856\pi$
$132$		0			0
$133$	9574.96	+	3485.00i	0.541295	+	0.197015i
$134$			9789.24i			0.545179i
$135$		0			0
$136$	−8868.68			−0.479492
$137$	6175.92	−	16968.2i	0.329049	−	0.904054i	−0.659304	−	0.751876i	$-0.729149\pi$
$137$	6175.92	−	16968.2i	0.329049	−	0.904054i	0.988353	−	0.152178i	$-0.0486287\pi$
$138$		0			0
$139$	12180.0	+	10220.3i	0.630404	+	0.528972i	0.901055	−	0.433706i	$-0.142794\pi$
$139$	12180.0	+	10220.3i	0.630404	+	0.528972i	−0.270650	+	0.962678i	$0.587239\pi$
$140$	8292.58	+	1462.21i	0.423091	+	0.0746024i
$141$		0			0
$142$	−14369.1	+	12057.1i	−0.712609	+	0.597950i
$143$	−1698.47	+	980.611i	−0.0830587	+	0.0479540i
$144$		0			0
$145$	30074.8	−	52091.1i	1.43043	−	2.47758i
$146$	−16407.7	+	2893.13i	−0.769738	+	0.135726i
$147$		0			0
$148$	−11352.4	+	4131.94i	−0.518280	+	0.188639i
$149$	−4838.44	−	13293.5i	−0.217938	−	0.598780i	0.781754	−	0.623587i	$-0.214325\pi$
$149$	−4838.44	−	13293.5i	−0.217938	−	0.598780i	−0.999692	+	0.0248069i	$0.992103\pi$
$150$		0			0
$151$	−1016.71	−	5766.02i	−0.0445904	−	0.252885i	0.954362	−	0.298653i	$-0.0965374\pi$
$151$	−1016.71	−	5766.02i	−0.0445904	−	0.252885i	−0.998952	+	0.0457686i	$0.985426\pi$
$152$	−8036.85	−	4640.08i	−0.347855	−	0.200834i
$153$		0			0
$154$	−645.264	−	1117.63i	−0.0272079	−	0.0471255i
$155$	32817.4	+	39110.2i	1.36597	+	1.62790i
$156$		0			0
$157$	−5308.10	+	30103.7i	−0.215347	+	1.22130i	0.664955	+	0.746883i	$0.268451\pi$
$157$	−5308.10	+	30103.7i	−0.215347	+	1.22130i	−0.880303	+	0.474412i	$0.842661\pi$
$158$	−4527.49	+	5395.65i	−0.181361	+	0.216137i
$159$		0			0
$160$	−7206.56	−	2622.97i	−0.281506	−	0.102460i
$161$			8451.31i			0.326041i
$162$		0			0
$163$	24783.8			0.932809			0.466405	−	0.884572i	$-0.345549\pi$
$163$	24783.8			0.932809			0.466405	+	0.884572i	$0.345549\pi$
$164$	1658.11	−	4555.63i	0.0616490	−	0.169379i
$165$		0			0
$166$	23992.5	+	20132.1i	0.870681	+	0.730588i
$167$	46851.0	+	8261.09i	1.67991	+	0.296213i	0.930608	−	0.366017i	$-0.119279\pi$
$167$	46851.0	+	8261.09i	1.67991	+	0.296213i	0.749301	+	0.662230i	$0.230390\pi$
$168$		0			0
$169$	−13142.7	+	11028.1i	−0.460164	+	0.386124i
$170$	−40674.0	+	23483.2i	−1.40741	+	0.812566i
$171$		0			0
$172$	7777.03	−	13470.2i	0.262880	−	0.455321i
$173$	−2045.69	+	360.711i	−0.0683515	+	0.0120522i	−0.207719	−	0.978188i	$-0.566604\pi$
$173$	−2045.69	+	360.711i	−0.0683515	+	0.0120522i	0.139368	+	0.990241i	$0.455493\pi$
$174$		0			0
$175$	27312.2	−	9940.84i	0.891828	−	0.324599i
$176$	401.997	+	1104.48i	0.0129777	+	0.0356559i
$177$		0			0
$178$	3449.39	+	19562.5i	0.108869	+	0.617424i
$179$	16467.1	+	9507.30i	0.513939	+	0.296723i	0.734451	−	0.678661i	$-0.237440\pi$
$179$	16467.1	+	9507.30i	0.513939	+	0.296723i	−0.220512	+	0.975384i	$0.570773\pi$
$180$		0			0
$181$	18376.7	+	31829.5i	0.560934	+	0.971566i	0.997415	+	0.0718525i	$0.0228911\pi$
$181$	18376.7	+	31829.5i	0.560934	+	0.971566i	−0.436482	+	0.899713i	$0.643776\pi$
$182$	4823.69	+	5748.65i	0.145625	+	0.173549i
$183$		0			0
$184$	1336.59	−	7580.18i	0.0394787	−	0.223895i
$185$	−41124.2	+	49009.9i	−1.20158	+	1.43199i
$186$		0			0
$187$	6763.96	+	2461.88i	0.193427	+	0.0704018i
$188$			25207.2i			0.713196i
$189$		0			0
$190$	−49145.4			−1.36137
$191$	2106.78	−	5788.32i	0.0577500	−	0.158667i	−0.907463	−	0.420132i	$-0.861984\pi$
$191$	2106.78	−	5788.32i	0.0577500	−	0.158667i	0.965213	+	0.261466i	$0.0842058\pi$
$192$		0			0
$193$	−24419.1	−	20490.1i	−0.655565	−	0.550084i	0.253189	−	0.967417i	$-0.418521\pi$
$193$	−24419.1	−	20490.1i	−0.655565	−	0.550084i	−0.908754	+	0.417333i	$0.862965\pi$
$194$	5615.34	+	990.136i	0.149201	+	0.0263082i
$195$		0			0
$196$	10931.4	−	9172.57i	0.284555	−	0.238770i
$197$	19300.3	−	11143.0i	0.497314	−	0.287124i	−0.230290	−	0.973122i	$-0.573967\pi$
$197$	19300.3	−	11143.0i	0.497314	−	0.287124i	0.727604	+	0.685998i	$0.240634\pi$
$198$		0			0
$199$	−7630.55	+	13216.5i	−0.192686	+	0.333742i	−0.946139	−	0.323759i	$-0.895053\pi$
$199$	−7630.55	+	13216.5i	−0.192686	+	0.333742i	0.753454	+	0.657501i	$0.228386\pi$
$200$	−26069.2	+	4596.70i	−0.651729	+	0.114917i
$201$		0			0
$202$	46213.4	−	16820.3i	1.13257	−	0.412222i
$203$	12064.2	+	33146.1i	0.292756	+	0.804340i
$204$		0			0
$205$	−4458.20	−	25283.7i	−0.106085	−	0.601636i
$206$	32478.1	+	18751.2i	0.765343	+	0.441871i
$207$		0			0
$208$	−3417.32	−	5918.97i	−0.0789876	−	0.136811i
$209$	4841.49	+	5769.86i	0.110837	+	0.132091i
$210$		0			0
$211$	−3131.77	+	17761.2i	−0.0703438	+	0.398939i	0.929223	+	0.369519i	$0.120477\pi$
$211$	−3131.77	+	17761.2i	−0.0703438	+	0.398939i	−0.999567	+	0.0294207i	$0.990634\pi$
$212$	17020.6	−	20284.4i	0.378708	−	0.451327i
$213$		0			0
$214$	−27962.1	−	10177.4i	−0.610580	−	0.222233i
$215$		−	82370.4i		−	1.78195i
$216$		0			0
$217$	−29939.9			−0.635815
$218$	−10288.4	+	28267.1i	−0.216488	+	0.594796i
$219$		0			0
$220$	4768.18	+	4000.98i	0.0985161	+	0.0826648i
$221$	−41220.3	−	7268.25i	−0.843969	−	0.148814i
$222$		0			0
$223$	26982.1	−	22640.7i	0.542583	−	0.455282i	−0.329837	−	0.944038i	$-0.606994\pi$
$223$	26982.1	−	22640.7i	0.542583	−	0.455282i	0.872420	+	0.488756i	$0.162549\pi$
$224$	3894.81	−	2248.67i	0.0776230	−	0.0448157i
$225$		0			0
$226$	−19954.6	+	34562.4i	−0.390685	+	0.676686i
$227$	−43109.9	+	7601.44i	−0.836614	+	0.147518i	−0.575512	−	0.817793i	$-0.695197\pi$
$227$	−43109.9	+	7601.44i	−0.836614	+	0.147518i	−0.261102	+	0.965311i	$0.584086\pi$
$228$		0			0
$229$	−36596.7	+	13320.1i	−0.697864	+	0.254002i	−0.666499	−	0.745506i	$-0.732208\pi$
$229$	−36596.7	+	13320.1i	−0.697864	+	0.254002i	−0.0313656	+	0.999508i	$0.509986\pi$
$230$	−13941.4	−	38303.7i	−0.263543	−	0.724078i
$231$		0			0
$232$	−5578.54	−	31637.5i	−0.103644	−	0.587795i
$233$	13129.6	+	7580.39i	0.241847	+	0.139630i	0.616025	−	0.787726i	$-0.288742\pi$
$233$	13129.6	+	7580.39i	0.241847	+	0.139630i	−0.374178	+	0.927357i	$0.622075\pi$
$234$		0			0
$235$	66745.5	+	115607.i	1.20861	+	2.09337i
$236$	−25051.4	−	29855.1i	−0.449788	−	0.536036i
$237$		0			0
$238$	4782.67	−	27123.9i	0.0844338	−	0.478848i
$239$	−12810.9	+	15267.4i	−0.224277	+	0.267282i	−0.866435	−	0.499289i	$-0.833595\pi$
$239$	−12810.9	+	15267.4i	−0.224277	+	0.267282i	0.642159	+	0.766572i	$0.278039\pi$
$240$		0			0
$241$	61204.6	+	22276.7i	1.05378	+	0.383545i	0.810088	−	0.586308i	$-0.199419\pi$
$241$	61204.6	+	22276.7i	1.05378	+	0.383545i	0.243692	+	0.969853i	$0.421641\pi$
$242$			40457.0i			0.690818i
$243$		0			0
$244$	−17663.3			−0.296682
$245$	25846.6	−	71012.8i	0.430597	−	1.18305i
$246$		0			0
$247$	−33551.3	−	28152.9i	−0.549941	−	0.461455i
$248$	26853.8	+	4735.05i	0.436618	+	0.0769876i
$249$		0			0
$250$	−50016.8	+	41969.0i	−0.800268	+	0.671505i
$251$	75304.6	−	43477.1i	1.19529	−	0.690102i	0.235790	−	0.971804i	$-0.424232\pi$
$251$	75304.6	−	43477.1i	1.19529	−	0.690102i	0.959502	+	0.281702i	$0.0908990\pi$
$252$		0			0
$253$	−3123.59	+	5410.22i	−0.0487992	+	0.0845227i
$254$	30990.8	−	5464.51i	0.480358	−	0.0847001i
$255$		0			0
$256$	−3848.98	+	1400.91i	−0.0587308	+	0.0213763i
$257$	−12558.6	−	34504.6i	−0.190141	−	0.522409i	0.807589	−	0.589746i	$-0.200772\pi$
$257$	−12558.6	−	34504.6i	−0.190141	−	0.522409i	−0.997730	+	0.0673367i	$0.978550\pi$
$258$		0			0
$259$	−6514.99	−	36948.3i	−0.0971212	−	0.550802i
$260$	−31345.4	−	18097.3i	−0.463689	−	0.267711i
$261$		0			0
$262$	−2646.82	−	4584.43i	−0.0385586	−	0.0667855i
$263$	−44991.3	−	53618.5i	−0.650455	−	0.775182i	0.335528	−	0.942030i	$-0.391085\pi$
$263$	−44991.3	−	53618.5i	−0.650455	−	0.775182i	−0.985983	+	0.166849i	$0.946641\pi$
$264$		0			0
$265$	24350.4	−	138098.i	0.346748	−	1.96651i
$266$	18525.2	−	22077.5i	0.261819	−	0.312023i
$267$		0			0
$268$	26018.4	+	9469.91i	0.362252	+	0.131849i
$269$		−	27399.8i		−	0.378654i	−0.981914	−	0.189327i	$-0.939369\pi$
$269$		−	27399.8i		−	0.378654i	0.981914	−	0.189327i	$-0.0606306\pi$
$270$		0			0
$271$	−80278.7			−1.09310			−0.546552	−	0.837425i	$-0.684060\pi$
$271$	−80278.7			−1.09310			−0.546552	+	0.837425i	$0.684060\pi$
$272$	−8579.37	+	23571.6i	−0.115963	+	0.318605i
$273$		0			0
$274$	−39124.5	−	32829.3i	−0.521132	−	0.437281i
$275$	21158.4	+	3730.80i	0.279781	+	0.0493329i
$276$		0			0
$277$	14943.4	−	12539.0i	0.194756	−	0.163420i	−0.540195	−	0.841540i	$-0.681650\pi$
$277$	14943.4	−	12539.0i	0.194756	−	0.163420i	0.734951	+	0.678120i	$0.237205\pi$
$278$	38946.7	−	22485.9i	0.503942	−	0.290951i
$279$		0			0
$280$	11908.4	−	20626.0i	0.151893	−	0.263086i
$281$	6479.42	−	1142.50i	0.0820585	−	0.0144691i	−0.132468	−	0.991187i	$-0.542290\pi$
$281$	6479.42	−	1142.50i	0.0820585	−	0.0144691i	0.214527	+	0.976718i	$0.431179\pi$
$282$		0			0
$283$	22664.0	−	8249.01i	0.282985	−	0.102998i	−0.196628	−	0.980478i	$-0.562999\pi$
$283$	22664.0	−	8249.01i	0.282985	−	0.102998i	0.479613	+	0.877480i	$0.340777\pi$
$284$	18145.6	+	49854.6i	0.224975	+	0.618114i
$285$		0			0
$286$	963.256	+	5462.90i	0.0117763	+	0.0667869i
$287$	13038.7	+	7527.89i	0.158296	+	0.0913923i
$288$		0			0
$289$	35049.5	+	60707.6i	0.419649	+	0.726854i
$290$	−109357.	−	130326.i	−1.30032	−	1.54966i
$291$		0			0
$292$	−8183.00	+	46408.1i	−0.0959725	+	0.544287i
$293$	−40800.2	+	48623.8i	−0.475256	+	0.566388i	−0.949404	−	0.314057i	$-0.898312\pi$
$293$	−40800.2	+	48623.8i	−0.475256	+	0.566388i	0.474148	+	0.880445i	$0.342756\pi$
$294$		0			0
$295$	−193945.	−	70590.1i	−2.22861	−	0.811147i
$296$			34170.2i			0.389999i
$297$		0			0
$298$	−40012.8			−0.450574
$299$	12424.5	−	34136.1i	0.138975	−	0.381832i
$300$		0			0
$301$	37003.2	+	31049.3i	0.408419	+	0.342704i
$302$	−16308.8	−	2875.68i	−0.178816	−	0.0315302i
$303$		0			0
$304$	−20107.3	+	16872.0i	−0.217574	+	0.182566i
$305$	−81008.2	+	46770.1i	−0.870822	+	0.502769i
$306$		0			0
$307$	26678.0	−	46207.7i	0.283059	−	0.490272i	−0.689078	−	0.724687i	$-0.741984\pi$
$307$	26678.0	−	46207.7i	0.283059	−	0.490272i	0.972137	+	0.234415i	$0.0753175\pi$
$308$	−3594.71	+	633.844i	−0.0378933	+	0.00668161i
$309$		0			0
$310$	135696.	−	49389.3i	1.41203	−	0.513937i
$311$	10062.8	+	27647.2i	0.104039	+	0.285845i	0.980780	−	0.195118i	$-0.0625091\pi$
$311$	10062.8	+	27647.2i	0.104039	+	0.285845i	−0.876741	+	0.480964i	$0.840287\pi$
$312$		0			0
$313$	−25540.7	−	144848.i	−0.260701	−	1.47851i	−0.781002	−	0.624528i	$-0.785291\pi$
$313$	−25540.7	−	144848.i	−0.260701	−	1.47851i	0.520301	−	0.853983i	$-0.325820\pi$
$314$	74876.3	+	43229.8i	0.759425	+	0.438454i
$315$		0			0
$316$	9961.05	+	17253.0i	0.0997541	+	0.172779i
$317$	−73982.5	−	88168.9i	−0.736225	−	0.877399i	0.259874	−	0.965643i	$-0.416319\pi$
$317$	−73982.5	−	88168.9i	−0.736225	−	0.877399i	−0.996099	+	0.0882440i	$0.971874\pi$
$318$		0			0
$319$	−4527.69	+	25677.8i	−0.0444934	+	0.252334i
$320$	−13943.0	+	16616.6i	−0.136162	+	0.162271i
$321$		0			0
$322$	22462.3	+	8175.62i	0.216642	+	0.0788513i
$323$			160747.i			1.54077i
$324$		0			0
$325$	−124933.			−1.18279
$326$	23975.3	−	65871.7i	0.225595	−	0.619817i
$327$		0			0
$328$	−10504.2	−	8814.04i	−0.0976368	−	0.0819270i
$329$	−77093.4	−	13593.6i	−0.712238	−	0.125587i
$330$		0			0
$331$	−45867.3	+	38487.3i	−0.418646	+	0.351286i	−0.827648	−	0.561248i	$-0.810322\pi$
$331$	−45867.3	+	38487.3i	−0.418646	+	0.351286i	0.409001	+	0.912534i	$0.365877\pi$
$332$	76718.0	−	44293.1i	0.696019	−	0.401847i
$333$		0			0
$334$	67279.4	−	116531.i	0.603100	−	1.04460i
$335$	144402.	−	25462.0i	1.28672	−	0.226883i
$336$		0			0
$337$	−56576.9	+	20592.3i	−0.498172	+	0.181320i	−0.578872	−	0.815419i	$-0.696507\pi$
$337$	−56576.9	+	20592.3i	−0.498172	+	0.181320i	0.0806994	+	0.996738i	$0.474285\pi$
$338$	16597.0	+	45599.8i	0.145277	+	0.399144i
$339$		0			0
$340$	23067.6	+	130823.i	0.199546	+	1.13168i
$341$	−19166.4	−	11065.7i	−0.164828	−	0.0951637i
$342$		0			0
$343$	51984.1	+	90039.1i	0.441857	+	0.765320i
$344$	−28278.5	−	33701.0i	−0.238968	−	0.284791i
$345$		0			0
$346$	−1020.24	+	5786.09i	−0.00852220	+	0.0483318i
$347$	16062.2	−	19142.1i	0.133397	−	0.158976i	−0.695211	−	0.718806i	$-0.744689\pi$
$347$	16062.2	−	19142.1i	0.133397	−	0.158976i	0.828608	+	0.559830i	$0.189134\pi$
$348$		0			0
$349$	−127113.	−	46265.2i	−1.04361	−	0.379843i	−0.237362	−	0.971421i	$-0.576283\pi$
$349$	−127113.	−	46265.2i	−1.04361	−	0.379843i	−0.806247	+	0.591579i	$0.798505\pi$
$350$		−	82208.5i		−	0.671089i
$351$		0			0
$352$	3324.42			0.0268306
$353$	−70858.1	+	194681.i	−0.568643	+	1.56233i	0.237981	+	0.971270i	$0.423515\pi$
$353$	−70858.1	+	194681.i	−0.568643	+	1.56233i	−0.806624	+	0.591065i	$0.798708\pi$
$354$		0			0
$355$	215229.	+	180599.i	1.70783	+	1.43304i
$356$	55331.0	+	9756.35i	0.436585	+	0.0769817i
$357$		0			0
$358$	41199.0	−	34570.0i	0.321455	−	0.269733i
$359$	9886.99	−	5708.26i	0.0767141	−	0.0442909i	−0.461152	−	0.887321i	$-0.652564\pi$
$359$	9886.99	−	5708.26i	0.0767141	−	0.0442909i	0.537866	+	0.843030i	$0.319230\pi$
$360$		0			0
$361$	−18942.3	+	32809.0i	−0.145351	+	0.251755i
$362$	102375.	−	18051.5i	0.781228	−	0.137752i
$363$		0			0
$364$	19945.4	−	7259.52i	0.150536	−	0.0547905i
$365$	85353.5	+	234507.i	0.640672	+	1.76023i
$366$		0			0
$367$	32552.8	+	184616.i	0.241688	+	1.37068i	0.828059	+	0.560640i	$0.189445\pi$
$367$	32552.8	+	184616.i	0.241688	+	1.37068i	−0.586371	+	0.810043i	$0.699444\pi$
$368$	−18854.0	−	10885.4i	−0.139222	−	0.0803799i
$369$		0			0
$370$	90478.4	+	156713.i	0.660908	+	1.14473i
$371$	52858.8	+	62994.6i	0.384034	+	0.457674i
$372$		0			0
$373$	13751.3	−	77987.7i	0.0988387	−	0.560542i	−0.894665	−	0.446739i	$-0.852585\pi$
$373$	13751.3	−	77987.7i	0.0988387	−	0.560542i	0.993503	−	0.113804i	$-0.0363035\pi$
$374$	13086.6	−	15596.0i	0.0935587	−	0.111499i
$375$		0			0
$376$	66997.0	+	24384.9i	0.473892	+	0.172483i
$377$		−	151618.i		−	1.06676i
$378$		0			0
$379$	−122815.			−0.855015			−0.427507	−	0.904012i	$-0.640608\pi$
$379$	−122815.			−0.855015			−0.427507	+	0.904012i	$0.640608\pi$
$380$	−47542.2	+	130621.i	−0.329240	+	0.904579i
$381$		0			0
$382$	−13346.5	−	11199.0i	−0.0914617	−	0.0767455i
$383$	−95401.9	−	16821.9i	−0.650369	−	0.114678i	−0.161276	−	0.986909i	$-0.551561\pi$
$383$	−95401.9	−	16821.9i	−0.650369	−	0.114678i	−0.489093	+	0.872232i	$0.662672\pi$
$384$		0			0
$385$	−14807.9	+	12425.3i	−0.0999015	+	0.0838273i
$386$	−78082.2	+	45080.8i	−0.524055	+	0.302564i
$387$		0			0
$388$	8063.80	−	13966.9i	0.0535644	−	0.0927762i
$389$	−207400.	+	36570.3i	−1.37060	+	0.241674i	−0.810008	−	0.586419i	$-0.800537\pi$
$389$	−207400.	+	36570.3i	−1.37060	+	0.241674i	−0.560591	+	0.828093i	$0.689426\pi$
$390$		0			0
$391$	−125286.	+	45600.4i	−0.819500	+	0.298274i
$392$	−13804.5	−	37927.5i	−0.0898355	−	0.246821i
$393$		0			0
$394$	−10945.8	−	62076.8i	−0.0705108	−	0.399886i
$395$	91367.8	+	52751.2i	0.585597	+	0.338095i
$396$		0			0
$397$	96424.6	+	167012.i	0.611796	+	1.05966i	0.990938	+	0.134323i	$0.0428860\pi$
$397$	96424.6	+	167012.i	0.611796	+	1.05966i	−0.379141	+	0.925339i	$0.623781\pi$
$398$	27745.9	+	33066.2i	0.175159	+	0.208746i
$399$		0			0
$400$	−13001.4	+	73734.7i	−0.0812589	+	0.460842i
$401$	15527.7	−	18505.2i	0.0965650	−	0.115082i	−0.715598	−	0.698513i	$-0.753846\pi$
$401$	15527.7	−	18505.2i	0.0965650	−	0.115082i	0.812163	+	0.583431i	$0.198290\pi$
$402$		0			0
$403$	120932.	+	44015.6i	0.744612	+	0.271017i
$404$		−	139100.i		−	0.852245i
$405$		0			0
$406$	99768.0			0.605256
$407$	9485.39	−	26060.9i	0.0572620	−	0.157326i
$408$		0			0
$409$	−129469.	−	108637.i	−0.773961	−	0.649430i	0.167759	−	0.985828i	$-0.446347\pi$
$409$	−129469.	−	108637.i	−0.773961	−	0.649430i	−0.941720	+	0.336398i	$0.890791\pi$
$410$	−71513.2	−	12609.7i	−0.425421	−	0.0750131i
$411$		0			0
$412$	81256.7	−	68182.5i	0.478701	−	0.401678i
$413$	104818.	−	60516.7i	0.614520	−	0.354793i
$414$		0			0
$415$	234565.	−	406279.i	1.36197	−	2.35900i
$416$	−19037.6	+	3356.84i	−0.110008	+	0.0193974i
$417$		0			0
$418$	20019.0	−	7286.32i	0.114575	−	0.0417019i
$419$	−16582.6	−	45560.4i	−0.0944551	−	0.259513i	0.883463	−	0.468500i	$-0.155206\pi$
$419$	−16582.6	−	45560.4i	−0.0944551	−	0.259513i	−0.977918	+	0.208987i	$0.932983\pi$
$420$		0			0
$421$	−31948.4	−	181189.i	−0.180254	−	1.02227i	−0.931903	−	0.362708i	$-0.881852\pi$
$421$	−31948.4	−	181189.i	−0.180254	−	1.02227i	0.751649	−	0.659564i	$-0.229259\pi$
$422$	44177.0	+	25505.6i	0.248068	+	0.143222i
$423$		0			0
$424$	−37447.6	−	64861.1i	−0.208301	−	0.360788i
$425$	294735.	+	351252.i	1.63175	+	1.94465i
$426$		0			0
$427$	9525.38	−	54021.1i	0.0522428	−	0.296284i
$428$	−54099.9	+	64473.8i	−0.295331	+	0.351962i
$429$		0			0
$430$	−218928.	−	79683.4i	−1.18404	−	0.430954i
$431$			137027.i			0.737651i	0.929499	+	0.368825i	$0.120240\pi$
$431$			137027.i			0.737651i	−0.929499	+	0.368825i	$0.879760\pi$
$432$		0			0
$433$	−113894.			−0.607471			−0.303735	−	0.952756i	$-0.598234\pi$
$433$	−113894.			−0.607471			−0.303735	+	0.952756i	$0.598234\pi$
$434$	−28963.2	+	79575.8i	−0.153768	+	0.422475i
$435$		0			0
$436$	65177.0	+	54690.0i	0.342863	+	0.287697i
$437$	−137393.	−	24226.1i	−0.719452	−	0.126859i
$438$		0			0
$439$	220226.	−	184792.i	1.14272	−	0.958857i	0.143197	−	0.989694i	$-0.454262\pi$
$439$	220226.	−	184792.i	1.14272	−	0.958857i	0.999524	+	0.0308371i	$0.00981731\pi$
$440$	15246.6	−	8802.65i	0.0787533	−	0.0454682i
$441$		0			0
$442$	−59193.6	+	102526.i	−0.302991	+	0.524796i
$443$	−178409.	+	31458.4i	−0.909098	+	0.160298i	−0.608594	−	0.793482i	$-0.708266\pi$
$443$	−178409.	+	31458.4i	−0.909098	+	0.160298i	−0.300504	+	0.953781i	$0.597155\pi$
$444$		0			0
$445$	279596.	−	101764.i	1.41192	−	0.513897i
$446$	−34073.7	−	93616.7i	−0.171297	−	0.470634i
$447$		0			0
$448$	−2208.88	−	12527.2i	−0.0110056	−	0.0624161i
$449$	−210245.	−	121385.i	−1.04288	−	0.602104i	−0.122229	−	0.992502i	$-0.539004\pi$
$449$	−210245.	−	121385.i	−1.04288	−	0.602104i	−0.920646	+	0.390398i	$0.872338\pi$
$450$		0			0
$451$	5564.59	+	9638.16i	0.0273578	+	0.0473850i
$452$	72558.1	+	86471.4i	0.355148	+	0.423249i
$453$		0			0
$454$	−21500.1	+	121933.i	−0.104311	+	0.591576i
$455$	72252.3	−	86106.9i	0.349003	−	0.415925i
$456$		0			0
$457$	253917.	+	92418.3i	1.21579	+	0.442513i	0.868710	−	0.495321i	$-0.164950\pi$
$457$	253917.	+	92418.3i	1.21579	+	0.442513i	0.347084	+	0.937834i	$0.387172\pi$
$458$			110154.i			0.525134i
$459$		0			0
$460$	−115292.			−0.544860
$461$	103651.	−	284779.i	0.487722	−	1.34000i	−0.415016	−	0.909814i	$-0.636224\pi$
$461$	103651.	−	284779.i	0.487722	−	1.34000i	0.902738	−	0.430190i	$-0.141554\pi$
$462$		0			0
$463$	27480.3	+	23058.7i	0.128192	+	0.107566i	0.704629	−	0.709575i	$-0.251113\pi$
$463$	27480.3	+	23058.7i	0.128192	+	0.107566i	−0.576438	+	0.817141i	$0.695558\pi$
$464$	−89484.2	−	15778.5i	−0.415634	−	0.0732874i
$465$		0			0
$466$	32848.9	−	27563.5i	0.151269	−	0.126929i
$467$	−8908.51	+	5143.33i	−0.0408481	+	0.0235836i	−0.520285	−	0.853993i	$-0.674174\pi$
$467$	−8908.51	+	5143.33i	−0.0408481	+	0.0235836i	0.479437	+	0.877576i	$0.340841\pi$
$468$		0			0
$469$	−42993.7	+	74467.3i	−0.195461	+	0.338548i
$470$	371833.	−	65564.3i	1.68327	−	0.296805i
$471$		0			0
$472$	−103585.	+	37701.7i	−0.464955	+	0.169230i
$473$	12212.3	+	33553.0i	0.0545851	+	0.149971i
$474$		0			0
$475$	83316.5	+	472511.i	0.369270	+	2.09423i
$476$	−67464.5	−	38950.7i	−0.297757	−	0.171910i
$477$		0			0
$478$	28185.6	+	48818.9i	0.123359	+	0.213664i
$479$	47147.7	+	56188.5i	0.205490	+	0.244893i	0.858940	−	0.512076i	$-0.171124\pi$
$479$	47147.7	+	56188.5i	0.205490	+	0.244893i	−0.653450	+	0.756969i	$0.726679\pi$
$480$		0			0
$481$	−28003.9	+	158818.i	−0.121040	+	0.686450i
$482$	118416.	−	141123.i	0.509702	−	0.607440i
$483$		0			0
$484$	107529.	+	39137.3i	0.459023	+	0.167071i
$485$		−	85407.7i		−	0.363089i
$486$		0			0
$487$	380836.			1.60576			0.802879	−	0.596143i	$-0.203301\pi$
$487$	380836.			1.60576			0.802879	+	0.596143i	$0.203301\pi$
$488$	−17087.1	+	46946.4i	−0.0717510	+	0.197134i
$489$		0			0
$490$	−163738.	−	137393.i	−0.681958	−	0.572231i
$491$	49659.2	+	8756.25i	0.205985	+	0.0363208i	0.275689	−	0.961247i	$-0.411094\pi$
$491$	49659.2	+	8756.25i	0.205985	+	0.0363208i	−0.0697032	+	0.997568i	$0.522205\pi$
$492$		0			0
$493$	−426278.	+	357690.i	−1.75388	+	1.47168i
$494$	−107283.	+	61939.9i	−0.439620	+	0.253815i
$495$		0			0
$496$	38562.8	−	66792.8i	0.156749	−	0.271498i
$497$	−162260.	+	28610.8i	−0.656900	+	0.115829i
$498$		0			0
$499$	−337063.	+	122681.i	−1.35366	+	0.492693i	−0.914089	−	0.405514i	$-0.867093\pi$
$499$	−337063.	+	122681.i	−1.35366	+	0.492693i	−0.439573	+	0.898207i	$0.644870\pi$
$500$	63162.3	+	173537.i	0.252649	+	0.694148i
$501$		0			0
$502$	−42707.7	−	242207.i	−0.169472	−	0.961125i
$503$	97150.7	+	56090.0i	0.383981	+	0.221692i	0.679549	−	0.733630i	$-0.262176\pi$
$503$	97150.7	+	56090.0i	0.383981	+	0.221692i	−0.295568	+	0.955322i	$0.595509\pi$
$504$		0			0
$505$	−368319.	−	637948.i	−1.44425	−	2.50151i
$506$	11357.9	+	13535.8i	0.0443604	+	0.0528667i
$507$		0			0
$508$	15456.0	−	87655.2i	0.0598920	−	0.339665i
$509$	229653.	−	273689.i	0.886413	−	1.05639i	−0.111624	−	0.993751i	$-0.535605\pi$
$509$	229653.	−	273689.i	0.886413	−	1.05639i	0.998036	−	0.0626352i	$-0.0199505\pi$
$510$		0			0
$511$	−137521.	−	50053.6i	−0.526656	−	0.191687i
$512$			11585.2i			0.0441942i
$513$		0			0
$514$	−103857.			−0.393106
$515$	192125.	−	527860.i	0.724386	−	1.99023i
$516$		0			0
$517$	−44328.2	−	37195.7i	−0.165844	−	0.139159i
$518$	−104506.	−	18427.2i	−0.389476	−	0.0686751i
$519$		0			0
$520$	−78422.7	+	65804.5i	−0.290025	+	0.243360i
$521$	−278941.	+	161047.i	−1.02763	+	0.593302i	−0.916305	−	0.400482i	$-0.868843\pi$
$521$	−278941.	+	161047.i	−1.02763	+	0.593302i	−0.111325	+	0.993784i	$0.535509\pi$
$522$		0			0
$523$	108461.	−	187860.i	0.396525	−	0.686801i	−0.596770	−	0.802413i	$-0.703549\pi$
$523$	108461.	−	187860.i	0.396525	−	0.686801i	0.993295	+	0.115611i	$0.0368827\pi$
$524$	−14745.2	+	2599.98i	−0.0537017	+	0.00946906i
$525$		0			0
$526$	−186034.	+	67710.8i	−0.672389	+	0.244729i
$527$	−161545.	−	443842.i	−0.581666	−	1.59811i
$528$		0			0
$529$	28500.4	+	161634.i	0.101845	+	0.577591i
$530$	−343488.	−	198313.i	−1.22281	−	0.705991i
$531$		0			0
$532$	−40757.8	−	70594.7i	−0.144008	−	0.249430i
$533$	−41598.3	−	49574.9i	−0.146427	−	0.174505i
$534$		0			0
$535$	−77397.5	+	438943.i	−0.270408	+	1.53356i
$536$	50339.2	−	59991.9i	0.175217	−	0.208816i
$537$		0			0
$538$	−72824.6	−	26506.0i	−0.251602	−	0.0915755i
$539$			32758.6i			0.112758i
$540$		0			0
$541$	−316743.			−1.08221			−0.541106	−	0.840955i	$-0.681994\pi$
$541$	−316743.			−1.08221			−0.541106	+	0.840955i	$0.681994\pi$
$542$	−77659.9	+	213369.i	−0.264362	+	0.726327i
$543$		0			0
$544$	54350.4	+	45605.4i	0.183656	+	0.154106i
$545$	443730.	+	78241.6i	1.49392	+	0.263418i
$546$		0			0
$547$	39894.6	−	33475.5i	0.133333	−	0.111880i	−0.573682	−	0.819078i	$-0.694486\pi$
$547$	39894.6	−	33475.5i	0.133333	−	0.111880i	0.707016	+	0.707198i	$0.250041\pi$
$548$	−125104.	+	72228.7i	−0.416590	+	0.240519i
$549$		0			0
$550$	30384.1	−	52626.8i	0.100443	−	0.173973i
$551$	−573438.	+	101113.i	−1.88879	+	0.333045i
$552$		0			0
$553$	−58138.3	+	21160.6i	−0.190113	+	0.0691955i
$554$	−18870.9	−	51847.5i	−0.0614857	−	0.168930i
$555$		0			0
$556$	−22087.9	−	125267.i	−0.0714505	−	0.405216i
$557$	−142300.	−	82157.1i	−0.458665	−	0.264810i	0.252818	−	0.967514i	$-0.418643\pi$
$557$	−142300.	−	82157.1i	−0.458665	−	0.264810i	−0.711483	+	0.702704i	$0.751976\pi$
$558$		0			0
$559$	−103815.	−	179813.i	−0.332228	−	0.575435i
$560$	−43300.8	−	51603.9i	−0.138077	−	0.164553i
$561$		0			0
$562$	3231.47	−	18326.6i	0.0102312	−	0.0580241i
$563$	297776.	−	354876.i	0.939449	−	1.11959i	−0.0532025	−	0.998584i	$-0.516943\pi$
$563$	297776.	−	354876.i	0.939449	−	1.11959i	0.992652	−	0.121008i	$-0.0386127\pi$
$564$		0			0
$565$	561736.	+	204455.i	1.75969	+	0.640473i
$566$		−	68217.4i		−	0.212943i
$567$		0			0
$568$	150060.			0.465123
$569$	12912.6	−	35477.2i	0.0398833	−	0.109578i	−0.918152	−	0.396227i	$-0.870319\pi$
$569$	12912.6	−	35477.2i	0.0398833	−	0.109578i	0.958036	+	0.286649i	$0.0925414\pi$
$570$		0			0
$571$	−355124.	−	297984.i	−1.08920	−	0.913948i	−0.0925485	−	0.995708i	$-0.529501\pi$
$571$	−355124.	−	297984.i	−1.08920	−	0.913948i	−0.996652	+	0.0817604i	$0.973946\pi$
$572$	15451.4	+	2724.50i	0.0472254	+	0.00832712i
$573$		0			0
$574$	32621.4	−	27372.6i	0.0990099	−	0.0830792i
$575$	−344639.	+	198977.i	−1.04239	+	0.601822i
$576$		0			0
$577$	92607.3	−	160401.i	0.278159	−	0.481786i	−0.692768	−	0.721161i	$-0.743609\pi$
$577$	92607.3	−	160401.i	0.278159	−	0.481786i	0.970927	+	0.239374i	$0.0769423\pi$
$578$	195258.	−	34429.2i	0.584458	−	0.103056i
$579$		0			0
$580$	−452177.	+	164579.i	−1.34416	+	0.489236i
$581$	94093.4	+	258520.i	0.278745	+	0.765845i
$582$		0			0
$583$	10555.5	+	59863.4i	0.0310558	+	0.176126i
$584$	115430.	+	66643.4i	0.338448	+	0.195403i
$585$		0			0
$586$	89765.6	+	155479.i	0.261406	+	0.452768i
$587$	133194.	+	158735.i	0.386553	+	0.460676i	0.923871	−	0.382704i	$-0.125007\pi$
$587$	133194.	+	158735.i	0.386553	+	0.460676i	−0.537318	+	0.843380i	$0.680562\pi$
$588$		0			0
$589$	85824.1	−	486733.i	0.247388	−	1.40301i
$590$	−375236.	+	447189.i	−1.07795	+	1.28466i
$591$		0			0
$592$	90819.3	+	33055.5i	0.259140	+	0.0943193i
$593$			405120.i			1.15206i	0.817429	+	0.576029i	$0.195399\pi$
$593$			405120.i			1.15206i	−0.817429	+	0.576029i	$0.804601\pi$
$594$		0			0
$595$	−412546.			−1.16530
$596$	−38707.5	+	106348.i	−0.108969	+	0.299390i
$597$		0			0
$598$	−78709.5	−	66045.1i	−0.220103	−	0.184688i
$599$	221080.	+	38982.4i	0.616165	+	0.108646i	0.473015	−	0.881055i	$-0.343166\pi$
$599$	221080.	+	38982.4i	0.616165	+	0.108646i	0.143150	+	0.989701i	$0.454277\pi$
$600$		0			0
$601$	396010.	−	332292.i	1.09637	−	0.919964i	0.0991945	−	0.995068i	$-0.468373\pi$
$601$	396010.	−	332292.i	1.09637	−	0.919964i	0.997176	+	0.0751043i	$0.0239290\pi$
$602$	118321.	−	68312.4i	0.326488	−	0.188498i
$603$		0			0
$604$	−23419.9	+	40564.4i	−0.0641965	+	0.111192i
$605$	596785.	−	105229.i	1.63045	−	0.287492i
$606$		0			0
$607$	548701.	−	199711.i	1.48922	−	0.542031i	0.535975	−	0.844234i	$-0.319944\pi$
$607$	548701.	−	199711.i	1.48922	−	0.542031i	0.953244	+	0.302203i	$0.0977220\pi$
$608$	25392.0	+	69763.9i	0.0686894	+	0.188723i
$609$		0			0
$610$	45942.4	+	260552.i	0.123468	+	0.700221i
$611$	291407.	+	168244.i	0.780582	+	0.450669i
$612$		0			0
$613$	359959.	+	623468.i	0.957927	+	1.65918i	0.727524	+	0.686082i	$0.240671\pi$
$613$	359959.	+	623468.i	0.957927	+	1.65918i	0.230403	+	0.973095i	$0.425996\pi$
$614$	−97005.4	−	115607.i	−0.257312	−	0.306652i
$615$		0			0
$616$	−1792.78	+	10167.4i	−0.00472461	+	0.0267946i
$617$	258721.	−	308331.i	0.679611	−	0.809929i	−0.310446	−	0.950591i	$-0.600478\pi$
$617$	258721.	−	308331.i	0.679611	−	0.809929i	0.990058	+	0.140662i	$0.0449229\pi$
$618$		0			0
$619$	−446744.	−	162601.i	−1.16594	−	0.424368i	−0.314726	−	0.949183i	$-0.601913\pi$
$619$	−446744.	−	162601.i	−1.16594	−	0.424368i	−0.851217	+	0.524814i	$0.824135\pi$
$620$		−	408438.i		−	1.06253i
$621$		0			0
$622$	83216.7			0.215095
$623$	−59677.4	+	163962.i	−0.153757	+	0.422443i
$624$		0			0
$625$	189072.	+	158650.i	0.484023	+	0.406144i
$626$	−409693.	−	72239.9i	−1.04547	−	0.184344i
$627$		0			0
$628$	187332.	−	157190.i	0.475000	−	0.398572i
$629$	512586.	−	295942.i	1.29558	−	0.748006i
$630$		0			0
$631$	−126509.	+	219120.i	−0.317733	+	0.550329i	−0.980015	−	0.198925i	$-0.936255\pi$
$631$	−126509.	+	219120.i	−0.317733	+	0.550329i	0.662282	+	0.749255i	$0.269588\pi$
$632$	55492.2	−	9784.76i	0.138930	−	0.0244972i
$633$		0			0
$634$	−305909.	+	111342.i	−0.761051	+	0.277000i
$635$	−161215.	−	442935.i	−0.399814	−	1.09848i
$636$		0			0
$637$	−33078.0	−	187595.i	−0.0815193	−	0.462319i
$638$	63867.8	+	36874.1i	0.156906	+	0.0905899i
$639$		0			0
$640$	30676.3	+	53132.8i	0.0748932	+	0.129719i
$641$	262760.	+	313145.i	0.639504	+	0.762132i	0.984292	−	0.176549i	$-0.0564934\pi$
$641$	262760.	+	313145.i	0.639504	+	0.762132i	−0.344787	+	0.938681i	$0.612049\pi$
$642$		0			0
$643$	−24638.0	+	139729.i	−0.0595915	+	0.337960i	−0.999998	−	0.00209281i	$-0.999334\pi$
$643$	−24638.0	+	139729.i	−0.0595915	+	0.337960i	0.940406	+	0.340053i	$0.110445\pi$
$644$	43459.2	−	51792.6i	0.104788	−	0.124881i
$645$		0			0
$646$	427243.	+	155504.i	1.02379	+	0.372628i
$647$			340407.i			0.813186i	0.913609	+	0.406593i	$0.133283\pi$
$647$			340407.i			0.813186i	−0.913609	+	0.406593i	$0.866717\pi$
$648$		0			0
$649$	89467.5			0.212411
$650$	−120857.	+	332053.i	−0.286053	+	0.785923i
$651$		0			0
$652$	−151884.	−	127446.i	−0.357287	−	0.299799i
$653$	−413322.	−	72879.9i	−0.969310	−	0.170915i	−0.333491	−	0.942753i	$-0.608227\pi$
$653$	−413322.	−	72879.9i	−0.969310	−	0.170915i	−0.635819	+	0.771838i	$0.719338\pi$
$654$		0			0
$655$	−60740.8	+	50967.6i	−0.141579	+	0.118799i
$656$	−33587.9	+	19392.0i	−0.0780504	+	0.0450624i
$657$		0			0
$658$	−110708.	+	191753.i	−0.255699	+	0.442883i
$659$	−540473.	+	95299.9i	−1.24452	+	0.219443i	−0.756853	−	0.653585i	$-0.773264\pi$
$659$	−540473.	+	95299.9i	−1.24452	+	0.219443i	−0.487670	+	0.873028i	$0.662153\pi$
$660$		0			0
$661$	577773.	−	210292.i	1.32237	−	0.481305i	0.418156	−	0.908375i	$-0.362676\pi$
$661$	577773.	−	210292.i	1.32237	−	0.481305i	0.904219	+	0.427070i	$0.140454\pi$
$662$	57922.3	+	159140.i	0.132169	+	0.363132i
$663$		0			0
$664$	−43509.3	−	246753.i	−0.0986837	−	0.559663i
$665$	−373852.	−	215843.i	−0.845388	−	0.488085i
$666$		0			0
$667$	−241478.	−	418253.i	−0.542783	−	0.940128i
$668$	−244638.	−	291549.i	−0.548241	−	0.653369i
$669$		0			0
$670$	72017.3	−	408430.i	0.160431	−	0.909847i
$671$	26063.9	−	31061.8i	0.0578888	−	0.0689892i
$672$		0			0
$673$	831958.	+	302808.i	1.83684	+	0.668555i	0.990782	+	0.135465i	$0.0432528\pi$
$673$	831958.	+	302808.i	1.83684	+	0.668555i	0.846058	+	0.533090i	$0.178969\pi$
$674$			170294.i			0.374868i
$675$		0			0
$676$	137253.			0.300351
$677$	−88016.3	+	241823.i	−0.192037	+	0.527618i	−0.997921	−	0.0644563i	$-0.979469\pi$
$677$	−88016.3	+	241823.i	−0.192037	+	0.527618i	0.805883	+	0.592075i	$0.201691\pi$
$678$		0			0
$679$	38367.6	+	32194.2i	0.0832195	+	0.0698294i
$680$	370022.	+	65244.9i	0.800221	+	0.141101i
$681$		0			0
$682$	−47952.3	+	40236.7i	−0.103096	+	0.0865075i
$683$	−314393.	+	181515.i	−0.673956	+	0.389109i	−0.797574	−	0.603221i	$-0.793884\pi$
$683$	−314393.	+	181515.i	−0.673956	+	0.389109i	0.123618	+	0.992330i	$0.460550\pi$
$684$		0			0
$685$	−382505.	+	662518.i	−0.815185	+	1.41194i
$686$	289599.	−	51064.1i	0.615387	−	0.108509i
$687$		0			0
$688$	−116928.	+	42558.4i	−0.247026	+	0.0899101i
$689$	−120894.	−	332154.i	−0.254664	−	0.699683i
$690$		0			0
$691$	−45340.3	−	257138.i	−0.0949573	−	0.538530i	−0.994760	−	0.102234i	$-0.967401\pi$
$691$	−45340.3	−	257138.i	−0.0949573	−	0.538530i	0.899803	−	0.436296i	$-0.143710\pi$
$692$	14391.6	+	8309.00i	0.0300537	+	0.0173515i
$693$		0			0
$694$	−35338.8	−	61208.5i	−0.0733723	−	0.127085i
$695$	−432992.	−	516020.i	−0.896417	−	1.06831i
$696$		0			0
$697$	−41244.5	+	233909.i	−0.0848987	+	0.481484i
$698$	−245932.	+	293091.i	−0.504783	+	0.601577i
$699$		0			0
$700$	−218498.	−	79526.7i	−0.445914	−	0.162299i
$701$		−	374534.i		−	0.762176i	−0.924539	−	0.381088i	$-0.875550\pi$
$701$		−	374534.i		−	0.762176i	0.924539	−	0.381088i	$-0.124450\pi$
$702$		0			0
$703$	619345.			1.25320
$704$	3215.98	−	8835.82i	0.00648885	−	0.0178280i
$705$		0			0
$706$	448887.	+	376661.i	0.900590	+	0.755685i
$707$	425422.	+	75013.3i	0.851100	+	0.150072i
$708$		0			0
$709$	−427788.	+	358957.i	−0.851012	+	0.714084i	−0.960012	−	0.279958i	$-0.909680\pi$
$709$	−427788.	+	358957.i	−0.851012	+	0.714084i	0.109000	+	0.994042i	$0.465235\pi$
$710$	688212.	−	397339.i	1.36523	−	0.788216i
$711$		0			0
$712$	79457.0	−	137624.i	0.156737	−	0.271477i
$713$	403704.	−	71184.0i	0.794117	−	0.140024i
$714$		0			0
$715$	78078.2	−	28418.1i	0.152728	−	0.0555883i
$716$	−52027.0	−	142943.i	−0.101485	−	0.278828i
$717$		0			0
$718$	−5607.24	−	31800.2i	−0.0108768	−	0.0616852i
$719$	156648.	+	90440.6i	0.303017	+	0.174947i	0.643797	−	0.765196i	$-0.277358\pi$
$719$	156648.	+	90440.6i	0.303017	+	0.174947i	−0.340781	+	0.940143i	$0.610691\pi$
$720$		0			0
$721$	164709.	+	285284.i	0.316844	+	0.548790i
$722$	68877.1	+	82084.6i	0.132130	+	0.157466i
$723$		0			0
$724$	51057.4	−	289561.i	0.0974051	−	0.552412i
$725$	−1.06764e6	+	1.27236e6i	−2.03117	+	2.42066i
$726$		0			0
$727$	−570109.	−	207503.i	−1.07867	−	0.392604i	−0.259258	−	0.965808i	$-0.583478\pi$
$727$	−570109.	−	207503.i	−1.07867	−	0.392604i	−0.819413	+	0.573204i	$0.805700\pi$
$728$		−	60034.6i		−	0.113276i
$729$		0			0
$730$	705854.			1.32455
$731$	−260633.	+	716083.i	−0.487747	+	1.34007i
$732$		0			0
$733$	46094.5	+	38677.9i	0.0857908	+	0.0719871i	0.684674	−	0.728849i	$-0.259944\pi$
$733$	46094.5	+	38677.9i	0.0857908	+	0.0719871i	−0.598884	+	0.800836i	$0.704389\pi$
$734$	522173.	+	92073.1i	0.969219	+	0.170899i
$735$		0			0
$736$	−47170.6	+	39580.9i	−0.0870796	+	0.0730684i
$737$	−55046.0	+	31780.8i	−0.101342	+	0.0585100i
$738$		0			0
$739$	−128656.	+	222839.i	−0.235581	+	0.408039i	−0.959441	−	0.281908i	$-0.909033\pi$
$739$	−128656.	+	222839.i	−0.235581	+	0.408039i	0.723860	+	0.689947i	$0.242366\pi$
$740$	504047.	−	88877.1i	0.920466	−	0.162303i
$741$		0			0
$742$	218565.	−	79551.1i	0.396984	−	0.144490i
$743$	246217.	+	676475.i	0.446005	+	1.22539i	0.935483	+	0.353373i	$0.114965\pi$
$743$	246217.	+	676475.i	0.446005	+	1.22539i	−0.489478	+	0.872016i	$0.662813\pi$
$744$		0			0
$745$	104074.	+	590232.i	0.187512	+	1.06343i
$746$	−193977.	−	111993.i	−0.348556	−	0.201239i
$747$		0			0
$748$	−28792.2	−	49869.6i	−0.0514602	−	0.0891318i
$749$	−168011.	−	200228.i	−0.299484	−	0.356911i
$750$		0			0
$751$	1891.59	−	10727.7i	0.00335387	−	0.0190207i	−0.983085	−	0.183150i	$-0.941370\pi$
$751$	1891.59	−	10727.7i	0.00335387	−	0.0190207i	0.986439	+	0.164130i	$0.0524816\pi$
$752$	129623.	−	154479.i	0.229217	−	0.273170i
$753$		0			0
$754$	−402978.	−	146672.i	−0.708825	−	0.257991i
$755$			248052.i			0.435160i
$756$		0			0
$757$	299286.			0.522270			0.261135	−	0.965302i	$-0.415903\pi$
$757$	299286.			0.522270			0.261135	+	0.965302i	$0.415903\pi$
$758$	−118809.	+	326425.i	−0.206781	+	0.568126i
$759$		0			0
$760$	301180.	+	252720.i	0.521434	+	0.437535i
$761$	544360.	+	95985.3i	0.939976	+	0.165743i	0.622586	−	0.782552i	$-0.286082\pi$
$761$	544360.	+	95985.3i	0.939976	+	0.165743i	0.317391	+	0.948295i	$0.397193\pi$
$762$		0			0
$763$	−202411.	+	169843.i	−0.347685	+	0.291742i
$764$	−42676.4	+	24639.2i	−0.0731140	+	0.0422124i
$765$		0			0
$766$	−137000.	+	237291.i	−0.233487	+	0.404412i
$767$	−512344.	+	90340.0i	−0.870905	+	0.153564i
$768$		0			0
$769$	−380525.	+	138500.i	−0.643474	+	0.234205i	−0.643085	−	0.765795i	$-0.722346\pi$
$769$	−380525.	+	138500.i	−0.643474	+	0.234205i	−0.000388607		1.00000i	$0.500124\pi$
$770$	18699.8	+	51377.2i	0.0315395	+	0.0866541i
$771$		0			0
$772$	44282.9	+	251141.i	0.0743022	+	0.421389i
$773$	867332.	+	500754.i	1.45153	+	0.838042i	0.998569	−	0.0534876i	$-0.0170338\pi$
$773$	867332.	+	500754.i	1.45153	+	0.838042i	0.452963	+	0.891529i	$0.350367\pi$
$774$		0			0
$775$	−704903.	−	1.22093e6i	−1.17362	−	2.03276i
$776$	−29321.2	−	34943.7i	−0.0486921	−	0.0580290i
$777$		0			0
$778$	−103436.	+	586617.i	−0.170889	+	0.969160i
$779$	−159757.	+	190391.i	−0.263260	+	0.313741i
$780$		0			0
$781$	−114447.	−	41655.5i	−0.187631	−	0.0682920i
$782$			377105.i			0.616664i
$783$		0			0
$784$	−114160.			−0.185730
$785$	442933.	−	1.21695e6i	0.718784	−	1.97484i
$786$		0			0
$787$	813406.	+	682528.i	1.31328	+	1.10197i	0.987683	+	0.156465i	$0.0500099\pi$
$787$	813406.	+	682528.i	1.31328	+	1.10197i	0.325598	+	0.945508i	$0.394435\pi$
$788$	−175580.	−	30959.4i	−0.282762	−	0.0498586i
$789$		0			0
$790$	228592.	−	191812.i	0.366275	−	0.307341i
$791$	−303592.	+	175279.i	−0.485219	+	0.280141i
$792$		0			0
$793$	−117893.	+	204196.i	−0.187474	+	0.324714i
$794$	537173.	−	94718.1i	0.852066	−	0.150242i
$795$		0			0
$796$	114726.	−	41756.8i	0.181065	−	0.0659024i
$797$	137866.	+	378783.i	0.217040	+	0.596312i	0.999657	−	0.0261912i	$-0.00833787\pi$
$797$	137866.	+	378783.i	0.217040	+	0.596312i	−0.782617	+	0.622503i	$0.786116\pi$
$798$		0			0
$799$	−214451.	−	1.21621e6i	−0.335920	−	1.90509i
$800$	183399.	+	105885.i	0.286560	+	0.165446i
$801$		0			0
$802$	−34163.0	−	59172.0i	−0.0531138	−	0.0919958i
$803$	−69536.2	−	82870.0i	−0.107840	−	0.128519i
$804$		0			0
$805$	62174.4	−	352609.i	0.0959445	−	0.544128i
$806$	233974.	−	278839.i	0.360161	−	0.429223i
$807$		0			0
$808$	−369707.	−	134562.i	−0.566285	−	0.206111i
$809$		−	350362.i		−	0.535328i	−0.963512	−	0.267664i	$-0.913748\pi$
$809$		−	350362.i		−	0.535328i	0.963512	−	0.267664i	$-0.0862518\pi$
$810$		0			0
$811$	928027.			1.41097			0.705486	−	0.708723i	$-0.250729\pi$
$811$	928027.			1.41097			0.705486	+	0.708723i	$0.250729\pi$
$812$	96513.5	−	265169.i	0.146378	−	0.402170i
$813$		0			0
$814$	−60090.0	−	50421.5i	−0.0906888	−	0.0760969i
$815$	−1.03404e6	−	182329.i	−1.55676	−	0.274499i
$816$		0			0
$817$	−610841.	+	512556.i	−0.915132	+	0.767887i
$818$	−413987.	+	239016.i	−0.618701	+	0.357207i
$819$		0			0
$820$	−102695.	+	177873.i	−0.152729	+	0.264535i
$821$	−328299.	+	57887.9i	−0.487061	+	0.0858819i	−0.411785	−	0.911281i	$-0.635095\pi$
$821$	−328299.	+	57887.9i	−0.487061	+	0.0858819i	−0.0752753	+	0.997163i	$0.523984\pi$
$822$		0			0
$823$	204886.	−	74572.3i	0.302491	−	0.110098i	−0.186316	−	0.982490i	$-0.559655\pi$
$823$	204886.	−	74572.3i	0.302491	−	0.110098i	0.488806	+	0.872392i	$0.337432\pi$
$824$	−102613.	−	281927.i	−0.151129	−	0.415223i
$825$		0			0
$826$	−59445.7	−	337133.i	−0.0871286	−	0.494131i
$827$	398393.	+	230012.i	0.582506	+	0.336310i	0.762129	−	0.647425i	$-0.224154\pi$
$827$	398393.	+	230012.i	0.582506	+	0.336310i	−0.179622	+	0.983736i	$0.557488\pi$
$828$		0			0
$829$	−647870.	−	1.12214e6i	−0.942711	−	1.63282i	−0.760271	−	0.649606i	$-0.774934\pi$
$829$	−647870.	−	1.12214e6i	−0.942711	−	1.63282i	−0.182440	−	0.983217i	$-0.558400\pi$
$830$	−852916.	−	1.01647e6i	−1.23808	−	1.47549i
$831$		0			0
$832$	−9494.58	+	53846.4i	−0.0137160	+	0.0777876i
$833$	−449392.	+	535564.i	−0.647642	+	0.771830i
$834$		0			0
$835$	−1.89396e6	−	689345.i	−2.71642	−	0.988697i
$836$		−	60256.1i		−	0.0862162i
$837$		0			0
$838$	−137135.			−0.195280
$839$	129441.	−	355636.i	0.183886	−	0.505222i	−0.813159	−	0.582041i	$-0.802254\pi$
$839$	129441.	−	355636.i	0.183886	−	0.505222i	0.997045	+	0.0768192i	$0.0244764\pi$
$840$		0			0
$841$	−1.00232e6	−	841049.i	−1.41715	−	1.18913i
$842$	−512478.	−	90363.8i	−0.722855	−	0.127459i
$843$		0			0
$844$	110526.	−	92742.3i	0.155160	−	0.130195i
$845$	629478.	−	363429.i	0.881590	−	0.508986i
$846$		0			0
$847$	−177685.	+	307759.i	−0.247676	+	0.428987i
$848$	−208617.	+	36784.8i	−0.290107	+	0.0511537i
$849$		0			0
$850$	1.21870e6	−	443569.i	1.68678	−	0.613936i
$851$	175694.	+	482715.i	0.242604	+	0.666549i
$852$		0			0
$853$	81624.8	+	462917.i	0.112182	+	0.636217i	0.988107	+	0.153769i	$0.0491412\pi$
$853$	81624.8	+	462917.i	0.112182	+	0.636217i	−0.875925	+	0.482448i	$0.839748\pi$
$854$	−134365.	−	77576.0i	−0.184235	−	0.106368i
$855$		0			0
$856$	119027.	+	206160.i	0.162441	+	0.281357i
$857$	275329.	+	328124.i	0.374878	+	0.446762i	0.920191	−	0.391471i	$-0.128034\pi$
$857$	275329.	+	328124.i	0.374878	+	0.446762i	−0.545313	+	0.838233i	$0.683589\pi$
$858$		0			0
$859$	35852.1	−	203327.i	0.0485879	−	0.275555i	−0.950828	−	0.309718i	$-0.899765\pi$
$859$	35852.1	−	203327.i	0.0485879	−	0.275555i	0.999416	+	0.0341627i	$0.0108764\pi$
$860$	−423573.	+	504795.i	−0.572706	+	0.682525i
$861$		0			0
$862$	364197.	+	132557.i	0.490142	+	0.178397i
$863$		−	1.22796e6i		−	1.64878i	−0.566023	−	0.824390i	$-0.691519\pi$
$863$		−	1.22796e6i		−	1.64878i	0.566023	−	0.824390i	$-0.308481\pi$
$864$		0			0
$865$	88004.8			0.117618
$866$	−110179.	+	302714.i	−0.146914	+	0.403642i
$867$		0			0
$868$	183482.	+	153960.i	0.243531	+	0.204347i
$869$	−45038.9	−	7941.57i	−0.0596414	−	0.0105164i
$870$		0			0
$871$	283135.	−	237578.i	0.373213	−	0.313163i
$872$	208409.	−	120325.i	0.274083	−	0.158242i
$873$		0			0
$874$	−197300.	+	341734.i	−0.258289	+	0.447369i
$875$	−564806.	+	99590.5i	−0.737705	+	0.130077i
$876$		0			0
$877$	−13247.3	+	4821.62i	−0.0172238	+	0.00626894i	−0.350618	−	0.936519i	$-0.614028\pi$
$877$	−13247.3	+	4821.62i	−0.0172238	+	0.00626894i	0.333394	+	0.942788i	$0.391806\pi$
$878$	−278107.	−	764093.i	−0.360764	−	0.991191i
$879$		0			0
$880$	−8646.87	−	49038.8i	−0.0111659	−	0.0633249i
$881$	−665335.	−	384131.i	−0.857213	−	0.494912i	0.00586512	−	0.999983i	$-0.498133\pi$
$881$	−665335.	−	384131.i	−0.857213	−	0.494912i	−0.863078	+	0.505071i	$0.831466\pi$
$882$		0			0
$883$	678306.	+	1.17486e6i	0.869971	+	1.50683i	0.862026	+	0.506865i	$0.169196\pi$
$883$	678306.	+	1.17486e6i	0.869971	+	1.50683i	0.00794492	+	0.999968i	$0.497471\pi$
$884$	215237.	+	256509.i	0.275431	+	0.328246i
$885$		0			0
$886$	−88977.8	+	504618.i	−0.113348	+	0.642829i
$887$	−34310.2	+	40889.3i	−0.0436090	+	0.0519711i	−0.787408	−	0.616432i	$-0.788577\pi$
$887$	−34310.2	+	40889.3i	−0.0436090	+	0.0519711i	0.743799	+	0.668403i	$0.233022\pi$
$888$		0			0
$889$	259749.	+	94540.7i	0.328662	+	0.119623i
$890$		−	841569.i		−	1.06245i
$891$		0			0
$892$	−281781.			−0.354146
$893$	441984.	−	1.21434e6i	0.554247	−	1.52278i
$894$		0			0
$895$	−617104.	−	517812.i	−0.770394	−	0.646437i
$896$	−35432.1	−	6247.64i	−0.0441348	−	0.00778216i
$897$		0			0
$898$	−526009.	+	441374.i	−0.652290	+	0.547336i
$899$	1.48172e6	−	855469.i	1.83335	−	1.05849i
$900$		0			0
$901$	−648653.	+	1.12350e6i	−0.799030	+	1.38396i
$902$	30999.9	−	5466.11i	0.0381019	−	0.00671840i
$903$		0			0
$904$	300020.	−	109198.i	0.367124	−	0.133622i
$905$	−532559.	−	1.46319e6i	−0.650235	−	1.78651i
$906$		0			0
$907$	294.186	+	1668.41i	0.000357608	+	0.00202810i	0.984986	−	0.172634i	$-0.0552278\pi$
$907$	294.186	+	1668.41i	0.000357608	+	0.00202810i	−0.984628	+	0.174662i	$0.944117\pi$
$908$	303282.	+	175100.i	0.367853	+	0.212380i
$909$		0			0
$910$	−158964.	−	275334.i	−0.191962	−	0.332489i
$911$	137089.	+	163377.i	0.165184	+	0.196858i	0.842286	−	0.539030i	$-0.181209\pi$
$911$	137089.	+	163377.i	0.165184	+	0.196858i	−0.677103	+	0.735889i	$0.736765\pi$
$912$		0			0
$913$	−35313.3	+	200271.i	−0.0423639	+	0.240258i
$914$	491269.	−	585471.i	0.588067	−	0.700831i
$915$		0			0
$916$	292774.	+	106561.i	0.348932	+	0.127001i
$917$		−	46498.6i		−	0.0552970i
$918$		0			0
$919$	67384.9			0.0797868			0.0398934	−	0.999204i	$-0.487298\pi$
$919$	67384.9			0.0797868			0.0398934	+	0.999204i	$0.487298\pi$
$920$	−111531.	+	306430.i	−0.131771	+	0.362039i
$921$		0			0
$922$	−656631.	−	550979.i	−0.772430	−	0.648146i
$923$	697455.	+	122980.i	0.818677	+	0.144355i
$924$		0			0
$925$	1.35334e6	−	1.13559e6i	1.58170	−	1.32720i
$926$	87870.6	−	50732.1i	0.102476	−	0.0591644i
$927$		0			0
$928$	−128502.	+	222572.i	−0.149216	+	0.258449i
$929$	−70523.8	+	12435.2i	−0.0817155	+	0.0144086i	−0.214356	−	0.976756i	$-0.568765\pi$
$929$	−70523.8	+	12435.2i	−0.0817155	+	0.0144086i	0.132641	+	0.991164i	$0.457654\pi$
$930$		0			0
$931$	−687448.	+	250211.i	−0.793123	+	0.288673i
$932$	−41482.4	−	113972.i	−0.0477564	−	0.131210i
$933$		0			0
$934$	5052.31	+	28653.1i	0.00579157	+	0.0328456i
$935$	−264097.	−	152476.i	−0.302092	−	0.174413i
$936$		0			0
$937$	350885.	+	607751.i	0.399655	+	0.692223i	0.993683	−	0.112221i	$-0.0357965\pi$
$937$	350885.	+	607751.i	0.399655	+	0.692223i	−0.594028	+	0.804444i	$0.702463\pi$
$938$	156332.	+	186309.i	0.177681	+	0.211752i
$939$		0			0
$940$	185444.	−	1.05170e6i	0.209873	−	1.19025i
$941$	−612619.	+	730091.i	−0.691849	+	0.824514i	−0.991578	−	0.129511i	$-0.958659\pi$
$941$	−612619.	+	730091.i	−0.691849	+	0.824514i	0.299729	+	0.954024i	$0.403104\pi$
$942$		0			0
$943$	−193710.	−	70504.5i	−0.217835	−	0.0792855i
$944$			311784.i			0.349873i
$945$		0			0
$946$	100993.			0.112852
$947$	−124361.	+	341678.i	−0.138670	+	0.380993i	−0.989516	−	0.144422i	$-0.953868\pi$
$947$	−124361.	+	341678.i	−0.138670	+	0.380993i	0.850846	+	0.525415i	$0.176090\pi$
$948$		0			0
$949$	481883.	+	404348.i	0.535068	+	0.448976i
$950$	1.33646e6	+	235655.i	1.48085	+	0.261113i
$951$		0			0
$952$	−168789.	+	141631.i	−0.186239	+	0.156273i
$953$	838648.	−	484194.i	0.923409	−	0.533130i	0.0386879	−	0.999251i	$-0.487682\pi$
$953$	838648.	−	484194.i	0.923409	−	0.533130i	0.884721	+	0.466121i	$0.154349\pi$
$954$		0			0
$955$	−130483.	+	226003.i	−0.143070	+	0.247804i
$956$	157019.	−	27686.8i	0.171806	−	0.0302940i
$957$		0			0
$958$	194950.	−	70956.2i	0.212419	−	0.0773142i
$959$	−153438.	−	421567.i	−0.166838	−	0.458384i
$960$		0			0
$961$	91810.9	+	520685.i	0.0994140	+	0.563805i
$962$	395024.	+	228067.i	0.426848	+	0.246441i
$963$		0			0
$964$	−260530.	−	451252.i	−0.280352	−	0.485584i
$965$	868083.	+	1.03454e6i	0.932194	+	1.11095i
$966$		0			0
$967$	173986.	−	986724.i	0.186064	−	1.05522i	−0.738517	−	0.674234i	$-0.764474\pi$
$967$	173986.	−	986724.i	0.186064	−	1.05522i	0.924581	−	0.380985i	$-0.124415\pi$
$968$	208042.	−	247935.i	0.222025	−	0.264599i
$969$		0			0
$970$	−227001.	−	82621.6i	−0.241259	−	0.0878113i
$971$			1.09369e6i			1.15999i	0.814620	+	0.579995i	$0.196946\pi$
$971$			1.09369e6i			1.15999i	−0.814620	+	0.579995i	$0.803054\pi$
$972$		0			0
$973$	395026.			0.417254
$974$	368413.	−	1.01221e6i	0.388344	−	1.06697i
$975$		0			0
$976$	108247.	+	90829.8i	0.113636	+	0.0953518i
$977$	−1.20016e6	−	211620.i	−1.25733	−	0.221701i	−0.495002	−	0.868892i	$-0.664833\pi$
$977$	−1.20016e6	−	211620.i	−1.25733	−	0.221701i	−0.762328	+	0.647191i	$0.775944\pi$
$978$		0			0
$979$	−98803.5	+	82906.0i	−0.103088	+	0.0865008i
$980$	−523566.	+	302281.i	−0.545154	+	0.314745i
$981$		0			0
$982$	71312.1	−	123516.i	0.0739503	−	0.128086i
$983$	−1.56087e6	+	275223.i	−1.61532	+	0.284824i	−0.907020	−	0.421087i	$-0.861649\pi$
$983$	−1.56087e6	+	275223.i	−1.61532	+	0.284824i	−0.708300	+	0.705912i	$0.750537\pi$
$984$		0			0
$985$	−887229.	+	322925.i	−0.914457	+	0.332835i
$986$	538314.	+	1.47901e6i	0.553709	+	1.52130i
$987$		0			0
$988$	60843.7	+	345062.i	0.0623307	+	0.353495i
$989$	−572766.	−	330687.i	−0.585578	−	0.338084i
$990$		0			0
$991$	−175298.	−	303625.i	−0.178496	−	0.309165i	0.762869	−	0.646553i	$-0.223790\pi$
$991$	−175298.	−	303625.i	−0.178496	−	0.309165i	−0.941366	+	0.337388i	$0.890457\pi$
$992$	−140220.	−	167108.i	−0.142491	−	0.169814i
$993$		0			0
$994$	−80923.7	+	458941.i	−0.0819036	+	0.464498i
$995$	415596.	−	495287.i	0.419783	−	0.500278i
$996$		0			0
$997$	−293282.	−	106746.i	−0.295050	−	0.107389i	0.190254	−	0.981735i	$-0.439069\pi$
$997$	−293282.	−	106746.i	−0.295050	−	0.107389i	−0.485304	+	0.874346i	$0.661291\pi$
$998$			1.01454e6i			1.01861i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.17.7		72
3.2	odd	2		54.5.f.a.23.4	✓	72
27.7	even	9		54.5.f.a.47.4	yes	72
27.20	odd	18	inner	162.5.f.a.143.7		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.23.4	✓	72	3.2	odd	2
54.5.f.a.47.4	yes	72	27.7	even	9
162.5.f.a.17.7		72	1.1	even	1	trivial
162.5.f.a.143.7		72	27.20	odd	18	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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-41.7224 - 7.35678i) q^{5} +(19.0320 - 15.9698i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(-59.9146 + 103.775i) q^{10} +(18.0860 - 3.18905i) q^{11} +(-100.351 + 36.5247i) q^{13} +(-24.0341 - 66.0331i) q^{14} +(11.1135 + 63.0277i) q^{16} +(339.433 + 195.972i) q^{17} +(205.064 + 355.182i) q^{19} +(217.859 + 259.634i) q^{20} +(9.02000 - 51.1549i) q^{22} +(-218.656 + 260.583i) q^{23} +(1099.33 + 400.122i) q^{25} +302.051i q^{26} -198.756 q^{28} +(-485.587 + 1334.14i) q^{29} +(-923.152 - 774.616i) q^{31} +(178.269 + 31.4337i) q^{32} +(849.225 - 712.585i) q^{34} +(-911.547 + 526.282i) q^{35} +(755.062 - 1307.80i) q^{37} +(1142.40 - 201.435i) q^{38} +(900.820 - 327.872i) q^{40} +(207.264 + 569.453i) q^{41} +(337.617 + 1914.72i) q^{43} +(-127.237 - 73.4600i) q^{44} +(481.070 + 833.237i) q^{46} +(-2025.36 - 2413.73i) q^{47} +(-309.745 + 1756.65i) q^{49} +(2126.93 - 2534.78i) q^{50} +(802.807 + 292.198i) q^{52} +3309.93i q^{53} -778.052 q^{55} +(-192.273 + 528.265i) q^{56} +(3076.20 + 2581.24i) q^{58} +(4797.62 + 845.950i) q^{59} +(1691.36 - 1419.22i) q^{61} +(-2951.85 + 1704.25i) q^{62} +(256.000 - 443.405i) q^{64} +(4455.58 - 785.639i) q^{65} +(-3252.29 + 1183.74i) q^{67} +(-1072.42 - 2946.45i) q^{68} +(516.968 + 2931.87i) q^{70} +(-5743.28 - 3315.88i) q^{71} +(-2945.25 - 5101.32i) q^{73} +(-2745.52 - 3271.98i) q^{74} +(569.745 - 3231.18i) q^{76} +(293.285 - 349.523i) q^{77} +(-2340.08 - 851.720i) q^{79} -2711.42i q^{80} +1714.03 q^{82} +(-3787.29 + 10405.5i) q^{83} +(-12720.2 - 10673.6i) q^{85} +(5415.65 + 954.924i) q^{86} +(-318.332 + 267.112i) q^{88} +(-6082.16 + 3511.54i) q^{89} +(-1326.59 + 2297.72i) q^{91} +(2680.00 - 472.556i) q^{92} +(-8374.63 + 3048.11i) q^{94} +(-5942.78 - 16327.6i) q^{95} +(350.066 + 1985.32i) q^{97} +(4369.27 + 2522.60i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5} - 720 q^{11} + 288 q^{14} - 288 q^{20} - 1008 q^{22} - 4716 q^{23} - 882 q^{25} + 6084 q^{29} + 3330 q^{31} + 288 q^{34} - 5346 q^{35} - 576 q^{38} + 13356 q^{41} + 1260 q^{43} - 16578 q^{47}+ \cdots - 82944 q^{98}+O(q^{100}) \) 72 * q + 18 * q^5 - 720 * q^11 + 288 * q^14 - 288 * q^20 - 1008 * q^22 - 4716 * q^23 - 882 * q^25 + 6084 * q^29 + 3330 * q^31 + 288 * q^34 - 5346 * q^35 - 576 * q^38 + 13356 * q^41 + 1260 * q^43 - 16578 * q^47 - 5904 * q^49 - 15552 * q^50 + 2304 * q^56 + 40104 * q^59 + 8352 * q^61 + 18432 * q^64 + 19674 * q^65 - 24192 * q^67 - 10224 * q^68 + 14400 * q^70 - 39528 * q^71 - 12222 * q^73 - 33120 * q^74 + 9792 * q^76 - 28206 * q^77 + 11304 * q^79 + 30078 * q^83 - 52200 * q^85 + 46224 * q^86 - 16128 * q^88 + 102222 * q^89 + 12078 * q^91 + 27504 * q^92 + 4032 * q^94 - 46728 * q^95 + 49680 * q^97 - 82944 * q^98

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