LMFDB - Embedded newform 108.5.f.a.91.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(19,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			91.21
Character	$\chi$	$=$	108.91
Dual form			108.5.f.a.19.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.93519 - 0.717143i) q^{2} +(14.9714 - 5.64418i) q^{4} +(5.51579 - 9.55363i) q^{5} +(-10.3188 + 5.95759i) q^{7} +(54.8676 - 32.9476i) q^{8} +O(q^{10})$	\(q+(3.93519 - 0.717143i) q^{2} +(14.9714 - 5.64418i) q^{4} +(5.51579 - 9.55363i) q^{5} +(-10.3188 + 5.95759i) q^{7} +(54.8676 - 32.9476i) q^{8} +(14.8544 - 41.5509i) q^{10} +(189.995 - 109.694i) q^{11} +(18.5350 - 32.1036i) q^{13} +(-36.3341 + 30.8443i) q^{14} +(192.286 - 169.003i) q^{16} -284.021 q^{17} +45.4901i q^{19} +(28.6568 - 174.163i) q^{20} +(669.000 - 567.918i) q^{22} +(174.319 + 100.643i) q^{23} +(251.652 + 435.874i) q^{25} +(49.9160 - 139.626i) q^{26} +(-120.862 + 147.435i) q^{28} +(-614.153 - 1063.74i) q^{29} +(1311.83 + 757.384i) q^{31} +(635.484 - 802.954i) q^{32} +(-1117.68 + 203.683i) q^{34} +131.443i q^{35} -1521.29 q^{37} +(32.6229 + 179.012i) q^{38} +(-12.1303 - 705.917i) q^{40} +(-1316.97 + 2281.07i) q^{41} +(34.6057 - 19.9796i) q^{43} +(2225.36 - 2714.63i) q^{44} +(758.153 + 271.038i) q^{46} +(-2498.36 + 1442.43i) q^{47} +(-1129.51 + 1956.38i) q^{49} +(1302.88 + 1534.78i) q^{50} +(96.2969 - 585.252i) q^{52} -1415.13 q^{53} -2420.19i q^{55} +(-369.883 + 666.859i) q^{56} +(-3179.66 - 3745.60i) q^{58} +(2453.33 + 1416.43i) q^{59} +(2628.64 + 4552.93i) q^{61} +(5705.44 + 2039.68i) q^{62} +(1924.92 - 3615.51i) q^{64} +(-204.471 - 354.154i) q^{65} +(-805.917 - 465.296i) q^{67} +(-4252.19 + 1603.07i) q^{68} +(94.2635 + 517.254i) q^{70} -1162.75i q^{71} -2162.87 q^{73} +(-5986.57 + 1090.98i) q^{74} +(256.754 + 681.051i) q^{76} +(-1307.02 + 2263.82i) q^{77} +(-6482.54 + 3742.70i) q^{79} +(-553.978 - 2769.22i) q^{80} +(-3546.69 + 9920.88i) q^{82} +(-966.756 + 558.157i) q^{83} +(-1566.60 + 2713.43i) q^{85} +(121.852 - 103.441i) q^{86} +(6810.44 - 12278.5i) q^{88} +6739.71 q^{89} +441.696i q^{91} +(3177.85 + 522.881i) q^{92} +(-8797.09 + 7467.91i) q^{94} +(434.596 + 250.914i) q^{95} +(-6023.28 - 10432.6i) q^{97} +(-3041.85 + 8508.73i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.93519	−	0.717143i	0.983797	−	0.179286i
$2$	3.93519	−	0.717143i	0.983797	−	0.179286i
$3$		0			0
$3$		0			0
$4$	14.9714	−	5.64418i	0.935713	−	0.352761i
$5$	5.51579	−	9.55363i	0.220632	−	0.382145i	−0.734368	−	0.678751i	$-0.762521\pi$
$5$	5.51579	−	9.55363i	0.220632	−	0.382145i	0.955000	+	0.296606i	$0.0958548\pi$
$6$		0			0
$7$	−10.3188	+	5.95759i	−0.210589	+	0.121583i	−0.601585	−	0.798809i	$-0.705464\pi$
$7$	−10.3188	+	5.95759i	−0.210589	+	0.121583i	0.390996	+	0.920392i	$0.372131\pi$
$8$	54.8676	−	32.9476i	0.857307	−	0.514806i
$9$		0			0
$10$	14.8544	−	41.5509i	0.148544	−	0.415509i
$11$	189.995	−	109.694i	1.57021	−	0.906559i	0.574063	−	0.818811i	$-0.305367\pi$
$11$	189.995	−	109.694i	1.57021	−	0.906559i	0.996143	−	0.0877473i	$-0.0279668\pi$
$12$		0			0
$13$	18.5350	−	32.1036i	0.109675	−	0.189962i	−0.805964	−	0.591965i	$-0.798352\pi$
$13$	18.5350	−	32.1036i	0.109675	−	0.189962i	0.915639	+	0.402003i	$0.131686\pi$
$14$	−36.3341	+	30.8443i	−0.185378	+	0.157369i
$15$		0			0
$16$	192.286	−	169.003i	0.751119	−	0.660167i
$17$	−284.021			−0.982771			−0.491386	−	0.870942i	$-0.663509\pi$
$17$	−284.021			−0.982771			−0.491386	+	0.870942i	$0.663509\pi$
$18$		0			0
$19$			45.4901i			0.126011i	0.998013	+	0.0630057i	$0.0200686\pi$
$19$			45.4901i			0.126011i	−0.998013	+	0.0630057i	$0.979931\pi$
$20$	28.6568	−	174.163i	0.0716419	−	0.435409i
$21$		0			0
$22$	669.000	−	567.918i	1.38223	−	1.17338i
$23$	174.319	+	100.643i	0.329525	+	0.190252i	0.655630	−	0.755082i	$-0.272403\pi$
$23$	174.319	+	100.643i	0.329525	+	0.190252i	−0.326105	+	0.945334i	$0.605736\pi$
$24$		0			0
$25$	251.652	+	435.874i	0.402643	+	0.697399i
$26$	49.9160	−	139.626i	0.0738402	−	0.206547i
$27$		0			0
$28$	−120.862	+	147.435i	−0.154161	+	0.188055i
$29$	−614.153	−	1063.74i	−0.730265	−	1.26486i	−0.956770	−	0.290846i	$-0.906063\pi$
$29$	−614.153	−	1063.74i	−0.730265	−	1.26486i	0.226505	−	0.974010i	$-0.427270\pi$
$30$		0			0
$31$	1311.83	+	757.384i	1.36507	+	0.788121i	0.990293	−	0.138996i	$-0.0443875\pi$
$31$	1311.83	+	757.384i	1.36507	+	0.788121i	0.374773	+	0.927117i	$0.377721\pi$
$32$	635.484	−	802.954i	0.620590	−	0.784135i
$33$		0			0
$34$	−1117.68	+	203.683i	−0.966847	+	0.176197i
$35$			131.443i			0.107301i
$36$		0			0
$37$	−1521.29			−1.11124			−0.555622	−	0.831435i	$-0.687520\pi$
$37$	−1521.29			−1.11124			−0.555622	+	0.831435i	$0.687520\pi$
$38$	32.6229	+	179.012i	0.0225920	+	0.123970i
$39$		0			0
$40$	−12.1303	−	705.917i	−0.00758145	−	0.441198i
$41$	−1316.97	+	2281.07i	−0.783447	+	1.35697i	0.146476	+	0.989214i	$0.453207\pi$
$41$	−1316.97	+	2281.07i	−0.783447	+	1.35697i	−0.929923	+	0.367755i	$0.880126\pi$
$42$		0			0
$43$	34.6057	−	19.9796i	0.0187159	−	0.0108056i	−0.490613	−	0.871378i	$-0.663227\pi$
$43$	34.6057	−	19.9796i	0.0187159	−	0.0108056i	0.509329	+	0.860572i	$0.329894\pi$
$44$	2225.36	−	2714.63i	1.14946	−	1.40219i
$45$		0			0
$46$	758.153	+	271.038i	0.358295	+	0.128090i
$47$	−2498.36	+	1442.43i	−1.13099	+	0.652978i	−0.944184	−	0.329419i	$-0.893147\pi$
$47$	−2498.36	+	1442.43i	−1.13099	+	0.652978i	−0.186807	+	0.982397i	$0.559814\pi$
$48$		0			0
$49$	−1129.51	+	1956.38i	−0.470435	+	0.814817i
$50$	1302.88	+	1534.78i	0.521153	+	0.613911i
$51$		0			0
$52$	96.2969	−	585.252i	0.0356128	−	0.216439i
$53$	−1415.13			−0.503783			−0.251892	−	0.967755i	$-0.581053\pi$
$53$	−1415.13			−0.503783			−0.251892	+	0.967755i	$0.581053\pi$
$54$		0			0
$55$		−	2420.19i		−	0.800062i
$56$	−369.883	+	666.859i	−0.117947	+	0.212646i
$57$		0			0
$58$	−3179.66	−	3745.60i	−0.945203	−	1.11344i
$59$	2453.33	+	1416.43i	0.704778	+	0.406904i	0.809125	−	0.587637i	$-0.199942\pi$
$59$	2453.33	+	1416.43i	0.704778	+	0.406904i	−0.104346	+	0.994541i	$0.533275\pi$
$60$		0			0
$61$	2628.64	+	4552.93i	0.706433	+	1.22358i	0.966172	+	0.257899i	$0.0830300\pi$
$61$	2628.64	+	4552.93i	0.706433	+	1.22358i	−0.259739	+	0.965679i	$0.583637\pi$
$62$	5705.44	+	2039.68i	1.48425	+	0.530614i
$63$		0			0
$64$	1924.92	−	3615.51i	0.469950	−	0.882693i
$65$	−204.471	−	354.154i	−0.0483954	−	0.0838233i
$66$		0			0
$67$	−805.917	−	465.296i	−0.179531	−	0.103653i	0.407541	−	0.913187i	$-0.366386\pi$
$67$	−805.917	−	465.296i	−0.179531	−	0.103653i	−0.587073	+	0.809534i	$0.699720\pi$
$68$	−4252.19	+	1603.07i	−0.919592	+	0.346684i
$69$		0			0
$70$	94.2635	+	517.254i	0.0192375	+	0.105562i
$71$		−	1162.75i		−	0.230659i	−0.993327	−	0.115329i	$-0.963208\pi$
$71$		−	1162.75i		−	0.230659i	0.993327	−	0.115329i	$-0.0367923\pi$
$72$		0			0
$73$	−2162.87			−0.405867			−0.202934	−	0.979192i	$-0.565048\pi$
$73$	−2162.87			−0.405867			−0.202934	+	0.979192i	$0.565048\pi$
$74$	−5986.57	+	1090.98i	−1.09324	+	0.199230i
$75$		0			0
$76$	256.754	+	681.051i	0.0444519	+	0.117911i
$77$	−1307.02	+	2263.82i	−0.220445	+	0.381822i
$78$		0			0
$79$	−6482.54	+	3742.70i	−1.03870	+	0.599695i	−0.919466	−	0.393171i	$-0.871378\pi$
$79$	−6482.54	+	3742.70i	−1.03870	+	0.599695i	−0.119237	+	0.992866i	$0.538045\pi$
$80$	−553.978	−	2769.22i	−0.0865591	−	0.432690i
$81$		0			0
$82$	−3546.69	+	9920.88i	−0.527467	+	1.47544i
$83$	−966.756	+	558.157i	−0.140333	+	0.0810215i	−0.568523	−	0.822667i	$-0.692485\pi$
$83$	−966.756	+	558.157i	−0.140333	+	0.0810215i	0.428190	+	0.903689i	$0.359152\pi$
$84$		0			0
$85$	−1566.60	+	2713.43i	−0.216830	+	0.375561i
$86$	121.852	−	103.441i	0.0164754	−	0.0139861i
$87$		0			0
$88$	6810.44	−	12278.5i	0.879447	−	1.58555i
$89$	6739.71			0.850866			0.425433	−	0.904990i	$-0.360122\pi$
$89$	6739.71			0.850866			0.425433	+	0.904990i	$0.360122\pi$
$90$		0			0
$91$			441.696i			0.0533385i
$92$	3177.85	+	522.881i	0.375455	+	0.0617771i
$93$		0			0
$94$	−8797.09	+	7467.91i	−0.995596	+	0.845168i
$95$	434.596	+	250.914i	0.0481546	+	0.0278021i
$96$		0			0
$97$	−6023.28	−	10432.6i	−0.640161	−	1.10879i	−0.985396	−	0.170276i	$-0.945534\pi$
$97$	−6023.28	−	10432.6i	−0.640161	−	1.10879i	0.345235	−	0.938516i	$-0.387799\pi$
$98$	−3041.85	+	8508.73i	−0.316727	+	0.885957i
$99$		0			0
$100$	6227.74	+	5105.28i	0.622774	+	0.510528i
$101$	−4777.60	−	8275.04i	−0.468346	−	0.811199i	0.530999	−	0.847372i	$-0.321817\pi$
$101$	−4777.60	−	8275.04i	−0.468346	−	0.811199i	−0.999346	+	0.0361728i	$0.988483\pi$
$102$		0			0
$103$	9962.26	+	5751.71i	0.939039	+	0.542154i	0.889659	−	0.456626i	$-0.150942\pi$
$103$	9962.26	+	5751.71i	0.939039	+	0.542154i	0.0493798	+	0.998780i	$0.484276\pi$
$104$	−40.7622	−	2372.13i	−0.00376870	−	0.219317i
$105$		0			0
$106$	−5568.79	+	1014.85i	−0.495620	+	0.0903211i
$107$		−	6602.72i		−	0.576707i	−0.957524	−	0.288353i	$-0.906892\pi$
$107$		−	6602.72i		−	0.576707i	0.957524	−	0.288353i	$-0.0931078\pi$
$108$		0			0
$109$	12045.3			1.01383			0.506913	−	0.861997i	$-0.330786\pi$
$109$	12045.3			1.01383			0.506913	+	0.861997i	$0.330786\pi$
$110$	−1735.62	−	9523.89i	−0.143440	−	0.787099i
$111$		0			0
$112$	−977.325	+	2889.48i	−0.0779117	+	0.230347i
$113$	1865.35	−	3230.88i	0.146084	−	0.253025i	−0.783693	−	0.621149i	$-0.786666\pi$
$113$	1865.35	−	3230.88i	0.146084	−	0.253025i	0.929777	+	0.368124i	$0.120000\pi$
$114$		0			0
$115$	1923.01	−	1110.25i	0.145407	−	0.0839510i
$116$	−15198.7	−	12459.4i	−1.12951	−	0.925933i
$117$		0			0
$118$	10670.1	+	3814.54i	0.766311	+	0.273954i
$119$	2930.77	−	1692.08i	0.206960	−	0.119489i
$120$		0			0
$121$	16744.9	−	29003.0i	1.14370	−	1.98094i
$122$	13609.3	+	16031.5i	0.914356	+	1.07710i
$123$		0			0
$124$	23914.7	+	3934.92i	1.55533	+	0.255913i
$125$	12447.0			0.796607
$126$		0			0
$127$		−	26549.7i		−	1.64608i	−0.567980	−	0.823042i	$-0.692275\pi$
$127$		−	26549.7i		−	1.64608i	0.567980	−	0.823042i	$-0.307725\pi$
$128$	4982.07	−	15608.2i	0.304082	−	0.952646i
$129$		0			0
$130$	−1058.61	−	1247.03i	−0.0626396	−	0.0737886i
$131$	−1142.84	−	659.821i	−0.0665954	−	0.0384489i	0.466333	−	0.884609i	$-0.345575\pi$
$131$	−1142.84	−	659.821i	−0.0665954	−	0.0384489i	−0.532928	+	0.846161i	$0.678908\pi$
$132$		0			0
$133$	−271.011	−	469.405i	−0.0153209	−	0.0265366i
$134$	−3505.12	−	1253.07i	−0.195206	−	0.0697856i
$135$		0			0
$136$	−15583.6	+	9357.79i	−0.842537	+	0.505936i
$137$	12906.5	+	22354.7i	0.687648	+	1.19104i	0.972597	+	0.232499i	$0.0746901\pi$
$137$	12906.5	+	22354.7i	0.687648	+	1.19104i	−0.284949	+	0.958543i	$0.591977\pi$
$138$		0			0
$139$	11377.8	+	6569.00i	0.588885	+	0.339993i	0.764656	−	0.644438i	$-0.222909\pi$
$139$	11377.8	+	6569.00i	0.588885	+	0.339993i	−0.175772	+	0.984431i	$0.556242\pi$
$140$	741.889	+	1967.89i	0.0378515	+	0.100403i
$141$		0			0
$142$	−833.858	−	4575.64i	−0.0413538	−	0.226921i
$143$		−	8132.70i		−	0.397706i
$144$		0			0
$145$	−13550.2			−0.644478
$146$	−8511.29	+	1551.08i	−0.399291	+	0.0727662i
$147$		0			0
$148$	−22775.9	+	8586.46i	−1.03981	+	0.392004i
$149$	12968.2	−	22461.6i	0.584128	−	1.01174i	−0.410856	−	0.911700i	$-0.634770\pi$
$149$	12968.2	−	22461.6i	0.584128	−	1.01174i	0.994984	−	0.100038i	$-0.0318965\pi$
$150$		0			0
$151$	−24591.2	+	14197.8i	−1.07852	+	0.622681i	−0.930496	−	0.366303i	$-0.880623\pi$
$151$	−24591.2	+	14197.8i	−1.07852	+	0.622681i	−0.148020	+	0.988984i	$0.547290\pi$
$152$	1498.79	+	2495.93i	0.0648714	+	0.108030i
$153$		0			0
$154$	−3519.88	+	9845.88i	−0.148418	+	0.415158i
$155$	14471.5	−	8355.15i	0.602353	−	0.347769i
$156$		0			0
$157$	2760.19	−	4780.78i	0.111980	−	0.193954i	−0.804589	−	0.593832i	$-0.797614\pi$
$157$	2760.19	−	4780.78i	0.111980	−	0.193954i	0.916568	+	0.399878i	$0.130948\pi$
$158$	−22826.0	+	19377.1i	−0.914356	+	0.776203i
$159$		0			0
$160$	−4165.93	−	10500.1i	−0.162732	−	0.410161i
$161$	−2398.36			−0.0925257
$162$		0			0
$163$			407.281i			0.0153292i	0.999971	+	0.00766459i	$0.00243974\pi$
$163$			407.281i			0.0153292i	−0.999971	+	0.00766459i	$0.997560\pi$
$164$	−6842.21	+	41584.0i	−0.254395	+	1.54610i
$165$		0			0
$166$	−3404.09	+	2889.76i	−0.123534	+	0.104868i
$167$	−20561.9	−	11871.4i	−0.737277	−	0.425667i	0.0838016	−	0.996482i	$-0.473294\pi$
$167$	−20561.9	−	11871.4i	−0.737277	−	0.425667i	−0.821078	+	0.570816i	$0.806627\pi$
$168$		0			0
$169$	13593.4	+	23544.5i	0.475943	+	0.824357i
$170$	−4218.95	+	11801.3i	−0.145984	+	0.408351i
$171$		0			0
$172$	405.328	−	494.444i	0.0137009	−	0.0167132i
$173$	−1413.25	−	2447.82i	−0.0472200	−	0.0817874i	0.841449	−	0.540336i	$-0.181703\pi$
$173$	−1413.25	−	2447.82i	−0.0472200	−	0.0817874i	−0.888669	+	0.458549i	$0.848370\pi$
$174$		0			0
$175$	−5193.52	−	2998.48i	−0.169584	−	0.0979095i
$176$	17994.9	−	53202.2i	0.580931	−	1.71753i
$177$		0			0
$178$	26522.0	−	4833.34i	0.837080	−	0.152548i
$179$			45743.4i			1.42765i	0.700323	+	0.713826i	$0.253039\pi$
$179$			45743.4i			1.42765i	−0.700323	+	0.713826i	$0.746961\pi$
$180$		0			0
$181$	−24226.2			−0.739483			−0.369742	−	0.929135i	$-0.620554\pi$
$181$	−24226.2			−0.739483			−0.369742	+	0.929135i	$0.620554\pi$
$182$	316.759	+	1738.16i	0.00956283	+	0.0524743i
$183$		0			0
$184$	12880.4	−	221.334i	0.380447	−	0.00653752i
$185$	−8391.13	+	14533.9i	−0.245176	+	0.424657i
$186$		0			0
$187$	−53962.5	+	31155.3i	−1.54315	+	0.890940i
$188$	−29262.6	+	35696.4i	−0.827938	+	1.00997i
$189$		0			0
$190$	1890.16	+	675.726i	0.0523589	+	0.0187182i
$191$	−19504.6	+	11261.0i	−0.534651	+	0.308681i	−0.742908	−	0.669393i	$-0.766554\pi$
$191$	−19504.6	+	11261.0i	−0.534651	+	0.308681i	0.208257	+	0.978074i	$0.433221\pi$
$192$		0			0
$193$	−9144.35	+	15838.5i	−0.245493	+	0.425205i	−0.962270	−	0.272097i	$-0.912283\pi$
$193$	−9144.35	+	15838.5i	−0.245493	+	0.425205i	0.716777	+	0.697302i	$0.245616\pi$
$194$	−31184.4	−	36734.8i	−0.828579	−	0.976055i
$195$		0			0
$196$	−5868.28	+	35664.9i	−0.152756	+	0.928387i
$197$	−36300.2			−0.935356			−0.467678	−	0.883899i	$-0.654909\pi$
$197$	−36300.2			−0.935356			−0.467678	+	0.883899i	$0.654909\pi$
$198$		0			0
$199$		−	47336.5i		−	1.19533i	−0.801744	−	0.597667i	$-0.796094\pi$
$199$		−	47336.5i		−	1.19533i	0.801744	−	0.597667i	$-0.203906\pi$
$200$	28168.6	+	15624.1i	0.704214	+	0.390602i
$201$		0			0
$202$	−24735.1	−	29137.6i	−0.606194	−	0.714088i
$203$	12674.7	+	7317.73i	0.307571	+	0.177576i
$204$		0			0
$205$	14528.3	+	25163.8i	0.345706	+	0.598781i
$206$	43328.2	+	15489.7i	1.02102	+	0.365014i
$207$		0			0
$208$	−1861.57	−	9305.56i	−0.0430280	−	0.215088i
$209$	4989.97	+	8642.89i	0.114237	+	0.197864i
$210$		0			0
$211$	40261.7	+	23245.1i	0.904330	+	0.522115i	0.878602	−	0.477554i	$-0.158476\pi$
$211$	40261.7	+	23245.1i	0.904330	+	0.522115i	0.0257275	+	0.999669i	$0.491810\pi$
$212$	−21186.5	+	7987.24i	−0.471397	+	0.177715i
$213$		0			0
$214$	−4735.09	−	25982.9i	−0.103395	−	0.567363i
$215$		−	440.814i		−	0.00953626i
$216$		0			0
$217$	−18048.7			−0.383290
$218$	47400.4	−	8638.18i	0.997400	−	0.181765i
$219$		0			0
$220$	−13660.0	−	36233.6i	−0.282231	−	0.748629i
$221$	−5264.34	+	9118.10i	−0.107785	+	0.186689i
$222$		0			0
$223$	71531.9	−	41298.9i	1.43843	−	0.830480i	0.440693	−	0.897658i	$-0.354733\pi$
$223$	71531.9	−	41298.9i	1.43843	−	0.830480i	0.997741	+	0.0671780i	$0.0213996\pi$
$224$	−1773.79	+	12071.5i	−0.0353514	+	0.240583i
$225$		0			0
$226$	5023.49	−	14051.8i	0.0983533	−	0.275116i
$227$	25722.3	−	14850.8i	0.499182	−	0.288203i	−0.229194	−	0.973381i	$-0.573609\pi$
$227$	25722.3	−	14850.8i	0.499182	−	0.288203i	0.728376	+	0.685178i	$0.240276\pi$
$228$		0			0
$229$	−22667.9	+	39262.0i	−0.432256	+	0.748690i	−0.997067	−	0.0765307i	$-0.975616\pi$
$229$	−22667.9	+	39262.0i	−0.432256	+	0.748690i	0.564811	+	0.825220i	$0.308949\pi$
$230$	6771.21	−	5748.13i	0.128000	−	0.108660i
$231$		0			0
$232$	−68744.9	−	38130.3i	−1.27722	−	0.708425i
$233$	−50931.3			−0.938151			−0.469075	−	0.883158i	$-0.655413\pi$
$233$	−50931.3			−0.938151			−0.469075	+	0.883158i	$0.655413\pi$
$234$		0			0
$235$			31824.5i			0.576270i
$236$	44724.5	+	7358.94i	0.803010	+	0.132127i
$237$		0			0
$238$	10319.7	−	8760.43i	0.182184	−	0.154658i
$239$	−31946.2	−	18444.1i	−0.559272	−	0.322896i	0.193581	−	0.981084i	$-0.437990\pi$
$239$	−31946.2	−	18444.1i	−0.559272	−	0.322896i	−0.752853	+	0.658188i	$0.771323\pi$
$240$		0			0
$241$	−4193.64	−	7263.59i	−0.0722033	−	0.125060i	0.827663	−	0.561225i	$-0.189670\pi$
$241$	−4193.64	−	7263.59i	−0.0722033	−	0.125060i	−0.899867	+	0.436165i	$0.856336\pi$
$242$	45094.9	−	126141.i	0.770011	−	2.15389i
$243$		0			0
$244$	65052.0	+	53327.3i	1.09265	+	0.895715i
$245$	12460.3	+	21581.9i	0.207586	+	0.359549i
$246$		0			0
$247$	1460.40	+	843.160i	0.0239374	+	0.0138203i
$248$	96930.9	−	1665.64i	1.57601	−	0.0270818i
$249$		0			0
$250$	48981.2	−	8926.26i	0.783699	−	0.142820i
$251$			1475.47i			0.0234198i	0.999931	+	0.0117099i	$0.00372746\pi$
$251$			1475.47i			0.0234198i	−0.999931	+	0.0117099i	$0.996273\pi$
$252$		0			0
$253$	44159.6			0.689897
$254$	−19039.9	−	104478.i	−0.295119	−	1.61941i
$255$		0			0
$256$	8412.13	−	64993.9i	0.128359	−	0.991728i
$257$	17336.5	−	30027.8i	0.262480	−	0.454629i	−0.704420	−	0.709783i	$-0.748793\pi$
$257$	17336.5	−	30027.8i	0.262480	−	0.454629i	0.966900	+	0.255154i	$0.0821263\pi$
$258$		0			0
$259$	15698.0	−	9063.23i	0.234015	−	0.135109i
$260$	−5060.12	−	4148.11i	−0.0748539	−	0.0613626i
$261$		0			0
$262$	−4970.49	−	1776.94i	−0.0724097	−	0.0258863i
$263$	−16482.5	+	9516.19i	−0.238294	+	0.137579i	−0.614392	−	0.789001i	$-0.710599\pi$
$263$	−16482.5	+	9516.19i	−0.238294	+	0.137579i	0.376099	+	0.926580i	$0.377265\pi$
$264$		0			0
$265$	−7805.54	+	13519.6i	−0.111151	+	0.192518i
$266$	−1403.11	−	1652.84i	−0.0198303	−	0.0233598i
$267$		0			0
$268$	−14691.9	−	2417.40i	−0.204555	−	0.0336573i
$269$	−58724.1			−0.811544			−0.405772	−	0.913974i	$-0.632997\pi$
$269$	−58724.1			−0.811544			−0.405772	+	0.913974i	$0.632997\pi$
$270$		0			0
$271$			31474.1i			0.428563i	0.976772	+	0.214281i	$0.0687409\pi$
$271$			31474.1i			0.428563i	−0.976772	+	0.214281i	$0.931259\pi$
$272$	−54613.4	+	48000.3i	−0.738178	+	0.648793i
$273$		0			0
$274$	66820.8	+	78714.0i	0.890043	+	1.04846i
$275$	95625.2	+	55209.2i	1.26447	+	0.730040i
$276$		0			0
$277$	−33265.8	−	57618.0i	−0.433549	−	0.750929i	0.563627	−	0.826029i	$-0.309405\pi$
$277$	−33265.8	−	57618.0i	−0.433549	−	0.750929i	−0.997176	+	0.0751008i	$0.976072\pi$
$278$	49484.8	+	17690.7i	0.640299	+	0.228905i
$279$		0			0
$280$	4330.73	+	7211.98i	0.0552389	+	0.0919895i
$281$	−61859.9	−	107145.i	−0.783424	−	1.35693i	−0.929936	−	0.367721i	$-0.880138\pi$
$281$	−61859.9	−	107145.i	−0.783424	−	1.35693i	0.146512	−	0.989209i	$-0.453195\pi$
$282$		0			0
$283$	47401.9	+	27367.5i	0.591865	+	0.341713i	0.765835	−	0.643038i	$-0.222326\pi$
$283$	47401.9	+	27367.5i	0.591865	+	0.341713i	−0.173970	+	0.984751i	$0.555659\pi$
$284$	−6562.78	−	17408.0i	−0.0813675	−	0.215830i
$285$		0			0
$286$	−5832.30	−	32003.7i	−0.0713030	−	0.391262i
$287$		−	31383.9i		−	0.381016i
$288$		0			0
$289$	−2853.15			−0.0341609
$290$	−53322.4	+	9717.39i	−0.634036	+	0.115546i
$291$		0			0
$292$	−32381.2	+	12207.6i	−0.379776	+	0.143174i
$293$	−44309.0	+	76745.4i	−0.516127	+	0.893958i	0.483698	+	0.875235i	$0.339293\pi$
$293$	−44309.0	+	76745.4i	−0.516127	+	0.893958i	−0.999825	+	0.0187226i	$0.994040\pi$
$294$		0			0
$295$	27064.1	−	15625.5i	0.310993	−	0.179552i
$296$	−83469.8	+	50122.9i	−0.952677	+	0.572075i
$297$		0			0
$298$	34924.2	−	97690.7i	0.393273	−	1.10007i
$299$	6462.01	−	3730.84i	0.0722812	−	0.0417316i
$300$		0			0
$301$	−238.061	+	412.333i	−0.00262757	+	0.00455109i
$302$	−86589.3	+	73506.3i	−0.949403	+	0.805955i
$303$		0			0
$304$	7687.95	+	8747.13i	0.0831886	+	0.0946495i
$305$	57996.0			0.623446
$306$		0			0
$307$			123447.i			1.30980i	0.755716	+	0.654900i	$0.227289\pi$
$307$			123447.i			1.30980i	−0.755716	+	0.654900i	$0.772711\pi$
$308$	−6790.48	+	41269.7i	−0.0715813	+	0.435040i
$309$		0			0
$310$	50956.4	−	43257.2i	0.530243	−	0.450127i
$311$	−52431.9	−	30271.6i	−0.542094	−	0.312978i	0.203833	−	0.979006i	$-0.434660\pi$
$311$	−52431.9	−	30271.6i	−0.542094	−	0.312978i	−0.745927	+	0.666027i	$0.767993\pi$
$312$		0			0
$313$	26193.1	+	45367.8i	0.267361	+	0.463083i	0.968180	−	0.250257i	$-0.0805150\pi$
$313$	26193.1	+	45367.8i	0.267361	+	0.463083i	−0.700818	+	0.713340i	$0.747182\pi$
$314$	7433.35	−	20792.7i	0.0753920	−	0.210888i
$315$		0			0
$316$	−75928.4	+	92622.1i	−0.760378	+	0.927557i
$317$	−12998.7	−	22514.4i	−0.129354	−	0.224048i	0.794072	−	0.607823i	$-0.207957\pi$
$317$	−12998.7	−	22514.4i	−0.129354	−	0.224048i	−0.923427	+	0.383775i	$0.874624\pi$
$318$		0			0
$319$	−233372.	−	134737.i	−2.29333	−	1.32406i
$320$	−23923.8	−	38332.3i	−0.233631	−	0.374339i
$321$		0			0
$322$	−9437.99	+	1719.97i	−0.0910265	+	0.0165885i
$323$		−	12920.1i		−	0.123840i
$324$		0			0
$325$	18657.5			0.176639
$326$	292.079	+	1602.73i	0.00274830	+	0.0150808i
$327$		0			0
$328$	2896.29	+	168548.i	0.0269212	+	1.56666i
$329$	17186.8	−	29768.4i	0.158783	−	0.275019i
$330$		0			0
$331$	−37439.2	+	21615.5i	−0.341720	+	0.197292i	−0.661032	−	0.750357i	$-0.729881\pi$
$331$	−37439.2	+	21615.5i	−0.341720	+	0.197292i	0.319312	+	0.947650i	$0.396548\pi$
$332$	−11323.4	+	13812.9i	−0.102731	+	0.125317i
$333$		0			0
$334$	−89428.5	−	31970.5i	−0.801647	−	0.286587i
$335$	−8890.54	+	5132.95i	−0.0792206	+	0.0457381i
$336$		0			0
$337$	−5926.38	+	10264.8i	−0.0521831	+	0.0903837i	−0.890937	−	0.454127i	$-0.849951\pi$
$337$	−5926.38	+	10264.8i	−0.0521831	+	0.0903837i	0.838754	+	0.544511i	$0.183285\pi$
$338$	70377.3	+	82903.5i	0.616027	+	0.725671i
$339$		0			0
$340$	−8139.12	+	49466.1i	−0.0704076	+	0.427907i
$341$	332321.			2.85791
$342$		0			0
$343$		−	55525.0i		−	0.471955i
$344$	1240.45	−	2236.41i	0.0104825	−	0.0188988i
$345$		0			0
$346$	−7316.83	−	8619.12i	−0.0611182	−	0.0719964i
$347$	25222.5	+	14562.2i	0.209473	+	0.120940i	0.601067	−	0.799199i	$-0.294743\pi$
$347$	25222.5	+	14562.2i	0.209473	+	0.120940i	−0.391593	+	0.920138i	$0.628076\pi$
$348$		0			0
$349$	−59988.4	−	103903.i	−0.492512	−	0.853055i	0.507451	−	0.861681i	$-0.330588\pi$
$349$	−59988.4	−	103903.i	−0.492512	−	0.853055i	−0.999963	+	0.00862528i	$0.997254\pi$
$350$	−22587.8	−	8075.08i	−0.184390	−	0.0659191i
$351$		0			0
$352$	32659.8	−	222266.i	0.263589	−	1.79385i
$353$	77379.0	+	134024.i	0.620975	+	1.07556i	0.989305	+	0.145865i	$0.0465964\pi$
$353$	77379.0	+	134024.i	0.620975	+	1.07556i	−0.368330	+	0.929695i	$0.620070\pi$
$354$		0			0
$355$	−11108.5	−	6413.49i	−0.0881451	−	0.0508906i
$356$	100903.	−	38040.2i	0.796167	−	0.300153i
$357$		0			0
$358$	32804.5	+	180009.i	0.255957	+	1.40452i
$359$		−	66839.6i		−	0.518615i	−0.965795	−	0.259307i	$-0.916506\pi$
$359$		−	66839.6i		−	0.518615i	0.965795	−	0.259307i	$-0.0834942\pi$
$360$		0			0
$361$	128252.			0.984121
$362$	−95334.7	+	17373.6i	−0.727501	+	0.132579i
$363$		0			0
$364$	2493.01	+	6612.82i	0.0188158	+	0.0499096i
$365$	−11929.9	+	20663.2i	−0.0895472	+	0.155100i
$366$		0			0
$367$	81901.3	−	47285.7i	0.608077	−	0.351073i	−0.164136	−	0.986438i	$-0.552483\pi$
$367$	81901.3	−	47285.7i	0.608077	−	0.351073i	0.772212	+	0.635364i	$0.219150\pi$
$368$	50528.1	−	10108.1i	0.373110	−	0.0746403i
$369$		0			0
$370$	−22597.8	+	63211.2i	−0.165068	+	0.461732i
$371$	14602.5	−	8430.74i	0.106091	−	0.0612517i
$372$		0			0
$373$	90530.4	−	156803.i	0.650694	−	1.12704i	−0.332260	−	0.943188i	$-0.607811\pi$
$373$	90530.4	−	156803.i	0.650694	−	1.12704i	0.982955	−	0.183848i	$-0.0588554\pi$
$374$	−190010.	+	161301.i	−1.35842	+	1.15317i
$375$		0			0
$376$	−89554.6	+	161457.i	−0.633450	+	1.14204i
$377$	−45533.4			−0.320366
$378$		0			0
$379$		−	51191.3i		−	0.356384i	−0.983996	−	0.178192i	$-0.942975\pi$
$379$		−	51191.3i		−	0.356384i	0.983996	−	0.178192i	$-0.0570248\pi$
$380$	7922.71	+	1303.60i	0.0548664	+	0.00902769i
$381$		0			0
$382$	−68678.6	+	58301.7i	−0.470646	+	0.399535i
$383$	−132128.	−	76284.0i	−0.900734	−	0.520039i	−0.0232957	−	0.999729i	$-0.507416\pi$
$383$	−132128.	−	76284.0i	−0.900734	−	0.520039i	−0.877438	+	0.479690i	$0.840749\pi$
$384$		0			0
$385$	14418.5	+	24973.5i	0.0972742	+	0.168484i
$386$	−24626.3	+	68885.2i	−0.165282	+	0.462329i
$387$		0			0
$388$	−149061.	−	122195.i	−0.990147	−	0.811687i
$389$	33948.4	+	58800.3i	0.224347	+	0.388580i	0.956123	−	0.292965i	$-0.0946418\pi$
$389$	33948.4	+	58800.3i	0.224347	+	0.388580i	−0.731776	+	0.681545i	$0.761308\pi$
$390$		0			0
$391$	−49510.2	−	28584.7i	−0.323848	−	0.186974i
$392$	2484.03	+	144556.i	0.0161653	+	0.940731i
$393$		0			0
$394$	−142848.	+	26032.5i	−0.920201	+	0.167696i
$395$			82575.7i			0.529247i
$396$		0			0
$397$	−126087.			−0.799998			−0.399999	−	0.916516i	$-0.630990\pi$
$397$	−126087.			−0.799998			−0.399999	+	0.916516i	$0.630990\pi$
$398$	−33947.0	−	186278.i	−0.214306	−	1.17597i
$399$		0			0
$400$	122053.	+	41282.8i	0.762833	+	0.258017i
$401$	35445.4	−	61393.2i	0.220430	−	0.381796i	−0.734509	−	0.678599i	$-0.762587\pi$
$401$	35445.4	−	61393.2i	0.220430	−	0.381796i	0.954939	+	0.296803i	$0.0959206\pi$
$402$		0			0
$403$	48629.5	−	28076.3i	0.299426	−	0.172874i
$404$	−118233.	−	96923.5i	−0.724398	−	0.593836i
$405$		0			0
$406$	55125.1	+	19707.1i	0.334424	+	0.119556i
$407$	−289038.	+	166876.i	−1.74488	+	1.00741i
$408$		0			0
$409$	−21772.1	+	37710.4i	−0.130153	+	0.225432i	−0.923735	−	0.383031i	$-0.874880\pi$
$409$	−21772.1	+	37710.4i	−0.130153	+	0.225432i	0.793582	+	0.608463i	$0.208214\pi$
$410$	75217.6	+	88605.3i	0.447458	+	0.527099i
$411$		0			0
$412$	181613.	+	29882.5i	1.06992	+	0.176044i
$413$	−33754.1			−0.197891
$414$		0			0
$415$			12314.7i			0.0715036i
$416$	−13999.0	−	35284.1i	−0.0808930	−	0.203888i
$417$		0			0
$418$	25834.7	+	30432.9i	0.147860	+	0.174177i
$419$	182385.	+	105300.i	1.03887	+	0.599792i	0.919513	−	0.393060i	$-0.128583\pi$
$419$	182385.	+	105300.i	1.03887	+	0.599792i	0.119357	+	0.992851i	$0.461917\pi$
$420$		0			0
$421$	−42063.0	−	72855.3i	−0.237321	−	0.411052i	0.722624	−	0.691242i	$-0.242936\pi$
$421$	−42063.0	−	72855.3i	−0.237321	−	0.411052i	−0.959945	+	0.280190i	$0.909603\pi$
$422$	175107.	+	62600.4i	0.983285	+	0.351522i
$423$		0			0
$424$	−77644.7	+	46625.0i	−0.431897	+	0.259350i
$425$	−71474.4	−	123797.i	−0.395706	−	0.685383i
$426$		0			0
$427$	−54249.0	−	31320.7i	−0.297533	−	0.171781i
$428$	−37266.9	−	98852.0i	−0.203440	−	0.539632i
$429$		0			0
$430$	−316.126	−	1734.69i	−0.00170972	−	0.00938175i
$431$		−	150083.i		−	0.807933i	−0.914774	−	0.403967i	$-0.867631\pi$
$431$		−	150083.i		−	0.807933i	0.914774	−	0.403967i	$-0.132369\pi$
$432$		0			0
$433$	71221.5			0.379871			0.189935	−	0.981797i	$-0.439172\pi$
$433$	71221.5			0.379871			0.189935	+	0.981797i	$0.439172\pi$
$434$	−71025.1	+	12943.5i	−0.377079	+	0.0687183i
$435$		0			0
$436$	180335.	−	67985.7i	0.948651	−	0.357639i
$437$	−4578.26	+	7929.78i	−0.0239739	+	0.0415239i
$438$		0			0
$439$	94609.3	−	54622.7i	0.490913	−	0.283429i	−0.234040	−	0.972227i	$-0.575195\pi$
$439$	94609.3	−	54622.7i	0.490913	−	0.283429i	0.724953	+	0.688798i	$0.241861\pi$
$440$	−79739.3	−	132790.i	−0.411876	−	0.685899i
$441$		0			0
$442$	−14177.2	+	39656.7i	−0.0725680	+	0.202989i
$443$	199756.	−	115329.i	1.01787	−	0.587666i	0.104382	−	0.994537i	$-0.466713\pi$
$443$	199756.	−	115329.i	1.01787	−	0.587666i	0.913486	+	0.406871i	$0.133380\pi$
$444$		0			0
$445$	37174.8	−	64388.7i	0.187728	−	0.325154i
$446$	251874.	−	213818.i	1.26623	−	1.07491i
$447$		0			0
$448$	1676.80	+	48775.7i	0.00835458	+	0.243023i
$449$	9751.64			0.0483710			0.0241855	−	0.999707i	$-0.492301\pi$
$449$	9751.64			0.0483710			0.0241855	+	0.999707i	$0.492301\pi$
$450$		0			0
$451$			577854.i			2.84096i
$452$	9691.23	−	58899.1i	0.0474353	−	0.288292i
$453$		0			0
$454$	90572.1	−	76887.2i	0.439423	−	0.373029i
$455$	4219.80	+	2436.30i	0.0203831	+	0.0117682i
$456$		0			0
$457$	−33069.5	−	57278.1i	−0.158342	−	0.274256i	0.775929	−	0.630820i	$-0.217281\pi$
$457$	−33069.5	−	57278.1i	−0.158342	−	0.274256i	−0.934271	+	0.356564i	$0.883948\pi$
$458$	−61046.1	+	170760.i	−0.291023	+	0.814056i
$459$		0			0
$460$	22523.8	−	27475.9i	0.106445	−	0.129848i
$461$	−86994.6	−	150679.i	−0.409346	−	0.709008i	0.585471	−	0.810694i	$-0.300910\pi$
$461$	−86994.6	−	150679.i	−0.409346	−	0.709008i	−0.994817	+	0.101686i	$0.967576\pi$
$462$		0			0
$463$	150682.	+	86996.3i	0.702909	+	0.405825i	0.808430	−	0.588592i	$-0.200318\pi$
$463$	150682.	+	86996.3i	0.702909	+	0.405825i	−0.105521	+	0.994417i	$0.533651\pi$
$464$	−297869.	−	100750.i	−1.38353	−	0.467960i
$465$		0			0
$466$	−200424.	+	36525.0i	−0.922950	+	0.168197i
$467$		−	172090.i		−	0.789080i	−0.918879	−	0.394540i	$-0.870904\pi$
$467$		−	172090.i		−	0.789080i	0.918879	−	0.394540i	$-0.129096\pi$
$468$		0			0
$469$	11088.2			0.0504097
$470$	22822.7	+	125236.i	0.103317	+	0.566933i
$471$		0			0
$472$	181277.	−	3115.02i	0.813688	−	0.0139822i
$473$	4383.27	−	7592.05i	0.0195919	−	0.0339341i
$474$		0			0
$475$	−19828.0	+	11447.7i	−0.0878802	+	0.0507376i
$476$	34327.3	−	41874.6i	0.151505	−	0.184815i
$477$		0			0
$478$	−138941.	−	49671.2i	−0.608101	−	0.217395i
$479$	189138.	−	109199.i	0.824343	−	0.475935i	−0.0275690	−	0.999620i	$-0.508777\pi$
$479$	189138.	−	109199.i	0.824343	−	0.475935i	0.851912	+	0.523685i	$0.175443\pi$
$480$		0			0
$481$	−28197.2	+	48839.0i	−0.121875	+	0.211094i
$482$	−21711.8	−	25576.2i	−0.0934548	−	0.110088i
$483$		0			0
$484$	86996.3	−	528726.i	0.371373	−	2.25705i
$485$	−132893.			−0.564959
$486$		0			0
$487$		−	392112.i		−	1.65330i	−0.562716	−	0.826650i	$-0.690243\pi$
$487$		−	392112.i		−	1.65330i	0.562716	−	0.826650i	$-0.309757\pi$
$488$	294235.	+	163201.i	1.23553	+	0.685306i
$489$		0			0
$490$	64511.1	+	75993.1i	0.268684	+	0.316506i
$491$	181620.	+	104859.i	0.753358	+	0.434951i	0.826906	−	0.562340i	$-0.190099\pi$
$491$	181620.	+	104859.i	0.753358	+	0.434951i	−0.0735480	+	0.997292i	$0.523432\pi$
$492$		0			0
$493$	174432.	+	302125.i	0.717683	+	1.24306i
$494$	6351.60	+	2270.68i	0.0260273	+	0.00930470i
$495$		0			0
$496$	380247.	−	76067.9i	1.54562	−	0.309199i
$497$	6927.19	+	11998.2i	0.0280443	+	0.0485741i
$498$		0			0
$499$	−117681.	−	67943.0i	−0.472611	−	0.272862i	0.244721	−	0.969594i	$-0.421304\pi$
$499$	−117681.	−	67943.0i	−0.472611	−	0.272862i	−0.717332	+	0.696731i	$0.754637\pi$
$500$	186349.	−	70253.0i	0.745395	−	0.281012i
$501$		0			0
$502$	1058.12	+	5806.24i	0.00419883	+	0.0230403i
$503$			232332.i			0.918275i	0.888365	+	0.459137i	$0.151841\pi$
$503$			232332.i			0.918275i	−0.888365	+	0.459137i	$0.848159\pi$
$504$		0			0
$505$	−105409.			−0.413328
$506$	173776.	−	31668.7i	0.678718	−	0.123689i
$507$		0			0
$508$	−149851.	−	397486.i	−0.580675	−	1.54026i
$509$	−72659.4	+	125850.i	−0.280451	+	0.485755i	−0.971496	−	0.237057i	$-0.923817\pi$
$509$	−72659.4	+	125850.i	−0.280451	+	0.485755i	0.691045	+	0.722812i	$0.257151\pi$
$510$		0			0
$511$	22318.3	−	12885.5i	0.0854711	−	0.0493467i
$512$	−13506.6	−	261796.i	−0.0515234	−	0.998672i
$513$		0			0
$514$	46688.3	−	130598.i	0.176719	−	0.494321i
$515$	109899.	−	63450.5i	0.414363	−	0.239233i
$516$		0			0
$517$	−316450.	+	548108.i	−1.18393	+	2.05062i
$518$	55274.9	−	46923.2i	0.206001	−	0.174875i
$519$		0			0
$520$	−22887.3	−	12694.8i	−0.0846425	−	0.0469481i
$521$	−443088.			−1.63235			−0.816177	−	0.577803i	$-0.803910\pi$
$521$	−443088.			−1.63235			−0.816177	+	0.577803i	$0.803910\pi$
$522$		0			0
$523$			73202.4i			0.267622i	0.991007	+	0.133811i	$0.0427215\pi$
$523$			73202.4i			0.267622i	−0.991007	+	0.133811i	$0.957278\pi$
$524$	−20834.1	−	3428.04i	−0.0758775	−	0.0124848i
$525$		0			0
$526$	−58037.4	+	49268.3i	−0.209767	+	0.178072i
$527$	−372587.	−	215113.i	−1.34155	−	0.774543i
$528$		0			0
$529$	−119662.	−	207261.i	−0.427609	−	0.740640i
$530$	−21020.8	+	58799.9i	−0.0748338	+	0.209327i
$531$		0			0
$532$	−6706.83	−	5498.02i	−0.0236970	−	0.0194260i
$533$	48820.3	+	84559.2i	0.171849	+	0.297651i
$534$		0			0
$535$	−63079.9	−	36419.2i	−0.220386	−	0.127240i
$536$	−59549.1	+	1023.28i	−0.207274	+	0.00356176i
$537$		0			0
$538$	−231090.	+	42113.6i	−0.798394	+	0.145498i
$539$			495602.i			1.70591i
$540$		0			0
$541$	438165.			1.49707			0.748536	−	0.663094i	$-0.230757\pi$
$541$	438165.			1.49707			0.748536	+	0.663094i	$0.230757\pi$
$542$	22571.4	+	123856.i	0.0768351	+	0.421619i
$543$		0			0
$544$	−180491.	+	228056.i	−0.609898	+	0.770625i
$545$	66439.2	−	115076.i	0.223682	−	0.387429i
$546$		0			0
$547$	270221.	−	156012.i	0.903118	−	0.521416i	0.0249077	−	0.999690i	$-0.492071\pi$
$547$	270221.	−	156012.i	0.903118	−	0.521416i	0.878211	+	0.478274i	$0.158737\pi$
$548$	319402.	+	261834.i	1.06359	+	0.871898i
$549$		0			0
$550$	415896.	+	148682.i	1.37486	+	0.491510i
$551$	48389.8	−	27937.9i	0.159386	−	0.0920217i
$552$		0			0
$553$	44594.9	−	77240.6i	0.145826	−	0.252578i
$554$	−172227.	−	202881.i	−0.561155	−	0.661032i
$555$		0			0
$556$	207419.	+	34128.6i	0.670963	+	0.110400i
$557$	−312549.			−1.00741			−0.503707	−	0.863874i	$-0.668031\pi$
$557$	−312549.			−1.00741			−0.503707	+	0.863874i	$0.668031\pi$
$558$		0			0
$559$		−	1481.29i		−	0.00474042i
$560$	22214.3	+	25274.7i	0.0708363	+	0.0805955i
$561$		0			0
$562$	−320268.	−	377272.i	−1.01401	−	1.19449i
$563$	−74780.6	−	43174.6i	−0.235924	−	0.136211i	0.377378	−	0.926059i	$-0.376826\pi$
$563$	−74780.6	−	43174.6i	−0.235924	−	0.136211i	−0.613302	+	0.789849i	$0.710159\pi$
$564$		0			0
$565$	−20577.7	−	35641.7i	−0.0644615	−	0.111651i
$566$	206162.	+	73702.3i	0.643539	+	0.230064i
$567$		0			0
$568$	−38309.8	−	63797.4i	−0.118744	−	0.197745i
$569$	277479.	+	480608.i	0.857049	+	1.48445i	0.874731	+	0.484609i	$0.161038\pi$
$569$	277479.	+	480608.i	0.857049	+	1.48445i	−0.0176822	+	0.999844i	$0.505629\pi$
$570$		0			0
$571$	262848.	+	151755.i	0.806181	+	0.465449i	0.845628	−	0.533773i	$-0.179226\pi$
$571$	262848.	+	151755.i	0.806181	+	0.465449i	−0.0394467	+	0.999222i	$0.512560\pi$
$572$	−45902.4	−	121758.i	−0.140295	−	0.372139i
$573$		0			0
$574$	−22506.8	−	123502.i	−0.0683108	−	0.374843i
$575$			101308.i			0.306414i
$576$		0			0
$577$	−500884.			−1.50448			−0.752238	−	0.658892i	$-0.771026\pi$
$577$	−500884.			−1.50448			−0.752238	+	0.658892i	$0.771026\pi$
$578$	−11227.7	+	2046.12i	−0.0336074	+	0.00612456i
$579$		0			0
$580$	−202865.	+	76479.5i	−0.603047	+	0.227347i
$581$	6650.54	−	11519.1i	0.0197017	−	0.0341244i
$582$		0			0
$583$	−268867.	+	155230.i	−0.791043	+	0.456709i
$584$	−118671.	+	71261.2i	−0.347953	+	0.208943i
$585$		0			0
$586$	−119327.	+	333783.i	−0.347490	+	0.972007i
$587$	−498580.	+	287855.i	−1.44697	+	0.835406i	−0.998300	−	0.0582932i	$-0.981434\pi$
$587$	−498580.	+	287855.i	−1.44697	+	0.835406i	−0.448666	+	0.893699i	$0.648101\pi$
$588$		0			0
$589$	−34453.5	+	59675.2i	−0.0993122	+	0.172014i
$590$	95296.8	−	80898.1i	0.273763	−	0.232399i
$591$		0			0
$592$	−292524.	+	257103.i	−0.834676	+	0.733607i
$593$	138143.			0.392843			0.196421	−	0.980520i	$-0.437068\pi$
$593$	138143.			0.392843			0.196421	+	0.980520i	$0.437068\pi$
$594$		0			0
$595$		−	37332.6i		−	0.105452i
$596$	67375.1	−	409477.i	0.189674	−	1.15275i
$597$		0			0
$598$	22753.7	−	19315.8i	0.0636282	−	0.0540144i
$599$	−165665.	−	95646.9i	−0.461719	−	0.266574i	0.251048	−	0.967975i	$-0.419225\pi$
$599$	−165665.	−	95646.9i	−0.461719	−	0.266574i	−0.712767	+	0.701401i	$0.752558\pi$
$600$		0			0
$601$	203120.	+	351814.i	0.562346	+	0.974012i	0.997291	+	0.0735551i	$0.0234345\pi$
$601$	203120.	+	351814.i	0.562346	+	0.974012i	−0.434945	+	0.900457i	$0.643232\pi$
$602$	−641.112	+	1793.33i	−0.00176905	+	0.00494843i
$603$		0			0
$604$	−288031.	+	351358.i	−0.789524	+	0.963110i
$605$	−184722.	−	319948.i	−0.504671	−	0.874117i
$606$		0			0
$607$	−59466.9	−	34333.2i	−0.161398	−	0.0931831i	0.417126	−	0.908849i	$-0.363038\pi$
$607$	−59466.9	−	34333.2i	−0.161398	−	0.0931831i	−0.578523	+	0.815666i	$0.696371\pi$
$608$	36526.5	+	28908.2i	0.0988100	+	0.0782014i
$609$		0			0
$610$	228225.	−	41591.4i	0.613344	−	0.111775i
$611$			106942.i			0.286461i
$612$		0			0
$613$	−572114.			−1.52252			−0.761258	−	0.648450i	$-0.775418\pi$
$613$	−572114.			−1.52252			−0.761258	+	0.648450i	$0.775418\pi$
$614$	88529.3	+	485788.i	0.234828	+	1.28858i
$615$		0			0
$616$	2874.39	+	167274.i	0.00757504	+	0.440825i
$617$	10190.4	−	17650.3i	0.0267684	−	0.0463642i	−0.852331	−	0.523003i	$-0.824812\pi$
$617$	10190.4	−	17650.3i	0.0267684	−	0.0463642i	0.879099	+	0.476639i	$0.158145\pi$
$618$		0			0
$619$	−388604.	+	224361.i	−1.01421	+	0.585552i	−0.912420	−	0.409254i	$-0.865789\pi$
$619$	−388604.	+	224361.i	−1.01421	+	0.585552i	−0.101786	+	0.994806i	$0.532456\pi$
$620$	169501.	−	206768.i	0.440951	−	0.537899i
$621$		0			0
$622$	−228038.	−	81523.2i	−0.589423	−	0.210717i
$623$	−69546.0	+	40152.4i	−0.179183	+	0.103451i
$624$		0			0
$625$	−88627.6	+	153508.i	−0.226887	+	0.392979i
$626$	135610.	+	159747.i	0.346053	+	0.407646i
$627$		0			0
$628$	14340.3	−	87154.1i	0.0363612	−	0.220988i
$629$	432079.			1.09210
$630$		0			0
$631$		−	402529.i		−	1.01097i	−0.862835	−	0.505486i	$-0.831313\pi$
$631$		−	402529.i		−	1.01097i	0.862835	−	0.505486i	$-0.168687\pi$
$632$	−232369.	+	418937.i	−0.581760	+	1.04885i
$633$		0			0
$634$	−67298.3	−	79276.4i	−0.167427	−	0.197227i
$635$	−253646.	−	146443.i	−0.629043	−	0.363178i
$636$		0			0
$637$	41871.2	+	72523.0i	0.103190	+	0.178730i
$638$	−1.01499e6	−	362856.i	−2.49356	−	0.891441i
$639$		0			0
$640$	−121634.	−	133688.i	−0.296959	−	0.326387i
$641$	176906.	+	306411.i	0.430554	+	0.745741i	0.996921	−	0.0784117i	$-0.0249849\pi$
$641$	176906.	+	306411.i	0.430554	+	0.745741i	−0.566367	+	0.824153i	$0.691652\pi$
$642$		0			0
$643$	227886.	+	131570.i	0.551184	+	0.318226i	0.749599	−	0.661892i	$-0.230246\pi$
$643$	227886.	+	131570.i	0.551184	+	0.318226i	−0.198415	+	0.980118i	$0.563580\pi$
$644$	−35906.8	+	13536.8i	−0.0865775	+	0.0326395i
$645$		0			0
$646$	−9265.58	−	50843.2i	−0.0222028	−	0.121834i
$647$		−	265174.i		−	0.633464i	−0.948515	−	0.316732i	$-0.897414\pi$
$647$		−	265174.i		−	0.633464i	0.948515	−	0.316732i	$-0.102586\pi$
$648$		0			0
$649$	621494.			1.47553
$650$	73420.8	−	13380.1i	0.173777	−	0.0316689i
$651$		0			0
$652$	2298.77	+	6097.57i	0.00540754	+	0.0143437i
$653$	−2938.96	+	5090.43i	−0.00689235	+	0.0119379i	−0.869451	−	0.494019i	$-0.835527\pi$
$653$	−2938.96	+	5090.43i	−0.00689235	+	0.0119379i	0.862559	+	0.505957i	$0.168861\pi$
$654$		0			0
$655$	−12607.4	+	7278.87i	−0.0293861	+	0.0169661i
$656$	132270.	+	661190.i	0.307365	+	1.53645i
$657$		0			0
$658$	46285.0	−	129470.i	0.106903	−	0.299031i
$659$	480334.	−	277321.i	1.10604	−	0.638575i	0.168242	−	0.985746i	$-0.446191\pi$
$659$	480334.	−	277321.i	1.10604	−	0.638575i	0.937802	+	0.347171i	$0.112858\pi$
$660$		0			0
$661$	410614.	−	711204.i	0.939789	−	1.62776i	0.173926	−	0.984759i	$-0.444355\pi$
$661$	410614.	−	711204.i	0.939789	−	1.62776i	0.765863	−	0.643004i	$-0.222312\pi$
$662$	−131829.	+	111910.i	−0.300812	+	0.255361i
$663$		0			0
$664$	−34653.7	+	62477.0i	−0.0785984	+	0.141705i
$665$	−5979.36			−0.0135211
$666$		0			0
$667$		−	247241.i		−	0.555736i
$668$	−374845.	−	61676.8i	−0.840039	−	0.138219i
$669$		0			0
$670$	−31304.9	+	26574.9i	−0.0697368	+	0.0592001i
$671$	998855.	+	576689.i	2.21849	+	1.28085i
$672$		0			0
$673$	−258432.	−	447618.i	−0.570580	−	0.988274i	−0.996506	−	0.0835158i	$-0.973385\pi$
$673$	−258432.	−	447618.i	−0.570580	−	0.988274i	0.425926	−	0.904758i	$-0.359948\pi$
$674$	−15960.1	+	44643.9i	−0.0351330	+	0.0982749i
$675$		0			0
$676$	336402.	+	275770.i	0.736148	+	0.603468i
$677$	−345343.	−	598152.i	−0.753483	−	1.30507i	−0.946125	−	0.323801i	$-0.895039\pi$
$677$	−345343.	−	598152.i	−0.753483	−	1.30507i	0.192642	−	0.981269i	$-0.438294\pi$
$678$		0			0
$679$	124307.	+	71768.4i	0.269621	+	0.155666i
$680$	3445.26	+	200495.i	0.00745083	+	0.433597i
$681$		0			0
$682$	1.30774e6	−	238321.i	2.81160	−	0.512382i
$683$		−	764551.i		−	1.63895i	−0.573117	−	0.819474i	$-0.694266\pi$
$683$		−	764551.i		−	1.63895i	0.573117	−	0.819474i	$-0.305734\pi$
$684$		0			0
$685$	284757.			0.606868
$686$	−39819.4	−	218502.i	−0.0846148	−	0.464308i
$687$		0			0
$688$	3277.60	−	9690.27i	0.00692435	−	0.0204719i
$689$	−26229.4	+	45430.7i	−0.0552523	+	0.0956998i
$690$		0			0
$691$	−278107.	+	160565.i	−0.582445	+	0.336275i	−0.762105	−	0.647454i	$-0.775834\pi$
$691$	−278107.	+	160565.i	−0.582445	+	0.336275i	0.179659	+	0.983729i	$0.442500\pi$
$692$	−34974.2	−	28670.6i	−0.0730358	−	0.0598722i
$693$		0			0
$694$	109698.	+	39216.9i	0.227762	+	0.0814244i
$695$	125516.	−	72466.4i	0.259853	−	0.150026i
$696$		0			0
$697$	374048.	−	647870.i	0.769949	−	1.33359i
$698$	−310579.	−	365858.i	−0.637472	−	0.750933i
$699$		0			0
$700$	−94678.2	−	15578.3i	−0.193221	−	0.0317925i
$701$	621799.			1.26536			0.632680	−	0.774413i	$-0.281955\pi$
$701$	621799.			1.26536			0.632680	+	0.774413i	$0.281955\pi$
$702$		0			0
$703$		−	69203.8i		−	0.140029i
$704$	−30873.9	−	898079.i	−0.0622940	−	1.81205i
$705$		0			0
$706$	400616.	+	471920.i	0.803745	+	0.946801i
$707$	98598.6	+	56925.9i	0.197257	+	0.113886i
$708$		0			0
$709$	262435.	+	454550.i	0.522070	+	0.904252i	0.999670	+	0.0256748i	$0.00817343\pi$
$709$	262435.	+	454550.i	0.522070	+	0.904252i	−0.477600	+	0.878577i	$0.658493\pi$
$710$	−48313.4	−	17271.9i	−0.0958409	−	0.0342629i
$711$		0			0
$712$	369792.	−	222057.i	0.729454	−	0.438031i
$713$	152451.	+	264053.i	0.299882	+	0.519412i
$714$		0			0
$715$	−77696.8	−	44858.2i	−0.151982	−	0.0877466i
$716$	258184.	+	684843.i	0.503620	+	1.33587i
$717$		0			0
$718$	−47933.5	−	263026.i	−0.0929801	−	0.510211i
$719$		−	348658.i		−	0.674438i	−0.941426	−	0.337219i	$-0.890514\pi$
$719$		−	348658.i		−	0.674438i	0.941426	−	0.337219i	$-0.109486\pi$
$720$		0			0
$721$	−137065.			−0.263668
$722$	504694.	−	91974.7i	0.968175	−	0.176439i
$723$		0			0
$724$	−362701.	+	136737.i	−0.691944	+	0.260861i
$725$	309106.	−	535387.i	0.588073	−	1.01857i
$726$		0			0
$727$	−523789.	+	302410.i	−0.991032	+	0.572173i	−0.905583	−	0.424170i	$-0.860566\pi$
$727$	−523789.	+	302410.i	−0.991032	+	0.572173i	−0.0854497	+	0.996342i	$0.527233\pi$
$728$	14552.8	+	24234.8i	0.0274590	+	0.0457275i
$729$		0			0
$730$	−32128.0	+	89869.2i	−0.0602890	+	0.168642i
$731$	−9828.75	+	5674.63i	−0.0183935	+	0.0106195i
$732$		0			0
$733$	237805.	−	411891.i	0.442602	−	0.766609i	−0.555280	−	0.831664i	$-0.687389\pi$
$733$	237805.	−	411891.i	0.442602	−	0.766609i	0.997882	+	0.0650546i	$0.0207222\pi$
$734$	288386.	−	244813.i	0.535282	−	0.454404i
$735$		0			0
$736$	191589.	−	76013.1i	0.353683	−	0.140324i
$737$	−204160.			−0.375868
$738$		0			0
$739$		−	844449.i		−	1.54627i	−0.634244	−	0.773133i	$-0.718688\pi$
$739$		−	844449.i		−	1.54627i	0.634244	−	0.773133i	$-0.281312\pi$
$740$	−43595.3	+	264954.i	−0.0796116	+	0.483845i
$741$		0			0
$742$	51417.4	−	43648.6i	0.0933905	−	0.0792798i
$743$	−537216.	−	310162.i	−0.973131	−	0.561837i	−0.0729415	−	0.997336i	$-0.523239\pi$
$743$	−537216.	−	310162.i	−0.973131	−	0.561837i	−0.900189	+	0.435499i	$0.856572\pi$
$744$		0			0
$745$	−143060.	−	247787.i	−0.257754	−	0.446443i
$746$	243804.	−	681974.i	0.438090	−	1.22543i
$747$		0			0
$748$	−632049.	+	771013.i	−1.12966	+	1.37803i
$749$	39336.3	+	68132.4i	0.0701180	+	0.121448i
$750$		0			0
$751$	632847.	+	365374.i	1.12207	+	0.647825i	0.941928	−	0.335816i	$-0.109012\pi$
$751$	632847.	+	365374.i	1.12207	+	0.647825i	0.180139	+	0.983641i	$0.442345\pi$
$752$	−236626.	+	699589.i	−0.418434	+	1.23711i
$753$		0			0
$754$	−179182.	+	32653.9i	−0.315176	+	0.0574371i
$755$			313247.i			0.549533i
$756$		0			0
$757$	−769023.			−1.34198			−0.670992	−	0.741465i	$-0.734132\pi$
$757$	−769023.			−1.34198			−0.670992	+	0.741465i	$0.734132\pi$
$758$	−36711.5	−	201447.i	−0.0638945	−	0.350609i
$759$		0			0
$760$	32112.2	−	551.810i	0.0555960	−	0.000955349i
$761$	137697.	−	238498.i	0.237769	−	0.411828i	−0.722305	−	0.691575i	$-0.756917\pi$
$761$	137697.	−	238498.i	0.237769	−	0.411828i	0.960074	+	0.279747i	$0.0902505\pi$
$762$		0			0
$763$	−124293.	+	71760.8i	−0.213500	+	0.123264i
$764$	−228452.	+	278680.i	−0.391389	+	0.477441i
$765$		0			0
$766$	−574654.	−	205437.i	−0.979375	−	0.350124i
$767$	90945.2	−	52507.2i	0.154593	−	0.0892541i
$768$		0			0
$769$	26421.1	−	45762.6i	0.0446784	−	0.0773853i	−0.842821	−	0.538193i	$-0.819107\pi$
$769$	26421.1	−	45762.6i	0.0446784	−	0.0773853i	0.887500	+	0.460808i	$0.152440\pi$
$770$	74649.0	+	87935.4i	0.125905	+	0.148314i
$771$		0			0
$772$	−47508.6	+	288737.i	−0.0797145	+	0.484471i
$773$	195309.			0.326861			0.163430	−	0.986555i	$-0.447744\pi$
$773$	195309.			0.326861			0.163430	+	0.986555i	$0.447744\pi$
$774$		0			0
$775$			762389.i			1.26933i
$776$	−674213.	−	373961.i	−1.11963	−	0.621017i
$777$		0			0
$778$	175761.	+	207045.i	0.290379	+	0.342062i
$779$	−103766.	−	59909.3i	−0.170994	−	0.0987232i
$780$		0			0
$781$	−127546.	−	220917.i	−0.209106	−	0.362182i
$782$	−215331.	−	76980.4i	−0.352122	−	0.125883i
$783$		0			0
$784$	113443.	+	567076.i	0.184563	+	0.922590i
$785$	−30449.2	−	52739.6i	−0.0494125	−	0.0855849i
$786$		0			0
$787$	677438.	+	391119.i	1.09375	+	0.631480i	0.934574	−	0.355770i	$-0.115781\pi$
$787$	677438.	+	391119.i	1.09375	+	0.631480i	0.159181	+	0.987249i	$0.449115\pi$
$788$	−543466.	+	204885.i	−0.875225	+	0.329958i
$789$		0			0
$790$	59218.6	+	324951.i	0.0948864	+	0.520672i
$791$			44451.9i			0.0710456i
$792$		0			0
$793$	194887.			0.309911
$794$	−496176.	+	90422.3i	−0.787036	+	0.143428i
$795$		0			0
$796$	−267176.	−	708694.i	−0.421668	−	1.11849i
$797$	−586714.	+	1.01622e6i	−0.923655	+	1.59982i	−0.129944	+	0.991521i	$0.541480\pi$
$797$	−586714.	+	1.01622e6i	−0.923655	+	1.59982i	−0.793711	+	0.608296i	$0.791854\pi$
$798$		0			0
$799$	709586.	−	409680.i	1.11151	−	0.641728i
$800$	509908.	+	74926.0i	0.796731	+	0.117072i
$801$		0			0
$802$	95456.6	−	267013.i	0.148408	−	0.415130i
$803$	−410934.	+	237253.i	−0.637295	+	0.367943i
$804$		0			0
$805$	−13228.8	+	22913.0i	−0.0204141	+	0.0353583i
$806$	171232.	−	145360.i	0.263581	−	0.223756i
$807$		0			0
$808$	−534778.	−	296622.i	−0.819126	−	0.454340i
$809$	421614.			0.644196			0.322098	−	0.946706i	$-0.395612\pi$
$809$	421614.			0.644196			0.322098	+	0.946706i	$0.395612\pi$
$810$		0			0
$811$		−	504037.i		−	0.766339i	−0.923678	−	0.383169i	$-0.874833\pi$
$811$		−	504037.i		−	0.766339i	0.923678	−	0.383169i	$-0.125167\pi$
$812$	231061.	+	38018.6i	0.350440	+	0.0576612i
$813$		0			0
$814$	−1.01774e6	+	863970.i	−1.53600	+	1.30392i
$815$	3891.01	+	2246.48i	0.00585797	+	0.00338210i
$816$		0			0
$817$	908.875	+	1574.22i	0.00136163	+	0.00235842i
$818$	−58633.6	+	164011.i	−0.0876275	+	0.245113i
$819$		0			0
$820$	359538.	+	294737.i	0.534709	+	0.438335i
$821$	−35777.1	−	61967.7i	−0.0530785	−	0.0919346i	0.838265	−	0.545262i	$-0.183570\pi$
$821$	−35777.1	−	61967.7i	−0.0530785	−	0.0919346i	−0.891344	+	0.453328i	$0.850237\pi$
$822$		0			0
$823$	−703826.	−	406354.i	−1.03912	−	0.599936i	−0.119536	−	0.992830i	$-0.538141\pi$
$823$	−703826.	−	406354.i	−1.03912	−	0.599936i	−0.919584	+	0.392893i	$0.871474\pi$
$824$	736111.	−	12649.2i	1.08415	−	0.0186298i
$825$		0			0
$826$	−132829.	+	24206.5i	−0.194685	+	0.0354790i
$827$			375951.i			0.549693i	0.961488	+	0.274847i	$0.0886271\pi$
$827$			375951.i			0.549693i	−0.961488	+	0.274847i	$0.911373\pi$
$828$		0			0
$829$	423699.			0.616522			0.308261	−	0.951302i	$-0.400253\pi$
$829$	423699.			0.616522			0.308261	+	0.951302i	$0.400253\pi$
$830$	8831.40	+	48460.7i	0.0128196	+	0.0703450i
$831$		0			0
$832$	−80392.5	−	128810.i	−0.116137	−	0.186082i
$833$	320806.	−	555652.i	0.462330	−	0.800779i
$834$		0			0
$835$	−226830.	+	130961.i	−0.325333	+	0.187831i
$836$	123489.	+	101232.i	0.176691	+	0.144845i
$837$		0			0
$838$	793234.	+	283579.i	1.12957	+	0.403819i
$839$	−959899.	+	554198.i	−1.36365	+	0.787302i	−0.990107	−	0.140313i	$-0.955189\pi$
$839$	−959899.	+	554198.i	−1.36365	+	0.787302i	−0.373539	+	0.927614i	$0.621856\pi$
$840$		0			0
$841$	−400727.	+	694079.i	−0.566573	+	0.981334i
$842$	−217773.	−	256534.i	−0.307171	−	0.361843i
$843$		0			0
$844$	733974.	+	120768.i	1.03038	+	0.169537i
$845$	299914.			0.420032
$846$		0			0
$847$			399036.i			0.556218i
$848$	−272110.	+	239160.i	−0.378401	+	0.332581i
$849$		0			0
$850$	−370046.	−	435909.i	−0.512174	−	0.603334i
$851$	−265190.	−	153108.i	−0.366183	−	0.211416i
$852$		0			0
$853$	254659.	+	441083.i	0.349995	+	0.606209i	0.986248	−	0.165272i	$-0.0528501\pi$
$853$	254659.	+	441083.i	0.349995	+	0.606209i	−0.636253	+	0.771480i	$0.719517\pi$
$854$	−235941.	−	84348.4i	−0.323510	−	0.115654i
$855$		0			0
$856$	−217543.	−	362276.i	−0.296892	−	0.494415i
$857$	−328394.	−	568795.i	−0.447130	−	0.774452i	0.551068	−	0.834460i	$-0.314220\pi$
$857$	−328394.	−	568795.i	−0.447130	−	0.774452i	−0.998198	+	0.0600088i	$0.980887\pi$
$858$		0			0
$859$	−916830.	−	529332.i	−1.24252	−	0.717368i	−0.272912	−	0.962039i	$-0.587987\pi$
$859$	−916830.	−	529332.i	−1.24252	−	0.717368i	−0.969606	+	0.244671i	$0.921320\pi$
$860$	−2488.03	−	6599.60i	−0.00336403	−	0.00892321i
$861$		0			0
$862$	−107631.	−	590603.i	−0.144851	−	0.794842i
$863$			676878.i			0.908844i	0.890787	+	0.454422i	$0.150154\pi$
$863$			676878.i			0.908844i	−0.890787	+	0.454422i	$0.849846\pi$
$864$		0			0
$865$	−31180.7			−0.0416729
$866$	280270.	−	51076.0i	0.373716	−	0.0681053i
$867$		0			0
$868$	−270215.	+	101870.i	−0.358649	+	0.135210i
$869$	−821100.	+	1.42219e6i	−1.08732	+	1.88329i
$870$		0			0
$871$	−29875.4	+	17248.6i	−0.0393801	+	0.0227361i
$872$	660896.	−	396862.i	0.869161	−	0.521924i
$873$		0			0
$874$	−12329.5	+	34488.5i	−0.0161408	+	0.0451493i
$875$	−128438.	+	74154.0i	−0.167756	+	0.0968541i
$876$		0			0
$877$	−737914.	+	1.27810e6i	−0.959415	+	1.66176i	−0.235490	+	0.971877i	$0.575669\pi$
$877$	−737914.	+	1.27810e6i	−0.959415	+	1.66176i	−0.723925	+	0.689879i	$0.757664\pi$
$878$	333133.	−	282799.i	0.432144	−	0.366850i
$879$		0			0
$880$	−409018.	−	465369.i	−0.528175	−	0.600942i
$881$	−599513.			−0.772408			−0.386204	−	0.922413i	$-0.626214\pi$
$881$	−599513.			−0.772408			−0.386204	+	0.922413i	$0.626214\pi$
$882$		0			0
$883$		−	729187.i		−	0.935229i	−0.883933	−	0.467614i	$-0.845114\pi$
$883$		−	729187.i		−	0.935229i	0.883933	−	0.467614i	$-0.154886\pi$
$884$	−27350.3	+	166224.i	−0.0349992	+	0.212710i
$885$		0			0
$886$	703369.	−	597094.i	0.896015	−	0.760634i
$887$	1.26218e6	+	728722.i	1.60426	+	0.926221i	0.990621	+	0.136636i	$0.0436290\pi$
$887$	1.26218e6	+	728722.i	1.60426	+	0.926221i	0.613641	+	0.789585i	$0.289704\pi$
$888$		0			0
$889$	158172.	+	273962.i	0.200137	+	0.346647i
$890$	100114.	−	280041.i	0.126391	−	0.353543i
$891$		0			0
$892$	837834.	−	1.02204e6i	1.05300	−	1.28452i
$893$	−65616.2	−	113651.i	−0.0822826	−	0.142518i
$894$		0			0
$895$	437015.	+	252311.i	0.545570	+	0.314985i
$896$	41577.7	+	190739.i	0.0517898	+	0.237588i
$897$		0			0
$898$	38374.5	−	6993.32i	0.0475872	−	0.00867223i
$899$		−	1.86060e6i		−	2.30215i
$900$		0			0
$901$	401926.			0.495104
$902$	414404.	+	2.27397e6i	0.509344	+	2.79493i
$903$		0			0
$904$	−4102.27	−	238729.i	−0.00501981	−	0.292125i
$905$	−133627.	+	231448.i	−0.163153	+	0.282590i
$906$		0			0
$907$	−3010.76	+	1738.27i	−0.00365984	+	0.00211301i	−0.501829	−	0.864967i	$-0.667339\pi$
$907$	−3010.76	+	1738.27i	−0.00365984	+	0.00211301i	0.498169	+	0.867080i	$0.334006\pi$
$908$	301279.	−	367519.i	0.365424	−	0.445767i
$909$		0			0
$910$	18352.9	+	6561.11i	0.0221627	+	0.00792309i
$911$	712683.	−	411468.i	0.858736	−	0.495791i	−0.00485282	−	0.999988i	$-0.501545\pi$
$911$	712683.	−	411468.i	0.858736	−	0.495791i	0.863589	+	0.504197i	$0.168211\pi$
$912$		0			0
$913$	−122453.	+	212094.i	−0.146901	+	0.254441i
$914$	−171211.	−	201685.i	−0.204946	−	0.241424i
$915$		0			0
$916$	−117769.	+	715750.i	−0.140359	+	0.853042i
$917$	15723.8			0.0186990
$918$		0			0
$919$			873279.i			1.03400i	0.855984	+	0.517002i	$0.172952\pi$
$919$			873279.i			1.03400i	−0.855984	+	0.517002i	$0.827048\pi$
$920$	68931.1	−	124276.i	0.0814403	−	0.146828i
$921$		0			0
$922$	−450398.	−	530563.i	−0.529828	−	0.624130i
$923$	−37328.5	−	21551.6i	−0.0438164	−	0.0252974i
$924$		0			0
$925$	−382837.	−	663092.i	−0.447435	−	0.774980i
$926$	655351.	+	234286.i	0.764279	+	0.273228i
$927$		0			0
$928$	−1.24442e6	−	182856.i	−1.44501	−	0.212330i
$929$	172980.	+	299611.i	0.200431	+	0.347157i	0.948667	−	0.316275i	$-0.102432\pi$
$929$	172980.	+	299611.i	0.200431	+	0.347157i	−0.748236	+	0.663433i	$0.769099\pi$
$930$		0			0
$931$	−88995.8	−	51381.7i	−0.102676	−	0.0592802i
$932$	−762513.	+	287465.i	−0.877840	+	0.330943i
$933$		0			0
$934$	−123413.	−	677205.i	−0.141471	−	0.776295i
$935$			687384.i			0.786278i
$936$		0			0
$937$	−1.10958e6			−1.26380			−0.631901	−	0.775049i	$-0.717725\pi$
$937$	−1.10958e6			−1.26380			−0.631901	+	0.775049i	$0.717725\pi$
$938$	43634.0	−	7951.80i	0.0495929	−	0.00903774i
$939$		0			0
$940$	179623.	+	476458.i	0.203286	+	0.539224i
$941$	161271.	−	279330.i	0.182129	−	0.315456i	−0.760477	−	0.649365i	$-0.775035\pi$
$941$	161271.	−	279330.i	0.182129	−	0.315456i	0.942605	+	0.333909i	$0.108368\pi$
$942$		0			0
$943$	−459147.	+	265089.i	−0.516331	+	0.298104i
$944$	711124.	−	142259.i	0.797997	−	0.159638i
$945$		0			0
$946$	11804.4	−	33019.6i	0.0131905	−	0.0368969i
$947$	120742.	−	69710.2i	0.134635	−	0.0777314i	−0.431170	−	0.902271i	$-0.641899\pi$
$947$	120742.	−	69710.2i	0.134635	−	0.0777314i	0.565805	+	0.824539i	$0.308566\pi$
$948$		0			0
$949$	−40088.8	+	69435.9i	−0.0445134	+	0.0770995i
$950$	−69817.2	+	59268.3i	−0.0773597	+	0.0656712i
$951$		0			0
$952$	105054.	−	189402.i	0.115915	−	0.208983i
$953$	−1.68438e6			−1.85462			−0.927308	−	0.374300i	$-0.877883\pi$
$953$	−1.68438e6			−1.85462			−0.927308	+	0.374300i	$0.877883\pi$
$954$		0			0
$955$			248453.i			0.272419i
$956$	−582382.	−	95824.8i	−0.637224	−	0.104848i
$957$		0			0
$958$	665983.	−	565357.i	0.725658	−	0.616016i
$959$	−266360.	−	153783.i	−0.289622	−	0.167213i
$960$		0			0
$961$	685501.	+	1.18732e6i	0.742269	+	1.28565i
$962$	−75936.8	+	212412.i	−0.0820545	+	0.229525i
$963$		0			0
$964$	−103782.	−	85076.6i	−0.111678	−	0.0915495i
$965$	100877.	+	174723.i	0.108327	+	0.187628i
$966$		0			0
$967$	−39280.8	−	22678.8i	−0.0420075	−	0.0242530i	0.478849	−	0.877897i	$-0.341054\pi$
$967$	−39280.8	−	22678.8i	−0.0420075	−	0.0242530i	−0.520857	+	0.853644i	$0.674387\pi$
$968$	−36825.3	−	2.14303e6i	−0.0393003	−	2.28706i
$969$		0			0
$970$	−522957.	+	95302.9i	−0.555805	+	0.101289i
$971$			1.18319e6i			1.25492i	0.778648	+	0.627461i	$0.215906\pi$
$971$			1.18319e6i			1.25492i	−0.778648	+	0.627461i	$0.784094\pi$
$972$		0			0
$973$	−156541.			−0.165350
$974$	−281200.	−	1.54303e6i	−0.296413	−	1.62651i
$975$		0			0
$976$	1.27491e6	+	431220.i	1.33838	+	0.452688i
$977$	562965.	−	975083.i	0.589783	−	1.02153i	−0.404478	−	0.914548i	$-0.632547\pi$
$977$	562965.	−	975083.i	0.589783	−	1.02153i	0.994261	−	0.106986i	$-0.0341199\pi$
$978$		0			0
$979$	1.28051e6	−	739303.i	1.33604	−	0.771360i
$980$	308361.	+	252784.i	0.321076	+	0.263206i
$981$		0			0
$982$	789909.	+	282390.i	0.819132	+	0.292838i
$983$	1.17197e6	−	676638.i	1.21286	−	0.700243i	0.249476	−	0.968381i	$-0.419741\pi$
$983$	1.17197e6	−	676638.i	1.21286	−	0.700243i	0.963381	+	0.268137i	$0.0864081\pi$
$984$		0			0
$985$	−200225.	+	346799.i	−0.206369	+	0.357442i
$986$	903090.	+	1.06383e6i	0.928918	+	1.09425i
$987$		0			0
$988$	26623.2	+	4380.56i	0.0272738	+	0.00448761i
$989$	8043.24			0.00822316
$990$		0			0
$991$			1.02847e6i			1.04724i	0.851953	+	0.523619i	$0.175418\pi$
$991$			1.02847e6i			1.04724i	−0.851953	+	0.523619i	$0.824582\pi$
$992$	1.44179e6	−	572032.i	1.46514	−	0.581296i
$993$		0			0
$994$	35864.2	+	42247.5i	0.0362985	+	0.0427591i
$995$	−452235.	−	261098.i	−0.456791	−	0.263729i
$996$		0			0
$997$	−564030.	−	976929.i	−0.567430	−	0.982817i	−0.996819	−	0.0796977i	$-0.974605\pi$
$997$	−564030.	−	976929.i	−0.567430	−	0.982817i	0.429389	−	0.903119i	$-0.358729\pi$
$998$	−511821.	−	182975.i	−0.513874	−	0.183709i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.91.21		44
3.2	odd	2		36.5.f.a.31.2	yes	44
4.3	odd	2	inner	108.5.f.a.91.7		44
9.2	odd	6		36.5.f.a.7.16	yes	44
9.4	even	3		324.5.d.e.163.10		22
9.5	odd	6		324.5.d.f.163.13		22
9.7	even	3	inner	108.5.f.a.19.7		44
12.11	even	2		36.5.f.a.31.16	yes	44
36.7	odd	6	inner	108.5.f.a.19.21		44
36.11	even	6		36.5.f.a.7.2	✓	44
36.23	even	6		324.5.d.f.163.14		22
36.31	odd	6		324.5.d.e.163.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.2	✓	44	36.11	even	6
36.5.f.a.7.16	yes	44	9.2	odd	6
36.5.f.a.31.2	yes	44	3.2	odd	2
36.5.f.a.31.16	yes	44	12.11	even	2
108.5.f.a.19.7		44	9.7	even	3	inner
108.5.f.a.19.21		44	36.7	odd	6	inner
108.5.f.a.91.7		44	4.3	odd	2	inner
108.5.f.a.91.21		44	1.1	even	1	trivial
324.5.d.e.163.9		22	36.31	odd	6
324.5.d.e.163.10		22	9.4	even	3
324.5.d.f.163.13		22	9.5	odd	6
324.5.d.f.163.14		22	36.23	even	6

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.93519 - 0.717143i) q^{2} +(14.9714 - 5.64418i) q^{4} +(5.51579 - 9.55363i) q^{5} +(-10.3188 + 5.95759i) q^{7} +(54.8676 - 32.9476i) q^{8} +O(q^{10})\)	\(q+(3.93519 - 0.717143i) q^{2} +(14.9714 - 5.64418i) q^{4} +(5.51579 - 9.55363i) q^{5} +(-10.3188 + 5.95759i) q^{7} +(54.8676 - 32.9476i) q^{8} +(14.8544 - 41.5509i) q^{10} +(189.995 - 109.694i) q^{11} +(18.5350 - 32.1036i) q^{13} +(-36.3341 + 30.8443i) q^{14} +(192.286 - 169.003i) q^{16} -284.021 q^{17} +45.4901i q^{19} +(28.6568 - 174.163i) q^{20} +(669.000 - 567.918i) q^{22} +(174.319 + 100.643i) q^{23} +(251.652 + 435.874i) q^{25} +(49.9160 - 139.626i) q^{26} +(-120.862 + 147.435i) q^{28} +(-614.153 - 1063.74i) q^{29} +(1311.83 + 757.384i) q^{31} +(635.484 - 802.954i) q^{32} +(-1117.68 + 203.683i) q^{34} +131.443i q^{35} -1521.29 q^{37} +(32.6229 + 179.012i) q^{38} +(-12.1303 - 705.917i) q^{40} +(-1316.97 + 2281.07i) q^{41} +(34.6057 - 19.9796i) q^{43} +(2225.36 - 2714.63i) q^{44} +(758.153 + 271.038i) q^{46} +(-2498.36 + 1442.43i) q^{47} +(-1129.51 + 1956.38i) q^{49} +(1302.88 + 1534.78i) q^{50} +(96.2969 - 585.252i) q^{52} -1415.13 q^{53} -2420.19i q^{55} +(-369.883 + 666.859i) q^{56} +(-3179.66 - 3745.60i) q^{58} +(2453.33 + 1416.43i) q^{59} +(2628.64 + 4552.93i) q^{61} +(5705.44 + 2039.68i) q^{62} +(1924.92 - 3615.51i) q^{64} +(-204.471 - 354.154i) q^{65} +(-805.917 - 465.296i) q^{67} +(-4252.19 + 1603.07i) q^{68} +(94.2635 + 517.254i) q^{70} -1162.75i q^{71} -2162.87 q^{73} +(-5986.57 + 1090.98i) q^{74} +(256.754 + 681.051i) q^{76} +(-1307.02 + 2263.82i) q^{77} +(-6482.54 + 3742.70i) q^{79} +(-553.978 - 2769.22i) q^{80} +(-3546.69 + 9920.88i) q^{82} +(-966.756 + 558.157i) q^{83} +(-1566.60 + 2713.43i) q^{85} +(121.852 - 103.441i) q^{86} +(6810.44 - 12278.5i) q^{88} +6739.71 q^{89} +441.696i q^{91} +(3177.85 + 522.881i) q^{92} +(-8797.09 + 7467.91i) q^{94} +(434.596 + 250.914i) q^{95} +(-6023.28 - 10432.6i) q^{97} +(-3041.85 + 8508.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

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