LMFDB - Embedded newform 108.3.k.a.77.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(5,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.k (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			77.5
Character	$\chi$	$=$	108.77
Dual form			108.3.k.a.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.15561 + 2.08647i) q^{3} +(2.92426 + 0.515626i) q^{5} +(0.715829 - 0.600652i) q^{7} +(0.293266 + 8.99522i) q^{9} +O(q^{10})$	\(q+(2.15561 + 2.08647i) q^{3} +(2.92426 + 0.515626i) q^{5} +(0.715829 - 0.600652i) q^{7} +(0.293266 + 8.99522i) q^{9} +(5.89850 - 1.04007i) q^{11} +(-9.53387 + 3.47005i) q^{13} +(5.22771 + 7.21288i) q^{15} +(6.81408 + 3.93411i) q^{17} +(-2.29223 - 3.97026i) q^{19} +(2.79629 + 0.198789i) q^{21} +(22.9203 - 27.3153i) q^{23} +(-15.2069 - 5.53485i) q^{25} +(-18.1361 + 20.0020i) q^{27} +(3.20583 - 8.80793i) q^{29} +(-41.5801 - 34.8898i) q^{31} +(14.8849 + 10.0651i) q^{33} +(2.40298 - 1.38736i) q^{35} +(-9.21875 + 15.9673i) q^{37} +(-27.7914 - 12.4121i) q^{39} +(-3.70267 - 10.1730i) q^{41} +(-9.70581 - 55.0444i) q^{43} +(-3.78058 + 26.4556i) q^{45} +(-46.8929 - 55.8847i) q^{47} +(-8.35713 + 47.3957i) q^{49} +(6.48005 + 22.6978i) q^{51} +44.8133i q^{53} +17.7851 q^{55} +(3.34269 - 13.3410i) q^{57} +(81.5042 + 14.3714i) q^{59} +(47.6825 - 40.0104i) q^{61} +(5.61292 + 6.26289i) q^{63} +(-29.6688 + 5.23141i) q^{65} +(-31.9873 + 11.6424i) q^{67} +(106.400 - 11.0585i) q^{69} +(60.7133 + 35.0528i) q^{71} +(68.4607 + 118.577i) q^{73} +(-21.2317 - 43.6597i) q^{75} +(3.59760 - 4.28745i) q^{77} +(41.4241 + 15.0772i) q^{79} +(-80.8280 + 5.27599i) q^{81} +(-31.4310 + 86.3561i) q^{83} +(17.8976 + 15.0179i) q^{85} +(25.2880 - 12.2976i) q^{87} +(-86.0608 + 49.6872i) q^{89} +(-4.74033 + 8.21049i) q^{91} +(-16.8336 - 161.964i) q^{93} +(-4.65591 - 12.7920i) q^{95} +(-4.81594 - 27.3125i) q^{97} +(11.0855 + 52.7533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q - 9 * q^5 + 6 * q^9	$ 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) $ 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.15561	+	2.08647i	0.718535	+	0.695491i
$3$	2.15561	+	2.08647i	0.718535	+	0.695491i
$4$		0			0
$5$	2.92426	+	0.515626i	0.584852	+	0.103125i	0.458242	−	0.888827i	$-0.348479\pi$
$5$	2.92426	+	0.515626i	0.584852	+	0.103125i	0.126610	+	0.991953i	$0.459590\pi$
$6$		0			0
$7$	0.715829	−	0.600652i	0.102261	−	0.0858074i	−0.590224	−	0.807240i	$-0.700960\pi$
$7$	0.715829	−	0.600652i	0.102261	−	0.0858074i	0.692485	+	0.721432i	$0.256516\pi$
$8$		0			0
$9$	0.293266	+	8.99522i	0.0325852	+	0.999469i
$10$		0			0
$11$	5.89850	−	1.04007i	0.536228	−	0.0945514i	0.101025	−	0.994884i	$-0.467788\pi$
$11$	5.89850	−	1.04007i	0.536228	−	0.0945514i	0.435203	+	0.900332i	$0.356677\pi$
$12$		0			0
$13$	−9.53387	+	3.47005i	−0.733375	+	0.266927i	−0.681593	−	0.731732i	$-0.738712\pi$
$13$	−9.53387	+	3.47005i	−0.733375	+	0.266927i	−0.0517821	+	0.998658i	$0.516490\pi$
$14$		0			0
$15$	5.22771	+	7.21288i	0.348514	+	0.480858i
$16$		0			0
$17$	6.81408	+	3.93411i	0.400828	+	0.231418i	0.686841	−	0.726807i	$-0.258997\pi$
$17$	6.81408	+	3.93411i	0.400828	+	0.231418i	−0.286013	+	0.958226i	$0.592330\pi$
$18$		0			0
$19$	−2.29223	−	3.97026i	−0.120644	−	0.208961i	0.799378	−	0.600828i	$-0.205163\pi$
$19$	−2.29223	−	3.97026i	−0.120644	−	0.208961i	−0.920022	+	0.391867i	$0.871829\pi$
$20$		0			0
$21$	2.79629	+	0.198789i	0.133157	+	0.00946615i
$22$		0			0
$23$	22.9203	−	27.3153i	0.996534	−	1.18762i	0.0143130	−	0.999898i	$-0.495444\pi$
$23$	22.9203	−	27.3153i	0.996534	−	1.18762i	0.982221	−	0.187726i	$-0.0601117\pi$
$24$		0			0
$25$	−15.2069	−	5.53485i	−0.608275	−	0.221394i
$26$		0			0
$27$	−18.1361	+	20.0020i	−0.671708	+	0.740816i
$28$		0			0
$29$	3.20583	−	8.80793i	0.110546	−	0.303722i	−0.872068	−	0.489385i	$-0.837221\pi$
$29$	3.20583	−	8.80793i	0.110546	−	0.303722i	0.982613	+	0.185663i	$0.0594434\pi$
$30$		0			0
$31$	−41.5801	−	34.8898i	−1.34129	−	1.12548i	−0.981292	−	0.192527i	$-0.938332\pi$
$31$	−41.5801	−	34.8898i	−1.34129	−	1.12548i	−0.360002	−	0.932952i	$-0.617224\pi$
$32$		0			0
$33$	14.8849	+	10.0651i	0.451058	+	0.305003i
$34$		0			0
$35$	2.40298	−	1.38736i	0.0686566	−	0.0396389i
$36$		0			0
$37$	−9.21875	+	15.9673i	−0.249155	+	0.431550i	−0.963292	−	0.268457i	$-0.913486\pi$
$37$	−9.21875	+	15.9673i	−0.249155	+	0.431550i	0.714136	+	0.700007i	$0.246820\pi$
$38$		0			0
$39$	−27.7914	−	12.4121i	−0.712600	−	0.318259i
$40$		0			0
$41$	−3.70267	−	10.1730i	−0.0903090	−	0.248122i	0.886313	−	0.463087i	$-0.153258\pi$
$41$	−3.70267	−	10.1730i	−0.0903090	−	0.248122i	−0.976622	+	0.214965i	$0.931036\pi$
$42$		0			0
$43$	−9.70581	−	55.0444i	−0.225716	−	1.28010i	−0.861311	−	0.508078i	$-0.830356\pi$
$43$	−9.70581	−	55.0444i	−0.225716	−	1.28010i	0.635594	−	0.772023i	$-0.280755\pi$
$44$		0			0
$45$	−3.78058	+	26.4556i	−0.0840130	+	0.587902i
$46$		0			0
$47$	−46.8929	−	55.8847i	−0.997720	−	1.18904i	−0.981946	−	0.189161i	$-0.939423\pi$
$47$	−46.8929	−	55.8847i	−0.997720	−	1.18904i	−0.0157742	−	0.999876i	$-0.505021\pi$
$48$		0			0
$49$	−8.35713	+	47.3957i	−0.170554	+	0.967258i
$50$		0			0
$51$	6.48005	+	22.6978i	0.127060	+	0.445054i
$52$		0			0
$53$			44.8133i			0.845534i	0.906238	+	0.422767i	$0.138941\pi$
$53$			44.8133i			0.845534i	−0.906238	+	0.422767i	$0.861059\pi$
$54$		0			0
$55$	17.7851			0.323365
$56$		0			0
$57$	3.34269	−	13.3410i	0.0586437	−	0.234052i
$58$		0			0
$59$	81.5042	+	14.3714i	1.38143	+	0.243583i	0.814490	−	0.580178i	$-0.197017\pi$
$59$	81.5042	+	14.3714i	1.38143	+	0.243583i	0.566937	+	0.823761i	$0.308128\pi$
$60$		0			0
$61$	47.6825	−	40.0104i	0.781681	−	0.655908i	−0.161990	−	0.986792i	$-0.551791\pi$
$61$	47.6825	−	40.0104i	0.781681	−	0.655908i	0.943671	+	0.330884i	$0.107347\pi$
$62$		0			0
$63$	5.61292	+	6.26289i	0.0890940	+	0.0994109i
$64$		0			0
$65$	−29.6688	+	5.23141i	−0.456443	+	0.0804832i
$66$		0			0
$67$	−31.9873	+	11.6424i	−0.477423	+	0.173768i	−0.569512	−	0.821983i	$-0.692868\pi$
$67$	−31.9873	+	11.6424i	−0.477423	+	0.173768i	0.0920892	+	0.995751i	$0.470646\pi$
$68$		0			0
$69$	106.400	−	11.0585i	1.54203	−	0.160269i
$70$		0			0
$71$	60.7133	+	35.0528i	0.855117	+	0.493702i	0.862374	−	0.506272i	$-0.168977\pi$
$71$	60.7133	+	35.0528i	0.855117	+	0.493702i	−0.00725708	+	0.999974i	$0.502310\pi$
$72$		0			0
$73$	68.4607	+	118.577i	0.937818	+	1.62435i	0.769530	+	0.638611i	$0.220491\pi$
$73$	68.4607	+	118.577i	0.937818	+	1.62435i	0.168288	+	0.985738i	$0.446176\pi$
$74$		0			0
$75$	−21.2317	−	43.6597i	−0.283090	−	0.582129i
$76$		0			0
$77$	3.59760	−	4.28745i	0.0467221	−	0.0556812i
$78$		0			0
$79$	41.4241	+	15.0772i	0.524356	+	0.190850i	0.590617	−	0.806952i	$-0.298885\pi$
$79$	41.4241	+	15.0772i	0.524356	+	0.190850i	−0.0662604	+	0.997802i	$0.521107\pi$
$80$		0			0
$81$	−80.8280	+	5.27599i	−0.997876	+	0.0651357i
$82$		0			0
$83$	−31.4310	+	86.3561i	−0.378687	+	1.04043i	0.593214	+	0.805045i	$0.297859\pi$
$83$	−31.4310	+	86.3561i	−0.378687	+	1.04043i	−0.971901	+	0.235390i	$0.924363\pi$
$84$		0			0
$85$	17.8976	+	15.0179i	0.210560	+	0.176681i
$86$		0			0
$87$	25.2880	−	12.2976i	0.290667	−	0.141351i
$88$		0			0
$89$	−86.0608	+	49.6872i	−0.966975	+	0.558283i	−0.898313	−	0.439357i	$-0.855206\pi$
$89$	−86.0608	+	49.6872i	−0.966975	+	0.558283i	−0.0686623	+	0.997640i	$0.521873\pi$
$90$		0			0
$91$	−4.74033	+	8.21049i	−0.0520915	+	0.0902252i
$92$		0			0
$93$	−16.8336	−	161.964i	−0.181006	−	1.74155i
$94$		0			0
$95$	−4.65591	−	12.7920i	−0.0490096	−	0.134653i
$96$		0			0
$97$	−4.81594	−	27.3125i	−0.0496488	−	0.281573i	0.949868	−	0.312651i	$-0.101217\pi$
$97$	−4.81594	−	27.3125i	−0.0496488	−	0.281573i	−0.999517	+	0.0310783i	$0.990106\pi$
$98$		0			0
$99$	11.0855	+	52.7533i	0.111974	+	0.532862i
$100$		0			0
$101$	−114.677	−	136.666i	−1.13541	−	1.35313i	−0.926988	−	0.375092i	$-0.877611\pi$
$101$	−114.677	−	136.666i	−1.13541	−	1.35313i	−0.208424	−	0.978039i	$-0.566833\pi$
$102$		0			0
$103$	−0.915345	+	5.19118i	−0.00888684	+	0.0503998i	−0.988929	−	0.148391i	$-0.952590\pi$
$103$	−0.915345	+	5.19118i	−0.00888684	+	0.0503998i	0.980042	+	0.198791i	$0.0637016\pi$
$104$		0			0
$105$	8.07457	+	2.02315i	0.0769007	+	0.0192681i
$106$		0			0
$107$			153.946i			1.43875i	0.694623	+	0.719374i	$0.255571\pi$
$107$			153.946i			1.43875i	−0.694623	+	0.719374i	$0.744429\pi$
$108$		0			0
$109$	145.335			1.33335			0.666675	−	0.745348i	$-0.267717\pi$
$109$	145.335			1.33335			0.666675	+	0.745348i	$0.267717\pi$
$110$		0			0
$111$	−53.1874	+	15.1846i	−0.479166	+	0.136798i
$112$		0			0
$113$	−62.4372	−	11.0094i	−0.552542	−	0.0974280i	−0.109596	−	0.993976i	$-0.534956\pi$
$113$	−62.4372	−	11.0094i	−0.552542	−	0.0974280i	−0.442946	+	0.896548i	$0.646067\pi$
$114$		0			0
$115$	81.1094	−	68.0589i	0.705299	−	0.591816i
$116$		0			0
$117$	−34.0098	−	84.7416i	−0.290682	−	0.724288i
$118$		0			0
$119$	7.24074	−	1.27674i	0.0608466	−	0.0107289i
$120$		0			0
$121$	−79.9922	+	29.1148i	−0.661092	+	0.240618i
$122$		0			0
$123$	13.2442	−	29.6545i	0.107676	−	0.241093i
$124$		0			0
$125$	−105.904	−	61.1436i	−0.847230	−	0.489149i
$126$		0			0
$127$	32.0199	+	55.4601i	0.252125	+	0.436694i	0.964111	−	0.265501i	$-0.0855372\pi$
$127$	32.0199	+	55.4601i	0.252125	+	0.436694i	−0.711986	+	0.702194i	$0.752204\pi$
$128$		0			0
$129$	93.9267	−	138.905i	0.728114	−	1.07678i
$130$		0			0
$131$	77.4031	−	92.2454i	0.590863	−	0.704164i	−0.384908	−	0.922955i	$-0.625767\pi$
$131$	77.4031	−	92.2454i	0.590863	−	0.704164i	0.975772	+	0.218791i	$0.0702114\pi$
$132$		0			0
$133$	−4.02559	−	1.46519i	−0.0302676	−	0.0110165i
$134$		0			0
$135$	−63.3483	+	49.1397i	−0.469247	+	0.363998i
$136$		0			0
$137$	−55.4867	+	152.448i	−0.405012	+	1.11276i	0.554767	+	0.832006i	$0.312807\pi$
$137$	−55.4867	+	152.448i	−0.405012	+	1.11276i	−0.959779	+	0.280756i	$0.909415\pi$
$138$		0			0
$139$	−81.5779	−	68.4520i	−0.586892	−	0.492461i	0.300311	−	0.953841i	$-0.402910\pi$
$139$	−81.5779	−	68.4520i	−0.586892	−	0.492461i	−0.887202	+	0.461381i	$0.847354\pi$
$140$		0			0
$141$	15.5195	−	218.306i	0.110067	−	1.54827i
$142$		0			0
$143$	−52.6265	+	30.3839i	−0.368018	+	0.212475i
$144$		0			0
$145$	13.9163	−	24.1037i	0.0959743	−	0.166232i
$146$		0			0
$147$	−116.904	+	84.7294i	−0.795268	+	0.576390i
$148$		0			0
$149$	5.26909	+	14.4767i	0.0353630	+	0.0971590i	0.956118	−	0.292983i	$-0.0946480\pi$
$149$	5.26909	+	14.4767i	0.0353630	+	0.0971590i	−0.920755	+	0.390142i	$0.872426\pi$
$150$		0			0
$151$	0.522463	+	2.96303i	0.00346002	+	0.0196227i	0.986489	−	0.163828i	$-0.0523843\pi$
$151$	0.522463	+	2.96303i	0.00346002	+	0.0196227i	−0.983029	+	0.183451i	$0.941273\pi$
$152$		0			0
$153$	−33.3899	+	62.4479i	−0.218234	+	0.408156i
$154$		0			0
$155$	−103.601	−	123.467i	−0.668393	−	0.796560i
$156$		0			0
$157$	−9.84877	+	55.8551i	−0.0627310	+	0.355765i	0.937244	+	0.348675i	$0.113368\pi$
$157$	−9.84877	+	55.8551i	−0.0627310	+	0.355765i	−0.999975	+	0.00709063i	$0.997743\pi$
$158$		0			0
$159$	−93.5017	+	96.5998i	−0.588061	+	0.607546i
$160$		0			0
$161$		−	33.3202i		−	0.206958i
$162$		0			0
$163$	−68.0676			−0.417592			−0.208796	−	0.977959i	$-0.566955\pi$
$163$	−68.0676			−0.417592			−0.208796	+	0.977959i	$0.566955\pi$
$164$		0			0
$165$	38.3376	+	37.1080i	0.232349	+	0.224897i
$166$		0			0
$167$	105.878	+	18.6691i	0.633998	+	0.111791i	0.481405	−	0.876498i	$-0.340127\pi$
$167$	105.878	+	18.6691i	0.633998	+	0.111791i	0.152593	+	0.988289i	$0.451238\pi$
$168$		0			0
$169$	−50.6080	+	42.4652i	−0.299456	+	0.251273i
$170$		0			0
$171$	35.0411	−	21.7835i	0.204919	−	0.127389i
$172$		0			0
$173$	265.492	−	46.8135i	1.53464	−	0.270598i	0.658472	−	0.752606i	$-0.271203\pi$
$173$	265.492	−	46.8135i	1.53464	−	0.270598i	0.876167	+	0.482007i	$0.160092\pi$
$174$		0			0
$175$	−14.2100	+	5.17203i	−0.0812002	+	0.0295545i
$176$		0			0
$177$	145.705	+	201.035i	0.823194	+	1.13579i
$178$		0			0
$179$	187.227	+	108.096i	1.04596	+	0.603887i	0.921517	−	0.388339i	$-0.126951\pi$
$179$	187.227	+	108.096i	1.04596	+	0.603887i	0.124447	+	0.992226i	$0.460284\pi$
$180$		0			0
$181$	−62.0552	−	107.483i	−0.342847	−	0.593828i	0.642114	−	0.766610i	$-0.278058\pi$
$181$	−62.0552	−	107.483i	−0.342847	−	0.593828i	−0.984960	+	0.172782i	$0.944724\pi$
$182$		0			0
$183$	186.265	+	13.2417i	1.01784	+	0.0723589i
$184$		0			0
$185$	−35.1912	+	41.9393i	−0.190223	+	0.226699i
$186$		0			0
$187$	44.2846	+	16.1183i	0.236816	+	0.0861940i
$188$		0			0
$189$	−0.968095	+	25.2115i	−0.00512220	+	0.133394i
$190$		0			0
$191$	−34.5227	+	94.8505i	−0.180747	+	0.496599i	−0.996668	−	0.0815645i	$-0.974008\pi$
$191$	−34.5227	+	94.8505i	−0.180747	+	0.496599i	0.815921	+	0.578164i	$0.196231\pi$
$192$		0			0
$193$	149.819	+	125.713i	0.776264	+	0.651362i	0.942305	−	0.334756i	$-0.108654\pi$
$193$	149.819	+	125.713i	0.776264	+	0.651362i	−0.166041	+	0.986119i	$0.553098\pi$
$194$		0			0
$195$	−74.8694	−	50.6262i	−0.383945	−	0.259622i
$196$		0			0
$197$	213.741	−	123.403i	1.08498	−	0.626412i	0.152743	−	0.988266i	$-0.451189\pi$
$197$	213.741	−	123.403i	1.08498	−	0.626412i	0.932235	+	0.361854i	$0.117856\pi$
$198$		0			0
$199$	−79.4674	+	137.642i	−0.399334	+	0.691666i	−0.993644	−	0.112570i	$-0.964092\pi$
$199$	−79.4674	+	137.642i	−0.399334	+	0.691666i	0.594310	+	0.804236i	$0.297425\pi$
$200$		0			0
$201$	−93.2436	−	41.6442i	−0.463899	−	0.207185i
$202$		0			0
$203$	−2.99568	−	8.23055i	−0.0147570	−	0.0405446i
$204$		0			0
$205$	−5.58211	−	31.6577i	−0.0272298	−	0.154428i
$206$		0			0
$207$	252.429	+	198.162i	1.21947	+	0.957306i
$208$		0			0
$209$	−17.6501	−	21.0345i	−0.0844501	−	0.100644i
$210$		0			0
$211$	60.4264	−	342.695i	0.286381	−	1.62415i	−0.413930	−	0.910309i	$-0.635844\pi$
$211$	60.4264	−	342.695i	0.286381	−	1.62415i	0.700311	−	0.713838i	$-0.253045\pi$
$212$		0			0
$213$	57.7371	+	202.237i	0.271066	+	0.949468i
$214$		0			0
$215$		−	165.969i		−	0.771947i
$216$		0			0
$217$	−50.7209			−0.233737
$218$		0			0
$219$	−99.8343	+	398.448i	−0.455864	+	1.81940i
$220$		0			0
$221$	−78.6161	−	13.8621i	−0.355729	−	0.0627246i
$222$		0			0
$223$	−120.247	+	100.900i	−0.539226	+	0.452465i	−0.871273	−	0.490798i	$-0.836705\pi$
$223$	−120.247	+	100.900i	−0.539226	+	0.452465i	0.332047	+	0.943263i	$0.392261\pi$
$224$		0			0
$225$	45.3275	−	138.412i	0.201456	−	0.615166i
$226$		0			0
$227$	357.998	−	63.1248i	1.57709	−	0.278083i	0.684518	−	0.728996i	$-0.260013\pi$
$227$	357.998	−	63.1248i	1.57709	−	0.278083i	0.892568	+	0.450914i	$0.148902\pi$
$228$		0			0
$229$	−84.0632	+	30.5965i	−0.367088	+	0.133609i	−0.518977	−	0.854788i	$-0.673687\pi$
$229$	−84.0632	+	30.5965i	−0.367088	+	0.133609i	0.151888	+	0.988398i	$0.451465\pi$
$230$		0			0
$231$	16.7007	−	1.73576i	0.0722972	−	0.00751412i
$232$		0			0
$233$	−160.610	−	92.7281i	−0.689312	−	0.397975i	0.114042	−	0.993476i	$-0.463620\pi$
$233$	−160.610	−	92.7281i	−0.689312	−	0.397975i	−0.803354	+	0.595501i	$0.796953\pi$
$234$		0			0
$235$	−108.311	−	187.601i	−0.460899	−	0.798301i
$236$		0			0
$237$	57.8360	+	118.931i	0.244034	+	0.501817i
$238$		0			0
$239$	19.8929	−	23.7075i	0.0832341	−	0.0991945i	−0.722820	−	0.691036i	$-0.757154\pi$
$239$	19.8929	−	23.7075i	0.0832341	−	0.0991945i	0.806054	+	0.591842i	$0.201599\pi$
$240$		0			0
$241$	−329.180	−	119.812i	−1.36589	−	0.497144i	−0.448020	−	0.894023i	$-0.647871\pi$
$241$	−329.180	−	119.812i	−1.36589	−	0.497144i	−0.917871	+	0.396880i	$0.870093\pi$
$242$		0			0
$243$	−185.241	−	157.272i	−0.762310	−	0.647212i
$244$		0			0
$245$	−48.8769	+	134.288i	−0.199497	+	0.548115i
$246$		0			0
$247$	35.6308	+	29.8978i	0.144254	+	0.121044i
$248$		0			0
$249$	−247.932	+	120.570i	−0.995712	+	0.484215i
$250$		0			0
$251$	41.0932	−	23.7252i	0.163718	−	0.0945226i	−0.415902	−	0.909409i	$-0.636534\pi$
$251$	41.0932	−	23.7252i	0.163718	−	0.0945226i	0.579620	+	0.814887i	$0.303201\pi$
$252$		0			0
$253$	106.786	−	184.958i	0.422078	−	0.731060i
$254$		0			0
$255$	7.24580	+	69.7155i	0.0284149	+	0.273394i
$256$		0			0
$257$	39.9077	+	109.645i	0.155283	+	0.426636i	0.992801	−	0.119773i	$-0.0382167\pi$
$257$	39.9077	+	109.645i	0.155283	+	0.426636i	−0.837519	+	0.546409i	$0.815994\pi$
$258$		0			0
$259$	2.99176	+	16.9671i	0.0115512	+	0.0655102i
$260$		0			0
$261$	80.1695	+	26.2540i	0.307163	+	0.100590i
$262$		0			0
$263$	−205.463	−	244.861i	−0.781227	−	0.931030i	0.217762	−	0.976002i	$-0.430124\pi$
$263$	−205.463	−	244.861i	−0.781227	−	0.931030i	−0.998988	+	0.0449723i	$0.985680\pi$
$264$		0			0
$265$	−23.1069	+	131.046i	−0.0871959	+	0.494512i
$266$		0			0
$267$	−289.184	−	72.4574i	−1.08309	−	0.271376i
$268$		0			0
$269$		−	347.341i		−	1.29123i	−0.763662	−	0.645616i	$-0.776601\pi$
$269$		−	347.341i		−	1.29123i	0.763662	−	0.645616i	$-0.223399\pi$
$270$		0			0
$271$	−464.981			−1.71580			−0.857898	−	0.513821i	$-0.828230\pi$
$271$	−464.981			−1.71580			−0.857898	+	0.513821i	$0.828230\pi$
$272$		0			0
$273$	−27.3492	+	7.80801i	−0.100180	+	0.0286008i
$274$		0			0
$275$	−95.4545	−	16.8312i	−0.347107	−	0.0612044i
$276$		0			0
$277$	−104.098	+	87.3486i	−0.375805	+	0.315338i	−0.811053	−	0.584973i	$-0.801105\pi$
$277$	−104.098	+	87.3486i	−0.375805	+	0.315338i	0.435248	+	0.900311i	$0.356661\pi$
$278$		0			0
$279$	301.648	−	384.254i	1.08117	−	1.37726i
$280$		0			0
$281$	531.265	−	93.6763i	1.89062	−	0.333367i	0.896626	−	0.442789i	$-0.146011\pi$
$281$	531.265	−	93.6763i	1.89062	−	0.333367i	0.993995	+	0.109422i	$0.0349000\pi$
$282$		0			0
$283$	279.334	−	101.669i	0.987048	−	0.359256i	0.202471	−	0.979288i	$-0.435103\pi$
$283$	279.334	−	101.669i	0.987048	−	0.359256i	0.784576	+	0.620032i	$0.212881\pi$
$284$		0			0
$285$	16.6539	−	37.2890i	0.0584346	−	0.130838i
$286$		0			0
$287$	−8.76090	−	5.05811i	−0.0305258	−	0.0176241i
$288$		0			0
$289$	−113.546	−	196.667i	−0.392891	−	0.680507i
$290$		0			0
$291$	46.6056	−	68.9234i	0.160157	−	0.236850i
$292$		0			0
$293$	−345.127	+	411.306i	−1.17791	+	1.40378i	−0.282071	+	0.959393i	$0.591021\pi$
$293$	−345.127	+	411.306i	−1.17791	+	1.40378i	−0.895837	+	0.444383i	$0.853423\pi$
$294$		0			0
$295$	230.929	+	84.0514i	0.782811	+	0.284920i
$296$		0			0
$297$	−86.1725	+	136.845i	−0.290143	+	0.460757i
$298$		0			0
$299$	−123.734	+	339.955i	−0.413825	+	1.13697i
$300$		0			0
$301$	−40.0102	−	33.5725i	−0.132924	−	0.111537i
$302$		0			0
$303$	37.9529	−	533.868i	0.125257	−	1.76194i
$304$		0			0
$305$	160.067	−	92.4145i	0.524809	−	0.302998i
$306$		0			0
$307$	15.9704	−	27.6615i	0.0520208	−	0.0901027i	−0.838842	−	0.544374i	$-0.816767\pi$
$307$	15.9704	−	27.6615i	0.0520208	−	0.0901027i	0.890863	+	0.454272i	$0.150100\pi$
$308$		0			0
$309$	−12.8044	+	9.28029i	−0.0414381	+	0.0300333i
$310$		0			0
$311$	−121.282	−	333.220i	−0.389975	−	1.07145i	−0.967012	−	0.254730i	$-0.918013\pi$
$311$	−121.282	−	333.220i	−0.389975	−	1.07145i	0.577037	−	0.816718i	$-0.304209\pi$
$312$		0			0
$313$	72.9700	+	413.834i	0.233131	+	1.32215i	0.846514	+	0.532366i	$0.178697\pi$
$313$	72.9700	+	413.834i	0.233131	+	1.32215i	−0.613383	+	0.789786i	$0.710192\pi$
$314$		0			0
$315$	13.1843	+	21.2085i	0.0418551	+	0.0673285i
$316$		0			0
$317$	162.451	+	193.602i	0.512464	+	0.610731i	0.958782	−	0.284144i	$-0.0917093\pi$
$317$	162.451	+	193.602i	0.512464	+	0.610731i	−0.446318	+	0.894875i	$0.647265\pi$
$318$		0			0
$319$	9.74875	−	55.2879i	0.0305603	−	0.173316i
$320$		0			0
$321$	−321.204	+	331.847i	−1.00064	+	1.03379i
$322$		0			0
$323$		−	36.0716i		−	0.111677i
$324$		0			0
$325$	164.187			0.505190
$326$		0			0
$327$	313.285	+	303.238i	0.958059	+	0.927333i
$328$		0			0
$329$	−67.1345	−	11.8376i	−0.204056	−	0.0359806i
$330$		0			0
$331$	−121.834	+	102.231i	−0.368080	+	0.308855i	−0.808001	−	0.589181i	$-0.799451\pi$
$331$	−121.834	+	102.231i	−0.368080	+	0.308855i	0.439922	+	0.898036i	$0.355006\pi$
$332$		0			0
$333$	−146.333	−	78.2420i	−0.439439	−	0.234961i
$334$		0			0
$335$	−99.5424	+	17.5520i	−0.297142	+	0.0523941i
$336$		0			0
$337$	499.639	−	181.854i	1.48261	−	0.539626i	0.531117	−	0.847298i	$-0.321772\pi$
$337$	499.639	−	181.854i	1.48261	−	0.539626i	0.951492	+	0.307673i	$0.0995501\pi$
$338$		0			0
$339$	−111.619	−	154.005i	−0.329260	−	0.454293i
$340$		0			0
$341$	−281.548	−	162.552i	−0.825654	−	0.476692i
$342$		0			0
$343$	45.3800	+	78.6004i	0.132303	+	0.229156i
$344$		0			0
$345$	316.843	+	22.5245i	0.918385	+	0.0652884i
$346$		0			0
$347$	−57.0006	+	67.9306i	−0.164267	+	0.195765i	−0.841898	−	0.539636i	$-0.818562\pi$
$347$	−57.0006	+	67.9306i	−0.164267	+	0.195765i	0.677632	+	0.735401i	$0.263006\pi$
$348$		0			0
$349$	54.9200	+	19.9893i	0.157364	+	0.0572758i	0.419501	−	0.907755i	$-0.362205\pi$
$349$	54.9200	+	19.9893i	0.157364	+	0.0572758i	−0.262137	+	0.965031i	$0.584427\pi$
$350$		0			0
$351$	103.499	−	253.630i	0.294870	−	0.722593i
$352$		0			0
$353$	−154.431	+	424.296i	−0.437482	+	1.20197i	0.503643	+	0.863912i	$0.331993\pi$
$353$	−154.431	+	424.296i	−0.437482	+	1.20197i	−0.941125	+	0.338060i	$0.890229\pi$
$354$		0			0
$355$	159.467	+	133.809i	0.449204	+	0.376927i
$356$		0			0
$357$	18.2721	+	12.3555i	0.0511822	+	0.0346091i
$358$		0			0
$359$	−354.208	+	204.502i	−0.986653	+	0.569644i	−0.904272	−	0.426956i	$-0.859586\pi$
$359$	−354.208	+	204.502i	−0.986653	+	0.569644i	−0.0823810	+	0.996601i	$0.526252\pi$
$360$		0			0
$361$	169.991	−	294.434i	0.470890	−	0.815606i
$362$		0			0
$363$	−233.179	−	104.142i	−0.642366	−	0.286891i
$364$		0			0
$365$	139.055	+	382.052i	0.380974	+	1.04672i
$366$		0			0
$367$	94.4979	+	535.924i	0.257487	+	1.46028i	0.789606	+	0.613614i	$0.210285\pi$
$367$	94.4979	+	535.924i	0.257487	+	1.46028i	−0.532119	+	0.846670i	$0.678604\pi$
$368$		0			0
$369$	90.4225	−	36.2897i	0.245047	−	0.0983461i
$370$		0			0
$371$	26.9172	+	32.0786i	0.0725530	+	0.0864654i
$372$		0			0
$373$	−39.2174	+	222.413i	−0.105140	+	0.596281i	0.886024	+	0.463640i	$0.153457\pi$
$373$	−39.2174	+	222.413i	−0.105140	+	0.596281i	−0.991164	+	0.132641i	$0.957654\pi$
$374$		0			0
$375$	−100.712	−	352.767i	−0.268566	−	0.940711i
$376$		0			0
$377$			95.0981i			0.252250i
$378$		0			0
$379$	174.665			0.460857			0.230428	−	0.973089i	$-0.425987\pi$
$379$	174.665			0.460857			0.230428	+	0.973089i	$0.425987\pi$
$380$		0			0
$381$	−46.6937	+	186.359i	−0.122556	+	0.489130i
$382$		0			0
$383$	−567.725	−	100.105i	−1.48231	−	0.261372i	−0.626810	−	0.779172i	$-0.715640\pi$
$383$	−567.725	−	100.105i	−1.48231	−	0.261372i	−0.855501	+	0.517800i	$0.826751\pi$
$384$		0			0
$385$	12.7311	−	10.6826i	0.0330677	−	0.0277471i
$386$		0			0
$387$	492.290	−	103.449i	1.27207	−	0.267309i
$388$		0			0
$389$	674.651	−	118.959i	1.73432	−	0.305808i	0.784855	−	0.619679i	$-0.212737\pi$
$389$	674.651	−	118.959i	1.73432	−	0.305808i	0.949465	+	0.313872i	$0.101626\pi$
$390$		0			0
$391$	263.642	−	95.9579i	0.674277	−	0.245417i
$392$		0			0
$393$	359.318	−	37.3453i	0.914295	−	0.0950261i
$394$		0			0
$395$	113.361	+	65.4489i	0.286989	+	0.165693i
$396$		0			0
$397$	28.9985	+	50.2268i	0.0730440	+	0.126516i	0.900234	−	0.435406i	$-0.143395\pi$
$397$	28.9985	+	50.2268i	0.0730440	+	0.126516i	−0.827190	+	0.561922i	$0.810062\pi$
$398$		0			0
$399$	−5.62049	−	11.5577i	−0.0140864	−	0.0289666i
$400$		0			0
$401$	21.2804	−	25.3610i	0.0530683	−	0.0632443i	−0.738857	−	0.673862i	$-0.764634\pi$
$401$	21.2804	−	25.3610i	0.0530683	−	0.0632443i	0.791926	+	0.610618i	$0.209079\pi$
$402$		0			0
$403$	517.489	+	188.350i	1.28409	+	0.467371i
$404$		0			0
$405$	−239.083	−	26.2486i	−0.590327	−	0.0648115i
$406$		0			0
$407$	−37.7698	+	103.772i	−0.0928004	+	0.254967i
$408$		0			0
$409$	151.962	+	127.512i	0.371546	+	0.311764i	0.809373	−	0.587295i	$-0.199807\pi$
$409$	151.962	+	127.512i	0.371546	+	0.311764i	−0.437827	+	0.899059i	$0.644252\pi$
$410$		0			0
$411$	−437.687	+	212.847i	−1.06493	+	0.517876i
$412$		0			0
$413$	66.9752	−	38.6682i	0.162168	−	0.0936275i
$414$		0			0
$415$	−136.440	+	236.321i	−0.328771	+	0.569448i
$416$		0			0
$417$	−33.0266	−	317.766i	−0.0792004	−	0.762028i
$418$		0			0
$419$	124.159	+	341.125i	0.296323	+	0.814140i	0.995107	+	0.0988073i	$0.0315027\pi$
$419$	124.159	+	341.125i	0.296323	+	0.814140i	−0.698784	+	0.715333i	$0.746275\pi$
$420$		0			0
$421$	−82.0540	−	465.352i	−0.194903	−	1.10535i	−0.912557	−	0.408949i	$-0.865895\pi$
$421$	−82.0540	−	465.352i	−0.194903	−	1.10535i	0.717655	−	0.696399i	$-0.245216\pi$
$422$		0			0
$423$	488.943	−	438.201i	1.15589	−	1.03594i
$424$		0			0
$425$	−81.8462	−	97.5405i	−0.192579	−	0.229507i
$426$		0			0
$427$	10.1002	−	57.2812i	0.0236539	−	0.134148i
$428$		0			0
$429$	−176.837	−	44.3080i	−0.412208	−	0.103282i
$430$		0			0
$431$		−	144.354i		−	0.334927i	−0.985878	−	0.167464i	$-0.946442\pi$
$431$		−	144.354i		−	0.334927i	0.985878	−	0.167464i	$-0.0535577\pi$
$432$		0			0
$433$	−25.2858			−0.0583967			−0.0291984	−	0.999574i	$-0.509295\pi$
$433$	−25.2858			−0.0583967			−0.0291984	+	0.999574i	$0.509295\pi$
$434$		0			0
$435$	80.2897	−	22.9221i	0.184574	−	0.0526945i
$436$		0			0
$437$	−160.988	−	28.3865i	−0.368393	−	0.0649576i
$438$		0			0
$439$	−119.871	+	100.583i	−0.273054	+	0.229119i	−0.769024	−	0.639220i	$-0.779257\pi$
$439$	−119.871	+	100.583i	−0.273054	+	0.229119i	0.495970	+	0.868340i	$0.334813\pi$
$440$		0			0
$441$	−428.785	−	61.2747i	−0.972302	−	0.138945i
$442$		0			0
$443$	−522.960	+	92.2120i	−1.18050	+	0.208153i	−0.729251	−	0.684246i	$-0.760131\pi$
$443$	−522.960	+	92.2120i	−1.18050	+	0.208153i	−0.451246	+	0.892400i	$0.649020\pi$
$444$		0			0
$445$	−277.284	+	100.923i	−0.623111	+	0.226794i
$446$		0			0
$447$	−18.8472	+	42.1998i	−0.0421637	+	0.0944068i
$448$		0			0
$449$	−210.795	−	121.703i	−0.469477	−	0.271052i	0.246544	−	0.969132i	$-0.420705\pi$
$449$	−210.795	−	121.703i	−0.469477	−	0.271052i	−0.716021	+	0.698079i	$0.754038\pi$
$450$		0			0
$451$	−32.4208	−	56.1545i	−0.0718865	−	0.124511i
$452$		0			0
$453$	−5.05606	+	7.47723i	−0.0111613	+	0.0165060i
$454$		0			0
$455$	−18.0955	+	21.5654i	−0.0397704	+	0.0473965i
$456$		0			0
$457$	−610.104	−	222.060i	−1.33502	−	0.485908i	−0.426780	−	0.904356i	$-0.640352\pi$
$457$	−610.104	−	222.060i	−1.33502	−	0.485908i	−0.908241	+	0.418448i	$0.862574\pi$
$458$		0			0
$459$	−202.271	+	64.9460i	−0.440678	+	0.141495i
$460$		0			0
$461$	10.4561	−	28.7278i	0.0226813	−	0.0623162i	−0.927835	−	0.372990i	$-0.878333\pi$
$461$	10.4561	−	28.7278i	0.0226813	−	0.0623162i	0.950517	+	0.310674i	$0.100555\pi$
$462$		0			0
$463$	−6.55388	−	5.49936i	−0.0141553	−	0.0118777i	0.635683	−	0.771951i	$-0.280719\pi$
$463$	−6.55388	−	5.49936i	−0.0141553	−	0.0118777i	−0.649838	+	0.760073i	$0.725163\pi$
$464$		0			0
$465$	34.2873	−	482.306i	0.0737362	−	1.03722i
$466$		0			0
$467$	−92.6402	+	53.4858i	−0.198373	+	0.114531i	−0.595896	−	0.803061i	$-0.703203\pi$
$467$	−92.6402	+	53.4858i	−0.198373	+	0.114531i	0.397523	+	0.917592i	$0.369870\pi$
$468$		0			0
$469$	−15.9044	+	27.5472i	−0.0339113	+	0.0587361i
$470$		0			0
$471$	−137.770	+	99.8524i	−0.292506	+	0.212001i
$472$		0			0
$473$	−114.499	−	314.585i	−0.242071	−	0.665084i
$474$		0			0
$475$	12.8829	+	73.0624i	0.0271218	+	0.153816i
$476$		0			0
$477$	−403.106	+	13.1422i	−0.845085	+	0.0275519i
$478$		0			0
$479$	−367.547	−	438.026i	−0.767322	−	0.914459i	0.230965	−	0.972962i	$-0.425812\pi$
$479$	−367.547	−	438.026i	−0.767322	−	0.914459i	−0.998287	+	0.0585028i	$0.981367\pi$
$480$		0			0
$481$	32.4830	−	184.220i	0.0675322	−	0.382994i
$482$		0			0
$483$	69.5217	−	71.8252i	0.143937	−	0.148706i
$484$		0			0
$485$		−	82.3522i		−	0.169798i
$486$		0			0
$487$	−51.4408			−0.105628			−0.0528140	−	0.998604i	$-0.516819\pi$
$487$	−51.4408			−0.105628			−0.0528140	+	0.998604i	$0.516819\pi$
$488$		0			0
$489$	−146.727	−	142.021i	−0.300055	−	0.290432i
$490$		0			0
$491$	520.792	+	91.8297i	1.06068	+	0.187026i	0.676656	−	0.736299i	$-0.263428\pi$
$491$	520.792	+	91.8297i	1.06068	+	0.187026i	0.384020	+	0.923325i	$0.374539\pi$
$492$		0			0
$493$	56.4961	−	47.4059i	0.114597	−	0.0961580i
$494$		0			0
$495$	5.21576	+	159.980i	0.0105369	+	0.323193i
$496$		0			0
$497$	64.5149	−	11.3757i	0.129809	−	0.0228888i
$498$		0			0
$499$	−11.9189	+	4.33813i	−0.0238856	+	0.00869364i	−0.353935	−	0.935270i	$-0.615157\pi$
$499$	−11.9189	+	4.33813i	−0.0238856	+	0.00869364i	0.330050	+	0.943964i	$0.392934\pi$
$500$		0			0
$501$	189.278	+	261.154i	0.377800	+	0.521265i
$502$		0			0
$503$	239.874	+	138.491i	0.476886	+	0.275330i	0.719118	−	0.694888i	$-0.244546\pi$
$503$	239.874	+	138.491i	0.476886	+	0.275330i	−0.242232	+	0.970218i	$0.577879\pi$
$504$		0			0
$505$	−264.876	−	458.778i	−0.524506	−	0.908471i
$506$		0			0
$507$	−197.693	−	14.0541i	−0.389927	−	0.0277201i
$508$		0			0
$509$	−160.021	+	190.705i	−0.314382	+	0.374666i	−0.899977	−	0.435938i	$-0.856417\pi$
$509$	−160.021	+	190.705i	−0.314382	+	0.374666i	0.585594	+	0.810604i	$0.300861\pi$
$510$		0			0
$511$	120.230	+	43.7601i	0.235284	+	0.0856362i
$512$		0			0
$513$	120.985	+	26.1558i	0.235839	+	0.0509860i
$514$		0			0
$515$	−5.35341	+	14.7084i	−0.0103950	+	0.0285600i
$516$		0			0
$517$	−334.721	−	280.865i	−0.647430	−	0.543259i
$518$		0			0
$519$	669.972	+	453.031i	1.29089	+	0.872893i
$520$		0			0
$521$	770.317	−	444.742i	1.47853	−	0.853632i	0.478829	−	0.877908i	$-0.341061\pi$
$521$	770.317	−	444.742i	1.47853	−	0.853632i	0.999705	+	0.0242755i	$0.00772790\pi$
$522$		0			0
$523$	−236.647	+	409.884i	−0.452479	+	0.783717i	−0.998539	−	0.0540291i	$-0.982794\pi$
$523$	−236.647	+	409.884i	−0.452479	+	0.783717i	0.546060	+	0.837746i	$0.316127\pi$
$524$		0			0
$525$	−41.4225	−	18.5000i	−0.0789001	−	0.0352381i
$526$		0			0
$527$	−146.070	−	401.323i	−0.277172	−	0.761523i
$528$		0			0
$529$	−128.928	−	731.188i	−0.243721	−	1.38221i
$530$		0			0
$531$	−105.371	+	737.363i	−0.198439	+	1.38863i
$532$		0			0
$533$	70.6015	+	84.1396i	0.132461	+	0.157860i
$534$		0			0
$535$	−79.3786	+	450.178i	−0.148371	+	0.841455i
$536$		0			0
$537$	178.050	+	623.657i	0.331563	+	1.16137i
$538$		0			0
$539$			288.255i			0.534797i
$540$		0			0
$541$	−54.9995			−0.101663			−0.0508314	−	0.998707i	$-0.516187\pi$
$541$	−54.9995			−0.101663			−0.0508314	+	0.998707i	$0.516187\pi$
$542$		0			0
$543$	90.4933	−	361.167i	0.166654	−	0.665133i
$544$		0			0
$545$	424.998	+	74.9386i	0.779813	+	0.137502i
$546$		0			0
$547$	572.073	−	480.027i	1.04584	−	0.877562i	0.0531884	−	0.998584i	$-0.483062\pi$
$547$	572.073	−	480.027i	1.04584	−	0.877562i	0.992650	+	0.121022i	$0.0386172\pi$
$548$		0			0
$549$	373.886	+	417.181i	0.681031	+	0.759893i
$550$		0			0
$551$	−42.3183	+	7.46185i	−0.0768027	+	0.0135424i
$552$		0			0
$553$	38.7087	−	14.0888i	0.0699976	−	0.0254771i
$554$		0			0
$555$	−163.363	+	16.9790i	−0.294349	+	0.0305928i
$556$		0			0
$557$	30.6029	+	17.6686i	0.0549424	+	0.0317210i	0.527220	−	0.849729i	$-0.323235\pi$
$557$	30.6029	+	17.6686i	0.0549424	+	0.0317210i	−0.472277	+	0.881450i	$0.656568\pi$
$558$		0			0
$559$	283.540	+	491.106i	0.507228	+	0.878544i
$560$		0			0
$561$	61.8298	+	127.143i	0.110214	+	0.226637i
$562$		0			0
$563$	438.510	−	522.596i	0.778882	−	0.928235i	−0.220001	−	0.975500i	$-0.570606\pi$
$563$	438.510	−	522.596i	0.778882	−	0.928235i	0.998882	+	0.0472647i	$0.0150504\pi$
$564$		0			0
$565$	−176.906	−	64.3885i	−0.313108	−	0.113962i
$566$		0			0
$567$	−54.6900	+	52.3262i	−0.0964550	+	0.0922860i
$568$		0			0
$569$	309.078	−	849.184i	0.543195	−	1.49242i	−0.299538	−	0.954084i	$-0.596833\pi$
$569$	309.078	−	849.184i	0.543195	−	1.49242i	0.842733	−	0.538331i	$-0.180945\pi$
$570$		0			0
$571$	−495.403	−	415.692i	−0.867606	−	0.728008i	0.0959867	−	0.995383i	$-0.469399\pi$
$571$	−495.403	−	415.692i	−0.867606	−	0.728008i	−0.963593	+	0.267375i	$0.913844\pi$
$572$		0			0
$573$	−272.320	+	132.429i	−0.475254	+	0.231116i
$574$		0			0
$575$	−499.733	+	288.521i	−0.869100	+	0.501775i
$576$		0			0
$577$	165.488	−	286.633i	0.286807	−	0.496765i	−0.686239	−	0.727377i	$-0.740739\pi$
$577$	165.488	−	286.633i	0.286807	−	0.496765i	0.973046	+	0.230612i	$0.0740727\pi$
$578$		0			0
$579$	60.6537	+	583.580i	0.104756	+	1.00791i
$580$		0			0
$581$	29.3707	+	80.6952i	0.0505519	+	0.138890i
$582$		0			0
$583$	46.6088	+	264.331i	0.0799464	+	0.453399i
$584$		0			0
$585$	−55.7585	−	265.343i	−0.0953137	−	0.453578i
$586$		0			0
$587$	−9.19148	−	10.9540i	−0.0156584	−	0.0186610i	0.758158	−	0.652070i	$-0.226099\pi$
$587$	−9.19148	−	10.9540i	−0.0156584	−	0.0186610i	−0.773817	+	0.633409i	$0.781655\pi$
$588$		0			0
$589$	−43.2106	+	245.059i	−0.0733626	+	0.416060i
$590$		0			0
$591$	718.218	+	179.955i	1.21526	+	0.304493i
$592$		0			0
$593$			834.096i			1.40657i	0.710908	+	0.703285i	$0.248284\pi$
$593$			834.096i			1.40657i	−0.710908	+	0.703285i	$0.751716\pi$
$594$		0			0
$595$	21.8321			0.0366927
$596$		0			0
$597$	−458.486	+	130.894i	−0.767983	+	0.219254i
$598$		0			0
$599$	764.371	+	134.779i	1.27608	+	0.225007i	0.770314	−	0.637665i	$-0.220100\pi$
$599$	764.371	+	134.779i	1.27608	+	0.225007i	0.505764	+	0.862672i	$0.331211\pi$
$600$		0			0
$601$	−327.998	+	275.223i	−0.545754	+	0.457942i	−0.873500	−	0.486824i	$-0.838155\pi$
$601$	−327.998	+	275.223i	−0.545754	+	0.457942i	0.327746	+	0.944766i	$0.393711\pi$
$602$		0			0
$603$	−114.107	−	284.319i	−0.189232	−	0.471507i
$604$		0			0
$605$	−248.930	+	43.8931i	−0.411455	+	0.0725507i
$606$		0			0
$607$	−1085.37	+	395.041i	−1.78808	+	0.650809i	−0.788733	+	0.614736i	$0.789263\pi$
$607$	−1085.37	+	395.041i	−1.78808	+	0.650809i	−0.999349	+	0.0360730i	$0.988515\pi$
$608$		0			0
$609$	10.7153	−	23.9922i	0.0175950	−	0.0393961i
$610$		0			0
$611$	640.993	+	370.077i	1.04909	+	0.605691i
$612$		0			0
$613$	496.301	+	859.619i	0.809627	+	1.40231i	0.913123	+	0.407685i	$0.133664\pi$
$613$	496.301	+	859.619i	0.809627	+	1.40231i	−0.103496	+	0.994630i	$0.533003\pi$
$614$		0			0
$615$	54.0201	−	79.8884i	0.0878376	−	0.129900i
$616$		0			0
$617$	623.221	−	742.726i	1.01008	−	1.20377i	0.0311651	−	0.999514i	$-0.490078\pi$
$617$	623.221	−	742.726i	1.01008	−	1.20377i	0.978918	−	0.204255i	$-0.0654773\pi$
$618$		0			0
$619$	−666.834	−	242.708i	−1.07728	−	0.392096i	−0.258383	−	0.966043i	$-0.583190\pi$
$619$	−666.834	−	242.708i	−1.07728	−	0.392096i	−0.818893	+	0.573946i	$0.805412\pi$
$620$		0			0
$621$	130.677	+	953.847i	0.210431	+	1.53598i
$622$		0			0
$623$	−31.7601	+	87.2601i	−0.0509792	+	0.140064i
$624$		0			0
$625$	31.7560	+	26.6464i	0.0508095	+	0.0426343i
$626$		0			0
$627$	5.84139	−	82.1685i	0.00931641	−	0.131050i
$628$		0			0
$629$	−125.635	+	72.5352i	−0.199737	+	0.115318i
$630$		0			0
$631$	27.0548	−	46.8602i	0.0428760	−	0.0742634i	−0.843791	−	0.536672i	$-0.819681\pi$
$631$	27.0548	−	46.8602i	0.0428760	−	0.0742634i	0.886667	+	0.462408i	$0.153015\pi$
$632$		0			0
$633$	845.279	−	612.637i	1.33535	−	0.967831i
$634$		0			0
$635$	65.0379	+	178.690i	0.102422	+	0.281402i
$636$		0			0
$637$	−84.7893	−	480.864i	−0.133107	−	0.754888i
$638$		0			0
$639$	−297.503	+	556.409i	−0.465576	+	0.870750i
$640$		0			0
$641$	182.928	+	218.005i	0.285380	+	0.340102i	0.889621	−	0.456699i	$-0.150968\pi$
$641$	182.928	+	218.005i	0.285380	+	0.340102i	−0.604242	+	0.796801i	$0.706524\pi$
$642$		0			0
$643$	143.731	−	815.136i	0.223531	−	1.26771i	−0.641942	−	0.766753i	$-0.721871\pi$
$643$	143.731	−	815.136i	0.223531	−	1.26771i	0.865473	−	0.500955i	$-0.167018\pi$
$644$		0			0
$645$	346.289	−	357.763i	0.536882	−	0.554671i
$646$		0			0
$647$		−	592.934i		−	0.916436i	−0.888840	−	0.458218i	$-0.848488\pi$
$647$		−	592.934i		−	0.916436i	0.888840	−	0.458218i	$-0.151512\pi$
$648$		0			0
$649$	495.700			0.763791
$650$		0			0
$651$	−109.334	−	105.828i	−0.167948	−	0.162562i
$652$		0			0
$653$	−50.0324	−	8.82206i	−0.0766193	−	0.0135100i	0.135207	−	0.990817i	$-0.456830\pi$
$653$	−50.0324	−	8.82206i	−0.0766193	−	0.0135100i	−0.211826	+	0.977307i	$0.567941\pi$
$654$		0			0
$655$	273.911	−	229.839i	0.418185	−	0.350899i
$656$		0			0
$657$	−1046.55	+	650.594i	−1.59293	+	0.990250i
$658$		0			0
$659$	−17.8256	+	3.14313i	−0.0270494	+	0.00476954i	−0.187157	−	0.982330i	$-0.559927\pi$
$659$	−17.8256	+	3.14313i	−0.0270494	+	0.00476954i	0.160107	+	0.987100i	$0.448816\pi$
$660$		0			0
$661$	−901.414	+	328.088i	−1.36371	+	0.496351i	−0.917200	−	0.398427i	$-0.869556\pi$
$661$	−901.414	+	328.088i	−1.36371	+	0.496351i	−0.446512	+	0.894778i	$0.647334\pi$
$662$		0			0
$663$	−140.542	−	193.912i	−0.211979	−	0.292476i
$664$		0			0
$665$	−11.0164	−	6.36031i	−0.0165660	−	0.00956437i
$666$		0			0
$667$	−167.113	−	289.449i	−0.250545	−	0.433956i
$668$		0			0
$669$	−469.730	−	33.3933i	−0.702138	−	0.0499153i
$670$		0			0
$671$	239.642	−	285.594i	0.357142	−	0.425625i
$672$		0			0
$673$	936.382	+	340.815i	1.39136	+	0.506412i	0.925601	−	0.378502i	$-0.123561\pi$
$673$	936.382	+	340.815i	1.39136	+	0.506412i	0.465755	+	0.884914i	$0.345783\pi$
$674$		0			0
$675$	386.502	−	203.788i	0.572596	−	0.301908i
$676$		0			0
$677$	206.246	−	566.655i	0.304647	−	0.837010i	−0.689030	−	0.724732i	$-0.741963\pi$
$677$	206.246	−	566.655i	0.304647	−	0.837010i	0.993677	−	0.112277i	$-0.0358144\pi$
$678$		0			0
$679$	−19.8527	−	16.6584i	−0.0292381	−	0.0245337i
$680$		0			0
$681$	903.411	+	610.882i	1.32659	+	0.897036i
$682$		0			0
$683$	−413.524	+	238.748i	−0.605452	+	0.349558i	−0.771184	−	0.636613i	$-0.780335\pi$
$683$	−413.524	+	238.748i	−0.605452	+	0.349558i	0.165731	+	0.986171i	$0.447002\pi$
$684$		0			0
$685$	−240.864	+	417.189i	−0.351626	+	0.609034i
$686$		0			0
$687$	−245.046	−	109.442i	−0.356690	−	0.159304i
$688$		0			0
$689$	−155.504	−	427.244i	−0.225696	−	0.620093i
$690$		0			0
$691$	−71.3995	−	404.927i	−0.103328	−	0.586001i	−0.991875	−	0.127216i	$-0.959396\pi$
$691$	−71.3995	−	404.927i	−0.103328	−	0.586001i	0.888547	−	0.458785i	$-0.151715\pi$
$692$		0			0
$693$	39.6217	+	31.1039i	0.0571741	+	0.0448829i
$694$		0			0
$695$	−203.260	−	242.235i	−0.292460	−	0.348540i
$696$		0			0
$697$	14.7914	−	83.8863i	0.0212216	−	0.120353i
$698$		0			0
$699$	−152.737	−	534.993i	−0.218507	−	0.765369i
$700$		0			0
$701$			857.375i			1.22307i	0.791216	+	0.611537i	$0.209448\pi$
$701$			857.375i			1.22307i	−0.791216	+	0.611537i	$0.790552\pi$
$702$		0			0
$703$	84.5260			0.120236
$704$		0			0
$705$	157.947	−	630.382i	0.224039	−	0.894158i
$706$		0			0
$707$	−164.178	−	28.9489i	−0.232217	−	0.0409461i
$708$		0			0
$709$	507.834	−	426.123i	0.716268	−	0.601020i	−0.210082	−	0.977684i	$-0.567373\pi$
$709$	507.834	−	426.123i	0.716268	−	0.601020i	0.926350	+	0.376664i	$0.122929\pi$
$710$		0			0
$711$	−123.474	+	377.041i	−0.173662	+	0.530297i
$712$		0			0
$713$	−1906.06	+	336.089i	−2.67329	+	0.471373i
$714$		0			0
$715$	−169.560	+	61.7150i	−0.237147	+	0.0863146i
$716$		0			0
$717$	92.3464	−	9.59791i	0.128795	−	0.0133862i
$718$		0			0
$719$	273.812	+	158.085i	0.380823	+	0.219868i	0.678176	−	0.734899i	$-0.262771\pi$
$719$	273.812	+	158.085i	0.380823	+	0.219868i	−0.297353	+	0.954768i	$0.596104\pi$
$720$		0			0
$721$	2.46286	+	4.26580i	0.00341589	+	0.00591650i
$722$		0			0
$723$	−459.598	−	945.091i	−0.635682	−	1.30718i
$724$		0			0
$725$	−97.5012	+	116.197i	−0.134484	+	0.160272i
$726$		0			0
$727$	−357.493	−	130.117i	−0.491738	−	0.178978i	0.0842365	−	0.996446i	$-0.473155\pi$
$727$	−357.493	−	130.117i	−0.491738	−	0.178978i	−0.575974	+	0.817468i	$0.695377\pi$
$728$		0			0
$729$	−71.1629	−	725.518i	−0.0976171	−	0.995224i
$730$		0			0
$731$	150.414	−	413.260i	0.205765	−	0.565336i
$732$		0			0
$733$	382.389	+	320.862i	0.521676	+	0.437738i	0.865216	−	0.501400i	$-0.167181\pi$
$733$	382.389	+	320.862i	0.521676	+	0.437738i	−0.343540	+	0.939138i	$0.611626\pi$
$734$		0			0
$735$	−385.548	+	187.492i	−0.524555	+	0.255091i
$736$		0			0
$737$	−176.568	+	101.942i	−0.239577	+	0.138320i
$738$		0			0
$739$	384.461	−	665.906i	0.520245	−	0.901090i	−0.479478	−	0.877554i	$-0.659174\pi$
$739$	384.461	−	665.906i	0.520245	−	0.901090i	0.999723	−	0.0235367i	$-0.00749264\pi$
$740$		0			0
$741$	14.4250	+	138.791i	0.0194670	+	0.187302i
$742$		0			0
$743$	−121.256	−	333.147i	−0.163197	−	0.448381i	0.830959	−	0.556334i	$-0.187793\pi$
$743$	−121.256	−	333.147i	−0.163197	−	0.448381i	−0.994156	+	0.107953i	$0.965570\pi$
$744$		0			0
$745$	7.94362	+	45.0505i	0.0106626	+	0.0604705i
$746$		0			0
$747$	−786.009	−	257.404i	−1.05222	−	0.344583i
$748$		0			0
$749$	92.4679	+	110.199i	0.123455	+	0.147128i
$750$		0			0
$751$	−56.1994	+	318.723i	−0.0748327	+	0.424398i	0.924258	+	0.381768i	$0.124685\pi$
$751$	−56.1994	+	318.723i	−0.0748327	+	0.424398i	−0.999091	+	0.0426296i	$0.986426\pi$
$752$		0			0
$753$	138.083	+	34.5977i	0.183377	+	0.0459465i
$754$		0			0
$755$			8.93408i			0.0118332i
$756$		0			0
$757$	−158.961			−0.209988			−0.104994	−	0.994473i	$-0.533482\pi$
$757$	−158.961			−0.209988			−0.104994	+	0.994473i	$0.533482\pi$
$758$		0			0
$759$	616.098	−	175.892i	0.811723	−	0.231741i
$760$		0			0
$761$	−39.6236	−	6.98671i	−0.0520678	−	0.00918096i	0.147554	−	0.989054i	$-0.452860\pi$
$761$	−39.6236	−	6.98671i	−0.0520678	−	0.00918096i	−0.199621	+	0.979873i	$0.563971\pi$
$762$		0			0
$763$	104.035	−	87.2958i	0.136350	−	0.114411i
$764$		0			0
$765$	−129.840	+	165.397i	−0.169726	+	0.216206i
$766$		0			0
$767$	−826.920	+	145.808i	−1.07812	+	0.190102i
$768$		0			0
$769$	−387.461	+	141.024i	−0.503851	+	0.183387i	−0.581425	−	0.813600i	$-0.697505\pi$
$769$	−387.461	+	141.024i	−0.503851	+	0.183387i	0.0775744	+	0.996987i	$0.475282\pi$
$770$		0			0
$771$	−142.747	+	319.618i	−0.185145	+	0.414551i
$772$		0			0
$773$	−1135.88	−	655.799i	−1.46944	−	0.848382i	−0.470028	−	0.882651i	$-0.655756\pi$
$773$	−1135.88	−	655.799i	−1.46944	−	0.848382i	−0.999413	+	0.0342695i	$0.989090\pi$
$774$		0			0
$775$	439.193	+	760.705i	0.566701	+	0.981555i
$776$		0			0
$777$	−28.9524	+	42.8167i	−0.0372618	+	0.0551051i
$778$		0			0
$779$	−31.9021	+	38.0194i	−0.0409526	+	0.0488054i
$780$		0			0
$781$	394.575	+	143.614i	0.505218	+	0.183884i
$782$		0			0
$783$	118.035	+	223.865i	0.150748	+	0.285906i
$784$		0			0
$785$	−57.6007	+	158.257i	−0.0733767	+	0.201601i
$786$		0			0
$787$	−355.669	−	298.441i	−0.451930	−	0.379214i	0.388222	−	0.921566i	$-0.373089\pi$
$787$	−355.669	−	298.441i	−0.451930	−	0.379214i	−0.840151	+	0.542352i	$0.817534\pi$
$788$		0			0
$789$	67.9990	−	956.515i	0.0861838	−	1.21231i
$790$		0			0
$791$	−51.3071	+	29.6222i	−0.0648636	+	0.0374490i
$792$		0			0
$793$	−315.761	+	546.915i	−0.398186	+	0.689678i
$794$		0			0
$795$	−323.233	+	234.271i	−0.406582	+	0.294681i
$796$		0			0
$797$	279.835	+	768.839i	0.351110	+	0.964667i	0.982014	+	0.188806i	$0.0604618\pi$
$797$	279.835	+	768.839i	0.351110	+	0.964667i	−0.630904	+	0.775861i	$0.717316\pi$
$798$		0			0
$799$	−99.6749	−	565.285i	−0.124750	−	0.707490i
$800$		0			0
$801$	−472.186	−	759.564i	−0.589496	−	0.948270i
$802$		0			0
$803$	527.144	+	628.226i	0.656468	+	0.782349i
$804$		0			0
$805$	17.1808	−	97.4370i	0.0213426	−	0.121040i
$806$		0			0
$807$	724.718	−	748.731i	0.898040	−	0.927795i
$808$		0			0
$809$			787.781i			0.973771i	0.873466	+	0.486886i	$0.161867\pi$
$809$			787.781i			0.973771i	−0.873466	+	0.486886i	$0.838133\pi$
$810$		0			0
$811$	781.305			0.963384			0.481692	−	0.876341i	$-0.340022\pi$
$811$	781.305			0.963384			0.481692	+	0.876341i	$0.340022\pi$
$812$		0			0
$813$	−1002.31	−	970.169i	−1.23286	−	1.19332i
$814$		0			0
$815$	−199.047	−	35.0974i	−0.244230	−	0.0430643i
$816$		0			0
$817$	−196.292	+	164.709i	−0.240260	+	0.201602i
$818$		0			0
$819$	−75.2454	−	40.2325i	−0.0918747	−	0.0491239i
$820$		0			0
$821$	−262.358	+	46.2608i	−0.319559	+	0.0563469i	−0.331127	−	0.943586i	$-0.607429\pi$
$821$	−262.358	+	46.2608i	−0.319559	+	0.0563469i	0.0115678	+	0.999933i	$0.496318\pi$
$822$		0			0
$823$	1115.33	−	405.945i	1.35519	−	0.493251i	0.440629	−	0.897689i	$-0.354755\pi$
$823$	1115.33	−	405.945i	1.35519	−	0.493251i	0.914565	+	0.404439i	$0.132533\pi$
$824$		0			0
$825$	−170.644	−	235.445i	−0.206842	−	0.285387i
$826$		0			0
$827$	678.939	+	391.985i	0.820966	+	0.473985i	0.850749	−	0.525572i	$-0.176148\pi$
$827$	678.939	+	391.985i	0.820966	+	0.473985i	−0.0297836	+	0.999556i	$0.509482\pi$
$828$		0			0
$829$	489.138	+	847.212i	0.590034	+	1.02197i	0.994227	+	0.107295i	$0.0342190\pi$
$829$	489.138	+	847.212i	0.590034	+	1.02197i	−0.404193	+	0.914674i	$0.632448\pi$
$830$		0			0
$831$	−406.645	−	28.9085i	−0.489344	−	0.0347876i
$832$		0			0
$833$	−243.406	+	290.080i	−0.292204	+	0.348235i
$834$		0			0
$835$	299.987	+	109.187i	0.359266	+	0.130762i
$836$		0			0
$837$	1451.97	−	198.920i	1.73473	−	0.237659i
$838$		0			0
$839$	355.297	−	976.171i	0.423477	−	1.16349i	−0.526227	−	0.850344i	$-0.676394\pi$
$839$	355.297	−	976.171i	0.423477	−	1.16349i	0.949704	−	0.313149i	$-0.101384\pi$
$840$		0			0
$841$	576.941	+	484.111i	0.686018	+	0.575637i
$842$		0			0
$843$	1340.65	+	906.540i	1.59033	+	1.07537i
$844$		0			0
$845$	−169.887	+	98.0844i	−0.201050	+	0.116076i
$846$		0			0
$847$	−39.7729	+	68.8886i	−0.0469573	+	0.0813325i
$848$		0			0
$849$	814.265	+	363.664i	0.959087	+	0.428345i
$850$		0			0
$851$	224.857	+	617.790i	0.264227	+	0.725957i
$852$		0			0
$853$	164.358	+	932.120i	0.192682	+	1.09275i	0.915681	+	0.401906i	$0.131652\pi$
$853$	164.358	+	932.120i	0.192682	+	1.09275i	−0.722999	+	0.690849i	$0.757237\pi$
$854$		0			0
$855$	113.702	−	45.6324i	0.132984	−	0.0533713i
$856$		0			0
$857$	−194.366	−	231.636i	−0.226798	−	0.270287i	0.640631	−	0.767849i	$-0.278673\pi$
$857$	−194.366	−	231.636i	−0.226798	−	0.270287i	−0.867428	+	0.497562i	$0.834229\pi$
$858$		0			0
$859$	−150.742	+	854.900i	−0.175485	+	0.995227i	0.762097	+	0.647463i	$0.224170\pi$
$859$	−150.742	+	854.900i	−0.175485	+	0.995227i	−0.937582	+	0.347764i	$0.886941\pi$
$860$		0			0
$861$	−8.33144	−	29.1827i	−0.00967647	−	0.0338939i
$862$		0			0
$863$		−	179.663i		−	0.208184i	−0.994568	−	0.104092i	$-0.966806\pi$
$863$		−	179.663i		−	0.208184i	0.994568	−	0.104092i	$-0.0331936\pi$
$864$		0			0
$865$	800.508			0.925442
$866$		0			0
$867$	165.580	−	660.845i	0.190981	−	0.762221i
$868$		0			0
$869$	260.022	+	45.8488i	0.299219	+	0.0527605i
$870$		0			0
$871$	264.563	−	221.995i	0.303747	−	0.254874i
$872$		0			0
$873$	244.270	−	51.3303i	0.279805	−	0.0587976i
$874$		0			0
$875$	−112.535	+	19.8429i	−0.128611	+	0.0226777i
$876$		0			0
$877$	573.067	−	208.579i	0.653440	−	0.237833i	0.00603862	−	0.999982i	$-0.498078\pi$
$877$	573.067	−	208.579i	0.653440	−	0.237833i	0.647402	+	0.762149i	$0.275856\pi$
$878$		0			0
$879$	−1602.14	+	166.516i	−1.82268	+	0.189438i
$880$		0			0
$881$	662.997	+	382.782i	0.752551	+	0.434485i	0.826615	−	0.562768i	$-0.190264\pi$
$881$	662.997	+	382.782i	0.752551	+	0.434485i	−0.0740639	+	0.997253i	$0.523597\pi$
$882$		0			0
$883$	−256.800	−	444.790i	−0.290826	−	0.503726i	0.683179	−	0.730251i	$-0.260597\pi$
$883$	−256.800	−	444.790i	−0.290826	−	0.503726i	−0.974005	+	0.226525i	$0.927263\pi$
$884$		0			0
$885$	322.421	+	663.009i	0.364318	+	0.749163i
$886$		0			0
$887$	−213.850	+	254.857i	−0.241094	+	0.287325i	−0.873000	−	0.487721i	$-0.837828\pi$
$887$	−213.850	+	254.857i	−0.241094	+	0.287325i	0.631906	+	0.775045i	$0.282273\pi$
$888$		0			0
$889$	56.2329	+	20.4671i	0.0632541	+	0.0230226i
$890$		0			0
$891$	−471.277	+	115.187i	−0.528930	+	0.129278i
$892$		0			0
$893$	−114.388	+	314.278i	−0.128094	+	0.351935i
$894$		0			0
$895$	491.765	+	412.640i	0.549458	+	0.461050i
$896$		0			0
$897$	−976.029	+	474.643i	−1.08810	+	0.529145i
$898$		0			0
$899$	−440.606	+	254.384i	−0.490107	+	0.282963i
$900$		0			0
$901$	−176.300	+	305.361i	−0.195672	+	0.338914i
$902$		0			0
$903$	−16.1980	−	155.849i	−0.0179380	−	0.172591i
$904$		0			0
$905$	−126.045	−	346.305i	−0.139276	−	0.382658i
$906$		0			0
$907$	−142.000	−	805.323i	−0.156560	−	0.887897i	−0.957345	−	0.288946i	$-0.906695\pi$
$907$	−142.000	−	805.323i	−0.156560	−	0.887897i	0.800785	−	0.598952i	$-0.204416\pi$
$908$		0			0
$909$	1195.71	−	1071.62i	1.31541	−	1.17890i
$910$		0			0
$911$	1004.82	+	1197.50i	1.10299	+	1.31449i	0.945007	+	0.327049i	$0.106054\pi$
$911$	1004.82	+	1197.50i	1.10299	+	1.31449i	0.157982	+	0.987442i	$0.449501\pi$
$912$		0			0
$913$	−95.5801	+	542.062i	−0.104688	+	0.593715i
$914$		0			0
$915$	537.861	+	134.765i	0.587826	+	0.147285i
$916$		0			0
$917$		−	112.524i		−	0.122709i
$918$		0			0
$919$	−826.055			−0.898863			−0.449431	−	0.893315i	$-0.648373\pi$
$919$	−826.055			−0.898863			−0.449431	+	0.893315i	$0.648373\pi$
$920$		0			0
$921$	92.1408	−	26.3055i	0.100044	−	0.0285619i
$922$		0			0
$923$	−700.468	−	123.511i	−0.758903	−	0.133815i
$924$		0			0
$925$	228.565	−	191.789i	0.247098	−	0.207340i
$926$		0			0
$927$	−46.9642	−	6.71133i	−0.0506626	−	0.00723984i
$928$		0			0
$929$	−1285.74	+	226.711i	−1.38401	+	0.244038i	−0.815556	−	0.578678i	$-0.803569\pi$
$929$	−1285.74	+	226.711i	−1.38401	+	0.244038i	−0.568453	+	0.822716i	$0.692458\pi$
$930$		0			0
$931$	207.330	−	75.4618i	0.222696	−	0.0810545i
$932$		0			0
$933$	433.818	−	971.344i	0.464971	−	1.04110i
$934$		0			0
$935$	121.189	+	69.9684i	0.129614	+	0.0748325i
$936$		0			0
$937$	−409.103	−	708.588i	−0.436610	−	0.756230i	0.560816	−	0.827941i	$-0.310488\pi$
$937$	−409.103	−	708.588i	−0.436610	−	0.756230i	−0.997425	+	0.0717104i	$0.977154\pi$
$938$		0			0
$939$	−706.158	+	1044.31i	−0.752032	+	1.11215i
$940$		0			0
$941$	−120.852	+	144.026i	−0.128430	+	0.153056i	−0.826427	−	0.563044i	$-0.809630\pi$
$941$	−120.852	+	144.026i	−0.128430	+	0.153056i	0.697997	+	0.716100i	$0.254075\pi$
$942$		0			0
$943$	−362.745	−	132.028i	−0.384671	−	0.140009i
$944$		0			0
$945$	−15.8307	+	73.2259i	−0.0167520	+	0.0774877i
$946$		0			0
$947$	431.659	−	1185.97i	0.455817	−	1.25235i	−0.472755	−	0.881194i	$-0.656740\pi$
$947$	431.659	−	1185.97i	0.455817	−	1.25235i	0.928572	−	0.371153i	$-0.121037\pi$
$948$		0			0
$949$	−1064.16	−	892.940i	−1.12135	−	0.940928i
$950$		0			0
$951$	−53.7641	+	756.278i	−0.0565343	+	0.795245i
$952$		0			0
$953$	789.863	−	456.027i	0.828817	−	0.478518i	−0.0246304	−	0.999697i	$-0.507841\pi$
$953$	789.863	−	456.027i	0.828817	−	0.478518i	0.853447	+	0.521179i	$0.174508\pi$
$954$		0			0
$955$	−149.861	+	259.567i	−0.156922	+	0.271798i
$956$		0			0
$957$	136.371	−	98.8384i	0.142499	−	0.103279i
$958$		0			0
$959$	51.8494	+	142.455i	0.0540661	+	0.148545i
$960$		0			0
$961$	344.727	+	1955.05i	0.358717	+	2.03439i
$962$		0			0
$963$	−1384.78	+	45.1472i	−1.43798	+	0.0468818i
$964$		0			0
$965$	373.289	+	444.868i	0.386828	+	0.461003i
$966$		0			0
$967$	172.790	−	979.942i	0.178687	−	1.01338i	−0.755115	−	0.655592i	$-0.772419\pi$
$967$	172.790	−	979.942i	0.178687	−	1.01338i	0.933802	−	0.357791i	$-0.116470\pi$
$968$		0			0
$969$	75.2623	−	77.7560i	0.0776701	−	0.0802436i
$970$		0			0
$971$		−	1477.87i		−	1.52201i	−0.648746	−	0.761005i	$-0.724706\pi$
$971$		−	1477.87i		−	1.52201i	0.648746	−	0.761005i	$-0.275294\pi$
$972$		0			0
$973$	−99.5116			−0.102273
$974$		0			0
$975$	353.922	+	342.571i	0.362997	+	0.351355i
$976$		0			0
$977$	−150.970	−	26.6200i	−0.154524	−	0.0272467i	0.0958511	−	0.995396i	$-0.469443\pi$
$977$	−150.970	−	26.6200i	−0.154524	−	0.0272467i	−0.250375	+	0.968149i	$0.580554\pi$
$978$		0			0
$979$	−455.952	+	382.589i	−0.465732	+	0.390796i
$980$		0			0
$981$	42.6219	+	1307.32i	0.0434474	+	1.33264i
$982$		0			0
$983$	−84.1552	+	14.8388i	−0.0856106	+	0.0150955i	−0.216289	−	0.976329i	$-0.569395\pi$
$983$	−84.1552	+	14.8388i	−0.0856106	+	0.0150955i	0.130679	+	0.991425i	$0.458284\pi$
$984$		0			0
$985$	688.664	−	250.653i	0.699151	−	0.254470i
$986$		0			0
$987$	−120.017	−	165.592i	−0.121597	−	0.167773i
$988$		0			0
$989$	−1726.02	−	996.515i	−1.74521	−	1.00760i
$990$		0			0
$991$	−793.570	−	1374.50i	−0.800777	−	1.38699i	−0.919106	−	0.394011i	$-0.871087\pi$
$991$	−793.570	−	1374.50i	−0.800777	−	1.38699i	0.118329	−	0.992974i	$-0.462246\pi$
$992$		0			0
$993$	−475.929	−	33.8340i	−0.479284	−	0.0340725i
$994$		0			0
$995$	−303.355	+	361.524i	−0.304879	+	0.363341i
$996$		0			0
$997$	453.729	+	165.144i	0.455094	+	0.165641i	0.559388	−	0.828906i	$-0.311036\pi$
$997$	453.729	+	165.144i	0.455094	+	0.165641i	−0.104294	+	0.994546i	$0.533258\pi$
$998$		0			0
$999$	−152.187	−	473.979i	−0.152339	−	0.474454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.k.a.77.5	✓	36
3.2	odd	2		324.3.k.a.17.3		36
4.3	odd	2		432.3.bc.b.401.2		36
27.7	even	9		324.3.k.a.305.3		36
27.13	even	9		2916.3.c.b.1457.23		36
27.14	odd	18		2916.3.c.b.1457.14		36
27.20	odd	18	inner	108.3.k.a.101.5	yes	36
108.47	even	18		432.3.bc.b.209.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.77.5	✓	36	1.1	even	1	trivial
108.3.k.a.101.5	yes	36	27.20	odd	18	inner
324.3.k.a.17.3		36	3.2	odd	2
324.3.k.a.305.3		36	27.7	even	9
432.3.bc.b.209.2		36	108.47	even	18
432.3.bc.b.401.2		36	4.3	odd	2
2916.3.c.b.1457.14		36	27.14	odd	18
2916.3.c.b.1457.23		36	27.13	even	9

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.15561 + 2.08647i) q^{3} +(2.92426 + 0.515626i) q^{5} +(0.715829 - 0.600652i) q^{7} +(0.293266 + 8.99522i) q^{9} +O(q^{10})\)	\(q+(2.15561 + 2.08647i) q^{3} +(2.92426 + 0.515626i) q^{5} +(0.715829 - 0.600652i) q^{7} +(0.293266 + 8.99522i) q^{9} +(5.89850 - 1.04007i) q^{11} +(-9.53387 + 3.47005i) q^{13} +(5.22771 + 7.21288i) q^{15} +(6.81408 + 3.93411i) q^{17} +(-2.29223 - 3.97026i) q^{19} +(2.79629 + 0.198789i) q^{21} +(22.9203 - 27.3153i) q^{23} +(-15.2069 - 5.53485i) q^{25} +(-18.1361 + 20.0020i) q^{27} +(3.20583 - 8.80793i) q^{29} +(-41.5801 - 34.8898i) q^{31} +(14.8849 + 10.0651i) q^{33} +(2.40298 - 1.38736i) q^{35} +(-9.21875 + 15.9673i) q^{37} +(-27.7914 - 12.4121i) q^{39} +(-3.70267 - 10.1730i) q^{41} +(-9.70581 - 55.0444i) q^{43} +(-3.78058 + 26.4556i) q^{45} +(-46.8929 - 55.8847i) q^{47} +(-8.35713 + 47.3957i) q^{49} +(6.48005 + 22.6978i) q^{51} +44.8133i q^{53} +17.7851 q^{55} +(3.34269 - 13.3410i) q^{57} +(81.5042 + 14.3714i) q^{59} +(47.6825 - 40.0104i) q^{61} +(5.61292 + 6.26289i) q^{63} +(-29.6688 + 5.23141i) q^{65} +(-31.9873 + 11.6424i) q^{67} +(106.400 - 11.0585i) q^{69} +(60.7133 + 35.0528i) q^{71} +(68.4607 + 118.577i) q^{73} +(-21.2317 - 43.6597i) q^{75} +(3.59760 - 4.28745i) q^{77} +(41.4241 + 15.0772i) q^{79} +(-80.8280 + 5.27599i) q^{81} +(-31.4310 + 86.3561i) q^{83} +(17.8976 + 15.0179i) q^{85} +(25.2880 - 12.2976i) q^{87} +(-86.0608 + 49.6872i) q^{89} +(-4.74033 + 8.21049i) q^{91} +(-16.8336 - 161.964i) q^{93} +(-4.65591 - 12.7920i) q^{95} +(-4.81594 - 27.3125i) q^{97} +(11.0855 + 52.7533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q - 9 * q^5 + 6 * q^9	\( 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) \) 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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