LMFDB - Embedded newform 216.2.q.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (of order $9$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	216.49
Dual form			216.2.q.a.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.278117 - 1.70958i) q^{3} +(2.42978 - 0.884366i) q^{5} +(-0.245784 - 1.39391i) q^{7} +(-2.84530 + 0.950925i) q^{9} +O(q^{10})$	\(q+(-0.278117 - 1.70958i) q^{3} +(2.42978 - 0.884366i) q^{5} +(-0.245784 - 1.39391i) q^{7} +(-2.84530 + 0.950925i) q^{9} +(-1.99234 - 0.725153i) q^{11} +(1.59088 + 1.33491i) q^{13} +(-2.18765 - 3.90793i) q^{15} +(1.93552 - 3.35242i) q^{17} +(1.22285 + 2.11804i) q^{19} +(-2.31464 + 0.807856i) q^{21} +(1.45350 - 8.24321i) q^{23} +(1.29148 - 1.08368i) q^{25} +(2.41701 + 4.59979i) q^{27} +(-0.797932 + 0.669544i) q^{29} +(-1.54023 + 8.73507i) q^{31} +(-0.685600 + 3.60774i) q^{33} +(-1.82993 - 3.16952i) q^{35} +(-4.97082 + 8.60972i) q^{37} +(1.83967 - 3.09099i) q^{39} +(9.25295 + 7.76415i) q^{41} +(5.70613 + 2.07686i) q^{43} +(-6.07248 + 4.82682i) q^{45} +(0.665477 + 3.77411i) q^{47} +(4.69528 - 1.70894i) q^{49} +(-6.26953 - 2.37656i) q^{51} -3.73190 q^{53} -5.48224 q^{55} +(3.28086 - 2.67963i) q^{57} +(-5.04377 + 1.83578i) q^{59} +(-1.85946 - 10.5455i) q^{61} +(2.02483 + 3.73237i) q^{63} +(5.04603 + 1.83660i) q^{65} +(11.3245 + 9.50236i) q^{67} +(-14.4966 - 0.192291i) q^{69} +(2.68331 - 4.64763i) q^{71} +(-5.25081 - 9.09467i) q^{73} +(-2.21182 - 1.90650i) q^{75} +(-0.521112 + 2.95537i) q^{77} +(-6.10688 + 5.12428i) q^{79} +(7.19148 - 5.41134i) q^{81} +(-9.32482 + 7.82445i) q^{83} +(1.73812 - 9.85735i) q^{85} +(1.36656 + 1.17791i) q^{87} +(-7.20496 - 12.4794i) q^{89} +(1.46973 - 2.54564i) q^{91} +(15.3616 + 0.203764i) q^{93} +(4.84439 + 4.06492i) q^{95} +(10.6595 + 3.87974i) q^{97} +(6.35838 + 0.168711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) $ 24 * q - 3 * q^7 + 6 * q^9	$ 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) $ 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.278117	−	1.70958i	−0.160571	−	0.987024i
$3$	−0.278117	−	1.70958i	−0.160571	−	0.987024i
$4$		0			0
$5$	2.42978	−	0.884366i	1.08663	−	0.395500i	0.264258	−	0.964452i	$-0.414873\pi$
$5$	2.42978	−	0.884366i	1.08663	−	0.395500i	0.822371	+	0.568952i	$0.192651\pi$
$6$		0			0
$7$	−0.245784	−	1.39391i	−0.0928975	−	0.526848i	−0.995371	−	0.0961034i	$-0.969362\pi$
$7$	−0.245784	−	1.39391i	−0.0928975	−	0.526848i	0.902474	−	0.430745i	$-0.141749\pi$
$8$		0			0
$9$	−2.84530	+	0.950925i	−0.948434	+	0.316975i
$10$		0			0
$11$	−1.99234	−	0.725153i	−0.600714	−	0.218642i	0.0237215	−	0.999719i	$-0.492449\pi$
$11$	−1.99234	−	0.725153i	−0.600714	−	0.218642i	−0.624435	+	0.781077i	$0.714671\pi$
$12$		0			0
$13$	1.59088	+	1.33491i	0.441231	+	0.370237i	0.836170	−	0.548471i	$-0.184790\pi$
$13$	1.59088	+	1.33491i	0.441231	+	0.370237i	−0.394939	+	0.918707i	$0.629234\pi$
$14$		0			0
$15$	−2.18765	−	3.90793i	−0.564850	−	1.00902i
$16$		0			0
$17$	1.93552	−	3.35242i	0.469433	−	0.813082i	−0.529956	−	0.848025i	$-0.677792\pi$
$17$	1.93552	−	3.35242i	0.469433	−	0.813082i	0.999389	+	0.0349427i	$0.0111249\pi$
$18$		0			0
$19$	1.22285	+	2.11804i	0.280542	+	0.485913i	0.971518	−	0.236964i	$-0.0761525\pi$
$19$	1.22285	+	2.11804i	0.280542	+	0.485913i	−0.690976	+	0.722877i	$0.742819\pi$
$20$		0			0
$21$	−2.31464	+	0.807856i	−0.505095	+	0.176289i
$22$		0			0
$23$	1.45350	−	8.24321i	0.303076	−	1.71883i	−0.329350	−	0.944208i	$-0.606830\pi$
$23$	1.45350	−	8.24321i	0.303076	−	1.71883i	0.632426	−	0.774621i	$-0.282059\pi$
$24$		0			0
$25$	1.29148	−	1.08368i	0.258296	−	0.216736i
$26$		0			0
$27$	2.41701	+	4.59979i	0.465153	+	0.885230i
$28$		0			0
$29$	−0.797932	+	0.669544i	−0.148172	+	0.124331i	−0.713861	−	0.700288i	$-0.753055\pi$
$29$	−0.797932	+	0.669544i	−0.148172	+	0.124331i	0.565688	+	0.824619i	$0.308611\pi$
$30$		0			0
$31$	−1.54023	+	8.73507i	−0.276633	+	1.56886i	0.457093	+	0.889419i	$0.348891\pi$
$31$	−1.54023	+	8.73507i	−0.276633	+	1.56886i	−0.733726	+	0.679446i	$0.762220\pi$
$32$		0			0
$33$	−0.685600	+	3.60774i	−0.119348	+	0.628026i
$34$		0			0
$35$	−1.82993	−	3.16952i	−0.309314	−	0.535747i
$36$		0			0
$37$	−4.97082	+	8.60972i	−0.817198	+	1.41543i	0.0905404	+	0.995893i	$0.471141\pi$
$37$	−4.97082	+	8.60972i	−0.817198	+	1.41543i	−0.907739	+	0.419536i	$0.862193\pi$
$38$		0			0
$39$	1.83967	−	3.09099i	0.294584	−	0.494955i
$40$		0			0
$41$	9.25295	+	7.76415i	1.44507	+	1.21256i	0.936083	+	0.351780i	$0.114424\pi$
$41$	9.25295	+	7.76415i	1.44507	+	1.21256i	0.508985	+	0.860775i	$0.330021\pi$
$42$		0			0
$43$	5.70613	+	2.07686i	0.870176	+	0.316718i	0.738239	−	0.674540i	$-0.235658\pi$
$43$	5.70613	+	2.07686i	0.870176	+	0.316718i	0.131938	+	0.991258i	$0.457880\pi$
$44$		0			0
$45$	−6.07248	+	4.82682i	−0.905231	+	0.719540i
$46$		0			0
$47$	0.665477	+	3.77411i	0.0970698	+	0.550510i	0.994093	+	0.108528i	$0.0346136\pi$
$47$	0.665477	+	3.77411i	0.0970698	+	0.550510i	−0.897024	+	0.441983i	$0.854275\pi$
$48$		0			0
$49$	4.69528	−	1.70894i	0.670754	−	0.244134i
$50$		0			0
$51$	−6.26953	−	2.37656i	−0.877910	−	0.332785i
$52$		0			0
$53$	−3.73190			−0.512616			−0.256308	−	0.966595i	$-0.582506\pi$
$53$	−3.73190			−0.512616			−0.256308	+	0.966595i	$0.582506\pi$
$54$		0			0
$55$	−5.48224			−0.739225
$56$		0			0
$57$	3.28086	−	2.67963i	0.434561	−	0.354925i
$58$		0			0
$59$	−5.04377	+	1.83578i	−0.656643	+	0.238998i	−0.648786	−	0.760971i	$-0.724723\pi$
$59$	−5.04377	+	1.83578i	−0.656643	+	0.238998i	−0.00785651	+	0.999969i	$0.502501\pi$
$60$		0			0
$61$	−1.85946	−	10.5455i	−0.238079	−	1.35021i	−0.836031	−	0.548682i	$-0.815130\pi$
$61$	−1.85946	−	10.5455i	−0.238079	−	1.35021i	0.597952	−	0.801532i	$-0.295981\pi$
$62$		0			0
$63$	2.02483	+	3.73237i	0.255105	+	0.470234i
$64$		0			0
$65$	5.04603	+	1.83660i	0.625883	+	0.227803i
$66$		0			0
$67$	11.3245	+	9.50236i	1.38350	+	1.16090i	0.967895	+	0.251356i	$0.0808763\pi$
$67$	11.3245	+	9.50236i	1.38350	+	1.16090i	0.415610	+	0.909543i	$0.363568\pi$
$68$		0			0
$69$	−14.4966	−	0.192291i	−1.74519	−	0.0231491i
$70$		0			0
$71$	2.68331	−	4.64763i	0.318450	−	0.551572i	−0.661715	−	0.749756i	$-0.730171\pi$
$71$	2.68331	−	4.64763i	0.318450	−	0.551572i	0.980165	+	0.198184i	$0.0635043\pi$
$72$		0			0
$73$	−5.25081	−	9.09467i	−0.614561	−	1.06445i	−0.990461	−	0.137791i	$-0.956000\pi$
$73$	−5.25081	−	9.09467i	−0.614561	−	1.06445i	0.375901	−	0.926660i	$-0.377333\pi$
$74$		0			0
$75$	−2.21182	−	1.90650i	−0.255399	−	0.220143i
$76$		0			0
$77$	−0.521112	+	2.95537i	−0.0593862	+	0.336796i
$78$		0			0
$79$	−6.10688	+	5.12428i	−0.687077	+	0.576526i	−0.918065	−	0.396431i	$-0.870249\pi$
$79$	−6.10688	+	5.12428i	−0.687077	+	0.576526i	0.230988	+	0.972957i	$0.425804\pi$
$80$		0			0
$81$	7.19148	−	5.41134i	0.799054	−	0.601260i
$82$		0			0
$83$	−9.32482	+	7.82445i	−1.02353	+	0.858845i	−0.990067	−	0.140594i	$-0.955099\pi$
$83$	−9.32482	+	7.82445i	−1.02353	+	0.858845i	−0.0334649	+	0.999440i	$0.510654\pi$
$84$		0			0
$85$	1.73812	−	9.85735i	0.188525	−	1.06918i
$86$		0			0
$87$	1.36656	+	1.17791i	0.146510	+	0.126286i
$88$		0			0
$89$	−7.20496	−	12.4794i	−0.763724	−	1.32281i	−0.940918	−	0.338633i	$-0.890035\pi$
$89$	−7.20496	−	12.4794i	−0.763724	−	1.32281i	0.177194	−	0.984176i	$-0.443298\pi$
$90$		0			0
$91$	1.46973	−	2.54564i	0.154069	−	0.266856i
$92$		0			0
$93$	15.3616	+	0.203764i	1.59293	+	0.0211294i
$94$		0			0
$95$	4.84439	+	4.06492i	0.497024	+	0.417052i
$96$		0			0
$97$	10.6595	+	3.87974i	1.08231	+	0.393928i	0.820766	−	0.571265i	$-0.193547\pi$
$97$	10.6595	+	3.87974i	1.08231	+	0.393928i	0.261541	+	0.965192i	$0.415769\pi$
$98$		0			0
$99$	6.35838	+	0.168711i	0.639041	+	0.0169561i
$100$		0			0
$101$	0.0926500	+	0.525444i	0.00921902	+	0.0522836i	0.989070	−	0.147445i	$-0.0471050\pi$
$101$	0.0926500	+	0.525444i	0.00921902	+	0.0522836i	−0.979851	+	0.199729i	$0.935994\pi$
$102$		0			0
$103$	1.39538	−	0.507876i	0.137491	−	0.0500425i	−0.272358	−	0.962196i	$-0.587804\pi$
$103$	1.39538	−	0.507876i	0.137491	−	0.0500425i	0.409849	+	0.912153i	$0.365581\pi$
$104$		0			0
$105$	−4.90961	+	4.00990i	−0.479129	+	0.391326i
$106$		0			0
$107$	−0.416489			−0.0402635			−0.0201317	−	0.999797i	$-0.506409\pi$
$107$	−0.416489			−0.0402635			−0.0201317	+	0.999797i	$0.506409\pi$
$108$		0			0
$109$	−17.2057			−1.64800			−0.824002	−	0.566586i	$-0.808264\pi$
$109$	−17.2057			−1.64800			−0.824002	+	0.566586i	$0.808264\pi$
$110$		0			0
$111$	16.1014	+	6.10349i	1.52828	+	0.579318i
$112$		0			0
$113$	10.1681	−	3.70087i	0.956531	−	0.348149i	0.183858	−	0.982953i	$-0.441141\pi$
$113$	10.1681	−	3.70087i	0.956531	−	0.348149i	0.772673	+	0.634804i	$0.218919\pi$
$114$		0			0
$115$	−3.75834	−	21.3146i	−0.350467	−	1.98759i
$116$		0			0
$117$	−5.79593	−	2.28541i	−0.535834	−	0.211286i
$118$		0			0
$119$	−5.14870	−	1.87397i	−0.471980	−	0.171787i
$120$		0			0
$121$	−4.98291	−	4.18116i	−0.452992	−	0.380105i
$122$		0			0
$123$	10.7000	−	17.9780i	0.964786	−	1.62102i
$124$		0			0
$125$	−4.28464	+	7.42122i	−0.383230	+	0.663774i
$126$		0			0
$127$	−0.0422583	−	0.0731936i	−0.00374982	−	0.00649488i	0.864144	−	0.503244i	$-0.167860\pi$
$127$	−0.0422583	−	0.0731936i	−0.00374982	−	0.00649488i	−0.867894	+	0.496749i	$0.834527\pi$
$128$		0			0
$129$	1.96358	−	10.3327i	0.172884	−	0.909741i
$130$		0			0
$131$	0.176083	−	0.998617i	0.0153845	−	0.0872496i	−0.976149	−	0.217102i	$-0.930339\pi$
$131$	0.176083	−	0.998617i	0.0153845	−	0.0872496i	0.991533	+	0.129853i	$0.0414505\pi$
$132$		0			0
$133$	2.65180	−	2.22513i	0.229941	−	0.192943i
$134$		0			0
$135$	9.94068	+	9.03894i	0.855558	+	0.777948i
$136$		0			0
$137$	−0.572591	+	0.480461i	−0.0489198	+	0.0410486i	−0.666920	−	0.745130i	$-0.732388\pi$
$137$	−0.572591	+	0.480461i	−0.0489198	+	0.0410486i	0.618000	+	0.786178i	$0.287943\pi$
$138$		0			0
$139$	−0.0126135	+	0.0715348i	−0.00106986	+	0.00606750i	−0.985338	−	0.170614i	$-0.945425\pi$
$139$	−0.0126135	+	0.0715348i	−0.00106986	+	0.00606750i	0.984268	+	0.176681i	$0.0565361\pi$
$140$		0			0
$141$	6.26704	−	2.18733i	0.527780	−	0.184206i
$142$		0			0
$143$	−2.20157	−	3.81322i	−0.184104	−	0.318878i
$144$		0			0
$145$	−1.34667	+	2.33250i	−0.111835	+	0.193704i
$146$		0			0
$147$	−4.22740	−	7.55164i	−0.348670	−	0.622849i
$148$		0			0
$149$	−5.86114	−	4.91808i	−0.480163	−	0.402905i	0.370322	−	0.928903i	$-0.379247\pi$
$149$	−5.86114	−	4.91808i	−0.480163	−	0.402905i	−0.850485	+	0.525999i	$0.823692\pi$
$150$		0			0
$151$	−14.5372	−	5.29110i	−1.18302	−	0.430583i	−0.325751	−	0.945456i	$-0.605617\pi$
$151$	−14.5372	−	5.29110i	−1.18302	−	0.430583i	−0.857267	+	0.514872i	$0.827839\pi$
$152$		0			0
$153$	−2.31924	+	11.3792i	−0.187500	+	0.919954i
$154$		0			0
$155$	3.98259	+	22.5864i	0.319889	+	1.81418i
$156$		0			0
$157$	−0.236318	+	0.0860127i	−0.0188602	+	0.00686456i	−0.351433	−	0.936213i	$-0.614306\pi$
$157$	−0.236318	+	0.0860127i	−0.0188602	+	0.00686456i	0.332573	+	0.943078i	$0.392083\pi$
$158$		0			0
$159$	1.03791	+	6.37997i	0.0823113	+	0.505965i
$160$		0			0
$161$	−11.8475			−0.933717
$162$		0			0
$163$	2.08013			0.162929			0.0814643	−	0.996676i	$-0.474040\pi$
$163$	2.08013			0.162929			0.0814643	+	0.996676i	$0.474040\pi$
$164$		0			0
$165$	1.52471	+	9.37231i	0.118698	+	0.729633i
$166$		0			0
$167$	2.65547	−	0.966512i	0.205486	−	0.0747910i	−0.237226	−	0.971454i	$-0.576238\pi$
$167$	2.65547	−	0.966512i	0.205486	−	0.0747910i	0.442713	+	0.896663i	$0.354016\pi$
$168$		0			0
$169$	−1.50850	−	8.55514i	−0.116039	−	0.658088i
$170$		0			0
$171$	−5.49349	−	4.86363i	−0.420098	−	0.371931i
$172$		0			0
$173$	−5.27324	−	1.91930i	−0.400917	−	0.145922i	0.133689	−	0.991023i	$-0.457318\pi$
$173$	−5.27324	−	1.91930i	−0.400917	−	0.145922i	−0.534606	+	0.845102i	$0.679540\pi$
$174$		0			0
$175$	−1.82798	−	1.53386i	−0.138182	−	0.115949i
$176$		0			0
$177$	4.54117	+	8.11214i	0.341335	+	0.609746i
$178$		0			0
$179$	0.261810	−	0.453468i	0.0195686	−	0.0338938i	−0.856075	−	0.516851i	$-0.827104\pi$
$179$	0.261810	−	0.453468i	0.0195686	−	0.0338938i	0.875644	+	0.482957i	$0.160437\pi$
$180$		0			0
$181$	2.44721	+	4.23870i	0.181900	+	0.315060i	0.942527	−	0.334129i	$-0.108442\pi$
$181$	2.44721	+	4.23870i	0.181900	+	0.315060i	−0.760628	+	0.649188i	$0.775109\pi$
$182$		0			0
$183$	−17.5112	+	6.11177i	−1.29446	+	0.451795i
$184$		0			0
$185$	−4.46384	+	25.3157i	−0.328188	+	1.86125i
$186$		0			0
$187$	−6.28724	+	5.27562i	−0.459769	+	0.385792i
$188$		0			0
$189$	5.81763	−	4.49964i	0.423170	−	0.327301i
$190$		0			0
$191$	−10.8417	+	9.09725i	−0.784477	+	0.658254i	−0.944372	−	0.328880i	$-0.893329\pi$
$191$	−10.8417	+	9.09725i	−0.784477	+	0.658254i	0.159895	+	0.987134i	$0.448884\pi$
$192$		0			0
$193$	−2.00475	+	11.3695i	−0.144305	+	0.818396i	0.823617	+	0.567146i	$0.191953\pi$
$193$	−2.00475	+	11.3695i	−0.144305	+	0.818396i	−0.967922	+	0.251250i	$0.919158\pi$
$194$		0			0
$195$	1.73643	−	9.13736i	0.124348	−	0.654340i
$196$		0			0
$197$	8.58339	+	14.8669i	0.611541	+	1.05922i	0.990981	+	0.134004i	$0.0427835\pi$
$197$	8.58339	+	14.8669i	0.611541	+	1.05922i	−0.379439	+	0.925217i	$0.623883\pi$
$198$		0			0
$199$	7.09229	−	12.2842i	0.502759	−	0.870804i	−0.497236	−	0.867615i	$-0.665652\pi$
$199$	7.09229	−	12.2842i	0.502759	−	0.870804i	0.999995	−	0.00318864i	$-0.00101498\pi$
$200$		0			0
$201$	13.0955	−	22.0028i	0.923684	−	1.55196i
$202$		0			0
$203$	1.12940	+	0.947681i	0.0792685	+	0.0665142i
$204$		0			0
$205$	29.3489	+	10.6821i	2.04982	+	0.746073i
$206$		0			0
$207$	3.70303	+	24.8366i	0.257378	+	1.72626i
$208$		0			0
$209$	−0.900436	−	5.10662i	−0.0622844	−	0.353233i
$210$		0			0
$211$	−1.69567	+	0.617173i	−0.116735	+	0.0424880i	−0.399727	−	0.916634i	$-0.630895\pi$
$211$	−1.69567	+	0.617173i	−0.116735	+	0.0424880i	0.282992	+	0.959122i	$0.408673\pi$
$212$		0			0
$213$	−8.69175	−	3.29474i	−0.595549	−	0.225752i
$214$		0			0
$215$	15.7013			1.07082
$216$		0			0
$217$	12.5545			0.852252
$218$		0			0
$219$	−14.0877	+	11.5060i	−0.951958	+	0.777506i
$220$		0			0
$221$	7.55436	−	2.74956i	0.508162	−	0.184956i
$222$		0			0
$223$	−4.03626	−	22.8907i	−0.270288	−	1.53288i	−0.753543	−	0.657398i	$-0.771657\pi$
$223$	−4.03626	−	22.8907i	−0.270288	−	1.53288i	0.483256	−	0.875479i	$-0.339454\pi$
$224$		0			0
$225$	−2.64416	+	4.31151i	−0.176277	+	0.287434i
$226$		0			0
$227$	−6.33464	−	2.30562i	−0.420445	−	0.153029i	0.123129	−	0.992391i	$-0.460707\pi$
$227$	−6.33464	−	2.30562i	−0.420445	−	0.153029i	−0.543574	+	0.839361i	$0.682929\pi$
$228$		0			0
$229$	−5.87666	−	4.93111i	−0.388341	−	0.325857i	0.427626	−	0.903956i	$-0.359350\pi$
$229$	−5.87666	−	4.93111i	−0.388341	−	0.325857i	−0.815966	+	0.578099i	$0.803795\pi$
$230$		0			0
$231$	5.19737	+	0.0689404i	0.341962	+	0.00453595i
$232$		0			0
$233$	−5.49573	+	9.51888i	−0.360037	+	0.623603i	−0.987967	−	0.154668i	$-0.950569\pi$
$233$	−5.49573	+	9.51888i	−0.360037	+	0.623603i	0.627929	+	0.778270i	$0.283903\pi$
$234$		0			0
$235$	4.95465	+	8.58171i	0.323206	+	0.559809i
$236$		0			0
$237$	10.4588	+	9.01502i	0.679370	+	0.585588i
$238$		0			0
$239$	3.71043	−	21.0429i	0.240008	−	1.36115i	−0.591799	−	0.806086i	$-0.701582\pi$
$239$	3.71043	−	21.0429i	0.240008	−	1.36115i	0.831806	−	0.555066i	$-0.187307\pi$
$240$		0			0
$241$	−21.4255	+	17.9781i	−1.38014	+	1.15807i	−0.410974	+	0.911647i	$0.634811\pi$
$241$	−21.4255	+	17.9781i	−1.38014	+	1.15807i	−0.969162	+	0.246424i	$0.920744\pi$
$242$		0			0
$243$	−11.2512	−	10.7894i	−0.721763	−	0.692140i
$244$		0			0
$245$	9.89713	−	8.30468i	0.632305	−	0.530567i
$246$		0			0
$247$	−0.881979	+	5.00195i	−0.0561190	+	0.318267i
$248$		0			0
$249$	15.9699	+	13.7654i	1.01205	+	0.872345i
$250$		0			0
$251$	11.1783	+	19.3613i	0.705565	+	1.22207i	0.966487	+	0.256715i	$0.0826400\pi$
$251$	11.1783	+	19.3613i	0.705565	+	1.22207i	−0.260922	+	0.965360i	$0.584027\pi$
$252$		0			0
$253$	−8.87346	+	15.3693i	−0.557870	+	0.966258i
$254$		0			0
$255$	−17.3353	−	0.229944i	−1.08558	−	0.0143996i
$256$		0			0
$257$	−13.7122	−	11.5059i	−0.855344	−	0.717719i	0.105616	−	0.994407i	$-0.466319\pi$
$257$	−13.7122	−	11.5059i	−0.855344	−	0.717719i	−0.960960	+	0.276688i	$0.910763\pi$
$258$		0			0
$259$	13.2229	+	4.81275i	0.821632	+	0.299050i
$260$		0			0
$261$	1.63367	−	2.66383i	0.101122	−	0.164887i
$262$		0			0
$263$	−4.58969	−	26.0294i	−0.283013	−	1.60504i	−0.712299	−	0.701876i	$-0.752346\pi$
$263$	−4.58969	−	26.0294i	−0.283013	−	1.60504i	0.429286	−	0.903168i	$-0.358765\pi$
$264$		0			0
$265$	−9.06768	+	3.30037i	−0.557023	+	0.202740i
$266$		0			0
$267$	−19.3306	+	15.7882i	−1.18301	+	0.966219i
$268$		0			0
$269$	−4.30073			−0.262220			−0.131110	−	0.991368i	$-0.541854\pi$
$269$	−4.30073			−0.262220			−0.131110	+	0.991368i	$0.541854\pi$
$270$		0			0
$271$	−2.97894			−0.180957			−0.0904787	−	0.995898i	$-0.528840\pi$
$271$	−2.97894			−0.180957			−0.0904787	+	0.995898i	$0.528840\pi$
$272$		0			0
$273$	−4.76073	−	1.80462i	−0.288132	−	0.109221i
$274$		0			0
$275$	−3.35891	+	1.22254i	−0.202550	+	0.0737221i
$276$		0			0
$277$	1.08403	+	6.14785i	0.0651332	+	0.369389i	0.999900	+	0.0141273i	$0.00449702\pi$
$277$	1.08403	+	6.14785i	0.0651332	+	0.369389i	−0.934767	+	0.355261i	$0.884392\pi$
$278$		0			0
$279$	−3.92398	−	26.3185i	−0.234923	−	1.57565i
$280$		0			0
$281$	2.23973	+	0.815197i	0.133611	+	0.0486306i	0.407960	−	0.913000i	$-0.366240\pi$
$281$	2.23973	+	0.815197i	0.133611	+	0.0486306i	−0.274349	+	0.961630i	$0.588462\pi$
$282$		0			0
$283$	−0.00910269	−	0.00763807i	−0.000541099	−	0.000454036i	0.642517	−	0.766271i	$-0.277890\pi$
$283$	−0.00910269	−	0.00763807i	−0.000541099	−	0.000454036i	−0.643058	+	0.765817i	$0.722335\pi$
$284$		0			0
$285$	5.60199	−	9.41237i	0.331833	−	0.557541i
$286$		0			0
$287$	8.54829	−	14.8061i	0.504590	−	0.873975i
$288$		0			0
$289$	1.00750	+	1.74504i	0.0592646	+	0.102649i
$290$		0			0
$291$	3.66812	−	19.3022i	0.215029	−	1.13152i
$292$		0			0
$293$	−0.905379	+	5.13466i	−0.0528928	+	0.299970i	−0.999766	−	0.0216376i	$-0.993112\pi$
$293$	−0.905379	+	5.13466i	−0.0528928	+	0.299970i	0.946873	+	0.321607i	$0.104223\pi$
$294$		0			0
$295$	−10.6317	+	8.92107i	−0.619003	+	0.519405i
$296$		0			0
$297$	−1.47995	−	10.9171i	−0.0858754	−	0.633472i
$298$		0			0
$299$	13.3163	−	11.1737i	0.770100	−	0.646190i
$300$		0			0
$301$	1.49248	−	8.46428i	0.0860252	−	0.487873i
$302$		0			0
$303$	0.872519	−	0.304527i	0.0501249	−	0.0174946i
$304$		0			0
$305$	−13.8441	−	23.9788i	−0.792713	−	1.37302i
$306$		0			0
$307$	10.1440	−	17.5700i	0.578951	−	1.00277i	−0.416649	−	0.909067i	$-0.636796\pi$
$307$	10.1440	−	17.5700i	0.578951	−	1.00277i	0.995600	−	0.0937049i	$-0.0298710\pi$
$308$		0			0
$309$	−1.25633	−	2.24426i	−0.0714702	−	0.127671i
$310$		0			0
$311$	−8.13067	−	6.82244i	−0.461048	−	0.386865i	0.382468	−	0.923969i	$-0.375074\pi$
$311$	−8.13067	−	6.82244i	−0.461048	−	0.386865i	−0.843516	+	0.537103i	$0.819519\pi$
$312$		0			0
$313$	5.88285	+	2.14118i	0.332518	+	0.121027i	0.502884	−	0.864354i	$-0.332272\pi$
$313$	5.88285	+	2.14118i	0.332518	+	0.121027i	−0.170365	+	0.985381i	$0.554495\pi$
$314$		0			0
$315$	8.22067	+	7.27813i	0.463182	+	0.410076i
$316$		0			0
$317$	−3.02412	−	17.1507i	−0.169852	−	0.963277i	−0.943920	−	0.330175i	$-0.892892\pi$
$317$	−3.02412	−	17.1507i	−0.169852	−	0.963277i	0.774068	−	0.633102i	$-0.218219\pi$
$318$		0			0
$319$	2.07527	−	0.755338i	0.116193	−	0.0422908i
$320$		0			0
$321$	0.115833	+	0.712019i	0.00646515	+	0.0397410i
$322$		0			0
$323$	9.46745			0.526783
$324$		0			0
$325$	3.50121			0.194212
$326$		0			0
$327$	4.78519	+	29.4144i	0.264622	+	1.62662i
$328$		0			0
$329$	5.09720	−	1.85523i	0.281018	−	0.102282i
$330$		0			0
$331$	3.55468	+	20.1596i	0.195383	+	1.10807i	0.911872	+	0.410474i	$0.134637\pi$
$331$	3.55468	+	20.1596i	0.195383	+	1.10807i	−0.716489	+	0.697598i	$0.754252\pi$
$332$		0			0
$333$	5.95629	−	29.2241i	0.326403	−	1.60147i
$334$		0			0
$335$	35.9195	+	13.0736i	1.96249	+	0.714289i
$336$		0			0
$337$	16.9649	+	14.2352i	0.924136	+	0.775442i	0.974755	−	0.223276i	$-0.0716752\pi$
$337$	16.9649	+	14.2352i	0.924136	+	0.775442i	−0.0506197	+	0.998718i	$0.516120\pi$
$338$		0			0
$339$	−9.15484	−	16.3538i	−0.497223	−	0.888217i
$340$		0			0
$341$	9.40292	−	16.2863i	0.509197	−	0.881955i
$342$		0			0
$343$	−8.49007	−	14.7052i	−0.458421	−	0.794008i
$344$		0			0
$345$	−35.3936	+	12.3531i	−1.90553	+	0.665069i
$346$		0			0
$347$	−0.196028	+	1.11173i	−0.0105234	+	0.0596809i	−0.989617	−	0.143728i	$-0.954091\pi$
$347$	−0.196028	+	1.11173i	−0.0105234	+	0.0596809i	0.979094	+	0.203409i	$0.0652021\pi$
$348$		0			0
$349$	−9.55881	+	8.02079i	−0.511671	+	0.429343i	−0.861717	−	0.507389i	$-0.830611\pi$
$349$	−9.55881	+	8.02079i	−0.511671	+	0.429343i	0.350046	+	0.936733i	$0.386166\pi$
$350$		0			0
$351$	−2.29513	+	10.5442i	−0.122505	+	0.562808i
$352$		0			0
$353$	20.3466	−	17.0729i	1.08294	−	0.908696i	0.0867801	−	0.996227i	$-0.472342\pi$
$353$	20.3466	−	17.0729i	1.08294	−	0.908696i	0.996162	+	0.0875314i	$0.0278978\pi$
$354$		0			0
$355$	2.40964	−	13.6657i	0.127890	−	0.725301i
$356$		0			0
$357$	−1.77176	+	9.32327i	−0.0937713	+	0.493440i
$358$		0			0
$359$	7.47495	+	12.9470i	0.394513	+	0.683317i	0.993039	−	0.117787i	$-0.0375800\pi$
$359$	7.47495	+	12.9470i	0.394513	+	0.683317i	−0.598526	+	0.801103i	$0.704247\pi$
$360$		0			0
$361$	6.50926	−	11.2744i	0.342592	−	0.593388i
$362$		0			0
$363$	−5.76218	+	9.68152i	−0.302436	+	0.508148i
$364$		0			0
$365$	−20.8013	−	17.4544i	−1.08879	−	0.913603i
$366$		0			0
$367$	22.7509	+	8.28066i	1.18759	+	0.432247i	0.858876	−	0.512183i	$-0.171163\pi$
$367$	22.7509	+	8.28066i	1.18759	+	0.432247i	0.328712	+	0.944430i	$0.393385\pi$
$368$		0			0
$369$	−33.7105	−	13.2925i	−1.75490	−	0.691978i
$370$		0			0
$371$	0.917241	+	5.20193i	0.0476208	+	0.270071i
$372$		0			0
$373$	16.8087	−	6.11786i	0.870320	−	0.316771i	0.132023	−	0.991247i	$-0.457853\pi$
$373$	16.8087	−	6.11786i	0.870320	−	0.316771i	0.738297	+	0.674476i	$0.235630\pi$
$374$		0			0
$375$	13.8788	+	5.26095i	0.716697	+	0.271674i
$376$		0			0
$377$	−2.16319			−0.111410
$378$		0			0
$379$	37.2231			1.91202			0.956010	−	0.293334i	$-0.0947648\pi$
$379$	37.2231			1.91202			0.956010	+	0.293334i	$0.0947648\pi$
$380$		0			0
$381$	−0.113377	+	0.0926002i	−0.00580849	+	0.00474405i
$382$		0			0
$383$	−21.9881	+	8.00300i	−1.12354	+	0.408934i	−0.835942	−	0.548818i	$-0.815078\pi$
$383$	−21.9881	+	8.00300i	−1.12354	+	0.408934i	−0.287595	+	0.957752i	$0.592856\pi$
$384$		0			0
$385$	1.34745	+	7.64175i	0.0686722	+	0.389460i
$386$		0			0
$387$	−18.2106	−	0.483194i	−0.925697	−	0.0245621i
$388$		0			0
$389$	−4.90844	−	1.78653i	−0.248868	−	0.0905805i	0.214574	−	0.976708i	$-0.431164\pi$
$389$	−4.90844	−	1.78653i	−0.248868	−	0.0905805i	−0.463442	+	0.886127i	$0.653386\pi$
$390$		0			0
$391$	−24.8215	−	20.8277i	−1.25528	−	1.05330i
$392$		0			0
$393$	−1.75618	−	0.0232949i	−0.0885877	−	0.00117507i
$394$		0			0
$395$	−10.3066	+	17.8516i	−0.518581	+	0.898209i
$396$		0			0
$397$	17.1043	+	29.6256i	0.858442	+	1.48686i	0.873415	+	0.486977i	$0.161900\pi$
$397$	17.1043	+	29.6256i	0.858442	+	1.48686i	−0.0149734	+	0.999888i	$0.504766\pi$
$398$		0			0
$399$	−4.54154	−	3.91462i	−0.227361	−	0.195976i
$400$		0			0
$401$	−5.67724	+	32.1972i	−0.283508	+	1.60785i	0.427060	+	0.904223i	$0.359549\pi$
$401$	−5.67724	+	32.1972i	−0.283508	+	1.60785i	−0.710567	+	0.703629i	$0.751562\pi$
$402$		0			0
$403$	−14.1108	+	11.8404i	−0.702910	+	0.589812i
$404$		0			0
$405$	12.6881	−	19.5082i	0.630476	−	0.969372i
$406$		0			0
$407$	16.1469	−	13.5489i	0.800374	−	0.671594i
$408$		0			0
$409$	3.13626	−	17.7866i	0.155078	−	0.879491i	−0.803636	−	0.595121i	$-0.797104\pi$
$409$	3.13626	−	17.7866i	0.155078	−	0.879491i	0.958714	−	0.284371i	$-0.0917846\pi$
$410$		0			0
$411$	0.980632	+	0.845264i	0.0483710	+	0.0416938i
$412$		0			0
$413$	3.79859	+	6.57935i	0.186916	+	0.323749i
$414$		0			0
$415$	−15.7375	+	27.2582i	−0.772525	+	1.33805i
$416$		0			0
$417$	0.125802	+	0.00166870i	0.00616056	+	8.17167e-5i
$418$		0			0
$419$	8.10008	+	6.79677i	0.395715	+	0.332044i	0.818835	−	0.574030i	$-0.194621\pi$
$419$	8.10008	+	6.79677i	0.395715	+	0.332044i	−0.423120	+	0.906074i	$0.639065\pi$
$420$		0			0
$421$	14.0408	+	5.11045i	0.684309	+	0.249068i	0.660696	−	0.750653i	$-0.270261\pi$
$421$	14.0408	+	5.11045i	0.684309	+	0.249068i	0.0236122	+	0.999721i	$0.492483\pi$
$422$		0			0
$423$	−5.48238	−	10.1057i	−0.266562	−	0.491354i
$424$		0			0
$425$	−1.13327	−	6.42709i	−0.0549716	−	0.311760i
$426$		0			0
$427$	−14.2424	+	5.18383i	−0.689240	+	0.250863i
$428$		0			0
$429$	−5.90670	+	4.82427i	−0.285178	+	0.232918i
$430$		0			0
$431$	2.20497			0.106210			0.0531048	−	0.998589i	$-0.483088\pi$
$431$	2.20497			0.106210			0.0531048	+	0.998589i	$0.483088\pi$
$432$		0			0
$433$	−6.38398			−0.306794			−0.153397	−	0.988165i	$-0.549021\pi$
$433$	−6.38398			−0.306794			−0.153397	+	0.988165i	$0.549021\pi$
$434$		0			0
$435$	4.36213	+	1.65353i	0.209148	+	0.0792807i
$436$		0			0
$437$	19.2369	−	7.00166i	0.920226	−	0.334935i
$438$		0			0
$439$	1.72428	+	9.77890i	0.0822955	+	0.466721i	0.997907	+	0.0646581i	$0.0205957\pi$
$439$	1.72428	+	9.77890i	0.0822955	+	0.466721i	−0.915612	+	0.402063i	$0.868293\pi$
$440$		0			0
$441$	−11.7344	+	9.32731i	−0.558781	+	0.444157i
$442$		0			0
$443$	−6.82027	−	2.48238i	−0.324041	−	0.117941i	0.174877	−	0.984590i	$-0.444047\pi$
$443$	−6.82027	−	2.48238i	−0.324041	−	0.117941i	−0.498918	+	0.866649i	$0.666269\pi$
$444$		0			0
$445$	−28.5428	−	23.9502i	−1.35306	−	1.13535i
$446$		0			0
$447$	−6.77774	+	11.3879i	−0.320576	+	0.538627i
$448$		0			0
$449$	−1.51154	+	2.61806i	−0.0713339	+	0.123554i	−0.899486	−	0.436949i	$-0.856059\pi$
$449$	−1.51154	+	2.61806i	−0.0713339	+	0.123554i	0.828152	+	0.560503i	$0.189392\pi$
$450$		0			0
$451$	−12.8048	−	22.1786i	−0.602956	−	1.04435i
$452$		0			0
$453$	−5.00249	+	26.3239i	−0.235038	+	1.23681i
$454$		0			0
$455$	1.31983	−	7.48511i	0.0618745	−	0.350908i
$456$		0			0
$457$	−21.3187	+	17.8885i	−0.997248	+	0.836790i	−0.986601	−	0.163153i	$-0.947834\pi$
$457$	−21.3187	+	17.8885i	−0.997248	+	0.836790i	−0.0106471	+	0.999943i	$0.503389\pi$
$458$		0			0
$459$	20.0986	+	0.800170i	0.938124	+	0.0373487i
$460$		0			0
$461$	−20.9390	+	17.5699i	−0.975227	+	0.818313i	−0.983362	−	0.181654i	$-0.941855\pi$
$461$	−20.9390	+	17.5699i	−0.975227	+	0.818313i	0.00813531	+	0.999967i	$0.497410\pi$
$462$		0			0
$463$	−3.60742	+	20.4587i	−0.167651	+	0.950795i	0.778638	+	0.627473i	$0.215911\pi$
$463$	−3.60742	+	20.4587i	−0.167651	+	0.950795i	−0.946289	+	0.323322i	$0.895200\pi$
$464$		0			0
$465$	37.5055	−	13.0902i	1.73928	−	0.607043i
$466$		0			0
$467$	−2.66334	−	4.61304i	−0.123245	−	0.213466i	0.797801	−	0.602921i	$-0.205997\pi$
$467$	−2.66334	−	4.61304i	−0.123245	−	0.213466i	−0.921045	+	0.389455i	$0.872663\pi$
$468$		0			0
$469$	10.4621	−	18.1208i	0.483093	−	0.836742i
$470$		0			0
$471$	0.212769	+	0.380082i	0.00980390	+	0.0175133i
$472$		0			0
$473$	−9.86251	−	8.27563i	−0.453479	−	0.380514i
$474$		0			0
$475$	3.87458	+	1.41023i	0.177778	+	0.0647059i
$476$		0			0
$477$	10.6184	−	3.54876i	0.486182	−	0.162487i
$478$		0			0
$479$	−1.43810	−	8.15589i	−0.0657086	−	0.372652i	−0.999875	−	0.0158142i	$-0.994966\pi$
$479$	−1.43810	−	8.15589i	−0.0657086	−	0.372652i	0.934166	−	0.356838i	$-0.116145\pi$
$480$		0			0
$481$	−19.4012	+	7.06145i	−0.884617	+	0.321974i
$482$		0			0
$483$	3.29500	+	20.2543i	0.149928	+	0.921601i
$484$		0			0
$485$	29.3313			1.33186
$486$		0			0
$487$	24.1730			1.09539			0.547693	−	0.836680i	$-0.315506\pi$
$487$	24.1730			1.09539			0.547693	+	0.836680i	$0.315506\pi$
$488$		0			0
$489$	−0.578521	−	3.55614i	−0.0261616	−	0.160814i
$490$		0			0
$491$	−38.1657	+	13.8912i	−1.72239	+	0.626900i	−0.998043	−	0.0625322i	$-0.980082\pi$
$491$	−38.1657	+	13.8912i	−1.72239	+	0.626900i	−0.724350	+	0.689432i	$0.757860\pi$
$492$		0			0
$493$	0.700181	+	3.97092i	0.0315346	+	0.178841i
$494$		0			0
$495$	15.5986	−	5.21320i	0.701106	−	0.234316i
$496$		0			0
$497$	−7.13789	−	2.59798i	−0.320178	−	0.116535i
$498$		0			0
$499$	20.8373	+	17.4846i	0.932806	+	0.782717i	0.976319	−	0.216336i	$-0.0694107\pi$
$499$	20.8373	+	17.4846i	0.932806	+	0.782717i	−0.0435134	+	0.999053i	$0.513855\pi$
$500$		0			0
$501$	−2.39086	−	4.27092i	−0.106816	−	0.190811i
$502$		0			0
$503$	−13.4402	+	23.2791i	−0.599270	+	1.03797i	0.393659	+	0.919256i	$0.371209\pi$
$503$	−13.4402	+	23.2791i	−0.599270	+	1.03797i	−0.992929	+	0.118709i	$0.962124\pi$
$504$		0			0
$505$	0.689803	+	1.19477i	0.0306959	+	0.0531668i
$506$		0			0
$507$	−14.2061	+	4.95823i	−0.630916	+	0.220203i
$508$		0			0
$509$	5.15594	−	29.2408i	0.228533	−	1.29608i	−0.627281	−	0.778793i	$-0.715832\pi$
$509$	5.15594	−	29.2408i	0.228533	−	1.29608i	0.855814	−	0.517283i	$-0.173057\pi$
$510$		0			0
$511$	−11.3866	+	9.55448i	−0.503713	+	0.422665i
$512$		0			0
$513$	−6.78692	+	10.7442i	−0.299650	+	0.474368i
$514$		0			0
$515$	2.94131	−	2.46805i	0.129609	−	0.108755i
$516$		0			0
$517$	1.41095	−	8.00188i	0.0620534	−	0.351922i
$518$		0			0
$519$	−1.81461	+	9.54879i	−0.0796527	+	0.419145i
$520$		0			0
$521$	19.7615	+	34.2280i	0.865769	+	1.49956i	0.866282	+	0.499556i	$0.166503\pi$
$521$	19.7615	+	34.2280i	0.865769	+	1.49956i	−0.000512875		1.00000i	$0.500163\pi$
$522$		0			0
$523$	−3.77869	+	6.54488i	−0.165231	+	0.286188i	−0.936737	−	0.350034i	$-0.886170\pi$
$523$	−3.77869	+	6.54488i	−0.165231	+	0.286188i	0.771507	+	0.636221i	$0.219503\pi$
$524$		0			0
$525$	−2.11385	+	3.55166i	−0.0922561	+	0.155007i
$526$		0			0
$527$	26.3025	+	22.0704i	1.14576	+	0.961403i
$528$		0			0
$529$	−44.2249	−	16.0966i	−1.92282	−	0.699851i
$530$		0			0
$531$	12.6054	−	10.0196i	0.547026	−	0.434814i
$532$		0			0
$533$	4.35592	+	24.7037i	0.188676	+	1.07003i
$534$		0			0
$535$	−1.01197	+	0.368328i	−0.0437515	+	0.0159242i
$536$		0			0
$537$	−0.848051	−	0.321466i	−0.0365961	−	0.0138723i
$538$		0			0
$539$	−10.5938			−0.456309
$540$		0			0
$541$	2.89649			0.124530			0.0622650	−	0.998060i	$-0.480168\pi$
$541$	2.89649			0.124530			0.0622650	+	0.998060i	$0.480168\pi$
$542$		0			0
$543$	6.56576	−	5.36255i	0.281764	−	0.230129i
$544$		0			0
$545$	−41.8059	+	15.2161i	−1.79077	+	0.651787i
$546$		0			0
$547$	−2.59815	−	14.7349i	−0.111089	−	0.630017i	−0.988613	−	0.150483i	$-0.951917\pi$
$547$	−2.59815	−	14.7349i	−0.111089	−	0.630017i	0.877524	−	0.479533i	$-0.159194\pi$
$548$		0			0
$549$	15.3187	+	28.2369i	0.653786	+	1.20512i
$550$		0			0
$551$	−2.39388	−	0.871300i	−0.101983	−	0.0371186i
$552$		0			0
$553$	8.64375	+	7.25297i	0.367570	+	0.308427i
$554$		0			0
$555$	44.5206	+	0.590543i	1.88979	+	0.0250672i
$556$		0			0
$557$	−10.7114	+	18.5527i	−0.453856	+	0.786102i	−0.998622	−	0.0524865i	$-0.983285\pi$
$557$	−10.7114	+	18.5527i	−0.453856	+	0.786102i	0.544766	+	0.838588i	$0.316619\pi$
$558$		0			0
$559$	6.30535	+	10.9212i	0.266688	+	0.461917i
$560$		0			0
$561$	10.7677	+	9.28128i	0.454611	+	0.391856i
$562$		0			0
$563$	7.65262	−	43.4002i	0.322520	−	1.82910i	−0.204042	−	0.978962i	$-0.565408\pi$
$563$	7.65262	−	43.4002i	0.322520	−	1.82910i	0.526561	−	0.850137i	$-0.323481\pi$
$564$		0			0
$565$	21.4332	−	17.9846i	0.901701	−	0.756617i
$566$		0			0
$567$	−9.31046	−	8.69425i	−0.391003	−	0.365124i
$568$		0			0
$569$	22.4926	−	18.8735i	0.942940	−	0.791220i	−0.0351549	−	0.999382i	$-0.511192\pi$
$569$	22.4926	−	18.8735i	0.942940	−	0.791220i	0.978094	+	0.208162i	$0.0667480\pi$
$570$		0			0
$571$	5.20125	−	29.4977i	0.217665	−	1.23444i	−0.658555	−	0.752532i	$-0.728832\pi$
$571$	5.20125	−	29.4977i	0.217665	−	1.23444i	0.876221	−	0.481910i	$-0.160057\pi$
$572$		0			0
$573$	18.5677	+	16.0046i	0.775677	+	0.668601i
$574$		0			0
$575$	−7.05585	−	12.2211i	−0.294249	−	0.509655i
$576$		0			0
$577$	18.7784	−	32.5251i	0.781755	−	1.35404i	−0.149164	−	0.988812i	$-0.547658\pi$
$577$	18.7784	−	32.5251i	0.781755	−	1.35404i	0.930919	−	0.365226i	$-0.119008\pi$
$578$		0			0
$579$	19.9946	+	0.265219i	0.830948	+	0.0110221i
$580$		0			0
$581$	13.1985	+	11.0748i	0.547565	+	0.459461i
$582$		0			0
$583$	7.43522	+	2.70620i	0.307935	+	0.112079i
$584$		0			0
$585$	−16.1039	−	0.427297i	−0.665816	−	0.0176665i
$586$		0			0
$587$	−4.06466	−	23.0518i	−0.167766	−	0.951451i	−0.946166	−	0.323682i	$-0.895079\pi$
$587$	−4.06466	−	23.0518i	−0.167766	−	0.951451i	0.778400	−	0.627769i	$-0.216032\pi$
$588$		0			0
$589$	−20.3847	+	7.41944i	−0.839939	+	0.305713i
$590$		0			0
$591$	23.0289	−	18.8087i	0.947281	−	0.773686i
$592$		0			0
$593$	−3.10744			−0.127607			−0.0638037	−	0.997962i	$-0.520323\pi$
$593$	−3.10744			−0.127607			−0.0638037	+	0.997962i	$0.520323\pi$
$594$		0			0
$595$	−14.1675			−0.580809
$596$		0			0
$597$	−22.9733	−	8.70836i	−0.940233	−	0.356409i
$598$		0			0
$599$	−18.8508	+	6.86114i	−0.770224	+	0.280339i	−0.697090	−	0.716983i	$-0.745522\pi$
$599$	−18.8508	+	6.86114i	−0.770224	+	0.280339i	−0.0731340	+	0.997322i	$0.523300\pi$
$600$		0			0
$601$	−6.44368	−	36.5439i	−0.262843	−	1.49066i	−0.775107	−	0.631829i	$-0.782304\pi$
$601$	−6.44368	−	36.5439i	−0.262843	−	1.49066i	0.512264	−	0.858828i	$-0.328807\pi$
$602$		0			0
$603$	−41.2576	−	16.2684i	−1.68014	−	0.662499i
$604$		0			0
$605$	−15.8050	−	5.75256i	−0.642566	−	0.233875i
$606$		0			0
$607$	−24.1436	−	20.2588i	−0.979957	−	0.822281i	0.00412615	−	0.999991i	$-0.498687\pi$
$607$	−24.1436	−	20.2588i	−0.979957	−	0.822281i	−0.984083	+	0.177710i	$0.943131\pi$
$608$		0			0
$609$	1.30603	−	2.19437i	0.0529229	−	0.0889202i
$610$		0			0
$611$	−3.97939	+	6.89251i	−0.160989	+	0.278841i
$612$		0			0
$613$	−16.5827	−	28.7220i	−0.669767	−	1.16007i	−0.977969	−	0.208750i	$-0.933061\pi$
$613$	−16.5827	−	28.7220i	−0.669767	−	1.16007i	0.308202	−	0.951321i	$-0.400273\pi$
$614$		0			0
$615$	10.0995	−	53.1451i	0.407250	−	2.14302i
$616$		0			0
$617$	−1.65400	+	9.38030i	−0.0665875	+	0.377636i	0.933243	+	0.359245i	$0.116966\pi$
$617$	−1.65400	+	9.38030i	−0.0665875	+	0.377636i	−0.999831	+	0.0183917i	$0.994145\pi$
$618$		0			0
$619$	22.2981	−	18.7103i	0.896237	−	0.752032i	−0.0732141	−	0.997316i	$-0.523326\pi$
$619$	22.2981	−	18.7103i	0.896237	−	0.752032i	0.969451	+	0.245284i	$0.0788812\pi$
$620$		0			0
$621$	41.4302	−	13.2381i	1.66254	−	0.531227i
$622$		0			0
$623$	−15.6242	+	13.1103i	−0.625971	+	0.525252i
$624$		0			0
$625$	−5.31142	+	30.1226i	−0.212457	+	1.20490i
$626$		0			0
$627$	−8.47974	+	2.95960i	−0.338648	+	0.118195i
$628$		0			0
$629$	19.2423	+	33.3286i	0.767240	+	1.32890i
$630$		0			0
$631$	4.17030	−	7.22318i	0.166017	−	0.287550i	−0.770999	−	0.636837i	$-0.780243\pi$
$631$	4.17030	−	7.22318i	0.166017	−	0.287550i	0.937016	+	0.349286i	$0.113576\pi$
$632$		0			0
$633$	1.52670	+	2.72723i	0.0606809	+	0.108398i
$634$		0			0
$635$	−0.167408	−	0.140472i	−0.00664339	−	0.00557446i
$636$		0			0
$637$	9.75090	+	3.54904i	0.386345	+	0.140618i
$638$		0			0
$639$	−3.21528	+	15.7755i	−0.127194	+	0.624071i
$640$		0			0
$641$	1.90981	+	10.8311i	0.0754330	+	0.427802i	0.999014	+	0.0443983i	$0.0141371\pi$
$641$	1.90981	+	10.8311i	0.0754330	+	0.427802i	−0.923581	+	0.383404i	$0.874752\pi$
$642$		0			0
$643$	−7.45557	+	2.71361i	−0.294019	+	0.107014i	−0.484818	−	0.874615i	$-0.661114\pi$
$643$	−7.45557	+	2.71361i	−0.294019	+	0.107014i	0.190799	+	0.981629i	$0.438892\pi$
$644$		0			0
$645$	−4.36681	−	26.8426i	−0.171943	−	1.05693i
$646$		0			0
$647$	−7.52146			−0.295699			−0.147849	−	0.989010i	$-0.547235\pi$
$647$	−7.52146			−0.295699			−0.147849	+	0.989010i	$0.547235\pi$
$648$		0			0
$649$	11.3801			0.446709
$650$		0			0
$651$	−3.49161	−	21.4628i	−0.136847	−	0.841193i
$652$		0			0
$653$	23.5518	−	8.57214i	0.921652	−	0.335454i	0.162757	−	0.986666i	$-0.447961\pi$
$653$	23.5518	−	8.57214i	0.921652	−	0.335454i	0.758896	+	0.651212i	$0.225739\pi$
$654$		0			0
$655$	−0.455300	−	2.58214i	−0.0177901	−	0.100892i
$656$		0			0
$657$	23.5885	+	20.8840i	0.920275	+	0.814761i
$658$		0			0
$659$	−30.5262	−	11.1106i	−1.18913	−	0.432808i	−0.329712	−	0.944081i	$-0.606952\pi$
$659$	−30.5262	−	11.1106i	−1.18913	−	0.432808i	−0.859418	+	0.511273i	$0.829174\pi$
$660$		0			0
$661$	−24.7123	−	20.7361i	−0.961197	−	0.806540i	0.0199502	−	0.999801i	$-0.493649\pi$
$661$	−24.7123	−	20.7361i	−0.961197	−	0.806540i	−0.981147	+	0.193261i	$0.938094\pi$
$662$		0			0
$663$	−6.80159	−	12.1501i	−0.264152	−	0.471869i
$664$		0			0
$665$	4.47546	−	7.75173i	0.173551	−	0.300599i
$666$		0			0
$667$	4.35940	+	7.55070i	0.168797	+	0.292364i
$668$		0			0
$669$	−38.0109	+	13.2666i	−1.46959	+	0.512916i
$670$		0			0
$671$	−3.94243	+	22.3586i	−0.152196	+	0.863145i
$672$		0			0
$673$	16.1895	−	13.5846i	0.624061	−	0.523649i	−0.275016	−	0.961440i	$-0.588683\pi$
$673$	16.1895	−	13.5846i	0.624061	−	0.523649i	0.899077	+	0.437790i	$0.144239\pi$
$674$		0			0
$675$	8.10623	+	3.32128i	0.312009	+	0.127836i
$676$		0			0
$677$	−39.0139	+	32.7366i	−1.49943	+	1.25817i	−0.617696	+	0.786417i	$0.711934\pi$
$677$	−39.0139	+	32.7366i	−1.49943	+	1.25817i	−0.881731	+	0.471752i	$0.843622\pi$
$678$		0			0
$679$	2.78807	−	15.8119i	0.106996	−	0.606807i
$680$		0			0
$681$	−2.17986	+	11.4708i	−0.0835324	+	0.439561i
$682$		0			0
$683$	−4.73422	−	8.19991i	−0.181150	−	0.313761i	0.761123	−	0.648608i	$-0.224649\pi$
$683$	−4.73422	−	8.19991i	−0.181150	−	0.313761i	−0.942272	+	0.334847i	$0.891315\pi$
$684$		0			0
$685$	−0.966365	+	1.67379i	−0.0369229	+	0.0639523i
$686$		0			0
$687$	−6.79570	+	11.4180i	−0.259272	+	0.435625i
$688$		0			0
$689$	−5.93701	−	4.98174i	−0.226182	−	0.189789i
$690$		0			0
$691$	−15.4877	−	5.63705i	−0.589179	−	0.214444i	0.0301894	−	0.999544i	$-0.490389\pi$
$691$	−15.4877	−	5.63705i	−0.589179	−	0.214444i	−0.619368	+	0.785101i	$0.712611\pi$
$692$		0			0
$693$	−1.32762	−	8.90447i	−0.0504321	−	0.338253i
$694$		0			0
$695$	0.0326149	+	0.184968i	0.00123715	+	0.00701625i
$696$		0			0
$697$	43.9380	−	15.9921i	1.66427	−	0.605745i
$698$		0			0
$699$	17.8017	+	6.74800i	0.673323	+	0.255233i
$700$		0			0
$701$	23.6066			0.891607			0.445804	−	0.895131i	$-0.352918\pi$
$701$	23.6066			0.891607			0.445804	+	0.895131i	$0.352918\pi$
$702$		0			0
$703$	−24.3144			−0.917033
$704$		0			0
$705$	13.2931	−	10.8571i	0.500648	−	0.408901i
$706$		0			0
$707$	0.709650	−	0.258291i	0.0266891	−	0.00971404i
$708$		0			0
$709$	0.0376114	+	0.213305i	0.00141253	+	0.00801083i	0.985506	−	0.169641i	$-0.0542609\pi$
$709$	0.0376114	+	0.213305i	0.00141253	+	0.00801083i	−0.984093	+	0.177652i	$0.943150\pi$
$710$		0			0
$711$	12.5031	−	20.3873i	0.468903	−	0.764583i
$712$		0			0
$713$	69.7663	+	25.3929i	2.61277	+	0.950970i
$714$		0			0
$715$	−8.72159	−	7.31829i	−0.326169	−	0.273688i
$716$		0			0
$717$	−37.0064	−	0.490871i	−1.38203	−	0.0183319i
$718$		0			0
$719$	5.99911	−	10.3908i	0.223729	−	0.387510i	−0.732208	−	0.681081i	$-0.761510\pi$
$719$	5.99911	−	10.3908i	0.223729	−	0.387510i	0.955937	+	0.293571i	$0.0948435\pi$
$720$		0			0
$721$	−1.05089	−	1.82020i	−0.0391374	−	0.0677879i
$722$		0			0
$723$	36.6937	+	31.6285i	1.36465	+	1.17627i
$724$		0			0
$725$	−0.304941	+	1.72941i	−0.0113252	+	0.0642286i
$726$		0			0
$727$	−10.3729	+	8.70393i	−0.384711	+	0.322811i	−0.814548	−	0.580095i	$-0.803015\pi$
$727$	−10.3729	+	8.70393i	−0.384711	+	0.322811i	0.429838	+	0.902906i	$0.358571\pi$
$728$		0			0
$729$	−15.3162	+	22.2355i	−0.567265	+	0.823535i
$730$		0			0
$731$	18.0069	−	15.1096i	0.666008	−	0.558847i
$732$		0			0
$733$	−1.82017	+	10.3227i	−0.0672296	+	0.381278i	0.932565	+	0.361003i	$0.117565\pi$
$733$	−1.82017	+	10.3227i	−0.0672296	+	0.381278i	−0.999794	+	0.0202755i	$0.993546\pi$
$734$		0			0
$735$	−16.9501	−	14.6102i	−0.625212	−	0.538906i
$736$		0			0
$737$	−15.6716	−	27.1439i	−0.577269	−	0.999859i
$738$		0			0
$739$	−19.2321	+	33.3110i	−0.707465	+	1.22537i	0.258329	+	0.966057i	$0.416828\pi$
$739$	−19.2321	+	33.3110i	−0.707465	+	1.22537i	−0.965794	+	0.259309i	$0.916505\pi$
$740$		0			0
$741$	8.79651	+	0.116681i	0.323148	+	0.00428639i
$742$		0			0
$743$	6.10477	+	5.12251i	0.223962	+	0.187927i	0.747864	−	0.663852i	$-0.231080\pi$
$743$	6.10477	+	5.12251i	0.223962	+	0.187927i	−0.523901	+	0.851779i	$0.675524\pi$
$744$		0			0
$745$	−18.5906	−	6.76643i	−0.681108	−	0.247903i
$746$		0			0
$747$	19.0915	−	31.1301i	0.698520	−	1.13899i
$748$		0			0
$749$	0.102366	+	0.580548i	0.00374038	+	0.0212127i
$750$		0			0
$751$	33.2299	−	12.0947i	1.21258	−	0.441341i	0.344979	−	0.938610i	$-0.387886\pi$
$751$	33.2299	−	12.0947i	1.21258	−	0.441341i	0.867596	+	0.497269i	$0.165664\pi$
$752$		0			0
$753$	29.9908	−	24.4948i	1.09292	−	0.892640i
$754$		0			0
$755$	−40.0013			−1.45580
$756$		0			0
$757$	−2.27205			−0.0825791			−0.0412895	−	0.999147i	$-0.513147\pi$
$757$	−2.27205			−0.0825791			−0.0412895	+	0.999147i	$0.513147\pi$
$758$		0			0
$759$	28.7428	+	10.8954i	1.04330	+	0.395478i
$760$		0			0
$761$	18.7690	−	6.83137i	0.680377	−	0.247637i	0.0213676	−	0.999772i	$-0.493198\pi$
$761$	18.7690	−	6.83137i	0.680377	−	0.247637i	0.659009	+	0.752135i	$0.270976\pi$
$762$		0			0
$763$	4.22888	+	23.9831i	0.153096	+	0.868248i
$764$		0			0
$765$	4.42814	+	29.7000i	0.160100	+	1.07380i
$766$		0			0
$767$	−10.4746	−	3.81245i	−0.378217	−	0.137660i
$768$		0			0
$769$	24.6676	+	20.6986i	0.889537	+	0.746410i	0.968117	−	0.250498i	$-0.0805943\pi$
$769$	24.6676	+	20.6986i	0.889537	+	0.746410i	−0.0785806	+	0.996908i	$0.525039\pi$
$770$		0			0
$771$	−15.8566	+	26.6420i	−0.571062	+	0.959490i
$772$		0			0
$773$	5.04006	−	8.72964i	0.181278	−	0.313983i	−0.761038	−	0.648708i	$-0.775310\pi$
$773$	5.04006	−	8.72964i	0.181278	−	0.313983i	0.942316	+	0.334724i	$0.108643\pi$
$774$		0			0
$775$	7.47686	+	12.9503i	0.268577	+	0.465189i
$776$		0			0
$777$	4.55024	−	23.9441i	0.163239	−	0.858989i
$778$		0			0
$779$	−5.12981	+	29.0926i	−0.183794	+	1.04235i
$780$		0			0
$781$	−8.71631	+	7.31385i	−0.311894	+	0.261710i
$782$		0			0
$783$	−5.00837	−	2.05203i	−0.178984	−	0.0733334i
$784$		0			0
$785$	−0.498133	+	0.417983i	−0.0177791	+	0.0149185i
$786$		0			0
$787$	−0.0850424	+	0.482300i	−0.00303144	+	0.0171921i	−0.986286	−	0.165045i	$-0.947223\pi$
$787$	−0.0850424	+	0.482300i	−0.00303144	+	0.0171921i	0.983255	+	0.182238i	$0.0583340\pi$
$788$		0			0
$789$	−43.2229	+	15.0857i	−1.53877	+	0.537064i
$790$		0			0
$791$	−7.65783	−	13.2637i	−0.272281	−	0.471605i
$792$		0			0
$793$	11.1191	−	19.2588i	0.394851	−	0.683901i
$794$		0			0
$795$	8.16411	+	14.5840i	0.289551	+	0.517241i
$796$		0			0
$797$	−33.1609	−	27.8253i	−1.17462	−	0.985623i	−1.00000		0.000987700i	$-0.999686\pi$
$797$	−33.1609	−	27.8253i	−1.17462	−	0.985623i	−0.174621	−	0.984636i	$-0.555870\pi$
$798$		0			0
$799$	13.9405	+	5.07391i	0.493178	+	0.179502i
$800$		0			0
$801$	32.3672	+	28.6562i	1.14364	+	1.01252i
$802$		0			0
$803$	3.86638	+	21.9273i	0.136442	+	0.773799i
$804$		0			0
$805$	−28.7868	+	10.4776i	−1.01460	+	0.369285i
$806$		0			0
$807$	1.19611	+	7.35242i	0.0421049	+	0.258817i
$808$		0			0
$809$	−1.01221			−0.0355874			−0.0177937	−	0.999842i	$-0.505664\pi$
$809$	−1.01221			−0.0355874			−0.0177937	+	0.999842i	$0.505664\pi$
$810$		0			0
$811$	−50.1980			−1.76269			−0.881346	−	0.472472i	$-0.843362\pi$
$811$	−50.1980			−1.76269			−0.881346	+	0.472472i	$0.843362\pi$
$812$		0			0
$813$	0.828493	+	5.09272i	0.0290565	+	0.178609i
$814$		0			0
$815$	5.05425	−	1.83960i	0.177043	−	0.0644383i
$816$		0			0
$817$	2.57888	+	14.6255i	0.0902235	+	0.511683i
$818$		0			0
$819$	−1.76110	+	8.64072i	−0.0615379	+	0.301931i
$820$		0			0
$821$	−9.40675	−	3.42378i	−0.328298	−	0.119491i	0.172613	−	0.984990i	$-0.444779\pi$
$821$	−9.40675	−	3.42378i	−0.328298	−	0.119491i	−0.500910	+	0.865499i	$0.667001\pi$
$822$		0			0
$823$	27.5812	+	23.1434i	0.961421	+	0.806728i	0.981184	−	0.193077i	$-0.0618467\pi$
$823$	27.5812	+	23.1434i	0.961421	+	0.806728i	−0.0197629	+	0.999805i	$0.506291\pi$
$824$		0			0
$825$	3.02420	+	5.40230i	0.105289	+	0.188084i
$826$		0			0
$827$	27.1307	−	46.9918i	0.943428	−	1.63407i	0.184561	−	0.982821i	$-0.440914\pi$
$827$	27.1307	−	46.9918i	0.943428	−	1.63407i	0.758868	−	0.651245i	$-0.225753\pi$
$828$		0			0
$829$	1.48912	+	2.57923i	0.0517192	+	0.0895803i	0.890726	−	0.454541i	$-0.150197\pi$
$829$	1.48912	+	2.57923i	0.0517192	+	0.0895803i	−0.839007	+	0.544121i	$0.816863\pi$
$830$		0			0
$831$	10.2087	−	3.56306i	0.354137	−	0.123601i
$832$		0			0
$833$	3.35872	−	19.0483i	0.116373	−	0.659983i
$834$		0			0
$835$	5.59745	−	4.69681i	0.193708	−	0.162540i
$836$		0			0
$837$	−43.9022	+	14.0280i	−1.51748	+	0.484878i
$838$		0			0
$839$	−23.2584	+	19.5161i	−0.802967	+	0.673770i	−0.948918	−	0.315522i	$-0.897820\pi$
$839$	−23.2584	+	19.5161i	−0.802967	+	0.673770i	0.145951	+	0.989292i	$0.453376\pi$
$840$		0			0
$841$	−4.84739	+	27.4909i	−0.167151	+	0.947963i
$842$		0			0
$843$	0.770732	−	4.05572i	0.0265454	−	0.139686i
$844$		0			0
$845$	−11.2312	−	19.4530i	−0.386365	−	0.669204i
$846$		0			0
$847$	−4.60344	+	7.97339i	−0.158176	+	0.273969i
$848$		0			0
$849$	−0.0105262	+	0.0176860i	−0.000361260	+	0.000606983i
$850$		0			0
$851$	63.7466	+	53.4898i	2.18521	+	1.83361i
$852$		0			0
$853$	−15.5715	−	5.66757i	−0.533159	−	0.194054i	0.0613893	−	0.998114i	$-0.480447\pi$
$853$	−15.5715	−	5.66757i	−0.533159	−	0.194054i	−0.594548	+	0.804060i	$0.702669\pi$
$854$		0			0
$855$	−17.6492	−	6.95928i	−0.603589	−	0.238002i
$856$		0			0
$857$	0.658235	+	3.73303i	0.0224849	+	0.127518i	0.993984	−	0.109525i	$-0.0349329\pi$
$857$	0.658235	+	3.73303i	0.0224849	+	0.127518i	−0.971499	+	0.237043i	$0.923822\pi$
$858$		0			0
$859$	−6.87400	+	2.50193i	−0.234538	+	0.0853647i	−0.456615	−	0.889664i	$-0.650938\pi$
$859$	−6.87400	+	2.50193i	−0.234538	+	0.0853647i	0.222078	+	0.975029i	$0.428716\pi$
$860$		0			0
$861$	−27.6895	−	10.4961i	−0.943657	−	0.357707i
$862$		0			0
$863$	−49.3163			−1.67875			−0.839373	−	0.543557i	$-0.817077\pi$
$863$	−49.3163			−1.67875			−0.839373	+	0.543557i	$0.817077\pi$
$864$		0			0
$865$	−14.5101			−0.493360
$866$		0			0
$867$	2.70307	−	2.20772i	0.0918012	−	0.0749781i
$868$		0			0
$869$	15.8829	−	5.78089i	0.538789	−	0.196103i
$870$		0			0
$871$	5.33111	+	30.2343i	0.180638	+	1.02445i
$872$		0			0
$873$	−34.0188	−	0.902643i	−1.15136	−	0.0305498i
$874$		0			0
$875$	11.3976	+	4.14839i	0.385309	+	0.140241i
$876$		0			0
$877$	30.8256	+	25.8658i	1.04091	+	0.873425i	0.992108	−	0.125384i	$-0.0400161\pi$
$877$	30.8256	+	25.8658i	1.04091	+	0.873425i	0.0487991	+	0.998809i	$0.484461\pi$
$878$		0			0
$879$	9.02989	+	0.119777i	0.304571	+	0.00403997i
$880$		0			0
$881$	−4.03667	+	6.99172i	−0.135999	+	0.235557i	−0.925979	−	0.377576i	$-0.876758\pi$
$881$	−4.03667	+	6.99172i	−0.135999	+	0.235557i	0.789980	+	0.613133i	$0.210091\pi$
$882$		0			0
$883$	9.05527	+	15.6842i	0.304734	+	0.527815i	0.977202	−	0.212311i	$-0.0680991\pi$
$883$	9.05527	+	15.6842i	0.304734	+	0.527815i	−0.672468	+	0.740126i	$0.734766\pi$
$884$		0			0
$885$	18.2081	+	15.6946i	0.612059	+	0.527569i
$886$		0			0
$887$	3.38170	−	19.1786i	0.113546	−	0.643954i	−0.873913	−	0.486082i	$-0.838426\pi$
$887$	3.38170	−	19.1786i	0.113546	−	0.643954i	0.987460	−	0.157872i	$-0.0504633\pi$
$888$		0			0
$889$	−0.0916388	+	0.0768940i	−0.00307347	+	0.00257894i
$890$		0			0
$891$	−18.2519	+	5.56631i	−0.611463	+	0.186478i
$892$		0			0
$893$	−7.17995	+	6.02469i	−0.240268	+	0.201609i
$894$		0			0
$895$	0.235107	−	1.33336i	0.00785877	−	0.0445693i
$896$		0			0
$897$	−22.8057	−	19.6576i	−0.761461	−	0.656348i
$898$		0			0
$899$	−4.61952	−	8.00124i	−0.154069	−	0.266856i
$900$		0			0
$901$	−7.22318	+	12.5109i	−0.240639	+	0.416799i
$902$		0			0
$903$	−14.8854	−	0.197448i	−0.495356	−	0.00657064i
$904$		0			0
$905$	9.69474	+	8.13485i	0.322264	+	0.270412i
$906$		0			0
$907$	−3.68496	−	1.34122i	−0.122357	−	0.0445344i	0.280116	−	0.959966i	$-0.409627\pi$
$907$	−3.68496	−	1.34122i	−0.122357	−	0.0445344i	−0.402473	+	0.915432i	$0.631849\pi$
$908$		0			0
$909$	−0.763275	−	1.40694i	−0.0253162	−	0.0466654i
$910$		0			0
$911$	−3.15327	−	17.8831i	−0.104473	−	0.592493i	−0.991430	−	0.130642i	$-0.958296\pi$
$911$	−3.15327	−	17.8831i	−0.104473	−	0.592493i	0.886957	−	0.461852i	$-0.152815\pi$
$912$		0			0
$913$	24.2522	−	8.82706i	0.802629	−	0.292133i
$914$		0			0
$915$	−37.1432	+	30.3365i	−1.22792	+	1.00289i
$916$		0			0
$917$	−1.43526			−0.0473964
$918$		0			0
$919$	5.65763			0.186628			0.0933140	−	0.995637i	$-0.470254\pi$
$919$	5.65763			0.186628			0.0933140	+	0.995637i	$0.470254\pi$
$920$		0			0
$921$	−32.8585	−	12.4555i	−1.08272	−	0.410422i
$922$		0			0
$923$	10.4730	−	3.81185i	0.344722	−	0.125469i
$924$		0			0
$925$	2.91047	+	16.5061i	0.0956956	+	0.542717i
$926$		0			0
$927$	−3.48732	+	2.77196i	−0.114539	+	0.0910431i
$928$		0			0
$929$	−16.1286	−	5.87034i	−0.529163	−	0.192600i	0.0636016	−	0.997975i	$-0.479741\pi$
$929$	−16.1286	−	5.87034i	−0.529163	−	0.192600i	−0.592765	+	0.805376i	$0.701964\pi$
$930$		0			0
$931$	9.36125	+	7.85502i	0.306802	+	0.257438i
$932$		0			0
$933$	−9.40221	+	15.7974i	−0.307814	+	0.517185i
$934$		0			0
$935$	−10.6110	+	18.3788i	−0.347017	+	0.601051i
$936$		0			0
$937$	−9.09417	−	15.7516i	−0.297094	−	0.514581i	0.678376	−	0.734715i	$-0.262684\pi$
$937$	−9.09417	−	15.7516i	−0.297094	−	0.514581i	−0.975470	+	0.220134i	$0.929351\pi$
$938$		0			0
$939$	2.02439	−	10.6527i	0.0660636	−	0.347637i
$940$		0			0
$941$	−4.33218	+	24.5690i	−0.141225	+	0.800928i	0.829096	+	0.559107i	$0.188856\pi$
$941$	−4.33218	+	24.5690i	−0.141225	+	0.800928i	−0.970321	+	0.241821i	$0.922255\pi$
$942$		0			0
$943$	77.4507	−	64.9888i	2.52214	−	2.11633i
$944$		0			0
$945$	10.1562	−	16.0780i	0.330381	−	0.523018i
$946$		0			0
$947$	32.2233	−	27.0386i	1.04712	−	0.878636i	0.0543305	−	0.998523i	$-0.482698\pi$
$947$	32.2233	−	27.0386i	1.04712	−	0.878636i	0.992788	+	0.119887i	$0.0382531\pi$
$948$		0			0
$949$	3.78713	−	21.4779i	0.122935	−	0.697202i
$950$		0			0
$951$	−28.4793	+	9.93987i	−0.923505	+	0.322322i
$952$		0			0
$953$	−9.09208	−	15.7479i	−0.294521	−	0.510126i	0.680352	−	0.732885i	$-0.261827\pi$
$953$	−9.09208	−	15.7479i	−0.294521	−	0.510126i	−0.974873	+	0.222759i	$0.928494\pi$
$954$		0			0
$955$	−18.2976	+	31.6923i	−0.592095	+	1.02554i
$956$		0			0
$957$	−1.86848	−	3.33777i	−0.0603993	−	0.107895i
$958$		0			0
$959$	0.810453	+	0.680051i	0.0261709	+	0.0219600i
$960$		0			0
$961$	−44.7986	−	16.3054i	−1.44512	−	0.525980i
$962$		0			0
$963$	1.18504	−	0.396050i	0.0381873	−	0.0127625i
$964$		0			0
$965$	5.18372	+	29.3983i	0.166870	+	0.946365i
$966$		0			0
$967$	17.8221	−	6.48673i	0.573121	−	0.208599i	−0.0391685	−	0.999233i	$-0.512471\pi$
$967$	17.8221	−	6.48673i	0.573121	−	0.208599i	0.612290	+	0.790634i	$0.290249\pi$
$968$		0			0
$969$	−2.63306	−	16.1853i	−0.0845861	−	0.519948i
$970$		0			0
$971$	51.8323			1.66338			0.831688	−	0.555243i	$-0.187375\pi$
$971$	51.8323			1.66338			0.831688	+	0.555243i	$0.187375\pi$
$972$		0			0
$973$	0.102813			0.00329604
$974$		0			0
$975$	−0.973747	−	5.98558i	−0.0311849	−	0.191692i
$976$		0			0
$977$	28.8109	−	10.4863i	0.921744	−	0.335487i	0.162812	−	0.986657i	$-0.447944\pi$
$977$	28.8109	−	10.4863i	0.921744	−	0.335487i	0.758932	+	0.651170i	$0.225721\pi$
$978$		0			0
$979$	5.30530	+	30.0878i	0.169558	+	0.961611i
$980$		0			0
$981$	48.9553	−	16.3613i	1.56302	−	0.522376i
$982$		0			0
$983$	39.3321	+	14.3157i	1.25450	+	0.456600i	0.881919	−	0.471401i	$-0.156251\pi$
$983$	39.3321	+	14.3157i	1.25450	+	0.456600i	0.372579	+	0.928001i	$0.378474\pi$
$984$		0			0
$985$	34.0035	+	28.5323i	1.08344	+	0.909115i
$986$		0			0
$987$	−4.58928	−	8.19808i	−0.146078	−	0.260948i
$988$		0			0
$989$	25.4139	−	44.0181i	0.808114	−	1.39969i
$990$		0			0
$991$	0.830287	+	1.43810i	0.0263749	+	0.0456827i	0.878912	−	0.476985i	$-0.158270\pi$
$991$	0.830287	+	1.43810i	0.0263749	+	0.0456827i	−0.852537	+	0.522667i	$0.824937\pi$
$992$		0			0
$993$	33.4758	−	11.6837i	1.06232	−	0.370772i
$994$		0			0
$995$	6.36893	−	36.1200i	0.201909	−	1.14508i
$996$		0			0
$997$	29.0498	−	24.3756i	0.920015	−	0.771984i	−0.0539828	−	0.998542i	$-0.517192\pi$
$997$	29.0498	−	24.3756i	0.920015	−	0.771984i	0.973998	+	0.226558i	$0.0727472\pi$
$998$		0			0
$999$	−51.6174	−	2.05500i	−1.63310	−	0.0650173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.a.49.2	✓	24
3.2	odd	2		648.2.q.a.361.1		24
4.3	odd	2		432.2.u.e.49.3		24
27.4	even	9		5832.2.a.h.1.3		12
27.11	odd	18		648.2.q.a.289.1		24
27.16	even	9	inner	216.2.q.a.97.2	yes	24
27.23	odd	18		5832.2.a.i.1.10		12
108.43	odd	18		432.2.u.e.97.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.a.49.2	✓	24	1.1	even	1	trivial
216.2.q.a.97.2	yes	24	27.16	even	9	inner
432.2.u.e.49.3		24	4.3	odd	2
432.2.u.e.97.3		24	108.43	odd	18
648.2.q.a.289.1		24	27.11	odd	18
648.2.q.a.361.1		24	3.2	odd	2
5832.2.a.h.1.3		12	27.4	even	9
5832.2.a.i.1.10		12	27.23	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.278117 - 1.70958i) q^{3} +(2.42978 - 0.884366i) q^{5} +(-0.245784 - 1.39391i) q^{7} +(-2.84530 + 0.950925i) q^{9} +O(q^{10})\)	\(q+(-0.278117 - 1.70958i) q^{3} +(2.42978 - 0.884366i) q^{5} +(-0.245784 - 1.39391i) q^{7} +(-2.84530 + 0.950925i) q^{9} +(-1.99234 - 0.725153i) q^{11} +(1.59088 + 1.33491i) q^{13} +(-2.18765 - 3.90793i) q^{15} +(1.93552 - 3.35242i) q^{17} +(1.22285 + 2.11804i) q^{19} +(-2.31464 + 0.807856i) q^{21} +(1.45350 - 8.24321i) q^{23} +(1.29148 - 1.08368i) q^{25} +(2.41701 + 4.59979i) q^{27} +(-0.797932 + 0.669544i) q^{29} +(-1.54023 + 8.73507i) q^{31} +(-0.685600 + 3.60774i) q^{33} +(-1.82993 - 3.16952i) q^{35} +(-4.97082 + 8.60972i) q^{37} +(1.83967 - 3.09099i) q^{39} +(9.25295 + 7.76415i) q^{41} +(5.70613 + 2.07686i) q^{43} +(-6.07248 + 4.82682i) q^{45} +(0.665477 + 3.77411i) q^{47} +(4.69528 - 1.70894i) q^{49} +(-6.26953 - 2.37656i) q^{51} -3.73190 q^{53} -5.48224 q^{55} +(3.28086 - 2.67963i) q^{57} +(-5.04377 + 1.83578i) q^{59} +(-1.85946 - 10.5455i) q^{61} +(2.02483 + 3.73237i) q^{63} +(5.04603 + 1.83660i) q^{65} +(11.3245 + 9.50236i) q^{67} +(-14.4966 - 0.192291i) q^{69} +(2.68331 - 4.64763i) q^{71} +(-5.25081 - 9.09467i) q^{73} +(-2.21182 - 1.90650i) q^{75} +(-0.521112 + 2.95537i) q^{77} +(-6.10688 + 5.12428i) q^{79} +(7.19148 - 5.41134i) q^{81} +(-9.32482 + 7.82445i) q^{83} +(1.73812 - 9.85735i) q^{85} +(1.36656 + 1.17791i) q^{87} +(-7.20496 - 12.4794i) q^{89} +(1.46973 - 2.54564i) q^{91} +(15.3616 + 0.203764i) q^{93} +(4.84439 + 4.06492i) q^{95} +(10.6595 + 3.87974i) q^{97} +(6.35838 + 0.168711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) \) 24 * q - 3 * q^7 + 6 * q^9	\( 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) \) 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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