LMFDB - Embedded newform 432.2.u.e.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	432.49
Dual form			432.2.u.e.97.3

$q$-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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

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	$0.0306380\pi$
$7$	0.245784	+	1.39391i	0.0928975	+	0.526848i	−0.902474	+	0.430745i	$0.858251\pi$
$8$		0			0
$9$	−2.84530	+	0.950925i	−0.948434	+	0.316975i
$10$		0			0
$11$	1.99234	+	0.725153i	0.600714	+	0.218642i	0.624435	−	0.781077i	$-0.285329\pi$
$11$	1.99234	+	0.725153i	0.600714	+	0.218642i	−0.0237215	+	0.999719i	$0.507551\pi$
$12$		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	0.690976	−	0.722877i	$-0.257181\pi$
$19$	−1.22285	−	2.11804i	−0.280542	−	0.485913i	−0.971518	+	0.236964i	$0.923847\pi$
$20$		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	$0.393170\pi$
$23$	−1.45350	+	8.24321i	−0.303076	+	1.71883i	−0.632426	+	0.774621i	$0.717941\pi$
$24$		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	$-0.651109\pi$
$31$	1.54023	−	8.73507i	0.276633	−	1.56886i	0.733726	−	0.679446i	$-0.237780\pi$
$32$		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	−0.131938	−	0.991258i	$-0.542120\pi$
$43$	−5.70613	−	2.07686i	−0.870176	−	0.316718i	−0.738239	+	0.674540i	$0.764342\pi$
$44$		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	$-0.965386\pi$
$47$	−0.665477	−	3.77411i	−0.0970698	−	0.550510i	0.897024	−	0.441983i	$-0.145725\pi$
$48$		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	0.00785651	−	0.999969i	$-0.497499\pi$
$59$	5.04377	−	1.83578i	0.656643	−	0.238998i	0.648786	+	0.760971i	$0.275277\pi$
$60$		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	$-0.919124\pi$
$67$	−11.3245	−	9.50236i	−1.38350	−	1.16090i	−0.415610	−	0.909543i	$-0.636432\pi$
$68$		0			0
$69$	−14.4966	−	0.192291i	−1.74519	−	0.0231491i
$70$		0			0
$71$	−2.68331	+	4.64763i	−0.318450	+	0.551572i	−0.980165	−	0.198184i	$-0.936496\pi$
$71$	−2.68331	+	4.64763i	−0.318450	+	0.551572i	0.661715	+	0.749756i	$0.269829\pi$
$72$		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	−0.230988	−	0.972957i	$-0.574196\pi$
$79$	6.10688	−	5.12428i	0.687077	−	0.576526i	0.918065	+	0.396431i	$0.129751\pi$
$80$		0			0
$81$	7.19148	−	5.41134i	0.799054	−	0.601260i
$82$		0			0
$83$	9.32482	−	7.82445i	1.02353	−	0.858845i	0.0334649	−	0.999440i	$-0.489346\pi$
$83$	9.32482	−	7.82445i	1.02353	−	0.858845i	0.990067	+	0.140594i	$0.0449014\pi$
$84$		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	−0.409849	−	0.912153i	$-0.634419\pi$
$103$	−1.39538	+	0.507876i	−0.137491	+	0.0500425i	0.272358	+	0.962196i	$0.412196\pi$
$104$		0			0
$105$	−4.90961	+	4.00990i	−0.479129	+	0.391326i
$106$		0			0
$107$	0.416489			0.0402635			0.0201317	−	0.999797i	$-0.493591\pi$
$107$	0.416489			0.0402635			0.0201317	+	0.999797i	$0.493591\pi$
$108$		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	0.867894	−	0.496749i	$-0.165473\pi$
$127$	0.0422583	+	0.0731936i	0.00374982	+	0.00649488i	−0.864144	+	0.503244i	$0.832140\pi$
$128$		0			0
$129$	1.96358	−	10.3327i	0.172884	−	0.909741i
$130$		0			0
$131$	−0.176083	+	0.998617i	−0.0153845	+	0.0872496i	−0.991533	−	0.129853i	$-0.958549\pi$
$131$	−0.176083	+	0.998617i	−0.0153845	+	0.0872496i	0.976149	+	0.217102i	$0.0696606\pi$
$132$		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	−0.984268	−	0.176681i	$-0.943464\pi$
$139$	0.0126135	−	0.0715348i	0.00106986	−	0.00606750i	0.985338	+	0.170614i	$0.0545750\pi$
$140$		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	0.857267	−	0.514872i	$-0.172161\pi$
$151$	14.5372	+	5.29110i	1.18302	+	0.430583i	0.325751	+	0.945456i	$0.394383\pi$
$152$		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	$-0.525960\pi$
$163$	−2.08013			−0.162929			−0.0814643	+	0.996676i	$0.525960\pi$
$164$		0			0
$165$	1.52471	+	9.37231i	0.118698	+	0.729633i
$166$		0			0
$167$	−2.65547	+	0.966512i	−0.205486	+	0.0747910i	−0.442713	−	0.896663i	$-0.645984\pi$
$167$	−2.65547	+	0.966512i	−0.205486	+	0.0747910i	0.237226	+	0.971454i	$0.423762\pi$
$168$		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	−0.875644	−	0.482957i	$-0.839563\pi$
$179$	−0.261810	+	0.453468i	−0.0195686	+	0.0338938i	0.856075	+	0.516851i	$0.172896\pi$
$180$		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	−0.159895	−	0.987134i	$-0.551116\pi$
$191$	10.8417	−	9.09725i	0.784477	−	0.658254i	0.944372	+	0.328880i	$0.106671\pi$
$192$		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	$0.334348\pi$
$199$	−7.09229	+	12.2842i	−0.502759	+	0.870804i	−0.999995	+	0.00318864i	$0.998985\pi$
$200$		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	−0.282992	−	0.959122i	$-0.591327\pi$
$211$	1.69567	−	0.617173i	0.116735	−	0.0424880i	0.399727	+	0.916634i	$0.369105\pi$
$212$		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	$0.228343\pi$
$223$	4.03626	+	22.8907i	0.270288	+	1.53288i	−0.483256	+	0.875479i	$0.660546\pi$
$224$		0			0
$225$	−2.64416	+	4.31151i	−0.176277	+	0.287434i
$226$		0			0
$227$	6.33464	+	2.30562i	0.420445	+	0.153029i	0.543574	−	0.839361i	$-0.317071\pi$
$227$	6.33464	+	2.30562i	0.420445	+	0.153029i	−0.123129	+	0.992391i	$0.539293\pi$
$228$		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	$0.298418\pi$
$239$	−3.71043	+	21.0429i	−0.240008	+	1.36115i	−0.831806	+	0.555066i	$0.812693\pi$
$240$		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	$-0.917360\pi$
$251$	−11.1783	−	19.3613i	−0.705565	−	1.22207i	0.260922	−	0.965360i	$-0.415973\pi$
$252$		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	$0.247654\pi$
$263$	4.58969	+	26.0294i	0.283013	+	1.60504i	−0.429286	+	0.903168i	$0.641235\pi$
$264$		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	$-0.471160\pi$
$271$	2.97894			0.180957			0.0904787	+	0.995898i	$0.471160\pi$
$272$		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	0.643058	−	0.765817i	$-0.277665\pi$
$283$	0.00910269	+	0.00763807i	0.000541099	+	0.000454036i	−0.642517	+	0.766271i	$0.722110\pi$
$284$		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	$0.363204\pi$
$307$	−10.1440	+	17.5700i	−0.578951	+	1.00277i	−0.995600	+	0.0937049i	$0.970129\pi$
$308$		0			0
$309$	−1.25633	−	2.24426i	−0.0714702	−	0.127671i
$310$		0			0
$311$	8.13067	+	6.82244i	0.461048	+	0.386865i	0.843516	−	0.537103i	$-0.180481\pi$
$311$	8.13067	+	6.82244i	0.461048	+	0.386865i	−0.382468	+	0.923969i	$0.624926\pi$
$312$		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	$-0.865363\pi$
$331$	−3.55468	−	20.1596i	−0.195383	−	1.10807i	0.716489	−	0.697598i	$-0.245748\pi$
$332$		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	−0.979094	−	0.203409i	$-0.934798\pi$
$347$	0.196028	−	1.11173i	0.0105234	−	0.0596809i	0.989617	+	0.143728i	$0.0459090\pi$
$348$		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	0.598526	−	0.801103i	$-0.295753\pi$
$359$	−7.47495	−	12.9470i	−0.394513	−	0.683317i	−0.993039	+	0.117787i	$0.962420\pi$
$360$		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	−0.328712	−	0.944430i	$-0.606615\pi$
$367$	−22.7509	−	8.28066i	−1.18759	−	0.432247i	−0.858876	+	0.512183i	$0.828837\pi$
$368$		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	$-0.905235\pi$
$379$	−37.2231			−1.91202			−0.956010	+	0.293334i	$0.905235\pi$
$380$		0			0
$381$	−0.113377	+	0.0926002i	−0.00580849	+	0.00474405i
$382$		0			0
$383$	21.9881	−	8.00300i	1.12354	−	0.408934i	0.287595	−	0.957752i	$-0.407144\pi$
$383$	21.9881	−	8.00300i	1.12354	−	0.408934i	0.835942	+	0.548818i	$0.184922\pi$
$384$		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	0.423120	−	0.906074i	$-0.360935\pi$
$419$	−8.10008	−	6.79677i	−0.395715	−	0.332044i	−0.818835	+	0.574030i	$0.805379\pi$
$420$		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	$-0.516912\pi$
$431$	−2.20497			−0.106210			−0.0531048	+	0.998589i	$0.516912\pi$
$432$		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	$-0.979404\pi$
$439$	−1.72428	−	9.77890i	−0.0822955	−	0.466721i	0.915612	−	0.402063i	$-0.131707\pi$
$440$		0			0
$441$	−11.7344	+	9.32731i	−0.558781	+	0.444157i
$442$		0			0
$443$	6.82027	+	2.48238i	0.324041	+	0.117941i	0.498918	−	0.866649i	$-0.333731\pi$
$443$	6.82027	+	2.48238i	0.324041	+	0.117941i	−0.174877	+	0.984590i	$0.555953\pi$
$444$		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	$-0.784089\pi$
$463$	3.60742	−	20.4587i	0.167651	−	0.950795i	0.946289	−	0.323322i	$-0.104800\pi$
$464$		0			0
$465$	37.5055	−	13.0902i	1.73928	−	0.607043i
$466$		0			0
$467$	2.66334	+	4.61304i	0.123245	+	0.213466i	0.921045	−	0.389455i	$-0.127337\pi$
$467$	2.66334	+	4.61304i	0.123245	+	0.213466i	−0.797801	+	0.602921i	$0.794003\pi$
$468$		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	$0.00503403\pi$
$479$	1.43810	+	8.15589i	0.0657086	+	0.372652i	−0.934166	+	0.356838i	$0.883855\pi$
$480$		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	$-0.684494\pi$
$487$	−24.1730			−1.09539			−0.547693	+	0.836680i	$0.684494\pi$
$488$		0			0
$489$	−0.578521	−	3.55614i	−0.0261616	−	0.160814i
$490$		0			0
$491$	38.1657	−	13.8912i	1.72239	−	0.626900i	0.724350	−	0.689432i	$-0.242140\pi$
$491$	38.1657	−	13.8912i	1.72239	−	0.626900i	0.998043	+	0.0625322i	$0.0199176\pi$
$492$		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	0.0435134	−	0.999053i	$-0.486145\pi$
$499$	−20.8373	−	17.4846i	−0.932806	−	0.782717i	−0.976319	+	0.216336i	$0.930589\pi$
$500$		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	$-0.628791\pi$
$503$	13.4402	−	23.2791i	0.599270	−	1.03797i	0.992929	−	0.118709i	$-0.0378756\pi$
$504$		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	−0.771507	−	0.636221i	$-0.780497\pi$
$523$	3.77869	−	6.54488i	0.165231	−	0.286188i	0.936737	+	0.350034i	$0.113830\pi$
$524$		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	$0.0480830\pi$
$547$	2.59815	+	14.7349i	0.111089	+	0.630017i	−0.877524	+	0.479533i	$0.840806\pi$
$548$		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	$0.434592\pi$
$563$	−7.65262	+	43.4002i	−0.322520	+	1.82910i	−0.526561	+	0.850137i	$0.676519\pi$
$564$		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	$0.271168\pi$
$571$	−5.20125	+	29.4977i	−0.217665	+	1.23444i	−0.876221	+	0.481910i	$0.839943\pi$
$572$		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	$0.104921\pi$
$587$	4.06466	+	23.0518i	0.167766	+	0.951451i	−0.778400	+	0.627769i	$0.783968\pi$
$588$		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	0.0731340	−	0.997322i	$-0.476700\pi$
$599$	18.8508	−	6.86114i	0.770224	−	0.280339i	0.697090	+	0.716983i	$0.254478\pi$
$600$		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	0.984083	−	0.177710i	$-0.0568690\pi$
$607$	24.1436	+	20.2588i	0.979957	+	0.822281i	−0.00412615	+	0.999991i	$0.501313\pi$
$608$		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	−0.969451	−	0.245284i	$-0.921119\pi$
$619$	−22.2981	+	18.7103i	−0.896237	+	0.752032i	0.0732141	+	0.997316i	$0.476674\pi$
$620$		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	−0.937016	−	0.349286i	$-0.886424\pi$
$631$	−4.17030	+	7.22318i	−0.166017	+	0.287550i	0.770999	+	0.636837i	$0.219757\pi$
$632$		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	−0.190799	−	0.981629i	$-0.561108\pi$
$643$	7.45557	−	2.71361i	0.294019	−	0.107014i	0.484818	+	0.874615i	$0.338886\pi$
$644$		0			0
$645$	−4.36681	−	26.8426i	−0.171943	−	1.05693i
$646$		0			0
$647$	7.52146			0.295699			0.147849	−	0.989010i	$-0.452765\pi$
$647$	7.52146			0.295699			0.147849	+	0.989010i	$0.452765\pi$
$648$		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	0.859418	−	0.511273i	$-0.170826\pi$
$659$	30.5262	+	11.1106i	1.18913	+	0.432808i	0.329712	+	0.944081i	$0.393048\pi$
$660$		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	0.942272	−	0.334847i	$-0.108685\pi$
$683$	4.73422	+	8.19991i	0.181150	+	0.313761i	−0.761123	+	0.648608i	$0.775351\pi$
$684$		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	0.619368	−	0.785101i	$-0.287389\pi$
$691$	15.4877	+	5.63705i	0.589179	+	0.214444i	−0.0301894	+	0.999544i	$0.509611\pi$
$692$		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	−0.955937	−	0.293571i	$-0.905156\pi$
$719$	−5.99911	+	10.3908i	−0.223729	+	0.387510i	0.732208	+	0.681081i	$0.238490\pi$
$720$		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	−0.429838	−	0.902906i	$-0.641429\pi$
$727$	10.3729	−	8.70393i	0.384711	−	0.322811i	0.814548	+	0.580095i	$0.196985\pi$
$728$		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	$-0.583172\pi$
$739$	19.2321	−	33.3110i	0.707465	−	1.22537i	0.965794	−	0.259309i	$-0.0834948\pi$
$740$		0			0
$741$	8.79651	+	0.116681i	0.323148	+	0.00428639i
$742$		0			0
$743$	−6.10477	−	5.12251i	−0.223962	−	0.187927i	0.523901	−	0.851779i	$-0.324476\pi$
$743$	−6.10477	−	5.12251i	−0.223962	−	0.187927i	−0.747864	+	0.663852i	$0.768920\pi$
$744$		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	−0.867596	−	0.497269i	$-0.834336\pi$
$751$	−33.2299	+	12.0947i	−1.21258	+	0.441341i	−0.344979	+	0.938610i	$0.612114\pi$
$752$		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	−0.983255	−	0.182238i	$-0.941666\pi$
$787$	0.0850424	−	0.482300i	0.00303144	−	0.0171921i	0.986286	+	0.165045i	$0.0527771\pi$
$788$		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	$-0.156638\pi$
$811$	50.1980			1.76269			0.881346	+	0.472472i	$0.156638\pi$
$812$		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	0.0197629	−	0.999805i	$-0.493709\pi$
$823$	−27.5812	−	23.1434i	−0.961421	−	0.806728i	−0.981184	+	0.193077i	$0.938153\pi$
$824$		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	$0.559086\pi$
$827$	−27.1307	+	46.9918i	−0.943428	+	1.63407i	−0.758868	+	0.651245i	$0.774247\pi$
$828$		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	−0.145951	−	0.989292i	$-0.546624\pi$
$839$	23.2584	−	19.5161i	0.802967	−	0.673770i	0.948918	+	0.315522i	$0.102180\pi$
$840$		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	−0.222078	−	0.975029i	$-0.571284\pi$
$859$	6.87400	−	2.50193i	0.234538	−	0.0853647i	0.456615	+	0.889664i	$0.349062\pi$
$860$		0			0
$861$	−27.6895	−	10.4961i	−0.943657	−	0.357707i
$862$		0			0
$863$	49.3163			1.67875			0.839373	−	0.543557i	$-0.182923\pi$
$863$	49.3163			1.67875			0.839373	+	0.543557i	$0.182923\pi$
$864$		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	0.672468	−	0.740126i	$-0.265234\pi$
$883$	−9.05527	−	15.6842i	−0.304734	−	0.527815i	−0.977202	+	0.212311i	$0.931901\pi$
$884$		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	$0.161574\pi$
$887$	−3.38170	+	19.1786i	−0.113546	+	0.643954i	−0.987460	+	0.157872i	$0.949537\pi$
$888$		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	0.402473	−	0.915432i	$-0.368151\pi$
$907$	3.68496	+	1.34122i	0.122357	+	0.0445344i	−0.280116	+	0.959966i	$0.590373\pi$
$908$		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	$0.0417037\pi$
$911$	3.15327	+	17.8831i	0.104473	+	0.592493i	−0.886957	+	0.461852i	$0.847185\pi$
$912$		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	$-0.529746\pi$
$919$	−5.65763			−0.186628			−0.0933140	+	0.995637i	$0.529746\pi$
$920$		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	−0.992788	−	0.119887i	$-0.961747\pi$
$947$	−32.2233	+	27.0386i	−1.04712	+	0.878636i	−0.0543305	+	0.998523i	$0.517302\pi$
$948$		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	−0.612290	−	0.790634i	$-0.709751\pi$
$967$	−17.8221	+	6.48673i	−0.573121	+	0.208599i	0.0391685	+	0.999233i	$0.487529\pi$
$968$		0			0
$969$	−2.63306	−	16.1853i	−0.0845861	−	0.519948i
$970$		0			0
$971$	−51.8323			−1.66338			−0.831688	−	0.555243i	$-0.812625\pi$
$971$	−51.8323			−1.66338			−0.831688	+	0.555243i	$0.812625\pi$
$972$		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	−0.372579	−	0.928001i	$-0.621526\pi$
$983$	−39.3321	−	14.3157i	−1.25450	−	0.456600i	−0.881919	+	0.471401i	$0.843749\pi$
$984$		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	0.852537	−	0.522667i	$-0.175063\pi$
$991$	−0.830287	−	1.43810i	−0.0263749	−	0.0456827i	−0.878912	+	0.476985i	$0.841730\pi$
$992$		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	432.2.u.e.49.3		24
4.3	odd	2		216.2.q.a.49.2	✓	24
12.11	even	2		648.2.q.a.361.1		24
27.16	even	9	inner	432.2.u.e.97.3		24
108.11	even	18		648.2.q.a.289.1		24
108.23	even	18		5832.2.a.i.1.10		12
108.31	odd	18		5832.2.a.h.1.3		12
108.43	odd	18		216.2.q.a.97.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.a.49.2	✓	24	4.3	odd	2
216.2.q.a.97.2	yes	24	108.43	odd	18
432.2.u.e.49.3		24	1.1	even	1	trivial
432.2.u.e.97.3		24	27.16	even	9	inner
648.2.q.a.289.1		24	108.11	even	18
648.2.q.a.361.1		24	12.11	even	2
5832.2.a.h.1.3		12	108.31	odd	18
5832.2.a.i.1.10		12	108.23	even	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not 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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Database

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