LMFDB - Embedded newform 432.2.k.c.325.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.k (of order $4$, degree $2$, 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:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			325.7
Character	$\chi$	$=$	432.325
Dual form			432.2.k.c.109.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.680919 + 1.23950i) q^{2} +(-1.07270 + 1.68799i) q^{4} +(2.24693 + 2.24693i) q^{5} +3.93534i q^{7} +(-2.82268 - 0.180219i) q^{8} +O(q^{10})$	\(q+(0.680919 + 1.23950i) q^{2} +(-1.07270 + 1.68799i) q^{4} +(2.24693 + 2.24693i) q^{5} +3.93534i q^{7} +(-2.82268 - 0.180219i) q^{8} +(-1.25508 + 4.31505i) q^{10} +(-3.47488 - 3.47488i) q^{11} +(4.14540 - 4.14540i) q^{13} +(-4.87784 + 2.67965i) q^{14} +(-1.69864 - 3.62141i) q^{16} -0.326940 q^{17} +(-0.108711 + 0.108711i) q^{19} +(-6.20309 + 1.38253i) q^{20} +(1.94098 - 6.67320i) q^{22} +4.30494i q^{23} +5.09743i q^{25} +(7.96088 + 2.31552i) q^{26} +(-6.64283 - 4.22144i) q^{28} +(-2.75677 + 2.75677i) q^{29} +4.45679 q^{31} +(3.33209 - 4.57134i) q^{32} +(-0.222619 - 0.405240i) q^{34} +(-8.84246 + 8.84246i) q^{35} +(4.76428 + 4.76428i) q^{37} +(-0.208769 - 0.0607231i) q^{38} +(-5.93744 - 6.74732i) q^{40} -9.19359i q^{41} +(5.45288 + 5.45288i) q^{43} +(9.59306 - 2.13807i) q^{44} +(-5.33596 + 2.93132i) q^{46} -3.67052 q^{47} -8.48693 q^{49} +(-6.31824 + 3.47094i) q^{50} +(2.55064 + 11.4442i) q^{52} +(2.59909 + 2.59909i) q^{53} -15.6156i q^{55} +(0.709223 - 11.1082i) q^{56} +(-5.29414 - 1.53987i) q^{58} +(-0.326100 - 0.326100i) q^{59} +(8.26951 - 8.26951i) q^{61} +(3.03472 + 5.52418i) q^{62} +(7.93504 + 1.01740i) q^{64} +18.6289 q^{65} +(4.31646 - 4.31646i) q^{67} +(0.350708 - 0.551872i) q^{68} +(-16.9812 - 4.93919i) q^{70} -6.88192i q^{71} +3.15046i q^{73} +(-2.66121 + 9.14939i) q^{74} +(-0.0668889 - 0.300116i) q^{76} +(13.6748 - 13.6748i) q^{77} -10.2305 q^{79} +(4.32036 - 11.9538i) q^{80} +(11.3954 - 6.26009i) q^{82} +(1.07814 - 1.07814i) q^{83} +(-0.734612 - 0.734612i) q^{85} +(-3.04585 + 10.4718i) q^{86} +(9.18222 + 10.4347i) q^{88} +5.77030i q^{89} +(16.3136 + 16.3136i) q^{91} +(-7.26671 - 4.61790i) q^{92} +(-2.49933 - 4.54960i) q^{94} -0.488531 q^{95} +2.82365 q^{97} +(-5.77891 - 10.5195i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{4}+O(q^{10}) $ 24 * q + 16 * q^4	$ 24 q + 16 q^{4} - 4 q^{10} + 16 q^{13} - 20 q^{16} - 16 q^{19} - 12 q^{22} - 12 q^{28} + 32 q^{31} + 28 q^{34} - 8 q^{37} - 36 q^{40} - 64 q^{46} - 16 q^{49} - 36 q^{52} - 32 q^{58} - 16 q^{61} + 16 q^{64} + 48 q^{67} - 24 q^{70} + 16 q^{76} - 48 q^{79} - 16 q^{82} - 16 q^{85} - 60 q^{88} + 96 q^{91} + 84 q^{94} + 8 q^{97}+O(q^{100}) $ 24 * q + 16 * q^4 - 4 * q^10 + 16 * q^13 - 20 * q^16 - 16 * q^19 - 12 * q^22 - 12 * q^28 + 32 * q^31 + 28 * q^34 - 8 * q^37 - 36 * q^40 - 64 * q^46 - 16 * q^49 - 36 * q^52 - 32 * q^58 - 16 * q^61 + 16 * q^64 + 48 * q^67 - 24 * q^70 + 16 * q^76 - 48 * q^79 - 16 * q^82 - 16 * q^85 - 60 * q^88 + 96 * q^91 + 84 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.680919	+	1.23950i	0.481482	+	0.876456i
$2$	0.680919	+	1.23950i	0.481482	+	0.876456i
$3$		0			0
$3$		0			0
$4$	−1.07270	+	1.68799i	−0.536349	+	0.843996i
$5$	2.24693	+	2.24693i	1.00486	+	1.00486i	0.999988	+	0.00487156i	$0.00155067\pi$
$5$	2.24693	+	2.24693i	1.00486	+	1.00486i	0.00487156	+	0.999988i	$0.498449\pi$
$6$		0			0
$7$			3.93534i			1.48742i	0.668502	+	0.743710i	$0.266936\pi$
$7$			3.93534i			1.48742i	−0.668502	+	0.743710i	$0.733064\pi$
$8$	−2.82268	−	0.180219i	−0.997968	−	0.0637170i
$9$		0			0
$10$	−1.25508	+	4.31505i	−0.396893	+	1.36454i
$11$	−3.47488	−	3.47488i	−1.04771	−	1.04771i	−0.998803	−	0.0489112i	$-0.984425\pi$
$11$	−3.47488	−	3.47488i	−1.04771	−	1.04771i	−0.0489112	−	0.998803i	$-0.515575\pi$
$12$		0			0
$13$	4.14540	−	4.14540i	1.14973	−	1.14973i	0.163120	−	0.986606i	$-0.447844\pi$
$13$	4.14540	−	4.14540i	1.14973	−	1.14973i	0.986606	−	0.163120i	$-0.0521558\pi$
$14$	−4.87784	+	2.67965i	−1.30366	+	0.716167i
$15$		0			0
$16$	−1.69864	−	3.62141i	−0.424659	−	0.905353i
$17$	−0.326940			−0.0792945			−0.0396473	−	0.999214i	$-0.512623\pi$
$17$	−0.326940			−0.0792945			−0.0396473	+	0.999214i	$0.512623\pi$
$18$		0			0
$19$	−0.108711	+	0.108711i	−0.0249399	+	0.0249399i	−0.719467	−	0.694527i	$-0.755614\pi$
$19$	−0.108711	+	0.108711i	−0.0249399	+	0.0249399i	0.694527	+	0.719467i	$0.255614\pi$
$20$	−6.20309	+	1.38253i	−1.38705	+	0.309142i
$21$		0			0
$22$	1.94098	−	6.67320i	0.413819	−	1.42273i
$23$			4.30494i			0.897643i	0.893622	+	0.448821i	$0.148156\pi$
$23$			4.30494i			0.897643i	−0.893622	+	0.448821i	$0.851844\pi$
$24$		0			0
$25$			5.09743i			1.01949i
$26$	7.96088	+	2.31552i	1.56126	+	0.454111i
$27$		0			0
$28$	−6.64283	−	4.22144i	−1.25538	−	0.797777i
$29$	−2.75677	+	2.75677i	−0.511919	+	0.511919i	−0.915114	−	0.403195i	$-0.867900\pi$
$29$	−2.75677	+	2.75677i	−0.511919	+	0.511919i	0.403195	+	0.915114i	$0.367900\pi$
$30$		0			0
$31$	4.45679			0.800464			0.400232	−	0.916414i	$-0.368930\pi$
$31$	4.45679			0.800464			0.400232	+	0.916414i	$0.368930\pi$
$32$	3.33209	−	4.57134i	0.589036	−	0.808107i
$33$		0			0
$34$	−0.222619	−	0.405240i	−0.0381789	−	0.0694981i
$35$	−8.84246	+	8.84246i	−1.49465	+	1.49465i
$36$		0			0
$37$	4.76428	+	4.76428i	0.783242	+	0.783242i	0.980377	−	0.197134i	$-0.0631635\pi$
$37$	4.76428	+	4.76428i	0.783242	+	0.783242i	−0.197134	+	0.980377i	$0.563163\pi$
$38$	−0.208769	−	0.0607231i	−0.0338668	−	0.00985059i
$39$		0			0
$40$	−5.93744	−	6.74732i	−0.938791	−	1.06684i
$41$		−	9.19359i		−	1.43580i	−0.696148	−	0.717898i	$-0.745104\pi$
$41$		−	9.19359i		−	1.43580i	0.696148	−	0.717898i	$-0.254896\pi$
$42$		0			0
$43$	5.45288	+	5.45288i	0.831556	+	0.831556i	0.987730	−	0.156173i	$-0.0499158\pi$
$43$	5.45288	+	5.45288i	0.831556	+	0.831556i	−0.156173	+	0.987730i	$0.549916\pi$
$44$	9.59306	−	2.13807i	1.44621	−	0.322326i
$45$		0			0
$46$	−5.33596	+	2.93132i	−0.786744	+	0.432199i
$47$	−3.67052			−0.535401			−0.267700	−	0.963502i	$-0.586264\pi$
$47$	−3.67052			−0.535401			−0.267700	+	0.963502i	$0.586264\pi$
$48$		0			0
$49$	−8.48693			−1.21242
$50$	−6.31824	+	3.47094i	−0.893534	+	0.490865i
$51$		0			0
$52$	2.55064	+	11.4442i	0.353710	+	1.58702i
$53$	2.59909	+	2.59909i	0.357012	+	0.357012i	0.862710	−	0.505698i	$-0.168765\pi$
$53$	2.59909	+	2.59909i	0.357012	+	0.357012i	−0.505698	+	0.862710i	$0.668765\pi$
$54$		0			0
$55$		−	15.6156i		−	2.10561i
$56$	0.709223	−	11.1082i	0.0947739	−	1.48440i
$57$		0			0
$58$	−5.29414	−	1.53987i	−0.695154	−	0.202194i
$59$	−0.326100	−	0.326100i	−0.0424546	−	0.0424546i	0.685561	−	0.728015i	$-0.259557\pi$
$59$	−0.326100	−	0.326100i	−0.0424546	−	0.0424546i	−0.728015	+	0.685561i	$0.759557\pi$
$60$		0			0
$61$	8.26951	−	8.26951i	1.05880	−	1.05880i	0.0606422	−	0.998160i	$-0.480685\pi$
$61$	8.26951	−	8.26951i	1.05880	−	1.05880i	0.998160	−	0.0606422i	$-0.0193149\pi$
$62$	3.03472	+	5.52418i	0.385409	+	0.701571i
$63$		0			0
$64$	7.93504	+	1.01740i	0.991880	+	0.127175i
$65$	18.6289			2.31063
$66$		0			0
$67$	4.31646	−	4.31646i	0.527340	−	0.527340i	−0.392438	−	0.919778i	$-0.628368\pi$
$67$	4.31646	−	4.31646i	0.527340	−	0.527340i	0.919778	+	0.392438i	$0.128368\pi$
$68$	0.350708	−	0.551872i	0.0425296	−	0.0669243i
$69$		0			0
$70$	−16.9812	−	4.93919i	−2.02964	−	0.590346i
$71$		−	6.88192i		−	0.816733i	−0.912818	−	0.408367i	$-0.866099\pi$
$71$		−	6.88192i		−	0.816733i	0.912818	−	0.408367i	$-0.133901\pi$
$72$		0			0
$73$			3.15046i			0.368734i	0.982857	+	0.184367i	$0.0590235\pi$
$73$			3.15046i			0.368734i	−0.982857	+	0.184367i	$0.940977\pi$
$74$	−2.66121	+	9.14939i	−0.309360	+	1.06359i
$75$		0			0
$76$	−0.0668889	−	0.300116i	−0.00767268	−	0.0344257i
$77$	13.6748	−	13.6748i	1.55839	−	1.55839i
$78$		0			0
$79$	−10.2305			−1.15102			−0.575512	−	0.817794i	$-0.695197\pi$
$79$	−10.2305			−1.15102			−0.575512	+	0.817794i	$0.695197\pi$
$80$	4.32036	−	11.9538i	0.483030	−	1.33648i
$81$		0			0
$82$	11.3954	−	6.26009i	1.25841	−	0.691311i
$83$	1.07814	−	1.07814i	0.118341	−	0.118341i	−0.645456	−	0.763797i	$-0.723333\pi$
$83$	1.07814	−	1.07814i	0.118341	−	0.118341i	0.763797	+	0.645456i	$0.223333\pi$
$84$		0			0
$85$	−0.734612	−	0.734612i	−0.0796799	−	0.0796799i
$86$	−3.04585	+	10.4718i	−0.328443	+	1.12920i
$87$		0			0
$88$	9.18222	+	10.4347i	0.978828	+	1.11234i
$89$			5.77030i			0.611650i	0.952088	+	0.305825i	$0.0989323\pi$
$89$			5.77030i			0.611650i	−0.952088	+	0.305825i	$0.901068\pi$
$90$		0			0
$91$	16.3136	+	16.3136i	1.71013	+	1.71013i
$92$	−7.26671	−	4.61790i	−0.757607	−	0.481450i
$93$		0			0
$94$	−2.49933	−	4.54960i	−0.257786	−	0.469255i
$95$	−0.488531			−0.0501222
$96$		0			0
$97$	2.82365			0.286698			0.143349	−	0.989672i	$-0.454213\pi$
$97$	2.82365			0.286698			0.143349	+	0.989672i	$0.454213\pi$
$98$	−5.77891	−	10.5195i	−0.583758	−	1.06263i
$99$		0			0
$100$	−8.60442	−	5.46801i	−0.860442	−	0.546801i
$101$	−3.00490	−	3.00490i	−0.298998	−	0.298998i	0.541623	−	0.840621i	$-0.317810\pi$
$101$	−3.00490	−	3.00490i	−0.298998	−	0.298998i	−0.840621	+	0.541623i	$0.817810\pi$
$102$		0			0
$103$		−	7.42721i		−	0.731825i	−0.930649	−	0.365912i	$-0.880757\pi$
$103$		−	7.42721i		−	0.731825i	0.930649	−	0.365912i	$-0.119243\pi$
$104$	−12.4482	+	10.9540i	−1.22065	+	1.07413i
$105$		0			0
$106$	−1.45179	+	4.99133i	−0.141010	+	0.484801i
$107$	−3.48970	−	3.48970i	−0.337362	−	0.337362i	0.518011	−	0.855374i	$-0.326672\pi$
$107$	−3.48970	−	3.48970i	−0.337362	−	0.337362i	−0.855374	+	0.518011i	$0.826672\pi$
$108$		0			0
$109$	−11.9987	+	11.9987i	−1.14927	+	1.14927i	−0.162571	+	0.986697i	$0.551979\pi$
$109$	−11.9987	+	11.9987i	−1.14927	+	1.14927i	−0.986697	+	0.162571i	$0.948021\pi$
$110$	19.3555	−	10.6330i	1.84548	−	1.01382i
$111$		0			0
$112$	14.2515	−	6.68472i	1.34664	−	0.631646i
$113$	2.81801			0.265096			0.132548	−	0.991177i	$-0.457684\pi$
$113$	2.81801			0.265096			0.132548	+	0.991177i	$0.457684\pi$
$114$		0			0
$115$	−9.67292	+	9.67292i	−0.902005	+	0.902005i
$116$	−1.69622	−	7.61058i	−0.157490	−	0.706625i
$117$		0			0
$118$	0.182152	−	0.626248i	0.0167684	−	0.0576508i
$119$		−	1.28662i		−	0.117944i
$120$		0			0
$121$			13.1495i			1.19541i
$122$	15.8809	+	4.61915i	1.43779	+	0.418198i
$123$		0			0
$124$	−4.78080	+	7.52303i	−0.429328	+	0.675588i
$125$	−0.218919	+	0.218919i	−0.0195807	+	0.0195807i
$126$		0			0
$127$	−11.8717			−1.05344			−0.526722	−	0.850038i	$-0.676579\pi$
$127$	−11.8717			−1.05344			−0.526722	+	0.850038i	$0.676579\pi$
$128$	4.14206	+	10.5282i	0.366110	+	0.930572i
$129$		0			0
$130$	12.6848	+	23.0904i	1.11253	+	2.02516i
$131$	8.54865	−	8.54865i	0.746899	−	0.746899i	−0.226996	−	0.973896i	$-0.572891\pi$
$131$	8.54865	−	8.54865i	0.746899	−	0.746899i	0.973896	+	0.226996i	$0.0728906\pi$
$132$		0			0
$133$	−0.427813	−	0.427813i	−0.0370961	−	0.0370961i
$134$	8.28940	+	2.41107i	0.716095	+	0.208285i
$135$		0			0
$136$	0.922846	+	0.0589207i	0.0791334	+	0.00505241i
$137$			4.96667i			0.424332i	0.977234	+	0.212166i	$0.0680517\pi$
$137$			4.96667i			0.424332i	−0.977234	+	0.212166i	$0.931948\pi$
$138$		0			0
$139$	−2.10134	−	2.10134i	−0.178234	−	0.178234i	0.612352	−	0.790585i	$-0.290224\pi$
$139$	−2.10134	−	2.10134i	−0.178234	−	0.178234i	−0.790585	+	0.612352i	$0.790224\pi$
$140$	−5.44071	−	24.4113i	−0.459824	−	2.06313i
$141$		0			0
$142$	8.53010	−	4.68603i	0.715830	−	0.393243i
$143$	−28.8095			−2.40917
$144$		0			0
$145$	−12.3885			−1.02881
$146$	−3.90499	+	2.14521i	−0.323179	+	0.177539i
$147$		0			0
$148$	−13.1527	+	2.93143i	−1.08114	+	0.240962i
$149$	7.78968	+	7.78968i	0.638155	+	0.638155i	0.950100	−	0.311945i	$-0.100980\pi$
$149$	7.78968	+	7.78968i	0.638155	+	0.638155i	−0.311945	+	0.950100i	$0.600980\pi$
$150$		0			0
$151$		−	2.99839i		−	0.244005i	−0.992530	−	0.122003i	$-0.961068\pi$
$151$		−	2.99839i		−	0.244005i	0.992530	−	0.122003i	$-0.0389316\pi$
$152$	0.326447	−	0.287263i	0.0264783	−	0.0233001i
$153$		0			0
$154$	26.2613	+	7.63844i	2.11620	+	0.615523i
$155$	10.0141	+	10.0141i	0.804354	+	0.804354i
$156$		0			0
$157$	13.5844	−	13.5844i	1.08415	−	1.08415i	0.0880321	−	0.996118i	$-0.471942\pi$
$157$	13.5844	−	13.5844i	1.08415	−	1.08415i	0.996118	−	0.0880321i	$-0.0280578\pi$
$158$	−6.96616	−	12.6807i	−0.554198	−	1.00882i
$159$		0			0
$160$	17.7585	−	2.78451i	1.40393	−	0.220135i
$161$	−16.9414			−1.33517
$162$		0			0
$163$	7.38524	−	7.38524i	0.578457	−	0.578457i	−0.356021	−	0.934478i	$-0.615867\pi$
$163$	7.38524	−	7.38524i	0.578457	−	0.578457i	0.934478	+	0.356021i	$0.115867\pi$
$164$	15.5187	+	9.86195i	1.21181	+	0.770089i
$165$		0			0
$166$	2.07047	+	0.602223i	0.160700	+	0.0467416i
$167$			4.04079i			0.312686i	0.987703	+	0.156343i	$0.0499705\pi$
$167$			4.04079i			0.312686i	−0.987703	+	0.156343i	$0.950030\pi$
$168$		0			0
$169$		−	21.3686i		−	1.64374i
$170$	0.410337	−	1.41076i	0.0314714	−	0.108200i
$171$		0			0
$172$	−15.0537	+	3.35512i	−1.14784	+	0.255826i
$173$	6.71115	−	6.71115i	0.510239	−	0.510239i	−0.404360	−	0.914600i	$-0.632506\pi$
$173$	6.71115	−	6.71115i	0.510239	−	0.510239i	0.914600	+	0.404360i	$0.132506\pi$
$174$		0			0
$175$	−20.0601			−1.51640
$176$	−6.68141	+	18.4865i	−0.503630	+	1.39347i
$177$		0			0
$178$	−7.15226	+	3.92910i	−0.536084	+	0.294499i
$179$	3.48970	−	3.48970i	0.260833	−	0.260833i	−0.564560	−	0.825392i	$-0.690954\pi$
$179$	3.48970	−	3.48970i	0.260833	−	0.260833i	0.825392	+	0.564560i	$0.190954\pi$
$180$		0			0
$181$	−17.4293	−	17.4293i	−1.29551	−	1.29551i	−0.931328	−	0.364181i	$-0.881349\pi$
$181$	−17.4293	−	17.4293i	−1.29551	−	1.29551i	−0.364181	−	0.931328i	$-0.618651\pi$
$182$	−9.11237	+	31.3288i	−0.675454	+	2.32225i
$183$		0			0
$184$	0.775832	−	12.1515i	0.0571951	−	0.895819i
$185$			21.4100i			1.57410i
$186$		0			0
$187$	1.13607	+	1.13607i	0.0830780	+	0.0830780i
$188$	3.93736	−	6.19581i	0.287162	−	0.451876i
$189$		0			0
$190$	−0.332650	−	0.605532i	−0.0241330	−	0.0439299i
$191$	3.50685			0.253747			0.126873	−	0.991919i	$-0.459506\pi$
$191$	3.50685			0.253747			0.126873	+	0.991919i	$0.459506\pi$
$192$		0			0
$193$	−10.4842			−0.754666			−0.377333	−	0.926078i	$-0.623159\pi$
$193$	−10.4842			−0.754666			−0.377333	+	0.926078i	$0.623159\pi$
$194$	1.92268	+	3.49990i	0.138040	+	0.251278i
$195$		0			0
$196$	9.10391	−	14.3259i	0.650280	−	1.02328i
$197$	−5.28098	−	5.28098i	−0.376255	−	0.376255i	0.493494	−	0.869749i	$-0.335719\pi$
$197$	−5.28098	−	5.28098i	−0.376255	−	0.376255i	−0.869749	+	0.493494i	$0.835719\pi$
$198$		0			0
$199$		−	9.93981i		−	0.704614i	−0.935884	−	0.352307i	$-0.885397\pi$
$199$		−	9.93981i		−	0.704614i	0.935884	−	0.352307i	$-0.114603\pi$
$200$	0.918653	−	14.3884i	0.0649586	−	1.01741i
$201$		0			0
$202$	1.67846	−	5.77065i	0.118096	−	0.406021i
$203$	−10.8488	−	10.8488i	−0.761438	−	0.761438i
$204$		0			0
$205$	20.6574	−	20.6574i	1.44277	−	1.44277i
$206$	9.20600	−	5.05733i	0.641412	−	0.352361i
$207$		0			0
$208$	−22.0537	−	7.97068i	−1.52915	−	0.552667i
$209$	0.755511			0.0522598
$210$		0			0
$211$	−10.9210	+	10.9210i	−0.751830	+	0.751830i	−0.974821	−	0.222991i	$-0.928418\pi$
$211$	−10.9210	+	10.9210i	−0.751830	+	0.751830i	0.222991	+	0.974821i	$0.428418\pi$
$212$	−7.17528	+	1.59920i	−0.492800	+	0.109834i
$213$		0			0
$214$	1.94927	−	6.70167i	0.133249	−	0.458117i
$215$			24.5045i			1.67120i
$216$		0			0
$217$			17.5390i			1.19063i
$218$	−23.0425	−	6.70220i	−1.56063	−	0.453930i
$219$		0			0
$220$	26.3591	+	16.7509i	1.77713	+	1.12934i
$221$	−1.35529	+	1.35529i	−0.0911670	+	0.0911670i
$222$		0			0
$223$	−8.89438			−0.595612			−0.297806	−	0.954626i	$-0.596255\pi$
$223$	−8.89438			−0.595612			−0.297806	+	0.954626i	$0.596255\pi$
$224$	17.9898	+	13.1129i	1.20199	+	0.876144i
$225$		0			0
$226$	1.91884	+	3.49291i	0.127639	+	0.232345i
$227$	−19.5902	+	19.5902i	−1.30025	+	1.30025i	−0.372028	+	0.928222i	$0.621337\pi$
$227$	−19.5902	+	19.5902i	−1.30025	+	1.30025i	−0.928222	+	0.372028i	$0.878663\pi$
$228$		0			0
$229$	8.88839	+	8.88839i	0.587361	+	0.587361i	0.936916	−	0.349555i	$-0.113667\pi$
$229$	8.88839	+	8.88839i	0.587361	+	0.587361i	−0.349555	+	0.936916i	$0.613667\pi$
$230$	−18.5760	−	5.40307i	−1.22487	−	0.356268i
$231$		0			0
$232$	8.27829	−	7.28465i	0.543496	−	0.478261i
$233$		−	13.5181i		−	0.885602i	−0.896620	−	0.442801i	$-0.853985\pi$
$233$		−	13.5181i		−	0.885602i	0.896620	−	0.442801i	$-0.146015\pi$
$234$		0			0
$235$	−8.24742	−	8.24742i	−0.538003	−	0.538003i
$236$	0.900262	−	0.200647i	0.0586021	−	0.0130610i
$237$		0			0
$238$	1.59476	−	0.876084i	0.103373	−	0.0567881i
$239$	5.79042			0.374551			0.187276	−	0.982307i	$-0.440034\pi$
$239$	5.79042			0.374551			0.187276	+	0.982307i	$0.440034\pi$
$240$		0			0
$241$	−28.3050			−1.82329			−0.911643	−	0.410984i	$-0.865185\pi$
$241$	−28.3050			−1.82329			−0.911643	+	0.410984i	$0.865185\pi$
$242$	−16.2988	+	8.95376i	−1.04772	+	0.575569i
$243$		0			0
$244$	5.08818	+	22.8295i	0.325737	+	1.46151i
$245$	−19.0696	−	19.0696i	−1.21831	−	1.21831i
$246$		0			0
$247$			0.901296i			0.0573481i
$248$	−12.5801	−	0.803198i	−0.798837	−	0.0510031i
$249$		0			0
$250$	−0.420415	−	0.122283i	−0.0265894	−	0.00773385i
$251$	12.6583	+	12.6583i	0.798982	+	0.798982i	0.982935	−	0.183953i	$-0.0588893\pi$
$251$	12.6583	+	12.6583i	0.798982	+	0.798982i	−0.183953	+	0.982935i	$0.558889\pi$
$252$		0			0
$253$	14.9591	−	14.9591i	0.940473	−	0.940473i
$254$	−8.08368	−	14.7149i	−0.507215	−	0.923297i
$255$		0			0
$256$	−10.2293	+	12.3029i	−0.639329	+	0.768933i
$257$	−24.8277			−1.54871			−0.774356	−	0.632750i	$-0.781926\pi$
$257$	−24.8277			−1.54871			−0.774356	+	0.632750i	$0.781926\pi$
$258$		0			0
$259$	−18.7491	+	18.7491i	−1.16501	+	1.16501i
$260$	−19.9832	+	31.4454i	−1.23930	+	1.95016i
$261$		0			0
$262$	16.4170	+	4.77508i	1.01424	+	0.295005i
$263$		−	28.3171i		−	1.74610i	−0.487626	−	0.873052i	$-0.662137\pi$
$263$		−	28.3171i		−	1.74610i	0.487626	−	0.873052i	$-0.337863\pi$
$264$		0			0
$265$			11.6800i			0.717495i
$266$	0.238966	−	0.821579i	0.0146520	−	0.0503742i
$267$		0			0
$268$	2.65589	+	11.9164i	0.162235	+	0.727911i
$269$	−16.4900	+	16.4900i	−1.00541	+	1.00541i	−0.00542517	+	0.999985i	$0.501727\pi$
$269$	−16.4900	+	16.4900i	−1.00541	+	1.00541i	−0.999985	+	0.00542517i	$0.998273\pi$
$270$		0			0
$271$	15.2088			0.923867			0.461933	−	0.886915i	$-0.347156\pi$
$271$	15.2088			0.923867			0.461933	+	0.886915i	$0.347156\pi$
$272$	0.555352	+	1.18398i	0.0336731	+	0.0717896i
$273$		0			0
$274$	−6.15617	+	3.38190i	−0.371908	+	0.204308i
$275$	17.7129	−	17.7129i	1.06813	−	1.06813i
$276$		0			0
$277$	3.25572	+	3.25572i	0.195617	+	0.195617i	0.798118	−	0.602501i	$-0.205829\pi$
$277$	3.25572	+	3.25572i	0.195617	+	0.195617i	−0.602501	+	0.798118i	$0.705829\pi$
$278$	1.17376	−	4.03545i	0.0703975	−	0.242030i
$279$		0			0
$280$	26.5530	−	23.3659i	1.58685	−	1.39638i
$281$		−	13.1484i		−	0.784367i	−0.919887	−	0.392183i	$-0.871720\pi$
$281$		−	13.1484i		−	0.784367i	0.919887	−	0.392183i	$-0.128280\pi$
$282$		0			0
$283$	9.18485	+	9.18485i	0.545983	+	0.545983i	0.925276	−	0.379294i	$-0.123833\pi$
$283$	9.18485	+	9.18485i	0.545983	+	0.545983i	−0.379294	+	0.925276i	$0.623833\pi$
$284$	11.6166	+	7.38222i	0.689320	+	0.438054i
$285$		0			0
$286$	−19.6169	−	35.7092i	−1.15997	−	2.11153i
$287$	36.1799			2.13563
$288$		0			0
$289$	−16.8931			−0.993712
$290$	−8.43560	−	15.3556i	−0.495355	−	0.901709i
$291$		0			0
$292$	−5.31796	−	3.37950i	−0.311210	−	0.197770i
$293$	14.6906	+	14.6906i	0.858234	+	0.858234i	0.991130	−	0.132896i	$-0.0424277\pi$
$293$	14.6906	+	14.6906i	0.858234	+	0.858234i	−0.132896	+	0.991130i	$0.542428\pi$
$294$		0			0
$295$		−	1.46545i		−	0.0853219i
$296$	−12.5894	−	14.3066i	−0.731745	−	0.831557i
$297$		0			0
$298$	−4.35113	+	14.9594i	−0.252054	+	0.866576i
$299$	17.8457	+	17.8457i	1.03204	+	1.03204i
$300$		0			0
$301$	−21.4590	+	21.4590i	−1.23687	+	1.23687i
$302$	3.71649	−	2.04166i	0.213860	−	0.117484i
$303$		0			0
$304$	0.578345	+	0.209026i	0.0331704	+	0.0119885i
$305$	37.1621			2.12789
$306$		0			0
$307$	23.7587	−	23.7587i	1.35598	−	1.35598i	0.477173	−	0.878809i	$-0.341662\pi$
$307$	23.7587	−	23.7587i	1.35598	−	1.35598i	0.878809	−	0.477173i	$-0.158338\pi$
$308$	8.41404	+	37.7520i	0.479434	+	2.15112i
$309$		0			0
$310$	−5.59365	+	19.2313i	−0.317698	+	1.09226i
$311$			8.59248i			0.487235i	0.969871	+	0.243617i	$0.0783341\pi$
$311$			8.59248i			0.487235i	−0.969871	+	0.243617i	$0.921666\pi$
$312$		0			0
$313$			8.35592i			0.472304i	0.971716	+	0.236152i	$0.0758864\pi$
$313$			8.35592i			0.472304i	−0.971716	+	0.236152i	$0.924114\pi$
$314$	26.0876	+	7.58790i	1.47221	+	0.428210i
$315$		0			0
$316$	10.9743	−	17.2690i	0.617350	−	0.971459i
$317$	−23.6909	+	23.6909i	−1.33061	+	1.33061i	−0.425790	+	0.904822i	$0.640004\pi$
$317$	−23.6909	+	23.6909i	−1.33061	+	1.33061i	−0.904822	+	0.425790i	$0.859996\pi$
$318$		0			0
$319$	19.1588			1.07269
$320$	15.5435	+	20.1156i	0.868907	+	1.12449i
$321$		0			0
$322$	−11.5357	−	20.9988i	−0.642862	−	1.17022i
$323$	0.0355418	−	0.0355418i	0.00197760	−	0.00197760i
$324$		0			0
$325$	21.1309	+	21.1309i	1.17213	+	1.17213i
$326$	14.1827	+	4.12522i	0.785508	+	0.228475i
$327$		0			0
$328$	−1.65686	+	25.9506i	−0.0914846	+	1.43288i
$329$		−	14.4448i		−	0.796366i
$330$		0			0
$331$	4.37674	+	4.37674i	0.240567	+	0.240567i	0.817085	−	0.576518i	$-0.195589\pi$
$331$	4.37674	+	4.37674i	0.240567	+	0.240567i	−0.576518	+	0.817085i	$0.695589\pi$
$332$	0.663372	+	2.97641i	0.0364073	+	0.163352i
$333$		0			0
$334$	−5.00854	+	2.75145i	−0.274055	+	0.150553i
$335$	19.3976			1.05981
$336$		0			0
$337$	−0.946967			−0.0515846			−0.0257923	−	0.999667i	$-0.508211\pi$
$337$	−0.946967			−0.0515846			−0.0257923	+	0.999667i	$0.508211\pi$
$338$	26.4863	−	14.5503i	1.44067	−	0.791432i
$339$		0			0
$340$	2.02804	−	0.452002i	0.109986	−	0.0245133i
$341$	−15.4868	−	15.4868i	−0.838657	−	0.838657i
$342$		0			0
$343$		−	5.85157i		−	0.315955i
$344$	−14.4090	−	16.3744i	−0.776883	−	0.882851i
$345$		0			0
$346$	12.8882	+	3.74869i	0.692873	+	0.201531i
$347$	−17.3176	−	17.3176i	−0.929656	−	0.929656i	0.0680274	−	0.997683i	$-0.478329\pi$
$347$	−17.3176	−	17.3176i	−0.929656	−	0.929656i	−0.997683	+	0.0680274i	$0.978329\pi$
$348$		0			0
$349$	−0.862655	+	0.862655i	−0.0461769	+	0.0461769i	−0.729818	−	0.683641i	$-0.760395\pi$
$349$	−0.862655	+	0.862655i	−0.0461769	+	0.0461769i	0.683641	+	0.729818i	$0.260395\pi$
$350$	−13.6593	−	24.8645i	−0.730122	−	1.32906i
$351$		0			0
$352$	−27.4634	+	4.30624i	−1.46381	+	0.229523i
$353$	−19.2982			−1.02714			−0.513570	−	0.858048i	$-0.671677\pi$
$353$	−19.2982			−1.02714			−0.513570	+	0.858048i	$0.671677\pi$
$354$		0			0
$355$	15.4632	−	15.4632i	0.820702	−	0.820702i
$356$	−9.74021	−	6.18979i	−0.516230	−	0.328058i
$357$		0			0
$358$	6.70167	+	1.94927i	0.354194	+	0.103022i
$359$		−	23.4266i		−	1.23641i	−0.786018	−	0.618203i	$-0.787861\pi$
$359$		−	23.4266i		−	1.23641i	0.786018	−	0.618203i	$-0.212139\pi$
$360$		0			0
$361$			18.9764i			0.998756i
$362$	9.73559	−	33.4715i	0.511691	−	1.75922i
$363$		0			0
$364$	−45.0367	+	10.0376i	−2.36056	+	0.526115i
$365$	−7.07889	+	7.07889i	−0.370526	+	0.370526i
$366$		0			0
$367$	−1.53294			−0.0800186			−0.0400093	−	0.999199i	$-0.512739\pi$
$367$	−1.53294			−0.0800186			−0.0400093	+	0.999199i	$0.512739\pi$
$368$	15.5900	−	7.31253i	0.812684	−	0.381192i
$369$		0			0
$370$	−26.5376	+	14.5785i	−1.37963	+	0.757900i
$371$	−10.2283	+	10.2283i	−0.531027	+	0.531027i
$372$		0			0
$373$	−14.7693	−	14.7693i	−0.764727	−	0.764727i	0.212446	−	0.977173i	$-0.431857\pi$
$373$	−14.7693	−	14.7693i	−0.764727	−	0.764727i	−0.977173	+	0.212446i	$0.931857\pi$
$374$	−0.634585	+	2.18173i	−0.0328136	+	0.112815i
$375$		0			0
$376$	10.3607	+	0.661497i	0.534313	+	0.0341141i
$377$			22.8558i			1.17713i
$378$		0			0
$379$	−18.8578	−	18.8578i	−0.968659	−	0.968659i	0.0308646	−	0.999524i	$-0.490174\pi$
$379$	−18.8578	−	18.8578i	−0.968659	−	0.968659i	−0.999524	+	0.0308646i	$0.990174\pi$
$380$	0.524046	−	0.824636i	0.0268830	−	0.0423029i
$381$		0			0
$382$	2.38788	+	4.34673i	0.122175	+	0.222398i
$383$	−0.241783			−0.0123546			−0.00617728	−	0.999981i	$-0.501966\pi$
$383$	−0.241783			−0.0123546			−0.00617728	+	0.999981i	$0.501966\pi$
$384$		0			0
$385$	61.4529			3.13193
$386$	−7.13886	−	12.9951i	−0.363359	−	0.661431i
$387$		0			0
$388$	−3.02892	+	4.76629i	−0.153770	+	0.241972i
$389$	22.1081	+	22.1081i	1.12093	+	1.12093i	0.991602	+	0.129325i	$0.0412809\pi$
$389$	22.1081	+	22.1081i	1.12093	+	1.12093i	0.129325	+	0.991602i	$0.458719\pi$
$390$		0			0
$391$		−	1.40746i		−	0.0711781i
$392$	23.9559	+	1.52950i	1.20995	+	0.0772516i
$393$		0			0
$394$	2.94983	−	10.1417i	0.148610	−	0.510930i
$395$	−22.9873	−	22.9873i	−1.15662	−	1.15662i
$396$		0			0
$397$	−7.22027	+	7.22027i	−0.362375	+	0.362375i	−0.864687	−	0.502312i	$-0.832483\pi$
$397$	−7.22027	+	7.22027i	−0.362375	+	0.362375i	0.502312	+	0.864687i	$0.332483\pi$
$398$	12.3203	−	6.76820i	0.617563	−	0.339259i
$399$		0			0
$400$	18.4599	−	8.65868i	0.922995	−	0.432934i
$401$	−35.9448			−1.79500			−0.897499	−	0.441017i	$-0.854618\pi$
$401$	−35.9448			−1.79500			−0.897499	+	0.441017i	$0.854618\pi$
$402$		0			0
$403$	18.4752	−	18.4752i	0.920314	−	0.920314i
$404$	8.29559	−	1.84889i	0.412721	−	0.0919859i
$405$		0			0
$406$	6.05990	−	20.8342i	0.300748	−	1.03399i
$407$		−	33.1105i		−	1.64123i
$408$		0			0
$409$		−	15.5816i		−	0.770460i	−0.922821	−	0.385230i	$-0.874122\pi$
$409$		−	15.5816i		−	0.770460i	0.922821	−	0.385230i	$-0.125878\pi$
$410$	39.6707	+	11.5387i	1.95920	+	0.569857i
$411$		0			0
$412$	12.5371	+	7.96716i	0.617657	+	0.392514i
$413$	1.28332	−	1.28332i	0.0631479	−	0.0631479i
$414$		0			0
$415$	4.84501			0.237832
$416$	−5.13718	−	32.7629i	−0.251871	−	1.60633i
$417$		0			0
$418$	0.514442	+	0.936452i	0.0251622	+	0.0458034i
$419$	17.7897	−	17.7897i	0.869084	−	0.869084i	−0.123287	−	0.992371i	$-0.539344\pi$
$419$	17.7897	−	17.7897i	0.869084	−	0.869084i	0.992371	+	0.123287i	$0.0393436\pi$
$420$		0			0
$421$	−17.1522	−	17.1522i	−0.835945	−	0.835945i	0.152377	−	0.988322i	$-0.451307\pi$
$421$	−17.1522	−	17.1522i	−0.835945	−	0.835945i	−0.988322	+	0.152377i	$0.951307\pi$
$422$	−20.9728	−	6.10019i	−1.02094	−	0.296953i
$423$		0			0
$424$	−6.86799	−	7.80480i	−0.333539	−	0.379035i
$425$		−	1.66655i		−	0.0808397i
$426$		0			0
$427$	32.5433	+	32.5433i	1.57488	+	1.57488i
$428$	9.63399	−	2.14719i	0.465676	−	0.103788i
$429$		0			0
$430$	−30.3733	+	16.6856i	−1.46473	+	0.804651i
$431$	36.1086			1.73929			0.869645	−	0.493677i	$-0.164347\pi$
$431$	36.1086			1.73929			0.869645	+	0.493677i	$0.164347\pi$
$432$		0			0
$433$	13.7206			0.659372			0.329686	−	0.944091i	$-0.393057\pi$
$433$	13.7206			0.659372			0.329686	+	0.944091i	$0.393057\pi$
$434$	−21.7395	+	11.9426i	−1.04353	+	0.573265i
$435$		0			0
$436$	−7.38273	−	33.1247i	−0.353569	−	1.58639i
$437$	−0.467993	−	0.467993i	−0.0223871	−	0.0223871i
$438$		0			0
$439$			28.1895i			1.34541i	0.739909	+	0.672707i	$0.234868\pi$
$439$			28.1895i			1.34541i	−0.739909	+	0.672707i	$0.765132\pi$
$440$	−2.81423	+	44.0779i	−0.134163	+	2.10133i
$441$		0			0
$442$	−2.60273	−	0.757036i	−0.123799	−	0.0360085i
$443$	−1.74454	−	1.74454i	−0.0828854	−	0.0828854i	0.664449	−	0.747334i	$-0.268666\pi$
$443$	−1.74454	−	1.74454i	−0.0828854	−	0.0828854i	−0.747334	+	0.664449i	$0.768666\pi$
$444$		0			0
$445$	−12.9655	+	12.9655i	−0.614623	+	0.614623i
$446$	−6.05635	−	11.0245i	−0.286777	−	0.522027i
$447$		0			0
$448$	−4.00382	+	31.2271i	−0.189163	+	1.47534i
$449$	−1.12449			−0.0530679			−0.0265339	−	0.999648i	$-0.508447\pi$
$449$	−1.12449			−0.0530679			−0.0265339	+	0.999648i	$0.508447\pi$
$450$		0			0
$451$	−31.9466	+	31.9466i	−1.50431	+	1.50431i
$452$	−3.02287	+	4.75678i	−0.142184	+	0.223740i
$453$		0			0
$454$	−37.6214	−	10.9426i	−1.76566	−	0.513564i
$455$			73.3110i			3.43687i
$456$		0			0
$457$		−	37.2983i		−	1.74474i	−0.488843	−	0.872372i	$-0.662581\pi$
$457$		−	37.2983i		−	1.74474i	0.488843	−	0.872372i	$-0.337419\pi$
$458$	−4.96484	+	17.0694i	−0.231992	+	0.797600i
$459$		0			0
$460$	−5.95169	−	26.7040i	−0.277499	−	1.24508i
$461$	3.09234	−	3.09234i	0.144025	−	0.144025i	−0.631418	−	0.775443i	$-0.717527\pi$
$461$	3.09234	−	3.09234i	0.144025	−	0.144025i	0.775443	+	0.631418i	$0.217527\pi$
$462$		0			0
$463$	−4.58611			−0.213134			−0.106567	−	0.994305i	$-0.533986\pi$
$463$	−4.58611			−0.213134			−0.106567	+	0.994305i	$0.533986\pi$
$464$	14.6661	+	5.30065i	0.680858	+	0.246076i
$465$		0			0
$466$	16.7557	−	9.20476i	0.776191	−	0.426402i
$467$	24.4064	−	24.4064i	1.12939	−	1.12939i	0.139116	−	0.990276i	$-0.455574\pi$
$467$	24.4064	−	24.4064i	1.12939	−	1.12939i	0.990276	−	0.139116i	$-0.0444261\pi$
$468$		0			0
$469$	16.9868	+	16.9868i	0.784376	+	0.784376i
$470$	4.60682	−	15.8385i	0.212497	−	0.730574i
$471$		0			0
$472$	0.861707	+	0.979246i	0.0396633	+	0.0450734i
$473$		−	37.8962i		−	1.74247i
$474$		0			0
$475$	−0.554144	−	0.554144i	−0.0254259	−	0.0254259i
$476$	2.17180	+	1.38016i	0.0995445	+	0.0632593i
$477$		0			0
$478$	3.94281	+	7.17720i	0.180340	+	0.328277i
$479$	1.12295			0.0513089			0.0256545	−	0.999671i	$-0.491833\pi$
$479$	1.12295			0.0513089			0.0256545	+	0.999671i	$0.491833\pi$
$480$		0			0
$481$	39.4996			1.80103
$482$	−19.2734	−	35.0839i	−0.877880	−	1.59803i
$483$		0			0
$484$	−22.1963	−	14.1055i	−1.00892	−	0.641157i
$485$	6.34455	+	6.34455i	0.288091	+	0.288091i
$486$		0			0
$487$			19.5301i			0.884991i	0.896771	+	0.442496i	$0.145907\pi$
$487$			19.5301i			0.884991i	−0.896771	+	0.442496i	$0.854093\pi$
$488$	−24.8325	+	21.8518i	−1.12411	+	0.989187i
$489$		0			0
$490$	10.6518	−	36.6215i	0.481200	−	1.65439i
$491$	22.6135	+	22.6135i	1.02053	+	1.02053i	0.999785	+	0.0207472i	$0.00660451\pi$
$491$	22.6135	+	22.6135i	1.02053	+	1.02053i	0.0207472	+	0.999785i	$0.493395\pi$
$492$		0			0
$493$	0.901296	−	0.901296i	0.0405924	−	0.0405924i
$494$	−1.11715	+	0.613710i	−0.0502631	+	0.0276121i
$495$		0			0
$496$	−7.57047	−	16.1399i	−0.339924	−	0.724703i
$497$	27.0827			1.21483
$498$		0			0
$499$	−12.4100	+	12.4100i	−0.555547	+	0.555547i	−0.928036	−	0.372489i	$-0.878504\pi$
$499$	−12.4100	+	12.4100i	−0.555547	+	0.555547i	0.372489	+	0.928036i	$0.378504\pi$
$500$	−0.134699	−	0.604368i	−0.00602394	−	0.0270281i
$501$		0			0
$502$	−7.07061	+	24.3091i	−0.315577	+	1.08497i
$503$		−	11.7678i		−	0.524698i	−0.964973	−	0.262349i	$-0.915503\pi$
$503$		−	11.7678i		−	0.524698i	0.964973	−	0.262349i	$-0.0844972\pi$
$504$		0			0
$505$		−	13.5036i		−	0.600903i
$506$	28.7277	+	8.35582i	1.27710	+	0.371462i
$507$		0			0
$508$	12.7348	−	20.0394i	0.565014	−	0.889103i
$509$	15.3964	−	15.3964i	0.682434	−	0.682434i	−0.278114	−	0.960548i	$-0.589709\pi$
$509$	15.3964	−	15.3964i	0.682434	−	0.682434i	0.960548	+	0.278114i	$0.0897092\pi$
$510$		0			0
$511$	−12.3982			−0.548462
$512$	−22.2147	−	4.30184i	−0.981762	−	0.190116i
$513$		0			0
$514$	−16.9057	−	30.7739i	−0.745678	−	1.35738i
$515$	16.6885	−	16.6885i	0.735381	−	0.735381i
$516$		0			0
$517$	12.7546	+	12.7546i	0.560947	+	0.560947i
$518$	−36.0060	−	10.4728i	−1.58201	−	0.460148i
$519$		0			0
$520$	−52.5833	−	3.35727i	−2.30593	−	0.147226i
$521$		−	11.8344i		−	0.518474i	−0.965814	−	0.259237i	$-0.916529\pi$
$521$		−	11.8344i		−	0.518474i	0.965814	−	0.259237i	$-0.0834711\pi$
$522$		0			0
$523$	−1.49118	−	1.49118i	−0.0652049	−	0.0652049i	0.673752	−	0.738957i	$-0.264681\pi$
$523$	−1.49118	−	1.49118i	−0.0652049	−	0.0652049i	−0.738957	+	0.673752i	$0.764681\pi$
$524$	5.25993	+	23.6002i	0.229781	+	1.03098i
$525$		0			0
$526$	35.0989	−	19.2816i	1.53038	−	0.840719i
$527$	−1.45710			−0.0634724
$528$		0			0
$529$	4.46747			0.194238
$530$	−14.4773	+	7.95311i	−0.628852	+	0.345461i
$531$		0			0
$532$	1.18106	−	0.263231i	0.0512054	−	0.0114125i
$533$	−38.1111	−	38.1111i	−1.65077	−	1.65077i
$534$		0			0
$535$		−	15.6823i		−	0.678003i
$536$	−12.9619	+	11.4061i	−0.559869	+	0.492668i
$537$		0			0
$538$	−31.6676	−	9.21090i	−1.36529	−	0.397110i
$539$	29.4910	+	29.4910i	1.27027	+	1.27027i
$540$		0			0
$541$	7.54651	−	7.54651i	0.324450	−	0.324450i	−0.526021	−	0.850471i	$-0.676317\pi$
$541$	7.54651	−	7.54651i	0.324450	−	0.324450i	0.850471	+	0.526021i	$0.176317\pi$
$542$	10.3559	+	18.8512i	0.444826	+	0.809728i
$543$		0			0
$544$	−1.08939	+	1.49455i	−0.0467073	+	0.0640784i
$545$	−53.9206			−2.30971
$546$		0			0
$547$	8.75678	−	8.75678i	0.374413	−	0.374413i	−0.494669	−	0.869082i	$-0.664711\pi$
$547$	8.75678	−	8.75678i	0.374413	−	0.374413i	0.869082	+	0.494669i	$0.164711\pi$
$548$	−8.38371	−	5.32774i	−0.358134	−	0.227590i
$549$		0			0
$550$	34.0162	+	9.89403i	1.45045	+	0.421883i
$551$		−	0.599379i		−	0.0255344i
$552$		0			0
$553$		−	40.2606i		−	1.71206i
$554$	−1.81857	+	6.25233i	−0.0772636	+	0.265636i
$555$		0			0
$556$	5.80116	−	1.29294i	0.246024	−	0.0548330i
$557$	19.9006	−	19.9006i	0.843215	−	0.843215i	−0.146061	−	0.989276i	$-0.546659\pi$
$557$	19.9006	−	19.9006i	0.843215	−	0.843215i	0.989276	+	0.146061i	$0.0466595\pi$
$558$		0			0
$559$	45.2087			1.91212
$560$	47.0423	+	17.0021i	1.98790	+	0.718469i
$561$		0			0
$562$	16.2974	−	8.95299i	0.687463	−	0.377659i
$563$	−24.1922	+	24.1922i	−1.01958	+	1.01958i	−0.0197747	+	0.999804i	$0.506295\pi$
$563$	−24.1922	+	24.1922i	−1.01958	+	1.01958i	−0.999804	+	0.0197747i	$0.993705\pi$
$564$		0			0
$565$	6.33188	+	6.33188i	0.266384	+	0.266384i
$566$	−5.13044	+	17.6387i	−0.215649	+	0.741411i
$567$		0			0
$568$	−1.24025	+	19.4254i	−0.0520398	+	0.815073i
$569$			38.1466i			1.59919i	0.600540	+	0.799594i	$0.294952\pi$
$569$			38.1466i			1.59919i	−0.600540	+	0.799594i	$0.705048\pi$
$570$		0			0
$571$	−22.3968	−	22.3968i	−0.937277	−	0.937277i	0.0608686	−	0.998146i	$-0.480613\pi$
$571$	−22.3968	−	22.3968i	−0.937277	−	0.937277i	−0.998146	+	0.0608686i	$0.980613\pi$
$572$	30.9039	−	48.6302i	1.29216	−	2.03333i
$573$		0			0
$574$	24.6356	+	44.8448i	1.02827	+	1.87179i
$575$	−21.9441			−0.915134
$576$		0			0
$577$	−26.2349			−1.09217			−0.546086	−	0.837729i	$-0.683883\pi$
$577$	−26.2349			−1.09217			−0.546086	+	0.837729i	$0.683883\pi$
$578$	−11.5028	−	20.9389i	−0.478455	−	0.870945i
$579$		0			0
$580$	13.2892	−	20.9118i	0.551803	−	0.868314i
$581$	4.24285	+	4.24285i	0.176023	+	0.176023i
$582$		0			0
$583$		−	18.0630i		−	0.748094i
$584$	0.567773	−	8.89275i	0.0234946	−	0.367985i
$585$		0			0
$586$	−8.20582	+	28.2120i	−0.338979	+	1.16543i
$587$	3.63391	+	3.63391i	0.149988	+	0.149988i	0.778113	−	0.628125i	$-0.216177\pi$
$587$	3.63391	+	3.63391i	0.149988	+	0.149988i	−0.628125	+	0.778113i	$0.716177\pi$
$588$		0			0
$589$	−0.484500	+	0.484500i	−0.0199635	+	0.0199635i
$590$	1.81642	−	0.997854i	0.0747809	−	0.0410810i
$591$		0			0
$592$	9.16064	−	25.3462i	0.376500	−	1.04172i
$593$	13.6076			0.558796			0.279398	−	0.960175i	$-0.409865\pi$
$593$	13.6076			0.558796			0.279398	+	0.960175i	$0.409865\pi$
$594$		0			0
$595$	2.89095	−	2.89095i	0.118517	−	0.118517i
$596$	−21.5049	+	4.79294i	−0.880875	+	0.196327i
$597$		0			0
$598$	−9.96819	+	34.2711i	−0.407629	+	1.40145i
$599$			5.25611i			0.214759i	0.994218	+	0.107379i	$0.0342459\pi$
$599$			5.25611i			0.214759i	−0.994218	+	0.107379i	$0.965754\pi$
$600$		0			0
$601$			34.7190i			1.41622i	0.706103	+	0.708109i	$0.250451\pi$
$601$			34.7190i			1.41622i	−0.706103	+	0.708109i	$0.749549\pi$
$602$	−41.2101	−	11.9865i	−1.67960	−	0.488532i
$603$		0			0
$604$	5.06126	+	3.21637i	0.205940	+	0.130872i
$605$	−29.5461	+	29.5461i	−1.20122	+	1.20122i
$606$		0			0
$607$	−14.2796			−0.579590			−0.289795	−	0.957089i	$-0.593587\pi$
$607$	−14.2796			−0.579590			−0.289795	+	0.957089i	$0.593587\pi$
$608$	0.134719	+	0.859186i	0.00546359	+	0.0348446i
$609$		0			0
$610$	25.3044	+	46.0622i	1.02454	+	1.86501i
$611$	−15.2158	+	15.2158i	−0.615564	+	0.615564i
$612$		0			0
$613$	−15.3421	−	15.3421i	−0.619660	−	0.619660i	0.325784	−	0.945444i	$-0.394372\pi$
$613$	−15.3421	−	15.3421i	−0.619660	−	0.619660i	−0.945444	+	0.325784i	$0.894372\pi$
$614$	45.6266	+	13.2711i	1.84134	+	0.535577i
$615$		0			0
$616$	−41.0641	+	36.1352i	−1.65452	+	1.45593i
$617$			43.4143i			1.74779i	0.486112	+	0.873897i	$0.338415\pi$
$617$			43.4143i			1.74779i	−0.486112	+	0.873897i	$0.661585\pi$
$618$		0			0
$619$	9.34752	+	9.34752i	0.375709	+	0.375709i	0.869551	−	0.493843i	$-0.164408\pi$
$619$	9.34752	+	9.34752i	0.375709	+	0.375709i	−0.493843	+	0.869551i	$0.664408\pi$
$620$	−27.6459	+	6.16163i	−1.11029	+	0.247457i
$621$		0			0
$622$	−10.6503	+	5.85078i	−0.427040	+	0.234595i
$623$	−22.7081			−0.909781
$624$		0			0
$625$	24.5034			0.980134
$626$	−10.3571	+	5.68970i	−0.413954	+	0.227406i
$627$		0			0
$628$	8.35837	+	37.5022i	0.333535	+	1.49650i
$629$	−1.55763	−	1.55763i	−0.0621068	−	0.0621068i
$630$		0			0
$631$			35.7747i			1.42417i	0.702095	+	0.712084i	$0.252248\pi$
$631$			35.7747i			1.42417i	−0.702095	+	0.712084i	$0.747752\pi$
$632$	28.8775	+	1.84373i	1.14868	+	0.0733397i
$633$		0			0
$634$	−45.4963	−	13.2332i	−1.80689	−	0.525556i
$635$	−26.6750	−	26.6750i	−1.05856	−	1.05856i
$636$		0			0
$637$	−35.1817	+	35.1817i	−1.39395	+	1.39395i
$638$	13.0456	+	23.7473i	0.516481	+	0.940165i
$639$		0			0
$640$	−14.3493	+	32.9631i	−0.567205	+	1.30298i
$641$	27.8292			1.09919			0.549593	−	0.835432i	$-0.314783\pi$
$641$	27.8292			1.09919			0.549593	+	0.835432i	$0.314783\pi$
$642$		0			0
$643$	1.87219	−	1.87219i	0.0738321	−	0.0738321i	−0.669226	−	0.743059i	$-0.733374\pi$
$643$	1.87219	−	1.87219i	0.0738321	−	0.0738321i	0.743059	+	0.669226i	$0.233374\pi$
$644$	18.1730	−	28.5970i	0.716118	−	1.12688i
$645$		0			0
$646$	0.0682550	+	0.0198528i	0.00268546	+	0.000781098i
$647$		−	22.2507i		−	0.874767i	−0.899275	−	0.437383i	$-0.855905\pi$
$647$		−	22.2507i		−	0.874767i	0.899275	−	0.437383i	$-0.144095\pi$
$648$		0			0
$649$			2.26632i			0.0889607i
$650$	−11.8032	+	40.5800i	−0.462960	+	1.59168i
$651$		0			0
$652$	4.54409	+	20.3884i	0.177960	+	0.798470i
$653$	4.80129	−	4.80129i	0.187889	−	0.187889i	−0.606894	−	0.794783i	$-0.707585\pi$
$653$	4.80129	−	4.80129i	0.187889	−	0.187889i	0.794783	+	0.606894i	$0.207585\pi$
$654$		0			0
$655$	38.4165			1.50106
$656$	−33.2938	+	15.6166i	−1.29990	+	0.609724i
$657$		0			0
$658$	17.9042	−	9.83572i	0.697979	−	0.383436i
$659$	−24.9687	+	24.9687i	−0.972642	+	0.972642i	−0.999636	−	0.0269940i	$-0.991407\pi$
$659$	−24.9687	+	24.9687i	−0.972642	+	0.972642i	0.0269940	+	0.999636i	$0.491407\pi$
$660$		0			0
$661$	5.42481	+	5.42481i	0.211001	+	0.211001i	0.804692	−	0.593692i	$-0.202330\pi$
$661$	5.42481	+	5.42481i	0.211001	+	0.211001i	−0.593692	+	0.804692i	$0.702330\pi$
$662$	−2.44474	+	8.40515i	−0.0950176	+	0.326675i
$663$		0			0
$664$	−3.23754	+	2.84894i	−0.125641	+	0.110560i
$665$		−	1.92254i		−	0.0745528i
$666$		0			0
$667$	−11.8677	−	11.8677i	−0.459520	−	0.459520i
$668$	−6.82082	−	4.33455i	−0.263905	−	0.167709i
$669$		0			0
$670$	13.2082	+	24.0433i	0.510278	+	0.928872i
$671$	−57.4710			−2.21864
$672$		0			0
$673$	−28.3041			−1.09104			−0.545521	−	0.838097i	$-0.683668\pi$
$673$	−28.3041			−1.09104			−0.545521	+	0.838097i	$0.683668\pi$
$674$	−0.644808	−	1.17376i	−0.0248371	−	0.0452116i
$675$		0			0
$676$	36.0701	+	22.9221i	1.38731	+	0.881619i
$677$	4.48694	+	4.48694i	0.172447	+	0.172447i	0.788054	−	0.615607i	$-0.211089\pi$
$677$	4.48694	+	4.48694i	0.172447	+	0.172447i	−0.615607	+	0.788054i	$0.711089\pi$
$678$		0			0
$679$			11.1120i			0.426440i
$680$	1.94118	+	2.20597i	0.0744410	+	0.0845949i
$681$		0			0
$682$	8.65056	−	29.7411i	0.331247	−	1.13884i
$683$	11.5502	+	11.5502i	0.441955	+	0.441955i	0.892669	−	0.450713i	$-0.148830\pi$
$683$	11.5502	+	11.5502i	0.441955	+	0.441955i	−0.450713	+	0.892669i	$0.648830\pi$
$684$		0			0
$685$	−11.1598	+	11.1598i	−0.426394	+	0.426394i
$686$	7.25299	−	3.98445i	0.276921	−	0.152127i
$687$		0			0
$688$	10.4847	−	29.0096i	0.399725	−	1.10598i
$689$	21.5485			0.820933
$690$		0			0
$691$	−11.0962	+	11.0962i	−0.422118	+	0.422118i	−0.885932	−	0.463815i	$-0.846480\pi$
$691$	−11.0962	+	11.0962i	−0.422118	+	0.422118i	0.463815	+	0.885932i	$0.346480\pi$
$692$	4.12933	+	18.5274i	0.156974	+	0.704306i
$693$		0			0
$694$	9.67319	−	33.2569i	0.367189	−	1.26242i
$695$		−	9.44316i		−	0.358200i
$696$		0			0
$697$			3.00575i			0.113851i
$698$	−1.65666	−	0.481859i	−0.0627053	−	0.0182386i
$699$		0			0
$700$	21.5185	−	33.8614i	0.813322	−	1.27984i
$701$	−3.52654	+	3.52654i	−0.133196	+	0.133196i	−0.770561	−	0.637366i	$-0.780024\pi$
$701$	−3.52654	+	3.52654i	−0.133196	+	0.133196i	0.637366	+	0.770561i	$0.280024\pi$
$702$		0			0
$703$	−1.03585			−0.0390680
$704$	−24.0379	−	31.1086i	−0.905964	−	1.17245i
$705$		0			0
$706$	−13.1405	−	23.9201i	−0.494550	−	0.900243i
$707$	11.8253	−	11.8253i	0.444736	−	0.444736i
$708$		0			0
$709$	8.22384	+	8.22384i	0.308853	+	0.308853i	0.844464	−	0.535612i	$-0.179919\pi$
$709$	8.22384	+	8.22384i	0.308853	+	0.308853i	−0.535612	+	0.844464i	$0.679919\pi$
$710$	29.6958	+	8.63739i	1.11446	+	0.324155i
$711$		0			0
$712$	1.03992	−	16.2877i	0.0389725	−	0.610407i
$713$			19.1862i			0.718530i
$714$		0			0
$715$	−64.7330	−	64.7330i	−2.42088	−	2.42088i
$716$	2.14719	+	9.63399i	0.0802443	+	0.360039i
$717$		0			0
$718$	29.0371	−	15.9516i	1.08366	−	0.595308i
$719$	−37.5128			−1.39899			−0.699496	−	0.714637i	$-0.746592\pi$
$719$	−37.5128			−1.39899			−0.699496	+	0.714637i	$0.746592\pi$
$720$		0			0
$721$	29.2286			1.08853
$722$	−23.5211	+	12.9214i	−0.875365	+	0.480884i
$723$		0			0
$724$	48.1169	−	10.7241i	1.78825	−	0.398559i
$725$	−14.0524	−	14.0524i	−0.521894	−	0.521894i
$726$		0			0
$727$			52.5708i			1.94974i	0.222765	+	0.974872i	$0.428492\pi$
$727$			52.5708i			1.94974i	−0.222765	+	0.974872i	$0.571508\pi$
$728$	−43.1079	−	48.9880i	−1.59769	−	1.81561i
$729$		0			0
$730$	−13.5944	−	3.95410i	−0.503151	−	0.146348i
$731$	−1.78276	−	1.78276i	−0.0659379	−	0.0659379i
$732$		0			0
$733$	0.339705	−	0.339705i	0.0125473	−	0.0125473i	−0.700805	−	0.713353i	$-0.747176\pi$
$733$	0.339705	−	0.339705i	0.0125473	−	0.0125473i	0.713353	+	0.700805i	$0.247176\pi$
$734$	−1.04381	−	1.90007i	−0.0385276	−	0.0701328i
$735$		0			0
$736$	19.6794	+	14.3445i	0.725391	+	0.528744i
$737$	−29.9983			−1.10500
$738$		0			0
$739$	26.8772	−	26.8772i	0.988693	−	0.988693i	−0.0112434	−	0.999937i	$-0.503579\pi$
$739$	26.8772	−	26.8772i	0.988693	−	0.988693i	0.999937	+	0.0112434i	$0.00357897\pi$
$740$	−36.1400	−	22.9665i	−1.32853	−	0.844266i
$741$		0			0
$742$	−19.6426	−	5.71329i	−0.721102	−	0.209742i
$743$		−	14.2143i		−	0.521474i	−0.965410	−	0.260737i	$-0.916035\pi$
$743$		−	14.2143i		−	0.521474i	0.965410	−	0.260737i	$-0.0839655\pi$
$744$		0			0
$745$			35.0058i			1.28251i
$746$	8.24980	−	28.3632i	0.302047	−	1.03845i
$747$		0			0
$748$	−3.13635	+	0.699020i	−0.114676	+	0.0255587i
$749$	13.7332	−	13.7332i	0.501799	−	0.501799i
$750$		0			0
$751$	24.3087			0.887037			0.443519	−	0.896265i	$-0.353730\pi$
$751$	24.3087			0.887037			0.443519	+	0.896265i	$0.353730\pi$
$752$	6.23488	+	13.2925i	0.227363	+	0.484727i
$753$		0			0
$754$	−28.3296	+	15.5629i	−1.03170	+	0.566769i
$755$	6.73718	−	6.73718i	0.245191	−	0.245191i
$756$		0			0
$757$	−32.1423	−	32.1423i	−1.16823	−	1.16823i	−0.982624	−	0.185606i	$-0.940575\pi$
$757$	−32.1423	−	32.1423i	−1.16823	−	1.16823i	−0.185606	−	0.982624i	$-0.559425\pi$
$758$	10.5335	−	36.2148i	0.382594	−	1.31538i
$759$		0			0
$760$	1.37897	+	0.0880425i	0.0500204	+	0.00319364i
$761$			44.1704i			1.60117i	0.599216	+	0.800587i	$0.295479\pi$
$761$			44.1704i			1.60117i	−0.599216	+	0.800587i	$0.704521\pi$
$762$		0			0
$763$	−47.2190	−	47.2190i	−1.70944	−	1.70944i
$764$	−3.76180	+	5.91954i	−0.136097	+	0.214161i
$765$		0			0
$766$	−0.164635	−	0.299689i	−0.00594850	−	0.0108282i
$767$	−2.70363			−0.0976224
$768$		0			0
$769$	−31.4844			−1.13536			−0.567678	−	0.823251i	$-0.692158\pi$
$769$	−31.4844			−1.13536			−0.567678	+	0.823251i	$0.692158\pi$
$770$	41.8444	+	76.1706i	1.50797	+	2.74500i
$771$		0			0
$772$	11.2463	−	17.6972i	0.404765	−	0.636935i
$773$	20.6072	+	20.6072i	0.741188	+	0.741188i	0.972807	−	0.231619i	$-0.0744022\pi$
$773$	20.6072	+	20.6072i	0.741188	+	0.741188i	−0.231619	+	0.972807i	$0.574402\pi$
$774$		0			0
$775$			22.7182i			0.816062i
$776$	−7.97025	−	0.508874i	−0.286115	−	0.0182675i
$777$		0			0
$778$	−12.3491	+	42.4568i	−0.442736	+	1.52215i
$779$	0.999440	+	0.999440i	0.0358086	+	0.0358086i
$780$		0			0
$781$	−23.9138	+	23.9138i	−0.855703	+	0.855703i
$782$	1.74454	−	0.958364i	0.0623845	−	0.0342710i
$783$		0			0
$784$	14.4162	+	30.7347i	0.514864	+	1.09767i
$785$	61.0463			2.17884
$786$		0			0
$787$	17.9633	−	17.9633i	0.640321	−	0.640321i	−0.310313	−	0.950634i	$-0.600434\pi$
$787$	17.9633	−	17.9633i	0.640321	−	0.640321i	0.950634	+	0.310313i	$0.100434\pi$
$788$	14.5792	−	3.24936i	0.519361	−	0.115754i
$789$		0			0
$790$	12.8402	−	44.1452i	0.456833	−	1.57061i
$791$			11.0898i			0.394309i
$792$		0			0
$793$		−	68.5608i		−	2.43466i
$794$	−13.8659	−	4.03307i	−0.492083	−	0.143128i
$795$		0			0
$796$	16.7783	+	10.6624i	0.594692	+	0.377919i
$797$	−3.15069	+	3.15069i	−0.111603	+	0.111603i	−0.760703	−	0.649100i	$-0.775146\pi$
$797$	−3.15069	+	3.15069i	−0.111603	+	0.111603i	0.649100	+	0.760703i	$0.275146\pi$
$798$		0			0
$799$	1.20004			0.0424543
$800$	23.3021	+	16.9851i	0.823853	+	0.600514i
$801$		0			0
$802$	−24.4755	−	44.5534i	−0.864260	−	1.57324i
$803$	10.9475	−	10.9475i	0.386328	−	0.386328i
$804$		0			0
$805$	−38.0663	−	38.0663i	−1.34166	−	1.34166i
$806$	35.4800	+	10.3198i	1.24973	+	0.363499i
$807$		0			0
$808$	7.94032	+	9.02340i	0.279340	+	0.317442i
$809$		−	49.4194i		−	1.73749i	−0.495257	−	0.868746i	$-0.664926\pi$
$809$		−	49.4194i		−	1.73749i	0.495257	−	0.868746i	$-0.335074\pi$
$810$		0			0
$811$	−11.3643	−	11.3643i	−0.399054	−	0.399054i	0.478845	−	0.877899i	$-0.341056\pi$
$811$	−11.3643	−	11.3643i	−0.399054	−	0.399054i	−0.877899	+	0.478845i	$0.841056\pi$
$812$	29.9502	−	6.67521i	1.05105	−	0.234254i
$813$		0			0
$814$	41.0404	−	22.5456i	1.43846	−	0.790223i
$815$	33.1883			1.16254
$816$		0			0
$817$	−1.18557			−0.0414779
$818$	19.3133	−	10.6098i	0.675274	−	0.370963i
$819$		0			0
$820$	12.7104	+	57.0287i	0.443865	+	1.99153i
$821$	−10.7322	−	10.7322i	−0.374557	−	0.374557i	0.494577	−	0.869134i	$-0.335323\pi$
$821$	−10.7322	−	10.7322i	−0.374557	−	0.374557i	−0.869134	+	0.494577i	$0.835323\pi$
$822$		0			0
$823$		−	1.72914i		−	0.0602739i	−0.999546	−	0.0301370i	$-0.990406\pi$
$823$		−	1.72914i		−	0.0602739i	0.999546	−	0.0301370i	$-0.00959435\pi$
$824$	−1.33852	+	20.9646i	−0.0466297	+	0.730338i
$825$		0			0
$826$	2.46450	+	0.716830i	0.0857509	+	0.0249417i
$827$	−14.7644	−	14.7644i	−0.513410	−	0.513410i	0.402160	−	0.915570i	$-0.368260\pi$
$827$	−14.7644	−	14.7644i	−0.513410	−	0.513410i	−0.915570	+	0.402160i	$0.868260\pi$
$828$		0			0
$829$	−12.9876	+	12.9876i	−0.451080	+	0.451080i	−0.895713	−	0.444633i	$-0.853334\pi$
$829$	−12.9876	+	12.9876i	−0.451080	+	0.451080i	0.444633	+	0.895713i	$0.353334\pi$
$830$	3.29906	+	6.00537i	0.114512	+	0.208450i
$831$		0			0
$832$	37.1114	−	28.6764i	1.28661	−	0.994174i
$833$	2.77471			0.0961381
$834$		0			0
$835$	−9.07939	+	9.07939i	−0.314205	+	0.314205i
$836$	−0.810435	+	1.27530i	−0.0280295	+	0.0441071i
$837$		0			0
$838$	34.1636	+	9.93691i	1.18016	+	0.343265i
$839$			43.9697i			1.51800i	0.651089	+	0.759001i	$0.274312\pi$
$839$			43.9697i			1.51800i	−0.651089	+	0.759001i	$0.725688\pi$
$840$		0			0
$841$			13.8005i			0.475878i
$842$	9.58079	−	32.9393i	0.330176	−	1.13516i
$843$		0			0
$844$	−6.71960	−	30.1494i	−0.231298	−	1.03778i
$845$	48.0139	−	48.0139i	1.65173	−	1.65173i
$846$		0			0
$847$	−51.7479			−1.77808
$848$	4.99747	−	13.8273i	0.171614	−	0.474831i
$849$		0			0
$850$	2.06568	−	1.13479i	0.0708524	−	0.0389229i
$851$	−20.5099	+	20.5099i	−0.703072	+	0.703072i
$852$		0			0
$853$	14.7069	+	14.7069i	0.503553	+	0.503553i	0.912540	−	0.408987i	$-0.134118\pi$
$853$	14.7069	+	14.7069i	0.503553	+	0.503553i	−0.408987	+	0.912540i	$0.634118\pi$
$854$	−18.1779	+	62.4967i	−0.622037	+	2.13859i
$855$		0			0
$856$	9.22140	+	10.4792i	0.315181	+	0.358172i
$857$		−	12.0017i		−	0.409971i	−0.978765	−	0.204985i	$-0.934285\pi$
$857$		−	12.0017i		−	0.409971i	0.978765	−	0.204985i	$-0.0657147\pi$
$858$		0			0
$859$	12.8440	+	12.8440i	0.438231	+	0.438231i	0.891416	−	0.453185i	$-0.149712\pi$
$859$	12.8440	+	12.8440i	0.438231	+	0.438231i	−0.453185	+	0.891416i	$0.649712\pi$
$860$	−41.3635	−	26.2860i	−1.41048	−	0.896344i
$861$		0			0
$862$	24.5870	+	44.7565i	0.837438	+	1.52441i
$863$	26.2593			0.893877			0.446938	−	0.894565i	$-0.352514\pi$
$863$	26.2593			0.893877			0.446938	+	0.894565i	$0.352514\pi$
$864$		0			0
$865$	30.1590			1.02544
$866$	9.34265	+	17.0067i	0.317476	+	0.577910i
$867$		0			0
$868$	−29.6057	−	18.8141i	−1.00488	−	0.638591i
$869$	35.5498	+	35.5498i	1.20594	+	1.20594i
$870$		0			0
$871$		−	35.7869i		−	1.21259i
$872$	36.0309	−	31.7061i	1.22016	−	1.07370i
$873$		0			0
$874$	0.261410	−	0.898740i	0.00884231	−	0.0304003i
$875$	−0.861521	−	0.861521i	−0.0291247	−	0.0291247i
$876$		0			0
$877$	5.26743	−	5.26743i	0.177868	−	0.177868i	−0.612558	−	0.790426i	$-0.709859\pi$
$877$	5.26743	−	5.26743i	0.177868	−	0.177868i	0.790426	+	0.612558i	$0.209859\pi$
$878$	−34.9408	+	19.1948i	−1.17919	+	0.647793i
$879$		0			0
$880$	−56.5507	+	26.5253i	−1.90632	+	0.894167i
$881$	5.66368			0.190814			0.0954071	−	0.995438i	$-0.469585\pi$
$881$	5.66368			0.190814			0.0954071	+	0.995438i	$0.469585\pi$
$882$		0			0
$883$	−17.9671	+	17.9671i	−0.604640	+	0.604640i	−0.941540	−	0.336900i	$-0.890621\pi$
$883$	−17.9671	+	17.9671i	−0.604640	+	0.604640i	0.336900	+	0.941540i	$0.390621\pi$
$884$	−0.833905	−	3.74155i	−0.0280472	−	0.125842i
$885$		0			0
$886$	0.974457	−	3.35023i	0.0327375	−	0.112553i
$887$		−	38.0932i		−	1.27905i	−0.768772	−	0.639523i	$-0.779132\pi$
$887$		−	38.0932i		−	1.27905i	0.768772	−	0.639523i	$-0.220868\pi$
$888$		0			0
$889$		−	46.7193i		−	1.56691i
$890$	−24.8991	−	7.24221i	−0.834619	−	0.242759i
$891$		0			0
$892$	9.54099	−	15.0136i	0.319456	−	0.502694i
$893$	0.399024	−	0.399024i	0.0133528	−	0.0133528i
$894$		0			0
$895$	15.6823			0.524200
$896$	−41.4321	+	16.3004i	−1.38415	+	0.544559i
$897$		0			0
$898$	−0.765685	−	1.39380i	−0.0255512	−	0.0465116i
$899$	−12.2863	+	12.2863i	−0.409772	+	0.409772i
$900$		0			0
$901$	−0.849745	−	0.849745i	−0.0283091	−	0.0283091i
$902$	−61.3507	−	17.8446i	−2.04275	−	0.594160i
$903$		0			0
$904$	−7.95433	−	0.507858i	−0.264557	−	0.0168911i
$905$		−	78.3250i		−	2.60361i
$906$		0			0
$907$	−25.7306	−	25.7306i	−0.854372	−	0.854372i	0.136296	−	0.990668i	$-0.456480\pi$
$907$	−25.7306	−	25.7306i	−0.854372	−	0.854372i	−0.990668	+	0.136296i	$0.956480\pi$
$908$	−12.0537	−	54.0826i	−0.400018	−	1.79479i
$909$		0			0
$910$	−90.8687	+	49.9189i	−3.01227	+	1.65479i
$911$	2.17398			0.0720271			0.0360136	−	0.999351i	$-0.488534\pi$
$911$	2.17398			0.0720271			0.0360136	+	0.999351i	$0.488534\pi$
$912$		0			0
$913$	−7.49279			−0.247975
$914$	46.2311	−	25.3972i	1.52919	−	0.840063i
$915$		0			0
$916$	−24.5381	+	5.46897i	−0.810761	+	0.180700i
$917$	33.6419	+	33.6419i	1.11095	+	1.11095i
$918$		0			0
$919$		−	8.61338i		−	0.284129i	−0.989857	−	0.142065i	$-0.954626\pi$
$919$		−	8.61338i		−	0.284129i	0.989857	−	0.142065i	$-0.0453741\pi$
$920$	29.0468	−	25.5603i	0.957645	−	0.842699i
$921$		0			0
$922$	5.93857	+	1.72731i	0.195576	+	0.0568858i
$923$	−28.5283	−	28.5283i	−0.939019	−	0.939019i
$924$		0			0
$925$	−24.2856	+	24.2856i	−0.798505	+	0.798505i
$926$	−3.12277	−	5.68446i	−0.102621	−	0.186803i
$927$		0			0
$928$	3.41632	+	21.7879i	0.112146	+	0.715224i
$929$	−5.86822			−0.192530			−0.0962650	−	0.995356i	$-0.530690\pi$
$929$	−5.86822			−0.192530			−0.0962650	+	0.995356i	$0.530690\pi$
$930$		0			0
$931$	0.922618	−	0.922618i	0.0302376	−	0.0302376i
$932$	22.8185	+	14.5009i	0.747445	+	0.474992i
$933$		0			0
$934$	46.8704	+	13.6328i	1.53364	+	0.446080i
$935$			5.10537i			0.166963i
$936$		0			0
$937$			11.7635i			0.384296i	0.981366	+	0.192148i	$0.0615454\pi$
$937$			11.7635i			0.384296i	−0.981366	+	0.192148i	$0.938455\pi$
$938$	−9.48841	+	32.6216i	−0.309807	+	1.06513i
$939$		0			0
$940$	22.7686	−	5.07459i	0.742629	−	0.165515i
$941$	40.7052	−	40.7052i	1.32695	−	1.32695i	0.418934	−	0.908017i	$-0.362404\pi$
$941$	40.7052	−	40.7052i	1.32695	−	1.32695i	0.908017	−	0.418934i	$-0.137596\pi$
$942$		0			0
$943$	39.5779			1.28883
$944$	−0.627018	+	1.73487i	−0.0204077	+	0.0564652i
$945$		0			0
$946$	46.9721	−	25.8042i	1.52720	−	0.838967i
$947$	−6.21975	+	6.21975i	−0.202115	+	0.202115i	−0.800906	−	0.598791i	$-0.795648\pi$
$947$	−6.21975	+	6.21975i	−0.202115	+	0.202115i	0.598791	+	0.800906i	$0.295648\pi$
$948$		0			0
$949$	13.0599	+	13.0599i	0.423943	+	0.423943i
$950$	0.309532	−	1.06419i	0.0100425	−	0.0345268i
$951$		0			0
$952$	−0.231873	+	3.63172i	−0.00751505	+	0.117705i
$953$			39.5189i			1.28014i	0.768316	+	0.640071i	$0.221095\pi$
$953$			39.5189i			1.28014i	−0.768316	+	0.640071i	$0.778905\pi$
$954$		0			0
$955$	7.87967	+	7.87967i	0.254980	+	0.254980i
$956$	−6.21137	+	9.77418i	−0.200890	+	0.316120i
$957$		0			0
$958$	0.764638	+	1.39189i	0.0247043	+	0.0449700i
$959$	−19.5456			−0.631159
$960$		0			0
$961$	−11.1370			−0.359258
$962$	26.8961	+	48.9596i	0.867164	+	1.57852i
$963$		0			0
$964$	30.3627	−	47.7786i	0.977918	−	1.53885i
$965$	−23.5572	−	23.5572i	−0.758334	−	0.758334i
$966$		0			0
$967$			57.8455i			1.86018i	0.367326	+	0.930092i	$0.380273\pi$
$967$			57.8455i			1.86018i	−0.367326	+	0.930092i	$0.619727\pi$
$968$	2.36979	−	37.1169i	0.0761679	−	1.19298i
$969$		0			0
$970$	−3.54392	+	12.1842i	−0.113788	+	0.391210i
$971$	7.90060	+	7.90060i	0.253542	+	0.253542i	0.822421	−	0.568879i	$-0.192623\pi$
$971$	7.90060	+	7.90060i	0.253542	+	0.253542i	−0.568879	+	0.822421i	$0.692623\pi$
$972$		0			0
$973$	8.26951	−	8.26951i	0.265108	−	0.265108i
$974$	−24.2074	+	13.2984i	−0.775656	+	0.426108i
$975$		0			0
$976$	−43.9942	−	15.9004i	−1.40822	−	0.508960i
$977$	17.1759			0.549507			0.274753	−	0.961515i	$-0.411404\pi$
$977$	17.1759			0.549507			0.274753	+	0.961515i	$0.411404\pi$
$978$		0			0
$979$	20.0511	−	20.0511i	0.640835	−	0.640835i
$980$	52.6452	−	11.7334i	1.68169	−	0.374809i
$981$		0			0
$982$	−12.6314	+	43.4273i	−0.403083	+	1.38582i
$983$			22.1702i			0.707120i	0.935412	+	0.353560i	$0.115029\pi$
$983$			22.1702i			0.707120i	−0.935412	+	0.353560i	$0.884971\pi$
$984$		0			0
$985$		−	23.7321i		−	0.756166i
$986$	1.73086	+	0.503443i	0.0551219	+	0.0160329i
$987$		0			0
$988$	−1.52138	−	0.966819i	−0.0484016	−	0.0307586i
$989$	−23.4743	+	23.4743i	−0.746440	+	0.746440i
$990$		0			0
$991$	−7.23742			−0.229904			−0.114952	−	0.993371i	$-0.536671\pi$
$991$	−7.23742			−0.229904			−0.114952	+	0.993371i	$0.536671\pi$
$992$	14.8504	−	20.3735i	0.471502	−	0.646860i
$993$		0			0
$994$	18.4411	+	33.5689i	0.584917	+	1.06474i
$995$	22.3341	−	22.3341i	0.708039	−	0.708039i
$996$		0			0
$997$	−13.5321	−	13.5321i	−0.428566	−	0.428566i	0.459573	−	0.888140i	$-0.348002\pi$
$997$	−13.5321	−	13.5321i	−0.428566	−	0.428566i	−0.888140	+	0.459573i	$0.848002\pi$
$998$	−23.8323	−	6.93192i	−0.754399	−	0.219426i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.c.325.7	yes	24
3.2	odd	2	inner	432.2.k.c.325.6	yes	24
4.3	odd	2		1728.2.k.c.433.10		24
12.11	even	2		1728.2.k.c.433.3		24
16.3	odd	4		1728.2.k.c.1297.10		24
16.13	even	4	inner	432.2.k.c.109.7	yes	24
48.29	odd	4	inner	432.2.k.c.109.6	✓	24
48.35	even	4		1728.2.k.c.1297.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.c.109.6	✓	24	48.29	odd	4	inner
432.2.k.c.109.7	yes	24	16.13	even	4	inner
432.2.k.c.325.6	yes	24	3.2	odd	2	inner
432.2.k.c.325.7	yes	24	1.1	even	1	trivial
1728.2.k.c.433.3		24	12.11	even	2
1728.2.k.c.433.10		24	4.3	odd	2
1728.2.k.c.1297.3		24	48.35	even	4
1728.2.k.c.1297.10		24	16.3	odd	4

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.680919 + 1.23950i) q^{2} +(-1.07270 + 1.68799i) q^{4} +(2.24693 + 2.24693i) q^{5} +3.93534i q^{7} +(-2.82268 - 0.180219i) q^{8} +O(q^{10})\)	\(q+(0.680919 + 1.23950i) q^{2} +(-1.07270 + 1.68799i) q^{4} +(2.24693 + 2.24693i) q^{5} +3.93534i q^{7} +(-2.82268 - 0.180219i) q^{8} +(-1.25508 + 4.31505i) q^{10} +(-3.47488 - 3.47488i) q^{11} +(4.14540 - 4.14540i) q^{13} +(-4.87784 + 2.67965i) q^{14} +(-1.69864 - 3.62141i) q^{16} -0.326940 q^{17} +(-0.108711 + 0.108711i) q^{19} +(-6.20309 + 1.38253i) q^{20} +(1.94098 - 6.67320i) q^{22} +4.30494i q^{23} +5.09743i q^{25} +(7.96088 + 2.31552i) q^{26} +(-6.64283 - 4.22144i) q^{28} +(-2.75677 + 2.75677i) q^{29} +4.45679 q^{31} +(3.33209 - 4.57134i) q^{32} +(-0.222619 - 0.405240i) q^{34} +(-8.84246 + 8.84246i) q^{35} +(4.76428 + 4.76428i) q^{37} +(-0.208769 - 0.0607231i) q^{38} +(-5.93744 - 6.74732i) q^{40} -9.19359i q^{41} +(5.45288 + 5.45288i) q^{43} +(9.59306 - 2.13807i) q^{44} +(-5.33596 + 2.93132i) q^{46} -3.67052 q^{47} -8.48693 q^{49} +(-6.31824 + 3.47094i) q^{50} +(2.55064 + 11.4442i) q^{52} +(2.59909 + 2.59909i) q^{53} -15.6156i q^{55} +(0.709223 - 11.1082i) q^{56} +(-5.29414 - 1.53987i) q^{58} +(-0.326100 - 0.326100i) q^{59} +(8.26951 - 8.26951i) q^{61} +(3.03472 + 5.52418i) q^{62} +(7.93504 + 1.01740i) q^{64} +18.6289 q^{65} +(4.31646 - 4.31646i) q^{67} +(0.350708 - 0.551872i) q^{68} +(-16.9812 - 4.93919i) q^{70} -6.88192i q^{71} +3.15046i q^{73} +(-2.66121 + 9.14939i) q^{74} +(-0.0668889 - 0.300116i) q^{76} +(13.6748 - 13.6748i) q^{77} -10.2305 q^{79} +(4.32036 - 11.9538i) q^{80} +(11.3954 - 6.26009i) q^{82} +(1.07814 - 1.07814i) q^{83} +(-0.734612 - 0.734612i) q^{85} +(-3.04585 + 10.4718i) q^{86} +(9.18222 + 10.4347i) q^{88} +5.77030i q^{89} +(16.3136 + 16.3136i) q^{91} +(-7.26671 - 4.61790i) q^{92} +(-2.49933 - 4.54960i) q^{94} -0.488531 q^{95} +2.82365 q^{97} +(-5.77891 - 10.5195i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{4}+O(q^{10}) \) 24 * q + 16 * q^4	\( 24 q + 16 q^{4} - 4 q^{10} + 16 q^{13} - 20 q^{16} - 16 q^{19} - 12 q^{22} - 12 q^{28} + 32 q^{31} + 28 q^{34} - 8 q^{37} - 36 q^{40} - 64 q^{46} - 16 q^{49} - 36 q^{52} - 32 q^{58} - 16 q^{61} + 16 q^{64} + 48 q^{67} - 24 q^{70} + 16 q^{76} - 48 q^{79} - 16 q^{82} - 16 q^{85} - 60 q^{88} + 96 q^{91} + 84 q^{94} + 8 q^{97}+O(q^{100}) \) 24 * q + 16 * q^4 - 4 * q^10 + 16 * q^13 - 20 * q^16 - 16 * q^19 - 12 * q^22 - 12 * q^28 + 32 * q^31 + 28 * q^34 - 8 * q^37 - 36 * q^40 - 64 * q^46 - 16 * q^49 - 36 * q^52 - 32 * q^58 - 16 * q^61 + 16 * q^64 + 48 * q^67 - 24 * q^70 + 16 * q^76 - 48 * q^79 - 16 * q^82 - 16 * q^85 - 60 * q^88 + 96 * q^91 + 84 * q^94 + 8 * q^97

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