LMFDB - Embedded newform 432.2.l.b.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(107,432)]

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([2, 1, 2]))

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

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

chi := DirichletCharacter("432.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.l (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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.1
Character	$\chi$	$=$	432.323
Dual form			432.2.l.b.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41076 + 0.0987658i) q^{2} +(1.98049 - 0.278670i) q^{4} +(0.0308139 + 0.0308139i) q^{5} +2.10616 q^{7} +(-2.76648 + 0.588741i) q^{8} +O(q^{10})$	\(q+(-1.41076 + 0.0987658i) q^{2} +(1.98049 - 0.278670i) q^{4} +(0.0308139 + 0.0308139i) q^{5} +2.10616 q^{7} +(-2.76648 + 0.588741i) q^{8} +(-0.0465144 - 0.0404277i) q^{10} +(2.05680 - 2.05680i) q^{11} +(0.0744247 + 0.0744247i) q^{13} +(-2.97129 + 0.208017i) q^{14} +(3.84469 - 1.10381i) q^{16} +1.91418i q^{17} +(0.131716 - 0.131716i) q^{19} +(0.0696135 + 0.0524397i) q^{20} +(-2.69851 + 3.10480i) q^{22} +2.90032i q^{23} -4.99810i q^{25} +(-0.112346 - 0.0976449i) q^{26} +(4.17124 - 0.586924i) q^{28} +(6.63495 - 6.63495i) q^{29} +5.33291i q^{31} +(-5.31491 + 1.93693i) q^{32} +(-0.189056 - 2.70045i) q^{34} +(0.0648991 + 0.0648991i) q^{35} +(3.75340 - 3.75340i) q^{37} +(-0.172811 + 0.198829i) q^{38} +(-0.103387 - 0.0671045i) q^{40} +2.42313 q^{41} +(7.02341 + 7.02341i) q^{43} +(3.50031 - 4.64664i) q^{44} +(-0.286453 - 4.09166i) q^{46} +9.23178 q^{47} -2.56407 q^{49} +(0.493641 + 7.05112i) q^{50} +(0.168137 + 0.126658i) q^{52} +(5.34161 + 5.34161i) q^{53} +0.126756 q^{55} +(-5.82665 + 1.23999i) q^{56} +(-8.70502 + 10.0156i) q^{58} +(8.08106 - 8.08106i) q^{59} +(-9.29703 - 9.29703i) q^{61} +(-0.526709 - 7.52346i) q^{62} +(7.30677 - 3.25747i) q^{64} +0.00458663i q^{65} +(-6.10817 + 6.10817i) q^{67} +(0.533425 + 3.79102i) q^{68} +(-0.0979669 - 0.0851473i) q^{70} +8.70439i q^{71} -6.34509i q^{73} +(-4.92444 + 5.66585i) q^{74} +(0.224157 - 0.297568i) q^{76} +(4.33196 - 4.33196i) q^{77} +6.95551i q^{79} +(0.152482 + 0.0844572i) q^{80} +(-3.41846 + 0.239323i) q^{82} +(-8.86872 - 8.86872i) q^{83} +(-0.0589834 + 0.0589834i) q^{85} +(-10.6020 - 9.21468i) q^{86} +(-4.47917 + 6.90101i) q^{88} -17.3073 q^{89} +(0.156751 + 0.156751i) q^{91} +(0.808232 + 5.74406i) q^{92} +(-13.0238 + 0.911784i) q^{94} +0.00811737 q^{95} -8.51092 q^{97} +(3.61729 - 0.253243i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) $ 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.41076	+	0.0987658i	−0.997558	+	0.0698380i
$2$	−1.41076	+	0.0987658i	−0.997558	+	0.0698380i
$3$		0			0
$3$		0			0
$4$	1.98049	−	0.278670i	0.990245	−	0.139335i
$5$	0.0308139	+	0.0308139i	0.0137804	+	0.0137804i	0.713963	−	0.700183i	$-0.246898\pi$
$5$	0.0308139	+	0.0308139i	0.0137804	+	0.0137804i	−0.700183	+	0.713963i	$0.746898\pi$
$6$		0			0
$7$	2.10616			0.796055			0.398028	−	0.917373i	$-0.369695\pi$
$7$	2.10616			0.796055			0.398028	+	0.917373i	$0.369695\pi$
$8$	−2.76648	+	0.588741i	−0.978097	+	0.208151i
$9$		0			0
$10$	−0.0465144	−	0.0404277i	−0.0147091	−	0.0127844i
$11$	2.05680	−	2.05680i	0.620149	−	0.620149i	−0.325420	−	0.945569i	$-0.605506\pi$
$11$	2.05680	−	2.05680i	0.620149	−	0.620149i	0.945569	+	0.325420i	$0.105506\pi$
$12$		0			0
$13$	0.0744247	+	0.0744247i	0.0206417	+	0.0206417i	0.717352	−	0.696711i	$-0.245354\pi$
$13$	0.0744247	+	0.0744247i	0.0206417	+	0.0206417i	−0.696711	+	0.717352i	$0.745354\pi$
$14$	−2.97129	+	0.208017i	−0.794112	+	0.0555949i
$15$		0			0
$16$	3.84469	−	1.10381i	0.961172	−	0.275951i
$17$			1.91418i			0.464257i	0.972685	+	0.232129i	$0.0745691\pi$
$17$			1.91418i			0.464257i	−0.972685	+	0.232129i	$0.925431\pi$
$18$		0			0
$19$	0.131716	−	0.131716i	0.0302177	−	0.0302177i	−0.691836	−	0.722054i	$-0.743198\pi$
$19$	0.131716	−	0.131716i	0.0302177	−	0.0302177i	0.722054	+	0.691836i	$0.243198\pi$
$20$	0.0696135	+	0.0524397i	0.0155661	+	0.0117259i
$21$		0			0
$22$	−2.69851	+	3.10480i	−0.575325	+	0.661945i
$23$			2.90032i			0.604759i	0.953188	+	0.302380i	$0.0977810\pi$
$23$			2.90032i			0.604759i	−0.953188	+	0.302380i	$0.902219\pi$
$24$		0			0
$25$		−	4.99810i		−	0.999620i
$26$	−0.112346	−	0.0976449i	−0.0220329	−	0.0191497i
$27$		0			0
$28$	4.17124	−	0.586924i	0.788290	−	0.110918i
$29$	6.63495	−	6.63495i	1.23208	−	1.23208i	0.268916	−	0.963163i	$-0.413334\pi$
$29$	6.63495	−	6.63495i	1.23208	−	1.23208i	0.963163	−	0.268916i	$-0.0866656\pi$
$30$		0			0
$31$			5.33291i			0.957819i	0.877864	+	0.478910i	$0.158968\pi$
$31$			5.33291i			0.957819i	−0.877864	+	0.478910i	$0.841032\pi$
$32$	−5.31491	+	1.93693i	−0.939553	+	0.342404i
$33$		0			0
$34$	−0.189056	−	2.70045i	−0.0324228	−	0.463124i
$35$	0.0648991	+	0.0648991i	0.0109700	+	0.0109700i
$36$		0			0
$37$	3.75340	−	3.75340i	0.617055	−	0.617055i	−0.327720	−	0.944775i	$-0.606280\pi$
$37$	3.75340	−	3.75340i	0.617055	−	0.617055i	0.944775	+	0.327720i	$0.106280\pi$
$38$	−0.172811	+	0.198829i	−0.0280336	+	0.0322543i
$39$		0			0
$40$	−0.103387	−	0.0671045i	−0.0163470	−	0.0106101i
$41$	2.42313			0.378430			0.189215	−	0.981936i	$-0.439406\pi$
$41$	2.42313			0.378430			0.189215	+	0.981936i	$0.439406\pi$
$42$		0			0
$43$	7.02341	+	7.02341i	1.07106	+	1.07106i	0.997274	+	0.0737859i	$0.0235081\pi$
$43$	7.02341	+	7.02341i	1.07106	+	1.07106i	0.0737859	+	0.997274i	$0.476492\pi$
$44$	3.50031	−	4.64664i	0.527691	−	0.700508i
$45$		0			0
$46$	−0.286453	−	4.09166i	−0.0422351	−	0.603282i
$47$	9.23178			1.34659			0.673297	−	0.739372i	$-0.264878\pi$
$47$	9.23178			1.34659			0.673297	+	0.739372i	$0.264878\pi$
$48$		0			0
$49$	−2.56407			−0.366296
$50$	0.493641	+	7.05112i	0.0698114	+	0.997179i
$51$		0			0
$52$	0.168137	+	0.126658i	0.0233165	+	0.0175642i
$53$	5.34161	+	5.34161i	0.733726	+	0.733726i	0.971356	−	0.237630i	$-0.0763704\pi$
$53$	5.34161	+	5.34161i	0.733726	+	0.733726i	−0.237630	+	0.971356i	$0.576370\pi$
$54$		0			0
$55$	0.126756			0.0170918
$56$	−5.82665	+	1.23999i	−0.778619	+	0.165700i
$57$		0			0
$58$	−8.70502	+	10.0156i	−1.14303	+	1.31512i
$59$	8.08106	−	8.08106i	1.05206	−	1.05206i	0.0534959	−	0.998568i	$-0.482964\pi$
$59$	8.08106	−	8.08106i	1.05206	−	1.05206i	0.998568	−	0.0534959i	$-0.0170364\pi$
$60$		0			0
$61$	−9.29703	−	9.29703i	−1.19036	−	1.19036i	−0.976966	−	0.213397i	$-0.931547\pi$
$61$	−9.29703	−	9.29703i	−1.19036	−	1.19036i	−0.213397	−	0.976966i	$-0.568453\pi$
$62$	−0.526709	−	7.52346i	−0.0668921	−	0.955481i
$63$		0			0
$64$	7.30677	−	3.25747i	0.913346	−	0.407184i
$65$			0.00458663i			0.000568902i
$66$		0			0
$67$	−6.10817	+	6.10817i	−0.746231	+	0.746231i	−0.973769	−	0.227538i	$-0.926932\pi$
$67$	−6.10817	+	6.10817i	−0.746231	+	0.746231i	0.227538	+	0.973769i	$0.426932\pi$
$68$	0.533425	+	3.79102i	0.0646873	+	0.459729i
$69$		0			0
$70$	−0.0979669	−	0.0851473i	−0.0117093	−	0.0101771i
$71$			8.70439i			1.03302i	0.856281	+	0.516511i	$0.172769\pi$
$71$			8.70439i			1.03302i	−0.856281	+	0.516511i	$0.827231\pi$
$72$		0			0
$73$		−	6.34509i		−	0.742636i	−0.928506	−	0.371318i	$-0.878906\pi$
$73$		−	6.34509i		−	0.742636i	0.928506	−	0.371318i	$-0.121094\pi$
$74$	−4.92444	+	5.66585i	−0.572454	+	0.658642i
$75$		0			0
$76$	0.224157	−	0.297568i	0.0257126	−	0.0341334i
$77$	4.33196	−	4.33196i	0.493673	−	0.493673i
$78$		0			0
$79$			6.95551i			0.782556i	0.920272	+	0.391278i	$0.127967\pi$
$79$			6.95551i			0.782556i	−0.920272	+	0.391278i	$0.872033\pi$
$80$	0.152482	+	0.0844572i	0.0170480	+	0.00944260i
$81$		0			0
$82$	−3.41846	+	0.239323i	−0.377506	+	0.0264288i
$83$	−8.86872	−	8.86872i	−0.973469	−	0.973469i	0.0261884	−	0.999657i	$-0.491663\pi$
$83$	−8.86872	−	8.86872i	−0.973469	−	0.973469i	−0.999657	+	0.0261884i	$0.991663\pi$
$84$		0			0
$85$	−0.0589834	+	0.0589834i	−0.00639765	+	0.00639765i
$86$	−10.6020	−	9.21468i	−1.14325	−	0.993644i
$87$		0			0
$88$	−4.47917	+	6.90101i	−0.477481	+	0.735651i
$89$	−17.3073			−1.83457			−0.917287	−	0.398228i	$-0.869625\pi$
$89$	−17.3073			−1.83457			−0.917287	+	0.398228i	$0.869625\pi$
$90$		0			0
$91$	0.156751	+	0.156751i	0.0164319	+	0.0164319i
$92$	0.808232	+	5.74406i	0.0842640	+	0.598860i
$93$		0			0
$94$	−13.0238	+	0.911784i	−1.34331	+	0.0940434i
$95$	0.00811737			0.000832825
$96$		0			0
$97$	−8.51092			−0.864153			−0.432076	−	0.901837i	$-0.642219\pi$
$97$	−8.51092			−0.864153			−0.432076	+	0.901837i	$0.642219\pi$
$98$	3.61729	−	0.253243i	0.365402	−	0.0255814i
$99$		0			0
$100$	−1.39282	−	9.89869i	−0.139282	−	0.989869i
$101$	5.17522	+	5.17522i	0.514954	+	0.514954i	0.916040	−	0.401086i	$-0.131367\pi$
$101$	5.17522	+	5.17522i	0.514954	+	0.514954i	−0.401086	+	0.916040i	$0.631367\pi$
$102$		0			0
$103$	−9.15061			−0.901636			−0.450818	−	0.892616i	$-0.648868\pi$
$103$	−9.15061			−0.901636			−0.450818	+	0.892616i	$0.648868\pi$
$104$	−0.249711	−	0.162077i	−0.0244862	−	0.0158930i
$105$		0			0
$106$	−8.06330	−	7.00816i	−0.783177	−	0.680693i
$107$	−9.24890	+	9.24890i	−0.894125	+	0.894125i	−0.994908	−	0.100783i	$-0.967865\pi$
$107$	−9.24890	+	9.24890i	−0.894125	+	0.894125i	0.100783	+	0.994908i	$0.467865\pi$
$108$		0			0
$109$	−1.49292	−	1.49292i	−0.142995	−	0.142995i	0.631985	−	0.774981i	$-0.282240\pi$
$109$	−1.49292	−	1.49292i	−0.142995	−	0.142995i	−0.774981	+	0.631985i	$0.782240\pi$
$110$	−0.178823	+	0.0125192i	−0.0170501	+	0.00119366i
$111$		0			0
$112$	8.09754	−	2.32480i	0.765146	−	0.219673i
$113$			0.884042i			0.0831637i	0.999135	+	0.0415818i	$0.0132397\pi$
$113$			0.884042i			0.0831637i	−0.999135	+	0.0415818i	$0.986760\pi$
$114$		0			0
$115$	−0.0893702	+	0.0893702i	−0.00833382	+	0.00833382i
$116$	11.2915	−	14.9894i	1.04839	−	1.39173i
$117$		0			0
$118$	−10.6023	+	12.1986i	−0.976021	+	1.12297i
$119$			4.03158i			0.369575i
$120$		0			0
$121$			2.53913i			0.230830i
$122$	14.0341	+	12.1977i	1.27059	+	1.10432i
$123$		0			0
$124$	1.48612	+	10.5618i	0.133458	+	0.948476i
$125$	0.308080	−	0.308080i	0.0275556	−	0.0275556i
$126$		0			0
$127$			4.56069i			0.404696i	0.979314	+	0.202348i	$0.0648572\pi$
$127$			4.56069i			0.404696i	−0.979314	+	0.202348i	$0.935143\pi$
$128$	−9.98637	+	5.31718i	−0.882679	+	0.469976i
$129$		0			0
$130$	−0.000453002	−	0.00647064i	−3.97309e−5	−	0.000567513i
$131$	−11.0544	−	11.0544i	−0.965827	−	0.965827i	0.0336081	−	0.999435i	$-0.489300\pi$
$131$	−11.0544	−	11.0544i	−0.965827	−	0.965827i	−0.999435	+	0.0336081i	$0.989300\pi$
$132$		0			0
$133$	0.277416	−	0.277416i	0.0240550	−	0.0240550i
$134$	8.01388	−	9.22044i	0.692294	−	0.796525i
$135$		0			0
$136$	−1.12696	−	5.29554i	−0.0966358	−	0.454089i
$137$	−18.9150			−1.61602			−0.808009	−	0.589170i	$-0.799455\pi$
$137$	−18.9150			−1.61602			−0.808009	+	0.589170i	$0.799455\pi$
$138$		0			0
$139$	−2.78849	−	2.78849i	−0.236516	−	0.236516i	0.578890	−	0.815406i	$-0.303486\pi$
$139$	−2.78849	−	2.78849i	−0.236516	−	0.236516i	−0.815406	+	0.578890i	$0.803486\pi$
$140$	0.146618	+	0.110447i	0.0123914	+	0.00933445i
$141$		0			0
$142$	−0.859696	−	12.2798i	−0.0721441	−	1.03050i
$143$	0.306154			0.0256019
$144$		0			0
$145$	0.408898			0.0339571
$146$	0.626677	+	8.95140i	0.0518642	+	0.740823i
$147$		0			0
$148$	6.38761	−	8.47953i	0.525058	−	0.697013i
$149$	−6.26182	−	6.26182i	−0.512988	−	0.512988i	0.402453	−	0.915441i	$-0.368158\pi$
$149$	−6.26182	−	6.26182i	−0.512988	−	0.512988i	−0.915441	+	0.402453i	$0.868158\pi$
$150$		0			0
$151$	16.8846			1.37405			0.687025	−	0.726634i	$-0.258916\pi$
$151$	16.8846			1.37405			0.687025	+	0.726634i	$0.258916\pi$
$152$	−0.286843	+	0.441936i	−0.0232660	+	0.0358457i
$153$		0			0
$154$	−5.68351	+	6.53921i	−0.457990	+	0.526945i
$155$	−0.164328	+	0.164328i	−0.0131991	+	0.0131991i
$156$		0			0
$157$	3.81853	+	3.81853i	0.304752	+	0.304752i	0.842870	−	0.538118i	$-0.180864\pi$
$157$	3.81853	+	3.81853i	0.304752	+	0.304752i	−0.538118	+	0.842870i	$0.680864\pi$
$158$	−0.686967	−	9.81256i	−0.0546521	−	0.780646i
$159$		0			0
$160$	−0.223458	−	0.104089i	−0.0176659	−	0.00822895i
$161$			6.10856i			0.481422i
$162$		0			0
$163$	−3.17616	+	3.17616i	−0.248776	+	0.248776i	−0.820468	−	0.571692i	$-0.806287\pi$
$163$	−3.17616	+	3.17616i	−0.248776	+	0.248776i	0.571692	+	0.820468i	$0.306287\pi$
$164$	4.79900	−	0.675254i	0.374739	−	0.0527285i
$165$		0			0
$166$	13.3876	+	11.6357i	1.03908	+	0.903107i
$167$			23.6279i			1.82839i	0.405279	+	0.914193i	$0.367174\pi$
$167$			23.6279i			1.82839i	−0.405279	+	0.914193i	$0.632826\pi$
$168$		0			0
$169$		−	12.9889i		−	0.999148i
$170$	0.0773859	−	0.0890370i	0.00593523	−	0.00682883i
$171$		0			0
$172$	15.8670	+	11.9526i	1.20985	+	0.911376i
$173$	7.41133	−	7.41133i	0.563473	−	0.563473i	−0.366819	−	0.930292i	$-0.619553\pi$
$173$	7.41133	−	7.41133i	0.563473	−	0.563473i	0.930292	+	0.366819i	$0.119553\pi$
$174$		0			0
$175$		−	10.5268i		−	0.795753i
$176$	5.63745	−	10.1781i	0.424939	−	0.767201i
$177$		0			0
$178$	24.4165	−	1.70937i	1.83009	−	0.128123i
$179$	−7.02123	−	7.02123i	−0.524792	−	0.524792i	0.394223	−	0.919015i	$-0.371014\pi$
$179$	−7.02123	−	7.02123i	−0.524792	−	0.524792i	−0.919015	+	0.394223i	$0.871014\pi$
$180$		0			0
$181$	−4.82455	+	4.82455i	−0.358606	+	0.358606i	−0.863299	−	0.504693i	$-0.831606\pi$
$181$	−4.82455	+	4.82455i	−0.358606	+	0.358606i	0.504693	+	0.863299i	$0.331606\pi$
$182$	−0.236619	−	0.205656i	−0.0175394	−	0.0152442i
$183$		0			0
$184$	−1.70754	−	8.02367i	−0.125881	−	0.591513i
$185$	0.231314			0.0170065
$186$		0			0
$187$	3.93709	+	3.93709i	0.287909	+	0.287909i
$188$	18.2835	−	2.57262i	1.33346	−	0.187628i
$189$		0			0
$190$	−0.0114517		0.000801719i	−0.000830791		5.81628e-5i
$191$	−4.29118			−0.310499			−0.155249	−	0.987875i	$-0.549618\pi$
$191$	−4.29118			−0.310499			−0.155249	+	0.987875i	$0.549618\pi$
$192$		0			0
$193$	23.6296			1.70090			0.850448	−	0.526058i	$-0.176331\pi$
$193$	23.6296			1.70090			0.850448	+	0.526058i	$0.176331\pi$
$194$	12.0069	−	0.840587i	0.862043	−	0.0603507i
$195$		0			0
$196$	−5.07812	+	0.714529i	−0.362723	+	0.0510378i
$197$	8.58568	+	8.58568i	0.611705	+	0.611705i	0.943390	−	0.331685i	$-0.107617\pi$
$197$	8.58568	+	8.58568i	0.611705	+	0.611705i	−0.331685	+	0.943390i	$0.607617\pi$
$198$		0			0
$199$	−2.66685			−0.189048			−0.0945241	−	0.995523i	$-0.530133\pi$
$199$	−2.66685			−0.189048			−0.0945241	+	0.995523i	$0.530133\pi$
$200$	2.94259	+	13.8271i	0.208072	+	0.977725i
$201$		0			0
$202$	−7.81213	−	6.78986i	−0.549660	−	0.477733i
$203$	13.9743	−	13.9743i	0.980804	−	0.980804i
$204$		0			0
$205$	0.0746662	+	0.0746662i	0.00521491	+	0.00521491i
$206$	12.9093	−	0.903767i	0.899435	−	0.0629684i
$207$		0			0
$208$	0.368290	+	0.203989i	0.0255363	+	0.0141441i
$209$		−	0.541828i		−	0.0374790i
$210$		0			0
$211$	8.32429	−	8.32429i	0.573068	−	0.573068i	−0.359917	−	0.932985i	$-0.617195\pi$
$211$	8.32429	−	8.32429i	0.573068	−	0.573068i	0.932985	+	0.359917i	$0.117195\pi$
$212$	12.0675	+	9.09046i	0.828803	+	0.624335i
$213$		0			0
$214$	12.1345	−	13.9615i	0.829498	−	0.954386i
$215$			0.432837i			0.0295193i
$216$		0			0
$217$			11.2320i			0.762477i
$218$	2.25360	+	1.95870i	0.152633	+	0.132660i
$219$		0			0
$220$	0.251039	−	0.0353231i	0.0169251	−	0.00238148i
$221$	−0.142463	+	0.142463i	−0.00958307	+	0.00958307i
$222$		0			0
$223$			13.9106i			0.931522i	0.884911	+	0.465761i	$0.154219\pi$
$223$			13.9106i			0.931522i	−0.884911	+	0.465761i	$0.845781\pi$
$224$	−11.1941	+	4.07949i	−0.747936	+	0.272572i
$225$		0			0
$226$	−0.0873131	−	1.24717i	−0.00580798	−	0.0829606i
$227$	2.28603	+	2.28603i	0.151729	+	0.151729i	0.778890	−	0.627161i	$-0.215783\pi$
$227$	2.28603	+	2.28603i	0.151729	+	0.151729i	−0.627161	+	0.778890i	$0.715783\pi$
$228$		0			0
$229$	9.26006	−	9.26006i	0.611922	−	0.611922i	−0.331525	−	0.943447i	$-0.607563\pi$
$229$	9.26006	−	9.26006i	0.611922	−	0.611922i	0.943447	+	0.331525i	$0.107563\pi$
$230$	0.117253	−	0.134907i	0.00773145	−	0.00889549i
$231$		0			0
$232$	−14.4492	+	22.2617i	−0.948634	+	1.46155i
$233$	−24.4667			−1.60286			−0.801432	−	0.598086i	$-0.795928\pi$
$233$	−24.4667			−1.60286			−0.801432	+	0.598086i	$0.795928\pi$
$234$		0			0
$235$	0.284467	+	0.284467i	0.0185566	+	0.0185566i
$236$	13.7525	−	18.2564i	0.895212	−	1.18839i
$237$		0			0
$238$	−0.398182	−	5.68760i	−0.0258103	−	0.368672i
$239$	−11.5010			−0.743941			−0.371970	−	0.928245i	$-0.621318\pi$
$239$	−11.5010			−0.743941			−0.371970	+	0.928245i	$0.621318\pi$
$240$		0			0
$241$	−19.9860			−1.28741			−0.643705	−	0.765274i	$-0.722604\pi$
$241$	−19.9860			−1.28741			−0.643705	+	0.765274i	$0.722604\pi$
$242$	−0.250780	−	3.58211i	−0.0161207	−	0.230267i
$243$		0			0
$244$	−21.0035	−	15.8219i	−1.34461	−	1.01289i
$245$	−0.0790091	−	0.0790091i	−0.00504770	−	0.00504770i
$246$		0			0
$247$	0.0196059			0.00124749
$248$	−3.13970	−	14.7534i	−0.199371	−	0.936840i
$249$		0			0
$250$	−0.404200	+	0.465056i	−0.0255638	+	0.0294127i
$251$	−6.46279	+	6.46279i	−0.407928	+	0.407928i	−0.881015	−	0.473087i	$-0.843139\pi$
$251$	−6.46279	+	6.46279i	−0.407928	+	0.407928i	0.473087	+	0.881015i	$0.343139\pi$
$252$		0			0
$253$	5.96539	+	5.96539i	0.375041	+	0.375041i
$254$	−0.450440	−	6.43404i	−0.0282631	−	0.403708i
$255$		0			0
$256$	13.5632	−	8.48757i	0.847702	−	0.530473i
$257$			22.7997i			1.42221i	0.703087	+	0.711104i	$0.251804\pi$
$257$			22.7997i			1.42221i	−0.703087	+	0.711104i	$0.748196\pi$
$258$		0			0
$259$	7.90527	−	7.90527i	0.491210	−	0.491210i
$260$	0.00127816	+	0.00908378i	7.92679e−5	+	0.000563352i
$261$		0			0
$262$	16.6869	+	14.5033i	1.03092	+	0.896017i
$263$		−	4.81857i		−	0.297126i	−0.988903	−	0.148563i	$-0.952535\pi$
$263$		−	4.81857i		−	0.297126i	0.988903	−	0.148563i	$-0.0474647\pi$
$264$		0			0
$265$			0.329192i			0.0202221i
$266$	−0.363968	+	0.418766i	−0.0223163	+	0.0256762i
$267$		0			0
$268$	−10.3950	+	13.7993i	−0.634976	+	0.842928i
$269$	5.96497	−	5.96497i	0.363691	−	0.363691i	−0.501479	−	0.865170i	$-0.667211\pi$
$269$	5.96497	−	5.96497i	0.363691	−	0.363691i	0.865170	+	0.501479i	$0.167211\pi$
$270$		0			0
$271$		−	15.6430i		−	0.950242i	−0.879920	−	0.475121i	$-0.842404\pi$
$271$		−	15.6430i		−	0.950242i	0.879920	−	0.475121i	$-0.157596\pi$
$272$	2.11289	+	7.35943i	0.128112	+	0.446231i
$273$		0			0
$274$	26.6845	−	1.86816i	1.61207	−	0.112859i
$275$	−10.2801	−	10.2801i	−0.619913	−	0.619913i
$276$		0			0
$277$	−2.96248	+	2.96248i	−0.177998	+	0.177998i	−0.790483	−	0.612485i	$-0.790170\pi$
$277$	−2.96248	+	2.96248i	−0.177998	+	0.177998i	0.612485	+	0.790483i	$0.290170\pi$
$278$	4.20929	+	3.65848i	0.252457	+	0.219421i
$279$		0			0
$280$	−0.217751	−	0.141333i	−0.0130131	−	0.00844626i
$281$	−0.848328			−0.0506070			−0.0253035	−	0.999680i	$-0.508055\pi$
$281$	−0.848328			−0.0506070			−0.0253035	+	0.999680i	$0.508055\pi$
$282$		0			0
$283$	−10.2802	−	10.2802i	−0.611093	−	0.611093i	0.332138	−	0.943231i	$-0.392230\pi$
$283$	−10.2802	−	10.2802i	−0.611093	−	0.611093i	−0.943231	+	0.332138i	$0.892230\pi$
$284$	2.42565	+	17.2390i	0.143936	+	1.02294i
$285$		0			0
$286$	−0.431910	+	0.0302375i	−0.0255394	+	0.00178798i
$287$	5.10352			0.301251
$288$		0			0
$289$	13.3359			0.784465
$290$	−0.576857	+	0.0403851i	−0.0338742	+	0.00237149i
$291$		0			0
$292$	−1.76818	−	12.5664i	−0.103475	−	0.735392i
$293$	−21.0142	−	21.0142i	−1.22766	−	1.22766i	−0.964847	−	0.262813i	$-0.915350\pi$
$293$	−21.0142	−	21.0142i	−1.22766	−	1.22766i	−0.262813	−	0.964847i	$-0.584650\pi$
$294$		0			0
$295$	0.498018			0.0289957
$296$	−8.17390	+	12.5935i	−0.475098	+	0.731980i
$297$		0			0
$298$	9.45238	+	8.21547i	0.547562	+	0.475910i
$299$	−0.215856	+	0.215856i	−0.0124833	+	0.0124833i
$300$		0			0
$301$	14.7925	+	14.7925i	0.852623	+	0.852623i
$302$	−23.8201	+	1.66762i	−1.37070	+	0.0959609i
$303$		0			0
$304$	0.361018	−	0.651796i	0.0207058	−	0.0373831i
$305$		−	0.572955i		−	0.0328073i
$306$		0			0
$307$	−1.15465	+	1.15465i	−0.0658995	+	0.0658995i	−0.739288	−	0.673389i	$-0.764838\pi$
$307$	−1.15465	+	1.15465i	−0.0658995	+	0.0658995i	0.673389	+	0.739288i	$0.264838\pi$
$308$	7.37222	−	9.78660i	0.420071	−	0.557643i
$309$		0			0
$310$	0.215597	−	0.248057i	0.0122451	−	0.0140887i
$311$			26.9469i			1.52802i	0.645204	+	0.764010i	$0.276772\pi$
$311$			26.9469i			1.52802i	−0.645204	+	0.764010i	$0.723228\pi$
$312$		0			0
$313$			28.3493i			1.60240i	0.598398	+	0.801199i	$0.295804\pi$
$313$			28.3493i			1.60240i	−0.598398	+	0.801199i	$0.704196\pi$
$314$	−5.76418	−	5.00990i	−0.325291	−	0.282725i
$315$		0			0
$316$	1.93829	+	13.7753i	0.109037	+	0.774923i
$317$	−1.68264	+	1.68264i	−0.0945063	+	0.0945063i	−0.752779	−	0.658273i	$-0.771287\pi$
$317$	−1.68264	+	1.68264i	−0.0945063	+	0.0945063i	0.658273	+	0.752779i	$0.271287\pi$
$318$		0			0
$319$		−	27.2936i		−	1.52815i
$320$	0.325525	+	0.124774i	0.0181974	+	0.00697511i
$321$		0			0
$322$	−0.603316	−	8.61771i	−0.0336215	−	0.480246i
$323$	0.252129	+	0.252129i	0.0140288	+	0.0140288i
$324$		0			0
$325$	0.371982	−	0.371982i	0.0206339	−	0.0206339i
$326$	4.16711	−	4.79450i	0.230795	−	0.265543i
$327$		0			0
$328$	−6.70354	+	1.42660i	−0.370141	+	0.0787707i
$329$	19.4436			1.07196
$330$		0			0
$331$	7.67191	+	7.67191i	0.421686	+	0.421686i	0.885784	−	0.464098i	$-0.153621\pi$
$331$	7.67191	+	7.67191i	0.421686	+	0.421686i	−0.464098	+	0.885784i	$0.653621\pi$
$332$	−20.0359	−	15.0930i	−1.09961	−	0.828335i
$333$		0			0
$334$	−2.33363	−	33.3334i	−0.127691	−	1.82392i
$335$	−0.376433			−0.0205667
$336$		0			0
$337$	−0.100240			−0.00546042			−0.00273021	−	0.999996i	$-0.500869\pi$
$337$	−0.100240			−0.00546042			−0.00273021	+	0.999996i	$0.500869\pi$
$338$	1.28286	+	18.3243i	0.0697784	+	0.996708i
$339$		0			0
$340$	−0.100379	+	0.133253i	−0.00544383	+	0.00722666i
$341$	10.9687	+	10.9687i	0.593991	+	0.593991i
$342$		0			0
$343$	−20.1435			−1.08765
$344$	−23.5651	−	15.2951i	−1.27054	−	0.824658i
$345$		0			0
$346$	−9.72363	+	11.1876i	−0.522746	+	0.601449i
$347$	7.60868	−	7.60868i	0.408455	−	0.408455i	−0.472744	−	0.881200i	$-0.656737\pi$
$347$	7.60868	−	7.60868i	0.408455	−	0.408455i	0.881200	+	0.472744i	$0.156737\pi$
$348$		0			0
$349$	−14.8930	−	14.8930i	−0.797203	−	0.797203i	0.185451	−	0.982654i	$-0.440625\pi$
$349$	−14.8930	−	14.8930i	−0.797203	−	0.797203i	−0.982654	+	0.185451i	$0.940625\pi$
$350$	1.03969	+	14.8508i	0.0555738	+	0.793810i
$351$		0			0
$352$	−6.94784	+	14.9156i	−0.370321	+	0.795004i
$353$		−	23.0134i		−	1.22488i	−0.790518	−	0.612439i	$-0.790189\pi$
$353$		−	23.0134i		−	1.22488i	0.790518	−	0.612439i	$-0.209811\pi$
$354$		0			0
$355$	−0.268216	+	0.268216i	−0.0142354	+	0.0142354i
$356$	−34.2770	+	4.82303i	−1.81668	+	0.255620i
$357$		0			0
$358$	10.5987	+	9.21182i	0.560161	+	0.486860i
$359$		−	18.8225i		−	0.993412i	−0.867919	−	0.496706i	$-0.834543\pi$
$359$		−	18.8225i		−	0.993412i	0.867919	−	0.496706i	$-0.165457\pi$
$360$		0			0
$361$			18.9653i			0.998174i
$362$	6.32979	−	7.28279i	0.332686	−	0.382775i
$363$		0			0
$364$	0.354125	+	0.266762i	0.0185612	+	0.0139821i
$365$	0.195517	−	0.195517i	0.0102338	−	0.0102338i
$366$		0			0
$367$		−	13.9567i		−	0.728532i	−0.931295	−	0.364266i	$-0.881320\pi$
$367$		−	13.9567i		−	0.728532i	0.931295	−	0.364266i	$-0.118680\pi$
$368$	3.20139	+	11.1508i	0.166884	+	0.581277i
$369$		0			0
$370$	−0.326328	+	0.0228459i	−0.0169650	+	0.00118770i
$371$	11.2503	+	11.2503i	0.584087	+	0.584087i
$372$		0			0
$373$	−13.6909	+	13.6909i	−0.708889	+	0.708889i	−0.966302	−	0.257413i	$-0.917130\pi$
$373$	−13.6909	+	13.6909i	−0.708889	+	0.708889i	0.257413	+	0.966302i	$0.417130\pi$
$374$	−5.94315	−	5.16545i	−0.307313	−	0.267099i
$375$		0			0
$376$	−25.5395	+	5.43513i	−1.31710	+	0.280295i
$377$	0.987609			0.0508645
$378$		0			0
$379$	−23.3116	−	23.3116i	−1.19743	−	1.19743i	−0.974932	−	0.222503i	$-0.928577\pi$
$379$	−23.3116	−	23.3116i	−1.19743	−	1.19743i	−0.222503	−	0.974932i	$-0.571423\pi$
$380$	0.0160764	−	0.00226207i	0.000824701	−	0.000116042i
$381$		0			0
$382$	6.05383	−	0.423822i	0.309741	−	0.0216846i
$383$	3.01708			0.154166			0.0770828	−	0.997025i	$-0.475439\pi$
$383$	3.01708			0.154166			0.0770828	+	0.997025i	$0.475439\pi$
$384$		0			0
$385$	0.266969			0.0136060
$386$	−33.3357	+	2.33380i	−1.69674	+	0.118787i
$387$		0			0
$388$	−16.8558	+	2.37174i	−0.855723	+	0.120407i
$389$	19.0490	+	19.0490i	0.965823	+	0.965823i	0.999435	−	0.0336122i	$-0.0107011\pi$
$389$	19.0490	+	19.0490i	0.965823	+	0.965823i	−0.0336122	+	0.999435i	$0.510701\pi$
$390$		0			0
$391$	−5.55175			−0.280764
$392$	7.09344	−	1.50957i	0.358273	−	0.0762450i
$393$		0			0
$394$	−12.9603	−	11.2644i	−0.652931	−	0.567491i
$395$	−0.214326	+	0.214326i	−0.0107839	+	0.0107839i
$396$		0			0
$397$	21.2871	+	21.2871i	1.06837	+	1.06837i	0.997485	+	0.0708831i	$0.0225817\pi$
$397$	21.2871	+	21.2871i	1.06837	+	1.06837i	0.0708831	+	0.997485i	$0.477418\pi$
$398$	3.76229	−	0.263394i	0.188587	−	0.0132027i
$399$		0			0
$400$	−5.51693	−	19.2161i	−0.275847	−	0.960807i
$401$			9.00579i			0.449728i	0.974390	+	0.224864i	$0.0721937\pi$
$401$			9.00579i			0.449728i	−0.974390	+	0.224864i	$0.927806\pi$
$402$		0			0
$403$	−0.396901	+	0.396901i	−0.0197710	+	0.0197710i
$404$	11.6917	+	8.80730i	0.581682	+	0.438180i
$405$		0			0
$406$	−18.3342	+	21.0946i	−0.909912	+	1.04691i
$407$		−	15.4400i		−	0.765332i
$408$		0			0
$409$			10.9855i			0.543200i	0.962410	+	0.271600i	$0.0875528\pi$
$409$			10.9855i			0.543200i	−0.962410	+	0.271600i	$0.912447\pi$
$410$	−0.112711	−	0.0979617i	−0.00556638	−	0.00483798i
$411$		0			0
$412$	−18.1227	+	2.55000i	−0.892841	+	0.125629i
$413$	17.0200	−	17.0200i	0.837501	−	0.837501i
$414$		0			0
$415$		−	0.546560i		−	0.0268296i
$416$	−0.539717	−	0.251406i	−0.0264618	−	0.0123262i
$417$		0			0
$418$	0.0535140	+	0.764389i	0.00261746	+	0.0373875i
$419$	3.26249	+	3.26249i	0.159383	+	0.159383i	0.782293	−	0.622910i	$-0.214050\pi$
$419$	3.26249	+	3.26249i	0.159383	+	0.159383i	−0.622910	+	0.782293i	$0.714050\pi$
$420$		0			0
$421$	−16.2146	+	16.2146i	−0.790251	+	0.790251i	−0.981535	−	0.191284i	$-0.938735\pi$
$421$	−16.2146	+	16.2146i	−0.790251	+	0.790251i	0.191284	+	0.981535i	$0.438735\pi$
$422$	−10.9214	+	12.5657i	−0.531647	+	0.611691i
$423$		0			0
$424$	−17.9222	−	11.6326i	−0.870381	−	0.564929i
$425$	9.56728			0.464081
$426$		0			0
$427$	−19.5811	−	19.5811i	−0.947594	−	0.947594i
$428$	−15.7400	+	20.8948i	−0.760821	+	1.00999i
$429$		0			0
$430$	−0.0427495	−	0.610630i	−0.00206156	−	0.0294472i
$431$	28.9348			1.39374			0.696869	−	0.717198i	$-0.254576\pi$
$431$	28.9348			1.39374			0.696869	+	0.717198i	$0.254576\pi$
$432$		0			0
$433$	−16.4156			−0.788884			−0.394442	−	0.918921i	$-0.629062\pi$
$433$	−16.4156			−0.788884			−0.394442	+	0.918921i	$0.629062\pi$
$434$	−1.10934	−	15.8456i	−0.0532498	−	0.760615i
$435$		0			0
$436$	−3.37274	−	2.54067i	−0.161525	−	0.121676i
$437$	0.382019	+	0.382019i	0.0182745	+	0.0182745i
$438$		0			0
$439$	−1.99348			−0.0951434			−0.0475717	−	0.998868i	$-0.515148\pi$
$439$	−1.99348			−0.0951434			−0.0475717	+	0.998868i	$0.515148\pi$
$440$	−0.350668	+	0.0746265i	−0.0167174	+	0.00355768i
$441$		0			0
$442$	0.186910	−	0.215051i	0.00889041	−	0.0102289i
$443$	−5.76437	+	5.76437i	−0.273874	+	0.273874i	−0.830657	−	0.556784i	$-0.812035\pi$
$443$	−5.76437	+	5.76437i	−0.273874	+	0.273874i	0.556784	+	0.830657i	$0.312035\pi$
$444$		0			0
$445$	−0.533306	−	0.533306i	−0.0252811	−	0.0252811i
$446$	−1.37389	−	19.6245i	−0.0650556	−	0.929247i
$447$		0			0
$448$	15.3893	−	6.86078i	0.727074	−	0.324141i
$449$		−	32.3341i		−	1.52594i	−0.646433	−	0.762971i	$-0.723740\pi$
$449$		−	32.3341i		−	1.52594i	0.646433	−	0.762971i	$-0.276260\pi$
$450$		0			0
$451$	4.98391	−	4.98391i	0.234683	−	0.234683i
$452$	0.246356	+	1.75084i	0.0115876	+	0.0823524i
$453$		0			0
$454$	−3.45082	−	2.99926i	−0.161955	−	0.140762i
$455$			0.00966020i			0.000452877i
$456$		0			0
$457$		−	31.7821i		−	1.48670i	−0.668900	−	0.743352i	$-0.733235\pi$
$457$		−	31.7821i		−	1.48670i	0.668900	−	0.743352i	$-0.266765\pi$
$458$	−12.1492	+	13.9783i	−0.567693	+	0.653163i
$459$		0			0
$460$	−0.152092	+	0.201902i	−0.00709133	+	0.00941372i
$461$	−16.5539	+	16.5539i	−0.770993	+	0.770993i	−0.978280	−	0.207287i	$-0.933537\pi$
$461$	−16.5539	+	16.5539i	−0.770993	+	0.770993i	0.207287	+	0.978280i	$0.433537\pi$
$462$		0			0
$463$			19.9659i			0.927896i	0.885862	+	0.463948i	$0.153568\pi$
$463$			19.9659i			0.927896i	−0.885862	+	0.463948i	$0.846432\pi$
$464$	18.1856	−	32.8330i	0.844246	−	1.52423i
$465$		0			0
$466$	34.5166	−	2.41647i	1.59895	−	0.111941i
$467$	19.7660	+	19.7660i	0.914662	+	0.914662i	0.996635	−	0.0819722i	$-0.0261219\pi$
$467$	19.7660	+	19.7660i	0.914662	+	0.914662i	−0.0819722	+	0.996635i	$0.526122\pi$
$468$		0			0
$469$	−12.8648	+	12.8648i	−0.594041	+	0.594041i
$470$	−0.429411	−	0.373219i	−0.0198072	−	0.0172153i
$471$		0			0
$472$	−17.5984	+	27.1137i	−0.810032	+	1.24801i
$473$	28.8915			1.32843
$474$		0			0
$475$	−0.658330	−	0.658330i	−0.0302063	−	0.0302063i
$476$	1.12348	+	7.98451i	0.0514946	+	0.365969i
$477$		0			0
$478$	16.2252	−	1.13591i	0.742124	−	0.0519553i
$479$	17.4640			0.797949			0.398974	−	0.916962i	$-0.369366\pi$
$479$	17.4640			0.797949			0.398974	+	0.916962i	$0.369366\pi$
$480$		0			0
$481$	0.558691			0.0254741
$482$	28.1954	−	1.97393i	1.28427	−	0.0899101i
$483$		0			0
$484$	0.707580	+	5.02873i	0.0321627	+	0.228579i
$485$	−0.262255	−	0.262255i	−0.0119084	−	0.0119084i
$486$		0			0
$487$	1.39496			0.0632119			0.0316059	−	0.999500i	$-0.489938\pi$
$487$	1.39496			0.0632119			0.0316059	+	0.999500i	$0.489938\pi$
$488$	31.1935	+	20.2465i	1.41207	+	0.916514i
$489$		0			0
$490$	0.119266	+	0.103659i	0.00538790	+	0.00468286i
$491$	15.2226	−	15.2226i	0.686984	−	0.686984i	−0.274580	−	0.961564i	$-0.588539\pi$
$491$	15.2226	−	15.2226i	0.686984	−	0.686984i	0.961564	+	0.274580i	$0.0885388\pi$
$492$		0			0
$493$	12.7005	+	12.7005i	0.572002	+	0.572002i
$494$	−0.0276592	+	0.00193639i	−0.00124445	+	8.71223e-5i
$495$		0			0
$496$	5.88650	+	20.5034i	0.264312	+	0.920629i
$497$			18.3329i			0.822342i
$498$		0			0
$499$	4.59095	−	4.59095i	0.205519	−	0.205519i	−0.596841	−	0.802360i	$-0.703578\pi$
$499$	4.59095	−	4.59095i	0.205519	−	0.205519i	0.802360	+	0.596841i	$0.203578\pi$
$500$	0.524298	−	0.696003i	0.0234473	−	0.0311262i
$501$		0			0
$502$	8.47915	−	9.75576i	0.378443	−	0.435421i
$503$		−	38.8293i		−	1.73131i	−0.500639	−	0.865656i	$-0.666901\pi$
$503$		−	38.8293i		−	1.73131i	0.500639	−	0.865656i	$-0.333099\pi$
$504$		0			0
$505$			0.318938i			0.0141925i
$506$	−9.00491	−	7.82656i	−0.400317	−	0.347933i
$507$		0			0
$508$	1.27093	+	9.03240i	0.0563882	+	0.400748i
$509$	−18.1695	+	18.1695i	−0.805351	+	0.805351i	−0.983926	−	0.178575i	$-0.942851\pi$
$509$	−18.1695	+	18.1695i	−0.805351	+	0.805351i	0.178575	+	0.983926i	$0.442851\pi$
$510$		0			0
$511$		−	13.3638i		−	0.591179i
$512$	−18.2962	+	13.3135i	−0.808585	+	0.588380i
$513$		0			0
$514$	−2.25183	−	32.1650i	−0.0993241	−	1.41874i
$515$	−0.281966	−	0.281966i	−0.0124249	−	0.0124249i
$516$		0			0
$517$	18.9879	−	18.9879i	0.835089	−	0.835089i
$518$	−10.3717	+	11.9332i	−0.455705	+	0.524315i
$519$		0			0
$520$	−0.00270034	−	0.0126888i	−0.000118418	−	0.000556441i
$521$	26.3085			1.15260			0.576298	−	0.817239i	$-0.304497\pi$
$521$	26.3085			1.15260			0.576298	+	0.817239i	$0.304497\pi$
$522$		0			0
$523$	3.24829	+	3.24829i	0.142038	+	0.142038i	0.774550	−	0.632512i	$-0.217976\pi$
$523$	3.24829	+	3.24829i	0.142038	+	0.142038i	−0.632512	+	0.774550i	$0.717976\pi$
$524$	−24.9737	−	18.8126i	−1.09098	−	0.821832i
$525$		0			0
$526$	0.475910	+	6.79785i	0.0207506	+	0.296400i
$527$	−10.2082			−0.444675
$528$		0			0
$529$	14.5881			0.634266
$530$	−0.0325129	−	0.464410i	−0.00141227	−	0.0201727i
$531$		0			0
$532$	0.472112	−	0.626727i	0.0204686	−	0.0271720i
$533$	0.180341	+	0.180341i	0.00781144	+	0.00781144i
$534$		0			0
$535$	−0.569990			−0.0246428
$536$	13.3020	−	20.4942i	0.574557	−	0.885215i
$537$		0			0
$538$	−7.82601	+	9.00428i	−0.337403	+	0.388202i
$539$	−5.27379	+	5.27379i	−0.227158	+	0.227158i
$540$		0			0
$541$	−17.6700	−	17.6700i	−0.759694	−	0.759694i	0.216572	−	0.976267i	$-0.430512\pi$
$541$	−17.6700	−	17.6700i	−0.759694	−	0.759694i	−0.976267	+	0.216572i	$0.930512\pi$
$542$	1.54499	+	22.0685i	0.0663630	+	0.947922i
$543$		0			0
$544$	−3.70764	−	10.1737i	−0.158964	−	0.436194i
$545$		−	0.0920051i		−	0.00394107i
$546$		0			0
$547$	−7.42676	+	7.42676i	−0.317545	+	0.317545i	−0.847824	−	0.530278i	$-0.822087\pi$
$547$	−7.42676	+	7.42676i	−0.317545	+	0.317545i	0.530278	+	0.847824i	$0.322087\pi$
$548$	−37.4610	+	5.27104i	−1.60025	+	0.225168i
$549$		0			0
$550$	15.5181	+	13.4874i	0.661693	+	0.575106i
$551$		−	1.74786i		−	0.0744614i
$552$		0			0
$553$			14.6495i			0.622958i
$554$	3.88676	−	4.47194i	0.165132	−	0.189994i
$555$		0			0
$556$	−6.29964	−	4.74551i	−0.267164	−	0.201254i
$557$	7.47821	−	7.47821i	0.316862	−	0.316862i	−0.530699	−	0.847561i	$-0.678070\pi$
$557$	7.47821	−	7.47821i	0.316862	−	0.316862i	0.847561	+	0.530699i	$0.178070\pi$
$558$		0			0
$559$			1.04543i			0.0442170i
$560$	0.321153	+	0.177881i	0.0135712	+	0.00751683i
$561$		0			0
$562$	1.19679	−	0.0837858i	0.0504834	−	0.00353429i
$563$	5.93310	+	5.93310i	0.250050	+	0.250050i	0.820991	−	0.570941i	$-0.193421\pi$
$563$	5.93310	+	5.93310i	0.250050	+	0.250050i	−0.570941	+	0.820991i	$0.693421\pi$
$564$		0			0
$565$	−0.0272408	+	0.0272408i	−0.00114603	+	0.00114603i
$566$	15.5182	+	13.4875i	0.652279	+	0.566924i
$567$		0			0
$568$	−5.12463	−	24.0805i	−0.215025	−	1.01039i
$569$	−11.6799			−0.489647			−0.244823	−	0.969568i	$-0.578730\pi$
$569$	−11.6799			−0.489647			−0.244823	+	0.969568i	$0.578730\pi$
$570$		0			0
$571$	24.0478	+	24.0478i	1.00637	+	1.00637i	0.999980	+	0.00638923i	$0.00203377\pi$
$571$	24.0478	+	24.0478i	1.00637	+	1.00637i	0.00638923	+	0.999980i	$0.497966\pi$
$572$	0.606335	−	0.0853158i	0.0253521	−	0.00356723i
$573$		0			0
$574$	−7.19984	+	0.504053i	−0.300516	+	0.0210388i
$575$	14.4961			0.604529
$576$		0			0
$577$	24.6975			1.02817			0.514085	−	0.857739i	$-0.328132\pi$
$577$	24.6975			1.02817			0.514085	+	0.857739i	$0.328132\pi$
$578$	−18.8138	+	1.31713i	−0.782550	+	0.0547854i
$579$		0			0
$580$	0.809818	−	0.113947i	0.0336259	−	0.00473141i
$581$	−18.6790	−	18.6790i	−0.774935	−	0.774935i
$582$		0			0
$583$	21.9733			0.910039
$584$	3.73561	+	17.5535i	0.154581	+	0.726370i
$585$		0			0
$586$	31.7214	+	27.5705i	1.31040	+	1.13893i
$587$	−31.5251	+	31.5251i	−1.30118	+	1.30118i	−0.373583	+	0.927597i	$0.621871\pi$
$587$	−31.5251	+	31.5251i	−1.30118	+	1.30118i	−0.927597	+	0.373583i	$0.878129\pi$
$588$		0			0
$589$	0.702430	+	0.702430i	0.0289431	+	0.0289431i
$590$	−0.702584	+	0.0491871i	−0.0289249	+	0.00202500i
$591$		0			0
$592$	10.2876	−	18.5737i	0.422818	−	0.763373i
$593$		−	36.2500i		−	1.48861i	−0.667840	−	0.744305i	$-0.732781\pi$
$593$		−	36.2500i		−	1.48861i	0.667840	−	0.744305i	$-0.267219\pi$
$594$		0			0
$595$	−0.124229	+	0.124229i	−0.00509288	+	0.00509288i
$596$	−14.1465	−	10.6565i	−0.579461	−	0.436507i
$597$		0			0
$598$	0.283202	−	0.325840i	0.0115810	−	0.0133246i
$599$			20.6764i			0.844816i	0.906406	+	0.422408i	$0.138815\pi$
$599$			20.6764i			0.844816i	−0.906406	+	0.422408i	$0.861185\pi$
$600$		0			0
$601$			16.9807i			0.692659i	0.938113	+	0.346329i	$0.112572\pi$
$601$			16.9807i			0.692659i	−0.938113	+	0.346329i	$0.887428\pi$
$602$	−22.3296	−	19.4076i	−0.910087	−	0.790996i
$603$		0			0
$604$	33.4398	−	4.70523i	1.36065	−	0.191453i
$605$	−0.0782406	+	0.0782406i	−0.00318093	+	0.00318093i
$606$		0			0
$607$		−	2.81828i		−	0.114390i	−0.998363	−	0.0571951i	$-0.981784\pi$
$607$		−	2.81828i		−	0.114390i	0.998363	−	0.0571951i	$-0.0182157\pi$
$608$	−0.444935	+	0.955184i	−0.0180445	+	0.0387378i
$609$		0			0
$610$	0.0565884	+	0.808303i	0.00229120	+	0.0327272i
$611$	0.687073	+	0.687073i	0.0277960	+	0.0277960i
$612$		0			0
$613$	27.2262	−	27.2262i	1.09965	−	1.09965i	0.105203	−	0.994451i	$-0.466451\pi$
$613$	27.2262	−	27.2262i	1.09965	−	1.09965i	0.994451	−	0.105203i	$-0.0335494\pi$
$614$	1.51490	−	1.74298i	0.0611363	−	0.0703408i
$615$		0			0
$616$	−9.43386	+	14.5347i	−0.380101	+	0.585618i
$617$	31.6978			1.27610			0.638052	−	0.769993i	$-0.279741\pi$
$617$	31.6978			1.27610			0.638052	+	0.769993i	$0.279741\pi$
$618$		0			0
$619$	−6.74642	−	6.74642i	−0.271162	−	0.271162i	0.558406	−	0.829568i	$-0.311413\pi$
$619$	−6.74642	−	6.74642i	−0.271162	−	0.271162i	−0.829568	+	0.558406i	$0.811413\pi$
$620$	−0.279656	+	0.371243i	−0.0112313	+	0.0149095i
$621$		0			0
$622$	−2.66144	−	38.0157i	−0.106714	−	1.52429i
$623$	−36.4521			−1.46042
$624$		0			0
$625$	−24.9715			−0.998861
$626$	−2.79994	−	39.9941i	−0.111908	−	1.59848i
$627$		0			0
$628$	8.62668	+	6.49846i	0.344242	+	0.259317i
$629$	7.18469	+	7.18469i	0.286472	+	0.286472i
$630$		0			0
$631$	27.6749			1.10172			0.550861	−	0.834597i	$-0.314300\pi$
$631$	27.6749			1.10172			0.550861	+	0.834597i	$0.314300\pi$
$632$	−4.09500	−	19.2423i	−0.162890	−	0.765416i
$633$		0			0
$634$	2.20761	−	2.53998i	0.0876754	−	0.100876i
$635$	−0.140533	+	0.140533i	−0.00557687	+	0.00557687i
$636$		0			0
$637$	−0.190830	−	0.190830i	−0.00756098	−	0.00756098i
$638$	2.69567	+	38.5047i	0.106723	+	1.52442i
$639$		0			0
$640$	−0.471562	−	0.143876i	−0.0186401	−	0.00568720i
$641$			11.8975i			0.469925i	0.972004	+	0.234962i	$0.0754967\pi$
$641$			11.8975i			0.469925i	−0.972004	+	0.234962i	$0.924503\pi$
$642$		0			0
$643$	−6.83513	+	6.83513i	−0.269551	+	0.269551i	−0.828919	−	0.559368i	$-0.811044\pi$
$643$	−6.83513	+	6.83513i	−0.269551	+	0.269551i	0.559368	+	0.828919i	$0.311044\pi$
$644$	1.70227	+	12.0979i	0.0670788	+	0.476726i
$645$		0			0
$646$	−0.380595	−	0.330791i	−0.0149743	−	0.0130148i
$647$		−	48.8234i		−	1.91945i	−0.280949	−	0.959723i	$-0.590649\pi$
$647$		−	48.8234i		−	1.91945i	0.280949	−	0.959723i	$-0.409351\pi$
$648$		0			0
$649$		−	33.2423i		−	1.30487i
$650$	−0.488039	+	0.561517i	−0.0191425	+	0.0220245i
$651$		0			0
$652$	−5.40526	+	7.17546i	−0.211686	+	0.281013i
$653$	−22.4800	+	22.4800i	−0.879711	+	0.879711i	−0.993504	−	0.113794i	$-0.963700\pi$
$653$	−22.4800	+	22.4800i	−0.879711	+	0.879711i	0.113794	+	0.993504i	$0.463700\pi$
$654$		0			0
$655$		−	0.681258i		−	0.0266190i
$656$	9.31619	−	2.67467i	0.363736	−	0.104428i
$657$		0			0
$658$	−27.4303	+	1.92037i	−1.06935	+	0.0748637i
$659$	26.0850	+	26.0850i	1.01613	+	1.01613i	0.999868	+	0.0162578i	$0.00517525\pi$
$659$	26.0850	+	26.0850i	1.01613	+	1.01613i	0.0162578	+	0.999868i	$0.494825\pi$
$660$		0			0
$661$	−24.1472	+	24.1472i	−0.939218	+	0.939218i	−0.998256	−	0.0590379i	$-0.981197\pi$
$661$	−24.1472	+	24.1472i	−0.939218	+	0.939218i	0.0590379	+	0.998256i	$0.481197\pi$
$662$	−11.5809	−	10.0655i	−0.450106	−	0.391207i
$663$		0			0
$664$	29.7565	+	19.3137i	1.15478	+	0.749517i
$665$	0.0170965			0.000662975
$666$		0			0
$667$	19.2435	+	19.2435i	0.745112	+	0.745112i
$668$	6.58440	+	46.7949i	0.254758	+	1.81055i
$669$		0			0
$670$	0.531057	−	0.0371787i	0.0205165	−	0.00143634i
$671$	−38.2443			−1.47640
$672$		0			0
$673$	14.1208			0.544316			0.272158	−	0.962253i	$-0.412263\pi$
$673$	14.1208			0.544316			0.272158	+	0.962253i	$0.412263\pi$
$674$	0.141415	−	0.00990029i	0.00544709	−	0.000381345i
$675$		0			0
$676$	−3.61962	−	25.7244i	−0.139216	−	0.989401i
$677$	−17.2082	−	17.2082i	−0.661363	−	0.661363i	0.294338	−	0.955701i	$-0.404901\pi$
$677$	−17.2082	−	17.2082i	−0.661363	−	0.661363i	−0.955701	+	0.294338i	$0.904901\pi$
$678$		0			0
$679$	−17.9254			−0.687913
$680$	0.128450	−	0.197902i	0.00492584	−	0.00758920i
$681$		0			0
$682$	−16.5576	−	14.3909i	−0.634023	−	0.551057i
$683$	9.88736	−	9.88736i	0.378329	−	0.378329i	−0.492170	−	0.870499i	$-0.663796\pi$
$683$	9.88736	−	9.88736i	0.378329	−	0.378329i	0.870499	+	0.492170i	$0.163796\pi$
$684$		0			0
$685$	−0.582845	−	0.582845i	−0.0222694	−	0.0222694i
$686$	28.4177	−	1.98949i	1.08499	−	0.0759591i
$687$		0			0
$688$	34.7553	+	19.2503i	1.32503	+	0.733912i
$689$			0.795096i			0.0302907i
$690$		0			0
$691$	11.5507	−	11.5507i	0.439408	−	0.439408i	−0.452405	−	0.891813i	$-0.649434\pi$
$691$	11.5507	−	11.5507i	0.439408	−	0.439408i	0.891813	+	0.452405i	$0.149434\pi$
$692$	12.6128	−	16.7434i	0.479465	−	0.636488i
$693$		0			0
$694$	−9.98254	+	11.4855i	−0.378932	+	0.435984i
$695$		−	0.171848i		−	0.00651858i
$696$		0			0
$697$			4.63832i			0.175689i
$698$	22.4813	+	19.5395i	0.850931	+	0.739581i
$699$		0			0
$700$	−2.93351	−	20.8483i	−0.110876	−	0.787991i
$701$	−23.5792	+	23.5792i	−0.890575	+	0.890575i	−0.994577	−	0.104002i	$-0.966835\pi$
$701$	−23.5792	+	23.5792i	−0.890575	+	0.890575i	0.104002	+	0.994577i	$0.466835\pi$
$702$		0			0
$703$		−	0.988766i		−	0.0372920i
$704$	8.32859	−	21.7286i	0.313896	−	0.818926i
$705$		0			0
$706$	2.27293	+	32.4663i	0.0855430	+	1.22189i
$707$	10.8999	+	10.8999i	0.409932	+	0.409932i
$708$		0			0
$709$	34.7965	−	34.7965i	1.30681	−	1.30681i	0.383102	−	0.923706i	$-0.374856\pi$
$709$	34.7965	−	34.7965i	1.30681	−	1.30681i	0.923706	−	0.383102i	$-0.125144\pi$
$710$	0.351898	−	0.404880i	0.0132065	−	0.0151949i
$711$		0			0
$712$	47.8803	−	10.1895i	1.79439	−	0.381869i
$713$	−15.4672			−0.579250
$714$		0			0
$715$	0.00943379	+	0.00943379i	0.000352804	+	0.000352804i
$716$	−15.8621	−	11.9489i	−0.592794	−	0.446551i
$717$		0			0
$718$	1.85902	+	26.5540i	0.0693779	+	0.990986i
$719$	−30.3872			−1.13325			−0.566626	−	0.823975i	$-0.691751\pi$
$719$	−30.3872			−1.13325			−0.566626	+	0.823975i	$0.691751\pi$
$720$		0			0
$721$	−19.2727			−0.717752
$722$	−1.87312	−	26.7555i	−0.0697104	−	0.995737i
$723$		0			0
$724$	−8.21053	+	10.8994i	−0.305142	+	0.405075i
$725$	−33.1622	−	33.1622i	−1.23161	−	1.23161i
$726$		0			0
$727$	−49.4115			−1.83257			−0.916285	−	0.400528i	$-0.868827\pi$
$727$	−49.4115			−1.83257			−0.916285	+	0.400528i	$0.868827\pi$
$728$	−0.525933	−	0.341361i	−0.0194924	−	0.0126517i
$729$		0			0
$730$	−0.256517	+	0.295138i	−0.00949412	+	0.0109235i
$731$	−13.4441	+	13.4441i	−0.497248	+	0.497248i
$732$		0			0
$733$	−9.80255	−	9.80255i	−0.362065	−	0.362065i	0.502507	−	0.864573i	$-0.332411\pi$
$733$	−9.80255	−	9.80255i	−0.362065	−	0.362065i	−0.864573	+	0.502507i	$0.832411\pi$
$734$	1.37844	+	19.6895i	0.0508792	+	0.726753i
$735$		0			0
$736$	−5.61772	−	15.4150i	−0.207072	−	0.568203i
$737$			25.1266i			0.925549i
$738$		0			0
$739$	23.4230	−	23.4230i	0.861630	−	0.861630i	−0.129897	−	0.991527i	$-0.541465\pi$
$739$	23.4230	−	23.4230i	0.861630	−	0.861630i	0.991527	+	0.129897i	$0.0414648\pi$
$740$	0.458114	−	0.0644601i	0.0168406	−	0.00236960i
$741$		0			0
$742$	−16.9826	−	14.7603i	−0.623452	−	0.541869i
$743$		−	21.8087i		−	0.800083i	−0.916497	−	0.400042i	$-0.868996\pi$
$743$		−	21.8087i		−	0.800083i	0.916497	−	0.400042i	$-0.131004\pi$
$744$		0			0
$745$		−	0.385902i		−	0.0141384i
$746$	17.9624	−	20.6668i	0.657651	−	0.756665i
$747$		0			0
$748$	8.89453	+	6.70023i	0.325216	+	0.244985i
$749$	−19.4797	+	19.4797i	−0.711773	+	0.711773i
$750$		0			0
$751$			36.4038i			1.32839i	0.747557	+	0.664197i	$0.231226\pi$
$751$			36.4038i			1.32839i	−0.747557	+	0.664197i	$0.768774\pi$
$752$	35.4933	−	10.1901i	1.29431	−	0.371595i
$753$		0			0
$754$	−1.39328	+	0.0975420i	−0.0507403	+	0.00355227i
$755$	0.520281	+	0.520281i	0.0189350	+	0.0189350i
$756$		0			0
$757$	−3.56764	+	3.56764i	−0.129668	+	0.129668i	−0.768962	−	0.639294i	$-0.779227\pi$
$757$	−3.56764	+	3.56764i	−0.129668	+	0.129668i	0.639294	+	0.768962i	$0.279227\pi$
$758$	35.1894	+	30.5847i	1.27814	+	1.11088i
$759$		0			0
$760$	−0.0224565	+	0.00477903i	−0.000814583	+	0.000173354i
$761$	21.3343			0.773368			0.386684	−	0.922212i	$-0.373620\pi$
$761$	21.3343			0.773368			0.386684	+	0.922212i	$0.373620\pi$
$762$		0			0
$763$	−3.14433	−	3.14433i	−0.113832	−	0.113832i
$764$	−8.49864	+	1.19582i	−0.307470	+	0.0432633i
$765$		0			0
$766$	−4.25638	+	0.297984i	−0.153789	+	0.0107666i
$767$	1.20286			0.0434328
$768$		0			0
$769$	7.41504			0.267393			0.133697	−	0.991022i	$-0.457315\pi$
$769$	7.41504			0.267393			0.133697	+	0.991022i	$0.457315\pi$
$770$	−0.376630	+	0.0263674i	−0.0135728	+	0.000950216i
$771$		0			0
$772$	46.7982	−	6.58486i	1.68431	−	0.236994i
$773$	−1.14034	−	1.14034i	−0.0410152	−	0.0410152i	0.686302	−	0.727317i	$-0.259233\pi$
$773$	−1.14034	−	1.14034i	−0.0410152	−	0.0410152i	−0.727317	+	0.686302i	$0.759233\pi$
$774$		0			0
$775$	26.6544			0.957455
$776$	23.5452	−	5.01073i	0.845225	−	0.179875i
$777$		0			0
$778$	−28.7550	−	24.9922i	−1.03092	−	0.896013i
$779$	0.319166	−	0.319166i	0.0114353	−	0.0114353i
$780$		0			0
$781$	17.9032	+	17.9032i	0.640627	+	0.640627i
$782$	7.83218	−	0.548323i	0.280078	−	0.0196080i
$783$		0			0
$784$	−9.85805	+	2.83024i	−0.352073	+	0.101080i
$785$			0.235328i			0.00839921i
$786$		0			0
$787$	−22.9976	+	22.9976i	−0.819775	+	0.819775i	−0.986075	−	0.166300i	$-0.946818\pi$
$787$	−22.9976	+	22.9976i	−0.819775	+	0.819775i	0.166300	+	0.986075i	$0.446818\pi$
$788$	19.3964	+	14.6113i	0.690969	+	0.520506i
$789$		0			0
$790$	0.281195	−	0.323531i	0.0100045	−	0.0115107i
$791$			1.86194i			0.0662029i
$792$		0			0
$793$		−	1.38386i		−	0.0491422i
$794$	−32.1334	−	27.9285i	−1.14037	−	0.991147i
$795$		0			0
$796$	−5.28168	+	0.743171i	−0.187204	+	0.0263410i
$797$	−11.2884	+	11.2884i	−0.399854	+	0.399854i	−0.878182	−	0.478327i	$-0.841243\pi$
$797$	−11.2884	+	11.2884i	−0.399854	+	0.399854i	0.478327	+	0.878182i	$0.341243\pi$
$798$		0			0
$799$			17.6713i			0.625166i
$800$	9.68097	+	26.5645i	0.342274	+	0.939196i
$801$		0			0
$802$	−0.889464	−	12.7050i	−0.0314081	−	0.448629i
$803$	−13.0506	−	13.0506i	−0.460545	−	0.460545i
$804$		0			0
$805$	−0.188228	+	0.188228i	−0.00663418	+	0.00663418i
$806$	0.520731	−	0.599132i	0.0183420	−	0.0211035i
$807$		0			0
$808$	−17.3640	−	11.2703i	−0.610863	−	0.396486i
$809$	−3.12757			−0.109959			−0.0549797	−	0.998487i	$-0.517509\pi$
$809$	−3.12757			−0.109959			−0.0549797	+	0.998487i	$0.517509\pi$
$810$		0			0
$811$	15.1849	+	15.1849i	0.533213	+	0.533213i	0.921527	−	0.388314i	$-0.126942\pi$
$811$	15.1849	+	15.1849i	0.533213	+	0.533213i	−0.388314	+	0.921527i	$0.626942\pi$
$812$	23.7818	−	31.5702i	0.834576	−	1.10790i
$813$		0			0
$814$	1.52494	+	21.7821i	0.0534492	+	0.763463i
$815$	−0.195740			−0.00685647
$816$		0			0
$817$	1.85019			0.0647300
$818$	−1.08500	−	15.4980i	−0.0379360	−	0.541874i
$819$		0			0
$820$	0.168683	+	0.127069i	0.00589066	+	0.00443743i
$821$	−5.26935	−	5.26935i	−0.183901	−	0.183901i	0.609152	−	0.793053i	$-0.291510\pi$
$821$	−5.26935	−	5.26935i	−0.183901	−	0.183901i	−0.793053	+	0.609152i	$0.791510\pi$
$822$		0			0
$823$	41.6290			1.45110			0.725549	−	0.688171i	$-0.241586\pi$
$823$	41.6290			1.45110			0.725549	+	0.688171i	$0.241586\pi$
$824$	25.3149	−	5.38734i	0.881887	−	0.187677i
$825$		0			0
$826$	−22.3302	+	25.6922i	−0.776967	+	0.893945i
$827$	−18.9578	+	18.9578i	−0.659226	+	0.659226i	−0.955197	−	0.295971i	$-0.904357\pi$
$827$	−18.9578	+	18.9578i	−0.659226	+	0.659226i	0.295971	+	0.955197i	$0.404357\pi$
$828$		0			0
$829$	−26.9361	−	26.9361i	−0.935530	−	0.935530i	0.0625139	−	0.998044i	$-0.480088\pi$
$829$	−26.9361	−	26.9361i	−0.935530	−	0.935530i	−0.998044	+	0.0625139i	$0.980088\pi$
$830$	0.0539814	+	0.771065i	0.00187372	+	0.0267641i
$831$		0			0
$832$	0.786241	+	0.301368i	0.0272580	+	0.0104480i
$833$		−	4.90810i		−	0.170056i
$834$		0			0
$835$	−0.728069	+	0.728069i	−0.0251959	+	0.0251959i
$836$	−0.150991	−	1.07308i	−0.00522213	−	0.0371134i
$837$		0			0
$838$	−4.92481	−	4.28037i	−0.170125	−	0.147863i
$839$		−	8.57105i		−	0.295905i	−0.988994	−	0.147953i	$-0.952732\pi$
$839$		−	8.57105i		−	0.295905i	0.988994	−	0.147953i	$-0.0472683\pi$
$840$		0			0
$841$		−	59.0452i		−	2.03604i
$842$	21.2735	−	24.4763i	0.733132	−	0.843511i
$843$		0			0
$844$	14.1665	−	18.8059i	0.487630	−	0.647326i
$845$	0.400239	−	0.400239i	0.0137687	−	0.0137687i
$846$		0			0
$847$			5.34783i			0.183754i
$848$	26.4329	+	14.6407i	0.907710	+	0.502764i
$849$		0			0
$850$	−13.4971	+	0.944920i	−0.462948	+	0.0324105i
$851$	10.8861	+	10.8861i	0.373170	+	0.373170i
$852$		0			0
$853$	−6.98782	+	6.98782i	−0.239258	+	0.239258i	−0.816543	−	0.577285i	$-0.804112\pi$
$853$	−6.98782	+	6.98782i	−0.239258	+	0.239258i	0.577285	+	0.816543i	$0.304112\pi$
$854$	29.5581	+	25.6903i	1.01146	+	0.879102i
$855$		0			0
$856$	20.1417	−	31.0321i	0.688428	−	1.06065i
$857$	30.2504			1.03333			0.516666	−	0.856187i	$-0.327173\pi$
$857$	30.2504			1.03333			0.516666	+	0.856187i	$0.327173\pi$
$858$		0			0
$859$	21.6567	+	21.6567i	0.738917	+	0.738917i	0.972369	−	0.233451i	$-0.0750019\pi$
$859$	21.6567	+	21.6567i	0.738917	+	0.738917i	−0.233451	+	0.972369i	$0.575002\pi$
$860$	0.120619	+	0.857230i	0.00411306	+	0.0292313i
$861$		0			0
$862$	−40.8200	+	2.85776i	−1.39034	+	0.0973358i
$863$	−15.3679			−0.523131			−0.261565	−	0.965186i	$-0.584239\pi$
$863$	−15.3679			−0.523131			−0.261565	+	0.965186i	$0.584239\pi$
$864$		0			0
$865$	0.456744			0.0155298
$866$	23.1585	−	1.62130i	0.786958	−	0.0550940i
$867$		0			0
$868$	3.13002	+	22.2448i	0.106240	+	0.755039i
$869$	14.3061	+	14.3061i	0.485301	+	0.485301i
$870$		0			0
$871$	−0.909197			−0.0308070
$872$	5.00905	+	3.25117i	0.169628	+	0.110099i
$873$		0			0
$874$	−0.576668	−	0.501207i	−0.0195061	−	0.0169536i
$875$	0.648868	−	0.648868i	0.0219357	−	0.0219357i
$876$		0			0
$877$	−17.1484	−	17.1484i	−0.579060	−	0.579060i	0.355584	−	0.934644i	$-0.384282\pi$
$877$	−17.1484	−	17.1484i	−0.579060	−	0.579060i	−0.934644	+	0.355584i	$0.884282\pi$
$878$	2.81232	−	0.196887i	0.0949111	−	0.00664462i
$879$		0			0
$880$	0.487338	−	0.139914i	0.0164281	−	0.00471651i
$881$		−	19.1271i		−	0.644409i	−0.946670	−	0.322204i	$-0.895576\pi$
$881$		−	19.1271i		−	0.644409i	0.946670	−	0.322204i	$-0.104424\pi$
$882$		0			0
$883$	−37.7452	+	37.7452i	−1.27023	+	1.27023i	−0.324259	+	0.945968i	$0.605115\pi$
$883$	−37.7452	+	37.7452i	−1.27023	+	1.27023i	−0.945968	+	0.324259i	$0.894885\pi$
$884$	−0.242446	+	0.321846i	−0.00815433	+	0.0108248i
$885$		0			0
$886$	7.56283	−	8.70147i	0.254078	−	0.292332i
$887$		−	15.5731i		−	0.522895i	−0.965218	−	0.261447i	$-0.915800\pi$
$887$		−	15.5731i		−	0.522895i	0.965218	−	0.261447i	$-0.0841998\pi$
$888$		0			0
$889$			9.60556i			0.322160i
$890$	0.805040	+	0.699695i	0.0269850	+	0.0234538i
$891$		0			0
$892$	3.87646	+	27.5498i	0.129793	+	0.922435i
$893$	1.21597	−	1.21597i	0.0406910	−	0.0406910i
$894$		0			0
$895$		−	0.432703i		−	0.0144637i
$896$	−21.0329	+	11.1988i	−0.702661	+	0.374127i
$897$		0			0
$898$	3.19351	+	45.6157i	0.106569	+	1.52222i
$899$	35.3836	+	35.3836i	1.18011	+	1.18011i
$900$		0			0
$901$	−10.2248	+	10.2248i	−0.340638	+	0.340638i
$902$	−6.53886	+	7.52334i	−0.217720	+	0.250500i
$903$		0			0
$904$	−0.520472	−	2.44568i	−0.0173106	−	0.0813421i
$905$	−0.297327			−0.00988347
$906$		0			0
$907$	−19.6157	−	19.6157i	−0.651330	−	0.651330i	0.301984	−	0.953313i	$-0.402351\pi$
$907$	−19.6157	−	19.6157i	−0.651330	−	0.651330i	−0.953313	+	0.301984i	$0.902351\pi$
$908$	5.16451	+	3.89041i	0.171390	+	0.129108i
$909$		0			0
$910$	−0.000954097	−	0.0136282i	−3.16280e−5	−	0.000451771i
$911$	30.3457			1.00540			0.502699	−	0.864462i	$-0.332340\pi$
$911$	30.3457			1.00540			0.502699	+	0.864462i	$0.332340\pi$
$912$		0			0
$913$	−36.4824			−1.20739
$914$	3.13898	+	44.8369i	0.103828	+	1.48307i
$915$		0			0
$916$	15.7590	−	20.9200i	0.520691	−	0.691215i
$917$	−23.2824	−	23.2824i	−0.768852	−	0.768852i
$918$		0			0
$919$	−38.5944			−1.27311			−0.636557	−	0.771230i	$-0.719642\pi$
$919$	−38.5944			−1.27311			−0.636557	+	0.771230i	$0.719642\pi$
$920$	0.194625	−	0.299856i	0.00641658	−	0.00988598i
$921$		0			0
$922$	21.7187	−	24.9886i	0.715266	−	0.822955i
$923$	−0.647822	+	0.647822i	−0.0213233	+	0.0213233i
$924$		0			0
$925$	−18.7599	−	18.7599i	−0.616820	−	0.616820i
$926$	−1.97195	−	28.1672i	−0.0648024	−	0.925630i
$927$		0			0
$928$	−22.4128	+	48.1156i	−0.735735	+	1.57947i
$929$			2.41090i			0.0790990i	0.999218	+	0.0395495i	$0.0125923\pi$
$929$			2.41090i			0.0790990i	−0.999218	+	0.0395495i	$0.987408\pi$
$930$		0			0
$931$	−0.337730	+	0.337730i	−0.0110686	+	0.0110686i
$932$	−48.4560	+	6.81812i	−1.58723	+	0.223335i
$933$		0			0
$934$	−29.8373	−	25.9329i	−0.976307	−	0.848551i
$935$			0.242634i			0.00793499i
$936$		0			0
$937$		−	33.5635i		−	1.09647i	−0.836324	−	0.548236i	$-0.815300\pi$
$937$		−	33.5635i		−	1.09647i	0.836324	−	0.548236i	$-0.184700\pi$
$938$	16.8786	−	19.4198i	0.551104	−	0.634078i
$939$		0			0
$940$	0.642657	+	0.484112i	0.0209612	+	0.0157900i
$941$	−15.9764	+	15.9764i	−0.520815	+	0.520815i	−0.917818	−	0.397003i	$-0.870050\pi$
$941$	−15.9764	+	15.9764i	−0.520815	+	0.520815i	0.397003	+	0.917818i	$0.370050\pi$
$942$		0			0
$943$			7.02787i			0.228859i
$944$	22.1492	−	39.9890i	0.720895	−	1.30153i
$945$		0			0
$946$	−40.7590	+	2.85349i	−1.32519	+	0.0927751i
$947$	−17.3815	−	17.3815i	−0.564822	−	0.564822i	0.365851	−	0.930673i	$-0.380778\pi$
$947$	−17.3815	−	17.3815i	−0.564822	−	0.564822i	−0.930673	+	0.365851i	$0.880778\pi$
$948$		0			0
$949$	0.472231	−	0.472231i	0.0153293	−	0.0153293i
$950$	0.993767	+	0.863726i	0.0322421	+	0.0280230i
$951$		0			0
$952$	−2.37356	−	11.1533i	−0.0769275	−	0.361480i
$953$	9.05205			0.293225			0.146612	−	0.989194i	$-0.453163\pi$
$953$	9.05205			0.293225			0.146612	+	0.989194i	$0.453163\pi$
$954$		0			0
$955$	−0.132228	−	0.132228i	−0.00427880	−	0.00427880i
$956$	−22.7777	+	3.20499i	−0.736684	+	0.103657i
$957$		0			0
$958$	−24.6375	+	1.72484i	−0.796000	+	0.0557271i
$959$	−39.8381			−1.28644
$960$		0			0
$961$	2.56005			0.0825824
$962$	−0.788180	+	0.0551796i	−0.0254119	+	0.00177906i
$963$		0			0
$964$	−39.5820	+	5.56949i	−1.27485	+	0.179381i
$965$	0.728120	+	0.728120i	0.0234390	+	0.0234390i
$966$		0			0
$967$	4.09093			0.131555			0.0657777	−	0.997834i	$-0.479047\pi$
$967$	4.09093			0.131555			0.0657777	+	0.997834i	$0.479047\pi$
$968$	−1.49489	−	7.02445i	−0.0480477	−	0.225774i
$969$		0			0
$970$	0.395880	+	0.344077i	0.0127109	+	0.0110476i
$971$	−27.6702	+	27.6702i	−0.887978	+	0.887978i	−0.994329	−	0.106351i	$-0.966083\pi$
$971$	−27.6702	+	27.6702i	−0.887978	+	0.887978i	0.106351	+	0.994329i	$0.466083\pi$
$972$		0			0
$973$	−5.87301	−	5.87301i	−0.188280	−	0.188280i
$974$	−1.96796	+	0.137775i	−0.0630575	+	0.00441459i
$975$		0			0
$976$	−46.0063	−	25.4820i	−1.47262	−	0.815660i
$977$			0.367175i			0.0117470i	0.999983	+	0.00587349i	$0.00186960\pi$
$977$			0.367175i			0.0117470i	−0.999983	+	0.00587349i	$0.998130\pi$
$978$		0			0
$979$	−35.5977	+	35.5977i	−1.13771	+	1.13771i
$980$	−0.178494	−	0.134459i	−0.00570179	−	0.00429514i
$981$		0			0
$982$	−19.9719	+	22.9789i	−0.637329	+	0.733285i
$983$		−	37.1872i		−	1.18609i	−0.805170	−	0.593044i	$-0.797926\pi$
$983$		−	37.1872i		−	1.18609i	0.805170	−	0.593044i	$-0.202074\pi$
$984$		0			0
$985$			0.529117i			0.0168591i
$986$	−19.1718	−	16.6630i	−0.610553	−	0.530658i
$987$		0			0
$988$	0.0388292	−	0.00546356i	0.00123532	−	0.000173819i
$989$	−20.3702	+	20.3702i	−0.647733	+	0.647733i
$990$		0			0
$991$			47.3429i			1.50390i	0.659222	+	0.751949i	$0.270886\pi$
$991$			47.3429i			1.50390i	−0.659222	+	0.751949i	$0.729114\pi$
$992$	−10.3295	−	28.3440i	−0.327961	−	0.899922i
$993$		0			0
$994$	−1.81066	−	25.8633i	−0.0574307	−	0.820334i
$995$	−0.0821761	−	0.0821761i	−0.00260516	−	0.00260516i
$996$		0			0
$997$	12.9204	−	12.9204i	0.409192	−	0.409192i	−0.472265	−	0.881457i	$-0.656563\pi$
$997$	12.9204	−	12.9204i	0.409192	−	0.409192i	0.881457	+	0.472265i	$0.156563\pi$
$998$	−6.02330	+	6.93016i	−0.190664	+	0.219370i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.b.323.1	yes	32
3.2	odd	2	inner	432.2.l.b.323.16	yes	32
4.3	odd	2		1728.2.l.b.431.9		32
12.11	even	2		1728.2.l.b.431.8		32
16.5	even	4		1728.2.l.b.1295.8		32
16.11	odd	4	inner	432.2.l.b.107.16	yes	32
48.5	odd	4		1728.2.l.b.1295.9		32
48.11	even	4	inner	432.2.l.b.107.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.b.107.1	✓	32	48.11	even	4	inner
432.2.l.b.107.16	yes	32	16.11	odd	4	inner
432.2.l.b.323.1	yes	32	1.1	even	1	trivial
432.2.l.b.323.16	yes	32	3.2	odd	2	inner
1728.2.l.b.431.8		32	12.11	even	2
1728.2.l.b.431.9		32	4.3	odd	2
1728.2.l.b.1295.8		32	16.5	even	4
1728.2.l.b.1295.9		32	48.5	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.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41076 + 0.0987658i) q^{2} +(1.98049 - 0.278670i) q^{4} +(0.0308139 + 0.0308139i) q^{5} +2.10616 q^{7} +(-2.76648 + 0.588741i) q^{8} +O(q^{10})\)	\(q+(-1.41076 + 0.0987658i) q^{2} +(1.98049 - 0.278670i) q^{4} +(0.0308139 + 0.0308139i) q^{5} +2.10616 q^{7} +(-2.76648 + 0.588741i) q^{8} +(-0.0465144 - 0.0404277i) q^{10} +(2.05680 - 2.05680i) q^{11} +(0.0744247 + 0.0744247i) q^{13} +(-2.97129 + 0.208017i) q^{14} +(3.84469 - 1.10381i) q^{16} +1.91418i q^{17} +(0.131716 - 0.131716i) q^{19} +(0.0696135 + 0.0524397i) q^{20} +(-2.69851 + 3.10480i) q^{22} +2.90032i q^{23} -4.99810i q^{25} +(-0.112346 - 0.0976449i) q^{26} +(4.17124 - 0.586924i) q^{28} +(6.63495 - 6.63495i) q^{29} +5.33291i q^{31} +(-5.31491 + 1.93693i) q^{32} +(-0.189056 - 2.70045i) q^{34} +(0.0648991 + 0.0648991i) q^{35} +(3.75340 - 3.75340i) q^{37} +(-0.172811 + 0.198829i) q^{38} +(-0.103387 - 0.0671045i) q^{40} +2.42313 q^{41} +(7.02341 + 7.02341i) q^{43} +(3.50031 - 4.64664i) q^{44} +(-0.286453 - 4.09166i) q^{46} +9.23178 q^{47} -2.56407 q^{49} +(0.493641 + 7.05112i) q^{50} +(0.168137 + 0.126658i) q^{52} +(5.34161 + 5.34161i) q^{53} +0.126756 q^{55} +(-5.82665 + 1.23999i) q^{56} +(-8.70502 + 10.0156i) q^{58} +(8.08106 - 8.08106i) q^{59} +(-9.29703 - 9.29703i) q^{61} +(-0.526709 - 7.52346i) q^{62} +(7.30677 - 3.25747i) q^{64} +0.00458663i q^{65} +(-6.10817 + 6.10817i) q^{67} +(0.533425 + 3.79102i) q^{68} +(-0.0979669 - 0.0851473i) q^{70} +8.70439i q^{71} -6.34509i q^{73} +(-4.92444 + 5.66585i) q^{74} +(0.224157 - 0.297568i) q^{76} +(4.33196 - 4.33196i) q^{77} +6.95551i q^{79} +(0.152482 + 0.0844572i) q^{80} +(-3.41846 + 0.239323i) q^{82} +(-8.86872 - 8.86872i) q^{83} +(-0.0589834 + 0.0589834i) q^{85} +(-10.6020 - 9.21468i) q^{86} +(-4.47917 + 6.90101i) q^{88} -17.3073 q^{89} +(0.156751 + 0.156751i) q^{91} +(0.808232 + 5.74406i) q^{92} +(-13.0238 + 0.911784i) q^{94} +0.00811737 q^{95} -8.51092 q^{97} +(3.61729 - 0.253243i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) \) 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

Introduction

L-functions

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