LMFDB - Embedded newform 25.3.c.a.18.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [25,3,Mod(7,25)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("25.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	25.c (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.681200660901$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			18.1
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	25.18
Dual form			25.3.c.a.7.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 + 1.22474i) q^{2} +(1.22474 + 1.22474i) q^{3} +1.00000i q^{4} -3.00000 q^{6} +(4.89898 - 4.89898i) q^{7} +(-6.12372 - 6.12372i) q^{8} -6.00000i q^{9} -3.00000 q^{11} +(-1.22474 + 1.22474i) q^{12} +(7.34847 + 7.34847i) q^{13} +12.0000i q^{14} +11.0000 q^{16} +(-13.4722 + 13.4722i) q^{17} +(7.34847 + 7.34847i) q^{18} -5.00000i q^{19} +12.0000 q^{21} +(3.67423 - 3.67423i) q^{22} +(-17.1464 - 17.1464i) q^{23} -15.0000i q^{24} -18.0000 q^{26} +(18.3712 - 18.3712i) q^{27} +(4.89898 + 4.89898i) q^{28} +30.0000i q^{29} -38.0000 q^{31} +(11.0227 - 11.0227i) q^{32} +(-3.67423 - 3.67423i) q^{33} -33.0000i q^{34} +6.00000 q^{36} +(-19.5959 + 19.5959i) q^{37} +(6.12372 + 6.12372i) q^{38} +18.0000i q^{39} +57.0000 q^{41} +(-14.6969 + 14.6969i) q^{42} +(-4.89898 - 4.89898i) q^{43} -3.00000i q^{44} +42.0000 q^{46} +(-7.34847 + 7.34847i) q^{47} +(13.4722 + 13.4722i) q^{48} +1.00000i q^{49} -33.0000 q^{51} +(-7.34847 + 7.34847i) q^{52} +(31.8434 + 31.8434i) q^{53} +45.0000i q^{54} -60.0000 q^{56} +(6.12372 - 6.12372i) q^{57} +(-36.7423 - 36.7423i) q^{58} -90.0000i q^{59} -28.0000 q^{61} +(46.5403 - 46.5403i) q^{62} +(-29.3939 - 29.3939i) q^{63} +71.0000i q^{64} +9.00000 q^{66} +(47.7650 - 47.7650i) q^{67} +(-13.4722 - 13.4722i) q^{68} -42.0000i q^{69} +42.0000 q^{71} +(-36.7423 + 36.7423i) q^{72} +(13.4722 + 13.4722i) q^{73} -48.0000i q^{74} +5.00000 q^{76} +(-14.6969 + 14.6969i) q^{77} +(-22.0454 - 22.0454i) q^{78} +80.0000i q^{79} -9.00000 q^{81} +(-69.8105 + 69.8105i) q^{82} +(111.452 + 111.452i) q^{83} +12.0000i q^{84} +12.0000 q^{86} +(-36.7423 + 36.7423i) q^{87} +(18.3712 + 18.3712i) q^{88} +15.0000i q^{89} +72.0000 q^{91} +(17.1464 - 17.1464i) q^{92} +(-46.5403 - 46.5403i) q^{93} -18.0000i q^{94} +27.0000 q^{96} +(53.8888 - 53.8888i) q^{97} +(-1.22474 - 1.22474i) q^{98} +18.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{6} - 12 q^{11} + 44 q^{16} + 48 q^{21} - 72 q^{26} - 152 q^{31} + 24 q^{36} + 228 q^{41} + 168 q^{46} - 132 q^{51} - 240 q^{56} - 112 q^{61} + 36 q^{66} + 168 q^{71} + 20 q^{76} - 36 q^{81}+ \cdots + 108 q^{96}+O(q^{100}) $ 4 * q - 12 * q^6 - 12 * q^11 + 44 * q^16 + 48 * q^21 - 72 * q^26 - 152 * q^31 + 24 * q^36 + 228 * q^41 + 168 * q^46 - 132 * q^51 - 240 * q^56 - 112 * q^61 + 36 * q^66 + 168 * q^71 + 20 * q^76 - 36 * q^81 + 48 * q^86 + 288 * q^91 + 108 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.22474	+	1.22474i	−0.612372	+	0.612372i	−0.943564	−	0.331191i	$-0.892549\pi$
$2$	−1.22474	+	1.22474i	−0.612372	+	0.612372i	0.331191	+	0.943564i	$0.392549\pi$
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i	0.881127	−	0.472879i	$-0.156785\pi$
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i	−0.472879	+	0.881127i	$0.656785\pi$
$4$			1.00000i			0.250000i
$5$		0			0
$5$		0			0
$6$	−3.00000			−0.500000
$7$	4.89898	−	4.89898i	0.699854	−	0.699854i	−0.264525	−	0.964379i	$-0.585215\pi$
$7$	4.89898	−	4.89898i	0.699854	−	0.699854i	0.964379	+	0.264525i	$0.0852151\pi$
$8$	−6.12372	−	6.12372i	−0.765466	−	0.765466i
$9$		−	6.00000i		−	0.666667i
$10$		0			0
$11$	−3.00000			−0.272727			−0.136364	−	0.990659i	$-0.543542\pi$
$11$	−3.00000			−0.272727			−0.136364	+	0.990659i	$0.543542\pi$
$12$	−1.22474	+	1.22474i	−0.102062	+	0.102062i
$13$	7.34847	+	7.34847i	0.565267	+	0.565267i	0.930799	−	0.365532i	$-0.119113\pi$
$13$	7.34847	+	7.34847i	0.565267	+	0.565267i	−0.365532	+	0.930799i	$0.619113\pi$
$14$			12.0000i			0.857143i
$15$		0			0
$16$	11.0000			0.687500
$17$	−13.4722	+	13.4722i	−0.792482	+	0.792482i	−0.981897	−	0.189415i	$-0.939341\pi$
$17$	−13.4722	+	13.4722i	−0.792482	+	0.792482i	0.189415	+	0.981897i	$0.439341\pi$
$18$	7.34847	+	7.34847i	0.408248	+	0.408248i
$19$		−	5.00000i		−	0.263158i	−0.991306	−	0.131579i	$-0.957995\pi$
$19$		−	5.00000i		−	0.263158i	0.991306	−	0.131579i	$-0.0420047\pi$
$20$		0			0
$21$	12.0000			0.571429
$22$	3.67423	−	3.67423i	0.167011	−	0.167011i
$23$	−17.1464	−	17.1464i	−0.745497	−	0.745497i	0.228133	−	0.973630i	$-0.426738\pi$
$23$	−17.1464	−	17.1464i	−0.745497	−	0.745497i	−0.973630	+	0.228133i	$0.926738\pi$
$24$		−	15.0000i		−	0.625000i
$25$		0			0
$26$	−18.0000			−0.692308
$27$	18.3712	−	18.3712i	0.680414	−	0.680414i
$28$	4.89898	+	4.89898i	0.174964	+	0.174964i
$29$			30.0000i			1.03448i	0.855840	+	0.517241i	$0.173041\pi$
$29$			30.0000i			1.03448i	−0.855840	+	0.517241i	$0.826959\pi$
$30$		0			0
$31$	−38.0000			−1.22581			−0.612903	−	0.790158i	$-0.709998\pi$
$31$	−38.0000			−1.22581			−0.612903	+	0.790158i	$0.709998\pi$
$32$	11.0227	−	11.0227i	0.344459	−	0.344459i
$33$	−3.67423	−	3.67423i	−0.111340	−	0.111340i
$34$		−	33.0000i		−	0.970588i
$35$		0			0
$36$	6.00000			0.166667
$37$	−19.5959	+	19.5959i	−0.529619	+	0.529619i	−0.920459	−	0.390839i	$-0.872185\pi$
$37$	−19.5959	+	19.5959i	−0.529619	+	0.529619i	0.390839	+	0.920459i	$0.372185\pi$
$38$	6.12372	+	6.12372i	0.161151	+	0.161151i
$39$			18.0000i			0.461538i
$40$		0			0
$41$	57.0000			1.39024			0.695122	−	0.718892i	$-0.255350\pi$
$41$	57.0000			1.39024			0.695122	+	0.718892i	$0.255350\pi$
$42$	−14.6969	+	14.6969i	−0.349927	+	0.349927i
$43$	−4.89898	−	4.89898i	−0.113930	−	0.113930i	0.647844	−	0.761773i	$-0.275671\pi$
$43$	−4.89898	−	4.89898i	−0.113930	−	0.113930i	−0.761773	+	0.647844i	$0.775671\pi$
$44$		−	3.00000i		−	0.0681818i
$45$		0			0
$46$	42.0000			0.913043
$47$	−7.34847	+	7.34847i	−0.156350	+	0.156350i	−0.780947	−	0.624597i	$-0.785263\pi$
$47$	−7.34847	+	7.34847i	−0.156350	+	0.156350i	0.624597	+	0.780947i	$0.285263\pi$
$48$	13.4722	+	13.4722i	0.280671	+	0.280671i
$49$			1.00000i			0.0204082i
$50$		0			0
$51$	−33.0000			−0.647059
$52$	−7.34847	+	7.34847i	−0.141317	+	0.141317i
$53$	31.8434	+	31.8434i	0.600818	+	0.600818i	0.940530	−	0.339711i	$-0.110329\pi$
$53$	31.8434	+	31.8434i	0.600818	+	0.600818i	−0.339711	+	0.940530i	$0.610329\pi$
$54$			45.0000i			0.833333i
$55$		0			0
$56$	−60.0000			−1.07143
$57$	6.12372	−	6.12372i	0.107434	−	0.107434i
$58$	−36.7423	−	36.7423i	−0.633489	−	0.633489i
$59$		−	90.0000i		−	1.52542i	−0.646738	−	0.762712i	$-0.723867\pi$
$59$		−	90.0000i		−	1.52542i	0.646738	−	0.762712i	$-0.276133\pi$
$60$		0			0
$61$	−28.0000			−0.459016			−0.229508	−	0.973307i	$-0.573712\pi$
$61$	−28.0000			−0.459016			−0.229508	+	0.973307i	$0.573712\pi$
$62$	46.5403	−	46.5403i	0.750650	−	0.750650i
$63$	−29.3939	−	29.3939i	−0.466569	−	0.466569i
$64$			71.0000i			1.10938i
$65$		0			0
$66$	9.00000			0.136364
$67$	47.7650	−	47.7650i	0.712911	−	0.712911i	−0.254232	−	0.967143i	$-0.581823\pi$
$67$	47.7650	−	47.7650i	0.712911	−	0.712911i	0.967143	+	0.254232i	$0.0818227\pi$
$68$	−13.4722	−	13.4722i	−0.198120	−	0.198120i
$69$		−	42.0000i		−	0.608696i
$70$		0			0
$71$	42.0000			0.591549			0.295775	−	0.955258i	$-0.404422\pi$
$71$	42.0000			0.591549			0.295775	+	0.955258i	$0.404422\pi$
$72$	−36.7423	+	36.7423i	−0.510310	+	0.510310i
$73$	13.4722	+	13.4722i	0.184551	+	0.184551i	0.793335	−	0.608785i	$-0.208343\pi$
$73$	13.4722	+	13.4722i	0.184551	+	0.184551i	−0.608785	+	0.793335i	$0.708343\pi$
$74$		−	48.0000i		−	0.648649i
$75$		0			0
$76$	5.00000			0.0657895
$77$	−14.6969	+	14.6969i	−0.190869	+	0.190869i
$78$	−22.0454	−	22.0454i	−0.282633	−	0.282633i
$79$			80.0000i			1.01266i	0.862340	+	0.506329i	$0.168998\pi$
$79$			80.0000i			1.01266i	−0.862340	+	0.506329i	$0.831002\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−69.8105	+	69.8105i	−0.851347	+	0.851347i
$83$	111.452	+	111.452i	1.34279	+	1.34279i	0.893268	+	0.449525i	$0.148407\pi$
$83$	111.452	+	111.452i	1.34279	+	1.34279i	0.449525	+	0.893268i	$0.351593\pi$
$84$			12.0000i			0.142857i
$85$		0			0
$86$	12.0000			0.139535
$87$	−36.7423	+	36.7423i	−0.422326	+	0.422326i
$88$	18.3712	+	18.3712i	0.208763	+	0.208763i
$89$			15.0000i			0.168539i	0.996443	+	0.0842697i	$0.0268557\pi$
$89$			15.0000i			0.168539i	−0.996443	+	0.0842697i	$0.973144\pi$
$90$		0			0
$91$	72.0000			0.791209
$92$	17.1464	−	17.1464i	0.186374	−	0.186374i
$93$	−46.5403	−	46.5403i	−0.500433	−	0.500433i
$94$		−	18.0000i		−	0.191489i
$95$		0			0
$96$	27.0000			0.281250
$97$	53.8888	−	53.8888i	0.555554	−	0.555554i	−0.372484	−	0.928039i	$-0.621494\pi$
$97$	53.8888	−	53.8888i	0.555554	−	0.555554i	0.928039	+	0.372484i	$0.121494\pi$
$98$	−1.22474	−	1.22474i	−0.0124974	−	0.0124974i
$99$			18.0000i			0.181818i
$100$		0			0
$101$	−48.0000			−0.475248			−0.237624	−	0.971357i	$-0.576369\pi$
$101$	−48.0000			−0.475248			−0.237624	+	0.971357i	$0.576369\pi$
$102$	40.4166	−	40.4166i	0.396241	−	0.396241i
$103$	−90.6311	−	90.6311i	−0.879914	−	0.879914i	0.113611	−	0.993525i	$-0.463758\pi$
$103$	−90.6311	−	90.6311i	−0.879914	−	0.879914i	−0.993525	+	0.113611i	$0.963758\pi$
$104$		−	90.0000i		−	0.865385i
$105$		0			0
$106$	−78.0000			−0.735849
$107$	−25.7196	+	25.7196i	−0.240370	+	0.240370i	−0.817003	−	0.576633i	$-0.804366\pi$
$107$	−25.7196	+	25.7196i	−0.240370	+	0.240370i	0.576633	+	0.817003i	$0.304366\pi$
$108$	18.3712	+	18.3712i	0.170103	+	0.170103i
$109$		−	40.0000i		−	0.366972i	−0.983022	−	0.183486i	$-0.941262\pi$
$109$		−	40.0000i		−	0.366972i	0.983022	−	0.183486i	$-0.0587383\pi$
$110$		0			0
$111$	−48.0000			−0.432432
$112$	53.8888	−	53.8888i	0.481150	−	0.481150i
$113$	−84.5074	−	84.5074i	−0.747853	−	0.747853i	0.226223	−	0.974076i	$-0.427362\pi$
$113$	−84.5074	−	84.5074i	−0.747853	−	0.747853i	−0.974076	+	0.226223i	$0.927362\pi$
$114$			15.0000i			0.131579i
$115$		0			0
$116$	−30.0000			−0.258621
$117$	44.0908	−	44.0908i	0.376845	−	0.376845i
$118$	110.227	+	110.227i	0.934127	+	0.934127i
$119$			132.000i			1.10924i
$120$		0			0
$121$	−112.000			−0.925620
$122$	34.2929	−	34.2929i	0.281089	−	0.281089i
$123$	69.8105	+	69.8105i	0.567565	+	0.567565i
$124$		−	38.0000i		−	0.306452i
$125$		0			0
$126$	72.0000			0.571429
$127$	−154.318	+	154.318i	−1.21510	+	1.21510i	−0.245774	+	0.969327i	$0.579042\pi$
$127$	−154.318	+	154.318i	−1.21510	+	1.21510i	−0.969327	+	0.245774i	$0.920958\pi$
$128$	−42.8661	−	42.8661i	−0.334891	−	0.334891i
$129$		−	12.0000i		−	0.0930233i
$130$		0			0
$131$	162.000			1.23664			0.618321	−	0.785926i	$-0.287813\pi$
$131$	162.000			1.23664			0.618321	+	0.785926i	$0.287813\pi$
$132$	3.67423	−	3.67423i	0.0278351	−	0.0278351i
$133$	−24.4949	−	24.4949i	−0.184172	−	0.184172i
$134$			117.000i			0.873134i
$135$		0			0
$136$	165.000			1.21324
$137$	−50.2145	+	50.2145i	−0.366529	+	0.366529i	−0.866210	−	0.499680i	$-0.833451\pi$
$137$	−50.2145	+	50.2145i	−0.366529	+	0.366529i	0.499680	+	0.866210i	$0.333451\pi$
$138$	51.4393	+	51.4393i	0.372748	+	0.372748i
$139$		−	185.000i		−	1.33094i	−0.746427	−	0.665468i	$-0.768232\pi$
$139$		−	185.000i		−	1.33094i	0.746427	−	0.665468i	$-0.231768\pi$
$140$		0			0
$141$	−18.0000			−0.127660
$142$	−51.4393	+	51.4393i	−0.362248	+	0.362248i
$143$	−22.0454	−	22.0454i	−0.154164	−	0.154164i
$144$		−	66.0000i		−	0.458333i
$145$		0			0
$146$	−33.0000			−0.226027
$147$	−1.22474	+	1.22474i	−0.00833160	+	0.00833160i
$148$	−19.5959	−	19.5959i	−0.132405	−	0.132405i
$149$			150.000i			1.00671i	0.864079	+	0.503356i	$0.167901\pi$
$149$			150.000i			1.00671i	−0.864079	+	0.503356i	$0.832099\pi$
$150$		0			0
$151$	52.0000			0.344371			0.172185	−	0.985065i	$-0.444917\pi$
$151$	52.0000			0.344371			0.172185	+	0.985065i	$0.444917\pi$
$152$	−30.6186	+	30.6186i	−0.201438	+	0.201438i
$153$	80.8332	+	80.8332i	0.528321	+	0.528321i
$154$		−	36.0000i		−	0.233766i
$155$		0			0
$156$	−18.0000			−0.115385
$157$	188.611	−	188.611i	1.20134	−	1.20134i	0.227584	−	0.973759i	$-0.426918\pi$
$157$	188.611	−	188.611i	1.20134	−	1.20134i	0.973759	−	0.227584i	$-0.0730825\pi$
$158$	−97.9796	−	97.9796i	−0.620124	−	0.620124i
$159$			78.0000i			0.490566i
$160$		0			0
$161$	−168.000			−1.04348
$162$	11.0227	−	11.0227i	0.0680414	−	0.0680414i
$163$	99.2043	+	99.2043i	0.608616	+	0.608616i	0.942584	−	0.333969i	$-0.108388\pi$
$163$	99.2043	+	99.2043i	0.608616	+	0.608616i	−0.333969	+	0.942584i	$0.608388\pi$
$164$			57.0000i			0.347561i
$165$		0			0
$166$	−273.000			−1.64458
$167$	17.1464	−	17.1464i	0.102673	−	0.102673i	−0.653904	−	0.756577i	$-0.726870\pi$
$167$	17.1464	−	17.1464i	0.102673	−	0.102673i	0.756577	+	0.653904i	$0.226870\pi$
$168$	−73.4847	−	73.4847i	−0.437409	−	0.437409i
$169$		−	61.0000i		−	0.360947i
$170$		0			0
$171$	−30.0000			−0.175439
$172$	4.89898	−	4.89898i	0.0284824	−	0.0284824i
$173$	−78.3837	−	78.3837i	−0.453085	−	0.453085i	0.443292	−	0.896377i	$-0.353810\pi$
$173$	−78.3837	−	78.3837i	−0.453085	−	0.453085i	−0.896377	+	0.443292i	$0.853810\pi$
$174$		−	90.0000i		−	0.517241i
$175$		0			0
$176$	−33.0000			−0.187500
$177$	110.227	−	110.227i	0.622752	−	0.622752i
$178$	−18.3712	−	18.3712i	−0.103209	−	0.103209i
$179$		−	195.000i		−	1.08939i	−0.838636	−	0.544693i	$-0.816646\pi$
$179$		−	195.000i		−	1.08939i	0.838636	−	0.544693i	$-0.183354\pi$
$180$		0			0
$181$	262.000			1.44751			0.723757	−	0.690055i	$-0.242414\pi$
$181$	262.000			1.44751			0.723757	+	0.690055i	$0.242414\pi$
$182$	−88.1816	+	88.1816i	−0.484514	+	0.484514i
$183$	−34.2929	−	34.2929i	−0.187393	−	0.187393i
$184$			210.000i			1.14130i
$185$		0			0
$186$	114.000			0.612903
$187$	40.4166	−	40.4166i	0.216131	−	0.216131i
$188$	−7.34847	−	7.34847i	−0.0390876	−	0.0390876i
$189$		−	180.000i		−	0.952381i
$190$		0			0
$191$	−18.0000			−0.0942408			−0.0471204	−	0.998889i	$-0.515004\pi$
$191$	−18.0000			−0.0942408			−0.0471204	+	0.998889i	$0.515004\pi$
$192$	−86.9569	+	86.9569i	−0.452900	+	0.452900i
$193$	86.9569	+	86.9569i	0.450554	+	0.450554i	0.895538	−	0.444984i	$-0.146791\pi$
$193$	86.9569	+	86.9569i	0.450554	+	0.450554i	−0.444984	+	0.895538i	$0.646791\pi$
$194$			132.000i			0.680412i
$195$		0			0
$196$	−1.00000			−0.00510204
$197$	−129.823	+	129.823i	−0.659000	+	0.659000i	−0.955143	−	0.296144i	$-0.904299\pi$
$197$	−129.823	+	129.823i	−0.659000	+	0.659000i	0.296144	+	0.955143i	$0.404299\pi$
$198$	−22.0454	−	22.0454i	−0.111340	−	0.111340i
$199$			200.000i			1.00503i	0.864570	+	0.502513i	$0.167591\pi$
$199$			200.000i			1.00503i	−0.864570	+	0.502513i	$0.832409\pi$
$200$		0			0
$201$	117.000			0.582090
$202$	58.7878	−	58.7878i	0.291028	−	0.291028i
$203$	146.969	+	146.969i	0.723987	+	0.723987i
$204$		−	33.0000i		−	0.161765i
$205$		0			0
$206$	222.000			1.07767
$207$	−102.879	+	102.879i	−0.496998	+	0.496998i
$208$	80.8332	+	80.8332i	0.388621	+	0.388621i
$209$			15.0000i			0.0717703i
$210$		0			0
$211$	−103.000			−0.488152			−0.244076	−	0.969756i	$-0.578485\pi$
$211$	−103.000			−0.488152			−0.244076	+	0.969756i	$0.578485\pi$
$212$	−31.8434	+	31.8434i	−0.150205	+	0.150205i
$213$	51.4393	+	51.4393i	0.241499	+	0.241499i
$214$		−	63.0000i		−	0.294393i
$215$		0			0
$216$	−225.000			−1.04167
$217$	−186.161	+	186.161i	−0.857886	+	0.857886i
$218$	48.9898	+	48.9898i	0.224724	+	0.224724i
$219$			33.0000i			0.150685i
$220$		0			0
$221$	−198.000			−0.895928
$222$	58.7878	−	58.7878i	0.264810	−	0.264810i
$223$	−200.858	−	200.858i	−0.900709	−	0.900709i	0.0947882	−	0.995497i	$-0.469783\pi$
$223$	−200.858	−	200.858i	−0.900709	−	0.900709i	−0.995497	+	0.0947882i	$0.969783\pi$
$224$		−	108.000i		−	0.482143i
$225$		0			0
$226$	207.000			0.915929
$227$	274.343	−	274.343i	1.20856	−	1.20856i	0.237065	−	0.971494i	$-0.423815\pi$
$227$	274.343	−	274.343i	1.20856	−	1.20856i	0.971494	−	0.237065i	$-0.0761854\pi$
$228$	6.12372	+	6.12372i	0.0268584	+	0.0268584i
$229$		−	20.0000i		−	0.0873362i	−0.999046	−	0.0436681i	$-0.986096\pi$
$229$		−	20.0000i		−	0.0873362i	0.999046	−	0.0436681i	$-0.0139044\pi$
$230$		0			0
$231$	−36.0000			−0.155844
$232$	183.712	−	183.712i	0.791861	−	0.791861i
$233$	−102.879	−	102.879i	−0.441539	−	0.441539i	0.450990	−	0.892529i	$-0.351071\pi$
$233$	−102.879	−	102.879i	−0.441539	−	0.441539i	−0.892529	+	0.450990i	$0.851071\pi$
$234$			108.000i			0.461538i
$235$		0			0
$236$	90.0000			0.381356
$237$	−97.9796	+	97.9796i	−0.413416	+	0.413416i
$238$	−161.666	−	161.666i	−0.679270	−	0.679270i
$239$		−	210.000i		−	0.878661i	−0.898325	−	0.439331i	$-0.855216\pi$
$239$		−	210.000i		−	0.878661i	0.898325	−	0.439331i	$-0.144784\pi$
$240$		0			0
$241$	−43.0000			−0.178423			−0.0892116	−	0.996013i	$-0.528435\pi$
$241$	−43.0000			−0.178423			−0.0892116	+	0.996013i	$0.528435\pi$
$242$	137.171	−	137.171i	0.566824	−	0.566824i
$243$	−176.363	−	176.363i	−0.725775	−	0.725775i
$244$		−	28.0000i		−	0.114754i
$245$		0			0
$246$	−171.000			−0.695122
$247$	36.7423	−	36.7423i	0.148754	−	0.148754i
$248$	232.702	+	232.702i	0.938313	+	0.938313i
$249$			273.000i			1.09639i
$250$		0			0
$251$	−123.000			−0.490040			−0.245020	−	0.969518i	$-0.578795\pi$
$251$	−123.000			−0.490040			−0.245020	+	0.969518i	$0.578795\pi$
$252$	29.3939	−	29.3939i	0.116642	−	0.116642i
$253$	51.4393	+	51.4393i	0.203317	+	0.203317i
$254$		−	378.000i		−	1.48819i
$255$		0			0
$256$	−179.000			−0.699219
$257$	4.89898	−	4.89898i	0.0190622	−	0.0190622i	−0.697511	−	0.716574i	$-0.745709\pi$
$257$	4.89898	−	4.89898i	0.0190622	−	0.0190622i	0.716574	+	0.697511i	$0.245709\pi$
$258$	14.6969	+	14.6969i	0.0569649	+	0.0569649i
$259$			192.000i			0.741313i
$260$		0			0
$261$	180.000			0.689655
$262$	−198.409	+	198.409i	−0.757285	+	0.757285i
$263$	7.34847	+	7.34847i	0.0279409	+	0.0279409i	0.720939	−	0.692998i	$-0.243711\pi$
$263$	7.34847	+	7.34847i	0.0279409	+	0.0279409i	−0.692998	+	0.720939i	$0.743711\pi$
$264$			45.0000i			0.170455i
$265$		0			0
$266$	60.0000			0.225564
$267$	−18.3712	+	18.3712i	−0.0688059	+	0.0688059i
$268$	47.7650	+	47.7650i	0.178228	+	0.178228i
$269$			120.000i			0.446097i	0.974807	+	0.223048i	$0.0716008\pi$
$269$			120.000i			0.446097i	−0.974807	+	0.223048i	$0.928399\pi$
$270$		0			0
$271$	−58.0000			−0.214022			−0.107011	−	0.994258i	$-0.534128\pi$
$271$	−58.0000			−0.214022			−0.107011	+	0.994258i	$0.534128\pi$
$272$	−148.194	+	148.194i	−0.544831	+	0.544831i
$273$	88.1816	+	88.1816i	0.323010	+	0.323010i
$274$		−	123.000i		−	0.448905i
$275$		0			0
$276$	42.0000			0.152174
$277$	−276.792	+	276.792i	−0.999250	+	0.999250i	−1.00000		0.000749391i	$-0.999761\pi$
$277$	−276.792	+	276.792i	−0.999250	+	0.999250i	0.000749391		1.00000i	$0.499761\pi$
$278$	226.578	+	226.578i	0.815028	+	0.815028i
$279$			228.000i			0.817204i
$280$		0			0
$281$	462.000			1.64413			0.822064	−	0.569395i	$-0.192822\pi$
$281$	462.000			1.64413			0.822064	+	0.569395i	$0.192822\pi$
$282$	22.0454	−	22.0454i	0.0781752	−	0.0781752i
$283$	−72.2599	−	72.2599i	−0.255336	−	0.255336i	0.567818	−	0.823154i	$-0.307788\pi$
$283$	−72.2599	−	72.2599i	−0.255336	−	0.255336i	−0.823154	+	0.567818i	$0.807788\pi$
$284$			42.0000i			0.147887i
$285$		0			0
$286$	54.0000			0.188811
$287$	279.242	−	279.242i	0.972968	−	0.972968i
$288$	−66.1362	−	66.1362i	−0.229640	−	0.229640i
$289$		−	74.0000i		−	0.256055i
$290$		0			0
$291$	132.000			0.453608
$292$	−13.4722	+	13.4722i	−0.0461376	+	0.0461376i
$293$	−4.89898	−	4.89898i	−0.0167201	−	0.0167201i	0.698697	−	0.715417i	$-0.253763\pi$
$293$	−4.89898	−	4.89898i	−0.0167201	−	0.0167201i	−0.715417	+	0.698697i	$0.753763\pi$
$294$		−	3.00000i		−	0.0102041i
$295$		0			0
$296$	240.000			0.810811
$297$	−55.1135	+	55.1135i	−0.185567	+	0.185567i
$298$	−183.712	−	183.712i	−0.616482	−	0.616482i
$299$		−	252.000i		−	0.842809i
$300$		0			0
$301$	−48.0000			−0.159468
$302$	−63.6867	+	63.6867i	−0.210883	+	0.210883i
$303$	−58.7878	−	58.7878i	−0.194019	−	0.194019i
$304$		−	55.0000i		−	0.180921i
$305$		0			0
$306$	−198.000			−0.647059
$307$	−86.9569	+	86.9569i	−0.283247	+	0.283247i	−0.834403	−	0.551155i	$-0.814187\pi$
$307$	−86.9569	+	86.9569i	−0.283247	+	0.283247i	0.551155	+	0.834403i	$0.314187\pi$
$308$	−14.6969	−	14.6969i	−0.0477173	−	0.0477173i
$309$		−	222.000i		−	0.718447i
$310$		0			0
$311$	−528.000			−1.69775			−0.848875	−	0.528594i	$-0.822719\pi$
$311$	−528.000			−1.69775			−0.848875	+	0.528594i	$0.822719\pi$
$312$	110.227	−	110.227i	0.353292	−	0.353292i
$313$	191.060	+	191.060i	0.610416	+	0.610416i	0.943054	−	0.332638i	$-0.107939\pi$
$313$	191.060	+	191.060i	0.610416	+	0.610416i	−0.332638	+	0.943054i	$0.607939\pi$
$314$			462.000i			1.47134i
$315$		0			0
$316$	−80.0000			−0.253165
$317$	200.858	−	200.858i	0.633622	−	0.633622i	−0.315353	−	0.948975i	$-0.602123\pi$
$317$	200.858	−	200.858i	0.633622	−	0.633622i	0.948975	+	0.315353i	$0.102123\pi$
$318$	−95.5301	−	95.5301i	−0.300409	−	0.300409i
$319$		−	90.0000i		−	0.282132i
$320$		0			0
$321$	−63.0000			−0.196262
$322$	205.757	−	205.757i	0.638997	−	0.638997i
$323$	67.3610	+	67.3610i	0.208548	+	0.208548i
$324$		−	9.00000i		−	0.0277778i
$325$		0			0
$326$	−243.000			−0.745399
$327$	48.9898	−	48.9898i	0.149816	−	0.149816i
$328$	−349.052	−	349.052i	−1.06418	−	1.06418i
$329$			72.0000i			0.218845i
$330$		0			0
$331$	−313.000			−0.945619			−0.472810	−	0.881165i	$-0.656760\pi$
$331$	−313.000			−0.945619			−0.472810	+	0.881165i	$0.656760\pi$
$332$	−111.452	+	111.452i	−0.335698	+	0.335698i
$333$	117.576	+	117.576i	0.353080	+	0.353080i
$334$			42.0000i			0.125749i
$335$		0			0
$336$	132.000			0.392857
$337$	194.734	−	194.734i	0.577847	−	0.577847i	−0.356463	−	0.934310i	$-0.616017\pi$
$337$	194.734	−	194.734i	0.577847	−	0.577847i	0.934310	+	0.356463i	$0.116017\pi$
$338$	74.7094	+	74.7094i	0.221034	+	0.221034i
$339$		−	207.000i		−	0.610619i
$340$		0			0
$341$	114.000			0.334311
$342$	36.7423	−	36.7423i	0.107434	−	0.107434i
$343$	244.949	+	244.949i	0.714137	+	0.714137i
$344$			60.0000i			0.174419i
$345$		0			0
$346$	192.000			0.554913
$347$	−99.2043	+	99.2043i	−0.285891	+	0.285891i	−0.835453	−	0.549562i	$-0.814795\pi$
$347$	−99.2043	+	99.2043i	−0.285891	+	0.285891i	0.549562	+	0.835453i	$0.314795\pi$
$348$	−36.7423	−	36.7423i	−0.105581	−	0.105581i
$349$			100.000i			0.286533i	0.989684	+	0.143266i	$0.0457606\pi$
$349$			100.000i			0.286533i	−0.989684	+	0.143266i	$0.954239\pi$
$350$		0			0
$351$	270.000			0.769231
$352$	−33.0681	+	33.0681i	−0.0939435	+	0.0939435i
$353$	−396.817	−	396.817i	−1.12413	−	1.12413i	−0.991114	−	0.133014i	$-0.957534\pi$
$353$	−396.817	−	396.817i	−1.12413	−	1.12413i	−0.133014	−	0.991114i	$-0.542466\pi$
$354$			270.000i			0.762712i
$355$		0			0
$356$	−15.0000			−0.0421348
$357$	−161.666	+	161.666i	−0.452847	+	0.452847i
$358$	238.825	+	238.825i	0.667110	+	0.667110i
$359$		−	540.000i		−	1.50418i	−0.659061	−	0.752089i	$-0.729046\pi$
$359$		−	540.000i		−	1.50418i	0.659061	−	0.752089i	$-0.270954\pi$
$360$		0			0
$361$	336.000			0.930748
$362$	−320.883	+	320.883i	−0.886418	+	0.886418i
$363$	−137.171	−	137.171i	−0.377883	−	0.377883i
$364$			72.0000i			0.197802i
$365$		0			0
$366$	84.0000			0.229508
$367$	−44.0908	+	44.0908i	−0.120138	+	0.120138i	−0.764620	−	0.644481i	$-0.777073\pi$
$367$	−44.0908	+	44.0908i	−0.120138	+	0.120138i	0.644481	+	0.764620i	$0.277073\pi$
$368$	−188.611	−	188.611i	−0.512529	−	0.512529i
$369$		−	342.000i		−	0.926829i
$370$		0			0
$371$	312.000			0.840970
$372$	46.5403	−	46.5403i	0.125108	−	0.125108i
$373$	350.277	+	350.277i	0.939081	+	0.939081i	0.998248	−	0.0591675i	$-0.0188446\pi$
$373$	350.277	+	350.277i	0.939081	+	0.939081i	−0.0591675	+	0.998248i	$0.518845\pi$
$374$			99.0000i			0.264706i
$375$		0			0
$376$	90.0000			0.239362
$377$	−220.454	+	220.454i	−0.584759	+	0.584759i
$378$	220.454	+	220.454i	0.583212	+	0.583212i
$379$			505.000i			1.33245i	0.745749	+	0.666227i	$0.232092\pi$
$379$			505.000i			1.33245i	−0.745749	+	0.666227i	$0.767908\pi$
$380$		0			0
$381$	−378.000			−0.992126
$382$	22.0454	−	22.0454i	0.0577105	−	0.0577105i
$383$	142.070	+	142.070i	0.370941	+	0.370941i	0.867820	−	0.496879i	$-0.165521\pi$
$383$	142.070	+	142.070i	0.370941	+	0.370941i	−0.496879	+	0.867820i	$0.665521\pi$
$384$		−	105.000i		−	0.273438i
$385$		0			0
$386$	−213.000			−0.551813
$387$	−29.3939	+	29.3939i	−0.0759532	+	0.0759532i
$388$	53.8888	+	53.8888i	0.138889	+	0.138889i
$389$			690.000i			1.77378i	0.461982	+	0.886889i	$0.347139\pi$
$389$			690.000i			1.77378i	−0.461982	+	0.886889i	$0.652861\pi$
$390$		0			0
$391$	462.000			1.18159
$392$	6.12372	−	6.12372i	0.0156217	−	0.0156217i
$393$	198.409	+	198.409i	0.504857	+	0.504857i
$394$		−	318.000i		−	0.807107i
$395$		0			0
$396$	−18.0000			−0.0454545
$397$	421.312	−	421.312i	1.06124	−	1.06124i	0.0632416	−	0.997998i	$-0.479856\pi$
$397$	421.312	−	421.312i	1.06124	−	1.06124i	0.997998	−	0.0632416i	$-0.0201439\pi$
$398$	−244.949	−	244.949i	−0.615450	−	0.615450i
$399$		−	60.0000i		−	0.150376i
$400$		0			0
$401$	−573.000			−1.42893			−0.714464	−	0.699672i	$-0.753329\pi$
$401$	−573.000			−1.42893			−0.714464	+	0.699672i	$0.753329\pi$
$402$	−143.295	+	143.295i	−0.356456	+	0.356456i
$403$	−279.242	−	279.242i	−0.692908	−	0.692908i
$404$		−	48.0000i		−	0.118812i
$405$		0			0
$406$	−360.000			−0.886700
$407$	58.7878	−	58.7878i	0.144442	−	0.144442i
$408$	202.083	+	202.083i	0.495301	+	0.495301i
$409$		−	365.000i		−	0.892421i	−0.894928	−	0.446210i	$-0.852773\pi$
$409$		−	365.000i		−	0.892421i	0.894928	−	0.446210i	$-0.147227\pi$
$410$		0			0
$411$	−123.000			−0.299270
$412$	90.6311	−	90.6311i	0.219978	−	0.219978i
$413$	−440.908	−	440.908i	−1.06757	−	1.06757i
$414$		−	252.000i		−	0.608696i
$415$		0			0
$416$	162.000			0.389423
$417$	226.578	−	226.578i	0.543352	−	0.543352i
$418$	−18.3712	−	18.3712i	−0.0439502	−	0.0439502i
$419$			645.000i			1.53938i	0.638418	+	0.769690i	$0.279589\pi$
$419$			645.000i			1.53938i	−0.638418	+	0.769690i	$0.720411\pi$
$420$		0			0
$421$	−8.00000			−0.0190024			−0.00950119	−	0.999955i	$-0.503024\pi$
$421$	−8.00000			−0.0190024			−0.00950119	+	0.999955i	$0.503024\pi$
$422$	126.149	−	126.149i	0.298931	−	0.298931i
$423$	44.0908	+	44.0908i	0.104234	+	0.104234i
$424$		−	390.000i		−	0.919811i
$425$		0			0
$426$	−126.000			−0.295775
$427$	−137.171	+	137.171i	−0.321245	+	0.321245i
$428$	−25.7196	−	25.7196i	−0.0600926	−	0.0600926i
$429$		−	54.0000i		−	0.125874i
$430$		0			0
$431$	12.0000			0.0278422			0.0139211	−	0.999903i	$-0.495569\pi$
$431$	12.0000			0.0278422			0.0139211	+	0.999903i	$0.495569\pi$
$432$	202.083	−	202.083i	0.467784	−	0.467784i
$433$	−439.683	−	439.683i	−1.01544	−	1.01544i	−0.999879	−	0.0155561i	$-0.995048\pi$
$433$	−439.683	−	439.683i	−1.01544	−	1.01544i	−0.0155561	−	0.999879i	$-0.504952\pi$
$434$		−	456.000i		−	1.05069i
$435$		0			0
$436$	40.0000			0.0917431
$437$	−85.7321	+	85.7321i	−0.196183	+	0.196183i
$438$	−40.4166	−	40.4166i	−0.0922753	−	0.0922753i
$439$		−	10.0000i		−	0.0227790i	−0.999935	−	0.0113895i	$-0.996375\pi$
$439$		−	10.0000i		−	0.0227790i	0.999935	−	0.0113895i	$-0.00362548\pi$
$440$		0			0
$441$	6.00000			0.0136054
$442$	242.499	−	242.499i	0.548641	−	0.548641i
$443$	86.9569	+	86.9569i	0.196291	+	0.196291i	0.798408	−	0.602117i	$-0.205676\pi$
$443$	86.9569	+	86.9569i	0.196291	+	0.196291i	−0.602117	+	0.798408i	$0.705676\pi$
$444$		−	48.0000i		−	0.108108i
$445$		0			0
$446$	492.000			1.10314
$447$	−183.712	+	183.712i	−0.410988	+	0.410988i
$448$	347.828	+	347.828i	0.776401	+	0.776401i
$449$			75.0000i			0.167038i	0.996506	+	0.0835189i	$0.0266159\pi$
$449$			75.0000i			0.167038i	−0.996506	+	0.0835189i	$0.973384\pi$
$450$		0			0
$451$	−171.000			−0.379157
$452$	84.5074	−	84.5074i	0.186963	−	0.186963i
$453$	63.6867	+	63.6867i	0.140589	+	0.140589i
$454$			672.000i			1.48018i
$455$		0			0
$456$	−75.0000			−0.164474
$457$	−209.431	+	209.431i	−0.458274	+	0.458274i	−0.898089	−	0.439814i	$-0.855044\pi$
$457$	−209.431	+	209.431i	−0.458274	+	0.458274i	0.439814	+	0.898089i	$0.355044\pi$
$458$	24.4949	+	24.4949i	0.0534823	+	0.0534823i
$459$			495.000i			1.07843i
$460$		0			0
$461$	−228.000			−0.494577			−0.247289	−	0.968942i	$-0.579540\pi$
$461$	−228.000			−0.494577			−0.247289	+	0.968942i	$0.579540\pi$
$462$	44.0908	−	44.0908i	0.0954347	−	0.0954347i
$463$	436.009	+	436.009i	0.941704	+	0.941704i	0.998392	−	0.0566875i	$-0.0180539\pi$
$463$	436.009	+	436.009i	0.941704	+	0.941704i	−0.0566875	+	0.998392i	$0.518054\pi$
$464$			330.000i			0.711207i
$465$		0			0
$466$	252.000			0.540773
$467$	−533.989	+	533.989i	−1.14344	+	1.14344i	−0.155629	+	0.987816i	$0.549741\pi$
$467$	−533.989	+	533.989i	−1.14344	+	1.14344i	−0.987816	+	0.155629i	$0.950259\pi$
$468$	44.0908	+	44.0908i	0.0942111	+	0.0942111i
$469$		−	468.000i		−	0.997868i
$470$		0			0
$471$	462.000			0.980892
$472$	−551.135	+	551.135i	−1.16766	+	1.16766i
$473$	14.6969	+	14.6969i	0.0310718	+	0.0310718i
$474$		−	240.000i		−	0.506329i
$475$		0			0
$476$	−132.000			−0.277311
$477$	191.060	−	191.060i	0.400545	−	0.400545i
$478$	257.196	+	257.196i	0.538068	+	0.538068i
$479$		−	270.000i		−	0.563674i	−0.959462	−	0.281837i	$-0.909056\pi$
$479$		−	270.000i		−	0.563674i	0.959462	−	0.281837i	$-0.0909438\pi$
$480$		0			0
$481$	−288.000			−0.598753
$482$	52.6640	−	52.6640i	0.109261	−	0.109261i
$483$	−205.757	−	205.757i	−0.425998	−	0.425998i
$484$		−	112.000i		−	0.231405i
$485$		0			0
$486$	432.000			0.888889
$487$	−80.8332	+	80.8332i	−0.165982	+	0.165982i	−0.785211	−	0.619229i	$-0.787445\pi$
$487$	−80.8332	+	80.8332i	−0.165982	+	0.165982i	0.619229	+	0.785211i	$0.287445\pi$
$488$	171.464	+	171.464i	0.351361	+	0.351361i
$489$			243.000i			0.496933i
$490$		0			0
$491$	582.000			1.18534			0.592668	−	0.805447i	$-0.298075\pi$
$491$	582.000			1.18534			0.592668	+	0.805447i	$0.298075\pi$
$492$	−69.8105	+	69.8105i	−0.141891	+	0.141891i
$493$	−404.166	−	404.166i	−0.819809	−	0.819809i
$494$			90.0000i			0.182186i
$495$		0			0
$496$	−418.000			−0.842742
$497$	205.757	−	205.757i	0.413998	−	0.413998i
$498$	−334.355	−	334.355i	−0.671396	−	0.671396i
$499$		−	250.000i		−	0.501002i	−0.968116	−	0.250501i	$-0.919405\pi$
$499$		−	250.000i		−	0.501002i	0.968116	−	0.250501i	$-0.0805953\pi$
$500$		0			0
$501$	42.0000			0.0838323
$502$	150.644	−	150.644i	0.300087	−	0.300087i
$503$	460.504	+	460.504i	0.915515	+	0.915515i	0.996699	−	0.0811841i	$-0.0258702\pi$
$503$	460.504	+	460.504i	0.915515	+	0.915515i	−0.0811841	+	0.996699i	$0.525870\pi$
$504$			360.000i			0.714286i
$505$		0			0
$506$	−126.000			−0.249012
$507$	74.7094	−	74.7094i	0.147356	−	0.147356i
$508$	−154.318	−	154.318i	−0.303775	−	0.303775i
$509$		−	390.000i		−	0.766208i	−0.923705	−	0.383104i	$-0.874855\pi$
$509$		−	390.000i		−	0.766208i	0.923705	−	0.383104i	$-0.125145\pi$
$510$		0			0
$511$	132.000			0.258317
$512$	390.694	−	390.694i	0.763073	−	0.763073i
$513$	−91.8559	−	91.8559i	−0.179056	−	0.179056i
$514$			12.0000i			0.0233463i
$515$		0			0
$516$	12.0000			0.0232558
$517$	22.0454	−	22.0454i	0.0426410	−	0.0426410i
$518$	−235.151	−	235.151i	−0.453959	−	0.453959i
$519$		−	192.000i		−	0.369942i
$520$		0			0
$521$	−183.000			−0.351248			−0.175624	−	0.984457i	$-0.556194\pi$
$521$	−183.000			−0.351248			−0.175624	+	0.984457i	$0.556194\pi$
$522$	−220.454	+	220.454i	−0.422326	+	0.422326i
$523$	−476.426	−	476.426i	−0.910948	−	0.910948i	0.0853989	−	0.996347i	$-0.472784\pi$
$523$	−476.426	−	476.426i	−0.910948	−	0.910948i	−0.996347	+	0.0853989i	$0.972784\pi$
$524$			162.000i			0.309160i
$525$		0			0
$526$	−18.0000			−0.0342205
$527$	511.943	−	511.943i	0.971430	−	0.971430i
$528$	−40.4166	−	40.4166i	−0.0765466	−	0.0765466i
$529$			59.0000i			0.111531i
$530$		0			0
$531$	−540.000			−1.01695
$532$	24.4949	−	24.4949i	0.0460430	−	0.0460430i
$533$	418.863	+	418.863i	0.785859	+	0.785859i
$534$		−	45.0000i		−	0.0842697i
$535$		0			0
$536$	−585.000			−1.09142
$537$	238.825	−	238.825i	0.444740	−	0.444740i
$538$	−146.969	−	146.969i	−0.273177	−	0.273177i
$539$		−	3.00000i		−	0.00556586i
$540$		0			0
$541$	−568.000			−1.04991			−0.524954	−	0.851131i	$-0.675917\pi$
$541$	−568.000			−1.04991			−0.524954	+	0.851131i	$0.675917\pi$
$542$	71.0352	−	71.0352i	0.131061	−	0.131061i
$543$	320.883	+	320.883i	0.590945	+	0.590945i
$544$			297.000i			0.545956i
$545$		0			0
$546$	−216.000			−0.395604
$547$	−160.442	+	160.442i	−0.293312	+	0.293312i	−0.838387	−	0.545075i	$-0.816501\pi$
$547$	−160.442	+	160.442i	−0.293312	+	0.293312i	0.545075	+	0.838387i	$0.316501\pi$
$548$	−50.2145	−	50.2145i	−0.0916324	−	0.0916324i
$549$			168.000i			0.306011i
$550$		0			0
$551$	150.000			0.272232
$552$	−257.196	+	257.196i	−0.465936	+	0.465936i
$553$	391.918	+	391.918i	0.708713	+	0.708713i
$554$		−	678.000i		−	1.22383i
$555$		0			0
$556$	185.000			0.332734
$557$	66.1362	−	66.1362i	0.118736	−	0.118736i	−0.645242	−	0.763978i	$-0.723243\pi$
$557$	66.1362	−	66.1362i	0.118736	−	0.118736i	0.763978	+	0.645242i	$0.223243\pi$
$558$	−279.242	−	279.242i	−0.500433	−	0.500433i
$559$		−	72.0000i		−	0.128801i
$560$		0			0
$561$	99.0000			0.176471
$562$	−565.832	+	565.832i	−1.00682	+	1.00682i
$563$	191.060	+	191.060i	0.339361	+	0.339361i	0.856127	−	0.516766i	$-0.172864\pi$
$563$	191.060	+	191.060i	0.339361	+	0.339361i	−0.516766	+	0.856127i	$0.672864\pi$
$564$		−	18.0000i		−	0.0319149i
$565$		0			0
$566$	177.000			0.312721
$567$	−44.0908	+	44.0908i	−0.0777616	+	0.0777616i
$568$	−257.196	−	257.196i	−0.452811	−	0.452811i
$569$			45.0000i			0.0790861i	0.999218	+	0.0395431i	$0.0125902\pi$
$569$			45.0000i			0.0790861i	−0.999218	+	0.0395431i	$0.987410\pi$
$570$		0			0
$571$	542.000			0.949212			0.474606	−	0.880198i	$-0.342591\pi$
$571$	542.000			0.949212			0.474606	+	0.880198i	$0.342591\pi$
$572$	22.0454	−	22.0454i	0.0385409	−	0.0385409i
$573$	−22.0454	−	22.0454i	−0.0384737	−	0.0384737i
$574$			684.000i			1.19164i
$575$		0			0
$576$	426.000			0.739583
$577$	549.910	−	549.910i	0.953051	−	0.953051i	−0.0458952	−	0.998946i	$-0.514614\pi$
$577$	549.910	−	549.910i	0.953051	−	0.953051i	0.998946	+	0.0458952i	$0.0146140\pi$
$578$	90.6311	+	90.6311i	0.156801	+	0.156801i
$579$			213.000i			0.367876i
$580$		0			0
$581$	1092.00			1.87952
$582$	−161.666	+	161.666i	−0.277777	+	0.277777i
$583$	−95.5301	−	95.5301i	−0.163860	−	0.163860i
$584$		−	165.000i		−	0.282534i
$585$		0			0
$586$	12.0000			0.0204778
$587$	−417.638	+	417.638i	−0.711479	+	0.711479i	−0.966845	−	0.255366i	$-0.917804\pi$
$587$	−417.638	+	417.638i	−0.711479	+	0.711479i	0.255366	+	0.966845i	$0.417804\pi$
$588$	−1.22474	−	1.22474i	−0.00208290	−	0.00208290i
$589$			190.000i			0.322581i
$590$		0			0
$591$	−318.000			−0.538071
$592$	−215.555	+	215.555i	−0.364113	+	0.364113i
$593$	331.906	+	331.906i	0.559706	+	0.559706i	0.929224	−	0.369517i	$-0.120477\pi$
$593$	331.906	+	331.906i	0.559706	+	0.559706i	−0.369517	+	0.929224i	$0.620477\pi$
$594$		−	135.000i		−	0.227273i
$595$		0			0
$596$	−150.000			−0.251678
$597$	−244.949	+	244.949i	−0.410300	+	0.410300i
$598$	308.636	+	308.636i	0.516113	+	0.516113i
$599$		−	900.000i		−	1.50250i	−0.660015	−	0.751252i	$-0.729450\pi$
$599$		−	900.000i		−	1.50250i	0.660015	−	0.751252i	$-0.270550\pi$
$600$		0			0
$601$	577.000			0.960067			0.480033	−	0.877250i	$-0.340625\pi$
$601$	577.000			0.960067			0.480033	+	0.877250i	$0.340625\pi$
$602$	58.7878	−	58.7878i	0.0976541	−	0.0976541i
$603$	−286.590	−	286.590i	−0.475274	−	0.475274i
$604$			52.0000i			0.0860927i
$605$		0			0
$606$	144.000			0.237624
$607$	127.373	−	127.373i	0.209841	−	0.209841i	−0.594359	−	0.804200i	$-0.702594\pi$
$607$	127.373	−	127.373i	0.209841	−	0.209841i	0.804200	+	0.594359i	$0.202594\pi$
$608$	−55.1135	−	55.1135i	−0.0906472	−	0.0906472i
$609$			360.000i			0.591133i
$610$		0			0
$611$	−108.000			−0.176759
$612$	−80.8332	+	80.8332i	−0.132080	+	0.132080i
$613$	−237.601	−	237.601i	−0.387603	−	0.387603i	0.486229	−	0.873832i	$-0.338372\pi$
$613$	−237.601	−	237.601i	−0.387603	−	0.387603i	−0.873832	+	0.486229i	$0.838372\pi$
$614$		−	213.000i		−	0.346906i
$615$		0			0
$616$	180.000			0.292208
$617$	−656.463	+	656.463i	−1.06396	+	1.06396i	−0.0661502	+	0.997810i	$0.521072\pi$
$617$	−656.463	+	656.463i	−1.06396	+	1.06396i	−0.997810	+	0.0661502i	$0.978928\pi$
$618$	271.893	+	271.893i	0.439957	+	0.439957i
$619$			470.000i			0.759289i	0.925132	+	0.379645i	$0.123954\pi$
$619$			470.000i			0.759289i	−0.925132	+	0.379645i	$0.876046\pi$
$620$		0			0
$621$	−630.000			−1.01449
$622$	646.665	−	646.665i	1.03965	−	1.03965i
$623$	73.4847	+	73.4847i	0.117953	+	0.117953i
$624$			198.000i			0.317308i
$625$		0			0
$626$	−468.000			−0.747604
$627$	−18.3712	+	18.3712i	−0.0293001	+	0.0293001i
$628$	188.611	+	188.611i	0.300336	+	0.300336i
$629$		−	528.000i		−	0.839428i
$630$		0			0
$631$	−838.000			−1.32805			−0.664025	−	0.747710i	$-0.731153\pi$
$631$	−838.000			−1.32805			−0.664025	+	0.747710i	$0.731153\pi$
$632$	489.898	−	489.898i	0.775155	−	0.775155i
$633$	−126.149	−	126.149i	−0.199287	−	0.199287i
$634$			492.000i			0.776025i
$635$		0			0
$636$	−78.0000			−0.122642
$637$	−7.34847	+	7.34847i	−0.0115361	+	0.0115361i
$638$	110.227	+	110.227i	0.172770	+	0.172770i
$639$		−	252.000i		−	0.394366i
$640$		0			0
$641$	−618.000			−0.964119			−0.482059	−	0.876139i	$-0.660111\pi$
$641$	−618.000			−0.964119			−0.482059	+	0.876139i	$0.660111\pi$
$642$	77.1589	−	77.1589i	0.120185	−	0.120185i
$643$	−249.848	−	249.848i	−0.388566	−	0.388566i	0.485610	−	0.874176i	$-0.338598\pi$
$643$	−249.848	−	249.848i	−0.388566	−	0.388566i	−0.874176	+	0.485610i	$0.838598\pi$
$644$		−	168.000i		−	0.260870i
$645$		0			0
$646$	−165.000			−0.255418
$647$	421.312	−	421.312i	0.651178	−	0.651178i	−0.302099	−	0.953277i	$-0.597687\pi$
$647$	421.312	−	421.312i	0.651178	−	0.651178i	0.953277	+	0.302099i	$0.0976872\pi$
$648$	55.1135	+	55.1135i	0.0850517	+	0.0850517i
$649$			270.000i			0.416025i
$650$		0			0
$651$	−456.000			−0.700461
$652$	−99.2043	+	99.2043i	−0.152154	+	0.152154i
$653$	−519.292	−	519.292i	−0.795240	−	0.795240i	0.187101	−	0.982341i	$-0.440091\pi$
$653$	−519.292	−	519.292i	−0.795240	−	0.795240i	−0.982341	+	0.187101i	$0.940091\pi$
$654$			120.000i			0.183486i
$655$		0			0
$656$	627.000			0.955793
$657$	80.8332	−	80.8332i	0.123034	−	0.123034i
$658$	−88.1816	−	88.1816i	−0.134015	−	0.134015i
$659$			885.000i			1.34294i	0.741030	+	0.671472i	$0.234338\pi$
$659$			885.000i			1.34294i	−0.741030	+	0.671472i	$0.765662\pi$
$660$		0			0
$661$	922.000			1.39486			0.697428	−	0.716655i	$-0.254328\pi$
$661$	922.000			1.39486			0.697428	+	0.716655i	$0.254328\pi$
$662$	383.345	−	383.345i	0.579071	−	0.579071i
$663$	−242.499	−	242.499i	−0.365761	−	0.365761i
$664$		−	1365.00i		−	2.05572i
$665$		0			0
$666$	−288.000			−0.432432
$667$	514.393	−	514.393i	0.771204	−	0.771204i
$668$	17.1464	+	17.1464i	0.0256683	+	0.0256683i
$669$		−	492.000i		−	0.735426i
$670$		0			0
$671$	84.0000			0.125186
$672$	132.272	−	132.272i	0.196834	−	0.196834i
$673$	−78.3837	−	78.3837i	−0.116469	−	0.116469i	0.646470	−	0.762939i	$-0.276244\pi$
$673$	−78.3837	−	78.3837i	−0.116469	−	0.116469i	−0.762939	+	0.646470i	$0.776244\pi$
$674$			477.000i			0.707715i
$675$		0			0
$676$	61.0000			0.0902367
$677$	−705.453	+	705.453i	−1.04203	+	1.04203i	−0.0429510	+	0.999077i	$0.513676\pi$
$677$	−705.453	+	705.453i	−1.04203	+	1.04203i	−0.999077	+	0.0429510i	$0.986324\pi$
$678$	253.522	+	253.522i	0.373927	+	0.373927i
$679$		−	528.000i		−	0.777614i
$680$		0			0
$681$	672.000			0.986784
$682$	−139.621	+	139.621i	−0.204723	+	0.204723i
$683$	−133.497	−	133.497i	−0.195457	−	0.195457i	0.602592	−	0.798049i	$-0.294135\pi$
$683$	−133.497	−	133.497i	−0.195457	−	0.195457i	−0.798049	+	0.602592i	$0.794135\pi$
$684$		−	30.0000i		−	0.0438596i
$685$		0			0
$686$	−600.000			−0.874636
$687$	24.4949	−	24.4949i	0.0356549	−	0.0356549i
$688$	−53.8888	−	53.8888i	−0.0783267	−	0.0783267i
$689$			468.000i			0.679245i
$690$		0			0
$691$	−893.000			−1.29233			−0.646165	−	0.763198i	$-0.723628\pi$
$691$	−893.000			−1.29233			−0.646165	+	0.763198i	$0.723628\pi$
$692$	78.3837	−	78.3837i	0.113271	−	0.113271i
$693$	88.1816	+	88.1816i	0.127246	+	0.127246i
$694$		−	243.000i		−	0.350144i
$695$		0			0
$696$	450.000			0.646552
$697$	−767.915	+	767.915i	−1.10174	+	1.10174i
$698$	−122.474	−	122.474i	−0.175465	−	0.175465i
$699$		−	252.000i		−	0.360515i
$700$		0			0
$701$	402.000			0.573466			0.286733	−	0.958010i	$-0.407431\pi$
$701$	402.000			0.573466			0.286733	+	0.958010i	$0.407431\pi$
$702$	−330.681	+	330.681i	−0.471056	+	0.471056i
$703$	97.9796	+	97.9796i	0.139374	+	0.139374i
$704$		−	213.000i		−	0.302557i
$705$		0			0
$706$	972.000			1.37677
$707$	−235.151	+	235.151i	−0.332604	+	0.332604i
$708$	110.227	+	110.227i	0.155688	+	0.155688i
$709$			1060.00i			1.49506i	0.664226	+	0.747532i	$0.268761\pi$
$709$			1060.00i			1.49506i	−0.664226	+	0.747532i	$0.731239\pi$
$710$		0			0
$711$	480.000			0.675105
$712$	91.8559	−	91.8559i	0.129011	−	0.129011i
$713$	651.564	+	651.564i	0.913835	+	0.913835i
$714$		−	396.000i		−	0.554622i
$715$		0			0
$716$	195.000			0.272346
$717$	257.196	−	257.196i	0.358712	−	0.358712i
$718$	661.362	+	661.362i	0.921117	+	0.921117i
$719$			1320.00i			1.83588i	0.396716	+	0.917942i	$0.370150\pi$
$719$			1320.00i			1.83588i	−0.396716	+	0.917942i	$0.629850\pi$
$720$		0			0
$721$	−888.000			−1.23162
$722$	−411.514	+	411.514i	−0.569964	+	0.569964i
$723$	−52.6640	−	52.6640i	−0.0728410	−	0.0728410i
$724$			262.000i			0.361878i
$725$		0			0
$726$	336.000			0.462810
$727$	−31.8434	+	31.8434i	−0.0438011	+	0.0438011i	−0.728668	−	0.684867i	$-0.759860\pi$
$727$	−31.8434	+	31.8434i	−0.0438011	+	0.0438011i	0.684867	+	0.728668i	$0.259860\pi$
$728$	−440.908	−	440.908i	−0.605643	−	0.605643i
$729$		−	351.000i		−	0.481481i
$730$		0			0
$731$	132.000			0.180575
$732$	34.2929	−	34.2929i	0.0468482	−	0.0468482i
$733$	815.680	+	815.680i	1.11280	+	1.11280i	0.992771	+	0.120026i	$0.0382978\pi$
$733$	815.680	+	815.680i	1.11280	+	1.11280i	0.120026	+	0.992771i	$0.461702\pi$
$734$		−	108.000i		−	0.147139i
$735$		0			0
$736$	−378.000			−0.513587
$737$	−143.295	+	143.295i	−0.194430	+	0.194430i
$738$	418.863	+	418.863i	0.567565	+	0.567565i
$739$		−	710.000i		−	0.960758i	−0.877061	−	0.480379i	$-0.840499\pi$
$739$		−	710.000i		−	0.960758i	0.877061	−	0.480379i	$-0.159501\pi$
$740$		0			0
$741$	90.0000			0.121457
$742$	−382.120	+	382.120i	−0.514987	+	0.514987i
$743$	−800.983	−	800.983i	−1.07804	−	1.07804i	−0.996685	−	0.0813540i	$-0.974076\pi$
$743$	−800.983	−	800.983i	−1.07804	−	1.07804i	−0.0813540	−	0.996685i	$-0.525924\pi$
$744$			570.000i			0.766129i
$745$		0			0
$746$	−858.000			−1.15013
$747$	668.711	−	668.711i	0.895195	−	0.895195i
$748$	40.4166	+	40.4166i	0.0540329	+	0.0540329i
$749$			252.000i			0.336449i
$750$		0			0
$751$	502.000			0.668442			0.334221	−	0.942495i	$-0.391527\pi$
$751$	502.000			0.668442			0.334221	+	0.942495i	$0.391527\pi$
$752$	−80.8332	+	80.8332i	−0.107491	+	0.107491i
$753$	−150.644	−	150.644i	−0.200058	−	0.200058i
$754$		−	540.000i		−	0.716180i
$755$		0			0
$756$	180.000			0.238095
$757$	4.89898	−	4.89898i	0.00647157	−	0.00647157i	−0.703864	−	0.710335i	$-0.748543\pi$
$757$	4.89898	−	4.89898i	0.00647157	−	0.00647157i	0.710335	+	0.703864i	$0.248543\pi$
$758$	−618.496	−	618.496i	−0.815958	−	0.815958i
$759$			126.000i			0.166008i
$760$		0			0
$761$	747.000			0.981603			0.490802	−	0.871271i	$-0.336704\pi$
$761$	747.000			0.981603			0.490802	+	0.871271i	$0.336704\pi$
$762$	462.954	−	462.954i	0.607551	−	0.607551i
$763$	−195.959	−	195.959i	−0.256827	−	0.256827i
$764$		−	18.0000i		−	0.0235602i
$765$		0			0
$766$	−348.000			−0.454308
$767$	661.362	−	661.362i	0.862271	−	0.862271i
$768$	−219.229	−	219.229i	−0.285455	−	0.285455i
$769$		−	1255.00i		−	1.63199i	−0.578059	−	0.815995i	$-0.696190\pi$
$769$		−	1255.00i		−	1.63199i	0.578059	−	0.815995i	$-0.303810\pi$
$770$		0			0
$771$	12.0000			0.0155642
$772$	−86.9569	+	86.9569i	−0.112638	+	0.112638i
$773$	−17.1464	−	17.1464i	−0.0221817	−	0.0221817i	0.695929	−	0.718111i	$-0.254993\pi$
$773$	−17.1464	−	17.1464i	−0.0221817	−	0.0221817i	−0.718111	+	0.695929i	$0.754993\pi$
$774$		−	72.0000i		−	0.0930233i
$775$		0			0
$776$	−660.000			−0.850515
$777$	−235.151	+	235.151i	−0.302640	+	0.302640i
$778$	−845.074	−	845.074i	−1.08621	−	1.08621i
$779$		−	285.000i		−	0.365854i
$780$		0			0
$781$	−126.000			−0.161332
$782$	−565.832	+	565.832i	−0.723570	+	0.723570i
$783$	551.135	+	551.135i	0.703876	+	0.703876i
$784$			11.0000i			0.0140306i
$785$		0			0
$786$	−486.000			−0.618321
$787$	592.777	−	592.777i	0.753210	−	0.753210i	−0.221867	−	0.975077i	$-0.571215\pi$
$787$	592.777	−	592.777i	0.753210	−	0.753210i	0.975077	+	0.221867i	$0.0712150\pi$
$788$	−129.823	−	129.823i	−0.164750	−	0.164750i
$789$			18.0000i			0.0228137i
$790$		0			0
$791$	−828.000			−1.04678
$792$	110.227	−	110.227i	0.139176	−	0.139176i
$793$	−205.757	−	205.757i	−0.259467	−	0.259467i
$794$			1032.00i			1.29975i
$795$		0			0
$796$	−200.000			−0.251256
$797$	605.024	−	605.024i	0.759127	−	0.759127i	−0.217037	−	0.976163i	$-0.569639\pi$
$797$	605.024	−	605.024i	0.759127	−	0.759127i	0.976163	+	0.217037i	$0.0696391\pi$
$798$	73.4847	+	73.4847i	0.0920861	+	0.0920861i
$799$		−	198.000i		−	0.247810i
$800$		0			0
$801$	90.0000			0.112360
$802$	701.779	−	701.779i	0.875036	−	0.875036i
$803$	−40.4166	−	40.4166i	−0.0503320	−	0.0503320i
$804$			117.000i			0.145522i
$805$		0			0
$806$	684.000			0.848635
$807$	−146.969	+	146.969i	−0.182118	+	0.182118i
$808$	293.939	+	293.939i	0.363786	+	0.363786i
$809$		−	90.0000i		−	0.111248i	−0.998452	−	0.0556242i	$-0.982285\pi$
$809$		−	90.0000i		−	0.111248i	0.998452	−	0.0556242i	$-0.0177149\pi$
$810$		0			0
$811$	−278.000			−0.342787			−0.171393	−	0.985203i	$-0.554827\pi$
$811$	−278.000			−0.342787			−0.171393	+	0.985203i	$0.554827\pi$
$812$	−146.969	+	146.969i	−0.180997	+	0.180997i
$813$	−71.0352	−	71.0352i	−0.0873742	−	0.0873742i
$814$			144.000i			0.176904i
$815$		0			0
$816$	−363.000			−0.444853
$817$	−24.4949	+	24.4949i	−0.0299815	+	0.0299815i
$818$	447.032	+	447.032i	0.546494	+	0.546494i
$819$		−	432.000i		−	0.527473i
$820$		0			0
$821$	42.0000			0.0511571			0.0255786	−	0.999673i	$-0.491857\pi$
$821$	42.0000			0.0511571			0.0255786	+	0.999673i	$0.491857\pi$
$822$	150.644	−	150.644i	0.183265	−	0.183265i
$823$	778.938	+	778.938i	0.946461	+	0.946461i	0.998638	−	0.0521765i	$-0.0166158\pi$
$823$	778.938	+	778.938i	0.946461	+	0.946461i	−0.0521765	+	0.998638i	$0.516616\pi$
$824$			1110.00i			1.34709i
$825$		0			0
$826$	1080.00			1.30751
$827$	−674.834	+	674.834i	−0.816003	+	0.816003i	−0.985526	−	0.169523i	$-0.945777\pi$
$827$	−674.834	+	674.834i	−0.816003	+	0.816003i	0.169523	+	0.985526i	$0.445777\pi$
$828$	−102.879	−	102.879i	−0.124249	−	0.124249i
$829$		−	170.000i		−	0.205066i	−0.994730	−	0.102533i	$-0.967305\pi$
$829$		−	170.000i		−	0.205066i	0.994730	−	0.102533i	$-0.0326948\pi$
$830$		0			0
$831$	−678.000			−0.815884
$832$	−521.741	+	521.741i	−0.627093	+	0.627093i
$833$	−13.4722	−	13.4722i	−0.0161731	−	0.0161731i
$834$			555.000i			0.665468i
$835$		0			0
$836$	−15.0000			−0.0179426
$837$	−698.105	+	698.105i	−0.834056	+	0.834056i
$838$	−789.960	−	789.960i	−0.942674	−	0.942674i
$839$		−	360.000i		−	0.429082i	−0.976715	−	0.214541i	$-0.931174\pi$
$839$		−	360.000i		−	0.429082i	0.976715	−	0.214541i	$-0.0688256\pi$
$840$		0			0
$841$	−59.0000			−0.0701546
$842$	9.79796	−	9.79796i	0.0116365	−	0.0116365i
$843$	565.832	+	565.832i	0.671212	+	0.671212i
$844$		−	103.000i		−	0.122038i
$845$		0			0
$846$	−108.000			−0.127660
$847$	−548.686	+	548.686i	−0.647799	+	0.647799i
$848$	350.277	+	350.277i	0.413063	+	0.413063i
$849$		−	177.000i		−	0.208481i
$850$		0			0
$851$	672.000			0.789659
$852$	−51.4393	+	51.4393i	−0.0603747	+	0.0603747i
$853$	521.741	+	521.741i	0.611655	+	0.611655i	0.943377	−	0.331722i	$-0.107630\pi$
$853$	521.741	+	521.741i	0.611655	+	0.611655i	−0.331722	+	0.943377i	$0.607630\pi$
$854$		−	336.000i		−	0.393443i
$855$		0			0
$856$	315.000			0.367991
$857$	280.467	−	280.467i	0.327266	−	0.327266i	−0.524280	−	0.851546i	$-0.675666\pi$
$857$	280.467	−	280.467i	0.327266	−	0.327266i	0.851546	+	0.524280i	$0.175666\pi$
$858$	66.1362	+	66.1362i	0.0770818	+	0.0770818i
$859$			335.000i			0.389988i	0.980804	+	0.194994i	$0.0624688\pi$
$859$			335.000i			0.389988i	−0.980804	+	0.194994i	$0.937531\pi$
$860$		0			0
$861$	684.000			0.794425
$862$	−14.6969	+	14.6969i	−0.0170498	+	0.0170498i
$863$	−849.973	−	849.973i	−0.984905	−	0.984905i	0.0149828	−	0.999888i	$-0.495231\pi$
$863$	−849.973	−	849.973i	−0.984905	−	0.984905i	−0.999888	+	0.0149828i	$0.995231\pi$
$864$		−	405.000i		−	0.468750i
$865$		0			0
$866$	1077.00			1.24365
$867$	90.6311	−	90.6311i	0.104534	−	0.104534i
$868$	−186.161	−	186.161i	−0.214471	−	0.214471i
$869$		−	240.000i		−	0.276180i
$870$		0			0
$871$	702.000			0.805970
$872$	−244.949	+	244.949i	−0.280905	+	0.280905i
$873$	−323.333	−	323.333i	−0.370370	−	0.370370i
$874$		−	210.000i		−	0.240275i
$875$		0			0
$876$	−33.0000			−0.0376712
$877$	151.868	−	151.868i	0.173168	−	0.173168i	−0.615202	−	0.788370i	$-0.710925\pi$
$877$	151.868	−	151.868i	0.173168	−	0.173168i	0.788370	+	0.615202i	$0.210925\pi$
$878$	12.2474	+	12.2474i	0.0139493	+	0.0139493i
$879$		−	12.0000i		−	0.0136519i
$880$		0			0
$881$	162.000			0.183882			0.0919410	−	0.995764i	$-0.470693\pi$
$881$	162.000			0.183882			0.0919410	+	0.995764i	$0.470693\pi$
$882$	−7.34847	+	7.34847i	−0.00833160	+	0.00833160i
$883$	295.164	+	295.164i	0.334274	+	0.334274i	0.854207	−	0.519933i	$-0.174043\pi$
$883$	295.164	+	295.164i	0.334274	+	0.334274i	−0.519933	+	0.854207i	$0.674043\pi$
$884$		−	198.000i		−	0.223982i
$885$		0			0
$886$	−213.000			−0.240406
$887$	−509.494	+	509.494i	−0.574401	+	0.574401i	−0.933355	−	0.358954i	$-0.883133\pi$
$887$	−509.494	+	509.494i	−0.574401	+	0.574401i	0.358954	+	0.933355i	$0.383133\pi$
$888$	293.939	+	293.939i	0.331012	+	0.331012i
$889$			1512.00i			1.70079i
$890$		0			0
$891$	27.0000			0.0303030
$892$	200.858	−	200.858i	0.225177	−	0.225177i
$893$	36.7423	+	36.7423i	0.0411448	+	0.0411448i
$894$		−	450.000i		−	0.503356i
$895$		0			0
$896$	−420.000			−0.468750
$897$	308.636	−	308.636i	0.344075	−	0.344075i
$898$	−91.8559	−	91.8559i	−0.102289	−	0.102289i
$899$		−	1140.00i		−	1.26808i
$900$		0			0
$901$	−858.000			−0.952275
$902$	209.431	−	209.431i	0.232186	−	0.232186i
$903$	−58.7878	−	58.7878i	−0.0651027	−	0.0651027i
$904$			1035.00i			1.14491i
$905$		0			0
$906$	−156.000			−0.172185
$907$	494.797	−	494.797i	0.545531	−	0.545531i	−0.379614	−	0.925145i	$-0.623943\pi$
$907$	494.797	−	494.797i	0.545531	−	0.545531i	0.925145	+	0.379614i	$0.123943\pi$
$908$	274.343	+	274.343i	0.302140	+	0.302140i
$909$			288.000i			0.316832i
$910$		0			0
$911$	−828.000			−0.908891			−0.454446	−	0.890774i	$-0.650163\pi$
$911$	−828.000			−0.908891			−0.454446	+	0.890774i	$0.650163\pi$
$912$	67.3610	−	67.3610i	0.0738607	−	0.0738607i
$913$	−334.355	−	334.355i	−0.366216	−	0.366216i
$914$		−	513.000i		−	0.561269i
$915$		0			0
$916$	20.0000			0.0218341
$917$	793.635	−	793.635i	0.865469	−	0.865469i
$918$	−606.249	−	606.249i	−0.660402	−	0.660402i
$919$			1270.00i			1.38194i	0.722885	+	0.690968i	$0.242816\pi$
$919$			1270.00i			1.38194i	−0.722885	+	0.690968i	$0.757184\pi$
$920$		0			0
$921$	−213.000			−0.231270
$922$	279.242	−	279.242i	0.302865	−	0.302865i
$923$	308.636	+	308.636i	0.334383	+	0.334383i
$924$		−	36.0000i		−	0.0389610i
$925$		0			0
$926$	−1068.00			−1.15335
$927$	−543.787	+	543.787i	−0.586609	+	0.586609i
$928$	330.681	+	330.681i	0.356337	+	0.356337i
$929$		−	570.000i		−	0.613563i	−0.951780	−	0.306781i	$-0.900748\pi$
$929$		−	570.000i		−	0.613563i	0.951780	−	0.306781i	$-0.0992521\pi$
$930$		0			0
$931$	5.00000			0.00537057
$932$	102.879	−	102.879i	0.110385	−	0.110385i
$933$	−646.665	−	646.665i	−0.693103	−	0.693103i
$934$		−	1308.00i		−	1.40043i
$935$		0			0
$936$	−540.000			−0.576923
$937$	317.209	−	317.209i	0.338537	−	0.338537i	−0.517280	−	0.855816i	$-0.673055\pi$
$937$	317.209	−	317.209i	0.338537	−	0.338537i	0.855816	+	0.517280i	$0.173055\pi$
$938$	573.181	+	573.181i	0.611067	+	0.611067i
$939$			468.000i			0.498403i
$940$		0			0
$941$	−1518.00			−1.61318			−0.806589	−	0.591113i	$-0.798689\pi$
$941$	−1518.00			−1.61318			−0.806589	+	0.591113i	$0.798689\pi$
$942$	−565.832	+	565.832i	−0.600671	+	0.600671i
$943$	−977.346	−	977.346i	−1.03642	−	1.03642i
$944$		−	990.000i		−	1.04873i
$945$		0			0
$946$	−36.0000			−0.0380550
$947$	−436.009	+	436.009i	−0.460411	+	0.460411i	−0.898790	−	0.438379i	$-0.855553\pi$
$947$	−436.009	+	436.009i	−0.460411	+	0.460411i	0.438379	+	0.898790i	$0.355553\pi$
$948$	−97.9796	−	97.9796i	−0.103354	−	0.103354i
$949$			198.000i			0.208641i
$950$		0			0
$951$	492.000			0.517350
$952$	808.332	−	808.332i	0.849088	−	0.849088i
$953$	429.885	+	429.885i	0.451087	+	0.451087i	0.895715	−	0.444629i	$-0.146664\pi$
$953$	429.885	+	429.885i	0.451087	+	0.451087i	−0.444629	+	0.895715i	$0.646664\pi$
$954$			468.000i			0.490566i
$955$		0			0
$956$	210.000			0.219665
$957$	110.227	−	110.227i	0.115180	−	0.115180i
$958$	330.681	+	330.681i	0.345179	+	0.345179i
$959$			492.000i			0.513034i
$960$		0			0
$961$	483.000			0.502601
$962$	352.727	−	352.727i	0.366660	−	0.366660i
$963$	154.318	+	154.318i	0.160247	+	0.160247i
$964$		−	43.0000i		−	0.0446058i
$965$		0			0
$966$	504.000			0.521739
$967$	−533.989	+	533.989i	−0.552212	+	0.552212i	−0.927079	−	0.374867i	$-0.877688\pi$
$967$	−533.989	+	533.989i	−0.552212	+	0.552212i	0.374867	+	0.927079i	$0.377688\pi$
$968$	685.857	+	685.857i	0.708530	+	0.708530i
$969$			165.000i			0.170279i
$970$		0			0
$971$	1467.00			1.51081			0.755407	−	0.655256i	$-0.227439\pi$
$971$	1467.00			1.51081			0.755407	+	0.655256i	$0.227439\pi$
$972$	176.363	−	176.363i	0.181444	−	0.181444i
$973$	−906.311	−	906.311i	−0.931461	−	0.931461i
$974$		−	198.000i		−	0.203285i
$975$		0			0
$976$	−308.000			−0.315574
$977$	1039.81	−	1039.81i	1.06429	−	1.06429i	0.0665006	−	0.997786i	$-0.478817\pi$
$977$	1039.81	−	1039.81i	1.06429	−	1.06429i	0.997786	−	0.0665006i	$-0.0211834\pi$
$978$	−297.613	−	297.613i	−0.304308	−	0.304308i
$979$		−	45.0000i		−	0.0459653i
$980$		0			0
$981$	−240.000			−0.244648
$982$	−712.802	+	712.802i	−0.725867	+	0.725867i
$983$	−715.251	−	715.251i	−0.727621	−	0.727621i	0.242525	−	0.970145i	$-0.422024\pi$
$983$	−715.251	−	715.251i	−0.727621	−	0.727621i	−0.970145	+	0.242525i	$0.922024\pi$
$984$		−	855.000i		−	0.868902i
$985$		0			0
$986$	990.000			1.00406
$987$	−88.1816	+	88.1816i	−0.0893431	+	0.0893431i
$988$	36.7423	+	36.7423i	0.0371886	+	0.0371886i
$989$			168.000i			0.169869i
$990$		0			0
$991$	1832.00			1.84864			0.924319	−	0.381621i	$-0.124634\pi$
$991$	1832.00			1.84864			0.924319	+	0.381621i	$0.124634\pi$
$992$	−418.863	+	418.863i	−0.422241	+	0.422241i
$993$	−383.345	−	383.345i	−0.386047	−	0.386047i
$994$			504.000i			0.507042i
$995$		0			0
$996$	−273.000			−0.274096
$997$	−1293.33	+	1293.33i	−1.29722	+	1.29722i	−0.367002	+	0.930220i	$0.619616\pi$
$997$	−1293.33	+	1293.33i	−1.29722	+	1.29722i	−0.930220	+	0.367002i	$0.880384\pi$
$998$	306.186	+	306.186i	0.306800	+	0.306800i
$999$			720.000i			0.720721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.c.a.18.1	yes	4
3.2	odd	2		225.3.g.e.118.2		4
4.3	odd	2		400.3.p.j.193.1		4
5.2	odd	4	inner	25.3.c.a.7.1	✓	4
5.3	odd	4	inner	25.3.c.a.7.2	yes	4
5.4	even	2	inner	25.3.c.a.18.2	yes	4
15.2	even	4		225.3.g.e.82.2		4
15.8	even	4		225.3.g.e.82.1		4
15.14	odd	2		225.3.g.e.118.1		4
20.3	even	4		400.3.p.j.257.2		4
20.7	even	4		400.3.p.j.257.1		4
20.19	odd	2		400.3.p.j.193.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.c.a.7.1	✓	4	5.2	odd	4	inner
25.3.c.a.7.2	yes	4	5.3	odd	4	inner
25.3.c.a.18.1	yes	4	1.1	even	1	trivial
25.3.c.a.18.2	yes	4	5.4	even	2	inner
225.3.g.e.82.1		4	15.8	even	4
225.3.g.e.82.2		4	15.2	even	4
225.3.g.e.118.1		4	15.14	odd	2
225.3.g.e.118.2		4	3.2	odd	2
400.3.p.j.193.1		4	4.3	odd	2
400.3.p.j.193.2		4	20.19	odd	2
400.3.p.j.257.1		4	20.7	even	4
400.3.p.j.257.2		4	20.3	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 1.22474i) q^{2} +(1.22474 + 1.22474i) q^{3} +1.00000i q^{4} -3.00000 q^{6} +(4.89898 - 4.89898i) q^{7} +(-6.12372 - 6.12372i) q^{8} -6.00000i q^{9} -3.00000 q^{11} +(-1.22474 + 1.22474i) q^{12} +(7.34847 + 7.34847i) q^{13} +12.0000i q^{14} +11.0000 q^{16} +(-13.4722 + 13.4722i) q^{17} +(7.34847 + 7.34847i) q^{18} -5.00000i q^{19} +12.0000 q^{21} +(3.67423 - 3.67423i) q^{22} +(-17.1464 - 17.1464i) q^{23} -15.0000i q^{24} -18.0000 q^{26} +(18.3712 - 18.3712i) q^{27} +(4.89898 + 4.89898i) q^{28} +30.0000i q^{29} -38.0000 q^{31} +(11.0227 - 11.0227i) q^{32} +(-3.67423 - 3.67423i) q^{33} -33.0000i q^{34} +6.00000 q^{36} +(-19.5959 + 19.5959i) q^{37} +(6.12372 + 6.12372i) q^{38} +18.0000i q^{39} +57.0000 q^{41} +(-14.6969 + 14.6969i) q^{42} +(-4.89898 - 4.89898i) q^{43} -3.00000i q^{44} +42.0000 q^{46} +(-7.34847 + 7.34847i) q^{47} +(13.4722 + 13.4722i) q^{48} +1.00000i q^{49} -33.0000 q^{51} +(-7.34847 + 7.34847i) q^{52} +(31.8434 + 31.8434i) q^{53} +45.0000i q^{54} -60.0000 q^{56} +(6.12372 - 6.12372i) q^{57} +(-36.7423 - 36.7423i) q^{58} -90.0000i q^{59} -28.0000 q^{61} +(46.5403 - 46.5403i) q^{62} +(-29.3939 - 29.3939i) q^{63} +71.0000i q^{64} +9.00000 q^{66} +(47.7650 - 47.7650i) q^{67} +(-13.4722 - 13.4722i) q^{68} -42.0000i q^{69} +42.0000 q^{71} +(-36.7423 + 36.7423i) q^{72} +(13.4722 + 13.4722i) q^{73} -48.0000i q^{74} +5.00000 q^{76} +(-14.6969 + 14.6969i) q^{77} +(-22.0454 - 22.0454i) q^{78} +80.0000i q^{79} -9.00000 q^{81} +(-69.8105 + 69.8105i) q^{82} +(111.452 + 111.452i) q^{83} +12.0000i q^{84} +12.0000 q^{86} +(-36.7423 + 36.7423i) q^{87} +(18.3712 + 18.3712i) q^{88} +15.0000i q^{89} +72.0000 q^{91} +(17.1464 - 17.1464i) q^{92} +(-46.5403 - 46.5403i) q^{93} -18.0000i q^{94} +27.0000 q^{96} +(53.8888 - 53.8888i) q^{97} +(-1.22474 - 1.22474i) q^{98} +18.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{6} - 12 q^{11} + 44 q^{16} + 48 q^{21} - 72 q^{26} - 152 q^{31} + 24 q^{36} + 228 q^{41} + 168 q^{46} - 132 q^{51} - 240 q^{56} - 112 q^{61} + 36 q^{66} + 168 q^{71} + 20 q^{76} - 36 q^{81}+ \cdots + 108 q^{96}+O(q^{100}) \) 4 * q - 12 * q^6 - 12 * q^11 + 44 * q^16 + 48 * q^21 - 72 * q^26 - 152 * q^31 + 24 * q^36 + 228 * q^41 + 168 * q^46 - 132 * q^51 - 240 * q^56 - 112 * q^61 + 36 * q^66 + 168 * q^71 + 20 * q^76 - 36 * q^81 + 48 * q^86 + 288 * q^91 + 108 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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