LMFDB - Embedded newform 25.5.c.b.18.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,5,Mod(7,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	25.c (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:	$2.58424907710$
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			18.2
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	25.18
Dual form			25.5.c.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.67423 - 3.67423i) q^{2} +(-8.57321 - 8.57321i) q^{3} -11.0000i q^{4} -63.0000 q^{6} +(34.2929 - 34.2929i) q^{7} +(18.3712 + 18.3712i) q^{8} +66.0000i q^{9} +O(q^{10})$	\(q+(3.67423 - 3.67423i) q^{2} +(-8.57321 - 8.57321i) q^{3} -11.0000i q^{4} -63.0000 q^{6} +(34.2929 - 34.2929i) q^{7} +(18.3712 + 18.3712i) q^{8} +66.0000i q^{9} +117.000 q^{11} +(-94.3054 + 94.3054i) q^{12} +(-51.4393 - 51.4393i) q^{13} -252.000i q^{14} +311.000 q^{16} +(-180.037 + 180.037i) q^{17} +(242.499 + 242.499i) q^{18} +595.000i q^{19} -588.000 q^{21} +(429.885 - 429.885i) q^{22} +(-124.924 - 124.924i) q^{23} -315.000i q^{24} -378.000 q^{26} +(-128.598 + 128.598i) q^{27} +(-377.221 - 377.221i) q^{28} -1170.00i q^{29} +322.000 q^{31} +(848.748 - 848.748i) q^{32} +(-1003.07 - 1003.07i) q^{33} +1323.00i q^{34} +726.000 q^{36} +(-578.080 + 578.080i) q^{37} +(2186.17 + 2186.17i) q^{38} +882.000i q^{39} -63.0000 q^{41} +(-2160.45 + 2160.45i) q^{42} +(1259.04 + 1259.04i) q^{43} -1287.00i q^{44} -918.000 q^{46} +(462.954 - 462.954i) q^{47} +(-2666.27 - 2666.27i) q^{48} +49.0000i q^{49} +3087.00 q^{51} +(-565.832 + 565.832i) q^{52} +(1491.74 + 1491.74i) q^{53} +945.000i q^{54} +1260.00 q^{56} +(5101.06 - 5101.06i) q^{57} +(-4298.85 - 4298.85i) q^{58} -1890.00i q^{59} -5908.00 q^{61} +(1183.10 - 1183.10i) q^{62} +(2263.33 + 2263.33i) q^{63} -1261.00i q^{64} -7371.00 q^{66} +(-4772.83 + 4772.83i) q^{67} +(1980.41 + 1980.41i) q^{68} +2142.00i q^{69} +2682.00 q^{71} +(-1212.50 + 1212.50i) q^{72} +(-1808.95 - 1808.95i) q^{73} +4248.00i q^{74} +6545.00 q^{76} +(4012.26 - 4012.26i) q^{77} +(3240.67 + 3240.67i) q^{78} -6520.00i q^{79} +7551.00 q^{81} +(-231.477 + 231.477i) q^{82} +(-2494.81 - 2494.81i) q^{83} +6468.00i q^{84} +9252.00 q^{86} +(-10030.7 + 10030.7i) q^{87} +(2149.43 + 2149.43i) q^{88} -5985.00i q^{89} -3528.00 q^{91} +(-1374.16 + 1374.16i) q^{92} +(-2760.57 - 2760.57i) q^{93} -3402.00i q^{94} -14553.0 q^{96} +(3463.58 - 3463.58i) q^{97} +(180.037 + 180.037i) q^{98} +7722.00i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 252 q^{6}+O(q^{10}) $ 4 * q - 252 * q^6	$ 4 q - 252 q^{6} + 468 q^{11} + 1244 q^{16} - 2352 q^{21} - 1512 q^{26} + 1288 q^{31} + 2904 q^{36} - 252 q^{41} - 3672 q^{46} + 12348 q^{51} + 5040 q^{56} - 23632 q^{61} - 29484 q^{66} + 10728 q^{71} + 26180 q^{76} + 30204 q^{81} + 37008 q^{86} - 14112 q^{91} - 58212 q^{96}+O(q^{100}) $ 4 * q - 252 * q^6 + 468 * q^11 + 1244 * q^16 - 2352 * q^21 - 1512 * q^26 + 1288 * q^31 + 2904 * q^36 - 252 * q^41 - 3672 * q^46 + 12348 * q^51 + 5040 * q^56 - 23632 * q^61 - 29484 * q^66 + 10728 * q^71 + 26180 * q^76 + 30204 * q^81 + 37008 * q^86 - 14112 * q^91 - 58212 * q^96

Display 100 coefficients 10 coefficients

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 $

$2$	3.67423	−	3.67423i	0.918559	−	0.918559i	−0.0783660	−	0.996925i	$-0.524970\pi$
$2$	3.67423	−	3.67423i	0.918559	−	0.918559i	0.996925	+	0.0783660i	$0.0249703\pi$
$3$	−8.57321	−	8.57321i	−0.952579	−	0.952579i	0.0463461	−	0.998925i	$-0.485242\pi$
$3$	−8.57321	−	8.57321i	−0.952579	−	0.952579i	−0.998925	+	0.0463461i	$0.985242\pi$
$4$		−	11.0000i		−	0.687500i
$5$		0			0
$5$		0			0
$6$	−63.0000			−1.75000
$7$	34.2929	−	34.2929i	0.699854	−	0.699854i	−0.264525	−	0.964379i	$-0.585215\pi$
$7$	34.2929	−	34.2929i	0.699854	−	0.699854i	0.964379	+	0.264525i	$0.0852151\pi$
$8$	18.3712	+	18.3712i	0.287050	+	0.287050i
$9$			66.0000i			0.814815i
$10$		0			0
$11$	117.000			0.966942			0.483471	−	0.875360i	$-0.339376\pi$
$11$	117.000			0.966942			0.483471	+	0.875360i	$0.339376\pi$
$12$	−94.3054	+	94.3054i	−0.654898	+	0.654898i
$13$	−51.4393	−	51.4393i	−0.304374	−	0.304374i	0.538348	−	0.842723i	$-0.319049\pi$
$13$	−51.4393	−	51.4393i	−0.304374	−	0.304374i	−0.842723	+	0.538348i	$0.819049\pi$
$14$		−	252.000i		−	1.28571i
$15$		0			0
$16$	311.000			1.21484
$17$	−180.037	+	180.037i	−0.622967	+	0.622967i	−0.946289	−	0.323322i	$-0.895200\pi$
$17$	−180.037	+	180.037i	−0.622967	+	0.622967i	0.323322	+	0.946289i	$0.395200\pi$
$18$	242.499	+	242.499i	0.748455	+	0.748455i
$19$			595.000i			1.64820i	0.566445	+	0.824100i	$0.308318\pi$
$19$			595.000i			1.64820i	−0.566445	+	0.824100i	$0.691682\pi$
$20$		0			0
$21$	−588.000			−1.33333
$22$	429.885	−	429.885i	0.888193	−	0.888193i
$23$	−124.924	−	124.924i	−0.236151	−	0.236151i	0.579103	−	0.815254i	$-0.303403\pi$
$23$	−124.924	−	124.924i	−0.236151	−	0.236151i	−0.815254	+	0.579103i	$0.803403\pi$
$24$		−	315.000i		−	0.546875i
$25$		0			0
$26$	−378.000			−0.559172
$27$	−128.598	+	128.598i	−0.176404	+	0.176404i
$28$	−377.221	−	377.221i	−0.481150	−	0.481150i
$29$		−	1170.00i		−	1.39120i	−0.718429	−	0.695600i	$-0.755138\pi$
$29$		−	1170.00i		−	1.39120i	0.718429	−	0.695600i	$-0.244862\pi$
$30$		0			0
$31$	322.000			0.335068			0.167534	−	0.985866i	$-0.446420\pi$
$31$	322.000			0.335068			0.167534	+	0.985866i	$0.446420\pi$
$32$	848.748	−	848.748i	0.828856	−	0.828856i
$33$	−1003.07	−	1003.07i	−0.921089	−	0.921089i
$34$			1323.00i			1.14446i
$35$		0			0
$36$	726.000			0.560185
$37$	−578.080	+	578.080i	−0.422264	+	0.422264i	−0.885983	−	0.463718i	$-0.846515\pi$
$37$	−578.080	+	578.080i	−0.422264	+	0.422264i	0.463718	+	0.885983i	$0.346515\pi$
$38$	2186.17	+	2186.17i	1.51397	+	1.51397i
$39$			882.000i			0.579882i
$40$		0			0
$41$	−63.0000			−0.0374777			−0.0187388	−	0.999824i	$-0.505965\pi$
$41$	−63.0000			−0.0374777			−0.0187388	+	0.999824i	$0.505965\pi$
$42$	−2160.45	+	2160.45i	−1.22474	+	1.22474i
$43$	1259.04	+	1259.04i	0.680929	+	0.680929i	0.960210	−	0.279281i	$-0.0900959\pi$
$43$	1259.04	+	1259.04i	0.680929	+	0.680929i	−0.279281	+	0.960210i	$0.590096\pi$
$44$		−	1287.00i		−	0.664773i
$45$		0			0
$46$	−918.000			−0.433837
$47$	462.954	−	462.954i	0.209576	−	0.209576i	−0.594511	−	0.804087i	$-0.702654\pi$
$47$	462.954	−	462.954i	0.209576	−	0.209576i	0.804087	+	0.594511i	$0.202654\pi$
$48$	−2666.27	−	2666.27i	−1.15724	−	1.15724i
$49$			49.0000i			0.0204082i
$50$		0			0
$51$	3087.00			1.18685
$52$	−565.832	+	565.832i	−0.209257	+	0.209257i
$53$	1491.74	+	1491.74i	0.531057	+	0.531057i	0.920887	−	0.389830i	$-0.127466\pi$
$53$	1491.74	+	1491.74i	0.531057	+	0.531057i	−0.389830	+	0.920887i	$0.627466\pi$
$54$			945.000i			0.324074i
$55$		0			0
$56$	1260.00			0.401786
$57$	5101.06	−	5101.06i	1.57004	−	1.57004i
$58$	−4298.85	−	4298.85i	−1.27790	−	1.27790i
$59$		−	1890.00i		−	0.542947i	−0.962446	−	0.271474i	$-0.912489\pi$
$59$		−	1890.00i		−	0.542947i	0.962446	−	0.271474i	$-0.0875110\pi$
$60$		0			0
$61$	−5908.00			−1.58775			−0.793873	−	0.608084i	$-0.791938\pi$
$61$	−5908.00			−1.58775			−0.793873	+	0.608084i	$0.791938\pi$
$62$	1183.10	−	1183.10i	0.307779	−	0.307779i
$63$	2263.33	+	2263.33i	0.570252	+	0.570252i
$64$		−	1261.00i		−	0.307861i
$65$		0			0
$66$	−7371.00			−1.69215
$67$	−4772.83	+	4772.83i	−1.06323	+	1.06323i	−0.0653668	+	0.997861i	$0.520822\pi$
$67$	−4772.83	+	4772.83i	−1.06323	+	1.06323i	−0.997861	+	0.0653668i	$0.979178\pi$
$68$	1980.41	+	1980.41i	0.428290	+	0.428290i
$69$			2142.00i			0.449905i
$70$		0			0
$71$	2682.00			0.532037			0.266019	−	0.963968i	$-0.414292\pi$
$71$	2682.00			0.532037			0.266019	+	0.963968i	$0.414292\pi$
$72$	−1212.50	+	1212.50i	−0.233892	+	0.233892i
$73$	−1808.95	−	1808.95i	−0.339454	−	0.339454i	0.516708	−	0.856162i	$-0.327157\pi$
$73$	−1808.95	−	1808.95i	−0.339454	−	0.339454i	−0.856162	+	0.516708i	$0.827157\pi$
$74$			4248.00i			0.775749i
$75$		0			0
$76$	6545.00			1.13314
$77$	4012.26	−	4012.26i	0.676719	−	0.676719i
$78$	3240.67	+	3240.67i	0.532655	+	0.532655i
$79$		−	6520.00i		−	1.04470i	−0.852730	−	0.522352i	$-0.825055\pi$
$79$		−	6520.00i		−	1.04470i	0.852730	−	0.522352i	$-0.174945\pi$
$80$		0			0
$81$	7551.00			1.15089
$82$	−231.477	+	231.477i	−0.0344255	+	0.0344255i
$83$	−2494.81	−	2494.81i	−0.362143	−	0.362143i	0.502458	−	0.864602i	$-0.332429\pi$
$83$	−2494.81	−	2494.81i	−0.362143	−	0.362143i	−0.864602	+	0.502458i	$0.832429\pi$
$84$			6468.00i			0.916667i
$85$		0			0
$86$	9252.00			1.25095
$87$	−10030.7	+	10030.7i	−1.32523	+	1.32523i
$88$	2149.43	+	2149.43i	0.277560	+	0.277560i
$89$		−	5985.00i		−	0.755586i	−0.925890	−	0.377793i	$-0.876683\pi$
$89$		−	5985.00i		−	0.755586i	0.925890	−	0.377793i	$-0.123317\pi$
$90$		0			0
$91$	−3528.00			−0.426036
$92$	−1374.16	+	1374.16i	−0.162354	+	0.162354i
$93$	−2760.57	−	2760.57i	−0.319179	−	0.319179i
$94$		−	3402.00i		−	0.385016i
$95$		0			0
$96$	−14553.0			−1.57910
$97$	3463.58	−	3463.58i	0.368113	−	0.368113i	−0.498675	−	0.866789i	$-0.666180\pi$
$97$	3463.58	−	3463.58i	0.368113	−	0.368113i	0.866789	+	0.498675i	$0.166180\pi$
$98$	180.037	+	180.037i	0.0187461	+	0.0187461i
$99$			7722.00i			0.787879i
$100$		0			0
$101$	−18648.0			−1.82806			−0.914028	−	0.405651i	$-0.867045\pi$
$101$	−18648.0			−1.82806			−0.914028	+	0.405651i	$0.867045\pi$
$102$	11342.4	−	11342.4i	1.09019	−	1.09019i
$103$	7492.99	+	7492.99i	0.706286	+	0.706286i	0.965752	−	0.259466i	$-0.0835466\pi$
$103$	7492.99	+	7492.99i	0.706286	+	0.706286i	−0.259466	+	0.965752i	$0.583547\pi$
$104$		−	1890.00i		−	0.174741i
$105$		0			0
$106$	10962.0			0.975614
$107$	−1466.02	+	1466.02i	−0.128048	+	0.128048i	−0.768226	−	0.640178i	$-0.778860\pi$
$107$	−1466.02	+	1466.02i	−0.128048	+	0.128048i	0.640178	+	0.768226i	$0.278860\pi$
$108$	1414.58	+	1414.58i	0.121277	+	0.121277i
$109$			20960.0i			1.76416i	0.471098	+	0.882081i	$0.343858\pi$
$109$			20960.0i			1.76416i	−0.471098	+	0.882081i	$0.656142\pi$
$110$		0			0
$111$	9912.00			0.804480
$112$	10665.1	−	10665.1i	0.850214	−	0.850214i
$113$	−17779.6	−	17779.6i	−1.39241	−	1.39241i	−0.819904	−	0.572501i	$-0.805973\pi$
$113$	−17779.6	−	17779.6i	−1.39241	−	1.39241i	−0.572501	−	0.819904i	$-0.694027\pi$
$114$		−	37485.0i		−	2.88435i
$115$		0			0
$116$	−12870.0			−0.956451
$117$	3394.99	−	3394.99i	0.248009	−	0.248009i
$118$	−6944.30	−	6944.30i	−0.498729	−	0.498729i
$119$			12348.0i			0.871972i
$120$		0			0
$121$	−952.000			−0.0650229
$122$	−21707.4	+	21707.4i	−1.45844	+	1.45844i
$123$	540.112	+	540.112i	0.0357005	+	0.0357005i
$124$		−	3542.00i		−	0.230359i
$125$		0			0
$126$	16632.0			1.04762
$127$	3402.34	−	3402.34i	0.210946	−	0.210946i	−0.593724	−	0.804669i	$-0.702343\pi$
$127$	3402.34	−	3402.34i	0.210946	−	0.210946i	0.804669	+	0.593724i	$0.202343\pi$
$128$	8946.76	+	8946.76i	0.546067	+	0.546067i
$129$		−	21588.0i		−	1.29728i
$130$		0			0
$131$	18522.0			1.07931			0.539654	−	0.841887i	$-0.318555\pi$
$131$	18522.0			1.07931			0.539654	+	0.841887i	$0.318555\pi$
$132$	−11033.7	+	11033.7i	−0.633249	+	0.633249i
$133$	20404.2	+	20404.2i	1.15350	+	1.15350i
$134$			35073.0i			1.95327i
$135$		0			0
$136$	−6615.00			−0.357645
$137$	−4037.98	+	4037.98i	−0.215141	+	0.215141i	−0.806447	−	0.591306i	$-0.798613\pi$
$137$	−4037.98	+	4037.98i	−0.215141	+	0.215141i	0.591306	+	0.806447i	$0.298613\pi$
$138$	7870.21	+	7870.21i	0.413265	+	0.413265i
$139$			13615.0i			0.704674i	0.935873	+	0.352337i	$0.114613\pi$
$139$			13615.0i			0.704674i	−0.935873	+	0.352337i	$0.885387\pi$
$140$		0			0
$141$	−7938.00			−0.399276
$142$	9854.30	−	9854.30i	0.488707	−	0.488707i
$143$	−6018.40	−	6018.40i	−0.294312	−	0.294312i
$144$			20526.0i			0.989873i
$145$		0			0
$146$	−13293.0			−0.623616
$147$	420.087	−	420.087i	0.0194404	−	0.0194404i
$148$	6358.88	+	6358.88i	0.290307	+	0.290307i
$149$		−	16650.0i		−	0.749966i	−0.927032	−	0.374983i	$-0.877649\pi$
$149$		−	16650.0i		−	0.749966i	0.927032	−	0.374983i	$-0.122351\pi$
$150$		0			0
$151$	15052.0			0.660146			0.330073	−	0.943955i	$-0.392927\pi$
$151$	15052.0			0.660146			0.330073	+	0.943955i	$0.392927\pi$
$152$	−10930.8	+	10930.8i	−0.473115	+	0.473115i
$153$	−11882.5	−	11882.5i	−0.507603	−	0.507603i
$154$		−	29484.0i		−	1.24321i
$155$		0			0
$156$	9702.00			0.398669
$157$	−11539.5	+	11539.5i	−0.468155	+	0.468155i	−0.901316	−	0.433162i	$-0.857398\pi$
$157$	−11539.5	+	11539.5i	−0.468155	+	0.468155i	0.433162	+	0.901316i	$0.357398\pi$
$158$	−23956.0	−	23956.0i	−0.959622	−	0.959622i
$159$		−	25578.0i		−	1.01175i
$160$		0			0
$161$	−8568.00			−0.330543
$162$	27744.1	−	27744.1i	1.05716	−	1.05716i
$163$	−5838.36	−	5838.36i	−0.219743	−	0.219743i	0.588647	−	0.808390i	$-0.299661\pi$
$163$	−5838.36	−	5838.36i	−0.219743	−	0.219743i	−0.808390	+	0.588647i	$0.799661\pi$
$164$			693.000i			0.0257659i
$165$		0			0
$166$	−18333.0			−0.665300
$167$	33898.5	−	33898.5i	1.21548	−	1.21548i	0.246280	−	0.969199i	$-0.420792\pi$
$167$	33898.5	−	33898.5i	1.21548	−	1.21548i	0.969199	−	0.246280i	$-0.0792083\pi$
$168$	−10802.2	−	10802.2i	−0.382733	−	0.382733i
$169$		−	23269.0i		−	0.814712i
$170$		0			0
$171$	−39270.0			−1.34298
$172$	13849.4	−	13849.4i	0.468139	−	0.468139i
$173$	17695.1	+	17695.1i	0.591236	+	0.591236i	0.937965	−	0.346729i	$-0.112708\pi$
$173$	17695.1	+	17695.1i	0.591236	+	0.591236i	−0.346729	+	0.937965i	$0.612708\pi$
$174$			73710.0i			2.43460i
$175$		0			0
$176$	36387.0			1.17468
$177$	−16203.4	+	16203.4i	−0.517201	+	0.517201i
$178$	−21990.3	−	21990.3i	−0.694050	−	0.694050i
$179$			7605.00i			0.237352i	0.992933	+	0.118676i	$0.0378650\pi$
$179$			7605.00i			0.237352i	−0.992933	+	0.118676i	$0.962135\pi$
$180$		0			0
$181$	6622.00			0.202131			0.101065	−	0.994880i	$-0.467775\pi$
$181$	6622.00			0.202131			0.101065	+	0.994880i	$0.467775\pi$
$182$	−12962.7	+	12962.7i	−0.391339	+	0.391339i
$183$	50650.5	+	50650.5i	1.51245	+	1.51245i
$184$		−	4590.00i		−	0.135574i
$185$		0			0
$186$	−20286.0			−0.586368
$187$	−21064.4	+	21064.4i	−0.602373	+	0.602373i
$188$	−5092.49	−	5092.49i	−0.144084	−	0.144084i
$189$			8820.00i			0.246914i
$190$		0			0
$191$	−34938.0			−0.957704			−0.478852	−	0.877896i	$-0.658947\pi$
$191$	−34938.0			−0.957704			−0.478852	+	0.877896i	$0.658947\pi$
$192$	−10810.8	+	10810.8i	−0.293262	+	0.293262i
$193$	8699.36	+	8699.36i	0.233546	+	0.233546i	0.814171	−	0.580625i	$-0.197192\pi$
$193$	8699.36	+	8699.36i	0.233546	+	0.233546i	−0.580625	+	0.814171i	$0.697192\pi$
$194$		−	25452.0i		−	0.676267i
$195$		0			0
$196$	539.000			0.0140306
$197$	20671.2	−	20671.2i	0.532640	−	0.532640i	−0.388717	−	0.921357i	$-0.627082\pi$
$197$	20671.2	−	20671.2i	0.532640	−	0.532640i	0.921357	+	0.388717i	$0.127082\pi$
$198$	28372.4	+	28372.4i	0.723713	+	0.723713i
$199$		−	32200.0i		−	0.813111i	−0.913626	−	0.406555i	$-0.866730\pi$
$199$		−	32200.0i		−	0.813111i	0.913626	−	0.406555i	$-0.133270\pi$
$200$		0			0
$201$	81837.0			2.02562
$202$	−68517.1	+	68517.1i	−1.67918	+	1.67918i
$203$	−40122.6	−	40122.6i	−0.973638	−	0.973638i
$204$		−	33957.0i		−	0.815960i
$205$		0			0
$206$	55062.0			1.29753
$207$	8244.98	−	8244.98i	0.192419	−	0.192419i
$208$	−15997.6	−	15997.6i	−0.369767	−	0.369767i
$209$			69615.0i			1.59371i
$210$		0			0
$211$	33017.0			0.741605			0.370803	−	0.928712i	$-0.379083\pi$
$211$	33017.0			0.741605			0.370803	+	0.928712i	$0.379083\pi$
$212$	16409.1	−	16409.1i	0.365102	−	0.365102i
$213$	−22993.4	−	22993.4i	−0.506808	−	0.506808i
$214$			10773.0i			0.235239i
$215$		0			0
$216$	−4725.00			−0.101273
$217$	11042.3	−	11042.3i	0.234498	−	0.234498i
$218$	77012.0	+	77012.0i	1.62049	+	1.62049i
$219$			31017.0i			0.646713i
$220$		0			0
$221$	18522.0			0.379231
$222$	36419.0	−	36419.0i	0.738962	−	0.738962i
$223$	−43174.7	−	43174.7i	−0.868200	−	0.868200i	0.124073	−	0.992273i	$-0.460404\pi$
$223$	−43174.7	−	43174.7i	−0.868200	−	0.868200i	−0.992273	+	0.124073i	$0.960404\pi$
$224$		−	58212.0i		−	1.16016i
$225$		0			0
$226$	−130653.			−2.55801
$227$	14608.8	−	14608.8i	0.283506	−	0.283506i	−0.551000	−	0.834505i	$-0.685754\pi$
$227$	14608.8	−	14608.8i	0.283506	−	0.283506i	0.834505	+	0.551000i	$0.185754\pi$
$228$	−56111.7	−	56111.7i	−1.07940	−	1.07940i
$229$			35980.0i			0.686104i	0.939316	+	0.343052i	$0.111461\pi$
$229$			35980.0i			0.686104i	−0.939316	+	0.343052i	$0.888539\pi$
$230$		0			0
$231$	−68796.0			−1.28926
$232$	21494.3	−	21494.3i	0.399344	−	0.399344i
$233$	60977.6	+	60977.6i	1.12320	+	1.12320i	0.991257	+	0.131947i	$0.0421228\pi$
$233$	60977.6	+	60977.6i	1.12320	+	1.12320i	0.131947	+	0.991257i	$0.457877\pi$
$234$		−	24948.0i		−	0.455621i
$235$		0			0
$236$	−20790.0			−0.373276
$237$	−55897.4	+	55897.4i	−0.995164	+	0.995164i
$238$	45369.4	+	45369.4i	0.800958	+	0.800958i
$239$		−	89010.0i		−	1.55827i	−0.626856	−	0.779136i	$-0.715658\pi$
$239$		−	89010.0i		−	1.55827i	0.626856	−	0.779136i	$-0.284342\pi$
$240$		0			0
$241$	3437.00			0.0591760			0.0295880	−	0.999562i	$-0.490580\pi$
$241$	3437.00			0.0591760			0.0295880	+	0.999562i	$0.490580\pi$
$242$	−3497.87	+	3497.87i	−0.0597273	+	0.0597273i
$243$	−54319.9	−	54319.9i	−0.919912	−	0.919912i
$244$			64988.0i			1.09157i
$245$		0			0
$246$	3969.00			0.0655860
$247$	30606.4	−	30606.4i	0.501670	−	0.501670i
$248$	5915.52	+	5915.52i	0.0961810	+	0.0961810i
$249$			42777.0i			0.689940i
$250$		0			0
$251$	−102123.			−1.62097			−0.810487	−	0.585756i	$-0.800798\pi$
$251$	−102123.			−1.62097			−0.810487	+	0.585756i	$0.800798\pi$
$252$	24896.6	−	24896.6i	0.392048	−	0.392048i
$253$	−14616.1	−	14616.1i	−0.228345	−	0.228345i
$254$		−	25002.0i		−	0.387532i
$255$		0			0
$256$	85921.0			1.31105
$257$	1748.94	−	1748.94i	0.0264794	−	0.0264794i	−0.693743	−	0.720223i	$-0.744040\pi$
$257$	1748.94	−	1748.94i	0.0264794	−	0.0264794i	0.720223	+	0.693743i	$0.244040\pi$
$258$	−79319.4	−	79319.4i	−1.19163	−	1.19163i
$259$			39648.0i			0.591047i
$260$		0			0
$261$	77220.0			1.13357
$262$	68054.2	−	68054.2i	0.991407	−	0.991407i
$263$	9501.57	+	9501.57i	0.137367	+	0.137367i	0.772447	−	0.635079i	$-0.219033\pi$
$263$	9501.57	+	9501.57i	0.137367	+	0.137367i	−0.635079	+	0.772447i	$0.719033\pi$
$264$		−	36855.0i		−	0.528796i
$265$		0			0
$266$	149940.			2.11911
$267$	−51310.7	+	51310.7i	−0.719756	+	0.719756i
$268$	52501.1	+	52501.1i	0.730969	+	0.730969i
$269$		−	47880.0i		−	0.661682i	−0.943686	−	0.330841i	$-0.892668\pi$
$269$		−	47880.0i		−	0.661682i	0.943686	−	0.330841i	$-0.107332\pi$
$270$		0			0
$271$	54782.0			0.745932			0.372966	−	0.927845i	$-0.378341\pi$
$271$	54782.0			0.745932			0.372966	+	0.927845i	$0.378341\pi$
$272$	−55991.7	+	55991.7i	−0.756808	+	0.756808i
$273$	30246.3	+	30246.3i	0.405833	+	0.405833i
$274$			29673.0i			0.395239i
$275$		0			0
$276$	23562.0			0.309310
$277$	−72409.4	+	72409.4i	−0.943703	+	0.943703i	−0.998498	−	0.0547949i	$-0.982549\pi$
$277$	−72409.4	+	72409.4i	−0.943703	+	0.943703i	0.0547949	+	0.998498i	$0.482549\pi$
$278$	50024.7	+	50024.7i	0.647284	+	0.647284i
$279$			21252.0i			0.273018i
$280$		0			0
$281$	−128178.			−1.62331			−0.811654	−	0.584139i	$-0.801432\pi$
$281$	−128178.			−1.62331			−0.811654	+	0.584139i	$0.801432\pi$
$282$	−29166.1	+	29166.1i	−0.366758	+	0.366758i
$283$	−28643.1	−	28643.1i	−0.357641	−	0.357641i	0.505302	−	0.862943i	$-0.331381\pi$
$283$	−28643.1	−	28643.1i	−0.357641	−	0.357641i	−0.862943	+	0.505302i	$0.831381\pi$
$284$		−	29502.0i		−	0.365776i
$285$		0			0
$286$	−44226.0			−0.540687
$287$	−2160.45	+	2160.45i	−0.0262289	+	0.0262289i
$288$	56017.4	+	56017.4i	0.675364	+	0.675364i
$289$			18694.0i			0.223824i
$290$		0			0
$291$	−59388.0			−0.701314
$292$	−19898.4	+	19898.4i	−0.233374	+	0.233374i
$293$	−39402.5	−	39402.5i	−0.458974	−	0.458974i	0.439344	−	0.898319i	$-0.355211\pi$
$293$	−39402.5	−	39402.5i	−0.458974	−	0.458974i	−0.898319	+	0.439344i	$0.855211\pi$
$294$		−	3087.00i		−	0.0357143i
$295$		0			0
$296$	−21240.0			−0.242421
$297$	−15046.0	+	15046.0i	−0.170572	+	0.170572i
$298$	−61176.0	−	61176.0i	−0.688888	−	0.688888i
$299$			12852.0i			0.143757i
$300$		0			0
$301$	86352.0			0.953102
$302$	55304.6	−	55304.6i	0.606383	−	0.606383i
$303$	159873.	+	159873.i	1.74137	+	1.74137i
$304$			185045.i			2.00230i
$305$		0			0
$306$	−87318.0			−0.932526
$307$	98411.9	−	98411.9i	1.04417	−	1.04417i	0.0451911	−	0.998978i	$-0.485610\pi$
$307$	98411.9	−	98411.9i	1.04417	−	1.04417i	0.998978	−	0.0451911i	$-0.0143897\pi$
$308$	−44134.9	−	44134.9i	−0.465244	−	0.465244i
$309$		−	128478.i		−	1.34559i
$310$		0			0
$311$	112392.			1.16202			0.581011	−	0.813895i	$-0.302657\pi$
$311$	112392.			1.16202			0.581011	+	0.813895i	$0.302657\pi$
$312$	−16203.4	+	16203.4i	−0.166455	+	0.166455i
$313$	−11625.3	−	11625.3i	−0.118663	−	0.118663i	0.645282	−	0.763945i	$-0.276740\pi$
$313$	−11625.3	−	11625.3i	−0.118663	−	0.118663i	−0.763945	+	0.645282i	$0.776740\pi$
$314$			84798.0i			0.860055i
$315$		0			0
$316$	−71720.0			−0.718234
$317$	75233.6	−	75233.6i	0.748675	−	0.748675i	−0.225555	−	0.974230i	$-0.572420\pi$
$317$	75233.6	−	75233.6i	0.748675	−	0.748675i	0.974230	+	0.225555i	$0.0724196\pi$
$318$	−93979.6	−	93979.6i	−0.929350	−	0.929350i
$319$		−	136890.i		−	1.34521i
$320$		0			0
$321$	25137.0			0.243951
$322$	−31480.8	+	31480.8i	−0.303623	+	0.303623i
$323$	−107122.	−	107122.i	−1.02677	−	1.02677i
$324$		−	83061.0i		−	0.791238i
$325$		0			0
$326$	−42903.0			−0.403694
$327$	179695.	−	179695.i	1.68050	−	1.68050i
$328$	−1157.38	−	1157.38i	−0.0107580	−	0.0107580i
$329$		−	31752.0i		−	0.293345i
$330$		0			0
$331$	19247.0			0.175674			0.0878369	−	0.996135i	$-0.472005\pi$
$331$	19247.0			0.175674			0.0878369	+	0.996135i	$0.472005\pi$
$332$	−27442.9	+	27442.9i	−0.248974	+	0.248974i
$333$	−38153.3	−	38153.3i	−0.344067	−	0.344067i
$334$		−	249102.i		−	2.23298i
$335$		0			0
$336$	−182868.			−1.61979
$337$	−76053.0	+	76053.0i	−0.669663	+	0.669663i	−0.957638	−	0.287975i	$-0.907018\pi$
$337$	−76053.0	+	76053.0i	−0.669663	+	0.669663i	0.287975	+	0.957638i	$0.407018\pi$
$338$	−85495.8	−	85495.8i	−0.748361	−	0.748361i
$339$			304857.i			2.65275i
$340$		0			0
$341$	37674.0			0.323991
$342$	−144287.	+	144287.i	−1.23360	+	1.23360i
$343$	84017.5	+	84017.5i	0.714137	+	0.714137i
$344$			46260.0i			0.390921i
$345$		0			0
$346$	130032.			1.08617
$347$	−128227.	+	128227.i	−1.06493	+	1.06493i	−0.0671894	+	0.997740i	$0.521403\pi$
$347$	−128227.	+	128227.i	−1.06493	+	1.06493i	−0.997740	+	0.0671894i	$0.978597\pi$
$348$	110337.	+	110337.i	0.911095	+	0.911095i
$349$		−	83300.0i		−	0.683902i	−0.939718	−	0.341951i	$-0.888912\pi$
$349$		−	83300.0i		−	0.683902i	0.939718	−	0.341951i	$-0.111088\pi$
$350$		0			0
$351$	13230.0			0.107385
$352$	99303.5	−	99303.5i	0.801455	−	0.801455i
$353$	157096.	+	157096.i	1.26071	+	1.26071i	0.950750	+	0.309958i	$0.100315\pi$
$353$	157096.	+	157096.i	1.26071	+	1.26071i	0.309958	+	0.950750i	$0.399685\pi$
$354$			119070.i			0.950158i
$355$		0			0
$356$	−65835.0			−0.519466
$357$	105862.	−	105862.i	0.830623	−	0.830623i
$358$	27942.6	+	27942.6i	0.218022	+	0.218022i
$359$			58860.0i			0.456700i	0.973579	+	0.228350i	$0.0733331\pi$
$359$			58860.0i			0.456700i	−0.973579	+	0.228350i	$0.926667\pi$
$360$		0			0
$361$	−223704.			−1.71656
$362$	24330.8	−	24330.8i	0.185669	−	0.185669i
$363$	8161.70	+	8161.70i	0.0619395	+	0.0619395i
$364$			38808.0i			0.292899i
$365$		0			0
$366$	372204.			2.77855
$367$	−65122.1	+	65122.1i	−0.483500	+	0.483500i	−0.906248	−	0.422747i	$-0.861066\pi$
$367$	−65122.1	+	65122.1i	−0.483500	+	0.483500i	0.422747	+	0.906248i	$0.361066\pi$
$368$	−38851.4	−	38851.4i	−0.286887	−	0.286887i
$369$		−	4158.00i		−	0.0305374i
$370$		0			0
$371$	102312.			0.743325
$372$	−30366.3	+	30366.3i	−0.219435	+	0.219435i
$373$	8080.87	+	8080.87i	0.0580818	+	0.0580818i	0.735551	−	0.677469i	$-0.236923\pi$
$373$	8080.87	+	8080.87i	0.0580818	+	0.0580818i	−0.677469	+	0.735551i	$0.736923\pi$
$374$			154791.i			1.10663i
$375$		0			0
$376$	17010.0			0.120317
$377$	−60184.0	+	60184.0i	−0.423446	+	0.423446i
$378$	32406.7	+	32406.7i	0.226805	+	0.226805i
$379$		−	133895.i		−	0.932150i	−0.884745	−	0.466075i	$-0.845668\pi$
$379$		−	133895.i		−	0.932150i	0.884745	−	0.466075i	$-0.154332\pi$
$380$		0			0
$381$	−58338.0			−0.401885
$382$	−128370.	+	128370.i	−0.879707	+	0.879707i
$383$	720.150	+	720.150i	0.00490937	+	0.00490937i	0.709557	−	0.704648i	$-0.248895\pi$
$383$	720.150	+	720.150i	0.00490937	+	0.00490937i	−0.704648	+	0.709557i	$0.748895\pi$
$384$		−	153405.i		−	1.04034i
$385$		0			0
$386$	63927.0			0.429052
$387$	−83096.5	+	83096.5i	−0.554831	+	0.554831i
$388$	−38099.4	−	38099.4i	−0.253078	−	0.253078i
$389$			86490.0i			0.571566i	0.958294	+	0.285783i	$0.0922537\pi$
$389$			86490.0i			0.571566i	−0.958294	+	0.285783i	$0.907746\pi$
$390$		0			0
$391$	44982.0			0.294229
$392$	−900.187	+	900.187i	−0.00585815	+	0.00585815i
$393$	−158793.	−	158793.i	−1.02813	−	1.02813i
$394$		−	151902.i		−	0.978523i
$395$		0			0
$396$	84942.0			0.541667
$397$	72906.6	−	72906.6i	0.462579	−	0.462579i	−0.436921	−	0.899500i	$-0.643931\pi$
$397$	72906.6	−	72906.6i	0.462579	−	0.462579i	0.899500	+	0.436921i	$0.143931\pi$
$398$	−118310.	−	118310.i	−0.746890	−	0.746890i
$399$		−	349860.i		−	2.19760i
$400$		0			0
$401$	−79173.0			−0.492366			−0.246183	−	0.969223i	$-0.579176\pi$
$401$	−79173.0			−0.492366			−0.246183	+	0.969223i	$0.579176\pi$
$402$	300688.	−	300688.i	1.86065	−	1.86065i
$403$	−16563.4	−	16563.4i	−0.101986	−	0.101986i
$404$			205128.i			1.25679i
$405$		0			0
$406$	−294840.			−1.78869
$407$	−67635.3	+	67635.3i	−0.408305	+	0.408305i
$408$	56711.8	+	56711.8i	0.340685	+	0.340685i
$409$			127435.i			0.761802i	0.924616	+	0.380901i	$0.124386\pi$
$409$			127435.i			0.761802i	−0.924616	+	0.380901i	$0.875614\pi$
$410$		0			0
$411$	69237.0			0.409878
$412$	82422.9	−	82422.9i	0.485572	−	0.485572i
$413$	−64813.5	−	64813.5i	−0.379984	−	0.379984i
$414$		−	60588.0i		−	0.353497i
$415$		0			0
$416$	−87318.0			−0.504565
$417$	116724.	−	116724.i	0.671258	−	0.671258i
$418$	255782.	+	255782.i	1.46392	+	1.46392i
$419$			234045.i			1.33313i	0.745449	+	0.666563i	$0.232235\pi$
$419$			234045.i			1.33313i	−0.745449	+	0.666563i	$0.767765\pi$
$420$		0			0
$421$	−87368.0			−0.492933			−0.246467	−	0.969151i	$-0.579270\pi$
$421$	−87368.0			−0.492933			−0.246467	+	0.969151i	$0.579270\pi$
$422$	121312.	−	121312.i	0.681208	−	0.681208i
$423$	30554.9	+	30554.9i	0.170766	+	0.170766i
$424$			54810.0i			0.304879i
$425$		0			0
$426$	−168966.			−0.931065
$427$	−202602.	+	202602.i	−1.11119	+	1.11119i
$428$	16126.2	+	16126.2i	0.0880329	+	0.0880329i
$429$			103194.i			0.560712i
$430$		0			0
$431$	−116028.			−0.624609			−0.312305	−	0.949982i	$-0.601101\pi$
$431$	−116028.			−0.624609			−0.312305	+	0.949982i	$0.601101\pi$
$432$	−39994.0	+	39994.0i	−0.214303	+	0.214303i
$433$	−144381.	−	144381.i	−0.770080	−	0.770080i	0.208040	−	0.978120i	$-0.433291\pi$
$433$	−144381.	−	144381.i	−0.770080	−	0.770080i	−0.978120	+	0.208040i	$0.933291\pi$
$434$		−	81144.0i		−	0.430801i
$435$		0			0
$436$	230560.			1.21286
$437$	74329.8	−	74329.8i	0.389224	−	0.389224i
$438$	113964.	+	113964.i	0.594044	+	0.594044i
$439$			85190.0i			0.442038i	0.975270	+	0.221019i	$0.0709383\pi$
$439$			85190.0i			0.442038i	−0.975270	+	0.221019i	$0.929062\pi$
$440$		0			0
$441$	−3234.00			−0.0166289
$442$	68054.2	−	68054.2i	0.348346	−	0.348346i
$443$	−153212.	−	153212.i	−0.780702	−	0.780702i	0.199248	−	0.979949i	$-0.436150\pi$
$443$	−153212.	−	153212.i	−0.780702	−	0.780702i	−0.979949	+	0.199248i	$0.936150\pi$
$444$		−	109032.i		−	0.553080i
$445$		0			0
$446$	−317268.			−1.59498
$447$	−142744.	+	142744.i	−0.714402	+	0.714402i
$448$	−43243.3	−	43243.3i	−0.215458	−	0.215458i
$449$		−	208125.i		−	1.03236i	−0.856480	−	0.516180i	$-0.827353\pi$
$449$		−	208125.i		−	1.03236i	0.856480	−	0.516180i	$-0.172647\pi$
$450$		0			0
$451$	−7371.00			−0.0362388
$452$	−195576.	+	195576.i	−0.957279	+	0.957279i
$453$	−129044.	−	129044.i	−0.628842	−	0.628842i
$454$		−	107352.i		−	0.520833i
$455$		0			0
$456$	187425.			0.901359
$457$	214395.	−	214395.i	1.02656	−	1.02656i	0.0269187	−	0.999638i	$-0.491430\pi$
$457$	214395.	−	214395.i	1.02656	−	1.02656i	0.999638	−	0.0269187i	$-0.00856953\pi$
$458$	132199.	+	132199.i	0.630227	+	0.630227i
$459$		−	46305.0i		−	0.219787i
$460$		0			0
$461$	332892.			1.56640			0.783198	−	0.621773i	$-0.213587\pi$
$461$	332892.			1.56640			0.783198	+	0.621773i	$0.213587\pi$
$462$	−252773.	+	252773.i	−1.18426	+	1.18426i
$463$	226710.	+	226710.i	1.05757	+	1.05757i	0.998238	+	0.0593309i	$0.0188967\pi$
$463$	226710.	+	226710.i	1.05757	+	1.05757i	0.0593309	+	0.998238i	$0.481103\pi$
$464$		−	363870.i		−	1.69009i
$465$		0			0
$466$	448092.			2.06346
$467$	−70266.1	+	70266.1i	−0.322190	+	0.322190i	−0.849607	−	0.527417i	$-0.823161\pi$
$467$	−70266.1	+	70266.1i	−0.322190	+	0.322190i	0.527417	+	0.849607i	$0.323161\pi$
$468$	−37344.9	−	37344.9i	−0.170506	−	0.170506i
$469$			327348.i			1.48821i
$470$		0			0
$471$	197862.			0.891909
$472$	34721.5	−	34721.5i	0.155853	−	0.155853i
$473$	147307.	+	147307.i	0.658419	+	0.658419i
$474$			410760.i			1.82823i
$475$		0			0
$476$	135828.			0.599481
$477$	−98454.8	+	98454.8i	−0.432713	+	0.432713i
$478$	−327044.	−	327044.i	−1.43136	−	1.43136i
$479$		−	5670.00i		−	0.0247122i	−0.999924	−	0.0123561i	$-0.996067\pi$
$479$		−	5670.00i		−	0.0247122i	0.999924	−	0.0123561i	$-0.00393317\pi$
$480$		0			0
$481$	59472.0			0.257053
$482$	12628.3	−	12628.3i	0.0543566	−	0.0543566i
$483$	73455.3	+	73455.3i	0.314868	+	0.314868i
$484$			10472.0i			0.0447032i
$485$		0			0
$486$	−399168.			−1.68999
$487$	291830.	−	291830.i	1.23047	−	1.23047i	0.266689	−	0.963783i	$-0.414070\pi$
$487$	291830.	−	291830.i	1.23047	−	1.23047i	0.963783	−	0.266689i	$-0.0859297\pi$
$488$	−108537.	−	108537.i	−0.455762	−	0.455762i
$489$			100107.i			0.418646i
$490$		0			0
$491$	−47538.0			−0.197187			−0.0985934	−	0.995128i	$-0.531434\pi$
$491$	−47538.0			−0.197187			−0.0985934	+	0.995128i	$0.531434\pi$
$492$	5941.24	−	5941.24i	0.0245441	−	0.0245441i
$493$	210644.	+	210644.i	0.866672	+	0.866672i
$494$		−	224910.i		−	0.921626i
$495$		0			0
$496$	100142.			0.407055
$497$	91973.4	−	91973.4i	0.372349	−	0.372349i
$498$	157173.	+	157173.i	0.633751	+	0.633751i
$499$			275150.i			1.10502i	0.833508	+	0.552508i	$0.186329\pi$
$499$			275150.i			1.10502i	−0.833508	+	0.552508i	$0.813671\pi$
$500$		0			0
$501$	−581238.			−2.31568
$502$	−375224.	+	375224.i	−1.48896	+	1.48896i
$503$	61932.9	+	61932.9i	0.244785	+	0.244785i	0.818826	−	0.574041i	$-0.194625\pi$
$503$	61932.9	+	61932.9i	0.244785	+	0.244785i	−0.574041	+	0.818826i	$0.694625\pi$
$504$			83160.0i			0.327381i
$505$		0			0
$506$	−107406.			−0.419496
$507$	−199490.	+	199490.i	−0.776078	+	0.776078i
$508$	−37425.8	−	37425.8i	−0.145025	−	0.145025i
$509$		−	184590.i		−	0.712480i	−0.934395	−	0.356240i	$-0.884059\pi$
$509$		−	184590.i		−	0.712480i	0.934395	−	0.356240i	$-0.115941\pi$
$510$		0			0
$511$	−124068.			−0.475136
$512$	172546.	−	172546.i	0.658210	−	0.658210i
$513$	−76515.9	−	76515.9i	−0.290748	−	0.290748i
$514$		−	12852.0i		−	0.0486457i
$515$		0			0
$516$	−237468.			−0.891878
$517$	54165.6	−	54165.6i	0.202648	−	0.202648i
$518$	145676.	+	145676.i	0.542911	+	0.542911i
$519$		−	303408.i		−	1.12640i
$520$		0			0
$521$	216657.			0.798173			0.399087	−	0.916913i	$-0.369327\pi$
$521$	216657.			0.798173			0.399087	+	0.916913i	$0.369327\pi$
$522$	283724.	−	283724.i	1.04125	−	1.04125i
$523$	−164700.	−	164700.i	−0.602130	−	0.602130i	0.338747	−	0.940877i	$-0.389997\pi$
$523$	−164700.	−	164700.i	−0.602130	−	0.602130i	−0.940877	+	0.338747i	$0.889997\pi$
$524$		−	203742.i		−	0.742024i
$525$		0			0
$526$	69822.0			0.252360
$527$	−57972.1	+	57972.1i	−0.208736	+	0.208736i
$528$	−311954.	−	311954.i	−1.11898	−	1.11898i
$529$		−	248629.i		−	0.888465i
$530$		0			0
$531$	124740.			0.442402
$532$	224447.	−	224447.i	0.793031	−	0.793031i
$533$	3240.67	+	3240.67i	0.0114073	+	0.0114073i
$534$			377055.i			1.32228i
$535$		0			0
$536$	−175365.			−0.610398
$537$	65199.3	−	65199.3i	0.226097	−	0.226097i
$538$	−175922.	−	175922.i	−0.607794	−	0.607794i
$539$			5733.00i			0.0197335i
$540$		0			0
$541$	−472888.			−1.61571			−0.807856	−	0.589380i	$-0.799372\pi$
$541$	−472888.			−1.61571			−0.807856	+	0.589380i	$0.799372\pi$
$542$	201282.	−	201282.i	0.685182	−	0.685182i
$543$	−56771.8	−	56771.8i	−0.192545	−	0.192545i
$544$			305613.i			1.03270i
$545$		0			0
$546$	222264.			0.745562
$547$	180347.	−	180347.i	0.602747	−	0.602747i	−0.338294	−	0.941041i	$-0.609850\pi$
$547$	180347.	−	180347.i	0.602747	−	0.602747i	0.941041	+	0.338294i	$0.109850\pi$
$548$	44417.8	+	44417.8i	0.147910	+	0.147910i
$549$		−	389928.i		−	1.29372i
$550$		0			0
$551$	696150.			2.29298
$552$	−39351.1	+	39351.1i	−0.129145	+	0.129145i
$553$	−223589.	−	223589.i	−0.731141	−	0.731141i
$554$			532098.i			1.73369i
$555$		0			0
$556$	149765.			0.484463
$557$	−212275.	+	212275.i	−0.684209	+	0.684209i	−0.960946	−	0.276737i	$-0.910747\pi$
$557$	−212275.	+	212275.i	−0.684209	+	0.684209i	0.276737	+	0.960946i	$0.410747\pi$
$558$	78084.8	+	78084.8i	0.250783	+	0.250783i
$559$		−	129528.i		−	0.414515i
$560$		0			0
$561$	361179.			1.14762
$562$	−470956.	+	470956.i	−1.49110	+	1.49110i
$563$	240427.	+	240427.i	0.758520	+	0.758520i	0.976053	−	0.217533i	$-0.0698011\pi$
$563$	240427.	+	240427.i	0.758520	+	0.758520i	−0.217533	+	0.976053i	$0.569801\pi$
$564$			87318.0i			0.274502i
$565$		0			0
$566$	−210483.			−0.657028
$567$	258945.	−	258945.i	0.805456	−	0.805456i
$568$	49271.5	+	49271.5i	0.152721	+	0.152721i
$569$		−	390555.i		−	1.20631i	−0.797625	−	0.603153i	$-0.793911\pi$
$569$		−	390555.i		−	1.20631i	0.797625	−	0.603153i	$-0.206089\pi$
$570$		0			0
$571$	−255418.			−0.783392			−0.391696	−	0.920095i	$-0.628112\pi$
$571$	−255418.			−0.783392			−0.391696	+	0.920095i	$0.628112\pi$
$572$	−66202.4	+	66202.4i	−0.202340	+	0.202340i
$573$	299531.	+	299531.i	0.912289	+	0.912289i
$574$			15876.0i			0.0481856i
$575$		0			0
$576$	83226.0			0.250850
$577$	−402264.	+	402264.i	−1.20826	+	1.20826i	−0.236666	+	0.971591i	$0.576055\pi$
$577$	−402264.	+	402264.i	−1.20826	+	1.20826i	−0.971591	+	0.236666i	$0.923945\pi$
$578$	68686.1	+	68686.1i	0.205595	+	0.205595i
$579$		−	149163.i		−	0.444943i
$580$		0			0
$581$	−171108.			−0.506895
$582$	−218205.	+	218205.i	−0.644198	+	0.644198i
$583$	174533.	+	174533.i	0.513501	+	0.513501i
$584$		−	66465.0i		−	0.194880i
$585$		0			0
$586$	−289548.			−0.843190
$587$	250586.	−	250586.i	0.727246	−	0.727246i	−0.242824	−	0.970070i	$-0.578074\pi$
$587$	250586.	−	250586.i	0.727246	−	0.727246i	0.970070	+	0.242824i	$0.0780738\pi$
$588$	−4620.96	−	4620.96i	−0.0133653	−	0.0133653i
$589$			191590.i			0.552258i
$590$		0			0
$591$	−354438.			−1.01476
$592$	−179783.	+	179783.i	−0.512985	+	0.512985i
$593$	88552.7	+	88552.7i	0.251821	+	0.251821i	0.821717	−	0.569896i	$-0.193016\pi$
$593$	88552.7	+	88552.7i	0.251821	+	0.251821i	−0.569896	+	0.821717i	$0.693016\pi$
$594$			110565.i			0.313361i
$595$		0			0
$596$	−183150.			−0.515602
$597$	−276057.	+	276057.i	−0.774553	+	0.774553i
$598$	47221.3	+	47221.3i	0.132049	+	0.132049i
$599$			569700.i			1.58779i	0.608056	+	0.793894i	$0.291950\pi$
$599$			569700.i			1.58779i	−0.608056	+	0.793894i	$0.708050\pi$
$600$		0			0
$601$	343777.			0.951761			0.475880	−	0.879510i	$-0.342129\pi$
$601$	343777.			0.951761			0.475880	+	0.879510i	$0.342129\pi$
$602$	317278.	−	317278.i	0.875480	−	0.875480i
$603$	−315007.	−	315007.i	−0.866334	−	0.866334i
$604$		−	165572.i		−	0.453851i
$605$		0			0
$606$	1.17482e6			3.19910
$607$	−184290.	+	184290.i	−0.500177	+	0.500177i	−0.911493	−	0.411316i	$-0.865069\pi$
$607$	−184290.	+	184290.i	−0.500177	+	0.500177i	0.411316	+	0.911493i	$0.365069\pi$
$608$	505005.	+	505005.i	1.36612	+	1.36612i
$609$			687960.i			1.85493i
$610$		0			0
$611$	−47628.0			−0.127579
$612$	−130707.	+	130707.i	−0.348977	+	0.348977i
$613$	−33364.5	−	33364.5i	−0.0887899	−	0.0887899i	0.661317	−	0.750107i	$-0.269998\pi$
$613$	−33364.5	−	33364.5i	−0.0887899	−	0.0887899i	−0.750107	+	0.661317i	$0.769998\pi$
$614$		−	723177.i		−	1.91826i
$615$		0			0
$616$	147420.			0.388504
$617$	11669.4	−	11669.4i	0.0306533	−	0.0306533i	−0.691614	−	0.722267i	$-0.743100\pi$
$617$	11669.4	−	11669.4i	0.0306533	−	0.0306533i	0.722267	+	0.691614i	$0.243100\pi$
$618$	−472058.	−	472058.i	−1.23600	−	1.23600i
$619$		−	144130.i		−	0.376160i	−0.982154	−	0.188080i	$-0.939774\pi$
$619$		−	144130.i		−	0.376160i	0.982154	−	0.188080i	$-0.0602265\pi$
$620$		0			0
$621$	32130.0			0.0833158
$622$	412955.	−	412955.i	1.06739	−	1.06739i
$623$	−205243.	−	205243.i	−0.528800	−	0.528800i
$624$			274302.i			0.704466i
$625$		0			0
$626$	−85428.0			−0.217998
$627$	596824.	−	596824.i	1.51814	−	1.51814i
$628$	126935.	+	126935.i	0.321856	+	0.321856i
$629$		−	208152.i		−	0.526113i
$630$		0			0
$631$	−326878.			−0.820969			−0.410485	−	0.911867i	$-0.634640\pi$
$631$	−326878.			−0.820969			−0.410485	+	0.911867i	$0.634640\pi$
$632$	119780.	−	119780.i	0.299882	−	0.299882i
$633$	−283062.	−	283062.i	−0.706438	−	0.706438i
$634$		−	552852.i		−	1.37540i
$635$		0			0
$636$	−281358.			−0.695577
$637$	2520.52	−	2520.52i	0.00621172	−	0.00621172i
$638$	−502966.	−	502966.i	−1.23566	−	1.23566i
$639$			177012.i			0.433512i
$640$		0			0
$641$	209862.			0.510761			0.255381	−	0.966841i	$-0.417799\pi$
$641$	209862.			0.510761			0.255381	+	0.966841i	$0.417799\pi$
$642$	92359.2	−	92359.2i	0.224084	−	0.224084i
$643$	120059.	+	120059.i	0.290385	+	0.290385i	0.837232	−	0.546847i	$-0.184172\pi$
$643$	120059.	+	120059.i	0.290385	+	0.290385i	−0.546847	+	0.837232i	$0.684172\pi$
$644$			94248.0i			0.227248i
$645$		0			0
$646$	−787185.			−1.88630
$647$	−294027.	+	294027.i	−0.702390	+	0.702390i	−0.964923	−	0.262533i	$-0.915442\pi$
$647$	−294027.	+	294027.i	−0.702390	+	0.702390i	0.262533	+	0.964923i	$0.415442\pi$
$648$	138721.	+	138721.i	0.330363	+	0.330363i
$649$		−	221130.i		−	0.524999i
$650$		0			0
$651$	−189336.			−0.446757
$652$	−64221.9	+	64221.9i	−0.151073	+	0.151073i
$653$	406576.	+	406576.i	0.953489	+	0.953489i	0.998965	−	0.0454768i	$-0.0144807\pi$
$653$	406576.	+	406576.i	0.953489	+	0.953489i	−0.0454768	+	0.998965i	$0.514481\pi$
$654$		−	1.32048e6i		−	3.08728i
$655$		0			0
$656$	−19593.0			−0.0455295
$657$	119391.	−	119391.i	0.276592	−	0.276592i
$658$	−116664.	−	116664.i	−0.269455	−	0.269455i
$659$			802485.i			1.84785i	0.382577	+	0.923924i	$0.375037\pi$
$659$			802485.i			1.84785i	−0.382577	+	0.923924i	$0.624963\pi$
$660$		0			0
$661$	532042.			1.21771			0.608854	−	0.793282i	$-0.291630\pi$
$661$	532042.			1.21771			0.608854	+	0.793282i	$0.291630\pi$
$662$	70718.0	−	70718.0i	0.161367	−	0.161367i
$663$	−158793.	−	158793.i	−0.361247	−	0.361247i
$664$		−	91665.0i		−	0.207906i
$665$		0			0
$666$	−280368.			−0.632092
$667$	−146161.	+	146161.i	−0.328534	+	0.328534i
$668$	−372883.	−	372883.i	−0.835642	−	0.835642i
$669$			740292.i			1.65406i
$670$		0			0
$671$	−691236.			−1.53526
$672$	−499064.	+	499064.i	−1.10514	+	1.10514i
$673$	−181203.	−	181203.i	−0.400070	−	0.400070i	0.478187	−	0.878258i	$-0.341294\pi$
$673$	−181203.	−	181203.i	−0.400070	−	0.400070i	−0.878258	+	0.478187i	$0.841294\pi$
$674$			558873.i			1.23025i
$675$		0			0
$676$	−255959.			−0.560115
$677$	235798.	−	235798.i	0.514473	−	0.514473i	−0.401421	−	0.915894i	$-0.631484\pi$
$677$	235798.	−	235798.i	0.514473	−	0.514473i	0.915894	+	0.401421i	$0.131484\pi$
$678$	1.12012e6	+	1.12012e6i	2.43671	+	2.43671i
$679$		−	237552.i		−	0.515251i
$680$		0			0
$681$	−250488.			−0.540123
$682$	138423.	−	138423.i	0.297605	−	0.297605i
$683$	−233237.	−	233237.i	−0.499983	−	0.499983i	0.411449	−	0.911433i	$-0.365023\pi$
$683$	−233237.	−	233237.i	−0.499983	−	0.499983i	−0.911433	+	0.411449i	$0.865023\pi$
$684$			431970.i			0.923297i
$685$		0			0
$686$	617400.			1.31195
$687$	308464.	−	308464.i	0.653569	−	0.653569i
$688$	391561.	+	391561.i	0.827222	+	0.827222i
$689$		−	153468.i		−	0.323280i
$690$		0			0
$691$	138187.			0.289408			0.144704	−	0.989475i	$-0.453777\pi$
$691$	138187.			0.289408			0.144704	+	0.989475i	$0.453777\pi$
$692$	194646.	−	194646.i	0.406475	−	0.406475i
$693$	264809.	+	264809.i	0.551400	+	0.551400i
$694$			942273.i			1.95640i
$695$		0			0
$696$	−368550.			−0.760813
$697$	11342.4	−	11342.4i	0.0233474	−	0.0233474i
$698$	−306064.	−	306064.i	−0.628204	−	0.628204i
$699$		−	1.04555e6i		−	2.13988i
$700$		0			0
$701$	649602.			1.32194			0.660969	−	0.750413i	$-0.270145\pi$
$701$	649602.			1.32194			0.660969	+	0.750413i	$0.270145\pi$
$702$	48610.1	−	48610.1i	0.0986399	−	0.0986399i
$703$	−343957.	−	343957.i	−0.695975	−	0.695975i
$704$		−	147537.i		−	0.297684i
$705$		0			0
$706$	1.15441e6			2.31607
$707$	−639493.	+	639493.i	−1.27937	+	1.27937i
$708$	178237.	+	178237.i	0.355575	+	0.355575i
$709$			439060.i			0.873437i	0.899598	+	0.436718i	$0.143859\pi$
$709$			439060.i			0.873437i	−0.899598	+	0.436718i	$0.856141\pi$
$710$		0			0
$711$	430320.			0.851241
$712$	109951.	−	109951.i	0.216891	−	0.216891i
$713$	−40225.5	−	40225.5i	−0.0791266	−	0.0791266i
$714$		−	777924.i		−	1.52595i
$715$		0			0
$716$	83655.0			0.163180
$717$	−763102.	+	763102.i	−1.48438	+	1.48438i
$718$	216265.	+	216265.i	0.419506	+	0.419506i
$719$		−	413280.i		−	0.799441i	−0.916637	−	0.399721i	$-0.869107\pi$
$719$		−	413280.i		−	0.799441i	0.916637	−	0.399721i	$-0.130893\pi$
$720$		0			0
$721$	513912.			0.988595
$722$	−821941.	+	821941.i	−1.57676	+	1.57676i
$723$	−29466.1	−	29466.1i	−0.0563698	−	0.0563698i
$724$		−	72842.0i		−	0.138965i
$725$		0			0
$726$	59976.0			0.113790
$727$	330532.	−	330532.i	0.625380	−	0.625380i	−0.321522	−	0.946902i	$-0.604194\pi$
$727$	330532.	−	330532.i	0.625380	−	0.625380i	0.946902	+	0.321522i	$0.104194\pi$
$728$	−64813.5	−	64813.5i	−0.122293	−	0.122293i
$729$			319761.i			0.601687i
$730$		0			0
$731$	−453348.			−0.848393
$732$	557156.	−	557156.i	1.03981	−	1.03981i
$733$	−571542.	−	571542.i	−1.06375	−	1.06375i	−0.997824	−	0.0659269i	$-0.979000\pi$
$733$	−571542.	−	571542.i	−1.06375	−	1.06375i	−0.0659269	−	0.997824i	$-0.521000\pi$
$734$			478548.i			0.888246i
$735$		0			0
$736$	−212058.			−0.391470
$737$	−558421.	+	558421.i	−1.02808	+	1.02808i
$738$	−15277.5	−	15277.5i	−0.0280504	−	0.0280504i
$739$		−	781310.i		−	1.43065i	−0.698790	−	0.715327i	$-0.746278\pi$
$739$		−	781310.i		−	1.43065i	0.698790	−	0.715327i	$-0.253722\pi$
$740$		0			0
$741$	−524790.			−0.955761
$742$	375918.	−	375918.i	0.682788	−	0.682788i
$743$	−400763.	−	400763.i	−0.725956	−	0.725956i	0.243855	−	0.969812i	$-0.421588\pi$
$743$	−400763.	−	400763.i	−0.725956	−	0.725956i	−0.969812	+	0.243855i	$0.921588\pi$
$744$		−	101430.i		−	0.183240i
$745$		0			0
$746$	59382.0			0.106703
$747$	164657.	−	164657.i	0.295080	−	0.295080i
$748$	231708.	+	231708.i	0.414132	+	0.414132i
$749$			100548.i			0.179230i
$750$		0			0
$751$	−258698.			−0.458684			−0.229342	−	0.973346i	$-0.573657\pi$
$751$	−258698.			−0.458684			−0.229342	+	0.973346i	$0.573657\pi$
$752$	143979.	−	143979.i	0.254602	−	0.254602i
$753$	875522.	+	875522.i	1.54411	+	1.54411i
$754$			442260.i			0.777920i
$755$		0			0
$756$	97020.0			0.169753
$757$	615101.	−	615101.i	1.07338	−	1.07338i	0.0762981	−	0.997085i	$-0.475690\pi$
$757$	615101.	−	615101.i	1.07338	−	1.07338i	0.997085	−	0.0762981i	$-0.0243101\pi$
$758$	−491962.	−	491962.i	−0.856235	−	0.856235i
$759$			250614.i			0.435033i
$760$		0			0
$761$	−547533.			−0.945455			−0.472728	−	0.881209i	$-0.656731\pi$
$761$	−547533.			−0.945455			−0.472728	+	0.881209i	$0.656731\pi$
$762$	−214347.	+	214347.i	−0.369155	+	0.369155i
$763$	718778.	+	718778.i	1.23466	+	1.23466i
$764$			384318.i			0.658422i
$765$		0			0
$766$	5292.00			0.00901908
$767$	−97220.2	+	97220.2i	−0.165259	+	0.165259i
$768$	−736619.	−	736619.i	−1.24888	−	1.24888i
$769$		−	136255.i		−	0.230409i	−0.993342	−	0.115205i	$-0.963248\pi$
$769$		−	136255.i		−	0.230409i	0.993342	−	0.115205i	$-0.0367524\pi$
$770$		0			0
$771$	−29988.0			−0.0504474
$772$	95693.0	−	95693.0i	0.160563	−	0.160563i
$773$	425351.	+	425351.i	0.711851	+	0.711851i	0.966922	−	0.255071i	$-0.0820990\pi$
$773$	425351.	+	425351.i	0.711851	+	0.711851i	−0.255071	+	0.966922i	$0.582099\pi$
$774$			610632.i			1.01929i
$775$		0			0
$776$	127260.			0.211334
$777$	339911.	−	339911.i	0.563019	−	0.563019i
$778$	317785.	+	317785.i	0.525017	+	0.525017i
$779$		−	37485.0i		−	0.0617707i
$780$		0			0
$781$	313794.			0.514449
$782$	165274.	−	165274.i	0.270266	−	0.270266i
$783$	150460.	+	150460.i	0.245413	+	0.245413i
$784$			15239.0i			0.0247927i
$785$		0			0
$786$	−1.16689e6			−1.88879
$787$	421836.	−	421836.i	0.681074	−	0.681074i	−0.279168	−	0.960242i	$-0.590059\pi$
$787$	421836.	−	421836.i	0.681074	−	0.681074i	0.960242	+	0.279168i	$0.0900586\pi$
$788$	−227384.	−	227384.i	−0.366190	−	0.366190i
$789$		−	162918.i		−	0.261707i
$790$		0			0
$791$	−1.21943e6			−1.94896
$792$	−141862.	+	141862.i	−0.226160	+	0.226160i
$793$	303903.	+	303903.i	0.483269	+	0.483269i
$794$		−	535752.i		−	0.849812i
$795$		0			0
$796$	−354200.			−0.559014
$797$	666602.	−	666602.i	1.04942	−	1.04942i	0.0507075	−	0.998714i	$-0.483852\pi$
$797$	666602.	−	666602.i	1.04942	−	1.04942i	0.998714	−	0.0507075i	$-0.0161476\pi$
$798$	−1.28547e6	−	1.28547e6i	−2.01862	−	2.01862i
$799$			166698.i			0.261118i
$800$		0			0
$801$	395010.			0.615663
$802$	−290900.	+	290900.i	−0.452267	+	0.452267i
$803$	−211647.	−	211647.i	−0.328232	−	0.328232i
$804$		−	900207.i		−	1.39261i
$805$		0			0
$806$	−121716.			−0.187360
$807$	−410485.	+	410485.i	−0.630305	+	0.630305i
$808$	−342586.	−	342586.i	−0.524743	−	0.524743i
$809$		−	698490.i		−	1.06724i	−0.845724	−	0.533621i	$-0.820831\pi$
$809$		−	698490.i		−	1.06724i	0.845724	−	0.533621i	$-0.179169\pi$
$810$		0			0
$811$	578242.			0.879160			0.439580	−	0.898203i	$-0.355127\pi$
$811$	578242.			0.879160			0.439580	+	0.898203i	$0.355127\pi$
$812$	−441349.	+	441349.i	−0.669376	+	0.669376i
$813$	−469658.	−	469658.i	−0.710560	−	0.710560i
$814$			497016.i			0.750104i
$815$		0			0
$816$	960057.			1.44184
$817$	−749127.	+	749127.i	−1.12231	+	1.12231i
$818$	468226.	+	468226.i	0.699760	+	0.699760i
$819$		−	232848.i		−	0.347140i
$820$		0			0
$821$	720882.			1.06949			0.534746	−	0.845013i	$-0.320407\pi$
$821$	720882.			1.06949			0.534746	+	0.845013i	$0.320407\pi$
$822$	254393.	−	254393.i	0.376497	−	0.376497i
$823$	−145073.	−	145073.i	−0.214185	−	0.214185i	0.591858	−	0.806042i	$-0.298395\pi$
$823$	−145073.	−	145073.i	−0.214185	−	0.214185i	−0.806042	+	0.591858i	$0.798395\pi$
$824$			275310.i			0.405478i
$825$		0			0
$826$	−476280.			−0.698075
$827$	488126.	−	488126.i	0.713708	−	0.713708i	−0.253601	−	0.967309i	$-0.581615\pi$
$827$	488126.	−	488126.i	0.713708	−	0.713708i	0.967309	+	0.253601i	$0.0816149\pi$
$828$	−90694.8	−	90694.8i	−0.132288	−	0.132288i
$829$		−	248570.i		−	0.361693i	−0.983511	−	0.180846i	$-0.942116\pi$
$829$		−	248570.i		−	0.361693i	0.983511	−	0.180846i	$-0.0578837\pi$
$830$		0			0
$831$	1.24156e6			1.79790
$832$	−64864.9	+	64864.9i	−0.0937051	+	0.0937051i
$833$	−8821.84	−	8821.84i	−0.0127136	−	0.0127136i
$834$		−	857745.i		−	1.23318i
$835$		0			0
$836$	765765.			1.09568
$837$	−41408.6	+	41408.6i	−0.0591071	+	0.0591071i
$838$	859936.	+	859936.i	1.22455	+	1.22455i
$839$			1.35324e6i			1.92243i	0.275797	+	0.961216i	$0.411058\pi$
$839$			1.35324e6i			1.92243i	−0.275797	+	0.961216i	$0.588942\pi$
$840$		0			0
$841$	−661619.			−0.935440
$842$	−321011.	+	321011.i	−0.452788	+	0.452788i
$843$	1.09890e6	+	1.09890e6i	1.54633	+	1.54633i
$844$		−	363187.i		−	0.509853i
$845$		0			0
$846$	224532.			0.313717
$847$	−32646.8	+	32646.8i	−0.0455065	+	0.0455065i
$848$	463931.	+	463931.i	0.645151	+	0.645151i
$849$			491127.i			0.681363i
$850$		0			0
$851$	144432.			0.199436
$852$	−252927.	+	252927.i	−0.348430	+	0.348430i
$853$	−934703.	−	934703.i	−1.28462	−	1.28462i	−0.938007	−	0.346616i	$-0.887331\pi$
$853$	−934703.	−	934703.i	−1.28462	−	1.28462i	−0.346616	−	0.938007i	$-0.612669\pi$
$854$			1.48882e6i			2.04139i
$855$		0			0
$856$	−53865.0			−0.0735122
$857$	771409.	−	771409.i	1.05032	−	1.05032i	0.0516590	−	0.998665i	$-0.483549\pi$
$857$	771409.	−	771409.i	1.05032	−	1.05032i	0.998665	−	0.0516590i	$-0.0164509\pi$
$858$	379159.	+	379159.i	0.515047	+	0.515047i
$859$			178535.i			0.241956i	0.992655	+	0.120978i	$0.0386031\pi$
$859$			178535.i			0.241956i	−0.992655	+	0.120978i	$0.961397\pi$
$860$		0			0
$861$	37044.0			0.0499703
$862$	−426314.	+	426314.i	−0.573740	+	0.573740i
$863$	−356085.	−	356085.i	−0.478114	−	0.478114i	0.426414	−	0.904528i	$-0.359777\pi$
$863$	−356085.	−	356085.i	−0.478114	−	0.478114i	−0.904528	+	0.426414i	$0.859777\pi$
$864$			218295.i			0.292426i
$865$		0			0
$866$	−1.06098e6			−1.41473
$867$	160268.	−	160268.i	0.213210	−	0.213210i
$868$	−121465.	−	121465.i	−0.161218	−	0.161218i
$869$		−	762840.i		−	1.01017i
$870$		0			0
$871$	491022.			0.647239
$872$	−385060.	+	385060.i	−0.506402	+	0.506402i
$873$	228596.	+	228596.i	0.299944	+	0.299944i
$874$		−	546210.i		−	0.715051i
$875$		0			0
$876$	341187.			0.444615
$877$	−699540.	+	699540.i	−0.909522	+	0.909522i	−0.996233	−	0.0867112i	$-0.972364\pi$
$877$	−699540.	+	699540.i	−0.909522	+	0.909522i	0.0867112	+	0.996233i	$0.472364\pi$
$878$	313008.	+	313008.i	0.406038	+	0.406038i
$879$			675612.i			0.874419i
$880$		0			0
$881$	−775278.			−0.998862			−0.499431	−	0.866354i	$-0.666458\pi$
$881$	−775278.			−0.998862			−0.499431	+	0.866354i	$0.666458\pi$
$882$	−11882.5	+	11882.5i	−0.0152746	+	0.0152746i
$883$	655867.	+	655867.i	0.841190	+	0.841190i	0.989014	−	0.147823i	$-0.0472268\pi$
$883$	655867.	+	655867.i	0.841190	+	0.841190i	−0.147823	+	0.989014i	$0.547227\pi$
$884$		−	203742.i		−	0.260721i
$885$		0			0
$886$	−1.12587e6			−1.43424
$887$	−391762.	+	391762.i	−0.497937	+	0.497937i	−0.910795	−	0.412858i	$-0.864531\pi$
$887$	−391762.	+	391762.i	−0.497937	+	0.497937i	0.412858	+	0.910795i	$0.364531\pi$
$888$	182095.	+	182095.i	0.230926	+	0.230926i
$889$		−	233352.i		−	0.295262i
$890$		0			0
$891$	883467.			1.11285
$892$	−474922.	+	474922.i	−0.596887	+	0.596887i
$893$	275457.	+	275457.i	0.345423	+	0.345423i
$894$			1.04895e6i			1.31244i
$895$		0			0
$896$	613620.			0.764335
$897$	110183.	−	110183.i	0.136940	−	0.136940i
$898$	−764700.	−	764700.i	−0.948284	−	0.948284i
$899$		−	376740.i		−	0.466146i
$900$		0			0
$901$	−537138.			−0.661662
$902$	−27082.8	+	27082.8i	−0.0332874	+	0.0332874i
$903$	−740314.	−	740314.i	−0.907905	−	0.907905i
$904$		−	653265.i		−	0.799379i
$905$		0			0
$906$	−948276.			−1.15526
$907$	24039.3	−	24039.3i	0.0292218	−	0.0292218i	−0.692345	−	0.721567i	$-0.743422\pi$
$907$	24039.3	−	24039.3i	0.0292218	−	0.0292218i	0.721567	+	0.692345i	$0.243422\pi$
$908$	−160696.	−	160696.i	−0.194910	−	0.194910i
$909$		−	1.23077e6i		−	1.48953i
$910$		0			0
$911$	259092.			0.312189			0.156094	−	0.987742i	$-0.450110\pi$
$911$	259092.			0.312189			0.156094	+	0.987742i	$0.450110\pi$
$912$	1.58643e6	−	1.58643e6i	1.90735	−	1.90735i
$913$	−291892.	−	291892.i	−0.350172	−	0.350172i
$914$		−	1.57548e6i		−	1.88590i
$915$		0			0
$916$	395780.			0.471697
$917$	635172.	−	635172.i	0.755358	−	0.755358i
$918$	−170135.	−	170135.i	−0.201887	−	0.201887i
$919$			190270.i			0.225289i	0.993635	+	0.112644i	$0.0359321\pi$
$919$			190270.i			0.225289i	−0.993635	+	0.112644i	$0.964068\pi$
$920$		0			0
$921$	−1.68741e6			−1.98931
$922$	1.22312e6	−	1.22312e6i	1.43883	−	1.43883i
$923$	−137960.	−	137960.i	−0.161939	−	0.161939i
$924$			756756.i			0.886364i
$925$		0			0
$926$	1.66597e6			1.94288
$927$	−494537.	+	494537.i	−0.575492	+	0.575492i
$928$	−993035.	−	993035.i	−1.15310	−	1.15310i
$929$			529830.i			0.613911i	0.951724	+	0.306955i	$0.0993102\pi$
$929$			529830.i			0.613911i	−0.951724	+	0.306955i	$0.900690\pi$
$930$		0			0
$931$	−29155.0			−0.0336367
$932$	670754.	−	670754.i	0.772202	−	0.772202i
$933$	−963561.	−	963561.i	−1.10692	−	1.10692i
$934$			516348.i			0.591901i
$935$		0			0
$936$	124740.			0.142382
$937$	−533005.	+	533005.i	−0.607089	+	0.607089i	−0.942184	−	0.335095i	$-0.891231\pi$
$937$	−533005.	+	533005.i	−0.607089	+	0.607089i	0.335095	+	0.942184i	$0.391231\pi$
$938$	1.20275e6	+	1.20275e6i	1.36701	+	1.36701i
$939$			199332.i			0.226072i
$940$		0			0
$941$	892962.			1.00845			0.504224	−	0.863573i	$-0.331778\pi$
$941$	892962.			1.00845			0.504224	+	0.863573i	$0.331778\pi$
$942$	726991.	−	726991.i	0.819271	−	0.819271i
$943$	7870.21	+	7870.21i	0.00885040	+	0.00885040i
$944$		−	587790.i		−	0.659596i
$945$		0			0
$946$	1.08248e6			1.20959
$947$	125203.	−	125203.i	0.139610	−	0.139610i	−0.633848	−	0.773458i	$-0.718526\pi$
$947$	125203.	−	125203.i	0.139610	−	0.139610i	0.773458	+	0.633848i	$0.218526\pi$
$948$	614871.	+	614871.i	0.684175	+	0.684175i
$949$			186102.i			0.206642i
$950$		0			0
$951$	−1.28999e6			−1.42635
$952$	−226847.	+	226847.i	−0.250299	+	0.250299i
$953$	−205827.	−	205827.i	−0.226629	−	0.226629i	0.584654	−	0.811283i	$-0.301230\pi$
$953$	−205827.	−	205827.i	−0.226629	−	0.226629i	−0.811283	+	0.584654i	$0.801230\pi$
$954$			723492.i			0.794945i
$955$		0			0
$956$	−979110.			−1.07131
$957$	−1.17359e6	+	1.17359e6i	−1.28142	+	1.28142i
$958$	−20832.9	−	20832.9i	−0.0226996	−	0.0226996i
$959$			276948.i			0.301135i
$960$		0			0
$961$	−819837.			−0.887730
$962$	218514.	−	218514.i	0.236118	−	0.236118i
$963$	−96757.3	−	96757.3i	−0.104335	−	0.104335i
$964$		−	37807.0i		−	0.0406835i
$965$		0			0
$966$	539784.			0.578450
$967$	−521217.	+	521217.i	−0.557398	+	0.557398i	−0.928566	−	0.371168i	$-0.878958\pi$
$967$	−521217.	+	521217.i	−0.557398	+	0.557398i	0.371168	+	0.928566i	$0.378958\pi$
$968$	−17489.4	−	17489.4i	−0.0186648	−	0.0186648i
$969$			1.83676e6i			1.95617i
$970$		0			0
$971$	−290493.			−0.308104			−0.154052	−	0.988063i	$-0.549232\pi$
$971$	−290493.			−0.308104			−0.154052	+	0.988063i	$0.549232\pi$
$972$	−597519.	+	597519.i	−0.632440	+	0.632440i
$973$	466897.	+	466897.i	0.493169	+	0.493169i
$974$		−	2.14450e6i		−	2.26052i
$975$		0			0
$976$	−1.83739e6			−1.92886
$977$	291187.	−	291187.i	0.305058	−	0.305058i	−0.537931	−	0.842989i	$-0.680794\pi$
$977$	291187.	−	291187.i	0.305058	−	0.305058i	0.842989	+	0.537931i	$0.180794\pi$
$978$	367817.	+	367817.i	0.384551	+	0.384551i
$979$		−	700245.i		−	0.730608i
$980$		0			0
$981$	−1.38336e6			−1.43746
$982$	−174666.	+	174666.i	−0.181128	+	0.181128i
$983$	651427.	+	651427.i	0.674153	+	0.674153i	0.958671	−	0.284517i	$-0.0918333\pi$
$983$	651427.	+	651427.i	0.674153	+	0.674153i	−0.284517	+	0.958671i	$0.591833\pi$
$984$			19845.0i			0.0204956i
$985$		0			0
$986$	1.54791e6			1.59218
$987$	−272217.	+	272217.i	−0.279435	+	0.279435i
$988$	−336670.	−	336670.i	−0.344898	−	0.344898i
$989$		−	314568.i		−	0.321604i
$990$		0			0
$991$	1.47651e6			1.50345			0.751726	−	0.659475i	$-0.229222\pi$
$991$	1.47651e6			1.50345			0.751726	+	0.659475i	$0.229222\pi$
$992$	273297.	−	273297.i	0.277723	−	0.277723i
$993$	−165009.	−	165009.i	−0.167343	−	0.167343i
$994$		−	675864.i		−	0.684048i
$995$		0			0
$996$	470547.			0.474334
$997$	945660.	−	945660.i	0.951359	−	0.951359i	−0.0475113	−	0.998871i	$-0.515129\pi$
$997$	945660.	−	945660.i	0.951359	−	0.951359i	0.998871	+	0.0475113i	$0.0151290\pi$
$998$	1.01097e6	+	1.01097e6i	1.01502	+	1.01502i
$999$		−	148680.i		−	0.148978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.5.c.b.18.2	yes	4
3.2	odd	2		225.5.g.f.118.1		4
4.3	odd	2		400.5.p.j.193.2		4
5.2	odd	4	inner	25.5.c.b.7.2	yes	4
5.3	odd	4	inner	25.5.c.b.7.1	✓	4
5.4	even	2	inner	25.5.c.b.18.1	yes	4
15.2	even	4		225.5.g.f.82.1		4
15.8	even	4		225.5.g.f.82.2		4
15.14	odd	2		225.5.g.f.118.2		4
20.3	even	4		400.5.p.j.257.1		4
20.7	even	4		400.5.p.j.257.2		4
20.19	odd	2		400.5.p.j.193.1		4

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

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

\(f(q)\)	\(=\)	\(q+(3.67423 - 3.67423i) q^{2} +(-8.57321 - 8.57321i) q^{3} -11.0000i q^{4} -63.0000 q^{6} +(34.2929 - 34.2929i) q^{7} +(18.3712 + 18.3712i) q^{8} +66.0000i q^{9} +O(q^{10})\)	\(q+(3.67423 - 3.67423i) q^{2} +(-8.57321 - 8.57321i) q^{3} -11.0000i q^{4} -63.0000 q^{6} +(34.2929 - 34.2929i) q^{7} +(18.3712 + 18.3712i) q^{8} +66.0000i q^{9} +117.000 q^{11} +(-94.3054 + 94.3054i) q^{12} +(-51.4393 - 51.4393i) q^{13} -252.000i q^{14} +311.000 q^{16} +(-180.037 + 180.037i) q^{17} +(242.499 + 242.499i) q^{18} +595.000i q^{19} -588.000 q^{21} +(429.885 - 429.885i) q^{22} +(-124.924 - 124.924i) q^{23} -315.000i q^{24} -378.000 q^{26} +(-128.598 + 128.598i) q^{27} +(-377.221 - 377.221i) q^{28} -1170.00i q^{29} +322.000 q^{31} +(848.748 - 848.748i) q^{32} +(-1003.07 - 1003.07i) q^{33} +1323.00i q^{34} +726.000 q^{36} +(-578.080 + 578.080i) q^{37} +(2186.17 + 2186.17i) q^{38} +882.000i q^{39} -63.0000 q^{41} +(-2160.45 + 2160.45i) q^{42} +(1259.04 + 1259.04i) q^{43} -1287.00i q^{44} -918.000 q^{46} +(462.954 - 462.954i) q^{47} +(-2666.27 - 2666.27i) q^{48} +49.0000i q^{49} +3087.00 q^{51} +(-565.832 + 565.832i) q^{52} +(1491.74 + 1491.74i) q^{53} +945.000i q^{54} +1260.00 q^{56} +(5101.06 - 5101.06i) q^{57} +(-4298.85 - 4298.85i) q^{58} -1890.00i q^{59} -5908.00 q^{61} +(1183.10 - 1183.10i) q^{62} +(2263.33 + 2263.33i) q^{63} -1261.00i q^{64} -7371.00 q^{66} +(-4772.83 + 4772.83i) q^{67} +(1980.41 + 1980.41i) q^{68} +2142.00i q^{69} +2682.00 q^{71} +(-1212.50 + 1212.50i) q^{72} +(-1808.95 - 1808.95i) q^{73} +4248.00i q^{74} +6545.00 q^{76} +(4012.26 - 4012.26i) q^{77} +(3240.67 + 3240.67i) q^{78} -6520.00i q^{79} +7551.00 q^{81} +(-231.477 + 231.477i) q^{82} +(-2494.81 - 2494.81i) q^{83} +6468.00i q^{84} +9252.00 q^{86} +(-10030.7 + 10030.7i) q^{87} +(2149.43 + 2149.43i) q^{88} -5985.00i q^{89} -3528.00 q^{91} +(-1374.16 + 1374.16i) q^{92} +(-2760.57 - 2760.57i) q^{93} -3402.00i q^{94} -14553.0 q^{96} +(3463.58 - 3463.58i) q^{97} +(180.037 + 180.037i) q^{98} +7722.00i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 252 q^{6}+O(q^{10}) \) 4 * q - 252 * q^6	\( 4 q - 252 q^{6} + 468 q^{11} + 1244 q^{16} - 2352 q^{21} - 1512 q^{26} + 1288 q^{31} + 2904 q^{36} - 252 q^{41} - 3672 q^{46} + 12348 q^{51} + 5040 q^{56} - 23632 q^{61} - 29484 q^{66} + 10728 q^{71} + 26180 q^{76} + 30204 q^{81} + 37008 q^{86} - 14112 q^{91} - 58212 q^{96}+O(q^{100}) \) 4 * q - 252 * q^6 + 468 * q^11 + 1244 * q^16 - 2352 * q^21 - 1512 * q^26 + 1288 * q^31 + 2904 * q^36 - 252 * q^41 - 3672 * q^46 + 12348 * q^51 + 5040 * q^56 - 23632 * q^61 - 29484 * q^66 + 10728 * q^71 + 26180 * q^76 + 30204 * q^81 + 37008 * q^86 - 14112 * q^91 - 58212 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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