LMFDB - Embedded newform 450.6.f.e.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,6,Mod(107,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("450.107");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	450.f (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:	$72.1727189158$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3457x^{8} + 2937456x^{4} + 12960000 $ x^12 + 3457x^8 + 2937456x^4 + 12960000
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.2
Root			$-4.38999 + 4.38999i$ of defining polynomial
Character	$\chi$	$=$	450.107
Dual form			450.6.f.e.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.82843 + 2.82843i) q^{2} -16.0000i q^{4} +(9.67825 + 9.67825i) q^{7} +(45.2548 + 45.2548i) q^{8} +O(q^{10})$	\(q+(-2.82843 + 2.82843i) q^{2} -16.0000i q^{4} +(9.67825 + 9.67825i) q^{7} +(45.2548 + 45.2548i) q^{8} +479.171i q^{11} +(177.573 - 177.573i) q^{13} -54.7484 q^{14} -256.000 q^{16} +(1380.00 - 1380.00i) q^{17} +121.286i q^{19} +(-1355.30 - 1355.30i) q^{22} +(1694.88 + 1694.88i) q^{23} +1004.51i q^{26} +(154.852 - 154.852i) q^{28} -7043.95 q^{29} +443.600 q^{31} +(724.077 - 724.077i) q^{32} +7806.47i q^{34} +(-4792.67 - 4792.67i) q^{37} +(-343.047 - 343.047i) q^{38} -1025.44i q^{41} +(-6318.40 + 6318.40i) q^{43} +7666.73 q^{44} -9587.68 q^{46} +(12832.1 - 12832.1i) q^{47} -16619.7i q^{49} +(-2841.17 - 2841.17i) q^{52} +(16707.1 + 16707.1i) q^{53} +875.975i q^{56} +(19923.3 - 19923.3i) q^{58} +41366.2 q^{59} -35702.6 q^{61} +(-1254.69 + 1254.69i) q^{62} +4096.00i q^{64} +(40179.3 + 40179.3i) q^{67} +(-22080.0 - 22080.0i) q^{68} -32974.0i q^{71} +(-20366.1 + 20366.1i) q^{73} +27111.4 q^{74} +1940.57 q^{76} +(-4637.53 + 4637.53i) q^{77} +27180.7i q^{79} +(2900.40 + 2900.40i) q^{82} +(32286.4 + 32286.4i) q^{83} -35742.3i q^{86} +(-21684.8 + 21684.8i) q^{88} +64897.3 q^{89} +3437.20 q^{91} +(27118.1 - 27118.1i) q^{92} +72589.4i q^{94} +(-22306.4 - 22306.4i) q^{97} +(47007.5 + 47007.5i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 144 q^{7}+O(q^{10}) $ 12 * q - 144 * q^7	$ 12 q - 144 q^{7} + 276 q^{13} - 3072 q^{16} - 384 q^{22} - 2304 q^{28} - 58512 q^{31} - 25764 q^{37} - 16080 q^{43} - 60672 q^{46} - 4416 q^{52} - 23952 q^{58} - 145200 q^{61} - 33552 q^{67} + 158988 q^{73} - 86016 q^{76} + 75024 q^{82} - 6144 q^{88} - 465024 q^{91} + 631116 q^{97}+O(q^{100}) $ 12 * q - 144 * q^7 + 276 * q^13 - 3072 * q^16 - 384 * q^22 - 2304 * q^28 - 58512 * q^31 - 25764 * q^37 - 16080 * q^43 - 60672 * q^46 - 4416 * q^52 - 23952 * q^58 - 145200 * q^61 - 33552 * q^67 + 158988 * q^73 - 86016 * q^76 + 75024 * q^82 - 6144 * q^88 - 465024 * q^91 + 631116 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.82843	+	2.82843i	−0.500000	+	0.500000i
$2$	−2.82843	+	2.82843i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	16.0000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	9.67825	+	9.67825i	0.0746538	+	0.0746538i	0.743448	−	0.668794i	$-0.233189\pi$
$7$	9.67825	+	9.67825i	0.0746538	+	0.0746538i	−0.668794	+	0.743448i	$0.733189\pi$
$8$	45.2548	+	45.2548i	0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$			479.171i			1.19401i	0.802237	+	0.597006i	$0.203643\pi$
$11$			479.171i			1.19401i	−0.802237	+	0.597006i	$0.796357\pi$
$12$		0			0
$13$	177.573	−	177.573i	0.291420	−	0.291420i	−0.546221	−	0.837641i	$-0.683934\pi$
$13$	177.573	−	177.573i	0.291420	−	0.291420i	0.837641	+	0.546221i	$0.183934\pi$
$14$	−54.7484			−0.0746538
$15$		0			0
$16$	−256.000			−0.250000
$17$	1380.00	−	1380.00i	1.15813	−	1.15813i	0.173254	−	0.984877i	$-0.444572\pi$
$17$	1380.00	−	1380.00i	1.15813	−	1.15813i	0.984877	−	0.173254i	$-0.0554281\pi$
$18$		0			0
$19$			121.286i			0.0770770i	0.999257	+	0.0385385i	$0.0122702\pi$
$19$			121.286i			0.0770770i	−0.999257	+	0.0385385i	$0.987730\pi$
$20$		0			0
$21$		0			0
$22$	−1355.30	−	1355.30i	−0.597006	−	0.597006i
$23$	1694.88	+	1694.88i	0.668065	+	0.668065i	0.957268	−	0.289203i	$-0.0933901\pi$
$23$	1694.88	+	1694.88i	0.668065	+	0.668065i	−0.289203	+	0.957268i	$0.593390\pi$
$24$		0			0
$25$		0			0
$26$			1004.51i			0.291420i
$27$		0			0
$28$	154.852	−	154.852i	0.0373269	−	0.0373269i
$29$	−7043.95			−1.55533			−0.777663	−	0.628682i	$-0.783595\pi$
$29$	−7043.95			−1.55533			−0.777663	+	0.628682i	$0.783595\pi$
$30$		0			0
$31$	443.600			0.0829063			0.0414531	−	0.999140i	$-0.486801\pi$
$31$	443.600			0.0829063			0.0414531	+	0.999140i	$0.486801\pi$
$32$	724.077	−	724.077i	0.125000	−	0.125000i
$33$		0			0
$34$			7806.47i			1.15813i
$35$		0			0
$36$		0			0
$37$	−4792.67	−	4792.67i	−0.575537	−	0.575537i	0.358133	−	0.933670i	$-0.383413\pi$
$37$	−4792.67	−	4792.67i	−0.575537	−	0.575537i	−0.933670	+	0.358133i	$0.883413\pi$
$38$	−343.047	−	343.047i	−0.0385385	−	0.0385385i
$39$		0			0
$40$		0			0
$41$		−	1025.44i		−	0.0952692i	−0.998865	−	0.0476346i	$-0.984832\pi$
$41$		−	1025.44i		−	0.0952692i	0.998865	−	0.0476346i	$-0.0151683\pi$
$42$		0			0
$43$	−6318.40	+	6318.40i	−0.521118	+	0.521118i	−0.917909	−	0.396791i	$-0.870124\pi$
$43$	−6318.40	+	6318.40i	−0.521118	+	0.521118i	0.396791	+	0.917909i	$0.370124\pi$
$44$	7666.73			0.597006
$45$		0			0
$46$	−9587.68			−0.668065
$47$	12832.1	−	12832.1i	0.847332	−	0.847332i	−0.142468	−	0.989799i	$-0.545504\pi$
$47$	12832.1	−	12832.1i	0.847332	−	0.847332i	0.989799	+	0.142468i	$0.0455037\pi$
$48$		0			0
$49$		−	16619.7i		−	0.988854i
$50$		0			0
$51$		0			0
$52$	−2841.17	−	2841.17i	−0.145710	−	0.145710i
$53$	16707.1	+	16707.1i	0.816980	+	0.816980i	0.985669	−	0.168689i	$-0.0539534\pi$
$53$	16707.1	+	16707.1i	0.816980	+	0.816980i	−0.168689	+	0.985669i	$0.553953\pi$
$54$		0			0
$55$		0			0
$56$			875.975i			0.0373269i
$57$		0			0
$58$	19923.3	−	19923.3i	0.777663	−	0.777663i
$59$	41366.2			1.54709			0.773545	−	0.633741i	$-0.218482\pi$
$59$	41366.2			1.54709			0.773545	+	0.633741i	$0.218482\pi$
$60$		0			0
$61$	−35702.6			−1.22850			−0.614250	−	0.789111i	$-0.710541\pi$
$61$	−35702.6			−1.22850			−0.614250	+	0.789111i	$0.710541\pi$
$62$	−1254.69	+	1254.69i	−0.0414531	+	0.0414531i
$63$		0			0
$64$			4096.00i			0.125000i
$65$		0			0
$66$		0			0
$67$	40179.3	+	40179.3i	1.09349	+	1.09349i	0.995153	+	0.0983373i	$0.0313524\pi$
$67$	40179.3	+	40179.3i	1.09349	+	1.09349i	0.0983373	+	0.995153i	$0.468648\pi$
$68$	−22080.0	−	22080.0i	−0.579065	−	0.579065i
$69$		0			0
$70$		0			0
$71$		−	32974.0i		−	0.776293i	−0.921598	−	0.388147i	$-0.873115\pi$
$71$		−	32974.0i		−	0.776293i	0.921598	−	0.388147i	$-0.126885\pi$
$72$		0			0
$73$	−20366.1	+	20366.1i	−0.447302	+	0.447302i	−0.894457	−	0.447154i	$-0.852437\pi$
$73$	−20366.1	+	20366.1i	−0.447302	+	0.447302i	0.447154	+	0.894457i	$0.352437\pi$
$74$	27111.4			0.575537
$75$		0			0
$76$	1940.57			0.0385385
$77$	−4637.53	+	4637.53i	−0.0891374	+	0.0891374i
$78$		0			0
$79$			27180.7i			0.489997i	0.969523	+	0.244999i	$0.0787875\pi$
$79$			27180.7i			0.489997i	−0.969523	+	0.244999i	$0.921212\pi$
$80$		0			0
$81$		0			0
$82$	2900.40	+	2900.40i	0.0476346	+	0.0476346i
$83$	32286.4	+	32286.4i	0.514428	+	0.514428i	0.915880	−	0.401452i	$-0.131494\pi$
$83$	32286.4	+	32286.4i	0.514428	+	0.514428i	−0.401452	+	0.915880i	$0.631494\pi$
$84$		0			0
$85$		0			0
$86$		−	35742.3i		−	0.521118i
$87$		0			0
$88$	−21684.8	+	21684.8i	−0.298503	+	0.298503i
$89$	64897.3			0.868464			0.434232	−	0.900801i	$-0.357020\pi$
$89$	64897.3			0.868464			0.434232	+	0.900801i	$0.357020\pi$
$90$		0			0
$91$	3437.20			0.0435112
$92$	27118.1	−	27118.1i	0.334033	−	0.334033i
$93$		0			0
$94$			72589.4i			0.847332i
$95$		0			0
$96$		0			0
$97$	−22306.4	−	22306.4i	−0.240713	−	0.240713i	0.576432	−	0.817145i	$-0.304445\pi$
$97$	−22306.4	−	22306.4i	−0.240713	−	0.240713i	−0.817145	+	0.576432i	$0.804445\pi$
$98$	47007.5	+	47007.5i	0.494427	+	0.494427i
$99$		0			0
$100$		0			0
$101$			43450.0i			0.423825i	0.977289	+	0.211913i	$0.0679692\pi$
$101$			43450.0i			0.423825i	−0.977289	+	0.211913i	$0.932031\pi$
$102$		0			0
$103$	60897.1	−	60897.1i	0.565592	−	0.565592i	−0.365298	−	0.930891i	$-0.619033\pi$
$103$	60897.1	−	60897.1i	0.565592	−	0.565592i	0.930891	+	0.365298i	$0.119033\pi$
$104$	16072.1			0.145710
$105$		0			0
$106$	−94509.6			−0.816980
$107$	163755.	−	163755.i	1.38273	−	1.38273i	0.542983	−	0.839744i	$-0.317295\pi$
$107$	163755.	−	163755.i	1.38273	−	1.38273i	0.839744	−	0.542983i	$-0.182705\pi$
$108$		0			0
$109$			196077.i			1.58074i	0.612629	+	0.790371i	$0.290112\pi$
$109$			196077.i			1.58074i	−0.612629	+	0.790371i	$0.709888\pi$
$110$		0			0
$111$		0			0
$112$	−2477.63	−	2477.63i	−0.0186634	−	0.0186634i
$113$	6940.19	+	6940.19i	0.0511299	+	0.0511299i	0.732209	−	0.681080i	$-0.238489\pi$
$113$	6940.19	+	6940.19i	0.0511299	+	0.0511299i	−0.681080	+	0.732209i	$0.738489\pi$
$114$		0			0
$115$		0			0
$116$			112703.i			0.777663i
$117$		0			0
$118$	−117001.	+	117001.i	−0.773545	+	0.773545i
$119$	26712.0			0.172918
$120$		0			0
$121$	−68553.5			−0.425663
$122$	100982.	−	100982.i	0.614250	−	0.614250i
$123$		0			0
$124$		−	7097.60i		−	0.0414531i
$125$		0			0
$126$		0			0
$127$	138770.	+	138770.i	0.763458	+	0.763458i	0.976946	−	0.213488i	$-0.0684824\pi$
$127$	138770.	+	138770.i	0.763458	+	0.763458i	−0.213488	+	0.976946i	$0.568482\pi$
$128$	−11585.2	−	11585.2i	−0.0625000	−	0.0625000i
$129$		0			0
$130$		0			0
$131$			377088.i			1.91984i	0.280275	+	0.959920i	$0.409574\pi$
$131$			377088.i			1.91984i	−0.280275	+	0.959920i	$0.590426\pi$
$132$		0			0
$133$	−1173.83	+	1173.83i	−0.00575409	+	0.00575409i
$134$	−227288.			−1.09349
$135$		0			0
$136$	124904.			0.579065
$137$	−96793.5	+	96793.5i	−0.440600	+	0.440600i	−0.892214	−	0.451613i	$-0.850849\pi$
$137$	−96793.5	+	96793.5i	−0.440600	+	0.440600i	0.451613	+	0.892214i	$0.350849\pi$
$138$		0			0
$139$			338833.i			1.48747i	0.668475	+	0.743735i	$0.266948\pi$
$139$			338833.i			1.48747i	−0.668475	+	0.743735i	$0.733052\pi$
$140$		0			0
$141$		0			0
$142$	93264.6	+	93264.6i	0.388147	+	0.388147i
$143$	85087.9	+	85087.9i	0.347959	+	0.347959i
$144$		0			0
$145$		0			0
$146$		−	115208.i		−	0.447302i
$147$		0			0
$148$	−76682.8	+	76682.8i	−0.287769	+	0.287769i
$149$	421623.			1.55582			0.777909	−	0.628377i	$-0.216280\pi$
$149$	421623.			1.55582			0.777909	+	0.628377i	$0.216280\pi$
$150$		0			0
$151$	−529841.			−1.89105			−0.945525	−	0.325550i	$-0.894451\pi$
$151$	−529841.			−1.89105			−0.945525	+	0.325550i	$0.894451\pi$
$152$	−5488.76	+	5488.76i	−0.0192693	+	0.0192693i
$153$		0			0
$154$		−	26233.8i		−	0.0891374i
$155$		0			0
$156$		0			0
$157$	110529.	+	110529.i	0.357871	+	0.357871i	0.863028	−	0.505157i	$-0.168565\pi$
$157$	110529.	+	110529.i	0.357871	+	0.357871i	−0.505157	+	0.863028i	$0.668565\pi$
$158$	−76878.8	−	76878.8i	−0.244999	−	0.244999i
$159$		0			0
$160$		0			0
$161$			32806.9i			0.0997472i
$162$		0			0
$163$	−245678.	+	245678.i	−0.724265	+	0.724265i	−0.969471	−	0.245206i	$-0.921144\pi$
$163$	−245678.	+	245678.i	−0.724265	+	0.724265i	0.245206	+	0.969471i	$0.421144\pi$
$164$	−16407.1			−0.0476346
$165$		0			0
$166$	−182639.			−0.514428
$167$	−349737.	+	349737.i	−0.970400	+	0.970400i	−0.999574	−	0.0291739i	$-0.990712\pi$
$167$	−349737.	+	349737.i	−0.970400	+	0.970400i	0.0291739	+	0.999574i	$0.490712\pi$
$168$		0			0
$169$			308228.i			0.830149i
$170$		0			0
$171$		0			0
$172$	101094.	+	101094.i	0.260559	+	0.260559i
$173$	143942.	+	143942.i	0.365655	+	0.365655i	0.865890	−	0.500235i	$-0.166753\pi$
$173$	143942.	+	143942.i	0.365655	+	0.365655i	−0.500235	+	0.865890i	$0.666753\pi$
$174$		0			0
$175$		0			0
$176$		−	122668.i		−	0.298503i
$177$		0			0
$178$	−183557.	+	183557.i	−0.434232	+	0.434232i
$179$	583232.			1.36053			0.680267	−	0.732965i	$-0.261864\pi$
$179$	583232.			1.36053			0.680267	+	0.732965i	$0.261864\pi$
$180$		0			0
$181$	753570.			1.70973			0.854864	−	0.518853i	$-0.173641\pi$
$181$	753570.			1.70973			0.854864	+	0.518853i	$0.173641\pi$
$182$	−9721.86	+	9721.86i	−0.0217556	+	0.0217556i
$183$		0			0
$184$			153403.i			0.334033i
$185$		0			0
$186$		0			0
$187$	661257.	+	661257.i	1.38282	+	1.38282i
$188$	−205314.	−	205314.i	−0.423666	−	0.423666i
$189$		0			0
$190$		0			0
$191$			511363.i			1.01425i	0.861872	+	0.507126i	$0.169292\pi$
$191$			511363.i			1.01425i	−0.861872	+	0.507126i	$0.830708\pi$
$192$		0			0
$193$	−9207.24	+	9207.24i	−0.0177925	+	0.0177925i	−0.715947	−	0.698155i	$-0.754005\pi$
$193$	−9207.24	+	9207.24i	−0.0177925	+	0.0177925i	0.698155	+	0.715947i	$0.254005\pi$
$194$	126184.			0.240713
$195$		0			0
$196$	−265915.			−0.494427
$197$	−227109.	+	227109.i	−0.416935	+	0.416935i	−0.884146	−	0.467211i	$-0.845259\pi$
$197$	−227109.	+	227109.i	−0.416935	+	0.416935i	0.467211	+	0.884146i	$0.345259\pi$
$198$		0			0
$199$		−	738531.i		−	1.32201i	−0.750380	−	0.661007i	$-0.770130\pi$
$199$		−	738531.i		−	1.32201i	0.750380	−	0.661007i	$-0.229870\pi$
$200$		0			0
$201$		0			0
$202$	−122895.	−	122895.i	−0.211913	−	0.211913i
$203$	−68173.1	−	68173.1i	−0.116111	−	0.116111i
$204$		0			0
$205$		0			0
$206$			344486.i			0.565592i
$207$		0			0
$208$	−45458.8	+	45458.8i	−0.0728550	+	0.0728550i
$209$	−58116.5			−0.0920309
$210$		0			0
$211$	−579506.			−0.896091			−0.448045	−	0.894011i	$-0.647880\pi$
$211$	−579506.			−0.896091			−0.448045	+	0.894011i	$0.647880\pi$
$212$	267314.	−	267314.i	0.408490	−	0.408490i
$213$		0			0
$214$			926341.i			1.38273i
$215$		0			0
$216$		0			0
$217$	4293.27	+	4293.27i	0.00618926	+	0.00618926i
$218$	−554590.	−	554590.i	−0.790371	−	0.790371i
$219$		0			0
$220$		0			0
$221$		−	490103.i		−	0.675005i
$222$		0			0
$223$	768537.	−	768537.i	1.03491	−	1.03491i	0.0355417	−	0.999368i	$-0.488684\pi$
$223$	768537.	−	768537.i	1.03491	−	1.03491i	0.999368	−	0.0355417i	$-0.0113157\pi$
$224$	14015.6			0.0186634
$225$		0			0
$226$	−39259.6			−0.0511299
$227$	701571.	−	701571.i	0.903664	−	0.903664i	−0.0920868	−	0.995751i	$-0.529354\pi$
$227$	701571.	−	701571.i	0.903664	−	0.903664i	0.995751	+	0.0920868i	$0.0293537\pi$
$228$		0			0
$229$		−	34830.3i		−	0.0438902i	−0.999759	−	0.0219451i	$-0.993014\pi$
$229$		−	34830.3i		−	0.0438902i	0.999759	−	0.0219451i	$-0.00698591\pi$
$230$		0			0
$231$		0			0
$232$	−318773.	−	318773.i	−0.388831	−	0.388831i
$233$	803689.	+	803689.i	0.969836	+	0.969836i	0.999558	−	0.0297224i	$-0.00946234\pi$
$233$	803689.	+	803689.i	0.969836	+	0.969836i	−0.0297224	+	0.999558i	$0.509462\pi$
$234$		0			0
$235$		0			0
$236$		−	661859.i		−	0.773545i
$237$		0			0
$238$	−75553.0	+	75553.0i	−0.0864588	+	0.0864588i
$239$	−1.11216e6			−1.25943			−0.629715	−	0.776826i	$-0.716828\pi$
$239$	−1.11216e6			−1.25943			−0.629715	+	0.776826i	$0.716828\pi$
$240$		0			0
$241$	967616.			1.07315			0.536575	−	0.843853i	$-0.319718\pi$
$241$	967616.			1.07315			0.536575	+	0.843853i	$0.319718\pi$
$242$	193899.	−	193899.i	0.212832	−	0.212832i
$243$		0			0
$244$			571242.i			0.614250i
$245$		0			0
$246$		0			0
$247$	21537.1	+	21537.1i	0.0224618	+	0.0224618i
$248$	20075.0	+	20075.0i	0.0207266	+	0.0207266i
$249$		0			0
$250$		0			0
$251$			419861.i			0.420651i	0.977631	+	0.210325i	$0.0674523\pi$
$251$			419861.i			0.420651i	−0.977631	+	0.210325i	$0.932548\pi$
$252$		0			0
$253$	−812136.	+	812136.i	−0.797678	+	0.797678i
$254$	−784999.			−0.763458
$255$		0			0
$256$	65536.0			0.0625000
$257$	−165167.	+	165167.i	−0.155988	+	0.155988i	−0.780786	−	0.624798i	$-0.785181\pi$
$257$	−165167.	+	165167.i	−0.155988	+	0.155988i	0.624798	+	0.780786i	$0.285181\pi$
$258$		0			0
$259$		−	92769.3i		−	0.0859320i
$260$		0			0
$261$		0			0
$262$	−1.06657e6	−	1.06657e6i	−0.959920	−	0.959920i
$263$	433781.	+	433781.i	0.386706	+	0.386706i	0.873511	−	0.486805i	$-0.161838\pi$
$263$	433781.	+	433781.i	0.386706	+	0.386706i	−0.486805	+	0.873511i	$0.661838\pi$
$264$		0			0
$265$		0			0
$266$		−	6640.19i		−	0.00575409i
$267$		0			0
$268$	642868.	−	642868.i	0.546745	−	0.546745i
$269$	643503.			0.542213			0.271106	−	0.962549i	$-0.412610\pi$
$269$	643503.			0.542213			0.271106	+	0.962549i	$0.412610\pi$
$270$		0			0
$271$	981970.			0.812223			0.406111	−	0.913824i	$-0.366885\pi$
$271$	981970.			0.812223			0.406111	+	0.913824i	$0.366885\pi$
$272$	−353281.	+	353281.i	−0.289533	+	0.289533i
$273$		0			0
$274$		−	547547.i		−	0.440600i
$275$		0			0
$276$		0			0
$277$	−1.09057e6	−	1.09057e6i	−0.853991	−	0.853991i	0.136631	−	0.990622i	$-0.456373\pi$
$277$	−1.09057e6	−	1.09057e6i	−0.853991	−	0.853991i	−0.990622	+	0.136631i	$0.956373\pi$
$278$	−958363.	−	958363.i	−0.743735	−	0.743735i
$279$		0			0
$280$		0			0
$281$		−	272068.i		−	0.205548i	−0.994705	−	0.102774i	$-0.967228\pi$
$281$		−	272068.i		−	0.205548i	0.994705	−	0.102774i	$-0.0327718\pi$
$282$		0			0
$283$	1.62568e6	−	1.62568e6i	1.20661	−	1.20661i	0.234497	−	0.972117i	$-0.424656\pi$
$283$	1.62568e6	−	1.62568e6i	1.20661	−	1.20661i	0.972117	−	0.234497i	$-0.0753443\pi$
$284$	−527584.			−0.388147
$285$		0			0
$286$	−481330.			−0.347959
$287$	9924.51	−	9924.51i	0.00711220	−	0.00711220i
$288$		0			0
$289$		−	2.38896e6i		−	1.68253i
$290$		0			0
$291$		0			0
$292$	325858.	+	325858.i	0.223651	+	0.223651i
$293$	1.02737e6	+	1.02737e6i	0.699127	+	0.699127i	0.964222	−	0.265095i	$-0.0854035\pi$
$293$	1.02737e6	+	1.02737e6i	0.699127	+	0.699127i	−0.265095	+	0.964222i	$0.585403\pi$
$294$		0			0
$295$		0			0
$296$		−	433783.i		−	0.287769i
$297$		0			0
$298$	−1.19253e6	+	1.19253e6i	−0.777909	+	0.777909i
$299$	601930.			0.389375
$300$		0			0
$301$	−122302.			−0.0778068
$302$	1.49862e6	−	1.49862e6i	0.945525	−	0.945525i
$303$		0			0
$304$		−	31049.1i		−	0.0192693i
$305$		0			0
$306$		0			0
$307$	−891251.	−	891251.i	−0.539702	−	0.539702i	0.383739	−	0.923441i	$-0.374636\pi$
$307$	−891251.	−	891251.i	−0.539702	−	0.539702i	−0.923441	+	0.383739i	$0.874636\pi$
$308$	74200.5	+	74200.5i	0.0445687	+	0.0445687i
$309$		0			0
$310$		0			0
$311$		−	1.42354e6i		−	0.834579i	−0.908774	−	0.417289i	$-0.862980\pi$
$311$		−	1.42354e6i		−	0.834579i	0.908774	−	0.417289i	$-0.137020\pi$
$312$		0			0
$313$	854680.	−	854680.i	0.493109	−	0.493109i	−0.416176	−	0.909284i	$-0.636630\pi$
$313$	854680.	−	854680.i	0.493109	−	0.493109i	0.909284	+	0.416176i	$0.136630\pi$
$314$	−625245.			−0.357871
$315$		0			0
$316$	434892.			0.244999
$317$	−1.68305e6	+	1.68305e6i	−0.940697	+	0.940697i	−0.998337	−	0.0576401i	$-0.981642\pi$
$317$	−1.68305e6	+	1.68305e6i	−0.940697	+	0.940697i	0.0576401	+	0.998337i	$0.481642\pi$
$318$		0			0
$319$		−	3.37525e6i		−	1.85708i
$320$		0			0
$321$		0			0
$322$	−92791.9	−	92791.9i	−0.0498736	−	0.0498736i
$323$	167374.	+	167374.i	0.0892653	+	0.0892653i
$324$		0			0
$325$		0			0
$326$		−	1.38977e6i		−	0.724265i
$327$		0			0
$328$	46406.3	−	46406.3i	0.0238173	−	0.0238173i
$329$	248385.			0.126513
$330$		0			0
$331$	−2.20398e6			−1.10570			−0.552850	−	0.833280i	$-0.686460\pi$
$331$	−2.20398e6			−1.10570			−0.552850	+	0.833280i	$0.686460\pi$
$332$	516582.	−	516582.i	0.257214	−	0.257214i
$333$		0			0
$334$		−	1.97841e6i		−	0.970400i
$335$		0			0
$336$		0			0
$337$	468533.	+	468533.i	0.224732	+	0.224732i	0.810488	−	0.585755i	$-0.199202\pi$
$337$	468533.	+	468533.i	0.224732	+	0.224732i	−0.585755	+	0.810488i	$0.699202\pi$
$338$	−871802.	−	871802.i	−0.415074	−	0.415074i
$339$		0			0
$340$		0			0
$341$			212560.i			0.0989910i
$342$		0			0
$343$	323512.	−	323512.i	0.148475	−	0.148475i
$344$	−571876.			−0.260559
$345$		0			0
$346$	−814257.			−0.365655
$347$	−2.03791e6	+	2.03791e6i	−0.908575	+	0.908575i	−0.996157	−	0.0875826i	$-0.972086\pi$
$347$	−2.03791e6	+	2.03791e6i	−0.908575	+	0.908575i	0.0875826	+	0.996157i	$0.472086\pi$
$348$		0			0
$349$			407443.i			0.179062i	0.995984	+	0.0895310i	$0.0285368\pi$
$349$			407443.i			0.179062i	−0.995984	+	0.0895310i	$0.971463\pi$
$350$		0			0
$351$		0			0
$352$	346957.	+	346957.i	0.149251	+	0.149251i
$353$	−2.07267e6	−	2.07267e6i	−0.885306	−	0.885306i	0.108762	−	0.994068i	$-0.465311\pi$
$353$	−2.07267e6	−	2.07267e6i	−0.885306	−	0.885306i	−0.994068	+	0.108762i	$0.965311\pi$
$354$		0			0
$355$		0			0
$356$		−	1.03836e6i		−	0.434232i
$357$		0			0
$358$	−1.64963e6	+	1.64963e6i	−0.680267	+	0.680267i
$359$	1.15572e6			0.473279			0.236640	−	0.971597i	$-0.423954\pi$
$359$	1.15572e6			0.473279			0.236640	+	0.971597i	$0.423954\pi$
$360$		0			0
$361$	2.46139e6			0.994059
$362$	−2.13142e6	+	2.13142e6i	−0.854864	+	0.854864i
$363$		0			0
$364$		−	54995.1i		−	0.0217556i
$365$		0			0
$366$		0			0
$367$	−628091.	−	628091.i	−0.243421	−	0.243421i	0.574843	−	0.818264i	$-0.305063\pi$
$367$	−628091.	−	628091.i	−0.243421	−	0.243421i	−0.818264	+	0.574843i	$0.805063\pi$
$368$	−433889.	−	433889.i	−0.167016	−	0.167016i
$369$		0			0
$370$		0			0
$371$			323391.i			0.121981i
$372$		0			0
$373$	2.26018e6	−	2.26018e6i	0.841144	−	0.841144i	−0.147863	−	0.989008i	$-0.547240\pi$
$373$	2.26018e6	−	2.26018e6i	0.841144	−	0.841144i	0.989008	+	0.147863i	$0.0472396\pi$
$374$	−3.74063e6			−1.38282
$375$		0			0
$376$	1.16143e6			0.423666
$377$	−1.25082e6	+	1.25082e6i	−0.453253	+	0.453253i
$378$		0			0
$379$		−	172752.i		−	0.0617769i	−0.999523	−	0.0308885i	$-0.990166\pi$
$379$		−	172752.i		−	0.0617769i	0.999523	−	0.0308885i	$-0.00983366\pi$
$380$		0			0
$381$		0			0
$382$	−1.44635e6	−	1.44635e6i	−0.507126	−	0.507126i
$383$	404160.	+	404160.i	0.140785	+	0.140785i	0.773987	−	0.633202i	$-0.218260\pi$
$383$	404160.	+	404160.i	0.140785	+	0.140785i	−0.633202	+	0.773987i	$0.718260\pi$
$384$		0			0
$385$		0			0
$386$		−	52084.0i		−	0.0177925i
$387$		0			0
$388$	−356902.	+	356902.i	−0.120357	+	0.120357i
$389$	−2.31395e6			−0.775319			−0.387660	−	0.921803i	$-0.626716\pi$
$389$	−2.31395e6			−0.775319			−0.387660	+	0.921803i	$0.626716\pi$
$390$		0			0
$391$	4.67787e6			1.54741
$392$	752120.	−	752120.i	0.247213	−	0.247213i
$393$		0			0
$394$		−	1.28472e6i		−	0.416935i
$395$		0			0
$396$		0			0
$397$	−858541.	−	858541.i	−0.273391	−	0.273391i	0.557072	−	0.830464i	$-0.311925\pi$
$397$	−858541.	−	858541.i	−0.273391	−	0.273391i	−0.830464	+	0.557072i	$0.811925\pi$
$398$	2.08888e6	+	2.08888e6i	0.661007	+	0.661007i
$399$		0			0
$400$		0			0
$401$		−	1.38617e6i		−	0.430482i	−0.976561	−	0.215241i	$-0.930946\pi$
$401$		−	1.38617e6i		−	0.430482i	0.976561	−	0.215241i	$-0.0690537\pi$
$402$		0			0
$403$	78771.5	−	78771.5i	0.0241605	−	0.0241605i
$404$	695200.			0.211913
$405$		0			0
$406$	385645.			0.116111
$407$	2.29651e6	−	2.29651e6i	0.687198	−	0.687198i
$408$		0			0
$409$		−	340398.i		−	0.100619i	−0.998734	−	0.0503094i	$-0.983979\pi$
$409$		−	340398.i		−	0.100619i	0.998734	−	0.0503094i	$-0.0160207\pi$
$410$		0			0
$411$		0			0
$412$	−974353.	−	974353.i	−0.282796	−	0.282796i
$413$	400352.	+	400352.i	0.115496	+	0.115496i
$414$		0			0
$415$		0			0
$416$		−	257154.i		−	0.0728550i
$417$		0			0
$418$	164378.	−	164378.i	0.0460154	−	0.0460154i
$419$	1.30762e6			0.363869			0.181934	−	0.983311i	$-0.441764\pi$
$419$	1.30762e6			0.363869			0.181934	+	0.983311i	$0.441764\pi$
$420$		0			0
$421$	476804.			0.131110			0.0655548	−	0.997849i	$-0.479118\pi$
$421$	476804.			0.131110			0.0655548	+	0.997849i	$0.479118\pi$
$422$	1.63909e6	−	1.63909e6i	0.448045	−	0.448045i
$423$		0			0
$424$			1.51215e6i			0.408490i
$425$		0			0
$426$		0			0
$427$	−345539.	−	345539.i	−0.0917122	−	0.0917122i
$428$	−2.62009e6	−	2.62009e6i	−0.691363	−	0.691363i
$429$		0			0
$430$		0			0
$431$			1.30974e6i			0.339619i	0.985477	+	0.169809i	$0.0543152\pi$
$431$			1.30974e6i			0.339619i	−0.985477	+	0.169809i	$0.945685\pi$
$432$		0			0
$433$	3.62876e6	−	3.62876e6i	0.930118	−	0.930118i	−0.0675951	−	0.997713i	$-0.521533\pi$
$433$	3.62876e6	−	3.62876e6i	0.930118	−	0.930118i	0.997713	+	0.0675951i	$0.0215326\pi$
$434$	−24286.4			−0.00618926
$435$		0			0
$436$	3.13724e6			0.790371
$437$	−205564.	+	205564.i	−0.0514925	+	0.0514925i
$438$		0			0
$439$			883070.i			0.218692i	0.994004	+	0.109346i	$0.0348757\pi$
$439$			883070.i			0.218692i	−0.994004	+	0.109346i	$0.965124\pi$
$440$		0			0
$441$		0			0
$442$	1.38622e6	+	1.38622e6i	0.337502	+	0.337502i
$443$	70500.7	+	70500.7i	0.0170681	+	0.0170681i	0.715589	−	0.698521i	$-0.246158\pi$
$443$	70500.7	+	70500.7i	0.0170681	+	0.0170681i	−0.698521	+	0.715589i	$0.746158\pi$
$444$		0			0
$445$		0			0
$446$			4.34750e6i			1.03491i
$447$		0			0
$448$	−39642.1	+	39642.1i	−0.00933172	+	0.00933172i
$449$	−5.66675e6			−1.32653			−0.663267	−	0.748383i	$-0.730831\pi$
$449$	−5.66675e6			−1.32653			−0.663267	+	0.748383i	$0.730831\pi$
$450$		0			0
$451$	491363.			0.113753
$452$	111043.	−	111043.i	0.0255650	−	0.0255650i
$453$		0			0
$454$			3.96869e6i			0.903664i
$455$		0			0
$456$		0			0
$457$	1.60863e6	+	1.60863e6i	0.360301	+	0.360301i	0.863924	−	0.503623i	$-0.168000\pi$
$457$	1.60863e6	+	1.60863e6i	0.360301	+	0.360301i	−0.503623	+	0.863924i	$0.668000\pi$
$458$	98514.9	+	98514.9i	0.0219451	+	0.0219451i
$459$		0			0
$460$		0			0
$461$			8.33450e6i			1.82653i	0.407364	+	0.913266i	$0.366448\pi$
$461$			8.33450e6i			1.82653i	−0.407364	+	0.913266i	$0.633552\pi$
$462$		0			0
$463$	−4.82641e6	+	4.82641e6i	−1.04634	+	1.04634i	−0.0474636	+	0.998873i	$0.515114\pi$
$463$	−4.82641e6	+	4.82641e6i	−1.04634	+	1.04634i	−0.998873	+	0.0474636i	$0.984886\pi$
$464$	1.80325e6			0.388831
$465$		0			0
$466$	−4.54635e6			−0.969836
$467$	−1.57887e6	+	1.57887e6i	−0.335007	+	0.335007i	−0.854484	−	0.519477i	$-0.826127\pi$
$467$	−1.57887e6	+	1.57887e6i	−0.335007	+	0.335007i	0.519477	+	0.854484i	$0.326127\pi$
$468$		0			0
$469$			777730.i			0.163266i
$470$		0			0
$471$		0			0
$472$	1.87202e6	+	1.87202e6i	0.386773	+	0.386773i
$473$	−3.02759e6	−	3.02759e6i	−0.622221	−	0.622221i
$474$		0			0
$475$		0			0
$476$		−	427392.i		−	0.0864588i
$477$		0			0
$478$	3.14568e6	−	3.14568e6i	0.629715	−	0.629715i
$479$	−5.33389e6			−1.06220			−0.531099	−	0.847310i	$-0.678221\pi$
$479$	−5.33389e6			−1.06220			−0.531099	+	0.847310i	$0.678221\pi$
$480$		0			0
$481$	−1.70210e6			−0.335446
$482$	−2.73683e6	+	2.73683e6i	−0.536575	+	0.536575i
$483$		0			0
$484$			1.09686e6i			0.212832i
$485$		0			0
$486$		0			0
$487$	2.16333e6	+	2.16333e6i	0.413334	+	0.413334i	0.882898	−	0.469565i	$-0.155589\pi$
$487$	2.16333e6	+	2.16333e6i	0.413334	+	0.413334i	−0.469565	+	0.882898i	$0.655589\pi$
$488$	−1.61572e6	−	1.61572e6i	−0.307125	−	0.307125i
$489$		0			0
$490$		0			0
$491$		−	8.45785e6i		−	1.58328i	−0.610991	−	0.791638i	$-0.709229\pi$
$491$		−	8.45785e6i		−	1.58328i	0.610991	−	0.791638i	$-0.290771\pi$
$492$		0			0
$493$	−9.72067e6	+	9.72067e6i	−1.80127	+	1.80127i
$494$	−121832.			−0.0224618
$495$		0			0
$496$	−113562.			−0.0207266
$497$	319131.	−	319131.i	0.0579532	−	0.0579532i
$498$		0			0
$499$			2.50745e6i			0.450797i	0.974267	+	0.225398i	$0.0723684\pi$
$499$			2.50745e6i			0.450797i	−0.974267	+	0.225398i	$0.927632\pi$
$500$		0			0
$501$		0			0
$502$	−1.18755e6	−	1.18755e6i	−0.210325	−	0.210325i
$503$	4.75292e6	+	4.75292e6i	0.837607	+	0.837607i	0.988543	−	0.150937i	$-0.0482290\pi$
$503$	4.75292e6	+	4.75292e6i	0.837607	+	0.837607i	−0.150937	+	0.988543i	$0.548229\pi$
$504$		0			0
$505$		0			0
$506$		−	4.59413e6i		−	0.797678i
$507$		0			0
$508$	2.22031e6	−	2.22031e6i	0.381729	−	0.381729i
$509$	7.64193e6			1.30740			0.653700	−	0.756754i	$-0.273216\pi$
$509$	7.64193e6			1.30740			0.653700	+	0.756754i	$0.273216\pi$
$510$		0			0
$511$	−394217.			−0.0667856
$512$	−185364.	+	185364.i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	934325.i		−	0.155988i
$515$		0			0
$516$		0			0
$517$	6.14877e6	+	6.14877e6i	1.01172	+	1.01172i
$518$	262391.	+	262391.i	0.0429660	+	0.0429660i
$519$		0			0
$520$		0			0
$521$			3.21226e6i			0.518461i	0.965815	+	0.259231i	$0.0834689\pi$
$521$			3.21226e6i			0.518461i	−0.965815	+	0.259231i	$0.916531\pi$
$522$		0			0
$523$	2.16299e6	−	2.16299e6i	0.345780	−	0.345780i	−0.512755	−	0.858535i	$-0.671375\pi$
$523$	2.16299e6	−	2.16299e6i	0.345780	−	0.345780i	0.858535	+	0.512755i	$0.171375\pi$
$524$	6.03341e6			0.959920
$525$		0			0
$526$	−2.45384e6			−0.386706
$527$	612169.	−	612169.i	0.0960163	−	0.0960163i
$528$		0			0
$529$		−	691118.i		−	0.107377i
$530$		0			0
$531$		0			0
$532$	18781.3	+	18781.3i	0.00287704	+	0.00287704i
$533$	−182092.	−	182092.i	−0.0277633	−	0.0277633i
$534$		0			0
$535$		0			0
$536$			3.63661e6i			0.546745i
$537$		0			0
$538$	−1.82010e6	+	1.82010e6i	−0.271106	+	0.271106i
$539$	7.96365e6			1.18070
$540$		0			0
$541$	−1.21690e7			−1.78756			−0.893780	−	0.448506i	$-0.851956\pi$
$541$	−1.21690e7			−1.78756			−0.893780	+	0.448506i	$0.851956\pi$
$542$	−2.77743e6	+	2.77743e6i	−0.406111	+	0.406111i
$543$		0			0
$544$		−	1.99846e6i		−	0.289533i
$545$		0			0
$546$		0			0
$547$	−6.29790e6	−	6.29790e6i	−0.899969	−	0.899969i	0.0954641	−	0.995433i	$-0.469567\pi$
$547$	−6.29790e6	−	6.29790e6i	−0.899969	−	0.899969i	−0.995433	+	0.0954641i	$0.969567\pi$
$548$	1.54870e6	+	1.54870e6i	0.220300	+	0.220300i
$549$		0			0
$550$		0			0
$551$		−	854329.i		−	0.119880i
$552$		0			0
$553$	−263062.	+	263062.i	−0.0365801	+	0.0365801i
$554$	6.16919e6			0.853991
$555$		0			0
$556$	5.42132e6			0.743735
$557$	−25868.2	+	25868.2i	−0.00353287	+	0.00353287i	−0.708871	−	0.705338i	$-0.750795\pi$
$557$	−25868.2	+	25868.2i	−0.00353287	+	0.00353287i	0.705338	+	0.708871i	$0.250795\pi$
$558$		0			0
$559$			2.24396e6i			0.303728i
$560$		0			0
$561$		0			0
$562$	769526.	+	769526.i	0.102774	+	0.102774i
$563$	−587908.	−	587908.i	−0.0781697	−	0.0781697i	0.666941	−	0.745111i	$-0.267603\pi$
$563$	−587908.	−	587908.i	−0.0781697	−	0.0781697i	−0.745111	+	0.666941i	$0.767603\pi$
$564$		0			0
$565$		0			0
$566$			9.19622e6i			1.20661i
$567$		0			0
$568$	1.49223e6	−	1.49223e6i	0.194073	−	0.194073i
$569$	1.96394e6			0.254301			0.127150	−	0.991883i	$-0.459417\pi$
$569$	1.96394e6			0.254301			0.127150	+	0.991883i	$0.459417\pi$
$570$		0			0
$571$	1.36566e6			0.175289			0.0876443	−	0.996152i	$-0.472066\pi$
$571$	1.36566e6			0.175289			0.0876443	+	0.996152i	$0.472066\pi$
$572$	1.36141e6	−	1.36141e6i	0.173979	−	0.173979i
$573$		0			0
$574$			56141.5i			0.00711220i
$575$		0			0
$576$		0			0
$577$	1.00497e7	+	1.00497e7i	1.25665	+	1.25665i	0.952684	+	0.303962i	$0.0983097\pi$
$577$	1.00497e7	+	1.00497e7i	1.25665	+	1.25665i	0.303962	+	0.952684i	$0.401690\pi$
$578$	6.75700e6	+	6.75700e6i	0.841267	+	0.841267i
$579$		0			0
$580$		0			0
$581$			624951.i			0.0768079i
$582$		0			0
$583$	−8.00555e6	+	8.00555e6i	−0.975484	+	0.975484i
$584$	−1.84333e6			−0.223651
$585$		0			0
$586$	−5.81166e6			−0.699127
$587$	6.34891e6	−	6.34891e6i	0.760508	−	0.760508i	−0.215906	−	0.976414i	$-0.569270\pi$
$587$	6.34891e6	−	6.34891e6i	0.760508	−	0.760508i	0.976414	+	0.215906i	$0.0692704\pi$
$588$		0			0
$589$			53802.3i			0.00639017i
$590$		0			0
$591$		0			0
$592$	1.22692e6	+	1.22692e6i	0.143884	+	0.143884i
$593$	−1.63841e6	−	1.63841e6i	−0.191331	−	0.191331i	0.604940	−	0.796271i	$-0.293197\pi$
$593$	−1.63841e6	−	1.63841e6i	−0.191331	−	0.191331i	−0.796271	+	0.604940i	$0.793197\pi$
$594$		0			0
$595$		0			0
$596$		−	6.74597e6i		−	0.777909i
$597$		0			0
$598$	−1.70252e6	+	1.70252e6i	−0.194688	+	0.194688i
$599$	4.20108e6			0.478403			0.239202	−	0.970970i	$-0.423114\pi$
$599$	4.20108e6			0.478403			0.239202	+	0.970970i	$0.423114\pi$
$600$		0			0
$601$	−6.19973e6			−0.700142			−0.350071	−	0.936723i	$-0.613843\pi$
$601$	−6.19973e6			−0.700142			−0.350071	+	0.936723i	$0.613843\pi$
$602$	345922.	−	345922.i	0.0389034	−	0.0389034i
$603$		0			0
$604$			8.47745e6i			0.945525i
$605$		0			0
$606$		0			0
$607$	−4.38869e6	−	4.38869e6i	−0.483462	−	0.483462i	0.422773	−	0.906236i	$-0.361057\pi$
$607$	−4.38869e6	−	4.38869e6i	−0.483462	−	0.483462i	−0.906236	+	0.422773i	$0.861057\pi$
$608$	87820.1	+	87820.1i	0.00963463	+	0.00963463i
$609$		0			0
$610$		0			0
$611$		−	4.55728e6i		−	0.493859i
$612$		0			0
$613$	4.75066e6	−	4.75066e6i	0.510626	−	0.510626i	−0.404092	−	0.914718i	$-0.632412\pi$
$613$	4.75066e6	−	4.75066e6i	0.510626	−	0.510626i	0.914718	+	0.404092i	$0.132412\pi$
$614$	5.04168e6			0.539702
$615$		0			0
$616$	−419741.			−0.0445687
$617$	1.24103e7	−	1.24103e7i	1.31241	−	1.31241i	0.392772	−	0.919636i	$-0.371516\pi$
$617$	1.24103e7	−	1.24103e7i	1.31241	−	1.31241i	0.919636	−	0.392772i	$-0.128484\pi$
$618$		0			0
$619$			1.61901e7i			1.69833i	0.528125	+	0.849166i	$0.322895\pi$
$619$			1.61901e7i			1.69833i	−0.528125	+	0.849166i	$0.677105\pi$
$620$		0			0
$621$		0			0
$622$	4.02637e6	+	4.02637e6i	0.417289	+	0.417289i
$623$	628092.	+	628092.i	0.0648341	+	0.0648341i
$624$		0			0
$625$		0			0
$626$			4.83480e6i			0.493109i
$627$		0			0
$628$	1.76846e6	−	1.76846e6i	0.178935	−	0.178935i
$629$	−1.32278e7			−1.33310
$630$		0			0
$631$	−1.03850e7			−1.03832			−0.519162	−	0.854676i	$-0.673756\pi$
$631$	−1.03850e7			−1.03832			−0.519162	+	0.854676i	$0.673756\pi$
$632$	−1.23006e6	+	1.23006e6i	−0.122499	+	0.122499i
$633$		0			0
$634$		−	9.52079e6i		−	0.940697i
$635$		0			0
$636$		0			0
$637$	−2.95121e6	−	2.95121e6i	−0.288172	−	0.288172i
$638$	9.54666e6	+	9.54666e6i	0.928538	+	0.928538i
$639$		0			0
$640$		0			0
$641$			1.19326e7i			1.14707i	0.819180	+	0.573537i	$0.194429\pi$
$641$			1.19326e7i			1.14707i	−0.819180	+	0.573537i	$0.805571\pi$
$642$		0			0
$643$	1.03095e7	−	1.03095e7i	0.983359	−	0.983359i	−0.0165048	−	0.999864i	$-0.505254\pi$
$643$	1.03095e7	−	1.03095e7i	0.983359	−	0.983359i	0.999864	+	0.0165048i	$0.00525387\pi$
$644$	524910.			0.0498736
$645$		0			0
$646$	−946812.			−0.0892653
$647$	7.30615e6	−	7.30615e6i	0.686164	−	0.686164i	−0.275218	−	0.961382i	$-0.588750\pi$
$647$	7.30615e6	−	7.30615e6i	0.686164	−	0.686164i	0.961382	+	0.275218i	$0.0887499\pi$
$648$		0			0
$649$			1.98215e7i			1.84724i
$650$		0			0
$651$		0			0
$652$	3.93085e6	+	3.93085e6i	0.362133	+	0.362133i
$653$	−4.82186e6	−	4.82186e6i	−0.442519	−	0.442519i	0.450339	−	0.892858i	$-0.351303\pi$
$653$	−4.82186e6	−	4.82186e6i	−0.442519	−	0.442519i	−0.892858	+	0.450339i	$0.851303\pi$
$654$		0			0
$655$		0			0
$656$			262514.i			0.0238173i
$657$		0			0
$658$	−702538.	+	702538.i	−0.0632565	+	0.0632565i
$659$	2.46721e6			0.221306			0.110653	−	0.993859i	$-0.464706\pi$
$659$	2.46721e6			0.221306			0.110653	+	0.993859i	$0.464706\pi$
$660$		0			0
$661$	3.92026e6			0.348989			0.174494	−	0.984658i	$-0.444171\pi$
$661$	3.92026e6			0.348989			0.174494	+	0.984658i	$0.444171\pi$
$662$	6.23380e6	−	6.23380e6i	0.552850	−	0.552850i
$663$		0			0
$664$			2.92223e6i			0.257214i
$665$		0			0
$666$		0			0
$667$	−1.19386e7	−	1.19386e7i	−1.03906	−	1.03906i
$668$	5.59580e6	+	5.59580e6i	0.485200	+	0.485200i
$669$		0			0
$670$		0			0
$671$		−	1.71076e7i		−	1.46684i
$672$		0			0
$673$	−1.04432e7	+	1.04432e7i	−0.888787	+	0.888787i	−0.994407	−	0.105619i	$-0.966318\pi$
$673$	−1.04432e7	+	1.04432e7i	−0.888787	+	0.888787i	0.105619	+	0.994407i	$0.466318\pi$
$674$	−2.65043e6			−0.224732
$675$		0			0
$676$	4.93166e6			0.415074
$677$	6.24464e6	−	6.24464e6i	0.523643	−	0.523643i	−0.395026	−	0.918670i	$-0.629265\pi$
$677$	6.24464e6	−	6.24464e6i	0.523643	−	0.523643i	0.918670	+	0.395026i	$0.129265\pi$
$678$		0			0
$679$		−	431774.i		−	0.0359403i
$680$		0			0
$681$		0			0
$682$	−601211.	−	601211.i	−0.0494955	−	0.0494955i
$683$	−6.24335e6	−	6.24335e6i	−0.512113	−	0.512113i	0.403060	−	0.915173i	$-0.367946\pi$
$683$	−6.24335e6	−	6.24335e6i	−0.512113	−	0.512113i	−0.915173	+	0.403060i	$0.867946\pi$
$684$		0			0
$685$		0			0
$686$			1.83006e6i			0.148475i
$687$		0			0
$688$	1.61751e6	−	1.61751e6i	0.130279	−	0.130279i
$689$	5.93347e6			0.476169
$690$		0			0
$691$	3.85776e6			0.307355			0.153677	−	0.988121i	$-0.450888\pi$
$691$	3.85776e6			0.307355			0.153677	+	0.988121i	$0.450888\pi$
$692$	2.30307e6	−	2.30307e6i	0.182827	−	0.182827i
$693$		0			0
$694$		−	1.15281e7i		−	0.908575i
$695$		0			0
$696$		0			0
$697$	−1.41512e6	−	1.41512e6i	−0.110334	−	0.110334i
$698$	−1.15242e6	−	1.15242e6i	−0.0895310	−	0.0895310i
$699$		0			0
$700$		0			0
$701$		−	2.09792e6i		−	0.161248i	−0.996745	−	0.0806240i	$-0.974309\pi$
$701$		−	2.09792e6i		−	0.161248i	0.996745	−	0.0806240i	$-0.0256913\pi$
$702$		0			0
$703$	581282.	−	581282.i	0.0443607	−	0.0443607i
$704$	−1.96268e6			−0.149251
$705$		0			0
$706$	1.17248e7			0.885306
$707$	−420520.	+	420520.i	−0.0316401	+	0.0316401i
$708$		0			0
$709$			1.90774e7i			1.42529i	0.701525	+	0.712645i	$0.252503\pi$
$709$			1.90774e7i			1.42529i	−0.701525	+	0.712645i	$0.747497\pi$
$710$		0			0
$711$		0			0
$712$	2.93692e6	+	2.93692e6i	0.217116	+	0.217116i
$713$	751848.	+	751848.i	0.0553868	+	0.0553868i
$714$		0			0
$715$		0			0
$716$		−	9.33172e6i		−	0.680267i
$717$		0			0
$718$	−3.26888e6	+	3.26888e6i	−0.236640	+	0.236640i
$719$	3.36879e6			0.243025			0.121513	−	0.992590i	$-0.461226\pi$
$719$	3.36879e6			0.243025			0.121513	+	0.992590i	$0.461226\pi$
$720$		0			0
$721$	1.17875e6			0.0844472
$722$	−6.96186e6	+	6.96186e6i	−0.497030	+	0.497030i
$723$		0			0
$724$		−	1.20571e7i		−	0.854864i
$725$		0			0
$726$		0			0
$727$	3.67673e6	+	3.67673e6i	0.258004	+	0.258004i	0.824242	−	0.566238i	$-0.191602\pi$
$727$	3.67673e6	+	3.67673e6i	0.258004	+	0.258004i	−0.566238	+	0.824242i	$0.691602\pi$
$728$	155550.	+	155550.i	0.0108778	+	0.0108778i
$729$		0			0
$730$		0			0
$731$			1.74388e7i			1.20705i
$732$		0			0
$733$	−2.83561e6	+	2.83561e6i	−0.194933	+	0.194933i	−0.797824	−	0.602891i	$-0.794016\pi$
$733$	−2.83561e6	+	2.83561e6i	−0.194933	+	0.194933i	0.602891	+	0.797824i	$0.294016\pi$
$734$	3.55302e6			0.243421
$735$		0			0
$736$	2.45445e6			0.167016
$737$	−1.92527e7	+	1.92527e7i	−1.30564	+	1.30564i
$738$		0			0
$739$		−	5.14600e6i		−	0.346624i	−0.984867	−	0.173312i	$-0.944553\pi$
$739$		−	5.14600e6i		−	0.346624i	0.984867	−	0.173312i	$-0.0554469\pi$
$740$		0			0
$741$		0			0
$742$	−914688.	−	914688.i	−0.0609906	−	0.0609906i
$743$	6.09111e6	+	6.09111e6i	0.404785	+	0.404785i	0.879915	−	0.475130i	$-0.157599\pi$
$743$	6.09111e6	+	6.09111e6i	0.404785	+	0.404785i	−0.475130	+	0.879915i	$0.657599\pi$
$744$		0			0
$745$		0			0
$746$			1.27855e7i			0.841144i
$747$		0			0
$748$	1.05801e7	−	1.05801e7i	0.691411	−	0.691411i
$749$	3.16973e6			0.206451
$750$		0			0
$751$	−1.72672e7			−1.11717			−0.558587	−	0.829446i	$-0.688656\pi$
$751$	−1.72672e7			−1.11717			−0.558587	+	0.829446i	$0.688656\pi$
$752$	−3.28502e6	+	3.28502e6i	−0.211833	+	0.211833i
$753$		0			0
$754$		−	7.07569e6i		−	0.453253i
$755$		0			0
$756$		0			0
$757$	6.87707e6	+	6.87707e6i	0.436178	+	0.436178i	0.890724	−	0.454545i	$-0.150198\pi$
$757$	6.87707e6	+	6.87707e6i	0.436178	+	0.436178i	−0.454545	+	0.890724i	$0.650198\pi$
$758$	488618.	+	488618.i	0.0308885	+	0.0308885i
$759$		0			0
$760$		0			0
$761$		−	1.68325e7i		−	1.05363i	−0.849980	−	0.526815i	$-0.823386\pi$
$761$		−	1.68325e7i		−	1.05363i	0.849980	−	0.526815i	$-0.176614\pi$
$762$		0			0
$763$	−1.89768e6	+	1.89768e6i	−0.118008	+	0.118008i
$764$	8.18181e6			0.507126
$765$		0			0
$766$	−2.28628e6			−0.140785
$767$	7.34553e6	−	7.34553e6i	0.450853	−	0.450853i
$768$		0			0
$769$		−	1.54410e7i		−	0.941587i	−0.882243	−	0.470794i	$-0.843968\pi$
$769$		−	1.54410e7i		−	0.941587i	0.882243	−	0.470794i	$-0.156032\pi$
$770$		0			0
$771$		0			0
$772$	147316.	+	147316.i	0.00889624	+	0.00889624i
$773$	−1.30729e7	−	1.30729e7i	−0.786904	−	0.786904i	0.194081	−	0.980985i	$-0.437827\pi$
$773$	−1.30729e7	−	1.30729e7i	−0.786904	−	0.786904i	−0.980985	+	0.194081i	$0.937827\pi$
$774$		0			0
$775$		0			0
$776$		−	2.01894e6i		−	0.120357i
$777$		0			0
$778$	6.54485e6	−	6.54485e6i	0.387660	−	0.387660i
$779$	124372.			0.00734307
$780$		0			0
$781$	1.58002e7			0.926903
$782$	−1.32310e7	+	1.32310e7i	−0.773707	+	0.773707i
$783$		0			0
$784$			4.25463e6i			0.247213i
$785$		0			0
$786$		0			0
$787$	−417501.	−	417501.i	−0.0240282	−	0.0240282i	0.694991	−	0.719019i	$-0.255409\pi$
$787$	−417501.	−	417501.i	−0.0240282	−	0.0240282i	−0.719019	+	0.694991i	$0.755409\pi$
$788$	3.63374e6	+	3.63374e6i	0.208467	+	0.208467i
$789$		0			0
$790$		0			0
$791$			134338.i			0.00763408i
$792$		0			0
$793$	−6.33983e6	+	6.33983e6i	−0.358009	+	0.358009i
$794$	4.85664e6			0.273391
$795$		0			0
$796$	−1.18165e7			−0.661007
$797$	−1.52951e7	+	1.52951e7i	−0.852918	+	0.852918i	−0.990492	−	0.137573i	$-0.956070\pi$
$797$	−1.52951e7	+	1.52951e7i	−0.852918	+	0.852918i	0.137573	+	0.990492i	$0.456070\pi$
$798$		0			0
$799$		−	3.54167e7i		−	1.96264i
$800$		0			0
$801$		0			0
$802$	3.92067e6	+	3.92067e6i	0.215241	+	0.215241i
$803$	−9.75885e6	−	9.75885e6i	−0.534084	−	0.534084i
$804$		0			0
$805$		0			0
$806$			445599.i			0.0241605i
$807$		0			0
$808$	−1.96632e6	+	1.96632e6i	−0.105956	+	0.105956i
$809$	−3.34054e7			−1.79451			−0.897254	−	0.441514i	$-0.854442\pi$
$809$	−3.34054e7			−1.79451			−0.897254	+	0.441514i	$0.854442\pi$
$810$		0			0
$811$	−1.81302e7			−0.967945			−0.483973	−	0.875083i	$-0.660807\pi$
$811$	−1.81302e7			−0.967945			−0.483973	+	0.875083i	$0.660807\pi$
$812$	−1.09077e6	+	1.09077e6i	−0.0580554	+	0.0580554i
$813$		0			0
$814$			1.29910e7i			0.687198i
$815$		0			0
$816$		0			0
$817$	−766330.	−	766330.i	−0.0401662	−	0.0401662i
$818$	962792.	+	962792.i	0.0503094	+	0.0503094i
$819$		0			0
$820$		0			0
$821$		−	3.30929e6i		−	0.171347i	−0.996323	−	0.0856735i	$-0.972696\pi$
$821$		−	3.30929e6i		−	0.171347i	0.996323	−	0.0856735i	$-0.0273042\pi$
$822$		0			0
$823$	−1.07231e7	+	1.07231e7i	−0.551850	+	0.551850i	−0.926974	−	0.375125i	$-0.877600\pi$
$823$	−1.07231e7	+	1.07231e7i	−0.551850	+	0.551850i	0.375125	+	0.926974i	$0.377600\pi$
$824$	5.51177e6			0.282796
$825$		0			0
$826$	−2.26474e6			−0.115496
$827$	−2.08247e6	+	2.08247e6i	−0.105880	+	0.105880i	−0.758062	−	0.652182i	$-0.773854\pi$
$827$	−2.08247e6	+	2.08247e6i	−0.105880	+	0.105880i	0.652182	+	0.758062i	$0.273854\pi$
$828$		0			0
$829$		−	2.31856e7i		−	1.17174i	−0.810404	−	0.585872i	$-0.800752\pi$
$829$		−	2.31856e7i		−	1.17174i	0.810404	−	0.585872i	$-0.199248\pi$
$830$		0			0
$831$		0			0
$832$	727340.	+	727340.i	0.0364275	+	0.0364275i
$833$	−2.29352e7	−	2.29352e7i	−1.14522	−	1.14522i
$834$		0			0
$835$		0			0
$836$			929863.i			0.0460154i
$837$		0			0
$838$	−3.69850e6	+	3.69850e6i	−0.181934	+	0.181934i
$839$	−3.40410e7			−1.66954			−0.834771	−	0.550598i	$-0.814400\pi$
$839$	−3.40410e7			−1.66954			−0.834771	+	0.550598i	$0.814400\pi$
$840$		0			0
$841$	2.91061e7			1.41904
$842$	−1.34861e6	+	1.34861e6i	−0.0655548	+	0.0655548i
$843$		0			0
$844$			9.27210e6i			0.448045i
$845$		0			0
$846$		0			0
$847$	−663478.	−	663478.i	−0.0317774	−	0.0317774i
$848$	−4.27702e6	−	4.27702e6i	−0.204245	−	0.204245i
$849$		0			0
$850$		0			0
$851$		−	1.62460e7i		−	0.768993i
$852$		0			0
$853$	5.07882e6	−	5.07882e6i	0.238996	−	0.238996i	−0.577438	−	0.816434i	$-0.695948\pi$
$853$	5.07882e6	−	5.07882e6i	0.238996	−	0.238996i	0.816434	+	0.577438i	$0.195948\pi$
$854$	1.95466e6			0.0917122
$855$		0			0
$856$	1.48215e7			0.691363
$857$	−2.78606e7	+	2.78606e7i	−1.29580	+	1.29580i	−0.364663	+	0.931139i	$0.618816\pi$
$857$	−2.78606e7	+	2.78606e7i	−1.29580	+	1.29580i	−0.931139	+	0.364663i	$0.881184\pi$
$858$		0			0
$859$			4.83134e6i			0.223401i	0.993742	+	0.111700i	$0.0356297\pi$
$859$			4.83134e6i			0.223401i	−0.993742	+	0.111700i	$0.964370\pi$
$860$		0			0
$861$		0			0
$862$	−3.70450e6	−	3.70450e6i	−0.169809	−	0.169809i
$863$	2.21932e7	+	2.21932e7i	1.01436	+	1.01436i	0.999895	+	0.0144652i	$0.00460457\pi$
$863$	2.21932e7	+	2.21932e7i	1.01436	+	1.01436i	0.0144652	+	0.999895i	$0.495395\pi$
$864$		0			0
$865$		0			0
$866$			2.05273e7i			0.930118i
$867$		0			0
$868$	68692.3	−	68692.3i	0.00309463	−	0.00309463i
$869$	−1.30242e7			−0.585062
$870$		0			0
$871$	1.42695e7			0.637330
$872$	−8.87344e6	+	8.87344e6i	−0.395185	+	0.395185i
$873$		0			0
$874$		−	1.16285e6i		−	0.0514925i
$875$		0			0
$876$		0			0
$877$	1.41235e6	+	1.41235e6i	0.0620074	+	0.0620074i	0.737430	−	0.675423i	$-0.236039\pi$
$877$	1.41235e6	+	1.41235e6i	0.0620074	+	0.0620074i	−0.675423	+	0.737430i	$0.736039\pi$
$878$	−2.49770e6	−	2.49770e6i	−0.109346	−	0.109346i
$879$		0			0
$880$		0			0
$881$			2.50777e7i			1.08855i	0.838908	+	0.544274i	$0.183195\pi$
$881$			2.50777e7i			1.08855i	−0.838908	+	0.544274i	$0.816805\pi$
$882$		0			0
$883$	1.84135e7	−	1.84135e7i	0.794759	−	0.794759i	−0.187505	−	0.982264i	$-0.560040\pi$
$883$	1.84135e7	−	1.84135e7i	0.794759	−	0.794759i	0.982264	+	0.187505i	$0.0600399\pi$
$884$	−7.84165e6			−0.337502
$885$		0			0
$886$	−398812.			−0.0170681
$887$	3.11782e7	−	3.11782e7i	1.33058	−	1.33058i	0.425733	−	0.904849i	$-0.360016\pi$
$887$	3.11782e7	−	3.11782e7i	1.33058	−	1.33058i	0.904849	−	0.425733i	$-0.139984\pi$
$888$		0			0
$889$			2.68609e6i			0.113990i
$890$		0			0
$891$		0			0
$892$	−1.22966e7	−	1.22966e7i	−0.517455	−	0.517455i
$893$	1.55635e6	+	1.55635e6i	0.0653098	+	0.0653098i
$894$		0			0
$895$		0			0
$896$		−	224250.i		−	0.00933172i
$897$		0			0
$898$	1.60280e7	−	1.60280e7i	0.663267	−	0.663267i
$899$	−3.12470e6			−0.128946
$900$		0			0
$901$	4.61117e7			1.89234
$902$	−1.38978e6	+	1.38978e6i	−0.0568763	+	0.0568763i
$903$		0			0
$904$			628154.i			0.0255650i
$905$		0			0
$906$		0			0
$907$	−2.01780e7	−	2.01780e7i	−0.814441	−	0.814441i	0.170855	−	0.985296i	$-0.445347\pi$
$907$	−2.01780e7	−	2.01780e7i	−0.814441	−	0.814441i	−0.985296	+	0.170855i	$0.945347\pi$
$908$	−1.12251e7	−	1.12251e7i	−0.451832	−	0.451832i
$909$		0			0
$910$		0			0
$911$		−	2.83269e7i		−	1.13085i	−0.824801	−	0.565423i	$-0.808713\pi$
$911$		−	2.83269e7i		−	1.13085i	0.824801	−	0.565423i	$-0.191287\pi$
$912$		0			0
$913$	−1.54707e7	+	1.54707e7i	−0.614232	+	0.614232i
$914$	−9.09979e6			−0.360301
$915$		0			0
$916$	−557284.			−0.0219451
$917$	−3.64956e6	+	3.64956e6i	−0.143323	+	0.143323i
$918$		0			0
$919$		−	3.33527e7i		−	1.30269i	−0.758780	−	0.651346i	$-0.774204\pi$
$919$		−	3.33527e7i		−	1.30269i	0.758780	−	0.651346i	$-0.225796\pi$
$920$		0			0
$921$		0			0
$922$	−2.35735e7	−	2.35735e7i	−0.913266	−	0.913266i
$923$	−5.85530e6	−	5.85530e6i	−0.226227	−	0.226227i
$924$		0			0
$925$		0			0
$926$		−	2.73023e7i		−	1.04634i
$927$		0			0
$928$	−5.10036e6	+	5.10036e6i	−0.194416	+	0.194416i
$929$	−6.74711e6			−0.256495			−0.128247	−	0.991742i	$-0.540935\pi$
$929$	−6.74711e6			−0.256495			−0.128247	+	0.991742i	$0.540935\pi$
$930$		0			0
$931$	2.01572e6			0.0762179
$932$	1.28590e7	−	1.28590e7i	0.484918	−	0.484918i
$933$		0			0
$934$		−	8.93144e6i		−	0.335007i
$935$		0			0
$936$		0			0
$937$	−3.35505e7	−	3.35505e7i	−1.24839	−	1.24839i	−0.956431	−	0.291959i	$-0.905693\pi$
$937$	−3.35505e7	−	3.35505e7i	−1.24839	−	1.24839i	−0.291959	−	0.956431i	$-0.594307\pi$
$938$	−2.19975e6	−	2.19975e6i	−0.0816332	−	0.0816332i
$939$		0			0
$940$		0			0
$941$			3.88609e6i			0.143067i	0.997438	+	0.0715334i	$0.0227892\pi$
$941$			3.88609e6i			0.143067i	−0.997438	+	0.0715334i	$0.977211\pi$
$942$		0			0
$943$	1.73800e6	−	1.73800e6i	0.0636461	−	0.0636461i
$944$	−1.05898e7			−0.386773
$945$		0			0
$946$	1.71266e7			0.622221
$947$	1.38895e7	−	1.38895e7i	0.503281	−	0.503281i	−0.409175	−	0.912456i	$-0.634183\pi$
$947$	1.38895e7	−	1.38895e7i	0.503281	−	0.503281i	0.912456	+	0.409175i	$0.134183\pi$
$948$		0			0
$949$			7.23296e6i			0.260706i
$950$		0			0
$951$		0			0
$952$	1.20885e6	+	1.20885e6i	0.0432294	+	0.0432294i
$953$	2.32501e7	+	2.32501e7i	0.829263	+	0.829263i	0.987415	−	0.158152i	$-0.0505535\pi$
$953$	2.32501e7	+	2.32501e7i	0.829263	+	0.829263i	−0.158152	+	0.987415i	$0.550553\pi$
$954$		0			0
$955$		0			0
$956$			1.77946e7i			0.629715i
$957$		0			0
$958$	1.50865e7	−	1.50865e7i	0.531099	−	0.531099i
$959$	−1.87358e6			−0.0657849
$960$		0			0
$961$	−2.84324e7			−0.993127
$962$	4.81427e6	−	4.81427e6i	0.167723	−	0.167723i
$963$		0			0
$964$		−	1.54819e7i		−	0.536575i
$965$		0			0
$966$		0			0
$967$	1.98191e7	+	1.98191e7i	0.681583	+	0.681583i	0.960357	−	0.278774i	$-0.0899280\pi$
$967$	1.98191e7	+	1.98191e7i	0.681583	+	0.681583i	−0.278774	+	0.960357i	$0.589928\pi$
$968$	−3.10238e6	−	3.10238e6i	−0.106416	−	0.106416i
$969$		0			0
$970$		0			0
$971$			3.25338e7i			1.10735i	0.832732	+	0.553677i	$0.186776\pi$
$971$			3.25338e7i			1.10735i	−0.832732	+	0.553677i	$0.813224\pi$
$972$		0			0
$973$	−3.27931e6	+	3.27931e6i	−0.111045	+	0.111045i
$974$	−1.22377e7			−0.413334
$975$		0			0
$976$	9.13987e6			0.307125
$977$	−1.01626e7	+	1.01626e7i	−0.340618	+	0.340618i	−0.856600	−	0.515981i	$-0.827427\pi$
$977$	−1.01626e7	+	1.01626e7i	−0.340618	+	0.340618i	0.515981	+	0.856600i	$0.327427\pi$
$978$		0			0
$979$			3.10969e7i			1.03696i
$980$		0			0
$981$		0			0
$982$	2.39224e7	+	2.39224e7i	0.791638	+	0.791638i
$983$	5.47881e6	+	5.47881e6i	0.180843	+	0.180843i	0.791723	−	0.610880i	$-0.209184\pi$
$983$	5.47881e6	+	5.47881e6i	0.180843	+	0.180843i	−0.610880	+	0.791723i	$0.709184\pi$
$984$		0			0
$985$		0			0
$986$		−	5.49884e7i		−	1.80127i
$987$		0			0
$988$	344593.	−	344593.i	0.0112309	−	0.0112309i
$989$	−2.14178e7			−0.696282
$990$		0			0
$991$	1.66714e7			0.539246			0.269623	−	0.962966i	$-0.413101\pi$
$991$	1.66714e7			0.539246			0.269623	+	0.962966i	$0.413101\pi$
$992$	321201.	−	321201.i	0.0103633	−	0.0103633i
$993$		0			0
$994$			1.80528e6i			0.0579532i
$995$		0			0
$996$		0			0
$997$	5.58846e6	+	5.58846e6i	0.178055	+	0.178055i	0.790507	−	0.612452i	$-0.209817\pi$
$997$	5.58846e6	+	5.58846e6i	0.178055	+	0.178055i	−0.612452	+	0.790507i	$0.709817\pi$
$998$	−7.09214e6	−	7.09214e6i	−0.225398	−	0.225398i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.6.f.e.107.2		12
3.2	odd	2	inner	450.6.f.e.107.5		12
5.2	odd	4		90.6.f.c.53.3	yes	12
5.3	odd	4	inner	450.6.f.e.143.5		12
5.4	even	2		90.6.f.c.17.4	yes	12
15.2	even	4		90.6.f.c.53.4	yes	12
15.8	even	4	inner	450.6.f.e.143.2		12
15.14	odd	2		90.6.f.c.17.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.6.f.c.17.3	✓	12	15.14	odd	2
90.6.f.c.17.4	yes	12	5.4	even	2
90.6.f.c.53.3	yes	12	5.2	odd	4
90.6.f.c.53.4	yes	12	15.2	even	4
450.6.f.e.107.2		12	1.1	even	1	trivial
450.6.f.e.107.5		12	3.2	odd	2	inner
450.6.f.e.143.2		12	15.8	even	4	inner
450.6.f.e.143.5		12	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	450.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.82843 + 2.82843i) q^{2} -16.0000i q^{4} +(9.67825 + 9.67825i) q^{7} +(45.2548 + 45.2548i) q^{8} +O(q^{10})\)	\(q+(-2.82843 + 2.82843i) q^{2} -16.0000i q^{4} +(9.67825 + 9.67825i) q^{7} +(45.2548 + 45.2548i) q^{8} +479.171i q^{11} +(177.573 - 177.573i) q^{13} -54.7484 q^{14} -256.000 q^{16} +(1380.00 - 1380.00i) q^{17} +121.286i q^{19} +(-1355.30 - 1355.30i) q^{22} +(1694.88 + 1694.88i) q^{23} +1004.51i q^{26} +(154.852 - 154.852i) q^{28} -7043.95 q^{29} +443.600 q^{31} +(724.077 - 724.077i) q^{32} +7806.47i q^{34} +(-4792.67 - 4792.67i) q^{37} +(-343.047 - 343.047i) q^{38} -1025.44i q^{41} +(-6318.40 + 6318.40i) q^{43} +7666.73 q^{44} -9587.68 q^{46} +(12832.1 - 12832.1i) q^{47} -16619.7i q^{49} +(-2841.17 - 2841.17i) q^{52} +(16707.1 + 16707.1i) q^{53} +875.975i q^{56} +(19923.3 - 19923.3i) q^{58} +41366.2 q^{59} -35702.6 q^{61} +(-1254.69 + 1254.69i) q^{62} +4096.00i q^{64} +(40179.3 + 40179.3i) q^{67} +(-22080.0 - 22080.0i) q^{68} -32974.0i q^{71} +(-20366.1 + 20366.1i) q^{73} +27111.4 q^{74} +1940.57 q^{76} +(-4637.53 + 4637.53i) q^{77} +27180.7i q^{79} +(2900.40 + 2900.40i) q^{82} +(32286.4 + 32286.4i) q^{83} -35742.3i q^{86} +(-21684.8 + 21684.8i) q^{88} +64897.3 q^{89} +3437.20 q^{91} +(27118.1 - 27118.1i) q^{92} +72589.4i q^{94} +(-22306.4 - 22306.4i) q^{97} +(47007.5 + 47007.5i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 144 q^{7}+O(q^{10}) \) 12 * q - 144 * q^7	\( 12 q - 144 q^{7} + 276 q^{13} - 3072 q^{16} - 384 q^{22} - 2304 q^{28} - 58512 q^{31} - 25764 q^{37} - 16080 q^{43} - 60672 q^{46} - 4416 q^{52} - 23952 q^{58} - 145200 q^{61} - 33552 q^{67} + 158988 q^{73} - 86016 q^{76} + 75024 q^{82} - 6144 q^{88} - 465024 q^{91} + 631116 q^{97}+O(q^{100}) \) 12 * q - 144 * q^7 + 276 * q^13 - 3072 * q^16 - 384 * q^22 - 2304 * q^28 - 58512 * q^31 - 25764 * q^37 - 16080 * q^43 - 60672 * q^46 - 4416 * q^52 - 23952 * q^58 - 145200 * q^61 - 33552 * q^67 + 158988 * q^73 - 86016 * q^76 + 75024 * q^82 - 6144 * q^88 - 465024 * q^91 + 631116 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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