LMFDB - Embedded newform 90.5.g.e.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,5,Mod(37,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("90.37");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	90.g (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:	$9.30329667755$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.1
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	90.37
Dual form			90.5.g.e.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +8.00000i q^{4} +(-24.6742 - 4.02270i) q^{5} +(44.4393 + 44.4393i) q^{7} +(-16.0000 + 16.0000i) q^{8} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +8.00000i q^{4} +(-24.6742 - 4.02270i) q^{5} +(44.4393 + 44.4393i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(-41.3031 - 57.3939i) q^{10} -167.439 q^{11} +(-223.621 + 223.621i) q^{13} +177.757i q^{14} -64.0000 q^{16} +(71.0148 + 71.0148i) q^{17} -272.211i q^{19} +(32.1816 - 197.394i) q^{20} +(-334.879 - 334.879i) q^{22} +(-87.6821 + 87.6821i) q^{23} +(592.636 + 198.514i) q^{25} -894.484 q^{26} +(-355.514 + 355.514i) q^{28} +839.832i q^{29} +403.787 q^{31} +(-128.000 - 128.000i) q^{32} +284.059i q^{34} +(-917.739 - 1275.27i) q^{35} +(-207.589 - 207.589i) q^{37} +(544.422 - 544.422i) q^{38} +(459.151 - 330.424i) q^{40} +1386.39 q^{41} +(568.393 - 568.393i) q^{43} -1339.51i q^{44} -350.729 q^{46} +(2642.77 + 2642.77i) q^{47} +1548.70i q^{49} +(788.243 + 1582.30i) q^{50} +(-1788.97 - 1788.97i) q^{52} +(1378.64 - 1378.64i) q^{53} +(4131.44 + 673.559i) q^{55} -1422.06 q^{56} +(-1679.66 + 1679.66i) q^{58} +327.503i q^{59} -4205.66 q^{61} +(807.573 + 807.573i) q^{62} -512.000i q^{64} +(6417.24 - 4618.11i) q^{65} +(2832.99 + 2832.99i) q^{67} +(-568.118 + 568.118i) q^{68} +(715.064 - 4386.02i) q^{70} -5339.03 q^{71} +(6865.24 - 6865.24i) q^{73} -830.357i q^{74} +2177.69 q^{76} +(-7440.88 - 7440.88i) q^{77} +4666.69i q^{79} +(1579.15 + 257.453i) q^{80} +(2772.78 + 2772.78i) q^{82} +(-4111.98 + 4111.98i) q^{83} +(-1466.56 - 2037.91i) q^{85} +2273.57 q^{86} +(2679.03 - 2679.03i) q^{88} +9911.62i q^{89} -19875.1 q^{91} +(-701.457 - 701.457i) q^{92} +10571.1i q^{94} +(-1095.03 + 6716.60i) q^{95} +(-10688.9 - 10688.9i) q^{97} +(-3097.40 + 3097.40i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 84 q^{5} - 28 q^{7} - 64 q^{8}+O(q^{10}) $ 4 * q + 8 * q^2 - 84 * q^5 - 28 * q^7 - 64 * q^8	$ 4 q + 8 q^{2} - 84 q^{5} - 28 q^{7} - 64 q^{8} - 224 q^{10} - 464 q^{11} - 336 q^{13} - 256 q^{16} - 392 q^{17} - 224 q^{20} - 928 q^{22} - 968 q^{23} + 1136 q^{25} - 1344 q^{26} + 224 q^{28} - 560 q^{31} - 512 q^{32} + 2296 q^{35} + 2256 q^{37} - 1232 q^{38} + 896 q^{40} - 392 q^{41} + 216 q^{43} - 3872 q^{46} + 9072 q^{47} + 3976 q^{50} - 2688 q^{52} + 4280 q^{53} + 10500 q^{55} + 896 q^{56} - 2192 q^{58} - 4536 q^{61} - 1120 q^{62} + 12912 q^{65} - 2248 q^{67} + 3136 q^{68} + 9856 q^{70} - 18064 q^{71} + 20524 q^{73} - 4928 q^{76} - 7336 q^{77} + 5376 q^{80} - 784 q^{82} + 336 q^{83} + 15944 q^{85} + 864 q^{86} + 7424 q^{88} - 52752 q^{91} - 7744 q^{92} - 23104 q^{95} - 40404 q^{97} - 23912 q^{98}+O(q^{100}) $ 4 * q + 8 * q^2 - 84 * q^5 - 28 * q^7 - 64 * q^8 - 224 * q^10 - 464 * q^11 - 336 * q^13 - 256 * q^16 - 392 * q^17 - 224 * q^20 - 928 * q^22 - 968 * q^23 + 1136 * q^25 - 1344 * q^26 + 224 * q^28 - 560 * q^31 - 512 * q^32 + 2296 * q^35 + 2256 * q^37 - 1232 * q^38 + 896 * q^40 - 392 * q^41 + 216 * q^43 - 3872 * q^46 + 9072 * q^47 + 3976 * q^50 - 2688 * q^52 + 4280 * q^53 + 10500 * q^55 + 896 * q^56 - 2192 * q^58 - 4536 * q^61 - 1120 * q^62 + 12912 * q^65 - 2248 * q^67 + 3136 * q^68 + 9856 * q^70 - 18064 * q^71 + 20524 * q^73 - 4928 * q^76 - 7336 * q^77 + 5376 * q^80 - 784 * q^82 + 336 * q^83 + 15944 * q^85 + 864 * q^86 + 7424 * q^88 - 52752 * q^91 - 7744 * q^92 - 23104 * q^95 - 40404 * q^97 - 23912 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			8.00000i			0.500000i
$5$	−24.6742	−	4.02270i	−0.986969	−	0.160908i
$5$	−24.6742	−	4.02270i	−0.986969	−	0.160908i
$6$		0			0
$7$	44.4393	+	44.4393i	0.906924	+	0.906924i	0.996023	−	0.0890986i	$-0.0283986\pi$
$7$	44.4393	+	44.4393i	0.906924	+	0.906924i	−0.0890986	+	0.996023i	$0.528399\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$		0			0
$10$	−41.3031	−	57.3939i	−0.413031	−	0.573939i
$11$	−167.439			−1.38380			−0.691898	−	0.721995i	$-0.743225\pi$
$11$	−167.439			−1.38380			−0.691898	+	0.721995i	$0.743225\pi$
$12$		0			0
$13$	−223.621	+	223.621i	−1.32320	+	1.32320i	−0.412031	+	0.911170i	$0.635180\pi$
$13$	−223.621	+	223.621i	−1.32320	+	1.32320i	−0.911170	+	0.412031i	$0.864820\pi$
$14$			177.757i			0.906924i
$15$		0			0
$16$	−64.0000			−0.250000
$17$	71.0148	+	71.0148i	0.245726	+	0.245726i	0.819214	−	0.573488i	$-0.194410\pi$
$17$	71.0148	+	71.0148i	0.245726	+	0.245726i	−0.573488	+	0.819214i	$0.694410\pi$
$18$		0			0
$19$		−	272.211i		−	0.754048i	−0.926204	−	0.377024i	$-0.876947\pi$
$19$		−	272.211i		−	0.754048i	0.926204	−	0.377024i	$-0.123053\pi$
$20$	32.1816	−	197.394i	0.0804541	−	0.493485i
$21$		0			0
$22$	−334.879	−	334.879i	−0.691898	−	0.691898i
$23$	−87.6821	+	87.6821i	−0.165751	+	0.165751i	−0.785109	−	0.619358i	$-0.787393\pi$
$23$	−87.6821	+	87.6821i	−0.165751	+	0.165751i	0.619358	+	0.785109i	$0.287393\pi$
$24$		0			0
$25$	592.636	+	198.514i	0.948217	+	0.317623i
$26$	−894.484			−1.32320
$27$		0			0
$28$	−355.514	+	355.514i	−0.453462	+	0.453462i
$29$			839.832i			0.998611i	0.866426	+	0.499306i	$0.166412\pi$
$29$			839.832i			0.998611i	−0.866426	+	0.499306i	$0.833588\pi$
$30$		0			0
$31$	403.787			0.420173			0.210087	−	0.977683i	$-0.432625\pi$
$31$	403.787			0.420173			0.210087	+	0.977683i	$0.432625\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$		0			0
$34$			284.059i			0.245726i
$35$	−917.739	−	1275.27i	−0.749175	−	1.04104i
$36$		0			0
$37$	−207.589	−	207.589i	−0.151636	−	0.151636i	0.627212	−	0.778848i	$-0.284196\pi$
$37$	−207.589	−	207.589i	−0.151636	−	0.151636i	−0.778848	+	0.627212i	$0.784196\pi$
$38$	544.422	−	544.422i	0.377024	−	0.377024i
$39$		0			0
$40$	459.151	−	330.424i	0.286969	−	0.206515i
$41$	1386.39			0.824742			0.412371	−	0.911016i	$-0.364701\pi$
$41$	1386.39			0.824742			0.412371	+	0.911016i	$0.364701\pi$
$42$		0			0
$43$	568.393	−	568.393i	0.307406	−	0.307406i	−0.536497	−	0.843902i	$-0.680253\pi$
$43$	568.393	−	568.393i	0.307406	−	0.307406i	0.843902	+	0.536497i	$0.180253\pi$
$44$		−	1339.51i		−	0.691898i
$45$		0			0
$46$	−350.729			−0.165751
$47$	2642.77	+	2642.77i	1.19637	+	1.19637i	0.975247	+	0.221119i	$0.0709709\pi$
$47$	2642.77	+	2642.77i	1.19637	+	1.19637i	0.221119	+	0.975247i	$0.429029\pi$
$48$		0			0
$49$			1548.70i			0.645023i
$50$	788.243	+	1582.30i	0.315297	+	0.632920i
$51$		0			0
$52$	−1788.97	−	1788.97i	−0.661600	−	0.661600i
$53$	1378.64	−	1378.64i	0.490792	−	0.490792i	−0.417763	−	0.908556i	$-0.637186\pi$
$53$	1378.64	−	1378.64i	0.490792	−	0.490792i	0.908556	+	0.417763i	$0.137186\pi$
$54$		0			0
$55$	4131.44	+	673.559i	1.36576	+	0.222664i
$56$	−1422.06			−0.453462
$57$		0			0
$58$	−1679.66	+	1679.66i	−0.499306	+	0.499306i
$59$			327.503i			0.0940829i	0.998893	+	0.0470415i	$0.0149793\pi$
$59$			327.503i			0.0940829i	−0.998893	+	0.0470415i	$0.985021\pi$
$60$		0			0
$61$	−4205.66			−1.13025			−0.565125	−	0.825005i	$-0.691172\pi$
$61$	−4205.66			−1.13025			−0.565125	+	0.825005i	$0.691172\pi$
$62$	807.573	+	807.573i	0.210087	+	0.210087i
$63$		0			0
$64$		−	512.000i		−	0.125000i
$65$	6417.24	−	4618.11i	1.51887	−	1.09304i
$66$		0			0
$67$	2832.99	+	2832.99i	0.631097	+	0.631097i	0.948343	−	0.317246i	$-0.102758\pi$
$67$	2832.99	+	2832.99i	0.631097	+	0.631097i	−0.317246	+	0.948343i	$0.602758\pi$
$68$	−568.118	+	568.118i	−0.122863	+	0.122863i
$69$		0			0
$70$	715.064	−	4386.02i	0.145931	−	0.895106i
$71$	−5339.03			−1.05912			−0.529560	−	0.848272i	$-0.677643\pi$
$71$	−5339.03			−1.05912			−0.529560	+	0.848272i	$0.677643\pi$
$72$		0			0
$73$	6865.24	−	6865.24i	1.28828	−	1.28828i	0.352447	−	0.935832i	$-0.385350\pi$
$73$	6865.24	−	6865.24i	1.28828	−	1.28828i	0.935832	−	0.352447i	$-0.114650\pi$
$74$		−	830.357i		−	0.151636i
$75$		0			0
$76$	2177.69			0.377024
$77$	−7440.88	−	7440.88i	−1.25500	−	1.25500i
$78$		0			0
$79$			4666.69i			0.747748i	0.927480	+	0.373874i	$0.121971\pi$
$79$			4666.69i			0.747748i	−0.927480	+	0.373874i	$0.878029\pi$
$80$	1579.15	+	257.453i	0.246742	+	0.0402270i
$81$		0			0
$82$	2772.78	+	2772.78i	0.412371	+	0.412371i
$83$	−4111.98	+	4111.98i	−0.596890	+	0.596890i	−0.939484	−	0.342594i	$-0.888695\pi$
$83$	−4111.98	+	4111.98i	−0.596890	+	0.596890i	0.342594	+	0.939484i	$0.388695\pi$
$84$		0			0
$85$	−1466.56	−	2037.91i	−0.202985	−	0.282063i
$86$	2273.57			0.307406
$87$		0			0
$88$	2679.03	−	2679.03i	0.345949	−	0.345949i
$89$			9911.62i			1.25131i	0.780100	+	0.625654i	$0.215168\pi$
$89$			9911.62i			1.25131i	−0.780100	+	0.625654i	$0.784832\pi$
$90$		0			0
$91$	−19875.1			−2.40009
$92$	−701.457	−	701.457i	−0.0828754	−	0.0828754i
$93$		0			0
$94$			10571.1i			1.19637i
$95$	−1095.03	+	6716.60i	−0.121332	+	0.744222i
$96$		0			0
$97$	−10688.9	−	10688.9i	−1.13603	−	1.13603i	−0.989156	−	0.146871i	$-0.953080\pi$
$97$	−10688.9	−	10688.9i	−1.13603	−	1.13603i	−0.146871	−	0.989156i	$-0.546920\pi$
$98$	−3097.40	+	3097.40i	−0.322511	+	0.322511i
$99$		0			0
$100$	−1588.11	+	4741.09i	−0.158811	+	0.474109i
$101$	1763.09			0.172835			0.0864177	−	0.996259i	$-0.472458\pi$
$101$	1763.09			0.172835			0.0864177	+	0.996259i	$0.472458\pi$
$102$		0			0
$103$	−2414.27	+	2414.27i	−0.227568	+	0.227568i	−0.811676	−	0.584108i	$-0.801444\pi$
$103$	−2414.27	+	2414.27i	−0.227568	+	0.227568i	0.584108	+	0.811676i	$0.301444\pi$
$104$		−	7155.87i		−	0.661600i
$105$		0			0
$106$	5514.54			0.490792
$107$	−4279.03	−	4279.03i	−0.373747	−	0.373747i	0.495093	−	0.868840i	$-0.335134\pi$
$107$	−4279.03	−	4279.03i	−0.373747	−	0.373747i	−0.868840	+	0.495093i	$0.835134\pi$
$108$		0			0
$109$			11819.5i			0.994827i	0.867514	+	0.497413i	$0.165717\pi$
$109$			11819.5i			0.994827i	−0.867514	+	0.497413i	$0.834283\pi$
$110$	6915.76	+	9609.99i	0.571550	+	0.794214i
$111$		0			0
$112$	−2844.11	−	2844.11i	−0.226731	−	0.226731i
$113$	−1620.60	+	1620.60i	−0.126917	+	0.126917i	−0.767712	−	0.640795i	$-0.778605\pi$
$113$	−1620.60	+	1620.60i	−0.126917	+	0.126917i	0.640795	+	0.767712i	$0.278605\pi$
$114$		0			0
$115$	2516.21	−	1810.77i	0.190262	−	0.136920i
$116$	−6718.66			−0.499306
$117$		0			0
$118$	−655.005	+	655.005i	−0.0470415	+	0.0470415i
$119$			6311.69i			0.445710i
$120$		0			0
$121$	13394.9			0.914891
$122$	−8411.32	−	8411.32i	−0.565125	−	0.565125i
$123$		0			0
$124$			3230.29i			0.210087i
$125$	−13824.3	−	7282.19i	−0.884753	−	0.466060i
$126$		0			0
$127$	−11572.5	−	11572.5i	−0.717494	−	0.717494i	0.250597	−	0.968091i	$-0.419373\pi$
$127$	−11572.5	−	11572.5i	−0.717494	−	0.717494i	−0.968091	+	0.250597i	$0.919373\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$		0			0
$130$	22070.7	+	3598.24i	1.30596	+	0.212914i
$131$	−65.6230			−0.00382396			−0.00191198	−	0.999998i	$-0.500609\pi$
$131$	−65.6230			−0.00382396			−0.00191198	+	0.999998i	$0.500609\pi$
$132$		0			0
$133$	12096.9	−	12096.9i	0.683864	−	0.683864i
$134$			11332.0i			0.631097i
$135$		0			0
$136$	−2272.47			−0.122863
$137$	−579.439	−	579.439i	−0.0308721	−	0.0308721i	0.691502	−	0.722374i	$-0.256949\pi$
$137$	−579.439	−	579.439i	−0.0308721	−	0.0308721i	−0.722374	+	0.691502i	$0.756949\pi$
$138$		0			0
$139$			36158.2i			1.87145i	0.352734	+	0.935724i	$0.385252\pi$
$139$			36158.2i			1.87145i	−0.352734	+	0.935724i	$0.614748\pi$
$140$	10202.2	−	7341.91i	0.520519	−	0.374587i
$141$		0			0
$142$	−10678.1	−	10678.1i	−0.529560	−	0.529560i
$143$	37442.9	−	37442.9i	1.83104	−	1.83104i
$144$		0			0
$145$	3378.40	−	20722.2i	0.160685	−	0.985599i
$146$	27461.0			1.28828
$147$		0			0
$148$	1660.71	−	1660.71i	0.0758178	−	0.0758178i
$149$			2143.94i			0.0965695i	0.998834	+	0.0482847i	$0.0153755\pi$
$149$			2143.94i			0.0965695i	−0.998834	+	0.0482847i	$0.984625\pi$
$150$		0			0
$151$	−8940.59			−0.392114			−0.196057	−	0.980593i	$-0.562814\pi$
$151$	−8940.59			−0.392114			−0.196057	+	0.980593i	$0.562814\pi$
$152$	4355.38	+	4355.38i	0.188512	+	0.188512i
$153$		0			0
$154$		−	29763.5i		−	1.25500i
$155$	−9963.13	−	1624.31i	−0.414698	−	0.0676093i
$156$		0			0
$157$	18032.9	+	18032.9i	0.731586	+	0.731586i	0.970934	−	0.239348i	$-0.0769337\pi$
$157$	18032.9	+	18032.9i	0.731586	+	0.731586i	−0.239348	+	0.970934i	$0.576934\pi$
$158$	−9333.39	+	9333.39i	−0.373874	+	0.373874i
$159$		0			0
$160$	2643.40	+	3673.21i	0.103258	+	0.143485i
$161$	−7793.06			−0.300647
$162$		0			0
$163$	−6859.00	+	6859.00i	−0.258158	+	0.258158i	−0.824305	−	0.566147i	$-0.808434\pi$
$163$	−6859.00	+	6859.00i	−0.258158	+	0.258158i	0.566147	+	0.824305i	$0.308434\pi$
$164$			11091.1i			0.412371i
$165$		0			0
$166$	−16447.9			−0.596890
$167$	37439.2	+	37439.2i	1.34244	+	1.34244i	0.893627	+	0.448811i	$0.148152\pi$
$167$	37439.2	+	37439.2i	1.34244	+	1.34244i	0.448811	+	0.893627i	$0.351848\pi$
$168$		0			0
$169$		−	71451.6i		−	2.50172i
$170$	1142.69	−	7008.94i	0.0395393	−	0.242524i
$171$		0			0
$172$	4547.14	+	4547.14i	0.153703	+	0.153703i
$173$	32638.2	−	32638.2i	1.09052	−	1.09052i	0.0950500	−	0.995472i	$-0.469699\pi$
$173$	32638.2	−	32638.2i	1.09052	−	1.09052i	0.995472	−	0.0950500i	$-0.0303011\pi$
$174$		0			0
$175$	17514.5	+	35158.1i	0.571901	+	1.14802i
$176$	10716.1			0.345949
$177$		0			0
$178$	−19823.2	+	19823.2i	−0.625654	+	0.625654i
$179$			6396.19i			0.199625i	0.995006	+	0.0998126i	$0.0318243\pi$
$179$			6396.19i			0.199625i	−0.995006	+	0.0998126i	$0.968176\pi$
$180$		0			0
$181$	49025.9			1.49647			0.748236	−	0.663432i	$-0.230901\pi$
$181$	49025.9			1.49647			0.748236	+	0.663432i	$0.230901\pi$
$182$	−39750.2	−	39750.2i	−1.20004	−	1.20004i
$183$		0			0
$184$		−	2805.83i		−	0.0828754i
$185$	4287.04	+	5957.18i	0.125260	+	0.174059i
$186$		0			0
$187$	−11890.7	−	11890.7i	−0.340034	−	0.340034i
$188$	−21142.2	+	21142.2i	−0.598183	+	0.598183i
$189$		0			0
$190$	−15623.3	+	11243.2i	−0.432777	+	0.311445i
$191$	−39949.0			−1.09506			−0.547531	−	0.836785i	$-0.684432\pi$
$191$	−39949.0			−1.09506			−0.547531	+	0.836785i	$0.684432\pi$
$192$		0			0
$193$	−23749.1	+	23749.1i	−0.637577	+	0.637577i	−0.949957	−	0.312380i	$-0.898874\pi$
$193$	−23749.1	+	23749.1i	−0.637577	+	0.637577i	0.312380	+	0.949957i	$0.398874\pi$
$194$		−	42755.5i		−	1.13603i
$195$		0			0
$196$	−12389.6			−0.322511
$197$	2725.09	+	2725.09i	0.0702181	+	0.0702181i	0.741344	−	0.671126i	$-0.234189\pi$
$197$	2725.09	+	2725.09i	0.0702181	+	0.0702181i	−0.671126	+	0.741344i	$0.734189\pi$
$198$		0			0
$199$			63212.5i			1.59624i	0.602502	+	0.798118i	$0.294171\pi$
$199$			63212.5i			1.59624i	−0.602502	+	0.798118i	$0.705829\pi$
$200$	−12658.4	+	6305.94i	−0.316460	+	0.157649i
$201$		0			0
$202$	3526.19	+	3526.19i	0.0864177	+	0.0864177i
$203$	−37321.5	+	37321.5i	−0.905665	+	0.905665i
$204$		0			0
$205$	−34208.1	−	5577.04i	−0.813995	−	0.132708i
$206$	−9657.07			−0.227568
$207$		0			0
$208$	14311.7	−	14311.7i	0.330800	−	0.330800i
$209$			45578.9i			1.04345i
$210$		0			0
$211$	15470.2			0.347480			0.173740	−	0.984792i	$-0.444415\pi$
$211$	15470.2			0.347480			0.173740	+	0.984792i	$0.444415\pi$
$212$	11029.1	+	11029.1i	0.245396	+	0.245396i
$213$		0			0
$214$		−	17116.1i		−	0.373747i
$215$	−16311.1	+	11738.2i	−0.352864	+	0.253936i
$216$		0			0
$217$	17944.0	+	17944.0i	0.381065	+	0.381065i
$218$	−23639.1	+	23639.1i	−0.497413	+	0.497413i
$219$		0			0
$220$	−5388.47	+	33051.5i	−0.111332	+	0.682882i
$221$	−31760.8			−0.650289
$222$		0			0
$223$	28817.8	−	28817.8i	0.579496	−	0.579496i	−0.355268	−	0.934764i	$-0.615611\pi$
$223$	28817.8	−	28817.8i	0.579496	−	0.579496i	0.934764	+	0.355268i	$0.115611\pi$
$224$		−	11376.5i		−	0.226731i
$225$		0			0
$226$	−6482.41			−0.126917
$227$	−884.237	−	884.237i	−0.0171600	−	0.0171600i	0.698475	−	0.715635i	$-0.253862\pi$
$227$	−884.237	−	884.237i	−0.0171600	−	0.0171600i	−0.715635	+	0.698475i	$0.753862\pi$
$228$		0			0
$229$		−	12076.4i		−	0.230285i	−0.993349	−	0.115143i	$-0.963268\pi$
$229$		−	12076.4i		−	0.230285i	0.993349	−	0.115143i	$-0.0367325\pi$
$230$	8653.96	+	1410.88i	0.163591	+	0.0266706i
$231$		0			0
$232$	−13437.3	−	13437.3i	−0.249653	−	0.249653i
$233$	24695.8	−	24695.8i	0.454894	−	0.454894i	−0.442081	−	0.896975i	$-0.645760\pi$
$233$	24695.8	−	24695.8i	0.454894	−	0.454894i	0.896975	+	0.442081i	$0.145760\pi$
$234$		0			0
$235$	−54577.3	−	75839.5i	−0.988271	−	1.37328i
$236$	−2620.02			−0.0470415
$237$		0			0
$238$	−12623.4	+	12623.4i	−0.222855	+	0.222855i
$239$		−	48187.8i		−	0.843608i	−0.906687	−	0.421804i	$-0.861397\pi$
$239$		−	48187.8i		−	0.843608i	0.906687	−	0.421804i	$-0.138603\pi$
$240$		0			0
$241$	−55184.2			−0.950125			−0.475062	−	0.879952i	$-0.657574\pi$
$241$	−55184.2			−0.950125			−0.475062	+	0.879952i	$0.657574\pi$
$242$	26789.8	+	26789.8i	0.457445	+	0.457445i
$243$		0			0
$244$		−	33645.3i		−	0.565125i
$245$	6229.96	−	38213.0i	0.103789	−	0.636618i
$246$		0			0
$247$	60872.1	+	60872.1i	0.997756	+	0.997756i
$248$	−6460.59	+	6460.59i	−0.105043	+	0.105043i
$249$		0			0
$250$	−13084.2	−	42212.9i	−0.209347	−	0.675407i
$251$	69667.8			1.10582			0.552910	−	0.833241i	$-0.313517\pi$
$251$	69667.8			1.10582			0.552910	+	0.833241i	$0.313517\pi$
$252$		0			0
$253$	14681.4	−	14681.4i	0.229365	−	0.229365i
$254$		−	46289.8i		−	0.717494i
$255$		0			0
$256$	4096.00			0.0625000
$257$	11614.4	+	11614.4i	0.175846	+	0.175846i	0.789542	−	0.613696i	$-0.210318\pi$
$257$	11614.4	+	11614.4i	0.175846	+	0.175846i	−0.613696	+	0.789542i	$0.710318\pi$
$258$		0			0
$259$		−	18450.2i		−	0.275044i
$260$	36944.9	+	51337.9i	0.546522	+	0.759436i
$261$		0			0
$262$	−131.246	−	131.246i	−0.00191198	−	0.00191198i
$263$	−86811.6	+	86811.6i	−1.25507	+	1.25507i	−0.301646	+	0.953420i	$0.597536\pi$
$263$	−86811.6	+	86811.6i	−1.25507	+	1.25507i	−0.953420	+	0.301646i	$0.902464\pi$
$264$		0			0
$265$	−39562.6	+	28470.9i	−0.563370	+	0.405425i
$266$	48387.5			0.683864
$267$		0			0
$268$	−22663.9	+	22663.9i	−0.315548	+	0.315548i
$269$		−	93439.3i		−	1.29129i	−0.763636	−	0.645647i	$-0.776588\pi$
$269$		−	93439.3i		−	1.29129i	0.763636	−	0.645647i	$-0.223412\pi$
$270$		0			0
$271$	−10856.5			−0.147826			−0.0739131	−	0.997265i	$-0.523549\pi$
$271$	−10856.5			−0.147826			−0.0739131	+	0.997265i	$0.523549\pi$
$272$	−4544.95	−	4544.95i	−0.0614315	−	0.0614315i
$273$		0			0
$274$		−	2317.76i		−	0.0308721i
$275$	−99230.5	−	33239.1i	−1.31214	−	0.439525i
$276$		0			0
$277$	65214.7	+	65214.7i	0.849935	+	0.849935i	0.990125	−	0.140189i	$-0.0447711\pi$
$277$	65214.7	+	65214.7i	0.849935	+	0.849935i	−0.140189	+	0.990125i	$0.544771\pi$
$278$	−72316.5	+	72316.5i	−0.935724	+	0.935724i
$279$		0			0
$280$	35088.2	+	5720.51i	0.447553	+	0.0729657i
$281$	8669.34			0.109793			0.0548963	−	0.998492i	$-0.482517\pi$
$281$	8669.34			0.109793			0.0548963	+	0.998492i	$0.482517\pi$
$282$		0			0
$283$	−23747.0	+	23747.0i	−0.296508	+	0.296508i	−0.839645	−	0.543136i	$-0.817237\pi$
$283$	−23747.0	+	23747.0i	−0.296508	+	0.296508i	0.543136	+	0.839645i	$0.317237\pi$
$284$		−	42712.2i		−	0.529560i
$285$		0			0
$286$	149772.			1.83104
$287$	61610.2	+	61610.2i	0.747978	+	0.747978i
$288$		0			0
$289$		−	73434.8i		−	0.879238i
$290$	48201.2	−	34687.6i	0.573142	−	0.412457i
$291$		0			0
$292$	54921.9	+	54921.9i	0.644139	+	0.644139i
$293$	55077.2	−	55077.2i	0.641559	−	0.641559i	−0.309380	−	0.950939i	$-0.600121\pi$
$293$	55077.2	−	55077.2i	0.641559	−	0.641559i	0.950939	+	0.309380i	$0.100121\pi$
$294$		0			0
$295$	1317.45	−	8080.88i	0.0151387	−	0.0928569i
$296$	6642.86			0.0758178
$297$		0			0
$298$	−4287.88	+	4287.88i	−0.0482847	+	0.0482847i
$299$		−	39215.1i		−	0.438643i
$300$		0			0
$301$	50517.9			0.557587
$302$	−17881.2	−	17881.2i	−0.196057	−	0.196057i
$303$		0			0
$304$			17421.5i			0.188512i
$305$	103771.	+	16918.1i	1.11552	+	0.181866i
$306$		0			0
$307$	11961.1	+	11961.1i	0.126910	+	0.126910i	0.767709	−	0.640799i	$-0.221397\pi$
$307$	11961.1	+	11961.1i	0.126910	+	0.126910i	−0.640799	+	0.767709i	$0.721397\pi$
$308$	59527.1	−	59527.1i	0.627499	−	0.627499i
$309$		0			0
$310$	−16677.6	−	23174.9i	−0.173545	−	0.241154i
$311$	65284.5			0.674977			0.337489	−	0.941330i	$-0.390423\pi$
$311$	65284.5			0.674977			0.337489	+	0.941330i	$0.390423\pi$
$312$		0			0
$313$	−6418.45	+	6418.45i	−0.0655151	+	0.0655151i	−0.739105	−	0.673590i	$-0.764751\pi$
$313$	−6418.45	+	6418.45i	−0.0655151	+	0.0655151i	0.673590	+	0.739105i	$0.264751\pi$
$314$			72131.4i			0.731586i
$315$		0			0
$316$	−37333.5			−0.373874
$317$	−22100.1	−	22100.1i	−0.219926	−	0.219926i	0.588541	−	0.808467i	$-0.299702\pi$
$317$	−22100.1	−	22100.1i	−0.219926	−	0.219926i	−0.808467	+	0.588541i	$0.799702\pi$
$318$		0			0
$319$		−	140621.i		−	1.38187i
$320$	−2059.62	+	12633.2i	−0.0201135	+	0.123371i
$321$		0			0
$322$	−15586.1	−	15586.1i	−0.150323	−	0.150323i
$323$	19331.0	−	19331.0i	0.185289	−	0.185289i
$324$		0			0
$325$	−176918.	+	88133.8i	−1.67496	+	0.834403i
$326$	−27436.0			−0.258158
$327$		0			0
$328$	−22182.3	+	22182.3i	−0.206185	+	0.206185i
$329$			234886.i			2.17003i
$330$		0			0
$331$	−49108.7			−0.448231			−0.224116	−	0.974563i	$-0.571949\pi$
$331$	−49108.7			−0.448231			−0.224116	+	0.974563i	$0.571949\pi$
$332$	−32895.8	−	32895.8i	−0.298445	−	0.298445i
$333$		0			0
$334$			149757.i			1.34244i
$335$	−58505.6	−	81298.2i	−0.521324	−	0.724422i
$336$		0			0
$337$	−142816.	−	142816.i	−1.25753	−	1.25753i	−0.952269	−	0.305260i	$-0.901257\pi$
$337$	−142816.	−	142816.i	−1.25753	−	1.25753i	−0.305260	−	0.952269i	$-0.598743\pi$
$338$	142903.	−	142903.i	1.25086	−	1.25086i
$339$		0			0
$340$	16303.3	−	11732.5i	0.141032	−	0.101492i
$341$	−67609.8			−0.581434
$342$		0			0
$343$	37875.6	−	37875.6i	0.321937	−	0.321937i
$344$			18188.6i			0.153703i
$345$		0			0
$346$	130553.			1.09052
$347$	21400.3	+	21400.3i	0.177730	+	0.177730i	0.790366	−	0.612635i	$-0.209891\pi$
$347$	21400.3	+	21400.3i	0.177730	+	0.177730i	−0.612635	+	0.790366i	$0.709891\pi$
$348$		0			0
$349$		−	34091.2i		−	0.279893i	−0.990159	−	0.139946i	$-0.955307\pi$
$349$		−	34091.2i		−	0.279893i	0.990159	−	0.139946i	$-0.0446930\pi$
$350$	−35287.3	+	105345.i	−0.288060	+	0.859961i
$351$		0			0
$352$	21432.2	+	21432.2i	0.172974	+	0.172974i
$353$	−28.7539	+	28.7539i	−0.000230753	+	0.000230753i	−0.707222	−	0.706991i	$-0.750052\pi$
$353$	−28.7539	+	28.7539i	−0.000230753	+	0.000230753i	0.706991	+	0.707222i	$0.250052\pi$
$354$		0			0
$355$	131736.	+	21477.3i	1.04532	+	0.170421i
$356$	−79292.9			−0.625654
$357$		0			0
$358$	−12792.4	+	12792.4i	−0.0998126	+	0.0998126i
$359$		−	173943.i		−	1.34964i	−0.737984	−	0.674818i	$-0.764222\pi$
$359$		−	173943.i		−	1.34964i	0.737984	−	0.674818i	$-0.235778\pi$
$360$		0			0
$361$	56222.1			0.431412
$362$	98051.9	+	98051.9i	0.748236	+	0.748236i
$363$		0			0
$364$		−	159001.i		−	1.20004i
$365$	−197011.	+	141778.i	−1.47879	+	1.06420i
$366$		0			0
$367$	−41954.1	−	41954.1i	−0.311489	−	0.311489i	0.533997	−	0.845486i	$-0.320689\pi$
$367$	−41954.1	−	41954.1i	−0.311489	−	0.311489i	−0.845486	+	0.533997i	$0.820689\pi$
$368$	5611.66	−	5611.66i	0.0414377	−	0.0414377i
$369$		0			0
$370$	−3340.28	+	20488.4i	−0.0243994	+	0.149660i
$371$	122531.			0.890223
$372$		0			0
$373$	−65875.2	+	65875.2i	−0.473483	+	0.473483i	−0.903040	−	0.429557i	$-0.858670\pi$
$373$	−65875.2	+	65875.2i	−0.473483	+	0.473483i	0.429557	+	0.903040i	$0.358670\pi$
$374$		−	47562.7i		−	0.340034i
$375$		0			0
$376$	−84568.7			−0.598183
$377$	−187804.	−	187804.i	−1.32136	−	1.32136i
$378$		0			0
$379$		−	10837.0i		−	0.0754448i	−0.999288	−	0.0377224i	$-0.987990\pi$
$379$		−	10837.0i		−	0.0754448i	0.999288	−	0.0377224i	$-0.0120103\pi$
$380$	−53732.8	−	8760.20i	−0.372111	−	0.0606662i
$381$		0			0
$382$	−79898.0	−	79898.0i	−0.547531	−	0.547531i
$383$	−22327.5	+	22327.5i	−0.152210	+	0.152210i	−0.779104	−	0.626894i	$-0.784326\pi$
$383$	−22327.5	+	22327.5i	−0.152210	+	0.152210i	0.626894	+	0.779104i	$0.284326\pi$
$384$		0			0
$385$	153666.	+	213531.i	1.03671	+	1.44058i
$386$	−94996.5			−0.637577
$387$		0			0
$388$	85511.0	−	85511.0i	0.568013	−	0.568013i
$389$			203884.i			1.34736i	0.739023	+	0.673680i	$0.235287\pi$
$389$			203884.i			1.34736i	−0.739023	+	0.673680i	$0.764713\pi$
$390$		0			0
$391$	−12453.5			−0.0814585
$392$	−24779.2	−	24779.2i	−0.161256	−	0.161256i
$393$		0			0
$394$			10900.4i			0.0702181i
$395$	18772.7	−	115147.i	0.120319	−	0.738004i
$396$		0			0
$397$	117299.	+	117299.i	0.744238	+	0.744238i	0.973390	−	0.229153i	$-0.0735955\pi$
$397$	117299.	+	117299.i	0.744238	+	0.744238i	−0.229153	+	0.973390i	$0.573596\pi$
$398$	−126425.	+	126425.i	−0.798118	+	0.798118i
$399$		0			0
$400$	−37928.7	−	12704.9i	−0.237054	−	0.0794057i
$401$	−43093.1			−0.267990			−0.133995	−	0.990982i	$-0.542781\pi$
$401$	−43093.1			−0.267990			−0.133995	+	0.990982i	$0.542781\pi$
$402$		0			0
$403$	−90295.2	+	90295.2i	−0.555974	+	0.555974i
$404$			14104.7i			0.0864177i
$405$		0			0
$406$	−149286.			−0.905665
$407$	34758.6	+	34758.6i	0.209833	+	0.209833i
$408$		0			0
$409$			186090.i			1.11244i	0.831036	+	0.556219i	$0.187748\pi$
$409$			186090.i			1.11244i	−0.831036	+	0.556219i	$0.812252\pi$
$410$	−57262.2	−	79570.3i	−0.340644	−	0.473351i
$411$		0			0
$412$	−19314.1	−	19314.1i	−0.113784	−	0.113784i
$413$	−14554.0	+	14554.0i	−0.0853261	+	0.0853261i
$414$		0			0
$415$	118001.	−	84918.6i	0.685157	−	0.493068i
$416$	57247.0			0.330800
$417$		0			0
$418$	−91157.7	+	91157.7i	−0.521724	+	0.521724i
$419$			101699.i			0.579278i	0.957136	+	0.289639i	$0.0935352\pi$
$419$			101699.i			0.579278i	−0.957136	+	0.289639i	$0.906465\pi$
$420$		0			0
$421$	−22533.0			−0.127132			−0.0635659	−	0.997978i	$-0.520247\pi$
$421$	−22533.0			−0.127132			−0.0635659	+	0.997978i	$0.520247\pi$
$422$	30940.3	+	30940.3i	0.173740	+	0.173740i
$423$		0			0
$424$			44116.3i			0.245396i
$425$	27988.5	+	56183.4i	0.154953	+	0.311050i
$426$		0			0
$427$	−186897.	−	186897.i	−1.02505	−	1.02505i
$428$	34232.2	−	34232.2i	0.186873	−	0.186873i
$429$		0			0
$430$	−56098.6	−	9145.90i	−0.303400	−	0.0494641i
$431$	−210598.			−1.13370			−0.566852	−	0.823820i	$-0.691839\pi$
$431$	−210598.			−1.13370			−0.566852	+	0.823820i	$0.691839\pi$
$432$		0			0
$433$	123405.	−	123405.i	0.658201	−	0.658201i	−0.296754	−	0.954954i	$-0.595904\pi$
$433$	123405.	−	123405.i	0.658201	−	0.658201i	0.954954	+	0.296754i	$0.0959040\pi$
$434$			71776.0i			0.381065i
$435$		0			0
$436$	−94556.3			−0.497413
$437$	23868.1	+	23868.1i	0.124984	+	0.124984i
$438$		0			0
$439$			265180.i			1.37598i	0.725721	+	0.687989i	$0.241506\pi$
$439$			265180.i			1.37598i	−0.725721	+	0.687989i	$0.758494\pi$
$440$	−76879.9	+	55326.0i	−0.397107	+	0.285775i
$441$		0			0
$442$	−63521.6	−	63521.6i	−0.325145	−	0.325145i
$443$	99815.9	−	99815.9i	0.508619	−	0.508619i	−0.405484	−	0.914102i	$-0.632897\pi$
$443$	99815.9	−	99815.9i	0.508619	−	0.508619i	0.914102	+	0.405484i	$0.132897\pi$
$444$		0			0
$445$	39871.5	−	244562.i	0.201346	−	1.23500i
$446$	115271.			0.579496
$447$		0			0
$448$	22752.9	−	22752.9i	0.113366	−	0.113366i
$449$		−	182934.i		−	0.907408i	−0.891152	−	0.453704i	$-0.850102\pi$
$449$		−	182934.i		−	0.907408i	0.891152	−	0.453704i	$-0.149898\pi$
$450$		0			0
$451$	−232136.			−1.14127
$452$	−12964.8	−	12964.8i	−0.0634585	−	0.0634585i
$453$		0			0
$454$		−	3536.95i		−	0.0171600i
$455$	490403.	+	79951.7i	2.36881	+	0.386193i
$456$		0			0
$457$	147497.	+	147497.i	0.706239	+	0.706239i	0.965742	−	0.259503i	$-0.0835588\pi$
$457$	147497.	+	147497.i	0.706239	+	0.706239i	−0.259503	+	0.965742i	$0.583559\pi$
$458$	24152.8	−	24152.8i	0.115143	−	0.115143i
$459$		0			0
$460$	14486.2	+	20129.7i	0.0684601	+	0.0951308i
$461$	354912.			1.67001			0.835006	−	0.550241i	$-0.185464\pi$
$461$	354912.			1.67001			0.835006	+	0.550241i	$0.185464\pi$
$462$		0			0
$463$	182475.	−	182475.i	0.851221	−	0.851221i	−0.139063	−	0.990284i	$-0.544409\pi$
$463$	182475.	−	182475.i	0.851221	−	0.851221i	0.990284	+	0.139063i	$0.0444090\pi$
$464$		−	53749.3i		−	0.249653i
$465$		0			0
$466$	98783.0			0.454894
$467$	−4348.30	−	4348.30i	−0.0199382	−	0.0199382i	0.697067	−	0.717006i	$-0.254488\pi$
$467$	−4348.30	−	4348.30i	−0.0199382	−	0.0199382i	−0.717006	+	0.697067i	$0.754488\pi$
$468$		0			0
$469$			251792.i			1.14471i
$470$	42524.4	−	260833.i	0.192505	−	1.18078i
$471$		0			0
$472$	−5240.04	−	5240.04i	−0.0235207	−	0.0235207i
$473$	−95171.3	+	95171.3i	−0.425386	+	0.425386i
$474$		0			0
$475$	54037.8	−	161322.i	0.239503	−	0.715001i
$476$	−50493.5			−0.222855
$477$		0			0
$478$	96375.5	−	96375.5i	0.421804	−	0.421804i
$479$			77346.0i			0.337106i	0.985693	+	0.168553i	$0.0539095\pi$
$479$			77346.0i			0.337106i	−0.985693	+	0.168553i	$0.946091\pi$
$480$		0			0
$481$	92842.6			0.401289
$482$	−110368.	−	110368.i	−0.475062	−	0.475062i
$483$		0			0
$484$			107159.i			0.457445i
$485$	220742.	+	306738.i	0.938428	+	1.30402i
$486$		0			0
$487$	77225.6	+	77225.6i	0.325614	+	0.325614i	0.850916	−	0.525302i	$-0.176048\pi$
$487$	77225.6	+	77225.6i	0.325614	+	0.325614i	−0.525302	+	0.850916i	$0.676048\pi$
$488$	67290.6	−	67290.6i	0.282562	−	0.282562i
$489$		0			0
$490$	88885.9	−	63966.1i	0.370204	−	0.266414i
$491$	−340217.			−1.41121			−0.705607	−	0.708603i	$-0.749326\pi$
$491$	−340217.			−1.41121			−0.705607	+	0.708603i	$0.749326\pi$
$492$		0			0
$493$	−59640.5	+	59640.5i	−0.245385	+	0.245385i
$494$			243488.i			0.997756i
$495$		0			0
$496$	−25842.4			−0.105043
$497$	−237263.	−	237263.i	−0.960542	−	0.960542i
$498$		0			0
$499$		−	331024.i		−	1.32941i	−0.747108	−	0.664703i	$-0.768558\pi$
$499$		−	331024.i		−	1.32941i	0.747108	−	0.664703i	$-0.231442\pi$
$500$	58257.5	−	110594.i	0.233030	−	0.442377i
$501$		0			0
$502$	139336.	+	139336.i	0.552910	+	0.552910i
$503$	123301.	−	123301.i	0.487338	−	0.487338i	−0.420127	−	0.907465i	$-0.638015\pi$
$503$	123301.	−	123301.i	0.487338	−	0.487338i	0.907465	+	0.420127i	$0.138015\pi$
$504$		0			0
$505$	−43503.0	−	7092.40i	−0.170583	−	0.0278106i
$506$	58725.7			0.229365
$507$		0			0
$508$	92579.7	−	92579.7i	0.358747	−	0.358747i
$509$		−	364729.i		−	1.40778i	−0.710309	−	0.703890i	$-0.751445\pi$
$509$		−	364729.i		−	1.40778i	0.710309	−	0.703890i	$-0.248555\pi$
$510$		0			0
$511$	610173.			2.33674
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$		0			0
$514$			46457.8i			0.175846i
$515$	69282.1	−	49858.3i	0.261220	−	0.187985i
$516$		0			0
$517$	−442504.	−	442504.i	−1.65553	−	1.65553i
$518$	36900.5	−	36900.5i	0.137522	−	0.137522i
$519$		0			0
$520$	−28785.9	+	176566.i	−0.106457	+	0.652979i
$521$	203461.			0.749560			0.374780	−	0.927114i	$-0.377718\pi$
$521$	203461.			0.749560			0.374780	+	0.927114i	$0.377718\pi$
$522$		0			0
$523$	72655.5	−	72655.5i	0.265623	−	0.265623i	−0.561711	−	0.827334i	$-0.689857\pi$
$523$	72655.5	−	72655.5i	0.265623	−	0.265623i	0.827334	+	0.561711i	$0.189857\pi$
$524$		−	524.984i		−	0.00191198i
$525$		0			0
$526$	−347247.			−1.25507
$527$	28674.8	+	28674.8i	0.103248	+	0.103248i
$528$		0			0
$529$			264465.i			0.945053i
$530$	−136067.	−	22183.4i	−0.484397	−	0.0789725i
$531$		0			0
$532$	96775.0	+	96775.0i	0.341932	+	0.341932i
$533$	−310026.	+	310026.i	−1.09130	+	1.09130i
$534$		0			0
$535$	88368.4	+	122795.i	0.308738	+	0.429015i
$536$	−90655.8			−0.315548
$537$		0			0
$538$	186879.	−	186879.i	0.645647	−	0.645647i
$539$		−	259313.i		−	0.892580i
$540$		0			0
$541$	−91367.2			−0.312173			−0.156087	−	0.987743i	$-0.549888\pi$
$541$	−91367.2			−0.312173			−0.156087	+	0.987743i	$0.549888\pi$
$542$	−21713.0	−	21713.0i	−0.0739131	−	0.0739131i
$543$		0			0
$544$		−	18179.8i		−	0.0614315i
$545$	47546.5	−	291638.i	0.160076	−	0.981863i
$546$		0			0
$547$	−9895.50	−	9895.50i	−0.0330722	−	0.0330722i	0.690377	−	0.723450i	$-0.257445\pi$
$547$	−9895.50	−	9895.50i	−0.0330722	−	0.0330722i	−0.723450	+	0.690377i	$0.757445\pi$
$548$	4635.51	−	4635.51i	0.0154361	−	0.0154361i
$549$		0			0
$550$	−131983.	−	264939.i	−0.436307	−	0.875832i
$551$	228612.			0.753001
$552$		0			0
$553$	−207384.	+	207384.i	−0.678150	+	0.678150i
$554$			260859.i			0.849935i
$555$		0			0
$556$	−289266.			−0.935724
$557$	306800.	+	306800.i	0.988883	+	0.988883i	0.999939	−	0.0110558i	$-0.00351924\pi$
$557$	306800.	+	306800.i	0.988883	+	0.988883i	−0.0110558	+	0.999939i	$0.503519\pi$
$558$		0			0
$559$			254209.i			0.813518i
$560$	58735.3	+	81617.4i	0.187294	+	0.260259i
$561$		0			0
$562$	17338.7	+	17338.7i	0.0548963	+	0.0548963i
$563$	−331132.	+	331132.i	−1.04468	+	1.04468i	−0.0457279	+	0.998954i	$0.514561\pi$
$563$	−331132.	+	331132.i	−1.04468	+	1.04468i	−0.998954	+	0.0457279i	$0.985439\pi$
$564$		0			0
$565$	46506.4	−	33467.9i	0.145685	−	0.104841i
$566$	−94988.2			−0.296508
$567$		0			0
$568$	85424.5	−	85424.5i	0.264780	−	0.264780i
$569$			257399.i			0.795028i	0.917596	+	0.397514i	$0.130127\pi$
$569$			257399.i			0.795028i	−0.917596	+	0.397514i	$0.869873\pi$
$570$		0			0
$571$	−622495.			−1.90925			−0.954626	−	0.297807i	$-0.903745\pi$
$571$	−622495.			−1.90925			−0.954626	+	0.297807i	$0.903745\pi$
$572$	299543.	+	299543.i	0.915520	+	0.915520i
$573$		0			0
$574$			246441.i			0.747978i
$575$	−69369.7	+	34557.4i	−0.209814	+	0.104521i
$576$		0			0
$577$	−23928.8	−	23928.8i	−0.0718736	−	0.0718736i	0.670256	−	0.742130i	$-0.266184\pi$
$577$	−23928.8	−	23928.8i	−0.0718736	−	0.0718736i	−0.742130	+	0.670256i	$0.766184\pi$
$578$	146870.	−	146870.i	0.439619	−	0.439619i
$579$		0			0
$580$	165778.	+	27027.2i	0.492799	+	0.0803424i
$581$	−365467.			−1.08267
$582$		0			0
$583$	−230838.	+	230838.i	−0.679156	+	0.679156i
$584$			219688.i			0.644139i
$585$		0			0
$586$	220309.			0.641559
$587$	−181136.	−	181136.i	−0.525690	−	0.525690i	0.393595	−	0.919284i	$-0.371231\pi$
$587$	−181136.	−	181136.i	−0.525690	−	0.525690i	−0.919284	+	0.393595i	$0.871231\pi$
$588$		0			0
$589$		−	109915.i		−	0.316831i
$590$	18796.6	−	13526.9i	0.0539978	−	0.0388591i
$591$		0			0
$592$	13285.7	+	13285.7i	0.0379089	+	0.0379089i
$593$	235890.	−	235890.i	0.670812	−	0.670812i	−0.287091	−	0.957903i	$-0.592688\pi$
$593$	235890.	−	235890.i	0.670812	−	0.670812i	0.957903	+	0.287091i	$0.0926883\pi$
$594$		0			0
$595$	25390.1	−	155736.i	0.0717183	−	0.439902i
$596$	−17151.5			−0.0482847
$597$		0			0
$598$	78430.2	−	78430.2i	0.219322	−	0.219322i
$599$		−	141629.i		−	0.394728i	−0.980330	−	0.197364i	$-0.936762\pi$
$599$		−	141629.i		−	0.394728i	0.980330	−	0.197364i	$-0.0632381\pi$
$600$		0			0
$601$	−564417.			−1.56261			−0.781306	−	0.624148i	$-0.785446\pi$
$601$	−564417.			−1.56261			−0.781306	+	0.624148i	$0.785446\pi$
$602$	101036.	+	101036.i	0.278794	+	0.278794i
$603$		0			0
$604$		−	71524.7i		−	0.196057i
$605$	−330509.	−	53883.8i	−0.902969	−	0.147213i
$606$		0			0
$607$	247253.	+	247253.i	0.671064	+	0.671064i	0.957961	−	0.286898i	$-0.0926240\pi$
$607$	247253.	+	247253.i	0.671064	+	0.671064i	−0.286898	+	0.957961i	$0.592624\pi$
$608$	−34843.0	+	34843.0i	−0.0942560	+	0.0942560i
$609$		0			0
$610$	173707.	+	241379.i	0.466828	+	0.648694i
$611$	−1.18196e6			−3.16606
$612$		0			0
$613$	−163758.	+	163758.i	−0.435794	+	0.435794i	−0.890594	−	0.454800i	$-0.849711\pi$
$613$	−163758.	+	163758.i	−0.435794	+	0.435794i	0.454800	+	0.890594i	$0.349711\pi$
$614$			47844.5i			0.126910i
$615$		0			0
$616$	238108.			0.627499
$617$	−273782.	−	273782.i	−0.719176	−	0.719176i	0.249260	−	0.968437i	$-0.419812\pi$
$617$	−273782.	−	273782.i	−0.719176	−	0.719176i	−0.968437	+	0.249260i	$0.919812\pi$
$618$		0			0
$619$		−	428345.i		−	1.11792i	−0.829194	−	0.558962i	$-0.811200\pi$
$619$		−	428345.i		−	1.11792i	0.829194	−	0.558962i	$-0.188800\pi$
$620$	12994.5	−	79705.0i	0.0338047	−	0.207349i
$621$		0			0
$622$	130569.	+	130569.i	0.337489	+	0.337489i
$623$	−440465.	+	440465.i	−1.13484	+	1.13484i
$624$		0			0
$625$	311809.	+	235293.i	0.798231	+	0.602351i
$626$	−25673.8			−0.0655151
$627$		0			0
$628$	−144263.	+	144263.i	−0.365793	+	0.365793i
$629$		−	29483.8i		−	0.0745216i
$630$		0			0
$631$	108870.			0.273432			0.136716	−	0.990610i	$-0.456345\pi$
$631$	108870.			0.273432			0.136716	+	0.990610i	$0.456345\pi$
$632$	−74667.1	−	74667.1i	−0.186937	−	0.186937i
$633$		0			0
$634$		−	88400.5i		−	0.219926i
$635$	238989.	+	332094.i	0.592694	+	0.823595i
$636$		0			0
$637$	−346322.	−	346322.i	−0.853495	−	0.853495i
$638$	281242.	−	281242.i	0.690937	−	0.690937i
$639$		0			0
$640$	−29385.7	+	21147.2i	−0.0717423	+	0.0516288i
$641$	501643.			1.22090			0.610448	−	0.792056i	$-0.290989\pi$
$641$	501643.			1.22090			0.610448	+	0.792056i	$0.290989\pi$
$642$		0			0
$643$	−117251.	+	117251.i	−0.283592	+	0.283592i	−0.834540	−	0.550948i	$-0.814266\pi$
$643$	−117251.	+	117251.i	−0.283592	+	0.283592i	0.550948	+	0.834540i	$0.314266\pi$
$644$		−	62344.5i		−	0.150323i
$645$		0			0
$646$	77324.1			0.185289
$647$	362031.	+	362031.i	0.864843	+	0.864843i	0.991896	−	0.127053i	$-0.0405519\pi$
$647$	362031.	+	362031.i	0.864843	+	0.864843i	−0.127053	+	0.991896i	$0.540552\pi$
$648$		0			0
$649$		−	54836.8i		−	0.130192i
$650$	−530103.	−	177568.i	−1.25468	−	0.420279i
$651$		0			0
$652$	−54872.0	−	54872.0i	−0.129079	−	0.129079i
$653$	411293.	−	411293.i	0.964552	−	0.964552i	−0.0348413	−	0.999393i	$-0.511093\pi$
$653$	411293.	−	411293.i	0.964552	−	0.964552i	0.999393	+	0.0348413i	$0.0110926\pi$
$654$		0			0
$655$	1619.20	+	263.982i	0.00377413	+	0.000615306i
$656$	−88729.0			−0.206185
$657$		0			0
$658$	−469772.	+	469772.i	−1.08501	+	1.08501i
$659$		−	291952.i		−	0.672265i	−0.941815	−	0.336133i	$-0.890881\pi$
$659$		−	291952.i		−	0.672265i	0.941815	−	0.336133i	$-0.109119\pi$
$660$		0			0
$661$	757270.			1.73320			0.866599	−	0.499006i	$-0.166301\pi$
$661$	757270.			1.73320			0.866599	+	0.499006i	$0.166301\pi$
$662$	−98217.4	−	98217.4i	−0.224116	−	0.224116i
$663$		0			0
$664$		−	131583.i		−	0.298445i
$665$	−347143.	+	249819.i	−0.784992	+	0.564914i
$666$		0			0
$667$	−73638.3	−	73638.3i	−0.165521	−	0.165521i
$668$	−299514.	+	299514.i	−0.671219	+	0.671219i
$669$		0			0
$670$	45585.2	−	279608.i	0.101549	−	0.622873i
$671$	704193.			1.56404
$672$		0			0
$673$	310335.	−	310335.i	0.685173	−	0.685173i	−0.275988	−	0.961161i	$-0.589005\pi$
$673$	310335.	−	310335.i	0.685173	−	0.685173i	0.961161	+	0.275988i	$0.0890050\pi$
$674$		−	571265.i		−	1.25753i
$675$		0			0
$676$	571613.			1.25086
$677$	−9203.97	−	9203.97i	−0.0200816	−	0.0200816i	0.696995	−	0.717076i	$-0.254520\pi$
$677$	−9203.97	−	9203.97i	−0.0200816	−	0.0200816i	−0.717076	+	0.696995i	$0.754520\pi$
$678$		0			0
$679$		−	950012.i		−	2.06058i
$680$	56071.5	+	9141.49i	0.121262	+	0.0197697i
$681$		0			0
$682$	−135220.	−	135220.i	−0.290717	−	0.290717i
$683$	421590.	−	421590.i	0.903750	−	0.903750i	−0.0920080	−	0.995758i	$-0.529329\pi$
$683$	421590.	−	421590.i	0.903750	−	0.903750i	0.995758	+	0.0920080i	$0.0293285\pi$
$684$		0			0
$685$	11966.3	+	16628.1i	0.0255023	+	0.0354374i
$686$	151502.			0.321937
$687$		0			0
$688$	−36377.1	+	36377.1i	−0.0768514	+	0.0768514i
$689$			616584.i			1.29883i
$690$		0			0
$691$	102275.			0.214197			0.107098	−	0.994248i	$-0.465844\pi$
$691$	102275.			0.214197			0.107098	+	0.994248i	$0.465844\pi$
$692$	261106.	+	261106.i	0.545261	+	0.545261i
$693$		0			0
$694$			85601.3i			0.177730i
$695$	145454.	−	892177.i	0.301131	−	1.84706i
$696$		0			0
$697$	98454.3	+	98454.3i	0.202660	+	0.202660i
$698$	68182.4	−	68182.4i	0.139946	−	0.139946i
$699$		0			0
$700$	−281265.	+	140116.i	−0.574010	+	0.285951i
$701$	685359.			1.39471			0.697353	−	0.716728i	$-0.254361\pi$
$701$	685359.			1.39471			0.697353	+	0.716728i	$0.254361\pi$
$702$		0			0
$703$	−56508.1	+	56508.1i	−0.114341	+	0.114341i
$704$			85728.9i			0.172974i
$705$		0			0
$706$	−115.016			−0.000230753
$707$	78350.6	+	78350.6i	0.156749	+	0.156749i
$708$		0			0
$709$		−	164715.i		−	0.327673i	−0.986487	−	0.163837i	$-0.947613\pi$
$709$		−	164715.i		−	0.327673i	0.986487	−	0.163837i	$-0.0523870\pi$
$710$	220518.	+	306428.i	0.437449	+	0.607871i
$711$		0			0
$712$	−158586.	−	158586.i	−0.312827	−	0.312827i
$713$	−35404.9	+	35404.9i	−0.0696441	+	0.0696441i
$714$		0			0
$715$	−1.07450e6	+	773254.i	−2.10181	+	1.51255i
$716$	−51169.5			−0.0998126
$717$		0			0
$718$	347885.	−	347885.i	0.674818	−	0.674818i
$719$			782798.i			1.51423i	0.653282	+	0.757115i	$0.273392\pi$
$719$			782798.i			1.51423i	−0.653282	+	0.757115i	$0.726608\pi$
$720$		0			0
$721$	−214577.			−0.412774
$722$	112444.	+	112444.i	0.215706	+	0.215706i
$723$		0			0
$724$			392208.i			0.748236i
$725$	−166719.	+	497715.i	−0.317182	+	0.946900i
$726$		0			0
$727$	659110.	+	659110.i	1.24706	+	1.24706i	0.957010	+	0.290054i	$0.0936732\pi$
$727$	659110.	+	659110.i	1.24706	+	1.24706i	0.290054	+	0.957010i	$0.406327\pi$
$728$	318002.	−	318002.i	0.600021	−	0.600021i
$729$		0			0
$730$	−677578.	−	110467.i	−1.27149	−	0.207295i
$731$	80728.6			0.151075
$732$		0			0
$733$	356952.	−	356952.i	0.664358	−	0.664358i	−0.292046	−	0.956404i	$-0.594336\pi$
$733$	356952.	−	356952.i	0.664358	−	0.664358i	0.956404	+	0.292046i	$0.0943361\pi$
$734$		−	167816.i		−	0.311489i
$735$		0			0
$736$	22446.6			0.0414377
$737$	−474354.	−	474354.i	−0.873309	−	0.873309i
$738$		0			0
$739$			231725.i			0.424311i	0.977236	+	0.212156i	$0.0680483\pi$
$739$			231725.i			0.424311i	−0.977236	+	0.212156i	$0.931952\pi$
$740$	−47657.4	+	34296.3i	−0.0870296	+	0.0626302i
$741$		0			0
$742$	245062.	+	245062.i	0.445111	+	0.445111i
$743$	35964.9	−	35964.9i	0.0651480	−	0.0651480i	−0.673782	−	0.738930i	$-0.735331\pi$
$743$	35964.9	−	35964.9i	0.0651480	−	0.0651480i	0.738930	+	0.673782i	$0.235331\pi$
$744$		0			0
$745$	8624.43	−	52900.1i	0.0155388	−	0.0953111i
$746$	−263501.			−0.473483
$747$		0			0
$748$	95125.3	−	95125.3i	0.170017	−	0.170017i
$749$		−	380314.i		−	0.677920i
$750$		0			0
$751$	702045.			1.24476			0.622379	−	0.782716i	$-0.286166\pi$
$751$	702045.			1.24476			0.622379	+	0.782716i	$0.286166\pi$
$752$	−169137.	−	169137.i	−0.299091	−	0.299091i
$753$		0			0
$754$		−	751216.i		−	1.32136i
$755$	220602.	+	35965.3i	0.387004	+	0.0630943i
$756$		0			0
$757$	−111880.	−	111880.i	−0.195236	−	0.195236i	0.602718	−	0.797954i	$-0.294084\pi$
$757$	−111880.	−	111880.i	−0.195236	−	0.195236i	−0.797954	+	0.602718i	$0.794084\pi$
$758$	21673.9	−	21673.9i	0.0377224	−	0.0377224i
$759$		0			0
$760$	−89945.3	−	124986.i	−0.155722	−	0.216389i
$761$	579015.			0.999817			0.499908	−	0.866078i	$-0.333367\pi$
$761$	579015.			0.999817			0.499908	+	0.866078i	$0.333367\pi$
$762$		0			0
$763$	−525252.	+	525252.i	−0.902232	+	0.902232i
$764$		−	319592.i		−	0.547531i
$765$		0			0
$766$	−89310.0			−0.152210
$767$	−73236.4	−	73236.4i	−0.124491	−	0.124491i
$768$		0			0
$769$			472110.i			0.798344i	0.916876	+	0.399172i	$0.130702\pi$
$769$			472110.i			0.798344i	−0.916876	+	0.399172i	$0.869298\pi$
$770$	−119730.	+	734392.i	−0.201939	+	1.23864i
$771$		0			0
$772$	−189993.	−	189993.i	−0.318789	−	0.318789i
$773$	20353.7	−	20353.7i	0.0340631	−	0.0340631i	−0.689870	−	0.723933i	$-0.742332\pi$
$773$	20353.7	−	20353.7i	0.0340631	−	0.0340631i	0.723933	+	0.689870i	$0.242332\pi$
$774$		0			0
$775$	239298.	+	80157.4i	0.398416	+	0.133457i
$776$	342044.			0.568013
$777$		0			0
$778$	−407768.	+	407768.i	−0.673680	+	0.673680i
$779$		−	377391.i		−	0.621895i
$780$		0			0
$781$	893963.			1.46561
$782$	−24906.9	−	24906.9i	−0.0407293	−	0.0407293i
$783$		0			0
$784$		−	99116.8i		−	0.161256i
$785$	−372406.	−	517488.i	−0.604335	−	0.839771i
$786$		0			0
$787$	640630.	+	640630.i	1.03433	+	1.03433i	0.999390	+	0.0349373i	$0.0111232\pi$
$787$	640630.	+	640630.i	1.03433	+	1.03433i	0.0349373	+	0.999390i	$0.488877\pi$
$788$	−21800.7	+	21800.7i	−0.0351090	+	0.0351090i
$789$		0			0
$790$	267840.	−	192749.i	0.429161	−	0.308843i
$791$	−144037.			−0.230208
$792$		0			0
$793$	940474.	−	940474.i	1.49555	−	1.49555i
$794$			469194.i			0.744238i
$795$		0			0
$796$	−505700.			−0.798118
$797$	−542782.	−	542782.i	−0.854494	−	0.854494i	0.136189	−	0.990683i	$-0.456515\pi$
$797$	−542782.	−	542782.i	−0.854494	−	0.854494i	−0.990683	+	0.136189i	$0.956515\pi$
$798$		0			0
$799$			375352.i			0.587956i
$800$	−50447.5	−	101267.i	−0.0788243	−	0.158230i
$801$		0			0
$802$	−86186.2	−	86186.2i	−0.133995	−	0.133995i
$803$	−1.14951e6	+	1.14951e6i	−1.78271	+	1.78271i
$804$		0			0
$805$	192288.	+	31349.2i	0.296729	+	0.0483765i
$806$	−361181.			−0.555974
$807$		0			0
$808$	−28209.5	+	28209.5i	−0.0432088	+	0.0432088i
$809$		−	1.09699e6i		−	1.67613i	−0.545571	−	0.838065i	$-0.683687\pi$
$809$		−	1.09699e6i		−	1.67613i	0.545571	−	0.838065i	$-0.316313\pi$
$810$		0			0
$811$	−711398.			−1.08161			−0.540805	−	0.841148i	$-0.681880\pi$
$811$	−711398.			−1.08161			−0.540805	+	0.841148i	$0.681880\pi$
$812$	−298572.	−	298572.i	−0.452832	−	0.452832i
$813$		0			0
$814$			139034.i			0.209833i
$815$	196832.	−	141649.i	0.296334	−	0.213254i
$816$		0			0
$817$	−154723.	−	154723.i	−0.231798	−	0.231798i
$818$	−372179.	+	372179.i	−0.556219	+	0.556219i
$819$		0			0
$820$	44616.3	−	273665.i	0.0663538	−	0.406997i
$821$	566243.			0.840071			0.420036	−	0.907508i	$-0.362018\pi$
$821$	566243.			0.840071			0.420036	+	0.907508i	$0.362018\pi$
$822$		0			0
$823$	−678523.	+	678523.i	−1.00176	+	1.00176i	−0.00176504	+	0.999998i	$0.500562\pi$
$823$	−678523.	+	678523.i	−1.00176	+	1.00176i	−0.999998	+	0.00176504i	$0.999438\pi$
$824$		−	77256.6i		−	0.113784i
$825$		0			0
$826$	−58215.9			−0.0853261
$827$	822466.	+	822466.i	1.20256	+	1.20256i	0.973385	+	0.229174i	$0.0736026\pi$
$827$	822466.	+	822466.i	1.20256	+	1.20256i	0.229174	+	0.973385i	$0.426397\pi$
$828$		0			0
$829$		−	1.26805e6i		−	1.84514i	−0.385832	−	0.922569i	$-0.626086\pi$
$829$		−	1.26805e6i		−	1.84514i	0.385832	−	0.922569i	$-0.373914\pi$
$830$	405839.	+	66165.0i	0.589112	+	0.0960445i
$831$		0			0
$832$	114494.	+	114494.i	0.165400	+	0.165400i
$833$	−109981.	+	109981.i	−0.158499	+	0.158499i
$834$		0			0
$835$	−773178.	−	1.07439e6i	−1.10894	−	1.54095i
$836$	−364631.			−0.521724
$837$		0			0
$838$	−203397.	+	203397.i	−0.289639	+	0.289639i
$839$			487091.i			0.691968i	0.938240	+	0.345984i	$0.112455\pi$
$839$			487091.i			0.691968i	−0.938240	+	0.345984i	$0.887545\pi$
$840$		0			0
$841$	1962.99			0.00277541
$842$	−45065.9	−	45065.9i	−0.0635659	−	0.0635659i
$843$		0			0
$844$			123761.i			0.173740i
$845$	−287429.	+	1.76301e6i	−0.402547	+	2.46912i
$846$		0			0
$847$	595260.	+	595260.i	0.829736	+	0.829736i
$848$	−88232.7	+	88232.7i	−0.122698	+	0.122698i
$849$		0			0
$850$	−56389.8	+	168344.i	−0.0780482	+	0.233002i
$851$	36403.7			0.0502675
$852$		0			0
$853$	10645.4	−	10645.4i	0.0146307	−	0.0146307i	−0.699754	−	0.714384i	$-0.746707\pi$
$853$	10645.4	−	10645.4i	0.0146307	−	0.0146307i	0.714384	+	0.699754i	$0.246707\pi$
$854$		−	747586.i		−	1.02505i
$855$		0			0
$856$	136929.			0.186873
$857$	692563.	+	692563.i	0.942970	+	0.942970i	0.998459	−	0.0554896i	$-0.0176720\pi$
$857$	692563.	+	692563.i	0.942970	+	0.942970i	−0.0554896	+	0.998459i	$0.517672\pi$
$858$		0			0
$859$			745974.i			1.01097i	0.862836	+	0.505484i	$0.168686\pi$
$859$			745974.i			1.01097i	−0.862836	+	0.505484i	$0.831314\pi$
$860$	−93905.5	−	130489.i	−0.126968	−	0.176432i
$861$		0			0
$862$	−421196.	−	421196.i	−0.566852	−	0.566852i
$863$	−259362.	+	259362.i	−0.348245	+	0.348245i	−0.859456	−	0.511211i	$-0.829197\pi$
$863$	−259362.	+	259362.i	−0.348245	+	0.348245i	0.511211	+	0.859456i	$0.329197\pi$
$864$		0			0
$865$	−936618.	+	674030.i	−1.25179	+	0.900838i
$866$	493621.			0.658201
$867$		0			0
$868$	−143552.	+	143552.i	−0.190533	+	0.190533i
$869$		−	781388.i		−	1.03473i
$870$		0			0
$871$	−1.26703e6			−1.67013
$872$	−189113.	−	189113.i	−0.248707	−	0.248707i
$873$		0			0
$874$			95472.3i			0.124984i
$875$	−290725.	−	937956.i	−0.379723	−	1.22509i
$876$		0			0
$877$	−191986.	−	191986.i	−0.249615	−	0.249615i	0.571197	−	0.820813i	$-0.306479\pi$
$877$	−191986.	−	191986.i	−0.249615	−	0.249615i	−0.820813	+	0.571197i	$0.806479\pi$
$878$	−530360.	+	530360.i	−0.687989	+	0.687989i
$879$		0			0
$880$	−264412.	−	43107.8i	−0.341441	−	0.0556660i
$881$	−1.08074e6			−1.39241			−0.696207	−	0.717841i	$-0.745130\pi$
$881$	−1.08074e6			−1.39241			−0.696207	+	0.717841i	$0.745130\pi$
$882$		0			0
$883$	294604.	−	294604.i	0.377848	−	0.377848i	−0.492477	−	0.870325i	$-0.663909\pi$
$883$	294604.	−	294604.i	0.377848	−	0.377848i	0.870325	+	0.492477i	$0.163909\pi$
$884$		−	254086.i		−	0.325145i
$885$		0			0
$886$	399264.			0.508619
$887$	373328.	+	373328.i	0.474507	+	0.474507i	0.903370	−	0.428862i	$-0.141085\pi$
$887$	373328.	+	373328.i	0.474507	+	0.474507i	−0.428862	+	0.903370i	$0.641085\pi$
$888$		0			0
$889$		−	1.02854e6i		−	1.30143i
$890$	568866.	−	409380.i	0.718175	−	0.516829i
$891$		0			0
$892$	230542.	+	230542.i	0.289748	+	0.289748i
$893$	719392.	−	719392.i	0.902117	−	0.902117i
$894$		0			0
$895$	25730.0	−	157821.i	0.0321213	−	0.197024i
$896$	91011.7			0.113366
$897$		0			0
$898$	365869.	−	365869.i	0.453704	−	0.453704i
$899$			339113.i			0.419590i
$900$		0			0
$901$	195807.			0.241201
$902$	−464273.	−	464273.i	−0.570637	−	0.570637i
$903$		0			0
$904$		−	51859.3i		−	0.0634585i
$905$	−1.20968e6	−	197217.i	−1.47697	−	0.240795i
$906$		0			0
$907$	−342694.	−	342694.i	−0.416574	−	0.416574i	0.467447	−	0.884021i	$-0.345174\pi$
$907$	−342694.	−	342694.i	−0.416574	−	0.416574i	−0.884021	+	0.467447i	$0.845174\pi$
$908$	7073.89	−	7073.89i	0.00857999	−	0.00857999i
$909$		0			0
$910$	820903.	+	1.14071e6i	0.991309	+	1.37750i
$911$	−653388.			−0.787290			−0.393645	−	0.919263i	$-0.628786\pi$
$911$	−653388.			−0.787290			−0.393645	+	0.919263i	$0.628786\pi$
$912$		0			0
$913$	688506.	−	688506.i	0.825974	−	0.825974i
$914$			589989.i			0.706239i
$915$		0			0
$916$	96611.0			0.115143
$917$	−2916.24	−	2916.24i	−0.00346804	−	0.00346804i
$918$		0			0
$919$		−	316752.i		−	0.375050i	−0.982260	−	0.187525i	$-0.939953\pi$
$919$		−	316752.i		−	0.375050i	0.982260	−	0.187525i	$-0.0600465\pi$
$920$	−11287.0	+	69231.7i	−0.0133353	+	0.0817955i
$921$		0			0
$922$	709825.	+	709825.i	0.835006	+	0.835006i
$923$	1.19392e6	−	1.19392e6i	1.40143	−	1.40143i
$924$		0			0
$925$	−81815.4	−	164234.i	−0.0956206	−	0.191947i
$926$	729901.			0.851221
$927$		0			0
$928$	107499.	−	107499.i	0.124826	−	0.124826i
$929$			1.39646e6i			1.61807i	0.587759	+	0.809036i	$0.300010\pi$
$929$			1.39646e6i			1.61807i	−0.587759	+	0.809036i	$0.699990\pi$
$930$		0			0
$931$	421574.			0.486378
$932$	197566.	+	197566.i	0.227447	+	0.227447i
$933$		0			0
$934$		−	17393.2i		−	0.0199382i
$935$	245560.	+	341226.i	0.280889	+	0.390318i
$936$		0			0
$937$	81884.2	+	81884.2i	0.0932655	+	0.0932655i	0.752200	−	0.658935i	$-0.228993\pi$
$937$	81884.2	+	81884.2i	0.0932655	+	0.0932655i	−0.658935	+	0.752200i	$0.728993\pi$
$938$	−503585.	+	503585.i	−0.572357	+	0.572357i
$939$		0			0
$940$	606716.	−	436618.i	0.686641	−	0.494136i
$941$	−1.67094e6			−1.88705			−0.943524	−	0.331305i	$-0.892511\pi$
$941$	−1.67094e6			−1.88705			−0.943524	+	0.331305i	$0.892511\pi$
$942$		0			0
$943$	−121562.	+	121562.i	−0.136702	+	0.136702i
$944$		−	20960.2i		−	0.0235207i
$945$		0			0
$946$	−380685.			−0.425386
$947$	−689602.	−	689602.i	−0.768950	−	0.768950i	0.208971	−	0.977922i	$-0.432988\pi$
$947$	−689602.	−	689602.i	−0.768950	−	0.768950i	−0.977922	+	0.208971i	$0.932988\pi$
$948$		0			0
$949$			3.07042e6i			3.40930i
$950$	430720.	−	214569.i	0.477252	−	0.237749i
$951$		0			0
$952$	−100987.	−	100987.i	−0.111427	−	0.111427i
$953$	−150337.	+	150337.i	−0.165532	+	0.165532i	−0.785012	−	0.619480i	$-0.787343\pi$
$953$	−150337.	+	150337.i	−0.165532	+	0.165532i	0.619480	+	0.785012i	$0.287343\pi$
$954$		0			0
$955$	985710.	+	160703.i	1.08079	+	0.176204i
$956$	385502.			0.421804
$957$		0			0
$958$	−154692.	+	154692.i	−0.168553	+	0.168553i
$959$		−	51499.7i		−	0.0559974i
$960$		0			0
$961$	−760477.			−0.823454
$962$	185685.	+	185685.i	0.200644	+	0.200644i
$963$		0			0
$964$		−	441473.i		−	0.475062i
$965$	681527.	−	490456.i	0.731861	−	0.526678i
$966$		0			0
$967$	−312723.	−	312723.i	−0.334432	−	0.334432i	0.519835	−	0.854267i	$-0.325993\pi$
$967$	−312723.	−	312723.i	−0.334432	−	0.334432i	−0.854267	+	0.519835i	$0.825993\pi$
$968$	−214319.	+	214319.i	−0.228723	+	0.228723i
$969$		0			0
$970$	−171993.	+	1.05496e6i	−0.182796	+	1.12122i
$971$	−1.16534e6			−1.23598			−0.617992	−	0.786185i	$-0.712054\pi$
$971$	−1.16534e6			−1.23598			−0.617992	+	0.786185i	$0.712054\pi$
$972$		0			0
$973$	−1.60685e6	+	1.60685e6i	−1.69726	+	1.69726i
$974$			308903.i			0.325614i
$975$		0			0
$976$	269162.			0.282562
$977$	748461.	+	748461.i	0.784115	+	0.784115i	0.980522	−	0.196407i	$-0.0629274\pi$
$977$	748461.	+	748461.i	0.784115	+	0.784115i	−0.196407	+	0.980522i	$0.562927\pi$
$978$		0			0
$979$		−	1.65959e6i		−	1.73156i
$980$	305704.	+	49839.7i	0.318309	+	0.0518947i
$981$		0			0
$982$	−680434.	−	680434.i	−0.705607	−	0.705607i
$983$	542812.	−	542812.i	0.561749	−	0.561749i	−0.368055	−	0.929804i	$-0.619976\pi$
$983$	542812.	−	542812.i	0.561749	−	0.561749i	0.929804	+	0.368055i	$0.119976\pi$
$984$		0			0
$985$	−56277.3	−	78201.8i	−0.0580044	−	0.0806017i
$986$	−238562.			−0.245385
$987$		0			0
$988$	−486977.	+	486977.i	−0.498878	+	0.498878i
$989$			99675.8i			0.101905i
$990$		0			0
$991$	1.08269e6			1.10245			0.551224	−	0.834357i	$-0.314161\pi$
$991$	1.08269e6			1.10245			0.551224	+	0.834357i	$0.314161\pi$
$992$	−51684.7	−	51684.7i	−0.0525217	−	0.0525217i
$993$		0			0
$994$		−	949050.i		−	0.960542i
$995$	254285.	−	1.55972e6i	0.256847	−	1.57544i
$996$		0			0
$997$	25593.2	+	25593.2i	0.0257475	+	0.0257475i	0.719863	−	0.694116i	$-0.244204\pi$
$997$	25593.2	+	25593.2i	0.0257475	+	0.0257475i	−0.694116	+	0.719863i	$0.744204\pi$
$998$	662047.	−	662047.i	0.664703	−	0.664703i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.5.g.e.37.1		4
3.2	odd	2		30.5.f.a.7.1	✓	4
5.2	odd	4		450.5.g.f.343.1		4
5.3	odd	4	inner	90.5.g.e.73.1		4
5.4	even	2		450.5.g.f.307.1		4
12.11	even	2		240.5.bg.b.97.2		4
15.2	even	4		150.5.f.e.43.2		4
15.8	even	4		30.5.f.a.13.1	yes	4
15.14	odd	2		150.5.f.e.7.2		4
60.23	odd	4		240.5.bg.b.193.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.5.f.a.7.1	✓	4	3.2	odd	2
30.5.f.a.13.1	yes	4	15.8	even	4
90.5.g.e.37.1		4	1.1	even	1	trivial
90.5.g.e.73.1		4	5.3	odd	4	inner
150.5.f.e.7.2		4	15.14	odd	2
150.5.f.e.43.2		4	15.2	even	4
240.5.bg.b.97.2		4	12.11	even	2
240.5.bg.b.193.2		4	60.23	odd	4
450.5.g.f.307.1		4	5.4	even	2
450.5.g.f.343.1		4	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	90.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +8.00000i q^{4} +(-24.6742 - 4.02270i) q^{5} +(44.4393 + 44.4393i) q^{7} +(-16.0000 + 16.0000i) q^{8} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +8.00000i q^{4} +(-24.6742 - 4.02270i) q^{5} +(44.4393 + 44.4393i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(-41.3031 - 57.3939i) q^{10} -167.439 q^{11} +(-223.621 + 223.621i) q^{13} +177.757i q^{14} -64.0000 q^{16} +(71.0148 + 71.0148i) q^{17} -272.211i q^{19} +(32.1816 - 197.394i) q^{20} +(-334.879 - 334.879i) q^{22} +(-87.6821 + 87.6821i) q^{23} +(592.636 + 198.514i) q^{25} -894.484 q^{26} +(-355.514 + 355.514i) q^{28} +839.832i q^{29} +403.787 q^{31} +(-128.000 - 128.000i) q^{32} +284.059i q^{34} +(-917.739 - 1275.27i) q^{35} +(-207.589 - 207.589i) q^{37} +(544.422 - 544.422i) q^{38} +(459.151 - 330.424i) q^{40} +1386.39 q^{41} +(568.393 - 568.393i) q^{43} -1339.51i q^{44} -350.729 q^{46} +(2642.77 + 2642.77i) q^{47} +1548.70i q^{49} +(788.243 + 1582.30i) q^{50} +(-1788.97 - 1788.97i) q^{52} +(1378.64 - 1378.64i) q^{53} +(4131.44 + 673.559i) q^{55} -1422.06 q^{56} +(-1679.66 + 1679.66i) q^{58} +327.503i q^{59} -4205.66 q^{61} +(807.573 + 807.573i) q^{62} -512.000i q^{64} +(6417.24 - 4618.11i) q^{65} +(2832.99 + 2832.99i) q^{67} +(-568.118 + 568.118i) q^{68} +(715.064 - 4386.02i) q^{70} -5339.03 q^{71} +(6865.24 - 6865.24i) q^{73} -830.357i q^{74} +2177.69 q^{76} +(-7440.88 - 7440.88i) q^{77} +4666.69i q^{79} +(1579.15 + 257.453i) q^{80} +(2772.78 + 2772.78i) q^{82} +(-4111.98 + 4111.98i) q^{83} +(-1466.56 - 2037.91i) q^{85} +2273.57 q^{86} +(2679.03 - 2679.03i) q^{88} +9911.62i q^{89} -19875.1 q^{91} +(-701.457 - 701.457i) q^{92} +10571.1i q^{94} +(-1095.03 + 6716.60i) q^{95} +(-10688.9 - 10688.9i) q^{97} +(-3097.40 + 3097.40i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 84 q^{5} - 28 q^{7} - 64 q^{8}+O(q^{10}) \) 4 * q + 8 * q^2 - 84 * q^5 - 28 * q^7 - 64 * q^8	\( 4 q + 8 q^{2} - 84 q^{5} - 28 q^{7} - 64 q^{8} - 224 q^{10} - 464 q^{11} - 336 q^{13} - 256 q^{16} - 392 q^{17} - 224 q^{20} - 928 q^{22} - 968 q^{23} + 1136 q^{25} - 1344 q^{26} + 224 q^{28} - 560 q^{31} - 512 q^{32} + 2296 q^{35} + 2256 q^{37} - 1232 q^{38} + 896 q^{40} - 392 q^{41} + 216 q^{43} - 3872 q^{46} + 9072 q^{47} + 3976 q^{50} - 2688 q^{52} + 4280 q^{53} + 10500 q^{55} + 896 q^{56} - 2192 q^{58} - 4536 q^{61} - 1120 q^{62} + 12912 q^{65} - 2248 q^{67} + 3136 q^{68} + 9856 q^{70} - 18064 q^{71} + 20524 q^{73} - 4928 q^{76} - 7336 q^{77} + 5376 q^{80} - 784 q^{82} + 336 q^{83} + 15944 q^{85} + 864 q^{86} + 7424 q^{88} - 52752 q^{91} - 7744 q^{92} - 23104 q^{95} - 40404 q^{97} - 23912 q^{98}+O(q^{100}) \) 4 * q + 8 * q^2 - 84 * q^5 - 28 * q^7 - 64 * q^8 - 224 * q^10 - 464 * q^11 - 336 * q^13 - 256 * q^16 - 392 * q^17 - 224 * q^20 - 928 * q^22 - 968 * q^23 + 1136 * q^25 - 1344 * q^26 + 224 * q^28 - 560 * q^31 - 512 * q^32 + 2296 * q^35 + 2256 * q^37 - 1232 * q^38 + 896 * q^40 - 392 * q^41 + 216 * q^43 - 3872 * q^46 + 9072 * q^47 + 3976 * q^50 - 2688 * q^52 + 4280 * q^53 + 10500 * q^55 + 896 * q^56 - 2192 * q^58 - 4536 * q^61 - 1120 * q^62 + 12912 * q^65 - 2248 * q^67 + 3136 * q^68 + 9856 * q^70 - 18064 * q^71 + 20524 * q^73 - 4928 * q^76 - 7336 * q^77 + 5376 * q^80 - 784 * q^82 + 336 * q^83 + 15944 * q^85 + 864 * q^86 + 7424 * q^88 - 52752 * q^91 - 7744 * q^92 - 23104 * q^95 - 40404 * q^97 - 23912 * q^98

Introduction

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