LMFDB - Embedded newform 333.3.i.b.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,3,Mod(154,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("333.154");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	333.i (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:	$9.07359280320$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 111)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.2
Character	$\chi$	$=$	333.253
Dual form			333.3.i.b.154.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.61593 - 2.61593i) q^{2} +9.68620i q^{4} +(2.59767 - 2.59767i) q^{5} +8.77260 q^{7} +(14.8747 - 14.8747i) q^{8} +O(q^{10})$	\(q+(-2.61593 - 2.61593i) q^{2} +9.68620i q^{4} +(2.59767 - 2.59767i) q^{5} +8.77260 q^{7} +(14.8747 - 14.8747i) q^{8} -13.5907 q^{10} +15.8888i q^{11} +(-8.87012 + 8.87012i) q^{13} +(-22.9485 - 22.9485i) q^{14} -39.0776 q^{16} +(-11.5706 + 11.5706i) q^{17} +(0.137103 - 0.137103i) q^{19} +(25.1616 + 25.1616i) q^{20} +(41.5640 - 41.5640i) q^{22} +(-29.9582 + 29.9582i) q^{23} +11.5042i q^{25} +46.4072 q^{26} +84.9731i q^{28} +(26.9667 + 26.9667i) q^{29} +(-14.3673 - 14.3673i) q^{31} +(42.7256 + 42.7256i) q^{32} +60.5358 q^{34} +(22.7883 - 22.7883i) q^{35} +(-24.5549 + 27.6777i) q^{37} -0.717304 q^{38} -77.2792i q^{40} -36.6404i q^{41} +(7.36240 - 7.36240i) q^{43} -153.902 q^{44} +156.737 q^{46} +32.4457 q^{47} +27.9585 q^{49} +(30.0942 - 30.0942i) q^{50} +(-85.9177 - 85.9177i) q^{52} -25.5762 q^{53} +(41.2739 + 41.2739i) q^{55} +(130.490 - 130.490i) q^{56} -141.086i q^{58} +(74.7967 - 74.7967i) q^{59} +(-34.3143 - 34.3143i) q^{61} +75.1680i q^{62} -67.2238i q^{64} +46.0833i q^{65} +112.443i q^{67} +(-112.075 - 112.075i) q^{68} -119.226 q^{70} -8.35647 q^{71} +76.1200i q^{73} +(136.637 - 8.16913i) q^{74} +(1.32801 + 1.32801i) q^{76} +139.386i q^{77} +(74.1682 - 74.1682i) q^{79} +(-101.511 + 101.511i) q^{80} +(-95.8487 + 95.8487i) q^{82} +84.0855 q^{83} +60.1133i q^{85} -38.5191 q^{86} +(236.341 + 236.341i) q^{88} +(67.6874 + 67.6874i) q^{89} +(-77.8140 + 77.8140i) q^{91} +(-290.181 - 290.181i) q^{92} +(-84.8756 - 84.8756i) q^{94} -0.712298i q^{95} +(75.8877 - 75.8877i) q^{97} +(-73.1375 - 73.1375i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} - 20 q^{5} + 60 q^{8}+O(q^{10}) $ 24 * q - 8 * q^2 - 20 * q^5 + 60 * q^8	$ 24 q - 8 q^{2} - 20 q^{5} + 60 q^{8} + 24 q^{10} - 32 q^{13} - 60 q^{14} - 40 q^{16} + 8 q^{17} - 48 q^{19} - 104 q^{20} + 32 q^{22} + 44 q^{23} - 88 q^{26} + 88 q^{29} + 192 q^{32} - 56 q^{34} - 60 q^{35} + 56 q^{37} - 160 q^{38} - 8 q^{43} - 536 q^{44} + 480 q^{46} - 88 q^{47} - 32 q^{49} - 172 q^{50} - 488 q^{52} - 104 q^{53} - 208 q^{55} + 80 q^{56} + 456 q^{59} - 96 q^{61} + 44 q^{68} - 1080 q^{70} + 528 q^{71} - 136 q^{74} - 24 q^{76} + 160 q^{79} - 48 q^{80} - 392 q^{82} - 280 q^{83} + 288 q^{86} + 1424 q^{88} + 92 q^{89} + 320 q^{91} - 48 q^{92} - 56 q^{94} + 352 q^{97} + 664 q^{98}+O(q^{100}) $ 24 * q - 8 * q^2 - 20 * q^5 + 60 * q^8 + 24 * q^10 - 32 * q^13 - 60 * q^14 - 40 * q^16 + 8 * q^17 - 48 * q^19 - 104 * q^20 + 32 * q^22 + 44 * q^23 - 88 * q^26 + 88 * q^29 + 192 * q^32 - 56 * q^34 - 60 * q^35 + 56 * q^37 - 160 * q^38 - 8 * q^43 - 536 * q^44 + 480 * q^46 - 88 * q^47 - 32 * q^49 - 172 * q^50 - 488 * q^52 - 104 * q^53 - 208 * q^55 + 80 * q^56 + 456 * q^59 - 96 * q^61 + 44 * q^68 - 1080 * q^70 + 528 * q^71 - 136 * q^74 - 24 * q^76 + 160 * q^79 - 48 * q^80 - 392 * q^82 - 280 * q^83 + 288 * q^86 + 1424 * q^88 + 92 * q^89 + 320 * q^91 - 48 * q^92 - 56 * q^94 + 352 * q^97 + 664 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.61593	−	2.61593i	−1.30797	−	1.30797i	−0.922881	−	0.385084i	$-0.874172\pi$
$2$	−2.61593	−	2.61593i	−1.30797	−	1.30797i	−0.385084	−	0.922881i	$-0.625828\pi$
$3$		0			0
$3$		0			0
$4$			9.68620i			2.42155i
$5$	2.59767	−	2.59767i	0.519535	−	0.519535i	−0.397896	−	0.917431i	$-0.630259\pi$
$5$	2.59767	−	2.59767i	0.519535	−	0.519535i	0.917431	+	0.397896i	$0.130259\pi$
$6$		0			0
$7$	8.77260			1.25323			0.626614	−	0.779330i	$-0.284440\pi$
$7$	8.77260			1.25323			0.626614	+	0.779330i	$0.284440\pi$
$8$	14.8747	−	14.8747i	1.85934	−	1.85934i
$9$		0			0
$10$	−13.5907			−1.35907
$11$			15.8888i			1.44444i	0.691665	+	0.722219i	$0.256878\pi$
$11$			15.8888i			1.44444i	−0.691665	+	0.722219i	$0.743122\pi$
$12$		0			0
$13$	−8.87012	+	8.87012i	−0.682317	+	0.682317i	−0.960522	−	0.278205i	$-0.910261\pi$
$13$	−8.87012	+	8.87012i	−0.682317	+	0.682317i	0.278205	+	0.960522i	$0.410261\pi$
$14$	−22.9485	−	22.9485i	−1.63918	−	1.63918i
$15$		0			0
$16$	−39.0776			−2.44235
$17$	−11.5706	+	11.5706i	−0.680623	+	0.680623i	−0.960141	−	0.279517i	$-0.909826\pi$
$17$	−11.5706	+	11.5706i	−0.680623	+	0.680623i	0.279517	+	0.960141i	$0.409826\pi$
$18$		0			0
$19$	0.137103	−	0.137103i	0.00721595	−	0.00721595i	−0.703490	−	0.710706i	$-0.748376\pi$
$19$	0.137103	−	0.137103i	0.00721595	−	0.00721595i	0.710706	+	0.703490i	$0.248376\pi$
$20$	25.1616	+	25.1616i	1.25808	+	1.25808i
$21$		0			0
$22$	41.5640	−	41.5640i	1.88927	−	1.88927i
$23$	−29.9582	+	29.9582i	−1.30253	+	1.30253i	−0.375846	+	0.926682i	$0.622648\pi$
$23$	−29.9582	+	29.9582i	−1.30253	+	1.30253i	−0.926682	+	0.375846i	$0.877352\pi$
$24$		0			0
$25$			11.5042i			0.460167i
$26$	46.4072			1.78489
$27$		0			0
$28$			84.9731i			3.03475i
$29$	26.9667	+	26.9667i	0.929887	+	0.929887i	0.997698	−	0.0678115i	$-0.0216017\pi$
$29$	26.9667	+	26.9667i	0.929887	+	0.929887i	−0.0678115	+	0.997698i	$0.521602\pi$
$30$		0			0
$31$	−14.3673	−	14.3673i	−0.463463	−	0.463463i	0.436326	−	0.899789i	$-0.356279\pi$
$31$	−14.3673	−	14.3673i	−0.463463	−	0.463463i	−0.899789	+	0.436326i	$0.856279\pi$
$32$	42.7256	+	42.7256i	1.33517	+	1.33517i
$33$		0			0
$34$	60.5358			1.78046
$35$	22.7883	−	22.7883i	0.651096	−	0.651096i
$36$		0			0
$37$	−24.5549	+	27.6777i	−0.663646	+	0.748047i
$37$	−24.5549	+	27.6777i	−0.663646	+	0.748047i
$38$	−0.717304			−0.0188764
$39$		0			0
$40$		−	77.2792i		−	1.93198i
$41$		−	36.6404i		−	0.893667i	−0.894617	−	0.446834i	$-0.852552\pi$
$41$		−	36.6404i		−	0.893667i	0.894617	−	0.446834i	$-0.147448\pi$
$42$		0			0
$43$	7.36240	−	7.36240i	0.171219	−	0.171219i	−0.616296	−	0.787515i	$-0.711368\pi$
$43$	7.36240	−	7.36240i	0.171219	−	0.171219i	0.787515	+	0.616296i	$0.211368\pi$
$44$	−153.902			−3.49778
$45$		0			0
$46$	156.737			3.40732
$47$	32.4457			0.690333			0.345167	−	0.938541i	$-0.387822\pi$
$47$	32.4457			0.690333			0.345167	+	0.938541i	$0.387822\pi$
$48$		0			0
$49$	27.9585			0.570581
$50$	30.0942	−	30.0942i	0.601883	−	0.601883i
$51$		0			0
$52$	−85.9177	−	85.9177i	−1.65226	−	1.65226i
$53$	−25.5762			−0.482570			−0.241285	−	0.970454i	$-0.577569\pi$
$53$	−25.5762			−0.482570			−0.241285	+	0.970454i	$0.577569\pi$
$54$		0			0
$55$	41.2739	+	41.2739i	0.750435	+	0.750435i
$56$	130.490	−	130.490i	2.33017	−	2.33017i
$57$		0			0
$58$		−	141.086i		−	2.43252i
$59$	74.7967	−	74.7967i	1.26774	−	1.26774i	0.320487	−	0.947253i	$-0.396153\pi$
$59$	74.7967	−	74.7967i	1.26774	−	1.26774i	0.947253	−	0.320487i	$-0.103847\pi$
$60$		0			0
$61$	−34.3143	−	34.3143i	−0.562530	−	0.562530i	0.367495	−	0.930025i	$-0.380215\pi$
$61$	−34.3143	−	34.3143i	−0.562530	−	0.562530i	−0.930025	+	0.367495i	$0.880215\pi$
$62$			75.1680i			1.21239i
$63$		0			0
$64$		−	67.2238i		−	1.05037i
$65$			46.0833i			0.708974i
$66$		0			0
$67$			112.443i			1.67825i	0.543939	+	0.839125i	$0.316932\pi$
$67$			112.443i			1.67825i	−0.543939	+	0.839125i	$0.683068\pi$
$68$	−112.075	−	112.075i	−1.64816	−	1.64816i
$69$		0			0
$70$	−119.226			−1.70322
$71$	−8.35647			−0.117697			−0.0588484	−	0.998267i	$-0.518743\pi$
$71$	−8.35647			−0.117697			−0.0588484	+	0.998267i	$0.518743\pi$
$72$		0			0
$73$			76.1200i			1.04274i	0.853331	+	0.521370i	$0.174579\pi$
$73$			76.1200i			1.04274i	−0.853331	+	0.521370i	$0.825421\pi$
$74$	136.637	−	8.16913i	1.84645	−	0.110394i
$75$		0			0
$76$	1.32801	+	1.32801i	0.0174738	+	0.0174738i
$77$			139.386i			1.81021i
$78$		0			0
$79$	74.1682	−	74.1682i	0.938838	−	0.938838i	−0.0593965	−	0.998234i	$-0.518918\pi$
$79$	74.1682	−	74.1682i	0.938838	−	0.938838i	0.998234	+	0.0593965i	$0.0189176\pi$
$80$	−101.511	+	101.511i	−1.26889	+	1.26889i
$81$		0			0
$82$	−95.8487	+	95.8487i	−1.16889	+	1.16889i
$83$	84.0855			1.01308			0.506539	−	0.862217i	$-0.330924\pi$
$83$	84.0855			1.01308			0.506539	+	0.862217i	$0.330924\pi$
$84$		0			0
$85$			60.1133i			0.707215i
$86$	−38.5191			−0.447896
$87$		0			0
$88$	236.341	+	236.341i	2.68570	+	2.68570i
$89$	67.6874	+	67.6874i	0.760533	+	0.760533i	0.976419	−	0.215886i	$-0.0692639\pi$
$89$	67.6874	+	67.6874i	0.760533	+	0.760533i	−0.215886	+	0.976419i	$0.569264\pi$
$90$		0			0
$91$	−77.8140	+	77.8140i	−0.855098	+	0.855098i
$92$	−290.181	−	290.181i	−3.15414	−	3.15414i
$93$		0			0
$94$	−84.8756	−	84.8756i	−0.902932	−	0.902932i
$95$		−	0.712298i		−	0.00749787i
$96$		0			0
$97$	75.8877	−	75.8877i	0.782347	−	0.782347i	−0.197879	−	0.980226i	$-0.563405\pi$
$97$	75.8877	−	75.8877i	0.782347	−	0.782347i	0.980226	+	0.197879i	$0.0634053\pi$
$98$	−73.1375	−	73.1375i	−0.746301	−	0.746301i
$99$		0			0
$100$	−111.432			−1.11432
$101$			9.60810i			0.0951297i	0.998868	+	0.0475649i	$0.0151461\pi$
$101$			9.60810i			0.0951297i	−0.998868	+	0.0475649i	$0.984854\pi$
$102$		0			0
$103$	−26.2374	−	26.2374i	−0.254732	−	0.254732i	0.568176	−	0.822907i	$-0.307649\pi$
$103$	−26.2374	−	26.2374i	−0.254732	−	0.254732i	−0.822907	+	0.568176i	$0.807649\pi$
$104$			263.881i			2.53731i
$105$		0			0
$106$	66.9056	+	66.9056i	0.631185	+	0.631185i
$107$	−177.423			−1.65816			−0.829080	−	0.559130i	$-0.811135\pi$
$107$	−177.423			−1.65816			−0.829080	+	0.559130i	$0.811135\pi$
$108$		0			0
$109$	110.435	−	110.435i	1.01316	−	1.01316i	0.0132505	−	0.999912i	$-0.495782\pi$
$109$	110.435	−	110.435i	1.01316	−	1.01316i	0.999912	−	0.0132505i	$-0.00421788\pi$
$110$		−	215.940i		−	1.96309i
$111$		0			0
$112$	−342.812			−3.06082
$113$	−28.0979	−	28.0979i	−0.248654	−	0.248654i	0.571764	−	0.820418i	$-0.306259\pi$
$113$	−28.0979	−	28.0979i	−0.248654	−	0.248654i	−0.820418	+	0.571764i	$0.806259\pi$
$114$		0			0
$115$			155.643i			1.35342i
$116$	−261.205	+	261.205i	−2.25177	+	2.25177i
$117$		0			0
$118$	−391.326			−3.31632
$119$	−101.504	+	101.504i	−0.852976	+	0.852976i
$120$		0			0
$121$	−131.454			−1.08640
$122$			179.528i			1.47154i
$123$		0			0
$124$	139.165	−	139.165i	1.12230	−	1.12230i
$125$	94.8260	+	94.8260i	0.758608	+	0.758608i
$126$		0			0
$127$	−58.5675			−0.461161			−0.230581	−	0.973053i	$-0.574063\pi$
$127$	−58.5675			−0.461161			−0.230581	+	0.973053i	$0.574063\pi$
$128$	−4.95072	+	4.95072i	−0.0386775	+	0.0386775i
$129$		0			0
$130$	120.551	−	120.551i	0.927314	−	0.927314i
$131$	50.6386	+	50.6386i	0.386554	+	0.386554i	0.873457	−	0.486902i	$-0.161873\pi$
$131$	50.6386	+	50.6386i	0.386554	+	0.386554i	−0.486902	+	0.873457i	$0.661873\pi$
$132$		0			0
$133$	1.20275	−	1.20275i	0.00904323	−	0.00904323i
$134$	294.142	−	294.142i	2.19509	−	2.19509i
$135$		0			0
$136$			344.218i			2.53102i
$137$	−78.8056			−0.575223			−0.287612	−	0.957747i	$-0.592861\pi$
$137$	−78.8056			−0.575223			−0.287612	+	0.957747i	$0.592861\pi$
$138$		0			0
$139$		−	3.06647i		−	0.0220609i	−0.999939	−	0.0110305i	$-0.996489\pi$
$139$		−	3.06647i		−	0.0220609i	0.999939	−	0.0110305i	$-0.00351117\pi$
$140$	220.732	+	220.732i	1.57666	+	1.57666i
$141$		0			0
$142$	21.8600	+	21.8600i	0.153943	+	0.153943i
$143$	−140.936	−	140.936i	−0.985563	−	0.985563i
$144$		0			0
$145$	140.101			0.966217
$146$	199.125	−	199.125i	1.36387	−	1.36387i
$147$		0			0
$148$	−268.092	−	237.844i	−1.81143	−	1.60705i
$149$	52.8285			0.354554			0.177277	−	0.984161i	$-0.443271\pi$
$149$	52.8285			0.354554			0.177277	+	0.984161i	$0.443271\pi$
$150$		0			0
$151$			48.5129i			0.321277i	0.987013	+	0.160639i	$0.0513554\pi$
$151$			48.5129i			0.321277i	−0.987013	+	0.160639i	$0.948645\pi$
$152$		−	4.07873i		−	0.0268338i
$153$		0			0
$154$	364.625	−	364.625i	2.36769	−	2.36769i
$155$	−74.6433			−0.481570
$156$		0			0
$157$	251.155			1.59971			0.799857	−	0.600191i	$-0.204909\pi$
$157$	251.155			1.59971			0.799857	+	0.600191i	$0.204909\pi$
$158$	−388.038			−2.45594
$159$		0			0
$160$	221.974			1.38734
$161$	−262.811	+	262.811i	−1.63237	+	1.63237i
$162$		0			0
$163$	−145.719	−	145.719i	−0.893983	−	0.893983i	0.100912	−	0.994895i	$-0.467824\pi$
$163$	−145.719	−	145.719i	−0.893983	−	0.893983i	−0.994895	+	0.100912i	$0.967824\pi$
$164$	354.906			2.16406
$165$		0			0
$166$	−219.962	−	219.962i	−1.32507	−	1.32507i
$167$	33.6724	−	33.6724i	0.201631	−	0.201631i	−0.599067	−	0.800699i	$-0.704462\pi$
$167$	33.6724	−	33.6724i	0.201631	−	0.201631i	0.800699	+	0.599067i	$0.204462\pi$
$168$		0			0
$169$			11.6421i			0.0688881i
$170$	157.252	−	157.252i	0.925013	−	0.925013i
$171$		0			0
$172$	71.3136	+	71.3136i	0.414614	+	0.414614i
$173$		−	188.865i		−	1.09170i	−0.837882	−	0.545852i	$-0.816206\pi$
$173$		−	188.865i		−	1.09170i	0.837882	−	0.545852i	$-0.183794\pi$
$174$		0			0
$175$			100.922i			0.576695i
$176$		−	620.897i		−	3.52782i
$177$		0			0
$178$		−	354.131i		−	1.98950i
$179$	−226.059	−	226.059i	−1.26290	−	1.26290i	−0.949682	−	0.313214i	$-0.898594\pi$
$179$	−226.059	−	226.059i	−1.26290	−	1.26290i	−0.313214	−	0.949682i	$-0.601406\pi$
$180$		0			0
$181$	70.9118			0.391778			0.195889	−	0.980626i	$-0.437241\pi$
$181$	70.9118			0.391778			0.195889	+	0.980626i	$0.437241\pi$
$182$	407.112			2.23688
$183$		0			0
$184$			891.237i			4.84368i
$185$	8.11211	+	135.683i	0.0438492	+	0.733423i
$186$		0			0
$187$	−183.843	−	183.843i	−0.983117	−	0.983117i
$188$			314.275i			1.67168i
$189$		0			0
$190$	−1.86332	+	1.86332i	−0.00980696	+	0.00980696i
$191$	73.0712	−	73.0712i	0.382572	−	0.382572i	−0.489456	−	0.872028i	$-0.662805\pi$
$191$	73.0712	−	73.0712i	0.382572	−	0.382572i	0.872028	+	0.489456i	$0.162805\pi$
$192$		0			0
$193$	130.664	−	130.664i	0.677016	−	0.677016i	−0.282307	−	0.959324i	$-0.591100\pi$
$193$	130.664	−	130.664i	0.677016	−	0.677016i	0.959324	+	0.282307i	$0.0910998\pi$
$194$	−397.034			−2.04657
$195$		0			0
$196$			270.811i			1.38169i
$197$	215.706			1.09495			0.547476	−	0.836821i	$-0.315589\pi$
$197$	215.706			1.09495			0.547476	+	0.836821i	$0.315589\pi$
$198$		0			0
$199$	103.916	+	103.916i	0.522191	+	0.522191i	0.918232	−	0.396042i	$-0.129616\pi$
$199$	103.916	+	103.916i	0.522191	+	0.522191i	−0.396042	+	0.918232i	$0.629616\pi$
$200$	171.121	+	171.121i	0.855606	+	0.855606i
$201$		0			0
$202$	25.1341	−	25.1341i	0.124426	−	0.124426i
$203$	236.568	+	236.568i	1.16536	+	1.16536i
$204$		0			0
$205$	−95.1797	−	95.1797i	−0.464291	−	0.464291i
$206$			137.270i			0.666360i
$207$		0			0
$208$	346.623	−	346.623i	1.66646	−	1.66646i
$209$	2.17840	+	2.17840i	0.0104230	+	0.0104230i
$210$		0			0
$211$	−52.9679			−0.251033			−0.125516	−	0.992092i	$-0.540059\pi$
$211$	−52.9679			−0.251033			−0.125516	+	0.992092i	$0.540059\pi$
$212$		−	247.736i		−	1.16857i
$213$		0			0
$214$	464.127	+	464.127i	2.16882	+	2.16882i
$215$		−	38.2502i		−	0.177908i
$216$		0			0
$217$	−126.039	−	126.039i	−0.580825	−	0.580825i
$218$	−577.779			−2.65036
$219$		0			0
$220$	−399.787	+	399.787i	−1.81722	+	1.81722i
$221$		−	205.265i		−	0.928801i
$222$		0			0
$223$	−152.152			−0.682298			−0.341149	−	0.940009i	$-0.610816\pi$
$223$	−152.152			−0.682298			−0.341149	+	0.940009i	$0.610816\pi$
$224$	374.814	+	374.814i	1.67328	+	1.67328i
$225$		0			0
$226$			147.004i			0.650462i
$227$	−40.6102	+	40.6102i	−0.178899	+	0.178899i	−0.790876	−	0.611976i	$-0.790375\pi$
$227$	−40.6102	+	40.6102i	−0.178899	+	0.178899i	0.611976	+	0.790876i	$0.290375\pi$
$228$		0			0
$229$	68.0529			0.297174			0.148587	−	0.988899i	$-0.452527\pi$
$229$	68.0529			0.297174			0.148587	+	0.988899i	$0.452527\pi$
$230$	407.151	−	407.151i	1.77022	−	1.77022i
$231$		0			0
$232$	802.244			3.45795
$233$			55.5360i			0.238352i	0.992873	+	0.119176i	$0.0380253\pi$
$233$			55.5360i			0.238352i	−0.992873	+	0.119176i	$0.961975\pi$
$234$		0			0
$235$	84.2832	−	84.2832i	0.358652	−	0.358652i
$236$	724.495	+	724.495i	3.06989	+	3.06989i
$237$		0			0
$238$	531.056			2.23133
$239$	−106.305	+	106.305i	−0.444793	+	0.444793i	−0.893619	−	0.448826i	$-0.851842\pi$
$239$	−106.305	+	106.305i	−0.444793	+	0.444793i	0.448826	+	0.893619i	$0.351842\pi$
$240$		0			0
$241$	−259.438	+	259.438i	−1.07651	+	1.07651i	−0.0796876	+	0.996820i	$0.525392\pi$
$241$	−259.438	+	259.438i	−1.07651	+	1.07651i	−0.996820	+	0.0796876i	$0.974608\pi$
$242$	343.875	+	343.875i	1.42097	+	1.42097i
$243$		0			0
$244$	332.375	−	332.375i	1.36219	−	1.36219i
$245$	72.6270	−	72.6270i	0.296437	−	0.296437i
$246$		0			0
$247$			2.43224i			0.00984712i
$248$	−427.420			−1.72347
$249$		0			0
$250$		−	496.116i		−	1.98447i
$251$	−300.709	−	300.709i	−1.19804	−	1.19804i	−0.974752	−	0.223291i	$-0.928320\pi$
$251$	−300.709	−	300.709i	−1.19804	−	1.19804i	−0.223291	−	0.974752i	$-0.571680\pi$
$252$		0			0
$253$	−475.999	−	475.999i	−1.88142	−	1.88142i
$254$	153.209	+	153.209i	0.603183	+	0.603183i
$255$		0			0
$256$	−242.994			−0.949195
$257$	110.390	−	110.390i	0.429534	−	0.429534i	−0.458935	−	0.888470i	$-0.651769\pi$
$257$	110.390	−	110.390i	0.429534	−	0.429534i	0.888470	+	0.458935i	$0.151769\pi$
$258$		0			0
$259$	−215.410	+	242.806i	−0.831700	+	0.937474i
$260$	−446.372			−1.71682
$261$		0			0
$262$		−	264.934i		−	1.01120i
$263$			303.282i			1.15316i	0.817040	+	0.576581i	$0.195613\pi$
$263$			303.282i			1.15316i	−0.817040	+	0.576581i	$0.804387\pi$
$264$		0			0
$265$	−66.4387	+	66.4387i	−0.250712	+	0.250712i
$266$	−6.29262			−0.0236565
$267$		0			0
$268$	−1089.14			−4.06396
$269$	301.305			1.12009			0.560047	−	0.828461i	$-0.310783\pi$
$269$	301.305			1.12009			0.560047	+	0.828461i	$0.310783\pi$
$270$		0			0
$271$	170.236			0.628178			0.314089	−	0.949393i	$-0.398301\pi$
$271$	170.236			0.628178			0.314089	+	0.949393i	$0.398301\pi$
$272$	452.151	−	452.151i	1.66232	−	1.66232i
$273$		0			0
$274$	206.150	+	206.150i	0.752373	+	0.752373i
$275$	−182.788			−0.664683
$276$		0			0
$277$	8.64065	+	8.64065i	0.0311937	+	0.0311937i	0.722532	−	0.691338i	$-0.242978\pi$
$277$	8.64065	+	8.64065i	0.0311937	+	0.0311937i	−0.691338	+	0.722532i	$0.742978\pi$
$278$	−8.02167	+	8.02167i	−0.0288549	+	0.0288549i
$279$		0			0
$280$		−	677.940i		−	2.42121i
$281$	14.4554	−	14.4554i	0.0514426	−	0.0514426i	−0.680918	−	0.732360i	$-0.738419\pi$
$281$	14.4554	−	14.4554i	0.0514426	−	0.0514426i	0.732360	+	0.680918i	$0.238419\pi$
$282$		0			0
$283$	−28.0386	−	28.0386i	−0.0990762	−	0.0990762i	0.655831	−	0.754907i	$-0.272318\pi$
$283$	−28.0386	−	28.0386i	−0.0990762	−	0.0990762i	−0.754907	+	0.655831i	$0.772318\pi$
$284$		−	80.9424i		−	0.285009i
$285$		0			0
$286$			737.356i			2.57817i
$287$		−	321.431i		−	1.11997i
$288$		0			0
$289$			21.2427i			0.0735042i
$290$	−366.496	−	366.496i	−1.26378	−	1.26378i
$291$		0			0
$292$	−737.313			−2.52504
$293$	234.945			0.801859			0.400930	−	0.916109i	$-0.368687\pi$
$293$	234.945			0.801859			0.400930	+	0.916109i	$0.368687\pi$
$294$		0			0
$295$		−	388.595i		−	1.31727i
$296$	46.4513	+	776.945i	0.156930	+	2.62481i
$297$		0			0
$298$	−138.196	−	138.196i	−0.463744	−	0.463744i
$299$		−	531.465i		−	1.77747i
$300$		0			0
$301$	64.5874	−	64.5874i	0.214576	−	0.214576i
$302$	126.906	−	126.906i	0.420220	−	0.420220i
$303$		0			0
$304$	−5.35766	+	5.35766i	−0.0176239	+	0.0176239i
$305$	−178.275			−0.584508
$306$		0			0
$307$			504.579i			1.64358i	0.569791	+	0.821790i	$0.307024\pi$
$307$			504.579i			1.64358i	−0.569791	+	0.821790i	$0.692976\pi$
$308$	−1350.12			−4.38351
$309$		0			0
$310$	195.262	+	195.262i	0.629877	+	0.629877i
$311$	−71.6566	−	71.6566i	−0.230407	−	0.230407i	0.582455	−	0.812863i	$-0.302092\pi$
$311$	−71.6566	−	71.6566i	−0.230407	−	0.230407i	−0.812863	+	0.582455i	$0.802092\pi$
$312$		0			0
$313$	279.378	−	279.378i	0.892580	−	0.892580i	−0.102185	−	0.994765i	$-0.532583\pi$
$313$	279.378	−	279.378i	0.892580	−	0.892580i	0.994765	+	0.102185i	$0.0325834\pi$
$314$	−657.004	−	657.004i	−2.09237	−	2.09237i
$315$		0			0
$316$	718.408	+	718.408i	2.27344	+	2.27344i
$317$			139.128i			0.438890i	0.975625	+	0.219445i	$0.0704247\pi$
$317$			139.128i			0.438890i	−0.975625	+	0.219445i	$0.929575\pi$
$318$		0			0
$319$	−428.469	+	428.469i	−1.34316	+	1.34316i
$320$	−174.626	−	174.626i	−0.545705	−	0.545705i
$321$		0			0
$322$	1374.99			4.27016
$323$			3.17273i			0.00982268i
$324$		0			0
$325$	−102.043	−	102.043i	−0.313980	−	0.313980i
$326$			762.383i			2.33860i
$327$		0			0
$328$	−545.014	−	545.014i	−1.66163	−	1.66163i
$329$	284.633			0.865145
$330$		0			0
$331$	398.103	−	398.103i	1.20273	−	1.20273i	0.229394	−	0.973334i	$-0.426325\pi$
$331$	398.103	−	398.103i	1.20273	−	1.20273i	0.973334	−	0.229394i	$-0.0736746\pi$
$332$			814.469i			2.45322i
$333$		0			0
$334$	−176.169			−0.527454
$335$	292.089	+	292.089i	0.871909	+	0.871909i
$336$		0			0
$337$			51.7944i			0.153692i	0.997043	+	0.0768462i	$0.0244851\pi$
$337$			51.7944i			0.153692i	−0.997043	+	0.0768462i	$0.975515\pi$
$338$	30.4549	−	30.4549i	0.0901033	−	0.0901033i
$339$		0			0
$340$	−582.269			−1.71256
$341$	228.280	−	228.280i	0.669443	−	0.669443i
$342$		0			0
$343$	−184.589			−0.538160
$344$		−	219.027i		−	0.636706i
$345$		0			0
$346$	−494.057	+	494.057i	−1.42791	+	1.42791i
$347$	273.343	+	273.343i	0.787733	+	0.787733i	0.981122	−	0.193389i	$-0.0619479\pi$
$347$	273.343	+	273.343i	0.787733	+	0.787733i	−0.193389	+	0.981122i	$0.561948\pi$
$348$		0			0
$349$	234.794			0.672763			0.336382	−	0.941726i	$-0.390797\pi$
$349$	234.794			0.672763			0.336382	+	0.941726i	$0.390797\pi$
$350$	264.004	−	264.004i	0.754297	−	0.754297i
$351$		0			0
$352$	−678.858	+	678.858i	−1.92857	+	1.92857i
$353$	237.028	+	237.028i	0.671468	+	0.671468i	0.958054	−	0.286587i	$-0.0925206\pi$
$353$	237.028	+	237.028i	0.671468	+	0.671468i	−0.286587	+	0.958054i	$0.592521\pi$
$354$		0			0
$355$	−21.7074	+	21.7074i	−0.0611476	+	0.0611476i
$356$	−655.634	+	655.634i	−1.84167	+	1.84167i
$357$		0			0
$358$			1182.71i			3.30365i
$359$	62.3602			0.173705			0.0868527	−	0.996221i	$-0.472319\pi$
$359$	62.3602			0.173705			0.0868527	+	0.996221i	$0.472319\pi$
$360$		0			0
$361$			360.962i			0.999896i
$362$	−185.500	−	185.500i	−0.512432	−	0.512432i
$363$		0			0
$364$	−753.721	−	753.721i	−2.07066	−	2.07066i
$365$	197.735	+	197.735i	0.541739	+	0.541739i
$366$		0			0
$367$	−195.476			−0.532633			−0.266316	−	0.963886i	$-0.585807\pi$
$367$	−195.476			−0.532633			−0.266316	+	0.963886i	$0.585807\pi$
$368$	1170.69	−	1170.69i	3.18123	−	3.18123i
$369$		0			0
$370$	333.718	−	376.159i	0.901939	−	1.01665i
$371$	−224.370			−0.604771
$372$		0			0
$373$			67.2411i			0.180271i	0.995930	+	0.0901355i	$0.0287300\pi$
$373$			67.2411i			0.180271i	−0.995930	+	0.0901355i	$0.971270\pi$
$374$			961.841i			2.57177i
$375$		0			0
$376$	482.620	−	482.620i	1.28356	−	1.28356i
$377$	−478.396			−1.26895
$378$		0			0
$379$	−18.4375			−0.0486479			−0.0243239	−	0.999704i	$-0.507743\pi$
$379$	−18.4375			−0.0486479			−0.0243239	+	0.999704i	$0.507743\pi$
$380$	6.89946			0.0181565
$381$		0			0
$382$	−382.298			−1.00078
$383$	−409.659	+	409.659i	−1.06961	+	1.06961i	−0.0722181	+	0.997389i	$0.523008\pi$
$383$	−409.659	+	409.659i	−1.06961	+	1.06961i	−0.997389	+	0.0722181i	$0.976992\pi$
$384$		0			0
$385$	362.080	+	362.080i	0.940467	+	0.940467i
$386$	−683.617			−1.77103
$387$		0			0
$388$	735.063	+	735.063i	1.89449	+	1.89449i
$389$	−241.446	+	241.446i	−0.620683	+	0.620683i	−0.945706	−	0.325023i	$-0.894628\pi$
$389$	−241.446	+	241.446i	−0.620683	+	0.620683i	0.325023	+	0.945706i	$0.394628\pi$
$390$		0			0
$391$		−	693.267i		−	1.77306i
$392$	415.874	−	415.874i	1.06090	−	1.06090i
$393$		0			0
$394$	−564.271	−	564.271i	−1.43216	−	1.43216i
$395$		−	385.330i		−	0.975518i
$396$		0			0
$397$		−	333.251i		−	0.839423i	−0.907658	−	0.419711i	$-0.862131\pi$
$397$		−	333.251i		−	0.839423i	0.907658	−	0.419711i	$-0.137869\pi$
$398$		−	543.674i		−	1.36602i
$399$		0			0
$400$		−	449.556i		−	1.12389i
$401$	109.530	+	109.530i	0.273142	+	0.273142i	0.830364	−	0.557222i	$-0.188133\pi$
$401$	109.530	+	109.530i	0.273142	+	0.273142i	−0.557222	+	0.830364i	$0.688133\pi$
$402$		0			0
$403$	254.880			0.632457
$404$	−93.0660			−0.230361
$405$		0			0
$406$		−	1237.69i		−	3.04850i
$407$	−439.766	−	390.148i	−1.08051	−	0.958595i
$408$		0			0
$409$	472.714	+	472.714i	1.15578	+	1.15578i	0.985374	+	0.170407i	$0.0545083\pi$
$409$	472.714	+	472.714i	1.15578	+	1.15578i	0.170407	+	0.985374i	$0.445492\pi$
$410$			497.967i			1.21455i
$411$		0			0
$412$	254.140	−	254.140i	0.616845	−	0.616845i
$413$	656.161	−	656.161i	1.58877	−	1.58877i
$414$		0			0
$415$	218.427	−	218.427i	0.526330	−	0.526330i
$416$	−757.961			−1.82202
$417$		0			0
$418$		−	11.3971i		−	0.0272658i
$419$	−270.311			−0.645134			−0.322567	−	0.946547i	$-0.604546\pi$
$419$	−270.311			−0.645134			−0.322567	+	0.946547i	$0.604546\pi$
$420$		0			0
$421$	2.45553	+	2.45553i	0.00583262	+	0.00583262i	0.710017	−	0.704184i	$-0.248687\pi$
$421$	2.45553	+	2.45553i	0.00583262	+	0.00583262i	−0.704184	+	0.710017i	$0.748687\pi$
$422$	138.560	+	138.560i	0.328342	+	0.328342i
$423$		0			0
$424$	−380.439	+	380.439i	−0.897261	+	0.897261i
$425$	−133.110	−	133.110i	−0.313201	−	0.313201i
$426$		0			0
$427$	−301.026	−	301.026i	−0.704979	−	0.704979i
$428$		−	1718.56i		−	4.01532i
$429$		0			0
$430$	−100.060	+	100.060i	−0.232698	+	0.232698i
$431$	118.266	+	118.266i	0.274399	+	0.274399i	0.830868	−	0.556469i	$-0.187844\pi$
$431$	118.266	+	118.266i	0.274399	+	0.274399i	−0.556469	+	0.830868i	$0.687844\pi$
$432$		0			0
$433$	332.897			0.768816			0.384408	−	0.923163i	$-0.374406\pi$
$433$	332.897			0.768816			0.384408	+	0.923163i	$0.374406\pi$
$434$			659.418i			1.51940i
$435$		0			0
$436$	1069.69	+	1069.69i	2.45342	+	2.45342i
$437$			8.21471i			0.0187980i
$438$		0			0
$439$	39.8745	+	39.8745i	0.0908303	+	0.0908303i	0.751062	−	0.660232i	$-0.229542\pi$
$439$	39.8745	+	39.8745i	0.0908303	+	0.0908303i	−0.660232	+	0.751062i	$0.729542\pi$
$440$	1227.87			2.79062
$441$		0			0
$442$	−536.959	+	536.959i	−1.21484	+	1.21484i
$443$		−	99.0599i		−	0.223611i	−0.993730	−	0.111806i	$-0.964337\pi$
$443$		−	99.0599i		−	0.223611i	0.993730	−	0.111806i	$-0.0356634\pi$
$444$		0			0
$445$	351.660			0.790247
$446$	398.020	+	398.020i	0.892422	+	0.892422i
$447$		0			0
$448$		−	589.728i		−	1.31636i
$449$	99.8679	−	99.8679i	0.222423	−	0.222423i	−0.587095	−	0.809518i	$-0.699729\pi$
$449$	99.8679	−	99.8679i	0.222423	−	0.222423i	0.809518	+	0.587095i	$0.199729\pi$
$450$		0			0
$451$	582.172			1.29085
$452$	272.162	−	272.162i	0.602128	−	0.602128i
$453$		0			0
$454$	212.467			0.467989
$455$			404.271i			0.888507i
$456$		0			0
$457$	−310.411	+	310.411i	−0.679237	+	0.679237i	−0.959828	−	0.280591i	$-0.909470\pi$
$457$	−310.411	+	310.411i	−0.679237	+	0.679237i	0.280591	+	0.959828i	$0.409470\pi$
$458$	−178.022	−	178.022i	−0.388694	−	0.388694i
$459$		0			0
$460$	−1507.59			−3.27737
$461$	−173.439	+	173.439i	−0.376224	+	0.376224i	−0.869738	−	0.493514i	$-0.835712\pi$
$461$	−173.439	+	173.439i	−0.376224	+	0.376224i	0.493514	+	0.869738i	$0.335712\pi$
$462$		0			0
$463$	308.429	−	308.429i	0.666153	−	0.666153i	−0.290670	−	0.956823i	$-0.593878\pi$
$463$	308.429	−	308.429i	0.666153	−	0.666153i	0.956823	+	0.290670i	$0.0938782\pi$
$464$	−1053.79	−	1053.79i	−2.27111	−	2.27111i
$465$		0			0
$466$	145.278	−	145.278i	0.311756	−	0.311756i
$467$	−72.9534	+	72.9534i	−0.156217	+	0.156217i	−0.780888	−	0.624671i	$-0.785233\pi$
$467$	−72.9534	+	72.9534i	−0.156217	+	0.156217i	0.624671	+	0.780888i	$0.285233\pi$
$468$		0			0
$469$			986.415i			2.10323i
$470$	−440.958			−0.938209
$471$		0			0
$472$		−	2225.16i		−	4.71431i
$473$	116.980	+	116.980i	0.247314	+	0.247314i
$474$		0			0
$475$	1.57726	+	1.57726i	0.00332054	+	0.00332054i
$476$	−983.189	−	983.189i	−2.06552	−	2.06552i
$477$		0			0
$478$	556.175			1.16355
$479$	272.615	−	272.615i	0.569133	−	0.569133i	−0.362752	−	0.931886i	$-0.618163\pi$
$479$	272.615	−	272.615i	0.569133	−	0.569133i	0.931886	+	0.362752i	$0.118163\pi$
$480$		0			0
$481$	−27.6999	−	463.309i	−0.0575882	−	0.963221i
$482$	1357.35			2.81607
$483$		0			0
$484$		−	1273.29i		−	2.63077i
$485$		−	394.263i		−	0.812913i
$486$		0			0
$487$	348.005	−	348.005i	0.714590	−	0.714590i	−0.252902	−	0.967492i	$-0.581385\pi$
$487$	348.005	−	348.005i	0.714590	−	0.714590i	0.967492	+	0.252902i	$0.0813850\pi$
$488$	−1020.83			−2.09187
$489$		0			0
$490$	−379.975			−0.775458
$491$	196.137			0.399465			0.199732	−	0.979850i	$-0.435993\pi$
$491$	196.137			0.399465			0.199732	+	0.979850i	$0.435993\pi$
$492$		0			0
$493$	−624.042			−1.26580
$494$	6.36257	−	6.36257i	0.0128797	−	0.0128797i
$495$		0			0
$496$	561.442	+	561.442i	1.13194	+	1.13194i
$497$	−73.3080			−0.147501
$498$		0			0
$499$	161.329	+	161.329i	0.323304	+	0.323304i	0.850033	−	0.526729i	$-0.176582\pi$
$499$	161.329	+	161.329i	0.323304	+	0.323304i	−0.526729	+	0.850033i	$0.676582\pi$
$500$	−918.503	+	918.503i	−1.83701	+	1.83701i
$501$		0			0
$502$			1573.27i			3.13400i
$503$	−174.337	+	174.337i	−0.346595	+	0.346595i	−0.858840	−	0.512245i	$-0.828814\pi$
$503$	−174.337	+	174.337i	−0.346595	+	0.346595i	0.512245	+	0.858840i	$0.328814\pi$
$504$		0			0
$505$	24.9587	+	24.9587i	0.0494232	+	0.0494232i
$506$			2490.36i			4.92167i
$507$		0			0
$508$		−	567.296i		−	1.11672i
$509$		−	559.403i		−	1.09902i	−0.835486	−	0.549512i	$-0.814814\pi$
$509$		−	559.403i		−	1.09902i	0.835486	−	0.549512i	$-0.185186\pi$
$510$		0			0
$511$			667.770i			1.30679i
$512$	655.458	+	655.458i	1.28019	+	1.28019i
$513$		0			0
$514$	−577.547			−1.12363
$515$	−136.312			−0.264684
$516$		0			0
$517$			515.523i			0.997143i
$518$	1198.66	−	71.6645i	2.31402	−	0.138348i
$519$		0			0
$520$	685.476	+	685.476i	1.31822	+	1.31822i
$521$		−	71.5121i		−	0.137259i	−0.997642	−	0.0686297i	$-0.978137\pi$
$521$		−	71.5121i		−	0.137259i	0.997642	−	0.0686297i	$-0.0218627\pi$
$522$		0			0
$523$	−479.153	+	479.153i	−0.916162	+	0.916162i	−0.996748	−	0.0805858i	$-0.974321\pi$
$523$	−479.153	+	479.153i	−0.916162	+	0.916162i	0.0805858	+	0.996748i	$0.474321\pi$
$524$	−490.496	+	490.496i	−0.936060	+	0.936060i
$525$		0			0
$526$	793.364	−	793.364i	1.50830	−	1.50830i
$527$	332.477			0.630887
$528$		0			0
$529$		−	1265.98i		−	2.39316i
$530$	347.598			0.655845
$531$		0			0
$532$	11.6501	+	11.6501i	0.0218986	+	0.0218986i
$533$	325.004	+	325.004i	0.609764	+	0.609764i
$534$		0			0
$535$	−460.888	+	460.888i	−0.861472	+	0.861472i
$536$	1672.55	+	1672.55i	3.12043	+	3.12043i
$537$		0			0
$538$	−788.194	−	788.194i	−1.46504	−	1.46504i
$539$			444.227i			0.824169i
$540$		0			0
$541$	−717.898	+	717.898i	−1.32698	+	1.32698i	−0.418996	+	0.907988i	$0.637618\pi$
$541$	−717.898	+	717.898i	−1.32698	+	1.32698i	−0.907988	+	0.418996i	$0.862382\pi$
$542$	−445.327	−	445.327i	−0.821636	−	0.821636i
$543$		0			0
$544$	−988.720			−1.81750
$545$		−	573.747i		−	1.05275i
$546$		0			0
$547$	321.416	+	321.416i	0.587598	+	0.587598i	0.936980	−	0.349382i	$-0.113609\pi$
$547$	321.416	+	321.416i	0.587598	+	0.587598i	−0.349382	+	0.936980i	$0.613609\pi$
$548$		−	763.327i		−	1.39293i
$549$		0			0
$550$	478.160	+	478.160i	0.869382	+	0.869382i
$551$	7.39444			0.0134200
$552$		0			0
$553$	650.648	−	650.648i	1.17658	−	1.17658i
$554$		−	45.2067i		−	0.0816006i
$555$		0			0
$556$	29.7024			0.0534216
$557$	−63.7956	−	63.7956i	−0.114534	−	0.114534i	0.647517	−	0.762051i	$-0.275808\pi$
$557$	−63.7956	−	63.7956i	−0.114534	−	0.114534i	−0.762051	+	0.647517i	$0.775808\pi$
$558$		0			0
$559$			130.611i			0.233651i
$560$	−890.514	+	890.514i	−1.59020	+	1.59020i
$561$		0			0
$562$	−75.6285			−0.134570
$563$	−337.078	+	337.078i	−0.598718	+	0.598718i	−0.939971	−	0.341254i	$-0.889149\pi$
$563$	−337.078	+	337.078i	−0.598718	+	0.598718i	0.341254	+	0.939971i	$0.389149\pi$
$564$		0			0
$565$	−145.978			−0.258369
$566$			146.694i			0.259177i
$567$		0			0
$568$	−124.300	+	124.300i	−0.218838	+	0.218838i
$569$	−115.210	−	115.210i	−0.202478	−	0.202478i	0.598583	−	0.801061i	$-0.295731\pi$
$569$	−115.210	−	115.210i	−0.202478	−	0.202478i	−0.801061	+	0.598583i	$0.795731\pi$
$570$		0			0
$571$	−197.491			−0.345868			−0.172934	−	0.984933i	$-0.555325\pi$
$571$	−197.491			−0.345868			−0.172934	+	0.984933i	$0.555325\pi$
$572$	1365.13	−	1365.13i	2.38659	−	2.38659i
$573$		0			0
$574$	−840.842	+	840.842i	−1.46488	+	1.46488i
$575$	−344.644	−	344.644i	−0.599381	−	0.599381i
$576$		0			0
$577$	−301.724	+	301.724i	−0.522918	+	0.522918i	−0.918451	−	0.395534i	$-0.870560\pi$
$577$	−301.724	+	301.724i	−0.522918	+	0.522918i	0.395534	+	0.918451i	$0.370560\pi$
$578$	55.5695	−	55.5695i	0.0961410	−	0.0961410i
$579$		0			0
$580$			1357.05i			2.33974i
$581$	737.649			1.26962
$582$		0			0
$583$		−	406.376i		−	0.697042i
$584$	1132.26	+	1132.26i	1.93880	+	1.93880i
$585$		0			0
$586$	−614.600	−	614.600i	−1.04880	−	1.04880i
$587$	−291.937	−	291.937i	−0.497338	−	0.497338i	0.413270	−	0.910608i	$-0.364386\pi$
$587$	−291.937	−	291.937i	−0.497338	−	0.497338i	−0.910608	+	0.413270i	$0.864386\pi$
$588$		0			0
$589$	−3.93961			−0.00668865
$590$	−1016.54	+	1016.54i	−1.72294	+	1.72294i
$591$		0			0
$592$	959.547	−	1081.58i	1.62086	−	1.82699i
$593$	−392.112			−0.661234			−0.330617	−	0.943765i	$-0.607257\pi$
$593$	−392.112			−0.661234			−0.330617	+	0.943765i	$0.607257\pi$
$594$		0			0
$595$			527.349i			0.886302i
$596$			511.707i			0.858569i
$597$		0			0
$598$	−1390.27	+	1390.27i	−2.32487	+	2.32487i
$599$	−378.580			−0.632021			−0.316010	−	0.948756i	$-0.602343\pi$
$599$	−378.580			−0.632021			−0.316010	+	0.948756i	$0.602343\pi$
$600$		0			0
$601$	247.544			0.411887			0.205944	−	0.978564i	$-0.433974\pi$
$601$	247.544			0.411887			0.205944	+	0.978564i	$0.433974\pi$
$602$	−337.912			−0.561316
$603$		0			0
$604$	−469.905			−0.777989
$605$	−341.475	+	341.475i	−0.564422	+	0.564422i
$606$		0			0
$607$	42.1232	+	42.1232i	0.0693957	+	0.0693957i	0.740953	−	0.671557i	$-0.234374\pi$
$607$	42.1232	+	42.1232i	0.0693957	+	0.0693957i	−0.671557	+	0.740953i	$0.734374\pi$
$608$	11.7156			0.0192691
$609$		0			0
$610$	466.355	+	466.355i	0.764516	+	0.764516i
$611$	−287.797	+	287.797i	−0.471026	+	0.471026i
$612$		0			0
$613$		−	959.180i		−	1.56473i	−0.622819	−	0.782366i	$-0.714013\pi$
$613$		−	959.180i		−	1.56473i	0.622819	−	0.782366i	$-0.285987\pi$
$614$	1319.94	−	1319.94i	2.14975	−	2.14975i
$615$		0			0
$616$	2073.33	+	2073.33i	3.36579	+	3.36579i
$617$		−	319.988i		−	0.518619i	−0.965794	−	0.259310i	$-0.916505\pi$
$617$		−	319.988i		−	0.518619i	0.965794	−	0.259310i	$-0.0834950\pi$
$618$		0			0
$619$		−	975.608i		−	1.57610i	−0.615609	−	0.788052i	$-0.711090\pi$
$619$		−	975.608i		−	1.57610i	0.615609	−	0.788052i	$-0.288910\pi$
$620$		−	723.010i		−	1.16615i
$621$		0			0
$622$			374.898i			0.602729i
$623$	593.795	+	593.795i	0.953121	+	0.953121i
$624$		0			0
$625$	205.049			0.328079
$626$	−1461.67			−2.33493
$627$		0			0
$628$			2432.74i			3.87379i
$629$	−36.1331	−	604.363i	−0.0574453	−	0.960831i
$630$		0			0
$631$	744.750	+	744.750i	1.18027	+	1.18027i	0.979674	+	0.200594i	$0.0642873\pi$
$631$	744.750	+	744.750i	1.18027	+	1.18027i	0.200594	+	0.979674i	$0.435713\pi$
$632$		−	2206.46i		−	3.49123i
$633$		0			0
$634$	363.950	−	363.950i	0.574054	−	0.574054i
$635$	−152.139	+	152.139i	−0.239589	+	0.239589i
$636$		0			0
$637$	−247.995	+	247.995i	−0.389317	+	0.389317i
$638$	2241.69			3.51362
$639$		0			0
$640$			25.7207i			0.0401886i
$641$	1254.80			1.95756			0.978782	−	0.204905i	$-0.0656886\pi$
$641$	1254.80			1.95756			0.978782	+	0.204905i	$0.0656886\pi$
$642$		0			0
$643$	−751.162	−	751.162i	−1.16821	−	1.16821i	−0.982628	−	0.185587i	$-0.940581\pi$
$643$	−751.162	−	751.162i	−1.16821	−	1.16821i	−0.185587	−	0.982628i	$-0.559419\pi$
$644$	−2545.64	−	2545.64i	−3.95285	−	3.95285i
$645$		0			0
$646$	8.29964	−	8.29964i	0.0128477	−	0.0128477i
$647$	−617.954	−	617.954i	−0.955106	−	0.955106i	0.0439284	−	0.999035i	$-0.486013\pi$
$647$	−617.954	−	617.954i	−0.955106	−	0.955106i	−0.999035	+	0.0439284i	$0.986013\pi$
$648$		0			0
$649$	1188.43	+	1188.43i	1.83117	+	1.83117i
$650$			533.877i			0.821350i
$651$		0			0
$652$	1411.46	−	1411.46i	2.16482	−	2.16482i
$653$	−208.459	−	208.459i	−0.319233	−	0.319233i	0.529239	−	0.848472i	$-0.322477\pi$
$653$	−208.459	−	208.459i	−0.319233	−	0.319233i	−0.848472	+	0.529239i	$0.822477\pi$
$654$		0			0
$655$	263.085			0.401657
$656$			1431.82i			2.18265i
$657$		0			0
$658$	−744.580	−	744.580i	−1.13158	−	1.13158i
$659$			401.967i			0.609965i	0.952358	+	0.304983i	$0.0986506\pi$
$659$			401.967i			0.609965i	−0.952358	+	0.304983i	$0.901349\pi$
$660$		0			0
$661$	−358.765	−	358.765i	−0.542761	−	0.542761i	0.381576	−	0.924337i	$-0.375381\pi$
$661$	−358.765	−	358.765i	−0.542761	−	0.542761i	−0.924337	+	0.381576i	$0.875381\pi$
$662$	−2082.82			−3.14625
$663$		0			0
$664$	1250.75	−	1250.75i	1.88366	−	1.88366i
$665$		−	6.24870i		−	0.00939654i
$666$		0			0
$667$	−1615.75			−2.42241
$668$	326.158	+	326.158i	0.488260	+	0.488260i
$669$		0			0
$670$		−	1528.17i		−	2.28085i
$671$	545.214	−	545.214i	0.812539	−	0.812539i
$672$		0			0
$673$	569.680			0.846479			0.423240	−	0.906018i	$-0.360893\pi$
$673$	569.680			0.846479			0.423240	+	0.906018i	$0.360893\pi$
$674$	135.490	−	135.490i	0.201024	−	0.201024i
$675$		0			0
$676$	−112.768			−0.166816
$677$			267.108i			0.394546i	0.980349	+	0.197273i	$0.0632085\pi$
$677$			267.108i			0.394546i	−0.980349	+	0.197273i	$0.936791\pi$
$678$		0			0
$679$	665.732	−	665.732i	0.980460	−	0.980460i
$680$	894.167	+	894.167i	1.31495	+	1.31495i
$681$		0			0
$682$	−1194.33			−1.75122
$683$	288.154	−	288.154i	0.421894	−	0.421894i	−0.463961	−	0.885855i	$-0.653572\pi$
$683$	288.154	−	288.154i	0.421894	−	0.421894i	0.885855	+	0.463961i	$0.153572\pi$
$684$		0			0
$685$	−204.711	+	204.711i	−0.298849	+	0.298849i
$686$	482.872	+	482.872i	0.703895	+	0.703895i
$687$		0			0
$688$	−287.705	+	287.705i	−0.418176	+	0.418176i
$689$	226.864	−	226.864i	0.329266	−	0.329266i
$690$		0			0
$691$		−	762.354i		−	1.10326i	−0.834088	−	0.551631i	$-0.814006\pi$
$691$		−	762.354i		−	1.10326i	0.834088	−	0.551631i	$-0.185994\pi$
$692$	1829.38			2.64362
$693$		0			0
$694$		−	1430.10i		−	2.06066i
$695$	−7.96568	−	7.96568i	−0.0114614	−	0.0114614i
$696$		0			0
$697$	423.951	+	423.951i	0.608251	+	0.608251i
$698$	−614.206	−	614.206i	−0.879951	−	0.879951i
$699$		0			0
$700$	−977.546			−1.39649
$701$	−58.7311	+	58.7311i	−0.0837819	+	0.0837819i	−0.747756	−	0.663974i	$-0.768869\pi$
$701$	−58.7311	+	58.7311i	−0.0837819	+	0.0837819i	0.663974	+	0.747756i	$0.268869\pi$
$702$		0			0
$703$	0.428150	+	7.16125i	0.000609033	+	0.0101867i
$704$	1068.11			1.51720
$705$		0			0
$706$		−	1240.10i		−	1.75651i
$707$			84.2880i			0.119219i
$708$		0			0
$709$	−60.6102	+	60.6102i	−0.0854869	+	0.0854869i	−0.748557	−	0.663070i	$-0.769253\pi$
$709$	−60.6102	+	60.6102i	−0.0854869	+	0.0854869i	0.663070	+	0.748557i	$0.269253\pi$
$710$	113.570			0.159958
$711$		0			0
$712$	2013.66			2.82817
$713$	860.838			1.20735
$714$		0			0
$715$	−732.209			−1.02407
$716$	2189.65	−	2189.65i	3.05817	−	3.05817i
$717$		0			0
$718$	−163.130	−	163.130i	−0.227201	−	0.227201i
$719$	88.0182			0.122418			0.0612088	−	0.998125i	$-0.480504\pi$
$719$	88.0182			0.122418			0.0612088	+	0.998125i	$0.480504\pi$
$720$		0			0
$721$	−230.170	−	230.170i	−0.319237	−	0.319237i
$722$	944.253	−	944.253i	1.30783	−	1.30783i
$723$		0			0
$724$			686.865i			0.948709i
$725$	−310.230	+	310.230i	−0.427903	+	0.427903i
$726$		0			0
$727$	−648.541	−	648.541i	−0.892079	−	0.892079i	0.102640	−	0.994719i	$-0.467271\pi$
$727$	−648.541	−	648.541i	−0.892079	−	0.892079i	−0.994719	+	0.102640i	$0.967271\pi$
$728$			2314.92i			3.17983i
$729$		0			0
$730$		−	1034.52i		−	1.41715i
$731$			170.375i			0.233071i
$732$		0			0
$733$		−	861.223i		−	1.17493i	−0.809250	−	0.587465i	$-0.800126\pi$
$733$		−	861.223i		−	1.17493i	0.809250	−	0.587465i	$-0.199874\pi$
$734$	511.352	+	511.352i	0.696665	+	0.696665i
$735$		0			0
$736$	−2559.96			−3.47820
$737$	−1786.58			−2.42413
$738$		0			0
$739$		−	589.510i		−	0.797712i	−0.917013	−	0.398856i	$-0.869407\pi$
$739$		−	589.510i		−	0.797712i	0.917013	−	0.398856i	$-0.130593\pi$
$740$	−1314.26	+	78.5755i	−1.77602	+	0.106183i
$741$		0			0
$742$	586.936	+	586.936i	0.791019	+	0.791019i
$743$			1213.46i			1.63318i	0.577216	+	0.816592i	$0.304139\pi$
$743$			1213.46i			1.63318i	−0.577216	+	0.816592i	$0.695861\pi$
$744$		0			0
$745$	137.231	−	137.231i	0.184203	−	0.184203i
$746$	175.898	−	175.898i	0.235788	−	0.235788i
$747$		0			0
$748$	1780.74	−	1780.74i	2.38067	−	2.38067i
$749$	−1556.46			−2.07805
$750$		0			0
$751$			677.119i			0.901624i	0.892619	+	0.450812i	$0.148865\pi$
$751$			677.119i			0.901624i	−0.892619	+	0.450812i	$0.851135\pi$
$752$	−1267.90			−1.68604
$753$		0			0
$754$	1251.45	+	1251.45i	1.65975	+	1.65975i
$755$	126.021	+	126.021i	0.166915	+	0.166915i
$756$		0			0
$757$	−725.717	+	725.717i	−0.958675	+	0.958675i	−0.999179	−	0.0405045i	$-0.987103\pi$
$757$	−725.717	+	725.717i	−0.958675	+	0.958675i	0.0405045	+	0.999179i	$0.487103\pi$
$758$	48.2313	+	48.2313i	0.0636297	+	0.0636297i
$759$		0			0
$760$	−10.5952	−	10.5952i	−0.0139411	−	0.0139411i
$761$			875.415i			1.15035i	0.818031	+	0.575174i	$0.195066\pi$
$761$			875.415i			1.15035i	−0.818031	+	0.575174i	$0.804934\pi$
$762$		0			0
$763$	968.800	−	968.800i	1.26972	−	1.26972i
$764$	707.782	+	707.782i	0.926416	+	0.926416i
$765$		0			0
$766$	2143.28			2.79802
$767$			1326.91i			1.73000i
$768$		0			0
$769$	247.960	+	247.960i	0.322445	+	0.322445i	0.849705	−	0.527259i	$-0.176780\pi$
$769$	247.960	+	247.960i	0.322445	+	0.322445i	−0.527259	+	0.849705i	$0.676780\pi$
$770$		−	1894.35i		−	2.46020i
$771$		0			0
$772$	1265.64	+	1265.64i	1.63943	+	1.63943i
$773$	1041.50			1.34735			0.673673	−	0.739029i	$-0.264715\pi$
$773$	1041.50			1.34735			0.673673	+	0.739029i	$0.264715\pi$
$774$		0			0
$775$	165.285	−	165.285i	0.213270	−	0.213270i
$776$		−	2257.61i		−	2.90930i
$777$		0			0
$778$	1263.21			1.62366
$779$	−5.02350	−	5.02350i	−0.00644866	−	0.00644866i
$780$		0			0
$781$		−	132.774i		−	0.170006i
$782$	−1813.54	+	1813.54i	−2.31910	+	2.31910i
$783$		0			0
$784$	−1092.55			−1.39356
$785$	652.419	−	652.419i	0.831107	−	0.831107i
$786$		0			0
$787$	−1179.77			−1.49907			−0.749535	−	0.661965i	$-0.769723\pi$
$787$	−1179.77			−1.49907			−0.749535	+	0.661965i	$0.769723\pi$
$788$			2089.37i			2.65148i
$789$		0			0
$790$	−1008.00	+	1008.00i	−1.27594	+	1.27594i
$791$	−246.492	−	246.492i	−0.311620	−	0.311620i
$792$		0			0
$793$	608.744			0.767647
$794$	−871.762	+	871.762i	−1.09794	+	1.09794i
$795$		0			0
$796$	−1006.55	+	1006.55i	−1.26451	+	1.26451i
$797$	781.483	+	781.483i	0.980531	+	0.980531i	0.999814	−	0.0192831i	$-0.00613837\pi$
$797$	781.483	+	781.483i	0.980531	+	0.980531i	−0.0192831	+	0.999814i	$0.506138\pi$
$798$		0			0
$799$	−375.416	+	375.416i	−0.469857	+	0.469857i
$800$	−491.523	+	491.523i	−0.614403	+	0.614403i
$801$		0			0
$802$		−	573.045i		−	0.714520i
$803$	−1209.46			−1.50617
$804$		0			0
$805$			1365.39i			1.69614i
$806$	−666.749	−	666.749i	−0.827232	−	0.827232i
$807$		0			0
$808$	142.918	+	142.918i	0.176878	+	0.176878i
$809$	−448.584	−	448.584i	−0.554492	−	0.554492i	0.373242	−	0.927734i	$-0.378246\pi$
$809$	−448.584	−	448.584i	−0.554492	−	0.554492i	−0.927734	+	0.373242i	$0.878246\pi$
$810$		0			0
$811$	1077.05			1.32806			0.664028	−	0.747708i	$-0.268845\pi$
$811$	1077.05			1.32806			0.664028	+	0.747708i	$0.268845\pi$
$812$	−2291.45	+	2291.45i	−2.82198	+	2.82198i
$813$		0			0
$814$	129.798	+	2171.00i	0.159457	+	2.66707i
$815$	−757.062			−0.928910
$816$		0			0
$817$		−	2.01881i		−	0.00247101i
$818$		−	2473.18i		−	3.02344i
$819$		0			0
$820$	921.929	−	921.929i	1.12430	−	1.12430i
$821$	1226.08			1.49340			0.746701	−	0.665160i	$-0.231637\pi$
$821$	1226.08			1.49340			0.746701	+	0.665160i	$0.231637\pi$
$822$		0			0
$823$	258.978			0.314675			0.157338	−	0.987545i	$-0.449709\pi$
$823$	258.978			0.314675			0.157338	+	0.987545i	$0.449709\pi$
$824$	−780.546			−0.947264
$825$		0			0
$826$	−3432.94			−4.15611
$827$	402.713	−	402.713i	0.486956	−	0.486956i	−0.420388	−	0.907344i	$-0.638106\pi$
$827$	402.713	−	402.713i	0.486956	−	0.486956i	0.907344	+	0.420388i	$0.138106\pi$
$828$		0			0
$829$	−475.969	−	475.969i	−0.574148	−	0.574148i	0.359137	−	0.933285i	$-0.383071\pi$
$829$	−475.969	−	475.969i	−0.574148	−	0.574148i	−0.933285	+	0.359137i	$0.883071\pi$
$830$	−1142.78			−1.37684
$831$		0			0
$832$	596.283	+	596.283i	0.716687	+	0.716687i
$833$	−323.496	+	323.496i	−0.388351	+	0.388351i
$834$		0			0
$835$		−	174.940i		−	0.209509i
$836$	−21.1004	+	21.1004i	−0.0252398	+	0.0252398i
$837$		0			0
$838$	707.115	+	707.115i	0.843813	+	0.843813i
$839$		−	1598.69i		−	1.90547i	−0.303806	−	0.952734i	$-0.598258\pi$
$839$		−	1598.69i		−	1.90547i	0.303806	−	0.952734i	$-0.401742\pi$
$840$		0			0
$841$			613.407i			0.729378i
$842$		−	12.8470i		−	0.0152577i
$843$		0			0
$844$		−	513.057i		−	0.607888i
$845$	30.2424	+	30.2424i	0.0357898	+	0.0357898i
$846$		0			0
$847$	−1153.20			−1.36151
$848$	999.457			1.17861
$849$		0			0
$850$			696.415i			0.819311i
$851$	−93.5544	−	1564.79i	−0.109935	−	1.83877i
$852$		0			0
$853$	−141.549	−	141.549i	−0.165942	−	0.165942i	0.619251	−	0.785193i	$-0.287436\pi$
$853$	−141.549	−	141.549i	−0.165942	−	0.165942i	−0.785193	+	0.619251i	$0.787436\pi$
$854$			1574.93i			1.84418i
$855$		0			0
$856$	−2639.12	+	2639.12i	−3.08308	+	3.08308i
$857$	−41.6961	+	41.6961i	−0.0486535	+	0.0486535i	−0.731015	−	0.682361i	$-0.760953\pi$
$857$	−41.6961	+	41.6961i	−0.0486535	+	0.0486535i	0.682361	+	0.731015i	$0.260953\pi$
$858$		0			0
$859$	550.302	−	550.302i	0.640631	−	0.640631i	−0.310080	−	0.950711i	$-0.600356\pi$
$859$	550.302	−	550.302i	0.640631	−	0.640631i	0.950711	+	0.310080i	$0.100356\pi$
$860$	370.499			0.430813
$861$		0			0
$862$		−	618.751i		−	0.717808i
$863$	−835.133			−0.967710			−0.483855	−	0.875148i	$-0.660764\pi$
$863$	−835.133			−0.967710			−0.483855	+	0.875148i	$0.660764\pi$
$864$		0			0
$865$	−490.609	−	490.609i	−0.567178	−	0.567178i
$866$	−870.836	−	870.836i	−1.00558	−	1.00558i
$867$		0			0
$868$	1220.84	−	1220.84i	1.40650	−	1.40650i
$869$	1178.44	+	1178.44i	1.35609	+	1.35609i
$870$		0			0
$871$	−997.380	−	997.380i	−1.14510	−	1.14510i
$872$		−	3285.37i		−	3.76762i
$873$		0			0
$874$	21.4891	−	21.4891i	0.0245871	−	0.0245871i
$875$	831.870	+	831.870i	0.950709	+	0.950709i
$876$		0			0
$877$	79.8398			0.0910374			0.0455187	−	0.998963i	$-0.485506\pi$
$877$	79.8398			0.0910374			0.0455187	+	0.998963i	$0.485506\pi$
$878$		−	208.618i		−	0.237606i
$879$		0			0
$880$	−1612.89	−	1612.89i	−1.83283	−	1.83283i
$881$		−	302.520i		−	0.343383i	−0.985151	−	0.171692i	$-0.945077\pi$
$881$		−	302.520i		−	0.343383i	0.985151	−	0.171692i	$-0.0549232\pi$
$882$		0			0
$883$	−798.287	−	798.287i	−0.904062	−	0.904062i	0.0917222	−	0.995785i	$-0.470763\pi$
$883$	−798.287	−	798.287i	−0.904062	−	0.904062i	−0.995785	+	0.0917222i	$0.970763\pi$
$884$	1988.24			2.24914
$885$		0			0
$886$	−259.134	+	259.134i	−0.292476	+	0.292476i
$887$			1536.02i			1.73171i	0.500298	+	0.865854i	$0.333224\pi$
$887$			1536.02i			1.73171i	−0.500298	+	0.865854i	$0.666776\pi$
$888$		0			0
$889$	−513.789			−0.577940
$890$	−919.918	−	919.918i	−1.03362	−	1.03362i
$891$		0			0
$892$		−	1473.78i		−	1.65222i
$893$	4.44840	−	4.44840i	0.00498141	−	0.00498141i
$894$		0			0
$895$	−1174.45			−1.31224
$896$	−43.4306	+	43.4306i	−0.0484717	+	0.0484717i
$897$		0			0
$898$	−522.495			−0.581843
$899$		−	774.880i		−	0.861936i
$900$		0			0
$901$	295.932	−	295.932i	0.328448	−	0.328448i
$902$	−1522.92	−	1522.92i	−1.68838	−	1.68838i
$903$		0			0
$904$	−835.896			−0.924664
$905$	184.206	−	184.206i	0.203542	−	0.203542i
$906$		0			0
$907$	489.219	−	489.219i	0.539382	−	0.539382i	−0.383965	−	0.923347i	$-0.625442\pi$
$907$	489.219	−	489.219i	0.539382	−	0.539382i	0.923347	+	0.383965i	$0.125442\pi$
$908$	−393.358	−	393.358i	−0.433214	−	0.433214i
$909$		0			0
$910$	1057.54	−	1057.54i	1.16214	−	1.16214i
$911$	978.801	−	978.801i	1.07443	−	1.07443i	0.0774272	−	0.996998i	$-0.475329\pi$
$911$	978.801	−	978.801i	1.07443	−	1.07443i	0.996998	−	0.0774272i	$-0.0246705\pi$
$912$		0			0
$913$			1336.02i			1.46333i
$914$	1624.03			1.77684
$915$		0			0
$916$			659.173i			0.719622i
$917$	444.232	+	444.232i	0.484441	+	0.484441i
$918$		0			0
$919$	63.5400	+	63.5400i	0.0691403	+	0.0691403i	0.740831	−	0.671691i	$-0.234432\pi$
$919$	63.5400	+	63.5400i	0.0691403	+	0.0691403i	−0.671691	+	0.740831i	$0.734432\pi$
$920$	2315.14	+	2315.14i	2.51646	+	2.51646i
$921$		0			0
$922$	907.411			0.984176
$923$	74.1229	−	74.1229i	0.0803065	−	0.0803065i
$924$		0			0
$925$	−318.410	−	282.484i	−0.344227	−	0.305388i
$926$	−1613.66			−1.74261
$927$		0			0
$928$			2304.34i			2.48312i
$929$		−	463.766i		−	0.499210i	−0.968348	−	0.249605i	$-0.919699\pi$
$929$		−	463.766i		−	0.499210i	0.968348	−	0.249605i	$-0.0803008\pi$
$930$		0			0
$931$	3.83319	−	3.83319i	0.00411728	−	0.00411728i
$932$	−537.932			−0.577181
$933$		0			0
$934$	381.682			0.408653
$935$	−955.128			−1.02153
$936$		0			0
$937$	1163.74			1.24198			0.620990	−	0.783818i	$-0.286731\pi$
$937$	1163.74			1.24198			0.620990	+	0.783818i	$0.286731\pi$
$938$	2580.39	−	2580.39i	2.75095	−	2.75095i
$939$		0			0
$940$	816.384	+	816.384i	0.868494	+	0.868494i
$941$	−755.592			−0.802967			−0.401484	−	0.915866i	$-0.631505\pi$
$941$	−755.592			−0.802967			−0.401484	+	0.915866i	$0.631505\pi$
$942$		0			0
$943$	1097.68	+	1097.68i	1.16403	+	1.16403i
$944$	−2922.88	+	2922.88i	−3.09627	+	3.09627i
$945$		0			0
$946$		−	612.022i		−	0.646958i
$947$	275.233	−	275.233i	0.290637	−	0.290637i	−0.546695	−	0.837332i	$-0.684114\pi$
$947$	275.233	−	275.233i	0.290637	−	0.290637i	0.837332	+	0.546695i	$0.184114\pi$
$948$		0			0
$949$	−675.193	−	675.193i	−0.711478	−	0.711478i
$950$		−	8.25200i		−	0.00868632i
$951$		0			0
$952$			3019.69i			3.17194i
$953$			845.497i			0.887195i	0.896226	+	0.443597i	$0.146298\pi$
$953$			845.497i			0.887195i	−0.896226	+	0.443597i	$0.853702\pi$
$954$		0			0
$955$		−	379.630i		−	0.397519i
$956$	−1029.70	−	1029.70i	−1.07709	−	1.07709i
$957$		0			0
$958$	−1426.28			−1.48881
$959$	−691.330			−0.720886
$960$		0			0
$961$		−	548.159i		−	0.570405i
$962$	−1139.52	+	1284.45i	−1.18454	+	1.33518i
$963$		0			0
$964$	−2512.97	−	2512.97i	−2.60682	−	2.60682i
$965$		−	678.846i		−	0.703467i
$966$		0			0
$967$	−1311.52	+	1311.52i	−1.35628	+	1.35628i	−0.477823	+	0.878456i	$0.658574\pi$
$967$	−1311.52	+	1311.52i	−1.35628	+	1.35628i	−0.878456	+	0.477823i	$0.841426\pi$
$968$	−1955.34	+	1955.34i	−2.01998	+	2.01998i
$969$		0			0
$970$	−1031.36	+	1031.36i	−1.06326	+	1.06326i
$971$	−252.661			−0.260208			−0.130104	−	0.991500i	$-0.541531\pi$
$971$	−252.661			−0.260208			−0.130104	+	0.991500i	$0.541531\pi$
$972$		0			0
$973$		−	26.9009i		−	0.0276474i
$974$	−1820.72			−1.86932
$975$		0			0
$976$	1340.92	+	1340.92i	1.37390	+	1.37390i
$977$	168.389	+	168.389i	0.172353	+	0.172353i	0.788012	−	0.615659i	$-0.211110\pi$
$977$	168.389	+	168.389i	0.172353	+	0.172353i	−0.615659	+	0.788012i	$0.711110\pi$
$978$		0			0
$979$	−1075.47	+	1075.47i	−1.09854	+	1.09854i
$980$	703.479	+	703.479i	0.717836	+	0.717836i
$981$		0			0
$982$	−513.082	−	513.082i	−0.522486	−	0.522486i
$983$			673.903i			0.685557i	0.939416	+	0.342779i	$0.111368\pi$
$983$			673.903i			0.685557i	−0.939416	+	0.342779i	$0.888632\pi$
$984$		0			0
$985$	560.333	−	560.333i	0.568866	−	0.568866i
$986$	1632.45	+	1632.45i	1.65563	+	1.65563i
$987$		0			0
$988$	−23.5591			−0.0238453
$989$			441.128i			0.446034i
$990$		0			0
$991$	521.436	+	521.436i	0.526171	+	0.526171i	0.919428	−	0.393257i	$-0.128652\pi$
$991$	521.436	+	521.436i	0.526171	+	0.526171i	−0.393257	+	0.919428i	$0.628652\pi$
$992$		−	1227.71i		−	1.23761i
$993$		0			0
$994$	191.769	+	191.769i	0.192926	+	0.192926i
$995$	539.879			0.542592
$996$		0			0
$997$	−646.551	+	646.551i	−0.648497	+	0.648497i	−0.952630	−	0.304133i	$-0.901633\pi$
$997$	−646.551	+	646.551i	−0.648497	+	0.648497i	0.304133	+	0.952630i	$0.401633\pi$
$998$		−	844.049i		−	0.845741i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.3.i.b.253.2		24
3.2	odd	2		111.3.f.a.31.11	✓	24
37.6	odd	4	inner	333.3.i.b.154.2		24
111.80	even	4		111.3.f.a.43.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.3.f.a.31.11	✓	24	3.2	odd	2
111.3.f.a.43.11	yes	24	111.80	even	4
333.3.i.b.154.2		24	37.6	odd	4	inner
333.3.i.b.253.2		24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.61593 - 2.61593i) q^{2} +9.68620i q^{4} +(2.59767 - 2.59767i) q^{5} +8.77260 q^{7} +(14.8747 - 14.8747i) q^{8} +O(q^{10})\)	\(q+(-2.61593 - 2.61593i) q^{2} +9.68620i q^{4} +(2.59767 - 2.59767i) q^{5} +8.77260 q^{7} +(14.8747 - 14.8747i) q^{8} -13.5907 q^{10} +15.8888i q^{11} +(-8.87012 + 8.87012i) q^{13} +(-22.9485 - 22.9485i) q^{14} -39.0776 q^{16} +(-11.5706 + 11.5706i) q^{17} +(0.137103 - 0.137103i) q^{19} +(25.1616 + 25.1616i) q^{20} +(41.5640 - 41.5640i) q^{22} +(-29.9582 + 29.9582i) q^{23} +11.5042i q^{25} +46.4072 q^{26} +84.9731i q^{28} +(26.9667 + 26.9667i) q^{29} +(-14.3673 - 14.3673i) q^{31} +(42.7256 + 42.7256i) q^{32} +60.5358 q^{34} +(22.7883 - 22.7883i) q^{35} +(-24.5549 + 27.6777i) q^{37} -0.717304 q^{38} -77.2792i q^{40} -36.6404i q^{41} +(7.36240 - 7.36240i) q^{43} -153.902 q^{44} +156.737 q^{46} +32.4457 q^{47} +27.9585 q^{49} +(30.0942 - 30.0942i) q^{50} +(-85.9177 - 85.9177i) q^{52} -25.5762 q^{53} +(41.2739 + 41.2739i) q^{55} +(130.490 - 130.490i) q^{56} -141.086i q^{58} +(74.7967 - 74.7967i) q^{59} +(-34.3143 - 34.3143i) q^{61} +75.1680i q^{62} -67.2238i q^{64} +46.0833i q^{65} +112.443i q^{67} +(-112.075 - 112.075i) q^{68} -119.226 q^{70} -8.35647 q^{71} +76.1200i q^{73} +(136.637 - 8.16913i) q^{74} +(1.32801 + 1.32801i) q^{76} +139.386i q^{77} +(74.1682 - 74.1682i) q^{79} +(-101.511 + 101.511i) q^{80} +(-95.8487 + 95.8487i) q^{82} +84.0855 q^{83} +60.1133i q^{85} -38.5191 q^{86} +(236.341 + 236.341i) q^{88} +(67.6874 + 67.6874i) q^{89} +(-77.8140 + 77.8140i) q^{91} +(-290.181 - 290.181i) q^{92} +(-84.8756 - 84.8756i) q^{94} -0.712298i q^{95} +(75.8877 - 75.8877i) q^{97} +(-73.1375 - 73.1375i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} - 20 q^{5} + 60 q^{8}+O(q^{10}) \) 24 * q - 8 * q^2 - 20 * q^5 + 60 * q^8	\( 24 q - 8 q^{2} - 20 q^{5} + 60 q^{8} + 24 q^{10} - 32 q^{13} - 60 q^{14} - 40 q^{16} + 8 q^{17} - 48 q^{19} - 104 q^{20} + 32 q^{22} + 44 q^{23} - 88 q^{26} + 88 q^{29} + 192 q^{32} - 56 q^{34} - 60 q^{35} + 56 q^{37} - 160 q^{38} - 8 q^{43} - 536 q^{44} + 480 q^{46} - 88 q^{47} - 32 q^{49} - 172 q^{50} - 488 q^{52} - 104 q^{53} - 208 q^{55} + 80 q^{56} + 456 q^{59} - 96 q^{61} + 44 q^{68} - 1080 q^{70} + 528 q^{71} - 136 q^{74} - 24 q^{76} + 160 q^{79} - 48 q^{80} - 392 q^{82} - 280 q^{83} + 288 q^{86} + 1424 q^{88} + 92 q^{89} + 320 q^{91} - 48 q^{92} - 56 q^{94} + 352 q^{97} + 664 q^{98}+O(q^{100}) \) 24 * q - 8 * q^2 - 20 * q^5 + 60 * q^8 + 24 * q^10 - 32 * q^13 - 60 * q^14 - 40 * q^16 + 8 * q^17 - 48 * q^19 - 104 * q^20 + 32 * q^22 + 44 * q^23 - 88 * q^26 + 88 * q^29 + 192 * q^32 - 56 * q^34 - 60 * q^35 + 56 * q^37 - 160 * q^38 - 8 * q^43 - 536 * q^44 + 480 * q^46 - 88 * q^47 - 32 * q^49 - 172 * q^50 - 488 * q^52 - 104 * q^53 - 208 * q^55 + 80 * q^56 + 456 * q^59 - 96 * q^61 + 44 * q^68 - 1080 * q^70 + 528 * q^71 - 136 * q^74 - 24 * q^76 + 160 * q^79 - 48 * q^80 - 392 * q^82 - 280 * q^83 + 288 * q^86 + 1424 * q^88 + 92 * q^89 + 320 * q^91 - 48 * q^92 - 56 * q^94 + 352 * q^97 + 664 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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