LMFDB - Embedded newform 225.4.p.b.68.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(32,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.32");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.p (of order $12$, degree $4$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			68.3
Character	$\chi$	$=$	225.68
Dual form			225.4.p.b.182.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11026 + 4.14355i) q^{2} +(4.87317 - 1.80338i) q^{3} +(-9.00816 - 5.20086i) q^{4} +(2.06189 + 22.1945i) q^{6} +(14.5845 + 3.90791i) q^{7} +(7.28515 - 7.28515i) q^{8} +(20.4957 - 17.5763i) q^{9} +O(q^{10})$	\(q+(-1.11026 + 4.14355i) q^{2} +(4.87317 - 1.80338i) q^{3} +(-9.00816 - 5.20086i) q^{4} +(2.06189 + 22.1945i) q^{6} +(14.5845 + 3.90791i) q^{7} +(7.28515 - 7.28515i) q^{8} +(20.4957 - 17.5763i) q^{9} +(42.5632 - 24.5739i) q^{11} +(-53.2775 - 9.09960i) q^{12} +(33.7651 - 9.04733i) q^{13} +(-32.3853 + 56.0930i) q^{14} +(-19.5089 - 33.7905i) q^{16} +(-18.9033 - 18.9033i) q^{17} +(50.0730 + 104.439i) q^{18} -53.7656i q^{19} +(78.1204 - 7.25747i) q^{21} +(54.5669 + 203.647i) q^{22} +(45.7984 + 170.922i) q^{23} +(22.3639 - 48.6397i) q^{24} +149.952i q^{26} +(68.1821 - 122.614i) q^{27} +(-111.055 - 111.055i) q^{28} +(110.003 + 190.531i) q^{29} +(-22.1047 + 38.2864i) q^{31} +(241.286 - 64.6525i) q^{32} +(163.102 - 196.510i) q^{33} +(99.3145 - 57.3392i) q^{34} +(-276.040 + 51.7355i) q^{36} +(-169.138 + 169.138i) q^{37} +(222.781 + 59.6939i) q^{38} +(148.227 - 104.980i) q^{39} +(42.1171 + 24.3163i) q^{41} +(-56.6624 + 331.754i) q^{42} +(92.3811 - 344.771i) q^{43} -511.222 q^{44} -759.073 q^{46} +(-137.261 + 512.264i) q^{47} +(-156.007 - 129.485i) q^{48} +(-99.6102 - 57.5100i) q^{49} +(-126.209 - 58.0293i) q^{51} +(-351.215 - 94.1079i) q^{52} +(-198.516 + 198.516i) q^{53} +(432.358 + 418.650i) q^{54} +(134.720 - 77.7807i) q^{56} +(-96.9596 - 262.009i) q^{57} +(-911.609 + 244.265i) q^{58} +(64.3921 - 111.530i) q^{59} +(-33.4727 - 57.9764i) q^{61} +(-134.100 - 134.100i) q^{62} +(367.606 - 176.247i) q^{63} +759.421i q^{64} +(633.166 + 894.000i) q^{66} +(-18.6925 - 69.7613i) q^{67} +(71.9705 + 268.597i) q^{68} +(531.420 + 750.341i) q^{69} -1038.75i q^{71} +(21.2676 - 277.360i) q^{72} +(-339.210 - 339.210i) q^{73} +(-513.044 - 888.619i) q^{74} +(-279.627 + 484.329i) q^{76} +(716.797 - 192.065i) q^{77} +(270.421 + 730.744i) q^{78} +(297.681 - 171.866i) q^{79} +(111.144 - 720.478i) q^{81} +(-147.517 + 147.517i) q^{82} +(841.890 + 225.584i) q^{83} +(-741.466 - 340.917i) q^{84} +(1326.01 + 765.572i) q^{86} +(879.665 + 730.114i) q^{87} +(131.055 - 489.104i) q^{88} +230.315 q^{89} +527.804 q^{91} +(476.383 - 1777.88i) q^{92} +(-38.6751 + 226.440i) q^{93} +(-1970.20 - 1137.50i) q^{94} +(1059.24 - 750.193i) q^{96} +(-553.082 - 148.198i) q^{97} +(348.889 - 348.889i) q^{98} +(440.442 - 1251.76i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.11026	+	4.14355i	−0.392537	+	1.46497i	0.433398	+	0.901203i	$0.357314\pi$
$2$	−1.11026	+	4.14355i	−0.392537	+	1.46497i	−0.825935	+	0.563765i	$0.809352\pi$
$3$	4.87317	−	1.80338i	0.937843	−	0.347060i
$3$	4.87317	−	1.80338i	0.937843	−	0.347060i
$4$	−9.00816	−	5.20086i	−1.12602	−	0.650108i
$5$		0			0
$5$		0			0
$6$	2.06189	+	22.1945i	0.140294	+	1.51014i
$7$	14.5845	+	3.90791i	0.787490	+	0.211007i	0.630084	−	0.776527i	$-0.283020\pi$
$7$	14.5845	+	3.90791i	0.787490	+	0.211007i	0.157406	+	0.987534i	$0.449687\pi$
$8$	7.28515	−	7.28515i	0.321961	−	0.321961i
$9$	20.4957	−	17.5763i	0.759098	−	0.650976i
$10$		0			0
$11$	42.5632	−	24.5739i	1.16666	−	0.673573i	0.213771	−	0.976884i	$-0.431425\pi$
$11$	42.5632	−	24.5739i	1.16666	−	0.673573i	0.952892	+	0.303310i	$0.0980919\pi$
$12$	−53.2775	−	9.09960i	−1.28166	−	0.218902i
$13$	33.7651	−	9.04733i	0.720366	−	0.193021i	0.120031	−	0.992770i	$-0.461701\pi$
$13$	33.7651	−	9.04733i	0.720366	−	0.193021i	0.600335	+	0.799749i	$0.295034\pi$
$14$	−32.3853	+	56.0930i	−0.618238	+	1.07082i
$15$		0			0
$16$	−19.5089	−	33.7905i	−0.304827	−	0.527976i
$17$	−18.9033	−	18.9033i	−0.269690	−	0.269690i	0.559285	−	0.828975i	$-0.311076\pi$
$17$	−18.9033	−	18.9033i	−0.269690	−	0.269690i	−0.828975	+	0.559285i	$0.811076\pi$
$18$	50.0730	+	104.439i	0.655685	+	1.36759i
$19$		−	53.7656i		−	0.649193i	−0.945853	−	0.324596i	$-0.894772\pi$
$19$		−	53.7656i		−	0.649193i	0.945853	−	0.324596i	$-0.105228\pi$
$20$		0			0
$21$	78.1204	−	7.25747i	0.811774	−	0.0754148i
$22$	54.5669	+	203.647i	0.528805	+	1.97353i
$23$	45.7984	+	170.922i	0.415201	+	1.54955i	0.784432	+	0.620214i	$0.212954\pi$
$23$	45.7984	+	170.922i	0.415201	+	1.54955i	−0.369231	+	0.929338i	$0.620379\pi$
$24$	22.3639	−	48.6397i	0.190209	−	0.413689i
$25$		0			0
$26$			149.952i			1.13108i
$27$	68.1821	−	122.614i	0.485987	−	0.873966i
$28$	−111.055	−	111.055i	−0.749552	−	0.749552i
$29$	110.003	+	190.531i	0.704382	+	1.22003i	0.966914	+	0.255103i	$0.0821092\pi$
$29$	110.003	+	190.531i	0.704382	+	1.22003i	−0.262532	+	0.964923i	$0.584557\pi$
$30$		0			0
$31$	−22.1047	+	38.2864i	−0.128068	+	0.221821i	−0.922928	−	0.384972i	$-0.874211\pi$
$31$	−22.1047	+	38.2864i	−0.128068	+	0.221821i	0.794860	+	0.606793i	$0.207544\pi$
$32$	241.286	−	64.6525i	1.33293	−	0.357158i
$33$	163.102	−	196.510i	0.860376	−	1.03661i
$34$	99.3145	−	57.3392i	0.500950	−	0.289224i
$35$		0			0
$36$	−276.040	+	51.7355i	−1.27796	+	0.239516i
$37$	−169.138	+	169.138i	−0.751516	+	0.751516i	−0.974762	−	0.223246i	$-0.928335\pi$
$37$	−169.138	+	169.138i	−0.751516	+	0.751516i	0.223246	+	0.974762i	$0.428335\pi$
$38$	222.781	+	59.6939i	0.951047	+	0.254832i
$39$	148.227	−	104.980i	0.608600	−	0.431034i
$40$		0			0
$41$	42.1171	+	24.3163i	0.160429	+	0.0926237i	0.578065	−	0.815991i	$-0.303808\pi$
$41$	42.1171	+	24.3163i	0.160429	+	0.0926237i	−0.417636	+	0.908614i	$0.637141\pi$
$42$	−56.6624	+	331.754i	−0.208171	+	1.21883i
$43$	92.3811	−	344.771i	0.327628	−	1.22272i	−0.584016	−	0.811742i	$-0.698520\pi$
$43$	92.3811	−	344.771i	0.327628	−	1.22272i	0.911644	−	0.410981i	$-0.134814\pi$
$44$	−511.222			−1.75158
$45$		0			0
$46$	−759.073			−2.43303
$47$	−137.261	+	512.264i	−0.425990	+	1.58982i	0.335761	+	0.941947i	$0.391007\pi$
$47$	−137.261	+	512.264i	−0.425990	+	1.58982i	−0.761751	+	0.647870i	$0.775660\pi$
$48$	−156.007	−	129.485i	−0.469119	−	0.389365i
$49$	−99.6102	−	57.5100i	−0.290409	−	0.167667i
$50$		0			0
$51$	−126.209	−	58.0293i	−0.346525	−	0.159328i
$52$	−351.215	−	94.1079i	−0.936631	−	0.250969i
$53$	−198.516	+	198.516i	−0.514496	+	0.514496i	−0.915901	−	0.401405i	$-0.868522\pi$
$53$	−198.516	+	198.516i	−0.514496	+	0.514496i	0.401405	+	0.915901i	$0.368522\pi$
$54$	432.358	+	418.650i	1.08956	+	1.05502i
$55$		0			0
$56$	134.720	−	77.7807i	0.321477	−	0.185605i
$57$	−96.9596	−	262.009i	−0.225309	−	0.608841i
$58$	−911.609	+	244.265i	−2.06379	+	0.552992i
$59$	64.3921	−	111.530i	0.142087	−	0.246102i	−0.786195	−	0.617978i	$-0.787952\pi$
$59$	64.3921	−	111.530i	0.142087	−	0.246102i	0.928282	+	0.371876i	$0.121285\pi$
$60$		0			0
$61$	−33.4727	−	57.9764i	−0.0702581	−	0.121691i	0.828756	−	0.559610i	$-0.189049\pi$
$61$	−33.4727	−	57.9764i	−0.0702581	−	0.121691i	−0.899014	+	0.437919i	$0.855716\pi$
$62$	−134.100	−	134.100i	−0.274689	−	0.274689i
$63$	367.606	−	176.247i	0.735143	−	0.352462i
$64$			759.421i			1.48324i
$65$		0			0
$66$	633.166	+	894.000i	1.18087	+	1.66733i
$67$	−18.6925	−	69.7613i	−0.0340843	−	0.127204i	0.946787	−	0.321860i	$-0.104308\pi$
$67$	−18.6925	−	69.7613i	−0.0340843	−	0.127204i	−0.980872	+	0.194655i	$0.937641\pi$
$68$	71.9705	+	268.597i	0.128349	+	0.479003i
$69$	531.420	+	750.341i	0.927181	+	1.30914i
$70$		0			0
$71$		−	1038.75i		−	1.73629i	−0.496313	−	0.868143i	$-0.665313\pi$
$71$		−	1038.75i		−	1.73629i	0.496313	−	0.868143i	$-0.334687\pi$
$72$	21.2676	−	277.360i	0.0348112	−	0.453989i
$73$	−339.210	−	339.210i	−0.543857	−	0.543857i	0.380800	−	0.924657i	$-0.375649\pi$
$73$	−339.210	−	339.210i	−0.543857	−	0.543857i	−0.924657	+	0.380800i	$0.875649\pi$
$74$	−513.044	−	888.619i	−0.805949	−	1.39594i
$75$		0			0
$76$	−279.627	+	484.329i	−0.422045	+	0.731004i
$77$	716.797	−	192.065i	1.06086	−	0.284258i
$78$	270.421	+	730.744i	0.392553	+	1.06078i
$79$	297.681	−	171.866i	0.423946	−	0.244766i	−0.272818	−	0.962066i	$-0.587956\pi$
$79$	297.681	−	171.866i	0.423946	−	0.244766i	0.696764	+	0.717300i	$0.254622\pi$
$80$		0			0
$81$	111.144	−	720.478i	0.152461	−	0.988310i
$82$	−147.517	+	147.517i	−0.198665	+	0.198665i
$83$	841.890	+	225.584i	1.11337	+	0.298326i	0.768196	−	0.640214i	$-0.221155\pi$
$83$	841.890	+	225.584i	1.11337	+	0.298326i	0.345170	+	0.938540i	$0.387821\pi$
$84$	−741.466	−	340.917i	−0.963102	−	0.442822i
$85$		0			0
$86$	1326.01	+	765.572i	1.66264	+	0.959928i
$87$	879.665	+	730.114i	1.08402	+	0.899730i
$88$	131.055	−	489.104i	0.158756	−	0.592485i
$89$	230.315			0.274307			0.137153	−	0.990550i	$-0.456205\pi$
$89$	230.315			0.274307			0.137153	+	0.990550i	$0.456205\pi$
$90$		0			0
$91$	527.804			0.608010
$92$	476.383	−	1777.88i	0.539851	−	2.01475i
$93$	−38.6751	+	226.440i	−0.0431228	+	0.252481i
$94$	−1970.20	−	1137.50i	−2.16181	−	1.24812i
$95$		0			0
$96$	1059.24	−	750.193i	1.12612	−	0.797565i
$97$	−553.082	−	148.198i	−0.578938	−	0.155126i	−0.0425454	−	0.999095i	$-0.513547\pi$
$97$	−553.082	−	148.198i	−0.578938	−	0.155126i	−0.536393	+	0.843969i	$0.680213\pi$
$98$	348.889	−	348.889i	0.359624	−	0.359624i
$99$	440.442	−	1251.76i	0.447132	−	1.27078i
$100$		0			0
$101$	−122.461	+	70.7028i	−0.120647	+	0.0696554i	−0.559109	−	0.829094i	$-0.688857\pi$
$101$	−122.461	+	70.7028i	−0.120647	+	0.0696554i	0.438462	+	0.898750i	$0.355523\pi$
$102$	380.572	−	458.526i	0.369434	−	0.445106i
$103$	−115.727	+	31.0089i	−0.110708	+	0.0296641i	−0.313748	−	0.949506i	$-0.601585\pi$
$103$	−115.727	+	31.0089i	−0.110708	+	0.0296641i	0.203040	+	0.979170i	$0.434918\pi$
$104$	180.073	−	311.895i	0.169784	−	0.294075i
$105$		0			0
$106$	−602.157	−	1042.97i	−0.551761	−	0.955678i
$107$	−940.778	−	940.778i	−0.849985	−	0.849985i	0.140146	−	0.990131i	$-0.455243\pi$
$107$	−940.778	−	940.778i	−0.849985	−	0.849985i	−0.990131	+	0.140146i	$0.955243\pi$
$108$	−1251.89	+	749.921i	−1.11540	+	0.668159i
$109$			1052.78i			0.925121i	0.886588	+	0.462560i	$0.153069\pi$
$109$			1052.78i			0.925121i	−0.886588	+	0.462560i	$0.846931\pi$
$110$		0			0
$111$	−519.219	+	1129.26i	−0.443982	+	0.965625i
$112$	−152.478	−	569.057i	−0.128642	−	0.480097i
$113$	−303.543	−	1132.84i	−0.252699	−	0.943085i	−0.969356	−	0.245659i	$-0.920996\pi$
$113$	−303.543	−	1132.84i	−0.252699	−	0.943085i	0.716657	−	0.697425i	$-0.245671\pi$
$114$	1193.30	−	110.859i	0.980374	−	0.0910779i
$115$		0			0
$116$		−	2288.45i		−	1.83170i
$117$	533.019	−	778.898i	0.421176	−	0.615463i
$118$	390.640	+	390.640i	0.304757	+	0.304757i
$119$	−201.823	−	349.568i	−0.155471	−	0.269284i
$120$		0			0
$121$	542.252	−	939.209i	0.407402	−	0.705641i
$122$	277.392	−	74.3270i	0.205852	−	0.0551578i
$123$	249.095	+	42.5446i	0.182603	+	0.0311880i
$124$	398.245	−	229.927i	0.288415	−	0.166517i
$125$		0			0
$126$	322.152	+	1718.88i	0.227774	+	1.21532i
$127$	−2.78116	+	2.78116i	−0.00194321	+	0.00194321i	−0.708078	−	0.706135i	$-0.750437\pi$
$127$	−2.78116	+	2.78116i	−0.00194321	+	0.00194321i	0.706135	+	0.708078i	$0.250437\pi$
$128$	−1216.41	−	325.937i	−0.839974	−	0.225070i
$129$	−171.563	−	1846.73i	−0.117095	−	1.26043i
$130$		0			0
$131$	−455.461	−	262.961i	−0.303770	−	0.175381i	0.340365	−	0.940293i	$-0.389449\pi$
$131$	−455.461	−	262.961i	−0.303770	−	0.175381i	−0.644135	+	0.764912i	$0.722783\pi$
$132$	−2491.27	+	921.926i	−1.64271	+	0.607904i
$133$	210.111	−	784.145i	0.136984	−	0.511233i
$134$	309.813			0.199730
$135$		0			0
$136$	−275.427			−0.173659
$137$	−482.495	+	1800.69i	−0.300893	+	1.12295i	0.635531	+	0.772075i	$0.280781\pi$
$137$	−482.495	+	1800.69i	−0.300893	+	1.12295i	−0.936424	+	0.350871i	$0.885885\pi$
$138$	−3699.09	+	1368.89i	−2.28180	+	0.844406i
$139$	2076.42	+	1198.82i	1.26705	+	0.731531i	0.974428	−	0.224698i	$-0.0721395\pi$
$139$	2076.42	+	1198.82i	1.26705	+	0.731531i	0.292620	+	0.956229i	$0.405473\pi$
$140$		0			0
$141$	254.910	+	2743.89i	0.152250	+	1.63884i
$142$	4304.10	+	1153.28i	2.54360	+	0.681557i
$143$	1214.82	−	1214.82i	0.710410	−	0.710410i
$144$	−993.761	−	349.662i	−0.575093	−	0.202351i
$145$		0			0
$146$	1782.15	−	1028.92i	1.01022	−	0.583249i
$147$	−589.130	−	100.621i	−0.330548	−	0.0564565i
$148$	2403.28	−	643.958i	1.33479	−	0.357655i
$149$	−1086.72	+	1882.25i	−0.597498	+	1.03490i	0.395691	+	0.918384i	$0.370505\pi$
$149$	−1086.72	+	1882.25i	−0.597498	+	1.03490i	−0.993189	+	0.116513i	$0.962828\pi$
$150$		0			0
$151$	−1316.04	−	2279.46i	−0.709260	−	1.22847i	−0.965132	−	0.261763i	$-0.915696\pi$
$151$	−1316.04	−	2279.46i	−0.709260	−	1.22847i	0.255873	−	0.966711i	$-0.417637\pi$
$152$	−391.690	−	391.690i	−0.209015	−	0.209015i
$153$	−719.687	−	55.1846i	−0.380282	−	0.0291595i
$154$			3183.33i			1.66571i
$155$		0			0
$156$	−1881.25	+	174.770i	−0.965514	+	0.0896974i
$157$	−749.861	−	2798.52i	−0.381181	−	1.42259i	−0.844100	−	0.536186i	$-0.819865\pi$
$157$	−749.861	−	2798.52i	−0.381181	−	1.42259i	0.462919	−	0.886401i	$-0.346802\pi$
$158$	381.633	+	1424.28i	0.192159	+	0.717147i
$159$	−609.404	+	1325.40i	−0.303955	+	0.661077i
$160$		0			0
$161$			2671.79i			1.30787i
$162$	2861.94	+	1260.45i	1.38800	+	0.611298i
$163$	1097.25	+	1097.25i	0.527259	+	0.527259i	0.919754	−	0.392495i	$-0.128388\pi$
$163$	1097.25	+	1097.25i	0.527259	+	0.527259i	−0.392495	+	0.919754i	$0.628388\pi$
$164$	−252.932	−	438.091i	−0.120431	−	0.208592i
$165$		0			0
$166$	−1869.44	+	3237.96i	−0.874075	+	1.51394i
$167$	−3359.65	+	900.215i	−1.55675	+	0.417130i	−0.931633	−	0.363401i	$-0.881616\pi$
$167$	−3359.65	+	900.215i	−1.55675	+	0.417130i	−0.625117	+	0.780531i	$0.714949\pi$
$168$	516.247	−	621.990i	0.237079	−	0.285640i
$169$	−844.431	+	487.532i	−0.384356	+	0.221908i
$170$		0			0
$171$	−945.002	−	1101.96i	−0.422609	−	0.492801i
$172$	−2625.29	+	2625.29i	−1.16382	+	1.16382i
$173$	−854.813	−	229.047i	−0.375666	−	0.100659i	0.0660452	−	0.997817i	$-0.478962\pi$
$173$	−854.813	−	229.047i	−0.375666	−	0.100659i	−0.441711	+	0.897157i	$0.645628\pi$
$174$	−4001.93	+	2834.32i	−1.74359	+	1.23488i
$175$		0			0
$176$	−1660.73	−	958.821i	−0.711261	−	0.410647i
$177$	112.663	−	659.631i	0.0478432	−	0.280118i
$178$	−255.710	+	954.321i	−0.107676	+	0.401851i
$179$	1948.94			0.813803			0.406901	−	0.913472i	$-0.366609\pi$
$179$	1948.94			0.813803			0.406901	+	0.913472i	$0.366609\pi$
$180$		0			0
$181$	1591.17			0.653431			0.326716	−	0.945123i	$-0.394058\pi$
$181$	1591.17			0.653431			0.326716	+	0.945123i	$0.394058\pi$
$182$	−586.001	+	2186.98i	−0.238666	+	0.890715i
$183$	−267.672	−	222.165i	−0.108125	−	0.0897428i
$184$	1578.84	+	911.544i	0.632574	+	0.365217i
$185$		0			0
$186$	−895.326	−	411.660i	−0.352949	−	0.162281i
$187$	−1269.11	−	340.058i	−0.496293	−	0.132981i
$188$	3900.68	−	3900.68i	1.51323	−	1.51323i
$189$	1473.57	−	1521.82i	0.567123	−	0.585693i
$190$		0			0
$191$	−1725.63	+	996.295i	−0.653730	+	0.377431i	−0.789884	−	0.613257i	$-0.789859\pi$
$191$	−1725.63	+	996.295i	−0.653730	+	0.377431i	0.136154	+	0.990688i	$0.456526\pi$
$192$	1369.52	+	3700.79i	0.514775	+	1.39105i
$193$	−2376.60	+	636.807i	−0.886379	+	0.237504i	−0.673157	−	0.739500i	$-0.735062\pi$
$193$	−2376.60	+	636.807i	−0.886379	+	0.237504i	−0.213221	+	0.977004i	$0.568396\pi$
$194$	1228.13	−	2127.19i	0.454509	−	0.787233i
$195$		0			0
$196$	598.203	+	1036.12i	0.218004	+	0.377594i
$197$	−497.126	−	497.126i	−0.179790	−	0.179790i	0.611474	−	0.791265i	$-0.290577\pi$
$197$	−497.126	−	497.126i	−0.179790	−	0.179790i	−0.791265	+	0.611474i	$0.790577\pi$
$198$	4697.75	+	3214.78i	1.68613	+	1.15386i
$199$		−	1269.73i		−	0.452305i	−0.974092	−	0.226152i	$-0.927385\pi$
$199$		−	1269.73i		−	0.452305i	0.974092	−	0.226152i	$-0.0726148\pi$
$200$		0			0
$201$	−216.898	−	306.249i	−0.0761133	−	0.107468i
$202$	−156.997	−	585.922i	−0.0546846	−	0.204086i
$203$	859.766	+	3208.69i	0.297260	+	1.10939i
$204$	835.107	+	1179.13i	0.286614	+	0.404685i
$205$		0			0
$206$		−	513.949i		−	0.173828i
$207$	3942.85	+	2698.19i	1.32390	+	0.905976i
$208$	−964.434	−	964.434i	−0.321498	−	0.321498i
$209$	−1321.23	−	2288.44i	−0.437279	−	0.757389i
$210$		0			0
$211$	−676.141	+	1171.11i	−0.220604	+	0.382098i	−0.954992	−	0.296633i	$-0.904136\pi$
$211$	−676.141	+	1171.11i	−0.220604	+	0.382098i	0.734387	+	0.678731i	$0.237470\pi$
$212$	2820.72	−	755.809i	0.913810	−	0.244855i
$213$	−1873.25	−	5061.99i	−0.602596	−	1.62836i
$214$	4942.67	−	2853.65i	1.57885	−	0.911550i
$215$		0			0
$216$	−396.544	−	1389.98i	−0.124914	−	0.437852i
$217$	−472.006	+	472.006i	−0.147658	+	0.147658i
$218$	−4362.26	−	1168.86i	−1.35527	−	0.363144i
$219$	−2264.76	−	1041.31i	−0.698804	−	0.321301i
$220$		0			0
$221$	−809.296	−	467.247i	−0.246331	−	0.142219i
$222$	−4102.67	−	3405.18i	−1.24033	−	1.02946i
$223$	26.4940	−	98.8770i	0.00795592	−	0.0296919i	−0.961834	−	0.273634i	$-0.911774\pi$
$223$	26.4940	−	98.8770i	0.00795592	−	0.0296919i	0.969790	+	0.243943i	$0.0784408\pi$
$224$	3771.70			1.12503
$225$		0			0
$226$	5031.00			1.48078
$227$	375.911	−	1402.92i	0.109912	−	0.410198i	−0.888944	−	0.458016i	$-0.848560\pi$
$227$	375.911	−	1402.92i	0.109912	−	0.410198i	0.998856	+	0.0478183i	$0.0152268\pi$
$228$	−489.245	+	2864.49i	−0.142110	+	0.832042i
$229$	−4802.27	−	2772.59i	−1.38578	−	0.800079i	−0.392941	−	0.919564i	$-0.628542\pi$
$229$	−4802.27	−	2772.59i	−1.38578	−	0.800079i	−0.992836	+	0.119485i	$0.961876\pi$
$230$		0			0
$231$	3146.71	−	2228.62i	0.896270	−	0.634773i
$232$	2189.44	+	586.658i	0.619585	+	0.166017i
$233$	870.893	−	870.893i	0.244867	−	0.244867i	−0.573993	−	0.818860i	$-0.694606\pi$
$233$	870.893	−	870.893i	0.244867	−	0.244867i	0.818860	+	0.573993i	$0.194606\pi$
$234$	2635.62	+	3073.37i	0.736306	+	0.858601i
$235$		0			0
$236$	−1160.11	+	669.790i	−0.319986	+	0.184744i
$237$	1140.71	−	1374.37i	0.312647	−	0.376687i
$238$	1672.53	−	448.153i	0.455521	−	0.122057i
$239$	45.9510	−	79.5895i	0.0124365	−	0.0215406i	−0.859740	−	0.510732i	$-0.829375\pi$
$239$	45.9510	−	79.5895i	0.0124365	−	0.0215406i	0.872177	+	0.489191i	$0.162708\pi$
$240$		0			0
$241$	−979.248	−	1696.11i	−0.261738	−	0.453344i	0.704966	−	0.709241i	$-0.250962\pi$
$241$	−979.248	−	1696.11i	−0.261738	−	0.453344i	−0.966704	+	0.255898i	$0.917629\pi$
$242$	3289.62	+	3289.62i	0.873821	+	0.873821i
$243$	−757.670	−	3711.45i	−0.200019	−	0.979792i
$244$			696.348i			0.182701i
$245$		0			0
$246$	−452.847	+	984.905i	−0.117368	+	0.255265i
$247$	−486.435	−	1815.40i	−0.125308	−	0.467656i
$248$	117.886	+	439.958i	0.0301847	+	0.112651i
$249$	4509.49	−	418.937i	1.14770	−	0.106623i
$250$		0			0
$251$			1167.85i			0.293681i	0.989160	+	0.146840i	$0.0469104\pi$
$251$			1167.85i			0.293681i	−0.989160	+	0.146840i	$0.953090\pi$
$252$	−4228.10	−	324.204i	−1.05692	−	0.0810435i
$253$	6149.55	+	6149.55i	1.52814	+	1.52814i
$254$	−8.43606	−	14.6117i	−0.00208396	−	0.00360952i
$255$		0			0
$256$	−336.610	+	583.026i	−0.0821802	+	0.142340i
$257$	25.3091	−	6.78155i	0.00614295	−	0.00164600i	−0.255746	−	0.966744i	$-0.582321\pi$
$257$	25.3091	−	6.78155i	0.00614295	−	0.00164600i	0.261889	+	0.965098i	$0.415654\pi$
$258$	7842.49	+	1339.47i	1.89245	+	0.323224i
$259$	−3127.77	+	1805.82i	−0.750387	+	0.433236i
$260$		0			0
$261$	5603.43	+	1971.61i	1.32890	+	0.467584i
$262$	1595.27	−	1595.27i	0.376169	−	0.376169i
$263$	576.639	+	154.510i	0.135198	+	0.0362262i	0.325783	−	0.945444i	$-0.394372\pi$
$263$	576.639	+	154.510i	0.135198	+	0.0362262i	−0.190585	+	0.981671i	$0.561039\pi$
$264$	−243.385	−	2619.83i	−0.0567399	−	0.610755i
$265$		0			0
$266$	3015.87	+	1741.21i	0.695168	+	0.401356i
$267$	1122.36	−	415.344i	0.257257	−	0.0952009i
$268$	−194.434	+	725.638i	−0.0443170	+	0.165393i
$269$	−6123.85			−1.38802			−0.694011	−	0.719965i	$-0.744158\pi$
$269$	−6123.85			−1.38802			−0.694011	+	0.719965i	$0.744158\pi$
$270$		0			0
$271$	−122.463			−0.0274505			−0.0137253	−	0.999906i	$-0.504369\pi$
$271$	−122.463			−0.0274505			−0.0137253	+	0.999906i	$0.504369\pi$
$272$	−269.968	+	1007.53i	−0.0601809	+	0.224598i
$273$	2572.08	−	951.830i	0.570218	−	0.211016i
$274$	−6925.58	−	3998.49i	−1.52697	−	0.881596i
$275$		0			0
$276$	−884.701	−	9523.04i	−0.192945	−	2.07688i
$277$	1496.60	+	401.012i	0.324627	+	0.0869836i	0.417452	−	0.908699i	$-0.362923\pi$
$277$	1496.60	+	401.012i	0.324627	+	0.0869836i	−0.0928250	+	0.995682i	$0.529590\pi$
$278$	−7272.76	+	7272.76i	−1.56903	+	1.56903i
$279$	219.886	+	1173.23i	0.0471836	+	0.251753i
$280$		0			0
$281$	−2397.24	+	1384.04i	−0.508922	+	0.293826i	−0.732390	−	0.680885i	$-0.761595\pi$
$281$	−2397.24	+	1384.04i	−0.508922	+	0.293826i	0.223468	+	0.974711i	$0.428262\pi$
$282$	−11652.5	−	1990.20i	−2.46062	−	0.420265i
$283$	−5947.68	+	1593.68i	−1.24930	+	0.334750i	−0.822067	−	0.569391i	$-0.807179\pi$
$283$	−5947.68	+	1593.68i	−1.24930	+	0.334750i	−0.427236	+	0.904140i	$0.640513\pi$
$284$	−5402.37	+	9357.18i	−1.12877	+	1.95509i
$285$		0			0
$286$	3684.91	+	6382.46i	0.761866	+	1.31959i
$287$	519.232	+	519.232i	0.106792	+	0.106792i
$288$	3808.97	−	5566.03i	0.779325	−	1.13882i
$289$		−	4198.33i		−	0.854535i
$290$		0			0
$291$	−2962.52	+	275.222i	−0.596791	+	0.0554426i
$292$	1291.47	+	4819.85i	0.258828	+	0.965960i
$293$	1828.92	+	6825.62i	0.364664	+	1.36094i	0.867876	+	0.496781i	$0.165485\pi$
$293$	1828.92	+	6825.62i	0.364664	+	1.36094i	−0.503212	+	0.864163i	$0.667848\pi$
$294$	1071.02	−	2329.38i	0.212459	−	0.462081i
$295$		0			0
$296$			2464.39i			0.483918i
$297$	−111.053	−	6894.35i	−0.0216968	−	1.34697i
$298$	−6592.65	−	6592.65i	−1.28155	−	1.28155i
$299$	3092.77	+	5356.84i	0.598193	+	1.03610i
$300$		0			0
$301$	2694.67	−	4667.30i	0.516007	−	0.893750i
$302$	10906.2	−	2922.31i	2.07809	−	0.556821i
$303$	−469.269	+	565.391i	−0.0889730	+	0.107197i
$304$	−1816.76	+	1048.91i	−0.342758	+	0.197892i
$305$		0			0
$306$	1027.70	−	2920.79i	0.191993	−	0.545655i
$307$	−496.221	+	496.221i	−0.0922502	+	0.0922502i	−0.751726	−	0.659476i	$-0.770778\pi$
$307$	−496.221	+	496.221i	−0.0922502	+	0.0922502i	0.659476	+	0.751726i	$0.270778\pi$
$308$	−7455.93	−	1997.81i	−1.37935	−	0.369597i
$309$	−508.037	+	359.811i	−0.0935314	+	0.0662426i
$310$		0			0
$311$	2763.77	+	1595.66i	0.503920	+	0.290938i	0.730331	−	0.683094i	$-0.239366\pi$
$311$	2763.77	+	1595.66i	0.503920	+	0.290938i	−0.226411	+	0.974032i	$0.572699\pi$
$312$	315.061	−	1844.66i	0.0571692	−	0.334722i
$313$	1129.32	−	4214.66i	0.203938	−	0.761108i	−0.785832	−	0.618440i	$-0.787765\pi$
$313$	1129.32	−	4214.66i	0.203938	−	0.761108i	0.989771	−	0.142669i	$-0.0455683\pi$
$314$	12428.4			2.23367
$315$		0			0
$316$	−3575.42			−0.636496
$317$	1041.92	−	3888.50i	0.184606	−	0.688959i	−0.810109	−	0.586280i	$-0.800592\pi$
$317$	1041.92	−	3888.50i	0.184606	−	0.688959i	0.994715	−	0.102679i	$-0.0327414\pi$
$318$	−4815.28	−	3996.64i	−0.849143	−	0.704781i
$319$	9364.18	+	5406.41i	1.64355	+	0.948906i
$320$		0			0
$321$	−6281.15	−	2888.00i	−1.09215	−	0.502156i
$322$	−11070.7	−	2966.39i	−1.91598	−	0.513386i
$323$	−1016.35	+	1016.35i	−0.175081	+	0.175081i
$324$	−4748.31	+	5912.13i	−0.814182	+	1.01374i
$325$		0			0
$326$	−5764.75	+	3328.28i	−0.979386	+	0.565449i
$327$	1898.56	+	5130.39i	0.321073	+	0.867618i
$328$	483.977	−	129.681i	0.0814731	−	0.0218306i
$329$	−4003.77	+	6934.73i	−0.670926	+	1.16208i
$330$		0			0
$331$	−324.017	−	561.214i	−0.0538054	−	0.0931937i	0.837868	−	0.545873i	$-0.183802\pi$
$331$	−324.017	−	561.214i	−0.0538054	−	0.0931937i	−0.891674	+	0.452679i	$0.850468\pi$
$332$	−6410.65	−	6410.65i	−1.05973	−	1.05973i
$333$	−493.765	+	6439.41i	−0.0812558	+	1.05969i
$334$		−	14920.4i		−	2.44433i
$335$		0			0
$336$	−1769.28	−	2498.14i	−0.287268	−	0.405609i
$337$	2911.92	+	10867.4i	0.470689	+	1.75664i	0.637303	+	0.770614i	$0.280050\pi$
$337$	2911.92	+	10867.4i	0.470689	+	1.75664i	−0.166614	+	0.986022i	$0.553283\pi$
$338$	−1082.58	−	4040.23i	−0.174214	−	0.650177i
$339$	−3522.16	−	4973.12i	−0.564299	−	0.796764i
$340$		0			0
$341$			2172.79i			0.345054i
$342$	5615.23	−	2692.20i	0.887828	−	0.425666i
$343$	−4890.10	−	4890.10i	−0.769798	−	0.769798i
$344$	−1838.70	−	3184.72i	−0.288186	−	0.499152i
$345$		0			0
$346$	1898.13	−	3287.66i	0.294926	−	0.510826i
$347$	−9499.02	+	2545.25i	−1.46955	+	0.393765i	−0.902777	−	0.430109i	$-0.858475\pi$
$347$	−9499.02	+	2545.25i	−1.46955	+	0.393765i	−0.566774	+	0.823874i	$0.691809\pi$
$348$	−4126.94	−	11152.0i	−0.635710	−	1.71785i
$349$	8795.71	−	5078.20i	1.34906	−	0.778883i	0.360947	−	0.932586i	$-0.382453\pi$
$349$	8795.71	−	5078.20i	1.34906	−	0.778883i	0.988117	+	0.153703i	$0.0491200\pi$
$350$		0			0
$351$	1192.85	−	4756.94i	0.181394	−	0.723381i
$352$	8681.16	−	8681.16i	1.31451	−	1.31451i
$353$	−4215.36	−	1129.50i	−0.635584	−	0.170304i	−0.0733816	−	0.997304i	$-0.523379\pi$
$353$	−4215.36	−	1129.50i	−0.635584	−	0.170304i	−0.562202	+	0.827000i	$0.690046\pi$
$354$	2608.13	+	1199.19i	0.391584	+	0.180045i
$355$		0			0
$356$	−2074.71	−	1197.83i	−0.308875	−	0.178329i
$357$	−1613.92	−	1339.54i	−0.239266	−	0.198589i
$358$	−2163.84	+	8075.54i	−0.319448	+	1.19219i
$359$	−5672.13			−0.833881			−0.416941	−	0.908934i	$-0.636898\pi$
$359$	−5672.13			−0.833881			−0.416941	+	0.908934i	$0.636898\pi$
$360$		0			0
$361$	3968.27			0.578549
$362$	−1766.62	+	6593.12i	−0.256496	+	0.957256i
$363$	948.742	−	5554.81i	0.137179	−	0.803174i
$364$	−4754.54	−	2745.04i	−0.684631	−	0.395272i
$365$		0			0
$366$	1217.74	−	862.451i	0.173913	−	0.123172i
$367$	4082.14	+	1093.81i	0.580616	+	0.155576i	0.537161	−	0.843480i	$-0.319497\pi$
$367$	4082.14	+	1093.81i	0.580616	+	0.155576i	0.0434549	+	0.999055i	$0.486164\pi$
$368$	4882.05	−	4882.05i	0.691562	−	0.691562i
$369$	1290.61	−	241.886i	0.182077	−	0.0341249i
$370$		0			0
$371$	−3671.04	+	2119.48i	−0.513723	+	0.296598i
$372$	1526.07	−	1838.66i	0.212697	−	0.256264i
$373$	223.349	−	59.8461i	0.0310042	−	0.00830755i	−0.243284	−	0.969955i	$-0.578225\pi$
$373$	223.349	−	59.8461i	0.0310042	−	0.00830755i	0.274288	+	0.961648i	$0.411558\pi$
$374$	2818.10	−	4881.09i	0.389627	−	0.674853i
$375$		0			0
$376$	2731.96	+	4731.89i	0.374707	+	0.649012i
$377$	5438.07	+	5438.07i	0.742904	+	0.742904i
$378$	4669.69	+	7795.43i	0.635404	+	1.06072i
$379$			7586.66i			1.02823i	0.857720	+	0.514117i	$0.171880\pi$
$379$			7586.66i			1.02823i	−0.857720	+	0.514117i	$0.828120\pi$
$380$		0			0
$381$	−8.53759	+	18.5685i	−0.00114802	+	0.00249684i
$382$	−2212.30	−	8256.40i	−0.296311	−	1.10585i
$383$	1160.64	+	4331.56i	0.154846	+	0.577891i	0.999119	+	0.0419781i	$0.0133660\pi$
$383$	1160.64	+	4331.56i	0.154846	+	0.577891i	−0.844273	+	0.535913i	$0.819967\pi$
$384$	−6515.58	+	605.305i	−0.865877	+	0.0804410i
$385$		0			0
$386$		−	10554.6i		−	1.39175i
$387$	−4166.40	−	8690.03i	−0.547261	−	1.14144i
$388$	4211.50	+	4211.50i	0.551047	+	0.551047i
$389$	−1695.52	−	2936.72i	−0.220993	−	0.382771i	0.734117	−	0.679023i	$-0.237596\pi$
$389$	−1695.52	−	2936.72i	−0.220993	−	0.382771i	−0.955110	+	0.296252i	$0.904263\pi$
$390$		0			0
$391$	2365.25	−	4096.73i	0.305923	−	0.529874i
$392$	−1144.64	+	306.706i	−0.147483	+	0.0395179i
$393$	−2693.76	−	460.084i	−0.345756	−	0.0590539i
$394$	2611.81	−	1507.93i	0.333962	−	0.192813i
$395$		0			0
$396$	−10477.8	+	8985.41i	−1.32962	+	1.14024i
$397$	1130.27	−	1130.27i	0.142889	−	0.142889i	−0.632044	−	0.774933i	$-0.717784\pi$
$397$	1130.27	−	1130.27i	0.142889	−	0.142889i	0.774933	+	0.632044i	$0.217784\pi$
$398$	5261.19	+	1409.73i	0.662612	+	0.177546i
$399$	−390.202	−	4200.18i	−0.0489587	−	0.526998i
$400$		0			0
$401$	6469.25	+	3735.03i	0.805634	+	0.465133i	0.845437	−	0.534075i	$-0.179340\pi$
$401$	6469.25	+	3735.03i	0.805634	+	0.465133i	−0.0398035	+	0.999208i	$0.512673\pi$
$402$	1509.77	−	558.710i	0.187315	−	0.0693183i
$403$	−399.977	+	1492.73i	−0.0494399	+	0.184512i
$404$	1470.86			0.181134
$405$		0			0
$406$	−14249.9			−1.74190
$407$	−3042.68	+	11355.4i	−0.370565	+	1.38297i
$408$	−1342.20	+	496.698i	−0.162865	+	0.0602702i
$409$	8609.85	+	4970.90i	1.04090	+	0.600966i	0.920089	−	0.391709i	$-0.128116\pi$
$409$	8609.85	+	4970.90i	1.04090	+	0.600966i	0.120815	+	0.992675i	$0.461449\pi$
$410$		0			0
$411$	896.052	+	9645.22i	0.107540	+	1.15758i
$412$	1203.76	+	322.547i	0.143944	+	0.0385697i
$413$	1374.98	−	1374.98i	0.163822	−	0.163822i
$414$	−15557.7	+	13341.7i	−1.84691	+	1.58384i
$415$		0			0
$416$	7562.12	−	4365.99i	0.891258	−	0.514568i
$417$	12280.7	+	2097.50i	1.44218	+	0.246319i
$418$	10949.2	−	2933.82i	1.28120	−	0.343296i
$419$	1659.67	−	2874.63i	0.193508	−	0.335167i	−0.752902	−	0.658133i	$-0.771347\pi$
$419$	1659.67	−	2874.63i	0.193508	−	0.335167i	0.946411	+	0.322966i	$0.104680\pi$
$420$		0			0
$421$	5046.60	+	8740.97i	0.584219	+	1.01190i	0.994972	+	0.100150i	$0.0319324\pi$
$421$	5046.60	+	8740.97i	0.584219	+	1.01190i	−0.410753	+	0.911747i	$0.634734\pi$
$422$	−4101.87	−	4101.87i	−0.473165	−	0.473165i
$423$	6190.48	+	12911.7i	0.711564	+	1.48414i
$424$			2892.44i			0.331295i
$425$		0			0
$426$	23054.4	−	2141.78i	2.62204	−	0.243591i
$427$	−261.617	−	976.367i	−0.0296499	−	0.110655i
$428$	3581.82	+	13367.5i	0.404518	+	1.50968i
$429$	3729.26	−	8110.83i	0.419698	−	0.912808i
$430$		0			0
$431$			4785.97i			0.534877i	0.963575	+	0.267439i	$0.0861773\pi$
$431$			4785.97i			0.534877i	−0.963575	+	0.267439i	$0.913823\pi$
$432$	−5473.34	+	88.1636i	−0.609575	+	0.00981892i
$433$	5732.64	+	5732.64i	0.636243	+	0.636243i	0.949627	−	0.313384i	$-0.101463\pi$
$433$	5732.64	+	5732.64i	0.636243	+	0.636243i	−0.313384	+	0.949627i	$0.601463\pi$
$434$	−1431.73	−	2479.84i	−0.158353	−	0.274276i
$435$		0			0
$436$	5475.37	−	9483.62i	0.601428	−	1.04170i
$437$	9189.71	−	2462.38i	1.00596	−	0.269546i
$438$	6829.18	−	8228.02i	0.745002	−	0.897602i
$439$	−14876.1	+	8588.72i	−1.61731	+	0.933753i	−0.629694	+	0.776843i	$0.716820\pi$
$439$	−14876.1	+	8588.72i	−1.61731	+	0.933753i	−0.987613	+	0.156910i	$0.949847\pi$
$440$		0			0
$441$	−3052.39	+	572.079i	−0.329596	+	0.0617729i
$442$	2834.60	−	2834.60i	0.305041	−	0.305041i
$443$	−6720.19	−	1800.67i	−0.720736	−	0.193121i	−0.120236	−	0.992745i	$-0.538365\pi$
$443$	−6720.19	−	1800.67i	−0.720736	−	0.193121i	−0.600500	+	0.799625i	$0.705032\pi$
$444$	10550.3	−	7472.15i	1.12769	−	0.798677i
$445$		0			0
$446$	380.287	+	219.559i	0.0403747	+	0.0233103i
$447$	−1901.35	+	11132.3i	−0.201188	+	1.17794i
$448$	−2967.75	+	11075.8i	−0.312975	+	1.16804i
$449$	3397.64			0.357115			0.178558	−	0.983929i	$-0.442857\pi$
$449$	3397.64			0.357115			0.178558	+	0.983929i	$0.442857\pi$
$450$		0			0
$451$	2390.19			0.249555
$452$	−3157.38	+	11783.5i	−0.328563	+	1.22621i
$453$	−10524.0	−	8734.86i	−1.09153	−	0.905959i
$454$	5395.71	+	3115.21i	0.557782	+	0.322036i
$455$		0			0
$456$	−2615.14	−	1202.41i	−0.268564	−	0.123482i
$457$	−8373.74	−	2243.74i	−0.857127	−	0.229666i	−0.196614	−	0.980481i	$-0.562995\pi$
$457$	−8373.74	−	2243.74i	−0.857127	−	0.229666i	−0.660513	+	0.750815i	$0.729661\pi$
$458$	16820.2	−	16820.2i	1.71606	−	1.71606i
$459$	−3606.68	+	1028.94i	−0.366765	+	0.104634i
$460$		0			0
$461$	7004.05	−	4043.79i	0.707617	−	0.408543i	−0.102561	−	0.994727i	$-0.532704\pi$
$461$	7004.05	−	4043.79i	0.707617	−	0.408543i	0.810178	+	0.586184i	$0.199370\pi$
$462$	5740.75	+	15512.9i	0.578103	+	1.56218i
$463$	7287.87	−	1952.78i	0.731525	−	0.196012i	0.126217	−	0.992003i	$-0.459716\pi$
$463$	7287.87	−	1952.78i	0.731525	−	0.196012i	0.605308	+	0.795991i	$0.293050\pi$
$464$	4292.09	−	7434.12i	0.429430	−	0.743794i
$465$		0			0
$466$	2641.67	+	4575.51i	0.262603	+	0.454842i
$467$	−9156.39	−	9156.39i	−0.907296	−	0.907296i	0.0887572	−	0.996053i	$-0.471710\pi$
$467$	−9156.39	−	9156.39i	−0.907296	−	0.907296i	−0.996053	+	0.0887572i	$0.971710\pi$
$468$	−8852.46	+	4244.28i	−0.874370	+	0.419214i
$469$		−	1090.48i		−	0.107364i
$470$		0			0
$471$	−8700.99	−	12285.4i	−0.851211	−	1.20187i
$472$	−343.410	−	1281.62i	−0.0334888	−	0.124982i
$473$	−4540.33	−	16944.7i	−0.441362	−	1.64719i
$474$	4428.27	+	6252.51i	0.429108	+	0.605881i
$475$		0			0
$476$			4198.62i			0.404293i
$477$	−579.529	+	7557.90i	−0.0556286	+	0.725477i
$478$	278.766	+	278.766i	0.0266746	+	0.0266746i
$479$	−383.279	−	663.859i	−0.0365605	−	0.0633246i	0.847166	−	0.531328i	$-0.178307\pi$
$479$	−383.279	−	663.859i	−0.0365605	−	0.0633246i	−0.883727	+	0.468003i	$0.844973\pi$
$480$		0			0
$481$	−4180.71	+	7241.20i	−0.396307	+	0.686425i
$482$	8115.13	−	2174.44i	0.766876	−	0.205484i
$483$	4818.25	+	13020.1i	0.453909	+	1.22657i
$484$	−9769.39	+	5640.36i	−0.917486	+	0.529711i
$485$		0			0
$486$	16219.8	+	981.234i	1.51388	+	0.0915837i
$487$	−3894.85	+	3894.85i	−0.362408	+	0.362408i	−0.864699	−	0.502291i	$-0.832491\pi$
$487$	−3894.85	+	3894.85i	−0.362408	+	0.362408i	0.502291	+	0.864699i	$0.332491\pi$
$488$	−666.221	−	178.513i	−0.0618000	−	0.0165593i
$489$	7325.84	+	3368.33i	0.677476	+	0.311495i
$490$		0			0
$491$	−12685.9	−	7324.19i	−1.16600	−	0.673190i	−0.213265	−	0.976994i	$-0.568410\pi$
$491$	−12685.9	−	7324.19i	−1.16600	−	0.673190i	−0.952734	+	0.303805i	$0.901743\pi$
$492$	−2022.62	−	1678.76i	−0.185339	−	0.153830i
$493$	1522.24	−	5681.09i	0.139064	−	0.518993i
$494$	8062.27			0.734289
$495$		0			0
$496$	1724.96			0.156155
$497$	4059.32	−	15149.6i	0.366369	−	1.36731i
$498$	−3270.83	+	19150.4i	−0.294316	+	1.72320i
$499$	11810.8	+	6818.95i	1.05956	+	0.611739i	0.925311	−	0.379208i	$-0.123803\pi$
$499$	11810.8	+	6818.95i	1.05956	+	0.611739i	0.134252	+	0.990947i	$0.457137\pi$
$500$		0			0
$501$	−14748.7	+	10445.6i	−1.31522	+	0.931488i
$502$	−4839.04	−	1296.62i	−0.430233	−	0.115281i
$503$	−12517.9	+	12517.9i	−1.10964	+	1.10964i	−0.116438	+	0.993198i	$0.537148\pi$
$503$	−12517.9	+	12517.9i	−1.10964	+	1.10964i	−0.993198	+	0.116438i	$0.962852\pi$
$504$	1394.08	−	3962.05i	0.123209	−	0.350166i
$505$		0			0
$506$	−32308.6	+	18653.4i	−2.83852	+	1.63882i
$507$	−3235.85	+	3898.66i	−0.283450	+	0.341510i
$508$	39.5175	−	10.5887i	0.00345139	−	0.000924798i
$509$	3526.64	−	6108.32i	0.307103	−	0.531918i	−0.670624	−	0.741797i	$-0.733974\pi$
$509$	3526.64	−	6108.32i	0.307103	−	0.531918i	0.977727	+	0.209879i	$0.0673070\pi$
$510$		0			0
$511$	−3621.62	−	6272.83i	−0.313524	−	0.543040i
$512$	−9165.88	−	9165.88i	−0.791169	−	0.791169i
$513$	−6592.41	−	3665.85i	−0.567372	−	0.315499i
$514$			112.399i			0.00964534i
$515$		0			0
$516$	−8059.11	+	17527.9i	−0.687563	+	1.49539i
$517$	6746.06	+	25176.6i	0.573871	+	2.14172i
$518$	−4009.86	−	14965.0i	−0.340122	−	1.26935i
$519$	−4578.71	+	425.368i	−0.387251	+	0.0359760i
$520$		0			0
$521$		−	17522.3i		−	1.47344i	−0.676196	−	0.736722i	$-0.736373\pi$
$521$		−	17522.3i		−	1.47344i	0.676196	−	0.736722i	$-0.263627\pi$
$522$	−14390.7	+	21029.1i	−1.20664	+	1.76326i
$523$	5784.54	+	5784.54i	0.483633	+	0.483633i	0.906290	−	0.422657i	$-0.138902\pi$
$523$	5784.54	+	5784.54i	0.483633	+	0.483633i	−0.422657	+	0.906290i	$0.638902\pi$
$524$	2735.25	+	4737.58i	0.228034	+	0.394966i
$525$		0			0
$526$	−1280.44	+	2217.79i	−0.106140	+	0.183841i
$527$	1141.59	−	305.889i	0.0943615	−	0.0252841i
$528$	−9822.13	−	1677.58i	−0.809570	−	0.138272i
$529$	−16579.9	+	9572.40i	−1.36269	+	0.786751i
$530$		0			0
$531$	−640.539	−	3417.67i	−0.0523484	−	0.279311i
$532$	−5970.95	+	5970.95i	−0.486604	+	0.486604i
$533$	1642.09	+	439.995i	0.133446	+	0.0357567i
$534$	474.884	+	5111.71i	0.0384836	+	0.414243i
$535$		0			0
$536$	−644.399	−	372.044i	−0.0519287	−	0.0299811i
$537$	9497.53	−	3514.68i	0.763219	−	0.282439i
$538$	6799.08	−	25374.5i	0.544850	−	2.03341i
$539$	−5652.97			−0.451745
$540$		0			0
$541$	10105.8			0.803113			0.401557	−	0.915834i	$-0.368469\pi$
$541$	10105.8			0.803113			0.401557	+	0.915834i	$0.368469\pi$
$542$	135.966	−	507.432i	0.0107753	−	0.0402141i
$543$	7754.07	−	2869.49i	0.612816	−	0.226780i
$544$	−5783.25	−	3338.96i	−0.455799	−	0.263156i
$545$		0			0
$546$	1088.28	+	11714.3i	0.0853002	+	0.918182i
$547$	635.040	+	170.158i	0.0496386	+	0.0133006i	0.283553	−	0.958957i	$-0.408487\pi$
$547$	635.040	+	170.158i	0.0496386	+	0.0133006i	−0.233914	+	0.972257i	$0.575154\pi$
$548$	13711.6	−	13711.6i	1.06885	−	1.06885i
$549$	−1705.06	−	599.937i	−0.132550	−	0.0466388i
$550$		0			0
$551$	10244.0	−	5914.38i	0.792032	−	0.457280i
$552$	9337.82	+	1594.87i	0.720007	+	0.122975i
$553$	5013.18	−	1343.28i	0.385501	−	0.103295i
$554$	−3323.23	+	5756.00i	−0.254856	+	0.441424i
$555$		0			0
$556$	−12469.8	−	21598.4i	−0.951148	−	1.64744i
$557$	6427.65	+	6427.65i	0.488956	+	0.488956i	0.907977	−	0.419021i	$-0.137627\pi$
$557$	6427.65	+	6427.65i	0.488956	+	0.488956i	−0.419021	+	0.907977i	$0.637627\pi$
$558$	−5105.46	−	391.479i	−0.387332	−	0.0297001i
$559$		−	12477.0i		−	0.944046i
$560$		0			0
$561$	−6797.86	+	631.529i	−0.511597	+	0.0475280i
$562$	−3073.31	−	11469.7i	−0.230675	−	0.860892i
$563$	970.932	+	3623.57i	0.0726819	+	0.271253i	0.992698	−	0.120629i	$-0.0384911\pi$
$563$	970.932	+	3623.57i	0.0726819	+	0.271253i	−0.920016	+	0.391881i	$0.871824\pi$
$564$	11974.3	−	26043.1i	0.893988	−	1.94435i
$565$		0			0
$566$		−	26413.9i		−	1.96159i
$567$	4436.54	−	10073.5i	0.328602	−	0.746114i
$568$	−7567.41	−	7567.41i	−0.559017	−	0.559017i
$569$	−4162.66	−	7209.93i	−0.306692	−	0.531206i	0.670945	−	0.741507i	$-0.265889\pi$
$569$	−4162.66	−	7209.93i	−0.306692	−	0.531206i	−0.977637	+	0.210302i	$0.932555\pi$
$570$		0			0
$571$	−13072.8	+	22642.7i	−0.958107	+	1.65949i	−0.231013	+	0.972951i	$0.574204\pi$
$571$	−13072.8	+	22642.7i	−0.958107	+	1.65949i	−0.727093	+	0.686539i	$0.759129\pi$
$572$	−17261.5	+	4625.19i	−1.26178	+	0.338093i
$573$	−6612.62	+	7967.09i	−0.482105	+	0.580855i
$574$	−2727.95	+	1574.98i	−0.198367	+	0.114527i
$575$		0			0
$576$	13347.8	+	15564.8i	0.965556	+	1.12593i
$577$	17789.3	−	17789.3i	1.28349	−	1.28349i	0.344829	−	0.938665i	$-0.387937\pi$
$577$	17789.3	−	17789.3i	1.28349	−	1.28349i	0.938665	−	0.344829i	$-0.112063\pi$
$578$	17396.0	+	4661.25i	1.25187	+	0.335437i
$579$	−10433.2	+	7389.17i	−0.748855	+	0.530369i
$580$		0			0
$581$	11397.0	+	6580.06i	0.813816	+	0.469857i
$582$	2148.78	−	12580.9i	0.153041	−	0.896043i
$583$	−3571.17	+	13327.8i	−0.253693	+	0.946794i
$584$	−4942.39			−0.350202
$585$		0			0
$586$	−30312.9			−2.13688
$587$	1709.74	−	6380.84i	0.120219	−	0.448664i	−0.879405	−	0.476074i	$-0.842059\pi$
$587$	1709.74	−	6380.84i	0.120219	−	0.448664i	0.999624	+	0.0274104i	$0.00872610\pi$
$588$	4783.66	+	3970.40i	0.335501	+	0.278463i
$589$	2058.49	+	1188.47i	0.144005	+	0.0831411i
$590$		0			0
$591$	−3319.08	−	1526.07i	−0.231013	−	0.106217i
$592$	9014.94	+	2415.55i	0.625865	+	0.167700i
$593$	−1466.22	+	1466.22i	−0.101535	+	0.101535i	−0.756050	−	0.654514i	$-0.772873\pi$
$593$	−1466.22	+	1466.22i	−0.101535	+	0.101535i	0.654514	+	0.756050i	$0.272873\pi$
$594$	28690.4	+	7194.38i	1.98179	+	0.496951i
$595$		0			0
$596$	19578.6	−	11303.7i	1.34559	−	0.776877i
$597$	−2289.80	−	6187.61i	−0.156977	−	0.424191i
$598$	−25630.2	+	6867.58i	−1.75267	+	0.469626i
$599$	−8093.94	+	14019.1i	−0.552102	+	0.956269i	0.446020	+	0.895023i	$0.352841\pi$
$599$	−8093.94	+	14019.1i	−0.552102	+	0.956269i	−0.998123	+	0.0612464i	$0.980492\pi$
$600$		0			0
$601$	−4667.92	−	8085.07i	−0.316819	−	0.548747i	0.663003	−	0.748617i	$-0.269282\pi$
$601$	−4667.92	−	8085.07i	−0.316819	−	0.548747i	−0.979823	+	0.199869i	$0.935948\pi$
$602$	16347.4	+	16347.4i	1.10676	+	1.10676i
$603$	−1609.26	−	1101.26i	−0.108680	−	0.0743726i
$604$			27378.3i			1.84438i
$605$		0			0
$606$	−1821.71	−	2572.18i	−0.122116	−	0.172422i
$607$	−1299.92	−	4851.38i	−0.0869230	−	0.324401i	0.908748	−	0.417344i	$-0.137039\pi$
$607$	−1299.92	−	4851.38i	−0.0869230	−	0.324401i	−0.995671	+	0.0929433i	$0.970372\pi$
$608$	−3476.07	−	12972.9i	−0.231864	−	0.865329i
$609$	9976.27	+	14086.0i	0.663807	+	0.937265i
$610$		0			0
$611$			18538.5i			1.22747i
$612$	6196.05	+	4240.10i	0.409249	+	0.280059i
$613$	−17030.5	−	17030.5i	−1.12212	−	1.12212i	−0.991423	−	0.130693i	$-0.958280\pi$
$613$	−17030.5	−	17030.5i	−1.12212	−	1.12212i	−0.130693	−	0.991423i	$-0.541720\pi$
$614$	−1505.18	−	2607.05i	−0.0989320	−	0.171355i
$615$		0			0
$616$	3822.75	−	6621.19i	0.250037	−	0.433077i
$617$	−6255.15	+	1676.06i	−0.408141	+	0.109361i	−0.457047	−	0.889442i	$-0.651093\pi$
$617$	−6255.15	+	1676.06i	−0.408141	+	0.109361i	0.0489065	+	0.998803i	$0.484426\pi$
$618$	−926.844	−	2504.56i	−0.0603287	−	0.163023i
$619$	10407.7	−	6008.87i	0.675799	−	0.390173i	−0.122472	−	0.992472i	$-0.539082\pi$
$619$	10407.7	−	6008.87i	0.675799	−	0.390173i	0.798270	+	0.602300i	$0.205749\pi$
$620$		0			0
$621$	24080.1	+	6038.29i	1.55604	+	0.390191i
$622$	−9680.22	+	9680.22i	−0.624022	+	0.624022i
$623$	3359.03	+	900.049i	0.216014	+	0.0578807i
$624$	−6439.10	−	2960.62i	−0.413093	−	0.189935i
$625$		0			0
$626$	16209.9	+	9358.77i	1.03495	+	0.597526i
$627$	−10565.5	−	8769.27i	−0.672959	−	0.558550i
$628$	−7799.85	+	29109.4i	−0.495618	+	1.84967i
$629$	6394.53			0.405352
$630$		0			0
$631$	1233.51			0.0778212			0.0389106	−	0.999243i	$-0.487611\pi$
$631$	1233.51			0.0778212			0.0389106	+	0.999243i	$0.487611\pi$
$632$	916.580	−	3420.72i	0.0576892	−	0.215299i
$633$	−1183.00	+	6926.37i	−0.0742812	+	0.434910i
$634$	14955.4	+	8634.51i	0.936838	+	0.540884i
$635$		0			0
$636$	12382.8	−	8770.01i	0.772031	−	0.546782i
$637$	−3883.66	−	1040.62i	−0.241564	−	0.0647268i
$638$	−32798.5	+	32798.5i	−2.03527	+	2.03527i
$639$	−18257.3	−	21289.8i	−1.13028	−	1.31801i
$640$		0			0
$641$	22917.1	−	13231.2i	1.41212	−	0.815291i	0.416536	−	0.909119i	$-0.363244\pi$
$641$	22917.1	−	13231.2i	1.41212	−	0.815291i	0.995588	+	0.0938285i	$0.0299105\pi$
$642$	18940.3	−	22819.9i	1.16435	−	1.40285i
$643$	23058.6	−	6178.54i	1.41422	−	0.378939i	0.530791	−	0.847503i	$-0.321895\pi$
$643$	23058.6	−	6178.54i	1.41422	−	0.378939i	0.883430	+	0.468564i	$0.155228\pi$
$644$	13895.6	−	24067.9i	0.850255	−	1.47269i
$645$		0			0
$646$	−3082.88	−	5339.70i	−0.187762	−	0.325213i
$647$	−11613.4	−	11613.4i	−0.705670	−	0.705670i	0.259951	−	0.965622i	$-0.416294\pi$
$647$	−11613.4	−	11613.4i	−0.705670	−	0.705670i	−0.965622	+	0.259951i	$0.916294\pi$
$648$	−4439.09	−	6058.49i	−0.269111	−	0.367284i
$649$		−	6329.46i		−	0.382825i
$650$		0			0
$651$	−1448.96	+	3151.38i	−0.0872340	+	0.189727i
$652$	−4177.55	−	15590.8i	−0.250929	−	0.936479i
$653$	4917.23	+	18351.3i	0.294680	+	1.09976i	0.941471	+	0.337094i	$0.109444\pi$
$653$	4917.23	+	18351.3i	0.294680	+	1.09976i	−0.646791	+	0.762667i	$0.723889\pi$
$654$	−23365.9	+	2170.72i	−1.39706	+	0.129789i
$655$		0			0
$656$		−	1897.54i		−	0.112937i
$657$	−12914.4	−	990.260i	−0.766879	−	0.0588032i
$658$	−24289.2	−	24289.2i	−1.43904	−	1.43904i
$659$	−10618.4	−	18391.6i	−0.627670	−	1.08716i	−0.988018	−	0.154338i	$-0.950675\pi$
$659$	−10618.4	−	18391.6i	−0.627670	−	1.08716i	0.360348	−	0.932818i	$-0.382658\pi$
$660$		0			0
$661$	7686.03	−	13312.6i	0.452272	−	0.783359i	−0.546254	−	0.837619i	$-0.683947\pi$
$661$	7686.03	−	13312.6i	0.452272	−	0.783359i	0.998527	+	0.0542605i	$0.0172801\pi$
$662$	2685.16	−	719.488i	0.157646	−	0.0422412i
$663$	−4786.46	−	817.511i	−0.280378	−	0.0478876i
$664$	7776.70	−	4489.88i	0.454510	−	0.262411i
$665$		0			0
$666$	−26133.9	−	9195.38i	−1.52052	−	0.535006i
$667$	−27528.0	+	27528.0i	−1.59803	+	1.59803i
$668$	34946.1	+	9363.79i	2.02411	+	0.542359i
$669$	−49.2027	−	529.624i	−0.00284347	−	0.0306075i
$670$		0			0
$671$	−2849.41	−	1645.11i	−0.163935	−	0.0946479i
$672$	18380.2	−	6801.80i	1.05510	−	0.390454i
$673$	7929.17	−	29592.1i	0.454156	−	1.69493i	−0.236401	−	0.971656i	$-0.575968\pi$
$673$	7929.17	−	29592.1i	0.454156	−	1.69493i	0.690557	−	0.723278i	$-0.257365\pi$
$674$	−48262.8			−2.75818
$675$		0			0
$676$	10142.4			0.577057
$677$	8227.98	−	30707.2i	0.467100	−	1.74324i	−0.182731	−	0.983163i	$-0.558494\pi$
$677$	8227.98	−	30707.2i	0.467100	−	1.74324i	0.649831	−	0.760079i	$-0.274840\pi$
$678$	24516.9	−	9072.79i	1.38874	−	0.513921i
$679$	−7487.30	−	4322.79i	−0.423175	−	0.244320i
$680$		0			0
$681$	−698.112	−	7514.57i	−0.0392830	−	0.422847i
$682$	−9003.09	−	2412.37i	−0.505493	−	0.135446i
$683$	10544.6	−	10544.6i	0.590742	−	0.590742i	−0.347090	−	0.937832i	$-0.612830\pi$
$683$	10544.6	−	10544.6i	0.590742	−	0.590742i	0.937832	+	0.347090i	$0.112830\pi$
$684$	2781.59	+	14841.5i	0.155492	+	0.829646i
$685$		0			0
$686$	25691.7	−	14833.1i	1.42990	−	0.825555i
$687$	−28402.3	−	4851.02i	−1.57732	−	0.269400i
$688$	−13452.2	+	3604.51i	−0.745438	+	0.199739i
$689$	−4906.87	+	8498.95i	−0.271316	+	0.469933i
$690$		0			0
$691$	1725.29	+	2988.28i	0.0949825	+	0.164515i	0.909601	−	0.415482i	$-0.136387\pi$
$691$	1725.29	+	2988.28i	0.0949825	+	0.164515i	−0.814619	+	0.579997i	$0.803054\pi$
$692$	6509.06	+	6509.06i	0.357568	+	0.357568i
$693$	11315.4	−	16535.2i	0.620256	−	0.906377i
$694$		−	42185.6i		−	2.30741i
$695$		0			0
$696$	11727.5	−	1089.50i	0.638691	−	0.0593351i
$697$	−336.493	−	1255.81i	−0.0182864	−	0.0682457i
$698$	11276.3	+	42083.6i	0.611481	+	2.28208i
$699$	2673.46	−	5814.56i	0.144663	−	0.314631i
$700$		0			0
$701$			33118.2i			1.78439i	0.451650	+	0.892195i	$0.350835\pi$
$701$			33118.2i			1.78439i	−0.451650	+	0.892195i	$0.649165\pi$
$702$	18386.3	+	10224.1i	0.988526	+	0.549691i
$703$	9093.79	+	9093.79i	0.487879	+	0.487879i
$704$	18661.9	+	32323.4i	0.999074	+	1.73045i
$705$		0			0
$706$	9360.31	−	16212.5i	0.498980	−	0.864259i
$707$	−2062.33	+	552.601i	−0.109706	+	0.0293956i
$708$	−4445.53	+	5356.12i	−0.235979	+	0.284315i
$709$	24955.0	−	14407.8i	1.32187	−	0.763181i	0.337842	−	0.941203i	$-0.390303\pi$
$709$	24955.0	−	14407.8i	1.32187	−	0.763181i	0.984027	+	0.178021i	$0.0569696\pi$
$710$		0			0
$711$	3080.39	−	8754.66i	0.162481	−	0.461780i
$712$	1677.88	−	1677.88i	0.0883161	−	0.0883161i
$713$	−7556.35	−	2024.72i	−0.396897	−	0.106348i
$714$	7342.35	−	5200.13i	0.384846	−	0.272563i
$715$		0			0
$716$	−17556.4	−	10136.2i	−0.916358	−	0.529060i
$717$	80.3973	−	470.720i	0.00418758	−	0.0245180i
$718$	6297.55	−	23502.8i	0.327329	−	1.22161i
$719$	−11652.8			−0.604418			−0.302209	−	0.953242i	$-0.597724\pi$
$719$	−11652.8			−0.604418			−0.302209	+	0.953242i	$0.597724\pi$
$720$		0			0
$721$	−1809.00			−0.0934407
$722$	−4405.82	+	16442.7i	−0.227102	+	0.847555i
$723$	−7830.76	−	6499.47i	−0.402807	−	0.334326i
$724$	−14333.6	−	8275.48i	−0.735777	−	0.424801i
$725$		0			0
$726$	21963.3	+	10098.5i	1.12278	+	0.516238i
$727$	12169.8	+	3260.88i	0.620841	+	0.166354i	0.555510	−	0.831510i	$-0.312523\pi$
$727$	12169.8	+	3260.88i	0.620841	+	0.166354i	0.0653308	+	0.997864i	$0.479190\pi$
$728$	3845.13	−	3845.13i	0.195755	−	0.195755i
$729$	−10385.4	−	16720.2i	−0.527633	−	0.849472i
$730$		0			0
$731$	−8263.62	+	4771.00i	−0.418113	+	0.241398i
$732$	1255.78	+	3393.43i	0.0634084	+	0.171345i
$733$	−26234.6	+	7029.55i	−1.32196	+	0.354219i	−0.849713	−	0.527246i	$-0.823225\pi$
$733$	−26234.6	+	7029.55i	−1.32196	+	0.354219i	−0.472250	+	0.881465i	$0.656558\pi$
$734$	−9064.49	+	15700.2i	−0.455826	+	0.789514i
$735$		0			0
$736$	22101.0	+	38280.1i	1.10687	+	1.91715i
$737$	−2509.92	−	2509.92i	−0.125446	−	0.125446i
$738$	−430.648	+	5616.27i	−0.0214802	+	0.280132i
$739$			18361.9i			0.914008i	0.889465	+	0.457004i	$0.151077\pi$
$739$			18361.9i			0.914008i	−0.889465	+	0.457004i	$0.848923\pi$
$740$		0			0
$741$	−5644.33	−	7969.53i	−0.279824	−	0.395098i
$742$	−4706.35	−	17564.3i	−0.232851	−	0.869013i
$743$	−3625.64	−	13531.1i	−0.179020	−	0.668112i	−0.995832	−	0.0912077i	$-0.970927\pi$
$743$	−3625.64	−	13531.1i	−0.179020	−	0.668112i	0.816812	−	0.576904i	$-0.195739\pi$
$744$	1367.89	+	1931.40i	0.0674051	+	0.0951728i
$745$		0			0
$746$			991.903i			0.0486811i
$747$	21220.0	−	10173.9i	1.03936	−	0.498316i
$748$	9663.78	+	9663.78i	0.472384	+	0.472384i
$749$	−10044.3	−	17397.3i	−0.490002	−	0.848708i
$750$		0			0
$751$	−12757.5	+	22096.6i	−0.619876	+	1.07366i	0.369632	+	0.929178i	$0.379484\pi$
$751$	−12757.5	+	22096.6i	−0.619876	+	1.07366i	−0.989508	+	0.144478i	$0.953850\pi$
$752$	19987.5	−	5355.62i	0.969239	−	0.259707i
$753$	2106.07	+	5691.12i	0.101925	+	0.275426i
$754$	−28570.6	+	16495.3i	−1.37995	+	0.796713i
$755$		0			0
$756$	−21188.9	+	6044.95i	−1.01936	+	0.290810i
$757$	14733.2	−	14733.2i	0.707382	−	0.707382i	−0.258602	−	0.965984i	$-0.583262\pi$
$757$	14733.2	−	14733.2i	0.707382	−	0.707382i	0.965984	+	0.258602i	$0.0832617\pi$
$758$	−31435.7	−	8423.18i	−1.50633	−	0.403620i
$759$	41057.8	+	18877.9i	1.96351	+	0.902797i
$760$		0			0
$761$	1768.38	+	1020.97i	0.0842361	+	0.0486337i	0.541526	−	0.840684i	$-0.317847\pi$
$761$	1768.38	+	1020.97i	0.0842361	+	0.0486337i	−0.457290	+	0.889317i	$0.651180\pi$
$762$	−67.4608	−	55.9919i	−0.00320715	−	0.00266191i
$763$	−4114.18	+	15354.3i	−0.195207	+	0.728523i
$764$	20726.4			0.981484
$765$		0			0
$766$	−19236.7			−0.907375
$767$	1165.15	−	4348.41i	0.0548517	−	0.204709i
$768$	−588.944	+	3448.22i	−0.0276715	+	0.162014i
$769$	−7810.71	−	4509.51i	−0.366270	−	0.211466i	0.305558	−	0.952174i	$-0.401157\pi$
$769$	−7810.71	−	4509.51i	−0.366270	−	0.211466i	−0.671828	+	0.740708i	$0.734490\pi$
$770$		0			0
$771$	111.106	−	78.6896i	0.00518986	−	0.00367566i
$772$	24720.7	+	6623.89i	1.15248	+	0.308807i
$773$	12401.6	−	12401.6i	0.577042	−	0.577042i	−0.357045	−	0.934087i	$-0.616216\pi$
$773$	12401.6	−	12401.6i	0.577042	−	0.577042i	0.934087	+	0.357045i	$0.116216\pi$
$774$	40633.4	−	7615.51i	1.88700	−	0.353661i
$775$		0			0
$776$	−5108.93	+	2949.64i	−0.236340	+	0.136451i
$777$	−11985.6	+	14440.6i	−0.553386	+	0.666737i
$778$	14050.9	−	3764.94i	0.647494	−	0.173496i
$779$	1307.38	−	2264.45i	0.0601306	−	0.104149i
$780$		0			0
$781$	−25526.0	−	44212.3i	−1.16952	−	2.02566i
$782$	14349.0	+	14349.0i	0.656162	+	0.656162i
$783$	30862.0	−	497.120i	1.40858	−	0.0226892i
$784$			4487.83i			0.204438i
$785$		0			0
$786$	4897.16	−	10650.9i	0.222234	−	0.483341i
$787$	8582.02	+	32028.5i	0.388712	+	1.45069i	0.832232	+	0.554427i	$0.187063\pi$
$787$	8582.02	+	32028.5i	0.388712	+	1.45069i	−0.443521	+	0.896264i	$0.646271\pi$
$788$	1892.70	+	7063.67i	0.0855645	+	0.319331i
$789$	3088.70	−	286.944i	0.139367	−	0.0129474i
$790$		0			0
$791$		−	17708.1i		−	0.795991i
$792$	−5910.60	−	12328.0i	−0.265182	−	0.553100i
$793$	−1654.74	−	1654.74i	−0.0741004	−	0.0741004i
$794$	3428.45	+	5938.26i	0.153238	+	0.265417i
$795$		0			0
$796$	−6603.69	+	11437.9i	−0.294047	+	0.509305i
$797$	8323.68	−	2230.32i	0.369937	−	0.0991243i	−0.0690608	−	0.997612i	$-0.522000\pi$
$797$	8323.68	−	2230.32i	0.369937	−	0.0991243i	0.438998	+	0.898488i	$0.355334\pi$
$798$	17836.9	+	3046.48i	0.791253	+	0.135143i
$799$	12278.2	−	7088.80i	0.543642	−	0.313872i
$800$		0			0
$801$	4720.45	−	4048.09i	0.208226	−	0.178567i
$802$	−22658.9	+	22658.9i	−0.997646	+	0.997646i
$803$	−22773.6	−	6102.17i	−1.00083	−	0.268170i
$804$	361.088	+	3886.80i	0.0158390	+	0.170494i
$805$		0			0
$806$	−5741.14	−	3314.65i	−0.250897	−	0.144856i
$807$	−29842.6	+	11043.6i	−1.30175	+	0.481727i
$808$	−377.065	+	1407.23i	−0.0164172	+	0.0612699i
$809$	23450.0			1.01911			0.509554	−	0.860439i	$-0.329810\pi$
$809$	23450.0			1.01911			0.509554	+	0.860439i	$0.329810\pi$
$810$		0			0
$811$	12488.0			0.540705			0.270352	−	0.962761i	$-0.412860\pi$
$811$	12488.0			0.540705			0.270352	+	0.962761i	$0.412860\pi$
$812$	8943.05	−	33375.9i	0.386502	−	1.44244i
$813$	−596.783	+	220.847i	−0.0257443	+	0.00952699i
$814$	−43673.7	−	25215.0i	−1.88054	−	1.08573i
$815$		0			0
$816$	501.364	+	5396.75i	0.0215089	+	0.231524i
$817$	−18536.8	−	4966.92i	−0.793783	−	0.212693i
$818$	−30156.4	+	30156.4i	−1.28899	+	1.28899i
$819$	10817.7	−	9276.87i	0.461539	−	0.395800i
$820$		0			0
$821$	−7534.17	+	4349.85i	−0.320273	+	0.184910i	−0.651514	−	0.758636i	$-0.725866\pi$
$821$	−7534.17	+	4349.85i	−0.320273	+	0.184910i	0.331241	+	0.943546i	$0.392533\pi$
$822$	−40960.3	−	6995.88i	−1.73802	−	0.296848i
$823$	−29156.6	+	7812.50i	−1.23492	+	0.330895i	−0.816492	−	0.577356i	$-0.804084\pi$
$823$	−29156.6	+	7812.50i	−1.23492	+	0.330895i	−0.418425	+	0.908251i	$0.637418\pi$
$824$	−617.183	+	1068.99i	−0.0260930	+	0.0451943i
$825$		0			0
$826$	4170.72	+	7223.89i	0.175687	+	0.304299i
$827$	26730.4	+	26730.4i	1.12395	+	1.12395i	0.991141	+	0.132810i	$0.0424001\pi$
$827$	26730.4	+	26730.4i	1.12395	+	1.12395i	0.132810	+	0.991141i	$0.457600\pi$
$828$	−21484.9	−	44812.0i	−0.901755	−	1.88083i
$829$			39741.7i			1.66500i	0.554025	+	0.832500i	$0.313091\pi$
$829$			39741.7i			1.66500i	−0.554025	+	0.832500i	$0.686909\pi$
$830$		0			0
$831$	8016.35	−	744.728i	0.334638	−	0.0310883i
$832$	6870.73	+	25641.9i	0.286298	+	1.06848i
$833$	795.833	+	2970.09i	0.0331020	+	0.123538i
$834$	−22325.9	+	48557.0i	−0.926957	+	2.01605i
$835$		0			0
$836$			27486.1i			1.13711i
$837$	3187.31	+	5320.80i	0.131624	+	0.219730i
$838$	10068.5	+	10068.5i	0.415049	+	0.415049i
$839$	14713.2	+	25484.1i	0.605431	+	1.04864i	0.991983	+	0.126370i	$0.0403328\pi$
$839$	14713.2	+	25484.1i	0.605431	+	1.04864i	−0.386552	+	0.922268i	$0.626334\pi$
$840$		0			0
$841$	−12006.9	+	20796.6i	−0.492309	+	0.852704i
$842$	−41821.7	+	11206.1i	−1.71172	+	0.458655i
$843$	−9186.19	+	11067.8i	−0.375314	+	0.452190i
$844$	12181.6	−	7033.04i	0.496810	−	0.286833i
$845$		0			0
$846$	−60373.5	+	11315.2i	−2.45353	+	0.459840i
$847$	11578.8	−	11578.8i	0.469721	−	0.469721i
$848$	10580.8	+	2835.11i	0.428473	+	0.114809i
$849$	−26110.1	+	18492.2i	−1.05547	+	0.747526i
$850$		0			0
$851$	−36655.6	−	21163.1i	−1.47654	−	0.852482i
$852$	−9452.17	+	55341.7i	−0.380077	+	2.22532i
$853$	4857.73	−	18129.3i	0.194989	−	0.727709i	−0.797281	−	0.603609i	$-0.793729\pi$
$853$	4857.73	−	18129.3i	0.194989	−	0.727709i	0.992270	−	0.124100i	$-0.0396044\pi$
$854$	4336.09			0.173745
$855$		0			0
$856$	−13707.4			−0.547324
$857$	−4197.56	+	15665.5i	−0.167312	+	0.624415i	0.830422	+	0.557134i	$0.188099\pi$
$857$	−4197.56	+	15665.5i	−0.167312	+	0.624415i	−0.997734	+	0.0672811i	$0.978568\pi$
$858$	29467.2	+	24457.5i	1.17249	+	0.973155i
$859$	601.750	+	347.420i	0.0239016	+	0.0137996i	0.511903	−	0.859043i	$-0.328941\pi$
$859$	601.750	+	347.420i	0.0239016	+	0.0137996i	−0.488002	+	0.872843i	$0.662274\pi$
$860$		0			0
$861$	3466.68	+	1593.94i	0.137217	+	0.0630908i
$862$	−19830.9	−	5313.68i	−0.783578	−	0.209959i
$863$	15470.7	−	15470.7i	0.610228	−	0.610228i	−0.332777	−	0.943006i	$-0.607986\pi$
$863$	15470.7	−	15470.7i	0.610228	−	0.610228i	0.943006	+	0.332777i	$0.107986\pi$
$864$	8524.11	−	33993.2i	0.335644	−	1.33851i
$865$		0			0
$866$	−30118.3	+	17388.8i	−1.18182	+	0.682327i
$867$	−7571.18	−	20459.2i	−0.296575	−	0.801420i
$868$	6706.75	−	1797.07i	0.262260	−	0.0702724i
$869$	8446.85	−	14630.4i	0.329735	−	0.571118i
$870$		0			0
$871$	−1262.31	−	2186.38i	−0.0491063	−	0.0850547i
$872$	7669.67	+	7669.67i	0.297853	+	0.297853i
$873$	−13940.6	+	6683.75i	−0.540454	+	0.259119i
$874$			40812.0i			1.57950i
$875$		0			0
$876$	14985.6	+	21158.9i	0.577986	+	0.816090i
$877$	−5050.52	−	18848.8i	−0.194463	−	0.725746i	−0.992405	−	0.123012i	$-0.960745\pi$
$877$	−5050.52	−	18848.8i	−0.194463	−	0.725746i	0.797942	−	0.602734i	$-0.205922\pi$
$878$	−19071.5	−	71175.7i	−0.733065	−	2.73584i
$879$	21221.8	+	29964.2i	0.814327	+	1.14979i
$880$		0			0
$881$			22685.6i			0.867533i	0.901025	+	0.433766i	$0.142816\pi$
$881$			22685.6i			0.867533i	−0.901025	+	0.433766i	$0.857184\pi$
$882$	1018.51	−	13282.9i	0.0388834	−	0.507096i
$883$	6561.23	+	6561.23i	0.250060	+	0.250060i	0.820995	−	0.570935i	$-0.193419\pi$
$883$	6561.23	+	6561.23i	0.250060	+	0.250060i	−0.570935	+	0.820995i	$0.693419\pi$
$884$	4860.18	+	8418.08i	0.184916	+	0.320284i
$885$		0			0
$886$	14922.3	−	25846.3i	0.565831	−	0.980048i
$887$	−12631.0	+	3384.46i	−0.478137	+	0.128116i	−0.489835	−	0.871815i	$-0.662943\pi$
$887$	−12631.0	+	3384.46i	−0.478137	+	0.128116i	0.0116982	+	0.999932i	$0.496276\pi$
$888$	4444.22	+	12009.4i	0.167949	+	0.453839i
$889$	−51.4304	+	29.6933i	−0.00194029	+	0.00112023i
$890$		0			0
$891$	−12974.3	−	33397.1i	−0.487829	−	1.25572i
$892$	−752.908	+	752.908i	−0.0282615	+	0.0282615i
$893$	27542.2	+	7379.90i	1.03210	+	0.276550i
$894$	−44016.2	−	20238.1i	−1.64667	−	0.757118i
$895$		0			0
$896$	−16467.1	−	9507.27i	−0.613980	−	0.354482i
$897$	24732.0	+	20527.4i	0.920601	+	0.764091i
$898$	−3772.27	+	14078.3i	−0.140181	+	0.523162i
$899$	−9726.35			−0.360836
$900$		0			0
$901$	7505.21			0.277508
$902$	−2653.73	+	9903.87i	−0.0979597	+	0.365591i
$903$	4714.68	−	27604.1i	0.173748	−	1.01728i
$904$	−10464.3	−	6041.54i	−0.384996	−	0.222277i
$905$		0			0
$906$	47877.8	−	33908.9i	1.75567	−	1.24343i
$907$	12250.7	+	3282.57i	0.448488	+	0.120172i	0.475992	−	0.879450i	$-0.342089\pi$
$907$	12250.7	+	3282.57i	0.448488	+	0.120172i	−0.0275041	+	0.999622i	$0.508756\pi$
$908$	−10682.7	+	10682.7i	−0.390436	+	0.390436i
$909$	−1267.22	+	3601.52i	−0.0462387	+	0.131413i
$910$		0			0
$911$	−19788.0	+	11424.6i	−0.719655	+	0.415493i	−0.814626	−	0.579987i	$-0.803058\pi$
$911$	−19788.0	+	11424.6i	−0.719655	+	0.415493i	0.0949706	+	0.995480i	$0.469724\pi$
$912$	−6961.82	+	8387.82i	−0.252773	+	0.304549i
$913$	41377.0	−	11086.9i	1.49987	−	0.401888i
$914$	18594.1	−	32205.9i	0.672908	−	1.16551i
$915$		0			0
$916$	28839.8	+	49951.9i	1.04028	+	1.80181i
$917$	−5615.06	−	5615.06i	−0.202209	−	0.202209i
$918$	−259.124	−	16086.9i	−0.00931631	−	0.578372i
$919$		−	34032.1i		−	1.22156i	−0.791800	−	0.610780i	$-0.790856\pi$
$919$		−	34032.1i		−	1.22156i	0.791800	−	0.610780i	$-0.209144\pi$
$920$		0			0
$921$	−1523.30	+	3313.04i	−0.0544998	+	0.118533i
$922$	8979.34	+	33511.3i	0.320736	+	1.19700i
$923$	−9397.87	−	35073.3i	−0.335140	−	1.25076i
$924$	−39936.8	+	3710.18i	−1.42189	+	0.132095i
$925$		0			0
$926$			32365.8i			1.14860i
$927$	−1826.88	+	2669.61i	−0.0647276	+	0.0945861i
$928$	38860.6	+	38860.6i	1.37463	+	1.37463i
$929$	10629.2	+	18410.4i	0.375386	+	0.650188i	0.990385	−	0.138340i	$-0.0441767\pi$
$929$	10629.2	+	18410.4i	0.375386	+	0.650188i	−0.614998	+	0.788528i	$0.710843\pi$
$930$		0			0
$931$	−3092.05	+	5355.60i	−0.108849	+	0.188531i
$932$	−12374.5	+	3315.75i	−0.434916	+	0.116535i
$933$	16345.9	+	2791.82i	0.573570	+	0.0979638i
$934$	48106.0	−	27774.0i	1.68531	−	0.973012i
$935$		0			0
$936$	−1791.27	−	9557.51i	−0.0625528	−	0.333757i
$937$	376.587	−	376.587i	0.0131297	−	0.0131297i	−0.700511	−	0.713641i	$-0.747045\pi$
$937$	376.587	−	376.587i	0.0131297	−	0.0131297i	0.713641	+	0.700511i	$0.247045\pi$
$938$	4518.48	+	1210.72i	0.157285	+	0.0421445i
$939$	−2097.28	−	22575.4i	−0.0728883	−	0.784579i
$940$		0			0
$941$	24030.3	+	13873.9i	0.832481	+	0.480633i	0.854701	−	0.519120i	$-0.173740\pi$
$941$	24030.3	+	13873.9i	0.832481	+	0.480633i	−0.0222206	+	0.999753i	$0.507074\pi$
$942$	60565.6	−	22413.0i	2.09483	−	0.775219i
$943$	−2227.30	+	8312.38i	−0.0769149	+	0.287050i
$944$	−5024.89			−0.173248
$945$		0			0
$946$	75252.4			2.58633
$947$	−3256.28	+	12152.6i	−0.111737	+	0.417008i	−0.999022	−	0.0442131i	$-0.985922\pi$
$947$	−3256.28	+	12152.6i	−0.111737	+	0.417008i	0.887285	+	0.461221i	$0.152589\pi$
$948$	−17423.6	+	6447.82i	−0.596933	+	0.220903i
$949$	−14522.4	−	8384.52i	−0.496752	−	0.286800i
$950$		0			0
$951$	−1934.97	−	20828.3i	−0.0659788	−	0.710204i
$952$	−4016.97	−	1076.34i	−0.136755	−	0.0366434i
$953$	−1723.37	+	1723.37i	−0.0585787	+	0.0585787i	−0.735789	−	0.677211i	$-0.763189\pi$
$953$	−1723.37	+	1723.37i	−0.0585787	+	0.0585787i	0.677211	+	0.735789i	$0.263189\pi$
$954$	−30673.1	−	10792.6i	−1.04096	−	0.366271i
$955$		0			0
$956$	−827.868	+	477.970i	−0.0280075	+	0.0161701i
$957$	55383.1	+	9459.24i	1.87072	+	0.319513i
$958$	3176.28	−	851.080i	0.107120	−	0.0287027i
$959$	−14073.9	+	24376.7i	−0.473900	+	0.820819i
$960$		0			0
$961$	13918.3	+	24107.1i	0.467197	+	0.809209i
$962$	−25362.6	−	25362.6i	−0.850025	−	0.850025i
$963$	−35817.3	−	2746.42i	−1.19854	−	0.0919025i
$964$			20371.7i			0.680632i
$965$		0			0
$966$	−59299.0	+	5508.95i	−1.97507	+	0.183486i
$967$	−8142.30	−	30387.5i	−0.270774	−	1.01054i	−0.958621	−	0.284687i	$-0.908110\pi$
$967$	−8142.30	−	30387.5i	−0.270774	−	1.01054i	0.687846	−	0.725856i	$-0.258556\pi$
$968$	−2891.88	−	10792.7i	−0.0960214	−	0.358357i
$969$	−3119.98	+	6785.69i	−0.103435	+	0.224962i
$970$		0			0
$971$		−	51764.9i		−	1.71083i	−0.517943	−	0.855415i	$-0.673302\pi$
$971$		−	51764.9i		−	1.71083i	0.517943	−	0.855415i	$-0.326698\pi$
$972$	−12477.5	+	37373.9i	−0.411746	+	1.23330i
$973$	25598.7	+	25598.7i	0.843430	+	0.843430i
$974$	−11814.2	−	20462.8i	−0.388657	−	0.673174i
$975$		0			0
$976$	−1306.03	+	2262.12i	−0.0428331	+	0.0741891i
$977$	−36283.3	+	9722.09i	−1.18813	+	0.318359i	−0.798148	−	0.602462i	$-0.794187\pi$
$977$	−36283.3	+	9722.09i	−1.18813	+	0.318359i	−0.389985	+	0.920821i	$0.627520\pi$
$978$	−22090.5	+	26615.3i	−0.722265	+	0.870208i
$979$	9802.93	−	5659.73i	0.320024	−	0.184766i
$980$		0			0
$981$	18504.0	+	21577.4i	0.602231	+	0.702258i
$982$	44432.8	−	44432.8i	1.44390	−	1.44390i
$983$	49244.5	+	13195.0i	1.59782	+	0.428134i	0.944382	−	0.328849i	$-0.106661\pi$
$983$	49244.5	+	13195.0i	1.59782	+	0.428134i	0.653435	+	0.756983i	$0.273327\pi$
$984$	2124.64	−	1504.75i	0.0688324	−	0.0487498i
$985$		0			0
$986$	21849.8	+	12615.0i	0.705720	+	0.407448i
$987$	−7005.12	+	41014.4i	−0.225912	+	1.32270i
$988$	−5059.76	+	18883.3i	−0.162928	+	0.608054i
$989$	63159.8			2.03070
$990$		0			0
$991$	61805.9			1.98116			0.990580	−	0.136936i	$-0.0437255\pi$
$991$	61805.9			1.98116			0.990580	+	0.136936i	$0.0437255\pi$
$992$	−2858.24	+	10667.1i	−0.0914812	+	0.341413i
$993$	−2591.07	−	2150.57i	−0.0828048	−	0.0687273i
$994$	58266.3	+	33640.1i	1.85925	+	1.07344i
$995$		0			0
$996$	−42801.0	−	19679.4i	−1.36165	−	0.626070i
$997$	11218.8	+	3006.06i	0.356371	+	0.0954892i	0.432562	−	0.901604i	$-0.357610\pi$
$997$	11218.8	+	3006.06i	0.356371	+	0.0954892i	−0.0761919	+	0.997093i	$0.524276\pi$
$998$	−41367.7	+	41367.7i	−1.31210	+	1.31210i
$999$	9206.49	+	32270.8i	0.291572	+	1.02203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.p.b.68.3		64
5.2	odd	4	inner	225.4.p.b.32.3		64
5.3	odd	4		45.4.l.a.32.14	yes	64
5.4	even	2		45.4.l.a.23.14	yes	64
9.2	odd	6	inner	225.4.p.b.218.3		64
15.8	even	4		135.4.m.a.17.3		64
15.14	odd	2		135.4.m.a.98.3		64
45.2	even	12	inner	225.4.p.b.182.3		64
45.29	odd	6		45.4.l.a.38.14	yes	64
45.34	even	6		135.4.m.a.8.3		64
45.38	even	12		45.4.l.a.2.14	✓	64
45.43	odd	12		135.4.m.a.62.3		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.14	✓	64	45.38	even	12
45.4.l.a.23.14	yes	64	5.4	even	2
45.4.l.a.32.14	yes	64	5.3	odd	4
45.4.l.a.38.14	yes	64	45.29	odd	6
135.4.m.a.8.3		64	45.34	even	6
135.4.m.a.17.3		64	15.8	even	4
135.4.m.a.62.3		64	45.43	odd	12
135.4.m.a.98.3		64	15.14	odd	2
225.4.p.b.32.3		64	5.2	odd	4	inner
225.4.p.b.68.3		64	1.1	even	1	trivial
225.4.p.b.182.3		64	45.2	even	12	inner
225.4.p.b.218.3		64	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11026 + 4.14355i) q^{2} +(4.87317 - 1.80338i) q^{3} +(-9.00816 - 5.20086i) q^{4} +(2.06189 + 22.1945i) q^{6} +(14.5845 + 3.90791i) q^{7} +(7.28515 - 7.28515i) q^{8} +(20.4957 - 17.5763i) q^{9} +O(q^{10})\)	\(q+(-1.11026 + 4.14355i) q^{2} +(4.87317 - 1.80338i) q^{3} +(-9.00816 - 5.20086i) q^{4} +(2.06189 + 22.1945i) q^{6} +(14.5845 + 3.90791i) q^{7} +(7.28515 - 7.28515i) q^{8} +(20.4957 - 17.5763i) q^{9} +(42.5632 - 24.5739i) q^{11} +(-53.2775 - 9.09960i) q^{12} +(33.7651 - 9.04733i) q^{13} +(-32.3853 + 56.0930i) q^{14} +(-19.5089 - 33.7905i) q^{16} +(-18.9033 - 18.9033i) q^{17} +(50.0730 + 104.439i) q^{18} -53.7656i q^{19} +(78.1204 - 7.25747i) q^{21} +(54.5669 + 203.647i) q^{22} +(45.7984 + 170.922i) q^{23} +(22.3639 - 48.6397i) q^{24} +149.952i q^{26} +(68.1821 - 122.614i) q^{27} +(-111.055 - 111.055i) q^{28} +(110.003 + 190.531i) q^{29} +(-22.1047 + 38.2864i) q^{31} +(241.286 - 64.6525i) q^{32} +(163.102 - 196.510i) q^{33} +(99.3145 - 57.3392i) q^{34} +(-276.040 + 51.7355i) q^{36} +(-169.138 + 169.138i) q^{37} +(222.781 + 59.6939i) q^{38} +(148.227 - 104.980i) q^{39} +(42.1171 + 24.3163i) q^{41} +(-56.6624 + 331.754i) q^{42} +(92.3811 - 344.771i) q^{43} -511.222 q^{44} -759.073 q^{46} +(-137.261 + 512.264i) q^{47} +(-156.007 - 129.485i) q^{48} +(-99.6102 - 57.5100i) q^{49} +(-126.209 - 58.0293i) q^{51} +(-351.215 - 94.1079i) q^{52} +(-198.516 + 198.516i) q^{53} +(432.358 + 418.650i) q^{54} +(134.720 - 77.7807i) q^{56} +(-96.9596 - 262.009i) q^{57} +(-911.609 + 244.265i) q^{58} +(64.3921 - 111.530i) q^{59} +(-33.4727 - 57.9764i) q^{61} +(-134.100 - 134.100i) q^{62} +(367.606 - 176.247i) q^{63} +759.421i q^{64} +(633.166 + 894.000i) q^{66} +(-18.6925 - 69.7613i) q^{67} +(71.9705 + 268.597i) q^{68} +(531.420 + 750.341i) q^{69} -1038.75i q^{71} +(21.2676 - 277.360i) q^{72} +(-339.210 - 339.210i) q^{73} +(-513.044 - 888.619i) q^{74} +(-279.627 + 484.329i) q^{76} +(716.797 - 192.065i) q^{77} +(270.421 + 730.744i) q^{78} +(297.681 - 171.866i) q^{79} +(111.144 - 720.478i) q^{81} +(-147.517 + 147.517i) q^{82} +(841.890 + 225.584i) q^{83} +(-741.466 - 340.917i) q^{84} +(1326.01 + 765.572i) q^{86} +(879.665 + 730.114i) q^{87} +(131.055 - 489.104i) q^{88} +230.315 q^{89} +527.804 q^{91} +(476.383 - 1777.88i) q^{92} +(-38.6751 + 226.440i) q^{93} +(-1970.20 - 1137.50i) q^{94} +(1059.24 - 750.193i) q^{96} +(-553.082 - 148.198i) q^{97} +(348.889 - 348.889i) q^{98} +(440.442 - 1251.76i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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