LMFDB - Embedded newform 405.3.g.f.163.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(82,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.82"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 256x^{12} + 15630x^{8} + 235936x^{4} + 28561 $ x^16 + 256x^12 + 15630x^8 + 235936*x^4 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.2
Root			$1.96165 + 1.96165i$ of defining polynomial
Character	$\chi$	$=$	405.163
Dual form			405.3.g.f.82.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96165 + 1.96165i) q^{2} -3.69616i q^{4} +(-0.453215 + 4.97942i) q^{5} +(6.04960 - 6.04960i) q^{7} +(-0.596019 - 0.596019i) q^{8} +(-8.87884 - 10.6569i) q^{10} -0.445449 q^{11} +(2.66383 + 2.66383i) q^{13} +23.7344i q^{14} +17.1230 q^{16} +(14.8395 - 14.8395i) q^{17} -29.1331i q^{19} +(18.4047 + 1.67516i) q^{20} +(0.873817 - 0.873817i) q^{22} +(14.5548 + 14.5548i) q^{23} +(-24.5892 - 4.51349i) q^{25} -10.4510 q^{26} +(-22.3603 - 22.3603i) q^{28} -40.1018i q^{29} +15.2931 q^{31} +(-31.2054 + 31.2054i) q^{32} +58.2198i q^{34} +(27.3817 + 32.8653i) q^{35} +(6.61115 - 6.61115i) q^{37} +(57.1490 + 57.1490i) q^{38} +(3.23795 - 2.69770i) q^{40} +42.4361 q^{41} +(25.7093 + 25.7093i) q^{43} +1.64645i q^{44} -57.1029 q^{46} +(-52.9832 + 52.9832i) q^{47} -24.1953i q^{49} +(57.0894 - 39.3816i) q^{50} +(9.84595 - 9.84595i) q^{52} +(44.8558 + 44.8558i) q^{53} +(0.201884 - 2.21808i) q^{55} -7.21135 q^{56} +(78.6658 + 78.6658i) q^{58} -70.7920i q^{59} +107.011 q^{61} +(-29.9998 + 29.9998i) q^{62} -53.9361i q^{64} +(-14.4716 + 12.0570i) q^{65} +(-89.6252 + 89.6252i) q^{67} +(-54.8491 - 54.8491i) q^{68} +(-118.184 - 10.7568i) q^{70} -71.1649 q^{71} +(77.9049 + 77.9049i) q^{73} +25.9376i q^{74} -107.681 q^{76} +(-2.69479 + 2.69479i) q^{77} +67.2537i q^{79} +(-7.76041 + 85.2627i) q^{80} +(-83.2449 + 83.2449i) q^{82} +(-22.7178 - 22.7178i) q^{83} +(67.1665 + 80.6174i) q^{85} -100.865 q^{86} +(0.265496 + 0.265496i) q^{88} -104.971i q^{89} +32.2302 q^{91} +(53.7969 - 53.7969i) q^{92} -207.869i q^{94} +(145.066 + 13.2035i) q^{95} +(105.410 - 105.410i) q^{97} +(47.4628 + 47.4628i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 40 q^{7} - 56 q^{10} - 44 q^{13} - 32 q^{16} + 32 q^{22} - 92 q^{25} + 176 q^{28} + 320 q^{31} + 4 q^{37} - 528 q^{40} + 256 q^{43} - 16 q^{46} - 308 q^{52} - 364 q^{55} + 492 q^{58} + 8 q^{61} + 88 q^{67}+ \cdots + 304 q^{97}+O(q^{100}) $ 16 * q + 40 * q^7 - 56 * q^10 - 44 * q^13 - 32 * q^16 + 32 * q^22 - 92 * q^25 + 176 * q^28 + 320 * q^31 + 4 * q^37 - 528 * q^40 + 256 * q^43 - 16 * q^46 - 308 * q^52 - 364 * q^55 + 492 * q^58 + 8 * q^61 + 88 * q^67 - 36 * q^70 + 364 * q^73 - 912 * q^76 + 32 * q^82 + 64 * q^85 + 840 * q^88 + 224 * q^91 + 304 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−1.96165	+	1.96165i	−0.980826	+	0.980826i	−0.999820	−	0.0189931i	$-0.993954\pi$
$2$	−1.96165	+	1.96165i	−0.980826	+	0.980826i	0.0189931	+	0.999820i	$0.493954\pi$
$3$		0			0
$3$		0			0
$4$		−	3.69616i		−	0.924041i
$5$	−0.453215	+	4.97942i	−0.0906430	+	0.995883i
$5$	−0.453215	+	4.97942i	−0.0906430	+	0.995883i
$6$		0			0
$7$	6.04960	−	6.04960i	0.864229	−	0.864229i	−0.127597	−	0.991826i	$-0.540727\pi$
$7$	6.04960	−	6.04960i	0.864229	−	0.864229i	0.991826	+	0.127597i	$0.0407266\pi$
$8$	−0.596019	−	0.596019i	−0.0745024	−	0.0745024i
$9$		0			0
$10$	−8.87884	−	10.6569i	−0.887884	−	1.06569i
$11$	−0.445449			−0.0404954			−0.0202477	−	0.999795i	$-0.506445\pi$
$11$	−0.445449			−0.0404954			−0.0202477	+	0.999795i	$0.506445\pi$
$12$		0			0
$13$	2.66383	+	2.66383i	0.204910	+	0.204910i	0.802100	−	0.597190i	$-0.203716\pi$
$13$	2.66383	+	2.66383i	0.204910	+	0.204910i	−0.597190	+	0.802100i	$0.703716\pi$
$14$			23.7344i			1.69532i
$15$		0			0
$16$	17.1230			1.07019
$17$	14.8395	−	14.8395i	0.872910	−	0.872910i	−0.119878	−	0.992789i	$-0.538250\pi$
$17$	14.8395	−	14.8395i	0.872910	−	0.872910i	0.992789	+	0.119878i	$0.0382504\pi$
$18$		0			0
$19$		−	29.1331i		−	1.53332i	−0.642054	−	0.766660i	$-0.721917\pi$
$19$		−	29.1331i		−	1.53332i	0.642054	−	0.766660i	$-0.278083\pi$
$20$	18.4047	+	1.67516i	0.920237	+	0.0837578i
$21$		0			0
$22$	0.873817	−	0.873817i	0.0397190	−	0.0397190i
$23$	14.5548	+	14.5548i	0.632817	+	0.632817i	0.948774	−	0.315956i	$-0.102325\pi$
$23$	14.5548	+	14.5548i	0.632817	+	0.632817i	−0.315956	+	0.948774i	$0.602325\pi$
$24$		0			0
$25$	−24.5892	−	4.51349i	−0.983568	−	0.180540i
$26$	−10.4510			−0.401962
$27$		0			0
$28$	−22.3603	−	22.3603i	−0.798583	−	0.798583i
$29$		−	40.1018i		−	1.38282i	−0.722463	−	0.691410i	$-0.756990\pi$
$29$		−	40.1018i		−	1.38282i	0.722463	−	0.691410i	$-0.243010\pi$
$30$		0			0
$31$	15.2931			0.493327			0.246663	−	0.969101i	$-0.420666\pi$
$31$	15.2931			0.493327			0.246663	+	0.969101i	$0.420666\pi$
$32$	−31.2054	+	31.2054i	−0.975167	+	0.975167i
$33$		0			0
$34$			58.2198i			1.71235i
$35$	27.3817	+	32.8653i	0.782335	+	0.939007i
$36$		0			0
$37$	6.61115	−	6.61115i	0.178680	−	0.178680i	−0.612100	−	0.790780i	$-0.709675\pi$
$37$	6.61115	−	6.61115i	0.178680	−	0.178680i	0.790780	+	0.612100i	$0.209675\pi$
$38$	57.1490	+	57.1490i	1.50392	+	1.50392i
$39$		0			0
$40$	3.23795	−	2.69770i	0.0809488	−	0.0674426i
$41$	42.4361			1.03503			0.517513	−	0.855675i	$-0.326858\pi$
$41$	42.4361			1.03503			0.517513	+	0.855675i	$0.326858\pi$
$42$		0			0
$43$	25.7093	+	25.7093i	0.597890	+	0.597890i	0.939751	−	0.341860i	$-0.111057\pi$
$43$	25.7093	+	25.7093i	0.597890	+	0.597890i	−0.341860	+	0.939751i	$0.611057\pi$
$44$			1.64645i			0.0374194i
$45$		0			0
$46$	−57.1029			−1.24137
$47$	−52.9832	+	52.9832i	−1.12730	+	1.12730i	−0.136689	+	0.990614i	$0.543646\pi$
$47$	−52.9832	+	52.9832i	−1.12730	+	1.12730i	−0.990614	+	0.136689i	$0.956354\pi$
$48$		0			0
$49$		−	24.1953i		−	0.493782i
$50$	57.0894	−	39.3816i	1.14179	−	0.787631i
$51$		0			0
$52$	9.84595	−	9.84595i	0.189345	−	0.189345i
$53$	44.8558	+	44.8558i	0.846336	+	0.846336i	0.989674	−	0.143338i	$-0.0457836\pi$
$53$	44.8558	+	44.8558i	0.846336	+	0.846336i	−0.143338	+	0.989674i	$0.545784\pi$
$54$		0			0
$55$	0.201884	−	2.21808i	0.00367062	−	0.0403287i
$56$	−7.21135			−0.128774
$57$		0			0
$58$	78.6658	+	78.6658i	1.35631	+	1.35631i
$59$		−	70.7920i		−	1.19986i	−0.800051	−	0.599932i	$-0.795194\pi$
$59$		−	70.7920i		−	1.19986i	0.800051	−	0.599932i	$-0.204806\pi$
$60$		0			0
$61$	107.011			1.75429			0.877143	−	0.480230i	$-0.159447\pi$
$61$	107.011			1.75429			0.877143	+	0.480230i	$0.159447\pi$
$62$	−29.9998	+	29.9998i	−0.483868	+	0.483868i
$63$		0			0
$64$		−	53.9361i		−	0.842751i
$65$	−14.4716	+	12.0570i	−0.222640	+	0.185493i
$66$		0			0
$67$	−89.6252	+	89.6252i	−1.33769	+	1.33769i	−0.439398	+	0.898293i	$0.644808\pi$
$67$	−89.6252	+	89.6252i	−1.33769	+	1.33769i	−0.898293	+	0.439398i	$0.855192\pi$
$68$	−54.8491	−	54.8491i	−0.806605	−	0.806605i
$69$		0			0
$70$	−118.184	−	10.7568i	−1.68834	−	0.153669i
$71$	−71.1649			−1.00232			−0.501161	−	0.865354i	$-0.667094\pi$
$71$	−71.1649			−1.00232			−0.501161	+	0.865354i	$0.667094\pi$
$72$		0			0
$73$	77.9049	+	77.9049i	1.06719	+	1.06719i	0.997574	+	0.0696171i	$0.0221777\pi$
$73$	77.9049	+	77.9049i	1.06719	+	1.06719i	0.0696171	+	0.997574i	$0.477822\pi$
$74$			25.9376i			0.350508i
$75$		0			0
$76$	−107.681			−1.41685
$77$	−2.69479	+	2.69479i	−0.0349973	+	0.0349973i
$78$		0			0
$79$			67.2537i			0.851313i	0.904885	+	0.425657i	$0.139957\pi$
$79$			67.2537i			0.851313i	−0.904885	+	0.425657i	$0.860043\pi$
$80$	−7.76041	+	85.2627i	−0.0970051	+	1.06578i
$81$		0			0
$82$	−83.2449	+	83.2449i	−1.01518	+	1.01518i
$83$	−22.7178	−	22.7178i	−0.273708	−	0.273708i	0.556883	−	0.830591i	$-0.311997\pi$
$83$	−22.7178	−	22.7178i	−0.273708	−	0.273708i	−0.830591	+	0.556883i	$0.811997\pi$
$84$		0			0
$85$	67.1665	+	80.6174i	0.790194	+	0.948440i
$86$	−100.865			−1.17285
$87$		0			0
$88$	0.265496	+	0.265496i	0.00301700	+	0.00301700i
$89$		−	104.971i		−	1.17945i	−0.807603	−	0.589727i	$-0.799235\pi$
$89$		−	104.971i		−	1.17945i	0.807603	−	0.589727i	$-0.200765\pi$
$90$		0			0
$91$	32.2302			0.354178
$92$	53.7969	−	53.7969i	0.584749	−	0.584749i
$93$		0			0
$94$		−	207.869i		−	2.21138i
$95$	145.066	+	13.2035i	1.52701	+	0.138985i
$96$		0			0
$97$	105.410	−	105.410i	1.08670	−	1.08670i	0.0908350	−	0.995866i	$-0.471046\pi$
$97$	105.410	−	105.410i	1.08670	−	1.08670i	0.995866	−	0.0908350i	$-0.0289536\pi$
$98$	47.4628	+	47.4628i	0.484315	+	0.484315i
$99$		0			0
$100$	−16.6826	+	90.8857i	−0.166826	+	0.908857i
$101$	−6.17204			−0.0611093			−0.0305546	−	0.999533i	$-0.509727\pi$
$101$	−6.17204			−0.0611093			−0.0305546	+	0.999533i	$0.509727\pi$
$102$		0			0
$103$	13.8280	+	13.8280i	0.134253	+	0.134253i	0.771040	−	0.636787i	$-0.219737\pi$
$103$	13.8280	+	13.8280i	0.134253	+	0.134253i	−0.636787	+	0.771040i	$0.719737\pi$
$104$		−	3.17539i		−	0.0305326i
$105$		0			0
$106$	−175.983			−1.66022
$107$	47.8849	−	47.8849i	0.447522	−	0.447522i	−0.447008	−	0.894530i	$-0.647510\pi$
$107$	47.8849	−	47.8849i	0.447522	−	0.447522i	0.894530	+	0.447008i	$0.147510\pi$
$108$		0			0
$109$		−	60.2436i		−	0.552694i	−0.961058	−	0.276347i	$-0.910876\pi$
$109$		−	60.2436i		−	0.552694i	0.961058	−	0.276347i	$-0.0891239\pi$
$110$	3.95507	+	4.74713i	0.0359552	+	0.0431557i
$111$		0			0
$112$	103.587	−	103.587i	0.924888	−	0.924888i
$113$	−56.8175	−	56.8175i	−0.502810	−	0.502810i	0.409500	−	0.912310i	$-0.365703\pi$
$113$	−56.8175	−	56.8175i	−0.502810	−	0.502810i	−0.912310	+	0.409500i	$0.865703\pi$
$114$		0			0
$115$	−79.0709	+	65.8780i	−0.687573	+	0.572852i
$116$	−148.223			−1.27778
$117$		0			0
$118$	138.869	+	138.869i	1.17686	+	1.17686i
$119$		−	179.546i		−	1.50879i
$120$		0			0
$121$	−120.802			−0.998360
$122$	−209.919	+	209.919i	−1.72065	+	1.72065i
$123$		0			0
$124$		−	56.5259i		−	0.455854i
$125$	33.6187	−	120.394i	0.268950	−	0.963154i
$126$		0			0
$127$	113.537	−	113.537i	0.893994	−	0.893994i	−0.100902	−	0.994896i	$-0.532173\pi$
$127$	113.537	−	113.537i	0.893994	−	0.893994i	0.994896	+	0.100902i	$0.0321730\pi$
$128$	−19.0176	−	19.0176i	−0.148575	−	0.148575i
$129$		0			0
$130$	4.73656	−	52.0400i	0.0364350	−	0.400308i
$131$	79.3967			0.606081			0.303041	−	0.952978i	$-0.401998\pi$
$131$	79.3967			0.606081			0.303041	+	0.952978i	$0.401998\pi$
$132$		0			0
$133$	−176.243	−	176.243i	−1.32514	−	1.32514i
$134$		−	351.627i		−	2.62408i
$135$		0			0
$136$	−17.6892			−0.130068
$137$	69.7872	−	69.7872i	0.509396	−	0.509396i	−0.404945	−	0.914341i	$-0.632709\pi$
$137$	69.7872	−	69.7872i	0.509396	−	0.509396i	0.914341	+	0.404945i	$0.132709\pi$
$138$		0			0
$139$		−	85.8108i		−	0.617344i	−0.951169	−	0.308672i	$-0.900116\pi$
$139$		−	85.8108i		−	0.617344i	0.951169	−	0.308672i	$-0.0998845\pi$
$140$	121.475	−	101.207i	0.867681	−	0.722910i
$141$		0			0
$142$	139.601	−	139.601i	0.983105	−	0.983105i
$143$	−1.18660	−	1.18660i	−0.00829791	−	0.00829791i
$144$		0			0
$145$	199.683	+	18.1747i	1.37713	+	0.125343i
$146$	−305.645			−2.09346
$147$		0			0
$148$	−24.4359	−	24.4359i	−0.165108	−	0.165108i
$149$			135.293i			0.908006i	0.891000	+	0.454003i	$0.150004\pi$
$149$			135.293i			0.908006i	−0.891000	+	0.454003i	$0.849996\pi$
$150$		0			0
$151$	144.205			0.954999			0.477500	−	0.878632i	$-0.341543\pi$
$151$	144.205			0.954999			0.477500	+	0.878632i	$0.341543\pi$
$152$	−17.3639	+	17.3639i	−0.114236	+	0.114236i
$153$		0			0
$154$		−	10.5725i		−	0.0686525i
$155$	−6.93107	+	76.1509i	−0.0447166	+	0.491296i
$156$		0			0
$157$	45.4271	−	45.4271i	0.289345	−	0.289345i	−0.547477	−	0.836821i	$-0.684411\pi$
$157$	45.4271	−	45.4271i	0.289345	−	0.289345i	0.836821	+	0.547477i	$0.184411\pi$
$158$	−131.929	−	131.929i	−0.834991	−	0.834991i
$159$		0			0
$160$	−141.242	−	169.527i	−0.882761	−	1.05955i
$161$	176.101			1.09380
$162$		0			0
$163$	−18.1117	−	18.1117i	−0.111115	−	0.111115i	0.649364	−	0.760478i	$-0.275035\pi$
$163$	−18.1117	−	18.1117i	−0.111115	−	0.111115i	−0.760478	+	0.649364i	$0.775035\pi$
$164$		−	156.851i		−	0.956408i
$165$		0			0
$166$	89.1287			0.536920
$167$	−31.0302	+	31.0302i	−0.185810	+	0.185810i	−0.793882	−	0.608072i	$-0.791943\pi$
$167$	−31.0302	+	31.0302i	−0.185810	+	0.185810i	0.608072	+	0.793882i	$0.291943\pi$
$168$		0			0
$169$		−	154.808i		−	0.916024i
$170$	−289.901	−	26.3861i	−1.70530	−	0.155212i
$171$		0			0
$172$	95.0258	−	95.0258i	0.552475	−	0.552475i
$173$	57.0256	+	57.0256i	0.329628	+	0.329628i	0.852445	−	0.522817i	$-0.175119\pi$
$173$	57.0256	+	57.0256i	0.329628	+	0.329628i	−0.522817	+	0.852445i	$0.675119\pi$
$174$		0			0
$175$	−176.060	+	121.450i	−1.00605	+	0.694000i
$176$	−7.62744			−0.0433377
$177$		0			0
$178$	205.917	+	205.917i	1.15684	+	1.15684i
$179$		−	55.1405i		−	0.308047i	−0.988067	−	0.154024i	$-0.950777\pi$
$179$		−	55.1405i		−	0.308047i	0.988067	−	0.154024i	$-0.0492232\pi$
$180$		0			0
$181$	−180.687			−0.998270			−0.499135	−	0.866524i	$-0.666349\pi$
$181$	−180.687			−0.998270			−0.499135	+	0.866524i	$0.666349\pi$
$182$	−63.2245	+	63.2245i	−0.347387	+	0.347387i
$183$		0			0
$184$		−	17.3499i		−	0.0942928i
$185$	29.9234	+	35.9160i	0.161748	+	0.194140i
$186$		0			0
$187$	−6.61024	+	6.61024i	−0.0353489	+	0.0353489i
$188$	195.835	+	195.835i	1.04167	+	1.04167i
$189$		0			0
$190$	−310.469	+	258.668i	−1.63405	+	1.36141i
$191$	190.289			0.996278			0.498139	−	0.867097i	$-0.334017\pi$
$191$	190.289			0.996278			0.498139	+	0.867097i	$0.334017\pi$
$192$		0			0
$193$	6.44405	+	6.44405i	0.0333889	+	0.0333889i	0.723604	−	0.690215i	$-0.242484\pi$
$193$	6.44405	+	6.44405i	0.0333889	+	0.0333889i	−0.690215	+	0.723604i	$0.742484\pi$
$194$			413.556i			2.13173i
$195$		0			0
$196$	−89.4299			−0.456275
$197$	−116.112	+	116.112i	−0.589403	+	0.589403i	−0.937470	−	0.348067i	$-0.886838\pi$
$197$	−116.112	+	116.112i	−0.589403	+	0.589403i	0.348067	+	0.937470i	$0.386838\pi$
$198$		0			0
$199$			281.684i			1.41550i	0.706465	+	0.707748i	$0.250289\pi$
$199$			281.684i			1.41550i	−0.706465	+	0.707748i	$0.749711\pi$
$200$	11.9655	+	17.3458i	0.0598275	+	0.0867288i
$201$		0			0
$202$	12.1074	−	12.1074i	0.0599376	−	0.0599376i
$203$	−242.600	−	242.600i	−1.19507	−	1.19507i
$204$		0			0
$205$	−19.2327	+	211.307i	−0.0938179	+	1.03077i
$206$	−54.2516			−0.263357
$207$		0			0
$208$	45.6128	+	45.6128i	0.219292	+	0.219292i
$209$			12.9773i			0.0620924i
$210$		0			0
$211$	−240.852			−1.14148			−0.570739	−	0.821132i	$-0.693343\pi$
$211$	−240.852			−1.14148			−0.570739	+	0.821132i	$0.693343\pi$
$212$	165.794	−	165.794i	0.782049	−	0.782049i
$213$		0			0
$214$			187.867i			0.877883i
$215$	−139.669	+	116.365i	−0.649624	+	0.541235i
$216$		0			0
$217$	92.5173	−	92.5173i	0.426347	−	0.426347i
$218$	118.177	+	118.177i	0.542097	+	0.542097i
$219$		0			0
$220$	−8.19838	−	0.746198i	−0.0372654	−	0.00339181i
$221$	79.0597			0.357736
$222$		0			0
$223$	53.9338	+	53.9338i	0.241856	+	0.241856i	0.817618	−	0.575762i	$-0.195294\pi$
$223$	53.9338	+	53.9338i	0.241856	+	0.241856i	−0.575762	+	0.817618i	$0.695294\pi$
$224$			377.560i			1.68554i
$225$		0			0
$226$	222.913			0.986339
$227$	5.95126	−	5.95126i	0.0262170	−	0.0262170i	−0.693877	−	0.720094i	$-0.744099\pi$
$227$	5.95126	−	5.95126i	0.0262170	−	0.0262170i	0.720094	+	0.693877i	$0.244099\pi$
$228$		0			0
$229$			216.480i			0.945328i	0.881243	+	0.472664i	$0.156708\pi$
$229$			216.480i			0.945328i	−0.881243	+	0.472664i	$0.843292\pi$
$230$	25.8799	−	284.339i	0.112521	−	1.23626i
$231$		0			0
$232$	−23.9014	+	23.9014i	−0.103023	+	0.103023i
$233$	85.0860	+	85.0860i	0.365176	+	0.365176i	0.865714	−	0.500538i	$-0.166865\pi$
$233$	85.0860	+	85.0860i	0.365176	+	0.365176i	−0.500538	+	0.865714i	$0.666865\pi$
$234$		0			0
$235$	−239.813	−	287.838i	−1.02048	−	1.22484i
$236$	−261.659			−1.10872
$237$		0			0
$238$	352.207	+	352.207i	1.47986	+	1.47986i
$239$		−	267.134i		−	1.11772i	−0.829263	−	0.558858i	$-0.811240\pi$
$239$		−	267.134i		−	1.11772i	0.829263	−	0.558858i	$-0.188760\pi$
$240$		0			0
$241$	−282.000			−1.17013			−0.585063	−	0.810988i	$-0.698930\pi$
$241$	−282.000			−1.17013			−0.585063	+	0.810988i	$0.698930\pi$
$242$	236.971	−	236.971i	0.979218	−	0.979218i
$243$		0			0
$244$		−	395.532i		−	1.62103i
$245$	120.479	+	10.9657i	0.491749	+	0.0447579i
$246$		0			0
$247$	77.6055	−	77.6055i	0.314192	−	0.314192i
$248$	−9.11500	−	9.11500i	−0.0367540	−	0.0367540i
$249$		0			0
$250$	170.223	+	302.120i	0.680894	+	1.20848i
$251$	29.8384			0.118878			0.0594390	−	0.998232i	$-0.481069\pi$
$251$	29.8384			0.118878			0.0594390	+	0.998232i	$0.481069\pi$
$252$		0			0
$253$	−6.48343	−	6.48343i	−0.0256262	−	0.0256262i
$254$			445.441i			1.75371i
$255$		0			0
$256$	290.356			1.13420
$257$	110.717	−	110.717i	0.430806	−	0.430806i	−0.458096	−	0.888902i	$-0.651469\pi$
$257$	110.717	−	110.717i	0.430806	−	0.430806i	0.888902	+	0.458096i	$0.151469\pi$
$258$		0			0
$259$		−	79.9897i		−	0.308840i
$260$	44.5648	+	53.4894i	0.171403	+	0.205729i
$261$		0			0
$262$	−155.749	+	155.749i	−0.594461	+	0.594461i
$263$	−19.7336	−	19.7336i	−0.0750328	−	0.0750328i	0.668594	−	0.743627i	$-0.266896\pi$
$263$	−19.7336	−	19.7336i	−0.0750328	−	0.0750328i	−0.743627	+	0.668594i	$0.766896\pi$
$264$		0			0
$265$	−243.685	+	203.026i	−0.919566	+	0.766138i
$266$	691.457			2.59946
$267$		0			0
$268$	331.270	+	331.270i	1.23608	+	1.23608i
$269$			100.763i			0.374584i	0.982304	+	0.187292i	$0.0599711\pi$
$269$			100.763i			0.374584i	−0.982304	+	0.187292i	$0.940029\pi$
$270$		0			0
$271$	−342.248			−1.26291			−0.631453	−	0.775414i	$-0.717541\pi$
$271$	−342.248			−1.26291			−0.631453	+	0.775414i	$0.717541\pi$
$272$	254.097	−	254.097i	0.934179	−	0.934179i
$273$		0			0
$274$			273.797i			0.999258i
$275$	10.9532	+	2.01053i	0.0398300	+	0.00731103i
$276$		0			0
$277$	−161.049	+	161.049i	−0.581405	+	0.581405i	−0.935289	−	0.353884i	$-0.884861\pi$
$277$	−161.049	+	161.049i	−0.581405	+	0.581405i	0.353884	+	0.935289i	$0.384861\pi$
$278$	168.331	+	168.331i	0.605507	+	0.605507i
$279$		0			0
$280$	3.26829	−	35.9083i	0.0116725	−	0.128244i
$281$	509.668			1.81376			0.906882	−	0.421384i	$-0.138456\pi$
$281$	509.668			1.81376			0.906882	+	0.421384i	$0.138456\pi$
$282$		0			0
$283$	−254.961	−	254.961i	−0.900923	−	0.900923i	0.0945934	−	0.995516i	$-0.469845\pi$
$283$	−254.961	−	254.961i	−0.900923	−	0.900923i	−0.995516	+	0.0945934i	$0.969845\pi$
$284$			263.037i			0.926187i
$285$		0			0
$286$	4.65540			0.0162776
$287$	256.721	−	256.721i	0.894500	−	0.894500i
$288$		0			0
$289$		−	151.420i		−	0.523945i
$290$	−427.362	+	356.057i	−1.47366	+	1.22778i
$291$		0			0
$292$	287.949	−	287.949i	0.986128	−	0.986128i
$293$	−140.223	−	140.223i	−0.478576	−	0.478576i	0.426100	−	0.904676i	$-0.359887\pi$
$293$	−140.223	−	140.223i	−0.478576	−	0.478576i	−0.904676	+	0.426100i	$0.859887\pi$
$294$		0			0
$295$	352.503	+	32.0840i	1.19493	+	0.108759i
$296$	−7.88075			−0.0266241
$297$		0			0
$298$	−265.398	−	265.398i	−0.890596	−	0.890596i
$299$			77.5430i			0.259341i
$300$		0			0
$301$	311.062			1.03343
$302$	−282.880	+	282.880i	−0.936689	+	0.936689i
$303$		0			0
$304$		−	498.846i		−	1.64094i
$305$	−48.4992	+	532.855i	−0.159014	+	1.74706i
$306$		0			0
$307$	123.104	−	123.104i	0.400990	−	0.400990i	−0.477592	−	0.878582i	$-0.658490\pi$
$307$	123.104	−	123.104i	0.400990	−	0.400990i	0.878582	+	0.477592i	$0.158490\pi$
$308$	9.96039	+	9.96039i	0.0323389	+	0.0323389i
$309$		0			0
$310$	−135.785	−	162.978i	−0.438017	−	0.525735i
$311$	−248.018			−0.797485			−0.398742	−	0.917063i	$-0.630553\pi$
$311$	−248.018			−0.797485			−0.398742	+	0.917063i	$0.630553\pi$
$312$		0			0
$313$	127.568	+	127.568i	0.407567	+	0.407567i	0.880889	−	0.473322i	$-0.156945\pi$
$313$	127.568	+	127.568i	0.407567	+	0.407567i	−0.473322	+	0.880889i	$0.656945\pi$
$314$			178.224i			0.567594i
$315$		0			0
$316$	248.581			0.786649
$317$	−235.473	+	235.473i	−0.742817	+	0.742817i	−0.973119	−	0.230302i	$-0.926028\pi$
$317$	−235.473	+	235.473i	−0.742817	+	0.742817i	0.230302	+	0.973119i	$0.426028\pi$
$318$		0			0
$319$			17.8633i			0.0559978i
$320$	268.570	+	24.4446i	0.839282	+	0.0763894i
$321$		0			0
$322$	−345.450	+	345.450i	−1.07283	+	1.07283i
$323$	−432.319	−	432.319i	−1.33845	−	1.33845i
$324$		0			0
$325$	−53.4782	−	77.5246i	−0.164548	−	0.238537i
$326$	71.0576			0.217968
$327$		0			0
$328$	−25.2927	−	25.2927i	−0.0771120	−	0.0771120i
$329$			641.055i			1.94849i
$330$		0			0
$331$	17.7617			0.0536608			0.0268304	−	0.999640i	$-0.491459\pi$
$331$	17.7617			0.0536608			0.0268304	+	0.999640i	$0.491459\pi$
$332$	−83.9686	+	83.9686i	−0.252918	+	0.252918i
$333$		0			0
$334$		−	121.741i		−	0.364494i
$335$	−405.662	−	486.901i	−1.21093	−	1.45344i
$336$		0			0
$337$	−195.549	+	195.549i	−0.580265	+	0.580265i	−0.934976	−	0.354711i	$-0.884579\pi$
$337$	−195.549	+	195.549i	−0.580265	+	0.580265i	0.354711	+	0.934976i	$0.384579\pi$
$338$	303.680	+	303.680i	0.898460	+	0.898460i
$339$		0			0
$340$	297.975	−	248.258i	0.876398	−	0.730172i
$341$	−6.81232			−0.0199775
$342$		0			0
$343$	150.058	+	150.058i	0.437488	+	0.437488i
$344$		−	30.6464i		−	0.0890885i
$345$		0			0
$346$	−223.729			−0.646616
$347$	−223.633	+	223.633i	−0.644475	+	0.644475i	−0.951652	−	0.307177i	$-0.900615\pi$
$347$	−223.633	+	223.633i	−0.644475	+	0.644475i	0.307177	+	0.951652i	$0.400615\pi$
$348$		0			0
$349$		−	675.814i		−	1.93643i	−0.250120	−	0.968215i	$-0.580470\pi$
$349$		−	675.814i		−	1.93643i	0.250120	−	0.968215i	$-0.419530\pi$
$350$	107.125	−	583.611i	0.306072	−	1.66746i
$351$		0			0
$352$	13.9004	−	13.9004i	0.0394898	−	0.0394898i
$353$	293.602	+	293.602i	0.831735	+	0.831735i	0.987754	−	0.156019i	$-0.0498661\pi$
$353$	293.602	+	293.602i	0.831735	+	0.831735i	−0.156019	+	0.987754i	$0.549866\pi$
$354$		0			0
$355$	32.2530	−	354.360i	0.0908535	−	0.998196i
$356$	−387.991			−1.08986
$357$		0			0
$358$	108.167	+	108.167i	0.302141	+	0.302141i
$359$		−	206.110i		−	0.574122i	−0.957912	−	0.287061i	$-0.907322\pi$
$359$		−	206.110i		−	0.574122i	0.957912	−	0.287061i	$-0.0926783\pi$
$360$		0			0
$361$	−487.736			−1.35107
$362$	354.445	−	354.445i	0.979130	−	0.979130i
$363$		0			0
$364$		−	119.128i		−	0.327275i
$365$	−423.229	+	352.614i	−1.15953	+	0.966064i
$366$		0			0
$367$	−130.805	+	130.805i	−0.356417	+	0.356417i	−0.862490	−	0.506073i	$-0.831097\pi$
$367$	−130.805	+	130.805i	−0.356417	+	0.356417i	0.506073	+	0.862490i	$0.331097\pi$
$368$	249.222	+	249.222i	0.677234	+	0.677234i
$369$		0			0
$370$	−129.154	−	11.7553i	−0.349065	−	0.0317711i
$371$	542.719			1.46286
$372$		0			0
$373$	172.185	+	172.185i	0.461623	+	0.461623i	0.899187	−	0.437564i	$-0.144159\pi$
$373$	172.185	+	172.185i	0.461623	+	0.461623i	−0.437564	+	0.899187i	$0.644159\pi$
$374$		−	25.9340i		−	0.0693422i
$375$		0			0
$376$	63.1580			0.167973
$377$	106.824	−	106.824i	0.283354	−	0.283354i
$378$		0			0
$379$			240.778i			0.635297i	0.948208	+	0.317649i	$0.102893\pi$
$379$			240.778i			0.635297i	−0.948208	+	0.317649i	$0.897107\pi$
$380$	48.8025	−	536.187i	0.128428	−	1.41102i
$381$		0			0
$382$	−373.281	+	373.281i	−0.977175	+	0.977175i
$383$	119.769	+	119.769i	0.312712	+	0.312712i	0.845959	−	0.533247i	$-0.179028\pi$
$383$	119.769	+	119.769i	0.312712	+	0.312712i	−0.533247	+	0.845959i	$0.679028\pi$
$384$		0			0
$385$	−12.1972	−	14.6398i	−0.0316810	−	0.0380255i
$386$	−25.2820			−0.0654974
$387$		0			0
$388$	−389.613	−	389.613i	−1.00416	−	1.00416i
$389$			147.816i			0.379989i	0.981785	+	0.189995i	$0.0608470\pi$
$389$			147.816i			0.379989i	−0.981785	+	0.189995i	$0.939153\pi$
$390$		0			0
$391$	431.971			1.10479
$392$	−14.4209	+	14.4209i	−0.0367879	+	0.0367879i
$393$		0			0
$394$		−	455.544i		−	1.15620i
$395$	−334.884	−	30.4804i	−0.847809	−	0.0771656i
$396$		0			0
$397$	154.690	−	154.690i	0.389647	−	0.389647i	−0.484915	−	0.874561i	$-0.661149\pi$
$397$	154.690	−	154.690i	0.389647	−	0.389647i	0.874561	+	0.484915i	$0.161149\pi$
$398$	−552.566	−	552.566i	−1.38836	−	1.38836i
$399$		0			0
$400$	−421.041	−	77.2846i	−1.05260	−	0.193212i
$401$	708.918			1.76787			0.883937	−	0.467606i	$-0.154883\pi$
$401$	708.918			1.76787			0.883937	+	0.467606i	$0.154883\pi$
$402$		0			0
$403$	40.7383	+	40.7383i	0.101088	+	0.101088i
$404$			22.8129i			0.0564675i
$405$		0			0
$406$	951.793			2.34432
$407$	−2.94493	+	2.94493i	−0.00723571	+	0.00723571i
$408$		0			0
$409$		−	167.538i		−	0.409629i	−0.978801	−	0.204814i	$-0.934341\pi$
$409$		−	167.538i		−	0.409629i	0.978801	−	0.204814i	$-0.0656590\pi$
$410$	−376.783	−	452.239i	−0.918984	−	1.10302i
$411$		0			0
$412$	51.1107	−	51.1107i	0.124055	−	0.124055i
$413$	−428.263	−	428.263i	−1.03696	−	1.03696i
$414$		0			0
$415$	123.417	−	102.825i	0.297391	−	0.247772i
$416$	−166.252			−0.399643
$417$		0			0
$418$	−25.4570	−	25.4570i	−0.0609019	−	0.0609019i
$419$		−	141.227i		−	0.337058i	−0.985697	−	0.168529i	$-0.946098\pi$
$419$		−	141.227i		−	0.337058i	0.985697	−	0.168529i	$-0.0539017\pi$
$420$		0			0
$421$	−576.339			−1.36898			−0.684488	−	0.729024i	$-0.739974\pi$
$421$	−576.339			−1.36898			−0.684488	+	0.729024i	$0.739974\pi$
$422$	472.467	−	472.467i	1.11959	−	1.11959i
$423$		0			0
$424$		−	53.4698i		−	0.126108i
$425$	−431.869	+	297.913i	−1.01616	+	0.700971i
$426$		0			0
$427$	647.376	−	647.376i	1.51610	−	1.51610i
$428$	−176.990	−	176.990i	−0.413529	−	0.413529i
$429$		0			0
$430$	45.7137	−	502.251i	0.106311	−	1.16803i
$431$	449.009			1.04179			0.520893	−	0.853622i	$-0.325599\pi$
$431$	449.009			1.04179			0.520893	+	0.853622i	$0.325599\pi$
$432$		0			0
$433$	542.261	+	542.261i	1.25233	+	1.25233i	0.954671	+	0.297663i	$0.0962072\pi$
$433$	542.261	+	542.261i	1.25233	+	1.25233i	0.297663	+	0.954671i	$0.403793\pi$
$434$			362.974i			0.836345i
$435$		0			0
$436$	−222.670			−0.510712
$437$	424.026	−	424.026i	0.970311	−	0.970311i
$438$		0			0
$439$			458.923i			1.04538i	0.852522	+	0.522692i	$0.175072\pi$
$439$			458.923i			1.04538i	−0.852522	+	0.522692i	$0.824928\pi$
$440$	−1.44234	+	1.20169i	−0.00327805	+	0.00273111i
$441$		0			0
$442$	−155.088	+	155.088i	−0.350877	+	0.350877i
$443$	−166.912	−	166.912i	−0.376777	−	0.376777i	0.493161	−	0.869938i	$-0.335841\pi$
$443$	−166.912	−	166.912i	−0.376777	−	0.376777i	−0.869938	+	0.493161i	$0.835841\pi$
$444$		0			0
$445$	522.696	+	47.5746i	1.17460	+	0.106909i
$446$	−211.599			−0.474437
$447$		0			0
$448$	−326.292	−	326.292i	−0.728329	−	0.728329i
$449$			267.125i			0.594933i	0.954732	+	0.297467i	$0.0961417\pi$
$449$			267.125i			0.594933i	−0.954732	+	0.297467i	$0.903858\pi$
$450$		0			0
$451$	−18.9031			−0.0419138
$452$	−210.007	+	210.007i	−0.464617	+	0.464617i
$453$		0			0
$454$			23.3486i			0.0514286i
$455$	−14.6072	+	160.488i	−0.0321038	+	0.352720i
$456$		0			0
$457$	−61.7372	+	61.7372i	−0.135092	+	0.135092i	−0.771419	−	0.636327i	$-0.780453\pi$
$457$	−61.7372	+	61.7372i	−0.135092	+	0.135092i	0.636327	+	0.771419i	$0.280453\pi$
$458$	−424.659	−	424.659i	−0.927203	−	0.927203i
$459$		0			0
$460$	243.496	+	292.259i	0.529339	+	0.635346i
$461$	−456.501			−0.990241			−0.495121	−	0.868824i	$-0.664876\pi$
$461$	−456.501			−0.990241			−0.495121	+	0.868824i	$0.664876\pi$
$462$		0			0
$463$	−522.907	−	522.907i	−1.12939	−	1.12939i	−0.990277	−	0.139112i	$-0.955575\pi$
$463$	−522.907	−	522.907i	−1.12939	−	1.12939i	−0.139112	−	0.990277i	$-0.544425\pi$
$464$		−	686.664i		−	1.47988i
$465$		0			0
$466$	−333.818			−0.716349
$467$	−200.076	+	200.076i	−0.428428	+	0.428428i	−0.888093	−	0.459664i	$-0.847970\pi$
$467$	−200.076	+	200.076i	−0.428428	+	0.428428i	0.459664	+	0.888093i	$0.347970\pi$
$468$		0			0
$469$			1084.39i			2.31214i
$470$	1035.07	+	94.2095i	2.20227	+	0.200446i
$471$		0			0
$472$	−42.1934	+	42.1934i	−0.0893928	+	0.0893928i
$473$	−11.4522	−	11.4522i	−0.0242118	−	0.0242118i
$474$		0			0
$475$	−131.492	+	716.359i	−0.276825	+	1.50812i
$476$	−663.631			−1.39418
$477$		0			0
$478$	524.025	+	524.025i	1.09629	+	1.09629i
$479$		−	527.960i		−	1.10221i	−0.834435	−	0.551107i	$-0.814206\pi$
$479$		−	527.960i		−	1.10221i	0.834435	−	0.551107i	$-0.185794\pi$
$480$		0			0
$481$	35.2220			0.0732266
$482$	553.187	−	553.187i	1.14769	−	1.14769i
$483$		0			0
$484$			446.503i			0.922526i
$485$	477.107	+	572.654i	0.983726	+	1.18073i
$486$		0			0
$487$	2.96411	−	2.96411i	0.00608646	−	0.00608646i	−0.704057	−	0.710143i	$-0.748630\pi$
$487$	2.96411	−	2.96411i	0.00608646	−	0.00608646i	0.710143	+	0.704057i	$0.248630\pi$
$488$	−63.7808	−	63.7808i	−0.130698	−	0.130698i
$489$		0			0
$490$	−257.848	+	214.826i	−0.526221	+	0.438421i
$491$	−790.825			−1.61064			−0.805320	−	0.592840i	$-0.798007\pi$
$491$	−790.825			−1.61064			−0.805320	+	0.592840i	$0.798007\pi$
$492$		0			0
$493$	−595.089	−	595.089i	−1.20708	−	1.20708i
$494$			304.470i			0.616337i
$495$		0			0
$496$	261.865			0.527953
$497$	−430.519	+	430.519i	−0.866236	+	0.866236i
$498$		0			0
$499$			587.934i			1.17822i	0.808052	+	0.589112i	$0.200522\pi$
$499$			587.934i			1.17822i	−0.808052	+	0.589112i	$0.799478\pi$
$500$	−444.997	−	124.260i	−0.889994	−	0.248521i
$501$		0			0
$502$	−58.5325	+	58.5325i	−0.116599	+	0.116599i
$503$	282.741	+	282.741i	0.562109	+	0.562109i	0.929906	−	0.367797i	$-0.119888\pi$
$503$	282.741	+	282.741i	0.562109	+	0.562109i	−0.367797	+	0.929906i	$0.619888\pi$
$504$		0			0
$505$	2.79726	−	30.7332i	0.00553913	−	0.0608577i
$506$	25.4365			0.0502697
$507$		0			0
$508$	−419.652	−	419.652i	−0.826087	−	0.826087i
$509$		−	524.061i		−	1.02959i	−0.857313	−	0.514795i	$-0.827868\pi$
$509$		−	524.061i		−	1.02959i	0.857313	−	0.514795i	$-0.172132\pi$
$510$		0			0
$511$	942.587			1.84459
$512$	−493.507	+	493.507i	−0.963882	+	0.963882i
$513$		0			0
$514$			434.377i			0.845092i
$515$	−75.1226	+	62.5885i	−0.145869	+	0.121531i
$516$		0			0
$517$	23.6014	−	23.6014i	0.0456506	−	0.0456506i
$518$	156.912	+	156.912i	0.302919	+	0.302919i
$519$		0			0
$520$	15.8116	+	1.43913i	0.0304069	+	0.00276756i
$521$	−149.033			−0.286051			−0.143026	−	0.989719i	$-0.545683\pi$
$521$	−149.033			−0.286051			−0.143026	+	0.989719i	$0.545683\pi$
$522$		0			0
$523$	−529.426	−	529.426i	−1.01229	−	1.01229i	−0.999924	−	0.0123638i	$-0.996064\pi$
$523$	−529.426	−	529.426i	−1.01229	−	1.01229i	−0.0123638	−	0.999924i	$-0.503936\pi$
$524$		−	293.463i		−	0.560044i
$525$		0			0
$526$	77.4211			0.147188
$527$	226.942	−	226.942i	0.430630	−	0.430630i
$528$		0			0
$529$		−	105.316i		−	0.199084i
$530$	79.7581	−	876.293i	0.150487	−	1.65338i
$531$		0			0
$532$	−651.425	+	651.425i	−1.22448	+	1.22448i
$533$	113.043	+	113.043i	0.212087	+	0.212087i
$534$		0			0
$535$	216.737	+	260.141i	0.405115	+	0.486245i
$536$	106.837			0.199322
$537$		0			0
$538$	−197.662	−	197.662i	−0.367402	−	0.367402i
$539$			10.7778i			0.0199959i
$540$		0			0
$541$	−95.0214			−0.175640			−0.0878202	−	0.996136i	$-0.527990\pi$
$541$	−95.0214			−0.175640			−0.0878202	+	0.996136i	$0.527990\pi$
$542$	671.371	−	671.371i	1.23869	−	1.23869i
$543$		0			0
$544$			926.142i			1.70247i
$545$	299.978	+	27.3033i	0.550419	+	0.0500978i
$546$		0			0
$547$	437.531	−	437.531i	0.799875	−	0.799875i	−0.183201	−	0.983075i	$-0.558646\pi$
$547$	437.531	−	437.531i	0.799875	−	0.799875i	0.983075	+	0.183201i	$0.0586459\pi$
$548$	−257.945	−	257.945i	−0.470703	−	0.470703i
$549$		0			0
$550$	−25.4304	+	17.5425i	−0.0462371	+	0.0318954i
$551$	−1168.29			−2.12030
$552$		0			0
$553$	406.858	+	406.858i	0.735729	+	0.735729i
$554$		−	631.845i		−	1.14051i
$555$		0			0
$556$	−317.171			−0.570451
$557$	−591.236	+	591.236i	−1.06147	+	1.06147i	−0.0634822	+	0.997983i	$0.520221\pi$
$557$	−591.236	+	591.236i	−1.06147	+	1.06147i	−0.997983	+	0.0634822i	$0.979779\pi$
$558$		0			0
$559$			136.970i			0.245027i
$560$	468.858	+	562.753i	0.837246	+	1.00492i
$561$		0			0
$562$	−999.791	+	999.791i	−1.77899	+	1.77899i
$563$	−526.655	−	526.655i	−0.935444	−	0.935444i	0.0625946	−	0.998039i	$-0.480062\pi$
$563$	−526.655	−	526.655i	−0.935444	−	0.935444i	−0.998039	+	0.0625946i	$0.980062\pi$
$564$		0			0
$565$	308.669	−	257.168i	0.546316	−	0.455164i
$566$	1000.29			1.76730
$567$		0			0
$568$	42.4156	+	42.4156i	0.0746754	+	0.0746754i
$569$		−	590.957i		−	1.03859i	−0.854595	−	0.519294i	$-0.826195\pi$
$569$		−	590.957i		−	1.03859i	0.854595	−	0.519294i	$-0.173805\pi$
$570$		0			0
$571$	−380.609			−0.666565			−0.333283	−	0.942827i	$-0.608156\pi$
$571$	−380.609			−0.666565			−0.333283	+	0.942827i	$0.608156\pi$
$572$	−4.38587	+	4.38587i	−0.00766761	+	0.00766761i
$573$		0			0
$574$			1007.20i			1.75470i
$575$	−292.198	−	423.584i	−0.508170	−	0.736667i
$576$		0			0
$577$	−156.284	+	156.284i	−0.270856	+	0.270856i	−0.829445	−	0.558589i	$-0.811343\pi$
$577$	−156.284	+	156.284i	−0.270856	+	0.270856i	0.558589	+	0.829445i	$0.311343\pi$
$578$	297.034	+	297.034i	0.513899	+	0.513899i
$579$		0			0
$580$	67.1768	−	738.063i	0.115822	−	1.27252i
$581$	−274.867			−0.473093
$582$		0			0
$583$	−19.9810	−	19.9810i	−0.0342727	−	0.0342727i
$584$		−	92.8656i		−	0.159017i
$585$		0			0
$586$	550.137			0.938800
$587$	−717.351	+	717.351i	−1.22206	+	1.22206i	−0.255166	+	0.966897i	$0.582130\pi$
$587$	−717.351	+	717.351i	−1.22206	+	1.22206i	−0.966897	+	0.255166i	$0.917870\pi$
$588$		0			0
$589$		−	445.536i		−	0.756427i
$590$	−754.426	+	628.551i	−1.27869	+	1.06534i
$591$		0			0
$592$	113.203	−	113.203i	0.191221	−	0.191221i
$593$	336.299	+	336.299i	0.567115	+	0.567115i	0.931319	−	0.364204i	$-0.118659\pi$
$593$	336.299	+	336.299i	0.567115	+	0.567115i	−0.364204	+	0.931319i	$0.618659\pi$
$594$		0			0
$595$	894.033	+	81.3728i	1.50258	+	0.136761i
$596$	500.065			0.839035
$597$		0			0
$598$	−152.112	−	152.112i	−0.254369	−	0.254369i
$599$			427.985i			0.714500i	0.934009	+	0.357250i	$0.116286\pi$
$599$			427.985i			0.714500i	−0.934009	+	0.357250i	$0.883714\pi$
$600$		0			0
$601$	17.0151			0.0283112			0.0141556	−	0.999900i	$-0.495494\pi$
$601$	17.0151			0.0283112			0.0141556	+	0.999900i	$0.495494\pi$
$602$	−610.195	+	610.195i	−1.01361	+	1.01361i
$603$		0			0
$604$		−	533.005i		−	0.882459i
$605$	54.7491	−	601.521i	0.0904943	−	0.994250i
$606$		0			0
$607$	209.591	−	209.591i	0.345290	−	0.345290i	−0.513062	−	0.858352i	$-0.671489\pi$
$607$	209.591	−	209.591i	0.345290	−	0.345290i	0.858352	+	0.513062i	$0.171489\pi$
$608$	909.108	+	909.108i	1.49524	+	1.49524i
$609$		0			0
$610$	−950.137	−	1140.41i	−1.55760	−	1.86953i
$611$	−282.277			−0.461991
$612$		0			0
$613$	−229.232	−	229.232i	−0.373951	−	0.373951i	0.494963	−	0.868914i	$-0.335181\pi$
$613$	−229.232	−	229.232i	−0.373951	−	0.373951i	−0.868914	+	0.494963i	$0.835181\pi$
$614$			482.974i			0.786603i
$615$		0			0
$616$	3.21229			0.00521476
$617$	−89.8034	+	89.8034i	−0.145548	+	0.145548i	−0.776126	−	0.630578i	$-0.782818\pi$
$617$	−89.8034	+	89.8034i	−0.145548	+	0.145548i	0.630578	+	0.776126i	$0.282818\pi$
$618$		0			0
$619$			1157.67i			1.87022i	0.354351	+	0.935112i	$0.384702\pi$
$619$			1157.67i			1.87022i	−0.354351	+	0.935112i	$0.615298\pi$
$620$	281.466	+	25.6184i	0.453978	+	0.0413200i
$621$		0			0
$622$	486.525	−	486.525i	0.782194	−	0.782194i
$623$	−635.035	−	635.035i	−1.01932	−	1.01932i
$624$		0			0
$625$	584.257	+	221.966i	0.934811	+	0.355146i
$626$	−500.490			−0.799505
$627$		0			0
$628$	−167.906	−	167.906i	−0.267366	−	0.267366i
$629$		−	196.212i		−	0.311943i
$630$		0			0
$631$	−1139.80			−1.80634			−0.903169	−	0.429285i	$-0.858766\pi$
$631$	−1139.80			−1.80634			−0.903169	+	0.429285i	$0.858766\pi$
$632$	40.0845	−	40.0845i	0.0634249	−	0.0634249i
$633$		0			0
$634$		−	923.832i		−	1.45715i
$635$	513.892	+	616.806i	0.809279	+	0.971348i
$636$		0			0
$637$	64.4522	−	64.4522i	0.101181	−	0.101181i
$638$	−35.0416	−	35.0416i	−0.0549242	−	0.0549242i
$639$		0			0
$640$	103.316	−	86.0774i	0.161431	−	0.134496i
$641$	762.768			1.18997			0.594983	−	0.803738i	$-0.297159\pi$
$641$	762.768			1.18997			0.594983	+	0.803738i	$0.297159\pi$
$642$		0			0
$643$	−321.892	−	321.892i	−0.500610	−	0.500610i	0.411018	−	0.911627i	$-0.365173\pi$
$643$	−321.892	−	321.892i	−0.500610	−	0.500610i	−0.911627	+	0.411018i	$0.865173\pi$
$644$		−	650.900i		−	1.01071i
$645$		0			0
$646$	1696.12			2.62557
$647$	19.2194	−	19.2194i	0.0297054	−	0.0297054i	−0.692098	−	0.721803i	$-0.743313\pi$
$647$	19.2194	−	19.2194i	0.0297054	−	0.0297054i	0.721803	+	0.692098i	$0.243313\pi$
$648$		0			0
$649$			31.5343i			0.0485890i
$650$	256.982	+	47.1706i	0.395357	+	0.0725701i
$651$		0			0
$652$	−66.9437	+	66.9437i	−0.102674	+	0.102674i
$653$	897.572	+	897.572i	1.37454	+	1.37454i	0.853589	+	0.520948i	$0.174421\pi$
$653$	897.572	+	897.572i	1.37454	+	1.37454i	0.520948	+	0.853589i	$0.325579\pi$
$654$		0			0
$655$	−35.9837	+	395.349i	−0.0549370	+	0.603586i
$656$	726.634			1.10767
$657$		0			0
$658$	−1257.53	−	1257.53i	−1.91114	−	1.91114i
$659$			785.804i			1.19242i	0.802829	+	0.596209i	$0.203327\pi$
$659$			785.804i			1.19242i	−0.802829	+	0.596209i	$0.796673\pi$
$660$		0			0
$661$	368.211			0.557051			0.278526	−	0.960429i	$-0.410154\pi$
$661$	368.211			0.557051			0.278526	+	0.960429i	$0.410154\pi$
$662$	−34.8423	+	34.8423i	−0.0526319	+	0.0526319i
$663$		0			0
$664$			27.0804i			0.0407838i
$665$	957.466	−	797.713i	1.43980	−	1.19957i
$666$		0			0
$667$	583.673	−	583.673i	0.875072	−	0.875072i
$668$	114.693	+	114.693i	0.171696	+	0.171696i
$669$		0			0
$670$	1750.90	+	159.363i	2.61328	+	0.237855i
$671$	−47.6682			−0.0710405
$672$		0			0
$673$	−583.994	−	583.994i	−0.867748	−	0.867748i	0.124475	−	0.992223i	$-0.460275\pi$
$673$	−583.994	−	583.994i	−0.867748	−	0.867748i	−0.992223	+	0.124475i	$0.960275\pi$
$674$		−	767.200i		−	1.13828i
$675$		0			0
$676$	−572.196			−0.846444
$677$	−510.053	+	510.053i	−0.753401	+	0.753401i	−0.975112	−	0.221711i	$-0.928836\pi$
$677$	−510.053	+	510.053i	−0.753401	+	0.753401i	0.221711	+	0.975112i	$0.428836\pi$
$678$		0			0
$679$		−	1275.38i		−	1.87832i
$680$	8.01702	−	88.0820i	0.0117897	−	0.129532i
$681$		0			0
$682$	13.3634	−	13.3634i	0.0195944	−	0.0195944i
$683$	−264.640	−	264.640i	−0.387467	−	0.387467i	0.486316	−	0.873783i	$-0.338340\pi$
$683$	−264.640	−	264.640i	−0.387467	−	0.387467i	−0.873783	+	0.486316i	$0.838340\pi$
$684$		0			0
$685$	315.871	+	379.128i	0.461126	+	0.553472i
$686$	−588.725			−0.858200
$687$		0			0
$688$	440.221	+	440.221i	0.639856	+	0.639856i
$689$			238.976i			0.346845i
$690$		0			0
$691$	484.032			0.700480			0.350240	−	0.936660i	$-0.386100\pi$
$691$	484.032			0.700480			0.350240	+	0.936660i	$0.386100\pi$
$692$	210.776	−	210.776i	0.304590	−	0.304590i
$693$		0			0
$694$		−	877.380i		−	1.26424i
$695$	427.288	+	38.8907i	0.614802	+	0.0559579i
$696$		0			0
$697$	629.730	−	629.730i	0.903486	−	0.903486i
$698$	1325.71	+	1325.71i	1.89930	+	1.89930i
$699$		0			0
$700$	448.899	+	650.745i	0.641284	+	0.929636i
$701$	394.513			0.562787			0.281393	−	0.959593i	$-0.409203\pi$
$701$	394.513			0.562787			0.281393	+	0.959593i	$0.409203\pi$
$702$		0			0
$703$	−192.603	−	192.603i	−0.273973	−	0.273973i
$704$			24.0258i			0.0341275i
$705$		0			0
$706$	−1151.89			−1.63158
$707$	−37.3384	+	37.3384i	−0.0528124	+	0.0528124i
$708$		0			0
$709$			113.025i			0.159415i	0.996818	+	0.0797074i	$0.0253986\pi$
$709$			113.025i			0.159415i	−0.996818	+	0.0797074i	$0.974601\pi$
$710$	631.862	+	758.400i	0.889946	+	1.06817i
$711$		0			0
$712$	−62.5649	+	62.5649i	−0.0878721	+	0.0878721i
$713$	222.588	+	222.588i	0.312186	+	0.312186i
$714$		0			0
$715$	6.44637	−	5.37080i	0.00901590	−	0.00751161i
$716$	−203.808			−0.284649
$717$		0			0
$718$	404.316	+	404.316i	0.563115	+	0.563115i
$719$			242.271i			0.336955i	0.985705	+	0.168478i	$0.0538851\pi$
$719$			242.271i			0.336955i	−0.985705	+	0.168478i	$0.946115\pi$
$720$		0			0
$721$	167.308			0.232050
$722$	956.768	−	956.768i	1.32516	−	1.32516i
$723$		0			0
$724$			667.849i			0.922443i
$725$	−180.999	+	986.070i	−0.249654	+	1.36010i
$726$		0			0
$727$	297.287	−	297.287i	0.408923	−	0.408923i	−0.472440	−	0.881363i	$-0.656627\pi$
$727$	297.287	−	297.287i	0.408923	−	0.408923i	0.881363	+	0.472440i	$0.156627\pi$
$728$	−19.2098	−	19.2098i	−0.0263871	−	0.0263871i
$729$		0			0
$730$	138.523	−	1521.93i	0.189757	−	2.08484i
$731$	763.025			1.04381
$732$		0			0
$733$	102.972	+	102.972i	0.140480	+	0.140480i	0.773850	−	0.633369i	$-0.218329\pi$
$733$	102.972	+	102.972i	0.140480	+	0.140480i	−0.633369	+	0.773850i	$0.718329\pi$
$734$		−	513.188i		−	0.699167i
$735$		0			0
$736$	−908.375			−1.23421
$737$	39.9235	−	39.9235i	0.0541703	−	0.0541703i
$738$		0			0
$739$		−	951.239i		−	1.28720i	−0.765363	−	0.643599i	$-0.777441\pi$
$739$		−	951.239i		−	1.28720i	0.765363	−	0.643599i	$-0.222559\pi$
$740$	132.751	−	110.602i	0.179394	−	0.149462i
$741$		0			0
$742$	−1064.63	+	1064.63i	−1.43481	+	1.43481i
$743$	98.0333	+	98.0333i	0.131942	+	0.131942i	0.769994	−	0.638051i	$-0.220259\pi$
$743$	98.0333	+	98.0333i	0.131942	+	0.131942i	−0.638051	+	0.769994i	$0.720259\pi$
$744$		0			0
$745$	−673.679	−	61.3167i	−0.904268	−	0.0823043i
$746$	−675.536			−0.905544
$747$		0			0
$748$	24.4325	+	24.4325i	0.0326638	+	0.0326638i
$749$		−	579.369i		−	0.773523i
$750$		0			0
$751$	144.613			0.192560			0.0962800	−	0.995354i	$-0.469306\pi$
$751$	144.613			0.192560			0.0962800	+	0.995354i	$0.469306\pi$
$752$	−907.233	+	907.233i	−1.20643	+	1.20643i
$753$		0			0
$754$			419.104i			0.555841i
$755$	−65.3558	+	718.056i	−0.0865640	+	0.951068i
$756$		0			0
$757$	−509.399	+	509.399i	−0.672918	+	0.672918i	−0.958388	−	0.285470i	$-0.907850\pi$
$757$	−509.399	+	509.399i	−0.672918	+	0.672918i	0.285470	+	0.958388i	$0.407850\pi$
$758$	−472.322	−	472.322i	−0.623116	−	0.623116i
$759$		0			0
$760$	−78.5924	−	94.3315i	−0.103411	−	0.124120i
$761$	−648.413			−0.852054			−0.426027	−	0.904710i	$-0.640087\pi$
$761$	−648.413			−0.852054			−0.426027	+	0.904710i	$0.640087\pi$
$762$		0			0
$763$	−364.450	−	364.450i	−0.477654	−	0.477654i
$764$		−	703.340i		−	0.920601i
$765$		0			0
$766$	−469.889			−0.613433
$767$	188.578	−	188.578i	0.245864	−	0.245864i
$768$		0			0
$769$			416.812i			0.542019i	0.962577	+	0.271009i	$0.0873574\pi$
$769$			416.812i			0.542019i	−0.962577	+	0.271009i	$0.912643\pi$
$770$	52.6448	+	4.79161i	0.0683699	+	0.00622287i
$771$		0			0
$772$	23.8183	−	23.8183i	0.0308527	−	0.0308527i
$773$	−114.629	−	114.629i	−0.148292	−	0.148292i	0.629063	−	0.777354i	$-0.283439\pi$
$773$	−114.629	−	114.629i	−0.148292	−	0.148292i	−0.777354	+	0.629063i	$0.783439\pi$
$774$		0			0
$775$	−376.046	−	69.0254i	−0.485220	−	0.0890650i
$776$	−125.653			−0.161924
$777$		0			0
$778$	−289.963	−	289.963i	−0.372703	−	0.372703i
$779$		−	1236.29i		−	1.58703i
$780$		0			0
$781$	31.7004			0.0405895
$782$	−847.377	+	847.377i	−1.08360	+	1.08360i
$783$		0			0
$784$		−	414.297i		−	0.528440i
$785$	205.612	+	246.789i	0.261926	+	0.314380i
$786$		0			0
$787$	−671.451	+	671.451i	−0.853178	+	0.853178i	−0.990523	−	0.137345i	$-0.956143\pi$
$787$	−671.451	+	671.451i	−0.853178	+	0.853178i	0.137345	+	0.990523i	$0.456143\pi$
$788$	429.170	+	429.170i	0.544632	+	0.544632i
$789$		0			0
$790$	716.719	−	597.135i	0.907239	−	0.755867i
$791$	−687.447			−0.869085
$792$		0			0
$793$	285.060	+	285.060i	0.359471	+	0.359471i
$794$			606.895i			0.764352i
$795$		0			0
$796$	1041.15			1.30798
$797$	−194.568	+	194.568i	−0.244126	+	0.244126i	−0.818555	−	0.574429i	$-0.805224\pi$
$797$	−194.568	+	194.568i	−0.244126	+	0.244126i	0.574429	+	0.818555i	$0.305224\pi$
$798$		0			0
$799$			1572.49i			1.96807i
$800$	908.160	−	626.469i	1.13520	−	0.783087i
$801$		0			0
$802$	−1390.65	+	1390.65i	−1.73398	+	1.73398i
$803$	−34.7027	−	34.7027i	−0.0432163	−	0.0432163i
$804$		0			0
$805$	−79.8118	+	876.882i	−0.0991451	+	1.08929i
$806$	−159.829			−0.198299
$807$		0			0
$808$	3.67865	+	3.67865i	0.00455279	+	0.00455279i
$809$			724.904i			0.896049i	0.894021	+	0.448025i	$0.147872\pi$
$809$			724.904i			0.896049i	−0.894021	+	0.448025i	$0.852128\pi$
$810$		0			0
$811$	331.996			0.409366			0.204683	−	0.978828i	$-0.434384\pi$
$811$	331.996			0.409366			0.204683	+	0.978828i	$0.434384\pi$
$812$	−896.689	+	896.689i	−1.10430	+	1.10430i
$813$		0			0
$814$		−	11.5539i		−	0.0141940i
$815$	98.3940	−	81.9771i	0.120729	−	0.100585i
$816$		0			0
$817$	748.990	−	748.990i	0.916757	−	0.916757i
$818$	328.652	+	328.652i	0.401775	+	0.401775i
$819$		0			0
$820$	781.026	+	71.0871i	0.952470	+	0.0866916i
$821$	719.613			0.876508			0.438254	−	0.898851i	$-0.355597\pi$
$821$	719.613			0.876508			0.438254	+	0.898851i	$0.355597\pi$
$822$		0			0
$823$	290.454	+	290.454i	0.352921	+	0.352921i	0.861195	−	0.508274i	$-0.169716\pi$
$823$	290.454	+	290.454i	0.352921	+	0.352921i	−0.508274	+	0.861195i	$0.669716\pi$
$824$		−	16.4835i		−	0.0200043i
$825$		0			0
$826$	1680.21			2.03415
$827$	185.364	−	185.364i	0.224140	−	0.224140i	−0.586099	−	0.810239i	$-0.699337\pi$
$827$	185.364	−	185.364i	0.224140	−	0.224140i	0.810239	+	0.586099i	$0.199337\pi$
$828$		0			0
$829$		−	601.887i		−	0.726040i	−0.931781	−	0.363020i	$-0.881746\pi$
$829$		−	601.887i		−	0.726040i	0.931781	−	0.363020i	$-0.118254\pi$
$830$	−40.3945	+	443.809i	−0.0486680	+	0.534710i
$831$		0			0
$832$	143.676	−	143.676i	0.172688	−	0.172688i
$833$	−359.046	−	359.046i	−0.431028	−	0.431028i
$834$		0			0
$835$	−140.449	−	168.576i	−0.168202	−	0.201887i
$836$	47.9663			0.0573759
$837$		0			0
$838$	277.039	+	277.039i	0.330595	+	0.330595i
$839$			168.066i			0.200317i	0.994971	+	0.100159i	$0.0319350\pi$
$839$			168.066i			0.200317i	−0.994971	+	0.100159i	$0.968065\pi$
$840$		0			0
$841$	−767.152			−0.912191
$842$	1130.58	−	1130.58i	1.34273	−	1.34273i
$843$		0			0
$844$			890.227i			1.05477i
$845$	770.854	+	70.1613i	0.912253	+	0.0830311i
$846$		0			0
$847$	−730.801	+	730.801i	−0.862811	+	0.862811i
$848$	768.067	+	768.067i	0.905739	+	0.905739i
$849$		0			0
$850$	262.775	−	1431.58i	0.309147	−	1.68421i
$851$	192.448			0.226143
$852$		0			0
$853$	318.997	+	318.997i	0.373971	+	0.373971i	0.868921	−	0.494950i	$-0.164814\pi$
$853$	318.997	+	318.997i	0.373971	+	0.373971i	−0.494950	+	0.868921i	$0.664814\pi$
$854$			2539.86i			2.97407i
$855$		0			0
$856$	−57.0806			−0.0666830
$857$	−680.909	+	680.909i	−0.794526	+	0.794526i	−0.982226	−	0.187700i	$-0.939897\pi$
$857$	−680.909	+	680.909i	−0.794526	+	0.794526i	0.187700	+	0.982226i	$0.439897\pi$
$858$		0			0
$859$			329.452i			0.383530i	0.981441	+	0.191765i	$0.0614211\pi$
$859$			329.452i			0.383530i	−0.981441	+	0.191765i	$0.938579\pi$
$860$	430.106	+	516.240i	0.500123	+	0.600279i
$861$		0			0
$862$	−880.801	+	880.801i	−1.02181	+	1.02181i
$863$	−271.802	−	271.802i	−0.314950	−	0.314950i	0.531874	−	0.846824i	$-0.321488\pi$
$863$	−271.802	−	271.802i	−0.314950	−	0.314950i	−0.846824	+	0.531874i	$0.821488\pi$
$864$		0			0
$865$	−309.799	+	258.110i	−0.358150	+	0.298393i
$866$	−2127.45			−2.45664
$867$		0			0
$868$	−341.959	−	341.959i	−0.393962	−	0.393962i
$869$		−	29.9581i		−	0.0344743i
$870$		0			0
$871$	−477.493			−0.548212
$872$	−35.9064	+	35.9064i	−0.0411770	+	0.0411770i
$873$		0			0
$874$			1663.58i			1.90341i
$875$	−524.957	−	931.717i	−0.599951	−	1.06482i
$876$		0			0
$877$	−515.213	+	515.213i	−0.587473	+	0.587473i	−0.936946	−	0.349474i	$-0.886360\pi$
$877$	−515.213	+	515.213i	−0.587473	+	0.587473i	0.349474	+	0.936946i	$0.386360\pi$
$878$	−900.248	−	900.248i	−1.02534	−	1.02534i
$879$		0			0
$880$	3.45687	−	37.9802i	0.00392826	−	0.0431593i
$881$	−1330.41			−1.51011			−0.755055	−	0.655661i	$-0.772390\pi$
$881$	−1330.41			−1.51011			−0.755055	+	0.655661i	$0.772390\pi$
$882$		0			0
$883$	−678.846	−	678.846i	−0.768795	−	0.768795i	0.209099	−	0.977894i	$-0.432947\pi$
$883$	−678.846	−	678.846i	−0.768795	−	0.768795i	−0.977894	+	0.209099i	$0.932947\pi$
$884$		−	292.218i		−	0.330563i
$885$		0			0
$886$	654.848			0.739106
$887$	803.393	−	803.393i	0.905742	−	0.905742i	−0.0901829	−	0.995925i	$-0.528745\pi$
$887$	803.393	−	803.393i	0.905742	−	0.905742i	0.995925	+	0.0901829i	$0.0287452\pi$
$888$		0			0
$889$		−	1373.71i		−	1.54523i
$890$	−1118.67	+	932.024i	−1.25694	+	1.04722i
$891$		0			0
$892$	199.348	−	199.348i	0.223485	−	0.223485i
$893$	1543.56	+	1543.56i	1.72852	+	1.72852i
$894$		0			0
$895$	274.568	+	24.9905i	0.306779	+	0.0279223i
$896$	−230.098			−0.256805
$897$		0			0
$898$	−524.007	−	524.007i	−0.583526	−	0.583526i
$899$		−	613.282i		−	0.682182i
$900$		0			0
$901$	1331.27			1.47755
$902$	37.0814	−	37.0814i	0.0411102	−	0.0411102i
$903$		0			0
$904$			67.7287i			0.0749211i
$905$	81.8900	−	899.716i	0.0904862	−	0.994161i
$906$		0			0
$907$	−1079.59	+	1079.59i	−1.19029	+	1.19029i	−0.213305	+	0.976986i	$0.568423\pi$
$907$	−1079.59	+	1079.59i	−1.19029	+	1.19029i	−0.976986	+	0.213305i	$0.931577\pi$
$908$	−21.9968	−	21.9968i	−0.0242256	−	0.0242256i
$909$		0			0
$910$	−286.167	−	343.475i	−0.314469	−	0.377445i
$911$	1792.53			1.96765			0.983825	−	0.179133i	$-0.0573294\pi$
$911$	1792.53			1.96765			0.983825	+	0.179133i	$0.0573294\pi$
$912$		0			0
$913$	10.1196	+	10.1196i	0.0110839	+	0.0110839i
$914$		−	242.214i		−	0.265004i
$915$		0			0
$916$	800.146			0.873522
$917$	480.318	−	480.318i	0.523793	−	0.523793i
$918$		0			0
$919$			1164.78i			1.26744i	0.773563	+	0.633719i	$0.218473\pi$
$919$			1164.78i			1.26744i	−0.773563	+	0.633719i	$0.781527\pi$
$920$	86.3923	+	7.86322i	0.0939046	+	0.00854698i
$921$		0			0
$922$	895.497	−	895.497i	0.971255	−	0.971255i
$923$	−189.571	−	189.571i	−0.205386	−	0.205386i
$924$		0			0
$925$	−192.402	+	132.724i	−0.208003	+	0.143485i
$926$	2051.52			2.21547
$927$		0			0
$928$	1251.39	+	1251.39i	1.34848	+	1.34848i
$929$		−	822.723i		−	0.885600i	−0.896620	−	0.442800i	$-0.853985\pi$
$929$		−	822.723i		−	0.885600i	0.896620	−	0.442800i	$-0.146015\pi$
$930$		0			0
$931$	−704.884			−0.757126
$932$	314.492	−	314.492i	0.337438	−	0.337438i
$933$		0			0
$934$		−	784.959i		−	0.840428i
$935$	−29.9193	−	35.9110i	−0.0319992	−	0.0384075i
$936$		0			0
$937$	857.665	−	857.665i	0.915331	−	0.915331i	−0.0813546	−	0.996685i	$-0.525925\pi$
$937$	857.665	−	857.665i	0.915331	−	0.915331i	0.996685	+	0.0813546i	$0.0259246\pi$
$938$	−2127.20	−	2127.20i	−2.26781	−	2.26781i
$939$		0			0
$940$	−1063.90	+	886.388i	−1.13181	+	0.942966i
$941$	−168.157			−0.178700			−0.0893501	−	0.996000i	$-0.528479\pi$
$941$	−168.157			−0.178700			−0.0893501	+	0.996000i	$0.528479\pi$
$942$		0			0
$943$	617.649	+	617.649i	0.654983	+	0.654983i
$944$		−	1212.17i		−	1.28408i
$945$		0			0
$946$	44.9304			0.0474952
$947$	−565.892	+	565.892i	−0.597562	+	0.597562i	−0.939663	−	0.342101i	$-0.888862\pi$
$947$	−565.892	+	565.892i	−0.597562	+	0.597562i	0.342101	+	0.939663i	$0.388862\pi$
$948$		0			0
$949$			415.051i			0.437356i
$950$	−1147.31	−	1663.19i	−1.20769	−	1.75072i
$951$		0			0
$952$	−107.013	+	107.013i	−0.112408	+	0.112408i
$953$	−387.854	−	387.854i	−0.406982	−	0.406982i	0.473703	−	0.880685i	$-0.342917\pi$
$953$	−387.854	−	387.854i	−0.406982	−	0.406982i	−0.880685	+	0.473703i	$0.842917\pi$
$954$		0			0
$955$	−86.2418	+	947.528i	−0.0903055	+	0.992176i
$956$	−987.372			−1.03282
$957$		0			0
$958$	1035.68	+	1035.68i	1.08108	+	1.08108i
$959$		−	844.370i		−	0.880469i
$960$		0			0
$961$	−727.120			−0.756629
$962$	−69.0933	+	69.0933i	−0.0718225	+	0.0718225i
$963$		0			0
$964$			1042.32i			1.08124i
$965$	−35.0082	+	29.1671i	−0.0362779	+	0.0302250i
$966$		0			0
$967$	−944.809	+	944.809i	−0.977051	+	0.977051i	−0.999743	−	0.0226911i	$-0.992777\pi$
$967$	−944.809	+	944.809i	−0.977051	+	0.977051i	0.0226911	+	0.999743i	$0.492777\pi$
$968$	72.0000	+	72.0000i	0.0743802	+	0.0743802i
$969$		0			0
$970$	−2059.27	−	187.430i	−2.12295	−	0.193226i
$971$	−1177.49			−1.21266			−0.606328	−	0.795215i	$-0.707358\pi$
$971$	−1177.49			−1.21266			−0.606328	+	0.795215i	$0.707358\pi$
$972$		0			0
$973$	−519.121	−	519.121i	−0.533526	−	0.533526i
$974$			11.6291i			0.0119395i
$975$		0			0
$976$	1832.36			1.87742
$977$	256.140	−	256.140i	0.262170	−	0.262170i	−0.563765	−	0.825935i	$-0.690648\pi$
$977$	256.140	−	256.140i	0.262170	−	0.262170i	0.825935	+	0.563765i	$0.190648\pi$
$978$		0			0
$979$			46.7594i			0.0477624i
$980$	40.5310	−	445.309i	0.0413581	−	0.454397i
$981$		0			0
$982$	1551.32	−	1551.32i	1.57976	−	1.57976i
$983$	480.914	+	480.914i	0.489231	+	0.489231i	0.908063	−	0.418833i	$-0.137561\pi$
$983$	480.914	+	480.914i	0.489231	+	0.489231i	−0.418833	+	0.908063i	$0.637561\pi$
$984$		0			0
$985$	−525.548	−	630.795i	−0.533551	−	0.640401i
$986$	2334.72			2.36787
$987$		0			0
$988$	−286.843	−	286.843i	−0.290327	−	0.290327i
$989$			748.387i			0.756711i
$990$		0			0
$991$	809.023			0.816370			0.408185	−	0.912899i	$-0.366162\pi$
$991$	809.023			0.816370			0.408185	+	0.912899i	$0.366162\pi$
$992$	−477.228	+	477.228i	−0.481076	+	0.481076i
$993$		0			0
$994$		−	1689.06i		−	1.69925i
$995$	−1402.62	−	127.663i	−1.40967	−	0.128305i
$996$		0			0
$997$	75.4865	−	75.4865i	0.0757137	−	0.0757137i	−0.668236	−	0.743950i	$-0.732950\pi$
$997$	75.4865	−	75.4865i	0.0757137	−	0.0757137i	0.743950	+	0.668236i	$0.232950\pi$
$998$	−1153.32	−	1153.32i	−1.15563	−	1.15563i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.g.f.163.2	yes	16
3.2	odd	2	inner	405.3.g.f.163.7	yes	16
5.2	odd	4	inner	405.3.g.f.82.2	✓	16
9.2	odd	6		405.3.l.m.28.1		16
9.4	even	3		405.3.l.m.298.1		16
9.5	odd	6		405.3.l.j.298.4		16
9.7	even	3		405.3.l.j.28.4		16
15.2	even	4	inner	405.3.g.f.82.7	yes	16
45.2	even	12		405.3.l.j.352.4		16
45.7	odd	12		405.3.l.m.352.1		16
45.22	odd	12		405.3.l.j.217.4		16
45.32	even	12		405.3.l.m.217.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.f.82.2	✓	16	5.2	odd	4	inner
405.3.g.f.82.7	yes	16	15.2	even	4	inner
405.3.g.f.163.2	yes	16	1.1	even	1	trivial
405.3.g.f.163.7	yes	16	3.2	odd	2	inner
405.3.l.j.28.4		16	9.7	even	3
405.3.l.j.217.4		16	45.22	odd	12
405.3.l.j.298.4		16	9.5	odd	6
405.3.l.j.352.4		16	45.2	even	12
405.3.l.m.28.1		16	9.2	odd	6
405.3.l.m.217.1		16	45.32	even	12
405.3.l.m.298.1		16	9.4	even	3
405.3.l.m.352.1		16	45.7	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96165 + 1.96165i) q^{2} -3.69616i q^{4} +(-0.453215 + 4.97942i) q^{5} +(6.04960 - 6.04960i) q^{7} +(-0.596019 - 0.596019i) q^{8} +(-8.87884 - 10.6569i) q^{10} -0.445449 q^{11} +(2.66383 + 2.66383i) q^{13} +23.7344i q^{14} +17.1230 q^{16} +(14.8395 - 14.8395i) q^{17} -29.1331i q^{19} +(18.4047 + 1.67516i) q^{20} +(0.873817 - 0.873817i) q^{22} +(14.5548 + 14.5548i) q^{23} +(-24.5892 - 4.51349i) q^{25} -10.4510 q^{26} +(-22.3603 - 22.3603i) q^{28} -40.1018i q^{29} +15.2931 q^{31} +(-31.2054 + 31.2054i) q^{32} +58.2198i q^{34} +(27.3817 + 32.8653i) q^{35} +(6.61115 - 6.61115i) q^{37} +(57.1490 + 57.1490i) q^{38} +(3.23795 - 2.69770i) q^{40} +42.4361 q^{41} +(25.7093 + 25.7093i) q^{43} +1.64645i q^{44} -57.1029 q^{46} +(-52.9832 + 52.9832i) q^{47} -24.1953i q^{49} +(57.0894 - 39.3816i) q^{50} +(9.84595 - 9.84595i) q^{52} +(44.8558 + 44.8558i) q^{53} +(0.201884 - 2.21808i) q^{55} -7.21135 q^{56} +(78.6658 + 78.6658i) q^{58} -70.7920i q^{59} +107.011 q^{61} +(-29.9998 + 29.9998i) q^{62} -53.9361i q^{64} +(-14.4716 + 12.0570i) q^{65} +(-89.6252 + 89.6252i) q^{67} +(-54.8491 - 54.8491i) q^{68} +(-118.184 - 10.7568i) q^{70} -71.1649 q^{71} +(77.9049 + 77.9049i) q^{73} +25.9376i q^{74} -107.681 q^{76} +(-2.69479 + 2.69479i) q^{77} +67.2537i q^{79} +(-7.76041 + 85.2627i) q^{80} +(-83.2449 + 83.2449i) q^{82} +(-22.7178 - 22.7178i) q^{83} +(67.1665 + 80.6174i) q^{85} -100.865 q^{86} +(0.265496 + 0.265496i) q^{88} -104.971i q^{89} +32.2302 q^{91} +(53.7969 - 53.7969i) q^{92} -207.869i q^{94} +(145.066 + 13.2035i) q^{95} +(105.410 - 105.410i) q^{97} +(47.4628 + 47.4628i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 40 q^{7} - 56 q^{10} - 44 q^{13} - 32 q^{16} + 32 q^{22} - 92 q^{25} + 176 q^{28} + 320 q^{31} + 4 q^{37} - 528 q^{40} + 256 q^{43} - 16 q^{46} - 308 q^{52} - 364 q^{55} + 492 q^{58} + 8 q^{61} + 88 q^{67}+ \cdots + 304 q^{97}+O(q^{100}) \) 16 * q + 40 * q^7 - 56 * q^10 - 44 * q^13 - 32 * q^16 + 32 * q^22 - 92 * q^25 + 176 * q^28 + 320 * q^31 + 4 * q^37 - 528 * q^40 + 256 * q^43 - 16 * q^46 - 308 * q^52 - 364 * q^55 + 492 * q^58 + 8 * q^61 + 88 * q^67 - 36 * q^70 + 364 * q^73 - 912 * q^76 + 32 * q^82 + 64 * q^85 + 840 * q^88 + 224 * q^91 + 304 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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