LMFDB - Embedded newform 405.3.g.f.82.2

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			82.2
Root			$1.96165 - 1.96165i$ of defining polynomial
Character	$\chi$	$=$	405.82
Dual form			405.3.g.f.163.2

$q$-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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

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

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	0.0189931	−	0.999820i	$-0.493954\pi$
$2$	−1.96165	−	1.96165i	−0.980826	−	0.980826i	−0.999820	+	0.0189931i	$0.993954\pi$
$3$		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	0.991826	−	0.127597i	$-0.0407266\pi$
$7$	6.04960	+	6.04960i	0.864229	+	0.864229i	−0.127597	+	0.991826i	$0.540727\pi$
$8$	−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	−0.597190	−	0.802100i	$-0.703716\pi$
$13$	2.66383	−	2.66383i	0.204910	−	0.204910i	0.802100	+	0.597190i	$0.203716\pi$
$14$		−	23.7344i		−	1.69532i
$15$		0			0
$16$	17.1230			1.07019
$17$	14.8395	+	14.8395i	0.872910	+	0.872910i	0.992789	−	0.119878i	$-0.0382504\pi$
$17$	14.8395	+	14.8395i	0.872910	+	0.872910i	−0.119878	+	0.992789i	$0.538250\pi$
$18$		0			0
$19$			29.1331i			1.53332i	0.642054	+	0.766660i	$0.278083\pi$
$19$			29.1331i			1.53332i	−0.642054	+	0.766660i	$0.721917\pi$
$20$	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	−0.315956	−	0.948774i	$-0.602325\pi$
$23$	14.5548	−	14.5548i	0.632817	−	0.632817i	0.948774	+	0.315956i	$0.102325\pi$
$24$		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	$0.243010\pi$
$29$			40.1018i			1.38282i	−0.722463	+	0.691410i	$0.756990\pi$
$30$		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	0.790780	−	0.612100i	$-0.209675\pi$
$37$	6.61115	+	6.61115i	0.178680	+	0.178680i	−0.612100	+	0.790780i	$0.709675\pi$
$38$	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	−0.341860	−	0.939751i	$-0.611057\pi$
$43$	25.7093	−	25.7093i	0.597890	−	0.597890i	0.939751	+	0.341860i	$0.111057\pi$
$44$		−	1.64645i		−	0.0374194i
$45$		0			0
$46$	−57.1029			−1.24137
$47$	−52.9832	−	52.9832i	−1.12730	−	1.12730i	−0.990614	−	0.136689i	$-0.956354\pi$
$47$	−52.9832	−	52.9832i	−1.12730	−	1.12730i	−0.136689	−	0.990614i	$-0.543646\pi$
$48$		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	−0.143338	−	0.989674i	$-0.545784\pi$
$53$	44.8558	−	44.8558i	0.846336	−	0.846336i	0.989674	+	0.143338i	$0.0457836\pi$
$54$		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	$0.204806\pi$
$59$			70.7920i			1.19986i	−0.800051	+	0.599932i	$0.795194\pi$
$60$		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	−0.898293	−	0.439398i	$-0.855192\pi$
$67$	−89.6252	−	89.6252i	−1.33769	−	1.33769i	−0.439398	−	0.898293i	$-0.644808\pi$
$68$	−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	0.0696171	−	0.997574i	$-0.477822\pi$
$73$	77.9049	−	77.9049i	1.06719	−	1.06719i	0.997574	−	0.0696171i	$-0.0221777\pi$
$74$		−	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	$-0.860043\pi$
$79$		−	67.2537i		−	0.851313i	0.904885	−	0.425657i	$-0.139957\pi$
$80$	−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	−0.830591	−	0.556883i	$-0.811997\pi$
$83$	−22.7178	+	22.7178i	−0.273708	+	0.273708i	0.556883	+	0.830591i	$0.311997\pi$
$84$		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	$0.200765\pi$
$89$			104.971i			1.17945i	−0.807603	+	0.589727i	$0.799235\pi$
$90$		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	0.995866	+	0.0908350i	$0.0289536\pi$
$97$	105.410	+	105.410i	1.08670	+	1.08670i	0.0908350	+	0.995866i	$0.471046\pi$
$98$	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	−0.636787	−	0.771040i	$-0.719737\pi$
$103$	13.8280	−	13.8280i	0.134253	−	0.134253i	0.771040	+	0.636787i	$0.219737\pi$
$104$			3.17539i			0.0305326i
$105$		0			0
$106$	−175.983			−1.66022
$107$	47.8849	+	47.8849i	0.447522	+	0.447522i	0.894530	−	0.447008i	$-0.147510\pi$
$107$	47.8849	+	47.8849i	0.447522	+	0.447522i	−0.447008	+	0.894530i	$0.647510\pi$
$108$		0			0
$109$			60.2436i			0.552694i	0.961058	+	0.276347i	$0.0891239\pi$
$109$			60.2436i			0.552694i	−0.961058	+	0.276347i	$0.910876\pi$
$110$	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	−0.912310	−	0.409500i	$-0.865703\pi$
$113$	−56.8175	+	56.8175i	−0.502810	+	0.502810i	0.409500	+	0.912310i	$0.365703\pi$
$114$		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	0.994896	−	0.100902i	$-0.0321730\pi$
$127$	113.537	+	113.537i	0.893994	+	0.893994i	−0.100902	+	0.994896i	$0.532173\pi$
$128$	−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	0.914341	−	0.404945i	$-0.132709\pi$
$137$	69.7872	+	69.7872i	0.509396	+	0.509396i	−0.404945	+	0.914341i	$0.632709\pi$
$138$		0			0
$139$			85.8108i			0.617344i	0.951169	+	0.308672i	$0.0998845\pi$
$139$			85.8108i			0.617344i	−0.951169	+	0.308672i	$0.900116\pi$
$140$	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	$-0.849996\pi$
$149$		−	135.293i		−	0.908006i	0.891000	−	0.454003i	$-0.150004\pi$
$150$		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	0.836821	−	0.547477i	$-0.184411\pi$
$157$	45.4271	+	45.4271i	0.289345	+	0.289345i	−0.547477	+	0.836821i	$0.684411\pi$
$158$	−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	−0.760478	−	0.649364i	$-0.775035\pi$
$163$	−18.1117	+	18.1117i	−0.111115	+	0.111115i	0.649364	+	0.760478i	$0.275035\pi$
$164$			156.851i			0.956408i
$165$		0			0
$166$	89.1287			0.536920
$167$	−31.0302	−	31.0302i	−0.185810	−	0.185810i	0.608072	−	0.793882i	$-0.291943\pi$
$167$	−31.0302	−	31.0302i	−0.185810	−	0.185810i	−0.793882	+	0.608072i	$0.791943\pi$
$168$		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	−0.522817	−	0.852445i	$-0.675119\pi$
$173$	57.0256	−	57.0256i	0.329628	−	0.329628i	0.852445	+	0.522817i	$0.175119\pi$
$174$		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	$0.0492232\pi$
$179$			55.1405i			0.308047i	−0.988067	+	0.154024i	$0.950777\pi$
$180$		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	−0.690215	−	0.723604i	$-0.742484\pi$
$193$	6.44405	−	6.44405i	0.0333889	−	0.0333889i	0.723604	+	0.690215i	$0.242484\pi$
$194$		−	413.556i		−	2.13173i
$195$		0			0
$196$	−89.4299			−0.456275
$197$	−116.112	−	116.112i	−0.589403	−	0.589403i	0.348067	−	0.937470i	$-0.386838\pi$
$197$	−116.112	−	116.112i	−0.589403	−	0.589403i	−0.937470	+	0.348067i	$0.886838\pi$
$198$		0			0
$199$		−	281.684i		−	1.41550i	−0.706465	−	0.707748i	$-0.749711\pi$
$199$		−	281.684i		−	1.41550i	0.706465	−	0.707748i	$-0.250289\pi$
$200$	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	−0.575762	−	0.817618i	$-0.695294\pi$
$223$	53.9338	−	53.9338i	0.241856	−	0.241856i	0.817618	+	0.575762i	$0.195294\pi$
$224$		−	377.560i		−	1.68554i
$225$		0			0
$226$	222.913			0.986339
$227$	5.95126	+	5.95126i	0.0262170	+	0.0262170i	0.720094	−	0.693877i	$-0.244099\pi$
$227$	5.95126	+	5.95126i	0.0262170	+	0.0262170i	−0.693877	+	0.720094i	$0.744099\pi$
$228$		0			0
$229$		−	216.480i		−	0.945328i	−0.881243	−	0.472664i	$-0.843292\pi$
$229$		−	216.480i		−	0.945328i	0.881243	−	0.472664i	$-0.156708\pi$
$230$	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	−0.500538	−	0.865714i	$-0.666865\pi$
$233$	85.0860	−	85.0860i	0.365176	−	0.365176i	0.865714	+	0.500538i	$0.166865\pi$
$234$		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	$0.188760\pi$
$239$			267.134i			1.11772i	−0.829263	+	0.558858i	$0.811240\pi$
$240$		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	0.888902	−	0.458096i	$-0.151469\pi$
$257$	110.717	+	110.717i	0.430806	+	0.430806i	−0.458096	+	0.888902i	$0.651469\pi$
$258$		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	−0.743627	−	0.668594i	$-0.766896\pi$
$263$	−19.7336	+	19.7336i	−0.0750328	+	0.0750328i	0.668594	+	0.743627i	$0.266896\pi$
$264$		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	$-0.940029\pi$
$269$		−	100.763i		−	0.374584i	0.982304	−	0.187292i	$-0.0599711\pi$
$270$		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	0.353884	−	0.935289i	$-0.384861\pi$
$277$	−161.049	−	161.049i	−0.581405	−	0.581405i	−0.935289	+	0.353884i	$0.884861\pi$
$278$	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	−0.995516	−	0.0945934i	$-0.969845\pi$
$283$	−254.961	+	254.961i	−0.900923	+	0.900923i	0.0945934	+	0.995516i	$0.469845\pi$
$284$		−	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	−0.904676	−	0.426100i	$-0.859887\pi$
$293$	−140.223	+	140.223i	−0.478576	+	0.478576i	0.426100	+	0.904676i	$0.359887\pi$
$294$		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	0.878582	−	0.477592i	$-0.158490\pi$
$307$	123.104	+	123.104i	0.400990	+	0.400990i	−0.477592	+	0.878582i	$0.658490\pi$
$308$	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	−0.473322	−	0.880889i	$-0.656945\pi$
$313$	127.568	−	127.568i	0.407567	−	0.407567i	0.880889	+	0.473322i	$0.156945\pi$
$314$		−	178.224i		−	0.567594i
$315$		0			0
$316$	248.581			0.786649
$317$	−235.473	−	235.473i	−0.742817	−	0.742817i	0.230302	−	0.973119i	$-0.426028\pi$
$317$	−235.473	−	235.473i	−0.742817	−	0.742817i	−0.973119	+	0.230302i	$0.926028\pi$
$318$		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	0.354711	−	0.934976i	$-0.384579\pi$
$337$	−195.549	−	195.549i	−0.580265	−	0.580265i	−0.934976	+	0.354711i	$0.884579\pi$
$338$	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	0.307177	−	0.951652i	$-0.400615\pi$
$347$	−223.633	−	223.633i	−0.644475	−	0.644475i	−0.951652	+	0.307177i	$0.900615\pi$
$348$		0			0
$349$			675.814i			1.93643i	0.250120	+	0.968215i	$0.419530\pi$
$349$			675.814i			1.93643i	−0.250120	+	0.968215i	$0.580470\pi$
$350$	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	−0.156019	−	0.987754i	$-0.549866\pi$
$353$	293.602	−	293.602i	0.831735	−	0.831735i	0.987754	+	0.156019i	$0.0498661\pi$
$354$		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	$0.0926783\pi$
$359$			206.110i			0.574122i	−0.957912	+	0.287061i	$0.907322\pi$
$360$		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	0.506073	−	0.862490i	$-0.331097\pi$
$367$	−130.805	−	130.805i	−0.356417	−	0.356417i	−0.862490	+	0.506073i	$0.831097\pi$
$368$	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	−0.437564	−	0.899187i	$-0.644159\pi$
$373$	172.185	−	172.185i	0.461623	−	0.461623i	0.899187	+	0.437564i	$0.144159\pi$
$374$			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	$-0.897107\pi$
$379$		−	240.778i		−	0.635297i	0.948208	−	0.317649i	$-0.102893\pi$
$380$	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	−0.533247	−	0.845959i	$-0.679028\pi$
$383$	119.769	−	119.769i	0.312712	−	0.312712i	0.845959	+	0.533247i	$0.179028\pi$
$384$		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	$-0.939153\pi$
$389$		−	147.816i		−	0.379989i	0.981785	−	0.189995i	$-0.0608470\pi$
$390$		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	0.874561	−	0.484915i	$-0.161149\pi$
$397$	154.690	+	154.690i	0.389647	+	0.389647i	−0.484915	+	0.874561i	$0.661149\pi$
$398$	−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	$0.0656590\pi$
$409$			167.538i			0.409629i	−0.978801	+	0.204814i	$0.934341\pi$
$410$	−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	$0.0539017\pi$
$419$			141.227i			0.337058i	−0.985697	+	0.168529i	$0.946098\pi$
$420$		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	0.297663	−	0.954671i	$-0.403793\pi$
$433$	542.261	−	542.261i	1.25233	−	1.25233i	0.954671	−	0.297663i	$-0.0962072\pi$
$434$		−	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	$-0.824928\pi$
$439$		−	458.923i		−	1.04538i	0.852522	−	0.522692i	$-0.175072\pi$
$440$	−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	−0.869938	−	0.493161i	$-0.835841\pi$
$443$	−166.912	+	166.912i	−0.376777	+	0.376777i	0.493161	+	0.869938i	$0.335841\pi$
$444$		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	$-0.903858\pi$
$449$		−	267.125i		−	0.594933i	0.954732	−	0.297467i	$-0.0961417\pi$
$450$		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	0.636327	−	0.771419i	$-0.280453\pi$
$457$	−61.7372	−	61.7372i	−0.135092	−	0.135092i	−0.771419	+	0.636327i	$0.780453\pi$
$458$	−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	−0.139112	+	0.990277i	$0.544425\pi$
$463$	−522.907	+	522.907i	−1.12939	+	1.12939i	−0.990277	+	0.139112i	$0.955575\pi$
$464$			686.664i			1.47988i
$465$		0			0
$466$	−333.818			−0.716349
$467$	−200.076	−	200.076i	−0.428428	−	0.428428i	0.459664	−	0.888093i	$-0.347970\pi$
$467$	−200.076	−	200.076i	−0.428428	−	0.428428i	−0.888093	+	0.459664i	$0.847970\pi$
$468$		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	$0.185794\pi$
$479$			527.960i			1.10221i	−0.834435	+	0.551107i	$0.814206\pi$
$480$		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	0.710143	−	0.704057i	$-0.248630\pi$
$487$	2.96411	+	2.96411i	0.00608646	+	0.00608646i	−0.704057	+	0.710143i	$0.748630\pi$
$488$	−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	$-0.799478\pi$
$499$		−	587.934i		−	1.17822i	0.808052	−	0.589112i	$-0.200522\pi$
$500$	−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	−0.367797	−	0.929906i	$-0.619888\pi$
$503$	282.741	−	282.741i	0.562109	−	0.562109i	0.929906	+	0.367797i	$0.119888\pi$
$504$		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	$0.172132\pi$
$509$			524.061i			1.02959i	−0.857313	+	0.514795i	$0.827868\pi$
$510$		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	−0.0123638	+	0.999924i	$0.503936\pi$
$523$	−529.426	+	529.426i	−1.01229	+	1.01229i	−0.999924	+	0.0123638i	$0.996064\pi$
$524$			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	0.983075	−	0.183201i	$-0.0586459\pi$
$547$	437.531	+	437.531i	0.799875	+	0.799875i	−0.183201	+	0.983075i	$0.558646\pi$
$548$	−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	−0.997983	−	0.0634822i	$-0.979779\pi$
$557$	−591.236	−	591.236i	−1.06147	−	1.06147i	−0.0634822	−	0.997983i	$-0.520221\pi$
$558$		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	−0.998039	−	0.0625946i	$-0.980062\pi$
$563$	−526.655	+	526.655i	−0.935444	+	0.935444i	0.0625946	+	0.998039i	$0.480062\pi$
$564$		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	$0.173805\pi$
$569$			590.957i			1.03859i	−0.854595	+	0.519294i	$0.826195\pi$
$570$		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	0.558589	−	0.829445i	$-0.311343\pi$
$577$	−156.284	−	156.284i	−0.270856	−	0.270856i	−0.829445	+	0.558589i	$0.811343\pi$
$578$	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	−0.966897	−	0.255166i	$-0.917870\pi$
$587$	−717.351	−	717.351i	−1.22206	−	1.22206i	−0.255166	−	0.966897i	$-0.582130\pi$
$588$		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	−0.364204	−	0.931319i	$-0.618659\pi$
$593$	336.299	−	336.299i	0.567115	−	0.567115i	0.931319	+	0.364204i	$0.118659\pi$
$594$		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	$-0.883714\pi$
$599$		−	427.985i		−	0.714500i	0.934009	−	0.357250i	$-0.116286\pi$
$600$		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	0.858352	−	0.513062i	$-0.171489\pi$
$607$	209.591	+	209.591i	0.345290	+	0.345290i	−0.513062	+	0.858352i	$0.671489\pi$
$608$	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	−0.868914	−	0.494963i	$-0.835181\pi$
$613$	−229.232	+	229.232i	−0.373951	+	0.373951i	0.494963	+	0.868914i	$0.335181\pi$
$614$		−	482.974i		−	0.786603i
$615$		0			0
$616$	3.21229			0.00521476
$617$	−89.8034	−	89.8034i	−0.145548	−	0.145548i	0.630578	−	0.776126i	$-0.282818\pi$
$617$	−89.8034	−	89.8034i	−0.145548	−	0.145548i	−0.776126	+	0.630578i	$0.782818\pi$
$618$		0			0
$619$		−	1157.67i		−	1.87022i	−0.354351	−	0.935112i	$-0.615298\pi$
$619$		−	1157.67i		−	1.87022i	0.354351	−	0.935112i	$-0.384702\pi$
$620$	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	−0.911627	−	0.411018i	$-0.865173\pi$
$643$	−321.892	+	321.892i	−0.500610	+	0.500610i	0.411018	+	0.911627i	$0.365173\pi$
$644$			650.900i			1.01071i
$645$		0			0
$646$	1696.12			2.62557
$647$	19.2194	+	19.2194i	0.0297054	+	0.0297054i	0.721803	−	0.692098i	$-0.243313\pi$
$647$	19.2194	+	19.2194i	0.0297054	+	0.0297054i	−0.692098	+	0.721803i	$0.743313\pi$
$648$		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	0.520948	−	0.853589i	$-0.325579\pi$
$653$	897.572	−	897.572i	1.37454	−	1.37454i	0.853589	−	0.520948i	$-0.174421\pi$
$654$		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	$-0.796673\pi$
$659$		−	785.804i		−	1.19242i	0.802829	−	0.596209i	$-0.203327\pi$
$660$		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	−0.992223	−	0.124475i	$-0.960275\pi$
$673$	−583.994	+	583.994i	−0.867748	+	0.867748i	0.124475	+	0.992223i	$0.460275\pi$
$674$			767.200i			1.13828i
$675$		0			0
$676$	−572.196			−0.846444
$677$	−510.053	−	510.053i	−0.753401	−	0.753401i	0.221711	−	0.975112i	$-0.428836\pi$
$677$	−510.053	−	510.053i	−0.753401	−	0.753401i	−0.975112	+	0.221711i	$0.928836\pi$
$678$		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	−0.873783	−	0.486316i	$-0.838340\pi$
$683$	−264.640	+	264.640i	−0.387467	+	0.387467i	0.486316	+	0.873783i	$0.338340\pi$
$684$		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	$-0.974601\pi$
$709$		−	113.025i		−	0.159415i	0.996818	−	0.0797074i	$-0.0253986\pi$
$710$	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	$-0.946115\pi$
$719$		−	242.271i		−	0.336955i	0.985705	−	0.168478i	$-0.0538851\pi$
$720$		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	0.881363	−	0.472440i	$-0.156627\pi$
$727$	297.287	+	297.287i	0.408923	+	0.408923i	−0.472440	+	0.881363i	$0.656627\pi$
$728$	−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	−0.633369	−	0.773850i	$-0.718329\pi$
$733$	102.972	−	102.972i	0.140480	−	0.140480i	0.773850	+	0.633369i	$0.218329\pi$
$734$			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	$0.222559\pi$
$739$			951.239i			1.28720i	−0.765363	+	0.643599i	$0.777441\pi$
$740$	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	−0.638051	−	0.769994i	$-0.720259\pi$
$743$	98.0333	−	98.0333i	0.131942	−	0.131942i	0.769994	+	0.638051i	$0.220259\pi$
$744$		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	0.285470	−	0.958388i	$-0.407850\pi$
$757$	−509.399	−	509.399i	−0.672918	−	0.672918i	−0.958388	+	0.285470i	$0.907850\pi$
$758$	−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	$-0.912643\pi$
$769$		−	416.812i		−	0.542019i	0.962577	−	0.271009i	$-0.0873574\pi$
$770$	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	−0.777354	−	0.629063i	$-0.783439\pi$
$773$	−114.629	+	114.629i	−0.148292	+	0.148292i	0.629063	+	0.777354i	$0.283439\pi$
$774$		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	0.137345	−	0.990523i	$-0.456143\pi$
$787$	−671.451	−	671.451i	−0.853178	−	0.853178i	−0.990523	+	0.137345i	$0.956143\pi$
$788$	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	0.574429	−	0.818555i	$-0.305224\pi$
$797$	−194.568	−	194.568i	−0.244126	−	0.244126i	−0.818555	+	0.574429i	$0.805224\pi$
$798$		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	$-0.852128\pi$
$809$		−	724.904i		−	0.896049i	0.894021	−	0.448025i	$-0.147872\pi$
$810$		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	−0.508274	−	0.861195i	$-0.669716\pi$
$823$	290.454	−	290.454i	0.352921	−	0.352921i	0.861195	+	0.508274i	$0.169716\pi$
$824$			16.4835i			0.0200043i
$825$		0			0
$826$	1680.21			2.03415
$827$	185.364	+	185.364i	0.224140	+	0.224140i	0.810239	−	0.586099i	$-0.199337\pi$
$827$	185.364	+	185.364i	0.224140	+	0.224140i	−0.586099	+	0.810239i	$0.699337\pi$
$828$		0			0
$829$			601.887i			0.726040i	0.931781	+	0.363020i	$0.118254\pi$
$829$			601.887i			0.726040i	−0.931781	+	0.363020i	$0.881746\pi$
$830$	−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	$-0.968065\pi$
$839$		−	168.066i		−	0.200317i	0.994971	−	0.100159i	$-0.0319350\pi$
$840$		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	−0.494950	−	0.868921i	$-0.664814\pi$
$853$	318.997	−	318.997i	0.373971	−	0.373971i	0.868921	+	0.494950i	$0.164814\pi$
$854$		−	2539.86i		−	2.97407i
$855$		0			0
$856$	−57.0806			−0.0666830
$857$	−680.909	−	680.909i	−0.794526	−	0.794526i	0.187700	−	0.982226i	$-0.439897\pi$
$857$	−680.909	−	680.909i	−0.794526	−	0.794526i	−0.982226	+	0.187700i	$0.939897\pi$
$858$		0			0
$859$		−	329.452i		−	0.383530i	−0.981441	−	0.191765i	$-0.938579\pi$
$859$		−	329.452i		−	0.383530i	0.981441	−	0.191765i	$-0.0614211\pi$
$860$	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	−0.846824	−	0.531874i	$-0.821488\pi$
$863$	−271.802	+	271.802i	−0.314950	+	0.314950i	0.531874	+	0.846824i	$0.321488\pi$
$864$		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	0.349474	−	0.936946i	$-0.386360\pi$
$877$	−515.213	−	515.213i	−0.587473	−	0.587473i	−0.936946	+	0.349474i	$0.886360\pi$
$878$	−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	−0.977894	−	0.209099i	$-0.932947\pi$
$883$	−678.846	+	678.846i	−0.768795	+	0.768795i	0.209099	+	0.977894i	$0.432947\pi$
$884$			292.218i			0.330563i
$885$		0			0
$886$	654.848			0.739106
$887$	803.393	+	803.393i	0.905742	+	0.905742i	0.995925	−	0.0901829i	$-0.0287452\pi$
$887$	803.393	+	803.393i	0.905742	+	0.905742i	−0.0901829	+	0.995925i	$0.528745\pi$
$888$		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	−0.976986	−	0.213305i	$-0.931577\pi$
$907$	−1079.59	−	1079.59i	−1.19029	−	1.19029i	−0.213305	−	0.976986i	$-0.568423\pi$
$908$	−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	$-0.781527\pi$
$919$		−	1164.78i		−	1.26744i	0.773563	−	0.633719i	$-0.218473\pi$
$920$	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	$0.146015\pi$
$929$			822.723i			0.885600i	−0.896620	+	0.442800i	$0.853985\pi$
$930$		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	0.996685	−	0.0813546i	$-0.0259246\pi$
$937$	857.665	+	857.665i	0.915331	+	0.915331i	−0.0813546	+	0.996685i	$0.525925\pi$
$938$	−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	0.342101	−	0.939663i	$-0.388862\pi$
$947$	−565.892	−	565.892i	−0.597562	−	0.597562i	−0.939663	+	0.342101i	$0.888862\pi$
$948$		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	−0.880685	−	0.473703i	$-0.842917\pi$
$953$	−387.854	+	387.854i	−0.406982	+	0.406982i	0.473703	+	0.880685i	$0.342917\pi$
$954$		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	0.0226911	−	0.999743i	$-0.492777\pi$
$967$	−944.809	−	944.809i	−0.977051	−	0.977051i	−0.999743	+	0.0226911i	$0.992777\pi$
$968$	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	0.825935	−	0.563765i	$-0.190648\pi$
$977$	256.140	+	256.140i	0.262170	+	0.262170i	−0.563765	+	0.825935i	$0.690648\pi$
$978$		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	−0.418833	−	0.908063i	$-0.637561\pi$
$983$	480.914	−	480.914i	0.489231	−	0.489231i	0.908063	+	0.418833i	$0.137561\pi$
$984$		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	0.743950	−	0.668236i	$-0.232950\pi$
$997$	75.4865	+	75.4865i	0.0757137	+	0.0757137i	−0.668236	+	0.743950i	$0.732950\pi$
$998$	−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.82.2	✓	16
3.2	odd	2	inner	405.3.g.f.82.7	yes	16
5.3	odd	4	inner	405.3.g.f.163.2	yes	16
9.2	odd	6		405.3.l.j.352.4		16
9.4	even	3		405.3.l.j.217.4		16
9.5	odd	6		405.3.l.m.217.1		16
9.7	even	3		405.3.l.m.352.1		16
15.8	even	4	inner	405.3.g.f.163.7	yes	16
45.13	odd	12		405.3.l.m.298.1		16
45.23	even	12		405.3.l.j.298.4		16
45.38	even	12		405.3.l.m.28.1		16
45.43	odd	12		405.3.l.j.28.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.f.82.2	✓	16	1.1	even	1	trivial
405.3.g.f.82.7	yes	16	3.2	odd	2	inner
405.3.g.f.163.2	yes	16	5.3	odd	4	inner
405.3.g.f.163.7	yes	16	15.8	even	4	inner
405.3.l.j.28.4		16	45.43	odd	12
405.3.l.j.217.4		16	9.4	even	3
405.3.l.j.298.4		16	45.23	even	12
405.3.l.j.352.4		16	9.2	odd	6
405.3.l.m.28.1		16	45.38	even	12
405.3.l.m.217.1		16	9.5	odd	6
405.3.l.m.298.1		16	45.13	odd	12
405.3.l.m.352.1		16	9.7	even	3

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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