LMFDB - Embedded newform 300.2.w.a.67.2

Newspace parameters

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			67.2
Character	$\chi$	$=$	300.67
Dual form			300.2.w.a.103.2

$q$-expansion

$f(q)$	$=$	$q+(-1.37859 - 0.315398i) q^{2} +(0.987688 + 0.156434i) q^{3} +(1.80105 + 0.869612i) q^{4} +(2.22681 + 0.203301i) q^{5} +(-1.31228 - 0.527175i) q^{6} +(2.91192 - 2.91192i) q^{7} +(-2.20864 - 1.76689i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})$	\(q+(-1.37859 - 0.315398i) q^{2} +(0.987688 + 0.156434i) q^{3} +(1.80105 + 0.869612i) q^{4} +(2.22681 + 0.203301i) q^{5} +(-1.31228 - 0.527175i) q^{6} +(2.91192 - 2.91192i) q^{7} +(-2.20864 - 1.76689i) q^{8} +(0.951057 + 0.309017i) q^{9} +(-3.00574 - 0.982600i) q^{10} +(-2.79799 + 0.909123i) q^{11} +(1.64284 + 1.14065i) q^{12} +(-0.922241 - 1.81000i) q^{13} +(-4.93278 + 3.09595i) q^{14} +(2.16759 + 0.549147i) q^{15} +(2.48755 + 3.13243i) q^{16} +(0.653515 + 4.12613i) q^{17} +(-1.21366 - 0.725971i) q^{18} +(-2.04108 - 1.48293i) q^{19} +(3.83379 + 2.30261i) q^{20} +(3.33160 - 2.42055i) q^{21} +(4.14404 - 0.370831i) q^{22} +(0.577981 - 1.13435i) q^{23} +(-1.90505 - 2.09064i) q^{24} +(4.91734 + 0.905424i) q^{25} +(0.700527 + 2.78613i) q^{26} +(0.891007 + 0.453990i) q^{27} +(7.77676 - 2.71227i) q^{28} +(-4.10725 - 5.65314i) q^{29} +(-2.81503 - 1.44070i) q^{30} +(-4.56619 + 6.28482i) q^{31} +(-2.44136 - 5.10292i) q^{32} +(-2.90576 + 0.460228i) q^{33} +(0.400441 - 5.89438i) q^{34} +(7.07629 - 5.89230i) q^{35} +(1.44417 + 1.38360i) q^{36} +(9.09435 - 4.63380i) q^{37} +(2.34611 + 2.68812i) q^{38} +(-0.627740 - 1.93199i) q^{39} +(-4.55901 - 4.38354i) q^{40} +(-1.48215 + 4.56160i) q^{41} +(-5.35636 + 2.28618i) q^{42} +(4.56222 + 4.56222i) q^{43} +(-5.82991 - 0.795794i) q^{44} +(2.05500 + 0.881472i) q^{45} +(-1.15457 + 1.38152i) q^{46} +(-0.753158 + 4.75525i) q^{47} +(1.96690 + 3.48300i) q^{48} -9.95861i q^{49} +(-6.49345 - 2.79913i) q^{50} +4.17756i q^{51} +(-0.0870029 - 4.06189i) q^{52} +(0.396929 - 2.50611i) q^{53} +(-1.08515 - 0.906891i) q^{54} +(-6.41542 + 1.45561i) q^{55} +(-11.5764 + 1.28635i) q^{56} +(-1.78397 - 1.78397i) q^{57} +(3.87924 + 9.08881i) q^{58} +(-1.41128 + 4.34348i) q^{59} +(3.42639 + 2.87400i) q^{60} +(3.01297 + 9.27297i) q^{61} +(8.27714 - 7.22405i) q^{62} +(3.66924 - 1.86957i) q^{63} +(1.75620 + 7.80485i) q^{64} +(-1.68568 - 4.21801i) q^{65} +(4.15103 + 0.282004i) q^{66} +(-14.9494 + 2.36776i) q^{67} +(-2.41112 + 7.99966i) q^{68} +(0.748317 - 1.02997i) q^{69} +(-11.6138 + 5.89124i) q^{70} +(3.33031 + 4.58377i) q^{71} +(-1.55454 - 2.36292i) q^{72} +(-7.97187 - 4.06187i) q^{73} +(-13.9989 + 3.51980i) q^{74} +(4.71516 + 1.66352i) q^{75} +(-2.38651 - 4.44578i) q^{76} +(-5.50025 + 10.7948i) q^{77} +(0.256055 + 2.86141i) q^{78} +(-7.70950 + 5.60128i) q^{79} +(4.90247 + 7.48103i) q^{80} +(0.809017 + 0.587785i) q^{81} +(3.48201 - 5.82113i) q^{82} +(-2.36463 - 14.9297i) q^{83} +(8.10531 - 1.46233i) q^{84} +(0.616405 + 9.32095i) q^{85} +(-4.85054 - 7.72837i) q^{86} +(-3.17233 - 6.22606i) q^{87} +(7.78609 + 2.93582i) q^{88} +(3.68014 - 1.19575i) q^{89} +(-2.55499 - 1.86333i) q^{90} +(-7.95608 - 2.58509i) q^{91} +(2.02742 - 1.54040i) q^{92} +(-5.49313 + 5.49313i) q^{93} +(2.53810 - 6.31802i) q^{94} +(-4.24361 - 3.71716i) q^{95} +(-1.61303 - 5.42200i) q^{96} +(-17.8238 - 2.82302i) q^{97} +(-3.14092 + 13.7289i) q^{98} -2.94198 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240q + 12q^{8} + O(q^{10}) $	$ 240q + 12q^{8} + 8q^{10} + 8q^{12} + 4q^{13} + 20q^{17} - 20q^{20} - 12q^{22} + 20q^{25} + 4q^{28} - 8q^{30} - 20q^{32} - 8q^{33} - 4q^{37} - 76q^{38} - 92q^{40} - 20q^{42} - 140q^{44} - 4q^{45} - 16q^{48} - 164q^{50} - 172q^{52} - 4q^{53} - 120q^{58} + 20q^{60} - 44q^{62} - 60q^{64} - 20q^{65} + 16q^{68} - 44q^{70} + 12q^{72} - 44q^{73} - 48q^{77} + 24q^{78} - 4q^{80} + 60q^{81} + 24q^{82} + 80q^{84} - 64q^{85} + 60q^{88} - 260q^{89} + 48q^{90} + 144q^{92} - 64q^{93} + 40q^{94} - 20q^{96} - 180q^{97} + 256q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{20}\right)$

Coefficient data

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

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

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

$2$	−1.37859	−	0.315398i	−0.974814	−	0.223020i
$2$	−1.37859	−	0.315398i	−0.974814	−	0.223020i
$3$	0.987688	+	0.156434i	0.570242	+	0.0903175i
$3$	0.987688	+	0.156434i	0.570242	+	0.0903175i
$4$	1.80105	+	0.869612i	0.900524	+	0.434806i
$5$	2.22681	+	0.203301i	0.995858	+	0.0909190i
$5$	2.22681	+	0.203301i	0.995858	+	0.0909190i
$6$	−1.31228	−	0.527175i	−0.535737	−	0.215218i
$7$	2.91192	−	2.91192i	1.10060	−	1.10060i	0.106266	−	0.994338i	$-0.466110\pi$
$7$	2.91192	−	2.91192i	1.10060	−	1.10060i	0.994338	−	0.106266i	$-0.0338896\pi$
$8$	−2.20864	−	1.76689i	−0.780873	−	0.624690i
$9$	0.951057	+	0.309017i	0.317019	+	0.103006i
$10$	−3.00574	−	0.982600i	−0.950500	−	0.310725i
$11$	−2.79799	+	0.909123i	−0.843627	+	0.274111i	−0.698774	−	0.715342i	$-0.746271\pi$
$11$	−2.79799	+	0.909123i	−0.843627	+	0.274111i	−0.144853	+	0.989453i	$0.546271\pi$
$12$	1.64284	+	1.14065i	0.474246	+	0.329278i
$13$	−0.922241	−	1.81000i	−0.255784	−	0.502004i	0.727030	−	0.686606i	$-0.240900\pi$
$13$	−0.922241	−	1.81000i	−0.255784	−	0.502004i	−0.982813	+	0.184602i	$0.940900\pi$
$14$	−4.93278	+	3.09595i	−1.31834	+	0.827427i
$15$	2.16759	+	0.549147i	0.559669	+	0.141789i
$16$	2.48755	+	3.13243i	0.621887	+	0.783107i
$17$	0.653515	+	4.12613i	0.158501	+	1.00073i	0.930814	+	0.365492i	$0.119099\pi$
$17$	0.653515	+	4.12613i	0.158501	+	1.00073i	−0.772314	+	0.635241i	$0.780901\pi$
$18$	−1.21366	−	0.725971i	−0.286062	−	0.171113i
$19$	−2.04108	−	1.48293i	−0.468256	−	0.340208i	0.328505	−	0.944502i	$-0.393455\pi$
$19$	−2.04108	−	1.48293i	−0.468256	−	0.340208i	−0.796761	+	0.604294i	$0.793455\pi$
$20$	3.83379	+	2.30261i	0.857262	+	0.514880i
$21$	3.33160	−	2.42055i	0.727015	−	0.528207i
$22$	4.14404	−	0.370831i	0.883511	−	0.0790615i
$23$	0.577981	−	1.13435i	0.120517	−	0.236529i	−0.822864	−	0.568238i	$-0.807625\pi$
$23$	0.577981	−	1.13435i	0.120517	−	0.236529i	0.943382	+	0.331709i	$0.107625\pi$
$24$	−1.90505	−	2.09064i	−0.388866	−	0.426751i
$25$	4.91734	+	0.905424i	0.983467	+	0.181085i
$26$	0.700527	+	2.78613i	0.137385	+	0.546405i
$27$	0.891007	+	0.453990i	0.171474	+	0.0873705i
$28$	7.77676	−	2.71227i	1.46967	−	0.512571i
$29$	−4.10725	−	5.65314i	−0.762697	−	1.04976i	−0.996985	−	0.0775947i	$-0.975276\pi$
$29$	−4.10725	−	5.65314i	−0.762697	−	1.04976i	0.234288	−	0.972167i	$-0.424724\pi$
$30$	−2.81503	−	1.44070i	−0.513951	−	0.263035i
$31$	−4.56619	+	6.28482i	−0.820111	+	1.12879i	0.169572	+	0.985518i	$0.445761\pi$
$31$	−4.56619	+	6.28482i	−0.820111	+	1.12879i	−0.989684	+	0.143269i	$0.954239\pi$
$32$	−2.44136	−	5.10292i	−0.431576	−	0.902077i
$33$	−2.90576	+	0.460228i	−0.505829	+	0.0801154i
$34$	0.400441	−	5.89438i	0.0686750	−	1.01088i
$35$	7.07629	−	5.89230i	1.19611	−	0.995980i
$36$	1.44417	+	1.38360i	0.240696	+	0.230601i
$37$	9.09435	−	4.63380i	1.49510	−	0.761792i	0.500517	−	0.865726i	$-0.333143\pi$
$37$	9.09435	−	4.63380i	1.49510	−	0.761792i	0.994584	+	0.103934i	$0.0331431\pi$
$38$	2.34611	+	2.68812i	0.380590	+	0.436070i
$39$	−0.627740	−	1.93199i	−0.100519	−	0.309365i
$40$	−4.55901	−	4.38354i	−0.720843	−	0.693099i
$41$	−1.48215	+	4.56160i	−0.231474	+	0.712402i	0.766096	+	0.642726i	$0.222197\pi$
$41$	−1.48215	+	4.56160i	−0.231474	+	0.712402i	−0.997570	+	0.0696763i	$0.977803\pi$
$42$	−5.35636	+	2.28618i	−0.826505	+	0.352765i
$43$	4.56222	+	4.56222i	0.695733	+	0.695733i	0.963487	−	0.267755i	$-0.0862817\pi$
$43$	4.56222	+	4.56222i	0.695733	+	0.695733i	−0.267755	+	0.963487i	$0.586282\pi$
$44$	−5.82991	−	0.795794i	−0.878892	−	0.119970i
$45$	2.05500	+	0.881472i	0.306341	+	0.131402i
$46$	−1.15457	+	1.38152i	−0.170233	+	0.203694i
$47$	−0.753158	+	4.75525i	−0.109859	+	0.693625i	0.869867	+	0.493286i	$0.164204\pi$
$47$	−0.753158	+	4.75525i	−0.109859	+	0.693625i	−0.979727	+	0.200339i	$0.935796\pi$
$48$	1.96690	+	3.48300i	0.283898	+	0.502728i
$49$		−	9.95861i		−	1.42266i
$50$	−6.49345	−	2.79913i	−0.918312	−	0.395857i
$51$			4.17756i			0.584976i
$52$	−0.0870029	−	4.06189i	−0.0120651	−	0.563283i
$53$	0.396929	−	2.50611i	0.0545224	−	0.344241i	−0.945314	−	0.326161i	$-0.894245\pi$
$53$	0.396929	−	2.50611i	0.0545224	−	0.344241i	0.999837	−	0.0180797i	$-0.00575525\pi$
$54$	−1.08515	−	0.906891i	−0.147670	−	0.123412i
$55$	−6.41542	+	1.45561i	−0.865055	+	0.196274i
$56$	−11.5764	+	1.28635i	−1.54697	+	0.171896i
$57$	−1.78397	−	1.78397i	−0.236293	−	0.236293i
$58$	3.87924	+	9.08881i	0.509369	+	1.19342i
$59$	−1.41128	+	4.34348i	−0.183733	+	0.565473i	−0.999924	−	0.0123093i	$-0.996082\pi$
$59$	−1.41128	+	4.34348i	−0.183733	+	0.565473i	0.816191	+	0.577782i	$0.196082\pi$
$60$	3.42639	+	2.87400i	0.442344	+	0.371032i
$61$	3.01297	+	9.27297i	0.385771	+	1.18728i	0.935919	+	0.352215i	$0.114571\pi$
$61$	3.01297	+	9.27297i	0.385771	+	1.18728i	−0.550148	+	0.835067i	$0.685429\pi$
$62$	8.27714	−	7.22405i	1.05120	−	0.917456i
$63$	3.66924	−	1.86957i	0.462281	−	0.235544i
$64$	1.75620	+	7.80485i	0.219525	+	0.975607i
$65$	−1.68568	−	4.21801i	−0.209083	−	0.523180i
$66$	4.15103	+	0.282004i	0.510956	+	0.0347123i
$67$	−14.9494	+	2.36776i	−1.82636	+	0.289268i	−0.972788	−	0.231699i	$-0.925572\pi$
$67$	−14.9494	+	2.36776i	−1.82636	+	0.289268i	−0.853577	+	0.520966i	$0.825572\pi$
$68$	−2.41112	+	7.99966i	−0.292391	+	0.970101i
$69$	0.748317	−	1.02997i	0.0900868	−	0.123994i
$70$	−11.6138	+	5.89124i	−1.38811	+	0.704138i
$71$	3.33031	+	4.58377i	0.395235	+	0.543994i	0.959540	−	0.281572i	$-0.0908559\pi$
$71$	3.33031	+	4.58377i	0.395235	+	0.543994i	−0.564305	+	0.825566i	$0.690856\pi$
$72$	−1.55454	−	2.36292i	−0.183205	−	0.278473i
$73$	−7.97187	−	4.06187i	−0.933037	−	0.475406i	−0.0797309	−	0.996816i	$-0.525406\pi$
$73$	−7.97187	−	4.06187i	−0.933037	−	0.475406i	−0.853306	+	0.521410i	$0.825406\pi$
$74$	−13.9989	+	3.51980i	−1.62734	+	0.409168i
$75$	4.71516	+	1.66352i	0.544459	+	0.192086i
$76$	−2.38651	−	4.44578i	−0.273752	−	0.509966i
$77$	−5.50025	+	10.7948i	−0.626812	+	1.23019i
$78$	0.256055	+	2.86141i	0.0289926	+	0.323991i
$79$	−7.70950	+	5.60128i	−0.867387	+	0.630193i	−0.929884	−	0.367852i	$-0.880093\pi$
$79$	−7.70950	+	5.60128i	−0.867387	+	0.630193i	0.0624977	+	0.998045i	$0.480093\pi$
$80$	4.90247	+	7.48103i	0.548113	+	0.836405i
$81$	0.809017	+	0.587785i	0.0898908	+	0.0653095i
$82$	3.48201	−	5.82113i	0.384524	−	0.642836i
$83$	−2.36463	−	14.9297i	−0.259552	−	1.63874i	−0.681281	−	0.732022i	$-0.738577\pi$
$83$	−2.36463	−	14.9297i	−0.259552	−	1.63874i	0.421729	−	0.906722i	$-0.361423\pi$
$84$	8.10531	−	1.46233i	0.884362	−	0.159553i
$85$	0.616405	+	9.32095i	0.0668585	+	1.01100i
$86$	−4.85054	−	7.72837i	−0.523047	−	0.833372i
$87$	−3.17233	−	6.22606i	−0.340110	−	0.667503i
$88$	7.78609	+	2.93582i	0.830000	+	0.312959i
$89$	3.68014	−	1.19575i	0.390095	−	0.126749i	−0.107401	−	0.994216i	$-0.534253\pi$
$89$	3.68014	−	1.19575i	0.390095	−	0.126749i	0.497496	+	0.867466i	$0.334253\pi$
$90$	−2.55499	−	1.86333i	−0.269320	−	0.196413i
$91$	−7.95608	−	2.58509i	−0.834024	−	0.270991i
$92$	2.02742	−	1.54040i	0.211373	−	0.160598i
$93$	−5.49313	+	5.49313i	−0.569611	+	0.569611i
$94$	2.53810	−	6.31802i	0.261785	−	0.651654i
$95$	−4.24361	−	3.71716i	−0.435386	−	0.381373i
$96$	−1.61303	−	5.42200i	−0.164630	−	0.553381i
$97$	−17.8238	−	2.82302i	−1.80973	−	0.286634i	−0.842162	−	0.539225i	$-0.818717\pi$
$97$	−17.8238	−	2.82302i	−1.80973	−	0.286634i	−0.967573	+	0.252591i	$0.918717\pi$
$98$	−3.14092	+	13.7289i	−0.317281	+	1.38683i
$99$	−2.94198			−0.295681
$100$	8.06899	+	5.90689i	0.806899	+	0.590689i
$101$	−1.75718			−0.174846			−0.0874230	−	0.996171i	$-0.527863\pi$
$101$	−1.75718			−0.174846			−0.0874230	+	0.996171i	$0.527863\pi$
$102$	1.31759	−	5.75916i	0.130461	−	0.570242i
$103$	6.32547	+	1.00186i	0.623267	+	0.0987158i	0.460077	−	0.887879i	$-0.347822\pi$
$103$	6.32547	+	1.00186i	0.623267	+	0.0987158i	0.163190	+	0.986595i	$0.447822\pi$
$104$	−1.16117	+	5.62714i	−0.113862	+	0.551787i
$105$	7.91093	−	4.71278i	0.772027	−	0.459920i
$106$	−1.33763	+	3.32972i	−0.129922	+	0.323411i
$107$	8.34389	−	8.34389i	0.806634	−	0.806634i	−0.177489	−	0.984123i	$-0.556797\pi$
$107$	8.34389	−	8.34389i	0.806634	−	0.806634i	0.984123	+	0.177489i	$0.0567973\pi$
$108$	1.20995	+	1.59249i	0.116428	+	0.153237i
$109$	−10.2590	−	3.33335i	−0.982635	−	0.319277i	−0.226729	−	0.973958i	$-0.572803\pi$
$109$	−10.2590	−	3.33335i	−0.982635	−	0.319277i	−0.755906	+	0.654680i	$0.772803\pi$
$110$	9.30336	+	0.0167168i	0.887040	+	0.00159388i
$111$	9.70727	−	3.15408i	0.921373	−	0.299372i
$112$	16.3649	+	1.87783i	1.54634	+	0.177439i
$113$	5.40831	+	10.6144i	0.508771	+	0.998519i	0.992378	+	0.123233i	$0.0393264\pi$
$113$	5.40831	+	10.6144i	0.508771	+	0.998519i	−0.483607	+	0.875285i	$0.660674\pi$
$114$	1.89671	+	3.02203i	0.177643	+	0.283039i
$115$	1.51767	−	2.40848i	0.141523	−	0.224592i
$116$	−2.48131	−	13.7533i	−0.230384	−	1.27696i
$117$	−0.317783	−	2.00640i	−0.0293790	−	0.185492i
$118$	3.31551	−	5.54278i	0.305218	−	0.510255i
$119$	13.9180	+	10.1120i	1.27586	+	0.926965i
$120$	−3.81714	−	5.04276i	−0.348456	−	0.460339i
$121$	−1.89692	+	1.37819i	−0.172447	+	0.125290i
$122$	−1.22899	−	13.7340i	−0.111268	−	1.24341i
$123$	−2.17750	+	4.27358i	−0.196338	+	0.385336i
$124$	−13.6893	+	7.34845i	−1.22933	+	0.659910i
$125$	10.7659	+	3.01590i	0.962930	+	0.269751i
$126$	−5.64805	+	1.42011i	−0.503169	+	0.126513i
$127$	5.19941	+	2.64923i	0.461373	+	0.235081i	0.669197	−	0.743085i	$-0.266638\pi$
$127$	5.19941	+	2.64923i	0.461373	+	0.235081i	−0.207824	+	0.978166i	$0.566638\pi$
$128$	0.0405449	−	11.3136i	0.00358370	−	0.999994i
$129$	3.79237	+	5.21974i	0.333899	+	0.459573i
$130$	0.993515	+	6.34659i	0.0871370	+	0.556633i
$131$	7.90202	−	10.8762i	0.690403	−	0.950258i	−0.309597	−	0.950868i	$-0.600194\pi$
$131$	7.90202	−	10.8762i	0.690403	−	0.950258i	1.00000		0.000610176i	$0.000194225\pi$
$132$	−5.63364	−	1.69800i	−0.490346	−	0.147791i
$133$	−10.2617	+	1.62529i	−0.889799	+	0.140930i
$134$	21.3560	+	1.45084i	1.84488	+	0.125334i
$135$	1.89180	+	1.19209i	0.162820	+	0.102599i
$136$	5.84703	−	10.2678i	0.501379	−	0.880459i
$137$	−10.7331	+	5.46880i	−0.916994	+	0.467232i	−0.847767	−	0.530369i	$-0.822053\pi$
$137$	−10.7331	+	5.46880i	−0.916994	+	0.467232i	−0.0692269	+	0.997601i	$0.522053\pi$
$138$	−1.35648	+	1.18389i	−0.115471	+	0.100780i
$139$	−2.59947	−	8.00036i	−0.220485	−	0.678582i	−0.998719	−	0.0506073i	$-0.983884\pi$
$139$	−2.59947	−	8.00036i	−0.220485	−	0.678582i	0.778234	−	0.627974i	$-0.216116\pi$
$140$	17.8688	−	4.45868i	1.51019	−	0.376827i
$141$	−1.48777	+	4.57889i	−0.125293	+	0.385612i
$142$	−3.14543	−	7.36954i	−0.263959	−	0.618438i
$143$	4.22594	+	4.22594i	0.353391	+	0.353391i
$144$	1.39783	+	3.74781i	0.116486	+	0.312317i
$145$	−7.99676	−	13.4235i	−0.664095	−	1.11476i
$146$	9.70888	+	8.11399i	0.803512	+	0.671518i
$147$	1.55787	−	9.83600i	0.128491	−	0.811260i
$148$	20.4090	−	0.437146i	1.67761	−	0.0359332i
$149$		−	5.29270i		−	0.433595i	−0.976217	−	0.216797i	$-0.930439\pi$
$149$		−	5.29270i		−	0.433595i	0.976217	−	0.216797i	$-0.0695611\pi$
$150$	−5.97562	−	3.78047i	−0.487908	−	0.308674i
$151$			2.46259i			0.200403i	0.994967	+	0.100202i	$0.0319488\pi$
$151$			2.46259i			0.200403i	−0.994967	+	0.100202i	$0.968051\pi$
$152$	1.88784	+	6.88164i	0.153124	+	0.558174i
$153$	−0.653515	+	4.12613i	−0.0528335	+	0.333578i
$154$	10.9873	−	13.1470i	0.885381	−	1.05941i
$155$	−11.4457	+	13.0668i	−0.919343	+	1.04955i
$156$	0.549488	−	4.02549i	0.0439942	−	0.322297i
$157$	10.9985	+	10.9985i	0.877778	+	0.877778i	0.993304	−	0.115527i	$-0.0368556\pi$
$157$	10.9985	+	10.9985i	0.877778	+	0.877778i	−0.115527	+	0.993304i	$0.536856\pi$
$158$	12.3949	−	5.29034i	0.986086	−	0.420877i
$159$	0.784084	−	2.41316i	0.0621819	−	0.191376i
$160$	−4.39902	−	11.8595i	−0.347773	−	0.937579i
$161$	−1.62011	−	4.98619i	−0.127683	−	0.392967i
$162$	−0.929921	−	1.06548i	−0.0730615	−	0.0837120i
$163$	−3.25666	+	1.65935i	−0.255082	+	0.129971i	−0.576856	−	0.816846i	$-0.695721\pi$
$163$	−3.25666	+	1.65935i	−0.255082	+	0.129971i	0.321775	+	0.946816i	$0.395721\pi$
$164$	−6.63625	+	6.92676i	−0.518204	+	0.540889i
$165$	−6.56414	+	0.434094i	−0.511018	+	0.0337942i
$166$	−1.44892	+	21.3278i	−0.112458	+	1.65536i
$167$	−13.9909	+	2.21594i	−1.08265	+	0.171475i	−0.672171	−	0.740396i	$-0.734638\pi$
$167$	−13.9909	+	2.21594i	−1.08265	+	0.171475i	−0.410478	+	0.911871i	$0.634638\pi$
$168$	−11.6352	−	0.540443i	−0.897672	−	0.0416961i
$169$	5.21564	−	7.17871i	0.401203	−	0.552208i
$170$	2.09004	−	13.0442i	0.160298	−	1.00045i
$171$	−1.48293	−	2.04108i	−0.113403	−	0.156085i
$172$	4.24942	+	12.1841i	0.324015	+	0.929033i
$173$	−21.7320	−	11.0730i	−1.65226	−	0.841866i	−0.996194	−	0.0871591i	$-0.972221\pi$
$173$	−21.7320	−	11.0730i	−1.65226	−	0.841866i	−0.656062	−	0.754707i	$-0.727779\pi$
$174$	2.40968	+	9.58376i	0.182677	+	0.726543i
$175$	16.9554	−	11.6824i	1.28171	−	0.883106i
$176$	−9.80791	−	6.50302i	−0.739299	−	0.490184i
$177$	−2.07338	+	4.06923i	−0.155845	+	0.305862i
$178$	−5.45057	+	0.487747i	−0.408537	+	0.0365582i
$179$	9.28423	−	6.74539i	0.693936	−	0.504174i	−0.184016	−	0.982923i	$-0.558910\pi$
$179$	9.28423	−	6.74539i	0.693936	−	0.504174i	0.877952	+	0.478750i	$0.158910\pi$
$180$	2.93461	+	3.37462i	0.218733	+	0.251530i
$181$	9.77894	+	7.10482i	0.726863	+	0.528097i	0.888570	−	0.458742i	$-0.151700\pi$
$181$	9.77894	+	7.10482i	0.726863	+	0.528097i	−0.161706	+	0.986839i	$0.551700\pi$
$182$	10.1529	+	6.07312i	0.752582	+	0.450170i
$183$	1.52526	+	9.63014i	0.112751	+	0.711880i
$184$	−3.28083	+	1.48415i	−0.241866	+	0.109413i
$185$	21.1934	−	8.46969i	1.55817	−	0.622704i
$186$	9.30533	−	5.84028i	0.682300	−	0.428230i
$187$	−5.57969	−	10.9508i	−0.408027	−	0.800799i
$188$	−5.49170	+	7.90948i	−0.400523	+	0.576858i
$189$	3.91653	−	1.27256i	0.284886	−	0.0925649i
$190$	4.67784	+	6.46288i	0.339366	+	0.468867i
$191$	−1.72388	−	0.560124i	−0.124736	−	0.0405291i	0.245984	−	0.969274i	$-0.420889\pi$
$191$	−1.72388	−	0.560124i	−0.124736	−	0.0405291i	−0.370720	+	0.928745i	$0.620889\pi$
$192$	0.513631	+	7.98349i	0.0370681	+	0.576159i
$193$	11.3881	−	11.3881i	0.819731	−	0.819731i	−0.166338	−	0.986069i	$-0.553194\pi$
$193$	11.3881	−	11.3881i	0.819731	−	0.819731i	0.986069	+	0.166338i	$0.0531941\pi$
$194$	23.6815	+	9.51339i	1.70023	+	0.683022i
$195$	−1.00508	−	4.42978i	−0.0719754	−	0.317223i
$196$	8.66013	−	17.9359i	0.618580	−	1.28114i
$197$	4.46632	+	0.707396i	0.318212	+	0.0503999i	0.313498	−	0.949589i	$-0.398499\pi$
$197$	4.46632	+	0.707396i	0.318212	+	0.0503999i	0.00471472	+	0.999989i	$0.498499\pi$
$198$	4.05581	+	0.927896i	0.288234	+	0.0659427i
$199$	−0.389180			−0.0275883			−0.0137941	−	0.999905i	$-0.504391\pi$
$199$	−0.389180			−0.0275883			−0.0137941	+	0.999905i	$0.504391\pi$
$200$	−9.26085	−	10.6882i	−0.654841	−	0.755766i
$201$	−15.1358			−1.06760
$202$	2.42244	+	0.554211i	0.170442	+	0.0389942i
$203$	−28.4215	−	4.50153i	−1.99480	−	0.315945i
$204$	−3.63286	+	7.52399i	−0.254351	+	0.526785i
$205$	−4.22785	+	9.85648i	−0.295286	+	0.688406i
$206$	−8.40428	−	3.37619i	−0.585554	−	0.235231i
$207$	0.900227	−	0.900227i	0.0625701	−	0.0625701i
$208$	3.37557	−	7.39132i	0.234054	−	0.512496i
$209$	7.05910	+	2.29364i	0.488288	+	0.158655i
$210$	−12.3924	+	4.00192i	−0.855154	+	0.276159i
$211$	−10.6305	+	3.45406i	−0.731833	+	0.237787i	−0.651146	−	0.758952i	$-0.725712\pi$
$211$	−10.6305	+	3.45406i	−0.731833	+	0.237787i	−0.0806873	+	0.996739i	$0.525712\pi$
$212$	2.89423	−	4.16845i	0.198777	−	0.286291i
$213$	2.57224	+	5.04831i	0.176247	+	0.345905i
$214$	−14.1345	+	8.87120i	−0.966214	+	0.606423i
$215$	9.23169	+	11.0867i	0.629596	+	0.756106i
$216$	−1.16576	−	2.57701i	−0.0793202	−	0.175344i
$217$	5.00452	+	31.5973i	0.339729	+	2.14497i
$218$	13.0917	+	7.83102i	0.886681	+	0.530383i
$219$	−7.23831	−	5.25894i	−0.489120	−	0.355366i
$220$	−12.8203	−	2.95731i	−0.864344	−	0.199382i
$221$	6.86560	−	4.98815i	0.461830	−	0.335539i
$222$	−14.3772	+	1.28655i	−0.964933	+	0.0863476i
$223$	0.846437	−	1.66123i	0.0566816	−	0.111244i	−0.860928	−	0.508727i	$-0.830116\pi$
$223$	0.846437	−	1.66123i	0.0566816	−	0.111244i	0.917610	+	0.397483i	$0.130116\pi$
$224$	−21.9684	−	7.75024i	−1.46782	−	0.517835i
$225$	4.39687	+	2.38065i	0.293125	+	0.158710i
$226$	−4.10810	−	16.3387i	−0.273267	−	1.08684i
$227$	5.62529	+	2.86623i	0.373364	+	0.190238i	0.630596	−	0.776111i	$-0.282811\pi$
$227$	5.62529	+	2.86623i	0.373364	+	0.190238i	−0.257232	+	0.966350i	$0.582811\pi$
$228$	−1.66166	−	4.76438i	−0.110046	−	0.315529i
$229$	−3.59408	−	4.94683i	−0.237503	−	0.326895i	0.673582	−	0.739112i	$-0.264755\pi$
$229$	−3.59408	−	4.94683i	−0.237503	−	0.326895i	−0.911086	+	0.412217i	$0.864755\pi$
$230$	−2.85188	+	2.84165i	−0.188047	+	0.187373i
$231$	−7.12122	+	9.80151i	−0.468542	+	0.644892i
$232$	−0.917037	+	19.7428i	−0.0602064	+	1.29618i
$233$	−3.82896	+	0.606447i	−0.250843	+	0.0397297i	−0.280590	−	0.959828i	$-0.590530\pi$
$233$	−3.82896	+	0.606447i	−0.250843	+	0.0397297i	0.0297465	+	0.999557i	$0.490530\pi$
$234$	−0.194721	+	2.86624i	−0.0127293	+	0.187372i
$235$	−2.64388	+	10.4359i	−0.172468	+	0.680764i
$236$	−6.31893	+	6.59555i	−0.411327	+	0.429334i
$237$	−8.49082	+	4.32629i	−0.551538	+	0.281023i
$238$	−15.9979	−	18.3300i	−1.03699	−	1.18816i
$239$	6.49825	+	19.9996i	0.420337	+	1.29366i	0.907389	+	0.420291i	$0.138072\pi$
$239$	6.49825	+	19.9996i	0.420337	+	1.29366i	−0.487052	+	0.873373i	$0.661928\pi$
$240$	3.67182	+	8.15584i	0.237015	+	0.526457i
$241$	−5.27854	+	16.2457i	−0.340021	+	1.04648i	0.624175	+	0.781285i	$0.285435\pi$
$241$	−5.27854	+	16.2457i	−0.340021	+	1.04648i	−0.964196	+	0.265192i	$0.914565\pi$
$242$	3.04977	−	1.30169i	0.196046	−	0.0836756i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−2.63738	+	19.3212i	−0.168841	+	1.23691i
$245$	2.02459	−	22.1759i	0.129347	−	1.41677i
$246$	4.34977	−	5.20476i	0.277331	−	0.331843i
$247$	−0.801739	+	5.06198i	−0.0510134	+	0.322086i
$248$	21.1897	−	5.81296i	1.34554	−	0.369124i
$249$		−	15.1158i		−	0.957923i
$250$	−13.8906	−	7.55325i	−0.878518	−	0.477709i
$251$		−	7.43789i		−	0.469475i	−0.972059	−	0.234738i	$-0.924577\pi$
$251$		−	7.43789i		−	0.469475i	0.972059	−	0.234738i	$-0.0754231\pi$
$252$	8.23428	−	0.176373i	0.518711	−	0.0111104i
$253$	−0.585922	+	3.69937i	−0.0368366	+	0.232577i
$254$	−6.33232	−	5.29210i	−0.397325	−	0.332056i
$255$	−0.849302	+	9.30262i	−0.0531854	+	0.582553i
$256$	−3.62419	+	15.5841i	−0.226512	+	0.974008i
$257$	−15.5114	−	15.5114i	−0.967577	−	0.967577i	0.0319134	−	0.999491i	$-0.489840\pi$
$257$	−15.5114	−	15.5114i	−0.967577	−	0.967577i	−0.999491	+	0.0319134i	$0.989840\pi$
$258$	−3.58184	−	8.39202i	−0.222996	−	0.522464i
$259$	12.9888	−	39.9753i	0.807083	−	2.48395i
$260$	0.632048	−	9.06273i	0.0391979	−	0.562047i
$261$	−2.15931	−	6.64567i	−0.133658	−	0.411356i
$262$	−14.3240	+	12.5016i	−0.884940	+	0.772351i
$263$	3.45964	−	1.76277i	0.213330	−	0.108697i	−0.344061	−	0.938947i	$-0.611803\pi$
$263$	3.45964	−	1.76277i	0.213330	−	0.108697i	0.557391	+	0.830250i	$0.311803\pi$
$264$	7.23097	+	4.11769i	0.445035	+	0.253426i
$265$	1.39338	−	5.49993i	0.0855946	−	0.337858i
$266$	14.6593	+	0.995894i	0.898819	+	0.0610622i
$267$	3.82189	−	0.605328i	0.233896	−	0.0370455i
$268$	−28.9837	−	8.73577i	−1.77046	−	0.533622i
$269$	−12.4449	+	17.1289i	−0.758778	+	1.04437i	0.238537	+	0.971133i	$0.423332\pi$
$269$	−12.4449	+	17.1289i	−0.758778	+	1.04437i	−0.997315	+	0.0732344i	$0.976668\pi$
$270$	−2.23205	−	2.24008i	−0.135838	−	0.136327i
$271$	9.84582	+	13.5516i	0.598091	+	0.823202i	0.995532	−	0.0944262i	$-0.0301016\pi$
$271$	9.84582	+	13.5516i	0.598091	+	0.823202i	−0.397441	+	0.917628i	$0.630102\pi$
$272$	−11.2991	+	12.3110i	−0.685111	+	0.746466i
$273$	−7.45373	−	3.79787i	−0.451120	−	0.229857i
$274$	16.5215	−	4.15406i	0.998100	−	0.250956i
$275$	−14.5818	+	1.93710i	−0.879317	+	0.116811i
$276$	2.24343	−	1.20428i	0.135039	−	0.0724892i
$277$	4.43885	−	8.71174i	0.266705	−	0.523438i	−0.718349	−	0.695683i	$-0.755102\pi$
$277$	4.43885	−	8.71174i	0.266705	−	0.523438i	0.985054	+	0.172245i	$0.0551021\pi$
$278$	1.06033	+	11.8491i	0.0635941	+	0.710663i
$279$	−6.28482	+	4.56619i	−0.376262	+	0.273370i
$280$	−26.0400	+	0.510950i	−1.55619	+	0.0305351i
$281$	21.0726	+	15.3101i	1.25708	+	0.913325i	0.998611	−	0.0526937i	$-0.0167807\pi$
$281$	21.0726	+	15.3101i	1.25708	+	0.913325i	0.258473	+	0.966018i	$0.416781\pi$
$282$	3.49520	−	5.84319i	0.208136	−	0.347957i
$283$	2.50556	+	15.8195i	0.148940	+	0.940369i	0.943063	+	0.332613i	$0.107930\pi$
$283$	2.50556	+	15.8195i	0.148940	+	0.940369i	−0.794124	+	0.607756i	$0.792070\pi$
$284$	2.01194	+	11.1517i	0.119387	+	0.661730i
$285$	−3.60988	−	4.33524i	−0.213831	−	0.256798i
$286$	−4.49301	−	7.15871i	−0.265677	−	0.423303i
$287$	8.96712	+	17.5990i	0.529312	+	1.03883i
$288$	−0.744986	−	5.60758i	−0.0438987	−	0.330430i
$289$	−0.429893	+	0.139681i	−0.0252878	+	0.00821651i
$290$	6.79056	+	21.0277i	0.398755	+	1.23479i
$291$	−17.1628	−	5.57652i	−1.00610	−	0.326901i
$292$	−10.8255	−	14.2481i	−0.633513	−	0.833805i
$293$	14.9114	−	14.9114i	0.871133	−	0.871133i	−0.121463	−	0.992596i	$-0.538759\pi$
$293$	14.9114	−	14.9114i	0.871133	−	0.871133i	0.992596	+	0.121463i	$0.0387587\pi$
$294$	−5.24993	+	13.0685i	−0.306182	+	0.762171i
$295$	−4.02569	+	9.38518i	−0.234385	+	0.546426i
$296$	−28.2736	−	5.83430i	−1.64337	−	0.339112i
$297$	−2.90576	−	0.460228i	−0.168610	−	0.0267051i
$298$	−1.66931	+	7.29649i	−0.0967003	+	0.422674i
$299$	−2.58622			−0.149565
$300$	7.04561	+	7.09643i	0.406779	+	0.409713i
$301$	26.5697			1.53145
$302$	0.776697	−	3.39492i	0.0446939	−	0.195356i
$303$	−1.73555	−	0.274884i	−0.0997046	−	0.0157917i
$304$	−0.432115	−	10.0824i	−0.0247835	−	0.578266i
$305$	4.82410	+	21.2617i	0.276227	+	1.21744i
$306$	2.20230	−	5.48214i	0.125897	−	0.313393i
$307$	7.01043	−	7.01043i	0.400106	−	0.400106i	−0.478164	−	0.878270i	$-0.658698\pi$
$307$	7.01043	−	7.01043i	0.400106	−	0.400106i	0.878270	+	0.478164i	$0.158698\pi$
$308$	−19.2935	+	14.6590i	−1.09935	+	0.835272i
$309$	6.09087	+	1.97904i	0.346497	+	0.112584i
$310$	19.9003	−	14.4038i	1.13026	−	0.818082i
$311$	28.3183	−	9.20117i	1.60578	−	0.521751i	0.637255	−	0.770653i	$-0.280070\pi$
$311$	28.3183	−	9.20117i	1.60578	−	0.521751i	0.968529	+	0.248902i	$0.0800698\pi$
$312$	−2.02715	+	5.37622i	−0.114765	+	0.304368i
$313$	−6.28630	−	12.3376i	−0.355323	−	0.697360i	0.642287	−	0.766465i	$-0.277986\pi$
$313$	−6.28630	−	12.3376i	−0.355323	−	0.697360i	−0.997609	+	0.0691042i	$0.977986\pi$
$314$	−11.6936	−	18.6314i	−0.659908	−	1.05143i
$315$	8.55077	−	3.41721i	0.481781	−	0.192538i
$316$	−18.7561	+	3.38390i	−1.05511	+	0.190359i
$317$	−4.59264	−	28.9968i	−0.257949	−	1.62862i	−0.687924	−	0.725783i	$-0.741478\pi$
$317$	−4.59264	−	28.9968i	−0.257949	−	1.62862i	0.429975	−	0.902841i	$-0.358522\pi$
$318$	−1.84204	+	3.07948i	−0.103297	+	0.172688i
$319$	16.6315	+	12.0835i	0.931183	+	0.676544i
$320$	2.32399	+	17.7369i	0.129915	+	0.991525i
$321$	9.54643	−	6.93589i	0.532830	−	0.387124i
$322$	0.660843	+	7.38491i	0.0368273	+	0.411545i
$323$	4.78490	−	9.39089i	0.266239	−	0.522523i
$324$	0.945934	+	1.76216i	0.0525519	+	0.0978978i
$325$	−2.89615	−	9.73540i	−0.160650	−	0.540023i
$326$	5.01298	−	1.26043i	0.277643	−	0.0698088i
$327$	−9.61125	−	4.89718i	−0.531504	−	0.270815i
$328$	11.3334	−	7.45614i	0.625782	−	0.411697i
$329$	11.6538	+	16.0401i	0.642495	+	0.884318i
$330$	9.18620	+	1.47188i	0.505684	+	0.0810242i
$331$	4.96767	−	6.83741i	0.273048	−	0.375818i	−0.650368	−	0.759619i	$-0.725385\pi$
$331$	4.96767	−	6.83741i	0.273048	−	0.375818i	0.923416	+	0.383801i	$0.125385\pi$
$332$	8.72421	−	28.9454i	0.478803	−	1.58858i
$333$	10.0812	−	1.59670i	0.552444	−	0.0874986i
$334$	19.9867	+	1.35782i	1.09362	+	0.0742964i
$335$	−33.7709	+	2.23331i	−1.84510	+	0.122019i
$336$	15.8697	+	4.41476i	0.865764	+	0.240845i
$337$	27.5810	−	14.0532i	1.50243	−	0.765527i	0.507085	−	0.861896i	$-0.330723\pi$
$337$	27.5810	−	14.0532i	1.50243	−	0.765527i	0.995346	+	0.0963694i	$0.0307230\pi$
$338$	−9.45440	+	8.25153i	−0.514252	+	0.448824i
$339$	3.68126	+	11.3298i	0.199939	+	0.615348i
$340$	−6.99544	+	17.3235i	−0.379381	+	0.939500i
$341$	7.06249	−	21.7361i	0.382455	−	1.17708i
$342$	1.40061	+	3.28154i	0.0757364	+	0.177445i
$343$	−8.61524	−	8.61524i	−0.465179	−	0.465179i
$344$	−2.01537	−	18.1373i	−0.108662	−	0.977896i
$345$	1.87575	−	2.14141i	0.100987	−	0.115290i
$346$	26.4673	+	22.1195i	1.42289	+	1.18915i
$347$	−4.63833	+	29.2853i	−0.248999	+	1.57212i	0.473532	+	0.880777i	$0.342979\pi$
$347$	−4.63833	+	29.2853i	−0.248999	+	1.57212i	−0.722530	+	0.691339i	$0.757021\pi$
$348$	−0.299273	−	13.9721i	−0.0160427	−	0.748985i
$349$		−	20.0990i		−	1.07587i	−0.842985	−	0.537937i	$-0.819204\pi$
$349$		−	20.0990i		−	1.07587i	0.842985	−	0.537937i	$-0.180796\pi$
$350$	−27.0593	+	10.7576i	−1.44638	+	0.575016i
$351$		−	2.03141i		−	0.108429i
$352$	11.4701	+	12.0584i	0.611358	+	0.642716i
$353$	−2.20264	+	13.9069i	−0.117235	+	0.740190i	0.857111	+	0.515132i	$0.172257\pi$
$353$	−2.20264	+	13.9069i	−0.117235	+	0.740190i	−0.974345	+	0.225058i	$0.927743\pi$
$354$	4.14177	−	4.95588i	0.220133	−	0.263402i
$355$	6.48406	+	10.8842i	0.344138	+	0.577675i
$356$	7.66796	+	1.04669i	0.406401	+	0.0554746i
$357$	12.1647	+	12.1647i	0.643826	+	0.643826i
$358$	−14.9267	+	6.37093i	−0.788899	+	0.336714i
$359$	5.68610	−	17.5000i	0.300101	−	0.923616i	−0.681359	−	0.731949i	$-0.738611\pi$
$359$	5.68610	−	17.5000i	0.300101	−	0.923616i	0.981460	−	0.191667i	$-0.0613893\pi$
$360$	−2.98129	−	5.57781i	−0.157128	−	0.293976i
$361$	−3.90440	−	12.0165i	−0.205495	−	0.632447i
$362$	−11.2404	−	12.8789i	−0.590780	−	0.676901i
$363$	−2.08916	+	1.06448i	−0.109653	+	0.0558708i
$364$	−12.0813	−	11.5746i	−0.633230	−	0.606672i
$365$	−16.9260	−	10.6657i	−0.885949	−	0.558268i
$366$	0.934604	−	13.7571i	0.0488526	−	0.719096i
$367$	−0.168050	+	0.0266165i	−0.00877212	+	0.00138937i	−0.160819	−	0.986984i	$-0.551414\pi$
$367$	−0.168050	+	0.0266165i	−0.00877212	+	0.00138937i	0.152047	+	0.988373i	$0.451414\pi$
$368$	4.99103	−	1.01127i	0.260176	−	0.0527163i
$369$	−2.81922	+	3.88033i	−0.146763	+	0.202002i
$370$	−31.8885	+	4.99192i	−1.65780	+	0.259517i
$371$	−6.14178	−	8.45344i	−0.318865	−	0.438880i
$372$	−14.6703	+	5.11650i	−0.760619	+	0.265278i
$373$	0.278937	+	0.142126i	0.0144428	+	0.00735898i	0.461197	−	0.887298i	$-0.347420\pi$
$373$	0.278937	+	0.142126i	0.0144428	+	0.00735898i	−0.446754	+	0.894657i	$0.647420\pi$
$374$	4.23829	+	16.8565i	0.219157	+	0.871628i
$375$	10.1615	+	4.66293i	0.524740	+	0.240793i
$376$	10.0655	−	9.17190i	0.519087	−	0.473005i
$377$	−6.44431	+	12.6477i	−0.331899	+	0.651389i
$378$	−5.80067	+	0.519076i	−0.298354	+	0.0266984i
$379$	5.42966	−	3.94488i	0.278903	−	0.202635i	−0.439536	−	0.898225i	$-0.644857\pi$
$379$	5.42966	−	3.94488i	0.278903	−	0.202635i	0.718439	+	0.695590i	$0.244857\pi$
$380$	−4.41047	−	10.3851i	−0.226252	−	0.532743i
$381$	4.72097	+	3.42998i	0.241863	+	0.175723i
$382$	2.19987	+	1.31589i	0.112555	+	0.0673269i
$383$	−4.11650	−	25.9905i	−0.210343	−	1.32805i	−0.836333	−	0.548222i	$-0.815305\pi$
$383$	−4.11650	−	25.9905i	−0.210343	−	1.32805i	0.625989	−	0.779832i	$-0.284695\pi$
$384$	1.80989	−	11.1680i	0.0923605	−	0.569915i
$385$	−14.4426	+	22.9198i	−0.736063	+	1.16810i
$386$	−19.2913	+	12.1078i	−0.981902	+	0.616269i
$387$	2.92913	+	5.74874i	0.148896	+	0.292225i
$388$	−29.6466	−	20.5842i	−1.50508	−	1.04500i
$389$	3.28723	−	1.06809i	0.166669	−	0.0541541i	−0.224494	−	0.974476i	$-0.572073\pi$
$389$	3.28723	−	1.06809i	0.166669	−	0.0541541i	0.391163	+	0.920321i	$0.372073\pi$
$390$	−0.0115428	+	6.42387i	−0.000584490	+	0.325286i
$391$	5.05820	+	1.64351i	0.255804	+	0.0831159i
$392$	−17.5958	+	21.9950i	−0.888720	+	1.11092i
$393$	9.50614	−	9.50614i	0.479522	−	0.479522i
$394$	−5.93414	−	2.38388i	−0.298958	−	0.120098i
$395$	−18.3063	+	10.9056i	−0.921091	+	0.548721i
$396$	−5.29866	−	2.55839i	−0.266268	−	0.128564i
$397$	−7.27135	−	1.15167i	−0.364938	−	0.0578006i	−0.0287275	−	0.999587i	$-0.509146\pi$
$397$	−7.27135	−	1.15167i	−0.364938	−	0.0578006i	−0.336211	+	0.941787i	$0.609146\pi$
$398$	0.536522	+	0.122747i	0.0268934	+	0.00615273i
$399$	−10.3896			−0.520130
$400$	9.39595	+	17.6555i	0.469797	+	0.882774i
$401$	5.47950			0.273633			0.136817	−	0.990596i	$-0.456313\pi$
$401$	5.47950			0.273633			0.136817	+	0.990596i	$0.456313\pi$
$402$	20.8661	+	4.77380i	1.04071	+	0.238095i
$403$	15.5866	+	2.46868i	0.776426	+	0.122974i
$404$	−3.16477	−	1.52807i	−0.157453	−	0.0760241i
$405$	1.68203	+	1.47336i	0.0835806	+	0.0732118i
$406$	37.7620	+	15.1699i	1.87410	+	0.752868i
$407$	−21.2332	+	21.2332i	−1.05249	+	1.05249i
$408$	7.38129	−	9.22674i	0.365428	−	0.456792i
$409$	2.38942	+	0.776370i	0.118149	+	0.0383890i	0.367495	−	0.930026i	$-0.380216\pi$
$409$	2.38942	+	0.776370i	0.118149	+	0.0383890i	−0.249346	+	0.968415i	$0.580216\pi$
$410$	8.93720	−	12.2546i	0.441377	−	0.605214i
$411$	−11.4565	+	3.72244i	−0.565108	+	0.183615i
$412$	10.5212	+	7.30510i	0.518345	+	0.359896i
$413$	8.53834	+	16.7574i	0.420144	+	0.824579i
$414$	−1.52498	+	0.957119i	−0.0749486	+	0.0470398i
$415$	−2.23035	−	33.7262i	−0.109484	−	1.65556i
$416$	−6.98475	+	9.12499i	−0.342456	+	0.447389i
$417$	−1.31594	−	8.30851i	−0.0644418	−	0.406869i
$418$	−9.00824	−	5.38843i	−0.440607	−	0.263557i
$419$	−1.06381	−	0.772904i	−0.0519706	−	0.0377589i	0.561497	−	0.827479i	$-0.310226\pi$
$419$	−1.06381	−	0.772904i	−0.0519706	−	0.0377589i	−0.613467	+	0.789720i	$0.710226\pi$
$420$	18.3463	−	1.60850i	0.895205	−	0.0784868i
$421$	−25.4702	+	18.5052i	−1.24134	+	0.901887i	−0.997687	−	0.0679755i	$-0.978346\pi$
$421$	−25.4702	+	18.5052i	−1.24134	+	0.901887i	−0.243654	+	0.969862i	$0.578346\pi$
$422$	15.7445	−	1.40891i	0.766433	−	0.0685846i
$423$	−2.18575	+	4.28978i	−0.106275	+	0.208576i
$424$	−5.30470	+	4.83377i	−0.257619	+	0.234749i
$425$	−0.522344	+	20.8813i	−0.0253374	+	1.01289i
$426$	−1.95386	−	7.77086i	−0.0946646	−	0.376500i
$427$	35.7757	+	18.2286i	1.73131	+	0.882146i
$428$	22.2837	−	7.77180i	1.07712	−	0.375664i
$429$	3.51283	+	4.83499i	0.169601	+	0.233436i
$430$	−9.23003	−	18.1957i	−0.445112	−	0.877475i
$431$	20.7812	−	28.6029i	1.00100	−	1.37775i	0.0762831	−	0.997086i	$-0.475695\pi$
$431$	20.7812	−	28.6029i	1.00100	−	1.37775i	0.924713	−	0.380666i	$-0.124305\pi$
$432$	0.794331	+	3.92034i	0.0382173	+	0.188617i
$433$	22.9677	−	3.63773i	1.10376	−	0.174818i	0.422144	−	0.906529i	$-0.361278\pi$
$433$	22.9677	−	3.63773i	1.10376	−	0.174818i	0.681615	+	0.731711i	$0.261278\pi$
$434$	3.06652	−	45.1383i	0.147198	−	2.16671i
$435$	−5.79841	−	14.5092i	−0.278013	−	0.695661i
$436$	−15.5782	−	14.9249i	−0.746063	−	0.714773i
$437$	−2.86188	+	1.45820i	−0.136902	+	0.0697551i
$438$	8.32004	+	9.53289i	0.397547	+	0.455499i
$439$	9.85832	+	30.3408i	0.470512	+	1.44809i	0.851916	+	0.523679i	$0.175441\pi$
$439$	9.85832	+	30.3408i	0.470512	+	1.44809i	−0.381404	+	0.924409i	$0.624559\pi$
$440$	16.7413	+	8.12042i	0.798108	+	0.387126i
$441$	3.07738	−	9.47120i	0.146542	−	0.451009i
$442$	−11.0381	+	4.71124i	−0.525030	+	0.224091i
$443$	−8.31661	−	8.31661i	−0.395134	−	0.395134i	0.481379	−	0.876513i	$-0.340136\pi$
$443$	−8.31661	−	8.31661i	−0.395134	−	0.395134i	−0.876513	+	0.481379i	$0.840136\pi$
$444$	20.2261	+	2.76090i	0.959888	+	0.131027i
$445$	8.43807	−	1.91453i	0.400003	−	0.0907574i
$446$	−1.69084	+	2.02319i	−0.0800637	+	0.0958010i
$447$	0.827960	−	5.22753i	0.0391612	−	0.247254i
$448$	27.8411	+	17.6132i	1.31537	+	0.832147i
$449$		−	0.214086i		−	0.0101034i	−0.999987	−	0.00505168i	$-0.998392\pi$
$449$		−	0.214086i		−	0.0101034i	0.999987	−	0.00505168i	$-0.00160801\pi$
$450$	−5.31066	−	4.66872i	−0.250347	−	0.220085i
$451$		−	14.1108i		−	0.664451i
$452$	0.510212	+	23.8202i	0.0239983	+	1.12041i
$453$	−0.385235	+	2.43228i	−0.0180999	+	0.114278i
$454$	−6.85100	−	5.72557i	−0.321533	−	0.268715i
$455$	−17.1911	−	7.37397i	−0.805931	−	0.345697i
$456$	0.788074	+	7.09223i	0.0369049	+	0.332124i
$457$	−4.54935	−	4.54935i	−0.212810	−	0.212810i	0.592650	−	0.805460i	$-0.298082\pi$
$457$	−4.54935	−	4.54935i	−0.212810	−	0.212810i	−0.805460	+	0.592650i	$0.798082\pi$
$458$	3.39456	+	7.95324i	0.158617	+	0.371630i
$459$	−1.29094	+	3.97310i	−0.0602558	+	0.185448i
$460$	4.82784	−	3.01801i	0.225099	−	0.140715i
$461$	9.39860	+	28.9259i	0.437737	+	1.34721i	0.890256	+	0.455460i	$0.150525\pi$
$461$	9.39860	+	28.9259i	0.437737	+	1.34721i	−0.452520	+	0.891754i	$0.649475\pi$
$462$	12.9087	−	11.2663i	0.600565	−	0.524156i
$463$	14.7207	−	7.50059i	0.684131	−	0.348582i	−0.0771362	−	0.997021i	$-0.524578\pi$
$463$	14.7207	−	7.50059i	0.684131	−	0.348582i	0.761267	+	0.648438i	$0.224578\pi$
$464$	7.49107	−	26.9281i	0.347764	−	1.25011i
$465$	−13.3489	+	11.1154i	−0.619041	+	0.515464i
$466$	5.46985	+	0.371600i	0.253386	+	0.0172140i
$467$	23.1722	−	3.67012i	1.07228	−	0.169833i	0.404760	−	0.914423i	$-0.367355\pi$
$467$	23.1722	−	3.67012i	1.07228	−	0.169833i	0.667522	+	0.744590i	$0.267355\pi$
$468$	1.17245	−	3.88997i	0.0541964	−	0.179814i
$469$	−36.6369	+	50.4264i	−1.69174	+	2.32847i
$470$	6.93631	−	13.5530i	0.319948	−	0.625154i
$471$	9.14256	+	12.5837i	0.421267	+	0.579824i
$472$	10.7915	−	7.09961i	0.496718	−	0.326786i
$473$	−16.9127	−	8.61745i	−0.777647	−	0.396231i
$474$	13.0699	−	3.28621i	0.600321	−	0.150941i
$475$	−8.69401	−	9.14013i	−0.398908	−	0.419378i
$476$	16.2734	+	30.3154i	0.745890	+	1.38950i
$477$	1.15193	−	2.26080i	0.0527434	−	0.103515i
$478$	−2.65064	−	29.6208i	−0.121237	−	1.35483i
$479$	13.8011	−	10.0271i	0.630587	−	0.458148i	−0.226016	−	0.974124i	$-0.572570\pi$
$479$	13.8011	−	10.0271i	0.630587	−	0.458148i	0.856604	+	0.515975i	$0.172570\pi$
$480$	−2.48962	−	12.4017i	−0.113635	−	0.566057i
$481$	−16.7744	−	12.1873i	−0.764845	−	0.555693i
$482$	12.4008	−	20.7314i	0.564842	−	0.944288i
$483$	−0.820153	−	5.17824i	−0.0373182	−	0.235618i
$484$	−4.61494	+	0.832609i	−0.209770	+	0.0378458i
$485$	−39.1163	−	9.90991i	−1.77618	−	0.449986i
$486$	−0.751794	−	1.19783i	−0.0341021	−	0.0543348i
$487$	5.36443	+	10.5283i	0.243086	+	0.477082i	0.980024	−	0.198877i	$-0.0637295\pi$
$487$	5.36443	+	10.5283i	0.243086	+	0.477082i	−0.736939	+	0.675959i	$0.763729\pi$
$488$	9.72974	−	25.8043i	0.440445	−	1.16810i
$489$	−3.47615	+	1.12947i	−0.157197	+	0.0510764i
$490$	−9.78533	+	29.9330i	−0.442056	+	1.35224i
$491$	−6.63918	−	2.15720i	−0.299622	−	0.0973530i	0.155348	−	0.987860i	$-0.450350\pi$
$491$	−6.63918	−	2.15720i	−0.299622	−	0.0973530i	−0.454970	+	0.890507i	$0.650350\pi$
$492$	−7.63814	+	5.80335i	−0.344354	+	0.261635i
$493$	20.6414	−	20.6414i	0.929644	−	0.929644i
$494$	2.70181	−	6.72556i	0.121560	−	0.302597i
$495$	−6.55123	−	0.598108i	−0.294456	−	0.0268830i
$496$	−31.0453	+	1.33055i	−1.39398	+	0.0597435i
$497$	23.0452	+	3.65000i	1.03372	+	0.163725i
$498$	−4.76748	+	20.8385i	−0.213636	+	0.933797i
$499$	−37.1988			−1.66525			−0.832624	−	0.553839i	$-0.813162\pi$
$499$	−37.1988			−1.66525			−0.832624	+	0.553839i	$0.813162\pi$
$500$	16.7672	+	14.7939i	0.749853	+	0.661605i
$501$	−14.1653			−0.632859
$502$	−2.34589	+	10.2538i	−0.104702	+	0.457651i
$503$	2.11162	+	0.334448i	0.0941526	+	0.0149123i	0.203333	−	0.979110i	$-0.434823\pi$
$503$	2.11162	+	0.334448i	0.0941526	+	0.0149123i	−0.109180	+	0.994022i	$0.534823\pi$
$504$	−11.4074	−	2.35393i	−0.508124	−	0.104852i
$505$	−3.91290	−	0.357237i	−0.174122	−	0.0158968i
$506$	1.97452	−	4.91513i	0.0877782	−	0.218504i
$507$	6.27442	−	6.27442i	0.278657	−	0.278657i
$508$	7.06059	+	9.29287i	0.313263	+	0.412304i
$509$	−10.9355	−	3.55317i	−0.484709	−	0.157491i	0.0564609	−	0.998405i	$-0.482018\pi$
$509$	−10.9355	−	3.55317i	−0.484709	−	0.157491i	−0.541170	+	0.840913i	$0.682018\pi$
$510$	4.10487	−	12.5567i	0.181767	−	0.556019i
$511$	−35.0414	+	11.3856i	−1.55014	+	0.503670i
$512$	9.91150	−	20.3411i	0.438030	−	0.898960i
$513$	−1.14538	−	2.24793i	−0.0505698	−	0.0992488i
$514$	16.4917	+	26.2763i	0.727419	+	1.15900i
$515$	13.8819	+	3.51691i	0.611710	+	0.154974i
$516$	2.29108	+	12.6989i	0.100859	+	0.559038i
$517$	−2.21578	−	13.9899i	−0.0974499	−	0.615274i
$518$	−30.5144	+	51.0132i	−1.34073	+	2.24139i
$519$	−19.7323	−	14.3363i	−0.866151	−	0.629295i
$520$	−3.72970	+	12.2945i	−0.163558	+	0.539149i
$521$	−19.5545	+	14.2072i	−0.856698	+	0.622428i	−0.926985	−	0.375099i	$-0.877609\pi$
$521$	−19.5545	+	14.2072i	−0.856698	+	0.622428i	0.0702864	+	0.997527i	$0.477609\pi$
$522$	0.880781	+	9.84272i	0.0385508	+	0.430804i
$523$	−0.167730	+	0.329188i	−0.00733431	+	0.0143944i	−0.894645	−	0.446778i	$-0.852571\pi$
$523$	−0.167730	+	0.329188i	−0.00733431	+	0.0143944i	0.887310	+	0.461173i	$0.152571\pi$
$524$	23.6900	−	12.7169i	1.03490	−	0.555539i
$525$	18.5742	−	8.88614i	0.810645	−	0.387823i
$526$	−5.32541	+	1.33899i	−0.232199	+	0.0583826i
$527$	−28.9160	−	14.7335i	−1.25960	−	0.641799i
$528$	−8.66986	−	7.95725i	−0.377307	−	0.346295i
$529$	12.5664	+	17.2961i	0.546364	+	0.752005i
$530$	−3.65557	+	7.14271i	−0.158788	+	0.310259i
$531$	−2.68442	+	3.69478i	−0.116494	+	0.160340i
$532$	−19.8951	−	5.99645i	−0.862563	−	0.259979i
$533$	9.62340	−	1.52420i	0.416836	−	0.0660203i
$534$	−5.45976	−	0.370914i	−0.236267	−	0.0160510i
$535$	20.2765	−	16.8839i	0.876632	−	0.729955i
$536$	37.2015	+	21.1845i	1.60686	+	0.915030i
$537$	10.2251	−	5.20997i	0.441247	−	0.224827i
$538$	22.5589	−	19.6887i	0.972582	−	0.848842i
$539$	9.05360	+	27.8641i	0.389966	+	1.20019i
$540$	2.37057	+	3.79215i	0.102013	+	0.163188i
$541$	9.02234	−	27.7679i	0.387901	−	1.19384i	−0.546453	−	0.837490i	$-0.684022\pi$
$541$	9.02234	−	27.7679i	0.387901	−	1.19384i	0.934354	−	0.356346i	$-0.115978\pi$
$542$	−9.29925	−	21.7875i	−0.399437	−	0.935855i
$543$	8.54711	+	8.54711i	0.366792	+	0.366792i
$544$	19.4598	−	13.4082i	0.834333	−	0.574872i
$545$	−22.1672	−	9.50840i	−0.949537	−	0.407295i
$546$	9.07784	+	7.58661i	0.388496	+	0.324677i
$547$	3.50210	−	22.1114i	0.149739	−	0.945415i	−0.792354	−	0.610062i	$-0.791145\pi$
$547$	3.50210	−	22.1114i	0.149739	−	0.945415i	0.942093	−	0.335353i	$-0.108855\pi$
$548$	−24.0866	+	0.515919i	−1.02893	+	0.0220390i
$549$			9.75018i			0.416127i
$550$	20.7134	+	1.92861i	0.883222	+	0.0822361i
$551$			17.6293i			0.751033i
$552$	−3.47261	+	0.952642i	−0.147804	+	0.0405471i
$553$	−6.13898	+	38.7600i	−0.261056	+	1.64824i
$554$	−8.86704	+	10.6100i	−0.376725	+	0.450774i
$555$	22.2574	−	5.05004i	0.944776	−	0.214362i
$556$	2.27543	−	16.6696i	0.0964997	−	0.706947i
$557$	−1.54450	−	1.54450i	−0.0654426	−	0.0654426i	0.673628	−	0.739071i	$-0.264735\pi$
$557$	−1.54450	−	1.54450i	−0.0654426	−	0.0654426i	−0.739071	+	0.673628i	$0.764735\pi$
$558$	10.1044	−	4.31270i	0.427753	−	0.182571i
$559$	4.05015	−	12.4651i	0.171303	−	0.527217i
$560$	36.0598	+	7.50858i	1.52381	+	0.317295i
$561$	−3.79792	−	11.6888i	−0.160348	−	0.493501i
$562$	−24.2218	−	27.7527i	−1.02173	−	1.17068i
$563$	−33.8732	+	17.2592i	−1.42758	+	0.727391i	−0.985515	−	0.169590i	$-0.945756\pi$
$563$	−33.8732	+	17.2592i	−1.42758	+	0.727391i	−0.442070	+	0.896981i	$0.645756\pi$
$564$	−6.66140	+	6.95301i	−0.280496	+	0.292775i
$565$	9.88534	+	24.7357i	0.415879	+	1.04064i
$566$	1.53528	−	22.5989i	0.0645325	−	0.949901i
$567$	4.06738	−	0.644210i	0.170814	−	0.0270543i
$568$	0.743567	−	16.0082i	0.0311994	−	0.671689i
$569$	−4.84171	+	6.66404i	−0.202975	+	0.279371i	−0.898354	−	0.439272i	$-0.855236\pi$
$569$	−4.84171	+	6.66404i	−0.202975	+	0.279371i	0.695379	+	0.718643i	$0.255236\pi$
$570$	3.60923	+	7.11509i	0.151174	+	0.298018i
$571$	−3.79165	−	5.21876i	−0.158676	−	0.218398i	0.722276	−	0.691605i	$-0.243096\pi$
$571$	−3.79165	−	5.21876i	−0.158676	−	0.218398i	−0.880951	+	0.473207i	$0.843096\pi$
$572$	3.93619	+	11.2860i	0.164580	+	0.471893i
$573$	−1.61504	−	0.822902i	−0.0674691	−	0.0343772i
$574$	−6.81135	−	27.0900i	−0.284300	−	1.13072i
$575$	3.86920	−	5.05468i	0.161357	−	0.210795i
$576$	−0.741586	+	7.96555i	−0.0308994	+	0.331898i
$577$	7.18802	−	14.1073i	0.299241	−	0.587294i	−0.691607	−	0.722274i	$-0.743097\pi$
$577$	7.18802	−	14.1073i	0.299241	−	0.587294i	0.990848	+	0.134980i	$0.0430971\pi$
$578$	0.636704	−	0.0569758i	0.0264834	−	0.00236988i
$579$	13.0294	−	9.46638i	0.541481	−	0.393409i
$580$	−2.72934	−	31.1304i	−0.113330	−	1.29262i
$581$	−50.3597	−	36.5885i	−2.08927	−	1.51794i
$582$	21.9017	+	13.1009i	0.907854	+	0.543048i
$583$	1.16776	+	7.37294i	0.0483637	+	0.305356i
$584$	10.4301	+	23.0566i	0.431602	+	0.954090i
$585$	−0.299737	−	4.53247i	−0.0123926	−	0.187395i
$586$	−25.2598	+	15.8537i	−1.04347	+	0.654912i
$587$	−6.18104	−	12.1310i	−0.255119	−	0.500699i	0.727553	−	0.686051i	$-0.240657\pi$
$587$	−6.18104	−	12.1310i	−0.255119	−	0.500699i	−0.982672	+	0.185352i	$0.940657\pi$
$588$	11.3593	−	16.3604i	0.468450	−	0.674690i
$589$	18.6399	−	6.05648i	0.768045	−	0.249553i
$590$	8.50986	−	11.6687i	0.350345	−	0.480391i
$591$	4.30067	+	1.39737i	0.176906	+	0.0574803i
$592$	37.1377	+	16.9606i	1.52635	+	0.697075i
$593$	23.0428	−	23.0428i	0.946253	−	0.946253i	−0.0523746	−	0.998628i	$-0.516679\pi$
$593$	23.0428	−	23.0428i	0.946253	−	0.946253i	0.998628	+	0.0523746i	$0.0166790\pi$
$594$	3.86072	+	1.55094i	0.158407	+	0.0636358i
$595$	28.9368	+	25.3470i	1.18629	+	1.03912i
$596$	4.60259	−	9.53240i	0.188530	−	0.390462i
$597$	−0.384389	−	0.0608812i	−0.0157320	−	0.00249170i
$598$	3.56535	+	0.815687i	0.145798	+	0.0333559i
$599$	−18.7963			−0.767998			−0.383999	−	0.923334i	$-0.625453\pi$
$599$	−18.7963			−0.767998			−0.383999	+	0.923334i	$0.625453\pi$
$600$	−7.47484	−	12.0053i	−0.305159	−	0.490113i
$601$	−19.7593			−0.805998			−0.402999	−	0.915200i	$-0.632032\pi$
$601$	−19.7593			−0.805998			−0.402999	+	0.915200i	$0.632032\pi$
$602$	−36.6289	−	8.38003i	−1.49288	−	0.341544i
$603$	−14.9494	−	2.36776i	−0.608788	−	0.0964226i
$604$	−2.14150	+	4.43525i	−0.0871365	+	0.180468i
$605$	−4.50427	+	2.68333i	−0.183124	+	0.109093i
$606$	2.30592	+	0.926341i	0.0936715	+	0.0376300i
$607$	19.6308	−	19.6308i	0.796789	−	0.796789i	−0.185799	−	0.982588i	$-0.559487\pi$
$607$	19.6308	−	19.6308i	0.796789	−	0.796789i	0.982588	+	0.185799i	$0.0594873\pi$
$608$	−2.58426	+	14.0358i	−0.104806	+	0.569229i
$609$	−27.3674	−	8.89221i	−1.10898	−	0.360330i
$610$	0.0554018	−	30.8327i	0.00224316	−	1.24838i
$611$	9.30160	−	3.02227i	0.376303	−	0.122268i
$612$	−4.76514	+	6.86305i	−0.192619	+	0.277422i
$613$	16.9009	+	33.1698i	0.682620	+	1.33972i	0.928832	+	0.370501i	$0.120814\pi$
$613$	16.9009	+	33.1698i	0.682620	+	1.33972i	−0.246212	+	0.969216i	$0.579186\pi$
$614$	−11.8756	+	7.45347i	−0.479261	+	0.300797i
$615$	−5.71769	+	9.07375i	−0.230560	+	0.365889i
$616$	31.2214	−	14.1236i	1.25795	−	0.569057i
$617$	−2.10927	−	13.3174i	−0.0849160	−	0.536139i	−0.993072	−	0.117507i	$-0.962510\pi$
$617$	−2.10927	−	13.3174i	−0.0849160	−	0.536139i	0.908156	−	0.418632i	$-0.137490\pi$
$618$	−7.77265	−	4.64935i	−0.312662	−	0.187024i
$619$	3.48666	+	2.53321i	0.140141	+	0.101818i	0.655647	−	0.755068i	$-0.272396\pi$
$619$	3.48666	+	2.53321i	0.140141	+	0.101818i	−0.515506	+	0.856886i	$0.672396\pi$
$620$	−31.9773	+	13.5805i	−1.28424	+	0.545407i
$621$	1.02997	−	0.748317i	0.0413313	−	0.0300289i
$622$	−41.9415	+	3.75316i	−1.68170	+	0.150488i
$623$	7.23436	−	14.1982i	0.289839	−	0.568840i
$624$	4.49027	−	6.77226i	0.179755	−	0.271108i
$625$	23.3604	+	8.90455i	0.934417	+	0.356182i
$626$	4.77502	+	18.9912i	0.190848	+	0.759041i
$627$	6.61339	+	3.36969i	0.264113	+	0.134572i
$628$	10.2444	+	29.3733i	0.408797	+	1.17212i
$629$	25.0629	+	34.4962i	0.999325	+	1.37545i
$630$	−12.8658	+	2.01406i	−0.512587	+	0.0802419i
$631$	0.543515	−	0.748085i	0.0216370	−	0.0297808i	−0.798061	−	0.602576i	$-0.794141\pi$
$631$	0.543515	−	0.748085i	0.0216370	−	0.0297808i	0.819698	+	0.572795i	$0.194141\pi$
$632$	26.9244	+	1.25061i	1.07099	+	0.0497468i
$633$	−11.0399	+	1.74856i	−0.438799	+	0.0694989i
$634$	−2.81414	+	41.4234i	−0.111764	+	1.64513i
$635$	11.0395	+	6.95638i	0.438089	+	0.276055i
$636$	3.51069	−	3.66438i	0.139208	−	0.145302i
$637$	−18.0251	+	9.18424i	−0.714180	+	0.363893i
$638$	−19.1169	−	21.9037i	−0.756847	−	0.867177i
$639$	1.75085	+	5.38855i	0.0692624	+	0.213168i
$640$	2.39036	−	25.1850i	0.0944872	−	0.995526i
$641$	0.925645	−	2.84884i	0.0365608	−	0.112523i	−0.931111	−	0.364737i	$-0.881159\pi$
$641$	0.925645	−	2.84884i	0.0365608	−	0.112523i	0.967671	+	0.252215i	$0.0811589\pi$
$642$	−15.3482	+	6.55086i	−0.605746	+	0.258542i
$643$	18.1860	+	18.1860i	0.717184	+	0.717184i	0.968028	−	0.250843i	$-0.0807079\pi$
$643$	18.1860	+	18.1860i	0.717184	+	0.717184i	−0.250843	+	0.968028i	$0.580708\pi$
$644$	1.41815	−	10.3892i	0.0558830	−	0.409393i
$645$	7.38369	+	12.3944i	0.290732	+	0.488027i
$646$	−9.55830	+	11.4371i	−0.376066	+	0.449986i
$647$	−3.07874	+	19.4384i	−0.121038	+	0.764203i	0.850265	+	0.526356i	$0.176442\pi$
$647$	−3.07874	+	19.4384i	−0.121038	+	0.764203i	−0.971302	+	0.237848i	$0.923558\pi$
$648$	−0.748277	−	2.72765i	−0.0293951	−	0.107152i
$649$		−	13.4361i		−	0.527412i
$650$	0.922097	+	14.3346i	0.0361676	+	0.562250i
$651$			31.9912i			1.25383i
$652$	−7.30840	+	0.156541i	−0.286219	+	0.00613062i
$653$	−5.10462	+	32.2293i	−0.199759	+	1.26123i	0.660287	+	0.751013i	$0.270435\pi$
$653$	−5.10462	+	32.2293i	−0.199759	+	1.26123i	−0.860046	+	0.510216i	$0.829565\pi$
$654$	11.7055	+	9.78260i	0.457720	+	0.382530i
$655$	19.8074	−	22.6127i	0.773940	−	0.883551i
$656$	−17.9758	+	6.70447i	−0.701838	+	0.261766i
$657$	−6.32651	−	6.32651i	−0.246821	−	0.246821i
$658$	−11.0069	−	25.7884i	−0.429092	−	1.00533i
$659$	3.81602	−	11.7445i	0.148651	−	0.457500i	−0.848812	−	0.528696i	$-0.822681\pi$
$659$	3.81602	−	11.7445i	0.148651	−	0.457500i	0.997462	+	0.0711952i	$0.0226813\pi$
$660$	−12.1998	−	4.92643i	−0.474878	−	0.191761i
$661$	−14.4254	−	44.3968i	−0.561083	−	1.72683i	−0.679313	−	0.733848i	$-0.737722\pi$
$661$	−14.4254	−	44.3968i	−0.561083	−	1.72683i	0.118231	−	0.992986i	$-0.462278\pi$
$662$	−9.00491	+	7.85923i	−0.349986	+	0.305458i
$663$	7.56139	−	3.85272i	0.293660	−	0.149627i
$664$	−21.1565	+	37.1523i	−0.821030	+	1.44179i
$665$	−23.1812	+	1.53300i	−0.898927	+	0.0594471i
$666$	−14.4014	−	0.978376i	−0.558044	−	0.0379113i
$667$	−8.78657	+	1.39166i	−0.340217	+	0.0538851i
$668$	−27.1253	−	8.17564i	−1.04951	−	0.316325i
$669$	1.09589	−	1.50836i	0.0423695	−	0.0583167i
$670$	47.2607	+	7.57244i	1.82584	+	0.292549i
$671$	−16.8605	−	23.2066i	−0.650894	−	0.895879i
$672$	−20.4855	−	11.0914i	−0.790245	−	0.427861i
$673$	−23.1435	−	11.7922i	−0.892115	−	0.454555i	−0.0530536	−	0.998592i	$-0.516895\pi$
$673$	−23.1435	−	11.7922i	−0.892115	−	0.454555i	−0.839062	+	0.544036i	$0.816895\pi$
$674$	−42.4553	+	10.6747i	−1.63532	+	0.411174i
$675$	3.97033	+	3.03916i	0.152818	+	0.116977i
$676$	15.6363	−	8.39362i	0.601396	−	0.322831i
$677$	−10.6821	+	20.9649i	−0.410547	+	0.805745i	−0.999998	−	0.00205983i	$-0.999344\pi$
$677$	−10.6821	+	20.9649i	−0.410547	+	0.805745i	0.589450	+	0.807805i	$0.299344\pi$
$678$	−1.50159	−	16.7802i	−0.0576681	−	0.644440i
$679$	−60.1220	+	43.6812i	−2.30727	+	1.67633i
$680$	15.1077	−	21.6758i	0.579353	−	0.831228i
$681$	5.10766	+	3.71093i	0.195726	+	0.142203i
$682$	−16.5918	+	27.7378i	−0.635334	+	1.06214i
$683$	5.16155	+	32.5887i	0.197501	+	1.24697i	0.864775	+	0.502160i	$0.167461\pi$
$683$	5.16155	+	32.5887i	0.197501	+	1.24697i	−0.667274	+	0.744813i	$0.732539\pi$
$684$	−0.895884	−	4.96566i	−0.0342550	−	0.189867i
$685$	−25.0124	+	9.99592i	−0.955676	+	0.381924i
$686$	9.15970	+	14.5942i	0.349719	+	0.557208i
$687$	−2.77598	−	5.44816i	−0.105910	−	0.207860i
$688$	−2.94207	+	25.6396i	−0.112165	+	0.977500i
$689$	−4.90213	+	1.59280i	−0.186756	+	0.0606808i
$690$	−3.26130	+	2.36053i	−0.124156	+	0.0898639i
$691$	12.2625	+	3.98433i	0.466487	+	0.151571i	0.532824	−	0.846226i	$-0.321131\pi$
$691$	12.2625	+	3.98433i	0.466487	+	0.151571i	−0.0663361	+	0.997797i	$0.521131\pi$
$692$	−29.5112	−	38.8415i	−1.12185	−	1.47653i
$693$	−8.56684	+	8.56684i	−0.325427	+	0.325427i
$694$	15.6309	−	38.9096i	0.593341	−	1.47699i
$695$	−4.16205	−	18.3437i	−0.157875	−	0.695817i
$696$	−3.99420	+	19.3563i	−0.151400	+	0.733698i
$697$	−19.7904	−	3.13449i	−0.749613	−	0.118727i
$698$	−6.33918	+	27.7084i	−0.239942	+	1.04878i
$699$	−3.87668			−0.146630
$700$	40.6967	−	6.29589i	1.53819	−	0.237962i
$701$	−10.1632			−0.383857			−0.191929	−	0.981409i	$-0.561474\pi$
$701$	−10.1632			−0.383857			−0.191929	+	0.981409i	$0.561474\pi$
$702$	−0.640703	+	2.80049i	−0.0241818	+	0.105698i
$703$	−25.4339	−	4.02834i	−0.959259	−	0.151932i
$704$	−12.0094	−	20.2413i	−0.452622	−	0.762874i
$705$	−4.24387	+	9.89383i	−0.159833	+	0.372623i
$706$	7.42276	−	18.4773i	0.279359	−	0.695402i
$707$	−5.11678	+	5.11678i	−0.192436	+	0.192436i
$708$	−7.27290	+	5.52585i	−0.273332	+	0.207674i
$709$	19.1758	+	6.23061i	0.720164	+	0.233995i	0.646094	−	0.763258i	$-0.276401\pi$
$709$	19.1758	+	6.23061i	0.720164	+	0.233995i	0.0740695	+	0.997253i	$0.476401\pi$
$710$	−5.50603	−	17.0500i	−0.206638	−	0.639876i
$711$	−9.06306	+	2.94477i	−0.339891	+	0.110437i
$712$	−10.2409	−	3.86142i	−0.383793	−	0.144713i
$713$	4.49003	+	8.81217i	0.168153	+	0.330019i
$714$	−12.9335	−	20.6070i	−0.484025	−	0.771197i
$715$	8.55121	+	10.2695i	0.319797	+	0.384057i
$716$	22.5872	−	4.07509i	0.844124	−	0.152293i
$717$	3.28963	+	20.7699i	0.122853	+	0.775666i
$718$	−13.3583	+	22.3321i	−0.498528	+	0.833425i
$719$	−4.47990	−	3.25484i	−0.167072	−	0.121385i	0.501107	−	0.865385i	$-0.332926\pi$
$719$	−4.47990	−	3.25484i	−0.167072	−	0.121385i	−0.668179	+	0.744000i	$0.732926\pi$
$720$	2.35076	+	8.62983i	0.0876076	+	0.321615i
$721$	21.3366	−	15.5020i	0.794617	−	0.577323i
$722$	1.59260	+	17.7973i	0.0592705	+	0.662348i
$723$	−7.75494	+	15.2199i	−0.288409	+	0.566035i
$724$	11.4339	+	21.3000i	0.424938	+	0.791609i
$725$	−15.0782	−	31.5172i	−0.559991	−	1.17052i
$726$	3.21585	−	0.808572i	0.119351	−	0.0300089i
$727$	−20.1834	−	10.2839i	−0.748560	−	0.381410i	0.0377137	−	0.999289i	$-0.487992\pi$
$727$	−20.1834	−	10.2839i	−0.748560	−	0.381410i	−0.786274	+	0.617878i	$0.787992\pi$
$728$	13.0046	+	19.7671i	0.481982	+	0.732616i
$729$	0.587785	+	0.809017i	0.0217698	+	0.0299636i
$730$	19.9702	+	20.0421i	0.739131	+	0.741792i
$731$	−15.8428	+	21.8058i	−0.585969	+	0.806517i
$732$	−5.62741	+	18.6707i	−0.207995	+	0.690090i
$733$	−20.5076	+	3.24809i	−0.757467	+	0.119971i	−0.523210	−	0.852204i	$-0.675266\pi$
$733$	−20.5076	+	3.24809i	−0.757467	+	0.119971i	−0.234257	+	0.972175i	$0.575266\pi$
$734$	0.240067	+	0.0163092i	0.00886104	+	0.000601984i
$735$	5.46874	−	21.5862i	0.201718	−	0.796217i
$736$	−7.19957	−	0.180025i	−0.265380	−	0.00663580i
$737$	39.6759	−	20.2159i	1.46148	−	0.744661i
$738$	5.11042	−	4.46023i	0.188117	−	0.164183i
$739$	−12.0568	−	37.1070i	−0.443517	−	1.36500i	−0.884102	−	0.467293i	$-0.845229\pi$
$739$	−12.0568	−	37.1070i	−0.443517	−	1.36500i	0.440586	−	0.897710i	$-0.354771\pi$
$740$	45.5357	+	3.17572i	1.67393	+	0.116742i
$741$	−1.58374	+	4.87424i	−0.0581800	+	0.179060i
$742$	5.80083	+	13.5910i	0.212955	+	0.498940i
$743$	13.7818	+	13.7818i	0.505605	+	0.505605i	0.913174	−	0.407569i	$-0.133623\pi$
$743$	13.7818	+	13.7818i	0.505605	+	0.505605i	−0.407569	+	0.913174i	$0.633623\pi$
$744$	21.8381	−	2.42660i	0.800624	−	0.0889637i
$745$	1.07601	−	11.7858i	0.0394220	−	0.431799i
$746$	−0.339715	−	0.283910i	−0.0124379	−	0.0103947i
$747$	2.36463	−	14.9297i	0.0865172	−	0.546248i
$748$	−0.526380	−	24.5750i	−0.0192463	−	0.898551i
$749$		−	48.5935i		−	1.77557i
$750$	−12.5380	−	9.63322i	−0.457822	−	0.351756i
$751$		−	5.44983i		−	0.198867i	−0.995044	−	0.0994336i	$-0.968297\pi$
$751$		−	5.44983i		−	0.198867i	0.995044	−	0.0994336i	$-0.0317031\pi$
$752$	−16.7690	+	9.46971i	−0.611502	+	0.345325i
$753$	1.16354	−	7.34632i	0.0424018	−	0.267715i
$754$	12.8731	−	15.4035i	0.468812	−	0.560962i
$755$	−0.500648	+	5.48372i	−0.0182204	+	0.199573i
$756$	8.16049	+	1.11392i	0.296794	+	0.0405130i
$757$	10.0153	+	10.0153i	0.364012	+	0.364012i	0.865288	−	0.501275i	$-0.167136\pi$
$757$	10.0153	+	10.0153i	0.364012	+	0.364012i	−0.501275	+	0.865288i	$0.667136\pi$
$758$	−8.72951	+	3.72589i	−0.317070	+	0.135330i
$759$	−1.15742	+	3.56216i	−0.0420116	+	0.129298i
$760$	2.80481	+	15.7079i	0.101741	+	0.569784i
$761$	8.57919	+	26.4040i	0.310995	+	0.957145i	0.977372	+	0.211529i	$0.0678444\pi$
$761$	8.57919	+	26.4040i	0.310995	+	0.957145i	−0.666376	+	0.745616i	$0.732156\pi$
$762$	−5.42649	−	6.21754i	−0.196581	−	0.225238i
$763$	−39.5799	+	20.1670i	−1.43289	+	0.730094i
$764$	−2.61771	−	2.50792i	−0.0947053	−	0.0907333i
$765$	−2.29410	+	9.05523i	−0.0829432	+	0.327393i
$766$	−2.52238	+	37.1287i	−0.0911373	+	1.34152i
$767$	9.16324	−	1.45132i	0.330866	−	0.0524040i
$768$	−6.01747	+	14.8253i	−0.217137	+	0.534963i
$769$	−5.13191	+	7.06347i	−0.185061	+	0.254715i	−0.891460	−	0.453099i	$-0.850318\pi$
$769$	−5.13191	+	7.06347i	−0.185061	+	0.254715i	0.706399	+	0.707814i	$0.250318\pi$
$770$	27.1394	−	27.0420i	0.978034	−	0.974526i
$771$	−12.8939	−	17.7470i	−0.464364	−	0.639142i
$772$	30.4137	−	10.6073i	1.09461	−	0.381764i
$773$	38.1655	+	19.4463i	1.37272	+	0.699434i	0.975850	−	0.218442i	$-0.0700974\pi$
$773$	38.1655	+	19.4463i	1.37272	+	0.699434i	0.396867	+	0.917876i	$0.370097\pi$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37859 - 0.315398i) q^{2} +(0.987688 + 0.156434i) q^{3} +(1.80105 + 0.869612i) q^{4} +(2.22681 + 0.203301i) q^{5} +(-1.31228 - 0.527175i) q^{6} +(2.91192 - 2.91192i) q^{7} +(-2.20864 - 1.76689i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})\)	\(q+(-1.37859 - 0.315398i) q^{2} +(0.987688 + 0.156434i) q^{3} +(1.80105 + 0.869612i) q^{4} +(2.22681 + 0.203301i) q^{5} +(-1.31228 - 0.527175i) q^{6} +(2.91192 - 2.91192i) q^{7} +(-2.20864 - 1.76689i) q^{8} +(0.951057 + 0.309017i) q^{9} +(-3.00574 - 0.982600i) q^{10} +(-2.79799 + 0.909123i) q^{11} +(1.64284 + 1.14065i) q^{12} +(-0.922241 - 1.81000i) q^{13} +(-4.93278 + 3.09595i) q^{14} +(2.16759 + 0.549147i) q^{15} +(2.48755 + 3.13243i) q^{16} +(0.653515 + 4.12613i) q^{17} +(-1.21366 - 0.725971i) q^{18} +(-2.04108 - 1.48293i) q^{19} +(3.83379 + 2.30261i) q^{20} +(3.33160 - 2.42055i) q^{21} +(4.14404 - 0.370831i) q^{22} +(0.577981 - 1.13435i) q^{23} +(-1.90505 - 2.09064i) q^{24} +(4.91734 + 0.905424i) q^{25} +(0.700527 + 2.78613i) q^{26} +(0.891007 + 0.453990i) q^{27} +(7.77676 - 2.71227i) q^{28} +(-4.10725 - 5.65314i) q^{29} +(-2.81503 - 1.44070i) q^{30} +(-4.56619 + 6.28482i) q^{31} +(-2.44136 - 5.10292i) q^{32} +(-2.90576 + 0.460228i) q^{33} +(0.400441 - 5.89438i) q^{34} +(7.07629 - 5.89230i) q^{35} +(1.44417 + 1.38360i) q^{36} +(9.09435 - 4.63380i) q^{37} +(2.34611 + 2.68812i) q^{38} +(-0.627740 - 1.93199i) q^{39} +(-4.55901 - 4.38354i) q^{40} +(-1.48215 + 4.56160i) q^{41} +(-5.35636 + 2.28618i) q^{42} +(4.56222 + 4.56222i) q^{43} +(-5.82991 - 0.795794i) q^{44} +(2.05500 + 0.881472i) q^{45} +(-1.15457 + 1.38152i) q^{46} +(-0.753158 + 4.75525i) q^{47} +(1.96690 + 3.48300i) q^{48} -9.95861i q^{49} +(-6.49345 - 2.79913i) q^{50} +4.17756i q^{51} +(-0.0870029 - 4.06189i) q^{52} +(0.396929 - 2.50611i) q^{53} +(-1.08515 - 0.906891i) q^{54} +(-6.41542 + 1.45561i) q^{55} +(-11.5764 + 1.28635i) q^{56} +(-1.78397 - 1.78397i) q^{57} +(3.87924 + 9.08881i) q^{58} +(-1.41128 + 4.34348i) q^{59} +(3.42639 + 2.87400i) q^{60} +(3.01297 + 9.27297i) q^{61} +(8.27714 - 7.22405i) q^{62} +(3.66924 - 1.86957i) q^{63} +(1.75620 + 7.80485i) q^{64} +(-1.68568 - 4.21801i) q^{65} +(4.15103 + 0.282004i) q^{66} +(-14.9494 + 2.36776i) q^{67} +(-2.41112 + 7.99966i) q^{68} +(0.748317 - 1.02997i) q^{69} +(-11.6138 + 5.89124i) q^{70} +(3.33031 + 4.58377i) q^{71} +(-1.55454 - 2.36292i) q^{72} +(-7.97187 - 4.06187i) q^{73} +(-13.9989 + 3.51980i) q^{74} +(4.71516 + 1.66352i) q^{75} +(-2.38651 - 4.44578i) q^{76} +(-5.50025 + 10.7948i) q^{77} +(0.256055 + 2.86141i) q^{78} +(-7.70950 + 5.60128i) q^{79} +(4.90247 + 7.48103i) q^{80} +(0.809017 + 0.587785i) q^{81} +(3.48201 - 5.82113i) q^{82} +(-2.36463 - 14.9297i) q^{83} +(8.10531 - 1.46233i) q^{84} +(0.616405 + 9.32095i) q^{85} +(-4.85054 - 7.72837i) q^{86} +(-3.17233 - 6.22606i) q^{87} +(7.78609 + 2.93582i) q^{88} +(3.68014 - 1.19575i) q^{89} +(-2.55499 - 1.86333i) q^{90} +(-7.95608 - 2.58509i) q^{91} +(2.02742 - 1.54040i) q^{92} +(-5.49313 + 5.49313i) q^{93} +(2.53810 - 6.31802i) q^{94} +(-4.24361 - 3.71716i) q^{95} +(-1.61303 - 5.42200i) q^{96} +(-17.8238 - 2.82302i) q^{97} +(-3.14092 + 13.7289i) q^{98} -2.94198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240q + 12q^{8} + O(q^{10}) \)	\( 240q + 12q^{8} + 8q^{10} + 8q^{12} + 4q^{13} + 20q^{17} - 20q^{20} - 12q^{22} + 20q^{25} + 4q^{28} - 8q^{30} - 20q^{32} - 8q^{33} - 4q^{37} - 76q^{38} - 92q^{40} - 20q^{42} - 140q^{44} - 4q^{45} - 16q^{48} - 164q^{50} - 172q^{52} - 4q^{53} - 120q^{58} + 20q^{60} - 44q^{62} - 60q^{64} - 20q^{65} + 16q^{68} - 44q^{70} + 12q^{72} - 44q^{73} - 48q^{77} + 24q^{78} - 4q^{80} + 60q^{81} + 24q^{82} + 80q^{84} - 64q^{85} + 60q^{88} - 260q^{89} + 48q^{90} + 144q^{92} - 64q^{93} + 40q^{94} - 20q^{96} - 180q^{97} + 256q^{98} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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