LMFDB - Embedded newform 570.2.n.a.179.3

Newspace parameters

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.n (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.3
Character	$\chi$	$=$	570.179
Dual form			570.2.n.a.449.3

$q$-expansion

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.66274 - 0.485072i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.14569 + 1.92026i) q^{5} +(1.19744 + 1.25145i) q^{6} -4.59876i q^{7} -1.00000i q^{8} +(2.52941 + 1.61310i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.66274 - 0.485072i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.14569 + 1.92026i) q^{5} +(1.19744 + 1.25145i) q^{6} -4.59876i q^{7} -1.00000i q^{8} +(2.52941 + 1.61310i) q^{9} +(1.95233 - 1.09015i) q^{10} +1.39284i q^{11} +(-0.411285 - 1.68251i) q^{12} +(3.11593 + 5.39696i) q^{13} +(-2.29938 + 3.98265i) q^{14} +(2.83645 - 2.63715i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.239870 - 0.415466i) q^{17} +(-1.38398 - 2.66169i) q^{18} +(-2.43225 - 3.61720i) q^{19} +(-2.23584 - 0.0320694i) q^{20} +(-2.23073 + 7.64655i) q^{21} +(0.696421 - 1.20624i) q^{22} +(-2.13813 - 3.70335i) q^{23} +(-0.485072 + 1.66274i) q^{24} +(-2.37478 - 4.40005i) q^{25} -6.23187i q^{26} +(-3.42328 - 3.90911i) q^{27} +(3.98265 - 2.29938i) q^{28} +(-1.35342 - 2.34419i) q^{29} +(-3.77501 + 0.865610i) q^{30} -4.16041i q^{31} +(0.866025 - 0.500000i) q^{32} +(0.675629 - 2.31593i) q^{33} +(-0.415466 + 0.239870i) q^{34} +(8.83081 + 5.26877i) q^{35} +(-0.132279 + 2.99708i) q^{36} -2.07106 q^{37} +(0.297794 + 4.34871i) q^{38} +(-2.56308 - 10.4852i) q^{39} +(1.92026 + 1.14569i) q^{40} +(5.51368 - 9.54997i) q^{41} +(5.75515 - 5.50674i) q^{42} +(-5.15633 - 2.97701i) q^{43} +(-1.20624 + 0.696421i) q^{44} +(-5.99549 + 3.00901i) q^{45} +4.27626i q^{46} +(-3.19735 - 5.53798i) q^{47} +(1.25145 - 1.19744i) q^{48} -14.1486 q^{49} +(-0.143404 + 4.99794i) q^{50} +(-0.600372 + 0.574459i) q^{51} +(-3.11593 + 5.39696i) q^{52} +(6.58345 - 3.80096i) q^{53} +(1.01009 + 5.09703i) q^{54} +(-2.67461 - 1.59577i) q^{55} -4.59876 q^{56} +(2.28960 + 7.19428i) q^{57} +2.70684i q^{58} +(-0.292964 + 0.507429i) q^{59} +(3.70206 + 1.13787i) q^{60} +(-4.04082 - 6.99890i) q^{61} +(-2.08020 + 3.60302i) q^{62} +(7.41826 - 11.6322i) q^{63} -1.00000 q^{64} +(-13.9335 - 0.199853i) q^{65} +(-1.74308 + 1.66784i) q^{66} +(7.23104 + 12.5245i) q^{67} +0.479739 q^{68} +(1.75876 + 7.19485i) q^{69} +(-5.01332 - 8.97829i) q^{70} +(-5.36334 + 9.28957i) q^{71} +(1.61310 - 2.52941i) q^{72} +(-7.91151 - 4.56771i) q^{73} +(1.79359 + 1.03553i) q^{74} +(1.81430 + 8.46808i) q^{75} +(1.91646 - 3.91499i) q^{76} +6.40535 q^{77} +(-3.02291 + 10.3620i) q^{78} +(-9.30867 - 5.37436i) q^{79} +(-1.09015 - 1.95233i) q^{80} +(3.79583 + 8.16037i) q^{81} +(-9.54997 + 5.51368i) q^{82} -5.37122 q^{83} +(-7.73747 + 1.89140i) q^{84} +(0.522986 + 0.936608i) q^{85} +(2.97701 + 5.15633i) q^{86} +(1.11328 + 4.55429i) q^{87} +1.39284 q^{88} +(0.964199 + 1.67004i) q^{89} +(6.69675 + 0.391869i) q^{90} +(24.8193 - 14.3294i) q^{91} +(2.13813 - 3.70335i) q^{92} +(-2.01810 + 6.91768i) q^{93} +6.39471i q^{94} +(9.73257 - 0.526357i) q^{95} +(-1.68251 + 0.411285i) q^{96} +(7.30058 - 12.6450i) q^{97} +(12.2531 + 7.07431i) q^{98} +(-2.24679 + 3.52307i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80q + 40q^{4} + O(q^{10}) $	$ 80q + 40q^{4} + 30q^{15} - 40q^{16} + 8q^{19} + 8q^{25} - 4q^{30} + 48q^{39} + 12q^{45} - 128q^{49} - 36q^{54} + 12q^{55} + 30q^{60} - 24q^{61} - 80q^{64} + 4q^{66} + 36q^{70} + 16q^{76} + 24q^{79} + 32q^{81} - 8q^{85} - 54q^{90} + 24q^{91} - 60q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.66274	−	0.485072i	−0.959984	−	0.280057i
$3$	−1.66274	−	0.485072i	−0.959984	−	0.280057i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.14569	+	1.92026i	−0.512369	+	0.858765i
$5$	−1.14569	+	1.92026i	−0.512369	+	0.858765i
$6$	1.19744	+	1.25145i	0.488852	+	0.510904i
$7$		−	4.59876i		−	1.73817i	−0.494664	−	0.869085i	$-0.664709\pi$
$7$		−	4.59876i		−	1.73817i	0.494664	−	0.869085i	$-0.335291\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.52941	+	1.61310i	0.843137	+	0.537699i
$10$	1.95233	−	1.09015i	0.617380	−	0.344734i
$11$			1.39284i			0.419958i	0.977706	+	0.209979i	$0.0673395\pi$
$11$			1.39284i			0.419958i	−0.977706	+	0.209979i	$0.932661\pi$
$12$	−0.411285	−	1.68251i	−0.118728	−	0.485699i
$13$	3.11593	+	5.39696i	0.864205	+	1.49685i	0.867835	+	0.496853i	$0.165511\pi$
$13$	3.11593	+	5.39696i	0.864205	+	1.49685i	−0.00362967	+	0.999993i	$0.501155\pi$
$14$	−2.29938	+	3.98265i	−0.614536	+	1.06441i
$15$	2.83645	−	2.63715i	0.732369	−	0.680908i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.239870	−	0.415466i	0.0581769	−	0.100765i	−0.835470	−	0.549536i	$-0.814805\pi$
$17$	0.239870	−	0.415466i	0.0581769	−	0.100765i	0.893647	+	0.448770i	$0.148138\pi$
$18$	−1.38398	−	2.66169i	−0.326208	−	0.627366i
$19$	−2.43225	−	3.61720i	−0.557997	−	0.829843i
$19$	−2.43225	−	3.61720i	−0.557997	−	0.829843i
$20$	−2.23584	−	0.0320694i	−0.499949	−	0.00717094i
$21$	−2.23073	+	7.64655i	−0.486786	+	1.66861i
$22$	0.696421	−	1.20624i	0.148477	−	0.257170i
$23$	−2.13813	−	3.70335i	−0.445831	−	0.772201i	0.552279	−	0.833659i	$-0.313758\pi$
$23$	−2.13813	−	3.70335i	−0.445831	−	0.772201i	−0.998110	+	0.0614580i	$0.980425\pi$
$24$	−0.485072	+	1.66274i	−0.0990149	+	0.339405i
$25$	−2.37478	−	4.40005i	−0.474956	−	0.880010i
$26$		−	6.23187i		−	1.22217i
$27$	−3.42328	−	3.90911i	−0.658811	−	0.752308i
$28$	3.98265	−	2.29938i	0.752649	−	0.434542i
$29$	−1.35342	−	2.34419i	−0.251324	−	0.435305i	0.712567	−	0.701604i	$-0.247533\pi$
$29$	−1.35342	−	2.34419i	−0.251324	−	0.435305i	−0.963891	+	0.266299i	$0.914199\pi$
$30$	−3.77501	+	0.865610i	−0.689220	+	0.158038i
$31$		−	4.16041i		−	0.747232i	−0.927584	−	0.373616i	$-0.878118\pi$
$31$		−	4.16041i		−	0.747232i	0.927584	−	0.373616i	$-0.121882\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.675629	−	2.31593i	0.117612	−	0.403152i
$34$	−0.415466	+	0.239870i	−0.0712519	+	0.0411373i
$35$	8.83081	+	5.26877i	1.49268	+	0.890584i
$36$	−0.132279	+	2.99708i	−0.0220465	+	0.499514i
$37$	−2.07106			−0.340480			−0.170240	−	0.985403i	$-0.554454\pi$
$37$	−2.07106			−0.340480			−0.170240	+	0.985403i	$0.554454\pi$
$38$	0.297794	+	4.34871i	0.0483085	+	0.705455i
$39$	−2.56308	−	10.4852i	−0.410421	−	1.67897i
$40$	1.92026	+	1.14569i	0.303619	+	0.181150i
$41$	5.51368	−	9.54997i	0.861092	−	1.49145i	−0.00978488	−	0.999952i	$-0.503115\pi$
$41$	5.51368	−	9.54997i	0.861092	−	1.49145i	0.870876	−	0.491502i	$-0.163552\pi$
$42$	5.75515	−	5.50674i	0.888038	−	0.849708i
$43$	−5.15633	−	2.97701i	−0.786333	−	0.453989i	0.0523373	−	0.998629i	$-0.483333\pi$
$43$	−5.15633	−	2.97701i	−0.786333	−	0.453989i	−0.838670	+	0.544640i	$0.816666\pi$
$44$	−1.20624	+	0.696421i	−0.181847	+	0.104989i
$45$	−5.99549	+	3.00901i	−0.893755	+	0.448556i
$46$			4.27626i			0.630500i
$47$	−3.19735	−	5.53798i	−0.466382	−	0.807798i	0.532881	−	0.846190i	$-0.321109\pi$
$47$	−3.19735	−	5.53798i	−0.466382	−	0.807798i	−0.999263	+	0.0383929i	$0.987776\pi$
$48$	1.25145	−	1.19744i	0.180632	−	0.172835i
$49$	−14.1486			−2.02123
$50$	−0.143404	+	4.99794i	−0.0202804	+	0.706816i
$51$	−0.600372	+	0.574459i	−0.0840689	+	0.0804403i
$52$	−3.11593	+	5.39696i	−0.432102	+	0.748423i
$53$	6.58345	−	3.80096i	0.904307	−	0.522102i	0.0257120	−	0.999669i	$-0.491815\pi$
$53$	6.58345	−	3.80096i	0.904307	−	0.522102i	0.878595	+	0.477567i	$0.158481\pi$
$54$	1.01009	+	5.09703i	0.137457	+	0.693618i
$55$	−2.67461	−	1.59577i	−0.360645	−	0.215173i
$56$	−4.59876			−0.614536
$57$	2.28960	+	7.19428i	0.303265	+	0.952906i
$58$			2.70684i			0.355425i
$59$	−0.292964	+	0.507429i	−0.0381407	+	0.0660617i	−0.884466	−	0.466605i	$-0.845477\pi$
$59$	−0.292964	+	0.507429i	−0.0381407	+	0.0660617i	0.846325	+	0.532667i	$0.178810\pi$
$60$	3.70206	+	1.13787i	0.477934	+	0.146898i
$61$	−4.04082	−	6.99890i	−0.517374	−	0.896118i	−0.999796	−	0.0201790i	$-0.993576\pi$
$61$	−4.04082	−	6.99890i	−0.517374	−	0.896118i	0.482423	−	0.875939i	$-0.339757\pi$
$62$	−2.08020	+	3.60302i	−0.264186	+	0.457584i
$63$	7.41826	−	11.6322i	0.934612	−	1.46551i
$64$	−1.00000			−0.125000
$65$	−13.9335	−	0.199853i	−1.72823	−	0.0247887i
$66$	−1.74308	+	1.66784i	−0.214558	+	0.205297i
$67$	7.23104	+	12.5245i	0.883412	+	1.53011i	0.847523	+	0.530758i	$0.178093\pi$
$67$	7.23104	+	12.5245i	0.883412	+	1.53011i	0.0358883	+	0.999356i	$0.488574\pi$
$68$	0.479739			0.0581769
$69$	1.75876	+	7.19485i	0.211730	+	0.866158i
$70$	−5.01332	−	8.97829i	−0.599207	−	1.07311i
$71$	−5.36334	+	9.28957i	−0.636511	+	1.10247i	0.349682	+	0.936868i	$0.386290\pi$
$71$	−5.36334	+	9.28957i	−0.636511	+	1.10247i	−0.986193	+	0.165601i	$0.947044\pi$
$72$	1.61310	−	2.52941i	0.190105	−	0.298094i
$73$	−7.91151	−	4.56771i	−0.925972	−	0.534610i	−0.0404369	−	0.999182i	$-0.512875\pi$
$73$	−7.91151	−	4.56771i	−0.925972	−	0.534610i	−0.885536	+	0.464572i	$0.846208\pi$
$74$	1.79359	+	1.03553i	0.208501	+	0.120378i
$75$	1.81430	+	8.46808i	0.209497	+	0.977809i
$76$	1.91646	−	3.91499i	0.219833	−	0.449081i
$77$	6.40535			0.729957
$78$	−3.02291	+	10.3620i	−0.342277	+	1.17326i
$79$	−9.30867	−	5.37436i	−1.04731	−	0.604663i	−0.125413	−	0.992105i	$-0.540026\pi$
$79$	−9.30867	−	5.37436i	−1.04731	−	0.604663i	−0.921894	+	0.387442i	$0.873359\pi$
$80$	−1.09015	−	1.95233i	−0.121882	−	0.218277i
$81$	3.79583	+	8.16037i	0.421759	+	0.906708i
$82$	−9.54997	+	5.51368i	−1.05462	+	0.608884i
$83$	−5.37122			−0.589568			−0.294784	−	0.955564i	$-0.595248\pi$
$83$	−5.37122			−0.589568			−0.294784	+	0.955564i	$0.595248\pi$
$84$	−7.73747	+	1.89140i	−0.844227	+	0.206369i
$85$	0.522986	+	0.936608i	0.0567258	+	0.101589i
$86$	2.97701	+	5.15633i	0.321019	+	0.556021i
$87$	1.11328	+	4.55429i	0.119356	+	0.488271i
$88$	1.39284			0.148477
$89$	0.964199	+	1.67004i	0.102205	+	0.177024i	0.912593	−	0.408870i	$-0.134077\pi$
$89$	0.964199	+	1.67004i	0.102205	+	0.177024i	−0.810388	+	0.585894i	$0.800744\pi$
$90$	6.69675	+	0.391869i	0.705899	+	0.0413066i
$91$	24.8193	−	14.3294i	2.60177	−	1.50213i
$92$	2.13813	−	3.70335i	0.222915	−	0.386101i
$93$	−2.01810	+	6.91768i	−0.209267	+	0.717330i
$94$			6.39471i			0.659564i
$95$	9.73257	−	0.526357i	0.998541	−	0.0540031i
$96$	−1.68251	+	0.411285i	−0.171721	+	0.0419766i
$97$	7.30058	−	12.6450i	0.741261	−	1.28390i	−0.210660	−	0.977559i	$-0.567561\pi$
$97$	7.30058	−	12.6450i	0.741261	−	1.28390i	0.951921	−	0.306343i	$-0.0991053\pi$
$98$	12.2531	+	7.07431i	1.23775	+	0.714613i
$99$	−2.24679	+	3.52307i	−0.225811	+	0.354082i
$100$	2.62316	−	4.25664i	0.262316	−	0.425664i
$101$	13.5006	−	7.79457i	1.34336	−	0.775589i	0.356061	−	0.934463i	$-0.384120\pi$
$101$	13.5006	−	7.79457i	1.34336	−	0.775589i	0.987299	+	0.158874i	$0.0507863\pi$
$102$	0.807167	−	0.197310i	0.0799214	−	0.0195366i
$103$	14.6267			1.44121			0.720605	−	0.693345i	$-0.243864\pi$
$103$	14.6267			1.44121			0.720605	+	0.693345i	$0.243864\pi$
$104$	5.39696	−	3.11593i	0.529215	−	0.305543i
$105$	−12.1276	−	13.0442i	−1.18353	−	1.27298i
$106$	−7.60192			−0.738364
$107$		−	5.90734i		−	0.571084i	−0.958366	−	0.285542i	$-0.907826\pi$
$107$		−	5.90734i		−	0.571084i	0.958366	−	0.285542i	$-0.0921737\pi$
$108$	1.67375	−	4.91920i	0.161056	−	0.473351i
$109$	−3.32769	−	1.92124i	−0.318735	−	0.184022i	0.332094	−	0.943246i	$-0.392245\pi$
$109$	−3.32769	−	1.92124i	−0.318735	−	0.184022i	−0.650829	+	0.759225i	$0.725578\pi$
$110$	1.51840	+	2.71928i	0.144774	+	0.259273i
$111$	3.44363	+	1.00461i	0.326855	+	0.0953537i
$112$	3.98265	+	2.29938i	0.376325	+	0.217271i
$113$			13.9360i			1.31098i	0.755202	+	0.655492i	$0.227539\pi$
$113$			13.9360i			1.31098i	−0.755202	+	0.655492i	$0.772461\pi$
$114$	1.61429	−	7.37523i	0.151192	−	0.690754i
$115$	9.56102	+	0.137137i	0.891570	+	0.0127881i
$116$	1.35342	−	2.34419i	0.125662	−	0.217653i
$117$	−0.824345	+	18.6774i	−0.0762107	+	1.72673i
$118$	0.507429	−	0.292964i	0.0467126	−	0.0269696i
$119$	−1.91063	−	1.10310i	−0.175147	−	0.101121i
$120$	−2.63715	−	2.83645i	−0.240737	−	0.258931i
$121$	9.05999			0.823636
$122$			8.08164i			0.731677i
$123$	−13.8002	+	13.2046i	−1.24433	+	1.19062i
$124$	3.60302	−	2.08020i	0.323561	−	0.186808i
$125$	11.1700	+	0.480910i	0.999074	+	0.0430139i
$126$	−12.2405	+	6.36462i	−1.09047	+	0.567005i
$127$	2.52200	+	4.36823i	0.223791	+	0.387617i	0.955956	−	0.293510i	$-0.0948234\pi$
$127$	2.52200	+	4.36823i	0.223791	+	0.387617i	−0.732165	+	0.681127i	$0.761490\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	7.12957	+	7.45118i	0.627724	+	0.656040i
$130$	11.9668	+	7.13980i	1.04956	+	0.626202i
$131$	−6.42795	−	3.71118i	−0.561612	−	0.324247i	0.192180	−	0.981360i	$-0.438444\pi$
$131$	−6.42795	−	3.71118i	−0.561612	−	0.324247i	−0.753792	+	0.657113i	$0.771778\pi$
$132$	2.34347	−	0.572855i	0.203973	−	0.0498606i
$133$	−16.6346	+	11.1854i	−1.44241	+	0.969894i
$134$		−	14.4621i		−	1.24933i
$135$	11.4285	−	2.09495i	0.983611	−	0.180305i
$136$	−0.415466	−	0.239870i	−0.0356260	−	0.0205687i
$137$	−4.75833	−	8.24166i	−0.406531	−	0.704133i	0.587967	−	0.808885i	$-0.299928\pi$
$137$	−4.75833	−	8.24166i	−0.406531	−	0.704133i	−0.994498	+	0.104752i	$0.966595\pi$
$138$	2.07429	−	7.11031i	0.176576	−	0.605269i
$139$	−2.16277	−	3.74604i	−0.183444	−	0.317735i	0.759607	−	0.650382i	$-0.225391\pi$
$139$	−2.16277	−	3.74604i	−0.183444	−	0.317735i	−0.943051	+	0.332648i	$0.892058\pi$
$140$	−0.147480	+	10.2821i	−0.0124643	+	0.868995i
$141$	2.63005	+	10.7592i	0.221490	+	0.906086i
$142$	9.28957	−	5.36334i	0.779563	−	0.450081i
$143$	−7.51711	+	4.34000i	−0.628612	+	0.362929i
$144$	−2.66169	+	1.38398i	−0.221807	+	0.115332i
$145$	6.05205	+	0.0868068i	0.502596	+	0.00720891i
$146$	4.56771	+	7.91151i	0.378027	+	0.654761i
$147$	23.5255	+	6.86310i	1.94035	+	0.566059i
$148$	−1.03553	−	1.79359i	−0.0851200	−	0.147432i
$149$	−8.69619	−	5.02075i	−0.712420	−	0.411316i	0.0995366	−	0.995034i	$-0.468264\pi$
$149$	−8.69619	−	5.02075i	−0.712420	−	0.411316i	−0.811956	+	0.583718i	$0.801597\pi$
$150$	2.66281	−	8.24072i	0.217417	−	0.672852i
$151$			8.52964i			0.694132i	0.937841	+	0.347066i	$0.112822\pi$
$151$			8.52964i			0.694132i	−0.937841	+	0.347066i	$0.887178\pi$
$152$	−3.61720	+	2.43225i	−0.293394	+	0.197282i
$153$	1.27692	−	0.663952i	0.103233	−	0.0536773i
$154$	−5.54719	−	3.20267i	−0.447006	−	0.258079i
$155$	7.98906	+	4.76655i	0.641697	+	0.382858i
$156$	7.79890	−	7.46229i	0.624412	−	0.597461i
$157$	−3.83879	−	2.21633i	−0.306369	−	0.176882i	0.338932	−	0.940811i	$-0.389934\pi$
$157$	−3.83879	−	2.21633i	−0.306369	−	0.176882i	−0.645300	+	0.763929i	$0.723268\pi$
$158$	5.37436	+	9.30867i	0.427561	+	0.740558i
$159$	−12.7903	+	3.12656i	−1.01434	+	0.247952i
$160$	−0.0320694	+	2.23584i	−0.00253531	+	0.176759i
$161$	−17.0308	+	9.83275i	−1.34222	+	0.774929i
$162$	0.792902	−	8.96500i	0.0622962	−	0.704357i
$163$		−	13.3074i		−	1.04232i	−0.853460	−	0.521158i	$-0.825500\pi$
$163$		−	13.3074i		−	1.04232i	0.853460	−	0.521158i	$-0.174500\pi$
$164$	11.0274			0.861092
$165$	3.67313	+	3.95073i	0.285953	+	0.307564i
$166$	4.65161	+	2.68561i	0.361035	+	0.208444i
$167$	9.26118	−	5.34695i	0.716652	−	0.413759i	−0.0968673	−	0.995297i	$-0.530882\pi$
$167$	9.26118	−	5.34695i	0.716652	−	0.413759i	0.813519	+	0.581538i	$0.197549\pi$
$168$	7.64655	+	2.23073i	0.589944	+	0.172105i
$169$	−12.9181	+	22.3748i	−0.993700	+	1.72114i
$170$	0.0153850	−	1.07262i	0.00117997	−	0.0822662i
$171$	−0.317269	−	13.0728i	−0.0242621	−	0.999706i
$172$		−	5.95401i		−	0.453989i
$173$	−16.5086	−	9.53126i	−1.25513	−	0.724648i	−0.283004	−	0.959119i	$-0.591331\pi$
$173$	−16.5086	−	9.53126i	−1.25513	−	0.724648i	−0.972123	+	0.234471i	$0.924664\pi$
$174$	1.31301	−	4.50077i	0.0995392	−	0.341202i
$175$	−20.2348	+	10.9211i	−1.52961	+	0.825554i
$176$	−1.20624	−	0.696421i	−0.0909235	−	0.0524947i
$177$	0.733263	−	0.701614i	0.0551155	−	0.0527365i
$178$		−	1.92840i		−	0.144540i
$179$	10.6080			0.792881			0.396440	−	0.918060i	$-0.370245\pi$
$179$	10.6080			0.792881			0.396440	+	0.918060i	$0.370245\pi$
$180$	−5.60362	−	3.68774i	−0.417669	−	0.274868i
$181$	−3.00128	+	1.73279i	−0.223083	+	0.128797i	−0.607377	−	0.794414i	$-0.707778\pi$
$181$	−3.00128	+	1.73279i	−0.223083	+	0.128797i	0.384294	+	0.923211i	$0.374445\pi$
$182$	−28.6589			−2.12434
$183$	3.32386	+	13.5974i	0.245707	+	1.00515i
$184$	−3.70335	+	2.13813i	−0.273014	+	0.157625i
$185$	2.37280	−	3.97697i	0.174451	−	0.292393i
$186$	5.20657	−	4.98184i	0.381764	−	0.365286i
$187$	0.578679	+	0.334100i	0.0423172	+	0.0244318i
$188$	3.19735	−	5.53798i	0.233191	−	0.403899i
$189$	−17.9771	+	15.7429i	−1.30764	+	1.14513i
$190$	−8.69183	−	4.41045i	−0.630572	−	0.319967i
$191$			12.3355i			0.892563i	0.894893	+	0.446281i	$0.147252\pi$
$191$			12.3355i			0.892563i	−0.894893	+	0.446281i	$0.852748\pi$
$192$	1.66274	+	0.485072i	0.119998	+	0.0350071i
$193$	6.20828	−	10.7531i	0.446882	−	0.774022i	−0.551300	−	0.834307i	$-0.685868\pi$
$193$	6.20828	−	10.7531i	0.446882	−	0.774022i	0.998181	+	0.0602858i	$0.0192012\pi$
$194$	−12.6450	+	7.30058i	−0.907856	+	0.524151i
$195$	23.0708	+	7.09103i	1.65213	+	0.507799i
$196$	−7.07431	−	12.2531i	−0.505308	−	0.875219i
$197$	−1.06295			−0.0757323			−0.0378661	−	0.999283i	$-0.512056\pi$
$197$	−1.06295			−0.0757323			−0.0378661	+	0.999283i	$0.512056\pi$
$198$	3.70731	−	1.92767i	0.263467	−	0.136994i
$199$	−1.54641	−	2.67846i	−0.109622	−	0.189871i	0.805995	−	0.591922i	$-0.201631\pi$
$199$	−1.54641	−	2.67846i	−0.109622	−	0.189871i	−0.915617	+	0.402051i	$0.868297\pi$
$200$	−4.40005	+	2.37478i	−0.311130	+	0.167922i
$201$	−5.94804	−	24.3326i	−0.419542	−	1.71629i
$202$	−15.5891			−1.09685
$203$	−10.7804	+	6.22406i	−0.756634	+	0.436843i
$204$	−0.797682	−	0.232708i	−0.0558489	−	0.0162928i
$205$	12.0214	+	21.5290i	0.839613	+	1.50365i
$206$	−12.6671	−	7.31335i	−0.882558	−	0.509545i
$207$	0.565659	−	12.8163i	0.0393160	−	0.890794i
$208$	−6.23187			−0.432102
$209$	5.03819	−	3.38774i	0.348499	−	0.234335i
$210$	3.98074	+	17.3604i	0.274697	+	1.19798i
$211$	7.20865	+	4.16192i	0.496264	+	0.286518i	0.727169	−	0.686458i	$-0.240835\pi$
$211$	7.20865	+	4.16192i	0.496264	+	0.286518i	−0.230905	+	0.972976i	$0.574169\pi$
$212$	6.58345	+	3.80096i	0.452154	+	0.261051i
$213$	13.4239	−	12.8445i	0.919794	−	0.880093i
$214$	−2.95367	+	5.11591i	−0.201909	+	0.349716i
$215$	11.6242	−	6.49075i	0.792763	−	0.442665i
$216$	−3.90911	+	3.42328i	−0.265981	+	0.232925i
$217$	−19.1327			−1.29882
$218$	1.92124	+	3.32769i	0.130123	+	0.225380i
$219$	10.9391	+	11.4326i	0.739197	+	0.772542i
$220$	0.0446676	−	3.11417i	0.00301149	−	0.209957i
$221$	2.98967			0.201107
$222$	−2.47997	−	2.59184i	−0.166445	−	0.173953i
$223$	−5.54000	+	9.59556i	−0.370986	+	0.642566i	−0.989717	−	0.143036i	$-0.954314\pi$
$223$	−5.54000	+	9.59556i	−0.370986	+	0.642566i	0.618732	+	0.785602i	$0.287647\pi$
$224$	−2.29938	−	3.98265i	−0.153634	−	0.266102i
$225$	1.09092	−	14.9603i	0.0727278	−	0.997352i
$226$	6.96798	−	12.0689i	0.463503	−	0.802811i
$227$			9.47873i			0.629126i	0.949237	+	0.314563i	$0.101858\pi$
$227$			9.47873i			0.629126i	−0.949237	+	0.314563i	$0.898142\pi$
$228$	−5.08563	+	5.58000i	−0.336804	+	0.369544i
$229$	−15.6438			−1.03377			−0.516885	−	0.856055i	$-0.672908\pi$
$229$	−15.6438			−1.03377			−0.516885	+	0.856055i	$0.672908\pi$
$230$	−8.21152	−	4.89927i	−0.541451	−	0.323049i
$231$	−10.6504	−	3.10706i	−0.700747	−	0.204429i
$232$	−2.34419	+	1.35342i	−0.153904	+	0.0888563i
$233$	7.00038	−	12.1250i	0.458610	−	0.794336i	−0.540278	−	0.841487i	$-0.681681\pi$
$233$	7.00038	−	12.1250i	0.458610	−	0.794336i	0.998888	+	0.0471506i	$0.0150141\pi$
$234$	10.0526	−	15.7630i	0.657160	−	1.03046i
$235$	14.2975	+	0.205075i	0.932668	+	0.0133776i
$236$	−0.585929			−0.0381407
$237$	12.8709	+	13.4515i	0.836058	+	0.873772i
$238$	1.10310	+	1.91063i	0.0715036	+	0.123848i
$239$		−	6.56660i		−	0.424758i	−0.977187	−	0.212379i	$-0.931879\pi$
$239$		−	6.56660i		−	0.424758i	0.977187	−	0.212379i	$-0.0681211\pi$
$240$	0.865610	+	3.77501i	0.0558749	+	0.243676i
$241$	9.33253	−	5.38814i	0.601161	−	0.347080i	−0.168337	−	0.985729i	$-0.553840\pi$
$241$	9.33253	−	5.38814i	0.601161	−	0.347080i	0.769498	+	0.638649i	$0.220506\pi$
$242$	−7.84618	−	4.53000i	−0.504372	−	0.291199i
$243$	−2.35311	−	15.4098i	−0.150952	−	0.988541i
$244$	4.04082	−	6.99890i	0.258687	−	0.448059i
$245$	16.2100	−	27.1690i	1.03562	−	1.73576i
$246$	18.5536	−	4.53539i	1.18294	−	0.289166i
$247$	11.9431	−	24.3977i	0.759923	−	1.55239i
$248$	−4.16041			−0.264186
$249$	8.93094	+	2.60543i	0.565975	+	0.165112i
$250$	−9.43304	−	6.00148i	−0.596598	−	0.379567i
$251$	5.05969	−	2.92121i	0.319365	−	0.184385i	−0.331745	−	0.943369i	$-0.607637\pi$
$251$	5.05969	−	2.92121i	0.319365	−	0.184385i	0.651109	+	0.758984i	$0.274304\pi$
$252$	13.7829	+	0.608319i	0.868239	+	0.0383205i
$253$	5.15818	−	2.97807i	0.324292	−	0.187230i
$254$		−	5.04399i		−	0.316488i
$255$	−0.415267	−	1.81102i	−0.0260050	−	0.113411i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−23.3067	+	13.4561i	−1.45383	+	0.839371i	−0.998696	−	0.0510509i	$-0.983743\pi$
$257$	−23.3067	+	13.4561i	−1.45383	+	0.839371i	−0.455137	+	0.890422i	$0.650410\pi$
$258$	−2.44880	−	10.0177i	−0.152456	−	0.623675i
$259$			9.52431i			0.591812i
$260$	−6.79365	−	12.1666i	−0.421324	−	0.754544i
$261$	0.358058	−	8.11262i	0.0221632	−	0.502158i
$262$	3.71118	+	6.42795i	0.229277	+	0.397120i
$263$	3.27942	−	5.68013i	0.202218	−	0.350252i	−0.747025	−	0.664796i	$-0.768518\pi$
$263$	3.27942	−	5.68013i	0.202218	−	0.350252i	0.949243	+	0.314544i	$0.101852\pi$
$264$	−2.31593	−	0.675629i	−0.142536	−	0.0415821i
$265$	−0.243789	+	16.9967i	−0.0149759	+	1.04410i
$266$	19.9987	−	1.36948i	1.22620	−	0.0839683i
$267$	−0.793122	−	3.24455i	−0.0485383	−	0.198563i
$268$	−7.23104	+	12.5245i	−0.441706	+	0.765057i
$269$	−10.5970	+	18.3545i	−0.646108	+	1.11909i	0.337937	+	0.941169i	$0.390271\pi$
$269$	−10.5970	+	18.3545i	−0.646108	+	1.11909i	−0.984045	+	0.177922i	$0.943062\pi$
$270$	−10.9449	−	3.89998i	−0.666083	−	0.237345i
$271$	3.82071	−	6.61767i	0.232092	−	0.401995i	−0.726332	−	0.687344i	$-0.758776\pi$
$271$	3.82071	−	6.61767i	0.232092	−	0.401995i	0.958423	+	0.285350i	$0.0921097\pi$
$272$	0.239870	+	0.415466i	0.0145442	+	0.0251914i
$273$	−48.2189	+	11.7870i	−2.91834	+	0.713381i
$274$			9.51665i			0.574922i
$275$	6.12857	−	3.30769i	0.369567	−	0.199461i
$276$	−5.35154	+	5.12056i	−0.322125	+	0.308221i
$277$			9.73807i			0.585104i	0.956250	+	0.292552i	$0.0945044\pi$
$277$			9.73807i			0.585104i	−0.956250	+	0.292552i	$0.905496\pi$
$278$			4.32555i			0.259429i
$279$	6.71115	−	10.5234i	0.401786	−	0.630018i
$280$	5.26877	−	8.83081i	0.314869	−	0.527742i
$281$	10.2574	+	17.7663i	0.611904	+	1.05985i	0.990919	+	0.134459i	$0.0429296\pi$
$281$	10.2574	+	17.7663i	0.611904	+	1.05985i	−0.379015	+	0.925391i	$0.623737\pi$
$282$	3.10190	−	10.6327i	0.184715	−	0.633171i
$283$	0.395082	+	0.228101i	0.0234852	+	0.0135592i	0.511697	−	0.859166i	$-0.329017\pi$
$283$	0.395082	+	0.228101i	0.0234852	+	0.0135592i	−0.488211	+	0.872725i	$0.662351\pi$
$284$	−10.7267			−0.636511
$285$	−16.4381	−	3.84580i	−0.973707	−	0.227806i
$286$	8.68001			0.513260
$287$	−43.9180	−	25.3561i	−2.59240	−	1.49672i
$288$	2.99708	+	0.132279i	0.176605	+	0.00779461i
$289$	8.38493	+	14.5231i	0.493231	+	0.854301i
$290$	−5.19783	−	3.10120i	−0.305227	−	0.182109i
$291$	−18.2727	+	17.4840i	−1.07116	+	1.02493i
$292$		−	9.13543i		−	0.534610i
$293$		−	21.4226i		−	1.25152i	−0.780015	−	0.625761i	$-0.784788\pi$
$293$		−	21.4226i		−	1.25152i	0.780015	−	0.625761i	$-0.215212\pi$
$294$	−16.9421	−	17.7064i	−0.988084	−	1.03266i
$295$	−0.638748	−	1.14392i	−0.0371893	−	0.0666019i
$296$			2.07106i			0.120378i
$297$	5.44477	−	4.76809i	0.315938	−	0.276673i
$298$	5.02075	+	8.69619i	0.290844	+	0.503757i
$299$	13.3245	−	23.0788i	0.770578	−	1.33468i
$300$	−6.42642	+	5.80527i	−0.371029	+	0.335167i
$301$	−13.6906	+	23.7127i	−0.789110	+	1.36678i
$302$	4.26482	−	7.38688i	0.245413	−	0.425067i
$303$	−26.2289	+	6.41159i	−1.50681	+	0.368336i
$304$	4.34871	−	0.297794i	0.249416	−	0.0170796i
$305$	18.0692	+	0.259174i	1.03464	+	0.0148402i
$306$	−1.43782	−	0.0634594i	−0.0821946	−	0.00362773i
$307$	1.61128	−	2.79083i	0.0919608	−	0.159281i	−0.816375	−	0.577522i	$-0.804020\pi$
$307$	1.61128	−	2.79083i	0.0919608	−	0.159281i	0.908336	+	0.418241i	$0.137353\pi$
$308$	3.20267	+	5.54719i	0.182489	+	0.316081i
$309$	−24.3204	−	7.09500i	−1.38354	−	0.403621i
$310$	−4.53545	−	8.12248i	−0.257596	−	0.461326i
$311$			18.9599i			1.07512i	0.843227	+	0.537558i	$0.180653\pi$
$311$			18.9599i			1.07512i	−0.843227	+	0.537558i	$0.819347\pi$
$312$	−10.4852	+	2.56308i	−0.593607	+	0.145106i
$313$	21.1307	−	12.1998i	1.19438	−	0.689575i	0.235083	−	0.971975i	$-0.424464\pi$
$313$	21.1307	−	12.1998i	1.19438	−	0.689575i	0.959297	+	0.282400i	$0.0911306\pi$
$314$	2.21633	+	3.83879i	0.125075	+	0.216635i
$315$	13.8377	+	27.5718i	0.779666	+	1.55350i
$316$		−	10.7487i		−	0.604663i
$317$	5.31295	−	3.06743i	0.298405	−	0.172284i	−0.343321	−	0.939218i	$-0.611552\pi$
$317$	5.31295	−	3.06743i	0.298405	−	0.172284i	0.641726	+	0.766934i	$0.278219\pi$
$318$	12.6400	+	3.68748i	0.708817	+	0.206784i
$319$	3.26509	−	1.88510i	0.182810	−	0.105545i
$320$	1.14569	−	1.92026i	0.0640461	−	0.107346i
$321$	−2.86549	+	9.82238i	−0.159936	+	0.548232i
$322$	19.6655			1.09592
$323$	−2.08625	+	0.142863i	−0.116082	+	0.00794913i
$324$	−5.16918	+	7.36747i	−0.287176	+	0.409304i
$325$	16.3472	−	26.5268i	0.906780	−	1.47144i
$326$	−6.65370	+	11.5245i	−0.368514	+	0.638285i
$327$	4.60114	+	4.80870i	0.254444	+	0.265922i
$328$	−9.54997	−	5.51368i	−0.527309	−	0.304442i
$329$	−25.4679	+	14.7039i	−1.40409	+	0.810651i
$330$	−1.20566	−	5.25799i	−0.0663693	−	0.289443i
$331$			13.0072i			0.714940i	0.933925	+	0.357470i	$0.116361\pi$
$331$			13.0072i			0.714940i	−0.933925	+	0.357470i	$0.883639\pi$
$332$	−2.68561	−	4.65161i	−0.147392	−	0.255290i
$333$	−5.23856	−	3.34082i	−0.287071	−	0.183076i
$334$	−10.6939			−0.585144
$335$	−32.3349	−	0.463791i	−1.76664	−	0.0253396i
$336$	−5.50674	−	5.75515i	−0.300417	−	0.313969i
$337$	−4.67204	+	8.09221i	−0.254502	+	0.440811i	−0.964760	−	0.263131i	$-0.915245\pi$
$337$	−4.67204	+	8.09221i	−0.254502	+	0.440811i	0.710258	+	0.703941i	$0.248578\pi$
$338$	22.3748	−	12.9181i	1.21703	−	0.702652i
$339$	6.75994	−	23.1719i	0.367150	−	1.25852i
$340$	−0.549634	+	0.921223i	−0.0298081	+	0.0499603i
$341$	5.79479			0.313806
$342$	−6.26166	+	11.4801i	−0.338592	+	0.620770i
$343$			32.8748i			1.77507i
$344$	−2.97701	+	5.15633i	−0.160509	+	0.278011i
$345$	−15.8310	−	4.86581i	−0.852311	−	0.261966i
$346$	9.53126	+	16.5086i	0.512403	+	0.887509i
$347$	−16.1143	+	27.9108i	−0.865062	+	1.49833i	0.00192381	+	0.999998i	$0.499388\pi$
$347$	−16.1143	+	27.9108i	−0.865062	+	1.49833i	−0.866986	+	0.498333i	$0.833946\pi$
$348$	−3.38749	+	3.24127i	−0.181588	+	0.173751i
$349$	11.9647			0.640457			0.320228	−	0.947340i	$-0.396240\pi$
$349$	11.9647			0.640457			0.320228	+	0.947340i	$0.396240\pi$
$350$	22.9844	+	0.659482i	1.22857	+	0.0352508i
$351$	10.4306	−	30.6558i	0.556743	−	1.63629i
$352$	0.696421	+	1.20624i	0.0371193	+	0.0642926i
$353$	3.69736			0.196791			0.0983954	−	0.995147i	$-0.468629\pi$
$353$	3.69736			0.196791			0.0983954	+	0.995147i	$0.468629\pi$
$354$	−0.985832	+	0.240984i	−0.0523964	+	0.0128081i
$355$	−11.6936	−	20.9420i	−0.620634	−	1.11148i
$356$	−0.964199	+	1.67004i	−0.0511025	+	0.0885121i
$357$	2.64180	+	2.76097i	0.139819	+	0.146126i
$358$	−9.18682	−	5.30401i	−0.485538	−	0.280326i
$359$	2.86979	+	1.65687i	0.151462	+	0.0874464i	0.573815	−	0.818985i	$-0.305463\pi$
$359$	2.86979	+	1.65687i	0.151462	+	0.0874464i	−0.422354	+	0.906431i	$0.638796\pi$
$360$	3.00901	+	5.99549i	0.158589	+	0.315990i
$361$	−7.16828	+	17.5959i	−0.377278	+	0.926100i
$362$	3.46558			0.182147
$363$	−15.0644	−	4.39475i	−0.790677	−	0.230665i
$364$	24.8193	+	14.3294i	1.30089	+	0.751067i
$365$	17.8353	−	9.95895i	0.933545	−	0.521275i
$366$	3.92018	−	13.4377i	0.204911	−	0.702398i
$367$	−13.4156	+	7.74551i	−0.700290	+	0.404312i	−0.807455	−	0.589929i	$-0.799156\pi$
$367$	−13.4156	+	7.74551i	−0.700290	+	0.404312i	0.107166	+	0.994241i	$0.465822\pi$
$368$	4.27626			0.222915
$369$	29.3514	−	15.2617i	1.52797	−	0.794491i
$370$	−4.04339	+	2.25776i	−0.210206	+	0.117375i
$371$	−17.4797	−	30.2758i	−0.907501	−	1.57184i
$372$	−6.99994	+	1.71112i	−0.362930	+	0.0887172i
$373$	−4.72434			−0.244617			−0.122308	−	0.992492i	$-0.539030\pi$
$373$	−4.72434			−0.244617			−0.122308	+	0.992492i	$0.539030\pi$
$374$	−0.334100	−	0.578679i	−0.0172759	−	0.0299228i
$375$	−18.3395	−	6.21788i	−0.947049	−	0.321090i
$376$	−5.53798	+	3.19735i	−0.285600	+	0.164891i
$377$	8.43433	−	14.6087i	0.434390	−	0.752386i
$378$	23.4400	−	4.64519i	1.20563	−	0.238923i
$379$			9.54162i			0.490120i	0.969508	+	0.245060i	$0.0788077\pi$
$379$			9.54162i			0.490120i	−0.969508	+	0.245060i	$0.921192\pi$
$380$	5.32212	+	8.16548i	0.273019	+	0.418880i
$381$	−2.07452	−	8.48658i	−0.106281	−	0.434780i
$382$	6.16773	−	10.6828i	0.315569	−	0.546581i
$383$	−3.26903	−	1.88738i	−0.167040	−	0.0964404i	0.414150	−	0.910209i	$-0.364079\pi$
$383$	−3.26903	−	1.88738i	−0.167040	−	0.0964404i	−0.581189	+	0.813768i	$0.697412\pi$
$384$	−1.19744	−	1.25145i	−0.0611066	−	0.0638630i
$385$	−7.33856	+	12.2999i	−0.374007	+	0.626862i
$386$	−10.7531	+	6.20828i	−0.547316	+	0.315993i
$387$	−8.24026	−	15.8477i	−0.418876	−	0.805586i
$388$	14.6012			0.741261
$389$	17.3261	−	10.0032i	0.878468	−	0.507183i	0.00831472	−	0.999965i	$-0.497353\pi$
$389$	17.3261	−	10.0032i	0.878468	−	0.507183i	0.870153	+	0.492782i	$0.164020\pi$
$390$	−16.4344	−	17.6764i	−0.832186	−	0.895079i
$391$	−2.05149			−0.103748
$392$			14.1486i			0.714613i
$393$	8.88782	+	9.28874i	0.448331	+	0.468555i
$394$	0.920544	+	0.531476i	0.0463763	+	0.0267754i
$395$	20.9850	−	11.7177i	1.05587	−	0.589580i
$396$	−4.17446	−	0.184244i	−0.209775	−	0.00925859i
$397$	24.4000	+	14.0874i	1.22460	+	0.707024i	0.965896	−	0.258932i	$-0.0833705\pi$
$397$	24.4000	+	14.0874i	1.22460	+	0.707024i	0.258706	+	0.965956i	$0.416704\pi$
$398$			3.09282i			0.155029i
$399$	33.0848	−	10.5293i	1.65631	−	0.527127i
$400$	4.99794	+	0.143404i	0.249897	+	0.00717021i
$401$	5.25498	−	9.10189i	0.262421	−	0.454527i	−0.704464	−	0.709740i	$-0.748812\pi$
$401$	5.25498	−	9.10189i	0.262421	−	0.454527i	0.966885	+	0.255213i	$0.0821457\pi$
$402$	−7.01515	+	24.0467i	−0.349884	+	1.19934i
$403$	22.4536	−	12.9636i	1.11849	−	0.645761i
$404$	13.5006	+	7.79457i	0.671680	+	0.387795i
$405$	−20.0189	−	2.06030i	−0.994746	−	0.102377i
$406$	12.4481			0.617789
$407$		−	2.88466i		−	0.142987i
$408$	0.574459	+	0.600372i	0.0284399	+	0.0297229i
$409$	0.617398	−	0.356455i	0.0305284	−	0.0176256i	−0.484658	−	0.874704i	$-0.661056\pi$
$409$	0.617398	−	0.356455i	0.0305284	−	0.0176256i	0.515187	+	0.857078i	$0.327723\pi$
$410$	0.353641	−	24.6554i	0.0174651	−	1.21764i
$411$	3.91406	+	16.0119i	0.193066	+	0.789808i
$412$	7.31335	+	12.6671i	0.360303	+	0.624063i
$413$	2.33355	+	1.34727i	0.114826	+	0.0662950i
$414$	−6.89802	+	10.8164i	−0.339019	+	0.531597i
$415$	6.15376	−	10.3141i	0.302076	−	0.506300i
$416$	5.39696	+	3.11593i	0.264608	+	0.152771i
$417$	1.77903	+	7.27779i	0.0871197	+	0.356395i
$418$	−6.05707	+	0.414779i	−0.296261	+	0.0202875i
$419$			27.4307i			1.34008i	0.742325	+	0.670040i	$0.233723\pi$
$419$			27.4307i			1.34008i	−0.742325	+	0.670040i	$0.766277\pi$
$420$	5.23278	−	17.0249i	0.255333	−	0.830730i
$421$	9.13416	+	5.27361i	0.445172	+	0.257020i	0.705789	−	0.708422i	$-0.250593\pi$
$421$	9.13416	+	5.27361i	0.445172	+	0.257020i	−0.260617	+	0.965442i	$0.583926\pi$
$422$	−4.16192	−	7.20865i	−0.202599	−	0.350912i
$423$	0.845885	−	19.1655i	0.0411284	−	0.931857i
$424$	−3.80096	−	6.58345i	−0.184591	−	0.319721i
$425$	−2.39771	−	0.0687966i	−0.116306	−	0.00333713i
$426$	−18.0477	+	4.41172i	−0.874416	+	0.213749i
$427$	−32.1863	+	18.5828i	−1.55760	+	0.899283i
$428$	5.11591	−	2.95367i	0.247287	−	0.142771i
$429$	14.6042	−	3.56996i	0.705098	−	0.172359i
$430$	−13.3122	−	0.190942i	−0.641972	−	0.00920804i
$431$	−10.8918	−	18.8652i	−0.524640	−	0.908702i	−0.999588	−	0.0286889i	$-0.990867\pi$
$431$	−10.8918	−	18.8652i	−0.524640	−	0.908702i	0.474949	−	0.880013i	$-0.342467\pi$
$432$	5.09703	−	1.01009i	0.245231	−	0.0485982i
$433$	−7.67259	−	13.2893i	−0.368721	−	0.638644i	0.620645	−	0.784092i	$-0.286871\pi$
$433$	−7.67259	−	13.2893i	−0.368721	−	0.638644i	−0.989366	+	0.145448i	$0.953538\pi$
$434$	16.5694	+	9.56637i	0.795359	+	0.459200i
$435$	−10.0209	−	3.08002i	−0.480465	−	0.147676i
$436$		−	3.84249i		−	0.184022i
$437$	−8.19528	+	16.7415i	−0.392033	+	0.800856i
$438$	−3.75727	−	15.3705i	−0.179529	−	0.734429i
$439$	−20.9419	−	12.0908i	−0.999502	−	0.577063i	−0.0914012	−	0.995814i	$-0.529135\pi$
$439$	−20.9419	−	12.0908i	−0.999502	−	0.577063i	−0.908101	+	0.418751i	$0.862468\pi$
$440$	−1.59577	+	2.67461i	−0.0760752	+	0.127507i
$441$	−35.7877	−	22.8231i	−1.70417	−	1.08682i
$442$	−2.58913	−	1.49484i	−0.123153	−	0.0711021i
$443$	3.71967	+	6.44266i	0.176727	+	0.306100i	0.940758	−	0.339080i	$-0.110116\pi$
$443$	3.71967	+	6.44266i	0.176727	+	0.306100i	−0.764031	+	0.645180i	$0.776782\pi$
$444$	0.851796	+	3.48458i	0.0404245	+	0.165371i
$445$	−4.31159	−	0.0618427i	−0.204389	−	0.00293162i
$446$	9.59556	−	5.54000i	0.454363	−	0.262327i
$447$	12.0241	+	12.5665i	0.568720	+	0.594374i
$448$			4.59876i			0.217271i
$449$	−12.6975			−0.599231			−0.299615	−	0.954060i	$-0.596858\pi$
$449$	−12.6975			−0.599231			−0.299615	+	0.954060i	$0.596858\pi$
$450$	−8.42490	+	12.4105i	−0.397154	+	0.585038i
$451$	13.3016	+	7.67968i	0.626347	+	0.361622i
$452$	−12.0689	+	6.96798i	−0.567673	+	0.327746i
$453$	4.13749	−	14.1826i	0.194396	−	0.666355i
$454$	4.73937	−	8.20882i	0.222430	−	0.385259i
$455$	−0.919075	+	64.0766i	−0.0430869	+	3.00396i
$456$	7.19428	−	2.28960i	0.336903	−	0.107220i
$457$		−	4.90753i		−	0.229565i	−0.993391	−	0.114782i	$-0.963383\pi$
$457$		−	4.90753i		−	0.229565i	0.993391	−	0.114782i	$-0.0366170\pi$
$458$	13.5479	+	7.82189i	0.633052	+	0.365493i
$459$	−2.44525	+	0.484582i	−0.114134	+	0.0226184i
$460$	4.66175	+	8.34865i	0.217355	+	0.389258i
$461$	−16.9981	−	9.81383i	−0.791678	−	0.457076i	0.0488748	−	0.998805i	$-0.484436\pi$
$461$	−16.9981	−	9.81383i	−0.791678	−	0.457076i	−0.840553	+	0.541729i	$0.817770\pi$
$462$	7.67001	+	8.01600i	0.356841	+	0.372938i
$463$		−	38.5459i		−	1.79138i	−0.444680	−	0.895689i	$-0.646683\pi$
$463$		−	38.5459i		−	1.79138i	0.444680	−	0.895689i	$-0.353317\pi$
$464$	2.70684			0.125662
$465$	−10.9716	−	11.8008i	−0.508796	−	0.547249i
$466$	−12.1250	+	7.00038i	−0.561681	+	0.324286i
$467$	−37.1729			−1.72016			−0.860079	−	0.510161i	$-0.829586\pi$
$467$	−37.1729			−1.72016			−0.860079	+	0.510161i	$0.829586\pi$
$468$	−16.5873	+	8.62481i	−0.766748	+	0.398682i
$469$	57.5973	−	33.2538i	2.65960	−	1.53552i
$470$	−12.2795	−	7.32637i	−0.566411	−	0.337940i
$471$	5.30783	+	5.54726i	0.244572	+	0.255604i
$472$	0.507429	+	0.292964i	0.0233563	+	0.0134848i
$473$	4.14650	−	7.18195i	0.190656	−	0.330226i
$474$	−4.42079	−	18.0849i	−0.203054	−	0.830665i
$475$	−10.1398	+	19.2921i	−0.465245	+	0.885182i
$476$		−	2.20621i		−	0.101121i
$477$	22.7836	+	1.00557i	1.04319	+	0.0460421i
$478$	−3.28330	+	5.68684i	−0.150175	+	0.260110i
$479$	3.84357	−	2.21908i	0.175617	−	0.101393i	−0.409615	−	0.912259i	$-0.634337\pi$
$479$	3.84357	−	2.21908i	0.175617	−	0.101393i	0.585232	+	0.810866i	$0.301004\pi$
$480$	1.13787	−	3.70206i	0.0519362	−	0.168975i
$481$	−6.45329	−	11.1774i	−0.294245	−	0.509647i
$482$	−10.7763			−0.490846
$483$	33.0874	−	8.08813i	1.50553	−	0.368023i
$484$	4.53000	+	7.84618i	0.205909	+	0.356645i
$485$	15.9174	+	28.5062i	0.722771	+	1.29440i
$486$	−5.66706	+	14.5219i	−0.257063	+	0.658725i
$487$	1.58405			0.0717800			0.0358900	−	0.999356i	$-0.488573\pi$
$487$	1.58405			0.0717800			0.0358900	+	0.999356i	$0.488573\pi$
$488$	−6.99890	+	4.04082i	−0.316825	+	0.182919i
$489$	−6.45504	+	22.1267i	−0.291907	+	1.00061i
$490$	−27.6227	+	15.4241i	−1.24787	+	0.696788i
$491$	12.0182	+	6.93869i	0.542372	+	0.313139i	0.746040	−	0.665901i	$-0.231953\pi$
$491$	12.0182	+	6.93869i	0.542372	+	0.313139i	−0.203668	+	0.979040i	$0.565286\pi$
$492$	−18.3356	−	5.34906i	−0.826634	−	0.241154i
$493$	−1.29858			−0.0584850
$494$	−22.5419	+	15.1575i	−1.01421	+	0.681968i
$495$	−4.19107	−	8.35077i	−0.188374	−	0.375339i
$496$	3.60302	+	2.08020i	0.161780	+	0.0934040i
$497$	42.7205	+	24.6647i	1.91628	+	1.10636i
$498$	−6.43171	−	6.72184i	−0.288212	−	0.301213i
$499$	11.7673	−	20.3816i	0.526778	−	0.912407i	−0.472735	−	0.881205i	$-0.656733\pi$
$499$	11.7673	−	20.3816i	0.526778	−	0.912407i	0.999513	−	0.0312021i	$-0.00993354\pi$
$500$	5.16852	+	9.91395i	0.231143	+	0.443365i
$501$	−17.9926	+	4.39824i	−0.803850	+	0.196499i
$502$	−5.84242			−0.260760
$503$	12.7244	+	22.0393i	0.567353	+	0.982684i	0.996827	+	0.0796045i	$0.0253657\pi$
$503$	12.7244	+	22.0393i	0.567353	+	0.982684i	−0.429474	+	0.903079i	$0.641301\pi$
$504$	−11.6322	−	7.41826i	−0.518137	−	0.330435i
$505$	−0.499935	+	34.8548i	−0.0222468	+	1.55102i
$506$	−5.95615			−0.264783
$507$	32.3328	−	30.9373i	1.43595	−	1.37397i
$508$	−2.52200	+	4.36823i	−0.111896	+	0.193809i
$509$	−11.5167	−	19.9475i	−0.510468	−	0.884157i	−0.999926	−	0.0121304i	$-0.996139\pi$
$509$	−11.5167	−	19.9475i	−0.510468	−	0.884157i	0.489458	−	0.872027i	$-0.337195\pi$
$510$	−0.545879	+	1.77602i	−0.0241719	+	0.0786437i
$511$	−21.0058	+	36.3832i	−0.929243	+	1.60950i
$512$			1.00000i			0.0441942i
$513$	−5.81374	+	21.8906i	−0.256683	+	0.966496i
$514$	26.9123			1.18705
$515$	−16.7577	+	28.0870i	−0.738432	+	1.23766i
$516$	−2.88813	+	9.89998i	−0.127143	+	0.435822i
$517$	7.71353	−	4.45341i	0.339241	−	0.195861i
$518$	4.76216	−	8.24830i	0.209237	−	0.362409i
$519$	22.8262	+	23.8559i	1.00196	+	1.04716i
$520$	−0.199853	+	13.9335i	−0.00876412	+	0.611022i
$521$	−3.36747			−0.147532			−0.0737659	−	0.997276i	$-0.523502\pi$
$521$	−3.36747			−0.147532			−0.0737659	+	0.997276i	$0.523502\pi$
$522$	−4.36640	+	6.84670i	−0.191112	+	0.299672i
$523$	4.73639	+	8.20368i	0.207108	+	0.358722i	0.950802	−	0.309798i	$-0.100261\pi$
$523$	4.73639	+	8.20368i	0.207108	+	0.358722i	−0.743694	+	0.668520i	$0.766928\pi$
$524$		−	7.42235i		−	0.324247i
$525$	38.9427	−	8.34354i	1.69960	−	0.364142i
$526$	−5.68013	+	3.27942i	−0.247665	+	0.142990i
$527$	−1.72851	−	0.997956i	−0.0752951	−	0.0434717i
$528$	1.66784	+	1.74308i	0.0725835	+	0.0758577i
$529$	2.35681	−	4.08212i	0.102470	−	0.177483i
$530$	8.70946	−	14.5976i	0.378315	−	0.634081i
$531$	−1.55956	+	0.810916i	−0.0676791	+	0.0351908i
$532$	−18.0041	−	8.81335i	−0.780578	−	0.382107i
$533$	68.7210			2.97664
$534$	−0.935412	+	3.20643i	−0.0404793	+	0.138756i
$535$	11.3436	+	6.76800i	0.490428	+	0.292606i
$536$	12.5245	−	7.23104i	0.540977	−	0.312333i
$537$	−17.6384	−	5.14566i	−0.761152	−	0.222051i
$538$	18.3545	−	10.5970i	0.791317	−	0.456867i
$539$		−	19.7068i		−	0.848832i
$540$	7.52854	+	8.84992i	0.323977	+	0.380840i
$541$	−3.84845	−	6.66571i	−0.165458	−	0.286581i	0.771360	−	0.636399i	$-0.219577\pi$
$541$	−3.84845	−	6.66571i	−0.165458	−	0.286581i	−0.936818	+	0.349818i	$0.886243\pi$
$542$	−6.61767	+	3.82071i	−0.284253	+	0.164114i
$543$	5.83087	−	1.42534i	0.250227	−	0.0611672i
$544$		−	0.479739i		−	0.0205687i
$545$	7.50179	−	4.18887i	0.321341	−	0.179432i
$546$	47.6523	+	13.9016i	2.03933	+	0.594935i
$547$	1.44871	+	2.50924i	0.0619423	+	0.107287i	0.895334	−	0.445396i	$-0.146937\pi$
$547$	1.44871	+	2.50924i	0.0619423	+	0.107287i	−0.833391	+	0.552683i	$0.813604\pi$
$548$	4.75833	−	8.24166i	0.203266	−	0.352066i
$549$	1.06903	−	24.2213i	0.0456251	−	1.03374i
$550$	−6.96134	−	0.199739i	−0.296833	−	0.00851691i
$551$	−5.18755	+	10.5973i	−0.220997	+	0.451458i
$552$	7.19485	−	1.75876i	0.306233	−	0.0748579i
$553$	−24.7154	+	42.8084i	−1.05101	+	1.82040i
$554$	4.86904	−	8.43342i	0.206865	−	0.358302i
$555$	−5.87446	+	5.46169i	−0.249357	+	0.231836i
$556$	2.16277	−	3.74604i	0.0917221	−	0.158867i
$557$	15.8962	+	27.5330i	0.673544	+	1.16661i	0.976892	+	0.213732i	$0.0685621\pi$
$557$	15.8962	+	27.5330i	0.673544	+	1.16661i	−0.303348	+	0.952880i	$0.598105\pi$
$558$	−11.0737	+	5.75794i	−0.468788	+	0.243753i
$559$		−	37.1046i		−	1.56936i
$560$	−8.97829	+	5.01332i	−0.379402	+	0.211852i
$561$	−0.800130	−	0.836223i	−0.0337815	−	0.0353054i
$562$		−	20.5148i		−	0.865363i
$563$			9.81574i			0.413684i	0.978374	+	0.206842i	$0.0663186\pi$
$563$			9.81574i			0.413684i	−0.978374	+	0.206842i	$0.933681\pi$
$564$	−8.00269	+	7.65728i	−0.336974	+	0.322429i
$565$	−26.7606	−	15.9663i	−1.12583	−	0.671708i
$566$	−0.228101	−	0.395082i	−0.00958779	−	0.0166065i
$567$	37.5276	−	17.4561i	1.57601	−	0.733088i
$568$	9.28957	+	5.36334i	0.389782	+	0.225041i
$569$	36.0591			1.51167			0.755837	−	0.654760i	$-0.227230\pi$
$569$	36.0591			1.51167			0.755837	+	0.654760i	$0.227230\pi$
$570$	12.3129	+	11.5496i	0.515730	+	0.483759i
$571$	−13.7104			−0.573764			−0.286882	−	0.957966i	$-0.592619\pi$
$571$	−13.7104			−0.573764			−0.286882	+	0.957966i	$0.592619\pi$
$572$	−7.51711	−	4.34000i	−0.314306	−	0.181465i
$573$	5.98359	−	20.5107i	0.249968	−	0.856845i
$574$	25.3561	+	43.9180i	1.05834	+	1.83310i
$575$	−11.2173	+	18.2025i	−0.467795	+	0.759097i
$576$	−2.52941	−	1.61310i	−0.105392	−	0.0672124i
$577$			34.0427i			1.41722i	0.705602	+	0.708608i	$0.250677\pi$
$577$			34.0427i			1.41722i	−0.705602	+	0.708608i	$0.749323\pi$
$578$		−	16.7699i		−	0.697534i
$579$	−15.5388	+	14.8681i	−0.645769	+	0.617896i
$580$	2.95085	+	5.28463i	0.122527	+	0.219433i
$581$			24.7010i			1.02477i
$582$	24.5666	−	6.00524i	1.01832	−	0.248925i
$583$	5.29413	+	9.16971i	0.219261	+	0.379771i
$584$	−4.56771	+	7.91151i	−0.189013	+	0.327381i
$585$	−34.9210	−	22.9815i	−1.44381	−	0.950169i
$586$	−10.7113	+	18.5525i	−0.442480	+	0.766398i
$587$	12.6616	−	21.9305i	0.522599	−	0.905168i	−0.477055	−	0.878873i	$-0.658296\pi$
$587$	12.6616	−	21.9305i	0.522599	−	0.905168i	0.999654	−	0.0262946i	$-0.00837079\pi$
$588$	5.81912	+	23.8052i	0.239976	+	0.981711i
$589$	−15.0490	+	10.1192i	−0.620085	+	0.416953i
$590$	−0.0187904	+	1.31004i	−0.000773589	+	0.0539336i
$591$	1.76741	+	0.515609i	0.0727017	+	0.0212093i
$592$	1.03553	−	1.79359i	0.0425600	−	0.0737161i
$593$	−10.3969	−	18.0080i	−0.426951	−	0.739500i	0.569650	−	0.821888i	$-0.307079\pi$
$593$	−10.3969	−	18.0080i	−0.426951	−	0.739500i	−0.996600	+	0.0823874i	$0.973746\pi$
$594$	−7.09935	+	1.40690i	−0.291290	+	0.0577259i
$595$	4.30724	−	2.40509i	0.176580	−	0.0985990i
$596$		−	10.0415i		−	0.411316i
$597$	1.27203	+	5.20370i	0.0520607	+	0.212973i
$598$	−23.0788	+	13.3245i	−0.943762	+	0.544881i
$599$	2.18111	+	3.77780i	0.0891178	+	0.154357i	0.907138	−	0.420832i	$-0.138262\pi$
$599$	2.18111	+	3.77780i	0.0891178	+	0.154357i	−0.818021	+	0.575189i	$0.804929\pi$
$600$	8.46808	−	1.81430i	0.345708	−	0.0740685i
$601$		−	5.12913i		−	0.209221i	−0.994513	−	0.104611i	$-0.966640\pi$
$601$		−	5.12913i		−	0.209221i	0.994513	−	0.104611i	$-0.0333597\pi$
$602$	23.7127	−	13.6906i	0.966459	−	0.557985i
$603$	−1.91303	+	43.3440i	−0.0779045	+	1.76510i
$604$	−7.38688	+	4.26482i	−0.300568	+	0.173533i
$605$	−10.3800	+	17.3975i	−0.422005	+	0.707310i
$606$	25.9207	+	7.56186i	1.05296	+	0.307180i
$607$	−3.49534			−0.141871			−0.0709357	−	0.997481i	$-0.522599\pi$
$607$	−3.49534			−0.141871			−0.0709357	+	0.997481i	$0.522599\pi$
$608$	−3.91499	−	1.91646i	−0.158774	−	0.0777227i
$609$	20.9441	−	5.11972i	0.848697	−	0.207462i
$610$	−15.5188	−	9.25906i	−0.628339	−	0.374889i
$611$	19.9255	−	34.5120i	0.806099	−	1.39621i
$612$	1.21346	+	0.773867i	0.0490511	+	0.0312817i
$613$	−20.1711	−	11.6458i	−0.814705	−	0.470370i	0.0338824	−	0.999426i	$-0.489213\pi$
$613$	−20.1711	−	11.6458i	−0.814705	−	0.470370i	−0.848587	+	0.529056i	$0.822546\pi$
$614$	−2.79083	+	1.61128i	−0.112629	+	0.0650261i
$615$	−9.54539	−	41.6284i	−0.384907	−	1.67862i
$616$		−	6.40535i		−	0.258079i
$617$	19.1437	+	33.1578i	0.770696	+	1.33488i	0.937182	+	0.348840i	$0.113424\pi$
$617$	19.1437	+	33.1578i	0.770696	+	1.33488i	−0.166486	+	0.986044i	$0.553242\pi$
$618$	17.5146	+	18.3046i	0.704539	+	0.736321i
$619$	32.6821			1.31360			0.656801	−	0.754064i	$-0.271909\pi$
$619$	32.6821			1.31360			0.656801	+	0.754064i	$0.271909\pi$
$620$	−0.133422	+	9.30200i	−0.00535836	+	0.373577i
$621$	−7.15737	+	21.0358i	−0.287215	+	0.844137i
$622$	9.47994	−	16.4197i	0.380111	−	0.658371i
$623$	7.68013	−	4.43412i	0.307698	−	0.177649i
$624$	10.3620	+	3.02291i	0.414811	+	0.121013i
$625$	−13.7208	+	20.8983i	−0.548834	+	0.835932i
$626$	−24.3997			−0.975207
$627$	−10.0205	+	3.18905i	−0.400180	+	0.127359i
$628$		−	4.43265i		−	0.176882i
$629$	−0.496785	+	0.860456i	−0.0198081	+	0.0343086i
$630$	1.80211	−	30.7968i	0.0717979	−	1.22697i
$631$	−16.1683	−	28.0042i	−0.643648	−	1.11483i	−0.984612	−	0.174755i	$-0.944087\pi$
$631$	−16.1683	−	28.0042i	−0.643648	−	1.11483i	0.340964	−	0.940076i	$-0.389247\pi$
$632$	−5.37436	+	9.30867i	−0.213781	+	0.370279i
$633$	−9.96728	−	10.4169i	−0.396164	−	0.414035i
$634$	−6.13487			−0.243647
$635$	−11.2776	−	0.161758i	−0.447536	−	0.00641917i
$636$	−9.10284	−	9.51346i	−0.360951	−	0.377233i
$637$	−44.0862	−	76.3595i	−1.74676	−	3.02547i
$638$	−3.77020			−0.149264
$639$	−28.5511	+	14.8455i	−1.12946	+	0.587281i
$640$	−1.95233	+	1.09015i	−0.0771725	+	0.0430918i
$641$	3.96930	−	6.87504i	0.156778	−	0.271548i	−0.776927	−	0.629591i	$-0.783223\pi$
$641$	3.96930	−	6.87504i	0.156778	−	0.271548i	0.933705	+	0.358043i	$0.116556\pi$
$642$	7.39277	−	7.07368i	0.291769	−	0.279176i
$643$	13.4682	+	7.77586i	0.531134	+	0.306650i	0.741478	−	0.670977i	$-0.234125\pi$
$643$	13.4682	+	7.77586i	0.531134	+	0.306650i	−0.210344	+	0.977627i	$0.567459\pi$
$644$	−17.0308	−	9.83275i	−0.671108	−	0.387465i
$645$	−22.4765	+	5.15385i	−0.885010	+	0.202933i
$646$	1.87818	+	0.919402i	0.0738959	+	0.0361734i
$647$	−21.8361			−0.858465			−0.429232	−	0.903194i	$-0.641216\pi$
$647$	−21.8361			−0.858465			−0.429232	+	0.903194i	$0.641216\pi$
$648$	8.16037	−	3.79583i	0.320570	−	0.149114i
$649$	−0.706768	−	0.408053i	−0.0277431	−	0.0160175i
$650$	−27.4205	+	14.7993i	−1.07552	+	0.580477i
$651$	31.8128	+	9.28076i	1.24684	+	0.363742i
$652$	11.5245	−	6.65370i	0.451336	−	0.260579i
$653$	−33.4523			−1.30909			−0.654544	−	0.756024i	$-0.727139\pi$
$653$	−33.4523			−1.30909			−0.654544	+	0.756024i	$0.727139\pi$
$654$	−1.58036	−	6.46503i	−0.0617969	−	0.252803i
$655$	14.4909	−	8.09145i	0.566205	−	0.316159i
$656$	5.51368	+	9.54997i	0.215273	+	0.372864i
$657$	−12.6433	−	24.3157i	−0.493262	−	0.948644i
$658$	29.4078			1.14643
$659$	21.0910	+	36.5306i	0.821587	+	1.42303i	0.904500	+	0.426473i	$0.140244\pi$
$659$	21.0910	+	36.5306i	0.821587	+	1.42303i	−0.0829133	+	0.996557i	$0.526422\pi$
$660$	−1.58487	+	5.15639i	−0.0616909	+	0.200712i
$661$	12.7480	−	7.36004i	0.495838	−	0.286272i	−0.231155	−	0.972917i	$-0.574250\pi$
$661$	12.7480	−	7.36004i	0.495838	−	0.286272i	0.726993	+	0.686645i	$0.240917\pi$
$662$	6.50359	−	11.2646i	0.252769	−	0.437809i
$663$	−4.97105	−	1.45021i	−0.193060	−	0.0563214i
$664$			5.37122i			0.208444i
$665$	−2.42059	−	44.7578i	−0.0938666	−	1.73563i
$666$	2.86631	+	5.51252i	0.111067	+	0.213606i
$667$	−5.78757	+	10.0244i	−0.224096	+	0.388145i
$668$	9.26118	+	5.34695i	0.358326	+	0.206880i
$669$	13.8661	−	13.2676i	0.536095	−	0.512956i
$670$	27.7709	+	16.5691i	1.07288	+	0.640119i
$671$	9.74836	−	5.62822i	0.376331	−	0.217275i
$672$	1.89140	+	7.73747i	0.0729625	+	0.298479i
$673$	−20.7866			−0.801263			−0.400632	−	0.916239i	$-0.631209\pi$
$673$	−20.7866			−0.801263			−0.400632	+	0.916239i	$0.631209\pi$
$674$	8.09221	−	4.67204i	0.311700	−	0.179960i
$675$	−9.07073	+	24.3459i	−0.349132	+	0.937073i
$676$	−25.8362			−0.993700
$677$		−	22.3672i		−	0.859641i	−0.902914	−	0.429821i	$-0.858577\pi$
$677$		−	22.3672i		−	0.859641i	0.902914	−	0.429821i	$-0.141423\pi$
$678$	−17.4402	+	16.6875i	−0.669788	+	0.640878i
$679$	−58.1512	−	33.5736i	−2.23164	−	1.28844i
$680$	0.936608	−	0.522986i	0.0359173	−	0.0200556i
$681$	4.59787	−	15.7607i	0.176191	−	0.603950i
$682$	−5.01844	−	2.89740i	−0.192166	−	0.110947i
$683$			39.9738i			1.52956i	0.644294	+	0.764778i	$0.277151\pi$
$683$			39.9738i			1.52956i	−0.644294	+	0.764778i	$0.722849\pi$
$684$	11.1628	−	6.81119i	0.426820	−	0.260432i
$685$	21.2777	+	0.305194i	0.812979	+	0.0116609i
$686$	16.4374	−	28.4704i	0.627583	−	1.08701i
$687$	26.0115	+	7.58836i	0.992402	+	0.289514i
$688$	5.15633	−	2.97701i	0.196583	−	0.113497i
$689$	41.0272	+	23.6871i	1.56301	+	0.902406i
$690$	11.2771	+	12.1294i	0.429313	+	0.461758i
$691$	−25.0769			−0.953970			−0.476985	−	0.878911i	$-0.658270\pi$
$691$	−25.0769			−0.953970			−0.476985	+	0.878911i	$0.658270\pi$
$692$		−	19.0625i		−	0.724648i
$693$	16.2018	+	10.3325i	0.615454	+	0.392497i
$694$	27.9108	−	16.1143i	1.05948	−	0.611691i
$695$	9.67123	+	0.138718i	0.366851	+	0.00526187i
$696$	4.55429	−	1.11328i	0.172630	−	0.0421989i
$697$	−2.64513	−	4.58150i	−0.100191	−	0.173537i
$698$	−10.3618	−	5.98236i	−0.392198	−	0.226436i
$699$	−17.5213	+	16.7651i	−0.662717	+	0.634113i
$700$	−19.5753	−	12.0633i	−0.739877	−	0.455950i
$701$	−14.2018	−	8.19942i	−0.536395	−	0.309688i	0.207222	−	0.978294i	$-0.433558\pi$
$701$	−14.2018	−	8.19942i	−0.536395	−	0.309688i	−0.743617	+	0.668606i	$0.766891\pi$
$702$	−24.3611	+	21.3335i	−0.919449	+	0.805179i
$703$	5.03734	+	7.49144i	0.189987	+	0.282545i
$704$		−	1.39284i		−	0.0524947i
$705$	−23.6736	−	7.27632i	−0.891600	−	0.274042i
$706$	−3.20201	−	1.84868i	−0.120509	−	0.0695760i
$707$	−35.8454	−	62.0861i	−1.34811	−	2.33499i
$708$	0.974247	+	0.284218i	0.0366145	+	0.0106816i
$709$	8.91758	+	15.4457i	0.334907	+	0.580076i	0.983467	−	0.181088i	$-0.0579618\pi$
$709$	8.91758	+	15.4457i	0.334907	+	0.580076i	−0.648560	+	0.761163i	$0.724628\pi$
$710$	−0.343998	+	23.9831i	−0.0129100	+	0.900070i
$711$	−14.8761	−	28.6098i	−0.557896	−	1.07295i
$712$	1.67004	−	0.964199i	0.0625875	−	0.0361349i
$713$	−15.4074	+	8.89549i	−0.577013	+	0.333139i
$714$	−0.907381	−	3.71197i	−0.0339579	−	0.138917i
$715$	0.278363	−	19.4071i	0.0104102	−	0.725784i
$716$	5.30401	+	9.18682i	0.198220	+	0.343327i
$717$	−3.18527	+	10.9185i	−0.118956	+	0.407761i
$718$	−1.65687	−	2.86979i	−0.0618339	−	0.107099i
$719$	−19.2354	−	11.1056i	−0.717360	−	0.414168i	0.0964201	−	0.995341i	$-0.469261\pi$
$719$	−19.2354	−	11.1056i	−0.717360	−	0.414168i	−0.813780	+	0.581173i	$0.802594\pi$
$720$	0.391869	−	6.69675i	0.0146041	−	0.249573i
$721$		−	67.2647i		−	2.50507i
$722$	15.0059	−	11.6544i	0.558460	−	0.433730i
$723$	−18.1312	+	4.43212i	−0.674307	+	0.164832i
$724$	−3.00128	−	1.73279i	−0.111542	−	0.0643986i
$725$	−7.10048	+	11.5220i	−0.263705	+	0.427918i
$726$	10.8488	+	11.3382i	0.402636	+	0.420799i
$727$	21.2331	+	12.2589i	0.787492	+	0.454659i	0.839079	−	0.544010i	$-0.183095\pi$
$727$	21.2331	+	12.2589i	0.787492	+	0.454659i	−0.0515868	+	0.998669i	$0.516428\pi$
$728$	−14.3294	−	24.8193i	−0.531085	−	0.919866i
$729$	−3.56227	+	26.7640i	−0.131936	+	0.991258i
$730$	−20.4253	−	0.292968i	−0.755976	−	0.0108432i
$731$	−2.47369	+	1.42819i	−0.0914929	+	0.0528234i
$732$	−10.1138	+	9.67727i	−0.373817	+	0.357682i
$733$		−	12.5596i		−	0.463899i	−0.972728	−	0.231949i	$-0.925490\pi$
$733$		−	12.5596i		−	0.463899i	0.972728	−	0.231949i	$-0.0745104\pi$
$734$	15.4910			0.571784
$735$	−40.1319	+	37.3120i	−1.48029	+	1.37627i
$736$	−3.70335	−	2.13813i	−0.136507	−	0.0788125i
$737$	−17.4447	+	10.0717i	−0.642583	+	0.370995i
$738$	−33.0499	−	1.45869i	−1.21658	−	0.0536950i
$739$	12.6272	−	21.8709i	0.464498	−	0.804534i	−0.534681	−	0.845054i	$-0.679568\pi$
$739$	12.6272	−	21.8709i	0.464498	−	0.804534i	0.999179	+	0.0405203i	$0.0129016\pi$
$740$	4.63055	+	0.0664177i	0.170223	+	0.00244156i
$741$	−31.6930	+	34.7738i	−1.16427	+	1.27745i
$742$			34.9594i			1.28340i
$743$	−4.75202	−	2.74358i	−0.174335	−	0.100652i	0.410294	−	0.911954i	$-0.365426\pi$
$743$	−4.75202	−	2.74358i	−0.174335	−	0.100652i	−0.584628	+	0.811301i	$0.698760\pi$
$744$	6.91768	+	2.01810i	0.253614	+	0.0739871i
$745$	19.6043	−	10.9467i	0.718245	−	0.401056i
$746$	4.09140	+	2.36217i	0.149797	+	0.0864851i
$747$	−13.5860	−	8.66430i	−0.497086	−	0.317010i
$748$			0.668201i			0.0244318i
$749$	−27.1665			−0.992641
$750$	12.7735	+	14.5546i	0.466424	+	0.531459i
$751$	−26.3926	+	15.2378i	−0.963078	+	0.556034i	−0.897119	−	0.441789i	$-0.854344\pi$
$751$	−26.3926	+	15.2378i	−0.963078	+	0.556034i	−0.0659593	+	0.997822i	$0.521011\pi$
$752$	6.39471			0.233191
$753$	−9.82994	+	2.40290i	−0.358223	+	0.0875666i
$754$	−14.6087	+	8.43433i	−0.532017	+	0.307160i
$755$	−16.3791	−	9.77234i	−0.596097	−	0.355652i
$756$	−22.6223	−	7.69717i	−0.822764	−	0.279943i
$757$	42.0539	+	24.2798i	1.52847	+	0.882465i	0.999426	+	0.0338722i	$0.0107839\pi$
$757$	42.0539	+	24.2798i	1.52847	+	0.882465i	0.529047	+	0.848592i	$0.322549\pi$
$758$	4.77081	−	8.26329i	0.173284	−	0.300136i
$759$	−10.0213	+	2.44968i	−0.363750	+	0.0889176i
$760$	−0.526357	−	9.73257i	−0.0190930	−	0.353037i
$761$		−	33.3844i		−	1.21018i	−0.796156	−	0.605092i	$-0.793136\pi$
$761$		−	33.3844i		−	1.21018i	0.796156	−	0.605092i	$-0.206864\pi$
$762$	−2.44670	+	8.38685i	−0.0886346	+	0.303824i
$763$	−8.83534	+	15.3033i	−0.319861	+	0.554015i
$764$	−10.6828	+	6.16773i	−0.386491	+	0.223141i
$765$	−0.187995	+	3.21269i	−0.00679697	+	0.116155i
$766$	1.88738	+	3.26903i	0.0681937	+	0.118115i
$767$	−3.65143			−0.131846
$768$	0.411285	+	1.68251i	0.0148410	+	0.0607124i
$769$	21.7336	+	37.6437i	0.783734	+	1.35747i	0.929753	+	0.368185i	$0.120021\pi$
$769$	21.7336	+	37.6437i	0.783734	+	1.35747i	−0.146019	+	0.989282i	$0.546646\pi$
$770$	12.5053	−	6.98277i	0.450661	−	0.251641i
$771$	45.2802	−	11.0686i	1.63073	−	0.398627i
$772$	12.4166			0.446882
$773$	−21.3590	+	12.3316i	−0.768230	+	0.443538i	−0.832243	−	0.554411i	$-0.812943\pi$
$773$	−21.3590	+	12.3316i	−0.768230	+	0.443538i	0.0640129	+	0.997949i	$0.479610\pi$
$774$	−0.787591	+	17.8447i	−0.0283094	+	0.641413i
$775$	−18.3060	+	9.88006i	−0.657571	+	0.354902i
$776$

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.66274 - 0.485072i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.14569 + 1.92026i) q^{5} +(1.19744 + 1.25145i) q^{6} -4.59876i q^{7} -1.00000i q^{8} +(2.52941 + 1.61310i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.66274 - 0.485072i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.14569 + 1.92026i) q^{5} +(1.19744 + 1.25145i) q^{6} -4.59876i q^{7} -1.00000i q^{8} +(2.52941 + 1.61310i) q^{9} +(1.95233 - 1.09015i) q^{10} +1.39284i q^{11} +(-0.411285 - 1.68251i) q^{12} +(3.11593 + 5.39696i) q^{13} +(-2.29938 + 3.98265i) q^{14} +(2.83645 - 2.63715i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.239870 - 0.415466i) q^{17} +(-1.38398 - 2.66169i) q^{18} +(-2.43225 - 3.61720i) q^{19} +(-2.23584 - 0.0320694i) q^{20} +(-2.23073 + 7.64655i) q^{21} +(0.696421 - 1.20624i) q^{22} +(-2.13813 - 3.70335i) q^{23} +(-0.485072 + 1.66274i) q^{24} +(-2.37478 - 4.40005i) q^{25} -6.23187i q^{26} +(-3.42328 - 3.90911i) q^{27} +(3.98265 - 2.29938i) q^{28} +(-1.35342 - 2.34419i) q^{29} +(-3.77501 + 0.865610i) q^{30} -4.16041i q^{31} +(0.866025 - 0.500000i) q^{32} +(0.675629 - 2.31593i) q^{33} +(-0.415466 + 0.239870i) q^{34} +(8.83081 + 5.26877i) q^{35} +(-0.132279 + 2.99708i) q^{36} -2.07106 q^{37} +(0.297794 + 4.34871i) q^{38} +(-2.56308 - 10.4852i) q^{39} +(1.92026 + 1.14569i) q^{40} +(5.51368 - 9.54997i) q^{41} +(5.75515 - 5.50674i) q^{42} +(-5.15633 - 2.97701i) q^{43} +(-1.20624 + 0.696421i) q^{44} +(-5.99549 + 3.00901i) q^{45} +4.27626i q^{46} +(-3.19735 - 5.53798i) q^{47} +(1.25145 - 1.19744i) q^{48} -14.1486 q^{49} +(-0.143404 + 4.99794i) q^{50} +(-0.600372 + 0.574459i) q^{51} +(-3.11593 + 5.39696i) q^{52} +(6.58345 - 3.80096i) q^{53} +(1.01009 + 5.09703i) q^{54} +(-2.67461 - 1.59577i) q^{55} -4.59876 q^{56} +(2.28960 + 7.19428i) q^{57} +2.70684i q^{58} +(-0.292964 + 0.507429i) q^{59} +(3.70206 + 1.13787i) q^{60} +(-4.04082 - 6.99890i) q^{61} +(-2.08020 + 3.60302i) q^{62} +(7.41826 - 11.6322i) q^{63} -1.00000 q^{64} +(-13.9335 - 0.199853i) q^{65} +(-1.74308 + 1.66784i) q^{66} +(7.23104 + 12.5245i) q^{67} +0.479739 q^{68} +(1.75876 + 7.19485i) q^{69} +(-5.01332 - 8.97829i) q^{70} +(-5.36334 + 9.28957i) q^{71} +(1.61310 - 2.52941i) q^{72} +(-7.91151 - 4.56771i) q^{73} +(1.79359 + 1.03553i) q^{74} +(1.81430 + 8.46808i) q^{75} +(1.91646 - 3.91499i) q^{76} +6.40535 q^{77} +(-3.02291 + 10.3620i) q^{78} +(-9.30867 - 5.37436i) q^{79} +(-1.09015 - 1.95233i) q^{80} +(3.79583 + 8.16037i) q^{81} +(-9.54997 + 5.51368i) q^{82} -5.37122 q^{83} +(-7.73747 + 1.89140i) q^{84} +(0.522986 + 0.936608i) q^{85} +(2.97701 + 5.15633i) q^{86} +(1.11328 + 4.55429i) q^{87} +1.39284 q^{88} +(0.964199 + 1.67004i) q^{89} +(6.69675 + 0.391869i) q^{90} +(24.8193 - 14.3294i) q^{91} +(2.13813 - 3.70335i) q^{92} +(-2.01810 + 6.91768i) q^{93} +6.39471i q^{94} +(9.73257 - 0.526357i) q^{95} +(-1.68251 + 0.411285i) q^{96} +(7.30058 - 12.6450i) q^{97} +(12.2531 + 7.07431i) q^{98} +(-2.24679 + 3.52307i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80q + 40q^{4} + O(q^{10}) \)	\( 80q + 40q^{4} + 30q^{15} - 40q^{16} + 8q^{19} + 8q^{25} - 4q^{30} + 48q^{39} + 12q^{45} - 128q^{49} - 36q^{54} + 12q^{55} + 30q^{60} - 24q^{61} - 80q^{64} + 4q^{66} + 36q^{70} + 16q^{76} + 24q^{79} + 32q^{81} - 8q^{85} - 54q^{90} + 24q^{91} - 60q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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