LMFDB - Embedded newform 300.2.w.a.67.1

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			67.1
Character	$\chi$	$=$	300.67
Dual form			300.2.w.a.103.1

$q$-expansion

$f(q)$	$=$	$q+(-1.38407 + 0.290430i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(1.83130 - 0.803952i) q^{4} +(0.979302 + 2.01022i) q^{5} +(1.41246 - 0.0703383i) q^{6} +(-0.0808033 + 0.0808033i) q^{7} +(-2.30116 + 1.64459i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})$	\(q+(-1.38407 + 0.290430i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(1.83130 - 0.803952i) q^{4} +(0.979302 + 2.01022i) q^{5} +(1.41246 - 0.0703383i) q^{6} +(-0.0808033 + 0.0808033i) q^{7} +(-2.30116 + 1.64459i) q^{8} +(0.951057 + 0.309017i) q^{9} +(-1.93925 - 2.49786i) q^{10} +(-0.521065 + 0.169304i) q^{11} +(-1.93452 + 0.507575i) q^{12} +(-0.379036 - 0.743901i) q^{13} +(0.0883697 - 0.135305i) q^{14} +(-0.652778 - 2.13866i) q^{15} +(2.70732 - 2.94455i) q^{16} +(0.514721 + 3.24982i) q^{17} +(-1.40608 - 0.151486i) q^{18} +(2.87295 + 2.08732i) q^{19} +(3.40951 + 2.89400i) q^{20} +(0.0924489 - 0.0671680i) q^{21} +(0.672020 - 0.385662i) q^{22} +(-3.38282 + 6.63917i) q^{23} +(2.53010 - 1.26436i) q^{24} +(-3.08194 + 3.93722i) q^{25} +(0.740664 + 0.919527i) q^{26} +(-0.891007 - 0.453990i) q^{27} +(-0.0830132 + 0.212937i) q^{28} +(4.57530 + 6.29737i) q^{29} +(1.52462 + 2.77047i) q^{30} +(-1.38542 + 1.90687i) q^{31} +(-2.89194 + 4.86176i) q^{32} +(0.541135 - 0.0857074i) q^{33} +(-1.65626 - 4.34849i) q^{34} +(-0.241563 - 0.0833013i) q^{35} +(1.99011 - 0.198701i) q^{36} +(0.401778 - 0.204716i) q^{37} +(-4.58259 - 2.05461i) q^{38} +(0.257998 + 0.794036i) q^{39} +(-5.55951 - 3.01527i) q^{40} +(1.29216 - 3.97687i) q^{41} +(-0.108448 + 0.119815i) q^{42} +(2.31395 + 2.31395i) q^{43} +(-0.818115 + 0.728959i) q^{44} +(0.310180 + 2.21445i) q^{45} +(2.75385 - 10.1715i) q^{46} +(-0.528548 + 3.33712i) q^{47} +(-3.13462 + 2.48478i) q^{48} +6.98694i q^{49} +(3.12213 - 6.34447i) q^{50} -3.29033i q^{51} +(-1.29219 - 1.05758i) q^{52} +(2.22344 - 14.0382i) q^{53} +(1.36507 + 0.369579i) q^{54} +(-0.850619 - 0.881654i) q^{55} +(0.0530527 - 0.318829i) q^{56} +(-2.51105 - 2.51105i) q^{57} +(-8.16149 - 7.38719i) q^{58} +(-1.80325 + 5.54984i) q^{59} +(-2.91481 - 3.39173i) q^{60} +(-2.07653 - 6.39089i) q^{61} +(1.36371 - 3.04161i) q^{62} +(-0.101818 + 0.0518789i) q^{63} +(2.59064 - 7.56892i) q^{64} +(1.12421 - 1.49045i) q^{65} +(-0.724077 + 0.275787i) q^{66} +(12.2481 - 1.93991i) q^{67} +(3.55531 + 5.53758i) q^{68} +(4.37977 - 6.02824i) q^{69} +(0.358533 + 0.0451376i) q^{70} +(-9.28233 - 12.7760i) q^{71} +(-2.69674 + 0.853002i) q^{72} +(1.31572 + 0.670391i) q^{73} +(-0.496633 + 0.400030i) q^{74} +(3.65991 - 3.40662i) q^{75} +(6.93934 + 1.51280i) q^{76} +(0.0284234 - 0.0557842i) q^{77} +(-0.587700 - 1.02407i) q^{78} +(-4.21793 + 3.06451i) q^{79} +(8.57048 + 2.55870i) q^{80} +(0.809017 + 0.587785i) q^{81} +(-0.633441 + 5.87955i) q^{82} +(-0.973158 - 6.14428i) q^{83} +(0.115302 - 0.197329i) q^{84} +(-6.02877 + 4.21725i) q^{85} +(-3.87472 - 2.53063i) q^{86} +(-3.53385 - 6.93557i) q^{87} +(0.920617 - 1.24654i) q^{88} +(9.70119 - 3.15211i) q^{89} +(-1.07245 - 2.97487i) q^{90} +(0.0907370 + 0.0294822i) q^{91} +(-0.857397 + 14.8779i) q^{92} +(1.66666 - 1.66666i) q^{93} +(-0.237653 - 4.77231i) q^{94} +(-1.38248 + 7.81937i) q^{95} +(3.61688 - 4.34950i) q^{96} +(-1.70626 - 0.270245i) q^{97} +(-2.02922 - 9.67042i) q^{98} -0.547881 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 $

$2$	−1.38407	+	0.290430i	−0.978685	+	0.205365i
$2$	−1.38407	+	0.290430i	−0.978685	+	0.205365i
$3$	−0.987688	−	0.156434i	−0.570242	−	0.0903175i
$3$	−0.987688	−	0.156434i	−0.570242	−	0.0903175i
$4$	1.83130	−	0.803952i	0.915650	−	0.401976i
$5$	0.979302	+	2.01022i	0.437957	+	0.898996i
$5$	0.979302	+	2.01022i	0.437957	+	0.898996i
$6$	1.41246	−	0.0703383i	0.576636	−	0.0287155i
$7$	−0.0808033	+	0.0808033i	−0.0305408	+	0.0305408i	−0.722212	−	0.691671i	$-0.756875\pi$
$7$	−0.0808033	+	0.0808033i	−0.0305408	+	0.0305408i	0.691671	+	0.722212i	$0.256875\pi$
$8$	−2.30116	+	1.64459i	−0.813582	+	0.581451i
$9$	0.951057	+	0.309017i	0.317019	+	0.103006i
$10$	−1.93925	−	2.49786i	−0.613245	−	0.789893i
$11$	−0.521065	+	0.169304i	−0.157107	+	0.0510472i	−0.386515	−	0.922283i	$-0.626321\pi$
$11$	−0.521065	+	0.169304i	−0.157107	+	0.0510472i	0.229408	+	0.973330i	$0.426321\pi$
$12$	−1.93452	+	0.507575i	−0.558448	+	0.146524i
$13$	−0.379036	−	0.743901i	−0.105126	−	0.206321i	0.832452	−	0.554098i	$-0.186937\pi$
$13$	−0.379036	−	0.743901i	−0.105126	−	0.206321i	−0.937577	+	0.347777i	$0.886937\pi$
$14$	0.0883697	−	0.135305i	0.0236178	−	0.0361618i
$15$	−0.652778	−	2.13866i	−0.168547	−	0.552201i
$16$	2.70732	−	2.94455i	0.676831	−	0.736139i
$17$	0.514721	+	3.24982i	0.124838	+	0.788197i	0.968076	+	0.250656i	$0.0806465\pi$
$17$	0.514721	+	3.24982i	0.124838	+	0.788197i	−0.843238	+	0.537540i	$0.819354\pi$
$18$	−1.40608	−	0.151486i	−0.331415	−	0.0357055i
$19$	2.87295	+	2.08732i	0.659100	+	0.478864i	0.866359	−	0.499422i	$-0.166454\pi$
$19$	2.87295	+	2.08732i	0.659100	+	0.478864i	−0.207259	+	0.978286i	$0.566454\pi$
$20$	3.40951	+	2.89400i	0.762390	+	0.647118i
$21$	0.0924489	−	0.0671680i	0.0201740	−	0.0146573i
$22$	0.672020	−	0.385662i	0.143275	−	0.0822235i
$23$	−3.38282	+	6.63917i	−0.705367	+	1.38436i	0.208367	+	0.978051i	$0.433185\pi$
$23$	−3.38282	+	6.63917i	−0.705367	+	1.38436i	−0.913735	+	0.406311i	$0.866815\pi$
$24$	2.53010	−	1.26436i	0.516454	−	0.258087i
$25$	−3.08194	+	3.93722i	−0.616387	+	0.787443i
$26$	0.740664	+	0.919527i	0.145256	+	0.180334i
$27$	−0.891007	−	0.453990i	−0.171474	−	0.0873705i
$28$	−0.0830132	+	0.212937i	−0.0156880	+	0.0402413i
$29$	4.57530	+	6.29737i	0.849613	+	1.16939i	0.983948	+	0.178455i	$0.0571100\pi$
$29$	4.57530	+	6.29737i	0.849613	+	1.16939i	−0.134335	+	0.990936i	$0.542890\pi$
$30$	1.52462	+	2.77047i	0.278357	+	0.505817i
$31$	−1.38542	+	1.90687i	−0.248829	+	0.342484i	−0.915101	−	0.403225i	$-0.867889\pi$
$31$	−1.38542	+	1.90687i	−0.248829	+	0.342484i	0.666272	+	0.745709i	$0.267889\pi$
$32$	−2.89194	+	4.86176i	−0.511227	+	0.859446i
$33$	0.541135	−	0.0857074i	0.0941996	−	0.0149197i
$34$	−1.65626	−	4.34849i	−0.284045	−	0.745759i
$35$	−0.241563	−	0.0833013i	−0.0408316	−	0.0140805i
$36$	1.99011	−	0.198701i	0.331684	−	0.0331168i
$37$	0.401778	−	0.204716i	0.0660518	−	0.0336551i	−0.420653	−	0.907222i	$-0.638199\pi$
$37$	0.401778	−	0.204716i	0.0660518	−	0.0336551i	0.486704	+	0.873567i	$0.338199\pi$
$38$	−4.58259	−	2.05461i	−0.743393	−	0.333301i
$39$	0.257998	+	0.794036i	0.0413128	+	0.127148i
$40$	−5.55951	−	3.01527i	−0.879036	−	0.476756i
$41$	1.29216	−	3.97687i	0.201802	−	0.621083i	−0.798028	−	0.602621i	$-0.794123\pi$
$41$	1.29216	−	3.97687i	0.201802	−	0.621083i	0.999830	−	0.0184617i	$-0.00587687\pi$
$42$	−0.108448	+	0.119815i	−0.0167339	+	0.0184879i
$43$	2.31395	+	2.31395i	0.352875	+	0.352875i	0.861178	−	0.508303i	$-0.169727\pi$
$43$	2.31395	+	2.31395i	0.352875	+	0.352875i	−0.508303	+	0.861178i	$0.669727\pi$
$44$	−0.818115	+	0.728959i	−0.123335	+	0.109895i
$45$	0.310180	+	2.21445i	0.0462390	+	0.330111i
$46$	2.75385	−	10.1715i	0.406033	−	1.49971i
$47$	−0.528548	+	3.33712i	−0.0770966	+	0.486769i	0.918683	+	0.394995i	$0.129254\pi$
$47$	−0.528548	+	3.33712i	−0.0770966	+	0.486769i	−0.995780	+	0.0917738i	$0.970746\pi$
$48$	−3.13462	+	2.48478i	−0.452444	+	0.358648i
$49$			6.98694i			0.998135i
$50$	3.12213	−	6.34447i	0.441536	−	0.897244i
$51$		−	3.29033i		−	0.460738i
$52$	−1.29219	−	1.05758i	−0.179194	−	0.146660i
$53$	2.22344	−	14.0382i	0.305413	−	1.92830i	−0.0616376	−	0.998099i	$-0.519632\pi$
$53$	2.22344	−	14.0382i	0.305413	−	1.92830i	0.367050	−	0.930201i	$-0.380368\pi$
$54$	1.36507	+	0.369579i	0.185762	+	0.0502934i
$55$	−0.850619	−	0.881654i	−0.114697	−	0.118882i
$56$	0.0530527	−	0.318829i	0.00708946	−	0.0426054i
$57$	−2.51105	−	2.51105i	−0.332597	−	0.332597i
$58$	−8.16149	−	7.38719i	−1.07166	−	0.969985i
$59$	−1.80325	+	5.54984i	−0.234763	+	0.722528i	0.762389	+	0.647119i	$0.224026\pi$
$59$	−1.80325	+	5.54984i	−0.234763	+	0.722528i	−0.997153	+	0.0754088i	$0.975974\pi$
$60$	−2.91481	−	3.39173i	−0.376301	−	0.437871i
$61$	−2.07653	−	6.39089i	−0.265872	−	0.818269i	−0.991491	−	0.130173i	$-0.958447\pi$
$61$	−2.07653	−	6.39089i	−0.265872	−	0.818269i	0.725619	−	0.688096i	$-0.241553\pi$
$62$	1.36371	−	3.04161i	0.173191	−	0.386285i
$63$	−0.101818	+	0.0518789i	−0.0128279	+	0.00653613i
$64$	2.59064	−	7.56892i	0.323830	−	0.946115i
$65$	1.12421	−	1.49045i	0.139441	−	0.184867i
$66$	−0.724077	+	0.275787i	−0.0891277	+	0.0339471i
$67$	12.2481	−	1.93991i	1.49634	−	0.236998i	0.646046	−	0.763298i	$-0.276421\pi$
$67$	12.2481	−	1.93991i	1.49634	−	0.236998i	0.850298	+	0.526301i	$0.176421\pi$
$68$	3.55531	+	5.53758i	0.431144	+	0.671531i
$69$	4.37977	−	6.02824i	0.527262	−	0.725714i
$70$	0.358533	+	0.0451376i	0.0428529	+	0.00539498i
$71$	−9.28233	−	12.7760i	−1.10161	−	1.51624i	−0.833233	−	0.552923i	$-0.813512\pi$
$71$	−9.28233	−	12.7760i	−1.10161	−	1.51624i	−0.268378	−	0.963314i	$-0.586488\pi$
$72$	−2.69674	+	0.853002i	−0.317813	+	0.100527i
$73$	1.31572	+	0.670391i	0.153993	+	0.0784633i	0.529289	−	0.848442i	$-0.322459\pi$
$73$	1.31572	+	0.670391i	0.153993	+	0.0784633i	−0.375296	+	0.926905i	$0.622459\pi$
$74$	−0.496633	+	0.400030i	−0.0577324	+	0.0465025i
$75$	3.65991	−	3.40662i	0.422610	−	0.393363i
$76$	6.93934	+	1.51280i	0.795997	+	0.173530i
$77$	0.0284234	−	0.0557842i	0.00323915	−	0.00635719i
$78$	−0.587700	−	1.02407i	−0.0665439	−	0.115953i
$79$	−4.21793	+	3.06451i	−0.474554	+	0.344784i	−0.799214	−	0.601047i	$-0.794750\pi$
$79$	−4.21793	+	3.06451i	−0.474554	+	0.344784i	0.324659	+	0.945831i	$0.394750\pi$
$80$	8.57048	+	2.55870i	0.958208	+	0.286071i
$81$	0.809017	+	0.587785i	0.0898908	+	0.0653095i
$82$	−0.633441	+	5.87955i	−0.0699519	+	0.649288i
$83$	−0.973158	−	6.14428i	−0.106818	−	0.674422i	−0.981750	−	0.190176i	$-0.939094\pi$
$83$	−0.973158	−	6.14428i	−0.106818	−	0.674422i	0.874932	−	0.484246i	$-0.160906\pi$
$84$	0.115302	−	0.197329i	0.0125805	−	0.0215304i
$85$	−6.02877	+	4.21725i	−0.653912	+	0.457425i
$86$	−3.87472	−	2.53063i	−0.417821	−	0.272885i
$87$	−3.53385	−	6.93557i	−0.378868	−	0.743571i
$88$	0.920617	−	1.24654i	0.0981380	−	0.132881i
$89$	9.70119	−	3.15211i	1.02832	−	0.334123i	0.254197	−	0.967153i	$-0.418189\pi$
$89$	9.70119	−	3.15211i	1.02832	−	0.334123i	0.774127	+	0.633030i	$0.218189\pi$
$90$	−1.07245	−	2.97487i	−0.113047	−	0.313579i
$91$	0.0907370	+	0.0294822i	0.00951182	+	0.00309058i
$92$	−0.857397	+	14.8779i	−0.0893899	+	1.55113i
$93$	1.66666	−	1.66666i	0.172825	−	0.172825i
$94$	−0.237653	−	4.77231i	−0.0245121	−	0.492226i
$95$	−1.38248	+	7.81937i	−0.141839	+	0.802250i
$96$	3.61688	−	4.34950i	0.369146	−	0.443919i
$97$	−1.70626	−	0.270245i	−0.173244	−	0.0274392i	0.0692096	−	0.997602i	$-0.477952\pi$
$97$	−1.70626	−	0.270245i	−0.173244	−	0.0274392i	−0.242454	+	0.970163i	$0.577952\pi$
$98$	−2.02922	−	9.67042i	−0.204982	−	0.976860i
$99$	−0.547881			−0.0550641
$100$	−2.47862	+	9.68795i	−0.247862	+	0.968795i
$101$	−11.4729			−1.14160			−0.570798	−	0.821091i	$-0.693366\pi$
$101$	−11.4729			−1.14160			−0.570798	+	0.821091i	$0.693366\pi$
$102$	0.955611	+	4.55405i	0.0946196	+	0.450918i
$103$	11.2138	+	1.77608i	1.10492	+	0.175003i	0.682136	−	0.731225i	$-0.261051\pi$
$103$	11.2138	+	1.77608i	1.10492	+	0.175003i	0.422789	+	0.906228i	$0.361051\pi$
$104$	2.09563	+	1.08847i	0.205494	+	0.106733i
$105$	0.225558	+	0.120064i	0.0220122	+	0.0117171i
$106$	0.999735	+	20.0757i	0.0971028	+	1.94992i
$107$	2.58147	−	2.58147i	0.249560	−	0.249560i	−0.571230	−	0.820790i	$-0.693534\pi$
$107$	2.58147	−	2.58147i	0.249560	−	0.249560i	0.820790	+	0.571230i	$0.193534\pi$
$108$	−1.99669	−	0.115067i	−0.192131	−	0.0110723i
$109$	4.86280	+	1.58002i	0.465772	+	0.151338i	0.532495	−	0.846433i	$-0.321255\pi$
$109$	4.86280	+	1.58002i	0.465772	+	0.151338i	−0.0667234	+	0.997772i	$0.521255\pi$
$110$	1.43337	+	0.973225i	0.136667	+	0.0927934i
$111$	−0.428856	+	0.139344i	−0.0407052	+	0.0132259i
$112$	0.0191691	+	0.456690i	0.00181131	+	0.0431532i
$113$	−7.03160	−	13.8003i	−0.661477	−	1.29822i	−0.941105	−	0.338114i	$-0.890211\pi$
$113$	−7.03160	−	13.8003i	−0.661477	−	1.29822i	0.279628	−	0.960108i	$-0.409789\pi$
$114$	4.20475	+	2.74618i	0.393811	+	0.257204i
$115$	−16.6590	−	0.298460i	−1.55346	−	0.0278316i
$116$	13.4415	+	7.85404i	1.24802	+	0.729230i
$117$	−0.130607	−	0.824620i	−0.0120746	−	0.0762362i
$118$	0.883986	−	8.20509i	0.0813775	−	0.755339i
$119$	−0.304187	−	0.221005i	−0.0278848	−	0.0202595i
$120$	5.01937	+	3.84785i	0.458204	+	0.351259i
$121$	−8.65634	+	6.28920i	−0.786940	+	0.571745i
$122$	4.73016	+	8.24235i	0.428249	+	0.746227i
$123$	−1.89837	+	3.72577i	−0.171171	+	0.335941i
$124$	−1.00409	+	4.60586i	−0.0901701	+	0.413619i
$125$	−10.9328	−	2.33964i	−0.977859	−	0.209263i
$126$	0.125856	−	0.101375i	0.0112122	−	0.00903121i
$127$	9.45960	+	4.81991i	0.839404	+	0.427698i	0.820172	−	0.572117i	$-0.193878\pi$
$127$	9.45960	+	4.81991i	0.839404	+	0.427698i	0.0192321	+	0.999815i	$0.493878\pi$
$128$	−1.38739	+	11.2283i	−0.122629	+	0.992453i
$129$	−1.92348	−	2.64745i	−0.169353	−	0.233095i
$130$	−1.12311	+	2.38939i	−0.0985037	+	0.209563i
$131$	13.0987	−	18.0288i	1.14444	−	1.57518i	0.387257	−	0.921972i	$-0.373422\pi$
$131$	13.0987	−	18.0288i	1.14444	−	1.57518i	0.757178	−	0.653209i	$-0.226578\pi$
$132$	0.922077	−	0.592003i	0.0802565	−	0.0515272i
$133$	−0.400806	+	0.0634815i	−0.0347543	+	0.00550454i
$134$	−16.3888	+	6.24219i	−1.41578	+	0.539243i
$135$	0.0400547	−	2.23571i	0.00344736	−	0.192419i
$136$	−6.52908	−	6.63184i	−0.559864	−	0.568675i
$137$	−6.60920	+	3.36756i	−0.564662	+	0.287710i	−0.712927	−	0.701238i	$-0.752631\pi$
$137$	−6.60920	+	3.36756i	−0.564662	+	0.287710i	0.148265	+	0.988948i	$0.452631\pi$
$138$	−4.31113	+	9.61552i	−0.366987	+	0.818527i
$139$	−2.89675	−	8.91529i	−0.245699	−	0.756185i	−0.995521	−	0.0945444i	$-0.969861\pi$
$139$	−2.89675	−	8.91529i	−0.245699	−	0.756185i	0.749821	−	0.661640i	$-0.230139\pi$
$140$	−0.509344	+	0.0416553i	−0.0430475	+	0.00352051i
$141$	1.04408	−	3.21335i	0.0879275	−	0.270613i
$142$	16.5579	+	14.9871i	1.38951	+	1.25769i
$143$	0.323448	+	0.323448i	0.0270481	+	0.0270481i
$144$	3.48473	−	1.96383i	0.290395	−	0.163652i
$145$	−8.17846	+	15.3644i	−0.679184	+	1.27594i
$146$	−2.01575	−	0.545744i	−0.166824	−	0.0451661i
$147$	1.09300	−	6.90092i	0.0901490	−	0.569178i
$148$	0.571194	−	0.697906i	0.0469518	−	0.0573675i
$149$			20.8441i			1.70762i	0.520587	+	0.853809i	$0.325713\pi$
$149$			20.8441i			1.70762i	−0.520587	+	0.853809i	$0.674287\pi$
$150$	−4.07618	+	5.77795i	−0.332819	+	0.471768i
$151$			19.3780i			1.57696i	0.615062	+	0.788479i	$0.289131\pi$
$151$			19.3780i			1.57696i	−0.615062	+	0.788479i	$0.710869\pi$
$152$	−10.0439	−	0.0784231i	−0.814667	−	0.00636095i
$153$	−0.514721	+	3.24982i	−0.0416127	+	0.262732i
$154$	−0.0231386	+	0.0854642i	−0.00186456	+	0.00688690i
$155$	−5.18997	−	0.917596i	−0.416868	−	0.0737031i
$156$	1.11084	+	1.24670i	0.0889383	+	0.0998160i
$157$	−11.0581	−	11.0581i	−0.882529	−	0.882529i	0.111262	−	0.993791i	$-0.464511\pi$
$157$	−11.0581	−	11.0581i	−0.882529	−	0.882529i	−0.993791	+	0.111262i	$0.964511\pi$
$158$	4.94789	−	5.46651i	0.393633	−	0.434892i
$159$	−4.39213	+	13.5176i	−0.348318	+	1.07201i
$160$	−12.6053	−	1.05229i	−0.996534	−	0.0831907i
$161$	−0.263123	−	0.809810i	−0.0207370	−	0.0638219i
$162$	−1.29045	−	0.578573i	−0.101387	−	0.0454570i
$163$	18.5208	−	9.43684i	1.45066	−	0.739150i	0.461663	−	0.887056i	$-0.347253\pi$
$163$	18.5208	−	9.43684i	1.45066	−	0.739150i	0.989002	+	0.147905i	$0.0472530\pi$
$164$	−0.830872	−	8.32168i	−0.0648802	−	0.649814i
$165$	0.702225	+	1.00387i	0.0546682	+	0.0781508i
$166$	3.13140	+	8.22147i	0.243044	+	0.638110i
$167$	16.9741	−	2.68843i	1.31349	−	0.208037i	0.539905	−	0.841726i	$-0.318460\pi$
$167$	16.9741	−	2.68843i	1.31349	−	0.208037i	0.773587	+	0.633690i	$0.218460\pi$
$168$	−0.102275	+	0.306605i	−0.00789072	+	0.0236551i
$169$	7.23149	−	9.95329i	0.556268	−	0.765638i
$170$	7.11942	−	7.58791i	0.546035	−	0.581966i
$171$	2.08732	+	2.87295i	0.159621	+	0.219700i
$172$	6.09785	+	2.37724i	0.464957	+	0.181263i
$173$	11.8394	+	6.03246i	0.900130	+	0.458639i	0.841881	−	0.539663i	$-0.181448\pi$
$173$	11.8394	+	6.03246i	0.900130	+	0.458639i	0.0582491	+	0.998302i	$0.481448\pi$
$174$	6.90539	+	8.57298i	0.523497	+	0.649916i
$175$	−0.0691094	−	0.567171i	−0.00522418	−	0.0428741i
$176$	−0.912166	+	1.99267i	−0.0687571	+	0.150203i
$177$	2.64924	−	5.19942i	0.199129	−	0.390812i
$178$	−12.5117	+	7.18026i	−0.937789	+	0.538183i
$179$	11.9838	−	8.70672i	0.895709	−	0.650771i	−0.0416514	−	0.999132i	$-0.513262\pi$
$179$	11.9838	−	8.70672i	0.895709	−	0.650771i	0.937360	+	0.348362i	$0.113262\pi$
$180$	2.34834	+	3.80595i	0.175035	+	0.283679i
$181$	2.28163	+	1.65770i	0.169592	+	0.123216i	0.669344	−	0.742953i	$-0.266575\pi$
$181$	2.28163	+	1.65770i	0.169592	+	0.123216i	−0.499752	+	0.866169i	$0.666575\pi$
$182$	−0.134149	−	0.0144527i	−0.00994378	−	0.00107131i
$183$	1.05120	+	6.63705i	0.0777073	+	0.490625i
$184$	−3.13430	−	20.8411i	−0.231064	−	1.53643i
$185$	0.804985	+	0.607181i	0.0591836	+	0.0446408i
$186$	−1.82273	+	2.79083i	−0.133649	+	0.204634i
$187$	−0.818412	−	1.60622i	−0.0598482	−	0.117459i
$188$	1.71495	+	6.53619i	0.125076	+	0.476701i
$189$	0.108680	−	0.0353123i	0.00790532	−	0.00256859i
$190$	−0.357532	−	11.2241i	−0.0259381	−	0.814279i
$191$	0.659670	+	0.214340i	0.0477320	+	0.0155091i	0.332786	−	0.943002i	$-0.392011\pi$
$191$	0.659670	+	0.214340i	0.0477320	+	0.0155091i	−0.285054	+	0.958512i	$0.592011\pi$
$192$	−3.74279	+	7.07047i	−0.270112	+	0.510267i
$193$	0.643179	−	0.643179i	0.0462971	−	0.0462971i	−0.683579	−	0.729876i	$-0.739578\pi$
$193$	0.643179	−	0.643179i	0.0462971	−	0.0462971i	0.729876	+	0.683579i	$0.239578\pi$
$194$	2.44007	−	0.121511i	0.175187	−	0.00872401i
$195$	−1.34353	+	1.29623i	−0.0962119	+	0.0928252i
$196$	5.61716	+	12.7952i	0.401226	+	0.913942i
$197$	4.69155	+	0.743068i	0.334259	+	0.0529414i	0.321308	−	0.946975i	$-0.395877\pi$
$197$	4.69155	+	0.743068i	0.334259	+	0.0529414i	0.0129509	+	0.999916i	$0.495877\pi$
$198$	0.758305	−	0.159121i	0.0538904	−	0.0113082i
$199$	−17.8531			−1.26557			−0.632786	−	0.774327i	$-0.718089\pi$
$199$	−17.8531			−1.26557			−0.632786	+	0.774327i	$0.718089\pi$
$200$	0.616908	−	14.1287i	0.0436220	−	0.999048i
$201$	−12.4008			−0.874684
$202$	15.8793	−	3.33207i	1.11726	−	0.234444i
$203$	−0.878547	−	0.139148i	−0.0616619	−	0.00976629i
$204$	−2.64527	−	6.02558i	−0.185206	−	0.421875i
$205$	9.25978	−	1.29703i	0.646731	−	0.0905883i
$206$	−16.0365	+	0.798589i	−1.11731	+	0.0556403i
$207$	−5.26887	+	5.26887i	−0.366212	+	0.366212i
$208$	−3.21663	−	0.897886i	−0.223033	−	0.0622572i
$209$	−1.85039	−	0.601227i	−0.127994	−	0.0415878i
$210$	−0.347058	−	0.100669i	−0.0239493	−	0.00694681i
$211$	3.94777	−	1.28271i	0.271776	−	0.0883053i	−0.169958	−	0.985451i	$-0.554363\pi$
$211$	3.94777	−	1.28271i	0.271776	−	0.0883053i	0.441734	+	0.897146i	$0.354363\pi$
$212$	−7.21428	−	27.4958i	−0.495479	−	1.88842i
$213$	7.16944	+	14.0708i	0.491242	+	0.964117i
$214$	−2.82320	+	4.32267i	−0.192990	+	0.295492i
$215$	−2.38549	+	6.91761i	−0.162689	+	0.471777i
$216$	2.79697	−	0.420638i	0.190310	−	0.0286208i
$217$	−0.0421347	−	0.266028i	−0.00286029	−	0.0180592i
$218$	−7.18934	−	0.774553i	−0.486924	−	0.0524594i
$219$	−1.19465	−	0.867961i	−0.0807266	−	0.0586513i
$220$	−2.26655	−	0.930717i	−0.152810	−	0.0627489i
$221$	2.22244	−	1.61470i	0.149498	−	0.108617i
$222$	0.553097	−	0.317414i	0.0371214	−	0.0213034i
$223$	−5.03433	+	9.88043i	−0.337124	+	0.661643i	−0.995877	−	0.0907167i	$-0.971084\pi$
$223$	−5.03433	+	9.88043i	−0.337124	+	0.661643i	0.658753	+	0.752359i	$0.271084\pi$
$224$	−0.159168	−	0.626524i	−0.0106349	−	0.0418614i
$225$	−4.14776	+	2.79214i	−0.276517	+	0.186143i
$226$	13.7402	+	17.0584i	0.913988	+	1.13471i
$227$	−7.98815	−	4.07017i	−0.530192	−	0.270147i	0.168335	−	0.985730i	$-0.446161\pi$
$227$	−7.98815	−	4.07017i	−0.530192	−	0.270147i	−0.698527	+	0.715583i	$0.746161\pi$
$228$	−6.61725	−	2.57972i	−0.438238	−	0.170846i
$229$	−11.2030	−	15.4196i	−0.740315	−	1.01896i	−0.998600	−	0.0528873i	$-0.983158\pi$
$229$	−11.2030	−	15.4196i	−0.740315	−	1.01896i	0.258286	−	0.966069i	$-0.416842\pi$
$230$	23.1439	−	4.42518i	1.52606	−	0.291788i
$231$	−0.0368001	+	0.0506510i	−0.00242127	+	0.00333259i
$232$	−20.8851	−	6.96672i	−1.37117	−	0.457388i
$233$	20.2185	−	3.20229i	1.32456	−	0.209789i	0.546222	−	0.837640i	$-0.316065\pi$
$233$	20.2185	−	3.20229i	1.32456	−	0.209789i	0.778333	+	0.627851i	$0.216065\pi$
$234$	0.420264	+	1.10340i	0.0274735	+	0.0721315i
$235$	−7.22594	+	2.20555i	−0.471368	+	0.143874i
$236$	1.15951	+	11.6132i	0.0754775	+	0.755952i
$237$	4.64540	−	2.36695i	0.301751	−	0.153750i
$238$	0.485203	+	0.217541i	0.0314510	+	0.0141011i
$239$	−1.41153	−	4.34425i	−0.0913044	−	0.281006i	0.894969	−	0.446129i	$-0.147198\pi$
$239$	−1.41153	−	4.34425i	−0.0913044	−	0.281006i	−0.986273	+	0.165123i	$0.947198\pi$
$240$	−8.06469	−	3.86791i	−0.520574	−	0.249673i
$241$	−5.60469	+	17.2495i	−0.361030	+	1.11113i	0.591401	+	0.806378i	$0.298575\pi$
$241$	−5.60469	+	17.2495i	−0.361030	+	1.11113i	−0.952430	+	0.304757i	$0.901425\pi$
$242$	10.1544	−	11.2188i	0.652750	−	0.721169i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−8.94071	−	10.0342i	−0.572370	−	0.642374i
$245$	−14.0453	+	6.84232i	−0.897319	+	0.437140i
$246$	1.54541	−	5.70807i	0.0985315	−	0.363933i
$247$	0.463807	−	2.92836i	0.0295113	−	0.186327i
$248$	0.0520519	−	6.66646i	0.00330530	−	0.423320i
$249$			6.22086i			0.394231i
$250$	15.8113	+	0.0630033i	0.999992	+	0.00398468i
$251$		−	16.9015i		−	1.06681i	−0.845859	−	0.533406i	$-0.820912\pi$
$251$		−	16.9015i		−	1.06681i	0.845859	−	0.533406i	$-0.179088\pi$
$252$	−0.144751	+	0.176863i	−0.00911848	+	0.0111413i
$253$	0.638632	−	4.03217i	0.0401505	−	0.253500i
$254$	−14.4926	−	3.92374i	−0.909346	−	0.246197i
$255$	6.61427	−	3.22222i	0.414202	−	0.201784i
$256$	−1.34081	−	15.9437i	−0.0838004	−	0.996483i
$257$	−13.4787	−	13.4787i	−0.840776	−	0.840776i	0.148184	−	0.988960i	$-0.452657\pi$
$257$	−13.4787	−	13.4787i	−0.840776	−	0.840776i	−0.988960	+	0.148184i	$0.952657\pi$
$258$	3.43113	+	3.10562i	0.213613	+	0.193347i
$259$	−0.0159232	+	0.0490067i	−0.000989421	+	0.00304513i
$260$	0.860518	−	3.63327i	0.0533671	−	0.225326i
$261$	2.40538	+	7.40300i	0.148889	+	0.458234i
$262$	−12.8934	+	28.7573i	−0.796555	+	1.77663i
$263$	−12.5493	+	6.39419i	−0.773823	+	0.394283i	−0.795865	−	0.605475i	$-0.792983\pi$
$263$	−12.5493	+	6.39419i	−0.773823	+	0.394283i	0.0220417	+	0.999757i	$0.492983\pi$
$264$	−1.10428	+	1.08717i	−0.0679639	+	0.0669108i
$265$	30.3973	−	9.27808i	1.86729	−	0.569948i
$266$	0.536307	−	0.204269i	0.0328831	−	0.0125245i
$267$	−10.0749	+	1.59570i	−0.616571	+	0.0976552i
$268$	20.8704	−	13.3994i	1.27486	−	0.818501i
$269$	5.30034	−	7.29529i	0.323167	−	0.444802i	−0.616264	−	0.787540i	$-0.711354\pi$
$269$	5.30034	−	7.29529i	0.323167	−	0.444802i	0.939431	+	0.342738i	$0.111354\pi$
$270$	0.593879	+	3.10601i	0.0361423	+	0.189026i
$271$	6.50668	+	8.95567i	0.395253	+	0.544018i	0.959545	−	0.281557i	$-0.0908508\pi$
$271$	6.50668	+	8.95567i	0.395253	+	0.544018i	−0.564292	+	0.825575i	$0.690851\pi$
$272$	10.9628	+	7.28269i	0.664717	+	0.441578i
$273$	−0.0850078	−	0.0433137i	−0.00514491	−	0.00262146i
$274$	8.16956	−	6.58045i	0.493541	−	0.397540i
$275$	0.939302	−	2.57333i	0.0566421	−	0.155178i
$276$	3.17426	−	14.5606i	0.191068	−	0.876447i
$277$	12.5869	−	24.7032i	0.756274	−	1.48427i	−0.114943	−	0.993372i	$-0.536668\pi$
$277$	12.5869	−	24.7032i	0.756274	−	1.48427i	0.871217	−	0.490899i	$-0.163332\pi$
$278$	6.59858	+	11.4981i	0.395756	+	0.689609i
$279$	−1.90687	+	1.38542i	−0.114161	+	0.0829430i
$280$	0.692870	−	0.205583i	0.0414069	−	0.0122859i
$281$	7.95866	+	5.78231i	0.474774	+	0.344943i	0.799299	−	0.600934i	$-0.205204\pi$
$281$	7.95866	+	5.78231i	0.474774	+	0.344943i	−0.324525	+	0.945877i	$0.605204\pi$
$282$	−0.511827	+	4.75073i	−0.0304788	+	0.282902i
$283$	−2.38077	−	15.0316i	−0.141522	−	0.893535i	−0.951628	−	0.307252i	$-0.900591\pi$
$283$	−2.38077	−	15.0316i	−0.141522	−	0.893535i	0.810106	−	0.586283i	$-0.199409\pi$
$284$	−27.2701	−	15.9342i	−1.61818	−	0.945521i
$285$	2.58868	−	7.50683i	0.153340	−	0.444666i
$286$	−0.541615	−	0.353736i	−0.0320263	−	0.0209169i
$287$	0.216933	+	0.425755i	0.0128052	+	0.0251315i
$288$	−4.25276	+	3.73015i	−0.250596	+	0.219801i
$289$	5.87157	−	1.90779i	0.345387	−	0.112223i
$290$	6.85729	−	23.6406i	0.402674	−	1.38823i
$291$	1.64297	+	0.533835i	0.0963129	+	0.0312940i
$292$	2.94843	+	0.169915i	0.172544	+	0.00994350i
$293$	−18.5529	+	18.5529i	−1.08387	+	1.08387i	−0.0877260	+	0.996145i	$0.527960\pi$
$293$	−18.5529	+	18.5529i	−1.08387	+	1.08387i	−0.996145	+	0.0877260i	$0.972040\pi$
$294$	0.491450	+	9.86880i	0.0286619	+	0.575560i
$295$	−12.9223	+	1.81004i	−0.752366	+	0.105385i
$296$	−0.587879	+	1.13184i	−0.0341698	+	0.0657870i
$297$	0.541135	+	0.0857074i	0.0313999	+	0.00497325i
$298$	−6.05377	−	28.8497i	−0.350685	−	1.67122i
$299$	6.22109			0.359775
$300$	3.96363	−	9.18094i	0.228840	−	0.530062i
$301$	−0.373950			−0.0215541
$302$	−5.62795	−	26.8205i	−0.323852	−	1.54335i
$303$	11.3316	+	1.79476i	0.650986	+	0.103106i
$304$	13.9242	−	2.80851i	0.798609	−	0.161079i
$305$	10.8135	−	10.4329i	0.619180	−	0.597384i
$306$	−0.231436	−	4.64747i	−0.0132303	−	0.265678i
$307$	−7.59845	+	7.59845i	−0.433667	+	0.433667i	−0.889874	−	0.456207i	$-0.849208\pi$
$307$	−7.59845	+	7.59845i	−0.433667	+	0.433667i	0.456207	+	0.889874i	$0.349208\pi$
$308$	0.00720410	−	0.125009i	0.000410492	−	0.00712303i
$309$	−10.7979	−	3.50844i	−0.614269	−	0.199588i
$310$	7.44977	−	0.237305i	0.423119	−	0.0134780i
$311$	−18.8976	+	6.14019i	−1.07158	+	0.348178i	−0.791104	−	0.611682i	$-0.790493\pi$
$311$	−18.8976	+	6.14019i	−1.07158	+	0.348178i	−0.280479	+	0.959860i	$0.590493\pi$
$312$	−1.89956	−	1.40290i	−0.107541	−	0.0794236i
$313$	−1.19984	−	2.35482i	−0.0678190	−	0.133102i	0.854608	−	0.519273i	$-0.173797\pi$
$313$	−1.19984	−	2.35482i	−0.0678190	−	0.133102i	−0.922427	+	0.386171i	$0.873797\pi$
$314$	18.5167	+	12.0935i	1.04496	+	0.682477i
$315$	−0.203998	−	0.153871i	−0.0114940	−	0.00866966i
$316$	−5.26058	+	9.00305i	−0.295931	+	0.506461i
$317$	2.11922	+	13.3802i	0.119027	+	0.751508i	0.972934	+	0.231082i	$0.0742267\pi$
$317$	2.11922	+	13.3802i	0.119027	+	0.751508i	−0.853907	+	0.520426i	$0.825773\pi$
$318$	2.15310	−	19.9849i	0.120740	−	1.12070i
$319$	−3.45020	−	2.50672i	−0.193174	−	0.140349i
$320$	17.7522	−	2.20451i	0.992377	−	0.123236i
$321$	−2.95352	+	2.14586i	−0.164849	+	0.119770i
$322$	0.599374	+	1.04441i	0.0334018	+	0.0582029i
$323$	−5.30465	+	10.4110i	−0.295158	+	0.579281i
$324$	1.95410	+	0.426001i	0.108561	+	0.0236667i
$325$	4.09706	+	0.800307i	0.227264	+	0.0443930i
$326$	−22.8934	+	18.4403i	−1.26795	+	1.02131i
$327$	−4.55576	−	2.32128i	−0.251934	−	0.128367i
$328$	3.56685	+	11.2765i	0.196947	+	0.622639i
$329$	−0.226942	−	0.312359i	−0.0125117	−	0.0172209i
$330$	−1.26348	−	1.18547i	−0.0695524	−	0.0652581i
$331$	1.74817	−	2.40616i	0.0960883	−	0.132254i	−0.758266	−	0.651946i	$-0.773953\pi$
$331$	1.74817	−	2.40616i	0.0960883	−	0.132254i	0.854354	+	0.519691i	$0.173953\pi$
$332$	−6.72185	−	10.4696i	−0.368909	−	0.574596i
$333$	0.445374	−	0.0705403i	0.0244063	−	0.00386558i
$334$	−22.7125	+	8.65075i	−1.24277	+	0.473348i
$335$	15.8942	+	22.7216i	0.868395	+	1.24141i
$336$	0.0525090	−	0.454066i	0.00286460	−	0.0247714i
$337$	7.68126	−	3.91380i	0.418425	−	0.213198i	−0.232086	−	0.972695i	$-0.574555\pi$
$337$	7.68126	−	3.91380i	0.418425	−	0.213198i	0.650511	+	0.759497i	$0.274555\pi$
$338$	−7.11815	+	15.8763i	−0.387176	+	0.863557i
$339$	4.78619	+	14.7304i	0.259950	+	0.800044i
$340$	−7.65002	+	12.5699i	−0.414881	+	0.681699i
$341$	0.399054	−	1.22816i	0.0216100	−	0.0665087i
$342$	−3.72339	−	3.37014i	−0.201338	−	0.182236i
$343$	−1.13019	−	1.13019i	−0.0610246	−	0.0610246i
$344$	−9.13028	−	1.51926i	−0.492272	−	0.0819131i
$345$	16.4072	+	2.90082i	0.883332	+	0.156175i
$346$	−18.1385	−	4.91084i	−0.975133	−	0.264008i
$347$	−4.55737	+	28.7741i	−0.244653	+	1.54468i	0.493321	+	0.869847i	$0.335783\pi$
$347$	−4.55737	+	28.7741i	−0.244653	+	1.54468i	−0.737974	+	0.674829i	$0.764217\pi$
$348$	−12.0474	−	9.86007i	−0.645809	−	0.528555i
$349$			24.7013i			1.32223i	0.750284	+	0.661115i	$0.229917\pi$
$349$			24.7013i			1.32223i	−0.750284	+	0.661115i	$0.770083\pi$
$350$	0.260376	+	0.764932i	0.0139177	+	0.0408874i
$351$			0.834899i			0.0445636i
$352$	0.683771	−	3.02291i	0.0364451	−	0.161122i
$353$	0.908260	−	5.73453i	0.0483418	−	0.305218i	−0.951656	−	0.307165i	$-0.900620\pi$
$353$	0.908260	−	5.73453i	0.0483418	−	0.305218i	0.999998	+	0.00194675i	$0.000619670\pi$
$354$	−2.15666	+	7.96578i	−0.114625	+	0.423377i
$355$	16.5924	−	31.1711i	0.880632	−	1.65439i
$356$	15.2317	−	13.5717i	0.807276	−	0.719301i
$357$	0.265869	+	0.265869i	0.0140713	+	0.0140713i
$358$	−14.0577	+	15.5312i	−0.742971	+	0.820847i
$359$	−4.60845	+	14.1833i	−0.243225	+	0.748568i	0.752699	+	0.658365i	$0.228752\pi$
$359$	−4.60845	+	14.1833i	−0.243225	+	0.748568i	−0.995923	+	0.0902033i	$0.971248\pi$
$360$	−4.35564	−	4.58568i	−0.229562	−	0.241686i
$361$	−1.97439	−	6.07654i	−0.103915	−	0.319818i
$362$	−3.63938	−	1.63172i	−0.191282	−	0.0857613i
$363$	9.53362	−	4.85762i	0.500385	−	0.254959i
$364$	0.189869	−	0.0189573i	0.00995184	−	0.000993635i
$365$	−0.0591473	+	3.30139i	−0.00309591	+	0.172803i
$366$	−3.38254	−	8.88083i	−0.176808	−	0.464209i
$367$	−19.7109	+	3.12190i	−1.02890	+	0.162962i	−0.647989	−	0.761649i	$-0.724390\pi$
$367$	−19.7109	+	3.12190i	−1.02890	+	0.162962i	−0.380912	+	0.924611i	$0.624390\pi$
$368$	10.3910	+	27.9353i	0.541668	+	1.45623i
$369$	2.45784	−	3.38293i	0.127950	−	0.176108i
$370$	−1.29050	−	0.606589i	−0.0670898	−	0.0315351i
$371$	0.954674	+	1.31400i	0.0495642	+	0.0682193i
$372$	1.71225	−	4.39208i	0.0887758	−	0.227719i
$373$	30.1435	+	15.3589i	1.56077	+	0.795253i	0.999476	−	0.0323617i	$-0.0103029\pi$
$373$	30.1435	+	15.3589i	1.56077	+	0.795253i	0.561296	+	0.827615i	$0.310303\pi$
$374$	1.59924	+	1.98543i	0.0826945	+	0.102664i
$375$	10.4322	+	4.02110i	0.538716	+	0.207649i
$376$	−4.27192	−	8.54848i	−0.220308	−	0.440854i
$377$	2.95041	−	5.79050i	0.151954	−	0.298226i
$378$	−0.140165	+	0.0804388i	−0.00720932	+	0.00413732i
$379$	−11.0434	+	8.02353i	−0.567264	+	0.412141i	−0.834110	−	0.551598i	$-0.814018\pi$
$379$	−11.0434	+	8.02353i	−0.567264	+	0.412141i	0.266846	+	0.963739i	$0.414018\pi$
$380$	3.75466	+	15.4311i	0.192610	+	0.791596i
$381$	−8.58914	−	6.24037i	−0.440035	−	0.319704i
$382$	−0.975280	−	0.105073i	−0.0498997	−	0.00537601i
$383$	3.32987	+	21.0240i	0.170148	+	1.07427i	0.913936	+	0.405858i	$0.133027\pi$
$383$	3.32987	+	21.0240i	0.170148	+	1.07427i	−0.743788	+	0.668416i	$0.766973\pi$
$384$	3.12680	−	10.8730i	0.159564	−	0.554863i
$385$	0.139973	+	0.00250775i	0.00713370	+	0.000127807i
$386$	−0.703407	+	1.07700i	−0.0358025	+	0.0548181i
$387$	1.48565	+	2.91575i	0.0755198	+	0.148216i
$388$	−3.34193	+	0.876850i	−0.169661	+	0.0445153i
$389$	−5.57557	+	1.81161i	−0.282693	+	0.0918524i	−0.446932	−	0.894568i	$-0.647483\pi$
$389$	−5.57557	+	1.81161i	−0.282693	+	0.0918524i	0.164239	+	0.986421i	$0.447483\pi$
$390$	1.48307	−	2.18428i	0.0750982	−	0.110605i
$391$	−23.3173	−	7.57625i	−1.17921	−	0.383147i
$392$	−11.4907	−	16.0780i	−0.580366	−	0.812064i
$393$	−15.7577	+	15.7577i	−0.794872	+	0.794872i
$394$	−6.70924	+	0.334109i	−0.338007	+	0.0168322i
$395$	−10.2909	−	5.47788i	−0.517794	−	0.275622i
$396$	−1.00333	+	0.440470i	−0.0504194	+	0.0221344i
$397$	8.40000	+	1.33043i	0.421584	+	0.0667723i	0.363622	−	0.931547i	$-0.381540\pi$
$397$	8.40000	+	1.33043i	0.421584	+	0.0667723i	0.0579615	+	0.998319i	$0.481540\pi$
$398$	24.7099	−	5.18508i	1.23860	−	0.259905i
$399$	0.405802			0.0203155
$400$	3.24955	+	19.7342i	0.162478	+	0.986712i
$401$	20.6802			1.03272			0.516360	−	0.856372i	$-0.327287\pi$
$401$	20.6802			1.03272			0.516360	+	0.856372i	$0.327287\pi$
$402$	17.1636	−	3.60156i	0.856040	−	0.179630i
$403$	1.94365	+	0.307843i	0.0968199	+	0.0153348i
$404$	−21.0103	+	9.22365i	−1.04530	+	0.458894i
$405$	−0.389304	+	2.20192i	−0.0193446	+	0.109414i
$406$	1.25638	−	0.0625659i	0.0623533	−	0.00310509i
$407$	−0.174693	+	0.174693i	−0.00865921	+	0.00865921i
$408$	5.41124	+	7.57156i	0.267897	+	0.374848i
$409$	−24.9795	−	8.11632i	−1.23515	−	0.401326i	−0.382575	−	0.923924i	$-0.624963\pi$
$409$	−24.9795	−	8.11632i	−1.23515	−	0.401326i	−0.852579	+	0.522598i	$0.824963\pi$
$410$	−12.4395	+	4.48450i	−0.614343	+	0.221474i
$411$	7.05464	−	2.29219i	0.347980	−	0.113065i
$412$	21.9636	−	5.76278i	1.08207	−	0.283912i
$413$	−0.302737	−	0.594154i	−0.0148967	−	0.0292364i
$414$	5.76225	−	8.82273i	0.283199	−	0.433613i
$415$	11.3983	−	7.97336i	0.559521	−	0.391397i
$416$	4.71282	+	0.308531i	0.231065	+	0.0151270i
$417$	1.46643	+	9.25868i	0.0718114	+	0.453399i
$418$	2.73568	+	0.294732i	0.133807	+	0.0144158i
$419$	27.5322	+	20.0033i	1.34504	+	0.977227i	0.999242	+	0.0389168i	$0.0123907\pi$
$419$	27.5322	+	20.0033i	1.34504	+	0.977227i	0.345795	+	0.938310i	$0.387609\pi$
$420$	0.509590	+	0.0385366i	0.0248654	+	0.00188039i
$421$	−3.66642	+	2.66381i	−0.178690	+	0.129826i	−0.673535	−	0.739155i	$-0.735225\pi$
$421$	−3.66642	+	2.66381i	−0.178690	+	0.129826i	0.494845	+	0.868981i	$0.335225\pi$
$422$	−5.09146	+	2.92191i	−0.247848	+	0.142236i
$423$	−1.53390	+	3.01046i	−0.0745810	+	0.146373i
$424$	17.9707	+	35.9608i	0.872733	+	1.74641i
$425$	−14.3816	−	7.98917i	−0.697609	−	0.387532i
$426$	−14.0096	−	17.3928i	−0.678767	−	0.842683i
$427$	0.684195	+	0.348615i	0.0331105	+	0.0168706i
$428$	2.65207	−	6.80282i	0.128193	−	0.328827i
$429$	−0.268868	−	0.370065i	−0.0129811	−	0.0178669i
$430$	1.29260	−	10.2673i	0.0623347	−	0.495132i
$431$	6.87989	−	9.46936i	0.331393	−	0.456123i	−0.610510	−	0.792009i	$-0.709036\pi$
$431$	6.87989	−	9.46936i	0.331393	−	0.456123i	0.941903	+	0.335885i	$0.109036\pi$
$432$	−3.74904	+	1.39452i	−0.180376	+	0.0670938i
$433$	−16.1360	+	2.55570i	−0.775448	+	0.122819i	−0.531601	−	0.846995i	$-0.678409\pi$
$433$	−16.1360	+	2.55570i	−0.775448	+	0.122819i	−0.243847	+	0.969814i	$0.578409\pi$
$434$	0.135580	+	0.355964i	0.00650805	+	0.0170868i
$435$	10.4813	−	13.8958i	0.502539	−	0.666253i
$436$	10.1755	−	1.01597i	0.487318	−	0.0486560i
$437$	−23.5767	+	12.0130i	−1.12783	+	0.574657i
$438$	1.90555	+	0.854357i	0.0910509	+	0.0408228i
$439$	−7.35130	−	22.6250i	−0.350858	−	1.07983i	−0.958372	−	0.285522i	$-0.907833\pi$
$439$	−7.35130	−	22.6250i	−0.350858	−	1.07983i	0.607514	−	0.794309i	$-0.292167\pi$
$440$	3.40737	+	0.629904i	0.162440	+	0.0300295i
$441$	−2.15908	+	6.64498i	−0.102814	+	0.316427i
$442$	−2.60706	+	2.88032i	−0.124005	+	0.137003i
$443$	−28.7205	−	28.7205i	−1.36455	−	1.36455i	−0.868016	−	0.496536i	$-0.834605\pi$
$443$	−28.7205	−	28.7205i	−1.36455	−	1.36455i	−0.496536	−	0.868016i	$-0.665395\pi$
$444$	−0.673338	+	0.599959i	−0.0319552	+	0.0284728i
$445$	15.8368	+	16.4146i	0.750737	+	0.778128i
$446$	4.09829	−	15.1373i	0.194060	−	0.716773i
$447$	3.26074	−	20.5875i	0.154228	−	0.973755i
$448$	0.402261	+	0.820926i	0.0190051	+	0.0387851i
$449$			16.4871i			0.778074i	0.921222	+	0.389037i	$0.127192\pi$
$449$			16.4871i			0.778074i	−0.921222	+	0.389037i	$0.872808\pi$
$450$	4.92987	−	5.06916i	0.232396	−	0.238962i
$451$			2.29098i			0.107878i
$452$	−23.9717	−	19.6194i	−1.12754	−	0.922819i
$453$	3.03139	−	19.1394i	0.142427	−	0.899248i
$454$	12.2383	+	3.31340i	0.574370	+	0.155505i
$455$	0.0295932	+	0.211273i	0.00138735	+	0.00990463i
$456$	9.90797	+	1.64867i	0.463983	+	0.0772060i
$457$	12.2230	+	12.2230i	0.571769	+	0.571769i	0.932623	−	0.360853i	$-0.117514\pi$
$457$	12.2230	+	12.2230i	0.571769	+	0.571769i	−0.360853	+	0.932623i	$0.617514\pi$
$458$	19.9841	+	18.0881i	0.933793	+	0.845202i
$459$	1.01677	−	3.12929i	0.0474586	−	0.146063i
$460$	−30.7475	+	12.8464i	−1.43361	+	0.598968i
$461$	7.32565	+	22.5460i	0.341189	+	1.05007i	0.963592	+	0.267376i	$0.0861566\pi$
$461$	7.32565	+	22.5460i	0.341189	+	1.05007i	−0.622403	+	0.782697i	$0.713843\pi$
$462$	0.0362233	−	0.0807923i	0.00168526	−	0.00375880i
$463$	17.2393	−	8.78385i	0.801178	−	0.408220i	−0.00493114	−	0.999988i	$-0.501570\pi$
$463$	17.2393	−	8.78385i	0.801178	−	0.408220i	0.806109	+	0.591767i	$0.201570\pi$
$464$	30.9298	+	3.57677i	1.43588	+	0.166047i
$465$	4.98252	+	1.71819i	0.231059	+	0.0796791i
$466$	−27.0537	+	10.3042i	−1.25324	+	0.477335i
$467$	25.3795	−	4.01972i	1.17442	−	0.186011i	0.461428	−	0.887178i	$-0.347337\pi$
$467$	25.3795	−	4.01972i	1.17442	−	0.186011i	0.712997	+	0.701167i	$0.247337\pi$
$468$	−0.902136	−	1.40513i	−0.0417012	−	0.0649520i
$469$	−0.832936	+	1.14644i	−0.0384614	+	0.0529376i
$470$	9.36064	−	5.15127i	0.431774	−	0.237610i
$471$	9.19205	+	12.6518i	0.423547	+	0.582963i
$472$	−4.97765	−	15.7367i	−0.229115	−	0.724338i
$473$	−1.59748	−	0.813959i	−0.0734524	−	0.0374259i
$474$	−5.74212	+	4.62519i	−0.263744	+	0.212442i
$475$	−17.0725	+	4.87844i	−0.783339	+	0.223838i
$476$	−0.734736	−	0.160175i	−0.0336765	−	0.00734159i
$477$	6.45267	−	12.6641i	0.295447	−	0.579848i
$478$	3.21536	+	5.60279i	0.147067	+	0.256266i
$479$	27.4905	−	19.9730i	1.25607	−	0.912590i	0.257515	−	0.966274i	$-0.417096\pi$
$479$	27.4905	−	19.9730i	1.25607	−	0.912590i	0.998558	+	0.0536842i	$0.0170964\pi$
$480$	12.2855	+	3.01123i	0.560752	+	0.137443i
$481$	−0.304577	−	0.221288i	−0.0138875	−	0.0100899i
$482$	2.74752	−	25.5022i	0.125146	−	1.16159i
$483$	0.133201	+	0.841001i	0.00606088	+	0.0382669i
$484$	−10.7961	+	18.4767i	−0.490734	+	0.839850i
$485$	−1.12769	−	3.69460i	−0.0512058	−	0.167763i
$486$	1.18405	+	0.773320i	0.0537096	+	0.0350785i
$487$	−12.2987	−	24.1375i	−0.557307	−	1.09378i	−0.982078	−	0.188475i	$-0.939645\pi$
$487$	−12.2987	−	24.1375i	−0.557307	−	1.09378i	0.424771	−	0.905301i	$-0.360355\pi$
$488$	15.2888	+	11.2914i	0.692092	+	0.511138i
$489$	−19.7691	+	6.42336i	−0.893988	+	0.290474i
$490$	17.4524	−	13.5494i	0.788419	−	0.612101i
$491$	1.87731	+	0.609975i	0.0847218	+	0.0275278i	0.351071	−	0.936349i	$-0.385818\pi$
$491$	1.87731	+	0.609975i	0.0847218	+	0.0275278i	−0.266349	+	0.963877i	$0.585818\pi$
$492$	−0.481154	+	8.34920i	−0.0216921	+	0.376411i
$493$	−18.1103	+	18.1103i	−0.815647	+	0.815647i
$494$	0.208543	+	4.18776i	0.00938282	+	0.188416i
$495$	−0.536540	−	1.10136i	−0.0241157	−	0.0495024i
$496$	1.86410	+	9.24196i	0.0837004	+	0.414976i
$497$	1.78239	+	0.282303i	0.0799511	+	0.0126630i
$498$	−1.80673	−	8.61011i	−0.0809614	−	0.385828i
$499$	15.8221			0.708297			0.354148	−	0.935189i	$-0.384771\pi$
$499$	15.8221			0.708297			0.354148	+	0.935189i	$0.384771\pi$
$500$	−21.9022	+	4.50487i	−0.979496	+	0.201464i
$501$	−17.1856			−0.767798
$502$	4.90870	+	23.3928i	0.219086	+	1.04407i
$503$	−16.5176	−	2.61613i	−0.736482	−	0.116647i	−0.223086	−	0.974799i	$-0.571613\pi$
$503$	−16.5176	−	2.61613i	−0.736482	−	0.116647i	−0.513397	+	0.858151i	$0.671613\pi$
$504$	0.148980	−	0.286831i	0.00663609	−	0.0127764i
$505$	−11.2354	−	23.0630i	−0.499970	−	1.02629i
$506$	0.287151	+	5.76628i	0.0127654	+	0.256342i
$507$	−8.69949	+	8.69949i	−0.386358	+	0.386358i
$508$	21.1983	+	1.22164i	0.940524	+	0.0542013i
$509$	−18.6546	−	6.06124i	−0.826850	−	0.268660i	−0.135132	−	0.990828i	$-0.543146\pi$
$509$	−18.6546	−	6.06124i	−0.826850	−	0.268660i	−0.691718	+	0.722168i	$0.743146\pi$
$510$	−8.21878	+	6.38077i	−0.363934	+	0.282545i
$511$	−0.160484	+	0.0521444i	−0.00709939	+	0.00230673i
$512$	6.48631	+	21.6778i	0.286657	+	0.958033i
$513$	−1.61219	−	3.16411i	−0.0711801	−	0.139699i
$514$	22.5700	+	14.7408i	0.995522	+	0.650189i
$515$	7.41134	+	24.2814i	0.326583	+	1.06997i
$516$	−5.65090	−	3.30188i	−0.248767	−	0.145357i
$517$	−0.289581	−	1.82834i	−0.0127358	−	0.0804104i
$518$	0.00780585	−	0.0724533i	0.000342969	−	0.00318341i
$519$	−10.7499	−	7.81027i	−0.471869	−	0.342833i
$520$	−0.135806	+	5.27862i	−0.00595548	+	0.231483i
$521$	18.9520	−	13.7694i	0.830303	−	0.603250i	−0.0893421	−	0.996001i	$-0.528476\pi$
$521$	18.9520	−	13.7694i	0.830303	−	0.603250i	0.919645	+	0.392751i	$0.128476\pi$
$522$	−5.47927	−	9.54767i	−0.239821	−	0.417890i
$523$	0.561777	−	1.10255i	0.0245648	−	0.0482111i	−0.878398	−	0.477930i	$-0.841387\pi$
$523$	0.561777	−	1.10255i	0.0245648	−	0.0482111i	0.902963	+	0.429719i	$0.141387\pi$
$524$	9.49333	−	43.5468i	0.414718	−	1.90235i
$525$	−0.0204665	+	0.570999i	−0.000893231	+	0.0249204i
$526$	15.5120	−	12.4947i	0.676357	−	0.544795i
$527$	−6.91009	−	3.52086i	−0.301008	−	0.153371i
$528$	1.21266	−	1.82544i	0.0527742	−	0.0794421i
$529$	−19.1160	−	26.3109i	−0.831129	−	1.14395i
$530$	−39.3774	+	21.6698i	−1.71044	+	0.941276i
$531$	−3.42999	+	4.72098i	−0.148849	+	0.204873i
$532$	−0.682960	+	0.438482i	−0.0296101	+	0.0190106i
$533$	−3.44817	+	0.546137i	−0.149357	+	0.0236558i
$534$	13.4809	−	5.13460i	0.583374	−	0.222196i
$535$	7.71735	+	2.66127i	0.333650	+	0.115057i
$536$	−24.9945	+	24.6072i	−1.07960	+	1.06287i
$537$	−13.1983	+	6.72485i	−0.569547	+	0.290199i
$538$	−5.21727	+	11.6366i	−0.224932	+	0.501688i
$539$	−1.18292	−	3.64065i	−0.0509520	−	0.156814i
$540$	−1.72405	−	4.12646i	−0.0741913	−	0.177574i
$541$	5.99846	−	18.4614i	0.257894	−	0.793716i	−0.735352	−	0.677686i	$-0.762983\pi$
$541$	5.99846	−	18.4614i	0.257894	−	0.793716i	0.993246	−	0.116030i	$-0.0370170\pi$
$542$	−11.6067	−	10.5055i	−0.498550	−	0.451252i
$543$	−1.99422	−	1.99422i	−0.0855800	−	0.0855800i
$544$	−17.2884	−	6.89582i	−0.741233	−	0.295656i
$545$	1.58597	+	11.3226i	0.0679354	+	0.485007i
$546$	0.130236	+	0.0352603i	0.00557360	+	0.00150900i
$547$	0.958973	−	6.05472i	0.0410027	−	0.258881i	−0.958668	−	0.284526i	$-0.908164\pi$
$547$	0.958973	−	6.05472i	0.0410027	−	0.258881i	0.999671	+	0.0256447i	$0.00816387\pi$
$548$	−9.39609	+	11.4805i	−0.401381	+	0.490422i
$549$		−	6.71978i		−	0.286793i
$550$	−0.552687	+	3.83447i	−0.0235666	+	0.163503i
$551$			27.6421i			1.17759i
$552$	−0.164553	+	21.0748i	−0.00700385	+	0.897005i
$553$	0.0932005	−	0.588445i	0.00396329	−	0.0250232i
$554$	−10.2466	+	37.8466i	−0.435337	+	1.60795i
$555$	−0.700090	−	0.725633i	−0.0297172	−	0.0308014i
$556$	−12.4723	−	13.9977i	−0.528943	−	0.593636i
$557$	−4.22564	−	4.22564i	−0.179046	−	0.179046i	0.611894	−	0.790940i	$-0.290408\pi$
$557$	−4.22564	−	4.22564i	−0.179046	−	0.179046i	−0.790940	+	0.611894i	$0.790408\pi$
$558$	2.23687	−	2.47133i	0.0946944	−	0.104620i
$559$	0.844279	−	2.59842i	0.0357092	−	0.109902i
$560$	−0.899274	+	0.485772i	−0.0380013	+	0.0205276i
$561$	0.557067	+	1.71448i	0.0235194	+	0.0723852i
$562$	−12.6947	−	5.69168i	−0.535494	−	0.240089i
$563$	−7.19657	+	3.66683i	−0.303299	+	0.154539i	−0.599016	−	0.800737i	$-0.704441\pi$
$563$	−7.19657	+	3.66683i	−0.303299	+	0.154539i	0.295717	+	0.955276i	$0.404441\pi$
$564$	−0.671353	−	6.72400i	−0.0282691	−	0.283131i
$565$	20.8555	−	27.6497i	0.877398	−	1.16323i
$566$	7.66078	+	20.1133i	0.322006	+	0.845426i
$567$	−0.112866	+	0.0178763i	−0.00473994	+	0.000750732i
$568$	42.3715	+	14.1340i	1.77787	+	0.593050i
$569$	20.6135	−	28.3720i	0.864161	−	1.18942i	−0.116400	−	0.993202i	$-0.537135\pi$
$569$	20.6135	−	28.3720i	0.864161	−	1.18942i	0.980561	−	0.196214i	$-0.0628646\pi$
$570$	−1.40270	+	11.1418i	−0.0587527	+	0.466679i
$571$	5.87123	+	8.08106i	0.245703	+	0.338182i	0.914001	−	0.405713i	$-0.132977\pi$
$571$	5.87123	+	8.08106i	0.245703	+	0.338182i	−0.668297	+	0.743894i	$0.732977\pi$
$572$	0.852368	+	0.332294i	0.0356393	+	0.0138939i
$573$	−0.618018	−	0.314896i	−0.0258181	−	0.0131550i
$574$	−0.423903	−	0.526271i	−0.0176934	−	0.0219661i
$575$	−15.7142	−	33.7804i	−0.655327	−	1.40874i
$576$	4.80277	−	6.39792i	0.200115	−	0.266580i
$577$	−12.4104	+	24.3568i	−0.516651	+	1.01399i	0.474376	+	0.880323i	$0.342674\pi$
$577$	−12.4104	+	24.3568i	−0.516651	+	1.01399i	−0.991027	+	0.133663i	$0.957326\pi$
$578$	−7.57259	+	4.34580i	−0.314978	+	0.180761i
$579$	−0.735876	+	0.534645i	−0.0305820	+	0.0222191i
$580$	−2.62501	+	34.7119i	−0.108998	+	1.44133i
$581$	0.575112	+	0.417843i	0.0238597	+	0.0173351i
$582$	−2.42903	−	0.261695i	−0.100687	−	0.0108476i
$583$	1.21818	+	7.69128i	0.0504518	+	0.318540i
$584$	−4.13019	+	0.621141i	−0.170908	+	0.0257030i
$585$	1.52976	−	1.07010i	0.0632478	−	0.0442432i
$586$	20.2902	−	31.0668i	0.838179	−	1.28336i
$587$	16.2223	+	31.8381i	0.669566	+	1.31410i	0.936597	+	0.350409i	$0.113958\pi$
$587$	16.2223	+	31.8381i	0.669566	+	1.31410i	−0.267030	+	0.963688i	$0.586042\pi$
$588$	−3.54640	−	13.5164i	−0.146251	−	0.557406i
$589$	−7.96049	+	2.58652i	−0.328006	+	0.106576i
$590$	17.3597	−	6.25825i	0.714687	−	0.257648i
$591$	−4.51755	−	1.46784i	−0.185827	−	0.0603789i
$592$	0.484944	−	1.73729i	0.0199311	−	0.0714021i
$593$	−12.3866	+	12.3866i	−0.508656	+	0.508656i	−0.914114	−	0.405458i	$-0.867112\pi$
$593$	−12.3866	+	12.3866i	−0.508656	+	0.508656i	0.405458	+	0.914114i	$0.367112\pi$
$594$	−0.773861	+	0.0385370i	−0.0317519	+	0.00158119i
$595$	0.146377	−	0.827913i	0.00600086	−	0.0339411i
$596$	16.7577	+	38.1719i	0.686421	+	1.56358i
$597$	17.6333	+	2.79284i	0.721683	+	0.114303i
$598$	−8.61043	+	1.80679i	−0.352107	+	0.0738853i
$599$	10.8175			0.441989			0.220995	−	0.975275i	$-0.429070\pi$
$599$	10.8175			0.441989			0.220995	+	0.975275i	$0.429070\pi$
$600$	−2.81952	+	13.8582i	−0.115107	+	0.565759i
$601$	11.1241			0.453761			0.226881	−	0.973923i	$-0.427147\pi$
$601$	11.1241			0.453761			0.226881	+	0.973923i	$0.427147\pi$
$602$	0.517573	−	0.108606i	0.0210947	−	0.00442647i
$603$	12.2481	+	1.93991i	0.498782	+	0.0789992i
$604$	15.5790	+	35.4869i	0.633899	+	1.44394i
$605$	−21.1198	−	11.2421i	−0.858643	−	0.457056i
$606$	−16.2050	+	0.806984i	−0.658285	+	0.0327815i
$607$	23.0754	−	23.0754i	0.936602	−	0.936602i	−0.0615046	−	0.998107i	$-0.519590\pi$
$607$	23.0754	−	23.0754i	0.936602	−	0.936602i	0.998107	+	0.0615046i	$0.0195899\pi$
$608$	−18.4564	+	7.93119i	−0.748507	+	0.321652i
$609$	0.845963	+	0.274870i	0.0342802	+	0.0111383i
$610$	−11.9366	+	17.5804i	−0.483301	+	0.711810i
$611$	2.68282	−	0.871702i	0.108535	−	0.0352653i
$612$	1.67009	+	6.36521i	0.0675094	+	0.257298i
$613$	−14.3058	−	28.0768i	−0.577807	−	1.13401i	−0.976215	−	0.216802i	$-0.930437\pi$
$613$	−14.3058	−	28.0768i	−0.577807	−	1.13401i	0.398408	−	0.917208i	$-0.369563\pi$
$614$	8.30997	−	12.7236i	0.335363	−	0.513483i
$615$	−9.34868	−	0.167490i	−0.376975	−	0.00675385i
$616$	0.0263353	+	0.175113i	0.00106108	+	0.00705550i
$617$	2.38218	+	15.0405i	0.0959030	+	0.605508i	0.988094	+	0.153850i	$0.0491672\pi$
$617$	2.38218	+	15.0405i	0.0959030	+	0.605508i	−0.892191	+	0.451658i	$0.850833\pi$
$618$	15.9639	+	1.71990i	0.642164	+	0.0691844i
$619$	16.5938	+	12.0561i	0.666962	+	0.484576i	0.869007	−	0.494800i	$-0.164759\pi$
$619$	16.5938	+	12.0561i	0.666962	+	0.484576i	−0.202045	+	0.979376i	$0.564759\pi$
$620$	−10.2421	+	2.49209i	−0.411332	+	0.100085i
$621$	6.02824	−	4.37977i	0.241905	−	0.175754i
$622$	24.3723	−	13.9869i	0.977238	−	0.560823i
$623$	−0.529187	+	1.03859i	−0.0212014	+	0.0416102i
$624$	3.03657	+	1.39002i	0.121560	+	0.0556455i
$625$	−6.00334	−	24.2685i	−0.240133	−	0.970740i
$626$	2.34457	+	2.91076i	0.0937080	+	0.116338i
$627$	1.73355	+	0.883290i	0.0692314	+	0.0352752i
$628$	−29.1408	−	11.3605i	−1.16284	−	0.453332i
$629$	0.872093	+	1.20033i	0.0347726	+	0.0478604i
$630$	0.327037	+	0.153721i	0.0130295	+	0.00612440i
$631$	−15.9680	+	21.9780i	−0.635675	+	0.874931i	−0.998376	−	0.0569743i	$-0.981855\pi$
$631$	−15.9680	+	21.9780i	−0.635675	+	0.874931i	0.362701	+	0.931906i	$0.381855\pi$
$632$	4.66626	−	13.9887i	0.185614	−	0.556440i
$633$	−4.09983	+	0.649349i	−0.162954	+	0.0258093i
$634$	−6.81917	−	17.9037i	−0.270824	−	0.711046i
$635$	−0.425251	+	23.7360i	−0.0168756	+	0.941934i
$636$	2.82418	+	28.2858i	0.111986	+	1.12161i
$637$	5.19759	−	2.64830i	0.205936	−	0.104930i
$638$	5.50335	+	2.46743i	0.217880	+	0.0976866i
$639$	−4.88001	−	15.0191i	−0.193050	−	0.594148i
$640$	−23.9300	+	8.20697i	−0.945917	+	0.324409i
$641$	11.5391	−	35.5136i	0.455765	−	1.40270i	−0.414469	−	0.910063i	$-0.636033\pi$
$641$	11.5391	−	35.5136i	0.455765	−	1.40270i	0.870234	−	0.492638i	$-0.163967\pi$
$642$	3.46465	−	3.82781i	0.136739	−	0.151072i
$643$	−32.3947	−	32.3947i	−1.27752	−	1.27752i	−0.942051	−	0.335471i	$-0.891105\pi$
$643$	−32.3947	−	32.3947i	−1.27752	−	1.27752i	−0.335471	−	0.942051i	$-0.608895\pi$
$644$	−1.13291	−	1.27147i	−0.0446427	−	0.0501028i
$645$	3.43827	−	6.45927i	0.135382	−	0.254333i
$646$	4.31835	−	15.9501i	0.169903	−	0.627549i
$647$	1.56537	−	9.88334i	0.0615410	−	0.388554i	−0.937622	−	0.347656i	$-0.886978\pi$
$647$	1.56537	−	9.88334i	0.0615410	−	0.388554i	0.999163	−	0.0408988i	$-0.0130221\pi$
$648$	−2.82834	−	0.0220838i	−0.111108	−	0.000867533i
$649$		−	3.19713i		−	0.125498i
$650$	−5.90306	+	0.0822307i	−0.231537	+	0.00322535i
$651$			0.269344i			0.0105564i
$652$	26.3305	−	32.1716i	1.03118	−	1.25994i
$653$	3.02216	−	19.0811i	0.118266	−	0.746703i	−0.855272	−	0.518179i	$-0.826610\pi$
$653$	3.02216	−	19.0811i	0.118266	−	0.746703i	0.973538	−	0.228524i	$-0.0733899\pi$
$654$	6.97966	+	1.88968i	0.272926	+	0.0738922i
$655$	49.0692	+	8.67554i	1.91729	+	0.338981i
$656$	−8.21181	−	14.5715i	−0.320617	−	0.568922i
$657$	1.04416	+	1.04416i	0.0407365	+	0.0407365i
$658$	0.404822	+	0.366415i	0.0157816	+	0.0142844i
$659$	9.26020	−	28.5000i	0.360726	−	1.11020i	−0.591888	−	0.806020i	$-0.701617\pi$
$659$	9.26020	−	28.5000i	0.360726	−	1.11020i	0.952614	−	0.304181i	$-0.0983828\pi$
$660$	2.09304	+	1.27382i	0.0814716	+	0.0495835i
$661$	−11.0378	−	33.9707i	−0.429319	−	1.32131i	−0.898797	−	0.438365i	$-0.855558\pi$
$661$	−11.0378	−	33.9707i	−0.429319	−	1.32131i	0.469478	−	0.882944i	$-0.344442\pi$
$662$	−1.72078	+	3.83801i	−0.0668798	+	0.149169i
$663$	−2.44768	+	1.24715i	−0.0950599	+	0.0484355i
$664$	12.3442	+	12.5385i	0.479048	+	0.486588i
$665$	−0.520122	−	0.743539i	−0.0201694	−	0.0288332i
$666$	−0.595942	+	0.226983i	−0.0230923	+	0.00879540i
$667$	−57.2867	+	9.07332i	−2.21815	+	0.351320i
$668$	28.9232	−	18.5696i	1.11907	−	0.718481i
$669$	6.51799	−	8.97124i	0.252000	−	0.346848i
$670$	−28.5978	−	26.8321i	−1.10483	−	1.03661i
$671$	2.16401	+	2.97851i	0.0835407	+	0.114984i
$672$	0.0591985	+	0.643710i	0.00228363	+	0.0248317i
$673$	14.5989	+	7.43852i	0.562747	+	0.286734i	0.712133	−	0.702045i	$-0.247729\pi$
$673$	14.5989	+	7.43852i	0.562747	+	0.286734i	−0.149385	+	0.988779i	$0.547729\pi$
$674$	−9.49472	+	7.64784i	−0.365723	+	0.294584i
$675$	4.53348	−	2.10892i	0.174494	−	0.0811722i
$676$	5.24106	−	24.0412i	0.201579	−	0.924663i
$677$	−19.3278	+	37.9329i	−0.742827	+	1.45788i	0.140973	+	0.990013i	$0.454977\pi$
$677$	−19.3278	+	37.9329i	−0.742827	+	1.45788i	−0.883800	+	0.467866i	$0.845023\pi$
$678$	−10.9026	−	18.9978i	−0.418710	−	0.729606i
$679$	0.159708	−	0.116035i	0.00612903	−	0.00445300i
$680$	6.93749	−	19.6194i	0.266041	−	0.752370i
$681$	7.25309	+	5.26968i	0.277939	+	0.201935i
$682$	−0.195623	+	1.81576i	−0.00749080	+	0.0695290i
$683$	−4.71709	−	29.7825i	−0.180494	−	1.13960i	−0.897005	−	0.442020i	$-0.854262\pi$
$683$	−4.71709	−	29.7825i	−0.180494	−	1.13960i	0.716511	−	0.697576i	$-0.245738\pi$
$684$	6.13222	+	3.58313i	0.234471	+	0.137004i
$685$	−13.2419	−	9.98807i	−0.505948	−	0.381625i
$686$	1.89251	+	1.23602i	0.0722562	+	0.0471915i
$687$	8.65291	+	16.9823i	0.330129	+	0.647915i
$688$	13.0782	−	0.548944i	0.498601	−	0.0209283i
$689$	−11.2858	+	3.66698i	−0.429955	+	0.139701i
$690$	−23.5512	+	0.750200i	−0.896577	+	0.0285596i
$691$	21.6237	+	7.02595i	0.822603	+	0.267280i	0.689926	−	0.723880i	$-0.257643\pi$
$691$	21.6237	+	7.02595i	0.822603	+	0.267280i	0.132676	+	0.991159i	$0.457643\pi$
$692$	26.5312	+	1.52896i	1.00857	+	0.0581225i
$693$	0.0442706	−	0.0442706i	0.00168170	−	0.00168170i
$694$	−2.04915	−	41.1490i	−0.0777848	−	1.56200i
$695$	15.0849	−	14.5539i	0.572201	−	0.552059i
$696$	19.5381	+	10.1481i	0.740590	+	0.384662i
$697$	13.5892	+	2.15232i	0.514728	+	0.0815249i
$698$	−7.17401	−	34.1883i	−0.271540	−	1.29405i
$699$	−20.4705			−0.774265
$700$	−0.582538	−	0.983099i	−0.0220179	−	0.0371577i
$701$	24.5720			0.928072			0.464036	−	0.885816i	$-0.346401\pi$
$701$	24.5720			0.928072			0.464036	+	0.885816i	$0.346401\pi$
$702$	−0.242480	−	1.15556i	−0.00915182	−	0.0436138i
$703$	1.58159	+	0.250500i	0.0596510	+	0.00944778i
$704$	−0.0684418	+	4.38251i	−0.00257950	+	0.165172i
$705$	7.48200	−	1.04801i	0.281788	−	0.0394704i
$706$	0.408385	+	8.20078i	0.0153698	+	0.308640i
$707$	0.927047	−	0.927047i	0.0348652	−	0.0348652i
$708$	0.671465	−	11.6516i	0.0252352	−	0.437892i
$709$	23.7263	+	7.70913i	0.891059	+	0.289522i	0.718542	−	0.695484i	$-0.244810\pi$
$709$	23.7263	+	7.70913i	0.891059	+	0.289522i	0.172517	+	0.985007i	$0.444810\pi$
$710$	−13.9120	+	47.9619i	−0.522108	+	1.79998i
$711$	−4.95848	+	1.61111i	−0.185957	+	0.0604212i
$712$	−17.1400	+	23.2080i	−0.642350	+	0.869756i
$713$	−7.97338	−	15.6486i	−0.298606	−	0.586046i
$714$	−0.445198	−	0.290765i	−0.0166611	−	0.0108816i
$715$	−0.333448	+	0.966955i	−0.0124702	+	0.0361621i
$716$	14.9461	−	25.5790i	0.558562	−	0.955932i
$717$	0.714563	+	4.51157i	0.0266859	+	0.168488i
$718$	2.25914	−	20.9692i	0.0843104	−	0.782563i
$719$	−40.3089	−	29.2861i	−1.50327	−	1.09219i	−0.969057	−	0.246836i	$-0.920609\pi$
$719$	−40.3089	−	29.2861i	−1.50327	−	1.09219i	−0.534210	−	0.845352i	$-0.679391\pi$
$720$	7.36033	+	5.08189i	0.274303	+	0.189391i
$721$	−1.04962	+	0.762595i	−0.0390900	+	0.0284005i
$722$	4.49750	+	7.83694i	0.167380	+	0.291661i
$723$	8.23409	−	16.1603i	0.306229	−	0.601009i
$724$	5.51106	+	1.20143i	0.204817	+	0.0446507i
$725$	−38.8949	−	1.39412i	−1.44452	−	0.0517763i
$726$	−11.7844	+	9.49214i	−0.437360	+	0.352286i
$727$	12.3755	+	6.30561i	0.458981	+	0.233862i	0.668164	−	0.744014i	$-0.267081\pi$
$727$	12.3755	+	6.30561i	0.458981	+	0.233862i	−0.209183	+	0.977876i	$0.567081\pi$
$728$	−0.257286	+	0.0813820i	−0.00953566	+	0.00301622i
$729$	0.587785	+	0.809017i	0.0217698	+	0.0299636i
$730$	−0.876959	−	4.58653i	−0.0324577	−	0.169755i
$731$	−6.32889	+	8.71097i	−0.234082	+	0.322187i
$732$	7.26094	+	11.3093i	0.268372	+	0.418004i
$733$	−20.2370	+	3.20522i	−0.747470	+	0.118388i	−0.518538	−	0.855055i	$-0.673523\pi$
$733$	−20.2370	+	3.20522i	−0.747470	+	0.118388i	−0.228932	+	0.973442i	$0.573523\pi$
$734$	26.3746	−	10.0456i	0.973504	−	0.370789i
$735$	14.9427	−	4.56092i	0.551170	−	0.168232i
$736$	−22.4951	−	35.6465i	−0.829181	−	1.31395i
$737$	−6.05363	+	3.08448i	−0.222988	+	0.113618i
$738$	−2.41932	+	5.39604i	−0.0890564	+	0.198631i
$739$	0.864509	+	2.66068i	0.0318015	+	0.0978749i	0.965697	−	0.259670i	$-0.0836139\pi$
$739$	0.864509	+	2.66068i	0.0318015	+	0.0978749i	−0.933896	+	0.357545i	$0.883614\pi$
$740$	1.96231	+	0.464762i	0.0721361	+	0.0170850i
$741$	−0.916193	+	2.81975i	−0.0336572	+	0.103586i
$742$	−1.70296	−	1.54140i	−0.0625177	−	0.0565865i
$743$	−12.0348	−	12.0348i	−0.441514	−	0.441514i	0.451007	−	0.892520i	$-0.351065\pi$
$743$	−12.0348	−	12.0348i	−0.441514	−	0.441514i	−0.892520	+	0.451007i	$0.851065\pi$
$744$	−1.09427	+	6.57624i	−0.0401181	+	0.241097i
$745$	−41.9012	+	20.4127i	−1.53514	+	0.747863i
$746$	−46.1814	−	12.5032i	−1.69082	−	0.457774i
$747$	0.973158	−	6.14428i	0.0356060	−	0.224807i
$748$	−2.79008	−	2.28351i	−0.102016	−	0.0834936i
$749$			0.417182i			0.0152435i
$750$	−15.6067	−	2.53565i	−0.569878	−	0.0925890i
$751$		−	15.7846i		−	0.575988i	−0.957632	−	0.287994i	$-0.907012\pi$
$751$		−	15.7846i		−	0.575988i	0.957632	−	0.287994i	$-0.0929883\pi$
$752$	8.39538	+	10.5910i	0.306148	+	0.386214i
$753$	−2.64398	+	16.6934i	−0.0963518	+	0.608341i
$754$	−2.40183	+	8.87135i	−0.0874697	+	0.323075i
$755$	−38.9539	+	18.9769i	−1.41768	+	0.690640i
$756$	0.170637	−	0.152041i	0.00620600	−	0.00552968i
$757$	29.9500	+	29.9500i	1.08855	+	1.08855i	0.995678	+	0.0928725i	$0.0296049\pi$
$757$	29.9500	+	29.9500i	1.08855	+	1.08855i	0.0928725	+	0.995678i	$0.470395\pi$
$758$	12.9546	−	14.3125i	0.470533	−	0.519853i
$759$	−1.26154	+	3.88262i	−0.0457910	+	0.140930i
$760$	−9.67836	−	20.2672i	−0.351071	−	0.735168i
$761$	2.86616	+	8.82112i	0.103898	+	0.319765i	0.989470	−	0.144736i	$-0.0462334\pi$
$761$	2.86616	+	8.82112i	0.103898	+	0.319765i	−0.885572	+	0.464502i	$0.846233\pi$
$762$	13.7004	+	6.14257i	0.496312	+	0.222522i
$763$	−0.520601	+	0.265259i	−0.0188470	+	0.00960304i
$764$	1.38037	−	0.137822i	0.0499401	−	0.00498624i
$765$	−7.03691	+	2.14785i	−0.254420	+	0.0776558i
$766$	−10.7148	−	28.1315i	−0.387140	−	1.01643i
$767$	4.81203	−	0.762150i	0.173752	−	0.0275197i
$768$	−1.16985	+	15.9572i	−0.0422133	+	0.575805i
$769$	−4.01537	+	5.52668i	−0.144798	+	0.199297i	−0.875256	−	0.483661i	$-0.839307\pi$
$769$	−4.01537	+	5.52668i	−0.144798	+	0.199297i	0.730458	+	0.682958i	$0.239307\pi$
$770$	−0.194461	+	0.0371816i	−0.00700790	+	0.00133993i
$771$	11.2042	+	15.4213i	0.403509	+	0.555383i
$772$	0.660769	−	1.69494i	0.0237816	−	0.0610022i
$773$	9.38905	+	4.78396i	0.337701	+	0.172067i	0.614614

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)

\(f(q)\)	\(=\)	\(q+(-1.38407 + 0.290430i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(1.83130 - 0.803952i) q^{4} +(0.979302 + 2.01022i) q^{5} +(1.41246 - 0.0703383i) q^{6} +(-0.0808033 + 0.0808033i) q^{7} +(-2.30116 + 1.64459i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})\)	\(q+(-1.38407 + 0.290430i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(1.83130 - 0.803952i) q^{4} +(0.979302 + 2.01022i) q^{5} +(1.41246 - 0.0703383i) q^{6} +(-0.0808033 + 0.0808033i) q^{7} +(-2.30116 + 1.64459i) q^{8} +(0.951057 + 0.309017i) q^{9} +(-1.93925 - 2.49786i) q^{10} +(-0.521065 + 0.169304i) q^{11} +(-1.93452 + 0.507575i) q^{12} +(-0.379036 - 0.743901i) q^{13} +(0.0883697 - 0.135305i) q^{14} +(-0.652778 - 2.13866i) q^{15} +(2.70732 - 2.94455i) q^{16} +(0.514721 + 3.24982i) q^{17} +(-1.40608 - 0.151486i) q^{18} +(2.87295 + 2.08732i) q^{19} +(3.40951 + 2.89400i) q^{20} +(0.0924489 - 0.0671680i) q^{21} +(0.672020 - 0.385662i) q^{22} +(-3.38282 + 6.63917i) q^{23} +(2.53010 - 1.26436i) q^{24} +(-3.08194 + 3.93722i) q^{25} +(0.740664 + 0.919527i) q^{26} +(-0.891007 - 0.453990i) q^{27} +(-0.0830132 + 0.212937i) q^{28} +(4.57530 + 6.29737i) q^{29} +(1.52462 + 2.77047i) q^{30} +(-1.38542 + 1.90687i) q^{31} +(-2.89194 + 4.86176i) q^{32} +(0.541135 - 0.0857074i) q^{33} +(-1.65626 - 4.34849i) q^{34} +(-0.241563 - 0.0833013i) q^{35} +(1.99011 - 0.198701i) q^{36} +(0.401778 - 0.204716i) q^{37} +(-4.58259 - 2.05461i) q^{38} +(0.257998 + 0.794036i) q^{39} +(-5.55951 - 3.01527i) q^{40} +(1.29216 - 3.97687i) q^{41} +(-0.108448 + 0.119815i) q^{42} +(2.31395 + 2.31395i) q^{43} +(-0.818115 + 0.728959i) q^{44} +(0.310180 + 2.21445i) q^{45} +(2.75385 - 10.1715i) q^{46} +(-0.528548 + 3.33712i) q^{47} +(-3.13462 + 2.48478i) q^{48} +6.98694i q^{49} +(3.12213 - 6.34447i) q^{50} -3.29033i q^{51} +(-1.29219 - 1.05758i) q^{52} +(2.22344 - 14.0382i) q^{53} +(1.36507 + 0.369579i) q^{54} +(-0.850619 - 0.881654i) q^{55} +(0.0530527 - 0.318829i) q^{56} +(-2.51105 - 2.51105i) q^{57} +(-8.16149 - 7.38719i) q^{58} +(-1.80325 + 5.54984i) q^{59} +(-2.91481 - 3.39173i) q^{60} +(-2.07653 - 6.39089i) q^{61} +(1.36371 - 3.04161i) q^{62} +(-0.101818 + 0.0518789i) q^{63} +(2.59064 - 7.56892i) q^{64} +(1.12421 - 1.49045i) q^{65} +(-0.724077 + 0.275787i) q^{66} +(12.2481 - 1.93991i) q^{67} +(3.55531 + 5.53758i) q^{68} +(4.37977 - 6.02824i) q^{69} +(0.358533 + 0.0451376i) q^{70} +(-9.28233 - 12.7760i) q^{71} +(-2.69674 + 0.853002i) q^{72} +(1.31572 + 0.670391i) q^{73} +(-0.496633 + 0.400030i) q^{74} +(3.65991 - 3.40662i) q^{75} +(6.93934 + 1.51280i) q^{76} +(0.0284234 - 0.0557842i) q^{77} +(-0.587700 - 1.02407i) q^{78} +(-4.21793 + 3.06451i) q^{79} +(8.57048 + 2.55870i) q^{80} +(0.809017 + 0.587785i) q^{81} +(-0.633441 + 5.87955i) q^{82} +(-0.973158 - 6.14428i) q^{83} +(0.115302 - 0.197329i) q^{84} +(-6.02877 + 4.21725i) q^{85} +(-3.87472 - 2.53063i) q^{86} +(-3.53385 - 6.93557i) q^{87} +(0.920617 - 1.24654i) q^{88} +(9.70119 - 3.15211i) q^{89} +(-1.07245 - 2.97487i) q^{90} +(0.0907370 + 0.0294822i) q^{91} +(-0.857397 + 14.8779i) q^{92} +(1.66666 - 1.66666i) q^{93} +(-0.237653 - 4.77231i) q^{94} +(-1.38248 + 7.81937i) q^{95} +(3.61688 - 4.34950i) q^{96} +(-1.70626 - 0.270245i) q^{97} +(-2.02922 - 9.67042i) q^{98} -0.547881 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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