LMFDB - Embedded newform 300.2.r.a.59.19

Newspace parameters

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.r (of order $10$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			59.19
Character	$\chi$	$=$	300.59
Dual form			300.2.r.a.239.19

$q$-expansion

$f(q)$	$=$	$q+(-0.723120 + 1.21536i) q^{2} +(-1.44187 + 0.959691i) q^{3} +(-0.954195 - 1.75770i) q^{4} +(1.84864 + 1.25798i) q^{5} +(-0.123723 - 2.44636i) q^{6} +2.80461 q^{7} +(2.82623 + 0.111339i) q^{8} +(1.15799 - 2.76750i) q^{9} +O(q^{10})$	\(q+(-0.723120 + 1.21536i) q^{2} +(-1.44187 + 0.959691i) q^{3} +(-0.954195 - 1.75770i) q^{4} +(1.84864 + 1.25798i) q^{5} +(-0.123723 - 2.44636i) q^{6} +2.80461 q^{7} +(2.82623 + 0.111339i) q^{8} +(1.15799 - 2.76750i) q^{9} +(-2.86569 + 1.33709i) q^{10} +(1.50008 + 1.08987i) q^{11} +(3.06268 + 1.61865i) q^{12} +(2.01229 + 2.76969i) q^{13} +(-2.02807 + 3.40861i) q^{14} +(-3.87278 - 0.0397234i) q^{15} +(-2.17902 + 3.35438i) q^{16} +(-0.345387 + 1.06299i) q^{17} +(2.52615 + 3.40861i) q^{18} +(-7.11064 - 2.31039i) q^{19} +(0.447192 - 4.44972i) q^{20} +(-4.04389 + 2.69156i) q^{21} +(-2.40932 + 1.03503i) q^{22} +(1.23722 - 1.70289i) q^{23} +(-4.18192 + 2.55177i) q^{24} +(1.83496 + 4.65112i) q^{25} +(-4.82129 + 0.442845i) q^{26} +(0.986279 + 5.10169i) q^{27} +(-2.67615 - 4.92967i) q^{28} +(-3.56932 + 1.15974i) q^{29} +(2.84876 - 4.67809i) q^{30} +(8.53887 + 2.77445i) q^{31} +(-2.50108 - 5.07391i) q^{32} +(-3.20886 - 0.131842i) q^{33} +(-1.04216 - 1.18844i) q^{34} +(5.18472 + 3.52815i) q^{35} +(-5.96939 + 0.605342i) q^{36} +(4.97454 + 6.84687i) q^{37} +(7.94980 - 6.97130i) q^{38} +(-5.55951 - 2.06235i) q^{39} +(5.08464 + 3.76118i) q^{40} +(-3.81439 - 5.25005i) q^{41} +(-0.346995 - 6.86110i) q^{42} -7.87791 q^{43} +(0.484300 - 3.67664i) q^{44} +(5.62217 - 3.65940i) q^{45} +(1.17496 + 2.73507i) q^{46} +(0.999744 - 0.324837i) q^{47} +(-0.0772933 - 6.92777i) q^{48} +0.865841 q^{49} +(-6.97968 - 1.13318i) q^{50} +(-0.522140 - 1.86416i) q^{51} +(2.94816 - 6.17983i) q^{52} +(0.595625 + 1.83314i) q^{53} +(-6.91358 - 2.49045i) q^{54} +(1.40207 + 3.90186i) q^{55} +(7.92649 + 0.312264i) q^{56} +(12.4699 - 3.49274i) q^{57} +(1.17154 - 5.17664i) q^{58} +(6.91365 - 5.02306i) q^{59} +(3.62556 + 6.84509i) q^{60} +(-0.730226 - 0.530540i) q^{61} +(-9.54658 + 8.37154i) q^{62} +(3.24770 - 7.76177i) q^{63} +(7.97521 + 0.629343i) q^{64} +(0.235797 + 7.65159i) q^{65} +(2.48063 - 3.80458i) q^{66} +(0.462733 - 1.42415i) q^{67} +(2.19799 - 0.407214i) q^{68} +(-0.149667 + 3.64271i) q^{69} +(-8.03715 + 3.75002i) q^{70} +(1.11003 + 3.41631i) q^{71} +(3.58087 - 7.69268i) q^{72} +(7.45432 - 10.2600i) q^{73} +(-11.9186 + 1.09475i) q^{74} +(-7.10941 - 4.94532i) q^{75} +(2.72397 + 14.7029i) q^{76} +(4.20714 + 3.05667i) q^{77} +(6.52669 - 5.26548i) q^{78} +(-4.76272 + 1.54750i) q^{79} +(-8.24799 + 3.45987i) q^{80} +(-6.31813 - 6.40946i) q^{81} +(9.13896 - 0.839431i) q^{82} +(5.84619 + 1.89954i) q^{83} +(8.58961 + 4.53967i) q^{84} +(-1.97572 + 1.53060i) q^{85} +(5.69668 - 9.57449i) q^{86} +(4.03351 - 5.09764i) q^{87} +(4.11823 + 3.24725i) q^{88} +(9.96050 - 13.7094i) q^{89} +(0.381974 + 9.47914i) q^{90} +(5.64370 + 7.76789i) q^{91} +(-4.17373 - 0.549778i) q^{92} +(-14.9746 + 4.19428i) q^{93} +(-0.328142 + 1.44994i) q^{94} +(-10.2386 - 13.2161i) q^{95} +(8.47562 + 4.91567i) q^{96} +(-16.7757 + 5.45075i) q^{97} +(-0.626107 + 1.05231i) q^{98} +(4.75330 - 2.88942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224q - 6q^{4} - 7q^{6} - 6q^{9} + O(q^{10}) $	$ 224q - 6q^{4} - 7q^{6} - 6q^{9} - 5q^{12} - 20q^{13} + 6q^{16} - 24q^{21} - 10q^{22} - 28q^{24} - 20q^{25} - 50q^{28} - 25q^{30} - 10q^{33} - 14q^{34} - 25q^{36} - 60q^{37} - 20q^{40} - 85q^{42} - 30q^{45} + 6q^{46} - 70q^{48} + 88q^{49} + 40q^{52} - 46q^{54} + 50q^{58} + 10q^{60} - 28q^{61} + 18q^{64} + 64q^{66} - 42q^{69} - 40q^{70} - 5q^{72} - 20q^{73} - 80q^{76} - 85q^{78} + 18q^{81} - 48q^{84} - 20q^{85} + 50q^{88} - 60q^{90} + 60q^{94} + 44q^{96} - 120q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.723120	+	1.21536i	−0.511323	+	0.859389i
$2$	−0.723120	+	1.21536i	−0.511323	+	0.859389i
$3$	−1.44187	+	0.959691i	−0.832465	+	0.554078i
$3$	−1.44187	+	0.959691i	−0.832465	+	0.554078i
$4$	−0.954195	−	1.75770i	−0.477097	−	0.878850i
$5$	1.84864	+	1.25798i	0.826738	+	0.562587i
$5$	1.84864	+	1.25798i	0.826738	+	0.562587i
$6$	−0.123723	−	2.44636i	−0.0505097	−	0.998724i
$7$	2.80461			1.06004			0.530022	−	0.847984i	$-0.322184\pi$
$7$	2.80461			1.06004			0.530022	+	0.847984i	$0.322184\pi$
$8$	2.82623	+	0.111339i	0.999225	+	0.0393644i
$9$	1.15799	−	2.76750i	0.385996	−	0.922501i
$10$	−2.86569	+	1.33709i	−0.906211	+	0.422826i
$11$	1.50008	+	1.08987i	0.452291	+	0.328609i	0.790500	−	0.612462i	$-0.209821\pi$
$11$	1.50008	+	1.08987i	0.452291	+	0.328609i	−0.338209	+	0.941071i	$0.609821\pi$
$12$	3.06268	+	1.61865i	0.884118	+	0.467263i
$13$	2.01229	+	2.76969i	0.558110	+	0.768173i	0.991085	−	0.133234i	$-0.0425360\pi$
$13$	2.01229	+	2.76969i	0.558110	+	0.768173i	−0.432975	+	0.901406i	$0.642536\pi$
$14$	−2.02807	+	3.40861i	−0.542025	+	0.910989i
$15$	−3.87278	−	0.0397234i	−0.999947	−	0.0102565i
$16$	−2.17902	+	3.35438i	−0.544756	+	0.838595i
$17$	−0.345387	+	1.06299i	−0.0837686	+	0.257813i	−0.984164	−	0.177259i	$-0.943277\pi$
$17$	−0.345387	+	1.06299i	−0.0837686	+	0.257813i	0.900396	+	0.435072i	$0.143277\pi$
$18$	2.52615	+	3.40861i	0.595418	+	0.803416i
$19$	−7.11064	−	2.31039i	−1.63129	−	0.530039i	−0.656725	−	0.754130i	$-0.728059\pi$
$19$	−7.11064	−	2.31039i	−1.63129	−	0.530039i	−0.974568	+	0.224090i	$0.928059\pi$
$20$	0.447192	−	4.44972i	0.0999951	−	0.994988i
$21$	−4.04389	+	2.69156i	−0.882449	+	0.587346i
$22$	−2.40932	+	1.03503i	−0.513670	+	0.220669i
$23$	1.23722	−	1.70289i	0.257979	−	0.355078i	−0.660307	−	0.750996i	$-0.729574\pi$
$23$	1.23722	−	1.70289i	0.257979	−	0.355078i	0.918286	+	0.395918i	$0.129574\pi$
$24$	−4.18192	+	2.55177i	−0.853631	+	0.520879i
$25$	1.83496	+	4.65112i	0.366992	+	0.930224i
$26$	−4.82129	+	0.442845i	−0.945533	+	0.0868490i
$27$	0.986279	+	5.10169i	0.189809	+	0.981821i
$28$	−2.67615	−	4.92967i	−0.505744	−	0.931619i
$29$	−3.56932	+	1.15974i	−0.662806	+	0.215359i	−0.621052	−	0.783769i	$-0.713294\pi$
$29$	−3.56932	+	1.15974i	−0.662806	+	0.215359i	−0.0417538	+	0.999128i	$0.513294\pi$
$30$	2.84876	−	4.67809i	0.520111	−	0.854099i
$31$	8.53887	+	2.77445i	1.53363	+	0.498306i	0.949610	−	0.313435i	$-0.101480\pi$
$31$	8.53887	+	2.77445i	1.53363	+	0.498306i	0.584018	+	0.811741i	$0.301480\pi$
$32$	−2.50108	−	5.07391i	−0.442132	−	0.896950i
$33$	−3.20886	−	0.131842i	−0.558591	−	0.0229507i
$34$	−1.04216	−	1.18844i	−0.178729	−	0.203816i
$35$	5.18472	+	3.52815i	0.876378	+	0.596366i
$36$	−5.96939	+	0.605342i	−0.994898	+	0.100890i
$37$	4.97454	+	6.84687i	0.817809	+	1.12562i	0.990071	+	0.140567i	$0.0448924\pi$
$37$	4.97454	+	6.84687i	0.817809	+	1.12562i	−0.172262	+	0.985051i	$0.555108\pi$
$38$	7.94980	−	6.97130i	1.28963	−	1.13089i
$39$	−5.55951	−	2.06235i	−0.890234	−	0.330240i
$40$	5.08464	+	3.76118i	0.803951	+	0.594695i
$41$	−3.81439	−	5.25005i	−0.595707	−	0.819921i	0.399600	−	0.916690i	$-0.369149\pi$
$41$	−3.81439	−	5.25005i	−0.595707	−	0.819921i	−0.995307	+	0.0967691i	$0.969149\pi$
$42$	−0.346995	−	6.86110i	−0.0535424	−	1.05869i
$43$	−7.87791			−1.20137			−0.600685	−	0.799486i	$-0.705105\pi$
$43$	−7.87791			−1.20137			−0.600685	+	0.799486i	$0.705105\pi$
$44$	0.484300	−	3.67664i	0.0730110	−	0.554275i
$45$	5.62217	−	3.65940i	0.838104	−	0.545510i
$46$	1.17496	+	2.73507i	0.173239	+	0.403264i
$47$	0.999744	−	0.324837i	0.145828	−	0.0473823i	−0.235194	−	0.971949i	$-0.575572\pi$
$47$	0.999744	−	0.324837i	0.145828	−	0.0473823i	0.381021	+	0.924566i	$0.375572\pi$
$48$	−0.0772933	−	6.92777i	−0.0111563	−	0.999938i
$49$	0.865841			0.123692
$50$	−6.97968	−	1.13318i	−0.987075	−	0.160256i
$51$	−0.522140	−	1.86416i	−0.0731142	−	0.261035i
$52$	2.94816	−	6.17983i	0.408836	−	0.856988i
$53$	0.595625	+	1.83314i	0.0818153	+	0.251802i	0.983594	−	0.180396i	$-0.0577381\pi$
$53$	0.595625	+	1.83314i	0.0818153	+	0.251802i	−0.901779	+	0.432198i	$0.857738\pi$
$54$	−6.91358	−	2.49045i	−0.940820	−	0.338908i
$55$	1.40207	+	3.90186i	0.189055	+	0.526127i
$56$	7.92649	+	0.312264i	1.05922	+	0.0417280i
$57$	12.4699	−	3.49274i	1.65168	−	0.462624i
$58$	1.17154	−	5.17664i	0.153831	−	0.679726i
$59$	6.91365	−	5.02306i	0.900081	−	0.653947i	−0.0384059	−	0.999262i	$-0.512228\pi$
$59$	6.91365	−	5.02306i	0.900081	−	0.653947i	0.938487	+	0.345315i	$0.112228\pi$
$60$	3.62556	+	6.84509i	0.468058	+	0.883698i
$61$	−0.730226	−	0.530540i	−0.0934959	−	0.0679287i	0.540055	−	0.841630i	$-0.318403\pi$
$61$	−0.730226	−	0.530540i	−0.0934959	−	0.0679287i	−0.633551	+	0.773701i	$0.718403\pi$
$62$	−9.54658	+	8.37154i	−1.21242	+	1.06319i
$63$	3.24770	−	7.76177i	0.409172	−	0.977891i
$64$	7.97521	+	0.629343i	0.996901	+	0.0786678i
$65$	0.235797	+	7.65159i	0.0292470	+	0.949063i
$66$	2.48063	−	3.80458i	0.305344	−	0.468312i
$67$	0.462733	−	1.42415i	0.0565319	−	0.173987i	−0.918804	−	0.394715i	$-0.870843\pi$
$67$	0.462733	−	1.42415i	0.0565319	−	0.173987i	0.975335	+	0.220728i	$0.0708433\pi$
$68$	2.19799	−	0.407214i	0.266545	−	0.0493820i
$69$	−0.149667	+	3.64271i	−0.0180178	+	0.438530i
$70$	−8.03715	+	3.75002i	−0.960623	+	0.448213i
$71$	1.11003	+	3.41631i	0.131736	+	0.405442i	0.995068	−	0.0991946i	$-0.0316266\pi$
$71$	1.11003	+	3.41631i	0.131736	+	0.405442i	−0.863332	+	0.504636i	$0.831627\pi$
$72$	3.58087	−	7.69268i	0.422010	−	0.906591i
$73$	7.45432	−	10.2600i	0.872462	−	1.20084i	−0.105990	−	0.994367i	$-0.533801\pi$
$73$	7.45432	−	10.2600i	0.872462	−	1.20084i	0.978452	−	0.206474i	$-0.0661987\pi$
$74$	−11.9186	+	1.09475i	−1.38551	+	0.127262i
$75$	−7.10941	−	4.94532i	−0.820924	−	0.571037i
$76$	2.72397	+	14.7029i	0.312461	+	1.68654i
$77$	4.20714	+	3.05667i	0.479448	+	0.348340i
$78$	6.52669	−	5.26548i	0.739002	−	0.596198i
$79$	−4.76272	+	1.54750i	−0.535848	+	0.174108i	−0.564425	−	0.825484i	$-0.690902\pi$
$79$	−4.76272	+	1.54750i	−0.535848	+	0.174108i	0.0285776	+	0.999592i	$0.490902\pi$
$80$	−8.24799	+	3.45987i	−0.922153	+	0.386825i
$81$	−6.31813	−	6.40946i	−0.702015	−	0.712162i
$82$	9.13896	−	0.839431i	1.00923	−	0.0926996i
$83$	5.84619	+	1.89954i	0.641703	+	0.208502i	0.611752	−	0.791050i	$-0.290465\pi$
$83$	5.84619	+	1.89954i	0.641703	+	0.208502i	0.0299505	+	0.999551i	$0.490465\pi$
$84$	8.58961	+	4.53967i	0.937204	+	0.495319i
$85$	−1.97572	+	1.53060i	−0.214297	+	0.166017i
$86$	5.69668	−	9.57449i	0.614288	−	1.03244i
$87$	4.03351	−	5.09764i	0.432437	−	0.546525i
$88$	4.11823	+	3.24725i	0.439005	+	0.346158i
$89$	9.96050	−	13.7094i	1.05581	−	1.45320i	0.172150	−	0.985071i	$-0.444929\pi$
$89$	9.96050	−	13.7094i	1.05581	−	1.45320i	0.883661	−	0.468128i	$-0.155071\pi$
$90$	0.381974	+	9.47914i	0.0402636	+	0.999189i
$91$	5.64370	+	7.76789i	0.591621	+	0.814296i
$92$	−4.17373	−	0.549778i	−0.435141	−	0.0573183i
$93$	−14.9746	+	4.19428i	−1.55279	+	0.434927i
$94$	−0.328142	+	1.44994i	−0.0338453	+	0.149550i
$95$	−10.2386	−	13.2161i	−1.05046	−	1.35595i
$96$	8.47562	+	4.91567i	0.865040	+	0.501704i
$97$	−16.7757	+	5.45075i	−1.70331	+	0.553440i	−0.989198	−	0.146588i	$-0.953171\pi$
$97$	−16.7757	+	5.45075i	−1.70331	+	0.553440i	−0.714115	+	0.700028i	$0.753171\pi$
$98$	−0.626107	+	1.05231i	−0.0632464	+	0.106299i
$99$	4.75330	−	2.88942i	0.477724	−	0.290397i
$100$	6.42437	−	7.66339i	0.642437	−	0.766339i
$101$		−	6.81866i		−	0.678482i	−0.940700	−	0.339241i	$-0.889830\pi$
$101$		−	6.81866i		−	0.678482i	0.940700	−	0.339241i	$-0.110170\pi$
$102$	2.64319	+	0.713425i	0.261715	+	0.0706396i
$103$	−4.18192	−	12.8706i	−0.412057	−	1.26818i	−0.914857	−	0.403778i	$-0.867697\pi$
$103$	−4.18192	−	12.8706i	−0.412057	−	1.26818i	0.502800	−	0.864403i	$-0.332303\pi$
$104$	5.37884	+	8.05183i	0.527439	+	0.789547i
$105$	−10.8616	−	0.111409i	−1.05999	−	0.0108724i
$106$	−2.65864	−	0.601685i	−0.258230	−	0.0584409i
$107$			9.81778i			0.949120i	0.880223	+	0.474560i	$0.157393\pi$
$107$			9.81778i			0.949120i	−0.880223	+	0.474560i	$0.842607\pi$
$108$	8.02614	−	6.60159i	0.772316	−	0.635238i
$109$	1.78582	−	1.29748i	0.171051	−	0.124276i	−0.498966	−	0.866622i	$-0.666287\pi$
$109$	1.78582	−	1.29748i	0.171051	−	0.124276i	0.670017	+	0.742346i	$0.266287\pi$
$110$	−5.75603	−	1.11749i	−0.548816	−	0.106549i
$111$	−13.7435	−	5.09828i	−1.30448	−	0.483907i
$112$	−6.11132	+	9.40772i	−0.577465	+	0.888946i
$113$	−12.5977	+	9.15275i	−1.18509	+	0.861018i	−0.992737	−	0.120308i	$-0.961612\pi$
$113$	−12.5977	+	9.15275i	−1.18509	+	0.861018i	−0.192353	+	0.981326i	$0.561612\pi$
$114$	−4.77230	+	17.6811i	−0.446967	+	1.65598i
$115$	4.42940	−	1.59163i	0.413043	−	0.148421i
$116$	5.44431	+	5.16718i	0.505491	+	0.479760i
$117$	9.99532	−	2.36177i	0.924068	−	0.218346i
$118$	1.10542	+	12.0348i	0.101762	+	1.10790i
$119$	−0.968675	+	2.98128i	−0.0887983	+	0.273293i
$120$	−10.9410	−	0.543461i	−0.998769	−	0.0496109i
$121$	−2.33677	−	7.19183i	−0.212433	−	0.653803i
$122$	1.17284	−	0.503842i	0.106184	−	0.0456158i
$123$	10.5383	+	3.90927i	0.950205	+	0.352487i
$124$	−3.27110	−	17.6562i	−0.293753	−	1.58557i
$125$	−2.45884	+	10.9066i	−0.219926	+	0.975517i
$126$	7.08485	+	9.55981i	0.631169	+	0.851656i
$127$	−1.96048	−	1.42437i	−0.173964	−	0.126392i	0.497396	−	0.867524i	$-0.334290\pi$
$127$	−1.96048	−	1.42437i	−0.173964	−	0.126392i	−0.671360	+	0.741131i	$0.734290\pi$
$128$	−6.53191	+	9.23765i	−0.577345	+	0.816501i
$129$	11.3589	−	7.56036i	1.00010	−	0.665653i
$130$	−9.46994	−	5.24644i	−0.830569	−	0.460143i
$131$	−1.27975	+	3.93867i	−0.111812	+	0.344123i	−0.991269	−	0.131856i	$-0.957906\pi$
$131$	−1.27975	+	3.93867i	−0.111812	+	0.344123i	0.879457	+	0.475979i	$0.157906\pi$
$132$	2.83014	+	5.76602i	0.246332	+	0.501868i
$133$	−19.9426	−	6.47974i	−1.72924	−	0.561865i
$134$	1.39624	+	1.59222i	0.120617	+	0.137546i
$135$	−4.59456	+	10.6719i	−0.395437	+	0.918493i
$136$	−1.09450	+	2.96581i	−0.0938523	+	0.254316i
$137$	2.61762	−	1.90181i	0.223638	−	0.162483i	−0.470325	−	0.882494i	$-0.655863\pi$
$137$	2.61762	−	1.90181i	0.223638	−	0.162483i	0.693963	+	0.720011i	$0.255863\pi$
$138$	−4.31897	−	2.81601i	−0.367655	−	0.239715i
$139$	4.14436	−	5.70423i	0.351520	−	0.483826i	−0.596241	−	0.802805i	$-0.703340\pi$
$139$	4.14436	−	5.70423i	0.351520	−	0.483826i	0.947762	+	0.318979i	$0.103340\pi$
$140$	1.25420	−	12.4797i	0.105999	−	1.05473i
$141$	−1.12976	+	1.42782i	−0.0951429	+	0.120244i
$142$	−4.95473	−	1.12132i	−0.415792	−	0.0940993i
$143$			6.34789i			0.530838i
$144$	6.75997	+	9.91478i	0.563331	+	0.826232i
$145$	−8.05733	−	2.34619i	−0.669125	−	0.194841i
$146$	7.07920	+	16.4789i	0.585879	+	1.36380i
$147$	−1.24843	+	0.830940i	−0.102969	+	0.0685348i
$148$	7.28806	−	15.2770i	0.599075	−	1.25576i
$149$		−	20.1075i		−	1.64727i	−0.567122	−	0.823634i	$-0.691943\pi$
$149$		−	20.1075i		−	1.64727i	0.567122	−	0.823634i	$-0.308057\pi$
$150$	11.1513	−	5.06443i	0.910500	−	0.413509i
$151$		−	7.94771i		−	0.646776i	−0.946267	−	0.323388i	$-0.895178\pi$
$151$		−	7.94771i		−	0.646776i	0.946267	−	0.323388i	$-0.104822\pi$
$152$	−19.8391	−	7.32139i	−1.60916	−	0.593844i
$153$	2.54188	+	2.18679i	0.205499	+	0.176791i
$154$	−6.75722	+	2.90285i	−0.544512	+	0.233918i
$155$	12.2951	+	15.8707i	0.987568	+	1.27477i
$156$	1.67986	+	11.7398i	0.134497	+	0.939940i
$157$		−	21.0927i		−	1.68338i	−0.539959	−	0.841691i	$-0.681560\pi$
$157$		−	21.0927i		−	1.68338i	0.539959	−	0.841691i	$-0.318440\pi$
$158$	1.56325	−	6.90744i	0.124365	−	0.549527i
$159$	−2.61807	−	2.07154i	−0.207626	−	0.164284i
$160$	1.75930	−	12.5262i	0.139085	−	0.990280i
$161$	3.46993	−	4.77595i	0.273469	−	0.376398i
$162$	12.3586	−	3.04399i	0.970981	−	0.239159i
$163$	−4.21409	+	3.06171i	−0.330073	+	0.239812i	−0.740461	−	0.672099i	$-0.765393\pi$
$163$	−4.21409	+	3.06171i	−0.330073	+	0.239812i	0.410389	+	0.911911i	$0.365393\pi$
$164$	−5.58835	+	11.7141i	−0.436377	+	0.914720i
$165$	−5.76619	−	4.28042i	−0.448897	−	0.333230i
$166$	−6.53612	+	5.73162i	−0.507301	+	0.444860i
$167$	5.01679	+	1.63005i	0.388211	+	0.126137i	0.496618	−	0.867969i	$-0.334575\pi$
$167$	5.01679	+	1.63005i	0.388211	+	0.126137i	−0.108407	+	0.994107i	$0.534575\pi$
$168$	−11.7287	+	7.15674i	−0.904885	+	0.552154i
$169$	0.395392	−	1.21689i	0.0304148	−	0.0936070i
$170$	−0.431545	−	3.50802i	−0.0330980	−	0.269053i
$171$	−14.6280	+	17.0033i	−1.11863	+	1.30028i
$172$	7.51706	+	13.8470i	0.573171	+	1.05582i
$173$	13.1367	+	9.54436i	0.998764	+	0.725644i	0.961823	−	0.273673i	$-0.0882386\pi$
$173$	13.1367	+	9.54436i	0.998764	+	0.725644i	0.0369410	+	0.999317i	$0.488239\pi$
$174$	3.27876	+	8.58836i	0.248562	+	0.651082i
$175$	5.14635	+	13.0446i	0.389027	+	0.986078i
$176$	−6.92455	+	2.65698i	−0.521958	+	0.200277i
$177$	−5.14801	+	13.8776i	−0.386948	+	1.04310i
$178$	9.45926	+	22.0192i	0.709002	+	1.65041i
$179$	2.97647	+	9.16063i	0.222472	+	0.684697i	0.998538	+	0.0540466i	$0.0172119\pi$
$179$	2.97647	+	9.16063i	0.222472	+	0.684697i	−0.776067	+	0.630651i	$0.782788\pi$
$180$	−11.7968	−	6.39032i	−0.879279	−	0.476306i
$181$	−3.65420	+	11.2465i	−0.271614	+	0.835943i	0.718481	+	0.695546i	$0.244838\pi$
$181$	−3.65420	+	11.2465i	−0.271614	+	0.835943i	−0.990095	+	0.140396i	$0.955162\pi$
$182$	−13.5218	+	1.24201i	−1.00231	+	0.0920637i
$183$	1.56205	+	0.0641795i	0.115470	+	0.00474429i
$184$	3.68629	−	4.67502i	0.271757	−	0.344647i
$185$	0.582908	+	18.9153i	0.0428563	+	1.39068i
$186$	5.73085	−	21.2325i	0.420207	−	1.55684i
$187$	−1.67663	+	1.21814i	−0.122607	+	0.0890795i
$188$	−1.52492	−	1.44729i	−0.111216	−	0.105555i
$189$	2.76613	+	14.3083i	0.201206	+	1.04077i
$190$	23.4661	−	2.88673i	1.70241	−	0.209425i
$191$	16.3988	−	11.9144i	1.18657	−	0.862096i	0.193675	−	0.981066i	$-0.437959\pi$
$191$	16.3988	−	11.9144i	1.18657	−	0.862096i	0.992898	+	0.118970i	$0.0379591\pi$
$192$	−12.1032	+	6.74630i	−0.873473	+	0.486872i
$193$			7.83027i			0.563635i	0.959468	+	0.281818i	$0.0909373\pi$
$193$			7.83027i			0.563635i	−0.959468	+	0.281818i	$0.909063\pi$
$194$	5.50622	−	24.3300i	0.395323	−	1.74679i
$195$	−7.68315	−	10.8063i	−0.550202	−	0.773856i
$196$	−0.826181	−	1.52189i	−0.0590129	−	0.108706i
$197$	−4.59514	−	14.1424i	−0.327390	−	1.00760i	−0.970350	−	0.241703i	$-0.922294\pi$
$197$	−4.59514	−	14.1424i	−0.327390	−	1.00760i	0.642960	−	0.765900i	$-0.277706\pi$
$198$	0.0744765	+	7.86636i	0.00529281	+	0.559038i
$199$			14.5552i			1.03179i	0.856652	+	0.515894i	$0.172540\pi$
$199$			14.5552i			1.03179i	−0.856652	+	0.515894i	$0.827460\pi$
$200$	4.66817	+	13.3495i	0.330090	+	0.943950i
$201$	0.699539	+	2.49752i	0.0493417	+	0.176161i
$202$	8.28711	+	4.93071i	0.583079	+	0.346923i
$203$	−10.0106	+	3.25263i	−0.702603	+	0.228290i
$204$	−2.77841	+	2.69654i	−0.194528	+	0.188795i
$205$	−0.446963	−	14.5039i	−0.0312173	−	1.01300i
$206$	18.6665	+	4.22448i	1.30055	+	0.294333i
$207$	−3.28007	−	5.39595i	−0.227981	−	0.375044i
$208$	−13.6754	+	0.714784i	−0.948219	+	0.0495613i
$209$	−8.14851	−	11.2155i	−0.563644	−	0.775790i
$210$	7.98967	−	13.1202i	0.551340	−	0.905382i
$211$	5.00382	−	6.88717i	0.344477	−	0.474132i	−0.601265	−	0.799049i	$-0.705337\pi$
$211$	5.00382	−	6.88717i	0.344477	−	0.474132i	0.945742	+	0.324917i	$0.105337\pi$
$212$	2.65378	−	2.79611i	0.182262	−	0.192037i
$213$	−4.87912	−	3.86060i	−0.334312	−	0.264524i
$214$	−11.9321	−	7.09943i	−0.815663	−	0.485307i
$215$	−14.5634	−	9.91028i	−0.993219	−	0.675875i
$216$	2.21944	+	14.5284i	0.151014	+	0.988532i
$217$	23.9482	+	7.78125i	1.62571	+	0.528226i
$218$	0.285535	+	3.10865i	0.0193389	+	0.210544i
$219$	−0.901750	+	21.9474i	−0.0609346	+	1.48307i
$220$	5.52045	−	6.18756i	0.372189	−	0.417165i
$221$	−3.63917	+	1.18244i	−0.244797	+	0.0795394i
$222$	16.1345	−	13.0166i	1.08287	−	0.873620i
$223$	−1.64427	−	1.19463i	−0.110109	−	0.0799987i	0.531368	−	0.847141i	$-0.321678\pi$
$223$	−1.64427	−	1.19463i	−0.110109	−	0.0799987i	−0.641477	+	0.767142i	$0.721678\pi$
$224$	−7.01455	−	14.2304i	−0.468679	−	0.950806i
$225$	14.9968	+	0.307680i	0.999790	+	0.0205120i
$226$	−2.01424	−	21.9292i	−0.133985	−	1.45871i
$227$	15.1887	−	20.9054i	1.00811	−	1.38754i	0.0878937	−	0.996130i	$-0.471986\pi$
$227$	15.1887	−	20.9054i	1.00811	−	1.38754i	0.920215	−	0.391413i	$-0.128014\pi$
$228$	−18.0379	−	18.5856i	−1.19459	−	1.23086i
$229$	−0.894624	−	2.75337i	−0.0591184	−	0.181948i	0.917136	−	0.398574i	$-0.130495\pi$
$229$	−0.894624	−	2.75337i	−0.0591184	−	0.181948i	−0.976255	+	0.216626i	$0.930495\pi$
$230$	−1.26858	+	6.53425i	−0.0836475	+	0.430856i
$231$	−8.99961	−	0.369765i	−0.592131	−	0.0243288i
$232$	−10.2169	+	2.88030i	−0.670770	+	0.189101i
$233$	−5.73497	+	17.6504i	−0.375710	+	1.15632i	0.567288	+	0.823520i	$0.307993\pi$
$233$	−5.73497	+	17.6504i	−0.375710	+	1.15632i	−0.942998	+	0.332798i	$0.892007\pi$
$234$	−4.35742	+	13.8557i	−0.284853	+	0.905778i
$235$	2.25681	+	0.657154i	0.147218	+	0.0428680i
$236$	−15.4260	−	7.35915i	−1.00415	−	0.479040i
$237$	5.38211	−	6.80204i	0.349605	−	0.441840i
$238$	−2.92285	−	3.33311i	−0.189460	−	0.216053i
$239$	−7.59666	−	5.51929i	−0.491387	−	0.357013i	0.314331	−	0.949314i	$-0.398220\pi$
$239$	−7.59666	−	5.51929i	−0.491387	−	0.357013i	−0.805717	+	0.592300i	$0.798220\pi$
$240$	8.57213	−	12.9042i	0.553329	−	0.832963i
$241$	16.9165	−	12.2905i	1.08969	−	0.791704i	0.110340	−	0.993894i	$-0.464806\pi$
$241$	16.9165	−	12.2905i	1.08969	−	0.791704i	0.979346	+	0.202190i	$0.0648059\pi$
$242$	10.4304	+	2.36055i	0.670493	+	0.151742i
$243$	15.2610	+	3.17816i	0.978996	+	0.203879i
$244$	−0.235753	+	1.78976i	−0.0150925	+	0.114578i
$245$	1.60063	+	1.08921i	0.102261	+	0.0695873i
$246$	−12.3716	+	9.98093i	−0.788785	+	0.636361i
$247$	−7.90966	−	24.3434i	−0.503280	−	1.54894i
$248$	23.8240	+	8.79196i	1.51282	+	0.558290i
$249$	−10.2524	+	2.87164i	−0.649721	+	0.181983i
$250$	−11.4774	−	10.8752i	−0.725895	−	0.687806i
$251$	−8.22153			−0.518938			−0.259469	−	0.965751i	$-0.583548\pi$
$251$	−8.22153			−0.518938			−0.259469	+	0.965751i	$0.583548\pi$
$252$	−16.7418	+	1.69775i	−1.05463	+	0.106948i
$253$	3.71187	−	1.20606i	0.233363	−	0.0758244i
$254$	3.14878	−	1.35269i	0.197572	−	0.0848755i
$255$	1.37983	−	4.10301i	0.0864084	−	0.256940i
$256$	−6.50371	−	14.6185i	−0.406482	−	0.913659i
$257$	11.5351			0.719538			0.359769	−	0.933041i	$-0.382855\pi$
$257$	11.5351			0.719538			0.359769	+	0.933041i	$0.382855\pi$
$258$	0.974678	+	19.2722i	0.0606808	+	1.19984i
$259$	13.9516	+	19.2028i	0.866913	+	1.19320i
$260$	13.2242	−	7.71557i	0.820131	−	0.478499i
$261$	−0.923635	+	11.2211i	−0.0571716	+	0.694566i
$262$	−3.86148	−	4.40349i	−0.238563	−	0.272048i
$263$	−10.6114	−	14.6054i	−0.654330	−	0.900608i	0.344947	−	0.938622i	$-0.387897\pi$
$263$	−10.6114	−	14.6054i	−0.654330	−	0.900608i	−0.999277	+	0.0380143i	$0.987897\pi$
$264$	−9.05432	−	0.729889i	−0.557255	−	0.0449216i
$265$	−1.20497	+	4.13811i	−0.0740205	+	0.254202i
$266$	22.2961	−	19.5518i	1.36706	−	1.19880i
$267$	−1.20492	+	29.3263i	−0.0737401	+	1.79474i
$268$	−2.94476	+	0.545567i	−0.179880	+	0.0333258i
$269$	−6.82911	−	2.21891i	−0.416378	−	0.135289i	0.0933334	−	0.995635i	$-0.470248\pi$
$269$	−6.82911	−	2.21891i	−0.416378	−	0.135289i	−0.509711	+	0.860346i	$0.670248\pi$
$270$	−9.64780	−	13.3011i	−0.587147	−	0.809481i
$271$	9.40434	−	3.05565i	0.571273	−	0.185618i	−0.00911443	−	0.999958i	$-0.502901\pi$
$271$	9.40434	−	3.05565i	0.571273	−	0.185618i	0.580387	+	0.814341i	$0.302901\pi$
$272$	−2.81307	−	3.47484i	−0.170567	−	0.210693i
$273$	−15.5923	−	5.78409i	−0.943687	−	0.350069i
$274$	0.418531	+	4.55659i	0.0252844	+	0.275274i
$275$	−2.31654	+	8.97693i	−0.139693	+	0.541329i
$276$	6.54560	−	3.21278i	0.393999	−	0.193387i
$277$	1.96968	−	2.71103i	0.118347	−	0.162890i	−0.745734	−	0.666244i	$-0.767901\pi$
$277$	1.96968	−	2.71103i	0.118347	−	0.162890i	0.864080	+	0.503354i	$0.167901\pi$
$278$	3.93581	+	9.16173i	0.236054	+	0.549484i
$279$	17.5662	−	20.4186i	1.05166	−	1.22243i
$280$	14.2604	+	10.5486i	0.852223	+	0.630402i
$281$	−12.3397	−	4.00940i	−0.736122	−	0.239181i	−0.0831232	−	0.996539i	$-0.526490\pi$
$281$	−12.3397	−	4.00940i	−0.736122	−	0.239181i	−0.652999	+	0.757359i	$0.726490\pi$
$282$	−0.918359	−	2.40555i	−0.0546875	−	0.143248i
$283$	0.0785686	−	0.241809i	0.00467042	−	0.0143741i	−0.948694	−	0.316195i	$-0.897595\pi$
$283$	0.0785686	−	0.241809i	0.00467042	−	0.0143741i	0.953365	+	0.301821i	$0.0975945\pi$
$284$	4.94567	−	5.21092i	0.293472	−	0.309211i
$285$	27.4462	+	9.23008i	1.62577	+	0.546743i
$286$	−7.71497	−	4.59029i	−0.456196	−	0.271429i
$287$	−10.6979	−	14.7244i	−0.631475	−	0.869151i
$288$	−16.9383	+	1.04621i	−0.998098	+	0.0616486i
$289$	12.7426	+	9.25806i	0.749567	+	0.544592i
$290$	8.67788	−	8.09597i	0.509583	−	0.475412i
$291$	18.9573	−	23.9588i	1.11130	−	1.40449i
$292$	−25.1469	−	3.31243i	−1.47161	−	0.193845i
$293$	10.3849			0.606691			0.303345	−	0.952881i	$-0.401896\pi$
$293$	10.3849			0.606691			0.303345	+	0.952881i	$0.401896\pi$
$294$	−0.107124	−	2.11816i	−0.00624762	−	0.123534i
$295$	19.0998	−	0.588594i	1.11203	−	0.0342693i
$296$	13.2969	+	19.9047i	0.772866	+	1.15694i
$297$	−4.08069	+	8.72786i	−0.236786	+	0.506442i
$298$	24.4378	+	14.5401i	1.41564	+	0.842286i
$299$	7.20614			0.416742
$300$	−1.90863	+	17.2150i	−0.110195	+	0.993910i
$301$	−22.0945			−1.27350
$302$	9.65932	+	5.74715i	0.555832	+	0.330711i
$303$	6.54380	+	9.83163i	0.375932	+	0.564812i
$304$	23.2442	−	18.8174i	1.33315	−	1.07925i
$305$	−0.682517	−	1.89939i	−0.0390808	−	0.108759i
$306$	−4.49581	+	1.50798i	−0.257009	+	0.0862056i
$307$	−17.0538			−0.973314			−0.486657	−	0.873593i	$-0.661784\pi$
$307$	−17.0538			−0.973314			−0.486657	+	0.873593i	$0.661784\pi$
$308$	1.35827	−	10.3116i	0.0773948	−	0.587555i
$309$	18.3816	+	14.5444i	1.04569	+	0.827405i
$310$	−28.1795	+	3.46655i	−1.60049	+	0.196887i
$311$	−19.8576	−	14.4274i	−1.12602	−	0.818102i	−0.140910	−	0.990022i	$-0.545003\pi$
$311$	−19.8576	−	14.4274i	−1.12602	−	0.818102i	−0.985111	+	0.171920i	$0.945003\pi$
$312$	−15.4829	−	6.44768i	−0.876545	−	0.365028i
$313$	5.67018	+	7.80433i	0.320497	+	0.441127i	0.938619	−	0.344956i	$-0.112106\pi$
$313$	5.67018	+	7.80433i	0.320497	+	0.441127i	−0.618122	+	0.786083i	$0.712106\pi$
$314$	25.6352	+	15.2526i	1.44668	+	0.860752i
$315$	15.7680	−	10.2632i	0.888426	−	0.578265i
$316$	7.26461	+	6.89482i	0.408666	+	0.387864i
$317$	−5.41442	+	16.6639i	−0.304104	+	0.935936i	0.675906	+	0.736988i	$0.263753\pi$
$317$	−5.41442	+	16.6639i	−0.304104	+	0.935936i	−0.980010	+	0.198948i	$0.936247\pi$
$318$	4.41084	−	1.68392i	0.247348	−	0.0944293i
$319$	−6.61824	−	2.15040i	−0.370550	−	0.120399i
$320$	13.9516	+	11.1961i	0.779919	+	0.625881i
$321$	−9.42203	−	14.1560i	−0.525887	−	0.790109i
$322$	3.29532	+	7.67080i	0.183641	+	0.427477i
$323$	4.91184	−	6.76057i	0.273302	−	0.376168i
$324$	−5.23718	+	17.2213i	−0.290955	+	0.956737i
$325$	−9.18966	+	14.4417i	−0.509751	+	0.801081i
$326$	−0.673790	−	7.33561i	−0.0373178	−	0.406282i
$327$	−1.32975	+	3.58463i	−0.0735354	+	0.198231i
$328$	−10.1958	−	15.2626i	−0.562970	−	0.842735i
$329$	2.80389	−	0.911040i	0.154584	−	0.0502273i
$330$	9.37190	−	3.91273i	0.515906	−	0.215389i
$331$	−24.1449	−	7.84515i	−1.32712	−	0.431208i	−0.442188	−	0.896922i	$-0.645798\pi$
$331$	−24.1449	−	7.84515i	−1.32712	−	0.431208i	−0.884935	+	0.465714i	$0.845798\pi$
$332$	−2.23958	−	12.0884i	−0.122913	−	0.663436i
$333$	24.7092	−	5.83847i	1.35405	−	0.319946i
$334$	−5.60884	+	4.91848i	−0.306902	+	0.269127i
$335$	2.64698	−	2.05063i	0.144620	−	0.112038i
$336$	−0.216778	−	19.4297i	−0.0118262	−	1.05998i
$337$	6.24918	+	8.60126i	0.340415	+	0.468540i	0.944562	−	0.328332i	$-0.106486\pi$
$337$	6.24918	+	8.60126i	0.340415	+	0.468540i	−0.604148	+	0.796872i	$0.706486\pi$
$338$	1.19304	+	1.36050i	0.0648930	+	0.0740015i
$339$	9.38042	−	25.2870i	0.509475	−	1.37340i
$340$	4.57556	+	2.01224i	0.248145	+	0.109129i
$341$	9.78520	+	13.4682i	0.529898	+	0.729343i
$342$	−10.0873	−	30.0738i	−0.545460	−	1.62620i
$343$	−17.2039			−0.928925
$344$	−22.2648	−	0.877122i	−1.20044	−	0.0472913i
$345$	−4.85914	+	6.54578i	−0.261607	+	0.352413i
$346$	−21.0992	+	9.06407i	−1.13430	+	0.487287i
$347$	−30.8425	+	10.0213i	−1.65571	+	0.537974i	−0.979967	−	0.199161i	$-0.936178\pi$
$347$	−30.8425	+	10.0213i	−1.65571	+	0.537974i	−0.675746	+	0.737135i	$0.736178\pi$
$348$	−12.8089	−	2.22555i	−0.686628	−	0.119302i
$349$	−3.26785			−0.174924			−0.0874621	−	0.996168i	$-0.527876\pi$
$349$	−3.26785			−0.174924			−0.0874621	+	0.996168i	$0.527876\pi$
$350$	−19.5753	−	3.17814i	−1.04634	−	0.169879i
$351$	−12.1454	+	12.9978i	−0.648273	+	0.693771i
$352$	1.77810	−	10.3371i	0.0947731	−	0.550971i
$353$	−5.15615	−	15.8690i	−0.274434	−	0.844621i	−0.989369	−	0.145430i	$-0.953544\pi$
$353$	−5.15615	−	15.8690i	−0.274434	−	0.844621i	0.714935	−	0.699191i	$-0.246456\pi$
$354$	−13.1436	−	16.2918i	−0.698575	−	0.865901i
$355$	−2.24562	+	7.71193i	−0.119185	+	0.409307i
$356$	−33.6014	−	4.42609i	−1.78087	−	0.234582i
$357$	−1.46440	−	5.22825i	−0.0775042	−	0.276708i
$358$	−13.2858	−	3.00676i	−0.702176	−	0.158912i
$359$	−7.34053	+	5.33320i	−0.387418	+	0.281476i	−0.764397	−	0.644746i	$-0.776963\pi$
$359$	−7.34053	+	5.33320i	−0.387418	+	0.281476i	0.376979	+	0.926222i	$0.376963\pi$
$360$	16.2970	−	9.71634i	0.858928	−	0.512096i
$361$	29.8520	+	21.6888i	1.57116	+	1.14151i
$362$	−11.0261	−	12.5737i	−0.579517	−	0.660859i
$363$	10.2713	+	8.12712i	0.539101	+	0.426563i
$364$	8.26843	−	17.3320i	0.433384	−	0.908445i
$365$	26.6873	−	9.58965i	1.39687	−	0.501945i
$366$	−1.20755	+	1.85204i	−0.0631196	+	0.0968076i
$367$	3.80297	−	11.7043i	0.198513	−	0.610961i	−0.801404	−	0.598123i	$-0.795913\pi$
$367$	3.80297	−	11.7043i	0.198513	−	0.610961i	0.999918	−	0.0128379i	$-0.00408653\pi$
$368$	3.01621	+	7.86076i	0.157231	+	0.409771i
$369$	−18.9465	+	4.47683i	−0.986318	+	0.233055i
$370$	−23.4104	−	12.9696i	−1.21705	−	0.674257i
$371$	1.67050	+	5.14126i	0.0867278	+	0.266921i
$372$	21.6610	+	22.3187i	1.12307	+	1.15717i
$373$	−0.909305	+	1.25155i	−0.0470820	+	0.0648029i	−0.831909	−	0.554912i	$-0.812752\pi$
$373$	−0.909305	+	1.25155i	−0.0470820	+	0.0648029i	0.784827	+	0.619715i	$0.212752\pi$
$374$	−0.268077	−	2.91857i	−0.0138619	−	0.150916i
$375$	−6.92164	−	18.0857i	−0.357432	−	0.933939i
$376$	2.86168	−	0.806753i	0.147580	−	0.0416051i
$377$	−10.3946	−	7.55215i	−0.535351	−	0.388955i
$378$	−19.3899	−	6.98475i	−0.997309	−	0.359257i
$379$	6.13362	−	1.99293i	0.315063	−	0.102370i	−0.147217	−	0.989104i	$-0.547032\pi$
$379$	6.13362	−	1.99293i	0.315063	−	0.102370i	0.462280	+	0.886734i	$0.347032\pi$
$380$	−13.4604	+	30.6072i	−0.690504	+	1.57012i
$381$	4.19371	+	0.172306i	0.214850	+	0.00882752i
$382$	2.62200	+	28.5459i	0.134153	+	1.46054i
$383$	13.7803	+	4.47749i	0.704140	+	0.228789i	0.639133	−	0.769096i	$-0.279293\pi$
$383$	13.7803	+	4.47749i	0.704140	+	0.228789i	0.0650064	+	0.997885i	$0.479293\pi$
$384$	0.552885	−	19.5881i	0.0282143	−	0.999602i
$385$	3.93227	+	10.9432i	0.200407	+	0.557717i
$386$	−9.51659	−	5.66223i	−0.484382	−	0.288200i
$387$	−9.12252	+	21.8021i	−0.463724	+	1.10827i
$388$	25.5881	+	24.2856i	1.29904	+	1.23291i
$389$	−12.9514	+	17.8261i	−0.656663	+	0.903819i	−0.999365	−	0.0356248i	$-0.988658\pi$
$389$	−12.9514	+	17.8261i	−0.656663	+	0.903819i	0.342702	+	0.939444i	$0.388658\pi$
$390$	18.6894	−	1.52352i	0.946374	−	0.0771466i
$391$	1.38284	+	1.90331i	0.0699332	+	0.0962548i
$392$	2.44707	+	0.0964023i	0.123596	+	0.00486905i
$393$	−1.93467	−	6.90722i	−0.0975911	−	0.348423i
$394$	20.5109	+	4.64190i	1.03332	+	0.233855i
$395$	−10.7513	−	3.13064i	−0.540956	−	0.157520i
$396$	−9.61430	−	5.59780i	−0.483137	−	0.281300i
$397$	−17.5994	+	5.71840i	−0.883290	+	0.286998i	−0.715323	−	0.698794i	$-0.753720\pi$
$397$	−17.5994	+	5.71840i	−0.883290	+	0.286998i	−0.167967	+	0.985793i	$0.553720\pi$
$398$	−17.6898	−	10.5251i	−0.886707	−	0.527577i
$399$	34.9732	−	9.79577i	1.75085	−	0.490402i
$400$	−19.6000	−	3.97976i	−0.980002	−	0.198988i
$401$		−	17.2591i		−	0.861877i	−0.902381	−	0.430939i	$-0.858183\pi$
$401$		−	17.2591i		−	0.861877i	0.902381	−	0.430939i	$-0.141817\pi$
$402$	−3.54123	−	0.955814i	−0.176620	−	0.0476717i
$403$	9.49838	+	29.2330i	0.473148	+	1.45620i
$404$	−11.9852	+	6.50633i	−0.596284	+	0.323702i
$405$	−3.61698	−	19.7969i	−0.179729	−	0.983716i
$406$	3.28572	−	14.5185i	0.163068	−	0.720539i
$407$			15.6925i			0.777846i
$408$	−1.26813	−	5.32669i	−0.0627820	−	0.263711i
$409$	−5.74671	+	4.17523i	−0.284156	+	0.206452i	−0.720728	−	0.693218i	$-0.756192\pi$
$409$	−5.74671	+	4.17523i	−0.284156	+	0.206452i	0.436572	+	0.899669i	$0.356192\pi$
$410$	17.9507	+	9.94484i	0.886520	+	0.491141i
$411$	−1.94912	+	5.25428i	−0.0961430	+	0.259174i
$412$	−18.6324	+	19.6317i	−0.917950	+	0.967183i
$413$	19.3901	−	14.0877i	0.954125	−	0.693212i
$414$	8.92990	−	0.0845458i	0.438881	−	0.00415520i
$415$	8.41792	+	10.8660i	0.413220	+	0.533390i
$416$	9.02024	−	17.1374i	0.442254	−	0.840231i
$417$	−0.501344	+	12.2021i	−0.0245509	+	0.597538i
$418$	19.5232	−	1.79324i	0.954909	−	0.0877102i
$419$	−0.662387	+	2.03862i	−0.0323597	+	0.0995929i	−0.965932	−	0.258797i	$-0.916674\pi$
$419$	−0.662387	+	2.03862i	−0.0323597	+	0.0995929i	0.933572	+	0.358390i	$0.116674\pi$
$420$	10.1683	+	19.1978i	0.496162	+	0.936758i
$421$	−4.44421	−	13.6779i	−0.216597	−	0.666618i	−0.999036	−	0.0438909i	$-0.986025\pi$
$421$	−4.44421	−	13.6779i	−0.216597	−	0.666618i	0.782439	−	0.622727i	$-0.213975\pi$
$422$	4.75202	+	11.0617i	0.231325	+	0.538474i
$423$	0.258704	−	3.14295i	0.0125786	−	0.152815i
$424$	1.47927	+	5.24721i	0.0718399	+	0.254827i
$425$	−5.57787	+	0.344111i	−0.270566	+	0.0166918i
$426$	8.22020	−	3.13820i	0.398270	−	0.152047i
$427$	−2.04800	−	1.48796i	−0.0991097	−	0.0720074i
$428$	17.2567	−	9.36807i	0.834135	−	0.452823i
$429$	−6.09202	−	9.15285i	−0.294125	−	0.441904i
$430$	22.5757	−	10.5335i	1.08870	−	0.507970i
$431$	−5.45008	+	16.7736i	−0.262521	+	0.807957i	0.729733	+	0.683732i	$0.239644\pi$
$431$	−5.45008	+	16.7736i	−0.262521	+	0.807957i	−0.992254	+	0.124225i	$0.960356\pi$
$432$	−19.2621	−	7.80836i	−0.926750	−	0.375680i
$433$	−2.32032	−	0.753918i	−0.111508	−	0.0362310i	0.252732	−	0.967536i	$-0.418671\pi$
$433$	−2.32032	−	0.753918i	−0.111508	−	0.0362310i	−0.364239	+	0.931305i	$0.618671\pi$
$434$	−26.7744	+	23.4789i	−1.28521	+	1.12702i
$435$	13.8693	−	4.34964i	0.664980	−	0.208549i
$436$	−3.98460	−	1.90090i	−0.190828	−	0.0910365i
$437$	−12.7318	+	9.25020i	−0.609045	+	0.442497i
$438$	−26.0219	−	16.9666i	−1.24338	−	0.810694i
$439$	−19.5188	+	26.8653i	−0.931579	+	1.28221i	0.0276608	+	0.999617i	$0.491194\pi$
$439$	−19.5188	+	26.8653i	−0.931579	+	1.28221i	−0.959240	+	0.282592i	$0.908806\pi$
$440$	3.52816	+	11.1837i	0.168198	+	0.533161i
$441$	1.00263	−	2.39622i	0.0477444	−	0.114106i
$442$	1.19447	−	5.27794i	0.0568152	−	0.251046i
$443$			25.0316i			1.18929i	0.803990	+	0.594643i	$0.202707\pi$
$443$			25.0316i			1.18929i	−0.803990	+	0.594643i	$0.797293\pi$
$444$	4.15275	+	29.0218i	0.197081	+	1.37731i
$445$	35.6596	−	12.8137i	1.69043	−	0.607429i
$446$	2.64092	−	1.13452i	0.125051	−	0.0537210i
$447$	19.2969	+	28.9924i	0.912714	+	1.37129i
$448$	22.3674	+	1.76506i	1.05676	+	0.0833913i
$449$			32.0071i			1.51051i	0.655433	+	0.755253i	$0.272486\pi$
$449$			32.0071i			1.51051i	−0.655433	+	0.755253i	$0.727514\pi$
$450$	−11.2185	+	18.0041i	−0.528843	+	0.848720i
$451$		−	12.0327i		−	0.566598i
$452$	28.1084	+	13.4094i	1.32211	+	0.630727i
$453$	7.62735	+	11.4596i	0.358364	+	0.538418i
$454$	14.4244	+	33.5769i	0.676969	+	1.57584i
$455$	0.661319	+	21.4597i	0.0310031	+	1.00605i
$456$	35.6317	−	8.48291i	1.66861	−	0.397249i
$457$		−	27.8514i		−	1.30283i	−0.758721	−	0.651416i	$-0.774175\pi$
$457$		−	27.8514i		−	1.30283i	0.758721	−	0.651416i	$-0.225825\pi$
$458$	3.99325	+	0.903728i	0.186593	+	0.0422284i
$459$	−5.76370	−	0.713651i	−0.269026	−	0.0333104i
$460$	−7.02412	−	6.26682i	−0.327501	−	0.292192i
$461$	2.72769	−	3.75434i	0.127041	−	0.174857i	−0.740758	−	0.671771i	$-0.765534\pi$
$461$	2.72769	−	3.75434i	0.127041	−	0.174857i	0.867800	+	0.496914i	$0.165534\pi$
$462$	6.95720	−	10.6704i	0.323678	−	0.496431i
$463$	−12.0343	+	8.74343i	−0.559281	+	0.406341i	−0.831196	−	0.555980i	$-0.812343\pi$
$463$	−12.0343	+	8.74343i	−0.559281	+	0.406341i	0.271915	+	0.962321i	$0.412343\pi$
$464$	3.88742	−	14.5000i	0.180469	−	0.673143i
$465$	−32.9590	−	11.0840i	−1.52844	−	0.514009i
$466$	−17.3045	−	19.7334i	−0.801617	−	0.914133i
$467$	6.19271	+	2.01213i	0.286564	+	0.0931104i	0.448772	−	0.893646i	$-0.351861\pi$
$467$	6.19271	+	2.01213i	0.286564	+	0.0931104i	−0.162208	+	0.986757i	$0.551861\pi$
$468$	−13.6888	−	15.3152i	−0.632763	−	0.707945i
$469$	1.29779	−	3.99418i	0.0599262	−	0.184434i
$470$	−2.43062	+	2.26763i	−0.112116	+	0.104598i
$471$	20.2425	+	30.4130i	0.932725	+	1.40136i
$472$	20.0989	−	13.4266i	0.925126	−	0.618009i
$473$	−11.8175	−	8.58592i	−0.543369	−	0.394781i
$474$	4.37501	+	11.4599i	0.200951	+	0.526370i
$475$	−2.30185	−	37.3119i	−0.105616	−	1.71199i
$476$	6.16450	−	1.14208i	0.282549	−	0.0523470i
$477$	5.76296	+	0.474364i	0.263868	+	0.0217196i
$478$	12.2012	−	5.24155i	0.558071	−	0.239743i
$479$	−5.73304	−	17.6445i	−0.261949	−	0.806197i	−0.992381	−	0.123211i	$-0.960681\pi$
$479$	−5.73304	−	17.6445i	−0.261949	−	0.806197i	0.730431	−	0.682986i	$-0.239319\pi$
$480$	9.48457	+	19.7495i	0.432909	+	0.901437i
$481$	−8.95343	+	27.5558i	−0.408241	+	1.25644i
$482$	2.70478	+	29.4471i	0.123199	+	1.34128i
$483$	−0.419758	+	10.2164i	−0.0190997	+	0.464861i
$484$	−10.4114	+	10.9697i	−0.473243	+	0.498625i
$485$	−37.8692	−	11.0270i	−1.71955	−	0.500712i
$486$	−14.8982	+	16.2494i	−0.675795	+	0.737090i
$487$	15.6066	−	11.3389i	0.707203	−	0.513813i	−0.175067	−	0.984556i	$-0.556014\pi$
$487$	15.6066	−	11.3389i	0.707203	−	0.513813i	0.882270	+	0.470744i	$0.156014\pi$
$488$	−2.00472	−	1.58073i	−0.0907494	−	0.0715565i
$489$	3.13787	−	8.45882i	0.141899	−	0.382521i
$490$	−2.48123	+	1.15771i	−0.112091	+	0.0523000i
$491$	−4.69454	+	3.41078i	−0.211862	+	0.153926i	−0.688656	−	0.725089i	$-0.741799\pi$
$491$	−4.69454	+	3.41078i	−0.211862	+	0.153926i	0.476794	+	0.879015i	$0.341799\pi$
$492$	−3.18425	−	22.2534i	−0.143557	−	1.00326i
$493$		−	4.19471i		−	0.188920i
$494$	35.3056	+	7.99015i	1.58848	+	0.359494i
$495$	12.4220	+	0.638062i	0.558327	+	0.0286787i
$496$	−27.9130	+	22.5970i	−1.25333	+	1.01464i
$497$	3.11319	+	9.58142i	0.139646	+	0.429786i
$498$	3.92366	−	14.5369i	0.175823	−	0.651415i
$499$			20.7222i			0.927654i	0.885926	+	0.463827i	$0.153524\pi$
$499$			20.7222i			0.927654i	−0.885926	+	0.463827i	$0.846476\pi$
$500$	21.5168	−	6.08512i	0.962259	−	0.272135i
$501$	−8.79792	+	2.46424i	−0.393062	+	0.110094i
$502$	5.94515	−	9.99211i	0.265345	−	0.445970i
$503$	−33.8991	+	11.0145i	−1.51149	+	0.491111i	−0.943343	−	0.331819i	$-0.892338\pi$
$503$	−33.8991	+	11.0145i	−1.51149	+	0.491111i	−0.568142	+	0.822931i	$0.692338\pi$
$504$	10.0430	−	21.5750i	0.447349	−	0.961026i
$505$	8.57775	−	12.6053i	0.381705	−	0.560927i
$506$	−1.21833	+	5.38338i	−0.0541615	+	0.239321i
$507$	0.597735	+	2.13405i	0.0265463	+	0.0947767i
$508$	−0.632939	+	4.80506i	−0.0280821	+	0.213190i
$509$	−2.25059	−	3.09767i	−0.0997557	−	0.137302i	0.756221	−	0.654316i	$-0.227043\pi$
$509$	−2.25059	−	3.09767i	−0.0997557	−	0.137302i	−0.855977	+	0.517014i	$0.827043\pi$
$510$	3.98885	+	4.64396i	0.176629	+	0.205638i
$511$	20.9065	−	28.7753i	0.924847	−	1.27294i
$512$	22.4697	+	2.66663i	0.993031	+	0.117849i
$513$	4.77381	−	38.5550i	0.210769	−	1.70224i
$514$	−8.34125	+	14.0193i	−0.367917	+	0.618363i
$515$	8.46015	−	29.0540i	0.372799	−	1.28027i
$516$	−24.1275	−	12.7516i	−1.06215	−	0.561356i
$517$	1.85373	+	0.602312i	0.0815268	+	0.0264897i
$518$	−33.4270	+	3.07033i	−1.46870	+	0.134903i
$519$	−28.1010	−	1.15458i	−1.23350	−	0.0506806i
$520$	−0.185505	+	21.6514i	−0.00813494	+	0.949479i
$521$	27.7287	−	9.00962i	1.21482	−	0.394718i	0.369626	−	0.929181i	$-0.379486\pi$
$521$	27.7287	−	9.00962i	1.21482	−	0.394718i	0.845192	+	0.534462i	$0.179486\pi$
$522$	−12.9697	−	9.23672i	−0.567669	−	0.404280i
$523$	−5.18001	−	3.76350i	−0.226506	−	0.164566i	0.468744	−	0.883334i	$-0.344707\pi$
$523$	−5.18001	−	3.76350i	−0.226506	−	0.164566i	−0.695250	+	0.718768i	$0.744707\pi$
$524$	8.14413	−	1.50884i	0.355778	−	0.0659139i
$525$	−19.9391	−	13.8697i	−0.870215	−	0.605324i
$526$	25.4242	−	2.33526i	1.10855	−	0.101822i
$527$	−5.89843	+	8.11849i	−0.256940	+	0.353647i
$528$	7.43444	−	10.4765i	0.323542	−	0.455929i
$529$	5.73827	+	17.6606i	0.249490	+	0.767851i
$530$	−4.15796	−	4.45682i	−0.180610	−	0.193592i
$531$	−5.89542	−	24.9502i	−0.255839	−	1.08275i
$532$	7.63967	+	41.2360i	0.331222	+	1.78781i
$533$	6.86533	−	21.1293i	0.297370	−	0.915212i
$534$	−34.7706	−	22.6708i	−1.50467	−	0.981062i
$535$	−12.3506	+	18.1496i	−0.533963	+	0.784674i
$536$	1.46636	−	3.97345i	0.0633369	−	0.171627i
$537$	−13.0831	−	10.3520i	−0.564575	−	0.446720i
$538$	7.63504	−	6.69528i	0.329170	−	0.288654i
$539$	1.29883	+	0.943656i	0.0559446	+	0.0406461i
$540$	23.1422	−	2.10723i	0.995880	−	0.0906809i
$541$	18.7149	−	13.5972i	0.804617	−	0.584589i	−0.107648	−	0.994189i	$-0.534332\pi$
$541$	18.7149	−	13.5972i	0.804617	−	0.584589i	0.912265	+	0.409600i	$0.134332\pi$
$542$	−3.08675	+	13.6392i	−0.132587	+	0.585856i
$543$	−5.52424	−	19.7228i	−0.237068	−	0.846388i
$544$	6.25736	−	0.906160i	0.268282	−	0.0388513i
$545$	4.93355	−	0.152036i	0.211330	−	0.00651252i
$546$	18.3048	−	14.7676i	0.783374	−	0.631995i
$547$	−1.11144	−	3.42065i	−0.0475216	−	0.146256i	0.924480	−	0.381230i	$-0.124500\pi$
$547$	−1.11144	−	3.42065i	−0.0475216	−	0.146256i	−0.972002	+	0.234974i	$0.924500\pi$
$548$	−5.84054	−	2.78629i	−0.249495	−	0.119025i
$549$	−2.31386	+	1.40654i	−0.0987533	+	0.0600298i
$550$	−9.23505	−	9.30682i	−0.393784	−	0.396844i
$551$	28.0596			1.19538
$552$	−0.828571	+	10.2785i	−0.0352663	+	0.437481i
$553$	−13.3576	+	4.34014i	−0.568022	+	0.184561i
$554$	1.87056	+	4.35427i	0.0794726	+	0.184995i
$555$	−18.9933	−	26.7140i	−0.806221	−	1.13395i
$556$	−13.9809	−	1.84161i	−0.592921	−	0.0781016i
$557$	−28.3445			−1.20100			−0.600498	−	0.799626i	$-0.705031\pi$
$557$	−28.3445			−1.20100			−0.600498	+	0.799626i	$0.705031\pi$
$558$	12.1134	+	36.1143i	0.512803	+	1.52884i
$559$	−15.8527	−	21.8193i	−0.670497	−	0.922860i
$560$	−23.1324	+	9.70359i	−0.977522	+	0.410052i
$561$	1.24845	−	3.36546i	0.0527094	−	0.142090i
$562$	13.7959	−	12.0978i	0.581946	−	0.510317i
$563$	−18.1788	−	25.0210i	−0.766146	−	1.05451i	−0.996678	−	0.0814444i	$-0.974047\pi$
$563$	−18.1788	−	25.0210i	−0.766146	−	1.05451i	0.230532	−	0.973065i	$-0.425953\pi$
$564$	3.58769	+	0.623363i	0.151069	+	0.0262483i
$565$	−34.8026	+	1.07250i	−1.46416	+	0.0451206i
$566$	0.237071	+	0.270346i	0.00996482	+	0.0113635i
$567$	−17.7199	−	17.9760i	−0.744166	−	0.754923i
$568$	2.75683	+	9.77889i	0.115674	+	0.410313i
$569$	33.1483	+	10.7705i	1.38965	+	0.451524i	0.905829	−	0.423644i	$-0.139249\pi$
$569$	33.1483	+	10.7705i	1.38965	+	0.451524i	0.483819	+	0.875168i	$0.339249\pi$
$570$	−31.0647	+	26.6825i	−1.30116	+	1.11761i
$571$	18.3366	−	5.95791i	0.767361	−	0.249331i	0.100926	−	0.994894i	$-0.467819\pi$
$571$	18.3366	−	5.95791i	0.767361	−	0.249331i	0.666435	+	0.745563i	$0.267819\pi$
$572$	11.1577	−	6.05713i	0.466527	−	0.253261i
$573$	−12.2108	+	32.9168i	−0.510112	+	1.37512i
$574$	25.6312	−	2.35428i	1.06983	−	0.0982656i
$575$	10.1906	+	2.62974i	0.424978	+	0.109668i
$576$	10.9769	−	21.3426i	0.457370	−	0.889276i
$577$	−19.8382	+	27.3049i	−0.825874	+	1.13672i	0.162803	+	0.986659i	$0.447946\pi$
$577$	−19.8382	+	27.3049i	−0.825874	+	1.13672i	−0.988677	+	0.150059i	$0.952054\pi$
$578$	−20.4663	+	8.79218i	−0.851287	+	0.365706i
$579$	−7.51464	−	11.2902i	−0.312298	−	0.469207i
$580$	3.56436	+	16.4011i	0.148002	+	0.681019i
$581$	16.3963	+	5.32747i	0.680232	+	0.221021i
$582$	15.4101	+	40.3650i	0.638767	+	1.67318i
$583$	−1.10441	+	3.39902i	−0.0457399	+	0.140773i
$584$	22.2100	−	28.1672i	0.919056	−	1.16557i
$585$	21.4488	+	8.20787i	0.886800	+	0.339354i
$586$	−7.50951	+	12.6213i	−0.310215	+	0.521383i
$587$	−11.2432	−	15.4749i	−0.464057	−	0.638719i	0.511287	−	0.859410i	$-0.329169\pi$
$587$	−11.2432	−	15.4749i	−0.464057	−	0.638719i	−0.975344	+	0.220691i	$0.929169\pi$
$588$	2.65179	+	1.40149i	0.109358	+	0.0577965i
$589$	−54.3068	−	39.4562i	−2.23767	−	1.62577i
$590$	−13.0961	+	23.6387i	−0.539158	+	0.973191i
$591$	20.1979	+	15.9816i	0.830831	+	0.657394i
$592$	−33.8066	+	1.76700i	−1.38944	+	0.0726232i
$593$	8.54639			0.350958			0.175479	−	0.984483i	$-0.443853\pi$
$593$	8.54639			0.350958			0.175479	+	0.984483i	$0.443853\pi$
$594$	−7.65666	−	11.2708i	−0.314156	−	0.462447i
$595$	−5.54113	+	4.29274i	−0.227164	+	0.175985i
$596$	−35.3429	+	19.1864i	−1.44770	+	0.785907i
$597$	−13.9685	−	20.9867i	−0.571691	−	0.858928i
$598$	−5.21090	+	8.75804i	−0.213090	+	0.358143i
$599$	−34.9700			−1.42884			−0.714419	−	0.699719i	$-0.753309\pi$
$599$	−34.9700			−1.42884			−0.714419	+	0.699719i	$0.753309\pi$
$600$	−19.5423	−	14.7682i	−0.797810	−	0.602909i
$601$	−25.6951			−1.04813			−0.524063	−	0.851679i	$-0.675585\pi$
$601$	−25.6951			−1.04813			−0.524063	+	0.851679i	$0.675585\pi$
$602$	15.9770	−	26.8527i	0.651172	−	1.09444i
$603$	−3.40549	−	2.92976i	−0.138682	−	0.119309i
$604$	−13.9697	+	7.58366i	−0.568419	+	0.308575i
$605$	4.72735	−	16.2347i	0.192194	−	0.660036i
$606$	−16.6809	+	0.843624i	−0.677616	+	0.0342699i
$607$	33.7114			1.36830			0.684152	−	0.729340i	$-0.260173\pi$
$607$	33.7114			1.36830			0.684152	+	0.729340i	$0.260173\pi$
$608$	6.06156	+	41.8573i	0.245829	+	1.69754i
$609$	11.3124	−	14.2969i	0.458402	−	0.579340i
$610$	2.80198	+	0.543985i	0.113449	+	0.0220253i
$611$	2.91147	+	2.11531i	0.117786	+	0.0855763i
$612$	1.41827	−	6.55448i	0.0573303	−	0.264949i
$613$	13.7296	+	18.8972i	0.554535	+	0.763252i	0.990619	−	0.136654i	$-0.0436349\pi$
$613$	13.7296	+	18.8972i	0.554535	+	0.763252i	−0.436084	+	0.899906i	$0.643635\pi$
$614$	12.3320	−	20.7265i	0.497678	−	0.836455i
$615$	14.5637	+	20.4838i	0.587266	+	0.825987i
$616$	11.5500	+	9.10728i	0.465364	+	0.366943i
$617$	2.44863	−	7.53611i	0.0985782	−	0.303392i	−0.889591	−	0.456757i	$-0.849011\pi$
$617$	2.44863	−	7.53611i	0.0985782	−	0.303392i	0.988170	+	0.153365i	$0.0490109\pi$
$618$	−30.9688	+	11.8229i	−1.24575	+	0.475587i
$619$	17.1069	+	5.55838i	0.687586	+	0.223410i	0.631913	−	0.775039i	$-0.282270\pi$
$619$	17.1069	+	5.55838i	0.687586	+	0.223410i	0.0556723	+	0.998449i	$0.482270\pi$
$620$	16.1640	−	36.7549i	0.649163	−	1.47611i
$621$	9.90788	+	4.63241i	0.397590	+	0.185892i
$622$	31.8939	−	13.7014i	1.27883	−	0.549375i
$623$	27.9353	−	38.4497i	1.11920	−	1.54045i
$624$	19.0322	−	14.1548i	0.761898	−	0.566645i
$625$	−18.2658	+	17.0692i	−0.730634	+	0.682770i
$626$	−13.5853	+	1.24783i	−0.542977	+	0.0498735i
$627$	22.5125	+	8.35120i	0.899062	+	0.333515i
$628$	−37.0747	+	20.1266i	−1.47944	+	0.803137i
$629$	−8.99630	+	2.92307i	−0.358706	+	0.116551i
$630$	1.07129	+	26.5853i	0.0426811	+	1.05918i
$631$	36.7577	+	11.9433i	1.46330	+	0.475455i	0.929076	−	0.369888i	$-0.120604\pi$
$631$	36.7577	+	11.9433i	1.46330	+	0.475455i	0.534224	+	0.845343i	$0.320604\pi$
$632$	−13.6329	+	3.84332i	−0.542286	+	0.152879i
$633$	−0.605313	+	14.7325i	−0.0240590	+	0.585565i
$634$	−16.3373	−	18.6304i	−0.648837	−	0.739909i
$635$	−1.83239	−	5.09940i	−0.0727161	−	0.202363i
$636$	−1.14301	+	6.57843i	−0.0453232	+	0.260852i
$637$	1.74233	+	2.39811i	0.0690335	+	0.0950165i
$638$	7.39928	−	6.48854i	0.292940	−	0.256884i
$639$	10.7400	+	0.884041i	0.424870	+	0.0349721i
$640$	−23.6960	+	8.86009i	−0.936665	+	0.350226i
$641$	22.8319	+	31.4254i	0.901806	+	1.24123i	0.969888	+	0.243550i	$0.0783120\pi$
$641$	22.8319	+	31.4254i	0.901806	+	1.24123i	−0.0680821	+	0.997680i	$0.521688\pi$
$642$	24.0178	−	1.21468i	0.947909	−	0.0479397i
$643$	17.5439			0.691864			0.345932	−	0.938260i	$-0.387563\pi$
$643$	17.5439			0.691864			0.345932	+	0.938260i	$0.387563\pi$
$644$	−11.7057	−	1.54191i	−0.461269	−	0.0607599i
$645$	30.5094	+	0.312937i	1.20131	+	0.0123219i
$646$	4.66467	+	10.8584i	0.183529	+	0.427216i
$647$	17.8336	−	5.79448i	0.701110	−	0.227804i	0.0632959	−	0.997995i	$-0.479839\pi$
$647$	17.8336	−	5.79448i	0.701110	−	0.227804i	0.637814	+	0.770190i	$0.279839\pi$
$648$	−17.1429	−	18.8181i	−0.673437	−	0.739245i
$649$	15.8455			0.621991
$650$	−10.9066	−	21.6118i	−0.427792	−	0.847685i
$651$	−41.9978	+	11.7633i	−1.64603	+	0.461041i
$652$	9.40263	+	4.48563i	0.368236	+	0.175671i
$653$	−1.36907	−	4.21357i	−0.0535759	−	0.164890i	0.920688	−	0.390299i	$-0.127628\pi$
$653$	−1.36907	−	4.21357i	−0.0535759	−	0.164890i	−0.974264	+	0.225409i	$0.927628\pi$
$654$	−3.39505	−	4.20825i	−0.132757	−	0.164555i
$655$	−7.32058	+	5.67129i	−0.286039	+	0.221595i
$656$	25.9223	−	1.35490i	1.01210	−	0.0529000i
$657$	−19.7625	−	32.5108i	−0.771010	−	1.26837i
$658$	−0.920310	+	4.06653i	−0.0358774	+	0.158530i
$659$	9.45627	−	6.87038i	0.368364	−	0.267632i	−0.388168	−	0.921589i	$-0.626892\pi$
$659$	9.45627	−	6.87038i	0.368364	−	0.267632i	0.756532	+	0.653956i	$0.226892\pi$
$660$	−2.02164	+	14.2196i	−0.0786921	+	0.553497i
$661$	−2.32708	−	1.69072i	−0.0905129	−	0.0657615i	0.541608	−	0.840631i	$-0.317816\pi$
$661$	−2.32708	−	1.69072i	−0.0905129	−	0.0657615i	−0.632121	+	0.774869i	$0.717816\pi$
$662$	26.9943	−	23.6717i	1.04916	−	0.920028i
$663$	4.11244	−	5.19740i	0.159714	−	0.201850i
$664$	16.3112	+	6.01946i	0.632998	+	0.233600i
$665$	−28.7153	−	37.0662i	−1.11353	−	1.43736i
$666$	−10.7719	+	34.2524i	−0.417401	+	1.32725i
$667$	−2.44113	+	7.51303i	−0.0945210	+	0.290906i
$668$	−1.92185	−	10.3734i	−0.0743586	−	0.401359i
$669$	3.51731	+	0.144515i	0.135987	+	0.00558728i
$670$	0.578165	+	4.69988i	0.0223364	+	0.181572i
$671$	−0.517177	−	1.59171i	−0.0199654	−	0.0614471i
$672$	23.7708	+	13.7865i	0.916979	+	0.531828i
$673$	17.4636	−	24.0366i	0.673172	−	0.926542i	−0.326655	−	0.945144i	$-0.605921\pi$
$673$	17.4636	−	24.0366i	0.673172	−	0.926542i	0.999827	+	0.0186014i	$0.00592136\pi$
$674$	−14.9725	+	1.37525i	−0.576720	+	0.0529728i
$675$	−21.9188	+	13.9487i	−0.843655	+	0.536886i
$676$	−2.51621	+	0.466170i	−0.0967773	+	0.0179296i
$677$	−22.0160	−	15.9956i	−0.846144	−	0.614760i	0.0779360	−	0.996958i	$-0.475167\pi$
$677$	−22.0160	−	15.9956i	−0.846144	−	0.614760i	−0.924080	+	0.382199i	$0.875167\pi$
$678$	23.9496	+	29.6861i	0.919778	+	1.14009i
$679$	−47.0493	+	15.2872i	−1.80559	+	0.586670i
$680$	−5.75427	+	4.10586i	−0.220666	+	0.157453i
$681$	−1.83738	+	44.7194i	−0.0704085	+	1.71365i
$682$	−23.4445	+	2.15343i	−0.897738	+	0.0824589i
$683$	8.56408	+	2.78264i	0.327695	+	0.106475i	0.468244	−	0.883599i	$-0.344887\pi$
$683$	8.56408	+	2.78264i	0.327695	+	0.106475i	−0.140549	+	0.990074i	$0.544887\pi$
$684$	43.8447	+	9.48722i	1.67645	+	0.362753i
$685$	7.23149	−	0.222851i	0.276301	−	0.00851471i
$686$	12.4405	−	20.9089i	0.474981	−	0.798307i
$687$	3.93232	+	3.11144i	0.150027	+	0.118709i
$688$	17.1662	−	26.4255i	0.654454	−	1.00746i
$689$	−3.87866	+	5.33852i	−0.147765	+	0.203381i
$690$	−4.44173	−	10.6390i	−0.169094	−	0.405019i
$691$	−9.28419	−	12.7786i	−0.353187	−	0.486121i	0.595048	−	0.803690i	$-0.297133\pi$
$691$	−9.28419	−	12.7786i	−0.353187	−	0.486121i	−0.948235	+	0.317570i	$0.897133\pi$
$692$	4.24117	−	32.1975i	0.161225	−	1.22397i
$693$	13.3311	−	8.10369i	0.506408	−	0.307834i
$694$	10.1233	−	44.7313i	0.384276	−	1.69798i
$695$	14.8373	−	5.33154i	0.562810	−	0.202237i
$696$	11.9672	−	13.9580i	0.453616	−	0.529078i
$697$	6.89820	−	2.24136i	0.261288	−	0.0848976i
$698$	2.36305	−	3.97161i	0.0894428	−	0.150328i
$699$	−8.66986	−	30.9534i	−0.327924	−	1.17077i
$700$	18.0179	−	21.4928i	0.681011	−	0.812352i
$701$			38.6678i			1.46046i	0.683201	+	0.730231i	$0.260587\pi$
$701$			38.6678i			1.46046i	−0.683201	+	0.730231i	$0.739413\pi$
$702$	−7.01440	−	24.1600i	−0.264741	−	0.911860i
$703$	−19.5533	−	60.1787i	−0.737465	−	2.26968i
$704$	11.2775	+	9.63602i	0.425039	+	0.363171i
$705$	−3.88469	+	1.21831i	−0.146306	+	0.0458841i
$706$	23.0150	+	5.20861i	0.866182	+	0.196029i
$707$		−	19.1237i		−	0.719220i
$708$	29.3048	−	4.19325i	1.10134	−	0.157592i
$709$	−26.7600	+	19.4423i	−1.00499	+	0.730171i	−0.963153	−	0.268953i	$-0.913322\pi$
$709$	−26.7600	+	19.4423i	−1.00499	+	0.730171i	−0.0418412	+	0.999124i	$0.513322\pi$
$710$	−7.74892	−	8.30588i	−0.290812	−	0.311714i
$711$	−1.23245	+	14.9728i	−0.0462206	+	0.561525i
$712$	29.6771	−	37.6371i	1.11220	−	1.41051i
$713$	15.2891	−	11.1082i	0.572581	−	0.416004i
$714$	7.41313	+	2.00088i	0.277429	+	0.0748810i
$715$	−7.98554	+	11.7350i	−0.298642	+	0.438864i
$716$	13.2615	−	13.9728i	0.495606	−	0.522187i
$717$	16.2502	+	0.667670i	0.606875	+	0.0249346i
$718$	−1.17368	−	12.7779i	−0.0438012	−	0.476868i
$719$	11.1272	−	34.2459i	0.414973	−	1.27716i	−0.497302	−	0.867578i	$-0.665676\pi$
$719$	11.1272	−	34.2459i	0.414973	−	1.27716i	0.912275	−	0.409579i	$-0.134324\pi$
$720$	0.0241457	+	26.8328i	0.000899856	+	1.00000i
$721$	−11.7287	−	36.0971i	−0.436798	−	1.34433i
$722$	−47.9463	+	20.5974i	−1.78438	+	0.766554i
$723$	−12.5963	+	33.9560i	−0.468460	+	1.26284i
$724$	23.2547	−	4.30833i	0.864255	−	0.160118i
$725$	−11.9437	−	14.4733i	−0.443576	−	0.537523i
$726$	−17.3047	+	6.60638i	−0.642238	+	0.245186i
$727$	−7.26585	−	5.27895i	−0.269475	−	0.195785i	0.444838	−	0.895611i	$-0.353261\pi$
$727$	−7.26585	−	5.27895i	−0.269475	−	0.195785i	−0.714314	+	0.699825i	$0.753261\pi$
$728$	15.0856	+	22.5822i	0.559108	+	0.836954i
$729$	−25.0545	+	10.0634i	−0.927945	+	0.372718i
$730$	−7.64322	+	39.3691i	−0.282888	+	1.45711i
$731$	2.72093	−	8.37415i	0.100637	−	0.309729i
$732$	−1.37769	−	2.80685i	−0.0509208	−	0.103744i
$733$	18.4725	+	6.00207i	0.682296	+	0.221692i	0.629601	−	0.776919i	$-0.283219\pi$
$733$	18.4725	+	6.00207i	0.682296	+	0.221692i	0.0526960	+	0.998611i	$0.483219\pi$
$734$	11.4750	+	13.0856i	0.423548	+	0.482998i
$735$	−3.35321	−	0.0343941i	−0.123685	−	0.00126865i
$736$	−11.7347	−	2.01850i	−0.432548	−	0.0744030i
$737$	2.24627	−	1.63201i	0.0827426	−	0.0601160i
$738$	8.25967	−	26.2641i	0.304042	−	0.966796i
$739$	5.22131	−	7.18652i	0.192069	−	0.264360i	−0.702111	−	0.712067i	$-0.747759\pi$
$739$	5.22131	−	7.18652i	0.192069	−	0.264360i	0.894180	+	0.447707i	$0.147759\pi$
$740$	32.6912	−	19.0735i	1.20175	−	0.701154i
$741$	34.7669	+	27.5093i	1.27719	+	1.01058i
$742$	−7.45644	−	1.68749i	−0.273735	−	0.0619498i
$743$			38.1796i			1.40067i	0.713813	+	0.700337i	$0.246967\pi$
$743$			38.1796i			1.40067i	−0.713813	+	0.700337i	$0.753033\pi$
$744$	−42.7886	+	10.1868i	−1.56871	+	0.373465i
$745$	25.2948	−	37.1715i	0.926731	−	1.36186i
$746$	−0.863547	−	2.01015i	−0.0316167	−	0.0735970i
$747$	12.0268	−	13.9797i	0.440037	−	0.511490i
$748$	3.74097	+	1.78467i	0.136783	+	0.0652540i
$749$			27.5350i			1.00611i
$750$	26.9857	+	4.66583i	0.985380	+	0.170372i
$751$			25.5204i			0.931254i	0.884981	+	0.465627i	$0.154171\pi$
$751$			25.5204i			0.931254i	−0.884981	+	0.465627i	$0.845829\pi$
$752$	−1.08884	+	4.06135i	−0.0397060	+	0.148102i
$753$	11.8544	−	7.89013i	0.431998	−	0.287532i
$754$	16.6951	−	7.17211i	0.608001	−	0.261193i
$755$	9.99808	−	14.6925i	0.363867	−	0.534714i
$756$	22.5102	−	18.5149i	0.818688	−	0.673380i
$757$		−	24.9324i		−	0.906184i	−0.891464	−	0.453092i	$-0.850321\pi$
$757$		−	24.9324i		−	0.906184i	0.891464	−	0.453092i	$-0.149679\pi$
$758$	−2.01321	+	8.89568i	−0.0731232	+	0.323106i
$759$	−4.19460	+	5.30123i	−0.152254	+	0.192423i
$760$	−27.4652	−	38.4919i	−0.996269	−	1.39625i
$761$	−26.6111	+	36.6270i	−0.964650	+	1.32773i	−0.0199469	+	0.999801i	$0.506350\pi$
$761$	−26.6111	+	36.6270i	−0.964650	+	1.32773i	−0.944703	+	0.327926i	$0.893650\pi$
$762$	−3.24197	+	4.97227i	−0.117444	+	0.180126i
$763$	5.00854	−	3.63892i	0.181321	−	0.131738i
$764$	−36.5896	−	17.4555i	−1.32376	−	0.631517i
$765$	1.94808	+	7.24023i	0.0704330	+	0.261771i
$766$	−15.4066	+	13.5102i	−0.556661	+	0.488145i
$767$	27.8246	+	9.04076i	1.00469	+	0.326443i
$768$	23.4068	+	14.8365i	0.844620	+	0.535367i
$769$	7.78339	−	23.9548i	0.280676	−	0.863833i	−0.706985	−	0.707229i	$-0.749945\pi$
$769$	7.78339	−	23.9548i	0.280676	−	0.863833i	0.987661	−	0.156605i	$-0.0500548\pi$
$770$	−16.1434	−	3.13413i	−0.581768	−	0.112946i
$771$	−16.6321	+	11.0701i	−0.598991	+	0.398680i
$772$	13.7633	−	7.47160i	0.495351	−	0.268909i
$773$	12.5760	+	9.13698i	0.452326	+	0.328634i	0.790514	−	0.612445i	$-0.209814\pi$
$773$	12.5760	+	9.13698i	0.452326	+	0.328634i	−0.338187	+	0.941079i	$0.609814\pi$
$774$	−19.9008	−

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.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.723120 + 1.21536i) q^{2} +(-1.44187 + 0.959691i) q^{3} +(-0.954195 - 1.75770i) q^{4} +(1.84864 + 1.25798i) q^{5} +(-0.123723 - 2.44636i) q^{6} +2.80461 q^{7} +(2.82623 + 0.111339i) q^{8} +(1.15799 - 2.76750i) q^{9} +O(q^{10})\)	\(q+(-0.723120 + 1.21536i) q^{2} +(-1.44187 + 0.959691i) q^{3} +(-0.954195 - 1.75770i) q^{4} +(1.84864 + 1.25798i) q^{5} +(-0.123723 - 2.44636i) q^{6} +2.80461 q^{7} +(2.82623 + 0.111339i) q^{8} +(1.15799 - 2.76750i) q^{9} +(-2.86569 + 1.33709i) q^{10} +(1.50008 + 1.08987i) q^{11} +(3.06268 + 1.61865i) q^{12} +(2.01229 + 2.76969i) q^{13} +(-2.02807 + 3.40861i) q^{14} +(-3.87278 - 0.0397234i) q^{15} +(-2.17902 + 3.35438i) q^{16} +(-0.345387 + 1.06299i) q^{17} +(2.52615 + 3.40861i) q^{18} +(-7.11064 - 2.31039i) q^{19} +(0.447192 - 4.44972i) q^{20} +(-4.04389 + 2.69156i) q^{21} +(-2.40932 + 1.03503i) q^{22} +(1.23722 - 1.70289i) q^{23} +(-4.18192 + 2.55177i) q^{24} +(1.83496 + 4.65112i) q^{25} +(-4.82129 + 0.442845i) q^{26} +(0.986279 + 5.10169i) q^{27} +(-2.67615 - 4.92967i) q^{28} +(-3.56932 + 1.15974i) q^{29} +(2.84876 - 4.67809i) q^{30} +(8.53887 + 2.77445i) q^{31} +(-2.50108 - 5.07391i) q^{32} +(-3.20886 - 0.131842i) q^{33} +(-1.04216 - 1.18844i) q^{34} +(5.18472 + 3.52815i) q^{35} +(-5.96939 + 0.605342i) q^{36} +(4.97454 + 6.84687i) q^{37} +(7.94980 - 6.97130i) q^{38} +(-5.55951 - 2.06235i) q^{39} +(5.08464 + 3.76118i) q^{40} +(-3.81439 - 5.25005i) q^{41} +(-0.346995 - 6.86110i) q^{42} -7.87791 q^{43} +(0.484300 - 3.67664i) q^{44} +(5.62217 - 3.65940i) q^{45} +(1.17496 + 2.73507i) q^{46} +(0.999744 - 0.324837i) q^{47} +(-0.0772933 - 6.92777i) q^{48} +0.865841 q^{49} +(-6.97968 - 1.13318i) q^{50} +(-0.522140 - 1.86416i) q^{51} +(2.94816 - 6.17983i) q^{52} +(0.595625 + 1.83314i) q^{53} +(-6.91358 - 2.49045i) q^{54} +(1.40207 + 3.90186i) q^{55} +(7.92649 + 0.312264i) q^{56} +(12.4699 - 3.49274i) q^{57} +(1.17154 - 5.17664i) q^{58} +(6.91365 - 5.02306i) q^{59} +(3.62556 + 6.84509i) q^{60} +(-0.730226 - 0.530540i) q^{61} +(-9.54658 + 8.37154i) q^{62} +(3.24770 - 7.76177i) q^{63} +(7.97521 + 0.629343i) q^{64} +(0.235797 + 7.65159i) q^{65} +(2.48063 - 3.80458i) q^{66} +(0.462733 - 1.42415i) q^{67} +(2.19799 - 0.407214i) q^{68} +(-0.149667 + 3.64271i) q^{69} +(-8.03715 + 3.75002i) q^{70} +(1.11003 + 3.41631i) q^{71} +(3.58087 - 7.69268i) q^{72} +(7.45432 - 10.2600i) q^{73} +(-11.9186 + 1.09475i) q^{74} +(-7.10941 - 4.94532i) q^{75} +(2.72397 + 14.7029i) q^{76} +(4.20714 + 3.05667i) q^{77} +(6.52669 - 5.26548i) q^{78} +(-4.76272 + 1.54750i) q^{79} +(-8.24799 + 3.45987i) q^{80} +(-6.31813 - 6.40946i) q^{81} +(9.13896 - 0.839431i) q^{82} +(5.84619 + 1.89954i) q^{83} +(8.58961 + 4.53967i) q^{84} +(-1.97572 + 1.53060i) q^{85} +(5.69668 - 9.57449i) q^{86} +(4.03351 - 5.09764i) q^{87} +(4.11823 + 3.24725i) q^{88} +(9.96050 - 13.7094i) q^{89} +(0.381974 + 9.47914i) q^{90} +(5.64370 + 7.76789i) q^{91} +(-4.17373 - 0.549778i) q^{92} +(-14.9746 + 4.19428i) q^{93} +(-0.328142 + 1.44994i) q^{94} +(-10.2386 - 13.2161i) q^{95} +(8.47562 + 4.91567i) q^{96} +(-16.7757 + 5.45075i) q^{97} +(-0.626107 + 1.05231i) q^{98} +(4.75330 - 2.88942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224q - 6q^{4} - 7q^{6} - 6q^{9} + O(q^{10}) \)	\( 224q - 6q^{4} - 7q^{6} - 6q^{9} - 5q^{12} - 20q^{13} + 6q^{16} - 24q^{21} - 10q^{22} - 28q^{24} - 20q^{25} - 50q^{28} - 25q^{30} - 10q^{33} - 14q^{34} - 25q^{36} - 60q^{37} - 20q^{40} - 85q^{42} - 30q^{45} + 6q^{46} - 70q^{48} + 88q^{49} + 40q^{52} - 46q^{54} + 50q^{58} + 10q^{60} - 28q^{61} + 18q^{64} + 64q^{66} - 42q^{69} - 40q^{70} - 5q^{72} - 20q^{73} - 80q^{76} - 85q^{78} + 18q^{81} - 48q^{84} - 20q^{85} + 50q^{88} - 60q^{90} + 60q^{94} + 44q^{96} - 120q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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