LMFDB - Embedded newform 930.2.br.a.11.14

Newspace parameters

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.14
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.14

$q$-expansion

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(-1.43042 - 0.976675i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.66222 - 0.486849i) q^{6} +(0.122441 + 1.16495i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.09221 + 2.79411i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(-1.43042 - 0.976675i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.66222 - 0.486849i) q^{6} +(0.122441 + 1.16495i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.09221 + 2.79411i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-0.519826 - 0.231441i) q^{11} +(-1.73131 + 0.0506337i) q^{12} +(0.447115 + 2.10351i) q^{13} +(0.476438 + 1.07010i) q^{14} +(1.72712 + 0.130615i) q^{15} +(0.309017 - 0.951057i) q^{16} +(5.00147 - 2.22680i) q^{17} +(1.90218 + 2.31985i) q^{18} +(3.58590 + 0.762207i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(0.962635 - 1.78595i) q^{21} +(-0.565903 - 0.0594788i) q^{22} +(5.52033 + 4.01076i) q^{23} +(-1.63093 + 0.583160i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.07525 + 1.86239i) q^{26} +(1.16662 - 5.06350i) q^{27} +(0.783797 + 0.870495i) q^{28} +(-3.19081 - 9.82031i) q^{29} +(1.68295 - 0.409487i) q^{30} +(4.19859 + 3.65676i) q^{31} -1.00000i q^{32} +(0.517527 + 0.838760i) q^{33} +(4.06856 - 3.66335i) q^{34} +(-0.688512 - 0.947655i) q^{35} +(2.52596 + 1.61850i) q^{36} +(-1.33670 - 0.771745i) q^{37} +(3.64593 - 0.383203i) q^{38} +(1.41488 - 3.44559i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-1.22627 - 1.10414i) q^{41} +(0.363630 - 1.99601i) q^{42} +(-1.07851 + 5.07399i) q^{43} +(-0.556586 + 0.118306i) q^{44} +(-2.34294 - 1.87367i) q^{45} +(6.48954 + 2.10858i) q^{46} +(-0.408277 - 0.132657i) q^{47} +(-1.37090 + 1.05860i) q^{48} +(5.50492 - 1.17011i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-9.32907 - 1.69955i) q^{51} +(1.59814 + 1.43897i) q^{52} +(-0.499825 + 4.75551i) q^{53} +(-0.455184 - 5.17618i) q^{54} +(0.565903 - 0.0594788i) q^{55} +(1.01443 + 0.585683i) q^{56} +(-4.38492 - 4.59254i) q^{57} +(-6.06929 - 8.35366i) q^{58} +(2.81688 - 2.53633i) q^{59} +(1.47404 - 0.909505i) q^{60} -5.66315i q^{61} +(5.12309 + 2.18035i) q^{62} +(-3.12127 + 1.61448i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.43897 - 1.59814i) q^{65} +(0.751389 + 0.637784i) q^{66} +(6.10033 + 10.5661i) q^{67} +(2.73740 - 4.74131i) q^{68} +(-3.97919 - 11.1286i) q^{69} +(-0.947655 - 0.688512i) q^{70} +(10.1259 + 1.06427i) q^{71} +(2.90247 + 0.758722i) q^{72} +(1.02323 - 2.29822i) q^{73} +(-1.50976 - 0.320909i) q^{74} +(-1.56104 + 0.750444i) q^{75} +(3.34907 - 1.49110i) q^{76} +(0.205970 - 0.633909i) q^{77} +(0.280888 - 3.71417i) q^{78} +(0.346214 + 0.777609i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-6.61415 + 6.10352i) q^{81} +(-1.50745 - 0.671159i) q^{82} +(2.23296 - 2.47995i) q^{83} +(-0.270969 - 2.01069i) q^{84} +(-3.21800 + 4.42920i) q^{85} +(0.542226 + 5.15893i) q^{86} +(-5.02705 + 17.1636i) q^{87} +(-0.492786 + 0.284510i) q^{88} +(10.6012 - 7.70220i) q^{89} +(-2.80726 - 1.05796i) q^{90} +(-2.39574 + 0.778422i) q^{91} +6.82351 q^{92} +(-2.43428 - 9.33136i) q^{93} -0.429288 q^{94} +(-3.48659 + 1.13286i) q^{95} +(-0.976675 + 1.43042i) q^{96} +(0.672915 - 0.488901i) q^{97} +(4.87391 - 2.81395i) q^{98} +(0.0789143 - 1.70524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176q + 44q^{4} + 4q^{7} - 4q^{9} + O(q^{10}) $	$ 176q + 44q^{4} + 4q^{7} - 4q^{9} - 22q^{10} - 38q^{13} - 44q^{16} + 12q^{18} + 8q^{19} - 18q^{21} - 4q^{22} + 88q^{25} - 90q^{27} + 36q^{28} + 24q^{31} + 18q^{33} + 14q^{34} + 4q^{36} - 42q^{37} - 42q^{39} + 22q^{40} - 12q^{42} - 34q^{43} - 8q^{45} + 10q^{46} + 22q^{49} + 26q^{51} - 2q^{52} + 4q^{55} + 114q^{57} + 32q^{63} + 44q^{64} - 42q^{66} + 20q^{67} + 16q^{69} + 8q^{70} - 12q^{72} - 28q^{73} + 12q^{76} - 92q^{78} - 56q^{79} - 124q^{81} - 32q^{82} - 12q^{84} - 36q^{87} - 6q^{88} + 24q^{90} - 140q^{91} - 104q^{93} - 36q^{94} + 88q^{97} - 60q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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 $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	−1.43042	−	0.976675i	−0.825854	−	0.563884i
$3$	−1.43042	−	0.976675i	−0.825854	−	0.563884i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−1.66222	−	0.486849i	−0.678599	−	0.198755i
$7$	0.122441	+	1.16495i	0.0462784	+	0.440310i	0.992987	+	0.118220i	$0.0377187\pi$
$7$	0.122441	+	1.16495i	0.0462784	+	0.440310i	−0.946709	+	0.322090i	$0.895615\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	1.09221	+	2.79411i	0.364070	+	0.931371i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	−0.519826	−	0.231441i	−0.156733	−	0.0697822i	0.326871	−	0.945069i	$-0.394006\pi$
$11$	−0.519826	−	0.231441i	−0.156733	−	0.0697822i	−0.483604	+	0.875287i	$0.660673\pi$
$12$	−1.73131	+	0.0506337i	−0.499786	+	0.0146167i
$13$	0.447115	+	2.10351i	0.124007	+	0.583409i	0.995642	+	0.0932532i	$0.0297266\pi$
$13$	0.447115	+	2.10351i	0.124007	+	0.583409i	−0.871635	+	0.490155i	$0.836940\pi$
$14$	0.476438	+	1.07010i	0.127333	+	0.285995i
$15$	1.72712	+	0.130615i	0.445940	+	0.0337246i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	5.00147	−	2.22680i	1.21304	−	0.540078i	0.302357	−	0.953195i	$-0.402226\pi$
$17$	5.00147	−	2.22680i	1.21304	−	0.540078i	0.910678	+	0.413117i	$0.135560\pi$
$18$	1.90218	+	2.31985i	0.448349	+	0.546794i
$19$	3.58590	+	0.762207i	0.822663	+	0.174862i	0.599966	−	0.800025i	$-0.295181\pi$
$19$	3.58590	+	0.762207i	0.822663	+	0.174862i	0.222697	+	0.974888i	$0.428514\pi$
$20$	−0.406737	+	0.913545i	−0.0909491	+	0.204275i
$21$	0.962635	−	1.78595i	0.210064	−	0.389727i
$22$	−0.565903	−	0.0594788i	−0.120651	−	0.0126809i
$23$	5.52033	+	4.01076i	1.15107	+	0.836300i	0.988623	−	0.150417i	$-0.0480616\pi$
$23$	5.52033	+	4.01076i	1.15107	+	0.836300i	0.162446	+	0.986717i	$0.448062\pi$
$24$	−1.63093	+	0.583160i	−0.332912	+	0.119037i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.07525	+	1.86239i	0.210874	+	0.365245i
$27$	1.16662	−	5.06350i	0.224516	−	0.974470i
$28$	0.783797	+	0.870495i	0.148124	+	0.164508i
$29$	−3.19081	−	9.82031i	−0.592519	−	1.82359i	−0.566707	−	0.823919i	$-0.691783\pi$
$29$	−3.19081	−	9.82031i	−0.592519	−	1.82359i	−0.0258119	−	0.999667i	$-0.508217\pi$
$30$	1.68295	−	0.409487i	0.307263	−	0.0747617i
$31$	4.19859	+	3.65676i	0.754088	+	0.656773i
$31$	4.19859	+	3.65676i	0.754088	+	0.656773i
$32$		−	1.00000i		−	0.176777i
$33$	0.517527	+	0.838760i	0.0900899	+	0.146009i
$34$	4.06856	−	3.66335i	0.697753	−	0.628260i
$35$	−0.688512	−	0.947655i	−0.116380	−	0.160183i
$36$	2.52596	+	1.61850i	0.420993	+	0.269750i
$37$	−1.33670	−	0.771745i	−0.219752	−	0.126874i	0.386083	−	0.922464i	$-0.373828\pi$
$37$	−1.33670	−	0.771745i	−0.219752	−	0.126874i	−0.605836	+	0.795590i	$0.707161\pi$
$38$	3.64593	−	0.383203i	0.591448	−	0.0621637i
$39$	1.41488	−	3.44559i	0.226563	−	0.551736i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	−1.22627	−	1.10414i	−0.191511	−	0.172437i	0.567797	−	0.823169i	$-0.307796\pi$
$41$	−1.22627	−	1.10414i	−0.191511	−	0.172437i	−0.759308	+	0.650731i	$0.774462\pi$
$42$	0.363630	−	1.99601i	0.0561093	−	0.307992i
$43$	−1.07851	+	5.07399i	−0.164471	+	0.773777i	0.816146	+	0.577845i	$0.196106\pi$
$43$	−1.07851	+	5.07399i	−0.164471	+	0.773777i	−0.980618	+	0.195931i	$0.937227\pi$
$44$	−0.556586	+	0.118306i	−0.0839085	+	0.0178353i
$45$	−2.34294	−	1.87367i	−0.349265	−	0.279310i
$46$	6.48954	+	2.10858i	0.956830	+	0.310893i
$47$	−0.408277	−	0.132657i	−0.0595533	−	0.0193500i	0.279089	−	0.960265i	$-0.409968\pi$
$47$	−0.408277	−	0.132657i	−0.0595533	−	0.0193500i	−0.338642	+	0.940915i	$0.609968\pi$
$48$	−1.37090	+	1.05860i	−0.197872	+	0.152796i
$49$	5.50492	−	1.17011i	0.786417	−	0.167158i
$50$	0.207912	−	0.978148i	0.0294032	−	0.138331i
$51$	−9.32907	−	1.69955i	−1.30633	−	0.237985i
$52$	1.59814	+	1.43897i	0.221621	+	0.199549i
$53$	−0.499825	+	4.75551i	−0.0686562	+	0.653220i	0.905033	+	0.425341i	$0.139846\pi$
$53$	−0.499825	+	4.75551i	−0.0686562	+	0.653220i	−0.973689	+	0.227879i	$0.926821\pi$
$54$	−0.455184	−	5.17618i	−0.0619427	−	0.704388i
$55$	0.565903	−	0.0594788i	0.0763064	−	0.00802012i
$56$	1.01443	+	0.585683i	0.135559	+	0.0782652i
$57$	−4.38492	−	4.59254i	−0.580797	−	0.608297i
$58$	−6.06929	−	8.35366i	−0.796936	−	1.09689i
$59$	2.81688	−	2.53633i	0.366727	−	0.330202i	−0.465079	−	0.885269i	$-0.653974\pi$
$59$	2.81688	−	2.53633i	0.366727	−	0.330202i	0.831806	+	0.555067i	$0.187307\pi$
$60$	1.47404	−	0.909505i	0.190298	−	0.117417i
$61$		−	5.66315i		−	0.725092i	−0.931966	−	0.362546i	$-0.881908\pi$
$61$		−	5.66315i		−	0.725092i	0.931966	−	0.362546i	$-0.118092\pi$
$62$	5.12309	+	2.18035i	0.650633	+	0.276904i
$63$	−3.12127	+	1.61448i	−0.393243	+	0.203406i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−1.43897	−	1.59814i	−0.178482	−	0.198224i
$66$	0.751389	+	0.637784i	0.0924896	+	0.0785057i
$67$	6.10033	+	10.5661i	0.745274	+	1.29085i	0.950067	+	0.312047i	$0.101015\pi$
$67$	6.10033	+	10.5661i	0.745274	+	1.29085i	−0.204792	+	0.978805i	$0.565652\pi$
$68$	2.73740	−	4.74131i	0.331958	−	0.574968i
$69$	−3.97919	−	11.1286i	−0.479039	−	1.33973i
$70$	−0.947655	−	0.688512i	−0.113266	−	0.0822929i
$71$	10.1259	+	1.06427i	1.20172	+	0.126306i	0.684155	−	0.729336i	$-0.260171\pi$
$71$	10.1259	+	1.06427i	1.20172	+	0.126306i	0.517567	+	0.855643i	$0.326838\pi$
$72$	2.90247	+	0.758722i	0.342060	+	0.0894163i
$73$	1.02323	−	2.29822i	0.119760	−	0.268986i	−0.843711	−	0.536798i	$-0.819634\pi$
$73$	1.02323	−	2.29822i	0.119760	−	0.268986i	0.963471	+	0.267812i	$0.0863005\pi$
$74$	−1.50976	−	0.320909i	−0.175506	−	0.0373050i
$75$	−1.56104	+	0.750444i	−0.180253	+	0.0866538i
$76$	3.34907	−	1.49110i	0.384165	−	0.171041i
$77$	0.205970	−	0.633909i	0.0234724	−	0.0722406i
$78$	0.280888	−	3.71417i	0.0318043	−	0.420547i
$79$	0.346214	+	0.777609i	0.0389521	+	0.0874878i	0.931974	−	0.362526i	$-0.118086\pi$
$79$	0.346214	+	0.777609i	0.0389521	+	0.0874878i	−0.893022	+	0.450014i	$0.851419\pi$
$80$	0.207912	+	0.978148i	0.0232452	+	0.109360i
$81$	−6.61415	+	6.10352i	−0.734906	+	0.678169i
$82$	−1.50745	−	0.671159i	−0.166470	−	0.0741171i
$83$	2.23296	−	2.47995i	0.245099	−	0.272210i	−0.608025	−	0.793918i	$-0.708038\pi$
$83$	2.23296	−	2.47995i	0.245099	−	0.272210i	0.853125	+	0.521707i	$0.174705\pi$
$84$	−0.270969	−	2.01069i	−0.0295652	−	0.219384i
$85$	−3.21800	+	4.42920i	−0.349041	+	0.480414i
$86$	0.542226	+	5.15893i	0.0584697	+	0.556302i
$87$	−5.02705	+	17.1636i	−0.538956	+	1.84013i
$88$	−0.492786	+	0.284510i	−0.0525312	+	0.0303289i
$89$	10.6012	−	7.70220i	1.12372	−	0.816431i	0.138952	−	0.990299i	$-0.455626\pi$
$89$	10.6012	−	7.70220i	1.12372	−	0.816431i	0.984769	+	0.173868i	$0.0556265\pi$
$90$	−2.80726	−	1.05796i	−0.295912	−	0.111518i
$91$	−2.39574	+	0.778422i	−0.251141	+	0.0816008i
$92$	6.82351			0.711400
$93$	−2.43428	−	9.33136i	−0.252423	−	0.967617i
$94$	−0.429288			−0.0442776
$95$	−3.48659	+	1.13286i	−0.357716	+	0.116229i
$96$	−0.976675	+	1.43042i	−0.0996815	+	0.145992i
$97$	0.672915	−	0.488901i	0.0683242	−	0.0496404i	−0.553099	−	0.833116i	$-0.686555\pi$
$97$	0.672915	−	0.488901i	0.0683242	−	0.0496404i	0.621423	+	0.783475i	$0.286555\pi$
$98$	4.87391	−	2.81395i	0.492339	−	0.284252i
$99$	0.0789143	−	1.70524i	0.00793119	−	0.171383i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−9.35065	+	12.8701i	−0.930424	+	1.28062i	0.0292699	+	0.999572i	$0.490682\pi$
$101$	−9.35065	+	12.8701i	−0.930424	+	1.28062i	−0.959694	+	0.281047i	$0.909318\pi$
$102$	−9.39767	+	1.26647i	−0.930508	+	0.125399i
$103$	−2.88696	+	3.20629i	−0.284460	+	0.315925i	−0.868393	−	0.495877i	$-0.834847\pi$
$103$	−2.88696	+	3.20629i	−0.284460	+	0.315925i	0.583932	+	0.811802i	$0.301513\pi$
$104$	1.96458	+	0.874688i	0.192643	+	0.0857703i
$105$	0.0593106	+	2.02800i	0.00578812	+	0.197912i
$106$	0.994173	+	4.67722i	0.0965626	+	0.454291i
$107$	−1.88572	−	4.23539i	−0.182299	−	0.409450i	0.799161	−	0.601117i	$-0.205277\pi$
$107$	−1.88572	−	4.23539i	−0.182299	−	0.409450i	−0.981460	+	0.191667i	$0.938611\pi$
$108$	−2.03243	−	4.78218i	−0.195571	−	0.460165i
$109$	0.311319	−	0.958142i	0.0298190	−	0.0917734i	−0.935039	−	0.354544i	$-0.884636\pi$
$109$	0.311319	−	0.958142i	0.0298190	−	0.0917734i	0.964858	+	0.262770i	$0.0846362\pi$
$110$	0.519826	−	0.231441i	0.0495635	−	0.0220671i
$111$	1.15830	+	2.40944i	0.109941	+	0.228694i
$112$	1.14577	+	0.243541i	0.108265	+	0.0230124i
$113$	−6.93779	+	15.5825i	−0.652653	+	1.46588i	0.218983	+	0.975729i	$0.429726\pi$
$113$	−6.93779	+	15.5825i	−0.652653	+	1.46588i	−0.871636	+	0.490154i	$0.836941\pi$
$114$	−5.58948	−	3.01275i	−0.523503	−	0.282170i
$115$	−6.78613	−	0.713251i	−0.632809	−	0.0665110i
$116$	−8.35366	−	6.06929i	−0.775618	−	0.563519i
$117$	−5.38910	+	3.54677i	−0.498223	+	0.327899i
$118$	1.89524	−	3.28266i	0.174471	−	0.302193i
$119$	3.20649	+	5.55381i	0.293939	+	0.509117i
$120$	1.12084	−	1.32050i	0.102319	−	0.120544i
$121$	−7.14378	−	7.93397i	−0.649435	−	0.721270i
$122$	−1.75001	−	5.38598i	−0.158438	−	0.487623i
$123$	0.675698	+	2.77705i	0.0609256	+	0.250398i
$124$	5.54612	+	0.490512i	0.498056	+	0.0440492i
$125$			1.00000i			0.0894427i
$126$	−2.46960	+	2.49999i	−0.220010	+	0.222717i
$127$	−11.2462	+	10.1261i	−0.997937	+	0.898547i	−0.994841	−	0.101449i	$-0.967652\pi$
$127$	−11.2462	+	10.1261i	−0.997937	+	0.898547i	−0.00309626	+	0.999995i	$0.500986\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	6.49837	−	6.20459i	0.572149	−	0.546284i
$130$	−1.86239	−	1.07525i	−0.163342	−	0.0943058i
$131$	−12.4646	+	1.31008i	−1.08904	+	0.114463i	−0.631988	−	0.774978i	$-0.717761\pi$
$131$	−12.4646	+	1.31008i	−1.08904	+	0.114463i	−0.457051	+	0.889441i	$0.651094\pi$
$132$	0.911699	+	0.374376i	0.0793532	+	0.0325853i
$133$	−0.448871	+	4.27072i	−0.0389221	+	0.370319i
$134$	9.06686	+	8.16384i	0.783257	+	0.705248i
$135$	1.52142	+	4.96843i	0.130943	+	0.427614i
$136$	1.13827	−	5.35516i	0.0976062	−	0.459201i
$137$	4.64789	−	0.987941i	0.397096	−	0.0844055i	−0.00503517	−	0.999987i	$-0.501603\pi$
$137$	4.64789	−	0.987941i	0.397096	−	0.0844055i	0.402132	+	0.915582i	$0.368269\pi$
$138$	−7.22338	−	9.35433i	−0.614895	−	0.796293i
$139$	4.27398	+	1.38870i	0.362514	+	0.117788i	0.484610	−	0.874730i	$-0.338961\pi$
$139$	4.27398	+	1.38870i	0.362514	+	0.117788i	−0.122096	+	0.992518i	$0.538961\pi$
$140$	−1.11404	−	0.361972i	−0.0941532	−	0.0305922i
$141$	0.454445	+	0.588510i	0.0382712	+	0.0495614i
$142$	9.95918	−	2.11689i	0.835756	−	0.177645i
$143$	0.254417	−	1.19694i	0.0212755	−	0.100093i
$144$	2.99487	−	0.175325i	0.249573	−	0.0146104i
$145$	7.67348	+	6.90923i	0.637248	+	0.573781i
$146$	0.262964	−	2.50193i	0.0217630	−	0.207061i
$147$	−9.01717	−	3.70277i	−0.743723	−	0.305399i
$148$	−1.53503	+	0.161339i	−0.126179	+	0.0132619i
$149$	−15.4834	−	8.93935i	−1.26845	−	0.732340i	−0.293756	−	0.955880i	$-0.594905\pi$
$149$	−15.4834	−	8.93935i	−1.26845	−	0.732340i	−0.974695	+	0.223540i	$0.928239\pi$
$150$	−1.25273	+	1.19610i	−0.102285	+	0.0976612i
$151$	0.434637	+	0.598227i	0.0353703	+	0.0486830i	0.826336	−	0.563178i	$-0.190421\pi$
$151$	0.434637	+	0.598227i	0.0353703	+	0.0486830i	−0.790966	+	0.611861i	$0.790421\pi$
$152$	2.72438	−	2.45304i	0.220976	−	0.198968i
$153$	11.6846	+	11.5426i	0.944643	+	0.933160i
$154$		−	0.666531i		−	0.0537106i
$155$	−5.46446	−	1.06755i	−0.438916	−	0.0857478i
$156$	−0.880603	−	3.61919i	−0.0705047	−	0.289767i
$157$	4.49248	+	13.8264i	0.358539	+	1.10347i	0.953929	+	0.300033i	$0.0969976\pi$
$157$	4.49248	+	13.8264i	0.358539	+	1.10347i	−0.595390	+	0.803437i	$0.703002\pi$
$158$	0.569563	+	0.632564i	0.0453120	+	0.0503241i
$159$	5.35955	−	6.31422i	0.425040	−	0.500750i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−3.99641	+	6.92199i	−0.314961	+	0.545529i
$162$	−4.40434	+	7.84868i	−0.346038	+	0.616651i
$163$	−1.48950	−	1.08219i	−0.116667	−	0.0847633i	0.527922	−	0.849293i	$-0.322971\pi$
$163$	−1.48950	−	1.08219i	−0.116667	−	0.0847633i	−0.644589	+	0.764530i	$0.722971\pi$
$164$	−1.64107	−	0.172483i	−0.128146	−	0.0134687i
$165$	−0.867572	−	0.467624i	−0.0675404	−	0.0364045i
$166$	1.35732	−	3.04860i	0.105349	−	0.236617i
$167$	−8.07631	−	1.71667i	−0.624964	−	0.132840i	−0.115465	−	0.993312i	$-0.536836\pi$
$167$	−8.07631	−	1.71667i	−0.624964	−	0.132840i	−0.509499	+	0.860471i	$0.670169\pi$
$168$	−0.879044	−	1.82855i	−0.0678197	−	0.141075i
$169$	7.65125	−	3.40656i	0.588558	−	0.262043i
$170$	−1.69180	+	5.20684i	−0.129755	+	0.399346i
$171$	1.78687	+	10.8519i	0.136645	+	0.829867i
$172$	2.10989	+	4.73888i	0.160877	+	0.361336i
$173$	2.62903	+	12.3686i	0.199881	+	0.940368i	0.957670	+	0.287868i	$0.0929464\pi$
$173$	2.62903	+	12.3686i	0.199881	+	0.940368i	−0.757789	+	0.652500i	$0.773720\pi$
$174$	0.522828	+	17.8770i	0.0396355	+	1.35525i
$175$	1.07010	+	0.476438i	0.0808917	+	0.0360153i
$176$	−0.380749	+	0.422865i	−0.0287000	+	0.0318746i
$177$	−6.50650	+	0.876845i	−0.489059	+	0.0659077i
$178$	7.70220	−	10.6012i	0.577304	−	0.794591i
$179$	−0.510614	−	4.85816i	−0.0381651	−	0.363116i	−0.996892	−	0.0787862i	$-0.974896\pi$
$179$	−0.510614	−	4.85816i	−0.0381651	−	0.363116i	0.958726	−	0.284330i	$-0.0917711\pi$
$180$	−2.99679	−	0.138685i	−0.223368	−	0.0103369i
$181$	10.9043	−	6.29562i	0.810513	−	0.467950i	−0.0366213	−	0.999329i	$-0.511660\pi$
$181$	10.9043	−	6.29562i	0.810513	−	0.467950i	0.847134	+	0.531380i	$0.178326\pi$
$182$	−2.03794	+	1.48065i	−0.151062	+	0.109753i
$183$	−5.53106	+	8.10069i	−0.408868	+	0.598820i
$184$	6.48954	−	2.10858i	0.478415	−	0.155447i
$185$	1.54349			0.113480
$186$	−5.19869	−	8.12241i	−0.381186	−	0.595564i
$187$	−3.11527			−0.227811
$188$	−0.408277	+	0.132657i	−0.0297766	+	0.00967502i
$189$	6.04156	+	0.739074i	0.439459	+	0.0537597i
$190$	−2.96587	+	2.15483i	−0.215167	+	0.156328i
$191$	−15.8368	+	9.14337i	−1.14591	+	0.661591i	−0.947887	−	0.318606i	$-0.896785\pi$
$191$	−15.8368	+	9.14337i	−1.14591	+	0.661591i	−0.198022	+	0.980198i	$0.563452\pi$
$192$	−0.486849	+	1.66222i	−0.0351353	+	0.119960i
$193$	−1.65439	−	15.7405i	−0.119086	−	1.13303i	−0.876939	−	0.480601i	$-0.840419\pi$
$193$	−1.65439	−	15.7405i	−0.119086	−	1.13303i	0.757854	−	0.652425i	$-0.226248\pi$
$194$	0.488901	−	0.672915i	0.0351011	−	0.0483125i
$195$	0.497471	+	3.69141i	0.0356246	+	0.264347i
$196$	3.76580	−	4.18235i	0.268986	−	0.298739i
$197$	−16.5671	−	7.37615i	−1.18036	−	0.525529i	−0.279712	−	0.960084i	$-0.590239\pi$
$197$	−16.5671	−	7.37615i	−1.18036	−	0.525529i	−0.900645	+	0.434555i	$0.856906\pi$
$198$	−0.451895	−	1.64616i	−0.0321148	−	0.116988i
$199$	−4.21524	−	19.8311i	−0.298810	−	1.40579i	−0.829633	−	0.558309i	$-0.811451\pi$
$199$	−4.21524	−	19.8311i	−0.298810	−	1.40579i	0.530823	−	0.847483i	$-0.321883\pi$
$200$	−0.406737	−	0.913545i	−0.0287606	−	0.0645974i
$201$	1.59359	−	21.0720i	0.112403	−	1.48630i
$202$	−4.91593	+	15.1297i	−0.345883	+	1.06452i
$203$	11.0495	−	4.91955i	0.775521	−	0.345284i
$204$	−8.54635	+	4.10852i	−0.598364	+	0.287654i
$205$	1.61405	+	0.343077i	0.112730	+	0.0239615i
$206$	−1.75486	+	3.94148i	−0.122267	+	0.274616i
$207$	−5.17714	+	19.8050i	−0.359836	+	1.37654i
$208$	2.13872	+	0.224789i	0.148294	+	0.0155863i
$209$	−1.68764	−	1.22614i	−0.116736	−	0.0848140i
$210$	0.683094	+	1.91041i	0.0471380	+	0.131831i
$211$	−8.73743	+	15.1337i	−0.601510	+	1.04185i	0.391083	+	0.920355i	$0.372101\pi$
$211$	−8.73743	+	15.1337i	−0.601510	+	1.04185i	−0.992593	+	0.121490i	$0.961233\pi$
$212$	2.39085	+	4.14108i	0.164205	+	0.284411i
$213$	−13.4448	−	11.4121i	−0.921226	−	0.781942i
$214$	−3.10223	−	3.44537i	−0.212064	−	0.235521i
$215$	−1.60298	−	4.93346i	−0.109322	−	0.336459i
$216$	−3.41073	−	3.92006i	−0.232071	−	0.266727i
$217$	−3.74586	+	5.33888i	−0.254285	+	0.362427i
$218$		−	1.00745i		−	0.0682331i
$219$	−3.70827	+	2.28805i	−0.250581	+	0.154612i
$220$	0.422865	−	0.380749i	0.0285095	−	0.0256701i
$221$	6.92032	+	9.52501i	0.465511	+	0.640722i
$222$	1.84617	+	1.93358i	0.123907	+	0.129773i
$223$	11.8538	+	6.84380i	0.793790	+	0.458295i	0.841295	−	0.540576i	$-0.181794\pi$
$223$	11.8538	+	6.84380i	0.793790	+	0.458295i	−0.0475051	+	0.998871i	$0.515127\pi$
$224$	1.16495	−	0.122441i	0.0778365	−	0.00818094i
$225$	2.96588	+	0.451175i	0.197725	+	0.0300783i
$226$	−1.78296	+	16.9638i	−0.118601	+	1.12841i
$227$	12.8460	+	11.5666i	0.852620	+	0.767703i	0.974392	−	0.224856i	$-0.0721910\pi$
$227$	12.8460	+	11.5666i	0.852620	+	0.767703i	−0.121772	+	0.992558i	$0.538858\pi$
$228$	−6.24691	−	1.13805i	−0.413712	−	0.0753692i
$229$	3.74095	−	17.5998i	0.247209	−	1.16303i	−0.662917	−	0.748693i	$-0.730682\pi$
$229$	3.74095	−	17.5998i	0.247209	−	1.16303i	0.910126	−	0.414332i	$-0.135985\pi$
$230$	−6.67440	+	1.41869i	−0.440097	+	0.0935454i
$231$	−0.913747	+	0.705592i	−0.0601201	+	0.0464245i
$232$	−9.82031	−	3.19081i	−0.644735	−	0.209487i
$233$	−24.9434	−	8.10459i	−1.63409	−	0.530949i	−0.658887	−	0.752242i	$-0.728972\pi$
$233$	−24.9434	−	8.10459i	−1.63409	−	0.530949i	−0.975207	+	0.221293i	$0.928972\pi$
$234$	−4.02933	+	5.03850i	−0.263406	+	0.329377i
$235$	0.419907	−	0.0892539i	0.0273917	−	0.00582228i
$236$	0.788087	−	3.70766i	0.0513001	−	0.241348i
$237$	0.264240	−	1.45045i	0.0171642	−	0.0942166i
$238$	4.76578	+	4.29113i	0.308920	+	0.278152i
$239$	−1.54501	+	14.6997i	−0.0999381	+	0.950848i	0.823556	+	0.567235i	$0.191987\pi$
$239$	−1.54501	+	14.6997i	−0.0999381	+	0.950848i	−0.923494	+	0.383613i	$0.874680\pi$
$240$	0.657931	−	1.60223i	0.0424693	−	0.103423i
$241$	−3.01041	+	0.316407i	−0.193918	+	0.0203816i	−0.200989	−	0.979593i	$-0.564416\pi$
$241$	−3.01041	+	0.316407i	−0.193918	+	0.0203816i	0.00707169	+	0.999975i	$0.497749\pi$
$242$	−9.24587	−	5.33811i	−0.594347	−	0.343147i
$243$	15.4222	−	2.27073i	0.989334	−	0.145668i
$244$	−3.32872	−	4.58159i	−0.213099	−	0.293306i
$245$	−4.18235	+	3.76580i	−0.267200	+	0.240588i
$246$	1.50078	+	2.43233i	0.0956863	+	0.155080i
$247$			7.88378i			0.501633i
$248$	5.42625	−	1.24734i	0.344567	−	0.0792062i
$249$	−5.61619	+	1.36650i	−0.355911	+	0.0865986i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−8.51058	−	9.45196i	−0.537183	−	0.596602i	0.412056	−	0.911159i	$-0.364811\pi$
$251$	−8.51058	−	9.45196i	−0.537183	−	0.596602i	−0.949239	+	0.314556i	$0.898144\pi$
$252$	−1.57619	+	3.14078i	−0.0992907	+	0.197851i
$253$	−1.94136	−	3.36253i	−0.122052	−	0.211400i
$254$	−7.56661	+	13.1058i	−0.474772	+	0.822328i
$255$	8.92899	−	3.19268i	0.559155	−	0.199933i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	9.15701	+	0.962441i	0.571199	+	0.0600354i	0.385725	−	0.922614i	$-0.373951\pi$
$257$	9.15701	+	0.962441i	0.571199	+	0.0600354i	0.185474	+	0.982649i	$0.440618\pi$
$258$	4.26299	−	7.90903i	0.265402	−	0.492394i
$259$	0.735376	−	1.65168i	0.0456941	−	0.102631i
$260$	−2.10351	−	0.447115i	−0.130454	−	0.0277289i
$261$	23.9540	−	19.6413i	1.48272	−	1.21577i
$262$	−11.4497	+	5.09775i	−0.707366	+	0.314940i
$263$	−8.49185	+	26.1352i	−0.523630	+	1.61157i	0.243379	+	0.969931i	$0.421744\pi$
$263$	−8.49185	+	26.1352i	−0.523630	+	1.61157i	−0.767009	+	0.641637i	$0.778256\pi$
$264$	0.982766	+	0.0743226i	0.0604851	+	0.00457424i
$265$	−1.94490	−	4.36831i	−0.119474	−	0.268343i
$266$	0.892824	+	4.20041i	0.0547426	+	0.257544i
$267$	−22.6867	+	0.663492i	−1.38840	+	0.0406051i
$268$	11.1459	+	4.96246i	0.680842	+	0.303130i
$269$	3.12757	−	3.47352i	0.190692	−	0.211784i	−0.640216	−	0.768195i	$-0.721155\pi$
$269$	3.12757	−	3.47352i	0.190692	−	0.211784i	0.830908	+	0.556411i	$0.187822\pi$
$270$	2.98229	+	4.25511i	0.181496	+	0.258958i
$271$	12.0604	−	16.5997i	0.732618	−	1.00836i	−0.266392	−	0.963865i	$-0.585831\pi$
$271$	12.0604	−	16.5997i	0.732618	−	1.00836i	0.999010	−	0.0444972i	$-0.0141686\pi$
$272$	−0.572272	−	5.44480i	−0.0346991	−	0.330140i
$273$	4.18718	+	1.22639i	0.253420	+	0.0742242i
$274$	4.11512	−	2.37587i	0.248604	−	0.143531i
$275$	−0.460347	+	0.334462i	−0.0277600	+	0.0201688i
$276$	−9.76049	−	6.66435i	−0.587512	−	0.401147i
$277$	28.9704	−	9.41307i	1.74067	−	0.565576i	0.745744	−	0.666233i	$-0.232094\pi$
$277$	28.9704	−	9.41307i	1.74067	−	0.565576i	0.994921	+	0.100656i	$0.0320942\pi$
$278$	4.49393			0.269528
$279$	−5.63166	+	15.7253i	−0.337158	+	0.941448i
$280$	−1.17137			−0.0700025
$281$	−6.09864	+	1.98157i	−0.363815	+	0.118211i	−0.485219	−	0.874393i	$-0.661260\pi$
$281$	−6.09864	+	1.98157i	−0.363815	+	0.118211i	0.121405	+	0.992603i	$0.461260\pi$
$282$	0.614062	+	0.419275i	0.0365669	+	0.0249674i
$283$	12.5885	−	9.14610i	0.748310	−	0.543679i	−0.146993	−	0.989138i	$-0.546959\pi$
$283$	12.5885	−	9.14610i	0.748310	−	0.543679i	0.895303	+	0.445459i	$0.146959\pi$
$284$	8.81759	−	5.09084i	0.523227	−	0.302085i
$285$	6.09373	+	1.78480i	0.360961	+	0.105722i
$286$	−0.127909	−	1.21698i	−0.00756344	−	0.0719613i
$287$	1.13612	−	1.56373i	0.0670630	−	0.0923042i
$288$	2.79411	−	1.09221i	0.164645	−	0.0643591i
$289$	8.68088	−	9.64109i	0.510640	−	0.567123i
$290$	9.43298	+	4.19984i	0.553924	+	0.246623i
$291$	−1.44005	+	0.0421155i	−0.0844172	+	0.00246886i
$292$	−0.523046	−	2.46074i	−0.0306090	−	0.144004i
$293$	−12.2895	−	27.6027i	−0.717960	−	1.61257i	−0.788484	−	0.615055i	$-0.789134\pi$
$293$	−12.2895	−	27.6027i	−0.717960	−	1.61257i	0.0705235	−	0.997510i	$-0.477533\pi$
$294$	−9.72005	−	0.735088i	−0.566885	−	0.0428712i
$295$	−1.17133	+	3.60497i	−0.0681972	+	0.209889i
$296$	−1.41005	+	0.627794i	−0.0819573	+	0.0364898i
$297$	−1.77834	+	2.36213i	−0.103190	+	0.137065i
$298$	−17.4880	−	3.71719i	−1.01305	−	0.215331i
$299$	−5.96844	+	13.4053i	−0.345164	+	0.775251i
$300$	−0.821805	+	1.52468i	−0.0474469	+	0.0880272i
$301$	−6.04300	−	0.635145i	−0.348313	−	0.0366091i
$302$	0.598227	+	0.434637i	0.0344241	+	0.0250106i
$303$	25.9452	−	9.27706i	1.49051	−	0.532953i
$304$	1.83301	−	3.17486i	0.105130	−	0.182091i
$305$	2.83158	+	4.90443i	0.162136	+	0.280827i
$306$	14.6796	+	7.36688i	0.839174	+	0.421137i
$307$	−13.6916	−	15.2061i	−0.781421	−	0.867856i	0.212590	−	0.977142i	$-0.431810\pi$
$307$	−13.6916	−	15.2061i	−0.781421	−	0.867856i	−0.994010	+	0.109286i	$0.965144\pi$
$308$	−0.205970	−	0.633909i	−0.0117362	−	0.0361203i
$309$	7.26107	−	1.76673i	0.413068	−	0.100506i
$310$	−5.52690	+	0.673310i	−0.313907	+	0.0382414i
$311$		−	32.8476i		−	1.86262i	−0.364230	−	0.931309i	$-0.618668\pi$
$311$		−	32.8476i		−	1.86262i	0.364230	−	0.931309i	$-0.381332\pi$
$312$	−1.95589	−	3.16993i	−0.110731	−	0.179462i
$313$	13.2534	−	11.9334i	0.749125	−	0.674515i	−0.203359	−	0.979104i	$-0.565186\pi$
$313$	13.2534	−	11.9334i	0.749125	−	0.674515i	0.952484	+	0.304589i	$0.0985192\pi$
$314$	8.54521	+	11.7615i	0.482234	+	0.663738i
$315$	1.89586	−	2.95882i	0.106819	−	0.166711i
$316$	0.737160	+	0.425599i	0.0414685	+	0.0239418i
$317$	−27.4340	+	2.88343i	−1.54085	+	0.161950i	−0.836524	−	0.547930i	$-0.815416\pi$
$317$	−27.4340	+	2.88343i	−1.54085	+	0.161950i	−0.704323	+	0.709880i	$0.748749\pi$
$318$	3.14603	−	7.66137i	0.176421	−	0.429628i
$319$	−0.614160	+	5.84334i	−0.0343863	+	0.327164i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	−1.43923	+	7.90012i	−0.0803300	+	0.440942i
$322$	−1.66180	+	7.81816i	−0.0926086	+	0.435689i
$323$	19.6321	−	4.17293i	1.09236	−	0.232188i
$324$	−1.76340	+	8.82556i	−0.0979666	+	0.490309i
$325$	2.04525	+	0.664542i	0.113450	+	0.0368622i
$326$	−1.75101	−	0.568938i	−0.0969796	−	0.0315106i
$327$	−1.38111	+	1.06649i	−0.0763756	+	0.0589770i
$328$	−1.61405	+	0.343077i	−0.0891209	+	0.0189432i
$329$	0.104549	−	0.491865i	0.00576398	−	0.0271174i
$330$	−0.969613	−	0.176642i	−0.0533755	−	0.00972385i
$331$	2.86711	+	2.58156i	0.157591	+	0.141895i	0.744154	−	0.668008i	$-0.232853\pi$
$331$	2.86711	+	2.58156i	0.157591	+	0.141895i	−0.586563	+	0.809903i	$0.699519\pi$
$332$	0.348823	−	3.31883i	0.0191441	−	0.182144i
$333$	0.696384	−	4.57780i	0.0381616	−	0.250862i
$334$	−8.21151	+	0.863065i	−0.449314	+	0.0472248i
$335$	−10.5661	−	6.10033i	−0.577287	−	0.333297i
$336$	−1.40107	−	1.46741i	−0.0764348	−	0.0800538i
$337$	6.05519	+	8.33426i	0.329847	+	0.453996i	0.941442	−	0.337175i	$-0.109472\pi$
$337$	6.05519	+	8.33426i	0.329847	+	0.453996i	−0.611594	+	0.791171i	$0.709472\pi$
$338$	6.22409	−	5.60419i	0.338546	−	0.304828i
$339$	25.1431	−	15.5136i	1.36558	−	0.842585i
$340$			5.47479i			0.296912i
$341$	−1.33621	−	2.87260i	−0.0723598	−	0.155560i
$342$	5.05284	+	9.76861i	0.273226	+	0.528226i
$343$	4.57095	+	14.0679i	0.246808	+	0.759597i
$344$	3.47101	+	3.85495i	0.187145	+	0.207845i
$345$	9.01040	+	7.64809i	0.485104	+	0.411759i
$346$	6.32246	+	10.9508i	0.339898	+	0.588720i
$347$	14.3911	−	24.9261i	0.772554	−	1.33810i	−0.163605	−	0.986526i	$-0.552312\pi$
$347$	14.3911	−	24.9261i	0.772554	−	1.33810i	0.936159	−	0.351577i	$-0.114354\pi$
$348$	6.02153	+	16.8404i	0.322788	+	0.902743i
$349$	−12.5161	−	9.09349i	−0.669973	−	0.486764i	0.200043	−	0.979787i	$-0.435892\pi$
$349$	−12.5161	−	9.09349i	−0.669973	−	0.486764i	−0.870016	+	0.493023i	$0.835892\pi$
$350$	1.16495	+	0.122441i	0.0622692	+	0.00654475i
$351$	11.1727	+	0.190034i	0.596356	+	0.0101433i
$352$	−0.231441	+	0.519826i	−0.0123359	+	0.0277068i
$353$	7.48355	+	1.59068i	0.398309	+	0.0846632i	0.402711	−	0.915327i	$-0.368068\pi$
$353$	7.48355	+	1.59068i	0.398309	+	0.0846632i	−0.00440211	+	0.999990i	$0.501401\pi$
$354$	−5.91709	+	2.84455i	−0.314490	+	0.151186i
$355$	−9.30142	+	4.14126i	−0.493668	+	0.219795i
$356$	4.04929	−	12.4624i	0.214612	−	0.660507i
$357$	0.837632	−	11.0760i	0.0443322	−	0.586204i
$358$	−1.98688	−	4.46260i	−0.105010	−	0.235856i
$359$	−1.09807	−	5.16601i	−0.0579539	−	0.272652i	0.939624	−	0.342208i	$-0.111175\pi$
$359$	−1.09807	−	5.16601i	−0.0579539	−	0.272652i	−0.997578	+	0.0695567i	$0.977842\pi$
$360$	−2.89298	+	0.794163i	−0.152473	+	0.0418561i
$361$	−5.07962	−	2.26159i	−0.267348	−	0.119031i
$362$	8.42518	−	9.35711i	0.442818	−	0.491799i
$363$	2.46970	+	18.3261i	0.129626	+	0.961870i
$364$	−1.48065	+	2.03794i	−0.0776070	+	0.106817i
$365$	0.262964	+	2.50193i	0.0137641	+	0.130957i
$366$	−2.75710	+	9.41341i	−0.144116	+	0.492047i
$367$	−4.30266	+	2.48414i	−0.224597	+	0.129671i	−0.608077	−	0.793878i	$-0.708059\pi$
$367$	−4.30266	+	2.48414i	−0.224597	+	0.129671i	0.383480	+	0.923549i	$0.374725\pi$
$368$	5.52033	−	4.01076i	0.287767	−	0.209075i
$369$	1.74574	−	4.63229i	0.0908797	−	0.241147i
$370$	1.46795	−	0.476964i	0.0763148	−	0.0247962i
$371$	−5.60113			−0.290796
$372$	−7.45421	−	6.11839i	−0.386483	−	0.317224i
$373$	−33.1963			−1.71884			−0.859419	−	0.511271i	$-0.829175\pi$
$373$	−33.1963			−1.71884			−0.859419	+	0.511271i	$0.829175\pi$
$374$	−2.96280	+	0.962671i	−0.153203	+	0.0497785i
$375$	0.976675	−	1.43042i	0.0504353	−	0.0738666i
$376$	−0.347301	+	0.252329i	−0.0179107	+	0.0130129i
$377$	19.2305	−	11.1027i	0.990419	−	0.571819i
$378$	5.97425	−	1.16404i	0.307282	−	0.0598719i
$379$	2.07737	+	19.7648i	0.106707	+	1.01525i	0.908567	+	0.417739i	$0.137177\pi$
$379$	2.07737	+	19.7648i	0.106707	+	1.01525i	−0.801860	+	0.597512i	$0.796156\pi$
$380$	−2.15483	+	2.96587i	−0.110540	+	0.152146i
$381$	25.9767	−	3.50073i	1.33083	−	0.179348i
$382$	−12.2362	+	13.5897i	−0.626059	+	0.695309i
$383$	−15.2225	−	6.77751i	−0.777835	−	0.346315i	−0.0208806	−	0.999782i	$-0.506647\pi$
$383$	−15.2225	−	6.77751i	−0.777835	−	0.346315i	−0.756955	+	0.653467i	$0.773314\pi$
$384$	0.0506337	+	1.73131i	0.00258389	+	0.0883506i
$385$	0.138580	+	0.651966i	0.00706267	+	0.0332273i
$386$	−6.43750	−	14.4589i	−0.327660	−	0.735937i
$387$	−15.3553	+	2.52839i	−0.780553	+	0.128525i
$388$	0.257031	−	0.791059i	0.0130488	−	0.0401599i
$389$	18.9726	−	8.44715i	0.961950	−	0.428288i	0.135176	−	0.990822i	$-0.456840\pi$
$389$	18.9726	−	8.44715i	0.961950	−	0.428288i	0.826774	+	0.562534i	$0.190174\pi$
$390$	1.61383	+	3.35701i	0.0817195	+	0.169989i
$391$	36.5409	+	7.76702i	1.84795	+	0.392795i
$392$	2.28907	−	5.14134i	0.115616	−	0.259677i
$393$	19.1092	+	10.2999i	0.963931	+	0.519562i
$394$	−18.0356	−	1.89562i	−0.908621	−	0.0954999i
$395$	−0.688634	−	0.500322i	−0.0346490	−	0.0251739i
$396$	−0.938470	−	1.42595i	−0.0471599	−	0.0716567i
$397$	2.36809	−	4.10165i	0.118851	−	0.205856i	−0.800462	−	0.599384i	$-0.795412\pi$
$397$	2.36809	−	4.10165i	0.118851	−	0.205856i	0.919313	+	0.393528i	$0.128746\pi$
$398$	−10.1371	−	17.5579i	−0.508126	−	0.880100i
$399$	4.81318	−	5.67053i	0.240961	−	0.283882i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	5.38252	+	16.5657i	0.268790	+	0.827251i	0.990796	+	0.135364i	$0.0432204\pi$
$401$	5.38252	+	16.5657i	0.268790	+	0.827251i	−0.722006	+	0.691887i	$0.756780\pi$
$402$	−4.99601	−	20.5331i	−0.249178	−	1.02410i
$403$	−5.81477	+	10.4668i	−0.289654	+	0.521386i
$404$			15.9083i			0.791466i
$405$	2.67626	−	8.59288i	0.132984	−	0.426984i
$406$	8.98846	−	8.09324i	0.446090	−	0.401661i
$407$	0.516238	+	0.710541i	0.0255890	+	0.0352202i
$408$	−6.85846	+	6.54841i	−0.339544	+	0.324194i
$409$	−22.7494	−	13.1343i	−1.12488	−	0.649452i	−0.182240	−	0.983254i	$-0.558335\pi$
$409$	−22.7494	−	13.1343i	−1.12488	−	0.649452i	−0.942643	+	0.333802i	$0.891668\pi$
$410$	1.64107	−	0.172483i	0.0810466	−	0.00851834i
$411$	−7.61335	−	3.12631i	−0.375539	−	0.154210i
$412$	−0.450987	+	4.29085i	−0.0222185	+	0.211395i
$413$	3.29960	+	2.97097i	0.162363	+	0.146192i
$414$	1.19633	+	20.4355i	0.0587966	+	1.00435i
$415$	−0.693824	+	3.26418i	−0.0340585	+	0.160233i
$416$	2.10351	−	0.447115i	0.103133	−	0.0219216i
$417$	−4.75729	−	6.16072i	−0.232965	−	0.301692i
$418$	−1.98394	−	0.644621i	−0.0970377	−	0.0315294i
$419$	5.07827	+	1.65003i	0.248090	+	0.0806092i	0.430422	−	0.902628i	$-0.358365\pi$
$419$	5.07827	+	1.65003i	0.248090	+	0.0806092i	−0.182333	+	0.983237i	$0.558365\pi$
$420$	1.24001	+	1.60582i	0.0605063	+	0.0783562i
$421$	8.11085	−	1.72401i	0.395299	−	0.0840233i	−0.00597357	−	0.999982i	$-0.501901\pi$
$421$	8.11085	−	1.72401i	0.395299	−	0.0840233i	0.401272	+	0.915959i	$0.368568\pi$
$422$	−3.63323	+	17.0930i	−0.176863	+	0.832074i
$423$	−0.0752650	−	1.28566i	−0.00365951	−	0.0625110i
$424$	3.55350	+	3.19959i	0.172573	+	0.155386i
$425$	0.572272	−	5.44480i	0.0277593	−	0.264112i
$426$	−16.3133	−	6.69884i	−0.790384	−	0.324560i
$427$	6.59729	−	0.693403i	0.319265	−	0.0335561i
$428$	−4.01507	−	2.31810i	−0.194076	−	0.112050i
$429$	−1.53295	+	1.46365i	−0.0740113	+	0.0706655i
$430$	−3.04905	−	4.19665i	−0.147038	−	0.202381i
$431$	−19.2853	+	17.3645i	−0.928938	+	0.836420i	−0.986806	−	0.161904i	$-0.948236\pi$
$431$	−19.2853	+	17.3645i	−0.928938	+	0.836420i	0.0578680	+	0.998324i	$0.481570\pi$
$432$	−4.45517	−	2.67423i	−0.214349	−	0.128664i
$433$		−	5.55549i		−	0.266980i	−0.991050	−	0.133490i	$-0.957382\pi$
$433$		−	5.55549i		−	0.266980i	0.991050	−	0.133490i	$-0.0426184\pi$
$434$	−1.91272	+	6.23511i	−0.0918134	+	0.299295i
$435$	−4.22823	−	17.3776i	−0.202728	−	0.833193i
$436$	−0.311319	−	0.958142i	−0.0149095	−	0.0458867i
$437$	16.7384	+	18.5898i	0.800704	+	0.889272i
$438$	−2.81972	+	3.32199i	−0.134732	+	0.158731i
$439$	19.1175	+	33.1126i	0.912430	+	1.58038i	0.810620	+	0.585572i	$0.199130\pi$
$439$	19.1175	+	33.1126i	0.912430	+	1.58038i	0.101810	+	0.994804i	$0.467537\pi$
$440$	0.284510	−	0.492786i	0.0135635	−	0.0234927i
$441$	9.28194	+	14.1034i	0.441997	+	0.671589i
$442$	9.52501	+	6.92032i	0.453059	+	0.329166i
$443$	−13.1871	−	1.38602i	−0.626537	−	0.0658517i	−0.214061	−	0.976820i	$-0.568669\pi$
$443$	−13.1871	−	1.38602i	−0.626537	−	0.0658517i	−0.412476	+	0.910969i	$0.635336\pi$
$444$	2.35332	+	1.26845i	0.111684	+	0.0601978i
$445$	−5.32978	+	11.9709i	−0.252656	+	0.567474i
$446$	13.3885	+	2.84581i	0.633964	+	0.134753i
$447$	13.4170	+	27.9093i	0.634601	+	1.32007i
$448$	1.07010	−	0.476438i	0.0505573	−	0.0225096i
$449$	6.03767	−	18.5820i	0.284935	−	0.876940i	−0.701483	−	0.712686i	$-0.747478\pi$
$449$	6.03767	−	18.5820i	0.284935	−	0.876940i	0.986418	−	0.164254i	$-0.0525216\pi$
$450$	2.96014	−	0.487414i	0.139542	−	0.0229769i
$451$	0.381903	+	0.857769i	0.0179831	+	0.0403908i
$452$	3.54639	+	16.6845i	0.166808	+	0.784772i
$453$	−0.0374410	−	1.28022i	−0.00175913	−	0.0601498i
$454$	15.7916	+	7.03086i	0.741135	+	0.329975i
$455$	1.68556	−	1.87200i	0.0790202	−	0.0877608i
$456$	−6.29284	+	0.848050i	−0.294689	+	0.0397136i
$457$	8.32696	−	11.4611i	0.389519	−	0.536126i	−0.568556	−	0.822644i	$-0.692498\pi$
$457$	8.32696	−	11.4611i	0.389519	−	0.536126i	0.958075	+	0.286518i	$0.0924978\pi$
$458$	−1.88078	−	17.8944i	−0.0878829	−	0.836150i
$459$	−5.44057	−	27.9228i	−0.253944	−	1.30332i
$460$	−5.90933	+	3.41175i	−0.275524	+	0.159074i
$461$	−23.3216	+	16.9441i	−1.08619	+	0.789166i	−0.978752	−	0.205045i	$-0.934266\pi$
$461$	−23.3216	+	16.9441i	−1.08619	+	0.789166i	−0.107442	+	0.994211i	$0.534266\pi$
$462$	−0.650985	+	0.953421i	−0.0302866	+	0.0443572i
$463$	−30.0461	+	9.76257i	−1.39636	+	0.453705i	−0.908012	−	0.418943i	$-0.862401\pi$
$463$	−30.0461	+	9.76257i	−1.39636	+	0.453705i	−0.488349	+	0.872649i	$0.662401\pi$
$464$	−10.3257			−0.479358
$465$	6.77383	+	6.86405i	0.314129	+	0.318313i
$466$	−26.2270			−1.21494
$467$	2.95370	−	0.959715i	0.136681	−	0.0444103i	−0.239878	−	0.970803i	$-0.577107\pi$
$467$	2.95370	−	0.959715i	0.136681	−	0.0444103i	0.376559	+	0.926393i	$0.377107\pi$
$468$	−2.27514	+	6.03703i	−0.105168	+	0.279062i
$469$	−11.5620	+	8.40030i	−0.533885	+	0.387890i
$470$	0.371774	−	0.214644i	0.0171487	−	0.00990078i
$471$	7.07780	−	24.1653i	0.326128	−	1.11348i
$472$	−0.396214	−	3.76972i	−0.0182372	−	0.173516i
$473$	1.73497	−	2.38798i	0.0797740	−	0.109800i
$474$	−0.196906	−	1.46111i	−0.00904418	−	0.0671111i
$475$	2.45304	−	2.72438i	0.112553	−	0.125003i
$476$	5.85856	+	2.60840i	0.268527	+	0.119556i
$477$	−13.8334	+	3.79746i	−0.633386	+	0.173874i
$478$	3.07308	+	14.4577i	0.140560	+	0.661281i
$479$	−8.08892	−	18.1680i	−0.369592	−	0.830118i	−0.998609	−	0.0527261i	$-0.983209\pi$
$479$	−8.08892	−	18.1680i	−0.369592	−	0.830118i	0.629017	−	0.777392i	$-0.283458\pi$
$480$	0.130615	−	1.72712i	0.00596173	−	0.0788318i
$481$	1.02571	−	3.15682i	0.0467685	−	0.143939i
$482$	−2.76530	+	1.23119i	−0.125956	+	0.0560791i
$483$	12.4771	−	5.99816i	0.567727	−	0.272926i
$484$	−10.4429	−	2.21971i	−0.474678	−	0.100896i
$485$	−0.338311	+	0.759858i	−0.0153619	+	0.0345034i
$486$	13.9657	−	6.92531i	0.633496	−	0.314139i
$487$	−17.9348	−	1.88503i	−0.812705	−	0.0854188i	−0.310948	−	0.950427i	$-0.600646\pi$
$487$	−17.9348	−	1.88503i	−0.812705	−	0.0854188i	−0.501758	+	0.865008i	$0.667313\pi$
$488$	−4.58159	−	3.32872i	−0.207399	−	0.150684i
$489$	1.07367	+	3.00274i	0.0485530	+	0.135789i
$490$	−2.81395	+	4.87391i	−0.127121	+	0.220181i
$491$	−0.426512	−	0.738741i	−0.0192482	−	0.0333389i	0.856241	−	0.516577i	$-0.172794\pi$
$491$	−0.426512	−	0.738741i	−0.0192482	−	0.0333389i	−0.875489	+	0.483238i	$0.839461\pi$
$492$	2.17896	+	1.84951i	0.0982351	+	0.0833825i
$493$	−37.8266	−	42.0107i	−1.70363	−	1.89207i
$494$	2.43622	+	7.49792i	0.109611	+	0.337347i
$495$	0.784276	+	1.51624i	0.0352506	+	0.0681497i
$496$	4.77522	−	2.86309i	0.214414	−	0.128557i
$497$			11.9265i			0.534975i
$498$	−4.91904	+	3.03512i	−0.220427	+	0.136007i
$499$	−7.37273	+	6.63843i	−0.330049	+	0.297177i	−0.817448	−	0.576002i	$-0.804612\pi$
$499$	−7.37273	+	6.63843i	−0.330049	+	0.297177i	0.487400	+	0.873179i	$0.337945\pi$
$500$	0.587785	+	0.809017i	0.0262866	+	0.0361803i
$501$	9.87590	+	10.3435i	0.441223	+	0.462114i
$502$	−11.0149	−	6.35943i	−0.491617	−	0.283835i
$503$	32.0836	−	3.37213i	1.43054	−	0.150356i	0.642644	−	0.766165i	$-0.277838\pi$
$503$	32.0836	−	3.37213i	1.43054	−	0.150356i	0.787895	+	0.615810i	$0.211171\pi$
$504$	−0.528491	+	3.47413i	−0.0235409	+	0.154750i
$505$	1.66287	−	15.8211i	0.0739966	−	0.704031i
$506$	−2.88542	−	2.59804i	−0.128273	−	0.115497i
$507$	−14.2716	−	2.59998i	−0.633825	−	0.115469i
$508$	−3.14637	+	14.8025i	−0.139598	+	0.656756i
$509$	6.94827	−	1.47690i	0.307977	−	0.0654625i	−0.0513307	−	0.998682i	$-0.516346\pi$
$509$	6.94827	−	1.47690i	0.307977	−	0.0654625i	0.359307	+	0.933219i	$0.383013\pi$
$510$	7.50538	−	5.79563i	0.332344	−	0.256635i
$511$	2.80259	+	0.910618i	0.123979	+	0.0402834i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	8.04282	−	17.2680i	0.355099	−	0.762401i
$514$	9.00625	−	1.91434i	0.397248	−	0.0844378i
$515$	0.897032	−	4.22021i	0.0395280	−	0.185964i
$516$	1.61032	−	8.83927i	0.0708905	−	0.389127i
$517$	0.181531	+	0.163451i	0.00798370	+	0.00718856i
$518$	0.188987	−	1.79809i	0.00830359	−	0.0790034i
$519$	8.31949	−	20.2600i	0.365185	−	0.889316i
$520$	−2.13872	+	0.224789i	−0.0937892	+	0.00985764i
$521$	5.15742	+	2.97764i	0.225951	+	0.130453i	0.608703	−	0.793398i	$-0.291690\pi$
$521$	5.15742	+	2.97764i	0.225951	+	0.130453i	−0.382752	+	0.923851i	$0.625024\pi$
$522$	16.7121	−	26.0822i	0.731470	−	1.14159i
$523$	−11.8967	−	16.3744i	−0.520207	−	0.716004i	0.465392	−	0.885105i	$-0.345914\pi$
$523$	−11.8967	−	16.3744i	−0.520207	−	0.716004i	−0.985599	+	0.169101i	$0.945914\pi$
$524$	−9.31404	+	8.38640i	−0.406886	+	0.366362i
$525$	−1.06536	−	1.72664i	−0.0464963	−	0.0753569i
$526$			27.4802i			1.19819i
$527$	29.1420	+	8.93976i	1.26944	+	0.389422i
$528$	0.957633	−	0.233006i	0.0416756	−	0.0101403i
$529$	7.28051	+	22.4071i	0.316544	+	0.974222i
$530$	−3.19959	−	3.55350i	−0.138981	−	0.154354i
$531$	10.1634	+	5.10048i	0.441055	+	0.221342i
$532$	2.14712	+	3.71893i	0.0930896	+	0.161236i
$533$	1.77428	−	3.07314i	0.0768526	−	0.133113i
$534$	−21.3713	+	7.64159i	−0.924826	+	0.330684i
$535$	3.75077	+	2.72509i	0.162160	+	0.117816i
$536$	12.1338	+	1.27532i	0.524102	+	0.0550853i
$537$	−4.01446	+	7.44793i	−0.173237	+	0.321402i
$538$	1.90112	−	4.26999i	0.0819632	−	0.184092i
$539$	−3.13241	−	0.665814i	−0.134922	−	0.0286787i
$540$	4.15123	+	3.12527i	0.178640	+	0.134490i
$541$	0.527913	−	0.235042i	0.0226967	−	0.0101052i	−0.395357	−	0.918528i	$-0.629379\pi$
$541$	0.527913	−	0.235042i	0.0226967	−	0.0101052i	0.418054	+	0.908422i	$0.362712\pi$
$542$	6.34053	−	19.5142i	0.272349	−	0.838205i
$543$	−21.7466	−	1.64460i	−0.933234	−	0.0705767i
$544$	−2.22680	−	5.00147i	−0.0954732	−	0.214436i
$545$	0.209461	+	0.985435i	0.00897231	+	0.0422114i
$546$	4.36122	−	0.127548i	0.186643	−	0.00545854i
$547$	−16.0945	−	7.16573i	−0.688151	−	0.306384i	0.0327096	−	0.999465i	$-0.489586\pi$
$547$	−16.0945	−	7.16573i	−0.688151	−	0.306384i	−0.720860	+	0.693081i	$0.756253\pi$
$548$	3.17953	−	3.53122i	0.135823	−	0.150846i
$549$	15.8235	−	6.18536i	0.675330	−	0.263985i
$550$	−0.334462	+	0.460347i	−0.0142615	+	0.0196293i
$551$	−3.95683	−	37.6468i	−0.168567	−	1.60381i
$552$	−11.3422	−	3.32202i	−0.482755	−	0.141394i
$553$	−0.863484	+	0.498533i	−0.0367191	+	0.0211998i
$554$	24.6437	−	17.9047i	1.04701	−	0.760699i
$555$	−2.20784	−	1.50749i	−0.0937176	−	0.0639893i
$556$	4.27398	−	1.38870i	0.181257	−	0.0588940i
$557$	−18.8652			−0.799343			−0.399672	−	0.916658i	$-0.630876\pi$
$557$	−18.8652			−0.799343			−0.399672	+	0.916658i	$0.630876\pi$
$558$	−0.496645	+	16.6959i	−0.0210246	+	0.706794i
$559$	−11.1554			−0.471824
$560$	−1.11404	+	0.361972i	−0.0470766	+	0.0152961i
$561$	4.45615	+	3.04261i	0.188139	+	0.128459i
$562$	−5.18782	+	3.76917i	−0.218835	+	0.158993i
$563$	−9.19574	+	5.30916i	−0.387554	+	0.223755i	−0.681100	−	0.732191i	$-0.738498\pi$
$563$	−9.19574	+	5.30916i	−0.387554	+	0.223755i	0.293546	+	0.955945i	$0.405165\pi$
$564$	0.713571	+	0.208998i	0.0300468	+	0.00880041i
$565$	−1.78296	−	16.9638i	−0.0750099	−	0.713671i
$566$	9.14610	−	12.5885i	0.384439	−	0.529135i
$567$	−7.92014	−	6.95783i	−0.332615	−	0.292201i
$568$	6.81287	−	7.56646i	0.285862	−	0.317481i
$569$	26.4747	+	11.7873i	1.10988	+	0.494149i	0.878031	−	0.478604i	$-0.158857\pi$
$569$	26.4747	+	11.7873i	1.10988	+	0.494149i	0.231846	+	0.972753i	$0.425524\pi$
$570$	6.34701	−	0.185624i	0.265847	−	0.00777493i
$571$	−5.05028	−	23.7597i	−0.211348	−	0.994312i	−0.948056	−	0.318102i	$-0.896954\pi$
$571$	−5.05028	−	23.7597i	−0.211348	−	0.994312i	0.736709	−	0.676210i	$-0.236379\pi$
$572$	−0.497716	−	1.11789i	−0.0208105	−	0.0467412i
$573$	31.5834	+	2.38852i	1.31941	+	0.0997819i
$574$	0.597293	−	1.83828i	0.0249305	−	0.0767283i
$575$	6.23358	−	2.77537i	0.259958	−	0.115741i
$576$	2.31985	−	1.90218i	0.0966604	−	0.0792576i
$577$	31.4854	+	6.69244i	1.31076	+	0.278610i	0.809720	−	0.586816i	$-0.199619\pi$
$577$	31.4854	+	6.69244i	1.31076	+	0.278610i	0.501036	+	0.865426i	$0.332952\pi$
$578$	5.27674	−	11.8518i	0.219484	−	0.492968i
$579$	−13.0069	+	24.1313i	−0.540547	+	1.00286i
$580$	10.2691	+	1.07933i	0.426402	+	0.0448167i
$581$	3.16243	+	2.29764i	0.131200	+	0.0953221i
$582$	−1.35655	+	0.485054i	−0.0562310	+	0.0201061i
$583$	1.36044	−	2.35636i	0.0563439	−	0.0975904i
$584$	−1.25786	−	2.17867i	−0.0520505	−	0.0901541i
$585$	2.89372	−	5.76614i	0.119640	−	0.238401i
$586$	−20.2177	−	22.4540i	−0.835186	−	0.927568i
$587$	9.02095	+	27.7636i	0.372335	+	1.14593i	0.945259	+	0.326320i	$0.105809\pi$
$587$	9.02095	+	27.7636i	0.372335	+	1.14593i	−0.572925	+	0.819608i	$0.694191\pi$
$588$	−9.47148	+	2.30455i	−0.390597	+	0.0950381i
$589$	12.2685	+	16.3130i	0.505516	+	0.672164i
$590$			3.79049i			0.156052i
$591$	16.4938	+	26.7317i	0.678466	+	1.09959i
$592$	−1.14704	+	1.03280i	−0.0471429	+	0.0424476i
$593$	19.6006	+	26.9779i	0.804900	+	1.10785i	0.992090	+	0.125526i	$0.0400617\pi$
$593$	19.6006	+	26.9779i	0.804900	+	1.10785i	−0.187191	+	0.982324i	$0.559938\pi$
$594$	−0.961365	+	2.79606i	−0.0394453	+	0.114724i
$595$	−5.55381	−	3.20649i	−0.227684	−	0.131453i
$596$	−17.7808	+	1.86883i	−0.728329	+	0.0765504i
$597$	−13.3390	+	32.4838i	−0.545929	+	1.32947i
$598$	−1.53385	+	14.5936i	−0.0627237	+	0.596776i
$599$	17.3303	+	15.6043i	0.708097	+	0.637574i	0.942360	−	0.334599i	$-0.108601\pi$
$599$	17.3303	+	15.6043i	0.708097	+	0.637574i	−0.234263	+	0.972173i	$0.575268\pi$
$600$	−0.310432	+	1.70400i	−0.0126734	+	0.0695657i
$601$	−4.22756	+	19.8891i	−0.172446	+	0.811293i	0.803846	+	0.594837i	$0.202783\pi$
$601$	−4.22756	+	19.8891i	−0.172446	+	0.811293i	−0.976292	+	0.216457i	$0.930550\pi$
$602$	−5.94351	+	1.26333i	−0.242239	+	0.0514895i
$603$	−22.8600	+	28.5854i	−0.930931	+	1.16409i
$604$	0.703258	+	0.228502i	0.0286152	+	0.00929763i
$605$	10.1537	+	3.29913i	0.412806	+	0.134129i
$606$	21.8086	−	16.8405i	0.885914	−	0.684100i
$607$	14.7869	−	3.14305i	0.600181	−	0.127572i	0.102205	−	0.994763i	$-0.467410\pi$
$607$	14.7869	−	3.14305i	0.600181	−	0.127572i	0.497976	+	0.867191i	$0.334077\pi$
$608$	0.762207	−	3.58590i	0.0309116	−	0.145428i
$609$	−20.6102	−	3.75473i	−0.835168	−	0.152149i
$610$	4.20854	+	3.78939i	0.170399	+	0.153428i
$611$	0.0964990	−	0.918127i	0.00390393	−	0.0371434i
$612$	16.2376	+	2.47009i	0.656365	+	0.0998475i
$613$	−5.40291	+	0.567868i	−0.218221	+	0.0229360i	−0.213008	−	0.977050i	$-0.568326\pi$
$613$	−5.40291	+	0.567868i	−0.218221	+	0.0229360i	−0.00521317	+	0.999986i	$0.501659\pi$
$614$	−17.7204	−	10.2309i	−0.715138	−	0.412885i
$615$	−1.97370	−	2.06715i	−0.0795871	−	0.0833554i
$616$	−0.391777	−	0.539235i	−0.0157852	−	0.0217264i
$617$	6.79995	−	6.12270i	0.273756	−	0.246491i	−0.520805	−	0.853676i	$-0.674368\pi$
$617$	6.79995	−	6.12270i	0.273756	−	0.246491i	0.794560	+	0.607185i	$0.207701\pi$
$618$	6.35974	−	3.92405i	0.255826	−	0.157848i
$619$		−	26.6125i		−	1.06965i	−0.844963	−	0.534824i	$-0.820378\pi$
$619$		−	26.6125i		−	1.06965i	0.844963	−	0.534824i	$-0.179622\pi$
$620$	−5.04833	+	2.34826i	−0.202746	+	0.0943085i
$621$	26.7486	−	23.2731i	1.07338	−	0.933919i
$622$	−10.1505	−	31.2400i	−0.406997	−	1.25261i
$623$	10.2707	+	11.4068i	0.411487	+	0.457002i
$624$	−2.83973	−	2.41038i	−0.113680	−	0.0964924i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	8.91708	−	15.4448i	0.356398	−	0.617300i
$627$	1.21649	+	3.40218i	0.0485821	+	0.135870i
$628$	11.7615	+	8.54521i	0.469334	+	0.340991i
$629$	−8.40399	−	0.883295i	−0.335089	−	0.0352193i
$630$	0.888742	−	3.39986i	0.0354083	−	0.135454i
$631$	−4.89230	+	10.9883i	−0.194759	+	0.437437i	−0.984356	−	0.176189i	$-0.943623\pi$
$631$	−4.89230	+	10.9883i	−0.194759	+	0.437437i	0.789597	+	0.613626i	$0.210290\pi$
$632$	0.832598	+	0.176974i	0.0331190	+	0.00703966i
$633$	27.2789	−	13.1139i	1.08424	−	0.521231i
$634$	−25.2003	+	11.2199i	−1.00083	+	0.445598i
$635$	4.67642	−	14.3926i	0.185578	−	0.571151i
$636$	0.624562	−	8.25858i	0.0247655	−	0.327474i
$637$	4.92266	+	11.0565i	0.195043	+	0.438073i
$638$	1.22159	+	5.74713i	0.0483632	+	0.227531i
$639$	8.08591	+	29.4553i	0.319874	+	1.16523i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	18.2043	−	20.2180i	0.719028	−	0.798562i	−0.267255	−	0.963626i	$-0.586116\pi$
$641$	18.2043	−	20.2180i	0.719028	−	0.798562i	0.986283	+	0.165064i	$0.0527831\pi$
$642$	1.07248	+	7.95821i	0.0423275	+	0.314085i
$643$	−23.1182	+	31.8194i	−0.911692	+	1.25484i	0.0548934	+	0.998492i	$0.482518\pi$
$643$	−23.1182	+	31.8194i	−0.911692	+	1.25484i	−0.966586	+	0.256344i	$0.917482\pi$
$644$	0.835478	+	7.94904i	0.0329224	+	0.313236i
$645$	−2.52546	+	8.62252i	−0.0994397	+	0.339511i
$646$	17.3817	−	10.0353i	0.683874	−	0.394835i
$647$	0.346380	−	0.251660i	0.0136176	−	0.00989376i	−0.580956	−	0.813935i	$-0.697321\pi$
$647$	0.346380	−	0.251660i	0.0136176	−	0.00989376i	0.594573	+	0.804041i	$0.297321\pi$
$648$	1.05015	+	8.93852i	0.0412539	+	0.351138i
$649$	−2.05130	+	0.666508i	−0.0805206	+	0.0261627i
$650$	2.15050			0.0843497
$651$	10.5725	−	3.97836i	0.414369	−	0.155924i
$652$	−1.84112			−0.0721040
$653$	−13.1871	+	4.28474i	−0.516050	+	0.167675i	−0.555452	−	0.831549i	$-0.687455\pi$
$653$	−13.1871	+	4.28474i	−0.516050	+	0.167675i	0.0394022	+	0.999223i	$0.487455\pi$
$654$	−0.983952	+	1.44108i	−0.0384756	+	0.0563506i
$655$	10.1396	−	7.36688i	0.396188	−	0.287848i
$656$	−1.42904	+	0.825054i	−0.0557944	+	0.0322129i
$657$	7.53907	+	0.348890i	0.294127	+	0.0136115i
$658$	−0.0525625	−	0.500098i	−0.00204910	−	0.0194959i
$659$	18.8321	−	25.9202i	0.733595	−	1.00971i	−0.265366	−	0.964148i	$-0.585493\pi$
$659$	18.8321	−	25.9202i	0.733595	−	1.00971i	0.998962	−	0.0455599i	$-0.0145072\pi$
$660$	−0.976743	+	0.131630i	−0.0380197	+	0.00512370i
$661$	−0.371837	+	0.412966i	−0.0144628	+	0.0160625i	−0.750333	−	0.661060i	$-0.770107\pi$
$661$	−0.371837	+	0.412966i	−0.0144628	+	0.0160625i	0.735870	+	0.677123i	$0.236773\pi$
$662$	3.52453	+	1.56922i	0.136985	+	0.0609896i
$663$	−0.596139	−	20.3837i	−0.0231521	−	0.791637i
$664$	−0.693824	−	3.26418i	−0.0269256	−	0.126675i
$665$	−1.74663	−	3.92299i	−0.0677313	−	0.152127i
$666$	−0.752319	−	4.56894i	−0.0291518	−	0.177043i
$667$	21.7725	−	67.0089i	0.843036	−	2.59460i
$668$	−7.54291	+	3.35832i	−0.291844	+	0.129937i
$669$	−10.2718	−	21.3668i	−0.397130	−	0.826090i
$670$	−11.9340	−	2.53666i	−0.461053	−	0.0979997i
$671$	−1.31069	+	2.94385i	−0.0505986	+	0.113646i
$672$	−1.78595	−	0.962635i	−0.0688947	−	0.0371344i
$673$	−15.2554	−	1.60341i	−0.588053	−	0.0618068i	−0.194170	−	0.980968i	$-0.562202\pi$
$673$	−15.2554	−	1.60341i	−0.588053	−	0.0618068i	−0.393882	+	0.919161i	$0.628868\pi$
$674$	8.33426	+	6.05519i	0.321024	+	0.233237i
$675$	−3.80181	−	3.54207i	−0.146332	−	0.136334i
$676$	4.18767	−	7.25325i	0.161064	−	0.278971i
$677$	0.114376	+	0.198105i	0.00439582	+	0.00761378i	0.868215	−	0.496188i	$-0.165267\pi$
$677$	0.114376	+	0.198105i	0.00439582	+	0.00761378i	−0.863819	+	0.503802i	$0.831934\pi$
$678$	19.1185	−	22.5240i	0.734241	−	0.865028i
$679$	0.651938	+	0.724050i	0.0250191	+	0.0277865i
$680$	1.69180	+	5.20684i	0.0648777	+	0.199673i
$681$	−7.07840	−	29.0915i	−0.271245	−	1.11479i
$682$	−2.15849	−	2.31910i	−0.0826530	−	0.0888029i
$683$		−	11.8167i		−	0.452154i	−0.974109	−	0.226077i	$-0.927410\pi$
$683$		−	11.8167i		−	0.452154i	0.974109	−	0.226077i	$-0.0725900\pi$
$684$	7.82420	+	7.72909i	0.299166	+	0.295529i
$685$	−3.53122	+	3.17953i	−0.134921	+	0.121484i
$686$	8.69446	+	11.9669i	0.331956	+	0.456898i
$687$	−22.5404	+	21.5214i	−0.859969	+	0.821092i
$688$	4.49238	+	2.59367i	0.171270	+	0.0988829i
$689$	−10.2267	+	1.07487i	−0.389608	+	0.0409494i
$690$	10.9328	+	4.48940i	0.416204	+	0.170908i
$691$	2.30335	−	21.9149i	0.0876236	−	0.833683i	−0.859137	−	0.511745i	$-0.828999\pi$
$691$	2.30335	−	21.9149i	0.0876236	−	0.833683i	0.946761	−	0.321938i	$-0.104334\pi$
$692$	9.39701	+	8.46111i	0.357221	+	0.321643i
$693$	1.99618	−	0.116860i	0.0758285	−	0.00443914i
$694$	5.98415	−	28.1532i	0.227155	−	1.06868i
$695$	−4.39573	+	0.934341i	−0.166739	+	0.0354416i
$696$	10.9308	+	14.1555i	0.414331	+	0.536561i
$697$	−8.59184	−	2.79166i	−0.325439	−	0.105742i
$698$	−14.7136	−	4.78073i	−0.556917	−	0.180953i
$699$	27.7640	+	35.9545i	1.05013	+	1.35993i
$700$	1.14577	−	0.243541i	0.0433060	−	0.00920498i
$701$	−8.94605	+	42.0878i	−0.337888	+	1.58964i	0.401176	+	0.916001i	$0.368601\pi$
$701$	−8.94605	+	42.0878i	−0.337888	+	1.58964i	−0.739064	+	0.673635i	$0.764732\pi$
$702$	10.6846	−	3.27183i	0.403265	−	0.123487i
$703$	−4.20505	−	3.78624i	−0.158597	−	0.142801i
$704$	−0.0594788	+	0.565903i	−0.00224169	+	0.0213283i
$705$	−0.687816	−	0.282442i	−0.0259046	−	0.0106374i
$706$	7.60882	−	0.799720i	0.286362	−	0.0300978i
$707$	−16.1379	−	9.31721i	−0.606927	−	0.350410i
$708$	−4.74847	+	4.53381i	−0.178459	+	0.170391i
$709$	−22.8863	−	31.5003i	−0.859512	−	1.18302i	−0.981686	−	0.190508i	$-0.938986\pi$
$709$	−22.8863	−	31.5003i	−0.859512	−	1.18302i	0.122173	−	0.992509i	$-0.461014\pi$
$710$	−7.56646	+	6.81287i	−0.283964	+	0.255682i
$711$	−1.79459	+	1.81667i	−0.0673024	+	0.0681306i
$712$		−	13.1038i		−	0.491084i
$713$	8.51123	+	37.0260i	0.318748	+	1.38664i
$714$	−2.62604	−	10.7927i	−0.0982769	−	0.403908i
$715$	0.378138	+	1.16379i	0.0141416	+	0.0435232i
$716$	−3.26865	−	3.63021i	−0.122155	−	0.135667i
$717$	16.5669	−	19.5179i	0.618702	−	0.728908i
$718$	−2.64071	−	4.57385i	−0.0985505	−	0.170694i
$719$	20.4449	−	35.4115i	0.762464	−	1.32063i	−0.179113	−	0.983829i	$-0.557323\pi$
$719$	20.4449	−	35.4115i	0.762464	−	1.32063i	0.941577	−	0.336798i	$-0.109344\pi$
$720$	−2.50597	+	1.64927i	−0.0933921	+	0.0614648i
$721$	−4.08865	−	2.97058i	−0.152269	−	0.110630i
$722$	−5.52987	−	0.581213i	−0.205801	−	0.0216305i
$723$	4.61518	+	2.48760i	0.171641	+	0.0925148i
$724$	5.12132	−	11.5027i	0.190332	−	0.427493i
$725$	−10.1000	−	2.14683i	−0.375106	−	0.0797313i
$726$	8.01190	+	16.6660i	0.297349	+	0.618532i
$727$	4.72429	−	2.10339i	0.175214	−	0.0780104i	−0.317255	−	0.948340i	$-0.602761\pi$
$727$	4.72429	−	2.10339i	0.175214	−	0.0780104i	0.492469	+	0.870330i	$0.336094\pi$
$728$	−0.778422	+	2.39574i	−0.0288502	+	0.0887919i
$729$	−24.2780	−	11.8144i	−0.899185	−	0.437569i
$730$	1.02323	+	2.29822i	0.0378715	+	0.0850609i
$731$	5.90462	+	27.7791i	0.218390	+	1.02745i
$732$	0.286746	+	9.80467i	0.0105985	+	0.362391i
$733$	24.7784	+	11.0320i	0.915209	+	0.407477i	0.809635	−	0.586934i	$-0.199665\pi$
$733$	24.7784	+	11.0320i	0.915209	+	0.407477i	0.105575	+	0.994411i	$0.466332\pi$
$734$	−3.32443	+	3.69215i	−0.122707	+	0.136280i
$735$	9.66048	−	1.30189i	0.356332	−	0.0480209i
$736$	4.01076	−	5.52033i	0.147838	−	0.203482i
$737$	−0.725681	−	6.90440i	−0.0267308	−	0.254327i
$738$	0.228844	−	4.94503i	0.00842388	−	0.182029i
$739$	12.4505	−	7.18833i	0.458001	−	0.264427i	−0.253203	−	0.967413i	$-0.581484\pi$
$739$	12.4505	−	7.18833i	0.458001	−	0.264427i	0.711203	+	0.702986i	$0.248151\pi$
$740$	1.24871	−	0.907240i	0.0459034	−	0.0333508i
$741$	7.69989	−	11.2771i	0.282863	−	0.414275i
$742$	−5.32699	+	1.73084i	−0.195560	+	0.0635413i
$743$	−35.0045			−1.28419			−0.642096	−	0.766624i	$-0.721935\pi$
$743$	−35.0045			−1.28419			−0.642096	+	0.766624i	$0.721935\pi$
$744$	−8.98006	−	3.51546i	−0.329225	−	0.128883i
$745$	17.8787			0.655025
$746$	−31.5715	+	10.2582i	−1.15592	+	0.375580i
$747$	9.36814	+	3.53052i	0.342762	+	0.129175i
$748$	−2.52031	+	1.83111i	−0.0921515	+	0.0669520i
$749$	4.70312	−	2.71535i	0.171848	−	0.0992167i
$750$	0.486849	−	1.66222i	0.0177772	−	0.0606957i
$751$	2.35946	+	22.4487i	0.0860978	+	0.819166i	0.949314	+	0.314331i	$0.101780\pi$
$751$	2.35946	+	22.4487i	0.0860978	+	0.819166i	−0.863216	+	0.504835i	$0.831553\pi$
$752$	−0.252329	+	0.347301i	−0.00920149	+	0.0126648i
$753$	2.94222	+	21.8324i	0.107221	+	0.795615i
$754$	14.8583	−	16.5018i	0.541108	−	0.600962i
$755$	−0.675520	−	0.300761i	−0.0245847	−	0.0109458i
$756$	5.32214	−	2.95322i	0.193564	−	0.107407i
$757$	−2.59886	−	12.2267i	−0.0944572	−	0.444386i	−0.999806	−	0.0197166i	$-0.993724\pi$
$757$	−2.59886	−	12.2267i	−0.0944572	−	0.444386i	0.905348	−	0.424670i	$-0.139610\pi$
$758$	8.08336	+	18.1555i	0.293601	+	0.659438i
$759$	−0.507140	+	6.70591i	−0.0184080	+	0.243409i
$760$	−1.13286	+	3.48659i	−0.0410932	+	0.126472i
$761$	−8.95391	+	3.98654i	−0.324579	+	0.144512i	−0.562557	−	0.826759i	$-0.690182\pi$
$761$	−8.95391	+	3.98654i	−0.324579	+	0.144512i	0.237978	+	0.971271i	$0.423516\pi$
$762$	23.6235	−	11.3566i	0.855790	−	0.411407i
$763$	1.15431	+	0.245355i	0.0417887	+	0.00888245i
$764$	−7.43789	+	16.7058i	−0.269093	+	0.604394i
$765$	−15.8904	−	4.15385i	−0.574520	−	0.150183i
$766$	−16.5719	−	1.74177i	−0.598766	−	0.0629328i
$767$	6.59467	+	4.79131i	0.238120	+	0.173004i
$768$	0.583160	+	1.63093i	0.0210430	+	0.0588510i
$769$	−10.5137	+	18.2102i	−0.379133	+	0.656678i	−0.990936	−	0.134332i	$-0.957111\pi$
$769$	−10.5137	+	18.2102i	−0.379133	+	0.656678i	0.611803	+	0.791010i	$0.290444\pi$
$770$	0.333266	+	0.577233i	0.0120101	+	0.0208020i
$771$	−12.1584	−	10.3201i	−0.437874	−	0.371670i
$772$	−10.5905	−	11.7619i	−0.381159	−	0.423320i
$773$	11.0955	+	34.1484i	0.399077	+	1.22823i	0.925741	+	0.378159i

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(-1.43042 - 0.976675i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.66222 - 0.486849i) q^{6} +(0.122441 + 1.16495i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.09221 + 2.79411i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(-1.43042 - 0.976675i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.66222 - 0.486849i) q^{6} +(0.122441 + 1.16495i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.09221 + 2.79411i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-0.519826 - 0.231441i) q^{11} +(-1.73131 + 0.0506337i) q^{12} +(0.447115 + 2.10351i) q^{13} +(0.476438 + 1.07010i) q^{14} +(1.72712 + 0.130615i) q^{15} +(0.309017 - 0.951057i) q^{16} +(5.00147 - 2.22680i) q^{17} +(1.90218 + 2.31985i) q^{18} +(3.58590 + 0.762207i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(0.962635 - 1.78595i) q^{21} +(-0.565903 - 0.0594788i) q^{22} +(5.52033 + 4.01076i) q^{23} +(-1.63093 + 0.583160i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.07525 + 1.86239i) q^{26} +(1.16662 - 5.06350i) q^{27} +(0.783797 + 0.870495i) q^{28} +(-3.19081 - 9.82031i) q^{29} +(1.68295 - 0.409487i) q^{30} +(4.19859 + 3.65676i) q^{31} -1.00000i q^{32} +(0.517527 + 0.838760i) q^{33} +(4.06856 - 3.66335i) q^{34} +(-0.688512 - 0.947655i) q^{35} +(2.52596 + 1.61850i) q^{36} +(-1.33670 - 0.771745i) q^{37} +(3.64593 - 0.383203i) q^{38} +(1.41488 - 3.44559i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-1.22627 - 1.10414i) q^{41} +(0.363630 - 1.99601i) q^{42} +(-1.07851 + 5.07399i) q^{43} +(-0.556586 + 0.118306i) q^{44} +(-2.34294 - 1.87367i) q^{45} +(6.48954 + 2.10858i) q^{46} +(-0.408277 - 0.132657i) q^{47} +(-1.37090 + 1.05860i) q^{48} +(5.50492 - 1.17011i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-9.32907 - 1.69955i) q^{51} +(1.59814 + 1.43897i) q^{52} +(-0.499825 + 4.75551i) q^{53} +(-0.455184 - 5.17618i) q^{54} +(0.565903 - 0.0594788i) q^{55} +(1.01443 + 0.585683i) q^{56} +(-4.38492 - 4.59254i) q^{57} +(-6.06929 - 8.35366i) q^{58} +(2.81688 - 2.53633i) q^{59} +(1.47404 - 0.909505i) q^{60} -5.66315i q^{61} +(5.12309 + 2.18035i) q^{62} +(-3.12127 + 1.61448i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.43897 - 1.59814i) q^{65} +(0.751389 + 0.637784i) q^{66} +(6.10033 + 10.5661i) q^{67} +(2.73740 - 4.74131i) q^{68} +(-3.97919 - 11.1286i) q^{69} +(-0.947655 - 0.688512i) q^{70} +(10.1259 + 1.06427i) q^{71} +(2.90247 + 0.758722i) q^{72} +(1.02323 - 2.29822i) q^{73} +(-1.50976 - 0.320909i) q^{74} +(-1.56104 + 0.750444i) q^{75} +(3.34907 - 1.49110i) q^{76} +(0.205970 - 0.633909i) q^{77} +(0.280888 - 3.71417i) q^{78} +(0.346214 + 0.777609i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-6.61415 + 6.10352i) q^{81} +(-1.50745 - 0.671159i) q^{82} +(2.23296 - 2.47995i) q^{83} +(-0.270969 - 2.01069i) q^{84} +(-3.21800 + 4.42920i) q^{85} +(0.542226 + 5.15893i) q^{86} +(-5.02705 + 17.1636i) q^{87} +(-0.492786 + 0.284510i) q^{88} +(10.6012 - 7.70220i) q^{89} +(-2.80726 - 1.05796i) q^{90} +(-2.39574 + 0.778422i) q^{91} +6.82351 q^{92} +(-2.43428 - 9.33136i) q^{93} -0.429288 q^{94} +(-3.48659 + 1.13286i) q^{95} +(-0.976675 + 1.43042i) q^{96} +(0.672915 - 0.488901i) q^{97} +(4.87391 - 2.81395i) q^{98} +(0.0789143 - 1.70524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176q + 44q^{4} + 4q^{7} - 4q^{9} + O(q^{10}) \)	\( 176q + 44q^{4} + 4q^{7} - 4q^{9} - 22q^{10} - 38q^{13} - 44q^{16} + 12q^{18} + 8q^{19} - 18q^{21} - 4q^{22} + 88q^{25} - 90q^{27} + 36q^{28} + 24q^{31} + 18q^{33} + 14q^{34} + 4q^{36} - 42q^{37} - 42q^{39} + 22q^{40} - 12q^{42} - 34q^{43} - 8q^{45} + 10q^{46} + 22q^{49} + 26q^{51} - 2q^{52} + 4q^{55} + 114q^{57} + 32q^{63} + 44q^{64} - 42q^{66} + 20q^{67} + 16q^{69} + 8q^{70} - 12q^{72} - 28q^{73} + 12q^{76} - 92q^{78} - 56q^{79} - 124q^{81} - 32q^{82} - 12q^{84} - 36q^{87} - 6q^{88} + 24q^{90} - 140q^{91} - 104q^{93} - 36q^{94} + 88q^{97} - 60q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

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Fields

Representations

Groups

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