LMFDB - Embedded newform 77.2.n.a.24.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [77,2,Mod(17,77)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("77.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(77, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.n (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			24.2
Character	$\chi$	$=$	77.24
Dual form			77.2.n.a.61.2

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.373106 - 1.75533i) q^{2} +(-2.87300 + 0.301965i) q^{3} +(-1.11488 + 0.496374i) q^{4} +(-1.49503 - 1.34613i) q^{5} +(1.60198 + 4.93040i) q^{6} +(-1.89247 + 1.84893i) q^{7} +(-0.822345 - 1.13186i) q^{8} +(5.22852 - 1.11136i) q^{9} +(-1.80510 + 3.12652i) q^{10} +(-0.00719692 - 3.31662i) q^{11} +(3.05315 - 1.76274i) q^{12} +(1.45177 - 4.46807i) q^{13} +(3.95158 + 2.63205i) q^{14} +(4.70172 + 3.41600i) q^{15} +(-3.31315 + 3.67963i) q^{16} +(-0.563588 - 0.119794i) q^{17} +(-3.90159 - 8.76311i) q^{18} +(1.25928 + 0.560666i) q^{19} +(2.33496 + 0.758675i) q^{20} +(4.87876 - 5.88345i) q^{21} +(-5.81906 + 1.25008i) q^{22} +(0.408298 + 0.707192i) q^{23} +(2.70438 + 3.00352i) q^{24} +(-0.0995947 - 0.947580i) q^{25} +(-8.38459 - 0.881256i) q^{26} +(-6.44364 + 2.09366i) q^{27} +(1.19210 - 3.00071i) q^{28} +(0.425221 - 0.585266i) q^{29} +(4.24195 - 9.52759i) q^{30} +(-2.66938 + 2.40352i) q^{31} +(5.27188 + 3.04372i) q^{32} +(1.02218 + 9.52648i) q^{33} +1.03398i q^{34} +(5.31822 - 0.216702i) q^{35} +(-5.27750 + 3.83433i) q^{36} +(-1.01403 + 9.64787i) q^{37} +(0.514308 - 2.41963i) q^{38} +(-2.82172 + 13.2752i) q^{39} +(-0.294203 + 2.79915i) q^{40} +(2.23288 - 1.62228i) q^{41} +(-12.1477 - 6.36866i) q^{42} -8.37074i q^{43} +(1.65431 + 3.69404i) q^{44} +(-9.31284 - 5.37677i) q^{45} +(1.08902 - 0.980554i) q^{46} +(1.44091 - 3.23634i) q^{47} +(8.40758 - 11.5720i) q^{48} +(0.162880 - 6.99810i) q^{49} +(-1.62615 + 0.528369i) q^{50} +(1.65536 + 0.173986i) q^{51} +(0.599301 + 5.70196i) q^{52} +(-4.28163 - 4.75523i) q^{53} +(6.07923 + 10.5295i) q^{54} +(-4.45385 + 4.96814i) q^{55} +(3.64900 + 0.621549i) q^{56} +(-3.78720 - 1.23054i) q^{57} +(-1.18599 - 0.528035i) q^{58} +(-2.32108 - 5.21322i) q^{59} +(-6.93744 - 1.47460i) q^{60} +(9.07168 - 10.0751i) q^{61} +(5.21492 + 3.78886i) q^{62} +(-7.83998 + 11.7704i) q^{63} +(0.315602 - 0.971325i) q^{64} +(-8.18506 + 4.72565i) q^{65} +(16.3407 - 5.34865i) q^{66} +(-0.838413 + 1.45217i) q^{67} +(0.687794 - 0.146195i) q^{68} +(-1.38659 - 1.90847i) q^{69} +(-2.36464 - 9.25436i) q^{70} +(2.10176 + 6.46855i) q^{71} +(-5.55754 - 5.00403i) q^{72} +(5.68595 - 2.53155i) q^{73} +(17.3135 - 1.81972i) q^{74} +(0.572272 + 2.69233i) q^{75} -1.68224 q^{76} +(6.14583 + 6.26329i) q^{77} +24.3551 q^{78} +(-1.58831 - 7.47240i) q^{79} +(9.90655 - 1.04122i) q^{80} +(3.23078 - 1.43844i) q^{81} +(-3.68074 - 3.31415i) q^{82} +(-0.369293 - 1.13657i) q^{83} +(-2.51881 + 8.98101i) q^{84} +(0.681324 + 0.937762i) q^{85} +(-14.6934 + 3.12318i) q^{86} +(-1.04493 + 1.80987i) q^{87} +(-3.74803 + 2.73555i) q^{88} +(-12.6666 + 7.31306i) q^{89} +(-5.96331 + 18.3532i) q^{90} +(5.51376 + 11.1399i) q^{91} +(-0.806233 - 0.585763i) q^{92} +(6.94335 - 7.71137i) q^{93} +(-6.21844 - 1.32177i) q^{94} +(-1.12793 - 2.53337i) q^{95} +(-16.0652 - 7.15270i) q^{96} +(9.81655 + 3.18959i) q^{97} +(-12.3447 + 2.32513i) q^{98} +(-3.72357 - 17.3330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26}+ \cdots - 12 q^{99}+O(q^{100}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.373106	−	1.75533i	−0.263826	−	1.24120i	−0.887972	−	0.459897i	$-0.847886\pi$
$2$	−0.373106	−	1.75533i	−0.263826	−	1.24120i	0.624146	−	0.781307i	$-0.285447\pi$
$3$	−2.87300	+	0.301965i	−1.65873	+	0.174339i	−0.887050	−	0.461673i	$-0.847249\pi$
$3$	−2.87300	+	0.301965i	−1.65873	+	0.174339i	−0.771679	+	0.636013i	$0.780583\pi$
$4$	−1.11488	+	0.496374i	−0.557438	+	0.248187i
$5$	−1.49503	−	1.34613i	−0.668599	−	0.602009i	0.263306	−	0.964712i	$-0.415187\pi$
$5$	−1.49503	−	1.34613i	−0.668599	−	0.602009i	−0.931905	+	0.362703i	$0.881854\pi$
$6$	1.60198	+	4.93040i	0.654007	+	2.01283i
$7$	−1.89247	+	1.84893i	−0.715286	+	0.698832i
$7$	−1.89247	+	1.84893i	−0.715286	+	0.698832i
$8$	−0.822345	−	1.13186i	−0.290743	−	0.400173i
$9$	5.22852	−	1.11136i	1.74284	−	0.370452i
$10$	−1.80510	+	3.12652i	−0.570823	+	0.988694i
$11$	−0.00719692	−	3.31662i	−0.00216995	−	0.999998i
$11$	−0.00719692	−	3.31662i	−0.00216995	−	0.999998i
$12$	3.05315	−	1.76274i	0.881369	−	0.508859i
$13$	1.45177	−	4.46807i	0.402647	−	1.23922i	−0.520197	−	0.854046i	$-0.674141\pi$
$13$	1.45177	−	4.46807i	0.402647	−	1.23922i	0.922844	−	0.385174i	$-0.125859\pi$
$14$	3.95158	+	2.63205i	1.05610	+	0.703446i
$15$	4.70172	+	3.41600i	1.21398	+	0.882007i
$16$	−3.31315	+	3.67963i	−0.828289	+	0.919908i
$17$	−0.563588	−	0.119794i	−0.136690	−	0.0290544i	0.139058	−	0.990284i	$-0.455592\pi$
$17$	−0.563588	−	0.119794i	−0.136690	−	0.0290544i	−0.275749	+	0.961230i	$0.588926\pi$
$18$	−3.90159	−	8.76311i	−0.919613	−	2.06548i
$19$	1.25928	+	0.560666i	0.288898	+	0.128626i	0.546069	−	0.837740i	$-0.316124\pi$
$19$	1.25928	+	0.560666i	0.288898	+	0.128626i	−0.257171	+	0.966366i	$0.582790\pi$
$20$	2.33496	+	0.758675i	0.522113	+	0.169645i
$21$	4.87876	−	5.88345i	1.06463	−	1.28387i
$22$	−5.81906	+	1.25008i	−1.24063	+	0.266519i
$23$	0.408298	+	0.707192i	0.0851360	+	0.147460i	0.905449	−	0.424455i	$-0.139534\pi$
$23$	0.408298	+	0.707192i	0.0851360	+	0.147460i	−0.820313	+	0.571915i	$0.806201\pi$
$24$	2.70438	+	3.00352i	0.552029	+	0.613091i
$25$	−0.0995947	−	0.947580i	−0.0199189	−	0.189516i
$26$	−8.38459	−	0.881256i	−1.64435	−	0.172829i
$27$	−6.44364	+	2.09366i	−1.24008	+	0.402926i
$28$	1.19210	−	3.00071i	0.225286	−	0.567080i
$29$	0.425221	−	0.585266i	0.0789615	−	0.108681i	−0.767709	−	0.640798i	$-0.778603\pi$
$29$	0.425221	−	0.585266i	0.0789615	−	0.108681i	0.846671	+	0.532117i	$0.178603\pi$
$30$	4.24195	−	9.52759i	0.774471	−	1.73949i
$31$	−2.66938	+	2.40352i	−0.479434	+	0.431684i	−0.873079	−	0.487578i	$-0.837880\pi$
$31$	−2.66938	+	2.40352i	−0.479434	+	0.431684i	0.393645	+	0.919262i	$0.371214\pi$
$32$	5.27188	+	3.04372i	0.931945	+	0.538059i
$33$	1.02218	+	9.52648i	0.177938	+	1.65835i
$34$			1.03398i			0.177326i
$35$	5.31822	−	0.216702i	0.898943	−	0.0366293i
$36$	−5.27750	+	3.83433i	−0.879583	+	0.639054i
$37$	−1.01403	+	9.64787i	−0.166706	+	1.58610i	0.516768	+	0.856125i	$0.327135\pi$
$37$	−1.01403	+	9.64787i	−0.166706	+	1.58610i	−0.683474	+	0.729975i	$0.739532\pi$
$38$	0.514308	−	2.41963i	0.0834318	−	0.392516i
$39$	−2.82172	+	13.2752i	−0.451837	+	2.12573i
$40$	−0.294203	+	2.79915i	−0.0465176	+	0.442585i
$41$	2.23288	−	1.62228i	0.348717	−	0.253358i	−0.399614	−	0.916684i	$-0.630856\pi$
$41$	2.23288	−	1.62228i	0.348717	−	0.253358i	0.748331	+	0.663326i	$0.230856\pi$
$42$	−12.1477	−	6.36866i	−1.87443	−	0.982706i
$43$		−	8.37074i		−	1.27653i	−0.769819	−	0.638263i	$-0.779653\pi$
$43$		−	8.37074i		−	1.27653i	0.769819	−	0.638263i	$-0.220347\pi$
$44$	1.65431	+	3.69404i	0.249396	+	0.556898i
$45$	−9.31284	−	5.37677i	−1.38828	−	0.801522i
$46$	1.08902	−	0.980554i	0.160567	−	0.144575i
$47$	1.44091	−	3.23634i	0.210178	−	0.472068i	−0.777437	−	0.628960i	$-0.783481\pi$
$47$	1.44091	−	3.23634i	0.210178	−	0.472068i	0.987616	+	0.156892i	$0.0501475\pi$
$48$	8.40758	−	11.5720i	1.21353	−	1.67028i
$49$	0.162880	−	6.99810i	0.0232686	−	0.999729i
$50$	−1.62615	+	0.528369i	−0.229973	+	0.0747227i
$51$	1.65536	+	0.173986i	0.231797	+	0.0243629i
$52$	0.599301	+	5.70196i	0.0831080	+	0.790720i
$53$	−4.28163	−	4.75523i	−0.588127	−	0.653182i	0.373471	−	0.927642i	$-0.378168\pi$
$53$	−4.28163	−	4.75523i	−0.588127	−	0.653182i	−0.961598	+	0.274460i	$0.911501\pi$
$54$	6.07923	+	10.5295i	0.827278	+	1.43289i
$55$	−4.45385	+	4.96814i	−0.600557	+	0.669904i
$56$	3.64900	+	0.621549i	0.487618	+	0.0830580i
$57$	−3.78720	−	1.23054i	−0.501627	−	0.162989i
$58$	−1.18599	−	0.528035i	−0.155728	−	0.0693344i
$59$	−2.32108	−	5.21322i	−0.302179	−	0.678704i	0.697089	−	0.716985i	$-0.254478\pi$
$59$	−2.32108	−	5.21322i	−0.302179	−	0.678704i	−0.999267	+	0.0382811i	$0.987812\pi$
$60$	−6.93744	−	1.47460i	−0.895620	−	0.190370i
$61$	9.07168	−	10.0751i	1.16151	−	1.28999i	0.211637	−	0.977348i	$-0.432120\pi$
$61$	9.07168	−	10.0751i	1.16151	−	1.28999i	0.949872	−	0.312639i	$-0.101213\pi$
$62$	5.21492	+	3.78886i	0.662295	+	0.481186i
$63$	−7.83998	+	11.7704i	−0.987745	+	1.48293i
$64$	0.315602	−	0.971325i	0.0394503	−	0.121416i
$65$	−8.18506	+	4.72565i	−1.01523	+	0.586144i
$66$	16.3407	−	5.34865i	2.01140	−	0.658373i
$67$	−0.838413	+	1.45217i	−0.102428	+	0.177411i	−0.912685	−	0.408665i	$-0.865995\pi$
$67$	−0.838413	+	1.45217i	−0.102428	+	0.177411i	0.810256	+	0.586076i	$0.199328\pi$
$68$	0.687794	−	0.146195i	0.0834072	−	0.0177288i
$69$	−1.38659	−	1.90847i	−0.166926	−	0.229753i
$70$	−2.36464	−	9.25436i	−0.282629	−	1.10611i
$71$	2.10176	+	6.46855i	0.249433	+	0.767676i	0.994876	+	0.101106i	$0.0322381\pi$
$71$	2.10176	+	6.46855i	0.249433	+	0.767676i	−0.745443	+	0.666570i	$0.767762\pi$
$72$	−5.55754	−	5.00403i	−0.654963	−	0.589731i
$73$	5.68595	−	2.53155i	0.665490	−	0.296295i	−0.0460519	−	0.998939i	$-0.514664\pi$
$73$	5.68595	−	2.53155i	0.665490	−	0.296295i	0.711542	+	0.702644i	$0.247997\pi$
$74$	17.3135	−	1.81972i	2.01266	−	0.211539i
$75$	0.572272	+	2.69233i	0.0660802	+	0.310883i
$76$	−1.68224			−0.192966
$77$	6.14583	+	6.26329i	0.700382	+	0.713768i
$78$	24.3551			2.75767
$79$	−1.58831	−	7.47240i	−0.178699	−	0.840711i	−0.972567	−	0.232622i	$-0.925270\pi$
$79$	−1.58831	−	7.47240i	−0.178699	−	0.840711i	0.793869	−	0.608089i	$-0.208064\pi$
$80$	9.90655	−	1.04122i	1.10759	−	0.116412i
$81$	3.23078	−	1.43844i	0.358976	−	0.159826i
$82$	−3.68074	−	3.31415i	−0.406469	−	0.365987i
$83$	−0.369293	−	1.13657i	−0.0405351	−	0.124754i	0.928741	−	0.370729i	$-0.120892\pi$
$83$	−0.369293	−	1.13657i	−0.0405351	−	0.124754i	−0.969276	+	0.245974i	$0.920892\pi$
$84$	−2.51881	+	8.98101i	−0.274825	+	0.979908i
$85$	0.681324	+	0.937762i	0.0739000	+	0.101715i
$86$	−14.6934	+	3.12318i	−1.58443	+	0.336781i
$87$	−1.04493	+	1.80987i	−0.112028	+	0.194039i
$88$	−3.74803	+	2.73555i	−0.399541	+	0.291610i
$89$	−12.6666	+	7.31306i	−1.34266	+	0.775183i	−0.987197	−	0.159508i	$-0.949009\pi$
$89$	−12.6666	+	7.31306i	−1.34266	+	0.775183i	−0.355460	+	0.934691i	$0.615676\pi$
$90$	−5.96331	+	18.3532i	−0.628588	+	1.93460i
$91$	5.51376	+	11.1399i	0.577999	+	1.16778i
$92$	−0.806233	−	0.585763i	−0.0840556	−	0.0610700i
$93$	6.94335	−	7.71137i	0.719991	−	0.799631i
$94$	−6.21844	−	1.32177i	−0.641383	−	0.136330i
$95$	−1.12793	−	2.53337i	−0.115723	−	0.259918i
$96$	−16.0652	−	7.15270i	−1.63965	−	0.730019i
$97$	9.81655	+	3.18959i	0.996720	+	0.323854i	0.761554	−	0.648101i	$-0.224437\pi$
$97$	9.81655	+	3.18959i	0.996720	+	0.323854i	0.235166	+	0.971955i	$0.424437\pi$
$98$	−12.3447	+	2.32513i	−1.24701	+	0.234874i
$99$	−3.72357	−	17.3330i	−0.374233	−	1.74203i
$100$	0.581390	+	1.00700i	0.0581390	+	0.100700i
$101$	3.58942	+	3.98646i	0.357161	+	0.396667i	0.894770	−	0.446527i	$-0.147339\pi$
$101$	3.58942	+	3.98646i	0.357161	+	0.396667i	−0.537609	+	0.843194i	$0.680673\pi$
$102$	−0.312225	−	2.97062i	−0.0309149	−	0.294135i
$103$	9.47734	+	0.996109i	0.933830	+	0.0981495i	0.559207	−	0.829028i	$-0.311106\pi$
$103$	9.47734	+	0.996109i	0.933830	+	0.0981495i	0.374623	+	0.927177i	$0.377772\pi$
$104$	−6.25109	+	2.03110i	−0.612969	+	0.199166i
$105$	−15.2138	+	2.22850i	−1.48472	+	0.217479i
$106$	−6.74949	+	9.28987i	−0.655568	+	0.902312i
$107$	0.589718	−	1.32453i	0.0570102	−	0.128047i	−0.882794	−	0.469760i	$-0.844340\pi$
$107$	0.589718	−	1.32453i	0.0570102	−	0.128047i	0.939804	+	0.341713i	$0.111007\pi$
$108$	6.14461	−	5.53263i	0.591265	−	0.532378i
$109$	6.50025	+	3.75292i	0.622611	+	0.359465i	0.777885	−	0.628407i	$-0.216293\pi$
$109$	6.50025	+	3.75292i	0.622611	+	0.359465i	−0.155274	+	0.987871i	$0.549626\pi$
$110$	10.3825	+	5.96432i	0.989930	+	0.568676i
$111$		−	28.0246i		−	2.65997i
$112$	−0.533355	−	13.0894i	−0.0503973	−	1.23683i
$113$	−7.45715	+	5.41794i	−0.701509	+	0.509676i	−0.880423	−	0.474188i	$-0.842742\pi$
$113$	−7.45715	+	5.41794i	−0.701509	+	0.509676i	0.178914	+	0.983865i	$0.442742\pi$
$114$	−0.746966	+	7.10690i	−0.0699597	+	0.665622i
$115$	0.341557	−	1.60690i	0.0318504	−	0.149844i
$116$	−0.183557	+	0.863568i	−0.0170428	+	0.0801803i
$117$	2.62496	−	24.9748i	0.242678	−	2.30892i
$118$	−8.28491	+	6.01934i	−0.762688	+	0.554125i
$119$	1.28807	−	0.815331i	0.118077	−	0.0747413i
$120$		−	8.13082i		−	0.742239i
$121$	−10.9999	+	0.0477388i	−0.999991	+	0.00433989i
$122$	−21.0698	−	12.1647i	−1.90757	−	1.10134i
$123$	−5.92519	+	5.33507i	−0.534257	+	0.481047i
$124$	1.78298	−	4.00463i	0.160116	−	0.359626i
$125$	−7.03910	+	9.68849i	−0.629596	+	0.866565i
$126$	23.5860	+	9.37013i	2.10121	+	0.834758i
$127$	9.48419	−	3.08160i	0.841586	−	0.273448i	0.143668	−	0.989626i	$-0.454110\pi$
$127$	9.48419	−	3.08160i	0.841586	−	0.273448i	0.697918	+	0.716178i	$0.254110\pi$
$128$	10.2854	+	1.08104i	0.909113	+	0.0955517i
$129$	2.52767	+	24.0491i	0.222549	+	2.11741i
$130$	11.3490	+	12.6043i	0.995369	+	1.10547i
$131$	−6.87588	−	11.9094i	−0.600749	−	1.04053i	−0.992708	−	0.120545i	$-0.961536\pi$
$131$	−6.87588	−	11.9094i	−0.600749	−	1.04053i	0.391959	−	0.919983i	$-0.371797\pi$
$132$	−5.86830	−	10.1134i	−0.510770	−	0.880263i
$133$	−3.41977	+	1.26728i	−0.296532	+	0.109887i
$134$	2.86186	+	0.929874i	0.247227	+	0.0803289i
$135$	12.4518	+	5.54390i	1.07168	+	0.477143i
$136$	0.327873	+	0.736415i	0.0281149	+	0.0631471i
$137$	16.5515	+	3.51813i	1.41409	+	0.300574i	0.850715	−	0.525627i	$-0.176169\pi$
$137$	16.5515	+	3.51813i	1.41409	+	0.300574i	0.563375	+	0.826201i	$0.309503\pi$
$138$	−2.83265	+	3.14598i	−0.241131	+	0.267804i
$139$	−0.206041	−	0.149697i	−0.0174762	−	0.0126972i	0.579013	−	0.815318i	$-0.303438\pi$
$139$	−0.206041	−	0.149697i	−0.0174762	−	0.0126972i	−0.596489	+	0.802621i	$0.703438\pi$
$140$	−5.82158	+	2.88142i	−0.492014	+	0.243525i
$141$	−3.16248	+	9.73310i	−0.266329	+	0.819675i
$142$	10.5702	−	6.10273i	0.887035	−	0.512130i
$143$	−14.8293	−	4.78279i	−1.24009	−	0.399957i
$144$	−13.2335	+	22.9211i	−1.10279	+	1.91009i
$145$	−1.42357	+	0.302588i	−0.118221	+	0.0251286i
$146$	−6.56516	−	9.03616i	−0.543336	−	0.747838i
$147$	1.64523	+	20.1548i	0.135696	+	1.66234i
$148$	−3.65844	−	11.2595i	−0.300722	−	0.925526i
$149$	9.11952	+	8.21125i	0.747100	+	0.672692i	0.952002	−	0.306091i	$-0.0990211\pi$
$149$	9.11952	+	8.21125i	0.747100	+	0.672692i	−0.204902	+	0.978782i	$0.565688\pi$
$150$	4.51240	−	2.00905i	0.368436	−	0.164038i
$151$	−5.66217	+	0.595118i	−0.460781	+	0.0484301i	−0.332076	−	0.943253i	$-0.607749\pi$
$151$	−5.66217	+	0.595118i	−0.460781	+	0.0484301i	−0.128706	+	0.991683i	$0.541082\pi$
$152$	−0.400963	−	1.88638i	−0.0325224	−	0.153006i
$153$	−3.07987			−0.248992
$154$	8.70108	−	13.1248i	0.701153	−	1.05763i
$155$	7.22626			0.580427
$156$	−3.44358	−	16.2008i	−0.275707	−	1.29710i
$157$	7.38104	−	0.775779i	0.589071	−	0.0619139i	0.194697	−	0.980864i	$-0.437628\pi$
$157$	7.38104	−	0.775779i	0.589071	−	0.0619139i	0.394375	+	0.918950i	$0.370961\pi$
$158$	−12.5239	+	5.57600i	−0.996348	+	0.443603i
$159$	13.7371	+	12.3689i	1.08942	+	0.980917i
$160$	−3.78438	−	11.6471i	−0.299181	−	0.920786i
$161$	−2.08024	−	0.583424i	−0.163946	−	0.0459803i
$162$	−3.73035	−	5.13439i	−0.293084	−	0.403396i
$163$	10.7064	−	2.27571i	0.838589	−	0.178248i	0.231454	−	0.972846i	$-0.425652\pi$
$163$	10.7064	−	2.27571i	0.838589	−	0.178248i	0.607135	+	0.794598i	$0.292319\pi$
$164$	−1.68412	+	2.91699i	−0.131508	+	0.227778i
$165$	11.2957	−	15.6184i	0.879371	−	1.21589i
$166$	−1.85726	+	1.07229i	−0.144151	+	0.0832258i
$167$	−1.48944	+	4.58403i	−0.115256	+	0.354723i	−0.992000	−	0.126234i	$-0.959711\pi$
$167$	−1.48944	+	4.58403i	−0.115256	+	0.354723i	0.876744	+	0.480957i	$0.159711\pi$
$168$	−10.6713	−	0.683844i	−0.823306	−	0.0527597i
$169$	−7.33884	−	5.33198i	−0.564526	−	0.410152i
$170$	1.39187	−	1.54583i	0.106752	−	0.118560i
$171$	7.20724	+	1.53195i	0.551152	+	0.117151i
$172$	4.15502	+	9.33233i	0.316817	+	0.711583i
$173$	−15.5482	−	6.92252i	−1.18211	−	0.526310i	−0.280919	−	0.959731i	$-0.590639\pi$
$173$	−15.5482	−	6.92252i	−1.18211	−	0.526310i	−0.901191	+	0.433422i	$0.857306\pi$
$174$	3.56679	+	1.15892i	0.270398	+	0.0878576i
$175$	1.94049	+	1.60912i	0.146688	+	0.121638i
$176$	12.2278	+	10.9620i	0.921703	+	0.826290i
$177$	8.24267	+	14.2767i	0.619557	+	1.07310i
$178$	17.5628	+	19.5055i	1.31639	+	1.46200i
$179$	−2.08339	−	19.8222i	−0.155720	−	1.48158i	−0.741415	−	0.671046i	$-0.765845\pi$
$179$	−2.08339	−	19.8222i	−0.155720	−	1.48158i	0.585695	−	0.810531i	$-0.300822\pi$
$180$	13.0515	+	1.37177i	0.972805	+	0.102246i
$181$	−17.1058	+	5.55801i	−1.27146	+	0.413124i	−0.865566	−	0.500795i	$-0.833041\pi$
$181$	−17.1058	+	5.55801i	−1.27146	+	0.413124i	−0.405898	+	0.913919i	$0.633041\pi$
$182$	17.4970	−	13.8348i	1.29696	−	1.02551i
$183$	−23.0206	+	31.6852i	−1.70173	+	2.34224i
$184$	0.464682	−	1.04369i	0.0342568	−	0.0769420i
$185$	14.5033	−	13.0589i	1.06631	−	0.960107i
$186$	−16.1266	−	9.31069i	−1.18246	−	0.682693i
$187$	−0.393256	+	1.87007i	−0.0287577	+	0.136753i
$188$			4.32334i			0.315312i
$189$	8.32334	−	15.8761i	0.605434	−	1.15481i
$190$	−4.02605	+	2.92510i	−0.292081	+	0.212209i
$191$	2.54370	−	24.2017i	0.184055	−	1.75117i	−0.379591	−	0.925154i	$-0.623935\pi$
$191$	2.54370	−	24.2017i	0.184055	−	1.75117i	0.563647	−	0.826016i	$-0.309398\pi$
$192$	−0.613421	+	2.88592i	−0.0442698	+	0.208273i
$193$	3.86646	−	18.1903i	0.278314	−	1.30936i	−0.587592	−	0.809157i	$-0.699924\pi$
$193$	3.86646	−	18.1903i	0.278314	−	1.30936i	0.865906	−	0.500207i	$-0.166743\pi$
$194$	1.93616	−	18.4213i	0.139008	−	1.32257i
$195$	22.0887	−	16.0484i	1.58181	−	1.14925i
$196$	3.29209	+	7.88286i	0.235149	+	0.563062i
$197$			3.97471i			0.283187i	0.989925	+	0.141593i	$0.0452225\pi$
$197$			3.97471i			0.283187i	−0.989925	+	0.141593i	$0.954777\pi$
$198$	−29.0358	+	13.0031i	−2.06348	+	0.924093i
$199$	13.4921	+	7.78964i	0.956427	+	0.552193i	0.895071	−	0.445923i	$-0.147124\pi$
$199$	13.4921	+	7.78964i	0.956427	+	0.552193i	0.0613554	+	0.998116i	$0.480458\pi$
$200$	−0.990627	+	0.891965i	−0.0700479	+	0.0630714i
$201$	1.97026	−	4.42527i	0.138971	−	0.312134i
$202$	5.65830	−	7.78798i	0.398117	−	0.547961i
$203$	0.277402	+	1.89380i	0.0194698	+	0.132919i
$204$	−1.93189	+	0.627708i	−0.135259	+	0.0439484i
$205$	−5.52204	−	0.580389i	−0.385676	−	0.0405362i
$206$	−1.78756	−	17.0075i	−0.124545	−	1.18497i
$207$	2.92073	+	3.24380i	0.203005	+	0.225460i
$208$	11.6309	+	20.1454i	0.806460	+	1.39683i
$209$	1.85045	−	4.18057i	0.127998	−	0.289176i
$210$	9.58812	+	25.8738i	0.661643	+	1.78546i
$211$	−12.3212	−	4.00339i	−0.848223	−	0.275604i	−0.147522	−	0.989059i	$-0.547130\pi$
$211$	−12.3212	−	4.00339i	−0.848223	−	0.275604i	−0.700702	+	0.713454i	$0.747130\pi$
$212$	7.13386	+	3.17620i	0.489956	+	0.218142i
$213$	−7.99164	−	17.9495i	−0.547578	−	1.22988i
$214$	−2.54501	−	0.540958i	−0.173973	−	0.0369791i
$215$	−11.2681	+	12.5145i	−0.768480	+	0.853484i
$216$	7.66863	+	5.57158i	0.521784	+	0.379098i
$217$	0.607766	−	9.48408i	0.0412578	−	0.643822i
$218$	4.16232	−	12.8103i	0.281908	−	0.867623i
$219$	−15.5713	+	8.99010i	−1.05221	+	0.607494i
$220$	2.49943	−	7.74963i	0.168512	−	0.522480i
$221$	−1.35345	+	2.34424i	−0.0910428	+	0.157691i
$222$	−49.1923	+	10.4561i	−3.30157	+	0.701770i
$223$	0.691406	+	0.951639i	0.0463000	+	0.0637265i	0.831539	−	0.555466i	$-0.187460\pi$
$223$	0.691406	+	0.951639i	0.0463000	+	0.0637265i	−0.785239	+	0.619192i	$0.787460\pi$
$224$	−15.6045	+	3.98721i	−1.04262	+	0.266407i
$225$	−1.57383	−	4.84375i	−0.104922	−	0.322917i
$226$	12.2926	+	11.0683i	0.817689	+	0.736250i
$227$	−15.4048	+	6.85866i	−1.02245	+	0.455225i	−0.848312	−	0.529496i	$-0.822381\pi$
$227$	−15.4048	+	6.85866i	−1.02245	+	0.455225i	−0.174140	+	0.984721i	$0.555714\pi$
$228$	4.83307	−	0.507976i	0.320078	−	0.0336415i
$229$	1.22621	+	5.76885i	0.0810300	+	0.381216i	0.999911	−	0.0133179i	$-0.00423934\pi$
$229$	1.22621	+	5.76885i	0.0810300	+	0.381216i	−0.918881	+	0.394534i	$0.870906\pi$
$230$	−2.94807			−0.194390
$231$	−19.5483	−	16.1386i	−1.28618	−	1.06184i
$232$	−1.01212			−0.0664488
$233$	2.67058	+	12.5641i	0.174955	+	0.823101i	0.974833	+	0.222937i	$0.0715645\pi$
$233$	2.67058	+	12.5641i	0.174955	+	0.823101i	−0.799877	+	0.600164i	$0.795102\pi$
$234$	−44.8184	+	4.71060i	−2.92987	+	0.307942i
$235$	−6.51075	+	2.89877i	−0.424714	+	0.189095i
$236$	5.17542	+	4.65997i	0.336891	+	0.303338i
$237$	6.81962	+	20.9886i	0.442982	+	1.36336i
$238$	−1.91176	−	1.95677i	−0.123921	−	0.126839i
$239$	2.69800	+	3.71348i	0.174519	+	0.240205i	0.887312	−	0.461170i	$-0.152570\pi$
$239$	2.69800	+	3.71348i	0.174519	+	0.240205i	−0.712793	+	0.701375i	$0.752570\pi$
$240$	−28.1471	+	5.98286i	−1.81689	+	0.386192i
$241$	3.85526	−	6.67751i	0.248339	−	0.430136i	−0.714726	−	0.699405i	$-0.753449\pi$
$241$	3.85526	−	6.67751i	0.248339	−	0.430136i	0.963065	+	0.269268i	$0.0867819\pi$
$242$	4.18793	+	19.2906i	0.269210	+	1.24005i
$243$	8.75491	−	5.05465i	0.561628	−	0.324256i
$244$	−5.11276	+	15.7355i	−0.327311	+	1.00736i
$245$	−9.66390	+	10.2431i	−0.617404	+	0.654410i
$246$	11.5755	+	8.41011i	0.738028	+	0.536209i
$247$	4.33327	−	4.81258i	0.275719	−	0.306217i
$248$	4.91559	+	1.04484i	0.312140	+	0.0663475i
$249$	1.40418	+	3.15384i	0.0889864	+	0.199867i
$250$	19.6328	+	8.74109i	1.24169	+	0.552835i
$251$	17.6741	+	5.74265i	1.11558	+	0.362473i	0.808078	−	0.589076i	$-0.200508\pi$
$251$	17.6741	+	5.74265i	1.11558	+	0.362473i	0.307499	+	0.951549i	$0.400508\pi$
$252$	2.89808	−	17.0141i	0.182562	−	1.07179i
$253$	2.34255	−	1.35926i	0.147275	−	0.0854557i
$254$	−8.94783	−	15.4981i	−0.561437	−	0.972437i
$255$	−2.24062	−	2.48846i	−0.140313	−	0.155833i
$256$	−2.15349	−	20.4891i	−0.134593	−	1.28057i
$257$	19.1825	+	2.01617i	1.19657	+	0.125765i	0.681785	−	0.731552i	$-0.261204\pi$
$257$	19.1825	+	2.01617i	1.19657	+	0.125765i	0.514788	+	0.857317i	$0.327871\pi$
$258$	41.2710	−	13.4098i	2.56942	−	0.834856i
$259$	−15.9193	−	20.1332i	−0.989175	−	1.25102i
$260$	6.77963	−	9.33136i	0.420455	−	0.578707i
$261$	1.57284	−	3.53265i	0.0973561	−	0.218665i
$262$	−18.3394	+	16.5129i	−1.13301	+	1.02017i
$263$	11.3727	+	6.56600i	0.701268	+	0.404877i	0.807819	−	0.589430i	$-0.200648\pi$
$263$	11.3727	+	6.56600i	0.701268	+	0.404877i	−0.106552	+	0.994307i	$0.533981\pi$
$264$	9.94205	−	8.99101i	0.611891	−	0.553358i
$265$			12.8729i			0.790775i
$266$	3.50042	+	5.53000i	0.214625	+	0.339066i
$267$	34.1829	−	24.8353i	2.09196	−	1.51990i
$268$	0.213904	−	2.03516i	0.0130663	−	0.124317i
$269$	−4.93998	+	23.2408i	−0.301196	+	1.41701i	0.523784	+	0.851851i	$0.324520\pi$
$269$	−4.93998	+	23.2408i	−0.301196	+	1.41701i	−0.824979	+	0.565163i	$0.808813\pi$
$270$	5.08551	−	23.9255i	0.309494	−	1.45606i
$271$	−1.45215	+	13.8163i	−0.0882116	+	0.839278i	0.857547	+	0.514406i	$0.171988\pi$
$271$	−1.45215	+	13.8163i	−0.0882116	+	0.839278i	−0.945758	+	0.324871i	$0.894679\pi$
$272$	2.30805	−	1.67690i	0.139946	−	0.101677i
$273$	−19.2049	−	30.3400i	−1.16233	−	1.83626i
$274$		−	30.3659i		−	1.83447i
$275$	−3.14204	+	0.337137i	−0.189472	+	0.0203301i
$276$	2.49319	+	1.43944i	0.150072	+	0.0866443i
$277$	0.148588	−	0.133789i	0.00892780	−	0.00803863i	−0.664655	−	0.747151i	$-0.731421\pi$
$277$	0.148588	−	0.133789i	0.00892780	−	0.00803863i	0.673582	+	0.739112i	$0.264755\pi$
$278$	−0.185893	+	0.417522i	−0.0111491	+	0.0250413i
$279$	−11.2857	+	15.5335i	−0.675658	+	0.929964i
$280$	−4.61868	−	5.84128i	−0.276019	−	0.349083i
$281$	1.00492	−	0.326519i	0.0599486	−	0.0194785i	−0.278889	−	0.960323i	$-0.589966\pi$
$281$	1.00492	−	0.326519i	0.0599486	−	0.0194785i	0.338838	+	0.940845i	$0.389966\pi$
$282$	18.2647	+	1.91970i	1.08765	+	0.114316i
$283$	−1.63560	−	15.5617i	−0.0972266	−	0.925049i	−0.929036	−	0.369988i	$-0.879362\pi$
$283$	−1.63560	−	15.5617i	−0.0972266	−	0.925049i	0.831810	−	0.555061i	$-0.187305\pi$
$284$	−5.55402	−	6.16837i	−0.329571	−	0.366025i
$285$	4.00553	+	6.93778i	0.237267	+	0.410958i
$286$	−2.86245	+	27.8148i	−0.169260	+	1.64473i
$287$	−1.22616	+	7.19857i	−0.0723781	+	0.424918i
$288$	30.9468	+	10.0552i	1.82356	+	0.592509i
$289$	−15.2270	−	6.77949i	−0.895705	−	0.398794i
$290$	1.06228	+	2.38593i	0.0623794	+	0.140106i
$291$	−29.1661	−	6.19945i	−1.70975	−	0.363418i
$292$	−5.08253	+	5.64472i	−0.297432	+	0.330332i
$293$	2.16413	+	1.57233i	0.126430	+	0.0918565i	0.649203	−	0.760615i	$-0.275103\pi$
$293$	2.16413	+	1.57233i	0.126430	+	0.0918565i	−0.522773	+	0.852472i	$0.675103\pi$
$294$	34.7644	−	10.4078i	2.02750	−	0.606994i
$295$	−3.54761	+	10.9184i	−0.206550	+	0.635695i
$296$	11.7539	−	6.78613i	0.683183	−	0.394436i
$297$	6.99026	+	21.3560i	0.405616	+	1.23920i
$298$	11.0109	−	19.0714i	0.637843	−	1.10478i
$299$	3.75254	−	0.797627i	0.217015	−	0.0461280i
$300$	−1.97441	−	2.71755i	−0.113993	−	0.156898i
$301$	15.4769	+	15.8414i	0.892076	+	0.913081i
$302$	3.15722	+	9.71693i	0.181678	+	0.559146i
$303$	−11.5162	−	10.3692i	−0.661588	−	0.595696i
$304$	−6.23522	+	2.77610i	−0.357614	+	0.159220i
$305$	−27.1249	+	2.85094i	−1.55317	+	0.163245i
$306$	1.14912	+	5.40617i	0.0656907	+	0.309050i
$307$	−1.94883			−0.111226			−0.0556129	−	0.998452i	$-0.517711\pi$
$307$	−1.94883			−0.111226			−0.0556129	+	0.998452i	$0.517711\pi$
$308$	−9.96077	−	3.93215i	−0.567567	−	0.224055i
$309$	−27.5292			−1.56608
$310$	−2.69616	−	12.6845i	−0.153132	−	0.720429i
$311$	2.49357	−	0.262085i	0.141397	−	0.0148615i	−0.0335653	−	0.999437i	$-0.510686\pi$
$311$	2.49357	−	0.262085i	0.141397	−	0.0148615i	0.174963	+	0.984575i	$0.444019\pi$
$312$	17.3461	−	7.72296i	0.982027	−	0.437227i
$313$	−9.27255	−	8.34905i	−0.524116	−	0.471916i	0.364089	−	0.931364i	$-0.381380\pi$
$313$	−9.27255	−	8.34905i	−0.524116	−	0.471916i	−0.888205	+	0.459448i	$0.848047\pi$
$314$	−4.11566	−	12.6667i	−0.232260	−	0.714823i
$315$	27.5656	−	7.04346i	1.55314	−	0.396854i
$316$	5.47988	+	7.54240i	0.308267	+	0.424293i
$317$	−7.82085	+	1.66237i	−0.439263	+	0.0933682i	−0.422234	−	0.906487i	$-0.638754\pi$
$317$	−7.82085	+	1.66237i	−0.439263	+	0.0933682i	−0.0170286	+	0.999855i	$0.505421\pi$
$318$	16.5861	−	28.7279i	0.930101	−	1.61098i
$319$	−1.94416	−	1.40608i	−0.108852	−	0.0787255i
$320$	−1.77937	+	1.02732i	−0.0994698	+	0.0574289i
$321$	−1.29430	+	3.98345i	−0.0722408	+	0.222334i
$322$	−0.247948	+	3.86919i	−0.0138176	+	0.215621i
$323$	−0.642548	−	0.466839i	−0.0357524	−	0.0259756i
$324$	−2.88791	+	3.20735i	−0.160440	+	0.178186i
$325$	−4.37845	−	0.930667i	−0.242872	−	0.0516241i
$326$	−7.98924	−	17.9441i	−0.442483	−	0.993834i
$327$	−19.8085	−	8.81930i	−1.09541	−	0.487709i
$328$	−3.67239	−	1.19323i	−0.202774	−	0.0658852i
$329$	3.25690	+	8.78881i	0.179559	+	0.484543i
$330$	−31.6299	−	14.0004i	−1.74117	−	0.770695i
$331$	7.04778	+	12.2071i	0.387381	+	0.670964i	0.992096	−	0.125478i	$-0.0400464\pi$
$331$	7.04778	+	12.2071i	0.387381	+	0.670964i	−0.604715	+	0.796442i	$0.706713\pi$
$332$	0.975878	+	1.08382i	0.0535583	+	0.0594825i
$333$	5.42033	+	51.5710i	0.297032	+	2.82607i
$334$	8.60220	+	0.904127i	0.470691	+	0.0494716i
$335$	3.20828	−	1.04243i	0.175287	−	0.0569541i
$336$	5.48486	+	37.4448i	0.299224	+	2.04278i
$337$	10.1848	−	14.0182i	0.554802	−	0.763620i	−0.435852	−	0.900019i	$-0.643553\pi$
$337$	10.1848	−	14.0182i	0.554802	−	0.763620i	0.990654	+	0.136399i	$0.0435528\pi$
$338$	−6.62120	+	14.8715i	−0.360146	+	0.808901i
$339$	19.7884	−	17.8175i	1.07476	−	0.967716i
$340$	−1.22507	−	0.707296i	−0.0664389	−	0.0383585i
$341$	7.99076	+	8.83600i	0.432724	+	0.478496i
$342$		−	13.2227i		−	0.714999i
$343$	12.6308	+	13.5449i	0.681999	+	0.731353i
$344$	−9.47450	+	6.88363i	−0.510831	+	0.371140i
$345$	−0.496067	+	4.71976i	−0.0267074	+	0.254104i
$346$	−6.35015	+	29.8751i	−0.341386	+	1.60609i
$347$	−2.24522	+	10.5629i	−0.120530	+	0.567048i	0.875890	+	0.482510i	$0.160275\pi$
$347$	−2.24522	+	10.5629i	−0.120530	+	0.567048i	−0.996420	+	0.0845383i	$0.973058\pi$
$348$	0.266593	−	2.53646i	0.0142909	−	0.135969i
$349$	−9.73410	+	7.07224i	−0.521054	+	0.378568i	−0.817001	−	0.576636i	$-0.804365\pi$
$349$	−9.73410	+	7.07224i	−0.521054	+	0.378568i	0.295947	+	0.955204i	$0.404365\pi$
$350$	2.10053	−	4.00658i	0.112278	−	0.214160i
$351$			31.8302i			1.69897i
$352$	10.0569	−	17.5067i	0.536035	−	0.933111i
$353$	−0.0402959	−	0.0232648i	−0.00214473	−	0.00123826i	0.498927	−	0.866644i	$-0.333727\pi$
$353$	−0.0402959	−	0.0232648i	−0.00214473	−	0.00123826i	−0.501072	+	0.865406i	$0.667061\pi$
$354$	21.9849	−	19.7953i	1.16849	−	1.05211i
$355$	5.56534	−	12.4999i	0.295377	−	0.663428i
$356$	10.4917	−	14.4405i	0.556057	−	0.765347i
$357$	−3.45441	+	2.73140i	−0.182827	+	0.144561i
$358$	−34.0171	+	11.0528i	−1.79786	+	0.584159i
$359$	21.7857	+	2.28977i	1.14981	+	0.120849i	0.660197	−	0.751093i	$-0.270473\pi$
$359$	21.7857	+	2.28977i	1.14981	+	0.120849i	0.489609	+	0.871942i	$0.337140\pi$
$360$	1.57261	+	14.9624i	0.0828839	+	0.788587i
$361$	−11.4421	−	12.7077i	−0.602213	−	0.668826i
$362$	16.1384	+	27.9525i	0.848216	+	1.46915i
$363$	31.5883	−	3.45873i	1.65796	−	0.181536i
$364$	−11.6767	−	9.68272i	−0.612026	−	0.507513i
$365$	−11.9085	−	3.86930i	−0.623318	−	0.202528i
$366$	64.2070	+	28.5868i	3.35615	+	1.49426i
$367$	−9.83382	−	22.0871i	−0.513321	−	1.15294i	−0.965356	−	0.260938i	$-0.915968\pi$
$367$	−9.83382	−	22.0871i	−0.513321	−	1.15294i	0.452034	−	0.892001i	$-0.350698\pi$
$368$	−3.95496	−	0.840653i	−0.206167	−	0.0438221i
$369$	9.87171	−	10.9636i	0.513901	−	0.570745i
$370$	−28.3339	−	20.5858i	−1.47301	−	1.07020i
$371$	16.8950	+	1.08268i	0.877143	+	0.0562097i
$372$	−3.91324	+	12.0437i	−0.202892	+	0.624437i
$373$	−32.4952	+	18.7611i	−1.68254	+	0.971414i	−0.722574	+	0.691293i	$0.757041\pi$
$373$	−32.4952	+	18.7611i	−1.68254	+	0.971414i	−0.959965	+	0.280121i	$0.909625\pi$
$374$	3.42931	−	0.00744145i	0.177325	−	0.000384788i
$375$	17.2978	−	29.9606i	0.893253	−	1.54716i
$376$	−4.84800	+	1.03047i	−0.250017	+	0.0531427i
$377$	−1.99769	−	2.74959i	−0.102886	−	0.141611i
$378$	−30.9732	−	8.68672i	−1.59309	−	0.446797i
$379$	−4.13051	−	12.7124i	−0.212170	−	0.652992i	−0.999342	−	0.0362589i	$-0.988456\pi$
$379$	−4.13051	−	12.7124i	−0.212170	−	0.652992i	0.787173	−	0.616733i	$-0.211544\pi$
$380$	2.51500	+	2.26451i	0.129017	+	0.116167i
$381$	−26.3176	+	11.7173i	−1.34829	+	0.600297i
$382$	−43.4309	+	4.56477i	−2.22212	+	0.233554i
$383$	0.0692511	+	0.325801i	0.00353857	+	0.0166477i	0.979881	−	0.199580i	$-0.0639579\pi$
$383$	0.0692511	+	0.325801i	0.00353857	+	0.0166477i	−0.976343	+	0.216228i	$0.930625\pi$
$384$	−29.8765			−1.52463
$385$	−0.756992	−	17.6369i	−0.0385799	−	0.898861i
$386$	−33.3725			−1.69861
$387$	−9.30287	−	43.7665i	−0.472891	−	2.22478i
$388$	−12.5275	+	1.31669i	−0.635985	+	0.0668448i
$389$	−5.12540	+	2.28198i	−0.259868	+	0.115701i	−0.532536	−	0.846408i	$-0.678761\pi$
$389$	−5.12540	+	2.28198i	−0.259868	+	0.115701i	0.272667	+	0.962108i	$0.412094\pi$
$390$	−36.4116	−	32.7852i	−1.84377	−	1.66014i
$391$	−0.145394	−	0.447477i	−0.00735290	−	0.0226299i
$392$	−8.05482	+	5.57050i	−0.406830	+	0.281353i
$393$	23.3506	+	32.1394i	1.17788	+	1.62122i
$394$	6.97692	−	1.48299i	0.351492	−	0.0747120i
$395$	−7.68428	+	13.3096i	−0.386638	+	0.669677i
$396$	12.7550	+	17.4758i	0.640961	+	0.878194i
$397$	−0.206595	+	0.119278i	−0.0103687	+	0.00598639i	−0.505175	−	0.863017i	$-0.668572\pi$
$397$	−0.206595	+	0.119278i	−0.0103687	+	0.00598639i	0.494807	+	0.869003i	$0.335239\pi$
$398$	8.63940	−	26.5894i	0.433054	−	1.33280i
$399$	9.44235	−	4.67354i	0.472709	−	0.233970i
$400$	3.81672	+	2.77301i	0.190836	+	0.138650i
$401$	19.9927	−	22.2041i	0.998388	−	1.10882i	0.00432778	−	0.999991i	$-0.498622\pi$
$401$	19.9927	−	22.2041i	0.998388	−	1.10882i	0.994060	−	0.108832i	$-0.0347109\pi$
$402$	−8.50291	−	1.80735i	−0.424087	−	0.0901424i
$403$	6.86378	+	15.4163i	0.341909	+	0.767941i
$404$	−5.98053	−	2.66270i	−0.297543	−	0.132475i
$405$	−6.76645	−	2.19855i	−0.336228	−	0.109247i
$406$	3.22075	−	1.19352i	0.159843	−	0.0592335i
$407$	32.0056	+	3.29372i	1.58646	+	0.163264i
$408$	−1.16435	−	2.01672i	−0.0576440	−	0.0998424i
$409$	1.90917	+	2.12035i	0.0944026	+	0.104845i	0.788495	−	0.615041i	$-0.210861\pi$
$409$	1.90917	+	2.12035i	0.0944026	+	0.104845i	−0.694092	+	0.719886i	$0.744194\pi$
$410$	1.04153	+	9.90953i	0.0514377	+	0.489397i
$411$	−48.6148	−	5.10963i	−2.39799	−	0.252039i
$412$	−11.0605	+	3.59377i	−0.544912	+	0.177053i
$413$	14.0315	+	5.57435i	0.690444	+	0.274296i
$414$	4.60419	−	6.33713i	0.226284	−	0.311453i
$415$	−0.977865	+	2.19632i	−0.0480015	+	0.107813i
$416$	21.2531	−	19.1364i	1.04202	−	0.938238i
$417$	0.637159	+	0.367864i	0.0312018	+	0.0180144i
$418$	−8.02868	−	1.68835i	−0.392696	−	0.0825798i
$419$		−	12.7923i		−	0.624946i	−0.949927	−	0.312473i	$-0.898843\pi$
$419$		−	12.7923i		−	0.624946i	0.949927	−	0.312473i	$-0.101157\pi$
$420$	15.8553	−	10.0362i	0.773661	−	0.489719i
$421$	−12.9084	+	9.37849i	−0.629116	+	0.457079i	−0.856094	−	0.516820i	$-0.827115\pi$
$421$	−12.9084	+	9.37849i	−0.629116	+	0.457079i	0.226978	+	0.973900i	$0.427115\pi$
$422$	−2.43015	+	23.1213i	−0.118298	+	1.12553i
$423$	3.93710	−	18.5226i	0.191428	−	0.900600i
$424$	−1.86128	+	8.75665i	−0.0903919	+	0.425260i
$425$	−0.0573844	+	0.545976i	−0.00278355	+	0.0264837i
$426$	−28.5255	+	20.7250i	−1.38207	+	1.00413i
$427$	1.46037	+	35.8398i	0.0706721	+	1.73441i
$428$			1.76940i			0.0855274i
$429$	44.0490	+	9.26304i	2.12670	+	0.447224i
$430$	26.1713	+	15.1100i	1.26209	+	0.728669i
$431$	−11.8380	+	10.6590i	−0.570217	+	0.513426i	−0.903036	−	0.429565i	$-0.858667\pi$
$431$	−11.8380	+	10.6590i	−0.570217	+	0.513426i	0.332819	+	0.942991i	$0.392000\pi$
$432$	13.6449	−	30.6468i	0.656488	−	1.47450i
$433$	7.87012	−	10.8323i	0.378214	−	0.520567i	−0.576896	−	0.816817i	$-0.695736\pi$
$433$	7.87012	−	10.8323i	0.378214	−	0.520567i	0.955110	+	0.296251i	$0.0957363\pi$
$434$	−16.8744	+	2.47174i	−0.809999	+	0.118648i
$435$	3.99854	−	1.29920i	0.191715	−	0.0622921i
$436$	−9.10982	−	0.957481i	−0.436281	−	0.0458550i
$437$	0.117661	+	1.11947i	0.00562848	+	0.0535515i
$438$	21.5903	+	23.9785i	1.03163	+	1.14574i
$439$	−6.51975	−	11.2925i	−0.311171	−	0.538963i	0.667446	−	0.744659i	$-0.267388\pi$
$439$	−6.51975	−	11.2925i	−0.311171	−	0.538963i	−0.978616	+	0.205695i	$0.934054\pi$
$440$	9.28584	+	0.955613i	0.442685	+	0.0455571i
$441$	−6.92576	−	36.7707i	−0.329798	−	1.75099i
$442$	4.61989	+	1.50109i	0.219746	+	0.0713997i
$443$	−17.4780	−	7.78169i	−0.830404	−	0.369719i	−0.0529014	−	0.998600i	$-0.516847\pi$
$443$	−17.4780	−	7.78169i	−0.830404	−	0.369719i	−0.777502	+	0.628880i	$0.783514\pi$
$444$	13.9107	+	31.2439i	0.660172	+	1.48277i
$445$	28.7813	+	6.11766i	1.36437	+	0.290005i
$446$	1.41247	−	1.56871i	0.0668824	−	0.0742804i
$447$	−28.6799	−	20.8372i	−1.35651	−	0.985564i
$448$	1.19865	+	2.42173i	0.0566308	+	0.114416i
$449$	8.51490	−	26.2062i	0.401843	−	1.23674i	−0.521660	−	0.853153i	$-0.674687\pi$
$449$	8.51490	−	26.2062i	0.401843	−	1.23674i	0.923503	−	0.383591i	$-0.125313\pi$
$450$	−7.91517	+	4.56982i	−0.373125	+	0.215424i
$451$	−5.39656	−	7.39393i	−0.254114	−	0.348166i
$452$	5.62447	−	9.74186i	0.264553	−	0.458219i
$453$	16.0877	−	3.41955i	0.755868	−	0.160665i
$454$	17.7868	+	24.4814i	0.834776	+	1.14897i
$455$	6.75256	−	24.0768i	0.316565	−	1.12874i
$456$	1.72159	+	5.29851i	0.0806208	+	0.248125i
$457$	7.76318	+	6.99000i	0.363146	+	0.326978i	0.830424	−	0.557132i	$-0.188098\pi$
$457$	7.76318	+	6.99000i	0.363146	+	0.326978i	−0.467278	+	0.884111i	$0.654765\pi$
$458$	9.66871	−	4.30479i	0.451789	−	0.201150i
$459$	3.88237	−	0.408053i	0.181213	−	0.0190463i
$460$	0.416830	+	1.96103i	0.0194348	+	0.0914336i
$461$	37.8146			1.76120			0.880601	−	0.473858i	$-0.157139\pi$
$461$	37.8146			1.76120			0.880601	+	0.473858i	$0.157139\pi$
$462$	−21.0350	+	40.3350i	−0.978636	+	1.87656i
$463$	10.3030			0.478821			0.239410	−	0.970918i	$-0.423046\pi$
$463$	10.3030			0.478821			0.239410	+	0.970918i	$0.423046\pi$
$464$	0.744742	+	3.50373i	0.0345738	+	0.162657i
$465$	−20.7611	+	2.18208i	−0.962771	+	0.101191i
$466$	21.0577	−	9.37548i	0.975478	−	0.434311i
$467$	−2.74060	−	2.46765i	−0.126820	−	0.114189i	0.603280	−	0.797529i	$-0.293860\pi$
$467$	−2.74060	−	2.46765i	−0.126820	−	0.114189i	−0.730100	+	0.683340i	$0.760527\pi$
$468$	9.47036	+	29.1468i	0.437768	+	1.34731i
$469$	−1.09830	−	4.29837i	−0.0507150	−	0.198480i
$470$	7.51750	+	10.3469i	0.346756	+	0.477269i
$471$	−20.9715	+	4.45763i	−0.966316	+	0.205397i
$472$	−3.99192	+	6.91420i	−0.183743	+	0.318252i
$473$	−27.7625	+	0.0602435i	−1.27652	+	0.00277000i
$474$	34.2975	−	19.8016i	1.57533	−	0.909520i
$475$	0.405858	−	1.24910i	0.0186221	−	0.0573128i
$476$	−1.03132	+	1.54836i	−0.0472706	+	0.0709687i
$477$	−27.6713	−	20.1044i	−1.26698	−	0.920518i
$478$	5.51173	−	6.12140i	0.252101	−	0.279986i
$479$	20.8451	+	4.43076i	0.952437	+	0.202447i	0.657826	−	0.753170i	$-0.271476\pi$
$479$	20.8451	+	4.43076i	0.952437	+	0.202447i	0.294612	+	0.955617i	$0.404810\pi$
$480$	14.3895	+	32.3195i	0.656790	+	1.47517i
$481$	41.6353	+	18.5372i	1.89840	+	0.845224i
$482$	−13.1596	−	4.27583i	−0.599405	−	0.194759i
$483$	6.15272	+	1.04802i	0.279958	+	0.0476865i
$484$	12.2398	−	5.51329i	0.556355	−	0.250604i
$485$	−10.3825	−	17.9829i	−0.471443	−	0.816563i
$486$	−12.1391	−	13.4818i	−0.550640	−	0.611548i
$487$	3.34387	+	31.8148i	0.151525	+	1.44167i	0.760944	+	0.648818i	$0.224736\pi$
$487$	3.34387	+	31.8148i	0.151525	+	1.44167i	−0.609418	+	0.792849i	$0.708597\pi$
$488$	−18.8637	−	1.98265i	−0.853918	−	0.0897504i
$489$	−30.0723	+	9.77108i	−1.35992	+	0.441864i
$490$	21.5857	+	13.1415i	0.975144	+	0.593673i
$491$	18.9744	−	26.1160i	0.856303	−	1.17860i	−0.126135	−	0.992013i	$-0.540257\pi$
$491$	18.9744	−	26.1160i	0.856303	−	1.17860i	0.982438	−	0.186587i	$-0.0597428\pi$
$492$	3.95766	−	8.88905i	0.178425	−	0.400749i
$493$	−0.309761	+	0.278910i	−0.0139509	+	0.0125615i
$494$	−10.0644	−	5.81070i	−0.452820	−	0.261436i
$495$	−17.7657	+	30.9258i	−0.798507	+	1.39001i
$496$		−	17.7855i		−	0.798594i
$497$	−15.9374	−	8.35552i	−0.714892	−	0.374796i
$498$	5.01212	−	3.64152i	0.224598	−	0.163180i
$499$	−4.25839	+	40.5159i	−0.190632	+	1.81374i	0.312926	+	0.949778i	$0.398691\pi$
$499$	−4.25839	+	40.5159i	−0.190632	+	1.81374i	−0.503557	+	0.863962i	$0.667976\pi$
$500$	3.03860	−	14.2955i	0.135890	−	0.639314i
$501$	2.89495	−	13.6197i	0.129337	−	0.608483i
$502$	3.48593	−	33.1664i	0.155585	−	1.48029i
$503$	−11.2045	+	8.14051i	−0.499582	+	0.362967i	−0.808857	−	0.588005i	$-0.799914\pi$
$503$	−11.2045	+	8.14051i	−0.499582	+	0.362967i	0.309275	+	0.950973i	$0.399914\pi$
$504$	19.7696	−	0.805554i	0.880608	−	0.0358822i
$505$		−	10.7917i		−	0.480226i
$506$	−3.25996	−	3.60479i	−0.144923	−	0.160253i
$507$	22.6946	+	13.1027i	1.00790	+	0.581912i
$508$	−9.04406	+	8.14331i	−0.401265	+	0.361301i
$509$	−2.51875	+	5.65722i	−0.111642	+	0.250752i	−0.960722	−	0.277512i	$-0.910490\pi$
$509$	−2.51875	+	5.65722i	−0.111642	+	0.250752i	0.849080	+	0.528264i	$0.177157\pi$
$510$	−3.53207	+	4.86147i	−0.156403	+	0.215270i
$511$	−6.07982	+	15.3038i	−0.268955	+	0.677001i
$512$	−15.4898	+	5.03293i	−0.684557	+	0.222426i
$513$	−9.28816	−	0.976225i	−0.410082	−	0.0431014i
$514$	−3.61809	−	34.4239i	−0.159587	−	1.51837i
$515$	−12.8280	−	14.2470i	−0.565271	−	0.627797i
$516$	−14.7554	−	25.5571i	−0.649571	−	1.12509i
$517$	−10.7441	−	4.75565i	−0.472523	−	0.209153i
$518$	−29.4007	+	35.4553i	−1.29179	+	1.55782i
$519$	46.7605	+	15.1934i	2.05256	+	0.666916i
$520$	12.0797	+	5.37823i	0.529730	+	0.235851i
$521$	11.9001	+	26.7281i	0.521354	+	1.17098i	0.961938	+	0.273268i	$0.0881047\pi$
$521$	11.9001	+	26.7281i	0.521354	+	1.17098i	−0.440584	+	0.897711i	$0.645229\pi$
$522$	−6.78779	−	1.44279i	−0.297093	−	0.0631492i
$523$	−13.1228	+	14.5743i	−0.573819	+	0.637291i	−0.958273	−	0.285853i	$-0.907723\pi$
$523$	−13.1228	+	14.5743i	−0.573819	+	0.637291i	0.384454	+	0.923144i	$0.374390\pi$
$524$	13.5773	+	9.86446i	0.593126	+	0.430931i
$525$	−6.06094	−	4.03705i	−0.264521	−	0.176191i
$526$	7.28228	−	22.4126i	0.317522	−	0.977234i
$527$	1.79236	−	1.03482i	0.0780763	−	0.0450774i
$528$	−38.4405	−	27.8014i	−1.67291	−	1.20990i
$529$	11.1666	−	19.3411i	0.485504	−	0.840917i
$530$	22.5961	−	4.80295i	0.981513	−	0.208627i
$531$	−17.9295	−	24.6779i	−0.778076	−	1.07093i
$532$	3.18358	−	3.11034i	0.138026	−	0.134850i
$533$	−4.00686	−	12.3318i	−0.173556	−	0.534151i
$534$	−56.3480	−	50.7359i	−2.43841	−	2.19556i
$535$	−2.66464	+	1.18637i	−0.115202	+	0.0512914i
$536$	2.33312	−	0.245221i	0.100776	−	0.0105919i
$537$	11.9712	+	56.3200i	0.516595	+	2.43039i
$538$	42.6383			1.83827
$539$	−23.2112	−	0.489846i	−0.999777	−	0.0210991i
$540$	−16.6341			−0.715816
$541$	−6.27392	−	29.5165i	−0.269737	−	1.26901i	−0.879297	−	0.476273i	$-0.841987\pi$
$541$	−6.27392	−	29.5165i	−0.269737	−	1.26901i	0.609560	−	0.792740i	$-0.291346\pi$
$542$	24.7939	−	2.60594i	1.06499	−	0.111935i
$543$	47.4667	−	21.1335i	2.03699	−	0.906926i
$544$	−2.60655	−	2.34695i	−0.111755	−	0.100625i
$545$	−4.66615	−	14.3609i	−0.199876	−	0.615155i
$546$	−46.0912	+	45.0309i	−1.97252	+	1.92715i
$547$	−11.1154	−	15.2991i	−0.475261	−	0.654141i	0.502324	−	0.864679i	$-0.332478\pi$
$547$	−11.1154	−	15.2991i	−0.475261	−	0.654141i	−0.977586	+	0.210538i	$0.932478\pi$
$548$	−20.1992	+	4.29347i	−0.862866	+	0.183408i
$549$	36.2344	−	62.7598i	1.54645	−	2.67852i
$550$	1.76410	+	5.38953i	0.0752216	+	0.229810i
$551$	0.863609	−	0.498605i	0.0367910	−	0.0212413i
$552$	−1.01987	+	3.13885i	−0.0434087	+	0.133598i
$553$	16.8218	+	11.2046i	0.715336	+	0.476469i
$554$	−0.290284	−	0.210903i	−0.0123330	−	0.00896043i
$555$	−37.7248	+	41.8976i	−1.60133	+	1.77846i
$556$	0.304016	+	0.0646205i	0.0128931	+	0.00274052i
$557$	−13.8004	−	30.9961i	−0.584740	−	1.31335i	−0.927464	−	0.373911i	$-0.878016\pi$
$557$	−13.8004	−	30.9961i	−0.584740	−	1.31335i	0.342725	−	0.939436i	$-0.388650\pi$
$558$	31.4771	+	14.0145i	1.33253	+	0.593281i
$559$	−37.4011	−	12.1523i	−1.58190	−	0.513989i
$560$	−16.8227	+	20.2870i	−0.710889	+	0.857284i
$561$	0.565131	−	5.49146i	0.0238598	−	0.231850i
$562$	−0.948090	−	1.64214i	−0.0399928	−	0.0692695i
$563$	23.4280	+	26.0194i	0.987371	+	1.09659i	0.995322	+	0.0966179i	$0.0308025\pi$
$563$	23.4280	+	26.0194i	0.987371	+	1.09659i	−0.00795080	+	0.999968i	$0.502531\pi$
$564$	−1.30550	−	12.4210i	−0.0549713	−	0.523017i
$565$	18.4419	+	1.93833i	0.775859	+	0.0815460i
$566$	−26.7057	+	8.67720i	−1.12252	+	0.364730i
$567$	−3.45458	+	8.69570i	−0.145079	+	0.365185i
$568$	5.59312	−	7.69828i	0.234682	−	0.323012i
$569$	11.8947	−	26.7160i	0.498653	−	1.11999i	−0.472455	−	0.881355i	$-0.656632\pi$
$569$	11.8947	−	26.7160i	0.498653	−	1.11999i	0.971108	−	0.238639i	$-0.0767012\pi$
$570$	10.6836	−	9.61954i	0.447486	−	0.402918i
$571$	13.0386	+	7.52785i	0.545649	+	0.315031i	0.747365	−	0.664413i	$-0.231319\pi$
$571$	13.0386	+	7.52785i	0.545649	+	0.315031i	−0.201716	+	0.979444i	$0.564652\pi$
$572$	18.9069	−	2.02869i	0.790538	−	0.0848237i
$573$			70.2995i			2.93680i
$574$	13.0933	−	0.533515i	0.546505	−	0.0222685i
$575$	0.629457	−	0.457327i	0.0262502	−	0.0190719i
$576$	0.570646	−	5.42933i	0.0237769	−	0.226222i
$577$	4.68594	−	22.0456i	0.195078	−	0.917772i	−0.766287	−	0.642498i	$-0.777898\pi$
$577$	4.68594	−	22.0456i	0.195078	−	0.917772i	0.961366	−	0.275274i	$-0.0887685\pi$
$578$	−6.21894	+	29.2578i	−0.258674	+	1.21697i
$579$	−5.61553	+	53.4282i	−0.233374	+	2.22040i
$580$	1.43690	−	1.04397i	0.0596641	−	0.0433485i
$581$	2.80031	+	1.46812i	0.116177	+	0.0609078i
$582$			53.5091i			2.21803i
$583$	−15.7405	+	14.2348i	−0.651904	+	0.589543i
$584$	−7.54116	−	4.35389i	−0.312056	−	0.180165i
$585$	−37.5439	+	33.8046i	−1.55225	+	1.39765i
$586$	1.95250	−	4.38540i	0.0806572	−	0.181159i
$587$	−3.78610	+	5.21112i	−0.156269	+	0.215086i	−0.879972	−	0.475026i	$-0.842439\pi$
$587$	−3.78610	+	5.21112i	−0.156269	+	0.215086i	0.723703	+	0.690112i	$0.242439\pi$
$588$	−11.8385	−	21.6534i	−0.488213	−	0.892971i
$589$	−4.70905	+	1.53006i	−0.194033	+	0.0630451i
$590$	20.4890	+	2.15349i	0.843521	+	0.0886576i
$591$	−1.20022	−	11.4194i	−0.0493706	−	0.469730i
$592$	−32.1410	−	35.6962i	−1.32099	−	1.46710i
$593$	−20.6673	−	35.7968i	−0.848704	−	1.47000i	−0.882365	−	0.470565i	$-0.844050\pi$
$593$	−20.6673	−	35.7968i	−0.848704	−	1.47000i	0.0336616	−	0.999433i	$-0.489283\pi$
$594$	34.8787	−	20.2383i	1.43109	−	0.830386i
$595$	−3.02325	−	0.514962i	−0.123941	−	0.0211114i
$596$	−14.2430	−	4.62782i	−0.583415	−	0.189563i
$597$	−41.1149	−	18.3055i	−1.68272	−	0.749196i
$598$	−2.80019	−	6.28934i	−0.114508	−	0.257190i
$599$	37.2804	+	7.92420i	1.52324	+	0.323774i	0.892079	−	0.451880i	$-0.149247\pi$
$599$	37.2804	+	7.92420i	1.52324	+	0.323774i	0.631158	+	0.775654i	$0.282580\pi$
$600$	2.57673	−	2.86175i	0.105195	−	0.116830i
$601$	36.9913	+	26.8757i	1.50891	+	1.09628i	0.966660	+	0.256064i	$0.0824257\pi$
$601$	36.9913	+	26.8757i	1.50891	+	1.09628i	0.542245	+	0.840220i	$0.317574\pi$
$602$	22.0322	−	33.0776i	0.897967	−	1.34814i
$603$	−2.76978	+	8.52449i	−0.112794	+	0.347144i
$604$	6.01722	−	3.47404i	0.244837	−	0.141357i
$605$	16.5095	+	14.7360i	0.671205	+	0.599102i
$606$	−13.9046	+	24.0835i	−0.564836	+	0.978325i
$607$	−41.3262	+	8.78416i	−1.67738	+	0.356538i	−0.945682	−	0.325092i	$-0.894605\pi$
$607$	−41.3262	+	8.78416i	−1.67738	+	0.356538i	−0.731697	+	0.681630i	$0.761271\pi$
$608$	4.93224	+	6.78865i	0.200029	+	0.275316i
$609$	−1.36884	−	5.35714i	−0.0554681	−	0.217082i
$610$	15.1248	+	46.5494i	0.612386	+	1.88473i
$611$	−12.3683	−	11.1365i	−0.500369	−	0.450534i
$612$	3.43367	−	1.52877i	0.138798	−	0.0617967i
$613$	35.8988	−	3.77311i	1.44994	−	0.152395i	0.653413	−	0.757001i	$-0.273336\pi$
$613$	35.8988	−	3.77311i	1.44994	−	0.152395i	0.796524	+	0.604607i	$0.206670\pi$
$614$	0.727122	+	3.42084i	0.0293443	+	0.138054i
$615$	16.0401			0.646798
$616$	2.03518	−	12.1068i	0.0819997	−	0.487797i
$617$	−13.7471			−0.553439			−0.276720	−	0.960951i	$-0.589247\pi$
$617$	−13.7471			−0.553439			−0.276720	+	0.960951i	$0.589247\pi$
$618$	10.2713	+	48.3228i	0.413173	+	1.94383i
$619$	−23.7021	+	2.49119i	−0.952669	+	0.100130i	−0.568094	−	0.822964i	$-0.692319\pi$
$619$	−23.7021	+	2.49119i	−0.952669	+	0.100130i	−0.384576	+	0.923093i	$0.625652\pi$
$620$	−8.05638	+	3.58693i	−0.323552	+	0.144055i
$621$	−4.11155	−	3.70205i	−0.164991	−	0.148558i
$622$	−1.39041	−	4.27925i	−0.0557505	−	0.171582i
$623$	10.4498	−	37.2595i	0.418661	−	1.49277i
$624$	−39.4989	−	54.3656i	−1.58122	−	2.17637i
$625$	18.9058	−	4.01855i	0.756232	−	0.160742i
$626$	−11.1957	+	19.3915i	−0.447469	+	0.775038i
$627$	−4.05396	+	12.5696i	−0.161900	+	0.501980i
$628$	−7.84387	+	4.52866i	−0.313004	+	0.180713i
$629$	1.72726	−	5.31595i	0.0688703	−	0.211961i
$630$	−22.6485	−	45.7586i	−0.902337	−	1.82307i
$631$	−9.02470	−	6.55683i	−0.359267	−	0.261023i	0.393479	−	0.919334i	$-0.371271\pi$
$631$	−9.02470	−	6.55683i	−0.359267	−	0.261023i	−0.752747	+	0.658310i	$0.771271\pi$
$632$	−7.15158	+	7.94263i	−0.284474	+	0.315941i
$633$	36.6076	+	7.78118i	1.45502	+	0.309274i
$634$	5.83602	+	13.1079i	0.231778	+	0.520582i
$635$	−18.3274	−	8.15990i	−0.727302	−	0.323816i
$636$	−21.4547	−	6.97106i	−0.850734	−	0.276420i
$637$	−31.0316	−	10.8874i	−1.22952	−	0.431373i
$638$	−1.74276	+	3.93726i	−0.0689964	+	0.155878i
$639$	18.1779	+	31.4851i	0.719109	+	1.24553i
$640$	−13.9218	−	15.4618i	−0.550309	−	0.611180i
$641$	1.53462	+	14.6010i	0.0606139	+	0.576703i	0.982109	+	0.188313i	$0.0603019\pi$
$641$	1.53462	+	14.6010i	0.0606139	+	0.576703i	−0.921495	+	0.388390i	$0.873031\pi$
$642$	7.47516	+	0.785671i	0.295021	+	0.0310080i
$643$	41.6038	−	13.5179i	1.64069	−	0.533094i	0.664000	−	0.747733i	$-0.268858\pi$
$643$	41.6038	−	13.5179i	1.64069	−	0.533094i	0.976693	+	0.214639i	$0.0688575\pi$
$644$	2.60881	−	0.382135i	0.102801	−	0.0150582i
$645$	28.5944	−	39.3568i	1.12590	−	1.54967i
$646$	−0.579716	+	1.30206i	−0.0228086	+	0.0512290i
$647$	−27.1714	+	24.4653i	−1.06822	+	0.961829i	−0.999359	−	0.0357973i	$-0.988603\pi$
$647$	−27.1714	+	24.4653i	−1.06822	+	0.961829i	−0.0688602	+	0.997626i	$0.521936\pi$
$648$	−4.28492	−	2.47390i	−0.168328	−	0.0971840i
$649$	−17.2736	+	7.73564i	−0.678047	+	0.303651i
$650$			8.03284i			0.315074i
$651$	1.11775	+	27.4313i	0.0438079	+	1.07512i
$652$	−10.8067	+	7.85151i	−0.423222	+	0.307489i
$653$	0.804780	−	7.65697i	0.0314935	−	0.299641i	−0.967426	−	0.253156i	$-0.918531\pi$
$653$	0.804780	−	7.65697i	0.0314935	−	0.299641i	0.998919	−	0.0464847i	$-0.0148019\pi$
$654$	−8.09010	+	38.0609i	−0.316348	+	1.48830i
$655$	−5.75195	+	27.0608i	−0.224747	+	1.05735i
$656$	−1.42848	+	13.5910i	−0.0557726	+	0.530641i
$657$	26.9156	−	19.5553i	1.05008	−	0.762927i
$658$	14.2121	−	8.99608i	0.554044	−	0.350704i
$659$			49.2350i			1.91793i	0.283533	+	0.958963i	$0.408494\pi$
$659$			49.2350i			1.91793i	−0.283533	+	0.958963i	$0.591506\pi$
$660$	−4.84075	+	23.0195i	−0.188426	+	0.896031i
$661$	9.22894	+	5.32833i	0.358964	+	0.207248i	0.668626	−	0.743599i	$-0.266883\pi$
$661$	9.22894	+	5.32833i	0.358964	+	0.207248i	−0.309662	+	0.950847i	$0.600216\pi$
$662$	18.7979	−	16.9257i	0.730602	−	0.657837i
$663$	3.18058	−	7.14370i	0.123524	−	0.277438i
$664$	−0.982748	+	1.35264i	−0.0381380	+	0.0524925i
$665$	6.81860	+	2.70885i	0.264414	+	0.105045i
$666$	88.5017	−	28.7559i	3.42937	−	1.11427i
$667$	0.587513	+	0.0617501i	0.0227486	+	0.00239097i
$668$	−0.614854	−	5.84994i	−0.0237894	−	0.226341i
$669$	−2.27377	−	2.52528i	−0.0879091	−	0.0976330i
$670$	−3.02684	−	5.24264i	−0.116937	−	0.202541i
$671$	−33.4806	−	30.0148i	−1.29250	−	1.15871i
$672$	43.6278	−	16.1673i	1.68298	−	0.623667i
$673$	−15.7291	−	5.11069i	−0.606312	−	0.197003i	−0.0102583	−	0.999947i	$-0.503265\pi$
$673$	−15.7291	−	5.11069i	−0.606312	−	0.197003i	−0.596053	+	0.802945i	$0.703265\pi$
$674$	−28.4066	−	12.6474i	−1.09418	−	0.487160i
$675$	2.62567	+	5.89735i	0.101062	+	0.226989i
$676$	10.8285	+	2.30168i	0.416483	+	0.0885261i
$677$	8.72612	−	9.69133i	0.335372	−	0.372468i	−0.551745	−	0.834013i	$-0.686038\pi$
$677$	8.72612	−	9.69133i	0.335372	−	0.372468i	0.887117	+	0.461545i	$0.152705\pi$
$678$	−38.6588	−	28.0872i	−1.48468	−	1.07868i
$679$	−24.4749	+	12.1140i	−0.939259	+	0.464891i
$680$	0.501132	−	1.54233i	0.0192175	−	0.0591455i
$681$	42.1869	−	24.3566i	1.61661	−	0.933348i
$682$	12.5287	−	17.3232i	0.479748	−	0.663338i
$683$	−7.73841	+	13.4033i	−0.296102	+	0.512864i	−0.975241	−	0.221146i	$-0.929020\pi$
$683$	−7.73841	+	13.4033i	−0.296102	+	0.512864i	0.679139	+	0.734010i	$0.262354\pi$
$684$	−8.79560	+	1.86956i	−0.336308	+	0.0714845i
$685$	−20.0092	−	27.5403i	−0.764511	−	1.05226i
$686$	19.0630	−	27.2249i	0.727830	−	1.03945i
$687$	−5.26488	−	16.2036i	−0.200868	−	0.618207i
$688$	30.8012	+	27.7335i	1.17429	+	1.05733i
$689$	−27.4627	+	12.2272i	−1.04624	+	0.465818i
$690$	8.46982	−	0.890214i	0.322440	−	0.0338899i
$691$	−9.15726	−	43.0815i	−0.348359	−	1.63890i	−0.708292	−	0.705920i	$-0.750534\pi$
$691$	−9.15726	−	43.0815i	−0.348359	−	1.63890i	0.359933	−	0.932978i	$-0.382799\pi$
$692$	20.7705			0.789576
$693$	39.0943	+	25.9175i	1.48507	+	0.984525i
$694$	19.3791			0.735622
$695$	0.106525	+	0.501161i	0.00404073	+	0.0190101i
$696$	2.90782	−	0.305624i	0.110221	−	0.0115846i
$697$	−1.45276	+	0.646813i	−0.0550274	+	0.0244998i
$698$	16.0459	+	14.4478i	0.607348	+	0.546859i
$699$	−11.4665	−	35.2902i	−0.433703	−	1.33480i
$700$	−2.96214	−	0.830759i	−0.111958	−	0.0313997i
$701$	14.2779	+	19.6518i	0.539269	+	0.742240i	0.988507	−	0.151172i	$-0.0483048\pi$
$701$	14.2779	+	19.6518i	0.539269	+	0.742240i	−0.449239	+	0.893412i	$0.648305\pi$
$702$	55.8723	−	11.8760i	2.10877	−	0.448232i
$703$	−6.68618	+	11.5808i	−0.252174	+	0.436778i
$704$	−3.22378	−	1.03974i	−0.121501	−	0.0391868i
$705$	17.8301	−	10.2942i	0.671519	−	0.387702i
$706$	−0.0258028	+	0.0794127i	−0.000971100	+	0.00298874i
$707$	−14.1636	−	0.907640i	−0.532676	−	0.0341353i
$708$	−16.2761	−	11.8253i	−0.611695	−	0.444423i
$709$	15.3239	−	17.0189i	0.575501	−	0.639158i	−0.383169	−	0.923678i	$-0.625167\pi$
$709$	15.3239	−	17.0189i	0.575501	−	0.639158i	0.958670	+	0.284520i	$0.0918341\pi$
$710$	−24.0180	−	5.10518i	−0.901378	−	0.191594i
$711$	−16.6090	−	37.3044i	−0.622886	−	1.39902i
$712$	18.6937	+	8.32296i	0.700575	+	0.311916i
$713$	−2.78965	−	0.906412i	−0.104473	−	0.0339454i
$714$	6.08336	+	5.04453i	0.227664	+	0.188787i
$715$	15.7321	+	27.1127i	0.588346	+	1.01396i
$716$	12.1619	+	21.0651i	0.454513	+	0.787239i
$717$	−8.87270	−	9.85413i	−0.331357	−	0.368009i
$718$	−4.10909	−	39.0954i	−0.153350	−	1.45903i
$719$	38.7687	+	4.07476i	1.44583	+	0.151963i	0.794699	−	0.607003i	$-0.207629\pi$
$719$	38.7687	+	4.07476i	1.44583	+	0.151963i	0.651130	+	0.758966i	$0.274295\pi$
$720$	50.6394	−	16.4537i	1.88722	−	0.613195i
$721$	−19.7773	+	15.6379i	−0.736546	+	0.582385i
$722$	−18.0370	+	24.8259i	−0.671269	+	0.923923i
$723$	−9.05981	+	20.3487i	−0.336938	+	0.756775i
$724$	16.3120	−	14.6874i	0.606230	−	0.545852i
$725$	−0.596937	−	0.344641i	−0.0221697	−	0.0127997i
$726$	−17.8570	−	54.1574i	−0.662736	−	2.00997i
$727$			46.1620i			1.71205i	0.516933	+	0.856026i	$0.327074\pi$
$727$			46.1620i			1.71205i	−0.516933	+	0.856026i	$0.672926\pi$
$728$	8.07461	−	15.4016i	0.299265	−	0.570823i
$729$	−32.2099	+	23.4019i	−1.19296	+	0.866735i
$730$	−2.34876	+	22.3469i	−0.0869314	+	0.827097i
$731$	−1.00277	+	4.71765i	−0.0370887	+	0.174489i
$732$	9.93742	−	46.7519i	0.367297	−	1.72800i
$733$	−2.20052	+	20.9366i	−0.0812782	+	0.773310i	0.875642	+	0.482960i	$0.160438\pi$
$733$	−2.20052	+	20.9366i	−0.0812782	+	0.773310i	−0.956920	+	0.290350i	$0.906228\pi$
$734$	−35.1011	+	25.5024i	−1.29560	+	0.941312i
$735$	24.6713	−	32.3467i	0.910016	−	1.19313i
$736$			4.97098i			0.183233i
$737$	4.82234	+	2.77024i	0.177633	+	0.102043i
$738$	−22.9280	−	13.2375i	−0.843991	−	0.487279i
$739$	17.8957	−	16.1134i	0.658305	−	0.592741i	−0.270764	−	0.962646i	$-0.587276\pi$
$739$	17.8957	−	16.1134i	0.658305	−	0.592741i	0.929070	+	0.369905i	$0.120610\pi$
$740$	−9.68733	+	21.7581i	−0.356113	+	0.799843i
$741$	−10.9963	+	15.1351i	−0.403958	+	0.556000i
$742$	−4.40317	−	30.0602i	−0.161646	−	1.10354i
$743$	−21.1622	+	6.87601i	−0.776365	+	0.252256i	−0.670287	−	0.742102i	$-0.733829\pi$
$743$	−21.1622	+	6.87601i	−0.776365	+	0.252256i	−0.106078	+	0.994358i	$0.533829\pi$
$744$	−14.4380	−	1.51750i	−0.529323	−	0.0556341i
$745$	−2.58054	−	24.5522i	−0.0945436	−	0.899522i
$746$	45.0561	+	50.0399i	1.64962	+	1.83209i
$747$	−3.19398	−	5.53214i	−0.116862	−	0.202410i
$748$	−0.489823	−	2.28010i	−0.0179097	−	0.0833686i
$749$	1.33294	+	3.59698i	0.0487047	+	0.131431i
$750$	−59.0446	−	19.1848i	−2.15600	−	0.700528i
$751$	31.1338	+	13.8617i	1.13609	+	0.505819i	0.886590	−	0.462557i	$-0.153068\pi$
$751$	31.1338	+	13.8617i	1.13609	+	0.505819i	0.249498	+	0.968375i	$0.419734\pi$
$752$	7.13456	+	16.0245i	0.260171	+	0.584353i
$753$	−52.5117	−	11.1617i	−1.91363	−	0.406755i
$754$	−4.08108	+	4.53249i	−0.148624	+	0.165064i
$755$	9.26625	+	6.73232i	0.337233	+	0.245014i
$756$	−1.39901	+	21.8313i	−0.0508815	+	0.793997i
$757$	−3.02432	+	9.30790i	−0.109921	+	0.338301i	−0.990854	−	0.134940i	$-0.956916\pi$
$757$	−3.02432	+	9.30790i	−0.109921	+	0.338301i	0.880933	+	0.473241i	$0.156916\pi$
$758$	−20.7733	+	11.9935i	−0.754520	+	0.435622i
$759$	−6.31970	+	4.61252i	−0.229391	+	0.167424i
$760$	−1.93987	+	3.35996i	−0.0703666	+	0.121878i
$761$	2.87431	−	0.610954i	0.104194	−	0.0221471i	−0.155520	−	0.987833i	$-0.549705\pi$
$761$	2.87431	−	0.610954i	0.104194	−	0.0221471i	0.259713	+	0.965686i	$0.416372\pi$
$762$	30.3870	+	41.8241i	1.10081	+	1.51513i
$763$	−19.2404	+	4.91625i	−0.696550	+	0.177980i
$764$	9.17718	+	28.2445i	0.332019	+	1.02185i
$765$	4.60450	+	4.14591i	0.166476	+	0.149896i
$766$	0.546049	−	0.243117i	0.0197296	−	0.00878417i
$767$	−26.6627	+	2.80237i	−0.962735	+	0.101188i
$768$	12.3740	+	58.2149i	0.446507	+	2.10065i
$769$	−33.5697			−1.21055			−0.605277	−	0.796015i	$-0.706938\pi$
$769$	−33.5697			−1.21055			−0.605277	+	0.796015i	$0.706938\pi$
$770$	−30.6762	+	7.90922i	−1.10549	+	0.285029i
$771$	−55.7203			−2.00672
$772$	4.71856	+	22.1991i	0.169825	+	0.798963i
$773$	36.2358	−	3.80854i	1.30331	−	0.136984i	0.572693	−	0.819770i	$-0.305899\pi$
$773$	36.2358	−	3.80854i	1.30331	−	0.136984i	0.730618	+	0.682786i	$0.239232\pi$
$774$	−73.3537	+	32.6591i	−2.63664	+	1.17391i
$775$	2.54338	+	2.29007i	0.0913609	+	0.0822617i
$776$	−4.46242	−	13.7339i	−0.160191	−	0.493018i
$777$	51.8156	+	53.0356i	1.85887	+	1.90264i
$778$	5.91794	+	8.14534i	0.212168	+	0.292025i
$779$	3.72137	−	0.791001i	0.133332	−	0.0283406i
$780$	−16.6602	+	28.8562i	−0.596529	+	1.03322i
$781$	21.4386	−	7.01729i	0.767133	−	0.251098i
$782$	−0.731222	+	0.422171i	−0.0261484	+	0.0150968i
$783$	−1.51462	+	4.66152i	−0.0541280	+	0.166589i
$784$	25.2108	+	23.7851i	0.900386	+	0.849469i
$785$	−12.0792	−	8.77606i	−0.431125	−	0.313231i
$786$	47.7029	−	52.9794i	1.70151	−	1.88971i
$787$	−2.87993	−	0.612149i	−0.102659	−	0.0218208i	0.156296	−	0.987710i	$-0.450045\pi$
$787$	−2.87993	−	0.612149i	−0.102659	−	0.0218208i	−0.258955	+	0.965890i	$0.583378\pi$
$788$	−1.97295	−	4.43131i	−0.0702833	−	0.157859i
$789$	−34.6564	−	15.4300i	−1.23380	−	0.549323i
$790$	26.2297	+	8.52255i	0.933211	+	0.303219i
$791$	4.09501	−	24.0411i	0.145602	−	0.854802i
$792$	−16.5565	+	18.4683i	−0.588308	+	0.656241i
$793$	−31.8464	−	55.1596i	−1.13090	−	1.95878i
$794$	0.286454	+	0.318139i	0.0101659	+	0.0112903i
$795$	−3.88716	−	36.9838i	−0.137863	−	1.31168i
$796$	−18.9085	−	1.98737i	−0.670196	−	0.0704404i
$797$	−14.6246	+	4.75183i	−0.518031	+	0.168318i	−0.556352	−	0.830947i	$-0.687799\pi$
$797$	−14.6246	+	4.75183i	−0.518031	+	0.168318i	0.0383206	+	0.999265i	$0.487799\pi$
$798$	−11.7266	−	14.8307i	−0.415117	−	0.525001i
$799$	−1.19977	+	1.65135i	−0.0424450	+	0.0584205i
$800$	2.35912	−	5.29867i	0.0834074	−	0.187336i
$801$	−58.1001	+	52.3136i	−2.05287	+	1.84841i
$802$	−46.4350	−	26.8092i	−1.63968	−	0.946667i
$803$	−8.43709	−	18.8399i	−0.297739	−	0.664845i
$804$			5.91161i			0.208486i
$805$	2.32467	+	3.67252i	0.0819337	+	0.129439i
$806$	24.4997	−	17.8001i	0.862967	−	0.626982i
$807$	7.17467	−	68.2624i	0.252560	−	2.40295i
$808$	1.56037	−	7.34096i	0.0548936	−	0.258254i
$809$	1.05210	−	4.94974i	0.0369899	−	0.174024i	−0.955775	−	0.294099i	$-0.904980\pi$
$809$	1.05210	−	4.94974i	0.0369899	−	0.174024i	0.992765	+	0.120076i	$0.0383137\pi$
$810$	−1.33457	+	12.6976i	−0.0468922	+	0.446149i
$811$	23.4051	−	17.0048i	0.821865	−	0.597120i	−0.0953814	−	0.995441i	$-0.530407\pi$
$811$	23.4051	−	17.0048i	0.821865	−	0.597120i	0.917246	+	0.398321i	$0.130407\pi$
$812$	−1.24930	−	1.97366i	−0.0438420	−	0.0692619i
$813$		−	40.1326i		−	1.40751i
$814$	−6.15993	−	57.4092i	−0.215905	−	2.01219i
$815$	−19.0698	−	11.0100i	−0.667987	−	0.385662i
$816$	−6.12468	+	5.51469i	−0.214407	+	0.193053i
$817$	4.69318	−	10.5411i	0.164194	−	0.368785i
$818$	3.00959	−	4.14234i	0.105228	−	0.144834i
$819$	41.2092	+	52.1175i	1.43997	+	1.82113i
$820$	6.44447	−	2.09394i	0.225051	−	0.0731234i
$821$	−32.8361	−	3.45122i	−1.14599	−	0.120448i	−0.487559	−	0.873090i	$-0.662112\pi$
$821$	−32.8361	−	3.45122i	−1.14599	−	0.120448i	−0.658430	+	0.752642i	$0.728779\pi$
$822$	9.16944	+	87.2414i	0.319821	+	3.04289i
$823$	−3.15708	−	3.50630i	−0.110049	−	0.122222i	0.685603	−	0.727975i	$-0.259538\pi$
$823$	−3.15708	−	3.50630i	−0.110049	−	0.122222i	−0.795652	+	0.605753i	$0.792872\pi$
$824$	−6.66618	−	11.5462i	−0.232228	−	0.402230i
$825$	8.92530	−	1.91738i	0.310739	−	0.0667547i
$826$	4.54957	−	26.7097i	0.158300	−	0.929348i
$827$	30.7669	+	9.99677i	1.06987	+	0.347622i	0.790437	−	0.612544i	$-0.209854\pi$
$827$	30.7669	+	9.99677i	1.06987	+	0.347622i	0.279433	+	0.960165i	$0.409854\pi$
$828$	−4.86640	−	2.16666i	−0.169119	−	0.0752966i
$829$	−2.17733	−	4.89036i	−0.0756218	−	0.169849i	0.871779	−	0.489900i	$-0.162967\pi$
$829$	−2.17733	−	4.89036i	−0.0756218	−	0.169849i	−0.947400	+	0.320051i	$0.896300\pi$
$830$	4.22011	+	0.897012i	0.146482	+	0.0311358i
$831$	−0.386495	+	0.429246i	−0.0134074	+	0.0148904i
$832$	−3.88177	−	2.82027i	−0.134576	−	0.0977753i
$833$	−0.930131	+	3.92454i	−0.0322271	+	0.135977i
$834$	0.407994	−	1.25568i	0.0141277	−	0.0434805i
$835$	8.39748	−	4.84829i	0.290607	−	0.167782i
$836$	0.0121069	+	5.57933i	0.000418726	+	0.192965i
$837$	12.1683	−	21.0762i	0.420599	−	0.728499i
$838$	−22.4547	+	4.77290i	−0.775686	+	0.164877i
$839$	15.9054	+	21.8918i	0.549114	+	0.755790i	0.989892	−	0.141826i	$-0.0452973\pi$
$839$	15.9054	+	21.8918i	0.549114	+	0.755790i	−0.440778	+	0.897616i	$0.645297\pi$
$840$	15.0333	+	15.3873i	0.518700	+	0.530913i
$841$	8.79977	+	27.0829i	0.303440	+	0.933893i
$842$	21.2785	+	19.1593i	0.733306	+	0.660272i
$843$	−2.78854	+	1.24154i	−0.0960426	+	0.0427609i
$844$	15.7237	−	1.65263i	0.541233	−	0.0568859i
$845$	3.79425	+	17.8505i	0.130526	+	0.614077i
$846$	−33.9822			−1.16833
$847$	20.7287	−	20.4284i	0.712247	−	0.701929i
$848$	31.6832			1.08801
$849$	9.39819	+	44.2150i	0.322545	+	1.51745i
$850$	0.979777	−	0.102979i	0.0336061	−	0.00353214i
$851$	−7.23693	+	3.22209i	−0.248079	+	0.110452i
$852$	17.8194	+	16.0446i	0.610481	+	0.549680i
$853$	−7.86547	−	24.2074i	−0.269308	−	0.828846i	−0.990669	−	0.136287i	$-0.956483\pi$
$853$	−7.86547	−	24.2074i	−0.269308	−	0.828846i	0.721361	−	0.692559i	$-0.243517\pi$
$854$	62.3657	−	15.9355i	2.13411	−	0.545301i
$855$	−8.71286	−	11.9922i	−0.297974	−	0.410125i
$856$	−1.98413	+	0.421740i	−0.0678162	+	0.0144148i
$857$	−1.85885	+	3.21962i	−0.0634971	+	0.109980i	−0.896026	−	0.444001i	$-0.853559\pi$
$857$	−1.85885	+	3.21962i	−0.0634971	+	0.109980i	0.832529	+	0.553981i	$0.186892\pi$
$858$	−0.175281	−	80.7764i	−0.00598401	−	2.75766i
$859$	−3.89561	+	2.24913i	−0.132916	+	0.0767394i	−0.564984	−	0.825102i	$-0.691118\pi$
$859$	−3.89561	+	2.24913i	−0.132916	+	0.0767394i	0.432067	+	0.901841i	$0.357784\pi$
$860$	6.35067	−	19.5453i	0.216556	−	0.666491i
$861$	1.34905	−	21.0518i	0.0459756	−	0.717442i
$862$	23.1269	+	16.8027i	0.787705	+	0.572301i
$863$	−10.1288	+	11.2492i	−0.344789	+	0.382927i	−0.890451	−	0.455078i	$-0.849611\pi$
$863$	−10.1288	+	11.2492i	−0.344789	+	0.382927i	0.545663	+	0.838005i	$0.316278\pi$
$864$	−40.3426	−	8.57509i	−1.37248	−	0.291730i
$865$	13.9265	+	31.2794i	0.473515	+	1.06353i
$866$	−21.9506	−	9.77305i	−0.745912	−	0.332102i
$867$	45.7944	+	14.8795i	1.55526	+	0.505334i
$868$	4.03007	+	10.8752i	0.136790	+	0.369130i
$869$	−24.7717	+	5.32159i	−0.840321	+	0.180523i
$870$	−3.77241	−	6.53400i	−0.127897	−	0.221523i
$871$	5.27124	+	5.85431i	0.178609	+	0.198366i
$872$	−1.09766	−	10.4436i	−0.0371716	−	0.353664i
$873$	54.8708	+	5.76715i	1.85709	+	0.195188i
$874$	1.92113	−	0.624214i	0.0649833	−	0.0211144i
$875$	−4.59211	−	31.3500i	−0.155242	−	1.05982i
$876$	12.8976	−	17.7520i	0.435770	−	0.599786i
$877$	−9.29679	+	20.8809i	−0.313930	+	0.705099i	−0.999743	−	0.0226792i	$-0.992780\pi$
$877$	−9.29679	+	20.8809i	−0.313930	+	0.705099i	0.685812	+	0.727778i	$0.259447\pi$
$878$	−17.3895	+	15.6576i	−0.586868	+	0.528419i
$879$	−6.69233	−	3.86382i	−0.225727	−	0.130323i
$880$	−3.52463	−	32.8487i	−0.118815	−	1.10733i
$881$			29.6337i			0.998385i	0.866491	+	0.499193i	$0.166370\pi$
$881$			29.6337i			0.998385i	−0.866491	+	0.499193i	$0.833630\pi$
$882$	−61.9606	+	25.8764i	−2.08632	+	0.871303i
$883$	41.3114	−	30.0145i	1.39024	−	1.01007i	0.394401	−	0.918938i	$-0.370952\pi$
$883$	41.3114	−	30.0145i	1.39024	−	1.01007i	0.995839	−	0.0911305i	$-0.0290480\pi$
$884$	0.345305	−	3.28535i	0.0116138	−	0.110498i
$885$	6.89532	−	32.4399i	0.231784	−	1.09046i
$886$	−7.13828	+	33.5830i	−0.239815	+	1.12824i
$887$	2.75181	−	26.1817i	0.0923968	−	0.879097i	−0.845918	−	0.533314i	$-0.820947\pi$
$887$	2.75181	−	26.1817i	0.0923968	−	0.879097i	0.938314	−	0.345783i	$-0.112387\pi$
$888$	−31.7199	+	23.0458i	−1.06445	+	0.773368i
$889$	−12.2509	+	23.3675i	−0.410881	+	0.783720i
$890$		−	52.8032i		−	1.76997i
$891$	−4.79399	−	10.7049i	−0.160605	−	0.358628i
$892$	−1.24320	−	0.717762i	−0.0416254	−	0.0240325i
$893$	3.62900	−	3.26757i	0.121440	−	0.109345i
$894$	−25.8754	+	58.1171i	−0.865403	+	1.94373i
$895$	−23.5685	+	32.4393i	−0.787809	+	1.08433i
$896$	−21.4637	+	16.9713i	−0.717051	+	0.566970i
$897$	−10.5402	+	3.42472i	−0.351927	+	0.114348i
$898$	−49.1773	−	5.16875i	−1.64107	−	0.172483i
$899$	0.271623	+	2.58432i	0.00905914	+	0.0861920i
$900$	4.15894	+	4.61897i	0.138631	+	0.153966i
$901$	1.84343	+	3.19291i	0.0614135	+	0.106371i
$902$	−10.9653	+	12.2314i	−0.365104	+	0.407263i
$903$	−49.2488	−	40.8388i	−1.63890	−	1.35903i
$904$	12.2647	+	3.98504i	0.407918	+	0.132540i
$905$	33.0556	+	14.7173i	1.09880	+	0.489219i
$906$	−12.0049	−	26.9634i	−0.398835	−	0.895798i
$907$	10.5819	+	2.24924i	0.351365	+	0.0746849i	0.380213	−	0.924899i	$-0.375851\pi$
$907$	10.5819	+	2.24924i	0.351365	+	0.0746849i	−0.0288482	+	0.999584i	$0.509184\pi$
$908$	13.7700	−	15.2931i	0.456972	−	0.507519i
$909$	23.1977	+	16.8541i	0.769420	+	0.559016i
$910$	−44.7821	−	2.86976i	−1.48451	−	0.0951315i
$911$	11.0015	−	33.8591i	0.364496	−	1.12180i	−0.585801	−	0.810455i	$-0.699220\pi$
$911$	11.0015	−	33.8591i	0.364496	−	1.12180i	0.950296	−	0.311347i	$-0.100780\pi$
$912$	17.0755	−	9.85855i	0.565427	−	0.326449i
$913$	−3.76690	+	1.23298i	−0.124666	+	0.0408058i
$914$	9.37324	−	16.2349i	0.310039	−	0.537004i
$915$	77.0691	−	16.3815i	2.54783	−	0.541557i
$916$	−4.23058	−	5.82289i	−0.139782	−	0.192394i
$917$	35.0321	+	9.82507i	1.15686	+	0.324453i
$918$	−2.16480	−	6.66258i	−0.0714492	−	0.219898i
$919$	22.8686	+	20.5910i	0.754366	+	0.679234i	0.953721	−	0.300693i	$-0.0972181\pi$
$919$	22.8686	+	20.5910i	0.754366	+	0.679234i	−0.199355	+	0.979927i	$0.563885\pi$
$920$	−2.09966	+	0.934830i	−0.0692238	+	0.0308204i
$921$	5.59900	−	0.588479i	0.184493	−	0.0193910i
$922$	−14.1089	−	66.3770i	−0.464651	−	2.18601i
$923$	31.9532			1.05175
$924$	29.8047	+	8.28929i	0.980502	+	0.272698i
$925$	9.24312			0.303912
$926$	−3.84411	−	18.0851i	−0.126325	−	0.594314i
$927$	50.6595	−	5.32453i	1.66388	−	0.174880i
$928$	4.02310	−	1.79120i	0.132065	−	0.0587990i
$929$	−10.3496	−	9.31880i	−0.339559	−	0.305740i	0.481655	−	0.876361i	$-0.340036\pi$
$929$	−10.3496	−	9.31880i	−0.339559	−	0.305740i	−0.821214	+	0.570621i	$0.806703\pi$
$930$	11.5763	+	35.6283i	0.379603	+	1.16830i
$931$	4.12871	−	8.72122i	0.135313	−	0.285827i
$932$	−9.21385	−	12.6818i	−0.301810	−	0.415406i
$933$	−7.08490	+	1.50594i	−0.231949	+	0.0493023i
$934$	−3.30900	+	5.73135i	−0.108274	+	0.187536i
$935$	3.10529	−	2.26644i	0.101554	−	0.0741205i
$936$	−30.4266	+	17.5668i	−0.994526	+	0.574190i
$937$	11.9520	−	36.7843i	0.390453	−	1.20169i	−0.541993	−	0.840383i	$-0.682330\pi$
$937$	11.9520	−	36.7843i	0.390453	−	1.20169i	0.932446	−	0.361309i	$-0.117670\pi$
$938$	−7.13525	+	3.53163i	−0.232974	+	0.115312i
$939$	29.1612	+	21.1868i	0.951639	+	0.691406i
$940$	5.81980	−	6.46354i	0.189821	−	0.210817i
$941$	−44.1010	−	9.37395i	−1.43765	−	0.305582i	−0.577821	−	0.816163i	$-0.696097\pi$
$941$	−44.1010	−	9.37395i	−1.43765	−	0.305582i	−0.859830	+	0.510581i	$0.829430\pi$
$942$	15.6492	+	35.1487i	0.509879	+	1.14521i
$943$	2.05894	+	0.916701i	0.0670485	+	0.0298519i
$944$	26.8728	+	8.73151i	0.874636	+	0.284186i
$945$	−33.8150	+	12.5309i	−1.10000	+	0.407631i
$946$	10.4641	+	48.7098i	0.340218	+	1.58369i
$947$	18.1857	+	31.4985i	0.590956	+	1.02357i	0.994104	+	0.108431i	$0.0345825\pi$
$947$	18.1857	+	31.4985i	0.590956	+	1.02357i	−0.403148	+	0.915135i	$0.632084\pi$
$948$	−18.0212	−	20.0146i	−0.585302	−	0.650044i
$949$	−3.05648	−	29.0804i	−0.0992175	−	0.943991i
$950$	−2.34401	−	0.246366i	−0.0760499	−	0.00799316i
$951$	21.9673	−	7.13762i	0.712340	−	0.231453i
$952$	−1.98207	−	0.787427i	−0.0642394	−	0.0255207i
$953$	−17.2576	+	23.7531i	−0.559030	+	0.769439i	−0.991203	−	0.132352i	$-0.957747\pi$
$953$	−17.2576	+	23.7531i	−0.559030	+	0.769439i	0.432173	+	0.901791i	$0.357747\pi$
$954$	−24.9655	+	56.0733i	−0.808287	+	1.81544i
$955$	−36.3816	+	32.7581i	−1.17728	+	1.06003i
$956$	−4.85121	−	2.80085i	−0.156899	−	0.0905859i
$957$	6.01018	+	3.45261i	0.194281	+	0.111607i
$958$		−	38.2431i		−	1.23558i
$959$	−37.8280	+	23.9447i	−1.22153	+	0.773214i
$960$	4.80192	−	3.48880i	0.154981	−	0.112600i
$961$	−1.89171	+	17.9984i	−0.0610228	+	0.580594i
$962$	17.0045	−	79.9999i	0.548247	−	2.57930i
$963$	1.61133	−	7.58070i	0.0519243	−	0.244285i
$964$	−0.983592	+	9.35825i	−0.0316794	+	0.301409i
$965$	−30.2670	+	21.9903i	−0.974330	+	0.707892i
$966$	−0.456003	−	11.1911i	−0.0146717	−	0.360066i
$967$			10.3829i			0.333892i	0.985966	+	0.166946i	$0.0533906\pi$
$967$			10.3829i			0.333892i	−0.985966	+	0.166946i	$0.946609\pi$
$968$	9.09974	+	12.4111i	0.292477	+	0.398907i
$969$	1.98701	+	1.14720i	0.0638320	+	0.0368534i
$970$	−27.6922	+	24.9341i	−0.889142	+	0.800587i
$971$	−14.5597	+	32.7016i	−0.467243	+	1.04945i	0.514196	+	0.857673i	$0.328090\pi$
$971$	−14.5597	+	32.7016i	−0.467243	+	1.04945i	−0.981439	+	0.191773i	$0.938576\pi$
$972$	−7.25164	+	9.98102i	−0.232596	+	0.320141i
$973$	0.666707	−	0.0976583i	0.0213736	−	0.00313078i
$974$	54.5978	−	17.7399i	1.74943	−	0.568423i
$975$	12.8603	+	1.35167i	0.411860	+	0.0432882i
$976$	7.01685	+	66.7609i	0.224604	+	2.13696i
$977$	18.5824	+	20.6378i	0.594503	+	0.660262i	0.963042	−	0.269350i	$-0.0868087\pi$
$977$	18.5824	+	20.6378i	0.594503	+	0.660262i	−0.368540	+	0.929612i	$0.620142\pi$
$978$	28.3716	+	49.1411i	0.907224	+	1.57136i
$979$	24.3458	+	41.9576i	0.778095	+	1.34097i
$980$	5.68961	−	16.2167i	0.181748	−	0.518025i
$981$	38.1575	+	12.3981i	1.21827	+	0.395842i
$982$	−52.9217	−	23.5623i	−1.68880	−	0.751902i
$983$	−18.6056	−	41.7888i	−0.593425	−	1.33285i	−0.921565	−	0.388225i	$-0.873088\pi$
$983$	−18.6056	−	41.7888i	−0.593425	−	1.33285i	0.328140	−	0.944629i	$-0.393578\pi$
$984$	10.9111	+	2.31923i	0.347833	+	0.0739342i
$985$	5.35050	−	5.94233i	0.170481	−	0.189338i
$986$	0.605153	+	0.439669i	0.0192720	+	0.0140019i
$987$	−12.0110	−	24.2668i	−0.382314	−	0.772421i
$988$	−2.44221	+	7.51635i	−0.0776971	+	0.239127i
$989$	5.91972	−	3.41775i	0.188236	−	0.108678i
$990$	60.9134	+	19.6459i	1.93596	+	0.624389i
$991$	−23.2826	+	40.3267i	−0.739597	+	1.28102i	0.213079	+	0.977035i	$0.431651\pi$
$991$	−23.2826	+	40.3267i	−0.739597	+	1.28102i	−0.952677	+	0.303985i	$0.901683\pi$
$992$	−21.3883	+	4.54622i	−0.679078	+	0.144342i
$993$	−23.9344	−	32.9429i	−0.759536	−	1.04541i
$994$	−8.72031	+	31.0929i	−0.276591	+	0.986208i
$995$	−9.68517	−	29.8079i	−0.307041	−	0.944974i
$996$	−3.13098	−	2.81914i	−0.0992087	−	0.0893280i
$997$	51.9853	−	23.1454i	1.64639	−	0.733021i	0.646831	−	0.762634i	$-0.276094\pi$
$997$	51.9853	−	23.1454i	1.64639	−	0.733021i	0.999561	+	0.0296126i	$0.00942736\pi$
$998$	72.7075	−	7.64186i	2.30151	−	0.241899i
$999$	−13.6654	−	64.2904i	−0.432353	−	2.03406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.n.a.24.2	yes	48
3.2	odd	2		693.2.cg.a.640.5		48
7.2	even	3		539.2.s.d.68.2		48
7.3	odd	6		539.2.m.a.244.9		48
7.4	even	3		539.2.m.a.244.10		48
7.5	odd	6	inner	77.2.n.a.68.2	yes	48
7.6	odd	2		539.2.s.d.178.2		48
11.2	odd	10		847.2.r.a.360.5		48
11.3	even	5		847.2.r.a.766.2		48
11.4	even	5		847.2.i.b.241.20		48
11.5	even	5		847.2.r.c.94.5		48
11.6	odd	10	inner	77.2.n.a.17.2	✓	48
11.7	odd	10		847.2.i.b.241.5		48
11.8	odd	10		847.2.r.d.766.5		48
11.9	even	5		847.2.r.d.360.2		48
11.10	odd	2		847.2.r.c.717.5		48
21.5	even	6		693.2.cg.a.145.5		48
33.17	even	10		693.2.cg.a.325.5		48
77.5	odd	30		847.2.r.c.215.5		48
77.6	even	10		539.2.s.d.325.2		48
77.17	even	30		539.2.m.a.391.10		48
77.19	even	30		847.2.r.d.40.2		48
77.26	odd	30		847.2.i.b.362.5		48
77.39	odd	30		539.2.m.a.391.9		48
77.40	even	30		847.2.i.b.362.20		48
77.47	odd	30		847.2.r.a.40.5		48
77.54	even	6		847.2.r.c.838.5		48
77.61	even	30	inner	77.2.n.a.61.2	yes	48
77.68	even	30		847.2.r.a.481.2		48
77.72	odd	30		539.2.s.d.215.2		48
77.75	odd	30		847.2.r.d.481.5		48
231.215	odd	30		693.2.cg.a.523.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.17.2	✓	48	11.6	odd	10	inner
77.2.n.a.24.2	yes	48	1.1	even	1	trivial
77.2.n.a.61.2	yes	48	77.61	even	30	inner
77.2.n.a.68.2	yes	48	7.5	odd	6	inner
539.2.m.a.244.9		48	7.3	odd	6
539.2.m.a.244.10		48	7.4	even	3
539.2.m.a.391.9		48	77.39	odd	30
539.2.m.a.391.10		48	77.17	even	30
539.2.s.d.68.2		48	7.2	even	3
539.2.s.d.178.2		48	7.6	odd	2
539.2.s.d.215.2		48	77.72	odd	30
539.2.s.d.325.2		48	77.6	even	10
693.2.cg.a.145.5		48	21.5	even	6
693.2.cg.a.325.5		48	33.17	even	10
693.2.cg.a.523.5		48	231.215	odd	30
693.2.cg.a.640.5		48	3.2	odd	2
847.2.i.b.241.5		48	11.7	odd	10
847.2.i.b.241.20		48	11.4	even	5
847.2.i.b.362.5		48	77.26	odd	30
847.2.i.b.362.20		48	77.40	even	30
847.2.r.a.40.5		48	77.47	odd	30
847.2.r.a.360.5		48	11.2	odd	10
847.2.r.a.481.2		48	77.68	even	30
847.2.r.a.766.2		48	11.3	even	5
847.2.r.c.94.5		48	11.5	even	5
847.2.r.c.215.5		48	77.5	odd	30
847.2.r.c.717.5		48	11.10	odd	2
847.2.r.c.838.5		48	77.54	even	6
847.2.r.d.40.2		48	77.19	even	30
847.2.r.d.360.2		48	11.9	even	5
847.2.r.d.481.5		48	77.75	odd	30
847.2.r.d.766.5		48	11.8	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.n (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.373106 - 1.75533i) q^{2} +(-2.87300 + 0.301965i) q^{3} +(-1.11488 + 0.496374i) q^{4} +(-1.49503 - 1.34613i) q^{5} +(1.60198 + 4.93040i) q^{6} +(-1.89247 + 1.84893i) q^{7} +(-0.822345 - 1.13186i) q^{8} +(5.22852 - 1.11136i) q^{9} +(-1.80510 + 3.12652i) q^{10} +(-0.00719692 - 3.31662i) q^{11} +(3.05315 - 1.76274i) q^{12} +(1.45177 - 4.46807i) q^{13} +(3.95158 + 2.63205i) q^{14} +(4.70172 + 3.41600i) q^{15} +(-3.31315 + 3.67963i) q^{16} +(-0.563588 - 0.119794i) q^{17} +(-3.90159 - 8.76311i) q^{18} +(1.25928 + 0.560666i) q^{19} +(2.33496 + 0.758675i) q^{20} +(4.87876 - 5.88345i) q^{21} +(-5.81906 + 1.25008i) q^{22} +(0.408298 + 0.707192i) q^{23} +(2.70438 + 3.00352i) q^{24} +(-0.0995947 - 0.947580i) q^{25} +(-8.38459 - 0.881256i) q^{26} +(-6.44364 + 2.09366i) q^{27} +(1.19210 - 3.00071i) q^{28} +(0.425221 - 0.585266i) q^{29} +(4.24195 - 9.52759i) q^{30} +(-2.66938 + 2.40352i) q^{31} +(5.27188 + 3.04372i) q^{32} +(1.02218 + 9.52648i) q^{33} +1.03398i q^{34} +(5.31822 - 0.216702i) q^{35} +(-5.27750 + 3.83433i) q^{36} +(-1.01403 + 9.64787i) q^{37} +(0.514308 - 2.41963i) q^{38} +(-2.82172 + 13.2752i) q^{39} +(-0.294203 + 2.79915i) q^{40} +(2.23288 - 1.62228i) q^{41} +(-12.1477 - 6.36866i) q^{42} -8.37074i q^{43} +(1.65431 + 3.69404i) q^{44} +(-9.31284 - 5.37677i) q^{45} +(1.08902 - 0.980554i) q^{46} +(1.44091 - 3.23634i) q^{47} +(8.40758 - 11.5720i) q^{48} +(0.162880 - 6.99810i) q^{49} +(-1.62615 + 0.528369i) q^{50} +(1.65536 + 0.173986i) q^{51} +(0.599301 + 5.70196i) q^{52} +(-4.28163 - 4.75523i) q^{53} +(6.07923 + 10.5295i) q^{54} +(-4.45385 + 4.96814i) q^{55} +(3.64900 + 0.621549i) q^{56} +(-3.78720 - 1.23054i) q^{57} +(-1.18599 - 0.528035i) q^{58} +(-2.32108 - 5.21322i) q^{59} +(-6.93744 - 1.47460i) q^{60} +(9.07168 - 10.0751i) q^{61} +(5.21492 + 3.78886i) q^{62} +(-7.83998 + 11.7704i) q^{63} +(0.315602 - 0.971325i) q^{64} +(-8.18506 + 4.72565i) q^{65} +(16.3407 - 5.34865i) q^{66} +(-0.838413 + 1.45217i) q^{67} +(0.687794 - 0.146195i) q^{68} +(-1.38659 - 1.90847i) q^{69} +(-2.36464 - 9.25436i) q^{70} +(2.10176 + 6.46855i) q^{71} +(-5.55754 - 5.00403i) q^{72} +(5.68595 - 2.53155i) q^{73} +(17.3135 - 1.81972i) q^{74} +(0.572272 + 2.69233i) q^{75} -1.68224 q^{76} +(6.14583 + 6.26329i) q^{77} +24.3551 q^{78} +(-1.58831 - 7.47240i) q^{79} +(9.90655 - 1.04122i) q^{80} +(3.23078 - 1.43844i) q^{81} +(-3.68074 - 3.31415i) q^{82} +(-0.369293 - 1.13657i) q^{83} +(-2.51881 + 8.98101i) q^{84} +(0.681324 + 0.937762i) q^{85} +(-14.6934 + 3.12318i) q^{86} +(-1.04493 + 1.80987i) q^{87} +(-3.74803 + 2.73555i) q^{88} +(-12.6666 + 7.31306i) q^{89} +(-5.96331 + 18.3532i) q^{90} +(5.51376 + 11.1399i) q^{91} +(-0.806233 - 0.585763i) q^{92} +(6.94335 - 7.71137i) q^{93} +(-6.21844 - 1.32177i) q^{94} +(-1.12793 - 2.53337i) q^{95} +(-16.0652 - 7.15270i) q^{96} +(9.81655 + 3.18959i) q^{97} +(-12.3447 + 2.32513i) q^{98} +(-3.72357 - 17.3330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26}+ \cdots - 12 q^{99}+O(q^{100}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more