LMFDB - Embedded newform 684.2.ch.a.479.44

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [684,2,Mod(47,684)] 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("684.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(684, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.ch (of order $18$, degree $6$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$696$
Relative dimension:	$116$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			479.44
Character	$\chi$	$=$	684.479
Dual form			684.2.ch.a.347.44

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.538946 - 1.30749i) q^{2} +(1.73112 + 0.0568802i) q^{3} +(-1.41907 + 1.40934i) q^{4} +(-0.104190 + 0.286260i) q^{5} +(-0.858607 - 2.29408i) q^{6} +(-4.02200 + 2.32210i) q^{7} +(2.60750 + 1.09588i) q^{8} +(2.99353 + 0.196933i) q^{9} +(0.430435 - 0.0180508i) q^{10} -0.728900 q^{11} +(-2.53675 + 2.35901i) q^{12} +(-3.04039 + 1.10661i) q^{13} +(5.20377 + 4.00725i) q^{14} +(-0.196648 + 0.489623i) q^{15} +(0.0275475 - 3.99991i) q^{16} +(-1.52304 + 4.18452i) q^{17} +(-1.35586 - 4.02015i) q^{18} +(-2.92871 - 3.22841i) q^{19} +(-0.255583 - 0.553063i) q^{20} +(-7.09463 + 3.79106i) q^{21} +(0.392837 + 0.953031i) q^{22} +(-1.06224 + 6.02426i) q^{23} +(4.45155 + 2.04540i) q^{24} +(3.75913 + 3.15429i) q^{25} +(3.08549 + 3.37889i) q^{26} +(5.17095 + 0.511186i) q^{27} +(2.43490 - 8.96358i) q^{28} +(-4.38187 - 0.772642i) q^{29} +(0.746161 - 0.00676471i) q^{30} +4.05037i q^{31} +(-5.24469 + 2.11971i) q^{32} +(-1.26181 - 0.0414600i) q^{33} +(6.29206 - 0.263864i) q^{34} +(-0.245672 - 1.39328i) q^{35} +(-4.52559 + 3.93942i) q^{36} +7.38739 q^{37} +(-2.64270 + 5.56921i) q^{38} +(-5.32621 + 1.74274i) q^{39} +(-0.585381 + 0.632243i) q^{40} +(2.20219 + 2.62447i) q^{41} +(8.78040 + 7.23300i) q^{42} +(-9.24620 + 1.63035i) q^{43} +(1.03436 - 1.02726i) q^{44} +(-0.368270 + 0.836409i) q^{45} +(8.44916 - 1.85788i) q^{46} +(-1.11312 + 6.31285i) q^{47} +(0.275203 - 6.92274i) q^{48} +(7.28431 - 12.6168i) q^{49} +(2.09824 - 6.61503i) q^{50} +(-2.87458 + 7.15726i) q^{51} +(2.75496 - 5.85529i) q^{52} +(0.546835 - 0.651692i) q^{53} +(-2.11849 - 7.03648i) q^{54} +(0.0759441 - 0.208655i) q^{55} +(-13.0321 + 1.64727i) q^{56} +(-4.88631 - 5.75534i) q^{57} +(1.35137 + 6.14567i) q^{58} +(-1.95546 - 11.0900i) q^{59} +(-0.410985 - 0.971954i) q^{60} +(-1.42533 + 0.518777i) q^{61} +(5.29583 - 2.18293i) q^{62} +(-12.4973 + 6.15922i) q^{63} +(5.59812 + 5.71499i) q^{64} -0.985640i q^{65} +(0.625839 + 1.67215i) q^{66} +(1.65487 - 1.97220i) q^{67} +(-3.73608 - 8.08462i) q^{68} +(-2.18152 + 10.3683i) q^{69} +(-1.68929 + 1.07212i) q^{70} +(-1.43374 + 1.20305i) q^{71} +(7.58981 + 3.79404i) q^{72} +(-0.632028 - 3.58441i) q^{73} +(-3.98140 - 9.65895i) q^{74} +(6.32808 + 5.67426i) q^{75} +(8.70598 + 0.453815i) q^{76} +(2.93163 - 1.69258i) q^{77} +(5.14916 + 6.02475i) q^{78} +(1.21632 - 3.34182i) q^{79} +(1.14214 + 0.424636i) q^{80} +(8.92244 + 1.17905i) q^{81} +(2.24461 - 4.29379i) q^{82} +(2.03358 + 3.52226i) q^{83} +(4.72494 - 15.3785i) q^{84} +(-1.03917 - 0.871970i) q^{85} +(7.11487 + 11.2107i) q^{86} +(-7.54158 - 1.58677i) q^{87} +(-1.90061 - 0.798783i) q^{88} +(14.9076 + 2.62861i) q^{89} +(1.29208 + 0.0307313i) q^{90} +(9.65878 - 11.5109i) q^{91} +(-6.98280 - 10.0459i) q^{92} +(-0.230386 + 7.01166i) q^{93} +(8.85391 - 1.94688i) q^{94} +(1.22931 - 0.502005i) q^{95} +(-9.19975 + 3.37115i) q^{96} +(10.2471 - 8.59831i) q^{97} +(-20.4222 - 2.72442i) q^{98} +(-2.18198 - 0.143544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 696 q - 9 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{6} - 12 q^{10} - 3 q^{12} - 6 q^{13} - 9 q^{14} - 3 q^{16} - 12 q^{18} - 18 q^{20} - 30 q^{21} - 27 q^{22} - 18 q^{24} - 6 q^{25} - 72 q^{26} - 18 q^{29} + 63 q^{30}+ \cdots - 45 q^{98}+O(q^{100}) $ 696 * q - 9 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^6 - 12 * q^10 - 3 * q^12 - 6 * q^13 - 9 * q^14 - 3 * q^16 - 12 * q^18 - 18 * q^20 - 30 * q^21 - 27 * q^22 - 18 * q^24 - 6 * q^25 - 72 * q^26 - 18 * q^29 + 63 * q^30 - 9 * q^32 - 60 * q^33 - 39 * q^34 - 66 * q^36 - 48 * q^37 - 9 * q^38 - 33 * q^40 - 18 * q^41 - 27 * q^42 - 135 * q^44 - 6 * q^45 - 6 * q^46 - 18 * q^48 + 282 * q^49 - 3 * q^52 + 15 * q^54 + 45 * q^56 - 12 * q^57 - 6 * q^58 - 9 * q^60 - 6 * q^61 + 18 * q^62 + 12 * q^64 + 18 * q^66 - 9 * q^68 - 6 * q^69 - 45 * q^70 + 12 * q^72 + 12 * q^73 + 99 * q^74 - 3 * q^76 - 36 * q^77 + 69 * q^78 - 72 * q^81 - 12 * q^82 - 45 * q^84 - 6 * q^85 - 171 * q^86 - 45 * q^88 + 27 * q^90 - 9 * q^92 + 24 * q^93 - 6 * q^94 - 87 * q^96 - 42 * q^97 - 45 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.538946	−	1.30749i	−0.381092	−	0.924537i
$2$	−0.538946	−	1.30749i	−0.381092	−	0.924537i
$3$	1.73112	+	0.0568802i	0.999461	+	0.0328398i
$3$	1.73112	+	0.0568802i	0.999461	+	0.0328398i
$4$	−1.41907	+	1.40934i	−0.709537	+	0.704668i
$5$	−0.104190	+	0.286260i	−0.0465952	+	0.128019i	−0.960808	−	0.277216i	$-0.910588\pi$
$5$	−0.104190	+	0.286260i	−0.0465952	+	0.128019i	0.914212	+	0.405235i	$0.132810\pi$
$6$	−0.858607	−	2.29408i	−0.350525	−	0.936553i
$7$	−4.02200	+	2.32210i	−1.52017	+	0.877672i	−0.520455	+	0.853889i	$0.674238\pi$
$7$	−4.02200	+	2.32210i	−1.52017	+	0.877672i	−0.999717	+	0.0237829i	$0.992429\pi$
$8$	2.60750	+	1.09588i	0.921891	+	0.387450i
$9$	2.99353	+	0.196933i	0.997843	+	0.0656442i
$10$	0.430435	−	0.0180508i	0.136116	−	0.00570815i
$11$	−0.728900			−0.219772			−0.109886	−	0.993944i	$-0.535049\pi$
$11$	−0.728900			−0.219772			−0.109886	+	0.993944i	$0.535049\pi$
$12$	−2.53675	+	2.35901i	−0.732296	+	0.680987i
$13$	−3.04039	+	1.10661i	−0.843253	+	0.306919i	−0.727286	−	0.686334i	$-0.759219\pi$
$13$	−3.04039	+	1.10661i	−0.843253	+	0.306919i	−0.115966	+	0.993253i	$0.536996\pi$
$14$	5.20377	+	4.00725i	1.39077	+	1.07098i
$15$	−0.196648	+	0.489623i	−0.0507742	+	0.126420i
$16$	0.0275475	−	3.99991i	0.00688687	−	0.999976i
$17$	−1.52304	+	4.18452i	−0.369391	+	1.01489i	0.606202	+	0.795311i	$0.292692\pi$
$17$	−1.52304	+	4.18452i	−0.369391	+	1.01489i	−0.975594	+	0.219584i	$0.929530\pi$
$18$	−1.35586	−	4.02015i	−0.319580	−	0.947559i
$19$	−2.92871	−	3.22841i	−0.671893	−	0.740648i
$19$	−2.92871	−	3.22841i	−0.671893	−	0.740648i
$20$	−0.255583	−	0.553063i	−0.0571500	−	0.123669i
$21$	−7.09463	+	3.79106i	−1.54818	+	0.827276i
$22$	0.392837	+	0.953031i	0.0837532	+	0.203187i
$23$	−1.06224	+	6.02426i	−0.221492	+	1.25614i	0.647786	+	0.761822i	$0.275695\pi$
$23$	−1.06224	+	6.02426i	−0.221492	+	1.25614i	−0.869279	+	0.494323i	$0.835416\pi$
$24$	4.45155	+	2.04540i	0.908670	+	0.417516i
$25$	3.75913	+	3.15429i	0.751827	+	0.630857i
$26$	3.08549	+	3.37889i	0.605115	+	0.662654i
$27$	5.17095	+	0.511186i	0.995149	+	0.0983778i
$28$	2.43490	−	8.96358i	0.460152	−	1.69396i
$29$	−4.38187	−	0.772642i	−0.813693	−	0.143476i	−0.248709	−	0.968578i	$-0.580006\pi$
$29$	−4.38187	−	0.772642i	−0.813693	−	0.143476i	−0.564983	+	0.825102i	$0.691117\pi$
$30$	0.746161	−	0.00676471i	0.136230	−	0.00123506i
$31$			4.05037i			0.727468i	0.931503	+	0.363734i	$0.118498\pi$
$31$			4.05037i			0.727468i	−0.931503	+	0.363734i	$0.881502\pi$
$32$	−5.24469	+	2.11971i	−0.927140	+	0.374716i
$33$	−1.26181	−	0.0414600i	−0.219653	−	0.00721726i
$34$	6.29206	−	0.263864i	1.07908	−	0.0452524i
$35$	−0.245672	−	1.39328i	−0.0415262	−	0.235507i
$36$	−4.52559	+	3.93942i	−0.754264	+	0.656571i
$37$	7.38739			1.21448			0.607239	−	0.794519i	$-0.292277\pi$
$37$	7.38739			1.21448			0.607239	+	0.794519i	$0.292277\pi$
$38$	−2.64270	+	5.56921i	−0.428703	+	0.903445i
$39$	−5.32621	+	1.74274i	−0.852877	+	0.279061i
$40$	−0.585381	+	0.632243i	−0.0925568	+	0.0999665i
$41$	2.20219	+	2.62447i	0.343924	+	0.409873i	0.910085	−	0.414422i	$-0.136016\pi$
$41$	2.20219	+	2.62447i	0.343924	+	0.409873i	−0.566161	+	0.824295i	$0.691572\pi$
$42$	8.78040	+	7.23300i	1.35485	+	1.11608i
$43$	−9.24620	+	1.63035i	−1.41003	+	0.248627i	−0.826259	−	0.563290i	$-0.809535\pi$
$43$	−9.24620	+	1.63035i	−1.41003	+	0.248627i	−0.583773	+	0.811917i	$0.698424\pi$
$44$	1.03436	−	1.02726i	0.155936	−	0.154866i
$45$	−0.368270	+	0.836409i	−0.0548984	+	0.124684i
$46$	8.44916	−	1.85788i	1.24576	−	0.273929i
$47$	−1.11312	+	6.31285i	−0.162366	+	0.920823i	0.789373	+	0.613914i	$0.210406\pi$
$47$	−1.11312	+	6.31285i	−0.162366	+	0.920823i	−0.951739	+	0.306909i	$0.900705\pi$
$48$	0.275203	−	6.92274i	0.0397222	−	0.999211i
$49$	7.28431	−	12.6168i	1.04062	−	1.80240i
$50$	2.09824	−	6.61503i	0.296736	−	0.935506i
$51$	−2.87458	+	7.15726i	−0.402521	+	1.00222i
$52$	2.75496	−	5.85529i	0.382044	−	0.811983i
$53$	0.546835	−	0.651692i	0.0751135	−	0.0895168i	−0.727179	−	0.686448i	$-0.759169\pi$
$53$	0.546835	−	0.651692i	0.0751135	−	0.0895168i	0.802293	+	0.596931i	$0.203613\pi$
$54$	−2.11849	−	7.03648i	−0.288290	−	0.957543i
$55$	0.0759441	−	0.208655i	0.0102403	−	0.0281350i
$56$	−13.0321	+	1.64727i	−1.74149	+	0.220126i
$57$	−4.88631	−	5.75534i	−0.647208	−	0.762313i
$58$	1.35137	+	6.14567i	0.177443	+	0.806966i
$59$	−1.95546	−	11.0900i	−0.254579	−	1.44379i	−0.797150	−	0.603781i	$-0.793660\pi$
$59$	−1.95546	−	11.0900i	−0.254579	−	1.44379i	0.542570	−	0.840010i	$-0.317451\pi$
$60$	−0.410985	−	0.971954i	−0.0530579	−	0.125479i
$61$	−1.42533	+	0.518777i	−0.182495	+	0.0664226i	−0.431651	−	0.902041i	$-0.642069\pi$
$61$	−1.42533	+	0.518777i	−0.182495	+	0.0664226i	0.249156	+	0.968463i	$0.419847\pi$
$62$	5.29583	−	2.18293i	0.672571	−	0.277232i
$63$	−12.4973	+	6.15922i	−1.57451	+	0.775988i
$64$	5.59812	+	5.71499i	0.699764	+	0.714374i
$65$		−	0.985640i		−	0.122254i
$66$	0.625839	+	1.67215i	0.0770354	+	0.205828i
$67$	1.65487	−	1.97220i	0.202174	−	0.240942i	−0.655425	−	0.755260i	$-0.727510\pi$
$67$	1.65487	−	1.97220i	0.202174	−	0.240942i	0.857599	+	0.514318i	$0.171955\pi$
$68$	−3.73608	−	8.08462i	−0.453066	−	0.980404i
$69$	−2.18152	+	10.3683i	−0.262624	+	1.24819i
$70$	−1.68929	+	1.07212i	−0.201909	+	0.128142i
$71$	−1.43374	+	1.20305i	−0.170154	+	0.142776i	−0.723888	−	0.689917i	$-0.757647\pi$
$71$	−1.43374	+	1.20305i	−0.170154	+	0.142776i	0.553734	+	0.832693i	$0.313202\pi$
$72$	7.58981	+	3.79404i	0.894468	+	0.447131i
$73$	−0.632028	−	3.58441i	−0.0739732	−	0.419523i	−0.999196	−	0.0400981i	$-0.987233\pi$
$73$	−0.632028	−	3.58441i	−0.0739732	−	0.419523i	0.925223	−	0.379425i	$-0.123878\pi$
$74$	−3.98140	−	9.65895i	−0.462828	−	1.12283i
$75$	6.32808	+	5.67426i	0.730704	+	0.655207i
$76$	8.70598	+	0.453815i	0.998644	+	0.0520562i
$77$	2.93163	−	1.69258i	0.334091	−	0.192887i
$78$	5.14916	+	6.02475i	0.583027	+	0.682168i
$79$	1.21632	−	3.34182i	0.136847	−	0.375984i	−0.852273	−	0.523098i	$-0.824776\pi$
$79$	1.21632	−	3.34182i	0.136847	−	0.375984i	0.989120	+	0.147114i	$0.0469984\pi$
$80$	1.14214	+	0.424636i	0.127695	+	0.0474758i
$81$	8.92244	+	1.17905i	0.991382	+	0.131005i
$82$	2.24461	−	4.29379i	0.247876	−	0.474170i
$83$	2.03358	+	3.52226i	0.223214	+	0.386618i	0.955782	−	0.294076i	$-0.0950118\pi$
$83$	2.03358	+	3.52226i	0.223214	+	0.386618i	−0.732568	+	0.680694i	$0.761678\pi$
$84$	4.72494	−	15.3785i	0.515533	−	1.67793i
$85$	−1.03917	−	0.871970i	−0.112714	−	0.0945785i
$86$	7.11487	+	11.2107i	0.767217	+	1.20888i
$87$	−7.54158	−	1.58677i	−0.808542	−	0.170120i
$88$	−1.90061	−	0.798783i	−0.202605	−	0.0851506i
$89$	14.9076	+	2.62861i	1.58020	+	0.278632i	0.893758	−	0.448550i	$-0.148059\pi$
$89$	14.9076	+	2.62861i	1.58020	+	0.278632i	0.686444	+	0.727182i	$0.259171\pi$
$90$	1.29208	+	0.0307313i	0.136197	+	0.00323936i
$91$	9.65878	−	11.5109i	1.01252	−	1.20667i
$92$	−6.98280	−	10.0459i	−0.728007	−	1.04736i
$93$	−0.230386	+	7.01166i	−0.0238899	+	0.727075i
$94$	8.85391	−	1.94688i	0.913211	−	0.200805i
$95$	1.22931	−	0.502005i	0.126124	−	0.0515046i
$96$	−9.19975	+	3.37115i	−0.938945	+	0.344067i
$97$	10.2471	−	8.59831i	1.04043	−	0.873026i	0.0483766	−	0.998829i	$-0.484595\pi$
$97$	10.2471	−	8.59831i	1.04043	−	0.873026i	0.992055	+	0.125803i	$0.0401508\pi$
$98$	−20.4222	−	2.72442i	−2.06296	−	0.275208i
$99$	−2.18198	−	0.143544i	−0.219298	−	0.0144267i
$100$	−9.77994	+	0.821709i	−0.977994	+	0.0821709i
$101$	−2.64321	+	3.15006i	−0.263009	+	0.313442i	−0.881346	−	0.472471i	$-0.843362\pi$
$101$	−2.64321	+	3.15006i	−0.263009	+	0.313442i	0.618337	+	0.785913i	$0.287807\pi$
$102$	10.9073	−	0.0988858i	1.07998	−	0.00979116i
$103$	−5.84085	−	3.37222i	−0.575516	−	0.332274i	0.183833	−	0.982957i	$-0.441149\pi$
$103$	−5.84085	−	3.37222i	−0.575516	−	0.332274i	−0.759349	+	0.650683i	$0.774483\pi$
$104$	−9.14053	−	0.446398i	−0.896302	−	0.0437729i
$105$	−0.346037	−	2.42590i	−0.0337698	−	0.236743i
$106$	−1.14680	−	0.363756i	−0.111387	−	0.0353311i
$107$	−9.93237	+	17.2034i	−0.960198	+	1.66311i	−0.238201	+	0.971216i	$0.576558\pi$
$107$	−9.93237	+	17.2034i	−0.960198	+	1.66311i	−0.721997	+	0.691896i	$0.756776\pi$
$108$	−8.05839	+	6.56219i	−0.775419	+	0.631447i
$109$	11.9395	−	10.0185i	1.14360	−	0.959594i	0.144049	−	0.989571i	$-0.453988\pi$
$109$	11.9395	−	10.0185i	1.14360	−	0.959594i	0.999551	+	0.0299768i	$0.00954335\pi$
$110$	−0.313744	+	0.0131572i	−0.0299144	+	0.00125449i
$111$	12.7884	+	0.420196i	1.21382	+	0.0398833i
$112$	9.17739	+	16.1516i	0.867182	+	1.52618i
$113$	6.19538	−	3.57691i	0.582813	−	0.336487i	−0.179438	−	0.983769i	$-0.557428\pi$
$113$	6.19538	−	3.57691i	0.582813	−	0.336487i	0.762250	+	0.647282i	$0.224095\pi$
$114$	−4.89161	+	9.49064i	−0.458141	+	0.888879i
$115$	−1.61383	−	0.931744i	−0.150490	−	0.0868856i
$116$	7.30711	−	5.07909i	0.678448	−	0.471581i
$117$	−9.31943	+	2.71392i	−0.861581	+	0.250902i
$118$	−13.4462	+	8.53365i	−1.23782	+	0.785586i
$119$	−3.59121	−	20.3668i	−0.329206	−	1.86702i
$120$	−1.04932	+	1.06119i	−0.0957898	+	0.0968730i
$121$	−10.4687			−0.951700
$122$	1.44647	+	1.58402i	0.130958	+	0.143410i
$123$	3.66297	+	4.66852i	0.330279	+	0.420946i
$124$	−5.70833	−	5.74778i	−0.512623	−	0.516166i
$125$	−2.61370	+	1.50902i	−0.233777	+	0.134971i
$126$	14.7885	+	13.0206i	1.31746	+	1.15997i
$127$	8.73955	+	1.54102i	0.775509	+	0.136743i	0.547376	−	0.836887i	$-0.315627\pi$
$127$	8.73955	+	1.54102i	0.775509	+	0.136743i	0.228133	+	0.973630i	$0.426738\pi$
$128$	4.45523	−	10.3996i	0.393790	−	0.919200i
$129$	−16.0990	+	2.29641i	−1.41744	+	0.202187i
$130$	−1.28872	+	0.531206i	−0.113028	+	0.0465899i
$131$	1.97280	+	11.1883i	0.172364	+	0.977526i	0.941142	+	0.338010i	$0.109754\pi$
$131$	1.97280	+	11.1883i	0.172364	+	0.977526i	−0.768778	+	0.639515i	$0.779135\pi$
$132$	1.84904	−	1.71948i	0.160938	−	0.149661i
$133$	19.2760	+	6.18389i	1.67144	+	0.536211i
$134$	−3.47052	−	1.10082i	−0.299807	−	0.0950966i
$135$	−0.685093	+	1.42697i	−0.0589634	+	0.122814i
$136$	−8.55704	+	9.24207i	−0.733760	+	0.792501i
$137$	4.23980	+	11.6488i	0.362231	+	0.995221i	0.978239	+	0.207481i	$0.0665267\pi$
$137$	4.23980	+	11.6488i	0.362231	+	0.995221i	−0.616008	+	0.787740i	$0.711251\pi$
$138$	14.7322	−	2.73561i	1.25408	−	0.232871i
$139$	−7.14021	−	19.6176i	−0.605624	−	1.66394i	−0.739675	−	0.672965i	$-0.765021\pi$
$139$	−7.14021	−	19.6176i	−0.605624	−	1.66394i	0.134050	−	0.990975i	$-0.457202\pi$
$140$	2.31222	+	1.63093i	0.195418	+	0.137839i
$141$	−2.28603	+	10.8650i	−0.192518	+	0.914994i
$142$	2.34569	+	1.22623i	0.196846	+	0.102903i
$143$	2.21614	−	0.806609i	0.185323	−	0.0674520i
$144$	0.870176	−	11.9684i	0.0725147	−	0.997367i
$145$	0.677723	−	1.17385i	0.0562819	−	0.0974831i
$146$	−4.34596	+	2.75817i	−0.359674	+	0.228268i
$147$	13.3276	−	21.4268i	1.09925	−	1.76725i
$148$	−10.4833	+	10.4113i	−0.861718	+	0.855804i
$149$	0.297713	+	0.354801i	0.0243896	+	0.0290664i	0.778101	−	0.628139i	$-0.216183\pi$
$149$	0.297713	+	0.354801i	0.0243896	+	0.0290664i	−0.753712	+	0.657205i	$0.771739\pi$
$150$	4.00856	−	11.3320i	0.327298	−	0.925257i
$151$	7.36041	+	4.24954i	0.598982	+	0.345822i	0.768641	−	0.639680i	$-0.220933\pi$
$151$	7.36041	+	4.24954i	0.598982	+	0.345822i	−0.169659	+	0.985503i	$0.554267\pi$
$152$	−4.09869	−	11.6276i	−0.332448	−	0.943122i
$153$	−5.38333	+	12.2265i	−0.435217	+	0.988457i
$154$	−3.79303	−	2.92088i	−0.305651	−	0.235371i
$155$	−1.15946	−	0.422008i	−0.0931299	−	0.0338965i
$156$	5.10220	−	9.97950i	0.408503	−	0.798999i
$157$	−21.6166	−	7.86779i	−1.72519	−	0.627918i	−0.726922	−	0.686720i	$-0.759050\pi$
$157$	−21.6166	−	7.86779i	−1.72519	−	0.627918i	−0.998270	+	0.0588018i	$0.981272\pi$
$158$	−5.02494	+	0.210726i	−0.399763	+	0.0167645i
$159$	0.983703	−	1.09705i	0.0780127	−	0.0870018i
$160$	−0.0603439	−	1.72220i	−0.00477061	−	0.136152i
$161$	−9.71661	−	26.6962i	−0.765776	−	2.10395i
$162$	−3.26711	−	12.3015i	−0.256689	−	0.966494i
$163$	0.468730	−	0.270622i	0.0367138	−	0.0211967i	−0.481531	−	0.876429i	$-0.659919\pi$
$163$	0.468730	−	0.270622i	0.0367138	−	0.0211967i	0.518245	+	0.855232i	$0.326586\pi$
$164$	−6.82383	−	0.620692i	−0.532851	−	0.0484679i
$165$	0.143336	−	0.356886i	0.0111587	−	0.0277835i
$166$	3.50934	−	4.55719i	0.272378	−	0.353707i
$167$	1.91063	−	10.8357i	0.147849	−	0.838492i	−0.817187	−	0.576373i	$-0.804468\pi$
$167$	1.91063	−	10.8357i	0.147849	−	0.838492i	0.965036	−	0.262119i	$-0.0844214\pi$
$168$	−22.6538	+	2.11035i	−1.74778	+	0.162817i
$169$	−1.93919	+	1.62718i	−0.149169	+	0.125167i
$170$	−0.580037	+	1.82866i	−0.0444868	+	0.140252i
$171$	−8.13141	−	10.2411i	−0.621825	−	0.783156i
$172$	10.8233	−	15.3446i	0.825271	−	1.17001i
$173$	3.74599	+	4.46429i	0.284802	+	0.339414i	0.889411	−	0.457109i	$-0.151115\pi$
$173$	3.74599	+	4.46429i	0.284802	+	0.339414i	−0.604609	+	0.796523i	$0.706670\pi$
$174$	1.98980	+	10.7157i	0.150847	+	0.812358i
$175$	−22.4438	−	3.95745i	−1.69659	−	0.299155i
$176$	−0.0200794	+	2.91553i	−0.00151354	+	0.219766i
$177$	−2.75433	−	19.3093i	−0.207028	−	1.45137i
$178$	−4.59749	−	20.9083i	−0.344597	−	1.56714i
$179$	3.72746	+	6.45616i	0.278604	+	0.482556i	0.971038	−	0.238925i	$-0.0767951\pi$
$179$	3.72746	+	6.45616i	0.278604	+	0.482556i	−0.692434	+	0.721481i	$0.743462\pi$
$180$	−0.656178	−	1.70594i	−0.0489086	−	0.127153i
$181$	−22.2545	+	8.09997i	−1.65416	+	0.602066i	−0.989429	−	0.145016i	$-0.953677\pi$
$181$	−22.2545	+	8.09997i	−1.65416	+	0.602066i	−0.664733	+	0.747081i	$0.731454\pi$
$182$	−20.2560	−	6.42504i	−1.50147	−	0.476256i
$183$	−2.49692	+	0.816991i	−0.184578	+	0.0603937i
$184$	−9.37162	+	14.5442i	−0.690885	+	1.07221i
$185$	−0.769692	+	2.11471i	−0.0565889	+	0.155477i
$186$	9.29186	−	3.47768i	0.681312	−	0.254996i
$187$	1.11014	−	3.05010i	0.0811818	−	0.223045i
$188$	−7.31731	−	10.5272i	−0.533670	−	0.767773i
$189$	−21.9846	+	9.95147i	−1.59914	+	0.723863i
$190$	−1.31890	−	1.33676i	−0.0956829	−	0.0969785i
$191$	−2.75293	+	4.76822i	−0.199195	+	0.345016i	−0.948268	−	0.317472i	$-0.897166\pi$
$191$	−2.75293	+	4.76822i	−0.199195	+	0.345016i	0.749072	+	0.662488i	$0.230499\pi$
$192$	9.36592	+	10.2117i	0.675927	+	0.736968i
$193$	−3.51648	+	2.95067i	−0.253122	+	0.212394i	−0.760515	−	0.649320i	$-0.775053\pi$
$193$	−3.51648	+	2.95067i	−0.253122	+	0.212394i	0.507394	+	0.861714i	$0.330609\pi$
$194$	−16.7648	−	8.76394i	−1.20365	−	0.629214i
$195$	0.0560634	−	1.70626i	0.00401479	−	0.122188i
$196$	7.44432	+	28.1702i	0.531737	+	2.01216i
$197$	−7.99009	−	4.61308i	−0.569270	−	0.328668i	0.187587	−	0.982248i	$-0.439933\pi$
$197$	−7.99009	−	4.61308i	−0.569270	−	0.328668i	−0.756858	+	0.653579i	$0.773267\pi$
$198$	0.988288	+	2.93029i	0.0702345	+	0.208247i
$199$	7.00208	+	19.2380i	0.496364	+	1.36375i	0.894765	+	0.446538i	$0.147343\pi$
$199$	7.00208	+	19.2380i	0.496364	+	1.36375i	−0.398401	+	0.917211i	$0.630435\pi$
$200$	6.34524	+	12.3443i	0.448676	+	0.872877i
$201$	2.97695	−	3.31997i	0.209978	−	0.234173i
$202$	5.54323	+	1.75827i	0.390020	+	0.123712i
$203$	19.4180	−	7.06758i	1.36288	−	0.496047i
$204$	−6.00774	−	14.2079i	−0.420626	−	0.994754i
$205$	−0.980726	+	0.356955i	−0.0684969	+	0.0249308i
$206$	−1.26125	+	9.45431i	−0.0878753	+	0.658713i
$207$	−4.36622	+	17.8246i	−0.303473	+	1.23890i
$208$	4.34259	+	12.1918i	0.301104	+	0.845346i
$209$	2.13474	+	2.35319i	0.147663	+	0.162773i
$210$	−2.98535	+	1.75987i	−0.206009	+	0.121442i
$211$	−6.87736	+	1.21266i	−0.473457	+	0.0834832i	−0.405285	−	0.914190i	$-0.632828\pi$
$211$	−6.87736	+	1.21266i	−0.473457	+	0.0834832i	−0.0681719	+	0.997674i	$0.521717\pi$
$212$	0.142454	+	1.69547i	0.00978375	+	0.116446i
$213$	−2.55040	+	2.00107i	−0.174751	+	0.137111i
$214$	27.8463	+	3.71482i	1.90353	+	0.253940i
$215$	0.496657	−	2.81668i	0.0338717	−	0.192096i
$216$	12.9230	+	6.99963i	0.879302	+	0.476264i
$217$	−9.40537	−	16.2906i	−0.638478	−	1.10588i
$218$	−19.5338	−	10.2114i	−1.32300	−	0.691606i
$219$	−0.890232	−	6.24098i	−0.0601563	−	0.421726i
$220$	0.186294	+	0.403128i	0.0125599	+	0.0271789i
$221$		−	14.4080i		−	0.969186i
$222$	−6.34286	−	16.9472i	−0.425705	−	1.13742i
$223$	11.1725	−	1.97001i	0.748164	−	0.131922i	0.213449	−	0.976954i	$-0.431530\pi$
$223$	11.1725	−	1.97001i	0.748164	−	0.131922i	0.534715	+	0.845033i	$0.320419\pi$
$224$	16.1720	−	20.7042i	1.08053	−	1.38336i
$225$	10.6319	+	10.1827i	0.708793	+	0.678850i
$226$	−8.01575	−	6.17266i	−0.533200	−	0.410599i
$227$	0.416567	−	0.721515i	0.0276485	−	0.0478886i	−0.851870	−	0.523753i	$-0.824531\pi$
$227$	0.416567	−	0.721515i	0.0276485	−	0.0478886i	0.879519	+	0.475865i	$0.157865\pi$
$228$	15.0452	+	1.28081i	0.996396	+	0.0848234i
$229$	4.46586	+	7.73510i	0.295112	+	0.511149i	0.975011	−	0.222157i	$-0.0713096\pi$
$229$	4.46586	+	7.73510i	0.295112	+	0.511149i	−0.679899	+	0.733306i	$0.737976\pi$
$230$	−0.348483	+	2.61223i	−0.0229783	+	0.172245i
$231$	5.17127	−	2.76330i	0.340245	−	0.181812i
$232$	−10.5790	−	6.81664i	−0.694546	−	0.447535i
$233$	15.7924	+	18.8206i	1.03459	+	1.23298i	0.972010	+	0.234940i	$0.0754894\pi$
$233$	15.7924	+	18.8206i	1.03459	+	1.23298i	0.0625830	+	0.998040i	$0.480066\pi$
$234$	8.57110	+	10.7224i	0.560310	+	0.700947i
$235$	−1.69114	−	0.976379i	−0.110318	−	0.0636919i
$236$	18.4044	+	12.9816i	1.19803	+	0.845030i
$237$	2.29568	−	5.71590i	0.149120	−	0.371287i
$238$	−24.6939	+	15.6721i	−1.60067	+	1.01587i
$239$	6.43029	−	11.1376i	0.415941	−	0.720430i	−0.579586	−	0.814911i	$-0.696786\pi$
$239$	6.43029	−	11.1376i	0.415941	−	0.720430i	0.995527	+	0.0944807i	$0.0301191\pi$
$240$	1.95303	+	0.800060i	0.126067	+	0.0516436i
$241$	−17.1799	−	14.4156i	−1.10665	−	0.928592i	−0.108799	−	0.994064i	$-0.534700\pi$
$241$	−17.1799	−	14.4156i	−1.10665	−	0.928592i	−0.997854	+	0.0654716i	$0.979145\pi$
$242$	5.64206	+	13.6878i	0.362686	+	0.879882i
$243$	15.3787	+	2.54858i	0.986545	+	0.163491i
$244$	1.29152	−	2.74495i	0.0826810	−	0.175728i
$245$	2.85273	+	3.39975i	0.182254	+	0.217202i
$246$	4.12992	−	7.30538i	0.263314	−	0.465774i
$247$	12.4770	+	6.57468i	0.793895	+	0.418337i
$248$	−4.43870	+	10.5613i	−0.281858	+	0.670646i
$249$	3.32001	+	6.21311i	0.210397	+	0.393740i
$250$	3.38168	+	2.60412i	0.213876	+	0.164699i
$251$	−6.01767	−	5.04942i	−0.379832	−	0.318717i	0.432805	−	0.901488i	$-0.357524\pi$
$251$	−6.01767	−	5.04942i	−0.379832	−	0.318717i	−0.812636	+	0.582771i	$0.801968\pi$
$252$	9.05416	−	26.3532i	0.570358	−	1.66010i
$253$	0.774266	−	4.39108i	0.0486777	−	0.276065i
$254$	−2.69527	−	12.2574i	−0.169116	−	0.769099i
$255$	−1.74933	−	1.56859i	−0.109548	−	0.0982290i
$256$	−15.9985	−	0.220375i	−0.999905	−	0.0137734i
$257$	−1.98609	+	2.36693i	−0.123889	+	0.147645i	−0.824424	−	0.565973i	$-0.808500\pi$
$257$	−1.98609	+	2.36693i	−0.123889	+	0.147645i	0.700535	+	0.713618i	$0.252945\pi$
$258$	11.6790	+	19.8117i	0.727103	+	1.23342i
$259$	−29.7121	+	17.1543i	−1.84622	+	1.06591i
$260$	1.38910	+	1.39870i	0.0861481	+	0.0867435i
$261$	−12.9651	−	3.17586i	−0.802519	−	0.196581i
$262$	13.5654	−	8.60930i	0.838072	−	0.531884i
$263$	−9.61161	−	3.49834i	−0.592677	−	0.215717i	0.0282293	−	0.999601i	$-0.491013\pi$
$263$	−9.61161	−	3.49834i	−0.592677	−	0.215717i	−0.620907	+	0.783885i	$0.713235\pi$
$264$	−3.24474	−	1.49089i	−0.199700	−	0.0917582i
$265$	0.129579	+	0.224437i	0.00795995	+	0.0137870i
$266$	−2.30332	−	28.5360i	−0.141226	−	1.74965i
$267$	25.6573	+	5.39838i	1.57020	+	0.330375i
$268$	0.431102	+	5.13096i	0.0263338	+	0.313423i
$269$	−11.2293	+	1.98003i	−0.684663	+	0.120725i	−0.505151	−	0.863031i	$-0.668563\pi$
$269$	−11.2293	+	1.98003i	−0.684663	+	0.120725i	−0.179512	+	0.983756i	$0.557452\pi$
$270$	2.23499	+	0.126693i	0.136017	+	0.00771029i
$271$	0.874173	+	1.04180i	0.0531022	+	0.0632848i	0.791942	−	0.610597i	$-0.209070\pi$
$271$	0.874173	+	1.04180i	0.0531022	+	0.0632848i	−0.738840	+	0.673881i	$0.764626\pi$
$272$	16.6957	+	6.20729i	1.01233	+	0.376372i
$273$	17.3752	−	19.3773i	1.05160	−	1.17277i
$274$	12.9457	−	11.8216i	0.782076	−	0.714167i
$275$	−2.74003	−	2.29916i	−0.165230	−	0.138645i
$276$	−11.5166	−	17.7878i	−0.693220	−	1.07070i
$277$	25.8300			1.55198			0.775988	−	0.630748i	$-0.217252\pi$
$277$	25.8300			1.55198			0.775988	+	0.630748i	$0.217252\pi$
$278$	−21.8016	+	19.9086i	−1.30757	+	1.19404i
$279$	−0.797650	+	12.1249i	−0.0477540	+	0.725899i
$280$	0.886266	−	3.90219i	0.0529645	−	0.233201i
$281$	10.5160	+	28.8925i	0.627332	+	1.72358i	0.688285	+	0.725440i	$0.258364\pi$
$281$	10.5160	+	28.8925i	0.627332	+	1.72358i	−0.0609534	+	0.998141i	$0.519414\pi$
$282$	15.4379	−	2.86666i	0.919313	−	0.170707i
$283$	18.5822	−	3.27655i	1.10460	−	0.194771i	0.408530	−	0.912745i	$-0.366042\pi$
$283$	18.5822	−	3.27655i	1.10460	−	0.194771i	0.696070	+	0.717974i	$0.254930\pi$
$284$	0.339083	−	3.72784i	0.0201209	−	0.221207i
$285$	2.15663	−	0.799106i	0.127748	−	0.0473350i
$286$	−2.24902	−	2.46287i	−0.132987	−	0.145633i
$287$	−14.9515	−	5.44189i	−0.882558	−	0.321225i
$288$	−16.1176	+	5.31257i	−0.949738	+	0.313046i
$289$	−2.16779	−	1.81899i	−0.127517	−	0.106999i
$290$	−1.90006	−	0.253476i	−0.111575	−	0.0148846i
$291$	18.2279	−	14.3018i	1.06854	−	0.838387i
$292$	5.94853	+	4.19580i	0.348111	+	0.245541i
$293$	27.3830	+	15.8096i	1.59973	+	0.923605i	0.991538	+	0.129815i	$0.0414382\pi$
$293$	27.3830	+	15.8096i	1.59973	+	0.923605i	0.608192	+	0.793790i	$0.291895\pi$
$294$	−35.1983	−	5.87790i	−2.05281	−	0.342806i
$295$	3.37835	+	0.595695i	0.196695	+	0.0346827i
$296$	19.2626	+	8.09565i	1.11962	+	0.470550i
$297$	−3.76910	−	0.372603i	−0.218706	−	0.0216206i
$298$	0.303448	−	0.580477i	0.0175783	−	0.0336261i
$299$	−3.43689	−	19.4916i	−0.198761	−	1.12723i
$300$	−16.9770	+	0.866189i	−0.980165	+	0.0500095i
$301$	33.4023	−	28.0279i	1.92528	−	1.61550i
$302$	1.58937	−	11.9140i	0.0914582	−	0.685571i
$303$	−4.75488	+	5.30277i	−0.273161	+	0.304636i
$304$	−12.9940	+	11.6256i	−0.745258	+	0.666776i
$305$		−	0.462066i		−	0.0264578i
$306$	18.8874	+	0.449227i	1.07972	+	0.0256806i
$307$	17.5711	−	3.09827i	1.00284	−	0.176827i	0.351964	−	0.936013i	$-0.385514\pi$
$307$	17.5711	−	3.09827i	1.00284	−	0.176827i	0.650874	+	0.759186i	$0.274403\pi$
$308$	−1.77480	+	6.53355i	−0.101128	+	0.372284i
$309$	−9.91938	−	6.16993i	−0.564294	−	0.350995i
$310$	0.0731123	+	1.74342i	0.00415250	+	0.0990197i
$311$	−0.183448			−0.0104024			−0.00520119	−	0.999986i	$-0.501656\pi$
$311$	−0.183448			−0.0104024			−0.00520119	+	0.999986i	$0.501656\pi$
$312$	−15.7979	−	1.29268i	−0.894382	−	0.0731837i
$313$	2.52672	−	14.3298i	0.142819	−	0.809965i	−0.826274	−	0.563268i	$-0.809544\pi$
$313$	2.52672	−	14.3298i	0.142819	−	0.809965i	0.969093	−	0.246697i	$-0.0793452\pi$
$314$	1.36308	+	32.5038i	0.0769232	+	1.83430i
$315$	−0.461045	−	4.21919i	−0.0259770	−	0.237725i
$316$	2.98369	+	6.45650i	0.167846	+	0.363207i
$317$	8.36856	−	9.97326i	0.470025	−	0.560154i	−0.477996	−	0.878362i	$-0.658637\pi$
$317$	8.36856	−	9.97326i	0.470025	−	0.560154i	0.948021	+	0.318208i	$0.103081\pi$
$318$	−1.96455	−	0.694934i	−0.110166	−	0.0389699i
$319$	3.19394	+	0.563178i	0.178826	+	0.0315319i
$320$	−2.21924	+	1.00707i	−0.124059	+	0.0562970i
$321$	−18.1726	+	29.2161i	−1.01430	+	1.63068i
$322$	−29.6683	+	27.0922i	−1.65335	+	1.50979i
$323$	17.9699	−	7.33826i	0.999872	−	0.408312i
$324$	−14.3233	+	10.9015i	−0.795738	+	0.605641i
$325$	−14.9198	−	5.43036i	−0.827602	−	0.301222i
$326$	−0.606456	−	0.467011i	−0.0335885	−	0.0258654i
$327$	21.2386	−	16.6640i	1.17450	−	0.921521i
$328$	2.86612	+	9.25662i	0.158255	+	0.511112i
$329$	−10.1821	−	27.9750i	−0.561356	−	1.54231i
$330$	−0.543876	+	0.00493079i	−0.0299394	+	0.000271431i
$331$			18.7092i			1.02835i	0.857685	+	0.514175i	$0.171902\pi$
$331$			18.7092i			1.02835i	−0.857685	+	0.514175i	$0.828098\pi$
$332$	−7.84984	−	2.13236i	−0.430816	−	0.117028i
$333$	22.1144	+	1.45482i	1.21186	+	0.0797235i
$334$	−15.1973	+	3.34173i	−0.831561	+	0.182851i
$335$	0.392140	+	0.679206i	0.0214249	+	0.0371090i
$336$	14.9684	+	28.4823i	0.816595	+	1.55384i
$337$	−10.5371	−	3.83520i	−0.573993	−	0.208917i	0.0386814	−	0.999252i	$-0.487684\pi$
$337$	−10.5371	−	3.83520i	−0.573993	−	0.208917i	−0.612675	+	0.790335i	$0.709906\pi$
$338$	3.17264	+	1.65852i	0.172569	+	0.0902116i
$339$	10.9284	−	5.83965i	0.593548	−	0.317166i
$340$	2.70356	−	0.227153i	0.146621	−	0.0123191i
$341$		−	2.95231i		−	0.159877i
$342$	−9.00777	+	16.1512i	−0.487085	+	0.873355i
$343$			35.1502i			1.89793i
$344$	−25.8961	−	5.88153i	−1.39623	−	0.317111i
$345$	−2.74073	−	1.70475i	−0.147556	−	0.0917808i
$346$	3.81815	−	7.30387i	0.205265	−	0.392658i
$347$	27.3520	+	9.95530i	1.46833	+	0.534428i	0.947646	−	0.319322i	$-0.103455\pi$
$347$	27.3520	+	9.95530i	1.46833	+	0.534428i	0.520683	+	0.853750i	$0.325677\pi$
$348$	12.9384	−	8.37686i	0.693569	−	0.449047i
$349$	10.9108	+	18.8980i	0.584040	+	1.01159i	0.994994	+	0.0999309i	$0.0318622\pi$
$349$	10.9108	+	18.8980i	0.584040	+	1.01159i	−0.410955	+	0.911656i	$0.634805\pi$
$350$	6.92166	+	31.4780i	0.369978	+	1.68257i
$351$	−16.2874	+	4.16802i	−0.869356	+	0.222473i
$352$	3.82286	−	1.54506i	0.203759	−	0.0823519i
$353$			18.0102i			0.958588i	0.877654	+	0.479294i	$0.159107\pi$
$353$			18.0102i			0.958588i	−0.877654	+	0.479294i	$0.840893\pi$
$354$	−23.7623	+	14.0079i	−1.26295	+	0.744512i
$355$	−0.195004	−	0.535769i	−0.0103497	−	0.0284356i
$356$	−24.8596	+	17.2796i	−1.31756	+	0.915817i
$357$	−5.05834	−	35.4615i	−0.267716	−	1.87682i
$358$	6.43248	−	8.35315i	0.339967	−	0.441478i
$359$	32.7644	+	11.9253i	1.72924	+	0.629392i	0.998576	−	0.0533437i	$-0.0169879\pi$
$359$	32.7644	+	11.9253i	1.72924	+	0.629392i	0.730665	+	0.682736i	$0.239210\pi$
$360$	−1.87686	+	1.77736i	−0.0989194	+	0.0936750i
$361$	−1.84526	+	18.9102i	−0.0971192	+	0.995273i
$362$	22.5846	+	24.7321i	1.18702	+	1.29989i
$363$	−18.1225	−	0.595462i	−0.951187	−	0.0312537i
$364$	2.51617	+	29.9473i	0.131883	+	1.56966i
$365$	1.09192	+	0.192535i	0.0571539	+	0.0100778i
$366$	2.41391	+	2.82439i	0.126177	+	0.147633i
$367$	−12.3272	+	14.6909i	−0.643472	+	0.766861i	−0.984914	−	0.173042i	$-0.944640\pi$
$367$	−12.3272	+	14.6909i	−0.643472	+	0.766861i	0.341442	+	0.939903i	$0.389085\pi$
$368$	24.0672	+	4.41481i	1.25459	+	0.230138i
$369$	6.07548	+	8.29010i	0.316277	+	0.431566i
$370$	3.17979	−	0.133348i	0.165310	−	0.00693243i
$371$	−0.686073	+	3.89091i	−0.0356191	+	0.202006i
$372$	−9.55485	−	10.2748i	−0.495396	−	0.532722i
$373$	0.231768			0.0120005			0.00600025	−	0.999982i	$-0.498090\pi$
$373$	0.231768			0.0120005			0.00600025	+	0.999982i	$0.498090\pi$
$374$	−4.58628	+	0.192331i	−0.237151	+	0.00994518i
$375$	−4.61046	+	2.46362i	−0.238083	+	0.127221i
$376$	−9.82056	+	15.2409i	−0.506457	+	0.785989i
$377$	14.1776	−	2.49989i	0.730184	−	0.128751i
$378$	24.8600	+	23.3814i	1.27866	+	1.20261i
$379$			7.19225i			0.369441i	0.982791	+	0.184720i	$0.0591380\pi$
$379$			7.19225i			0.369441i	−0.982791	+	0.184720i	$0.940862\pi$
$380$	−1.03699	+	2.44489i	−0.0531962	+	0.125420i
$381$	15.0415	+	3.16479i	0.770600	+	0.162137i
$382$	7.71810	+	1.02963i	0.394892	+	0.0526804i
$383$	−6.54505	+	5.49195i	−0.334436	+	0.280625i	−0.794505	−	0.607258i	$-0.792269\pi$
$383$	−6.54505	+	5.49195i	−0.334436	+	0.280625i	0.460068	+	0.887884i	$0.347825\pi$
$384$	8.30405	−	17.7494i	0.423764	−	0.905773i
$385$	0.179070	+	1.01556i	0.00912628	+	0.0517577i
$386$	5.75318	+	3.00751i	0.292829	+	0.153078i
$387$	−27.9998	+	3.05963i	−1.42331	+	0.155530i
$388$	−2.42345	+	26.6432i	−0.123032	+	1.35260i
$389$	−20.7793	−	3.66396i	−1.05355	−	0.185770i	−0.380059	−	0.924962i	$-0.624096\pi$
$389$	−20.7793	−	3.66396i	−1.05355	−	0.185770i	−0.673495	+	0.739192i	$0.735208\pi$
$390$	−2.26113	+	0.846278i	−0.114497	+	0.0428529i
$391$	−23.5908	−	13.6201i	−1.19304	−	0.688800i
$392$	32.8203	−	24.9156i	1.65767	−	1.25843i
$393$	2.77875	+	19.4805i	0.140169	+	0.982659i
$394$	−1.72535	+	12.9332i	−0.0869216	+	0.651565i
$395$	0.829900	+	0.696369i	0.0417568	+	0.0350381i
$396$	3.29870	−	2.87145i	0.165766	−	0.144296i
$397$	−4.82177	−	1.75498i	−0.241998	−	0.0880799i	0.218174	−	0.975910i	$-0.429990\pi$
$397$	−4.82177	−	1.75498i	−0.241998	−	0.0880799i	−0.460172	+	0.887830i	$0.652212\pi$
$398$	21.3799	−	19.5234i	1.07168	−	0.978621i
$399$	33.0172	+	11.8015i	1.65293	+	0.590812i
$400$	12.7204	−	14.9493i	0.636020	−	0.747464i
$401$	−23.1018	+	4.07347i	−1.15365	+	0.203420i	−0.717569	−	0.696488i	$-0.754745\pi$
$401$	−23.1018	+	4.07347i	−1.15365	+	0.203420i	−0.436081	+	0.899907i	$0.643634\pi$
$402$	−5.94525	−	2.10306i	−0.296522	−	0.104891i
$403$	−4.48218	−	12.3147i	−0.223274	−	0.613439i
$404$	−0.688571	−	8.19534i	−0.0342577	−	0.407733i
$405$	−1.26714	+	2.43129i	−0.0629648	+	0.120812i
$406$	−19.7061	−	21.5799i	−0.977996	−	1.07099i
$407$	−5.38466			−0.266908
$408$	−15.3389	+	15.5124i	−0.759390	+	0.767977i
$409$	16.5319	+	13.8719i	0.817448	+	0.685920i	0.952373	−	0.304935i	$-0.0986349\pi$
$409$	16.5319	+	13.8719i	0.817448	+	0.685920i	−0.134925	+	0.990856i	$0.543079\pi$
$410$	0.995274	+	1.08991i	0.0491531	+	0.0538270i
$411$	6.67701	+	20.4065i	0.329353	+	1.00658i
$412$	13.0412	−	3.44629i	0.642493	−	0.169786i
$413$	33.6169	+	40.0631i	1.65418	+	1.97138i
$414$	25.6587	−	3.89770i	1.26106	−	0.191561i
$415$	−1.22016	+	0.215147i	−0.0598953	+	0.0105612i
$416$	13.6002	−	12.2486i	0.666806	−	0.600537i
$417$	−11.2447	−	34.3664i	−0.550654	−	1.68293i
$418$	1.92627	−	4.05940i	0.0942168	−	0.198552i
$419$	−19.3011	−	33.4306i	−0.942923	−	1.63319i	−0.759858	−	0.650089i	$-0.774731\pi$
$419$	−19.3011	−	33.4306i	−0.942923	−	1.63319i	−0.183065	−	0.983101i	$-0.558602\pi$
$420$	3.90996	+	2.95485i	0.190786	+	0.144182i
$421$	−22.0918	−	8.04074i	−1.07669	−	0.391882i	−0.258013	−	0.966141i	$-0.583068\pi$
$421$	−22.0918	−	8.04074i	−1.07669	−	0.391882i	−0.818673	+	0.574260i	$0.805290\pi$
$422$	5.29207	+	8.33854i	0.257614	+	0.405914i
$423$	−4.57538	+	18.6785i	−0.222462	+	0.908179i
$424$	2.14005	−	1.10003i	0.103930	−	0.0534220i
$425$	−18.9245	+	10.9261i	−0.917972	+	0.529992i
$426$	3.99092	+	2.25617i	0.193361	+	0.109312i
$427$	4.52802	−	5.39628i	0.219126	−	0.261144i
$428$	−10.1505	−	38.4109i	−0.490645	−	1.85666i
$429$	3.88228	−	1.27028i	0.187438	−	0.0613297i
$430$	−3.95046	+	0.868663i	−0.190508	+	0.0418907i
$431$	2.06553	−	11.7142i	0.0994932	−	0.564254i	−0.893784	−	0.448497i	$-0.851959\pi$
$431$	2.06553	−	11.7142i	0.0994932	−	0.564254i	0.993278	−	0.115757i	$-0.0369294\pi$
$432$	2.18714	−	20.6692i	0.105229	−	0.994448i
$433$	−4.88668	−	4.10041i	−0.234839	−	0.197053i	0.517772	−	0.855518i	$-0.326761\pi$
$433$	−4.88668	−	4.10041i	−0.234839	−	0.197053i	−0.752611	+	0.658465i	$0.771206\pi$
$434$	−16.2308	+	21.0772i	−0.779105	+	1.01174i
$435$	1.23999	−	1.99352i	0.0594528	−	0.0955822i
$436$	−2.82372	+	31.0437i	−0.135232	+	1.48673i
$437$	22.5598	−	14.2140i	1.07918	−	0.679947i
$438$	−7.68025	+	4.52752i	−0.366976	+	0.216333i
$439$	−0.651150	−	0.776010i	−0.0310777	−	0.0370369i	0.750282	−	0.661118i	$-0.229918\pi$
$439$	−0.651150	−	0.776010i	−0.0310777	−	0.0370369i	−0.781359	+	0.624081i	$0.785473\pi$
$440$	0.426684	−	0.460842i	0.0203414	−	0.0219698i
$441$	24.2905	−	36.3342i	1.15669	−	1.73020i
$442$	−18.8383	+	7.76512i	−0.896048	+	0.369349i
$443$	10.9215	+	9.16426i	0.518898	+	0.435407i	0.864247	−	0.503067i	$-0.167795\pi$
$443$	10.9215	+	9.16426i	0.518898	+	0.435407i	−0.345349	+	0.938474i	$0.612240\pi$
$444$	−18.7399	+	17.4269i	−0.889358	+	0.827044i
$445$	−2.30569	+	3.99357i	−0.109300	+	0.189313i
$446$	−8.59713	−	13.5462i	−0.407086	−	0.641431i
$447$	0.495196	+	0.631136i	0.0234219	+	0.0298517i
$448$	−35.7864	−	9.98628i	−1.69075	−	0.471807i
$449$	−18.9558	−	10.9441i	−0.894580	−	0.516486i	−0.0191423	−	0.999817i	$-0.506094\pi$
$449$	−18.9558	−	10.9441i	−0.894580	−	0.516486i	−0.875438	+	0.483331i	$0.839427\pi$
$450$	7.58386	−	19.3891i	0.357506	−	0.914010i
$451$	−1.60518	−	1.91297i	−0.0755848	−	0.0900784i
$452$	−3.75065	+	13.8073i	−0.176416	+	0.649439i
$453$	12.5000	+	7.77510i	0.587302	+	0.365306i
$454$	−1.16788	−	0.155801i	−0.0548115	−	0.00731209i
$455$	2.28876	+	3.96424i	0.107299	+	0.185846i
$456$	−6.43393	−	20.3618i	−0.301296	−	0.953531i
$457$	−12.4699	+	21.5985i	−0.583318	+	1.01034i	0.411765	+	0.911290i	$0.364912\pi$
$457$	−12.4699	+	21.5985i	−0.583318	+	1.01034i	−0.995083	+	0.0990458i	$0.968421\pi$
$458$	7.70673	−	10.0079i	0.360112	−	0.467637i
$459$	−10.0146	+	20.8594i	−0.467443	+	0.973632i
$460$	3.60328	−	0.952210i	0.168004	−	0.0443970i
$461$	30.7369	−	5.41975i	1.43156	−	0.252423i	0.596515	−	0.802602i	$-0.296552\pi$
$461$	30.7369	−	5.41975i	1.43156	−	0.252423i	0.835047	+	0.550179i	$0.185440\pi$
$462$	−6.40003	−	5.27214i	−0.297756	−	0.245282i
$463$		−	29.9071i		−	1.38990i	−0.719059	−	0.694949i	$-0.755427\pi$
$463$		−	29.9071i		−	1.38990i	0.719059	−	0.694949i	$-0.244573\pi$
$464$	−3.21120	+	17.5058i	−0.149076	+	0.812685i
$465$	−1.98315	−	0.796495i	−0.0919665	−	0.0369366i
$466$	16.0966	−	30.7917i	0.745660	−	1.42640i
$467$	13.1426	+	22.7637i	0.608168	+	1.05338i	0.991542	+	0.129785i	$0.0414286\pi$
$467$	13.1426	+	22.7637i	0.608168	+	1.05338i	−0.383374	+	0.923593i	$0.625238\pi$
$468$	9.40014	−	16.9855i	0.434522	−	0.785153i
$469$	−2.07624	+	11.7749i	−0.0958718	+	0.543716i
$470$	−0.365177	+	2.73737i	−0.0168443	+	0.126265i
$471$	−36.9733	−	14.8496i	−1.70364	−	0.684235i
$472$	7.05436	−	31.0601i	0.324703	−	1.42965i
$473$	6.73955	−	1.18836i	0.309885	−	0.0546411i
$474$	−8.71074	+	0.0789717i	−0.400098	+	0.00362729i
$475$	−0.826094	−	21.3740i	−0.0379038	−	0.980708i
$476$	33.7998	+	23.8408i	1.54921	+	1.09274i
$477$	1.76531	−	1.84317i	0.0808278	−	0.0843930i
$478$	−18.0279	−	2.40500i	−0.824576	−	0.110002i
$479$	19.7657	−	7.19412i	0.903117	−	0.328708i	0.151616	−	0.988439i	$-0.451552\pi$
$479$	19.7657	−	7.19412i	0.903117	−	0.328708i	0.751501	+	0.659732i	$0.229330\pi$
$480$	−0.00650333	−	2.98476i	−0.000296835	−	0.136235i
$481$	−22.4605	+	8.17497i	−1.02411	+	0.372746i
$482$	−9.58931	+	30.2318i	−0.436781	+	1.37702i
$483$	−15.3021	−	46.7669i	−0.696270	−	2.12797i
$484$	14.8559	−	14.7539i	0.675267	−	0.670633i
$485$	1.39371	+	3.82918i	0.0632850	+	0.173874i
$486$	−4.95604	−	21.4811i	−0.224811	−	0.974402i
$487$	4.64077	+	2.67935i	0.210293	+	0.121413i	0.601448	−	0.798912i	$-0.294591\pi$
$487$	4.64077	+	2.67935i	0.210293	+	0.121413i	−0.391154	+	0.920325i	$0.627924\pi$
$488$	−4.28506	−	0.209270i	−0.193976	−	0.00947323i
$489$	0.826820	−	0.441816i	0.0373901	−	0.0199796i
$490$	2.90768	−	5.56221i	0.131356	−	0.251275i
$491$	−18.5149	+	15.5358i	−0.835564	+	0.701121i	−0.956561	−	0.291532i	$-0.905835\pi$
$491$	−18.5149	+	15.5358i	−0.835564	+	0.701121i	0.120997	+	0.992653i	$0.461391\pi$
$492$	−11.7775	−	1.46263i	−0.530972	−	0.0659405i
$493$	9.90689	−	17.1592i	0.446184	−	0.772814i
$494$	1.87190	−	19.8570i	0.0842208	−	0.893410i
$495$	0.268432	−	0.609658i	0.0120651	−	0.0274021i
$496$	16.2011	+	0.111577i	0.727450	+	0.00500998i
$497$	2.97290	−	8.16797i	0.133353	−	0.366383i
$498$	6.33429	−	7.68942i	0.283846	−	0.344571i
$499$	6.23154	−	17.1210i	0.278962	−	0.766442i	−0.718519	−	0.695507i	$-0.755180\pi$
$499$	6.23154	−	17.1210i	0.278962	−	0.766442i	0.997481	−	0.0709344i	$-0.0225981\pi$
$500$	1.58232	−	5.82500i	0.0707636	−	0.260502i
$501$	3.92386	−	18.6492i	0.175305	−	0.833185i
$502$	−3.35889	+	10.5894i	−0.149914	+	0.472629i
$503$	−9.56357	+	3.48085i	−0.426418	+	0.155204i	−0.546309	−	0.837583i	$-0.683968\pi$
$503$	−9.56357	+	3.48085i	−0.426418	+	0.155204i	0.119891	+	0.992787i	$0.461745\pi$
$504$	−39.3364	+	2.36472i	−1.75218	+	0.105333i
$505$	−0.626339	−	1.08485i	−0.0278717	−	0.0482752i
$506$	−6.15859	+	1.35421i	−0.273783	+	0.0602018i
$507$	−3.44952	+	2.70653i	−0.153199	+	0.120201i
$508$	−14.5739	+	10.1301i	−0.646611	+	0.449452i
$509$	−15.2048	−	2.68102i	−0.673943	−	0.118834i	−0.173805	−	0.984780i	$-0.555606\pi$
$509$	−15.2048	−	2.68102i	−0.673943	−	0.118834i	−0.500138	+	0.865946i	$0.666717\pi$
$510$	−1.10813	+	3.13263i	−0.0490686	+	0.138715i
$511$	10.8654	+	12.9488i	0.480656	+	0.572823i
$512$	8.33418	+	21.0367i	0.368322	+	0.929698i
$513$	−13.4939	−	18.1911i	−0.595771	−	0.803155i
$514$	4.16514	+	1.32115i	0.183716	+	0.0582735i
$515$	1.57389	−	1.32065i	0.0693538	−	0.0581948i
$516$	19.6092	−	25.9476i	0.863249	−	1.14228i
$517$	0.811357	−	4.60143i	0.0356834	−	0.202371i
$518$	38.4423	+	29.6031i	1.68906	+	1.30068i
$519$	6.23081	+	7.94129i	0.273502	+	0.348584i
$520$	1.08014	−	2.57006i	0.0473672	−	0.112704i
$521$	37.6728	−	21.7504i	1.65047	−	0.952901i	0.673596	−	0.739100i	$-0.264749\pi$
$521$	37.6728	−	21.7504i	1.65047	−	0.952901i	0.976877	−	0.213801i	$-0.0685845\pi$
$522$	2.83507	+	18.6634i	0.124088	+	0.816874i
$523$	4.37854	+	12.0299i	0.191460	+	0.526033i	0.997864	−	0.0653332i	$-0.0208110\pi$
$523$	4.37854	+	12.0299i	0.191460	+	0.526033i	−0.806403	+	0.591366i	$0.798589\pi$
$524$	−18.5676	−	13.0967i	−0.811130	−	0.572132i
$525$	−38.6277	−	8.12741i	−1.68585	−	0.354709i
$526$	0.606082	+	14.4525i	0.0264264	+	0.630160i
$527$	−16.9488	−	6.16887i	−0.738303	−	0.268720i
$528$	−0.200596	+	5.04598i	−0.00872981	+	0.219598i
$529$	−13.5504	−	4.93194i	−0.589148	−	0.214432i
$530$	0.223614	−	0.290382i	0.00971315	−	0.0126134i
$531$	−3.66975	−	33.5833i	−0.159254	−	1.45739i
$532$	−36.0692	+	18.3909i	−1.56380	+	0.797348i
$533$	−9.59978	−	5.54244i	−0.415813	−	0.240070i
$534$	−6.76953	−	36.4561i	−0.292946	−	1.57761i
$535$	−3.88978	−	4.63566i	−0.168170	−	0.200417i
$536$	6.47635	−	3.32897i	0.279736	−	0.143790i
$537$	6.08545	+	11.3884i	0.262606	+	0.491445i
$538$	8.64086	+	13.6151i	0.372534	+	0.586989i
$539$	−5.30953	+	9.19638i	−0.228698	+	0.396116i
$540$	−1.03889	−	2.99051i	−0.0447065	−	0.128691i
$541$	0.0229040	−	0.00833637i	0.000984719	−	0.000358408i	−0.341528	−	0.939872i	$-0.610944\pi$
$541$	0.0229040	−	0.00833637i	0.000984719	−	0.000358408i	0.342512	+	0.939513i	$0.388722\pi$
$542$	0.891013	−	1.70445i	0.0382723	−	0.0732123i
$543$	−38.9858	+	12.7561i	−1.67304	+	0.547419i
$544$	−0.882102	−	25.1749i	−0.0378198	−	1.07937i
$545$	1.62390	+	4.46163i	0.0695603	+	0.191115i
$546$	−34.7000	−	12.2747i	−1.48502	−	0.525307i
$547$	−4.28621	−	11.7763i	−0.183265	−	0.503516i	0.813707	−	0.581275i	$-0.197446\pi$
$547$	−4.28621	−	11.7763i	−0.183265	−	0.503516i	−0.996972	+	0.0777586i	$0.975224\pi$
$548$	−22.4336	−	10.5552i	−0.958317	−	0.450894i
$549$	−4.36893	+	1.27228i	−0.186461	+	0.0542997i
$550$	−1.52941	+	4.82169i	−0.0652141	+	0.205598i
$551$	10.3388	+	16.4093i	0.440449	+	0.699060i
$552$	−17.0506	+	24.6446i	−0.725724	+	1.04894i
$553$	2.86800	+	16.2652i	0.121960	+	0.691668i
$554$	−13.9210	−	33.7726i	−0.591446	−	1.43486i
$555$	−1.45271	+	3.61703i	−0.0616642	+	0.153534i
$556$	37.7802	+	17.7758i	1.60224	+	0.753863i
$557$	−35.7848	−	6.30982i	−1.51625	−	0.267356i	−0.647292	−	0.762242i	$-0.724099\pi$
$557$	−35.7848	−	6.30982i	−1.51625	−	0.267356i	−0.868958	+	0.494886i	$0.835210\pi$
$558$	16.2831	−	5.49174i	0.689319	−	0.232484i
$559$	26.3079	−	15.1889i	1.11270	−	0.642420i
$560$	−5.57974	+	0.944284i	−0.235787	+	0.0399033i
$561$	2.09528	−	5.21692i	0.0884627	−	0.220259i
$562$	32.1091	−	29.3211i	1.35444	−	1.23683i
$563$	12.2701			0.517121			0.258561	−	0.965995i	$-0.416752\pi$
$563$	12.2701			0.517121			0.258561	+	0.965995i	$0.416752\pi$
$564$	−12.0683	−	18.6400i	−0.508168	−	0.784884i
$565$	0.378427	+	2.14617i	0.0159206	+	0.0902899i
$566$	−14.2989	−	22.5303i	−0.601027	−	0.947018i
$567$	−38.6239	+	15.9767i	−1.62205	+	0.670957i
$568$	−5.05688	+	1.56576i	−0.212182	+	0.0656977i
$569$	35.5590	+	20.5300i	1.49071	+	0.860663i	0.999944	−	0.0106278i	$-0.00338301\pi$
$569$	35.5590	+	20.5300i	1.49071	+	0.860663i	0.490768	+	0.871290i	$0.336716\pi$
$570$	−2.20713	−	2.38910i	−0.0924465	−	0.100068i
$571$	32.2837	−	18.6390i	1.35103	−	0.780017i	0.362636	−	0.931931i	$-0.381877\pi$
$571$	32.2837	−	18.6390i	1.35103	−	0.780017i	0.988394	+	0.151914i	$0.0485437\pi$
$572$	−2.00809	+	4.26792i	−0.0839623	+	0.178451i
$573$	−5.03687	+	8.09776i	−0.210418	+	0.338289i
$574$	0.942800	+	22.4818i	0.0393517	+	0.938374i
$575$	−22.9953	+	19.2954i	−0.958972	+	0.804673i
$576$	15.6327	+	18.2104i	0.651361	+	0.758768i
$577$	−2.49339	+	4.31867i	−0.103801	+	0.179789i	−0.913248	−	0.407405i	$-0.866434\pi$
$577$	−2.49339	+	4.31867i	−0.103801	+	0.179789i	0.809447	+	0.587193i	$0.199767\pi$
$578$	−1.21000	+	3.81470i	−0.0503292	+	0.158671i
$579$	−6.25527	+	4.90794i	−0.259960	+	0.203967i
$580$	0.692610	+	2.62092i	0.0287591	+	0.108828i
$581$	−16.3581	−	9.44435i	−0.678648	−	0.391818i
$582$	−28.5234	−	16.1250i	−1.18233	−	0.668402i
$583$	−0.398588	+	0.475018i	−0.0165078	+	0.0196733i
$584$	2.28005	−	10.0390i	0.0943491	−	0.415415i
$585$	0.194105	−	2.95054i	0.00802524	−	0.121990i
$586$	5.91296	−	44.3235i	0.244262	−	1.83099i
$587$	20.5858	−	17.2735i	0.849667	−	0.712955i	−0.110049	−	0.993926i	$-0.535101\pi$
$587$	20.5858	−	17.2735i	0.849667	−	0.712955i	0.959716	+	0.280971i	$0.0906564\pi$
$588$	11.2846	+	49.1894i	0.465371	+	2.02854i
$589$	13.0762	−	11.8624i	0.538797	−	0.488781i
$590$	−1.04188	−	4.73822i	−0.0428936	−	0.195069i
$591$	−13.5694	−	8.44026i	−0.558170	−	0.347186i
$592$	0.203504	−	29.5488i	0.00836396	−	1.21445i
$593$	1.21757	−	1.45105i	0.0499997	−	0.0595873i	−0.740465	−	0.672095i	$-0.765395\pi$
$593$	1.21757	−	1.45105i	0.0499997	−	0.0595873i	0.790465	+	0.612508i	$0.209839\pi$
$594$	1.54417	+	5.12889i	0.0633579	+	0.210441i
$595$	6.20436	+	1.09400i	0.254354	+	0.0448495i
$596$	−0.922511	−	0.0839112i	−0.0377875	−	0.00343714i
$597$	11.0271	+	33.7016i	0.451311	+	1.37931i
$598$	−23.6328	+	14.9986i	−0.966417	+	0.613339i
$599$	13.1730	+	11.0535i	0.538236	+	0.451633i	0.870934	−	0.491400i	$-0.163515\pi$
$599$	13.1730	+	11.0535i	0.538236	+	0.451633i	−0.332698	+	0.943033i	$0.607959\pi$
$600$	10.2822	+	21.7304i	0.419769	+	0.887141i
$601$	1.69778	+	2.94065i	0.0692540	+	0.119951i	0.898573	−	0.438824i	$-0.144605\pi$
$601$	1.69778	+	2.94065i	0.0692540	+	0.119951i	−0.829319	+	0.558775i	$0.811271\pi$
$602$	−54.6483	−	28.5678i	−2.22730	−	1.16434i
$603$	5.34229	−	5.57793i	0.217555	−	0.227151i
$604$	−16.4340	+	4.34288i	−0.668690	+	0.176709i
$605$	1.09074	−	2.99677i	0.0443447	−	0.121836i
$606$	9.49596	+	3.35907i	0.385747	+	0.136453i
$607$	13.4845	−	7.78527i	0.547319	−	0.315995i	−0.200721	−	0.979648i	$-0.564329\pi$
$607$	13.4845	−	7.78527i	0.547319	−	0.315995i	0.748040	+	0.663654i	$0.230995\pi$
$608$	22.2035	+	10.7240i	0.900471	+	0.434915i
$609$	34.0169	−	11.1303i	1.37843	−	0.451023i
$610$	−0.604148	+	0.249029i	−0.0244612	+	0.0100829i
$611$	−3.60153	−	20.4253i	−0.145702	−	0.826320i
$612$	−9.59194	−	24.9373i	−0.387731	−	1.00803i
$613$	30.4586	−	25.5578i	1.23021	−	1.03227i	0.231987	−	0.972719i	$-0.425477\pi$
$613$	30.4586	−	25.5578i	1.23021	−	1.03227i	0.998225	−	0.0595521i	$-0.0189672\pi$
$614$	−13.5209	−	21.3043i	−0.545657	−	0.859773i
$615$	−1.71805	+	0.562147i	−0.0692787	+	0.0226680i
$616$	9.49909	−	1.20070i	0.382729	−	0.0483775i
$617$	−21.9452	+	26.1533i	−0.883482	+	1.05289i	0.114746	+	0.993395i	$0.463395\pi$
$617$	−21.9452	+	26.1533i	−0.883482	+	1.05289i	−0.998228	+	0.0594984i	$0.981050\pi$
$618$	−2.72113	+	16.2948i	−0.109460	+	0.655472i
$619$		−	0.767559i		−	0.0308508i	−0.999881	−	0.0154254i	$-0.995090\pi$
$619$		−	0.767559i		−	0.0308508i	0.999881	−	0.0154254i	$-0.00491025\pi$
$620$	2.24011	−	1.03520i	0.0899649	−	0.0415748i
$621$	−8.57230	+	30.6081i	−0.343994	+	1.22826i
$622$	0.0988684	+	0.239857i	0.00396426	+	0.00961738i
$623$	−66.0622	+	24.0447i	−2.64673	+	0.963330i
$624$	6.82405	+	21.3524i	0.273181	+	0.854779i
$625$	4.10098	+	23.2578i	0.164039	+	0.930313i
$626$	−20.0978	+	4.41929i	−0.803270	+	0.176630i
$627$	3.56163	+	4.19507i	0.142238	+	0.167535i
$628$	41.7639	−	19.3000i	1.66656	−	0.770155i
$629$	−11.2513	+	30.9127i	−0.448618	+	1.23257i
$630$	−5.26809	+	2.87673i	−0.209886	+	0.114612i
$631$	−7.68470	+	9.15827i	−0.305923	+	0.364585i	−0.897000	−	0.442030i	$-0.854258\pi$
$631$	−7.68470	+	9.15827i	−0.305923	+	0.364585i	0.591077	+	0.806615i	$0.298703\pi$
$632$	6.83378	−	7.38086i	0.271833	−	0.293595i
$633$	−11.9745	+	1.70808i	−0.475943	+	0.0678900i
$634$	−17.5502	−	5.56679i	−0.697006	−	0.221085i
$635$	−1.35171	+	2.34122i	−0.0536408	+	0.0929086i
$636$	0.150165	+	2.94317i	0.00595442	+	0.116704i
$637$	−8.18526	+	46.4209i	−0.324312	+	1.83926i
$638$	−0.985010	−	4.47958i	−0.0389969	−	0.177348i
$639$	−4.52887	+	3.31902i	−0.179159	+	0.131298i
$640$	2.51279	+	2.35888i	0.0993267	+	0.0932431i
$641$	−34.3544	+	6.05761i	−1.35692	+	0.239261i	−0.804324	−	0.594191i	$-0.797473\pi$
$641$	−34.3544	+	6.05761i	−1.35692	+	0.239261i	−0.552592	+	0.833452i	$0.686361\pi$
$642$	47.9939	+	8.01469i	1.89417	+	0.316314i
$643$	10.0484	+	11.9752i	0.396269	+	0.472255i	0.926879	−	0.375361i	$-0.122481\pi$
$643$	10.0484	+	11.9752i	0.396269	+	0.472255i	−0.530609	+	0.847616i	$0.678037\pi$
$644$	51.4125	+	24.1899i	2.02594	+	0.953216i
$645$	1.01998	−	4.84775i	0.0401619	−	0.190880i
$646$	−19.2795	−	19.5406i	−0.758543	−	0.768814i
$647$	42.7677			1.68137			0.840686	−	0.541523i	$-0.182152\pi$
$647$	42.7677			1.68137			0.840686	+	0.541523i	$0.182152\pi$
$648$	21.9732	+	12.8522i	0.863187	+	0.504884i
$649$	1.42534	+	8.08348i	0.0559493	+	0.317304i
$650$	0.940802	+	22.4342i	0.0369013	+	0.879942i
$651$	−15.3552	−	28.7359i	−0.601817	−	1.12625i
$652$	−0.283767	+	1.04463i	−0.0111132	+	0.0409109i
$653$		−	0.165767i		−	0.00648698i	−0.999995	−	0.00324349i	$-0.998968\pi$
$653$		−	0.165767i		−	0.00648698i	0.999995	−	0.00324349i	$-0.00103244\pi$
$654$	−33.2345	−	18.7883i	−1.29957	−	0.734680i
$655$	−3.40831	−	0.600976i	−0.133174	−	0.0234821i
$656$	10.5583	−	8.73625i	0.412232	−	0.341093i
$657$	−1.18611	−	10.8545i	−0.0462744	−	0.423474i
$658$	−31.0896	+	28.3900i	−1.21200	+	1.10676i
$659$	−9.46081	−	7.93856i	−0.368541	−	0.309243i	0.439643	−	0.898173i	$-0.355105\pi$
$659$	−9.46081	−	7.93856i	−0.368541	−	0.309243i	−0.808184	+	0.588930i	$0.799549\pi$
$660$	0.299567	+	0.708457i	0.0116606	+	0.0275767i
$661$	−1.06288	+	6.02790i	−0.0413413	+	0.234458i	−0.998476	−	0.0551844i	$-0.982425\pi$
$661$	−1.06288	+	6.02790i	−0.0413413	+	0.234458i	0.957135	+	0.289643i	$0.0935364\pi$
$662$	24.4622	−	10.0832i	0.950748	−	0.391896i
$663$	0.819530	−	24.9419i	0.0318279	−	0.968663i
$664$	1.44260	+	11.4128i	0.0559837	+	0.442904i
$665$	−3.77856	+	4.87364i	−0.146526	+	0.188992i
$666$	−10.0163	−	29.6984i	−0.388123	−	1.15079i
$667$	9.30918	−	25.5768i	0.360453	−	0.990337i
$668$	12.5598	+	18.0694i	0.485954	+	0.699126i
$669$	19.4529	−	2.77482i	0.752093	−	0.107281i
$670$	0.676715	−	0.878775i	0.0261438	−	0.0339500i
$671$	1.03892	−	0.378137i	0.0401072	−	0.0145978i
$672$	29.1732	−	34.9215i	1.12538	−	1.34713i
$673$	−36.8676			−1.42114			−0.710570	−	0.703627i	$-0.751563\pi$
$673$	−36.8676			−1.42114			−0.710570	+	0.703627i	$0.751563\pi$
$674$	0.664442	+	15.8442i	0.0255933	+	0.610295i
$675$	17.8258	+	18.2323i	0.686117	+	0.701760i
$676$	0.458623	−	5.04206i	0.0176394	−	0.193925i
$677$	−10.3372	+	5.96816i	−0.397289	+	0.229375i	−0.685314	−	0.728248i	$-0.740335\pi$
$677$	−10.3372	+	5.96816i	−0.397289	+	0.229375i	0.288025	+	0.957623i	$0.407002\pi$
$678$	−13.5251	−	11.1415i	−0.519428	−	0.427888i
$679$	−21.2475	+	58.3771i	−0.815405	+	2.24031i
$680$	−1.75408	−	3.41247i	−0.0672657	−	0.130862i
$681$	0.762166	−	1.22533i	0.0292063	−	0.0469548i
$682$	−3.86013	+	1.59114i	−0.147812	+	0.0609278i
$683$	0.833395			0.0318890			0.0159445	−	0.999873i	$-0.494924\pi$
$683$	0.833395			0.0318890			0.0159445	+	0.999873i	$0.494924\pi$
$684$	25.9722	+	3.07300i	0.993073	+	0.117499i
$685$	−3.77632			−0.144286
$686$	45.9587	−	18.9441i	1.75471	−	0.723288i
$687$	7.29095	+	13.6444i	0.278167	+	0.520565i
$688$	6.26655	+	37.0288i	0.238910	+	1.41171i
$689$	−0.941421	+	2.58653i	−0.0358653	+	0.0985391i
$690$	−0.751849	+	4.50225i	−0.0286224	+	0.171398i
$691$	15.6165	−	9.01618i	0.594079	−	0.342991i	−0.172630	−	0.984987i	$-0.555226\pi$
$691$	15.6165	−	9.01618i	0.594079	−	0.342991i	0.766709	+	0.641995i	$0.221893\pi$
$692$	−11.6075	−	1.05582i	−0.441252	−	0.0401361i
$693$	9.10926	−	4.48945i	0.346032	−	0.170540i
$694$	−1.72474	−	41.1278i	−0.0654702	−	1.56119i
$695$	6.35966			0.241236
$696$	−17.9258	−	12.4021i	−0.679474	−	0.470102i
$697$	−14.3362	+	5.21793i	−0.543021	+	0.197643i
$698$	18.8287	−	24.4507i	0.712676	−	0.925474i
$699$	26.2679	+	33.4790i	0.993544	+	1.26629i
$700$	37.4268	−	26.0149i	1.41460	−	0.983272i
$701$	−8.81994	+	24.2326i	−0.333124	+	0.915252i	0.654170	+	0.756348i	$0.273018\pi$
$701$	−8.81994	+	24.2326i	−0.333124	+	0.915252i	−0.987294	+	0.158904i	$0.949204\pi$
$702$	14.2277	+	19.0493i	0.536989	+	0.718969i
$703$	−21.6355	−	23.8495i	−0.816000	−	0.899501i
$704$	−4.08047	−	4.16565i	−0.153788	−	0.156999i
$705$	−2.87202	−	1.78642i	−0.108167	−	0.0672804i
$706$	23.5482	−	9.70654i	0.886250	−	0.365310i
$707$	3.31624	−	18.8073i	0.124720	−	0.707323i
$708$	31.1218	+	23.5195i	1.16963	+	0.883918i
$709$	−17.5791	−	14.7506i	−0.660197	−	0.553971i	0.249949	−	0.968259i	$-0.419586\pi$
$709$	−17.5791	−	14.7506i	−0.660197	−	0.553971i	−0.910146	+	0.414288i	$0.864031\pi$
$710$	−0.595417	+	0.543716i	−0.0223456	+	0.0204053i
$711$	4.29921	−	9.76430i	0.161233	−	0.366190i
$712$	35.9909	+	23.1910i	1.34882	+	0.869118i
$713$	−24.4005	−	4.30246i	−0.913804	−	0.161128i
$714$	−43.6395	+	25.7256i	−1.63317	+	0.962756i
$715$			0.718433i			0.0268679i
$716$	−14.3884	−	3.90852i	−0.537721	−	0.146068i
$717$	11.7651	−	18.9147i	0.439375	−	0.706382i
$718$	−2.06604	−	49.2664i	−0.0771038	−	1.83860i
$719$	−2.90789	−	16.4915i	−0.108446	−	0.615027i	−0.989788	−	0.142548i	$-0.954470\pi$
$719$	−2.90789	−	16.4915i	−0.108446	−	0.615027i	0.881342	−	0.472479i	$-0.156641\pi$
$720$	3.33541	+	1.49609i	0.124303	+	0.0557558i
$721$	31.3225			1.16651
$722$	25.7194	−	7.77889i	0.957178	−	0.289500i
$723$	−28.9204	−	25.9323i	−1.07556	−	0.964434i
$724$	20.1652	−	42.8585i	0.749434	−	1.59282i
$725$	−14.0349	−	16.7261i	−0.521243	−	0.621193i
$726$	8.98851	+	24.0160i	0.333595	+	0.891318i
$727$	−40.6274	+	7.16370i	−1.50679	+	0.265687i	−0.865225	−	0.501385i	$-0.832824\pi$
$727$	−40.6274	+	7.16370i	−1.50679	+	0.265687i	−0.641562	+	0.767072i	$0.721713\pi$
$728$	37.7998	−	19.4298i	1.40095	−	0.720117i
$729$	26.4774	+	5.28663i	0.980644	+	0.195801i
$730$	−0.336748	−	1.53145i	−0.0124636	−	0.0566814i
$731$	7.26008	−	41.1740i	0.268524	−	1.52287i
$732$	2.39190	−	4.67837i	0.0884072	−	0.172917i
$733$	−9.87325	+	17.1010i	−0.364677	+	0.631639i	−0.988724	−	0.149748i	$-0.952154\pi$
$733$	−9.87325	+	17.1010i	−0.364677	+	0.631639i	0.624047	+	0.781386i	$0.285487\pi$
$734$	25.8520	+	8.20005i	0.954213	+	0.302669i
$735$	4.74503	+	6.04763i	0.175023	+	0.223070i
$736$	−7.19858	−	33.8470i	−0.265343	−	1.24762i
$737$	−1.20623	+	1.43753i	−0.0444322	+	0.0529522i
$738$	7.56490	−	12.4116i	0.278468	−	0.456876i
$739$	−5.76543	+	15.8404i	−0.212085	+	0.582698i	−0.999428	−	0.0338165i	$-0.989234\pi$
$739$	−5.76543	+	15.8404i	−0.212085	+	0.582698i	0.787343	+	0.616515i	$0.211456\pi$
$740$	−1.88809	−	4.08569i	−0.0694075	−	0.150193i
$741$	21.2252	+	12.0912i	0.779728	+	0.444182i
$742$	5.45709	−	1.19996i	0.200336	−	0.0440517i
$743$	7.52434	+	42.6727i	0.276041	+	1.56551i	0.735634	+	0.677379i	$0.236884\pi$
$743$	7.52434	+	42.6727i	0.276041	+	1.56551i	−0.459593	+	0.888130i	$0.652005\pi$
$744$	−8.28463	+	18.0304i	−0.303729	+	0.661028i
$745$	−0.132584	+	0.0482567i	−0.00485751	+	0.00176799i
$746$	−0.124911	−	0.303035i	−0.00457330	−	0.0110949i
$747$	5.39393	+	10.9445i	0.197353	+	0.400437i
$748$	2.72323	+	5.89288i	0.0995711	+	0.215465i
$749$		−	92.2559i		−	3.37096i
$750$	5.70596	+	4.70038i	0.208352	+	0.171634i
$751$	−5.60641	+	6.68145i	−0.204581	+	0.243810i	−0.858573	−	0.512692i	$-0.828648\pi$
$751$	−5.60641	+	6.68145i	−0.204581	+	0.243810i	0.653992	+	0.756501i	$0.273093\pi$
$752$	25.2201	+	4.62630i	0.919683	+	0.168704i
$753$	−10.1301	−	9.08342i	−0.369160	−	0.331018i
$754$	−10.9096	−	17.1898i	−0.397303	−	0.626016i
$755$	−1.98335	+	1.66423i	−0.0721816	+	0.0605676i
$756$	17.1728	−	45.1055i	0.624568	−	1.64047i
$757$	1.39931	+	7.93588i	0.0508588	+	0.288435i	0.999620	−	0.0275588i	$-0.00877336\pi$
$757$	1.39931	+	7.93588i	0.0508588	+	0.288435i	−0.948761	+	0.315993i	$0.897662\pi$
$758$	9.40381	−	3.87623i	0.341562	−	0.140791i
$759$	1.59011	−	7.55743i	0.0577174	−	0.274317i
$760$	3.75555	+	0.0381886i	0.136228	+	0.00138525i
$761$	−11.5931	+	6.69328i	−0.420249	+	0.242631i	−0.695184	−	0.718832i	$-0.744677\pi$
$761$	−11.5931	+	6.69328i	−0.420249	+	0.242631i	0.274935	+	0.961463i	$0.411344\pi$
$762$	−3.96862	−	21.3723i	−0.143768	−	0.774238i
$763$	−24.7569	+	68.0190i	−0.896260	+	2.46245i
$764$	−2.81340	−	10.6463i	−0.101785	−	0.385169i
$765$	−2.93908	−	2.81492i	−0.106263	−	0.101774i
$766$	10.7081	+	5.59774i	0.386900	+	0.202255i
$767$	18.2177	+	31.5539i	0.657802	+	1.13935i
$768$	−27.6827	−	1.29149i	−0.998914	−	0.0466027i
$769$	−17.4331	−	14.6281i	−0.628652	−	0.527502i	0.271858	−	0.962337i	$-0.412362\pi$
$769$	−17.4331	−	14.6281i	−0.628652	−	0.527502i	−0.900510	+	0.434836i	$0.856806\pi$
$770$	1.23133	−	0.781465i	0.0443739	−	0.0281620i
$771$	−3.57278	+	3.98446i	−0.128671	+	0.143497i
$772$	0.831654	−	9.14312i	0.0299319	−	0.329068i
$773$	−21.4876	−	3.78885i	−0.772856	−	0.136275i	−0.226707	−	0.973963i	$-0.572796\pi$
$773$	−21.4876	−	3.78885i	−0.772856	−	0.136275i	−0.546150	+	0.837688i	$0.683907\pi$
$774$	19.0908	+	34.9606i	0.686206	+	1.25663i
$775$	−12.7760	+	15.2259i	−0.458928	+	0.546930i
$776$	36.1419	−	11.1906i	1.29742	−	0.401719i
$777$	−52.4108	+	28.0060i	−1.88023	+	1.00471i
$778$	6.40834	+	29.1435i	0.229750	+	1.04485i
$779$	2.02327	−	14.7959i	0.0724913	−	0.530118i
$780$	2.32513	+	2.50032i	0.0832530	+	0.0895258i
$781$	1.04505	−	0.876904i	0.0373950	−	0.0313781i
$782$	−5.09409	+	38.1853i	−0.182164	+	1.36550i
$783$	−22.2634	−	6.23524i	−0.795631	−	0.222829i
$784$	−50.2653	−	29.4841i	−1.79519	−	1.05300i
$785$	4.50447	−	5.36822i	0.160771	−	0.191600i
$786$	23.9730	−	14.1321i	0.855087	−	0.504075i
$787$	−9.79399	−	5.65456i	−0.349118	−	0.201563i	0.315179	−	0.949032i	$-0.397936\pi$
$787$	−9.79399	−	5.65456i	−0.349118	−	0.201563i	−0.664297	+	0.747469i	$0.731269\pi$
$788$	17.8399	−	4.71441i	0.635521	−	0.167944i
$789$	−16.4398	−	6.60275i	−0.585274	−	0.235064i
$790$	0.463226	−	1.46039i	0.0164808	−	0.0519585i
$791$	−16.6119	+	28.7726i	−0.590650	+	1.02304i
$792$	−5.53222	−	2.76547i	−0.196579	−	0.0982668i
$793$	3.75947	−	3.15457i	0.133503	−	0.112022i
$794$	0.304048	+	7.25027i	0.0107902	+	0.257302i
$795$	0.211550	+	0.395897i	0.00750289	+	0.0140410i
$796$	−37.0493	−	17.4320i	−1.31318	−	0.617859i
$797$	−21.7076	+	12.5329i	−0.768923	+	0.443938i	−0.832490	−	0.554040i	$-0.813086\pi$
$797$	−21.7076	+	12.5329i	−0.768923	+	0.443938i	0.0635673	+	0.997978i	$0.479752\pi$
$798$	−2.36418	−	49.5301i	−0.0836911	−	1.75335i
$799$	−24.7209	−	14.2726i	−0.874562	−	0.504929i
$800$	−26.4017	−	8.57498i	−0.933441	−	0.303171i
$801$	44.1087	+	10.8046i	1.55850	+	0.381762i
$802$	17.7767	+	28.0101i	0.627716	+	0.989070i
$803$	0.460685	+	2.61267i	0.0162572	+	0.0921993i
$804$	0.454439	+	8.90681i	0.0160268	+	0.314119i
$805$	8.65442			0.305028
$806$	−13.6857	+	12.4974i	−0.482059	+	0.440201i
$807$	−19.5519	+	2.78894i	−0.688258	+	0.0981752i
$808$	−10.3442	+	5.31715i	−0.363909	+	0.187057i
$809$	45.9589	−	26.5344i	1.61583	−	0.932900i	0.627847	−	0.778337i	$-0.283936\pi$
$809$	45.9589	−	26.5344i	1.61583	−	0.932900i	0.987983	−	0.154563i	$-0.0493970\pi$
$810$	3.86182	+	0.346447i	0.135690	+	0.0121729i
$811$	−38.4268	−	6.77569i	−1.34935	−	0.237927i	−0.548178	−	0.836362i	$-0.684678\pi$
$811$	−38.4268	−	6.77569i	−1.34935	−	0.237927i	−0.801171	+	0.598435i	$0.795789\pi$
$812$	−17.5950	+	37.3959i	−0.617465	+	1.31234i
$813$	1.45404	+	1.85320i	0.0509953	+	0.0649945i
$814$	2.90204	+	7.04041i	0.101717	+	0.246766i
$815$	0.0286311	+	0.162375i	0.00100290	+	0.00568774i
$816$	28.5492	+	11.6952i	0.999421	+	0.409414i
$817$	32.3429	+	25.0757i	1.13154	+	0.877287i
$818$	9.22761	−	29.0915i	0.322636	−	1.01716i
$819$	31.1807	−	32.5560i	1.08954	−	1.13760i
$820$	0.888654	−	1.88872i	0.0310332	−	0.0659569i
$821$	−11.5853	−	31.8305i	−0.404331	−	1.11089i	−0.960125	−	0.279570i	$-0.909808\pi$
$821$	−11.5853	−	31.8305i	−0.404331	−	1.11089i	0.555794	−	0.831320i	$-0.312414\pi$
$822$	23.0829	−	19.7282i	0.805107	−	0.688099i
$823$	−1.53388	−	4.21430i	−0.0534676	−	0.146901i	0.910084	−	0.414424i	$-0.136017\pi$
$823$	−1.53388	−	4.21430i	−0.0534676	−	0.146901i	−0.963551	+	0.267523i	$0.913795\pi$
$824$	−11.5345	−	15.1939i	−0.401823	−	0.529305i
$825$	−4.61254	−	4.13597i	−0.160588	−	0.143996i
$826$	34.2645	−	65.5457i	1.19221	−	2.28063i
$827$	−42.9191	+	15.6213i	−1.49244	+	0.543205i	−0.954092	−	0.299515i	$-0.903175\pi$
$827$	−42.9191	+	15.6213i	−1.49244	+	0.543205i	−0.538352	+	0.842720i	$0.680953\pi$
$828$	−18.9249	−	31.4479i	−0.657684	−	1.09289i
$829$	2.62117	−	4.53999i	0.0910369	−	0.157680i	−0.816911	−	0.576764i	$-0.804315\pi$
$829$	2.62117	−	4.53999i	0.0910369	−	0.157680i	0.907948	+	0.419084i	$0.137649\pi$
$830$	0.938903	+	1.47940i	0.0325898	+	0.0513506i
$831$	44.7148	+	1.46922i	1.55114	+	0.0509666i
$832$	−23.3447	−	11.1809i	−0.809333	−	0.387627i
$833$	41.7009	+	49.6972i	1.44485	+	1.72191i
$834$	−38.8736	+	33.2240i	−1.34608	+	1.15045i
$835$	2.90276	+	1.67591i	0.100454	+	0.0579972i
$836$	−6.34579	−	0.330786i	−0.219474	−	0.0114405i
$837$	−2.07049	+	20.9442i	−0.0715667	+	0.723939i
$838$	−33.3080	+	43.2534i	−1.15060	+	1.49416i
$839$	−6.24570	−	2.27325i	−0.215625	−	0.0784812i	0.231949	−	0.972728i	$-0.425490\pi$
$839$	−6.24570	−	2.27325i	−0.215625	−	0.0784812i	−0.447574	+	0.894247i	$0.647712\pi$
$840$	1.75619	−	6.70474i	0.0605943	−	0.231336i
$841$	−8.64729	−	3.14736i	−0.298182	−	0.108530i
$842$	1.39305	+	33.2183i	0.0480075	+	1.14478i
$843$	16.5610	+	50.6144i	0.570392	+	1.74325i
$844$	8.05044	−	11.4134i	0.277108	−	0.392864i
$845$	−0.263750	−	0.724648i	−0.00907329	−	0.0249287i
$846$	26.8879	−	4.08441i	0.924423	−	0.140425i
$847$	42.1051	−	24.3094i	1.44675	−	0.835281i
$848$	−2.59164	−	2.20524i	−0.0889974	−	0.0757282i
$849$	32.3544	−	4.61513i	1.11040	−	0.158391i
$850$	24.4850	+	18.8551i	0.839829	+	0.646724i
$851$	−7.84717	+	44.5035i	−0.268998	+	1.52556i
$852$	0.799033	−	6.43404i	0.0273744	−	0.220427i
$853$	−1.95720	+	1.64229i	−0.0670134	+	0.0562309i	−0.675679	−	0.737196i	$-0.736150\pi$
$853$	−1.95720	+	1.64229i	−0.0670134	+	0.0562309i	0.608666	+	0.793427i	$0.291705\pi$
$854$	−9.49596	−	3.01205i	−0.324945	−	0.103070i
$855$	3.77883	−	1.26068i	0.129233	−	0.0431142i
$856$	−44.7514	+	33.9731i	−1.52957	+	1.16118i
$857$	0.487109	+	0.580514i	0.0166393	+	0.0198300i	0.774300	−	0.632819i	$-0.218102\pi$
$857$	0.487109	+	0.580514i	0.0166393	+	0.0198300i	−0.757661	+	0.652649i	$0.773658\pi$
$858$	−3.75322	−	4.39144i	−0.128133	−	0.149921i
$859$	17.2580	+	3.04306i	0.588837	+	0.103828i	0.460125	−	0.887854i	$-0.347805\pi$
$859$	17.2580	+	3.04306i	0.588837	+	0.103828i	0.128712	+	0.991682i	$0.458916\pi$
$860$	3.26486	+	4.69704i	0.111331	+	0.160168i
$861$	−25.5732	−	10.2710i	−0.871533	−	0.350035i
$862$	−16.4295	+	3.61266i	−0.559590	+	0.123048i
$863$	−23.3064	−	40.3679i	−0.793359	−	1.37414i	−0.923876	−	0.382692i	$-0.874997\pi$
$863$	−23.3064	−	40.3679i	−0.793359	−	1.37414i	0.130517	−	0.991446i	$-0.458336\pi$
$864$	−28.2036	+	8.27991i	−0.959506	+	0.281688i
$865$	−1.66824	+	0.607191i	−0.0567220	+	0.0206451i
$866$	−2.72760	+	8.59919i	−0.0926877	+	0.292212i
$867$	−3.64923	−	3.27219i	−0.123934	−	0.111129i
$868$	36.3058	+	9.86223i	1.23230	+	0.334746i
$869$	−0.886578	+	2.43585i	−0.0300751	+	0.0826306i
$870$	−3.27480	−	0.546873i	−0.111026	−	0.0185407i
$871$	−2.84899	+	7.82754i	−0.0965344	+	0.265226i
$872$	42.1113	−	13.0389i	1.42607	−	0.441553i
$873$	32.3682	−	23.7213i	1.09550	−	0.802845i
$874$	−30.7432	−	21.8362i	−1.03990	−	0.738619i
$875$	7.00820	−	12.1386i	0.236921	−	0.410358i
$876$	10.0589	+	7.60178i	0.339860	+	0.256840i
$877$	−1.73889	+	1.45911i	−0.0587183	+	0.0492705i	−0.671674	−	0.740846i	$-0.734425\pi$
$877$	−1.73889	+	1.45911i	−0.0587183	+	0.0492705i	0.612956	+	0.790117i	$0.289980\pi$
$878$	−0.663693	+	1.26960i	−0.0223986	+	0.0428470i
$879$	46.5039	+	28.9257i	1.56854	+	0.975641i
$880$	−0.832507	−	0.309517i	−0.0280638	−	0.0104338i
$881$	−8.74157	−	5.04695i	−0.294511	−	0.170036i	0.345463	−	0.938432i	$-0.387722\pi$
$881$	−8.74157	−	5.04695i	−0.294511	−	0.170036i	−0.639974	+	0.768396i	$0.721055\pi$
$882$	−60.5980	−	12.1774i	−2.04044	−	0.410035i
$883$	9.04875	+	24.8612i	0.304515	+	0.836648i	0.993701	+	0.112063i	$0.0357459\pi$
$883$	9.04875	+	24.8612i	0.304515	+	0.836648i	−0.689186	+	0.724584i	$0.742032\pi$
$884$	20.3057	+	20.4460i	0.682954	+	0.687674i
$885$	5.81444	+	1.22338i	0.195450	+	0.0411234i
$886$	6.09608	−	19.2189i	0.204802	−	0.645670i
$887$	−7.53521	+	2.74259i	−0.253008	+	0.0920872i	−0.465411	−	0.885095i	$-0.654093\pi$
$887$	−7.53521	+	2.74259i	−0.253008	+	0.0920872i	0.212403	+	0.977182i	$0.431871\pi$
$888$	32.8853	+	15.1102i	1.10356	+	0.507064i
$889$	−38.7288	+	14.0961i	−1.29892	+	0.472769i
$890$	6.46421	+	0.862354i	0.216681	+	0.0289062i
$891$	−6.50356	−	0.859408i	−0.217878	−	0.0287912i
$892$	−13.0782	+	18.5414i	−0.437890	+	0.620811i
$893$	23.6405	−	14.8949i	0.791098	−	0.498439i
$894$	0.558322	−	0.987613i	0.0186731	−	0.0330307i
$895$	−2.23650	+	0.394356i	−0.0747580	+	0.0131819i
$896$	6.22994	+	52.1725i	0.208128	+	1.74296i
$897$	−4.84097	−	33.9377i	−0.161635	−	1.13315i
$898$	−4.09323	+	30.6829i	−0.136593	+	1.02390i
$899$	3.12948	−	17.7482i	0.104374	−	0.591935i
$900$	−29.4384	+	0.533821i	−0.981279	+	0.0177940i
$901$	1.89417	+	3.28079i	0.0631039	+	0.109299i
$902$	−1.63610	+	3.12975i	−0.0544761	+	0.104209i
$903$	59.4176	−	46.6196i	1.97729	−	1.55140i
$904$	20.0743	−	2.53742i	0.667661	−	0.0843933i
$905$		−	7.21450i		−	0.239818i
$906$	3.42906	−	20.5340i	0.113923	−	0.682198i
$907$	40.9645	−	7.22314i	1.36020	−	0.239841i	0.554512	−	0.832176i	$-0.312905\pi$
$907$	40.9645	−	7.22314i	1.36020	−	0.239841i	0.805692	+	0.592335i	$0.201794\pi$
$908$	0.425717	+	1.61097i	0.0141279	+	0.0534618i
$909$	−8.53288	+	8.90926i	−0.283018	+	0.295501i
$910$	3.94970	−	5.12904i	0.130931	−	0.170026i
$911$	−17.3391	+	30.0322i	−0.574469	+	0.995010i	0.421630	+	0.906768i	$0.361458\pi$
$911$	−17.3391	+	30.0322i	−0.574469	+	0.995010i	−0.996099	+	0.0882417i	$0.971875\pi$
$912$	−23.1554	+	19.3862i	−0.766753	+	0.641943i
$913$	−1.48227	−	2.56737i	−0.0490561	−	0.0849677i
$914$	34.9605	+	4.66389i	1.15639	+	0.154268i
$915$	0.0262824	−	0.799890i	0.000868870	−	0.0264436i
$916$	−17.2387	−	4.68279i	−0.569584	−	0.154724i
$917$	−33.9149	−	40.4183i	−1.11997	−	1.33473i
$918$	32.6708	+	1.85199i	1.07830	+	0.0611247i
$919$	−9.62605	−	5.55760i	−0.317534	−	0.183328i	0.332759	−	0.943012i	$-0.392021\pi$
$919$	−9.62605	−	5.55760i	−0.317534	−	0.183328i	−0.650293	+	0.759684i	$0.725354\pi$
$920$	−3.18698	−	4.19808i	−0.105072	−	0.138407i
$921$	30.5939	−	4.36401i	1.00810	−	0.143799i
$922$	−23.6518	−	37.2674i	−0.778932	−	1.22734i
$923$	3.02782	−	5.24434i	0.0996620	−	0.172620i
$924$	−3.44401	+	11.2094i	−0.113300	+	0.368762i
$925$	27.7702	+	23.3019i	0.913077	+	0.766163i
$926$	−39.1033	+	16.1183i	−1.28501	+	0.529679i
$927$	−16.8207	−	11.2451i	−0.552463	−	0.369337i
$928$	24.6193	−	5.23604i	0.808169	−	0.171881i
$929$	−13.7436	−	16.3789i	−0.450912	−	0.537376i	0.491922	−	0.870639i	$-0.336295\pi$
$929$	−13.7436	−	16.3789i	−0.450912	−	0.537376i	−0.942834	+	0.333263i	$0.891850\pi$
$930$	0.0273996	+	3.02223i	0.000898467	+	0.0991027i
$931$	−62.0659	+	13.4343i	−2.03413	+	0.440290i
$932$	−48.9351	−	4.45112i	−1.60292	−	0.145801i
$933$	−0.317570	−	0.0104346i	−0.0103968	−	0.000341612i
$934$	22.6802	−	29.4523i	0.742119	−	0.963708i
$935$	0.757454	+	0.635579i	0.0247714	+	0.0207857i
$936$	−27.2745	−	3.13637i	−0.891496	−	0.102516i
$937$	−4.63304	+	26.2753i	−0.151355	+	0.858377i	0.810688	+	0.585478i	$0.199093\pi$
$937$	−4.63304	+	26.2753i	−0.151355	+	0.858377i	−0.962043	+	0.272898i	$0.912018\pi$
$938$	16.5146	−	3.63139i	0.539222	−	0.118569i
$939$	5.18913	−	24.6627i	0.169341	−	0.804838i
$940$	3.77590	−	0.997825i	0.123156	−	0.0325455i
$941$	−0.522171	+	0.622299i	−0.0170223	+	0.0202864i	−0.774488	−	0.632588i	$-0.781993\pi$
$941$	−0.522171	+	0.622299i	−0.0170223	+	0.0202864i	0.757466	+	0.652874i	$0.226437\pi$
$942$	0.510829	+	56.3455i	0.0166437	+	1.83584i
$943$	−18.1497	+	10.4787i	−0.591036	+	0.341235i
$944$	−44.4127	+	7.51616i	−1.44551	+	0.244630i
$945$	−0.558134	−	7.33014i	−0.0181561	−	0.238450i
$946$	−5.18603	−	8.17145i	−0.168612	−	0.265677i
$947$	−42.4940	−	15.4666i	−1.38087	−	0.502595i	−0.458428	−	0.888732i	$-0.651587\pi$
$947$	−42.4940	−	15.4666i	−1.38087	−	0.502595i	−0.922442	+	0.386136i	$0.873809\pi$
$948$	4.79787	+	11.3467i	0.155828	+	0.368523i
$949$	5.88816	+	10.1986i	0.191138	+	0.331060i
$950$	−27.5012	+	12.5996i	−0.892256	+	0.408784i
$951$	15.0542	−	16.7889i	0.488167	−	0.544417i
$952$	12.9554	−	57.0419i	0.419885	−	1.84874i
$953$	−17.6899	+	3.11921i	−0.573033	+	0.101041i	−0.452653	−	0.891687i	$-0.649522\pi$
$953$	−17.6899	+	3.11921i	−0.573033	+	0.101041i	−0.120380	+	0.992728i	$0.538411\pi$
$954$	−3.36134	−	1.31476i	−0.108827	−	0.0425668i
$955$	−1.07812	−	1.28486i	−0.0348872	−	0.0415770i
$956$	6.57153	+	24.8675i	0.212539	+	0.804272i
$957$	5.49705	+	1.15660i	0.177695	+	0.0373876i
$958$	−20.0589	−	21.9663i	−0.648074	−	0.709697i
$959$	−44.1021	−	37.0061i	−1.42413	−	1.19499i
$960$	−3.89905	+	1.61713i	−0.125841	+	0.0521925i
$961$	14.5945			0.470791
$962$	22.7937	+	24.9611i	0.734899	+	0.804779i
$963$	−33.1207	+	49.5428i	−1.06730	+	1.59649i
$964$	44.6960	−	3.75535i	1.43956	−	0.120952i
$965$	−0.478278	−	1.31406i	−0.0153963	−	0.0423010i
$966$	−52.9004	+	45.2122i	−1.70204	+	1.45468i
$967$	40.8078	−	7.19551i	1.31229	−	0.231392i	0.526653	−	0.850080i	$-0.323447\pi$
$967$	40.8078	−	7.19551i	1.31229	−	0.231392i	0.785636	+	0.618688i	$0.212336\pi$
$968$	−27.2972	−	11.4724i	−0.877364	−	0.368737i
$969$	31.5254	−	11.6813i	1.01274	−	0.375256i
$970$	4.25549	−	3.88598i	0.136636	−	0.124771i
$971$	−14.5865	−	5.30905i	−0.468103	−	0.170376i	0.0971899	−	0.995266i	$-0.469015\pi$
$971$	−14.5865	−	5.30905i	−0.468103	−	0.170376i	−0.565293	+	0.824890i	$0.691237\pi$
$972$	−25.4153	+	18.0571i	−0.815198	+	0.579183i
$973$	74.2718	+	62.3215i	2.38105	+	1.99793i
$974$	1.00211	−	7.51179i	0.0321096	−	0.240693i
$975$	−25.5190	−	10.2492i	−0.817263	−	0.328238i
$976$	2.03580	+	5.71547i	0.0651643	+	0.182948i
$977$	31.2224	+	18.0263i	0.998894	+	0.576712i	0.907921	−	0.419141i	$-0.137669\pi$
$977$	31.2224	+	18.0263i	0.998894	+	0.576712i	0.0909733	+	0.995853i	$0.471002\pi$
$978$	−1.02328	−	0.842946i	−0.0327210	−	0.0269544i
$979$	−10.8661	−	1.91599i	−0.347283	−	0.0612354i
$980$	−8.83963	−	0.804048i	−0.282372	−	0.0256844i
$981$	37.7143	−	27.6392i	1.20412	−	0.882453i
$982$	30.2915	+	15.8351i	0.966639	+	0.505318i
$983$	7.14539	+	40.5235i	0.227903	+	1.29250i	0.857058	+	0.515220i	$0.172290\pi$
$983$	7.14539	+	40.5235i	0.227903	+	1.29250i	−0.629155	+	0.777280i	$0.716599\pi$
$984$	4.43507	+	16.1873i	0.141385	+	0.516033i
$985$	2.15303	−	1.80661i	0.0686012	−	0.0575632i
$986$	−27.7749	−	3.70529i	−0.884532	−	0.118001i
$987$	−16.0351	−	49.0072i	−0.510404	−	1.55992i
$988$	−26.9718	+	8.25436i	−0.858086	+	0.262606i
$989$		−	57.4333i		−	1.82627i
$990$	−0.941794	−	0.0224000i	−0.0299322	−	0.000711920i
$991$	3.07566	−	0.542321i	0.0977014	−	0.0172274i	−0.124584	−	0.992209i	$-0.539760\pi$
$991$	3.07566	−	0.542321i	0.0977014	−	0.0172274i	0.222285	+	0.974982i	$0.428648\pi$
$992$	−8.58562	−	21.2429i	−0.272594	−	0.674464i
$993$	−1.06418	+	32.3878i	−0.0337709	+	1.02780i
$994$	−12.2818	+	0.515050i	−0.389555	+	0.0163364i
$995$	−6.23663			−0.197714
$996$	−13.4677	−	4.13786i	−0.426741	−	0.131113i
$997$	1.08648	−	6.16172i	0.0344091	−	0.195144i	−0.962758	−	0.270366i	$-0.912855\pi$
$997$	1.08648	−	6.16172i	0.0344091	−	0.195144i	0.997167	+	0.0752220i	$0.0239666\pi$
$998$	−25.7441	+	1.07960i	−0.814914	+	0.0341743i
$999$	38.1998	+	3.77633i	1.20859	+	0.119478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.ch.a.479.44	yes	696
4.3	odd	2	inner	684.2.ch.a.479.22	yes	696
9.5	odd	6		684.2.bs.a.23.6	✓	696
19.5	even	9		684.2.bs.a.119.18	yes	696
36.23	even	6		684.2.bs.a.23.18	yes	696
76.43	odd	18		684.2.bs.a.119.6	yes	696
171.5	odd	18	inner	684.2.ch.a.347.22	yes	696
684.347	even	18	inner	684.2.ch.a.347.44	yes	696

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.bs.a.23.6	✓	696	9.5	odd	6
684.2.bs.a.23.18	yes	696	36.23	even	6
684.2.bs.a.119.6	yes	696	76.43	odd	18
684.2.bs.a.119.18	yes	696	19.5	even	9
684.2.ch.a.347.22	yes	696	171.5	odd	18	inner
684.2.ch.a.347.44	yes	696	684.347	even	18	inner
684.2.ch.a.479.22	yes	696	4.3	odd	2	inner
684.2.ch.a.479.44	yes	696	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.ch (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.538946 - 1.30749i) q^{2} +(1.73112 + 0.0568802i) q^{3} +(-1.41907 + 1.40934i) q^{4} +(-0.104190 + 0.286260i) q^{5} +(-0.858607 - 2.29408i) q^{6} +(-4.02200 + 2.32210i) q^{7} +(2.60750 + 1.09588i) q^{8} +(2.99353 + 0.196933i) q^{9} +(0.430435 - 0.0180508i) q^{10} -0.728900 q^{11} +(-2.53675 + 2.35901i) q^{12} +(-3.04039 + 1.10661i) q^{13} +(5.20377 + 4.00725i) q^{14} +(-0.196648 + 0.489623i) q^{15} +(0.0275475 - 3.99991i) q^{16} +(-1.52304 + 4.18452i) q^{17} +(-1.35586 - 4.02015i) q^{18} +(-2.92871 - 3.22841i) q^{19} +(-0.255583 - 0.553063i) q^{20} +(-7.09463 + 3.79106i) q^{21} +(0.392837 + 0.953031i) q^{22} +(-1.06224 + 6.02426i) q^{23} +(4.45155 + 2.04540i) q^{24} +(3.75913 + 3.15429i) q^{25} +(3.08549 + 3.37889i) q^{26} +(5.17095 + 0.511186i) q^{27} +(2.43490 - 8.96358i) q^{28} +(-4.38187 - 0.772642i) q^{29} +(0.746161 - 0.00676471i) q^{30} +4.05037i q^{31} +(-5.24469 + 2.11971i) q^{32} +(-1.26181 - 0.0414600i) q^{33} +(6.29206 - 0.263864i) q^{34} +(-0.245672 - 1.39328i) q^{35} +(-4.52559 + 3.93942i) q^{36} +7.38739 q^{37} +(-2.64270 + 5.56921i) q^{38} +(-5.32621 + 1.74274i) q^{39} +(-0.585381 + 0.632243i) q^{40} +(2.20219 + 2.62447i) q^{41} +(8.78040 + 7.23300i) q^{42} +(-9.24620 + 1.63035i) q^{43} +(1.03436 - 1.02726i) q^{44} +(-0.368270 + 0.836409i) q^{45} +(8.44916 - 1.85788i) q^{46} +(-1.11312 + 6.31285i) q^{47} +(0.275203 - 6.92274i) q^{48} +(7.28431 - 12.6168i) q^{49} +(2.09824 - 6.61503i) q^{50} +(-2.87458 + 7.15726i) q^{51} +(2.75496 - 5.85529i) q^{52} +(0.546835 - 0.651692i) q^{53} +(-2.11849 - 7.03648i) q^{54} +(0.0759441 - 0.208655i) q^{55} +(-13.0321 + 1.64727i) q^{56} +(-4.88631 - 5.75534i) q^{57} +(1.35137 + 6.14567i) q^{58} +(-1.95546 - 11.0900i) q^{59} +(-0.410985 - 0.971954i) q^{60} +(-1.42533 + 0.518777i) q^{61} +(5.29583 - 2.18293i) q^{62} +(-12.4973 + 6.15922i) q^{63} +(5.59812 + 5.71499i) q^{64} -0.985640i q^{65} +(0.625839 + 1.67215i) q^{66} +(1.65487 - 1.97220i) q^{67} +(-3.73608 - 8.08462i) q^{68} +(-2.18152 + 10.3683i) q^{69} +(-1.68929 + 1.07212i) q^{70} +(-1.43374 + 1.20305i) q^{71} +(7.58981 + 3.79404i) q^{72} +(-0.632028 - 3.58441i) q^{73} +(-3.98140 - 9.65895i) q^{74} +(6.32808 + 5.67426i) q^{75} +(8.70598 + 0.453815i) q^{76} +(2.93163 - 1.69258i) q^{77} +(5.14916 + 6.02475i) q^{78} +(1.21632 - 3.34182i) q^{79} +(1.14214 + 0.424636i) q^{80} +(8.92244 + 1.17905i) q^{81} +(2.24461 - 4.29379i) q^{82} +(2.03358 + 3.52226i) q^{83} +(4.72494 - 15.3785i) q^{84} +(-1.03917 - 0.871970i) q^{85} +(7.11487 + 11.2107i) q^{86} +(-7.54158 - 1.58677i) q^{87} +(-1.90061 - 0.798783i) q^{88} +(14.9076 + 2.62861i) q^{89} +(1.29208 + 0.0307313i) q^{90} +(9.65878 - 11.5109i) q^{91} +(-6.98280 - 10.0459i) q^{92} +(-0.230386 + 7.01166i) q^{93} +(8.85391 - 1.94688i) q^{94} +(1.22931 - 0.502005i) q^{95} +(-9.19975 + 3.37115i) q^{96} +(10.2471 - 8.59831i) q^{97} +(-20.4222 - 2.72442i) q^{98} +(-2.18198 - 0.143544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 696 q - 9 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{6} - 12 q^{10} - 3 q^{12} - 6 q^{13} - 9 q^{14} - 3 q^{16} - 12 q^{18} - 18 q^{20} - 30 q^{21} - 27 q^{22} - 18 q^{24} - 6 q^{25} - 72 q^{26} - 18 q^{29} + 63 q^{30}+ \cdots - 45 q^{98}+O(q^{100}) \) 696 * q - 9 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^6 - 12 * q^10 - 3 * q^12 - 6 * q^13 - 9 * q^14 - 3 * q^16 - 12 * q^18 - 18 * q^20 - 30 * q^21 - 27 * q^22 - 18 * q^24 - 6 * q^25 - 72 * q^26 - 18 * q^29 + 63 * q^30 - 9 * q^32 - 60 * q^33 - 39 * q^34 - 66 * q^36 - 48 * q^37 - 9 * q^38 - 33 * q^40 - 18 * q^41 - 27 * q^42 - 135 * q^44 - 6 * q^45 - 6 * q^46 - 18 * q^48 + 282 * q^49 - 3 * q^52 + 15 * q^54 + 45 * q^56 - 12 * q^57 - 6 * q^58 - 9 * q^60 - 6 * q^61 + 18 * q^62 + 12 * q^64 + 18 * q^66 - 9 * q^68 - 6 * q^69 - 45 * q^70 + 12 * q^72 + 12 * q^73 + 99 * q^74 - 3 * q^76 - 36 * q^77 + 69 * q^78 - 72 * q^81 - 12 * q^82 - 45 * q^84 - 6 * q^85 - 171 * q^86 - 45 * q^88 + 27 * q^90 - 9 * q^92 + 24 * q^93 - 6 * q^94 - 87 * q^96 - 42 * q^97 - 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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