LMFDB - Embedded newform 342.2.x.c.281.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(29,342)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 17]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("342.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.x (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			281.1
Character	$\chi$	$=$	342.281
Dual form			342.2.x.c.185.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-1.73166 + 0.0369083i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.303424 - 0.833650i) q^{5} +(-1.30280 + 1.14136i) q^{6} +(0.619454 + 1.07293i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.99728 - 0.127825i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-1.73166 + 0.0369083i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.303424 - 0.833650i) q^{5} +(-1.30280 + 1.14136i) q^{6} +(0.619454 + 1.07293i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.99728 - 0.127825i) q^{9} +(-0.303424 - 0.833650i) q^{10} -4.47607i q^{11} +(-0.264352 + 1.71176i) q^{12} +(-1.65862 - 4.55702i) q^{13} +(1.16419 + 0.423732i) q^{14} +(-0.494657 + 1.45479i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.16819 - 3.20959i) q^{17} +(2.21388 - 2.02453i) q^{18} +(-4.29775 + 0.727574i) q^{19} +(-0.768296 - 0.443576i) q^{20} +(-1.11228 - 1.83508i) q^{21} +(-2.87716 - 3.42887i) q^{22} +(0.542537 + 0.0956639i) q^{23} +(0.897792 + 1.48121i) q^{24} +(3.22732 + 2.70804i) q^{25} +(-4.19978 - 2.42474i) q^{26} +(-5.18554 + 0.331974i) q^{27} +(1.16419 - 0.423732i) q^{28} +(-0.188302 + 1.06791i) q^{29} +(0.556194 + 1.43240i) q^{30} -3.17254i q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.165204 + 7.75102i) q^{33} +(-1.16819 - 3.20959i) q^{34} +(1.08240 - 0.190857i) q^{35} +(0.394588 - 2.97394i) q^{36} -0.210909i q^{37} +(-2.82459 + 3.31989i) q^{38} +(3.04036 + 7.82999i) q^{39} +(-0.873674 + 0.154052i) q^{40} +(6.75327 - 5.66667i) q^{41} +(-2.03162 - 0.690790i) q^{42} +(1.98350 + 11.2490i) q^{43} +(-4.40807 - 0.777261i) q^{44} +(0.802883 - 2.53746i) q^{45} +(0.477099 - 0.275453i) q^{46} +(9.59960 + 1.69267i) q^{47} +(1.63985 + 0.557579i) q^{48} +(2.73255 - 4.73292i) q^{49} +4.21296 q^{50} +(-1.90445 + 5.60102i) q^{51} +(-4.77581 + 0.842104i) q^{52} +(4.72793 + 3.96720i) q^{53} +(-3.75896 + 3.58751i) q^{54} +(-3.73147 - 1.35815i) q^{55} +(0.619454 - 1.07293i) q^{56} +(7.41537 - 1.41853i) q^{57} +(0.542194 + 0.939108i) q^{58} +(-0.254116 - 1.44116i) q^{59} +(1.34680 + 0.739765i) q^{60} +(-4.88723 + 1.77880i) q^{61} +(-2.03927 - 2.43031i) q^{62} +(1.99382 + 3.13667i) q^{63} +(-0.500000 + 0.866025i) q^{64} -4.30223 q^{65} +(5.10881 + 5.83143i) q^{66} +(-8.44468 + 10.0640i) q^{67} +(-2.95797 - 1.70779i) q^{68} +(-0.943019 - 0.145633i) q^{69} +(0.706488 - 0.841959i) q^{70} +(0.567184 - 0.475924i) q^{71} +(-1.60934 - 2.53180i) q^{72} +(1.49888 + 8.50059i) q^{73} +(-0.135570 - 0.161566i) q^{74} +(-5.68856 - 4.57028i) q^{75} +(-0.0297759 + 4.35880i) q^{76} +(4.80249 - 2.77272i) q^{77} +(7.36207 + 4.04382i) q^{78} +(-2.86755 + 7.87854i) q^{79} +(-0.570250 + 0.679597i) q^{80} +(8.96732 - 0.766254i) q^{81} +(1.53084 - 8.68184i) q^{82} +(-6.65002 + 3.83939i) q^{83} +(-2.00034 + 0.776727i) q^{84} +(-2.32121 - 1.94773i) q^{85} +(8.75015 + 7.34225i) q^{86} +(0.286660 - 1.85621i) q^{87} +(-3.87639 + 2.23803i) q^{88} +(-1.80010 + 10.2088i) q^{89} +(-1.01601 - 2.45989i) q^{90} +(3.86191 - 4.60245i) q^{91} +(0.188421 - 0.517683i) q^{92} +(0.117093 + 5.49375i) q^{93} +(8.44175 - 4.87385i) q^{94} +(-0.697497 + 3.80358i) q^{95} +(1.61460 - 0.626944i) q^{96} +(-2.59091 - 3.08772i) q^{97} +(-0.949006 - 5.38208i) q^{98} +(-0.572154 - 13.4160i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9}+O(q^{10}) $ 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9	$ 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9} + 3 q^{13} + 3 q^{14} + 27 q^{15} - 27 q^{17} - 18 q^{18} + 3 q^{19} + 18 q^{23} + 3 q^{24} - 6 q^{27} + 3 q^{28} + 57 q^{33} + 27 q^{34} + 9 q^{38} - 30 q^{39} + 9 q^{41} - 3 q^{43} - 9 q^{44} + 27 q^{45} - 30 q^{49} - 132 q^{50} - 66 q^{51} + 6 q^{52} + 27 q^{54} + 102 q^{57} - 54 q^{59} + 6 q^{60} - 24 q^{61} - 3 q^{62} - 30 q^{64} + 36 q^{65} - 63 q^{66} + 51 q^{67} - 18 q^{68} + 3 q^{69} - 18 q^{71} - 3 q^{72} - 66 q^{73} - 6 q^{74} + 3 q^{78} - 51 q^{79} - 30 q^{81} - 36 q^{83} + 60 q^{84} - 3 q^{86} + 54 q^{87} - 27 q^{89} + 36 q^{90} - 69 q^{91} + 69 q^{93} + 18 q^{94} - 27 q^{95} + 81 q^{97} + 60 q^{98} + 51 q^{99}+O(q^{100}) $ 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9 + 3 * q^13 + 3 * q^14 + 27 * q^15 - 27 * q^17 - 18 * q^18 + 3 * q^19 + 18 * q^23 + 3 * q^24 - 6 * q^27 + 3 * q^28 + 57 * q^33 + 27 * q^34 + 9 * q^38 - 30 * q^39 + 9 * q^41 - 3 * q^43 - 9 * q^44 + 27 * q^45 - 30 * q^49 - 132 * q^50 - 66 * q^51 + 6 * q^52 + 27 * q^54 + 102 * q^57 - 54 * q^59 + 6 * q^60 - 24 * q^61 - 3 * q^62 - 30 * q^64 + 36 * q^65 - 63 * q^66 + 51 * q^67 - 18 * q^68 + 3 * q^69 - 18 * q^71 - 3 * q^72 - 66 * q^73 - 6 * q^74 + 3 * q^78 - 51 * q^79 - 30 * q^81 - 36 * q^83 + 60 * q^84 - 3 * q^86 + 54 * q^87 - 27 * q^89 + 36 * q^90 - 69 * q^91 + 69 * q^93 + 18 * q^94 - 27 * q^95 + 81 * q^97 + 60 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−1.73166	+	0.0369083i	−0.999773	+	0.0213090i
$3$	−1.73166	+	0.0369083i	−0.999773	+	0.0213090i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.303424	−	0.833650i	0.135695	−	0.372819i	−0.853170	−	0.521633i	$-0.825323\pi$
$5$	0.303424	−	0.833650i	0.135695	−	0.372819i	0.988865	+	0.148813i	$0.0475453\pi$
$6$	−1.30280	+	1.14136i	−0.531867	+	0.465959i
$7$	0.619454	+	1.07293i	0.234132	+	0.405528i	0.959020	−	0.283338i	$-0.0914420\pi$
$7$	0.619454	+	1.07293i	0.234132	+	0.405528i	−0.724888	+	0.688866i	$0.758109\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.99728	−	0.127825i	0.999092	−	0.0426084i
$10$	−0.303424	−	0.833650i	−0.0959510	−	0.263623i
$11$		−	4.47607i		−	1.34959i	−0.738007	−	0.674793i	$-0.764233\pi$
$11$		−	4.47607i		−	1.34959i	0.738007	−	0.674793i	$-0.235767\pi$
$12$	−0.264352	+	1.71176i	−0.0763117	+	0.494142i
$13$	−1.65862	−	4.55702i	−0.460019	−	1.26389i	−0.925471	−	0.378818i	$-0.876331\pi$
$13$	−1.65862	−	4.55702i	−0.460019	−	1.26389i	0.465452	−	0.885073i	$-0.345892\pi$
$14$	1.16419	+	0.423732i	0.311144	+	0.113247i
$15$	−0.494657	+	1.45479i	−0.127720	+	0.375626i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.16819	−	3.20959i	0.283329	−	0.778439i	−0.713631	−	0.700522i	$-0.752951\pi$
$17$	1.16819	−	3.20959i	0.283329	−	0.778439i	0.996960	−	0.0779175i	$-0.0248271\pi$
$18$	2.21388	−	2.02453i	0.521817	−	0.477187i
$19$	−4.29775	+	0.727574i	−0.985971	+	0.166917i
$19$	−4.29775	+	0.727574i	−0.985971	+	0.166917i
$20$	−0.768296	−	0.443576i	−0.171796	−	0.0991865i
$21$	−1.11228	−	1.83508i	−0.242720	−	0.400447i
$22$	−2.87716	−	3.42887i	−0.613413	−	0.731037i
$23$	0.542537	+	0.0956639i	0.113127	+	0.0199473i	0.229925	−	0.973208i	$-0.426152\pi$
$23$	0.542537	+	0.0956639i	0.113127	+	0.0199473i	−0.116798	+	0.993156i	$0.537263\pi$
$24$	0.897792	+	1.48121i	0.183261	+	0.302350i
$25$	3.22732	+	2.70804i	0.645463	+	0.541608i
$26$	−4.19978	−	2.42474i	−0.823644	−	0.475531i
$27$	−5.18554	+	0.331974i	−0.997957	+	0.0638884i
$28$	1.16419	−	0.423732i	0.220012	−	0.0800778i
$29$	−0.188302	+	1.06791i	−0.0349668	+	0.198307i	−0.997287	−	0.0736124i	$-0.976547\pi$
$29$	−0.188302	+	1.06791i	−0.0349668	+	0.198307i	0.962320	+	0.271919i	$0.0876583\pi$
$30$	0.556194	+	1.43240i	0.101547	+	0.261519i
$31$		−	3.17254i		−	0.569805i	−0.958556	−	0.284903i	$-0.908039\pi$
$31$		−	3.17254i		−	0.569805i	0.958556	−	0.284903i	$-0.0919612\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.165204	+	7.75102i	0.0287584	+	1.34928i
$34$	−1.16819	−	3.20959i	−0.200344	−	0.550440i
$35$	1.08240	−	0.190857i	0.182959	−	0.0322607i
$36$	0.394588	−	2.97394i	0.0657647	−	0.495656i
$37$		−	0.210909i		−	0.0346733i	−0.999850	−	0.0173366i	$-0.994481\pi$
$37$		−	0.210909i		−	0.0346733i	0.999850	−	0.0173366i	$-0.00551870\pi$
$38$	−2.82459	+	3.31989i	−0.458209	+	0.538558i
$39$	3.04036	+	7.82999i	0.486847	+	1.25380i
$40$	−0.873674	+	0.154052i	−0.138140	+	0.0243578i
$41$	6.75327	−	5.66667i	1.05468	−	0.884985i	0.0611055	−	0.998131i	$-0.480537\pi$
$41$	6.75327	−	5.66667i	1.05468	−	0.884985i	0.993578	+	0.113147i	$0.0360930\pi$
$42$	−2.03162	−	0.690790i	−0.313486	−	0.106591i
$43$	1.98350	+	11.2490i	0.302481	+	1.71545i	0.635132	+	0.772403i	$0.280945\pi$
$43$	1.98350	+	11.2490i	0.302481	+	1.71545i	−0.332652	+	0.943050i	$0.607943\pi$
$44$	−4.40807	−	0.777261i	−0.664541	−	0.117177i
$45$	0.802883	−	2.53746i	0.119687	−	0.378263i
$46$	0.477099	−	0.275453i	0.0703444	−	0.0406134i
$47$	9.59960	+	1.69267i	1.40025	+	0.246901i	0.822244	−	0.569135i	$-0.192722\pi$
$47$	9.59960	+	1.69267i	1.40025	+	0.246901i	0.578002	+	0.816036i	$0.303833\pi$
$48$	1.63985	+	0.557579i	0.236692	+	0.0804796i
$49$	2.73255	−	4.73292i	0.390365	−	0.676131i
$50$	4.21296			0.595803
$51$	−1.90445	+	5.60102i	−0.266677	+	0.784300i
$52$	−4.77581	+	0.842104i	−0.662286	+	0.116779i
$53$	4.72793	+	3.96720i	0.649431	+	0.544937i	0.906898	−	0.421350i	$-0.138443\pi$
$53$	4.72793	+	3.96720i	0.649431	+	0.544937i	−0.257467	+	0.966287i	$0.582888\pi$
$54$	−3.75896	+	3.58751i	−0.511530	+	0.488198i
$55$	−3.73147	−	1.35815i	−0.503152	−	0.183132i
$56$	0.619454	−	1.07293i	0.0827781	−	0.143376i
$57$	7.41537	−	1.41853i	0.982190	−	0.187889i
$58$	0.542194	+	0.939108i	0.0711936	+	0.123311i
$59$	−0.254116	−	1.44116i	−0.0330831	−	0.187623i	0.963788	−	0.266670i	$-0.0859235\pi$
$59$	−0.254116	−	1.44116i	−0.0330831	−	0.187623i	−0.996871	+	0.0790468i	$0.974812\pi$
$60$	1.34680	+	0.739765i	0.173871	+	0.0955032i
$61$	−4.88723	+	1.77880i	−0.625745	+	0.227753i	−0.635378	−	0.772201i	$-0.719156\pi$
$61$	−4.88723	+	1.77880i	−0.625745	+	0.227753i	0.00963321	+	0.999954i	$0.496934\pi$
$62$	−2.03927	−	2.43031i	−0.258987	−	0.308649i
$63$	1.99382	+	3.13667i	0.251198	+	0.395184i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−4.30223			−0.533626
$66$	5.10881	+	5.83143i	0.628851	+	0.717800i
$67$	−8.44468	+	10.0640i	−1.03168	+	1.22951i	−0.0587858	+	0.998271i	$0.518723\pi$
$67$	−8.44468	+	10.0640i	−1.03168	+	1.22951i	−0.972897	+	0.231241i	$0.925722\pi$
$68$	−2.95797	−	1.70779i	−0.358707	−	0.207099i
$69$	−0.943019	−	0.145633i	−0.113526	−	0.0175322i
$70$	0.706488	−	0.841959i	0.0844414	−	0.100633i
$71$	0.567184	−	0.475924i	0.0673124	−	0.0564818i	−0.608511	−	0.793546i	$-0.708233\pi$
$71$	0.567184	−	0.475924i	0.0673124	−	0.0564818i	0.675823	+	0.737064i	$0.263788\pi$
$72$	−1.60934	−	2.53180i	−0.189662	−	0.298376i
$73$	1.49888	+	8.50059i	0.175431	+	0.994918i	0.937645	+	0.347594i	$0.113001\pi$
$73$	1.49888	+	8.50059i	0.175431	+	0.994918i	−0.762214	+	0.647325i	$0.775888\pi$
$74$	−0.135570	−	0.161566i	−0.0157597	−	0.0187817i
$75$	−5.68856	−	4.57028i	−0.656858	−	0.527731i
$76$	−0.0297759	+	4.35880i	−0.00341553	+	0.499988i
$77$	4.80249	−	2.77272i	0.547295	−	0.315981i
$78$	7.36207	+	4.04382i	0.833590	+	0.457872i
$79$	−2.86755	+	7.87854i	−0.322625	+	0.886405i	0.667297	+	0.744792i	$0.267451\pi$
$79$	−2.86755	+	7.87854i	−0.322625	+	0.886405i	−0.989922	+	0.141613i	$0.954771\pi$
$80$	−0.570250	+	0.679597i	−0.0637559	+	0.0759813i
$81$	8.96732	−	0.766254i	0.996369	−	0.0851393i
$82$	1.53084	−	8.68184i	0.169053	−	0.958749i
$83$	−6.65002	+	3.83939i	−0.729934	+	0.421428i	−0.818398	−	0.574652i	$-0.805138\pi$
$83$	−6.65002	+	3.83939i	−0.729934	+	0.421428i	0.0884640	+	0.996079i	$0.471804\pi$
$84$	−2.00034	+	0.776727i	−0.218256	+	0.0847478i
$85$	−2.32121	−	1.94773i	−0.251771	−	0.211261i
$86$	8.75015	+	7.34225i	0.943553	+	0.791735i
$87$	0.286660	−	1.85621i	0.0307332	−	0.199007i
$88$	−3.87639	+	2.23803i	−0.413225	+	0.238575i
$89$	−1.80010	+	10.2088i	−0.190810	+	1.08214i	0.727451	+	0.686160i	$0.240705\pi$
$89$	−1.80010	+	10.2088i	−0.190810	+	1.08214i	−0.918261	+	0.395976i	$0.870406\pi$
$90$	−1.01601	−	2.45989i	−0.107096	−	0.259295i
$91$	3.86191	−	4.60245i	0.404838	−	0.482468i
$92$	0.188421	−	0.517683i	0.0196443	−	0.0539722i
$93$	0.117093	+	5.49375i	0.0121420	+	0.569676i
$94$	8.44175	−	4.87385i	0.870700	−	0.502699i
$95$	−0.697497	+	3.80358i	−0.0715617	+	0.390239i
$96$	1.61460	−	0.626944i	0.164790	−	0.0639872i
$97$	−2.59091	−	3.08772i	−0.263067	−	0.313511i	0.618301	−	0.785941i	$-0.287821\pi$
$97$	−2.59091	−	3.08772i	−0.263067	−	0.313511i	−0.881368	+	0.472430i	$0.843377\pi$
$98$	−0.949006	−	5.38208i	−0.0958640	−	0.543672i
$99$	−0.572154	−	13.4160i	−0.0575036	−	1.34836i
$100$	3.22732	−	2.70804i	0.322732	−	0.270804i
$101$	9.42919	−	11.2373i	0.938240	−	1.11815i	−0.0545773	−	0.998510i	$-0.517381\pi$
$101$	9.42919	−	11.2373i	0.938240	−	1.11815i	0.992817	−	0.119641i	$-0.0381744\pi$
$102$	2.14137	+	5.51479i	0.212027	+	0.546046i
$103$	−14.1992	−	8.19789i	−1.39908	−	0.807762i	−0.404788	−	0.914411i	$-0.632655\pi$
$103$	−14.1992	−	8.19789i	−1.39908	−	0.807762i	−0.994297	+	0.106649i	$0.965988\pi$
$104$	−3.11719	+	3.71492i	−0.305665	+	0.364278i
$105$	−1.86730	+	0.370448i	−0.182230	+	0.0361520i
$106$	6.17187			0.599465
$107$	4.40279	−	7.62586i	0.425634	−	0.737219i	−0.570846	−	0.821057i	$-0.693385\pi$
$107$	4.40279	−	7.62586i	0.425634	−	0.737219i	0.996479	+	0.0838380i	$0.0267178\pi$
$108$	−0.573529	+	5.16440i	−0.0551878	+	0.496945i
$109$	−0.932997	−	1.11190i	−0.0893649	−	0.106501i	0.719509	−	0.694483i	$-0.244367\pi$
$109$	−0.932997	−	1.11190i	−0.0893649	−	0.106501i	−0.808874	+	0.587982i	$0.799922\pi$
$110$	−3.73147	+	1.35815i	−0.355782	+	0.129494i
$111$	0.00778431	+	0.365223i	0.000738854	+	0.0346654i
$112$	−0.215134	−	1.22009i	−0.0203283	−	0.115287i
$113$	−0.704329	−	1.21993i	−0.0662577	−	0.114762i	0.830993	−	0.556282i	$-0.187773\pi$
$113$	−0.704329	−	1.21993i	−0.0662577	−	0.114762i	−0.897251	+	0.441520i	$0.854439\pi$
$114$	4.76869	−	5.85317i	0.446629	−	0.548199i
$115$	0.244369	−	0.423259i	0.0227875	−	0.0394691i
$116$	1.01899	+	0.370883i	0.0946110	+	0.0344356i
$117$	−5.55385	−	13.4466i	−0.513453	−	1.24314i
$118$	−1.12103	−	0.940652i	−0.103199	−	0.0865941i
$119$	4.16729	−	0.734806i	0.382015	−	0.0673596i
$120$	1.50722	−	0.299012i	0.137590	−	0.0272959i
$121$	−9.03520			−0.821382
$122$	−2.60044	+	4.50409i	−0.235433	+	0.407781i
$123$	−11.4852	+	10.0620i	−1.03559	+	0.907258i
$124$	−3.12434	−	0.550906i	−0.280574	−	0.0494728i
$125$	7.07828	−	4.08665i	0.633101	−	0.365521i
$126$	3.54357	+	1.12123i	0.315686	+	0.0998869i
$127$	18.9156	+	3.33533i	1.67849	+	0.295963i	0.930102	−	0.367301i	$-0.119718\pi$
$127$	18.9156	+	3.33533i	1.67849	+	0.295963i	0.748386	+	0.663264i	$0.230829\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−3.84992	−	19.4062i	−0.338967	−	1.70862i
$130$	−3.29570	+	2.76542i	−0.289052	+	0.242543i
$131$	6.52579	−	1.15067i	0.570160	−	0.100535i	0.118867	−	0.992910i	$-0.462074\pi$
$131$	6.52579	−	1.15067i	0.570160	−	0.100535i	0.451294	+	0.892376i	$0.350963\pi$
$132$	7.66195	+	1.18326i	0.666887	+	0.102989i
$133$	−3.44289	−	4.16047i	−0.298537	−	0.360758i
$134$			13.1376i			1.13492i
$135$	−1.29666	+	4.42365i	−0.111599	+	0.380727i
$136$	−3.36368	+	0.593108i	−0.288433	+	0.0508586i
$137$	0.803123	+	2.20656i	0.0686154	+	0.188519i	0.969261	−	0.246035i	$-0.0791280\pi$
$137$	0.803123	+	2.20656i	0.0686154	+	0.188519i	−0.900645	+	0.434555i	$0.856906\pi$
$138$	−0.816006	+	0.494600i	−0.0694630	+	0.0421031i
$139$	18.0866	−	6.58299i	1.53409	−	0.558362i	0.569468	−	0.822014i	$-0.307149\pi$
$139$	18.0866	−	6.58299i	1.53409	−	0.558362i	0.964618	+	0.263652i	$0.0849271\pi$
$140$		−	1.09910i		−	0.0928909i
$141$	−16.6857	−	2.57682i	−1.40519	−	0.217007i
$142$	0.128570	−	0.729158i	0.0107894	−	0.0611896i
$143$	−20.3976	+	7.42410i	−1.70573	+	0.620835i
$144$	−2.86024	−	0.905012i	−0.238353	−	0.0754177i
$145$	0.833131	+	0.481008i	0.0691878	+	0.0399456i
$146$	6.61228	+	5.54836i	0.547236	+	0.459186i
$147$	−4.55716	+	8.29665i	−0.375868	+	0.684296i
$148$	−0.207705	−	0.0366240i	−0.0170733	−	0.00301048i
$149$	−3.89237	−	4.63875i	−0.318875	−	0.380021i	0.582668	−	0.812711i	$-0.302009\pi$
$149$	−3.89237	−	4.63875i	−0.318875	−	0.380021i	−0.901543	+	0.432690i	$0.857565\pi$
$150$	−7.29541	+	0.155493i	−0.595668	+	0.0126960i
$151$	5.85379	+	3.37968i	0.476374	+	0.275035i	0.718904	−	0.695109i	$-0.244644\pi$
$151$	5.85379	+	3.37968i	0.476374	+	0.275035i	−0.242530	+	0.970144i	$0.577977\pi$
$152$	2.77897	+	3.35817i	0.225404	+	0.272384i
$153$	3.09113	−	9.76934i	0.249903	−	0.789804i
$154$	1.89665	−	5.21101i	0.152837	−	0.419915i
$155$	−2.64479	−	0.962624i	−0.212434	−	0.0773198i
$156$	8.23899	−	1.63450i	0.659647	−	0.130865i
$157$	−6.96482	−	2.53499i	−0.555853	−	0.202314i	0.0487921	−	0.998809i	$-0.484463\pi$
$157$	−6.96482	−	2.53499i	−0.555853	−	0.202314i	−0.604645	+	0.796495i	$0.706685\pi$
$158$	2.86755	+	7.87854i	0.228130	+	0.626783i
$159$	−8.33358	−	6.69534i	−0.660896	−	0.530975i
$160$			0.887151i			0.0701355i
$161$	0.233437	+	0.641362i	0.0183974	+	0.0505464i
$162$	6.37683	−	6.35107i	0.501011	−	0.498987i
$163$	0.252807	+	0.437875i	0.0198014	+	0.0342970i	0.875756	−	0.482753i	$-0.160363\pi$
$163$	0.252807	+	0.437875i	0.0198014	+	0.0342970i	−0.855955	+	0.517050i	$0.827030\pi$
$164$	−4.40788	−	7.63468i	−0.344198	−	0.596168i
$165$	6.51176	+	2.21412i	0.506940	+	0.172369i
$166$	−2.62630	+	7.21569i	−0.203840	+	0.560046i
$167$	−2.65016	+	15.0298i	−0.205075	+	1.16304i	0.692246	+	0.721662i	$0.256621\pi$
$167$	−2.65016	+	15.0298i	−0.205075	+	1.16304i	−0.897321	+	0.441378i	$0.854490\pi$
$168$	−1.03308	+	1.88080i	−0.0797041	+	0.145107i
$169$	−8.05687	+	6.76052i	−0.619759	+	0.520040i
$170$	−3.03013			−0.232400
$171$	−12.7885	+	2.73010i	−0.977964	+	0.208776i
$172$	11.4225			0.870958
$173$	−4.20861	+	3.53144i	−0.319975	+	0.268491i	−0.788600	−	0.614906i	$-0.789194\pi$
$173$	−4.20861	+	3.53144i	−0.319975	+	0.268491i	0.468625	+	0.883397i	$0.344749\pi$
$174$	−0.973556	−	1.60620i	−0.0738051	−	0.121766i
$175$	−0.906352	+	5.14018i	−0.0685138	+	0.388561i
$176$	−1.53091	+	4.20613i	−0.115396	+	0.317049i
$177$	0.493233	+	2.48622i	0.0370736	+	0.186876i
$178$	5.18317	+	8.97751i	0.388495	+	0.672893i
$179$	−7.57995	−	13.1289i	−0.566552	−	0.981296i	−0.996903	−	0.0786351i	$-0.974944\pi$
$179$	−7.57995	−	13.1289i	−0.566552	−	0.981296i	0.430352	−	0.902661i	$-0.358390\pi$
$180$	−2.35949	−	1.23131i	−0.175866	−	0.0917765i
$181$	5.82467	+	16.0032i	0.432945	+	1.18951i	0.943996	+	0.329956i	$0.107034\pi$
$181$	5.82467	+	16.0032i	0.432945	+	1.18951i	−0.511052	+	0.859550i	$0.670744\pi$
$182$		−	6.00807i		−	0.445348i
$183$	8.39735	−	3.26066i	0.620750	−	0.241035i
$184$	−0.188421	−	0.517683i	−0.0138906	−	0.0381641i
$185$	−0.175824	−	0.0639949i	−0.0129269	−	0.00470500i
$186$	3.62101	+	4.13319i	0.265506	+	0.303060i
$187$	−14.3663	−	5.22892i	−1.05057	−	0.382376i
$188$	3.33391	−	9.15983i	0.243150	−	0.668050i
$189$	−3.56839	−	5.35806i	−0.259562	−	0.389741i
$190$	1.91058	+	3.36205i	0.138608	+	0.243909i
$191$	−20.1840	−	11.6533i	−1.46047	−	0.843200i	−0.461433	−	0.887175i	$-0.652665\pi$
$191$	−20.1840	−	11.6533i	−1.46047	−	0.843200i	−0.999033	+	0.0439745i	$0.985998\pi$
$192$	0.833865	−	1.51811i	0.0601790	−	0.109560i
$193$	−3.46196	−	4.12580i	−0.249197	−	0.296982i	0.626916	−	0.779087i	$-0.284317\pi$
$193$	−3.46196	−	4.12580i	−0.249197	−	0.296982i	−0.876113	+	0.482105i	$0.839872\pi$
$194$	−3.96950	−	0.699930i	−0.284994	−	0.0502521i
$195$	7.44998	−	0.158788i	0.533504	−	0.0113710i
$196$	−4.18651	−	3.51290i	−0.299037	−	0.250922i
$197$	15.2693	+	8.81574i	1.08789	+	0.628095i	0.933015	−	0.359838i	$-0.117168\pi$
$197$	15.2693	+	8.81574i	1.08789	+	0.628095i	0.154878	+	0.987934i	$0.450501\pi$
$198$	−9.06194	−	9.90949i	−0.644004	−	0.704237i
$199$	1.31891	−	0.480042i	0.0934947	−	0.0340293i	−0.294849	−	0.955544i	$-0.595269\pi$
$199$	1.31891	−	0.480042i	0.0934947	−	0.0340293i	0.388344	+	0.921514i	$0.373047\pi$
$200$	0.731573	−	4.14896i	0.0517300	−	0.293376i
$201$	14.2519	−	17.7391i	1.00525	−	1.25122i
$202$		−	14.6692i		−	1.03212i
$203$	−1.26244	+	0.459490i	−0.0886058	+	0.0322499i
$204$	5.18523	+	2.84813i	0.363038	+	0.199409i
$205$	−2.67491	−	7.34926i	−0.186824	−	0.513295i
$206$	−16.1467	+	2.84710i	−1.12499	+	0.198367i
$207$	1.63836	+	0.217381i	0.113874	+	0.0151090i
$208$			4.84948i			0.336251i
$209$	3.25667	+	19.2370i	0.225269	+	1.33065i
$210$	−1.19232	+	1.48406i	−0.0822778	+	0.102410i
$211$	19.8100	−	3.49304i	1.36378	−	0.240471i	0.556601	−	0.830780i	$-0.312105\pi$
$211$	19.8100	−	3.49304i	1.36378	−	0.240471i	0.807177	+	0.590309i	$0.200994\pi$
$212$	4.72793	−	3.96720i	0.324716	−	0.272469i
$213$	−0.964603	+	0.845071i	−0.0660935	+	0.0579033i
$214$	−1.52907	−	8.67180i	−0.104525	−	0.592792i
$215$	9.97955	+	1.75966i	0.680599	+	0.120008i
$216$	2.88027	+	4.32482i	0.195977	+	0.294267i
$217$	3.40390	−	1.96524i	0.231072	−	0.133409i
$218$	−1.42943	−	0.252048i	−0.0968135	−	0.0170708i
$219$	−2.90929	−	14.6648i	−0.196592	−	0.990954i
$220$	−1.98548	+	3.43894i	−0.133861	+	0.231854i
$221$	−16.5638			−1.11420
$222$	0.240724	+	0.274773i	0.0161563	+	0.0184416i
$223$	22.5993	−	3.98487i	1.51336	−	0.266847i	0.645542	−	0.763725i	$-0.276632\pi$
$223$	22.5993	−	3.98487i	1.51336	−	0.266847i	0.867820	+	0.496878i	$0.165520\pi$
$224$	−0.949059	−	0.796355i	−0.0634117	−	0.0532087i
$225$	10.0193	+	7.70421i	0.667954	+	0.513614i
$226$	−1.32371	−	0.481789i	−0.0880516	−	0.0320482i
$227$	4.64246	−	8.04098i	0.308131	−	0.533698i	−0.669823	−	0.742521i	$-0.733630\pi$
$227$	4.64246	−	8.04098i	0.308131	−	0.533698i	0.977953	+	0.208823i	$0.0669632\pi$
$228$	−0.109314	−	7.54904i	−0.00723950	−	0.499948i
$229$	−3.35704	−	5.81457i	−0.221840	−	0.384238i	0.733527	−	0.679660i	$-0.237873\pi$
$229$	−3.35704	−	5.81457i	−0.221840	−	0.384238i	−0.955367	+	0.295423i	$0.904540\pi$
$230$	−0.0848684	−	0.481313i	−0.00559606	−	0.0317368i
$231$	−8.21394	+	4.97865i	−0.540437	+	0.327571i
$232$	1.01899	−	0.370883i	0.0669001	−	0.0243496i
$233$	15.4023	+	18.3557i	1.00904	+	1.20252i	0.979185	+	0.202969i	$0.0650592\pi$
$233$	15.4023	+	18.3557i	1.00904	+	1.20252i	0.0298522	+	0.999554i	$0.490496\pi$
$234$	−12.8978	−	6.73078i	−0.843158	−	0.440005i
$235$	4.32384	−	7.48911i	0.282056	−	0.488536i
$236$	−1.46340			−0.0952589
$237$	4.67484	−	13.7488i	0.303663	−	0.893079i
$238$	2.72001	−	3.24158i	0.176312	−	0.210120i
$239$	−23.9547	−	13.8303i	−1.54950	−	0.894606i	−0.998179	−	0.0603145i	$-0.980790\pi$
$239$	−23.9547	−	13.8303i	−1.54950	−	0.894606i	−0.551324	−	0.834292i	$-0.685877\pi$
$240$	0.962395	−	1.19788i	0.0621223	−	0.0773226i
$241$	−3.61802	+	4.31178i	−0.233057	+	0.277746i	−0.869880	−	0.493264i	$-0.835804\pi$
$241$	−3.61802	+	4.31178i	−0.233057	+	0.277746i	0.636823	+	0.771010i	$0.280248\pi$
$242$	−6.92136	+	5.80771i	−0.444922	+	0.373334i
$243$	−15.5000	+	1.65786i	−0.994329	+	0.106352i
$244$	0.903123	+	5.12186i	0.0578165	+	0.327894i
$245$	−3.11648	−	3.71407i	−0.199104	−	0.237283i
$246$	−2.33046	+	15.0905i	−0.148585	+	0.962133i
$247$	10.4439	+	18.3782i	0.664530	+	1.16938i
$248$	−2.74750	+	1.58627i	−0.174466	+	0.100728i
$249$	11.3738	−	6.89395i	0.720788	−	0.436886i
$250$	2.79543	−	7.68038i	0.176799	−	0.485750i
$251$	3.73982	−	4.45694i	0.236055	−	0.281320i	−0.634992	−	0.772519i	$-0.718997\pi$
$251$	3.73982	−	4.45694i	0.236055	−	0.281320i	0.871048	+	0.491199i	$0.163441\pi$
$252$	3.43524	−	1.41885i	0.216400	−	0.0893794i
$253$	0.428198	−	2.42843i	0.0269206	−	0.152674i
$254$	16.6341	−	9.60370i	1.04372	−	0.602590i
$255$	4.09143	+	3.28713i	0.256216	+	0.205848i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−23.4318	−	19.6617i	−1.46164	−	1.22646i	−0.923497	−	0.383606i	$-0.874682\pi$
$257$	−23.4318	−	19.6617i	−1.46164	−	1.22646i	−0.538141	−	0.842855i	$-0.680873\pi$
$258$	−15.4233	−	12.3913i	−0.960210	−	0.771449i
$259$	0.226290	−	0.130649i	0.0140610	−	0.00811812i
$260$	−0.747074	+	4.23687i	−0.0463316	+	0.262759i
$261$	−0.427887	+	3.22490i	−0.0264855	+	0.199617i
$262$	4.25940	−	5.07616i	0.263147	−	0.313606i
$263$	−8.04155	+	22.0940i	−0.495863	+	1.36237i	0.399376	+	0.916787i	$0.369227\pi$
$263$	−8.04155	+	22.0940i	−0.495863	+	1.36237i	−0.895239	+	0.445586i	$0.852995\pi$
$264$	6.62998	−	4.01858i	0.408047	−	0.247327i
$265$	4.74182	−	2.73769i	0.291288	−	0.168175i
$266$	−5.31171	−	0.974056i	−0.325682	−	0.0597232i
$267$	2.74036	−	17.7447i	0.167707	−	1.08596i
$268$	8.44468	+	10.0640i	0.515841	+	0.614756i
$269$	−0.127109	−	0.720871i	−0.00774998	−	0.0439523i	0.980688	−	0.195581i	$-0.0626593\pi$
$269$	−0.127109	−	0.720871i	−0.00774998	−	0.0439523i	−0.988438	+	0.151629i	$0.951548\pi$
$270$	1.85016	+	4.22219i	0.112597	+	0.256954i
$271$	2.72379	−	2.28553i	0.165459	−	0.138836i	−0.556299	−	0.830982i	$-0.687779\pi$
$271$	2.72379	−	2.28553i	0.165459	−	0.138836i	0.721757	+	0.692146i	$0.243335\pi$
$272$	−2.19549	+	2.61648i	−0.133121	+	0.158647i
$273$	−6.51764	+	8.11240i	−0.394466	+	0.490985i
$274$	2.03358	+	1.17409i	0.122853	+	0.0709292i
$275$	12.1214	−	14.4457i	0.730946	−	0.871108i
$276$	−0.307174	+	0.903404i	−0.0184897	+	0.0543785i
$277$	28.7867			1.72962			0.864812	−	0.502096i	$-0.167437\pi$
$277$	28.7867			1.72962			0.864812	+	0.502096i	$0.167437\pi$
$278$	9.62368	−	16.6687i	0.577190	−	0.999722i
$279$	−0.405530	−	9.50898i	−0.0242785	−	0.569288i
$280$	−0.706488	−	0.841959i	−0.0422207	−	0.0503167i
$281$	−10.9956	+	4.00207i	−0.655943	+	0.238744i	−0.648484	−	0.761228i	$-0.724597\pi$
$281$	−10.9956	+	4.00207i	−0.655943	+	0.238744i	−0.00745919	+	0.999972i	$0.502374\pi$
$282$	−14.4383	+	8.75140i	−0.859790	+	0.521138i
$283$	2.17644	+	12.3432i	0.129376	+	0.733727i	0.978612	+	0.205714i	$0.0659516\pi$
$283$	2.17644	+	12.3432i	0.129376	+	0.733727i	−0.849236	+	0.528013i	$0.822937\pi$
$284$	−0.370203	−	0.641211i	−0.0219675	−	0.0380489i
$285$	1.06744	−	6.61224i	0.0632298	−	0.391675i
$286$	−10.8533	+	18.7985i	−0.641770	+	1.11158i
$287$	10.2633	+	3.73552i	0.605821	+	0.220501i
$288$	−2.77280	+	1.14524i	−0.163389	+	0.0674842i
$289$	4.08598	+	3.42855i	0.240352	+	0.201679i
$290$	0.947402	−	0.167052i	0.0556333	−	0.00980966i
$291$	4.60053	+	5.25126i	0.269688	+	0.307834i
$292$	8.63172			0.505133
$293$	−12.0705	+	20.9066i	−0.705164	+	1.22138i	0.261469	+	0.965212i	$0.415793\pi$
$293$	−12.0705	+	20.9066i	−0.705164	+	1.22138i	−0.966632	+	0.256167i	$0.917540\pi$
$294$	1.84200	+	9.28489i	0.107427	+	0.541506i
$295$	−1.27853	−	0.225439i	−0.0744389	−	0.0131256i
$296$	−0.182653	+	0.105455i	−0.0106165	+	0.00612943i
$297$	1.48594	+	23.2108i	0.0862228	+	1.34683i
$298$	−5.96346	−	1.05152i	−0.345454	−	0.0609128i
$299$	−0.463921	−	2.63103i	−0.0268292	−	0.152156i
$300$	−5.48866	+	4.80851i	−0.316888	+	0.277620i
$301$	−10.8406	+	9.09637i	−0.624844	+	0.524306i
$302$	6.65668	−	1.17375i	0.383049	−	0.0675418i
$303$	−15.9134	+	19.8071i	−0.914200	+	1.13789i
$304$	4.28741	+	0.786221i	0.245900	+	0.0450929i
$305$			4.61397i			0.264195i
$306$	−3.91167	−	9.47069i	−0.223615	−	0.541403i
$307$	−2.32061	+	0.409187i	−0.132444	+	0.0233535i	−0.239477	−	0.970902i	$-0.576976\pi$
$307$	−2.32061	+	0.409187i	−0.132444	+	0.0233535i	0.107033	+	0.994255i	$0.465865\pi$
$308$	−1.89665	−	5.21101i	−0.108072	−	0.296925i
$309$	24.8906	+	13.6719i	1.41598	+	0.777765i
$310$	−2.64479	+	0.962624i	−0.150214	+	0.0546734i
$311$		−	28.1873i		−	1.59835i	−0.601096	−	0.799176i	$-0.705269\pi$
$311$		−	28.1873i		−	1.59835i	0.601096	−	0.799176i	$-0.294731\pi$
$312$	5.26079	−	6.54802i	0.297834	−	0.370709i
$313$	−3.32552	+	18.8600i	−0.187970	+	1.06603i	0.734111	+	0.679030i	$0.237599\pi$
$313$	−3.32552	+	18.8600i	−0.187970	+	1.06603i	−0.922080	+	0.386998i	$0.873512\pi$
$314$	−6.96482	+	2.53499i	−0.393047	+	0.143058i
$315$	3.21986	−	0.710408i	0.181419	−	0.0400270i
$316$	7.26090	+	4.19208i	0.408458	+	0.235823i
$317$	3.58255	+	3.00612i	0.201216	+	0.168840i	0.737828	−	0.674989i	$-0.235852\pi$
$317$	3.58255	+	3.00612i	0.201216	+	0.168840i	−0.536612	+	0.843829i	$0.680296\pi$
$318$	−10.6876	+	0.227793i	−0.599329	+	0.0127740i
$319$	4.78006	+	0.842853i	0.267632	+	0.0471907i
$320$	0.570250	+	0.679597i	0.0318779	+	0.0379906i
$321$	−7.34267	+	13.3679i	−0.409828	+	0.746122i
$322$	0.591082	+	0.341261i	0.0329397	+	0.0190178i
$323$	−2.68539	+	14.6439i	−0.149419	+	0.814811i
$324$	0.802546	−	8.96415i	0.0445859	−	0.498008i
$325$	6.98771	−	19.1986i	0.387608	−	1.06495i
$326$	0.475122	+	0.172930i	0.0263146	+	0.00957773i
$327$	1.65667	+	1.89100i	0.0916141	+	0.104573i
$328$	−8.28411	−	3.01517i	−0.457414	−	0.166485i
$329$	4.13041	+	11.3482i	0.227717	+	0.625646i
$330$	6.41151	−	2.48956i	0.352942	−	0.137046i
$331$			1.38687i			0.0762292i	0.999273	+	0.0381146i	$0.0121352\pi$
$331$			1.38687i			0.0762292i	−0.999273	+	0.0381146i	$0.987865\pi$
$332$	2.62630	+	7.21569i	0.144137	+	0.396012i
$333$	−0.0269595	−	0.632153i	−0.00147737	−	0.0346418i
$334$	7.63083	+	13.2170i	0.417540	+	0.723201i
$335$	5.82752	+	10.0936i	0.318391	+	0.551470i
$336$	0.417570	+	2.10483i	0.0227803	+	0.114828i
$337$	1.13802	−	3.12667i	0.0619917	−	0.170321i	−0.904830	−	0.425773i	$-0.860002\pi$
$337$	1.13802	−	3.12667i	0.0619917	−	0.170321i	0.966822	+	0.255452i	$0.0822244\pi$
$338$	−1.82634	+	10.3577i	−0.0993401	+	0.563386i
$339$	1.26468	+	2.08651i	0.0686881	+	0.113324i
$340$	−2.32121	+	1.94773i	−0.125885	+	0.105630i
$341$	−14.2005			−0.769001
$342$	−8.04171	+	10.3117i	−0.434846	+	0.557592i
$343$	15.4431			0.833850
$344$	8.75015	−	7.34225i	0.471777	−	0.395868i
$345$	−0.407541	+	0.741959i	−0.0219413	+	0.0399457i
$346$	−0.954015	+	5.41049i	−0.0512882	+	0.290870i
$347$	−4.17304	+	11.4653i	−0.224021	+	0.615491i	−0.999881	−	0.0154129i	$-0.995094\pi$
$347$	−4.17304	+	11.4653i	−0.224021	+	0.615491i	0.775861	+	0.630904i	$0.217316\pi$
$348$	−1.77823	−	0.604633i	−0.0953233	−	0.0324117i
$349$	−1.35389	−	2.34501i	−0.0724722	−	0.125526i	0.827512	−	0.561448i	$-0.189756\pi$
$349$	−1.35389	−	2.34501i	−0.0724722	−	0.125526i	−0.899984	+	0.435922i	$0.856422\pi$
$350$	2.60974	+	4.52020i	0.139496	+	0.241615i
$351$	10.1137	+	23.0800i	0.539827	+	1.23192i
$352$	1.53091	+	4.20613i	0.0815976	+	0.224187i
$353$			23.8844i			1.27124i	0.772003	+	0.635619i	$0.219255\pi$
$353$			23.8844i			1.27124i	−0.772003	+	0.635619i	$0.780745\pi$
$354$	1.97595	+	1.58751i	0.105021	+	0.0843753i
$355$	−0.224657	−	0.617239i	−0.0119235	−	0.0327597i
$356$	9.74117	+	3.54550i	0.516281	+	0.187911i
$357$	−7.18920	+	1.42624i	−0.380493	+	0.0754847i
$358$	−14.2456	−	5.18499i	−0.752905	−	0.274035i
$359$	5.36332	−	14.7356i	0.283065	−	0.777716i	−0.713927	−	0.700220i	$-0.753085\pi$
$359$	5.36332	−	14.7356i	0.283065	−	0.777716i	0.996993	−	0.0774958i	$-0.0246924\pi$
$360$	−2.59895	+	0.573414i	−0.136977	+	0.0302216i
$361$	17.9413	−	6.25386i	0.944278	−	0.329150i
$362$	14.7486	+	8.51510i	0.775169	+	0.447544i
$363$	15.6459	−	0.333474i	0.821195	−	0.0175028i
$364$	−3.86191	−	4.60245i	−0.202419	−	0.241234i
$365$	7.54131	+	1.32974i	0.394730	+	0.0696016i
$366$	4.33683	−	7.89552i	0.226690	−	0.412706i
$367$	−14.8919	−	12.4958i	−0.777352	−	0.652276i	0.165228	−	0.986255i	$-0.447164\pi$
$367$	−14.8919	−	12.4958i	−0.777352	−	0.652276i	−0.942580	+	0.333979i	$0.891608\pi$
$368$	−0.477099	−	0.275453i	−0.0248705	−	0.0143590i
$369$	19.5171	−	17.8478i	1.01602	−	0.929119i
$370$	−0.175824	+	0.0639949i	−0.00914068	+	0.00332694i
$371$	−1.32778	+	7.53022i	−0.0689350	+	0.390950i
$372$	5.43062	+	0.838666i	0.281565	+	0.0434828i
$373$		−	19.6206i		−	1.01591i	−0.861382	−	0.507957i	$-0.830401\pi$
$373$		−	19.6206i		−	1.01591i	0.861382	−	0.507957i	$-0.169599\pi$
$374$	−14.3663	+	5.22892i	−0.742866	+	0.270381i
$375$	−12.1063	+	7.33792i	−0.625168	+	0.378929i
$376$	−3.33391	−	9.15983i	−0.171933	−	0.472382i
$377$	5.17883	−	0.913168i	0.266724	−	0.0470306i
$378$	−6.17763	−	1.81079i	−0.317743	−	0.0931372i
$379$			17.6869i			0.908513i	0.890871	+	0.454257i	$0.150095\pi$
$379$			17.6869i			0.908513i	−0.890871	+	0.454257i	$0.849905\pi$
$380$	3.62467	+	1.34738i	0.185942	+	0.0691194i
$381$	−32.8784	−	5.07751i	−1.68441	−	0.260129i
$382$	−22.9524	+	4.04714i	−1.17435	+	0.207069i
$383$	−10.2103	+	8.56745i	−0.521721	+	0.437776i	−0.865231	−	0.501373i	$-0.832829\pi$
$383$	−10.2103	+	8.56745i	−0.521721	+	0.437776i	0.343510	+	0.939149i	$0.388384\pi$
$384$	−0.337047	−	1.69894i	−0.0171998	−	0.0866987i
$385$	−0.854287	−	4.84490i	−0.0435385	−	0.246919i
$386$	−5.30403	−	0.935243i	−0.269968	−	0.0476026i
$387$	7.38299	+	33.4627i	0.375299	+	1.70101i
$388$	−3.49072	+	2.01537i	−0.177215	+	0.102315i
$389$	6.99128	+	1.23275i	0.354472	+	0.0625029i	0.348049	−	0.937476i	$-0.386844\pi$
$389$	6.99128	+	1.23275i	0.354472	+	0.0625029i	0.00642302	+	0.999979i	$0.497955\pi$
$390$	5.60495	−	4.91040i	0.283818	−	0.248648i
$391$	0.940830	−	1.62957i	0.0475798	−	0.0824107i
$392$	−5.46511			−0.276030
$393$	−11.2580	+	2.23343i	−0.567889	+	0.112661i
$394$	17.3636	−	3.06167i	0.874766	−	0.154245i
$395$	5.69786	+	4.78107i	0.286690	+	0.240562i
$396$	−13.3115	−	1.76620i	−0.668930	−	0.0887551i
$397$	−37.0408	−	13.4818i	−1.85903	−	0.676630i	−0.979719	−	0.200375i	$-0.935784\pi$
$397$	−37.0408	−	13.4818i	−1.85903	−	0.676630i	−0.879307	−	0.476255i	$-0.841994\pi$
$398$	0.701775	−	1.21551i	0.0351768	−	0.0609280i
$399$	6.11546	+	7.07743i	0.306156	+	0.354315i
$400$	−2.10648	−	3.64853i	−0.105324	−	0.182427i
$401$	2.81366	+	15.9570i	0.140507	+	0.796857i	0.970865	+	0.239626i	$0.0770249\pi$
$401$	2.81366	+	15.9570i	0.140507	+	0.796857i	−0.830358	+	0.557231i	$0.811864\pi$
$402$	−0.484887	−	22.7498i	−0.0241839	−	1.13466i
$403$	−14.4573	+	5.26204i	−0.720172	+	0.262121i
$404$	−9.42919	−	11.2373i	−0.469120	−	0.559075i
$405$	2.08211	−	7.70810i	0.103461	−	0.383019i
$406$	−0.671729	+	1.16347i	−0.0333374	+	0.0577420i
$407$	−0.944045			−0.0467946
$408$	5.80285	−	1.15121i	0.287284	−	0.0569933i
$409$	−20.7950	+	24.7826i	−1.02825	+	1.22542i	−0.0543293	+	0.998523i	$0.517302\pi$
$409$	−20.7950	+	24.7826i	−1.02825	+	1.22542i	−0.973919	+	0.226896i	$0.927142\pi$
$410$	−6.77312	−	3.91046i	−0.334500	−	0.193124i
$411$	−1.47217	−	3.79137i	−0.0726170	−	0.187014i
$412$	−10.5390	+	12.5599i	−0.519219	+	0.618781i
$413$	1.38885	−	1.16538i	0.0683408	−	0.0573447i
$414$	1.39479	−	0.886595i	0.0685501	−	0.0435738i
$415$	1.18293	+	6.70874i	0.0580679	+	0.329319i
$416$	3.11719	+	3.71492i	0.152833	+	0.182139i
$417$	−31.0768	+	12.0670i	−1.52184	+	0.590925i
$418$	14.8601	+	12.6431i	0.726830	+	0.618392i
$419$	25.9690	−	14.9932i	1.26867	−	0.732465i	0.293931	−	0.955827i	$-0.405036\pi$
$419$	25.9690	−	14.9932i	1.26867	−	0.732465i	0.974736	+	0.223362i	$0.0717032\pi$
$420$	0.0405659	+	1.90326i	0.00197941	+	0.0928698i
$421$	1.08521	−	2.98159i	0.0528898	−	0.145314i	−0.910435	−	0.413653i	$-0.864253\pi$
$421$	1.08521	−	2.98159i	0.0528898	−	0.145314i	0.963324	+	0.268339i	$0.0864749\pi$
$422$	12.9301	−	15.4095i	0.629426	−	0.750121i
$423$	28.9890	+	3.84633i	1.40949	+	0.187015i
$424$	1.07173	−	6.07811i	0.0520480	−	0.295179i
$425$	12.4618	−	7.19484i	0.604487	−	0.349001i
$426$	−0.195728	+	1.26740i	−0.00948303	+	0.0614056i
$427$	−4.93594	−	4.14174i	−0.238867	−	0.200433i
$428$	−6.74547	−	5.66012i	−0.326054	−	0.273592i
$429$	35.0476	−	13.6088i	1.69211	−	0.657041i
$430$	8.77587	−	5.06675i	0.423210	−	0.244340i
$431$	5.64856	−	32.0346i	0.272082	−	1.54305i	−0.476000	−	0.879445i	$-0.657914\pi$
$431$	5.64856	−	32.0346i	0.272082	−	1.54305i	0.748082	−	0.663607i	$-0.230975\pi$
$432$	4.98635	+	1.46160i	0.239906	+	0.0703215i
$433$	4.69210	−	5.59183i	0.225488	−	0.268726i	−0.641425	−	0.767186i	$-0.721656\pi$
$433$	4.69210	−	5.59183i	0.225488	−	0.268726i	0.866913	+	0.498460i	$0.166101\pi$
$434$	1.34431	−	3.69345i	0.0645287	−	0.177291i
$435$	−1.46045	−	0.802192i	−0.0700233	−	0.0384622i
$436$	−1.25702	+	0.725743i	−0.0602005	+	0.0347568i
$437$	−2.40129	−	0.0164038i	−0.114869	−	0.000784698i
$438$	−11.6550	−	9.36382i	−0.556897	−	0.447420i
$439$	5.35236	+	6.37870i	0.255454	+	0.304439i	0.878496	−	0.477750i	$-0.158548\pi$
$439$	5.35236	+	6.37870i	0.255454	+	0.304439i	−0.623041	+	0.782189i	$0.714103\pi$
$440$	0.689548	+	3.91062i	0.0328729	+	0.186432i
$441$	7.58523	−	14.5352i	0.361201	−	0.692150i
$442$	−12.6886	+	10.6470i	−0.603534	+	0.506425i
$443$	1.75838	−	2.09555i	0.0835431	−	0.0995628i	−0.722654	−	0.691210i	$-0.757078\pi$
$443$	1.75838	−	2.09555i	0.0835431	−	0.0995628i	0.806197	+	0.591648i	$0.201522\pi$
$444$	0.361026	+	0.0557542i	0.0171335	+	0.00264598i
$445$	7.96441	+	4.59825i	0.377549	+	0.217978i
$446$	14.7507	−	17.5791i	0.698464	−	0.832397i
$447$	6.91146	+	7.88906i	0.326901	+	0.373140i
$448$	−1.23891			−0.0585329
$449$	5.68003	−	9.83809i	0.268057	−	0.464288i	−0.700303	−	0.713846i	$-0.746952\pi$
$449$	5.68003	−	9.83809i	0.268057	−	0.464288i	0.968360	+	0.249557i	$0.0802851\pi$
$450$	12.6274	−	0.538522i	0.595262	−	0.0253862i
$451$	−25.3644	−	30.2281i	−1.19436	−	1.42339i
$452$	−1.32371	+	0.481789i	−0.0622619	+	0.0226615i
$453$	−10.2615	−	5.63640i	−0.482127	−	0.264821i
$454$	−1.61231	−	9.14386i	−0.0756694	−	0.429143i
$455$	−2.66503	−	4.61597i	−0.124939	−	0.216400i
$456$	−4.93617	−	5.71264i	−0.231157	−	0.267519i
$457$	14.2676	−	24.7122i	0.667409	−	1.15599i	−0.311218	−	0.950339i	$-0.600737\pi$
$457$	14.2676	−	24.7122i	0.667409	−	1.15599i	0.978626	−	0.205647i	$-0.0659299\pi$
$458$	−6.30918	−	2.29635i	−0.294809	−	0.107302i
$459$	−4.99222	+	17.0312i	−0.233017	+	0.794950i
$460$	−0.374395	−	0.314154i	−0.0174562	−	0.0146475i
$461$	−24.9650	+	4.40200i	−1.16274	+	0.205022i	−0.721529	−	0.692384i	$-0.756560\pi$
$461$	−24.9650	+	4.40200i	−1.16274	+	0.205022i	−0.441206	+	0.897406i	$0.645449\pi$
$462$	−3.09202	+	9.09369i	−0.143854	+	0.423077i
$463$	11.2354			0.522155			0.261078	−	0.965318i	$-0.415922\pi$
$463$	11.2354			0.522155			0.261078	+	0.965318i	$0.415922\pi$
$464$	0.542194	−	0.939108i	0.0251707	−	0.0435970i
$465$	4.61539	+	1.56932i	0.214034	+	0.0727755i
$466$	23.5977	+	4.16091i	1.09314	+	0.192750i
$467$	−7.68084	+	4.43453i	−0.355427	+	0.205206i	−0.667073	−	0.744993i	$-0.732453\pi$
$467$	−7.68084	+	4.43453i	−0.355427	+	0.205206i	0.311646	+	0.950198i	$0.399120\pi$
$468$	−14.2068	+	3.13449i	−0.656708	+	0.144892i
$469$	−16.0290	−	2.82635i	−0.740151	−	0.130509i
$470$	−1.50165	−	8.51630i	−0.0692661	−	0.392828i
$471$	12.1542	+	4.13267i	0.560038	+	0.190423i
$472$	−1.12103	+	0.940652i	−0.0515994	+	0.0432970i
$473$	50.3512	−	8.87828i	2.31515	−	0.408224i
$474$	−5.25640	−	13.5371i	−0.241435	−	0.621779i
$475$	−15.8405	−	9.29036i	−0.726812	−	0.426271i
$476$		−	4.23158i		−	0.193954i
$477$	14.6780	+	11.2865i	0.672060	+	0.516771i
$478$	−27.2403	+	4.80320i	−1.24594	+	0.219693i
$479$	−2.37559	−	6.52687i	−0.108543	−	0.298220i	0.873515	−	0.486797i	$-0.161835\pi$
$479$	−2.37559	−	6.52687i	−0.108543	−	0.298220i	−0.982058	+	0.188577i	$0.939613\pi$
$480$	−0.0327433	−	1.53624i	−0.00149452	−	0.0701195i
$481$	−0.961119	+	0.349819i	−0.0438233	+	0.0159504i
$482$			5.62863i			0.256377i
$483$	−0.427904	−	1.10200i	−0.0194703	−	0.0501429i
$484$	−1.56895	+	8.89793i	−0.0713157	+	0.404451i
$485$	−3.36022	+	1.22302i	−0.152580	+	0.0555345i
$486$	−10.8081	+	11.2332i	−0.490264	+	0.509550i
$487$	−35.9227	−	20.7400i	−1.62781	−	0.939818i	−0.984744	−	0.174008i	$-0.944328\pi$
$487$	−35.9227	−	20.7400i	−1.62781	−	0.939818i	−0.643068	−	0.765809i	$-0.722339\pi$
$488$	3.98410	+	3.34306i	0.180352	+	0.151333i
$489$	−0.453937	−	0.748919i	−0.0205277	−	0.0338673i
$490$	−4.77472	−	0.841912i	−0.215700	−	0.0380337i
$491$	6.99161	+	8.33228i	0.315527	+	0.376030i	0.900377	−	0.435111i	$-0.143291\pi$
$491$	6.99161	+	8.33228i	0.315527	+	0.376030i	−0.584850	+	0.811142i	$0.698847\pi$
$492$	7.91473	+	13.0580i	0.356824	+	0.588698i
$493$	3.20759	+	1.85190i	0.144463	+	0.0834055i
$494$	19.8138	+	7.36528i	0.891463	+	0.331380i
$495$	−11.3579	−	3.59376i	−0.510498	−	0.161527i
$496$	−1.08507	+	2.98121i	−0.0487212	+	0.133860i
$497$	0.861976	+	0.313734i	0.0386649	+	0.0140729i
$498$	4.28153	−	12.5920i	0.191860	−	0.564263i
$499$	5.52477	+	2.01085i	0.247323	+	0.0900180i	0.462707	−	0.886511i	$-0.346878\pi$
$499$	5.52477	+	2.01085i	0.247323	+	0.0900180i	−0.215384	+	0.976529i	$0.569100\pi$
$500$	−2.79543	−	7.68038i	−0.125015	−	0.343477i
$501$	4.03444	−	26.1243i	0.180246	−	1.16715i
$502$		−	5.81813i		−	0.259676i
$503$	−14.8965	−	40.9278i	−0.664202	−	1.82488i	−0.556769	−	0.830668i	$-0.687959\pi$
$503$	−14.8965	−	40.9278i	−0.664202	−	1.82488i	−0.107433	−	0.994212i	$-0.534263\pi$
$504$	1.71953	−	3.29504i	0.0765939	−	0.146773i
$505$	−6.50691	−	11.2703i	−0.289554	−	0.501522i
$506$	−1.23295	−	2.13553i	−0.0548112	−	0.0949358i
$507$	13.7022	−	12.0043i	0.608537	−	0.533128i
$508$	6.56932	−	18.0491i	0.291466	−	0.800797i
$509$	−1.34156	+	7.60836i	−0.0594635	+	0.337234i	−0.999997	−	0.00246670i	$-0.999215\pi$
$509$	−1.34156	+	7.60836i	−0.0594635	+	0.337234i	0.940533	+	0.339701i	$0.110326\pi$
$510$	5.24715	−	0.111837i	0.232348	−	0.00495222i
$511$	−8.19201	+	6.87392i	−0.362393	+	0.304084i
$512$	1.00000			0.0441942
$513$	22.0446	−	5.19960i	0.973293	−	0.229568i
$514$	−30.5881			−1.34918
$515$	−11.1425	+	9.34969i	−0.490998	+	0.411997i
$516$	−19.7799	+	0.421586i	−0.870761	+	0.0185593i
$517$	7.57650	−	42.9685i	0.333214	−	1.88975i
$518$	0.0893690	−	0.245539i	0.00392665	−	0.0107884i
$519$	7.15754	−	6.27059i	0.314181	−	0.275248i
$520$	2.15111	+	3.72584i	0.0943326	+	0.163389i
$521$	11.4415	+	19.8173i	0.501262	+	0.868211i	0.999999	+	0.00145749i	$0.000463932\pi$
$521$	11.4415	+	19.8173i	0.501262	+	0.868211i	−0.498737	+	0.866753i	$0.666203\pi$
$522$	1.74515	+	2.74546i	0.0763830	+	0.120166i
$523$	12.2540	+	33.6675i	0.535829	+	1.47218i	0.852033	+	0.523488i	$0.175369\pi$
$523$	12.2540	+	33.6675i	0.535829	+	1.47218i	−0.316204	+	0.948691i	$0.602408\pi$
$524$		−	6.62646i		−	0.289478i
$525$	1.37978	−	8.93448i	0.0602184	−	0.389933i
$526$	8.04155	+	22.0940i	0.350628	+	0.963343i
$527$	−10.1825	−	3.70614i	−0.443559	−	0.161442i
$528$	2.49576	−	7.34008i	0.108614	−	0.319436i
$529$	−21.3277	−	7.76266i	−0.927293	−	0.337507i
$530$	1.87269	−	5.14518i	0.0813446	−	0.223492i
$531$	−0.945872	−	4.28708i	−0.0410474	−	0.186043i
$532$	−4.69511	+	2.66813i	−0.203559	+	0.115678i
$533$	−37.0243	−	21.3760i	−1.60370	−	0.925896i
$534$	−9.30682	−	15.3547i	−0.402745	−	0.664462i
$535$	−5.02138	−	5.98425i	−0.217093	−	0.258722i
$536$	12.9380	+	2.28132i	0.558837	+	0.0985380i
$537$	13.6104	+	22.4549i	0.587334	+	0.969001i
$538$	−0.560738	−	0.470515i	−0.0241751	−	0.0202854i
$539$	−21.1849	−	12.2311i	−0.912497	−	0.526831i
$540$	4.13128	+	2.04512i	0.177782	+	0.0880081i
$541$	−38.9469	+	14.1755i	−1.67446	+	0.609452i	−0.992534	−	0.121972i	$-0.961078\pi$
$541$	−38.9469	+	14.1755i	−1.67446	+	0.609452i	−0.681923	+	0.731424i	$0.738856\pi$
$542$	0.617433	−	3.50164i	0.0265210	−	0.150408i
$543$	−10.6770	−	27.4970i	−0.458193	−	1.18001i
$544$			3.41557i			0.146441i
$545$	−1.21003	+	0.440415i	−0.0518320	+	0.0188653i
$546$	0.221748	+	10.4039i	0.00948992	+	0.445247i
$547$	−4.81543	−	13.2303i	−0.205893	−	0.565686i	0.793168	−	0.609002i	$-0.208430\pi$
$547$	−4.81543	−	13.2303i	−0.205893	−	0.565686i	−0.999061	+	0.0433160i	$0.986208\pi$
$548$	2.31250	−	0.407756i	0.0987851	−	0.0174185i
$549$	−14.4210	+	5.95628i	−0.615473	+	0.254208i
$550$		−	18.8575i		−	0.804087i
$551$	0.0322887	−	4.72663i	0.00137554	−	0.201361i
$552$	0.345388	+	0.889495i	0.0147007	+	0.0378594i
$553$	−10.2294	+	1.80372i	−0.434999	+	0.0767020i
$554$	22.0519	−	18.5037i	0.936895	−	0.786148i
$555$	0.306830	+	0.104328i	0.0130242	+	0.00442847i
$556$	−3.34227	−	18.9550i	−0.141744	−	0.803869i
$557$	26.0027	+	4.58498i	1.10177	+	0.194272i	0.694824	−	0.719180i	$-0.255482\pi$
$557$	26.0027	+	4.58498i	1.10177	+	0.194272i	0.406947	+	0.913452i	$0.366593\pi$
$558$	−6.42291	−	7.02363i	−0.271903	−	0.297334i
$559$	47.9720	−	27.6966i	2.02900	−	1.17144i
$560$	−1.08240	−	0.190857i	−0.0457398	−	0.00806516i
$561$	25.0706	+	8.52446i	1.05848	+	0.359903i
$562$	−5.85064	+	10.1336i	−0.246794	+	0.427460i
$563$	28.4692			1.19983			0.599917	−	0.800062i	$-0.295200\pi$
$563$	28.4692			1.19983			0.599917	+	0.800062i	$0.295200\pi$
$564$	−5.43511	+	15.9847i	−0.228859	+	0.673079i
$565$	−1.23071	+	0.217007i	−0.0517763	+	0.00912955i
$566$	9.60130	+	8.05645i	0.403573	+	0.338638i
$567$	6.37698	+	9.14662i	0.267808	+	0.384122i
$568$	−0.695754	−	0.253234i	−0.0291932	−	0.0106255i
$569$	−4.32951	+	7.49893i	−0.181502	+	0.314371i	−0.942392	−	0.334510i	$-0.891429\pi$
$569$	−4.32951	+	7.49893i	−0.181502	+	0.314371i	0.760890	+	0.648881i	$0.224763\pi$
$570$	−3.43256	−	5.75141i	−0.143774	−	0.240900i
$571$	7.96429	+	13.7946i	0.333295	+	0.577284i	0.983156	−	0.182769i	$-0.0585061\pi$
$571$	7.96429	+	13.7946i	0.333295	+	0.577284i	−0.649861	+	0.760053i	$0.725173\pi$
$572$	3.76932	+	21.3769i	0.157603	+	0.893811i
$573$	35.3819	+	19.4345i	1.47810	+	0.811888i
$574$	10.2633	−	3.73552i	0.428380	−	0.155918i
$575$	1.49188	+	1.77795i	0.0622156	+	0.0741456i
$576$	−1.38794	+	2.65963i	−0.0578307	+	0.110818i
$577$	−18.3765	+	31.8290i	−0.765024	+	1.32506i	0.175210	+	0.984531i	$0.443940\pi$
$577$	−18.3765	+	31.8290i	−0.765024	+	1.32506i	−0.940234	+	0.340529i	$0.889394\pi$
$578$	5.33387			0.221860
$579$	6.14720	+	7.01670i	0.255469	+	0.291604i
$580$	0.618373	−	0.736948i	0.0256765	−	0.0306001i
$581$	−8.23876	−	4.75665i	−0.341801	−	0.197339i
$582$	6.89965	+	1.06553i	0.286000	+	0.0441677i
$583$	17.7575	−	21.1625i	0.735440	−	0.876463i
$584$	6.61228	−	5.54836i	0.273618	−	0.229593i
$585$	−12.8950	+	0.549933i	−0.533141	+	0.0227369i
$586$	4.19203	+	23.7742i	0.173171	+	0.982101i
$587$	26.6146	+	31.7180i	1.09850	+	1.30914i	0.947195	+	0.320657i	$0.103904\pi$
$587$	26.6146	+	31.7180i	1.09850	+	1.30914i	0.151307	+	0.988487i	$0.451652\pi$
$588$	7.37926	+	5.92863i	0.304316	+	0.244492i
$589$	2.30826	+	13.6348i	0.0951101	+	0.561811i
$590$	−1.12432	+	0.649127i	−0.0462875	+	0.0267241i
$591$	−26.7666	−	14.7023i	−1.10103	−	0.604771i
$592$	−0.0721352	+	0.198190i	−0.00296474	+	0.00814556i
$593$	−26.5162	+	31.6007i	−1.08889	+	1.29769i	−0.137227	+	0.990540i	$0.543819\pi$
$593$	−26.5162	+	31.6007i	−1.08889	+	1.29769i	−0.951662	+	0.307147i	$0.900626\pi$
$594$	16.0579	+	16.8254i	0.658865	+	0.690354i
$595$	0.651884	−	3.69702i	0.0267247	−	0.151563i
$596$	−5.24418	+	3.02773i	−0.214810	+	0.124020i
$597$	−2.26618	+	0.879947i	−0.0927484	+	0.0360139i
$598$	−2.04657	−	1.71728i	−0.0836907	−	0.0702248i
$599$	−8.88160	−	7.45255i	−0.362892	−	0.304503i	0.443050	−	0.896497i	$-0.353896\pi$
$599$	−8.88160	−	7.45255i	−0.362892	−	0.304503i	−0.805942	+	0.591994i	$0.798341\pi$
$600$	−1.11370	+	7.21158i	−0.0454667	+	0.294411i
$601$	13.2730	−	7.66317i	0.541417	−	0.312587i	−0.204236	−	0.978922i	$-0.565471\pi$
$601$	13.2730	−	7.66317i	0.541417	−	0.312587i	0.745653	+	0.666334i	$0.232138\pi$
$602$	−2.45737	+	13.9365i	−0.100155	+	0.568007i
$603$	−24.0246	+	31.2440i	−0.978358	+	1.27235i
$604$	4.34484	−	5.17798i	0.176789	−	0.210689i
$605$	−2.74149	+	7.53219i	−0.111458	+	0.306227i
$606$	0.541416	+	25.4021i	0.0219935	+	1.03189i
$607$	−7.92492	+	4.57546i	−0.321663	+	0.185712i	−0.652133	−	0.758104i	$-0.726126\pi$
$607$	−7.92492	+	4.57546i	−0.321663	+	0.185712i	0.330471	+	0.943816i	$0.392792\pi$
$608$	3.78972	−	2.15361i	0.153693	−	0.0873405i
$609$	2.16915	−	0.842273i	0.0878984	−	0.0341306i
$610$	2.96580	+	3.53450i	0.120082	+	0.143108i
$611$	−8.20857	−	46.5531i	−0.332083	−	1.88334i
$612$	−9.08415	−	4.74060i	−0.367205	−	0.191627i
$613$	−24.9684	+	20.9509i	−1.00846	+	0.846201i	−0.988134	−	0.153592i	$-0.950916\pi$
$613$	−24.9684	+	20.9509i	−1.00846	+	0.846201i	−0.0203287	+	0.999793i	$0.506471\pi$
$614$	−1.51467	+	1.80512i	−0.0611272	+	0.0728486i
$615$	4.90328	+	12.6277i	0.197719	+	0.509197i
$616$	−4.80249	−	2.77272i	−0.193498	−	0.111716i
$617$	−2.57663	+	3.07070i	−0.103731	+	0.123622i	−0.815412	−	0.578881i	$-0.803490\pi$
$617$	−2.57663	+	3.07070i	−0.103731	+	0.123622i	0.711681	+	0.702503i	$0.247934\pi$
$618$	27.8554	−	5.52614i	1.12051	−	0.222294i
$619$	−0.932916			−0.0374971			−0.0187485	−	0.999824i	$-0.505968\pi$
$619$	−0.932916			−0.0374971			−0.0187485	+	0.999824i	$0.505968\pi$
$620$	−1.40726	+	2.43745i	−0.0565170	+	0.0978903i
$621$	−2.84510	−	0.315961i	−0.114170	−	0.0126791i
$622$	−18.1184	−	21.5927i	−0.726483	−	0.865788i
$623$	−12.0684	+	4.39254i	−0.483511	+	0.175984i
$624$	−0.178986	−	8.39765i	−0.00716519	−	0.336175i
$625$	2.39875	+	13.6040i	0.0959501	+	0.544160i
$626$	9.57545	+	16.5852i	0.382712	+	0.662877i
$627$	−6.34944	−	33.1917i	−0.253572	−	1.32555i
$628$	−3.70590	+	6.41881i	−0.147882	+	0.256138i
$629$	−0.676932	−	0.246383i	−0.0269910	−	0.00982394i
$630$	2.00991	−	2.61389i	0.0800769	−	0.104140i
$631$	7.28869	+	6.11594i	0.290158	+	0.243472i	0.776234	−	0.630445i	$-0.217128\pi$
$631$	7.28869	+	6.11594i	0.290158	+	0.243472i	−0.486076	+	0.873917i	$0.661572\pi$
$632$	8.25679	−	1.45590i	0.328438	−	0.0579124i
$633$	−34.1752	+	6.77990i	−1.35834	+	0.269477i
$634$	4.67669			0.185735
$635$	8.51993	−	14.7570i	0.338103	−	0.585612i
$636$	−8.04073	+	7.04434i	−0.318836	+	0.279326i
$637$	−26.1003	−	4.60219i	−1.03413	−	0.182345i
$638$	4.20351	−	2.42690i	0.166419	−	0.0960819i
$639$	1.63917	−	1.49898i	0.0648446	−	0.0592986i
$640$	0.873674	+	0.154052i	0.0345350	+	0.00608945i
$641$	0.419601	+	2.37967i	0.0165732	+	0.0939915i	0.991972	−	0.126455i	$-0.0403598\pi$
$641$	0.419601	+	2.37967i	0.0165732	+	0.0939915i	−0.975399	+	0.220446i	$0.929249\pi$
$642$	2.96789	+	14.9602i	0.117133	+	0.590430i
$643$	25.2829	−	21.2149i	0.997062	−	0.836634i	0.0104873	−	0.999945i	$-0.496662\pi$
$643$	25.2829	−	21.2149i	0.997062	−	0.836634i	0.986575	+	0.163311i	$0.0522173\pi$
$644$	0.672154	−	0.118519i	0.0264866	−	0.00467030i
$645$	−17.3461	−	2.67881i	−0.683002	−	0.105478i
$646$	7.35582	+	12.9440i	0.289411	+	0.509277i
$647$		−	3.07778i		−	0.121000i	−0.998168	−	0.0605000i	$-0.980730\pi$
$647$		−	3.07778i		−	0.121000i	0.998168	−	0.0605000i	$-0.0192695\pi$
$648$	−5.14726	−	7.38280i	−0.202203	−	0.290024i
$649$	−6.45075	+	1.13744i	−0.253214	+	0.0446484i
$650$	−6.98771	−	19.1986i	−0.274081	−	0.753030i
$651$	−5.82186	+	3.52876i	−0.228177	+	0.138303i
$652$	0.475122	−	0.172930i	0.0186072	−	0.00677247i
$653$		−	45.2152i		−	1.76941i	−0.466152	−	0.884704i	$-0.654360\pi$
$653$		−	45.2152i		−	1.76941i	0.466152	−	0.884704i	$-0.345640\pi$
$654$	2.48459	+	0.383703i	0.0971553	+	0.0150040i
$655$	1.02082	−	5.78936i	0.0398867	−	0.226209i
$656$	−8.28411	+	3.01517i	−0.323440	+	0.117723i
$657$	5.57915	+	25.2870i	0.217663	+	0.986540i
$658$	10.4586	+	6.03825i	0.407717	+	0.235395i
$659$	−6.21564	−	5.21554i	−0.242127	−	0.203169i	0.513646	−	0.858002i	$-0.328294\pi$
$659$	−6.21564	−	5.21554i	−0.242127	−	0.203169i	−0.755773	+	0.654833i	$0.772739\pi$
$660$	3.31124	−	6.02835i	0.128890	−	0.234653i
$661$	−6.42918	−	1.13364i	−0.250066	−	0.0440934i	0.0472098	−	0.998885i	$-0.484967\pi$
$661$	−6.42918	−	1.13364i	−0.250066	−	0.0440934i	−0.297276	+	0.954792i	$0.596078\pi$
$662$	0.891463	+	1.06240i	0.0346477	+	0.0412915i
$663$	28.6828	−	0.611340i	1.11395	−	0.0237425i
$664$	6.65002	+	3.83939i	0.258071	+	0.148997i
$665$	−4.51303	+	1.60778i	−0.175008	+	0.0623471i
$666$	−0.426993	−	0.466928i	−0.0165456	−	0.0180931i
$667$	−0.204322	+	0.561369i	−0.00791137	+	0.0217363i
$668$	14.3413	+	5.21979i	0.554880	+	0.201960i
$669$	−38.9872	+	7.73453i	−1.50733	+	0.299034i
$670$	10.9522	+	3.98626i	0.423119	+	0.154003i
$671$	7.96205	+	21.8756i	0.307372	+	0.844497i
$672$	1.67284	+	1.34399i	0.0645311	+	0.0518454i
$673$			21.4966i			0.828633i	0.910133	+	0.414316i	$0.135979\pi$
$673$			21.4966i			0.828633i	−0.910133	+	0.414316i	$0.864021\pi$
$674$	−1.13802	−	3.12667i	−0.0438348	−	0.120435i
$675$	−17.6344	−	12.9713i	−0.678747	−	0.499264i
$676$	5.25875	+	9.10842i	0.202260	+	0.350324i
$677$	−21.1179	−	36.5773i	−0.811627	−	1.40578i	−0.911724	−	0.410802i	$-0.865249\pi$
$677$	−21.1179	−	36.5773i	−0.811627	−	1.40578i	0.100097	−	0.994978i	$-0.468085\pi$
$678$	2.30999	+	0.785439i	0.0887145	+	0.0301646i
$679$	1.70795	−	4.69256i	0.0655452	−	0.180084i
$680$	−0.526176	+	2.98409i	−0.0201779	+	0.114435i
$681$	−7.74237	+	14.0956i	−0.296688	+	0.540143i
$682$	−10.8782	+	9.12791i	−0.416549	+	0.349526i
$683$	−3.03000			−0.115940			−0.0579699	−	0.998318i	$-0.518463\pi$
$683$	−3.03000			−0.115940			−0.0579699	+	0.998318i	$0.518463\pi$
$684$	0.467917	+	13.0683i	0.0178913	+	0.499680i
$685$	2.08319			0.0795944
$686$	11.8301	−	9.92665i	0.451676	−	0.379001i
$687$	6.02786	+	9.94494i	0.229977	+	0.379423i
$688$	1.98350	−	11.2490i	0.0756202	−	0.428863i
$689$	10.2368	−	28.1254i	0.389991	−	1.07149i
$690$	0.164727	+	0.830336i	0.00627107	+	0.0316104i
$691$	5.96076	+	10.3243i	0.226758	+	0.392756i	0.956845	−	0.290598i	$-0.0938541\pi$
$691$	5.96076	+	10.3243i	0.226758	+	0.392756i	−0.730088	+	0.683354i	$0.760521\pi$
$692$	2.74698	+	4.75790i	0.104424	+	0.180868i
$693$	14.0400	−	8.92449i	0.533334	−	0.339013i
$694$	4.17304	+	11.4653i	0.158406	+	0.435218i
$695$		−	17.0753i		−	0.647704i
$696$	−1.75086	+	0.679851i	−0.0663660	+	0.0257697i
$697$	−10.2985	−	28.2950i	−0.390085	−	1.07175i
$698$	−2.54449	−	0.926118i	−0.0963103	−	0.0350541i
$699$	−27.3490	−	31.2174i	−1.03443	−	1.18075i
$700$	4.90470	+	1.78517i	0.185380	+	0.0674729i
$701$	−2.47596	+	6.80264i	−0.0935157	+	0.256932i	−0.977628	−	0.210343i	$-0.932542\pi$
$701$	−2.47596	+	6.80264i	−0.0935157	+	0.256932i	0.884112	+	0.467275i	$0.154764\pi$
$702$	22.5830	+	11.1794i	0.852342	+	0.421938i
$703$	0.153452	+	0.906435i	0.00578755	+	0.0341868i
$704$	3.87639	+	2.23803i	0.146097	+	0.0843491i
$705$	−7.21100	+	13.1282i	−0.271582	+	0.494435i
$706$	15.3526	+	18.2965i	0.577803	+	0.688598i
$707$	17.8977	+	3.15585i	0.673113	+	0.118688i
$708$	2.53410	−	0.0540114i	0.0952373	−	0.00202987i
$709$	24.6990	+	20.7250i	0.927592	+	0.778342i	0.975383	−	0.220515i	$-0.0707739\pi$
$709$	24.6990	+	20.7250i	0.927592	+	0.778342i	−0.0477918	+	0.998857i	$0.515218\pi$
$710$	−0.568851	−	0.328426i	−0.0213486	−	0.0123256i
$711$	−7.58777	+	23.9807i	−0.284564	+	0.899347i
$712$	9.74117	−	3.54550i	0.365066	−	0.132873i
$713$	0.303498	−	1.72122i	0.0113661	−	0.0644602i
$714$	−4.59048	+	5.71370i	−0.171794	+	0.213830i
$715$			19.2571i			0.720173i
$716$	−14.2456	+	5.18499i	−0.532384	+	0.193772i
$717$	41.9918	+	23.0652i	1.56821	+	0.861384i
$718$	−5.36332	−	14.7356i	−0.200157	−	0.549928i
$719$	−39.7645	+	7.01156i	−1.48297	+	0.261487i	−0.855763	−	0.517368i	$-0.826912\pi$
$719$	−39.7645	+	7.01156i	−1.48297	+	0.261487i	−0.627204	+	0.778855i	$0.715801\pi$
$720$	−1.62233	+	2.10983i	−0.0604605	+	0.0786288i
$721$		−	20.3129i		−	0.756491i
$722$	9.72391	−	16.3232i	0.361887	−	0.607485i
$723$	6.10602	−	7.60007i	0.227085	−	0.282650i
$724$	16.7715	−	2.95726i	0.623307	−	0.109906i
$725$	−3.49967	+	2.93657i	−0.129974	+	0.109061i
$726$	11.7711	−	10.3124i	0.436866	−	0.382730i
$727$	−4.82355	−	27.3557i	−0.178896	−	1.01457i	−0.933550	−	0.358446i	$-0.883307\pi$
$727$	−4.82355	−	27.3557i	−0.178896	−	1.01457i	0.754655	−	0.656122i	$-0.227804\pi$
$728$	−5.91679	−	1.04329i	−0.219291	−	0.0386669i
$729$	26.7796	−	3.44292i	0.991837	−	0.127516i
$730$	6.63171	−	3.82882i	0.245451	−	0.141711i
$731$	38.4217	+	6.77478i	1.42108	+	0.250574i
$732$	−1.75294	−	8.83598i	−0.0647905	−	0.326587i
$733$	−23.1082	+	40.0245i	−0.853519	+	1.47834i	0.0244924	+	0.999700i	$0.492203\pi$
$733$	−23.1082	+	40.0245i	−0.853519	+	1.47834i	−0.878012	+	0.478639i	$0.841130\pi$
$734$	−19.4400			−0.717545
$735$	5.53375	+	6.31648i	0.204115	+	0.232987i
$736$	−0.542537	+	0.0956639i	−0.0199982	+	0.00352622i
$737$	45.0471	+	37.7990i	1.65933	+	1.39234i
$738$	3.47860	−	26.2175i	0.128049	−	0.965081i
$739$	−27.4644	−	9.99621i	−1.01029	−	0.367717i	−0.216748	−	0.976228i	$-0.569545\pi$
$739$	−27.4644	−	9.99621i	−1.01029	−	0.367717i	−0.793545	+	0.608511i	$0.791767\pi$
$740$	−0.0935543	+	0.162041i	−0.00343912	+	0.00595674i
$741$	−18.7636	−	31.4392i	−0.689297	−	1.15495i
$742$	3.82319	+	6.62197i	0.140354	+	0.243100i
$743$	3.90544	+	22.1488i	0.143277	+	0.812562i	0.968735	+	0.248098i	$0.0798056\pi$
$743$	3.90544	+	22.1488i	0.143277	+	0.812562i	−0.825458	+	0.564463i	$0.809083\pi$
$744$	4.69918	−	2.84828i	0.172280	−	0.104423i
$745$	−5.04812	+	1.83737i	−0.184949	+	0.0673159i
$746$	−12.6119	−	15.0302i	−0.461753	−	0.550296i
$747$	−19.4412	+	12.3577i	−0.711315	+	0.452146i
$748$	−7.64417	+	13.2401i	−0.279498	+	0.484105i
$749$	10.9093			0.398618
$750$	−4.55726	+	13.4030i	−0.166408	+	0.489407i
$751$	−5.47056	+	6.51956i	−0.199624	+	0.237902i	−0.856565	−	0.516040i	$-0.827406\pi$
$751$	−5.47056	+	6.51956i	−0.199624	+	0.237902i	0.656941	+	0.753942i	$0.271850\pi$
$752$	−8.44175	−	4.87385i	−0.307839	−	0.177731i
$753$	−6.31159	+	7.85593i	−0.230007	+	0.286286i
$754$	3.38024	−	4.02842i	0.123101	−	0.146706i
$755$	4.59365	−	3.85453i	0.167180	−	0.140281i
$756$	−5.89630	+	2.58376i	−0.214446	+	0.0939704i
$757$	−0.332147	−	1.88370i	−0.0120721	−	0.0684641i	0.978177	−	0.207775i	$-0.0666223\pi$
$757$	−0.332147	−	1.88370i	−0.0120721	−	0.0684641i	−0.990249	+	0.139311i	$0.955511\pi$
$758$	11.3689	+	13.5489i	0.412937	+	0.492119i
$759$	−0.651864	+	4.22102i	−0.0236611	+	0.153213i
$760$	3.64274	−	1.29774i	0.132136	−	0.0470740i
$761$	−45.9633	+	26.5369i	−1.66617	+	0.961962i	−0.696493	+	0.717564i	$0.745257\pi$
$761$	−45.9633	+	26.5369i	−1.66617	+	0.961962i	−0.969675	+	0.244398i	$0.921410\pi$
$762$	−28.4501	+	17.2443i	−1.03064	+	0.624693i
$763$	0.615041	−	1.68981i	0.0222660	−	0.0611752i
$764$	−14.9811	+	17.8538i	−0.541999	+	0.645929i
$765$	−7.20628	−	5.54117i	−0.260544	−	0.200342i
$766$	−2.31449	+	13.1261i	−0.0836257	+	0.474265i
$767$	−6.14593	+	3.54836i	−0.221917	+	0.128124i
$768$	−1.35025	−	1.08481i	−0.0487230	−	0.0391449i
$769$	1.47750	+	1.23977i	0.0532802	+	0.0447074i	0.669039	−	0.743227i	$-0.266706\pi$
$769$	1.47750	+	1.23977i	0.0532802	+	0.0447074i	−0.615759	+	0.787935i	$0.711150\pi$
$770$	−3.76867	−	3.16229i	−0.135813	−	0.113961i
$771$	41.3016	+	33.1824i	1.48744	+	1.19504i
$772$	−4.66428	+	2.69293i	−0.167871	+	0.0969205i
$773$	0.731672	−	4.14952i	0.0263164	−	0.149248i	−0.968818	−	0.247773i	$-0.920301\pi$
$773$	0.731672	−	4.14952i	0.0263164	−	0.149248i	0.995135	+	0.0985250i	$0.0314124\pi$
$774$	27.1651	+	20.8883i	0.976431	+	0.750813i
$775$	8.59137	−	10.2388i	0.308611	−	0.367788i
$776$	−1.37859	+	3.78766i	−0.0494886	+	0.135969i
$777$	−0.387035	+	0.234591i	−0.0138848	+	0.00841590i
$778$	6.14803	−	3.54956i	0.220417	−	0.127258i
$779$	−24.9009	+	29.2674i	−0.892169	+	1.04861i
$780$	1.13730	−	7.36437i	0.0407219	−	0.263687i
$781$	−2.13027	−	2.53876i	−0.0762270	−	0.0908438i
$782$	−0.326747	−	1.85307i	−0.0116844	−	0.0662658i
$783$	0.621928	−	5.60022i	0.0222259	−	0.200136i
$784$	−4.18651	+	3.51290i	−0.149518	+	0.125461i
$785$	−4.22658	+	5.03704i	−0.150853	+	0.179780i
$786$	−7.18848	+	8.94738i	−0.256404	+	0.319142i
$787$	18.1727	+	10.4920i	0.647785	+	0.373999i	0.787607	−	0.616178i	$-0.211320\pi$
$787$	18.1727	+	10.4920i	0.647785	+	0.373999i	−0.139822	+	0.990177i	$0.544653\pi$
$788$	11.3333	−	13.5065i	0.403732	−	0.481149i
$789$	13.1098	−	38.5560i	0.466720	−	1.37263i
$790$	7.43803			0.264633
$791$	0.872599	−	1.51139i	0.0310261	−	0.0537387i
$792$	−11.3325	+	7.20351i	−0.402684	+	0.255965i
$793$	16.2121	+	19.3208i	0.575709	+	0.686103i
$794$	−37.0408	+	13.4818i	−1.31453	+	0.478450i
$795$	−8.11017	+	4.91576i	−0.287638	+	0.174344i
$796$	−0.243724	−	1.38223i	−0.00863856	−	0.0489917i
$797$	−1.12076	−	1.94121i	−0.0396992	−	0.0687611i	0.845493	−	0.533986i	$-0.179307\pi$
$797$	−1.12076	−	1.94121i	−0.0396992	−	0.0687611i	−0.885192	+	0.465225i	$0.845973\pi$
$798$	9.23400	+	1.49068i	0.326880	+	0.0527697i
$799$	16.6470	−	28.8334i	0.588927	−	1.02005i
$800$	−3.95889	−	1.44092i	−0.139968	−	0.0509441i
$801$	−4.09043	+	30.8288i	−0.144528	+	1.08928i
$802$	12.4124	+	10.4152i	0.438296	+	0.367774i
$803$	38.0492	−	6.70910i	1.34273	−	0.236759i
$804$	−14.9947	−	17.1157i	−0.528824	−	0.603624i
$805$	0.605501			0.0213411
$806$	−7.69259	+	13.3240i	−0.270960	+	0.469317i
$807$	0.246716	+	1.24361i	0.00868480	+	0.0437772i
$808$	−14.4464	−	2.54728i	−0.508221	−	0.0896131i
$809$	−20.2910	+	11.7150i	−0.713395	+	0.411879i	−0.812317	−	0.583217i	$-0.801794\pi$
$809$	−20.2910	+	11.7150i	−0.713395	+	0.411879i	0.0989219	+	0.995095i	$0.468461\pi$
$810$	−3.35968	−	7.24310i	−0.118047	−	0.254497i
$811$	40.4082	+	7.12506i	1.41893	+	0.250195i	0.829896	−	0.557917i	$-0.188399\pi$
$811$	40.4082	+	7.12506i	1.41893	+	0.250195i	0.589029	+	0.808112i	$0.299511\pi$
$812$	0.233289	+	1.32305i	0.00818684	+	0.0464299i
$813$	−4.63232	+	4.05829i	−0.162463	+	0.142330i
$814$	−0.723180	+	0.606820i	−0.0253475	+	0.0212690i
$815$	0.441742	−	0.0778910i	0.0154735	−	0.00272840i
$816$	3.70526	−	4.61188i	0.129710	−	0.161448i
$817$	−16.7090	−	46.9021i	−0.584575	−	1.64090i
$818$			32.3513i			1.13114i
$819$	10.9869	−	14.2885i	0.383914	−	0.499279i
$820$	−7.70210	+	1.35809i	−0.268969	+	0.0474265i
$821$	4.40829	+	12.1117i	0.153851	+	0.422701i	0.992542	−	0.121907i	$-0.0389009\pi$
$821$	4.40829	+	12.1117i	0.153851	+	0.422701i	−0.838691	+	0.544607i	$0.816679\pi$
$822$	−3.56479	−	1.95806i	−0.124337	−	0.0682952i
$823$	35.1896	−	12.8080i	1.22663	−	0.446458i	0.354190	−	0.935174i	$-0.384757\pi$
$823$	35.1896	−	12.8080i	1.22663	−	0.446458i	0.872443	+	0.488716i	$0.162534\pi$
$824$			16.3958i			0.571174i
$825$	−20.4569	+	25.4624i	−0.712218	+	0.886486i
$826$	0.314826	−	1.78547i	0.0109542	−	0.0621244i
$827$	−23.4938	+	8.55105i	−0.816960	+	0.297349i	−0.716496	−	0.697592i	$-0.754255\pi$
$827$	−23.4938	+	8.55105i	−0.816960	+	0.297349i	−0.100464	+	0.994941i	$0.532033\pi$
$828$	0.498577	−	1.57572i	0.0173268	−	0.0547602i
$829$	−32.1180	−	18.5433i	−1.11550	−	0.644036i	−0.175254	−	0.984523i	$-0.556075\pi$
$829$	−32.1180	−	18.5433i	−1.11550	−	0.644036i	−0.940249	+	0.340487i	$0.889408\pi$
$830$	5.21848	+	4.37882i	0.181136	+	0.151991i
$831$	−49.8487	+	1.06247i	−1.72923	+	0.0368566i
$832$	4.77581	+	0.842104i	0.165571	+	0.0291947i
$833$	−11.9986	−	14.2993i	−0.415726	−	0.495443i
$834$	−16.0497	+	29.2197i	−0.555756	+	1.01179i
$835$	11.7255	+	6.76970i	0.405776	+	0.234275i
$836$	19.5103	+	0.133279i	0.674777	+	0.00460956i
$837$	1.05320	+	16.4513i	0.0364039	+	0.568641i
$838$	10.2559	−	28.1780i	0.354286	−	0.973392i
$839$	14.0569	+	5.11631i	0.485299	+	0.176635i	0.573070	−	0.819506i	$-0.305752\pi$
$839$	14.0569	+	5.11631i	0.485299	+	0.176635i	−0.0877710	+	0.996141i	$0.527974\pi$
$840$	1.25447	+	1.43191i	0.0432833	+	0.0494056i
$841$	26.1461	+	9.51640i	0.901590	+	0.328152i
$842$	−1.08521	−	2.98159i	−0.0373987	−	0.102752i
$843$	18.8929	−	7.33605i	0.650707	−	0.252667i
$844$		−	20.1156i		−	0.692408i
$845$	3.19126	+	8.76791i	0.109783	+	0.301625i
$846$	24.6792	−	15.6873i	0.848490	−	0.539341i
$847$	−5.59689	−	9.69410i	−0.192311	−	0.333093i
$848$	−3.08594	−	5.34500i	−0.105972	−	0.183548i
$849$	−4.22441	−	21.2939i	−0.144981	−	0.730803i
$850$	4.92156	−	13.5219i	0.168808	−	0.463796i
$851$	0.0201764	−	0.114426i	0.000691639	−	0.00392248i
$852$	0.664731	+	1.09669i	0.0227733	+	0.0375721i
$853$	24.3933	−	20.4684i	0.835212	−	0.700826i	−0.121269	−	0.992620i	$-0.538696\pi$
$853$	24.3933	−	20.4684i	0.835212	−	0.700826i	0.956481	+	0.291793i	$0.0942520\pi$
$854$	−6.44341			−0.220489
$855$	−1.60440	+	11.4895i	−0.0548692	+	0.392934i
$856$	−8.80558			−0.300969
$857$	38.8619	−	32.6090i	1.32750	−	1.11390i	0.342841	−	0.939393i	$-0.388611\pi$
$857$	38.8619	−	32.6090i	1.32750	−	1.11390i	0.984656	−	0.174509i	$-0.0558337\pi$
$858$	18.1004	−	32.9531i	0.617938	−	1.12500i
$859$	−8.50476	+	48.2329i	−0.290179	+	1.64568i	0.395999	+	0.918251i	$0.370398\pi$
$859$	−8.50476	+	48.2329i	−0.290179	+	1.64568i	−0.686178	+	0.727434i	$0.740713\pi$
$860$	3.46586	−	9.52237i	0.118185	−	0.324710i
$861$	−17.9103	−	6.08984i	−0.610382	−	0.207541i
$862$	−16.2644	−	28.1708i	−0.553967	−	0.959500i
$863$	19.1156	+	33.1092i	0.650702	+	1.12705i	0.982953	+	0.183858i	$0.0588588\pi$
$863$	19.1156	+	33.1092i	0.650702	+	1.12705i	−0.332250	+	0.943191i	$0.607808\pi$
$864$	4.75927	−	2.08551i	0.161914	−	0.0709505i
$865$	1.66700	+	4.58003i	0.0566795	+	0.155726i
$866$		−	7.29962i		−	0.248051i
$867$	−7.20206	−	5.78626i	−0.244595	−	0.196512i
$868$	−1.34431	−	3.69345i	−0.0456287	−	0.125364i
$869$	35.2649	+	12.8354i	1.19628	+	0.435410i
$870$	−1.63441	+	0.324245i	−0.0554117	+	0.0109929i
$871$	59.8684	+	21.7903i	2.02856	+	0.738336i
$872$	−0.496438	+	1.36395i	−0.0168115	+	0.0461892i
$873$	−8.16036	−	8.92358i	−0.276186	−	0.302017i
$874$	−1.85004	+	1.53095i	−0.0625785	+	0.0517853i
$875$	8.76934	+	5.06298i	0.296458	+	0.171160i
$876$	−14.9472	+	0.318582i	−0.505019	+	0.0107639i
$877$	18.2870	+	21.7936i	0.617509	+	0.735919i	0.980640	−	0.195819i	$-0.0627365\pi$
$877$	18.2870	+	21.7936i	0.617509	+	0.735919i	−0.363131	+	0.931738i	$0.618292\pi$
$878$	8.20030	+	1.44593i	0.276747	+	0.0487979i
$879$	20.1303	−	36.6486i	0.678977	−	1.23613i
$880$	3.04193	+	2.55248i	0.102543	+	0.0860440i
$881$	−24.5501	−	14.1740i	−0.827113	−	0.477534i	0.0257499	−	0.999668i	$-0.491803\pi$
$881$	−24.5501	−	14.1740i	−0.827113	−	0.477534i	−0.852863	+	0.522134i	$0.825136\pi$
$882$	−3.53240	−	16.0103i	−0.118942	−	0.539094i
$883$	−12.8113	+	4.66293i	−0.431134	+	0.156920i	−0.548466	−	0.836173i	$-0.684788\pi$
$883$	−12.8113	+	4.66293i	−0.431134	+	0.156920i	0.117332	+	0.993093i	$0.462566\pi$
$884$	−2.87627	+	16.3121i	−0.0967393	+	0.548636i
$885$	2.22230	+	0.343195i	0.0747017	+	0.0115364i
$886$		−	2.73555i		−	0.0919027i
$887$	−38.7919	+	14.1191i	−1.30250	+	0.474073i	−0.897812	−	0.440380i	$-0.854844\pi$
$887$	−38.7919	+	14.1191i	−1.30250	+	0.474073i	−0.404693	+	0.914453i	$0.632622\pi$
$888$	0.312400	−	0.189353i	0.0104835	−	0.00635426i
$889$	8.13878	+	22.3611i	0.272966	+	0.749968i
$890$	9.05679	−	1.59696i	0.303584	−	0.0535301i
$891$	−3.42981	−	40.1384i	−0.114903	−	1.34469i
$892$		−	22.9480i		−	0.768354i
$893$	−42.4882	−	0.290247i	−1.42181	−	0.00971273i
$894$	10.3655	+	1.60077i	0.346673	+	0.0535377i
$895$	−13.2448	+	2.33541i	−0.442725	+	0.0780643i
$896$	−0.949059	+	0.796355i	−0.0317058	+	0.0266044i
$897$	0.900459	+	4.53891i	0.0300654	+	0.151550i
$898$	−1.97265	−	11.1875i	−0.0658283	−	0.373331i
$899$	3.38800	+	0.597396i	0.112996	+	0.0199243i
$900$	9.32700	−	8.52927i	0.310900	−	0.284309i
$901$	18.2562	−	10.5402i	0.608203	−	0.351146i
$902$	−38.8605	−	6.85216i	−1.29391	−	0.228152i
$903$	18.4365	−	16.1519i	0.613530	−	0.537502i
$904$	−0.704329	+	1.21993i	−0.0234256	+	0.0405744i
$905$	15.1084			0.502219
$906$	−11.4838	+	2.27822i	−0.381523	+	0.0756889i
$907$	−37.1668	+	6.55350i	−1.23410	+	0.217606i	−0.752386	−	0.658722i	$-0.771097\pi$
$907$	−37.1668	+	6.55350i	−1.23410	+	0.217606i	−0.481716	+	0.876327i	$0.659986\pi$
$908$	−7.11266	−	5.96823i	−0.236042	−	0.198063i
$909$	26.8255	−	34.8865i	0.889745	−	1.15711i
$910$	−5.00862	−	1.82299i	−0.166034	−	0.0604315i
$911$	23.7579	−	41.1499i	0.787135	−	1.36336i	−0.140580	−	0.990069i	$-0.544897\pi$
$911$	23.7579	−	41.1499i	0.787135	−	1.36336i	0.927715	−	0.373289i	$-0.121770\pi$
$912$	−7.45334	−	1.20322i	−0.246805	−	0.0398427i
$913$	17.1854	+	29.7659i	0.568753	+	0.985109i
$914$	−4.95507	−	28.1016i	−0.163899	−	0.929519i
$915$	−0.170294	−	7.98981i	−0.00562973	−	0.264135i
$916$	−6.30918	+	2.29635i	−0.208461	+	0.0758737i
$917$	5.27701	+	6.28890i	0.174262	+	0.207678i
$918$	7.12321	+	16.2556i	0.235101	+	0.536516i
$919$	−21.1630	+	36.6553i	−0.698101	+	1.20915i	0.271023	+	0.962573i	$0.412638\pi$
$919$	−21.1630	+	36.6553i	−0.698101	+	1.20915i	−0.969124	+	0.246574i	$0.920695\pi$
$920$	−0.488738			−0.0161132
$921$	4.00340	−	0.794221i	0.131917	−	0.0261705i
$922$	−16.2947	+	19.4193i	−0.536639	+	0.639541i
$923$	−3.10954	−	1.79529i	−0.102352	−	0.0590928i
$924$	3.47668	+	8.95368i	0.114374	+	0.294555i
$925$	0.571151	−	0.680671i	0.0187793	−	0.0223803i
$926$	8.60685	−	7.22200i	0.282839	−	0.237330i
$927$	−43.6067	−	22.7563i	−1.43223	−	0.747416i
$928$	−0.188302	−	1.06791i	−0.00618132	−	0.0350560i
$929$	−8.67813	−	10.3422i	−0.284720	−	0.339316i	0.604661	−	0.796483i	$-0.293309\pi$
$929$	−8.67813	−	10.3422i	−0.284720	−	0.339316i	−0.889381	+	0.457167i	$0.848864\pi$
$930$	4.54434	−	1.76455i	0.149015	−	0.0578618i
$931$	−8.30027	+	22.3290i	−0.272031	+	0.731804i
$932$	20.7514	−	11.9809i	0.679736	−	0.392446i
$933$	1.04034	+	48.8107i	0.0340593	+	1.59799i
$934$	−3.03340	+	8.33420i	−0.0992559	+	0.272703i
$935$	−8.71817	+	10.3899i	−0.285115	+	0.339786i
$936$	−8.86821	+	11.5331i	−0.289867	+	0.376971i
$937$	−7.39263	+	41.9257i	−0.241507	+	1.36965i	0.586961	+	0.809615i	$0.300324\pi$
$937$	−7.39263	+	41.9257i	−0.241507	+	1.36965i	−0.828468	+	0.560037i	$0.810787\pi$
$938$	−14.0957	+	8.13814i	−0.460240	+	0.265720i
$939$	5.06257	−	32.7817i	0.165211	−	1.06979i
$940$	−6.62451	−	5.55862i	−0.216068	−	0.181302i
$941$	3.07263	+	2.57825i	0.100165	+	0.0840484i	0.691495	−	0.722381i	$-0.256952\pi$
$941$	3.07263	+	2.57825i	0.100165	+	0.0840484i	−0.591330	+	0.806430i	$0.701397\pi$
$942$	11.9671	−	4.64679i	0.389910	−	0.151401i
$943$	4.20600	−	2.42833i	0.136966	−	0.0790774i
$944$	−0.254116	+	1.44116i	−0.00827077	+	0.0469059i
$945$	−5.54947	+	1.34902i	−0.180524	+	0.0438837i
$946$	32.8644	−	39.1663i	1.06851	−	1.27341i
$947$	15.7009	−	43.1377i	0.510209	−	1.40179i	−0.370811	−	0.928709i	$-0.620920\pi$
$947$	15.7009	−	43.1377i	0.510209	−	1.40179i	0.881020	−	0.473080i	$-0.156858\pi$
$948$	−12.7281	−	6.99127i	−0.413390	−	0.227066i
$949$	36.2513	−	20.9297i	1.17677	−	0.679407i
$950$	−18.1063	+	3.06524i	−0.587444	+	0.0994495i
$951$	−6.31470	−	5.07334i	−0.204768	−	0.164514i
$952$	−2.72001	−	3.24158i	−0.0881560	−	0.105060i
$953$	−5.33398	−	30.2505i	−0.172785	−	0.979910i	−0.940670	−	0.339323i	$-0.889802\pi$
$953$	−5.33398	−	30.2505i	−0.172785	−	0.979910i	0.767885	−	0.640587i	$-0.221309\pi$
$954$	18.4988	−	0.788921i	0.598921	−	0.0255422i
$955$	−15.8391	+	13.2905i	−0.512540	+	0.430072i
$956$	−17.7799	+	21.1892i	−0.575042	+	0.685308i
$957$	−8.30853	−	1.28311i	−0.268577	−	0.0414770i
$958$	−6.01520	−	3.47288i	−0.194342	−	0.112204i
$959$	−1.86998	+	2.22856i	−0.0603848	+	0.0719638i
$960$	−1.01256	−	1.15578i	−0.0326802	−	0.0373027i
$961$	20.9350			0.675322
$962$	−0.511401	+	0.885772i	−0.0164882	+	0.0285584i
$963$	12.2216	−	23.4196i	0.393836	−	0.754685i
$964$	3.61802	+	4.31178i	0.116528	+	0.138873i
$965$	−4.48991	+	1.63419i	−0.144535	+	0.0526066i
$966$	−1.03615	−	0.569132i	−0.0333375	−	0.0183115i
$967$	−7.75812	−	43.9985i	−0.249484	−	1.41490i	−0.809844	−	0.586646i	$-0.800448\pi$
$967$	−7.75812	−	43.9985i	−0.249484	−	1.41490i	0.560359	−	0.828250i	$-0.310663\pi$
$968$	4.51760	+	7.82471i	0.145201	+	0.251496i
$969$	4.10970	−	25.4574i	0.132023	−	0.817810i
$970$	−1.78794	+	3.09680i	−0.0574072	+	0.0994322i
$971$	5.60597	+	2.04041i	0.179904	+	0.0654798i	0.430402	−	0.902637i	$-0.358372\pi$
$971$	5.60597	+	2.04041i	0.179904	+	0.0654798i	−0.250497	+	0.968117i	$0.580594\pi$
$972$	−1.05888	+	15.5525i	−0.0339637	+	0.498845i
$973$	18.2669	+	15.3277i	0.585609	+	0.491385i
$974$	−40.8498	+	7.20291i	−1.30891	+	0.230796i
$975$	−11.3917	+	33.5033i	−0.364827	+	1.07296i
$976$	5.20088			0.166476
$977$	−25.0971	+	43.4695i	−0.802929	+	1.39071i	0.114752	+	0.993394i	$0.463393\pi$
$977$	−25.0971	+	43.4695i	−0.802929	+	1.39071i	−0.917680	+	0.397319i	$0.869941\pi$
$978$	−0.829131	−	0.281920i	−0.0265127	−	0.00901481i
$979$	45.6955	+	8.05735i	1.46043	+	0.257514i
$980$	−4.19882	+	2.42419i	−0.134126	+	0.0774378i
$981$	−2.93858	−	3.21342i	−0.0938216	−	0.102597i
$982$	10.7118	+	1.88877i	0.341826	+	0.0602732i
$983$	−7.13674	−	40.4745i	−0.227627	−	1.29093i	−0.857600	−	0.514318i	$-0.828045\pi$
$983$	−7.13674	−	40.4745i	−0.227627	−	1.29093i	0.629973	−	0.776617i	$-0.283066\pi$
$984$	14.4565	+	4.91549i	0.460857	+	0.156700i
$985$	11.9823	−	10.0543i	0.381788	−	0.320358i
$986$	3.64754	−	0.643159i	0.116161	−	0.0204824i
$987$	−7.57129	−	19.4987i	−0.240997	−	0.620652i
$988$	19.9125	−	7.09390i	0.633502	−	0.225687i
$989$			6.29274i			0.200097i
$990$	−11.0106	+	4.54771i	−0.349941	+	0.144536i
$991$	−15.9662	+	2.81527i	−0.507183	+	0.0894301i	−0.421384	−	0.906882i	$-0.638456\pi$
$991$	−15.9662	+	2.81527i	−0.507183	+	0.0894301i	−0.0857993	+	0.996312i	$0.527344\pi$
$992$	1.08507	+	2.98121i	0.0344511	+	0.0946536i
$993$	−0.0511870	−	2.40158i	−0.00162437	−	0.0762119i
$994$	0.861976	−	0.313734i	0.0273402	−	0.00995103i
$995$		−	1.24516i		−	0.0394743i
$996$	−4.81416	−	12.3982i	−0.152543	−	0.392851i
$997$	−6.06749	+	34.4105i	−0.192159	+	1.08979i	0.724247	+	0.689541i	$0.242188\pi$
$997$	−6.06749	+	34.4105i	−0.192159	+	1.08979i	−0.916406	+	0.400250i	$0.868923\pi$
$998$	5.52477	−	2.01085i	0.174883	−	0.0636524i
$999$	0.0700163	+	1.09368i	0.00221522	+	0.0346024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.x.c.281.1	yes	60
9.5	odd	6		342.2.bf.c.167.1	yes	60
19.14	odd	18		342.2.bf.c.299.1	yes	60
171.14	even	18	inner	342.2.x.c.185.1	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.c.185.1	✓	60	171.14	even	18	inner
342.2.x.c.281.1	yes	60	1.1	even	1	trivial
342.2.bf.c.167.1	yes	60	9.5	odd	6
342.2.bf.c.299.1	yes	60	19.14	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-1.73166 + 0.0369083i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.303424 - 0.833650i) q^{5} +(-1.30280 + 1.14136i) q^{6} +(0.619454 + 1.07293i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.99728 - 0.127825i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-1.73166 + 0.0369083i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.303424 - 0.833650i) q^{5} +(-1.30280 + 1.14136i) q^{6} +(0.619454 + 1.07293i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.99728 - 0.127825i) q^{9} +(-0.303424 - 0.833650i) q^{10} -4.47607i q^{11} +(-0.264352 + 1.71176i) q^{12} +(-1.65862 - 4.55702i) q^{13} +(1.16419 + 0.423732i) q^{14} +(-0.494657 + 1.45479i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.16819 - 3.20959i) q^{17} +(2.21388 - 2.02453i) q^{18} +(-4.29775 + 0.727574i) q^{19} +(-0.768296 - 0.443576i) q^{20} +(-1.11228 - 1.83508i) q^{21} +(-2.87716 - 3.42887i) q^{22} +(0.542537 + 0.0956639i) q^{23} +(0.897792 + 1.48121i) q^{24} +(3.22732 + 2.70804i) q^{25} +(-4.19978 - 2.42474i) q^{26} +(-5.18554 + 0.331974i) q^{27} +(1.16419 - 0.423732i) q^{28} +(-0.188302 + 1.06791i) q^{29} +(0.556194 + 1.43240i) q^{30} -3.17254i q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.165204 + 7.75102i) q^{33} +(-1.16819 - 3.20959i) q^{34} +(1.08240 - 0.190857i) q^{35} +(0.394588 - 2.97394i) q^{36} -0.210909i q^{37} +(-2.82459 + 3.31989i) q^{38} +(3.04036 + 7.82999i) q^{39} +(-0.873674 + 0.154052i) q^{40} +(6.75327 - 5.66667i) q^{41} +(-2.03162 - 0.690790i) q^{42} +(1.98350 + 11.2490i) q^{43} +(-4.40807 - 0.777261i) q^{44} +(0.802883 - 2.53746i) q^{45} +(0.477099 - 0.275453i) q^{46} +(9.59960 + 1.69267i) q^{47} +(1.63985 + 0.557579i) q^{48} +(2.73255 - 4.73292i) q^{49} +4.21296 q^{50} +(-1.90445 + 5.60102i) q^{51} +(-4.77581 + 0.842104i) q^{52} +(4.72793 + 3.96720i) q^{53} +(-3.75896 + 3.58751i) q^{54} +(-3.73147 - 1.35815i) q^{55} +(0.619454 - 1.07293i) q^{56} +(7.41537 - 1.41853i) q^{57} +(0.542194 + 0.939108i) q^{58} +(-0.254116 - 1.44116i) q^{59} +(1.34680 + 0.739765i) q^{60} +(-4.88723 + 1.77880i) q^{61} +(-2.03927 - 2.43031i) q^{62} +(1.99382 + 3.13667i) q^{63} +(-0.500000 + 0.866025i) q^{64} -4.30223 q^{65} +(5.10881 + 5.83143i) q^{66} +(-8.44468 + 10.0640i) q^{67} +(-2.95797 - 1.70779i) q^{68} +(-0.943019 - 0.145633i) q^{69} +(0.706488 - 0.841959i) q^{70} +(0.567184 - 0.475924i) q^{71} +(-1.60934 - 2.53180i) q^{72} +(1.49888 + 8.50059i) q^{73} +(-0.135570 - 0.161566i) q^{74} +(-5.68856 - 4.57028i) q^{75} +(-0.0297759 + 4.35880i) q^{76} +(4.80249 - 2.77272i) q^{77} +(7.36207 + 4.04382i) q^{78} +(-2.86755 + 7.87854i) q^{79} +(-0.570250 + 0.679597i) q^{80} +(8.96732 - 0.766254i) q^{81} +(1.53084 - 8.68184i) q^{82} +(-6.65002 + 3.83939i) q^{83} +(-2.00034 + 0.776727i) q^{84} +(-2.32121 - 1.94773i) q^{85} +(8.75015 + 7.34225i) q^{86} +(0.286660 - 1.85621i) q^{87} +(-3.87639 + 2.23803i) q^{88} +(-1.80010 + 10.2088i) q^{89} +(-1.01601 - 2.45989i) q^{90} +(3.86191 - 4.60245i) q^{91} +(0.188421 - 0.517683i) q^{92} +(0.117093 + 5.49375i) q^{93} +(8.44175 - 4.87385i) q^{94} +(-0.697497 + 3.80358i) q^{95} +(1.61460 - 0.626944i) q^{96} +(-2.59091 - 3.08772i) q^{97} +(-0.949006 - 5.38208i) q^{98} +(-0.572154 - 13.4160i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9}+O(q^{10}) \) 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9	\( 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9} + 3 q^{13} + 3 q^{14} + 27 q^{15} - 27 q^{17} - 18 q^{18} + 3 q^{19} + 18 q^{23} + 3 q^{24} - 6 q^{27} + 3 q^{28} + 57 q^{33} + 27 q^{34} + 9 q^{38} - 30 q^{39} + 9 q^{41} - 3 q^{43} - 9 q^{44} + 27 q^{45} - 30 q^{49} - 132 q^{50} - 66 q^{51} + 6 q^{52} + 27 q^{54} + 102 q^{57} - 54 q^{59} + 6 q^{60} - 24 q^{61} - 3 q^{62} - 30 q^{64} + 36 q^{65} - 63 q^{66} + 51 q^{67} - 18 q^{68} + 3 q^{69} - 18 q^{71} - 3 q^{72} - 66 q^{73} - 6 q^{74} + 3 q^{78} - 51 q^{79} - 30 q^{81} - 36 q^{83} + 60 q^{84} - 3 q^{86} + 54 q^{87} - 27 q^{89} + 36 q^{90} - 69 q^{91} + 69 q^{93} + 18 q^{94} - 27 q^{95} + 81 q^{97} + 60 q^{98} + 51 q^{99}+O(q^{100}) \) 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9 + 3 * q^13 + 3 * q^14 + 27 * q^15 - 27 * q^17 - 18 * q^18 + 3 * q^19 + 18 * q^23 + 3 * q^24 - 6 * q^27 + 3 * q^28 + 57 * q^33 + 27 * q^34 + 9 * q^38 - 30 * q^39 + 9 * q^41 - 3 * q^43 - 9 * q^44 + 27 * q^45 - 30 * q^49 - 132 * q^50 - 66 * q^51 + 6 * q^52 + 27 * q^54 + 102 * q^57 - 54 * q^59 + 6 * q^60 - 24 * q^61 - 3 * q^62 - 30 * q^64 + 36 * q^65 - 63 * q^66 + 51 * q^67 - 18 * q^68 + 3 * q^69 - 18 * q^71 - 3 * q^72 - 66 * q^73 - 6 * q^74 + 3 * q^78 - 51 * q^79 - 30 * q^81 - 36 * q^83 + 60 * q^84 - 3 * q^86 + 54 * q^87 - 27 * q^89 + 36 * q^90 - 69 * q^91 + 69 * q^93 + 18 * q^94 - 27 * q^95 + 81 * q^97 + 60 * q^98 + 51 * q^99

Introduction

L-functions

Modular forms

Varieties

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