LMFDB - Embedded newform 945.2.bt.c.106.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(106,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 0, 0]))

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

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

chi := DirichletCharacter("945.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bt (of order $9$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			106.7
Character	$\chi$	$=$	945.106
Dual form			945.2.bt.c.526.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.215184 + 1.22037i) q^{2} +(1.68861 - 0.385473i) q^{3} +(0.436388 + 0.158832i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(0.107057 + 2.14368i) q^{6} +(-0.939693 + 0.342020i) q^{7} +(-1.52693 + 2.64473i) q^{8} +(2.70282 - 1.30183i) q^{9} +O(q^{10})$	\(q+(-0.215184 + 1.22037i) q^{2} +(1.68861 - 0.385473i) q^{3} +(0.436388 + 0.158832i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(0.107057 + 2.14368i) q^{6} +(-0.939693 + 0.342020i) q^{7} +(-1.52693 + 2.64473i) q^{8} +(2.70282 - 1.30183i) q^{9} +(-0.619598 - 1.07317i) q^{10} +(-0.799964 - 0.671250i) q^{11} +(0.798116 + 0.0999905i) q^{12} +(-0.162560 - 0.921924i) q^{13} +(-0.215184 - 1.22037i) q^{14} +(-1.04577 + 1.38071i) q^{15} +(-2.18748 - 1.83551i) q^{16} +(3.11722 + 5.39919i) q^{17} +(1.00711 + 3.57857i) q^{18} +(-3.45116 + 5.97759i) q^{19} +(-0.436388 + 0.158832i) q^{20} +(-1.45494 + 0.939765i) q^{21} +(0.991312 - 0.831810i) q^{22} +(7.51771 + 2.73622i) q^{23} +(-1.55893 + 5.05451i) q^{24} +(0.173648 - 0.984808i) q^{25} +1.16007 q^{26} +(4.06220 - 3.24015i) q^{27} -0.464394 q^{28} +(-1.19571 + 6.78120i) q^{29} +(-1.45994 - 1.57334i) q^{30} +(1.10234 + 0.401218i) q^{31} +(-1.96808 + 1.65142i) q^{32} +(-1.60958 - 0.825116i) q^{33} +(-7.25978 + 2.64235i) q^{34} +(0.500000 - 0.866025i) q^{35} +(1.38625 - 0.138807i) q^{36} +(-3.72444 - 6.45092i) q^{37} +(-6.55223 - 5.49797i) q^{38} +(-0.629877 - 1.49411i) q^{39} +(-0.530298 - 3.00747i) q^{40} +(0.0169991 + 0.0964067i) q^{41} +(-0.833781 - 1.97778i) q^{42} +(-3.46837 - 2.91031i) q^{43} +(-0.242479 - 0.419986i) q^{44} +(-1.23368 + 2.73460i) q^{45} +(-4.95689 + 8.58559i) q^{46} +(8.05063 - 2.93019i) q^{47} +(-4.40134 - 2.25625i) q^{48} +(0.766044 - 0.642788i) q^{49} +(1.16446 + 0.423830i) q^{50} +(7.34502 + 7.91553i) q^{51} +(0.0754920 - 0.428136i) q^{52} +1.15741 q^{53} +(3.08005 + 5.65461i) q^{54} +1.04428 q^{55} +(0.530298 - 3.00747i) q^{56} +(-3.52348 + 11.4242i) q^{57} +(-8.01827 - 2.91841i) q^{58} +(-9.99619 + 8.38780i) q^{59} +(-0.675665 + 0.436422i) q^{60} +(14.0056 - 5.09764i) q^{61} +(-0.726839 + 1.25892i) q^{62} +(-2.09457 + 2.14774i) q^{63} +(-4.44739 - 7.70310i) q^{64} +(0.717130 + 0.601743i) q^{65} +(1.35330 - 1.78673i) q^{66} +(-0.973855 - 5.52301i) q^{67} +(0.502754 + 2.85126i) q^{68} +(13.7492 + 1.72255i) q^{69} +(0.949279 + 0.796540i) q^{70} +(-2.90362 - 5.02922i) q^{71} +(-0.684052 + 9.13603i) q^{72} +(4.98848 - 8.64030i) q^{73} +(8.67395 - 3.15706i) q^{74} +(-0.0863920 - 1.72989i) q^{75} +(-2.45548 + 2.06039i) q^{76} +(0.981302 + 0.357165i) q^{77} +(1.95891 - 0.447175i) q^{78} +(-0.543518 + 3.08244i) q^{79} +2.85555 q^{80} +(5.61049 - 7.03721i) q^{81} -0.121310 q^{82} +(1.61898 - 9.18170i) q^{83} +(-0.784182 + 0.179011i) q^{84} +(-5.85847 - 2.13231i) q^{85} +(4.29798 - 3.60644i) q^{86} +(0.594879 + 11.9117i) q^{87} +(2.99676 - 1.09073i) q^{88} +(3.68857 - 6.38879i) q^{89} +(-3.07175 - 2.09399i) q^{90} +(0.468073 + 0.810726i) q^{91} +(2.84604 + 2.38811i) q^{92} +(2.01608 + 0.252580i) q^{93} +(1.84355 + 10.4553i) q^{94} +(-1.19858 - 6.79746i) q^{95} +(-2.68675 + 3.54725i) q^{96} +(4.32253 + 3.62703i) q^{97} +(0.619598 + 1.07317i) q^{98} +(-3.03601 - 0.772853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 9 q^{8}+O(q^{10}) $ 120 * q + 9 * q^8	$ 120 q + 9 q^{8} - 3 q^{10} - 24 q^{12} + 3 q^{13} + 6 q^{15} - 12 q^{16} + 60 q^{18} - 42 q^{19} + 9 q^{22} + 6 q^{23} - 60 q^{24} - 18 q^{26} - 42 q^{27} + 138 q^{28} - 18 q^{29} + 3 q^{30} - 21 q^{32} + 12 q^{33} + 39 q^{34} + 60 q^{35} + 6 q^{36} - 54 q^{37} - 117 q^{38} - 33 q^{39} - 9 q^{40} + 9 q^{41} + 3 q^{42} + 9 q^{43} + 24 q^{44} + 12 q^{45} - 24 q^{46} - 3 q^{47} + 180 q^{48} + 6 q^{51} + 39 q^{52} - 36 q^{53} - 48 q^{54} + 24 q^{55} + 9 q^{56} - 42 q^{57} - 27 q^{58} + 12 q^{59} + 15 q^{60} + 24 q^{61} - 27 q^{62} + 3 q^{63} - 123 q^{64} + 6 q^{65} - 75 q^{66} - 42 q^{67} - 111 q^{68} + 6 q^{69} + 30 q^{71} + 147 q^{72} - 66 q^{73} - 27 q^{74} - 24 q^{76} - 9 q^{77} - 15 q^{78} - 42 q^{79} - 174 q^{80} - 48 q^{81} + 132 q^{82} + 12 q^{83} - 15 q^{85} + 33 q^{86} + 42 q^{87} + 33 q^{88} + 57 q^{89} - 39 q^{90} - 42 q^{91} - 123 q^{92} - 72 q^{93} + 57 q^{94} - 21 q^{95} - 168 q^{96} + 93 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) $ 120 * q + 9 * q^8 - 3 * q^10 - 24 * q^12 + 3 * q^13 + 6 * q^15 - 12 * q^16 + 60 * q^18 - 42 * q^19 + 9 * q^22 + 6 * q^23 - 60 * q^24 - 18 * q^26 - 42 * q^27 + 138 * q^28 - 18 * q^29 + 3 * q^30 - 21 * q^32 + 12 * q^33 + 39 * q^34 + 60 * q^35 + 6 * q^36 - 54 * q^37 - 117 * q^38 - 33 * q^39 - 9 * q^40 + 9 * q^41 + 3 * q^42 + 9 * q^43 + 24 * q^44 + 12 * q^45 - 24 * q^46 - 3 * q^47 + 180 * q^48 + 6 * q^51 + 39 * q^52 - 36 * q^53 - 48 * q^54 + 24 * q^55 + 9 * q^56 - 42 * q^57 - 27 * q^58 + 12 * q^59 + 15 * q^60 + 24 * q^61 - 27 * q^62 + 3 * q^63 - 123 * q^64 + 6 * q^65 - 75 * q^66 - 42 * q^67 - 111 * q^68 + 6 * q^69 + 30 * q^71 + 147 * q^72 - 66 * q^73 - 27 * q^74 - 24 * q^76 - 9 * q^77 - 15 * q^78 - 42 * q^79 - 174 * q^80 - 48 * q^81 + 132 * q^82 + 12 * q^83 - 15 * q^85 + 33 * q^86 + 42 * q^87 + 33 * q^88 + 57 * q^89 - 39 * q^90 - 42 * q^91 - 123 * q^92 - 72 * q^93 + 57 * q^94 - 21 * q^95 - 168 * q^96 + 93 * q^97 + 3 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$1$

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 $

$2$	−0.215184	+	1.22037i	−0.152158	+	0.862931i	0.809180	+	0.587561i	$0.199912\pi$
$2$	−0.215184	+	1.22037i	−0.152158	+	0.862931i	−0.961338	+	0.275371i	$0.911199\pi$
$3$	1.68861	−	0.385473i	0.974921	−	0.222553i
$3$	1.68861	−	0.385473i	0.974921	−	0.222553i
$4$	0.436388	+	0.158832i	0.218194	+	0.0794161i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$	0.107057	+	2.14368i	0.0437057	+	0.875153i
$7$	−0.939693	+	0.342020i	−0.355170	+	0.129271i
$7$	−0.939693	+	0.342020i	−0.355170	+	0.129271i
$8$	−1.52693	+	2.64473i	−0.539852	+	0.935052i
$9$	2.70282	−	1.30183i	0.900941	−	0.433942i
$10$	−0.619598	−	1.07317i	−0.195934	−	0.339368i
$11$	−0.799964	−	0.671250i	−0.241198	−	0.202389i	0.514173	−	0.857687i	$-0.328099\pi$
$11$	−0.799964	−	0.671250i	−0.241198	−	0.202389i	−0.755371	+	0.655297i	$0.772543\pi$
$12$	0.798116	+	0.0999905i	0.230396	+	0.0288648i
$13$	−0.162560	−	0.921924i	−0.0450861	−	0.255696i	0.953931	−	0.300027i	$-0.0969955\pi$
$13$	−0.162560	−	0.921924i	−0.0450861	−	0.255696i	−0.999017	+	0.0443308i	$0.985884\pi$
$14$	−0.215184	−	1.22037i	−0.0575104	−	0.326157i
$15$	−1.04577	+	1.38071i	−0.270018	+	0.356497i
$16$	−2.18748	−	1.83551i	−0.546869	−	0.458878i
$17$	3.11722	+	5.39919i	0.756038	+	1.30950i	0.944857	+	0.327484i	$0.106201\pi$
$17$	3.11722	+	5.39919i	0.756038	+	1.30950i	−0.188819	+	0.982012i	$0.560466\pi$
$18$	1.00711	+	3.57857i	0.237377	+	0.843478i
$19$	−3.45116	+	5.97759i	−0.791751	+	1.37135i	0.133131	+	0.991098i	$0.457497\pi$
$19$	−3.45116	+	5.97759i	−0.791751	+	1.37135i	−0.924882	+	0.380254i	$0.875837\pi$
$20$	−0.436388	+	0.158832i	−0.0975793	+	0.0355160i
$21$	−1.45494	+	0.939765i	−0.317493	+	0.205074i
$22$	0.991312	−	0.831810i	0.211348	−	0.177342i
$23$	7.51771	+	2.73622i	1.56755	+	0.570542i	0.972450	−	0.233109i	$-0.0748900\pi$
$23$	7.51771	+	2.73622i	1.56755	+	0.570542i	0.595100	+	0.803651i	$0.297112\pi$
$24$	−1.55893	+	5.05451i	−0.318215	+	1.03175i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	1.16007			0.227508
$27$	4.06220	−	3.24015i	0.781771	−	0.623566i
$28$	−0.464394			−0.0877623
$29$	−1.19571	+	6.78120i	−0.222037	+	1.25924i	0.646231	+	0.763142i	$0.276344\pi$
$29$	−1.19571	+	6.78120i	−0.222037	+	1.25924i	−0.868268	+	0.496095i	$0.834767\pi$
$30$	−1.45994	−	1.57334i	−0.266547	−	0.287251i
$31$	1.10234	+	0.401218i	0.197985	+	0.0720608i	0.439110	−	0.898433i	$-0.355294\pi$
$31$	1.10234	+	0.401218i	0.197985	+	0.0720608i	−0.241124	+	0.970494i	$0.577516\pi$
$32$	−1.96808	+	1.65142i	−0.347911	+	0.291932i
$33$	−1.60958	−	0.825116i	−0.280192	−	0.143634i
$34$	−7.25978	+	2.64235i	−1.24504	+	0.453158i
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$	1.38625	−	0.138807i	0.231042	−	0.0231344i
$37$	−3.72444	−	6.45092i	−0.612295	−	1.06053i	−0.990853	−	0.134948i	$-0.956913\pi$
$37$	−3.72444	−	6.45092i	−0.612295	−	1.06053i	0.378558	−	0.925578i	$-0.376420\pi$
$38$	−6.55223	−	5.49797i	−1.06291	−	0.891889i
$39$	−0.629877	−	1.49411i	−0.100861	−	0.239249i
$40$	−0.530298	−	3.00747i	−0.0838475	−	0.475523i
$41$	0.0169991	+	0.0964067i	0.00265481	+	0.0150562i	0.986106	−	0.166115i	$-0.0531223\pi$
$41$	0.0169991	+	0.0964067i	0.00265481	+	0.0150562i	−0.983452	+	0.181171i	$0.942011\pi$
$42$	−0.833781	−	1.97778i	−0.128655	−	0.305179i
$43$	−3.46837	−	2.91031i	−0.528921	−	0.443817i	0.338808	−	0.940856i	$-0.389976\pi$
$43$	−3.46837	−	2.91031i	−0.528921	−	0.443817i	−0.867729	+	0.497038i	$0.834421\pi$
$44$	−0.242479	−	0.419986i	−0.0365551	−	0.0633152i
$45$	−1.23368	+	2.73460i	−0.183907	+	0.407650i
$46$	−4.95689	+	8.58559i	−0.730854	+	1.26588i
$47$	8.05063	−	2.93019i	1.17430	−	0.427412i	0.320118	−	0.947378i	$-0.396278\pi$
$47$	8.05063	−	2.93019i	1.17430	−	0.427412i	0.854187	+	0.519966i	$0.174055\pi$
$48$	−4.40134	−	2.25625i	−0.635279	−	0.325662i
$49$	0.766044	−	0.642788i	0.109435	−	0.0918268i
$50$	1.16446	+	0.423830i	0.164680	+	0.0599386i
$51$	7.34502	+	7.91553i	1.02851	+	1.10840i
$52$	0.0754920	−	0.428136i	0.0104689	−	0.0593718i
$53$	1.15741			0.158982			0.0794912	−	0.996836i	$-0.474670\pi$
$53$	1.15741			0.158982			0.0794912	+	0.996836i	$0.474670\pi$
$54$	3.08005	+	5.65461i	0.419142	+	0.769495i
$55$	1.04428			0.140811
$56$	0.530298	−	3.00747i	0.0708641	−	0.401890i
$57$	−3.52348	+	11.4242i	−0.466696	+	1.51317i
$58$	−8.01827	−	2.91841i	−1.05285	−	0.383206i
$59$	−9.99619	+	8.38780i	−1.30139	+	1.09200i	−0.311490	+	0.950249i	$0.600828\pi$
$59$	−9.99619	+	8.38780i	−1.30139	+	1.09200i	−0.989903	+	0.141749i	$0.954727\pi$
$60$	−0.675665	+	0.436422i	−0.0872279	+	0.0563418i
$61$	14.0056	−	5.09764i	1.79324	−	0.652685i	0.794256	−	0.607584i	$-0.207861\pi$
$61$	14.0056	−	5.09764i	1.79324	−	0.652685i	0.998982	−	0.0451017i	$-0.0143612\pi$
$62$	−0.726839	+	1.25892i	−0.0923086	+	0.159883i
$63$	−2.09457	+	2.14774i	−0.263891	+	0.270589i
$64$	−4.44739	−	7.70310i	−0.555924	−	0.962888i
$65$	0.717130	+	0.601743i	0.0889490	+	0.0746371i
$66$	1.35330	−	1.78673i	0.166580	−	0.219931i
$67$	−0.973855	−	5.52301i	−0.118975	−	0.674743i	−0.984705	−	0.174231i	$-0.944256\pi$
$67$	−0.973855	−	5.52301i	−0.118975	−	0.674743i	0.865730	−	0.500512i	$-0.166855\pi$
$68$	0.502754	+	2.85126i	0.0609679	+	0.345766i
$69$	13.7492	+	1.72255i	1.65521	+	0.207370i
$70$	0.949279	+	0.796540i	0.113461	+	0.0952047i
$71$	−2.90362	−	5.02922i	−0.344597	−	0.596859i	0.640684	−	0.767805i	$-0.278651\pi$
$71$	−2.90362	−	5.02922i	−0.344597	−	0.596859i	−0.985280	+	0.170946i	$0.945318\pi$
$72$	−0.684052	+	9.13603i	−0.0806163	+	1.07669i
$73$	4.98848	−	8.64030i	0.583858	−	1.01127i	−0.411159	−	0.911564i	$-0.634876\pi$
$73$	4.98848	−	8.64030i	0.583858	−	1.01127i	0.995017	−	0.0997074i	$-0.0317907\pi$
$74$	8.67395	−	3.15706i	1.00833	−	0.367001i
$75$	−0.0863920	−	1.72989i	−0.00997569	−	0.199751i
$76$	−2.45548	+	2.06039i	−0.281663	+	0.236343i
$77$	0.981302	+	0.357165i	0.111830	+	0.0407027i
$78$	1.95891	−	0.447175i	0.221802	−	0.0506325i
$79$	−0.543518	+	3.08244i	−0.0611505	+	0.346802i	0.938846	+	0.344336i	$0.111896\pi$
$79$	−0.543518	+	3.08244i	−0.0611505	+	0.346802i	−0.999997	+	0.00246565i	$0.999215\pi$
$80$	2.85555			0.319260
$81$	5.61049	−	7.03721i	0.623388	−	0.781913i
$82$	−0.121310			−0.0133964
$83$	1.61898	−	9.18170i	0.177706	−	1.00782i	−0.757267	−	0.653105i	$-0.773466\pi$
$83$	1.61898	−	9.18170i	0.177706	−	1.00782i	0.934974	−	0.354717i	$-0.115423\pi$
$84$	−0.784182	+	0.179011i	−0.0855613	+	0.0195317i
$85$	−5.85847	−	2.13231i	−0.635440	−	0.231281i
$86$	4.29798	−	3.60644i	0.463464	−	0.388892i
$87$	0.594879	+	11.9117i	0.0637777	+	1.27707i
$88$	2.99676	−	1.09073i	0.319456	−	0.116273i
$89$	3.68857	−	6.38879i	0.390988	−	0.677211i	−0.601592	−	0.798803i	$-0.705467\pi$
$89$	3.68857	−	6.38879i	0.390988	−	0.677211i	0.992580	+	0.121593i	$0.0388001\pi$
$90$	−3.07175	−	2.09399i	−0.323791	−	0.220726i
$91$	0.468073	+	0.810726i	0.0490674	+	0.0849872i
$92$	2.84604	+	2.38811i	0.296720	+	0.248978i
$93$	2.01608	+	0.252580i	0.209057	+	0.0261914i
$94$	1.84355	+	10.4553i	0.190147	+	1.07838i
$95$	−1.19858	−	6.79746i	−0.122971	−	0.697405i
$96$	−2.68675	+	3.54725i	−0.274216	+	0.362039i
$97$	4.32253	+	3.62703i	0.438886	+	0.368269i	0.835292	−	0.549806i	$-0.185298\pi$
$97$	4.32253	+	3.62703i	0.438886	+	0.368269i	−0.396406	+	0.918075i	$0.629743\pi$
$98$	0.619598	+	1.07317i	0.0625888	+	0.108407i
$99$	−3.03601	−	0.772853i	−0.305131	−	0.0776747i
$100$	0.232197	−	0.402177i	0.0232197	−	0.0402177i
$101$	−11.9382	+	4.34514i	−1.18789	+	0.432357i	−0.858983	−	0.512004i	$-0.828903\pi$
$101$	−11.9382	+	4.34514i	−1.18789	+	0.432357i	−0.328909	+	0.944362i	$0.606681\pi$
$102$	−11.2404	+	7.26034i	−1.11297	+	0.718881i
$103$	6.21150	−	5.21207i	0.612037	−	0.513560i	−0.283252	−	0.959046i	$-0.591413\pi$
$103$	6.21150	−	5.21207i	0.612037	−	0.513560i	0.895289	+	0.445485i	$0.146969\pi$
$104$	2.68646	+	0.977790i	0.263429	+	0.0958802i
$105$	0.510477	−	1.65512i	0.0498175	−	0.161523i
$106$	−0.249056	+	1.41247i	−0.0241905	+	0.137191i
$107$	−13.4677			−1.30197			−0.650987	−	0.759089i	$-0.725645\pi$
$107$	−13.4677			−1.30197			−0.650987	+	0.759089i	$0.725645\pi$
$108$	2.28733	−	0.768752i	0.220099	−	0.0739732i
$109$	−9.04286			−0.866149			−0.433074	−	0.901358i	$-0.642571\pi$
$109$	−9.04286			−0.866149			−0.433074	+	0.901358i	$0.642571\pi$
$110$	−0.224712	+	1.27441i	−0.0214255	+	0.121510i
$111$	−8.77579	−	9.45744i	−0.832961	−	0.897660i
$112$	2.68334	+	0.976655i	0.253552	+	0.0922852i
$113$	8.04952	−	6.75435i	0.757235	−	0.635396i	−0.180170	−	0.983635i	$-0.557665\pi$
$113$	8.04952	−	6.75435i	0.757235	−	0.635396i	0.937405	+	0.348240i	$0.113221\pi$
$114$	−13.1835	−	6.75824i	−1.23475	−	0.632967i
$115$	−7.51771	+	2.73622i	−0.701030	+	0.255154i
$116$	−1.59887	+	2.76932i	−0.148451	+	0.257125i
$117$	−1.63956	−	2.28017i	−0.151577	−	0.210802i
$118$	−8.08519	−	14.0040i	−0.744302	−	1.28917i
$119$	−4.77586	−	4.00743i	−0.437803	−	0.367360i
$120$	−2.05477	−	4.87404i	−0.187574	−	0.444937i
$121$	−1.72076	−	9.75893i	−0.156433	−	0.887176i
$122$	3.20721	+	18.1890i	0.290367	+	1.64675i
$123$	0.0658671	+	0.156241i	0.00593903	+	0.0140878i
$124$	0.417320	+	0.350173i	0.0374765	+	0.0314465i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	−2.17031	−	3.01831i	−0.193347	−	0.268892i
$127$	−5.08517	+	8.80777i	−0.451236	+	0.781563i	−0.998463	−	0.0554206i	$-0.982350\pi$
$127$	−5.08517	+	8.80777i	−0.451236	+	0.781563i	0.547227	+	0.836984i	$0.315683\pi$
$128$	5.52921	−	2.01247i	0.488718	−	0.177879i
$129$	−6.97857	−	3.57742i	−0.614429	−	0.314974i
$130$	−0.888664	+	0.745677i	−0.0779410	+	0.0654002i
$131$	17.8255	+	6.48794i	1.55742	+	0.566854i	0.970143	−	0.242533i	$-0.0779782\pi$
$131$	17.8255	+	6.48794i	1.55742	+	0.566854i	0.587276	+	0.809387i	$0.300200\pi$
$132$	−0.571346	−	0.615724i	−0.0497292	−	0.0535919i
$133$	1.19858	−	6.79746i	0.103930	−	0.589415i
$134$	6.94967			0.600360
$135$	−1.02910	+	5.09323i	−0.0885708	+	0.438355i
$136$	−19.0392			−1.63260
$137$	−1.48244	+	8.40735i	−0.126654	+	0.718288i	0.853658	+	0.520833i	$0.174379\pi$
$137$	−1.48244	+	8.40735i	−0.126654	+	0.718288i	−0.980312	+	0.197455i	$0.936732\pi$
$138$	−5.06076	+	16.4085i	−0.430801	+	1.39678i
$139$	−6.77666	−	2.46650i	−0.574789	−	0.209206i	0.0382371	−	0.999269i	$-0.487826\pi$
$139$	−6.77666	−	2.46650i	−0.574789	−	0.209206i	−0.613026	+	0.790063i	$0.710048\pi$
$140$	0.355747	−	0.298507i	0.0300661	−	0.0252284i
$141$	12.4649	−	8.05125i	1.04973	−	0.678037i
$142$	6.76232	−	2.46128i	0.567481	−	0.206546i
$143$	−0.488799	+	0.846625i	−0.0408754	+	0.0707983i
$144$	−8.30188	−	2.11334i	−0.691823	−	0.176112i
$145$	−3.44291	−	5.96329i	−0.285918	−	0.495224i
$146$	9.47092	+	7.94704i	0.783819	+	0.657702i
$147$	1.04577	−	1.38071i	0.0862541	−	0.113879i
$148$	−0.600687	−	3.40667i	−0.0493762	−	0.280026i
$149$	1.04888	+	5.94850i	0.0859276	+	0.487320i	0.997153	+	0.0754107i	$0.0240268\pi$
$149$	1.04888	+	5.94850i	0.0859276	+	0.487320i	−0.911225	+	0.411909i	$0.864862\pi$
$150$	2.12970	+	0.266816i	0.173889	+	0.0217854i
$151$	0.683909	+	0.573868i	0.0556557	+	0.0467007i	0.670191	−	0.742188i	$-0.266212\pi$
$151$	0.683909	+	0.573868i	0.0556557	+	0.0467007i	−0.614535	+	0.788889i	$0.710657\pi$
$152$	−10.5394	−	18.2548i	−0.854857	−	1.48066i
$153$	15.4541	+	10.5350i	1.24939	+	0.851701i
$154$	−0.647033	+	1.12069i	−0.0521394	+	0.0903081i
$155$	−1.10234	+	0.401218i	−0.0885418	+	0.0322266i
$156$	−0.0375581	−	0.752057i	−0.00300706	−	0.0602127i
$157$	1.78638	−	1.49895i	0.142569	−	0.119629i	−0.568714	−	0.822535i	$-0.692559\pi$
$157$	1.78638	−	1.49895i	0.142569	−	0.119629i	0.711283	+	0.702906i	$0.248115\pi$
$158$	−3.64476	−	1.32658i	−0.289962	−	0.105537i
$159$	1.95442	−	0.446150i	0.154995	−	0.0353820i
$160$	0.446128	−	2.53012i	0.0352695	−	0.200023i
$161$	−8.00018			−0.630503
$162$	7.38071	+	8.36117i	0.579884	+	0.656915i
$163$	−6.19199			−0.484994			−0.242497	−	0.970152i	$-0.577966\pi$
$163$	−6.19199			−0.484994			−0.242497	+	0.970152i	$0.577966\pi$
$164$	−0.00789429	+	0.0447708i	−0.000616441	+	0.00349601i
$165$	1.76338	−	0.402541i	0.137279	−	0.0313378i
$166$	10.8567	+	3.95151i	0.842642	+	0.306697i
$167$	18.1687	−	15.2453i	1.40593	−	1.17972i	0.447540	−	0.894264i	$-0.352300\pi$
$167$	18.1687	−	15.2453i	1.40593	−	1.17972i	0.958393	−	0.285454i	$-0.0921442\pi$
$168$	−0.263830	−	5.28287i	−0.0203549	−	0.407582i
$169$	11.3925	−	4.14653i	0.876345	−	0.318964i
$170$	3.86285	−	6.69065i	0.296267	−	0.513150i
$171$	−1.54609	+	20.6492i	−0.118232	+	1.57908i
$172$	−1.05130	−	1.82091i	−0.0801611	−	0.138843i
$173$	−9.71786	−	8.15425i	−0.738835	−	0.619956i	0.193689	−	0.981063i	$-0.437955\pi$
$173$	−9.71786	−	8.15425i	−0.738835	−	0.619956i	−0.932525	+	0.361107i	$0.882399\pi$
$174$	−14.6647	−	1.83724i	−1.11173	−	0.139281i
$175$	0.173648	+	0.984808i	0.0131266	+	0.0744445i
$176$	0.517817	+	2.93669i	0.0390319	+	0.221361i
$177$	−13.6464	+	18.0170i	−1.02573	+	1.35424i
$178$	7.00297	+	5.87619i	0.524895	+	0.440439i
$179$	−7.78019	−	13.4757i	−0.581519	−	1.00722i	−0.995300	−	0.0968436i	$-0.969125\pi$
$179$	−7.78019	−	13.4757i	−0.581519	−	1.00722i	0.413781	−	0.910377i	$-0.364208\pi$
$180$	−0.972707	+	0.997397i	−0.0725013	+	0.0743416i
$181$	3.82261	−	6.62095i	0.284132	−	0.492131i	−0.688266	−	0.725458i	$-0.741628\pi$
$181$	3.82261	−	6.62095i	0.284132	−	0.492131i	0.972398	+	0.233327i	$0.0749613\pi$
$182$	−1.09011	+	0.396767i	−0.0808041	+	0.0294103i
$183$	21.6851	−	14.0067i	1.60301	−	1.03541i
$184$	−18.7156	+	15.7043i	−1.37973	+	1.15773i
$185$	6.99966	+	2.54767i	0.514625	+	0.187308i
$186$	−0.742069	+	2.40601i	−0.0544111	+	0.176417i
$187$	1.13054	−	6.41160i	0.0826731	−	0.468862i
$188$	3.97861			0.290170
$189$	−2.70902	+	4.43409i	−0.197052	+	0.322533i
$190$	8.55333			0.620524
$191$	−0.0899084	+	0.509896i	−0.00650554	+	0.0368948i	−0.987888	−	0.155170i	$-0.950407\pi$
$191$	−0.0899084	+	0.509896i	−0.00650554	+	0.0368948i	0.981382	+	0.192065i	$0.0615185\pi$
$192$	−10.4792	−	11.2932i	−0.756275	−	0.815017i
$193$	−9.96036	−	3.62527i	−0.716962	−	0.260953i	−0.0423267	−	0.999104i	$-0.513477\pi$
$193$	−9.96036	−	3.62527i	−0.716962	−	0.260953i	−0.674636	+	0.738151i	$0.735699\pi$
$194$	−5.35646	+	4.49460i	−0.384571	+	0.322694i
$195$	1.44291	+	0.739677i	0.103329	+	0.0529694i
$196$	0.436388	−	0.158832i	0.0311706	−	0.0113452i
$197$	−3.29463	+	5.70647i	−0.234733	+	0.406569i	−0.959195	−	0.282745i	$-0.908755\pi$
$197$	−3.29463	+	5.70647i	−0.234733	+	0.406569i	0.724462	+	0.689315i	$0.242088\pi$
$198$	1.59647	−	3.53875i	0.113456	−	0.251488i
$199$	6.12639	+	10.6112i	0.434288	+	0.752209i	0.997237	−	0.0742822i	$-0.0236666\pi$
$199$	6.12639	+	10.6112i	0.434288	+	0.752209i	−0.562949	+	0.826492i	$0.690333\pi$
$200$	2.33940	+	1.96299i	0.165420	+	0.138804i
$201$	−3.77343	−	8.95082i	−0.266157	−	0.631342i
$202$	−2.73377	−	15.5040i	−0.192347	−	1.09086i
$203$	−1.19571	−	6.78120i	−0.0839223	−	0.475947i
$204$	1.94804	+	4.62087i	0.136390	+	0.323526i
$205$	−0.0749911	−	0.0629250i	−0.00523761	−	0.00439487i
$206$	5.02403	+	8.70188i	0.350041	+	0.606289i
$207$	23.8811	−	2.39124i	1.65985	−	0.166203i
$208$	−1.33661	+	2.31507i	−0.0926769	+	0.160521i
$209$	6.77326	−	2.46527i	0.468516	−	0.170526i
$210$	1.91001	+	0.979125i	0.131803	+	0.0675661i
$211$	−0.304561	+	0.255557i	−0.0209669	+	0.0175933i	−0.653211	−	0.757176i	$-0.726578\pi$
$211$	−0.304561	+	0.255557i	−0.0209669	+	0.0175933i	0.632244	+	0.774769i	$0.282134\pi$
$212$	0.505080	+	0.183834i	0.0346890	+	0.0126258i
$213$	−6.84172	−	7.37314i	−0.468787	−	0.505199i
$214$	2.89804	−	16.4356i	0.198106	−	1.12351i
$215$	4.52763			0.308782
$216$	2.36659	+	15.6909i	0.161026	+	1.06763i
$217$	−1.17308			−0.0796340
$218$	1.94588	−	11.0356i	0.131792	−	0.747427i
$219$	5.09301	−	16.5130i	0.344154	−	1.11585i
$220$	0.455711	+	0.165865i	0.0307240	+	0.0111826i
$221$	4.47091	−	3.75154i	0.300746	−	0.252356i
$222$	13.4300	−	8.67462i	0.901361	−	0.582202i
$223$	24.3869	−	8.87609i	1.63307	−	0.594387i	0.647258	−	0.762271i	$-0.275915\pi$
$223$	24.3869	−	8.87609i	1.63307	−	0.594387i	0.985807	+	0.167884i	$0.0536933\pi$
$224$	1.28457	−	2.22495i	0.0858293	−	0.148661i
$225$	−0.812710	−	2.88782i	−0.0541806	−	0.192521i
$226$	6.51067	+	11.2768i	0.433083	+	0.750122i
$227$	9.63430	+	8.08414i	0.639451	+	0.536563i	0.903850	−	0.427850i	$-0.140729\pi$
$227$	9.63430	+	8.08414i	0.639451	+	0.536563i	−0.264399	+	0.964413i	$0.585173\pi$
$228$	−3.35213	+	4.42572i	−0.222000	+	0.293101i
$229$	3.01760	+	17.1137i	0.199409	+	1.13090i	0.905999	+	0.423281i	$0.139122\pi$
$229$	3.01760	+	17.1137i	0.199409	+	1.13090i	−0.706590	+	0.707623i	$0.749767\pi$
$230$	−1.72151	−	9.76317i	−0.113513	−	0.643765i
$231$	1.79471	+	0.224848i	0.118084	+	0.0147939i
$232$	−16.1086	−	13.5168i	−1.05758	−	0.887419i
$233$	−7.68424	−	13.3095i	−0.503412	−	0.871935i	−0.999992	−	0.00394390i	$-0.998745\pi$
$233$	−7.68424	−	13.3095i	−0.503412	−	0.871935i	0.496581	−	0.867991i	$-0.334589\pi$
$234$	3.13546	−	1.51021i	0.204971	−	0.0987254i
$235$	−4.28365	+	7.41950i	−0.279434	+	0.483995i
$236$	−5.69447	+	2.07262i	−0.370678	+	0.134916i
$237$	0.270406	+	5.41456i	0.0175648	+	0.351713i
$238$	5.91823	−	4.96598i	0.383622	−	0.321897i
$239$	28.3123	+	10.3048i	1.83137	+	0.666564i	0.992502	+	0.122226i	$0.0390033\pi$
$239$	28.3123	+	10.3048i	1.83137	+	0.666564i	0.838866	+	0.544337i	$0.183219\pi$
$240$	4.82191	−	1.10074i	0.311253	−	0.0710522i
$241$	−0.703354	+	3.98892i	−0.0453070	+	0.256949i	−0.999045	−	0.0436898i	$-0.986089\pi$
$241$	−0.703354	+	3.98892i	−0.0453070	+	0.256949i	0.953738	+	0.300639i	$0.0971998\pi$
$242$	12.2798			0.789374
$243$	6.76129	−	14.0458i	0.433737	−	0.901040i
$244$	6.92156			0.443108
$245$	−0.173648	+	0.984808i	−0.0110940	+	0.0629171i
$246$	−0.204845	+	0.0467616i	−0.0130604	+	0.00298141i
$247$	6.07190	+	2.20999i	0.386346	+	0.140618i
$248$	−2.74430	+	2.30274i	−0.174264	+	0.146224i
$249$	−0.805462	−	16.1284i	−0.0510441	−	1.02210i
$250$	−1.16446	+	0.423830i	−0.0736471	+	0.0268054i
$251$	−10.4034	+	18.0192i	−0.656658	+	1.13736i	0.324818	+	0.945777i	$0.394697\pi$
$251$	−10.4034	+	18.0192i	−0.656658	+	1.13736i	−0.981475	+	0.191588i	$0.938636\pi$
$252$	−1.25518	+	0.604561i	−0.0790686	+	0.0380838i
$253$	−4.17721	−	7.23514i	−0.262619	−	0.454869i
$254$	−9.65449	−	8.10108i	−0.605776	−	0.508307i
$255$	−10.7146	−	1.34236i	−0.670976	−	0.0840619i
$256$	−1.82297	−	10.3386i	−0.113935	−	0.646160i
$257$	−2.08380	−	11.8178i	−0.129984	−	0.737176i	−0.978222	−	0.207561i	$-0.933448\pi$
$257$	−2.08380	−	11.8178i	−0.129984	−	0.737176i	0.848238	−	0.529615i	$-0.177664\pi$
$258$	5.86745	−	7.74663i	0.365291	−	0.482284i
$259$	5.70618	+	4.78805i	0.354565	+	0.297515i
$260$	0.217371	+	0.376497i	0.0134808	+	0.0233493i
$261$	5.59616	+	19.8850i	0.346394	+	1.23085i
$262$	−11.7534	+	20.3576i	−0.726130	+	1.25769i
$263$	−13.5400	+	4.92816i	−0.834913	+	0.303884i	−0.723874	−	0.689932i	$-0.757640\pi$
$263$	−13.5400	+	4.92816i	−0.834913	+	0.303884i	−0.111039	+	0.993816i	$0.535418\pi$
$264$	4.63992	−	2.99700i	0.285568	−	0.184452i
$265$	−0.886628	+	0.743969i	−0.0544651	+	0.0457016i
$266$	8.03750	+	2.92541i	0.492811	+	0.179368i
$267$	3.76586	−	12.2100i	0.230467	−	0.747242i
$268$	0.452253	−	2.56485i	0.0276258	−	0.156673i
$269$	10.9072			0.665022			0.332511	−	0.943099i	$-0.392104\pi$
$269$	10.9072			0.665022			0.332511	+	0.943099i	$0.392104\pi$
$270$	−5.99417	−	2.35186i	−0.364794	−	0.143130i
$271$	14.2063			0.862972			0.431486	−	0.902120i	$-0.357989\pi$
$271$	14.2063			0.862972			0.431486	+	0.902120i	$0.357989\pi$
$272$	3.09142	−	17.5323i	0.187445	−	1.06305i
$273$	1.10291	+	1.18857i	0.0667510	+	0.0719357i
$274$	−9.94107	−	3.61825i	−0.600562	−	0.218587i
$275$	−0.799964	+	0.671250i	−0.0482397	+	0.0404779i
$276$	5.72641	+	2.93552i	0.344689	+	0.176698i
$277$	14.3896	−	5.23738i	0.864586	−	0.314683i	0.128613	−	0.991695i	$-0.458947\pi$
$277$	14.3896	−	5.23738i	0.864586	−	0.314683i	0.735973	+	0.677011i	$0.236725\pi$
$278$	4.46828	−	7.73928i	0.267989	−	0.464171i
$279$	3.50173	−	0.350632i	0.209643	−	0.0209918i
$280$	1.52693	+	2.64473i	0.0912517	+	0.158053i
$281$	−11.6231	−	9.75291i	−0.693374	−	0.581810i	0.226506	−	0.974010i	$-0.427270\pi$
$281$	−11.6231	−	9.75291i	−0.693374	−	0.581810i	−0.919880	+	0.392200i	$0.871714\pi$
$282$	7.14325	+	16.9443i	0.425375	+	1.00902i
$283$	1.87973	+	10.6605i	0.111738	+	0.633699i	0.988314	+	0.152434i	$0.0487113\pi$
$283$	1.87973	+	10.6605i	0.111738	+	0.633699i	−0.876575	+	0.481265i	$0.840178\pi$
$284$	−0.468304	−	2.65588i	−0.0277887	−	0.157598i
$285$	−4.64416	−	11.0163i	−0.275097	−	0.652547i
$286$	−0.928013	−	0.778696i	−0.0548746	−	0.0460452i
$287$	−0.0489470	−	0.0847787i	−0.00288925	−	0.00500433i
$288$	−3.16952	+	7.02559i	−0.186766	+	0.413987i
$289$	−10.9342	+	18.9385i	−0.643187	+	1.11403i
$290$	8.01827	−	2.91841i	0.470849	−	0.171375i
$291$	8.69719	+	4.45843i	0.509839	+	0.261358i
$292$	3.54927	−	2.97819i	0.207705	−	0.174286i
$293$	0.245588	+	0.0893867i	0.0143474	+	0.00522203i	0.349184	−	0.937054i	$-0.386459\pi$
$293$	0.245588	+	0.0893867i	0.0143474	+	0.00522203i	−0.334836	+	0.942276i	$0.608681\pi$
$294$	1.45994	+	1.57334i	0.0851454	+	0.0917589i
$295$	2.26595	−	12.8509i	0.131929	−	0.748206i
$296$	22.7479			1.32219
$297$	−5.42456	−	0.134749i	−0.314765	−	0.00781896i
$298$	−7.48506			−0.433598
$299$	1.30051	−	7.37556i	0.0752104	−	0.426540i
$300$	0.237063	−	0.768627i	0.0136868	−	0.0443767i
$301$	4.25458	+	1.54854i	0.245230	+	0.0892564i
$302$	−0.847497	+	0.711135i	−0.0487680	+	0.0409212i
$303$	−18.4840	+	11.9391i	−1.06188	+	0.685883i
$304$	18.5213	−	6.74119i	1.06227	−	0.386634i
$305$	−7.45224	+	12.9077i	−0.426714	+	0.739091i
$306$	−16.1820	+	16.5928i	−0.925065	+	0.948546i
$307$	−10.9580	−	18.9798i	−0.625405	−	1.08323i	−0.988462	−	0.151467i	$-0.951600\pi$
$307$	−10.9580	−	18.9798i	−0.625405	−	1.08323i	0.363057	−	0.931767i	$-0.381733\pi$
$308$	0.371499	+	0.311725i	0.0211681	+	0.0177622i
$309$	8.47970	−	11.1955i	0.482394	−	0.636891i
$310$	−0.252428	−	1.43159i	−0.0143370	−	0.0813090i
$311$	−2.82706	−	16.0330i	−0.160308	−	0.909150i	−0.953771	−	0.300533i	$-0.902836\pi$
$311$	−2.82706	−	16.0330i	−0.160308	−	0.909150i	0.793464	−	0.608618i	$-0.208276\pi$
$312$	4.91329	+	0.615553i	0.278160	+	0.0348488i
$313$	11.6373	+	9.76483i	0.657777	+	0.551941i	0.909420	−	0.415880i	$-0.136526\pi$
$313$	11.6373	+	9.76483i	0.657777	+	0.551941i	−0.251642	+	0.967820i	$0.580971\pi$
$314$	1.44487	+	2.50259i	0.0815389	+	0.141229i
$315$	0.223995	−	2.99163i	0.0126207	−	0.168559i
$316$	−0.726776	+	1.25881i	−0.0408843	+	0.0708137i
$317$	26.8894	−	9.78695i	1.51026	−	0.549690i	0.551567	−	0.834131i	$-0.314030\pi$
$317$	26.8894	−	9.78695i	1.51026	−	0.549690i	0.958694	+	0.284441i	$0.0918080\pi$
$318$	0.123908	+	2.48111i	0.00694843	+	0.139134i
$319$	5.50840	−	4.62210i	0.308411	−	0.258788i
$320$	8.35836	+	3.04219i	0.467246	+	0.170064i
$321$	−22.7418	+	5.19144i	−1.26932	+	0.289758i
$322$	1.72151	−	9.76317i	0.0959361	−	0.544080i
$323$	−43.0322			−2.39437
$324$	3.56609	−	2.17983i	0.198116	−	0.121102i
$325$	−0.936146			−0.0519281
$326$	1.33242	−	7.55652i	0.0737958	−	0.418517i
$327$	−15.2699	+	3.48577i	−0.844426	+	0.192764i
$328$	−0.280926	−	0.102249i	−0.0155115	−	0.00564574i
$329$	−6.56293	+	5.50695i	−0.361826	+	0.303608i
$330$	0.111797	+	2.23860i	0.00615422	+	0.123231i
$331$	−33.9857	+	12.3698i	−1.86802	+	0.679905i	−0.896462	+	0.443121i	$0.853871\pi$
$331$	−33.9857	+	12.3698i	−1.86802	+	0.679905i	−0.971562	+	0.236784i	$0.923907\pi$
$332$	2.16485	−	3.74964i	0.118812	−	0.205788i
$333$	−18.4645	−	12.5871i	−1.01185	−	0.689770i
$334$	14.6953	+	25.4530i	0.804091	+	1.39273i
$335$	4.29614	+	3.60489i	0.234723	+	0.196956i
$336$	4.90759	+	0.614839i	0.267731	+	0.0335422i
$337$	−1.95577	−	11.0917i	−0.106537	−	0.604204i	−0.990595	−	0.136826i	$-0.956310\pi$
$337$	−1.95577	−	11.0917i	−0.106537	−	0.604204i	0.884058	−	0.467378i	$-0.154801\pi$
$338$	2.60881	+	14.7953i	0.141901	+	0.804759i
$339$	10.9889	−	14.5083i	0.596835	−	0.787985i
$340$	−2.21789	−	1.86103i	−0.120282	−	0.100928i
$341$	−0.612513	−	1.06090i	−0.0331694	−	0.0574511i
$342$	−24.8669	−	6.33017i	−1.34465	−	0.342296i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	12.9929	−	4.72904i	0.700532	−	0.254973i
$345$	−11.6398	+	7.51829i	−0.626663	+	0.404771i
$346$	12.0423	−	10.1047i	0.647399	−	0.543233i
$347$	22.6488	+	8.24347i	1.21585	+	0.442533i	0.868729	−	0.495288i	$-0.164937\pi$
$347$	22.6488	+	8.24347i	1.21585	+	0.442533i	0.347120	+	0.937821i	$0.387160\pi$
$348$	−1.63237	+	5.29262i	−0.0875042	+	0.283714i
$349$	−4.14072	+	23.4832i	−0.221648	+	1.25703i	0.647343	+	0.762199i	$0.275880\pi$
$349$	−4.14072	+	23.4832i	−0.221648	+	1.25703i	−0.868991	+	0.494828i	$0.835231\pi$
$350$	−1.23920			−0.0662378
$351$	−3.64752	−	3.21832i	−0.194690	−	0.171781i
$352$	2.68291			0.143000
$353$	1.83075	−	10.3827i	0.0974409	−	0.552615i	−0.896531	−	0.442981i	$-0.853921\pi$
$353$	1.83075	−	10.3827i	0.0974409	−	0.552615i	0.993972	−	0.109634i	$-0.0349679\pi$
$354$	−19.0509	−	20.5306i	−1.01254	−	1.09119i
$355$	5.45703	+	1.98619i	0.289629	+	0.105416i
$356$	2.62440	−	2.20213i	0.139093	−	0.116713i
$357$	−9.60934	−	4.92602i	−0.508580	−	0.260713i
$358$	18.1195	−	6.59495i	0.957645	−	0.348554i
$359$	3.17826	−	5.50491i	0.167742	−	0.290538i	−0.769883	−	0.638184i	$-0.779686\pi$
$359$	3.17826	−	5.50491i	0.167742	−	0.290538i	0.937626	+	0.347646i	$0.113019\pi$
$360$	−5.34851	−	7.43830i	−0.281891	−	0.392033i
$361$	−14.3210	−	24.8047i	−0.753738	−	1.30551i
$362$	7.25744	+	6.08971i	0.381442	+	0.320068i
$363$	−6.66750	−	15.8157i	−0.349953	−	0.830111i
$364$	0.0754920	+	0.428136i	0.00395686	+	0.0224404i
$365$	1.73248	+	9.82539i	0.0906822	+	0.514284i
$366$	12.4271	+	29.4778i	0.649574	+	1.54083i
$367$	20.6183	+	17.3008i	1.07626	+	0.903093i	0.995605	−	0.0936482i	$-0.0298529\pi$
$367$	20.6183	+	17.3008i	1.07626	+	0.903093i	0.0806595	+	0.996742i	$0.474297\pi$
$368$	−11.4225	−	19.7843i	−0.595436	−	1.03133i
$369$	0.171450	+	0.238440i	0.00892536	+	0.0124127i
$370$	−4.61531	+	7.99396i	−0.239939	+	0.415586i
$371$	−1.08761	+	0.395858i	−0.0564659	+	0.0205519i
$372$	0.839674	+	0.430441i	0.0435351	+	0.0223173i
$373$	26.4615	−	22.2038i	1.37013	−	1.14967i	0.397418	−	0.917638i	$-0.369906\pi$
$373$	26.4615	−	22.2038i	1.37013	−	1.14967i	0.972708	−	0.232034i	$-0.0745380\pi$
$374$	7.58124	+	2.75935i	0.392017	+	0.142682i
$375$	1.17814	+	1.26964i	0.0608386	+	0.0655642i
$376$	−4.54322	+	25.7659i	−0.234299	+	1.32878i
$377$	6.44613			0.331992
$378$	−4.82829	−	4.26016i	−0.248341	−	0.219119i
$379$	−26.4556			−1.35894			−0.679468	−	0.733706i	$-0.737789\pi$
$379$	−26.4556			−1.35894			−0.679468	+	0.733706i	$0.737789\pi$
$380$	0.556612	−	3.15670i	0.0285536	−	0.161935i
$381$	−5.19172	+	16.8331i	−0.265980	+	0.862386i
$382$	−0.602914	−	0.219443i	−0.0308478	−	0.0112277i
$383$	−17.3910	+	14.5928i	−0.888638	+	0.745656i	−0.967936	−	0.251195i	$-0.919176\pi$
$383$	−17.3910	+	14.5928i	−0.888638	+	0.745656i	0.0792988	+	0.996851i	$0.474732\pi$
$384$	8.56095	−	5.52964i	0.436874	−	0.282183i
$385$	−0.981302	+	0.357165i	−0.0500118	+	0.0182028i
$386$	6.56748	−	11.3752i	0.334276	−	0.578983i
$387$	−13.1631	−	3.35082i	−0.669118	−	0.170332i
$388$	1.31021	+	2.26935i	0.0665158	+	0.115209i
$389$	3.25733	+	2.73322i	0.165153	+	0.138580i	0.721619	−	0.692291i	$-0.243398\pi$
$389$	3.25733	+	2.73322i	0.165153	+	0.138580i	−0.556465	+	0.830871i	$0.687843\pi$
$390$	−1.21317	+	1.60172i	−0.0614313	+	0.0811060i
$391$	8.66100	+	49.1190i	0.438006	+	2.48405i
$392$	0.530298	+	3.00747i	0.0267841	+	0.151900i
$393$	32.6012	+	4.08439i	1.64451	+	0.206030i
$394$	−6.25505	−	5.24861i	−0.315125	−	0.264421i
$395$	−1.56500	−	2.71065i	−0.0787435	−	0.136388i
$396$	−1.20213	−	0.819481i	−0.0604091	−	0.0411805i
$397$	−7.16361	+	12.4077i	−0.359531	+	0.622727i	−0.987883	−	0.155203i	$-0.950397\pi$
$397$	−7.16361	+	12.4077i	−0.359531	+	0.622727i	0.628351	+	0.777930i	$0.283730\pi$
$398$	−14.2679	+	5.19309i	−0.715186	+	0.260306i
$399$	−0.596305	−	11.9403i	−0.0298526	−	0.597762i
$400$	−2.18748	+	1.83551i	−0.109374	+	0.0917756i
$401$	4.59277	+	1.67163i	0.229352	+	0.0834773i	0.454140	−	0.890930i	$-0.349947\pi$
$401$	4.59277	+	1.67163i	0.229352	+	0.0834773i	−0.224788	+	0.974408i	$0.572169\pi$
$402$	11.7353	−	2.67891i	0.585303	−	0.133612i
$403$	0.190696	−	1.08149i	0.00949926	−	0.0538730i
$404$	−5.89982			−0.293527
$405$	0.225549	+	8.99717i	0.0112076	+	0.447073i
$406$	8.53287			0.423479
$407$	−1.35076	+	7.66054i	−0.0669547	+	0.379719i
$408$	−32.1498	+	7.33908i	−1.59165	+	0.363339i
$409$	−15.1576	−	5.51693i	−0.749497	−	0.272795i	−0.0611029	−	0.998131i	$-0.519462\pi$
$409$	−15.1576	−	5.51693i	−0.749497	−	0.272795i	−0.688394	+	0.725337i	$0.741684\pi$
$410$	0.0929287	−	0.0779764i	0.00458942	−	0.00385098i
$411$	0.737532	+	14.7682i	0.0363798	+	0.728461i
$412$	3.53847	−	1.28790i	0.174328	−	0.0634501i
$413$	6.52455	−	11.3008i	0.321052	−	0.556078i
$414$	−2.22064	+	29.6583i	−0.109139	+	1.45763i
$415$	4.66167	+	8.07425i	0.228832	+	0.396349i
$416$	1.84241	+	1.54597i	0.0903318	+	0.0757973i
$417$	−12.3939	−	1.55275i	−0.606933	−	0.0760385i
$418$	1.55104	+	8.79636i	0.0758637	+	0.430244i
$419$	−2.58845	−	14.6798i	−0.126454	−	0.717156i	−0.980434	−	0.196850i	$-0.936929\pi$
$419$	−2.58845	−	14.6798i	−0.126454	−	0.717156i	0.853980	−	0.520306i	$-0.174182\pi$
$420$	0.485652	−	0.641193i	0.0236974	−	0.0312870i
$421$	5.36074	+	4.49819i	0.261266	+	0.219228i	0.764006	−	0.645210i	$-0.223230\pi$
$421$	5.36074	+	4.49819i	0.261266	+	0.219228i	−0.502739	+	0.864438i	$0.667674\pi$
$422$	−0.246338	−	0.426669i	−0.0119915	−	0.0207699i
$423$	17.9448	−	18.4003i	0.872507	−	0.894654i
$424$	−1.76729	+	3.06103i	−0.0858271	+	0.148657i
$425$	5.85847	−	2.13231i	0.284177	−	0.103432i
$426$	10.4702	−	6.76284i	0.507282	−	0.327661i
$427$	−11.4175	+	9.58042i	−0.552532	+	0.463629i
$428$	−5.87715	−	2.13911i	−0.284083	−	0.103398i
$429$	−0.499041	+	1.61804i	−0.0240939	+	0.0781197i
$430$	−0.974274	+	5.52538i	−0.0469837	+	0.266458i
$431$	−40.1826			−1.93553			−0.967763	−	0.251861i	$-0.918957\pi$
$431$	−40.1826			−1.93553			−0.967763	+	0.251861i	$0.918957\pi$
$432$	−14.8333	−	0.368468i	−0.713667	−	0.0177279i
$433$	−17.4421			−0.838215			−0.419107	−	0.907937i	$-0.637657\pi$
$433$	−17.4421			−0.838215			−0.419107	+	0.907937i	$0.637657\pi$
$434$	0.252428	−	1.43159i	0.0121170	−	0.0687187i
$435$	−8.11242	−	8.74253i	−0.388961	−	0.419172i
$436$	−3.94620	−	1.43630i	−0.188989	−	0.0687862i
$437$	−42.3008	+	35.4946i	−2.02352	+	1.69794i
$438$	19.0561	+	9.76870i	0.910535	+	0.466766i
$439$	6.87055	−	2.50068i	0.327914	−	0.119351i	−0.172817	−	0.984954i	$-0.555287\pi$
$439$	6.87055	−	2.50068i	0.327914	−	0.119351i	0.500731	+	0.865603i	$0.333065\pi$
$440$	−1.59454	+	2.76183i	−0.0760169	+	0.131665i
$441$	1.23368	−	2.73460i	0.0587468	−	0.130219i
$442$	3.61619	+	6.26343i	0.172005	+	0.297921i
$443$	−12.9778	−	10.8897i	−0.616596	−	0.517386i	0.280135	−	0.959961i	$-0.409621\pi$
$443$	−12.9778	−	10.8897i	−0.616596	−	0.517386i	−0.896732	+	0.442575i	$0.854065\pi$
$444$	−2.32751	−	5.52099i	−0.110459	−	0.262015i
$445$	1.28103	+	7.26507i	0.0607265	+	0.344397i
$446$	5.58445	+	31.6710i	0.264431	+	1.49966i
$447$	4.06413	+	9.64039i	0.192227	+	0.455975i
$448$	6.81379	+	5.71745i	0.321922	+	0.270124i
$449$	−8.17658	−	14.1623i	−0.385877	−	0.668358i	0.606014	−	0.795454i	$-0.292768\pi$
$449$	−8.17658	−	14.1623i	−0.385877	−	0.668358i	−0.991890	+	0.127096i	$0.959434\pi$
$450$	3.69909	−	0.370393i	0.174377	−	0.0174605i
$451$	0.0511143	−	0.0885326i	0.00240688	−	0.00416884i
$452$	4.58552	−	1.66899i	0.215685	−	0.0785029i
$453$	1.37607	+	0.705412i	0.0646533	+	0.0331432i
$454$	−11.9388	+	10.0178i	−0.560315	+	0.470160i
$455$	−0.879690	−	0.320181i	−0.0412405	−	0.0150103i
$456$	−24.8336	−	26.7626i	−1.16294	−	1.25327i
$457$	1.39324	−	7.90145i	0.0651730	−	0.369614i	−0.934726	−	0.355370i	$-0.884355\pi$
$457$	1.39324	−	7.90145i	0.0651730	−	0.369614i	0.999899	−	0.0142439i	$-0.00453413\pi$
$458$	−21.5344			−1.00623
$459$	30.1569	+	11.8323i	1.40761	+	0.552286i
$460$	−3.71524			−0.173224
$461$	3.76786	−	21.3686i	0.175487	−	0.995236i	−0.762093	−	0.647467i	$-0.775828\pi$
$461$	3.76786	−	21.3686i	0.175487	−	0.995236i	0.937580	−	0.347769i	$-0.113061\pi$
$462$	−0.660591	+	2.14183i	−0.0307335	+	0.0996470i
$463$	−14.8607	−	5.40886i	−0.690637	−	0.251371i	−0.0272290	−	0.999629i	$-0.508668\pi$
$463$	−14.8607	−	5.40886i	−0.690637	−	0.251371i	−0.663408	+	0.748258i	$0.730891\pi$
$464$	15.0626	−	12.6390i	0.699262	−	0.586750i
$465$	−1.70676	+	1.10242i	−0.0791491	+	0.0511236i
$466$	17.8960	−	6.51362i	0.829018	−	0.301738i
$467$	−9.38740	+	16.2595i	−0.434397	+	0.752398i	−0.997246	−	0.0741619i	$-0.976372\pi$
$467$	−9.38740	+	16.2595i	−0.434397	+	0.752398i	0.562849	+	0.826560i	$0.309705\pi$
$468$	−0.353318	−	1.25545i	−0.0163321	−	0.0580334i
$469$	2.80410	+	4.85685i	0.129482	+	0.224269i
$470$	−8.13276	−	6.82419i	−0.375136	−	0.314777i
$471$	2.43870	−	3.21974i	0.112369	−	0.148358i
$472$	−6.91992	−	39.2448i	−0.318515	−	1.80639i
$473$	0.821028	+	4.65628i	0.0377509	+	0.214096i
$474$	−6.66595	−	0.835131i	−0.306177	−	0.0383588i
$475$	5.28749	+	4.43673i	0.242606	+	0.203571i
$476$	−1.44762	−	2.50735i	−0.0663516	−	0.114924i
$477$	3.12827	−	1.50675i	0.143234	−	0.0689893i
$478$	−18.6680	+	32.3340i	−0.853856	+	1.47892i
$479$	−40.1166	+	14.6013i	−1.83298	+	0.667149i	−0.840950	+	0.541112i	$0.818003\pi$
$479$	−40.1166	+	14.6013i	−1.83298	+	0.667149i	−0.992026	+	0.126036i	$0.959774\pi$
$480$	−0.221954	−	4.44436i	−0.0101308	−	0.202856i
$481$	−5.34182	+	4.48232i	−0.243566	+	0.204376i
$482$	−4.71660	−	1.71670i	−0.214835	−	0.0781937i
$483$	−13.5092	+	3.08385i	−0.614690	+	0.140320i
$484$	0.799113	−	4.53200i	0.0363233	−	0.206000i
$485$	−5.64266			−0.256220
$486$	15.6862	+	11.2737i	0.711539	+	0.511386i
$487$	7.15087			0.324037			0.162018	−	0.986788i	$-0.448200\pi$
$487$	7.15087			0.324037			0.162018	+	0.986788i	$0.448200\pi$
$488$	−7.90383	+	44.8248i	−0.357789	+	2.02912i
$489$	−10.4559	+	2.38684i	−0.472831	+	0.107937i
$490$	−1.16446	−	0.423830i	−0.0526051	−	0.0191467i
$491$	−21.4488	+	17.9977i	−0.967970	+	0.812223i	−0.982231	−	0.187675i	$-0.939905\pi$
$491$	−21.4488	+	17.9977i	−0.967970	+	0.812223i	0.0142613	+	0.999898i	$0.495460\pi$
$492$	0.00392750	+	0.0786435i	0.000177065	+	0.00354552i
$493$	−40.3403	+	14.6827i	−1.81683	+	0.661274i
$494$	−4.00358	+	6.93441i	−0.180130	+	0.311994i
$495$	2.82250	−	1.35947i	0.126862	−	0.0611037i
$496$	−1.67490	−	2.90101i	−0.0752051	−	0.130259i
$497$	4.44861	+	3.73283i	0.199547	+	0.167440i
$498$	19.8559	+	2.48761i	0.889765	+	0.111473i
$499$	−1.89697	−	10.7582i	−0.0849200	−	0.481605i	−0.997374	−	0.0724256i	$-0.976926\pi$
$499$	−1.89697	−	10.7582i	−0.0849200	−	0.481605i	0.912454	−	0.409180i	$-0.134185\pi$
$500$	0.0806413	+	0.457339i	0.00360639	+	0.0204528i
$501$	24.8032	−	32.7469i	1.10812	−	1.46303i
$502$	−19.7515	−	16.5735i	−0.881552	−	0.739710i
$503$	−5.43334	−	9.41082i	−0.242261	−	0.419608i	0.719097	−	0.694910i	$-0.244556\pi$
$503$	−5.43334	−	9.41082i	−0.242261	−	0.419608i	−0.961358	+	0.275302i	$0.911222\pi$
$504$	−2.48191	−	8.81902i	−0.110553	−	0.392830i
$505$	6.35217	−	11.0023i	0.282668	−	0.489595i
$506$	9.72841	−	3.54085i	0.432481	−	0.157410i
$507$	17.6391	−	11.3934i	0.783381	−	0.505997i
$508$	−3.61807	+	3.03592i	−0.160526	+	0.134697i
$509$	−1.94438	−	0.707698i	−0.0861833	−	0.0313682i	0.298569	−	0.954388i	$-0.403491\pi$
$509$	−1.94438	−	0.707698i	−0.0861833	−	0.0313682i	−0.384752	+	0.923020i	$0.625713\pi$
$510$	3.94379	−	12.7869i	0.174634	−	0.566215i
$511$	−1.73248	+	9.82539i	−0.0766405	+	0.434650i
$512$	24.7773			1.09501
$513$	5.34895	+	35.4644i	0.236162	+	1.56579i
$514$	14.8705			0.655910
$515$	−1.40803	+	7.98535i	−0.0620453	+	0.351877i
$516$	−2.47716	−	2.66956i	−0.109051	−	0.117521i
$517$	−8.40710	−	3.05994i	−0.369744	−	0.134576i
$518$	−7.07107	+	5.93333i	−0.310685	+	0.260696i
$519$	−19.5529	−	10.0234i	−0.858279	−	0.439978i
$520$	−2.68646	+	0.977790i	−0.117809	+	0.0428789i
$521$	−20.5979	+	35.6767i	−0.902412	+	1.56302i	−0.0780574	+	0.996949i	$0.524872\pi$
$521$	−20.5979	+	35.6767i	−0.902412	+	1.56302i	−0.824354	+	0.566074i	$0.808462\pi$
$522$	−25.4712	+	2.55046i	−1.11485	+	0.111630i
$523$	5.47130	+	9.47657i	0.239243	+	0.414381i	0.960497	−	0.278289i	$-0.0897673\pi$
$523$	5.47130	+	9.47657i	0.239243	+	0.414381i	−0.721254	+	0.692671i	$0.756434\pi$
$524$	6.74833	+	5.66252i	0.294802	+	0.247368i
$525$	0.672841	+	1.59602i	0.0293652	+	0.0696561i
$526$	−3.10058	−	17.5843i	−0.135192	−	0.766711i
$527$	1.26998	+	7.20241i	0.0553212	+	0.313742i
$528$	2.00640	+	4.75932i	0.0873176	+	0.207123i
$529$	31.4100	+	26.3561i	1.36565	+	1.14592i
$530$	−0.717129	−	1.24210i	−0.0311501	−	0.0539535i
$531$	−16.0985	+	35.6840i	−0.698613	+	1.54856i
$532$	1.60270	−	2.77596i	0.0694859	−	0.120353i
$533$	0.0861163	−	0.0313438i	0.00373011	−	0.00135765i
$534$	14.0904	+	7.22315i	0.609751	+	0.312576i
$535$	10.3169	−	8.65688i	0.446037	−	0.374270i
$536$	16.0939	+	5.85768i	0.695149	+	0.253013i
$537$	−18.3322	−	19.7562i	−0.791094	−	0.852541i
$538$	−2.34705	+	13.3108i	−0.101189	+	0.573869i
$539$	−1.04428			−0.0449803
$540$	−1.25806	+	2.05917i	−0.0541381	+	0.0886125i
$541$	34.5196			1.48411			0.742057	−	0.670337i	$-0.233850\pi$
$541$	34.5196			1.48411			0.742057	+	0.670337i	$0.233850\pi$
$542$	−3.05697	+	17.3370i	−0.131308	+	0.744686i
$543$	3.90270	−	12.6537i	0.167481	−	0.543023i
$544$	−15.0513	−	5.47822i	−0.645318	−	0.234877i
$545$	6.92723	−	5.81264i	0.296730	−	0.248986i
$546$	−1.68783	+	1.09019i	−0.0722323	+	0.0466559i
$547$	2.15682	−	0.785018i	0.0922189	−	0.0335649i	−0.295499	−	0.955343i	$-0.595486\pi$
$547$	2.15682	−	0.785018i	0.0922189	−	0.0335649i	0.387718	+	0.921778i	$0.373264\pi$
$548$	−1.98228	+	3.43341i	−0.0846787	+	0.146668i
$549$	31.2185	−	32.0109i	1.33237	−	1.36619i
$550$	−0.647033	−	1.12069i	−0.0275896	−	0.0477866i
$551$	−36.4086	−	30.5505i	−1.55106	−	1.30149i
$552$	−25.5498	+	33.7327i	−1.08747	+	1.43576i
$553$	−0.543518	−	3.08244i	−0.0231127	−	0.131079i
$554$	3.29513	+	18.6876i	0.139997	+	0.793960i
$555$	12.8018	+	1.60385i	0.543405	+	0.0680795i
$556$	−2.56549	−	2.15271i	−0.108801	−	0.0912951i
$557$	14.6801	+	25.4267i	0.622017	+	1.07736i	0.989110	+	0.147180i	$0.0470197\pi$
$557$	14.6801	+	25.4267i	0.622017	+	1.07736i	−0.367093	+	0.930184i	$0.619647\pi$
$558$	−0.325617	+	4.34886i	−0.0137845	+	0.184102i
$559$	−2.11926	+	3.67067i	−0.0896353	+	0.155253i
$560$	−2.68334	+	0.976655i	−0.113392	+	0.0412712i
$561$	−0.562455	−	11.2625i	−0.0237469	−	0.475503i
$562$	14.4033	−	12.0858i	0.607565	−	0.509807i
$563$	6.02403	+	2.19257i	0.253883	+	0.0924057i	0.465826	−	0.884876i	$-0.345757\pi$
$563$	6.02403	+	2.19257i	0.253883	+	0.0924057i	−0.211944	+	0.977282i	$0.567979\pi$
$564$	6.71832	−	1.53364i	0.282892	−	0.0645781i
$565$	−1.82468	+	10.3483i	−0.0767648	+	0.435355i
$566$	−13.4142			−0.563841
$567$	−2.86527	+	8.53172i	−0.120330	+	0.358299i
$568$	17.7346			0.744125
$569$	4.04458	−	22.9379i	0.169557	−	0.961608i	−0.774683	−	0.632350i	$-0.782090\pi$
$569$	4.04458	−	22.9379i	0.169557	−	0.961608i	0.944240	−	0.329258i	$-0.106798\pi$
$570$	14.4433	−	3.29707i	0.604961	−	0.138099i
$571$	39.5114	+	14.3810i	1.65350	+	0.601826i	0.989322	−	0.145747i	$-0.0465585\pi$
$571$	39.5114	+	14.3810i	1.65350	+	0.601826i	0.664180	+	0.747572i	$0.268781\pi$
$572$	−0.347777	+	0.291820i	−0.0145413	+	0.0122016i
$573$	0.0447304	+	0.895673i	0.00186864	+	0.0374173i
$574$	0.113994	−	0.0414904i	0.00475801	−	0.00173178i
$575$	4.00009	−	6.92836i	0.166815	−	0.288933i
$576$	−22.0486	−	15.0304i	−0.918692	−	0.626266i
$577$	21.3509	+	36.9808i	0.888849	+	1.53953i	0.841237	+	0.540667i	$0.181828\pi$
$577$	21.3509	+	36.9808i	0.888849	+	1.53953i	0.0476125	+	0.998866i	$0.484839\pi$
$578$	−20.7592	−	17.4190i	−0.863467	−	0.724535i
$579$	−18.2166	−	2.28224i	−0.757057	−	0.0948465i
$580$	−0.555280	−	3.14915i	−0.0230568	−	0.130761i
$581$	1.61898	+	9.18170i	0.0671666	+	0.380921i
$582$	−7.31243	+	9.65440i	−0.303110	+	0.400188i
$583$	−0.925887	−	0.776911i	−0.0383463	−	0.0321764i
$584$	15.2342	+	26.3863i	0.630394	+	1.09187i
$585$	2.72164	+	0.692826i	0.112526	+	0.0286448i
$586$	−0.161931	+	0.280473i	−0.00668932	+	0.0115862i
$587$	−13.8473	+	5.04001i	−0.571540	+	0.208024i	−0.611591	−	0.791174i	$-0.709470\pi$
$587$	−13.8473	+	5.04001i	−0.571540	+	0.208024i	0.0400511	+	0.999198i	$0.487248\pi$
$588$	0.675665	−	0.436422i	0.0278639	−	0.0179977i
$589$	−6.20265	+	5.20464i	−0.255576	+	0.214454i
$590$	15.1952	+	5.53060i	0.625576	+	0.227691i
$591$	−3.36367	+	10.9060i	−0.138363	+	0.448613i
$592$	−3.69361	+	20.9475i	−0.151806	+	0.860937i
$593$	−26.0114			−1.06816			−0.534080	−	0.845434i	$-0.679342\pi$
$593$	−26.0114			−1.06816			−0.534080	+	0.845434i	$0.679342\pi$
$594$	1.33172	−	6.59097i	0.0546413	−	0.270431i
$595$	6.23445			0.255587
$596$	−0.487094	+	2.76245i	−0.0199522	+	0.113154i
$597$	14.4354	+	15.5567i	0.590803	+	0.636692i
$598$	8.72106	+	3.17421i	0.356631	+	0.129803i
$599$	−10.0941	+	8.46993i	−0.412433	+	0.346072i	−0.825276	−	0.564730i	$-0.808980\pi$
$599$	−10.0941	+	8.46993i	−0.412433	+	0.346072i	0.412843	+	0.910802i	$0.364536\pi$
$600$	4.70701	+	2.41295i	0.192163	+	0.0985083i
$601$	7.74874	−	2.82031i	0.316078	−	0.115043i	−0.179110	−	0.983829i	$-0.557322\pi$
$601$	7.74874	−	2.82031i	0.316078	−	0.115043i	0.495187	+	0.868786i	$0.335099\pi$
$602$	−2.80531	+	4.85894i	−0.114336	+	0.198036i
$603$	−9.82216	−	13.6599i	−0.399989	−	0.556275i
$604$	0.207301	+	0.359056i	0.00843496	+	0.0146098i
$605$	7.59110	+	6.36969i	0.308622	+	0.258965i
$606$	−10.5926	−	25.1264i	−0.430296	−	1.02069i
$607$	−6.38383	−	36.2045i	−0.259112	−	1.46950i	−0.785293	−	0.619124i	$-0.787488\pi$
$607$	−6.38383	−	36.2045i	−0.259112	−	1.46950i	0.526182	−	0.850372i	$-0.323623\pi$
$608$	−3.07932	−	17.4637i	−0.124883	−	0.708246i
$609$	−4.63305	−	10.9899i	−0.187741	−	0.445333i
$610$	−14.1485	−	11.8720i	−0.572857	−	0.480684i
$611$	−4.01012	−	6.94574i	−0.162232	−	0.280994i
$612$	5.07070	+	7.05194i	0.204971	+	0.285058i
$613$	10.3941	−	18.0031i	0.419813	−	0.727137i	−0.576107	−	0.817374i	$-0.695429\pi$
$613$	10.3941	−	18.0031i	0.419813	−	0.727137i	0.995920	+	0.0902367i	$0.0287624\pi$
$614$	25.5203	−	9.28864i	1.02992	−	0.374859i
$615$	−0.150887	−	0.0773489i	−0.00608434	−	0.00311901i
$616$	−2.44298	+	2.04991i	−0.0984306	+	0.0825931i
$617$	−17.8404	−	6.49338i	−0.718228	−	0.261414i	−0.0430546	−	0.999073i	$-0.513709\pi$
$617$	−17.8404	−	6.49338i	−0.718228	−	0.261414i	−0.675173	+	0.737659i	$0.735931\pi$
$618$	11.8380	+	12.7575i	0.476193	+	0.513181i
$619$	−4.27066	+	24.2201i	−0.171652	+	0.973488i	0.770285	+	0.637700i	$0.220114\pi$
$619$	−4.27066	+	24.2201i	−0.171652	+	0.973488i	−0.941937	+	0.335789i	$0.890997\pi$
$620$	−0.544773			−0.0218786
$621$	39.4042	−	13.2434i	1.58124	−	0.531439i
$622$	20.1746			0.808927
$623$	−1.28103	+	7.26507i	−0.0513233	+	0.291069i
$624$	−1.36461	+	4.42448i	−0.0546282	+	0.177121i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	−14.4209	+	12.1005i	−0.576373	+	0.483634i
$627$	10.4871	−	6.77378i	0.418815	−	0.270519i
$628$	1.01764	−	0.370389i	0.0406081	−	0.0147801i
$629$	23.2198	−	40.2179i	0.925836	−	1.60359i
$630$	3.60269	+	0.917107i	0.143535	+	0.0365384i
$631$	−12.9169	−	22.3728i	−0.514216	−	0.890647i	−0.999864	−	0.0164932i	$-0.994750\pi$
$631$	−12.9169	−	22.3728i	−0.514216	−	0.890647i	0.485648	−	0.874154i	$-0.338584\pi$
$632$	−7.32230	−	6.14414i	−0.291265	−	0.244401i
$633$	−0.415776	+	0.548937i	−0.0165256	+	0.0218183i
$634$	6.15752	+	34.9210i	0.244546	+	1.38689i
$635$	−1.76606	−	10.0158i	−0.0700840	−	0.397466i
$636$	0.923747	+	0.115730i	0.0366290	+	0.00458899i
$637$	−0.717130	−	0.601743i	−0.0284137	−	0.0238419i
$638$	4.45535	+	7.71689i	0.176389	+	0.305515i
$639$	−14.3952	−	9.81308i	−0.569463	−	0.388199i
$640$	−2.94203	+	5.09575i	−0.116294	+	0.201427i
$641$	−0.805447	+	0.293159i	−0.0318132	+	0.0115791i	−0.357878	−	0.933768i	$-0.616500\pi$
$641$	−0.805447	+	0.293159i	−0.0318132	+	0.0115791i	0.326065	+	0.945348i	$0.394277\pi$
$642$	−1.44181	−	28.8705i	−0.0569036	−	1.13943i
$643$	14.3184	−	12.0145i	0.564662	−	0.473807i	−0.315208	−	0.949023i	$-0.602074\pi$
$643$	14.3184	−	12.0145i	0.564662	−	0.473807i	0.879870	+	0.475215i	$0.157630\pi$
$644$	−3.49118	−	1.27069i	−0.137572	−	0.0500721i
$645$	7.64541	−	1.74528i	0.301038	−	0.0687202i
$646$	9.25984	−	52.5151i	0.364323	−	2.06618i
$647$	−28.6092			−1.12474			−0.562371	−	0.826885i	$-0.690111\pi$
$647$	−28.6092			−1.12474			−0.562371	+	0.826885i	$0.690111\pi$
$648$	10.0447	+	25.5836i	0.394591	+	1.00502i
$649$	13.6269			0.534903
$650$	0.201444	−	1.14244i	0.00790127	−	0.0448103i
$651$	−1.98088	+	0.452191i	−0.0776368	+	0.0177228i
$652$	−2.70211	−	0.983488i	−0.105823	−	0.0385164i
$653$	3.12896	−	2.62551i	0.122446	−	0.102744i	−0.579509	−	0.814966i	$-0.696755\pi$
$653$	3.12896	−	2.62551i	0.122446	−	0.102744i	0.701954	+	0.712222i	$0.252311\pi$
$654$	−0.968097	−	19.3850i	−0.0378556	−	0.758013i
$655$	−17.8255	+	6.48794i	−0.696499	+	0.253505i
$656$	0.139770	−	0.242090i	0.00545712	−	0.00945201i
$657$	2.23479	−	29.8473i	0.0871876	−	1.16446i
$658$	−5.30828	−	9.19421i	−0.206938	−	0.358428i
$659$	15.5617	+	13.0578i	0.606196	+	0.508659i	0.893431	−	0.449201i	$-0.148291\pi$
$659$	15.5617	+	13.0578i	0.606196	+	0.508659i	−0.287234	+	0.957860i	$0.592736\pi$
$660$	0.833456	+	0.104418i	0.0324422	+	0.00406446i
$661$	−7.96642	−	45.1798i	−0.309858	−	1.75729i	−0.599707	−	0.800220i	$-0.704716\pi$
$661$	−7.96642	−	45.1798i	−0.309858	−	1.75729i	0.289849	−	0.957072i	$-0.406395\pi$
$662$	−7.78253	−	44.1369i	−0.302477	−	1.71543i
$663$	6.10351	−	8.05830i	0.237041	−	0.312959i
$664$	21.8110	+	18.3016i	0.846431	+	0.710240i
$665$	3.45116	+	5.97759i	0.133830	+	0.231801i
$666$	19.3342	−	19.8250i	0.749185	−	0.768201i
$667$	−27.5439	+	47.7074i	−1.06650	+	1.84724i
$668$	10.3500	−	3.76710i	0.400455	−	0.145754i
$669$	37.7585	−	24.3887i	1.45983	−	0.942923i
$670$	−5.32375	+	4.46716i	−0.205675	+	0.172581i
$671$	−14.6258	−	5.32336i	−0.564623	−	0.205506i
$672$	1.31149	−	4.25224i	0.0505919	−	0.164034i
$673$	2.79371	−	15.8439i	0.107690	−	0.610739i	−0.882422	−	0.470459i	$-0.844089\pi$
$673$	2.79371	−	15.8439i	0.107690	−	0.610739i	0.990112	−	0.140280i	$-0.0448004\pi$
$674$	13.9568			0.537597
$675$	−2.48553	−	4.56313i	−0.0956680	−	0.175635i
$676$	5.63015			0.216544
$677$	1.47200	−	8.34811i	0.0565734	−	0.320844i	−0.943367	−	0.331751i	$-0.892361\pi$
$677$	1.47200	−	8.34811i	0.0565734	−	0.320844i	0.999941	+	0.0109069i	$0.00347184\pi$
$678$	15.3409	+	16.5325i	0.589164	+	0.634926i
$679$	−5.30236	−	1.92990i	−0.203486	−	0.0740629i
$680$	14.5849	−	12.2381i	0.559304	−	0.469311i
$681$	19.3848	+	9.93721i	0.742827	+	0.380795i
$682$	1.42650	−	0.519202i	0.0546234	−	0.0198813i
$683$	−20.5820	+	35.6490i	−0.787547	+	1.36407i	0.139918	+	0.990163i	$0.455316\pi$
$683$	−20.5820	+	35.6490i	−0.787547	+	1.36407i	−0.927465	+	0.373909i	$0.878017\pi$
$684$	−3.95445	+	8.76548i	−0.151202	+	0.335157i
$685$	−4.26852	−	7.39330i	−0.163092	−	0.282483i
$686$	−0.949279	−	0.796540i	−0.0362436	−	0.0304120i
$687$	11.6924	+	27.7352i	0.446094	+	1.05816i
$688$	2.24508	+	12.7325i	0.0855927	+	0.485420i
$689$	−0.188149	−	1.06704i	−0.00716789	−	0.0406511i
$690$	−6.67040	−	15.8226i	−0.253938	−	0.602357i
$691$	−9.39793	−	7.88580i	−0.357514	−	0.299990i	0.446285	−	0.894891i	$-0.352747\pi$
$691$	−9.39793	−	7.88580i	−0.357514	−	0.299990i	−0.803799	+	0.594901i	$0.797191\pi$
$692$	−2.94560	−	5.10193i	−0.111975	−	0.193946i
$693$	3.11725	−	0.312133i	0.118415	−	0.0118570i
$694$	−14.9337	+	25.8660i	−0.566877	+	0.981859i
$695$	6.77666	−	2.46650i	0.257053	−	0.0935598i
$696$	−32.4116	−	16.6151i	−1.22856	−	0.629795i
$697$	−0.467528	+	0.392303i	−0.0177089	+	0.0148595i
$698$	−27.7672	−	10.1064i	−1.05100	−	0.382534i
$699$	−18.1062	−	19.5125i	−0.684838	−	0.738031i
$700$	−0.0806413	+	0.457339i	−0.00304795	+	0.0172858i
$701$	−9.42113			−0.355831			−0.177916	−	0.984046i	$-0.556935\pi$
$701$	−9.42113			−0.355831			−0.177916	+	0.984046i	$0.556935\pi$
$702$	4.71243	−	3.75879i	0.177859	−	0.141866i
$703$	51.4146			1.93914
$704$	−1.61295	+	9.14752i	−0.0607905	+	0.344760i
$705$	−4.37341	+	14.1799i	−0.164712	+	0.534045i
$706$	12.2768	+	4.46838i	0.462042	+	0.168170i
$707$	9.73209	−	8.16619i	0.366013	−	0.307121i
$708$	−8.81681	+	5.69491i	−0.331356	+	0.214028i
$709$	7.61997	−	2.77344i	0.286174	−	0.104159i	−0.194945	−	0.980814i	$-0.562453\pi$
$709$	7.61997	−	2.77344i	0.286174	−	0.104159i	0.481119	+	0.876655i	$0.340231\pi$
$710$	−3.59816	+	6.23219i	−0.135036	+	0.233890i
$711$	2.54378	+	9.03885i	0.0953990	+	0.338984i
$712$	11.2644	+	19.5105i	0.422151	+	0.731188i
$713$	7.18922	+	6.03248i	0.269239	+	0.225918i
$714$	8.07934	−	10.6669i	0.302362	−	0.399200i
$715$	−0.169758	−	0.962746i	−0.00634859	−	0.0360047i
$716$	−1.25481	−	7.11637i	−0.0468944	−	0.265951i
$717$	51.7807	+	6.48725i	1.93378	+	0.242271i
$718$	6.03411	+	5.06322i	0.225191	+	0.188958i
$719$	20.3844	+	35.3068i	0.760210	+	1.31672i	0.942742	+	0.333522i	$0.108237\pi$
$719$	20.3844	+	35.3068i	0.760210	+	1.31672i	−0.182532	+	0.983200i	$0.558429\pi$
$720$	7.71804	−	3.71743i	0.287634	−	0.138540i
$721$	−4.05427	+	7.02220i	−0.150989	+	0.261520i
$722$	33.3526	−	12.1394i	1.24126	−	0.451780i
$723$	0.349927	+	7.00686i	0.0130139	+	0.260588i
$724$	2.71976	−	2.28215i	0.101079	−	0.0848154i
$725$	6.47055	+	2.35509i	0.240310	+	0.0874657i
$726$	20.7358	−	4.73352i	0.769577	−	0.175677i
$727$	−3.95412	+	22.4249i	−0.146650	+	0.831695i	0.819377	+	0.573255i	$0.194319\pi$
$727$	−3.95412	+	22.4249i	−0.146650	+	0.831695i	−0.966027	+	0.258440i	$0.916792\pi$
$728$	−2.85887			−0.105957
$729$	6.00292	−	26.3242i	0.222330	−	0.974971i
$730$	−12.3634			−0.457590
$731$	4.90162	−	27.7984i	0.181293	−	1.02816i
$732$	11.6878	−	2.66807i	0.431995	−	0.0986148i
$733$	7.27350	+	2.64734i	0.268653	+	0.0977817i	0.472834	−	0.881151i	$-0.343231\pi$
$733$	7.27350	+	2.64734i	0.268653	+	0.0977817i	−0.204181	+	0.978933i	$0.565453\pi$
$734$	−25.5501	+	21.4391i	−0.943070	+	0.791330i
$735$	0.0863920	+	1.72989i	0.00318662	+	0.0638081i
$736$	−19.3141	+	7.02977i	−0.711928	+	0.259121i
$737$	−2.92827	+	5.07191i	−0.107864	+	0.186826i
$738$	−0.327879	+	0.157924i	−0.0120694	+	0.00581328i
$739$	−14.4706	−	25.0638i	−0.532310	−	0.921988i	−0.999288	−	0.0377195i	$-0.987991\pi$
$739$	−14.4706	−	25.0638i	−0.532310	−	0.921988i	0.466978	−	0.884269i	$-0.345343\pi$
$740$	2.64992	+	2.22354i	0.0974129	+	0.0817391i
$741$	11.1050	+	1.39127i	0.407952	+	0.0511095i
$742$	−0.249056	−	1.41247i	−0.00914314	−	0.0518533i
$743$	7.60893	+	43.1524i	0.279145	+	1.58311i	0.725481	+	0.688242i	$0.241617\pi$
$743$	7.60893	+	43.1524i	0.279145	+	1.58311i	−0.446336	+	0.894865i	$0.647272\pi$
$744$	−3.74642	+	4.94630i	−0.137350	+	0.181340i
$745$	−4.62711	−	3.88260i	−0.169524	−	0.142248i
$746$	21.4028	+	37.0707i	0.783612	+	1.35726i
$747$	−7.57717	−	26.9241i	−0.277234	−	0.985102i
$748$	1.51172	−	2.61838i	0.0552740	−	0.0957374i
$749$	12.6555	−	4.60623i	0.462422	−	0.168308i
$750$	−1.80295	+	1.16455i	−0.0658345	+	0.0425235i
$751$	−23.9532	+	20.0991i	−0.874065	+	0.733428i	−0.964950	−	0.262433i	$-0.915475\pi$
$751$	−23.9532	+	20.0991i	−0.874065	+	0.733428i	0.0908847	+	0.995861i	$0.471031\pi$
$752$	−22.9890	−	8.36730i	−0.838321	−	0.305124i
$753$	−10.6214	+	34.4377i	−0.387066	+	1.25498i
$754$	−1.38710	+	7.86665i	−0.0505153	+	0.286487i
$755$	−0.892780			−0.0324916
$756$	−1.88646	+	1.50471i	−0.0686100	+	0.0547256i
$757$	6.11096			0.222107			0.111053	−	0.993814i	$-0.464578\pi$
$757$	6.11096			0.222107			0.111053	+	0.993814i	$0.464578\pi$
$758$	5.69283	−	32.2857i	0.206773	−	1.17267i
$759$	−9.84264	−	10.6071i	−0.357265	−	0.385015i
$760$	19.8076	+	7.20936i	0.718496	+	0.261511i
$761$	−0.777946	+	0.652774i	−0.0282005	+	0.0236631i	−0.656779	−	0.754083i	$-0.728082\pi$
$761$	−0.777946	+	0.652774i	−0.0282005	+	0.0236631i	0.628578	+	0.777746i	$0.283637\pi$
$762$	−19.4254	−	9.95804i	−0.703709	−	0.360742i
$763$	8.49751	−	3.09284i	0.307630	−	0.111968i
$764$	−0.120223	+	0.208232i	−0.00434951	+	0.00753357i
$765$	−18.6103	+	1.86346i	−0.672856	+	0.0673737i
$766$	−14.0663	−	24.3636i	−0.508236	−	0.880291i
$767$	9.35789	+	7.85221i	0.337894	+	0.283527i
$768$	−7.06351	−	16.7551i	−0.254883	−	0.604598i
$769$	−5.73929	−	32.5491i	−0.206964	−	1.17375i	−0.894319	−	0.447429i	$-0.852340\pi$
$769$	−5.73929	−	32.5491i	−0.206964	−	1.17375i	0.687355	−	0.726321i	$-0.258772\pi$
$770$	−0.224712	−	1.27441i	−0.00809807	−	0.0459264i
$771$	−8.07418	−	19.1525i	−0.290784	−	0.689759i
$772$	−3.77077	−	3.16405i	−0.135713	−	0.113877i
$773$	26.2958	+	45.5457i	0.945796	+	1.63817i	0.754150	+	0.656702i	$0.228049\pi$
$773$	26.2958	+	45.5457i	0.945796	+	1.63817i	0.191646	+	0.981464i	$0.438618\pi$
$774$	6.92173	−	15.3428i	0.248796	−	0.551485i
$775$	0.586541	−	1.01592i	0.0210692	−	0.0364929i
$776$	−16.1927	+	5.89367i	−0.581285	+	0.211570i
$777$	11.4812	+	5.88559i	0.411885	+	0.211144i
$778$	−4.03647	+	3.38700i	−0.144714	+	0.121430i
$779$	−0.634946	−	0.231102i	−0.0227493	−	0.00828007i
$780$	0.512184	+	0.551967i	0.0183391	+	0.0197636i
$781$	−1.05307	+	5.97225i	−0.0376818	+	0.213704i
$782$	−61.8070			−2.21021
$783$	17.1149	+	31.4208i	0.611635	+	1.12289i
$784$	−2.85555			−0.101984
$785$	−0.404939	+	2.29652i	−0.0144529	+	0.0819665i
$786$	−11.9997	+	38.9067i	−0.428016	+	1.38775i
$787$	19.8814	+	7.23624i	0.708696	+	0.257944i	0.671119	−	0.741350i	$-0.265814\pi$
$787$	19.8814	+	7.23624i	0.708696	+	0.257944i	0.0375768	+	0.999294i	$0.488036\pi$
$788$	−2.34411	+	1.96694i	−0.0835055	+	0.0700694i
$789$	−20.9642	+	13.5411i	−0.746344	+	0.482075i
$790$	3.64476	−	1.32658i	0.129675	−	0.0471977i
$791$	−5.25395	+	9.10011i	−0.186809	+	0.323563i
$792$	6.67977	−	6.84933i	0.237355	−	0.243380i
$793$	−6.97639	−	12.0835i	−0.247739	−	0.429096i
$794$	−13.6005	−	11.4122i	−0.482665	−	0.405004i
$795$	−1.21039	+	1.59805i	−0.0429281	+	0.0566768i
$796$	0.988080	+	5.60368i	0.0350216	+	0.198617i
$797$	0.0199400	+	0.113085i	0.000706311	+	0.00400569i	0.985159	−	0.171645i	$-0.0549082\pi$
$797$	0.0199400	+	0.113085i	0.000706311	+	0.00400569i	−0.984453	+	0.175651i	$0.943797\pi$
$798$	14.6999	+	1.84165i	0.520370	+	0.0651936i
$799$	40.9163	+	34.3328i	1.44751	+	1.21461i
$800$	1.28457	+	2.22495i	0.0454166	+	0.0786638i
$801$	1.65245	−	22.0697i	0.0583863	−	0.779793i
$802$	−3.02830	+	5.24517i	−0.106933	+	0.185213i
$803$	−9.79041	+	3.56342i	−0.345496	+	0.125750i
$804$	−0.225001	−	4.50538i	−0.00793518	−	0.158892i
$805$	6.12849	−	5.14242i	0.216001	−	0.181246i
$806$	1.27879	+	0.465440i	0.0450433	+	0.0163944i
$807$	18.4180	−	4.20442i	0.648344	−	0.148002i
$808$	6.73709	−	38.2079i	0.237010	−	1.34415i
$809$	−8.71629			−0.306448			−0.153224	−	0.988191i	$-0.548966\pi$
$809$	−8.71629			−0.306448			−0.153224	+	0.988191i	$0.548966\pi$
$810$	−11.0284	−	1.66080i	−0.387499	−	0.0583544i
$811$	−28.3260			−0.994661			−0.497331	−	0.867561i	$-0.665686\pi$
$811$	−28.3260			−0.994661			−0.497331	+	0.867561i	$0.665686\pi$
$812$	0.555280	−	3.14915i	0.0194865	−	0.110514i
$813$	23.9890	−	5.47615i	0.841329	−	0.192057i
$814$	−9.05803	−	3.29685i	−0.317484	−	0.115555i
$815$	4.74334	−	3.98014i	0.166152	−	0.139418i
$816$	−1.53802	−	30.7969i	−0.0538414	−	1.07811i
$817$	29.3665	−	10.6885i	1.02740	−	0.373944i
$818$	9.99437	−	17.3108i	0.349445	−	0.605257i
$819$	2.32054	+	1.58190i	0.0810864	+	0.0552760i
$820$	−0.0227307	−	0.0393707i	−0.000793791	−	0.00137489i
$821$	−16.4782	−	13.8268i	−0.575092	−	0.482559i	0.308239	−	0.951309i	$-0.400260\pi$
$821$	−16.4782	−	13.8268i	−0.575092	−	0.482559i	−0.883331	+	0.468750i	$0.844705\pi$
$822$	−18.1814	−	2.27782i	−0.634148	−	0.0794480i
$823$	−3.85188	−	21.8451i	−0.134268	−	0.761472i	−0.975367	−	0.220590i	$-0.929202\pi$
$823$	−3.85188	−	21.8451i	−0.134268	−	0.761472i	0.841099	−	0.540882i	$-0.181909\pi$
$824$	4.29994	+	24.3862i	0.149796	+	0.849533i
$825$	−1.09208	+	1.44184i	−0.0380214	+	0.0501986i
$826$	12.3872	+	10.3941i	0.431007	+	0.361658i
$827$	−9.26626	−	16.0496i	−0.322219	−	0.558100i	0.658726	−	0.752383i	$-0.271095\pi$
$827$	−9.26626	−	16.0496i	−0.322219	−	0.558100i	−0.980946	+	0.194282i	$0.937762\pi$
$828$	10.8012	+	2.74958i	0.375369	+	0.0955547i
$829$	−15.5610	+	26.9524i	−0.540456	+	0.936097i	0.458422	+	0.888735i	$0.348415\pi$
$829$	−15.5610	+	26.9524i	−0.540456	+	0.936097i	−0.998878	+	0.0473621i	$0.984919\pi$
$830$	−10.8567	+	3.95151i	−0.376841	+	0.137159i
$831$	22.2795	−	14.3907i	0.772869	−	0.499207i
$832$	−6.37871	+	5.35237i	−0.221142	+	0.185560i
$833$	5.85847	+	2.13231i	0.202984	+	0.0738801i
$834$	4.56190	−	14.7910i	0.157966	−	0.512172i
$835$	−4.11850	+	23.3572i	−0.142527	+	0.808308i
$836$	3.34733			0.115770
$837$	5.77791	−	1.94190i	0.199714	−	0.0671220i
$838$	18.4718			0.638097
$839$	3.69500	−	20.9554i	0.127566	−	0.723461i	−0.852185	−	0.523240i	$-0.824723\pi$
$839$	3.69500	−	20.9554i	0.127566	−	0.723461i	0.979751	−	0.200221i	$-0.0641659\pi$
$840$	3.59787	+	3.87733i	0.124138	+	0.133780i
$841$	−17.3039	−	6.29809i	−0.596685	−	0.217176i
$842$	−6.64300	+	5.57414i	−0.228933	+	0.192098i
$843$	−23.3863	−	11.9885i	−0.805468	−	0.412906i
$844$	−0.173498	+	0.0631480i	−0.00597204	+	0.00217364i
$845$	−6.06182	+	10.4994i	−0.208533	+	0.361189i
$846$	18.5937	+	25.8588i	0.639266	+	0.889042i
$847$	4.95474	+	8.58186i	0.170247	+	0.294876i
$848$	−2.53181	−	2.12444i	−0.0869426	−	0.0729535i
$849$	7.28345	+	17.2768i	0.249967	+	0.592938i
$850$	1.34155	+	7.60833i	0.0460149	+	0.260964i
$851$	−10.3481	−	58.6871i	−0.354729	−	2.01177i
$852$	−1.81455	−	4.30424i	−0.0621655	−	0.147461i
$853$	23.6907	+	19.8789i	0.811155	+	0.680640i	0.950883	−	0.309550i	$-0.100178\pi$
$853$	23.6907	+	19.8789i	0.811155	+	0.680640i	−0.139728	+	0.990190i	$0.544623\pi$
$854$	−9.23479	−	15.9951i	−0.316008	−	0.547342i
$855$	−12.0887	−	16.8120i	−0.413423	−	0.574958i
$856$	20.5643	−	35.6184i	0.702874	−	1.21741i
$857$	4.23273	−	1.54059i	0.144587	−	0.0526255i	−0.268713	−	0.963220i	$-0.586598\pi$
$857$	4.23273	−	1.54059i	0.144587	−	0.0526255i	0.413300	+	0.910595i	$0.364376\pi$
$858$	−1.86722	−	0.957191i	−0.0637458	−	0.0326780i
$859$	6.59660	−	5.53520i	0.225073	−	0.188859i	−0.523277	−	0.852163i	$-0.675291\pi$
$859$	6.59660	−	5.53520i	0.225073	−	0.188859i	0.748350	+	0.663304i	$0.230846\pi$
$860$	1.97580	+	0.719134i	0.0673744	+	0.0245223i
$861$	−0.115332	−	0.124291i	−0.00393051	−	0.00423581i
$862$	8.64665	−	49.0376i	0.294506	−	1.67023i
$863$	43.9069			1.49461			0.747304	−	0.664482i	$-0.231348\pi$
$863$	43.9069			1.49461			0.747304	+	0.664482i	$0.231348\pi$
$864$	−2.64391	+	13.0853i	−0.0899477	+	0.445170i
$865$	12.6858			0.431329
$866$	3.75327	−	21.2858i	0.127541	−	0.723322i
$867$	−11.1633	+	36.1947i	−0.379125	+	1.22924i
$868$	−0.511919	−	0.186323i	−0.0173757	−	0.00632422i
$869$	2.50388	−	2.10101i	0.0849384	−	0.0712718i
$870$	12.4148	−	8.01889i	0.420901	−	0.271866i
$871$	−4.93348	+	1.79564i	−0.167165	+	0.0608430i
$872$	13.8078	−	23.9159i	0.467593	−	0.809894i
$873$	16.4048	+	4.17603i	0.555218	+	0.141337i
$874$	−34.2141	−	59.2605i	−1.15731	−	2.00452i
$875$	−0.766044	−	0.642788i	−0.0258970	−	0.0217302i
$876$	4.84533	−	6.39716i	0.163709	−	0.216140i
$877$	−3.46399	−	19.6453i	−0.116971	−	0.663373i	−0.985756	−	0.168184i	$-0.946210\pi$
$877$	−3.46399	−	19.6453i	−0.116971	−	0.663373i	0.868785	−	0.495189i	$-0.164901\pi$
$878$	1.57332	+	8.92272i	0.0530968	+	0.301127i
$879$	0.449159	+	0.0562720i	0.0151498	+	0.00189801i
$880$	−2.28434	−	1.91679i	−0.0770050	−	0.0646149i
$881$	23.3439	+	40.4328i	0.786476	+	1.36222i	0.928113	+	0.372298i	$0.121430\pi$
$881$	23.3439	+	40.4328i	0.786476	+	1.36222i	−0.141637	+	0.989919i	$0.545237\pi$
$882$	3.07175	+	2.09399i	0.103431	+	0.0705083i
$883$	4.30521	−	7.45684i	0.144882	−	0.250943i	−0.784447	−	0.620196i	$-0.787053\pi$
$883$	4.30521	−	7.45684i	0.144882	−	0.250943i	0.929329	+	0.369253i	$0.120386\pi$
$884$	2.54692	−	0.927002i	0.0856621	−	0.0311784i
$885$	−1.12734	−	22.5736i	−0.0378950	−	0.758802i
$886$	16.0821	−	13.4945i	0.540288	−	0.453356i
$887$	−17.8898	−	6.51137i	−0.600682	−	0.218630i	0.0237390	−	0.999718i	$-0.492443\pi$
$887$	−17.8898	−	6.51137i	−0.600682	−	0.218630i	−0.624421	+	0.781088i	$0.714665\pi$
$888$	38.4124	−	8.76869i	1.28904	−	0.294258i
$889$	1.76606	−	10.0158i	0.0592318	−	0.335920i
$890$	−9.14172			−0.306431
$891$	−9.21192	+	1.86348i	−0.308611	+	0.0624289i
$892$	12.0519			0.403529
$893$	−10.2686	+	58.2359i	−0.343624	+	1.94879i
$894$	−12.6394	+	2.88529i	−0.422724	+	0.0964984i
$895$	14.6220	+	5.32196i	0.488759	+	0.177894i
$896$	−4.50746	+	3.78221i	−0.150584	+	0.126355i
$897$	−0.647019	−	12.9558i	−0.0216033	−	0.432581i
$898$	19.0427	−	6.93096i	0.635462	−	0.231289i
$899$	−4.03881	+	6.99542i	−0.134702	+	0.233310i
$900$	0.104022	−	1.38929i	0.00346741	−	0.0463098i
$901$	3.60791	+	6.24908i	0.120197	+	0.208187i
$902$	0.0970435	+	0.0814292i	0.00323119	+	0.00271129i
$903$	7.78126	+	0.974861i	0.258944	+	0.0324413i
$904$	5.57232	+	31.6022i	0.185333	+	1.05107i
$905$	1.32758	+	7.52906i	0.0441302	+	0.250275i
$906$	−1.15697	+	1.52752i	−0.0384378	+	0.0507484i
$907$	−15.5378	−	13.0378i	−0.515925	−	0.432913i	0.347283	−	0.937760i	$-0.387104\pi$
$907$	−15.5378	−	13.0378i	−0.515925	−	0.432913i	−0.863208	+	0.504848i	$0.831549\pi$
$908$	2.92027	+	5.05806i	0.0969126	+	0.167858i
$909$	−26.6101	+	27.2856i	−0.882602	+	0.905005i
$910$	0.580034	−	1.00465i	0.0192279	−	0.0333038i
$911$	−38.9702	+	14.1840i	−1.29114	+	0.469937i	−0.894101	−	0.447865i	$-0.852185\pi$
$911$	−38.9702	+	14.1840i	−1.29114	+	0.469937i	−0.397039	+	0.917802i	$0.629962\pi$
$912$	28.6767	−	18.5227i	0.949580	−	0.613348i
$913$	−7.45834	+	6.25829i	−0.246835	+	0.207119i
$914$	9.34288	+	3.40053i	0.309035	+	0.112480i
$915$	−7.60840	+	24.6687i	−0.251526	+	0.815521i
$916$	−1.40136	+	7.94750i	−0.0463022	+	0.262593i
$917$	−18.9695			−0.626427
$918$	−20.9291	+	34.2565i	−0.690763	+	1.13063i
$919$	24.1973			0.798196			0.399098	−	0.916908i	$-0.369323\pi$
$919$	24.1973			0.798196			0.399098	+	0.916908i	$0.369323\pi$
$920$	4.24248	−	24.0603i	0.139871	−	0.793245i
$921$	−25.8200	−	27.8255i	−0.850797	−	0.916881i
$922$	25.2668	+	9.19637i	0.832118	+	0.302866i
$923$	−4.16455	+	3.49447i	−0.137078	+	0.115022i
$924$	0.747479	+	0.383179i	0.0245903	+	0.0126057i
$925$	−6.99966	+	2.54767i	−0.230147	+	0.0837668i
$926$	9.79861	−	16.9717i	0.322002	−	0.557724i
$927$	10.0034	−	22.1736i	0.328554	−	0.728276i
$928$	−8.84534	−	15.3206i	−0.290363	−	0.502923i
$929$	23.1234	+	19.4028i	0.758655	+	0.636587i	0.937776	−	0.347240i	$-0.112881\pi$
$929$	23.1234	+	19.4028i	0.758655	+	0.636587i	−0.179122	+	0.983827i	$0.557326\pi$
$930$	−0.978094	−	2.32010i	−0.0320730	−	0.0760791i
$931$	1.19858	+	6.79746i	0.0392817	+	0.222778i
$932$	−1.23933	−	7.02861i	−0.0405957	−	0.230230i
$933$	−10.9541	−	25.9838i	−0.358621	−	0.850673i
$934$	−17.8225	−	14.9549i	−0.583171	−	0.489338i
$935$	3.25525	+	5.63826i	0.106458	+	0.184391i
$936$	8.53392	−	0.854509i	0.278940	−	0.0279305i
$937$	−9.46312	+	16.3906i	−0.309147	+	0.535458i	−0.978176	−	0.207778i	$-0.933377\pi$
$937$	−9.46312	+	16.3906i	−0.309147	+	0.535458i	0.669029	+	0.743236i	$0.266710\pi$
$938$	−6.53055	+	2.37693i	−0.213230	+	0.0776094i
$939$	23.4149	+	12.0032i	0.764117	+	0.391708i
$940$	−3.04779	+	2.55740i	−0.0994079	+	0.0834132i
$941$	12.5242	+	4.55845i	0.408278	+	0.148601i	0.537991	−	0.842951i	$-0.319183\pi$
$941$	12.5242	+	4.55845i	0.408278	+	0.148601i	−0.129713	+	0.991552i	$0.541406\pi$
$942$	3.40451	+	3.66895i	0.110925	+	0.119541i
$943$	−0.135996	+	0.771271i	−0.00442864	+	0.0251160i
$944$	37.2623			1.21279
$945$	−0.774949	−	5.13804i	−0.0252091	−	0.167140i
$946$	−5.85906			−0.190494
$947$	3.26602	−	18.5225i	0.106131	−	0.601902i	−0.884631	−	0.466292i	$-0.845590\pi$
$947$	3.26602	−	18.5225i	0.106131	−	0.601902i	0.990762	−	0.135610i	$-0.0432993\pi$
$948$	−0.742005	+	2.40580i	−0.0240992	+	0.0781367i
$949$	−8.77663	−	3.19443i	−0.284902	−	0.103696i
$950$	−6.55223	+	5.49797i	−0.212582	+	0.178378i
$951$	41.6332	−	26.8915i	1.35005	−	0.872016i
$952$	17.8910	−	6.51178i	0.579850	−	0.211048i
$953$	−15.0816	+	26.1221i	−0.488541	+	0.846177i	−0.999913	−	0.0131818i	$-0.995804\pi$
$953$	−15.0816	+	26.1221i	−0.488541	+	0.846177i	0.511372	+	0.859359i	$0.329137\pi$
$954$	1.16563	+	4.14188i	0.0377388	+	0.134098i
$955$	−0.258881	−	0.448395i	−0.00837719	−	0.0145097i
$956$	10.7184	+	8.99380i	0.346658	+	0.290880i
$957$	7.51986	−	9.92827i	0.243083	−	0.320935i
$958$	−9.18647	−	52.0991i	−0.296801	−	1.68324i
$959$	−1.48244	−	8.40735i	−0.0478706	−	0.271487i
$960$	15.2867	+	1.91517i	0.493376	+	0.0618117i
$961$	−22.6932	−	19.0419i	−0.732039	−	0.614254i
$962$	−4.32061	−	7.48351i	−0.139302	−	0.241278i
$963$	−36.4008	+	17.5326i	−1.17300	+	0.564982i
$964$	−0.940504	+	1.62900i	−0.0302916	+	0.0524666i
$965$	9.96036	−	3.62527i	0.320635	−	0.116702i
$966$	−0.856472	−	17.1498i	−0.0275565	−	0.551786i
$967$	−34.5683	+	29.0063i	−1.11164	+	0.932778i	−0.998152	−	0.0607609i	$-0.980647\pi$
$967$	−34.5683	+	29.0063i	−1.11164	+	0.932778i	−0.113490	+	0.993539i	$0.536203\pi$
$968$	28.4372	+	10.3503i	0.914006	+	0.332671i
$969$	−72.6647	+	16.5877i	−2.33432	+	0.532874i
$970$	1.21421	−	6.88613i	0.0389859	−	0.221100i
$971$	−39.8627			−1.27926			−0.639628	−	0.768684i	$-0.720912\pi$
$971$	−39.8627			−1.27926			−0.639628	+	0.768684i	$0.720912\pi$
$972$	5.18148	−	5.05552i	0.166196	−	0.162156i
$973$	7.21157			0.231192
$974$	−1.53875	+	8.72670i	−0.0493048	+	0.279622i
$975$	−1.58079	+	0.360859i	−0.0506257	+	0.0115567i
$976$	−39.9938	−	14.5565i	−1.28017	−	0.465944i
$977$	17.4320	−	14.6272i	0.557701	−	0.467966i	−0.319838	−	0.947472i	$-0.603629\pi$
$977$	17.4320	−	14.6272i	0.557701	−	0.467966i	0.877539	+	0.479506i	$0.159184\pi$
$978$	−0.662893	−	13.2736i	−0.0211970	−	0.424444i
$979$	−7.23920	+	2.63485i	−0.231366	+	0.0842103i
$980$	−0.232197	+	0.402177i	−0.00741727	+	0.0128471i
$981$	−24.4412	+	11.7722i	−0.780349	+	0.375859i
$982$	−17.3484	−	30.0482i	−0.553608	−	0.958878i
$983$	−1.13571	−	0.952971i	−0.0362234	−	0.0303950i	0.624496	−	0.781028i	$-0.285304\pi$
$983$	−1.13571	−	0.952971i	−0.0362234	−	0.0303950i	−0.660720	+	0.750633i	$0.729749\pi$
$984$	−0.513789	−	0.0643691i	−0.0163790	−	0.00205201i
$985$	−1.14421	−	6.48916i	−0.0364577	−	0.206762i
$986$	−9.23769	−	52.3895i	−0.294188	−	1.66842i
$987$	−8.95947	+	11.8289i	−0.285183	+	0.376519i
$988$	2.29869	+	1.92883i	0.0731310	+	0.0613642i
$989$	−18.1109	−	31.3691i	−0.575894	−	0.997478i
$990$	1.05170	+	3.73703i	0.0334252	+	0.118771i
$991$	7.06097	−	12.2300i	0.224299	−	0.388498i	−0.731810	−	0.681509i	$-0.761324\pi$
$991$	7.06097	−	12.2300i	0.224299	−	0.388498i	0.956109	+	0.293011i	$0.0946574\pi$
$992$	−2.83207	+	1.03079i	−0.0899182	+	0.0327276i
$993$	−52.6205	+	33.9883i	−1.66986	+	1.07859i
$994$	−5.51270	+	4.62570i	−0.174852	+	0.146718i
$995$	−11.5138	−	4.19070i	−0.365014	−	0.132854i
$996$	2.21022	−	7.16617i	0.0700334	−	0.227069i
$997$	−8.58494	+	48.6876i	−0.271888	+	1.54195i	0.476789	+	0.879018i	$0.341800\pi$
$997$	−8.58494	+	48.6876i	−0.271888	+	1.54195i	−0.748677	+	0.662935i	$0.769311\pi$
$998$	13.5372			0.428514
$999$	−36.0314	−	14.1372i	−1.13998	−	0.447281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bt.c.106.7	✓	120
27.13	even	9	inner	945.2.bt.c.526.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.bt.c.106.7	✓	120	1.1	even	1	trivial
945.2.bt.c.526.7	yes	120	27.13	even	9	inner

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bt (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.215184 + 1.22037i) q^{2} +(1.68861 - 0.385473i) q^{3} +(0.436388 + 0.158832i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(0.107057 + 2.14368i) q^{6} +(-0.939693 + 0.342020i) q^{7} +(-1.52693 + 2.64473i) q^{8} +(2.70282 - 1.30183i) q^{9} +O(q^{10})\)	\(q+(-0.215184 + 1.22037i) q^{2} +(1.68861 - 0.385473i) q^{3} +(0.436388 + 0.158832i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(0.107057 + 2.14368i) q^{6} +(-0.939693 + 0.342020i) q^{7} +(-1.52693 + 2.64473i) q^{8} +(2.70282 - 1.30183i) q^{9} +(-0.619598 - 1.07317i) q^{10} +(-0.799964 - 0.671250i) q^{11} +(0.798116 + 0.0999905i) q^{12} +(-0.162560 - 0.921924i) q^{13} +(-0.215184 - 1.22037i) q^{14} +(-1.04577 + 1.38071i) q^{15} +(-2.18748 - 1.83551i) q^{16} +(3.11722 + 5.39919i) q^{17} +(1.00711 + 3.57857i) q^{18} +(-3.45116 + 5.97759i) q^{19} +(-0.436388 + 0.158832i) q^{20} +(-1.45494 + 0.939765i) q^{21} +(0.991312 - 0.831810i) q^{22} +(7.51771 + 2.73622i) q^{23} +(-1.55893 + 5.05451i) q^{24} +(0.173648 - 0.984808i) q^{25} +1.16007 q^{26} +(4.06220 - 3.24015i) q^{27} -0.464394 q^{28} +(-1.19571 + 6.78120i) q^{29} +(-1.45994 - 1.57334i) q^{30} +(1.10234 + 0.401218i) q^{31} +(-1.96808 + 1.65142i) q^{32} +(-1.60958 - 0.825116i) q^{33} +(-7.25978 + 2.64235i) q^{34} +(0.500000 - 0.866025i) q^{35} +(1.38625 - 0.138807i) q^{36} +(-3.72444 - 6.45092i) q^{37} +(-6.55223 - 5.49797i) q^{38} +(-0.629877 - 1.49411i) q^{39} +(-0.530298 - 3.00747i) q^{40} +(0.0169991 + 0.0964067i) q^{41} +(-0.833781 - 1.97778i) q^{42} +(-3.46837 - 2.91031i) q^{43} +(-0.242479 - 0.419986i) q^{44} +(-1.23368 + 2.73460i) q^{45} +(-4.95689 + 8.58559i) q^{46} +(8.05063 - 2.93019i) q^{47} +(-4.40134 - 2.25625i) q^{48} +(0.766044 - 0.642788i) q^{49} +(1.16446 + 0.423830i) q^{50} +(7.34502 + 7.91553i) q^{51} +(0.0754920 - 0.428136i) q^{52} +1.15741 q^{53} +(3.08005 + 5.65461i) q^{54} +1.04428 q^{55} +(0.530298 - 3.00747i) q^{56} +(-3.52348 + 11.4242i) q^{57} +(-8.01827 - 2.91841i) q^{58} +(-9.99619 + 8.38780i) q^{59} +(-0.675665 + 0.436422i) q^{60} +(14.0056 - 5.09764i) q^{61} +(-0.726839 + 1.25892i) q^{62} +(-2.09457 + 2.14774i) q^{63} +(-4.44739 - 7.70310i) q^{64} +(0.717130 + 0.601743i) q^{65} +(1.35330 - 1.78673i) q^{66} +(-0.973855 - 5.52301i) q^{67} +(0.502754 + 2.85126i) q^{68} +(13.7492 + 1.72255i) q^{69} +(0.949279 + 0.796540i) q^{70} +(-2.90362 - 5.02922i) q^{71} +(-0.684052 + 9.13603i) q^{72} +(4.98848 - 8.64030i) q^{73} +(8.67395 - 3.15706i) q^{74} +(-0.0863920 - 1.72989i) q^{75} +(-2.45548 + 2.06039i) q^{76} +(0.981302 + 0.357165i) q^{77} +(1.95891 - 0.447175i) q^{78} +(-0.543518 + 3.08244i) q^{79} +2.85555 q^{80} +(5.61049 - 7.03721i) q^{81} -0.121310 q^{82} +(1.61898 - 9.18170i) q^{83} +(-0.784182 + 0.179011i) q^{84} +(-5.85847 - 2.13231i) q^{85} +(4.29798 - 3.60644i) q^{86} +(0.594879 + 11.9117i) q^{87} +(2.99676 - 1.09073i) q^{88} +(3.68857 - 6.38879i) q^{89} +(-3.07175 - 2.09399i) q^{90} +(0.468073 + 0.810726i) q^{91} +(2.84604 + 2.38811i) q^{92} +(2.01608 + 0.252580i) q^{93} +(1.84355 + 10.4553i) q^{94} +(-1.19858 - 6.79746i) q^{95} +(-2.68675 + 3.54725i) q^{96} +(4.32253 + 3.62703i) q^{97} +(0.619598 + 1.07317i) q^{98} +(-3.03601 - 0.772853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 9 q^{8}+O(q^{10}) \) 120 * q + 9 * q^8	\( 120 q + 9 q^{8} - 3 q^{10} - 24 q^{12} + 3 q^{13} + 6 q^{15} - 12 q^{16} + 60 q^{18} - 42 q^{19} + 9 q^{22} + 6 q^{23} - 60 q^{24} - 18 q^{26} - 42 q^{27} + 138 q^{28} - 18 q^{29} + 3 q^{30} - 21 q^{32} + 12 q^{33} + 39 q^{34} + 60 q^{35} + 6 q^{36} - 54 q^{37} - 117 q^{38} - 33 q^{39} - 9 q^{40} + 9 q^{41} + 3 q^{42} + 9 q^{43} + 24 q^{44} + 12 q^{45} - 24 q^{46} - 3 q^{47} + 180 q^{48} + 6 q^{51} + 39 q^{52} - 36 q^{53} - 48 q^{54} + 24 q^{55} + 9 q^{56} - 42 q^{57} - 27 q^{58} + 12 q^{59} + 15 q^{60} + 24 q^{61} - 27 q^{62} + 3 q^{63} - 123 q^{64} + 6 q^{65} - 75 q^{66} - 42 q^{67} - 111 q^{68} + 6 q^{69} + 30 q^{71} + 147 q^{72} - 66 q^{73} - 27 q^{74} - 24 q^{76} - 9 q^{77} - 15 q^{78} - 42 q^{79} - 174 q^{80} - 48 q^{81} + 132 q^{82} + 12 q^{83} - 15 q^{85} + 33 q^{86} + 42 q^{87} + 33 q^{88} + 57 q^{89} - 39 q^{90} - 42 q^{91} - 123 q^{92} - 72 q^{93} + 57 q^{94} - 21 q^{95} - 168 q^{96} + 93 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) \) 120 * q + 9 * q^8 - 3 * q^10 - 24 * q^12 + 3 * q^13 + 6 * q^15 - 12 * q^16 + 60 * q^18 - 42 * q^19 + 9 * q^22 + 6 * q^23 - 60 * q^24 - 18 * q^26 - 42 * q^27 + 138 * q^28 - 18 * q^29 + 3 * q^30 - 21 * q^32 + 12 * q^33 + 39 * q^34 + 60 * q^35 + 6 * q^36 - 54 * q^37 - 117 * q^38 - 33 * q^39 - 9 * q^40 + 9 * q^41 + 3 * q^42 + 9 * q^43 + 24 * q^44 + 12 * q^45 - 24 * q^46 - 3 * q^47 + 180 * q^48 + 6 * q^51 + 39 * q^52 - 36 * q^53 - 48 * q^54 + 24 * q^55 + 9 * q^56 - 42 * q^57 - 27 * q^58 + 12 * q^59 + 15 * q^60 + 24 * q^61 - 27 * q^62 + 3 * q^63 - 123 * q^64 + 6 * q^65 - 75 * q^66 - 42 * q^67 - 111 * q^68 + 6 * q^69 + 30 * q^71 + 147 * q^72 - 66 * q^73 - 27 * q^74 - 24 * q^76 - 9 * q^77 - 15 * q^78 - 42 * q^79 - 174 * q^80 - 48 * q^81 + 132 * q^82 + 12 * q^83 - 15 * q^85 + 33 * q^86 + 42 * q^87 + 33 * q^88 + 57 * q^89 - 39 * q^90 - 42 * q^91 - 123 * q^92 - 72 * q^93 + 57 * q^94 - 21 * q^95 - 168 * q^96 + 93 * q^97 + 3 * q^98 + 51 * q^99

Introduction

L-functions

Modular forms

Varieties

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