LMFDB - Embedded newform 354.2.e.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	354.25
Dual form			354.2.e.a.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.796093 + 0.605174i) q^{2} +(0.468408 + 0.883512i) q^{3} +(0.267528 + 0.963550i) q^{4} +(2.69226 + 2.55024i) q^{5} +(-0.161782 + 0.986827i) q^{6} +(1.09972 - 1.29469i) q^{7} +(-0.370138 + 0.928977i) q^{8} +(-0.561187 + 0.827689i) q^{9} +O(q^{10})$	\(q+(0.796093 + 0.605174i) q^{2} +(0.468408 + 0.883512i) q^{3} +(0.267528 + 0.963550i) q^{4} +(2.69226 + 2.55024i) q^{5} +(-0.161782 + 0.986827i) q^{6} +(1.09972 - 1.29469i) q^{7} +(-0.370138 + 0.928977i) q^{8} +(-0.561187 + 0.827689i) q^{9} +(0.599947 + 3.65951i) q^{10} +(-1.17064 - 0.704350i) q^{11} +(-0.725995 + 0.687699i) q^{12} +(-3.95550 - 5.83393i) q^{13} +(1.65899 - 0.365171i) q^{14} +(-0.992093 + 3.57320i) q^{15} +(-0.856857 + 0.515554i) q^{16} +(-2.70596 - 3.18570i) q^{17} +(-0.947653 + 0.319302i) q^{18} +(1.39322 - 0.644571i) q^{19} +(-1.73703 + 3.27639i) q^{20} +(1.65899 + 0.365171i) q^{21} +(-0.505683 - 1.26917i) q^{22} +(6.96978 + 2.34839i) q^{23} +(-0.994138 + 0.108119i) q^{24} +(0.473822 + 8.73914i) q^{25} +(0.381595 - 7.03811i) q^{26} +(-0.994138 - 0.108119i) q^{27} +(1.54170 + 0.713267i) q^{28} +(-4.99346 + 3.79593i) q^{29} +(-2.95220 + 2.24421i) q^{30} +(-2.98078 - 1.37906i) q^{31} +(-0.994138 - 0.108119i) q^{32} +(0.0739647 - 1.36420i) q^{33} +(-0.226291 - 4.17369i) q^{34} +(6.26249 - 0.681087i) q^{35} +(-0.947653 - 0.319302i) q^{36} +(0.201184 + 0.504934i) q^{37} +(1.49921 + 0.330001i) q^{38} +(3.30155 - 6.22739i) q^{39} +(-3.36562 + 1.55710i) q^{40} +(-2.08278 + 0.701771i) q^{41} +(1.09972 + 1.29469i) q^{42} +(-2.42978 + 1.46195i) q^{43} +(0.365498 - 1.31640i) q^{44} +(-3.62167 + 0.797189i) q^{45} +(4.12741 + 6.08747i) q^{46} +(7.38682 - 6.99717i) q^{47} +(-0.856857 - 0.515554i) q^{48} +(0.665637 + 4.06020i) q^{49} +(-4.91149 + 7.24391i) q^{50} +(1.54711 - 3.88296i) q^{51} +(4.56307 - 5.37206i) q^{52} +(1.60247 - 9.77463i) q^{53} +(-0.725995 - 0.687699i) q^{54} +(-1.35540 - 4.88170i) q^{55} +(0.795687 + 1.50083i) q^{56} +(1.22208 + 0.929001i) q^{57} -6.27246 q^{58} +(7.68030 - 0.114297i) q^{59} -3.70837 q^{60} +(-1.84013 - 1.39883i) q^{61} +(-1.53841 - 2.90175i) q^{62} +(0.454451 + 1.63679i) q^{63} +(-0.725995 - 0.687699i) q^{64} +(4.22870 - 25.7939i) q^{65} +(0.884460 - 1.04127i) q^{66} +(-0.570288 + 1.43131i) q^{67} +(2.34566 - 3.45959i) q^{68} +(1.18987 + 7.25789i) q^{69} +(5.39770 + 3.24769i) q^{70} +(-10.7010 + 10.1365i) q^{71} +(-0.561187 - 0.827689i) q^{72} +(-14.3957 + 3.16872i) q^{73} +(-0.145412 + 0.523726i) q^{74} +(-7.49919 + 4.51211i) q^{75} +(0.993801 + 1.16999i) q^{76} +(-2.19929 + 0.741026i) q^{77} +(6.39700 - 2.95957i) q^{78} +(0.264096 - 0.498137i) q^{79} +(-3.62167 - 0.797189i) q^{80} +(-0.370138 - 0.928977i) q^{81} +(-2.08278 - 0.701771i) q^{82} +(14.5653 - 1.58407i) q^{83} +(0.0919660 + 1.69621i) q^{84} +(0.839169 - 15.4776i) q^{85} +(-2.81906 - 0.306592i) q^{86} +(-5.69273 - 2.63374i) q^{87} +(1.08762 - 0.826790i) q^{88} +(1.93974 - 1.47455i) q^{89} +(-3.36562 - 1.55710i) q^{90} +(-11.9030 - 1.29453i) q^{91} +(-0.398180 + 7.34399i) q^{92} +(-0.177810 - 3.27952i) q^{93} +(10.1151 - 1.10008i) q^{94} +(5.39471 + 1.81769i) q^{95} +(-0.370138 - 0.928977i) q^{96} +(1.56981 + 0.345541i) q^{97} +(-1.92722 + 3.63513i) q^{98} +(1.23993 - 0.573653i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{6}{29}\right)$	$1$

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 $

$2$	0.796093	+	0.605174i	0.562923	+	0.427923i
$2$	0.796093	+	0.605174i	0.562923	+	0.427923i
$3$	0.468408	+	0.883512i	0.270436	+	0.510096i
$3$	0.468408	+	0.883512i	0.270436	+	0.510096i
$4$	0.267528	+	0.963550i	0.133764	+	0.481775i
$5$	2.69226	+	2.55024i	1.20401	+	1.14050i	0.986382	+	0.164471i	$0.0525919\pi$
$5$	2.69226	+	2.55024i	1.20401	+	1.14050i	0.217632	+	0.976031i	$0.430167\pi$
$6$	−0.161782	+	0.986827i	−0.0660472	+	0.402870i
$7$	1.09972	−	1.29469i	0.415654	−	0.489346i	−0.513994	−	0.857794i	$-0.671835\pi$
$7$	1.09972	−	1.29469i	0.415654	−	0.489346i	0.929649	+	0.368448i	$0.120111\pi$
$8$	−0.370138	+	0.928977i	−0.130864	+	0.328443i
$9$	−0.561187	+	0.827689i	−0.187062	+	0.275896i
$10$	0.599947	+	3.65951i	0.189720	+	1.15724i
$11$	−1.17064	−	0.704350i	−0.352961	−	0.212370i	0.328020	−	0.944671i	$-0.393619\pi$
$11$	−1.17064	−	0.704350i	−0.352961	−	0.212370i	−0.680981	+	0.732301i	$0.738446\pi$
$12$	−0.725995	+	0.687699i	−0.209577	+	0.198522i
$13$	−3.95550	−	5.83393i	−1.09706	−	1.61804i	−0.723331	−	0.690501i	$-0.757390\pi$
$13$	−3.95550	−	5.83393i	−1.09706	−	1.61804i	−0.373727	−	0.927539i	$-0.621920\pi$
$14$	1.65899	−	0.365171i	0.443384	−	0.0975961i
$15$	−0.992093	+	3.57320i	−0.256157	+	0.922595i
$16$	−0.856857	+	0.515554i	−0.214214	+	0.128888i
$17$	−2.70596	−	3.18570i	−0.656291	−	0.772646i	0.328852	−	0.944382i	$-0.393338\pi$
$17$	−2.70596	−	3.18570i	−0.656291	−	0.772646i	−0.985143	+	0.171736i	$0.945062\pi$
$18$	−0.947653	+	0.319302i	−0.223364	+	0.0752601i
$19$	1.39322	−	0.644571i	0.319626	−	0.147875i	−0.253515	−	0.967331i	$-0.581587\pi$
$19$	1.39322	−	0.644571i	0.319626	−	0.147875i	0.573141	+	0.819457i	$0.305725\pi$
$20$	−1.73703	+	3.27639i	−0.388412	+	0.732622i
$21$	1.65899	+	0.365171i	0.362021	+	0.0796869i
$22$	−0.505683	−	1.26917i	−0.107812	−	0.270588i
$23$	6.96978	+	2.34839i	1.45330	+	0.489673i	0.931609	−	0.363462i	$-0.118405\pi$
$23$	6.96978	+	2.34839i	1.45330	+	0.489673i	0.521690	+	0.853135i	$0.325302\pi$
$24$	−0.994138	+	0.108119i	−0.202928	+	0.0220697i
$25$	0.473822	+	8.73914i	0.0947645	+	1.74783i
$26$	0.381595	−	7.03811i	0.0748370	−	1.38029i
$27$	−0.994138	−	0.108119i	−0.191322	−	0.0208075i
$28$	1.54170	+	0.713267i	0.291354	+	0.134795i
$29$	−4.99346	+	3.79593i	−0.927262	+	0.704886i	−0.955586	−	0.294713i	$-0.904776\pi$
$29$	−4.99346	+	3.79593i	−0.927262	+	0.704886i	0.0283239	+	0.999599i	$0.490983\pi$
$30$	−2.95220	+	2.24421i	−0.538996	+	0.409734i
$31$	−2.98078	−	1.37906i	−0.535364	−	0.247686i	0.133528	−	0.991045i	$-0.457369\pi$
$31$	−2.98078	−	1.37906i	−0.535364	−	0.247686i	−0.668892	+	0.743359i	$0.733231\pi$
$32$	−0.994138	−	0.108119i	−0.175740	−	0.0191129i
$33$	0.0739647	−	1.36420i	0.0128756	−	0.237476i
$34$	−0.226291	−	4.17369i	−0.0388086	−	0.715782i
$35$	6.26249	−	0.681087i	1.05855	−	0.115125i
$36$	−0.947653	−	0.319302i	−0.157942	−	0.0532169i
$37$	0.201184	+	0.504934i	0.0330745	+	0.0830107i	0.944586	−	0.328263i	$-0.106463\pi$
$37$	0.201184	+	0.504934i	0.0330745	+	0.0830107i	−0.911512	+	0.411274i	$0.865084\pi$
$38$	1.49921	+	0.330001i	0.243204	+	0.0535332i
$39$	3.30155	−	6.22739i	0.528672	−	0.997181i
$40$	−3.36562	+	1.55710i	−0.532151	+	0.246199i
$41$	−2.08278	+	0.701771i	−0.325276	+	0.109598i	−0.477202	−	0.878794i	$-0.658349\pi$
$41$	−2.08278	+	0.701771i	−0.325276	+	0.109598i	0.151926	+	0.988392i	$0.451452\pi$
$42$	1.09972	+	1.29469i	0.169690	+	0.199775i
$43$	−2.42978	+	1.46195i	−0.370538	+	0.222945i	−0.688627	−	0.725115i	$-0.741786\pi$
$43$	−2.42978	+	1.46195i	−0.370538	+	0.222945i	0.318089	+	0.948061i	$0.396959\pi$
$44$	0.365498	−	1.31640i	0.0551008	−	0.198455i
$45$	−3.62167	+	0.797189i	−0.539886	+	0.118838i
$46$	4.12741	+	6.08747i	0.608553	+	0.897548i
$47$	7.38682	−	6.99717i	1.07748	−	1.02064i	0.0777590	−	0.996972i	$-0.475224\pi$
$47$	7.38682	−	6.99717i	1.07748	−	1.02064i	0.999720	−	0.0236699i	$-0.00753508\pi$
$48$	−0.856857	−	0.515554i	−0.123677	−	0.0744138i
$49$	0.665637	+	4.06020i	0.0950909	+	0.580029i
$50$	−4.91149	+	7.24391i	−0.694590	+	1.02444i
$51$	1.54711	−	3.88296i	0.216639	−	0.543722i
$52$	4.56307	−	5.37206i	0.632784	−	0.744971i
$53$	1.60247	−	9.77463i	0.220116	−	1.34265i	−0.613233	−	0.789902i	$-0.710131\pi$
$53$	1.60247	−	9.77463i	0.220116	−	1.34265i	0.833349	−	0.552747i	$-0.186420\pi$
$54$	−0.725995	−	0.687699i	−0.0987955	−	0.0935840i
$55$	−1.35540	−	4.88170i	−0.182762	−	0.658249i
$56$	0.795687	+	1.50083i	0.106328	+	0.200556i
$57$	1.22208	+	0.929001i	0.161868	+	0.123049i
$58$	−6.27246			−0.823614
$59$	7.68030	−	0.114297i	0.999889	−	0.0148802i
$59$	7.68030	−	0.114297i	0.999889	−	0.0148802i
$60$	−3.70837			−0.478748
$61$	−1.84013	−	1.39883i	−0.235604	−	0.179101i	0.480710	−	0.876880i	$-0.340379\pi$
$61$	−1.84013	−	1.39883i	−0.235604	−	0.179101i	−0.716314	+	0.697778i	$0.754172\pi$
$62$	−1.53841	−	2.90175i	−0.195378	−	0.368522i
$63$	0.454451	+	1.63679i	0.0572555	+	0.206216i
$64$	−0.725995	−	0.687699i	−0.0907494	−	0.0859624i
$65$	4.22870	−	25.7939i	0.524505	−	3.19934i
$66$	0.884460	−	1.04127i	0.108870	−	0.128171i
$67$	−0.570288	+	1.43131i	−0.0696718	+	0.174863i	−0.959689	−	0.281064i	$-0.909313\pi$
$67$	−0.570288	+	1.43131i	−0.0696718	+	0.174863i	0.890017	+	0.455927i	$0.150692\pi$
$68$	2.34566	−	3.45959i	0.284453	−	0.419537i
$69$	1.18987	+	7.25789i	0.143244	+	0.873747i
$70$	5.39770	+	3.24769i	0.645148	+	0.388173i
$71$	−10.7010	+	10.1365i	−1.26997	+	1.20298i	−0.301610	+	0.953431i	$0.597524\pi$
$71$	−10.7010	+	10.1365i	−1.26997	+	1.20298i	−0.968362	+	0.249550i	$0.919717\pi$
$72$	−0.561187	−	0.827689i	−0.0661365	−	0.0975441i
$73$	−14.3957	+	3.16872i	−1.68488	+	0.370871i	−0.951189	−	0.308608i	$-0.900137\pi$
$73$	−14.3957	+	3.16872i	−1.68488	+	0.370871i	−0.733695	+	0.679479i	$0.762206\pi$
$74$	−0.145412	+	0.523726i	−0.0169038	+	0.0608819i
$75$	−7.49919	+	4.51211i	−0.865932	+	0.521014i
$76$	0.993801	+	1.16999i	0.113997	+	0.134207i
$77$	−2.19929	+	0.741026i	−0.250632	+	0.0844478i
$78$	6.39700	−	2.95957i	0.724318	−	0.335105i
$79$	0.264096	−	0.498137i	0.0297131	−	0.0560448i	−0.868211	−	0.496195i	$-0.834730\pi$
$79$	0.264096	−	0.498137i	0.0297131	−	0.0560448i	0.897924	+	0.440150i	$0.145075\pi$
$80$	−3.62167	−	0.797189i	−0.404915	−	0.0891284i
$81$	−0.370138	−	0.928977i	−0.0411265	−	0.103220i
$82$	−2.08278	−	0.701771i	−0.230005	−	0.0774976i
$83$	14.5653	−	1.58407i	1.59875	−	0.173875i	0.735098	−	0.677960i	$-0.237136\pi$
$83$	14.5653	−	1.58407i	1.59875	−	0.173875i	0.863654	+	0.504086i	$0.168170\pi$
$84$	0.0919660	+	1.69621i	0.0100343	+	0.185072i
$85$	0.839169	−	15.4776i	0.0910207	−	1.67878i
$86$	−2.81906	−	0.306592i	−0.303988	−	0.0330606i
$87$	−5.69273	−	2.63374i	−0.610324	−	0.282366i
$88$	1.08762	−	0.826790i	0.115941	−	0.0881361i
$89$	1.93974	−	1.47455i	0.205612	−	0.156302i	−0.497301	−	0.867578i	$-0.665675\pi$
$89$	1.93974	−	1.47455i	0.205612	−	0.156302i	0.702913	+	0.711276i	$0.251882\pi$
$90$	−3.36562	−	1.55710i	−0.354768	−	0.164133i
$91$	−11.9030	−	1.29453i	−1.24778	−	0.135704i
$92$	−0.398180	+	7.34399i	−0.0415131	+	0.765664i
$93$	−0.177810	−	3.27952i	−0.0184381	−	0.340070i
$94$	10.1151	−	1.10008i	1.04329	−	0.113465i
$95$	5.39471	+	1.81769i	0.553485	+	0.186491i
$96$	−0.370138	−	0.928977i	−0.0377771	−	0.0948133i
$97$	1.56981	+	0.345541i	0.159390	+	0.0350844i	0.293948	−	0.955821i	$-0.405031\pi$
$97$	1.56981	+	0.345541i	0.159390	+	0.0350844i	−0.134559	+	0.990906i	$0.542962\pi$
$98$	−1.92722	+	3.63513i	−0.194679	+	0.367203i
$99$	1.23993	−	0.573653i	0.124618	−	0.0576543i
$100$	−8.29384	+	2.79452i	−0.829384	+	0.279452i
$101$	5.59063	+	6.58180i	0.556289	+	0.654914i	0.966376	−	0.257133i	$-0.0827777\pi$
$101$	5.59063	+	6.58180i	0.556289	+	0.654914i	−0.410087	+	0.912046i	$0.634502\pi$
$102$	3.58151	−	2.15492i	0.354622	−	0.213369i
$103$	−2.26391	+	8.15386i	−0.223069	+	0.803423i	0.764283	+	0.644881i	$0.223093\pi$
$103$	−2.26391	+	8.15386i	−0.223069	+	0.803423i	−0.987352	+	0.158542i	$0.949321\pi$
$104$	6.88366	−	1.51521i	0.674999	−	0.148578i
$105$	3.53515	+	5.21396i	0.344995	+	0.508830i
$106$	7.19107	−	6.81174i	0.698458	−	0.661615i
$107$	9.00760	+	5.41969i	0.870797	+	0.523941i	0.879434	−	0.476021i	$-0.157922\pi$
$107$	9.00760	+	5.41969i	0.870797	+	0.523941i	−0.00863651	+	0.999963i	$0.502749\pi$
$108$	−0.161782	−	0.986827i	−0.0155675	−	0.0949574i
$109$	8.72807	−	12.8729i	0.835998	−	1.23300i	−0.134264	−	0.990946i	$-0.542867\pi$
$109$	8.72807	−	12.8729i	0.835998	−	1.23300i	0.970262	−	0.242059i	$-0.0778227\pi$
$110$	1.87526	−	4.70654i	0.178799	−	0.448751i
$111$	−0.351879	+	0.414264i	−0.0333989	+	0.0393202i
$112$	−0.274820	+	1.67633i	−0.0259680	+	0.158398i
$113$	−4.50821	−	4.27040i	−0.424096	−	0.401725i	0.445663	−	0.895201i	$-0.352968\pi$
$113$	−4.50821	−	4.27040i	−0.424096	−	0.401725i	−0.869760	+	0.493475i	$0.835726\pi$
$114$	0.410682	+	1.47914i	0.0384639	+	0.138534i
$115$	12.7755	+	24.0971i	1.19132	+	2.24706i
$116$	−4.99346	−	3.79593i	−0.463631	−	0.352443i
$117$	7.04845			0.651630
$118$	6.18340	+	4.55693i	0.569228	+	0.419499i
$119$	−7.10028			−0.650881
$120$	−2.95220	−	2.24421i	−0.269498	−	0.204867i
$121$	−4.27821	−	8.06955i	−0.388928	−	0.733596i
$122$	−0.618377	−	2.22719i	−0.0559852	−	0.201641i
$123$	−1.59562	−	1.51145i	−0.143872	−	0.136283i
$124$	0.531346	−	3.24107i	0.0477163	−	0.291057i
$125$	−9.00753	+	10.6045i	−0.805658	+	0.948494i
$126$	−0.628755	+	1.57806i	−0.0560140	+	0.140584i
$127$	−7.94193	+	11.7135i	−0.704732	+	1.03940i	0.291823	+	0.956472i	$0.405738\pi$
$127$	−7.94193	+	11.7135i	−0.704732	+	1.03940i	−0.996555	+	0.0829300i	$0.973572\pi$
$128$	−0.161782	−	0.986827i	−0.0142996	−	0.0872240i
$129$	−2.42978	−	1.46195i	−0.213930	−	0.128717i
$130$	18.9762	−	17.9753i	1.66433	−	1.57653i
$131$	−5.43072	−	8.00972i	−0.474485	−	0.699812i	0.512848	−	0.858480i	$-0.328591\pi$
$131$	−5.43072	−	8.00972i	−0.474485	−	0.699812i	−0.987332	+	0.158667i	$0.949280\pi$
$132$	1.33426	−	0.293693i	0.116132	−	0.0255627i
$133$	0.697627	−	2.51263i	0.0604920	−	0.217872i
$134$	−1.32020	+	0.794336i	−0.114048	+	0.0686202i
$135$	−2.40074	−	2.82638i	−0.206623	−	0.243256i
$136$	3.96102	−	1.33462i	0.339655	−	0.114443i
$137$	−19.0383	+	8.80804i	−1.62655	+	0.752522i	−0.999647	−	0.0265754i	$-0.991540\pi$
$137$	−19.0383	+	8.80804i	−1.62655	+	0.752522i	−0.626903	+	0.779097i	$0.715678\pi$
$138$	−3.44504	+	6.49803i	−0.293261	+	0.553149i
$139$	1.75109	+	0.385444i	0.148526	+	0.0326929i	0.288611	−	0.957446i	$-0.406807\pi$
$139$	1.75109	+	0.385444i	0.148526	+	0.0326929i	−0.140085	+	0.990139i	$0.544738\pi$
$140$	2.33165	+	5.85201i	0.197061	+	0.494585i
$141$	9.64213	+	3.24881i	0.812014	+	0.273599i
$142$	−14.6533	+	1.59364i	−1.22968	+	0.133736i
$143$	0.521336	+	9.61548i	0.0435963	+	0.804087i
$144$	0.0541389	−	0.998533i	0.00451158	−	0.0832111i
$145$	−23.1242	−	2.51491i	−1.92036	−	0.208852i
$146$	−13.3779	−	6.18928i	−1.10716	−	0.512229i
$147$	−3.27545	+	2.48993i	−0.270154	+	0.205366i
$148$	−0.432707	+	0.328935i	−0.0355683	+	0.0270383i
$149$	1.21891	+	0.563928i	0.0998571	+	0.0461988i	0.469182	−	0.883102i	$-0.344549\pi$
$149$	1.21891	+	0.563928i	0.0998571	+	0.0461988i	−0.369325	+	0.929300i	$0.620411\pi$
$150$	−8.70067	−	0.946255i	−0.710407	−	0.0772614i
$151$	0.359438	−	6.62944i	0.0292506	−	0.539496i	−0.946782	−	0.321874i	$-0.895687\pi$
$151$	0.359438	−	6.62944i	0.0292506	−	0.539496i	0.976033	−	0.217622i	$-0.0698300\pi$
$152$	0.0831085	+	1.53285i	0.00674099	+	0.124330i
$153$	4.15532	−	0.451918i	0.335938	−	0.0365354i
$154$	−2.19929	−	0.741026i	−0.177224	−	0.0597136i
$155$	−4.50810	−	11.3145i	−0.362099	−	0.908801i
$156$	6.88366	+	1.51521i	0.551134	+	0.121314i
$157$	−5.85219	+	11.0384i	−0.467055	+	0.880960i	0.532352	+	0.846523i	$0.321308\pi$
$157$	−5.85219	+	11.0384i	−0.467055	+	0.880960i	−0.999407	+	0.0344363i	$0.989036\pi$
$158$	0.511704	−	0.236740i	0.0407090	−	0.0188340i
$159$	9.38661	−	3.16272i	0.744407	−	0.250820i
$160$	−2.40074	−	2.82638i	−0.189796	−	0.223445i
$161$	10.7052	−	6.44112i	0.843690	−	0.507631i
$162$	0.267528	−	0.963550i	0.0210190	−	0.0757036i
$163$	14.8614	−	3.27123i	1.16403	−	0.256223i	0.409390	−	0.912360i	$-0.365742\pi$
$163$	14.8614	−	3.27123i	1.16403	−	0.256223i	0.754642	+	0.656137i	$0.227811\pi$
$164$	−1.23339	−	1.81912i	−0.0963119	−	0.142049i
$165$	3.67816	−	3.48414i	0.286345	−	0.271240i
$166$	12.5540	+	7.55349i	0.974379	+	0.586264i
$167$	−0.988673	−	6.03064i	−0.0765058	−	0.466665i	−0.997097	−	0.0761377i	$-0.975741\pi$
$167$	−0.988673	−	6.03064i	−0.0765058	−	0.466665i	0.920592	−	0.390527i	$-0.127707\pi$
$168$	−0.953291	+	1.40600i	−0.0735480	+	0.108475i
$169$	−13.5769	+	34.0755i	−1.04438	+	2.62119i
$170$	10.0347	−	11.8137i	0.769625	−	0.906072i
$171$	−0.248351	+	1.51487i	−0.0189919	+	0.115845i
$172$	−2.05870	−	1.95010i	−0.156974	−	0.148694i
$173$	6.83245	+	24.6083i	0.519462	+	1.87093i	0.490667	+	0.871347i	$0.336753\pi$
$173$	6.83245	+	24.6083i	0.519462	+	1.87093i	0.0287945	+	0.999585i	$0.490833\pi$
$174$	−2.93807	−	5.54179i	−0.222735	−	0.420122i
$175$	11.8355	+	8.99713i	0.894682	+	0.680119i
$176$	1.36620			0.102981
$177$	3.69850	+	6.73210i	0.277996	+	0.506015i
$178$	2.43658			0.182629
$179$	−9.05941	−	6.88678i	−0.677132	−	0.514742i	0.209153	−	0.977883i	$-0.432929\pi$
$179$	−9.05941	−	6.88678i	−0.677132	−	0.514742i	−0.886285	+	0.463141i	$0.846722\pi$
$180$	−1.73703	−	3.27639i	−0.129471	−	0.244207i
$181$	−0.564181	−	2.03200i	−0.0419352	−	0.151037i	0.939618	−	0.342224i	$-0.111180\pi$
$181$	−0.564181	−	2.03200i	−0.0419352	−	0.151037i	−0.981554	+	0.191187i	$0.938766\pi$
$182$	−8.69251	−	8.23399i	−0.644332	−	0.610344i
$183$	0.373950	−	2.28100i	0.0276432	−	0.168616i
$184$	−4.76138	+	5.60553i	−0.351014	+	0.413245i
$185$	−0.746064	+	1.87248i	−0.0548517	+	0.137667i
$186$	1.84313	−	2.71841i	0.135145	−	0.199323i
$187$	0.923852	+	5.63525i	0.0675588	+	0.412090i
$188$	8.71831	+	5.24563i	0.635848	+	0.382577i
$189$	−1.23325	+	1.16820i	−0.0897058	+	0.0849739i
$190$	3.19467	+	4.71179i	0.231766	+	0.341829i
$191$	−4.68103	+	1.03037i	−0.338708	+	0.0745552i	−0.381068	−	0.924547i	$-0.624443\pi$
$191$	−4.68103	+	1.03037i	−0.338708	+	0.0745552i	0.0423598	+	0.999102i	$0.486512\pi$
$192$	0.267528	−	0.963550i	0.0193072	−	0.0695382i
$193$	6.70986	−	4.03719i	0.482986	−	0.290603i	−0.253161	−	0.967424i	$-0.581470\pi$
$193$	6.70986	−	4.03719i	0.482986	−	0.290603i	0.736148	+	0.676821i	$0.236643\pi$
$194$	1.04060	+	1.22509i	0.0747108	+	0.0879563i
$195$	24.7700	−	8.34598i	1.77382	−	0.597668i
$196$	−3.73413	+	1.72759i	−0.266724	+	0.123400i
$197$	−1.22081	+	2.30269i	−0.0869792	+	0.164060i	−0.923185	−	0.384355i	$-0.874424\pi$
$197$	−1.22081	+	2.30269i	−0.0869792	+	0.164060i	0.836206	+	0.548415i	$0.184769\pi$
$198$	1.33426	+	0.293693i	0.0948218	+	0.0208718i
$199$	1.66190	+	4.17105i	0.117809	+	0.295678i	0.976042	−	0.217582i	$-0.0698169\pi$
$199$	1.66190	+	4.17105i	0.117809	+	0.295678i	−0.858233	+	0.513260i	$0.828438\pi$
$200$	−8.29384	−	2.79452i	−0.586463	−	0.197602i
$201$	−1.53171	+	0.166584i	−0.108039	+	0.0117499i
$202$	0.467527	+	8.62303i	0.0328951	+	0.606714i
$203$	−0.576853	+	10.6394i	−0.0404871	+	0.746741i
$204$	4.15532	+	0.451918i	0.290930	+	0.0316406i
$205$	−7.39707	−	3.42225i	−0.516634	−	0.239020i
$206$	−6.73678	+	5.12117i	−0.469374	+	0.356809i
$207$	−5.85509	+	4.45092i	−0.406957	+	0.309360i
$208$	6.39700	+	2.95957i	0.443552	+	0.205209i
$209$	−2.08496	−	0.226753i	−0.144220	−	0.0156848i
$210$	−0.341043	+	6.29018i	−0.0235342	+	0.434063i
$211$	−0.895553	−	16.5175i	−0.0616524	−	1.13711i	−0.851688	−	0.524050i	$-0.824421\pi$
$211$	−0.895553	−	16.5175i	−0.0616524	−	1.13711i	0.790035	−	0.613061i	$-0.210062\pi$
$212$	9.84705	−	1.07093i	0.676298	−	0.0735519i
$213$	−13.9681	−	4.70642i	−0.957082	−	0.322478i
$214$	3.89103	+	9.76574i	0.265985	+	0.667572i
$215$	−10.2699	−	2.26058i	−0.700402	−	0.154170i
$216$	0.468408	−	0.883512i	0.0318712	−	0.0601154i
$217$	−5.06346	+	2.34261i	−0.343730	+	0.159027i
$218$	14.7387	−	4.96606i	0.998233	−	0.336344i
$219$	−9.54265	−	11.2345i	−0.644833	−	0.759156i
$220$	4.34116	−	2.61199i	0.292681	−	0.176100i
$221$	−7.88172	+	28.3874i	−0.530182	+	1.90954i
$222$	−0.530830	+	0.116845i	−0.0356270	+	0.00784210i
$223$	5.19349	+	7.65982i	0.347781	+	0.512939i	0.960842	−	0.277097i	$-0.0893722\pi$
$223$	5.19349	+	7.65982i	0.347781	+	0.512939i	−0.613061	+	0.790036i	$0.710062\pi$
$224$	−1.23325	+	1.16820i	−0.0824001	+	0.0780535i
$225$	−7.49919	−	4.51211i	−0.499946	−	0.300808i
$226$	−1.00462	−	6.12789i	−0.0668261	−	0.407621i
$227$	−3.62522	+	5.34681i	−0.240615	+	0.354880i	−0.928753	−	0.370700i	$-0.879118\pi$
$227$	−3.62522	+	5.34681i	−0.240615	+	0.354880i	0.688138	+	0.725580i	$0.258428\pi$
$228$	−0.568198	+	1.42607i	−0.0376298	+	0.0944438i
$229$	17.4121	−	20.4991i	1.15063	−	1.35462i	0.225825	−	0.974168i	$-0.427492\pi$
$229$	17.4121	−	20.4991i	1.15063	−	1.35462i	0.924800	−	0.380453i	$-0.124232\pi$
$230$	−4.41247	+	26.9149i	−0.290950	+	1.77472i
$231$	−1.68487	−	1.59599i	−0.110856	−	0.105009i
$232$	−1.67806	−	6.04383i	−0.110170	−	0.396797i
$233$	3.38519	+	6.38515i	0.221771	+	0.418305i	0.969285	−	0.245942i	$-0.0790972\pi$
$233$	3.38519	+	6.38515i	0.221771	+	0.418305i	−0.747513	+	0.664247i	$0.768752\pi$
$234$	5.61122	+	4.26554i	0.366817	+	0.278847i
$235$	37.7317			2.46134
$236$	2.16483	+	7.36977i	0.140918	+	0.479731i
$237$	0.563815			0.0366237
$238$	−5.65248	−	4.29690i	−0.366396	−	0.278527i
$239$	2.90758	+	5.48427i	0.188075	+	0.354748i	0.959562	−	0.281498i	$-0.0908313\pi$
$239$	2.90758	+	5.48427i	0.188075	+	0.354748i	−0.771486	+	0.636246i	$0.780486\pi$
$240$	−0.992093	−	3.57320i	−0.0640393	−	0.230649i
$241$	−14.6456	−	13.8730i	−0.943405	−	0.893640i	0.0510618	−	0.998695i	$-0.483739\pi$
$241$	−14.6456	−	13.8730i	−0.943405	−	0.893640i	−0.994466	+	0.105055i	$0.966498\pi$
$242$	1.47763	−	9.01317i	0.0949860	−	0.579389i
$243$	0.647386	−	0.762162i	0.0415298	−	0.0488927i
$244$	0.855554	−	2.14728i	0.0547712	−	0.137465i
$245$	−8.56243	+	12.6286i	−0.547034	+	0.806814i
$246$	−0.355570	−	2.16888i	−0.0226703	−	0.138283i
$247$	−9.27125	−	5.57832i	−0.589915	−	0.354940i
$248$	2.38441	−	2.25863i	0.151410	−	0.143423i
$249$	8.22207	+	12.1266i	0.521052	+	0.768495i
$250$	−13.5884	+	2.99103i	−0.859406	+	0.189170i
$251$	−7.58046	+	27.3023i	−0.478474	+	1.72331i	0.192017	+	0.981392i	$0.438497\pi$
$251$	−7.58046	+	27.3023i	−0.478474	+	1.72331i	−0.670492	+	0.741917i	$0.733917\pi$
$252$	−1.45555	+	0.875773i	−0.0916908	+	0.0551685i
$253$	−6.50501	−	7.65829i	−0.408966	−	0.481472i
$254$	−13.4112	+	4.51876i	−0.841494	+	0.283532i
$255$	14.0677	−	6.50841i	0.880953	−	0.407572i
$256$	0.468408	−	0.883512i	0.0292755	−	0.0552195i
$257$	15.3195	+	3.37208i	0.955606	+	0.210345i	0.665289	−	0.746586i	$-0.268308\pi$
$257$	15.3195	+	3.37208i	0.955606	+	0.210345i	0.290317	+	0.956931i	$0.406239\pi$
$258$	−1.04960	−	2.63429i	−0.0653450	−	0.164004i
$259$	0.874978	+	0.294814i	0.0543685	+	0.0183189i
$260$	25.9850	−	2.82604i	1.61152	−	0.175264i
$261$	−0.339584	−	6.26326i	−0.0210197	−	0.387686i
$262$	0.523913	−	9.66301i	0.0323675	−	0.596983i
$263$	3.76765	+	0.409757i	0.232323	+	0.0252667i	0.223540	−	0.974695i	$-0.428239\pi$
$263$	3.76765	+	0.409757i	0.232323	+	0.0252667i	0.00878320	+	0.999961i	$0.497204\pi$
$264$	1.23993	+	0.573653i	0.0763125	+	0.0353059i
$265$	29.2419	−	22.2291i	1.79632	−	1.36552i
$266$	2.07595	−	1.57810i	0.127285	−	0.0967594i
$267$	2.21138	+	1.02309i	0.135334	+	0.0626122i
$268$	−1.53171	−	0.166584i	−0.0935642	−	0.0101757i
$269$	−0.627421	+	11.5721i	−0.0382545	+	0.705564i	0.915011	+	0.403429i	$0.132182\pi$
$269$	−0.627421	+	11.5721i	−0.0382545	+	0.705564i	−0.953265	+	0.302134i	$0.902301\pi$
$270$	−0.200767	−	3.70293i	−0.0122183	−	0.225353i
$271$	−29.1981	+	3.17549i	−1.77366	+	0.192897i	−0.935691	−	0.352820i	$-0.885223\pi$
$271$	−29.1981	+	3.17549i	−1.77366	+	0.192897i	−0.837969	+	0.545717i	$0.816257\pi$
$272$	3.96102	+	1.33462i	0.240172	+	0.0809234i
$273$	−4.43175	−	11.1229i	−0.268222	−	0.673186i
$274$	−20.4866	−	4.50945i	−1.23764	−	0.272426i
$275$	5.60074	−	10.5641i	0.337737	−	0.637040i
$276$	−6.67501	+	3.08819i	−0.401789	+	0.185887i
$277$	−12.4308	+	4.18841i	−0.746892	+	0.251657i	−0.666909	−	0.745139i	$-0.732383\pi$
$277$	−12.4308	+	4.18841i	−0.746892	+	0.251657i	−0.0799826	+	0.996796i	$0.525486\pi$
$278$	1.16077	+	1.36656i	0.0696184	+	0.0819611i
$279$	2.81421	−	1.69325i	0.168482	−	0.101372i
$280$	−1.68527	+	6.06980i	−0.100714	+	0.362740i
$281$	−25.5681	+	5.62796i	−1.52526	+	0.335736i	−0.896917	−	0.442198i	$-0.854199\pi$
$281$	−25.5681	+	5.62796i	−1.52526	+	0.335736i	−0.628346	+	0.777934i	$0.716268\pi$
$282$	5.70994	+	8.42153i	0.340022	+	0.501495i
$283$	17.8188	−	16.8789i	1.05922	−	1.00334i	0.0592308	−	0.998244i	$-0.481135\pi$
$283$	17.8188	−	16.8789i	1.05922	−	1.00334i	0.999987	−	0.00510006i	$-0.00162341\pi$
$284$	−12.6298	−	7.59912i	−0.749443	−	0.450925i
$285$	0.920977	+	5.61771i	0.0545539	+	0.332764i
$286$	−5.40401	+	7.97032i	−0.319546	+	0.471295i
$287$	−1.38190	+	3.46830i	−0.0815709	+	0.204727i
$288$	0.647386	−	0.762162i	0.0381476	−	0.0449108i
$289$	−0.0761820	+	0.464689i	−0.00448129	+	0.0273347i
$290$	−16.8871	−	15.9963i	−0.991642	−	0.939334i
$291$	0.430022	+	1.54880i	0.0252083	+	0.0907922i
$292$	−6.90447	−	13.0232i	−0.404054	−	0.762126i
$293$	−13.6914	−	10.4079i	−0.799857	−	0.608036i	0.123339	−	0.992365i	$-0.460640\pi$
$293$	−13.6914	−	10.4079i	−0.799857	−	0.608036i	−0.923196	+	0.384329i	$0.874433\pi$
$294$	−4.11440			−0.239957
$295$	20.9688	+	19.2789i	1.22085	+	1.12246i
$296$	−0.543538			−0.0315925
$297$	1.08762	+	0.826790i	0.0631103	+	0.0479752i
$298$	0.629092	+	1.18659i	0.0364423	+	0.0687375i
$299$	−13.8686	−	49.9502i	−0.802043	−	2.88870i
$300$	−6.35389	−	6.01873i	−0.366842	−	0.347491i
$301$	−0.779303	+	4.75354i	−0.0449183	+	0.273989i
$302$	4.29811	−	5.06013i	0.247329	−	0.291178i
$303$	−3.19640	+	8.02236i	−0.183628	+	0.460873i
$304$	−0.861477	+	1.27058i	−0.0494091	+	0.0728729i
$305$	−1.38674	−	8.45877i	−0.0794048	−	0.484348i
$306$	3.58151	+	2.15492i	0.204741	+	0.123189i
$307$	−0.282835	+	0.267916i	−0.0161423	+	0.0152908i	−0.695728	−	0.718305i	$-0.744918\pi$
$307$	−0.282835	+	0.267916i	−0.0161423	+	0.0152908i	0.679586	+	0.733596i	$0.262160\pi$
$308$	−1.30239	−	1.92088i	−0.0742104	−	0.109452i
$309$	−8.26446	+	1.81915i	−0.470149	+	0.103488i
$310$	3.25836	−	11.7356i	0.185063	−	0.666536i
$311$	19.4449	−	11.6996i	1.10262	−	0.663425i	0.156643	−	0.987655i	$-0.449933\pi$
$311$	19.4449	−	11.6996i	1.10262	−	0.663425i	0.945978	+	0.324230i	$0.105105\pi$
$312$	4.56307	+	5.37206i	0.258333	+	0.304133i
$313$	18.1790	−	6.12523i	1.02754	−	0.346219i	0.245467	−	0.969405i	$-0.421059\pi$
$313$	18.1790	−	6.12523i	1.02754	−	0.346219i	0.782073	+	0.623186i	$0.214162\pi$
$314$	−11.3390	+	5.24600i	−0.639899	+	0.296049i
$315$	−2.95070	+	5.56561i	−0.166253	+	0.313587i
$316$	0.550633	+	0.121203i	0.0309755	+	0.00681823i
$317$	−1.07303	−	2.69311i	−0.0602675	−	0.151260i	0.895759	−	0.444540i	$-0.146633\pi$
$317$	−1.07303	−	2.69311i	−0.0602675	−	0.151260i	−0.956027	+	0.293279i	$0.905253\pi$
$318$	9.38661	+	3.16272i	0.526375	+	0.177356i
$319$	8.51920	−	0.926519i	0.476984	−	0.0518751i
$320$	−0.200767	−	3.70293i	−0.0112232	−	0.207000i
$321$	−0.569128	+	10.4969i	−0.0317656	+	0.585883i
$322$	12.4204	+	1.35079i	0.692159	+	0.0752768i
$323$	−5.82339	−	2.69419i	−0.324022	−	0.149909i
$324$	0.796093	−	0.605174i	0.0442274	−	0.0336208i
$325$	49.1093	−	37.3319i	2.72409	−	2.07080i
$326$	13.8107	+	6.38951i	0.764903	+	0.353882i
$327$	15.4617	+	1.68156i	0.855034	+	0.0929906i
$328$	0.118988	−	2.19461i	0.00657002	−	0.121177i
$329$	−0.935731	−	17.2585i	−0.0515885	−	0.951494i
$330$	5.03667	−	0.547771i	0.277260	−	0.0301538i
$331$	−3.32161	−	1.11918i	−0.182572	−	0.0615157i	0.226531	−	0.974004i	$-0.427262\pi$
$331$	−3.32161	−	1.11918i	−0.182572	−	0.0615157i	−0.409103	+	0.912488i	$0.634158\pi$
$332$	5.42297	+	13.6106i	0.297624	+	0.746981i
$333$	−0.530830	−	0.116845i	−0.0290893	−	0.00640304i
$334$	2.86251	−	5.39927i	0.156630	−	0.295435i
$335$	−5.18556	+	2.39909i	−0.283317	+	0.131077i
$336$	−1.60978	+	0.542399i	−0.0878208	+	0.0295903i
$337$	−17.2955	−	20.3619i	−0.942148	−	1.10918i	−0.993874	−	0.110521i	$-0.964748\pi$
$337$	−17.2955	−	20.3619i	−0.942148	−	1.10918i	0.0517256	−	0.998661i	$-0.483528\pi$
$338$	−31.4301	+	18.9109i	−1.70957	+	1.02862i
$339$	1.66127	−	5.98335i	0.0902277	−	0.324971i
$340$	15.1379	−	3.33211i	0.820968	−	0.180709i
$341$	2.51808	+	3.71389i	0.136362	+	0.201119i
$342$	−1.11447	+	1.05569i	−0.0602638	+	0.0570849i
$343$	16.1775	+	9.73370i	0.873505	+	0.525570i
$344$	−0.458763	−	2.79833i	−0.0247349	−	0.150876i
$345$	−15.3059	+	22.5746i	−0.824044	+	1.21537i
$346$	−9.45302	+	23.7253i	−0.508198	+	1.27548i
$347$	−3.46942	+	4.08451i	−0.186248	+	0.219268i	−0.847360	−	0.531019i	$-0.821809\pi$
$347$	−3.46942	+	4.08451i	−0.186248	+	0.219268i	0.661112	+	0.750288i	$0.270085\pi$
$348$	1.01477	−	6.18983i	0.0543974	−	0.331810i
$349$	10.9307	+	10.3541i	0.585108	+	0.554243i	0.921946	−	0.387319i	$-0.126599\pi$
$349$	10.9307	+	10.3541i	0.585108	+	0.554243i	−0.336838	+	0.941563i	$0.609357\pi$
$350$	3.97735	+	14.3251i	0.212598	+	0.765709i
$351$	3.30155	+	6.22739i	0.176224	+	0.332394i
$352$	1.08762	+	0.826790i	0.0579705	+	0.0440680i
$353$	23.4354			1.24734			0.623670	−	0.781688i	$-0.285641\pi$
$353$	23.4354			1.24734			0.623670	+	0.781688i	$0.285641\pi$
$354$	−1.12974	+	7.59761i	−0.0600451	+	0.403808i
$355$	−54.6603			−2.90107
$356$	1.93974	+	1.47455i	0.102806	+	0.0781511i
$357$	−3.32583	−	6.27318i	−0.176022	−	0.332012i
$358$	−3.04443	−	10.9650i	−0.160903	−	0.579520i
$359$	12.7733	+	12.0995i	0.674147	+	0.638586i	0.946157	−	0.323708i	$-0.104930\pi$
$359$	12.7733	+	12.0995i	0.674147	+	0.638586i	−0.272010	+	0.962295i	$0.587688\pi$
$360$	0.599947	−	3.65951i	0.0316200	−	0.192873i
$361$	−10.7748	+	12.6850i	−0.567093	+	0.667633i
$362$	0.780571	−	1.95909i	0.0410259	−	0.102967i
$363$	5.12560	−	7.55969i	0.269024	−	0.396781i
$364$	−1.93705	−	11.8155i	−0.101529	−	0.619301i
$365$	−46.8378	−	28.1814i	−2.45160	−	1.47508i
$366$	1.67810	−	1.58958i	0.0877156	−	0.0830887i
$367$	−11.2054	−	16.5267i	−0.584917	−	0.862688i	0.413949	−	0.910300i	$-0.364149\pi$
$367$	−11.2054	−	16.5267i	−0.584917	−	0.862688i	−0.998866	+	0.0476124i	$0.984839\pi$
$368$	−7.18283	+	1.58106i	−0.374431	+	0.0824184i
$369$	0.587982	−	2.11772i	0.0306091	−	0.110244i
$370$	−1.72711	+	1.03917i	−0.0897884	+	0.0540239i
$371$	−10.8928	−	12.8240i	−0.565527	−	0.665790i
$372$	3.11241	−	1.04869i	0.161371	−	0.0543722i
$373$	5.41432	−	2.50493i	0.280343	−	0.129700i	−0.274680	−	0.961536i	$-0.588572\pi$
$373$	5.41432	−	2.50493i	0.280343	−	0.129700i	0.555022	+	0.831835i	$0.312710\pi$
$374$	−2.67483	+	5.04527i	−0.138312	+	0.260885i
$375$	−13.5884	−	2.99103i	−0.701702	−	0.154456i
$376$	3.76606	+	9.45211i	0.194220	+	0.487455i
$377$	41.8968	+	14.1167i	2.15779	+	0.727046i
$378$	−1.68875	+	0.183662i	−0.0868597	+	0.00944657i
$379$	−1.63885	−	30.2269i	−0.0841822	−	1.55265i	−0.670095	−	0.742276i	$-0.733746\pi$
$379$	−1.63885	−	30.2269i	−0.0841822	−	1.55265i	0.585912	−	0.810374i	$-0.300736\pi$
$380$	−0.308197	+	5.68435i	−0.0158102	+	0.291601i
$381$	−14.0691	−	1.53010i	−0.720780	−	0.0783895i
$382$	−4.35009	−	2.01257i	−0.222570	−	0.102972i
$383$	4.52548	−	3.44018i	0.231241	−	0.175785i	−0.483137	−	0.875545i	$-0.660503\pi$
$383$	4.52548	−	3.44018i	0.231241	−	0.175785i	0.714378	+	0.699760i	$0.246710\pi$
$384$	0.796093	−	0.605174i	0.0406255	−	0.0308827i
$385$	−7.81084	−	3.61368i	−0.398077	−	0.184170i
$386$	7.78488	+	0.846656i	0.396240	+	0.0430937i
$387$	0.153521	−	2.83153i	0.00780391	−	0.143935i
$388$	0.0870222	+	1.60503i	0.00441788	+	0.0814831i
$389$	19.3957	−	2.10941i	0.983402	−	0.106951i	0.397732	−	0.917501i	$-0.369797\pi$
$389$	19.3957	−	2.10941i	0.983402	−	0.106951i	0.585669	+	0.810550i	$0.300832\pi$
$390$	24.7700	+	8.34598i	1.25428	+	0.422615i
$391$	−11.3787	−	28.5583i	−0.575443	−	1.44425i
$392$	−4.01821	−	0.884475i	−0.202950	−	0.0446728i
$393$	4.53289	−	8.54993i	0.228654	−	0.431287i
$394$	−2.36541	+	1.09436i	−0.119168	+	0.0551328i
$395$	1.98138	−	0.667605i	0.0996942	−	0.0335909i
$396$	0.884460	+	1.04127i	0.0444458	+	0.0523256i
$397$	−14.2065	+	8.54774i	−0.713001	+	0.428999i	−0.825314	−	0.564674i	$-0.809002\pi$
$397$	−14.2065	+	8.54774i	−0.713001	+	0.428999i	0.112312	+	0.993673i	$0.464174\pi$
$398$	−1.20119	+	4.32628i	−0.0602101	+	0.216857i
$399$	2.54671	−	0.560573i	0.127495	−	0.0280638i
$400$	−4.91149	−	7.24391i	−0.245575	−	0.362196i
$401$	−8.77894	+	8.31586i	−0.438399	+	0.415274i	−0.874804	−	0.484476i	$-0.839010\pi$
$401$	−8.77894	+	8.31586i	−0.438399	+	0.415274i	0.436405	+	0.899750i	$0.356252\pi$
$402$	−1.32020	−	0.794336i	−0.0658454	−	0.0396179i
$403$	3.74517	+	22.8445i	0.186560	+	1.13797i
$404$	−4.84624	+	7.14767i	−0.241110	+	0.355610i
$405$	1.37261	−	3.44499i	0.0682054	−	0.171183i
$406$	−6.89793	+	8.12087i	−0.342339	+	0.403032i
$407$	0.120136	−	0.732800i	0.00595494	−	0.0363235i
$408$	3.03453	+	2.87446i	0.150232	+	0.142307i
$409$	−9.22173	−	33.2137i	−0.455985	−	1.64231i	−0.732109	−	0.681188i	$-0.761464\pi$
$409$	−9.22173	−	33.2137i	−0.455985	−	1.64231i	0.276123	−	0.961122i	$-0.410950\pi$
$410$	−3.81770	−	7.20094i	−0.188543	−	0.355629i
$411$	−16.6997	−	12.6948i	−0.823736	−	0.626188i
$412$	−8.46231			−0.416908
$413$	8.29818	−	10.0693i	0.408327	−	0.495477i
$414$	−7.35478			−0.361468
$415$	43.2534	+	32.8804i	2.12322	+	1.61403i
$416$	3.30155	+	6.22739i	0.161872	+	0.305323i
$417$	0.479681	+	1.72765i	0.0234901	+	0.0846036i
$418$	−1.52260	−	1.44228i	−0.0744726	−	0.0705442i
$419$	5.65672	−	34.5044i	0.276349	−	1.68565i	−0.375120	−	0.926976i	$-0.622398\pi$
$419$	5.65672	−	34.5044i	0.276349	−	1.68565i	0.651468	−	0.758676i	$-0.274153\pi$
$420$	−4.07816	+	4.80118i	−0.198994	+	0.234273i
$421$	−7.98146	+	20.0319i	−0.388992	+	0.976297i	0.595889	+	0.803067i	$0.296800\pi$
$421$	−7.98146	+	20.0319i	−0.388992	+	0.976297i	−0.984881	+	0.173231i	$0.944579\pi$
$422$	9.28302	−	13.6914i	0.451890	−	0.666488i
$423$	1.64609	+	10.0407i	0.0800357	+	0.488196i
$424$	8.48727	+	5.10662i	0.412178	+	0.247999i
$425$	26.5581	−	25.1572i	1.28826	−	1.22030i
$426$	−8.27174	−	12.1999i	−0.400767	−	0.591088i
$427$	−3.83466	+	0.844073i	−0.185572	+	0.0408476i
$428$	−2.81236	+	10.1292i	−0.135940	+	0.489613i
$429$	−8.25120	+	4.96458i	−0.398372	+	0.239692i
$430$	−6.80776	−	8.01472i	−0.328299	−	0.386504i
$431$	−11.5636	+	3.89623i	−0.556999	+	0.187675i	−0.583701	−	0.811969i	$-0.698396\pi$
$431$	−11.5636	+	3.89623i	−0.556999	+	0.187675i	0.0267020	+	0.999643i	$0.491499\pi$
$432$	0.907575	−	0.419889i	0.0436657	−	0.0202019i
$433$	−5.69163	+	10.7356i	−0.273522	+	0.515918i	−0.981776	−	0.190040i	$-0.939138\pi$
$433$	−5.69163	+	10.7356i	−0.273522	+	0.515918i	0.708254	+	0.705958i	$0.249483\pi$
$434$	−5.44868	−	1.19934i	−0.261545	−	0.0575704i
$435$	−8.60962	−	21.6085i	−0.412800	−	1.03605i
$436$	14.7387	+	4.96606i	0.705857	+	0.237831i
$437$	11.2241	−	1.22070i	0.536922	−	0.0583938i
$438$	−0.798023	−	14.7187i	−0.0381310	−	0.703285i
$439$	−2.05832	+	37.9634i	−0.0982381	+	1.81189i	0.370796	+	0.928714i	$0.379085\pi$
$439$	−2.05832	+	37.9634i	−0.0982381	+	1.81189i	−0.469034	+	0.883180i	$0.655398\pi$
$440$	5.03667	+	0.547771i	0.240114	+	0.0261140i
$441$	−3.73413	−	1.72759i	−0.177816	−	0.0822664i
$442$	−23.4539	+	17.8292i	−1.11559	+	0.848048i
$443$	−9.14910	+	6.95496i	−0.434687	+	0.330440i	−0.799527	−	0.600630i	$-0.794917\pi$
$443$	−9.14910	+	6.95496i	−0.434687	+	0.330440i	0.364841	+	0.931070i	$0.381124\pi$
$444$	−0.493302	−	0.228226i	−0.0234111	−	0.0108311i
$445$	8.98275	+	0.976933i	0.425823	+	0.0463110i
$446$	−0.501027	+	9.24089i	−0.0237243	+	0.437569i
$447$	0.0727108	+	1.34107i	0.00343910	+	0.0634305i
$448$	−1.68875	+	0.183662i	−0.0797858	+	0.00867722i
$449$	−8.94615	−	3.01431i	−0.422195	−	0.142254i	0.100181	−	0.994969i	$-0.468058\pi$
$449$	−8.94615	−	3.01431i	−0.422195	−	0.142254i	−0.522376	+	0.852715i	$0.674954\pi$
$450$	−3.23944	−	8.13038i	−0.152709	−	0.383270i
$451$	2.93248	+	0.645488i	0.138085	+	0.0303948i
$452$	2.90867	−	5.48634i	0.136812	−	0.258056i
$453$	6.02555	−	2.78772i	0.283105	−	0.130978i
$454$	−6.12176	+	2.06266i	−0.287309	+	0.0968056i
$455$	−28.7447	−	33.8409i	−1.34757	−	1.58648i
$456$	−1.31536	+	0.791425i	−0.0615973	+	0.0370619i
$457$	7.00481	−	25.2290i	0.327671	−	1.18016i	−0.597894	−	0.801575i	$-0.703996\pi$
$457$	7.00481	−	25.2290i	0.327671	−	1.18016i	0.925565	−	0.378589i	$-0.123591\pi$
$458$	26.2672	−	5.78185i	1.22739	−	0.270168i
$459$	2.34566	+	3.45959i	0.109486	+	0.161480i
$460$	−19.8009	+	18.7565i	−0.923224	+	0.874524i
$461$	3.13455	+	1.88599i	0.145990	+	0.0878395i	0.586675	−	0.809823i	$-0.300437\pi$
$461$	3.13455	+	1.88599i	0.145990	+	0.0878395i	−0.440685	+	0.897662i	$0.645264\pi$
$462$	−0.375459	−	2.29020i	−0.0174679	−	0.106550i
$463$	−20.5704	+	30.3390i	−0.955986	+	1.40997i	−0.0443305	+	0.999017i	$0.514115\pi$
$463$	−20.5704	+	30.3390i	−0.955986	+	1.40997i	−0.911655	+	0.410956i	$0.865195\pi$
$464$	2.32168	−	5.82697i	0.107781	−	0.270510i
$465$	7.88485	−	9.28276i	0.365651	−	0.430478i
$466$	−1.16920	+	7.13181i	−0.0541622	+	0.330375i
$467$	−18.3533	−	17.3852i	−0.849289	−	0.804489i	0.133146	−	0.991096i	$-0.457492\pi$
$467$	−18.3533	−	17.3852i	−0.849289	−	0.804489i	−0.982435	+	0.186607i	$0.940251\pi$
$468$	1.88566	+	6.79154i	0.0871647	+	0.313939i
$469$	1.22595	+	2.31239i	0.0566091	+	0.106776i
$470$	30.0379	+	22.8342i	1.38555	+	1.05327i
$471$	−12.4938			−0.575682
$472$	−2.73659	+	7.17712i	−0.125962	+	0.330354i
$473$	3.87412			0.178132
$474$	0.448849	+	0.341206i	0.0206163	+	0.0156721i
$475$	6.29313	+	11.8701i	0.288749	+	0.544638i
$476$	−1.89953	−	6.84147i	−0.0870646	−	0.313578i
$477$	7.19107	+	6.81174i	0.329256	+	0.311888i
$478$	−1.00424	+	6.12558i	−0.0459328	+	0.280177i
$479$	0.279934	−	0.329563i	0.0127905	−	0.0150581i	−0.755730	−	0.654884i	$-0.772718\pi$
$479$	0.279934	−	0.329563i	0.0127905	−	0.0150581i	0.768520	+	0.639826i	$0.220993\pi$
$480$	1.37261	−	3.44499i	0.0626507	−	0.157241i
$481$	2.14996	−	3.17096i	0.0980299	−	0.144583i
$482$	−3.26364	−	19.9073i	−0.148655	−	0.906755i
$483$	10.7052	+	6.44112i	0.487104	+	0.293081i
$484$	6.63088	−	6.28110i	0.301403	−	0.285504i
$485$	3.34511	+	4.93367i	0.151894	+	0.224027i
$486$	0.976621	−	0.214970i	0.0443004	−	0.00975126i
$487$	−1.38628	+	4.99293i	−0.0628183	+	0.226251i	−0.988295	−	0.152553i	$-0.951251\pi$
$487$	−1.38628	+	4.99293i	−0.0628183	+	0.226251i	0.925477	+	0.378804i	$0.123664\pi$
$488$	1.98058	−	1.19167i	0.0896566	−	0.0539446i
$489$	9.85136	+	11.5979i	0.445494	+	0.524476i
$490$	−14.4590	+	4.87181i	−0.653192	+	0.220086i
$491$	28.8824	−	13.3624i	1.30344	−	0.603038i	0.359501	−	0.933145i	$-0.382947\pi$
$491$	28.8824	−	13.3624i	1.30344	−	0.603038i	0.943943	+	0.330107i	$0.107085\pi$
$492$	1.02948	−	1.94181i	0.0464127	−	0.0875436i
$493$	25.6048	+	5.63604i	1.15318	+	0.253834i
$494$	−4.00492	−	10.0516i	−0.180190	−	0.452242i
$495$	4.80117	+	1.61770i	0.215796	+	0.0727103i
$496$	3.26508	−	0.355099i	0.146606	−	0.0159444i
$497$	1.35555	+	25.0017i	0.0608049	+	1.12148i
$498$	−0.793201	+	14.6297i	−0.0355442	+	0.655574i
$499$	5.98943	+	0.651390i	0.268124	+	0.0291602i	0.241193	−	0.970477i	$-0.422461\pi$
$499$	5.98943	+	0.651390i	0.268124	+	0.0291602i	0.0269304	+	0.999637i	$0.491427\pi$
$500$	−12.6277	−	5.84221i	−0.564729	−	0.261271i
$501$	4.86504	−	3.69830i	0.217354	−	0.165228i
$502$	−22.5574	+	17.1477i	−1.00679	+	0.765340i
$503$	29.3075	+	13.5591i	1.30676	+	0.604570i	0.944807	−	0.327627i	$-0.106249\pi$
$503$	29.3075	+	13.5591i	1.30676	+	0.604570i	0.361950	+	0.932197i	$0.382111\pi$
$504$	−1.68875	−	0.183662i	−0.0752227	−	0.00818097i
$505$	−1.73376	+	31.9774i	−0.0771514	+	1.42297i
$506$	−0.543994	−	10.0334i	−0.0241835	−	0.446038i
$507$	−36.4656	+	3.96588i	−1.61950	+	0.176131i
$508$	−13.4112	−	4.51876i	−0.595026	−	0.200488i
$509$	14.1153	+	35.4268i	0.625651	+	1.57027i	0.809378	+	0.587288i	$0.199805\pi$
$509$	14.1153	+	35.4268i	0.625651	+	1.57027i	−0.183727	+	0.982977i	$0.558816\pi$
$510$	15.1379	+	3.33211i	0.670318	+	0.147548i
$511$	−11.7287	+	22.1226i	−0.518845	+	0.978646i
$512$	0.907575	−	0.419889i	0.0401095	−	0.0185567i
$513$	−1.45474	+	0.490159i	−0.0642283	+	0.0216410i
$514$	10.1551	+	11.9555i	0.447921	+	0.527333i
$515$	−26.8893	+	16.1788i	−1.18488	+	0.712922i
$516$	0.758627	−	2.73233i	0.0333967	−	0.120284i
$517$	−13.5758	+	2.98825i	−0.597061	+	0.131423i
$518$	0.518150	+	0.764214i	0.0227662	+	0.0335776i
$519$	−18.5413	+	17.5633i	−0.813874	+	0.770942i
$520$	22.3967	+	13.4757i	0.982162	+	0.590947i
$521$	−2.66333	−	16.2456i	−0.116683	−	0.711734i	−0.978768	−	0.204970i	$-0.934290\pi$
$521$	−2.66333	−	16.2456i	−0.116683	−	0.711734i	0.862085	−	0.506763i	$-0.169158\pi$
$522$	3.52002	−	5.19164i	0.154067	−	0.227232i
$523$	13.4937	−	33.8667i	0.590040	−	1.48089i	−0.265998	−	0.963974i	$-0.585701\pi$
$523$	13.4937	−	33.8667i	0.590040	−	1.48089i	0.856037	−	0.516914i	$-0.172919\pi$
$524$	6.26489	−	7.37560i	0.273683	−	0.322205i
$525$	−2.40522	+	14.6712i	−0.104972	+	0.640302i
$526$	2.75143	+	2.60629i	0.119968	+	0.113640i
$527$	3.67261	+	13.2275i	0.159981	+	0.576201i
$528$	0.639940	+	1.20706i	0.0278498	+	0.0525303i
$529$	24.7527	+	18.8165i	1.07621	+	0.818110i
$530$	36.7318			1.59553
$531$	−4.21548	+	6.42104i	−0.182936	+	0.278649i
$532$	2.60768			0.113057
$533$	12.3325	+	9.37494i	0.534181	+	0.406074i
$534$	1.14131	+	2.15274i	0.0493894	+	0.0931584i
$535$	10.4292	+	37.5627i	0.450895	+	1.62398i
$536$	−1.11857	−	1.05957i	−0.0483150	−	0.0457664i
$537$	1.84105	−	11.2299i	0.0794473	−	0.484607i
$538$	−7.50262	+	8.83277i	−0.323461	+	0.380808i
$539$	2.08059	−	5.22188i	0.0896172	−	0.224922i
$540$	2.08109	−	3.06937i	0.0895557	−	0.132085i
$541$	3.86629	+	23.5833i	0.166225	+	1.01393i	0.929762	+	0.368162i	$0.120013\pi$
$541$	3.86629	+	23.5833i	0.166225	+	1.01393i	−0.763537	+	0.645764i	$0.776539\pi$
$542$	−25.1662	−	15.1420i	−1.08098	−	0.650403i
$543$	1.53103	−	1.45026i	0.0657026	−	0.0622368i
$544$	2.34566	+	3.45959i	0.100569	+	0.148329i
$545$	56.3273	−	12.3986i	2.41280	−	0.531097i
$546$	3.20318	−	11.5368i	0.137083	−	0.493730i
$547$	−8.68686	+	5.22671i	−0.371423	+	0.223478i	−0.689011	−	0.724751i	$-0.741955\pi$
$547$	−8.68686	+	5.22671i	−0.371423	+	0.223478i	0.317588	+	0.948229i	$0.397127\pi$
$548$	−13.5803	−	15.9879i	−0.580120	−	0.682970i
$549$	2.19045	−	0.738048i	0.0934861	−	0.0314991i
$550$	10.8518	−	5.02060i	0.462724	−	0.214079i
$551$	−4.51023	+	8.50719i	−0.192142	+	0.362418i
$552$	−7.18283	−	1.58106i	−0.305721	−	0.0672944i
$553$	−0.354501	−	0.889731i	−0.0150749	−	0.0378352i
$554$	−12.4308	−	4.18841i	−0.528132	−	0.177948i
$555$	−2.00382	+	0.217929i	−0.0850575	+	0.00925056i
$556$	0.0970716	+	1.79038i	0.00411675	+	0.0759290i
$557$	−1.60606	+	29.6221i	−0.0680511	+	1.25513i	0.742655	+	0.669674i	$0.233566\pi$
$557$	−1.60606	+	29.6221i	−0.0680511	+	1.25513i	−0.810706	+	0.585454i	$0.800916\pi$
$558$	3.26508	+	0.355099i	0.138222	+	0.0150325i
$559$	18.1399	+	8.39241i	0.767236	+	0.354961i
$560$	−5.01492	+	3.81224i	−0.211919	+	0.161097i
$561$	−4.54607	+	3.45583i	−0.191935	+	0.145905i
$562$	−23.7605	−	10.9928i	−1.00227	−	0.463701i
$563$	−1.64318	−	0.178706i	−0.0692517	−	0.00753158i	0.0734276	−	0.997301i	$-0.476606\pi$
$563$	−1.64318	−	0.178706i	−0.0692517	−	0.00753158i	−0.142679	+	0.989769i	$0.545572\pi$
$564$	−0.550850	+	10.1598i	−0.0231950	+	0.427806i
$565$	−1.24670	−	22.9940i	−0.0524491	−	0.967366i
$566$	24.4001	−	2.65367i	1.02561	−	0.111542i
$567$	−1.60978	−	0.542399i	−0.0676045	−	0.0227786i
$568$	−5.45574	−	13.6929i	−0.228918	−	0.574540i
$569$	2.87968	+	0.633866i	0.120723	+	0.0265730i	0.274921	−	0.961467i	$-0.411348\pi$
$569$	2.87968	+	0.633866i	0.120723	+	0.0265730i	−0.154198	+	0.988040i	$0.549279\pi$
$570$	−2.66651	+	5.02957i	−0.111688	+	0.210666i
$571$	−14.3600	+	6.64363i	−0.600946	+	0.278027i	−0.696682	−	0.717380i	$-0.745341\pi$
$571$	−14.3600	+	6.64363i	−0.600946	+	0.278027i	0.0957368	+	0.995407i	$0.469479\pi$
$572$	−9.12553	+	3.07475i	−0.381557	+	0.128562i
$573$	−3.10298	−	3.65311i	−0.129629	−	0.152611i
$574$	−3.19905	+	1.92480i	−0.133526	+	0.0803397i
$575$	−17.2205	+	62.0226i	−0.718144	+	2.58652i
$576$	0.976621	−	0.214970i	0.0406925	−	0.00895710i
$577$	9.98796	+	14.7311i	0.415804	+	0.613266i	0.976697	−	0.214623i	$-0.0688523\pi$
$577$	9.98796	+	14.7311i	0.415804	+	0.613266i	−0.560893	+	0.827889i	$0.689542\pi$
$578$	−0.341866	+	0.323833i	−0.0142198	+	0.0134697i
$579$	6.70986	+	4.03719i	0.278852	+	0.167780i
$580$	−3.76314	−	22.9541i	−0.156256	−	0.953119i
$581$	13.9669	−	20.5996i	0.579443	−	0.854615i
$582$	−0.594956	+	1.49323i	−0.0246617	+	0.0618962i
$583$	−8.76068	+	10.3139i	−0.362830	+	0.427157i
$584$	2.38471	−	14.5461i	0.0986801	−	0.601922i
$585$	18.9762	+	17.9753i	0.784571	+	0.743185i
$586$	−4.60100	−	16.5713i	−0.190066	−	0.684554i
$587$	0.633315	+	1.19456i	0.0261397	+	0.0493047i	0.896238	−	0.443574i	$-0.146290\pi$
$587$	0.633315	+	1.19456i	0.0261397	+	0.0493047i	−0.870098	+	0.492878i	$0.835945\pi$
$588$	−3.27545	−	2.48993i	−0.135077	−	0.102683i
$589$	−5.04177			−0.207743
$590$	5.02604	+	28.0376i	0.206919	+	1.15429i
$591$	−2.60630			−0.107209
$592$	−0.432707	−	0.328935i	−0.0177841	−	0.0135192i
$593$	8.46009	+	15.9574i	0.347414	+	0.655293i	0.994220	−	0.107362i	$-0.0342403\pi$
$593$	8.46009	+	15.9574i	0.347414	+	0.655293i	−0.646806	+	0.762655i	$0.723895\pi$
$594$	0.365498	+	1.31640i	0.0149965	+	0.0540127i
$595$	−19.1158	−	18.1074i	−0.783670	−	0.742332i
$596$	−0.217280	+	1.32535i	−0.00890013	+	0.0542884i
$597$	−2.90673	+	3.42206i	−0.118964	+	0.140056i
$598$	19.1879	−	48.1580i	0.784651	−	1.96933i
$599$	3.20003	−	4.71969i	0.130750	−	0.192841i	−0.756679	−	0.653787i	$-0.773179\pi$
$599$	3.20003	−	4.71969i	0.130750	−	0.192841i	0.887428	+	0.460945i	$0.152490\pi$
$600$	−1.41591	−	8.63668i	−0.0578044	−	0.352591i
$601$	−13.4610	−	8.09919i	−0.549084	−	0.330373i	0.213832	−	0.976870i	$-0.431405\pi$
$601$	−13.4610	−	8.09919i	−0.549084	−	0.330373i	−0.762916	+	0.646498i	$0.776233\pi$
$602$	−3.49712	+	3.31264i	−0.142532	+	0.135013i
$603$	−0.864645	−	1.27526i	−0.0352111	−	0.0519324i
$604$	6.48396	−	1.42723i	0.263828	−	0.0580730i
$605$	9.06127	−	32.6358i	0.368393	−	1.32683i
$606$	−7.39956	+	4.45217i	−0.300587	+	0.180857i
$607$	11.9686	+	14.0905i	0.485790	+	0.571916i	0.949379	−	0.314134i	$-0.101714\pi$
$607$	11.9686	+	14.0905i	0.485790	+	0.571916i	−0.463588	+	0.886051i	$0.653438\pi$
$608$	−1.45474	+	0.490159i	−0.0589975	+	0.0198786i
$609$	−9.67026	+	4.47394i	−0.391859	+	0.181293i
$610$	4.01505	−	7.57319i	0.162565	−	0.306629i
$611$	−70.0395	−	15.4169i	−2.83350	−	0.623700i
$612$	1.54711	+	3.88296i	0.0625382	+	0.156959i
$613$	5.24594	+	1.76756i	0.211882	+	0.0713912i	0.423241	−	0.906017i	$-0.360892\pi$
$613$	5.24594	+	1.76756i	0.211882	+	0.0713912i	−0.211359	+	0.977408i	$0.567789\pi$
$614$	−0.387299	+	0.0421213i	−0.0156301	+	0.00169988i
$615$	−0.441252	−	8.13841i	−0.0177930	−	0.328172i
$616$	0.125644	−	2.31737i	0.00506234	−	0.0933694i
$617$	6.81345	+	0.741007i	0.274299	+	0.0298318i	0.244235	−	0.969716i	$-0.421463\pi$
$617$	6.81345	+	0.741007i	0.274299	+	0.0298318i	0.0300643	+	0.999548i	$0.490429\pi$
$618$	−7.68018	−	3.55323i	−0.308942	−	0.142932i
$619$	−11.1368	+	8.46596i	−0.447625	+	0.340276i	−0.804578	−	0.593847i	$-0.797609\pi$
$619$	−11.1368	+	8.46596i	−0.447625	+	0.340276i	0.356953	+	0.934122i	$0.383815\pi$
$620$	9.69602	−	7.37073i	0.389402	−	0.296015i
$621$	−6.67501	−	3.08819i	−0.267859	−	0.123925i
$622$	22.5603	+	2.45358i	0.904586	+	0.0983796i
$623$	0.224082	−	4.13295i	0.00897766	−	0.165583i
$624$	0.381595	+	7.03811i	0.0152760	+	0.281750i
$625$	−7.79124	+	0.847349i	−0.311650	+	0.0338939i
$626$	18.1790	+	6.12523i	0.726580	+	0.244813i
$627$	−0.776273	−	1.94830i	−0.0310014	−	0.0778075i
$628$	−12.2017	−	2.68579i	−0.486900	−	0.107175i
$629$	1.06417	−	2.00724i	0.0424314	−	0.0800340i
$630$	−5.71719	+	2.64506i	−0.227778	+	0.105382i
$631$	5.55096	−	1.87034i	0.220980	−	0.0744569i	−0.206634	−	0.978418i	$-0.566251\pi$
$631$	5.55096	−	1.87034i	0.220980	−	0.0744569i	0.427614	+	0.903961i	$0.359354\pi$
$632$	0.365006	+	0.429718i	0.0145192	+	0.0170933i
$633$	14.1739	−	8.52817i	0.563363	−	0.338964i
$634$	0.775566	−	2.79334i	0.0308017	−	0.110938i
$635$	−51.2539	+	11.2818i	−2.03395	+	0.447706i
$636$	5.55862	+	8.19835i	0.220414	+	0.325086i
$637$	21.0540	−	19.9434i	0.834190	−	0.790187i
$638$	7.34278	+	4.41801i	0.290704	+	0.174911i
$639$	−2.38462	−	14.5456i	−0.0943342	−	0.575413i
$640$	2.08109	−	3.06937i	0.0822622	−	0.121328i
$641$	−2.10977	+	5.29512i	−0.0833309	+	0.209145i	−0.964738	−	0.263213i	$-0.915218\pi$
$641$	−2.10977	+	5.29512i	−0.0833309	+	0.209145i	0.881407	+	0.472358i	$0.156597\pi$
$642$	−6.80556	+	8.01213i	−0.268594	+	0.316213i
$643$	6.24965	−	38.1212i	0.246462	−	1.50335i	−0.516151	−	0.856498i	$-0.672636\pi$
$643$	6.24965	−	38.1212i	0.246462	−	1.50335i	0.762613	−	0.646855i	$-0.223916\pi$
$644$	9.07029	+	8.59183i	0.357419	+	0.338566i
$645$	−2.81327	−	10.1325i	−0.110772	−	0.398965i
$646$	−3.00551	−	5.66899i	−0.118250	−	0.223044i
$647$	28.9022	+	21.9709i	1.13626	+	0.863765i	0.992058	−	0.125783i	$-0.0401442\pi$
$647$	28.9022	+	21.9709i	1.13626	+	0.863765i	0.144206	+	0.989548i	$0.453937\pi$
$648$	1.00000			0.0392837
$649$	−9.07136	−	5.27582i	−0.356082	−	0.207094i
$650$	61.6879			2.41960
$651$	−4.44149	−	3.37633i	−0.174076	−	0.132329i
$652$	7.12783	+	13.4445i	0.279147	+	0.526528i
$653$	−0.346512	−	1.24802i	−0.0135600	−	0.0488389i	0.956460	−	0.291862i	$-0.0942748\pi$
$653$	−0.346512	−	1.24802i	−0.0135600	−	0.0488389i	−0.970021	+	0.243023i	$0.921861\pi$
$654$	11.2913	+	10.6957i	0.441525	+	0.418235i
$655$	5.80581	−	35.4139i	0.226852	−	1.38373i
$656$	1.42285	−	1.67510i	0.0555528	−	0.0654018i
$657$	5.45594	−	13.6934i	0.212856	−	0.534230i
$658$	9.69949	−	14.3057i	0.378126	−	0.557694i
$659$	−1.15873	−	7.06792i	−0.0451376	−	0.275327i	0.954608	−	0.297864i	$-0.0962741\pi$
$659$	−1.15873	−	7.06792i	−0.0451376	−	0.275327i	−0.999746	+	0.0225365i	$0.992826\pi$
$660$	4.34116	+	2.61199i	0.168979	+	0.101672i
$661$	29.6589	−	28.0944i	1.15360	−	1.09275i	0.159180	−	0.987250i	$-0.449115\pi$
$661$	29.6589	−	28.0944i	1.15360	−	1.09275i	0.994420	−	0.105498i	$-0.0336436\pi$
$662$	−1.96701	−	2.90112i	−0.0764500	−	0.112755i
$663$	−28.7725	+	6.33330i	−1.11743	+	0.245965i
$664$	−3.91961	+	14.1172i	−0.152111	+	0.547853i
$665$	8.28599	−	4.98552i	0.321317	−	0.193330i
$666$	−0.351879	−	0.414264i	−0.0136350	−	0.0160524i
$667$	−43.7176	+	14.7302i	−1.69275	+	0.570355i
$668$	5.54632	−	2.56600i	0.214594	−	0.0992816i
$669$	−4.33487	+	8.17643i	−0.167596	+	0.316119i
$670$	−5.58006	−	1.22826i	−0.215576	−	0.0474520i
$671$	1.16886	+	2.93362i	0.0451233	+	0.113251i
$672$	−1.60978	−	0.542399i	−0.0620987	−	0.0209235i
$673$	13.8858	−	1.51018i	0.535260	−	0.0582130i	0.163502	−	0.986543i	$-0.447721\pi$
$673$	13.8858	−	1.51018i	0.535260	−	0.0582130i	0.371757	+	0.928330i	$0.378755\pi$
$674$	−1.44637	−	26.6768i	−0.0557122	−	1.02755i
$675$	0.473822	−	8.73914i	0.0182374	−	0.336370i
$676$	−36.4656	−	3.96588i	−1.40252	−	0.152534i
$677$	30.4526	+	14.0889i	1.17039	+	0.541480i	0.906141	−	0.422975i	$-0.139014\pi$
$677$	30.4526	+	14.0889i	1.17039	+	0.541480i	0.264248	+	0.964455i	$0.414876\pi$
$678$	4.94349	−	3.75794i	0.189854	−	0.144323i
$679$	2.17371	−	1.65241i	0.0834195	−	0.0634138i
$680$	14.0677	+	6.50841i	0.539471	+	0.249586i
$681$	−6.42205	−	0.698440i	−0.246094	−	0.0267643i
$682$	−0.242925	+	4.48048i	−0.00930207	+	0.171567i
$683$	−2.13600	−	39.3962i	−0.0817317	−	1.50745i	−0.695820	−	0.718216i	$-0.744959\pi$
$683$	−2.13600	−	39.3962i	−0.0817317	−	1.50745i	0.614088	−	0.789237i	$-0.289524\pi$
$684$	−1.52610	+	0.165973i	−0.0583518	+	0.00634614i
$685$	−73.7186	−	24.8387i	−2.81664	−	0.949037i
$686$	6.98824	+	17.5392i	0.266812	+	0.669648i
$687$	26.2672	+	5.78185i	1.00216	+	0.220591i
$688$	1.32826	−	2.50536i	0.0506394	−	0.0955161i
$689$	−63.3630	+	29.3149i	−2.41394	+	1.11681i
$690$	−25.8465	+	8.70869i	−0.983959	+	0.331534i
$691$	−8.04323	−	9.46922i	−0.305979	−	0.360226i	0.587585	−	0.809163i	$-0.300079\pi$
$691$	−8.04323	−	9.46922i	−0.305979	−	0.360226i	−0.893564	+	0.448936i	$0.851803\pi$
$692$	−21.8834	+	13.1668i	−0.831883	+	0.500527i
$693$	0.620872	−	2.23618i	0.0235850	−	0.0849454i
$694$	−5.23382	+	1.15205i	−0.198673	+	0.0437313i
$695$	3.73141	+	5.50342i	0.141540	+	0.208757i
$696$	4.55377	−	4.31356i	0.172610	−	0.163505i
$697$	7.87155	+	4.73616i	0.298156	+	0.179395i
$698$	2.43582	+	14.8578i	0.0921971	+	0.562377i
$699$	−4.05571	+	5.98172i	−0.153401	+	0.226249i
$700$	−5.50285	+	13.8111i	−0.207988	+	0.522011i
$701$	3.98205	−	4.68803i	0.150400	−	0.177065i	−0.681803	−	0.731536i	$-0.738804\pi$
$701$	3.98205	−	4.68803i	0.150400	−	0.177065i	0.832203	+	0.554472i	$0.187080\pi$
$702$	−1.14031	+	6.95560i	−0.0430383	+	0.262522i
$703$	0.605759	+	0.573805i	0.0228466	+	0.0216415i
$704$	0.365498	+	1.31640i	0.0137752	+	0.0496138i
$705$	17.6738	+	33.3364i	0.665635	+	1.25552i
$706$	18.6568	+	14.1825i	0.702156	+	0.533765i
$707$	14.6695			0.551703
$708$	−5.49726	+	5.36471i	−0.206600	+	0.201618i
$709$	−20.6536			−0.775661			−0.387830	−	0.921731i	$-0.626775\pi$
$709$	−20.6536			−0.775661			−0.387830	+	0.921731i	$0.626775\pi$
$710$	−43.5147	−	33.0790i	−1.63308	−	1.24143i
$711$	0.264096	+	0.498137i	0.00990436	+	0.0186816i
$712$	0.651853	+	2.34776i	0.0244292	+	0.0879861i
$713$	−17.5368	−	16.6118i	−0.656759	−	0.622115i
$714$	1.14870	−	7.00674i	0.0429889	−	0.262221i
$715$	−23.1182	+	27.2169i	−0.864573	+	1.01785i
$716$	4.21211	−	10.5716i	0.157414	−	0.395079i
$717$	−3.48348	+	5.13776i	−0.130093	+	0.191873i
$718$	2.84642	+	17.3624i	0.106227	+	0.647958i
$719$	−25.5854	−	15.3942i	−0.954174	−	0.574108i	−0.0488397	−	0.998807i	$-0.515552\pi$
$719$	−25.5854	−	15.3942i	−0.954174	−	0.574108i	−0.905335	+	0.424699i	$0.860380\pi$
$720$	2.69226	−	2.55024i	0.100334	−	0.0950419i
$721$	8.06704	+	11.8980i	0.300432	+	0.443104i
$722$	−16.2544	+	3.57786i	−0.604925	+	0.133154i
$723$	5.39688	−	19.4378i	0.200712	−	0.722899i
$724$	1.80699	−	1.08723i	0.0671564	−	0.0404067i
$725$	−35.5392	−	41.8399i	−1.31989	−	1.55390i
$726$	8.65538	−	2.91634i	0.321231	−	0.108235i
$727$	31.7791	−	14.7026i	1.17862	−	0.545289i	0.269981	−	0.962866i	$-0.412982\pi$
$727$	31.7791	−	14.7026i	1.17862	−	0.545289i	0.908642	+	0.417576i	$0.137120\pi$
$728$	5.60836	−	10.5785i	0.207860	−	0.392065i
$729$	0.976621	+	0.214970i	0.0361711	+	0.00796187i
$730$	−20.2326	−	50.7800i	−0.748843	−	1.87945i
$731$	11.2322	+	3.78457i	0.415438	+	0.139977i
$732$	2.29790	−	0.249911i	0.0849327	−	0.00923699i
$733$	0.209846	+	3.87039i	0.00775085	+	0.142956i	0.999847	+	0.0174780i	$0.00556369\pi$
$733$	0.209846	+	3.87039i	0.00775085	+	0.142956i	−0.992096	+	0.125478i	$0.959954\pi$
$734$	1.08101	−	19.9380i	0.0399007	−	0.735926i
$735$	−15.1683	−	1.64965i	−0.559490	−	0.0608482i
$736$	−6.67501	−	3.08819i	−0.246044	−	0.113832i
$737$	1.67575	−	1.27387i	0.0617270	−	0.0469236i
$738$	1.74968	−	1.33007i	0.0644065	−	0.0489606i
$739$	39.4727	+	18.2620i	1.45203	+	0.671779i	0.977976	−	0.208719i	$-0.0669293\pi$
$739$	39.4727	+	18.2620i	1.45203	+	0.671779i	0.474051	+	0.880498i	$0.342791\pi$
$740$	−2.00382	−	0.217929i	−0.0736620	−	0.00801122i
$741$	0.585786	−	10.8042i	0.0215194	−	0.396902i
$742$	−0.910933	−	16.8012i	−0.0334414	−	0.616791i
$743$	21.5904	−	2.34810i	0.792075	−	0.0861434i	0.296868	−	0.954918i	$-0.404058\pi$
$743$	21.5904	−	2.34810i	0.792075	−	0.0861434i	0.495207	+	0.868775i	$0.335092\pi$
$744$	3.11241	+	1.04869i	0.114106	+	0.0384469i
$745$	1.84347	+	4.62676i	0.0675394	+	0.169511i
$746$	5.82622	+	1.28245i	0.213313	+	0.0469537i
$747$	−6.86275	+	12.9445i	−0.251095	+	0.473615i
$748$	−5.18269	+	2.39777i	−0.189498	+	0.0876710i
$749$	16.9226	−	5.70189i	0.618339	−	0.208343i
$750$	−9.00753	−	10.6045i	−0.328909	−	0.387221i
$751$	−10.6114	+	6.38467i	−0.387216	+	0.232980i	−0.695829	−	0.718208i	$-0.744963\pi$
$751$	−10.6114	+	6.38467i	−0.387216	+	0.232980i	0.308613	+	0.951188i	$0.400135\pi$
$752$	−2.72203	+	9.80388i	−0.0992624	+	0.357511i
$753$	−27.6727	+	6.09122i	−1.00845	+	0.221976i
$754$	24.8107	+	36.5930i	0.903552	+	1.33264i
$755$	17.8744	−	16.9315i	0.650515	−	0.616200i
$756$	−1.45555	−	0.875773i	−0.0529377	−	0.0318516i
$757$	0.761180	+	4.64299i	0.0276656	+	0.168752i	0.997045	−	0.0768133i	$-0.0244745\pi$
$757$	0.761180	+	4.64299i	0.0276656	+	0.168752i	−0.969380	+	0.245566i	$0.921026\pi$
$758$	16.9878	−	25.0552i	0.617026	−	0.910046i
$759$	3.71919	−	9.33446i	0.134998	−	0.338819i
$760$	−3.68538	+	4.33876i	−0.133683	+	0.157383i
$761$	−1.52651	+	9.31129i	−0.0553359	+	0.337534i	0.944620	+	0.328166i	$0.106430\pi$
$761$	−1.52651	+	9.31129i	−0.0553359	+	0.337534i	−0.999956	+	0.00936852i	$0.997018\pi$
$762$	−10.2743	−	9.73233i	−0.372199	−	0.352565i
$763$	−7.06803	−	25.4567i	−0.255880	−	0.921596i
$764$	−2.24513	−	4.23476i	−0.0812258	−	0.153208i
$765$	12.3397	+	9.38038i	0.446142	+	0.339148i
$766$	5.68462			0.205394
$767$	−31.0462	−	44.3542i	−1.12101	−	1.60154i
$768$	1.00000			0.0360844
$769$	−8.38874	−	6.37696i	−0.302506	−	0.229959i	0.442898	−	0.896572i	$-0.353950\pi$
$769$	−8.38874	−	6.37696i	−0.302506	−	0.229959i	−0.745404	+	0.666613i	$0.767743\pi$
$770$	−4.03125	−	7.60374i	−0.145276	−	0.274020i
$771$	4.19652	+	15.1145i	0.151134	+	0.544335i
$772$	5.68511	+	5.38522i	0.204612	+	0.193818i
$773$	−5.11044	+	31.1723i	−0.183810	+	1.12119i	0.720228	+	0.693738i	$0.244037\pi$
$773$	−5.11044	+	31.1723i	−0.183810	+	1.12119i	−0.904038	+	0.427453i	$0.859411\pi$
$774$	1.83579	−	2.16125i	0.0659859	−	0.0776846i
$775$	10.6394	−	26.7029i	0.382179	−	0.959196i
$776$	−0.902045	+	1.33042i	−0.0323815	+	0.0477592i
$777$	0.149375	+	0.911147i	0.00535880	+	0.0326872i
$778$	16.7174	+	10.0585i	0.599346	+	0.360615i
$779$	−2.44943	+	2.32022i	−0.0877598	+	0.0831305i
$780$	14.6684	+	21.6343i	0.525214	+	0.774633i
$781$	19.6666	−	4.32895i	0.703728	−	0.154902i
$782$	8.22426	−	29.6211i	0.294099	−	1.05925i
$783$	5.37460	−	3.23379i	0.192073	−	0.115566i
$784$	−2.66361	−	3.13584i	−0.0951289	−	0.111994i
$785$	−43.9061	+	14.7937i	−1.56708	+	0.528010i
$786$	8.78280	−	4.06335i	0.313272	−	0.144935i
$787$	11.3436	−	21.3964i	0.404357	−	0.762698i	−0.594795	−	0.803877i	$-0.702767\pi$
$787$	11.3436	−	21.3964i	0.404357	−	0.762698i	0.999152	+	0.0411796i	$0.0131116\pi$
$788$	−2.54536	−	0.560276i	−0.0906748	−	0.0199590i
$789$	1.40277	+	3.52070i	0.0499401	+	0.125340i
$790$	1.98138	+	0.667605i	0.0704944	+	0.0237523i
$791$	−10.4866	+	1.14049i	−0.372860	+	0.0405510i
$792$	0.0739647	+	1.36420i	0.00262822	+	0.0484747i
$793$	−0.882037	+	16.2682i	−0.0313221	+	0.577701i
$794$	−16.4825	−	1.79258i	−0.584943	−	0.0636164i
$795$	33.3369	+	15.4233i	1.18234	+	0.547007i
$796$	−3.57441	+	2.71720i	−0.126692	+	0.0963085i
$797$	34.4799	−	26.2110i	1.22134	−	0.928440i	0.222425	−	0.974950i	$-0.428603\pi$
$797$	34.4799	−	26.2110i	1.22134	−	0.928440i	0.998918	+	0.0465095i	$0.0148098\pi$
$798$	2.36666	+	1.09493i	0.0837789	+	0.0387603i
$799$	−42.2793	−	4.59815i	−1.49573	−	0.162671i
$800$	0.473822	−	8.73914i	0.0167521	−	0.308975i
$801$	0.131914	+	2.43300i	0.00466094	+	0.0859659i
$802$	−12.0214	+	1.30741i	−0.424490	+	0.0461661i
$803$	19.0840	+	6.43016i	0.673460	+	0.226915i
$804$	−0.570288	−	1.43131i	−0.0201125	−	0.0504786i
$805$	45.2476	+	9.95975i	1.59477	+	0.351035i
$806$	−10.8434	+	20.4528i	−0.381943	+	0.720420i
$807$	−10.5180	+	4.86614i	−0.370250	+	0.171296i
$808$	−8.18365	+	2.75739i	−0.287900	+	0.0970047i
$809$	9.92983	+	11.6903i	0.349114	+	0.411009i	0.908491	−	0.417904i	$-0.137235\pi$
$809$	9.92983	+	11.6903i	0.349114	+	0.411009i	−0.559377	+	0.828914i	$0.688959\pi$
$810$	3.17754	−	1.91186i	0.111647	−	0.0671760i
$811$	3.04394	−	10.9633i	0.106887	−	0.384973i	−0.890684	−	0.454622i	$-0.849774\pi$
$811$	3.04394	−	10.9633i	0.106887	−	0.384973i	0.997572	+	0.0696493i	$0.0221880\pi$
$812$	−10.4059	+	2.29052i	−0.365177	+	0.0803815i
$813$	−16.4822	−	24.3095i	−0.578057	−	0.852571i
$814$	0.539111	−	0.510674i	0.0188958	−	0.0178991i
$815$	48.3530	+	29.0930i	1.69373	+	1.01908i
$816$	0.676220	+	4.12476i	0.0236724	+	0.144395i
$817$	−2.44288	+	3.60298i	−0.0854655	+	0.126052i
$818$	12.7587	−	32.0219i	0.446097	−	1.11962i
$819$	7.75131	−	9.12554i	0.270853	−	0.318872i
$820$	1.31858	−	8.04299i	0.0460469	−	0.280874i
$821$	−5.92983	−	5.61703i	−0.206952	−	0.196036i	0.577202	−	0.816601i	$-0.304144\pi$
$821$	−5.92983	−	5.61703i	−0.206952	−	0.196036i	−0.784155	+	0.620566i	$0.786903\pi$
$822$	−5.61196	−	20.2125i	−0.195740	−	0.704990i
$823$	−16.2928	−	30.7315i	−0.567931	−	1.07123i	−0.986610	−	0.163098i	$-0.947851\pi$
$823$	−16.2928	−	30.7315i	−0.567931	−	1.07123i	0.418679	−	0.908134i	$-0.362493\pi$
$824$	−6.73678	−	5.12117i	−0.234687	−	0.178404i
$825$	11.9570			0.416288
$826$	12.6998	−	2.99424i	0.441882	−	0.104183i
$827$	49.1413			1.70881			0.854405	−	0.519608i	$-0.173922\pi$
$827$	49.1413			1.70881			0.854405	+	0.519608i	$0.173922\pi$
$828$	−5.85509	−	4.45092i	−0.203478	−	0.154680i
$829$	−9.19240	−	17.3387i	−0.319265	−	0.602198i	0.670989	−	0.741467i	$-0.265870\pi$
$829$	−9.19240	−	17.3387i	−0.319265	−	0.602198i	−0.990255	+	0.139269i	$0.955525\pi$
$830$	14.5354	+	52.3516i	0.504530	+	1.81715i
$831$	−9.52318	−	9.02083i	−0.330355	−	0.312929i
$832$	−1.14031	+	6.95560i	−0.0395332	+	0.241142i
$833$	11.1334	−	13.1073i	0.385750	−	0.454140i
$834$	−0.663661	+	1.66566i	−0.0229807	+	0.0576772i
$835$	12.7178	−	18.7574i	0.440118	−	0.649126i
$836$	−0.339298	−	2.06962i	−0.0117349	−	0.0715794i
$837$	2.81421	+	1.69325i	0.0972732	+	0.0585273i
$838$	25.3845	−	24.0454i	0.876892	−	0.830636i
$839$	−9.28506	−	13.6944i	−0.320556	−	0.472785i	0.632936	−	0.774204i	$-0.281850\pi$
$839$	−9.28506	−	13.6944i	−0.320556	−	0.472785i	−0.953492	+	0.301420i	$0.902539\pi$
$840$	−6.15214	+	1.35419i	−0.212269	+	0.0467239i
$841$	2.76723	−	9.96668i	0.0954219	−	0.343679i
$842$	−18.4768	+	11.1171i	−0.636753	+	0.383121i
$843$	−16.9487	−	19.9535i	−0.583743	−	0.687235i
$844$	15.6758	−	5.28181i	0.539585	−	0.181807i
$845$	−123.453	+	57.1156i	−4.24692	+	1.96483i
$846$	−4.76594	+	8.98951i	−0.163856	+	0.309066i
$847$	−15.1524	−	3.33529i	−0.520642	−	0.114602i
$848$	3.66626	+	9.20162i	0.125900	+	0.315985i
$849$	23.2592	+	7.83692i	0.798252	+	0.268962i
$850$	36.3672	−	3.95517i	1.24739	−	0.135661i
$851$	0.216426	+	3.99174i	0.00741898	+	0.136835i
$852$	0.797993	−	14.7181i	0.0273388	−	0.504234i
$853$	5.86117	+	0.637441i	0.200683	+	0.0218256i	0.207908	−	0.978148i	$-0.433334\pi$
$853$	5.86117	+	0.637441i	0.200683	+	0.0218256i	−0.00722554	+	0.999974i	$0.502300\pi$
$854$	−3.56356	−	1.64868i	−0.121943	−	0.0564166i
$855$	−4.53192	+	3.44508i	−0.154988	+	0.117819i
$856$	−8.36882	+	6.36181i	−0.286040	+	0.217442i
$857$	20.2629	+	9.37460i	0.692167	+	0.320230i	0.734246	−	0.678884i	$-0.237536\pi$
$857$	20.2629	+	9.37460i	0.692167	+	0.320230i	−0.0420790	+	0.999114i	$0.513398\pi$
$858$	−9.57316	−	1.04114i	−0.326822	−	0.0355441i
$859$	−1.80503	+	33.2917i	−0.0615867	+	1.13590i	0.790487	+	0.612478i	$0.209827\pi$
$859$	−1.80503	+	33.2917i	−0.0615867	+	1.13590i	−0.852074	+	0.523421i	$0.824655\pi$
$860$	−0.569312	−	10.5003i	−0.0194134	−	0.358059i
$861$	−3.71158	+	0.403659i	−0.126490	+	0.0137566i
$862$	−11.5636	−	3.89623i	−0.393858	−	0.132706i
$863$	−10.4025	−	26.1082i	−0.354104	−	0.888733i	−0.992856	−	0.119321i	$-0.961928\pi$
$863$	−10.4025	−	26.1082i	−0.354104	−	0.888733i	0.638752	−	0.769413i	$-0.279451\pi$
$864$	0.976621	+	0.214970i	0.0332253	+	0.00731344i
$865$	−44.3623	+	83.6762i	−1.50836	+	2.84508i
$866$	−11.0279	+	5.10207i	−0.374745	+	0.173375i
$867$	−0.446243	+	0.150357i	−0.0151552	+	0.00510638i
$868$	−3.61184	−	4.25219i	−0.122594	−	0.144329i
$869$	−0.660024	+	0.397123i	−0.0223898	+	0.0134715i
$870$	6.22286	−	22.4127i	0.210975	−	0.759862i
$871$	10.6060	−	2.33455i	0.359369	−	0.0791031i
$872$	8.72807	+	12.8729i	0.295570	+	0.435933i
$873$	−1.16696	+	1.10540i	−0.0394955	+	0.0374121i
$874$	9.67417	+	5.82076i	0.327234	+	0.196890i
$875$	3.82376	+	23.3239i	0.129267	+	0.788491i
$876$	8.27205	−	12.2004i	0.279487	−	0.412212i
$877$	19.3232	−	48.4977i	0.652499	−	1.63765i	−0.112526	−	0.993649i	$-0.535894\pi$
$877$	19.3232	−	48.4977i	0.652499	−	1.63765i	0.765025	−	0.644001i	$-0.222727\pi$
$878$	−24.6131	+	28.9768i	−0.830651	+	0.977918i
$879$	2.78236	−	16.9716i	0.0938465	−	0.572439i
$880$	3.67816	+	3.48414i	0.123991	+	0.117450i
$881$	−6.00233	−	21.6184i	−0.202224	−	0.728344i	−0.993192	−	0.116487i	$-0.962837\pi$
$881$	−6.00233	−	21.6184i	−0.202224	−	0.728344i	0.790969	−	0.611857i	$-0.209577\pi$
$882$	−1.92722	−	3.63513i	−0.0648929	−	0.122401i
$883$	30.3025	+	23.0354i	1.01976	+	0.775201i	0.974640	−	0.223780i	$-0.0718398\pi$
$883$	30.3025	+	23.0354i	1.01976	+	0.775201i	0.0451203	+	0.998982i	$0.485633\pi$
$884$	−29.4613			−0.990889
$885$	−7.21116	+	27.5566i	−0.242401	+	0.926305i
$886$	−11.4925			−0.386098
$887$	−34.2679	−	26.0498i	−1.15060	−	0.874666i	−0.157001	−	0.987598i	$-0.550182\pi$
$887$	−34.2679	−	26.0498i	−1.15060	−	0.874666i	−0.993603	+	0.112933i	$0.963976\pi$
$888$	−0.254598	−	0.480222i	−0.00854374	−	0.0161152i
$889$	6.43140	+	23.1638i	0.215702	+	0.776890i
$890$	6.55989	+	6.21386i	0.219888	+	0.208289i
$891$	−0.221027	+	1.34820i	−0.00740468	+	0.0451665i
$892$	−5.99121	+	7.05340i	−0.200601	+	0.236165i
$893$	5.78127	−	14.5099i	0.193463	−	0.485555i
$894$	−0.753697	+	1.11162i	−0.0252074	+	0.0371781i
$895$	−6.82729	−	41.6446i	−0.228211	−	1.39203i
$896$	−1.45555	−	0.875773i	−0.0486264	−	0.0292575i
$897$	37.6355	−	35.6502i	1.25661	−	1.19033i
$898$	−5.29778	−	7.81365i	−0.176789	−	0.260745i
$899$	20.1192	−	4.42857i	0.671013	−	0.147701i
$900$	2.34140	−	8.43296i	0.0780467	−	0.281099i
$901$	−35.4752	+	21.3447i	−1.18185	+	0.711097i
$902$	1.94389	+	2.28853i	0.0647246	+	0.0761997i
$903$	−4.56484	+	1.53807i	−0.151908	+	0.0511839i
$904$	5.63576	−	2.60738i	0.187443	−	0.0867202i
$905$	3.66316	−	6.90945i	0.121768	−	0.229678i
$906$	6.48396	+	1.42723i	0.215415	+	0.0474164i
$907$	4.42574	+	11.1078i	0.146954	+	0.368828i	0.983966	−	0.178358i	$-0.0570785\pi$
$907$	4.42574	+	11.1078i	0.146954	+	0.368828i	−0.837011	+	0.547186i	$0.815699\pi$
$908$	−6.12176	−	2.06266i	−0.203158	−	0.0684519i
$909$	−8.58507	+	0.933683i	−0.284749	+	0.0309683i
$910$	−2.40383	−	44.3360i	−0.0796861	−	1.46972i
$911$	−2.81769	+	51.9693i	−0.0933543	+	1.72182i	0.459192	+	0.888337i	$0.348139\pi$
$911$	−2.81769	+	51.9693i	−0.0933543	+	1.72182i	−0.552546	+	0.833482i	$0.686344\pi$
$912$	−1.52610	−	0.165973i	−0.0505342	−	0.00549592i
$913$	−18.1665	−	8.40471i	−0.601223	−	0.278155i
$914$	20.8444	−	15.8455i	0.689473	−	0.524124i
$915$	6.82386	−	5.18736i	0.225590	−	0.171489i
$916$	24.4102	+	11.2934i	0.806535	+	0.373143i
$917$	−16.3423	−	1.77734i	−0.539672	−	0.0586928i
$918$	−0.226291	+	4.17369i	−0.00746871	+	0.137752i
$919$	2.57584	+	47.5086i	0.0849692	+	1.56716i	0.661410	+	0.750025i	$0.269958\pi$
$919$	2.57584	+	47.5086i	0.0849692	+	1.56716i	−0.576440	+	0.817139i	$0.695559\pi$
$920$	−27.1143	+	2.94886i	−0.893933	+	0.0972210i
$921$	−0.369189	−	0.124394i	−0.0121652	−	0.00409893i
$922$	1.35404	+	3.39837i	0.0445928	+	0.111919i
$923$	101.463	+	22.3338i	3.33971	+	0.735125i
$924$	1.08707	−	2.05043i	0.0357619	−	0.0674542i
$925$	−4.31736	+	1.99743i	−0.141954	+	0.0656749i
$926$	−34.7363	+	11.7040i	−1.14151	+	0.384618i
$927$	−5.47838	−	6.44965i	−0.179934	−	0.211834i
$928$	5.37460	−	3.23379i	0.176430	−	0.106154i
$929$	6.34091	−	22.8379i	0.208038	−	0.749287i	−0.783714	−	0.621121i	$-0.786677\pi$
$929$	6.34091	−	22.8379i	0.208038	−	0.749287i	0.991753	−	0.128165i	$-0.0409088\pi$
$930$	11.8948	−	2.61824i	0.390045	−	0.0858553i
$931$	3.54446	+	5.22769i	0.116165	+	0.171331i
$932$	−5.24678	+	4.97001i	−0.171864	+	0.162798i
$933$	19.4449	+	11.6996i	0.636599	+	0.383029i
$934$	−4.08988	−	24.9471i	−0.133825	−	0.816295i
$935$	−11.8840	+	17.5276i	−0.388648	+	0.573213i
$936$	−2.60890	+	6.54785i	−0.0852746	+	0.214023i
$937$	7.59081	−	8.93660i	0.247981	−	0.291946i	−0.624062	−	0.781375i	$-0.714519\pi$
$937$	7.59081	−	8.93660i	0.247981	−	0.291946i	0.872043	+	0.489429i	$0.162795\pi$
$938$	−0.423427	+	2.58279i	−0.0138254	+	0.0843310i
$939$	13.9269	+	13.1923i	0.454488	+	0.430514i
$940$	10.0943	+	36.3564i	0.329240	+	1.18581i
$941$	−2.80983	−	5.29990i	−0.0915978	−	0.172772i	0.833480	−	0.552550i	$-0.186345\pi$
$941$	−2.80983	−	5.29990i	−0.0915978	−	0.172772i	−0.925078	+	0.379778i	$0.876000\pi$
$942$	−9.94620	−	7.56090i	−0.324065	−	0.246348i
$943$	−16.1646			−0.526390
$944$	−6.52199	+	4.05754i	−0.212273	+	0.132062i
$945$	−6.29942			−0.204920
$946$	3.08416	+	2.34452i	0.100275	+	0.0762268i
$947$	2.28765	+	4.31496i	0.0743386	+	0.140217i	0.917895	−	0.396823i	$-0.129887\pi$
$947$	2.28765	+	4.31496i	0.0743386	+	0.140217i	−0.843557	+	0.537040i	$0.819542\pi$
$948$	0.150836	+	0.543264i	0.00489894	+	0.0176444i
$949$	75.4281	+	71.4493i	2.44850	+	2.31934i
$950$	−2.17356	+	13.2581i	−0.0705197	+	0.430151i
$951$	1.87678	−	2.20951i	0.0608587	−	0.0716483i
$952$	2.62808	−	6.59599i	0.0851767	−	0.213777i
$953$	−2.61759	+	3.86066i	−0.0847920	+	0.125059i	−0.867720	−	0.497054i	$-0.834415\pi$
$953$	−2.61759	+	3.86066i	−0.0847920	+	0.125059i	0.782928	+	0.622113i	$0.213725\pi$
$954$	1.60247	+	9.77463i	0.0518818	+	0.316465i
$955$	−15.2302	−	9.16373i	−0.492839	−	0.296531i
$956$	−4.50651	+	4.26879i	−0.145751	+	0.138063i
$957$	4.80906	+	7.09283i	0.155455	+	0.229279i
$958$	0.422297	−	0.0929545i	0.0136438	−	0.00300322i
$959$	−9.53306	+	34.3350i	−0.307839	+	1.10873i
$960$	3.17754	−	1.91186i	0.102555	−	0.0617051i
$961$	−13.0857	−	15.4057i	−0.422120	−	0.496958i
$962$	3.63056	−	1.22328i	0.117054	−	0.0394400i
$963$	−9.54076	+	4.41403i	−0.307447	+	0.142240i
$964$	9.44925	−	17.8232i	0.304340	−	0.574046i
$965$	28.3605	+	6.24261i	0.912956	+	0.200957i
$966$	4.62435	+	11.6063i	0.148786	+	0.373425i
$967$	14.6567	+	4.93843i	0.471329	+	0.158809i	0.544935	−	0.838478i	$-0.316554\pi$
$967$	14.6567	+	4.93843i	0.471329	+	0.158809i	−0.0736064	+	0.997287i	$0.523451\pi$
$968$	9.07995	−	0.987504i	0.291841	−	0.0317396i
$969$	−0.347379	−	6.40702i	−0.0111594	−	0.205823i
$970$	−0.322710	+	5.95204i	−0.0103616	+	0.191108i
$971$	43.9016	+	4.77458i	1.40887	+	0.153224i	0.780725	−	0.624875i	$-0.214850\pi$
$971$	43.9016	+	4.77458i	1.40887	+	0.153224i	0.628143	+	0.778098i	$0.283815\pi$
$972$	0.907575	+	0.419889i	0.0291105	+	0.0134679i
$973$	2.42474	−	1.84324i	0.0777334	−	0.0590914i
$974$	−4.12520	+	3.13589i	−0.132180	+	0.100481i
$975$	55.9864	+	25.9021i	1.79300	+	0.829530i
$976$	2.29790	+	0.249911i	0.0735539	+	0.00799946i
$977$	0.0216930	−	0.400104i	0.000694021	−	0.0128005i	−0.998166	−	0.0605380i	$-0.980718\pi$
$977$	0.0216930	−	0.400104i	0.000694021	−	0.0128005i	0.998860	+	0.0477376i	$0.0152011\pi$
$978$	0.823839	+	15.1948i	0.0263435	+	0.485876i
$979$	−3.30934	+	0.359912i	−0.105767	+	0.0115028i
$980$	−14.4590	−	4.87181i	−0.461877	−	0.155624i
$981$	5.75671	+	14.4483i	0.183798	+	0.461297i
$982$	31.0797	+	6.84115i	0.991792	+	0.218310i
$983$	−7.43384	+	14.0217i	−0.237103	+	0.447223i	−0.973298	−	0.229546i	$-0.926276\pi$
$983$	−7.43384	+	14.0217i	−0.237103	+	0.447223i	0.736195	+	0.676769i	$0.236621\pi$
$984$	1.99470	−	0.922845i	0.0635886	−	0.0294192i
$985$	−9.15916	+	3.08608i	−0.291835	+	0.0983307i
$986$	16.9730	+	19.9822i	0.540531	+	0.636362i
$987$	14.8098	−	8.91078i	0.471402	−	0.283633i
$988$	2.89467	−	10.4257i	0.0920918	−	0.331685i
$989$	−20.3682	+	4.48339i	−0.647673	+	0.142564i
$990$	2.84318	+	4.19338i	0.0903623	+	0.133274i
$991$	31.8075	−	30.1297i	1.01040	−	0.957101i	0.0113166	−	0.999936i	$-0.496398\pi$
$991$	31.8075	−	30.1297i	1.01040	−	0.957101i	0.999082	+	0.0428354i	$0.0136391\pi$
$992$	2.81421	+	1.69325i	0.0893511	+	0.0537608i
$993$	−0.567060	−	3.45891i	−0.0179951	−	0.109765i
$994$	−14.0512	+	20.7240i	−0.445678	+	0.657327i
$995$	−6.16293	+	15.4678i	−0.195378	+	0.490362i
$996$	−9.48499	+	11.1666i	−0.300543	+	0.353827i
$997$	6.32599	−	38.5869i	0.200346	−	1.22206i	−0.674727	−	0.738067i	$-0.735739\pi$
$997$	6.32599	−	38.5869i	0.200346	−	1.22206i	0.875073	−	0.483991i	$-0.160813\pi$
$998$	4.37394	+	4.14321i	0.138455	+	0.131151i
$999$	−0.145412	−	0.523726i	−0.00460063	−	0.0165700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.a.25.2	✓	56
59.26	even	29	inner	354.2.e.a.85.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.a.25.2	✓	56	1.1	even	1	trivial
354.2.e.a.85.2	yes	56	59.26	even	29	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.796093 + 0.605174i) q^{2} +(0.468408 + 0.883512i) q^{3} +(0.267528 + 0.963550i) q^{4} +(2.69226 + 2.55024i) q^{5} +(-0.161782 + 0.986827i) q^{6} +(1.09972 - 1.29469i) q^{7} +(-0.370138 + 0.928977i) q^{8} +(-0.561187 + 0.827689i) q^{9} +O(q^{10})\)	\(q+(0.796093 + 0.605174i) q^{2} +(0.468408 + 0.883512i) q^{3} +(0.267528 + 0.963550i) q^{4} +(2.69226 + 2.55024i) q^{5} +(-0.161782 + 0.986827i) q^{6} +(1.09972 - 1.29469i) q^{7} +(-0.370138 + 0.928977i) q^{8} +(-0.561187 + 0.827689i) q^{9} +(0.599947 + 3.65951i) q^{10} +(-1.17064 - 0.704350i) q^{11} +(-0.725995 + 0.687699i) q^{12} +(-3.95550 - 5.83393i) q^{13} +(1.65899 - 0.365171i) q^{14} +(-0.992093 + 3.57320i) q^{15} +(-0.856857 + 0.515554i) q^{16} +(-2.70596 - 3.18570i) q^{17} +(-0.947653 + 0.319302i) q^{18} +(1.39322 - 0.644571i) q^{19} +(-1.73703 + 3.27639i) q^{20} +(1.65899 + 0.365171i) q^{21} +(-0.505683 - 1.26917i) q^{22} +(6.96978 + 2.34839i) q^{23} +(-0.994138 + 0.108119i) q^{24} +(0.473822 + 8.73914i) q^{25} +(0.381595 - 7.03811i) q^{26} +(-0.994138 - 0.108119i) q^{27} +(1.54170 + 0.713267i) q^{28} +(-4.99346 + 3.79593i) q^{29} +(-2.95220 + 2.24421i) q^{30} +(-2.98078 - 1.37906i) q^{31} +(-0.994138 - 0.108119i) q^{32} +(0.0739647 - 1.36420i) q^{33} +(-0.226291 - 4.17369i) q^{34} +(6.26249 - 0.681087i) q^{35} +(-0.947653 - 0.319302i) q^{36} +(0.201184 + 0.504934i) q^{37} +(1.49921 + 0.330001i) q^{38} +(3.30155 - 6.22739i) q^{39} +(-3.36562 + 1.55710i) q^{40} +(-2.08278 + 0.701771i) q^{41} +(1.09972 + 1.29469i) q^{42} +(-2.42978 + 1.46195i) q^{43} +(0.365498 - 1.31640i) q^{44} +(-3.62167 + 0.797189i) q^{45} +(4.12741 + 6.08747i) q^{46} +(7.38682 - 6.99717i) q^{47} +(-0.856857 - 0.515554i) q^{48} +(0.665637 + 4.06020i) q^{49} +(-4.91149 + 7.24391i) q^{50} +(1.54711 - 3.88296i) q^{51} +(4.56307 - 5.37206i) q^{52} +(1.60247 - 9.77463i) q^{53} +(-0.725995 - 0.687699i) q^{54} +(-1.35540 - 4.88170i) q^{55} +(0.795687 + 1.50083i) q^{56} +(1.22208 + 0.929001i) q^{57} -6.27246 q^{58} +(7.68030 - 0.114297i) q^{59} -3.70837 q^{60} +(-1.84013 - 1.39883i) q^{61} +(-1.53841 - 2.90175i) q^{62} +(0.454451 + 1.63679i) q^{63} +(-0.725995 - 0.687699i) q^{64} +(4.22870 - 25.7939i) q^{65} +(0.884460 - 1.04127i) q^{66} +(-0.570288 + 1.43131i) q^{67} +(2.34566 - 3.45959i) q^{68} +(1.18987 + 7.25789i) q^{69} +(5.39770 + 3.24769i) q^{70} +(-10.7010 + 10.1365i) q^{71} +(-0.561187 - 0.827689i) q^{72} +(-14.3957 + 3.16872i) q^{73} +(-0.145412 + 0.523726i) q^{74} +(-7.49919 + 4.51211i) q^{75} +(0.993801 + 1.16999i) q^{76} +(-2.19929 + 0.741026i) q^{77} +(6.39700 - 2.95957i) q^{78} +(0.264096 - 0.498137i) q^{79} +(-3.62167 - 0.797189i) q^{80} +(-0.370138 - 0.928977i) q^{81} +(-2.08278 - 0.701771i) q^{82} +(14.5653 - 1.58407i) q^{83} +(0.0919660 + 1.69621i) q^{84} +(0.839169 - 15.4776i) q^{85} +(-2.81906 - 0.306592i) q^{86} +(-5.69273 - 2.63374i) q^{87} +(1.08762 - 0.826790i) q^{88} +(1.93974 - 1.47455i) q^{89} +(-3.36562 - 1.55710i) q^{90} +(-11.9030 - 1.29453i) q^{91} +(-0.398180 + 7.34399i) q^{92} +(-0.177810 - 3.27952i) q^{93} +(10.1151 - 1.10008i) q^{94} +(5.39471 + 1.81769i) q^{95} +(-0.370138 - 0.928977i) q^{96} +(1.56981 + 0.345541i) q^{97} +(-1.92722 + 3.63513i) q^{98} +(1.23993 - 0.573653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

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Database

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