LMFDB - Embedded newform 207.2.o.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29988 + 0.0619210i) q^{2} +(1.73131 + 0.0507847i) q^{3} +(-0.305085 + 0.0291321i) q^{4} +(-1.59287 - 1.51880i) q^{5} +(-2.25364 + 0.0411901i) q^{6} +(0.597259 + 3.09887i) q^{7} +(2.97099 - 0.427164i) q^{8} +(2.99484 + 0.175848i) q^{9} +O(q^{10})$	\(q+(-1.29988 + 0.0619210i) q^{2} +(1.73131 + 0.0507847i) q^{3} +(-0.305085 + 0.0291321i) q^{4} +(-1.59287 - 1.51880i) q^{5} +(-2.25364 + 0.0411901i) q^{6} +(0.597259 + 3.09887i) q^{7} +(2.97099 - 0.427164i) q^{8} +(2.99484 + 0.175848i) q^{9} +(2.16459 + 1.87562i) q^{10} +(5.77017 - 2.97473i) q^{11} +(-0.529675 + 0.0349429i) q^{12} +(0.586991 + 0.113133i) q^{13} +(-0.968251 - 3.99119i) q^{14} +(-2.68061 - 2.71039i) q^{15} +(-3.23362 + 0.623229i) q^{16} +(0.498465 + 1.09149i) q^{17} +(-3.90383 - 0.0431378i) q^{18} +(2.29054 + 1.04605i) q^{19} +(0.530206 + 0.416958i) q^{20} +(0.876662 + 5.39543i) q^{21} +(-7.31634 + 4.22409i) q^{22} +(-4.43144 - 1.83367i) q^{23} +(5.16539 - 0.588671i) q^{24} +(-0.00742427 - 0.155855i) q^{25} +(-0.770024 - 0.110713i) q^{26} +(5.17606 + 0.456539i) q^{27} +(-0.272491 - 0.928020i) q^{28} +(-0.128107 + 1.34159i) q^{29} +(3.65231 + 3.35721i) q^{30} +(3.48701 - 2.74222i) q^{31} +(-1.66914 + 0.404928i) q^{32} +(10.1410 - 4.85713i) q^{33} +(-0.715532 - 1.38794i) q^{34} +(3.75520 - 5.84321i) q^{35} +(-0.918804 + 0.0335974i) q^{36} +(-1.94758 + 6.63286i) q^{37} +(-3.04220 - 1.21791i) q^{38} +(1.01051 + 0.225678i) q^{39} +(-5.38117 - 3.83191i) q^{40} +(-7.43078 + 7.79318i) q^{41} +(-1.47365 - 6.95914i) q^{42} +(-1.53385 + 1.95045i) q^{43} +(-1.67373 + 1.07564i) q^{44} +(-4.50331 - 4.82866i) q^{45} +(5.87389 + 2.10915i) q^{46} +(-3.46639 - 2.00132i) q^{47} +(-5.63003 + 0.914781i) q^{48} +(-2.74772 + 1.10002i) q^{49} +(0.0193013 + 0.202133i) q^{50} +(0.807565 + 1.91501i) q^{51} +(-0.182378 - 0.0174150i) q^{52} +(-6.44700 - 7.44024i) q^{53} +(-6.75653 - 0.272940i) q^{54} +(-13.7091 - 4.02536i) q^{55} +(3.09818 + 8.95160i) q^{56} +(3.91250 + 1.92736i) q^{57} +(0.0834506 - 1.75184i) q^{58} +(0.762767 - 3.95761i) q^{59} +(0.896773 + 0.748809i) q^{60} +(-0.785782 + 1.96279i) q^{61} +(-4.36290 + 3.78048i) q^{62} +(1.24377 + 9.38566i) q^{63} +(8.46407 - 2.48528i) q^{64} +(-0.763172 - 1.07173i) q^{65} +(-12.8813 + 6.94164i) q^{66} +(-3.18925 + 6.18629i) q^{67} +(-0.183871 - 0.318475i) q^{68} +(-7.57906 - 3.39969i) q^{69} +(-4.51950 + 7.82801i) q^{70} +(-5.22568 - 8.13132i) q^{71} +(8.97276 - 0.756846i) q^{72} +(6.46681 - 14.1603i) q^{73} +(2.12092 - 8.74253i) q^{74} +(-0.00493865 - 0.270209i) q^{75} +(-0.729282 - 0.252407i) q^{76} +(12.6646 + 16.1043i) q^{77} +(-1.32752 - 0.230783i) q^{78} +(-0.600047 + 0.207678i) q^{79} +(6.09728 + 3.91849i) q^{80} +(8.93816 + 1.05327i) q^{81} +(9.17657 - 10.5903i) q^{82} +(-4.89683 + 4.66912i) q^{83} +(-0.424637 - 1.62053i) q^{84} +(0.863756 - 2.49566i) q^{85} +(1.87306 - 2.63034i) q^{86} +(-0.289924 + 2.31620i) q^{87} +(15.8724 - 11.3027i) q^{88} +(-0.587972 + 4.08944i) q^{89} +(6.15277 + 5.99783i) q^{90} +1.88658i q^{91} +(1.40538 + 0.430327i) q^{92} +(6.17635 - 4.57053i) q^{93} +(4.62982 + 2.38684i) q^{94} +(-2.05978 - 5.14508i) q^{95} +(-2.91035 + 0.616288i) q^{96} +(-18.6170 - 4.51643i) q^{97} +(3.50360 - 1.60004i) q^{98} +(17.8038 - 7.89417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.29988	+	0.0619210i	−0.919155	+	0.0437848i	−0.501824	−	0.864970i	$-0.667338\pi$
$2$	−1.29988	+	0.0619210i	−0.919155	+	0.0437848i	−0.417331	+	0.908754i	$0.637035\pi$
$3$	1.73131	+	0.0507847i	0.999570	+	0.0293206i
$3$	1.73131	+	0.0507847i	0.999570	+	0.0293206i
$4$	−0.305085	+	0.0291321i	−0.152542	+	0.0145660i
$5$	−1.59287	−	1.51880i	−0.712352	−	0.679226i	0.244550	−	0.969637i	$-0.421360\pi$
$5$	−1.59287	−	1.51880i	−0.712352	−	0.679226i	−0.956902	+	0.290410i	$0.906208\pi$
$6$	−2.25364	+	0.0411901i	−0.920044	+	0.0168158i
$7$	0.597259	+	3.09887i	0.225743	+	1.17126i	0.901046	+	0.433724i	$0.142801\pi$
$7$	0.597259	+	3.09887i	0.225743	+	1.17126i	−0.675303	+	0.737540i	$0.735987\pi$
$8$	2.97099	−	0.427164i	1.05040	−	0.151025i
$9$	2.99484	+	0.175848i	0.998281	+	0.0586159i
$10$	2.16459	+	1.87562i	0.684502	+	0.593124i
$11$	5.77017	−	2.97473i	1.73977	−	0.896914i	0.775770	−	0.631016i	$-0.217362\pi$
$11$	5.77017	−	2.97473i	1.73977	−	0.896914i	0.964001	−	0.265899i	$-0.0856687\pi$
$12$	−0.529675	+	0.0349429i	−0.152904	+	0.0100871i
$13$	0.586991	+	0.113133i	0.162802	+	0.0313775i	0.270001	−	0.962860i	$-0.412976\pi$
$13$	0.586991	+	0.113133i	0.162802	+	0.0313775i	−0.107199	+	0.994238i	$0.534188\pi$
$14$	−0.968251	−	3.99119i	−0.258776	−	1.06669i
$15$	−2.68061	−	2.71039i	−0.692130	−	0.699821i
$16$	−3.23362	+	0.623229i	−0.808405	+	0.155807i
$17$	0.498465	+	1.09149i	0.120896	+	0.264724i	0.960398	−	0.278631i	$-0.0898808\pi$
$17$	0.498465	+	1.09149i	0.120896	+	0.264724i	−0.839503	+	0.543356i	$0.817154\pi$
$18$	−3.90383	−	0.0431378i	−0.920141	−	0.0101677i
$19$	2.29054	+	1.04605i	0.525485	+	0.239981i	0.660451	−	0.750869i	$-0.270365\pi$
$19$	2.29054	+	1.04605i	0.525485	+	0.239981i	−0.134966	+	0.990850i	$0.543092\pi$
$20$	0.530206	+	0.416958i	0.118558	+	0.0932347i
$21$	0.876662	+	5.39543i	0.191303	+	1.17738i
$22$	−7.31634	+	4.22409i	−1.55985	+	0.900579i
$23$	−4.43144	−	1.83367i	−0.924019	−	0.382346i
$23$	−4.43144	−	1.83367i	−0.924019	−	0.382346i
$24$	5.16539	−	0.588671i	1.05438	−	0.120162i
$25$	−0.00742427	−	0.155855i	−0.00148485	−	0.0311709i
$26$	−0.770024	−	0.110713i	−0.151014	−	0.0217125i
$27$	5.17606	+	0.456539i	0.996133	+	0.0878609i
$28$	−0.272491	−	0.928020i	−0.0514960	−	0.175379i
$29$	−0.128107	+	1.34159i	−0.0237888	+	0.249127i	0.975753	+	0.218873i	$0.0702379\pi$
$29$	−0.128107	+	1.34159i	−0.0237888	+	0.249127i	−0.999542	+	0.0302548i	$0.990368\pi$
$30$	3.65231	+	3.35721i	0.666817	+	0.612939i
$31$	3.48701	−	2.74222i	0.626286	−	0.492517i	−0.253847	−	0.967244i	$-0.581696\pi$
$31$	3.48701	−	2.74222i	0.626286	−	0.492517i	0.880133	+	0.474728i	$0.157453\pi$
$32$	−1.66914	+	0.404928i	−0.295064	+	0.0715818i
$33$	10.1410	−	4.85713i	1.76532	−	0.845518i
$34$	−0.715532	−	1.38794i	−0.122713	−	0.238029i
$35$	3.75520	−	5.84321i	0.634745	−	0.987683i
$36$	−0.918804	+	0.0335974i	−0.153134	+	0.00559957i
$37$	−1.94758	+	6.63286i	−0.320181	+	1.09044i	0.629444	+	0.777046i	$0.283283\pi$
$37$	−1.94758	+	6.63286i	−0.320181	+	1.09044i	−0.949625	+	0.313390i	$0.898535\pi$
$38$	−3.04220	−	1.21791i	−0.493510	−	0.197572i
$39$	1.01051	+	0.225678i	0.161812	+	0.0361375i
$40$	−5.38117	−	3.83191i	−0.850838	−	0.605879i
$41$	−7.43078	+	7.79318i	−1.16049	+	1.21709i	−0.188501	+	0.982073i	$0.560363\pi$
$41$	−7.43078	+	7.79318i	−1.16049	+	1.21709i	−0.971991	+	0.235017i	$0.924486\pi$
$42$	−1.47365	−	6.95914i	−0.227389	−	1.07382i
$43$	−1.53385	+	1.95045i	−0.233911	+	0.297442i	−0.888811	−	0.458273i	$-0.848468\pi$
$43$	−1.53385	+	1.95045i	−0.233911	+	0.297442i	0.654901	+	0.755715i	$0.272710\pi$
$44$	−1.67373	+	1.07564i	−0.252324	+	0.162159i
$45$	−4.50331	−	4.82866i	−0.671314	−	0.719814i
$46$	5.87389	+	2.10915i	0.866058	+	0.310977i
$47$	−3.46639	−	2.00132i	−0.505625	−	0.291923i	0.225408	−	0.974264i	$-0.427628\pi$
$47$	−3.46639	−	2.00132i	−0.505625	−	0.291923i	−0.731034	+	0.682342i	$0.760962\pi$
$48$	−5.63003	+	0.914781i	−0.812625	+	0.132037i
$49$	−2.74772	+	1.10002i	−0.392531	+	0.157146i
$50$	0.0193013	+	0.202133i	0.00272962	+	0.0285859i
$51$	0.807565	+	1.91501i	0.113082	+	0.268155i
$52$	−0.182378	−	0.0174150i	−0.0252912	−	0.00241502i
$53$	−6.44700	−	7.44024i	−0.885564	−	1.02199i	−0.999593	−	0.0285176i	$-0.990921\pi$
$53$	−6.44700	−	7.44024i	−0.885564	−	1.02199i	0.114030	−	0.993477i	$-0.463624\pi$
$54$	−6.75653	−	0.272940i	−0.919448	−	0.0371424i
$55$	−13.7091	−	4.02536i	−1.84854	−	0.542780i
$56$	3.09818	+	8.95160i	0.414011	+	1.19621i
$57$	3.91250	+	1.92736i	0.518223	+	0.255285i
$58$	0.0834506	−	1.75184i	0.0109576	−	0.230028i
$59$	0.762767	−	3.95761i	0.0993038	−	0.515237i	−0.897880	−	0.440240i	$-0.854893\pi$
$59$	0.762767	−	3.95761i	0.0993038	−	0.515237i	0.997184	−	0.0749968i	$-0.0238947\pi$
$60$	0.896773	+	0.748809i	0.115773	+	0.0966708i
$61$	−0.785782	+	1.96279i	−0.100609	+	0.251309i	−0.970129	−	0.242588i	$-0.922004\pi$
$61$	−0.785782	+	1.96279i	−0.100609	+	0.251309i	0.869520	+	0.493897i	$0.164428\pi$
$62$	−4.36290	+	3.78048i	−0.554089	+	0.480121i
$63$	1.24377	+	9.38566i	0.156700	+	1.18248i
$64$	8.46407	−	2.48528i	1.05801	−	0.310660i
$65$	−0.763172	−	1.07173i	−0.0946598	−	0.132931i
$66$	−12.8813	+	6.94164i	−1.58558	+	0.854456i
$67$	−3.18925	+	6.18629i	−0.389629	+	0.755775i	−0.999320	−	0.0368640i	$-0.988263\pi$
$67$	−3.18925	+	6.18629i	−0.389629	+	0.755775i	0.609691	+	0.792639i	$0.291293\pi$
$68$	−0.183871	−	0.318475i	−0.0222977	−	0.0386207i
$69$	−7.57906	−	3.39969i	−0.912411	−	0.409274i
$70$	−4.51950	+	7.82801i	−0.540184	+	0.935626i
$71$	−5.22568	−	8.13132i	−0.620174	−	0.965010i	−0.999214	−	0.0396298i	$-0.987382\pi$
$71$	−5.22568	−	8.13132i	−0.620174	−	0.965010i	0.379040	−	0.925380i	$-0.376254\pi$
$72$	8.97276	−	0.756846i	1.05745	−	0.0891952i
$73$	6.46681	−	14.1603i	0.756882	−	1.65734i	0.00329427	−	0.999995i	$-0.498951\pi$
$73$	6.46681	−	14.1603i	0.756882	−	1.65734i	0.753588	−	0.657347i	$-0.228321\pi$
$74$	2.12092	−	8.74253i	0.246551	−	1.01630i
$75$	−0.00493865	−	0.270209i	−0.000570266	−	0.0312010i
$76$	−0.729282	−	0.252407i	−0.0836544	−	0.0289531i
$77$	12.6646	+	16.1043i	1.44326	+	1.83526i
$78$	−1.32752	−	0.230783i	−0.150313	−	0.0261310i
$79$	−0.600047	+	0.207678i	−0.0675105	+	0.0233656i	−0.360615	−	0.932715i	$-0.617433\pi$
$79$	−0.600047	+	0.207678i	−0.0675105	+	0.0233656i	0.293104	+	0.956081i	$0.405312\pi$
$80$	6.09728	+	3.91849i	0.681697	+	0.438100i
$81$	8.93816	+	1.05327i	0.993128	+	0.117030i
$82$	9.17657	−	10.5903i	1.01338	−	1.16951i
$83$	−4.89683	+	4.66912i	−0.537497	+	0.512503i	−0.909486	−	0.415735i	$-0.863524\pi$
$83$	−4.89683	+	4.66912i	−0.537497	+	0.512503i	0.371989	+	0.928237i	$0.378676\pi$
$84$	−0.424637	−	1.62053i	−0.0463316	−	0.176814i
$85$	0.863756	−	2.49566i	0.0936875	−	0.270692i
$86$	1.87306	−	2.63034i	0.201977	−	0.283637i
$87$	−0.289924	+	2.31620i	−0.0310831	+	0.248323i
$88$	15.8724	−	11.3027i	1.69201	−	1.20487i
$89$	−0.587972	+	4.08944i	−0.0623249	+	0.433479i	0.934638	+	0.355601i	$0.115724\pi$
$89$	−0.587972	+	4.08944i	−0.0623249	+	0.433479i	−0.996963	+	0.0778785i	$0.975185\pi$
$90$	6.15277	+	5.99783i	0.648558	+	0.632227i
$91$			1.88658i			0.197767i
$92$	1.40538	+	0.430327i	0.146521	+	0.0448647i
$93$	6.17635	−	4.57053i	0.640457	−	0.473942i
$94$	4.62982	+	2.38684i	0.477530	+	0.246184i
$95$	−2.05978	−	5.14508i	−0.211329	−	0.527874i
$96$	−2.91035	+	0.616288i	−0.297036	+	0.0628996i
$97$	−18.6170	−	4.51643i	−1.89027	−	0.458574i	−0.999995	−	0.00314367i	$-0.998999\pi$
$97$	−18.6170	−	4.51643i	−1.89027	−	0.458574i	−0.890272	−	0.455430i	$-0.849486\pi$
$98$	3.50360	−	1.60004i	0.353917	−	0.161628i
$99$	17.8038	−	7.89417i	1.78935	−	0.793394i
$100$	0.00680540	+	0.0473326i	0.000680540	+	0.00473326i
$101$	1.61825	+	1.69717i	0.161022	+	0.168875i	0.799302	−	0.600929i	$-0.205203\pi$
$101$	1.61825	+	1.69717i	0.161022	+	0.168875i	−0.638281	+	0.769804i	$0.720354\pi$
$102$	−1.16832	−	2.43928i	−0.115681	−	0.241525i
$103$	−3.75185	−	0.178723i	−0.369681	−	0.0176101i	−0.138080	−	0.990421i	$-0.544093\pi$
$103$	−3.75185	−	0.178723i	−0.369681	−	0.0176101i	−0.231601	+	0.972811i	$0.574396\pi$
$104$	1.79227	+	0.0853763i	0.175747	+	0.00837184i
$105$	6.79815	−	9.92568i	0.663432	−	0.968647i
$106$	8.84105	+	9.27222i	0.858718	+	0.900598i
$107$	2.28352	+	15.8822i	0.220756	+	1.53539i	0.735190	+	0.677861i	$0.237093\pi$
$107$	2.28352	+	15.8822i	0.220756	+	1.53539i	−0.514434	+	0.857530i	$0.671998\pi$
$108$	−1.59244	+	0.0115062i	−0.153232	+	0.00110719i
$109$	−2.88148	+	1.31593i	−0.275996	+	0.126043i	−0.548605	−	0.836082i	$-0.684841\pi$
$109$	−2.88148	+	1.31593i	−0.275996	+	0.126043i	0.272609	+	0.962125i	$0.412114\pi$
$110$	18.0695	+	4.38361i	1.72286	+	0.417961i
$111$	−3.70871	+	11.3846i	−0.352015	+	1.08058i
$112$	−3.86261	−	9.64834i	−0.364983	−	0.911683i
$113$	14.1816	+	7.31113i	1.33409	+	0.687773i	0.969889	−	0.243546i	$-0.0783108\pi$
$113$	14.1816	+	7.31113i	1.33409	+	0.687773i	0.364204	+	0.931319i	$0.381341\pi$
$114$	−5.20513	−	2.26308i	−0.487505	−	0.211957i
$115$	4.27373	+	9.65124i	0.398528	+	0.899983i
$116$		−	0.413032i		−	0.0383490i
$117$	1.73805	+	0.442037i	0.160683	+	0.0408663i
$118$	−0.746448	+	5.19166i	−0.0687161	+	0.477931i
$119$	−3.08466	+	2.19658i	−0.282771	+	0.201360i
$120$	−9.12185	−	6.90750i	−0.832707	−	0.630565i
$121$	18.0652	−	25.3690i	1.64229	−	2.30628i
$122$	0.899886	−	2.60005i	0.0814718	−	0.235397i
$123$	−13.2607	+	13.1150i	−1.19568	+	1.18254i
$124$	−0.983948	+	0.938193i	−0.0883612	+	0.0842522i
$125$	−7.43131	+	8.57618i	−0.664676	+	0.767077i
$126$	−2.19792	−	12.1232i	−0.195806	−	1.08002i
$127$	13.6862	+	8.79556i	1.21445	+	0.780480i	0.981398	−	0.191984i	$-0.0614922\pi$
$127$	13.6862	+	8.79556i	1.21445	+	0.780480i	0.233053	+	0.972464i	$0.425129\pi$
$128$	−7.60223	+	2.63116i	−0.671949	+	0.232564i
$129$	−2.75463	+	3.29894i	−0.242531	+	0.290455i
$130$	1.05840	+	1.34586i	0.0928275	+	0.118040i
$131$	−3.29072	−	1.13893i	−0.287512	−	0.0995087i	0.179506	−	0.983757i	$-0.442550\pi$
$131$	−3.29072	−	1.13893i	−0.287512	−	0.0995087i	−0.467017	+	0.884248i	$0.654671\pi$
$132$	−2.95237	+	1.77727i	−0.256971	+	0.154691i
$133$	−1.87354	+	7.72285i	−0.162457	+	0.669656i
$134$	3.76259	−	8.23892i	0.325038	−	0.711734i
$135$	−7.55139	−	8.58858i	−0.649920	−	0.739187i
$136$	1.94718	+	3.02987i	0.166969	+	0.259809i
$137$	4.67568	−	8.09851i	0.399470	−	0.691902i	−0.594191	−	0.804324i	$-0.702527\pi$
$137$	4.67568	−	8.09851i	0.399470	−	0.691902i	0.993661	+	0.112422i	$0.0358608\pi$
$138$	10.0624	+	3.94989i	0.856568	+	0.336237i
$139$	−8.26326	−	14.3124i	−0.700880	−	1.21396i	−0.968158	−	0.250341i	$-0.919457\pi$
$139$	−8.26326	−	14.3124i	−0.700880	−	1.21396i	0.267277	−	0.963620i	$-0.413876\pi$
$140$	−0.975431	+	1.89207i	−0.0824389	+	0.159909i
$141$	−5.89975	−	3.64094i	−0.496848	−	0.306623i
$142$	7.29627	+	10.2462i	0.612289	+	0.859840i
$143$	3.72357	−	1.09334i	0.311381	−	0.0914297i
$144$	−9.79377	+	1.29785i	−0.816147	+	0.108154i
$145$	2.24166	−	1.94241i	0.186160	−	0.161308i
$146$	−7.52926	+	18.8072i	−0.623126	+	1.55649i
$147$	−4.81301	+	1.76493i	−0.396970	+	0.145569i
$148$	0.400949	−	2.08032i	0.0329578	−	0.171001i
$149$	0.602847	−	12.6553i	0.0493872	−	1.03676i	−0.829131	−	0.559055i	$-0.811164\pi$
$149$	0.602847	−	12.6553i	0.0493872	−	1.03676i	0.878518	−	0.477710i	$-0.158533\pi$
$150$	0.0231513	+	0.350934i	0.00189029	+	0.0286536i
$151$	0.205419	+	0.593520i	0.0167168	+	0.0483000i	0.953051	−	0.302811i	$-0.0979251\pi$
$151$	0.205419	+	0.593520i	0.0167168	+	0.0483000i	−0.936334	+	0.351111i	$0.885804\pi$
$152$	7.25200	+	2.12938i	0.588215	+	0.172715i
$153$	1.30089	+	3.35648i	0.105171	+	0.271356i
$154$	−17.4597	−	20.1495i	−1.40694	−	1.62370i
$155$	−9.71922	−	0.928073i	−0.780666	−	0.0745446i
$156$	−0.314867	−	0.0394126i	−0.0252096	−	0.00315554i
$157$	1.70603	+	17.8663i	0.136156	+	1.42589i	0.762826	+	0.646604i	$0.223811\pi$
$157$	1.70603	+	17.8663i	0.136156	+	1.42589i	−0.626670	+	0.779285i	$0.715583\pi$
$158$	0.767130	−	0.307113i	0.0610296	−	0.0244326i
$159$	−10.7839	−	13.2087i	−0.855217	−	1.04752i
$160$	3.27371	+	1.89008i	0.258810	+	0.149424i
$161$	3.03558	−	14.8276i	0.239237	−	1.16858i
$162$	−11.6838	−	0.815671i	−0.917963	−	0.0640852i
$163$	−14.6959	+	9.44451i	−1.15108	+	0.739751i	−0.969853	−	0.243691i	$-0.921642\pi$
$163$	−14.6959	+	9.44451i	−1.15108	+	0.739751i	−0.181222	+	0.983442i	$0.558005\pi$
$164$	2.03999	−	2.59405i	0.159296	−	0.202562i
$165$	−23.5303	−	7.66535i	−1.83183	−	0.596746i
$166$	6.07619	−	6.37252i	0.471604	−	0.494604i
$167$	−8.10496	−	5.77152i	−0.627181	−	0.446613i	0.221760	−	0.975101i	$-0.428820\pi$
$167$	−8.10496	−	5.77152i	−0.627181	−	0.446613i	−0.848941	+	0.528488i	$0.822759\pi$
$168$	4.90929	+	15.6553i	0.378760	+	1.20783i
$169$	−11.7370	−	4.69880i	−0.902848	−	0.361446i
$170$	−0.968247	+	3.29755i	−0.0742612	+	0.252910i
$171$	6.67585	+	3.53555i	0.510515	+	0.270370i
$172$	0.411135	−	0.639739i	0.0313488	−	0.0487796i
$173$	−2.47736	−	4.80541i	−0.188350	−	0.365349i	0.775686	−	0.631119i	$-0.217404\pi$
$173$	−2.47736	−	4.80541i	−0.188350	−	0.365349i	−0.964036	+	0.265770i	$0.914374\pi$
$174$	0.233446	−	3.02874i	0.0176975	−	0.229608i
$175$	0.478539	−	0.116092i	0.0361742	−	0.00877576i
$176$	−16.8046	+	13.2153i	−1.26669	+	0.996138i
$177$	1.52157	−	6.81310i	0.114368	−	0.512104i
$178$	0.511072	−	5.35219i	0.0383065	−	0.401164i
$179$	−0.302687	−	1.03086i	−0.0226239	−	0.0770500i	0.947407	−	0.320030i	$-0.103693\pi$
$179$	−0.302687	−	1.03086i	−0.0226239	−	0.0770500i	−0.970031	+	0.242980i	$0.921875\pi$
$180$	1.51456	+	1.34196i	0.112889	+	0.100024i
$181$	16.7056	+	2.40190i	1.24172	+	0.178532i	0.731696	−	0.681631i	$-0.238729\pi$
$181$	16.7056	+	2.40190i	1.24172	+	0.178532i	0.510020	+	0.860163i	$0.329638\pi$
$182$	−0.116819	−	2.45233i	−0.00865919	−	0.181779i
$183$	−1.46011	+	3.35828i	−0.107934	+	0.248251i
$184$	−13.9490	−	3.55485i	−1.02834	−	0.262067i
$185$	13.1762	−	7.60728i	0.968734	−	0.559299i
$186$	−7.74551	+	6.32359i	−0.567928	+	0.463668i
$187$	6.12310	+	4.81526i	0.447766	+	0.352127i
$188$	1.11585	+	0.509590i	0.0813815	+	0.0371657i
$189$	1.67669	+	16.3126i	0.121961	+	1.18657i
$190$	2.99606	+	6.56046i	0.217357	+	0.475946i
$191$	−10.1376	+	1.95385i	−0.733528	+	0.141376i	−0.542318	−	0.840173i	$-0.682453\pi$
$191$	−10.1376	+	1.95385i	−0.733528	+	0.141376i	−0.191210	+	0.981549i	$0.561241\pi$
$192$	14.7801	−	3.87293i	1.06666	−	0.279505i
$193$	3.76612	+	15.5241i	0.271091	+	1.11745i	0.930682	+	0.365828i	$0.119214\pi$
$193$	3.76612	+	15.5241i	0.271091	+	1.11745i	−0.659591	+	0.751624i	$0.729271\pi$
$194$	24.4795	+	4.71804i	1.75753	+	0.338736i
$195$	−1.26686	−	1.89424i	−0.0907215	−	0.135649i
$196$	0.806242	−	0.415647i	0.0575887	−	0.0296891i
$197$	−1.12307	−	0.973149i	−0.0800157	−	0.0693340i	0.613935	−	0.789357i	$-0.289586\pi$
$197$	−1.12307	−	0.973149i	−0.0800157	−	0.0693340i	−0.693950	+	0.720023i	$0.744131\pi$
$198$	−22.6541	+	11.3639i	−1.60996	+	0.807599i
$199$	−0.536313	+	0.0771102i	−0.0380182	+	0.00546620i	−0.161298	−	0.986906i	$-0.551568\pi$
$199$	−0.536313	+	0.0771102i	−0.0380182	+	0.00546620i	0.123279	+	0.992372i	$0.460659\pi$
$200$	−0.0886329	−	0.459871i	−0.00626729	−	0.0325178i
$201$	−5.83574	+	10.5484i	−0.411621	+	0.744026i
$202$	−2.20862	−	2.10592i	−0.155398	−	0.148172i
$203$	−4.23394	+	0.404292i	−0.297164	+	0.0283757i
$204$	−0.302164	−	0.560715i	−0.0211557	−	0.0392579i
$205$	23.6725	−	1.12766i	1.65336	−	0.0787592i
$206$	4.88803			0.340565
$207$	−12.9490	−	6.27080i	−0.900019	−	0.435851i
$208$	−1.96861			−0.136499
$209$	16.3285	−	0.777823i	1.12947	−	0.0538031i
$210$	−8.22219	+	13.3232i	−0.567385	+	0.919385i
$211$	−4.41634	+	0.421709i	−0.304033	+	0.0290317i	−0.245958	−	0.969281i	$-0.579102\pi$
$211$	−4.41634	+	0.421709i	−0.304033	+	0.0290317i	−0.0580755	+	0.998312i	$0.518496\pi$
$212$	2.18363	+	2.08209i	0.149972	+	0.142998i
$213$	−8.63431	−	14.3432i	−0.591613	−	0.982779i
$214$	−3.95175	−	20.5036i	−0.270136	−	1.40160i
$215$	5.40557	−	0.777204i	0.368657	−	0.0530049i
$216$	15.5730	−	0.854653i	1.05961	−	0.0581518i
$217$	10.5804	+	9.16799i	0.718246	+	0.622364i
$218$	3.66411	−	1.88898i	0.248165	−	0.127938i
$219$	11.9152	−	24.1875i	0.805151	−	1.63444i
$220$	4.29971	+	0.828702i	0.289887	+	0.0558711i
$221$	0.169111	+	0.697085i	0.0113756	+	0.0468910i
$222$	4.11594	−	15.0283i	0.276244	−	1.00863i
$223$	−14.7087	+	2.83487i	−0.984967	+	0.189837i	−0.656211	−	0.754578i	$-0.727842\pi$
$223$	−14.7087	+	2.83487i	−0.984967	+	0.189837i	−0.328757	+	0.944415i	$0.606630\pi$
$224$	−2.25173	−	4.93059i	−0.150450	−	0.329439i
$225$	0.00517218	−	0.468065i	0.000344812	−	0.0312043i
$226$	−18.8871	−	8.62546i	−1.25635	−	0.573757i
$227$	−21.6811	−	17.0502i	−1.43902	−	1.13166i	−0.968423	−	0.249314i	$-0.919795\pi$
$227$	−21.6811	−	17.0502i	−1.43902	−	1.13166i	−0.470601	−	0.882346i	$-0.655963\pi$
$228$	−1.24979	−	0.474030i	−0.0827695	−	0.0313934i
$229$	7.92689	−	4.57659i	0.523824	−	0.302430i	−0.214674	−	0.976686i	$-0.568869\pi$
$229$	7.92689	−	4.57659i	0.523824	−	0.302430i	0.738498	+	0.674256i	$0.235536\pi$
$230$	−6.15296	−	12.2808i	−0.405714	−	0.809775i
$231$	21.1084	+	28.5247i	1.38883	+	1.87679i
$232$	0.192477	+	4.04058i	0.0126367	+	0.265277i
$233$	4.56708	+	0.656647i	0.299199	+	0.0430183i	0.290280	−	0.956942i	$-0.406252\pi$
$233$	4.56708	+	0.656647i	0.299199	+	0.0430183i	0.00891957	+	0.999960i	$0.497161\pi$
$234$	−2.28663	−	0.466974i	−0.149482	−	0.0305271i
$235$	2.48190	+	8.45258i	0.161901	+	0.551386i
$236$	−0.117415	+	1.22963i	−0.00764309	+	0.0800420i
$237$	−1.04941	+	0.329081i	−0.0681666	+	0.0213761i
$238$	3.87368	−	3.04630i	0.251094	−	0.197462i
$239$	3.68142	−	0.893102i	0.238131	−	0.0577700i	−0.114917	−	0.993375i	$-0.536660\pi$
$239$	3.68142	−	0.893102i	0.238131	−	0.0577700i	0.353048	+	0.935605i	$0.385145\pi$
$240$	10.3573	+	7.09375i	0.668558	+	0.457899i
$241$	−0.778766	−	1.51060i	−0.0501647	−	0.0973060i	0.862421	−	0.506193i	$-0.168947\pi$
$241$	−0.778766	−	1.51060i	−0.0501647	−	0.0973060i	−0.912585	+	0.408887i	$0.865917\pi$
$242$	−21.9118	+	34.0954i	−1.40854	+	2.19173i
$243$	15.4212	+	2.27746i	0.989270	+	0.146099i
$244$	0.182550	−	0.621708i	0.0116866	−	0.0398008i
$245$	6.04746	+	2.42104i	0.386358	+	0.154674i
$246$	16.4253	−	17.8691i	1.04724	−	1.13929i
$247$	1.22618	+	0.873159i	0.0780200	+	0.0555578i
$248$	9.18850	−	9.63663i	0.583471	−	0.611926i
$249$	−8.71504	+	7.83499i	−0.552293	+	0.496522i
$250$	9.12877	−	11.6082i	0.577354	−	0.734166i
$251$	−17.5086	+	11.2521i	−1.10514	+	0.710227i	−0.960228	−	0.279218i	$-0.909925\pi$
$251$	−17.5086	+	11.2521i	−1.10514	+	0.710227i	−0.144908	+	0.989445i	$0.546289\pi$
$252$	−0.652878	−	2.82719i	−0.0411274	−	0.178096i
$253$	−31.0248	+	2.60177i	−1.95051	+	0.163572i
$254$	−18.3350	−	10.5857i	−1.15044	−	0.664208i
$255$	1.62217	−	4.27689i	0.101584	−	0.267829i
$256$	−6.65993	+	2.66624i	−0.416246	+	0.166640i
$257$	2.35049	+	24.6155i	0.146620	+	1.53547i	0.706987	+	0.707227i	$0.250054\pi$
$257$	2.35049	+	24.6155i	0.146620	+	1.53547i	−0.560367	+	0.828244i	$0.689340\pi$
$258$	3.37641	−	4.45880i	0.210206	−	0.277593i
$259$	−21.7176	−	2.07378i	−1.34947	−	0.128858i
$260$	0.264054	+	0.304734i	0.0163759	+	0.0188988i
$261$	−0.619575	+	3.99533i	−0.0383507	+	0.247305i
$262$	4.34807	+	1.27671i	0.268625	+	0.0788754i
$263$	3.91120	+	11.3007i	0.241175	+	0.696830i	0.999014	+	0.0443885i	$0.0141340\pi$
$263$	3.91120	+	11.3007i	0.241175	+	0.696830i	−0.757839	+	0.652441i	$0.773745\pi$
$264$	28.0540	−	18.7624i	1.72661	−	1.15474i
$265$	−1.03098	+	21.6430i	−0.0633328	+	1.32952i
$266$	1.95718	−	10.1548i	0.120002	−	0.622631i
$267$	−1.22564	+	7.05020i	−0.0750080	+	0.431465i
$268$	0.792773	−	1.98025i	0.0484263	−	0.120963i
$269$	6.61353	−	5.73066i	0.403234	−	0.349404i	−0.429510	−	0.903062i	$-0.641314\pi$
$269$	6.61353	−	5.73066i	0.403234	−	0.349404i	0.832744	+	0.553658i	$0.186768\pi$
$270$	10.3477	+	10.6966i	0.629742	+	0.650972i
$271$	−2.25292	+	0.661517i	−0.136855	+	0.0401843i	−0.349443	−	0.936958i	$-0.613629\pi$
$271$	−2.25292	+	0.661517i	−0.136855	+	0.0401843i	0.212588	+	0.977142i	$0.431811\pi$
$272$	−2.29209	−	3.21879i	−0.138978	−	0.195168i
$273$	−0.0958094	+	3.26625i	−0.00579865	+	0.197682i
$274$	−5.57636	+	10.8166i	−0.336880	+	0.653457i
$275$	−0.506464	−	0.877222i	−0.0305409	−	0.0528984i
$276$	2.41130	+	0.816400i	0.145143	+	0.0491415i
$277$	6.88982	−	11.9335i	0.413969	−	0.717015i	−0.581351	−	0.813653i	$-0.697476\pi$
$277$	6.88982	−	11.9335i	0.413969	−	0.717015i	0.995320	+	0.0966379i	$0.0308089\pi$
$278$	11.6275	+	18.0927i	0.697371	+	1.08513i
$279$	10.9253	−	7.59932i	0.654078	−	0.454959i
$280$	8.66066	−	18.9642i	0.517574	−	1.13333i
$281$	3.12041	−	12.8625i	0.186148	−	0.767313i	−0.799801	−	0.600266i	$-0.795062\pi$
$281$	3.12041	−	12.8625i	0.186148	−	0.767313i	0.985949	−	0.167047i	$-0.0534233\pi$
$282$	7.89443	+	4.36748i	0.470106	+	0.260079i
$283$	5.70120	+	1.97320i	0.338901	+	0.117295i	0.491217	−	0.871037i	$-0.336552\pi$
$283$	5.70120	+	1.97320i	0.338901	+	0.117295i	−0.152316	+	0.988332i	$0.548673\pi$
$284$	1.83116	+	2.32851i	0.108659	+	0.138172i
$285$	−3.30482	−	9.01232i	−0.195761	−	0.533844i
$286$	−4.77251	+	1.65178i	−0.282204	+	0.0976718i
$287$	−28.5882	−	18.3725i	−1.68751	−	1.08449i
$288$	−5.07000	+	0.919181i	−0.298753	+	0.0541633i
$289$	10.1898	−	11.7596i	0.599398	−	0.691742i
$290$	−2.79362	+	2.66371i	−0.164047	+	0.156419i
$291$	−32.0023	−	8.76478i	−1.87601	−	0.513800i
$292$	−1.56041	+	4.50850i	−0.0913158	+	0.263840i
$293$	−10.3357	+	14.5144i	−0.603817	+	0.847942i	−0.997453	−	0.0713242i	$-0.977278\pi$
$293$	−10.3357	+	14.5144i	−0.603817	+	0.847942i	0.393636	+	0.919266i	$0.371217\pi$
$294$	6.14706	−	2.59223i	0.358504	−	0.151182i
$295$	−7.22579	+	5.14546i	−0.420702	+	0.299580i
$296$	−2.95293	+	20.5381i	−0.171636	+	1.19375i
$297$	31.2248	−	12.7631i	1.81185	−	0.740588i
$298$			16.4878i			0.955110i
$299$	−2.39377	−	1.57769i	−0.138435	−	0.0912400i
$300$	0.00937845	+	0.0822928i	0.000541465	+	0.00475118i
$301$	−6.96032	−	3.58829i	−0.401186	−	0.206826i
$302$	−0.303772	−	0.758787i	−0.0174801	−	0.0436633i
$303$	2.71549	+	3.02050i	0.156001	+	0.173523i
$304$	−8.05865	−	1.95501i	−0.462195	−	0.112127i
$305$	4.23272	−	1.93302i	0.242365	−	0.110684i
$306$	−1.89884	−	4.28248i	−0.108549	−	0.244813i
$307$	−2.61309	−	18.1744i	−0.149137	−	1.03727i	−0.917637	−	0.397419i	$-0.869906\pi$
$307$	−2.61309	−	18.1744i	−0.149137	−	1.03727i	0.768501	−	0.639849i	$-0.221003\pi$
$308$	−4.33293	−	4.54424i	−0.246891	−	0.258932i
$309$	−6.48652	−	0.499960i	−0.369005	−	0.0284417i
$310$	12.6913	+	0.604561i	0.720817	+	0.0343368i
$311$	−17.8835	−	0.851897i	−1.01408	−	0.0483067i	−0.466045	−	0.884761i	$-0.654321\pi$
$311$	−17.8835	−	0.851897i	−1.01408	−	0.0483067i	−0.548037	+	0.836454i	$0.684625\pi$
$312$	3.09863	+	0.238833i	0.175426	+	0.0135212i
$313$	−2.45038	−	2.56989i	−0.138504	−	0.145259i	0.650829	−	0.759225i	$-0.274422\pi$
$313$	−2.45038	−	2.56989i	−0.138504	−	0.145259i	−0.789332	+	0.613966i	$0.789573\pi$
$314$	−3.32394	−	23.1185i	−0.187581	−	1.30465i
$315$	12.2738	−	16.8391i	0.691548	−	0.948778i
$316$	0.177015	−	0.0808401i	0.00995788	−	0.00454761i
$317$	15.7969	+	3.83229i	0.887244	+	0.215243i	0.653383	−	0.757027i	$-0.273349\pi$
$317$	15.7969	+	3.83229i	0.887244	+	0.215243i	0.233860	+	0.972270i	$0.424864\pi$
$318$	14.8357	+	16.5020i	0.831943	+	0.925389i
$319$	3.25168	+	8.12230i	0.182059	+	0.454761i
$320$	−17.2568	−	8.89649i	−0.964683	−	0.497329i
$321$	3.14689	+	27.6129i	0.175642	+	1.54120i
$322$	−3.02776	+	19.4622i	−0.168730	+	1.08458i
$323$			3.02151i			0.168121i
$324$	−2.75758	−	0.0609507i	−0.153199	−	0.00338615i
$325$	0.0132743	−	0.0923251i	0.000736328	−	0.00512127i
$326$	18.5182	−	13.1867i	1.02563	−	0.730346i
$327$	−5.05556	+	2.13194i	−0.279573	+	0.117897i
$328$	−18.7478	+	26.3276i	−1.03517	+	1.45370i
$329$	4.13151	−	11.9372i	0.227778	−	0.658120i
$330$	31.0612	+	8.50703i	1.70986	+	0.468296i
$331$	13.1078	−	12.4982i	0.720469	−	0.686966i	−0.238288	−	0.971195i	$-0.576586\pi$
$331$	13.1078	−	12.4982i	0.720469	−	0.686966i	0.958756	+	0.284229i	$0.0917376\pi$
$332$	1.35793	−	1.56713i	0.0745260	−	0.0860076i
$333$	−6.99908	+	19.5219i	−0.383547	+	1.06979i
$334$	10.8929	+	7.00042i	0.596031	+	0.383046i
$335$	14.4758	−	5.01011i	0.790895	−	0.273732i
$336$	−6.19738	−	16.9004i	−0.338095	−	0.921992i
$337$	−0.0121733	−	0.0154796i	−0.000663123	−	0.000843229i	0.785721	−	0.618581i	$-0.212292\pi$
$337$	−0.0121733	−	0.0154796i	−0.000663123	−	0.000843229i	−0.786385	+	0.617737i	$0.788050\pi$
$338$	15.5477	+	5.38111i	0.845683	+	0.292694i
$339$	24.1814	+	13.3780i	1.31335	+	0.726594i
$340$	−0.190815	+	0.786551i	−0.0103484	+	0.0426567i
$341$	11.9633	−	26.1960i	0.647849	−	1.41859i
$342$	−8.89674	−	4.18242i	−0.481081	−	0.226159i
$343$	6.89355	+	10.7266i	0.372217	+	0.579180i
$344$	−3.72390	+	6.44999i	−0.200779	+	0.347760i
$345$	6.90900	+	16.9263i	0.371968	+	0.911281i
$346$	3.51783	+	6.09306i	0.189120	+	0.327565i
$347$	12.4170	−	24.0857i	0.666581	−	1.29299i	−0.276688	−	0.960960i	$-0.589237\pi$
$347$	12.4170	−	24.0857i	0.666581	−	1.29299i	0.943270	−	0.332028i	$-0.107733\pi$
$348$	0.0209757	−	0.715084i	0.00112442	−	0.0383325i
$349$	−5.57497	−	7.82895i	−0.298421	−	0.419074i	0.637954	−	0.770074i	$-0.279781\pi$
$349$	−5.57497	−	7.82895i	−0.298421	−	0.419074i	−0.936375	+	0.351000i	$0.885842\pi$
$350$	−0.614856	+	0.180538i	−0.0328654	+	0.00965016i
$351$	2.98665	+	0.853568i	0.159415	+	0.0455601i
$352$	−8.42664	+	7.30173i	−0.449142	+	0.389183i
$353$	−0.629546	+	1.57253i	−0.0335073	+	0.0836973i	−0.944178	−	0.329436i	$-0.893141\pi$
$353$	−0.629546	+	1.57253i	−0.0335073	+	0.0836973i	0.910671	+	0.413133i	$0.135566\pi$
$354$	−1.55599	+	8.95044i	−0.0826998	+	0.475711i
$355$	−4.02600	+	20.8889i	−0.213678	+	1.10867i
$356$	0.0602477	−	1.26475i	0.00319312	−	0.0670318i
$357$	−5.45205	+	3.64630i	−0.288553	+	0.192983i
$358$	0.457290	+	1.32125i	0.0241685	+	0.0698303i
$359$	16.4266	+	4.82329i	0.866963	+	0.254563i	0.684823	−	0.728709i	$-0.259879\pi$
$359$	16.4266	+	4.82329i	0.866963	+	0.254563i	0.182140	+	0.983273i	$0.441698\pi$
$360$	−15.4419	−	12.4222i	−0.813861	−	0.654710i
$361$	−8.29002	−	9.56720i	−0.436317	−	0.503537i
$362$	−21.8640	−	2.08776i	−1.14915	−	0.109730i
$363$	32.5648	−	43.0041i	1.70921	−	2.25713i
$364$	−0.0549600	−	0.575567i	−0.00288069	−	0.0301679i
$365$	−31.8074	+	12.7338i	−1.66488	+	0.666516i
$366$	1.69002	−	4.45578i	0.0883388	−	0.232907i
$367$	1.00048	+	0.577625i	0.0522244	+	0.0301518i	0.525885	−	0.850556i	$-0.323734\pi$
$367$	1.00048	+	0.577625i	0.0522244	+	0.0301518i	−0.473660	+	0.880708i	$0.657068\pi$
$368$	15.4724	+	3.16758i	0.806554	+	0.165121i
$369$	−23.6244	+	22.0326i	−1.22984	+	1.14697i
$370$	−16.6565	+	10.7045i	−0.865928	+	0.556498i
$371$	19.2058	−	24.4222i	0.997116	−	1.26794i
$372$	−1.75116	+	1.57433i	−0.0907935	+	0.0816252i
$373$	18.9190	−	19.8417i	0.979587	−	1.02736i	−0.0200326	−	0.999799i	$-0.506377\pi$
$373$	18.9190	−	19.8417i	0.979587	−	1.02736i	0.999620	−	0.0275624i	$-0.00877450\pi$
$374$	−8.25748	−	5.88012i	−0.426984	−	0.304054i
$375$	−13.3014	+	14.4706i	−0.686882	+	0.747259i
$376$	−11.1535	−	4.46519i	−0.575198	−	0.230275i
$377$	−0.226976	+	0.773009i	−0.0116899	+	0.0398120i
$378$	−3.18959	−	21.1007i	−0.164055	−	1.08530i
$379$	−2.59313	+	4.03499i	−0.133200	+	0.207264i	−0.901446	−	0.432891i	$-0.857493\pi$
$379$	−2.59313	+	4.03499i	−0.133200	+	0.207264i	0.768246	+	0.640155i	$0.221130\pi$
$380$	0.778295	+	1.50968i	0.0399257	+	0.0774450i
$381$	23.2483	+	15.9229i	1.19104	+	0.815753i
$382$	13.0566	−	3.16751i	0.668036	−	0.162064i
$383$	5.43877	−	4.27710i	0.277908	−	0.218549i	−0.469470	−	0.882949i	$-0.655555\pi$
$383$	5.43877	−	4.27710i	0.277908	−	0.218549i	0.747378	+	0.664399i	$0.231312\pi$
$384$	−13.2954	+	4.16926i	−0.678479	+	0.212762i
$385$	4.28619	−	44.8870i	0.218444	−	2.28765i
$386$	−5.85678	−	19.9464i	−0.298102	−	1.01524i
$387$	−4.93664	+	5.57158i	−0.250943	+	0.283219i
$388$	5.81133	+	0.835543i	0.295026	+	0.0424183i
$389$	1.44121	+	30.2548i	0.0730724	+	1.53398i	0.676429	+	0.736507i	$0.263526\pi$
$389$	1.44121	+	30.2548i	0.0730724	+	1.53398i	−0.603357	+	0.797471i	$0.706171\pi$
$390$	1.76406	+	2.38385i	0.0893266	+	0.120711i
$391$	−0.207497	−	5.75087i	−0.0104936	−	0.290834i
$392$	−7.69356	+	4.44188i	−0.388584	+	0.224349i
$393$	−5.63940	−	2.13895i	−0.284470	−	0.107896i
$394$	1.52012	+	1.19544i	0.0765826	+	0.0602252i
$395$	1.27122	+	0.580545i	0.0639618	+	0.0292104i
$396$	−5.20171	+	2.92706i	−0.261396	+	0.147090i
$397$	14.3943	+	31.5190i	0.722427	+	1.58189i	0.810471	+	0.585778i	$0.199211\pi$
$397$	14.3943	+	31.5190i	0.722427	+	1.58189i	−0.0880442	+	0.996117i	$0.528062\pi$
$398$	0.692369	−	0.133443i	0.0347053	−	0.00668890i
$399$	−3.63588	+	13.2755i	−0.182022	+	0.664605i
$400$	0.121140	+	0.499347i	0.00605701	+	0.0249673i
$401$	−17.8477	−	3.43987i	−0.891274	−	0.171779i	−0.276998	−	0.960870i	$-0.589340\pi$
$401$	−17.8477	−	3.43987i	−0.891274	−	0.171779i	−0.614276	+	0.789092i	$0.710552\pi$
$402$	6.93261	−	14.0730i	0.345767	−	0.701898i
$403$	2.35708	−	1.21516i	0.117414	−	0.0605314i
$404$	−0.543145	−	0.470638i	−0.0270225	−	0.0234151i
$405$	−12.6376	−	15.2530i	−0.627967	−	0.757926i
$406$	5.47858	−	0.787702i	0.271898	−	0.0390930i
$407$	8.49307	+	44.0662i	0.420986	+	2.18428i
$408$	3.21729	+	5.34452i	0.159280	+	0.264593i
$409$	2.17993	+	2.07856i	0.107791	+	0.102778i	0.742058	−	0.670335i	$-0.233850\pi$
$409$	2.17993	+	2.07856i	0.107791	+	0.102778i	−0.634268	+	0.773114i	$0.718698\pi$
$410$	−30.7016	+	2.93165i	−1.51624	+	0.144784i
$411$	8.50631	−	13.7835i	0.419585	−	0.679892i
$412$	1.14984	−	0.0547736i	0.0566485	−	0.00269850i
$413$	12.7197			0.625896
$414$	17.2205	+	7.34948i	0.846341	+	0.361207i
$415$	14.8914			0.730992
$416$	−1.02558	+	0.0488543i	−0.0502831	+	0.00239528i
$417$	−13.5794	−	25.1988i	−0.664985	−	1.23399i
$418$	−21.1770	+	2.02216i	−1.03580	+	0.0989068i
$419$	23.5773	+	22.4809i	1.15183	+	1.09827i	0.993840	+	0.110824i	$0.0353491\pi$
$419$	23.5773	+	22.4809i	1.15183	+	1.09827i	0.157987	+	0.987441i	$0.449499\pi$
$420$	−1.78486	+	3.22622i	−0.0870921	+	0.157423i
$421$	−2.84810	−	14.7774i	−0.138808	−	0.720204i	−0.982919	−	0.184037i	$-0.941084\pi$
$421$	−2.84810	−	14.7774i	−0.138808	−	0.720204i	0.844111	−	0.536168i	$-0.180129\pi$
$422$	5.71461	−	0.821637i	0.278183	−	0.0399966i
$423$	−10.0294	−	6.60320i	−0.487644	−	0.321059i
$424$	−22.3322	−	19.3509i	−1.08455	−	0.939765i
$425$	0.166412	−	0.0857915i	0.00807218	−	0.00416150i
$426$	12.1117	+	18.1098i	0.586815	+	0.877423i
$427$	−6.55174	−	1.26275i	−0.317061	−	0.0611085i
$428$	−1.15935	−	4.77890i	−0.0560392	−	0.230997i
$429$	6.50217	−	1.70381i	0.313928	−	0.0822605i
$430$	−6.97848	+	1.34499i	−0.336532	+	0.0648612i
$431$	−5.42763	−	11.8849i	−0.261440	−	0.572473i	0.732703	−	0.680549i	$-0.238259\pi$
$431$	−5.42763	−	11.8849i	−0.261440	−	0.572473i	−0.994143	+	0.108075i	$0.965531\pi$
$432$	−17.0219	+	1.74960i	−0.818968	+	0.0841775i
$433$	−12.7214	−	5.80966i	−0.611350	−	0.279194i	0.0855821	−	0.996331i	$-0.472725\pi$
$433$	−12.7214	−	5.80966i	−0.611350	−	0.279194i	−0.696932	+	0.717137i	$0.745452\pi$
$434$	−14.3210	−	11.2622i	−0.687430	−	0.540601i
$435$	3.97965	−	3.24907i	0.190810	−	0.155781i
$436$	0.840762	−	0.485414i	0.0402652	−	0.0232471i
$437$	−8.23227	−	8.83560i	−0.393803	−	0.422664i
$438$	−13.9906	+	32.1786i	−0.668496	+	1.53755i
$439$	1.05814	+	22.2130i	0.0505021	+	1.06017i	0.871859	+	0.489756i	$0.162914\pi$
$439$	1.05814	+	22.2130i	0.0505021	+	1.06017i	−0.821357	+	0.570414i	$0.806783\pi$
$440$	−42.4492	−	6.10327i	−2.02368	−	0.290962i
$441$	−8.42242	+	2.81121i	−0.401068	+	0.133867i
$442$	−0.262989	−	0.895657i	−0.0125091	−	0.0426020i
$443$	1.54784	−	16.2097i	0.0735400	−	0.770145i	−0.881208	−	0.472729i	$-0.843269\pi$
$443$	1.54784	−	16.2097i	0.0735400	−	0.770145i	0.954748	−	0.297416i	$-0.0961250\pi$
$444$	0.799815	−	3.58131i	0.0379575	−	0.169962i
$445$	7.14758	−	5.62092i	0.338828	−	0.266457i
$446$	18.9440	−	4.59577i	0.897026	−	0.217616i
$447$	1.68641	−	21.8796i	0.0797645	−	1.03487i
$448$	12.7568	+	24.7447i	0.602702	+	1.16908i
$449$	1.63618	−	2.54595i	0.0772162	−	0.120151i	−0.800498	−	0.599336i	$-0.795431\pi$
$449$	1.63618	−	2.54595i	0.0772162	−	0.120151i	0.877714	+	0.479185i	$0.159068\pi$
$450$	0.0222598	+	0.608750i	0.00104934	+	0.0286967i
$451$	−19.6943	+	67.0725i	−0.927366	+	3.15832i
$452$	−4.53958	−	1.81737i	−0.213524	−	0.0854821i
$453$	0.325502	+	1.03800i	0.0152934	+	0.0487694i
$454$	29.2386	+	20.8207i	1.37224	+	0.977164i
$455$	2.86533	−	3.00507i	0.134329	−	0.140880i
$456$	12.4473	+	4.05490i	0.582898	+	0.189888i
$457$	5.05113	−	6.42304i	0.236282	−	0.300457i	−0.653423	−	0.756993i	$-0.726668\pi$
$457$	5.05113	−	6.42304i	0.236282	−	0.300457i	0.889705	+	0.456536i	$0.150910\pi$
$458$	−10.0206	+	6.43987i	−0.468234	+	0.300916i
$459$	2.08178	+	5.87716i	0.0971691	+	0.274323i
$460$	−1.58501	−	2.81995i	−0.0739016	−	0.131481i
$461$	−22.4245	−	12.9468i	−1.04441	−	0.602993i	−0.123334	−	0.992365i	$-0.539359\pi$
$461$	−22.4245	−	12.9468i	−1.04441	−	0.602993i	−0.921080	+	0.389373i	$0.872692\pi$
$462$	−29.2047	−	35.7717i	−1.35873	−	1.66425i
$463$	20.6649	−	8.27297i	0.960379	−	0.384478i	0.162106	−	0.986773i	$-0.448171\pi$
$463$	20.6649	−	8.27297i	0.960379	−	0.384478i	0.798273	+	0.602296i	$0.205747\pi$
$464$	−0.421871	−	4.41804i	−0.0195849	−	0.205102i
$465$	−16.7798	−	2.10037i	−0.778145	−	0.0974021i
$466$	−5.97732	−	0.570765i	−0.276894	−	0.0264402i
$467$	−3.71329	−	4.28536i	−0.171831	−	0.198303i	0.663302	−	0.748352i	$-0.269155\pi$
$467$	−3.71329	−	4.28536i	−0.171831	−	0.198303i	−0.835132	+	0.550049i	$0.814609\pi$
$468$	−0.543130	−	0.0842258i	−0.0251062	−	0.00389334i
$469$	−21.0753	−	6.18827i	−0.973168	−	0.285748i
$470$	−3.74957	−	10.8337i	−0.172955	−	0.499720i
$471$	2.04632	+	31.0187i	0.0942895	+	1.42927i
$472$	0.575625	−	12.0839i	0.0264953	−	0.556204i
$473$	−3.04853	+	15.8173i	−0.140171	+	0.727278i
$474$	1.34373	−	0.492747i	0.0617197	−	0.0226326i
$475$	0.146027	−	0.364757i	0.00670016	−	0.0167362i
$476$	0.877094	−	0.760006i	0.0402015	−	0.0348348i
$477$	−17.9994	−	23.4160i	−0.824136	−	1.07215i
$478$	−4.73010	+	1.38888i	−0.216350	+	0.0635261i
$479$	5.44618	+	7.64809i	0.248842	+	0.349450i	0.920037	−	0.391831i	$-0.128158\pi$
$479$	5.44618	+	7.64809i	0.248842	+	0.349450i	−0.671195	+	0.741281i	$0.734219\pi$
$480$	5.57182	+	3.43856i	0.254317	+	0.156948i
$481$	−1.89361	+	3.67309i	−0.0863412	+	0.167478i
$482$	1.10584	+	1.91537i	0.0503697	+	0.0872429i
$483$	6.00854	−	25.5170i	0.273398	−	1.16107i
$484$	−4.77237	+	8.26599i	−0.216926	+	0.375727i
$485$	22.7948	+	35.4694i	1.03506	+	1.61058i
$486$	−20.1868	−	2.00553i	−0.915690	−	0.0909728i
$487$	1.49396	−	3.27131i	0.0676976	−	0.148237i	−0.872759	−	0.488152i	$-0.837671\pi$
$487$	1.49396	−	3.27131i	0.0676976	−	0.148237i	0.940456	+	0.339915i	$0.110398\pi$
$488$	−1.49612	+	6.16708i	−0.0677261	+	0.279171i
$489$	−25.9228	+	15.6050i	−1.17227	+	0.705683i
$490$	−8.01090	−	2.77260i	−0.361896	−	0.125253i
$491$	−0.541205	−	0.688198i	−0.0244243	−	0.0310580i	0.773688	−	0.633567i	$-0.218410\pi$
$491$	−0.541205	−	0.688198i	−0.0244243	−	0.0310580i	−0.798112	+	0.602509i	$0.794168\pi$
$492$	3.66358	−	4.38750i	0.165167	−	0.197804i
$493$	−1.52819	+	0.528910i	−0.0688260	+	0.0238209i
$494$	−1.64796	−	1.05908i	−0.0741451	−	0.0476501i
$495$	−40.3488	−	14.4660i	−1.81354	−	0.650200i
$496$	−9.56664	+	11.0405i	−0.429555	+	0.495733i
$497$	22.0768	−	21.0502i	0.990282	−	0.944232i
$498$	10.8434	−	10.7242i	0.485903	−	0.480563i
$499$	−2.31661	+	6.69341i	−0.103706	+	0.299638i	−0.984902	−	0.173112i	$-0.944618\pi$
$499$	−2.31661	+	6.69341i	−0.103706	+	0.299638i	0.881196	+	0.472751i	$0.156739\pi$
$500$	2.01734	−	2.83295i	0.0902181	−	0.126694i
$501$	−13.7391	−	10.4039i	−0.613816	−	0.464811i
$502$	22.0624	−	15.7106i	0.984694	−	0.701197i
$503$	1.39662	−	9.71367i	0.0622720	−	0.433111i	−0.934706	−	0.355423i	$-0.884337\pi$
$503$	1.39662	−	9.71367i	0.0622720	−	0.433111i	0.996978	−	0.0776885i	$-0.0247540\pi$
$504$	7.70443	+	27.3534i	0.343183	+	1.21842i
$505$		−	5.16115i		−	0.229668i
$506$	40.1675	−	5.30308i	1.78566	−	0.235751i
$507$	−20.0818	−	8.73112i	−0.891862	−	0.387762i
$508$	−4.43168	−	2.28469i	−0.196624	−	0.101367i
$509$	7.15870	+	17.8816i	0.317304	+	0.792587i	0.998187	+	0.0601945i	$0.0191721\pi$
$509$	7.15870	+	17.8816i	0.317304	+	0.792587i	−0.680883	+	0.732392i	$0.738404\pi$
$510$	−1.84380	+	5.65989i	−0.0816447	+	0.250624i
$511$	47.7434	+	11.5824i	2.11204	+	0.512377i
$512$	23.1274	−	10.5619i	1.02210	−	0.466776i
$513$	11.3784	+	6.46015i	0.502368	+	0.285223i
$514$	−4.57958	−	31.8517i	−0.201997	−	1.40492i
$515$	5.70476	+	5.98298i	0.251382	+	0.263641i
$516$	0.744290	−	1.08670i	0.0327655	−	0.0478395i
$517$	−25.9551	−	1.23639i	−1.14150	−	0.0543764i
$518$	28.3587	+	1.35089i	1.24601	+	0.0593548i
$519$	−4.04503	−	8.44545i	−0.177557	−	0.370714i
$520$	−2.72518	−	2.85809i	−0.119507	−	0.125335i
$521$	3.65335	+	25.4096i	0.160056	+	1.11322i	0.898523	+	0.438926i	$0.144641\pi$
$521$	3.65335	+	25.4096i	0.160056	+	1.11322i	−0.738467	+	0.674290i	$0.764450\pi$
$522$	0.557979	−	5.23182i	0.0244221	−	0.228991i
$523$	−3.19646	+	1.45978i	−0.139772	+	0.0638315i	−0.484073	−	0.875028i	$-0.660843\pi$
$523$	−3.19646	+	1.45978i	−0.139772	+	0.0638315i	0.344301	+	0.938859i	$0.388116\pi$
$524$	1.03713	+	0.251605i	0.0453072	+	0.0109914i
$525$	0.834393	−	0.176689i	0.0364159	−	0.00771134i
$526$	−5.78385	−	14.4474i	−0.252188	−	0.629935i
$527$	4.73124	+	2.43913i	0.206096	+	0.106250i
$528$	−29.7650	+	22.0263i	−1.29536	+	0.958570i
$529$	16.2753	+	16.2516i	0.707623	+	0.706590i
$530$		−	28.1972i		−	1.22481i
$531$	2.98030	−	11.7183i	0.129334	−	0.508530i
$532$	0.346607	−	2.41070i	0.0150273	−	0.104517i
$533$	−5.24346	+	3.73385i	−0.227120	+	0.161731i
$534$	1.15663	−	9.24033i	0.0500524	−	0.399868i
$535$	20.4845	−	28.7665i	0.885622	−	1.24368i
$536$	−6.83268	+	19.7417i	−0.295127	+	0.852713i
$537$	−0.471693	−	1.80010i	−0.0203550	−	0.0776802i
$538$	−8.24196	+	7.85869i	−0.355336	+	0.338812i
$539$	−12.5825	+	14.5210i	−0.541969	+	0.625465i
$540$	2.55402	+	2.40026i	0.109907	+	0.103291i
$541$	−25.1449	−	16.1596i	−1.08106	−	0.694757i	−0.126261	−	0.991997i	$-0.540298\pi$
$541$	−25.1449	−	16.1596i	−1.08106	−	0.694757i	−0.954803	+	0.297240i	$0.903934\pi$
$542$	2.88757	−	0.999397i	0.124032	−	0.0429278i
$543$	28.8005	+	5.00681i	1.23595	+	0.214863i
$544$	−1.27398	−	1.62000i	−0.0546214	−	0.0694568i
$545$	6.58845	+	2.28029i	0.282218	+	0.0976767i
$546$	−0.0777083	−	4.25167i	−0.00332561	−	0.181955i
$547$	6.61049	−	27.2488i	0.282644	−	1.16507i	−0.636539	−	0.771244i	$-0.719635\pi$
$547$	6.61049	−	27.2488i	0.282644	−	1.16507i	0.919183	−	0.393830i	$-0.128850\pi$
$548$	−1.19055	+	2.60695i	−0.0508579	+	0.111363i
$549$	−2.69844	+	5.74006i	−0.115167	+	0.244980i
$550$	0.712662	+	1.10892i	0.0303880	+	0.0472847i
$551$	−1.69681	+	2.93896i	−0.0722865	+	0.125204i
$552$	−23.9695	−	6.86294i	−1.02021	−	0.292106i
$553$	−1.00195	−	1.73543i	−0.0426073	−	0.0737980i
$554$	−8.21701	+	15.9388i	−0.349107	+	0.677174i
$555$	23.1984	−	12.5014i	0.984716	−	0.530654i
$556$	2.93794	+	4.12577i	0.124597	+	0.174971i
$557$	3.28157	−	0.963557i	0.139045	−	0.0408272i	−0.211470	−	0.977385i	$-0.567825\pi$
$557$	3.28157	−	0.963557i	0.139045	−	0.0408272i	0.350514	+	0.936557i	$0.386007\pi$
$558$	−13.7310	+	10.5547i	−0.581279	+	0.446817i
$559$	−1.12102	+	0.971369i	−0.0474141	+	0.0410845i
$560$	−8.50123	+	21.2351i	−0.359243	+	0.897345i
$561$	10.3564	+	8.64765i	0.437248	+	0.365104i
$562$	−3.25971	+	16.9130i	−0.137502	+	0.713430i
$563$	0.179556	−	3.76935i	0.00756739	−	0.158859i	−0.991921	−	0.126861i	$-0.959510\pi$
$563$	0.179556	−	3.76935i	0.00756739	−	0.158859i	0.999488	−	0.0319983i	$-0.0101871\pi$
$564$	1.90599	+	0.938924i	0.0802568	+	0.0395358i
$565$	−11.4853	−	33.1846i	−0.483191	−	1.39609i
$566$	−7.53307	−	2.21191i	−0.316639	−	0.0929735i
$567$	2.07443	+	28.3273i	0.0871180	+	1.18963i
$568$	−18.9989	−	21.9258i	−0.797174	−	0.919988i
$569$	10.1409	+	0.968343i	0.425131	+	0.0405951i	0.305429	−	0.952215i	$-0.401200\pi$
$569$	10.1409	+	0.968343i	0.425131	+	0.0405951i	0.119702	+	0.992810i	$0.461806\pi$
$570$	4.85393	+	11.5103i	0.203309	+	0.482114i
$571$	0.358867	+	3.75823i	0.0150181	+	0.157277i	0.999870	−	0.0161206i	$-0.00513155\pi$
$571$	0.358867	+	3.75823i	0.0150181	+	0.157277i	−0.984852	+	0.173397i	$0.944525\pi$
$572$	−1.10416	+	0.442037i	−0.0461671	+	0.0184825i
$573$	−17.6504	+	2.86789i	−0.737358	+	0.119808i
$574$	38.2989	+	22.1119i	1.59856	+	0.922931i
$575$	−0.252885	+	0.704274i	−0.0105460	+	0.0293702i
$576$	25.7856	−	5.95462i	1.07440	−	0.248109i
$577$	20.7665	−	13.3458i	0.864520	−	0.555593i	−0.0315518	−	0.999502i	$-0.510045\pi$
$577$	20.7665	−	13.3458i	0.864520	−	0.555593i	0.896072	+	0.443909i	$0.146409\pi$
$578$	−12.5173	+	15.9171i	−0.520652	+	0.662062i
$579$	5.73191	+	27.0683i	0.238210	+	1.12492i
$580$	−0.627311	+	0.657905i	−0.0260477	+	0.0273180i
$581$	−17.3937	−	12.3860i	−0.721612	−	0.513857i
$582$	42.1419	+	9.41156i	1.74684	+	0.390122i
$583$	−59.3330	−	23.7533i	−2.45732	−	0.983763i
$584$	13.1640	−	44.8326i	0.544732	−	1.85519i
$585$	−2.09712	−	3.34385i	−0.0867052	−	0.138251i
$586$	12.5364	−	19.5070i	0.517874	−	0.805828i
$587$	15.6932	+	30.4406i	0.647729	+	1.25642i	0.952658	+	0.304044i	$0.0983372\pi$
$587$	15.6932	+	30.4406i	0.647729	+	1.25642i	−0.304928	+	0.952375i	$0.598633\pi$
$588$	1.41696	−	0.678667i	0.0584345	−	0.0279878i
$589$	10.8556	−	2.63355i	0.447299	−	0.108513i
$590$	9.07406	−	7.13592i	0.373573	−	0.293781i
$591$	−1.89496	−	1.74185i	−0.0779484	−	0.0716503i
$592$	2.16395	−	22.6619i	0.0889379	−	0.931399i
$593$	10.2250	+	34.8230i	0.419889	+	1.43001i	0.849784	+	0.527131i	$0.176732\pi$
$593$	10.2250	+	34.8230i	0.419889	+	1.43001i	−0.429895	+	0.902879i	$0.641450\pi$
$594$	−39.7983	+	18.5239i	−1.63294	+	0.760047i
$595$	8.24962	+	1.18612i	0.338201	+	0.0486260i
$596$	0.184756	+	3.87851i	0.00756791	+	0.158870i
$597$	−0.932438	+	0.106265i	−0.0381622	+	0.00434913i
$598$	3.20930	+	1.90258i	0.131238	+	0.0778024i
$599$	23.0208	−	13.2911i	0.940603	−	0.543058i	0.0504540	−	0.998726i	$-0.483933\pi$
$599$	23.0208	−	13.2911i	0.940603	−	0.543058i	0.890149	+	0.455669i	$0.150600\pi$
$600$	−0.130096	−	0.800678i	−0.00531115	−	0.0326876i
$601$	16.4899	+	12.9678i	0.672637	+	0.528968i	0.895039	−	0.445987i	$-0.147147\pi$
$601$	16.4899	+	12.9678i	0.672637	+	0.528968i	−0.222402	+	0.974955i	$0.571390\pi$
$602$	9.26978	+	4.23337i	0.377808	+	0.172539i
$603$	−10.6391	+	17.9661i	−0.433260	+	0.731637i
$604$	−0.0799608	−	0.175090i	−0.00325356	−	0.00712430i
$605$	−67.3059	+	12.9721i	−2.73637	+	0.527393i
$606$	−3.71685	−	3.75815i	−0.150987	−	0.152664i
$607$	1.10601	+	4.55903i	0.0448916	+	0.185045i	0.989843	−	0.142165i	$-0.0454064\pi$
$607$	1.10601	+	4.55903i	0.0448916	+	0.185045i	−0.944951	+	0.327211i	$0.893891\pi$
$608$	−4.24679	−	0.818502i	−0.172230	−	0.0331946i
$609$	−7.35077	+	0.484934i	−0.297868	+	0.0196505i
$610$	−5.38234	+	2.77479i	−0.217925	+	0.112348i
$611$	−1.80832	−	1.56692i	−0.0731569	−	0.0633908i
$612$	−0.494663	−	0.986115i	−0.0199956	−	0.0398613i
$613$	42.4989	−	6.11041i	1.71651	−	0.246797i	0.787360	−	0.616493i	$-0.211447\pi$
$613$	42.4989	−	6.11041i	1.71651	−	0.246797i	0.929153	+	0.369696i	$0.120538\pi$
$614$	4.52208	+	23.4628i	0.182496	+	0.946881i
$615$	41.0416	−	0.750123i	1.65496	−	0.0302479i
$616$	44.5056	+	42.4360i	1.79318	+	1.70979i
$617$	−13.6511	+	1.30352i	−0.549573	+	0.0524778i	−0.366149	−	0.930556i	$-0.619324\pi$
$617$	−13.6511	+	1.30352i	−0.549573	+	0.0524778i	−0.183423	+	0.983034i	$0.558718\pi$
$618$	8.46267	+	0.248237i	0.340419	+	0.00998557i
$619$	−19.1678	+	0.913074i	−0.770418	+	0.0366995i	−0.429110	−	0.903252i	$-0.641173\pi$
$619$	−19.1678	+	0.913074i	−0.770418	+	0.0366995i	−0.341308	+	0.939952i	$0.610870\pi$
$620$	2.99222			0.120171
$621$	−22.1003	−	11.5143i	−0.886853	−	0.462052i
$622$	23.2992			0.934213
$623$	−13.0238	+	0.620401i	−0.521788	+	0.0248558i
$624$	−3.40827	−	0.0999754i	−0.136440	−	0.00400222i
$625$	24.0859	−	2.29993i	0.963438	−	0.0919971i
$626$	3.34434	+	3.18882i	0.133667	+	0.127451i
$627$	28.3091	−	0.517410i	1.13056	−	0.0206634i
$628$	−1.04097	−	5.40105i	−0.0415391	−	0.215525i
$629$	−8.21048	+	1.18049i	−0.327373	+	0.0470691i
$630$	−14.9117	+	22.6489i	−0.594098	+	0.902354i
$631$	−14.0704	−	12.1921i	−0.560135	−	0.485360i	0.328167	−	0.944620i	$-0.393569\pi$
$631$	−14.0704	−	12.1921i	−0.560135	−	0.485360i	−0.888302	+	0.459260i	$0.848115\pi$
$632$	−1.69402	+	0.873328i	−0.0673845	+	0.0347391i
$633$	−7.66745	+	0.505825i	−0.304754	+	0.0201048i
$634$	−20.7714	−	4.00337i	−0.824939	−	0.158994i
$635$	−8.44158	−	34.7967i	−0.334994	−	1.38086i
$636$	3.67480	+	3.71563i	0.145715	+	0.147334i
$637$	−1.73733	+	0.334844i	−0.0688357	+	0.0132670i
$638$	−4.72974	−	10.3567i	−0.187252	−	0.410025i
$639$	−14.2202	−	25.2709i	−0.562543	−	0.999703i
$640$	16.1055	+	7.35516i	0.636628	+	0.290738i
$641$	20.0658	+	15.7800i	0.792553	+	0.623271i	0.930134	−	0.367220i	$-0.119690\pi$
$641$	20.0658	+	15.7800i	0.792553	+	0.623271i	−0.137581	+	0.990491i	$0.543933\pi$
$642$	−5.80041	−	35.6987i	−0.228924	−	1.40892i
$643$	29.1207	−	16.8128i	1.14841	−	0.663033i	0.199908	−	0.979815i	$-0.435936\pi$
$643$	29.1207	−	16.8128i	1.14841	−	0.663033i	0.948498	+	0.316782i	$0.102602\pi$
$644$	−0.494150	+	4.61212i	−0.0194723	+	0.181743i
$645$	9.39817	−	1.07106i	0.370052	−	0.0421728i
$646$	−0.187095	−	3.92761i	−0.00736115	−	0.154530i
$647$	−13.5924	−	1.95430i	−0.534374	−	0.0768314i	−0.130155	−	0.991494i	$-0.541548\pi$
$647$	−13.5924	−	1.95430i	−0.534374	−	0.0768314i	−0.404219	+	0.914662i	$0.632457\pi$
$648$	27.0051	−	0.688794i	1.06086	−	0.0270584i
$649$	−7.37153	−	25.1051i	−0.289358	−	0.985462i
$650$	−0.0115382	+	0.120834i	−0.000452566	+	0.00473949i
$651$	17.8524	+	16.4099i	0.699689	+	0.643156i
$652$	4.20837	−	3.30950i	0.164813	−	0.129610i
$653$	30.5722	−	7.41674i	1.19638	−	0.290240i	0.412390	−	0.911008i	$-0.364694\pi$
$653$	30.5722	−	7.41674i	1.19638	−	0.290240i	0.783994	+	0.620768i	$0.213179\pi$
$654$	6.43962	−	3.08432i	0.251809	−	0.120606i
$655$	3.51188	+	6.81210i	0.137221	+	0.266171i
$656$	19.1714	−	29.8312i	0.748516	−	1.16471i
$657$	21.8571	−	41.2708i	0.852728	−	1.61013i
$658$	−4.63131	+	15.7728i	−0.180547	+	0.614888i
$659$	30.3288	+	12.1418i	1.18144	+	0.472979i	0.877437	−	0.479692i	$-0.159251\pi$
$659$	30.3288	+	12.1418i	1.18144	+	0.472979i	0.304006	+	0.952670i	$0.401676\pi$
$660$	7.40203	+	1.65310i	0.288124	+	0.0643467i
$661$	17.4934	+	12.4570i	0.680415	+	0.484522i	0.867252	−	0.497869i	$-0.165884\pi$
$661$	17.4934	+	12.4570i	0.680415	+	0.484522i	−0.186837	+	0.982391i	$0.559824\pi$
$662$	−16.2647	+	17.0579i	−0.632144	+	0.662974i
$663$	0.257382	+	1.21546i	0.00999587	+	0.0472044i
$664$	−12.5540	+	15.9637i	−0.487188	+	0.619510i
$665$	14.7137	−	9.45594i	0.570574	−	0.366686i
$666$	7.88916	−	25.8095i	0.305699	−	1.00010i
$667$	3.02773	−	5.71028i	0.117234	−	0.221103i
$668$	2.64084	+	1.52469i	0.102177	+	0.0589919i
$669$	−25.6092	+	4.16105i	−0.990110	+	0.160875i
$670$	−18.5066	+	7.40891i	−0.714970	+	0.286231i
$671$	1.30467	+	13.6631i	0.0503661	+	0.527458i
$672$	−3.64803	−	8.65072i	−0.140726	−	0.333709i
$673$	37.5921	+	3.58961i	1.44907	+	0.138369i	0.789720	−	0.613467i	$-0.210226\pi$
$673$	37.5921	+	3.58961i	1.44907	+	0.138369i	0.659350	+	0.751836i	$0.270832\pi$
$674$	0.0167824	+	0.0193679i	0.000646433	+	0.000746024i
$675$	0.0327252	−	0.810101i	0.00125959	−	0.0311808i
$676$	3.71767	+	1.09161i	0.142987	+	0.0419849i
$677$	8.35031	+	24.1266i	0.320929	+	0.927262i	0.983916	+	0.178632i	$0.0571671\pi$
$677$	8.35031	+	24.1266i	0.320929	+	0.927262i	−0.662987	+	0.748631i	$0.730712\pi$
$678$	−32.2614	−	15.8925i	−1.23899	−	0.610348i
$679$	2.87669	−	60.3891i	0.110397	−	2.31752i
$680$	1.50016	−	7.78355i	0.0575283	−	0.298485i
$681$	−36.6707	−	30.6202i	−1.40522	−	1.17337i
$682$	−13.9288	+	34.7924i	−0.533361	+	1.33227i
$683$	−20.1963	+	17.5002i	−0.772788	+	0.669625i	−0.949194	−	0.314693i	$-0.898099\pi$
$683$	−20.1963	+	17.5002i	−0.772788	+	0.669625i	0.176405	+	0.984318i	$0.443553\pi$
$684$	−2.13970	−	0.884162i	−0.0818134	−	0.0338068i
$685$	−19.7477	+	5.79845i	−0.754522	+	0.221548i
$686$	−9.62500	−	13.5164i	−0.367484	−	0.516059i
$687$	13.9563	−	7.52092i	0.532466	−	0.286941i
$688$	3.74432	−	7.26297i	0.142751	−	0.276898i
$689$	−2.94259	−	5.09672i	−0.112104	−	0.194169i
$690$	−10.0290	−	21.5744i	−0.381797	−	0.821322i
$691$	4.46011	−	7.72513i	0.169671	−	0.293878i	−0.768634	−	0.639689i	$-0.779063\pi$
$691$	4.46011	−	7.72513i	0.169671	−	0.293878i	0.938304	+	0.345811i	$0.112396\pi$
$692$	0.895797	+	1.39389i	0.0340531	+	0.0529876i
$693$	35.0965	+	50.4570i	1.33321	+	1.91670i
$694$	−14.6493	+	32.0774i	−0.556079	+	1.21764i
$695$	−8.57532	+	35.3479i	−0.325280	+	1.34082i
$696$	0.128036	+	7.00526i	0.00485320	+	0.265534i
$697$	−12.2101	−	4.22597i	−0.462491	−	0.160070i
$698$	7.73158	+	9.83150i	0.292644	+	0.372128i
$699$	7.87366	+	1.36879i	0.297809	+	0.0517725i
$700$	−0.142613	+	0.0493589i	−0.00539027	+	0.00186559i
$701$	2.48052	+	1.59413i	0.0936880	+	0.0602096i	0.586646	−	0.809844i	$-0.300448\pi$
$701$	2.48052	+	1.59413i	0.0936880	+	0.0602096i	−0.492958	+	0.870053i	$0.664084\pi$
$702$	−3.93514	−	0.924601i	−0.148522	−	0.0348968i
$703$	−11.3993	+	13.1555i	−0.429934	+	0.496170i
$704$	41.4461	−	39.5188i	1.56206	−	1.48942i
$705$	3.86767	+	14.7601i	0.145665	+	0.555896i
$706$	0.720963	−	2.08308i	0.0271338	−	0.0783979i
$707$	−4.29280	+	6.02839i	−0.161447	+	0.226721i
$708$	−0.265728	+	2.12290i	−0.00998668	+	0.0797835i
$709$	13.2037	−	9.40234i	0.495877	−	0.353112i	−0.304596	−	0.952482i	$-0.598521\pi$
$709$	13.2037	−	9.40234i	0.495877	−	0.353112i	0.800473	+	0.599369i	$0.204582\pi$
$710$	3.93986	−	27.4023i	0.147860	−	1.02839i
$711$	−1.83356	+	0.516446i	−0.0687641	+	0.0193683i
$712$			12.4008i			0.464741i
$713$	−20.4808	+	5.75795i	−0.767012	+	0.215637i
$714$	6.86124	−	5.07735i	0.256775	−	0.190015i
$715$	−7.59172	−	3.91381i	−0.283914	−	0.146368i
$716$	0.122376	+	0.305682i	0.00457342	+	0.0114239i
$717$	6.41901	−	1.35927i	0.239722	−	0.0507630i
$718$	−21.6513	−	5.25255i	−0.808020	−	0.196024i
$719$	34.2040	−	15.6204i	1.27559	−	0.582544i	0.341604	−	0.939844i	$-0.389030\pi$
$719$	34.2040	−	15.6204i	1.27559	−	0.582544i	0.933990	+	0.357300i	$0.116303\pi$
$720$	17.5713	+	12.8074i	0.654845	+	0.477305i
$721$	−1.68699	−	11.7333i	−0.0628267	−	0.436969i
$722$	11.3685	+	11.9229i	0.423090	+	0.443724i
$723$	−1.27157	−	2.65485i	−0.0472901	−	0.0987350i
$724$	−5.16659	−	0.246115i	−0.192015	−	0.00914680i
$725$	0.210044	+	0.0100056i	0.00780085	+	0.000371600i
$726$	−39.6675	+	57.9167i	−1.47220	+	2.14949i
$727$	−4.10709	−	4.30739i	−0.152323	−	0.159752i	0.643151	−	0.765739i	$-0.277627\pi$
$727$	−4.10709	−	4.30739i	−0.152323	−	0.159752i	−0.795474	+	0.605987i	$0.792778\pi$
$728$	0.805879	+	5.60501i	0.0298678	+	0.207735i
$729$	26.5831	+	4.72614i	0.984561	+	0.175042i
$730$	40.5574	−	18.5219i	1.50110	−	0.685528i
$731$	−2.89347	−	0.701948i	−0.107019	−	0.0259625i
$732$	0.347623	−	1.06710i	0.0128485	−	0.0394410i
$733$	9.42908	+	23.5527i	0.348271	+	0.869939i	0.994299	+	0.106625i	$0.0340045\pi$
$733$	9.42908	+	23.5527i	0.348271	+	0.869939i	−0.646028	+	0.763313i	$0.723571\pi$
$734$	−1.33627	−	0.688894i	−0.0493226	−	0.0254275i
$735$	10.3471	+	4.49868i	0.381657	+	0.165936i
$736$	8.13918	+	1.26622i	0.300014	+	0.0466736i
$737$			45.1831i			1.66434i
$738$	29.3447	−	30.1027i	1.08019	−	1.10809i
$739$	−0.879372	+	6.11617i	−0.0323482	+	0.224987i	−0.999582	−	0.0288993i	$-0.990800\pi$
$739$	−0.879372	+	6.11617i	−0.0323482	+	0.224987i	0.967234	+	0.253886i	$0.0817089\pi$
$740$	−3.79825	+	2.70472i	−0.139626	+	0.0994274i
$741$	2.07855	+	1.57398i	0.0763575	+	0.0578215i
$742$	−23.4530	+	32.9352i	−0.860989	+	1.20909i
$743$	2.46762	−	7.12972i	0.0905283	−	0.261564i	−0.890643	−	0.454703i	$-0.849745\pi$
$743$	2.46762	−	7.12972i	0.0905283	−	0.261564i	0.981171	+	0.193139i	$0.0618667\pi$
$744$	16.3975	−	16.2173i	0.601162	−	0.594556i
$745$	−20.1811	+	19.2427i	−0.739379	+	0.704996i
$746$	−23.3638	+	26.9633i	−0.855410	+	0.987196i
$747$	−15.4863	+	13.1222i	−0.566614	+	0.480115i
$748$	−2.00834	−	1.29068i	−0.0734324	−	0.0471921i
$749$	−47.8531	+	16.5621i	−1.74851	+	0.605167i
$750$	16.3942	−	19.6337i	0.598632	−	0.716922i
$751$	−26.8310	−	34.1184i	−0.979078	−	1.24500i	−0.969512	−	0.245045i	$-0.921197\pi$
$751$	−26.8310	−	34.1184i	−0.979078	−	1.24500i	−0.00956605	−	0.999954i	$-0.503045\pi$
$752$	12.4563	+	4.31116i	0.454233	+	0.157212i
$753$	−30.8843	+	18.5917i	−1.12548	+	0.677519i
$754$	0.247176	−	1.01888i	0.00900163	−	0.0371052i
$755$	0.574230	−	1.25739i	0.0208984	−	0.0457611i
$756$	−0.986754	−	4.92789i	−0.0358879	−	0.179226i
$757$	−22.6060	−	35.1756i	−0.821629	−	1.27848i	−0.957696	−	0.287780i	$-0.907083\pi$
$757$	−22.6060	−	35.1756i	−0.821629	−	1.27848i	0.136067	−	0.990700i	$-0.456554\pi$
$758$	3.12092	−	5.40558i	0.113357	−	0.196340i
$759$	−53.8456	+	2.92887i	−1.95447	+	0.106311i
$760$	−8.31738	−	14.4061i	−0.301703	−	0.522565i
$761$	8.58491	−	16.6524i	0.311203	−	0.603649i	−0.680419	−	0.732823i	$-0.738202\pi$
$761$	8.58491	−	16.6524i	0.311203	−	0.603649i	0.991622	+	0.129174i	$0.0412326\pi$
$762$	−31.2060	−	19.2583i	−1.13047	−	0.697654i
$763$	−5.79889	−	8.14340i	−0.209934	−	0.294811i
$764$	3.03590	−	0.891420i	0.109835	−	0.0322504i
$765$	3.02567	−	7.32222i	0.109393	−	0.264735i
$766$	−6.80492	+	5.89649i	−0.245872	+	0.213049i
$767$	0.895474	−	2.23679i	0.0323337	−	0.0807657i
$768$	−11.6658	+	4.27785i	−0.420953	+	0.154363i
$769$	−0.494339	+	2.56487i	−0.0178263	+	0.0924916i	−0.989752	−	0.142795i	$-0.954391\pi$
$769$	−0.494339	+	2.56487i	−0.0178263	+	0.0924916i	0.971926	+	0.235287i	$0.0756030\pi$
$770$	−2.79209	+	58.6132i	−0.100620	+	2.11227i
$771$	2.81933	+	42.7363i	0.101536	+	1.53911i
$772$	−1.60124	−	4.62647i	−0.0576297	−	0.166510i
$773$	−45.6343	−	13.3994i	−1.64135	−	0.481944i	−0.674711	−	0.738082i	$-0.735732\pi$
$773$	−45.6343	−	13.3994i	−1.64135	−	0.481944i	−0.966640	+	0.256137i	$0.917550\pi$
$774$	6.07205	−	7.54808i	0.218255	−	0.271310i
$775$	−0.453275	−	0.523108i	−0.0162821	−	0.0187906i
$776$	−57.2401	−	5.46577i	−2.05480	−	0.196210i
$777$	−37.4945	−	4.69327i	−1.34511	−	0.168370i
$778$	−3.74681	−	39.2384i	−0.134330	−	1.40677i
$779$	−25.1725	+	10.0776i	−0.901900	+	0.361066i
$780$	0.441682	+	0.540998i	0.0158148	+	0.0193709i
$781$	−54.3415	−	31.3741i	−1.94449	−	1.12265i
$782$	0.625821	+	7.46261i	0.0223793	+	0.266862i
$783$	−1.27558	+	6.88567i	−0.0455854	+	0.246074i
$784$	8.19951	−	5.26951i	0.292840	−	0.188197i
$785$	24.4178	−	31.0498i	0.871510	−	1.10822i
$786$	7.46301	+	2.43119i	0.266197	+	0.0867177i
$787$	−18.2744	+	19.1656i	−0.651412	+	0.683181i	−0.963755	−	0.266788i	$-0.914038\pi$
$787$	−18.2744	+	19.1656i	−0.651412	+	0.683181i	0.312343	+	0.949969i	$0.398886\pi$
$788$	0.370983	+	0.264176i	0.0132157	+	0.00941087i
$789$	6.19759	+	19.7636i	0.220640	+	0.703602i
$790$	−1.68838	−	0.675925i	−0.0600698	−	0.0240483i
$791$	−14.1862	+	48.3136i	−0.504402	+	1.71784i
$792$	49.5229	−	31.0587i	1.75972	−	1.10362i
$793$	−0.683303	+	1.06324i	−0.0242648	+	0.0377568i
$794$	−20.6625	−	40.0797i	−0.733286	−	1.42238i
$795$	−2.88408	+	37.4183i	−0.102288	+	1.32709i
$796$	0.161375	−	0.0391491i	0.00571977	−	0.00138760i
$797$	2.04915	−	1.61147i	0.0725848	−	0.0570813i	−0.581207	−	0.813755i	$-0.697419\pi$
$797$	2.04915	−	1.61147i	0.0725848	−	0.0570813i	0.653792	+	0.756674i	$0.273177\pi$
$798$	3.90418	−	17.4817i	0.138207	−	0.618845i
$799$	0.456540	−	4.78111i	0.0161512	−	0.169143i
$800$	0.0755019	+	0.257136i	0.00266940	+	0.00909113i
$801$	−2.48000	+	12.1438i	−0.0876265	+	0.429081i
$802$	23.4130	+	3.36627i	0.826740	+	0.118867i
$803$	−4.80858	−	100.944i	−0.169691	−	3.56225i
$804$	1.47310	−	3.38816i	0.0519522	−	0.119491i
$805$	−27.3555	+	19.0080i	−0.964153	+	0.669946i
$806$	−2.98868	+	1.72552i	−0.105272	+	0.0607787i
$807$	11.7411	−	9.58565i	0.413305	−	0.337431i
$808$	5.53277	+	4.35102i	0.194642	+	0.153068i
$809$	−10.1888	−	4.65306i	−0.358218	−	0.163593i	0.228173	−	0.973621i	$-0.426725\pi$
$809$	−10.1888	−	4.65306i	−0.358218	−	0.163593i	−0.586392	+	0.810028i	$0.699452\pi$
$810$	17.3719	+	19.0445i	0.610385	+	0.669156i
$811$	3.27900	+	7.18000i	0.115141	+	0.252124i	0.958425	−	0.285344i	$-0.0921080\pi$
$811$	3.27900	+	7.18000i	0.115141	+	0.252124i	−0.843284	+	0.537468i	$0.819381\pi$
$812$	1.27993	−	0.246687i	0.0449168	−	0.00865701i
$813$	−3.93409	+	1.03087i	−0.137975	+	0.0361544i
$814$	−13.7686	−	56.7550i	−0.482590	−	1.98926i
$815$	37.7530	+	7.27629i	1.32243	+	0.254877i
$816$	−3.80485	−	5.68912i	−0.133196	−	0.199159i
$817$	−5.55363	+	2.86310i	−0.194297	+	0.100167i
$818$	−2.96236	−	2.56690i	−0.103576	−	0.0897495i
$819$	−0.331751	+	5.65001i	−0.0115923	+	0.197427i
$820$	−7.18927	+	1.03366i	−0.251060	+	0.0360970i
$821$	−2.79177	−	14.4851i	−0.0974333	−	0.505532i	−0.997555	−	0.0698926i	$-0.977734\pi$
$821$	−2.79177	−	14.4851i	−0.0974333	−	0.505532i	0.900121	−	0.435640i	$-0.143478\pi$
$822$	−10.2037	+	18.4437i	−0.355895	+	0.643298i
$823$	−29.7487	−	28.3653i	−1.03698	−	0.988754i	−0.0370308	−	0.999314i	$-0.511790\pi$
$823$	−29.7487	−	28.3653i	−1.03698	−	0.988754i	−0.999944	+	0.0105604i	$0.996638\pi$
$824$	−11.2231	+	1.07167i	−0.390974	+	0.0373335i
$825$	−0.832295	−	1.54446i	−0.0289768	−	0.0537712i
$826$	−16.5341	+	0.787617i	−0.575295	+	0.0274047i
$827$	−25.8835			−0.900057			−0.450029	−	0.893014i	$-0.648586\pi$
$827$	−25.8835			−0.900057			−0.450029	+	0.893014i	$0.648586\pi$
$828$	4.13323	+	1.53589i	0.143640	+	0.0533760i
$829$	−29.0716			−1.00970			−0.504848	−	0.863208i	$-0.668452\pi$
$829$	−29.0716			−1.00970			−0.504848	+	0.863208i	$0.668452\pi$
$830$	−19.3571	+	0.922093i	−0.671896	+	0.0320063i
$831$	12.5344	−	20.3107i	0.434814	−	0.704569i
$832$	5.24950	−	0.501266i	0.181994	−	0.0173783i
$833$	−2.57030	−	2.45078i	−0.0890556	−	0.0849144i
$834$	19.2119	+	31.9146i	0.665254	+	1.10511i
$835$	4.14437	+	21.5030i	0.143422	+	0.744143i
$836$	−4.95892	+	0.712985i	−0.171508	+	0.0246591i
$837$	19.3009	−	12.6019i	0.667137	−	0.435586i
$838$	−32.0398	−	27.7626i	−1.10680	−	0.959044i
$839$	25.0194	−	12.8984i	0.863765	−	0.445302i	0.0313849	−	0.999507i	$-0.490008\pi$
$839$	25.0194	−	12.8984i	0.863765	−	0.445302i	0.832380	+	0.554206i	$0.186978\pi$
$840$	15.9573	−	32.3930i	0.550581	−	1.11767i
$841$	26.6925	+	5.14455i	0.920430	+	0.177398i
$842$	4.61723	+	19.0325i	0.159120	+	0.655902i
$843$	6.05561	−	22.1105i	0.208566	−	0.761525i
$844$	1.33507	−	0.257314i	0.0459551	−	0.00885713i
$845$	11.5590	+	25.3107i	0.397642	+	0.870715i
$846$	13.4459	+	7.96235i	0.462279	+	0.273751i
$847$	89.4050	+	40.8299i	3.07199	+	1.40293i
$848$	25.4841	+	20.0409i	0.875128	+	0.688208i
$849$	9.77031	+	3.70576i	0.335316	+	0.127181i
$850$	−0.211004	+	0.121823i	−0.00723738	+	0.00417850i
$851$	20.7931	−	25.8219i	0.712777	−	0.885164i
$852$	3.05204	+	4.12436i	0.104561	+	0.141298i
$853$	2.59647	+	54.5067i	0.0889016	+	1.86627i	0.400809	+	0.916162i	$0.368729\pi$
$853$	2.59647	+	54.5067i	0.0889016	+	1.86627i	−0.311907	+	0.950113i	$0.600968\pi$
$854$	8.59468	+	1.23573i	0.294104	+	0.0422858i
$855$	−5.26396	−	15.7709i	−0.180024	−	0.539354i
$856$	13.5686	+	46.2105i	0.463766	+	1.57944i
$857$	0.431067	−	4.51433i	0.0147250	−	0.154207i	−0.985119	−	0.171874i	$-0.945018\pi$
$857$	0.431067	−	4.51433i	0.0147250	−	0.154207i	0.999844	+	0.0176671i	$0.00562392\pi$
$858$	−8.34656	+	2.61737i	−0.284947	+	0.0893555i
$859$	−25.8489	+	20.3278i	−0.881953	+	0.693575i	−0.952698	−	0.303919i	$-0.901705\pi$
$859$	−25.8489	+	20.3278i	−0.881953	+	0.693575i	0.0707450	+	0.997494i	$0.477462\pi$
$860$	−1.62652	+	0.394589i	−0.0554638	+	0.0134554i
$861$	−48.5618	−	33.2603i	−1.65498	−	1.13351i
$862$	7.79120	+	15.1128i	0.265369	+	0.514745i
$863$	8.73417	−	13.5906i	0.297315	−	0.462631i	−0.660169	−	0.751117i	$-0.729516\pi$
$863$	8.73417	−	13.5906i	0.297315	−	0.462631i	0.957484	+	0.288486i	$0.0931519\pi$
$864$	−8.82441	+	1.33391i	−0.300212	+	0.0453804i
$865$	−3.35233	+	11.4170i	−0.113983	+	0.388189i
$866$	16.8960	+	6.76415i	0.574150	+	0.229855i
$867$	18.2388	−	19.8420i	0.619422	−	0.673870i
$868$	−3.49501	−	2.48879i	−0.118628	−	0.0844749i
$869$	−2.84458	+	2.98331i	−0.0964959	+	0.101202i
$870$	−4.97189	+	4.46983i	−0.168563	+	0.151541i
$871$	−2.57193	+	3.27048i	−0.0871467	+	0.110816i
$872$	−7.99874	+	5.14048i	−0.270872	+	0.174079i
$873$	−54.9607	−	16.7997i	−1.86014	−	0.568585i
$874$	11.2481	+	10.9755i	0.380472	+	0.371252i
$875$	−31.0149	−	17.9065i	−1.04850	−	0.605349i
$876$	−2.93050	+	7.72634i	−0.0990125	+	0.261049i
$877$	−44.2615	+	17.7196i	−1.49461	+	0.598350i	−0.967819	−	0.251647i	$-0.919028\pi$
$877$	−44.2615	+	17.7196i	−1.49461	+	0.598350i	−0.526787	+	0.849997i	$0.676603\pi$
$878$	−2.75091	−	28.8088i	−0.0928386	−	0.972250i
$879$	−18.6313	+	24.6040i	−0.628419	+	0.829873i
$880$	46.8388	+	4.47256i	1.57893	+	0.150770i
$881$	−7.49931	−	8.65466i	−0.252658	−	0.291583i	0.615225	−	0.788352i	$-0.289065\pi$
$881$	−7.49931	−	8.65466i	−0.252658	−	0.291583i	−0.867883	+	0.496769i	$0.834520\pi$
$882$	10.7741	−	4.17576i	0.362782	−	0.140605i
$883$	29.5127	+	8.66570i	0.993180	+	0.291624i	0.737654	−	0.675178i	$-0.235933\pi$
$883$	29.5127	+	8.66570i	0.993180	+	0.291624i	0.255525	+	0.966802i	$0.417752\pi$
$884$	−0.0719008	−	0.207744i	−0.00241828	−	0.00698717i
$885$	−12.7714	+	8.54141i	−0.429305	+	0.287116i
$886$	−1.00829	+	21.1665i	−0.0338740	+	0.711103i
$887$	2.35452	−	12.2164i	0.0790569	−	0.410186i	−0.920743	−	0.390170i	$-0.872416\pi$
$887$	2.35452	−	12.2164i	0.0790569	−	0.410186i	0.999800	−	0.0200160i	$-0.00637172\pi$
$888$	−6.15545	+	35.4078i	−0.206563	+	1.18821i
$889$	−19.0822	+	47.6649i	−0.639995	+	1.59863i
$890$	−8.94296	+	7.74912i	−0.299769	+	0.259751i
$891$	54.7079	−	20.5110i	1.83278	−	0.687145i
$892$	4.40482	−	1.29337i	0.147484	−	0.0433052i
$893$	−5.84641	−	8.21013i	−0.195643	−	0.274742i
$894$	−0.837326	+	28.5454i	−0.0280044	+	0.954699i
$895$	−1.08352	+	2.10174i	−0.0362182	+	0.0702535i
$896$	−12.6941	−	21.9869i	−0.424081	−	0.734530i
$897$	−4.06422	−	2.85303i	−0.135700	−	0.0952598i
$898$	−1.96920	+	3.41075i	−0.0657129	+	0.113818i
$899$	3.23223	+	5.02944i	0.107801	+	0.167741i
$900$	0.0120578	+	0.142950i	0.000401925	+	0.00476501i
$901$	4.90731	−	10.7455i	0.163486	−	0.357985i
$902$	21.4470	−	88.4058i	0.714107	−	2.94359i
$903$	−11.8682	−	6.56591i	−0.394949	−	0.218500i
$904$	45.2565	+	15.6634i	1.50521	+	0.520957i
$905$	−22.9618	−	29.1983i	−0.763276	−	0.970584i
$906$	−0.487388	−	1.32912i	−0.0161924	−	0.0441570i
$907$	−11.1833	+	3.87059i	−0.371337	+	0.128521i	−0.506361	−	0.862321i	$-0.669010\pi$
$907$	−11.1833	+	3.87059i	−0.371337	+	0.128521i	0.135025	+	0.990842i	$0.456889\pi$
$908$	7.11128	+	4.57014i	0.235996	+	0.151665i
$909$	4.54795	+	5.36732i	0.150846	+	0.178023i
$910$	−3.53851	+	4.08366i	−0.117301	+	0.135372i
$911$	26.7302	−	25.4872i	0.885612	−	0.844429i	−0.103036	−	0.994678i	$-0.532856\pi$
$911$	26.7302	−	25.4872i	0.885612	−	0.844429i	0.988648	+	0.150248i	$0.0480073\pi$
$912$	−13.8527	−	3.79397i	−0.458709	−	0.125631i
$913$	−14.3662	+	41.5084i	−0.475451	+	1.37373i
$914$	−6.16815	+	8.66196i	−0.204024	+	0.286512i
$915$	7.42630	−	3.13169i	0.245506	−	0.103530i
$916$	−2.28505	+	1.62718i	−0.0755002	+	0.0537634i
$917$	1.56399	−	10.8778i	0.0516474	−	0.359215i
$918$	−3.06999	−	7.51071i	−0.101325	−	0.247890i
$919$			32.1865i			1.06173i	0.847455	+	0.530867i	$0.178134\pi$
$919$			32.1865i			1.06173i	−0.847455	+	0.530867i	$0.821866\pi$
$920$	16.8199	+	26.8482i	0.554535	+	0.885158i
$921$	−3.60107	−	31.5982i	−0.118659	−	1.04119i
$922$	29.9509	+	15.4408i	0.986381	+	0.508515i
$923$	−2.14750	−	5.36421i	−0.0706860	−	0.176565i
$924$	−7.27085	−	8.08752i	−0.239193	−	0.266060i
$925$	1.04822	+	0.254296i	0.0344653	+	0.00836119i
$926$	−26.3496	+	12.0335i	−0.865903	+	0.395445i
$927$	−11.2048	−	1.19500i	−0.368013	−	0.0392490i
$928$	−0.329421	−	2.29117i	−0.0108138	−	0.0752115i
$929$	5.90743	+	6.19553i	0.193816	+	0.203269i	0.813470	−	0.581606i	$-0.197576\pi$
$929$	5.90743	+	6.19553i	0.193816	+	0.203269i	−0.619654	+	0.784875i	$0.712727\pi$
$930$	21.9418	+	1.69120i	0.719501	+	0.0554568i
$931$	−7.44444	−	0.354622i	−0.243982	−	0.0116223i
$932$	−1.41248	−	0.0672845i	−0.0462672	−	0.00220398i
$933$	−30.9186	−	2.38310i	−1.01223	−	0.0780193i
$934$	5.09219	+	5.34054i	0.166622	+	0.174748i
$935$	−2.43989	−	16.9698i	−0.0797930	−	0.554972i
$936$	5.35255	+	0.570855i	0.174954	+	0.0186590i
$937$	−17.1751	+	7.84362i	−0.561087	+	0.256240i	−0.675708	−	0.737169i	$-0.736162\pi$
$937$	−17.1751	+	7.84362i	−0.561087	+	0.256240i	0.114621	+	0.993409i	$0.463435\pi$
$938$	27.7786	+	6.73902i	0.907004	+	0.220037i
$939$	−4.11185	−	4.57370i	−0.134185	−	0.149257i
$940$	−1.00343	−	2.50645i	−0.0327284	−	0.0817515i
$941$	20.2100	+	10.4190i	0.658827	+	0.339649i	0.755008	−	0.655715i	$-0.227633\pi$
$941$	20.2100	+	10.4190i	0.658827	+	0.339649i	−0.0961818	+	0.995364i	$0.530663\pi$
$942$	−4.58069	−	40.1940i	−0.149247	−	1.30959i
$943$	47.2191	−	20.9094i	1.53767	−	0.680905i
$944$			13.2728i			0.431992i
$945$	22.1048	−	28.5304i	0.719069	−	0.928094i
$946$	2.98330	−	20.7493i	0.0969956	−	0.674619i
$947$	−43.1740	+	30.7440i	−1.40297	+	0.999047i	−0.406623	+	0.913596i	$0.633294\pi$
$947$	−43.1740	+	30.7440i	−1.40297	+	0.999047i	−0.996342	+	0.0854507i	$0.972767\pi$
$948$	0.310573	−	0.130969i	0.0100869	−	0.00425368i
$949$	5.39796	−	7.58037i	0.175225	−	0.246069i
$950$	−0.167231	+	0.483183i	−0.00542570	+	0.0156765i
$951$	27.1547	+	7.43711i	0.880551	+	0.241165i
$952$	−8.22621	+	7.84367i	−0.266613	+	0.254215i
$953$	26.3011	−	30.3531i	0.851976	−	0.983233i	−0.148008	−	0.988986i	$-0.547286\pi$
$953$	26.3011	−	30.3531i	0.851976	−	0.983233i	0.999983	+	0.00575369i	$0.00183147\pi$
$954$	24.8470	+	29.3235i	0.804453	+	0.949384i
$955$	19.1153	+	12.2847i	0.618557	+	0.397522i
$956$	−1.09713	+	0.379719i	−0.0354836	+	0.0122810i
$957$	5.21716	+	14.2273i	0.168647	+	0.459904i
$958$	−7.55297	−	9.60438i	−0.244025	−	0.310304i
$959$	27.8888	+	9.65242i	0.900578	+	0.311693i
$960$	−29.4250	−	16.2789i	−0.949686	−	0.525400i
$961$	−2.66903	+	11.0019i	−0.0860976	+	0.354899i
$962$	2.23403	−	4.89184i	0.0720279	−	0.157719i
$963$	4.04592	+	47.9663i	0.130378	+	1.54569i
$964$	0.281597	+	0.438173i	0.00906961	+	0.0141126i
$965$	17.5791	−	30.4479i	0.565891	−	0.980152i
$966$	−6.23035	+	33.5412i	−0.200458	+	1.07917i
$967$	−1.19555	−	2.07075i	−0.0384463	−	0.0665909i	0.846162	−	0.532926i	$-0.178908\pi$
$967$	−1.19555	−	2.07075i	−0.0384463	−	0.0665909i	−0.884608	+	0.466335i	$0.845574\pi$
$968$	42.8348	−	83.0880i	1.37676	−	2.67055i
$969$	−0.153447	+	5.23116i	−0.00492941	+	0.168049i
$970$	−31.8269	−	44.6946i	−1.02190	−	1.43506i
$971$	−42.9061	+	12.5984i	−1.37692	+	0.404301i	−0.884697	−	0.466167i	$-0.845635\pi$
$971$	−42.9061	+	12.5984i	−1.37692	+	0.404301i	−0.492226	+	0.870468i	$0.663816\pi$
$972$	−4.77112	−	0.245567i	−0.153034	−	0.00787657i
$973$	39.4170	−	34.1550i	1.26365	−	1.09496i
$974$	−1.73940	+	4.34482i	−0.0557341	+	0.139217i
$975$	0.0276706	−	0.159169i	0.000886170	−	0.00509748i
$976$	1.31765	−	6.83663i	0.0421770	−	0.218835i
$977$	−0.988665	+	20.7546i	−0.0316302	+	0.663999i	0.926264	+	0.376876i	$0.123002\pi$
$977$	−0.988665	+	20.7546i	−0.0316302	+	0.663999i	−0.957894	+	0.287123i	$0.907301\pi$
$978$	32.7303	−	21.8898i	1.04660	−	0.699960i
$979$	8.77226	+	25.3458i	0.280363	+	0.810055i
$980$	−1.91552	−	0.562447i	−0.0611890	−	0.0179667i
$981$	−8.86099	+	3.43430i	−0.282910	+	0.109649i
$982$	0.746117	+	0.861065i	0.0238095	+	0.0274777i
$983$	−32.3543	−	3.08946i	−1.03194	−	0.0985384i	−0.434680	−	0.900585i	$-0.643138\pi$
$983$	−32.3543	−	3.08946i	−1.03194	−	0.0985384i	−0.597261	+	0.802047i	$0.703744\pi$
$984$	−33.7952	+	44.6291i	−1.07735	+	1.42272i
$985$	0.310893	+	3.25582i	0.00990587	+	0.103739i
$986$	1.95371	−	0.782148i	0.0622188	−	0.0249087i
$987$	7.75914	−	20.4572i	0.246976	−	0.651158i
$988$	−0.399526	−	0.230666i	−0.0127106	−	0.00733848i
$989$	10.3737	−	5.83075i	0.329863	−	0.185407i
$990$	53.3444	+	16.3057i	1.69540	+	0.518229i
$991$	32.4415	−	20.8489i	1.03054	−	0.662286i	0.0879081	−	0.996129i	$-0.471982\pi$
$991$	32.4415	−	20.8489i	1.03054	−	0.662286i	0.942629	+	0.333843i	$0.108345\pi$
$992$	−4.70990	+	5.98912i	−0.149539	+	0.190155i
$993$	23.3283	−	20.9726i	0.740301	−	0.665546i
$994$	−27.3938	+	28.7298i	−0.868880	+	0.911255i
$995$	0.971390	+	0.691724i	0.0307951	+	0.0219291i
$996$	2.43058	−	2.64423i	0.0770158	−	0.0837855i
$997$	46.3991	+	18.5754i	1.46947	+	0.588289i	0.961920	−	0.273331i	$-0.0881254\pi$
$997$	46.3991	+	18.5754i	1.46947	+	0.588289i	0.507554	+	0.861620i	$0.330550\pi$
$998$	2.59686	−	8.84409i	0.0822021	−	0.279955i
$999$	−13.1090	+	33.4429i	−0.414749	+	1.05809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.11.8	✓	440
3.2	odd	2		621.2.s.a.494.15		440
9.4	even	3		621.2.s.a.287.15		440
9.5	odd	6	inner	207.2.o.a.149.8	yes	440
23.21	odd	22	inner	207.2.o.a.182.8	yes	440
69.44	even	22		621.2.s.a.251.15		440
207.67	odd	66		621.2.s.a.44.15		440
207.113	even	66	inner	207.2.o.a.113.8	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.8	✓	440	1.1	even	1	trivial
207.2.o.a.113.8	yes	440	207.113	even	66	inner
207.2.o.a.149.8	yes	440	9.5	odd	6	inner
207.2.o.a.182.8	yes	440	23.21	odd	22	inner
621.2.s.a.44.15		440	207.67	odd	66
621.2.s.a.251.15		440	69.44	even	22
621.2.s.a.287.15		440	9.4	even	3
621.2.s.a.494.15		440	3.2	odd	2

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29988 + 0.0619210i) q^{2} +(1.73131 + 0.0507847i) q^{3} +(-0.305085 + 0.0291321i) q^{4} +(-1.59287 - 1.51880i) q^{5} +(-2.25364 + 0.0411901i) q^{6} +(0.597259 + 3.09887i) q^{7} +(2.97099 - 0.427164i) q^{8} +(2.99484 + 0.175848i) q^{9} +O(q^{10})\)	\(q+(-1.29988 + 0.0619210i) q^{2} +(1.73131 + 0.0507847i) q^{3} +(-0.305085 + 0.0291321i) q^{4} +(-1.59287 - 1.51880i) q^{5} +(-2.25364 + 0.0411901i) q^{6} +(0.597259 + 3.09887i) q^{7} +(2.97099 - 0.427164i) q^{8} +(2.99484 + 0.175848i) q^{9} +(2.16459 + 1.87562i) q^{10} +(5.77017 - 2.97473i) q^{11} +(-0.529675 + 0.0349429i) q^{12} +(0.586991 + 0.113133i) q^{13} +(-0.968251 - 3.99119i) q^{14} +(-2.68061 - 2.71039i) q^{15} +(-3.23362 + 0.623229i) q^{16} +(0.498465 + 1.09149i) q^{17} +(-3.90383 - 0.0431378i) q^{18} +(2.29054 + 1.04605i) q^{19} +(0.530206 + 0.416958i) q^{20} +(0.876662 + 5.39543i) q^{21} +(-7.31634 + 4.22409i) q^{22} +(-4.43144 - 1.83367i) q^{23} +(5.16539 - 0.588671i) q^{24} +(-0.00742427 - 0.155855i) q^{25} +(-0.770024 - 0.110713i) q^{26} +(5.17606 + 0.456539i) q^{27} +(-0.272491 - 0.928020i) q^{28} +(-0.128107 + 1.34159i) q^{29} +(3.65231 + 3.35721i) q^{30} +(3.48701 - 2.74222i) q^{31} +(-1.66914 + 0.404928i) q^{32} +(10.1410 - 4.85713i) q^{33} +(-0.715532 - 1.38794i) q^{34} +(3.75520 - 5.84321i) q^{35} +(-0.918804 + 0.0335974i) q^{36} +(-1.94758 + 6.63286i) q^{37} +(-3.04220 - 1.21791i) q^{38} +(1.01051 + 0.225678i) q^{39} +(-5.38117 - 3.83191i) q^{40} +(-7.43078 + 7.79318i) q^{41} +(-1.47365 - 6.95914i) q^{42} +(-1.53385 + 1.95045i) q^{43} +(-1.67373 + 1.07564i) q^{44} +(-4.50331 - 4.82866i) q^{45} +(5.87389 + 2.10915i) q^{46} +(-3.46639 - 2.00132i) q^{47} +(-5.63003 + 0.914781i) q^{48} +(-2.74772 + 1.10002i) q^{49} +(0.0193013 + 0.202133i) q^{50} +(0.807565 + 1.91501i) q^{51} +(-0.182378 - 0.0174150i) q^{52} +(-6.44700 - 7.44024i) q^{53} +(-6.75653 - 0.272940i) q^{54} +(-13.7091 - 4.02536i) q^{55} +(3.09818 + 8.95160i) q^{56} +(3.91250 + 1.92736i) q^{57} +(0.0834506 - 1.75184i) q^{58} +(0.762767 - 3.95761i) q^{59} +(0.896773 + 0.748809i) q^{60} +(-0.785782 + 1.96279i) q^{61} +(-4.36290 + 3.78048i) q^{62} +(1.24377 + 9.38566i) q^{63} +(8.46407 - 2.48528i) q^{64} +(-0.763172 - 1.07173i) q^{65} +(-12.8813 + 6.94164i) q^{66} +(-3.18925 + 6.18629i) q^{67} +(-0.183871 - 0.318475i) q^{68} +(-7.57906 - 3.39969i) q^{69} +(-4.51950 + 7.82801i) q^{70} +(-5.22568 - 8.13132i) q^{71} +(8.97276 - 0.756846i) q^{72} +(6.46681 - 14.1603i) q^{73} +(2.12092 - 8.74253i) q^{74} +(-0.00493865 - 0.270209i) q^{75} +(-0.729282 - 0.252407i) q^{76} +(12.6646 + 16.1043i) q^{77} +(-1.32752 - 0.230783i) q^{78} +(-0.600047 + 0.207678i) q^{79} +(6.09728 + 3.91849i) q^{80} +(8.93816 + 1.05327i) q^{81} +(9.17657 - 10.5903i) q^{82} +(-4.89683 + 4.66912i) q^{83} +(-0.424637 - 1.62053i) q^{84} +(0.863756 - 2.49566i) q^{85} +(1.87306 - 2.63034i) q^{86} +(-0.289924 + 2.31620i) q^{87} +(15.8724 - 11.3027i) q^{88} +(-0.587972 + 4.08944i) q^{89} +(6.15277 + 5.99783i) q^{90} +1.88658i q^{91} +(1.40538 + 0.430327i) q^{92} +(6.17635 - 4.57053i) q^{93} +(4.62982 + 2.38684i) q^{94} +(-2.05978 - 5.14508i) q^{95} +(-2.91035 + 0.616288i) q^{96} +(-18.6170 - 4.51643i) q^{97} +(3.50360 - 1.60004i) q^{98} +(17.8038 - 7.89417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

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Database

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