LMFDB - Embedded newform 74.2.f.b.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			33.1
Root			$-2.14169 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	74.33
Dual form			74.2.f.b.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-0.238878 - 1.35474i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.266044 - 0.223238i) q^{5} -1.37564 q^{6} +(-0.365982 + 0.307095i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.04081 - 0.378824i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(-0.238878 - 1.35474i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.266044 - 0.223238i) q^{5} -1.37564 q^{6} +(-0.365982 + 0.307095i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.04081 - 0.378824i) q^{9} +(-0.173648 - 0.300767i) q^{10} +(-1.29268 + 2.23899i) q^{11} +(-0.238878 + 1.35474i) q^{12} +(4.21288 + 1.53336i) q^{13} +(0.238878 + 0.413749i) q^{14} +(-0.365982 - 0.307095i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.88864 + 0.687407i) q^{17} +(-0.192334 - 1.09078i) q^{18} +(0.611631 + 3.46873i) q^{19} +(-0.326352 + 0.118782i) q^{20} +(0.503461 + 0.422454i) q^{21} +(1.98050 + 1.66184i) q^{22} +(-2.60486 - 4.51175i) q^{23} +(1.29268 + 0.470498i) q^{24} +(-0.847296 + 4.80526i) q^{25} +(2.24162 - 3.88261i) q^{26} +(-2.82530 - 4.89356i) q^{27} +(0.448944 - 0.163402i) q^{28} +(-0.114111 + 0.197646i) q^{29} +(-0.365982 + 0.307095i) q^{30} -6.74658 q^{31} +(0.766044 - 0.642788i) q^{32} +(3.34205 + 1.21641i) q^{33} +(0.349006 + 1.97931i) q^{34} +(-0.0288122 + 0.163402i) q^{35} -1.10761 q^{36} +(2.42322 - 5.57925i) q^{37} +3.52224 q^{38} +(1.07095 - 6.07365i) q^{39} +(0.0603074 + 0.342020i) q^{40} +(-10.0701 - 3.66521i) q^{41} +(0.503461 - 0.422454i) q^{42} +8.85889 q^{43} +(1.98050 - 1.66184i) q^{44} +(0.192334 - 0.333132i) q^{45} +(-4.89554 + 1.78183i) q^{46} +(-3.72890 - 6.45864i) q^{47} +(0.687821 - 1.19134i) q^{48} +(-1.17590 + 6.66887i) q^{49} +(4.58512 + 1.66885i) q^{50} +(1.38241 + 2.39441i) q^{51} +(-3.43437 - 2.88178i) q^{52} +(3.35194 + 2.81261i) q^{53} +(-5.30983 + 1.93262i) q^{54} +(0.155916 + 0.884246i) q^{55} +(-0.0829614 - 0.470498i) q^{56} +(4.55314 - 1.65721i) q^{57} +(0.174828 + 0.146698i) q^{58} +(3.43016 + 2.87825i) q^{59} +(0.238878 + 0.413749i) q^{60} +(1.35175 + 0.491998i) q^{61} +(-1.17153 + 6.64409i) q^{62} +(-0.264583 + 0.458271i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.46312 - 0.532531i) q^{65} +(1.77827 - 3.08005i) q^{66} +(-8.06111 + 6.76408i) q^{67} +2.00984 q^{68} +(-5.49002 + 4.60667i) q^{69} +(0.155916 + 0.0567489i) q^{70} +(1.54193 + 8.74474i) q^{71} +(-0.192334 + 1.09078i) q^{72} +7.18667 q^{73} +(-5.07370 - 3.35524i) q^{74} +6.71229 q^{75} +(0.611631 - 3.46873i) q^{76} +(-0.214485 - 1.21641i) q^{77} +(-5.79541 - 2.10936i) q^{78} +(2.70857 - 2.27276i) q^{79} +0.347296 q^{80} +(-3.40919 + 2.86065i) q^{81} +(-5.35818 + 9.28064i) q^{82} +(-1.32932 + 0.483834i) q^{83} +(-0.328611 - 0.569170i) q^{84} +(-0.349006 + 0.604496i) q^{85} +(1.53833 - 8.72431i) q^{86} +(0.295018 + 0.107378i) q^{87} +(-1.29268 - 2.23899i) q^{88} +(2.92954 + 2.45818i) q^{89} +(-0.294673 - 0.247260i) q^{90} +(-2.01273 + 0.732572i) q^{91} +(0.904658 + 5.13057i) q^{92} +(1.61161 + 9.13989i) q^{93} +(-7.00804 + 2.55072i) q^{94} +(0.937074 + 0.786298i) q^{95} +(-1.05380 - 0.884246i) q^{96} +(-9.24175 - 16.0072i) q^{97} +(6.36336 + 2.31607i) q^{98} +(-0.497253 + 2.82006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 6 q^{30} + 42 q^{31} + 57 q^{33} - 3 q^{34} - 9 q^{35} + 24 q^{36} - 3 q^{37} + 42 q^{38} - 24 q^{39} + 12 q^{40} - 21 q^{41} - 33 q^{42} + 36 q^{43} - 3 q^{44} - 6 q^{45} + 3 q^{46} + 9 q^{47} - 12 q^{49} + 12 q^{50} + 3 q^{52} - 6 q^{53} - 27 q^{54} - 3 q^{56} - 36 q^{57} - 3 q^{58} - 6 q^{59} + 3 q^{60} - 18 q^{61} - 33 q^{62} + 36 q^{63} - 6 q^{64} + 3 q^{65} + 3 q^{66} - 27 q^{67} + 6 q^{68} - 12 q^{69} - 18 q^{71} + 6 q^{72} + 54 q^{73} + 3 q^{74} - 6 q^{75} - 3 q^{76} + 51 q^{77} - 33 q^{78} - 12 q^{79} - 36 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 3 q^{85} + 39 q^{87} + 3 q^{88} - 15 q^{89} - 15 q^{90} - 51 q^{91} - 6 q^{92} + 45 q^{93} - 12 q^{94} - 15 q^{95} + 6 q^{96} - 42 q^{97} + 51 q^{98} - 33 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	−0.238878	−	1.35474i	−0.137916	−	0.782162i	−0.972784	−	0.231712i	$-0.925567\pi$
$3$	−0.238878	−	1.35474i	−0.137916	−	0.782162i	0.834868	−	0.550450i	$-0.185544\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	0.266044	−	0.223238i	0.118979	−	0.0998350i	−0.581357	−	0.813649i	$-0.697478\pi$
$5$	0.266044	−	0.223238i	0.118979	−	0.0998350i	0.700336	+	0.713814i	$0.253034\pi$
$6$	−1.37564			−0.561604
$7$	−0.365982	+	0.307095i	−0.138328	+	0.116071i	−0.709326	−	0.704880i	$-0.751001\pi$
$7$	−0.365982	+	0.307095i	−0.138328	+	0.116071i	0.570998	+	0.820951i	$0.306556\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	1.04081	−	0.378824i	0.346937	−	0.126275i
$10$	−0.173648	−	0.300767i	−0.0549124	−	0.0951110i
$11$	−1.29268	+	2.23899i	−0.389758	+	0.675081i	−0.992417	−	0.122918i	$-0.960775\pi$
$11$	−1.29268	+	2.23899i	−0.389758	+	0.675081i	0.602659	+	0.797999i	$0.294108\pi$
$12$	−0.238878	+	1.35474i	−0.0689581	+	0.391081i
$13$	4.21288	+	1.53336i	1.16844	+	0.425278i	0.852106	−	0.523369i	$-0.175325\pi$
$13$	4.21288	+	1.53336i	1.16844	+	0.425278i	0.316336	+	0.948647i	$0.397547\pi$
$14$	0.238878	+	0.413749i	0.0638428	+	0.110579i
$15$	−0.365982	−	0.307095i	−0.0944962	−	0.0792917i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−1.88864	+	0.687407i	−0.458062	+	0.166721i	−0.560737	−	0.827994i	$-0.689482\pi$
$17$	−1.88864	+	0.687407i	−0.458062	+	0.166721i	0.102675	+	0.994715i	$0.467260\pi$
$18$	−0.192334	−	1.09078i	−0.0453335	−	0.257099i
$19$	0.611631	+	3.46873i	0.140318	+	0.795782i	0.971008	+	0.239047i	$0.0768350\pi$
$19$	0.611631	+	3.46873i	0.140318	+	0.795782i	−0.830690	+	0.556735i	$0.812054\pi$
$20$	−0.326352	+	0.118782i	−0.0729745	+	0.0265605i
$21$	0.503461	+	0.422454i	0.109864	+	0.0921869i
$22$	1.98050	+	1.66184i	0.422245	+	0.354305i
$23$	−2.60486	−	4.51175i	−0.543151	−	0.940765i	−0.998721	−	0.0505649i	$-0.983898\pi$
$23$	−2.60486	−	4.51175i	−0.543151	−	0.940765i	0.455570	−	0.890200i	$-0.349435\pi$
$24$	1.29268	+	0.470498i	0.263867	+	0.0960399i
$25$	−0.847296	+	4.80526i	−0.169459	+	0.961051i
$26$	2.24162	−	3.88261i	0.439619	−	0.761442i
$27$	−2.82530	−	4.89356i	−0.543729	−	0.941767i
$28$	0.448944	−	0.163402i	0.0848424	−	0.0308801i
$29$	−0.114111	+	0.197646i	−0.0211899	+	0.0367019i	−0.876426	−	0.481537i	$-0.840079\pi$
$29$	−0.114111	+	0.197646i	−0.0211899	+	0.0367019i	0.855236	+	0.518239i	$0.173412\pi$
$30$	−0.365982	+	0.307095i	−0.0668189	+	0.0560677i
$31$	−6.74658			−1.21172			−0.605861	−	0.795571i	$-0.707171\pi$
$31$	−6.74658			−1.21172			−0.605861	+	0.795571i	$0.707171\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	3.34205	+	1.21641i	0.581776	+	0.211749i
$34$	0.349006	+	1.97931i	0.0598540	+	0.339449i
$35$	−0.0288122	+	0.163402i	−0.00487015	+	0.0276200i
$36$	−1.10761			−0.184601
$37$	2.42322	−	5.57925i	0.398376	−	0.917222i
$37$	2.42322	−	5.57925i	0.398376	−	0.917222i
$38$	3.52224			0.571383
$39$	1.07095	−	6.07365i	0.171489	−	0.972563i
$40$	0.0603074	+	0.342020i	0.00953543	+	0.0540781i
$41$	−10.0701	−	3.66521i	−1.57268	−	0.572410i	−0.599086	−	0.800685i	$-0.704469\pi$
$41$	−10.0701	−	3.66521i	−1.57268	−	0.572410i	−0.973597	+	0.228275i	$0.926691\pi$
$42$	0.503461	−	0.422454i	0.0776857	−	0.0651860i
$43$	8.85889			1.35097			0.675484	−	0.737374i	$-0.263935\pi$
$43$	8.85889			1.35097			0.675484	+	0.737374i	$0.263935\pi$
$44$	1.98050	−	1.66184i	0.298572	−	0.250532i
$45$	0.192334	−	0.333132i	0.0286715	−	0.0496604i
$46$	−4.89554	+	1.78183i	−0.721807	+	0.262716i
$47$	−3.72890	−	6.45864i	−0.543916	−	0.942090i	−0.998674	−	0.0514750i	$-0.983608\pi$
$47$	−3.72890	−	6.45864i	−0.543916	−	0.942090i	0.454758	−	0.890615i	$-0.349726\pi$
$48$	0.687821	−	1.19134i	0.0992785	−	0.171955i
$49$	−1.17590	+	6.66887i	−0.167986	+	0.952696i
$50$	4.58512	+	1.66885i	0.648434	+	0.236011i
$51$	1.38241	+	2.39441i	0.193577	+	0.335285i
$52$	−3.43437	−	2.88178i	−0.476261	−	0.399631i
$53$	3.35194	+	2.81261i	0.460424	+	0.386342i	0.843287	−	0.537464i	$-0.180617\pi$
$53$	3.35194	+	2.81261i	0.460424	+	0.386342i	−0.382863	+	0.923805i	$0.625062\pi$
$54$	−5.30983	+	1.93262i	−0.722576	+	0.262996i
$55$	0.155916	+	0.884246i	0.0210238	+	0.119232i
$56$	−0.0829614	−	0.470498i	−0.0110862	−	0.0628729i
$57$	4.55314	−	1.65721i	0.603078	−	0.219502i
$58$	0.174828	+	0.146698i	0.0229560	+	0.0192624i
$59$	3.43016	+	2.87825i	0.446569	+	0.374716i	0.838161	−	0.545423i	$-0.183631\pi$
$59$	3.43016	+	2.87825i	0.446569	+	0.374716i	−0.391592	+	0.920139i	$0.628076\pi$
$60$	0.238878	+	0.413749i	0.0308390	+	0.0534147i
$61$	1.35175	+	0.491998i	0.173074	+	0.0629939i	0.427104	−	0.904203i	$-0.359534\pi$
$61$	1.35175	+	0.491998i	0.173074	+	0.0629939i	−0.254030	+	0.967196i	$0.581756\pi$
$62$	−1.17153	+	6.64409i	−0.148785	+	0.843800i
$63$	−0.264583	+	0.458271i	−0.0333343	+	0.0577367i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.46312	−	0.532531i	0.181477	−	0.0660523i
$66$	1.77827	−	3.08005i	0.218890	−	0.379128i
$67$	−8.06111	+	6.76408i	−0.984822	+	0.826363i	−0.984810	−	0.173637i	$-0.944448\pi$
$67$	−8.06111	+	6.76408i	−0.984822	+	0.826363i	−1.18267e−5		1.00000i	$0.500004\pi$
$68$	2.00984			0.243729
$69$	−5.49002	+	4.60667i	−0.660921	+	0.554578i
$70$	0.155916	+	0.0567489i	0.0186356	+	0.00678280i
$71$	1.54193	+	8.74474i	0.182994	+	1.03781i	0.928506	+	0.371318i	$0.121094\pi$
$71$	1.54193	+	8.74474i	0.182994	+	1.03781i	−0.745512	+	0.666492i	$0.767795\pi$
$72$	−0.192334	+	1.09078i	−0.0226668	+	0.128550i
$73$	7.18667			0.841136			0.420568	−	0.907261i	$-0.361831\pi$
$73$	7.18667			0.841136			0.420568	+	0.907261i	$0.361831\pi$
$74$	−5.07370	−	3.35524i	−0.589805	−	0.390038i
$75$	6.71229			0.775069
$76$	0.611631	−	3.46873i	0.0701589	−	0.397891i
$77$	−0.214485	−	1.21641i	−0.0244429	−	0.138622i
$78$	−5.79541	−	2.10936i	−0.656201	−	0.238838i
$79$	2.70857	−	2.27276i	0.304738	−	0.255705i	−0.477575	−	0.878591i	$-0.658484\pi$
$79$	2.70857	−	2.27276i	0.304738	−	0.255705i	0.782313	+	0.622885i	$0.214040\pi$
$80$	0.347296			0.0388289
$81$	−3.40919	+	2.86065i	−0.378799	+	0.317850i
$82$	−5.35818	+	9.28064i	−0.591712	+	1.02487i
$83$	−1.32932	+	0.483834i	−0.145912	+	0.0531077i	−0.413944	−	0.910302i	$-0.635849\pi$
$83$	−1.32932	+	0.483834i	−0.145912	+	0.0531077i	0.268032	+	0.963410i	$0.413627\pi$
$84$	−0.328611	−	0.569170i	−0.0358544	−	0.0621016i
$85$	−0.349006	+	0.604496i	−0.0378550	+	0.0655668i
$86$	1.53833	−	8.72431i	0.165882	−	0.940766i
$87$	0.295018	+	0.107378i	0.0316292	+	0.0115121i
$88$	−1.29268	−	2.23899i	−0.137800	−	0.238677i
$89$	2.92954	+	2.45818i	0.310531	+	0.260567i	0.784711	−	0.619861i	$-0.212811\pi$
$89$	2.92954	+	2.45818i	0.310531	+	0.260567i	−0.474180	+	0.880428i	$0.657256\pi$
$90$	−0.294673	−	0.247260i	−0.0310612	−	0.0260635i
$91$	−2.01273	+	0.732572i	−0.210991	+	0.0767944i
$92$	0.904658	+	5.13057i	0.0943172	+	0.534899i
$93$	1.61161	+	9.13989i	0.167116	+	0.947762i
$94$	−7.00804	+	2.55072i	−0.722824	+	0.263086i
$95$	0.937074	+	0.786298i	0.0961417	+	0.0806725i
$96$	−1.05380	−	0.884246i	−0.107553	−	0.0902480i
$97$	−9.24175	−	16.0072i	−0.938358	−	1.62528i	−0.768534	−	0.639809i	$-0.779013\pi$
$97$	−9.24175	−	16.0072i	−0.938358	−	1.62528i	−0.169824	−	0.985474i	$-0.554320\pi$
$98$	6.36336	+	2.31607i	0.642797	+	0.233959i
$99$	−0.497253	+	2.82006i	−0.0499758	+	0.283427i
$100$	2.43969	−	4.22567i	0.243969	−	0.422567i
$101$	−8.56431	−	14.8338i	−0.852180	−	1.47602i	−0.879236	−	0.476386i	$-0.841947\pi$
$101$	−8.56431	−	14.8338i	−0.852180	−	1.47602i	0.0270562	−	0.999634i	$-0.491387\pi$
$102$	2.59809	−	0.945627i	0.257249	−	0.0936310i
$103$	6.71012	−	11.6223i	0.661167	−	1.14518i	−0.319142	−	0.947707i	$-0.603395\pi$
$103$	6.71012	−	11.6223i	0.661167	−	1.14518i	0.980309	−	0.197468i	$-0.0632720\pi$
$104$	−3.43437	+	2.88178i	−0.336768	+	0.282582i
$105$	0.228251			0.0222750
$106$	3.35194	−	2.81261i	0.325569	−	0.273185i
$107$	19.2261	+	6.99774i	1.85866	+	0.676497i	0.979984	+	0.199079i	$0.0637949\pi$
$107$	19.2261	+	6.99774i	1.85866	+	0.676497i	0.878676	+	0.477418i	$0.158427\pi$
$108$	0.981216	+	5.56475i	0.0944176	+	0.535469i
$109$	1.85087	−	10.4968i	0.177281	−	1.00541i	−0.758197	−	0.652026i	$-0.773919\pi$
$109$	1.85087	−	10.4968i	0.177281	−	1.00541i	0.935478	−	0.353385i	$-0.114970\pi$
$110$	0.897887			0.0856102
$111$	−8.13730	−	1.95009i	−0.772359	−	0.185094i
$112$	−0.477756			−0.0451437
$113$	2.12063	−	12.0267i	0.199492	−	1.13138i	−0.706383	−	0.707830i	$-0.749674\pi$
$113$	2.12063	−	12.0267i	0.199492	−	1.13138i	0.905875	−	0.423546i	$-0.139215\pi$
$114$	−0.841386	−	4.77174i	−0.0788030	−	0.446914i
$115$	−1.70020	−	0.618823i	−0.158545	−	0.0577055i
$116$	0.174828	−	0.146698i	0.0162324	−	0.0136206i
$117$	4.96568			0.459077
$118$	3.43016	−	2.87825i	0.315772	−	0.264964i
$119$	0.480107	−	0.831570i	0.0440114	−	0.0762299i
$120$	0.448944	−	0.163402i	0.0409827	−	0.0149165i
$121$	2.15795	+	3.73768i	0.196177	+	0.339789i
$122$	0.719253	−	1.24578i	0.0651181	−	0.112788i
$123$	−2.55990	+	14.5179i	−0.230818	+	1.30904i
$124$	6.33971	+	2.30747i	0.569323	+	0.207217i
$125$	1.71554	+	2.97140i	0.153442	+	0.265770i
$126$	0.405364	+	0.340141i	0.0361127	+	0.0303022i
$127$	−5.40029	−	4.53138i	−0.479198	−	0.402095i	0.370938	−	0.928658i	$-0.379036\pi$
$127$	−5.40029	−	4.53138i	−0.479198	−	0.402095i	−0.850136	+	0.526563i	$0.823481\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	−2.11619	−	12.0015i	−0.186320	−	1.05668i
$130$	−0.270373	−	1.53336i	−0.0237133	−	0.134485i
$131$	−1.86532	+	0.678920i	−0.162974	+	0.0593175i	−0.422219	−	0.906494i	$-0.638749\pi$
$131$	−1.86532	+	0.678920i	−0.162974	+	0.0593175i	0.259245	+	0.965812i	$0.416526\pi$
$132$	−2.72446	−	2.28610i	−0.237134	−	0.198979i
$133$	−1.28908	−	1.08167i	−0.111777	−	0.0937923i
$134$	5.26152	+	9.11322i	0.454526	+	0.787262i
$135$	−1.84408	−	0.671192i	−0.158713	−	0.0577670i
$136$	0.349006	−	1.97931i	0.0299270	−	0.169724i
$137$	−8.69897	+	15.0671i	−0.743203	+	1.28727i	0.207826	+	0.978166i	$0.433361\pi$
$137$	−8.69897	+	15.0671i	−0.743203	+	1.28727i	−0.951029	+	0.309100i	$0.899972\pi$
$138$	3.58336	+	6.20656i	0.305036	+	0.528337i
$139$	−0.692602	+	0.252086i	−0.0587457	+	0.0213817i	−0.371226	−	0.928543i	$-0.621062\pi$
$139$	−0.692602	+	0.252086i	−0.0587457	+	0.0213817i	0.312480	+	0.949924i	$0.398840\pi$
$140$	0.0829614	−	0.143693i	0.00701152	−	0.0121443i
$141$	−7.85905	+	6.59453i	−0.661852	+	0.555360i
$142$	8.87964			0.745163
$143$	−8.87909	+	7.45044i	−0.742507	+	0.623037i
$144$	1.04081	+	0.378824i	0.0867342	+	0.0315687i
$145$	0.0137635	+	0.0780564i	0.00114299	+	0.00648223i
$146$	1.24795	−	7.07749i	0.103281	−	0.585737i
$147$	9.31551			0.768330
$148$	−4.18530	+	4.41398i	−0.344030	+	0.362827i
$149$	−19.0346			−1.55938			−0.779689	−	0.626167i	$-0.784623\pi$
$149$	−19.0346			−1.55938			−0.779689	+	0.626167i	$0.784623\pi$
$150$	1.16558	−	6.61032i	0.0951690	−	0.539730i
$151$	−1.12385	−	6.37365i	−0.0914574	−	0.518681i	−0.995775	−	0.0918214i	$-0.970731\pi$
$151$	−1.12385	−	6.37365i	−0.0914574	−	0.518681i	0.904318	−	0.426859i	$-0.140380\pi$
$152$	−3.30983	−	1.20468i	−0.268462	−	0.0977123i
$153$	−1.70531	+	1.43092i	−0.137866	+	0.115683i
$154$	−1.23517			−0.0995330
$155$	−1.79489	+	1.50609i	−0.144169	+	0.120972i
$156$	−3.08368	+	5.34108i	−0.246892	+	0.427629i
$157$	−11.3628	+	4.13571i	−0.906847	+	0.330065i	−0.752993	−	0.658028i	$-0.771391\pi$
$157$	−11.3628	+	4.13571i	−0.906847	+	0.330065i	−0.153854	+	0.988094i	$0.549169\pi$
$158$	−1.76789	−	3.06208i	−0.140646	−	0.243606i
$159$	3.00966	−	5.21289i	0.238682	−	0.413409i
$160$	0.0603074	−	0.342020i	0.00476772	−	0.0270391i
$161$	2.33887	+	0.851279i	0.184329	+	0.0670902i
$162$	2.22519	+	3.85415i	0.174828	+	0.302810i
$163$	11.2965	+	9.47892i	0.884813	+	0.742446i	0.967163	−	0.254157i	$-0.0817980\pi$
$163$	11.2965	+	9.47892i	0.884813	+	0.742446i	−0.0823498	+	0.996603i	$0.526242\pi$
$164$	8.20921	+	6.88834i	0.641031	+	0.537889i
$165$	1.16068	−	0.422454i	0.0903590	−	0.0328880i
$166$	0.245649	+	1.39315i	0.0190661	+	0.108129i
$167$	1.44239	+	8.18020i	0.111616	+	0.633003i	0.988370	+	0.152066i	$0.0485925\pi$
$167$	1.44239	+	8.18020i	0.111616	+	0.633003i	−0.876755	+	0.480937i	$0.840296\pi$
$168$	−0.617586	+	0.224783i	−0.0476478	+	0.0173424i
$169$	5.43855	+	4.56349i	0.418350	+	0.351038i
$170$	0.534708	+	0.448673i	0.0410102	+	0.0344117i
$171$	1.95063	+	3.37859i	0.149168	+	0.258367i
$172$	−8.32464	−	3.02992i	−0.634748	−	0.231029i
$173$	−1.14829	+	6.51227i	−0.0873028	+	0.495119i	0.909533	+	0.415632i	$0.136439\pi$
$173$	−1.14829	+	6.51227i	−0.0873028	+	0.495119i	−0.996836	+	0.0794872i	$0.974672\pi$
$174$	0.156976	−	0.271890i	0.0119003	−	0.0206119i
$175$	−1.16558	−	2.01884i	−0.0881093	−	0.152610i
$176$	−2.42945	+	0.884246i	−0.183126	+	0.0666526i
$177$	3.07990	−	5.33454i	0.231499	−	0.400968i
$178$	2.92954	−	2.45818i	0.219579	−	0.184248i
$179$	4.53985			0.339325			0.169662	−	0.985502i	$-0.445732\pi$
$179$	4.53985			0.339325			0.169662	+	0.985502i	$0.445732\pi$
$180$	−0.294673	+	0.247260i	−0.0219636	+	0.0184297i
$181$	1.46942	+	0.534826i	0.109221	+	0.0397533i	0.396053	−	0.918228i	$-0.370380\pi$
$181$	1.46942	+	0.534826i	0.109221	+	0.0397533i	−0.286831	+	0.957981i	$0.592602\pi$
$182$	0.371937	+	2.10936i	0.0275698	+	0.156356i
$183$	0.343627	−	1.94881i	0.0254016	−	0.144060i
$184$	5.20972			0.384066
$185$	−0.600813	−	2.02528i	−0.0441727	−	0.148902i
$186$	9.28089			0.680508
$187$	0.902307	−	5.11724i	0.0659832	−	0.374209i
$188$	1.29503	+	7.34450i	0.0944500	+	0.535653i
$189$	2.53680	+	0.923320i	0.184525	+	0.0671616i
$190$	0.937074	−	0.786298i	0.0679825	−	0.0570441i
$191$	23.0183			1.66555			0.832773	−	0.553615i	$-0.186752\pi$
$191$	23.0183			1.66555			0.832773	+	0.553615i	$0.186752\pi$
$192$	−1.05380	+	0.884246i	−0.0760517	+	0.0638150i
$193$	5.27705	−	9.14013i	0.379851	−	0.657921i	−0.611190	−	0.791484i	$-0.709309\pi$
$193$	5.27705	−	9.14013i	0.379851	−	0.657921i	0.991040	+	0.133564i	$0.0426420\pi$
$194$	−17.3688	+	6.32173i	−1.24701	+	0.453874i
$195$	−1.07095	−	1.85494i	−0.0766923	−	0.132835i
$196$	3.38587	−	5.86451i	0.241848	−	0.418893i
$197$	0.838489	−	4.75531i	0.0597399	−	0.338802i	−0.940259	−	0.340461i	$-0.889417\pi$
$197$	0.838489	−	4.75531i	0.0597399	−	0.338802i	0.999999	+	0.00165899i	$0.000528074\pi$
$198$	2.69087	+	0.979397i	0.191232	+	0.0696027i
$199$	−5.14608	−	8.91327i	−0.364796	−	0.631845i	0.623947	−	0.781466i	$-0.285528\pi$
$199$	−5.14608	−	8.91327i	−0.364796	−	0.631845i	−0.988743	+	0.149621i	$0.952195\pi$
$200$	−3.73783	−	3.13641i	−0.264304	−	0.221778i
$201$	11.0892	+	9.30495i	0.782173	+	0.656321i
$202$	−16.0956	+	5.85833i	−1.13248	+	0.412191i
$203$	−0.0189336	−	0.107378i	−0.00132888	−	0.00753644i
$204$	−0.480107	−	2.72282i	−0.0336142	−	0.190636i
$205$	−3.49730	+	1.27291i	−0.244262	+	0.0889042i
$206$	−10.2805	−	8.62636i	−0.716276	−	0.601027i
$207$	−4.42032	−	3.70909i	−0.307234	−	0.257800i
$208$	2.24162	+	3.88261i	0.155429	+	0.269210i
$209$	−8.55710	−	3.11453i	−0.591907	−	0.215437i
$210$	0.0396353	−	0.224783i	0.00273509	−	0.0155115i
$211$	−0.685470	+	1.18727i	−0.0471897	+	0.0817349i	−0.888655	−	0.458576i	$-0.848360\pi$
$211$	−0.685470	+	1.18727i	−0.0471897	+	0.0817349i	0.841466	+	0.540310i	$0.181693\pi$
$212$	−2.18782	−	3.78942i	−0.150260	−	0.260258i
$213$	11.4785	−	4.17785i	0.786497	−	0.286262i
$214$	10.2300	−	17.7189i	0.699309	−	1.21124i
$215$	2.35686	−	1.97764i	0.160736	−	0.134874i
$216$	5.65060			0.384475
$217$	2.46913	−	2.07184i	0.167615	−	0.140646i
$218$	−10.0159	−	3.64550i	−0.678365	−	0.246904i
$219$	−1.71674	−	9.73610i	−0.116006	−	0.657904i
$220$	0.155916	−	0.884246i	0.0105119	−	0.0596159i
$221$	−9.01064			−0.606121
$222$	−3.33349	+	7.67505i	−0.223729	+	0.515116i
$223$	−29.2612			−1.95947			−0.979736	−	0.200292i	$-0.935811\pi$
$223$	−29.2612			−1.95947			−0.979736	+	0.200292i	$0.935811\pi$
$224$	−0.0829614	+	0.470498i	−0.00554309	+	0.0314364i
$225$	0.938471	+	5.32234i	0.0625648	+	0.354822i
$226$	−11.4757	−	4.17683i	−0.763355	−	0.277838i
$227$	7.89376	−	6.62365i	0.523927	−	0.439627i	−0.342071	−	0.939674i	$-0.611128\pi$
$227$	7.89376	−	6.62365i	0.523927	−	0.439627i	0.865998	+	0.500047i	$0.166684\pi$
$228$	−4.84535			−0.320891
$229$	12.0022	−	10.0711i	0.793128	−	0.665514i	−0.153389	−	0.988166i	$-0.549019\pi$
$229$	12.0022	−	10.0711i	0.793128	−	0.665514i	0.946518	+	0.322652i	$0.104574\pi$
$230$	−0.904658	+	1.56691i	−0.0596514	+	0.103319i
$231$	−1.59668	+	0.581145i	−0.105054	+	0.0382366i
$232$	−0.114111	−	0.197646i	−0.00749175	−	0.0129761i
$233$	−3.60202	+	6.23888i	−0.235976	+	0.408723i	−0.959556	−	0.281518i	$-0.909162\pi$
$233$	−3.60202	+	6.23888i	−0.235976	+	0.408723i	0.723580	+	0.690241i	$0.242495\pi$
$234$	0.862281	−	4.89024i	0.0563691	−	0.319685i
$235$	−2.43387	−	0.885855i	−0.158768	−	0.0577868i
$236$	−2.23888	−	3.87785i	−0.145739	−	0.252427i
$237$	−3.72602	−	3.12651i	−0.242031	−	0.203088i
$238$	−0.735567	−	0.617214i	−0.0476797	−	0.0400081i
$239$	20.6291	−	7.50838i	1.33439	−	0.485677i	0.426346	−	0.904560i	$-0.359801\pi$
$239$	20.6291	−	7.50838i	1.33439	−	0.485677i	0.908040	+	0.418884i	$0.137579\pi$
$240$	−0.0829614	−	0.470498i	−0.00535514	−	0.0303705i
$241$	2.57180	+	14.5854i	0.165664	+	0.939527i	0.948377	+	0.317145i	$0.102724\pi$
$241$	2.57180	+	14.5854i	0.165664	+	0.939527i	−0.782713	+	0.622383i	$0.786165\pi$
$242$	4.05562	−	1.47612i	0.260705	−	0.0948889i
$243$	−8.29600	−	6.96117i	−0.532189	−	0.446559i
$244$	−1.10196	−	0.924653i	−0.0705457	−	0.0591949i
$245$	1.17590	+	2.03672i	0.0751256	+	0.130121i
$246$	13.8528	+	5.04202i	0.883224	+	0.321467i
$247$	−2.74210	+	15.5512i	−0.174475	+	0.989499i
$248$	3.37329	−	5.84271i	0.214204	−	0.371013i
$249$	0.973018	+	1.68532i	0.0616625	+	0.106803i
$250$	3.22416	−	1.17350i	0.203913	−	0.0742184i
$251$	−6.64493	+	11.5094i	−0.419424	+	0.726464i	−0.995882	−	0.0906631i	$-0.971101\pi$
$251$	−6.64493	+	11.5094i	−0.419424	+	0.726464i	0.576457	+	0.817127i	$0.304435\pi$
$252$	0.405364	−	0.340141i	0.0255356	−	0.0214269i
$253$	13.4690			0.846790
$254$	−5.40029	+	4.53138i	−0.338844	+	0.284324i
$255$	0.902307	+	0.328413i	0.0565046	+	0.0205660i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	3.03928	−	17.2366i	0.189585	−	1.07519i	−0.730336	−	0.683088i	$-0.760636\pi$
$257$	3.03928	−	17.2366i	0.189585	−	1.07519i	0.919921	−	0.392104i	$-0.128253\pi$
$258$	−12.1867			−0.758709
$259$	0.826504	+	2.78607i	0.0513565	+	0.173118i
$260$	−1.55702			−0.0965621
$261$	−0.0438948	+	0.248940i	−0.00271702	+	0.0154090i
$262$	0.344697	+	1.95487i	0.0212954	+	0.120772i
$263$	13.2811	+	4.83392i	0.818947	+	0.298072i	0.717314	−	0.696750i	$-0.245371\pi$
$263$	13.2811	+	4.83392i	0.818947	+	0.298072i	0.101633	+	0.994822i	$0.467593\pi$
$264$	−2.72446	+	2.28610i	−0.167679	+	0.140700i
$265$	1.51964			0.0933510
$266$	−1.28908	+	1.08167i	−0.0790385	+	0.0663211i
$267$	2.63040	−	4.55599i	0.160978	−	0.278822i
$268$	9.88842	−	3.59909i	0.604031	−	0.219849i
$269$	13.4051	+	23.2183i	0.817324	+	1.41565i	0.907647	+	0.419734i	$0.137876\pi$
$269$	13.4051	+	23.2183i	0.817324	+	1.41565i	−0.0903238	+	0.995912i	$0.528790\pi$
$270$	−0.981216	+	1.69952i	−0.0597149	+	0.103429i
$271$	−1.89500	+	10.7471i	−0.115113	+	0.652838i	0.871581	+	0.490251i	$0.163095\pi$
$271$	−1.89500	+	10.7471i	−0.115113	+	0.652838i	−0.986694	+	0.162587i	$0.948016\pi$
$272$	−1.88864	−	0.687407i	−0.114515	−	0.0416802i
$273$	1.47324	+	2.55173i	0.0891647	+	0.154438i
$274$	13.3276	+	11.1832i	0.805150	+	0.675601i
$275$	−9.66364	−	8.10875i	−0.582739	−	0.488976i
$276$	6.73451	−	2.45116i	0.405370	−	0.147543i
$277$	1.06680	+	6.05012i	0.0640978	+	0.363517i	0.999938	+	0.0110932i	$0.00353116\pi$
$277$	1.06680	+	6.05012i	0.0640978	+	0.363517i	−0.935841	+	0.352423i	$0.885358\pi$
$278$	0.127988	+	0.725854i	0.00767619	+	0.0435338i
$279$	−7.02191	+	2.55577i	−0.420391	+	0.153010i
$280$	−0.127104	−	0.106653i	−0.00759593	−	0.00637374i
$281$	2.26215	+	1.89817i	0.134948	+	0.113235i	0.707763	−	0.706449i	$-0.249704\pi$
$281$	2.26215	+	1.89817i	0.134948	+	0.113235i	−0.572815	+	0.819685i	$0.694149\pi$
$282$	5.12963	+	8.88478i	0.305465	+	0.529081i
$283$	−13.6016	−	4.95056i	−0.808529	−	0.294280i	−0.0955129	−	0.995428i	$-0.530449\pi$
$283$	−13.6016	−	4.95056i	−0.808529	−	0.294280i	−0.713016	+	0.701148i	$0.752671\pi$
$284$	1.54193	−	8.74474i	0.0914969	−	0.518905i
$285$	0.841386	−	1.45732i	0.0498394	−	0.0863244i
$286$	5.79541	+	10.0380i	0.342690	+	0.593556i
$287$	4.81104	−	1.75108i	0.283987	−	0.103363i
$288$	0.553803	−	0.959216i	0.0326332	−	0.0565223i
$289$	−9.92834	+	8.33086i	−0.584020	+	0.490051i
$290$	0.0792606			0.00465434
$291$	−19.4780	+	16.3440i	−1.14182	+	0.958100i
$292$	−6.75326	−	2.45799i	−0.395205	−	0.143843i
$293$	−2.18486	−	12.3910i	−0.127641	−	0.723888i	−0.979704	−	0.200449i	$-0.935760\pi$
$293$	−2.18486	−	12.3910i	−0.127641	−	0.723888i	0.852063	−	0.523439i	$-0.175351\pi$
$294$	1.61762	−	9.17398i	0.0943416	−	0.535038i
$295$	1.55511			0.0905419
$296$	3.62016	+	4.88820i	0.210417	+	0.284121i
$297$	14.6089			0.847691
$298$	−3.30533	+	18.7455i	−0.191473	+	1.08589i
$299$	−4.05581	−	23.0016i	−0.234554	−	1.33022i
$300$	−6.30749	−	2.29574i	−0.364163	−	0.132545i
$301$	−3.24220	+	2.72053i	−0.186877	+	0.156808i
$302$	−6.47198			−0.372420
$303$	−18.0502	+	15.1459i	−1.03696	+	0.870110i
$304$	−1.76112	+	3.05035i	−0.101007	+	0.174950i
$305$	0.469459	−	0.170869i	0.0268811	−	0.00978393i
$306$	1.11306	+	1.92787i	0.0636293	+	0.110209i
$307$	9.44985	−	16.3676i	0.539331	−	0.934149i	−0.459609	−	0.888121i	$-0.652010\pi$
$307$	9.44985	−	16.3676i	0.539331	−	0.934149i	0.998940	−	0.0460279i	$-0.0146563\pi$
$308$	−0.214485	+	1.21641i	−0.0122214	+	0.0693112i
$309$	−17.3481	−	6.31419i	−0.986898	−	0.359201i
$310$	1.17153	+	2.02915i	0.0665385	+	0.115248i
$311$	−0.0868584	−	0.0728829i	−0.00492529	−	0.00413281i	0.640322	−	0.768107i	$-0.278801\pi$
$311$	−0.0868584	−	0.0728829i	−0.00492529	−	0.00413281i	−0.645247	+	0.763974i	$0.723246\pi$
$312$	4.72446	+	3.96430i	0.267470	+	0.224434i
$313$	−8.62740	+	3.14012i	−0.487650	+	0.177490i	−0.574131	−	0.818764i	$-0.694660\pi$
$313$	−8.62740	+	3.14012i	−0.487650	+	0.177490i	0.0864813	+	0.996253i	$0.472438\pi$
$314$	2.09975	+	11.9083i	0.118496	+	0.672024i
$315$	0.0319126	+	0.180985i	0.00179807	+	0.0101974i
$316$	−3.32255	+	1.20931i	−0.186908	+	0.0680290i
$317$	20.1198	+	16.8826i	1.13004	+	0.948219i	0.999068	−	0.0431670i	$-0.0137447\pi$
$317$	20.1198	+	16.8826i	1.13004	+	0.948219i	0.130975	+	0.991386i	$0.458189\pi$
$318$	−4.61107	−	3.86915i	−0.258576	−	0.216971i
$319$	−0.295018	−	0.510986i	−0.0165178	−	0.0286097i
$320$	−0.326352	−	0.118782i	−0.0182436	−	0.00664014i
$321$	4.88744	−	27.7181i	0.272791	−	1.54707i
$322$	1.24449	−	2.15551i	0.0693525	−	0.120122i
$323$	−3.53958	−	6.13074i	−0.196948	−	0.341123i
$324$	4.18199	−	1.52212i	0.232333	−	0.0845623i
$325$	−10.9378	+	18.9447i	−0.606717	+	1.05087i
$326$	11.2965	−	9.47892i	0.625657	−	0.524989i
$327$	−14.6626			−0.810844
$328$	8.20921	−	6.88834i	0.453278	−	0.380345i
$329$	3.34813	+	1.21862i	0.184588	+	0.0671847i
$330$	−0.214485	−	1.21641i	−0.0118070	−	0.0669610i
$331$	−4.96254	+	28.1439i	−0.272766	+	1.54693i	0.473205	+	0.880952i	$0.343097\pi$
$331$	−4.96254	+	28.1439i	−0.272766	+	1.54693i	−0.745971	+	0.665979i	$0.768014\pi$
$332$	1.41464			0.0776383
$333$	0.408565	−	6.72491i	0.0223892	−	0.368523i
$334$	8.30639			0.454506
$335$	−0.634617	+	3.59909i	−0.0346728	+	0.196639i
$336$	0.114125	+	0.647237i	0.00622604	+	0.0353096i
$337$	9.18348	+	3.34251i	0.500256	+	0.182078i	0.579809	−	0.814752i	$-0.303127\pi$
$337$	9.18348	+	3.34251i	0.500256	+	0.182078i	−0.0795532	+	0.996831i	$0.525349\pi$
$338$	5.43855	−	4.56349i	0.295818	−	0.248221i
$339$	−16.7997			−0.912432
$340$	0.534708	−	0.448673i	0.0289986	−	0.0243327i
$341$	8.72118	−	15.1055i	0.472278	−	0.818010i
$342$	3.66599	−	1.33431i	0.198234	−	0.0721512i
$343$	−3.28977	−	5.69804i	−0.177631	−	0.307665i
$344$	−4.42945	+	7.67203i	−0.238820	+	0.413648i
$345$	−0.432206	+	2.45116i	−0.0232692	+	0.131966i
$346$	6.21394	+	2.26169i	0.334063	+	0.121589i
$347$	−8.28817	−	14.3555i	−0.444932	−	0.770645i	0.553115	−	0.833105i	$-0.313439\pi$
$347$	−8.28817	−	14.3555i	−0.444932	−	0.770645i	−0.998047	+	0.0624595i	$0.980106\pi$
$348$	−0.240501	−	0.201804i	−0.0128922	−	0.0108178i
$349$	14.3165	+	12.0129i	0.766342	+	0.643038i	0.939769	−	0.341809i	$-0.111040\pi$
$349$	14.3165	+	12.0129i	0.766342	+	0.643038i	−0.173427	+	0.984847i	$0.555484\pi$
$350$	−2.19057	+	0.797302i	−0.117091	+	0.0426176i
$351$	−4.39904	−	24.9482i	−0.234803	−	1.33164i
$352$	0.448944	+	2.54609i	0.0239288	+	0.135707i
$353$	−5.07813	+	1.84829i	−0.270282	+	0.0983745i	−0.473606	−	0.880737i	$-0.657048\pi$
$353$	−5.07813	+	1.84829i	−0.270282	+	0.0983745i	0.203324	+	0.979112i	$0.434826\pi$
$354$	−4.71867	−	3.95944i	−0.250795	−	0.210442i
$355$	2.36238	+	1.98227i	0.125382	+	0.105208i
$356$	−1.91212	−	3.31190i	−0.101342	−	0.175530i
$357$	−1.24125	−	0.451779i	−0.0656940	−	0.0239107i
$358$	0.788337	−	4.47088i	0.0416649	−	0.236294i
$359$	5.28319	−	9.15075i	0.278836	−	0.482958i	−0.692260	−	0.721649i	$-0.743385\pi$
$359$	5.28319	−	9.15075i	0.278836	−	0.482958i	0.971096	+	0.238690i	$0.0767180\pi$
$360$	0.192334	+	0.333132i	0.0101369	+	0.0175576i
$361$	6.19614	−	2.25521i	0.326113	−	0.118695i
$362$	0.781863	−	1.35423i	0.0410938	−	0.0711766i
$363$	4.54811	−	3.81632i	0.238714	−	0.200305i
$364$	2.14190			0.112266
$365$	1.91197	−	1.60434i	0.100077	−	0.0839748i
$366$	−1.85953	−	0.676813i	−0.0971991	−	0.0353776i
$367$	−0.0374864	−	0.212596i	−0.00195677	−	0.0110974i	0.983814	−	0.179194i	$-0.0573490\pi$
$367$	−0.0374864	−	0.212596i	−0.00195677	−	0.0110974i	−0.985771	+	0.168097i	$0.946238\pi$
$368$	0.904658	−	5.13057i	0.0471586	−	0.267450i
$369$	−11.8695			−0.617902
$370$	−2.09884	+	0.239999i	−0.109114	+	0.0124769i
$371$	−2.09049			−0.108533
$372$	1.61161	−	9.13989i	0.0835580	−	0.473881i
$373$	−3.43905	−	19.5038i	−0.178067	−	1.00987i	−0.934543	−	0.355849i	$-0.884192\pi$
$373$	−3.43905	−	19.5038i	−0.178067	−	1.00987i	0.756476	−	0.654021i	$-0.226919\pi$
$374$	−4.88281	−	1.77720i	−0.252484	−	0.0918967i
$375$	3.61568	−	3.03391i	0.186713	−	0.156671i
$376$	7.45780			0.384607
$377$	−0.783798	+	0.657684i	−0.0403676	+	0.0338725i
$378$	1.34980	−	2.33793i	0.0694264	−	0.120250i
$379$	21.7031	−	7.89927i	1.11481	−	0.405758i	0.282056	−	0.959398i	$-0.408984\pi$
$379$	21.7031	−	7.89927i	1.11481	−	0.405758i	0.832756	+	0.553640i	$0.186761\pi$
$380$	−0.611631	−	1.05938i	−0.0313760	−	0.0543449i
$381$	−4.84885	+	8.39845i	−0.248414	+	0.430266i
$382$	3.99708	−	22.6686i	0.204509	−	1.15983i
$383$	4.77929	+	1.73952i	0.244210	+	0.0888853i	0.461226	−	0.887283i	$-0.347410\pi$
$383$	4.77929	+	1.73952i	0.244210	+	0.0888853i	−0.217015	+	0.976168i	$0.569632\pi$
$384$	0.687821	+	1.19134i	0.0351002	+	0.0607954i
$385$	−0.328611	−	0.275737i	−0.0167475	−	0.0140529i
$386$	−8.08492	−	6.78405i	−0.411511	−	0.345299i
$387$	9.22042	−	3.35596i	0.468701	−	0.170593i
$388$	3.20963	+	18.2027i	0.162944	+	0.924102i
$389$	−5.06138	−	28.7045i	−0.256622	−	1.45538i	−0.791874	−	0.610684i	$-0.790895\pi$
$389$	−5.06138	−	28.7045i	−0.256622	−	1.45538i	0.535252	−	0.844692i	$-0.320217\pi$
$390$	−2.01273	+	0.732572i	−0.101918	+	0.0370952i
$391$	8.02104	+	6.73045i	0.405642	+	0.340374i
$392$	−5.18746	−	4.35280i	−0.262006	−	0.219849i
$393$	1.36535	+	2.36485i	0.0688726	+	0.119291i
$394$	−4.53746	−	1.65150i	−0.228594	−	0.0832014i
$395$	0.213234	−	1.20931i	0.0107290	−	0.0608470i
$396$	1.43178	−	2.47992i	0.0719498	−	0.124621i
$397$	7.99625	+	13.8499i	0.401320	+	0.695107i	0.993886	−	0.110416i	$-0.0352182\pi$
$397$	7.99625	+	13.8499i	0.401320	+	0.695107i	−0.592565	+	0.805522i	$0.701885\pi$
$398$	−9.67147	+	3.52013i	−0.484787	+	0.176448i
$399$	−1.15745	+	2.00476i	−0.0579448	+	0.100363i
$400$	−3.73783	+	3.13641i	−0.186891	+	0.156820i
$401$	−5.43983			−0.271652			−0.135826	−	0.990733i	$-0.543369\pi$
$401$	−5.43983			−0.271652			−0.135826	+	0.990733i	$0.543369\pi$
$402$	11.0892	−	9.30495i	0.553080	−	0.464089i
$403$	−28.4225	−	10.3450i	−1.41583	−	0.515319i
$404$	2.97435	+	16.8684i	0.147980	+	0.839234i
$405$	−0.268391	+	1.52212i	−0.0133365	+	0.0756348i
$406$	−0.109034			−0.00541128
$407$	9.35942	+	12.6378i	0.463929	+	0.626431i
$408$	−2.76483			−0.136879
$409$	−6.55076	+	37.1512i	−0.323914	+	1.83701i	0.193283	+	0.981143i	$0.438086\pi$
$409$	−6.55076	+	37.1512i	−0.323914	+	1.83701i	−0.517198	+	0.855866i	$0.673025\pi$
$410$	0.646275	+	3.66521i	0.0319173	+	0.181012i
$411$	22.4900	+	8.18569i	1.10935	+	0.403770i
$412$	−10.2805	+	8.62636i	−0.506484	+	0.424990i
$413$	−2.13927			−0.105267
$414$	−4.42032	+	3.70909i	−0.217247	+	0.182292i
$415$	−0.245649	+	0.425477i	−0.0120584	+	0.0208858i
$416$	4.21288	−	1.53336i	0.206553	−	0.0751792i
$417$	0.506960	+	0.878080i	0.0248259	+	0.0429998i
$418$	−4.55314	+	7.88627i	−0.222701	+	0.385730i
$419$	1.07518	−	6.09766i	0.0525261	−	0.297890i	−0.947216	−	0.320596i	$-0.896117\pi$
$419$	1.07518	−	6.09766i	0.0525261	−	0.297890i	0.999742	+	0.0227055i	$0.00722800\pi$
$420$	−0.214485	−	0.0780663i	−0.0104658	−	0.00380924i
$421$	5.05431	+	8.75433i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$421$	5.05431	+	8.75433i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$422$	1.05020	+	0.881223i	0.0511230	+	0.0428973i
$423$	−6.32776	−	5.30962i	−0.307666	−	0.258163i
$424$	−4.11176	+	1.49656i	−0.199685	+	0.0726793i
$425$	−1.70293	−	9.65782i	−0.0826044	−	0.468473i
$426$	−2.12115	−	12.0296i	−0.102770	−	0.582838i
$427$	−0.645808	+	0.235055i	−0.0312528	+	0.0113751i
$428$	−15.6733	−	13.1514i	−0.757597	−	0.635699i
$429$	12.2145	+	10.2491i	0.589719	+	0.494833i
$430$	−1.53833	−	2.66447i	−0.0741849	−	0.128492i
$431$	32.1170	+	11.6896i	1.54702	+	0.563070i	0.967716	−	0.252042i	$-0.0811020\pi$
$431$	32.1170	+	11.6896i	1.54702	+	0.563070i	0.579304	+	0.815111i	$0.303324\pi$
$432$	0.981216	−	5.56475i	0.0472088	−	0.267734i
$433$	0.343160	−	0.594370i	0.0164912	−	0.0285636i	−0.857662	−	0.514214i	$-0.828084\pi$
$433$	0.343160	−	0.594370i	0.0164912	−	0.0285636i	0.874153	+	0.485650i	$0.161417\pi$
$434$	−1.61161	−	2.79139i	−0.0773597	−	0.133991i
$435$	0.102459	−	0.0372919i	0.00491252	−	0.00178801i
$436$	−5.32937	+	9.23073i	−0.255230	+	0.442072i
$437$	14.0568	−	11.7951i	0.672430	−	0.564236i
$438$	−9.88629			−0.472385
$439$	16.4768	−	13.8257i	0.786393	−	0.659862i	−0.158456	−	0.987366i	$-0.550652\pi$
$439$	16.4768	−	13.8257i	0.786393	−	0.659862i	0.944850	+	0.327503i	$0.106207\pi$
$440$	−0.843738	−	0.307095i	−0.0402236	−	0.0146402i
$441$	1.30244	+	7.38649i	0.0620208	+	0.351738i
$442$	−1.56468	+	8.87374i	−0.0744243	+	0.422081i
$443$	−28.5971			−1.35869			−0.679344	−	0.733820i	$-0.737736\pi$
$443$	−28.5971			−1.35869			−0.679344	+	0.733820i	$0.737736\pi$
$444$	6.97959	+	4.61561i	0.331237	+	0.219047i
$445$	1.32815			0.0629602
$446$	−5.08115	+	28.8166i	−0.240599	+	1.36451i
$447$	4.54695	+	25.7870i	0.215063	+	1.21969i
$448$	0.448944	+	0.163402i	0.0212106	+	0.00772002i
$449$	−26.4813	+	22.2204i	−1.24973	+	1.04865i	−0.253031	+	0.967458i	$0.581427\pi$
$449$	−26.4813	+	22.2204i	−1.24973	+	1.04865i	−0.996699	+	0.0811896i	$0.974128\pi$
$450$	5.40444			0.254768
$451$	21.2238	−	17.8089i	0.999388	−	0.838587i
$452$	−6.10611	+	10.5761i	−0.287207	+	0.497458i
$453$	−8.36620	+	3.04505i	−0.393079	+	0.143069i
$454$	−5.15229	−	8.92402i	−0.241809	−	0.418825i
$455$	−0.371937	+	0.644213i	−0.0174367	+	0.0302012i
$456$	−0.841386	+	4.77174i	−0.0394015	+	0.223457i
$457$	−30.9238	−	11.2553i	−1.44655	−	0.526503i	−0.504928	−	0.863162i	$-0.668481\pi$
$457$	−30.9238	−	11.2553i	−1.44655	−	0.526503i	−0.941627	+	0.336659i	$0.890703\pi$
$458$	−7.83389	−	13.5687i	−0.366053	−	0.634023i
$459$	8.69983	+	7.30003i	0.406074	+	0.340736i
$460$	1.38602	+	1.16301i	0.0646234	+	0.0542255i
$461$	17.0455	−	6.20405i	0.793888	−	0.288952i	0.0869368	−	0.996214i	$-0.472292\pi$
$461$	17.0455	−	6.20405i	0.793888	−	0.288952i	0.706951	+	0.707262i	$0.250070\pi$
$462$	0.295055	+	1.67334i	0.0137272	+	0.0778509i
$463$	0.0589368	+	0.334247i	0.00273903	+	0.0155338i	0.986147	−	0.165876i	$-0.0530451\pi$
$463$	0.0589368	+	0.334247i	0.00273903	+	0.0155338i	−0.983408	+	0.181410i	$0.941934\pi$
$464$	−0.214458	+	0.0780564i	−0.00995598	+	0.00362368i
$465$	2.46913	+	2.07184i	0.114503	+	0.0960795i
$466$	5.51861	+	4.63067i	0.255645	+	0.214512i
$467$	7.10101	+	12.2993i	0.328596	+	0.569144i	0.982233	−	0.187663i	$-0.0600913\pi$
$467$	7.10101	+	12.2993i	0.328596	+	0.569144i	−0.653638	+	0.756808i	$0.726758\pi$
$468$	−4.66621	−	1.69836i	−0.215696	−	0.0785068i
$469$	0.873006	−	4.95106i	0.0403117	−	0.228619i
$470$	−1.29503	+	2.24306i	−0.0597354	+	0.103465i
$471$	8.31714	+	14.4057i	0.383233	+	0.663780i
$472$	−4.20771	+	1.53148i	−0.193676	+	0.0704922i
$473$	−11.4517	+	19.8350i	−0.526551	+	0.912013i
$474$	−3.72602	+	3.12651i	−0.171142	+	0.143605i
$475$	−17.1864			−0.788566
$476$	−0.735567	+	0.617214i	−0.0337147	+	0.0282900i
$477$	4.55421	+	1.65760i	0.208523	+	0.0758962i
$478$	−3.81210	−	21.6195i	−0.174362	−	0.988853i
$479$	−5.90065	+	33.4642i	−0.269608	+	1.52902i	0.485979	+	0.873971i	$0.338463\pi$
$479$	−5.90065	+	33.4642i	−0.269608	+	1.52902i	−0.755586	+	0.655049i	$0.772648\pi$
$480$	−0.477756			−0.0218065
$481$	18.7637	−	19.7890i	0.855553	−	0.902301i
$482$	14.8104			0.674595
$483$	0.594561	−	3.37192i	0.0270534	−	0.153428i
$484$	−0.749448	−	4.25033i	−0.0340658	−	0.193197i
$485$	−6.03213	−	2.19551i	−0.273905	−	0.0996932i
$486$	−8.29600	+	6.96117i	−0.376314	+	0.315765i
$487$	−25.3330			−1.14795			−0.573974	−	0.818874i	$-0.694599\pi$
$487$	−25.3330			−1.14795			−0.573974	+	0.818874i	$0.694599\pi$
$488$	−1.10196	+	0.924653i	−0.0498833	+	0.0418571i
$489$	10.1430	−	17.5682i	0.458683	−	0.794462i
$490$	2.20997	−	0.804364i	0.0998364	−	0.0363375i
$491$	−10.6344	−	18.4193i	−0.479922	−	0.831249i	0.519813	−	0.854280i	$-0.326002\pi$
$491$	−10.6344	−	18.4193i	−0.479922	−	0.831249i	−0.999735	+	0.0230308i	$0.992668\pi$
$492$	7.37094	−	12.7668i	0.332308	−	0.575574i
$493$	0.0796507	−	0.451722i	0.00358729	−	0.0203445i
$494$	14.8388	+	5.40087i	0.667628	+	0.242997i
$495$	0.497253	+	0.861267i	0.0223499	+	0.0387111i
$496$	−5.16818	−	4.33662i	−0.232058	−	0.194720i
$497$	−3.24979	−	2.72690i	−0.145773	−	0.122318i
$498$	1.82868	−	0.665583i	0.0819449	−	0.0298255i
$499$	2.85314	+	16.1810i	0.127724	+	0.724359i	0.979653	+	0.200701i	$0.0643220\pi$
$499$	2.85314	+	16.1810i	0.127724	+	0.724359i	−0.851928	+	0.523658i	$0.824567\pi$
$500$	−0.595800	−	3.37895i	−0.0266450	−	0.151111i
$501$	10.7375	−	3.90814i	0.479717	−	0.174603i
$502$	10.1806	+	8.54256i	0.454383	+	0.381273i
$503$	15.9979	+	13.4238i	0.713311	+	0.598539i	0.925526	−	0.378684i	$-0.123623\pi$
$503$	15.9979	+	13.4238i	0.713311	+	0.598539i	−0.212215	+	0.977223i	$0.568068\pi$
$504$	−0.264583	−	0.458271i	−0.0117855	−	0.0204130i
$505$	−5.58995	−	2.03458i	−0.248750	−	0.0905375i
$506$	2.33887	−	13.2644i	0.103975	−	0.589674i
$507$	4.88321	−	8.45796i	0.216871	−	0.375631i
$508$	3.52479	+	6.10511i	0.156387	+	0.270871i
$509$	−37.6746	+	13.7124i	−1.66990	+	0.607793i	−0.991871	−	0.127245i	$-0.959386\pi$
$509$	−37.6746	+	13.7124i	−1.66990	+	0.607793i	−0.678026	+	0.735038i	$0.737164\pi$
$510$	0.480107	−	0.831570i	0.0212595	−	0.0368226i
$511$	−2.63019	+	2.20699i	−0.116353	+	0.0976317i
$512$	1.00000			0.0441942
$513$	15.2464	−	12.7933i	0.673146	−	0.564837i
$514$	−16.4470	−	5.98622i	−0.725447	−	0.264041i
$515$	−0.809339	−	4.58999i	−0.0356637	−	0.202259i
$516$	−2.11619	+	12.0015i	−0.0931602	+	0.528338i
$517$	19.2811			0.847982
$518$	2.88726	−	0.330153i	0.126859	−	0.0145061i
$519$	9.09676			0.399303
$520$	−0.270373	+	1.53336i	−0.0118566	+	0.0672424i
$521$	1.59181	+	9.02760i	0.0697384	+	0.395506i	0.999618	+	0.0276419i	$0.00879982\pi$
$521$	1.59181	+	9.02760i	0.0697384	+	0.395506i	−0.929879	+	0.367864i	$0.880089\pi$
$522$	0.237536	+	0.0864559i	0.0103966	+	0.00378407i
$523$	22.7091	−	19.0552i	0.993000	−	0.833226i	0.00700102	−	0.999975i	$-0.497771\pi$
$523$	22.7091	−	19.0552i	0.993000	−	0.833226i	0.985999	+	0.166749i	$0.0533270\pi$
$524$	1.98503			0.0867164
$525$	−2.45658	+	2.06131i	−0.107214	+	0.0899631i
$526$	7.06672	−	12.2399i	0.308124	−	0.533686i
$527$	12.7418	−	4.63765i	0.555043	−	0.202019i
$528$	1.77827	+	3.08005i	0.0773892	+	0.134042i
$529$	−2.07059	+	3.58637i	−0.0900257	+	0.155929i
$530$	0.263884	−	1.49656i	0.0114624	−	0.0650063i
$531$	4.66049	+	1.69628i	0.202248	+	0.0736123i
$532$	0.841386	+	1.45732i	0.0364787	+	0.0631830i
$533$	−36.8039	−	30.8822i	−1.59415	−	1.33765i
$534$	−4.03001	−	3.38158i	−0.174395	−	0.146335i
$535$	6.67716	−	2.43029i	0.288679	−	0.105071i
$536$	−1.82731	−	10.3632i	−0.0789276	−	0.447621i
$537$	−1.08447	−	6.15034i	−0.0467984	−	0.265407i
$538$	25.1934	−	9.16963i	1.08616	−	0.395331i
$539$	−13.4115	−	11.2536i	−0.577673	−	0.484725i
$540$	1.50331	+	1.26143i	0.0646922	+	0.0542832i
$541$	−14.4930	−	25.1027i	−0.623104	−	1.07925i	−0.988904	−	0.148554i	$-0.952538\pi$
$541$	−14.4930	−	25.1027i	−0.623104	−	1.07925i	0.365800	−	0.930693i	$-0.380795\pi$
$542$	10.2547	+	3.73242i	0.440478	+	0.160321i
$543$	0.373540	−	2.11845i	0.0160301	−	0.0909113i
$544$	−1.00492	+	1.74058i	−0.0430857	+	0.0746266i
$545$	−1.85087	−	3.20580i	−0.0792825	−	0.137321i
$546$	2.76879	−	1.00776i	0.118493	−	0.0431281i
$547$	−2.68304	+	4.64717i	−0.114719	+	0.198699i	−0.917667	−	0.397350i	$-0.869930\pi$
$547$	−2.68304	+	4.64717i	−0.114719	+	0.198699i	0.802949	+	0.596048i	$0.203263\pi$
$548$	13.3276	−	11.1832i	0.569327	−	0.477722i
$549$	1.59330			0.0680003
$550$	−9.66364	+	8.10875i	−0.412059	+	0.345758i
$551$	−0.755374	−	0.274934i	−0.0321800	−	0.0117126i
$552$	−1.24449	−	7.05784i	−0.0529689	−	0.300401i
$553$	−0.293334	+	1.66358i	−0.0124738	+	0.0707426i
$554$	6.14345			0.261010
$555$	−2.60022	+	1.29774i	−0.110373	+	0.0550861i
$556$	0.737051			0.0312579
$557$	−2.03774	+	11.5566i	−0.0863416	+	0.489668i	0.910717	+	0.413030i	$0.135530\pi$
$557$	−2.03774	+	11.5566i	−0.0863416	+	0.489668i	−0.997059	+	0.0766376i	$0.975582\pi$
$558$	1.29760	+	7.35904i	0.0549316	+	0.311533i
$559$	37.3214	+	13.5839i	1.57853	+	0.574537i
$560$	−0.127104	+	0.106653i	−0.00537114	+	0.00450692i
$561$	−7.14808			−0.301792
$562$	2.26215	−	1.89817i	0.0954229	−	0.0800693i
$563$	−9.45929	+	16.3840i	−0.398662	+	0.690502i	−0.993561	−	0.113298i	$-0.963859\pi$
$563$	−9.45929	+	16.3840i	−0.398662	+	0.690502i	0.594899	+	0.803800i	$0.297192\pi$
$564$	9.64056	−	3.50888i	0.405941	−	0.147750i
$565$	−2.12063	−	3.67304i	−0.0892156	−	0.154526i
$566$	−7.23724	+	12.5353i	−0.304204	+	0.526897i
$567$	0.369210	−	2.09390i	0.0155054	−	0.0879353i
$568$	−8.34413	−	3.03702i	−0.350112	−	0.127430i
$569$	10.8074	+	18.7189i	0.453068	+	0.784737i	0.998575	−	0.0533694i	$-0.0169961\pi$
$569$	10.8074	+	18.7189i	0.453068	+	0.784737i	−0.545507	+	0.838107i	$0.683663\pi$
$570$	−1.28908	−	1.08167i	−0.0539936	−	0.0453060i
$571$	−26.8881	−	22.5618i	−1.12523	−	0.944181i	−0.126374	−	0.991983i	$-0.540334\pi$
$571$	−26.8881	−	22.5618i	−1.12523	−	0.944181i	−0.998857	+	0.0478018i	$0.984778\pi$
$572$	10.8918	−	3.96430i	0.455410	−	0.165756i
$573$	−5.49856	−	31.1839i	−0.229706	−	1.30273i
$574$	−0.889044	−	5.04202i	−0.0371080	−	0.210450i
$575$	23.8872	−	8.69423i	0.996165	−	0.362574i
$576$	−0.848476	−	0.711956i	−0.0353532	−	0.0296648i
$577$	−33.0040	−	27.6937i	−1.37398	−	1.15290i	−0.971382	−	0.237523i	$-0.923664\pi$
$577$	−33.0040	−	27.6937i	−1.37398	−	1.15290i	−0.402593	−	0.915379i	$-0.631891\pi$
$578$	6.48026	+	11.2241i	0.269543	+	0.466863i
$579$	−13.6431	−	4.96568i	−0.566988	−	0.206367i
$580$	0.0137635	−	0.0780564i	0.000571496	−	0.00324112i
$581$	0.337926	−	0.585304i	0.0140195	−	0.0242825i
$582$	12.7134	+	22.0202i	0.526985	+	0.912765i
$583$	−10.6304	+	3.86915i	−0.440266	+	0.160244i
$584$	−3.59334	+	6.22384i	−0.148693	+	0.257544i
$585$	1.32109	−	1.10853i	0.0546204	−	0.0458320i
$586$	−12.5821			−0.519762
$587$	−15.6463	+	13.1288i	−0.645790	+	0.541882i	−0.905790	−	0.423726i	$-0.860722\pi$
$587$	−15.6463	+	13.1288i	−0.645790	+	0.541882i	0.260000	+	0.965609i	$0.416277\pi$
$588$	−8.75371	−	3.18609i	−0.360997	−	0.131392i
$589$	−4.12642	−	23.4021i	−0.170026	−	0.964267i
$590$	0.270042	−	1.53148i	0.0111174	−	0.0630501i
$591$	−6.64252			−0.273237
$592$	5.44257	−	2.71633i	0.223688	−	0.111641i
$593$	−0.908005			−0.0372873			−0.0186436	−	0.999826i	$-0.505935\pi$
$593$	−0.908005			−0.0372873			−0.0186436	+	0.999826i	$0.505935\pi$
$594$	2.53680	−	14.3869i	0.104086	−	0.590302i
$595$	−0.0579080	−	0.328413i	−0.00237400	−	0.0134636i
$596$	17.8867	+	6.51023i	0.732668	+	0.266669i
$597$	−10.8459	+	9.10080i	−0.443894	+	0.372471i
$598$	−23.3565			−0.955117
$599$	−9.44037	+	7.92141i	−0.385723	+	0.323660i	−0.814944	−	0.579539i	$-0.803233\pi$
$599$	−9.44037	+	7.92141i	−0.385723	+	0.323660i	0.429221	+	0.903199i	$0.358788\pi$
$600$	−3.35615	+	5.81301i	−0.137014	+	0.237315i
$601$	32.2492	−	11.7377i	1.31547	−	0.478792i	0.413467	−	0.910519i	$-0.364318\pi$
$601$	32.2492	−	11.7377i	1.31547	−	0.478792i	0.902004	+	0.431727i	$0.142095\pi$
$602$	2.11619	+	3.66535i	0.0862496	+	0.149389i
$603$	−5.82769	+	10.0939i	−0.237322	+	0.411054i
$604$	−1.12385	+	6.37365i	−0.0457287	+	0.259340i
$605$	1.40850	+	0.512653i	0.0572637	+	0.0208423i
$606$	11.7814	+	20.4060i	0.478588	+	0.828938i
$607$	−3.12973	−	2.62616i	−0.127032	−	0.106593i	0.577058	−	0.816703i	$-0.304201\pi$
$607$	−3.12973	−	2.62616i	−0.127032	−	0.106593i	−0.704090	+	0.710110i	$0.748645\pi$
$608$	2.69820	+	2.26405i	0.109426	+	0.0918196i
$609$	−0.140947	+	0.0513003i	−0.00571144	+	0.00207879i
$610$	−0.0867525	−	0.491998i	−0.00351251	−	0.0199204i
$611$	−5.80596	−	32.9272i	−0.234884	−	1.33209i
$612$	2.09187	−	0.761377i	0.0845587	−	0.0307768i
$613$	15.2276	+	12.7775i	0.615036	+	0.516077i	0.896239	−	0.443572i	$-0.146289\pi$
$613$	15.2276	+	12.7775i	0.615036	+	0.516077i	−0.281202	+	0.959648i	$0.590733\pi$
$614$	−14.4780	−	12.1485i	−0.584285	−	0.490273i
$615$	2.55990	+	4.43388i	0.103225	+	0.178791i
$616$	1.16068	+	0.422454i	0.0467652	+	0.0170211i
$617$	0.664267	−	3.76724i	0.0267424	−	0.151664i	−0.968513	−	0.248964i	$-0.919910\pi$
$617$	0.664267	−	3.76724i	0.0267424	−	0.151664i	0.995255	+	0.0973009i	$0.0310209\pi$
$618$	−9.23072	+	15.9881i	−0.371314	+	0.643135i
$619$	5.97516	+	10.3493i	0.240162	+	0.415973i	0.960760	−	0.277380i	$-0.0894661\pi$
$619$	5.97516	+	10.3493i	0.240162	+	0.415973i	−0.720598	+	0.693353i	$0.756133\pi$
$620$	2.20176	−	0.801375i	0.0884248	−	0.0321840i
$621$	−14.7190	+	25.4941i	−0.590654	+	1.02304i
$622$	−0.0868584	+	0.0728829i	−0.00348271	+	0.00292234i
$623$	−1.82706			−0.0731995
$624$	4.72446	−	3.96430i	0.189130	−	0.158699i
$625$	−21.8059	−	7.93669i	−0.872235	−	0.317468i
$626$	1.59428	+	9.04161i	0.0637202	+	0.361375i
$627$	−2.17529	+	12.3367i	−0.0868727	+	0.492679i
$628$	12.0920			0.482523
$629$	−0.741374	+	12.2029i	−0.0295605	+	0.486562i
$630$	0.183777			0.00732186
$631$	−3.49888	+	19.8431i	−0.139288	+	0.789942i	0.832489	+	0.554041i	$0.186915\pi$
$631$	−3.49888	+	19.8431i	−0.139288	+	0.789942i	−0.971777	+	0.235901i	$0.924196\pi$
$632$	0.613983	+	3.48207i	0.0244229	+	0.138509i
$633$	1.77219	+	0.645024i	0.0704381	+	0.0256374i
$634$	20.1198	−	16.8826i	0.799061	−	0.670492i
$635$	−2.44829			−0.0971575
$636$	−4.61107	+	3.86915i	−0.182841	+	0.153422i
$637$	−15.1797	+	26.2920i	−0.601442	+	1.04173i
$638$	−0.554452	+	0.201804i	−0.0219510	+	0.00798950i
$639$	4.91758	+	8.51749i	0.194536	+	0.336947i
$640$	−0.173648	+	0.300767i	−0.00686405	+	0.0118889i
$641$	5.23531	−	29.6909i	0.206782	−	1.17272i	−0.687828	−	0.725874i	$-0.741435\pi$
$641$	5.23531	−	29.6909i	0.206782	−	1.17272i	0.894610	−	0.446848i	$-0.147453\pi$
$642$	−26.4483	−	9.62639i	−1.04383	−	0.379923i
$643$	6.52757	+	11.3061i	0.257422	+	0.445868i	0.965551	−	0.260215i	$-0.0837936\pi$
$643$	6.52757	+	11.3061i	0.257422	+	0.445868i	−0.708128	+	0.706084i	$0.750460\pi$
$644$	−1.90666	−	1.59988i	−0.0751331	−	0.0630442i
$645$	−3.24220	−	2.72053i	−0.127661	−	0.107121i
$646$	−6.65224	+	2.42122i	−0.261729	+	0.0952615i
$647$	8.16883	+	46.3278i	0.321150	+	1.82133i	0.535453	+	0.844565i	$0.320141\pi$
$647$	8.16883	+	46.3278i	0.321150	+	1.82133i	−0.214303	+	0.976767i	$0.568748\pi$
$648$	−0.772801	−	4.38277i	−0.0303585	−	0.172172i
$649$	−10.8785	+	3.95944i	−0.427017	+	0.155422i
$650$	16.7576	+	14.0613i	0.657287	+	0.551530i
$651$	−3.39664	−	2.85012i	−0.133125	−	0.111705i
$652$	−7.37329	−	12.7709i	−0.288760	−	0.500148i
$653$	25.9534	+	9.44628i	1.01564	+	0.369661i	0.795595	−	0.605829i	$-0.207158\pi$
$653$	25.9534	+	9.44628i	1.01564	+	0.369661i	0.220042	+	0.975491i	$0.429381\pi$
$654$	−2.54614	+	14.4399i	−0.0995618	+	0.564643i
$655$	−0.344697	+	0.597032i	−0.0134684	+	0.0233280i
$656$	−5.35818	−	9.28064i	−0.209202	−	0.362348i
$657$	7.47996	−	2.72248i	0.291821	−	0.106214i
$658$	1.78150	−	3.08565i	0.0694502	−	0.120291i
$659$	27.5226	−	23.0942i	1.07213	−	0.899624i	0.0768864	−	0.997040i	$-0.475502\pi$
$659$	27.5226	−	23.0942i	1.07213	−	0.899624i	0.995244	+	0.0974158i	$0.0310577\pi$
$660$	−1.23517			−0.0480790
$661$	30.2001	−	25.3409i	1.17465	−	0.985645i	0.174647	−	0.984631i	$-0.444122\pi$
$661$	30.2001	−	25.3409i	1.17465	−	0.985645i	0.999999	−	0.00101438i	$-0.000322887\pi$
$662$	26.8546	+	9.77429i	1.04373	+	0.379888i
$663$	2.15244	+	12.2071i	0.0835939	+	0.474085i
$664$	0.245649	−	1.39315i	0.00953304	−	0.0540645i
$665$	−0.584421			−0.0226629
$666$	−6.55180	−	1.57013i	−0.253877	−	0.0608411i
$667$	1.18897			0.0460372
$668$	1.44239	−	8.18020i	0.0558078	−	0.316501i
$669$	6.98984	+	39.6414i	0.270243	+	1.53262i
$670$	3.43421	+	1.24995i	0.132675	+	0.0482898i
$671$	−2.84896	+	2.39056i	−0.109983	+	0.0922867i
$672$	0.657221			0.0253529
$673$	11.6863	−	9.80600i	0.450475	−	0.377994i	−0.389137	−	0.921180i	$-0.627227\pi$
$673$	11.6863	−	9.80600i	0.450475	−	0.377994i	0.839612	+	0.543186i	$0.182782\pi$
$674$	4.88643	−	8.46354i	0.188218	−	0.326003i
$675$	25.9087	−	9.42999i	0.997226	−	0.362961i
$676$	−3.54976	−	6.14837i	−0.136529	−	0.236476i
$677$	−10.7029	+	18.5379i	−0.411345	+	0.712471i	−0.995037	−	0.0995043i	$-0.968274\pi$
$677$	−10.7029	+	18.5379i	−0.411345	+	0.712471i	0.583692	+	0.811975i	$0.301608\pi$
$678$	−2.91723	+	16.5444i	−0.112036	+	0.635385i
$679$	8.29805	+	3.02024i	0.318450	+	0.115906i
$680$	−0.349006	−	0.604496i	−0.0133838	−	0.0231814i
$681$	−10.8590	−	9.11178i	−0.416118	−	0.349164i
$682$	−13.3616	−	11.2117i	−0.511643	−	0.429319i
$683$	−11.8657	+	4.31877i	−0.454029	+	0.165253i	−0.558904	−	0.829232i	$-0.688778\pi$
$683$	−11.8657	+	4.31877i	−0.454029	+	0.165253i	0.104875	+	0.994485i	$0.466556\pi$
$684$	−0.677447	−	3.84199i	−0.0259028	−	0.146902i
$685$	1.04922	+	5.95045i	0.0400888	+	0.227355i
$686$	−6.18274	+	2.25033i	−0.236058	+	0.0859181i
$687$	−16.5108	−	13.8542i	−0.629925	−	0.528569i
$688$	6.78631	+	5.69439i	0.258725	+	0.217096i
$689$	9.80855	+	16.9889i	0.373676	+	0.647226i
$690$	2.33887	+	0.851279i	0.0890393	+	0.0324076i
$691$	−0.596082	+	3.38055i	−0.0226760	+	0.128602i	−0.994044	−	0.108977i	$-0.965243\pi$
$691$	−0.596082	+	3.38055i	−0.0226760	+	0.128602i	0.971368	+	0.237579i	$0.0763538\pi$
$692$	3.30637	−	5.72679i	0.125689	−	0.217700i
$693$	−0.684042	−	1.18480i	−0.0259846	−	0.0450067i
$694$	−15.5767	+	5.66944i	−0.591282	+	0.215209i
$695$	−0.127988	+	0.221681i	−0.00485485	+	0.00840884i
$696$	−0.240501	+	0.201804i	−0.00911616	+	0.00764937i
$697$	21.5382			0.815818
$698$	14.3165	−	12.0129i	0.541886	−	0.454696i
$699$	9.31253	+	3.38948i	0.352232	+	0.128202i
$700$	0.404801	+	2.29574i	0.0153000	+	0.0867708i
$701$	0.0325577	−	0.184644i	0.00122969	−	0.00697390i	−0.984187	−	0.177134i	$-0.943317\pi$
$701$	0.0325577	−	0.184644i	0.00122969	−	0.00697390i	0.985416	+	0.170160i	$0.0544285\pi$
$702$	−25.3331			−0.956134
$703$	20.8350	+	4.99308i	0.785808	+	0.188317i
$704$	2.58536			0.0974395
$705$	−0.618709	+	3.50888i	−0.0233019	+	0.132152i
$706$	0.938401	+	5.32193i	0.0353172	+	0.200294i
$707$	7.68978	+	2.79885i	0.289204	+	0.105262i
$708$	−4.71867	+	3.95944i	−0.177339	+	0.148805i
$709$	−48.4114			−1.81813			−0.909064	−	0.416656i	$-0.863202\pi$
$709$	−48.4114			−1.81813			−0.909064	+	0.416656i	$0.863202\pi$
$710$	2.36238	−	1.98227i	0.0886585	−	0.0743933i
$711$	1.95813	−	3.39158i	0.0734357	−	0.127194i
$712$	−3.59362	+	1.30797i	−0.134677	+	0.0490182i
$713$	17.5739	+	30.4389i	0.658148	+	1.13995i
$714$	−0.660456	+	1.14394i	−0.0247170	+	0.0428110i
$715$	−0.699012	+	3.96430i	−0.0261416	+	0.148256i
$716$	−4.26607	−	1.55272i	−0.159430	−	0.0580279i
$717$	−15.0998	−	26.1536i	−0.563911	−	0.976722i
$718$	−8.09432	−	6.79194i	−0.302077	−	0.253473i
$719$	−34.9152	−	29.2973i	−1.30212	−	1.09261i	−0.989775	−	0.142635i	$-0.954443\pi$
$719$	−34.9152	−	29.2973i	−1.30212	−	1.09261i	−0.312341	−	0.949970i	$-0.601113\pi$
$720$	0.361470	−	0.131564i	0.0134712	−	0.00490311i
$721$	1.11336	+	6.31419i	0.0414637	+	0.235153i
$722$	−1.14500	−	6.49362i	−0.0426125	−	0.241668i
$723$	19.1451	−	6.96825i	0.712015	−	0.259152i
$724$	−1.19788	−	1.00514i	−0.0445190	−	0.0373559i
$725$	−0.853053	−	0.715797i	−0.0316816	−	0.0265840i
$726$	−2.96857	−	5.14171i	−0.110174	−	0.190827i
$727$	−39.4113	−	14.3445i	−1.46168	−	0.532009i	−0.515854	−	0.856676i	$-0.672525\pi$
$727$	−39.4113	−	14.3445i	−1.46168	−	0.532009i	−0.945828	+	0.324667i	$0.894748\pi$
$728$	0.371937	−	2.10936i	0.0137849	−	0.0781780i
$729$	−14.1244	+	24.4643i	−0.523128	+	0.906084i
$730$	−1.24795	−	2.16152i	−0.0461888	−	0.0800013i
$731$	−16.7312	+	6.08967i	−0.618827	+	0.225234i
$732$	−0.989435	+	1.71375i	−0.0365706	+	0.0633421i
$733$	13.4938	−	11.3227i	0.498406	−	0.418212i	−0.358622	−	0.933483i	$-0.616753\pi$
$733$	13.4938	−	11.3227i	0.498406	−	0.418212i	0.857027	+	0.515271i	$0.172309\pi$
$734$	−0.215875			−0.00796811
$735$	2.47834	−	2.07957i	0.0914149	−	0.0767062i
$736$	−4.89554	−	1.78183i	−0.180452	−	0.0656791i
$737$	−4.72425	−	26.7925i	−0.174020	−	0.986916i
$738$	−2.06112	+	11.6892i	−0.0758708	+	0.430285i
$739$	39.4393			1.45080			0.725400	−	0.688328i	$-0.241655\pi$
$739$	39.4393			1.45080			0.725400	+	0.688328i	$0.241655\pi$
$740$	−0.128108	+	2.10863i	−0.00470933	+	0.0775149i
$741$	21.7229			0.798011
$742$	−0.363009	+	2.05873i	−0.0133265	+	0.0755783i
$743$	2.27755	+	12.9167i	0.0835554	+	0.473866i	0.997659	+	0.0683854i	$0.0217847\pi$
$743$	2.27755	+	12.9167i	0.0835554	+	0.473866i	−0.914104	+	0.405481i	$0.867104\pi$
$744$	−8.72118	−	3.17425i	−0.319734	−	0.116374i
$745$	−5.06406	+	4.24925i	−0.185533	+	0.155680i
$746$	−19.8047			−0.725102
$747$	−1.20029	+	1.00716i	−0.0439162	+	0.0368500i
$748$	−2.59809	+	4.50002i	−0.0949955	+	0.164537i
$749$	−9.18539	+	3.34321i	−0.335627	+	0.122158i
$750$	−2.35997	−	4.08758i	−0.0861738	−	0.149257i
$751$	19.9893	−	34.6226i	0.729421	−	1.26340i	−0.227707	−	0.973730i	$-0.573123\pi$
$751$	19.9893	−	34.6226i	0.729421	−	1.26340i	0.957128	−	0.289665i	$-0.0935440\pi$
$752$	1.29503	−	7.34450i	0.0472250	−	0.267826i
$753$	17.1796	+	6.25285i	0.626058	+	0.227866i
$754$	0.511588	+	0.886096i	0.0186309	+	0.0322697i
$755$	−1.72183	−	1.44479i	−0.0626639	−	0.0525813i
$756$	−2.06802	−	1.73527i	−0.0752131	−	0.0631113i
$757$	−26.2852	+	9.56703i	−0.955352	+	0.347720i	−0.772210	−	0.635367i	$-0.780849\pi$
$757$	−26.2852	+	9.56703i	−0.955352	+	0.347720i	−0.183141	+	0.983087i	$0.558627\pi$
$758$	−4.01057	−	22.7451i	−0.145670	−	0.826137i
$759$	−3.21745	−	18.2471i	−0.116786	−	0.662326i
$760$	−1.14949	+	0.418380i	−0.0416964	+	0.0151763i
$761$	−1.66744	−	1.39915i	−0.0604447	−	0.0507191i	0.612065	−	0.790808i	$-0.290339\pi$
$761$	−1.66744	−	1.39915i	−0.0604447	−	0.0507191i	−0.672510	+	0.740088i	$0.734784\pi$
$762$	7.42887	+	6.23356i	0.269119	+	0.225818i
$763$	2.54614	+	4.41004i	0.0921763	+	0.159654i
$764$	−21.6301	−	7.87272i	−0.782550	−	0.284825i
$765$	−0.134251	+	0.761377i	−0.00485387	+	0.0275276i
$766$	2.54301	−	4.40462i	0.0918826	−	0.159145i
$767$	10.0374	+	17.3854i	0.362431	+	0.627749i
$768$	1.29268	−	0.470498i	0.0466456	−	0.0169776i
$769$	20.6905	−	35.8370i	0.746118	−	1.29231i	−0.203553	−	0.979064i	$-0.565249\pi$
$769$	20.6905	−	35.8370i	0.746118	−	1.29231i	0.949671	−	0.313250i	$-0.101418\pi$
$770$	−0.328611	+	0.275737i	−0.0118423	+	0.00993687i
$771$	−24.0772			−0.867121
$772$	−8.08492	+	6.78405i	−0.290983	+	0.244163i
$773$	11.5459	+	4.20237i	0.415278	+	0.151149i	0.541205	−	0.840891i	$-0.317968\pi$
$773$	11.5459	+	4.20237i	0.415278	+	0.151149i	−0.125927	+	0.992040i	$0.540191\pi$
$774$	−1.70387	−	9.66310i	−0.0612442	−	0.347333i
$775$	5.71635	−	32.4191i	0.205338	−	1.16453i
$776$	18.4835			0.663519
$777$	3.57697	−	1.78523i	0.128323	−	0.0640448i
$778$	−29.1473			−1.04498
$779$	6.55446	−	37.1722i	0.234838	−	1.33183i
$780$	0.371937	+	2.10936i	0.0133175	+	0.0755271i
$781$	−21.5726	−	7.85179i	−0.771929	−	0.280959i
$782$	8.02104	−	6.73045i	0.286832	−	0.240681i
$783$	1.28959			0.0460862
$784$	−5.18746	+	4.35280i	−0.185266	+	0.155457i
$785$	−2.09975	+	3.63688i	−0.0749434	+	0.129806i
$786$	2.56601	−	0.933952i	0.0915266	−	0.0333130i
$787$	−12.0763	−	20.9167i	−0.430473	−	0.745601i	0.566441	−	0.824102i	$-0.308320\pi$
$787$	−12.0763	−	20.9167i	−0.430473	−	0.745601i	−0.996914	+	0.0785015i	$0.974986\pi$
$788$	−2.41433	+	4.18175i	−0.0860071	+	0.148969i
$789$	3.37617	−	19.1472i	0.120195	−	0.681658i
$790$	−1.15391	−	0.419989i	−0.0410543	−	0.0149425i
$791$	2.91723	+	5.05279i	0.103725	+	0.179657i
$792$	−2.19362	−	1.84066i	−0.0779468	−	0.0654052i
$793$	4.94036	+	4.14545i	0.175437	+	0.147209i
$794$	15.0280	−	5.46975i	0.533325	−	0.194114i
$795$	−0.363009	−	2.05873i	−0.0128746	−	0.0730156i
$796$	1.78721	+	10.1358i	0.0633461	+	0.359254i
$797$	30.9648	−	11.2703i	1.09683	−	0.399214i	0.270684	−	0.962668i	$-0.412750\pi$
$797$	30.9648	−	11.2703i	1.09683	−	0.399214i	0.826147	+	0.563455i	$0.190528\pi$
$798$	1.77331	+	1.48798i	0.0627745	+	0.0526741i
$799$	11.4823	+	9.63475i	0.406213	+	0.340853i
$800$	2.43969	+	4.22567i	0.0862562	+	0.149400i
$801$	3.98032	+	1.44872i	0.140638	+	0.0511879i
$802$	−0.944617	+	5.35719i	−0.0333556	+	0.189169i
$803$	−9.29008	+	16.0909i	−0.327840	+	0.567835i
$804$	−7.23797	−	12.5365i	−0.255263	−	0.442129i
$805$	0.812281	−	0.295646i	0.0286291	−	0.0104202i
$806$	−15.1233	+	26.1943i	−0.532696	+	0.922656i
$807$	28.2527	−	23.7068i	0.994542	−	0.834520i
$808$	17.1286			0.602582
$809$	27.3400	−	22.9410i	0.961224	−	0.806563i	−0.0199275	−	0.999801i	$-0.506344\pi$
$809$	27.3400	−	22.9410i	0.961224	−	0.806563i	0.981152	+	0.193238i	$0.0618991\pi$
$810$	1.45239	+	0.528627i	0.0510318	+	0.0185741i
$811$	5.88324	+	33.3655i	0.206589	+	1.17162i	0.894920	+	0.446226i	$0.147232\pi$
$811$	5.88324	+	33.3655i	0.206589	+	1.17162i	−0.688332	+	0.725396i	$0.741657\pi$
$812$	−0.0189336	+	0.107378i	−0.000664439	+	0.00376822i
$813$	15.0122			0.526501
$814$	14.0710	−	7.02270i	0.493189	−	0.246146i
$815$	5.12143			0.179396
$816$	−0.480107	+	2.72282i	−0.0168071	+	0.0953179i
$817$	5.41838	+	30.7291i	0.189565	+	1.07508i
$818$	35.4493	+	12.9025i	1.23945	+	0.451125i
$819$	−1.81735	+	1.52494i	−0.0635033	+	0.0532856i
$820$	3.72175			0.129969
$821$	−18.1645	+	15.2418i	−0.633945	+	0.531943i	−0.902152	−	0.431418i	$-0.858013\pi$
$821$	−18.1645	+	15.2418i	−0.633945	+	0.531943i	0.268207	+	0.963361i	$0.413569\pi$
$822$	11.9667	−	20.7269i	0.417386	−	0.722934i
$823$	−23.3126	+	8.48508i	−0.812625	+	0.295771i	−0.714708	−	0.699423i	$-0.753440\pi$
$823$	−23.3126	+	8.48508i	−0.812625	+	0.295771i	−0.0979172	+	0.995195i	$0.531218\pi$
$824$	6.71012	+	11.6223i	0.233758	+	0.404881i
$825$	−8.67685	+	15.0288i	−0.302089	+	0.523234i
$826$	−0.371481	+	2.10677i	−0.0129255	+	0.0733040i
$827$	−49.8660	−	18.1497i	−1.73401	−	0.631129i	−0.735108	−	0.677950i	$-0.762869\pi$
$827$	−49.8660	−	18.1497i	−1.73401	−	0.631129i	−0.998903	+	0.0468213i	$0.985091\pi$
$828$	2.88516	+	4.99725i	0.100266	+	0.173666i
$829$	−4.78684	−	4.01663i	−0.166254	−	0.139503i	0.555865	−	0.831273i	$-0.312387\pi$
$829$	−4.78684	−	4.01663i	−0.166254	−	0.139503i	−0.722119	+	0.691769i	$0.756832\pi$
$830$	0.376356	+	0.315801i	0.0130635	+	0.0109616i
$831$	7.94153	−	2.89048i	0.275489	−	0.100270i
$832$	−0.778508	−	4.41514i	−0.0269899	−	0.153067i
$833$	−2.36338	−	13.4034i	−0.0818863	−	0.464400i
$834$	0.952773	−	0.346781i	0.0329918	−	0.0120080i
$835$	2.20987	+	1.85430i	0.0764757	+	0.0641707i
$836$	6.97581	+	5.85340i	0.241264	+	0.202444i
$837$	19.0611	+	33.0148i	0.658849	+	1.14116i
$838$	−5.81832	−	2.11770i	−0.200991	−	0.0731546i
$839$	1.97545	−	11.2033i	0.0682002	−	0.386783i	−0.931532	−	0.363658i	$-0.881528\pi$
$839$	1.97545	−	11.2033i	0.0682002	−	0.386783i	0.999733	−	0.0231242i	$-0.00736132\pi$
$840$	−0.114125	+	0.197671i	−0.00393770	+	0.00682029i
$841$	14.4740	+	25.0696i	0.499102	+	0.864470i
$842$	9.49900	−	3.45735i	0.327357	−	0.119148i
$843$	2.03115	−	3.51806i	0.0699566	−	0.121168i
$844$	1.05020	−	0.881223i	0.0361494	−	0.0303329i
$845$	2.46564			0.0848206
$846$	−6.32776	+	5.30962i	−0.217553	+	0.182549i
$847$	−1.93760	−	0.705227i	−0.0665766	−	0.0242319i
$848$	0.759822	+	4.30917i	0.0260924	+	0.147977i
$849$	−3.45763	+	19.6092i	−0.118666	+	0.672986i
$850$	−9.80681			−0.336371
$851$	−31.4843	+	3.60017i	−1.07927	+	0.123412i
$852$	−12.2152			−0.418486
$853$	−0.162161	+	0.919663i	−0.00555230	+	0.0314886i	−0.987458	−	0.157882i	$-0.949534\pi$
$853$	−0.162161	+	0.919663i	−0.00555230	+	0.0314886i	0.981906	+	0.189370i	$0.0606447\pi$
$854$	0.119340	+	0.676813i	0.00408375	+	0.0231601i
$855$	1.27318	+	0.463401i	0.0435420	+	0.0158480i
$856$	−15.6733	+	13.1514i	−0.535702	+	0.449507i
$857$	34.2745			1.17080			0.585398	−	0.810746i	$-0.300938\pi$
$857$	34.2745			1.17080			0.585398	+	0.810746i	$0.300938\pi$
$858$	12.2145	−	10.2491i	0.416995	−	0.349900i
$859$	8.03105	−	13.9102i	0.274016	−	0.474609i	−0.695871	−	0.718167i	$-0.744981\pi$
$859$	8.03105	−	13.9102i	0.274016	−	0.474609i	0.969886	+	0.243558i	$0.0783146\pi$
$860$	−2.89112	+	1.05228i	−0.0985862	+	0.0358825i
$861$	−3.52151	−	6.09943i	−0.120013	−	0.207868i
$862$	17.0891	−	29.5992i	0.582057	−	1.00815i
$863$	−1.11602	+	6.32926i	−0.0379898	+	0.215451i	−0.997893	−	0.0648808i	$-0.979333\pi$
$863$	−1.11602	+	6.32926i	−0.0379898	+	0.215451i	0.959903	+	0.280331i	$0.0904444\pi$
$864$	−5.30983	−	1.93262i	−0.180644	−	0.0657490i
$865$	1.14829	+	1.98889i	0.0390430	+	0.0676245i
$866$	−0.525751	−	0.441157i	−0.0178657	−	0.0149911i
$867$	13.6578	+	11.4603i	0.463845	+	0.389212i
$868$	−3.02883	+	1.10241i	−0.102805	+	0.0374181i
$869$	1.58737	+	9.00241i	0.0538478	+	0.305386i
$870$	−0.0189336	−	0.107378i	−0.000641909	−	0.00364045i
$871$	−44.3322	+	16.1356i	−1.50214	+	0.546735i
$872$	8.16506	+	6.85130i	0.276504	+	0.232014i
$873$	−15.6828	−	13.1594i	−0.530783	−	0.445380i
$874$	−9.17495	−	15.8915i	−0.310347	−	0.537537i
$875$	−1.54036	−	0.560645i	−0.0520736	−	0.0189533i
$876$	−1.71674	+	9.73610i	−0.0580032	+	0.328952i
$877$	−21.9328	+	37.9888i	−0.740619	+	1.28279i	0.211595	+	0.977357i	$0.432134\pi$
$877$	−21.9328	+	37.9888i	−0.740619	+	1.28279i	−0.952214	+	0.305432i	$0.901199\pi$
$878$	−10.7545	−	18.6273i	−0.362945	−	0.628639i
$879$	−16.2647	+	5.91985i	−0.548594	+	0.199672i
$880$	−0.448944	+	0.777593i	−0.0151339	+	0.0262127i
$881$	−18.2452	+	15.3095i	−0.614696	+	0.515791i	−0.896131	−	0.443789i	$-0.853634\pi$
$881$	−18.2452	+	15.3095i	−0.614696	+	0.515791i	0.281436	+	0.959580i	$0.409189\pi$
$882$	7.50044			0.252553
$883$	5.99963	−	5.03429i	0.201904	−	0.169417i	−0.536230	−	0.844072i	$-0.680152\pi$
$883$	5.99963	−	5.03429i	0.201904	−	0.169417i	0.738133	+	0.674655i	$0.235708\pi$
$884$	8.46723	+	3.08182i	0.284784	+	0.103653i
$885$	−0.371481	−	2.10677i	−0.0124872	−	0.0708184i
$886$	−4.96583	+	28.1626i	−0.166830	+	0.946142i
$887$	−37.5492			−1.26078			−0.630389	−	0.776280i	$-0.717104\pi$
$887$	−37.5492			−1.26078			−0.630389	+	0.776280i	$0.717104\pi$
$888$	5.75748	−	6.07207i	0.193208	−	0.203765i
$889$	3.36798			0.112958
$890$	0.230630	−	1.30797i	0.00773075	−	0.0438433i
$891$	−1.99797	−	11.3311i	−0.0669346	−	0.379605i
$892$	27.4965	+	10.0079i	0.920651	+	0.335090i
$893$	20.1226	−	16.8849i	0.673377	−	0.565030i
$894$	26.1849			0.875752
$895$	1.20780	−	1.01347i	0.0403724	−	0.0338765i
$896$	0.238878	−	0.413749i	0.00798035	−	0.0138224i
$897$	−30.1925	+	10.9892i	−1.00810	+	0.366918i
$898$	17.2844	+	29.9375i	0.576789	+	0.999028i
$899$	0.769858	−	1.33343i	0.0256762	−	0.0444725i
$900$	0.938471	−	5.32234i	0.0312824	−	0.177411i
$901$	−8.26400	−	3.00785i	−0.275314	−	0.100206i
$902$	−13.8528	−	23.9938i	−0.461249	−	0.798907i
$903$	4.46010	+	3.74247i	0.148423	+	0.124542i
$904$	9.35511	+	7.84987i	0.311146	+	0.261083i
$905$	0.510325	−	0.185743i	0.0169638	−	0.00617431i
$906$	1.54601	+	8.76787i	0.0513628	+	0.291293i
$907$	5.69564	+	32.3016i	0.189120	+	1.07256i	0.920546	+	0.390634i	$0.127744\pi$
$907$	5.69564	+	32.3016i	0.189120	+	1.07256i	−0.731426	+	0.681921i	$0.761145\pi$
$908$	−9.68313	+	3.52437i	−0.321346	+	0.116960i
$909$	−14.5332	−	12.1948i	−0.482036	−	0.404477i
$910$	0.569840	+	0.478153i	0.0188900	+	0.0158506i
$911$	−16.8114	−	29.1181i	−0.556985	−	0.964727i	−0.997746	−	0.0671021i	$-0.978625\pi$
$911$	−16.8114	−	29.1181i	−0.556985	−	0.964727i	0.440761	−	0.897625i	$-0.354709\pi$
$912$	4.55314	+	1.65721i	0.150770	+	0.0548756i
$913$	0.635092	−	3.60179i	0.0210185	−	0.119202i
$914$	−16.4542	+	28.4995i	−0.544257	+	0.942680i
$915$	−0.343627	−	0.595180i	−0.0113600	−	0.0196760i
$916$	−14.7229	+	5.35869i	−0.486458	+	0.177056i
$917$	0.474180	−	0.821303i	0.0156588	−	0.0271218i
$918$	8.69983	−	7.30003i	0.287137	−	0.240937i
$919$	−29.1313			−0.960954			−0.480477	−	0.877007i	$-0.659536\pi$
$919$	−29.1313			−0.960954			−0.480477	+	0.877007i	$0.659536\pi$
$920$	1.38602	−	1.16301i	0.0456956	−	0.0383432i
$921$	−24.4313	−	8.89226i	−0.805038	−	0.293010i
$922$	−3.14988	−	17.8639i	−0.103736	−	0.588315i
$923$	−6.91287	+	39.2049i	−0.227540	+	1.29044i
$924$	1.69916			0.0558981
$925$	24.7565	+	16.3715i	0.813989	+	0.538291i
$926$	0.339403			0.0111535
$927$	2.58117	−	14.6385i	0.0847766	−	0.480792i
$928$	0.0396303	+	0.224755i	0.00130093	+	0.00737793i
$929$	−28.9996	−	10.5550i	−0.951446	−	0.346298i	−0.180770	−	0.983525i	$-0.557859\pi$
$929$	−28.9996	−	10.5550i	−0.951446	−	0.346298i	−0.770676	+	0.637228i	$0.780081\pi$
$930$	2.46913	−	2.07184i	0.0809659	−	0.0679385i
$931$	−23.8518			−0.781710
$932$	5.51861	−	4.63067i	0.180768	−	0.151683i
$933$	−0.0779891	+	0.135081i	−0.00255325	+	0.00442235i
$934$	13.3455	−	4.85738i	0.436679	−	0.158938i
$935$	−0.902307	−	1.56284i	−0.0295086	−	0.0511104i
$936$	−2.48284	+	4.30040i	−0.0811541	+	0.140563i
$937$	1.27251	−	7.21677i	0.0415711	−	0.235762i	−0.956942	−	0.290281i	$-0.906251\pi$
$937$	1.27251	−	7.21677i	0.0415711	−	0.235762i	0.998513	+	0.0545189i	$0.0173625\pi$
$938$	−4.72425	−	1.71949i	−0.154252	−	0.0561432i
$939$	6.31495	+	10.9378i	0.206081	+	0.356942i
$940$	1.98411	+	1.66486i	0.0647144	+	0.0543018i
$941$	32.3208	+	27.1204i	1.05363	+	0.884098i	0.993470	−	0.114090i	$-0.0363954\pi$
$941$	32.3208	+	27.1204i	1.05363	+	0.884098i	0.0601572	+	0.998189i	$0.480840\pi$
$942$	15.6311	−	5.68926i	0.509289	−	0.185366i
$943$	9.69464	+	54.9810i	0.315701	+	1.79043i
$944$	0.777554	+	4.40973i	0.0253072	+	0.143524i
$945$	0.881021	−	0.320666i	0.0286596	−	0.0104313i
$946$	17.5451	+	14.7221i	0.570439	+	0.478655i
$947$	−29.9494	−	25.1305i	−0.973224	−	0.816632i	0.00982951	−	0.999952i	$-0.496871\pi$
$947$	−29.9494	−	25.1305i	−0.973224	−	0.816632i	−0.983053	+	0.183320i	$0.941316\pi$
$948$	2.43199	+	4.21233i	0.0789874	+	0.136810i
$949$	30.2766	+	11.0198i	0.982819	+	0.357717i
$950$	−2.98438	+	16.9253i	−0.0968262	+	0.549129i
$951$	18.0653	−	31.2901i	0.585809	−	1.01465i
$952$	0.480107	+	0.831570i	0.0155604	+	0.0269514i
$953$	1.14509	−	0.416780i	0.0370932	−	0.0135008i	−0.323407	−	0.946260i	$-0.604828\pi$
$953$	1.14509	−	0.416780i	0.0370932	−	0.0135008i	0.360500	+	0.932759i	$0.382606\pi$
$954$	2.42325	−	4.19719i	0.0784555	−	0.135889i
$955$	6.12389	−	5.13855i	0.198164	−	0.166280i
$956$	−21.9530			−0.710012
$957$	−0.621782	+	0.521737i	−0.0200994	+	0.0168654i
$958$	31.9312	+	11.6220i	1.03165	+	0.375490i
$959$	−1.44336	−	8.18569i	−0.0466085	−	0.264330i
$960$	−0.0829614	+	0.470498i	−0.00267757	+	0.0151852i
$961$	14.5164			0.468270
$962$	−16.2301	−	21.9150i	−0.523278	−	0.706568i
$963$	22.6617			0.730262
$964$	2.57180	−	14.5854i	0.0828320	−	0.469764i
$965$	−0.636491	−	3.60972i	−0.0204894	−	0.116201i
$966$	−3.21745	−	1.17106i	−0.103520	−	0.0376781i
$967$	9.72067	−	8.15661i	0.312596	−	0.262299i	−0.472968	−	0.881080i	$-0.656817\pi$
$967$	9.72067	−	8.15661i	0.312596	−	0.262299i	0.785564	+	0.618781i	$0.212373\pi$
$968$	−4.31590			−0.138718
$969$	−7.46005	+	6.25972i	−0.239651	+	0.201091i
$970$	−3.20963	+	5.55924i	−0.103055	+	0.178496i
$971$	−0.827436	+	0.301162i	−0.0265537	+	0.00966475i	−0.355263	−	0.934766i	$-0.615609\pi$
$971$	−0.827436	+	0.301162i	−0.0265537	+	0.00966475i	0.328709	+	0.944431i	$0.393386\pi$
$972$	5.41483	+	9.37876i	0.173681	+	0.300824i
$973$	0.176065	−	0.304954i	0.00564439	−	0.00977638i
$974$	−4.39903	+	24.9481i	−0.140954	+	0.799389i
$975$	28.2781	+	10.2924i	0.905623	+	0.329620i
$976$	0.719253	+	1.24578i	0.0230227	+	0.0398765i
$977$	35.8592	+	30.0895i	1.14724	+	0.962647i	0.999651	−	0.0264023i	$-0.00840510\pi$
$977$	35.8592	+	30.0895i	1.14724	+	0.962647i	0.147586	+	0.989049i	$0.452850\pi$
$978$	−15.5400	−	13.0396i	−0.496914	−	0.416961i
$979$	−9.29081	+	3.38158i	−0.296935	+	0.108076i
$980$	−0.408386	−	2.31607i	−0.0130454	−	0.0739843i
$981$	−2.05004	−	11.6263i	−0.0654526	−	0.371200i
$982$	−19.9861	+	7.27433i	−0.637781	+	0.232133i
$983$	−26.4449	−	22.1899i	−0.843460	−	0.707747i	0.114879	−	0.993379i	$-0.463352\pi$
$983$	−26.4449	−	22.1899i	−0.843460	−	0.707747i	−0.958339	+	0.285633i	$0.907796\pi$
$984$	−11.2929	−	9.47590i	−0.360006	−	0.302081i
$985$	−0.838489	−	1.45231i	−0.0267165	−	0.0462743i
$986$	−0.431028	−	0.156881i	−0.0137267	−	0.00499612i
$987$	0.851123	−	4.82696i	0.0270915	−	0.153644i
$988$	7.89555	−	13.6755i	0.251191	−	0.435075i
$989$	−23.0762	−	39.9691i	−0.733780	−	1.27094i
$990$	0.934530	−	0.340141i	0.0297013	−	0.0108104i
$991$	23.7701	−	41.1711i	0.755083	−	1.30784i	−0.190249	−	0.981736i	$-0.560930\pi$
$991$	23.7701	−	41.1711i	0.755083	−	1.30784i	0.945333	−	0.326107i	$-0.105737\pi$
$992$	−5.16818	+	4.33662i	−0.164090	+	0.137688i
$993$	39.3133			1.24757
$994$	−3.24979	+	2.72690i	−0.103077	+	0.0864919i
$995$	−3.35887	−	1.22253i	−0.106483	−	0.0387567i
$996$	−0.337926	−	1.91647i	−0.0107076	−	0.0607257i
$997$	9.31464	−	52.8259i	0.294998	−	1.67301i	−0.372215	−	0.928147i	$-0.621401\pi$
$997$	9.31464	−	52.8259i	0.294998	−	1.67301i	0.667212	−	0.744868i	$-0.267487\pi$
$998$	16.4306			0.520101
$999$	−34.1487	+	3.90484i	−1.08042	+	0.123544i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.f.b.33.1	yes	12
3.2	odd	2		666.2.x.g.181.1		12
4.3	odd	2		592.2.bc.d.33.2		12
37.3	even	18		2738.2.a.q.1.3		6
37.9	even	9	inner	74.2.f.b.9.1	✓	12
37.34	even	9		2738.2.a.t.1.3		6
111.83	odd	18		666.2.x.g.379.1		12
148.83	odd	18		592.2.bc.d.305.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.9.1	✓	12	37.9	even	9	inner
74.2.f.b.33.1	yes	12	1.1	even	1	trivial
592.2.bc.d.33.2		12	4.3	odd	2
592.2.bc.d.305.2		12	148.83	odd	18
666.2.x.g.181.1		12	3.2	odd	2
666.2.x.g.379.1		12	111.83	odd	18
2738.2.a.q.1.3		6	37.3	even	18
2738.2.a.t.1.3		6	37.34	even	9

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.238878 - 1.35474i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.266044 - 0.223238i) q^{5} -1.37564 q^{6} +(-0.365982 + 0.307095i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.04081 - 0.378824i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.238878 - 1.35474i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.266044 - 0.223238i) q^{5} -1.37564 q^{6} +(-0.365982 + 0.307095i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.04081 - 0.378824i) q^{9} +(-0.173648 - 0.300767i) q^{10} +(-1.29268 + 2.23899i) q^{11} +(-0.238878 + 1.35474i) q^{12} +(4.21288 + 1.53336i) q^{13} +(0.238878 + 0.413749i) q^{14} +(-0.365982 - 0.307095i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.88864 + 0.687407i) q^{17} +(-0.192334 - 1.09078i) q^{18} +(0.611631 + 3.46873i) q^{19} +(-0.326352 + 0.118782i) q^{20} +(0.503461 + 0.422454i) q^{21} +(1.98050 + 1.66184i) q^{22} +(-2.60486 - 4.51175i) q^{23} +(1.29268 + 0.470498i) q^{24} +(-0.847296 + 4.80526i) q^{25} +(2.24162 - 3.88261i) q^{26} +(-2.82530 - 4.89356i) q^{27} +(0.448944 - 0.163402i) q^{28} +(-0.114111 + 0.197646i) q^{29} +(-0.365982 + 0.307095i) q^{30} -6.74658 q^{31} +(0.766044 - 0.642788i) q^{32} +(3.34205 + 1.21641i) q^{33} +(0.349006 + 1.97931i) q^{34} +(-0.0288122 + 0.163402i) q^{35} -1.10761 q^{36} +(2.42322 - 5.57925i) q^{37} +3.52224 q^{38} +(1.07095 - 6.07365i) q^{39} +(0.0603074 + 0.342020i) q^{40} +(-10.0701 - 3.66521i) q^{41} +(0.503461 - 0.422454i) q^{42} +8.85889 q^{43} +(1.98050 - 1.66184i) q^{44} +(0.192334 - 0.333132i) q^{45} +(-4.89554 + 1.78183i) q^{46} +(-3.72890 - 6.45864i) q^{47} +(0.687821 - 1.19134i) q^{48} +(-1.17590 + 6.66887i) q^{49} +(4.58512 + 1.66885i) q^{50} +(1.38241 + 2.39441i) q^{51} +(-3.43437 - 2.88178i) q^{52} +(3.35194 + 2.81261i) q^{53} +(-5.30983 + 1.93262i) q^{54} +(0.155916 + 0.884246i) q^{55} +(-0.0829614 - 0.470498i) q^{56} +(4.55314 - 1.65721i) q^{57} +(0.174828 + 0.146698i) q^{58} +(3.43016 + 2.87825i) q^{59} +(0.238878 + 0.413749i) q^{60} +(1.35175 + 0.491998i) q^{61} +(-1.17153 + 6.64409i) q^{62} +(-0.264583 + 0.458271i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.46312 - 0.532531i) q^{65} +(1.77827 - 3.08005i) q^{66} +(-8.06111 + 6.76408i) q^{67} +2.00984 q^{68} +(-5.49002 + 4.60667i) q^{69} +(0.155916 + 0.0567489i) q^{70} +(1.54193 + 8.74474i) q^{71} +(-0.192334 + 1.09078i) q^{72} +7.18667 q^{73} +(-5.07370 - 3.35524i) q^{74} +6.71229 q^{75} +(0.611631 - 3.46873i) q^{76} +(-0.214485 - 1.21641i) q^{77} +(-5.79541 - 2.10936i) q^{78} +(2.70857 - 2.27276i) q^{79} +0.347296 q^{80} +(-3.40919 + 2.86065i) q^{81} +(-5.35818 + 9.28064i) q^{82} +(-1.32932 + 0.483834i) q^{83} +(-0.328611 - 0.569170i) q^{84} +(-0.349006 + 0.604496i) q^{85} +(1.53833 - 8.72431i) q^{86} +(0.295018 + 0.107378i) q^{87} +(-1.29268 - 2.23899i) q^{88} +(2.92954 + 2.45818i) q^{89} +(-0.294673 - 0.247260i) q^{90} +(-2.01273 + 0.732572i) q^{91} +(0.904658 + 5.13057i) q^{92} +(1.61161 + 9.13989i) q^{93} +(-7.00804 + 2.55072i) q^{94} +(0.937074 + 0.786298i) q^{95} +(-1.05380 - 0.884246i) q^{96} +(-9.24175 - 16.0072i) q^{97} +(6.36336 + 2.31607i) q^{98} +(-0.497253 + 2.82006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 6 q^{30} + 42 q^{31} + 57 q^{33} - 3 q^{34} - 9 q^{35} + 24 q^{36} - 3 q^{37} + 42 q^{38} - 24 q^{39} + 12 q^{40} - 21 q^{41} - 33 q^{42} + 36 q^{43} - 3 q^{44} - 6 q^{45} + 3 q^{46} + 9 q^{47} - 12 q^{49} + 12 q^{50} + 3 q^{52} - 6 q^{53} - 27 q^{54} - 3 q^{56} - 36 q^{57} - 3 q^{58} - 6 q^{59} + 3 q^{60} - 18 q^{61} - 33 q^{62} + 36 q^{63} - 6 q^{64} + 3 q^{65} + 3 q^{66} - 27 q^{67} + 6 q^{68} - 12 q^{69} - 18 q^{71} + 6 q^{72} + 54 q^{73} + 3 q^{74} - 6 q^{75} - 3 q^{76} + 51 q^{77} - 33 q^{78} - 12 q^{79} - 36 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 3 q^{85} + 39 q^{87} + 3 q^{88} - 15 q^{89} - 15 q^{90} - 51 q^{91} - 6 q^{92} + 45 q^{93} - 12 q^{94} - 15 q^{95} + 6 q^{96} - 42 q^{97} + 51 q^{98} - 33 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Introduction

L-functions

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