LMFDB - Embedded newform 350.2.q.a.261.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(11,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 20]))

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

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

chi := DirichletCharacter("350.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.q (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			261.1
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	350.261
Dual form			350.2.q.a.291.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 + 0.994522i) q^{2} +(-0.604528 + 0.128496i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.11803 - 1.93649i) q^{5} +(-0.190983 - 0.587785i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.39169 + 1.06485i) q^{9} +O(q^{10})$	\(q+(0.104528 + 0.994522i) q^{2} +(-0.604528 + 0.128496i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.11803 - 1.93649i) q^{5} +(-0.190983 - 0.587785i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.39169 + 1.06485i) q^{9} +(2.04275 + 0.909491i) q^{10} +(3.52090 + 1.56760i) q^{11} +(0.564602 - 0.251377i) q^{12} +(4.73607 + 3.44095i) q^{13} +(-2.63611 - 0.225688i) q^{14} +(-0.427051 + 1.31433i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-5.15780 + 5.72831i) q^{17} +(-1.30902 - 2.26728i) q^{18} +(5.86889 + 1.24747i) q^{19} +(-0.690983 + 2.12663i) q^{20} +(-0.0315794 - 1.63486i) q^{21} +(-1.19098 + 3.66547i) q^{22} +(-0.153880 - 1.46407i) q^{23} +(0.309017 + 0.535233i) q^{24} +(-2.50000 - 4.33013i) q^{25} +(-2.92705 + 5.06980i) q^{26} +(2.80902 - 2.04087i) q^{27} +(-0.0510966 - 2.64526i) q^{28} +(1.07295 - 3.30220i) q^{29} +(-1.35177 - 0.287327i) q^{30} +(-3.24803 + 3.60730i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.32991 - 0.495239i) q^{33} +(-6.23607 - 4.53077i) q^{34} +(4.47214 + 3.87298i) q^{35} +(2.11803 - 1.53884i) q^{36} +(0.348943 - 0.155360i) q^{37} +(-0.627171 + 5.96713i) q^{38} +(-3.30524 - 1.47159i) q^{39} +(-2.18720 - 0.464905i) q^{40} +(-7.59017 - 5.51458i) q^{41} +(1.62260 - 0.202296i) q^{42} +2.23607 q^{43} +(-3.76988 - 0.801313i) q^{44} +(-0.611920 + 5.82203i) q^{45} +(1.43997 - 0.306074i) q^{46} +(6.18014 + 6.86374i) q^{47} +(-0.500000 + 0.363271i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(4.04508 - 2.93893i) q^{50} +(2.38197 - 4.12569i) q^{51} +(-5.34799 - 2.38108i) q^{52} +(0.230909 - 0.0490813i) q^{53} +(2.32331 + 2.58030i) q^{54} +(6.97214 - 5.06555i) q^{55} +(2.62543 - 0.327321i) q^{56} -3.70820 q^{57} +(3.39626 + 0.721898i) q^{58} +(0.556743 - 5.29706i) q^{59} +(0.144455 - 1.37440i) q^{60} +(-0.860904 - 8.19095i) q^{61} +(-3.92705 - 2.85317i) q^{62} +(-1.57072 - 6.74623i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(11.9585 - 5.32425i) q^{65} +(0.248983 - 2.36892i) q^{66} +(-0.669131 + 0.743145i) q^{67} +(3.85410 - 6.67550i) q^{68} +(0.281153 + 0.865300i) q^{69} +(-3.38430 + 4.85247i) q^{70} +(4.92705 - 15.1639i) q^{71} +(1.75181 + 1.94558i) q^{72} +(4.91667 + 2.18904i) q^{73} +(0.190983 + 0.330792i) q^{74} +(2.06773 + 2.29644i) q^{75} -6.00000 q^{76} +(-5.83320 + 8.36376i) q^{77} +(1.11803 - 3.44095i) q^{78} +(5.98489 + 6.64689i) q^{79} +(0.233733 - 2.22382i) q^{80} +(3.81953 - 4.24202i) q^{81} +(4.69098 - 8.12502i) q^{82} +(-1.78115 - 5.48183i) q^{83} +(0.370796 + 1.59257i) q^{84} +(5.32624 + 16.3925i) q^{85} +(0.233733 + 2.22382i) q^{86} +(-0.224307 + 2.13414i) q^{87} +(0.402863 - 3.83299i) q^{88} +(0.617745 + 5.87746i) q^{89} -5.85410 q^{90} +(-11.3079 + 10.5842i) q^{91} +(0.454915 + 1.40008i) q^{92} +(1.50000 - 2.59808i) q^{93} +(-6.18014 + 6.86374i) q^{94} +(8.97733 - 9.97033i) q^{95} +(-0.413545 - 0.459289i) q^{96} +(-3.47214 + 10.6861i) q^{97} +(1.90441 - 6.73597i) q^{98} -10.0902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9	\( 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9} + 5 q^{10} + 8 q^{11} + 2 q^{12} + 20 q^{13} - 4 q^{14} + 10 q^{15} + q^{16} + 14 q^{17} - 6 q^{18} - 6 q^{19} - 10 q^{20} + 15 q^{21} - 14 q^{22} + 7 q^{23} - 2 q^{24} - 20 q^{25} - 10 q^{26} + 18 q^{27} - 5 q^{28} + 22 q^{29} + 5 q^{30} + 6 q^{31} + 4 q^{32} + 6 q^{33} - 32 q^{34} + 8 q^{36} - q^{37} + 6 q^{38} - 5 q^{39} - 5 q^{40} - 16 q^{41} + 3 q^{42} - 7 q^{44} + 10 q^{45} + 13 q^{46} + 2 q^{47} - 4 q^{48} - 52 q^{49} + 10 q^{50} + 28 q^{51} - 10 q^{52} + 7 q^{53} - 11 q^{54} + 20 q^{55} - q^{56} + 24 q^{57} + 11 q^{58} - 15 q^{59} + 11 q^{61} - 18 q^{62} - 16 q^{63} - 2 q^{64} + 20 q^{65} - q^{66} - q^{67} + 4 q^{68} - 38 q^{69} - 25 q^{70} + 26 q^{71} - q^{72} + 4 q^{73} + 6 q^{74} - 15 q^{75} - 48 q^{76} - 40 q^{77} - 20 q^{79} - 5 q^{80} - 16 q^{81} + 42 q^{82} + 26 q^{83} + 8 q^{84} - 20 q^{85} - 5 q^{86} - 2 q^{87} - 8 q^{88} + q^{89} - 20 q^{90} - 10 q^{91} + 26 q^{92} + 12 q^{93} - 2 q^{94} - 30 q^{95} + 3 q^{96} + 8 q^{97} + 11 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9 + 5 * q^10 + 8 * q^11 + 2 * q^12 + 20 * q^13 - 4 * q^14 + 10 * q^15 + q^16 + 14 * q^17 - 6 * q^18 - 6 * q^19 - 10 * q^20 + 15 * q^21 - 14 * q^22 + 7 * q^23 - 2 * q^24 - 20 * q^25 - 10 * q^26 + 18 * q^27 - 5 * q^28 + 22 * q^29 + 5 * q^30 + 6 * q^31 + 4 * q^32 + 6 * q^33 - 32 * q^34 + 8 * q^36 - q^37 + 6 * q^38 - 5 * q^39 - 5 * q^40 - 16 * q^41 + 3 * q^42 - 7 * q^44 + 10 * q^45 + 13 * q^46 + 2 * q^47 - 4 * q^48 - 52 * q^49 + 10 * q^50 + 28 * q^51 - 10 * q^52 + 7 * q^53 - 11 * q^54 + 20 * q^55 - q^56 + 24 * q^57 + 11 * q^58 - 15 * q^59 + 11 * q^61 - 18 * q^62 - 16 * q^63 - 2 * q^64 + 20 * q^65 - q^66 - q^67 + 4 * q^68 - 38 * q^69 - 25 * q^70 + 26 * q^71 - q^72 + 4 * q^73 + 6 * q^74 - 15 * q^75 - 48 * q^76 - 40 * q^77 - 20 * q^79 - 5 * q^80 - 16 * q^81 + 42 * q^82 + 26 * q^83 + 8 * q^84 - 20 * q^85 - 5 * q^86 - 2 * q^87 - 8 * q^88 + q^89 - 20 * q^90 - 10 * q^91 + 26 * q^92 + 12 * q^93 - 2 * q^94 - 30 * q^95 + 3 * q^96 + 8 * q^97 + 11 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.104528	+	0.994522i	0.0739128	+	0.703233i
$2$	0.104528	+	0.994522i	0.0739128	+	0.703233i
$3$	−0.604528	+	0.128496i	−0.349025	+	0.0741875i	−0.379088	−	0.925361i	$-0.623762\pi$
$3$	−0.604528	+	0.128496i	−0.349025	+	0.0741875i	0.0300636	+	0.999548i	$0.490429\pi$
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i
$6$	−0.190983	−	0.587785i	−0.0779685	−	0.239962i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−2.39169	+	1.06485i	−0.797231	+	0.354950i
$10$	2.04275	+	0.909491i	0.645974	+	0.287606i
$11$	3.52090	+	1.56760i	1.06159	+	0.472651i	0.861832	−	0.507195i	$-0.169317\pi$
$11$	3.52090	+	1.56760i	1.06159	+	0.472651i	0.199759	+	0.979845i	$0.435984\pi$
$12$	0.564602	−	0.251377i	0.162987	−	0.0725663i
$13$	4.73607	+	3.44095i	1.31355	+	0.954349i	0.999989	+	0.00478088i	$0.00152181\pi$
$13$	4.73607	+	3.44095i	1.31355	+	0.954349i	0.313560	+	0.949568i	$0.398478\pi$
$14$	−2.63611	−	0.225688i	−0.704529	−	0.0603177i
$15$	−0.427051	+	1.31433i	−0.110264	+	0.339358i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	−5.15780	+	5.72831i	−1.25095	+	1.38932i	−0.361444	+	0.932394i	$0.617716\pi$
$17$	−5.15780	+	5.72831i	−1.25095	+	1.38932i	−0.889505	+	0.456926i	$0.848950\pi$
$18$	−1.30902	−	2.26728i	−0.308538	−	0.534404i
$19$	5.86889	+	1.24747i	1.34641	+	0.286189i	0.824042	−	0.566528i	$-0.191714\pi$
$19$	5.86889	+	1.24747i	1.34641	+	0.286189i	0.522372	+	0.852717i	$0.325047\pi$
$20$	−0.690983	+	2.12663i	−0.154508	+	0.475528i
$21$	−0.0315794	−	1.63486i	−0.00689120	−	0.356756i
$22$	−1.19098	+	3.66547i	−0.253918	+	0.781481i
$23$	−0.153880	−	1.46407i	−0.0320862	−	0.305280i	−0.998782	−	0.0493500i	$-0.984285\pi$
$23$	−0.153880	−	1.46407i	−0.0320862	−	0.305280i	0.966695	−	0.255930i	$-0.0823817\pi$
$24$	0.309017	+	0.535233i	0.0630778	+	0.109254i
$25$	−2.50000	−	4.33013i	−0.500000	−	0.866025i
$26$	−2.92705	+	5.06980i	−0.574042	+	0.994270i
$27$	2.80902	−	2.04087i	0.540596	−	0.392766i
$28$	−0.0510966	−	2.64526i	−0.00965635	−	0.499907i
$29$	1.07295	−	3.30220i	0.199242	−	0.613203i	−0.800659	−	0.599120i	$-0.795517\pi$
$29$	1.07295	−	3.30220i	0.199242	−	0.613203i	0.999901	−	0.0140826i	$-0.00448279\pi$
$30$	−1.35177	−	0.287327i	−0.246798	−	0.0524585i
$31$	−3.24803	+	3.60730i	−0.583363	+	0.647890i	−0.960504	−	0.278265i	$-0.910241\pi$
$31$	−3.24803	+	3.60730i	−0.583363	+	0.647890i	0.377141	+	0.926156i	$0.376907\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.32991	−	0.495239i	−0.405586	−	0.0862100i
$34$	−6.23607	−	4.53077i	−1.06948	−	0.777020i
$35$	4.47214	+	3.87298i	0.755929	+	0.654654i
$36$	2.11803	−	1.53884i	0.353006	−	0.256474i
$37$	0.348943	−	0.155360i	0.0573659	−	0.0255410i	−0.377853	−	0.925866i	$-0.623338\pi$
$37$	0.348943	−	0.155360i	0.0573659	−	0.0255410i	0.435219	+	0.900325i	$0.356671\pi$
$38$	−0.627171	+	5.96713i	−0.101741	+	0.967997i
$39$	−3.30524	−	1.47159i	−0.529262	−	0.235643i
$40$	−2.18720	−	0.464905i	−0.345827	−	0.0735079i
$41$	−7.59017	−	5.51458i	−1.18539	−	0.861233i	−0.192616	−	0.981274i	$-0.561697\pi$
$41$	−7.59017	−	5.51458i	−1.18539	−	0.861233i	−0.992769	+	0.120041i	$0.961697\pi$
$42$	1.62260	−	0.202296i	0.250373	−	0.0312149i
$43$	2.23607			0.340997			0.170499	−	0.985358i	$-0.445462\pi$
$43$	2.23607			0.340997			0.170499	+	0.985358i	$0.445462\pi$
$44$	−3.76988	−	0.801313i	−0.568331	−	0.120802i
$45$	−0.611920	+	5.82203i	−0.0912197	+	0.867897i
$46$	1.43997	−	0.306074i	0.212311	−	0.0451282i
$47$	6.18014	+	6.86374i	0.901465	+	1.00118i	0.999982	+	0.00604337i	$0.00192368\pi$
$47$	6.18014	+	6.86374i	0.901465	+	1.00118i	−0.0985163	+	0.995135i	$0.531410\pi$
$48$	−0.500000	+	0.363271i	−0.0721688	+	0.0524337i
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	4.04508	−	2.93893i	0.572061	−	0.415627i
$51$	2.38197	−	4.12569i	0.333542	−	0.577712i
$52$	−5.34799	−	2.38108i	−0.741633	−	0.330196i
$53$	0.230909	−	0.0490813i	0.0317178	−	0.00674183i	−0.192025	−	0.981390i	$-0.561506\pi$
$53$	0.230909	−	0.0490813i	0.0317178	−	0.00674183i	0.223743	+	0.974648i	$0.428172\pi$
$54$	2.32331	+	2.58030i	0.316163	+	0.351134i
$55$	6.97214	−	5.06555i	0.940123	−	0.683039i
$56$	2.62543	−	0.327321i	0.350837	−	0.0437402i
$57$	−3.70820			−0.491164
$58$	3.39626	+	0.721898i	0.445951	+	0.0947898i
$59$	0.556743	−	5.29706i	0.0724818	−	0.689619i	−0.896594	−	0.442854i	$-0.853966\pi$
$59$	0.556743	−	5.29706i	0.0724818	−	0.689619i	0.969076	−	0.246764i	$-0.0793674\pi$
$60$	0.144455	−	1.37440i	0.0186490	−	0.177434i
$61$	−0.860904	−	8.19095i	−0.110227	−	1.04874i	−0.900163	−	0.435554i	$-0.856553\pi$
$61$	−0.860904	−	8.19095i	−0.110227	−	1.04874i	0.789935	−	0.613190i	$-0.210114\pi$
$62$	−3.92705	−	2.85317i	−0.498736	−	0.362353i
$63$	−1.57072	−	6.74623i	−0.197892	−	0.849945i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	11.9585	−	5.32425i	1.48327	−	0.660392i
$66$	0.248983	−	2.36892i	0.0306477	−	0.291594i
$67$	−0.669131	+	0.743145i	−0.0817473	+	0.0907896i	−0.782631	−	0.622486i	$-0.786123\pi$
$67$	−0.669131	+	0.743145i	−0.0817473	+	0.0907896i	0.700883	+	0.713276i	$0.252789\pi$
$68$	3.85410	−	6.67550i	0.467379	−	0.809523i
$69$	0.281153	+	0.865300i	0.0338468	+	0.104170i
$70$	−3.38430	+	4.85247i	−0.404501	+	0.579982i
$71$	4.92705	−	15.1639i	0.584733	−	1.79962i	−0.0156051	−	0.999878i	$-0.504967\pi$
$71$	4.92705	−	15.1639i	0.584733	−	1.79962i	0.600338	−	0.799746i	$-0.295033\pi$
$72$	1.75181	+	1.94558i	0.206452	+	0.229289i
$73$	4.91667	+	2.18904i	0.575453	+	0.256208i	0.673763	−	0.738948i	$-0.264677\pi$
$73$	4.91667	+	2.18904i	0.575453	+	0.256208i	−0.0983100	+	0.995156i	$0.531344\pi$
$74$	0.190983	+	0.330792i	0.0222013	+	0.0384538i
$75$	2.06773	+	2.29644i	0.238761	+	0.265170i
$76$	−6.00000			−0.688247
$77$	−5.83320	+	8.36376i	−0.664755	+	0.953139i
$78$	1.11803	−	3.44095i	0.126592	−	0.389611i
$79$	5.98489	+	6.64689i	0.673352	+	0.747833i	0.978899	−	0.204344i	$-0.0655060\pi$
$79$	5.98489	+	6.64689i	0.673352	+	0.747833i	−0.305547	+	0.952177i	$0.598839\pi$
$80$	0.233733	−	2.22382i	0.0261321	−	0.248630i
$81$	3.81953	−	4.24202i	0.424393	−	0.471336i
$82$	4.69098	−	8.12502i	0.518032	−	0.897258i
$83$	−1.78115	−	5.48183i	−0.195507	−	0.601708i	−0.999970	−	0.00770622i	$-0.997547\pi$
$83$	−1.78115	−	5.48183i	−0.195507	−	0.601708i	0.804463	−	0.594002i	$-0.202453\pi$
$84$	0.370796	+	1.59257i	0.0404571	+	0.173763i
$85$	5.32624	+	16.3925i	0.577712	+	1.77801i
$86$	0.233733	+	2.22382i	0.0252041	+	0.239801i
$87$	−0.224307	+	2.13414i	−0.0240483	+	0.228804i
$88$	0.402863	−	3.83299i	0.0429454	−	0.408598i
$89$	0.617745	+	5.87746i	0.0654809	+	0.623009i	0.977218	+	0.212236i	$0.0680745\pi$
$89$	0.617745	+	5.87746i	0.0654809	+	0.623009i	−0.911738	+	0.410773i	$0.865259\pi$
$90$	−5.85410			−0.617077
$91$	−11.3079	+	10.5842i	−1.18539	+	1.10952i
$92$	0.454915	+	1.40008i	0.0474282	+	0.145969i
$93$	1.50000	−	2.59808i	0.155543	−	0.269408i
$94$	−6.18014	+	6.86374i	−0.637432	+	0.707940i
$95$	8.97733	−	9.97033i	0.921055	−	1.02293i
$96$	−0.413545	−	0.459289i	−0.0422073	−	0.0468760i
$97$	−3.47214	+	10.6861i	−0.352542	+	1.08501i	0.604879	+	0.796317i	$0.293221\pi$
$97$	−3.47214	+	10.6861i	−0.352542	+	1.08501i	−0.957421	+	0.288695i	$0.906779\pi$
$98$	1.90441	−	6.73597i	0.192374	−	0.680435i
$99$	−10.0902			−1.01410
$100$	3.34565	+	3.71572i	0.334565	+	0.371572i
$101$	−2.35410	−	4.07742i	−0.234242	−	0.405719i	0.724810	−	0.688949i	$-0.241927\pi$
$101$	−2.35410	−	4.07742i	−0.234242	−	0.405719i	−0.959052	+	0.283230i	$0.908594\pi$
$102$	4.35207	+	1.93767i	0.430919	+	0.191857i
$103$	1.97010	+	2.18802i	0.194120	+	0.215592i	0.832345	−	0.554258i	$-0.186998\pi$
$103$	1.97010	+	2.18802i	0.194120	+	0.215592i	−0.638225	+	0.769850i	$0.720331\pi$
$104$	1.80902	−	5.56758i	0.177389	−	0.545946i
$105$	−3.20120	−	1.76667i	−0.312405	−	0.172410i
$106$	0.0729490	+	0.224514i	0.00708543	+	0.0218067i
$107$	7.78115	−	13.4774i	0.752232	−	1.30290i	−0.194506	−	0.980901i	$-0.562310\pi$
$107$	7.78115	−	13.4774i	0.752232	−	1.30290i	0.946738	−	0.322003i	$-0.104356\pi$
$108$	−2.32331	+	2.58030i	−0.223561	+	0.248289i
$109$	0.129204	−	1.22930i	0.0123755	−	0.117745i	−0.986590	−	0.163218i	$-0.947813\pi$
$109$	0.129204	−	1.22930i	0.0123755	−	0.117745i	0.998966	+	0.0454725i	$0.0144793\pi$
$110$	5.76659	+	6.40445i	0.549823	+	0.610640i
$111$	−0.190983	+	0.138757i	−0.0181273	+	0.0131703i
$112$	0.599960	+	2.57683i	0.0566909	+	0.243487i
$113$	−5.19098	−	3.77147i	−0.488327	−	0.354790i	0.316214	−	0.948688i	$-0.397588\pi$
$113$	−5.19098	−	3.77147i	−0.488327	−	0.354790i	−0.804540	+	0.593898i	$0.797588\pi$
$114$	−0.387613	−	3.68789i	−0.0363033	−	0.345403i
$115$	−3.00721	−	1.33889i	−0.280423	−	0.124853i
$116$	−0.362937	+	3.45312i	−0.0336979	+	0.320614i
$117$	−14.9913	−	3.18650i	−1.38595	−	0.294592i
$118$	5.32624			0.490320
$119$	−12.3037	−	16.2645i	−1.12788	−	1.49096i
$120$	1.38197			0.126156
$121$	2.57890	+	2.86416i	0.234445	+	0.260378i
$122$	8.05609	−	1.71237i	0.729364	−	0.155031i
$123$	5.29708	+	2.35841i	0.477621	+	0.212651i
$124$	2.42705	−	4.20378i	0.217956	−	0.377510i
$125$	−11.1803			−1.00000
$126$	6.54508	−	2.26728i	0.583083	−	0.201986i
$127$	−7.28115	+	5.29007i	−0.646098	+	0.469418i	−0.861940	−	0.507011i	$-0.830750\pi$
$127$	−7.28115	+	5.29007i	−0.646098	+	0.469418i	0.215842	+	0.976428i	$0.430750\pi$
$128$	−0.669131	−	0.743145i	−0.0591433	−	0.0656853i
$129$	−1.35177	+	0.287327i	−0.119016	+	0.0252977i
$130$	6.54508	+	11.3364i	0.574042	+	0.994270i
$131$	6.64981	+	1.41346i	0.580997	+	0.123495i	0.489029	−	0.872267i	$-0.337351\pi$
$131$	6.64981	+	1.41346i	0.580997	+	0.123495i	0.0919675	+	0.995762i	$0.470684\pi$
$132$	2.38197			0.207324
$133$	−6.17547	+	14.6241i	−0.535481	+	1.26807i
$134$	−0.809017	−	0.587785i	−0.0698884	−	0.0507769i
$135$	−0.811552	−	7.72140i	−0.0698473	−	0.664552i
$136$	7.04179	+	3.13521i	0.603829	+	0.268842i
$137$	−0.258409	+	2.45859i	−0.0220773	+	0.210052i	0.977922	+	0.208970i	$0.0670111\pi$
$137$	−0.258409	+	2.45859i	−0.0220773	+	0.210052i	−0.999999	+	0.00108194i	$0.999656\pi$
$138$	−0.831171	+	0.370061i	−0.0707540	+	0.0315017i
$139$	−4.85410	+	3.52671i	−0.411720	+	0.299132i	−0.774298	−	0.632822i	$-0.781897\pi$
$139$	−4.85410	+	3.52671i	−0.411720	+	0.299132i	0.362578	+	0.931953i	$0.381897\pi$
$140$	−5.17965	−	2.85854i	−0.437760	−	0.241591i
$141$	−4.61803	−	3.35520i	−0.388909	−	0.282559i
$142$	15.5959	+	3.31500i	1.30877	+	0.278189i
$143$	11.2812	+	19.5395i	0.943377	+	1.63398i
$144$	−1.75181	+	1.94558i	−0.145984	+	0.162132i
$145$	−5.19508	−	5.76973i	−0.431428	−	0.479150i
$146$	−1.66312	+	5.11855i	−0.137641	+	0.423615i
$147$	4.26328	+	0.735384i	0.351629	+	0.0606534i
$148$	−0.309017	+	0.224514i	−0.0254010	+	0.0184549i
$149$	2.38197	−	4.12569i	0.195138	−	0.337989i	−0.751808	−	0.659383i	$-0.770818\pi$
$149$	2.38197	−	4.12569i	0.195138	−	0.337989i	0.946946	+	0.321393i	$0.104151\pi$
$150$	−2.06773	+	2.29644i	−0.168829	+	0.187504i
$151$	−8.80902	−	15.2577i	−0.716868	−	1.24165i	−0.962235	−	0.272221i	$-0.912242\pi$
$151$	−8.80902	−	15.2577i	−0.716868	−	1.24165i	0.245367	−	0.969430i	$-0.421091\pi$
$152$	−0.627171	−	5.96713i	−0.0508703	−	0.483998i
$153$	6.23607	−	19.1926i	0.504156	−	1.55163i
$154$	−8.92768	−	4.92700i	−0.719413	−	0.397029i
$155$	3.35410	+	10.3229i	0.269408	+	0.829152i
$156$	3.53897	+	0.752232i	0.283344	+	0.0602267i
$157$	0.690983	+	1.19682i	0.0551464	+	0.0955164i	0.892281	−	0.451481i	$-0.149104\pi$
$157$	0.690983	+	1.19682i	0.0551464	+	0.0955164i	−0.837134	+	0.546997i	$0.815771\pi$
$158$	−5.98489	+	6.64689i	−0.476132	+	0.528798i
$159$	−0.133284	+	0.0593421i	−0.0105701	+	0.00470613i
$160$	2.23607			0.176777
$161$	3.88071	+	0.332243i	0.305843	+	0.0261845i
$162$	4.61803	+	3.35520i	0.362827	+	0.263609i
$163$	−1.87800	+	0.836140i	−0.147096	+	0.0654915i	−0.478965	−	0.877834i	$-0.658988\pi$
$163$	−1.87800	+	0.836140i	−0.147096	+	0.0654915i	0.331868	+	0.943326i	$0.392321\pi$
$164$	8.57085	+	3.81599i	0.669271	+	0.297979i
$165$	−3.56395	+	3.95817i	−0.277453	+	0.308143i
$166$	5.26561	−	2.34440i	0.408691	−	0.181961i
$167$	0.0450850	+	0.138757i	0.00348878	+	0.0107374i	0.952786	−	0.303643i	$-0.0982031\pi$
$167$	0.0450850	+	0.138757i	0.00348878	+	0.0107374i	−0.949297	+	0.314381i	$0.898203\pi$
$168$	−1.54508	+	0.535233i	−0.119206	+	0.0412941i
$169$	6.57295	+	20.2295i	0.505611	+	1.55611i
$170$	−15.7459	+	7.01054i	−1.20766	+	0.537684i
$171$	−15.3649	+	3.26592i	−1.17499	+	0.249751i
$172$	−2.18720	+	0.464905i	−0.166773	+	0.0354486i
$173$	1.01478	+	9.65502i	0.0771526	+	0.734058i	0.962894	+	0.269879i	$0.0869837\pi$
$173$	1.01478	+	9.65502i	0.0771526	+	0.734058i	−0.885742	+	0.464179i	$0.846350\pi$
$174$	−2.14590			−0.162680
$175$	12.5000	−	4.33013i	0.944911	−	0.327327i
$176$	3.85410			0.290514
$177$	0.344086	+	3.27376i	0.0258631	+	0.246071i
$178$	−5.78069	+	1.22872i	−0.433281	+	0.0920967i
$179$	5.63798	−	1.19839i	0.421402	−	0.0895718i	0.00767029	−	0.999971i	$-0.497558\pi$
$179$	5.63798	−	1.19839i	0.421402	−	0.0895718i	0.413732	+	0.910399i	$0.364225\pi$
$180$	−0.611920	−	5.82203i	−0.0456098	−	0.433949i
$181$	−0.437694	−	1.34708i	−0.0325335	−	0.100128i	0.933471	−	0.358653i	$-0.116764\pi$
$181$	−0.437694	−	1.34708i	−0.0325335	−	0.100128i	−0.966005	+	0.258525i	$0.916764\pi$
$182$	−11.7082	−	10.1396i	−0.867870	−	0.751597i
$183$	1.57295	+	4.84104i	0.116276	+	0.357860i
$184$	−1.34486	+	0.598772i	−0.0991446	+	0.0441420i
$185$	0.0892780	−	0.849423i	0.00656385	−	0.0624508i
$186$	2.74064	+	1.22021i	0.200953	+	0.0894701i
$187$	−27.1398	+	12.0834i	−1.98466	+	0.883627i
$188$	−7.47214	−	5.42882i	−0.544962	−	0.395938i
$189$	3.89783	+	8.31848i	0.283525	+	0.605080i
$190$	10.8541	+	7.88597i	0.787439	+	0.572108i
$191$	−14.4011	+	6.41177i	−1.04202	+	0.463939i	−0.855115	−	0.518438i	$-0.826514\pi$
$191$	−14.4011	+	6.41177i	−1.04202	+	0.463939i	−0.186909	+	0.982377i	$0.559847\pi$
$192$	0.413545	−	0.459289i	0.0298451	−	0.0331463i
$193$	−11.8992	−	20.6100i	−0.856522	−	1.48354i	−0.875226	−	0.483715i	$-0.839287\pi$
$193$	−11.8992	−	20.6100i	−0.856522	−	1.48354i	0.0187034	−	0.999825i	$-0.494046\pi$
$194$	−10.9905	−	2.33611i	−0.789074	−	0.167723i
$195$	−6.54508	+	4.75528i	−0.468703	+	0.340533i
$196$	6.89813	+	1.18988i	0.492724	+	0.0849911i
$197$	7.37132	−	22.6866i	0.525185	−	1.61635i	−0.238765	−	0.971077i	$-0.576742\pi$
$197$	7.37132	−	22.6866i	0.525185	−	1.61635i	0.763950	−	0.645276i	$-0.223258\pi$
$198$	−1.05471	−	10.0349i	−0.0749550	−	0.713149i
$199$	11.2082	+	19.4132i	0.794529	+	1.37616i	0.923138	+	0.384468i	$0.125615\pi$
$199$	11.2082	+	19.4132i	0.794529	+	1.37616i	−0.128610	+	0.991695i	$0.541051\pi$
$200$	−3.34565	+	3.71572i	−0.236573	+	0.262741i
$201$	0.309017	−	0.535233i	0.0217964	−	0.0377524i
$202$	3.80902	−	2.76741i	0.268002	−	0.194714i
$203$	8.04289	+	4.43870i	0.564500	+	0.311536i
$204$	−1.47214	+	4.53077i	−0.103070	+	0.317217i
$205$	−19.1650	+	8.53281i	−1.33854	+	0.595957i
$206$	−1.97010	+	2.18802i	−0.137264	+	0.152447i
$207$	1.92705	+	3.33775i	0.133939	+	0.231990i
$208$	5.72618	+	1.21714i	0.397039	+	0.0843932i
$209$	18.7082	+	13.5923i	1.29407	+	0.940199i
$210$	1.42238	−	3.36833i	0.0981536	−	0.232437i
$211$	8.30902	−	6.03685i	0.572016	−	0.415594i	−0.263821	−	0.964572i	$-0.584983\pi$
$211$	8.30902	−	6.03685i	0.572016	−	0.415594i	0.835837	+	0.548978i	$0.184983\pi$
$212$	−0.215659	+	0.0960175i	−0.0148115	+	0.00659451i
$213$	−1.03003	+	9.80012i	−0.0705768	+	0.671493i
$214$	14.2169	+	6.32976i	0.971845	+	0.432693i
$215$	2.50000	−	4.33013i	0.170499	−	0.295312i
$216$	−2.80902	−	2.04087i	−0.191129	−	0.138864i
$217$	−7.74803	−	10.2423i	−0.525970	−	0.695291i
$218$	1.23607			0.0837171
$219$	−3.25355	−	0.691564i	−0.219855	−	0.0467315i
$220$	−5.76659	+	6.40445i	−0.388783	+	0.431788i
$221$	−44.1385	+	9.38193i	−2.96908	+	0.631097i
$222$	−0.157960	−	0.175433i	−0.0106016	−	0.0117743i
$223$	−8.59017	+	6.24112i	−0.575240	+	0.417937i	−0.837005	−	0.547195i	$-0.815696\pi$
$223$	−8.59017	+	6.24112i	−0.575240	+	0.417937i	0.261765	+	0.965132i	$0.415696\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$	10.5902	+	7.69421i	0.706011	+	0.512947i
$226$	3.20820	−	5.55677i	0.213407	−	0.369631i
$227$	−18.2200	−	8.11207i	−1.20930	−	0.538417i	−0.299756	−	0.954016i	$-0.596905\pi$
$227$	−18.2200	−	8.11207i	−1.20930	−	0.538417i	−0.909548	+	0.415599i	$0.863572\pi$
$228$	3.62717	−	0.770979i	0.240215	−	0.0510593i
$229$	8.24786	+	9.16018i	0.545034	+	0.605322i	0.951237	−	0.308461i	$-0.0998140\pi$
$229$	8.24786	+	9.16018i	0.545034	+	0.605322i	−0.406203	+	0.913783i	$0.633147\pi$
$230$	1.01722	−	3.13068i	0.0670736	−	0.206431i
$231$	2.45162	−	5.80568i	0.161305	−	0.381985i
$232$	−3.47214			−0.227957
$233$	25.2683	+	5.37094i	1.65538	+	0.351862i	0.938486	−	0.345318i	$-0.112229\pi$
$233$	25.2683	+	5.37094i	1.65538	+	0.351862i	0.716896	+	0.697180i	$0.245562\pi$
$234$	1.60203	−	15.2423i	0.104728	−	0.996419i
$235$	20.2012	−	4.29389i	1.31778	−	0.280103i
$236$	0.556743	+	5.29706i	0.0362409	+	0.344809i
$237$	−4.47214	−	3.24920i	−0.290496	−	0.211058i
$238$	14.8893	−	13.9364i	0.965131	−	0.903362i
$239$	−4.59017	+	3.33495i	−0.296913	+	0.215720i	−0.726261	−	0.687419i	$-0.758744\pi$
$239$	−4.59017	+	3.33495i	−0.296913	+	0.215720i	0.429347	+	0.903139i	$0.358744\pi$
$240$	0.144455	+	1.37440i	0.00932452	+	0.0887168i
$241$	1.13456	−	10.7946i	0.0730836	−	0.695344i	−0.895230	−	0.445605i	$-0.852989\pi$
$241$	1.13456	−	10.7946i	0.0730836	−	0.695344i	0.968313	−	0.249739i	$-0.0803448\pi$
$242$	−2.57890	+	2.86416i	−0.165778	+	0.184115i
$243$	−6.97214	+	12.0761i	−0.447263	+	0.774682i
$244$	2.54508	+	7.83297i	0.162932	+	0.501454i
$245$	−12.2984	+	9.68246i	−0.785714	+	0.618590i
$246$	−1.79180	+	5.51458i	−0.114241	+	0.351597i
$247$	23.5030	+	26.1027i	1.49546	+	1.66087i
$248$	4.43444	+	1.97434i	0.281587	+	0.125371i
$249$	1.78115	+	3.08505i	0.112876	+	0.195507i
$250$	−1.16866	−	11.1191i	−0.0739128	−	0.703233i
$251$	31.1803			1.96809			0.984043	−	0.177932i	$-0.0569407\pi$
$251$	31.1803			1.96809			0.984043	+	0.177932i	$0.0569407\pi$
$252$	2.93901	+	6.27223i	0.185140	+	0.395114i
$253$	1.75329	−	5.39607i	0.110228	−	0.339248i
$254$	−6.02218	−	6.68830i	−0.377865	−	0.419661i
$255$	−5.32624	−	9.22531i	−0.333542	−	0.577712i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	15.0172	−	26.0106i	0.936749	−	1.62250i	0.165263	−	0.986250i	$-0.447153\pi$
$257$	15.0172	−	26.0106i	0.936749	−	1.62250i	0.771486	−	0.636246i	$-0.219514\pi$
$258$	−0.427051	−	1.31433i	−0.0265870	−	0.0818265i
$259$	0.229164	+	0.984261i	0.0142396	+	0.0611590i
$260$	−10.5902	+	7.69421i	−0.656774	+	0.477175i
$261$	0.950181	+	9.04037i	0.0588148	+	0.559585i
$262$	−0.710624	+	6.76113i	−0.0439025	+	0.417704i
$263$	0.344086	−	3.27376i	0.0212173	−	0.201869i	−0.978778	−	0.204923i	$-0.934306\pi$
$263$	0.344086	−	3.27376i	0.0212173	−	0.201869i	0.999995	+	0.00305429i	$0.000972211\pi$
$264$	0.248983	+	2.36892i	0.0153239	+	0.145797i
$265$	0.163119	−	0.502029i	0.0100203	−	0.0308394i
$266$	−15.1895	−	4.61300i	−0.931327	−	0.282841i
$267$	−1.12868	−	3.47371i	−0.0690739	−	0.212588i
$268$	0.500000	−	0.866025i	0.0305424	−	0.0529009i
$269$	12.2626	−	13.6190i	0.747667	−	0.830368i	−0.242516	−	0.970147i	$-0.577973\pi$
$269$	12.2626	−	13.6190i	0.747667	−	0.830368i	0.990183	+	0.139779i	$0.0446393\pi$
$270$	7.59427	−	1.61421i	0.462173	−	0.0982378i
$271$	8.08990	+	8.98475i	0.491427	+	0.545785i	0.936940	−	0.349491i	$-0.113645\pi$
$271$	8.08990	+	8.98475i	0.491427	+	0.545785i	−0.445513	+	0.895275i	$0.646979\pi$
$272$	−2.38197	+	7.33094i	−0.144428	+	0.444503i
$273$	5.47591	−	7.85147i	0.331417	−	0.475192i
$274$	−2.47214			−0.149347
$275$	−2.01432	−	19.1649i	−0.121468	−	1.15569i
$276$	−0.454915	−	0.787936i	−0.0273827	−	0.0474282i
$277$	5.86168	+	2.60979i	0.352194	+	0.156807i	0.575206	−	0.818009i	$-0.304922\pi$
$277$	5.86168	+	2.60979i	0.352194	+	0.156807i	−0.223011	+	0.974816i	$0.571589\pi$
$278$	−4.01478	−	4.45887i	−0.240791	−	0.267425i
$279$	3.92705	−	12.0862i	0.235106	−	0.723583i
$280$	2.30146	−	5.45007i	0.137539	−	0.325704i
$281$	5.25329	+	16.1680i	0.313385	+	0.964500i	0.976414	+	0.215906i	$0.0692705\pi$
$281$	5.25329	+	16.1680i	0.313385	+	0.964500i	−0.663029	+	0.748594i	$0.730729\pi$
$282$	2.85410	−	4.94345i	0.169959	−	0.294378i
$283$	7.73669	−	8.59247i	0.459899	−	0.510769i	−0.467935	−	0.883763i	$-0.655002\pi$
$283$	7.73669	−	8.59247i	0.459899	−	0.510769i	0.927834	+	0.372994i	$0.121669\pi$
$284$	−1.66663	+	15.8569i	−0.0988963	+	0.940936i
$285$	−4.14590	+	7.18091i	−0.245582	+	0.425360i
$286$	−18.2533	+	13.2618i	−1.07934	+	0.784186i
$287$	18.1224	−	16.9625i	1.06973	−	1.00127i
$288$	−2.11803	−	1.53884i	−0.124806	−	0.0906771i
$289$	−4.43372	−	42.1840i	−0.260807	−	2.48141i
$290$	5.19508	−	5.76973i	0.305066	−	0.338810i
$291$	0.725874	−	6.90623i	0.0425515	−	0.404850i
$292$	−5.26436	−	1.11897i	−0.308073	−	0.0654830i
$293$	−1.09017			−0.0636884			−0.0318442	−	0.999493i	$-0.510138\pi$
$293$	−1.09017			−0.0636884			−0.0318442	+	0.999493i	$0.510138\pi$
$294$	−0.285721	+	4.31679i	−0.0166636	+	0.251760i
$295$	−9.63525	−	7.00042i	−0.560986	−	0.407580i
$296$	−0.255585	−	0.283856i	−0.0148556	−	0.0164988i
$297$	13.0895	−	2.78227i	0.759532	−	0.161444i
$298$	4.35207	+	1.93767i	0.252109	+	0.112246i
$299$	4.30902	−	7.46344i	0.249197	−	0.431622i
$300$	−2.50000	−	1.81636i	−0.144338	−	0.104867i
$301$	−1.11803	+	5.80948i	−0.0644424	+	0.334853i
$302$	14.2533	−	10.3556i	0.820185	−	0.595899i
$303$	1.94706	+	2.16243i	0.111855	+	0.124228i
$304$	5.86889	−	1.24747i	0.336604	−	0.0715473i
$305$	−16.8242	−	7.49063i	−0.963352	−	0.428912i
$306$	19.7394	+	4.19573i	1.12842	+	0.239854i
$307$	13.1246			0.749061			0.374531	−	0.927215i	$-0.377804\pi$
$307$	13.1246			0.749061			0.374531	+	0.927215i	$0.377804\pi$
$308$	3.96681	−	9.39378i	0.226030	−	0.535260i
$309$	−1.47214	−	1.06957i	−0.0837469	−	0.0608457i
$310$	−9.91572	+	4.41476i	−0.563175	+	0.250742i
$311$	3.27377	+	1.45758i	0.185639	+	0.0826517i	0.497451	−	0.867492i	$-0.334269\pi$
$311$	3.27377	+	1.45758i	0.185639	+	0.0826517i	−0.311812	+	0.950144i	$0.600936\pi$
$312$	−0.378188	+	3.59821i	−0.0214107	+	0.203709i
$313$	−20.5293	+	9.14024i	−1.16039	+	0.516637i	−0.894368	−	0.447331i	$-0.852374\pi$
$313$	−20.5293	+	9.14024i	−1.16039	+	0.516637i	−0.266017	+	0.963968i	$0.585708\pi$
$314$	−1.11803	+	0.812299i	−0.0630943	+	0.0458407i
$315$	−14.8201	−	4.50083i	−0.835019	−	0.253593i
$316$	−7.23607	−	5.25731i	−0.407061	−	0.295747i
$317$	−25.1801	−	5.35220i	−1.41426	−	0.300609i	−0.563476	−	0.826132i	$-0.690536\pi$
$317$	−25.1801	−	5.35220i	−1.41426	−	0.300609i	−0.850779	+	0.525523i	$0.823870\pi$
$318$	−0.0729490	−	0.126351i	−0.00409078	−	0.00708543i
$319$	8.95428	−	9.94474i	0.501344	−	0.556798i
$320$	0.233733	+	2.22382i	0.0130661	+	0.124315i
$321$	−2.97214	+	9.14729i	−0.165888	+	0.510552i
$322$	0.0752212	+	3.89418i	0.00419191	+	0.217014i
$323$	−37.4164	+	27.1846i	−2.08190	+	1.51259i
$324$	−2.85410	+	4.94345i	−0.158561	+	0.274636i
$325$	3.05960	−	29.1102i	0.169716	−	1.61474i
$326$	−1.02786	−	1.78031i	−0.0569281	−	0.0986024i
$327$	0.0798526	+	0.759747i	0.00441586	+	0.0420141i
$328$	−2.89919	+	8.92278i	−0.160081	+	0.492678i
$329$	−20.9226	+	12.6246i	−1.15350	+	0.696016i
$330$	−4.30902	−	3.13068i	−0.237204	−	0.172338i
$331$	27.8836	+	5.92685i	1.53262	+	0.325769i	0.895524	−	0.445013i	$-0.146801\pi$
$331$	27.8836	+	5.92685i	1.53262	+	0.325769i	0.637099	+	0.770782i	$0.280134\pi$
$332$	2.88197	+	4.99171i	0.158168	+	0.273956i
$333$	−0.669131	+	0.743145i	−0.0366681	+	0.0407241i
$334$	−0.133284	+	0.0593421i	−0.00729300	+	0.00324705i
$335$	0.690983	+	2.12663i	0.0377524	+	0.116190i
$336$	−0.693806	−	1.48067i	−0.0378502	−	0.0807774i
$337$	−18.3713	−	13.3475i	−1.00075	−	0.727087i	−0.0385009	−	0.999259i	$-0.512258\pi$
$337$	−18.3713	−	13.3475i	−1.00075	−	0.727087i	−0.962249	+	0.272171i	$0.912258\pi$
$338$	−19.4316	+	8.65150i	−1.05694	+	0.470579i
$339$	3.62272	+	1.61294i	0.196759	+	0.0876028i
$340$	−8.61803	−	14.9269i	−0.467379	−	0.809523i
$341$	−17.0908	+	7.60931i	−0.925518	+	0.412067i
$342$	−4.85410	−	14.9394i	−0.262480	−	0.807830i
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−0.690983	−	2.12663i	−0.0372553	−	0.114660i
$345$	1.98998	+	0.422984i	0.107137	+	0.0227727i
$346$	−9.49606	+	2.01845i	−0.510511	+	0.108512i
$347$	7.25434	−	1.54196i	0.389433	−	0.0827766i	−0.00903380	−	0.999959i	$-0.502876\pi$
$347$	7.25434	−	1.54196i	0.389433	−	0.0827766i	0.398467	+	0.917183i	$0.369542\pi$
$348$	−0.224307	−	2.13414i	−0.0120241	−	0.114402i
$349$	23.6180			1.26424			0.632122	−	0.774869i	$-0.282184\pi$
$349$	23.6180			1.26424			0.632122	+	0.774869i	$0.282184\pi$
$350$	5.61301	+	11.9789i	0.300028	+	0.640299i
$351$	20.3262			1.08493
$352$	0.402863	+	3.83299i	0.0214727	+	0.204299i
$353$	13.7278	−	2.91792i	0.730655	−	0.155305i	0.172461	−	0.985016i	$-0.444828\pi$
$353$	13.7278	−	2.91792i	0.730655	−	0.155305i	0.558193	+	0.829711i	$0.311495\pi$
$354$	−3.21986	+	0.684403i	−0.171134	+	0.0363756i
$355$	−23.8562	−	26.4950i	−1.26615	−	1.40621i
$356$	−1.82624	−	5.62058i	−0.0967904	−	0.297890i
$357$	9.52786	+	8.25137i	0.504268	+	0.436709i
$358$	1.78115	+	5.48183i	0.0941369	+	0.289723i
$359$	−1.61143	+	0.717456i	−0.0850481	+	0.0378659i	−0.448820	−	0.893622i	$-0.648156\pi$
$359$	−1.61143	+	0.717456i	−0.0850481	+	0.0378659i	0.363772	+	0.931488i	$0.381489\pi$
$360$	5.72618	−	1.21714i	0.301796	−	0.0641487i
$361$	15.5303	+	6.91452i	0.817383	+	0.363922i
$362$	1.29395	−	0.576105i	0.0680087	−	0.0302794i
$363$	−1.92705	−	1.40008i	−0.101144	−	0.0734854i
$364$	8.86022	−	12.7039i	0.464401	−	0.665867i
$365$	9.73607	−	7.07367i	0.509609	−	0.370253i
$366$	−4.65010	+	2.07036i	−0.243065	+	0.108219i
$367$	−22.0440	+	24.4824i	−1.15069	+	1.27797i	−0.195920	+	0.980620i	$0.562769\pi$
$367$	−22.0440	+	24.4824i	−1.15069	+	1.27797i	−0.954769	+	0.297349i	$0.903897\pi$
$368$	−0.736068	−	1.27491i	−0.0383702	−	0.0664591i
$369$	24.0256	+	5.10679i	1.25072	+	0.265849i
$370$	0.854102			0.0444026
$371$	0.0120623	+	0.624461i	0.000626242	+	0.0324204i
$372$	−0.927051	+	2.85317i	−0.0480654	+	0.147930i
$373$	0.172731	+	1.64342i	0.00894366	+	0.0850932i	0.998083	−	0.0618861i	$-0.0197116\pi$
$373$	0.172731	+	1.64342i	0.00894366	+	0.0850932i	−0.989140	+	0.146979i	$0.953045\pi$
$374$	−14.8541	−	25.7281i	−0.768087	−	1.33037i
$375$	6.75883	−	1.43663i	0.349025	−	0.0741875i
$376$	4.61803	−	7.99867i	0.238157	−	0.412500i
$377$	16.4443	−	11.9475i	0.846923	−	0.615326i
$378$	−7.86547	+	4.74599i	−0.404556	+	0.244108i
$379$	−1.87132	+	5.75934i	−0.0961234	+	0.295837i	−0.987545	−	0.157338i	$-0.949709\pi$
$379$	−1.87132	+	5.75934i	−0.0961234	+	0.295837i	0.891421	+	0.453175i	$0.149709\pi$
$380$	−6.70820	+	11.6190i	−0.344124	+	0.596040i
$381$	3.72191	−	4.13360i	0.190679	−	0.211771i
$382$	−7.88197	−	13.6520i	−0.403276	−	0.698495i
$383$	−19.5630	−	4.15823i	−0.999620	−	0.212476i	−0.321090	−	0.947049i	$-0.604049\pi$
$383$	−19.5630	−	4.15823i	−0.999620	−	0.212476i	−0.678530	+	0.734573i	$0.737383\pi$
$384$	0.500000	+	0.363271i	0.0255155	+	0.0185381i
$385$	9.67463	+	20.6469i	0.493065	+	1.05226i
$386$	19.2533	−	13.9883i	0.979967	−	0.711987i
$387$	−5.34799	+	2.38108i	−0.271854	+	0.121037i
$388$	1.17449	−	11.1745i	0.0596256	−	0.567300i
$389$	−6.47719	−	2.88383i	−0.328407	−	0.146216i	0.235909	−	0.971775i	$-0.424193\pi$
$389$	−6.47719	−	2.88383i	−0.328407	−	0.146216i	−0.564316	+	0.825559i	$0.690860\pi$
$390$	−5.41338	−	6.01217i	−0.274117	−	0.304438i
$391$	9.18034	+	6.66991i	0.464270	+	0.337312i
$392$	−0.462307	+	6.98472i	−0.0233500	+	0.352781i
$393$	−4.20163			−0.211944
$394$	23.3328	+	4.95955i	1.17549	+	0.249858i
$395$	19.5630	−	4.15823i	0.984319	−	0.209223i
$396$	9.86968	−	2.09786i	0.495970	−	0.105422i
$397$	−14.4510	−	16.0495i	−0.725277	−	0.805502i	0.261906	−	0.965093i	$-0.415649\pi$
$397$	−14.4510	−	16.0495i	−0.725277	−	0.805502i	−0.987183	+	0.159592i	$0.948982\pi$
$398$	−18.1353	+	13.1760i	−0.909038	+	0.660455i
$399$	1.85410	−	9.63420i	0.0928212	−	0.482313i
$400$	−4.04508	−	2.93893i	−0.202254	−	0.146946i
$401$	−10.2361	+	17.7294i	−0.511165	+	0.885363i	0.488751	+	0.872423i	$0.337453\pi$
$401$	−10.2361	+	17.7294i	−0.511165	+	0.885363i	−0.999916	+	0.0129404i	$0.995881\pi$
$402$	0.564602	+	0.251377i	0.0281598	+	0.0125375i
$403$	−27.7954	+	5.90810i	−1.38459	+	0.294304i
$404$	3.15040	+	3.49888i	0.156738	+	0.174076i
$405$	−3.94427	−	12.1392i	−0.195992	−	0.603203i
$406$	−3.57368	+	8.46280i	−0.177359	+	0.420002i
$407$	1.47214			0.0729711
$408$	−4.65983	−	0.990477i	−0.230696	−	0.0490359i
$409$	0.153880	−	1.46407i	0.00760888	−	0.0723937i	−0.990059	−	0.140656i	$-0.955079\pi$
$409$	0.153880	−	1.46407i	0.00760888	−	0.0723937i	0.997667	+	0.0682624i	$0.0217455\pi$
$410$	−10.4894	−	18.1681i	−0.518032	−	0.897258i
$411$	−0.159705	−	1.51949i	−0.00787768	−	0.0749511i
$412$	−2.38197	−	1.73060i	−0.117351	−	0.0852605i
$413$	13.4838	+	4.09499i	0.663494	+	0.201501i
$414$	−3.11803	+	2.26538i	−0.153243	+	0.111338i
$415$	−12.6069	−	2.67968i	−0.618848	−	0.131540i
$416$	−0.611920	+	5.82203i	−0.0300019	+	0.285449i
$417$	2.48127	−	2.75573i	0.121508	−	0.134949i
$418$	−11.5623	+	20.0265i	−0.565531	+	0.979528i
$419$	−3.78115	−	11.6372i	−0.184721	−	0.568514i	0.815222	−	0.579149i	$-0.196615\pi$
$419$	−3.78115	−	11.6372i	−0.184721	−	0.568514i	−0.999943	+	0.0106345i	$0.996615\pi$
$420$	3.49856	+	1.06250i	0.170712	+	0.0518448i
$421$	7.44427	−	22.9111i	0.362812	−	1.11662i	−0.588528	−	0.808476i	$-0.700293\pi$
$421$	7.44427	−	22.9111i	0.362812	−	1.11662i	0.951340	−	0.308143i	$-0.0997075\pi$
$422$	6.87231	+	7.63248i	0.334539	+	0.371543i
$423$	−22.0898	−	9.83503i	−1.07404	−	0.478196i
$424$	−0.118034	−	0.204441i	−0.00573224	−	0.00992853i
$425$	37.6988	+	8.01313i	1.82866	+	0.388694i
$426$	−9.85410			−0.477433
$427$	21.7112	+	1.85878i	1.05068	+	0.0899528i
$428$	−4.80902	+	14.8006i	−0.232453	+	0.715416i
$429$	−9.33054	−	10.3626i	−0.450483	−	0.500312i
$430$	4.56773	+	2.03368i	0.220275	+	0.0980729i
$431$	−18.0896	+	20.0905i	−0.871344	+	0.967726i	−0.999712	−	0.0240010i	$-0.992360\pi$
$431$	−18.0896	+	20.0905i	−0.871344	+	0.967726i	0.128368	+	0.991727i	$0.459026\pi$
$432$	1.73607	−	3.00696i	0.0835266	−	0.144672i
$433$	7.01722	+	21.5968i	0.337226	+	1.03788i	0.965615	+	0.259976i	$0.0837146\pi$
$433$	7.01722	+	21.5968i	0.337226	+	1.03788i	−0.628389	+	0.777899i	$0.716285\pi$
$434$	9.37628	−	8.77619i	0.450076	−	0.421271i
$435$	3.88197	+	2.82041i	0.186126	+	0.135228i
$436$	0.129204	+	1.22930i	0.00618776	+	0.0588726i
$437$	0.923281	−	8.78443i	0.0441665	−	0.420216i
$438$	0.347687	−	3.30802i	0.0166131	−	0.158063i
$439$	−0.412289	−	3.92266i	−0.0196775	−	0.187219i	0.980268	−	0.197674i	$-0.0633386\pi$
$439$	−0.412289	−	3.92266i	−0.0196775	−	0.187219i	−0.999945	+	0.0104551i	$0.996672\pi$
$440$	−6.97214	−	5.06555i	−0.332384	−	0.241491i
$441$	18.3126	−	0.707726i	0.872027	−	0.0337013i
$442$	−13.9443	−	42.9161i	−0.663261	−	2.04131i
$443$	−1.57295	+	2.72443i	−0.0747331	+	0.129441i	−0.900970	−	0.433881i	$-0.857144\pi$
$443$	−1.57295	+	2.72443i	−0.0747331	+	0.129441i	0.826237	+	0.563323i	$0.190477\pi$
$444$	0.157960	−	0.175433i	0.00749646	−	0.00832567i
$445$	12.0723	+	5.37494i	0.572282	+	0.254796i
$446$	−7.10485	−	7.89074i	−0.336424	−	0.373637i
$447$	−0.909830	+	2.80017i	−0.0430335	+	0.132443i
$448$	−1.12260	−	2.39578i	−0.0530380	−	0.113190i
$449$	4.96556			0.234339			0.117170	−	0.993112i	$-0.462618\pi$
$449$	4.96556			0.234339			0.117170	+	0.993112i	$0.462618\pi$
$450$	−6.54508	+	11.3364i	−0.308538	+	0.534404i
$451$	−18.0795	−	31.3147i	−0.851332	−	1.47455i
$452$	5.86168	+	2.60979i	0.275710	+	0.122754i
$453$	7.28586	+	8.09176i	0.342319	+	0.380184i
$454$	6.16312	−	18.9681i	0.289250	−	0.890218i
$455$	7.85358	+	33.7311i	0.368181	+	1.58134i
$456$	1.14590	+	3.52671i	0.0536616	+	0.165153i
$457$	5.38197	−	9.32184i	0.251758	−	0.436057i	−0.712252	−	0.701924i	$-0.752325\pi$
$457$	5.38197	−	9.32184i	0.251758	−	0.436057i	0.964010	+	0.265867i	$0.0856580\pi$
$458$	−8.24786	+	9.16018i	−0.385397	+	0.428027i
$459$	−2.79759	+	26.6173i	−0.130580	+	1.24239i
$460$	3.21986	+	0.684403i	0.150127	+	0.0319104i
$461$	−28.3713	+	20.6130i	−1.32138	+	0.960042i	−0.321470	+	0.946920i	$0.604177\pi$
$461$	−28.3713	+	20.6130i	−1.32138	+	0.960042i	−0.999914	+	0.0131222i	$0.995823\pi$
$462$	6.03014	+	1.83134i	0.280547	+	0.0852015i
$463$	−9.51722	−	6.91467i	−0.442303	−	0.321352i	0.344246	−	0.938879i	$-0.388134\pi$
$463$	−9.51722	−	6.91467i	−0.442303	−	0.321352i	−0.786549	+	0.617528i	$0.788134\pi$
$464$	−0.362937	−	3.45312i	−0.0168489	−	0.160307i
$465$	−3.35410	−	5.80948i	−0.155543	−	0.269408i
$466$	−2.70026	+	25.6913i	−0.125087	+	1.19013i
$467$	4.85705	+	1.03240i	0.224757	+	0.0477737i	0.318914	−	0.947784i	$-0.396682\pi$
$467$	4.85705	+	1.03240i	0.224757	+	0.0477737i	−0.0941563	+	0.995557i	$0.530015\pi$
$468$	15.3262			0.708456
$469$	−1.59618	−	2.11002i	−0.0737048	−	0.0974319i
$470$	6.38197	+	19.6417i	0.294378	+	0.906003i
$471$	−0.571506	−	0.634721i	−0.0263336	−	0.0292464i
$472$	−5.20985	+	1.10739i	−0.239803	+	0.0509716i
$473$	7.87297	+	3.50527i	0.361999	+	0.161172i
$474$	2.76393	−	4.78727i	0.126952	−	0.219887i
$475$	−9.27051	−	28.5317i	−0.425360	−	1.30912i
$476$	15.4164	+	13.3510i	0.706610	+	0.611942i
$477$	−0.500000	+	0.363271i	−0.0228934	+	0.0166330i
$478$	−3.79649	−	4.21643i	−0.173647	−	0.192855i
$479$	−5.58347	+	1.18680i	−0.255115	+	0.0542264i	−0.333694	−	0.942682i	$-0.608295\pi$
$479$	−5.58347	+	1.18680i	−0.255115	+	0.0542264i	0.0785787	+	0.996908i	$0.474962\pi$
$480$	−1.35177	+	0.287327i	−0.0616994	+	0.0131146i
$481$	2.18720	+	0.464905i	0.0997279	+	0.0211978i
$482$	10.8541			0.494391
$483$	−2.38869	+	0.297807i	−0.108689	+	0.0135507i
$484$	−3.11803	−	2.26538i	−0.141729	−	0.102972i
$485$	16.8116	+	18.6712i	0.763378	+	0.847817i
$486$	−12.7387	−	5.67165i	−0.577840	−	0.257271i
$487$	−4.24352	+	40.3744i	−0.192292	+	1.82954i	0.294075	+	0.955782i	$0.404988\pi$
$487$	−4.24352	+	40.3744i	−0.192292	+	1.82954i	−0.486367	+	0.873754i	$0.661678\pi$
$488$	−7.52402	+	3.34991i	−0.340596	+	0.151643i
$489$	1.02786	−	0.746787i	0.0464816	−	0.0337709i
$490$	−10.9149	−	11.2189i	−0.493087	−	0.506819i
$491$	17.1074	+	12.4292i	0.772046	+	0.560924i	0.902581	−	0.430520i	$-0.141670\pi$
$491$	17.1074	+	12.4292i	0.772046	+	0.560924i	−0.130536	+	0.991444i	$0.541670\pi$
$492$	−5.67167	−	1.20555i	−0.255698	−	0.0543504i
$493$	13.3820	+	23.1782i	0.602693	+	1.04390i
$494$	−23.5030	+	26.1027i	−1.05745	+	1.17441i
$495$	−11.2812	+	19.5395i	−0.507050	+	0.878237i
$496$	−1.50000	+	4.61653i	−0.0673520	+	0.207288i
$497$	36.9335	+	20.3828i	1.65669	+	0.914294i
$498$	−2.88197	+	2.09387i	−0.129144	+	0.0938286i
$499$	−6.00000	+	10.3923i	−0.268597	+	0.465223i	−0.968500	−	0.249015i	$-0.919893\pi$
$499$	−6.00000	+	10.3923i	−0.268597	+	0.465223i	0.699903	+	0.714238i	$0.253227\pi$
$500$	10.9360	−	2.32452i	0.489074	−	0.103956i
$501$	−0.0450850	−	0.0780895i	−0.00201425	−	0.00348878i
$502$	3.25923	+	31.0095i	0.145467	+	1.38402i
$503$	−5.70820	+	17.5680i	−0.254516	+	0.783320i	0.739408	+	0.673257i	$0.235105\pi$
$503$	−5.70820	+	17.5680i	−0.254516	+	0.783320i	−0.993925	+	0.110063i	$0.964895\pi$
$504$	−5.93066	+	3.57854i	−0.264173	+	0.159401i
$505$	−10.5279			−0.468484
$506$	5.54978	+	1.17964i	0.246718	+	0.0524415i
$507$	−6.57295	−	11.3847i	−0.291915	−	0.505611i
$508$	6.02218	−	6.68830i	0.267191	−	0.296745i
$509$	−5.03051	+	2.23973i	−0.222973	+	0.0992742i	−0.515183	−	0.857080i	$-0.672276\pi$
$509$	−5.03051	+	2.23973i	−0.222973	+	0.0992742i	0.292210	+	0.956354i	$0.405609\pi$
$510$	8.61803	−	6.26137i	0.381613	−	0.277258i
$511$	−8.14564	+	11.6794i	−0.360342	+	0.516665i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	19.0317	−	8.47347i	0.840271	−	0.374113i
$514$	27.4378	+	12.2161i	1.21023	+	0.538829i
$515$	6.43972	−	1.36881i	0.283768	−	0.0603168i
$516$	1.26249	−	0.562096i	0.0555780	−	0.0247449i
$517$	11.0000	+	33.8545i	0.483779	+	1.48892i
$518$	−0.954915	+	0.330792i	−0.0419566	+	0.0145342i
$519$	−1.85410	−	5.70634i	−0.0813860	−	0.250480i
$520$	−8.75903	−	9.72789i	−0.384109	−	0.426596i
$521$	20.1675	−	4.28673i	0.883553	−	0.187805i	0.256278	−	0.966603i	$-0.417504\pi$
$521$	20.1675	−	4.28673i	0.883553	−	0.187805i	0.627275	+	0.778798i	$0.284170\pi$
$522$	−8.89153	+	1.88995i	−0.389172	+	0.0827210i
$523$	−1.10046	−	10.4702i	−0.0481198	−	0.457829i	−0.991878	−	0.127193i	$-0.959403\pi$
$523$	−1.10046	−	10.4702i	−0.0481198	−	0.457829i	0.943758	−	0.330637i	$-0.107263\pi$
$524$	−6.79837			−0.296988
$525$	−7.00020	+	4.22389i	−0.305514	+	0.184346i
$526$	3.29180			0.143529
$527$	−3.91108	−	37.2114i	−0.170369	−	1.62096i
$528$	−2.32991	+	0.495239i	−0.101397	+	0.0215525i
$529$	20.3776	−	4.33139i	0.885981	−	0.188321i
$530$	0.516329	+	0.109749i	0.0224279	+	0.00476720i
$531$	4.30902	+	13.2618i	0.186995	+	0.575513i
$532$	3.00000	−	15.5885i	0.130066	−	0.675845i
$533$	−16.9721	−	52.2349i	−0.735145	−	2.26254i
$534$	3.33670	−	1.48560i	0.144393	−	0.0642880i
$535$	−17.3992	−	30.1363i	−0.752232	−	1.30290i
$536$	0.913545	+	0.406737i	0.0394592	+	0.0175683i
$537$	−3.25433	+	1.44892i	−0.140435	+	0.0625255i
$538$	14.8262	+	10.7719i	0.639205	+	0.464409i
$539$	−18.8131	−	19.3370i	−0.810337	−	0.832903i
$540$	2.39919	+	7.38394i	0.103245	+	0.317754i
$541$	−22.1407	+	9.85770i	−0.951905	+	0.423815i	−0.823127	−	0.567858i	$-0.807772\pi$
$541$	−22.1407	+	9.85770i	−0.951905	+	0.423815i	−0.128779	+	0.991673i	$0.541106\pi$
$542$	−8.08990	+	8.98475i	−0.347491	+	0.385928i
$543$	0.437694	+	0.758108i	0.0187833	+	0.0325335i
$544$	−7.53976	−	1.60263i	−0.323265	−	0.0687120i
$545$	−2.23607	−	1.62460i	−0.0957826	−	0.0695902i
$546$	8.38085	+	4.62521i	0.358667	+	0.197941i
$547$	−3.50658	+	10.7921i	−0.149930	+	0.461438i	−0.997612	−	0.0690669i	$-0.977998\pi$
$547$	−3.50658	+	10.7921i	−0.149930	+	0.461438i	0.847682	+	0.530505i	$0.177998\pi$
$548$	−0.258409	−	2.45859i	−0.0110387	−	0.105026i
$549$	10.7812	+	18.6735i	0.460128	+	0.796966i
$550$	18.8494	−	4.00656i	0.803741	−	0.170840i
$551$	10.4164	−	18.0417i	0.443754	−	0.768604i
$552$	0.736068	−	0.534785i	0.0313291	−	0.0227619i
$553$	−20.2616	+	12.2257i	−0.861610	+	0.519892i
$554$	−1.98278	+	6.10237i	−0.0842402	+	0.259265i
$555$	0.0551768	+	0.524972i	0.00234213	+	0.0222838i
$556$	4.01478	−	4.45887i	0.170265	−	0.189098i
$557$	−2.90983	−	5.03997i	−0.123293	−	0.213551i	0.797771	−	0.602960i	$-0.206012\pi$
$557$	−2.90983	−	5.03997i	−0.123293	−	0.213551i	−0.921065	+	0.389410i	$0.872679\pi$
$558$	12.4305	+	2.64218i	0.526225	+	0.111853i
$559$	10.5902	+	7.69421i	0.447916	+	0.325430i
$560$	5.66078	+	1.71916i	0.239212	+	0.0726480i
$561$	14.8541	−	10.7921i	0.627141	−	0.455644i
$562$	−15.5303	+	6.91452i	−0.655105	+	0.291672i
$563$	0.429764	−	4.08893i	0.0181124	−	0.172328i	−0.981726	−	0.190299i	$-0.939054\pi$
$563$	0.429764	−	4.08893i	0.0181124	−	0.172328i	0.999839	+	0.0179714i	$0.00572079\pi$
$564$	5.21470	+	2.32174i	0.219579	+	0.0977627i
$565$	−13.1071	+	5.83566i	−0.551420	+	0.245508i
$566$	9.35410	+	6.79615i	0.393182	+	0.285664i
$567$	9.11133	+	12.0445i	0.382640	+	0.505819i
$568$	−15.9443			−0.669007
$569$	−25.6964	−	5.46195i	−1.07725	−	0.228977i	−0.365075	−	0.930978i	$-0.618957\pi$
$569$	−25.6964	−	5.46195i	−1.07725	−	0.228977i	−0.712176	+	0.702001i	$0.752290\pi$
$570$	−7.57493	−	3.37258i	−0.317279	−	0.141262i
$571$	9.90336	−	2.10503i	0.414443	−	0.0880926i	0.00402895	−	0.999992i	$-0.498718\pi$
$571$	9.90336	−	2.10503i	0.414443	−	0.0880926i	0.410414	+	0.911899i	$0.365384\pi$
$572$	−15.0971	−	16.7671i	−0.631243	−	0.701066i
$573$	7.88197	−	5.72658i	0.329274	−	0.239231i
$574$	18.7639	+	16.2500i	0.783191	+	0.678264i
$575$	−5.95492	+	4.32650i	−0.248337	+	0.180427i
$576$	1.30902	−	2.26728i	0.0545424	−	0.0944702i
$577$	−7.09270	−	3.15788i	−0.295273	−	0.131464i	0.253753	−	0.967269i	$-0.418335\pi$
$577$	−7.09270	−	3.15788i	−0.295273	−	0.131464i	−0.549027	+	0.835805i	$0.685001\pi$
$578$	41.4895	−	8.81887i	1.72574	−	0.366817i
$579$	9.84171	+	10.9303i	0.409007	+	0.454249i
$580$	6.28115	+	4.56352i	0.260811	+	0.189490i
$581$	15.1328	−	1.88666i	0.627813	−	0.0782718i
$582$	6.94427			0.287849
$583$	0.889948	+	0.189164i	0.0368579	+	0.00783439i
$584$	0.562569	−	5.35248i	0.0232793	−	0.221487i
$585$	−22.9314	+	25.4680i	−0.948099	+	1.05297i
$586$	−0.113954	−	1.08420i	−0.00470739	−	0.0447878i
$587$	12.2082	+	8.86978i	0.503887	+	0.366095i	0.810500	−	0.585739i	$-0.199196\pi$
$587$	12.2082	+	8.86978i	0.503887	+	0.366095i	−0.306613	+	0.951834i	$0.599196\pi$
$588$	−4.32301	+	0.167072i	−0.178278	+	0.00688991i
$589$	−23.5623	+	17.1190i	−0.970868	+	0.705377i
$590$	5.95492	−	10.3142i	0.245160	−	0.424630i
$591$	−1.54103	+	14.6619i	−0.0633893	+	0.603109i
$592$	0.255585	−	0.283856i	0.0105045	−	0.0116664i
$593$	−1.55573	+	2.69460i	−0.0638861	+	0.110654i	−0.896199	−	0.443652i	$-0.853683\pi$
$593$	−1.55573	+	2.69460i	−0.0638861	+	0.110654i	0.832313	+	0.554306i	$0.187016\pi$
$594$	4.13525	+	12.7270i	0.169672	+	0.522195i
$595$	−45.2520	+	5.64173i	−1.85515	+	0.231289i
$596$	−1.47214	+	4.53077i	−0.0603010	+	0.185588i
$597$	−9.27020	−	10.2956i	−0.379404	−	0.421371i
$598$	7.87297	+	3.50527i	0.321950	+	0.143341i
$599$	−2.05573	−	3.56063i	−0.0839948	−	0.145483i	0.820968	−	0.570975i	$-0.193435\pi$
$599$	−2.05573	−	3.56063i	−0.0839948	−	0.145483i	−0.904962	+	0.425491i	$0.860101\pi$
$600$	1.54508	−	2.67617i	0.0630778	−	0.109254i
$601$	2.85410			0.116421			0.0582106	−	0.998304i	$-0.481461\pi$
$601$	2.85410			0.116421			0.0582106	+	0.998304i	$0.481461\pi$
$602$	−5.89452	−	0.504654i	−0.240243	−	0.0205682i
$603$	0.809017	−	2.48990i	0.0329457	−	0.101396i
$604$	11.7888	+	13.0928i	0.479678	+	0.532736i
$605$	8.42971	−	1.79179i	0.342716	−	0.0728466i
$606$	−1.94706	+	2.16243i	−0.0790938	+	0.0878425i
$607$	5.39919	−	9.35167i	0.219146	−	0.379572i	−0.735401	−	0.677632i	$-0.763006\pi$
$607$	5.39919	−	9.35167i	0.219146	−	0.379572i	0.954547	+	0.298060i	$0.0963395\pi$
$608$	1.85410	+	5.70634i	0.0751938	+	0.231423i
$609$	−5.43251	−	1.64984i	−0.220136	−	0.0668549i
$610$	5.69098	−	17.5150i	0.230421	−	0.709163i
$611$	5.65174	+	53.7727i	0.228645	+	2.17541i
$612$	−2.10942	+	20.0698i	−0.0852682	+	0.811273i
$613$	−1.35887	+	12.9288i	−0.0548842	+	0.522189i	0.932195	+	0.361956i	$0.117891\pi$
$613$	−1.35887	+	12.9288i	−0.0548842	+	0.522189i	−0.987079	+	0.160232i	$0.948776\pi$
$614$	1.37190	+	13.0527i	0.0553652	+	0.526765i
$615$	10.4894	−	7.62096i	0.422972	−	0.307307i
$616$	9.75697	+	2.96316i	0.393119	+	0.119389i
$617$	−9.12461	−	28.0827i	−0.367343	−	1.13057i	−0.948501	−	0.316775i	$-0.897400\pi$
$617$	−9.12461	−	28.0827i	−0.367343	−	1.13057i	0.581158	−	0.813791i	$-0.302600\pi$
$618$	0.909830	−	1.57587i	0.0365987	−	0.0633909i
$619$	21.9091	−	24.3325i	0.880601	−	0.978007i	−0.119288	−	0.992860i	$-0.538061\pi$
$619$	21.9091	−	24.3325i	0.880601	−	0.978007i	0.999890	+	0.0148528i	$0.00472796\pi$
$620$	−5.42705	−	9.39993i	−0.217956	−	0.377510i
$621$	−3.42023	−	3.79855i	−0.137249	−	0.152431i
$622$	−1.10739	+	3.40820i	−0.0444023	+	0.136656i
$623$	−15.5789	−	1.33378i	−0.624157	−	0.0534367i
$624$	−3.61803			−0.144837
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	−11.2361	−	19.4614i	−0.449084	−	0.777836i
$627$	−13.0562	−	5.81300i	−0.521415	−	0.232149i
$628$	−0.924716	−	1.02700i	−0.0369002	−	0.0409818i
$629$	−0.909830	+	2.80017i	−0.0362773	+	0.111650i
$630$	2.92705	−	15.2094i	0.116617	−	0.605957i
$631$	−8.10081	−	24.9317i	−0.322488	−	0.992517i	−0.972562	−	0.232645i	$-0.925262\pi$
$631$	−8.10081	−	24.9317i	−0.322488	−	0.992517i	0.650073	−	0.759871i	$-0.274738\pi$
$632$	4.47214	−	7.74597i	0.177892	−	0.308118i
$633$	−4.24732	+	4.71713i	−0.168816	+	0.187489i
$634$	2.69084	−	25.6016i	0.106867	−	1.01677i
$635$	2.10359	+	20.0144i	0.0834786	+	0.794246i
$636$	0.118034	−	0.0857567i	0.00468035	−	0.00340047i
$637$	−21.8446	−	34.6709i	−0.865514	−	1.37371i
$638$	10.8262	+	7.86572i	0.428615	+	0.311407i
$639$	4.36329	+	41.5140i	0.172609	+	1.64227i
$640$	−2.18720	+	0.464905i	−0.0864569	+	0.0183770i
$641$	1.47060	−	13.9918i	0.0580852	−	0.552643i	−0.926321	−	0.376734i	$-0.877047\pi$
$641$	1.47060	−	13.9918i	0.0580852	−	0.552643i	0.984406	−	0.175909i	$-0.0562864\pi$
$642$	−9.40786	−	1.99970i	−0.371298	−	0.0789219i
$643$	−11.9443			−0.471036			−0.235518	−	0.971870i	$-0.575679\pi$
$643$	−11.9443			−0.471036			−0.235518	+	0.971870i	$0.575679\pi$
$644$	−3.86498	+	0.481862i	−0.152302	+	0.0189880i
$645$	−0.954915	+	2.93893i	−0.0375997	+	0.115720i
$646$	−30.9468	−	34.3699i	−1.21758	−	1.35226i
$647$	−11.7170	+	2.49051i	−0.460641	+	0.0979122i	−0.432386	−	0.901689i	$-0.642328\pi$
$647$	−11.7170	+	2.49051i	−0.460641	+	0.0979122i	−0.0282547	+	0.999601i	$0.508995\pi$
$648$	−5.21470	−	2.32174i	−0.204853	−	0.0912064i
$649$	10.2639	−	17.7777i	0.402895	−	0.697834i
$650$	29.2705			1.14808
$651$	6.00000	+	5.19615i	0.235159	+	0.203653i
$652$	1.66312	−	1.20833i	0.0651328	−	0.0473217i
$653$	−30.6451	−	34.0348i	−1.19924	−	1.33189i	−0.929442	−	0.368967i	$-0.879711\pi$
$653$	−30.6451	−	34.0348i	−1.19924	−	1.33189i	−0.269793	−	0.962918i	$-0.586955\pi$
$654$	−0.747238	+	0.158830i	−0.0292193	+	0.00621076i
$655$	10.1719	−	11.2970i	0.397448	−	0.441411i
$656$	−9.17695	−	1.95062i	−0.358300	−	0.0761589i
$657$	−14.0902			−0.549710
$658$	−14.7424	−	19.4883i	−0.574720	−	0.759734i
$659$	13.1074	+	9.52308i	0.510591	+	0.370966i	0.813048	−	0.582197i	$-0.197807\pi$
$659$	13.1074	+	9.52308i	0.510591	+	0.370966i	−0.302456	+	0.953163i	$0.597807\pi$
$660$	2.66312	−	4.61266i	0.103662	−	0.179547i
$661$	2.27785	+	1.01417i	0.0885983	+	0.0394465i	0.450557	−	0.892748i	$-0.351225\pi$
$661$	2.27785	+	1.01417i	0.0885983	+	0.0394465i	−0.361959	+	0.932194i	$0.617892\pi$
$662$	−2.97975	+	28.3504i	−0.115811	+	1.10187i
$663$	25.4775	−	11.3433i	0.989462	−	0.440537i
$664$	−4.66312	+	3.38795i	−0.180964	+	0.131478i
$665$	21.4150	+	28.3090i	0.830439	+	1.09777i
$666$	−0.809017	−	0.587785i	−0.0313488	−	0.0227762i
$667$	−4.99976	−	1.06273i	−0.193591	−	0.0411491i
$668$	−0.0729490	−	0.126351i	−0.00282248	−	0.00488868i
$669$	4.39104	−	4.87674i	0.169767	−	0.188546i
$670$	−2.04275	+	0.909491i	−0.0789183	+	0.0351367i
$671$	9.80902	−	30.1891i	0.378673	−	1.16544i
$672$	1.40004	−	0.844778i	0.0540077	−	0.0325880i
$673$	30.6074	−	22.2376i	1.17983	−	0.857195i	0.187676	−	0.982231i	$-0.439905\pi$
$673$	30.6074	−	22.2376i	1.17983	−	0.857195i	0.992152	+	0.125036i	$0.0399045\pi$
$674$	11.3541	−	19.6659i	0.437344	−	0.757501i
$675$	−15.8598	−	7.06122i	−0.610443	−	0.271787i
$676$	−10.6353	−	18.4208i	−0.409048	−	0.708492i
$677$	1.07579	+	10.2354i	0.0413458	+	0.393379i	0.995551	+	0.0942257i	$0.0300375\pi$
$677$	1.07579	+	10.2354i	0.0413458	+	0.393379i	−0.954205	+	0.299153i	$0.903296\pi$
$678$	−1.22542	+	3.77147i	−0.0470622	+	0.144842i
$679$	−26.0273	−	14.3639i	−0.998837	−	0.551237i
$680$	13.9443	−	10.1311i	0.534738	−	0.388510i
$681$	12.0569	+	2.56277i	0.462021	+	0.0982055i
$682$	−9.35410	−	16.2018i	−0.358187	−	0.620398i
$683$	2.12806	−	2.36345i	0.0814281	−	0.0904350i	−0.701054	−	0.713108i	$-0.747287\pi$
$683$	2.12806	−	2.36345i	0.0814281	−	0.0904350i	0.782482	+	0.622673i	$0.213953\pi$
$684$	14.3502	−	6.38910i	0.548692	−	0.244293i
$685$	4.47214	+	3.24920i	0.170872	+	0.124145i
$686$	16.5483	+	8.31578i	0.631819	+	0.317498i
$687$	−6.16312	−	4.47777i	−0.235138	−	0.170838i
$688$	2.04275	−	0.909491i	0.0778791	−	0.0346740i
$689$	1.26249	+	0.562096i	0.0480970	+	0.0214142i
$690$	−0.212657	+	2.02330i	−0.00809572	+	0.0770256i
$691$	11.7428	−	5.22823i	0.446717	−	0.198891i	−0.171034	−	0.985265i	$-0.554711\pi$
$691$	11.7428	−	5.22823i	0.446717	−	0.198891i	0.617751	+	0.786374i	$0.288044\pi$
$692$	−3.00000	−	9.23305i	−0.114043	−	0.350988i
$693$	5.04508	−	26.2150i	0.191647	−	0.995827i
$694$	2.29180	+	7.05342i	0.0869954	+	0.267744i
$695$	1.40240	+	13.3429i	0.0531959	+	0.506125i
$696$	2.09901	−	0.446157i	0.0795626	−	0.0169115i
$697$	70.7378	−	15.0358i	2.67938	−	0.569521i
$698$	2.46876	+	23.4887i	0.0934438	+	0.889059i
$699$	−15.9656			−0.603873
$700$	−11.3266	+	6.83440i	−0.428104	+	0.258316i
$701$	−35.0132			−1.32243			−0.661214	−	0.750197i	$-0.729959\pi$
$701$	−35.0132			−1.32243			−0.661214	+	0.750197i	$0.729959\pi$
$702$	2.12467	+	20.2149i	0.0801905	+	0.762962i
$703$	2.24171	−	0.476491i	0.0845479	−	0.0179712i
$704$	−3.76988	+	0.801313i	−0.142083	+	0.0302006i
$705$	−11.6604	+	5.19156i	−0.439157	+	0.195525i
$706$	4.33688	+	13.3475i	0.163221	+	0.502342i
$707$	11.7705	−	4.07742i	0.442676	−	0.153347i
$708$	−1.01722	−	3.13068i	−0.0382295	−	0.117658i
$709$	−31.4410	+	13.9984i	−1.18079	+	0.525721i	−0.900780	−	0.434276i	$-0.857004\pi$
$709$	−31.4410	+	13.9984i	−1.18079	+	0.525721i	−0.280010	+	0.959997i	$0.590338\pi$
$710$	23.8562	−	26.4950i	0.895306	−	0.994338i
$711$	−21.3920	−	9.52431i	−0.802261	−	0.357190i
$712$	5.39890	−	2.40374i	0.202332	−	0.0900841i
$713$	5.78115	+	4.20025i	0.216506	+	0.157301i
$714$	−7.21024	+	10.3382i	−0.269836	+	0.386896i
$715$	50.4508			1.88675
$716$	−5.26561	+	2.34440i	−0.196785	+	0.0876144i
$717$	2.34636	−	2.60590i	0.0876264	−	0.0973189i
$718$	−0.881966	−	1.52761i	−0.0329147	−	0.0570099i
$719$	−25.3436	−	5.38696i	−0.945158	−	0.200900i	−0.290543	−	0.956862i	$-0.593836\pi$
$719$	−25.3436	−	5.38696i	−0.945158	−	0.200900i	−0.654615	+	0.755962i	$0.727169\pi$
$720$	1.80902	+	5.56758i	0.0674181	+	0.207492i
$721$	−6.66970	+	4.02447i	−0.248392	+	0.149879i
$722$	−5.25329	+	16.1680i	−0.195507	+	0.601709i
$723$	0.701198	+	6.67146i	0.0260778	+	0.248114i
$724$	0.708204	+	1.22665i	0.0263202	+	0.0455879i
$725$	−16.9813	+	3.60949i	−0.630670	+	0.134053i
$726$	1.19098	−	2.06284i	0.0442015	−	0.0765593i
$727$	−27.4164	+	19.9192i	−1.01682	+	0.738762i	−0.965628	−	0.259927i	$-0.916301\pi$
$727$	−27.4164	+	19.9192i	−1.01682	+	0.738762i	−0.0511901	+	0.998689i	$0.516301\pi$
$728$	13.5605	+	7.48375i	0.502585	+	0.277366i
$729$	−2.62868	+	8.09024i	−0.0973584	+	0.299638i
$730$	8.05261	+	8.94333i	0.298041	+	0.331008i
$731$	−11.5332	+	12.8089i	−0.426570	+	0.473754i
$732$	−2.54508	−	4.40822i	−0.0940690	−	0.162932i
$733$	−1.26357	−	0.268580i	−0.0466709	−	0.00992021i	0.184517	−	0.982829i	$-0.440928\pi$
$733$	−1.26357	−	0.268580i	−0.0466709	−	0.00992021i	−0.231188	+	0.972909i	$0.574261\pi$
$734$	−26.6525	−	19.3642i	−0.983761	−	0.714744i
$735$	6.19056	−	7.43362i	0.228342	−	0.274193i
$736$	1.19098	−	0.865300i	0.0439002	−	0.0318954i
$737$	−3.52090	+	1.56760i	−0.129694	+	0.0577435i
$738$	−2.56746	+	24.4278i	−0.0945095	+	0.899198i
$739$	−29.9434	−	13.3316i	−1.10148	−	0.490412i	−0.226229	−	0.974074i	$-0.572640\pi$
$739$	−29.9434	−	13.3316i	−1.10148	−	0.490412i	−0.875255	+	0.483662i	$0.839307\pi$
$740$	0.0892780	+	0.849423i	0.00328192	+	0.0312254i
$741$	−17.5623	−	12.7598i	−0.645167	−	0.468742i
$742$	−0.619779	+	0.0772701i	−0.0227528	+	0.00283668i
$743$	−36.2361			−1.32937			−0.664686	−	0.747123i	$-0.731435\pi$
$743$	−36.2361			−1.32937			−0.664686	+	0.747123i	$0.731435\pi$
$744$	−2.93444	−	0.623735i	−0.107582	−	0.0228672i
$745$	−5.32624	−	9.22531i	−0.195138	−	0.337989i
$746$	−1.61637	+	0.343569i	−0.0591793	+	0.0125790i
$747$	10.0973	+	11.2142i	0.369441	+	0.410305i
$748$	24.0344	−	17.4620i	0.878786	−	0.638476i
$749$	31.1246	+	26.9547i	1.13727	+	0.984903i
$750$	2.13525	+	6.57164i	0.0779685	+	0.239962i
$751$	−16.2533	+	28.1515i	−0.593091	+	1.02726i	0.400722	+	0.916200i	$0.368759\pi$
$751$	−16.2533	+	28.1515i	−0.593091	+	1.02726i	−0.993813	+	0.111064i	$0.964574\pi$
$752$	8.43757	+	3.75665i	0.307686	+	0.136991i
$753$	−18.8494	+	4.00656i	−0.686910	+	0.146007i
$754$	13.6009	+	15.1053i	0.495316	+	0.550104i
$755$	−39.3951			−1.43374
$756$	−5.54216	−	7.32629i	−0.201566	−	0.266455i
$757$	14.2016			0.516167			0.258083	−	0.966123i	$-0.416909\pi$
$757$	14.2016			0.516167			0.258083	+	0.966123i	$0.416909\pi$
$758$	−5.92340	−	1.25906i	−0.215147	−	0.0457310i
$759$	−0.366537	+	3.48737i	−0.0133045	+	0.126583i
$760$	−12.2565	−	5.45694i	−0.444590	−	0.197944i
$761$	−1.22967	−	11.6995i	−0.0445753	−	0.424106i	−0.993940	−	0.109928i	$-0.964938\pi$
$761$	−1.22967	−	11.6995i	−0.0445753	−	0.424106i	0.949364	−	0.314178i	$-0.101729\pi$
$762$	4.50000	+	3.26944i	0.163018	+	0.118439i
$763$	3.12920	+	0.950331i	0.113285	+	0.0344043i
$764$	12.7533	−	9.26581i	0.461398	−	0.335225i
$765$	−30.1943	−	33.5341i	−1.09168	−	1.21243i
$766$	2.09057	−	19.8904i	0.0755353	−	0.718671i
$767$	20.8637	−	23.1715i	0.753345	−	0.836675i
$768$	−0.309017	+	0.535233i	−0.0111507	+	0.0193136i
$769$	−2.12868	−	6.55139i	−0.0767621	−	0.236249i	0.905311	−	0.424749i	$-0.139638\pi$
$769$	−2.12868	−	6.55139i	−0.0767621	−	0.236249i	−0.982073	+	0.188500i	$0.939638\pi$
$770$	−19.5225	+	11.7798i	−0.703543	+	0.424515i
$771$	−5.73607	+	17.6538i	−0.206579	+	0.635786i
$772$	15.9242	+	17.6856i	0.573125	+	0.636520i
$773$	25.2423	+	11.2386i	0.907904	+	0.404225i	0.806918	−	0.590663i	$-0.201134\pi$
$773$	25.2423	+	11.2386i	0.907904	+	0.404225i	0.100986	+	0.994888i	$0.467800\pi$
$774$	−2.92705	−	5.06980i	−0.105211	−	0.182230i
$775$	23.7401	+	5.04612i	0.852771	+	0.181262i
$776$	11.2361			0.403351
$777$	−0.265010	−	0.565567i	−0.00950720	−	0.0202896i
$778$	2.19098	−	6.74315i	0.0785505	−	0.241754i
$779$	−37.6666	−	41.8330i	−1.34954	−	1.49882i
$780$	5.41338	−	6.01217i	0.193830	−	0.215270i
$781$	41.1186	−	45.6669i	1.47134	−	1.63409i
$782$	−5.67376	+	9.82724i	−0.202893	+	0.351422i
$783$	−3.72542	−	11.4657i	−0.133136	−	0.409750i
$784$	−6.99478	+	0.270327i	−0.249814	+	0.00965455i
$785$	3.09017			0.110293
$786$	−0.439190	−	4.17861i	−0.0156654	−	0.149046i
$787$	−0.630771	+	6.00138i	−0.0224846	+	0.213926i	0.977511	+	0.210885i	$0.0676346\pi$
$787$	−0.630771	+	6.00138i	−0.0224846	+	0.213926i	−0.999995	+	0.00304099i	$0.999032\pi$
$788$	−2.49343	+	23.7234i	−0.0888249	+	0.845112i
$789$	0.212657	+	2.02330i	0.00757079	+	0.0720313i
$790$	6.18034	+	19.0211i	0.219887	+	0.676741i
$791$	12.3941	−	11.6008i	0.440682	−	0.412478i
$792$	3.11803	+	9.59632i	0.110795	+	0.340990i
$793$	24.1074	−	41.7552i	0.856079	−	1.48277i
$794$	14.4510	−	16.0495i	0.512848	−	0.569576i
$795$	−0.0341011	+	0.324451i	−0.00120944	+	0.0115071i
$796$	−14.9995	−	16.6586i	−0.531643	−	0.590450i
$797$	−14.3090	+	44.0386i	−0.506851	+	1.55993i	0.290784	+	0.956789i	$0.406084\pi$
$797$	−14.3090	+	44.0386i	−0.506851	+	1.55993i	−0.797636	+	0.603140i	$0.793916\pi$
$798$	9.77523	+	0.836897i	0.346039	+	0.0296258i
$799$	−71.1935			−2.51864
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$	−7.73607	−	13.3993i	−0.273341	−	0.473440i
$802$	−18.7022	−	8.32677i	−0.660399	−	0.294028i
$803$	13.8795	+	15.4148i	0.489798	+	0.543976i
$804$	−0.190983	+	0.587785i	−0.00673545	+	0.0207296i
$805$	4.98215	−	7.14350i	0.175598	−	0.251775i
$806$	−8.78115	−	27.0256i	−0.309303	−	0.951937i
$807$	−5.66312	+	9.80881i	−0.199351	+	0.345286i
$808$	−3.15040	+	3.49888i	−0.110831	+	0.123090i
$809$	2.25027	−	21.4099i	0.0791154	−	0.752733i	−0.880998	−	0.473121i	$-0.843127\pi$
$809$	2.25027	−	21.4099i	0.0791154	−	0.752733i	0.960113	−	0.279612i	$-0.0902059\pi$
$810$	11.6604	−	5.19156i	0.409706	−	0.182413i
$811$	8.01722	−	5.82485i	0.281523	−	0.204538i	−0.438059	−	0.898946i	$-0.644334\pi$
$811$	8.01722	−	5.82485i	0.281523	−	0.204538i	0.719581	+	0.694408i	$0.244334\pi$
$812$	−8.78999	−	2.66950i	−0.308468	−	0.0936809i
$813$	−6.04508	−	4.39201i	−0.212010	−	0.154035i
$814$	0.153880	+	1.46407i	0.00539350	+	0.0513157i
$815$	−0.480491	+	4.57157i	−0.0168309	+	0.160135i
$816$	0.497966	−	4.73783i	0.0174323	−	0.165857i
$817$	13.1232	+	2.78943i	0.459124	+	0.0975897i
$818$	1.47214			0.0514720
$819$	15.7744	−	37.3553i	0.551204	−	1.30530i
$820$	16.9721	−	12.3310i	0.592693	−	0.430616i
$821$	−3.36870	−	3.74132i	−0.117568	−	0.130573i	0.681487	−	0.731830i	$-0.261333\pi$
$821$	−3.36870	−	3.74132i	−0.117568	−	0.130573i	−0.799056	+	0.601257i	$0.794667\pi$
$822$	1.49448	−	0.317661i	0.0521259	−	0.0110797i
$823$	6.92796	+	3.08452i	0.241493	+	0.107520i	0.523915	−	0.851771i	$-0.324471\pi$
$823$	6.92796	+	3.08452i	0.241493	+	0.107520i	−0.282421	+	0.959290i	$0.591138\pi$
$824$	1.47214	−	2.54981i	0.0512843	−	0.0888270i
$825$	3.68034	+	11.3269i	0.128133	+	0.394353i
$826$	−2.66312	+	13.8380i	−0.0926618	+	0.481485i
$827$	−8.33688	+	6.05710i	−0.289902	+	0.210626i	−0.723225	−	0.690613i	$-0.757341\pi$
$827$	−8.33688	+	6.05710i	−0.289902	+	0.210626i	0.433323	+	0.901239i	$0.357341\pi$
$828$	−2.57890	−	2.86416i	−0.0896229	−	0.0995363i
$829$	24.5964	−	5.22813i	0.854268	−	0.181580i	0.240093	−	0.970750i	$-0.422822\pi$
$829$	24.5964	−	5.22813i	0.854268	−	0.181580i	0.614175	+	0.789170i	$0.289489\pi$
$830$	1.34722	−	12.8179i	0.0467627	−	0.444917i
$831$	−3.87890	−	0.824486i	−0.134558	−	0.0286011i
$832$	−5.85410			−0.202954
$833$	48.4083	−	23.8337i	1.67725	−	0.825788i
$834$	3.00000	+	2.17963i	0.103882	+	0.0754743i
$835$	0.319109	+	0.0678287i	0.0110432	+	0.00234731i
$836$	−21.1254	−	9.40563i	−0.730637	−	0.325300i
$837$	−1.76173	+	16.7618i	−0.0608944	+	0.579372i
$838$	11.1782	−	4.97686i	0.386145	−	0.171923i
$839$	17.9443	−	13.0373i	0.619505	−	0.450097i	−0.233244	−	0.972418i	$-0.574934\pi$
$839$	17.9443	−	13.0373i	0.619505	−	0.450097i	0.852749	+	0.522322i	$0.174934\pi$
$840$	−0.690983	+	3.59045i	−0.0238412	+	0.123882i
$841$	13.7082	+	9.95959i	0.472697	+	0.343434i
$842$	23.5637	+	5.00863i	0.812060	+	0.172609i
$843$	−5.25329	−	9.09896i	−0.180933	−	0.313385i
$844$	−6.87231	+	7.63248i	−0.236555	+	0.262721i
$845$	46.5230	+	9.88876i	1.60044	+	0.340184i
$846$	7.47214	−	22.9969i	0.256897	−	0.790649i
$847$	−8.73074	+	5.26809i	−0.299992	+	0.181014i
$848$	0.190983	−	0.138757i	0.00655838	−	0.00476494i
$849$	−3.57295	+	6.18853i	−0.122623	+	0.212390i
$850$	−4.02863	+	38.3299i	−0.138181	+	1.31470i
$851$	−0.281153	−	0.486971i	−0.00963780	−	0.0166932i
$852$	−1.03003	−	9.80012i	−0.0352884	−	0.335747i
$853$	7.97214	−	24.5357i	0.272961	−	0.840087i	−0.716791	−	0.697288i	$-0.754390\pi$
$853$	7.97214	−	24.5357i	0.272961	−	0.840087i	0.989752	−	0.142799i	$-0.0456102\pi$
$854$	0.420835	+	21.7865i	0.0144007	+	0.745519i
$855$	−10.8541	+	33.4055i	−0.371202	+	1.14244i
$856$	−15.2222	−	3.23559i	−0.520285	−	0.110590i
$857$	−3.20820	−	5.55677i	−0.109590	−	0.189816i	0.806014	−	0.591896i	$-0.201621\pi$
$857$	−3.20820	−	5.55677i	−0.109590	−	0.189816i	−0.915604	+	0.402081i	$0.868287\pi$
$858$	9.33054	−	10.3626i	0.318539	−	0.353774i
$859$	−42.4035	+	18.8793i	−1.44679	+	0.644152i	−0.971793	−	0.235836i	$-0.924217\pi$
$859$	−42.4035	+	18.8793i	−1.44679	+	0.644152i	−0.474996	+	0.879988i	$0.657550\pi$
$860$	−1.54508	+	4.75528i	−0.0526870	+	0.162154i
$861$	−8.77587	+	12.5830i	−0.299081	+	0.428828i
$862$	−21.8713	−	15.8904i	−0.744940	−	0.541231i
$863$	21.0430	−	9.36895i	0.716312	−	0.318923i	−0.0160186	−	0.999872i	$-0.505099\pi$
$863$	21.0430	−	9.36895i	0.716312	−	0.318923i	0.732331	+	0.680949i	$0.238432\pi$
$864$	3.17195	+	1.41224i	0.107912	+	0.0480455i
$865$	19.8314	+	8.82952i	0.674289	+	0.300213i
$866$	−20.7450	+	9.23626i	−0.704943	+	0.313861i
$867$	8.10081	+	24.9317i	0.275118	+	0.846726i
$868$	9.70820	+	8.40755i	0.329518	+	0.285371i
$869$	10.6525	+	32.7849i	0.361360	+	1.11215i
$870$	−2.39919	+	4.15551i	−0.0813401	+	0.140885i
$871$	−5.72618	+	1.21714i	−0.194024	+	0.0412411i
$872$	−1.20906	+	0.256993i	−0.0409438	+	0.00870288i
$873$	−3.07485	−	29.2553i	−0.104068	−	0.990141i
$874$	8.83282			0.298774
$875$	5.59017	−	29.0474i	0.188982	−	0.981981i
$876$	3.32624			0.112383
$877$	−0.421714	−	4.01234i	−0.0142403	−	0.135487i	0.985092	−	0.172029i	$-0.0550324\pi$
$877$	−0.421714	−	4.01234i	−0.0142403	−	0.135487i	−0.999332	+	0.0365421i	$0.988366\pi$
$878$	3.85808	−	0.820060i	0.130204	−	0.0276757i
$879$	0.659039	−	0.140083i	0.0222288	−	0.00472488i
$880$	4.30902	−	7.46344i	0.145257	−	0.251592i
$881$	−4.23607	−	13.0373i	−0.142717	−	0.439237i	0.853994	−	0.520284i	$-0.174174\pi$
$881$	−4.23607	−	13.0373i	−0.142717	−	0.439237i	−0.996710	+	0.0810466i	$0.974174\pi$
$882$	2.61803	+	18.1383i	0.0881538	+	0.610747i
$883$	5.02786	+	15.4742i	0.169201	+	0.520747i	0.999321	−	0.0368371i	$-0.0117283\pi$
$883$	5.02786	+	15.4742i	0.169201	+	0.520747i	−0.830120	+	0.557584i	$0.811728\pi$
$884$	41.2234	−	18.3538i	1.38649	−	0.617306i
$885$	6.72432	+	2.99386i	0.226035	+	0.100637i
$886$	−2.87392	−	1.27955i	−0.0965513	−	0.0429874i
$887$	46.7047	−	20.7943i	1.56819	−	0.698203i	0.575377	−	0.817888i	$-0.304855\pi$
$887$	46.7047	−	20.7943i	1.56819	−	0.698203i	0.992812	+	0.119686i	$0.0381887\pi$
$888$	0.190983	+	0.138757i	0.00640897	+	0.00465639i
$889$	−10.1034	−	21.5620i	−0.338858	−	0.723167i
$890$	−4.08359	+	12.5680i	−0.136882	+	0.421280i
$891$	20.0980	−	8.94821i	0.673308	−	0.299776i
$892$	7.10485	−	7.89074i	0.237888	−	0.264201i
$893$	27.7082	+	47.9920i	0.927220	+	1.60599i
$894$	−2.87993	−	0.612149i	−0.0963194	−	0.0204733i
$895$	3.98278	−	12.2577i	0.133130	−	0.409731i
$896$	2.26531	−	1.36688i	0.0756788	−	0.0456643i
$897$	−1.64590	+	5.06555i	−0.0549549	+	0.169134i
$898$	0.519042	+	4.93836i	0.0173207	+	0.164795i
$899$	8.42705	+	14.5961i	0.281058	+	0.486807i
$900$	−11.9585	−	5.32425i	−0.398616	−	0.177475i
$901$	−0.909830	+	1.57587i	−0.0303108	+	0.0524999i
$902$	29.2533	−	21.2538i	0.974028	−	0.707673i
$903$	−0.0706138	−	3.65566i	−0.00234988	−	0.121653i
$904$	−1.98278	+	6.10237i	−0.0659463	+	0.202962i
$905$	−3.09797	−	0.658495i	−0.102980	−	0.0218891i
$906$	−7.28586	+	8.09176i	−0.242056	+	0.268831i
$907$	−17.1353	−	29.6791i	−0.568967	−	0.985479i	−0.996668	−	0.0815595i	$-0.974010\pi$
$907$	−17.1353	−	29.6791i	−0.568967	−	0.985479i	0.427702	−	0.903920i	$-0.359323\pi$
$908$	19.5084	+	4.14665i	0.647410	+	0.137611i
$909$	9.97214	+	7.24518i	0.330755	+	0.240307i
$910$	−32.7254	+	11.3364i	−1.08484	+	0.375799i
$911$	17.8262	−	12.9515i	0.590610	−	0.429103i	−0.251924	−	0.967747i	$-0.581063\pi$
$911$	17.8262	−	12.9515i	0.590610	−	0.429103i	0.842533	+	0.538644i	$0.181063\pi$
$912$	−3.38761	+	1.50826i	−0.112175	+	0.0499436i
$913$	2.32208	−	22.0931i	0.0768495	−	0.731174i
$914$	9.83334	+	4.37809i	0.325258	+	0.144814i
$915$	11.1332	+	2.36644i	0.368054	+	0.0782322i
$916$	−9.97214	−	7.24518i	−0.329489	−	0.239388i
$917$	−6.99719	+	16.5700i	−0.231067	+	0.547189i
$918$	−26.7639			−0.883341
$919$	15.4740	+	3.28909i	0.510439	+	0.108497i	0.455929	−	0.890016i	$-0.349307\pi$
$919$	15.4740	+	3.28909i	0.510439	+	0.108497i	0.0545098	+	0.998513i	$0.482640\pi$
$920$	−0.344086	+	3.27376i	−0.0113442	+	0.107933i
$921$	−7.93420	+	1.68647i	−0.261441	+	0.0555710i
$922$	−23.4657	−	26.0613i	−0.772800	−	0.858282i
$923$	75.5132	−	54.8635i	2.48555	−	1.80585i
$924$	−1.19098	+	6.18853i	−0.0391805	+	0.203588i
$925$	−1.54508	−	1.12257i	−0.0508021	−	0.0369099i
$926$	5.88197	−	10.1879i	0.193293	−	0.334794i
$927$	−7.04179	−	3.13521i	−0.231283	−	0.102974i
$928$	3.39626	−	0.721898i	0.111488	−	0.0236975i
$929$	11.8261	+	13.1342i	0.388000	+	0.430918i	0.905226	−	0.424931i	$-0.139702\pi$
$929$	11.8261	+	13.1342i	0.388000	+	0.430918i	−0.517225	+	0.855849i	$0.673035\pi$
$930$	5.42705	−	3.94298i	0.177960	−	0.129296i
$931$	−34.9067	−	23.3564i	−1.14402	−	0.765474i
$932$	−25.8328			−0.846182
$933$	−2.16638	−	0.460479i	−0.0709242	−	0.0150754i
$934$	−0.519042	+	4.93836i	−0.0169836	+	0.161588i
$935$	−6.94378	+	66.0657i	−0.227086	+	2.16058i
$936$	1.60203	+	15.2423i	0.0523639	+	0.498209i
$937$	−30.6803	−	22.2906i	−1.00228	−	0.728201i	−0.0397065	−	0.999211i	$-0.512642\pi$
$937$	−30.6803	−	22.2906i	−1.00228	−	0.728201i	−0.962576	+	0.271010i	$0.912642\pi$
$938$	1.93162	−	1.80800i	0.0630696	−	0.0590331i
$939$	11.2361	−	8.16348i	0.366675	−	0.266405i
$940$	−18.8670	+	8.40012i	−0.615373	+	0.273982i
$941$	−4.61228	+	43.8829i	−0.150356	+	1.43054i	0.615808	+	0.787896i	$0.288830\pi$
$941$	−4.61228	+	43.8829i	−0.150356	+	1.43054i	−0.766164	+	0.642645i	$0.777837\pi$
$942$	0.571506	−	0.634721i	0.0186207	−	0.0206803i
$943$	−6.90576	+	11.9611i	−0.224883	+	0.389508i
$944$	−1.64590	−	5.06555i	−0.0535694	−	0.164870i
$945$	20.4666	+	1.75223i	0.665777	+	0.0569999i
$946$	−2.66312	+	8.19624i	−0.0865855	+	0.266483i
$947$	20.7803	+	23.0789i	0.675270	+	0.749964i	0.979237	−	0.202719i	$-0.0649778\pi$
$947$	20.7803	+	23.0789i	0.675270	+	0.749964i	−0.303967	+	0.952683i	$0.598311\pi$
$948$	5.04996	+	2.24838i	0.164015	+	0.0730241i
$949$	15.7533	+	27.2855i	0.511373	+	0.885725i
$950$	27.4064	−	12.2021i	0.889180	−	0.395888i
$951$	15.9098			0.515912
$952$	−11.6664	+	16.7275i	−0.378110	+	0.542142i
$953$	−6.39261	+	19.6744i	−0.207077	+	0.637317i	0.792545	+	0.609814i	$0.208756\pi$
$953$	−6.39261	+	19.6744i	−0.207077	+	0.637317i	−0.999622	+	0.0275035i	$0.991244\pi$
$954$	−0.413545	−	0.459289i	−0.0133890	−	0.0148700i
$955$	−3.68455	+	35.0561i	−0.119229	+	1.13439i
$956$	3.79649	−	4.21643i	0.122787	−	0.136369i
$957$	−4.13525	+	7.16247i	−0.133674	+	0.231530i
$958$	−1.76393	−	5.42882i	−0.0569901	−	0.175397i
$959$	−6.25841	−	1.90066i	−0.202095	−	0.0613756i
$960$	−0.427051	−	1.31433i	−0.0137830	−	0.0424197i
$961$	0.777451	+	7.39695i	0.0250791	+	0.238611i
$962$	−0.233733	+	2.22382i	−0.00753585	+	0.0716988i
$963$	−4.25877	+	40.5195i	−0.137237	+	1.30572i
$964$	1.13456	+	10.7946i	0.0365418	+	0.347672i
$965$	−53.2148			−1.71304
$966$	−0.545862	−	2.34448i	−0.0175628	−	0.0754323i
$967$	−11.3090	−	34.8056i	−0.363673	−	1.11927i	−0.950808	−	0.309782i	$-0.899744\pi$
$967$	−11.3090	−	34.8056i	−0.363673	−	1.11927i	0.587134	−	0.809490i	$-0.300256\pi$
$968$	1.92705	−	3.33775i	0.0619378	−	0.107279i
$969$	19.1262	−	21.2417i	0.614421	−	0.682383i
$970$	−16.8116	+	18.6712i	−0.539789	+	0.599497i
$971$	−26.3001	−	29.2093i	−0.844012	−	0.937370i	0.154708	−	0.987960i	$-0.450556\pi$
$971$	−26.3001	−	29.2093i	−0.844012	−	0.937370i	−0.998719	+	0.0505902i	$0.983890\pi$
$972$	4.30902	−	13.2618i	0.138212	−	0.425372i
$973$	−6.73561	−	14.3747i	−0.215934	−	0.460831i
$974$	−40.5967			−1.30080
$975$	1.89094	+	17.9911i	0.0605585	+	0.576175i
$976$	−4.11803	−	7.13264i	−0.131815	−	0.228310i
$977$	−38.8122	−	17.2803i	−1.24171	−	0.552847i	−0.322487	−	0.946574i	$-0.604519\pi$
$977$	−38.8122	−	17.2803i	−1.24171	−	0.552847i	−0.919227	+	0.393727i	$0.871185\pi$
$978$	0.850137	+	0.944173i	0.0271844	+	0.0301913i
$979$	−7.03851	+	21.6623i	−0.224952	+	0.692330i
$980$	10.0165	−	12.0278i	0.319966	−	0.384216i
$981$	1.00000	+	3.07768i	0.0319275	+	0.0982629i
$982$	−10.5729	+	18.3129i	−0.337396	+	0.584388i
$983$	−12.8199	+	14.2380i	−0.408892	+	0.454120i	−0.912053	−	0.410072i	$-0.865503\pi$
$983$	−12.8199	+	14.2380i	−0.408892	+	0.454120i	0.503161	+	0.864192i	$0.332170\pi$
$984$	0.606095	−	5.76661i	0.0193216	−	0.183833i
$985$	−35.6910	−	39.6389i	−1.13721	−	1.26300i
$986$	−21.6525	+	15.7314i	−0.689555	+	0.500991i
$987$	11.0261	−	10.3204i	0.350964	−	0.328502i
$988$	−28.4164	−	20.6457i	−0.904046	−	0.656828i
$989$	−0.344086	−	3.27376i	−0.0109413	−	0.104100i
$990$	−20.6117	−	9.17692i	−0.655083	−	0.291662i
$991$	−1.85684	+	17.6666i	−0.0589844	+	0.561199i	0.924624	+	0.380881i	$0.124379\pi$
$991$	−1.85684	+	17.6666i	−0.0589844	+	0.561199i	−0.983608	+	0.180318i	$0.942287\pi$
$992$	−4.74803	−	1.00922i	−0.150750	−	0.0320429i
$993$	−17.6180			−0.559091
$994$	−16.4105	+	38.8617i	−0.520511	+	1.23262i
$995$	50.1246			1.58906
$996$	−2.38365	−	2.64731i	−0.0755288	−	0.0838832i
$997$	−14.8149	+	3.14901i	−0.469193	+	0.0997301i	−0.436440	−	0.899733i	$-0.643761\pi$
$997$	−14.8149	+	3.14901i	−0.469193	+	0.0997301i	−0.0327533	+	0.999463i	$0.510428\pi$
$998$	−10.9625	−	4.88084i	−0.347013	−	0.154500i
$999$	0.663119	−	1.14856i	0.0209802	−	0.0363387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.q.a.261.1	yes	8
7.4	even	3	inner	350.2.q.a.11.1	✓	8
25.16	even	5	inner	350.2.q.a.191.1	yes	8
175.116	even	15	inner	350.2.q.a.291.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.q.a.11.1	✓	8	7.4	even	3	inner
350.2.q.a.191.1	yes	8	25.16	even	5	inner
350.2.q.a.261.1	yes	8	1.1	even	1	trivial
350.2.q.a.291.1	yes	8	175.116	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 + 0.994522i) q^{2} +(-0.604528 + 0.128496i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.11803 - 1.93649i) q^{5} +(-0.190983 - 0.587785i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.39169 + 1.06485i) q^{9} +O(q^{10})\)	\(q+(0.104528 + 0.994522i) q^{2} +(-0.604528 + 0.128496i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.11803 - 1.93649i) q^{5} +(-0.190983 - 0.587785i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.39169 + 1.06485i) q^{9} +(2.04275 + 0.909491i) q^{10} +(3.52090 + 1.56760i) q^{11} +(0.564602 - 0.251377i) q^{12} +(4.73607 + 3.44095i) q^{13} +(-2.63611 - 0.225688i) q^{14} +(-0.427051 + 1.31433i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-5.15780 + 5.72831i) q^{17} +(-1.30902 - 2.26728i) q^{18} +(5.86889 + 1.24747i) q^{19} +(-0.690983 + 2.12663i) q^{20} +(-0.0315794 - 1.63486i) q^{21} +(-1.19098 + 3.66547i) q^{22} +(-0.153880 - 1.46407i) q^{23} +(0.309017 + 0.535233i) q^{24} +(-2.50000 - 4.33013i) q^{25} +(-2.92705 + 5.06980i) q^{26} +(2.80902 - 2.04087i) q^{27} +(-0.0510966 - 2.64526i) q^{28} +(1.07295 - 3.30220i) q^{29} +(-1.35177 - 0.287327i) q^{30} +(-3.24803 + 3.60730i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.32991 - 0.495239i) q^{33} +(-6.23607 - 4.53077i) q^{34} +(4.47214 + 3.87298i) q^{35} +(2.11803 - 1.53884i) q^{36} +(0.348943 - 0.155360i) q^{37} +(-0.627171 + 5.96713i) q^{38} +(-3.30524 - 1.47159i) q^{39} +(-2.18720 - 0.464905i) q^{40} +(-7.59017 - 5.51458i) q^{41} +(1.62260 - 0.202296i) q^{42} +2.23607 q^{43} +(-3.76988 - 0.801313i) q^{44} +(-0.611920 + 5.82203i) q^{45} +(1.43997 - 0.306074i) q^{46} +(6.18014 + 6.86374i) q^{47} +(-0.500000 + 0.363271i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(4.04508 - 2.93893i) q^{50} +(2.38197 - 4.12569i) q^{51} +(-5.34799 - 2.38108i) q^{52} +(0.230909 - 0.0490813i) q^{53} +(2.32331 + 2.58030i) q^{54} +(6.97214 - 5.06555i) q^{55} +(2.62543 - 0.327321i) q^{56} -3.70820 q^{57} +(3.39626 + 0.721898i) q^{58} +(0.556743 - 5.29706i) q^{59} +(0.144455 - 1.37440i) q^{60} +(-0.860904 - 8.19095i) q^{61} +(-3.92705 - 2.85317i) q^{62} +(-1.57072 - 6.74623i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(11.9585 - 5.32425i) q^{65} +(0.248983 - 2.36892i) q^{66} +(-0.669131 + 0.743145i) q^{67} +(3.85410 - 6.67550i) q^{68} +(0.281153 + 0.865300i) q^{69} +(-3.38430 + 4.85247i) q^{70} +(4.92705 - 15.1639i) q^{71} +(1.75181 + 1.94558i) q^{72} +(4.91667 + 2.18904i) q^{73} +(0.190983 + 0.330792i) q^{74} +(2.06773 + 2.29644i) q^{75} -6.00000 q^{76} +(-5.83320 + 8.36376i) q^{77} +(1.11803 - 3.44095i) q^{78} +(5.98489 + 6.64689i) q^{79} +(0.233733 - 2.22382i) q^{80} +(3.81953 - 4.24202i) q^{81} +(4.69098 - 8.12502i) q^{82} +(-1.78115 - 5.48183i) q^{83} +(0.370796 + 1.59257i) q^{84} +(5.32624 + 16.3925i) q^{85} +(0.233733 + 2.22382i) q^{86} +(-0.224307 + 2.13414i) q^{87} +(0.402863 - 3.83299i) q^{88} +(0.617745 + 5.87746i) q^{89} -5.85410 q^{90} +(-11.3079 + 10.5842i) q^{91} +(0.454915 + 1.40008i) q^{92} +(1.50000 - 2.59808i) q^{93} +(-6.18014 + 6.86374i) q^{94} +(8.97733 - 9.97033i) q^{95} +(-0.413545 - 0.459289i) q^{96} +(-3.47214 + 10.6861i) q^{97} +(1.90441 - 6.73597i) q^{98} -10.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9	\( 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9} + 5 q^{10} + 8 q^{11} + 2 q^{12} + 20 q^{13} - 4 q^{14} + 10 q^{15} + q^{16} + 14 q^{17} - 6 q^{18} - 6 q^{19} - 10 q^{20} + 15 q^{21} - 14 q^{22} + 7 q^{23} - 2 q^{24} - 20 q^{25} - 10 q^{26} + 18 q^{27} - 5 q^{28} + 22 q^{29} + 5 q^{30} + 6 q^{31} + 4 q^{32} + 6 q^{33} - 32 q^{34} + 8 q^{36} - q^{37} + 6 q^{38} - 5 q^{39} - 5 q^{40} - 16 q^{41} + 3 q^{42} - 7 q^{44} + 10 q^{45} + 13 q^{46} + 2 q^{47} - 4 q^{48} - 52 q^{49} + 10 q^{50} + 28 q^{51} - 10 q^{52} + 7 q^{53} - 11 q^{54} + 20 q^{55} - q^{56} + 24 q^{57} + 11 q^{58} - 15 q^{59} + 11 q^{61} - 18 q^{62} - 16 q^{63} - 2 q^{64} + 20 q^{65} - q^{66} - q^{67} + 4 q^{68} - 38 q^{69} - 25 q^{70} + 26 q^{71} - q^{72} + 4 q^{73} + 6 q^{74} - 15 q^{75} - 48 q^{76} - 40 q^{77} - 20 q^{79} - 5 q^{80} - 16 q^{81} + 42 q^{82} + 26 q^{83} + 8 q^{84} - 20 q^{85} - 5 q^{86} - 2 q^{87} - 8 q^{88} + q^{89} - 20 q^{90} - 10 q^{91} + 26 q^{92} + 12 q^{93} - 2 q^{94} - 30 q^{95} + 3 q^{96} + 8 q^{97} + 11 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9 + 5 * q^10 + 8 * q^11 + 2 * q^12 + 20 * q^13 - 4 * q^14 + 10 * q^15 + q^16 + 14 * q^17 - 6 * q^18 - 6 * q^19 - 10 * q^20 + 15 * q^21 - 14 * q^22 + 7 * q^23 - 2 * q^24 - 20 * q^25 - 10 * q^26 + 18 * q^27 - 5 * q^28 + 22 * q^29 + 5 * q^30 + 6 * q^31 + 4 * q^32 + 6 * q^33 - 32 * q^34 + 8 * q^36 - q^37 + 6 * q^38 - 5 * q^39 - 5 * q^40 - 16 * q^41 + 3 * q^42 - 7 * q^44 + 10 * q^45 + 13 * q^46 + 2 * q^47 - 4 * q^48 - 52 * q^49 + 10 * q^50 + 28 * q^51 - 10 * q^52 + 7 * q^53 - 11 * q^54 + 20 * q^55 - q^56 + 24 * q^57 + 11 * q^58 - 15 * q^59 + 11 * q^61 - 18 * q^62 - 16 * q^63 - 2 * q^64 + 20 * q^65 - q^66 - q^67 + 4 * q^68 - 38 * q^69 - 25 * q^70 + 26 * q^71 - q^72 + 4 * q^73 + 6 * q^74 - 15 * q^75 - 48 * q^76 - 40 * q^77 - 20 * q^79 - 5 * q^80 - 16 * q^81 + 42 * q^82 + 26 * q^83 + 8 * q^84 - 20 * q^85 - 5 * q^86 - 2 * q^87 - 8 * q^88 + q^89 - 20 * q^90 - 10 * q^91 + 26 * q^92 + 12 * q^93 - 2 * q^94 - 30 * q^95 + 3 * q^96 + 8 * q^97 + 11 * q^98 - 36 * q^99

Introduction

L-functions

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