LMFDB - Embedded newform 354.2.e.d.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			7.1
Character	$\chi$	$=$	354.7
Dual form			354.2.e.d.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.561187 + 0.827689i) q^{2} +(0.0541389 - 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(-1.35846 + 0.628489i) q^{5} +(0.856857 - 0.515554i) q^{6} +(-1.22687 + 4.41877i) q^{7} +(-0.976621 + 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +O(q^{10})$	\(q+(0.561187 + 0.827689i) q^{2} +(0.0541389 - 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(-1.35846 + 0.628489i) q^{5} +(0.856857 - 0.515554i) q^{6} +(-1.22687 + 4.41877i) q^{7} +(-0.976621 + 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +(-1.28254 - 0.771679i) q^{10} +(-1.60379 + 1.51919i) q^{11} +(0.907575 + 0.419889i) q^{12} +(2.46777 - 0.268386i) q^{13} +(-4.34587 + 1.46430i) q^{14} +(0.554022 + 1.39049i) q^{15} +(-0.725995 - 0.687699i) q^{16} +(0.837756 + 3.01732i) q^{17} +(-0.468408 - 0.883512i) q^{18} +(-1.86390 + 1.41690i) q^{19} +(-0.0810350 - 1.49460i) q^{20} +(4.34587 + 1.46430i) q^{21} +(-2.15744 - 0.474888i) q^{22} +(1.74200 - 3.28576i) q^{23} +(0.161782 + 0.986827i) q^{24} +(-1.78653 + 2.10326i) q^{25} +(1.60702 + 1.89193i) q^{26} +(-0.161782 + 0.986827i) q^{27} +(-3.65083 - 2.77529i) q^{28} +(1.77203 - 2.61355i) q^{29} +(-0.839983 + 1.23888i) q^{30} +(7.01795 + 5.33491i) q^{31} +(0.161782 - 0.986827i) q^{32} +(1.43013 + 1.68368i) q^{33} +(-2.02727 + 2.38668i) q^{34} +(-1.11051 - 6.77378i) q^{35} +(0.468408 - 0.883512i) q^{36} +(0.972755 + 0.214120i) q^{37} +(-2.21875 - 0.747584i) q^{38} +(-0.134390 - 2.47868i) q^{39} +(1.19159 - 0.905823i) q^{40} +(-2.99562 - 5.65033i) q^{41} +(1.22687 + 4.41877i) q^{42} +(5.32182 + 5.04109i) q^{43} +(-0.817667 - 2.05219i) q^{44} +(1.41844 - 0.477930i) q^{45} +(3.69718 - 0.402093i) q^{46} +(-11.3247 - 5.23937i) q^{47} +(-0.725995 + 0.687699i) q^{48} +(-12.0224 - 7.23362i) q^{49} +(-2.74342 - 0.298365i) q^{50} +(3.05825 - 0.673173i) q^{51} +(-0.664092 + 2.39184i) q^{52} +(7.81608 - 4.70278i) q^{53} +(-0.907575 + 0.419889i) q^{54} +(1.22388 - 3.07171i) q^{55} +(0.248277 - 4.57921i) q^{56} +(1.31391 + 1.93788i) q^{57} +3.15764 q^{58} +(7.68071 + 0.0817965i) q^{59} -1.49680 q^{60} +(-4.83899 - 7.13697i) q^{61} +(-0.477261 + 8.80256i) q^{62} +(1.69743 - 4.26022i) q^{63} +(0.907575 - 0.419889i) q^{64} +(-3.18368 + 1.91556i) q^{65} +(-0.590993 + 2.12856i) q^{66} +(4.81393 - 1.05963i) q^{67} +(-3.11311 - 0.338571i) q^{68} +(-3.18664 - 1.91733i) q^{69} +(4.98338 - 4.72051i) q^{70} +(0.887916 + 0.410793i) q^{71} +(0.994138 - 0.108119i) q^{72} +(8.55041 - 2.88097i) q^{73} +(0.368673 + 0.925300i) q^{74} +(2.00346 + 1.89777i) q^{75} +(-0.626367 - 2.25597i) q^{76} +(-4.74531 - 8.95061i) q^{77} +(1.97616 - 1.50224i) q^{78} +(0.796283 + 14.6866i) q^{79} +(1.41844 + 0.477930i) q^{80} +(0.976621 + 0.214970i) q^{81} +(2.99562 - 5.65033i) q^{82} +(1.91104 + 11.6568i) q^{83} +(-2.96887 + 3.49522i) q^{84} +(-3.03441 - 3.57238i) q^{85} +(-1.18592 + 7.23380i) q^{86} +(-2.51378 - 1.91092i) q^{87} +(1.23971 - 1.82844i) q^{88} +(-4.37398 + 6.45113i) q^{89} +(1.19159 + 0.905823i) q^{90} +(-1.84169 + 11.2338i) q^{91} +(2.40762 + 2.83447i) q^{92} +(5.70703 - 6.71883i) q^{93} +(-2.01871 - 12.3136i) q^{94} +(1.64152 - 3.09624i) q^{95} +(-0.976621 - 0.214970i) q^{96} +(11.0867 + 3.73553i) q^{97} +(-0.759611 - 14.0102i) q^{98} +(1.75864 - 1.33688i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9	\( 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9} + 2 q^{10} + 30 q^{11} - 3 q^{12} - 3 q^{13} + 7 q^{14} - 2 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 4 q^{19} - 2 q^{20} - 7 q^{21} - q^{22} + 2 q^{23} + 3 q^{24} - 67 q^{25} + 32 q^{26} - 3 q^{27} - 7 q^{28} + 4 q^{29} + 2 q^{30} - 6 q^{31} + 3 q^{32} + q^{33} + 26 q^{34} + 79 q^{35} - 3 q^{36} + 55 q^{37} + 4 q^{38} - 3 q^{39} + 2 q^{40} + q^{41} + 7 q^{42} + 51 q^{43} + q^{44} - 2 q^{45} - 31 q^{46} - 62 q^{47} - 3 q^{48} - 70 q^{49} + 9 q^{50} + 3 q^{51} - 32 q^{52} - 27 q^{53} + 3 q^{54} - 83 q^{55} + 7 q^{56} - 4 q^{57} - 120 q^{58} - 55 q^{59} + 56 q^{60} - 46 q^{61} - 23 q^{62} - 7 q^{63} - 3 q^{64} - 121 q^{65} - q^{66} + 8 q^{67} - 26 q^{68} - 27 q^{69} - 50 q^{70} - 61 q^{71} + 3 q^{72} + 49 q^{73} - 26 q^{74} - 9 q^{75} + 25 q^{76} + 77 q^{77} + 3 q^{78} - 5 q^{79} - 2 q^{80} - 3 q^{81} - q^{82} + 75 q^{83} - 7 q^{84} + 189 q^{85} + 65 q^{86} - 25 q^{87} - 30 q^{88} + 54 q^{89} + 2 q^{90} - 161 q^{91} + 2 q^{92} + 23 q^{93} + 33 q^{94} - 54 q^{95} + 3 q^{96} + 28 q^{97} + 12 q^{98} + q^{99}+O(q^{100}) \) 84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9 + 2 * q^10 + 30 * q^11 - 3 * q^12 - 3 * q^13 + 7 * q^14 - 2 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 4 * q^19 - 2 * q^20 - 7 * q^21 - q^22 + 2 * q^23 + 3 * q^24 - 67 * q^25 + 32 * q^26 - 3 * q^27 - 7 * q^28 + 4 * q^29 + 2 * q^30 - 6 * q^31 + 3 * q^32 + q^33 + 26 * q^34 + 79 * q^35 - 3 * q^36 + 55 * q^37 + 4 * q^38 - 3 * q^39 + 2 * q^40 + q^41 + 7 * q^42 + 51 * q^43 + q^44 - 2 * q^45 - 31 * q^46 - 62 * q^47 - 3 * q^48 - 70 * q^49 + 9 * q^50 + 3 * q^51 - 32 * q^52 - 27 * q^53 + 3 * q^54 - 83 * q^55 + 7 * q^56 - 4 * q^57 - 120 * q^58 - 55 * q^59 + 56 * q^60 - 46 * q^61 - 23 * q^62 - 7 * q^63 - 3 * q^64 - 121 * q^65 - q^66 + 8 * q^67 - 26 * q^68 - 27 * q^69 - 50 * q^70 - 61 * q^71 + 3 * q^72 + 49 * q^73 - 26 * q^74 - 9 * q^75 + 25 * q^76 + 77 * q^77 + 3 * q^78 - 5 * q^79 - 2 * q^80 - 3 * q^81 - q^82 + 75 * q^83 - 7 * q^84 + 189 * q^85 + 65 * q^86 - 25 * q^87 - 30 * q^88 + 54 * q^89 + 2 * q^90 - 161 * q^91 + 2 * q^92 + 23 * q^93 + 33 * q^94 - 54 * q^95 + 3 * q^96 + 28 * q^97 + 12 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{9}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	0.561187	+	0.827689i	0.396819	+	0.585265i
$2$	0.561187	+	0.827689i	0.396819	+	0.585265i
$3$	0.0541389	−	0.998533i	0.0312571	−	0.576504i
$3$	0.0541389	−	0.998533i	0.0312571	−	0.576504i
$4$	−0.370138	+	0.928977i	−0.185069	+	0.464488i
$5$	−1.35846	+	0.628489i	−0.607520	+	0.281069i	−0.699433	−	0.714698i	$-0.746564\pi$
$5$	−1.35846	+	0.628489i	−0.607520	+	0.281069i	0.0919128	+	0.995767i	$0.470702\pi$
$6$	0.856857	−	0.515554i	0.349810	−	0.210474i
$7$	−1.22687	+	4.41877i	−0.463712	+	1.67014i	0.248859	+	0.968540i	$0.419944\pi$
$7$	−1.22687	+	4.41877i	−0.463712	+	1.67014i	−0.712571	+	0.701600i	$0.752469\pi$
$8$	−0.976621	+	0.214970i	−0.345288	+	0.0760035i
$9$	−0.994138	−	0.108119i	−0.331379	−	0.0360397i
$10$	−1.28254	−	0.771679i	−0.405575	−	0.244026i
$11$	−1.60379	+	1.51919i	−0.483560	+	0.458052i	−0.890222	−	0.455526i	$-0.849451\pi$
$11$	−1.60379	+	1.51919i	−0.483560	+	0.458052i	0.406662	+	0.913578i	$0.366693\pi$
$12$	0.907575	+	0.419889i	0.261994	+	0.121212i
$13$	2.46777	−	0.268386i	0.684437	−	0.0744370i	0.240707	−	0.970598i	$-0.422621\pi$
$13$	2.46777	−	0.268386i	0.684437	−	0.0744370i	0.443729	+	0.896161i	$0.353655\pi$
$14$	−4.34587	+	1.46430i	−1.16148	+	0.391349i
$15$	0.554022	+	1.39049i	0.143048	+	0.359023i
$16$	−0.725995	−	0.687699i	−0.181499	−	0.171925i
$17$	0.837756	+	3.01732i	0.203186	+	0.731809i	0.992964	+	0.118416i	$0.0377817\pi$
$17$	0.837756	+	3.01732i	0.203186	+	0.731809i	−0.789778	+	0.613392i	$0.789804\pi$
$18$	−0.468408	−	0.883512i	−0.110405	−	0.208246i
$19$	−1.86390	+	1.41690i	−0.427608	+	0.325059i	−0.796745	−	0.604316i	$-0.793447\pi$
$19$	−1.86390	+	1.41690i	−0.427608	+	0.325059i	0.369137	+	0.929375i	$0.379653\pi$
$20$	−0.0810350	−	1.49460i	−0.0181200	−	0.334203i
$21$	4.34587	+	1.46430i	0.948347	+	0.319535i
$22$	−2.15744	−	0.474888i	−0.459968	−	0.101247i
$23$	1.74200	−	3.28576i	0.363232	−	0.685129i	−0.632781	−	0.774331i	$-0.718087\pi$
$23$	1.74200	−	3.28576i	0.363232	−	0.685129i	0.996014	+	0.0892016i	$0.0284315\pi$
$24$	0.161782	+	0.986827i	0.0330236	+	0.201435i
$25$	−1.78653	+	2.10326i	−0.357305	+	0.420652i
$26$	1.60702	+	1.89193i	0.315163	+	0.371038i
$27$	−0.161782	+	0.986827i	−0.0311350	+	0.189915i
$28$	−3.65083	−	2.77529i	−0.689942	−	0.524480i
$29$	1.77203	−	2.61355i	0.329057	−	0.485323i	−0.626790	−	0.779189i	$-0.715631\pi$
$29$	1.77203	−	2.61355i	0.329057	−	0.485323i	0.955847	+	0.293865i	$0.0949418\pi$
$30$	−0.839983	+	1.23888i	−0.153359	+	0.226188i
$31$	7.01795	+	5.33491i	1.26046	+	0.958178i	0.999973	−	0.00729962i	$-0.00232356\pi$
$31$	7.01795	+	5.33491i	1.26046	+	0.958178i	0.260488	+	0.965477i	$0.416117\pi$
$32$	0.161782	−	0.986827i	0.0285993	−	0.174448i
$33$	1.43013	+	1.68368i	0.248954	+	0.293091i
$34$	−2.02727	+	2.38668i	−0.347674	+	0.409313i
$35$	−1.11051	−	6.77378i	−0.187710	−	1.14498i
$36$	0.468408	−	0.883512i	0.0780681	−	0.147252i
$37$	0.972755	+	0.214120i	0.159920	+	0.0352010i	0.294209	−	0.955741i	$-0.404944\pi$
$37$	0.972755	+	0.214120i	0.159920	+	0.0352010i	−0.134289	+	0.990942i	$0.542875\pi$
$38$	−2.21875	−	0.747584i	−0.359929	−	0.121274i
$39$	−0.134390	−	2.47868i	−0.0215197	−	0.396907i
$40$	1.19159	−	0.905823i	0.188407	−	0.143223i
$41$	−2.99562	−	5.65033i	−0.467837	−	0.882434i	−0.999373	−	0.0353985i	$-0.988730\pi$
$41$	−2.99562	−	5.65033i	−0.467837	−	0.882434i	0.531536	−	0.847035i	$-0.321615\pi$
$42$	1.22687	+	4.41877i	0.189310	+	0.681832i
$43$	5.32182	+	5.04109i	0.811569	+	0.768759i	0.976033	−	0.217624i	$-0.0698306\pi$
$43$	5.32182	+	5.04109i	0.811569	+	0.768759i	−0.164463	+	0.986383i	$0.552589\pi$
$44$	−0.817667	−	2.05219i	−0.123268	−	0.309379i
$45$	1.41844	−	0.477930i	0.211449	−	0.0712455i
$46$	3.69718	−	0.402093i	0.545119	−	0.0592853i
$47$	−11.3247	−	5.23937i	−1.65188	−	0.764241i	−0.999982	−	0.00593370i	$-0.998111\pi$
$47$	−11.3247	−	5.23937i	−1.65188	−	0.764241i	−0.651897	−	0.758307i	$-0.726027\pi$
$48$	−0.725995	+	0.687699i	−0.104788	+	0.0992609i
$49$	−12.0224	−	7.23362i	−1.71748	−	1.03337i
$50$	−2.74342	−	0.298365i	−0.387978	−	0.0421952i
$51$	3.05825	−	0.673173i	0.428241	−	0.0942630i
$52$	−0.664092	+	2.39184i	−0.0920930	+	0.331689i
$53$	7.81608	−	4.70278i	1.07362	−	0.645976i	0.134971	−	0.990849i	$-0.456906\pi$
$53$	7.81608	−	4.70278i	1.07362	−	0.645976i	0.938649	+	0.344873i	$0.112078\pi$
$54$	−0.907575	+	0.419889i	−0.123505	+	0.0571397i
$55$	1.22388	−	3.07171i	0.165028	−	0.414189i
$56$	0.248277	−	4.57921i	0.0331775	−	0.611922i
$57$	1.31391	+	1.93788i	0.174032	+	0.256678i
$58$	3.15764			0.414619
$59$	7.68071	+	0.0817965i	0.999943	+	0.0106490i
$59$	7.68071	+	0.0817965i	0.999943	+	0.0106490i
$60$	−1.49680			−0.193236
$61$	−4.83899	−	7.13697i	−0.619569	−	0.913796i	0.380370	−	0.924834i	$-0.375797\pi$
$61$	−4.83899	−	7.13697i	−0.619569	−	0.913796i	−0.999939	+	0.0110386i	$0.996486\pi$
$62$	−0.477261	+	8.80256i	−0.0606122	+	1.11793i
$63$	1.69743	−	4.26022i	0.213856	−	0.536738i
$64$	0.907575	−	0.419889i	0.113447	−	0.0524861i
$65$	−3.18368	+	1.91556i	−0.394887	+	0.237596i
$66$	−0.590993	+	2.12856i	−0.0727462	+	0.262008i
$67$	4.81393	−	1.05963i	0.588115	−	0.129454i	0.0890630	−	0.996026i	$-0.471613\pi$
$67$	4.81393	−	1.05963i	0.588115	−	0.129454i	0.499052	+	0.866572i	$0.333682\pi$
$68$	−3.11311	−	0.338571i	−0.377520	−	0.0410578i
$69$	−3.18664	−	1.91733i	−0.383626	−	0.230820i
$70$	4.98338	−	4.72051i	0.595628	−	0.564209i
$71$	0.887916	+	0.410793i	0.105376	+	0.0487522i	0.471869	−	0.881669i	$-0.343580\pi$
$71$	0.887916	+	0.410793i	0.105376	+	0.0487522i	−0.366493	+	0.930421i	$0.619442\pi$
$72$	0.994138	−	0.108119i	0.117160	−	0.0127419i
$73$	8.55041	−	2.88097i	1.00075	−	0.337192i	0.229213	−	0.973376i	$-0.426385\pi$
$73$	8.55041	−	2.88097i	1.00075	−	0.337192i	0.771537	+	0.636184i	$0.219488\pi$
$74$	0.368673	+	0.925300i	0.0428574	+	0.107564i
$75$	2.00346	+	1.89777i	0.231339	+	0.219136i
$76$	−0.626367	−	2.25597i	−0.0718492	−	0.258778i
$77$	−4.74531	−	8.95061i	−0.540779	−	1.02002i
$78$	1.97616	−	1.50224i	0.223756	−	0.170095i
$79$	0.796283	+	14.6866i	0.0895889	+	1.65237i	0.605586	+	0.795780i	$0.292939\pi$
$79$	0.796283	+	14.6866i	0.0895889	+	1.65237i	−0.515998	+	0.856590i	$0.672579\pi$
$80$	1.41844	+	0.477930i	0.158587	+	0.0534341i
$81$	0.976621	+	0.214970i	0.108513	+	0.0238856i
$82$	2.99562	−	5.65033i	0.330811	−	0.623975i
$83$	1.91104	+	11.6568i	0.209764	+	1.27950i	0.856244	+	0.516571i	$0.172792\pi$
$83$	1.91104	+	11.6568i	0.209764	+	1.27950i	−0.646481	+	0.762930i	$0.723760\pi$
$84$	−2.96887	+	3.49522i	−0.323930	+	0.381360i
$85$	−3.03441	−	3.57238i	−0.329128	−	0.387479i
$86$	−1.18592	+	7.23380i	−0.127881	+	0.780041i
$87$	−2.51378	−	1.91092i	−0.269505	−	0.204872i
$88$	1.23971	−	1.82844i	0.132154	−	0.194912i
$89$	−4.37398	+	6.45113i	−0.463640	+	0.683819i	−0.985589	−	0.169159i	$-0.945895\pi$
$89$	−4.37398	+	6.45113i	−0.463640	+	0.683819i	0.521948	+	0.852977i	$0.325205\pi$
$90$	1.19159	+	0.905823i	0.125605	+	0.0954821i
$91$	−1.84169	+	11.2338i	−0.193061	+	1.17762i
$92$	2.40762	+	2.83447i	0.251011	+	0.295513i
$93$	5.70703	−	6.71883i	0.591791	−	0.696710i
$94$	−2.01871	−	12.3136i	−0.208214	−	1.27005i
$95$	1.64152	−	3.09624i	0.168417	−	0.317667i
$96$	−0.976621	−	0.214970i	−0.0996759	−	0.0219403i
$97$	11.0867	+	3.73553i	1.12568	+	0.379286i	0.819723	−	0.572760i	$-0.194127\pi$
$97$	11.0867	+	3.73553i	1.12568	+	0.379286i	0.305957	+	0.952045i	$0.401024\pi$
$98$	−0.759611	−	14.0102i	−0.0767323	−	1.41524i
$99$	1.75864	−	1.33688i	0.176750	−	0.134362i
$100$	−1.29262	−	2.43814i	−0.129262	−	0.243814i
$101$	−1.52413	−	5.48942i	−0.151657	−	0.546218i	−0.999863	−	0.0165521i	$-0.994731\pi$
$101$	−1.52413	−	5.48942i	−0.151657	−	0.546218i	0.848206	−	0.529666i	$-0.177683\pi$
$102$	2.27343	+	2.15351i	0.225103	+	0.213229i
$103$	−2.11146	−	5.29937i	−0.208048	−	0.522162i	0.787511	−	0.616301i	$-0.211370\pi$
$103$	−2.11146	−	5.29937i	−0.208048	−	0.522162i	−0.995559	+	0.0941389i	$0.969990\pi$
$104$	−2.35238	+	0.792610i	−0.230670	+	0.0777218i
$105$	−6.82397	+	0.742152i	−0.665951	+	0.0724266i
$106$	8.27872	+	3.83014i	0.804100	+	0.372016i
$107$	−5.79295	+	5.48737i	−0.560025	+	0.530484i	−0.914502	−	0.404581i	$-0.867417\pi$
$107$	−5.79295	+	5.48737i	−0.560025	+	0.530484i	0.354477	+	0.935065i	$0.384659\pi$
$108$	−0.856857	−	0.515554i	−0.0824511	−	0.0496092i
$109$	6.13801	+	0.667549i	0.587915	+	0.0639396i	0.397242	−	0.917714i	$-0.369967\pi$
$109$	6.13801	+	0.667549i	0.587915	+	0.0639396i	0.190673	+	0.981654i	$0.438933\pi$
$110$	3.22925	−	0.710811i	0.307897	−	0.0677732i
$111$	0.266469	−	0.959736i	0.0252922	−	0.0910941i
$112$	3.92949	−	2.36430i	0.371302	−	0.223405i
$113$	5.93315	−	2.74497i	0.558144	−	0.258225i	−0.120474	−	0.992717i	$-0.538441\pi$
$113$	5.93315	−	2.74497i	0.558144	−	0.258225i	0.678618	+	0.734492i	$0.262579\pi$
$114$	−0.866609	+	2.17502i	−0.0811653	+	0.203710i
$115$	−0.301367	+	5.55839i	−0.0281027	+	0.518323i
$116$	1.77203	+	2.61355i	0.164529	+	0.242662i
$117$	−2.48232			−0.229491
$118$	4.24261	+	6.40314i	0.390564	+	0.589457i
$119$	−14.3607			−1.31644
$120$	−0.839983	−	1.23888i	−0.0766796	−	0.113094i
$121$	−0.331327	+	6.11096i	−0.0301206	+	0.555542i
$122$	3.19162	−	8.01035i	0.288955	−	0.725223i
$123$	−5.80423	+	2.68532i	−0.523350	+	0.242127i
$124$	−7.55362	+	4.54486i	−0.678335	+	0.408140i
$125$	3.10722	−	11.1912i	0.277918	−	1.00097i
$126$	4.47872	−	0.985840i	0.398996	−	0.0878256i
$127$	8.87641	+	0.965368i	0.787654	+	0.0856625i	0.493100	−	0.869972i	$-0.335864\pi$
$127$	8.87641	+	0.965368i	0.787654	+	0.0856625i	0.294554	+	0.955635i	$0.404829\pi$
$128$	0.856857	+	0.515554i	0.0757362	+	0.0455690i
$129$	5.32182	−	5.04109i	0.468560	−	0.443843i
$130$	−3.37213	−	1.56011i	−0.295755	−	0.136831i
$131$	8.54362	−	0.929175i	0.746460	−	0.0811824i	0.273020	−	0.962008i	$-0.411978\pi$
$131$	8.54362	−	0.929175i	0.746460	−	0.0811824i	0.473440	+	0.880826i	$0.343012\pi$
$132$	−2.09345	+	0.705365i	−0.182211	+	0.0613941i
$133$	−3.97421	−	9.97451i	−0.344608	−	0.864900i
$134$	3.57855	+	3.38979i	0.309140	+	0.292833i
$135$	−0.400436	−	1.44224i	−0.0344640	−	0.124128i
$136$	−1.46681	−	2.76669i	−0.125778	−	0.237242i
$137$	−8.95701	+	6.80895i	−0.765249	+	0.581727i	−0.913317	−	0.407250i	$-0.866488\pi$
$137$	−8.95701	+	6.80895i	−0.765249	+	0.581727i	0.148067	+	0.988977i	$0.452695\pi$
$138$	−0.201342	−	3.71353i	−0.0171393	−	0.316116i
$139$	0.824474	+	0.277798i	0.0699310	+	0.0235625i	0.354050	−	0.935227i	$-0.384804\pi$
$139$	0.824474	+	0.277798i	0.0699310	+	0.0235625i	−0.284119	+	0.958789i	$0.591701\pi$
$140$	6.70373	+	1.47560i	0.566568	+	0.124711i
$141$	−5.84480	+	11.0245i	−0.492221	+	0.928427i
$142$	0.158277	+	0.965450i	0.0132824	+	0.0810188i
$143$	−3.55005	+	4.17944i	−0.296870	+	0.349502i
$144$	0.647386	+	0.762162i	0.0539489	+	0.0635135i
$145$	−0.764638	+	4.66409i	−0.0634997	+	0.387331i
$146$	7.18293	+	5.46032i	0.594463	+	0.451899i
$147$	−7.87389	+	11.6131i	−0.649427	+	0.957834i
$148$	−0.558966	+	0.824413i	−0.0459467	+	0.0677663i
$149$	13.1074	+	9.96400i	1.07380	+	0.816283i	0.983730	−	0.179652i	$-0.0574973\pi$
$149$	13.1074	+	9.96400i	1.07380	+	0.816283i	0.0900716	+	0.995935i	$0.471290\pi$
$150$	−0.446453	+	2.72325i	−0.0364528	+	0.222352i
$151$	6.01487	+	7.08126i	0.489484	+	0.576265i	0.950341	−	0.311209i	$-0.100734\pi$
$151$	6.01487	+	7.08126i	0.489484	+	0.576265i	−0.460858	+	0.887474i	$0.652458\pi$
$152$	1.51573	−	1.78446i	0.122942	−	0.144739i
$153$	−0.506615	−	3.09021i	−0.0409574	−	0.249829i
$154$	4.74531	−	8.95061i	0.382388	−	0.721261i
$155$	−12.8865	−	2.83653i	−1.03507	−	0.227836i
$156$	2.35238	+	0.792610i	0.188341	+	0.0634596i
$157$	−0.680569	−	12.5524i	−0.0543153	−	1.00179i	−0.890972	−	0.454059i	$-0.849976\pi$
$157$	−0.680569	−	12.5524i	−0.0543153	−	1.00179i	0.836656	−	0.547728i	$-0.184507\pi$
$158$	−11.7091	+	8.90099i	−0.931523	+	0.708125i
$159$	−4.27273	−	8.05922i	−0.338849	−	0.639137i
$160$	0.400436	+	1.44224i	0.0316572	+	0.114019i
$161$	12.3818	+	11.7287i	0.975826	+	0.924352i
$162$	0.370138	+	0.928977i	0.0290808	+	0.0729873i
$163$	−16.3480	+	5.50829i	−1.28048	+	0.431442i	−0.875648	−	0.482950i	$-0.839565\pi$
$163$	−16.3480	+	5.50829i	−1.28048	+	0.431442i	−0.404828	+	0.914393i	$0.632669\pi$
$164$	6.35782	−	0.691455i	0.496462	−	0.0539935i
$165$	−3.00095	−	1.38839i	−0.233623	−	0.108086i
$166$	−8.57576	+	8.12340i	−0.665608	+	0.630498i
$167$	−15.4599	−	9.30194i	−1.19633	−	0.719805i	−0.229021	−	0.973422i	$-0.573552\pi$
$167$	−15.4599	−	9.30194i	−1.19633	−	0.719805i	−0.967305	+	0.253616i	$0.918380\pi$
$168$	−4.55905	−	0.495826i	−0.351738	−	0.0382538i
$169$	−6.67820	+	1.46998i	−0.513708	+	0.113076i
$170$	1.25395	−	4.51632i	0.0961736	−	0.346386i
$171$	2.00617	−	1.20707i	0.153416	−	0.0923071i
$172$	−6.65286	+	3.07794i	−0.507276	+	0.234691i
$173$	3.70116	−	9.28920i	0.281394	−	0.706245i	−0.718548	−	0.695477i	$-0.755193\pi$
$173$	3.70116	−	9.28920i	0.281394	−	0.706245i	0.999942	−	0.0107679i	$-0.00342761\pi$
$174$	0.170951	−	3.15301i	0.0129598	−	0.239029i
$175$	−7.10201	−	10.4747i	−0.536861	−	0.791811i
$176$	2.20909			0.166516
$177$	0.497502	−	7.66502i	0.0373945	−	0.576138i
$178$	−7.79415			−0.584196
$179$	7.15568	+	10.5538i	0.534840	+	0.788830i	0.995092	−	0.0989583i	$-0.0315510\pi$
$179$	7.15568	+	10.5538i	0.534840	+	0.788830i	−0.460251	+	0.887789i	$0.652241\pi$
$180$	−0.0810350	+	1.49460i	−0.00603999	+	0.111401i
$181$	−1.64021	+	4.11663i	−0.121916	+	0.305986i	−0.977250	−	0.212091i	$-0.931973\pi$
$181$	−1.64021	+	4.11663i	−0.121916	+	0.305986i	0.855334	+	0.518077i	$0.173352\pi$
$182$	−10.3316	+	4.77992i	−0.765831	+	0.354311i
$183$	−7.38848	+	4.44550i	−0.546172	+	0.328621i
$184$	−0.994933	+	3.58342i	−0.0733474	+	0.264173i
$185$	−1.45602	+	0.320493i	−0.107048	+	0.0235631i
$186$	8.76381	+	0.953122i	0.642594	+	0.0698863i
$187$	−5.92746	−	3.56644i	−0.433459	−	0.260804i
$188$	9.05896	−	8.58111i	0.660693	−	0.625842i
$189$	−4.16208	−	1.92558i	−0.302747	−	0.140066i
$190$	3.48392	−	0.378900i	0.252750	−	0.0274883i
$191$	−19.9952	+	6.73715i	−1.44680	+	0.487483i	−0.929660	−	0.368418i	$-0.879899\pi$
$191$	−19.9952	+	6.73715i	−1.44680	+	0.487483i	−0.517139	+	0.855902i	$0.673003\pi$
$192$	−0.370138	−	0.928977i	−0.0267124	−	0.0670431i
$193$	−15.4956	−	14.6783i	−1.11540	−	1.05656i	−0.997983	−	0.0634815i	$-0.979780\pi$
$193$	−15.4956	−	14.6783i	−1.11540	−	1.05656i	−0.117418	−	0.993083i	$-0.537462\pi$
$194$	3.12983	+	11.2726i	0.224709	+	0.809328i
$195$	1.74039	+	3.28272i	0.124632	+	0.235080i
$196$	11.1698	−	8.49106i	0.797843	−	0.606504i
$197$	0.367511	+	6.77834i	0.0261841	+	0.482937i	0.981989	+	0.188936i	$0.0605040\pi$
$197$	0.367511	+	6.77834i	0.0261841	+	0.482937i	−0.955805	+	0.294001i	$0.905013\pi$
$198$	2.09345	+	0.705365i	0.148775	+	0.0501281i
$199$	−21.3426	−	4.69787i	−1.51294	−	0.333023i	−0.620505	−	0.784202i	$-0.713072\pi$
$199$	−21.3426	−	4.69787i	−1.51294	−	0.333023i	−0.892433	+	0.451179i	$0.851003\pi$
$200$	1.29262	−	2.43814i	0.0914020	−	0.172402i
$201$	−0.797451	−	4.86423i	−0.0562478	−	0.343097i
$202$	3.68821	−	4.34210i	0.259502	−	0.305509i
$203$	9.37463	+	11.0367i	0.657970	+	0.774622i
$204$	−0.506615	+	3.09021i	−0.0354701	+	0.216358i
$205$	7.62059	+	5.79302i	0.532245	+	0.404602i
$206$	3.20130	−	4.72157i	0.223045	−	0.328967i
$207$	−2.08704	+	3.07816i	−0.145060	+	0.213947i
$208$	−1.97616	−	1.50224i	−0.137022	−	0.104161i
$209$	0.836762	−	5.10402i	0.0578800	−	0.353053i
$210$	−4.44379	−	5.23164i	−0.306651	−	0.361017i
$211$	−3.00336	+	3.53583i	−0.206760	+	0.243417i	−0.855762	−	0.517370i	$-0.826911\pi$
$211$	−3.00336	+	3.53583i	−0.206760	+	0.243417i	0.649002	+	0.760787i	$0.275187\pi$
$212$	1.47574	+	9.00163i	0.101354	+	0.618235i
$213$	0.458262	−	0.864373i	0.0313996	−	0.0592259i
$214$	−7.79276	−	1.71532i	−0.532702	−	0.117257i
$215$	−10.3977	−	3.50340i	−0.709119	−	0.238930i
$216$	−0.0541389	−	0.998533i	−0.00368369	−	0.0679416i
$217$	−32.1838	+	24.4655i	−2.18478	+	1.66083i
$218$	2.89205	+	5.45499i	0.195874	+	0.369458i
$219$	−2.41383	−	8.69385i	−0.163112	−	0.587476i
$220$	2.40054	+	2.27392i	0.161845	+	0.153307i
$221$	2.87720	+	7.22123i	0.193541	+	0.485752i
$222$	0.943902	−	0.318038i	0.0633506	−	0.0213453i
$223$	25.9344	−	2.82054i	1.73670	−	0.188877i	0.815707	−	0.578465i	$-0.196348\pi$
$223$	25.9344	−	2.82054i	1.73670	−	0.188877i	0.920989	+	0.389588i	$0.127383\pi$
$224$	4.16208	+	1.92558i	0.278091	+	0.128658i
$225$	2.00346	−	1.89777i	0.133564	−	0.126518i
$226$	5.60159	+	3.37036i	0.372612	+	0.224193i
$227$	25.3115	+	2.75279i	1.67998	+	0.182709i	0.897819	−	0.440366i	$-0.145151\pi$
$227$	25.3115	+	2.75279i	1.67998	+	0.182709i	0.782162	+	0.623075i	$0.214117\pi$
$228$	−2.28657	+	0.503313i	−0.151432	+	0.0333327i
$229$	0.0139260	−	0.0501568i	0.000920254	−	0.00331446i	−0.963088	−	0.269185i	$-0.913246\pi$
$229$	0.0139260	−	0.0501568i	0.000920254	−	0.00331446i	0.964009	+	0.265871i	$0.0856594\pi$
$230$	−4.76975	+	2.86986i	−0.314508	+	0.189233i
$231$	−9.19439	+	4.25378i	−0.604947	+	0.279878i
$232$	−1.16876	+	2.93338i	−0.0767331	+	0.192586i
$233$	0.163669	−	3.01870i	0.0107223	−	0.197761i	−0.988264	−	0.152753i	$-0.951186\pi$
$233$	0.163669	−	3.01870i	0.0107223	−	0.197761i	0.998987	−	0.0450078i	$-0.0143313\pi$
$234$	−1.39305	−	2.05459i	−0.0910664	−	0.134313i
$235$	18.6770			1.21835
$236$	−2.91891	+	7.10492i	−0.190005	+	0.462491i
$237$	14.7082			0.955397
$238$	−8.05903	−	11.8862i	−0.522390	−	0.770467i
$239$	−0.318477	+	5.87396i	−0.0206006	+	0.379955i	0.969994	+	0.243128i	$0.0781734\pi$
$239$	−0.318477	+	5.87396i	−0.0206006	+	0.379955i	−0.990595	+	0.136828i	$0.956309\pi$
$240$	0.554022	−	1.39049i	0.0357619	−	0.0897557i
$241$	24.4536	−	11.3134i	1.57519	−	0.728762i	0.578951	−	0.815362i	$-0.303462\pi$
$241$	24.4536	−	11.3134i	1.57519	−	0.728762i	0.996243	+	0.0865998i	$0.0276001\pi$
$242$	−5.24391	+	3.15516i	−0.337091	+	0.202821i
$243$	0.267528	−	0.963550i	0.0171620	−	0.0618118i
$244$	8.42118	−	1.85364i	0.539111	−	0.118667i
$245$	20.8781	+	2.27063i	1.33385	+	0.145065i
$246$	−5.47987	−	3.29713i	−0.349384	−	0.210217i
$247$	−4.21941	+	3.99683i	−0.268474	+	0.254312i
$248$	−8.00072	−	3.70153i	−0.508046	−	0.235047i
$249$	11.7432	−	1.27715i	0.744194	−	0.0809359i
$250$	11.0066	−	3.70854i	0.696116	−	0.234549i
$251$	6.16086	+	15.4626i	0.388870	+	0.975991i	0.984915	+	0.173039i	$0.0553588\pi$
$251$	6.16086	+	15.4626i	0.388870	+	0.975991i	−0.596045	+	0.802951i	$0.703262\pi$
$252$	3.32937	+	3.15374i	0.209730	+	0.198667i
$253$	2.19789	+	7.91609i	0.138180	+	0.497680i
$254$	4.18230	+	7.88866i	0.262421	+	0.494979i
$255$	−3.73142	+	2.83655i	−0.233671	+	0.177632i
$256$	0.0541389	+	0.998533i	0.00338368	+	0.0624083i
$257$	3.06451	+	1.03255i	0.191159	+	0.0644089i	0.413253	−	0.910616i	$-0.364393\pi$
$257$	3.06451	+	1.03255i	0.191159	+	0.0644089i	−0.222094	+	0.975025i	$0.571289\pi$
$258$	7.15899	+	1.57581i	0.445699	+	0.0981058i
$259$	−2.13959	+	4.03569i	−0.132947	+	0.250765i
$260$	−0.601106	−	3.66659i	−0.0372790	−	0.227392i
$261$	−2.04421	+	2.40663i	−0.126534	+	0.148967i
$262$	5.56364	+	6.55002i	0.343723	+	0.404662i
$263$	1.62479	−	9.91075i	0.100189	−	0.611123i	−0.888233	−	0.459393i	$-0.848067\pi$
$263$	1.62479	−	9.91075i	0.100189	−	0.611123i	0.988422	−	0.151731i	$-0.0484846\pi$
$264$	−1.75864	−	1.33688i	−0.108237	−	0.0822794i
$265$	−7.66215	+	11.3008i	−0.470682	+	0.694205i
$266$	6.02552	−	8.88698i	0.369448	−	0.544895i
$267$	6.20487	+	4.71682i	0.379732	+	0.288665i
$268$	−0.797451	+	4.86423i	−0.0487121	+	0.297130i
$269$	0.119364	+	0.140526i	0.00727773	+	0.00856801i	0.765789	−	0.643092i	$-0.222349\pi$
$269$	0.119364	+	0.140526i	0.00727773	+	0.00856801i	−0.758511	+	0.651660i	$0.774073\pi$
$270$	0.969006	−	1.14080i	0.0589718	−	0.0694270i
$271$	−0.893657	−	5.45107i	−0.0542858	−	0.331129i	−0.999982	−	0.00607559i	$-0.998066\pi$
$271$	−0.893657	−	5.45107i	−0.0542858	−	0.331129i	0.945696	−	0.325053i	$-0.105382\pi$
$272$	1.46681	−	2.76669i	0.0889381	−	0.167755i
$273$	11.1176	+	2.44717i	0.672869	+	0.148110i
$274$	−10.6623	−	3.59253i	−0.644130	−	0.217033i
$275$	−0.330041	−	6.08725i	−0.0199022	−	0.367075i
$276$	2.96065	−	2.25063i	0.178210	−	0.135472i
$277$	−5.84712	−	11.0288i	−0.351319	−	0.662658i	0.643373	−	0.765553i	$-0.277534\pi$
$277$	−5.84712	−	11.0288i	−0.351319	−	0.662658i	−0.994692	+	0.102894i	$0.967190\pi$
$278$	0.232754	+	0.838304i	0.0139597	+	0.0502782i
$279$	−6.40001	−	6.06241i	−0.383158	−	0.362947i
$280$	2.54071	+	6.37669i	0.151836	+	0.381080i
$281$	2.55809	−	0.861921i	0.152603	−	0.0514179i	−0.241963	−	0.970285i	$-0.577791\pi$
$281$	2.55809	−	0.861921i	0.152603	−	0.0514179i	0.394566	+	0.918867i	$0.370895\pi$
$282$	−12.4048	+	1.34911i	−0.738698	+	0.0803382i
$283$	−26.3153	−	12.1747i	−1.56428	−	0.723713i	−0.569145	−	0.822237i	$-0.692726\pi$
$283$	−26.3153	−	12.1747i	−1.56428	−	0.723713i	−0.995135	+	0.0985245i	$0.968588\pi$
$284$	−0.710269	+	0.672803i	−0.0421467	+	0.0399235i
$285$	−3.00283	−	1.80674i	−0.177872	−	0.107022i
$286$	−5.45152	−	0.592889i	−0.322355	−	0.0350582i
$287$	28.6428	−	6.30475i	1.69073	−	0.372158i
$288$	−0.267528	+	0.963550i	−0.0157643	+	0.0567777i
$289$	6.16416	−	3.70885i	0.362598	−	0.218168i
$290$	−4.28952	+	1.98454i	−0.251889	+	0.116536i
$291$	4.33027	−	10.8682i	0.253845	−	0.637103i
$292$	−0.488480	+	9.00949i	−0.0285862	+	0.527241i
$293$	0.570507	+	0.841435i	0.0333294	+	0.0491572i	0.843989	−	0.536361i	$-0.180201\pi$
$293$	0.570507	+	0.841435i	0.0333294	+	0.0491572i	−0.810659	+	0.585518i	$0.800891\pi$
$294$	−14.0308			−0.818291
$295$	−10.4853	+	4.71612i	−0.610479	+	0.274583i
$296$	−0.996042			−0.0578938
$297$	−1.23971	−	1.82844i	−0.0719353	−	0.106097i
$298$	−0.891380	+	16.4405i	−0.0516363	+	0.952375i
$299$	3.41701	−	8.57604i	0.197611	−	0.495965i
$300$	−2.50454	+	1.15873i	−0.144600	+	0.0668990i
$301$	−28.8046	+	17.3312i	−1.66027	+	0.998951i
$302$	−2.48561	+	8.95236i	−0.143031	+	0.515150i
$303$	−5.56389	+	1.22470i	−0.319637	+	0.0703574i
$304$	2.32759	+	0.253140i	0.133496	+	0.0145186i
$305$	11.0591	+	6.65402i	0.633240	+	0.381008i
$306$	2.27343	−	2.15351i	0.129963	−	0.123108i
$307$	19.5547	+	9.04698i	1.11605	+	0.516338i	0.889166	−	0.457584i	$-0.151285\pi$
$307$	19.5547	+	9.04698i	1.11605	+	0.516338i	0.226881	+	0.973923i	$0.427147\pi$
$308$	10.0713	−	1.09532i	0.573867	−	0.0624118i
$309$	−5.40591	+	1.82146i	−0.307531	+	0.103619i
$310$	−4.88397	−	12.2578i	−0.277391	−	0.696199i
$311$	−4.01260	−	3.80094i	−0.227534	−	0.215531i	0.565436	−	0.824792i	$-0.308708\pi$
$311$	−4.01260	−	3.80094i	−0.227534	−	0.215531i	−0.792970	+	0.609260i	$0.791466\pi$
$312$	0.664092	+	2.39184i	0.0375968	+	0.135411i
$313$	−8.69138	−	16.3937i	−0.491266	−	0.926626i	−0.997919	−	0.0644758i	$-0.979462\pi$
$313$	−8.69138	−	16.3937i	−0.491266	−	0.926626i	0.506653	−	0.862150i	$-0.330882\pi$
$314$	10.0075	−	7.60752i	0.564757	−	0.429317i
$315$	0.371621	+	6.85414i	0.0209385	+	0.386187i
$316$	−13.9382	−	4.69634i	−0.784087	−	0.264190i
$317$	4.63148	+	1.01947i	0.260130	+	0.0572589i	0.343120	−	0.939291i	$-0.388516\pi$
$317$	4.63148	+	1.01947i	0.260130	+	0.0572589i	−0.0829905	+	0.996550i	$0.526447\pi$
$318$	4.27273	−	8.05922i	0.239603	−	0.451938i
$319$	1.12851	+	6.88361i	0.0631845	+	0.385408i
$320$	−0.969006	+	1.14080i	−0.0541691	+	0.0637728i
$321$	5.16570	+	6.08153i	0.288321	+	0.339438i
$322$	−2.75919	+	16.8303i	−0.153764	+	0.937917i
$323$	−5.83675	−	4.43698i	−0.324765	−	0.246880i
$324$	−0.561187	+	0.827689i	−0.0311771	+	0.0459827i
$325$	−3.84425	+	5.66985i	−0.213241	+	0.314507i
$326$	−13.7334	−	10.4399i	−0.760625	−	0.578212i
$327$	0.998876	−	6.09287i	0.0552380	−	0.336937i
$328$	4.14024	+	4.87426i	0.228606	+	0.269136i
$329$	37.0455	−	43.6134i	2.04239	−	2.40448i
$330$	−0.534941	−	3.26299i	−0.0294475	−	0.179622i
$331$	14.5801	−	27.5009i	0.801393	−	1.51159i	−0.0568724	−	0.998381i	$-0.518113\pi$
$331$	14.5801	−	27.5009i	0.801393	−	1.51159i	0.858265	−	0.513206i	$-0.171542\pi$
$332$	−11.5363	−	2.53932i	−0.633134	−	0.139363i
$333$	−0.943902	−	0.318038i	−0.0517255	−	0.0174284i
$334$	−0.976807	−	18.0161i	−0.0534485	−	0.985800i
$335$	−5.87355	+	4.46495i	−0.320906	+	0.243946i
$336$	−2.14809	−	4.05173i	−0.117188	−	0.221040i
$337$	−5.34201	−	19.2402i	−0.290998	−	1.04808i	−0.954085	−	0.299537i	$-0.903168\pi$
$337$	−5.34201	−	19.2402i	−0.290998	−	1.04808i	0.663087	−	0.748543i	$-0.269246\pi$
$338$	−4.96441	−	4.70254i	−0.270028	−	0.255784i
$339$	−2.41973	−	6.07306i	−0.131422	−	0.329843i
$340$	4.44181	−	1.49662i	0.240891	−	0.0811656i
$341$	−19.3600	+	2.10553i	−1.04840	+	0.114021i
$342$	2.12492	+	0.983091i	0.114902	+	0.0531595i
$343$	23.4080	−	22.1733i	1.26391	−	1.19724i
$344$	−6.28108	−	3.77920i	−0.338653	−	0.203761i
$345$	5.53393	+	0.601851i	0.297937	+	0.0324026i
$346$	9.76561	−	2.14957i	0.525003	−	0.115562i
$347$	5.00931	−	18.0419i	0.268914	−	0.968540i	−0.698556	−	0.715555i	$-0.746174\pi$
$347$	5.00931	−	18.0419i	0.268914	−	0.968540i	0.967470	−	0.252985i	$-0.0814124\pi$
$348$	2.70565	−	1.62793i	0.145038	−	0.0872664i
$349$	−1.63529	+	0.756564i	−0.0875349	+	0.0404979i	−0.463168	−	0.886271i	$-0.653287\pi$
$349$	−1.63529	+	0.756564i	−0.0875349	+	0.0404979i	0.375633	+	0.926768i	$0.377425\pi$
$350$	4.68422	−	11.7565i	0.250382	−	0.628412i
$351$	−0.134390	+	2.47868i	−0.00717322	+	0.132302i
$352$	1.23971	+	1.82844i	0.0660768	+	0.0974560i
$353$	−13.0473			−0.694439			−0.347220	−	0.937784i	$-0.612874\pi$
$353$	−13.0473			−0.694439			−0.347220	+	0.937784i	$0.612874\pi$
$354$	6.62344	−	3.88973i	0.352032	−	0.206737i
$355$	−1.46437			−0.0777209
$356$	−4.37398	−	6.45113i	−0.231820	−	0.341909i
$357$	−0.777472	+	14.3396i	−0.0411482	+	0.758934i
$358$	−4.71962	+	11.8453i	−0.249440	+	0.626046i
$359$	32.2515	−	14.9211i	1.70217	−	0.787507i	0.705260	−	0.708949i	$-0.250830\pi$
$359$	32.2515	−	14.9211i	1.70217	−	0.787507i	0.996910	−	0.0785586i	$-0.0250318\pi$
$360$	−1.28254	+	0.771679i	−0.0675959	+	0.0406711i
$361$	−3.61652	+	13.0255i	−0.190343	+	0.685554i
$362$	−4.32775	+	0.952611i	−0.227462	+	0.0500681i
$363$	6.08406	+	0.661682i	0.319330	+	0.0347293i
$364$	−9.75426	−	5.86894i	−0.511262	−	0.307616i
$365$	−9.80470	+	9.28751i	−0.513202	+	0.486130i
$366$	−7.82582	−	3.62061i	−0.409062	−	0.189252i
$367$	31.8525	−	3.46416i	1.66269	−	0.180828i	0.772055	−	0.635556i	$-0.219229\pi$
$367$	31.8525	−	3.46416i	1.66269	−	0.180828i	0.890630	+	0.454728i	$0.150264\pi$
$368$	−3.52430	+	1.18748i	−0.183717	+	0.0619015i
$369$	2.36715	+	5.94109i	0.123229	+	0.309281i
$370$	−1.08237	−	1.02527i	−0.0562696	−	0.0533014i
$371$	11.1912	+	40.3072i	0.581020	+	2.09264i
$372$	4.12925	+	7.78859i	0.214092	+	0.403820i
$373$	16.6462	−	12.6541i	0.861907	−	0.655205i	−0.0778809	−	0.996963i	$-0.524815\pi$
$373$	16.6462	−	12.6541i	0.861907	−	0.655205i	0.939788	+	0.341758i	$0.111022\pi$
$374$	−0.374516	−	6.90753i	−0.0193657	−	0.357180i
$375$	−11.0066	−	3.70854i	−0.568376	−	0.191508i
$376$	12.1863	+	2.68240i	0.628458	+	0.138334i
$377$	3.67152	−	6.92522i	0.189093	−	0.356667i
$378$	−0.741921	−	4.52552i	−0.0381603	−	0.232768i
$379$	−2.71963	+	3.20180i	−0.139698	+	0.164465i	−0.827562	−	0.561375i	$-0.810273\pi$
$379$	−2.71963	+	3.20180i	−0.139698	+	0.164465i	0.687864	+	0.725840i	$0.258549\pi$
$380$	2.26874	+	2.67097i	0.116384	+	0.137018i
$381$	1.44451	−	8.81113i	0.0740046	−	0.451408i
$382$	−16.7973	−	12.7690i	−0.859424	−	0.653317i
$383$	−17.0423	+	25.1355i	−0.870820	+	1.28436i	0.0867695	+	0.996228i	$0.472346\pi$
$383$	−17.0423	+	25.1355i	−0.870820	+	1.28436i	−0.957590	+	0.288135i	$0.906965\pi$
$384$	0.561187	−	0.827689i	0.0286380	−	0.0422378i
$385$	12.0717	+	9.17664i	0.615229	+	0.467685i
$386$	3.45307	−	21.0628i	0.175757	−	1.07207i
$387$	−4.74558	−	5.58693i	−0.241231	−	0.284000i
$388$	−7.57382	+	8.91659i	−0.384502	+	0.452671i
$389$	−0.287310	−	1.75252i	−0.0145672	−	0.0888561i	0.978542	−	0.206046i	$-0.0660596\pi$
$389$	−0.287310	−	1.75252i	−0.0145672	−	0.0888561i	−0.993110	+	0.117190i	$0.962611\pi$
$390$	−1.74039	+	3.28272i	−0.0881279	+	0.166227i
$391$	11.3736	+	2.50352i	0.575187	+	0.126608i
$392$	13.2963	+	4.48005i	0.671565	+	0.226277i
$393$	−0.465270	−	8.58140i	−0.0234698	−	0.432874i
$394$	−5.40412	+	4.10810i	−0.272256	+	0.206963i
$395$	−10.3121	−	19.4506i	−0.518856	−	0.978667i
$396$	0.590993	+	2.12856i	0.0296985	+	0.106964i
$397$	−24.3767	−	23.0908i	−1.22343	−	1.15889i	−0.982082	−	0.188455i	$-0.939652\pi$
$397$	−24.3767	−	23.0908i	−1.22343	−	1.15889i	−0.241347	−	0.970439i	$-0.577589\pi$
$398$	−8.08883	−	20.3014i	−0.405457	−	1.01762i
$399$	−10.1750	+	3.42837i	−0.509389	+	0.171633i
$400$	2.74342	−	0.298365i	0.137171	−	0.0149183i
$401$	−20.5756	−	9.51930i	−1.02750	−	0.475371i	−0.167610	−	0.985853i	$-0.553605\pi$
$401$	−20.5756	−	9.51930i	−1.02750	−	0.475371i	−0.859888	+	0.510482i	$0.829467\pi$
$402$	3.57855	−	3.38979i	0.178482	−	0.169067i
$403$	18.7505	+	11.2818i	0.934030	+	0.561987i
$404$	5.66369	+	0.615963i	0.281779	+	0.0306453i
$405$	−1.46180	+	0.321767i	−0.0726376	+	0.0159887i
$406$	−3.87401	+	13.9529i	−0.192264	+	0.692471i
$407$	−1.88538	+	1.13439i	−0.0934548	+	0.0562299i
$408$	−2.84204	+	1.31487i	−0.140702	+	0.0650957i
$409$	−4.08594	+	10.2549i	−0.202037	+	0.507074i	−0.994728	−	0.102550i	$-0.967300\pi$
$409$	−4.08594	+	10.2549i	−0.202037	+	0.507074i	0.792691	+	0.609623i	$0.208679\pi$
$410$	−0.518244	+	9.55844i	−0.0255942	+	0.472058i
$411$	6.31404	+	9.31251i	0.311448	+	0.459352i
$412$	5.70452			0.281042
$413$	−9.78465	+	33.8390i	−0.481471	+	1.66511i
$414$	−3.71898			−0.182778
$415$	−9.92223	−	14.6342i	−0.487063	−	0.718365i
$416$	0.134390	−	2.47868i	0.00658902	−	0.121527i
$417$	0.322026	−	0.808225i	0.0157697	−	0.0395790i
$418$	4.69412	−	2.17173i	0.229597	−	0.106223i
$419$	−5.07378	+	3.05279i	−0.247870	+	0.149139i	−0.634068	−	0.773278i	$-0.718616\pi$
$419$	−5.07378	+	3.05279i	−0.247870	+	0.149139i	0.386197	+	0.922416i	$0.373788\pi$
$420$	1.83637	−	6.61401i	0.0896057	−	0.322731i
$421$	5.56130	−	1.22413i	0.271041	−	0.0596607i	−0.0773701	−	0.997002i	$-0.524652\pi$
$421$	5.56130	−	1.22413i	0.271041	−	0.0596607i	0.348411	+	0.937342i	$0.386721\pi$
$422$	−4.61201	−	0.501587i	−0.224509	−	0.0244169i
$423$	10.6919	+	6.43308i	0.519856	+	0.312787i
$424$	−6.62238	+	6.27305i	−0.321611	+	0.304646i
$425$	−7.84290	−	3.62851i	−0.380436	−	0.176009i
$426$	0.972603	−	0.105777i	0.0471228	−	0.00512491i
$427$	37.4735	−	12.6263i	1.81347	−	0.611029i
$428$	−2.95345	−	7.41260i	−0.142760	−	0.358301i
$429$	3.98112	+	3.77111i	0.192210	+	0.182071i
$430$	−2.93534	−	10.5721i	−0.141555	−	0.509834i
$431$	8.57230	+	16.1691i	0.412913	+	0.778837i	0.999518	−	0.0310363i	$-0.00988073\pi$
$431$	8.57230	+	16.1691i	0.412913	+	0.778837i	−0.586605	+	0.809873i	$0.699536\pi$
$432$	0.796093	−	0.605174i	0.0383020	−	0.0291165i
$433$	−1.72017	−	31.7266i	−0.0826659	−	1.52468i	−0.686239	−	0.727376i	$-0.740740\pi$
$433$	−1.72017	−	31.7266i	−0.0826659	−	1.52468i	0.603573	−	0.797307i	$-0.293743\pi$
$434$	−38.3110	−	12.9085i	−1.83899	−	0.619627i
$435$	4.61585	+	1.01603i	0.221313	+	0.0487147i
$436$	−2.89205	+	5.45499i	−0.138504	+	0.261247i
$437$	1.40868	+	8.59259i	0.0673864	+	0.411039i
$438$	5.84119	−	6.87678i	0.279103	−	0.328585i
$439$	−12.1024	−	14.2481i	−0.577617	−	0.680023i	0.393308	−	0.919407i	$-0.371331\pi$
$439$	−12.1024	−	14.2481i	−0.577617	−	0.680023i	−0.970925	+	0.239383i	$0.923055\pi$
$440$	−0.534941	+	3.26299i	−0.0255023	+	0.155557i
$441$	11.1698	+	8.49106i	0.531895	+	0.404336i
$442$	−4.36228	+	6.43388i	−0.207493	+	0.306029i
$443$	−19.3620	+	28.5568i	−0.919917	+	1.35678i	0.0142341	+	0.999899i	$0.495469\pi$
$443$	−19.3620	+	28.5568i	−0.919917	+	1.35678i	−0.934151	+	0.356877i	$0.883841\pi$
$444$	0.792942	+	0.602779i	0.0376314	+	0.0286066i
$445$	1.88739	−	11.5126i	0.0894709	−	0.545748i
$446$	16.8886	+	19.8828i	0.799697	+	0.941477i
$447$	10.6590	−	12.5488i	0.504154	−	0.593536i
$448$	0.741921	+	4.52552i	0.0350525	+	0.213811i
$449$	−15.9481	+	30.0813i	−0.752638	+	1.41963i	0.149759	+	0.988722i	$0.452150\pi$
$449$	−15.9481	+	30.0813i	−0.752638	+	1.41963i	−0.902398	+	0.430904i	$0.858195\pi$
$450$	2.69508	+	0.593232i	0.127047	+	0.0279652i
$451$	13.3882	+	4.51103i	0.630428	+	0.212416i
$452$	0.353926	+	6.52778i	0.0166473	+	0.307041i
$453$	7.39651	−	5.62268i	0.347518	−	0.264177i
$454$	11.9260	+	22.4949i	0.559716	+	1.05574i
$455$	−4.55846	−	16.4181i	−0.213704	−	0.769693i
$456$	−1.69978	−	1.61012i	−0.0795996	−	0.0754007i
$457$	5.46645	+	13.7198i	0.255710	+	0.641783i	0.999650	−	0.0264633i	$-0.00842453\pi$
$457$	5.46645	+	13.7198i	0.255710	+	0.641783i	−0.743940	+	0.668246i	$0.767045\pi$
$458$	0.0493293	−	0.0166210i	0.00230501	−	0.000776648i
$459$	−3.11311	+	0.338571i	−0.145308	+	0.0158031i
$460$	−5.05207	−	2.33734i	−0.235554	−	0.108979i
$461$	9.80677	−	9.28947i	0.456747	−	0.432654i	−0.424415	−	0.905468i	$-0.639520\pi$
$461$	9.80677	−	9.28947i	0.456747	−	0.432654i	0.881162	+	0.472814i	$0.156762\pi$
$462$	−8.68058	−	5.22293i	−0.403857	−	0.242993i
$463$	−13.9687	−	1.51918i	−0.649179	−	0.0706025i	−0.222396	−	0.974956i	$-0.571388\pi$
$463$	−13.9687	−	1.51918i	−0.649179	−	0.0706025i	−0.426783	+	0.904354i	$0.640353\pi$
$464$	−3.08382	+	0.678800i	−0.143163	+	0.0315125i
$465$	−3.53004	+	12.7140i	−0.163701	+	0.589599i
$466$	2.59039	−	1.55859i	0.119997	−	0.0722001i
$467$	−10.8709	+	5.02944i	−0.503047	+	0.232735i	−0.654966	−	0.755659i	$-0.727317\pi$
$467$	−10.8709	+	5.02944i	−0.503047	+	0.232735i	0.151918	+	0.988393i	$0.451455\pi$
$468$	0.918803	−	2.30602i	0.0424717	−	0.106596i
$469$	−1.22380	+	22.5717i	−0.0565099	+	1.04226i
$470$	10.4813	+	15.4588i	0.483466	+	0.713059i
$471$	−12.5708			−0.579231
$472$	−7.51872	+	1.57124i	−0.346077	+	0.0723223i
$473$	−16.1934			−0.744574
$474$	8.25402	+	12.1738i	0.379120	+	0.559160i
$475$	0.349796	−	6.45160i	0.0160497	−	0.296020i
$476$	5.31544	−	13.3407i	0.243633	−	0.611472i
$477$	−8.27872	+	3.83014i	−0.379056	+	0.175370i
$478$	−5.04054	+	3.03279i	−0.230549	+	0.138717i
$479$	4.73725	−	17.0620i	0.216451	−	0.779585i	−0.772962	−	0.634453i	$-0.781226\pi$
$479$	4.73725	−	17.0620i	0.216451	−	0.779585i	0.989412	−	0.145132i	$-0.0463607\pi$
$480$	1.46180	−	0.321767i	0.0667219	−	0.0146866i
$481$	2.45800	+	0.267324i	0.112075	+	0.0121889i
$482$	23.0870	+	13.8910i	1.05159	+	0.632718i
$483$	12.3818	−	11.7287i	0.563394	−	0.533675i
$484$	−5.55431	−	2.56970i	−0.252468	−	0.116804i
$485$	−17.4085	+	1.89329i	−0.790478	+	0.0859697i
$486$	0.947653	−	0.319302i	0.0429864	−	0.0144838i
$487$	−11.9585	−	30.0137i	−0.541893	−	1.36005i	−0.903848	−	0.427853i	$-0.859270\pi$
$487$	−11.9585	−	30.0137i	−0.541893	−	1.36005i	0.361955	−	0.932195i	$-0.382109\pi$
$488$	6.26009	+	5.92988i	0.283381	+	0.268433i
$489$	4.61515	+	16.6223i	0.208704	+	0.751684i
$490$	9.83715	+	18.5548i	0.444397	+	0.838222i
$491$	5.53026	−	4.20400i	0.249577	−	0.189724i	−0.472904	−	0.881114i	$-0.656794\pi$
$491$	5.53026	−	4.20400i	0.249577	−	0.189724i	0.722482	+	0.691390i	$0.243001\pi$
$492$	−0.346235	−	6.38593i	−0.0156095	−	0.287900i
$493$	9.37044	+	3.15727i	0.422023	+	0.142196i
$494$	−5.67601	−	1.24938i	−0.255376	−	0.0562125i
$495$	−1.54882	+	2.92138i	−0.0696142	+	0.131306i
$496$	−1.42619	−	8.69936i	−0.0640377	−	0.390613i
$497$	−2.90456	+	3.41951i	−0.130287	+	0.153386i
$498$	7.64720	+	9.00298i	0.342679	+	0.403433i
$499$	0.409370	−	2.49705i	0.0183259	−	0.111783i	−0.976080	−	0.217414i	$-0.930238\pi$
$499$	0.409370	−	2.49705i	0.0183259	−	0.111783i	0.994405	+	0.105631i	$0.0336861\pi$
$500$	9.24626	+	7.02882i	0.413505	+	0.314338i
$501$	−10.1253	+	14.9337i	−0.452364	+	0.667187i
$502$	−9.34083	+	13.7767i	−0.416902	+	0.614884i
$503$	−34.6881	−	26.3692i	−1.54666	−	1.17574i	−0.917007	−	0.398871i	$-0.869402\pi$
$503$	−34.6881	−	26.3692i	−1.54666	−	1.17574i	−0.629657	−	0.776873i	$-0.716805\pi$
$504$	−0.741921	+	4.52552i	−0.0330478	+	0.201583i
$505$	5.52051	+	6.49924i	0.245659	+	0.289213i
$506$	−5.31863	+	6.26158i	−0.236442	+	0.278361i
$507$	1.10628	+	6.74799i	0.0491315	+	0.299689i
$508$	−4.18230	+	7.88866i	−0.185560	+	0.350003i
$509$	28.6981	+	6.31694i	1.27202	+	0.279993i	0.799147	−	0.601136i	$-0.205285\pi$
$509$	28.6981	+	6.31694i	1.27202	+	0.279993i	0.472876	+	0.881129i	$0.343216\pi$
$510$	−4.44181	−	1.49662i	−0.196687	−	0.0662715i
$511$	2.24014	+	41.3169i	0.0990979	+	1.82775i
$512$	−0.796093	+	0.605174i	−0.0351827	+	0.0267452i
$513$	−1.09669	−	2.06858i	−0.0484200	−	0.0913299i
$514$	0.865129	+	3.11591i	0.0381592	+	0.137437i
$515$	6.19892	+	5.87193i	0.273157	+	0.258748i
$516$	2.71325	+	6.80974i	0.119444	+	0.299782i
$517$	26.1220	−	8.80153i	1.14884	−	0.387091i
$518$	−4.54100	+	0.493864i	−0.199520	+	0.0216991i
$519$	−9.07520	−	4.19864i	−0.398357	−	0.184300i
$520$	2.69746	−	2.55517i	0.118291	−	0.112052i
$521$	−13.8942	−	8.35988i	−0.608717	−	0.366253i	0.177576	−	0.984107i	$-0.443175\pi$
$521$	−13.8942	−	8.35988i	−0.608717	−	0.366253i	−0.786293	+	0.617854i	$0.788002\pi$
$522$	−3.13913	−	0.341401i	−0.137396	−	0.0149427i
$523$	1.99662	−	0.439488i	0.0873059	−	0.0192175i	−0.171103	−	0.985253i	$-0.554733\pi$
$523$	1.99662	−	0.439488i	0.0873059	−	0.0192175i	0.258409	+	0.966036i	$0.416802\pi$
$524$	−2.29914	+	8.28075i	−0.100438	+	0.361746i
$525$	−10.8438	+	6.52451i	−0.473263	+	0.284753i
$526$	9.11483	−	4.21697i	0.397425	−	0.183869i
$527$	−10.2178	+	25.6448i	−0.445095	+	1.11710i
$528$	0.119598	−	2.20585i	0.00520481	−	0.0959971i
$529$	5.14563	+	7.58923i	0.223723	+	0.329967i
$530$	−13.6535			−0.593069
$531$	−7.62684	−	0.911748i	−0.330977	−	0.0395665i
$532$	10.7371			0.465512
$533$	−8.90897	−	13.1398i	−0.385890	−	0.569146i
$534$	−0.421967	+	7.78272i	−0.0182603	+	0.336791i
$535$	4.42071	−	11.0952i	0.191124	−	0.479685i
$536$	−4.47359	+	2.06970i	−0.193230	+	0.0893976i
$537$	10.9258	−	6.57381i	0.471481	−	0.283681i
$538$	−0.0493263	+	0.177657i	−0.00212661	+	0.00765935i
$539$	30.2705	−	6.66305i	1.30384	−	0.286998i
$540$	1.48802	+	0.161832i	0.0640343	+	0.00696415i
$541$	32.0427	+	19.2794i	1.37762	+	0.828888i	0.995458	−	0.0952058i	$-0.0303509\pi$
$541$	32.0427	+	19.2794i	1.37762	+	0.828888i	0.382165	+	0.924094i	$0.375178\pi$
$542$	4.01028	−	3.79874i	0.172256	−	0.163170i
$543$	4.02179	+	1.86068i	0.172592	+	0.0798493i
$544$	3.11311	−	0.338571i	0.133473	−	0.0145161i
$545$	−8.75777	+	2.95084i	−0.375142	+	0.126400i
$546$	4.21357	+	10.5753i	0.180324	+	0.452579i
$547$	10.7683	+	10.2003i	0.460418	+	0.436131i	0.882419	−	0.470464i	$-0.155914\pi$
$547$	10.7683	+	10.2003i	0.460418	+	0.436131i	−0.422001	+	0.906595i	$0.638672\pi$
$548$	−3.01002	−	10.8411i	−0.128582	−	0.463109i
$549$	4.03898	+	7.61832i	0.172379	+	0.325142i
$550$	4.85314	−	3.68926i	0.206938	−	0.157310i
$551$	0.400250	+	7.38218i	0.0170512	+	0.314491i
$552$	3.52430	+	1.18748i	0.150004	+	0.0505423i
$553$	−65.8736	−	14.4999i	−2.80123	−	0.616598i
$554$	5.84712	−	11.0288i	0.248420	−	0.468570i
$555$	0.241196	+	1.47123i	0.0102382	+	0.0624503i
$556$	−0.563237	+	0.663094i	−0.0238866	+	0.0281214i
$557$	22.7611	+	26.7964i	0.964418	+	1.13540i	0.990743	+	0.135747i	$0.0433435\pi$
$557$	22.7611	+	26.7964i	0.964418	+	1.13540i	−0.0263254	+	0.999653i	$0.508381\pi$
$558$	1.42619	−	8.69936i	0.0603753	−	0.368273i
$559$	14.4860	+	11.0120i	0.612692	+	0.465756i
$560$	−3.85211	+	5.68143i	−0.162781	+	0.240084i
$561$	−3.88211	+	5.72569i	−0.163903	+	0.241739i
$562$	2.14897	+	1.63360i	0.0906488	+	0.0689095i
$563$	5.66720	−	34.5684i	0.238844	−	1.45688i	−0.546310	−	0.837583i	$-0.683968\pi$
$563$	5.66720	−	34.5684i	0.238844	−	1.45688i	0.785154	−	0.619300i	$-0.212584\pi$
$564$	−8.07808	−	9.51025i	−0.340149	−	0.400454i
$565$	−6.33474	+	7.45784i	−0.266505	+	0.313754i
$566$	−4.69089	−	28.6131i	−0.197173	−	1.20270i
$567$	−2.14809	+	4.05173i	−0.0902113	+	0.170157i
$568$	−0.955465	−	0.210314i	−0.0400904	−	0.00882457i
$569$	0.515439	+	0.173672i	0.0216083	+	0.00728070i	0.330085	−	0.943951i	$-0.392923\pi$
$569$	0.515439	+	0.173672i	0.0216083	+	0.00728070i	−0.308477	+	0.951232i	$0.599819\pi$
$570$	−0.189728	−	3.49933i	−0.00794683	−	0.146571i
$571$	−21.1489	+	16.0770i	−0.885056	+	0.672802i	−0.945589	−	0.325364i	$-0.894513\pi$
$571$	−21.1489	+	16.0770i	−0.885056	+	0.672802i	0.0605331	+	0.998166i	$0.480720\pi$
$572$	−2.56860	−	4.84488i	−0.107398	−	0.202575i
$573$	5.64476	+	20.3306i	0.235813	+	0.849322i
$574$	21.2923	+	20.1692i	0.888725	+	0.841845i
$575$	3.79869	+	9.53399i	0.158416	+	0.397595i
$576$	−0.947653	+	0.319302i	−0.0394855	+	0.0133042i
$577$	16.8211	−	1.82940i	0.700272	−	0.0761591i	0.248945	−	0.968518i	$-0.419916\pi$
$577$	16.8211	−	1.82940i	0.700272	−	0.0761591i	0.451327	+	0.892359i	$0.350951\pi$
$578$	6.52902	+	3.02065i	0.271572	+	0.125642i
$579$	−15.4956	+	14.6783i	−0.643977	+	0.610008i
$580$	−4.04981	−	2.43669i	−0.168159	−	0.101178i
$581$	−53.8534	−	5.85691i	−2.23422	−	0.242986i
$582$	11.4256	−	2.51495i	0.473604	−	0.104248i
$583$	−5.39092	+	19.4163i	−0.223269	+	0.804143i
$584$	−7.73119	+	4.65170i	−0.319919	+	0.192489i
$585$	3.37213	−	1.56011i	0.139420	−	0.0645027i
$586$	−0.376285	+	0.944405i	−0.0155442	+	0.0390130i
$587$	1.36989	−	25.2661i	0.0565412	−	1.04284i	−0.823310	−	0.567592i	$-0.807875\pi$
$587$	1.36989	−	25.2661i	0.0565412	−	1.04284i	0.879851	−	0.475249i	$-0.157642\pi$
$588$	−7.87389	−	11.6131i	−0.324714	−	0.478917i
$589$	−20.6398			−0.850448
$590$	−9.78771	−	6.03195i	−0.402954	−	0.248332i
$591$	6.78830			0.279233
$592$	−0.558966	−	0.824413i	−0.0229734	−	0.0338832i
$593$	1.39361	−	25.7036i	0.0572287	−	1.05552i	−0.819052	−	0.573720i	$-0.805500\pi$
$593$	1.39361	−	25.7036i	0.0572287	−	1.05552i	0.876280	−	0.481801i	$-0.160017\pi$
$594$	0.817667	−	2.05219i	0.0335493	−	0.0842024i
$595$	19.5084	−	9.02553i	0.799765	−	0.370011i
$596$	−14.1079	+	8.48843i	−0.577881	+	0.347700i
$597$	−5.84644	+	21.0570i	−0.239279	+	0.861805i
$598$	9.01588	−	1.98455i	0.368687	−	0.0811541i
$599$	−15.1583	−	1.64857i	−0.619352	−	0.0673586i	−0.206936	−	0.978354i	$-0.566349\pi$
$599$	−15.1583	−	1.64857i	−0.619352	−	0.0673586i	−0.412415	+	0.910996i	$0.635315\pi$
$600$	−2.36458	−	1.42272i	−0.0965337	−	0.0580824i
$601$	−30.5267	+	28.9165i	−1.24521	+	1.17953i	−0.268897	+	0.963169i	$0.586659\pi$
$601$	−30.5267	+	28.9165i	−1.24521	+	1.17953i	−0.976314	+	0.216358i	$0.930582\pi$
$602$	−30.5096	−	14.1152i	−1.24348	−	0.575294i
$603$	−4.90027	+	0.532937i	−0.199555	+	0.0217029i
$604$	−8.80466	+	2.96663i	−0.358256	+	0.120711i
$605$	−3.39058	−	8.50971i	−0.137847	−	0.345969i
$606$	−4.13606	−	3.91788i	−0.168016	−	0.159153i
$607$	−6.41806	−	23.1158i	−0.260501	−	0.938240i	−0.971889	−	0.235440i	$-0.924347\pi$
$607$	−6.41806	−	23.1158i	−0.260501	−	0.938240i	0.711388	−	0.702800i	$-0.248067\pi$
$608$	1.09669	+	2.06858i	0.0444767	+	0.0838919i
$609$	11.5280	−	8.76337i	0.467139	−	0.355109i
$610$	0.698746	+	12.8876i	0.0282914	+	0.521804i
$611$	−29.3530	−	9.89017i	−1.18749	−	0.400114i
$612$	3.05825	+	0.673173i	0.123623	+	0.0272114i
$613$	20.9036	−	39.4283i	0.844288	−	1.59250i	0.0392821	−	0.999228i	$-0.487493\pi$
$613$	20.9036	−	39.4283i	0.844288	−	1.59250i	0.805006	−	0.593267i	$-0.202162\pi$
$614$	3.48577	+	21.2623i	0.140674	+	0.858076i
$615$	6.19709	−	7.29578i	0.249891	−	0.294194i
$616$	6.55849	+	7.72125i	0.264249	+	0.311098i
$617$	−5.42781	+	33.1082i	−0.218515	+	1.33288i	0.618534	+	0.785758i	$0.287727\pi$
$617$	−5.42781	+	33.1082i	−0.218515	+	1.33288i	−0.837050	+	0.547127i	$0.815722\pi$
$618$	−4.54133	−	3.45223i	−0.182679	−	0.138869i
$619$	−20.4800	+	30.2058i	−0.823162	+	1.21407i	0.151070	+	0.988523i	$0.451728\pi$
$619$	−20.4800	+	30.2058i	−0.823162	+	1.21407i	−0.974232	+	0.225550i	$0.927582\pi$
$620$	7.40486	−	10.9214i	0.297386	−	0.438612i
$621$	2.96065	+	2.25063i	0.118807	+	0.0903147i
$622$	0.894175	−	5.45423i	0.0358531	−	0.218694i
$623$	−23.1398	−	27.2423i	−0.927077	−	1.09144i
$624$	−1.60702	+	1.89193i	−0.0643324	+	0.0757379i
$625$	0.580250	+	3.53937i	0.0232100	+	0.141575i
$626$	8.69138	−	16.3937i	0.347377	−	0.655223i
$627$	−5.05124	−	1.11186i	−0.201727	−	0.0444035i
$628$	11.9127	+	4.01387i	0.475370	+	0.160171i
$629$	0.168863	+	3.11450i	0.00673301	+	0.124183i
$630$	−5.46455	+	4.15404i	−0.217713	+	0.165501i
$631$	14.9971	+	28.2875i	0.597025	+	1.12611i	0.979367	+	0.202088i	$0.0647728\pi$
$631$	14.9971	+	28.2875i	0.597025	+	1.12611i	−0.382342	+	0.924021i	$0.624882\pi$
$632$	−3.93485	−	14.1720i	−0.156520	−	0.563733i
$633$	3.36804	+	3.19038i	0.133868	+	0.126806i
$634$	1.75533	+	4.40554i	0.0697129	+	0.174966i
$635$	−12.6649	+	4.26731i	−0.502593	+	0.169343i
$636$	9.06832	−	0.986240i	0.359582	−	0.0391069i
$637$	−31.6099	−	14.6243i	−1.25243	−	0.579435i
$638$	−5.06418	+	4.79705i	−0.200493	+	0.189917i
$639$	−0.838296	−	0.504386i	−0.0331625	−	0.0199532i
$640$	−1.48802	−	0.161832i	−0.0588193	−	0.00639698i
$641$	47.7451	−	10.5095i	1.88582	−	0.415100i	0.886916	−	0.461931i	$-0.152843\pi$
$641$	47.7451	−	10.5095i	1.88582	−	0.415100i	0.998903	+	0.0468307i	$0.0149121\pi$
$642$	−2.13469	+	7.68847i	−0.0842496	+	0.303440i
$643$	18.3983	−	11.0699i	0.725558	−	0.436554i	−0.104287	−	0.994547i	$-0.533256\pi$
$643$	18.3983	−	11.0699i	0.725558	−	0.436554i	0.829845	+	0.557993i	$0.188429\pi$
$644$	−15.4787	+	7.16121i	−0.609946	+	0.282191i
$645$	−4.06118	+	10.1928i	−0.159909	+	0.401341i
$646$	0.396932	−	7.32098i	0.0156171	−	0.288040i
$647$	−20.2134	−	29.8125i	−0.794670	−	1.17205i	−0.981838	−	0.189723i	$-0.939241\pi$
$647$	−20.2134	−	29.8125i	−0.794670	−	1.17205i	0.187167	−	0.982328i	$-0.440069\pi$
$648$	−1.00000			−0.0392837
$649$	−12.4425	+	11.5373i	−0.488410	+	0.452877i
$650$	−6.85022			−0.268688
$651$	22.6872	+	33.4612i	0.889183	+	1.31145i
$652$	0.933953	−	17.2258i	0.0365764	−	0.674613i
$653$	−6.83558	+	17.1560i	−0.267497	+	0.671367i	−0.999955	−	0.00944492i	$-0.996994\pi$
$653$	−6.83558	+	17.1560i	−0.267497	+	0.671367i	0.732458	+	0.680812i	$0.238373\pi$
$654$	5.60356	−	2.59248i	0.219117	−	0.101374i
$655$	−11.0222	+	6.63181i	−0.430671	+	0.259126i
$656$	−1.71093	+	6.16220i	−0.0668005	+	0.240594i
$657$	−8.81178	+	1.93962i	−0.343780	+	0.0756717i
$658$	56.8878	+	6.18692i	2.21772	+	0.241191i
$659$	−40.2478	−	24.2163i	−1.56783	−	0.943333i	−0.992066	−	0.125718i	$-0.959877\pi$
$659$	−40.2478	−	24.2163i	−1.56783	−	0.943333i	−0.575765	−	0.817615i	$-0.695296\pi$
$660$	2.40054	−	2.27392i	0.0934410	−	0.0885120i
$661$	−28.5896	−	13.2270i	−1.11201	−	0.514469i	−0.224134	−	0.974558i	$-0.571955\pi$
$661$	−28.5896	−	13.2270i	−1.11201	−	0.514469i	−0.887873	+	0.460089i	$0.847817\pi$
$662$	30.9444	−	3.36540i	1.20269	−	0.130800i
$663$	7.36640	−	2.48203i	0.286087	−	0.0963941i
$664$	−4.37223	−	10.9735i	−0.169675	−	0.425853i
$665$	11.6677	+	11.0522i	0.452452	+	0.428586i
$666$	−0.266469	−	0.959736i	−0.0103255	−	0.0371890i
$667$	−5.50062	−	10.3753i	−0.212985	−	0.401732i
$668$	14.3636	−	10.9189i	0.555744	−	0.422466i
$669$	−1.41234	−	26.0491i	−0.0546042	−	1.00712i
$670$	−6.99175	−	2.35580i	−0.270115	−	0.0910123i
$671$	18.6031	+	4.09485i	0.718165	+	0.158080i
$672$	2.14809	−	4.05173i	0.0828643	−	0.156299i
$673$	4.45066	+	27.1478i	0.171560	+	1.04647i	0.922471	+	0.386067i	$0.126167\pi$
$673$	4.45066	+	27.1478i	0.171560	+	1.04647i	−0.750911	+	0.660404i	$0.770385\pi$
$674$	12.9270	−	15.2189i	0.497930	−	0.586209i
$675$	−1.78653	−	2.10326i	−0.0687634	−	0.0809546i
$676$	1.10628	−	6.74799i	0.0425491	−	0.259538i
$677$	26.1161	+	19.8530i	1.00372	+	0.763012i	0.971638	−	0.236473i	$-0.0759916\pi$
$677$	26.1161	+	19.8530i	1.00372	+	0.763012i	0.0320867	+	0.999485i	$0.489785\pi$
$678$	3.66868	−	5.41090i	0.140895	−	0.207805i
$679$	−30.1083	+	44.4065i	−1.15545	+	1.70416i
$680$	3.73142	+	2.83655i	0.143094	+	0.108777i
$681$	4.11909	−	25.1253i	0.157844	−	0.962804i
$682$	−12.6073	−	14.8425i	−0.482759	−	0.568348i
$683$	9.04375	−	10.6471i	0.346050	−	0.407401i	−0.561412	−	0.827537i	$-0.689742\pi$
$683$	9.04375	−	10.6471i	0.346050	−	0.407401i	0.907461	+	0.420136i	$0.138017\pi$
$684$	0.378782	+	2.31047i	0.0144831	+	0.0883430i
$685$	7.88837	−	14.8790i	0.301399	−	0.568499i
$686$	31.4888	+	6.93122i	1.20225	+	0.264635i
$687$	−0.0493293	−	0.0166210i	−0.00188203	−	0.000634130i
$688$	−0.396858	−	7.31962i	−0.0151301	−	0.279058i
$689$	18.0261	−	13.7031i	0.686741	−	0.522047i
$690$	2.60742	+	4.91812i	0.0992629	+	0.187230i
$691$	−5.97350	−	21.5146i	−0.227243	−	0.818454i	−0.985953	−	0.167025i	$-0.946584\pi$
$691$	−5.97350	−	21.5146i	−0.227243	−	0.818454i	0.758710	−	0.651429i	$-0.225830\pi$
$692$	7.25951	+	6.87658i	0.275965	+	0.261408i
$693$	3.74977	+	9.41120i	0.142442	+	0.357502i
$694$	17.7442	−	5.97873i	0.673562	−	0.226950i
$695$	−1.29460	+	0.140797i	−0.0491071	+	0.00534072i
$696$	2.86580	+	1.32586i	0.108628	+	0.0502566i
$697$	14.5393	−	13.7724i	0.550715	−	0.521665i
$698$	−1.54390	−	0.928934i	−0.0584375	−	0.0351607i
$699$	−3.00541	−	0.326858i	−0.113675	−	0.0123629i
$700$	12.3595	−	2.72052i	0.467144	−	0.102826i
$701$	−6.43459	+	23.1753i	−0.243031	+	0.875319i	0.736903	+	0.675998i	$0.236287\pi$
$701$	−6.43459	+	23.1753i	−0.243031	+	0.875319i	−0.979934	+	0.199320i	$0.936127\pi$
$702$	−2.12700	+	1.27977i	−0.0802783	+	0.0483019i
$703$	−2.11651	+	0.979200i	−0.0798255	+	0.0369312i
$704$	−0.817667	+	2.05219i	−0.0308170	+	0.0773448i
$705$	1.01115	−	18.6496i	0.0380822	−	0.702386i
$706$	−7.32199	−	10.7991i	−0.275567	−	0.406431i
$707$	26.1264			0.982586
$708$	6.93648	+	3.29928i	0.260689	+	0.123995i
$709$	26.2840			0.987118			0.493559	−	0.869712i	$-0.335696\pi$
$709$	26.2840			0.987118			0.493559	+	0.869712i	$0.335696\pi$
$710$	−0.821787	−	1.21205i	−0.0308411	−	0.0454873i
$711$	0.796283	−	14.6866i	0.0298630	−	0.550790i
$712$	2.88491	−	7.24058i	0.108117	−	0.271352i
$713$	29.7545	−	13.7659i	1.11432	−	0.515537i
$714$	−12.3051	+	7.40371i	−0.460505	+	0.277077i
$715$	2.19585	−	7.90875i	0.0821203	−	0.295771i
$716$	−12.4529	+	2.74108i	−0.465385	+	0.102439i
$717$	5.84811	+	0.636020i	0.218402	+	0.0237526i
$718$	30.4492	+	18.3207i	1.13635	+	0.683721i
$719$	9.25479	−	8.76660i	0.345145	−	0.326939i	−0.495416	−	0.868656i	$-0.664984\pi$
$719$	9.25479	−	8.76660i	0.345145	−	0.326939i	0.840561	+	0.541717i	$0.182226\pi$
$720$	−1.35846	−	0.628489i	−0.0506267	−	0.0234224i
$721$	26.0072	−	2.82845i	0.968558	−	0.105337i
$722$	−12.8106	+	4.31640i	−0.476762	+	0.160640i
$723$	−9.97295	−	25.0302i	−0.370898	−	0.930884i
$724$	−3.21714	−	3.04744i	−0.119564	−	0.113257i
$725$	2.33120	+	8.39621i	0.0865784	+	0.311827i
$726$	2.86663	+	5.40704i	0.106391	+	0.200674i
$727$	34.5089	−	26.2330i	1.27986	−	0.972928i	0.279948	−	0.960015i	$-0.409683\pi$
$727$	34.5089	−	26.2330i	1.27986	−	0.972928i	0.999917	−	0.0129129i	$-0.00411042\pi$
$728$	−0.616305	−	11.3671i	−0.0228418	−	0.421292i
$729$	−0.947653	−	0.319302i	−0.0350983	−	0.0118260i
$730$	−13.1894	−	2.90322i	−0.488163	−	0.107453i
$731$	−10.7522	+	20.2808i	−0.397685	+	0.750114i
$732$	−1.39501	−	8.50918i	−0.0515610	−	0.314508i
$733$	22.2604	−	26.2070i	0.822207	−	0.967976i	−0.177664	−	0.984091i	$-0.556854\pi$
$733$	22.2604	−	26.2070i	0.822207	−	0.967976i	0.999870	+	0.0161149i	$0.00512975\pi$
$734$	20.7424	+	24.4199i	0.765618	+	0.901355i
$735$	3.39762	−	20.7246i	0.125323	−	0.764437i
$736$	−2.96065	−	2.25063i	−0.109131	−	0.0829594i
$737$	−6.11074	+	9.01267i	−0.225092	+	0.331986i
$738$	−3.58897	+	5.29333i	−0.132112	+	0.194850i
$739$	3.48079	+	2.64603i	0.128043	+	0.0973358i	0.667236	−	0.744847i	$-0.267477\pi$
$739$	3.48079	+	2.64603i	0.128043	+	0.0973358i	−0.539193	+	0.842182i	$0.681271\pi$
$740$	0.241196	−	1.47123i	0.00886655	−	0.0540836i
$741$	3.76254	+	4.42960i	0.138220	+	0.162726i
$742$	−27.0814	+	31.8827i	−0.994190	+	1.17045i
$743$	−7.82597	−	47.7363i	−0.287107	−	1.75128i	−0.598620	−	0.801033i	$-0.704284\pi$
$743$	−7.82597	−	47.7363i	−0.287107	−	1.75128i	0.311513	−	0.950242i	$-0.399164\pi$
$744$	−4.12925	+	7.78859i	−0.151386	+	0.285544i
$745$	−24.0681	−	5.29779i	−0.881788	−	0.194096i
$746$	19.8153	+	6.67655i	0.725489	+	0.244446i
$747$	−0.639512	−	11.7951i	−0.0233985	−	0.431560i
$748$	5.50712	−	4.18640i	0.201360	−	0.153070i
$749$	−17.1403	−	32.3300i	−0.626292	−	1.18131i
$750$	−3.10722	−	11.1912i	−0.113460	−	0.408645i
$751$	−11.2563	−	10.6625i	−0.410749	−	0.389082i	0.454235	−	0.890882i	$-0.349913\pi$
$751$	−11.2563	−	10.6625i	−0.410749	−	0.389082i	−0.864984	+	0.501800i	$0.832671\pi$
$752$	4.61858	+	11.5918i	0.168422	+	0.422708i
$753$	15.7735	−	5.31470i	0.574817	−	0.193678i
$754$	7.79234	−	0.847468i	0.283780	−	0.0308630i
$755$	−12.6214	−	5.83930i	−0.459341	−	0.212514i
$756$	3.32937	−	3.15374i	0.121088	−	0.114701i
$757$	−22.2817	−	13.4065i	−0.809843	−	0.487266i	0.0494338	−	0.998777i	$-0.484258\pi$
$757$	−22.2817	−	13.4065i	−0.809843	−	0.487266i	−0.859277	+	0.511511i	$0.829086\pi$
$758$	−4.17631	−	0.454201i	−0.151691	−	0.0164973i
$759$	8.02347	−	1.76610i	0.291234	−	0.0641054i
$760$	−0.937544	+	3.37673i	−0.0340083	+	0.122487i
$761$	−33.8742	+	20.3814i	−1.22794	+	0.738826i	−0.973594	−	0.228288i	$-0.926687\pi$
$761$	−33.8742	+	20.3814i	−1.22794	+	0.738826i	−0.254345	+	0.967114i	$0.581860\pi$
$762$	8.10352	−	3.74909i	0.293559	−	0.135815i
$763$	−10.4803	+	26.3035i	−0.379412	+	0.952251i
$764$	1.14231	−	21.0687i	0.0413274	−	0.762239i
$765$	2.63038	+	3.87952i	0.0951015	+	0.140264i
$766$	−30.3683			−1.09725
$767$	18.9762	−	1.85954i	0.685191	−	0.0671442i
$768$	1.00000			0.0360844
$769$	1.62586	+	2.39797i	0.0586301	+	0.0864729i	0.855874	−	0.517184i	$-0.173020\pi$
$769$	1.62586	+	2.39797i	0.0586301	+	0.0864729i	−0.797244	+	0.603657i	$0.793710\pi$
$770$	−0.820942	+	15.1414i	−0.0295847	+	0.545658i
$771$	1.19695	−	3.00411i	0.0431070	−	0.108190i
$772$	19.3713	−	8.96211i	0.697188	−	0.322553i
$773$	−29.2649	+	17.6081i	−1.05258	+	0.633319i	−0.933137	−	0.359522i	$-0.882940\pi$
$773$	−29.2649	+	17.6081i	−1.05258	+	0.633319i	−0.119447	+	0.992841i	$0.538112\pi$
$774$	1.96108	−	7.06318i	0.0704896	−	0.253881i
$775$	−23.7585	+	5.22963i	−0.853429	+	0.187854i
$776$	−11.6305	−	1.26489i	−0.417510	−	0.0454070i
$777$	3.91394	+	2.35494i	0.140412	+	0.0844829i
$778$	1.28930	−	1.22129i	0.0462237	−	0.0437855i
$779$	13.5895	+	6.28717i	0.486894	+	0.225261i
$780$	−3.69375	+	0.401720i	−0.132258	+	0.0143839i
$781$	−2.04810	+	0.690085i	−0.0732868	+	0.0246932i
$782$	4.31058	+	10.8187i	0.154146	+	0.386877i
$783$	2.29243	+	2.17151i	0.0819249	+	0.0776034i
$784$	3.75363	+	13.5194i	0.134058	+	0.482834i
$785$	8.81353	+	16.6241i	0.314568	+	0.593339i
$786$	6.84162	−	5.20087i	0.244033	−	0.185509i
$787$	1.92035	+	35.4189i	0.0684532	+	1.26255i	0.807896	+	0.589326i	$0.200607\pi$
$787$	1.92035	+	35.4189i	0.0684532	+	1.26255i	−0.739442	+	0.673220i	$0.764911\pi$
$788$	−6.43295	−	2.16751i	−0.229164	−	0.0772145i
$789$	−9.80825	−	2.15896i	−0.349183	−	0.0768610i
$790$	10.3121	−	19.4506i	0.366887	−	0.692022i
$791$	4.85021	+	29.5850i	0.172454	+	1.05192i
$792$	−1.43013	+	1.68368i	−0.0508175	+	0.0598270i
$793$	−13.8570	−	16.3137i	−0.492076	−	0.579317i
$794$	5.43213	−	33.1345i	0.192779	−	1.17590i
$795$	10.8694	+	8.26273i	0.385499	+	0.293049i
$796$	12.2639	−	18.0879i	0.434683	−	0.641110i
$797$	−3.54893	+	5.23428i	−0.125710	+	0.185408i	−0.885336	−	0.464952i	$-0.846072\pi$
$797$	−3.54893	+	5.23428i	−0.125710	+	0.185408i	0.759626	+	0.650360i	$0.225382\pi$
$798$	−8.54773	−	6.49781i	−0.302586	−	0.230020i
$799$	6.32154	−	38.5597i	0.223640	−	1.36414i
$800$	1.78653	+	2.10326i	0.0631633	+	0.0743615i
$801$	5.04582	−	5.94040i	0.178285	−	0.209894i
$802$	−3.66776	−	22.3723i	−0.129513	−	0.789995i
$803$	−9.33631	+	17.6101i	−0.329471	+	0.621448i
$804$	4.81393	+	1.05963i	0.169774	+	0.0373701i
$805$	−24.1916	−	8.15108i	−0.852640	−	0.287288i
$806$	1.18472	+	21.8508i	0.0417298	+	0.769662i
$807$	0.146782	−	0.111581i	0.00516697	−	0.00392783i
$808$	2.66856	+	5.03344i	0.0938797	+	0.177076i
$809$	8.09793	+	29.1661i	0.284708	+	1.02543i	0.958169	+	0.286203i	$0.0923931\pi$
$809$	8.09793	+	29.1661i	0.284708	+	1.02543i	−0.673461	+	0.739223i	$0.735193\pi$
$810$	−1.08667	−	1.02935i	−0.0381816	−	0.0361675i
$811$	−13.8975	−	34.8801i	−0.488007	−	1.22481i	−0.942545	−	0.334078i	$-0.891575\pi$
$811$	−13.8975	−	34.8801i	−0.488007	−	1.22481i	0.454538	−	0.890727i	$-0.349804\pi$
$812$	−13.7227	+	4.62372i	−0.481573	+	0.162261i
$813$	−5.49145	+	0.597232i	−0.192594	+	0.0209458i
$814$	−1.99698	−	0.923900i	−0.0699940	−	0.0323827i
$815$	18.7462	−	17.7573i	0.656650	−	0.622012i
$816$	−2.68322	−	1.61444i	−0.0939315	−	0.0565167i
$817$	−17.0621	−	1.85561i	−0.596926	−	0.0649196i
$818$	−10.7809	+	2.37305i	−0.376944	+	0.0829717i
$819$	3.04548	−	10.9688i	0.106418	−	0.383282i
$820$	−8.20225	+	4.93513i	−0.286435	+	0.172342i
$821$	−6.00761	+	2.77942i	−0.209667	+	0.0970023i	−0.521912	−	0.852999i	$-0.674781\pi$
$821$	−6.00761	+	2.77942i	−0.209667	+	0.0970023i	0.312245	+	0.950002i	$0.398919\pi$
$822$	−4.16450	+	10.4521i	−0.145254	+	0.364559i
$823$	1.87600	−	34.6008i	0.0653933	−	1.20611i	−0.763164	−	0.646204i	$-0.776355\pi$
$823$	1.87600	−	34.6008i	0.0653933	−	1.20611i	0.828558	−	0.559904i	$-0.189162\pi$
$824$	3.20130	+	4.72157i	0.111523	+	0.164484i
$825$	−6.09619			−0.212242
$826$	−33.4992	+	10.8913i	−1.16559	+	0.378959i
$827$	−8.67312			−0.301594			−0.150797	−	0.988565i	$-0.548184\pi$
$827$	−8.67312			−0.301594			−0.150797	+	0.988565i	$0.548184\pi$
$828$	−2.08704	−	3.07816i	−0.0725298	−	0.106973i
$829$	0.659114	−	12.1566i	0.0228920	−	0.422218i	−0.964516	−	0.264024i	$-0.914950\pi$
$829$	0.659114	−	12.1566i	0.0228920	−	0.422218i	0.987408	−	0.158194i	$-0.0505671\pi$
$830$	6.54434	−	16.4250i	0.227157	−	0.570122i
$831$	−11.3292	+	5.24145i	−0.393006	+	0.181824i
$832$	2.12700	−	1.27977i	0.0737403	−	0.0443681i
$833$	11.7544	−	42.3354i	0.407265	−	1.46683i
$834$	0.849676	−	0.187028i	0.0294219	−	0.00647624i
$835$	26.8478	+	2.91987i	0.929107	+	0.101046i
$836$	4.43180	+	2.66653i	0.153277	+	0.0922237i
$837$	−6.40001	+	6.06241i	−0.221217	+	0.209547i
$838$	−5.37410	−	2.48632i	−0.185645	−	0.0858886i
$839$	39.3136	−	4.27562i	1.35726	−	0.147611i	0.599619	−	0.800285i	$-0.295319\pi$
$839$	39.3136	−	4.27562i	1.35726	−	0.147611i	0.757638	+	0.652675i	$0.226353\pi$
$840$	6.50489	−	2.19175i	0.224440	−	0.0756226i
$841$	7.04347	+	17.6778i	0.242878	+	0.609578i
$842$	4.13413	+	3.91606i	0.142472	+	0.134956i
$843$	−0.722165	−	2.60100i	−0.0248727	−	0.0895833i
$844$	−2.17304	−	4.09880i	−0.0747993	−	0.141086i
$845$	8.14818	−	6.19408i	0.280306	−	0.213083i
$846$	0.675545	+	12.4597i	0.0232257	+	0.428373i
$847$	−26.5965	−	8.96140i	−0.913866	−	0.307917i
$848$	−8.90853	−	1.96092i	−0.305920	−	0.0673382i
$849$	−13.5816	+	25.6175i	−0.466118	+	0.879191i
$850$	−1.39805	−	8.52775i	−0.0479529	−	0.292499i
$851$	2.39809	−	2.82325i	0.0822054	−	0.0967796i
$852$	0.633363	+	0.745652i	0.0216986	+	0.0255456i
$853$	−6.05954	+	36.9616i	−0.207475	+	1.26554i	0.653514	+	0.756915i	$0.273294\pi$
$853$	−6.05954	+	36.9616i	−0.207475	+	1.26554i	−0.860988	+	0.508625i	$0.830154\pi$
$854$	31.4803	+	23.9307i	1.07723	+	0.818891i
$855$	−1.96666	+	2.90061i	−0.0672584	+	0.0991987i
$856$	4.47789	−	6.60439i	0.153051	−	0.225733i
$857$	3.25893	+	2.47737i	0.111323	+	0.0846255i	0.659355	−	0.751832i	$-0.270830\pi$
$857$	3.25893	+	2.47737i	0.111323	+	0.0846255i	−0.548032	+	0.836458i	$0.684623\pi$
$858$	−0.887158	+	5.41143i	−0.0302871	+	0.184743i
$859$	24.1718	+	28.4572i	0.824730	+	0.970948i	0.999908	−	0.0135893i	$-0.00432574\pi$
$859$	24.1718	+	28.4572i	0.824730	+	0.970948i	−0.175177	+	0.984537i	$0.556050\pi$
$860$	7.10317	−	8.36250i	0.242216	−	0.285159i
$861$	−4.74482	−	28.9421i	−0.161703	−	0.986344i
$862$	−8.57230	+	16.1691i	−0.291974	+	0.550721i
$863$	3.95296	+	0.870112i	0.134560	+	0.0296190i	0.281740	−	0.959491i	$-0.409088\pi$
$863$	3.95296	+	0.870112i	0.134560	+	0.0296190i	−0.147180	+	0.989110i	$0.547020\pi$
$864$	0.947653	+	0.319302i	0.0322398	+	0.0108629i
$865$	0.810300	+	14.9451i	0.0275510	+	0.508149i
$866$	25.2944	−	19.2283i	0.859539	−	0.653405i
$867$	−3.36969	−	6.35591i	−0.114441	−	0.215858i
$868$	−10.8154	−	38.9537i	−0.367100	−	1.32217i
$869$	−23.5887	−	22.3444i	−0.800193	−	0.757983i
$870$	1.74940	+	4.39067i	0.0593103	+	0.148858i
$871$	11.5953	−	3.90691i	0.392891	−	0.132380i
$872$	−6.13801	+	0.667549i	−0.207859	+	0.0226061i
$873$	−10.6178	−	4.91231i	−0.359358	−	0.166257i
$874$	−6.32145	+	5.98800i	−0.213826	+	0.202547i
$875$	45.6392	+	27.4602i	1.54289	+	0.928324i
$876$	8.96983	+	0.975528i	0.303063	+	0.0329600i
$877$	6.11936	−	1.34697i	0.206636	−	0.0454841i	−0.110446	−	0.993882i	$-0.535228\pi$
$877$	6.11936	−	1.34697i	0.206636	−	0.0454841i	0.317082	+	0.948398i	$0.397297\pi$
$878$	5.00125	−	18.0129i	0.168784	−	0.607905i
$879$	0.871088	−	0.524116i	0.0293811	−	0.0176780i
$880$	−3.00095	+	1.38839i	−0.101162	+	0.0468025i
$881$	−14.1328	+	35.4707i	−0.476147	+	1.19504i	0.473241	+	0.880933i	$0.343084\pi$
$881$	−14.1328	+	35.4707i	−0.476147	+	1.19504i	−0.949388	+	0.314106i	$0.898295\pi$
$882$	−0.759611	+	14.0102i	−0.0255774	+	0.471748i
$883$	3.63692	+	5.36406i	0.122392	+	0.180515i	0.883949	−	0.467583i	$-0.154875\pi$
$883$	3.63692	+	5.36406i	0.122392	+	0.180515i	−0.761557	+	0.648098i	$0.775565\pi$
$884$	−7.77331			−0.261445
$885$	4.14154	+	10.7253i	0.139216	+	0.360526i
$886$	−34.5019			−1.15911
$887$	6.85508	+	10.1105i	0.230171	+	0.339477i	0.925183	−	0.379521i	$-0.123911\pi$
$887$	6.85508	+	10.1105i	0.230171	+	0.339477i	−0.695012	+	0.718998i	$0.744601\pi$
$888$	−0.0539246	+	0.994581i	−0.00180959	+	0.0333760i
$889$	−15.1559	+	38.0385i	−0.508313	+	1.27577i
$890$	10.5880	−	4.89853i	0.354911	−	0.164199i
$891$	−1.89287	+	1.13890i	−0.0634136	+	0.0381547i
$892$	−6.97910	+	25.1364i	−0.233678	+	0.841630i
$893$	28.5318	−	6.28033i	0.954781	−	0.210163i
$894$	16.3682	+	1.78015i	0.547433	+	0.0595370i
$895$	−16.3536	−	9.83966i	−0.546642	−	0.328903i
$896$	−3.32937	+	3.15374i	−0.111226	+	0.105359i
$897$	−8.37847	−	3.87629i	−0.279749	−	0.129426i
$898$	−33.8479	+	3.68118i	−1.12952	+	0.122843i
$899$	26.3790	−	8.88813i	0.879790	−	0.296436i
$900$	1.02143	+	2.56360i	0.0340478	+	0.0854534i
$901$	20.7378	+	19.6439i	0.690875	+	0.654432i
$902$	3.77958	+	13.6128i	0.125846	+	0.453258i
$903$	15.7463	+	29.7007i	0.524004	+	0.988376i
$904$	−5.20435	+	3.95624i	−0.173094	+	0.131583i
$905$	−0.359095	−	6.62311i	−0.0119367	−	0.220160i
$906$	8.80466	+	2.96663i	0.292515	+	0.0985598i
$907$	43.8000	+	9.64111i	1.45436	+	0.320128i	0.870676	−	0.491857i	$-0.163682\pi$
$907$	43.8000	+	9.64111i	1.45436	+	0.320128i	0.583679	+	0.811984i	$0.301613\pi$
$908$	−11.9260	+	22.4949i	−0.395779	+	0.746518i
$909$	0.921686	+	5.62203i	0.0305704	+	0.186471i
$910$	11.0309	−	12.9866i	0.365672	−	0.430502i
$911$	−11.0749	−	13.0383i	−0.366926	−	0.431979i	0.547454	−	0.836836i	$-0.315597\pi$
$911$	−11.0749	−	13.0383i	−0.366926	−	0.431979i	−0.914380	+	0.404857i	$0.867321\pi$
$912$	0.378782	−	2.31047i	0.0125427	−	0.0765072i
$913$	−20.7738	−	15.7918i	−0.687512	−	0.522633i
$914$	−8.28799	+	12.2239i	−0.274142	+	0.404330i
$915$	7.24298	−	10.6826i	0.239446	−	0.353156i
$916$	0.0414400	+	0.0315019i	0.00136922	+	0.00104085i
$917$	−6.37607	+	38.8923i	−0.210556	+	1.28434i
$918$	−2.02727	−	2.38668i	−0.0669098	−	0.0787723i
$919$	−15.2835	+	17.9931i	−0.504157	+	0.593539i	−0.954089	−	0.299524i	$-0.903172\pi$
$919$	−15.2835	+	17.9931i	−0.504157	+	0.593539i	0.449932	+	0.893063i	$0.351448\pi$
$920$	−0.900569	−	5.49323i	−0.0296909	−	0.181106i
$921$	10.0924	−	19.0363i	0.332555	−	0.627266i
$922$	13.1922	+	2.90383i	0.434463	+	0.0956325i
$923$	2.30142	+	0.775440i	0.0757523	+	0.0255239i
$924$	−0.548466	−	10.1159i	−0.0180432	−	0.332787i
$925$	−2.18820	+	1.66343i	−0.0719476	+	0.0546932i
$926$	−6.58163	−	12.4143i	−0.216286	−	0.407958i
$927$	1.52612	+	5.49659i	0.0501244	+	0.180532i
$928$	−2.29243	−	2.17151i	−0.0752528	−	0.0712833i
$929$	1.71241	+	4.29783i	0.0561824	+	0.141007i	0.954389	−	0.298567i	$-0.0965087\pi$
$929$	1.71241	+	4.29783i	0.0561824	+	0.141007i	−0.898206	+	0.439574i	$0.855129\pi$
$930$	−12.5043	+	4.21318i	−0.410032	+	0.138156i
$931$	32.6578	−	3.55175i	1.07032	−	0.116404i
$932$	2.74372	+	1.26938i	0.0898735	+	0.0415799i
$933$	−4.01260	+	3.80094i	−0.131367	+	0.124437i
$934$	−10.2634	−	6.17531i	−0.335830	−	0.202062i
$935$	10.2937	+	1.11950i	0.336639	+	0.0366117i
$936$	2.42429	−	0.533626i	0.0792403	−	0.0174421i
$937$	−0.950648	+	3.42392i	−0.0310563	+	0.111855i	−0.977454	−	0.211150i	$-0.932279\pi$
$937$	−0.950648	+	3.42392i	−0.0310563	+	0.111855i	0.946397	+	0.323005i	$0.104693\pi$
$938$	−19.3691	+	11.6540i	−0.632424	+	0.380517i
$939$	−16.8402	+	7.79110i	−0.549558	+	0.254253i
$940$	−6.91308	+	17.3505i	−0.225480	+	0.565911i
$941$	0.400032	−	7.37815i	0.0130407	−	0.240521i	−0.984745	−	0.174005i	$-0.944329\pi$
$941$	0.400032	−	7.37815i	0.0130407	−	0.240521i	0.997785	−	0.0665157i	$-0.0211882\pi$
$942$	−7.05456	−	10.4047i	−0.229850	−	0.339004i
$943$	−23.7840			−0.774515
$944$	−5.51991	−	5.34140i	−0.179658	−	0.173848i
$945$	6.86421			0.223293
$946$	−9.08754	−	13.4031i	−0.295461	−	0.435773i
$947$	1.91049	−	35.2369i	0.0620826	−	1.14505i	−0.787058	−	0.616879i	$-0.788397\pi$
$947$	1.91049	−	35.2369i	0.0620826	−	1.14505i	0.849141	−	0.528167i	$-0.177120\pi$
$948$	−5.44405	+	13.6635i	−0.176814	+	0.443771i
$949$	20.3273	−	9.40439i	0.659851	−	0.305279i
$950$	5.53622	−	3.33103i	0.179619	−	0.108073i
$951$	1.26871	−	4.56950i	0.0411409	−	0.148176i
$952$	14.0249	−	3.08712i	0.454551	−	0.100054i
$953$	23.0683	+	2.50883i	0.747257	+	0.0812691i	0.473821	−	0.880621i	$-0.342874\pi$
$953$	23.0683	+	2.50883i	0.747257	+	0.0812691i	0.273436	+	0.961890i	$0.411840\pi$
$954$	−7.81608	−	4.70278i	−0.253055	−	0.152258i
$955$	22.9283	−	21.7189i	0.741943	−	0.702806i
$956$	−5.33889	−	2.47004i	−0.172672	−	0.0798867i
$957$	6.93461	−	0.754185i	0.224164	−	0.0243793i
$958$	16.7806	−	5.65403i	0.542155	−	0.182673i
$959$	−19.0981	−	47.9327i	−0.616711	−	1.54783i
$960$	1.08667	+	1.02935i	0.0350721	+	0.0332220i
$961$	12.4970	+	45.0102i	0.403129	+	1.45194i
$962$	1.15814	+	2.18448i	0.0373399	+	0.0704305i
$963$	6.35228	−	4.82887i	0.204699	−	0.155608i
$964$	1.45871	+	26.9044i	0.0469819	+	0.866531i
$965$	30.2753	+	10.2009i	0.974596	+	0.328379i
$966$	16.6563	+	3.66632i	0.535906	+	0.117962i
$967$	0.117052	−	0.220784i	0.00376414	−	0.00709993i	−0.881623	−	0.471955i	$-0.843549\pi$
$967$	0.117052	−	0.220784i	0.00376414	−	0.00709993i	0.885387	+	0.464855i	$0.153893\pi$
$968$	−0.990096	−	6.03932i	−0.0318229	−	0.194111i
$969$	−4.74647	+	5.58797i	−0.152478	+	0.179512i
$970$	−11.3365	−	13.3463i	−0.363992	−	0.428525i
$971$	−3.12571	+	19.0660i	−0.100309	+	0.611856i	0.888054	+	0.459739i	$0.152057\pi$
$971$	−3.12571	+	19.0660i	−0.100309	+	0.611856i	−0.988363	+	0.152117i	$0.951391\pi$
$972$	0.796093	+	0.605174i	0.0255347	+	0.0194110i
$973$	−2.23904	+	3.30234i	−0.0717805	+	0.105868i
$974$	18.1310	−	26.7412i	0.580955	−	0.856844i
$975$	5.45341	+	4.14557i	0.174649	+	0.132765i
$976$	−1.39501	+	8.50918i	−0.0446532	+	0.272372i
$977$	20.2682	+	23.8616i	0.648438	+	0.763400i	0.983913	−	0.178649i	$-0.0571726\pi$
$977$	20.2682	+	23.8616i	0.648438	+	0.763400i	−0.335475	+	0.942049i	$0.608897\pi$
$978$	−11.1681	+	13.1481i	−0.357116	+	0.420430i
$979$	−2.78555	−	16.9911i	−0.0890267	−	0.543039i
$980$	−9.83715	+	18.5548i	−0.314236	+	0.592712i
$981$	−6.02986	−	1.32727i	−0.192519	−	0.0423765i
$982$	6.58311	+	2.21811i	0.210076	+	0.0707827i
$983$	2.51924	+	46.4646i	0.0803511	+	1.48199i	0.709500	+	0.704705i	$0.248921\pi$
$983$	2.51924	+	46.4646i	0.0803511	+	1.48199i	−0.629149	+	0.777284i	$0.716597\pi$
$984$	5.09126	−	3.87028i	0.162304	−	0.123380i
$985$	−4.75936	−	8.97711i	−0.151646	−	0.286034i
$986$	2.64533	+	9.52763i	0.0842446	+	0.303422i
$987$	−41.5438	−	39.3524i	−1.32235	−	1.25260i
$988$	−2.15120	−	5.39911i	−0.0684389	−	0.171769i
$989$	25.8345	−	8.70464i	0.821488	−	0.276791i
$990$	−3.28717	+	0.357501i	−0.104473	+	0.0113621i
$991$	−46.6763	−	21.5948i	−1.48272	−	0.685981i	−0.499154	−	0.866513i	$-0.666356\pi$
$991$	−46.6763	−	21.5948i	−1.48272	−	0.685981i	−0.983569	+	0.180533i	$0.942218\pi$
$992$	6.40001	−	6.06241i	0.203200	−	0.192482i
$993$	−26.6712	−	16.0476i	−0.846386	−	0.509254i
$994$	−4.46029	−	0.485086i	−0.141472	−	0.0153860i
$995$	31.9456	−	7.03175i	1.01274	−	0.222922i
$996$	−3.16016	+	11.3819i	−0.100133	+	0.360648i
$997$	30.8061	−	18.5354i	0.975638	−	0.587022i	0.0639710	−	0.997952i	$-0.479623\pi$
$997$	30.8061	−	18.5354i	0.975638	−	0.587022i	0.911667	+	0.410930i	$0.134796\pi$
$998$	2.29651	−	1.06248i	0.0726948	−	0.0336322i
$999$	−0.368673	+	0.925300i	−0.0116643	+	0.0292752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.d.7.1	✓	84
59.17	even	29	inner	354.2.e.d.253.1	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.d.7.1	✓	84	1.1	even	1	trivial
354.2.e.d.253.1	yes	84	59.17	even	29	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.561187 + 0.827689i) q^{2} +(0.0541389 - 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(-1.35846 + 0.628489i) q^{5} +(0.856857 - 0.515554i) q^{6} +(-1.22687 + 4.41877i) q^{7} +(-0.976621 + 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +O(q^{10})\)	\(q+(0.561187 + 0.827689i) q^{2} +(0.0541389 - 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(-1.35846 + 0.628489i) q^{5} +(0.856857 - 0.515554i) q^{6} +(-1.22687 + 4.41877i) q^{7} +(-0.976621 + 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +(-1.28254 - 0.771679i) q^{10} +(-1.60379 + 1.51919i) q^{11} +(0.907575 + 0.419889i) q^{12} +(2.46777 - 0.268386i) q^{13} +(-4.34587 + 1.46430i) q^{14} +(0.554022 + 1.39049i) q^{15} +(-0.725995 - 0.687699i) q^{16} +(0.837756 + 3.01732i) q^{17} +(-0.468408 - 0.883512i) q^{18} +(-1.86390 + 1.41690i) q^{19} +(-0.0810350 - 1.49460i) q^{20} +(4.34587 + 1.46430i) q^{21} +(-2.15744 - 0.474888i) q^{22} +(1.74200 - 3.28576i) q^{23} +(0.161782 + 0.986827i) q^{24} +(-1.78653 + 2.10326i) q^{25} +(1.60702 + 1.89193i) q^{26} +(-0.161782 + 0.986827i) q^{27} +(-3.65083 - 2.77529i) q^{28} +(1.77203 - 2.61355i) q^{29} +(-0.839983 + 1.23888i) q^{30} +(7.01795 + 5.33491i) q^{31} +(0.161782 - 0.986827i) q^{32} +(1.43013 + 1.68368i) q^{33} +(-2.02727 + 2.38668i) q^{34} +(-1.11051 - 6.77378i) q^{35} +(0.468408 - 0.883512i) q^{36} +(0.972755 + 0.214120i) q^{37} +(-2.21875 - 0.747584i) q^{38} +(-0.134390 - 2.47868i) q^{39} +(1.19159 - 0.905823i) q^{40} +(-2.99562 - 5.65033i) q^{41} +(1.22687 + 4.41877i) q^{42} +(5.32182 + 5.04109i) q^{43} +(-0.817667 - 2.05219i) q^{44} +(1.41844 - 0.477930i) q^{45} +(3.69718 - 0.402093i) q^{46} +(-11.3247 - 5.23937i) q^{47} +(-0.725995 + 0.687699i) q^{48} +(-12.0224 - 7.23362i) q^{49} +(-2.74342 - 0.298365i) q^{50} +(3.05825 - 0.673173i) q^{51} +(-0.664092 + 2.39184i) q^{52} +(7.81608 - 4.70278i) q^{53} +(-0.907575 + 0.419889i) q^{54} +(1.22388 - 3.07171i) q^{55} +(0.248277 - 4.57921i) q^{56} +(1.31391 + 1.93788i) q^{57} +3.15764 q^{58} +(7.68071 + 0.0817965i) q^{59} -1.49680 q^{60} +(-4.83899 - 7.13697i) q^{61} +(-0.477261 + 8.80256i) q^{62} +(1.69743 - 4.26022i) q^{63} +(0.907575 - 0.419889i) q^{64} +(-3.18368 + 1.91556i) q^{65} +(-0.590993 + 2.12856i) q^{66} +(4.81393 - 1.05963i) q^{67} +(-3.11311 - 0.338571i) q^{68} +(-3.18664 - 1.91733i) q^{69} +(4.98338 - 4.72051i) q^{70} +(0.887916 + 0.410793i) q^{71} +(0.994138 - 0.108119i) q^{72} +(8.55041 - 2.88097i) q^{73} +(0.368673 + 0.925300i) q^{74} +(2.00346 + 1.89777i) q^{75} +(-0.626367 - 2.25597i) q^{76} +(-4.74531 - 8.95061i) q^{77} +(1.97616 - 1.50224i) q^{78} +(0.796283 + 14.6866i) q^{79} +(1.41844 + 0.477930i) q^{80} +(0.976621 + 0.214970i) q^{81} +(2.99562 - 5.65033i) q^{82} +(1.91104 + 11.6568i) q^{83} +(-2.96887 + 3.49522i) q^{84} +(-3.03441 - 3.57238i) q^{85} +(-1.18592 + 7.23380i) q^{86} +(-2.51378 - 1.91092i) q^{87} +(1.23971 - 1.82844i) q^{88} +(-4.37398 + 6.45113i) q^{89} +(1.19159 + 0.905823i) q^{90} +(-1.84169 + 11.2338i) q^{91} +(2.40762 + 2.83447i) q^{92} +(5.70703 - 6.71883i) q^{93} +(-2.01871 - 12.3136i) q^{94} +(1.64152 - 3.09624i) q^{95} +(-0.976621 - 0.214970i) q^{96} +(11.0867 + 3.73553i) q^{97} +(-0.759611 - 14.0102i) q^{98} +(1.75864 - 1.33688i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9	\( 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9} + 2 q^{10} + 30 q^{11} - 3 q^{12} - 3 q^{13} + 7 q^{14} - 2 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 4 q^{19} - 2 q^{20} - 7 q^{21} - q^{22} + 2 q^{23} + 3 q^{24} - 67 q^{25} + 32 q^{26} - 3 q^{27} - 7 q^{28} + 4 q^{29} + 2 q^{30} - 6 q^{31} + 3 q^{32} + q^{33} + 26 q^{34} + 79 q^{35} - 3 q^{36} + 55 q^{37} + 4 q^{38} - 3 q^{39} + 2 q^{40} + q^{41} + 7 q^{42} + 51 q^{43} + q^{44} - 2 q^{45} - 31 q^{46} - 62 q^{47} - 3 q^{48} - 70 q^{49} + 9 q^{50} + 3 q^{51} - 32 q^{52} - 27 q^{53} + 3 q^{54} - 83 q^{55} + 7 q^{56} - 4 q^{57} - 120 q^{58} - 55 q^{59} + 56 q^{60} - 46 q^{61} - 23 q^{62} - 7 q^{63} - 3 q^{64} - 121 q^{65} - q^{66} + 8 q^{67} - 26 q^{68} - 27 q^{69} - 50 q^{70} - 61 q^{71} + 3 q^{72} + 49 q^{73} - 26 q^{74} - 9 q^{75} + 25 q^{76} + 77 q^{77} + 3 q^{78} - 5 q^{79} - 2 q^{80} - 3 q^{81} - q^{82} + 75 q^{83} - 7 q^{84} + 189 q^{85} + 65 q^{86} - 25 q^{87} - 30 q^{88} + 54 q^{89} + 2 q^{90} - 161 q^{91} + 2 q^{92} + 23 q^{93} + 33 q^{94} - 54 q^{95} + 3 q^{96} + 28 q^{97} + 12 q^{98} + q^{99}+O(q^{100}) \) 84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9 + 2 * q^10 + 30 * q^11 - 3 * q^12 - 3 * q^13 + 7 * q^14 - 2 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 4 * q^19 - 2 * q^20 - 7 * q^21 - q^22 + 2 * q^23 + 3 * q^24 - 67 * q^25 + 32 * q^26 - 3 * q^27 - 7 * q^28 + 4 * q^29 + 2 * q^30 - 6 * q^31 + 3 * q^32 + q^33 + 26 * q^34 + 79 * q^35 - 3 * q^36 + 55 * q^37 + 4 * q^38 - 3 * q^39 + 2 * q^40 + q^41 + 7 * q^42 + 51 * q^43 + q^44 - 2 * q^45 - 31 * q^46 - 62 * q^47 - 3 * q^48 - 70 * q^49 + 9 * q^50 + 3 * q^51 - 32 * q^52 - 27 * q^53 + 3 * q^54 - 83 * q^55 + 7 * q^56 - 4 * q^57 - 120 * q^58 - 55 * q^59 + 56 * q^60 - 46 * q^61 - 23 * q^62 - 7 * q^63 - 3 * q^64 - 121 * q^65 - q^66 + 8 * q^67 - 26 * q^68 - 27 * q^69 - 50 * q^70 - 61 * q^71 + 3 * q^72 + 49 * q^73 - 26 * q^74 - 9 * q^75 + 25 * q^76 + 77 * q^77 + 3 * q^78 - 5 * q^79 - 2 * q^80 - 3 * q^81 - q^82 + 75 * q^83 - 7 * q^84 + 189 * q^85 + 65 * q^86 - 25 * q^87 - 30 * q^88 + 54 * q^89 + 2 * q^90 - 161 * q^91 + 2 * q^92 + 23 * q^93 + 33 * q^94 - 54 * q^95 + 3 * q^96 + 28 * q^97 + 12 * q^98 + q^99

Introduction

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