LMFDB - Embedded newform 374.2.r.b.15.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [374,2,Mod(9,374)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(374, base_ring=CyclotomicField(40))

chi = DirichletCharacter(H, H._module([24, 5]))

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

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

chi := DirichletCharacter("374.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 374 = 2 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	374.r (of order $40$, degree $16$, 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:	$2.98640503560$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$10$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			15.10
Character	$\chi$	$=$	374.15
Dual form			374.2.r.b.25.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 - 0.987688i) q^{2} +(3.04661 - 0.239773i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(0.463220 - 0.755906i) q^{5} +(-0.713416 - 2.97159i) q^{6} +(0.353474 - 4.49131i) q^{7} +(0.453990 + 0.891007i) q^{8} +(6.26127 - 0.991688i) q^{9} +O(q^{10})$	\(q+(-0.156434 - 0.987688i) q^{2} +(3.04661 - 0.239773i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(0.463220 - 0.755906i) q^{5} +(-0.713416 - 2.97159i) q^{6} +(0.353474 - 4.49131i) q^{7} +(0.453990 + 0.891007i) q^{8} +(6.26127 - 0.991688i) q^{9} +(-0.819063 - 0.339267i) q^{10} +(-1.67560 + 2.86223i) q^{11} +(-2.82340 + 1.16949i) q^{12} +(-2.70255 + 3.71974i) q^{13} +(-4.49131 + 0.353474i) q^{14} +(1.23000 - 2.41402i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-3.00377 + 2.82443i) q^{17} +(-1.95896 - 6.02905i) q^{18} +(-1.89645 + 0.966289i) q^{19} +(-0.206960 + 0.862052i) q^{20} -13.7680i q^{21} +(3.08911 + 1.20722i) q^{22} +(1.56175 - 3.77039i) q^{23} +(1.59677 + 2.60569i) q^{24} +(1.91313 + 3.75473i) q^{25} +(4.09672 + 2.08738i) q^{26} +(9.92310 - 2.38232i) q^{27} +(1.05172 + 4.38072i) q^{28} +(2.60631 + 3.05160i) q^{29} +(-2.57671 - 0.837224i) q^{30} +(0.632736 - 2.63553i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.41860 + 9.12187i) q^{33} +(3.25955 + 2.52495i) q^{34} +(-3.23127 - 2.34766i) q^{35} +(-5.64838 + 2.87799i) q^{36} +(4.93779 - 4.21727i) q^{37} +(1.25106 + 1.72194i) q^{38} +(-7.34172 + 11.9806i) q^{39} +(0.883814 + 0.0695577i) q^{40} +(2.39334 - 2.80224i) q^{41} +(-13.5985 + 2.15379i) q^{42} +(-0.216497 + 0.216497i) q^{43} +(0.709109 - 3.23993i) q^{44} +(2.15072 - 5.19230i) q^{45} +(-3.96828 - 0.952701i) q^{46} +(-0.882584 - 0.286769i) q^{47} +(2.32382 - 1.98473i) q^{48} +(-13.1331 - 2.08008i) q^{49} +(3.40923 - 2.47695i) q^{50} +(-8.47408 + 9.32515i) q^{51} +(1.42081 - 4.37282i) q^{52} +(1.71537 + 10.8304i) q^{53} +(-3.90531 - 9.42825i) q^{54} +(1.38741 + 2.59244i) q^{55} +(4.16226 - 1.72406i) q^{56} +(-5.54605 + 3.39862i) q^{57} +(2.60631 - 3.05160i) q^{58} +(9.19884 + 4.68704i) q^{59} +(-0.423830 + 2.67596i) q^{60} +(8.10482 - 1.94580i) q^{61} +(-2.70207 - 0.212657i) q^{62} +(-2.24078 - 28.4719i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(1.55990 + 3.76593i) q^{65} +(9.70078 + 2.93723i) q^{66} -13.7307 q^{67} +(1.98396 - 3.61440i) q^{68} +(3.85399 - 11.8614i) q^{69} +(-1.81327 + 3.55874i) q^{70} +(-6.10996 - 3.74419i) q^{71} +(3.72616 + 5.12862i) q^{72} +(-8.27786 - 9.69213i) q^{73} +(-4.93779 - 4.21727i) q^{74} +(6.72885 + 10.9805i) q^{75} +(1.50503 - 1.50503i) q^{76} +(12.2629 + 8.53735i) q^{77} +(12.9816 + 5.37715i) q^{78} +(-10.3344 + 6.33296i) q^{79} +(-0.0695577 - 0.883814i) q^{80} +(11.5734 - 3.76043i) q^{81} +(-3.14214 - 1.92551i) q^{82} +(-0.559884 - 0.0886769i) q^{83} +(4.25455 + 13.0942i) q^{84} +(0.743595 + 3.57889i) q^{85} +(0.247699 + 0.179964i) q^{86} +(8.67211 + 8.67211i) q^{87} +(-3.31097 - 0.193542i) q^{88} +12.3896i q^{89} +(-5.46482 - 1.31199i) q^{90} +(15.7512 + 13.4528i) q^{91} +(-0.320195 + 4.06846i) q^{92} +(1.29577 - 8.18116i) q^{93} +(-0.145172 + 0.916578i) q^{94} +(-0.148049 + 1.88114i) q^{95} +(-2.32382 - 1.98473i) q^{96} +(-8.47997 - 2.03586i) q^{97} +13.2968i q^{98} +(-7.65293 + 19.5829i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{5} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^5 + 8 * q^9	$ 160 q + 8 q^{5} + 8 q^{9} + 8 q^{10} - 4 q^{11} - 8 q^{12} + 4 q^{14} - 8 q^{15} + 40 q^{16} - 12 q^{17} + 32 q^{18} + 12 q^{19} - 8 q^{22} + 32 q^{23} + 12 q^{24} - 8 q^{25} + 36 q^{27} - 4 q^{28} + 8 q^{29} - 40 q^{31} + 48 q^{33} + 8 q^{34} + 16 q^{35} - 12 q^{36} + 8 q^{37} - 16 q^{39} + 28 q^{41} + 60 q^{42} - 56 q^{43} - 8 q^{44} + 28 q^{46} - 116 q^{49} - 80 q^{50} + 8 q^{52} + 8 q^{53} - 8 q^{54} - 148 q^{57} + 8 q^{58} - 8 q^{59} + 8 q^{60} - 12 q^{61} - 40 q^{62} - 72 q^{63} + 144 q^{65} - 28 q^{66} - 256 q^{67} - 8 q^{69} + 8 q^{70} - 60 q^{71} - 8 q^{73} - 8 q^{74} - 116 q^{75} + 8 q^{76} - 60 q^{77} - 16 q^{78} + 40 q^{79} + 12 q^{80} - 16 q^{82} + 76 q^{83} - 56 q^{84} + 36 q^{85} - 8 q^{86} - 144 q^{87} - 4 q^{88} - 40 q^{90} + 44 q^{91} - 32 q^{92} - 40 q^{93} - 4 q^{94} + 36 q^{95} - 124 q^{97} - 176 q^{99}+O(q^{100}) $ 160 * q + 8 * q^5 + 8 * q^9 + 8 * q^10 - 4 * q^11 - 8 * q^12 + 4 * q^14 - 8 * q^15 + 40 * q^16 - 12 * q^17 + 32 * q^18 + 12 * q^19 - 8 * q^22 + 32 * q^23 + 12 * q^24 - 8 * q^25 + 36 * q^27 - 4 * q^28 + 8 * q^29 - 40 * q^31 + 48 * q^33 + 8 * q^34 + 16 * q^35 - 12 * q^36 + 8 * q^37 - 16 * q^39 + 28 * q^41 + 60 * q^42 - 56 * q^43 - 8 * q^44 + 28 * q^46 - 116 * q^49 - 80 * q^50 + 8 * q^52 + 8 * q^53 - 8 * q^54 - 148 * q^57 + 8 * q^58 - 8 * q^59 + 8 * q^60 - 12 * q^61 - 40 * q^62 - 72 * q^63 + 144 * q^65 - 28 * q^66 - 256 * q^67 - 8 * q^69 + 8 * q^70 - 60 * q^71 - 8 * q^73 - 8 * q^74 - 116 * q^75 + 8 * q^76 - 60 * q^77 - 16 * q^78 + 40 * q^79 + 12 * q^80 - 16 * q^82 + 76 * q^83 - 56 * q^84 + 36 * q^85 - 8 * q^86 - 144 * q^87 - 4 * q^88 - 40 * q^90 + 44 * q^91 - 32 * q^92 - 40 * q^93 - 4 * q^94 + 36 * q^95 - 124 * q^97 - 176 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/374\mathbb{Z}\right)^\times$.

$n$	$35$	$309$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$3$	3.04661	−	0.239773i	1.75896	−	0.138433i	0.842536	−	0.538640i	$-0.181062\pi$
$3$	3.04661	−	0.239773i	1.75896	−	0.138433i	0.916425	+	0.400207i	$0.131062\pi$
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	0.463220	−	0.755906i	0.207158	−	0.338051i	−0.732140	−	0.681155i	$-0.761478\pi$
$5$	0.463220	−	0.755906i	0.207158	−	0.338051i	0.939298	+	0.343103i	$0.111478\pi$
$6$	−0.713416	−	2.97159i	−0.291251	−	1.21315i
$7$	0.353474	−	4.49131i	0.133601	−	1.69756i	−0.456096	−	0.889931i	$-0.650753\pi$
$7$	0.353474	−	4.49131i	0.133601	−	1.69756i	0.589696	−	0.807625i	$-0.299247\pi$
$8$	0.453990	+	0.891007i	0.160510	+	0.315018i
$9$	6.26127	−	0.991688i	2.08709	−	0.330563i
$10$	−0.819063	−	0.339267i	−0.259010	−	0.107286i
$11$	−1.67560	+	2.86223i	−0.505212	+	0.862995i
$11$	−1.67560	+	2.86223i	−0.505212	+	0.862995i
$12$	−2.82340	+	1.16949i	−0.815046	+	0.337603i
$13$	−2.70255	+	3.71974i	−0.749553	+	1.03167i	0.248459	+	0.968642i	$0.420076\pi$
$13$	−2.70255	+	3.71974i	−0.749553	+	1.03167i	−0.998012	+	0.0630283i	$0.979924\pi$
$14$	−4.49131	+	0.353474i	−1.20035	+	0.0944698i
$15$	1.23000	−	2.41402i	0.317585	−	0.623296i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−3.00377	+	2.82443i	−0.728521	+	0.685024i
$17$	−3.00377	+	2.82443i	−0.728521	+	0.685024i
$18$	−1.95896	−	6.02905i	−0.461731	−	1.42106i
$19$	−1.89645	+	0.966289i	−0.435075	+	0.221682i	−0.657789	−	0.753202i	$-0.728508\pi$
$19$	−1.89645	+	0.966289i	−0.435075	+	0.221682i	0.222714	+	0.974884i	$0.428508\pi$
$20$	−0.206960	+	0.862052i	−0.0462777	+	0.192761i
$21$		−	13.7680i		−	3.00443i
$22$	3.08911	+	1.20722i	0.658601	+	0.257379i
$23$	1.56175	−	3.77039i	0.325647	−	0.786181i	−0.673259	−	0.739407i	$-0.735106\pi$
$23$	1.56175	−	3.77039i	0.325647	−	0.786181i	0.998905	−	0.0467740i	$-0.0148941\pi$
$24$	1.59677	+	2.60569i	0.325940	+	0.531885i
$25$	1.91313	+	3.75473i	0.382626	+	0.750946i
$26$	4.09672	+	2.08738i	0.803432	+	0.409369i
$27$	9.92310	−	2.38232i	1.90970	−	0.458479i
$28$	1.05172	+	4.38072i	0.198756	+	0.827878i
$29$	2.60631	+	3.05160i	0.483980	+	0.566668i	0.947638	−	0.319346i	$-0.103463\pi$
$29$	2.60631	+	3.05160i	0.483980	+	0.566668i	−0.463658	+	0.886014i	$0.653463\pi$
$30$	−2.57671	−	0.837224i	−0.470441	−	0.152856i
$31$	0.632736	−	2.63553i	0.113643	−	0.473356i	−0.886305	−	0.463103i	$-0.846736\pi$
$31$	0.632736	−	2.63553i	0.113643	−	0.473356i	0.999947	−	0.0102535i	$-0.00326384\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−4.41860	+	9.12187i	−0.769180	+	1.58791i
$34$	3.25955	+	2.52495i	0.559007	+	0.433025i
$35$	−3.23127	−	2.34766i	−0.546184	−	0.396826i
$36$	−5.64838	+	2.87799i	−0.941396	+	0.479665i
$37$	4.93779	−	4.21727i	0.811768	−	0.693316i	−0.143307	−	0.989678i	$-0.545774\pi$
$37$	4.93779	−	4.21727i	0.811768	−	0.693316i	0.955075	+	0.296363i	$0.0957737\pi$
$38$	1.25106	+	1.72194i	0.202949	+	0.279335i
$39$	−7.34172	+	11.9806i	−1.17562	+	1.91843i
$40$	0.883814	+	0.0695577i	0.139743	+	0.0109980i
$41$	2.39334	−	2.80224i	0.373777	−	0.437637i	−0.541353	−	0.840795i	$-0.682088\pi$
$41$	2.39334	−	2.80224i	0.373777	−	0.437637i	0.915130	+	0.403159i	$0.132088\pi$
$42$	−13.5985	+	2.15379i	−2.09830	+	0.332337i
$43$	−0.216497	+	0.216497i	−0.0330155	+	0.0330155i	−0.723422	−	0.690406i	$-0.757432\pi$
$43$	−0.216497	+	0.216497i	−0.0330155	+	0.0330155i	0.690406	+	0.723422i	$0.257432\pi$
$44$	0.709109	−	3.23993i	0.106902	−	0.488438i
$45$	2.15072	−	5.19230i	0.320611	−	0.774022i
$46$	−3.96828	−	0.952701i	−0.585091	−	0.140468i
$47$	−0.882584	−	0.286769i	−0.128738	−	0.0418295i	0.243939	−	0.969790i	$-0.421560\pi$
$47$	−0.882584	−	0.286769i	−0.128738	−	0.0418295i	−0.372677	+	0.927961i	$0.621560\pi$
$48$	2.32382	−	1.98473i	0.335415	−	0.286471i
$49$	−13.1331	−	2.08008i	−1.87616	−	0.297154i
$50$	3.40923	−	2.47695i	0.482137	−	0.350293i
$51$	−8.47408	+	9.32515i	−1.18661	+	1.30578i
$52$	1.42081	−	4.37282i	0.197032	−	0.606401i
$53$	1.71537	+	10.8304i	0.235624	+	1.48767i	0.767609	+	0.640919i	$0.221447\pi$
$53$	1.71537	+	10.8304i	0.235624	+	1.48767i	−0.531984	+	0.846754i	$0.678553\pi$
$54$	−3.90531	−	9.42825i	−0.531445	−	1.28302i
$55$	1.38741	+	2.59244i	0.187078	+	0.349564i
$56$	4.16226	−	1.72406i	0.556205	−	0.230388i
$57$	−5.54605	+	3.39862i	−0.734592	+	0.450159i
$58$	2.60631	−	3.05160i	0.342226	−	0.400695i
$59$	9.19884	+	4.68704i	1.19759	+	0.610201i	0.934980	−	0.354702i	$-0.115418\pi$
$59$	9.19884	+	4.68704i	1.19759	+	0.610201i	0.262608	+	0.964903i	$0.415418\pi$
$60$	−0.423830	+	2.67596i	−0.0547162	+	0.345465i
$61$	8.10482	−	1.94580i	1.03772	−	0.249134i	0.321425	−	0.946935i	$-0.395838\pi$
$61$	8.10482	−	1.94580i	1.03772	−	0.249134i	0.716291	+	0.697801i	$0.245838\pi$
$62$	−2.70207	−	0.212657i	−0.343163	−	0.0270075i
$63$	−2.24078	−	28.4719i	−0.282312	−	3.58712i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	1.55990	+	3.76593i	0.193482	+	0.467106i
$66$	9.70078	+	2.93723i	1.19408	+	0.361548i
$67$	−13.7307			−1.67748			−0.838738	−	0.544535i	$-0.816706\pi$
$67$	−13.7307			−1.67748			−0.838738	+	0.544535i	$0.816706\pi$
$68$	1.98396	−	3.61440i	0.240590	−	0.438311i
$69$	3.85399	−	11.8614i	0.463966	−	1.42794i
$70$	−1.81327	+	3.55874i	−0.216727	+	0.425351i
$71$	−6.10996	−	3.74419i	−0.725119	−	0.444353i	0.110349	−	0.993893i	$-0.464803\pi$
$71$	−6.10996	−	3.74419i	−0.725119	−	0.444353i	−0.835468	+	0.549540i	$0.814803\pi$
$72$	3.72616	+	5.12862i	0.439132	+	0.604413i
$73$	−8.27786	−	9.69213i	−0.968850	−	1.13438i	−0.990897	−	0.134621i	$-0.957018\pi$
$73$	−8.27786	−	9.69213i	−0.968850	−	1.13438i	0.0220467	−	0.999757i	$-0.492982\pi$
$74$	−4.93779	−	4.21727i	−0.574007	−	0.490248i
$75$	6.72885	+	10.9805i	0.776981	+	1.26792i
$76$	1.50503	−	1.50503i	0.172639	−	0.172639i
$77$	12.2629	+	8.53735i	1.39749	+	0.972922i
$78$	12.9816	+	5.37715i	1.46988	+	0.608843i
$79$	−10.3344	+	6.33296i	−1.16272	+	0.712514i	−0.963570	−	0.267456i	$-0.913817\pi$
$79$	−10.3344	+	6.33296i	−1.16272	+	0.712514i	−0.199146	+	0.979970i	$0.563817\pi$
$80$	−0.0695577	−	0.883814i	−0.00777678	−	0.0988134i
$81$	11.5734	−	3.76043i	1.28594	−	0.417826i
$82$	−3.14214	−	1.92551i	−0.346992	−	0.212637i
$83$	−0.559884	−	0.0886769i	−0.0614552	−	0.00973355i	0.125631	−	0.992077i	$-0.459904\pi$
$83$	−0.559884	−	0.0886769i	−0.0614552	−	0.00973355i	−0.187086	+	0.982343i	$0.559904\pi$
$84$	4.25455	+	13.0942i	0.464210	+	1.42869i
$85$	0.743595	+	3.57889i	0.0806542	+	0.388186i
$86$	0.247699	+	0.179964i	0.0267101	+	0.0194060i
$87$	8.67211	+	8.67211i	0.929748	+	0.929748i
$88$	−3.31097	−	0.193542i	−0.352951	−	0.0206317i
$89$			12.3896i			1.31329i	0.754199	+	0.656646i	$0.228025\pi$
$89$			12.3896i			1.31329i	−0.754199	+	0.656646i	$0.771975\pi$
$90$	−5.46482	−	1.31199i	−0.576043	−	0.138296i
$91$	15.7512	+	13.4528i	1.65118	+	1.41024i
$92$	−0.320195	+	4.06846i	−0.0333826	+	0.424167i
$93$	1.29577	−	8.18116i	0.134365	−	0.848347i
$94$	−0.145172	+	0.916578i	−0.0149733	+	0.0945378i
$95$	−0.148049	+	1.88114i	−0.0151895	+	0.193001i
$96$	−2.32382	−	1.98473i	−0.237174	−	0.202566i
$97$	−8.47997	−	2.03586i	−0.861010	−	0.206710i	−0.221186	−	0.975232i	$-0.570993\pi$
$97$	−8.47997	−	2.03586i	−0.861010	−	0.206710i	−0.639824	+	0.768521i	$0.720993\pi$
$98$			13.2968i			1.34318i
$99$	−7.65293	+	19.5829i	−0.769148	+	1.96815i
$100$	−2.97977	−	2.97977i	−0.297977	−	0.297977i
$101$	0.289337	+	0.210216i	0.0287901	+	0.0209173i	0.602087	−	0.798430i	$-0.294336\pi$
$101$	0.289337	+	0.210216i	0.0287901	+	0.0209173i	−0.573297	+	0.819348i	$0.694336\pi$
$102$	10.5360	+	6.91098i	1.04322	+	0.684289i
$103$	−0.664244	−	2.04433i	−0.0654499	−	0.201434i	0.912984	−	0.407996i	$-0.133772\pi$
$103$	−0.664244	−	2.04433i	−0.0654499	−	0.201434i	−0.978433	+	0.206562i	$0.933772\pi$
$104$	−4.54125	−	0.719263i	−0.445306	−	0.0705295i
$105$	−10.4073	−	6.37762i	−1.01565	−	0.622392i
$106$	10.4287	−	3.38850i	1.01293	−	0.329121i
$107$	−0.263162	−	3.34379i	−0.0254409	−	0.323257i	−0.996448	−	0.0842073i	$-0.973164\pi$
$107$	−0.263162	−	3.34379i	−0.0254409	−	0.323257i	0.971007	−	0.239049i	$-0.0768358\pi$
$108$	−8.70125	+	5.33213i	−0.837278	+	0.513084i
$109$	−9.55193	−	3.95654i	−0.914909	−	0.378968i	−0.124975	−	0.992160i	$-0.539885\pi$
$109$	−9.55193	−	3.95654i	−0.914909	−	0.378968i	−0.789934	+	0.613192i	$0.789885\pi$
$110$	2.34348	−	1.77587i	0.223442	−	0.169323i
$111$	14.0323	−	14.0323i	1.33189	−	1.33189i
$112$	−2.35396	−	3.84131i	−0.222428	−	0.362970i
$113$	1.99541	+	1.70424i	0.187712	+	0.160321i	0.738338	−	0.674431i	$-0.235611\pi$
$113$	1.99541	+	1.70424i	0.187712	+	0.160321i	−0.550626	+	0.834752i	$0.685611\pi$
$114$	4.22437	+	4.94611i	0.395649	+	0.463245i
$115$	−2.12663	−	2.92705i	−0.198309	−	0.272949i
$116$	−3.42175	−	2.09685i	−0.317701	−	0.194688i
$117$	−13.2326	+	25.9704i	−1.22335	+	2.40096i
$118$	3.19032	−	9.81880i	0.293693	−	0.903894i
$119$	11.6236	+	14.4892i	1.06554	+	1.32822i
$120$	2.70931			0.247325
$121$	−5.38475	−	9.59190i	−0.489522	−	0.871991i
$122$	−3.18971	−	7.70065i	−0.288783	−	0.697184i
$123$	6.61967	−	9.11119i	0.596876	−	0.821529i
$124$	0.212657	+	2.70207i	0.0190972	+	0.242653i
$125$	8.14349	+	0.640907i	0.728376	+	0.0573244i
$126$	−27.7708	+	6.66717i	−2.47402	+	0.593959i
$127$	−0.366652	+	2.31495i	−0.0325351	+	0.205418i	−0.998601	−	0.0528771i	$-0.983161\pi$
$127$	−0.366652	+	2.31495i	−0.0325351	+	0.205418i	0.966066	+	0.258296i	$0.0831608\pi$
$128$	0.891007	+	0.453990i	0.0787546	+	0.0401275i
$129$	−0.607671	+	0.711492i	−0.0535025	+	0.0626434i
$130$	3.47554	−	2.12982i	0.304825	−	0.186797i
$131$	10.9278	−	4.52646i	0.954770	−	0.395479i	0.149748	−	0.988724i	$-0.452154\pi$
$131$	10.9278	−	4.52646i	0.954770	−	0.395479i	0.805022	+	0.593245i	$0.202154\pi$
$132$	1.38353	−	10.0408i	0.120421	−	0.873942i
$133$	3.66956	+	8.85910i	0.318191	+	0.768181i
$134$	2.14796	+	13.5617i	0.185555	+	1.17155i
$135$	2.79576	−	8.60446i	0.240621	−	0.740554i
$136$	−3.88026	−	1.39411i	−0.332730	−	0.119544i
$137$	−6.76038	+	4.91170i	−0.577578	+	0.419635i	−0.837850	−	0.545900i	$-0.816188\pi$
$137$	−6.76038	+	4.91170i	−0.577578	+	0.419635i	0.260272	+	0.965535i	$0.416188\pi$
$138$	−12.3182	−	1.95102i	−1.04860	−	0.166082i
$139$	12.2412	−	10.4550i	1.03828	−	0.886778i	0.0446015	−	0.999005i	$-0.485798\pi$
$139$	12.2412	−	10.4550i	1.03828	−	0.886778i	0.993683	+	0.112226i	$0.0357982\pi$
$140$	3.79859	+	1.23424i	0.321039	+	0.104312i
$141$	−2.75765	−	0.662053i	−0.232236	−	0.0557549i
$142$	−2.74228	+	6.62045i	−0.230127	+	0.555576i
$143$	−6.11838	−	13.9681i	−0.511644	−	1.16807i
$144$	4.48258	−	4.48258i	0.373548	−	0.373548i
$145$	3.51402	−	0.556565i	0.291823	−	0.0462202i
$146$	−8.27786	+	9.69213i	−0.685081	+	0.802126i
$147$	−40.5102	−	3.18822i	−3.34122	−	0.262960i
$148$	−3.39291	+	5.53673i	−0.278896	+	0.455116i
$149$	10.8738	+	14.9664i	0.890813	+	1.22610i	0.973307	+	0.229507i	$0.0737113\pi$
$149$	10.8738	+	14.9664i	0.890813	+	1.22610i	−0.0824945	+	0.996592i	$0.526289\pi$
$150$	9.79267	−	8.36373i	0.799568	−	0.682896i
$151$	19.2991	−	9.83339i	1.57054	−	0.800230i	0.570757	−	0.821119i	$-0.306650\pi$
$151$	19.2991	−	9.83339i	1.57054	−	0.800230i	0.999782	+	0.0208892i	$0.00664974\pi$
$152$	−1.72194	−	1.25106i	−0.139668	−	0.101475i
$153$	−16.0065	+	20.6633i	−1.29405	+	1.67053i
$154$	6.51390	−	13.4475i	0.524905	−	1.08363i
$155$	−1.69912	−	1.69912i	−0.136477	−	0.136477i
$156$	3.28018	−	13.6629i	0.262625	−	1.09391i
$157$	−18.3096	−	5.94913i	−1.46126	−	0.474793i	−0.532806	−	0.846237i	$-0.678863\pi$
$157$	−18.3096	−	5.94913i	−1.46126	−	0.474793i	−0.928455	+	0.371445i	$0.878863\pi$
$158$	7.87165	+	9.21652i	0.626235	+	0.733227i
$159$	7.82291	+	32.5848i	0.620397	+	2.58414i
$160$	−0.862052	+	0.206960i	−0.0681512	+	0.0163616i
$161$	−16.3820	−	8.34703i	−1.29108	−	0.657838i
$162$	−5.52462	−	10.8427i	−0.434055	−	0.851881i
$163$	−5.12350	−	8.36080i	−0.401304	−	0.654868i	0.586611	−	0.809869i	$-0.300462\pi$
$163$	−5.12350	−	8.36080i	−0.401304	−	0.654868i	−0.987914	+	0.155001i	$0.950462\pi$
$164$	−1.41026	+	3.40467i	−0.110123	+	0.265860i
$165$	4.84849	+	7.56547i	0.377454	+	0.588971i
$166$			0.566863i			0.0439971i
$167$	2.52129	−	10.5019i	0.195104	−	0.812665i	−0.785849	−	0.618418i	$-0.787774\pi$
$167$	2.52129	−	10.5019i	0.195104	−	0.812665i	0.980953	−	0.194247i	$-0.0622262\pi$
$168$	12.2674	−	6.25055i	0.946450	−	0.482240i
$169$	−2.51548	−	7.74185i	−0.193498	−	0.595527i
$170$	3.41851	−	1.29430i	0.262188	−	0.0992685i
$171$	−10.9159	+	7.93088i	−0.834762	+	0.606490i
$172$	0.139000	−	0.272802i	0.0105986	−	0.0208010i
$173$	−13.9738	+	1.09976i	−1.06241	+	0.0836132i	−0.597596	−	0.801797i	$-0.703877\pi$
$173$	−13.9738	+	1.09976i	−1.06241	+	0.0836132i	−0.464810	+	0.885410i	$0.653877\pi$
$174$	7.20872	−	9.92196i	0.546492	−	0.752182i
$175$	17.5399	−	7.26527i	1.32589	−	0.549203i
$176$	0.326791	+	3.30049i	0.0246328	+	0.248783i
$177$	29.1491	+	12.0740i	2.19098	+	0.907534i
$178$	12.2370	−	1.93815i	0.917204	−	0.145271i
$179$	−6.34957	−	12.4617i	−0.474589	−	0.931434i	−0.996900	−	0.0786787i	$-0.974930\pi$
$179$	−6.34957	−	12.4617i	−0.474589	−	0.931434i	0.522311	−	0.852755i	$-0.325070\pi$
$180$	−0.440948	+	5.60278i	−0.0328663	+	0.417607i
$181$	−2.90582	−	12.1036i	−0.215988	−	0.899653i	−0.970061	−	0.242863i	$-0.921914\pi$
$181$	−2.90582	−	12.1036i	−0.215988	−	0.899653i	0.754073	−	0.656791i	$-0.228086\pi$
$182$	10.8232	−	17.6618i	0.802266	−	1.30918i
$183$	24.2257	−	7.87140i	1.79081	−	0.581871i
$184$	4.06846	−	0.320195i	0.299931	−	0.0236051i
$185$	−0.900579	−	5.68603i	−0.0662118	−	0.418045i
$186$	−8.28314			−0.607349
$187$	−3.05106	−	13.3301i	−0.223115	−	0.974792i
$188$	0.928004			0.0676816
$189$	−7.19220	−	45.4098i	−0.523156	−	3.30308i
$190$	1.88114	−	0.148049i	0.136472	−	0.0107406i
$191$	15.2749	−	4.96313i	1.10526	−	0.359120i	0.301133	−	0.953582i	$-0.402635\pi$
$191$	15.2749	−	4.96313i	1.10526	−	0.359120i	0.804123	+	0.594463i	$0.202635\pi$
$192$	−1.59677	+	2.60569i	−0.115237	+	0.188050i
$193$	−1.00696	−	4.19427i	−0.0724823	−	0.301910i	0.924340	−	0.381570i	$-0.124617\pi$
$193$	−1.00696	−	4.19427i	−0.0724823	−	0.301910i	−0.996822	+	0.0796599i	$0.974617\pi$
$194$	−0.684236	+	8.69404i	−0.0491253	+	0.624196i
$195$	5.65537	+	11.0993i	0.404990	+	0.794837i
$196$	13.1331	−	2.08008i	0.938079	−	0.148577i
$197$	−24.4000	−	10.1068i	−1.73843	−	0.720080i	−0.998897	−	0.0469547i	$-0.985048\pi$
$197$	−24.4000	−	10.1068i	−1.73843	−	0.720080i	−0.739529	−	0.673125i	$-0.764952\pi$
$198$	20.5390	+	4.49527i	1.45964	+	0.319465i
$199$	−11.7943	+	4.88537i	−0.836077	+	0.346315i	−0.759306	−	0.650734i	$-0.774461\pi$
$199$	−11.7943	+	4.88537i	−0.836077	+	0.346315i	−0.0767717	+	0.997049i	$0.524461\pi$
$200$	−2.47695	+	3.40923i	−0.175147	+	0.241069i
$201$	−41.8322	+	3.29226i	−2.95061	+	0.232218i
$202$	0.162365	−	0.318660i	0.0114240	−	0.0224208i
$203$	14.6269	−	10.6271i	1.02661	−	0.745876i
$204$	5.17770	−	11.4874i	0.362512	−	0.804277i
$205$	−1.00959	−	3.10719i	−0.0705127	−	0.217016i
$206$	−1.91525	+	0.975871i	−0.133442	+	0.0679921i
$207$	6.03947	−	25.1562i	0.419772	−	1.74848i
$208$			4.59785i			0.318804i
$209$	0.411942	−	7.04719i	0.0284946	−	0.487464i
$210$	−4.67103	+	11.2769i	−0.322332	+	0.778178i
$211$	15.0279	+	24.5233i	1.03456	+	1.68826i	0.637461	+	0.770483i	$0.279985\pi$
$211$	15.0279	+	24.5233i	1.03456	+	1.68826i	0.397104	+	0.917774i	$0.370015\pi$
$212$	−4.97820	−	9.77027i	−0.341904	−	0.671025i
$213$	−19.5124	−	9.94207i	−1.33697	−	0.681219i
$214$	−3.26146	+	0.783007i	−0.222949	+	0.0535252i
$215$	0.0633656	+	0.263937i	0.00432150	+	0.0180003i
$216$	6.62766	+	7.75999i	0.450955	+	0.528000i
$217$	−11.6133	−	3.77341i	−0.788365	−	0.256155i
$218$	−2.41358	+	10.0533i	−0.163468	+	0.680893i
$219$	−27.5433	−	27.5433i	−1.86121	−	1.86121i
$220$	−2.12061	−	2.03682i	−0.142971	−	0.137322i
$221$	−2.38830	−	18.8064i	−0.160654	−	1.26505i
$222$	−16.0547	−	11.6644i	−1.07752	−	0.782866i
$223$	−0.637496	+	0.324820i	−0.0426899	+	0.0217516i	−0.475205	−	0.879875i	$-0.657626\pi$
$223$	−0.637496	+	0.324820i	−0.0426899	+	0.0217516i	0.432515	+	0.901627i	$0.357626\pi$
$224$	−3.42578	+	2.92589i	−0.228895	+	0.195494i
$225$	15.7022	+	21.6122i	1.04681	+	1.44081i
$226$	1.37111	−	2.23744i	0.0912047	−	0.148833i
$227$	−0.188681	−	0.0148495i	−0.0125232	−	0.000985598i	0.0721959	−	0.997390i	$-0.476999\pi$
$227$	−0.188681	−	0.0148495i	−0.0125232	−	0.000985598i	−0.0847192	+	0.996405i	$0.526999\pi$
$228$	4.22437	−	4.94611i	0.279766	−	0.327564i
$229$	5.26566	−	0.833998i	0.347964	−	0.0551121i	0.0199938	−	0.999800i	$-0.493635\pi$
$229$	5.26566	−	0.833998i	0.347964	−	0.0551121i	0.327970	+	0.944688i	$0.393635\pi$
$230$	−2.55834	+	2.55834i	−0.168692	+	0.168692i
$231$	39.4073	+	23.0697i	2.59281	+	1.51787i
$232$	−1.53575	+	3.70764i	−0.100827	+	0.243418i
$233$	1.77782	+	0.426818i	0.116469	+	0.0279618i	0.291261	−	0.956644i	$-0.405925\pi$
$233$	1.77782	+	0.426818i	0.116469	+	0.0279618i	−0.174792	+	0.984605i	$0.555925\pi$
$234$	27.7207	+	9.00700i	1.81216	+	0.588806i
$235$	−0.625600	+	0.534313i	−0.0408097	+	0.0348547i
$236$	−10.1970	−	1.61505i	−0.663768	−	0.105130i
$237$	−29.9666	+	21.7720i	−1.94654	+	1.41424i
$238$	12.4925	−	13.7471i	0.809768	−	0.891094i
$239$	5.12010	−	15.7580i	0.331192	−	1.01930i	−0.637376	−	0.770553i	$-0.719980\pi$
$239$	5.12010	−	15.7580i	0.331192	−	1.01930i	0.968568	−	0.248750i	$-0.0800199\pi$
$240$	−0.423830	−	2.67596i	−0.0273581	−	0.172732i
$241$	−3.16634	−	7.64423i	−0.203962	−	0.492408i	0.788489	−	0.615049i	$-0.210864\pi$
$241$	−3.16634	−	7.64423i	−0.203962	−	0.492408i	−0.992451	+	0.122641i	$0.960864\pi$
$242$	−8.63145	+	6.81895i	−0.554850	+	0.438339i
$243$	6.07330	−	2.51564i	0.389603	−	0.161379i
$244$	−7.10686	+	4.35509i	−0.454970	+	0.278806i
$245$	−7.65586	+	8.96385i	−0.489115	+	0.572680i
$246$	−10.0346	−	5.11287i	−0.639780	−	0.325984i
$247$	1.53090	−	9.66574i	0.0974091	−	0.615017i
$248$	2.63553	−	0.632736i	0.167357	−	0.0401788i
$249$	−1.72701	−	0.135919i	−0.109445	−	0.00861349i
$250$	−0.640907	−	8.14349i	−0.0405345	−	0.515040i
$251$	−10.4596	+	14.3965i	−0.660206	+	0.908696i	−0.999488	−	0.0319886i	$-0.989816\pi$
$251$	−10.4596	+	14.3965i	−0.660206	+	0.908696i	0.339282	+	0.940685i	$0.389816\pi$
$252$	10.9294	+	26.3859i	0.688487	+	1.66216i
$253$	8.17488	+	10.7877i	0.513950	+	0.678220i
$254$	2.34380			0.147063
$255$	3.12357	+	10.7252i	0.195605	+	0.671638i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.25598	+	2.46499i	−0.0783457	+	0.153762i	−0.926856	−	0.375416i	$-0.877500\pi$
$257$	−1.25598	+	2.46499i	−0.0783457	+	0.153762i	0.848511	+	0.529178i	$0.177500\pi$
$258$	0.797793	+	0.488888i	0.0496684	+	0.0304368i
$259$	−17.1957	−	23.6679i	−1.06849	−	1.47065i
$260$	−2.64729	−	3.09958i	−0.164178	−	0.192228i
$261$	19.3451	+	16.5222i	1.19743	+	1.02270i
$262$	−6.18022	−	10.0852i	−0.381816	−	0.623066i
$263$	−13.5014	+	13.5014i	−0.832532	+	0.832532i	−0.987863	−	0.155330i	$-0.950356\pi$
$263$	−13.5014	+	13.5014i	−0.832532	+	0.832532i	0.155330	+	0.987863i	$0.450356\pi$
$264$	−10.1336	+	0.204236i	−0.623683	+	0.0125699i
$265$	8.98137	+	3.72021i	0.551721	+	0.228530i
$266$	8.17598	−	5.01025i	0.501302	−	0.307198i
$267$	2.97069	+	37.7462i	0.181803	+	2.31003i
$268$	13.0587	−	4.24303i	0.797687	−	0.259184i
$269$	18.4536	+	11.3084i	1.12514	+	0.689484i	0.955197	−	0.295970i	$-0.0956429\pi$
$269$	18.4536	+	11.3084i	1.12514	+	0.689484i	0.169939	+	0.985455i	$0.445643\pi$
$270$	−8.93588	−	1.41530i	−0.543820	−	0.0861327i
$271$	0.547029	+	1.68358i	0.0332296	+	0.102270i	0.966296	−	0.257435i	$-0.0828773\pi$
$271$	0.547029	+	1.68358i	0.0332296	+	0.102270i	−0.933066	+	0.359705i	$0.882877\pi$
$272$	−0.769943	+	4.05058i	−0.0466847	+	0.245602i
$273$	51.2135	+	37.2088i	3.09958	+	2.25198i
$274$	5.90879	+	5.90879i	0.356963	+	0.356963i
$275$	−13.9526	−	0.815593i	−0.841371	−	0.0491821i
$276$			12.4718i			0.750714i
$277$	−15.3325	−	3.68101i	−0.921242	−	0.221171i	−0.255030	−	0.966933i	$-0.582085\pi$
$277$	−15.3325	−	3.68101i	−0.921242	−	0.221171i	−0.666212	+	0.745763i	$0.732085\pi$
$278$	−12.2412	−	10.4550i	−0.734178	−	0.627047i
$279$	1.34810	−	17.1293i	0.0807088	−	1.02550i
$280$	0.624810	−	3.94490i	0.0373396	−	0.235753i
$281$	−4.21677	+	26.6236i	−0.251551	+	1.58823i	0.461513	+	0.887134i	$0.347307\pi$
$281$	−4.21677	+	26.6236i	−0.251551	+	1.58823i	−0.713064	+	0.701099i	$0.752693\pi$
$282$	−0.222511	+	2.82726i	−0.0132503	+	0.168361i
$283$	15.6953	+	13.4050i	0.932987	+	0.796846i	0.979370	−	0.202078i	$-0.0647693\pi$
$283$	15.6953	+	13.4050i	0.932987	+	0.796846i	−0.0463826	+	0.998924i	$0.514769\pi$
$284$	6.96793	+	1.67285i	0.413471	+	0.0992655i
$285$			5.76660i			0.341584i
$286$	−12.8390	+	8.22815i	−0.759187	+	0.486540i
$287$	−11.7398	−	11.7398i	−0.692976	−	0.692976i
$288$	−5.12862	−	3.72616i	−0.302207	−	0.219566i
$289$	1.04524	−	16.9678i	0.0614846	−	0.998108i
$290$	−1.09943	−	3.38369i	−0.0645605	−	0.198697i
$291$	−26.3233	−	4.16920i	−1.54310	−	0.244403i
$292$	10.8677	+	6.65976i	0.635987	+	0.389733i
$293$	−2.12557	+	0.690638i	−0.124177	+	0.0403475i	−0.370446	−	0.928854i	$-0.620795\pi$
$293$	−2.12557	+	0.690638i	−0.124177	+	0.0403475i	0.246269	+	0.969201i	$0.420795\pi$
$294$	3.18822	+	40.5102i	0.185941	+	2.36260i
$295$	7.80405	−	4.78233i	0.454369	−	0.278438i
$296$	5.99933	+	2.48500i	0.348704	+	0.144438i
$297$	−9.80835	+	32.3940i	−0.569138	+	1.87969i
$298$	13.0811	−	13.0811i	0.757770	−	0.757770i
$299$	9.80418	+	15.9990i	0.566991	+	0.925244i
$300$	−9.79267	−	8.36373i	−0.565380	−	0.482880i
$301$	0.895829	+	1.04888i	0.0516347	+	0.0604565i
$302$	−12.7314	−	17.5232i	−0.732608	−	1.00835i
$303$	0.931902	+	0.571070i	0.0535363	+	0.0328071i
$304$	−0.966289	+	1.89645i	−0.0554205	+	0.108769i
$305$	2.28347	−	7.02781i	0.130751	−	0.402411i
$306$	22.9129	+	12.5769i	1.30984	+	0.718976i
$307$	22.3664			1.27652			0.638259	−	0.769822i	$-0.279655\pi$
$307$	22.3664			1.27652			0.638259	+	0.769822i	$0.279655\pi$
$308$	−14.3009	−	4.33006i	−0.814869	−	0.246728i
$309$	−2.51387	−	6.06902i	−0.143009	−	0.345254i
$310$	−1.41240	+	1.94400i	−0.0802189	+	0.110412i
$311$	−1.09610	−	13.9273i	−0.0621541	−	0.789743i	−0.946457	−	0.322829i	$-0.895366\pi$
$311$	−1.09610	−	13.9273i	−0.0621541	−	0.789743i	0.884303	−	0.466913i	$-0.154634\pi$
$312$	−14.0079	−	1.10244i	−0.793039	−	0.0624135i
$313$	24.6250	−	5.91195i	1.39189	−	0.334163i	0.532909	−	0.846172i	$-0.321099\pi$
$313$	24.6250	−	5.91195i	1.39189	−	0.334163i	0.858980	+	0.512009i	$0.171099\pi$
$314$	−3.01165	+	19.0148i	−0.169957	+	1.07307i
$315$	−22.5600	−	11.4949i	−1.27111	−	0.647664i
$316$	7.87165	−	9.21652i	0.442815	−	0.518470i
$317$	23.9415	−	14.6714i	1.34469	−	0.824026i	0.351019	−	0.936368i	$-0.385835\pi$
$317$	23.9415	−	14.6714i	1.34469	−	0.824026i	0.993670	+	0.112342i	$0.0358354\pi$
$318$	30.9598	−	12.8240i	1.73614	−	0.719133i
$319$	−13.1015	+	2.34662i	−0.733544	+	0.131385i
$320$	0.339267	+	0.819063i	0.0189656	+	0.0457870i
$321$	−1.60350	−	10.1241i	−0.0894989	−	0.565074i
$322$	−5.68156	+	17.4860i	−0.316621	+	0.974459i
$323$	2.96728	−	8.25889i	0.165104	−	0.459537i
$324$	−9.84494	+	7.15277i	−0.546941	+	0.397376i
$325$	−19.1370	−	3.03100i	−1.06153	−	0.168130i
$326$	−7.45637	+	6.36834i	−0.412970	+	0.352710i
$327$	−30.0497	−	9.76373i	−1.66175	−	0.539935i
$328$	3.58337	+	0.860291i	0.197858	+	0.0475016i
$329$	−1.59994	+	3.86259i	−0.0882075	+	0.212952i
$330$	6.71386	−	5.97229i	0.369586	−	0.328764i
$331$	−1.23869	+	1.23869i	−0.0680843	+	0.0680843i	−0.740329	−	0.672245i	$-0.765330\pi$
$331$	−1.23869	+	1.23869i	−0.0680843	+	0.0680843i	0.672245	+	0.740329i	$0.265330\pi$
$332$	0.559884	−	0.0886769i	0.0307276	−	0.00486678i
$333$	26.7346	−	31.3023i	1.46505	−	1.71535i
$334$	−10.7671	−	0.847387i	−0.589148	−	0.0463669i
$335$	−6.36034	+	10.3791i	−0.347503	+	0.567073i
$336$	−8.09264	−	11.1386i	−0.441490	−	0.607658i
$337$	0.0138303	−	0.0118122i	0.000753382	−	0.000643449i	−0.649071	−	0.760728i	$-0.724842\pi$
$337$	0.0138303	−	0.0118122i	0.000753382	−	0.000643449i	0.649825	+	0.760084i	$0.274842\pi$
$338$	−7.25302	+	3.69560i	−0.394512	+	0.201014i
$339$	6.48786	+	4.71371i	0.352372	+	0.256013i
$340$	−1.81314	−	3.17395i	−0.0983313	−	0.172131i
$341$	6.48330	+	6.22713i	0.351090	+	0.337218i
$342$	9.54087	+	9.54087i	0.515911	+	0.515911i
$343$	−6.62247	+	27.5846i	−0.357580	+	1.48943i
$344$	−0.291188	−	0.0946126i	−0.0156998	−	0.00510117i
$345$	−7.18083	−	8.40768i	−0.386603	−	0.452654i
$346$	3.27220	+	13.6297i	0.175915	+	0.732737i
$347$	14.2387	−	3.41842i	0.764375	−	0.183510i	0.167530	−	0.985867i	$-0.446421\pi$
$347$	14.2387	−	3.41842i	0.764375	−	0.183510i	0.596845	+	0.802357i	$0.296421\pi$
$348$	−10.9275	−	5.56784i	−0.585775	−	0.298467i
$349$	0.940565	+	1.84596i	0.0503473	+	0.0988121i	0.914809	−	0.403886i	$-0.132341\pi$
$349$	0.940565	+	1.84596i	0.0503473	+	0.0988121i	−0.864462	+	0.502698i	$0.832341\pi$
$350$	−9.91967	−	16.1874i	−0.530229	−	0.865254i
$351$	−17.9560	+	43.3497i	−0.958422	+	2.31384i
$352$	3.20873	−	0.839077i	0.171026	−	0.0447230i
$353$			3.13315i			0.166761i	0.996518	+	0.0833805i	$0.0265717\pi$
$353$			3.13315i			0.166761i	−0.996518	+	0.0833805i	$0.973428\pi$
$354$	7.36538	−	30.6790i	0.391465	−	1.63057i
$355$	−5.66050	+	2.88417i	−0.300428	+	0.153076i
$356$	−3.82859	−	11.7832i	−0.202915	−	0.624507i
$357$	38.8868	+	41.3559i	2.05811	+	2.18879i
$358$	−11.3150	+	8.22084i	−0.598017	+	0.434485i
$359$	5.08519	−	9.98024i	0.268386	−	0.526737i	−0.717000	−	0.697073i	$-0.754485\pi$
$359$	5.08519	−	9.98024i	0.268386	−	0.526737i	0.985386	+	0.170336i	$0.0544853\pi$
$360$	5.60278	−	0.440948i	0.295292	−	0.0232400i
$361$	−8.50512	+	11.7063i	−0.447638	+	0.616120i
$362$	−11.5000	+	4.76346i	−0.604427	+	0.250362i
$363$	−18.7051	−	27.9316i	−0.981763	−	1.46603i
$364$	−19.1375	−	7.92700i	−1.00308	−	0.415488i
$365$	−11.1608	+	1.76770i	−0.584183	+	0.0925255i
$366$	−11.5642	−	22.6961i	−0.604472	−	1.18634i
$367$	0.514643	−	6.53916i	0.0268642	−	0.341342i	−0.968767	−	0.247972i	$-0.920236\pi$
$367$	0.514643	−	6.53916i	0.0268642	−	0.341342i	0.995631	−	0.0933700i	$-0.0297640\pi$
$368$	−0.952701	−	3.96828i	−0.0496629	−	0.206861i
$369$	12.2064	−	19.9190i	0.635440	−	1.03694i
$370$	−5.47514	+	1.77898i	−0.284639	+	0.0924849i
$371$	49.2491	−	3.87599i	2.55689	−	0.201231i
$372$	1.29577	+	8.18116i	0.0671824	+	0.424173i
$373$	−22.6738			−1.17400			−0.587002	−	0.809585i	$-0.699692\pi$
$373$	−22.6738			−1.17400			−0.587002	+	0.809585i	$0.699692\pi$
$374$	−12.6887	+	5.09878i	−0.656116	+	0.263652i
$375$	24.9637			1.28912
$376$	−0.145172	−	0.916578i	−0.00748666	−	0.0472689i
$377$	−18.3949	+	1.44771i	−0.947383	+	0.0745607i
$378$	−43.7256	+	14.2073i	−2.24900	+	0.730745i
$379$	−0.575943	+	0.939854i	−0.0295842	+	0.0482771i	−0.867091	−	0.498151i	$-0.834013\pi$
$379$	−0.575943	+	0.939854i	−0.0295842	+	0.0482771i	0.837506	+	0.546428i	$0.184013\pi$
$380$	−0.440501	−	1.83482i	−0.0225972	−	0.0941243i
$381$	−0.561982	+	7.14066i	−0.0287912	+	0.365827i
$382$	−7.29156	−	14.3105i	−0.373068	−	0.732188i
$383$	25.8898	−	4.10055i	1.32291	−	0.209528i	0.545281	−	0.838253i	$-0.316423\pi$
$383$	25.8898	−	4.10055i	1.32291	−	0.209528i	0.777628	+	0.628725i	$0.216423\pi$
$384$	2.82340	+	1.16949i	0.144081	+	0.0596804i
$385$	12.1338	−	5.31492i	0.618398	−	0.270873i
$386$	−3.98511	+	1.65069i	−0.202837	+	0.0840178i
$387$	−1.14085	+	1.57024i	−0.0579926	+	0.0798200i
$388$	8.69404	−	0.684236i	0.441373	−	0.0347368i
$389$	9.67654	−	18.9913i	0.490620	−	0.962896i	−0.504424	−	0.863456i	$-0.668295\pi$
$389$	9.67654	−	18.9913i	0.490620	−	0.962896i	0.995044	−	0.0994394i	$-0.0317049\pi$
$390$	10.0779	−	7.32206i	0.510317	−	0.370767i
$391$	5.95807	+	15.7364i	0.301312	+	0.795825i
$392$	−4.10894	−	12.6460i	−0.207533	−	0.638720i
$393$	32.2075	−	16.4106i	1.62466	−	0.827803i
$394$	−6.16537	+	25.6806i	−0.310607	+	1.29377i
$395$			10.7454i			0.540661i
$396$	1.22692	−	20.9893i	0.0616553	−	1.05475i
$397$	3.97257	−	9.59062i	0.199377	−	0.481340i	−0.792293	−	0.610141i	$-0.791113\pi$
$397$	3.97257	−	9.59062i	0.199377	−	0.481340i	0.991670	+	0.128801i	$0.0411129\pi$
$398$	6.67026	+	10.8849i	0.334350	+	0.545609i
$399$	13.3039	+	26.1103i	0.666027	+	1.30715i
$400$	3.75473	+	1.91313i	0.187737	+	0.0956566i
$401$	−16.0667	+	3.85727i	−0.802332	+	0.192623i	−0.613818	−	0.789448i	$-0.710367\pi$
$401$	−16.0667	+	3.85727i	−0.802332	+	0.192623i	−0.188514	+	0.982070i	$0.560367\pi$
$402$	9.79572	+	40.8021i	0.488566	+	2.03502i
$403$	8.09351	+	9.47628i	0.403166	+	0.472047i
$404$	−0.340136	−	0.110517i	−0.0169224	−	0.00549843i
$405$	2.51850	−	10.4903i	0.125145	−	0.521268i
$406$	−12.7844	−	12.7844i	−0.634480	−	0.634480i
$407$	3.79706	+	21.1996i	0.188213	+	1.05082i
$408$	−12.1559	−	3.31694i	−0.601808	−	0.164213i
$409$	−4.46801	−	3.24620i	−0.220929	−	0.160514i	0.471816	−	0.881697i	$-0.343599\pi$
$409$	−4.46801	−	3.24620i	−0.220929	−	0.160514i	−0.692745	+	0.721183i	$0.743599\pi$
$410$	−2.91100	+	1.48323i	−0.143764	+	0.0732515i
$411$	−19.4185	+	16.5850i	−0.957845	+	0.818077i
$412$	1.26347	+	1.73901i	0.0622466	+	0.0856751i
$413$	24.3025	−	39.6581i	1.19585	−	1.95145i
$414$	−25.7913	−	2.02982i	−1.26757	−	0.0997601i
$415$	−0.326381	+	0.382143i	−0.0160214	+	0.0187586i
$416$	4.54125	−	0.719263i	0.222653	−	0.0352648i
$417$	34.7873	−	34.7873i	1.70354	−	1.70354i
$418$	−7.02487	+	0.695553i	−0.343598	+	0.0340206i
$419$	−5.09807	+	12.3078i	−0.249057	+	0.601277i	−0.998124	−	0.0612170i	$-0.980502\pi$
$419$	−5.09807	+	12.3078i	−0.249057	+	0.601277i	0.749068	+	0.662494i	$0.230502\pi$
$420$	11.8687	+	2.84943i	0.579135	+	0.139038i
$421$	−20.1024	−	6.53168i	−0.979733	−	0.318334i	−0.224994	−	0.974360i	$-0.572236\pi$
$421$	−20.1024	−	6.53168i	−0.979733	−	0.318334i	−0.754739	+	0.656026i	$0.772236\pi$
$422$	21.8705	−	18.6792i	1.06464	−	0.909289i
$423$	−5.81048	−	0.920290i	−0.282515	−	0.0447460i
$424$	−8.87122	+	6.44532i	−0.430824	+	0.313012i
$425$	−16.3516	−	5.87484i	−0.793167	−	0.284972i
$426$	−6.76725	+	20.8275i	−0.327874	+	1.00909i
$427$	−5.87433	−	37.0891i	−0.284279	−	1.79487i
$428$	1.28357	+	3.09881i	0.0620437	+	0.149787i
$429$	−21.9895	−	41.0884i	−1.06166	−	1.98377i
$430$	0.250775	−	0.103874i	0.0120934	−	0.00500926i
$431$	−2.64866	+	1.62310i	−0.127581	+	0.0781820i	−0.584825	−	0.811160i	$-0.698837\pi$
$431$	−2.64866	+	1.62310i	−0.127581	+	0.0781820i	0.457243	+	0.889342i	$0.348837\pi$
$432$	6.62766	−	7.75999i	0.318873	−	0.373353i
$433$	−11.9149	−	6.07095i	−0.572594	−	0.291751i	0.143619	−	0.989633i	$-0.454126\pi$
$433$	−11.9149	−	6.07095i	−0.572594	−	0.291751i	−0.716213	+	0.697882i	$0.754126\pi$
$434$	−1.91022	+	12.0607i	−0.0916935	+	0.578930i
$435$	10.5724	−	2.53820i	0.506907	−	0.121698i
$436$	10.3071	+	0.811183i	0.493619	+	0.0388486i
$437$	0.681514	+	8.65945i	0.0326012	+	0.414238i
$438$	−22.8955	+	31.5129i	−1.09399	+	1.50575i
$439$	−1.05153	−	2.53863i	−0.0501869	−	0.121162i	0.896798	−	0.442441i	$-0.145887\pi$
$439$	−1.05153	−	2.53863i	−0.0501869	−	0.121162i	−0.946985	+	0.321279i	$0.895887\pi$
$440$	−1.68001	+	2.41313i	−0.0800912	+	0.115041i
$441$	−84.2927			−4.01394
$442$	−18.2012	+	5.30086i	−0.865745	+	0.252136i
$443$	5.64756	−	17.3814i	0.268324	−	0.825815i	−0.722585	−	0.691282i	$-0.757046\pi$
$443$	5.64756	−	17.3814i	0.268324	−	0.825815i	0.990909	−	0.134533i	$-0.0429536\pi$
$444$	−9.00931	+	17.6818i	−0.427563	+	0.839140i
$445$	9.36534	+	5.73909i	0.443960	+	0.272059i
$446$	0.420548	+	0.578834i	0.0199135	+	0.0274086i
$447$	36.7166	+	42.9897i	1.73664	+	2.03334i
$448$	3.42578	+	2.92589i	0.161853	+	0.138235i
$449$	0.639819	+	1.04409i	0.0301949	+	0.0492736i	0.867382	−	0.497644i	$-0.165801\pi$
$449$	0.639819	+	1.04409i	0.0301949	+	0.0492736i	−0.837187	+	0.546917i	$0.815801\pi$
$450$	18.8897	−	18.8897i	0.890470	−	0.890470i
$451$	4.01039	+	11.5457i	0.188842	+	0.543667i
$452$	−2.42439	−	1.00421i	−0.114033	−	0.0472342i
$453$	56.4391	−	34.5859i	2.65174	−	1.62499i
$454$	0.0148495	+	0.188681i	0.000696923	+	0.00885525i
$455$	17.4653	−	5.67483i	0.818788	−	0.266040i
$456$	−5.54605	−	3.39862i	−0.259718	−	0.159155i
$457$	37.2784	+	5.90432i	1.74381	+	0.276192i	0.945398	−	0.325919i	$-0.105674\pi$
$457$	37.2784	+	5.90432i	1.74381	+	0.276192i	0.798412	+	0.602112i	$0.205674\pi$
$458$	−1.64746	−	5.07036i	−0.0769807	−	0.236922i
$459$	−23.0780	+	35.1830i	−1.07719	+	1.64220i
$460$	2.92705	+	2.12663i	0.136475	+	0.0991546i
$461$	17.2699	+	17.2699i	0.804340	+	0.804340i	0.983771	−	0.179430i	$-0.0574255\pi$
$461$	17.2699	+	17.2699i	0.804340	+	0.804340i	−0.179430	+	0.983771i	$0.557425\pi$
$462$	16.6210	−	42.5310i	0.773278	−	1.97872i
$463$		−	13.0983i		−	0.608732i	−0.952555	−	0.304366i	$-0.901555\pi$
$463$		−	13.0983i		−	0.608732i	0.952555	−	0.304366i	$-0.0984445\pi$
$464$	3.90224	+	0.936844i	0.181157	+	0.0434919i
$465$	−5.58396	−	4.76915i	−0.258950	−	0.221164i
$466$	0.143450	−	1.82270i	0.00664519	−	0.0844352i
$467$	−1.65641	+	10.4581i	−0.0766493	+	0.483945i	0.919265	+	0.393640i	$0.128784\pi$
$467$	−1.65641	+	10.4581i	−0.0766493	+	0.483945i	−0.995914	+	0.0903051i	$0.971216\pi$
$468$	4.55964	−	28.7884i	0.210769	−	1.33074i
$469$	−4.85345	+	61.6690i	−0.224112	+	2.84761i
$470$	0.625600	+	0.534313i	0.0288568	+	0.0246460i
$471$	−57.2085	−	13.7345i	−2.63603	−	0.632854i
$472$			10.3241i			0.475205i
$473$	−0.256903	−	0.982426i	−0.0118124	−	0.0451720i
$474$	26.1917	+	26.1917i	1.20303	+	1.20303i
$475$	−7.25631	−	5.27202i	−0.332942	−	0.241897i
$476$	−15.5321	−	10.1882i	−0.711914	−	0.466974i
$477$	21.4808	+	66.1111i	0.983538	+	3.02702i
$478$	−16.3650	−	2.59196i	−0.748518	−	0.118554i
$479$	−6.10757	−	3.74273i	−0.279062	−	0.171010i	0.375924	−	0.926651i	$-0.377325\pi$
$479$	−6.10757	−	3.74273i	−0.279062	−	0.171010i	−0.654986	+	0.755641i	$0.727325\pi$
$480$	−2.57671	+	0.837224i	−0.117610	+	0.0382139i
$481$	2.34253	+	29.7647i	0.106810	+	1.35715i
$482$	−7.05479	+	4.32318i	−0.321337	+	0.196916i
$483$	−51.9108	−	21.5022i	−2.36202	−	0.978383i
$484$	8.08526	+	7.45846i	0.367512	+	0.339021i
$485$	−5.46700	+	5.46700i	−0.248244	+	0.248244i
$486$	−3.43475	−	5.60500i	−0.155803	−	0.254248i
$487$	23.3728	+	19.9622i	1.05912	+	0.904575i	0.995628	−	0.0934068i	$-0.0297757\pi$
$487$	23.3728	+	19.9622i	1.05912	+	0.904575i	0.0634938	+	0.997982i	$0.479776\pi$
$488$	5.41323	+	6.33808i	0.245045	+	0.286911i
$489$	−17.6140	−	24.2436i	−0.796533	−	1.09633i
$490$	10.0511	+	6.15934i	0.454064	+	0.278251i
$491$	−3.70673	+	7.27487i	−0.167282	+	0.328310i	−0.959396	−	0.282064i	$-0.908981\pi$
$491$	−3.70673	+	7.27487i	−0.167282	+	0.328310i	0.792113	+	0.610374i	$0.208981\pi$
$492$	−3.48017	+	10.7109i	−0.156898	+	0.482882i
$493$	−16.4478	−	1.80496i	−0.740770	−	0.0812913i
$494$	−9.78623			−0.440303
$495$	11.2578	+	14.8561i	0.506002	+	0.667731i
$496$	−1.03723	−	2.50411i	−0.0465732	−	0.112438i
$497$	−18.9760	+	26.1182i	−0.851191	+	1.17156i
$498$	0.135919	+	1.72701i	0.00609066	+	0.0773892i
$499$	−11.2784	−	0.887630i	−0.504891	−	0.0397358i	−0.176544	−	0.984293i	$-0.556492\pi$
$499$	−11.2784	−	0.887630i	−0.504891	−	0.0397358i	−0.328347	+	0.944557i	$0.606492\pi$
$500$	−7.94297	+	1.90694i	−0.355221	+	0.0852809i
$501$	5.16331	−	32.5999i	0.230680	−	1.45645i
$502$	15.8555	+	8.07876i	0.707664	+	0.360573i
$503$	0.337958	−	0.395698i	0.0150688	−	0.0176433i	−0.752820	−	0.658226i	$-0.771307\pi$
$503$	0.337958	−	0.395698i	0.0150688	−	0.0176433i	0.767889	+	0.640583i	$0.221307\pi$
$504$	24.3513	−	14.9225i	1.08469	−	0.664701i
$505$	0.292930	−	0.121336i	0.0130352	−	0.00539936i
$506$	9.37610	−	9.76181i	0.416818	−	0.433965i
$507$	−9.51997	−	22.9832i	−0.422797	−	1.02072i
$508$	−0.366652	−	2.31495i	−0.0162675	−	0.102709i
$509$	2.39564	−	7.37303i	0.106185	−	0.326804i	−0.883822	−	0.467824i	$-0.845038\pi$
$509$	2.39564	−	7.37303i	0.106185	−	0.326804i	0.990007	+	0.141020i	$0.0450382\pi$
$510$	10.1045	−	4.76290i	0.447436	−	0.210905i
$511$	−46.4564	+	33.7525i	−2.05511	+	1.49312i
$512$	−0.987688	−	0.156434i	−0.0436501	−	0.00691349i
$513$	−16.5166	+	14.1065i	−0.729227	+	0.622819i
$514$	2.63112	+	0.854904i	0.116054	+	0.0377082i
$515$	−1.85301	−	0.444869i	−0.0816536	−	0.0196033i
$516$	0.358067	−	0.864450i	0.0157630	−	0.0380553i
$517$	2.29965	−	2.04565i	0.101139	−	0.0899676i
$518$	−20.6865	+	20.6865i	−0.908911	+	0.908911i
$519$	−42.3089	+	6.70108i	−1.85716	+	0.294145i
$520$	−2.64729	+	3.09958i	−0.116091	+	0.135925i
$521$	−17.8079	−	1.40152i	−0.780180	−	0.0614015i	−0.317887	−	0.948129i	$-0.602973\pi$
$521$	−17.8079	−	1.40152i	−0.780180	−	0.0614015i	−0.462293	+	0.886727i	$0.652973\pi$
$522$	13.2926	−	21.6915i	0.581801	−	0.949413i
$523$	−18.9533	−	26.0869i	−0.828768	−	1.14070i	−0.988151	−	0.153485i	$-0.950950\pi$
$523$	−18.9533	−	26.0869i	−0.828768	−	1.14070i	0.159383	−	0.987217i	$-0.449050\pi$
$524$	−8.99424	+	7.68181i	−0.392915	+	0.335581i
$525$	51.6952	−	26.3400i	2.25616	−	1.14957i
$526$	15.4473	+	11.2231i	0.673533	+	0.489350i
$527$	5.54328	+	9.70365i	0.241469	+	0.422698i
$528$	1.78697	+	9.97694i	0.0777680	+	0.434190i
$529$	4.48666	+	4.48666i	0.195072	+	0.195072i
$530$	2.26941	−	9.45276i	0.0985768	−	0.410602i
$531$	62.2445	+	20.2245i	2.70118	+	0.877667i
$532$	−6.22757	−	7.29155i	−0.269999	−	0.316129i
$533$	3.95549	+	16.4758i	0.171331	+	0.713646i
$534$	36.8167	−	8.83891i	1.59322	−	0.382497i
$535$	−2.64949	−	1.34998i	−0.114548	−	0.0583649i
$536$	−6.23362	−	12.2342i	−0.269251	−	0.528436i
$537$	−22.3327	−	36.4436i	−0.963725	−	1.57266i
$538$	8.28238	−	19.9954i	0.357079	−	0.862064i
$539$	27.9595	−	34.1046i	1.20430	−	1.46899i
$540$			9.04727i			0.389332i
$541$	−2.42338	+	10.0941i	−0.104189	+	0.433979i	−0.999944	−	0.0105691i	$-0.996636\pi$
$541$	−2.42338	+	10.0941i	−0.104189	+	0.433979i	0.895755	+	0.444548i	$0.146636\pi$
$542$	1.57728	−	0.803664i	0.0677500	−	0.0345203i
$543$	−11.7550	−	36.1782i	−0.504456	−	1.55255i
$544$	4.12115	+	0.126814i	0.176693	+	0.00543710i
$545$	−7.41541	+	5.38761i	−0.317641	+	0.230780i
$546$	28.7391	−	56.4037i	1.22992	−	2.41386i
$547$	3.23478	−	0.254583i	0.138309	−	0.0108852i	−0.00911541	−	0.999958i	$-0.502902\pi$
$547$	3.23478	−	0.254583i	0.138309	−	0.0108852i	0.147425	+	0.989073i	$0.452902\pi$
$548$	4.91170	−	6.76038i	0.209817	−	0.288789i
$549$	48.8169	−	20.2206i	2.08345	−	0.862995i
$550$	1.37711	+	13.9084i	0.0587201	+	0.593055i
$551$	−7.89147	−	3.26875i	−0.336188	−	0.139254i
$552$	12.3182	−	1.95102i	0.524299	−	0.0830408i
$553$	24.7903	+	48.6538i	1.05419	+	2.06897i
$554$	−1.23716	+	15.7196i	−0.0525618	+	0.667861i
$555$	−4.10707	−	17.1072i	−0.174335	−	0.726159i
$556$	−8.41130	+	13.7260i	−0.356719	+	0.582112i
$557$	29.8059	−	9.68453i	1.26292	−	0.410347i	0.400385	−	0.916347i	$-0.368877\pi$
$557$	29.8059	−	9.68453i	1.26292	−	0.410347i	0.862533	+	0.506000i	$0.168877\pi$
$558$	−17.1293	+	1.34810i	−0.725140	+	0.0570698i
$559$	−0.220219	−	1.39041i	−0.00931426	−	0.0588079i
$560$	−3.99407			−0.168780
$561$	−12.4916	−	39.8800i	−0.527395	−	1.68373i
$562$	26.9555			1.13705
$563$	2.97016	+	18.7528i	0.125177	+	0.790337i	0.967779	+	0.251801i	$0.0810227\pi$
$563$	2.97016	+	18.7528i	0.125177	+	0.790337i	−0.842602	+	0.538537i	$0.818977\pi$
$564$	2.82726	−	0.222511i	0.119049	−	0.00936938i
$565$	2.21256	−	0.718903i	0.0930829	−	0.0302445i
$566$	10.7847	−	17.5990i	0.453315	−	0.739743i
$567$	−12.7984	−	53.3090i	−0.537481	−	2.23877i
$568$	0.562232	−	7.14384i	0.0235907	−	0.299749i
$569$	−3.79599	−	7.45005i	−0.159136	−	0.312322i	0.797647	−	0.603125i	$-0.206078\pi$
$569$	−3.79599	−	7.45005i	−0.159136	−	0.312322i	−0.956783	+	0.290802i	$0.906078\pi$
$570$	5.69560	−	0.902095i	0.238562	−	0.0377846i
$571$	16.8015	+	6.95939i	0.703119	+	0.291242i	0.705454	−	0.708756i	$-0.250743\pi$
$571$	16.8015	+	6.95939i	0.703119	+	0.291242i	−0.00233473	+	0.999997i	$0.500743\pi$
$572$	10.1353	+	11.3938i	0.423779	+	0.476398i
$573$	45.3468	−	18.7832i	1.89439	−	0.784681i
$574$	−9.75871	+	13.4317i	−0.407321	+	0.560629i
$575$	17.1446	−	1.34931i	0.714981	−	0.0562702i
$576$	−2.87799	+	5.64838i	−0.119916	+	0.235349i
$577$	37.7036	−	27.3933i	1.56962	−	1.14040i	0.642104	−	0.766617i	$-0.278062\pi$
$577$	37.7036	−	27.3933i	1.56962	−	1.14040i	0.927518	−	0.373780i	$-0.121938\pi$
$578$	−16.9224	+	1.62198i	−0.703881	+	0.0674657i
$579$	−4.07348	−	12.5369i	−0.169288	−	0.521014i
$580$	−3.17004	+	1.61522i	−0.131629	+	0.0670682i
$581$	−0.596180	+	2.48327i	−0.0247337	+	0.103023i
$582$			26.6514i			1.10474i
$583$	−33.8735	−	13.2376i	−1.40290	−	0.548247i
$584$	4.87768	−	11.7758i	0.201840	−	0.487285i
$585$	13.5016	+	22.0326i	0.558222	+	0.910935i
$586$	1.01465	+	1.99136i	0.0419147	+	0.0822622i
$587$	28.6586	+	14.6023i	1.18287	+	0.602701i	0.930985	−	0.365057i	$-0.118950\pi$
$587$	28.6586	+	14.6023i	1.18287	+	0.602701i	0.251882	+	0.967758i	$0.418950\pi$
$588$	39.5127	−	9.48616i	1.62948	−	0.391203i
$589$	1.34674	+	5.60956i	0.0554913	+	0.231138i
$590$	−5.94427	−	6.95984i	−0.244722	−	0.286532i
$591$	−76.7605	−	24.9410i	−3.15751	−	1.02594i
$592$	1.51591	−	6.31421i	0.0623034	−	0.259512i
$593$	−26.5560	−	26.5560i	−1.09053	−	1.09053i	−0.995472	−	0.0950537i	$-0.969698\pi$
$593$	−26.5560	−	26.5560i	−1.09053	−	1.09053i	−0.0950537	−	0.995472i	$-0.530302\pi$
$594$	33.5296	+	4.62005i	1.37573	+	0.189563i
$595$	16.3368	−	2.07467i	0.669742	−	0.0850533i
$596$	−14.9664	−	10.8738i	−0.613049	−	0.445406i
$597$	−34.7613	+	17.7118i	−1.42269	+	0.724895i
$598$	14.2683	−	12.1863i	0.583474	−	0.498334i
$599$	−23.9859	−	33.0138i	−0.980039	−	1.34891i	−0.936808	−	0.349843i	$-0.886235\pi$
$599$	−23.9859	−	33.0138i	−0.980039	−	1.34891i	−0.0432304	−	0.999065i	$-0.513765\pi$
$600$	−6.72885	+	10.9805i	−0.274704	+	0.448276i
$601$	39.5422	+	3.11204i	1.61296	+	0.126943i	0.852603	−	0.522560i	$-0.175023\pi$
$601$	39.5422	+	3.11204i	1.61296	+	0.126943i	0.760359	+	0.649503i	$0.225023\pi$
$602$	0.895829	−	1.04888i	0.0365113	−	0.0427492i
$603$	−85.9718	+	13.6166i	−3.50104	+	0.554511i
$604$	−15.3159	+	15.3159i	−0.623193	+	0.623193i
$605$	−9.74489	−	0.372795i	−0.396186	−	0.0151563i
$606$	0.418258	−	1.00976i	0.0169906	−	0.0410188i
$607$	14.9080	+	3.57909i	0.605097	+	0.145271i	0.524406	−	0.851468i	$-0.324287\pi$
$607$	14.9080	+	3.57909i	0.605097	+	0.145271i	0.0806908	+	0.996739i	$0.474287\pi$
$608$	2.02426	+	0.657722i	0.0820946	+	0.0266742i
$609$	42.0145	−	35.8838i	1.70251	−	1.45408i
$610$	−7.29850	−	1.15597i	−0.295508	−	0.0468038i
$611$	3.45193	−	2.50798i	0.139650	−	0.101462i
$612$	8.83773	−	24.5982i	0.357244	−	0.994325i
$613$	0.909961	−	2.80057i	0.0367530	−	0.113114i	−0.930997	−	0.365027i	$-0.881060\pi$
$613$	0.909961	−	2.80057i	0.0367530	−	0.113114i	0.967750	+	0.251913i	$0.0810597\pi$
$614$	−3.49888	−	22.0910i	−0.141203	−	0.891522i
$615$	−3.82084	−	9.22433i	−0.154071	−	0.371961i
$616$	−2.03960	+	14.8022i	−0.0821778	+	0.596397i
$617$	−40.3749	+	16.7238i	−1.62543	+	0.673276i	−0.994709	−	0.102732i	$-0.967241\pi$
$617$	−40.3749	+	16.7238i	−1.62543	+	0.673276i	−0.630723	+	0.776008i	$0.717241\pi$
$618$	−5.60104	+	3.43232i	−0.225307	+	0.138068i
$619$	−0.369403	+	0.432515i	−0.0148476	+	0.0173843i	−0.767780	−	0.640713i	$-0.778639\pi$
$619$	−0.369403	+	0.432515i	−0.0148476	+	0.0173843i	0.752933	+	0.658098i	$0.228639\pi$
$620$	2.14102	+	1.09090i	0.0859853	+	0.0438117i
$621$	6.51507	−	41.1345i	0.261441	−	1.65067i
$622$	−13.5843	+	3.26131i	−0.544682	+	0.130767i
$623$	55.6454	+	4.37939i	2.22938	+	0.175456i
$624$	1.10244	+	14.0079i	0.0441330	+	0.560763i
$625$	−8.12805	+	11.1873i	−0.325122	+	0.447492i
$626$	−9.69137	−	23.3970i	−0.387345	−	0.935133i
$627$	−0.434703	−	21.5688i	−0.0173604	−	0.861375i
$628$	19.2518			0.768231
$629$	−2.92061	+	26.6141i	−0.116452	+	1.06118i
$630$	−7.82421	+	24.0805i	−0.311724	+	0.959388i
$631$	−0.355455	+	0.697620i	−0.0141504	+	0.0277718i	−0.897974	−	0.440049i	$-0.854961\pi$
$631$	−0.355455	+	0.697620i	−0.0141504	+	0.0277718i	0.883823	+	0.467821i	$0.154961\pi$
$632$	−10.3344	−	6.33296i	−0.411082	−	0.251912i
$633$	51.6643	+	71.1097i	2.05347	+	2.82636i
$634$	−18.2360	−	21.3516i	−0.724245	−	0.847981i
$635$	1.58004	+	1.34948i	0.0627021	+	0.0535526i
$636$	−17.5093	−	28.5725i	−0.694288	−	1.13298i
$637$	43.2302	−	43.2302i	1.71284	−	1.71284i
$638$	4.36726	+	12.5731i	0.172901	+	0.497775i
$639$	−41.9692	−	17.3842i	−1.66027	−	0.687708i
$640$	0.755906	−	0.463220i	0.0298798	−	0.0183104i
$641$	2.63883	+	33.5296i	0.104228	+	1.32434i	0.797349	+	0.603518i	$0.206235\pi$
$641$	2.63883	+	33.5296i	0.104228	+	1.32434i	−0.693122	+	0.720821i	$0.743765\pi$
$642$	−9.74864	+	3.16753i	−0.384748	+	0.125012i
$643$	−17.3525	−	10.6336i	−0.684316	−	0.419349i	0.136425	−	0.990650i	$-0.456439\pi$
$643$	−17.3525	−	10.6336i	−0.684316	−	0.419349i	−0.820740	+	0.571301i	$0.806439\pi$
$644$	18.1595	+	2.87619i	0.715586	+	0.113338i
$645$	0.256335	+	0.788919i	0.0100932	+	0.0310637i
$646$	−8.62139	−	1.63877i	−0.339204	−	0.0644767i
$647$	−16.4847	−	11.9768i	−0.648081	−	0.470858i	0.214536	−	0.976716i	$-0.431176\pi$
$647$	−16.4847	−	11.9768i	−0.648081	−	0.470858i	−0.862617	+	0.505858i	$0.831176\pi$
$648$	8.60479	+	8.60479i	0.338028	+	0.338028i
$649$	−28.8290	+	18.4756i	−1.13164	+	0.725232i
$650$			19.3755i			0.759970i
$651$	−36.2861	−	8.71152i	−1.42216	−	0.341431i
$652$	7.45637	+	6.36834i	0.292014	+	0.249403i
$653$	−0.642885	+	8.16862i	−0.0251580	+	0.319663i	0.971442	+	0.237276i	$0.0762545\pi$
$653$	−0.642885	+	8.16862i	−0.0251580	+	0.319663i	−0.996600	+	0.0823873i	$0.973746\pi$
$654$	−4.94272	+	31.2071i	−0.193276	+	1.22029i
$655$	1.64041	−	10.3572i	0.0640963	−	0.404688i
$656$	0.289137	−	3.67383i	0.0112889	−	0.143439i
$657$	−61.4415	−	52.4760i	−2.39706	−	2.04728i
$658$	4.06532	+	0.975998i	0.158483	+	0.0380484i
$659$		−	17.9481i		−	0.699157i	−0.936907	−	0.349579i	$-0.886325\pi$
$659$		−	17.9481i		−	0.699157i	0.936907	−	0.349579i	$-0.113675\pi$
$660$	−6.94904	−	5.69693i	−0.270491	−	0.221753i
$661$	22.0906	+	22.0906i	0.859223	+	0.859223i	0.991247	−	0.132023i	$-0.0421474\pi$
$661$	22.0906	+	22.0906i	0.859223	+	0.859223i	−0.132023	+	0.991247i	$0.542147\pi$
$662$	1.41721	+	1.02966i	0.0550814	+	0.0400190i
$663$	−11.7855	−	56.7231i	−0.457711	−	2.20294i
$664$	−0.175170	−	0.539119i	−0.00679793	−	0.0209219i
$665$	8.39645	+	1.32987i	0.325600	+	0.0515700i
$666$	−35.0991	−	21.5087i	−1.36006	−	0.833447i
$667$	15.5761	−	5.06099i	0.603110	−	0.195962i
$668$	0.847387	+	10.7671i	0.0327864	+	0.416590i
$669$	−1.86432	+	1.14246i	−0.0720787	+	0.0441699i
$670$	11.2463	+	4.65838i	0.434484	+	0.179969i
$671$	−8.01110	+	26.4583i	−0.309265	+	1.02141i
$672$	−9.73546	+	9.73546i	−0.375554	+	0.375554i
$673$	11.3311	+	18.4907i	0.436782	+	0.712763i	0.992979	−	0.118287i	$-0.0377403\pi$
$673$	11.3311	+	18.4907i	0.436782	+	0.712763i	−0.556198	+	0.831050i	$0.687740\pi$
$674$	−0.0138303	−	0.0118122i	−0.000532722	−	0.000454987i
$675$	27.9292	+	32.7009i	1.07499	+	1.25866i
$676$	4.78472	+	6.58561i	0.184028	+	0.253293i
$677$	0.298861	+	0.183142i	0.0114861	+	0.00703872i	0.528230	−	0.849101i	$-0.322856\pi$
$677$	0.298861	+	0.183142i	0.0114861	+	0.00703872i	−0.516744	+	0.856140i	$0.672856\pi$
$678$	3.64075	−	7.14537i	0.139822	−	0.274416i
$679$	−12.1411	+	37.3665i	−0.465934	+	1.43400i
$680$	−2.85123	+	2.28733i	−0.109340	+	0.0877152i
$681$	−0.578398			−0.0221643
$682$	5.13625	−	7.37762i	0.196677	−	0.282504i
$683$	15.2115	+	36.7238i	0.582052	+	1.40520i	0.890949	+	0.454103i	$0.150040\pi$
$683$	15.2115	+	36.7238i	0.582052	+	1.40520i	−0.308897	+	0.951096i	$0.599960\pi$
$684$	7.93088	−	10.9159i	0.303245	−	0.417381i
$685$	0.581244	+	7.38540i	0.0222082	+	0.282182i
$686$	28.2809	+	2.22576i	1.07977	+	0.0849798i
$687$	15.8424	−	3.80343i	0.604426	−	0.145110i
$688$	−0.0478960	+	0.302403i	−0.00182602	+	0.0115290i
$689$	−44.9223	−	22.8890i	−1.71140	−	0.872003i
$690$	−7.18083	+	8.40768i	−0.273370	+	0.320075i
$691$	−18.5811	+	11.3865i	−0.706859	+	0.433164i	−0.828926	−	0.559358i	$-0.811048\pi$
$691$	−18.5811	+	11.3865i	−0.706859	+	0.433164i	0.122067	+	0.992522i	$0.461048\pi$
$692$	12.9500	−	5.36407i	0.492285	−	0.203911i
$693$	85.2477	+	41.2937i	3.23829	+	1.56862i
$694$	−5.60376	−	13.5287i	−0.212716	−	0.513541i
$695$	−2.23261	−	14.0961i	−0.0846876	−	0.534697i
$696$	−3.78985	+	11.6640i	−0.143654	+	0.442121i
$697$	0.725685	+	15.1771i	0.0274873	+	0.574873i
$698$	1.67610	−	1.21776i	0.0634413	−	0.0460928i
$699$	5.51867	+	0.874072i	0.208735	+	0.0330604i
$700$	−14.4364	+	12.3298i	−0.545643	+	0.466023i
$701$	14.3410	+	4.65969i	0.541654	+	0.175994i	0.567050	−	0.823683i	$-0.308085\pi$
$701$	14.3410	+	4.65969i	0.541654	+	0.175994i	−0.0253961	+	0.999677i	$0.508085\pi$
$702$	45.6249	+	10.9536i	1.72200	+	0.413416i
$703$	−5.28917	+	12.7692i	−0.199485	+	0.481599i
$704$	−1.33070	−	3.03796i	−0.0501528	−	0.114498i
$705$	−1.77785	+	1.77785i	−0.0669575	+	0.0669575i
$706$	3.09458	−	0.490133i	0.116466	−	0.0184464i
$707$	1.04642	−	1.22520i	0.0393546	−	0.0460783i
$708$	−31.4535	−	2.47544i	−1.18210	−	0.0930329i
$709$	8.89147	−	14.5096i	0.333926	−	0.544918i	−0.640973	−	0.767563i	$-0.721469\pi$
$709$	8.89147	−	14.5096i	0.333926	−	0.544918i	0.974900	+	0.222645i	$0.0714691\pi$
$710$	3.73416	+	5.13963i	0.140141	+	0.192887i
$711$	−58.4265	+	49.9009i	−2.19116	+	1.87143i
$712$	−11.0392	+	5.62474i	−0.413711	+	0.210796i
$713$	−8.94883	−	6.50170i	−0.335136	−	0.243491i
$714$	34.7635	−	44.8775i	1.30099	−	1.67950i
$715$	−13.3927	−	1.84539i	−0.500860	−	0.0690136i
$716$	9.88969	+	9.88969i	0.369595	+	0.369595i
$717$	11.8206	−	49.2363i	0.441448	−	1.83876i
$718$	−10.6529	−	3.46133i	−0.397561	−	0.129176i
$719$	15.2380	+	17.8414i	0.568281	+	0.665372i	0.967908	−	0.251307i	$-0.0808602\pi$
$719$	15.2380	+	17.8414i	0.568281	+	0.665372i	−0.399627	+	0.916678i	$0.630860\pi$
$720$	−1.31199	−	5.46482i	−0.0488949	−	0.203662i
$721$	−9.41653	+	2.26071i	−0.350690	+	0.0841932i
$722$	12.8927	+	6.56914i	0.479815	+	0.244478i
$723$	−11.4795	−	22.5298i	−0.426927	−	0.837892i
$724$	6.50381	+	10.6133i	0.241712	+	0.394439i
$725$	−6.47172	+	15.6241i	−0.240354	+	0.580265i
$726$	−24.6616	+	22.8443i	−0.915279	+	0.847831i
$727$			17.1837i			0.637309i	0.947871	+	0.318654i	$0.103231\pi$
$727$			17.1837i			0.637309i	−0.947871	+	0.318654i	$0.896769\pi$
$728$	−4.83564	+	20.1419i	−0.179221	+	0.746509i
$729$	−14.6282	+	7.45345i	−0.541786	+	0.276054i
$730$	3.49187	+	10.7469i	0.129240	+	0.397759i
$731$	0.0388269	−	1.26179i	0.00143607	−	0.0466688i
$732$	−20.6076	+	14.9723i	−0.761679	+	0.553392i
$733$	14.0381	−	27.5512i	0.518508	−	1.01763i	−0.472184	−	0.881500i	$-0.656534\pi$
$733$	14.0381	−	27.5512i	0.518508	−	1.01763i	0.990691	−	0.136128i	$-0.0434659\pi$
$734$	−6.53916	+	0.514643i	−0.241365	+	0.0189958i
$735$	−21.1751	+	29.1450i	−0.781056	+	1.07503i
$736$	−3.77039	+	1.56175i	−0.138978	+	0.0575668i
$737$	23.0072	−	39.3005i	0.847480	−	1.44765i
$738$	−21.5833	−	8.94010i	−0.794493	−	0.329090i
$739$	−17.7915	+	2.81790i	−0.654473	+	0.103658i	−0.474835	−	0.880075i	$-0.657492\pi$
$739$	−17.7915	+	2.81790i	−0.654473	+	0.103658i	−0.179637	+	0.983733i	$0.557492\pi$
$740$	2.61358	+	5.12944i	0.0960771	+	0.188562i
$741$	2.34648	−	29.8148i	0.0862000	−	1.09527i
$742$	−11.5325	−	48.0365i	−0.423373	−	1.76347i
$743$	4.58067	−	7.47498i	0.168049	−	0.274230i	−0.757519	−	0.652813i	$-0.773589\pi$
$743$	4.58067	−	7.47498i	0.168049	−	0.274230i	0.925567	+	0.378583i	$0.123589\pi$
$744$	7.87773	−	2.55963i	0.288812	−	0.0938406i
$745$	16.3501	−	1.28678i	0.599023	−	0.0471441i
$746$	3.54696	+	22.3946i	0.129864	+	0.819926i
$747$	−3.59353			−0.131480
$748$	7.02095	+	11.7348i	0.256711	+	0.429068i
$749$	−15.1110			−0.552145
$750$	−3.90519	−	24.6564i	−0.142597	−	0.900323i
$751$	−24.6301	+	1.93843i	−0.898764	+	0.0707343i	−0.519418	−	0.854521i	$-0.673851\pi$
$751$	−24.6301	+	1.93843i	−0.898764	+	0.0707343i	−0.379346	+	0.925255i	$0.623851\pi$
$752$	−0.882584	+	0.286769i	−0.0321845	+	0.0104574i
$753$	−28.4145	+	46.3683i	−1.03548	+	1.68976i
$754$	4.30747	+	17.9419i	0.156869	+	0.653406i
$755$	1.50661	−	19.1433i	0.0548312	−	0.696697i
$756$	20.8726	+	40.9648i	0.759129	+	1.48987i
$757$	−9.84484	+	1.55927i	−0.357817	+	0.0566726i	−0.332755	−	0.943013i	$-0.607978\pi$
$757$	−9.84484	+	1.55927i	−0.357817	+	0.0566726i	−0.0250618	+	0.999686i	$0.507978\pi$
$758$	1.01838	+	0.421827i	0.0369892	+	0.0153214i
$759$	27.4923	+	30.9059i	0.997906	+	1.12181i
$760$	−1.74332	+	0.722107i	−0.0632369	+	0.0261936i
$761$	1.82944	−	2.51801i	0.0663171	−	0.0912777i	−0.774570	−	0.632488i	$-0.782034\pi$
$761$	1.82944	−	2.51801i	0.0663171	−	0.0912777i	0.840887	+	0.541210i	$0.182034\pi$
$762$	7.14066	−	0.561982i	0.258679	−	0.0203585i
$763$	−21.1464	+	41.5021i	−0.765551	+	1.50248i
$764$	−12.9936	+	9.44044i	−0.470094	+	0.341543i
$765$	8.20500	+	21.6710i	0.296652	+	0.783517i
$766$	−8.10013	−	24.9296i	−0.292669	−	0.900744i
$767$	−42.2949	+	21.5503i	−1.52718	+	0.778138i
$768$	0.713416	−	2.97159i	0.0257432	−	0.107228i
$769$			12.4648i			0.449493i	0.974417	+	0.224746i	$0.0721553\pi$
$769$			12.4648i			0.449493i	−0.974417	+	0.224746i	$0.927845\pi$
$770$	−7.14764	−	11.1530i	−0.257583	−	0.401927i
$771$	−3.23543	+	7.81102i	−0.116521	+	0.281307i
$772$	2.25377	+	3.67782i	0.0811151	+	0.132368i
$773$	−9.87178	−	19.3745i	−0.355063	−	0.696851i	0.642525	−	0.766265i	$-0.277887\pi$
$773$	−9.87178	−	19.3745i	−0.355063	−	0.696851i	−0.997588	+	0.0694140i	$0.977887\pi$
$774$	1.72938	+	0.881163i	0.0621613	+	0.0316727i
$775$	11.1062	−	2.66637i	0.398948	−	0.0957789i
$776$	−2.03586	−	8.47997i	−0.0730831	−	0.304413i
$777$	−58.0635	−	67.9836i	−2.08302	−	2.43890i
$778$	−20.2712	−	6.58651i	−0.726758	−	0.236138i
$779$	−1.83107	+	7.62697i	−0.0656050	+	0.273264i
$780$	−8.80845	−	8.80845i	−0.315393	−	0.315393i
$781$	20.9546	−	11.2144i	0.749813	−	0.401282i
$782$	14.6106	−	8.34643i	0.522475	−	0.298468i
$783$	33.1326	+	24.0722i	1.18406	+	0.860271i
$784$	−11.8475	+	6.03663i	−0.423127	+	0.215594i
$785$	−12.9783	+	11.0845i	−0.463216	+	0.395624i
$786$	−21.2469	−	29.2438i	−0.757852	−	1.04309i
$787$	14.0638	−	22.9500i	0.501320	−	0.818080i	−0.497458	−	0.867488i	$-0.665733\pi$
$787$	14.0638	−	22.9500i	0.501320	−	0.818080i	0.998779	+	0.0494076i	$0.0157333\pi$
$788$	26.3289	+	2.07213i	0.937929	+	0.0738166i
$789$	−37.8962	+	44.3708i	−1.34914	+	1.57964i
$790$	10.6131	−	1.68095i	0.377598	−	0.0598057i
$791$	8.35959	−	8.35959i	0.297233	−	0.297233i
$792$	−20.9228	+	2.07163i	−0.743461	+	0.0736123i
$793$	−14.6658	+	35.4065i	−0.520799	+	1.25732i
$794$	−10.0940	−	2.42335i	−0.358222	−	0.0860016i
$795$	28.2547	+	9.18052i	1.00209	+	0.325599i
$796$	9.70741	−	8.29091i	0.344070	−	0.293863i
$797$	−17.2873	−	2.73804i	−0.612348	−	0.0969864i	−0.157445	−	0.987528i	$-0.550326\pi$
$797$	−17.2873	−	2.73804i	−0.612348	−	0.0969864i	−0.454902	+	0.890541i	$0.650326\pi$
$798$	23.7077	−	17.2247i	0.839244	−	0.609746i
$799$	3.46103	−	1.63141i	0.122443	−	0.0577150i
$800$	1.30221	−	4.00778i	0.0460400	−	0.141697i
$801$	12.2866	+	77.5744i	0.434125	+	2.74096i
$802$	6.32316	+	15.2655i	0.223279	+	0.539042i
$803$	41.6115	−	7.45305i	1.46844	−	0.263013i
$804$	38.7674	−	16.0580i	1.36722	−	0.566321i
$805$	−13.8980	+	8.51671i	−0.489840	+	0.300175i
$806$	8.09351	−	9.47628i	0.285082	−	0.333788i
$807$	58.9324	+	30.0276i	2.07452	+	1.05702i
$808$	−0.0559473	+	0.353237i	−0.00196822	+	0.0124268i
$809$	−9.64150	+	2.31472i	−0.338977	+	0.0813812i	−0.399360	−	0.916794i	$-0.630768\pi$
$809$	−9.64150	+	2.31472i	−0.338977	+	0.0813812i	0.0603831	+	0.998175i	$0.480768\pi$
$810$	−10.7551	−	0.846448i	−0.377897	−	0.0297412i
$811$	0.385589	+	4.89937i	0.0135399	+	0.172040i	0.999969	+	0.00785364i	$0.00249992\pi$
$811$	0.385589	+	4.89937i	0.0135399	+	0.172040i	−0.986429	+	0.164187i	$0.947500\pi$
$812$	−10.6271	+	14.6269i	−0.372938	+	0.513305i
$813$	2.07026	+	4.99805i	0.0726072	+	0.175289i
$814$	20.3446	−	7.06666i	0.713077	−	0.247686i
$815$	−8.69328			−0.304512
$816$	−1.37450	+	12.5251i	−0.0481170	+	0.438468i
$817$	0.201377	−	0.619774i	0.00704528	−	0.0216831i
$818$	−2.50728	+	4.92081i	−0.0876650	+	0.172052i
$819$	111.964	+	68.6115i	3.91233	+	2.39748i
$820$	1.92035	+	2.64314i	0.0670615	+	0.0923023i
$821$	−9.41615	−	11.0249i	−0.328626	−	0.384771i	0.571353	−	0.820704i	$-0.306419\pi$
$821$	−9.41615	−	11.0249i	−0.328626	−	0.384771i	−0.899979	+	0.435933i	$0.856419\pi$
$822$	19.4185	+	16.5850i	0.677299	+	0.578468i
$823$	−4.18949	−	6.83662i	−0.146036	−	0.238310i	0.771255	−	0.636526i	$-0.219629\pi$
$823$	−4.18949	−	6.83662i	−0.146036	−	0.238310i	−0.917291	+	0.398217i	$0.869629\pi$
$824$	1.51995	−	1.51995i	0.0529501	−	0.0529501i
$825$	−42.7035	+	0.860658i	−1.48675	+	0.0299643i
$826$	−42.9716	−	17.7994i	−1.49517	−	0.619321i
$827$	−8.50342	+	5.21090i	−0.295693	+	0.181201i	−0.662430	−	0.749124i	$-0.730475\pi$
$827$	−8.50342	+	5.21090i	−0.295693	+	0.181201i	0.366737	+	0.930325i	$0.380475\pi$
$828$	2.02982	+	25.7913i	0.0705411	+	0.896309i
$829$	−24.7656	+	8.04684i	−0.860146	+	0.279478i	−0.705690	−	0.708521i	$-0.749363\pi$
$829$	−24.7656	+	8.04684i	−0.860146	+	0.279478i	−0.154457	+	0.988000i	$0.549363\pi$
$830$	0.428495	+	0.262582i	0.0148733	+	0.00911435i
$831$	−47.5948	−	7.53828i	−1.65105	−	0.261500i
$832$	−1.42081	−	4.37282i	−0.0492579	−	0.151600i
$833$	45.3238	−	30.8454i	1.57038	−	1.06873i
$834$	−39.8009	−	28.9171i	−1.37819	−	1.00132i
$835$	−6.77057	−	6.77057i	−0.234305	−	0.234305i
$836$	1.78592	+	6.82957i	0.0617674	+	0.236206i
$837$		−	27.6600i		−	0.956071i
$838$	12.9538	+	3.10993i	0.447482	+	0.107431i
$839$	1.04371	+	0.891414i	0.0360329	+	0.0307750i	0.667282	−	0.744805i	$-0.267458\pi$
$839$	1.04371	+	0.891414i	0.0360329	+	0.0307750i	−0.631249	+	0.775580i	$0.717458\pi$
$840$	0.957672	−	12.1684i	0.0330428	−	0.419849i
$841$	2.01720	−	12.7361i	0.0695587	−	0.439176i
$842$	−3.30655	+	20.8767i	−0.113951	+	0.719459i
$843$	−6.46321	+	82.1229i	−0.222605	+	2.82846i
$844$	−21.8705	−	18.6792i	−0.752815	−	0.642965i
$845$	−7.01732	−	1.68471i	−0.241403	−	0.0579558i
$846$			5.88291i			0.202259i
$847$	−44.9836	+	20.7941i	−1.54565	+	0.714493i
$848$	7.75373	+	7.75373i	0.266264	+	0.266264i
$849$	51.0315	+	37.0766i	1.75140	+	1.27246i
$850$	−3.24457	+	17.0693i	−0.111288	+	0.585471i
$851$	−8.18919	−	25.2037i	−0.280722	−	0.863973i
$852$	21.6297	+	3.42580i	0.741020	+	0.117366i
$853$	24.4966	+	15.0116i	0.838749	+	0.513986i	0.874302	−	0.485382i	$-0.161319\pi$
$853$	24.4966	+	15.0116i	0.838749	+	0.513986i	−0.0355533	+	0.999368i	$0.511319\pi$
$854$	−35.7135	+	11.6040i	−1.22209	+	0.397081i
$855$	0.938530	+	11.9251i	0.0320970	+	0.407831i
$856$	2.85987	−	1.75253i	0.0977483	−	0.0599002i
$857$	32.9935	+	13.6664i	1.12704	+	0.466834i	0.866772	−	0.498704i	$-0.166190\pi$
$857$	32.9935	+	13.6664i	1.12704	+	0.466834i	0.260264	+	0.965538i	$0.416190\pi$
$858$	−37.1426	+	28.1464i	−1.26803	+	0.960902i
$859$	30.4916	−	30.4916i	1.04036	−	1.04036i	0.0412109	−	0.999150i	$-0.486878\pi$
$859$	30.4916	−	30.4916i	1.04036	−	1.04036i	0.999150	−	0.0412109i	$-0.0131216\pi$
$860$	−0.141825	−	0.231438i	−0.00483620	−	0.00789196i
$861$	−38.5813	−	32.9516i	−1.31485	−	1.12299i
$862$	2.01746	+	2.36214i	0.0687150	+	0.0804549i
$863$	−28.6993	−	39.5012i	−0.976936	−	1.34464i	−0.938464	−	0.345378i	$-0.887751\pi$
$863$	−28.6993	−	39.5012i	−0.976936	−	1.34464i	−0.0384723	−	0.999260i	$-0.512249\pi$
$864$	−8.70125	−	5.33213i	−0.296022	−	0.181403i
$865$	−5.64161	+	11.0723i	−0.191821	+	0.376469i
$866$	−4.13230	+	12.7179i	−0.140421	+	0.432172i
$867$	−0.884001	−	51.9450i	−0.0300223	−	1.76414i
$868$	12.2110			0.414468
$869$	−0.810021	−	40.1911i	−0.0274781	−	1.36339i
$870$	−4.16084	−	10.0452i	−0.141066	−	0.340563i
$871$	37.1080	−	51.0748i	1.25736	−	1.73060i
$872$	−0.811183	−	10.3071i	−0.0274701	−	0.349041i
$873$	−55.1143	−	4.33759i	−1.86534	−	0.146805i
$874$	8.44623	−	2.02776i	0.285698	−	0.0685900i
$875$	5.75702	−	36.3484i	0.194623	−	1.22880i
$876$	34.7066	+	17.6839i	1.17263	+	0.597484i
$877$	−32.9179	+	38.5419i	−1.11156	+	1.30147i	−0.162381	+	0.986728i	$0.551917\pi$
$877$	−32.9179	+	38.5419i	−1.11156	+	1.30147i	−0.949178	+	0.314740i	$0.898083\pi$
$878$	−2.34288	+	1.43572i	−0.0790682	+	0.0484531i
$879$	−6.31017	+	2.61376i	−0.212837	+	0.0881599i
$880$	2.64623	+	1.28183i	0.0892045	+	0.0432104i
$881$	10.8739	+	26.2519i	0.366351	+	0.884449i	0.994342	+	0.106228i	$0.0338774\pi$
$881$	10.8739	+	26.2519i	0.366351	+	0.884449i	−0.627991	+	0.778221i	$0.716123\pi$
$882$	13.1863	+	83.2550i	0.444005	+	2.80334i
$883$	0.459383	−	1.41384i	0.0154595	−	0.0475794i	−0.943029	−	0.332710i	$-0.892037\pi$
$883$	0.459383	−	1.41384i	0.0154595	−	0.0475794i	0.958489	+	0.285131i	$0.0920370\pi$
$884$	8.08290	+	17.1479i	0.271857	+	0.576747i
$885$	22.6292	−	16.4411i	0.760672	−	0.552661i
$886$	−18.0509	−	2.85898i	−0.606431	−	0.0960492i
$887$	−19.4575	+	16.6182i	−0.653317	+	0.557986i	−0.913128	−	0.407674i	$-0.866340\pi$
$887$	−19.4575	+	16.6182i	−0.653317	+	0.557986i	0.259810	+	0.965660i	$0.416340\pi$
$888$	18.8735	+	6.13236i	0.633352	+	0.205788i
$889$	10.2675	+	2.46502i	0.344363	+	0.0826741i
$890$	4.20337	−	10.1478i	0.140897	−	0.340156i
$891$	−8.62917	+	39.4268i	−0.289088	+	1.32085i
$892$	0.505920	−	0.505920i	0.0169394	−	0.0169394i
$893$	1.95088	−	0.308989i	0.0652836	−	0.0103399i
$894$	36.7166	−	42.9897i	1.22799	−	1.43779i
$895$	−12.3611	−	0.972843i	−0.413187	−	0.0325186i
$896$	2.35396	−	3.84131i	0.0786403	−	0.128329i
$897$	33.7056	+	46.3918i	1.12540	+	1.54898i
$898$	0.931145	−	0.795273i	0.0310727	−	0.0265386i
$899$	9.69170	−	4.93817i	0.323236	−	0.164697i
$900$	−21.6122	−	15.7022i	−0.720406	−	0.523405i
$901$	−35.7423	−	27.6871i	−1.19075	−	0.922392i
$902$	10.7762	−	5.76717i	0.358809	−	0.192026i
$903$	2.98073	+	2.98073i	0.0991926	+	0.0991926i
$904$	−0.612592	+	2.55163i	−0.0203745	+	0.0848660i
$905$	−10.4952	−	3.41010i	−0.348872	−	0.113356i
$906$	−42.9891	−	50.3338i	−1.42822	−	1.67223i
$907$	11.7290	+	48.8549i	0.389456	+	1.62220i	0.731030	+	0.682345i	$0.239040\pi$
$907$	11.7290	+	48.8549i	0.389456	+	1.62220i	−0.341575	+	0.939855i	$0.610960\pi$
$908$	0.184035	−	0.0441830i	0.00610742	−	0.00146626i
$909$	2.02009	+	1.02929i	0.0670021	+	0.0341393i
$910$	−8.33715	−	16.3626i	−0.276374	−	0.542414i
$911$	5.64599	+	9.21341i	0.187060	+	0.305254i	0.932398	−	0.361432i	$-0.117712\pi$
$911$	5.64599	+	9.21341i	0.187060	+	0.305254i	−0.745338	+	0.666686i	$0.767712\pi$
$912$	−2.48919	+	6.00943i	−0.0824252	+	0.198992i
$913$	1.19195	−	1.45393i	0.0394479	−	0.0481181i
$914$		−	37.7431i		−	1.24843i
$915$	5.27177	−	21.9585i	0.174279	−	0.725926i
$916$	−4.75022	+	2.42036i	−0.156952	+	0.0799708i
$917$	−16.4670	−	50.6803i	−0.543789	−	1.67361i
$918$	38.3600	+	17.2900i	1.26607	+	0.570655i
$919$	9.93951	−	7.22147i	0.327874	−	0.238214i	−0.411654	−	0.911340i	$-0.635049\pi$
$919$	9.93951	−	7.22147i	0.327874	−	0.238214i	0.739528	+	0.673126i	$0.235049\pi$
$920$	1.64255	−	3.22369i	0.0541534	−	0.106282i
$921$	68.1417	−	5.36287i	2.24535	−	0.176713i
$922$	14.3557	−	19.7589i	0.472779	−	0.650725i
$923$	30.4399	−	12.6086i	1.00194	−	0.415017i
$924$	−44.6075	−	9.76303i	−1.46748	−	0.321180i
$925$	25.2814	+	10.4719i	0.831247	+	0.344314i
$926$	−12.9371	+	2.04903i	−0.425139	+	0.0673354i
$927$	−6.18636	−	12.1414i	−0.203187	−	0.398776i
$928$	0.314866	−	4.00075i	0.0103360	−	0.131331i
$929$	−0.820798	−	3.41887i	−0.0269295	−	0.112169i	0.957286	−	0.289141i	$-0.0933698\pi$
$929$	−0.820798	−	3.41887i	−0.0269295	−	0.112169i	−0.984216	+	0.176972i	$0.943370\pi$
$930$	−3.83691	+	6.26127i	−0.125817	+	0.205315i
$931$	26.9162	−	8.74561i	0.882144	−	0.286626i
$932$	−1.82270	+	0.143450i	−0.0597047	+	0.00469886i
$933$	−6.67877	−	42.1681i	−0.218653	−	1.38052i
$934$	10.5885			0.346466
$935$	−11.4896	−	3.86844i	−0.375750	−	0.126512i
$936$	−29.1473			−0.952708
$937$	6.70838	+	42.3551i	0.219153	+	1.38368i	0.814478	+	0.580194i	$0.197023\pi$
$937$	6.70838	+	42.3551i	0.219153	+	1.38368i	−0.595325	+	0.803485i	$0.702977\pi$
$938$	61.6690	−	4.85345i	2.01356	−	0.158471i
$939$	73.6053	−	23.9158i	2.40202	−	0.780463i
$940$	0.429869	−	0.701483i	0.0140208	−	0.0228799i
$941$	−7.88337	−	32.8366i	−0.256990	−	1.07044i	−0.940309	−	0.340322i	$-0.889464\pi$
$941$	−7.88337	−	32.8366i	−0.256990	−	1.07044i	0.683318	−	0.730120i	$-0.260536\pi$
$942$	−4.61607	+	58.6527i	−0.150400	+	1.91101i
$943$	−6.82775	−	13.4002i	−0.222342	−	0.436371i
$944$	10.1970	−	1.61505i	0.331884	−	0.0525652i
$945$	−37.6571	−	15.5981i	−1.22498	−	0.507405i
$946$	−0.930142	+	0.407425i	−0.0302415	+	0.0132465i
$947$	−22.6264	+	9.37218i	−0.735260	+	0.304555i	−0.718712	−	0.695308i	$-0.755268\pi$
$947$	−22.6264	+	9.37218i	−0.735260	+	0.304555i	−0.0165487	+	0.999863i	$0.505268\pi$
$948$	21.7720	−	29.9666i	0.707121	−	0.973269i
$949$	58.4236	−	4.59803i	1.89651	−	0.149259i
$950$	−4.07197	+	7.99170i	−0.132112	+	0.259285i
$951$	69.4226	−	50.4385i	2.25118	−	1.63558i
$952$	−7.63297	+	16.9347i	−0.247386	+	0.548856i
$953$	−3.89851	−	11.9984i	−0.126285	−	0.388665i	0.867848	−	0.496830i	$-0.165503\pi$
$953$	−3.89851	−	11.9984i	−0.126285	−	0.388665i	−0.994133	+	0.108164i	$0.965503\pi$
$954$	61.9368	−	31.5584i	2.00528	−	1.02174i
$955$	3.32400	−	13.8454i	0.107562	−	0.448028i
$956$			16.5690i			0.535880i
$957$	−39.3525	+	10.2906i	−1.27209	+	0.332649i
$958$	−2.74121	+	6.61787i	−0.0885645	+	0.213814i
$959$	19.6704	+	32.0991i	0.635189	+	1.03653i
$960$	1.23000	+	2.41402i	0.0396982	+	0.0779121i
$961$	21.0755	+	10.7385i	0.679855	+	0.346404i
$962$	29.0318	−	6.96992i	0.936023	−	0.224719i
$963$	−4.96373	−	20.6754i	−0.159954	−	0.666256i
$964$	5.37357	+	6.29164i	0.173071	+	0.202640i
$965$	−3.63692	−	1.18171i	−0.117076	−	0.0380404i
$966$	−13.1168	+	54.6354i	−0.422026	+	1.75787i
$967$	27.3829	+	27.3829i	0.880575	+	0.880575i	0.993593	−	0.113018i	$-0.0360517\pi$
$967$	27.3829	+	27.3829i	0.880575	+	0.880575i	−0.113018	+	0.993593i	$0.536052\pi$
$968$	6.10182	−	9.15247i	0.196120	−	0.294172i
$969$	7.05988	−	25.8731i	0.226796	−	0.831163i
$970$	6.25492	+	4.54447i	0.200834	+	0.145914i
$971$	24.6635	−	12.5667i	0.791491	−	0.403285i	−0.0110074	−	0.999939i	$-0.503504\pi$
$971$	24.6635	−	12.5667i	0.791491	−	0.403285i	0.802498	+	0.596655i	$0.203504\pi$
$972$	−4.99868	+	4.26927i	−0.160333	+	0.136937i
$973$	−42.6295	−	58.6745i	−1.36664	−	1.88102i
$974$	16.0602	−	26.2078i	0.514601	−	0.839752i
$975$	−59.0296	−	4.64573i	−1.89046	−	0.148782i
$976$	5.41323	−	6.33808i	0.173273	−	0.202877i
$977$	−4.14945	+	0.657208i	−0.132753	+	0.0210259i	−0.222457	−	0.974942i	$-0.571408\pi$
$977$	−4.14945	+	0.657208i	−0.132753	+	0.0210259i	0.0897045	+	0.995968i	$0.471408\pi$
$978$	−21.1897	+	21.1897i	−0.677571	+	0.677571i
$979$	−35.4618	−	20.7599i	−1.13336	−	0.663490i
$980$	4.51117	−	10.8909i	0.144104	−	0.347898i
$981$	−63.7309	−	15.3004i	−2.03477	−	0.488505i
$982$	7.76517	+	2.52306i	0.247796	+	0.0805139i
$983$	−29.7704	+	25.4263i	−0.949528	+	0.810973i	−0.982074	−	0.188497i	$-0.939638\pi$
$983$	−29.7704	+	25.4263i	−0.949528	+	0.810973i	0.0325461	+	0.999470i	$0.489638\pi$
$984$	11.1234	+	1.76177i	0.354601	+	0.0561633i
$985$	−18.9423	+	13.7624i	−0.603553	+	0.438507i
$986$	0.790260	+	16.5276i	0.0251670	+	0.526347i
$987$	−3.94824	+	12.1514i	−0.125674	+	0.386784i
$988$	1.53090	+	9.66574i	0.0487045	+	0.307508i
$989$	0.478165	+	1.15439i	0.0152048	+	0.0367075i
$990$	12.9121	−	13.4432i	0.410372	−	0.427254i
$991$	−15.0665	+	6.24075i	−0.478603	+	0.198244i	−0.608925	−	0.793228i	$-0.708399\pi$
$991$	−15.0665	+	6.24075i	−0.478603	+	0.198244i	0.130322	+	0.991472i	$0.458399\pi$
$992$	−2.31102	+	1.41619i	−0.0733748	+	0.0449642i
$993$	−3.47679	+	4.07080i	−0.110333	+	0.129183i
$994$	28.7652	+	14.6566i	0.912376	+	0.464879i
$995$	−1.77048	+	11.1784i	−0.0561281	+	0.354379i
$996$	1.68449	−	0.404409i	0.0533750	−	0.0128142i
$997$	−43.8288	−	3.44940i	−1.38807	−	0.109244i	−0.637713	−	0.770274i	$-0.720120\pi$
$997$	−43.8288	−	3.44940i	−1.38807	−	0.109244i	−0.750359	+	0.661030i	$0.770120\pi$
$998$	0.887630	+	11.2784i	0.0280974	+	0.357012i
$999$	38.9513	−	53.6118i	1.23236	−	1.69620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	374.2.r.b.15.10	✓	160
11.3	even	5	inner	374.2.r.b.355.1	yes	160
17.8	even	8	inner	374.2.r.b.59.1	yes	160
187.25	even	40	inner	374.2.r.b.25.10	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.r.b.15.10	✓	160	1.1	even	1	trivial
374.2.r.b.25.10	yes	160	187.25	even	40	inner
374.2.r.b.59.1	yes	160	17.8	even	8	inner
374.2.r.b.355.1	yes	160	11.3	even	5	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:	\( N \)	\(=\)	\( 374 = 2 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	374.r (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 - 0.987688i) q^{2} +(3.04661 - 0.239773i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(0.463220 - 0.755906i) q^{5} +(-0.713416 - 2.97159i) q^{6} +(0.353474 - 4.49131i) q^{7} +(0.453990 + 0.891007i) q^{8} +(6.26127 - 0.991688i) q^{9} +O(q^{10})\)	\(q+(-0.156434 - 0.987688i) q^{2} +(3.04661 - 0.239773i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(0.463220 - 0.755906i) q^{5} +(-0.713416 - 2.97159i) q^{6} +(0.353474 - 4.49131i) q^{7} +(0.453990 + 0.891007i) q^{8} +(6.26127 - 0.991688i) q^{9} +(-0.819063 - 0.339267i) q^{10} +(-1.67560 + 2.86223i) q^{11} +(-2.82340 + 1.16949i) q^{12} +(-2.70255 + 3.71974i) q^{13} +(-4.49131 + 0.353474i) q^{14} +(1.23000 - 2.41402i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-3.00377 + 2.82443i) q^{17} +(-1.95896 - 6.02905i) q^{18} +(-1.89645 + 0.966289i) q^{19} +(-0.206960 + 0.862052i) q^{20} -13.7680i q^{21} +(3.08911 + 1.20722i) q^{22} +(1.56175 - 3.77039i) q^{23} +(1.59677 + 2.60569i) q^{24} +(1.91313 + 3.75473i) q^{25} +(4.09672 + 2.08738i) q^{26} +(9.92310 - 2.38232i) q^{27} +(1.05172 + 4.38072i) q^{28} +(2.60631 + 3.05160i) q^{29} +(-2.57671 - 0.837224i) q^{30} +(0.632736 - 2.63553i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.41860 + 9.12187i) q^{33} +(3.25955 + 2.52495i) q^{34} +(-3.23127 - 2.34766i) q^{35} +(-5.64838 + 2.87799i) q^{36} +(4.93779 - 4.21727i) q^{37} +(1.25106 + 1.72194i) q^{38} +(-7.34172 + 11.9806i) q^{39} +(0.883814 + 0.0695577i) q^{40} +(2.39334 - 2.80224i) q^{41} +(-13.5985 + 2.15379i) q^{42} +(-0.216497 + 0.216497i) q^{43} +(0.709109 - 3.23993i) q^{44} +(2.15072 - 5.19230i) q^{45} +(-3.96828 - 0.952701i) q^{46} +(-0.882584 - 0.286769i) q^{47} +(2.32382 - 1.98473i) q^{48} +(-13.1331 - 2.08008i) q^{49} +(3.40923 - 2.47695i) q^{50} +(-8.47408 + 9.32515i) q^{51} +(1.42081 - 4.37282i) q^{52} +(1.71537 + 10.8304i) q^{53} +(-3.90531 - 9.42825i) q^{54} +(1.38741 + 2.59244i) q^{55} +(4.16226 - 1.72406i) q^{56} +(-5.54605 + 3.39862i) q^{57} +(2.60631 - 3.05160i) q^{58} +(9.19884 + 4.68704i) q^{59} +(-0.423830 + 2.67596i) q^{60} +(8.10482 - 1.94580i) q^{61} +(-2.70207 - 0.212657i) q^{62} +(-2.24078 - 28.4719i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(1.55990 + 3.76593i) q^{65} +(9.70078 + 2.93723i) q^{66} -13.7307 q^{67} +(1.98396 - 3.61440i) q^{68} +(3.85399 - 11.8614i) q^{69} +(-1.81327 + 3.55874i) q^{70} +(-6.10996 - 3.74419i) q^{71} +(3.72616 + 5.12862i) q^{72} +(-8.27786 - 9.69213i) q^{73} +(-4.93779 - 4.21727i) q^{74} +(6.72885 + 10.9805i) q^{75} +(1.50503 - 1.50503i) q^{76} +(12.2629 + 8.53735i) q^{77} +(12.9816 + 5.37715i) q^{78} +(-10.3344 + 6.33296i) q^{79} +(-0.0695577 - 0.883814i) q^{80} +(11.5734 - 3.76043i) q^{81} +(-3.14214 - 1.92551i) q^{82} +(-0.559884 - 0.0886769i) q^{83} +(4.25455 + 13.0942i) q^{84} +(0.743595 + 3.57889i) q^{85} +(0.247699 + 0.179964i) q^{86} +(8.67211 + 8.67211i) q^{87} +(-3.31097 - 0.193542i) q^{88} +12.3896i q^{89} +(-5.46482 - 1.31199i) q^{90} +(15.7512 + 13.4528i) q^{91} +(-0.320195 + 4.06846i) q^{92} +(1.29577 - 8.18116i) q^{93} +(-0.145172 + 0.916578i) q^{94} +(-0.148049 + 1.88114i) q^{95} +(-2.32382 - 1.98473i) q^{96} +(-8.47997 - 2.03586i) q^{97} +13.2968i q^{98} +(-7.65293 + 19.5829i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{5} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^5 + 8 * q^9	\( 160 q + 8 q^{5} + 8 q^{9} + 8 q^{10} - 4 q^{11} - 8 q^{12} + 4 q^{14} - 8 q^{15} + 40 q^{16} - 12 q^{17} + 32 q^{18} + 12 q^{19} - 8 q^{22} + 32 q^{23} + 12 q^{24} - 8 q^{25} + 36 q^{27} - 4 q^{28} + 8 q^{29} - 40 q^{31} + 48 q^{33} + 8 q^{34} + 16 q^{35} - 12 q^{36} + 8 q^{37} - 16 q^{39} + 28 q^{41} + 60 q^{42} - 56 q^{43} - 8 q^{44} + 28 q^{46} - 116 q^{49} - 80 q^{50} + 8 q^{52} + 8 q^{53} - 8 q^{54} - 148 q^{57} + 8 q^{58} - 8 q^{59} + 8 q^{60} - 12 q^{61} - 40 q^{62} - 72 q^{63} + 144 q^{65} - 28 q^{66} - 256 q^{67} - 8 q^{69} + 8 q^{70} - 60 q^{71} - 8 q^{73} - 8 q^{74} - 116 q^{75} + 8 q^{76} - 60 q^{77} - 16 q^{78} + 40 q^{79} + 12 q^{80} - 16 q^{82} + 76 q^{83} - 56 q^{84} + 36 q^{85} - 8 q^{86} - 144 q^{87} - 4 q^{88} - 40 q^{90} + 44 q^{91} - 32 q^{92} - 40 q^{93} - 4 q^{94} + 36 q^{95} - 124 q^{97} - 176 q^{99}+O(q^{100}) \) 160 * q + 8 * q^5 + 8 * q^9 + 8 * q^10 - 4 * q^11 - 8 * q^12 + 4 * q^14 - 8 * q^15 + 40 * q^16 - 12 * q^17 + 32 * q^18 + 12 * q^19 - 8 * q^22 + 32 * q^23 + 12 * q^24 - 8 * q^25 + 36 * q^27 - 4 * q^28 + 8 * q^29 - 40 * q^31 + 48 * q^33 + 8 * q^34 + 16 * q^35 - 12 * q^36 + 8 * q^37 - 16 * q^39 + 28 * q^41 + 60 * q^42 - 56 * q^43 - 8 * q^44 + 28 * q^46 - 116 * q^49 - 80 * q^50 + 8 * q^52 + 8 * q^53 - 8 * q^54 - 148 * q^57 + 8 * q^58 - 8 * q^59 + 8 * q^60 - 12 * q^61 - 40 * q^62 - 72 * q^63 + 144 * q^65 - 28 * q^66 - 256 * q^67 - 8 * q^69 + 8 * q^70 - 60 * q^71 - 8 * q^73 - 8 * q^74 - 116 * q^75 + 8 * q^76 - 60 * q^77 - 16 * q^78 + 40 * q^79 + 12 * q^80 - 16 * q^82 + 76 * q^83 - 56 * q^84 + 36 * q^85 - 8 * q^86 - 144 * q^87 - 4 * q^88 - 40 * q^90 + 44 * q^91 - 32 * q^92 - 40 * q^93 - 4 * q^94 + 36 * q^95 - 124 * q^97 - 176 * q^99

Introduction

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