LMFDB - Embedded newform 380.2.n.a.31.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(31,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("380.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.n (of order $6$, degree $2$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.20
Character	$\chi$	$=$	380.31
Dual form			380.2.n.a.331.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41291 - 0.0606805i) q^{2} +(-0.600896 - 1.04078i) q^{3} +(1.99264 - 0.171472i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.912167 - 1.43407i) q^{6} +4.07590i q^{7} +(2.80501 - 0.363190i) q^{8} +(0.777849 - 1.34727i) q^{9} +O(q^{10})$	\(q+(1.41291 - 0.0606805i) q^{2} +(-0.600896 - 1.04078i) q^{3} +(1.99264 - 0.171472i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.912167 - 1.43407i) q^{6} +4.07590i q^{7} +(2.80501 - 0.363190i) q^{8} +(0.777849 - 1.34727i) q^{9} +(0.759006 + 1.19328i) q^{10} -0.526259i q^{11} +(-1.37583 - 1.97086i) q^{12} +(4.15082 + 2.39648i) q^{13} +(0.247328 + 5.75889i) q^{14} +(0.600896 - 1.04078i) q^{15} +(3.94119 - 0.683364i) q^{16} +(-2.96664 - 5.13837i) q^{17} +(1.01728 - 1.95078i) q^{18} +(-3.48412 - 2.61933i) q^{19} +(1.14482 + 1.63994i) q^{20} +(4.24213 - 2.44919i) q^{21} +(-0.0319337 - 0.743557i) q^{22} +(-1.08820 - 0.628273i) q^{23} +(-2.06352 - 2.70117i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(6.01016 + 3.13414i) q^{26} -5.47500 q^{27} +(0.698905 + 8.12179i) q^{28} +(-2.69537 - 1.55617i) q^{29} +(0.785857 - 1.50699i) q^{30} -0.0294402 q^{31} +(5.52709 - 1.20469i) q^{32} +(-0.547721 + 0.316227i) q^{33} +(-4.50340 - 7.08004i) q^{34} +(-3.52984 + 2.03795i) q^{35} +(1.31895 - 2.81801i) q^{36} +6.86336i q^{37} +(-5.08170 - 3.48946i) q^{38} -5.76014i q^{39} +(1.71704 + 2.24762i) q^{40} +(-6.78272 + 3.91600i) q^{41} +(5.84513 - 3.71791i) q^{42} +(4.46040 - 2.57522i) q^{43} +(-0.0902389 - 1.04864i) q^{44} +1.55570 q^{45} +(-1.57565 - 0.821661i) q^{46} +(0.907363 + 0.523866i) q^{47} +(-3.07948 - 3.69129i) q^{48} -9.61300 q^{49} +(-0.653905 + 1.25396i) q^{50} +(-3.56528 + 6.17525i) q^{51} +(8.68201 + 4.06356i) q^{52} +(2.74512 + 1.58490i) q^{53} +(-7.73569 + 0.332226i) q^{54} +(0.455754 - 0.263130i) q^{55} +(1.48033 + 11.4330i) q^{56} +(-0.632558 + 5.20015i) q^{57} +(-3.90275 - 2.03518i) q^{58} +(-1.03648 - 1.79524i) q^{59} +(1.01890 - 2.17694i) q^{60} +(-5.47760 + 9.48748i) q^{61} +(-0.0415963 + 0.00178645i) q^{62} +(5.49136 + 3.17044i) q^{63} +(7.73619 - 2.03750i) q^{64} +4.79296i q^{65} +(-0.754692 + 0.480036i) q^{66} +(1.00882 - 1.74733i) q^{67} +(-6.79252 - 9.73020i) q^{68} +1.51011i q^{69} +(-4.86368 + 3.09364i) q^{70} +(-2.94128 - 5.09445i) q^{71} +(1.69256 - 4.06163i) q^{72} +(-1.45468 - 2.51957i) q^{73} +(0.416473 + 9.69732i) q^{74} +1.20179 q^{75} +(-7.39173 - 4.62194i) q^{76} +2.14498 q^{77} +(-0.349528 - 8.13856i) q^{78} +(-6.81678 - 11.8070i) q^{79} +(2.56241 + 3.07149i) q^{80} +(0.956355 + 1.65646i) q^{81} +(-9.34575 + 5.94455i) q^{82} +8.72403i q^{83} +(8.03304 - 5.60776i) q^{84} +(2.96664 - 5.13837i) q^{85} +(6.14589 - 3.90921i) q^{86} +3.74039i q^{87} +(-0.191132 - 1.47616i) q^{88} +(-8.63922 - 4.98785i) q^{89} +(2.19806 - 0.0944006i) q^{90} +(-9.76782 + 16.9184i) q^{91} +(-2.27612 - 1.06532i) q^{92} +(0.0176905 + 0.0306408i) q^{93} +(1.31381 + 0.685117i) q^{94} +(0.526346 - 4.32700i) q^{95} +(-4.57502 - 5.02860i) q^{96} +(13.0162 - 7.51491i) q^{97} +(-13.5823 + 0.583322i) q^{98} +(-0.709015 - 0.409350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9	$ 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} + 18 q^{14} - 7 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{21} - 8 q^{24} - 20 q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{30} - 18 q^{32} - 6 q^{33} - 27 q^{34} - 14 q^{36} + 38 q^{38} + 36 q^{41} - 21 q^{42} - 8 q^{44} - 44 q^{45} - 18 q^{48} - 60 q^{49} - 33 q^{52} + 42 q^{53} + 9 q^{54} + 12 q^{57} - 62 q^{58} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 64 q^{64} + 2 q^{66} + 72 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} - 62 q^{76} - 28 q^{77} - 24 q^{78} + 7 q^{80} - 48 q^{81} - q^{82} - 4 q^{85} + 78 q^{86} - 18 q^{89} + 39 q^{90} + 16 q^{92} + 8 q^{96} + 30 q^{97} - 12 q^{98}+O(q^{100}) $ 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 + 18 * q^14 - 7 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^21 - 8 * q^24 - 20 * q^25 + 2 * q^26 + 8 * q^28 + 6 * q^30 - 18 * q^32 - 6 * q^33 - 27 * q^34 - 14 * q^36 + 38 * q^38 + 36 * q^41 - 21 * q^42 - 8 * q^44 - 44 * q^45 - 18 * q^48 - 60 * q^49 - 33 * q^52 + 42 * q^53 + 9 * q^54 + 12 * q^57 - 62 * q^58 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 64 * q^64 + 2 * q^66 + 72 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 - 62 * q^76 - 28 * q^77 - 24 * q^78 + 7 * q^80 - 48 * q^81 - q^82 - 4 * q^85 + 78 * q^86 - 18 * q^89 + 39 * q^90 + 16 * q^92 + 8 * q^96 + 30 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	1.41291	−	0.0606805i	0.999079	−	0.0429076i
$2$	1.41291	−	0.0606805i	0.999079	−	0.0429076i
$3$	−0.600896	−	1.04078i	−0.346927	−	0.600896i	0.638775	−	0.769394i	$-0.279442\pi$
$3$	−0.600896	−	1.04078i	−0.346927	−	0.600896i	−0.985702	+	0.168498i	$0.946108\pi$
$4$	1.99264	−	0.171472i	0.996318	−	0.0857362i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.912167	−	1.43407i	−0.372391	−	0.585456i
$7$			4.07590i			1.54055i	0.637714	+	0.770274i	$0.279880\pi$
$7$			4.07590i			1.54055i	−0.637714	+	0.770274i	$0.720120\pi$
$8$	2.80501	−	0.363190i	0.991722	−	0.128407i
$9$	0.777849	−	1.34727i	0.259283	−	0.449091i
$10$	0.759006	+	1.19328i	0.240019	+	0.377347i
$11$		−	0.526259i		−	0.158673i	−0.996848	−	0.0793365i	$-0.974720\pi$
$11$		−	0.526259i		−	0.158673i	0.996848	−	0.0793365i	$-0.0252802\pi$
$12$	−1.37583	−	1.97086i	−0.397168	−	0.568939i
$13$	4.15082	+	2.39648i	1.15123	+	0.664664i	0.949187	−	0.314713i	$-0.101908\pi$
$13$	4.15082	+	2.39648i	1.15123	+	0.664664i	0.202044	+	0.979376i	$0.435241\pi$
$14$	0.247328	+	5.75889i	0.0661012	+	1.53913i
$15$	0.600896	−	1.04078i	0.155151	−	0.268729i
$16$	3.94119	−	0.683364i	0.985299	−	0.170841i
$17$	−2.96664	−	5.13837i	−0.719516	−	1.24624i	−0.961192	−	0.275881i	$-0.911030\pi$
$17$	−2.96664	−	5.13837i	−0.719516	−	1.24624i	0.241676	−	0.970357i	$-0.422303\pi$
$18$	1.01728	−	1.95078i	0.239775	−	0.459803i
$19$	−3.48412	−	2.61933i	−0.799312	−	0.600916i
$19$	−3.48412	−	2.61933i	−0.799312	−	0.600916i
$20$	1.14482	+	1.63994i	0.255989	+	0.366701i
$21$	4.24213	−	2.44919i	0.925708	−	0.534458i
$22$	−0.0319337	−	0.743557i	−0.00680829	−	0.158527i
$23$	−1.08820	−	0.628273i	−0.226905	−	0.131004i	0.382238	−	0.924064i	$-0.375153\pi$
$23$	−1.08820	−	0.628273i	−0.226905	−	0.131004i	−0.609144	+	0.793060i	$0.708487\pi$
$24$	−2.06352	−	2.70117i	−0.421214	−	0.551373i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	6.01016	+	3.13414i	1.17869	+	0.614655i
$27$	−5.47500			−1.05366
$28$	0.698905	+	8.12179i	0.132081	+	1.53487i
$29$	−2.69537	−	1.55617i	−0.500518	−	0.288974i	0.228410	−	0.973565i	$-0.426647\pi$
$29$	−2.69537	−	1.55617i	−0.500518	−	0.288974i	−0.728927	+	0.684591i	$0.759981\pi$
$30$	0.785857	−	1.50699i	0.143477	−	0.275138i
$31$	−0.0294402			−0.00528761			−0.00264380	−	0.999997i	$-0.500842\pi$
$31$	−0.0294402			−0.00528761			−0.00264380	+	0.999997i	$0.500842\pi$
$32$	5.52709	−	1.20469i	0.977061	−	0.212961i
$33$	−0.547721	+	0.316227i	−0.0953460	+	0.0550480i
$34$	−4.50340	−	7.08004i	−0.772326	−	1.21422i
$35$	−3.52984	+	2.03795i	−0.596651	+	0.344477i
$36$	1.31895	−	2.81801i	0.219825	−	0.469668i
$37$			6.86336i			1.12833i	0.825662	+	0.564165i	$0.190802\pi$
$37$			6.86336i			1.12833i	−0.825662	+	0.564165i	$0.809198\pi$
$38$	−5.08170	−	3.48946i	−0.824360	−	0.566066i
$39$		−	5.76014i		−	0.922360i
$40$	1.71704	+	2.24762i	0.271487	+	0.355379i
$41$	−6.78272	+	3.91600i	−1.05928	+	0.611577i	−0.925234	−	0.379398i	$-0.876131\pi$
$41$	−6.78272	+	3.91600i	−1.05928	+	0.611577i	−0.134049	+	0.990975i	$0.542798\pi$
$42$	5.84513	−	3.71791i	0.901923	−	0.573685i
$43$	4.46040	−	2.57522i	0.680205	−	0.392717i	−0.119727	−	0.992807i	$-0.538202\pi$
$43$	4.46040	−	2.57522i	0.680205	−	0.392717i	0.799932	+	0.600090i	$0.204869\pi$
$44$	−0.0902389	−	1.04864i	−0.0136040	−	0.158089i
$45$	1.55570			0.231910
$46$	−1.57565	−	0.821661i	−0.232318	−	0.121147i
$47$	0.907363	+	0.523866i	0.132352	+	0.0764137i	0.564714	−	0.825286i	$-0.308986\pi$
$47$	0.907363	+	0.523866i	0.132352	+	0.0764137i	−0.432362	+	0.901700i	$0.642320\pi$
$48$	−3.07948	−	3.69129i	−0.444485	−	0.532792i
$49$	−9.61300			−1.37329
$50$	−0.653905	+	1.25396i	−0.0924761	+	0.177336i
$51$	−3.56528	+	6.17525i	−0.499239	+	0.864708i
$52$	8.68201	+	4.06356i	1.20398	+	0.563514i
$53$	2.74512	+	1.58490i	0.377071	+	0.217702i	0.676543	−	0.736403i	$-0.263477\pi$
$53$	2.74512	+	1.58490i	0.377071	+	0.217702i	−0.299472	+	0.954105i	$0.596811\pi$
$54$	−7.73569	+	0.332226i	−1.05269	+	0.0452102i
$55$	0.455754	−	0.263130i	0.0614538	−	0.0354804i
$56$	1.48033	+	11.4330i	0.197817	+	1.52779i
$57$	−0.632558	+	5.20015i	−0.0837844	+	0.688777i
$58$	−3.90275	−	2.03518i	−0.512456	−	0.267232i
$59$	−1.03648	−	1.79524i	−0.134938	−	0.233720i	0.790636	−	0.612287i	$-0.209750\pi$
$59$	−1.03648	−	1.79524i	−0.134938	−	0.233720i	−0.925574	+	0.378567i	$0.876417\pi$
$60$	1.01890	−	2.17694i	0.131540	−	0.281041i
$61$	−5.47760	+	9.48748i	−0.701335	+	1.21475i	0.266663	+	0.963790i	$0.414079\pi$
$61$	−5.47760	+	9.48748i	−0.701335	+	1.21475i	−0.967998	+	0.250958i	$0.919255\pi$
$62$	−0.0415963	+	0.00178645i	−0.00528274	+	0.000226879i
$63$	5.49136	+	3.17044i	0.691846	+	0.399438i
$64$	7.73619	−	2.03750i	0.967023	−	0.254688i
$65$			4.79296i			0.594493i
$66$	−0.754692	+	0.480036i	−0.0928962	+	0.0590884i
$67$	1.00882	−	1.74733i	0.123247	−	0.213471i	−0.797799	−	0.602923i	$-0.794002\pi$
$67$	1.00882	−	1.74733i	0.123247	−	0.213471i	0.921047	+	0.389453i	$0.127336\pi$
$68$	−6.79252	−	9.73020i	−0.823714	−	1.17996i
$69$			1.51011i			0.181795i
$70$	−4.86368	+	3.09364i	−0.581321	+	0.369760i
$71$	−2.94128	−	5.09445i	−0.349066	−	0.604601i	0.637018	−	0.770849i	$-0.280168\pi$
$71$	−2.94128	−	5.09445i	−0.349066	−	0.604601i	−0.986084	+	0.166249i	$0.946835\pi$
$72$	1.69256	−	4.06163i	0.199470	−	0.478667i
$73$	−1.45468	−	2.51957i	−0.170257	−	0.294894i	0.768253	−	0.640147i	$-0.221126\pi$
$73$	−1.45468	−	2.51957i	−0.170257	−	0.294894i	−0.938510	+	0.345253i	$0.887793\pi$
$74$	0.416473	+	9.69732i	0.0484140	+	1.12729i
$75$	1.20179			0.138771
$76$	−7.39173	−	4.62194i	−0.847889	−	0.530173i
$77$	2.14498			0.244443
$78$	−0.349528	−	8.13856i	−0.0395763	−	0.921510i
$79$	−6.81678	−	11.8070i	−0.766948	−	1.32839i	−0.939211	−	0.343342i	$-0.888441\pi$
$79$	−6.81678	−	11.8070i	−0.766948	−	1.32839i	0.172263	−	0.985051i	$-0.444892\pi$
$80$	2.56241	+	3.07149i	0.286486	+	0.343403i
$81$	0.956355	+	1.65646i	0.106262	+	0.184051i
$82$	−9.34575	+	5.94455i	−1.03207	+	0.656465i
$83$			8.72403i			0.957587i	0.877928	+	0.478793i	$0.158926\pi$
$83$			8.72403i			0.957587i	−0.877928	+	0.478793i	$0.841074\pi$
$84$	8.03304	−	5.60776i	0.876477	−	0.611856i
$85$	2.96664	−	5.13837i	0.321777	−	0.557335i
$86$	6.14589	−	3.90921i	0.662728	−	0.421541i
$87$			3.74039i			0.401012i
$88$	−0.191132	−	1.47616i	−0.0203747	−	0.157360i
$89$	−8.63922	−	4.98785i	−0.915755	−	0.528712i	−0.0334769	−	0.999439i	$-0.510658\pi$
$89$	−8.63922	−	4.98785i	−0.915755	−	0.528712i	−0.882278	+	0.470728i	$0.843991\pi$
$90$	2.19806	−	0.0944006i	0.231696	−	0.00995070i
$91$	−9.76782	+	16.9184i	−1.02395	+	1.77353i
$92$	−2.27612	−	1.06532i	−0.237302	−	0.111068i
$93$	0.0176905	+	0.0306408i	0.00183442	+	0.00317730i
$94$	1.31381	+	0.685117i	0.135509	+	0.0706644i
$95$	0.526346	−	4.32700i	0.0540020	−	0.443941i
$96$	−4.57502	−	5.02860i	−0.466936	−	0.513230i
$97$	13.0162	−	7.51491i	1.32160	−	0.763023i	0.337612	−	0.941285i	$-0.390381\pi$
$97$	13.0162	−	7.51491i	1.32160	−	0.763023i	0.983983	+	0.178262i	$0.0570474\pi$
$98$	−13.5823	+	0.583322i	−1.37202	+	0.0589244i
$99$	−0.709015	−	0.409350i	−0.0712587	−	0.0411412i
$100$	−0.847818	+	1.81141i	−0.0847818	+	0.181141i
$101$	4.96528	−	8.60011i	0.494064	−	0.855743i	−0.505913	−	0.862585i	$-0.668844\pi$
$101$	4.96528	−	8.60011i	0.494064	−	0.855743i	0.999977	+	0.00684126i	$0.00217766\pi$
$102$	−4.66271	+	8.94142i	−0.461677	+	0.885332i
$103$	−18.4650			−1.81941			−0.909706	−	0.415253i	$-0.863693\pi$
$103$	−18.4650			−1.81941			−0.909706	+	0.415253i	$0.863693\pi$
$104$	12.5135	+	5.21462i	1.22705	+	0.511335i
$105$	4.24213	+	2.44919i	0.413989	+	0.239017i
$106$	3.97478	+	2.07274i	0.386065	+	0.201322i
$107$	1.90643			0.184302			0.0921509	−	0.995745i	$-0.470626\pi$
$107$	1.90643			0.184302			0.0921509	+	0.995745i	$0.470626\pi$
$108$	−10.9097	+	0.938811i	−1.04978	+	0.0903372i
$109$	−16.1809	+	9.34203i	−1.54985	+	0.894805i	−0.551695	+	0.834046i	$0.686019\pi$
$109$	−16.1809	+	9.34203i	−1.54985	+	0.894805i	−0.998152	+	0.0607584i	$0.980648\pi$
$110$	0.627973	−	0.399434i	0.0598749	−	0.0380845i
$111$	7.14326	−	4.12417i	0.678009	−	0.391448i
$112$	2.78533	+	16.0639i	0.263189	+	1.51790i
$113$		−	4.61852i		−	0.434474i	−0.976119	−	0.217237i	$-0.930296\pi$
$113$		−	4.61852i		−	0.434474i	0.976119	−	0.217237i	$-0.0697044\pi$
$114$	−0.578201	+	7.38574i	−0.0541534	+	0.691738i
$115$		−	1.25655i		−	0.117173i
$116$	−5.63773	−	2.63870i	−0.523450	−	0.244997i
$117$	6.45743	−	3.72820i	0.596989	−	0.344672i
$118$	−1.57339	−	2.47362i	−0.144842	−	0.227715i
$119$	20.9435	−	12.0917i	1.91989	−	1.10845i
$120$	1.30752	−	3.13764i	0.119360	−	0.286426i
$121$	10.7231			0.974823
$122$	−7.16365	+	13.7373i	−0.648567	+	1.24372i
$123$	8.15141	+	4.70622i	0.734988	+	0.424346i
$124$	−0.0586635	+	0.00504818i	−0.00526814	+	0.000453340i
$125$	−1.00000			−0.0894427
$126$	7.95119	+	4.14633i	0.708348	+	0.369384i
$127$	1.30516	−	2.26061i	0.115814	−	0.200596i	−0.802291	−	0.596934i	$-0.796386\pi$
$127$	1.30516	−	2.26061i	0.115814	−	0.200596i	0.918105	+	0.396337i	$0.129719\pi$
$128$	10.8069	−	3.34825i	0.955205	−	0.295946i
$129$	−5.36047	−	3.09487i	−0.471963	−	0.272488i
$130$	0.290839	+	6.77202i	0.0255083	+	0.593946i
$131$	19.6463	−	11.3428i	1.71651	−	0.991026i	0.791419	−	0.611273i	$-0.209342\pi$
$131$	19.6463	−	11.3428i	1.71651	−	0.991026i	0.925088	−	0.379753i	$-0.123991\pi$
$132$	−1.03718	+	0.724044i	−0.0902753	+	0.0630199i
$133$	10.6761	−	14.2009i	0.925739	−	1.23138i
$134$	1.31935	−	2.53004i	0.113974	−	0.218562i
$135$	−2.73750	−	4.74149i	−0.235606	−	0.408082i
$136$	−10.1877	−	13.3357i	−0.873585	−	1.14353i
$137$	5.12884	−	8.88341i	0.438186	−	0.758961i	−0.559363	−	0.828923i	$-0.688954\pi$
$137$	5.12884	−	8.88341i	0.438186	−	0.758961i	0.997550	+	0.0699615i	$0.0222877\pi$
$138$	0.0916340	+	2.13364i	0.00780041	+	0.181628i
$139$	−4.38070	−	2.52920i	−0.371566	−	0.214524i	0.302576	−	0.953125i	$-0.402153\pi$
$139$	−4.38070	−	2.52920i	−0.371566	−	0.214524i	−0.674142	+	0.738601i	$0.735487\pi$
$140$	−6.68423	+	4.66617i	−0.564920	+	0.394363i
$141$		−	1.25916i		−	0.106040i
$142$	−4.46491	−	7.01953i	−0.374687	−	0.589066i
$143$	1.26117	−	2.18441i	0.105464	−	0.182669i
$144$	2.14498	−	5.84142i	0.178748	−	0.486785i
$145$		−	3.11235i		−	0.258466i
$146$	−2.20822	−	3.47166i	−0.182753	−	0.287317i
$147$	5.77641	+	10.0050i	0.476430	+	0.825201i
$148$	1.17688	+	13.6762i	0.0967388	+	1.12418i
$149$	4.88251	+	8.45676i	0.399991	+	0.692805i	0.993724	−	0.111857i	$-0.0356799\pi$
$149$	4.88251	+	8.45676i	0.399991	+	0.692805i	−0.593733	+	0.804662i	$0.702347\pi$
$150$	1.69802	−	0.0729253i	0.138643	−	0.00595433i
$151$	10.7452			0.874435			0.437217	−	0.899356i	$-0.355964\pi$
$151$	10.7452			0.874435			0.437217	+	0.899356i	$0.355964\pi$
$152$	−10.7243	−	6.08186i	−0.869857	−	0.493304i
$153$	−9.23039			−0.746233
$154$	3.03067	−	0.130159i	0.244218	−	0.0104885i
$155$	−0.0147201	−	0.0254959i	−0.00118235	−	0.00204788i
$156$	−0.987704	−	11.4779i	−0.0790796	−	0.918964i
$157$	8.70596	+	15.0792i	0.694811	+	1.20345i	0.970244	+	0.242128i	$0.0778455\pi$
$157$	8.70596	+	15.0792i	0.694811	+	1.20345i	−0.275433	+	0.961320i	$0.588821\pi$
$158$	−10.3480	−	16.2686i	−0.823240	−	1.29426i
$159$		−	3.80943i		−	0.302107i
$160$	3.80683	+	4.18426i	0.300957	+	0.330795i
$161$	2.56078	−	4.43540i	0.201818	−	0.349559i
$162$	1.45176	+	2.28239i	0.114061	+	0.179322i
$163$			20.3238i			1.59189i	0.605371	+	0.795943i	$0.293025\pi$
$163$			20.3238i			1.59189i	−0.605371	+	0.795943i	$0.706975\pi$
$164$	−12.8440	+	8.96622i	−1.00295	+	0.700144i
$165$	−0.547721	−	0.316227i	−0.0426400	−	0.0246182i
$166$	0.529379	+	12.3263i	0.0410878	+	0.956705i
$167$	−5.99886	+	10.3903i	−0.464206	+	0.804028i	−0.999165	−	0.0408499i	$-0.986993\pi$
$167$	−5.99886	+	10.3903i	−0.464206	+	0.804028i	0.534960	+	0.844878i	$0.320327\pi$
$168$	11.0097	−	8.41071i	0.849416	−	0.648901i
$169$	4.98623	+	8.63640i	0.383556	+	0.664338i
$170$	3.87980	−	7.44008i	0.297567	−	0.570628i
$171$	−6.23908	+	2.65662i	−0.477114	+	0.203157i
$172$	8.44638	−	5.89630i	0.644031	−	0.449589i
$173$	−18.5338	+	10.7005i	−1.40910	+	0.813543i	−0.995301	−	0.0968271i	$-0.969131\pi$
$173$	−18.5338	+	10.7005i	−1.40910	+	0.813543i	−0.413796	+	0.910370i	$0.635797\pi$
$174$	0.226969	+	5.28484i	0.0172065	+	0.400642i
$175$	−3.52984	−	2.03795i	−0.266831	−	0.154055i
$176$	−0.359627	−	2.07409i	−0.0271079	−	0.156340i
$177$	−1.24563	+	2.15750i	−0.0936276	+	0.162168i
$178$	−12.5091	−	6.52316i	−0.937598	−	0.488932i
$179$	2.84632			0.212744			0.106372	−	0.994326i	$-0.466077\pi$
$179$	2.84632			0.212744			0.106372	+	0.994326i	$0.466077\pi$
$180$	3.09994	−	0.266759i	0.231056	−	0.0198831i
$181$	−17.1859	−	9.92230i	−1.27742	−	0.737519i	−0.301047	−	0.953609i	$-0.597336\pi$
$181$	−17.1859	−	9.92230i	−1.27742	−	0.737519i	−0.976373	+	0.216091i	$0.930669\pi$
$182$	−12.7744	+	24.4969i	−0.946905	+	1.81583i
$183$	13.1659			0.973248
$184$	−3.28060	−	1.36709i	−0.241849	−	0.100783i
$185$	−5.94385	+	3.43168i	−0.437000	+	0.252302i
$186$	0.0268544	+	0.0422192i	0.00196906	+	0.00309566i
$187$	−2.70411	+	1.56122i	−0.197744	+	0.114168i
$188$	1.89787	+	0.888286i	0.138417	+	0.0647849i
$189$		−	22.3156i		−	1.62322i
$190$	0.481116	−	6.14561i	0.0349038	−	0.445849i
$191$			23.9808i			1.73519i	0.497274	+	0.867593i	$0.334334\pi$
$191$			23.9808i			1.73519i	−0.497274	+	0.867593i	$0.665666\pi$
$192$	−6.76924	−	6.82736i	−0.488527	−	0.492722i
$193$	20.6223	−	11.9063i	1.48443	−	0.857035i	0.484585	−	0.874744i	$-0.338971\pi$
$193$	20.6223	−	11.9063i	1.48443	−	0.857035i	0.999843	+	0.0177096i	$0.00563745\pi$
$194$	17.9347	−	11.4077i	1.28764	−	0.819027i
$195$	4.98842	−	2.88007i	0.357228	−	0.206246i
$196$	−19.1552	+	1.64836i	−1.36823	+	0.117740i
$197$	6.00910			0.428131			0.214065	−	0.976819i	$-0.431329\pi$
$197$	6.00910			0.428131			0.214065	+	0.976819i	$0.431329\pi$
$198$	−1.02662	−	0.535352i	−0.0729584	−	0.0380458i
$199$	10.5989	+	6.11926i	0.751334	+	0.433783i	0.826176	−	0.563413i	$-0.190512\pi$
$199$	10.5989	+	6.11926i	0.751334	+	0.433783i	−0.0748420	+	0.997195i	$0.523845\pi$
$200$	−1.08797	+	2.61081i	−0.0769314	+	0.184612i
$201$	−2.42479			−0.171032
$202$	6.49364	−	12.4525i	0.456891	−	0.876154i
$203$	6.34281	−	10.9861i	0.445178	−	0.771071i
$204$	−6.04542	+	12.9164i	−0.423264	+	0.904327i
$205$	−6.78272	−	3.91600i	−0.473726	−	0.273506i
$206$	−26.0894	+	1.12047i	−1.81774	+	0.0780667i
$207$	−1.69291	+	0.977403i	−0.117665	+	0.0679342i
$208$	17.9969	+	6.60847i	1.24786	+	0.458215i
$209$	−1.37845	+	1.83355i	−0.0953492	+	0.126829i
$210$	6.14237	+	3.20308i	0.423864	+	0.221033i
$211$	1.29776	+	2.24778i	0.0893412	+	0.154743i	0.907233	−	0.420629i	$-0.138191\pi$
$211$	1.29776	+	2.24778i	0.0893412	+	0.154743i	−0.817892	+	0.575372i	$0.804857\pi$
$212$	5.74179	+	2.68741i	0.394348	+	0.184572i
$213$	−3.53481	+	6.12247i	−0.242201	+	0.419505i
$214$	2.69362	−	0.115683i	0.184132	−	0.00790795i
$215$	4.46040	+	2.57522i	0.304197	+	0.175628i
$216$	−15.3574	+	1.98846i	−1.04494	+	0.135298i
$217$		−	0.119995i		−	0.00814581i
$218$	−22.2953	+	14.1813i	−1.51003	+	0.960481i
$219$	−1.74822	+	3.02800i	−0.118134	+	0.204613i
$220$	0.863032	−	0.602471i	0.0581856	−	0.0406186i
$221$		−	28.4380i		−	1.91294i
$222$	9.84254	−	6.26054i	0.660588	−	0.420180i
$223$	12.9684	+	22.4619i	0.868429	+	1.50416i	0.863602	+	0.504175i	$0.168203\pi$
$223$	12.9684	+	22.4619i	0.868429	+	1.50416i	0.00482702	+	0.999988i	$0.498464\pi$
$224$	4.91019	+	22.5279i	0.328076	+	1.50521i
$225$	0.777849	+	1.34727i	0.0518566	+	0.0898183i
$226$	−0.280254	−	6.52556i	−0.0186422	−	0.434074i
$227$	16.9275			1.12352			0.561760	−	0.827301i	$-0.310125\pi$
$227$	16.9275			1.12352			0.561760	+	0.827301i	$0.310125\pi$
$228$	−0.368775	+	10.4705i	−0.0244227	+	0.693424i
$229$	7.99595			0.528387			0.264194	−	0.964470i	$-0.414894\pi$
$229$	7.99595			0.528387			0.264194	+	0.964470i	$0.414894\pi$
$230$	−0.0762479	−	1.77539i	−0.00502764	−	0.117066i
$231$	−1.28891	−	2.23246i	−0.0848041	−	0.146885i
$232$	−8.12573	−	3.38615i	−0.533480	−	0.222312i
$233$	3.54033	+	6.13203i	0.231935	+	0.401722i	0.958377	−	0.285505i	$-0.0921612\pi$
$233$	3.54033	+	6.13203i	0.231935	+	0.401722i	−0.726443	+	0.687227i	$0.758828\pi$
$234$	8.89754	−	5.65945i	0.581651	−	0.369970i
$235$			1.04773i			0.0683465i
$236$	−2.37316	−	3.39953i	−0.154480	−	0.221290i
$237$	−8.19235	+	14.1896i	−0.532150	+	0.921711i
$238$	28.8576	−	18.3554i	1.87056	−	1.18980i
$239$		−	27.4126i		−	1.77317i	−0.462562	−	0.886587i	$-0.653070\pi$
$239$		−	27.4126i		−	1.77317i	0.462562	−	0.886587i	$-0.346930\pi$
$240$	1.65701	−	4.51255i	0.106960	−	0.291284i
$241$	5.47504	+	3.16102i	0.352678	+	0.203619i	0.665864	−	0.746073i	$-0.268063\pi$
$241$	5.47504	+	3.16102i	0.352678	+	0.203619i	−0.313186	+	0.949692i	$0.601396\pi$
$242$	15.1507	−	0.650681i	0.973925	−	0.0418273i
$243$	−7.06316	+	12.2337i	−0.453102	+	0.784795i
$244$	−9.28802	+	19.8443i	−0.594604	+	1.27040i
$245$	−4.80650	−	8.32510i	−0.307076	−	0.531871i
$246$	11.8028	+	6.15484i	0.752519	+	0.392418i
$247$	−8.18480	−	19.2220i	−0.520787	−	1.22307i
$248$	−0.0825800	+	0.0106924i	−0.00524384	+	0.000678966i
$249$	9.07981	−	5.24223i	0.575410	−	0.332213i
$250$	−1.41291	+	0.0606805i	−0.0893603	+	0.00383777i
$251$	−1.84965	−	1.06790i	−0.116749	−	0.0674050i	0.440488	−	0.897758i	$-0.354805\pi$
$251$	−1.84965	−	1.06790i	−0.116749	−	0.0674050i	−0.557237	+	0.830353i	$0.688139\pi$
$252$	11.4859	+	5.37591i	0.723545	+	0.338651i
$253$	−0.330634	+	0.572675i	−0.0207868	+	0.0360038i
$254$	1.70690	−	3.27324i	0.107101	−	0.205381i
$255$	−7.13056			−0.446533
$256$	15.0660	−	5.38654i	0.941627	−	0.336659i
$257$	−10.9456	−	6.31942i	−0.682765	−	0.394194i	0.118131	−	0.992998i	$-0.462310\pi$
$257$	−10.9456	−	6.31942i	−0.682765	−	0.394194i	−0.800896	+	0.598804i	$0.795643\pi$
$258$	−7.76167	−	4.04750i	−0.483221	−	0.251986i
$259$	−27.9744			−1.73825
$260$	0.821860	+	9.55062i	0.0509696	+	0.592304i
$261$	−4.19318	+	2.42093i	−0.259551	+	0.149852i
$262$	27.0702	−	17.2185i	1.67240	−	1.06376i
$263$	19.8571	−	11.4645i	1.22444	−	0.706932i	0.258581	−	0.965990i	$-0.416745\pi$
$263$	19.8571	−	11.4645i	1.22444	−	0.706932i	0.965862	+	0.259057i	$0.0834118\pi$
$264$	−1.42151	+	1.08595i	−0.0874881	+	0.0668354i
$265$			3.16979i			0.194719i
$266$	14.2227	−	20.7125i	0.872051	−	1.26997i
$267$			11.9887i			0.733698i
$268$	1.71060	−	3.65479i	0.104491	−	0.223252i
$269$	16.8520	−	9.72953i	1.02749	−	0.593220i	0.111224	−	0.993795i	$-0.464523\pi$
$269$	16.8520	−	9.72953i	1.02749	−	0.593220i	0.916264	+	0.400575i	$0.131190\pi$
$270$	−4.15556	−	6.53319i	−0.252899	−	0.397597i
$271$	5.77100	−	3.33189i	0.350563	−	0.202398i	−0.314370	−	0.949301i	$-0.601793\pi$
$271$	5.77100	−	3.33189i	0.350563	−	0.202398i	0.664933	+	0.746903i	$0.268460\pi$
$272$	−15.2035	−	18.2240i	−0.921846	−	1.10499i
$273$	23.4778			1.42094
$274$	6.70754	−	12.8627i	0.405218	−	0.777064i
$275$	0.455754	+	0.263130i	0.0274830	+	0.0158673i
$276$	0.258941	+	3.00909i	0.0155864	+	0.181126i
$277$	5.46800			0.328540			0.164270	−	0.986415i	$-0.447473\pi$
$277$	5.46800			0.328540			0.164270	+	0.986415i	$0.447473\pi$
$278$	−6.34301	−	3.30771i	−0.380429	−	0.198383i
$279$	−0.0229000	+	0.0396640i	−0.00137099	+	0.00237462i
$280$	−9.16107	+	6.99848i	−0.547479	+	0.418239i
$281$	11.1445	+	6.43427i	0.664824	+	0.383836i	0.794112	−	0.607771i	$-0.207936\pi$
$281$	11.1445	+	6.43427i	0.664824	+	0.383836i	−0.129289	+	0.991607i	$0.541269\pi$
$282$	−0.0764062	−	1.77907i	−0.00454992	−	0.105942i
$283$	−19.6239	+	11.3299i	−1.16652	+	0.673490i	−0.952858	−	0.303418i	$-0.901872\pi$
$283$	−19.6239	+	11.3299i	−1.16652	+	0.673490i	−0.213661	+	0.976908i	$0.568539\pi$
$284$	−6.73447	−	9.64704i	−0.399617	−	0.572447i
$285$	−4.81975	+	2.05227i	−0.285497	+	0.121566i
$286$	1.64937	−	3.16290i	0.0975292	−	0.187026i
$287$	−15.9613	−	27.6457i	−0.942163	−	1.63187i
$288$	2.67620	−	8.38357i	0.157697	−	0.494007i
$289$	−9.10190	+	15.7650i	−0.535406	+	0.927350i
$290$	−0.188859	−	4.39747i	−0.0110902	−	0.258228i
$291$	−15.6428	−	9.03135i	−0.916995	−	0.529427i
$292$	−3.33068	−	4.77116i	−0.194913	−	0.279211i
$293$			6.97690i			0.407595i	0.979013	+	0.203797i	$0.0653284\pi$
$293$			6.97690i			0.407595i	−0.979013	+	0.203797i	$0.934672\pi$
$294$	8.76866	+	13.7857i	0.511399	+	0.803999i
$295$	1.03648	−	1.79524i	0.0603463	−	0.104523i
$296$	2.49270	+	19.2518i	0.144885	+	1.11899i
$297$			2.88127i			0.167188i
$298$	7.41172	+	11.6524i	0.429349	+	0.675004i
$299$	−3.01129	−	5.21570i	−0.174147	−	0.301632i
$300$	2.39473	−	0.206074i	0.138260	−	0.0118977i
$301$	10.4963	+	18.1802i	0.604999	+	1.04789i
$302$	15.1821	−	0.652027i	0.873629	−	0.0375199i
$303$	−11.9345			−0.685616
$304$	−15.5216	−	7.94237i	−0.890222	−	0.455526i
$305$	−10.9552			−0.627293
$306$	−13.0417	+	0.560105i	−0.745546	+	0.0320191i
$307$	11.0859	+	19.2014i	0.632708	+	1.09588i	0.986996	+	0.160747i	$0.0513902\pi$
$307$	11.0859	+	19.2014i	0.632708	+	1.09588i	−0.354287	+	0.935137i	$0.615277\pi$
$308$	4.27417	−	0.367805i	0.243543	−	0.0209577i
$309$	11.0955	+	19.2180i	0.631204	+	1.09328i
$310$	−0.0223453	−	0.0351303i	−0.00126913	−	0.00199526i
$311$		−	13.6205i		−	0.772349i	−0.922426	−	0.386175i	$-0.873796\pi$
$311$		−	13.6205i		−	0.772349i	0.922426	−	0.386175i	$-0.126204\pi$
$312$	−2.09202	−	16.1572i	−0.118437	−	0.914724i
$313$	3.89964	−	6.75437i	0.220420	−	0.381779i	−0.734515	−	0.678592i	$-0.762590\pi$
$313$	3.89964	−	6.75437i	0.220420	−	0.381779i	0.954936	+	0.296813i	$0.0959237\pi$
$314$	13.2158	+	20.7772i	0.745809	+	1.17253i
$315$			6.34088i			0.357268i
$316$	−15.6079	−	22.3582i	−0.878015	−	1.25775i
$317$	−11.2971	−	6.52240i	−0.634510	−	0.366334i	0.147987	−	0.988989i	$-0.452721\pi$
$317$	−11.2971	−	6.52240i	−0.634510	−	0.366334i	−0.782497	+	0.622655i	$0.786054\pi$
$318$	−0.231158	−	5.38238i	−0.0129627	−	0.301829i
$319$	−0.818950	+	1.41846i	−0.0458524	+	0.0794187i
$320$	5.63262	+	5.68098i	0.314873	+	0.317577i
$321$	−1.14557	−	1.98418i	−0.0639393	−	0.110746i
$322$	3.34901	−	6.42222i	0.186633	−	0.357896i
$323$	−3.12296	+	25.6733i	−0.173766	+	1.42850i
$324$	2.18970	+	3.13672i	0.121650	+	0.174262i
$325$	−4.15082	+	2.39648i	−0.230246	+	0.132933i
$326$	1.23326	+	28.7158i	0.0683041	+	1.59042i
$327$	19.4460	+	11.2272i	1.07537	+	0.620864i
$328$	−17.6034	+	13.4479i	−0.971983	+	0.742533i
$329$	−2.13523	+	3.69832i	−0.117719	+	0.203895i
$330$	−0.793070	−	0.413564i	−0.0436571	−	0.0227660i
$331$	21.1929			1.16487			0.582434	−	0.812878i	$-0.302100\pi$
$331$	21.1929			1.16487			0.582434	+	0.812878i	$0.302100\pi$
$332$	1.49593	+	17.3838i	0.0820999	+	0.954061i
$333$	9.24683	+	5.33866i	0.506723	+	0.292557i
$334$	−7.84536	+	15.0446i	−0.429279	+	0.823205i
$335$	2.01765			0.110236
$336$	15.0454	−	12.5517i	0.820791	−	0.684749i
$337$	−15.7715	+	9.10568i	−0.859129	+	0.496018i	−0.863720	−	0.503971i	$-0.831872\pi$
$337$	−15.7715	+	9.10568i	−0.859129	+	0.496018i	0.00459171	+	0.999989i	$0.498538\pi$
$338$	7.56915	+	11.8999i	0.411708	+	0.647269i
$339$	−4.80687	+	2.77525i	−0.261073	+	0.150731i
$340$	5.03034	−	10.7476i	0.272809	−	0.582870i
$341$			0.0154932i			0.000839001i
$342$	−8.65406	+	4.13216i	−0.467958	+	0.223442i
$343$		−	10.6503i		−	0.575064i
$344$	11.5762	−	8.84348i	0.624147	−	0.476809i
$345$	−1.30779	+	0.755053i	−0.0704090	+	0.0406507i
$346$	−25.5373	+	16.2435i	−1.37289	+	0.873254i
$347$	17.3253	−	10.0027i	0.930068	−	0.536975i	0.0432350	−	0.999065i	$-0.486234\pi$
$347$	17.3253	−	10.0027i	0.930068	−	0.536975i	0.886833	+	0.462090i	$0.152900\pi$
$348$	0.641374	+	7.45323i	0.0343812	+	0.399535i
$349$	−32.2697			−1.72736			−0.863679	−	0.504042i	$-0.831846\pi$
$349$	−32.2697			−1.72736			−0.863679	+	0.504042i	$0.831846\pi$
$350$	−5.11101	−	2.66525i	−0.273195	−	0.142464i
$351$	−22.7257	−	13.1207i	−1.21301	−	0.700332i
$352$	−0.633977	−	2.90868i	−0.0337911	−	0.155033i
$353$	−16.6829			−0.887943			−0.443972	−	0.896041i	$-0.646431\pi$
$353$	−16.6829			−0.887943			−0.443972	+	0.896041i	$0.646431\pi$
$354$	−1.62905	+	3.12394i	−0.0865831	+	0.166036i
$355$	2.94128	−	5.09445i	0.156107	−	0.270386i
$356$	−18.0701	−	8.45759i	−0.957713	−	0.448251i
$357$	−25.1697	−	14.5317i	−1.33212	−	0.769102i
$358$	4.02160	−	0.172716i	0.212548	−	0.00912834i
$359$	0.668086	−	0.385719i	0.0352602	−	0.0203575i	−0.482266	−	0.876025i	$-0.660186\pi$
$359$	0.668086	−	0.385719i	0.0352602	−	0.0203575i	0.517526	+	0.855667i	$0.326853\pi$
$360$	4.36375	−	0.565013i	0.229990	−	0.0297788i
$361$	5.27821	+	18.2521i	0.277800	+	0.960639i
$362$	−24.8843	−	12.9765i	−1.30789	−	0.682028i
$363$	−6.44343	−	11.1604i	−0.338193	−	0.585767i
$364$	−16.5627	+	35.3870i	−0.868120	+	1.85479i
$365$	1.45468	−	2.51957i	0.0761412	−	0.131881i
$366$	18.6022	−	0.798912i	0.972352	−	0.0417598i
$367$	−23.6797	−	13.6715i	−1.23607	−	0.713645i	−0.267781	−	0.963480i	$-0.586291\pi$
$367$	−23.6797	−	13.6715i	−1.23607	−	0.713645i	−0.968289	+	0.249834i	$0.919624\pi$
$368$	−4.71815	−	1.73251i	−0.245951	−	0.0903132i
$369$			12.1842i			0.634286i
$370$	−8.18989	+	5.20934i	−0.425772	+	0.270821i
$371$	−6.45988	+	11.1888i	−0.335380	+	0.580896i
$372$	0.0405047	+	0.0580225i	0.00210007	+	0.00300833i
$373$			19.8125i			1.02585i	0.858433	+	0.512926i	$0.171439\pi$
$373$			19.8125i			1.02585i	−0.858433	+	0.512926i	$0.828561\pi$
$374$	−3.72594	+	2.36995i	−0.192664	+	0.122547i
$375$	0.600896	+	1.04078i	0.0310301	+	0.0537457i
$376$	2.73543	+	1.13991i	0.141069	+	0.0587862i
$377$	−7.45867	−	12.9188i	−0.384141	−	0.665352i
$378$	−1.35412	−	31.5299i	−0.0696485	−	1.62172i
$379$	−23.0142			−1.18216			−0.591079	−	0.806613i	$-0.701298\pi$
$379$	−23.0142			−1.18216			−0.591079	+	0.806613i	$0.701298\pi$
$380$	0.306855	−	8.71240i	0.0157413	−	0.446936i
$381$	−3.13706			−0.160717
$382$	1.45517	+	33.8827i	0.0744527	+	1.73359i
$383$	−17.7023	−	30.6612i	−0.904544	−	1.56672i	−0.821529	−	0.570167i	$-0.806878\pi$
$383$	−17.7023	−	30.6612i	−0.904544	−	1.56672i	−0.0830150	−	0.996548i	$-0.526455\pi$
$384$	−9.97862	−	9.23569i	−0.509219	−	0.471307i
$385$	1.07249	+	1.85761i	0.0546592	+	0.0946725i
$386$	28.4150	−	18.0739i	1.44629	−	0.919939i
$387$		−	8.01252i		−	0.407299i
$388$	24.6480	−	17.2064i	1.25131	−	0.873523i
$389$	14.4645	−	25.0532i	0.733377	−	1.27025i	−0.222055	−	0.975034i	$-0.571276\pi$
$389$	14.4645	−	25.0532i	0.733377	−	1.27025i	0.955432	−	0.295212i	$-0.0953903\pi$
$390$	6.87343	−	4.37198i	0.348050	−	0.221384i
$391$			7.45544i			0.377038i
$392$	−26.9646	+	3.49134i	−1.36192	+	0.176339i
$393$	−23.6108	−	13.6317i	−1.19101	−	0.687628i
$394$	8.49033	−	0.364636i	0.427736	−	0.0183701i
$395$	6.81678	−	11.8070i	0.342990	−	0.594075i
$396$	−1.48300	−	0.694109i	−0.0745236	−	0.0348803i
$397$	4.47707	+	7.75451i	0.224698	+	0.389188i	0.956229	−	0.292620i	$-0.0945273\pi$
$397$	4.47707	+	7.75451i	0.224698	+	0.389188i	−0.731531	+	0.681808i	$0.761194\pi$
$398$	15.3466	+	8.00282i	0.769254	+	0.401145i
$399$	−21.1953	−	2.57825i	−1.06109	−	0.129074i
$400$	−1.37879	+	3.75486i	−0.0689393	+	0.187743i
$401$	4.25671	−	2.45761i	0.212570	−	0.122727i	−0.389935	−	0.920842i	$-0.627503\pi$
$401$	4.25671	−	2.45761i	0.212570	−	0.122727i	0.602505	+	0.798115i	$0.294169\pi$
$402$	−3.42601	+	0.147138i	−0.170874	+	0.00733856i
$403$	−0.122201	−	0.0705527i	−0.00608726	−	0.00351448i
$404$	8.41931	−	17.9883i	0.418876	−	0.894951i
$405$	−0.956355	+	1.65646i	−0.0475217	+	0.0823099i
$406$	8.29519	−	15.9072i	0.411683	−	0.789462i
$407$	3.61191			0.179036
$408$	−7.75787	+	18.6165i	−0.384072	+	0.921655i
$409$	8.64534	+	4.99139i	0.427484	+	0.246808i	0.698274	−	0.715830i	$-0.253952\pi$
$409$	8.64534	+	4.99139i	0.427484	+	0.246808i	−0.270790	+	0.962638i	$0.587285\pi$
$410$	−9.82100	−	5.12139i	−0.485025	−	0.252927i
$411$	−12.3276			−0.608075
$412$	−36.7941	+	3.16624i	−1.81271	+	0.155990i
$413$	7.31722	−	4.22460i	0.360057	−	0.207879i
$414$	−2.33262	+	1.48371i	−0.114642	+	0.0729204i
$415$	−7.55523	+	4.36202i	−0.370872	+	0.214123i
$416$	25.8290	+	8.24511i	1.26637	+	0.404250i
$417$			6.07914i			0.297697i
$418$	−1.83636	+	2.67429i	−0.0898194	+	0.130804i
$419$			26.0564i			1.27294i	0.771302	+	0.636469i	$0.219606\pi$
$419$			26.0564i			1.27294i	−0.771302	+	0.636469i	$0.780394\pi$
$420$	8.87298	+	4.15294i	0.432957	+	0.202643i
$421$	15.4073	−	8.89543i	0.750908	−	0.433537i	−0.0751141	−	0.997175i	$-0.523932\pi$
$421$	15.4073	−	8.89543i	0.750908	−	0.433537i	0.826022	+	0.563638i	$0.190599\pi$
$422$	1.97001	+	3.09716i	0.0958986	+	0.150768i
$423$	1.41158	−	0.814977i	0.0686335	−	0.0396256i
$424$	8.27571	+	3.44865i	0.401904	+	0.167481i
$425$	5.93328			0.287806
$426$	−4.62286	+	8.86500i	−0.223978	+	0.429511i
$427$	−38.6701	−	22.3262i	−1.87138	−	1.08044i
$428$	3.79882	−	0.326901i	0.183623	−	0.0158013i
$429$	−3.03132			−0.146354
$430$	6.45842	+	3.36789i	0.311453	+	0.162414i
$431$	−3.90963	+	6.77168i	−0.188320	+	0.326180i	−0.944690	−	0.327964i	$-0.893638\pi$
$431$	−3.90963	+	6.77168i	−0.188320	+	0.326180i	0.756370	+	0.654144i	$0.226971\pi$
$432$	−21.5780	+	3.74142i	−1.03817	+	0.180009i
$433$	−12.8257	−	7.40491i	−0.616363	−	0.355857i	0.159089	−	0.987264i	$-0.449144\pi$
$433$	−12.8257	−	7.40491i	−0.616363	−	0.355857i	−0.775452	+	0.631407i	$0.782478\pi$
$434$	−0.00728138	−	0.169543i	−0.000349517	−	0.00813831i
$435$	−3.23927	+	1.87019i	−0.155311	+	0.0896690i
$436$	−30.6407	+	21.3898i	−1.46742	+	1.02439i
$437$	2.14577	+	5.03934i	0.102646	+	0.241064i
$438$	−2.28633	+	4.38438i	−0.109245	+	0.209494i
$439$	7.26776	+	12.5881i	0.346871	+	0.600799i	0.985692	−	0.168557i	$-0.0539108\pi$
$439$	7.26776	+	12.5881i	0.346871	+	0.600799i	−0.638821	+	0.769356i	$0.720577\pi$
$440$	1.18283	−	0.903607i	0.0563892	−	0.0430778i
$441$	−7.47746	+	12.9513i	−0.356070	+	0.616731i
$442$	−1.72563	−	40.1803i	−0.0820799	−	1.91118i
$443$	−13.7557	−	7.94188i	−0.653555	−	0.377330i	0.136262	−	0.990673i	$-0.456491\pi$
$443$	−13.7557	−	7.94188i	−0.653555	−	0.377330i	−0.789817	+	0.613343i	$0.789824\pi$
$444$	13.5267	−	9.44283i	0.641951	−	0.448137i
$445$		−	9.97571i		−	0.472894i
$446$	19.6862	+	30.9498i	0.932169	+	1.46552i
$447$	5.86776	−	10.1633i	0.277536	−	0.480706i
$448$	8.30466	+	31.5320i	0.392359	+	1.48975i
$449$			12.1366i			0.572764i	0.958116	+	0.286382i	$0.0924526\pi$
$449$			12.1366i			0.572764i	−0.958116	+	0.286382i	$0.907547\pi$
$450$	1.18078	+	1.85638i	0.0556627	+	0.0875105i
$451$	2.06083	+	3.56947i	0.0970408	+	0.168080i
$452$	−0.791949	−	9.20303i	−0.0372501	−	0.432874i
$453$	−6.45676	−	11.1834i	−0.303365	−	0.525444i
$454$	23.9171	−	1.02717i	1.12248	−	0.0482075i
$455$	−19.5356			−0.915845
$456$	0.114308	+	14.8162i	0.00535296	+	0.693834i
$457$	−27.9129			−1.30571			−0.652856	−	0.757482i	$-0.726429\pi$
$457$	−27.9129			−1.30571			−0.652856	+	0.757482i	$0.726429\pi$
$458$	11.2976	−	0.485199i	0.527900	−	0.0226718i
$459$	16.2423	+	28.1326i	0.758128	+	1.31312i
$460$	−0.215463	−	2.50384i	−0.0100460	−	0.116742i
$461$	15.6566	+	27.1180i	0.729200	+	1.26301i	0.957222	+	0.289355i	$0.0934409\pi$
$461$	15.6566	+	27.1180i	0.729200	+	1.26301i	−0.228022	+	0.973656i	$0.573226\pi$
$462$	−1.95658	−	3.07605i	−0.0910284	−	0.143111i
$463$		−	13.2760i		−	0.616988i	−0.951226	−	0.308494i	$-0.900175\pi$
$463$		−	13.2760i		−	0.616988i	0.951226	−	0.308494i	$-0.0998250\pi$
$464$	−11.6864	−	4.29126i	−0.542528	−	0.199217i
$465$	−0.0176905	+	0.0306408i	−0.000820376	+	0.00142093i
$466$	5.37426	+	8.44918i	0.248958	+	0.391401i
$467$			12.1070i			0.560247i	0.959964	+	0.280124i	$0.0903754\pi$
$467$			12.1070i			0.560247i	−0.959964	+	0.280124i	$0.909625\pi$
$468$	12.2280	−	8.53621i	0.565240	−	0.394587i
$469$	7.12197	+	4.11187i	0.328862	+	0.189868i
$470$	0.0635770	+	1.48035i	0.00293259	+	0.0682836i
$471$	10.4627	−	18.1220i	0.482098	−	0.835018i
$472$	−3.55935	−	4.65923i	−0.163833	−	0.214458i
$473$	−1.35523	−	2.34733i	−0.0623136	−	0.107930i
$474$	−10.7140	+	20.5457i	−0.492112	+	0.943696i
$475$	4.01047	−	1.70767i	0.184013	−	0.0783534i
$476$	39.6594	−	27.6857i	1.81778	−	1.26897i
$477$	4.27058	−	2.46562i	0.195536	−	0.112893i
$478$	−1.66341	−	38.7316i	−0.0760827	−	1.77154i
$479$	−3.31240	−	1.91242i	−0.151348	−	0.0873806i	0.422414	−	0.906403i	$-0.361183\pi$
$479$	−3.31240	−	1.91242i	−0.151348	−	0.0873806i	−0.573761	+	0.819023i	$0.694516\pi$
$480$	2.06739	−	6.47639i	0.0943629	−	0.295605i
$481$	−16.4479	+	28.4886i	−0.749960	+	1.29897i
$482$	7.92756	+	4.13401i	0.361090	+	0.188299i
$483$	−6.15505			−0.280064
$484$	21.3671	−	1.83871i	0.971233	−	0.0835776i
$485$	13.0162	+	7.51491i	0.591035	+	0.341234i
$486$	−9.23726	+	17.7138i	−0.419011	+	0.803514i
$487$	−2.55151			−0.115620			−0.0578099	−	0.998328i	$-0.518412\pi$
$487$	−2.55151			−0.115620			−0.0578099	+	0.998328i	$0.518412\pi$
$488$	−11.9190	+	28.6019i	−0.539547	+	1.29475i
$489$	21.1527	−	12.2125i	0.956557	−	0.552269i
$490$	−7.29633	−	11.4710i	−0.329614	−	0.518205i
$491$	−4.86667	+	2.80977i	−0.219630	+	0.126803i	−0.605779	−	0.795633i	$-0.707138\pi$
$491$	−4.86667	+	2.80977i	−0.219630	+	0.126803i	0.386149	+	0.922436i	$0.373805\pi$
$492$	17.0498	+	7.98004i	0.768664	+	0.359768i
$493$			18.4664i			0.831685i
$494$	−12.7308	−	26.6623i	−0.572786	−	1.19959i
$495$		−	0.818700i		−	0.0367978i
$496$	−0.116029	+	0.0201184i	−0.00520987	+	0.000903341i
$497$	20.7645	−	11.9884i	0.931416	−	0.537753i
$498$	12.5109	−	7.95778i	0.560625	−	0.356596i
$499$	30.3735	−	17.5362i	1.35971	−	0.785027i	0.370122	−	0.928983i	$-0.379316\pi$
$499$	30.3735	−	17.5362i	1.35971	−	0.785027i	0.989584	+	0.143956i	$0.0459824\pi$
$500$	−1.99264	+	0.171472i	−0.0891134	+	0.00766848i
$501$	14.4187			0.644182
$502$	−2.67819	−	1.39660i	−0.119534	−	0.0623335i
$503$	35.7628	+	20.6477i	1.59459	+	0.920635i	0.992506	+	0.122200i	$0.0389949\pi$
$503$	35.7628	+	20.6477i	1.59459	+	0.920635i	0.602081	+	0.798435i	$0.294338\pi$
$504$	16.5548	+	6.89871i	0.737410	+	0.307293i
$505$	9.93056			0.441904
$506$	−0.432407	+	0.829203i	−0.0192228	+	0.0368625i
$507$	5.99240	−	10.3791i	0.266132	−	0.460954i
$508$	2.21308	−	4.72837i	0.0981896	−	0.209787i
$509$	−14.8524	−	8.57503i	−0.658320	−	0.380081i	0.133316	−	0.991074i	$-0.457437\pi$
$509$	−14.8524	−	8.57503i	−0.658320	−	0.380081i	−0.791637	+	0.610992i	$0.790771\pi$
$510$	−10.0749	+	0.432686i	−0.446122	+	0.0191597i
$511$	10.2695	−	5.92912i	0.454298	−	0.262289i
$512$	20.9601	−	8.52492i	0.926314	−	0.376752i
$513$	19.0756	+	14.3408i	0.842206	+	0.633163i
$514$	−15.8486	−	8.26459i	−0.699050	−	0.364536i
$515$	−9.23251	−	15.9912i	−0.406833	−	0.704655i
$516$	−11.2122	−	5.24778i	−0.493588	−	0.231021i
$517$	0.275689	−	0.477508i	0.0121248	−	0.0210008i
$518$	−39.5254	+	1.69750i	−1.73664	+	0.0745840i
$519$	22.2737	+	12.8597i	0.977708	+	0.564480i
$520$	1.74075	+	13.4443i	0.0763370	+	0.589572i
$521$		−	18.9402i		−	0.829785i	−0.909870	−	0.414892i	$-0.863819\pi$
$521$		−	18.9402i		−	0.829785i	0.909870	−	0.414892i	$-0.136181\pi$
$522$	−5.77769	+	3.67501i	−0.252883	+	0.160851i
$523$	−8.59153	+	14.8810i	−0.375681	+	0.650699i	−0.990429	−	0.138025i	$-0.955925\pi$
$523$	−8.59153	+	14.8810i	−0.375681	+	0.650699i	0.614747	+	0.788724i	$0.289258\pi$
$524$	37.2030	−	25.9709i	1.62522	−	1.13454i
$525$			4.89839i			0.213783i
$526$	27.3607	−	17.4033i	1.19298	−	0.758819i
$527$	0.0873384	+	0.151274i	0.00380452	+	0.00658962i
$528$	−1.94258	+	1.62060i	−0.0845398	+	0.0705277i
$529$	−10.7105	−	18.5512i	−0.465676	−	0.806574i
$530$	0.192345	+	4.47863i	0.00835492	+	0.194539i
$531$	−3.22490			−0.139949
$532$	18.8386	−	30.1280i	0.816757	−	1.30621i
$533$	−37.5385			−1.62597
$534$	0.727482	+	16.9390i	0.0314812	+	0.733022i
$535$	0.953216	+	1.65102i	0.0412111	+	0.0713798i
$536$	2.19515	−	5.26769i	0.0948160	−	0.227529i
$537$	−1.71034	−	2.96240i	−0.0738067	−	0.127837i
$538$	23.2200	−	14.7696i	1.00109	−	0.636761i
$539$			5.05893i			0.217903i
$540$	−6.26787	−	8.97865i	−0.269726	−	0.386380i
$541$	1.69560	−	2.93687i	0.0728997	−	0.126266i	−0.827271	−	0.561803i	$-0.810108\pi$
$541$	1.69560	−	2.93687i	0.0728997	−	0.126266i	0.900171	+	0.435537i	$0.143441\pi$
$542$	7.95173	−	5.05785i	0.341556	−	0.217253i
$543$			23.8491i			1.02346i
$544$	−22.5870	−	24.8264i	−0.968410	−	1.06442i
$545$	−16.1809	−	9.34203i	−0.693113	−	0.400169i
$546$	33.1720	−	1.42464i	1.41963	−	0.0609691i
$547$	−3.01376	+	5.21999i	−0.128859	+	0.223191i	−0.923235	−	0.384236i	$-0.874465\pi$
$547$	−3.01376	+	5.21999i	−0.128859	+	0.223191i	0.794376	+	0.607427i	$0.207798\pi$
$548$	8.69665	−	18.5809i	0.371502	−	0.793735i
$549$	8.52149	+	14.7597i	0.363688	+	0.629927i
$550$	0.659906	+	0.344123i	0.0281385	+	0.0146735i
$551$	5.31487	+	12.4820i	0.226421	+	0.531749i
$552$	0.548455	+	4.23586i	0.0233438	+	0.180290i
$553$	48.1243	−	27.7846i	2.04645	−	1.18152i
$554$	7.72580	−	0.331801i	0.328238	−	0.0140969i
$555$	7.14326	+	4.12417i	0.303215	+	0.175061i
$556$	−9.16283	−	4.28860i	−0.388591	−	0.181877i
$557$	11.1446	−	19.3029i	0.472210	−	0.817892i	−0.527284	−	0.849689i	$-0.676790\pi$
$557$	11.1446	−	19.3029i	0.472210	−	0.817892i	0.999494	+	0.0317969i	$0.0101230\pi$
$558$	−0.0299488	+	0.0574312i	−0.00126784	+	0.00243126i
$559$	24.6858			1.04410
$560$	−12.5191	+	10.4441i	−0.529029	+	0.441345i
$561$	3.24978	+	1.87626i	0.137206	+	0.0792158i
$562$	16.1366	+	8.41479i	0.680681	+	0.354957i
$563$	−10.9572			−0.461792			−0.230896	−	0.972978i	$-0.574166\pi$
$563$	−10.9572			−0.461792			−0.230896	+	0.972978i	$0.574166\pi$
$564$	−0.215910	−	2.50904i	−0.00909147	−	0.105650i
$565$	3.99975	−	2.30926i	0.168271	−	0.0971513i
$566$	−27.0393	+	17.1989i	−1.13655	+	0.722922i
$567$	−6.75155	+	3.89801i	−0.283539	+	0.163701i
$568$	−10.1006	−	13.2218i	−0.423811	−	0.554773i
$569$			22.9811i			0.963418i	0.876331	+	0.481709i	$0.159984\pi$
$569$			22.9811i			0.963418i	−0.876331	+	0.481709i	$0.840016\pi$
$570$	−6.68534	+	3.19213i	−0.280018	+	0.133704i
$571$			32.5544i			1.36236i	0.732117	+	0.681179i	$0.238533\pi$
$571$			32.5544i			1.36236i	−0.732117	+	0.681179i	$0.761467\pi$
$572$	2.13848	−	4.56899i	0.0894145	−	0.191039i
$573$	24.9587	−	14.4099i	1.04267	−	0.601984i
$574$	−24.2294	−	38.0924i	−1.01132	−	1.58995i
$575$	1.08820	−	0.628273i	0.0453811	−	0.0262008i
$576$	3.27251	−	12.0076i	0.136355	−	0.500318i
$577$	8.63484			0.359473			0.179736	−	0.983715i	$-0.442475\pi$
$577$	8.63484			0.359473			0.179736	+	0.983715i	$0.442475\pi$
$578$	−11.9035	+	22.8268i	−0.495122	+	0.949469i
$579$	−24.7837	−	14.3089i	−1.02998	−	0.594657i
$580$	−0.533681	−	6.20177i	−0.0221599	−	0.257514i
$581$	−35.5583			−1.47521
$582$	−22.6499	−	11.8113i	−0.938867	−	0.489594i
$583$	0.834066	−	1.44464i	0.0345435	−	0.0598310i
$584$	−4.99547	−	6.53911i	−0.206714	−	0.270590i
$585$	6.45743	+	3.72820i	0.266982	+	0.154142i
$586$	0.423362	+	9.85774i	0.0174889	+	0.407220i
$587$	37.5112	−	21.6571i	1.54825	−	0.893885i	0.549979	−	0.835178i	$-0.314636\pi$
$587$	37.5112	−	21.6571i	1.54825	−	0.893885i	0.998275	−	0.0587070i	$-0.0186978\pi$
$588$	13.2259	+	18.9459i	0.545425	+	0.781315i
$589$	0.102573	+	0.0771135i	0.00422645	+	0.00317741i
$590$	1.35552	−	2.59941i	0.0558059	−	0.107016i
$591$	−3.61084	−	6.25416i	−0.148530	−	0.257262i
$592$	4.69018	+	27.0499i	0.192765	+	1.11174i
$593$	−19.5360	+	33.8373i	−0.802246	+	1.38953i	0.115889	+	0.993262i	$0.463028\pi$
$593$	−19.5360	+	33.8373i	−0.802246	+	1.38953i	−0.918135	+	0.396268i	$0.870305\pi$
$594$	0.174837	+	4.07097i	0.00717364	+	0.167034i
$595$	20.9435	+	12.0917i	0.858600	+	0.495713i
$596$	11.1792	+	16.0140i	0.457917	+	0.655960i
$597$		−	14.7081i		−	0.601964i
$598$	−4.57117	−	7.18659i	−0.186929	−	0.293882i
$599$	−8.73590	+	15.1310i	−0.356939	+	0.618237i	−0.987448	−	0.157945i	$-0.949513\pi$
$599$	−8.73590	+	15.1310i	−0.356939	+	0.618237i	0.630509	+	0.776182i	$0.282846\pi$
$600$	3.37104	−	0.436478i	0.137622	−	0.0178191i
$601$		−	23.3148i		−	0.951029i	−0.879708	−	0.475515i	$-0.842262\pi$
$601$		−	23.3148i		−	0.951029i	0.879708	−	0.475515i	$-0.157738\pi$
$602$	15.9336	+	25.0501i	0.649404	+	1.02096i
$603$	−1.56943	−	2.71832i	−0.0639119	−	0.110699i
$604$	21.4113	−	1.84251i	0.871215	−	0.0749707i
$605$	5.36153	+	9.28643i	0.217977	+	0.377547i
$606$	−16.8623	+	0.724189i	−0.684985	+	0.0294182i
$607$	1.37342			0.0557453			0.0278726	−	0.999611i	$-0.491127\pi$
$607$	1.37342			0.0557453			0.0278726	+	0.999611i	$0.491127\pi$
$608$	−22.4125	−	10.2800i	−0.908948	−	0.416909i
$609$	−15.2455			−0.617778
$610$	−15.4787	+	0.664767i	−0.626715	+	0.0269156i
$611$	2.51087	+	4.34895i	0.101579	+	0.175940i
$612$	−18.3928	+	1.58276i	−0.743485	+	0.0639792i
$613$	3.86267	+	6.69034i	0.156012	+	0.270220i	0.933427	−	0.358768i	$-0.116803\pi$
$613$	3.86267	+	6.69034i	0.156012	+	0.270220i	−0.777415	+	0.628988i	$0.783470\pi$
$614$	16.8286	+	26.4572i	0.679147	+	1.06773i
$615$			9.41244i			0.379546i
$616$	6.01670	−	0.779035i	0.242420	−	0.0313882i
$617$	6.10501	−	10.5742i	0.245779	−	0.425701i	−0.716572	−	0.697514i	$-0.754290\pi$
$617$	6.10501	−	10.5742i	0.245779	−	0.425701i	0.962350	+	0.271812i	$0.0876230\pi$
$618$	16.8432	+	26.4801i	0.677532	+	1.06519i
$619$		−	8.95263i		−	0.359836i	−0.983682	−	0.179918i	$-0.942417\pi$
$619$		−	8.95263i		−	0.359836i	0.983682	−	0.179918i	$-0.0575833\pi$
$620$	−0.0337036	−	0.0482800i	−0.00135357	−	0.00193897i
$621$	5.95789	+	3.43979i	0.239082	+	0.138034i
$622$	−0.826501	−	19.2446i	−0.0331397	−	0.771638i
$623$	20.3300	−	35.2126i	0.814505	−	1.41076i
$624$	−3.93627	−	22.7018i	−0.157577	−	0.908800i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	5.09998	−	9.77995i	0.203836	−	0.390886i
$627$	2.73663	+	0.332890i	0.109290	+	0.0132943i
$628$	19.9335	+	28.5545i	0.795432	+	1.13945i
$629$	35.2665	−	20.3611i	1.40617	−	0.811851i
$630$	0.384768	+	8.95910i	0.0153295	+	0.356939i
$631$	9.43410	+	5.44678i	0.375566	+	0.216833i	0.675887	−	0.737005i	$-0.263761\pi$
$631$	9.43410	+	5.44678i	0.375566	+	0.216833i	−0.300322	+	0.953838i	$0.597094\pi$
$632$	−23.4093	−	30.6430i	−0.931174	−	1.21891i
$633$	1.55963	−	2.70136i	0.0619898	−	0.107369i
$634$	−16.3576	−	8.53005i	−0.649644	−	0.338772i
$635$	2.61032			0.103588
$636$	−0.653212	−	7.59080i	−0.0259015	−	0.300995i
$637$	−39.9019	−	23.0373i	−1.58097	−	0.912773i
$638$	−1.07103	+	2.05386i	−0.0424025	+	0.0813130i
$639$	−9.15150			−0.362028
$640$	8.30312	+	7.68493i	0.328210	+	0.303774i
$641$	−12.1852	+	7.03511i	−0.481285	+	0.277870i	−0.720952	−	0.692985i	$-0.756295\pi$
$641$	−12.1852	+	7.03511i	−0.481285	+	0.277870i	0.239667	+	0.970855i	$0.422962\pi$
$642$	−1.73898	−	2.73396i	−0.0686323	−	0.107901i
$643$	31.6981	−	18.3009i	1.25005	−	0.721717i	0.278931	−	0.960311i	$-0.410020\pi$
$643$	31.6981	−	18.3009i	1.25005	−	0.721717i	0.971119	+	0.238595i	$0.0766867\pi$
$644$	4.34215	−	9.27724i	0.171105	−	0.365575i
$645$		−	6.18974i		−	0.243721i
$646$	−2.85459	+	36.4636i	−0.112312	+	1.43464i
$647$			10.2258i			0.402019i	0.979589	+	0.201010i	$0.0644223\pi$
$647$			10.2258i			0.402019i	−0.979589	+	0.201010i	$0.935578\pi$
$648$	3.28419	+	4.29904i	0.129015	+	0.168882i
$649$	−0.944761	+	0.545458i	−0.0370851	+	0.0214111i
$650$	−5.71933	+	3.63789i	−0.224330	+	0.142690i
$651$	−0.124889	+	0.0721046i	−0.00489478	+	0.00282600i
$652$	3.48498	+	40.4980i	0.136482	+	1.58602i
$653$	−17.9621			−0.702910			−0.351455	−	0.936205i	$-0.614313\pi$
$653$	−17.9621			−0.702910			−0.351455	+	0.936205i	$0.614313\pi$
$654$	28.1568	+	14.6830i	1.10102	+	0.574151i
$655$	19.6463	+	11.3428i	0.767646	+	0.443200i
$656$	−24.0560	+	20.0688i	−0.939227	+	0.783555i
$657$	−4.52607			−0.176579
$658$	−2.79247	+	5.35497i	−0.108862	+	0.208758i
$659$	−21.2416	+	36.7915i	−0.827454	+	1.43319i	0.0725760	+	0.997363i	$0.476878\pi$
$659$	−21.2416	+	36.7915i	−0.827454	+	1.43319i	−0.900030	+	0.435829i	$0.856455\pi$
$660$	−1.14563	−	0.536206i	−0.0445937	−	0.0208718i
$661$	−6.50692	−	3.75677i	−0.253090	−	0.146121i	0.368088	−	0.929791i	$-0.380012\pi$
$661$	−6.50692	−	3.75677i	−0.253090	−	0.146121i	−0.621178	+	0.783669i	$0.713346\pi$
$662$	29.9437	−	1.28600i	1.16380	−	0.0499817i
$663$	−29.5977	+	17.0882i	−1.14948	+	0.663652i
$664$	3.16848	+	24.4710i	0.122961	+	0.949660i
$665$	17.6365	+	2.14534i	0.683912	+	0.0831926i
$666$	13.3889	+	6.98195i	0.518810	+	0.270545i
$667$	1.95540	+	3.38686i	0.0757135	+	0.131140i
$668$	−10.1719	+	21.7328i	−0.393562	+	0.840866i
$669$	15.5853	−	26.9946i	0.602563	−	1.04367i
$670$	2.85076	−	0.122432i	0.110134	−	0.00472996i
$671$	4.99287	+	2.88264i	0.192748	+	0.111283i
$672$	20.4961	−	18.6473i	0.790655	−	0.719337i
$673$		−	14.0880i		−	0.543053i	−0.962431	−	0.271526i	$-0.912472\pi$
$673$		−	14.0880i		−	0.543053i	0.962431	−	0.271526i	$-0.0875284\pi$
$674$	−21.7312	+	13.8225i	−0.837055	+	0.532425i
$675$	2.73750	−	4.74149i	0.105366	−	0.182500i
$676$	11.4166	+	16.3542i	0.439101	+	0.629007i
$677$			15.4872i			0.595222i	0.954687	+	0.297611i	$0.0961898\pi$
$677$			15.4872i			0.595222i	−0.954687	+	0.297611i	$0.903810\pi$
$678$	−6.62328	+	4.21286i	−0.254365	+	0.161794i
$679$	30.6301	+	53.0528i	1.17547	+	2.03598i
$680$	6.45526	−	15.4906i	0.247548	−	0.594039i
$681$	−10.1717	−	17.6179i	−0.389779	−	0.675118i
$682$	0.000940133		0.0218905i	3.59996e−5		0.000838229i
$683$	−0.144140			−0.00551538			−0.00275769	−	0.999996i	$-0.500878\pi$
$683$	−0.144140			−0.00551538			−0.00275769	+	0.999996i	$0.500878\pi$
$684$	−11.9767	+	6.36351i	−0.457939	+	0.243315i
$685$	10.2577			0.391926
$686$	−0.646268	−	15.0480i	−0.0246746	−	0.574534i
$687$	−4.80473	−	8.32204i	−0.183312	−	0.317505i
$688$	15.8195	−	13.1975i	0.603113	−	0.503150i
$689$	7.59634	+	13.1572i	0.289397	+	0.501251i
$690$	−1.80197	+	1.14618i	−0.0686000	+	0.0436343i
$691$		−	43.9721i		−	1.67278i	−0.548138	−	0.836388i	$-0.684663\pi$
$691$		−	43.9721i		−	1.67278i	0.548138	−	0.836388i	$-0.315337\pi$
$692$	−35.0962	+	24.5002i	−1.33416	+	0.931358i
$693$	1.66847	−	2.88988i	0.0633800	−	0.109777i
$694$	23.8721	−	15.1843i	0.906171	−	0.576388i
$695$		−	5.05840i		−	0.191876i
$696$	1.35847	+	10.4918i	0.0514927	+	0.397692i
$697$	40.2438	+	23.2347i	1.52434	+	0.880079i
$698$	−45.5942	+	1.95814i	−1.72577	+	0.0741168i
$699$	4.25473	−	7.36941i	0.160929	−	0.278737i
$700$	−7.38313	−	3.45563i	−0.279056	−	0.130610i
$701$	−4.56023	−	7.89855i	−0.172238	−	0.298324i	0.766964	−	0.641690i	$-0.221766\pi$
$701$	−4.56023	−	7.89855i	−0.172238	−	0.298324i	−0.939202	+	0.343366i	$0.888433\pi$
$702$	−32.9056	−	17.1594i	−1.24194	−	0.647640i
$703$	17.9774	−	23.9128i	0.678031	−	0.901888i
$704$	−1.07225	−	4.07124i	−0.0404121	−	0.153441i
$705$	1.09046	−	0.629578i	0.0410691	−	0.0237113i
$706$	−23.5715	+	1.01233i	−0.887126	+	0.0380995i
$707$	35.0532	+	20.2380i	1.31831	+	0.761128i
$708$	−2.11214	+	4.51271i	−0.0793792	+	0.169598i
$709$	−0.987579	+	1.71054i	−0.0370893	+	0.0642405i	−0.883974	−	0.467536i	$-0.845142\pi$
$709$	−0.987579	+	1.71054i	−0.0370893	+	0.0642405i	0.846885	+	0.531776i	$0.178475\pi$
$710$	3.84664	−	7.37649i	0.144362	−	0.276835i
$711$	−21.2097			−0.795426
$712$	−26.0446	−	10.8533i	−0.976064	−	0.406745i
$713$	0.0320368	+	0.0184965i	0.00119979	+	0.000692698i
$714$	−36.4444	−	19.0048i	−1.36390	−	0.711235i
$715$	2.52234			0.0943301
$716$	5.67168	−	0.488066i	0.211961	−	0.0182399i
$717$	−28.5305	+	16.4721i	−1.06549	+	0.615162i
$718$	0.920540	−	0.585527i	0.0343542	−	0.0218517i
$719$	12.2551	−	7.07550i	0.457039	−	0.263872i	−0.253759	−	0.967267i	$-0.581667\pi$
$719$	12.2551	−	7.07550i	0.457039	−	0.263872i	0.710798	+	0.703396i	$0.248334\pi$
$720$	6.13131	−	1.06311i	0.228500	−	0.0396197i
$721$		−	75.2616i		−	2.80289i
$722$	8.56519	+	25.4684i	0.318763	+	0.947834i
$723$		−	7.59776i		−	0.282564i
$724$	−35.9467	−	16.8246i	−1.33595	−	0.625282i
$725$	2.69537	−	1.55617i	0.100104	−	0.0577948i
$726$	−9.78122	−	15.3776i	−0.363015	−	0.570716i
$727$	−41.4579	+	23.9357i	−1.53759	+	0.887728i	−0.538610	+	0.842555i	$0.681050\pi$
$727$	−41.4579	+	23.9357i	−1.53759	+	0.887728i	−0.998979	+	0.0451724i	$0.985616\pi$
$728$	−21.2543	+	51.0038i	−0.787736	+	1.89033i
$729$	22.7150			0.841297
$730$	1.90244	−	3.64820i	0.0704124	−	0.135026i
$731$	−26.4648	−	15.2795i	−0.978837	−	0.565132i
$732$	26.2348	−	2.25758i	0.969665	−	0.0834426i
$733$	33.3485			1.23175			0.615877	−	0.787843i	$-0.288802\pi$
$733$	33.3485			1.23175			0.615877	+	0.787843i	$0.288802\pi$
$734$	−34.2869	−	17.8797i	−1.26555	−	0.659951i
$735$	−5.77641	+	10.0050i	−0.213066	+	0.369041i
$736$	−6.77145	−	2.16158i	−0.249599	−	0.0796769i
$737$	−0.919550	−	0.530903i	−0.0338721	−	0.0195561i
$738$	0.739346	+	17.2153i	0.0272157	+	0.633702i
$739$	−4.60071	+	2.65622i	−0.169240	+	0.0977107i	−0.582227	−	0.813026i	$-0.697819\pi$
$739$	−4.60071	+	2.65622i	−0.169240	+	0.0977107i	0.412987	+	0.910737i	$0.364485\pi$
$740$	−11.2555	+	7.85730i	−0.413760	+	0.288840i
$741$	−15.0877	+	20.0690i	−0.554261	+	0.737254i
$742$	−8.44829	+	16.2008i	−0.310147	+	0.594751i
$743$	−13.5500	−	23.4694i	−0.497103	−	0.861007i	0.502892	−	0.864349i	$-0.332269\pi$
$743$	−13.5500	−	23.4694i	−0.497103	−	0.861007i	−0.999994	+	0.00334240i	$0.998936\pi$
$744$	0.0607504	+	0.0795228i	0.00222722	+	0.00291545i
$745$	−4.88251	+	8.45676i	−0.178881	+	0.309832i
$746$	1.20223	+	27.9933i	0.0440169	+	1.02491i
$747$	11.7537	+	6.78598i	0.430044	+	0.248286i
$748$	−5.12061	+	3.57463i	−0.187228	+	0.130701i
$749$			7.77044i			0.283926i
$750$	0.912167	+	1.43407i	0.0333076	+	0.0523648i
$751$	9.22783	−	15.9831i	0.336728	−	0.583231i	−0.647087	−	0.762416i	$-0.724013\pi$
$751$	9.22783	−	15.9831i	0.336728	−	0.583231i	0.983815	+	0.179186i	$0.0573463\pi$
$752$	3.93408	+	1.44460i	0.143461	+	0.0526791i
$753$			2.56678i			0.0935385i
$754$	−11.3224	−	17.8005i	−0.412336	−	0.648257i
$755$	5.37262	+	9.30564i	0.195530	+	0.338667i
$756$	−3.82651	−	44.4668i	−0.139169	−	1.61724i
$757$	1.38188	+	2.39348i	0.0502252	+	0.0869927i	0.890045	−	0.455873i	$-0.150673\pi$
$757$	1.38188	+	2.39348i	0.0502252	+	0.0869927i	−0.839820	+	0.542865i	$0.817339\pi$
$758$	−32.5170	+	1.39651i	−1.18107	+	0.0507236i
$759$	0.794707			0.0288460
$760$	−0.0951146	−	12.3285i	−0.00345017	−	0.447200i
$761$	9.16614			0.332272			0.166136	−	0.986103i	$-0.446871\pi$
$761$	9.16614			0.332272			0.166136	+	0.986103i	$0.446871\pi$
$762$	−4.43239	+	0.190359i	−0.160569	+	0.00689597i
$763$	−38.0772	−	65.9517i	−1.37849	−	2.38761i
$764$	4.11204	+	47.7849i	0.148768	+	1.72880i
$765$	−4.61520	−	7.99375i	−0.166863	−	0.289015i
$766$	−26.8723	−	42.2474i	−0.970935	−	1.52646i
$767$		−	9.93562i		−	0.358755i
$768$	−14.6593	−	12.4437i	−0.528973	−	0.449023i
$769$	0.0257927	−	0.0446742i	0.000930108	−	0.00161099i	−0.865560	−	0.500805i	$-0.833037\pi$
$769$	0.0257927	−	0.0446742i	0.000930108	−	0.00161099i	0.866490	+	0.499194i	$0.166371\pi$
$770$	1.62806	+	2.55956i	0.0586710	+	0.0922400i
$771$			15.1892i			0.547027i
$772$	39.0512	−	27.2611i	1.40548	−	0.981148i
$773$	−16.3980	−	9.46740i	−0.589796	−	0.340519i	0.175221	−	0.984529i	$-0.443936\pi$
$773$	−16.3980	−	9.46740i	−0.589796	−	0.340519i	−0.765017	+	0.644010i	$0.777269\pi$
$774$	−0.486204	−	11.3210i	−0.0174762	−	0.406924i
$775$	0.0147201	−	0.0254959i	0.000528761	−	0.000915841i
$776$	33.7813	−	25.8068i	1.21268	−	0.926409i
$777$	16.8097	+	29.1153i	0.603045	+	1.04450i
$778$	18.9167	−	36.2756i	0.678198	−	1.30054i
$779$	33.8891	+	4.12235i	1.21420	+	0.147699i
$780$	9.44626	−	6.59430i	0.338230	−	0.236114i
$781$	−2.68100	+	1.54788i	−0.0959338	+	0.0553874i
$782$	0.452400	+	10.5339i	0.0161778	+	0.376690i
$783$	14.7571	+	8.52004i	0.527377	+	0.304481i
$784$	−37.8867	+	6.56918i	−1.35310	+	0.234614i
$785$	−8.70596	+	15.0792i	−0.310729	+	0.538199i
$786$	−34.1871	−	17.8277i	−1.21941	−	0.635891i
$787$	23.8888			0.851543			0.425772	−	0.904831i	$-0.360003\pi$
$787$	23.8888			0.851543			0.425772	+	0.904831i	$0.360003\pi$
$788$	11.9740	−	1.03040i	0.426554	−	0.0367063i
$789$	−23.8641	−	13.7780i	−0.849585	−	0.490508i
$790$	8.91505	−	17.0959i	0.317183	−	0.608245i
$791$	18.8246			0.669327
$792$	−2.13747	−	0.890725i	−0.0759516	−	0.0316505i
$793$	−45.4731	+	26.2539i	−1.61480	+	0.932303i
$794$	6.79625	+	10.6848i	0.241190	+	0.379188i
$795$	3.29906	−	1.90471i	0.117006	−	0.0675532i
$796$	22.1690	+	10.3760i	0.785758	+	0.367769i
$797$		−	34.7913i		−	1.23237i	−0.787600	−	0.616186i	$-0.788677\pi$
$797$		−	34.7913i		−	1.23237i	0.787600	−	0.616186i	$-0.211323\pi$
$798$	−30.1036	−	2.35669i	−1.06565	−	0.0834259i
$799$		−	6.21649i		−	0.219923i
$800$	−1.72026	+	5.38894i	−0.0608202	+	0.190528i
$801$	−13.4400	+	7.75960i	−0.474880	+	0.274172i
$802$	5.86522	−	3.73069i	0.207108	−	0.131735i
$803$	−1.32595	+	0.765537i	−0.0467917	+	0.0270152i
$804$	−4.83173	+	0.415785i	−0.170402	+	0.0146636i
$805$	5.12156			0.180511
$806$	−0.176940	−	0.0922695i	−0.00623245	−	0.00325006i
$807$	−20.2526	−	11.6929i	−0.712927	−	0.411608i
$808$	10.8042	−	25.9268i	0.380090	−	0.912100i
$809$	5.81156			0.204324			0.102162	−	0.994768i	$-0.467424\pi$
$809$	5.81156			0.204324			0.102162	+	0.994768i	$0.467424\pi$
$810$	−1.25073	+	2.39846i	−0.0439462	+	0.0842732i
$811$	9.57870	−	16.5908i	0.336354	−	0.582581i	−0.647390	−	0.762159i	$-0.724140\pi$
$811$	9.57870	−	16.5908i	0.336354	−	0.582581i	0.983744	+	0.179577i	$0.0574730\pi$
$812$	10.7551	−	22.9789i	0.377430	−	0.806400i
$813$	−6.93554	−	4.00424i	−0.243240	−	0.140435i
$814$	5.10331	−	0.219173i	0.178871	−	0.00768200i
$815$	−17.6010	+	10.1619i	−0.616535	+	0.355957i
$816$	−9.83152	+	26.7742i	−0.344172	+	0.937286i
$817$	−22.2859	−	2.71091i	−0.779686	−	0.0948428i
$818$	12.5180	+	6.52778i	0.437681	+	0.228239i
$819$	15.1958	+	26.3199i	0.530983	+	0.919690i
$820$	−14.1870	−	6.64012i	−0.495431	−	0.231883i
$821$	−13.6571	+	23.6548i	−0.476637	+	0.825559i	−0.999642	−	0.0267704i	$-0.991478\pi$
$821$	−13.6571	+	23.6548i	−0.476637	+	0.825559i	0.523005	+	0.852330i	$0.324811\pi$
$822$	−17.4178	+	0.748045i	−0.607515	+	0.0260911i
$823$	42.4795	+	24.5256i	1.48074	+	0.854907i	0.999762	−	0.0218244i	$-0.00694747\pi$
$823$	42.4795	+	24.5256i	1.48074	+	0.854907i	0.480980	+	0.876731i	$0.340281\pi$
$824$	−51.7946	+	6.70630i	−1.80435	+	0.233625i
$825$		−	0.632454i		−	0.0220192i
$826$	10.0822	−	6.41300i	0.350806	−	0.223137i
$827$	−6.66089	+	11.5370i	−0.231622	+	0.401181i	−0.958286	−	0.285813i	$-0.907737\pi$
$827$	−6.66089	+	11.5370i	−0.231622	+	0.401181i	0.726664	+	0.686993i	$0.241070\pi$
$828$	−3.20576	+	2.23790i	−0.111408	+	0.0777722i
$829$		−	7.39280i		−	0.256763i	−0.991725	−	0.128381i	$-0.959022\pi$
$829$		−	7.39280i		−	0.256763i	0.991725	−	0.128381i	$-0.0409781\pi$
$830$	−10.4102	+	6.62160i	−0.361343	+	0.229839i
$831$	−3.28570	−	5.69100i	−0.113980	−	0.197418i
$832$	36.9944	+	10.0823i	1.28255	+	0.349541i
$833$	28.5183	+	49.3951i	0.988100	+	1.71144i
$834$	0.368885	+	8.58928i	0.0127735	+	0.297423i
$835$	−11.9977			−0.415198
$836$	−2.43234	+	3.88996i	−0.0841242	+	0.134537i
$837$	0.161185			0.00557136
$838$	1.58112	+	36.8154i	0.0546187	+	1.27177i
$839$	−4.27082	−	7.39728i	−0.147445	−	0.255383i	0.782837	−	0.622226i	$-0.213772\pi$
$839$	−4.27082	−	7.39728i	−0.147445	−	0.255383i	−0.930283	+	0.366844i	$0.880438\pi$
$840$	12.7887	+	5.32932i	0.441253	+	0.183879i
$841$	−9.65665	−	16.7258i	−0.332988	−	0.576752i
$842$	21.2294	−	13.5034i	0.731614	−	0.465357i
$843$		−	15.4653i		−	0.532653i
$844$	2.97139	+	4.25648i	0.102279	+	0.146514i
$845$	−4.98623	+	8.63640i	−0.171531	+	0.297101i
$846$	1.94499	−	1.23715i	0.0668700	−	0.0425340i
$847$			43.7061i			1.50176i
$848$	11.9021	+	4.37046i	0.408720	+	0.150082i
$849$	23.5838	+	13.6161i	0.809394	+	0.467304i
$850$	8.38320	−	0.360035i	0.287541	−	0.0123491i
$851$	4.31207	−	7.46872i	0.147816	−	0.256024i
$852$	−5.99375	+	12.8060i	−0.205343	+	0.438726i
$853$	−2.35270	−	4.07500i	−0.0805550	−	0.139525i	0.822933	−	0.568138i	$-0.192336\pi$
$853$	−2.35270	−	4.07500i	−0.0805550	−	0.139525i	−0.903488	+	0.428612i	$0.859003\pi$
$854$	−55.9921	−	29.1984i	−1.91601	−	0.999148i
$855$	−5.42024	−	4.07489i	−0.185368	−	0.139358i
$856$	5.34757	−	0.692396i	0.182776	−	0.0236656i
$857$	−24.0965	+	13.9121i	−0.823121	+	0.475229i	−0.851491	−	0.524369i	$-0.824301\pi$
$857$	−24.0965	+	13.9121i	−0.823121	+	0.475229i	0.0283708	+	0.999597i	$0.490968\pi$
$858$	−4.28299	+	0.183942i	−0.146219	+	0.00627969i
$859$	−35.3398	−	20.4035i	−1.20578	−	0.696157i	−0.243945	−	0.969789i	$-0.578442\pi$
$859$	−35.3398	−	20.4035i	−1.20578	−	0.696157i	−0.961834	+	0.273632i	$0.911775\pi$
$860$	9.32954	+	4.36663i	0.318135	+	0.148901i
$861$	−19.1821	+	33.2244i	−0.653724	+	1.13228i
$862$	−5.11305	+	9.80502i	−0.174151	+	0.333960i
$863$	−38.8455			−1.32232			−0.661158	−	0.750247i	$-0.729935\pi$
$863$	−38.8455			−1.32232			−0.661158	+	0.750247i	$0.729935\pi$
$864$	−30.2608	+	6.59566i	−1.02949	+	0.224389i
$865$	−18.5338	−	10.7005i	−0.630167	−	0.363827i
$866$	−18.5709	−	9.68421i	−0.631064	−	0.329083i
$867$	21.8772			0.742987
$868$	−0.0205759	−	0.239107i	−0.000698391	−	0.00811582i
$869$	−6.21355	+	3.58739i	−0.210780	+	0.121694i
$870$	−4.46332	+	2.83898i	−0.151321	+	0.0962504i
$871$	8.37490	−	4.83525i	0.283773	−	0.163836i
$872$	−41.9946	+	32.0812i	−1.42212	+	1.08641i
$873$		−	23.3819i		−	0.791356i
$874$	3.33757	+	6.98993i	0.112895	+	0.236438i
$875$		−	4.07590i		−	0.137791i
$876$	−2.96434	+	6.33347i	−0.100156	+	0.213988i
$877$	0.828727	−	0.478466i	0.0279841	−	0.0161566i	−0.485943	−	0.873991i	$-0.661524\pi$
$877$	0.828727	−	0.478466i	0.0279841	−	0.0161566i	0.513927	+	0.857834i	$0.328190\pi$
$878$	11.0326	+	17.3449i	0.372331	+	0.585362i
$879$	7.26143	−	4.19239i	0.244922	−	0.141406i
$880$	1.61640	−	1.34849i	0.0544889	−	0.0454576i
$881$	27.2907			0.919448			0.459724	−	0.888062i	$-0.347948\pi$
$881$	27.2907			0.919448			0.459724	+	0.888062i	$0.347948\pi$
$882$	−9.77909	+	18.7528i	−0.329279	+	0.631441i
$883$	11.9382	+	6.89250i	0.401751	+	0.231951i	0.687239	−	0.726431i	$-0.258822\pi$
$883$	11.9382	+	6.89250i	0.401751	+	0.231951i	−0.285488	+	0.958382i	$0.592156\pi$
$884$	−4.87633	−	56.6665i	−0.164009	−	1.90590i
$885$	−2.49127			−0.0837431
$886$	−19.9176	−	10.3865i	−0.669143	−	0.348940i
$887$	−15.7173	+	27.2231i	−0.527734	+	0.914062i	0.471743	+	0.881736i	$0.343625\pi$
$887$	−15.7173	+	27.2231i	−0.527734	+	0.914062i	−0.999477	+	0.0323261i	$0.989709\pi$
$888$	18.5391	−	14.1627i	0.622131	−	0.475269i
$889$	9.21402	+	5.31972i	0.309028	+	0.178418i
$890$	−0.605332	−	14.0948i	−0.0202908	−	0.472458i
$891$	0.871725	−	0.503290i	0.0292039	−	0.0168609i
$892$	29.6929	+	42.5347i	0.994192	+	1.42417i
$893$	−1.78918	−	4.20190i	−0.0598727	−	0.140611i
$894$	7.67391	−	14.7158i	0.256654	−	0.492171i
$895$	1.42316	+	2.46499i	0.0475710	+	0.0823954i
$896$	13.6471	+	44.0479i	0.455919	+	1.47154i
$897$	−3.61894	+	6.26818i	−0.120833	+	0.209288i
$898$	0.736458	+	17.1480i	0.0245759	+	0.572236i
$899$	0.0793521	+	0.0458140i	0.00264654	+	0.00152798i
$900$	1.78099	+	2.55125i	0.0593663	+	0.0850416i
$901$		−	18.8072i		−	0.626560i
$902$	3.12837	+	4.91829i	0.104163	+	0.163761i
$903$	12.6144	−	21.8488i	0.419781	−	0.727082i
$904$	−1.67740	−	12.9550i	−0.0557894	−	0.430877i
$905$		−	19.8446i		−	0.659657i
$906$	−9.80145	−	15.4094i	−0.325631	−	0.511943i
$907$	−19.8370	−	34.3586i	−0.658675	−	1.14086i	−0.980959	−	0.194216i	$-0.937784\pi$
$907$	−19.8370	−	34.3586i	−0.658675	−	1.14086i	0.322284	−	0.946643i	$-0.395550\pi$
$908$	33.7304	−	2.90260i	1.11938	−	0.0963263i
$909$	−7.72447	−	13.3792i	−0.256205	−	0.443759i
$910$	−27.6021	+	1.18543i	−0.915002	+	0.0392967i
$911$	−7.40424			−0.245313			−0.122657	−	0.992449i	$-0.539141\pi$
$911$	−7.40424			−0.245313			−0.122657	+	0.992449i	$0.539141\pi$
$912$	1.06056	+	20.9271i	0.0351188	+	0.692965i
$913$	4.59110			0.151943
$914$	−39.4385	+	1.69377i	−1.30451	+	0.0560250i
$915$	6.58293	+	11.4020i	0.217625	+	0.376937i
$916$	15.9330	−	1.37108i	0.526442	−	0.0453019i
$917$	46.2322	+	80.0766i	1.52672	+	2.64436i
$918$	24.6561	+	38.7632i	0.813772	+	1.27938i
$919$			1.24992i			0.0412311i	0.999787	+	0.0206155i	$0.00656259\pi$
$919$			1.24992i			0.0412311i	−0.999787	+	0.0206155i	$0.993437\pi$
$920$	−0.456364	−	3.52463i	−0.0150459	−	0.116203i
$921$	13.3230	−	23.0761i	0.439008	−	0.760383i
$922$	23.7669	+	37.3653i	0.782721	+	1.23056i
$923$		−	28.1949i		−	0.928047i
$924$	−2.95113	−	4.22746i	−0.0970852	−	0.139073i
$925$	−5.94385	−	3.43168i	−0.195433	−	0.112833i
$926$	−0.805595	−	18.7578i	−0.0264735	−	0.616420i
$927$	−14.3630	+	24.8774i	−0.471743	+	0.817082i
$928$	−16.7723	−	5.35403i	−0.550576	−	0.175755i
$929$	−22.6068	−	39.1561i	−0.741705	−	1.28467i	−0.951718	−	0.306973i	$-0.900684\pi$
$929$	−22.6068	−	39.1561i	−0.741705	−	1.28467i	0.210013	−	0.977699i	$-0.432649\pi$
$930$	−0.0231358	+	0.0443662i	−0.000758651	+	0.00145482i
$931$	33.4929	+	25.1796i	1.09768	+	0.825229i
$932$	8.10606	+	11.6118i	0.265523	+	0.380358i
$933$	−14.1760	+	8.18451i	−0.464101	+	0.267949i
$934$	0.734662	+	17.1062i	0.0240389	+	0.559731i
$935$	−2.70411	−	1.56122i	−0.0884340	−	0.0510574i
$936$	16.7591	−	12.8029i	0.547789	−	0.418476i
$937$	22.5518	−	39.0609i	0.736737	−	1.27607i	−0.217220	−	0.976123i	$-0.569699\pi$
$937$	22.5518	−	39.0609i	0.736737	−	1.27607i	0.953957	−	0.299943i	$-0.0969677\pi$
$938$	10.3122	+	5.37754i	0.336706	+	0.175583i
$939$	−9.37310			−0.305879
$940$	0.179657	+	2.08775i	0.00585977	+	0.0680948i
$941$	1.30148	+	0.751410i	0.0424270	+	0.0244953i	0.521063	−	0.853518i	$-0.325535\pi$
$941$	1.30148	+	0.751410i	0.0424270	+	0.0244953i	−0.478636	+	0.878013i	$0.658869\pi$
$942$	13.6833	−	26.2397i	0.445825	−	0.854935i
$943$	9.84128			0.320476
$944$	−5.31178	−	6.36709i	−0.172884	−	0.207231i
$945$	19.3258	−	11.1578i	0.628670	−	0.362963i
$946$	−2.05726	−	3.23433i	−0.0668872	−	0.105157i
$947$	−16.6125	+	9.59121i	−0.539833	+	0.311672i	−0.745011	−	0.667052i	$-0.767556\pi$
$947$	−16.6125	+	9.59121i	−0.539833	+	0.311672i	0.205179	+	0.978725i	$0.434222\pi$
$948$	−13.8912	+	29.6794i	−0.451167	+	0.963942i
$949$		−	13.9444i		−	0.452655i
$950$	5.56281	−	2.65615i	0.180481	−	0.0861768i
$951$			15.6771i			0.508366i
$952$	54.3552	−	41.5239i	1.76166	−	1.34580i
$953$	−8.37019	+	4.83253i	−0.271137	+	0.156541i	−0.629404	−	0.777078i	$-0.716701\pi$
$953$	−8.37019	+	4.83253i	−0.271137	+	0.156541i	0.358267	+	0.933619i	$0.383368\pi$
$954$	5.88433	−	3.74284i	0.190512	−	0.121179i
$955$	−20.7679	+	11.9904i	−0.672035	+	0.388000i
$956$	−4.70050	−	54.6233i	−0.152025	−	1.76664i
$957$	1.96841			0.0636298
$958$	−4.79618	−	2.50108i	−0.154958	−	0.0808061i
$959$	36.2079	+	20.9047i	1.16922	+	0.675047i
$960$	2.52805	−	9.27601i	0.0815923	−	0.299382i
$961$	−30.9991			−0.999972
$962$	−21.5107	+	41.2500i	−0.693534	+	1.32995i
$963$	1.48292	−	2.56849i	0.0477863	−	0.0827683i
$964$	11.4518	+	5.35994i	0.368837	+	0.172632i
$965$	20.6223	+	11.9063i	0.663856	+	0.383278i
$966$	−8.69653	+	0.373492i	−0.279806	+	0.0120169i
$967$	−8.09712	+	4.67488i	−0.260386	+	0.150334i	−0.624511	−	0.781016i	$-0.714702\pi$
$967$	−8.09712	+	4.67488i	−0.260386	+	0.150334i	0.364125	+	0.931350i	$0.381368\pi$
$968$	30.0783	−	3.89450i	0.966753	−	0.125174i
$969$	28.5969	−	12.1767i	0.918665	−	0.391171i
$970$	18.8468	+	9.82807i	0.605133	+	0.315560i
$971$	−10.5006	−	18.1876i	−0.336980	−	0.583667i	0.646883	−	0.762589i	$-0.276072\pi$
$971$	−10.5006	−	18.1876i	−0.336980	−	0.583667i	−0.983863	+	0.178922i	$0.942739\pi$
$972$	−11.9765	+	25.5885i	−0.384148	+	0.820753i
$973$	10.3088	−	17.8553i	0.330484	−	0.572415i
$974$	−3.60505	+	0.154827i	−0.115513	+	0.00496097i
$975$	4.98842	+	2.88007i	0.159757	+	0.0922360i
$976$	−15.1049	+	41.1352i	−0.483495	+	1.31671i
$977$			41.5054i			1.32788i	0.747788	+	0.663938i	$0.231116\pi$
$977$			41.5054i			1.32788i	−0.747788	+	0.663938i	$0.768884\pi$
$978$	29.1458	−	18.5387i	0.931980	−	0.592804i
$979$	−2.62490	+	4.54647i	−0.0838923	+	0.145306i
$980$	−11.0051	−	15.7647i	−0.351546	−	0.503585i
$981$			29.0668i			0.928031i
$982$	−6.70567	+	4.26527i	−0.213986	+	0.136110i
$983$	−26.3546	−	45.6476i	−0.840582	−	1.45593i	−0.889403	−	0.457123i	$-0.848880\pi$
$983$	−26.3546	−	45.6476i	−0.840582	−	1.45593i	0.0488213	−	0.998808i	$-0.484454\pi$
$984$	24.5741	+	10.2405i	0.783392	+	0.326455i
$985$	3.00455	+	5.20403i	0.0957330	+	0.165814i
$986$	1.12055	+	26.0914i	0.0356856	+	0.830919i
$987$	5.13220			0.163360
$988$	−19.6054	−	36.8990i	−0.623730	−	1.17391i
$989$	−6.47175			−0.205790
$990$	−0.0496792	−	1.15675i	−0.00157891	−	0.0367640i
$991$	−15.8565	−	27.4643i	−0.503698	−	0.872431i	−0.999991	−	0.00427550i	$-0.998639\pi$
$991$	−15.8565	−	27.4643i	−0.503698	−	0.872431i	0.496293	−	0.868155i	$-0.334694\pi$
$992$	−0.162718	+	0.0354662i	−0.00516632	+	0.00112605i
$993$	−12.7347	−	22.0572i	−0.404124	−	0.699964i
$994$	28.6109	−	18.1985i	0.907484	−	0.577223i
$995$			12.2385i			0.387987i
$996$	17.1939	−	12.0028i	0.544808	−	0.380323i
$997$	15.7747	−	27.3227i	0.499591	−	0.865317i	−0.500409	−	0.865789i	$-0.666817\pi$
$997$	15.7747	−	27.3227i	0.499591	−	0.865317i	1.00000		0.000472074i	$0.000150266\pi$
$998$	41.8510	−	26.6201i	1.32477	−	0.842646i
$999$		−	37.5769i		−	1.18888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.a.31.20	yes	40
4.3	odd	2	inner	380.2.n.a.31.15	✓	40
19.8	odd	6	inner	380.2.n.a.331.15	yes	40
76.27	even	6	inner	380.2.n.a.331.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.a.31.15	✓	40	4.3	odd	2	inner
380.2.n.a.31.20	yes	40	1.1	even	1	trivial
380.2.n.a.331.15	yes	40	19.8	odd	6	inner
380.2.n.a.331.20	yes	40	76.27	even	6	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41291 - 0.0606805i) q^{2} +(-0.600896 - 1.04078i) q^{3} +(1.99264 - 0.171472i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.912167 - 1.43407i) q^{6} +4.07590i q^{7} +(2.80501 - 0.363190i) q^{8} +(0.777849 - 1.34727i) q^{9} +O(q^{10})\)	\(q+(1.41291 - 0.0606805i) q^{2} +(-0.600896 - 1.04078i) q^{3} +(1.99264 - 0.171472i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.912167 - 1.43407i) q^{6} +4.07590i q^{7} +(2.80501 - 0.363190i) q^{8} +(0.777849 - 1.34727i) q^{9} +(0.759006 + 1.19328i) q^{10} -0.526259i q^{11} +(-1.37583 - 1.97086i) q^{12} +(4.15082 + 2.39648i) q^{13} +(0.247328 + 5.75889i) q^{14} +(0.600896 - 1.04078i) q^{15} +(3.94119 - 0.683364i) q^{16} +(-2.96664 - 5.13837i) q^{17} +(1.01728 - 1.95078i) q^{18} +(-3.48412 - 2.61933i) q^{19} +(1.14482 + 1.63994i) q^{20} +(4.24213 - 2.44919i) q^{21} +(-0.0319337 - 0.743557i) q^{22} +(-1.08820 - 0.628273i) q^{23} +(-2.06352 - 2.70117i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(6.01016 + 3.13414i) q^{26} -5.47500 q^{27} +(0.698905 + 8.12179i) q^{28} +(-2.69537 - 1.55617i) q^{29} +(0.785857 - 1.50699i) q^{30} -0.0294402 q^{31} +(5.52709 - 1.20469i) q^{32} +(-0.547721 + 0.316227i) q^{33} +(-4.50340 - 7.08004i) q^{34} +(-3.52984 + 2.03795i) q^{35} +(1.31895 - 2.81801i) q^{36} +6.86336i q^{37} +(-5.08170 - 3.48946i) q^{38} -5.76014i q^{39} +(1.71704 + 2.24762i) q^{40} +(-6.78272 + 3.91600i) q^{41} +(5.84513 - 3.71791i) q^{42} +(4.46040 - 2.57522i) q^{43} +(-0.0902389 - 1.04864i) q^{44} +1.55570 q^{45} +(-1.57565 - 0.821661i) q^{46} +(0.907363 + 0.523866i) q^{47} +(-3.07948 - 3.69129i) q^{48} -9.61300 q^{49} +(-0.653905 + 1.25396i) q^{50} +(-3.56528 + 6.17525i) q^{51} +(8.68201 + 4.06356i) q^{52} +(2.74512 + 1.58490i) q^{53} +(-7.73569 + 0.332226i) q^{54} +(0.455754 - 0.263130i) q^{55} +(1.48033 + 11.4330i) q^{56} +(-0.632558 + 5.20015i) q^{57} +(-3.90275 - 2.03518i) q^{58} +(-1.03648 - 1.79524i) q^{59} +(1.01890 - 2.17694i) q^{60} +(-5.47760 + 9.48748i) q^{61} +(-0.0415963 + 0.00178645i) q^{62} +(5.49136 + 3.17044i) q^{63} +(7.73619 - 2.03750i) q^{64} +4.79296i q^{65} +(-0.754692 + 0.480036i) q^{66} +(1.00882 - 1.74733i) q^{67} +(-6.79252 - 9.73020i) q^{68} +1.51011i q^{69} +(-4.86368 + 3.09364i) q^{70} +(-2.94128 - 5.09445i) q^{71} +(1.69256 - 4.06163i) q^{72} +(-1.45468 - 2.51957i) q^{73} +(0.416473 + 9.69732i) q^{74} +1.20179 q^{75} +(-7.39173 - 4.62194i) q^{76} +2.14498 q^{77} +(-0.349528 - 8.13856i) q^{78} +(-6.81678 - 11.8070i) q^{79} +(2.56241 + 3.07149i) q^{80} +(0.956355 + 1.65646i) q^{81} +(-9.34575 + 5.94455i) q^{82} +8.72403i q^{83} +(8.03304 - 5.60776i) q^{84} +(2.96664 - 5.13837i) q^{85} +(6.14589 - 3.90921i) q^{86} +3.74039i q^{87} +(-0.191132 - 1.47616i) q^{88} +(-8.63922 - 4.98785i) q^{89} +(2.19806 - 0.0944006i) q^{90} +(-9.76782 + 16.9184i) q^{91} +(-2.27612 - 1.06532i) q^{92} +(0.0176905 + 0.0306408i) q^{93} +(1.31381 + 0.685117i) q^{94} +(0.526346 - 4.32700i) q^{95} +(-4.57502 - 5.02860i) q^{96} +(13.0162 - 7.51491i) q^{97} +(-13.5823 + 0.583322i) q^{98} +(-0.709015 - 0.409350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9	\( 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} + 18 q^{14} - 7 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{21} - 8 q^{24} - 20 q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{30} - 18 q^{32} - 6 q^{33} - 27 q^{34} - 14 q^{36} + 38 q^{38} + 36 q^{41} - 21 q^{42} - 8 q^{44} - 44 q^{45} - 18 q^{48} - 60 q^{49} - 33 q^{52} + 42 q^{53} + 9 q^{54} + 12 q^{57} - 62 q^{58} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 64 q^{64} + 2 q^{66} + 72 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} - 62 q^{76} - 28 q^{77} - 24 q^{78} + 7 q^{80} - 48 q^{81} - q^{82} - 4 q^{85} + 78 q^{86} - 18 q^{89} + 39 q^{90} + 16 q^{92} + 8 q^{96} + 30 q^{97} - 12 q^{98}+O(q^{100}) \) 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 + 18 * q^14 - 7 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^21 - 8 * q^24 - 20 * q^25 + 2 * q^26 + 8 * q^28 + 6 * q^30 - 18 * q^32 - 6 * q^33 - 27 * q^34 - 14 * q^36 + 38 * q^38 + 36 * q^41 - 21 * q^42 - 8 * q^44 - 44 * q^45 - 18 * q^48 - 60 * q^49 - 33 * q^52 + 42 * q^53 + 9 * q^54 + 12 * q^57 - 62 * q^58 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 64 * q^64 + 2 * q^66 + 72 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 - 62 * q^76 - 28 * q^77 - 24 * q^78 + 7 * q^80 - 48 * q^81 - q^82 - 4 * q^85 + 78 * q^86 - 18 * q^89 + 39 * q^90 + 16 * q^92 + 8 * q^96 + 30 * q^97 - 12 * q^98

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