LMFDB - Embedded newform 299.2.i.b.231.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [299,2,Mod(231,299)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(299, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("299.231");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 299 = 13 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	299.i (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:	$2.38752702044$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			231.3
Character	$\chi$	$=$	299.231
Dual form			299.2.i.b.277.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98297 + 1.14487i) q^{2} +(-1.45233 - 2.51551i) q^{3} +(1.62146 - 2.80845i) q^{4} -3.03647i q^{5} +(5.75986 + 3.32545i) q^{6} +(3.97315 + 2.29390i) q^{7} +2.84596i q^{8} +(-2.71851 + 4.70860i) q^{9} +O(q^{10})$	\(q+(-1.98297 + 1.14487i) q^{2} +(-1.45233 - 2.51551i) q^{3} +(1.62146 - 2.80845i) q^{4} -3.03647i q^{5} +(5.75986 + 3.32545i) q^{6} +(3.97315 + 2.29390i) q^{7} +2.84596i q^{8} +(-2.71851 + 4.70860i) q^{9} +(3.47636 + 6.02123i) q^{10} +(3.76037 - 2.17105i) q^{11} -9.41955 q^{12} +(1.97024 - 3.01963i) q^{13} -10.5049 q^{14} +(-7.63824 + 4.40994i) q^{15} +(-0.0153361 - 0.0265629i) q^{16} +(1.74613 - 3.02438i) q^{17} -12.4494i q^{18} +(-2.36902 - 1.36775i) q^{19} +(-8.52775 - 4.92350i) q^{20} -13.3260i q^{21} +(-4.97114 + 8.61028i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(7.15902 - 4.13326i) q^{24} -4.22012 q^{25} +(-0.449857 + 8.24351i) q^{26} +7.07871 q^{27} +(12.8846 - 7.43892i) q^{28} +(2.49871 + 4.32790i) q^{29} +(10.0976 - 17.4896i) q^{30} +2.79864i q^{31} +(-4.86852 - 2.81084i) q^{32} +(-10.9226 - 6.30615i) q^{33} +7.99635i q^{34} +(6.96534 - 12.0643i) q^{35} +(8.81590 + 15.2696i) q^{36} +(-2.79410 + 1.61317i) q^{37} +6.26361 q^{38} +(-10.4573 - 0.570667i) q^{39} +8.64165 q^{40} +(-6.12192 + 3.53449i) q^{41} +(15.2565 + 26.4250i) q^{42} +(2.22441 - 3.85280i) q^{43} -14.0811i q^{44} +(14.2975 + 8.25466i) q^{45} +(1.98297 + 1.14487i) q^{46} -9.36585i q^{47} +(-0.0445461 + 0.0771561i) q^{48} +(7.02394 + 12.1658i) q^{49} +(8.36839 - 4.83149i) q^{50} -10.1438 q^{51} +(-5.28580 - 10.4295i) q^{52} -3.52914 q^{53} +(-14.0369 + 8.10420i) q^{54} +(-6.59232 - 11.4182i) q^{55} +(-6.52833 + 11.3074i) q^{56} +7.94571i q^{57} +(-9.90976 - 5.72140i) q^{58} +(4.75946 + 2.74788i) q^{59} +28.6021i q^{60} +(-4.75360 + 8.23348i) q^{61} +(-3.20408 - 5.54963i) q^{62} +(-21.6021 + 12.4720i) q^{63} +12.9335 q^{64} +(-9.16899 - 5.98257i) q^{65} +28.8789 q^{66} +(-0.907762 + 0.524097i) q^{67} +(-5.66254 - 9.80780i) q^{68} +(-1.45233 + 2.51551i) q^{69} +31.8977i q^{70} +(-4.62892 - 2.67251i) q^{71} +(-13.4005 - 7.73676i) q^{72} -3.36631i q^{73} +(3.69375 - 6.39776i) q^{74} +(6.12900 + 10.6157i) q^{75} +(-7.68253 + 4.43551i) q^{76} +19.9207 q^{77} +(21.3899 - 10.8407i) q^{78} -2.01122 q^{79} +(-0.0806574 + 0.0465676i) q^{80} +(-2.12507 - 3.68073i) q^{81} +(8.09307 - 14.0176i) q^{82} +4.04458i q^{83} +(-37.4253 - 21.6075i) q^{84} +(-9.18342 - 5.30205i) q^{85} +10.1867i q^{86} +(7.25789 - 12.5710i) q^{87} +(6.17872 + 10.7018i) q^{88} +(-8.28498 + 4.78334i) q^{89} -37.8021 q^{90} +(14.7548 - 7.47789i) q^{91} -3.24292 q^{92} +(7.03999 - 4.06454i) q^{93} +(10.7227 + 18.5722i) q^{94} +(-4.15314 + 7.19344i) q^{95} +16.3290i q^{96} +(7.21014 + 4.16278i) q^{97} +(-27.8566 - 16.0830i) q^{98} +23.6081i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9	$ 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9} + 23 q^{10} - 4 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} - 26 q^{16} + 13 q^{17} - 12 q^{19} + 6 q^{20} - 16 q^{22} - 15 q^{23} + 6 q^{24} - 52 q^{25} - 25 q^{26} + 54 q^{27} - 24 q^{28} - q^{29} + 20 q^{30} - 39 q^{32} - 18 q^{33} + 20 q^{35} + 23 q^{36} - 30 q^{37} + 18 q^{38} - 60 q^{39} + 124 q^{40} - 6 q^{41} - 12 q^{42} + 33 q^{43} + 18 q^{45} + 34 q^{48} + 48 q^{49} - 60 q^{50} + 20 q^{51} - 39 q^{52} + 62 q^{53} + 45 q^{54} - 16 q^{55} - 5 q^{56} - 66 q^{58} - 21 q^{59} - 18 q^{61} + 46 q^{62} - 117 q^{63} - 16 q^{64} - 4 q^{65} + 52 q^{66} + 24 q^{67} - 18 q^{68} - 3 q^{69} + 54 q^{71} - 54 q^{72} + 42 q^{74} + 4 q^{75} - 18 q^{76} - 20 q^{77} + 72 q^{79} + 114 q^{80} - 15 q^{81} + 14 q^{82} - 159 q^{84} - 39 q^{85} + 40 q^{87} + 93 q^{88} - 51 q^{89} - 78 q^{90} - 34 q^{91} - 32 q^{92} + 6 q^{93} + 8 q^{94} - 24 q^{95} - 6 q^{97} - 123 q^{98}+O(q^{100}) $ 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9 + 23 * q^10 - 4 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 - 26 * q^16 + 13 * q^17 - 12 * q^19 + 6 * q^20 - 16 * q^22 - 15 * q^23 + 6 * q^24 - 52 * q^25 - 25 * q^26 + 54 * q^27 - 24 * q^28 - q^29 + 20 * q^30 - 39 * q^32 - 18 * q^33 + 20 * q^35 + 23 * q^36 - 30 * q^37 + 18 * q^38 - 60 * q^39 + 124 * q^40 - 6 * q^41 - 12 * q^42 + 33 * q^43 + 18 * q^45 + 34 * q^48 + 48 * q^49 - 60 * q^50 + 20 * q^51 - 39 * q^52 + 62 * q^53 + 45 * q^54 - 16 * q^55 - 5 * q^56 - 66 * q^58 - 21 * q^59 - 18 * q^61 + 46 * q^62 - 117 * q^63 - 16 * q^64 - 4 * q^65 + 52 * q^66 + 24 * q^67 - 18 * q^68 - 3 * q^69 + 54 * q^71 - 54 * q^72 + 42 * q^74 + 4 * q^75 - 18 * q^76 - 20 * q^77 + 72 * q^79 + 114 * q^80 - 15 * q^81 + 14 * q^82 - 159 * q^84 - 39 * q^85 + 40 * q^87 + 93 * q^88 - 51 * q^89 - 78 * q^90 - 34 * q^91 - 32 * q^92 + 6 * q^93 + 8 * q^94 - 24 * q^95 - 6 * q^97 - 123 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/299\mathbb{Z}\right)^\times$.

$n$	$93$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.98297	+	1.14487i	−1.40217	+	0.809546i	−0.994616	−	0.103633i	$-0.966953\pi$
$2$	−1.98297	+	1.14487i	−1.40217	+	0.809546i	−0.407559	+	0.913179i	$0.633620\pi$
$3$	−1.45233	−	2.51551i	−0.838502	−	1.45233i	−0.891147	−	0.453714i	$-0.850099\pi$
$3$	−1.45233	−	2.51551i	−0.838502	−	1.45233i	0.0526455	−	0.998613i	$-0.483235\pi$
$4$	1.62146	−	2.80845i	0.810729	−	1.40422i
$5$		−	3.03647i		−	1.35795i	−0.734162	−	0.678974i	$-0.762425\pi$
$5$		−	3.03647i		−	1.35795i	0.734162	−	0.678974i	$-0.237575\pi$
$6$	5.75986	+	3.32545i	2.35145	+	1.35761i
$7$	3.97315	+	2.29390i	1.50171	+	0.867012i	0.999998	+	0.00197674i	$0.000629215\pi$
$7$	3.97315	+	2.29390i	1.50171	+	0.867012i	0.501711	+	0.865035i	$0.332704\pi$
$8$			2.84596i			1.00620i
$9$	−2.71851	+	4.70860i	−0.906170	+	1.56953i
$10$	3.47636	+	6.02123i	1.09932	+	1.90408i
$11$	3.76037	−	2.17105i	1.13379	−	0.654596i	0.188908	−	0.981995i	$-0.439505\pi$
$11$	3.76037	−	2.17105i	1.13379	−	0.654596i	0.944886	+	0.327398i	$0.106172\pi$
$12$	−9.41955			−2.71919
$13$	1.97024	−	3.01963i	0.546447	−	0.837494i
$13$	1.97024	−	3.01963i	0.546447	−	0.837494i
$14$	−10.5049			−2.80754
$15$	−7.63824	+	4.40994i	−1.97219	+	1.13864i
$16$	−0.0153361	−	0.0265629i	−0.00383403	−	0.00664073i
$17$	1.74613	−	3.02438i	0.423498	−	0.733519i	−0.572781	−	0.819708i	$-0.694136\pi$
$17$	1.74613	−	3.02438i	0.423498	−	0.733519i	0.996279	+	0.0861890i	$0.0274689\pi$
$18$		−	12.4494i		−	2.93435i
$19$	−2.36902	−	1.36775i	−0.543490	−	0.313784i	0.203002	−	0.979178i	$-0.434930\pi$
$19$	−2.36902	−	1.36775i	−0.543490	−	0.313784i	−0.746492	+	0.665394i	$0.768264\pi$
$20$	−8.52775	−	4.92350i	−1.90686	−	1.10093i
$21$		−	13.3260i		−	2.90796i
$22$	−4.97114	+	8.61028i	−1.05985	+	1.83572i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	7.15902	−	4.13326i	1.46133	−	0.843698i
$25$	−4.22012			−0.844024
$26$	−0.449857	+	8.24351i	−0.0882242	+	1.61669i
$27$	7.07871			1.36230
$28$	12.8846	−	7.43892i	2.43496	−	1.40582i
$29$	2.49871	+	4.32790i	0.463999	+	0.803670i	0.999156	−	0.0410829i	$-0.0130808\pi$
$29$	2.49871	+	4.32790i	0.463999	+	0.803670i	−0.535157	+	0.844753i	$0.679747\pi$
$30$	10.0976	−	17.4896i	1.84357	−	3.19315i
$31$			2.79864i			0.502651i	0.967903	+	0.251325i	$0.0808664\pi$
$31$			2.79864i			0.502651i	−0.967903	+	0.251325i	$0.919134\pi$
$32$	−4.86852	−	2.81084i	−0.860641	−	0.496891i
$33$	−10.9226	−	6.30615i	−1.90138	−	1.09776i
$34$			7.99635i			1.37136i
$35$	6.96534	−	12.0643i	1.17736	−	2.03924i
$36$	8.81590	+	15.2696i	1.46932	+	2.54493i
$37$	−2.79410	+	1.61317i	−0.459347	+	0.265204i	−0.711769	−	0.702413i	$-0.752106\pi$
$37$	−2.79410	+	1.61317i	−0.459347	+	0.265204i	0.252423	+	0.967617i	$0.418773\pi$
$38$	6.26361			1.01609
$39$	−10.4573	−	0.570667i	−1.67451	−	0.0913798i
$40$	8.64165			1.36636
$41$	−6.12192	+	3.53449i	−0.956083	+	0.551995i	−0.894965	−	0.446136i	$-0.852800\pi$
$41$	−6.12192	+	3.53449i	−0.956083	+	0.551995i	−0.0611176	+	0.998131i	$0.519466\pi$
$42$	15.2565	+	26.4250i	2.35413	+	4.07747i
$43$	2.22441	−	3.85280i	0.339220	−	0.587546i	−0.645066	−	0.764127i	$-0.723170\pi$
$43$	2.22441	−	3.85280i	0.339220	−	0.587546i	0.984286	+	0.176581i	$0.0565036\pi$
$44$		−	14.0811i		−	2.12280i
$45$	14.2975	+	8.25466i	2.13134	+	1.23053i
$46$	1.98297	+	1.14487i	0.292374	+	0.168802i
$47$		−	9.36585i		−	1.36615i	−0.730348	−	0.683075i	$-0.760642\pi$
$47$		−	9.36585i		−	1.36615i	0.730348	−	0.683075i	$-0.239358\pi$
$48$	−0.0445461	+	0.0771561i	−0.00642968	+	0.0111365i
$49$	7.02394	+	12.1658i	1.00342	+	1.73797i
$50$	8.36839	−	4.83149i	1.18347	−	0.683276i
$51$	−10.1438			−1.42041
$52$	−5.28580	−	10.4295i	−0.733008	−	1.44631i
$53$	−3.52914			−0.484765			−0.242382	−	0.970181i	$-0.577929\pi$
$53$	−3.52914			−0.484765			−0.242382	+	0.970181i	$0.577929\pi$
$54$	−14.0369	+	8.10420i	−1.91018	+	1.10284i
$55$	−6.59232	−	11.4182i	−0.888908	−	1.53963i
$56$	−6.52833	+	11.3074i	−0.872385	+	1.51102i
$57$			7.94571i			1.05243i
$58$	−9.90976	−	5.72140i	−1.30122	−	0.751257i
$59$	4.75946	+	2.74788i	0.619629	+	0.357743i	0.776725	−	0.629840i	$-0.216880\pi$
$59$	4.75946	+	2.74788i	0.619629	+	0.357743i	−0.157095	+	0.987583i	$0.550213\pi$
$60$			28.6021i			3.69252i
$61$	−4.75360	+	8.23348i	−0.608636	+	1.05419i	0.382829	+	0.923819i	$0.374950\pi$
$61$	−4.75360	+	8.23348i	−0.608636	+	1.05419i	−0.991465	+	0.130370i	$0.958384\pi$
$62$	−3.20408	−	5.54963i	−0.406919	−	0.704804i
$63$	−21.6021	+	12.4720i	−2.72161	+	1.57132i
$64$	12.9335			1.61669
$65$	−9.16899	−	5.98257i	−1.13727	−	0.742047i
$66$	28.8789			3.55475
$67$	−0.907762	+	0.524097i	−0.110901	+	0.0640286i	−0.554424	−	0.832234i	$-0.687062\pi$
$67$	−0.907762	+	0.524097i	−0.110901	+	0.0640286i	0.443524	+	0.896263i	$0.353728\pi$
$68$	−5.66254	−	9.80780i	−0.686683	−	1.18937i
$69$	−1.45233	+	2.51551i	−0.174840	+	0.302831i
$70$			31.8977i			3.81250i
$71$	−4.62892	−	2.67251i	−0.549352	−	0.317169i	0.199508	−	0.979896i	$-0.436065\pi$
$71$	−4.62892	−	2.67251i	−0.549352	−	0.317169i	−0.748861	+	0.662727i	$0.769399\pi$
$72$	−13.4005	−	7.73676i	−1.57926	−	0.911786i
$73$		−	3.36631i		−	0.393997i	−0.980404	−	0.196999i	$-0.936881\pi$
$73$		−	3.36631i		−	0.393997i	0.980404	−	0.196999i	$-0.0631194\pi$
$74$	3.69375	−	6.39776i	0.429389	−	0.743724i
$75$	6.12900	+	10.6157i	0.707716	+	1.22580i
$76$	−7.68253	+	4.43551i	−0.881247	+	0.508788i
$77$	19.9207			2.27017
$78$	21.3899	−	10.8407i	2.42193	−	1.22746i
$79$	−2.01122			−0.226280			−0.113140	−	0.993579i	$-0.536091\pi$
$79$	−2.01122			−0.226280			−0.113140	+	0.993579i	$0.536091\pi$
$80$	−0.0806574	+	0.0465676i	−0.00901777	+	0.00520641i
$81$	−2.12507	−	3.68073i	−0.236119	−	0.408970i
$82$	8.09307	−	14.0176i	0.893730	−	1.54799i
$83$			4.04458i			0.443950i	0.975052	+	0.221975i	$0.0712503\pi$
$83$			4.04458i			0.443950i	−0.975052	+	0.221975i	$0.928750\pi$
$84$	−37.4253	−	21.6075i	−4.08343	−	2.35757i
$85$	−9.18342	−	5.30205i	−0.996081	−	0.575088i
$86$			10.1867i			1.09846i
$87$	7.25789	−	12.5710i	0.778128	−	1.34776i
$88$	6.17872	+	10.7018i	0.658653	+	1.14082i
$89$	−8.28498	+	4.78334i	−0.878206	+	0.507033i	−0.870067	−	0.492934i	$-0.835924\pi$
$89$	−8.28498	+	4.78334i	−0.878206	+	0.507033i	−0.00813985	+	0.999967i	$0.502591\pi$
$90$	−37.8021			−3.98469
$91$	14.7548	−	7.47789i	1.54672	−	0.783896i
$92$	−3.24292			−0.338097
$93$	7.03999	−	4.06454i	0.730013	−	0.421473i
$94$	10.7227	+	18.5722i	1.10596	+	1.91558i
$95$	−4.15314	+	7.19344i	−0.426103	+	0.738032i
$96$			16.3290i			1.66658i
$97$	7.21014	+	4.16278i	0.732079	+	0.422666i	0.819182	−	0.573533i	$-0.194428\pi$
$97$	7.21014	+	4.16278i	0.732079	+	0.422666i	−0.0871031	+	0.996199i	$0.527761\pi$
$98$	−27.8566	−	16.0830i	−2.81394	−	1.62463i
$99$			23.6081i			2.37270i
$100$	−6.84275	+	11.8520i	−0.684275	+	1.18520i
$101$	6.09007	+	10.5483i	0.605984	+	1.04960i	0.991895	+	0.127059i	$0.0405539\pi$
$101$	6.09007	+	10.5483i	0.605984	+	1.04960i	−0.385911	+	0.922536i	$0.626113\pi$
$102$	20.1149	−	11.6133i	1.99167	−	1.14989i
$103$	16.2065			1.59688			0.798439	−	0.602075i	$-0.205659\pi$
$103$	16.2065			1.59688			0.798439	+	0.602075i	$0.205659\pi$
$104$	8.59373	+	5.60722i	0.842684	+	0.549833i
$105$	−40.4638			−3.94887
$106$	6.99820	−	4.04041i	0.679725	−	0.392439i
$107$	−2.63207	−	4.55888i	−0.254452	−	0.440724i	0.710295	−	0.703905i	$-0.248562\pi$
$107$	−2.63207	−	4.55888i	−0.254452	−	0.440724i	−0.964747	+	0.263181i	$0.915228\pi$
$108$	11.4778	−	19.8802i	1.10445	−	1.91297i
$109$		−	10.2428i		−	0.981078i	−0.871419	−	0.490539i	$-0.836800\pi$
$109$		−	10.2428i		−	0.981078i	0.871419	−	0.490539i	$-0.163200\pi$
$110$	26.1448	+	15.0947i	2.49281	+	1.43922i
$111$	8.11589	+	4.68571i	0.770326	+	0.444748i
$112$		−	0.140718i		−	0.0132966i
$113$	−10.1416	+	17.5657i	−0.954041	+	1.65245i	−0.217492	+	0.976062i	$0.569788\pi$
$113$	−10.1416	+	17.5657i	−0.954041	+	1.65245i	−0.736549	+	0.676384i	$0.763546\pi$
$114$	−9.09681	−	15.7561i	−0.851994	−	1.47570i
$115$	−2.62966	+	1.51823i	−0.245217	+	0.141576i
$116$	16.2062			1.50471
$117$	8.86209	+	17.4860i	0.819300	+	1.61658i
$118$	−12.5839			−1.15844
$119$	13.8752	−	8.01087i	1.27194	−	0.734355i
$120$	−12.5505	−	21.7381i	−1.14570	−	1.98441i
$121$	3.92692	−	6.80163i	0.356993	−	0.618330i
$122$		−	21.7690i		−	1.97088i
$123$	17.7821	+	10.2665i	1.60335	+	0.925697i
$124$	7.85983	+	4.53788i	0.705834	+	0.407513i
$125$		−	2.36808i		−	0.211807i
$126$	28.5576	−	49.4632i	2.54411	−	4.40653i
$127$	−3.19418	−	5.53247i	−0.283437	−	0.490928i	0.688792	−	0.724959i	$-0.258141\pi$
$127$	−3.19418	−	5.53247i	−0.283437	−	0.490928i	−0.972229	+	0.234032i	$0.924808\pi$
$128$	−15.9098	+	9.18555i	−1.40624	+	0.811896i
$129$	−12.9223			−1.13775
$130$	25.0311	+	1.36597i	2.19538	+	0.119804i
$131$	11.2463			0.982597			0.491298	−	0.870991i	$-0.336522\pi$
$131$	11.2463			0.982597			0.491298	+	0.870991i	$0.336522\pi$
$132$	−35.4210	+	20.4503i	−3.08300	+	1.77997i
$133$	−6.27498	−	10.8686i	−0.544110	−	0.942425i
$134$	1.20005	−	2.07854i	0.103668	−	0.179559i
$135$		−	21.4942i		−	1.84993i
$136$	8.60725	+	4.96940i	0.738065	+	0.426122i
$137$	−4.05971	−	2.34387i	−0.346844	−	0.200251i	0.316450	−	0.948609i	$-0.397509\pi$
$137$	−4.05971	−	2.34387i	−0.346844	−	0.200251i	−0.663294	+	0.748359i	$0.730842\pi$
$138$		−	6.65091i		−	0.566163i
$139$	1.61342	−	2.79453i	0.136849	−	0.237029i	−0.789454	−	0.613810i	$-0.789636\pi$
$139$	1.61342	−	2.79453i	0.136849	−	0.237029i	0.926302	+	0.376782i	$0.122969\pi$
$140$	−22.5880	−	39.1236i	−1.90904	−	3.30655i
$141$	−23.5599	+	13.6023i	−1.98410	+	1.14552i
$142$	12.2387			1.02705
$143$	0.853076	−	15.6324i	0.0713378	−	1.30725i
$144$	0.166766			0.0138971
$145$	13.1415	−	7.58725i	1.09134	−	0.630087i
$146$	3.85399	+	6.67531i	0.318959	+	0.552453i
$147$	20.4021	−	35.3375i	1.68274	−	2.91459i
$148$			10.4628i			0.860034i
$149$	−1.93151	−	1.11516i	−0.158235	−	0.0913573i	0.418791	−	0.908082i	$-0.362454\pi$
$149$	−1.93151	−	1.11516i	−0.158235	−	0.0913573i	−0.577027	+	0.816725i	$0.695787\pi$
$150$	−24.3073	−	14.0338i	−1.98468	−	1.14586i
$151$		−	15.3549i		−	1.24956i	−0.780800	−	0.624782i	$-0.785188\pi$
$151$		−	15.3549i		−	1.24956i	0.780800	−	0.624782i	$-0.214812\pi$
$152$	3.89257	−	6.74213i	0.315729	−	0.546859i
$153$	9.49372	+	16.4436i	0.767522	+	1.32939i
$154$	−39.5022	+	22.8066i	−3.18318	+	1.83781i
$155$	8.49797			0.682574
$156$	−18.5588	+	28.4435i	−1.48589	+	2.27731i
$157$	10.0350			0.800878			0.400439	−	0.916323i	$-0.368858\pi$
$157$	10.0350			0.800878			0.400439	+	0.916323i	$0.368858\pi$
$158$	3.98819	−	2.30258i	0.317284	−	0.183184i
$159$	5.12547	+	8.87757i	0.406476	+	0.704037i
$160$	−8.53502	+	14.7831i	−0.674753	+	1.16871i
$161$		−	4.58780i		−	0.361569i
$162$	8.42791	+	4.86586i	0.662159	+	0.382298i
$163$	−4.67451	−	2.69883i	−0.366136	−	0.211388i	0.305633	−	0.952149i	$-0.401132\pi$
$163$	−4.67451	−	2.69883i	−0.366136	−	0.211388i	−0.671769	+	0.740761i	$0.734465\pi$
$164$			22.9241i			1.79007i
$165$	−19.1484	+	33.1660i	−1.49070	+	2.58197i
$166$	−4.63052	−	8.02029i	−0.359398	−	0.622495i
$167$	8.40332	−	4.85166i	0.650268	−	0.375433i	−0.138291	−	0.990392i	$-0.544161\pi$
$167$	8.40332	−	4.85166i	0.650268	−	0.375433i	0.788559	+	0.614959i	$0.210827\pi$
$168$	37.9251			2.92599
$169$	−5.23629	−	11.8988i	−0.402792	−	0.915292i
$170$	24.2806			1.86224
$171$	12.8804	−	7.43651i	0.984989	−	0.568684i
$172$	−7.21358	−	12.4943i	−0.550031	−	0.952681i
$173$	−2.39562	+	4.14933i	−0.182135	+	0.315468i	−0.942607	−	0.333903i	$-0.891634\pi$
$173$	−2.39562	+	4.14933i	−0.182135	+	0.315468i	0.760472	+	0.649371i	$0.224968\pi$
$174$			33.2374i			2.51972i
$175$	−16.7672	−	9.68053i	−1.26748	−	0.731779i
$176$	−0.115339	−	0.0665910i	−0.00869400	−	0.00501948i
$177$		−	15.9633i		−	1.19987i
$178$	10.9526	−	18.9705i	0.820933	−	1.42190i
$179$	1.86290	+	3.22664i	0.139240	+	0.241170i	0.927209	−	0.374544i	$-0.122201\pi$
$179$	1.86290	+	3.22664i	0.139240	+	0.241170i	−0.787969	+	0.615714i	$0.788868\pi$
$180$	46.3656	−	26.7692i	3.45589	−	1.99526i
$181$	2.74455			0.204001			0.102000	−	0.994784i	$-0.467476\pi$
$181$	2.74455			0.204001			0.102000	+	0.994784i	$0.467476\pi$
$182$	−20.6971	+	31.7208i	−1.53417	+	2.35130i
$183$	27.6151			2.04137
$184$	2.46467	−	1.42298i	0.181698	−	0.104903i
$185$	4.89834	+	8.48417i	0.360133	+	0.623769i
$186$	−9.30675	+	16.1198i	−0.682404	+	1.18196i
$187$		−	15.1637i		−	1.10888i
$188$	−26.3035	−	15.1863i	−1.91838	−	1.10758i
$189$	28.1248	+	16.2378i	2.04577	+	1.18113i
$190$		−	19.0192i		−	1.37980i
$191$	−13.0025	+	22.5210i	−0.940826	+	1.62956i	−0.176927	+	0.984224i	$0.556616\pi$
$191$	−13.0025	+	22.5210i	−0.940826	+	1.62956i	−0.763900	+	0.645335i	$0.776718\pi$
$192$	−18.7837	−	32.5344i	−1.35560	−	2.34797i
$193$	−9.55127	+	5.51443i	−0.687516	+	0.396937i	−0.802681	−	0.596409i	$-0.796594\pi$
$193$	−9.55127	+	5.51443i	−0.687516	+	0.396937i	0.115165	+	0.993346i	$0.463260\pi$
$194$	−19.0634			−1.36867
$195$	−1.73281	+	31.7533i	−0.124089	+	2.27390i
$196$	45.5561			3.25401
$197$	−7.59634	+	4.38575i	−0.541217	+	0.312472i	−0.745572	−	0.666425i	$-0.767824\pi$
$197$	−7.59634	+	4.38575i	−0.541217	+	0.312472i	0.204355	+	0.978897i	$0.434490\pi$
$198$	−27.0282	−	46.8142i	−1.92081	−	3.32694i
$199$	−5.67974	+	9.83760i	−0.402626	+	0.697369i	−0.994042	−	0.108998i	$-0.965236\pi$
$199$	−5.67974	+	9.83760i	−0.402626	+	0.697369i	0.591416	+	0.806367i	$0.298569\pi$
$200$		−	12.0103i		−	0.849255i
$201$	2.63674	+	1.52232i	0.185981	+	0.107376i
$202$	−24.1529	−	13.9447i	−1.69939	−	0.981144i
$203$			22.9272i			1.60917i
$204$	−16.4477	+	28.4883i	−1.15157	+	1.99458i
$205$	10.7324	+	18.5890i	0.749580	+	1.29831i
$206$	−32.1372	+	18.5544i	−2.23910	+	1.29275i
$207$	5.43702			0.377899
$208$	−0.110426	−	0.00602606i	−0.00765666	−	0.000417832i
$209$	−11.8779			−0.821608
$210$	80.2387	−	46.3259i	5.53700	−	3.19679i
$211$	4.16581	+	7.21540i	0.286786	+	0.496729i	0.973041	−	0.230633i	$-0.0740797\pi$
$211$	4.16581	+	7.21540i	0.286786	+	0.496729i	−0.686254	+	0.727362i	$0.740746\pi$
$212$	−5.72235	+	9.91141i	−0.393013	+	0.680718i
$213$			15.5254i			1.06379i
$214$	10.4387	+	6.02676i	0.713572	+	0.411981i
$215$	−11.6989	−	6.75435i	−0.797857	−	0.460643i
$216$			20.1457i			1.37074i
$217$	−6.41980	+	11.1194i	−0.435804	+	0.754835i
$218$	11.7266	+	20.3111i	0.794227	+	1.37564i
$219$	−8.46798	+	4.88899i	−0.572213	+	0.330367i
$220$	−42.7567			−2.88265
$221$	−5.69220	−	11.2314i	−0.382899	−	0.755506i
$222$	−21.4581			−1.44017
$223$	0.631523	−	0.364610i	0.0422899	−	0.0244161i	−0.478706	−	0.877975i	$-0.658894\pi$
$223$	0.631523	−	0.364610i	0.0422899	−	0.0244161i	0.520996	+	0.853559i	$0.325561\pi$
$224$	−12.8956	−	22.3358i	−0.861621	−	1.49237i
$225$	11.4724	−	19.8709i	0.764830	−	1.32472i
$226$		−	46.4432i		−	3.08936i
$227$	9.42266	+	5.44018i	0.625404	+	0.361077i	0.778970	−	0.627061i	$-0.215742\pi$
$227$	9.42266	+	5.44018i	0.625404	+	0.361077i	−0.153566	+	0.988138i	$0.549076\pi$
$228$	22.3151	+	12.8836i	1.47785	+	0.853239i
$229$		−	21.3657i		−	1.41189i	−0.708268	−	0.705944i	$-0.750523\pi$
$229$		−	21.3657i		−	1.41189i	0.708268	−	0.705944i	$-0.249477\pi$
$230$	3.47636	−	6.02123i	0.229224	−	0.397028i
$231$	−28.9313	−	50.1106i	−1.90354	−	3.29703i
$232$	−12.3170	+	7.11122i	−0.808651	+	0.466875i
$233$	16.8099			1.10125			0.550626	−	0.834752i	$-0.314389\pi$
$233$	16.8099			1.10125			0.550626	+	0.834752i	$0.314389\pi$
$234$	−37.5925	−	24.5283i	−2.45750	−	1.60346i
$235$	−28.4391			−1.85516
$236$	15.4345	−	8.91114i	1.00470	−	0.580066i
$237$	2.92095	+	5.05923i	0.189736	+	0.328632i
$238$	−18.3428	+	31.7707i	−1.18899	+	2.05939i
$239$			7.59371i			0.491197i	0.969372	+	0.245598i	$0.0789844\pi$
$239$			7.59371i			0.491197i	−0.969372	+	0.245598i	$0.921016\pi$
$240$	0.234282	+	0.135263i	0.0151228	+	0.00873117i
$241$	17.0377	+	9.83673i	1.09750	+	0.633639i	0.935562	−	0.353162i	$-0.114894\pi$
$241$	17.0377	+	9.83673i	1.09750	+	0.633639i	0.161933	+	0.986802i	$0.448227\pi$
$242$			17.9833i			1.15601i
$243$	4.44547	−	7.69978i	0.285177	−	0.493941i
$244$	15.4155	+	26.7005i	0.986878	+	1.70932i
$245$	36.9411	−	21.3279i	2.36008	−	1.36259i
$246$	−47.0152			−2.99758
$247$	−8.79765	+	4.45875i	−0.559781	+	0.283703i
$248$	−7.96481			−0.505766
$249$	10.1742	−	5.87405i	0.644761	−	0.372253i
$250$	2.71114	+	4.69584i	0.171468	+	0.296991i
$251$	−3.36717	+	5.83211i	−0.212534	+	0.368120i	−0.952507	−	0.304517i	$-0.901505\pi$
$251$	−3.36717	+	5.83211i	−0.212534	+	0.368120i	0.739973	+	0.672637i	$0.234838\pi$
$252$			80.8911i			5.09566i
$253$	−3.76037	−	2.17105i	−0.236412	−	0.136493i
$254$	12.6679	+	7.31384i	0.794857	+	0.458911i
$255$			30.8012i			1.92885i
$256$	8.09900	−	14.0279i	0.506187	−	0.876742i
$257$	13.5010	+	23.3844i	0.842167	+	1.45868i	0.888059	+	0.459729i	$0.152054\pi$
$257$	13.5010	+	23.3844i	0.842167	+	1.45868i	−0.0458922	+	0.998946i	$0.514613\pi$
$258$	25.6246	−	14.7944i	1.59532	−	0.921057i
$259$	−14.8018			−0.919740
$260$	−31.6689	+	16.0501i	−1.96402	+	0.995388i
$261$	−27.1711			−1.68185
$262$	−22.3012	+	12.8756i	−1.37777	+	0.795457i
$263$	−13.6475	−	23.6381i	−0.841538	−	1.45759i	−0.888594	−	0.458695i	$-0.848317\pi$
$263$	−13.6475	−	23.6381i	−0.841538	−	1.45759i	0.0470558	−	0.998892i	$-0.485016\pi$
$264$	17.9470	−	31.0852i	1.10456	−	1.91316i
$265$			10.7161i			0.658286i
$266$	24.8862	+	14.3681i	1.52587	+	0.880963i
$267$	24.0650	+	13.8939i	1.47276	+	0.850296i
$268$			3.39920i			0.207639i
$269$	13.7934	−	23.8909i	0.841000	−	1.45666i	−0.0480498	−	0.998845i	$-0.515301\pi$
$269$	13.7934	−	23.8909i	0.841000	−	1.45666i	0.889050	−	0.457810i	$-0.151366\pi$
$270$	24.6081	+	42.6225i	1.49760	+	2.59392i
$271$	19.5743	−	11.3012i	1.18905	−	0.686501i	0.230963	−	0.972963i	$-0.425812\pi$
$271$	19.5743	−	11.3012i	1.18905	−	0.686501i	0.958092	+	0.286462i	$0.0924791\pi$
$272$	−0.107115			−0.00649481
$273$	−40.2394	−	26.2554i	−2.43540	−	1.58905i
$274$	10.7337			0.648448
$275$	−15.8692	+	9.16210i	−0.956950	+	0.552495i
$276$	4.70978	+	8.15757i	0.283495	+	0.491028i
$277$	−13.3130	+	23.0588i	−0.799902	+	1.38547i	0.119777	+	0.992801i	$0.461782\pi$
$277$	−13.3130	+	23.0588i	−0.799902	+	1.38547i	−0.919679	+	0.392671i	$0.871551\pi$
$278$			7.38863i			0.443141i
$279$	−13.1777	−	7.60813i	−0.788927	−	0.455487i
$280$	34.3345	+	19.8231i	2.05188	+	1.18465i
$281$			8.41612i			0.502064i	0.967979	+	0.251032i	$0.0807699\pi$
$281$			8.41612i			0.502064i	−0.967979	+	0.251032i	$0.919230\pi$
$282$	31.1457	−	53.9460i	1.85470	−	3.21244i
$283$	−2.61167	−	4.52355i	−0.155248	−	0.268897i	0.777901	−	0.628386i	$-0.216284\pi$
$283$	−2.61167	−	4.52355i	−0.155248	−	0.268897i	−0.933149	+	0.359489i	$0.882951\pi$
$284$	−15.0112	+	8.66673i	−0.890752	+	0.514276i
$285$	24.1269			1.42915
$286$	16.2055	+	31.9753i	0.958249	+	1.89074i
$287$	−32.4311			−1.91434
$288$	26.4702	−	15.2826i	1.55977	−	0.900536i
$289$	2.40209	+	4.16055i	0.141300	+	0.244738i
$290$	−17.3728	+	30.0906i	−1.02017	+	1.76698i
$291$		−	24.1829i		−	1.41763i
$292$	−9.45411	−	5.45834i	−0.553260	−	0.319425i
$293$	−15.5838	−	8.99732i	−0.910416	−	0.525629i	−0.0298513	−	0.999554i	$-0.509503\pi$
$293$	−15.5838	−	8.99732i	−0.910416	−	0.525629i	−0.880565	+	0.473925i	$0.842837\pi$
$294$			93.4312i			5.44902i
$295$	8.34384	−	14.4519i	0.485797	−	0.841425i
$296$	−4.59102	−	7.95188i	−0.266847	−	0.462193i
$297$	26.6186	−	15.3682i	1.54457	−	0.891755i
$298$	5.10685			0.295832
$299$	−3.60019	−	0.196466i	−0.208205	−	0.0113619i
$300$	39.7516			2.29506
$301$	17.6758	−	10.2052i	1.01882	−	0.588215i
$302$	17.5794	+	30.4484i	1.01158	+	1.75211i
$303$	17.6895	−	30.6392i	1.01624	−	1.76018i
$304$			0.0839041i			0.00481223i
$305$	25.0007	+	14.4341i	1.43153	+	0.826497i
$306$	−37.6516	−	21.7382i	−2.15240	−	1.24269i
$307$		−	5.88983i		−	0.336151i	−0.985774	−	0.168075i	$-0.946245\pi$
$307$		−	5.88983i		−	0.336151i	0.985774	−	0.168075i	$-0.0537552\pi$
$308$	32.3005	−	55.9462i	1.84049	−	3.18783i
$309$	−23.5372	−	40.7676i	−1.33899	−	2.31919i
$310$	−16.8513	+	9.72908i	−0.957087	+	0.552575i
$311$	−9.84313			−0.558153			−0.279076	−	0.960269i	$-0.590028\pi$
$311$	−9.84313			−0.558153			−0.279076	+	0.960269i	$0.590028\pi$
$312$	1.62409	−	29.7611i	0.0919461	−	1.68489i
$313$	16.2975			0.921189			0.460594	−	0.887611i	$-0.347636\pi$
$313$	16.2975			0.921189			0.460594	+	0.887611i	$0.347636\pi$
$314$	−19.8991	+	11.4888i	−1.12297	+	0.648348i
$315$	37.8707	+	65.5940i	2.13377	+	3.69580i
$316$	−3.26110	+	5.64840i	−0.183451	+	0.317747i
$317$			30.5451i			1.71558i	0.513998	+	0.857791i	$0.328164\pi$
$317$			30.5451i			1.71558i	−0.513998	+	0.857791i	$0.671836\pi$
$318$	−20.3273	−	11.7360i	−1.13990	−	0.658122i
$319$	18.7922	+	10.8497i	1.05216	+	0.607464i
$320$		−	39.2722i		−	2.19539i
$321$	−7.64526	+	13.2420i	−0.426717	+	0.739095i
$322$	5.25243	+	9.09748i	0.292707	+	0.506983i
$323$	−8.27321	+	4.77654i	−0.460334	+	0.265774i
$324$	−13.7828			−0.765713
$325$	−8.31466	+	12.7432i	−0.461214	+	0.706865i
$326$	12.3592			0.684515
$327$	−25.7657	+	14.8758i	−1.42485	+	0.822635i
$328$	−10.0590	−	17.4227i	−0.555416	−	0.962008i
$329$	21.4843	−	37.2119i	1.18447	−	2.05156i
$330$		−	87.6898i		−	4.82717i
$331$	−15.6575	−	9.03987i	−0.860615	−	0.496876i	0.00360345	−	0.999994i	$-0.498853\pi$
$331$	−15.6575	−	9.03987i	−0.860615	−	0.496876i	−0.864218	+	0.503117i	$0.832186\pi$
$332$	11.3590	+	6.55811i	0.623405	+	0.359923i
$333$		−	17.5417i		−	0.961279i
$334$	−11.1090	+	19.2414i	−0.607860	+	1.05284i
$335$	1.59140	+	2.75639i	0.0869476	+	0.150598i
$336$	−0.353977	+	0.204369i	−0.0193110	+	0.0111492i
$337$	−30.3938			−1.65565			−0.827827	−	0.560984i	$-0.810423\pi$
$337$	−30.3938			−1.65565			−0.827827	+	0.560984i	$0.810423\pi$
$338$	24.0060	+	17.6001i	1.30575	+	0.957320i
$339$	58.9156			3.19986
$340$	−29.7810	+	17.1941i	−1.61510	+	0.932481i
$341$	6.07599	+	10.5239i	0.329033	+	0.569902i
$342$	−17.0277	+	29.4928i	−0.920751	+	1.59479i
$343$			32.3342i			1.74588i
$344$	10.9649	+	6.33058i	0.591187	+	0.341322i
$345$	7.63824	+	4.40994i	0.411229	+	0.237423i
$346$		−	10.9707i		−	0.589788i
$347$	14.9354	−	25.8690i	0.801777	−	1.38872i	−0.116669	−	0.993171i	$-0.537222\pi$
$347$	14.9354	−	25.8690i	0.801777	−	1.38872i	0.918446	−	0.395547i	$-0.129445\pi$
$348$	−23.5367	−	40.7668i	−1.26170	−	2.18533i
$349$	17.0473	−	9.84226i	0.912521	−	0.526844i	0.0312793	−	0.999511i	$-0.490042\pi$
$349$	17.0473	−	9.84226i	0.912521	−	0.526844i	0.881241	+	0.472667i	$0.156709\pi$
$350$	44.3318			2.36963
$351$	13.9468	−	21.3751i	0.744423	−	1.14092i
$352$	−24.4099			−1.30105
$353$	0.638758	−	0.368787i	0.0339977	−	0.0196286i	−0.482905	−	0.875673i	$-0.660418\pi$
$353$	0.638758	−	0.368787i	0.0339977	−	0.0196286i	0.516903	+	0.856044i	$0.327085\pi$
$354$	18.2759	+	31.6548i	0.971352	+	1.68243i
$355$	−8.11499	+	14.0556i	−0.430699	+	0.745992i
$356$			31.0239i			1.64426i
$357$	−40.3028	−	23.2688i	−2.13305	−	1.23152i
$358$	−7.38816	−	4.26556i	−0.390476	−	0.225442i
$359$			6.52613i			0.344436i	0.985059	+	0.172218i	$0.0550934\pi$
$359$			6.52613i			0.344436i	−0.985059	+	0.172218i	$0.944907\pi$
$360$	−23.4924	+	40.6900i	−1.23816	+	2.14455i
$361$	−5.75850	−	9.97401i	−0.303079	−	0.524948i
$362$	−5.44237	+	3.14216i	−0.286045	+	0.165148i
$363$	−22.8127			−1.19736
$364$	2.92299	−	53.5631i	0.153206	−	2.80747i
$365$	−10.2217			−0.535028
$366$	−54.7601	+	31.6158i	−2.86236	+	1.65258i
$367$	2.26854	+	3.92922i	0.118417	+	0.205104i	0.919140	−	0.393930i	$-0.128885\pi$
$367$	2.26854	+	3.92922i	0.118417	+	0.205104i	−0.800724	+	0.599034i	$0.795552\pi$
$368$	−0.0153361	+	0.0265629i	−0.000799450	+	0.00138469i
$369$		−	38.4342i		−	2.00080i
$370$	−19.4266	−	11.2159i	−1.00994	−	0.583089i
$371$	−14.0218	−	8.09549i	−0.727976	−	0.420297i
$372$		−	26.3619i		−	1.36680i
$373$	−6.44751	+	11.1674i	−0.333840	+	0.578227i	−0.983261	−	0.182201i	$-0.941678\pi$
$373$	−6.44751	+	11.1674i	−0.333840	+	0.578227i	0.649422	+	0.760428i	$0.275011\pi$
$374$	17.3605	+	30.0692i	0.897689	+	1.55484i
$375$	−5.95691	+	3.43922i	−0.307613	+	0.177601i
$376$	26.6548			1.37462
$377$	17.9917	+	0.981825i	0.926619	+	0.0505665i
$378$	−74.3609			−3.82471
$379$	28.4270	−	16.4123i	1.46020	−	0.843044i	0.461176	−	0.887309i	$-0.347428\pi$
$379$	28.4270	−	16.4123i	1.46020	−	0.843044i	0.999020	+	0.0442643i	$0.0140944\pi$
$380$	13.4683	+	23.3277i	0.690908	+	1.19669i
$381$	−9.27798	+	16.0699i	−0.475325	+	0.823287i
$382$		−	59.5446i		−	3.04657i
$383$	8.49229	+	4.90302i	0.433936	+	0.250533i	0.701022	−	0.713140i	$-0.252728\pi$
$383$	8.49229	+	4.90302i	0.433936	+	0.250533i	−0.267086	+	0.963673i	$0.586061\pi$
$384$	46.2126	+	26.6809i	2.35828	+	1.36155i
$385$		−	60.4884i		−	3.08278i
$386$	12.6266	−	21.8699i	0.642678	−	1.11315i
$387$	12.0942	+	20.9477i	0.614782	+	1.06483i
$388$	23.3819	−	13.4995i	1.18704	−	0.685335i
$389$	8.60104			0.436090			0.218045	−	0.975939i	$-0.430032\pi$
$389$	8.60104			0.436090			0.218045	+	0.975939i	$0.430032\pi$
$390$	−32.9173	−	64.9498i	−1.66683	−	3.28886i
$391$	−3.49225			−0.176611
$392$	−34.6234	+	19.9898i	−1.74875	+	1.00964i
$393$	−16.3334	−	28.2902i	−0.823909	−	1.42705i
$394$	10.0422	−	17.3936i	0.505920	−	0.876279i
$395$			6.10699i			0.307276i
$396$	66.3021	+	38.2795i	3.33181	+	1.92362i
$397$	7.00815	+	4.04616i	0.351729	+	0.203071i	0.665447	−	0.746446i	$-0.268241\pi$
$397$	7.00815	+	4.04616i	0.351729	+	0.203071i	−0.313718	+	0.949516i	$0.601575\pi$
$398$		−	26.0103i		−	1.30378i
$399$	−18.2266	+	31.5695i	−0.912474	+	1.58045i
$400$	0.0647202	+	0.112099i	0.00323601	+	0.00560494i
$401$	21.9507	−	12.6732i	1.09616	−	0.632870i	0.160953	−	0.986962i	$-0.448543\pi$
$401$	21.9507	−	12.6732i	1.09616	−	0.632870i	0.935211	+	0.354092i	$0.115210\pi$
$402$	−6.97144			−0.347704
$403$	8.45085	+	5.51400i	0.420967	+	0.274672i
$404$	39.4991			1.96516
$405$	−11.1764	+	6.45270i	−0.555360	+	0.320637i
$406$	−26.2486	−	45.4640i	−1.30270	−	2.25634i
$407$	−7.00456	+	12.1322i	−0.347203	+	0.601373i
$408$		−	28.8688i		−	1.42922i
$409$	−9.74055	−	5.62371i	−0.481639	−	0.278075i	0.239460	−	0.970906i	$-0.423030\pi$
$409$	−9.74055	−	5.62371i	−0.481639	−	0.278075i	−0.721099	+	0.692832i	$0.756363\pi$
$410$	−42.5640	−	24.5743i	−2.10209	−	1.21364i
$411$			13.6163i			0.671642i
$412$	26.2782	−	45.5152i	1.29464	−	2.24237i
$413$	12.6067	+	21.8355i	0.620335	+	1.07445i
$414$	−10.7815	+	6.22469i	−0.529881	+	0.305927i
$415$	12.2812			0.602861
$416$	−18.0798	+	9.16307i	−0.886438	+	0.449257i
$417$	−9.37286			−0.458991
$418$	23.5535	−	13.5986i	1.15204	−	0.665130i
$419$	−3.17468	−	5.49870i	−0.155093	−	0.268629i	0.778000	−	0.628265i	$-0.216234\pi$
$419$	−3.17468	−	5.49870i	−0.155093	−	0.268629i	−0.933093	+	0.359635i	$0.882901\pi$
$420$	−65.6104	+	113.641i	−3.20146	+	5.54509i
$421$		−	2.29430i		−	0.111817i	−0.998436	−	0.0559087i	$-0.982194\pi$
$421$		−	2.29430i		−	0.111817i	0.998436	−	0.0559087i	$-0.0178056\pi$
$422$	−16.5214	−	9.53864i	−0.804249	−	0.464333i
$423$	44.1000	+	25.4612i	2.14422	+	1.23796i
$424$		−	10.0438i		−	0.487769i
$425$	−7.36886	+	12.7632i	−0.357442	+	0.619108i
$426$	−17.7746	−	30.7866i	−0.861184	−	1.49161i
$427$	−37.7735	+	21.8086i	−1.82799	+	1.05539i
$428$	−17.0712			−0.825166
$429$	−40.5624	+	20.5575i	−1.95837	+	0.992524i
$430$	30.9314			1.49165
$431$	−1.16499	+	0.672607i	−0.0561156	+	0.0323983i	−0.527795	−	0.849372i	$-0.676981\pi$
$431$	−1.16499	+	0.672607i	−0.0561156	+	0.0323983i	0.471680	+	0.881770i	$0.343648\pi$
$432$	−0.108560	−	0.188031i	−0.00522309	−	0.00904665i
$433$	−8.53461	+	14.7824i	−0.410147	+	0.710396i	−0.994906	−	0.100812i	$-0.967856\pi$
$433$	−8.53461	+	14.7824i	−0.410147	+	0.710396i	0.584758	+	0.811208i	$0.301189\pi$
$434$		−	29.3993i		−	1.41121i
$435$	−38.1715	−	22.0383i	−1.83018	−	1.05666i
$436$	−28.7662	−	16.6082i	−1.37765	−	0.795388i
$437$			2.73551i			0.130857i
$438$	11.1945	−	19.3895i	0.534895	−	0.926465i
$439$	16.2910	+	28.2169i	0.777529	+	1.34672i	0.933362	+	0.358937i	$0.116861\pi$
$439$	16.2910	+	28.2169i	0.777529	+	1.34672i	−0.155833	+	0.987783i	$0.549806\pi$
$440$	32.4958	−	18.7615i	1.54918	−	0.894417i
$441$	−76.3786			−3.63708
$442$	24.1460	+	15.7547i	1.14851	+	0.749377i
$443$	15.0615			0.715591			0.357796	−	0.933800i	$-0.383528\pi$
$443$	15.0615			0.715591			0.357796	+	0.933800i	$0.383528\pi$
$444$	26.3191	−	15.1954i	1.24905	−	0.721140i
$445$	14.5244	+	25.1571i	0.688524	+	1.19256i
$446$	−0.834863	+	1.44603i	−0.0395319	+	0.0684713i
$447$			6.47830i			0.306413i
$448$	51.3869	+	29.6682i	2.42780	+	1.40169i
$449$	24.4416	+	14.1113i	1.15347	+	0.665955i	0.949730	−	0.313070i	$-0.101357\pi$
$449$	24.4416	+	14.1113i	1.15347	+	0.665955i	0.203738	+	0.979025i	$0.434691\pi$
$450$			52.5379i			2.47666i
$451$	−15.3471	+	26.5820i	−0.722668	+	1.25170i
$452$	32.8883	+	56.9642i	1.54694	+	2.67937i
$453$	−38.6253	+	22.3003i	−1.81478	+	1.04776i
$454$	−24.9132			−1.16923
$455$	−22.7064	−	44.8024i	−1.06449	−	2.10037i
$456$	−22.6131			−1.05896
$457$	−19.5064	+	11.2620i	−0.912472	+	0.526816i	−0.881226	−	0.472696i	$-0.843281\pi$
$457$	−19.5064	+	11.2620i	−0.912472	+	0.526816i	−0.0312461	+	0.999512i	$0.509948\pi$
$458$	24.4610	+	42.3677i	1.14299	+	1.97971i
$459$	12.3603	−	21.4087i	0.576930	−	0.999272i
$460$			9.84700i			0.459119i
$461$	−20.8322	−	12.0275i	−0.970254	−	0.560176i	−0.0709401	−	0.997481i	$-0.522600\pi$
$461$	−20.8322	−	12.0275i	−0.970254	−	0.560176i	−0.899314	+	0.437304i	$0.855933\pi$
$462$	114.740	+	66.2453i	5.33820	+	3.08201i
$463$			27.5977i			1.28258i	0.767301	+	0.641288i	$0.221599\pi$
$463$			27.5977i			1.28258i	−0.767301	+	0.641288i	$0.778401\pi$
$464$	0.0766410	−	0.132746i	0.00355797	−	0.00616259i
$465$	−12.3418	−	21.3767i	−0.572339	−	0.991321i
$466$	−33.3336	+	19.2451i	−1.54415	+	0.891514i
$467$	12.3587			0.571895			0.285947	−	0.958245i	$-0.407692\pi$
$467$	12.3587			0.571895			0.285947	+	0.958245i	$0.407692\pi$
$468$	63.4779	+	3.46405i	2.93427	+	0.160126i
$469$	−4.80890			−0.222054
$470$	56.3940	−	32.5591i	2.60126	−	1.50184i
$471$	−14.5741	−	25.2430i	−0.671538	−	1.16314i
$472$	−7.82034	+	13.5452i	−0.359960	+	0.623470i
$473$		−	19.3173i		−	0.888208i
$474$	−11.5843	−	6.68821i	−0.532086	−	0.307200i
$475$	9.99755	+	5.77209i	0.458719	+	0.264841i
$476$		−	51.9571i		−	2.38145i
$477$	9.59401	−	16.6173i	0.439279	−	0.760854i
$478$	−8.69382	−	15.0581i	−0.397646	−	0.688743i
$479$	−12.4918	+	7.21212i	−0.570763	+	0.329530i	−0.757454	−	0.652888i	$-0.773557\pi$
$479$	−12.4918	+	7.21212i	−0.570763	+	0.329530i	0.186691	+	0.982419i	$0.440224\pi$
$480$	49.5826			2.26312
$481$	−0.633868	+	11.6155i	−0.0289019	+	0.529620i
$482$	−45.0471			−2.05184
$483$	−11.5406	+	6.66298i	−0.525117	+	0.303176i
$484$	−12.7347	−	22.0571i	−0.578849	−	1.00260i
$485$	12.6401	−	21.8934i	0.573959	−	0.994126i
$486$			20.3580i			0.923455i
$487$	−7.99046	−	4.61329i	−0.362082	−	0.209048i	0.307911	−	0.951415i	$-0.400370\pi$
$487$	−7.99046	−	4.61329i	−0.362082	−	0.209048i	−0.669994	+	0.742367i	$0.733703\pi$
$488$	−23.4321	−	13.5285i	−1.06072	−	0.612408i
$489$			15.6783i			0.708998i
$490$	−48.8355	+	84.5855i	−2.20616	+	3.82119i
$491$	7.81620	+	13.5381i	0.352740	+	0.610964i	0.986729	−	0.162379i	$-0.0519166\pi$
$491$	7.81620	+	13.5381i	0.352740	+	0.610964i	−0.633988	+	0.773343i	$0.718583\pi$
$492$	57.6657	−	33.2933i	2.59977	−	1.50098i
$493$	17.4523			0.786010
$494$	12.3408	−	18.9138i	0.555240	−	0.850970i
$495$	71.6852			3.22201
$496$	0.0743401	−	0.0429203i	0.00333797	−	0.00192718i
$497$	−12.2609	−	21.2366i	−0.549978	−	0.952590i
$498$	−13.4501	+	23.2962i	−0.602711	+	1.04393i
$499$			2.19369i			0.0982029i	0.998794	+	0.0491014i	$0.0156358\pi$
$499$			2.19369i			0.0982029i	−0.998794	+	0.0491014i	$0.984364\pi$
$500$	−6.65062	−	3.83974i	−0.297425	−	0.171718i
$501$	−24.4087	−	14.0924i	−1.09050	−	0.629602i
$502$		−	15.4199i		−	0.688224i
$503$	3.96506	−	6.86769i	0.176793	−	0.306215i	−0.763987	−	0.645232i	$-0.776761\pi$
$503$	3.96506	−	6.86769i	0.176793	−	0.306215i	0.940780	+	0.339016i	$0.110094\pi$
$504$	−35.4947	−	61.4786i	−1.58106	−	2.73848i
$505$	32.0296	−	18.4923i	1.42530	−	0.822895i
$506$	9.94229			0.441989
$507$	−22.3267	+	30.4529i	−0.991562	+	1.35246i
$508$	−20.7169			−0.919163
$509$	−33.4479	+	19.3112i	−1.48255	+	0.855952i	−0.999804	−	0.0198064i	$-0.993695\pi$
$509$	−33.4479	+	19.3112i	−1.48255	+	0.855952i	−0.482749	+	0.875759i	$0.660362\pi$
$510$	−35.2634	−	61.0781i	−1.56149	−	2.70458i
$511$	7.72198	−	13.3749i	0.341600	−	0.591669i
$512$			0.347013i			0.0153360i
$513$	−16.7696	−	9.68193i	−0.740396	−	0.427468i
$514$	−53.5441	−	30.9137i	−2.36173	−	1.36355i
$515$		−	49.2106i		−	2.16848i
$516$	−20.9530	+	36.2916i	−0.922403	+	1.59765i
$517$	−20.3337	−	35.2191i	−0.894277	−	1.54893i
$518$	29.3516	−	16.9462i	1.28964	−	0.744572i
$519$	13.9169			0.610883
$520$	17.0261	−	26.0946i	0.746645	−	1.14432i
$521$	24.7718			1.08527			0.542636	−	0.839968i	$-0.317426\pi$
$521$	24.7718			1.08527			0.542636	+	0.839968i	$0.317426\pi$
$522$	53.8796	−	31.1074i	2.35825	−	1.36153i
$523$	7.65950	+	13.2666i	0.334927	+	0.580110i	0.983471	−	0.181067i	$-0.0579551\pi$
$523$	7.65950	+	13.2666i	0.334927	+	0.580110i	−0.648544	+	0.761177i	$0.724622\pi$
$524$	18.2355	−	31.5847i	0.796620	−	1.37979i
$525$			56.2372i			2.45439i
$526$	54.1251	+	31.2491i	2.35997	+	1.36253i
$527$	8.46414	+	4.88678i	0.368704	+	0.212871i
$528$			0.386848i			0.0168354i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−12.2686	−	21.2498i	−0.532912	−	0.923031i
$531$	−25.8773	+	14.9403i	−1.12298	+	0.648353i
$532$	−40.6984			−1.76450
$533$	−1.38882	+	25.4497i	−0.0601563	+	1.10235i
$534$	−63.6271			−2.75341
$535$	−13.8429	+	7.99219i	−0.598480	+	0.345533i
$536$	−1.49156	−	2.58345i	−0.0644254	−	0.111588i
$537$	5.41108	−	9.37226i	0.233505	−	0.404443i
$538$			63.1668i			2.72331i
$539$	52.8252	+	30.4987i	2.27534	+	1.31367i
$540$	−60.3655	−	34.8520i	−2.59772	−	1.49979i
$541$			40.6683i			1.74847i	0.485506	+	0.874233i	$0.338635\pi$
$541$			40.6683i			1.74847i	−0.485506	+	0.874233i	$0.661365\pi$
$542$	−25.8769	+	44.8201i	−1.11151	+	1.92519i
$543$	−3.98599	−	6.90393i	−0.171055	−	0.296276i
$544$	−17.0021	+	9.81616i	−0.728958	+	0.420864i
$545$	−31.1018			−1.33225
$546$	109.853	+	5.99478i	4.70127	+	0.256553i
$547$	38.5317			1.64750			0.823749	−	0.566954i	$-0.191878\pi$
$547$	38.5317			1.64750			0.823749	+	0.566954i	$0.191878\pi$
$548$	−13.1653	+	7.60098i	−0.562393	+	0.324698i
$549$	−25.8454	−	44.7656i	−1.10306	−	1.91055i
$550$	20.9788	−	36.3364i	0.894540	−	1.54939i
$551$		−	13.6705i		−	0.582382i
$552$	−7.15902	−	4.13326i	−0.304708	−	0.175923i
$553$	−7.99087	−	4.61353i	−0.339806	−	0.196187i
$554$		−	60.9668i		−	2.59023i
$555$	14.2280	−	24.6436i	0.603945	−	1.04606i
$556$	−5.23219	−	9.06241i	−0.221894	−	0.384332i
$557$	30.6760	−	17.7108i	1.29978	−	0.750431i	0.319418	−	0.947614i	$-0.396513\pi$
$557$	30.6760	−	17.7108i	1.29978	−	0.750431i	0.980367	+	0.197183i	$0.0631793\pi$
$558$	34.8413			1.47495
$559$	−7.25137	−	14.3078i	−0.306700	−	0.605157i
$560$	−0.427285			−0.0180561
$561$	−38.1444	+	22.0227i	−1.61046	+	0.929798i
$562$	−9.63537	−	16.6890i	−0.406444	−	0.703981i
$563$	10.1951	−	17.6585i	0.429673	−	0.744215i	−0.567171	−	0.823600i	$-0.691962\pi$
$563$	10.1951	−	17.6585i	0.429673	−	0.744215i	0.996844	+	0.0793848i	$0.0252956\pi$
$564$			88.2222i			3.71482i
$565$	53.3378	+	30.7946i	2.24394	+	1.29554i
$566$	10.3578	+	5.98006i	0.435369	+	0.251360i
$567$		−	19.4988i		−	0.818871i
$568$	7.60585	−	13.1737i	0.319134	−	0.552757i
$569$	11.1924	+	19.3857i	0.469208	+	0.812692i	0.999380	−	0.0351978i	$-0.0112061\pi$
$569$	11.1924	+	19.3857i	0.469208	+	0.812692i	−0.530172	+	0.847890i	$0.677873\pi$
$570$	−47.8429	+	27.6221i	−2.00392	+	1.15696i
$571$	−9.65101			−0.403882			−0.201941	−	0.979398i	$-0.564725\pi$
$571$	−9.65101			−0.403882			−0.201941	+	0.979398i	$0.564725\pi$
$572$	−42.5196	−	27.7431i	−1.77783	−	1.16000i
$573$	75.5354			3.15554
$574$	64.3099	−	37.1294i	2.68424	−	1.54975i
$575$	2.11006	+	3.65473i	0.0879956	+	0.152413i
$576$	−35.1600	+	60.8989i	−1.46500	+	2.53745i
$577$		−	22.5663i		−	0.939447i	−0.882813	−	0.469724i	$-0.844354\pi$
$577$		−	22.5663i		−	0.939447i	0.882813	−	0.469724i	$-0.155646\pi$
$578$	−9.52658	−	5.50017i	−0.396254	−	0.228777i
$579$	27.7432	+	16.0175i	1.15297	+	0.665665i
$580$		−	49.2096i		−	2.04332i
$581$	−9.27785	+	16.0697i	−0.384910	+	0.666684i
$582$	27.6863	+	47.9540i	1.14763	+	1.98776i
$583$	−13.2709	+	7.66194i	−0.549624	+	0.317325i
$584$	9.58038			0.396439
$585$	53.0955	−	26.9094i	2.19523	−	1.11257i
$586$	41.2031			1.70208
$587$	−20.1851	+	11.6539i	−0.833130	+	0.481008i	−0.854923	−	0.518755i	$-0.826396\pi$
$587$	−20.1851	+	11.6539i	−0.833130	+	0.481008i	0.0217931	+	0.999763i	$0.493063\pi$
$588$	−66.1624	−	114.597i	−2.72849	−	4.72588i
$589$	3.82785	−	6.63003i	0.157724	−	0.273186i
$590$			38.2105i			1.57310i
$591$	22.0647	+	12.7391i	0.907622	+	0.524016i
$592$	0.0857011	+	0.0494796i	0.00352230	+	0.00203360i
$593$		−	0.994137i		−	0.0408243i	−0.999792	−	0.0204121i	$-0.993502\pi$
$593$		−	0.994137i		−	0.0408243i	0.999792	−	0.0204121i	$-0.00649784\pi$
$594$	−35.1893	+	60.9496i	−1.44383	+	2.50079i
$595$	−24.3247	−	42.1316i	−0.997216	−	1.72723i
$596$	−6.26372	+	3.61636i	−0.256572	+	0.148132i
$597$	32.9954			1.35041
$598$	7.36402	−	3.73217i	0.301137	−	0.152620i
$599$	11.3171			0.462404			0.231202	−	0.972906i	$-0.425734\pi$
$599$	11.3171			0.462404			0.231202	+	0.972906i	$0.425734\pi$
$600$	−30.2119	+	17.4429i	−1.23340	+	0.712102i
$601$	−10.3277	−	17.8881i	−0.421276	−	0.729671i	0.574789	−	0.818302i	$-0.305084\pi$
$601$	−10.3277	−	17.8881i	−0.421276	−	0.729671i	−0.996065	+	0.0886309i	$0.971751\pi$
$602$	−23.3672	+	40.4731i	−0.952375	+	1.64956i
$603$		−	5.69905i		−	0.232083i
$604$	−43.1234	−	24.8973i	−1.75467	−	1.01306i
$605$	−20.6529	−	11.9240i	−0.839660	−	0.484778i
$606$			81.0090i			3.29076i
$607$	−20.3204	+	35.1959i	−0.824778	+	1.42856i	0.0773103	+	0.997007i	$0.475367\pi$
$607$	−20.3204	+	35.1959i	−0.824778	+	1.42856i	−0.902089	+	0.431551i	$0.857967\pi$
$608$	7.68908	+	13.3179i	0.311833	+	0.540111i
$609$	57.6734	−	33.2977i	2.33704	−	1.34929i
$610$	−66.1009			−2.67635
$611$	−28.2814	−	18.4530i	−1.14414	−	0.746528i
$612$	61.5747			2.48901
$613$	0.497762	−	0.287383i	0.0201044	−	0.0116073i	−0.489914	−	0.871771i	$-0.662972\pi$
$613$	0.497762	−	0.287383i	0.0201044	−	0.0116073i	0.510019	+	0.860163i	$0.329639\pi$
$614$	6.74310	+	11.6794i	0.272129	+	0.471342i
$615$	31.1738	−	53.9946i	1.25705	−	2.17727i
$616$			56.6934i			2.28424i
$617$	−4.76072	−	2.74860i	−0.191660	−	0.110655i	0.401100	−	0.916034i	$-0.368628\pi$
$617$	−4.76072	−	2.74860i	−0.191660	−	0.110655i	−0.592759	+	0.805380i	$0.701961\pi$
$618$	93.3474	+	53.8941i	3.75498	+	2.16794i
$619$		−	29.5538i		−	1.18787i	−0.804514	−	0.593933i	$-0.797574\pi$
$619$		−	29.5538i		−	1.18787i	0.804514	−	0.593933i	$-0.202426\pi$
$620$	13.7791	−	23.8661i	0.553382	−	0.958486i
$621$	−3.53935	−	6.13034i	−0.142029	−	0.246002i
$622$	19.5187	−	11.2691i	0.782628	−	0.451850i
$623$	−43.8900			−1.75841
$624$	0.145216	+	0.286529i	0.00581330	+	0.0114703i
$625$	−28.2912			−1.13165
$626$	−32.3175	+	18.6585i	−1.29167	+	0.745745i
$627$	17.2505	+	29.8788i	0.688920	+	1.19324i
$628$	16.2713	−	28.1827i	0.649295	−	1.12461i
$629$			11.2672i			0.449253i
$630$	−150.193	−	86.7141i	−5.98384	−	3.45477i
$631$	29.0067	+	16.7471i	1.15474	+	0.666690i	0.950038	−	0.312135i	$-0.101044\pi$
$631$	29.0067	+	16.7471i	1.15474	+	0.666690i	0.204702	+	0.978824i	$0.434377\pi$
$632$		−	5.72384i		−	0.227682i
$633$	12.1003	−	20.9582i	0.480942	−	0.833016i
$634$	−34.9702	−	60.5701i	−1.38884	−	2.40555i
$635$	−16.7992	+	9.69900i	−0.666654	+	0.384893i
$636$	33.2429			1.31817
$637$	50.5751	+	2.75993i	2.00386	+	0.109353i
$638$	−49.6858			−1.96708
$639$	25.1676	−	14.5305i	0.995613	−	0.574818i
$640$	27.8916	+	48.3097i	1.10251	+	1.90961i
$641$	10.6912	−	18.5177i	0.422276	−	0.731404i	−0.573885	−	0.818936i	$-0.694564\pi$
$641$	10.6912	−	18.5177i	0.422276	−	0.731404i	0.996162	+	0.0875314i	$0.0278978\pi$
$642$		−	35.0113i		−	1.38179i
$643$	−23.4772	−	13.5546i	−0.925852	−	0.534541i	−0.0403547	−	0.999185i	$-0.512849\pi$
$643$	−23.4772	−	13.5546i	−0.925852	−	0.534541i	−0.885497	+	0.464644i	$0.846182\pi$
$644$	−12.8846	−	7.43892i	−0.507724	−	0.293135i
$645$			39.2381i			1.54500i
$646$	10.9370	−	18.9435i	0.430312	−	0.745322i
$647$	14.1426	+	24.4957i	0.556004	+	0.963027i	0.997825	+	0.0659236i	$0.0209994\pi$
$647$	14.1426	+	24.4957i	0.556004	+	0.963027i	−0.441821	+	0.897103i	$0.645667\pi$
$648$	10.4752	−	6.04785i	0.411504	−	0.237582i
$649$	23.8631			0.936710
$650$	1.89845	−	34.7886i	0.0744633	−	1.36452i
$651$	37.2946			1.46169
$652$	−15.1590	+	8.75207i	−0.593674	+	0.342758i
$653$	5.80184	+	10.0491i	0.227044	+	0.393251i	0.956931	−	0.290317i	$-0.0937607\pi$
$653$	5.80184	+	10.0491i	0.227044	+	0.393251i	−0.729887	+	0.683568i	$0.760427\pi$
$654$	34.0618	−	58.9968i	1.33192	−	2.30696i
$655$		−	34.1491i		−	1.33432i
$656$	0.187773	+	0.108411i	0.00733130	+	0.00423273i
$657$	15.8506	+	9.15136i	0.618391	+	0.357028i
$658$			98.3871i			3.83553i
$659$	3.47524	−	6.01929i	0.135376	−	0.234478i	−0.790365	−	0.612636i	$-0.790109\pi$
$659$	3.47524	−	6.01929i	0.135376	−	0.234478i	0.925741	+	0.378158i	$0.123442\pi$
$660$	62.0967	+	107.555i	2.41711	+	4.18656i
$661$	−12.8784	+	7.43536i	−0.500913	+	0.289202i	−0.729090	−	0.684417i	$-0.760057\pi$
$661$	−12.8784	+	7.43536i	−0.500913	+	0.289202i	0.228178	+	0.973620i	$0.426723\pi$
$662$	41.3979			1.60898
$663$	−19.9857	+	30.6304i	−0.776181	+	1.18959i
$664$	−11.5107			−0.446701
$665$	−33.0021	+	19.0537i	−1.27977	+	0.738873i
$666$	20.0830	+	34.7847i	0.778200	+	1.34788i
$667$	2.49871	−	4.32790i	0.0967505	−	0.167577i
$668$		−	31.4670i		−	1.21750i
$669$	−1.83436	−	1.05907i	−0.0709204	−	0.0409459i
$670$	−6.31142	−	3.64390i	−0.243831	−	0.140776i
$671$			41.2812i			1.59364i
$672$	−37.4572	+	64.8777i	−1.44494	+	2.50271i
$673$	−19.4060	−	33.6121i	−0.748045	−	1.29565i	−0.948759	−	0.316001i	$-0.897660\pi$
$673$	−19.4060	−	33.6121i	−0.748045	−	1.29565i	0.200714	−	0.979650i	$-0.435674\pi$
$674$	60.2700	−	34.7969i	2.32151	−	1.34033i
$675$	−29.8730			−1.14981
$676$	−41.9076	−	4.58754i	−1.61183	−	0.176444i
$677$	−27.8896			−1.07188			−0.535942	−	0.844255i	$-0.680043\pi$
$677$	−27.8896			−1.07188			−0.535942	+	0.844255i	$0.680043\pi$
$678$	−116.828	+	67.4508i	−4.48676	+	2.59043i
$679$	19.0980	+	33.0787i	0.732913	+	1.26944i
$680$	15.0894	−	26.1356i	0.578652	−	1.00225i
$681$		−	31.6037i		−	1.21106i
$682$	−24.0971	−	13.9124i	−0.922724	−	0.532735i
$683$	−25.7067	−	14.8418i	−0.983638	−	0.567904i	−0.0802718	−	0.996773i	$-0.525579\pi$
$683$	−25.7067	−	14.8418i	−0.983638	−	0.567904i	−0.903367	+	0.428869i	$0.858912\pi$
$684$		−	48.2319i		−	1.84419i
$685$	−7.11709	+	12.3272i	−0.271930	+	0.470997i
$686$	−37.0185	−	64.1180i	−1.41337	−	2.44803i
$687$	−53.7456	+	31.0301i	−2.05052	+	1.18387i
$688$	−0.136455			−0.00520231
$689$	−6.95326	+	10.6567i	−0.264898	+	0.405988i
$690$	−20.1953			−0.768820
$691$	−0.846355	+	0.488643i	−0.0321968	+	0.0185889i	−0.516012	−	0.856581i	$-0.672584\pi$
$691$	−0.846355	+	0.488643i	−0.0321968	+	0.0185889i	0.483815	+	0.875170i	$0.339251\pi$
$692$	7.76878	+	13.4559i	0.295325	+	0.511518i
$693$	−54.1546	+	93.7985i	−2.05716	+	3.56311i
$694$			68.3966i			2.59630i
$695$	−8.48548	−	4.89910i	−0.321873	−	0.185833i
$696$	35.7766	+	20.6557i	1.35611	+	0.782950i
$697$			24.6867i			0.935074i
$698$	−22.5362	+	39.0339i	−0.853009	+	1.47745i
$699$	−24.4134	−	42.2853i	−0.923401	−	1.59938i
$700$	−54.3745	+	31.3931i	−2.05516	+	1.18655i
$701$	−39.1601			−1.47906			−0.739528	−	0.673126i	$-0.764951\pi$
$701$	−39.1601			−1.47906			−0.739528	+	0.673126i	$0.764951\pi$
$702$	−3.18440	+	58.3534i	−0.120188	+	2.20241i
$703$	8.82569			0.332867
$704$	48.6349	−	28.0794i	1.83300	−	1.05828i
$705$	41.3029	+	71.5387i	1.55556	+	2.69430i
$706$	−0.844427	+	1.46259i	−0.0317804	+	0.0550453i
$707$			55.8800i			2.10158i
$708$	−44.8320	−	25.8838i	−1.68489	−	0.972772i
$709$	15.2209	+	8.78778i	0.571632	+	0.330032i	0.757801	−	0.652486i	$-0.226274\pi$
$709$	15.2209	+	8.78778i	0.571632	+	0.330032i	−0.186169	+	0.982518i	$0.559607\pi$
$710$		−	37.1624i		−	1.39468i
$711$	5.46752	−	9.47002i	0.205048	−	0.355153i
$712$	−13.6132	−	23.5787i	−0.510175	−	0.883649i
$713$	2.42369	−	1.39932i	0.0907680	−	0.0524049i
$714$	106.559			3.98787
$715$	−47.4673	−	2.59034i	−1.77518	−	0.0968731i
$716$	12.0824			0.451542
$717$	19.1020	−	11.0286i	0.713378	−	0.411869i
$718$	−7.47158	−	12.9412i	−0.278837	−	0.482960i
$719$	−18.8536	+	32.6554i	−0.703121	+	1.21784i	0.264244	+	0.964456i	$0.414878\pi$
$719$	−18.8536	+	32.6554i	−0.703121	+	1.21784i	−0.967365	+	0.253386i	$0.918456\pi$
$720$		−	0.506378i		−	0.0188716i
$721$	64.3910	+	37.1762i	2.39805	+	1.38451i
$722$	22.8379	+	13.1855i	0.849939	+	0.490712i
$723$		−	57.1446i		−	2.12523i
$724$	4.45017	−	7.70793i	0.165389	−	0.286463i
$725$	−10.5449	−	18.2642i	−0.391626	−	0.678317i
$726$	45.2370	−	26.1176i	1.67890	−	0.969315i
$727$	41.9807			1.55698			0.778489	−	0.627659i	$-0.215987\pi$
$727$	41.9807			1.55698			0.778489	+	0.627659i	$0.215987\pi$
$728$	21.2818	+	41.9915i	0.788754	+	1.55631i
$729$	−38.5755			−1.42872
$730$	20.2694	−	11.7025i	0.750202	−	0.433130i
$731$	−7.76821	−	13.4549i	−0.287317	−	0.497648i
$732$	44.7768	−	77.5557i	1.65500	−	2.86654i
$733$		−	39.2296i		−	1.44898i	−0.689285	−	0.724490i	$-0.742075\pi$
$733$		−	39.2296i		−	1.44898i	0.689285	−	0.724490i	$-0.257925\pi$
$734$	−8.99690	−	5.19436i	−0.332081	−	0.191727i
$735$	−107.301	−	61.9503i	−3.95786	−	2.28507i
$736$			5.62168i			0.207218i
$737$	−2.27568	+	3.94160i	−0.0838258	+	0.145191i
$738$	44.0022	+	76.2140i	1.61974	+	2.80548i
$739$	34.7159	−	20.0432i	1.27704	−	0.737302i	0.300740	−	0.953706i	$-0.402766\pi$
$739$	34.7159	−	20.0432i	1.27704	−	0.737302i	0.976304	+	0.216404i	$0.0694329\pi$
$740$	31.7698			1.16788
$741$	23.9931	+	15.6550i	0.881407	+	0.575100i
$742$	37.0732			1.36100
$743$	9.71566	−	5.60934i	0.356433	−	0.205787i	−0.311082	−	0.950383i	$-0.600691\pi$
$743$	9.71566	−	5.60934i	0.356433	−	0.205787i	0.667515	+	0.744596i	$0.267358\pi$
$744$	11.5675	+	20.0355i	0.424085	+	0.734538i
$745$	−3.38614	+	5.86496i	−0.124058	+	0.214876i
$746$		−	29.5263i		−	1.08103i
$747$	−19.0443	−	10.9952i	−0.696794	−	0.402294i
$748$	−42.5865	−	24.5873i	−1.55712	−	0.899001i
$749$		−	24.1508i		−	0.882451i
$750$	7.87493	−	13.6398i	0.287552	−	0.498054i
$751$	−10.0748	−	17.4501i	−0.367636	−	0.636764i	0.621559	−	0.783367i	$-0.286499\pi$
$751$	−10.0748	−	17.4501i	−0.367636	−	0.636764i	−0.989195	+	0.146603i	$0.953166\pi$
$752$	−0.248785	+	0.143636i	−0.00907224	+	0.00523786i
$753$	19.5609			0.712841
$754$	−36.8011	+	18.6512i	−1.34022	+	0.679238i
$755$	−46.6246			−1.69684
$756$	91.2062	−	52.6579i	3.31714	−	1.91515i
$757$	−14.5144	−	25.1398i	−0.527537	−	0.913720i	−0.999485	−	0.0320938i	$-0.989782\pi$
$757$	−14.5144	−	25.1398i	−0.527537	−	0.913720i	0.471948	−	0.881626i	$-0.343551\pi$
$758$	−37.5800	+	65.0904i	−1.36497	+	2.36419i
$759$			12.6123i			0.457798i
$760$	−20.4722	−	11.8196i	−0.742606	−	0.428744i
$761$	3.27060	+	1.88828i	0.118559	+	0.0684502i	0.558107	−	0.829769i	$-0.311528\pi$
$761$	3.27060	+	1.88828i	0.118559	+	0.0684502i	−0.439548	+	0.898219i	$0.644861\pi$
$762$		−	42.4883i		−	1.53919i
$763$	23.4958	−	40.6960i	0.850606	−	1.47329i
$764$	42.1659	+	73.0336i	1.52551	+	2.64226i
$765$	49.9304	−	28.8273i	1.80524	−	1.04225i
$766$	−22.4533			−0.811271
$767$	17.6749	−	8.95782i	0.638202	−	0.323448i
$768$	−47.0496			−1.69776
$769$	28.2746	−	16.3244i	1.01961	−	0.588672i	0.105618	−	0.994407i	$-0.466318\pi$
$769$	28.2746	−	16.3244i	1.01961	−	0.588672i	0.913991	+	0.405735i	$0.132984\pi$
$770$	69.2515	+	119.947i	2.49565	+	4.32259i
$771$	39.2156	−	67.9235i	1.41232	−	2.44620i
$772$			35.7657i			1.28723i
$773$	13.1959	+	7.61866i	0.474623	+	0.274024i	0.718173	−	0.695864i	$-0.244979\pi$
$773$	13.1959	+	7.61866i	0.474623	+	0.274024i	−0.243550	+	0.969888i	$0.578312\pi$
$774$	−47.9649	−	27.6925i	−1.72406	−	0.995388i
$775$		−	11.8106i		−	0.424249i
$776$	−11.8471	+	20.5198i	−0.425286	+	0.736616i
$777$	21.4971	+	37.2340i	0.771203	+	1.33576i
$778$	−17.0556	+	9.84708i	−0.611474	+	0.353035i
$779$	19.3373			0.692829
$780$	86.3678	+	56.3531i	3.09246	+	2.01777i
$781$	−23.2086			−0.830470
$782$	6.92504	−	3.99818i	0.247639	−	0.142974i
$783$	17.6876	+	30.6359i	0.632105	+	1.09484i
$784$	0.215440	−	0.373153i	0.00769428	−	0.0133269i
$785$		−	30.4709i		−	1.08755i
$786$	64.7773	+	37.3992i	2.31053	+	1.33398i
$787$	−36.9110	−	21.3105i	−1.31573	−	0.759639i	−0.332694	−	0.943035i	$-0.607958\pi$
$787$	−36.9110	−	21.3105i	−1.31573	−	0.759639i	−0.983039	+	0.183396i	$0.941291\pi$
$788$			28.4452i			1.01332i
$789$	−39.6412	+	68.6605i	−1.41126	+	2.44438i
$790$	−6.99172	−	12.1100i	−0.248754	−	0.430855i
$791$	−80.5881	+	46.5276i	−2.86538	+	1.65433i
$792$	−67.1876			−2.38741
$793$	15.4963	+	30.5760i	0.550289	+	1.08579i
$794$	−18.5293			−0.657581
$795$	26.9564	−	15.5633i	0.956046	−	0.551974i
$796$	18.4189	+	31.9025i	0.652842	+	1.13075i
$797$	18.6528	−	32.3075i	0.660715	−	1.14439i	−0.319713	−	0.947514i	$-0.603587\pi$
$797$	18.6528	−	32.3075i	0.660715	−	1.14439i	0.980428	−	0.196878i	$-0.0630802\pi$
$798$		−	83.4686i		−	2.95476i
$799$	−28.3259	−	16.3540i	−1.00210	−	0.578561i
$800$	20.5457	+	11.8621i	0.726401	+	0.419388i
$801$		−	52.0142i		−	1.83783i
$802$	−29.0184	+	50.2613i	−1.02467	+	1.77479i
$803$	−7.30844	−	12.6586i	−0.257909	−	0.446712i
$804$	8.55071	−	4.93676i	0.301560	−	0.174106i
$805$	−13.9307			−0.490992
$806$	−23.0706	−	1.25899i	−0.812628	−	0.0443459i
$807$	−80.1303			−2.82072
$808$	−30.0200	+	17.3321i	−1.05610	+	0.609740i
$809$	4.73733	+	8.20530i	0.166556	+	0.288483i	0.937207	−	0.348774i	$-0.113402\pi$
$809$	4.73733	+	8.20530i	0.166556	+	0.288483i	−0.770651	+	0.637258i	$0.780069\pi$
$810$	14.7750	−	25.5911i	0.519141	−	0.899178i
$811$			9.02137i			0.316783i	0.987376	+	0.158392i	$0.0506308\pi$
$811$			9.02137i			0.316783i	−0.987376	+	0.158392i	$0.949369\pi$
$812$	64.3897	+	37.1754i	2.25964	+	1.30460i
$813$	−56.8566	−	32.8262i	−1.99405	−	1.15126i
$814$		−	32.0772i		−	1.12431i
$815$	−8.19490	+	14.1940i	−0.287055	+	0.497193i
$816$	0.155566	+	0.269449i	0.00544591	+	0.00943259i
$817$	−10.5394	+	6.08490i	−0.368725	+	0.212884i
$818$	25.7537			0.900456
$819$	−4.90064	+	89.8031i	−0.171242	+	3.13797i
$820$	69.6083			2.43083
$821$	−14.5996	+	8.42909i	−0.509530	+	0.294177i	−0.732640	−	0.680616i	$-0.761712\pi$
$821$	−14.5996	+	8.42909i	−0.509530	+	0.294177i	0.223110	+	0.974793i	$0.428379\pi$
$822$	−15.5889	−	27.0007i	−0.543725	−	0.941759i
$823$	−10.9466	+	18.9601i	−0.381575	+	0.660908i	−0.991288	−	0.131715i	$-0.957952\pi$
$823$	−10.9466	+	18.9601i	−0.381575	+	0.660908i	0.609712	+	0.792623i	$0.291285\pi$
$824$			46.1231i			1.60678i
$825$	46.0946	+	26.6127i	1.60481	+	0.926536i
$826$	−49.9975	−	28.8661i	−1.73964	−	1.00438i
$827$		−	48.7650i		−	1.69573i	−0.530215	−	0.847863i	$-0.677889\pi$
$827$		−	48.7650i		−	1.69573i	0.530215	−	0.847863i	$-0.322111\pi$
$828$	8.81590	−	15.2696i	0.306374	−	0.530655i
$829$	−19.2395	−	33.3238i	−0.668215	−	1.15738i	−0.978403	−	0.206707i	$-0.933725\pi$
$829$	−19.2395	−	33.3238i	−0.668215	−	1.15738i	0.310188	−	0.950675i	$-0.399608\pi$
$830$	−24.3533	+	14.0604i	−0.845317	+	0.488044i
$831$	77.3395			2.68288
$832$	25.4822	−	39.0545i	0.883437	−	1.35397i
$833$	49.0587			1.69978
$834$	18.5861	−	10.7307i	0.643585	−	0.371574i
$835$	−14.7319	−	25.5164i	−0.509818	−	0.883031i
$836$	−19.2594	+	33.3583i	−0.666102	+	1.15372i
$837$			19.8108i			0.684760i
$838$	12.5906	+	7.26919i	0.434935	+	0.251110i
$839$	−12.4251	−	7.17364i	−0.428963	−	0.247662i	0.269942	−	0.962877i	$-0.412995\pi$
$839$	−12.4251	−	7.17364i	−0.428963	−	0.247662i	−0.698905	+	0.715215i	$0.746329\pi$
$840$		−	115.158i		−	3.97334i
$841$	2.01288	−	3.48641i	0.0694097	−	0.120221i
$842$	2.62668	+	4.54954i	0.0905213	+	0.156788i
$843$	21.1708	−	12.2230i	0.729161	−	0.420981i
$844$	27.0188			0.930024
$845$	−36.1303	+	15.8998i	−1.24292	+	0.546970i
$846$	−116.599			−4.00876
$847$	31.2045	−	18.0159i	1.07220	−	0.619034i
$848$	0.0541233	+	0.0937443i	0.00185860	+	0.00321919i
$849$	−7.58601	+	13.1394i	−0.260351	+	0.450941i
$850$		−	33.7456i		−	1.15746i
$851$	2.79410	+	1.61317i	0.0957804	+	0.0552988i
$852$	43.6024	+	25.1739i	1.49379	+	0.862442i
$853$		−	32.4427i		−	1.11082i	−0.831577	−	0.555409i	$-0.812562\pi$
$853$		−	32.4427i		−	1.11082i	0.831577	−	0.555409i	$-0.187438\pi$
$854$	49.9360	−	86.4916i	1.70877	−	2.95968i
$855$	−22.5807	−	39.1109i	−0.772243	−	1.33756i
$856$	12.9744	−	7.49076i	0.443455	−	0.256029i
$857$	−37.7965			−1.29111			−0.645553	−	0.763716i	$-0.723373\pi$
$857$	−37.7965			−1.29111			−0.645553	+	0.763716i	$0.723373\pi$
$858$	56.8985	−	87.2036i	1.94248	−	2.97708i
$859$	−26.7260			−0.911879			−0.455940	−	0.890011i	$-0.650697\pi$
$859$	−26.7260			−0.911879			−0.455940	+	0.890011i	$0.650697\pi$
$860$	−37.9385	+	21.9038i	−1.29369	+	0.746913i
$861$	47.1005	+	81.5805i	1.60518	+	2.78026i
$862$	1.54010	−	2.66752i	0.0524559	−	0.0908563i
$863$		−	22.3818i		−	0.761885i	−0.924599	−	0.380943i	$-0.875600\pi$
$863$		−	22.3818i		−	0.761885i	0.924599	−	0.380943i	$-0.124400\pi$
$864$	−34.4628	−	19.8971i	−1.17245	−	0.676914i
$865$	12.5993	+	7.27421i	0.428389	+	0.247330i
$866$		−	39.0841i		−	1.32813i
$867$	6.97726	−	12.0850i	0.236960	−	0.410427i
$868$	20.8189	+	36.0593i	0.706638	+	1.22393i
$869$	−7.56292	+	4.36646i	−0.256555	+	0.148122i
$870$	100.924			3.42165
$871$	−0.205935	+	3.77370i	−0.00697783	+	0.127867i
$872$	29.1504			0.987158
$873$	−39.2017	+	22.6331i	−1.32678	+	0.766015i
$874$	−3.13180	−	5.42444i	−0.105935	−	0.183484i
$875$	5.43213	−	9.40872i	0.183639	−	0.318073i
$876$			31.7092i			1.07135i
$877$	15.2106	+	8.78185i	0.513626	+	0.296542i	0.734323	−	0.678800i	$-0.237500\pi$
$877$	15.2106	+	8.78185i	0.513626	+	0.296542i	−0.220697	+	0.975342i	$0.570833\pi$
$878$	−64.6095	−	37.3023i	−2.18046	−	1.25889i
$879$			52.2682i			1.76296i
$880$	−0.202201	+	0.350223i	−0.00681620	+	0.0118060i
$881$	−1.56849	−	2.71670i	−0.0528438	−	0.0915281i	0.838394	−	0.545065i	$-0.183495\pi$
$881$	−1.56849	−	2.71670i	−0.0528438	−	0.0915281i	−0.891237	+	0.453537i	$0.850162\pi$
$882$	151.457	−	87.4436i	5.09982	−	2.94438i
$883$	−29.2554			−0.984522			−0.492261	−	0.870448i	$-0.663829\pi$
$883$	−29.2554			−0.984522			−0.492261	+	0.870448i	$0.663829\pi$
$884$	−40.7725	−	2.22499i	−1.37133	−	0.0748346i
$885$	−48.4719			−1.62937
$886$	−29.8665	+	17.2434i	−1.00338	+	0.579304i
$887$	−2.13588	−	3.69946i	−0.0717160	−	0.124216i	0.827937	−	0.560820i	$-0.189514\pi$
$887$	−2.13588	−	3.69946i	−0.0717160	−	0.124216i	−0.899653	+	0.436605i	$0.856181\pi$
$888$	−13.3353	+	23.0975i	−0.447504	+	0.775100i
$889$		−	29.3085i		−	0.982974i
$890$	−57.6032	−	33.2572i	−1.93086	−	1.11478i
$891$	−15.9821	−	9.22726i	−0.535420	−	0.309125i
$892$		−	2.36480i		−	0.0791794i
$893$	−12.8102	+	22.1879i	−0.428676	+	0.742489i
$894$	−7.41681	−	12.8463i	−0.248055	−	0.429644i
$895$	9.79757	−	5.65663i	0.327496	−	0.189080i
$896$	−84.2829			−2.81569
$897$	4.73445	+	9.34164i	0.158079	+	0.311908i
$898$	−64.6226			−2.15649
$899$	−12.1122	+	6.99299i	−0.403965	+	0.233229i
$900$	−37.2042	−	64.4395i	−1.24014	−	2.14798i
$901$	−6.16232	+	10.6735i	−0.205297	+	0.355584i
$902$		−	70.2819i		−	2.34013i
$903$	−51.3422	−	29.6425i	−1.70856	−	0.986439i
$904$	−49.9914	−	28.8625i	−1.66269	−	0.959953i
$905$		−	8.33373i		−	0.277023i
$906$	51.0620	−	88.4420i	1.69642	−	2.93829i
$907$	11.3079	+	19.5859i	0.375474	+	0.650340i	0.990398	−	0.138246i	$-0.0441466\pi$
$907$	11.3079	+	19.5859i	0.375474	+	0.650340i	−0.614924	+	0.788586i	$0.710813\pi$
$908$	30.5569	−	17.6420i	1.01407	−	0.585471i
$909$	−66.2236			−2.19650
$910$	96.3191	+	62.8461i	3.19295	+	2.08333i
$911$	13.4593			0.445926			0.222963	−	0.974827i	$-0.428427\pi$
$911$	13.4593			0.445926			0.222963	+	0.974827i	$0.428427\pi$
$912$	0.211061	−	0.121856i	0.00698894	−	0.00403506i
$913$	8.78098	+	15.2091i	0.290608	+	0.503348i
$914$	25.7871	−	44.6647i	0.852963	−	1.47738i
$915$		−	83.8524i		−	2.77208i
$916$	−60.0046	−	34.6436i	−1.98261	−	1.14466i
$917$	44.6834	+	25.7980i	1.47557	+	0.851923i
$918$			56.6038i			1.86820i
$919$	−19.5775	+	33.9093i	−0.645803	+	1.11856i	0.338312	+	0.941034i	$0.390144\pi$
$919$	−19.5775	+	33.9093i	−0.645803	+	1.11856i	−0.984115	+	0.177530i	$0.943189\pi$
$920$	−4.32082	−	7.48389i	−0.142453	−	0.246736i
$921$	−14.8159	+	8.55397i	−0.488201	+	0.281863i
$922$	55.0797			1.81395
$923$	−17.1901	+	8.71213i	−0.565819	+	0.286763i
$924$	−187.644			−6.17303
$925$	11.7914	−	6.80778i	0.387700	−	0.223838i
$926$	−31.5958	−	54.7256i	−1.03830	−	1.79839i
$927$	−44.0577	+	76.3101i	−1.44704	+	2.50635i
$928$		−	28.0939i		−	0.922228i
$929$	38.9290	+	22.4757i	1.27722	+	0.737404i	0.976336	−	0.216257i	$-0.0693850\pi$
$929$	38.9290	+	22.4757i	1.27722	+	0.737404i	0.300884	+	0.953661i	$0.402718\pi$
$930$	48.9471	+	28.2596i	1.60504	+	0.926670i
$931$		−	38.4281i		−	1.25943i
$932$	27.2565	−	47.2097i	0.892817	−	1.54640i
$933$	14.2955	+	24.7604i	0.468012	+	0.810621i
$934$	−24.5071	+	14.1492i	−0.801896	+	0.462975i
$935$	−46.0441			−1.50580
$936$	−49.7643	+	25.2211i	−1.62660	+	0.824378i
$937$	9.31704			0.304375			0.152187	−	0.988352i	$-0.451368\pi$
$937$	9.31704			0.304375			0.152187	+	0.988352i	$0.451368\pi$
$938$	9.53592	−	5.50557i	0.311359	−	0.179763i
$939$	−23.6693	−	40.9964i	−0.772418	−	1.33787i
$940$	−46.1128	+	79.8697i	−1.50403	+	2.60506i
$941$		−	54.1289i		−	1.76455i	−0.470732	−	0.882276i	$-0.656010\pi$
$941$		−	54.1289i		−	1.76455i	0.470732	−	0.882276i	$-0.343990\pi$
$942$	57.8000	+	33.3709i	1.88323	+	1.08728i
$943$	6.12192	+	3.53449i	0.199357	+	0.115099i
$944$		−	0.168567i		−	0.00548639i
$945$	49.3056	−	85.3998i	1.60391	−	2.77806i
$946$	22.1158	+	38.3056i	0.719045	+	1.24542i
$947$	−17.8706	+	10.3176i	−0.580715	+	0.335276i	−0.761418	−	0.648262i	$-0.775496\pi$
$947$	−17.8706	+	10.3176i	−0.580715	+	0.335276i	0.180702	+	0.983538i	$0.442163\pi$
$948$	18.9448			0.615298
$949$	−10.1650	−	6.63245i	−0.329970	−	0.215298i
$950$	−26.4332			−0.857605
$951$	76.8363	−	44.3615i	2.49159	−	1.43852i
$952$	22.7986	+	39.4883i	0.738906	+	1.27982i
$953$	−13.2276	+	22.9108i	−0.428483	+	0.742155i	−0.996739	−	0.0806976i	$-0.974285\pi$
$953$	−13.2276	+	22.9108i	−0.428483	+	0.742155i	0.568256	+	0.822852i	$0.307619\pi$
$954$			43.9356i			1.42247i
$955$	68.3841	+	39.4816i	2.21286	+	1.27759i
$956$	21.3265	+	12.3129i	0.689750	+	0.398227i
$957$		−	63.0290i		−	2.03744i
$958$	16.5139	−	28.6029i	0.533540	−	0.924118i
$959$	−10.7532	−	18.6251i	−0.347239	−	0.601436i
$960$	−98.7895	+	57.0362i	−3.18842	+	1.84083i
$961$	23.1676			0.747342
$962$	−12.0413	−	23.7589i	−0.388226	−	0.766017i
$963$	28.6213			0.922307
$964$	55.2519	−	31.8997i	1.77954	−	1.02742i
$965$	16.7444	+	29.0021i	0.539021	+	0.933611i
$966$	15.2565	−	26.4250i	0.490870	−	0.850212i
$967$			25.7100i			0.826776i	0.910555	+	0.413388i	$0.135655\pi$
$967$			25.7100i			0.826776i	−0.910555	+	0.413388i	$0.864345\pi$
$968$	19.3571	+	11.1758i	0.622162	+	0.359205i
$969$	24.0308	+	13.8742i	0.771981	+	0.445703i
$970$			57.8853i			1.85858i
$971$	30.0786	−	52.0976i	0.965267	−	1.67189i	0.256371	−	0.966579i	$-0.417473\pi$
$971$	30.0786	−	52.0976i	0.965267	−	1.67189i	0.708896	−	0.705313i	$-0.249193\pi$
$972$	−14.4163	−	24.9697i	−0.462403	−	0.800905i
$973$	12.8207	−	7.40205i	0.411013	−	0.237299i
$974$	21.1265			0.676937
$975$	44.1312	+	2.40828i	1.41333	+	0.0771267i
$976$	0.291607			0.00933411
$977$	−34.4613	+	19.8963i	−1.10252	+	0.636538i	−0.936881	−	0.349649i	$-0.886301\pi$
$977$	−34.4613	+	19.8963i	−1.10252	+	0.636538i	−0.165635	+	0.986187i	$0.552967\pi$
$978$	−17.9497	−	31.0897i	−0.573967	−	0.994140i
$979$	−20.7697	+	35.9742i	−0.663804	+	1.14974i
$980$		−	138.329i		−	4.41877i
$981$	48.2290	+	27.8450i	1.53983	+	0.889023i
$982$	−30.9987	−	17.8971i	−0.989207	−	0.571119i
$983$			25.3871i			0.809722i	0.914378	+	0.404861i	$0.132680\pi$
$983$			25.3871i			0.809722i	−0.914378	+	0.404861i	$0.867320\pi$
$984$	−29.2179	+	50.6070i	−0.931434	+	1.61329i
$985$	13.3172	+	23.0660i	0.424320	+	0.734944i
$986$	−34.6074	+	19.9806i	−1.10212	+	0.636311i
$987$	−124.809			−3.97272
$988$	−1.74286	+	31.9374i	−0.0554476	+	1.01606i
$989$	−4.44883			−0.141464
$990$	−142.150	+	82.0702i	−4.51782	+	2.60836i
$991$	−14.1062	−	24.4327i	−0.448099	−	0.776130i	0.550163	−	0.835057i	$-0.314565\pi$
$991$	−14.1062	−	24.4327i	−0.448099	−	0.776130i	−0.998262	+	0.0589268i	$0.981232\pi$
$992$	7.86653	−	13.6252i	0.249763	−	0.432602i
$993$			52.5154i			1.66653i
$994$	48.6262	+	28.0744i	1.54233	+	0.890465i
$995$	29.8715	+	17.2463i	0.946991	+	0.546746i
$996$		−	38.0981i		−	1.20718i
$997$	11.4683	−	19.8636i	0.363203	−	0.629087i	−0.625283	−	0.780398i	$-0.715016\pi$
$997$	11.4683	−	19.8636i	0.363203	−	0.629087i	0.988486	+	0.151312i	$0.0483497\pi$
$998$	−2.51149	−	4.35002i	−0.0794997	−	0.137698i
$999$	−19.7786	+	11.4192i	−0.625767	+	0.361287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	299.2.i.b.231.3	✓	30
13.2	odd	12		3887.2.a.u.1.5		30
13.4	even	6	inner	299.2.i.b.277.3	yes	30
13.11	odd	12		3887.2.a.u.1.26		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
299.2.i.b.231.3	✓	30	1.1	even	1	trivial
299.2.i.b.277.3	yes	30	13.4	even	6	inner
3887.2.a.u.1.5		30	13.2	odd	12
3887.2.a.u.1.26		30	13.11	odd	12

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:	\( N \)	\(=\)	\( 299 = 13 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	299.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98297 + 1.14487i) q^{2} +(-1.45233 - 2.51551i) q^{3} +(1.62146 - 2.80845i) q^{4} -3.03647i q^{5} +(5.75986 + 3.32545i) q^{6} +(3.97315 + 2.29390i) q^{7} +2.84596i q^{8} +(-2.71851 + 4.70860i) q^{9} +O(q^{10})\)	\(q+(-1.98297 + 1.14487i) q^{2} +(-1.45233 - 2.51551i) q^{3} +(1.62146 - 2.80845i) q^{4} -3.03647i q^{5} +(5.75986 + 3.32545i) q^{6} +(3.97315 + 2.29390i) q^{7} +2.84596i q^{8} +(-2.71851 + 4.70860i) q^{9} +(3.47636 + 6.02123i) q^{10} +(3.76037 - 2.17105i) q^{11} -9.41955 q^{12} +(1.97024 - 3.01963i) q^{13} -10.5049 q^{14} +(-7.63824 + 4.40994i) q^{15} +(-0.0153361 - 0.0265629i) q^{16} +(1.74613 - 3.02438i) q^{17} -12.4494i q^{18} +(-2.36902 - 1.36775i) q^{19} +(-8.52775 - 4.92350i) q^{20} -13.3260i q^{21} +(-4.97114 + 8.61028i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(7.15902 - 4.13326i) q^{24} -4.22012 q^{25} +(-0.449857 + 8.24351i) q^{26} +7.07871 q^{27} +(12.8846 - 7.43892i) q^{28} +(2.49871 + 4.32790i) q^{29} +(10.0976 - 17.4896i) q^{30} +2.79864i q^{31} +(-4.86852 - 2.81084i) q^{32} +(-10.9226 - 6.30615i) q^{33} +7.99635i q^{34} +(6.96534 - 12.0643i) q^{35} +(8.81590 + 15.2696i) q^{36} +(-2.79410 + 1.61317i) q^{37} +6.26361 q^{38} +(-10.4573 - 0.570667i) q^{39} +8.64165 q^{40} +(-6.12192 + 3.53449i) q^{41} +(15.2565 + 26.4250i) q^{42} +(2.22441 - 3.85280i) q^{43} -14.0811i q^{44} +(14.2975 + 8.25466i) q^{45} +(1.98297 + 1.14487i) q^{46} -9.36585i q^{47} +(-0.0445461 + 0.0771561i) q^{48} +(7.02394 + 12.1658i) q^{49} +(8.36839 - 4.83149i) q^{50} -10.1438 q^{51} +(-5.28580 - 10.4295i) q^{52} -3.52914 q^{53} +(-14.0369 + 8.10420i) q^{54} +(-6.59232 - 11.4182i) q^{55} +(-6.52833 + 11.3074i) q^{56} +7.94571i q^{57} +(-9.90976 - 5.72140i) q^{58} +(4.75946 + 2.74788i) q^{59} +28.6021i q^{60} +(-4.75360 + 8.23348i) q^{61} +(-3.20408 - 5.54963i) q^{62} +(-21.6021 + 12.4720i) q^{63} +12.9335 q^{64} +(-9.16899 - 5.98257i) q^{65} +28.8789 q^{66} +(-0.907762 + 0.524097i) q^{67} +(-5.66254 - 9.80780i) q^{68} +(-1.45233 + 2.51551i) q^{69} +31.8977i q^{70} +(-4.62892 - 2.67251i) q^{71} +(-13.4005 - 7.73676i) q^{72} -3.36631i q^{73} +(3.69375 - 6.39776i) q^{74} +(6.12900 + 10.6157i) q^{75} +(-7.68253 + 4.43551i) q^{76} +19.9207 q^{77} +(21.3899 - 10.8407i) q^{78} -2.01122 q^{79} +(-0.0806574 + 0.0465676i) q^{80} +(-2.12507 - 3.68073i) q^{81} +(8.09307 - 14.0176i) q^{82} +4.04458i q^{83} +(-37.4253 - 21.6075i) q^{84} +(-9.18342 - 5.30205i) q^{85} +10.1867i q^{86} +(7.25789 - 12.5710i) q^{87} +(6.17872 + 10.7018i) q^{88} +(-8.28498 + 4.78334i) q^{89} -37.8021 q^{90} +(14.7548 - 7.47789i) q^{91} -3.24292 q^{92} +(7.03999 - 4.06454i) q^{93} +(10.7227 + 18.5722i) q^{94} +(-4.15314 + 7.19344i) q^{95} +16.3290i q^{96} +(7.21014 + 4.16278i) q^{97} +(-27.8566 - 16.0830i) q^{98} +23.6081i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9	\( 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9} + 23 q^{10} - 4 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} - 26 q^{16} + 13 q^{17} - 12 q^{19} + 6 q^{20} - 16 q^{22} - 15 q^{23} + 6 q^{24} - 52 q^{25} - 25 q^{26} + 54 q^{27} - 24 q^{28} - q^{29} + 20 q^{30} - 39 q^{32} - 18 q^{33} + 20 q^{35} + 23 q^{36} - 30 q^{37} + 18 q^{38} - 60 q^{39} + 124 q^{40} - 6 q^{41} - 12 q^{42} + 33 q^{43} + 18 q^{45} + 34 q^{48} + 48 q^{49} - 60 q^{50} + 20 q^{51} - 39 q^{52} + 62 q^{53} + 45 q^{54} - 16 q^{55} - 5 q^{56} - 66 q^{58} - 21 q^{59} - 18 q^{61} + 46 q^{62} - 117 q^{63} - 16 q^{64} - 4 q^{65} + 52 q^{66} + 24 q^{67} - 18 q^{68} - 3 q^{69} + 54 q^{71} - 54 q^{72} + 42 q^{74} + 4 q^{75} - 18 q^{76} - 20 q^{77} + 72 q^{79} + 114 q^{80} - 15 q^{81} + 14 q^{82} - 159 q^{84} - 39 q^{85} + 40 q^{87} + 93 q^{88} - 51 q^{89} - 78 q^{90} - 34 q^{91} - 32 q^{92} + 6 q^{93} + 8 q^{94} - 24 q^{95} - 6 q^{97} - 123 q^{98}+O(q^{100}) \) 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9 + 23 * q^10 - 4 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 - 26 * q^16 + 13 * q^17 - 12 * q^19 + 6 * q^20 - 16 * q^22 - 15 * q^23 + 6 * q^24 - 52 * q^25 - 25 * q^26 + 54 * q^27 - 24 * q^28 - q^29 + 20 * q^30 - 39 * q^32 - 18 * q^33 + 20 * q^35 + 23 * q^36 - 30 * q^37 + 18 * q^38 - 60 * q^39 + 124 * q^40 - 6 * q^41 - 12 * q^42 + 33 * q^43 + 18 * q^45 + 34 * q^48 + 48 * q^49 - 60 * q^50 + 20 * q^51 - 39 * q^52 + 62 * q^53 + 45 * q^54 - 16 * q^55 - 5 * q^56 - 66 * q^58 - 21 * q^59 - 18 * q^61 + 46 * q^62 - 117 * q^63 - 16 * q^64 - 4 * q^65 + 52 * q^66 + 24 * q^67 - 18 * q^68 - 3 * q^69 + 54 * q^71 - 54 * q^72 + 42 * q^74 + 4 * q^75 - 18 * q^76 - 20 * q^77 + 72 * q^79 + 114 * q^80 - 15 * q^81 + 14 * q^82 - 159 * q^84 - 39 * q^85 + 40 * q^87 + 93 * q^88 - 51 * q^89 - 78 * q^90 - 34 * q^91 - 32 * q^92 + 6 * q^93 + 8 * q^94 - 24 * q^95 - 6 * q^97 - 123 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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