LMFDB - Embedded newform 310.2.s.a.277.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(23,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([15, 18]))

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

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

chi := DirichletCharacter("310.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.s (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			277.11
Character	$\chi$	$=$	310.277
Dual form			310.2.s.a.263.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 + 0.987688i) q^{2} +(-1.83857 - 0.291201i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(2.06347 + 0.861441i) q^{5} -1.86149i q^{6} +(1.91043 - 3.74943i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(0.442378 + 0.143737i) q^{9} +O(q^{10})$	\(q+(0.156434 + 0.987688i) q^{2} +(-1.83857 - 0.291201i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(2.06347 + 0.861441i) q^{5} -1.86149i q^{6} +(1.91043 - 3.74943i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(0.442378 + 0.143737i) q^{9} +(-0.528037 + 2.17283i) q^{10} +(-1.12989 + 0.367124i) q^{11} +(1.83857 - 0.291201i) q^{12} +(5.51343 + 0.873242i) q^{13} +(4.00213 + 1.30037i) q^{14} +(-3.54299 - 2.18471i) q^{15} +(0.809017 - 0.587785i) q^{16} +(2.53532 + 4.97584i) q^{17} +(-0.0727645 + 0.459417i) q^{18} +(2.91612 - 4.01370i) q^{19} +(-2.22868 - 0.181630i) q^{20} +(-4.60430 + 6.33728i) q^{21} +(-0.539358 - 1.05855i) q^{22} +(-0.739725 + 0.376909i) q^{23} +(0.575232 + 1.77038i) q^{24} +(3.51584 + 3.55512i) q^{25} +5.58216i q^{26} +(4.20431 + 2.14220i) q^{27} +(-0.658289 + 4.15628i) q^{28} +(-4.92950 - 3.58149i) q^{29} +(1.60356 - 3.84113i) q^{30} +(3.99622 + 3.87689i) q^{31} +(0.707107 + 0.707107i) q^{32} +(2.18429 - 0.345958i) q^{33} +(-4.51797 + 3.28250i) q^{34} +(7.17203 - 6.09113i) q^{35} -0.465144 q^{36} +(2.56906 - 2.56906i) q^{37} +(4.42046 + 2.25234i) q^{38} +(-9.88255 - 3.21104i) q^{39} +(-0.169248 - 2.22965i) q^{40} +(-7.80621 - 5.67154i) q^{41} +(-6.97953 - 3.55625i) q^{42} +(-0.0614603 - 0.388045i) q^{43} +(0.961143 - 0.698311i) q^{44} +(0.789014 + 0.677680i) q^{45} +(-0.487987 - 0.671656i) q^{46} +(1.30907 + 0.207336i) q^{47} +(-1.65860 + 0.845099i) q^{48} +(-6.29399 - 8.66293i) q^{49} +(-2.96135 + 4.02870i) q^{50} +(-3.21239 - 9.88673i) q^{51} +(-5.51343 + 0.873242i) q^{52} +(1.23348 - 0.628490i) q^{53} +(-1.45813 + 4.48766i) q^{54} +(-2.64775 - 0.215784i) q^{55} -4.20808 q^{56} +(-6.53029 + 6.53029i) q^{57} +(2.76625 - 5.42908i) q^{58} +(-5.46450 - 7.52124i) q^{59} +(4.04470 + 0.982934i) q^{60} +2.58265i q^{61} +(-3.20401 + 4.55349i) q^{62} +(1.38406 - 1.38406i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(10.6246 + 6.55141i) q^{65} +(0.683397 + 2.10328i) q^{66} +(-6.48765 - 6.48765i) q^{67} +(-3.94885 - 3.94885i) q^{68} +(1.46979 - 0.477565i) q^{69} +(7.13809 + 6.13087i) q^{70} +(-4.45973 + 13.7256i) q^{71} +(-0.0727645 - 0.459417i) q^{72} +(-0.989592 + 1.94218i) q^{73} +(2.93932 + 2.13554i) q^{74} +(-5.42887 - 7.56016i) q^{75} +(-1.53310 + 4.71838i) q^{76} +(-0.782073 + 4.93781i) q^{77} +(1.62553 - 10.2632i) q^{78} +(1.91575 - 5.89608i) q^{79} +(2.17573 - 0.515959i) q^{80} +(-8.23504 - 5.98311i) q^{81} +(4.38056 - 8.59732i) q^{82} +(0.351764 + 2.22095i) q^{83} +(2.42062 - 7.44992i) q^{84} +(0.945168 + 12.4515i) q^{85} +(0.373653 - 0.121407i) q^{86} +(8.02030 + 8.02030i) q^{87} +(0.840069 + 0.840069i) q^{88} +(2.09951 + 6.46163i) q^{89} +(-0.545908 + 0.885312i) q^{90} +(13.8072 - 19.0040i) q^{91} +(0.587049 - 0.587049i) q^{92} +(-6.21837 - 8.29164i) q^{93} +1.32539i q^{94} +(9.47490 - 5.77009i) q^{95} +(-1.09416 - 1.50598i) q^{96} +(5.61503 - 11.0201i) q^{97} +(7.57168 - 7.57168i) q^{98} -0.552608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 12 q^{7}+O(q^{10}) $ 128 * q + 12 * q^7	$ 128 q + 12 q^{7} + 8 q^{10} + 32 q^{16} + 8 q^{20} - 80 q^{21} - 20 q^{22} - 20 q^{23} + 40 q^{25} + 8 q^{28} - 32 q^{31} + 20 q^{33} - 48 q^{35} - 128 q^{36} + 52 q^{38} + 8 q^{41} - 20 q^{42} + 64 q^{45} - 40 q^{46} - 20 q^{47} - 20 q^{48} + 24 q^{50} - 16 q^{51} - 40 q^{53} - 40 q^{55} + 20 q^{60} - 8 q^{62} + 256 q^{63} - 160 q^{65} + 56 q^{66} + 8 q^{67} - 32 q^{70} + 56 q^{71} - 80 q^{73} - 160 q^{75} + 48 q^{76} - 20 q^{77} + 4 q^{78} - 96 q^{81} + 16 q^{82} - 240 q^{83} + 120 q^{85} + 40 q^{87} - 64 q^{90} + 80 q^{91} - 160 q^{93} + 32 q^{95} - 56 q^{97} - 176 q^{98}+O(q^{100}) $ 128 * q + 12 * q^7 + 8 * q^10 + 32 * q^16 + 8 * q^20 - 80 * q^21 - 20 * q^22 - 20 * q^23 + 40 * q^25 + 8 * q^28 - 32 * q^31 + 20 * q^33 - 48 * q^35 - 128 * q^36 + 52 * q^38 + 8 * q^41 - 20 * q^42 + 64 * q^45 - 40 * q^46 - 20 * q^47 - 20 * q^48 + 24 * q^50 - 16 * q^51 - 40 * q^53 - 40 * q^55 + 20 * q^60 - 8 * q^62 + 256 * q^63 - 160 * q^65 + 56 * q^66 + 8 * q^67 - 32 * q^70 + 56 * q^71 - 80 * q^73 - 160 * q^75 + 48 * q^76 - 20 * q^77 + 4 * q^78 - 96 * q^81 + 16 * q^82 - 240 * q^83 + 120 * q^85 + 40 * q^87 - 64 * q^90 + 80 * q^91 - 160 * q^93 + 32 * q^95 - 56 * q^97 - 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$3$	−1.83857	−	0.291201i	−1.06150	−	0.168125i	−0.398821	−	0.917029i	$-0.630581\pi$
$3$	−1.83857	−	0.291201i	−1.06150	−	0.168125i	−0.662679	+	0.748904i	$0.730581\pi$
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	2.06347	+	0.861441i	0.922813	+	0.385248i
$5$	2.06347	+	0.861441i	0.922813	+	0.385248i
$6$		−	1.86149i		−	0.759950i
$7$	1.91043	−	3.74943i	0.722075	−	1.41715i	−0.179160	−	0.983820i	$-0.557338\pi$
$7$	1.91043	−	3.74943i	0.722075	−	1.41715i	0.901235	−	0.433331i	$-0.142662\pi$
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$	0.442378	+	0.143737i	0.147459	+	0.0479124i
$10$	−0.528037	+	2.17283i	−0.166980	+	0.687108i
$11$	−1.12989	+	0.367124i	−0.340675	+	0.110692i	−0.474358	−	0.880332i	$-0.657320\pi$
$11$	−1.12989	+	0.367124i	−0.340675	+	0.110692i	0.133683	+	0.991024i	$0.457320\pi$
$12$	1.83857	−	0.291201i	0.530750	−	0.0840625i
$13$	5.51343	+	0.873242i	1.52915	+	0.242194i	0.863607	−	0.504165i	$-0.168200\pi$
$13$	5.51343	+	0.873242i	1.52915	+	0.242194i	0.665544	+	0.746359i	$0.268200\pi$
$14$	4.00213	+	1.30037i	1.06961	+	0.347538i
$15$	−3.54299	−	2.18471i	−0.914796	−	0.564089i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	2.53532	+	4.97584i	0.614905	+	1.20682i	0.963036	+	0.269373i	$0.0868164\pi$
$17$	2.53532	+	4.97584i	0.614905	+	1.20682i	−0.348131	+	0.937446i	$0.613184\pi$
$18$	−0.0727645	+	0.459417i	−0.0171508	+	0.108286i
$19$	2.91612	−	4.01370i	0.669004	−	0.920805i	−0.330733	−	0.943724i	$-0.607296\pi$
$19$	2.91612	−	4.01370i	0.669004	−	0.920805i	0.999737	+	0.0229191i	$0.00729603\pi$
$20$	−2.22868	−	0.181630i	−0.498348	−	0.0406138i
$21$	−4.60430	+	6.33728i	−1.00474	+	1.38291i
$22$	−0.539358	−	1.05855i	−0.114991	−	0.225683i
$23$	−0.739725	+	0.376909i	−0.154243	+	0.0785909i	−0.529408	−	0.848367i	$-0.677586\pi$
$23$	−0.739725	+	0.376909i	−0.154243	+	0.0785909i	0.375165	+	0.926958i	$0.377586\pi$
$24$	0.575232	+	1.77038i	0.117419	+	0.361378i
$25$	3.51584	+	3.55512i	0.703168	+	0.711024i
$26$			5.58216i			1.09475i
$27$	4.20431	+	2.14220i	0.809120	+	0.412267i
$28$	−0.658289	+	4.15628i	−0.124405	+	0.785462i
$29$	−4.92950	−	3.58149i	−0.915385	−	0.665066i	0.0269861	−	0.999636i	$-0.491409\pi$
$29$	−4.92950	−	3.58149i	−0.915385	−	0.665066i	−0.942371	+	0.334570i	$0.891409\pi$
$30$	1.60356	−	3.84113i	0.292769	−	0.701292i
$31$	3.99622	+	3.87689i	0.717741	+	0.696310i
$31$	3.99622	+	3.87689i	0.717741	+	0.696310i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	2.18429	−	0.345958i	0.380236	−	0.0602235i
$34$	−4.51797	+	3.28250i	−0.774825	+	0.562944i
$35$	7.17203	−	6.09113i	1.21229	−	1.02959i
$36$	−0.465144			−0.0775239
$37$	2.56906	−	2.56906i	0.422351	−	0.422351i	−0.463661	−	0.886013i	$-0.653465\pi$
$37$	2.56906	−	2.56906i	0.422351	−	0.422351i	0.886013	+	0.463661i	$0.153465\pi$
$38$	4.42046	+	2.25234i	0.717094	+	0.365378i
$39$	−9.88255	−	3.21104i	−1.58247	−	0.514177i
$40$	−0.169248	−	2.22965i	−0.0267604	−	0.352539i
$41$	−7.80621	−	5.67154i	−1.21912	−	0.885746i	−0.223098	−	0.974796i	$-0.571617\pi$
$41$	−7.80621	−	5.67154i	−1.21912	−	0.885746i	−0.996027	+	0.0890502i	$0.971617\pi$
$42$	−6.97953	−	3.55625i	−1.07696	−	0.548741i
$43$	−0.0614603	−	0.388045i	−0.00937260	−	0.0591763i	0.982559	−	0.185952i	$-0.0595370\pi$
$43$	−0.0614603	−	0.388045i	−0.00937260	−	0.0591763i	−0.991931	+	0.126776i	$0.959537\pi$
$44$	0.961143	−	0.698311i	0.144898	−	0.105274i
$45$	0.789014	+	0.677680i	0.117619	+	0.101023i
$46$	−0.487987	−	0.671656i	−0.0719497	−	0.0990303i
$47$	1.30907	+	0.207336i	0.190948	+	0.0302431i	0.251176	−	0.967942i	$-0.419183\pi$
$47$	1.30907	+	0.207336i	0.190948	+	0.0302431i	−0.0602281	+	0.998185i	$0.519183\pi$
$48$	−1.65860	+	0.845099i	−0.239398	+	0.121979i
$49$	−6.29399	−	8.66293i	−0.899141	−	1.23756i
$50$	−2.96135	+	4.02870i	−0.418798	+	0.569744i
$51$	−3.21239	−	9.88673i	−0.449825	−	1.38442i
$52$	−5.51343	+	0.873242i	−0.764576	+	0.121097i
$53$	1.23348	−	0.628490i	0.169432	−	0.0863298i	−0.367218	−	0.930135i	$-0.619690\pi$
$53$	1.23348	−	0.628490i	0.169432	−	0.0863298i	0.536650	+	0.843805i	$0.319690\pi$
$54$	−1.45813	+	4.48766i	−0.198426	+	0.610694i
$55$	−2.64775	−	0.215784i	−0.357023	−	0.0290963i
$56$	−4.20808			−0.562329
$57$	−6.53029	+	6.53029i	−0.864958	+	0.864958i
$58$	2.76625	−	5.42908i	0.363227	−	0.712873i
$59$	−5.46450	−	7.52124i	−0.711417	−	0.979182i	−0.999765	−	0.0216562i	$-0.993106\pi$
$59$	−5.46450	−	7.52124i	−0.711417	−	0.979182i	0.288348	−	0.957526i	$-0.406894\pi$
$60$	4.04470	+	0.982934i	0.522168	+	0.126896i
$61$			2.58265i			0.330675i	0.986237	+	0.165337i	$0.0528713\pi$
$61$			2.58265i			0.330675i	−0.986237	+	0.165337i	$0.947129\pi$
$62$	−3.20401	+	4.55349i	−0.406910	+	0.578294i
$63$	1.38406	−	1.38406i	0.174376	−	0.174376i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	10.6246	+	6.55141i	1.31782	+	0.812602i
$66$	0.683397	+	2.10328i	0.0841204	+	0.258896i
$67$	−6.48765	−	6.48765i	−0.792592	−	0.792592i	0.189323	−	0.981915i	$-0.439371\pi$
$67$	−6.48765	−	6.48765i	−0.792592	−	0.792592i	−0.981915	+	0.189323i	$0.939371\pi$
$68$	−3.94885	−	3.94885i	−0.478868	−	0.478868i
$69$	1.46979	−	0.477565i	0.176942	−	0.0574920i
$70$	7.13809	+	6.13087i	0.853165	+	0.732779i
$71$	−4.45973	+	13.7256i	−0.529272	+	1.62893i	0.226438	+	0.974026i	$0.427292\pi$
$71$	−4.45973	+	13.7256i	−0.529272	+	1.62893i	−0.755710	+	0.654907i	$0.772708\pi$
$72$	−0.0727645	−	0.459417i	−0.00857538	−	0.0541428i
$73$	−0.989592	+	1.94218i	−0.115823	+	0.227315i	−0.941639	−	0.336624i	$-0.890715\pi$
$73$	−0.989592	+	1.94218i	−0.115823	+	0.227315i	0.825816	+	0.563939i	$0.190715\pi$
$74$	2.93932	+	2.13554i	0.341689	+	0.248252i
$75$	−5.42887	−	7.56016i	−0.626872	−	0.872972i
$76$	−1.53310	+	4.71838i	−0.175858	+	0.541236i
$77$	−0.782073	+	4.93781i	−0.0891254	+	0.562716i
$78$	1.62553	−	10.2632i	0.184055	−	1.16208i
$79$	1.91575	−	5.89608i	0.215539	−	0.663361i	−0.783576	−	0.621296i	$-0.786606\pi$
$79$	1.91575	−	5.89608i	0.215539	−	0.663361i	0.999115	−	0.0420650i	$-0.0133936\pi$
$80$	2.17573	−	0.515959i	0.243254	−	0.0576860i
$81$	−8.23504	−	5.98311i	−0.915005	−	0.664790i
$82$	4.38056	−	8.59732i	0.483751	−	0.949416i
$83$	0.351764	+	2.22095i	0.0386112	+	0.243781i	0.999444	−	0.0333480i	$-0.0106170\pi$
$83$	0.351764	+	2.22095i	0.0386112	+	0.243781i	−0.960833	+	0.277129i	$0.910617\pi$
$84$	2.42062	−	7.44992i	0.264112	−	0.812852i
$85$	0.945168	+	12.4515i	0.102518	+	1.35056i
$86$	0.373653	−	0.121407i	0.0402920	−	0.0130917i
$87$	8.02030	+	8.02030i	0.859867	+	0.859867i
$88$	0.840069	+	0.840069i	0.0895517	+	0.0895517i
$89$	2.09951	+	6.46163i	0.222548	+	0.684931i	0.998531	+	0.0541780i	$0.0172538\pi$
$89$	2.09951	+	6.46163i	0.222548	+	0.684931i	−0.775984	+	0.630753i	$0.782746\pi$
$90$	−0.545908	+	0.885312i	−0.0575437	+	0.0933201i
$91$	13.8072	−	19.0040i	1.44739	−	1.99216i
$92$	0.587049	−	0.587049i	0.0612041	−	0.0612041i
$93$	−6.21837	−	8.29164i	−0.644815	−	0.859803i
$94$			1.32539i			0.136703i
$95$	9.47490	−	5.77009i	0.972104	−	0.591999i
$96$	−1.09416	−	1.50598i	−0.111672	−	0.153703i
$97$	5.61503	−	11.0201i	0.570120	−	1.11892i	−0.408406	−	0.912800i	$-0.633915\pi$
$97$	5.61503	−	11.0201i	0.570120	−	1.11892i	0.978526	−	0.206123i	$-0.0660846\pi$
$98$	7.57168	−	7.57168i	0.764855	−	0.764855i
$99$	−0.552608			−0.0555392
$100$	−4.44235	−	2.29466i	−0.444235	−	0.229466i
$101$	−3.47070	+	10.6817i	−0.345348	+	1.06287i	0.616050	+	0.787707i	$0.288732\pi$
$101$	−3.47070	+	10.6817i	−0.345348	+	1.06287i	−0.961397	+	0.275163i	$0.911268\pi$
$102$	9.26248	−	4.71947i	0.917122	−	0.467297i
$103$	−15.4523	+	2.44740i	−1.52256	+	0.241149i	−0.860946	−	0.508697i	$-0.830127\pi$
$103$	−15.4523	+	2.44740i	−1.52256	+	0.241149i	−0.661612	+	0.749846i	$0.730127\pi$
$104$	−1.72498	−	5.30895i	−0.169148	−	0.520585i
$105$	−14.9600	+	9.11047i	−1.45995	+	0.889090i
$106$	0.813712	+	1.11998i	0.0790346	+	0.108782i
$107$	2.59919	−	1.32435i	0.251273	−	0.128030i	−0.323818	−	0.946119i	$-0.604967\pi$
$107$	2.59919	−	1.32435i	0.251273	−	0.128030i	0.575091	+	0.818089i	$0.304967\pi$
$108$	−4.66051	−	0.738153i	−0.448458	−	0.0710288i
$109$	11.7018	+	16.1061i	1.12083	+	1.54269i	0.804416	+	0.594066i	$0.202478\pi$
$109$	11.7018	+	16.1061i	1.12083	+	1.54269i	0.316412	+	0.948622i	$0.397522\pi$
$110$	−0.201073	−	2.64891i	−0.0191715	−	0.252564i
$111$	−5.47152	+	3.97529i	−0.519334	+	0.377318i
$112$	−0.658289	−	4.15628i	−0.0622025	−	0.392731i
$113$	3.34152	+	1.70259i	0.314344	+	0.160166i	0.604043	−	0.796952i	$-0.293555\pi$
$113$	3.34152	+	1.70259i	0.314344	+	0.160166i	−0.289700	+	0.957118i	$0.593555\pi$
$114$	−7.47145	−	5.42833i	−0.699766	−	0.508410i
$115$	−1.85109	+	0.140512i	−0.172615	+	0.0131028i
$116$	5.79497	+	1.88290i	0.538050	+	0.174823i
$117$	2.31350	+	1.17879i	0.213883	+	0.108979i
$118$	6.57380	−	6.57380i	0.605168	−	0.605168i
$119$	23.5001			2.15425
$120$	−0.338103	+	4.14866i	−0.0308645	+	0.378719i
$121$	−7.75731	+	5.63602i	−0.705210	+	0.512365i
$122$	−2.55086	+	0.404016i	−0.230944	+	0.0365779i
$123$	12.7007	+	12.7007i	1.14518	+	1.14518i
$124$	−4.99865	−	2.45224i	−0.448892	−	0.220218i
$125$	4.19232	+	10.3646i	0.374972	+	0.927036i
$126$	1.58354	+	1.15051i	0.141073	+	0.102496i
$127$	−1.91497	+	12.0906i	−0.169926	+	1.07287i	0.744353	+	0.667786i	$0.232758\pi$
$127$	−1.91497	+	12.0906i	−0.169926	+	1.07287i	−0.914279	+	0.405085i	$0.867242\pi$
$128$	−0.891007	−	0.453990i	−0.0787546	−	0.0401275i
$129$			0.731345i			0.0643914i
$130$	−4.80870	+	11.5186i	−0.421751	+	1.01025i
$131$	−3.14125	−	9.66778i	−0.274453	−	0.844678i	−0.989364	−	0.145463i	$-0.953533\pi$
$131$	−3.14125	−	9.66778i	−0.274453	−	0.844678i	0.714911	−	0.699215i	$-0.246467\pi$
$132$	−1.97048	+	1.00401i	−0.171508	+	0.0873878i
$133$	−9.47803	−	18.6017i	−0.821849	−	1.61297i
$134$	5.39288	−	7.42267i	0.465874	−	0.641221i
$135$	6.83010	+	8.04214i	0.587842	+	0.692157i
$136$	3.28250	−	4.51797i	0.281472	−	0.387413i
$137$	−1.47834	+	9.33390i	−0.126303	+	0.797449i	0.840478	+	0.541845i	$0.182274\pi$
$137$	−1.47834	+	9.33390i	−0.126303	+	0.797449i	−0.966782	+	0.255603i	$0.917726\pi$
$138$	0.701611	+	1.37699i	0.0597251	+	0.117217i
$139$	−16.3138	+	11.8527i	−1.38372	+	1.00533i	−0.387195	+	0.921998i	$0.626556\pi$
$139$	−16.3138	+	11.8527i	−1.38372	+	1.00533i	−0.996522	+	0.0833310i	$0.973444\pi$
$140$	−4.93875	+	8.00928i	−0.417400	+	0.676908i
$141$	−2.34644	−	0.762406i	−0.197606	−	0.0642062i
$142$	−14.2543	−	2.25766i	−1.19619	−	0.189459i
$143$	−6.55017	+	1.03744i	−0.547752	+	0.0867555i
$144$	0.442378	−	0.143737i	0.0368648	−	0.0119781i
$145$	−7.08665	−	11.6368i	−0.588514	−	0.966382i
$146$	−2.07308	−	0.673584i	−0.171569	−	0.0557462i
$147$	9.04929	+	17.7602i	0.746373	+	1.46484i
$148$	−1.64944	+	3.23721i	−0.135583	+	0.266097i
$149$		−	15.5922i		−	1.27736i	−0.769471	−	0.638682i	$-0.779480\pi$
$149$		−	15.5922i		−	1.27736i	0.769471	−	0.638682i	$-0.220520\pi$
$150$	6.61782	−	6.54470i	0.540342	−	0.534373i
$151$	−12.9370	+	4.20350i	−1.05280	+	0.342076i	−0.783767	−	0.621055i	$-0.786705\pi$
$151$	−12.9370	+	4.20350i	−1.05280	+	0.342076i	−0.269034	+	0.963131i	$0.586705\pi$
$152$	−4.90012	−	0.776103i	−0.397452	−	0.0629503i
$153$	0.406355	+	2.56562i	0.0328518	+	0.207418i
$154$	−4.99936			−0.402860
$155$	4.90637	+	11.4424i	0.394089	+	0.919072i
$156$	10.3911			0.831956
$157$	−0.589503	−	3.72197i	−0.0470474	−	0.297046i	0.952934	−	0.303179i	$-0.0980479\pi$
$157$	−0.589503	−	3.72197i	−0.0470474	−	0.297046i	−0.999981	+	0.00613273i	$0.998048\pi$
$158$	6.12318	+	0.969817i	0.487134	+	0.0771545i
$159$	−2.45086	+	0.796333i	−0.194366	+	0.0631533i
$160$	0.849965	+	2.06823i	0.0671956	+	0.163508i
$161$			3.49360i			0.275335i
$162$	4.62120	−	9.06962i	0.363076	−	0.712577i
$163$	−9.36935	−	18.3884i	−0.733864	−	1.44029i	−0.891607	−	0.452810i	$-0.850422\pi$
$163$	−9.36935	−	18.3884i	−0.733864	−	1.44029i	0.157743	−	0.987480i	$-0.449578\pi$
$164$	9.17675	+	2.98171i	0.716584	+	0.232832i
$165$	4.80525	+	1.16776i	0.374088	+	0.0909102i
$166$	−2.13858	+	0.694867i	−0.165986	+	0.0539322i
$167$	4.34070	−	0.687499i	0.335893	−	0.0532002i	0.0137902	−	0.999905i	$-0.495610\pi$
$167$	4.34070	−	0.687499i	0.335893	−	0.0532002i	0.322103	+	0.946705i	$0.395610\pi$
$168$	7.73686	+	1.22540i	0.596912	+	0.0945416i
$169$	17.2717	+	5.61190i	1.32859	+	0.431685i
$170$	−12.1504	+	2.88138i	−0.931892	+	0.220992i
$171$	1.86695	−	1.35642i	0.142769	−	0.103728i
$172$	0.178365	+	0.350060i	0.0136002	+	0.0266918i
$173$	−0.594702	+	3.75480i	−0.0452144	+	0.285472i	−0.999927	−	0.0120561i	$-0.996162\pi$
$173$	−0.594702	+	3.75480i	−0.0452144	+	0.285472i	0.954713	+	0.297528i	$0.0961623\pi$
$174$	−6.66691	+	9.17621i	−0.505417	+	0.695647i
$175$	20.0464	−	6.39059i	1.51537	−	0.483083i
$176$	−0.698311	+	0.961143i	−0.0526372	+	0.0724489i
$177$	7.85668	+	15.4196i	0.590544	+	1.15901i
$178$	−6.05364	+	3.08448i	−0.453739	+	0.231192i
$179$	5.16699	+	15.9024i	0.386199	+	1.18860i	0.935607	+	0.353043i	$0.114853\pi$
$179$	5.16699	+	15.9024i	0.386199	+	1.18860i	−0.549408	+	0.835554i	$0.685147\pi$
$180$	−0.959811	−	0.400694i	−0.0715401	−	0.0298659i
$181$		−	19.4944i		−	1.44901i	−0.689271	−	0.724504i	$-0.742069\pi$
$181$		−	19.4944i		−	1.44901i	0.689271	−	0.724504i	$-0.257931\pi$
$182$	20.9299	+	10.6643i	1.55143	+	0.790492i
$183$	0.752072	−	4.74839i	0.0555947	−	0.351011i
$184$	0.671656	+	0.487987i	0.0495151	+	0.0359749i
$185$	7.51429	−	3.08810i	0.552461	−	0.227041i
$186$	7.21679	−	7.43891i	0.529161	−	0.545448i
$187$	−4.69138	−	4.69138i	−0.343068	−	0.343068i
$188$	−1.30907	+	0.207336i	−0.0954738	+	0.0151216i
$189$	16.0641	−	11.6712i	1.16849	−	0.848958i
$190$	7.18125	+	8.45561i	0.520983	+	0.613434i
$191$	2.90847			0.210449			0.105225	−	0.994448i	$-0.466444\pi$
$191$	2.90847			0.210449			0.105225	+	0.994448i	$0.466444\pi$
$192$	1.31627	−	1.31627i	0.0949937	−	0.0949937i
$193$	10.5594	+	5.38028i	0.760082	+	0.387281i	0.790663	−	0.612251i	$-0.209736\pi$
$193$	10.5594	+	5.38028i	0.760082	+	0.387281i	−0.0305811	+	0.999532i	$0.509736\pi$
$194$	11.7628	+	3.82197i	0.844521	+	0.274402i
$195$	−17.6263	−	15.1391i	−1.26224	−	1.08413i
$196$	8.66293	+	6.29399i	0.618781	+	0.449570i
$197$	−16.1506	−	8.22915i	−1.15068	−	0.586302i	−0.228686	−	0.973500i	$-0.573443\pi$
$197$	−16.1506	−	8.22915i	−1.15068	−	0.586302i	−0.921997	+	0.387198i	$0.873443\pi$
$198$	−0.0864470	−	0.545805i	−0.00614352	−	0.0387886i
$199$	−19.2052	+	13.9534i	−1.36142	+	0.989129i	−0.363065	+	0.931764i	$0.618270\pi$
$199$	−19.2052	+	13.9534i	−1.36142	+	0.989129i	−0.998353	+	0.0573649i	$0.981730\pi$
$200$	1.57148	−	4.74663i	0.111120	−	0.335637i
$201$	10.0388	+	13.8172i	0.708082	+	0.974591i
$202$	−11.0931	−	1.75698i	−0.780511	−	0.123621i
$203$	−22.8460	+	11.6406i	−1.60348	+	0.817012i
$204$	6.11033	+	8.41015i	0.427809	+	0.588828i
$205$	−11.2222	−	18.4277i	−0.783792	−	1.28704i
$206$	−4.83454	−	14.8792i	−0.336838	−	1.03668i
$207$	−0.381414	+	0.0604100i	−0.0265101	+	0.00419878i
$208$	4.97374	−	2.53425i	0.344867	−	0.175718i
$209$	−1.82138	+	5.60562i	−0.125987	+	0.387749i
$210$	−11.3386	−	13.3507i	−0.782435	−	0.921283i
$211$	3.65870			0.251875			0.125938	−	0.992038i	$-0.459806\pi$
$211$	3.65870			0.251875			0.125938	+	0.992038i	$0.459806\pi$
$212$	−0.978897	+	0.978897i	−0.0672309	+	0.0672309i
$213$	12.1964	−	23.9369i	0.835687	−	1.64013i
$214$	1.71465	+	2.36002i	0.117211	+	0.161327i
$215$	0.207456	−	0.853664i	0.0141484	−	0.0582194i
$216$		−	4.71861i		−	0.321061i
$217$	22.1706	−	7.57701i	1.50504	−	0.514361i
$218$	−14.0773	+	14.0773i	−0.953434	+	0.953434i
$219$	2.38500	−	3.28267i	0.161164	−	0.221823i
$220$	2.58485	−	0.612979i	0.174270	−	0.0413270i
$221$	9.63319	+	29.6479i	0.647999	+	1.99433i
$222$	−4.78228	−	4.78228i	−0.320966	−	0.320966i
$223$	9.20022	+	9.20022i	0.616092	+	0.616092i	0.944527	−	0.328435i	$-0.106521\pi$
$223$	9.20022	+	9.20022i	0.616092	+	0.616092i	−0.328435	+	0.944527i	$0.606521\pi$
$224$	4.00213	−	1.30037i	0.267403	−	0.0868846i
$225$	1.04433	+	2.07806i	0.0696218	+	0.138538i
$226$	−1.15890	+	3.56672i	−0.0770888	+	0.237255i
$227$	−0.892393	−	5.63435i	−0.0592302	−	0.373965i	−0.999443	−	0.0333767i	$-0.989374\pi$
$227$	−0.892393	−	5.63435i	−0.0592302	−	0.373965i	0.940213	−	0.340588i	$-0.110626\pi$
$228$	4.19270	−	8.22865i	0.277669	−	0.544955i
$229$	−13.7847	−	10.0152i	−0.910918	−	0.661820i	0.0303292	−	0.999540i	$-0.490344\pi$
$229$	−13.7847	−	10.0152i	−0.910918	−	0.661820i	−0.941247	+	0.337720i	$0.890344\pi$
$230$	−0.428356	−	1.80632i	−0.0282449	−	0.119105i
$231$	2.87579	−	8.85078i	0.189213	−	0.582339i
$232$	−0.953186	+	6.01818i	−0.0625797	+	0.395113i
$233$	−1.51839	+	9.58674i	−0.0994730	+	0.628048i	0.886702	+	0.462341i	$0.152990\pi$
$233$	−1.51839	+	9.58674i	−0.0994730	+	0.628048i	−0.986175	+	0.165707i	$0.947010\pi$
$234$	−0.802364	+	2.46942i	−0.0524522	+	0.161431i
$235$	2.52262	+	1.55552i	0.164558	+	0.101471i
$236$	7.52124	+	5.46450i	0.489591	+	0.355709i
$237$	−5.23920	+	10.2825i	−0.340322	+	0.667920i
$238$	3.67623	+	23.2108i	0.238294	+	1.50453i
$239$	−0.135481	+	0.416966i	−0.00876351	+	0.0269713i	−0.955343	−	0.295500i	$-0.904514\pi$
$239$	−0.135481	+	0.416966i	−0.00876351	+	0.0269713i	0.946579	+	0.322472i	$0.104514\pi$
$240$	−4.15048	+	0.315053i	−0.267912	+	0.0203366i
$241$	−4.50743	+	1.46455i	−0.290349	+	0.0943401i	−0.450570	−	0.892741i	$-0.648779\pi$
$241$	−4.50743	+	1.46455i	−0.290349	+	0.0943401i	0.160221	+	0.987081i	$0.448779\pi$
$242$	−6.78014	−	6.78014i	−0.435844	−	0.435844i
$243$	3.38875	+	3.38875i	0.217388	+	0.217388i
$244$	−0.798084	−	2.45625i	−0.0510921	−	0.157245i
$245$	−5.52487	−	23.2976i	−0.352971	−	1.48843i
$246$	−10.5575	+	14.5312i	−0.673123	+	0.926474i
$247$	19.5828	−	19.5828i	1.24602	−	1.24602i
$248$	1.64009	−	5.32072i	0.104146	−	0.337866i
$249$		−	4.18582i		−	0.265265i
$250$	−9.58115	+	5.76208i	−0.605965	+	0.364426i
$251$	−4.67696	−	6.43729i	−0.295207	−	0.406318i	0.635490	−	0.772109i	$-0.280798\pi$
$251$	−4.67696	−	6.43729i	−0.295207	−	0.406318i	−0.930697	+	0.365791i	$0.880798\pi$
$252$	−0.888624	+	1.74402i	−0.0559781	+	0.109863i
$253$	0.697436	−	0.697436i	0.0438474	−	0.0438474i
$254$	−12.2414			−0.768091
$255$	1.88814	−	23.1683i	0.118240	−	1.45085i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	14.8626	−	7.57287i	0.927103	−	0.472383i	0.0758392	−	0.997120i	$-0.475836\pi$
$257$	14.8626	−	7.57287i	0.927103	−	0.472383i	0.851264	+	0.524737i	$0.175836\pi$
$258$	−0.722341	+	0.114408i	−0.0449710	+	0.00712271i
$259$	−4.72451	−	14.5405i	−0.293567	−	0.903505i
$260$	−12.1291	−	2.94758i	−0.752213	−	0.182801i
$261$	−1.66591	−	2.29292i	−0.103117	−	0.141928i
$262$	9.05736	−	4.61495i	0.559565	−	0.285113i
$263$	9.99056	+	1.58235i	0.616044	+	0.0975718i	0.456655	−	0.889644i	$-0.349047\pi$
$263$	9.99056	+	1.58235i	0.616044	+	0.0975718i	0.159389	+	0.987216i	$0.449047\pi$
$264$	−1.29990	−	1.78916i	−0.0800032	−	0.110115i
$265$	3.08666	−	0.234302i	0.189612	−	0.0143930i
$266$	16.8900	−	12.2713i	1.03559	−	0.752401i
$267$	−1.97847	−	12.4915i	−0.121080	−	0.764470i
$268$	8.17491	+	4.16533i	0.499362	+	0.254438i
$269$	−6.77787	−	4.92441i	−0.413254	−	0.300247i	0.361664	−	0.932309i	$-0.382209\pi$
$269$	−6.77787	−	4.92441i	−0.413254	−	0.300247i	−0.774918	+	0.632062i	$0.782209\pi$
$270$	−6.87467	+	8.00408i	−0.418379	+	0.487113i
$271$	16.0512	+	5.21537i	0.975044	+	0.316811i	0.752850	−	0.658192i	$-0.228678\pi$
$271$	16.0512	+	5.21537i	0.975044	+	0.316811i	0.222194	+	0.975003i	$0.428678\pi$
$272$	4.97584	+	2.53532i	0.301705	+	0.153726i
$273$	−30.9195	+	30.9195i	−1.87133	+	1.87133i
$274$	−9.45025			−0.570910
$275$	−5.27768	−	2.72615i	−0.318256	−	0.164393i
$276$	−1.25028	+	0.908382i	−0.0752581	+	0.0546782i
$277$	−20.5903	+	3.26119i	−1.23715	+	0.195946i	−0.740531	−	0.672022i	$-0.765426\pi$
$277$	−20.5903	+	3.26119i	−1.23715	+	0.195946i	−0.496621	+	0.867968i	$0.665426\pi$
$278$	−14.2588	−	14.2588i	−0.855184	−	0.855184i
$279$	1.21058	+	2.28945i	0.0724758	+	0.137066i
$280$	−8.68327	−	3.62501i	−0.518924	−	0.216636i
$281$	0.0966261	+	0.0702030i	0.00576423	+	0.00418796i	0.590664	−	0.806918i	$-0.298866\pi$
$281$	0.0966261	+	0.0702030i	0.00576423	+	0.00418796i	−0.584899	+	0.811106i	$0.698866\pi$
$282$	0.385955	−	2.43682i	0.0229833	−	0.145111i
$283$	7.63932	+	3.89243i	0.454110	+	0.231381i	0.666058	−	0.745900i	$-0.267981\pi$
$283$	7.63932	+	3.89243i	0.454110	+	0.231381i	−0.211947	+	0.977281i	$0.567981\pi$
$284$		−	14.4320i		−	0.856380i
$285$	−19.1005	+	7.84962i	−1.13142	+	0.464971i
$286$	−2.04934	−	6.30723i	−0.121180	−	0.372954i
$287$	−36.1783	+	18.4337i	−2.13554	+	1.08811i
$288$	0.211171	+	0.414446i	0.0124434	+	0.0244215i
$289$	−8.33881	+	11.4774i	−0.490518	+	0.675141i
$290$	10.3849	−	8.81979i	0.609823	−	0.517916i
$291$	−13.5327	+	18.6262i	−0.793301	+	1.09189i
$292$	0.340990	−	2.15293i	0.0199549	−	0.125991i
$293$	5.82843	+	11.4389i	0.340500	+	0.668270i	0.996232	−	0.0867241i	$-0.0276399\pi$
$293$	5.82843	+	11.4389i	0.340500	+	0.668270i	−0.655732	+	0.754994i	$0.727640\pi$
$294$	−16.1260	+	11.7162i	−0.940485	+	0.683302i
$295$	−4.79675	−	20.2272i	−0.279277	−	1.17767i
$296$	−3.45538	−	1.12272i	−0.200840	−	0.0652569i
$297$	−5.53687	−	0.876954i	−0.321282	−	0.0508860i
$298$	15.4002	−	2.43916i	0.892112	−	0.141297i
$299$	−4.40756	+	1.43210i	−0.254896	+	0.0828206i
$300$	7.49938	+	5.51252i	0.432977	+	0.318266i
$301$	−1.57236	−	0.510891i	−0.0906295	−	0.0294473i
$302$	−6.17555	−	12.1202i	−0.355363	−	0.697439i
$303$	9.49166	−	18.6284i	0.545282	−	1.07018i
$304$		−	4.96120i		−	0.284544i
$305$	−2.22480	+	5.32924i	−0.127392	+	0.305151i
$306$	−2.47047	+	0.802703i	−0.141227	+	0.0458875i
$307$	3.76890	+	0.596936i	0.215103	+	0.0340689i	0.263056	−	0.964781i	$-0.415270\pi$
$307$	3.76890	+	0.596936i	0.215103	+	0.0340689i	−0.0479529	+	0.998850i	$0.515270\pi$
$308$	−0.782073	−	4.93781i	−0.0445627	−	0.281358i
$309$	29.1228			1.65674
$310$	−10.5340	+	6.63595i	−0.598288	+	0.376896i
$311$	−2.77229			−0.157202			−0.0786012	−	0.996906i	$-0.525045\pi$
$311$	−2.77229			−0.157202			−0.0786012	+	0.996906i	$0.525045\pi$
$312$	1.62553	+	10.2632i	0.0920276	+	0.581039i
$313$	−25.5204	−	4.04203i	−1.44250	−	0.228469i	−0.614374	−	0.789015i	$-0.710591\pi$
$313$	−25.5204	−	4.04203i	−1.44250	−	0.228469i	−0.828123	+	0.560546i	$0.810591\pi$
$314$	3.58393	−	1.16449i	0.202253	−	0.0657160i
$315$	4.04827	−	1.66369i	0.228094	−	0.0937384i
$316$			6.19951i			0.348750i
$317$	9.11437	−	17.8880i	0.511914	−	1.00469i	−0.479939	−	0.877302i	$-0.659341\pi$
$317$	9.11437	−	17.8880i	0.511914	−	1.00469i	0.991853	−	0.127386i	$-0.0406586\pi$
$318$	−1.16993	−	2.29611i	−0.0656063	−	0.128760i
$319$	6.88465	+	2.23696i	0.385466	+	0.125246i
$320$	−1.90980	+	1.16304i	−0.106761	+	0.0650161i
$321$	−5.16446	+	1.67803i	−0.288252	+	0.0936587i
$322$	−3.45059	+	0.546520i	−0.192294	+	0.0304564i
$323$	27.3648	+	4.33416i	1.52262	+	0.241159i
$324$	9.68087	+	3.14551i	0.537826	+	0.174750i
$325$	16.2799	+	22.6711i	0.903045	+	1.25757i
$326$	16.6963	−	12.1306i	0.924723	−	0.671851i
$327$	−16.8245	−	33.0199i	−0.930395	−	1.82600i
$328$	−1.50944	+	9.53021i	−0.0833447	+	0.526218i
$329$	3.27828	−	4.51217i	0.180738	−	0.248764i
$330$	−0.401679	+	4.92877i	−0.0221117	+	0.271320i
$331$	5.25636	−	7.23475i	0.288916	−	0.397658i	−0.639746	−	0.768586i	$-0.720960\pi$
$331$	5.25636	−	7.23475i	0.288916	−	0.397658i	0.928661	+	0.370928i	$0.120960\pi$
$332$	−1.02086	−	2.00355i	−0.0560270	−	0.109959i
$333$	1.50577	−	0.767227i	0.0825155	−	0.0420438i
$334$	1.35807	+	4.17971i	0.0743102	+	0.228703i
$335$	−7.79836	−	18.9758i	−0.426070	−	1.03676i
$336$			7.83330i			0.427342i
$337$	19.3116	+	9.83976i	1.05197	+	0.536006i	0.892430	−	0.451186i	$-0.148999\pi$
$337$	19.3116	+	9.83976i	1.05197	+	0.536006i	0.159540	+	0.987191i	$0.448999\pi$
$338$	−2.84093	+	17.9369i	−0.154526	+	0.975639i
$339$	−5.64782	−	4.10338i	−0.306748	−	0.222865i
$340$	−4.74665	−	11.5500i	−0.257423	−	0.626389i
$341$	−5.93859	−	2.91336i	−0.321592	−	0.157767i
$342$	1.63177	+	1.63177i	0.0882360	+	0.0882360i
$343$	−15.4113	+	2.44092i	−0.832134	+	0.131797i
$344$	−0.317848	+	0.230930i	−0.0171372	+	0.0124509i
$345$	3.44427	+	0.280698i	0.185433	+	0.0151122i
$346$	−3.80161			−0.204376
$347$	−24.4544	+	24.4544i	−1.31278	+	1.31278i	−0.393427	+	0.919356i	$0.628711\pi$
$347$	−24.4544	+	24.4544i	−1.31278	+	1.31278i	−0.919356	+	0.393427i	$0.871289\pi$
$348$	−10.1062	−	5.14935i	−0.541748	−	0.276034i
$349$	−10.0905	−	3.27860i	−0.540131	−	0.175499i	0.0262308	−	0.999656i	$-0.491650\pi$
$349$	−10.0905	−	3.27860i	−0.540131	−	0.175499i	−0.566362	+	0.824157i	$0.691650\pi$
$350$	9.44787	+	18.7999i	0.505010	+	1.00490i
$351$	21.3095	+	15.4823i	1.13742	+	0.826383i
$352$	−1.05855	−	0.539358i	−0.0564209	−	0.0287479i
$353$	−2.78293	−	17.5708i	−0.148121	−	0.935197i	−0.944049	−	0.329806i	$-0.893017\pi$
$353$	−2.78293	−	17.5708i	−0.148121	−	0.935197i	0.795928	−	0.605391i	$-0.206983\pi$
$354$	−14.0007	+	10.1721i	−0.744129	+	0.540641i
$355$	−21.0263	+	24.4807i	−1.11596	+	1.29930i
$356$	−3.99350	−	5.49659i	−0.211655	−	0.291319i
$357$	−43.2066	−	6.84326i	−2.28674	−	0.362184i
$358$	−14.8983	+	7.59105i	−0.787398	+	0.401199i
$359$	13.4216	+	18.4732i	0.708362	+	0.974977i	0.999831	+	0.0183967i	$0.00585618\pi$
$359$	13.4216	+	18.4732i	0.708362	+	0.974977i	−0.291468	+	0.956580i	$0.594144\pi$
$360$	0.245613	−	1.01068i	0.0129449	−	0.0532673i
$361$	−1.73467	−	5.33878i	−0.0912987	−	0.280988i
$362$	19.2544	−	3.04960i	1.01199	−	0.160283i
$363$	15.9036	−	8.10328i	0.834722	−	0.425312i
$364$	−7.25887	+	22.3405i	−0.380468	+	1.17096i
$365$	−3.71507	+	3.15517i	−0.194456	+	0.165149i
$366$	4.80758			0.251296
$367$	2.30910	−	2.30910i	0.120534	−	0.120534i	−0.644267	−	0.764801i	$-0.722837\pi$
$367$	2.30910	−	2.30910i	0.120534	−	0.120534i	0.764801	+	0.644267i	$0.222837\pi$
$368$	−0.376909	+	0.739725i	−0.0196477	+	0.0385608i
$369$	−2.63808	−	3.63101i	−0.137333	−	0.189023i
$370$	4.22557	+	6.93869i	0.219677	+	0.360725i
$371$		−	5.82554i		−	0.302447i
$372$	8.47628	+	5.96423i	0.439475	+	0.309231i
$373$	−0.547654	+	0.547654i	−0.0283565	+	0.0283565i	−0.721143	−	0.692786i	$-0.756383\pi$
$373$	−0.547654	+	0.547654i	−0.0283565	+	0.0283565i	0.692786	+	0.721143i	$0.256383\pi$
$374$	3.89973	−	5.36752i	0.201650	−	0.277548i
$375$	−4.68970	−	20.2768i	−0.242175	−	1.04709i
$376$	−0.409568	−	1.26052i	−0.0211218	−	0.0650063i
$377$	−24.0510	−	24.0510i	−1.23869	−	1.23869i
$378$	14.0405	+	14.0405i	0.722167	+	0.722167i
$379$	−9.03806	+	2.93664i	−0.464254	+	0.150845i	−0.531798	−	0.846871i	$-0.678484\pi$
$379$	−9.03806	+	2.93664i	−0.464254	+	0.150845i	0.0675444	+	0.997716i	$0.478484\pi$
$380$	−7.22811	+	8.41559i	−0.370794	+	0.431710i
$381$	7.04162	−	21.6719i	0.360753	−	1.11028i
$382$	0.454985	+	2.87266i	0.0232790	+	0.146978i
$383$	−0.0482434	+	0.0946829i	−0.00246512	+	0.00483807i	−0.892236	−	0.451570i	$-0.850864\pi$
$383$	−0.0482434	+	0.0946829i	−0.00246512	+	0.00483807i	0.889771	+	0.456408i	$0.150864\pi$
$384$	1.50598	+	1.09416i	0.0768516	+	0.0558359i
$385$	−5.86742	+	9.51533i	−0.299031	+	0.484946i
$386$	−3.66219	+	11.2711i	−0.186401	+	0.573682i
$387$	0.0285878	−	0.180497i	0.00145320	−	0.00917516i
$388$	−1.93481	+	12.2159i	−0.0982249	+	0.620168i
$389$	9.02186	−	27.7664i	0.457426	−	1.40781i	−0.410836	−	0.911709i	$-0.634763\pi$
$389$	9.02186	−	27.7664i	0.457426	−	1.40781i	0.868263	−	0.496105i	$-0.165237\pi$
$390$	12.1954	−	19.7775i	0.617537	−	1.00147i
$391$	−3.75087	−	2.72517i	−0.189690	−	0.137818i
$392$	−4.86132	+	9.54087i	−0.245534	+	0.481887i
$393$	2.96015	+	18.6896i	0.149320	+	0.942768i
$394$	5.60132	−	17.2391i	0.282190	−	0.868493i
$395$	9.03223	−	10.5161i	0.454461	−	0.529122i
$396$	0.525562	−	0.170765i	0.0264105	−	0.00858128i
$397$	24.4559	+	24.4559i	1.22741	+	1.22741i	0.964941	+	0.262467i	$0.0845361\pi$
$397$	24.4559	+	24.4559i	1.22741	+	1.22741i	0.262467	+	0.964941i	$0.415464\pi$
$398$	−16.7859	−	16.7859i	−0.841403	−	0.841403i
$399$	12.0092	+	36.9605i	0.601212	+	1.85034i
$400$	4.93402	+	0.809592i	0.246701	+	0.0404796i
$401$	22.8428	−	31.4405i	1.14072	−	1.57006i	0.374820	−	0.927098i	$-0.377705\pi$
$401$	22.8428	−	31.4405i	1.14072	−	1.57006i	0.765897	−	0.642964i	$-0.222295\pi$
$402$	−12.0767	+	12.0767i	−0.602330	+	0.602330i
$403$	18.6474	+	24.8646i	0.928893	+	1.23860i
$404$		−	11.2314i		−	0.558784i
$405$	−11.8387	−	19.4400i	−0.588269	−	0.965980i
$406$	−15.0712	−	20.7437i	−0.747972	−	1.02949i
$407$	−1.95960	+	3.84593i	−0.0971336	+	0.190635i
$408$	−7.35074	+	7.35074i	−0.363916	+	0.363916i
$409$	17.3373			0.857274			0.428637	−	0.903477i	$-0.358994\pi$
$409$	17.3373			0.857274			0.428637	+	0.903477i	$0.358994\pi$
$410$	16.4452	−	13.9668i	0.812173	−	0.689769i
$411$	5.43608	−	16.7305i	0.268142	−	0.825257i
$412$	13.9397	−	7.10263i	0.686760	−	0.349922i
$413$	−38.6399	+	6.11996i	−1.90135	+	0.301144i
$414$	−0.119332	−	0.367268i	−0.00586487	−	0.0180502i
$415$	−1.18736	+	4.88590i	−0.0582853	+	0.239839i
$416$	3.28111	+	4.51606i	0.160870	+	0.221418i
$417$	33.4456	−	17.0414i	1.63784	−	0.834519i
$418$	−5.82153	−	0.922040i	−0.284740	−	0.0450984i
$419$	−8.93797	−	12.3021i	−0.436648	−	0.600995i	0.532815	−	0.846232i	$-0.321134\pi$
$419$	−8.93797	−	12.3021i	−0.436648	−	0.600995i	−0.969463	+	0.245237i	$0.921134\pi$
$420$	11.4126	−	13.2875i	0.556875	−	0.648362i
$421$	24.7504	−	17.9822i	1.20626	−	0.876400i	0.211376	−	0.977405i	$-0.432206\pi$
$421$	24.7504	−	17.9822i	1.20626	−	0.876400i	0.994886	+	0.101005i	$0.0322057\pi$
$422$	0.572347	+	3.61366i	0.0278614	+	0.175910i
$423$	0.549302	+	0.279883i	0.0267080	+	0.0136084i
$424$	−1.11998	−	0.813712i	−0.0543909	−	0.0395173i
$425$	−8.77593	+	26.5076i	−0.425695	+	1.28581i
$426$	25.5501	+	8.30174i	1.23791	+	0.402220i
$427$	9.68348	+	4.93398i	0.468616	+	0.238772i
$428$	−2.06273	+	2.06273i	−0.0997059	+	0.0997059i
$429$	12.3451			0.596025
$430$	0.875607	+	0.0713593i	0.0422255	+	0.00344125i
$431$	11.4218	−	8.29844i	0.550170	−	0.399722i	−0.277678	−	0.960674i	$-0.589565\pi$
$431$	11.4218	−	8.29844i	0.550170	−	0.399722i	0.827848	+	0.560952i	$0.189565\pi$
$432$	4.66051	−	0.738153i	0.224229	−	0.0355144i
$433$	16.8339	+	16.8339i	0.808986	+	0.808986i	0.984480	−	0.175495i	$-0.0561525\pi$
$433$	16.8339	+	16.8339i	0.808986	+	0.808986i	−0.175495	+	0.984480i	$0.556152\pi$
$434$	10.9520	+	20.7124i	0.525711	+	0.994225i
$435$	9.64066	+	23.4587i	0.462234	+	1.12476i
$436$	−16.1061	−	11.7018i	−0.771344	−	0.560414i
$437$	−0.644330	+	4.06814i	−0.0308225	+	0.194606i
$438$	3.61536	+	1.84212i	0.172748	+	0.0880197i
$439$		−	20.1434i		−	0.961393i	−0.876887	−	0.480697i	$-0.840384\pi$
$439$		−	20.1434i		−	0.961393i	0.876887	−	0.480697i	$-0.159616\pi$
$440$	1.00979	+	2.45713i	0.0481399	+	0.117139i
$441$	−1.53913	−	4.73697i	−0.0732921	−	0.225570i
$442$	−27.7759	+	14.1525i	−1.32117	+	0.673168i
$443$	9.45018	+	18.5470i	0.448992	+	0.881196i	0.998942	+	0.0459983i	$0.0146469\pi$
$443$	9.45018	+	18.5470i	0.448992	+	0.881196i	−0.549950	+	0.835198i	$0.685353\pi$
$444$	3.97529	−	5.47152i	0.188659	−	0.259667i
$445$	−1.23403	+	15.1420i	−0.0584984	+	0.717799i
$446$	−7.64772	+	10.5262i	−0.362130	+	0.498429i
$447$	−4.54047	+	28.6674i	−0.214757	+	1.35592i
$448$	1.91043	+	3.74943i	0.0902593	+	0.177144i
$449$	7.32311	−	5.32055i	0.345599	−	0.251092i	−0.401421	−	0.915893i	$-0.631484\pi$
$449$	7.32311	−	5.32055i	0.345599	−	0.251092i	0.747020	+	0.664801i	$0.231484\pi$
$450$	−1.88911	+	1.35655i	−0.0890535	+	0.0639484i
$451$	10.9023	+	3.54238i	0.513370	+	0.166804i
$452$	−3.70410	−	0.586672i	−0.174226	−	0.0275947i
$453$	25.0097	−	3.96116i	1.17506	−	0.186111i
$454$	5.42538	−	1.76281i	0.254626	−	0.0827329i
$455$	44.8615	−	27.3201i	2.10314	−	1.28079i
$456$	8.78322	+	2.85384i	0.411312	+	0.133643i
$457$	−0.179013	−	0.351333i	−0.00837388	−	0.0164347i	0.886782	−	0.462189i	$-0.152936\pi$
$457$	−0.179013	−	0.351333i	−0.00837388	−	0.0164347i	−0.895156	+	0.445754i	$0.852936\pi$
$458$	7.73546	−	15.1817i	0.361454	−	0.709394i
$459$			26.3512i			1.22997i
$460$	1.71707	−	0.705652i	0.0800587	−	0.0329012i
$461$	12.0471	−	3.91434i	0.561089	−	0.182309i	−0.0147221	−	0.999892i	$-0.504686\pi$
$461$	12.0471	−	3.91434i	0.561089	−	0.182309i	0.575811	+	0.817583i	$0.304686\pi$
$462$	9.19168	+	1.45582i	0.427636	+	0.0677309i
$463$	4.42381	+	27.9308i	0.205592	+	1.29806i	0.847303	+	0.531110i	$0.178225\pi$
$463$	4.42381	+	27.9308i	0.205592	+	1.29806i	−0.641711	+	0.766947i	$0.721775\pi$
$464$	−6.09320			−0.282869
$465$	−5.68869	−	22.4663i	−0.263807	−	1.04185i
$466$	−9.70624			−0.449633
$467$	0.794112	+	5.01382i	0.0367471	+	0.232012i	0.999226	−	0.0393457i	$-0.0125273\pi$
$467$	0.794112	+	5.01382i	0.0367471	+	0.232012i	−0.962479	+	0.271358i	$0.912527\pi$
$468$	−2.56454	−	0.406183i	−0.118546	−	0.0187758i
$469$	−36.7192	+	11.9308i	−1.69553	+	0.550912i
$470$	−1.14174	+	2.73490i	−0.0526647	+	0.126152i
$471$			7.01478i			0.323224i
$472$	−4.22064	+	8.28348i	−0.194271	+	0.381278i
$473$	0.211904	+	0.415885i	0.00974335	+	0.0191224i
$474$	−10.9755	−	3.56616i	−0.504121	−	0.163799i
$475$	24.5218	−	3.74436i	1.12514	−	0.171803i
$476$	−22.3499	+	7.26194i	−1.02441	+	0.332850i
$477$	0.636002	−	0.100733i	0.0291206	−	0.00461224i
$478$	−0.433027	−	0.0685847i	−0.0198062	−	0.00313699i
$479$	−35.8739	−	11.6561i	−1.63912	−	0.532583i	−0.662779	−	0.748815i	$-0.730623\pi$
$479$	−35.8739	−	11.6561i	−1.63912	−	0.532583i	−0.976342	+	0.216233i	$0.930623\pi$
$480$	−0.960452	−	4.05009i	−0.0438384	−	0.184861i
$481$	16.4078	−	11.9209i	0.748130	−	0.543548i
$482$	−2.15164	−	4.22283i	−0.0980045	−	0.192345i
$483$	1.01734	−	6.42324i	0.0462906	−	0.292268i
$484$	5.63602	−	7.75731i	0.256183	−	0.352605i
$485$	21.0796	−	17.9027i	0.957177	−	0.812919i
$486$	−2.81691	+	3.87714i	−0.127778	+	0.175871i
$487$	−14.9877	−	29.4151i	−0.679159	−	1.33292i	−0.930951	−	0.365143i	$-0.881020\pi$
$487$	−14.9877	−	29.4151i	−0.679159	−	1.33292i	0.251792	−	0.967781i	$-0.418980\pi$
$488$	2.30116	−	1.17250i	0.104169	−	0.0530766i
$489$	11.8715	+	36.5367i	0.536848	+	1.65225i
$490$	22.1465	−	9.10140i	1.00048	−	0.411159i
$491$		−	25.8355i		−	1.16594i	−0.812494	−	0.582969i	$-0.801891\pi$
$491$		−	25.8355i		−	1.16594i	0.812494	−	0.582969i	$-0.198109\pi$
$492$	−16.0038	−	8.15436i	−0.721508	−	0.367627i
$493$	5.32308	−	33.6086i	0.239740	−	1.51366i
$494$	22.4051	+	16.2783i	1.00805	+	0.732393i
$495$	−1.14029	−	0.476039i	−0.0512523	−	0.0213964i
$496$	5.51178	+	0.787552i	0.247486	+	0.0353621i
$497$	42.9433	+	42.9433i	1.92627	+	1.92627i
$498$	4.13428	−	0.654806i	0.185262	−	0.0293426i
$499$	0.451953	−	0.328363i	0.0202322	−	0.0146996i	−0.577623	−	0.816304i	$-0.696020\pi$
$499$	0.451953	−	0.328363i	0.0202322	−	0.0146996i	0.597855	+	0.801604i	$0.296020\pi$
$500$	−7.18996	−	8.56180i	−0.321545	−	0.382895i
$501$	−8.18088			−0.365495
$502$	5.62640	−	5.62640i	0.251118	−	0.251118i
$503$	−2.82416	−	1.43898i	−0.125923	−	0.0641610i	0.389894	−	0.920860i	$-0.372512\pi$
$503$	−2.82416	−	1.43898i	−0.125923	−	0.0641610i	−0.515817	+	0.856699i	$0.672512\pi$
$504$	−1.86156	−	0.604859i	−0.0829206	−	0.0269425i
$505$	−16.3634	+	19.0516i	−0.728160	+	0.847787i
$506$	0.797953	+	0.579747i	0.0354733	+	0.0257729i
$507$	−30.1210	−	15.3474i	−1.33772	−	0.681602i
$508$	−1.91497	−	12.0906i	−0.0849631	−	0.536436i
$509$	−16.1365	+	11.7238i	−0.715237	+	0.519650i	−0.884859	−	0.465859i	$-0.845745\pi$
$509$	−16.1365	+	11.7238i	−0.715237	+	0.519650i	0.169622	+	0.985509i	$0.445745\pi$
$510$	23.1784	−	1.75942i	1.02636	−	0.0779084i
$511$	5.39154	+	7.42081i	0.238508	+	0.328278i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$	20.8584	−	10.6279i	0.920922	−	0.469233i
$514$	9.80466	+	13.4950i	0.432465	+	0.595237i
$515$	−33.9936	−	8.26107i	−1.49794	−	0.364026i
$516$	−0.225998	−	0.695551i	−0.00994901	−	0.0306199i
$517$	−1.55523	+	0.246324i	−0.0683987	+	0.0108333i
$518$	13.6224	−	6.94098i	0.598536	−	0.304969i
$519$	2.18681	−	6.73030i	0.0959901	−	0.295427i
$520$	1.01389	−	12.4408i	0.0444620	−	0.545567i
$521$	3.50606			0.153603			0.0768016	−	0.997046i	$-0.475529\pi$
$521$	3.50606			0.153603			0.0768016	+	0.997046i	$0.475529\pi$
$522$	2.00409	−	2.00409i	0.0877166	−	0.0877166i
$523$	−9.61590	+	18.8723i	−0.420474	+	0.825226i	0.579474	+	0.814991i	$0.303258\pi$
$523$	−9.61590	+	18.8723i	−0.420474	+	0.825226i	−0.999948	+	0.0102355i	$0.996742\pi$
$524$	5.97502	+	8.22391i	0.261020	+	0.359263i
$525$	−38.7178	+	5.91202i	−1.68978	+	0.258022i
$526$			10.1151i			0.441039i
$527$	−9.15911	+	29.7137i	−0.398977	+	1.29435i
$528$	1.56378	−	1.56378i	0.0680548	−	0.0680548i
$529$	−13.1139	+	18.0498i	−0.570171	+	0.784773i
$530$	0.714277	+	3.01201i	0.0310262	+	0.130833i
$531$	−1.33629	−	4.11268i	−0.0579901	−	0.178475i
$532$	14.7624	+	14.7624i	0.640030	+	0.640030i
$533$	−38.0864	−	38.0864i	−1.64970	−	1.64970i
$534$	12.0282	−	3.90821i	0.520513	−	0.169125i
$535$	6.50422	−	0.493720i	0.281202	−	0.0213454i
$536$	−2.83521	+	8.72587i	−0.122462	+	0.376900i
$537$	−4.86909	−	30.7422i	−0.210117	−	1.32663i
$538$	3.80349	−	7.46477i	0.163980	−	0.321829i
$539$	10.2919	+	7.47749i	0.443303	+	0.322078i
$540$	−8.98097	−	5.53792i	−0.386479	−	0.238314i
$541$	5.07322	−	15.6138i	0.218115	−	0.671288i	−0.780803	−	0.624777i	$-0.785190\pi$
$541$	5.07322	−	15.6138i	0.218115	−	0.671288i	0.998918	−	0.0465110i	$-0.0148102\pi$
$542$	−2.64019	+	16.6695i	−0.113406	+	0.716016i
$543$	−5.67679	+	35.8419i	−0.243614	+	1.53812i
$544$	−1.72571	+	5.31119i	−0.0739892	+	0.227715i
$545$	10.2719	+	43.3150i	0.439998	+	1.85541i
$546$	−35.3757	−	25.7019i	−1.51394	−	1.09994i
$547$	3.31719	−	6.51035i	0.141833	−	0.278362i	−0.809153	−	0.587599i	$-0.800073\pi$
$547$	3.31719	−	6.51035i	0.141833	−	0.278362i	0.950985	+	0.309236i	$0.100073\pi$
$548$	−1.47834	−	9.33390i	−0.0631517	−	0.398724i
$549$	−0.371224	+	1.14251i	−0.0158434	+	0.0487611i
$550$	1.86697	−	5.63917i	0.0796080	−	0.240455i
$551$	−28.7500	+	9.34145i	−1.22479	+	0.397959i
$552$	−1.09279	−	1.09279i	−0.0465120	−	0.0465120i
$553$	−18.4470	−	18.4470i	−0.784448	−	0.784448i
$554$	−6.44207	−	19.8267i	−0.273697	−	0.842354i
$555$	−14.7148	+	3.48952i	−0.624609	+	0.148122i
$556$	11.8527	−	16.3138i	0.502664	−	0.691858i
$557$	−1.45701	+	1.45701i	−0.0617354	+	0.0617354i	−0.737300	−	0.675565i	$-0.763900\pi$
$557$	−1.45701	+	1.45701i	−0.0617354	+	0.0617354i	0.675565	+	0.737300i	$0.263900\pi$
$558$	−2.07189	+	1.55383i	−0.0877101	+	0.0657788i
$559$		−	2.19313i		−	0.0927595i
$560$	2.22202	−	9.14344i	0.0938976	−	0.386381i
$561$	7.25931	+	9.99158i	0.306488	+	0.421845i
$562$	−0.0542230	+	0.106419i	−0.00228726	+	0.00448900i
$563$	−11.3738	+	11.3738i	−0.479347	+	0.479347i	−0.904923	−	0.425576i	$-0.860072\pi$
$563$	−11.3738	+	11.3738i	−0.479347	+	0.479347i	0.425576	+	0.904923i	$0.360072\pi$
$564$	2.46720			0.103888
$565$	5.42845	+	6.39176i	0.228377	+	0.268904i
$566$	−2.64945	+	8.15417i	−0.111365	+	0.342745i
$567$	−38.1657	+	19.4464i	−1.60281	+	0.816672i
$568$	14.2543	−	2.25766i	0.598097	−	0.0947293i
$569$	−9.66757	−	29.7537i	−0.405286	−	1.24734i	−0.920656	−	0.390374i	$-0.872346\pi$
$569$	−9.66757	−	29.7537i	−0.405286	−	1.24734i	0.515371	−	0.856967i	$-0.327654\pi$
$570$	−10.7410	−	17.6374i	−0.449889	−	0.738750i
$571$	11.9350	+	16.4271i	0.499462	+	0.687451i	0.982098	−	0.188370i	$-0.0603205\pi$
$571$	11.9350	+	16.4271i	0.499462	+	0.687451i	−0.482636	+	0.875821i	$0.660320\pi$
$572$	5.90899	−	3.01078i	0.247067	−	0.125887i
$573$	−5.34743	−	0.846949i	−0.223392	−	0.0353818i
$574$	−23.8663	−	32.8492i	−0.996161	−	1.37110i
$575$	−3.94071	−	1.30466i	−0.164339	−	0.0544080i
$576$	−0.376309	+	0.273405i	−0.0156795	+	0.0113919i
$577$	1.90013	+	11.9969i	0.0791034	+	0.499439i	0.995150	+	0.0983677i	$0.0313621\pi$
$577$	1.90013	+	11.9969i	0.0791034	+	0.499439i	−0.916047	+	0.401072i	$0.868638\pi$
$578$	−12.6406	−	6.44069i	−0.525778	−	0.267897i
$579$	−17.8475	−	12.9669i	−0.741716	−	0.538888i
$580$	10.3358	+	8.87734i	0.429169	+	0.368611i
$581$	8.99933	+	2.92406i	0.373355	+	0.121310i
$582$	−20.5138	−	10.4523i	−0.850325	−	0.433262i
$583$	−1.16297	+	1.16297i	−0.0481651	+	0.0481651i
$584$	2.17976			0.0901993
$585$	3.75840	+	4.42534i	0.155391	+	0.182965i
$586$	−10.3863	+	7.54611i	−0.429055	+	0.311727i
$587$	4.13577	−	0.655042i	0.170702	−	0.0270365i	−0.0704985	−	0.997512i	$-0.522459\pi$
$587$	4.13577	−	0.655042i	0.170702	−	0.0270365i	0.241200	+	0.970475i	$0.422459\pi$
$588$	−14.0946	−	14.0946i	−0.581251	−	0.581251i
$589$	27.2141	−	4.73412i	1.12134	−	0.195066i
$590$	19.2278	−	7.90192i	0.791596	−	0.325317i
$591$	27.2977	+	19.8329i	1.12288	+	0.815818i
$592$	0.568358	−	3.58847i	0.0233594	−	0.147485i
$593$	−36.4897	−	18.5924i	−1.49845	−	0.763499i	−0.503513	−	0.863988i	$-0.667959\pi$
$593$	−36.4897	−	18.5924i	−1.49845	−	0.763499i	−0.994938	+	0.100489i	$0.967959\pi$
$594$		−	5.60588i		−	0.230012i
$595$	48.4919	+	20.2440i	1.98797	+	0.829921i
$596$	4.81826	+	14.8291i	0.197363	+	0.607422i
$597$	39.3733	−	20.0617i	1.61144	−	0.821071i
$598$	−2.10396	−	4.12926i	−0.0860375	−	0.168858i
$599$	−18.0426	+	24.8335i	−0.737200	+	1.01467i	0.261575	+	0.965183i	$0.415758\pi$
$599$	−18.0426	+	24.8335i	−0.737200	+	1.01467i	−0.998775	+	0.0494856i	$0.984242\pi$
$600$	−4.27149	+	8.26940i	−0.174383	+	0.337597i
$601$	−24.7242	+	34.0300i	−1.00852	+	1.38811i	−0.0885761	+	0.996069i	$0.528232\pi$
$601$	−24.7242	+	34.0300i	−1.00852	+	1.38811i	−0.919947	+	0.392043i	$0.871768\pi$
$602$	0.258630	−	1.63292i	0.0105410	−	0.0665531i
$603$	−1.93747	−	3.80251i	−0.0789001	−	0.154850i
$604$	11.0049	−	7.99553i	0.447783	−	0.325334i
$605$	−20.8621	+	4.94731i	−0.848165	+	0.201137i
$606$	19.8839	+	6.46067i	0.807729	+	0.262447i
$607$	7.48093	+	1.18486i	0.303642	+	0.0480921i	0.306396	−	0.951904i	$-0.400877\pi$
$607$	7.48093	+	1.18486i	0.303642	+	0.0480921i	−0.00275448	+	0.999996i	$0.500877\pi$
$608$	4.90012	−	0.776103i	0.198726	−	0.0314751i
$609$	45.3938	−	14.7493i	1.83945	−	0.597673i
$610$	−5.61166	−	1.36374i	−0.227210	−	0.0552160i
$611$	7.03642	+	2.28627i	0.284663	+	0.0924927i
$612$	−1.17929	−	2.31448i	−0.0476698	−	0.0935573i
$613$	1.96481	−	3.85616i	0.0793580	−	0.155749i	−0.847918	−	0.530128i	$-0.822144\pi$
$613$	1.96481	−	3.85616i	0.0793580	−	0.155749i	0.927276	+	0.374379i	$0.122144\pi$
$614$			3.81588i			0.153997i
$615$	15.2667	+	37.1485i	0.615611	+	1.49797i
$616$	4.75468	−	1.54489i	0.191571	−	0.0622453i
$617$	−24.0710	−	3.81247i	−0.969061	−	0.153484i	−0.348213	−	0.937415i	$-0.613211\pi$
$617$	−24.0710	−	3.81247i	−0.969061	−	0.153484i	−0.620848	+	0.783931i	$0.713211\pi$
$618$	4.55581	+	28.7643i	0.183262	+	1.15707i
$619$	−17.2071			−0.691613			−0.345807	−	0.938306i	$-0.612395\pi$
$619$	−17.2071			−0.691613			−0.345807	+	0.938306i	$0.612395\pi$
$620$	−8.20212	−	9.36617i	−0.329405	−	0.376155i
$621$	−3.91745			−0.157202
$622$	−0.433682	−	2.73816i	−0.0173891	−	0.109790i
$623$	28.2384	+	4.47252i	1.13135	+	0.179188i
$624$	−9.88255	+	3.21104i	−0.395619	+	0.128544i
$625$	−0.277733	+	24.9985i	−0.0111093	+	0.999938i
$626$		−	25.8385i		−	1.03271i
$627$	4.98109	−	9.77594i	0.198926	−	0.390414i
$628$	1.71080	+	3.35764i	0.0682685	+	0.133984i
$629$	19.2966	+	6.26986i	0.769408	+	0.249996i
$630$	2.27650	+	3.73817i	0.0906978	+	0.148932i
$631$	−35.6697	+	11.5898i	−1.41999	+	0.461382i	−0.915599	−	0.402093i	$-0.868283\pi$
$631$	−35.6697	+	11.5898i	−1.41999	+	0.461382i	−0.504390	+	0.863476i	$0.668283\pi$
$632$	−6.12318	+	0.969817i	−0.243567	+	0.0385772i
$633$	−6.72678	−	1.06542i	−0.267366	−	0.0423465i
$634$	19.0935	+	6.20386i	0.758301	+	0.246387i
$635$	−14.3669	+	23.2991i	−0.570131	+	0.924596i
$636$	2.08483	−	1.51472i	0.0826688	−	0.0600624i
$637$	−27.1366	−	53.2587i	−1.07519	−	2.11018i
$638$	−1.13242	+	7.14982i	−0.0448330	+	0.283064i
$639$	−3.94577	+	5.43089i	−0.156092	+	0.214842i
$640$	−1.44748	−	1.70435i	−0.0572167	−	0.0673702i
$641$	−21.4388	+	29.5080i	−0.846782	+	1.16549i	0.137781	+	0.990463i	$0.456003\pi$
$641$	−21.4388	+	29.5080i	−0.846782	+	1.16549i	−0.984563	+	0.175032i	$0.943997\pi$
$642$	−2.46527	−	4.83837i	−0.0972966	−	0.190955i
$643$	36.4633	−	18.5790i	1.43797	−	0.732683i	0.450841	−	0.892604i	$-0.351124\pi$
$643$	36.4633	−	18.5790i	1.43797	−	0.732683i	0.987130	+	0.159922i	$0.0511241\pi$
$644$	−1.07958	−	3.32261i	−0.0425415	−	0.130929i
$645$	−0.630011	+	1.50911i	−0.0248066	+	0.0594212i
$646$			27.7059i			1.09007i
$647$	11.8188	+	6.02196i	0.464643	+	0.236748i	0.670608	−	0.741812i	$-0.266033\pi$
$647$	11.8188	+	6.02196i	0.464643	+	0.236748i	−0.205965	+	0.978559i	$0.566033\pi$
$648$	−1.59236	+	10.0538i	−0.0625537	+	0.394949i
$649$	8.93551	+	6.49203i	0.350750	+	0.254835i
$650$	−19.8452	+	19.6260i	−0.778394	+	0.769794i
$651$	−42.9687	+	7.47476i	−1.68408	+	0.292959i
$652$	14.5931	+	14.5931i	0.571510	+	0.571510i
$653$	36.5550	−	5.78975i	1.43051	−	0.226570i	0.607374	−	0.794416i	$-0.292223\pi$
$653$	36.5550	−	5.78975i	1.43051	−	0.226570i	0.823135	+	0.567846i	$0.192223\pi$
$654$	29.9814	−	21.7828i	1.17237	−	0.851773i
$655$	1.84633	−	22.6552i	0.0721421	−	0.885212i
$656$	−9.64900			−0.376730
$657$	−0.716938	+	0.716938i	−0.0279704	+	0.0279704i
$658$	4.96945	+	2.53206i	0.193729	+	0.0987101i
$659$	38.7022	+	12.5751i	1.50762	+	0.489856i	0.942230	−	0.334966i	$-0.108725\pi$
$659$	38.7022	+	12.5751i	1.50762	+	0.489856i	0.565392	+	0.824822i	$0.308725\pi$
$660$	−4.93092	+	0.374295i	−0.191936	+	0.0145694i
$661$	−12.2177	−	8.87670i	−0.475215	−	0.345264i	0.324256	−	0.945970i	$-0.394886\pi$
$661$	−12.2177	−	8.87670i	−0.475215	−	0.345264i	−0.799470	+	0.600706i	$0.794886\pi$
$662$	7.96796	+	4.05988i	0.309683	+	0.157792i
$663$	−9.07781	−	57.3150i	−0.352553	−	2.22593i
$664$	1.81919	−	1.32172i	0.0705981	−	0.0512925i
$665$	−3.53342	−	46.5488i	−0.137020	−	1.80509i
$666$	0.993335	+	1.36721i	0.0384909	+	0.0529782i
$667$	4.99637	+	0.791347i	0.193460	+	0.0306411i
$668$	−3.91580	+	1.99520i	−0.151507	+	0.0771966i
$669$	−14.2361	−	19.5944i	−0.550401	−	0.757562i
$670$	17.5223	−	10.6708i	0.676944	−	0.412250i
$671$	−0.948154	−	2.91812i	−0.0366031	−	0.112653i
$672$	−7.73686	+	1.22540i	−0.298456	+	0.0472708i
$673$	−29.0170	+	14.7849i	−1.11852	+	0.569916i	−0.912682	−	0.408670i	$-0.865993\pi$
$673$	−29.0170	+	14.7849i	−1.11852	+	0.569916i	−0.205841	+	0.978586i	$0.565993\pi$
$674$	−6.69761	+	20.6131i	−0.257982	+	0.793988i
$675$	7.16590	+	22.4785i	0.275816	+	0.865197i
$676$	−18.1605			−0.698481
$677$	0.595694	−	0.595694i	0.0228944	−	0.0228944i	−0.695567	−	0.718461i	$-0.744847\pi$
$677$	0.595694	−	0.595694i	0.0228944	−	0.0228944i	0.718461	+	0.695567i	$0.244847\pi$
$678$	3.16935	−	6.22020i	0.121718	−	0.238885i
$679$	−30.5920	−	42.1063i	−1.17401	−	1.61589i
$680$	10.6653	−	6.49503i	0.408996	−	0.249073i
$681$			10.6190i			0.406922i
$682$	1.94849	−	6.32122i	0.0746115	−	0.242052i
$683$	−4.84392	+	4.84392i	−0.185347	+	0.185347i	−0.793681	−	0.608334i	$-0.791838\pi$
$683$	−4.84392	+	4.84392i	−0.185347	+	0.185347i	0.608334	+	0.793681i	$0.291838\pi$
$684$	−1.35642	+	1.86695i	−0.0518638	+	0.0713844i
$685$	−11.0911	+	17.9867i	−0.423770	+	0.687238i
$686$	−4.82173	−	14.8398i	−0.184095	−	0.566585i
$687$	22.4277	+	22.4277i	0.855670	+	0.855670i
$688$	−0.277809	−	0.277809i	−0.0105914	−	0.0105914i
$689$	7.34954	−	2.38801i	0.279995	−	0.0909760i
$690$	0.261561	+	3.44578i	0.00995746	+	0.131179i
$691$	5.04970	−	15.5414i	0.192099	−	0.591221i	−0.807899	−	0.589321i	$-0.799395\pi$
$691$	5.04970	−	15.5414i	0.192099	−	0.591221i	0.999998	−	0.00190004i	$-0.000604801\pi$
$692$	−0.594702	−	3.75480i	−0.0226072	−	0.142736i
$693$	−1.05572	+	2.07197i	−0.0401035	+	0.0787075i
$694$	−27.9789	−	20.3278i	−1.06206	−	0.771634i
$695$	−43.8734	+	10.4043i	−1.66421	+	0.394657i
$696$	3.50500	−	10.7873i	0.132857	−	0.408891i
$697$	8.42947	−	53.2216i	0.319289	−	2.01591i
$698$	1.65973	−	10.4791i	0.0628218	−	0.396641i
$699$	5.58334	−	17.1837i	0.211181	−	0.649949i
$700$	−17.0905	+	12.2725i	−0.645960	+	0.463857i
$701$	35.9693	+	26.1332i	1.35854	+	0.987037i	0.998536	+	0.0540863i	$0.0172246\pi$
$701$	35.9693	+	26.1332i	1.35854	+	0.987037i	0.360004	+	0.932951i	$0.382775\pi$
$702$	−11.9581	+	23.4691i	−0.451330	+	0.885785i
$703$	−2.81974	−	17.8031i	−0.106349	−	0.671458i
$704$	0.367124	−	1.12989i	0.0138365	−	0.0425844i
$705$	−4.18506	−	3.59453i	−0.157618	−	0.135378i
$706$	16.9191	−	5.49734i	0.636758	−	0.206895i
$707$	33.4198	+	33.4198i	1.25688	+	1.25688i
$708$	−12.2371	−	12.2371i	−0.459897	−	0.459897i
$709$	−5.62806	−	17.3214i	−0.211366	−	0.650518i	−0.999392	−	0.0348757i	$-0.988896\pi$
$709$	−5.62806	−	17.3214i	−0.211366	−	0.650518i	0.788025	−	0.615643i	$-0.211104\pi$
$710$	−27.4685	−	16.9378i	−1.03088	−	0.635666i
$711$	1.69497	−	2.33293i	0.0635665	−	0.0874918i
$712$	4.80419	−	4.80419i	0.180045	−	0.180045i
$713$	−4.41733	−	1.36162i	−0.165430	−	0.0509932i
$714$		−	43.7452i		−	1.63712i
$715$	−14.4098	−	3.50184i	−0.538895	−	0.130961i
$716$	−9.82819	−	13.5273i	−0.367297	−	0.505541i
$717$	0.370512	−	0.727170i	0.0138370	−	0.0271567i
$718$	−16.1462	+	16.1462i	−0.602569	+	0.602569i
$719$	−6.14397			−0.229131			−0.114566	−	0.993416i	$-0.536548\pi$
$719$	−6.14397			−0.229131			−0.114566	+	0.993416i	$0.536548\pi$
$720$	1.03666	+	0.0844843i	0.0386339	+	0.00314854i
$721$	−20.3441	+	62.6128i	−0.757655	+	2.33182i
$722$	5.00169	−	2.54849i	0.186144	−	0.0948449i
$723$	8.71371	−	1.38012i	0.324066	−	0.0513271i
$724$	6.02410	+	18.5403i	0.223884	+	0.689044i
$725$	−4.59871	−	30.1169i	−0.170792	−	1.11851i
$726$	10.4914	+	14.4402i	0.389372	+	0.535925i
$727$	3.76889	−	1.92035i	0.139781	−	0.0712218i	−0.382701	−	0.923872i	$-0.625006\pi$
$727$	3.76889	−	1.92035i	0.139781	−	0.0712218i	0.522482	+	0.852650i	$0.325006\pi$
$728$	−23.2010	−	3.67468i	−0.859886	−	0.136193i
$729$	12.7057	+	17.4879i	0.470581	+	0.647699i
$730$	−3.69749	−	3.17576i	−0.136850	−	0.117540i
$731$	1.77503	−	1.28963i	0.0656518	−	0.0476988i
$732$	0.752072	+	4.74839i	0.0277974	+	0.175506i
$733$	−6.20941	−	3.16385i	−0.229350	−	0.116860i	0.335540	−	0.942026i	$-0.391081\pi$
$733$	−6.20941	−	3.16385i	−0.229350	−	0.116860i	−0.564890	+	0.825166i	$0.691081\pi$
$734$	2.64189	+	1.91945i	0.0975139	+	0.0708480i
$735$	3.37358	+	44.4432i	0.124436	+	1.63931i
$736$	−0.789579	−	0.256550i	−0.0291043	−	0.00945655i
$737$	9.71210	+	4.94856i	0.357750	+	0.182283i
$738$	3.17362	−	3.17362i	0.116822	−	0.116822i
$739$	−20.3094			−0.747093			−0.373547	−	0.927611i	$-0.621858\pi$
$739$	−20.3094			−0.747093			−0.373547	+	0.927611i	$0.621858\pi$
$740$	−6.19224	+	5.25900i	−0.227631	+	0.193325i
$741$	−41.7068	+	30.3018i	−1.53214	+	1.11316i
$742$	5.75382	−	0.911315i	0.211229	−	0.0334554i
$743$	−15.9341	−	15.9341i	−0.584565	−	0.584565i	0.351589	−	0.936154i	$-0.385641\pi$
$743$	−15.9341	−	15.9341i	−0.584565	−	0.584565i	−0.936154	+	0.351589i	$0.885641\pi$
$744$	−4.56482	+	9.30494i	−0.167355	+	0.341136i
$745$	13.4318	−	32.1741i	0.492101	−	1.17877i
$746$	−0.626583	−	0.455240i	−0.0229409	−	0.0166675i
$747$	−0.163621	+	1.03306i	−0.00598658	+	0.0377978i
$748$	5.91149	+	3.01205i	0.216145	+	0.110132i
$749$		−	12.2756i		−	0.448540i
$750$	19.2936	−	7.80396i	0.704501	−	0.284960i
$751$	−4.71976	−	14.5259i	−0.172227	−	0.530059i	0.827269	−	0.561805i	$-0.189893\pi$
$751$	−4.71976	−	14.5259i	−0.172227	−	0.530059i	−0.999496	+	0.0317466i	$0.989893\pi$
$752$	1.18093	−	0.601714i	0.0430641	−	0.0219422i
$753$	6.72439	+	13.1974i	0.245050	+	0.480938i
$754$	19.9924	−	27.5172i	0.728082	−	1.00212i
$755$	−30.3163	−	2.47069i	−1.10332	−	0.0899175i
$756$	−11.6712	+	16.0641i	−0.424479	+	0.584245i
$757$	3.04821	−	19.2456i	0.110789	−	0.699494i	−0.868297	−	0.496045i	$-0.834785\pi$
$757$	3.04821	−	19.2456i	0.110789	−	0.699494i	0.979086	−	0.203449i	$-0.0652150\pi$
$758$	−4.31435	−	8.46739i	−0.156704	−	0.307550i
$759$	−1.48538	+	1.07919i	−0.0539159	+	0.0391722i
$760$	−9.44270	−	5.82263i	−0.342523	−	0.211209i
$761$	−10.6809	−	3.47044i	−0.387183	−	0.125803i	0.108956	−	0.994047i	$-0.465249\pi$
$761$	−10.6809	−	3.47044i	−0.387183	−	0.125803i	−0.496139	+	0.868243i	$0.665249\pi$
$762$	22.5066	+	3.56470i	0.815328	+	0.129135i
$763$	82.7443	−	13.1054i	2.99554	−	0.474448i
$764$	−2.76612	+	0.898766i	−0.100075	+	0.0325162i
$765$	−1.37163	+	5.64414i	−0.0495914	+	0.204064i
$766$	−0.101064	−	0.0328377i	−0.00365160	−	0.00118648i
$767$	−23.5603	−	46.2397i	−0.850713	−	1.66962i
$768$	−0.845099	+	1.65860i	−0.0304949	+	0.0598496i
$769$			8.22562i			0.296623i	0.988941	+	0.148312i	$0.0473839\pi$
$769$			8.22562i			0.296623i	−0.988941	+	0.148312i	$0.952616\pi$
$770$	−10.3160	−	4.30665i	−0.371765	−	0.155201i
$771$	−29.5312	+	9.59526i	−1.06354	+	0.345565i
$772$	−11.7052	−	1.85392i	−0.421279	−	0.0667240i
$773$	−1.29546	−	8.17919i	−0.0465943	−	0.294185i	0.953377	−	0.301782i	$-0.0975816\pi$
$773$	−1.29546	−	8.17919i	−0.0465943	−	0.294185i	−0.999971	+	0.00759743i	$0.997582\pi$
$774$	0.182746			0.00656869
$775$	0.267257	+	27.8375i	0.00960016	+	0.999954i
$776$	−12.3682			−0.443991
$777$	4.45212	+	28.1096i	0.159719	+	1.00843i
$778$	28.8359	+	4.56716i	1.03382	+	0.163741i
$779$	−45.5277	+	14.7928i	−1.63120	+	0.530009i
$780$	21.4418	+	8.95134i	0.767740	+	0.320509i
$781$		−	17.1457i		−	0.613523i
$782$	2.10485	−	4.13101i	0.0752694	−	0.147724i
$783$	−13.0529	−	25.6177i	−0.466471	−	0.915502i
$784$	−10.1839	−	3.30894i	−0.363710	−	0.118177i
$785$	1.98984	−	8.18801i	0.0710203	−	0.292243i
$786$	−17.9965	+	5.84741i	−0.641913	+	0.208570i
$787$	14.9034	−	2.36046i	0.531248	−	0.0841414i	0.114953	−	0.993371i	$-0.463328\pi$
$787$	14.9034	−	2.36046i	0.531248	−	0.0841414i	0.416295	+	0.909230i	$0.363328\pi$
$788$	17.9031	+	2.83557i	0.637771	+	0.101013i
$789$	−17.9076	−	5.81852i	−0.637526	−	0.207145i
$790$	11.7996	+	7.27595i	0.419810	+	0.258867i
$791$	12.7675	−	9.27611i	0.453959	−	0.329821i
$792$	0.250879	+	0.492377i	0.00891459	+	0.0174959i
$793$	−2.25528	+	14.2393i	−0.0800874	+	0.505652i
$794$	−20.3291	+	27.9806i	−0.721452	+	0.992994i
$795$	−5.74328	−	0.468060i	−0.203693	−	0.0166004i
$796$	13.9534	−	19.2052i	0.494564	−	0.680709i
$797$	−21.8448	−	42.8729i	−0.773783	−	1.51864i	−0.853078	−	0.521784i	$-0.825267\pi$
$797$	−21.8448	−	42.8729i	−0.773783	−	1.51864i	0.0792944	−	0.996851i	$-0.474733\pi$
$798$	−34.6268	+	17.6433i	−1.22578	+	0.624564i
$799$	2.28724	+	7.03939i	0.0809167	+	0.249036i
$800$	−0.0277737	+	4.99992i	−0.000981948	+	0.176774i
$801$			3.16026i			0.111662i
$802$	34.6268	+	17.6432i	1.22271	+	0.623004i
$803$	0.405109	−	2.55776i	0.0142960	−	0.0902614i
$804$	−13.8172	−	10.0388i	−0.487296	−	0.354041i
$805$	−3.00953	+	7.20896i	−0.106072	+	0.254082i
$806$	−21.6414	+	22.3075i	−0.762286	+	0.785748i
$807$	11.0276	+	11.0276i	0.388190	+	0.388190i
$808$	11.0931	−	1.75698i	0.390256	−	0.0618104i
$809$	−23.9080	+	17.3702i	−0.840561	+	0.610704i	−0.922527	−	0.385931i	$-0.873880\pi$
$809$	−23.9080	+	17.3702i	−0.840561	+	0.610704i	0.0819660	+	0.996635i	$0.473880\pi$
$810$	17.3487	−	14.7340i	0.609570	−	0.517701i
$811$	11.5895			0.406962			0.203481	−	0.979079i	$-0.434774\pi$
$811$	11.5895			0.406962			0.203481	+	0.979079i	$0.434774\pi$
$812$	18.1307	−	18.1307i	0.636263	−	0.636263i
$813$	−27.9927	−	14.2630i	−0.981745	−	0.500224i
$814$	−4.10512	−	1.33384i	−0.143885	−	0.0467509i
$815$	−3.49290	−	46.0151i	−0.122351	−	1.61184i
$816$	−8.41015	−	6.11033i	−0.294414	−	0.213904i
$817$	−1.73672	−	0.884903i	−0.0607601	−	0.0309588i
$818$	2.71215	+	17.1238i	0.0948281	+	0.598721i
$819$	8.83957	−	6.42233i	0.308880	−	0.224414i
$820$	16.3674	+	14.0579i	0.571575	+	0.490923i
$821$	−20.5702	−	28.3124i	−0.717903	−	0.988109i	−0.999591	−	0.0286030i	$-0.990894\pi$
$821$	−20.5702	−	28.3124i	−0.717903	−	0.988109i	0.281687	−	0.959506i	$-0.409106\pi$
$822$	17.3750	+	2.75192i	0.606021	+	0.0959843i
$823$	21.6346	−	11.0234i	0.754134	−	0.384250i	−0.0342666	−	0.999413i	$-0.510910\pi$
$823$	21.6346	−	11.0234i	0.754134	−	0.384250i	0.788400	+	0.615162i	$0.210910\pi$
$824$	9.19584	+	12.6570i	0.320352	+	0.440927i
$825$	8.90954	+	6.54908i	0.310191	+	0.228010i
$826$	−12.0892	−	37.2068i	−0.420638	−	1.29459i
$827$	−17.9953	+	2.85018i	−0.625759	+	0.0991105i	−0.461258	−	0.887266i	$-0.652602\pi$
$827$	−17.9953	+	2.85018i	−0.625759	+	0.0991105i	−0.164502	+	0.986377i	$0.552602\pi$
$828$	0.344078	−	0.175317i	0.0119575	−	0.00609267i
$829$	−12.3268	+	37.9381i	−0.428128	+	1.31764i	0.471838	+	0.881685i	$0.343591\pi$
$829$	−12.3268	+	37.9381i	−0.428128	+	1.31764i	−0.899967	+	0.435959i	$0.856409\pi$
$830$	−5.01149	−	0.408421i	−0.173951	−	0.0141765i
$831$	38.8064			1.34618
$832$	−3.94718	+	3.94718i	−0.136844	+	0.136844i
$833$	27.1481	−	53.2812i	0.940626	−	1.84608i
$834$	22.0636	+	30.3679i	0.764000	+	1.05156i
$835$	9.54915	+	2.32062i	0.330462	+	0.0803082i
$836$		−	5.89409i		−	0.203852i
$837$	8.49625	+	24.8604i	0.293673	+	0.859299i
$838$	10.7524	−	10.7524i	0.371435	−	0.371435i
$839$	24.2440	−	33.3691i	0.836997	−	1.15203i	−0.149582	−	0.988749i	$-0.547793\pi$
$839$	24.2440	−	33.3691i	0.836997	−	1.15203i	0.986580	−	0.163279i	$-0.0522071\pi$
$840$	14.9092	+	9.19342i	0.514416	+	0.317203i
$841$	2.51139	+	7.72926i	0.0865996	+	0.266526i
$842$	21.6327	+	21.6327i	0.745511	+	0.745511i
$843$	−0.157211	−	0.157211i	−0.00541463	−	0.00541463i
$844$	−3.47963	+	1.13060i	−0.119774	+	0.0389169i
$845$	30.8053	+	26.4585i	1.05973	+	0.910201i
$846$	−0.190508	+	0.586323i	−0.00654979	+	0.0201582i
$847$	6.31205	+	39.8527i	0.216885	+	1.36936i
$848$	0.628490	−	1.23348i	0.0215824	−	0.0423579i
$849$	−12.9120	−	9.38108i	−0.443137	−	0.321958i
$850$	−27.5541	−	4.52118i	−0.945099	−	0.155075i
$851$	−0.932098	+	2.86870i	−0.0319519	+	0.0983378i
$852$	−4.20261	+	26.5342i	−0.143979	+	0.909048i
$853$	0.00927381	−	0.0585525i	0.000317529	−	0.00200480i	−0.987529	−	0.157437i	$-0.949677\pi$
$853$	0.00927381	−	0.0585525i	0.000317529	−	0.00200480i	0.987847	+	0.155432i	$0.0496769\pi$
$854$	−3.35840	+	10.3361i	−0.114922	+	0.353694i
$855$	5.02086	−	1.19066i	0.171710	−	0.0407198i
$856$	−2.36002	−	1.71465i	−0.0806637	−	0.0586056i
$857$	25.2475	−	49.5511i	0.862440	−	1.69263i	0.152579	−	0.988291i	$-0.451242\pi$
$857$	25.2475	−	49.5511i	0.862440	−	1.69263i	0.709861	−	0.704342i	$-0.248758\pi$
$858$	1.93119	+	12.1931i	0.0659298	+	0.416264i
$859$	0.0964604	−	0.296875i	0.00329119	−	0.0101292i	−0.949397	−	0.314077i	$-0.898305\pi$
$859$	0.0964604	−	0.296875i	0.00329119	−	0.0101292i	0.952689	+	0.303948i	$0.0983049\pi$
$860$	0.0664944	+	0.875990i	0.00226744	+	0.0298710i
$861$	71.8843	−	23.3566i	2.44981	−	0.795991i
$862$	9.98304	+	9.98304i	0.340024	+	0.340024i
$863$	19.5049	+	19.5049i	0.663955	+	0.663955i	0.956310	−	0.292355i	$-0.0944389\pi$
$863$	19.5049	+	19.5049i	0.663955	+	0.663955i	−0.292355	+	0.956310i	$0.594439\pi$
$864$	1.45813	+	4.48766i	0.0496066	+	0.152673i
$865$	−4.46169	+	7.23563i	−0.151702	+	0.246019i
$866$	−13.9932	+	19.2601i	−0.475510	+	0.654483i
$867$	18.6737	−	18.6737i	0.634193	−	0.634193i
$868$	−18.7441	+	14.0573i	−0.636216	+	0.477134i
$869$			7.36525i			0.249849i
$870$	−21.6617	+	13.1917i	−0.734402	+	0.447241i
$871$	−30.1039	−	41.4345i	−1.02003	−	1.40395i
$872$	9.03817	−	17.7384i	0.306071	−	0.600698i
$873$	4.06797	−	4.06797i	0.137680	−	0.137680i
$874$	−4.11885			−0.139322
$875$	46.8704	+	4.08200i	1.58451	+	0.137997i
$876$	−1.25387	+	3.85902i	−0.0423643	+	0.130384i
$877$	10.9406	−	5.57451i	0.369437	−	0.188238i	−0.259409	−	0.965768i	$-0.583528\pi$
$877$	10.9406	−	5.57451i	0.369437	−	0.188238i	0.628846	+	0.777530i	$0.283528\pi$
$878$	19.8954	−	3.15113i	0.671438	−	0.106345i
$879$	−7.38495	−	22.7285i	−0.249088	−	0.766615i
$880$	−2.26891	+	1.38174i	−0.0764850	+	0.0465784i
$881$	−22.8859	−	31.4998i	−0.771046	−	1.06125i	−0.996214	−	0.0869337i	$-0.972293\pi$
$881$	−22.8859	−	31.4998i	−0.771046	−	1.06125i	0.225168	−	0.974320i	$-0.427707\pi$
$882$	4.43788	−	2.26121i	0.149431	−	0.0761389i
$883$	35.0301	+	5.54823i	1.17886	+	0.186713i	0.714953	−	0.699172i	$-0.246448\pi$
$883$	35.0301	+	5.54823i	1.17886	+	0.186713i	0.463905	+	0.885885i	$0.346448\pi$
$884$	−18.3234	−	25.2200i	−0.616283	−	0.848241i
$885$	2.92898	+	38.5860i	0.0984564	+	1.29705i
$886$	−16.8404	+	12.2352i	−0.565763	+	0.411051i
$887$	1.64110	+	10.3615i	0.0551026	+	0.347904i	0.999801	+	0.0199629i	$0.00635480\pi$
$887$	1.64110	+	10.3615i	0.0551026	+	0.347904i	−0.944698	+	0.327941i	$0.893645\pi$
$888$	6.02603	+	3.07042i	0.202220	+	0.103036i
$889$	41.6746	+	30.2784i	1.39772	+	1.01550i
$890$	−15.1486	+	1.14990i	−0.507783	+	0.0385446i
$891$	11.5012	+	3.73698i	0.385306	+	0.125194i
$892$	−11.5930	−	5.90690i	−0.388161	−	0.197778i
$893$	4.64960	−	4.64960i	0.155593	−	0.155593i
$894$	−29.0247			−0.970732
$895$	−3.03699	+	37.2651i	−0.101515	+	1.24564i
$896$	−3.40441	+	2.47345i	−0.113733	+	0.0826322i
$897$	8.52064	−	1.34954i	0.284496	−	0.0450597i
$898$	6.40063	+	6.40063i	0.213592	+	0.213592i
$899$	−5.81430	−	33.4235i	−0.193918	−	1.11474i
$900$	−1.63537	−	1.65364i	−0.0545124	−	0.0551214i
$901$	6.25454	+	4.54419i	0.208369	+	0.151389i
$902$	−1.79327	+	11.3222i	−0.0597093	+	0.376990i
$903$	2.74213	+	1.39718i	0.0912523	+	0.0464954i
$904$		−	3.75027i		−	0.124732i
$905$	16.7933	−	40.2262i	0.558227	−	1.33716i
$906$	7.82477	+	24.0822i	0.259961	+	0.800077i
$907$	16.6853	−	8.50158i	0.554026	−	0.282290i	−0.154479	−	0.987996i	$-0.549370\pi$
$907$	16.6853	−	8.50158i	0.554026	−	0.282290i	0.708505	+	0.705706i	$0.249370\pi$
$908$	2.58982	+	5.08282i	0.0859464	+	0.168679i
$909$	−3.07072	+	4.22649i	−0.101849	+	0.140184i
$910$	34.0016	+	40.0354i	1.12714	+	1.32716i
$911$	−12.1902	+	16.7784i	−0.403880	+	0.555893i	−0.961712	−	0.274061i	$-0.911633\pi$
$911$	−12.1902	+	16.7784i	−0.403880	+	0.555893i	0.557833	+	0.829953i	$0.311633\pi$
$912$	−1.44471	+	9.12152i	−0.0478390	+	0.302044i
$913$	−1.21282	−	2.38029i	−0.0401385	−	0.0787762i
$914$	0.319004	−	0.231770i	0.0105517	−	0.00766626i
$915$	5.64234	−	9.15032i	0.186530	−	0.302500i
$916$	16.2049	+	5.26528i	0.535424	+	0.173970i
$917$	−42.2498	−	6.69171i	−1.39521	−	0.220980i
$918$	−26.0267	+	4.12223i	−0.859010	+	0.136054i
$919$	21.7367	−	7.06268i	0.717028	−	0.232976i	0.0722937	−	0.997383i	$-0.476968\pi$
$919$	21.7367	−	7.06268i	0.717028	−	0.232976i	0.644734	+	0.764407i	$0.276968\pi$
$920$	0.965572	+	1.58554i	0.0318340	+	0.0522737i
$921$	−6.75557	−	2.19502i	−0.222604	−	0.0723283i
$922$	5.75073	+	11.2864i	0.189390	+	0.371699i
$923$	−36.5742	+	71.7809i	−1.20385	+	2.36270i
$924$			9.30626i			0.306153i
$925$	18.1657	+	0.100907i	0.597286	+	0.00331782i
$926$	−26.8949	+	8.73869i	−0.883822	+	0.287171i
$927$	−7.18753	−	1.13839i	−0.236069	−	0.0373897i
$928$	−0.953186	−	6.01818i	−0.0312899	−	0.197556i
$929$	6.38567			0.209507			0.104754	−	0.994498i	$-0.466595\pi$
$929$	6.38567			0.209507			0.104754	+	0.994498i	$0.466595\pi$
$930$	21.2998	−	9.13316i	0.698449	−	0.299488i
$931$	−53.1244			−1.74108
$932$	−1.51839	−	9.58674i	−0.0497365	−	0.314024i
$933$	5.09706	+	0.807295i	0.166870	+	0.0264297i
$934$	−4.82787	+	1.56867i	−0.157973	+	0.0513284i
$935$	−5.63919	−	13.7219i	−0.184421	−	0.448754i
$936$		−	2.59651i		−	0.0848694i
$937$	−20.3719	+	39.9822i	−0.665522	+	1.30616i	0.273357	+	0.961913i	$0.411866\pi$
$937$	−20.3719	+	39.9822i	−0.665522	+	1.30616i	−0.938879	+	0.344248i	$0.888134\pi$
$938$	−17.5280	−	34.4007i	−0.572311	−	1.12322i
$939$	45.7440	+	14.8631i	1.49280	+	0.485040i
$940$	−2.87984	−	0.699854i	−0.0939300	−	0.0228267i
$941$	51.9215	−	16.8703i	1.69259	−	0.549956i	0.705304	−	0.708905i	$-0.250810\pi$
$941$	51.9215	−	16.8703i	1.69259	−	0.549956i	0.987287	+	0.158948i	$0.0508103\pi$
$942$	−6.92842	+	1.09735i	−0.225740	+	0.0357537i
$943$	7.91210	+	1.25315i	0.257653	+	0.0408083i
$944$	−8.84175	−	2.87286i	−0.287774	−	0.0935035i
$945$	43.2019	−	10.2450i	1.40536	−	0.333271i
$946$	−0.377615	+	0.274354i	−0.0122773	+	0.00892001i
$947$	21.6535	+	42.4973i	0.703643	+	1.38098i	0.914954	+	0.403558i	$0.132227\pi$
$947$	21.6535	+	42.4973i	0.703643	+	1.38098i	−0.211311	+	0.977419i	$0.567773\pi$
$948$	1.80530	−	11.3982i	0.0586336	−	0.370198i
$949$	−7.15205	+	9.84395i	−0.232165	+	0.319548i
$950$	7.53431	+	23.6341i	0.244445	+	0.766793i
$951$	−21.9664	+	30.2342i	−0.712310	+	0.980410i
$952$	−10.6688	−	20.9388i	−0.345779	−	0.678629i
$953$	22.2250	−	11.3242i	0.719940	−	0.366828i	−0.0553212	−	0.998469i	$-0.517618\pi$
$953$	22.2250	−	11.3242i	0.719940	−	0.366828i	0.775261	+	0.631641i	$0.217618\pi$
$954$	0.198985	+	0.612414i	0.00644239	+	0.0198276i
$955$	6.00155	+	2.50547i	0.194205	+	0.0810752i
$956$		−	0.438424i		−	0.0141797i
$957$	−12.0065	−	6.11762i	−0.388115	−	0.197755i
$958$	5.90072	−	37.2557i	0.190643	−	1.20368i
$959$	32.1725	+	23.3747i	1.03891	+	0.754809i
$960$	3.84998	−	1.58220i	0.124258	−	0.0510653i
$961$	0.939471	+	30.9858i	0.0303055	+	0.999541i
$962$	14.3409	+	14.3409i	0.462370	+	0.462370i
$963$	1.34018	−	0.212264i	0.0431868	−	0.00684012i
$964$	3.83425	−	2.78575i	0.123493	−	0.0897228i
$965$	17.1542	+	20.1984i	0.552215	+	0.650208i
$966$	6.50331			0.209240
$967$	−12.0665	+	12.0665i	−0.388034	+	0.388034i	−0.873986	−	0.485952i	$-0.838473\pi$
$967$	−12.0665	+	12.0665i	−0.388034	+	0.388034i	0.485952	+	0.873986i	$0.338473\pi$
$968$	8.54348	+	4.35312i	0.274598	+	0.139915i
$969$	−49.0501	−	15.9373i	−1.57571	−	0.511981i
$970$	20.9799	+	18.0195i	0.673623	+	0.578571i
$971$	28.0038	+	20.3459i	0.898684	+	0.652932i	0.938128	−	0.346290i	$-0.112559\pi$
$971$	28.0038	+	20.3459i	0.898684	+	0.652932i	−0.0394439	+	0.999222i	$0.512559\pi$
$972$	−4.27007	−	2.17571i	−0.136963	−	0.0697859i
$973$	13.2744	+	83.8110i	0.425557	+	2.68686i
$974$	26.7083	−	19.4047i	0.855790	−	0.621768i
$975$	−23.3299	−	46.4231i	−0.747154	−	1.48673i
$976$	1.51805	+	2.08941i	0.0485915	+	0.0668804i
$977$	−13.4557	−	2.13117i	−0.430485	−	0.0681822i	−0.0625680	−	0.998041i	$-0.519929\pi$
$977$	−13.4557	−	2.13117i	−0.430485	−	0.0681822i	−0.367917	+	0.929859i	$0.619929\pi$
$978$	−34.2298	+	17.4410i	−1.09455	+	0.557700i
$979$	−4.74443	−	6.53015i	−0.151633	−	0.208705i
$980$	12.4538	+	20.4501i	0.397823	+	0.653253i
$981$	2.86156	+	8.80698i	0.0913626	+	0.281185i
$982$	25.5174	−	4.04156i	0.814293	−	0.128971i
$983$	4.45273	−	2.26878i	0.142020	−	0.0723628i	−0.381536	−	0.924354i	$-0.624605\pi$
$983$	4.45273	−	2.26878i	0.142020	−	0.0723628i	0.523556	+	0.851991i	$0.324605\pi$
$984$	5.55041	−	17.0824i	0.176941	−	0.544568i
$985$	−26.2374	−	30.8934i	−0.835994	−	0.984346i
$986$	34.0276			1.08366
$987$	−7.34131	+	7.34131i	−0.233676	+	0.233676i
$988$	−12.5729	+	24.6757i	−0.399998	+	0.785039i
$989$	0.191721	+	0.263881i	0.00609638	+	0.00839094i
$990$	0.291797	−	1.20072i	0.00927393	−	0.0381614i
$991$			5.52082i			0.175375i	0.996148	+	0.0876873i	$0.0279476\pi$
$991$			5.52082i			0.175375i	−0.996148	+	0.0876873i	$0.972052\pi$
$992$	0.0843767	+	5.56712i	0.00267896	+	0.176756i
$993$	−11.7710	+	11.7710i	−0.373540	+	0.373540i
$994$	−35.6968	+	49.1324i	−1.13223	+	1.55838i
$995$	−51.6494	+	12.2483i	−1.63739	+	0.388297i
$996$	1.29349	+	3.98095i	0.0409857	+	0.126141i
$997$	−29.9849	−	29.9849i	−0.949633	−	0.949633i	0.0491581	−	0.998791i	$-0.484346\pi$
$997$	−29.9849	−	29.9849i	−0.949633	−	0.949633i	−0.998791	+	0.0491581i	$0.984346\pi$
$998$	0.395022	+	0.395022i	0.0125042	+	0.0125042i
$999$	16.3046	−	5.29769i	0.515855	−	0.167611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.s.a.277.11	yes	128
5.3	odd	4	inner	310.2.s.a.153.14	yes	128
31.15	odd	10	inner	310.2.s.a.77.14	✓	128
155.108	even	20	inner	310.2.s.a.263.11	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.s.a.77.14	✓	128	31.15	odd	10	inner
310.2.s.a.153.14	yes	128	5.3	odd	4	inner
310.2.s.a.263.11	yes	128	155.108	even	20	inner
310.2.s.a.277.11	yes	128	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.s (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 + 0.987688i) q^{2} +(-1.83857 - 0.291201i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(2.06347 + 0.861441i) q^{5} -1.86149i q^{6} +(1.91043 - 3.74943i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(0.442378 + 0.143737i) q^{9} +O(q^{10})\)	\(q+(0.156434 + 0.987688i) q^{2} +(-1.83857 - 0.291201i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(2.06347 + 0.861441i) q^{5} -1.86149i q^{6} +(1.91043 - 3.74943i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(0.442378 + 0.143737i) q^{9} +(-0.528037 + 2.17283i) q^{10} +(-1.12989 + 0.367124i) q^{11} +(1.83857 - 0.291201i) q^{12} +(5.51343 + 0.873242i) q^{13} +(4.00213 + 1.30037i) q^{14} +(-3.54299 - 2.18471i) q^{15} +(0.809017 - 0.587785i) q^{16} +(2.53532 + 4.97584i) q^{17} +(-0.0727645 + 0.459417i) q^{18} +(2.91612 - 4.01370i) q^{19} +(-2.22868 - 0.181630i) q^{20} +(-4.60430 + 6.33728i) q^{21} +(-0.539358 - 1.05855i) q^{22} +(-0.739725 + 0.376909i) q^{23} +(0.575232 + 1.77038i) q^{24} +(3.51584 + 3.55512i) q^{25} +5.58216i q^{26} +(4.20431 + 2.14220i) q^{27} +(-0.658289 + 4.15628i) q^{28} +(-4.92950 - 3.58149i) q^{29} +(1.60356 - 3.84113i) q^{30} +(3.99622 + 3.87689i) q^{31} +(0.707107 + 0.707107i) q^{32} +(2.18429 - 0.345958i) q^{33} +(-4.51797 + 3.28250i) q^{34} +(7.17203 - 6.09113i) q^{35} -0.465144 q^{36} +(2.56906 - 2.56906i) q^{37} +(4.42046 + 2.25234i) q^{38} +(-9.88255 - 3.21104i) q^{39} +(-0.169248 - 2.22965i) q^{40} +(-7.80621 - 5.67154i) q^{41} +(-6.97953 - 3.55625i) q^{42} +(-0.0614603 - 0.388045i) q^{43} +(0.961143 - 0.698311i) q^{44} +(0.789014 + 0.677680i) q^{45} +(-0.487987 - 0.671656i) q^{46} +(1.30907 + 0.207336i) q^{47} +(-1.65860 + 0.845099i) q^{48} +(-6.29399 - 8.66293i) q^{49} +(-2.96135 + 4.02870i) q^{50} +(-3.21239 - 9.88673i) q^{51} +(-5.51343 + 0.873242i) q^{52} +(1.23348 - 0.628490i) q^{53} +(-1.45813 + 4.48766i) q^{54} +(-2.64775 - 0.215784i) q^{55} -4.20808 q^{56} +(-6.53029 + 6.53029i) q^{57} +(2.76625 - 5.42908i) q^{58} +(-5.46450 - 7.52124i) q^{59} +(4.04470 + 0.982934i) q^{60} +2.58265i q^{61} +(-3.20401 + 4.55349i) q^{62} +(1.38406 - 1.38406i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(10.6246 + 6.55141i) q^{65} +(0.683397 + 2.10328i) q^{66} +(-6.48765 - 6.48765i) q^{67} +(-3.94885 - 3.94885i) q^{68} +(1.46979 - 0.477565i) q^{69} +(7.13809 + 6.13087i) q^{70} +(-4.45973 + 13.7256i) q^{71} +(-0.0727645 - 0.459417i) q^{72} +(-0.989592 + 1.94218i) q^{73} +(2.93932 + 2.13554i) q^{74} +(-5.42887 - 7.56016i) q^{75} +(-1.53310 + 4.71838i) q^{76} +(-0.782073 + 4.93781i) q^{77} +(1.62553 - 10.2632i) q^{78} +(1.91575 - 5.89608i) q^{79} +(2.17573 - 0.515959i) q^{80} +(-8.23504 - 5.98311i) q^{81} +(4.38056 - 8.59732i) q^{82} +(0.351764 + 2.22095i) q^{83} +(2.42062 - 7.44992i) q^{84} +(0.945168 + 12.4515i) q^{85} +(0.373653 - 0.121407i) q^{86} +(8.02030 + 8.02030i) q^{87} +(0.840069 + 0.840069i) q^{88} +(2.09951 + 6.46163i) q^{89} +(-0.545908 + 0.885312i) q^{90} +(13.8072 - 19.0040i) q^{91} +(0.587049 - 0.587049i) q^{92} +(-6.21837 - 8.29164i) q^{93} +1.32539i q^{94} +(9.47490 - 5.77009i) q^{95} +(-1.09416 - 1.50598i) q^{96} +(5.61503 - 11.0201i) q^{97} +(7.57168 - 7.57168i) q^{98} -0.552608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 12 q^{7}+O(q^{10}) \) 128 * q + 12 * q^7	\( 128 q + 12 q^{7} + 8 q^{10} + 32 q^{16} + 8 q^{20} - 80 q^{21} - 20 q^{22} - 20 q^{23} + 40 q^{25} + 8 q^{28} - 32 q^{31} + 20 q^{33} - 48 q^{35} - 128 q^{36} + 52 q^{38} + 8 q^{41} - 20 q^{42} + 64 q^{45} - 40 q^{46} - 20 q^{47} - 20 q^{48} + 24 q^{50} - 16 q^{51} - 40 q^{53} - 40 q^{55} + 20 q^{60} - 8 q^{62} + 256 q^{63} - 160 q^{65} + 56 q^{66} + 8 q^{67} - 32 q^{70} + 56 q^{71} - 80 q^{73} - 160 q^{75} + 48 q^{76} - 20 q^{77} + 4 q^{78} - 96 q^{81} + 16 q^{82} - 240 q^{83} + 120 q^{85} + 40 q^{87} - 64 q^{90} + 80 q^{91} - 160 q^{93} + 32 q^{95} - 56 q^{97} - 176 q^{98}+O(q^{100}) \) 128 * q + 12 * q^7 + 8 * q^10 + 32 * q^16 + 8 * q^20 - 80 * q^21 - 20 * q^22 - 20 * q^23 + 40 * q^25 + 8 * q^28 - 32 * q^31 + 20 * q^33 - 48 * q^35 - 128 * q^36 + 52 * q^38 + 8 * q^41 - 20 * q^42 + 64 * q^45 - 40 * q^46 - 20 * q^47 - 20 * q^48 + 24 * q^50 - 16 * q^51 - 40 * q^53 - 40 * q^55 + 20 * q^60 - 8 * q^62 + 256 * q^63 - 160 * q^65 + 56 * q^66 + 8 * q^67 - 32 * q^70 + 56 * q^71 - 80 * q^73 - 160 * q^75 + 48 * q^76 - 20 * q^77 + 4 * q^78 - 96 * q^81 + 16 * q^82 - 240 * q^83 + 120 * q^85 + 40 * q^87 - 64 * q^90 + 80 * q^91 - 160 * q^93 + 32 * q^95 - 56 * q^97 - 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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