LMFDB - Embedded newform 310.2.s.a.153.14

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			153.14
Character	$\chi$	$=$	310.153
Dual form			310.2.s.a.77.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987688 - 0.156434i) q^{2} +(0.291201 - 1.83857i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.06347 - 0.861441i) q^{5} -1.86149i q^{6} +(-3.74943 - 1.91043i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-0.442378 - 0.143737i) q^{9} +O(q^{10})$	\(q+(0.987688 - 0.156434i) q^{2} +(0.291201 - 1.83857i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.06347 - 0.861441i) q^{5} -1.86149i q^{6} +(-3.74943 - 1.91043i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-0.442378 - 0.143737i) q^{9} +(1.90331 - 1.17363i) q^{10} +(-1.12989 + 0.367124i) q^{11} +(-0.291201 - 1.83857i) q^{12} +(-0.873242 + 5.51343i) q^{13} +(-4.00213 - 1.30037i) q^{14} +(-0.982934 - 4.04470i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.97584 - 2.53532i) q^{17} +(-0.459417 - 0.0727645i) q^{18} +(-2.91612 + 4.01370i) q^{19} +(1.69628 - 1.45693i) q^{20} +(-4.60430 + 6.33728i) q^{21} +(-1.05855 + 0.539358i) q^{22} +(-0.376909 - 0.739725i) q^{23} +(-0.575232 - 1.77038i) q^{24} +(3.51584 - 3.55512i) q^{25} +5.58216i q^{26} +(2.14220 - 4.20431i) q^{27} +(-4.15628 - 0.658289i) 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} +(0.345958 + 2.18429i) q^{33} +(4.51797 - 3.28250i) q^{34} +(-9.38257 - 0.712209i) q^{35} -0.465144 q^{36} +(-2.56906 - 2.56906i) q^{37} +(-2.25234 + 4.42046i) q^{38} +(9.88255 + 3.21104i) q^{39} +(1.44748 - 1.70435i) q^{40} +(-7.80621 - 5.67154i) q^{41} +(-3.55625 + 6.97953i) q^{42} +(0.388045 - 0.0614603i) q^{43} +(-0.961143 + 0.698311i) q^{44} +(-1.03666 + 0.0844843i) q^{45} +(-0.487987 - 0.671656i) q^{46} +(0.207336 - 1.30907i) q^{47} +(-0.845099 - 1.65860i) q^{48} +(6.29399 + 8.66293i) q^{49} +(2.91641 - 4.06135i) q^{50} +(-3.21239 - 9.88673i) q^{51} +(0.873242 + 5.51343i) q^{52} +(0.628490 + 1.23348i) q^{53} +(1.45813 - 4.48766i) q^{54} +(-2.01524 + 1.73088i) q^{55} -4.20808 q^{56} +(6.53029 + 6.53029i) q^{57} +(5.42908 + 2.76625i) q^{58} +(5.46450 + 7.52124i) q^{59} +(-2.18471 - 3.54299i) q^{60} +2.58265i q^{61} +(4.55349 + 3.20401i) q^{62} +(1.38406 + 1.38406i) q^{63} +(0.587785 - 0.809017i) q^{64} +(2.94758 + 12.1291i) 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} +(-9.37847 + 0.764316i) q^{70} +(-4.45973 + 13.7256i) q^{71} +(-0.459417 + 0.0727645i) q^{72} +(-1.94218 - 0.989592i) q^{73} +(-2.93932 - 2.13554i) q^{74} +(-5.51252 - 7.49938i) q^{75} +(-1.53310 + 4.71838i) q^{76} +(4.93781 + 0.782073i) q^{77} +(10.2632 + 1.62553i) q^{78} +(-1.91575 + 5.89608i) q^{79} +(1.16304 - 1.90980i) q^{80} +(-8.23504 - 5.98311i) q^{81} +(-8.59732 - 4.38056i) q^{82} +(-2.22095 + 0.351764i) q^{83} +(-2.42062 + 7.44992i) q^{84} +(8.08349 - 9.51795i) 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} +(-1.01068 + 0.245613i) q^{90} +(13.8072 - 19.0040i) q^{91} +(-0.587049 - 0.587049i) q^{92} +(8.29164 - 6.21837i) q^{93} -1.32539i q^{94} +(-2.55978 + 10.7942i) q^{95} +(-1.09416 - 1.50598i) q^{96} +(-11.0201 - 5.61503i) 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 $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$3$	0.291201	−	1.83857i	0.168125	−	1.06150i	−0.748904	−	0.662679i	$-0.769419\pi$
$3$	0.291201	−	1.83857i	0.168125	−	1.06150i	0.917029	−	0.398821i	$-0.130581\pi$
$4$	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
$7$	−3.74943	−	1.91043i	−1.41715	−	0.722075i	−0.433331	−	0.901235i	$-0.642662\pi$
$7$	−3.74943	−	1.91043i	−1.41715	−	0.722075i	−0.983820	+	0.179160i	$0.942662\pi$
$8$	0.891007	−	0.453990i	0.315018	−	0.160510i
$9$	−0.442378	−	0.143737i	−0.147459	−	0.0479124i
$10$	1.90331	−	1.17363i	0.601879	−	0.371135i
$11$	−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	$0.457320\pi$
$12$	−0.291201	−	1.83857i	−0.0840625	−	0.530750i
$13$	−0.873242	+	5.51343i	−0.242194	+	1.52915i	0.504165	+	0.863607i	$0.331800\pi$
$13$	−0.873242	+	5.51343i	−0.242194	+	1.52915i	−0.746359	+	0.665544i	$0.768200\pi$
$14$	−4.00213	−	1.30037i	−1.06961	−	0.347538i
$15$	−0.982934	−	4.04470i	−0.253793	−	1.04434i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	4.97584	−	2.53532i	1.20682	−	0.614905i	0.269373	−	0.963036i	$-0.413184\pi$
$17$	4.97584	−	2.53532i	1.20682	−	0.614905i	0.937446	+	0.348131i	$0.113184\pi$
$18$	−0.459417	−	0.0727645i	−0.108286	−	0.0171508i
$19$	−2.91612	+	4.01370i	−0.669004	+	0.920805i	−0.999737	−	0.0229191i	$-0.992704\pi$
$19$	−2.91612	+	4.01370i	−0.669004	+	0.920805i	0.330733	+	0.943724i	$0.392704\pi$
$20$	1.69628	−	1.45693i	0.379300	−	0.325779i
$21$	−4.60430	+	6.33728i	−1.00474	+	1.38291i
$22$	−1.05855	+	0.539358i	−0.225683	+	0.114991i
$23$	−0.376909	−	0.739725i	−0.0785909	−	0.154243i	0.848367	−	0.529408i	$-0.177586\pi$
$23$	−0.376909	−	0.739725i	−0.0785909	−	0.154243i	−0.926958	+	0.375165i	$0.877586\pi$
$24$	−0.575232	−	1.77038i	−0.117419	−	0.361378i
$25$	3.51584	−	3.55512i	0.703168	−	0.711024i
$26$			5.58216i			1.09475i
$27$	2.14220	−	4.20431i	0.412267	−	0.809120i
$28$	−4.15628	−	0.658289i	−0.785462	−	0.124405i
$29$	4.92950	+	3.58149i	0.915385	+	0.665066i	0.942371	−	0.334570i	$-0.108591\pi$
$29$	4.92950	+	3.58149i	0.915385	+	0.665066i	−0.0269861	+	0.999636i	$0.508591\pi$
$30$	−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
$33$	0.345958	+	2.18429i	0.0602235	+	0.380236i
$34$	4.51797	−	3.28250i	0.774825	−	0.562944i
$35$	−9.38257	−	0.712209i	−1.58594	−	0.120385i
$36$	−0.465144			−0.0775239
$37$	−2.56906	−	2.56906i	−0.422351	−	0.422351i	0.463661	−	0.886013i	$-0.346535\pi$
$37$	−2.56906	−	2.56906i	−0.422351	−	0.422351i	−0.886013	+	0.463661i	$0.846535\pi$
$38$	−2.25234	+	4.42046i	−0.365378	+	0.717094i
$39$	9.88255	+	3.21104i	1.58247	+	0.514177i
$40$	1.44748	−	1.70435i	0.228867	−	0.269481i
$41$	−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	$0.971617\pi$
$42$	−3.55625	+	6.97953i	−0.548741	+	1.07696i
$43$	0.388045	−	0.0614603i	0.0591763	−	0.00937260i	−0.126776	−	0.991931i	$-0.540463\pi$
$43$	0.388045	−	0.0614603i	0.0591763	−	0.00937260i	0.185952	+	0.982559i	$0.440463\pi$
$44$	−0.961143	+	0.698311i	−0.144898	+	0.105274i
$45$	−1.03666	+	0.0844843i	−0.154536	+	0.0125942i
$46$	−0.487987	−	0.671656i	−0.0719497	−	0.0990303i
$47$	0.207336	−	1.30907i	0.0302431	−	0.190948i	−0.967942	−	0.251176i	$-0.919183\pi$
$47$	0.207336	−	1.30907i	0.0302431	−	0.190948i	0.998185	+	0.0602281i	$0.0191828\pi$
$48$	−0.845099	−	1.65860i	−0.121979	−	0.239398i
$49$	6.29399	+	8.66293i	0.899141	+	1.23756i
$50$	2.91641	−	4.06135i	0.412443	−	0.574361i
$51$	−3.21239	−	9.88673i	−0.449825	−	1.38442i
$52$	0.873242	+	5.51343i	0.121097	+	0.764576i
$53$	0.628490	+	1.23348i	0.0863298	+	0.169432i	0.930135	−	0.367218i	$-0.119690\pi$
$53$	0.628490	+	1.23348i	0.0863298	+	0.169432i	−0.843805	+	0.536650i	$0.819690\pi$
$54$	1.45813	−	4.48766i	0.198426	−	0.610694i
$55$	−2.01524	+	1.73088i	−0.271735	+	0.233392i
$56$	−4.20808			−0.562329
$57$	6.53029	+	6.53029i	0.864958	+	0.864958i
$58$	5.42908	+	2.76625i	0.712873	+	0.363227i
$59$	5.46450	+	7.52124i	0.711417	+	0.979182i	0.999765	+	0.0216562i	$0.00689392\pi$
$59$	5.46450	+	7.52124i	0.711417	+	0.979182i	−0.288348	+	0.957526i	$0.593106\pi$
$60$	−2.18471	−	3.54299i	−0.282044	−	0.457398i
$61$			2.58265i			0.330675i	0.986237	+	0.165337i	$0.0528713\pi$
$61$			2.58265i			0.330675i	−0.986237	+	0.165337i	$0.947129\pi$
$62$	4.55349	+	3.20401i	0.578294	+	0.406910i
$63$	1.38406	+	1.38406i	0.174376	+	0.174376i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	2.94758	+	12.1291i	0.365603	+	1.50443i
$66$	0.683397	+	2.10328i	0.0841204	+	0.258896i
$67$	−6.48765	+	6.48765i	−0.792592	+	0.792592i	−0.981915	−	0.189323i	$-0.939371\pi$
$67$	−6.48765	+	6.48765i	−0.792592	+	0.792592i	0.189323	+	0.981915i	$0.439371\pi$
$68$	3.94885	−	3.94885i	0.478868	−	0.478868i
$69$	−1.46979	+	0.477565i	−0.176942	+	0.0574920i
$70$	−9.37847	+	0.764316i	−1.12094	+	0.0913533i
$71$	−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	$0.772708\pi$
$72$	−0.459417	+	0.0727645i	−0.0541428	+	0.00857538i
$73$	−1.94218	−	0.989592i	−0.227315	−	0.115823i	0.336624	−	0.941639i	$-0.390715\pi$
$73$	−1.94218	−	0.989592i	−0.227315	−	0.115823i	−0.563939	+	0.825816i	$0.690715\pi$
$74$	−2.93932	−	2.13554i	−0.341689	−	0.248252i
$75$	−5.51252	−	7.49938i	−0.636531	−	0.865954i
$76$	−1.53310	+	4.71838i	−0.175858	+	0.541236i
$77$	4.93781	+	0.782073i	0.562716	+	0.0891254i
$78$	10.2632	+	1.62553i	1.16208	+	0.184055i
$79$	−1.91575	+	5.89608i	−0.215539	+	0.663361i	0.783576	+	0.621296i	$0.213394\pi$
$79$	−1.91575	+	5.89608i	−0.215539	+	0.663361i	−0.999115	+	0.0420650i	$0.986606\pi$
$80$	1.16304	−	1.90980i	0.130032	−	0.213522i
$81$	−8.23504	−	5.98311i	−0.915005	−	0.664790i
$82$	−8.59732	−	4.38056i	−0.949416	−	0.483751i
$83$	−2.22095	+	0.351764i	−0.243781	+	0.0386112i	−0.277129	−	0.960833i	$-0.589383\pi$
$83$	−2.22095	+	0.351764i	−0.243781	+	0.0386112i	0.0333480	+	0.999444i	$0.489383\pi$
$84$	−2.42062	+	7.44992i	−0.264112	+	0.812852i
$85$	8.08349	−	9.51795i	0.876777	−	1.03237i
$86$	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	$-0.982746\pi$
$89$	−2.09951	−	6.46163i	−0.222548	−	0.684931i	0.775984	−	0.630753i	$-0.217254\pi$
$90$	−1.01068	+	0.245613i	−0.106535	+	0.0258899i
$91$	13.8072	−	19.0040i	1.44739	−	1.99216i
$92$	−0.587049	−	0.587049i	−0.0612041	−	0.0612041i
$93$	8.29164	−	6.21837i	0.859803	−	0.644815i
$94$		−	1.32539i		−	0.136703i
$95$	−2.55978	+	10.7942i	−0.262627	+	1.10746i
$96$	−1.09416	−	1.50598i	−0.111672	−	0.153703i
$97$	−11.0201	−	5.61503i	−1.11892	−	0.570120i	−0.206123	−	0.978526i	$-0.566085\pi$
$97$	−11.0201	−	5.61503i	−1.11892	−	0.570120i	−0.912800	+	0.408406i	$0.866085\pi$
$98$	7.57168	+	7.57168i	0.764855	+	0.764855i
$99$	0.552608			0.0555392
$100$	2.24517	−	4.46757i	0.224517	−	0.446757i
$101$	−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	$0.911268\pi$
$102$	−4.71947	−	9.26248i	−0.467297	−	0.917122i
$103$	−2.44740	−	15.4523i	−0.241149	−	1.52256i	−0.749846	−	0.661612i	$-0.769873\pi$
$103$	−2.44740	−	15.4523i	−0.241149	−	1.52256i	0.508697	−	0.860946i	$-0.330127\pi$
$104$	1.72498	+	5.30895i	0.169148	+	0.520585i
$105$	−4.04166	+	17.0431i	−0.394426	+	1.66324i
$106$	0.813712	+	1.11998i	0.0790346	+	0.108782i
$107$	−1.32435	−	2.59919i	−0.128030	−	0.251273i	0.818089	−	0.575091i	$-0.195033\pi$
$107$	−1.32435	−	2.59919i	−0.128030	−	0.251273i	−0.946119	+	0.323818i	$0.895033\pi$
$108$	0.738153	−	4.66051i	0.0710288	−	0.448458i
$109$	−11.7018	−	16.1061i	−1.12083	−	1.54269i	−0.804416	−	0.594066i	$-0.797522\pi$
$109$	−11.7018	−	16.1061i	−1.12083	−	1.54269i	−0.316412	−	0.948622i	$-0.602478\pi$
$110$	−1.71966	+	2.02483i	−0.163963	+	0.193060i
$111$	−5.47152	+	3.97529i	−0.519334	+	0.377318i
$112$	−4.15628	+	0.658289i	−0.392731	+	0.0622025i
$113$	−1.70259	+	3.34152i	−0.160166	+	0.314344i	−0.957118	−	0.289700i	$-0.906445\pi$
$113$	−1.70259	+	3.34152i	−0.160166	+	0.314344i	0.796952	+	0.604043i	$0.206445\pi$
$114$	7.47145	+	5.42833i	0.699766	+	0.508410i
$115$	−1.41497	−	1.20172i	−0.131947	−	0.112061i
$116$	5.79497	+	1.88290i	0.538050	+	0.174823i
$117$	1.17879	−	2.31350i	0.108979	−	0.213883i
$118$	6.57380	+	6.57380i	0.605168	+	0.605168i
$119$	−23.5001			−2.15425
$120$	−2.71205	−	3.15761i	−0.247576	−	0.288249i
$121$	−7.75731	+	5.63602i	−0.705210	+	0.512365i
$122$	0.404016	+	2.55086i	0.0365779	+	0.230944i
$123$	−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
$127$	12.0906	+	1.91497i	1.07287	+	0.169926i	0.667786	−	0.744353i	$-0.267242\pi$
$127$	12.0906	+	1.91497i	1.07287	+	0.169926i	0.405085	+	0.914279i	$0.367242\pi$
$128$	0.453990	−	0.891007i	0.0401275	−	0.0787546i
$129$		−	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	$-0.246467\pi$
$132$	1.00401	+	1.97048i	0.0873878	+	0.171508i
$133$	18.6017	−	9.47803i	1.61297	−	0.821849i
$134$	−5.39288	+	7.42267i	−0.465874	+	0.641221i
$135$	0.798615	−	10.5209i	0.0687338	−	0.905492i
$136$	3.28250	−	4.51797i	0.281472	−	0.387413i
$137$	9.33390	+	1.47834i	0.797449	+	0.126303i	0.541845	−	0.840478i	$-0.317726\pi$
$137$	9.33390	+	1.47834i	0.797449	+	0.126303i	0.255603	+	0.966782i	$0.417726\pi$
$138$	−1.37699	+	0.701611i	−0.117217	+	0.0597251i
$139$	16.3138	−	11.8527i	1.38372	−	1.00533i	0.387195	−	0.921998i	$-0.373444\pi$
$139$	16.3138	−	11.8527i	1.38372	−	1.00533i	0.996522	−	0.0833310i	$-0.0265559\pi$
$140$	−9.14344	+	2.22202i	−0.772762	+	0.187795i
$141$	−2.34644	−	0.762406i	−0.197606	−	0.0642062i
$142$	−2.25766	+	14.2543i	−0.189459	+	1.19619i
$143$	−1.03744	−	6.55017i	−0.0867555	−	0.547752i
$144$	−0.442378	+	0.143737i	−0.0368648	+	0.0119781i
$145$	13.2571	+	3.14384i	1.10094	+	0.261082i
$146$	−2.07308	−	0.673584i	−0.171569	−	0.0557462i
$147$	17.7602	−	9.04929i	1.46484	−	0.746373i
$148$	−3.23721	−	1.64944i	−0.266097	−	0.135583i
$149$			15.5922i			1.27736i	0.769471	+	0.638682i	$0.220520\pi$
$149$			15.5922i			1.27736i	−0.769471	+	0.638682i	$0.779480\pi$
$150$	−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	$0.586705\pi$
$152$	−0.776103	+	4.90012i	−0.0629503	+	0.397452i
$153$	−2.56562	+	0.406355i	−0.207418	+	0.0328518i
$154$	4.99936			0.402860
$155$	11.5858	+	4.55735i	0.930593	+	0.366055i
$156$	10.3911			0.831956
$157$	−3.72197	+	0.589503i	−0.297046	+	0.0470474i	−0.303179	−	0.952934i	$-0.598048\pi$
$157$	−3.72197	+	0.589503i	−0.297046	+	0.0470474i	0.00613273	+	0.999981i	$0.498048\pi$
$158$	−0.969817	+	6.12318i	−0.0771545	+	0.487134i
$159$	2.45086	−	0.796333i	0.194366	−	0.0631533i
$160$	0.849965	−	2.06823i	0.0671956	−	0.163508i
$161$			3.49360i			0.275335i
$162$	−9.06962	−	4.62120i	−0.712577	−	0.363076i
$163$	18.3884	−	9.36935i	1.44029	−	0.733864i	0.452810	−	0.891607i	$-0.350422\pi$
$163$	18.3884	−	9.36935i	1.44029	−	0.733864i	0.987480	+	0.157743i	$0.0504217\pi$
$164$	−9.17675	−	2.98171i	−0.716584	−	0.232832i
$165$	2.59551	+	4.20921i	0.202060	+	0.327686i
$166$	−2.13858	+	0.694867i	−0.165986	+	0.0539322i
$167$	−0.687499	−	4.34070i	−0.0532002	−	0.335893i	−0.999905	−	0.0137902i	$-0.995610\pi$
$167$	−0.687499	−	4.34070i	−0.0532002	−	0.335893i	0.946705	−	0.322103i	$-0.104390\pi$
$168$	−1.22540	+	7.73686i	−0.0945416	+	0.596912i
$169$	−17.2717	−	5.61190i	−1.32859	−	0.431685i
$170$	6.49503	−	10.6653i	0.498146	−	0.817992i
$171$	1.86695	−	1.35642i	0.142769	−	0.103728i
$172$	0.350060	−	0.178365i	0.0266918	−	0.0136002i
$173$	−3.75480	−	0.594702i	−0.285472	−	0.0452144i	0.0120561	−	0.999927i	$-0.496162\pi$
$173$	−3.75480	−	0.594702i	−0.285472	−	0.0452144i	−0.297528	+	0.954713i	$0.596162\pi$
$174$	6.66691	−	9.17621i	0.505417	−	0.695647i
$175$	−19.9742	+	6.61290i	−1.50991	+	0.499888i
$176$	−0.698311	+	0.961143i	−0.0526372	+	0.0724489i
$177$	15.4196	−	7.85668i	1.15901	−	0.590544i
$178$	−3.08448	−	6.05364i	−0.231192	−	0.453739i
$179$	−5.16699	−	15.9024i	−0.386199	−	1.18860i	−0.935607	−	0.353043i	$-0.885147\pi$
$179$	−5.16699	−	15.9024i	−0.386199	−	1.18860i	0.549408	−	0.835554i	$-0.314853\pi$
$180$	−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	$-0.257931\pi$
$182$	10.6643	−	20.9299i	0.790492	−	1.55143i
$183$	4.74839	+	0.752072i	0.351011	+	0.0555947i
$184$	−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
$188$	−0.207336	−	1.30907i	−0.0151216	−	0.0954738i
$189$	−16.0641	+	11.6712i	−1.16849	+	0.848958i
$190$	−0.839673	+	11.0618i	−0.0609163	+	0.802505i
$191$	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
$193$	−5.38028	+	10.5594i	−0.387281	+	0.760082i	−0.999532	−	0.0305811i	$-0.990264\pi$
$193$	−5.38028	+	10.5594i	−0.387281	+	0.760082i	0.612251	+	0.790663i	$0.290264\pi$
$194$	−11.7628	−	3.82197i	−0.844521	−	0.274402i
$195$	23.1585	−	1.88735i	1.65841	−	0.135156i
$196$	8.66293	+	6.29399i	0.618781	+	0.449570i
$197$	−8.22915	+	16.1506i	−0.586302	+	1.15068i	0.387198	+	0.921997i	$0.373443\pi$
$197$	−8.22915	+	16.1506i	−0.586302	+	1.15068i	−0.973500	+	0.228686i	$0.926557\pi$
$198$	0.545805	−	0.0864470i	0.0387886	−	0.00614352i
$199$	19.2052	−	13.9534i	1.36142	−	0.989129i	0.363065	−	0.931764i	$-0.381730\pi$
$199$	19.2052	−	13.9534i	1.36142	−	0.989129i	0.998353	−	0.0573649i	$-0.0182698\pi$
$200$	1.51865	−	4.76379i	0.107385	−	0.336851i
$201$	10.0388	+	13.8172i	0.708082	+	0.974591i
$202$	−1.75698	+	11.0931i	−0.123621	+	0.780511i
$203$	−11.6406	−	22.8460i	−0.817012	−	1.60348i
$204$	−6.11033	−	8.41015i	−0.427809	−	0.588828i
$205$	−20.9936	−	4.97849i	−1.46626	−	0.347713i
$206$	−4.83454	−	14.8792i	−0.336838	−	1.03668i
$207$	0.0604100	+	0.381414i	0.00419878	+	0.0265101i
$208$	2.53425	+	4.97374i	0.175718	+	0.344867i
$209$	1.82138	−	5.60562i	0.125987	−	0.387749i
$210$	−1.32577	+	17.4656i	−0.0914869	+	1.20524i
$211$	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
$213$	23.9369	+	12.1964i	1.64013	+	0.835687i
$214$	−1.71465	−	2.36002i	−0.117211	−	0.161327i
$215$	0.747776	−	0.461099i	0.0509979	−	0.0314467i
$216$		−	4.71861i		−	0.321061i
$217$	−7.57701	−	22.1706i	−0.514361	−	1.50504i
$218$	−14.0773	−	14.0773i	−0.953434	−	0.953434i
$219$	−2.38500	+	3.28267i	−0.161164	+	0.221823i
$220$	−1.38174	+	2.26891i	−0.0931568	+	0.152970i
$221$	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	$-0.893479\pi$
$223$	−9.20022	+	9.20022i	−0.616092	+	0.616092i	0.328435	+	0.944527i	$0.393479\pi$
$224$	−4.00213	+	1.30037i	−0.267403	+	0.0868846i
$225$	−2.06633	+	1.06735i	−0.137756	+	0.0711566i
$226$	−1.15890	+	3.56672i	−0.0770888	+	0.237255i
$227$	−5.63435	+	0.892393i	−0.373965	+	0.0592302i	−0.340588	−	0.940213i	$-0.610626\pi$
$227$	−5.63435	+	0.892393i	−0.373965	+	0.0592302i	−0.0333767	+	0.999443i	$0.510626\pi$
$228$	8.22865	+	4.19270i	0.544955	+	0.277669i
$229$	13.7847	+	10.0152i	0.910918	+	0.661820i	0.941247	−	0.337720i	$-0.109656\pi$
$229$	13.7847	+	10.0152i	0.910918	+	0.661820i	−0.0303292	+	0.999540i	$0.509656\pi$
$230$	−1.58554	−	0.965572i	−0.104547	−	0.0636680i
$231$	2.87579	−	8.85078i	0.189213	−	0.582339i
$232$	6.01818	+	0.953186i	0.395113	+	0.0625797i
$233$	−9.58674	−	1.51839i	−0.628048	−	0.0994730i	−0.165707	−	0.986175i	$-0.552990\pi$
$233$	−9.58674	−	1.51839i	−0.628048	−	0.0994730i	−0.462341	+	0.886702i	$0.652990\pi$
$234$	0.802364	−	2.46942i	0.0524522	−	0.161431i
$235$	−0.699854	−	2.87984i	−0.0456534	−	0.187860i
$236$	7.52124	+	5.46450i	0.489591	+	0.355709i
$237$	10.2825	+	5.23920i	0.667920	+	0.340322i
$238$	−23.2108	+	3.67623i	−1.50453	+	0.238294i
$239$	0.135481	−	0.416966i	0.00876351	−	0.0269713i	−0.946579	−	0.322472i	$-0.895486\pi$
$239$	0.135481	−	0.416966i	0.00876351	−	0.0269713i	0.955343	+	0.295500i	$0.0954863\pi$
$240$	−3.17262	−	2.69447i	−0.204792	−	0.173927i
$241$	−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
$245$	20.4501	+	12.4538i	1.30651	+	0.795646i
$246$	−10.5575	+	14.5312i	−0.673123	+	0.926474i
$247$	−19.5828	−	19.5828i	−1.24602	−	1.24602i
$248$	5.32072	+	1.64009i	0.337866	+	0.104146i
$249$			4.18582i			0.265265i
$250$	2.51933	−	10.8928i	0.159336	−	0.688921i
$251$	−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	$0.880798\pi$
$252$	1.74402	+	0.888624i	0.109863	+	0.0559781i
$253$	0.697436	+	0.697436i	0.0438474	+	0.0438474i
$254$	12.2414			0.768091
$255$	−15.1455	−	17.6337i	−0.948449	−	1.10427i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−7.57287	−	14.8626i	−0.472383	−	0.927103i	−0.997120	−	0.0758392i	$-0.975836\pi$
$257$	−7.57287	−	14.8626i	−0.472383	−	0.927103i	0.524737	−	0.851264i	$-0.324164\pi$
$258$	−0.114408	−	0.722341i	−0.00712271	−	0.0449710i
$259$	4.72451	+	14.5405i	0.293567	+	0.903505i
$260$	6.55141	+	10.6246i	0.406301	+	0.658908i
$261$	−1.66591	−	2.29292i	−0.103117	−	0.141928i
$262$	−4.61495	−	9.05736i	−0.285113	−	0.559565i
$263$	−1.58235	+	9.99056i	−0.0975718	+	0.616044i	0.889644	+	0.456655i	$0.150953\pi$
$263$	−1.58235	+	9.99056i	−0.0975718	+	0.616044i	−0.987216	+	0.159389i	$0.949047\pi$
$264$	1.29990	+	1.78916i	0.0800032	+	0.110115i
$265$	2.35944	+	2.00385i	0.144939	+	0.123095i
$266$	16.8900	−	12.2713i	1.03559	−	0.752401i
$267$	−12.4915	+	1.97847i	−0.764470	+	0.121080i
$268$	−4.16533	+	8.17491i	−0.254438	+	0.499362i
$269$	6.77787	+	4.92441i	0.413254	+	0.300247i	0.774918	−	0.632062i	$-0.217791\pi$
$269$	6.77787	+	4.92441i	0.413254	+	0.300247i	−0.361664	+	0.932309i	$0.617791\pi$
$270$	−0.857043	−	10.5163i	−0.0521580	−	0.639999i
$271$	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	$0.428678\pi$
$272$	2.53532	−	4.97584i	0.153726	−	0.301705i
$273$	−30.9195	−	30.9195i	−1.87133	−	1.87133i
$274$	9.45025			0.570910
$275$	−2.66735	+	5.30764i	−0.160847	+	0.320063i
$276$	−1.25028	+	0.908382i	−0.0752581	+	0.0546782i
$277$	3.26119	+	20.5903i	0.195946	+	1.23715i	0.867968	+	0.496621i	$0.165426\pi$
$277$	3.26119	+	20.5903i	0.195946	+	1.23715i	−0.672022	+	0.740531i	$0.734574\pi$
$278$	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	$0.698866\pi$
$282$	−2.43682	−	0.385955i	−0.145111	−	0.0229833i
$283$	−3.89243	+	7.63932i	−0.231381	+	0.454110i	−0.977281	−	0.211947i	$-0.932019\pi$
$283$	−3.89243	+	7.63932i	−0.231381	+	0.454110i	0.745900	+	0.666058i	$0.232019\pi$
$284$			14.4320i			0.856380i
$285$	19.1005	+	7.84962i	1.13142	+	0.464971i
$286$	−2.04934	−	6.30723i	−0.121180	−	0.372954i
$287$	18.4337	+	36.1783i	1.08811	+	2.13554i
$288$	−0.414446	+	0.211171i	−0.0244215	+	0.0124434i
$289$	8.33881	−	11.4774i	0.490518	−	0.675141i
$290$	13.5857	+	1.03126i	0.797781	+	0.0605577i
$291$	−13.5327	+	18.6262i	−0.793301	+	1.09189i
$292$	−2.15293	−	0.340990i	−0.125991	−	0.0199549i
$293$	−11.4389	+	5.82843i	−0.668270	+	0.340500i	−0.754994	−	0.655732i	$-0.772360\pi$
$293$	−11.4389	+	5.82843i	−0.668270	+	0.340500i	0.0867241	+	0.996232i	$0.472360\pi$
$294$	16.1260	−	11.7162i	0.940485	−	0.683302i
$295$	17.7549	+	10.8125i	1.03373	+	0.629530i
$296$	−3.45538	−	1.12272i	−0.200840	−	0.0652569i
$297$	−0.876954	+	5.53687i	−0.0508860	+	0.321282i
$298$	2.43916	+	15.4002i	0.141297	+	0.892112i
$299$	4.40756	−	1.43210i	0.254896	−	0.0828206i
$300$	−7.56016	−	5.42887i	−0.436486	−	0.313436i
$301$	−1.57236	−	0.510891i	−0.0906295	−	0.0294473i
$302$	−12.1202	+	6.17555i	−0.697439	+	0.355363i
$303$	18.6284	+	9.49166i	1.07018	+	0.545282i
$304$			4.96120i			0.284544i
$305$	2.22480	+	5.32924i	0.127392	+	0.305151i
$306$	−2.47047	+	0.802703i	−0.141227	+	0.0458875i
$307$	0.596936	−	3.76890i	0.0340689	−	0.215103i	−0.964781	−	0.263056i	$-0.915270\pi$
$307$	0.596936	−	3.76890i	0.0340689	−	0.215103i	0.998850	+	0.0479529i	$0.0152697\pi$
$308$	4.93781	−	0.782073i	0.281358	−	0.0445627i
$309$	−29.1228			−1.65674
$310$	12.1561	+	2.68883i	0.690419	+	0.152715i
$311$	−2.77229			−0.157202			−0.0786012	−	0.996906i	$-0.525045\pi$
$311$	−2.77229			−0.157202			−0.0786012	+	0.996906i	$0.525045\pi$
$312$	10.2632	−	1.62553i	0.581039	−	0.0920276i
$313$	4.04203	−	25.5204i	0.228469	−	1.44250i	−0.560546	−	0.828123i	$-0.689409\pi$
$313$	4.04203	−	25.5204i	0.228469	−	1.44250i	0.789015	−	0.614374i	$-0.210591\pi$
$314$	−3.58393	+	1.16449i	−0.202253	+	0.0657160i
$315$	4.04827	+	1.66369i	0.228094	+	0.0937384i
$316$			6.19951i			0.348750i
$317$	−17.8880	−	9.11437i	−1.00469	−	0.511914i	−0.127386	−	0.991853i	$-0.540659\pi$
$317$	−17.8880	−	9.11437i	−1.00469	−	0.511914i	−0.877302	+	0.479939i	$0.840659\pi$
$318$	2.29611	−	1.16993i	0.128760	−	0.0656063i
$319$	−6.88465	−	2.23696i	−0.385466	−	0.125246i
$320$	0.515959	−	2.17573i	0.0288430	−	0.121627i
$321$	−5.16446	+	1.67803i	−0.288252	+	0.0936587i
$322$	0.546520	+	3.45059i	0.0304564	+	0.192294i
$323$	−4.33416	+	27.3648i	−0.241159	+	1.52262i
$324$	−9.68087	−	3.14551i	−0.537826	−	0.174750i
$325$	16.5307	+	22.4888i	0.916960	+	1.24746i
$326$	16.6963	−	12.1306i	0.924723	−	0.671851i
$327$	−33.0199	+	16.8245i	−1.82600	+	0.930395i
$328$	−9.53021	−	1.50944i	−0.526218	−	0.0833447i
$329$	−3.27828	+	4.51217i	−0.180738	+	0.248764i
$330$	3.22202	+	3.75136i	0.177366	+	0.206505i
$331$	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	$0.120960\pi$
$332$	−2.00355	+	1.02086i	−0.109959	+	0.0560270i
$333$	0.767227	+	1.50577i	0.0420438	+	0.0825155i
$334$	−1.35807	−	4.17971i	−0.0743102	−	0.228703i
$335$	−7.79836	+	18.9758i	−0.426070	+	1.03676i
$336$			7.83330i			0.427342i
$337$	9.83976	−	19.3116i	0.536006	−	1.05197i	−0.451186	−	0.892430i	$-0.648999\pi$
$337$	9.83976	−	19.3116i	0.536006	−	1.05197i	0.987191	−	0.159540i	$-0.0510012\pi$
$338$	−17.9369	−	2.84093i	−0.975639	−	0.154526i
$339$	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
$343$	−2.44092	−	15.4113i	−0.131797	−	0.832134i
$344$	0.317848	−	0.230930i	0.0171372	−	0.0124509i
$345$	−2.62148	+	2.25158i	−0.141136	+	0.121221i
$346$	−3.80161			−0.204376
$347$	24.4544	+	24.4544i	1.31278	+	1.31278i	0.919356	+	0.393427i	$0.128711\pi$
$347$	24.4544	+	24.4544i	1.31278	+	1.31278i	0.393427	+	0.919356i	$0.371289\pi$
$348$	5.14935	−	10.1062i	0.276034	−	0.541748i
$349$	10.0905	+	3.27860i	0.540131	+	0.175499i	0.566362	−	0.824157i	$-0.308350\pi$
$349$	10.0905	+	3.27860i	0.540131	+	0.175499i	−0.0262308	+	0.999656i	$0.508350\pi$
$350$	−18.6938	+	9.65614i	−0.999226	+	0.516142i
$351$	21.3095	+	15.4823i	1.13742	+	0.826383i
$352$	−0.539358	+	1.05855i	−0.0287479	+	0.0564209i
$353$	17.5708	−	2.78293i	0.935197	−	0.148121i	0.329806	−	0.944049i	$-0.393017\pi$
$353$	17.5708	−	2.78293i	0.935197	−	0.148121i	0.605391	+	0.795928i	$0.293017\pi$
$354$	14.0007	−	10.1721i	0.744129	−	0.540641i
$355$	2.62129	+	32.1643i	0.139123	+	1.70710i
$356$	−3.99350	−	5.49659i	−0.211655	−	0.291319i
$357$	−6.84326	+	43.2066i	−0.362184	+	2.28674i
$358$	−7.59105	−	14.8983i	−0.401199	−	0.787398i
$359$	−13.4216	−	18.4732i	−0.708362	−	0.974977i	−0.999831	−	0.0183967i	$-0.994144\pi$
$359$	−13.4216	−	18.4732i	−0.708362	−	0.974977i	0.291468	−	0.956580i	$-0.405856\pi$
$360$	−0.885312	+	0.545908i	−0.0466600	+	0.0287719i
$361$	−1.73467	−	5.33878i	−0.0912987	−	0.280988i
$362$	−3.04960	−	19.2544i	−0.160283	−	1.01199i
$363$	8.10328	+	15.9036i	0.425312	+	0.834722i
$364$	7.25887	−	22.3405i	0.380468	−	1.17096i
$365$	−4.86012	−	0.368921i	−0.254390	−	0.0193102i
$366$	4.80758			0.251296
$367$	−2.30910	−	2.30910i	−0.120534	−	0.120534i	0.644267	−	0.764801i	$-0.277163\pi$
$367$	−2.30910	−	2.30910i	−0.120534	−	0.120534i	−0.764801	+	0.644267i	$0.777163\pi$
$368$	−0.739725	−	0.376909i	−0.0385608	−	0.0196477i
$369$	2.63808	+	3.63101i	0.137333	+	0.189023i
$370$	−7.90486	−	1.87458i	−0.410954	−	0.0974550i
$371$		−	5.82554i		−	0.302447i
$372$	5.96423	−	8.47628i	0.309231	−	0.439475i
$373$	−0.547654	−	0.547654i	−0.0283565	−	0.0283565i	0.692786	−	0.721143i	$-0.256383\pi$
$373$	−0.547654	−	0.547654i	−0.0283565	−	0.0283565i	−0.721143	+	0.692786i	$0.756383\pi$
$374$	−3.89973	+	5.36752i	−0.201650	+	0.277548i
$375$	−17.8352	−	10.7261i	−0.921006	−	0.553891i
$376$	−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	−0.0675444	−	0.997716i	$-0.521516\pi$
$379$	9.03806	−	2.93664i	0.464254	−	0.150845i	0.531798	+	0.846871i	$0.321516\pi$
$380$	0.901105	+	11.0569i	0.0462257	+	0.567208i
$381$	7.04162	−	21.6719i	0.360753	−	1.11028i
$382$	2.87266	−	0.454985i	0.146978	−	0.0232790i
$383$	−0.0946829	−	0.0482434i	−0.00483807	−	0.00246512i	0.451570	−	0.892236i	$-0.350864\pi$
$383$	−0.0946829	−	0.0482434i	−0.00483807	−	0.00246512i	−0.456408	+	0.889771i	$0.650864\pi$
$384$	−1.50598	−	1.09416i	−0.0768516	−	0.0558359i
$385$	10.8627	−	2.63985i	0.553617	−	0.134539i
$386$	−3.66219	+	11.2711i	−0.186401	+	0.573682i
$387$	−0.180497	−	0.0285878i	−0.00917516	−	0.00145320i
$388$	−12.2159	−	1.93481i	−0.620168	−	0.0982249i
$389$	−9.02186	+	27.7664i	−0.457426	+	1.40781i	0.410836	+	0.911709i	$0.365237\pi$
$389$	−9.02186	+	27.7664i	−0.457426	+	1.40781i	−0.868263	+	0.496105i	$0.834763\pi$
$390$	22.5781	−	5.48690i	1.14329	−	0.277840i
$391$	−3.75087	−	2.72517i	−0.189690	−	0.137818i
$392$	9.54087	+	4.86132i	0.481887	+	0.245534i
$393$	−18.6896	+	2.96015i	−0.942768	+	0.149320i
$394$	−5.60132	+	17.2391i	−0.282190	+	0.868493i
$395$	1.12602	+	13.8167i	0.0566562	+	0.695194i
$396$	0.525562	−	0.170765i	0.0264105	−	0.00858128i
$397$	24.4559	−	24.4559i	1.22741	−	1.22741i	0.262467	−	0.964941i	$-0.415464\pi$
$397$	24.4559	−	24.4559i	1.22741	−	1.22741i	0.964941	−	0.262467i	$-0.0845361\pi$
$398$	16.7859	−	16.7859i	0.841403	−	0.841403i
$399$	−12.0092	−	36.9605i	−0.601212	−	1.85034i
$400$	0.754729	−	4.94271i	0.0377364	−	0.247136i
$401$	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
$403$	−24.8646	+	18.6474i	−1.23860	+	0.928893i
$404$			11.2314i			0.558784i
$405$	−22.1469	−	5.25198i	−1.10049	−	0.260973i
$406$	−15.0712	−	20.7437i	−0.747972	−	1.02949i
$407$	3.84593	+	1.95960i	0.190635	+	0.0971336i
$408$	−7.35074	−	7.35074i	−0.363916	−	0.363916i
$409$	−17.3373			−0.857274			−0.428637	−	0.903477i	$-0.641006\pi$
$409$	−17.3373			−0.857274			−0.428637	+	0.903477i	$0.641006\pi$
$410$	−21.5139	−	1.63307i	−1.06250	−	0.0806518i
$411$	5.43608	−	16.7305i	0.268142	−	0.825257i
$412$	−7.10263	−	13.9397i	−0.349922	−	0.686760i
$413$	−6.11996	−	38.6399i	−0.301144	−	1.90135i
$414$	0.119332	+	0.367268i	0.00586487	+	0.0180502i
$415$	−4.27985	+	2.63908i	−0.210090	+	0.129547i
$416$	3.28111	+	4.51606i	0.160870	+	0.221418i
$417$	−17.0414	−	33.4456i	−0.834519	−	1.63784i
$418$	0.922040	−	5.82153i	0.0450984	−	0.284740i
$419$	8.93797	+	12.3021i	0.436648	+	0.600995i	0.969463	−	0.245237i	$-0.0788658\pi$
$419$	8.93797	+	12.3021i	0.436648	+	0.600995i	−0.532815	+	0.846232i	$0.678866\pi$
$420$	1.42277	+	17.4579i	0.0694239	+	0.851859i
$421$	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	$0.0322057\pi$
$422$	3.61366	−	0.572347i	0.175910	−	0.0278614i
$423$	−0.279883	+	0.549302i	−0.0136084	+	0.0267080i
$424$	1.11998	+	0.813712i	0.0543909	+	0.0395173i
$425$	8.48091	−	26.6035i	0.411385	−	1.29046i
$426$	25.5501	+	8.30174i	1.23791	+	0.402220i
$427$	4.93398	−	9.68348i	0.238772	−	0.468616i
$428$	−2.06273	−	2.06273i	−0.0997059	−	0.0997059i
$429$	−12.3451			−0.596025
$430$	0.666437	−	0.572400i	0.0321385	−	0.0276036i
$431$	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	$0.189565\pi$
$432$	−0.738153	−	4.66051i	−0.0355144	−	0.224229i
$433$	−16.8339	+	16.8339i	−0.808986	+	0.808986i	−0.984480	−	0.175495i	$-0.943848\pi$
$433$	−16.8339	+	16.8339i	−0.808986	+	0.808986i	0.175495	+	0.984480i	$0.443848\pi$
$434$	−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
$437$	4.06814	+	0.644330i	0.194606	+	0.0308225i
$438$	−1.84212	+	3.61536i	−0.0880197	+	0.172748i
$439$			20.1434i			0.961393i	0.876887	+	0.480697i	$0.159616\pi$
$439$			20.1434i			0.961393i	−0.876887	+	0.480697i	$0.840384\pi$
$440$	−1.00979	+	2.45713i	−0.0481399	+	0.117139i
$441$	−1.53913	−	4.73697i	−0.0732921	−	0.225570i
$442$	14.1525	+	27.7759i	0.673168	+	1.32117i
$443$	−18.5470	+	9.45018i	−0.881196	+	0.448992i	−0.835198	−	0.549950i	$-0.814647\pi$
$443$	−18.5470	+	9.45018i	−0.881196	+	0.448992i	−0.0459983	+	0.998942i	$0.514647\pi$
$444$	−3.97529	+	5.47152i	−0.188659	+	0.259667i
$445$	−9.89859	−	11.5248i	−0.469238	−	0.546327i
$446$	−7.64772	+	10.5262i	−0.362130	+	0.498429i
$447$	28.6674	+	4.54047i	1.35592	+	0.214757i
$448$	−3.74943	+	1.91043i	−0.177144	+	0.0902593i
$449$	−7.32311	+	5.32055i	−0.345599	+	0.251092i	−0.747020	−	0.664801i	$-0.768516\pi$
$449$	−7.32311	+	5.32055i	−0.345599	+	0.251092i	0.401421	+	0.915893i	$0.368516\pi$
$450$	−1.87392	+	1.37745i	−0.0883376	+	0.0649338i
$451$	10.9023	+	3.54238i	0.513370	+	0.166804i
$452$	−0.586672	+	3.70410i	−0.0275947	+	0.174226i
$453$	3.96116	+	25.0097i	0.186111	+	1.17506i
$454$	−5.42538	+	1.76281i	−0.254626	+	0.0827329i
$455$	12.1200	−	51.1082i	0.568193	−	2.39599i
$456$	8.78322	+	2.85384i	0.411312	+	0.133643i
$457$	−0.351333	+	0.179013i	−0.0164347	+	0.00837388i	−0.462189	−	0.886782i	$-0.652936\pi$
$457$	−0.351333	+	0.179013i	−0.0164347	+	0.00837388i	0.445754	+	0.895156i	$0.352936\pi$
$458$	15.1817	+	7.73546i	0.709394	+	0.361454i
$459$		−	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	$0.304686\pi$
$462$	1.45582	−	9.19168i	0.0677309	−	0.427636i
$463$	−27.9308	+	4.42381i	−1.29806	+	0.205592i	−0.766947	−	0.641711i	$-0.778225\pi$
$463$	−27.9308	+	4.42381i	−1.29806	+	0.205592i	−0.531110	+	0.847303i	$0.678225\pi$
$464$	6.09320			0.282869
$465$	11.7528	−	19.9742i	0.545024	−	0.926281i
$466$	−9.70624			−0.449633
$467$	5.01382	−	0.794112i	0.232012	−	0.0367471i	−0.0393457	−	0.999226i	$-0.512527\pi$
$467$	5.01382	−	0.794112i	0.232012	−	0.0367471i	0.271358	+	0.962479i	$0.412527\pi$
$468$	0.406183	−	2.56454i	0.0187758	−	0.118546i
$469$	36.7192	−	11.9308i	1.69553	−	0.550912i
$470$	−1.14174	−	2.73490i	−0.0526647	−	0.126152i
$471$			7.01478i			0.323224i
$472$	8.28348	+	4.22064i	0.381278	+	0.194271i
$473$	−0.415885	+	0.211904i	−0.0191224	+	0.00974335i
$474$	10.9755	+	3.56616i	0.504121	+	0.163799i
$475$	4.01655	+	24.4787i	0.184292	+	1.12316i
$476$	−22.3499	+	7.26194i	−1.02441	+	0.332850i
$477$	−0.100733	−	0.636002i	−0.00461224	−	0.0291206i
$478$	0.0685847	−	0.433027i	0.00313699	−	0.0198062i
$479$	35.8739	+	11.6561i	1.63912	+	0.532583i	0.976342	−	0.216233i	$-0.0693771\pi$
$479$	35.8739	+	11.6561i	1.63912	+	0.532583i	0.662779	+	0.748815i	$0.269377\pi$
$480$	−3.55507	−	2.16499i	−0.162266	−	0.0988179i
$481$	16.4078	−	11.9209i	0.748130	−	0.543548i
$482$	−4.22283	+	2.15164i	−0.192345	+	0.0980045i
$483$	6.42324	+	1.01734i	0.292268	+	0.0462906i
$484$	−5.63602	+	7.75731i	−0.256183	+	0.352605i
$485$	−27.5767	−	2.09329i	−1.25219	−	0.0950512i
$486$	−2.81691	+	3.87714i	−0.127778	+	0.175871i
$487$	−29.4151	+	14.9877i	−1.33292	+	0.679159i	−0.967781	−	0.251792i	$-0.918980\pi$
$487$	−29.4151	+	14.9877i	−1.33292	+	0.679159i	−0.365143	+	0.930951i	$0.618980\pi$
$488$	1.17250	+	2.30116i	0.0530766	+	0.104169i
$489$	−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	$-0.198109\pi$
$492$	−8.15436	+	16.0038i	−0.367627	+	0.721508i
$493$	33.6086	+	5.32308i	1.51366	+	0.239740i
$494$	−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
$498$	0.654806	+	4.13428i	0.0293426	+	0.185262i
$499$	−0.451953	+	0.328363i	−0.0202322	+	0.0146996i	−0.597855	−	0.801604i	$-0.703980\pi$
$499$	−0.451953	+	0.328363i	−0.0202322	+	0.0146996i	0.577623	+	0.816304i	$0.303980\pi$
$500$	0.784301	−	11.1528i	0.0350750	−	0.498768i
$501$	−8.18088			−0.365495
$502$	−5.62640	−	5.62640i	−0.251118	−	0.251118i
$503$	1.43898	−	2.82416i	0.0641610	−	0.125923i	−0.856699	−	0.515817i	$-0.827488\pi$
$503$	1.43898	−	2.82416i	0.0641610	−	0.125923i	0.920860	+	0.389894i	$0.127488\pi$
$504$	1.86156	+	0.604859i	0.0829206	+	0.0269425i
$505$	2.03997	+	25.0312i	0.0907774	+	1.11388i
$506$	0.797953	+	0.579747i	0.0354733	+	0.0257729i
$507$	−15.3474	+	30.1210i	−0.681602	+	1.33772i
$508$	12.0906	−	1.91497i	0.536436	−	0.0849631i
$509$	16.1365	−	11.7238i	0.715237	−	0.519650i	−0.169622	−	0.985509i	$-0.554255\pi$
$509$	16.1365	−	11.7238i	0.715237	−	0.519650i	0.884859	+	0.465859i	$0.154255\pi$
$510$	−17.7176	−	15.0473i	−0.784547	−	0.666307i
$511$	5.39154	+	7.42081i	0.238508	+	0.328278i
$512$	0.156434	−	0.987688i	0.00691349	−	0.0436501i
$513$	10.6279	+	20.8584i	0.469233	+	0.920922i
$514$	−9.80466	−	13.4950i	−0.432465	−	0.595237i
$515$	−18.3614	−	29.7771i	−0.809098	−	1.31213i
$516$	−0.225998	−	0.695551i	−0.00994901	−	0.0306199i
$517$	0.246324	+	1.55523i	0.0108333	+	0.0683987i
$518$	6.94098	+	13.6224i	0.304969	+	0.598536i
$519$	−2.18681	+	6.73030i	−0.0959901	+	0.295427i
$520$	8.13280	+	9.46890i	0.356647	+	0.415239i
$521$	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
$523$	−18.8723	−	9.61590i	−0.825226	−	0.420474i	−0.0102355	−	0.999948i	$-0.503258\pi$
$523$	−18.8723	−	9.61590i	−0.825226	−	0.420474i	−0.814991	+	0.579474i	$0.803258\pi$
$524$	−5.97502	−	8.22391i	−0.261020	−	0.359263i
$525$	6.34178	+	38.6497i	0.276778	+	1.68681i
$526$			10.1151i			0.441039i
$527$	29.7137	+	9.15911i	1.29435	+	0.398977i
$528$	1.56378	+	1.56378i	0.0680548	+	0.0680548i
$529$	13.1139	−	18.0498i	0.570171	−	0.784773i
$530$	2.64387	+	1.61008i	0.114842	+	0.0699374i
$531$	−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
$535$	−4.97182	−	4.22251i	−0.214951	−	0.182555i
$536$	−2.83521	+	8.72587i	−0.122462	+	0.376900i
$537$	−30.7422	+	4.86909i	−1.32663	+	0.210117i
$538$	7.46477	+	3.80349i	0.321829	+	0.163980i
$539$	−10.2919	−	7.47749i	−0.443303	−	0.322078i
$540$	−2.49160	−	10.2527i	−0.107221	−	0.441207i
$541$	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	$-0.0148102\pi$
$542$	16.6695	+	2.64019i	0.716016	+	0.113406i
$543$	−35.8419	−	5.67679i	−1.53812	−	0.243614i
$544$	1.72571	−	5.31119i	0.0739892	−	0.227715i
$545$	−38.0208	−	23.1542i	−1.62863	−	0.991816i
$546$	−35.3757	−	25.7019i	−1.51394	−	1.09994i
$547$	−6.51035	−	3.31719i	−0.278362	−	0.141833i	0.309236	−	0.950985i	$-0.399927\pi$
$547$	−6.51035	−	3.31719i	−0.278362	−	0.141833i	−0.587599	+	0.809153i	$0.699927\pi$
$548$	9.33390	−	1.47834i	0.398724	−	0.0631517i
$549$	0.371224	−	1.14251i	0.0158434	−	0.0487611i
$550$	−1.80421	+	5.65956i	−0.0769318	+	0.241325i
$551$	−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
$555$	−7.86586	+	12.9163i	−0.333887	+	0.548266i
$556$	11.8527	−	16.3138i	0.502664	−	0.691858i
$557$	1.45701	+	1.45701i	0.0617354	+	0.0617354i	0.737300	−	0.675565i	$-0.236100\pi$
$557$	1.45701	+	1.45701i	0.0617354	+	0.0617354i	−0.675565	+	0.737300i	$0.736100\pi$
$558$	−1.55383	−	2.07189i	−0.0657788	−	0.0877101i
$559$			2.19313i			0.0927595i
$560$	−8.00928	+	4.93875i	−0.338454	+	0.208700i
$561$	7.25931	+	9.99158i	0.306488	+	0.421845i
$562$	0.106419	+	0.0542230i	0.00448900	+	0.00228726i
$563$	−11.3738	−	11.3738i	−0.479347	−	0.479347i	0.425576	−	0.904923i	$-0.360072\pi$
$563$	−11.3738	−	11.3738i	−0.479347	−	0.479347i	−0.904923	+	0.425576i	$0.860072\pi$
$564$	−2.46720			−0.103888
$565$	−0.634726	+	8.36181i	−0.0267031	+	0.351784i
$566$	−2.64945	+	8.15417i	−0.111365	+	0.342745i
$567$	19.4464	+	38.1657i	0.816672	+	1.60281i
$568$	2.25766	+	14.2543i	0.0947293	+	0.598097i
$569$	9.66757	+	29.7537i	0.405286	+	1.24734i	0.920656	+	0.390374i	$0.127654\pi$
$569$	9.66757	+	29.7537i	0.405286	+	1.24734i	−0.515371	+	0.856967i	$0.672346\pi$
$570$	20.0933	+	4.76500i	0.841617	+	0.199584i
$571$	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	$0.660320\pi$
$572$	−3.01078	−	5.90899i	−0.125887	−	0.247067i
$573$	0.846949	−	5.34743i	0.0353818	−	0.223392i
$574$	23.8663	+	32.8492i	0.996161	+	1.37110i
$575$	−3.95496	−	1.26080i	−0.164933	−	0.0525790i
$576$	−0.376309	+	0.273405i	−0.0156795	+	0.0113919i
$577$	11.9969	−	1.90013i	0.499439	−	0.0791034i	0.0983677	−	0.995150i	$-0.468638\pi$
$577$	11.9969	−	1.90013i	0.499439	−	0.0791034i	0.401072	+	0.916047i	$0.368638\pi$
$578$	6.44069	−	12.6406i	0.267897	−	0.525778i
$579$	17.8475	+	12.9669i	0.741716	+	0.538888i
$580$	13.5798	−	1.10671i	0.563870	−	0.0459536i
$581$	8.99933	+	2.92406i	0.373355	+	0.121310i
$582$	−10.4523	+	20.5138i	−0.433262	+	0.850325i
$583$	−1.16297	−	1.16297i	−0.0481651	−	0.0481651i
$584$	−2.17976			−0.0901993
$585$	0.439453	−	5.78931i	0.0181692	−	0.239358i
$586$	−10.3863	+	7.54611i	−0.429055	+	0.311727i
$587$	−0.655042	−	4.13577i	−0.0270365	−	0.170702i	0.970475	−	0.241200i	$-0.0775410\pi$
$587$	−0.655042	−	4.13577i	−0.0270365	−	0.170702i	−0.997512	+	0.0704985i	$0.977541\pi$
$588$	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
$592$	−3.58847	−	0.568358i	−0.147485	−	0.0233594i
$593$	18.5924	−	36.4897i	0.763499	−	1.49845i	−0.100489	−	0.994938i	$-0.532041\pi$
$593$	18.5924	−	36.4897i	0.763499	−	1.49845i	0.863988	−	0.503513i	$-0.167959\pi$
$594$			5.60588i			0.230012i
$595$	−48.4919	+	20.2440i	−1.98797	+	0.829921i
$596$	4.81826	+	14.8291i	0.197363	+	0.607422i
$597$	−20.0617	−	39.3733i	−0.821071	−	1.61144i
$598$	4.12926	−	2.10396i	0.168858	−	0.0860375i
$599$	18.0426	−	24.8335i	0.737200	−	1.01467i	−0.261575	−	0.965183i	$-0.584242\pi$
$599$	18.0426	−	24.8335i	0.737200	−	1.01467i	0.998775	−	0.0494856i	$-0.0157582\pi$
$600$	−8.31634	−	4.17936i	−0.339513	−	0.170622i
$601$	−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	$0.871768\pi$
$602$	−1.63292	−	0.258630i	−0.0665531	−	0.0105410i
$603$	3.80251	−	1.93747i	0.154850	−	0.0789001i
$604$	−11.0049	+	7.99553i	−0.447783	+	0.325334i
$605$	−11.1519	+	18.3122i	−0.453390	+	0.744498i
$606$	19.8839	+	6.46067i	0.807729	+	0.262447i
$607$	1.18486	−	7.48093i	0.0480921	−	0.303642i	−0.951904	−	0.306396i	$-0.900877\pi$
$607$	1.18486	−	7.48093i	0.0480921	−	0.303642i	0.999996	+	0.00275448i	$0.000876781\pi$
$608$	0.776103	+	4.90012i	0.0314751	+	0.198726i
$609$	−45.3938	+	14.7493i	−1.83945	+	0.597673i
$610$	3.03109	+	4.91559i	0.122725	+	0.199026i
$611$	7.03642	+	2.28627i	0.284663	+	0.0924927i
$612$	−2.31448	+	1.17929i	−0.0935573	+	0.0476698i
$613$	3.85616	+	1.96481i	0.155749	+	0.0793580i	0.530128	−	0.847918i	$-0.322144\pi$
$613$	3.85616	+	1.96481i	0.155749	+	0.0793580i	−0.374379	+	0.927276i	$0.622144\pi$
$614$		−	3.81588i		−	0.153997i
$615$	−15.2667	+	37.1485i	−0.615611	+	1.49797i
$616$	4.75468	−	1.54489i	0.191571	−	0.0622453i
$617$	−3.81247	+	24.0710i	−0.153484	+	0.969061i	0.783931	+	0.620848i	$0.213211\pi$
$617$	−3.81247	+	24.0710i	−0.153484	+	0.969061i	−0.937415	+	0.348213i	$0.886789\pi$
$618$	−28.7643	+	4.55581i	−1.15707	+	0.183262i
$619$	17.2071			0.691613			0.345807	−	0.938306i	$-0.387605\pi$
$619$	17.2071			0.691613			0.345807	+	0.938306i	$0.387605\pi$
$620$	12.4270	+	0.754094i	0.499082	+	0.0302851i
$621$	−3.91745			−0.157202
$622$	−2.73816	+	0.433682i	−0.109790	+	0.0173891i
$623$	−4.47252	+	28.2384i	−0.179188	+	1.13135i
$624$	9.88255	−	3.21104i	0.395619	−	0.128544i
$625$	−0.277733	−	24.9985i	−0.0111093	−	0.999938i
$626$		−	25.8385i		−	1.03271i
$627$	−9.77594	−	4.98109i	−0.390414	−	0.198926i
$628$	−3.35764	+	1.71080i	−0.133984	+	0.0682685i
$629$	−19.2966	−	6.26986i	−0.769408	−	0.249996i
$630$	4.25869	+	1.00992i	0.169670	+	0.0402361i
$631$	−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	$0.668283\pi$
$632$	0.969817	+	6.12318i	0.0385772	+	0.243567i
$633$	1.06542	−	6.72678i	0.0423465	−	0.267366i
$634$	−19.0935	−	6.20386i	−0.758301	−	0.246387i
$635$	26.5983	−	6.46388i	1.05552	−	0.256511i
$636$	2.08483	−	1.51472i	0.0826688	−	0.0600624i
$637$	−53.2587	+	27.1366i	−2.11018	+	1.07519i
$638$	−7.14982	−	1.13242i	−0.283064	−	0.0448330i
$639$	3.94577	−	5.43089i	0.156092	−	0.214842i
$640$	0.169248	−	2.22965i	0.00669011	−	0.0881348i
$641$	−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	$0.943997\pi$
$642$	−4.83837	+	2.46527i	−0.190955	+	0.0972966i
$643$	18.5790	+	36.4633i	0.732683	+	1.43797i	0.892604	+	0.450841i	$0.148876\pi$
$643$	18.5790	+	36.4633i	0.732683	+	1.43797i	−0.159922	+	0.987130i	$0.551124\pi$
$644$	1.07958	+	3.32261i	0.0425415	+	0.130929i
$645$	−0.630011	−	1.50911i	−0.0248066	−	0.0594212i
$646$			27.7059i			1.09007i
$647$	6.02196	−	11.8188i	0.236748	−	0.464643i	−0.741812	−	0.670608i	$-0.766033\pi$
$647$	6.02196	−	11.8188i	0.236748	−	0.464643i	0.978559	+	0.205965i	$0.0660333\pi$
$648$	−10.0538	−	1.59236i	−0.394949	−	0.0625537i
$649$	−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
$653$	5.78975	+	36.5550i	0.226570	+	1.43051i	0.794416	+	0.607374i	$0.207777\pi$
$653$	5.78975	+	36.5550i	0.226570	+	1.43051i	−0.567846	+	0.823135i	$0.692223\pi$
$654$	−29.9814	+	21.7828i	−1.17237	+	0.851773i
$655$	−14.8101	−	17.2432i	−0.578679	−	0.673748i
$656$	−9.64900			−0.376730
$657$	0.716938	+	0.716938i	0.0279704	+	0.0279704i
$658$	−2.53206	+	4.96945i	−0.0987101	+	0.193729i
$659$	−38.7022	−	12.5751i	−1.50762	−	0.489856i	−0.565392	−	0.824822i	$-0.691275\pi$
$659$	−38.7022	−	12.5751i	−1.50762	−	0.489856i	−0.942230	+	0.334966i	$0.891275\pi$
$660$	3.76920	+	3.20113i	0.146716	+	0.124604i
$661$	−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	$0.794886\pi$
$662$	4.05988	−	7.96796i	0.157792	−	0.309683i
$663$	57.3150	−	9.07781i	2.22593	−	0.352553i
$664$	−1.81919	+	1.32172i	−0.0705981	+	0.0512925i
$665$	30.2193	−	35.5819i	1.17185	−	1.37981i
$666$	0.993335	+	1.36721i	0.0384909	+	0.0529782i
$667$	0.791347	−	4.99637i	0.0306411	−	0.193460i
$668$	−1.99520	−	3.91580i	−0.0771966	−	0.151507i
$669$	14.2361	+	19.5944i	0.550401	+	0.757562i
$670$	−4.73388	+	19.9621i	−0.182886	+	0.771204i
$671$	−0.948154	−	2.91812i	−0.0366031	−	0.112653i
$672$	1.22540	+	7.73686i	0.0472708	+	0.298456i
$673$	−14.7849	−	29.0170i	−0.569916	−	1.11852i	−0.978586	−	0.205841i	$-0.934007\pi$
$673$	−14.7849	−	29.0170i	−0.569916	−	1.11852i	0.408670	−	0.912682i	$-0.365993\pi$
$674$	6.69761	−	20.6131i	0.257982	−	0.793988i
$675$	−7.41518	−	22.3975i	−0.285410	−	0.862079i
$676$	−18.1605			−0.698481
$677$	−0.595694	−	0.595694i	−0.0228944	−	0.0228944i	0.695567	−	0.718461i	$-0.255153\pi$
$677$	−0.595694	−	0.595694i	−0.0228944	−	0.0228944i	−0.718461	+	0.695567i	$0.755153\pi$
$678$	6.22020	+	3.16935i	0.238885	+	0.121718i
$679$	30.5920	+	42.1063i	1.17401	+	1.61589i
$680$	2.88138	−	12.1504i	0.110496	−	0.465946i
$681$			10.6190i			0.406922i
$682$	−6.32122	−	1.94849i	−0.242052	−	0.0746115i
$683$	−4.84392	−	4.84392i	−0.185347	−	0.185347i	0.608334	−	0.793681i	$-0.291838\pi$
$683$	−4.84392	−	4.84392i	−0.185347	−	0.185347i	−0.793681	+	0.608334i	$0.791838\pi$
$684$	1.35642	−	1.86695i	0.0518638	−	0.0713844i
$685$	20.5338	−	4.99008i	0.784554	−	0.190661i
$686$	−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
$690$	−2.23698	+	2.63395i	−0.0851606	+	0.100273i
$691$	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	$-0.000604801\pi$
$692$	−3.75480	+	0.594702i	−0.142736	+	0.0226072i
$693$	−2.07197	−	1.05572i	−0.0787075	−	0.0401035i
$694$	27.9789	+	20.3278i	1.06206	+	0.771634i
$695$	23.4527	−	38.5110i	0.889611	−	1.46080i
$696$	3.50500	−	10.7873i	0.132857	−	0.408891i
$697$	−53.2216	−	8.42947i	−2.01591	−	0.319289i
$698$	10.4791	+	1.65973i	0.396641	+	0.0628218i
$699$	−5.58334	+	17.1837i	−0.211181	+	0.649949i
$700$	−16.9531	+	12.4616i	−0.640767	+	0.471005i
$701$	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	$0.382775\pi$
$702$	23.4691	+	11.9581i	0.885785	+	0.451330i
$703$	17.8031	−	2.81974i	0.671458	−	0.106349i
$704$	−0.367124	+	1.12989i	−0.0138365	+	0.0425844i
$705$	−5.49859	+	0.448118i	−0.207089	+	0.0168771i
$706$	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	$0.0111035\pi$
$709$	5.62806	+	17.3214i	0.211366	+	0.650518i	−0.788025	+	0.615643i	$0.788896\pi$
$710$	7.62061	+	31.3582i	0.285996	+	1.17685i
$711$	1.69497	−	2.33293i	0.0635665	−	0.0874918i
$712$	−4.80419	−	4.80419i	−0.180045	−	0.180045i
$713$	1.36162	−	4.41733i	0.0509932	−	0.165430i
$714$			43.7452i			1.63712i
$715$	−7.78332	−	12.6224i	−0.291080	−	0.472051i
$716$	−9.82819	−	13.5273i	−0.367297	−	0.505541i
$717$	−0.727170	−	0.370512i	−0.0271567	−	0.0138370i
$718$	−16.1462	−	16.1462i	−0.602569	−	0.602569i
$719$	6.14397			0.229131			0.114566	−	0.993416i	$-0.463452\pi$
$719$	6.14397			0.229131			0.114566	+	0.993416i	$0.463452\pi$
$720$	−0.789014	+	0.677680i	−0.0294048	+	0.0252557i
$721$	−20.3441	+	62.6128i	−0.757655	+	2.33182i
$722$	−2.54849	−	5.00169i	−0.0948449	−	0.186144i
$723$	1.38012	+	8.71371i	0.0513271	+	0.324066i
$724$	−6.02410	−	18.5403i	−0.223884	−	0.689044i
$725$	30.0640	−	4.93300i	1.11655	−	0.183207i
$726$	10.4914	+	14.4402i	0.389372	+	0.535925i
$727$	−1.92035	−	3.76889i	−0.0712218	−	0.139781i	0.852650	−	0.522482i	$-0.174994\pi$
$727$	−1.92035	−	3.76889i	−0.0712218	−	0.139781i	−0.923872	+	0.382701i	$0.874994\pi$
$728$	3.67468	−	23.2010i	0.136193	−	0.859886i
$729$	−12.7057	−	17.4879i	−0.470581	−	0.647699i
$730$	−4.85800	+	0.395912i	−0.179802	+	0.0146533i
$731$	1.77503	−	1.28963i	0.0656518	−	0.0476988i
$732$	4.74839	−	0.752072i	0.175506	−	0.0277974i
$733$	3.16385	−	6.20941i	0.116860	−	0.229350i	−0.825166	−	0.564890i	$-0.808919\pi$
$733$	3.16385	−	6.20941i	0.116860	−	0.229350i	0.942026	+	0.335540i	$0.108919\pi$
$734$	−2.64189	−	1.91945i	−0.0975139	−	0.0708480i
$735$	28.8523	−	33.9723i	1.06423	−	1.25309i
$736$	−0.789579	−	0.256550i	−0.0291043	−	0.00945655i
$737$	4.94856	−	9.71210i	0.182283	−	0.357750i
$738$	3.17362	+	3.17362i	0.116822	+	0.116822i
$739$	20.3094			0.747093			0.373547	−	0.927611i	$-0.378142\pi$
$739$	20.3094			0.747093			0.373547	+	0.927611i	$0.378142\pi$
$740$	−8.10079	−	0.614912i	−0.297791	−	0.0226046i
$741$	−41.7068	+	30.3018i	−1.53214	+	1.11316i
$742$	−0.911315	−	5.75382i	−0.0334554	−	0.211229i
$743$	15.9341	−	15.9341i	0.584565	−	0.584565i	−0.351589	−	0.936154i	$-0.614359\pi$
$743$	15.9341	−	15.9341i	0.584565	−	0.584565i	0.936154	+	0.351589i	$0.114359\pi$
$744$	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
$747$	1.03306	+	0.163621i	0.0377978	+	0.00598658i
$748$	−3.01205	+	5.91149i	−0.110132	+	0.216145i
$749$			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	$0.989893\pi$
$752$	−0.601714	−	1.18093i	−0.0219422	−	0.0430641i
$753$	−13.1974	+	6.72439i	−0.480938	+	0.245050i
$754$	−19.9924	+	27.5172i	−0.728082	+	1.00212i
$755$	−23.0742	+	19.8183i	−0.839755	+	0.721262i
$756$	−11.6712	+	16.0641i	−0.424479	+	0.584245i
$757$	−19.2456	−	3.04821i	−0.699494	−	0.110789i	−0.203449	−	0.979086i	$-0.565215\pi$
$757$	−19.2456	−	3.04821i	−0.699494	−	0.110789i	−0.496045	+	0.868297i	$0.665215\pi$
$758$	8.46739	−	4.31435i	0.307550	−	0.156704i
$759$	1.48538	−	1.07919i	0.0539159	−	0.0391722i
$760$	2.61970	+	10.7798i	0.0950264	+	0.391026i
$761$	−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	$0.665249\pi$
$762$	3.56470	−	22.5066i	0.129135	−	0.815328i
$763$	13.1054	+	82.7443i	0.474448	+	2.99554i
$764$	2.76612	−	0.898766i	0.100075	−	0.0325162i
$765$	−4.94404	+	3.04863i	−0.178752	+	0.110224i
$766$	−0.101064	−	0.0328377i	−0.00365160	−	0.00118648i
$767$	−46.2397	+	23.5603i	−1.66962	+	0.850713i
$768$	−1.65860	−	0.845099i	−0.0598496	−	0.0304949i
$769$		−	8.22562i		−	0.296623i	−0.988941	−	0.148312i	$-0.952616\pi$
$769$		−	8.22562i		−	0.296623i	0.988941	−	0.148312i	$-0.0473839\pi$
$770$	10.3160	−	4.30665i	0.371765	−	0.155201i
$771$	−29.5312	+	9.59526i	−1.06354	+	0.345565i
$772$	−1.85392	+	11.7052i	−0.0667240	+	0.421279i
$773$	8.17919	−	1.29546i	0.294185	−	0.0465943i	−0.00759743	−	0.999971i	$-0.502418\pi$
$773$	8.17919	−	1.29546i	0.294185	−	0.0465943i	0.301782	+	0.953377i	$0.402418\pi$
$774$	−0.182746			−0.00656869
$775$	27.8329	−	0.576496i	0.999786	−	0.0207084i
$776$	−12.3682			−0.443991
$777$	28.1096	−	4.45212i	1.00843	−	0.159719i
$778$	−4.56716	+	28.8359i	−0.163741	+	1.03382i
$779$	45.5277	−	14.7928i	1.63120	−	0.530009i
$780$	21.4418	−	8.95134i	0.767740	−	0.320509i
$781$		−	17.1457i		−	0.613523i
$782$	−4.13101	−	2.10485i	−0.147724	−	0.0752694i
$783$	25.6177	−	13.0529i	0.915502	−	0.466471i
$784$	10.1839	+	3.30894i	0.363710	+	0.118177i
$785$	−7.17237	+	4.42268i	−0.255993	+	0.157852i
$786$	−17.9965	+	5.84741i	−0.641913	+	0.208570i
$787$	−2.36046	−	14.9034i	−0.0841414	−	0.531248i	−0.993371	−	0.114953i	$-0.963328\pi$
$787$	−2.36046	−	14.9034i	−0.0841414	−	0.531248i	0.909230	−	0.416295i	$-0.136672\pi$
$788$	−2.83557	+	17.9031i	−0.101013	+	0.637771i
$789$	17.9076	+	5.81852i	0.637526	+	0.207145i
$790$	3.27357	+	13.4705i	0.116468	+	0.479258i
$791$	12.7675	−	9.27611i	0.453959	−	0.329821i
$792$	0.492377	−	0.250879i	0.0174959	−	0.00891459i
$793$	−14.2393	−	2.25528i	−0.505652	−	0.0800874i
$794$	20.3291	−	27.9806i	0.721452	−	0.992994i
$795$	4.37129	−	3.75448i	0.155034	−	0.133158i
$796$	13.9534	−	19.2052i	0.494564	−	0.680709i
$797$	−42.8729	+	21.8448i	−1.51864	+	0.773783i	−0.996851	−	0.0792944i	$-0.974733\pi$
$797$	−42.8729	+	21.8448i	−1.51864	+	0.773783i	−0.521784	+	0.853078i	$0.674733\pi$
$798$	−17.6433	−	34.6268i	−0.624564	−	1.22578i
$799$	−2.28724	−	7.03939i	−0.0809167	−	0.249036i
$800$	−0.0277737	−	4.99992i	−0.000981948	−	0.176774i
$801$			3.16026i			0.111662i
$802$	17.6432	−	34.6268i	0.623004	−	1.22271i
$803$	2.55776	+	0.405109i	0.0902614	+	0.0142960i
$804$	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
$808$	1.75698	+	11.0931i	0.0618104	+	0.390256i
$809$	23.9080	−	17.3702i	0.840561	−	0.610704i	−0.0819660	−	0.996635i	$-0.526120\pi$
$809$	23.9080	−	17.3702i	0.840561	−	0.610704i	0.922527	+	0.385931i	$0.126120\pi$
$810$	−22.6958	−	1.72279i	−0.797449	−	0.0605326i
$811$	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
$813$	14.2630	−	27.9927i	0.500224	−	0.981745i
$814$	4.10512	+	1.33384i	0.143885	+	0.0467509i
$815$	29.8728	−	35.1739i	1.04640	−	1.23209i
$816$	−8.41015	−	6.11033i	−0.294414	−	0.213904i
$817$	−0.884903	+	1.73672i	−0.0309588	+	0.0607601i
$818$	−17.1238	+	2.71215i	−0.598721	+	0.0948281i
$819$	−8.83957	+	6.42233i	−0.308880	+	0.224414i
$820$	−21.5045	+	1.75255i	−0.750971	+	0.0612018i
$821$	−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	$-0.409106\pi$
$822$	2.75192	−	17.3750i	0.0959843	−	0.606021i
$823$	11.0234	+	21.6346i	0.384250	+	0.754134i	0.999413	−	0.0342666i	$-0.0109095\pi$
$823$	11.0234	+	21.6346i	0.384250	+	0.754134i	−0.615162	+	0.788400i	$0.710910\pi$
$824$	−9.19584	−	12.6570i	−0.320352	−	0.440927i
$825$	8.98175	+	6.44970i	0.312704	+	0.224550i
$826$	−12.0892	−	37.2068i	−0.420638	−	1.29459i
$827$	2.85018	+	17.9953i	0.0991105	+	0.625759i	0.986377	+	0.164502i	$0.0526016\pi$
$827$	2.85018	+	17.9953i	0.0991105	+	0.625759i	−0.887266	+	0.461258i	$0.847398\pi$
$828$	0.175317	+	0.344078i	0.00609267	+	0.0119575i
$829$	12.3268	−	37.9381i	0.428128	−	1.31764i	−0.471838	−	0.881685i	$-0.656409\pi$
$829$	12.3268	−	37.9381i	0.428128	−	1.31764i	0.899967	−	0.435959i	$-0.143591\pi$
$830$	−3.81432	+	3.27610i	−0.132397	+	0.113715i
$831$	38.8064			1.34618
$832$	3.94718	+	3.94718i	0.136844	+	0.136844i
$833$	53.2812	+	27.1481i	1.84608	+	0.940626i
$834$	−22.0636	−	30.3679i	−0.764000	−	1.05156i
$835$	−5.15789	−	8.36467i	−0.178496	−	0.289471i
$836$		−	5.89409i		−	0.203852i
$837$	24.8604	−	8.49625i	0.859299	−	0.293673i
$838$	10.7524	+	10.7524i	0.371435	+	0.371435i
$839$	−24.2440	+	33.3691i	−0.836997	+	1.15203i	0.149582	+	0.988749i	$0.452207\pi$
$839$	−24.2440	+	33.3691i	−0.836997	+	1.15203i	−0.986580	+	0.163279i	$0.947793\pi$
$840$	4.13627	+	17.0204i	0.142715	+	0.587260i
$841$	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
$845$	−40.4739	+	3.29850i	−1.39235	+	0.113472i
$846$	−0.190508	+	0.586323i	−0.00654979	+	0.0201582i
$847$	39.8527	−	6.31205i	1.36936	−	0.216885i
$848$	1.23348	+	0.628490i	0.0423579	+	0.0215824i
$849$	12.9120	+	9.38108i	0.443137	+	0.321958i
$850$	4.21479	−	27.6027i	0.144566	−	0.946763i
$851$	−0.932098	+	2.86870i	−0.0319519	+	0.0983378i
$852$	26.5342	+	4.20261i	0.909048	+	0.143979i
$853$	0.0585525	+	0.00927381i	0.00200480	+	0.000317529i	0.157437	−	0.987529i	$-0.449677\pi$
$853$	0.0585525	+	0.00927381i	0.00200480	+	0.000317529i	−0.155432	+	0.987847i	$0.549677\pi$
$854$	3.35840	−	10.3361i	0.114922	−	0.353694i
$855$	2.68392	−	4.40719i	0.0917881	−	0.150723i
$856$	−2.36002	−	1.71465i	−0.0806637	−	0.0586056i
$857$	−49.5511	−	25.2475i	−1.69263	−	0.862440i	−0.988291	−	0.152579i	$-0.951242\pi$
$857$	−49.5511	−	25.2475i	−1.69263	−	0.862440i	−0.704342	−	0.709861i	$-0.748758\pi$
$858$	−12.1931	+	1.93119i	−0.416264	+	0.0659298i
$859$	−0.0964604	+	0.296875i	−0.00329119	+	0.0101292i	−0.952689	−	0.303948i	$-0.901695\pi$
$859$	−0.0964604	+	0.296875i	−0.00329119	+	0.0101292i	0.949397	+	0.314077i	$0.101695\pi$
$860$	0.568689	−	0.669607i	0.0193921	−	0.0228334i
$861$	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	$-0.905561\pi$
$863$	−19.5049	+	19.5049i	−0.663955	+	0.663955i	0.292355	+	0.956310i	$0.405561\pi$
$864$	−1.45813	−	4.48766i	−0.0496066	−	0.152673i
$865$	−8.26023	+	2.00739i	−0.280856	+	0.0682532i
$866$	−13.9932	+	19.2601i	−0.475510	+	0.654483i
$867$	−18.6737	−	18.6737i	−0.634193	−	0.634193i
$868$	−14.0573	−	18.7441i	−0.477134	−	0.636216i
$869$		−	7.36525i		−	0.249849i
$870$	5.85222	−	24.6780i	0.198409	−	0.836663i
$871$	−30.1039	−	41.4345i	−1.02003	−	1.40395i
$872$	−17.7384	−	9.03817i	−0.600698	−	0.306071i
$873$	4.06797	+	4.06797i	0.137680	+	0.137680i
$874$	4.11885			0.139322
$875$	−35.5196	+	30.8521i	−1.20078	+	1.04299i
$876$	−1.25387	+	3.85902i	−0.0423643	+	0.130384i
$877$	−5.57451	−	10.9406i	−0.188238	−	0.369437i	0.777530	−	0.628846i	$-0.216472\pi$
$877$	−5.57451	−	10.9406i	−0.188238	−	0.369437i	−0.965768	+	0.259409i	$0.916472\pi$
$878$	3.15113	+	19.8954i	0.106345	+	0.671438i
$879$	7.38495	+	22.7285i	0.249088	+	0.766615i
$880$	−0.612979	+	2.58485i	−0.0206635	+	0.0871351i
$881$	−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	$-0.427707\pi$
$882$	−2.26121	−	4.43788i	−0.0761389	−	0.149431i
$883$	−5.54823	+	35.0301i	−0.186713	+	1.17886i	0.699172	+	0.714953i	$0.253552\pi$
$883$	−5.54823	+	35.0301i	−0.186713	+	1.17886i	−0.885885	+	0.463905i	$0.846448\pi$
$884$	18.3234	+	25.2200i	0.616283	+	0.848241i
$885$	25.0499	−	29.4951i	0.842042	−	0.991468i
$886$	−16.8404	+	12.2352i	−0.565763	+	0.411051i
$887$	10.3615	−	1.64110i	0.347904	−	0.0551026i	0.0199629	−	0.999801i	$-0.493645\pi$
$887$	10.3615	−	1.64110i	0.347904	−	0.0551026i	0.327941	+	0.944698i	$0.393645\pi$
$888$	−3.07042	+	6.02603i	−0.103036	+	0.202220i
$889$	−41.6746	−	30.2784i	−1.39772	−	1.01550i
$890$	−11.5796	−	9.83442i	−0.388149	−	0.329650i
$891$	11.5012	+	3.73698i	0.385306	+	0.125194i
$892$	−5.90690	+	11.5930i	−0.197778	+	0.388161i
$893$	4.64960	+	4.64960i	0.155593	+	0.155593i
$894$	29.0247			0.970732
$895$	−24.3609	−	28.3630i	−0.814294	−	0.948071i
$896$	−3.40441	+	2.47345i	−0.113733	+	0.0826322i
$897$	−1.34954	−	8.52064i	−0.0450597	−	0.284496i
$898$	−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
$902$	11.3222	+	1.79327i	0.376990	+	0.0597093i
$903$	−1.39718	+	2.74213i	−0.0464954	+	0.0912523i
$904$			3.75027i			0.124732i
$905$	−16.7933	−	40.2262i	−0.558227	−	1.33716i
$906$	7.82477	+	24.0822i	0.259961	+	0.800077i
$907$	−8.50158	−	16.6853i	−0.282290	−	0.554026i	0.705706	−	0.708505i	$-0.250630\pi$
$907$	−8.50158	−	16.6853i	−0.282290	−	0.554026i	−0.987996	+	0.154479i	$0.950630\pi$
$908$	−5.08282	+	2.58982i	−0.168679	+	0.0859464i
$909$	3.07072	−	4.22649i	0.101849	−	0.140184i
$910$	3.97567	−	52.3750i	0.131792	−	1.73621i
$911$	−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	$0.311633\pi$
$912$	9.12152	+	1.44471i	0.302044	+	0.0478390i
$913$	2.38029	−	1.21282i	0.0787762	−	0.0401385i
$914$	−0.319004	+	0.231770i	−0.0105517	+	0.00766626i
$915$	10.4460	−	2.53858i	0.345336	−	0.0839229i
$916$	16.2049	+	5.26528i	0.535424	+	0.173970i
$917$	−6.69171	+	42.2498i	−0.220980	+	1.39521i
$918$	−4.12223	−	26.0267i	−0.136054	−	0.859010i
$919$	−21.7367	+	7.06268i	−0.717028	+	0.232976i	−0.644734	−	0.764407i	$-0.723032\pi$
$919$	−21.7367	+	7.06268i	−0.717028	+	0.232976i	−0.0722937	+	0.997383i	$0.523032\pi$
$920$	−1.80632	−	0.428356i	−0.0595525	−	0.0141225i
$921$	−6.75557	−	2.19502i	−0.222604	−	0.0723283i
$922$	11.2864	−	5.75073i	0.371699	−	0.189390i
$923$	−71.7809	−	36.5742i	−2.36270	−	1.20385i
$924$		−	9.30626i		−	0.306153i
$925$	−18.1657	+	0.100907i	−0.597286	+	0.00331782i
$926$	−26.8949	+	8.73869i	−0.883822	+	0.287171i
$927$	−1.13839	+	7.18753i	−0.0373897	+	0.236069i
$928$	6.01818	−	0.953186i	0.197556	−	0.0312899i
$929$	−6.38567			−0.209507			−0.104754	−	0.994498i	$-0.533405\pi$
$929$	−6.38567			−0.209507			−0.104754	+	0.994498i	$0.533405\pi$
$930$	8.48346	−	21.5668i	0.278184	−	0.707204i
$931$	−53.1244			−1.74108
$932$	−9.58674	+	1.51839i	−0.314024	+	0.0497365i
$933$	−0.807295	+	5.09706i	−0.0264297	+	0.166870i
$934$	4.82787	−	1.56867i	0.157973	−	0.0513284i
$935$	−5.63919	+	13.7219i	−0.184421	+	0.448754i
$936$		−	2.59651i		−	0.0848694i
$937$	39.9822	+	20.3719i	1.30616	+	0.665522i	0.961913	−	0.273357i	$-0.0881340\pi$
$937$	39.9822	+	20.3719i	1.30616	+	0.665522i	0.344248	+	0.938879i	$0.388134\pi$
$938$	34.4007	−	17.5280i	1.12322	−	0.572311i
$939$	−45.7440	−	14.8631i	−1.49280	−	0.485040i
$940$	−1.55552	−	2.52262i	−0.0507355	−	0.0822789i
$941$	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	$0.0508103\pi$
$942$	1.09735	+	6.92842i	0.0357537	+	0.225740i
$943$	−1.25315	+	7.91210i	−0.0408083	+	0.257653i
$944$	8.84175	+	2.87286i	0.287774	+	0.0935035i
$945$	−23.0937	+	37.9215i	−0.751239	+	1.23359i
$946$	−0.377615	+	0.274354i	−0.0122773	+	0.00892001i
$947$	42.4973	−	21.6535i	1.38098	−	0.703643i	0.403558	−	0.914954i	$-0.367773\pi$
$947$	42.4973	−	21.6535i	1.38098	−	0.703643i	0.977419	+	0.211311i	$0.0677734\pi$
$948$	11.3982	+	1.80530i	0.370198	+	0.0586336i
$949$	7.15205	−	9.84395i	0.232165	−	0.319548i
$950$	7.79641	+	23.5490i	0.252949	+	0.764030i
$951$	−21.9664	+	30.2342i	−0.712310	+	0.980410i
$952$	−20.9388	+	10.6688i	−0.678629	+	0.345779i
$953$	11.3242	+	22.2250i	0.366828	+	0.719940i	0.998469	−	0.0553212i	$-0.0176183\pi$
$953$	11.3242	+	22.2250i	0.366828	+	0.719940i	−0.631641	+	0.775261i	$0.717618\pi$
$954$	−0.198985	−	0.612414i	−0.00644239	−	0.0198276i
$955$	6.00155	−	2.50547i	0.194205	−	0.0810752i
$956$		−	0.438424i		−	0.0141797i
$957$	−6.11762	+	12.0065i	−0.197755	+	0.388115i
$958$	37.2557	+	5.90072i	1.20368	+	0.190643i
$959$	−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
$963$	0.212264	+	1.34018i	0.00684012	+	0.0431868i
$964$	−3.83425	+	2.78575i	−0.123493	+	0.0897228i
$965$	−2.00577	+	26.4238i	−0.0645681	+	0.850613i
$966$	6.50331			0.209240
$967$	12.0665	+	12.0665i	0.388034	+	0.388034i	0.873986	−	0.485952i	$-0.161527\pi$
$967$	12.0665	+	12.0665i	0.388034	+	0.388034i	−0.485952	+	0.873986i	$0.661527\pi$
$968$	−4.35312	+	8.54348i	−0.139915	+	0.274598i
$969$	49.0501	+	15.9373i	1.57571	+	0.511981i
$970$	−27.5647	+	2.24643i	−0.885048	+	0.0721287i
$971$	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	$0.512559\pi$
$972$	−2.17571	+	4.27007i	−0.0697859	+	0.136963i
$973$	−83.8110	+	13.2744i	−2.68686	+	0.425557i
$974$	−26.7083	+	19.4047i	−0.855790	+	0.621768i
$975$	46.1611	−	23.8442i	1.47834	−	0.763624i
$976$	1.51805	+	2.08941i	0.0485915	+	0.0668804i
$977$	−2.13117	+	13.4557i	−0.0681822	+	0.430485i	0.929859	+	0.367917i	$0.119929\pi$
$977$	−2.13117	+	13.4557i	−0.0681822	+	0.430485i	−0.998041	+	0.0625680i	$0.980071\pi$
$978$	−17.4410	−	34.2298i	−0.557700	−	1.09455i
$979$	4.74443	+	6.53015i	0.151633	+	0.208705i
$980$	23.2976	+	5.52487i	0.744215	+	0.176486i
$981$	2.86156	+	8.80698i	0.0913626	+	0.281185i
$982$	−4.04156	−	25.5174i	−0.128971	−	0.814293i
$983$	2.26878	+	4.45273i	0.0723628	+	0.142020i	0.924354	−	0.381536i	$-0.124605\pi$
$983$	2.26878	+	4.45273i	0.0723628	+	0.142020i	−0.851991	+	0.523556i	$0.824605\pi$
$984$	−5.55041	+	17.0824i	−0.176941	+	0.544568i
$985$	−3.06783	+	40.4153i	−0.0977492	+	1.28774i
$986$	34.0276			1.08366
$987$	7.34131	+	7.34131i	0.233676	+	0.233676i
$988$	−24.6757	−	12.5729i	−0.785039	−	0.399998i
$989$	−0.191721	−	0.263881i	−0.00609638	−	0.00839094i
$990$	1.05178	−	0.648559i	0.0334279	−	0.0206126i
$991$			5.52082i			0.175375i	0.996148	+	0.0876873i	$0.0279476\pi$
$991$			5.52082i			0.175375i	−0.996148	+	0.0876873i	$0.972052\pi$
$992$	5.56712	−	0.0843767i	0.176756	−	0.00267896i
$993$	−11.7710	−	11.7710i	−0.373540	−	0.373540i
$994$	35.6968	−	49.1324i	1.13223	−	1.55838i
$995$	27.6094	−	45.3365i	0.875275	−	1.43726i
$996$	1.29349	+	3.98095i	0.0409857	+	0.126141i
$997$	−29.9849	+	29.9849i	−0.949633	+	0.949633i	−0.998791	−	0.0491581i	$-0.984346\pi$
$997$	−29.9849	+	29.9849i	−0.949633	+	0.949633i	0.0491581	+	0.998791i	$0.484346\pi$
$998$	−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.153.14	yes	128
5.2	odd	4	inner	310.2.s.a.277.11	yes	128
31.15	odd	10	inner	310.2.s.a.263.11	yes	128
155.77	even	20	inner	310.2.s.a.77.14	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.s.a.77.14	✓	128	155.77	even	20	inner
310.2.s.a.153.14	yes	128	1.1	even	1	trivial
310.2.s.a.263.11	yes	128	31.15	odd	10	inner
310.2.s.a.277.11	yes	128	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.987688 - 0.156434i) q^{2} +(0.291201 - 1.83857i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.06347 - 0.861441i) q^{5} -1.86149i q^{6} +(-3.74943 - 1.91043i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-0.442378 - 0.143737i) q^{9} +O(q^{10})\)	\(q+(0.987688 - 0.156434i) q^{2} +(0.291201 - 1.83857i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.06347 - 0.861441i) q^{5} -1.86149i q^{6} +(-3.74943 - 1.91043i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-0.442378 - 0.143737i) q^{9} +(1.90331 - 1.17363i) q^{10} +(-1.12989 + 0.367124i) q^{11} +(-0.291201 - 1.83857i) q^{12} +(-0.873242 + 5.51343i) q^{13} +(-4.00213 - 1.30037i) q^{14} +(-0.982934 - 4.04470i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.97584 - 2.53532i) q^{17} +(-0.459417 - 0.0727645i) q^{18} +(-2.91612 + 4.01370i) q^{19} +(1.69628 - 1.45693i) q^{20} +(-4.60430 + 6.33728i) q^{21} +(-1.05855 + 0.539358i) q^{22} +(-0.376909 - 0.739725i) q^{23} +(-0.575232 - 1.77038i) q^{24} +(3.51584 - 3.55512i) q^{25} +5.58216i q^{26} +(2.14220 - 4.20431i) q^{27} +(-4.15628 - 0.658289i) 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} +(0.345958 + 2.18429i) q^{33} +(4.51797 - 3.28250i) q^{34} +(-9.38257 - 0.712209i) q^{35} -0.465144 q^{36} +(-2.56906 - 2.56906i) q^{37} +(-2.25234 + 4.42046i) q^{38} +(9.88255 + 3.21104i) q^{39} +(1.44748 - 1.70435i) q^{40} +(-7.80621 - 5.67154i) q^{41} +(-3.55625 + 6.97953i) q^{42} +(0.388045 - 0.0614603i) q^{43} +(-0.961143 + 0.698311i) q^{44} +(-1.03666 + 0.0844843i) q^{45} +(-0.487987 - 0.671656i) q^{46} +(0.207336 - 1.30907i) q^{47} +(-0.845099 - 1.65860i) q^{48} +(6.29399 + 8.66293i) q^{49} +(2.91641 - 4.06135i) q^{50} +(-3.21239 - 9.88673i) q^{51} +(0.873242 + 5.51343i) q^{52} +(0.628490 + 1.23348i) q^{53} +(1.45813 - 4.48766i) q^{54} +(-2.01524 + 1.73088i) q^{55} -4.20808 q^{56} +(6.53029 + 6.53029i) q^{57} +(5.42908 + 2.76625i) q^{58} +(5.46450 + 7.52124i) q^{59} +(-2.18471 - 3.54299i) q^{60} +2.58265i q^{61} +(4.55349 + 3.20401i) q^{62} +(1.38406 + 1.38406i) q^{63} +(0.587785 - 0.809017i) q^{64} +(2.94758 + 12.1291i) 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} +(-9.37847 + 0.764316i) q^{70} +(-4.45973 + 13.7256i) q^{71} +(-0.459417 + 0.0727645i) q^{72} +(-1.94218 - 0.989592i) q^{73} +(-2.93932 - 2.13554i) q^{74} +(-5.51252 - 7.49938i) q^{75} +(-1.53310 + 4.71838i) q^{76} +(4.93781 + 0.782073i) q^{77} +(10.2632 + 1.62553i) q^{78} +(-1.91575 + 5.89608i) q^{79} +(1.16304 - 1.90980i) q^{80} +(-8.23504 - 5.98311i) q^{81} +(-8.59732 - 4.38056i) q^{82} +(-2.22095 + 0.351764i) q^{83} +(-2.42062 + 7.44992i) q^{84} +(8.08349 - 9.51795i) 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} +(-1.01068 + 0.245613i) q^{90} +(13.8072 - 19.0040i) q^{91} +(-0.587049 - 0.587049i) q^{92} +(8.29164 - 6.21837i) q^{93} -1.32539i q^{94} +(-2.55978 + 10.7942i) q^{95} +(-1.09416 - 1.50598i) q^{96} +(-11.0201 - 5.61503i) 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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