LMFDB - Embedded newform 124.4.e.b.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,4,Mod(5,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("124.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	124.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.31623684071$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.250722553392.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 46x^{4} - 24x^{3} + 2116x^{2} - 552x + 144 $ x^6 + 46x^4 - 24x^3 + 2116x^2 - 552x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.2
Root			$0.130629 - 0.226255i$ of defining polynomial
Character	$\chi$	$=$	124.25
Dual form			124.4.e.b.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36937 - 2.37182i) q^{3} +(-0.238743 + 0.413515i) q^{5} +(7.63063 + 13.2166i) q^{7} +(9.74964 - 16.8869i) q^{9} +O(q^{10})$	\(q+(-1.36937 - 2.37182i) q^{3} +(-0.238743 + 0.413515i) q^{5} +(7.63063 + 13.2166i) q^{7} +(9.74964 - 16.8869i) q^{9} +(24.8127 - 42.9769i) q^{11} +(4.05664 - 7.02631i) q^{13} +1.30771 q^{15} +(-25.1364 - 43.5375i) q^{17} +(-81.6871 - 141.486i) q^{19} +(20.8983 - 36.1970i) q^{21} +200.635 q^{23} +(62.3860 + 108.056i) q^{25} -127.350 q^{27} +90.6344 q^{29} +(-4.76141 - 172.535i) q^{31} -135.911 q^{33} -7.28703 q^{35} +(105.719 + 183.110i) q^{37} -22.2202 q^{39} +(-131.637 + 228.002i) q^{41} +(42.2922 + 73.2522i) q^{43} +(4.65531 + 8.06324i) q^{45} +19.3667 q^{47} +(55.0470 - 95.3442i) q^{49} +(-68.8420 + 119.238i) q^{51} +(-229.078 + 396.776i) q^{53} +(11.8477 + 20.5209i) q^{55} +(-223.720 + 387.494i) q^{57} +(34.1870 + 59.2136i) q^{59} -573.316 q^{61} +297.584 q^{63} +(1.93699 + 3.35496i) q^{65} +(446.743 - 773.781i) q^{67} +(-274.745 - 475.871i) q^{69} +(-487.761 + 844.827i) q^{71} +(-475.727 + 823.983i) q^{73} +(170.859 - 295.937i) q^{75} +757.347 q^{77} +(149.833 + 259.518i) q^{79} +(-88.8515 - 153.895i) q^{81} +(133.695 - 231.567i) q^{83} +24.0045 q^{85} +(-124.112 - 214.968i) q^{87} +901.640 q^{89} +123.819 q^{91} +(-402.702 + 247.558i) q^{93} +78.0088 q^{95} +29.7796 q^{97} +(-483.831 - 838.019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} - 3 q^{5} + 45 q^{7} - 38 q^{9}+O(q^{10}) $ 6 * q - 9 * q^3 - 3 * q^5 + 45 * q^7 - 38 * q^9	$ 6 q - 9 q^{3} - 3 q^{5} + 45 q^{7} - 38 q^{9} + 61 q^{11} + 113 q^{13} + 386 q^{15} + 123 q^{17} + 63 q^{19} + 43 q^{21} + 96 q^{23} + 4 q^{25} + 918 q^{27} + 332 q^{29} - 668 q^{31} - 1214 q^{33} + 278 q^{35} + 129 q^{37} - 14 q^{39} - 709 q^{41} + 107 q^{43} - 1214 q^{45} - 568 q^{47} + 262 q^{49} + 293 q^{51} - 1267 q^{53} + 909 q^{55} + 681 q^{57} - 989 q^{59} - 2500 q^{61} + 36 q^{63} - 551 q^{65} + 741 q^{67} + 440 q^{69} - 1089 q^{71} - 197 q^{73} - 500 q^{75} + 982 q^{77} + 677 q^{79} - 2423 q^{81} + q^{83} + 58 q^{85} + 1194 q^{87} - 564 q^{89} + 4054 q^{91} + 1439 q^{93} - 2094 q^{95} - 2092 q^{97} + 2086 q^{99}+O(q^{100}) $ 6 * q - 9 * q^3 - 3 * q^5 + 45 * q^7 - 38 * q^9 + 61 * q^11 + 113 * q^13 + 386 * q^15 + 123 * q^17 + 63 * q^19 + 43 * q^21 + 96 * q^23 + 4 * q^25 + 918 * q^27 + 332 * q^29 - 668 * q^31 - 1214 * q^33 + 278 * q^35 + 129 * q^37 - 14 * q^39 - 709 * q^41 + 107 * q^43 - 1214 * q^45 - 568 * q^47 + 262 * q^49 + 293 * q^51 - 1267 * q^53 + 909 * q^55 + 681 * q^57 - 989 * q^59 - 2500 * q^61 + 36 * q^63 - 551 * q^65 + 741 * q^67 + 440 * q^69 - 1089 * q^71 - 197 * q^73 - 500 * q^75 + 982 * q^77 + 677 * q^79 - 2423 * q^81 + q^83 + 58 * q^85 + 1194 * q^87 - 564 * q^89 + 4054 * q^91 + 1439 * q^93 - 2094 * q^95 - 2092 * q^97 + 2086 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−1.36937	−	2.37182i	−0.263536	−	0.456457i	0.703643	−	0.710553i	$-0.251555\pi$
$3$	−1.36937	−	2.37182i	−0.263536	−	0.456457i	−0.967179	+	0.254096i	$0.918222\pi$
$4$		0			0
$5$	−0.238743	+	0.413515i	−0.0213538	+	0.0369859i	−0.876505	−	0.481393i	$-0.840131\pi$
$5$	−0.238743	+	0.413515i	−0.0213538	+	0.0369859i	0.855151	+	0.518379i	$0.173464\pi$
$6$		0			0
$7$	7.63063	+	13.2166i	0.412015	+	0.713631i	0.995110	−	0.0987728i	$-0.0314917\pi$
$7$	7.63063	+	13.2166i	0.412015	+	0.713631i	−0.583095	+	0.812404i	$0.698158\pi$
$8$		0			0
$9$	9.74964	−	16.8869i	0.361098	−	0.625440i
$10$		0			0
$11$	24.8127	−	42.9769i	0.680120	−	1.17800i	−0.294824	−	0.955552i	$-0.595261\pi$
$11$	24.8127	−	42.9769i	0.680120	−	1.17800i	0.974944	−	0.222451i	$-0.0714056\pi$
$12$		0			0
$13$	4.05664	−	7.02631i	0.0865469	−	0.149904i	−0.819502	−	0.573076i	$-0.805750\pi$
$13$	4.05664	−	7.02631i	0.0865469	−	0.149904i	0.906049	+	0.423172i	$0.139083\pi$
$14$		0			0
$15$	1.30771			0.0225100
$16$		0			0
$17$	−25.1364	−	43.5375i	−0.358615	−	0.621140i	0.629114	−	0.777313i	$-0.283418\pi$
$17$	−25.1364	−	43.5375i	−0.358615	−	0.621140i	−0.987730	+	0.156173i	$0.950084\pi$
$18$		0			0
$19$	−81.6871	−	141.486i	−0.986332	−	1.70838i	−0.635860	−	0.771804i	$-0.719355\pi$
$19$	−81.6871	−	141.486i	−0.986332	−	1.70838i	−0.350472	−	0.936573i	$-0.613979\pi$
$20$		0			0
$21$	20.8983	−	36.1970i	0.217161	−	0.376135i
$22$		0			0
$23$	200.635			1.81893			0.909465	−	0.415780i	$-0.136491\pi$
$23$	200.635			1.81893			0.909465	+	0.415780i	$0.136491\pi$
$24$		0			0
$25$	62.3860	+	108.056i	0.499088	+	0.864446i
$26$		0			0
$27$	−127.350			−0.907720
$28$		0			0
$29$	90.6344			0.580358			0.290179	−	0.956972i	$-0.406285\pi$
$29$	90.6344			0.580358			0.290179	+	0.956972i	$0.406285\pi$
$30$		0			0
$31$	−4.76141	−	172.535i	−0.0275863	−	0.999619i
$31$	−4.76141	−	172.535i	−0.0275863	−	0.999619i
$32$		0			0
$33$	−135.911			−0.716943
$34$		0			0
$35$	−7.28703			−0.0351924
$36$		0			0
$37$	105.719	+	183.110i	0.469731	+	0.813599i	0.999401	−	0.0346054i	$-0.0110175\pi$
$37$	105.719	+	183.110i	0.469731	+	0.813599i	−0.529670	+	0.848204i	$0.677684\pi$
$38$		0			0
$39$	−22.2202			−0.0912328
$40$		0			0
$41$	−131.637	+	228.002i	−0.501421	+	0.868486i	0.498578	+	0.866845i	$0.333856\pi$
$41$	−131.637	+	228.002i	−0.501421	+	0.868486i	−0.999999	+	0.00164149i	$0.999477\pi$
$42$		0			0
$43$	42.2922	+	73.2522i	0.149988	+	0.259787i	0.931223	−	0.364450i	$-0.118743\pi$
$43$	42.2922	+	73.2522i	0.149988	+	0.259787i	−0.781235	+	0.624238i	$0.785410\pi$
$44$		0			0
$45$	4.65531	+	8.06324i	0.0154216	+	0.0267110i
$46$		0			0
$47$	19.3667			0.0601049			0.0300525	−	0.999548i	$-0.490433\pi$
$47$	19.3667			0.0601049			0.0300525	+	0.999548i	$0.490433\pi$
$48$		0			0
$49$	55.0470	−	95.3442i	0.160487	−	0.277972i
$50$		0			0
$51$	−68.8420	+	119.238i	−0.189016	+	0.327385i
$52$		0			0
$53$	−229.078	+	396.776i	−0.593705	+	1.02833i	0.400024	+	0.916505i	$0.369002\pi$
$53$	−229.078	+	396.776i	−0.593705	+	1.02833i	−0.993728	+	0.111822i	$0.964331\pi$
$54$		0			0
$55$	11.8477	+	20.5209i	0.0290463	+	0.0503097i
$56$		0			0
$57$	−223.720	+	387.494i	−0.519867	+	0.900437i
$58$		0			0
$59$	34.1870	+	59.2136i	0.0754367	+	0.130660i	0.901276	−	0.433245i	$-0.142632\pi$
$59$	34.1870	+	59.2136i	0.0754367	+	0.130660i	−0.825839	+	0.563905i	$0.809298\pi$
$60$		0			0
$61$	−573.316			−1.20337			−0.601686	−	0.798733i	$-0.705504\pi$
$61$	−573.316			−1.20337			−0.601686	+	0.798733i	$0.705504\pi$
$62$		0			0
$63$	297.584			0.595111
$64$		0			0
$65$	1.93699	+	3.35496i	0.00369621	+	0.00640203i
$66$		0			0
$67$	446.743	−	773.781i	0.814602	−	1.41093i	−0.0950119	−	0.995476i	$-0.530289\pi$
$67$	446.743	−	773.781i	0.814602	−	1.41093i	0.909614	−	0.415455i	$-0.136378\pi$
$68$		0			0
$69$	−274.745	−	475.871i	−0.479353	−	0.830264i
$70$		0			0
$71$	−487.761	+	844.827i	−0.815304	+	1.41215i	0.0938054	+	0.995591i	$0.470097\pi$
$71$	−487.761	+	844.827i	−0.815304	+	1.41215i	−0.909109	+	0.416557i	$0.863236\pi$
$72$		0			0
$73$	−475.727	+	823.983i	−0.762734	+	1.32109i	0.178702	+	0.983903i	$0.442810\pi$
$73$	−475.727	+	823.983i	−0.762734	+	1.32109i	−0.941436	+	0.337191i	$0.890523\pi$
$74$		0			0
$75$	170.859	−	295.937i	0.263055	−	0.455625i
$76$		0			0
$77$	757.347			1.12088
$78$		0			0
$79$	149.833	+	259.518i	0.213386	+	0.369595i	0.952772	−	0.303686i	$-0.0982175\pi$
$79$	149.833	+	259.518i	0.213386	+	0.369595i	−0.739386	+	0.673282i	$0.764884\pi$
$80$		0			0
$81$	−88.8515	−	153.895i	−0.121881	−	0.211105i
$82$		0			0
$83$	133.695	−	231.567i	0.176806	−	0.306238i	−0.763978	−	0.645242i	$-0.776757\pi$
$83$	133.695	−	231.567i	0.176806	−	0.306238i	0.940785	+	0.339004i	$0.110090\pi$
$84$		0			0
$85$	24.0045			0.0306312
$86$		0			0
$87$	−124.112	−	214.968i	−0.152945	−	0.264909i
$88$		0			0
$89$	901.640			1.07386			0.536930	−	0.843627i	$-0.319584\pi$
$89$	901.640			1.07386			0.536930	+	0.843627i	$0.319584\pi$
$90$		0			0
$91$	123.819			0.142635
$92$		0			0
$93$	−402.702	+	247.558i	−0.449013	+	0.276027i
$94$		0			0
$95$	78.0088			0.0842478
$96$		0			0
$97$	29.7796			0.0311718			0.0155859	−	0.999879i	$-0.495039\pi$
$97$	29.7796			0.0311718			0.0155859	+	0.999879i	$0.495039\pi$
$98$		0			0
$99$	−483.831	−	838.019i	−0.491180	−	0.850748i
$100$		0			0
$101$	969.046			0.954689			0.477345	−	0.878716i	$-0.341599\pi$
$101$	969.046			0.954689			0.477345	+	0.878716i	$0.341599\pi$
$102$		0			0
$103$	809.051	−	1401.32i	0.773963	−	1.34054i	−0.161412	−	0.986887i	$-0.551605\pi$
$103$	809.051	−	1401.32i	0.773963	−	1.34054i	0.935375	−	0.353656i	$-0.115062\pi$
$104$		0			0
$105$	9.97865	+	17.2835i	0.00927444	+	0.0160638i
$106$		0			0
$107$	−556.524	−	963.928i	−0.502815	−	0.870901i	−0.999995	−	0.00325347i	$-0.998964\pi$
$107$	−556.524	−	963.928i	−0.502815	−	0.870901i	0.497180	−	0.867648i	$-0.334369\pi$
$108$		0			0
$109$	−889.244			−0.781414			−0.390707	−	0.920515i	$-0.627769\pi$
$109$	−889.244			−0.781414			−0.390707	+	0.920515i	$0.627769\pi$
$110$		0			0
$111$	289.537	−	501.492i	0.247582	−	0.428824i
$112$		0			0
$113$	−64.8880	+	112.389i	−0.0540190	+	0.0935637i	−0.891770	−	0.452488i	$-0.850537\pi$
$113$	−64.8880	+	112.389i	−0.0540190	+	0.0935637i	0.837751	+	0.546052i	$0.183870\pi$
$114$		0			0
$115$	−47.9003	+	82.9657i	−0.0388411	+	0.0672747i
$116$		0			0
$117$	−79.1016	−	137.008i	−0.0625038	−	0.108260i
$118$		0			0
$119$	383.612	−	664.436i	0.295510	−	0.511838i
$120$		0			0
$121$	−565.843	−	980.069i	−0.425126	−	0.736340i
$122$		0			0
$123$	721.040			0.528569
$124$		0			0
$125$	−119.263			−0.0853373
$126$		0			0
$127$	−147.491	−	255.462i	−0.103053	−	0.178493i	0.809888	−	0.586584i	$-0.199528\pi$
$127$	−147.491	−	255.462i	−0.103053	−	0.178493i	−0.912941	+	0.408092i	$0.866194\pi$
$128$		0			0
$129$	115.827	−	200.619i	0.0790546	−	0.136927i
$130$		0			0
$131$	1425.49	+	2469.02i	0.950731	+	1.64671i	0.743848	+	0.668349i	$0.232999\pi$
$131$	1425.49	+	2469.02i	0.950731	+	1.64671i	0.206883	+	0.978366i	$0.433668\pi$
$132$		0			0
$133$	1246.65	−	2159.26i	0.812768	−	1.40775i
$134$		0			0
$135$	30.4038	−	52.6609i	0.0193833	−	0.0335728i
$136$		0			0
$137$	−978.678	+	1695.12i	−0.610322	+	1.05711i	0.380864	+	0.924631i	$0.375626\pi$
$137$	−978.678	+	1695.12i	−0.610322	+	1.05711i	−0.991186	+	0.132477i	$0.957707\pi$
$138$		0			0
$139$	−557.416			−0.340140			−0.170070	−	0.985432i	$-0.554399\pi$
$139$	−557.416			−0.340140			−0.170070	+	0.985432i	$0.554399\pi$
$140$		0			0
$141$	−26.5203	−	45.9345i	−0.0158398	−	0.0274353i
$142$		0			0
$143$	−201.313	−	348.684i	−0.117725	−	0.203905i
$144$		0			0
$145$	−21.6383	+	37.4786i	−0.0123928	+	0.0214650i
$146$		0			0
$147$	−301.519			−0.169176
$148$		0			0
$149$	767.388	+	1329.15i	0.421925	+	0.730796i	0.996128	−	0.0879173i	$-0.0280211\pi$
$149$	767.388	+	1329.15i	0.421925	+	0.730796i	−0.574202	+	0.818713i	$0.694688\pi$
$150$		0			0
$151$	−2423.59			−1.30615			−0.653075	−	0.757293i	$-0.726521\pi$
$151$	−2423.59			−1.30615			−0.653075	+	0.757293i	$0.726521\pi$
$152$		0			0
$153$	−980.282			−0.517981
$154$		0			0
$155$	72.4825	+	39.2226i	0.0375609	+	0.0203254i
$156$		0			0
$157$	−1172.57			−0.596058			−0.298029	−	0.954557i	$-0.596329\pi$
$157$	−1172.57			−0.596058			−0.298029	+	0.954557i	$0.596329\pi$
$158$		0			0
$159$	1254.77			0.625849
$160$		0			0
$161$	1530.97	+	2651.73i	0.749427	+	1.29805i
$162$		0			0
$163$	−655.148			−0.314817			−0.157408	−	0.987534i	$-0.550314\pi$
$163$	−655.148			−0.314817			−0.157408	+	0.987534i	$0.550314\pi$
$164$		0			0
$165$	32.4479	−	56.2013i	0.0153095	−	0.0265168i
$166$		0			0
$167$	819.906	+	1420.12i	0.379918	+	0.658037i	0.991050	−	0.133492i	$-0.0426190\pi$
$167$	819.906	+	1420.12i	0.379918	+	0.658037i	−0.611132	+	0.791528i	$0.709286\pi$
$168$		0			0
$169$	1065.59	+	1845.65i	0.485019	+	0.840078i
$170$		0			0
$171$	−3185.68			−1.42465
$172$		0			0
$173$	1285.44	−	2226.45i	0.564914	−	0.978460i	−0.432143	−	0.901805i	$-0.642243\pi$
$173$	1285.44	−	2226.45i	0.564914	−	0.978460i	0.997058	−	0.0766555i	$-0.0244242\pi$
$174$		0			0
$175$	−952.089	+	1649.07i	−0.411264	+	0.712330i
$176$		0			0
$177$	93.6293	−	162.171i	0.0397605	−	0.0688672i
$178$		0			0
$179$	1443.98	+	2501.04i	0.602949	+	1.04434i	0.992372	+	0.123279i	$0.0393410\pi$
$179$	1443.98	+	2501.04i	0.602949	+	1.04434i	−0.389423	+	0.921059i	$0.627326\pi$
$180$		0			0
$181$	557.964	−	966.422i	0.229133	−	0.396871i	−0.728418	−	0.685133i	$-0.759744\pi$
$181$	557.964	−	966.422i	0.229133	−	0.396871i	0.957552	+	0.288262i	$0.0930775\pi$
$182$		0			0
$183$	785.083	+	1359.80i	0.317131	+	0.549287i
$184$		0			0
$185$	−100.958			−0.0401222
$186$		0			0
$187$	−2494.81			−0.975606
$188$		0			0
$189$	−971.757	−	1683.13i	−0.373994	−	0.647777i
$190$		0			0
$191$	−2106.84	+	3649.16i	−0.798145	+	1.38243i	0.122678	+	0.992446i	$0.460852\pi$
$191$	−2106.84	+	3649.16i	−0.798145	+	1.38243i	−0.920823	+	0.389981i	$0.872482\pi$
$192$		0			0
$193$	829.495	+	1436.73i	0.309370	+	0.535844i	0.978225	−	0.207549i	$-0.0665486\pi$
$193$	829.495	+	1436.73i	0.309370	+	0.535844i	−0.668855	+	0.743393i	$0.733215\pi$
$194$		0			0
$195$	5.30491	−	9.18838i	0.00194817	−	0.00337432i
$196$		0			0
$197$	1172.41	−	2030.67i	0.424012	−	0.734411i	−0.572315	−	0.820034i	$-0.693955\pi$
$197$	1172.41	−	2030.67i	0.424012	−	0.734411i	0.996328	+	0.0856228i	$0.0272880\pi$
$198$		0			0
$199$	−280.764	+	486.298i	−0.100014	+	0.173230i	−0.911690	−	0.410878i	$-0.865222\pi$
$199$	−280.764	+	486.298i	−0.100014	+	0.173230i	0.811676	+	0.584108i	$0.198556\pi$
$200$		0			0
$201$	−2447.03			−0.858706
$202$		0			0
$203$	691.597	+	1197.88i	0.239116	+	0.414162i
$204$		0			0
$205$	−62.8548	−	108.868i	−0.0214145	−	0.0370910i
$206$		0			0
$207$	1956.12	−	3388.11i	0.656812	−	1.13763i
$208$		0			0
$209$	−8107.52			−2.68330
$210$		0			0
$211$	−1675.51	−	2902.07i	−0.546667	−	0.946856i	−0.998500	−	0.0547528i	$-0.982563\pi$
$211$	−1675.51	−	2902.07i	−0.546667	−	0.946856i	0.451833	−	0.892103i	$-0.350770\pi$
$212$		0			0
$213$	2671.70			0.859447
$214$		0			0
$215$	−40.3878			−0.0128113
$216$		0			0
$217$	2244.00	−	1379.48i	0.701994	−	0.431545i
$218$		0			0
$219$	2605.79			0.804030
$220$		0			0
$221$	−407.877			−0.124148
$222$		0			0
$223$	1804.39	+	3125.29i	0.541842	+	0.938498i	0.998798	+	0.0490091i	$0.0156063\pi$
$223$	1804.39	+	3125.29i	0.541842	+	0.938498i	−0.456956	+	0.889489i	$0.651060\pi$
$224$		0			0
$225$	2432.97			0.720879
$226$		0			0
$227$	1284.06	−	2224.06i	0.375445	−	0.650290i	−0.614948	−	0.788567i	$-0.710823\pi$
$227$	1284.06	−	2224.06i	0.375445	−	0.650290i	0.990394	+	0.138277i	$0.0441565\pi$
$228$		0			0
$229$	662.426	+	1147.36i	0.191154	+	0.331089i	0.945633	−	0.325235i	$-0.105444\pi$
$229$	662.426	+	1147.36i	0.191154	+	0.331089i	−0.754479	+	0.656325i	$0.772110\pi$
$230$		0			0
$231$	−1037.09	−	1796.29i	−0.295392	−	0.511633i
$232$		0			0
$233$	2926.03			0.822705			0.411353	−	0.911476i	$-0.365056\pi$
$233$	2926.03			0.822705			0.411353	+	0.911476i	$0.365056\pi$
$234$		0			0
$235$	−4.62367	+	8.00843i	−0.00128347	+	0.00222303i
$236$		0			0
$237$	410.353	−	710.752i	0.112470	−	0.194803i
$238$		0			0
$239$	−561.950	+	973.326i	−0.152090	+	0.263428i	−0.931996	−	0.362469i	$-0.881934\pi$
$239$	−561.950	+	973.326i	−0.152090	+	0.263428i	0.779906	+	0.625897i	$0.215267\pi$
$240$		0			0
$241$	−2508.00	−	4343.99i	−0.670352	−	1.16108i	−0.977804	−	0.209520i	$-0.932810\pi$
$241$	−2508.00	−	4343.99i	−0.670352	−	1.16108i	0.307453	−	0.951563i	$-0.400523\pi$
$242$		0			0
$243$	−1962.56	+	3399.26i	−0.518100	+	0.897376i
$244$		0			0
$245$	26.2842	+	45.5255i	0.00685401	+	0.0118715i
$246$		0			0
$247$	−1325.50			−0.341456
$248$		0			0
$249$	−732.313			−0.186379
$250$		0			0
$251$	1609.72	+	2788.12i	0.404800	+	0.701134i	0.994298	−	0.106635i	$-0.0340078\pi$
$251$	1609.72	+	2788.12i	0.404800	+	0.701134i	−0.589498	+	0.807770i	$0.700674\pi$
$252$		0			0
$253$	4978.31	−	8622.69i	1.23709	−	2.14270i
$254$		0			0
$255$	−32.8711	−	56.9344i	−0.00807242	−	0.0139818i
$256$		0			0
$257$	−930.796	+	1612.19i	−0.225920	+	0.391305i	−0.956595	−	0.291420i	$-0.905872\pi$
$257$	−930.796	+	1612.19i	−0.225920	+	0.391305i	0.730675	+	0.682725i	$0.239205\pi$
$258$		0			0
$259$	−1613.40	+	2794.49i	−0.387073	+	0.670430i
$260$		0			0
$261$	883.653	−	1530.53i	0.209566	−	0.362979i
$262$		0			0
$263$	3443.30			0.807311			0.403656	−	0.914911i	$-0.367739\pi$
$263$	3443.30			0.807311			0.403656	+	0.914911i	$0.367739\pi$
$264$		0			0
$265$	−109.382	−	189.455i	−0.0253557	−	0.0439174i
$266$		0			0
$267$	−1234.68	−	2138.53i	−0.283001	−	0.490171i
$268$		0			0
$269$	3448.08	−	5972.25i	0.781536	−	1.35366i	−0.149510	−	0.988760i	$-0.547770\pi$
$269$	3448.08	−	5972.25i	0.781536	−	1.35366i	0.931047	−	0.364900i	$-0.118897\pi$
$270$		0			0
$271$	−1324.92			−0.296985			−0.148492	−	0.988914i	$-0.547442\pi$
$271$	−1324.92			−0.296985			−0.148492	+	0.988914i	$0.547442\pi$
$272$		0			0
$273$	−169.554	−	293.676i	−0.0375893	−	0.0651066i
$274$		0			0
$275$	6191.87			1.35776
$276$		0			0
$277$	−2433.27			−0.527802			−0.263901	−	0.964550i	$-0.585009\pi$
$277$	−2433.27			−0.527802			−0.263901	+	0.964550i	$0.585009\pi$
$278$		0			0
$279$	−2960.00	−	1601.75i	−0.635163	−	0.343707i
$280$		0			0
$281$	4274.16			0.907384			0.453692	−	0.891158i	$-0.350107\pi$
$281$	4274.16			0.907384			0.453692	+	0.891158i	$0.350107\pi$
$282$		0			0
$283$	3559.40			0.747648			0.373824	−	0.927500i	$-0.378046\pi$
$283$	3559.40			0.747648			0.373824	+	0.927500i	$0.378046\pi$
$284$		0			0
$285$	−106.823	−	185.023i	−0.0222023	−	0.0384555i
$286$		0			0
$287$	−4017.89			−0.826372
$288$		0			0
$289$	1192.83	−	2066.04i	0.242790	−	0.420524i
$290$		0			0
$291$	−40.7794	−	70.6320i	−0.00821488	−	0.0142286i
$292$		0			0
$293$	−3587.94	−	6214.50i	−0.715392	−	1.23909i	−0.962808	−	0.270185i	$-0.912915\pi$
$293$	−3587.94	−	6214.50i	−0.715392	−	1.23909i	0.247417	−	0.968909i	$-0.420418\pi$
$294$		0			0
$295$	−32.6476			−0.00644344
$296$		0			0
$297$	−3159.89	+	5473.09i	−0.617358	+	1.06930i
$298$		0			0
$299$	813.906	−	1409.73i	0.157423	−	0.272664i
$300$		0			0
$301$	−645.432	+	1117.92i	−0.123595	+	0.214073i
$302$		0			0
$303$	−1326.98	−	2298.40i	−0.251595	−	0.435775i
$304$		0			0
$305$	136.875	−	237.075i	0.0256965	−	0.0445077i
$306$		0			0
$307$	−2286.55	−	3960.41i	−0.425082	−	0.736263i	0.571346	−	0.820709i	$-0.306421\pi$
$307$	−2286.55	−	3960.41i	−0.425082	−	0.736263i	−0.996428	+	0.0844461i	$0.973088\pi$
$308$		0			0
$309$	−4431.57			−0.815867
$310$		0			0
$311$	−4585.17			−0.836017			−0.418008	−	0.908443i	$-0.637272\pi$
$311$	−4585.17			−0.836017			−0.418008	+	0.908443i	$0.637272\pi$
$312$		0			0
$313$	4699.79	+	8140.27i	0.848715	+	1.47002i	0.882356	+	0.470583i	$0.155956\pi$
$313$	4699.79	+	8140.27i	0.848715	+	1.47002i	−0.0336414	+	0.999434i	$0.510710\pi$
$314$		0			0
$315$	−71.0459	+	123.055i	−0.0127079	+	0.0220107i
$316$		0			0
$317$	4139.99	+	7170.67i	0.733517	+	1.27049i	0.955371	+	0.295409i	$0.0954560\pi$
$317$	4139.99	+	7170.67i	0.733517	+	1.27049i	−0.221853	+	0.975080i	$0.571211\pi$
$318$		0			0
$319$	2248.89	−	3895.19i	0.394713	−	0.683663i
$320$		0			0
$321$	−1524.18	+	2639.95i	−0.265019	+	0.459027i
$322$		0			0
$323$	−4106.63	+	7112.90i	−0.707428	+	1.22530i
$324$		0			0
$325$	1012.31			0.172778
$326$		0			0
$327$	1217.71	+	2109.13i	0.205930	+	0.356682i
$328$		0			0
$329$	147.780	+	255.963i	0.0247641	+	0.0428927i
$330$		0			0
$331$	2338.78	−	4050.88i	0.388371	−	0.672679i	−0.603859	−	0.797091i	$-0.706371\pi$
$331$	2338.78	−	4050.88i	0.388371	−	0.672679i	0.992231	+	0.124412i	$0.0397044\pi$
$332$		0			0
$333$	4122.88			0.678476
$334$		0			0
$335$	213.313	+	369.469i	0.0347897	+	0.0602575i
$336$		0			0
$337$	−5526.87			−0.893377			−0.446688	−	0.894690i	$-0.647397\pi$
$337$	−5526.87			−0.893377			−0.446688	+	0.894690i	$0.647397\pi$
$338$		0			0
$339$	355.423			0.0569438
$340$		0			0
$341$	−7533.16	−	4076.43i	−1.19632	−	0.647364i
$342$		0			0
$343$	6914.78			1.08852
$344$		0			0
$345$	262.373			0.0409440
$346$		0			0
$347$	2917.70	+	5053.60i	0.451384	+	0.781819i	0.998472	−	0.0552554i	$-0.0175973\pi$
$347$	2917.70	+	5053.60i	0.451384	+	0.781819i	−0.547089	+	0.837075i	$0.684264\pi$
$348$		0			0
$349$	1884.24			0.289001			0.144500	−	0.989505i	$-0.453843\pi$
$349$	1884.24			0.289001			0.144500	+	0.989505i	$0.453843\pi$
$350$		0			0
$351$	−516.612	+	894.798i	−0.0785604	+	0.136071i
$352$		0			0
$353$	519.207	+	899.293i	0.0782850	+	0.135594i	0.902510	−	0.430669i	$-0.141722\pi$
$353$	519.207	+	899.293i	0.0782850	+	0.135594i	−0.824225	+	0.566262i	$0.808389\pi$
$354$		0			0
$355$	−232.899	−	403.393i	−0.0348197	−	0.0603095i
$356$		0			0
$357$	−2101.23			−0.311510
$358$		0			0
$359$	2809.77	−	4866.66i	0.413075	−	0.715466i	−0.582150	−	0.813082i	$-0.697788\pi$
$359$	2809.77	−	4866.66i	0.413075	−	0.715466i	0.995224	+	0.0976155i	$0.0311215\pi$
$360$		0			0
$361$	−9916.07	+	17175.1i	−1.44570	+	2.50403i
$362$		0			0
$363$	−1549.70	+	2684.16i	−0.224072	+	0.388104i
$364$		0			0
$365$	−227.153	−	393.440i	−0.0325745	−	0.0564208i
$366$		0			0
$367$	−6750.42	+	11692.1i	−0.960134	+	1.66300i	−0.237979	+	0.971270i	$0.576485\pi$
$367$	−6750.42	+	11692.1i	−0.960134	+	1.66300i	−0.722155	+	0.691731i	$0.756848\pi$
$368$		0			0
$369$	2566.83	+	4445.88i	0.362124	+	0.627217i
$370$		0			0
$371$	−6992.05			−0.978461
$372$		0			0
$373$	−21.7510			−0.00301937			−0.00150968	−	0.999999i	$-0.500481\pi$
$373$	−21.7510			−0.00301937			−0.00150968	+	0.999999i	$0.500481\pi$
$374$		0			0
$375$	163.315	+	282.869i	0.0224894	+	0.0389528i
$376$		0			0
$377$	367.671	−	636.825i	0.0502282	−	0.0869978i
$378$		0			0
$379$	−876.625	−	1518.36i	−0.118811	−	0.205786i	0.800486	−	0.599351i	$-0.204575\pi$
$379$	−876.625	−	1518.36i	−0.118811	−	0.205786i	−0.919297	+	0.393566i	$0.871241\pi$
$380$		0			0
$381$	−403.940	+	699.644i	−0.0543162	+	0.0940784i
$382$		0			0
$383$	4542.22	−	7867.36i	0.605996	−	1.04962i	−0.385897	−	0.922542i	$-0.626108\pi$
$383$	4542.22	−	7867.36i	0.605996	−	1.04962i	0.991893	−	0.127074i	$-0.0405587\pi$
$384$		0			0
$385$	−180.811	+	313.174i	−0.0239350	+	0.0414567i
$386$		0			0
$387$	1649.34			0.216642
$388$		0			0
$389$	3209.99	+	5559.87i	0.418388	+	0.724670i	0.995778	−	0.0917991i	$-0.0292618\pi$
$389$	3209.99	+	5559.87i	0.418388	+	0.724670i	−0.577389	+	0.816469i	$0.695928\pi$
$390$		0			0
$391$	−5043.25	−	8735.16i	−0.652296	−	1.12981i
$392$		0			0
$393$	3904.05	−	6762.02i	0.501103	−	0.867936i
$394$		0			0
$395$	−143.086			−0.0182264
$396$		0			0
$397$	7292.73	+	12631.4i	0.921944	+	1.59685i	0.796404	+	0.604765i	$0.206733\pi$
$397$	7292.73	+	12631.4i	0.921944	+	1.59685i	0.125540	+	0.992089i	$0.459934\pi$
$398$		0			0
$399$	−6828.50			−0.856773
$400$		0			0
$401$	−4285.19			−0.533647			−0.266823	−	0.963745i	$-0.585974\pi$
$401$	−4285.19			−0.533647			−0.266823	+	0.963745i	$0.585974\pi$
$402$		0			0
$403$	−1231.60	−	666.458i	−0.152234	−	0.0823787i
$404$		0			0
$405$	84.8506			0.0104105
$406$		0			0
$407$	10492.7			1.27789
$408$		0			0
$409$	5353.32	+	9272.22i	0.647199	+	1.12098i	0.983789	+	0.179331i	$0.0573932\pi$
$409$	5353.32	+	9272.22i	0.647199	+	1.12098i	−0.336589	+	0.941651i	$0.609273\pi$
$410$		0			0
$411$	5360.69			0.643366
$412$		0			0
$413$	−521.736	+	903.673i	−0.0621621	+	0.107668i
$414$		0			0
$415$	63.8375	+	110.570i	0.00755098	+	0.0130787i
$416$		0			0
$417$	763.309	+	1322.09i	0.0896389	+	0.155259i
$418$		0			0
$419$	−10542.6			−1.22921			−0.614605	−	0.788835i	$-0.710684\pi$
$419$	−10542.6			−1.22921			−0.614605	+	0.788835i	$0.710684\pi$
$420$		0			0
$421$	3377.69	−	5850.33i	0.391018	−	0.677262i	−0.601566	−	0.798823i	$-0.705456\pi$
$421$	3377.69	−	5850.33i	0.391018	−	0.677262i	0.992584	+	0.121560i	$0.0387898\pi$
$422$		0			0
$423$	188.819	−	327.044i	0.0217038	−	0.0375920i
$424$		0			0
$425$	3136.31	−	5432.26i	0.357961	−	0.620007i
$426$		0			0
$427$	−4374.76	−	7577.31i	−0.495807	−	0.858763i
$428$		0			0
$429$	−551.344	+	954.955i	−0.0620492	+	0.107472i
$430$		0			0
$431$	601.024	+	1041.00i	0.0671701	+	0.116342i	0.897655	−	0.440700i	$-0.145270\pi$
$431$	601.024	+	1041.00i	0.0671701	+	0.116342i	−0.830484	+	0.557042i	$0.811936\pi$
$432$		0			0
$433$	−3465.48			−0.384619			−0.192310	−	0.981334i	$-0.561598\pi$
$433$	−3465.48			−0.384619			−0.192310	+	0.981334i	$0.561598\pi$
$434$		0			0
$435$	118.523			0.0130638
$436$		0			0
$437$	−16389.3	−	28387.2i	−1.79407	−	3.10742i
$438$		0			0
$439$	4612.13	−	7988.45i	0.501424	−	0.868492i	−0.498575	−	0.866847i	$-0.666143\pi$
$439$	4612.13	−	7988.45i	0.501424	−	0.868492i	0.999999	−	0.00164509i	$-0.000523649\pi$
$440$		0			0
$441$	−1073.38	−	1859.14i	−0.115903	−	0.200750i
$442$		0			0
$443$	3540.87	−	6132.96i	0.379755	−	0.657755i	−0.611271	−	0.791421i	$-0.709342\pi$
$443$	3540.87	−	6132.96i	0.379755	−	0.657755i	0.991026	+	0.133666i	$0.0426749\pi$
$444$		0			0
$445$	−215.260	+	372.841i	−0.0229310	+	0.0397177i
$446$		0			0
$447$	2101.68	−	3640.21i	0.222385	−	0.385182i
$448$		0			0
$449$	−17378.4			−1.82658			−0.913292	−	0.407305i	$-0.866469\pi$
$449$	−17378.4			−1.82658			−0.913292	+	0.407305i	$0.866469\pi$
$450$		0			0
$451$	6532.55	+	11314.7i	0.682053	+	1.18135i
$452$		0			0
$453$	3318.79	+	5748.31i	0.344217	+	0.596201i
$454$		0			0
$455$	−29.5609	+	51.2009i	−0.00304579	+	0.00527547i
$456$		0			0
$457$	−12614.8			−1.29124			−0.645618	−	0.763660i	$-0.723400\pi$
$457$	−12614.8			−1.29124			−0.645618	+	0.763660i	$0.723400\pi$
$458$		0			0
$459$	3201.11	+	5544.48i	0.325522	+	0.563821i
$460$		0			0
$461$	2507.79			0.253361			0.126681	−	0.991944i	$-0.459568\pi$
$461$	2507.79			0.253361			0.126681	+	0.991944i	$0.459568\pi$
$462$		0			0
$463$	14109.8			1.41628			0.708140	−	0.706072i	$-0.249534\pi$
$463$	14109.8			1.41628			0.708140	+	0.706072i	$0.249534\pi$
$464$		0			0
$465$	−6.22654	−	225.626i	−0.000620965	−	0.0225014i
$466$		0			0
$467$	8600.97			0.852260			0.426130	−	0.904662i	$-0.359877\pi$
$467$	8600.97			0.852260			0.426130	+	0.904662i	$0.359877\pi$
$468$		0			0
$469$	13635.7			1.34251
$470$		0			0
$471$	1605.68	+	2781.12i	0.157083	+	0.272075i
$472$		0			0
$473$	4197.54			0.408040
$474$		0			0
$475$	10192.3	−	17653.5i	0.984533	−	1.70526i
$476$		0			0
$477$	4466.87	+	7736.84i	0.428771	+	0.742653i
$478$		0			0
$479$	−3727.78	−	6456.71i	−0.355588	−	0.615897i	0.631630	−	0.775270i	$-0.282386\pi$
$479$	−3727.78	−	6456.71i	−0.355588	−	0.615897i	−0.987218	+	0.159373i	$0.949053\pi$
$480$		0			0
$481$	1715.45			0.162615
$482$		0			0
$483$	4192.95	−	7262.40i	0.395001	−	0.684162i
$484$		0			0
$485$	−7.10968	+	12.3143i	−0.000665637	+	0.00115292i
$486$		0			0
$487$	−14.9386	+	25.8744i	−0.00139001	+	0.00240756i	−0.866720	−	0.498796i	$-0.833776\pi$
$487$	−14.9386	+	25.8744i	−0.00139001	+	0.00240756i	0.865330	+	0.501203i	$0.167109\pi$
$488$		0			0
$489$	897.141	+	1553.89i	0.0829655	+	0.143700i
$490$		0			0
$491$	527.380	−	913.449i	0.0484732	−	0.0839580i	−0.840771	−	0.541391i	$-0.817898\pi$
$491$	527.380	−	913.449i	0.0484732	−	0.0839580i	0.889244	+	0.457433i	$0.151231\pi$
$492$		0			0
$493$	−2278.22	−	3945.99i	−0.208125	−	0.360484i
$494$		0			0
$495$	462.044			0.0419542
$496$		0			0
$497$	−14887.7			−1.34367
$498$		0			0
$499$	−1648.40	−	2855.12i	−0.147881	−	0.256137i	0.782563	−	0.622571i	$-0.213912\pi$
$499$	−1648.40	−	2855.12i	−0.147881	−	0.256137i	−0.930444	+	0.366434i	$0.880579\pi$
$500$		0			0
$501$	2245.51	−	3889.34i	0.200244	−	0.346832i
$502$		0			0
$503$	1200.82	+	2079.88i	0.106445	+	0.184368i	0.914328	−	0.404975i	$-0.132720\pi$
$503$	1200.82	+	2079.88i	0.106445	+	0.184368i	−0.807883	+	0.589343i	$0.799387\pi$
$504$		0			0
$505$	−231.353	+	400.715i	−0.0203863	+	0.0353100i
$506$		0			0
$507$	2918.37	−	5054.76i	0.255640	−	0.442781i
$508$		0			0
$509$	−3252.01	+	5632.65i	−0.283189	+	0.490497i	−0.972168	−	0.234284i	$-0.924726\pi$
$509$	−3252.01	+	5632.65i	−0.283189	+	0.490497i	0.688980	+	0.724781i	$0.258059\pi$
$510$		0			0
$511$	−14520.4			−1.25703
$512$		0			0
$513$	10402.8	+	18018.2i	0.895313	+	1.55073i
$514$		0			0
$515$	386.310	+	669.109i	0.0330541	+	0.0572514i
$516$		0			0
$517$	480.542	−	832.323i	0.0408785	−	0.0708037i
$518$		0			0
$519$	−7040.98			−0.595500
$520$		0			0
$521$	−6494.70	−	11249.1i	−0.546138	−	0.945939i	−0.998534	−	0.0541216i	$-0.982764\pi$
$521$	−6494.70	−	11249.1i	−0.546138	−	0.945939i	0.452396	−	0.891817i	$-0.350569\pi$
$522$		0			0
$523$	1684.17			0.140810			0.0704049	−	0.997518i	$-0.477571\pi$
$523$	1684.17			0.140810			0.0704049	+	0.997518i	$0.477571\pi$
$524$		0			0
$525$	5215.05			0.433531
$526$		0			0
$527$	−7392.05	+	4544.20i	−0.611011	+	0.375614i
$528$		0			0
$529$	28087.6			2.30851
$530$		0			0
$531$	1333.24			0.108960
$532$		0			0
$533$	1068.01	+	1849.85i	0.0867929	+	0.150330i
$534$		0			0
$535$	531.464			0.0429480
$536$		0			0
$537$	3954.68	−	6849.70i	0.317797	−	0.550440i
$538$		0			0
$539$	−2731.73	−	4731.50i	−0.218301	−	0.378108i
$540$		0			0
$541$	−7920.08	−	13718.0i	−0.629410	−	1.09017i	−0.987670	−	0.156548i	$-0.949963\pi$
$541$	−7920.08	−	13718.0i	−0.629410	−	1.09017i	0.358260	−	0.933622i	$-0.383370\pi$
$542$		0			0
$543$	−3056.24			−0.241539
$544$		0			0
$545$	212.301	−	367.715i	0.0166862	−	0.0289013i
$546$		0			0
$547$	−8475.16	+	14679.4i	−0.662471	+	1.14743i	0.317493	+	0.948261i	$0.397159\pi$
$547$	−8475.16	+	14679.4i	−0.662471	+	1.14743i	−0.979964	+	0.199173i	$0.936174\pi$
$548$		0			0
$549$	−5589.63	+	9681.52i	−0.434535	+	0.752636i
$550$		0			0
$551$	−7403.66	−	12823.5i	−0.572426	−	0.991470i
$552$		0			0
$553$	−2286.63	+	3960.56i	−0.175836	+	0.304558i
$554$		0			0
$555$	138.250	+	239.455i	0.0105736	+	0.0183141i
$556$		0			0
$557$	−11592.8			−0.881875			−0.440938	−	0.897538i	$-0.645354\pi$
$557$	−11592.8			−0.881875			−0.440938	+	0.897538i	$0.645354\pi$
$558$		0			0
$559$	686.257			0.0519241
$560$		0			0
$561$	3416.32	+	5917.23i	0.257107	+	0.445322i
$562$		0			0
$563$	8446.82	−	14630.3i	0.632311	−	1.09519i	−0.354767	−	0.934955i	$-0.615440\pi$
$563$	8446.82	−	14630.3i	0.632311	−	1.09519i	0.987078	−	0.160240i	$-0.0512268\pi$
$564$		0			0
$565$	−30.9831	−	53.6643i	−0.00230702	−	0.00399588i
$566$		0			0
$567$	1355.99	−	2348.64i	0.100434	−	0.173957i
$568$		0			0
$569$	−1808.92	+	3133.14i	−0.133276	+	0.230840i	−0.924937	−	0.380119i	$-0.875883\pi$
$569$	−1808.92	+	3133.14i	−0.133276	+	0.230840i	0.791662	+	0.610960i	$0.209216\pi$
$570$		0			0
$571$	−11666.8	+	20207.4i	−0.855059	+	1.48101i	0.0215306	+	0.999768i	$0.493146\pi$
$571$	−11666.8	+	20207.4i	−0.855059	+	1.48101i	−0.876590	+	0.481238i	$0.840187\pi$
$572$		0			0
$573$	11540.2			0.841358
$574$		0			0
$575$	12516.8	+	21679.8i	0.907806	+	1.57237i
$576$		0			0
$577$	−2271.04	−	3933.55i	−0.163855	−	0.283806i	0.772393	−	0.635145i	$-0.219060\pi$
$577$	−2271.04	−	3933.55i	−0.163855	−	0.283806i	−0.936248	+	0.351339i	$0.885726\pi$
$578$		0			0
$579$	2271.77	−	3934.83i	0.163060	−	0.282428i
$580$		0			0
$581$	4080.71			0.291388
$582$		0			0
$583$	11368.1	+	19690.2i	0.807581	+	1.39877i
$584$		0			0
$585$	75.5398			0.00533878
$586$		0			0
$587$	−14841.2			−1.04355			−0.521774	−	0.853084i	$-0.674730\pi$
$587$	−14841.2			−1.04355			−0.521774	+	0.853084i	$0.674730\pi$
$588$		0			0
$589$	−24022.4	+	14767.6i	−1.68052	+	1.03308i
$590$		0			0
$591$	−6421.83			−0.446969
$592$		0			0
$593$	8188.97			0.567084			0.283542	−	0.958960i	$-0.408490\pi$
$593$	8188.97			0.567084			0.283542	+	0.958960i	$0.408490\pi$
$594$		0			0
$595$	183.169	+	317.259i	0.0126205	+	0.0218594i
$596$		0			0
$597$	1537.88			0.105429
$598$		0			0
$599$	859.077	−	1487.97i	0.0585993	−	0.101497i	−0.835238	−	0.549889i	$-0.814670\pi$
$599$	859.077	−	1487.97i	0.0585993	−	0.101497i	0.893837	+	0.448392i	$0.148003\pi$
$600$		0			0
$601$	−3208.82	−	5557.85i	−0.217788	−	0.377220i	0.736343	−	0.676608i	$-0.236551\pi$
$601$	−3208.82	−	5557.85i	−0.217788	−	0.377220i	−0.954131	+	0.299388i	$0.903217\pi$
$602$		0			0
$603$	−8711.17	−	15088.2i	−0.588302	−	1.01897i
$604$		0			0
$605$	540.364			0.0363123
$606$		0			0
$607$	−8019.09	+	13889.5i	−0.536219	+	0.928758i	0.462885	+	0.886418i	$0.346814\pi$
$607$	−8019.09	+	13889.5i	−0.536219	+	0.928758i	−0.999103	+	0.0423393i	$0.986519\pi$
$608$		0			0
$609$	1894.11	−	3280.69i	0.126031	−	0.218293i
$610$		0			0
$611$	78.5640	−	136.077i	0.00520189	−	0.00900995i
$612$		0			0
$613$	10060.0	+	17424.4i	0.662836	+	1.14807i	0.979867	+	0.199650i	$0.0639806\pi$
$613$	10060.0	+	17424.4i	0.662836	+	1.14807i	−0.317031	+	0.948415i	$0.602686\pi$
$614$		0			0
$615$	−172.143	+	298.161i	−0.0112870	+	0.0195496i
$616$		0			0
$617$	−10405.3	−	18022.5i	−0.678931	−	1.17594i	−0.975303	−	0.220871i	$-0.929110\pi$
$617$	−10405.3	−	18022.5i	−0.678931	−	1.17594i	0.296372	−	0.955073i	$-0.404223\pi$
$618$		0			0
$619$	−1370.98			−0.0890219			−0.0445109	−	0.999009i	$-0.514173\pi$
$619$	−1370.98			−0.0890219			−0.0445109	+	0.999009i	$0.514173\pi$
$620$		0			0
$621$	−25550.8			−1.65108
$622$		0			0
$623$	6880.08	+	11916.6i	0.442447	+	0.766341i
$624$		0			0
$625$	−7769.78	+	13457.6i	−0.497266	+	0.861290i
$626$		0			0
$627$	11102.2	+	19229.6i	0.707144	+	1.22481i
$628$		0			0
$629$	5314.77	−	9205.45i	0.336906	−	0.583538i
$630$		0			0
$631$	7827.48	−	13557.6i	0.493831	−	0.855340i	−0.506144	−	0.862449i	$-0.668930\pi$
$631$	7827.48	−	13557.6i	0.493831	−	0.855340i	0.999975	+	0.00710915i	$0.00226293\pi$
$632$		0			0
$633$	−4588.79	+	7948.01i	−0.288133	+	0.499060i
$634$		0			0
$635$	140.850			0.00880228
$636$		0			0
$637$	−446.612	−	773.555i	−0.0277793	−	0.0481152i
$638$		0			0
$639$	9510.99	+	16473.5i	0.588809	+	1.01985i
$640$		0			0
$641$	8347.27	−	14457.9i	0.514348	−	0.890878i	−0.485513	−	0.874229i	$-0.661367\pi$
$641$	8347.27	−	14457.9i	0.514348	−	0.890878i	0.999861	−	0.0166482i	$-0.00529954\pi$
$642$		0			0
$643$	−22961.1			−1.40824			−0.704121	−	0.710080i	$-0.748659\pi$
$643$	−22961.1			−1.40824			−0.704121	+	0.710080i	$0.748659\pi$
$644$		0			0
$645$	55.3059	+	95.7927i	0.00337623	+	0.00584780i
$646$		0			0
$647$	15397.3			0.935594			0.467797	−	0.883836i	$-0.345048\pi$
$647$	15397.3			0.935594			0.467797	+	0.883836i	$0.345048\pi$
$648$		0			0
$649$	3393.09			0.205224
$650$		0			0
$651$	−6344.75	−	3433.34i	−0.381982	−	0.206703i
$652$		0			0
$653$	27275.7			1.63458			0.817290	−	0.576227i	$-0.195475\pi$
$653$	27275.7			1.63458			0.817290	+	0.576227i	$0.195475\pi$
$654$		0			0
$655$	−1361.30			−0.0812069
$656$		0			0
$657$	9276.33	+	16067.1i	0.550843	+	0.954089i
$658$		0			0
$659$	−30271.0			−1.78936			−0.894681	−	0.446705i	$-0.852597\pi$
$659$	−30271.0			−1.78936			−0.894681	+	0.446705i	$0.852597\pi$
$660$		0			0
$661$	−3345.85	+	5795.18i	−0.196881	+	0.341008i	−0.947516	−	0.319710i	$-0.896415\pi$
$661$	−3345.85	+	5795.18i	−0.196881	+	0.341008i	0.750635	+	0.660718i	$0.229748\pi$
$662$		0			0
$663$	558.535	+	967.411i	0.0327175	+	0.0566684i
$664$		0			0
$665$	595.256	+	1031.01i	0.0347114	+	0.0601218i
$666$		0			0
$667$	18184.5			1.05563
$668$		0			0
$669$	4941.76	−	8559.38i	0.285590	−	0.494656i
$670$		0			0
$671$	−14225.5	+	24639.4i	−0.818437	+	1.41757i
$672$		0			0
$673$	15044.9	−	26058.4i	0.861718	−	1.49254i	−0.00855081	−	0.999963i	$-0.502722\pi$
$673$	15044.9	−	26058.4i	0.861718	−	1.49254i	0.870269	−	0.492576i	$-0.163945\pi$
$674$		0			0
$675$	−7944.83	−	13760.9i	−0.453032	−	0.784675i
$676$		0			0
$677$	−14051.5	+	24337.8i	−0.797698	+	1.38165i	0.123414	+	0.992355i	$0.460616\pi$
$677$	−14051.5	+	24337.8i	−0.797698	+	1.38165i	−0.921112	+	0.389298i	$0.872718\pi$
$678$		0			0
$679$	227.237	+	393.587i	0.0128433	+	0.0222452i
$680$		0			0
$681$	−7033.42			−0.395773
$682$		0			0
$683$	4679.27			0.262148			0.131074	−	0.991373i	$-0.458157\pi$
$683$	4679.27			0.262148			0.131074	+	0.991373i	$0.458157\pi$
$684$		0			0
$685$	−467.304	−	809.395i	−0.0260654	−	0.0451466i
$686$		0			0
$687$	1814.21	−	3142.31i	0.100752	−	0.174508i
$688$		0			0
$689$	1858.58	+	3219.15i	0.102767	+	0.177997i
$690$		0			0
$691$	−4663.69	+	8077.75i	−0.256751	+	0.444707i	−0.965370	−	0.260885i	$-0.915986\pi$
$691$	−4663.69	+	8077.75i	−0.256751	+	0.444707i	0.708618	+	0.705592i	$0.249319\pi$
$692$		0			0
$693$	7383.86	−	12789.2i	0.404747	−	0.701043i
$694$		0			0
$695$	133.079	−	230.500i	0.00726327	−	0.0125804i
$696$		0			0
$697$	13235.5			0.719269
$698$		0			0
$699$	−4006.82	−	6940.01i	−0.216812	−	0.375530i
$700$		0			0
$701$	−10032.8	−	17377.4i	−0.540563	−	0.936283i	−0.998872	−	0.0474897i	$-0.984878\pi$
$701$	−10032.8	−	17377.4i	−0.540563	−	0.936283i	0.458309	−	0.888793i	$-0.348455\pi$
$702$		0			0
$703$	17271.7	−	29915.5i	0.926622	−	1.60496i
$704$		0			0
$705$	25.3261			0.00135296
$706$		0			0
$707$	7394.43	+	12807.5i	0.393347	+	0.681296i
$708$		0			0
$709$	−13633.3			−0.722154			−0.361077	−	0.932536i	$-0.617591\pi$
$709$	−13633.3			−0.722154			−0.361077	+	0.932536i	$0.617591\pi$
$710$		0			0
$711$	5843.26			0.308213
$712$		0			0
$713$	−955.307	−	34616.6i	−0.0501775	−	1.81824i
$714$		0			0
$715$	192.248			0.0100555
$716$		0			0
$717$	3078.07			0.160325
$718$		0			0
$719$	9240.38	+	16004.8i	0.479288	+	0.830151i	0.999718	−	0.0237534i	$-0.00756164\pi$
$719$	9240.38	+	16004.8i	0.479288	+	0.830151i	−0.520430	+	0.853904i	$0.674228\pi$
$720$		0			0
$721$	24694.3			1.27554
$722$		0			0
$723$	−6868.78	+	11897.1i	−0.353323	+	0.611973i
$724$		0			0
$725$	5654.32	+	9793.56i	0.289650	+	0.501688i
$726$		0			0
$727$	−9264.31	−	16046.3i	−0.472619	−	0.818600i	0.526890	−	0.849934i	$-0.323358\pi$
$727$	−9264.31	−	16046.3i	−0.472619	−	0.818600i	−0.999509	+	0.0313332i	$0.990025\pi$
$728$		0			0
$729$	5951.92			0.302389
$730$		0			0
$731$	2126.14	−	3682.59i	0.107576	−	0.186328i
$732$		0			0
$733$	326.941	−	566.279i	0.0164746	−	0.0285348i	−0.857671	−	0.514200i	$-0.828089\pi$
$733$	326.941	−	566.279i	0.0164746	−	0.0285348i	0.874145	+	0.485665i	$0.161422\pi$
$734$		0			0
$735$	71.9855	−	124.683i	0.00361255	−	0.00625713i
$736$		0			0
$737$	−22169.8	−	38399.2i	−1.10805	−	1.91921i
$738$		0			0
$739$	−1422.52	+	2463.87i	−0.0708093	+	0.122645i	−0.899256	−	0.437422i	$-0.855892\pi$
$739$	−1422.52	+	2463.87i	−0.0708093	+	0.122645i	0.828447	+	0.560068i	$0.189225\pi$
$740$		0			0
$741$	1815.10	+	3143.85i	0.0899858	+	0.155860i
$742$		0			0
$743$	−24077.1			−1.18884			−0.594418	−	0.804156i	$-0.702617\pi$
$743$	−24077.1			−1.18884			−0.594418	+	0.804156i	$0.702617\pi$
$744$		0			0
$745$	−732.833			−0.0360388
$746$		0			0
$747$	−2606.96	−	4515.38i	−0.127689	−	0.221164i
$748$		0			0
$749$	8493.25	−	14710.7i	0.414335	−	0.717649i
$750$		0			0
$751$	−8764.25	−	15180.1i	−0.425848	−	0.737591i	0.570651	−	0.821193i	$-0.306691\pi$
$751$	−8764.25	−	15180.1i	−0.425848	−	0.737591i	−0.996499	+	0.0836018i	$0.973358\pi$
$752$		0			0
$753$	4408.62	−	7635.95i	0.213358	−	0.369548i
$754$		0			0
$755$	578.614	−	1002.19i	0.0278913	−	0.0483091i
$756$		0			0
$757$	14896.7	−	25801.8i	0.715229	−	1.23881i	−0.247642	−	0.968852i	$-0.579656\pi$
$757$	14896.7	−	25801.8i	0.715229	−	1.23881i	0.962871	−	0.269961i	$-0.0870109\pi$
$758$		0			0
$759$	−27268.6			−1.30407
$760$		0			0
$761$	4388.29	+	7600.74i	0.209035	+	0.362059i	0.951411	−	0.307925i	$-0.0996345\pi$
$761$	4388.29	+	7600.74i	0.209035	+	0.362059i	−0.742376	+	0.669983i	$0.766301\pi$
$762$		0			0
$763$	−6785.49	−	11752.8i	−0.321954	−	0.557641i
$764$		0			0
$765$	234.035	−	405.361i	0.0110609	−	0.0191580i
$766$		0			0
$767$	554.737			0.0261153
$768$		0			0
$769$	−10261.8	−	17773.9i	−0.481208	−	0.833477i	0.518559	−	0.855042i	$-0.326469\pi$
$769$	−10261.8	−	17773.9i	−0.481208	−	0.833477i	−0.999767	+	0.0215647i	$0.993135\pi$
$770$		0			0
$771$	5098.42			0.238152
$772$		0			0
$773$	−5217.38			−0.242763			−0.121382	−	0.992606i	$-0.538733\pi$
$773$	−5217.38			−0.242763			−0.121382	+	0.992606i	$0.538733\pi$
$774$		0			0
$775$	18346.4	−	11278.3i	0.850349	−	0.522745i
$776$		0			0
$777$	8837.38			0.408030
$778$		0			0
$779$	43012.2			1.97827
$780$		0			0
$781$	24205.4	+	41924.9i	1.10901	+	1.92086i
$782$		0			0
$783$	−11542.3			−0.526803
$784$		0			0
$785$	279.942	−	484.874i	0.0127281	−	0.0220457i
$786$		0			0
$787$	8670.02	+	15016.9i	0.392697	+	0.680171i	0.992804	−	0.119748i	$-0.0382087\pi$
$787$	8670.02	+	15016.9i	0.392697	+	0.680171i	−0.600107	+	0.799920i	$0.704875\pi$
$788$		0			0
$789$	−4715.15	−	8166.88i	−0.212755	−	0.368503i
$790$		0			0
$791$	−1980.55			−0.0890267
$792$		0			0
$793$	−2325.74	+	4028.30i	−0.104148	+	0.180390i
$794$		0			0
$795$	−299.568	+	518.867i	−0.0133643	+	0.0231476i
$796$		0			0
$797$	−1998.45	+	3461.41i	−0.0888188	+	0.153839i	−0.907012	−	0.421105i	$-0.861643\pi$
$797$	−1998.45	+	3461.41i	−0.0888188	+	0.153839i	0.818193	+	0.574943i	$0.194976\pi$
$798$		0			0
$799$	−486.810	−	843.179i	−0.0215545	−	0.0373336i
$800$		0			0
$801$	8790.67	−	15225.9i	0.387769	−	0.671635i
$802$		0			0
$803$	23608.1	+	40890.5i	1.03750	+	1.79700i
$804$		0			0
$805$	−1462.04			−0.0640125
$806$		0			0
$807$	−18886.8			−0.823851
$808$		0			0
$809$	6644.74	+	11509.0i	0.288772	+	0.500168i	0.973517	−	0.228615i	$-0.0734197\pi$
$809$	6644.74	+	11509.0i	0.288772	+	0.500168i	−0.684745	+	0.728783i	$0.740086\pi$
$810$		0			0
$811$	297.057	−	514.518i	0.0128620	−	0.0222776i	−0.859523	−	0.511097i	$-0.829239\pi$
$811$	297.057	−	514.518i	0.0128620	−	0.0222776i	0.872385	+	0.488820i	$0.162572\pi$
$812$		0			0
$813$	1814.30	+	3142.46i	0.0782661	+	0.135561i
$814$		0			0
$815$	156.412	−	270.913i	0.00672254	−	0.0116438i
$816$		0			0
$817$	6909.46	−	11967.5i	0.295877	−	0.512473i
$818$		0			0
$819$	1207.19	−	2090.92i	0.0515051	−	0.0892094i
$820$		0			0
$821$	−17947.4			−0.762935			−0.381468	−	0.924382i	$-0.624581\pi$
$821$	−17947.4			−0.762935			−0.381468	+	0.924382i	$0.624581\pi$
$822$		0			0
$823$	−542.957	−	940.429i	−0.0229967	−	0.0398315i	0.854298	−	0.519784i	$-0.173987\pi$
$823$	−542.957	−	940.429i	−0.0229967	−	0.0398315i	−0.877295	+	0.479952i	$0.840654\pi$
$824$		0			0
$825$	−8478.97	−	14686.0i	−0.357818	−	0.619759i
$826$		0			0
$827$	8372.84	−	14502.2i	0.352058	−	0.609782i	−0.634552	−	0.772880i	$-0.718815\pi$
$827$	8372.84	−	14502.2i	0.352058	−	0.609782i	0.986610	+	0.163098i	$0.0521486\pi$
$828$		0			0
$829$	−27351.4			−1.14590			−0.572952	−	0.819589i	$-0.694202\pi$
$829$	−27351.4			−1.14590			−0.572952	+	0.819589i	$0.694202\pi$
$830$		0			0
$831$	3332.06	+	5771.29i	0.139095	+	0.240919i
$832$		0			0
$833$	−5534.73			−0.230212
$834$		0			0
$835$	−782.987			−0.0324507
$836$		0			0
$837$	606.363	+	21972.3i	0.0250406	+	0.907375i
$838$		0			0
$839$	24861.5			1.02302			0.511509	−	0.859278i	$-0.329087\pi$
$839$	24861.5			1.02302			0.511509	+	0.859278i	$0.329087\pi$
$840$		0			0
$841$	−16174.4			−0.663185
$842$		0			0
$843$	−5852.91	−	10137.5i	−0.239128	−	0.414182i
$844$		0			0
$845$	−1017.61			−0.0414280
$846$		0			0
$847$	8635.48	−	14957.1i	0.350317	−	0.606767i
$848$		0			0
$849$	−4874.14	−	8442.26i	−0.197032	−	0.341269i
$850$		0			0
$851$	21210.9	+	36738.4i	0.854408	+	1.47988i
$852$		0			0
$853$	−25701.7			−1.03166			−0.515831	−	0.856690i	$-0.672517\pi$
$853$	−25701.7			−1.03166			−0.515831	+	0.856690i	$0.672517\pi$
$854$		0			0
$855$	760.558	−	1317.33i	0.0304217	−	0.0526919i
$856$		0			0
$857$	4717.83	−	8171.52i	0.188049	−	0.325711i	−0.756551	−	0.653935i	$-0.773117\pi$
$857$	4717.83	−	8171.52i	0.188049	−	0.325711i	0.944600	+	0.328225i	$0.106450\pi$
$858$		0			0
$859$	−14217.1	+	24624.8i	−0.564706	+	0.978099i	0.432371	+	0.901696i	$0.357677\pi$
$859$	−14217.1	+	24624.8i	−0.564706	+	0.978099i	−0.997077	+	0.0764034i	$0.975656\pi$
$860$		0			0
$861$	5501.99	+	9529.73i	0.217779	+	0.377203i
$862$		0			0
$863$	−15094.8	+	26145.0i	−0.595404	+	1.03127i	0.398086	+	0.917348i	$0.369674\pi$
$863$	−15094.8	+	26145.0i	−0.595404	+	1.03127i	−0.993490	+	0.113921i	$0.963659\pi$
$864$		0			0
$865$	613.779	+	1063.10i	0.0241261	+	0.0417877i
$866$		0			0
$867$	−6533.69			−0.255935
$868$		0			0
$869$	14871.0			0.580512
$870$		0			0
$871$	−3624.55	−	6277.91i	−0.141003	−	0.244224i
$872$		0			0
$873$	290.341	−	502.885i	0.0112561	−	0.0194961i
$874$		0			0
$875$	−910.048	−	1576.25i	−0.0351603	−	0.0608994i
$876$		0			0
$877$	−4470.95	+	7743.92i	−0.172148	+	0.298168i	−0.939170	−	0.343451i	$-0.888404\pi$
$877$	−4470.95	+	7743.92i	−0.172148	+	0.298168i	0.767023	+	0.641620i	$0.221737\pi$
$878$		0			0
$879$	−9826.45	+	17019.9i	−0.377062	+	0.653091i
$880$		0			0
$881$	−7450.21	+	12904.1i	−0.284908	+	0.493475i	−0.972587	−	0.232540i	$-0.925296\pi$
$881$	−7450.21	+	12904.1i	−0.284908	+	0.493475i	0.687679	+	0.726015i	$0.258630\pi$
$882$		0			0
$883$	−11379.5			−0.433693			−0.216847	−	0.976206i	$-0.569577\pi$
$883$	−11379.5			−0.433693			−0.216847	+	0.976206i	$0.569577\pi$
$884$		0			0
$885$	44.7066	+	77.4342i	0.00169808	+	0.00294115i
$886$		0			0
$887$	4433.05	+	7678.27i	0.167810	+	0.290655i	0.937650	−	0.347582i	$-0.112997\pi$
$887$	4433.05	+	7678.27i	0.167810	+	0.290655i	−0.769840	+	0.638237i	$0.779664\pi$
$888$		0			0
$889$	2250.90	−	3898.67i	0.0849187	−	0.147083i
$890$		0			0
$891$	−8818.59			−0.331576
$892$		0			0
$893$	−1582.01	−	2740.13i	−0.0592834	−	0.102682i
$894$		0			0
$895$	−1378.96			−0.0515010
$896$		0			0
$897$	−4458.16			−0.165946
$898$		0			0
$899$	−431.547	−	15637.6i	−0.0160099	−	0.580137i
$900$		0			0
$901$	23032.8			0.851647
$902$		0			0
$903$	3535.35			0.130287
$904$		0			0
$905$	266.420	+	461.453i	0.00978574	+	0.0169494i
$906$		0			0
$907$	5070.92			0.185642			0.0928210	−	0.995683i	$-0.470412\pi$
$907$	5070.92			0.185642			0.0928210	+	0.995683i	$0.470412\pi$
$908$		0			0
$909$	9447.85	−	16364.2i	0.344736	−	0.597101i
$910$		0			0
$911$	−794.035	−	1375.31i	−0.0288777	−	0.0500176i	0.851225	−	0.524800i	$-0.175860\pi$
$911$	−794.035	−	1375.31i	−0.0288777	−	0.0500176i	−0.880103	+	0.474783i	$0.842527\pi$
$912$		0			0
$913$	−6634.68	−	11491.6i	−0.240499	−	0.416557i
$914$		0			0
$915$	−749.732			−0.0270878
$916$		0			0
$917$	−21754.8	+	37680.4i	−0.783431	+	1.35694i
$918$		0			0
$919$	−40.8669	+	70.7835i	−0.00146689	+	0.00254073i	−0.866758	−	0.498729i	$-0.833800\pi$
$919$	−40.8669	+	70.7835i	−0.00146689	+	0.00254073i	0.865291	+	0.501270i	$0.167134\pi$
$920$		0			0
$921$	−6262.26	+	10846.6i	−0.224048	+	0.388063i
$922$		0			0
$923$	3957.34	+	6854.32i	0.141124	+	0.244434i
$924$		0			0
$925$	−13190.7	+	22847.0i	−0.468875	+	0.812115i
$926$		0			0
$927$	−15775.9	−	27324.7i	−0.558953	−	0.968135i
$928$		0			0
$929$	11515.5			0.406686			0.203343	−	0.979108i	$-0.434819\pi$
$929$	11515.5			0.406686			0.203343	+	0.979108i	$0.434819\pi$
$930$		0			0
$931$	−17986.5			−0.633174
$932$		0			0
$933$	6278.80	+	10875.2i	0.220320	+	0.381606i
$934$		0			0
$935$	595.617	−	1031.64i	0.0208329	−	0.0360836i
$936$		0			0
$937$	23444.8	+	40607.6i	0.817405	+	1.41579i	0.907588	+	0.419862i	$0.137921\pi$
$937$	23444.8	+	40607.6i	0.817405	+	1.41579i	−0.0901830	+	0.995925i	$0.528745\pi$
$938$		0			0
$939$	12871.5	−	22294.1i	0.447333	−	0.774804i
$940$		0			0
$941$	−22667.9	+	39262.0i	−0.785284	+	1.36015i	0.143545	+	0.989644i	$0.454150\pi$
$941$	−22667.9	+	39262.0i	−0.785284	+	1.36015i	−0.928829	+	0.370509i	$0.879183\pi$
$942$		0			0
$943$	−26411.1	+	45745.3i	−0.912050	+	1.57972i
$944$		0			0
$945$	928.000			0.0319448
$946$		0			0
$947$	5052.22	+	8750.71i	0.173363	+	0.300274i	0.939594	−	0.342292i	$-0.111203\pi$
$947$	5052.22	+	8750.71i	0.173363	+	0.300274i	−0.766230	+	0.642566i	$0.777870\pi$
$948$		0			0
$949$	3859.70	+	6685.20i	0.132025	+	0.228673i
$950$		0			0
$951$	11338.4	−	19638.6i	0.386616	−	0.669638i
$952$		0			0
$953$	33138.1			1.12639			0.563194	−	0.826325i	$-0.309572\pi$
$953$	33138.1			1.12639			0.563194	+	0.826325i	$0.309572\pi$
$954$		0			0
$955$	−1005.99	−	1742.42i	−0.0340869	−	0.0590402i
$956$		0			0
$957$	−12318.2			−0.416084
$958$		0			0
$959$	−29871.7			−1.00585
$960$		0			0
$961$	−29745.7	+	1643.02i	−0.998478	+	0.0551515i
$962$		0			0
$963$	−21703.6			−0.726262
$964$		0			0
$965$	−792.144			−0.0264249
$966$		0			0
$967$	−25690.9	−	44497.9i	−0.854356	−	1.47979i	−0.877241	−	0.480050i	$-0.840618\pi$
$967$	−25690.9	−	44497.9i	−0.854356	−	1.47979i	0.0228850	−	0.999738i	$-0.492715\pi$
$968$		0			0
$969$	22494.0			0.745730
$970$		0			0
$971$	4540.30	−	7864.03i	0.150057	−	0.259906i	−0.781191	−	0.624292i	$-0.785388\pi$
$971$	4540.30	−	7864.03i	0.150057	−	0.259906i	0.931248	+	0.364386i	$0.118721\pi$
$972$		0			0
$973$	−4253.43	−	7367.16i	−0.140143	−	0.242734i
$974$		0			0
$975$	−1386.23	−	2401.02i	−0.0455332	−	0.0788658i
$976$		0			0
$977$	−14758.9			−0.483295			−0.241647	−	0.970364i	$-0.577688\pi$
$977$	−14758.9			−0.483295			−0.241647	+	0.970364i	$0.577688\pi$
$978$		0			0
$979$	22372.1	−	38749.7i	0.730354	−	1.26501i
$980$		0			0
$981$	−8669.81	+	15016.6i	−0.282167	+	0.488727i
$982$		0			0
$983$	5804.17	−	10053.1i	0.188326	−	0.326190i	−0.756366	−	0.654148i	$-0.773027\pi$
$983$	5804.17	−	10053.1i	0.188326	−	0.326190i	0.944692	+	0.327958i	$0.106361\pi$
$984$		0			0
$985$	559.807	+	969.614i	0.0181086	+	0.0313649i
$986$		0			0
$987$	404.733	−	701.018i	0.0130525	−	0.0226075i
$988$		0			0
$989$	8485.32	+	14697.0i	0.272818	+	0.472535i
$990$		0			0
$991$	37943.7			1.21627			0.608134	−	0.793834i	$-0.291918\pi$
$991$	37943.7			1.21627			0.608134	+	0.793834i	$0.291918\pi$
$992$		0			0
$993$	−12810.6			−0.409399
$994$		0			0
$995$	−134.061	−	232.200i	−0.00427137	−	0.00739823i
$996$		0			0
$997$	9624.53	−	16670.2i	0.305729	−	0.529538i	−0.671694	−	0.740828i	$-0.734433\pi$
$997$	9624.53	−	16670.2i	0.305729	−	0.529538i	0.977423	+	0.211290i	$0.0677665\pi$
$998$		0			0
$999$	−13463.2	−	23319.0i	−0.426385	−	0.738520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.4.e.b.25.2	yes	6
3.2	odd	2		1116.4.i.d.397.2		6
4.3	odd	2		496.4.i.b.273.2		6
31.5	even	3	inner	124.4.e.b.5.2	✓	6
93.5	odd	6		1116.4.i.d.253.2		6
124.67	odd	6		496.4.i.b.129.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.4.e.b.5.2	✓	6	31.5	even	3	inner
124.4.e.b.25.2	yes	6	1.1	even	1	trivial
496.4.i.b.129.2		6	124.67	odd	6
496.4.i.b.273.2		6	4.3	odd	2
1116.4.i.d.253.2		6	93.5	odd	6
1116.4.i.d.397.2		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	124.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36937 - 2.37182i) q^{3} +(-0.238743 + 0.413515i) q^{5} +(7.63063 + 13.2166i) q^{7} +(9.74964 - 16.8869i) q^{9} +O(q^{10})\)	\(q+(-1.36937 - 2.37182i) q^{3} +(-0.238743 + 0.413515i) q^{5} +(7.63063 + 13.2166i) q^{7} +(9.74964 - 16.8869i) q^{9} +(24.8127 - 42.9769i) q^{11} +(4.05664 - 7.02631i) q^{13} +1.30771 q^{15} +(-25.1364 - 43.5375i) q^{17} +(-81.6871 - 141.486i) q^{19} +(20.8983 - 36.1970i) q^{21} +200.635 q^{23} +(62.3860 + 108.056i) q^{25} -127.350 q^{27} +90.6344 q^{29} +(-4.76141 - 172.535i) q^{31} -135.911 q^{33} -7.28703 q^{35} +(105.719 + 183.110i) q^{37} -22.2202 q^{39} +(-131.637 + 228.002i) q^{41} +(42.2922 + 73.2522i) q^{43} +(4.65531 + 8.06324i) q^{45} +19.3667 q^{47} +(55.0470 - 95.3442i) q^{49} +(-68.8420 + 119.238i) q^{51} +(-229.078 + 396.776i) q^{53} +(11.8477 + 20.5209i) q^{55} +(-223.720 + 387.494i) q^{57} +(34.1870 + 59.2136i) q^{59} -573.316 q^{61} +297.584 q^{63} +(1.93699 + 3.35496i) q^{65} +(446.743 - 773.781i) q^{67} +(-274.745 - 475.871i) q^{69} +(-487.761 + 844.827i) q^{71} +(-475.727 + 823.983i) q^{73} +(170.859 - 295.937i) q^{75} +757.347 q^{77} +(149.833 + 259.518i) q^{79} +(-88.8515 - 153.895i) q^{81} +(133.695 - 231.567i) q^{83} +24.0045 q^{85} +(-124.112 - 214.968i) q^{87} +901.640 q^{89} +123.819 q^{91} +(-402.702 + 247.558i) q^{93} +78.0088 q^{95} +29.7796 q^{97} +(-483.831 - 838.019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} - 3 q^{5} + 45 q^{7} - 38 q^{9}+O(q^{10}) \) 6 * q - 9 * q^3 - 3 * q^5 + 45 * q^7 - 38 * q^9	\( 6 q - 9 q^{3} - 3 q^{5} + 45 q^{7} - 38 q^{9} + 61 q^{11} + 113 q^{13} + 386 q^{15} + 123 q^{17} + 63 q^{19} + 43 q^{21} + 96 q^{23} + 4 q^{25} + 918 q^{27} + 332 q^{29} - 668 q^{31} - 1214 q^{33} + 278 q^{35} + 129 q^{37} - 14 q^{39} - 709 q^{41} + 107 q^{43} - 1214 q^{45} - 568 q^{47} + 262 q^{49} + 293 q^{51} - 1267 q^{53} + 909 q^{55} + 681 q^{57} - 989 q^{59} - 2500 q^{61} + 36 q^{63} - 551 q^{65} + 741 q^{67} + 440 q^{69} - 1089 q^{71} - 197 q^{73} - 500 q^{75} + 982 q^{77} + 677 q^{79} - 2423 q^{81} + q^{83} + 58 q^{85} + 1194 q^{87} - 564 q^{89} + 4054 q^{91} + 1439 q^{93} - 2094 q^{95} - 2092 q^{97} + 2086 q^{99}+O(q^{100}) \) 6 * q - 9 * q^3 - 3 * q^5 + 45 * q^7 - 38 * q^9 + 61 * q^11 + 113 * q^13 + 386 * q^15 + 123 * q^17 + 63 * q^19 + 43 * q^21 + 96 * q^23 + 4 * q^25 + 918 * q^27 + 332 * q^29 - 668 * q^31 - 1214 * q^33 + 278 * q^35 + 129 * q^37 - 14 * q^39 - 709 * q^41 + 107 * q^43 - 1214 * q^45 - 568 * q^47 + 262 * q^49 + 293 * q^51 - 1267 * q^53 + 909 * q^55 + 681 * q^57 - 989 * q^59 - 2500 * q^61 + 36 * q^63 - 551 * q^65 + 741 * q^67 + 440 * q^69 - 1089 * q^71 - 197 * q^73 - 500 * q^75 + 982 * q^77 + 677 * q^79 - 2423 * q^81 + q^83 + 58 * q^85 + 1194 * q^87 - 564 * q^89 + 4054 * q^91 + 1439 * q^93 - 2094 * q^95 - 2092 * q^97 + 2086 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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