LMFDB - Embedded newform 25.4.e.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(4,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("25.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.e (of order $10$, degree $4$, 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:	$1.47504775014$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	25.19
Dual form			25.4.e.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.95462 + 1.60985i) q^{2} +(-1.70326 - 2.34434i) q^{3} +(15.4845 - 11.2501i) q^{4} +(11.0057 + 1.96864i) q^{5} +(12.2131 + 8.87330i) q^{6} -24.5811i q^{7} +(-34.1117 + 46.9507i) q^{8} +(5.74864 - 17.6925i) q^{9} +O(q^{10})$	\(q+(-4.95462 + 1.60985i) q^{2} +(-1.70326 - 2.34434i) q^{3} +(15.4845 - 11.2501i) q^{4} +(11.0057 + 1.96864i) q^{5} +(12.2131 + 8.87330i) q^{6} -24.5811i q^{7} +(-34.1117 + 46.9507i) q^{8} +(5.74864 - 17.6925i) q^{9} +(-57.6981 + 7.96365i) q^{10} +(-0.0967445 - 0.297749i) q^{11} +(-52.7483 - 17.1390i) q^{12} +(39.6785 + 12.8923i) q^{13} +(39.5719 + 121.790i) q^{14} +(-14.1304 - 29.1541i) q^{15} +(46.1103 - 141.913i) q^{16} +(3.64505 - 5.01698i) q^{17} +96.9140i q^{18} +(-69.4577 - 50.4640i) q^{19} +(192.564 - 93.3319i) q^{20} +(-57.6263 + 41.8680i) q^{21} +(0.958664 + 1.31949i) q^{22} +(40.3641 - 13.1151i) q^{23} +168.170 q^{24} +(117.249 + 43.3323i) q^{25} -217.347 q^{26} +(-125.679 + 40.8355i) q^{27} +(-276.540 - 380.625i) q^{28} +(-186.418 + 135.441i) q^{29} +(116.944 + 121.700i) q^{30} +(195.159 + 141.791i) q^{31} +313.081i q^{32} +(-0.533243 + 0.733946i) q^{33} +(-9.98322 + 30.7252i) q^{34} +(48.3912 - 270.531i) q^{35} +(-110.028 - 338.632i) q^{36} +(137.713 + 44.7455i) q^{37} +(425.376 + 138.213i) q^{38} +(-37.3589 - 114.979i) q^{39} +(-467.851 + 449.570i) q^{40} +(7.44654 - 22.9181i) q^{41} +(218.115 - 300.210i) q^{42} +259.208i q^{43} +(-4.84776 - 3.52210i) q^{44} +(98.0976 - 183.400i) q^{45} +(-178.875 + 129.961i) q^{46} +(-179.081 - 246.484i) q^{47} +(-411.230 + 133.617i) q^{48} -261.229 q^{49} +(-650.683 - 25.9413i) q^{50} -17.9700 q^{51} +(759.443 - 246.758i) q^{52} +(221.987 + 305.538i) q^{53} +(556.952 - 404.649i) q^{54} +(-0.478577 - 3.46738i) q^{55} +(1154.10 + 838.502i) q^{56} +248.786i q^{57} +(705.591 - 971.163i) q^{58} +(69.6150 - 214.253i) q^{59} +(-546.789 - 292.468i) q^{60} +(166.679 + 512.985i) q^{61} +(-1195.20 - 388.344i) q^{62} +(-434.900 - 141.308i) q^{63} +(-135.133 - 415.895i) q^{64} +(411.308 + 220.001i) q^{65} +(1.46047 - 4.49487i) q^{66} +(-34.5641 + 47.5735i) q^{67} -118.693i q^{68} +(-99.4968 - 72.2886i) q^{69} +(195.755 + 1418.28i) q^{70} +(-29.2126 + 21.2242i) q^{71} +(634.579 + 873.424i) q^{72} +(-779.711 + 253.343i) q^{73} -754.347 q^{74} +(-98.1201 - 348.677i) q^{75} -1643.24 q^{76} +(-7.31898 + 2.37808i) q^{77} +(370.198 + 509.534i) q^{78} +(249.462 - 181.245i) q^{79} +(786.850 - 1471.07i) q^{80} +(-96.5572 - 70.1529i) q^{81} +125.538i q^{82} +(249.003 - 342.723i) q^{83} +(-421.294 + 1296.61i) q^{84} +(49.9927 - 48.0393i) q^{85} +(-417.286 - 1284.28i) q^{86} +(635.037 + 206.336i) q^{87} +(17.2796 + 5.61450i) q^{88} +(139.074 + 428.027i) q^{89} +(-190.788 + 1066.60i) q^{90} +(316.907 - 975.341i) q^{91} +(477.471 - 657.182i) q^{92} -699.025i q^{93} +(1284.08 + 932.940i) q^{94} +(-665.082 - 692.126i) q^{95} +(733.969 - 533.260i) q^{96} +(232.545 + 320.071i) q^{97} +(1294.29 - 420.540i) q^{98} -5.82407 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) $ 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9 - 5 * q^10 + 83 * q^11 - 165 * q^12 - 5 * q^13 + 31 * q^14 - 225 * q^15 + 89 * q^16 - 165 * q^17 - 115 * q^19 + 395 * q^20 + 138 * q^21 + 30 * q^22 + 75 * q^23 + 640 * q^24 + 595 * q^25 - 822 * q^26 + 595 * q^27 + 675 * q^28 + 125 * q^29 - 965 * q^30 + 633 * q^31 - 1285 * q^33 - 779 * q^34 + 190 * q^35 - 531 * q^36 - 1510 * q^37 + 255 * q^38 - 1241 * q^39 - 2470 * q^40 - 117 * q^41 + 1745 * q^42 + 516 * q^44 + 1725 * q^45 + 1233 * q^46 - 95 * q^47 + 1410 * q^48 + 1148 * q^49 + 2165 * q^50 - 2022 * q^51 + 1740 * q^52 + 2580 * q^53 + 1745 * q^54 - 315 * q^55 + 3160 * q^56 - 4230 * q^58 - 1905 * q^59 + 560 * q^60 - 567 * q^61 - 6880 * q^62 - 1950 * q^63 - 3612 * q^64 - 3170 * q^65 - 2774 * q^66 + 4195 * q^67 + 539 * q^69 + 3630 * q^70 + 2473 * q^71 + 215 * q^72 - 845 * q^73 + 3596 * q^74 + 2045 * q^75 - 3280 * q^76 + 3870 * q^77 + 9295 * q^78 + 775 * q^79 - 3670 * q^80 + 3309 * q^81 - 4625 * q^83 - 5694 * q^84 - 1460 * q^85 - 3897 * q^86 - 8485 * q^87 - 1650 * q^88 - 2410 * q^89 - 8845 * q^90 - 382 * q^91 + 4090 * q^92 + 5401 * q^94 + 3545 * q^95 + 6488 * q^96 + 5185 * q^97 + 5180 * q^98 + 6024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−4.95462	+	1.60985i	−1.75172	+	0.569169i	−0.996290	−	0.0860573i	$-0.972573\pi$
$2$	−4.95462	+	1.60985i	−1.75172	+	0.569169i	−0.755432	+	0.655227i	$0.772573\pi$
$3$	−1.70326	−	2.34434i	−0.327793	−	0.451168i	0.613034	−	0.790057i	$-0.289949\pi$
$3$	−1.70326	−	2.34434i	−0.327793	−	0.451168i	−0.940826	+	0.338889i	$0.889949\pi$
$4$	15.4845	−	11.2501i	1.93556	−	1.40627i
$5$	11.0057	+	1.96864i	0.984376	+	0.176080i
$5$	11.0057	+	1.96864i	0.984376	+	0.176080i
$6$	12.2131	+	8.87330i	0.830993	+	0.603752i
$7$		−	24.5811i		−	1.32725i	−0.748064	−	0.663626i	$-0.769017\pi$
$7$		−	24.5811i		−	1.32725i	0.748064	−	0.663626i	$-0.230983\pi$
$8$	−34.1117	+	46.9507i	−1.50754	+	2.07495i
$9$	5.74864	−	17.6925i	0.212912	−	0.655277i
$10$	−57.6981	+	7.96365i	−1.82457	+	0.251833i
$11$	−0.0967445	−	0.297749i	−0.00265178	−	0.00816133i	0.949722	−	0.313095i	$-0.101366\pi$
$11$	−0.0967445	−	0.297749i	−0.00265178	−	0.00816133i	−0.952374	+	0.304933i	$0.901366\pi$
$12$	−52.7483	−	17.1390i	−1.26893	−	0.412299i
$13$	39.6785	+	12.8923i	0.846527	+	0.275053i	0.699990	−	0.714152i	$-0.253188\pi$
$13$	39.6785	+	12.8923i	0.846527	+	0.275053i	0.146536	+	0.989205i	$0.453188\pi$
$14$	39.5719	+	121.790i	0.755431	+	2.32498i
$15$	−14.1304	−	29.1541i	−0.243230	−	0.501837i
$16$	46.1103	−	141.913i	0.720474	−	2.21739i
$17$	3.64505	−	5.01698i	0.0520032	−	0.0715762i	−0.782223	−	0.622998i	$-0.785914\pi$
$17$	3.64505	−	5.01698i	0.0520032	−	0.0715762i	0.834227	+	0.551422i	$0.185914\pi$
$18$			96.9140i			1.26905i
$19$	−69.4577	−	50.4640i	−0.838668	−	0.609328i	0.0833306	−	0.996522i	$-0.473444\pi$
$19$	−69.4577	−	50.4640i	−0.838668	−	0.609328i	−0.921998	+	0.387194i	$0.873444\pi$
$20$	192.564	−	93.3319i	2.15294	−	1.04348i
$21$	−57.6263	+	41.8680i	−0.598814	+	0.435064i
$22$	0.958664	+	1.31949i	0.00929036	+	0.0127871i
$23$	40.3641	−	13.1151i	0.365934	−	0.118899i	−0.120277	−	0.992740i	$-0.538378\pi$
$23$	40.3641	−	13.1151i	0.365934	−	0.118899i	0.486212	+	0.873841i	$0.338378\pi$
$24$	168.170			1.43031
$25$	117.249	+	43.3323i	0.937992	+	0.346658i
$26$	−217.347			−1.63943
$27$	−125.679	+	40.8355i	−0.895811	+	0.291067i
$28$	−276.540	−	380.625i	−1.86647	−	2.56898i
$29$	−186.418	+	135.441i	−1.19369	+	0.867265i	−0.993649	−	0.112522i	$-0.964107\pi$
$29$	−186.418	+	135.441i	−1.19369	+	0.867265i	−0.200039	+	0.979788i	$0.564107\pi$
$30$	116.944	+	121.700i	0.711701	+	0.740640i
$31$	195.159	+	141.791i	1.13069	+	0.821498i	0.985796	−	0.167949i	$-0.0537142\pi$
$31$	195.159	+	141.791i	1.13069	+	0.821498i	0.144899	+	0.989446i	$0.453714\pi$
$32$			313.081i			1.72955i
$33$	−0.533243	+	0.733946i	−0.00281290	+	0.00387162i
$34$	−9.98322	+	30.7252i	−0.0503561	+	0.154980i
$35$	48.3912	−	270.531i	0.233703	−	1.30652i
$36$	−110.028	−	338.632i	−0.509390	−	1.56774i
$37$	137.713	+	44.7455i	0.611887	+	0.198814i	0.598535	−	0.801097i	$-0.295750\pi$
$37$	137.713	+	44.7455i	0.611887	+	0.198814i	0.0133520	+	0.999911i	$0.495750\pi$
$38$	425.376	+	138.213i	1.81592	+	0.590029i
$39$	−37.3589	−	114.979i	−0.153390	−	0.472086i
$40$	−467.851	+	449.570i	−1.84934	+	1.77708i
$41$	7.44654	−	22.9181i	0.0283647	−	0.0872977i	−0.935872	−	0.352340i	$-0.885386\pi$
$41$	7.44654	−	22.9181i	0.0283647	−	0.0872977i	0.964237	+	0.265043i	$0.0853860\pi$
$42$	218.115	−	300.210i	0.801331	−	1.10294i
$43$			259.208i			0.919275i	0.888107	+	0.459637i	$0.152021\pi$
$43$			259.208i			0.919275i	−0.888107	+	0.459637i	$0.847979\pi$
$44$	−4.84776	−	3.52210i	−0.0166097	−	0.0120677i
$45$	98.0976	−	183.400i	0.324967	−	0.607549i
$46$	−178.875	+	129.961i	−0.573342	+	0.416557i
$47$	−179.081	−	246.484i	−0.555780	−	0.764965i	0.435003	−	0.900429i	$-0.356747\pi$
$47$	−179.081	−	246.484i	−0.555780	−	0.764965i	−0.990782	+	0.135464i	$0.956747\pi$
$48$	−411.230	+	133.617i	−1.23658	+	0.401790i
$49$	−261.229			−0.761599
$50$	−650.683	−	25.9413i	−1.84041	−	0.0733730i
$51$	−17.9700			−0.0493392
$52$	759.443	−	246.758i	2.02530	−	0.658061i
$53$	221.987	+	305.538i	0.575325	+	0.791867i	0.993173	−	0.116650i	$-0.0372156\pi$
$53$	221.987	+	305.538i	0.575325	+	0.791867i	−0.417848	+	0.908517i	$0.637216\pi$
$54$	556.952	−	404.649i	1.40355	−	1.01974i
$55$	−0.478577	−	3.46738i	−0.00117330	−	0.00850074i
$56$	1154.10	+	838.502i	2.75398	+	2.00088i
$57$			248.786i			0.578113i
$58$	705.591	−	971.163i	1.59739	−	2.19862i
$59$	69.6150	−	214.253i	0.153612	−	0.472769i	−0.844406	−	0.535704i	$-0.820046\pi$
$59$	69.6150	−	214.253i	0.153612	−	0.472769i	0.998018	+	0.0629355i	$0.0200462\pi$
$60$	−546.789	−	292.468i	−1.17650	−	0.629290i
$61$	166.679	+	512.985i	0.349854	+	1.07674i	0.958934	+	0.283630i	$0.0915387\pi$
$61$	166.679	+	512.985i	0.349854	+	1.07674i	−0.609080	+	0.793109i	$0.708461\pi$
$62$	−1195.20	−	388.344i	−2.44824	−	0.795480i
$63$	−434.900	−	141.308i	−0.869718	−	0.282589i
$64$	−135.133	−	415.895i	−0.263931	−	0.812296i
$65$	411.308	+	220.001i	0.784869	+	0.419812i
$66$	1.46047	−	4.49487i	0.00272381	−	0.00838303i
$67$	−34.5641	+	47.5735i	−0.0630251	+	0.0867466i	−0.839366	−	0.543567i	$-0.817074\pi$
$67$	−34.5641	+	47.5735i	−0.0630251	+	0.0867466i	0.776341	+	0.630313i	$0.217074\pi$
$68$		−	118.693i		−	0.211671i
$69$	−99.4968	−	72.2886i	−0.173594	−	0.126124i
$70$	195.755	+	1418.28i	0.334246	+	2.42167i
$71$	−29.2126	+	21.2242i	−0.0488295	+	0.0354767i	−0.611932	−	0.790910i	$-0.709608\pi$
$71$	−29.2126	+	21.2242i	−0.0488295	+	0.0354767i	0.563103	+	0.826387i	$0.309608\pi$
$72$	634.579	+	873.424i	1.03869	+	1.42964i
$73$	−779.711	+	253.343i	−1.25011	+	0.406186i	−0.857961	−	0.513714i	$-0.828269\pi$
$73$	−779.711	+	253.343i	−1.25011	+	0.406186i	−0.392152	+	0.919901i	$0.628269\pi$
$74$	−754.347			−1.18501
$75$	−98.1201	−	348.677i	−0.151066	−	0.536824i
$76$	−1643.24			−2.48017
$77$	−7.31898	+	2.37808i	−0.0108321	+	0.00351958i
$78$	370.198	+	509.534i	0.537394	+	0.739659i
$79$	249.462	−	181.245i	0.355274	−	0.258122i	−0.395804	−	0.918335i	$-0.629534\pi$
$79$	249.462	−	181.245i	0.355274	−	0.258122i	0.751078	+	0.660213i	$0.229534\pi$
$80$	786.850	−	1471.07i	1.09966	−	2.05588i
$81$	−96.5572	−	70.1529i	−0.132452	−	0.0962317i
$82$			125.538i			0.169066i
$83$	249.003	−	342.723i	0.329297	−	0.453238i	−0.611980	−	0.790873i	$-0.709627\pi$
$83$	249.003	−	342.723i	0.329297	−	0.453238i	0.941277	+	0.337635i	$0.109627\pi$
$84$	−421.294	+	1296.61i	−0.547225	+	1.68419i
$85$	49.9927	−	48.0393i	0.0637938	−	0.0613012i
$86$	−417.286	−	1284.28i	−0.523223	−	1.61031i
$87$	635.037	+	206.336i	0.782565	+	0.254271i
$88$	17.2796	+	5.61450i	0.0209320	+	0.00680122i
$89$	139.074	+	428.027i	0.165639	+	0.509784i	0.999083	−	0.0428203i	$-0.0136343\pi$
$89$	139.074	+	428.027i	0.165639	+	0.509784i	−0.833444	+	0.552604i	$0.813634\pi$
$90$	−190.788	+	1066.60i	−0.223454	+	1.24922i
$91$	316.907	−	975.341i	0.365065	−	1.12355i
$92$	477.471	−	657.182i	0.541084	−	0.744739i
$93$		−	699.025i		−	0.779415i
$94$	1284.08	+	932.940i	1.40897	+	1.02367i
$95$	−665.082	−	692.126i	−0.718274	−	0.747480i
$96$	733.969	−	533.260i	0.780316	−	0.566933i
$97$	232.545	+	320.071i	0.243416	+	0.335034i	0.913192	−	0.407530i	$-0.133610\pi$
$97$	232.545	+	320.071i	0.243416	+	0.335034i	−0.669776	+	0.742564i	$0.733610\pi$
$98$	1294.29	−	420.540i	1.33411	−	0.433479i
$99$	−5.82407			−0.00591253
$100$	2303.03	−	648.089i	2.30303	−	0.648089i
$101$	835.123			0.822751			0.411375	−	0.911466i	$-0.365049\pi$
$101$	835.123			0.822751			0.411375	+	0.911466i	$0.365049\pi$
$102$	89.0343	−	28.9290i	0.0864285	−	0.0280823i
$103$	−162.807	−	224.084i	−0.155746	−	0.214366i	0.724012	−	0.689787i	$-0.242296\pi$
$103$	−162.807	−	224.084i	−0.155746	−	0.214366i	−0.879758	+	0.475421i	$0.842296\pi$
$104$	−1958.81	+	1423.16i	−1.84689	+	1.34185i
$105$	−716.638	+	347.339i	−0.666064	+	0.322827i
$106$	−1591.73	−	1156.46i	−1.45852	−	1.05967i
$107$			1892.24i			1.70962i	0.518941	+	0.854810i	$0.326326\pi$
$107$			1892.24i			1.70962i	−0.518941	+	0.854810i	$0.673674\pi$
$108$	−1486.67	+	2046.22i	−1.32458	+	1.82313i
$109$	526.243	−	1619.61i	0.462430	−	1.42321i	−0.399756	−	0.916622i	$-0.630905\pi$
$109$	526.243	−	1619.61i	0.462430	−	1.42321i	0.862186	−	0.506592i	$-0.169095\pi$
$110$	7.95314	+	16.4091i	0.00689365	+	0.0142231i
$111$	−129.662	−	399.058i	−0.110874	−	0.341234i
$112$	−3488.37	−	1133.44i	−2.94304	−	0.956251i
$113$	−885.184	−	287.614i	−0.736912	−	0.239437i	−0.0835719	−	0.996502i	$-0.526633\pi$
$113$	−885.184	−	287.614i	−0.736912	−	0.239437i	−0.653340	+	0.757065i	$0.726633\pi$
$114$	−400.508	−	1232.64i	−0.329044	−	1.01269i
$115$	470.052	−	64.8779i	0.381153	−	0.0526078i
$116$	−1362.86	+	4194.46i	−1.09085	+	3.35729i
$117$	456.195	−	627.899i	0.360472	−	0.496147i
$118$			1173.61i			0.915591i
$119$	−123.323	−	89.5991i	−0.0949997	−	0.0690213i
$120$	1850.82	+	331.065i	1.40796	+	0.251849i
$121$	1076.72	−	782.285i	0.808957	−	0.587742i
$122$	−1651.66	−	2273.32i	−1.22569	−	1.68702i
$123$	−66.4112	+	21.5783i	−0.0486837	+	0.0158183i
$124$	4617.10			3.34378
$125$	1205.10	+	707.721i	0.862297	+	0.506404i
$126$	2382.25			1.68435
$127$	−1442.13	+	468.576i	−1.00762	+	0.327397i	−0.765908	−	0.642950i	$-0.777710\pi$
$127$	−1442.13	+	468.576i	−1.00762	+	0.327397i	−0.241716	+	0.970347i	$0.577710\pi$
$128$	−133.136	−	183.245i	−0.0919347	−	0.126537i
$129$	607.671	−	441.499i	0.414747	−	0.301332i
$130$	−2392.04	−	427.877i	−1.61382	−	0.288671i
$131$	249.445	+	181.233i	0.166367	+	0.120873i	0.667854	−	0.744293i	$-0.267213\pi$
$131$	249.445	+	181.233i	0.166367	+	0.120873i	−0.501486	+	0.865166i	$0.667213\pi$
$132$			17.3638i			0.0114495i
$133$	−1240.46	+	1707.34i	−0.808732	+	1.11312i
$134$	94.6659	−	291.352i	0.0610290	−	0.187828i
$135$	−1463.57	+	202.006i	−0.933066	+	0.128784i
$136$	111.212	+	342.275i	0.0701202	+	0.215808i
$137$	992.307	+	322.420i	0.618822	+	0.201067i	0.601617	−	0.798785i	$-0.294523\pi$
$137$	992.307	+	322.420i	0.618822	+	0.201067i	0.0172045	+	0.999852i	$0.494523\pi$
$138$	609.343	+	197.987i	0.375875	+	0.122129i
$139$	933.130	+	2871.88i	0.569403	+	1.75244i	0.654492	+	0.756069i	$0.272883\pi$
$139$	933.130	+	2871.88i	0.569403	+	1.75244i	−0.0850886	+	0.996373i	$0.527117\pi$
$140$	−2294.20	−	4733.44i	−1.38496	−	2.85749i
$141$	−272.820	+	839.653i	−0.162947	+	0.501500i
$142$	110.569	−	152.186i	0.0653435	−	0.0899376i
$143$		−	13.0615i		−	0.00763816i
$144$	−2245.72	−	1631.61i	−1.29961	−	0.944220i
$145$	−2318.29	+	1123.62i	−1.32775	+	0.643530i
$146$	3455.32	−	2510.44i	1.95866	−	1.42305i
$147$	444.941	+	612.408i	0.249647	+	0.343609i
$148$	2635.80	−	856.424i	1.46393	−	0.475660i
$149$	−2768.80			−1.52234			−0.761172	−	0.648550i	$-0.775376\pi$
$149$	−2768.80			−1.52234			−0.761172	+	0.648550i	$0.775376\pi$
$150$	1047.47	+	1569.60i	0.570169	+	0.854385i
$151$	−1947.75			−1.04971			−0.524854	−	0.851192i	$-0.675880\pi$
$151$	−1947.75			−1.04971			−0.524854	+	0.851192i	$0.675880\pi$
$152$	4738.64	−	1539.68i	2.52865	−	0.821607i
$153$	−67.8087	−	93.3307i	−0.0358301	−	0.0493160i
$154$	32.4344	−	23.5650i	0.0169717	−	0.0123307i
$155$	1868.71	+	1944.70i	0.968379	+	1.00776i
$156$	−1872.01	−	1360.10i	−0.960776	−	0.698044i
$157$		−	2213.57i		−	1.12523i	−0.826718	−	0.562617i	$-0.809795\pi$
$157$		−	2213.57i		−	1.12523i	0.826718	−	0.562617i	$-0.190205\pi$
$158$	−944.211	+	1299.60i	−0.475427	+	0.654369i
$159$	338.184	−	1040.82i	0.168678	−	0.519136i
$160$	−616.343	+	3445.67i	−0.304539	+	1.70252i
$161$	−322.383	−	992.192i	−0.157809	−	0.485687i
$162$	591.340	+	192.138i	0.286791	+	0.0931839i
$163$	1821.56	+	591.859i	0.875308	+	0.284405i	0.712008	−	0.702171i	$-0.247786\pi$
$163$	1821.56	+	591.859i	0.875308	+	0.284405i	0.163300	+	0.986576i	$0.447786\pi$
$164$	−142.526	−	438.650i	−0.0678622	−	0.208858i
$165$	−7.31356	+	7.02779i	−0.00345067	+	0.00331584i
$166$	−681.981	+	2098.92i	−0.318867	+	0.981373i
$167$	−652.079	+	897.510i	−0.302152	+	0.415877i	−0.932914	−	0.360100i	$-0.882743\pi$
$167$	−652.079	+	897.510i	−0.302152	+	0.415877i	0.630762	+	0.775977i	$0.282743\pi$
$168$		−	4133.79i		−	1.89838i
$169$	−369.237	−	268.266i	−0.168064	−	0.122106i
$170$	−170.359	+	318.498i	−0.0768583	+	0.143692i
$171$	−1292.12	+	938.780i	−0.577841	+	0.419826i
$172$	2916.12	+	4013.70i	1.29275	+	1.77931i
$173$	1668.83	−	542.235i	0.733403	−	0.238297i	0.0815786	−	0.996667i	$-0.474004\pi$
$173$	1668.83	−	542.235i	0.733403	−	0.238297i	0.651825	+	0.758370i	$0.274004\pi$
$174$	−3478.54			−1.51556
$175$	1065.15	−	2882.10i	0.460103	−	1.24495i
$176$	−46.7154			−0.0200074
$177$	−620.854	+	201.728i	−0.263651	+	0.0856654i
$178$	−1378.12	−	1896.82i	−0.580306	−	0.798723i
$179$	2460.43	−	1787.60i	1.02738	−	0.746435i	0.0595965	−	0.998223i	$-0.481019\pi$
$179$	2460.43	−	1787.60i	1.02738	−	0.746435i	0.967782	+	0.251788i	$0.0810186\pi$
$180$	−544.290	−	3943.47i	−0.225383	−	1.63294i
$181$	−326.276	−	237.053i	−0.133988	−	0.0973481i	0.518772	−	0.854912i	$-0.326389\pi$
$181$	−326.276	−	237.053i	−0.133988	−	0.0973481i	−0.652761	+	0.757564i	$0.726389\pi$
$182$			5342.62i			2.17594i
$183$	918.713	−	1264.50i	0.371111	−	0.510790i
$184$	−761.125	+	2342.50i	−0.304950	+	0.938541i
$185$	1427.53	+	763.560i	0.567319	+	0.303449i
$186$	1125.33	+	3463.40i	0.443619	+	1.36532i
$187$	−1.84644	−	0.599944i	−0.000722058	−	0.000234611i
$188$	−5545.96	−	1801.99i	−2.15149	−	0.699062i
$189$	1003.78	+	3089.32i	0.386319	+	1.18897i
$190$	4409.45	+	2358.54i	1.68366	+	0.900559i
$191$	−1.82439	+	5.61489i	−0.000691142	+	0.00212712i	−0.951401	−	0.307953i	$-0.900356\pi$
$191$	−1.82439	+	5.61489i	−0.000691142	+	0.00212712i	0.950710	+	0.310080i	$0.100356\pi$
$192$	−744.833	+	1025.18i	−0.279967	+	0.385342i
$193$		−	4750.58i		−	1.77179i	−0.463890	−	0.885893i	$-0.653547\pi$
$193$		−	4750.58i		−	1.77179i	0.463890	−	0.885893i	$-0.346453\pi$
$194$	−1667.44	−	1211.47i	−0.617089	−	0.448341i
$195$	−184.808	−	1338.96i	−0.0678685	−	0.491719i
$196$	−4044.99	+	2938.86i	−1.47412	+	1.07101i
$197$	−3043.27	−	4188.70i	−1.10063	−	1.51488i	−0.834549	−	0.550934i	$-0.814272\pi$
$197$	−3043.27	−	4188.70i	−1.10063	−	1.51488i	−0.266079	−	0.963951i	$-0.585728\pi$
$198$	28.8560	−	9.37589i	0.0103571	−	0.00336523i
$199$	−2049.83			−0.730192			−0.365096	−	0.930970i	$-0.618964\pi$
$199$	−2049.83			−0.730192			−0.365096	+	0.930970i	$0.618964\pi$
$200$	−6034.04	+	4026.79i	−2.13336	+	1.42368i
$201$	170.400			0.0597965
$202$	−4137.72	+	1344.43i	−1.44123	+	0.468284i
$203$	3329.27	+	4582.35i	1.15108	+	1.58433i
$204$	−278.256	+	202.165i	−0.0954990	+	0.0693841i
$205$	127.071	−	237.569i	0.0432930	−	0.0809393i
$206$	1167.39	+	848.158i	0.394834	+	0.286864i
$207$		−	789.535i		−	0.265104i
$208$	3659.18	−	5036.43i	1.21980	−	1.67891i
$209$	−8.30594	+	25.5631i	−0.00274897	+	0.00846045i
$210$	2991.50	−	2874.62i	0.983016	−	0.944607i
$211$	543.552	+	1672.88i	0.177344	+	0.545810i	0.999733	−	0.0231167i	$-0.00735894\pi$
$211$	543.552	+	1672.88i	0.177344	+	0.545810i	−0.822388	+	0.568926i	$0.807359\pi$
$212$	6874.70	+	2233.73i	2.22715	+	0.723646i
$213$	99.5133	+	32.3338i	0.0320119	+	0.0104013i
$214$	−3046.22	−	9375.31i	−0.973063	−	2.99478i
$215$	−510.286	+	2852.75i	−0.161866	+	0.904912i
$216$	2369.86	−	7293.68i	0.746522	−	2.29756i
$217$	3485.38	−	4797.21i	1.09034	−	1.50072i
$218$			8871.72i			2.75628i
$219$	1921.97	+	1396.40i	0.593036	+	0.430866i
$220$	−46.4190	−	48.3065i	−0.0142253	−	0.0148037i
$221$	209.311	−	152.073i	0.0637093	−	0.0462875i
$222$	1284.85	+	1768.45i	0.388439	+	0.534641i
$223$	−2880.43	+	935.909i	−0.864969	+	0.281045i	−0.707702	−	0.706511i	$-0.750268\pi$
$223$	−2880.43	+	935.909i	−0.864969	+	0.281045i	−0.157267	+	0.987556i	$0.550268\pi$
$224$	7695.87			2.29555
$225$	1440.68	−	1825.32i	0.426867	−	0.540837i
$226$	4848.76			1.42715
$227$	−154.776	+	50.2899i	−0.0452549	+	0.0147042i	−0.331557	−	0.943435i	$-0.607574\pi$
$227$	−154.776	+	50.2899i	−0.0452549	+	0.0147042i	0.286302	+	0.958139i	$0.407574\pi$
$228$	2798.87	+	3852.32i	0.812982	+	1.11897i
$229$	−4086.13	+	2968.74i	−1.17912	+	0.856682i	−0.992072	−	0.125669i	$-0.959892\pi$
$229$	−4086.13	+	2968.74i	−1.17912	+	0.856682i	−0.187049	+	0.982351i	$0.559892\pi$
$230$	−2224.48	+	1078.16i	−0.637731	+	0.309095i
$231$	18.0412	+	13.1077i	0.00513862	+	0.00373343i
$232$		−	13372.6i		−	3.78428i
$233$	2190.81	−	3015.39i	0.615986	−	0.847832i	−0.381067	−	0.924548i	$-0.624443\pi$
$233$	2190.81	−	3015.39i	0.615986	−	0.847832i	0.997053	+	0.0767152i	$0.0244432\pi$
$234$	−1249.45	+	3845.41i	−0.349055	+	1.07428i
$235$	−1485.67	−	3065.26i	−0.412401	−	0.850875i
$236$	−1332.42	−	4100.78i	−0.367514	−	1.13109i
$237$	−849.797	−	276.116i	−0.232913	−	0.0756779i
$238$	755.258	+	245.398i	0.205698	+	0.0668353i
$239$	235.510	+	724.824i	0.0637400	+	0.196171i	0.977855	−	0.209283i	$-0.0671131\pi$
$239$	235.510	+	724.824i	0.0637400	+	0.196171i	−0.914115	+	0.405455i	$0.867113\pi$
$240$	−4788.90	+	660.978i	−1.28801	+	0.177775i
$241$	−248.407	+	764.519i	−0.0663956	+	0.204345i	−0.978750	−	0.205056i	$-0.934262\pi$
$241$	−248.407	+	764.519i	−0.0663956	+	0.204345i	0.912355	+	0.409401i	$0.134262\pi$
$242$	−4075.39	+	5609.29i	−1.08254	+	1.48999i
$243$			3913.81i			1.03321i
$244$	8352.10	+	6068.16i	2.19135	+	1.59211i
$245$	−2874.99	−	514.264i	−0.749700	−	0.134103i
$246$	294.304	−	213.825i	0.0762770	−	0.0554185i
$247$	−2105.38	−	2897.81i	−0.542357	−	0.746490i
$248$	−13314.4	+	4326.11i	−3.40913	+	1.10769i
$249$	−1227.58			−0.312428
$250$	−7110.12	−	1566.46i	−1.79873	−	0.396286i
$251$	−3428.57			−0.862188			−0.431094	−	0.902307i	$-0.641872\pi$
$251$	−3428.57			−0.862188			−0.431094	+	0.902307i	$0.641872\pi$
$252$	−8323.94	+	2704.61i	−2.08079	+	0.676089i
$253$	−7.81000	−	10.7495i	−0.00194075	−	0.00267122i
$254$	6390.86	−	4643.23i	1.57873	−	1.14702i
$255$	−197.771	−	35.3763i	−0.0485683	−	0.00868765i
$256$	3784.89	+	2749.88i	0.924045	+	0.671358i
$257$			5337.53i			1.29551i	0.761849	+	0.647754i	$0.224292\pi$
$257$			5337.53i			1.29551i	−0.761849	+	0.647754i	$0.775708\pi$
$258$	−2300.03	+	3165.72i	−0.555014	+	0.763911i
$259$	1099.89	−	3385.12i	0.263876	−	0.812128i
$260$	8843.94	−	1220.67i	2.10953	−	0.291163i
$261$	1324.63	+	4076.80i	0.314148	+	0.966848i
$262$	−1527.66	−	496.368i	−0.360227	−	0.117045i
$263$	6258.22	+	2033.42i	1.46729	+	0.476753i	0.930290	−	0.366826i	$-0.119556\pi$
$263$	6258.22	+	2033.42i	1.46729	+	0.476753i	0.537005	+	0.843579i	$0.319556\pi$
$264$	−16.2695	−	50.0723i	−0.00379287	−	0.0116732i
$265$	1841.62	+	3799.66i	0.426904	+	0.880798i
$266$	3397.42	−	10456.2i	0.783118	−	2.41019i
$267$	766.559	−	1055.08i	0.175703	−	0.241834i
$268$			1125.50i			0.256534i
$269$	−2271.06	−	1650.02i	−0.514754	−	0.373990i	0.299870	−	0.953980i	$-0.403057\pi$
$269$	−2271.06	−	1650.02i	−0.514754	−	0.373990i	−0.814624	+	0.579990i	$0.803057\pi$
$270$	6926.23	−	3356.99i	1.56117	−	0.756667i
$271$	−5748.15	+	4176.27i	−1.28847	+	0.936127i	−0.999773	−	0.0212935i	$-0.993222\pi$
$271$	−5748.15	+	4176.27i	−1.28847	+	0.936127i	−0.288696	+	0.957421i	$0.593222\pi$
$272$	−543.900	−	748.614i	−0.121245	−	0.166880i
$273$	−2826.30	+	918.322i	−0.626578	+	0.203587i
$274$	−5435.56			−1.19844
$275$	1.55895	−	39.1029i	0.000341847	−	0.00857452i
$276$	−2353.91			−0.513366
$277$	3357.62	−	1090.96i	0.728302	−	0.236640i	0.0786830	−	0.996900i	$-0.474929\pi$
$277$	3357.62	−	1090.96i	0.728302	−	0.236640i	0.649619	+	0.760260i	$0.274929\pi$
$278$	−9246.61	−	12726.9i	−1.99487	−	2.74571i
$279$	3630.53	−	2637.74i	0.779048	−	0.566011i
$280$	11050.9	+	11500.3i	2.35864	+	2.45454i
$281$	−1473.09	−	1070.26i	−0.312731	−	0.227212i	0.420337	−	0.907368i	$-0.361912\pi$
$281$	−1473.09	−	1070.26i	−0.312731	−	0.227212i	−0.733067	+	0.680156i	$0.761912\pi$
$282$		−	4599.36i		−	0.971234i
$283$	524.340	−	721.691i	0.110137	−	0.151590i	−0.750390	−	0.660995i	$-0.770134\pi$
$283$	524.340	−	721.691i	0.110137	−	0.151590i	0.860527	+	0.509405i	$0.170134\pi$
$284$	−213.567	+	657.291i	−0.0446228	+	0.137335i
$285$	−489.768	+	2738.05i	−0.101794	+	0.569081i
$286$	21.0271	+	64.7148i	0.00434741	+	0.0133799i
$287$	−563.351	−	183.044i	−0.115866	−	0.0376472i
$288$	5539.19	+	1799.79i	1.13333	+	0.368242i
$289$	1506.32	+	4635.97i	0.306598	+	0.943612i
$290$	9677.36	−	9299.23i	1.95957	−	1.88300i
$291$	354.269	−	1090.33i	0.0713665	−	0.219643i
$292$	−9223.28	+	12694.8i	−1.84846	+	2.54419i
$293$		−	2936.32i		−	0.585466i	−0.956194	−	0.292733i	$-0.905435\pi$
$293$		−	2936.32i		−	0.585466i	0.956194	−	0.292733i	$-0.0945647\pi$
$294$	−3190.40	−	2317.96i	−0.632884	−	0.459817i
$295$	1187.94	−	2220.95i	0.234457	−	0.438334i
$296$	−6798.45	+	4939.36i	−1.33497	+	0.969914i
$297$	24.3175	+	33.4701i	0.00475098	+	0.00653917i
$298$	13718.4	−	4457.37i	2.66672	−	0.866471i
$299$	1770.67			0.342477
$300$	−5442.01	−	4295.23i	−1.04732	−	0.826617i
$301$	6371.60			1.22011
$302$	9650.39	−	3135.60i	1.83880	−	0.597462i
$303$	−1422.43	−	1957.81i	−0.269692	−	0.371199i
$304$	−10364.2	+	7530.04i	−1.95536	+	1.42065i
$305$	824.531	+	5973.87i	0.154795	+	1.12152i
$306$	486.215	+	353.256i	0.0908336	+	0.0659945i
$307$			1136.05i			0.211198i	0.994409	+	0.105599i	$0.0336759\pi$
$307$			1136.05i			0.211198i	−0.994409	+	0.105599i	$0.966324\pi$
$308$	−86.5770	+	119.163i	−0.0160168	+	0.0220453i
$309$	−248.027	+	763.349i	−0.0456627	+	0.140535i
$310$	−12389.5	−	6626.90i	−2.26992	−	1.21414i
$311$	−3255.80	−	10020.3i	−0.593631	−	1.82701i	−0.561424	−	0.827528i	$-0.689746\pi$
$311$	−3255.80	−	10020.3i	−0.593631	−	1.82701i	−0.0322076	−	0.999481i	$-0.510254\pi$
$312$	6672.72	+	2168.10i	1.21080	+	0.393412i
$313$	−4137.62	−	1344.39i	−0.747195	−	0.242778i	−0.0894210	−	0.995994i	$-0.528502\pi$
$313$	−4137.62	−	1344.39i	−0.747195	−	0.242778i	−0.657774	+	0.753216i	$0.728502\pi$
$314$	3563.52	+	10967.4i	0.640449	+	1.97110i
$315$	−4508.18	−	2411.34i	−0.806371	−	0.431314i
$316$	1823.76	−	5612.96i	0.324667	−	0.999221i
$317$	185.837	−	255.783i	0.0329264	−	0.0453193i	−0.792236	−	0.610214i	$-0.791083\pi$
$317$	185.837	−	255.783i	0.0329264	−	0.0453193i	0.825163	+	0.564895i	$0.191083\pi$
$318$			5701.31i			1.00539i
$319$	58.3622	+	42.4026i	0.0102434	+	0.00744229i
$320$	−668.476	−	4843.23i	−0.116778	−	0.846077i
$321$	4436.04	−	3222.97i	0.771326	−	0.560401i
$322$	3194.57	+	4396.94i	0.552877	+	0.760969i
$323$	−506.353	+	164.524i	−0.0872267	+	0.0283417i
$324$	−2284.37			−0.391696
$325$	4093.61	+	3230.97i	0.698685	+	0.551453i
$326$	−9977.92			−1.69517
$327$	−4693.24	+	1524.93i	−0.793690	+	0.257886i
$328$	822.007	+	1131.40i	0.138377	+	0.190460i
$329$	−6058.83	+	4402.00i	−1.01530	+	0.737660i
$330$	24.9222	−	46.5938i	0.00415734	−	0.00777244i
$331$	396.145	+	287.816i	0.0657828	+	0.0477940i	0.620191	−	0.784451i	$-0.287055\pi$
$331$	396.145	+	287.816i	0.0657828	+	0.0477940i	−0.554408	+	0.832245i	$0.687055\pi$
$332$		−	8108.22i		−	1.34035i
$333$	1583.32	−	2179.25i	0.260557	−	0.358625i
$334$	1785.95	−	5496.57i	0.292583	−	0.900477i
$335$	−474.056	+	455.533i	−0.0773147	+	0.0742938i
$336$	3284.44	+	10108.5i	0.533277	+	1.64126i
$337$	4078.51	+	1325.19i	0.659261	+	0.214207i	0.619493	−	0.785002i	$-0.287338\pi$
$337$	4078.51	+	1325.19i	0.659261	+	0.214207i	0.0397676	+	0.999209i	$0.487338\pi$
$338$	2261.30	+	734.739i	0.363900	+	0.118238i
$339$	833.435	+	2565.05i	0.133528	+	0.410957i
$340$	233.663	−	1306.29i	0.0372710	−	0.208363i
$341$	23.3376	−	71.8258i	0.00370617	−	0.0114064i
$342$	4890.66	−	6731.42i	0.773266	−	1.06431i
$343$		−	2010.03i		−	0.316418i
$344$	−12170.0	−	8842.02i	−1.90745	−	1.38584i
$345$	−952.717	−	991.457i	−0.148674	−	0.154720i
$346$	−7395.49	+	5373.14i	−1.14909	+	0.834861i
$347$	3089.90	+	4252.88i	0.478024	+	0.657943i	0.978124	−	0.208024i	$-0.0667033\pi$
$347$	3089.90	+	4252.88i	0.478024	+	0.657943i	−0.500100	+	0.865968i	$0.666703\pi$
$348$	12154.5	−	3949.25i	1.87228	−	0.608339i
$349$	12648.3			1.93996			0.969982	−	0.243176i	$-0.0781891\pi$
$349$	12648.3			1.93996			0.969982	+	0.243176i	$0.0781891\pi$
$350$	−637.664	+	15994.5i	−0.0973845	+	2.44269i
$351$	−5513.22			−0.838387
$352$	93.2196	−	30.2889i	0.0141154	−	0.00458637i
$353$	689.115	+	948.486i	0.103903	+	0.143011i	0.857802	−	0.513979i	$-0.171829\pi$
$353$	689.115	+	948.486i	0.103903	+	0.143011i	−0.753899	+	0.656990i	$0.771829\pi$
$354$	2751.34	−	1998.97i	0.413085	−	0.300124i
$355$	−363.286	+	176.077i	−0.0543133	+	0.0263245i
$356$	6968.86	+	5063.17i	1.03750	+	0.753785i
$357$			441.721i			0.0654855i
$358$	−9312.69	+	12817.8i	−1.37484	+	1.89230i
$359$	3288.39	−	10120.6i	0.483439	−	1.48787i	−0.350789	−	0.936454i	$-0.614087\pi$
$359$	3288.39	−	10120.6i	0.483439	−	1.48787i	0.834229	−	0.551419i	$-0.185913\pi$
$360$	5264.51	+	10861.9i	0.770733	+	1.59019i
$361$	158.210	+	486.922i	0.0230661	+	0.0709902i
$362$	1998.19	+	649.252i	0.290118	+	0.0942650i
$363$	−3667.88	−	1191.77i	−0.530341	−	0.172318i
$364$	−6065.57	−	18667.9i	−0.873413	−	2.68809i
$365$	−9079.97	+	1253.24i	−1.30210	+	0.179720i
$366$	−2516.21	+	7744.11i	−0.359357	+	1.10599i
$367$	−5151.43	+	7090.34i	−0.732704	+	1.00848i	0.266301	+	0.963890i	$0.414198\pi$
$367$	−5151.43	+	7090.34i	−0.732704	+	1.00848i	−0.999005	+	0.0445911i	$0.985802\pi$
$368$		−	6332.93i		−	0.897083i
$369$	−362.671	−	263.496i	−0.0511650	−	0.0371735i
$370$	−8302.09	−	1485.04i	−1.16650	−	0.208658i
$371$	7510.46	−	5456.67i	1.05101	−	0.763601i
$372$	−7864.14	−	10824.1i	−1.09607	−	1.50860i
$373$	−11053.9	+	3591.64i	−1.53445	+	0.498573i	−0.949839	−	0.312740i	$-0.898753\pi$
$373$	−11053.9	+	3591.64i	−1.53445	+	0.498573i	−0.584612	+	0.811313i	$0.698753\pi$
$374$	10.1142			0.00139838
$375$	−393.457	−	4030.59i	−0.0541815	−	0.555036i
$376$	17681.4			2.42512
$377$	−9142.94	+	2970.72i	−1.24903	+	0.405835i
$378$	−9946.70	−	13690.5i	−1.35345	−	1.86286i
$379$	−3620.89	+	2630.73i	−0.490746	+	0.356548i	−0.805471	−	0.592635i	$-0.798088\pi$
$379$	−3620.89	+	2630.73i	−0.490746	+	0.356548i	0.314725	+	0.949183i	$0.398088\pi$
$380$	−18085.0	−	3234.95i	−2.44142	−	0.436709i
$381$	3554.82	+	2582.73i	0.478003	+	0.347289i
$382$		−	30.7566i		−	0.00411949i
$383$	1257.06	−	1730.19i	0.167710	−	0.230832i	−0.716887	−	0.697189i	$-0.754434\pi$
$383$	1257.06	−	1730.19i	0.167710	−	0.230832i	0.884597	+	0.466357i	$0.154434\pi$
$384$	−202.825	+	624.230i	−0.0269540	+	0.0829560i
$385$	−85.2318	+	11.7639i	−0.0112826	+	0.00155726i
$386$	7647.75	+	23537.3i	1.00845	+	3.10368i
$387$	4586.03	+	1490.09i	0.602380	+	0.195725i
$388$	7201.69	+	2339.97i	0.942295	+	0.306170i
$389$	−3674.84	−	11310.0i	−0.478976	−	1.47414i	−0.840520	−	0.541781i	$-0.817750\pi$
$389$	−3674.84	−	11310.0i	−0.478976	−	1.47414i	0.361544	−	0.932355i	$-0.382250\pi$
$390$	3071.19	+	6336.55i	0.398758	+	0.822727i
$391$	81.3309	−	250.311i	0.0105194	−	0.0323753i
$392$	8910.95	−	12264.9i	1.14814	−	1.58028i
$393$		−	893.470i		−	0.114681i
$394$	21821.4	+	15854.2i	2.79022	+	2.02721i
$395$	3102.30	−	1503.62i	0.395173	−	0.191532i
$396$	−90.1827	+	65.5216i	−0.0114441	+	0.00831460i
$397$	3612.98	+	4972.84i	0.456751	+	0.628664i	0.973831	−	0.227273i	$-0.0729810\pi$
$397$	3612.98	+	4972.84i	0.456751	+	0.628664i	−0.517080	+	0.855937i	$0.672981\pi$
$398$	10156.1	−	3299.92i	1.27909	−	0.415603i
$399$	6115.41			0.767302
$400$	11555.8	−	14641.1i	1.44447	−	1.83014i
$401$	8095.13			1.00811			0.504054	−	0.863672i	$-0.331841\pi$
$401$	8095.13			1.00811			0.504054	+	0.863672i	$0.331841\pi$
$402$	−844.267	+	274.319i	−0.104747	+	0.0340343i
$403$	5915.59	+	8142.12i	0.731208	+	1.00642i
$404$	12931.5	−	9395.25i	1.59249	−	1.15701i
$405$	−924.570	−	962.165i	−0.113438	−	0.118050i
$406$	−23872.2	−	17344.2i	−2.91812	−	2.12014i
$407$		−	45.3326i		−	0.00552102i
$408$	612.986	−	843.703i	0.0743807	−	0.102376i
$409$	−1145.76	+	3526.28i	−0.138519	+	0.426317i	−0.996121	−	0.0879972i	$-0.971953\pi$
$409$	−1145.76	+	3526.28i	−0.138519	+	0.426317i	0.857602	+	0.514314i	$0.171953\pi$
$410$	−247.139	+	1381.63i	−0.0297691	+	0.166424i
$411$	−934.297	−	2875.47i	−0.112130	−	0.345101i
$412$	−5041.96	−	1638.23i	−0.602912	−	0.195898i
$413$	−5266.56	−	1711.21i	−0.627483	−	0.203882i
$414$	1271.04	+	3911.84i	0.150889	+	0.464388i
$415$	3415.14	−	3281.70i	0.403958	−	0.388174i
$416$	−4036.35	+	12422.6i	−0.475717	+	1.46411i
$417$	5143.29	−	7079.13i	0.604000	−	0.831335i
$418$		−	140.027i		−	0.0163850i
$419$	−9919.42	−	7206.88i	−1.15655	−	0.840284i	−0.167214	−	0.985921i	$-0.553477\pi$
$419$	−9919.42	−	7206.88i	−1.15655	−	0.840284i	−0.989338	+	0.145636i	$0.953477\pi$
$420$	−7189.16	+	13440.7i	−0.835227	+	1.56152i
$421$	4245.07	−	3084.23i	0.491430	−	0.357045i	−0.314304	−	0.949322i	$-0.601771\pi$
$421$	4245.07	−	3084.23i	0.491430	−	0.357045i	0.805734	+	0.592277i	$0.201771\pi$
$422$	−5386.18	−	7413.45i	−0.621316	−	0.855168i
$423$	−5390.38	+	1751.44i	−0.619597	+	0.201319i
$424$	−21917.6			−2.51041
$425$	644.775	−	430.287i	0.0735910	−	0.0491106i
$426$	−545.103			−0.0619961
$427$	12609.7	−	4097.15i	1.42910	−	0.464344i
$428$	21287.9	+	29300.3i	2.40418	+	3.30907i
$429$	−30.6206	+	22.2471i	−0.00344610	+	0.00250374i
$430$	−2064.24	−	14955.8i	−0.231503	−	1.67728i
$431$	−4898.54	−	3559.00i	−0.547458	−	0.397752i	0.279389	−	0.960178i	$-0.409868\pi$
$431$	−4898.54	−	3559.00i	−0.547458	−	0.397752i	−0.826847	+	0.562426i	$0.809868\pi$
$432$			19718.4i			2.19607i
$433$	253.120	−	348.390i	0.0280928	−	0.0386664i	−0.794740	−	0.606951i	$-0.792393\pi$
$433$	253.120	−	348.390i	0.0280928	−	0.0386664i	0.822832	+	0.568284i	$0.192393\pi$
$434$	−9545.91	+	29379.3i	−1.05580	+	3.24943i
$435$	6582.80	+	3521.02i	0.725566	+	0.388092i
$436$	−10072.2	−	30999.1i	−1.10636	−	3.40502i
$437$	−3465.43	−	1125.99i	−0.379346	−	0.123257i
$438$	−11770.6	−	3824.51i	−1.28407	−	0.417220i
$439$	1330.90	+	4096.09i	0.144694	+	0.445321i	0.996971	−	0.0777684i	$-0.0247795\pi$
$439$	1330.90	+	4096.09i	0.144694	+	0.445321i	−0.852278	+	0.523089i	$0.824779\pi$
$440$	179.121	+	95.8086i	0.0194074	+	0.0103807i
$441$	−1501.71	+	4621.78i	−0.162154	+	0.499059i
$442$	−792.239	+	1090.42i	−0.0852556	+	0.117344i
$443$		−	5335.30i		−	0.572207i	−0.958199	−	0.286103i	$-0.907640\pi$
$443$		−	5335.30i		−	0.572207i	0.958199	−	0.286103i	$-0.0923601\pi$
$444$	−6497.21	−	4720.50i	−0.694468	−	0.504561i
$445$	687.975	+	4984.50i	0.0732880	+	0.530984i
$446$	12764.8	−	9274.15i	1.35522	−	0.984627i
$447$	4716.00	+	6491.01i	0.499014	+	0.686833i
$448$	−10223.2	+	3321.70i	−1.07812	+	0.350303i
$449$	−9655.82			−1.01489			−0.507446	−	0.861684i	$-0.669410\pi$
$449$	−9655.82			−1.01489			−0.507446	+	0.861684i	$0.669410\pi$
$450$	−4199.50	+	11363.1i	−0.439926	+	1.19036i
$451$	−7.54425			−0.000787682
$452$	−16942.3	+	5504.89i	−1.76305	+	0.572850i
$453$	3317.54	+	4566.20i	0.344087	+	0.473595i
$454$	685.899	−	498.335i	0.0709049	−	0.0515154i
$455$	5407.86	−	10110.4i	0.557197	−	1.04172i
$456$	−11680.7	−	8486.50i	−1.19956	−	0.871528i
$457$		−	7165.86i		−	0.733489i	−0.930322	−	0.366745i	$-0.880472\pi$
$457$		−	7165.86i		−	0.733489i	0.930322	−	0.366745i	$-0.119528\pi$
$458$	15466.0	−	21287.1i	1.57790	−	2.17179i
$459$	−253.234	+	779.375i	−0.0257516	+	0.0792552i
$460$	6548.63	−	6292.75i	0.663764	−	0.637829i
$461$	1078.91	+	3320.55i	0.109002	+	0.335473i	0.990649	−	0.136436i	$-0.0435649\pi$
$461$	1078.91	+	3320.55i	0.109002	+	0.335473i	−0.881647	+	0.471910i	$0.843565\pi$
$462$	−110.489	−	35.8999i	−0.0111264	−	0.00361518i
$463$	−3628.92	−	1179.11i	−0.364255	−	0.118354i	0.121170	−	0.992632i	$-0.461335\pi$
$463$	−3628.92	−	1179.11i	−0.364255	−	0.118354i	−0.485425	+	0.874278i	$0.661335\pi$
$464$	10625.0	+	32700.4i	1.06304	+	3.27172i
$465$	1376.13	−	7693.23i	0.137239	−	0.767237i
$466$	−6000.29	+	18467.0i	−0.596477	+	1.83577i
$467$	−10335.8	+	14226.1i	−1.02417	+	1.40964i	−0.114926	+	0.993374i	$0.536663\pi$
$467$	−10335.8	+	14226.1i	−1.02417	+	1.40964i	−0.909241	+	0.416271i	$0.863337\pi$
$468$		−	14854.9i		−	1.46724i
$469$	1169.41	+	849.623i	0.115135	+	0.0836502i
$470$	12295.5	+	12795.5i	1.20670	+	1.25577i
$471$	−5189.35	+	3770.28i	−0.507670	+	0.368844i
$472$	7684.65	+	10577.0i	0.749395	+	1.03145i
$473$	77.1788	−	25.0769i	0.00750251	−	0.00243771i
$474$	4654.93			0.451072
$475$	−5957.12	−	8926.60i	−0.575435	−	0.862275i
$476$	−2917.59			−0.280940
$477$	6681.86	−	2171.07i	0.641386	−	0.208399i
$478$	−2333.72	−	3212.09i	−0.223309	−	0.307359i
$479$	2243.92	−	1630.30i	0.214044	−	0.155512i	−0.475597	−	0.879663i	$-0.657768\pi$
$479$	2243.92	−	1630.30i	0.214044	−	0.155512i	0.689642	+	0.724151i	$0.257768\pi$
$480$	9127.60	−	4423.95i	0.867950	−	0.420677i
$481$	4887.36	+	3550.87i	0.463294	+	0.336603i
$482$		−	4187.80i		−	0.395745i
$483$	−1776.93	+	2445.74i	−0.167398	+	0.230403i
$484$	7871.69	−	24226.6i	0.739264	−	2.27522i
$485$	1929.21	+	3980.39i	0.180620	+	0.372660i
$486$	−6300.66	−	19391.4i	−0.588073	−	1.80990i
$487$	−15199.2	−	4938.51i	−1.41425	−	0.459518i	−0.500481	−	0.865748i	$-0.666843\pi$
$487$	−15199.2	−	4938.51i	−1.41425	−	0.459518i	−0.913771	+	0.406229i	$0.866843\pi$
$488$	−29770.8	−	9673.10i	−2.76160	−	0.897297i
$489$	−1715.07	−	5278.43i	−0.158605	−	0.488137i
$490$	15072.4	−	2080.33i	1.38959	−	0.191796i
$491$	−3879.98	+	11941.3i	−0.356621	+	1.09757i	0.598442	+	0.801166i	$0.295787\pi$
$491$	−3879.98	+	11941.3i	−0.356621	+	1.09757i	−0.955064	+	0.296401i	$0.904213\pi$
$492$	−785.584	+	1081.26i	−0.0719855	+	0.0990796i
$493$			1428.94i			0.130540i
$494$	15096.4	+	10968.2i	1.37494	+	0.998951i
$495$	−64.0977	−	11.4655i	−0.00582015	−	0.00104108i
$496$	29120.8	−	21157.5i	2.63622	−	1.91532i
$497$	521.713	+	718.076i	0.0470866	+	0.0648091i
$498$	6082.18	−	1976.22i	0.547287	−	0.177824i
$499$	771.410			0.0692045			0.0346023	−	0.999401i	$-0.488984\pi$
$499$	771.410			0.0692045			0.0346023	+	0.999401i	$0.488984\pi$
$500$	26622.3	−	2598.81i	2.38117	−	0.232445i
$501$	3214.73			0.286674
$502$	16987.2	−	5519.49i	1.51031	−	0.490731i
$503$	3181.29	+	4378.68i	0.282002	+	0.388142i	0.926396	−	0.376552i	$-0.122890\pi$
$503$	3181.29	+	4378.68i	0.282002	+	0.388142i	−0.644394	+	0.764694i	$0.722890\pi$
$504$	21469.7	−	15598.6i	1.89749	−	1.37861i
$505$	9191.08	+	1644.05i	0.809896	+	0.144870i
$506$	56.0008	+	40.6870i	0.00492004	+	0.00357462i
$507$			1322.54i			0.115850i
$508$	−17059.1	+	23479.8i	−1.48991	+	2.05068i
$509$	−3518.30	+	10828.2i	−0.306377	+	0.942932i	0.672783	+	0.739840i	$0.265099\pi$
$509$	−3518.30	+	10828.2i	−0.306377	+	0.942932i	−0.979160	+	0.203091i	$0.934901\pi$
$510$	1036.83	−	143.106i	0.0900229	−	0.0124252i
$511$	6227.45	+	19166.1i	0.539112	+	1.65922i
$512$	−21456.3	−	6971.56i	−1.85203	−	0.601762i
$513$	10790.1	+	3505.91i	0.928643	+	0.301734i
$514$	−8592.63	−	26445.4i	−0.737364	−	2.26937i
$515$	−1350.66	−	2786.70i	−0.115567	−	0.238440i
$516$	4442.55	−	13672.8i	0.379016	−	1.16649i
$517$	−56.0652	+	77.1671i	−0.00476933	+	0.00656442i
$518$			18542.7i			1.57281i
$519$	−4113.64	−	2988.73i	−0.347916	−	0.252776i
$520$	−24359.6	+	11806.6i	−2.05431	+	0.995680i
$521$	−18950.0	+	13767.9i	−1.59350	+	1.15774i	−0.694775	+	0.719227i	$0.744496\pi$
$521$	−18950.0	+	13767.9i	−1.59350	+	1.15774i	−0.898723	+	0.438517i	$0.855504\pi$
$522$	−13126.1	−	18066.5i	−1.10060	−	1.51485i
$523$	−5123.65	+	1664.78i	−0.428378	+	0.139188i	−0.515267	−	0.857029i	$-0.672307\pi$
$523$	−5123.65	+	1664.78i	−0.428378	+	0.139188i	0.0868893	+	0.996218i	$0.472307\pi$
$524$	5901.43			0.491994
$525$	−8570.86	+	2411.90i	−0.712501	+	0.200502i
$526$	−34280.6			−2.84165
$527$	1422.73	−	462.271i	0.117599	−	0.0382104i
$528$	79.5685	+	109.517i	0.00655828	+	0.00902670i
$529$	−8386.06	+	6092.83i	−0.689246	+	0.500767i
$530$	−15241.4	−	15861.2i	−1.24914	−	1.29993i
$531$	−3390.47	−	2463.32i	−0.277089	−	0.201317i
$532$			40392.7i			3.29181i
$533$	590.936	−	813.353i	0.0480230	−	0.0660980i
$534$	−2099.49	+	6461.56i	−0.170138	+	0.523631i
$535$	−3725.12	+	20825.3i	−0.301030	+	1.68291i
$536$	−1054.57	−	3245.62i	−0.0849820	−	0.261548i
$537$	−8381.50	−	2723.31i	−0.673535	−	0.218845i
$538$	13908.5	+	4519.15i	1.11457	+	0.362146i
$539$	25.2724	+	77.7805i	0.00201959	+	0.00621567i
$540$	−20390.0	+	19593.3i	−1.62490	+	1.56141i
$541$	5437.27	−	16734.2i	0.432101	−	1.32987i	−0.463928	−	0.885873i	$-0.653560\pi$
$541$	5437.27	−	16734.2i	0.432101	−	1.32987i	0.896029	−	0.443996i	$-0.146440\pi$
$542$	21756.7	−	29945.5i	1.72423	−	2.37319i
$543$			1168.66i			0.0923612i
$544$	1570.72	+	1141.20i	0.123794	+	0.0899419i
$545$	8980.06	−	16788.9i	0.705805	−	1.31955i
$546$	12524.9	−	9099.87i	0.981715	−	0.713257i
$547$	−7899.24	−	10872.4i	−0.617454	−	0.849852i	0.379711	−	0.925105i	$-0.376023\pi$
$547$	−7899.24	−	10872.4i	−0.617454	−	0.849852i	−0.997164	+	0.0752532i	$0.976023\pi$
$548$	18992.7	−	6171.09i	1.48052	−	0.481051i
$549$	10034.2			0.780050
$550$	55.2259	+	196.250i	0.00428153	+	0.0152148i
$551$	19783.0			1.52956
$552$	6788.01	−	2205.56i	0.523400	−	0.170063i
$553$	−4455.19	−	6132.04i	−0.342593	−	0.471538i
$554$	−14879.4	+	10810.5i	−1.14109	+	0.829054i
$555$	−641.414	−	4647.15i	−0.0490567	−	0.355425i
$556$	46758.1	+	33971.7i	3.56652	+	2.59123i
$557$		−	7225.52i		−	0.549650i	−0.961494	−	0.274825i	$-0.911380\pi$
$557$		−	7225.52i		−	0.549650i	0.961494	−	0.274825i	$-0.0886199\pi$
$558$	−13741.5	+	18913.6i	−1.04252	+	1.43491i
$559$	−3341.79	+	10285.0i	−0.252849	+	0.778190i
$560$	−36160.5	−	19341.6i	−2.72868	−	1.45952i
$561$	1.73849	+	5.35053i	0.000130836	+	0.000402673i
$562$	9021.59	+	2931.29i	0.677140	+	0.220016i
$563$	17743.1	+	5765.08i	1.32821	+	0.431561i	0.885306	−	0.465008i	$-0.153949\pi$
$563$	17743.1	+	5765.08i	1.32821	+	0.431561i	0.442903	+	0.896570i	$0.353949\pi$
$564$	5221.74	+	16070.9i	0.389849	+	1.19983i
$565$	−9175.82	−	4907.98i	−0.683238	−	0.365452i
$566$	−1436.09	+	4419.82i	−0.106649	+	0.328231i
$567$	−1724.43	+	2373.48i	−0.127724	+	0.175797i
$568$		−	2095.55i		−	0.154801i
$569$	−9092.98	−	6606.44i	−0.669943	−	0.486742i	0.200063	−	0.979783i	$-0.435885\pi$
$569$	−9092.98	−	6606.44i	−0.669943	−	0.486742i	−0.870006	+	0.493041i	$0.835885\pi$
$570$	−1981.24	−	14354.4i	−0.145588	−	1.05481i
$571$	16544.6	−	12020.4i	1.21256	−	0.880976i	0.217099	−	0.976150i	$-0.430341\pi$
$571$	16544.6	−	12020.4i	1.21256	−	0.880976i	0.995461	+	0.0951736i	$0.0303406\pi$
$572$	−146.944	−	202.251i	−0.0107413	−	0.0147841i
$573$	16.2706	−	5.28664i	0.00118624	−	0.000385432i
$574$	3085.86			0.224393
$575$	5300.95	+	211.337i	0.384461	+	0.0153276i
$576$	−8135.05			−0.588473
$577$	10726.4	−	3485.22i	0.773910	−	0.251459i	0.104672	−	0.994507i	$-0.466621\pi$
$577$	10726.4	−	3485.22i	0.773910	−	0.251459i	0.669238	+	0.743048i	$0.266621\pi$
$578$	−14926.5	−	20544.5i	−1.07415	−	1.47844i
$579$	−11137.0	+	8091.49i	−0.799373	+	0.580779i
$580$	−23256.6	+	43479.8i	−1.66496	+	3.11276i
$581$	−8424.50	−	6120.76i	−0.601562	−	0.437060i
$582$			5972.49i			0.425374i
$583$	69.4977	−	95.6554i	0.00493705	−	0.00679527i
$584$	14702.6	−	45250.0i	1.04178	−	3.20626i
$585$	6256.83	−	6012.35i	0.442202	−	0.424923i
$586$	4727.04	+	14548.3i	0.333229	+	1.02557i
$587$	9479.89	+	3080.20i	0.666570	+	0.216582i	0.622706	−	0.782456i	$-0.286033\pi$
$587$	9479.89	+	3080.20i	0.666570	+	0.216582i	0.0438641	+	0.999038i	$0.486033\pi$
$588$	13779.4	+	4477.18i	0.966414	+	0.314007i
$589$	−6399.93	−	19697.0i	−0.447716	−	1.37793i
$590$	−2310.41	+	12916.4i	−0.161217	+	0.901285i
$591$	−4636.24	+	14268.9i	−0.322690	+	0.993137i
$592$	12699.9	−	17480.0i	0.881697	−	1.21355i
$593$			1820.59i			0.126075i	0.998011	+	0.0630376i	$0.0200788\pi$
$593$			1820.59i			0.126075i	−0.998011	+	0.0630376i	$0.979921\pi$
$594$	−174.366	−	126.684i	−0.0120443	−	0.00875070i
$595$	−1180.86	−	1228.87i	−0.0813621	−	0.0846705i
$596$	−42873.5	+	31149.4i	−2.94659	+	2.14082i
$597$	3491.39	+	4805.48i	0.239352	+	0.329439i
$598$	−8773.00	+	2850.52i	−0.599924	+	0.194927i
$599$	23623.2			1.61138			0.805692	−	0.592335i	$-0.201794\pi$
$599$	23623.2			1.61138			0.805692	+	0.592335i	$0.201794\pi$
$600$	19717.7	+	7287.17i	1.34162	+	0.495829i
$601$	−22682.2			−1.53948			−0.769740	−	0.638357i	$-0.779614\pi$
$601$	−22682.2			−1.53948			−0.769740	+	0.638357i	$0.779614\pi$
$602$	−31568.9	+	10257.3i	−2.13729	+	0.694449i
$603$	642.996	+	885.008i	0.0434242	+	0.0597683i
$604$	−30160.0	+	21912.5i	−2.03178	+	1.47617i
$605$	13390.1	−	6489.88i	0.899808	−	0.436118i
$606$	10199.4	+	7410.30i	0.683700	+	0.496737i
$607$		−	24236.3i		−	1.62063i	−0.585997	−	0.810313i	$-0.699297\pi$
$607$		−	24236.3i		−	1.62063i	0.585997	−	0.810313i	$-0.300703\pi$
$608$	15799.3	−	21745.9i	1.05386	−	1.45051i
$609$	5071.96	−	15609.9i	0.337482	−	1.03866i
$610$	−13702.3	−	28270.9i	−0.909491	−	1.87648i
$611$	−3927.92	−	12088.9i	−0.260076	−	0.800432i
$612$	−2099.97	−	682.321i	−0.138703	−	0.0450673i
$613$	−6269.40	−	2037.05i	−0.413081	−	0.134218i	0.0951016	−	0.995468i	$-0.469682\pi$
$613$	−6269.40	−	2037.05i	−0.413081	−	0.134218i	−0.508182	+	0.861249i	$0.669682\pi$
$614$	−1828.87	−	5628.69i	−0.120207	−	0.369960i
$615$	−773.378	+	106.744i	−0.0507083	+	0.00699891i
$616$	138.010	−	424.752i	0.00902694	−	0.0277821i
$617$	−2143.76	+	2950.64i	−0.139878	+	0.192525i	−0.873209	−	0.487347i	$-0.837965\pi$
$617$	−2143.76	+	2950.64i	−0.139878	+	0.192525i	0.733331	+	0.679872i	$0.237965\pi$
$618$		−	4181.39i		−	0.272169i
$619$	910.502	+	661.519i	0.0591215	+	0.0429543i	0.616953	−	0.787000i	$-0.288367\pi$
$619$	910.502	+	661.519i	0.0591215	+	0.0429543i	−0.557832	+	0.829954i	$0.688367\pi$
$620$	50814.3	+	9089.40i	3.29153	+	0.588773i
$621$	−4537.35	+	3296.58i	−0.293201	+	0.213023i
$622$	32262.5	+	44405.5i	2.07976	+	2.86254i
$623$	10521.3	−	3418.59i	0.676612	−	0.219844i
$624$	−18039.6			−1.15731
$625$	11869.6	+	10161.3i	0.759656	+	0.650325i
$626$	22664.6			1.44706
$627$	74.0756	−	24.0686i	0.00471817	−	0.00153303i
$628$	−24902.9	−	34275.9i	−1.58238	−	2.17796i
$629$	726.456	−	527.801i	0.0460504	−	0.0334576i
$630$	26218.2	+	4689.78i	1.65803	+	0.296580i
$631$	12323.8	+	8953.80i	0.777503	+	0.564889i	0.904229	−	0.427049i	$-0.140447\pi$
$631$	12323.8	+	8953.80i	0.777503	+	0.564889i	−0.126725	+	0.991938i	$0.540447\pi$
$632$			17895.0i			1.12630i
$633$	2995.99	−	4123.62i	0.188120	−	0.258925i
$634$	−508.980	+	1566.48i	−0.0318836	+	0.0981275i
$635$	−16794.0	+	2317.96i	−1.04953	+	0.144859i
$636$	−6472.81	−	19921.2i	−0.403559	−	1.24203i
$637$	−10365.2	−	3367.85i	−0.644714	−	0.209480i
$638$	−357.425	−	116.134i	−0.0221796	−	0.00720658i
$639$	207.576	+	638.853i	0.0128507	+	0.0395503i
$640$	−1104.50	−	2278.83i	−0.0682176	−	0.140748i
$641$	6459.99	−	19881.8i	0.398057	−	1.22509i	−0.528499	−	0.848934i	$-0.677245\pi$
$641$	6459.99	−	19881.8i	0.398057	−	1.22509i	0.926555	−	0.376158i	$-0.122755\pi$
$642$	−16790.4	+	23110.0i	−1.03219	+	1.42068i
$643$		−	9509.49i		−	0.583231i	−0.956536	−	0.291616i	$-0.905807\pi$
$643$		−	9509.49i		−	0.583231i	0.956536	−	0.291616i	$-0.0941928\pi$
$644$	−16154.2	−	11736.7i	−0.988456	−	0.718156i
$645$	7556.96	−	3662.70i	0.461326	−	0.223595i
$646$	2243.93	−	1630.31i	0.136666	−	0.0992935i
$647$	7223.96	+	9942.92i	0.438954	+	0.604168i	0.969979	−	0.243188i	$-0.0781932\pi$
$647$	7223.96	+	9942.92i	0.438954	+	0.604168i	−0.531026	+	0.847356i	$0.678193\pi$
$648$	6587.46	−	2140.40i	0.399352	−	0.129757i
$649$	−70.5284			−0.00426577
$650$	−25483.7	−	9418.13i	−1.53777	−	0.568322i
$651$	−17182.8			−1.03448
$652$	34864.4	−	11328.1i	2.09416	−	0.680435i
$653$	−1532.13	−	2108.79i	−0.0918175	−	0.126376i	0.760637	−	0.649178i	$-0.224887\pi$
$653$	−1532.13	−	2108.79i	−0.0918175	−	0.126376i	−0.852454	+	0.522802i	$0.824887\pi$
$654$	20798.3	−	15110.9i	1.24354	−	0.903488i
$655$	2388.53	+	2485.65i	0.142485	+	0.148278i
$656$	−2909.01	−	2113.52i	−0.173137	−	0.125791i
$657$			15251.4i			0.905653i
$658$	22932.6	−	31564.1i	1.35867	−	1.87005i
$659$	−5704.38	+	17556.3i	−0.337194	+	1.03778i	0.628437	+	0.777861i	$0.283695\pi$
$659$	−5704.38	+	17556.3i	−0.337194	+	1.03778i	−0.965631	+	0.259917i	$0.916305\pi$
$660$	−34.1831	+	191.100i	−0.00201602	+	0.0112706i
$661$	−2072.61	−	6378.82i	−0.121959	−	0.375352i	0.871376	−	0.490616i	$-0.163228\pi$
$661$	−2072.61	−	6378.82i	−0.121959	−	0.375352i	−0.993335	+	0.115265i	$0.963228\pi$
$662$	−2426.09	−	788.285i	−0.142436	−	0.0462803i
$663$	−713.022	−	231.675i	−0.0417669	−	0.0135709i
$664$	7597.19	+	23381.8i	0.444018	+	1.36655i
$665$	−17013.2	+	16348.4i	−0.992095	+	0.953330i
$666$	−4336.47	+	13346.3i	−0.252304	+	0.776513i
$667$	−5748.28	+	7911.82i	−0.333694	+	0.459291i
$668$			21233.5i			1.22986i
$669$	7100.22	+	5158.61i	0.410329	+	0.298122i
$670$	1615.43	−	3020.15i	0.0931482	−	0.174147i
$671$	136.616	−	99.2570i	0.00785989	−	0.00571054i
$672$	−13108.1	−	18041.7i	−0.752463	−	1.03568i
$673$	4341.57	−	1410.66i	0.248670	−	0.0807979i	−0.182030	−	0.983293i	$-0.558267\pi$
$673$	4341.57	−	1410.66i	0.248670	−	0.0807979i	0.430700	+	0.902495i	$0.358267\pi$
$674$	−22340.8			−1.27676
$675$	−16505.2	−	658.026i	−0.941164	−	0.0375221i
$676$	−8735.47			−0.497011
$677$	−4243.68	+	1378.86i	−0.240913	+	0.0782773i	−0.426985	−	0.904259i	$-0.640424\pi$
$677$	−4243.68	+	1378.86i	−0.240913	+	0.0782773i	0.186072	+	0.982536i	$0.440424\pi$
$678$	−8258.71	−	11367.1i	−0.467808	−	0.643883i
$679$	7867.68	−	5716.21i	0.444674	−	0.323075i
$680$	550.145	+	3985.90i	0.0310252	+	0.224783i
$681$	381.521	+	277.191i	0.0214683	+	0.0155977i
$682$			393.440i			0.0220903i
$683$	−12877.8	+	17724.7i	−0.721456	+	0.992998i	0.278019	+	0.960576i	$0.410322\pi$
$683$	−12877.8	+	17724.7i	−0.721456	+	0.992998i	−0.999474	+	0.0324227i	$0.989678\pi$
$684$	−9446.41	+	29073.1i	−0.528059	+	1.62520i
$685$	10286.3	+	5501.94i	0.573749	+	0.306888i
$686$	3235.85	+	9958.93i	0.180095	+	0.554276i
$687$	13919.5	+	4522.71i	0.773015	+	0.251168i
$688$	36784.9	+	11952.2i	2.03839	+	0.662313i
$689$	4869.00	+	14985.2i	0.269222	+	0.828581i
$690$	6316.45	+	3378.56i	0.348497	+	0.186405i
$691$	6857.02	−	21103.7i	0.377501	−	1.16183i	−0.564274	−	0.825587i	$-0.690844\pi$
$691$	6857.02	−	21103.7i	0.377501	−	1.16183i	0.941776	−	0.336242i	$-0.109156\pi$
$692$	19740.7	−	27170.8i	1.08444	−	1.49260i
$693$			143.162i			0.00784742i
$694$	−22155.8	−	16097.1i	−1.21185	−	0.880458i
$695$	4616.02	+	33443.9i	0.251936	+	1.82532i
$696$	−31349.8	+	22777.0i	−1.70735	+	1.24046i
$697$	−87.8366	−	120.897i	−0.00477338	−	0.00657000i
$698$	−62667.5	+	20361.9i	−3.39828	+	1.10417i
$699$	−10800.6			−0.584431
$700$	−15930.7	−	56611.0i	−0.860178	−	3.05671i
$701$	−7568.64			−0.407794			−0.203897	−	0.978992i	$-0.565361\pi$
$701$	−7568.64			−0.407794			−0.203897	+	0.978992i	$0.565361\pi$
$702$	27315.9	−	8875.47i	1.46862	−	0.477184i
$703$	−7307.16	−	10057.4i	−0.392027	−	0.539578i
$704$	−110.759	+	80.4712i	−0.00592953	+	0.00430806i
$705$	−4655.53	+	8703.85i	−0.248706	+	0.464973i
$706$	−4941.23	−	3590.01i	−0.263407	−	0.191377i
$707$		−	20528.2i		−	1.09200i
$708$	−7344.14	+	10108.3i	−0.389844	+	0.536575i
$709$	−4823.23	+	14844.4i	−0.255487	+	0.786308i	0.738246	+	0.674531i	$0.235654\pi$
$709$	−4823.23	+	14844.4i	−0.255487	+	0.786308i	−0.993733	+	0.111777i	$0.964346\pi$
$710$	1516.49	−	1457.23i	0.0801588	−	0.0770267i
$711$	−1772.60	−	5455.51i	−0.0934990	−	0.287760i
$712$	−24840.2	−	8071.08i	−1.30748	−	0.424827i
$713$	9737.00	+	3163.74i	0.511436	+	0.166176i
$714$	−711.106	−	2188.56i	−0.0372723	−	0.114712i
$715$	25.7133	−	143.750i	0.00134493	−	0.00751882i
$716$	17987.6	−	55360.3i	0.938868	−	2.88954i
$717$	1298.10	−	1786.68i	0.0676128	−	0.0930610i
$718$			55437.7i			2.88150i
$719$	19142.6	+	13907.9i	0.992904	+	0.721387i	0.960555	−	0.278090i	$-0.0897013\pi$
$719$	19142.6	+	13907.9i	0.992904	+	0.721387i	0.0323486	+	0.999477i	$0.489701\pi$
$720$	−21503.6	−	22378.0i	−1.11304	−	1.15830i
$721$	−5508.23	+	4001.96i	−0.284518	+	0.206714i
$722$	−1567.75	−	2157.82i	−0.0808109	−	0.111227i
$723$	2215.39	−	719.825i	0.113958	−	0.0370271i
$724$	−7719.09			−0.396240
$725$	−27726.3	+	7802.36i	−1.42031	+	0.399686i
$726$	20091.5			1.02709
$727$	−13723.9	+	4459.16i	−0.700125	+	0.227484i	−0.637385	−	0.770545i	$-0.719984\pi$
$727$	−13723.9	+	4459.16i	−0.700125	+	0.227484i	−0.0627401	+	0.998030i	$0.519984\pi$
$728$	34982.7	+	48149.6i	1.78097	+	2.45129i
$729$	6568.25	−	4772.11i	0.333701	−	0.242448i
$730$	42970.3	−	20826.8i	2.17863	−	1.05594i
$731$	1300.44	+	944.824i	0.0657982	+	0.0478052i
$732$		−	29915.8i		−	1.51055i
$733$	6187.77	−	8516.74i	0.311802	−	0.429158i	−0.624140	−	0.781312i	$-0.714551\pi$
$733$	6187.77	−	8516.74i	0.311802	−	0.429158i	0.935942	+	0.352154i	$0.114551\pi$
$734$	14109.0	−	43423.0i	0.709498	−	2.18361i
$735$	3691.25	+	7615.88i	0.185243	+	0.382199i
$736$	4106.09	+	12637.2i	0.205642	+	0.632901i
$737$	17.5088	+	5.68896i	0.000875096	+	0.000284336i
$738$	2221.08	+	721.674i	0.110785	+	0.0359962i
$739$	−5206.56	−	16024.2i	−0.259170	−	0.797643i	−0.992979	−	0.118287i	$-0.962260\pi$
$739$	−5206.56	−	16024.2i	−0.259170	−	0.797643i	0.733810	−	0.679355i	$-0.237740\pi$
$740$	30694.7	−	4236.58i	1.52481	−	0.210459i
$741$	−3207.43	+	9871.45i	−0.159012	+	0.489388i
$742$	−28427.0	+	39126.5i	−1.40645	+	1.93582i
$743$		−	27544.9i		−	1.36006i	−0.733184	−	0.680030i	$-0.761967\pi$
$743$		−	27544.9i		−	1.36006i	0.733184	−	0.680030i	$-0.238033\pi$
$744$	32819.8	+	23844.9i	1.61725	+	1.17500i
$745$	−30472.5	−	5450.77i	−1.49856	−	0.268055i
$746$	48986.0	−	35590.4i	2.40416	−	1.74672i
$747$	−4632.20	−	6375.67i	−0.226885	−	0.312281i
$748$	−35.3406	+	11.4829i	−0.00172751	+	0.000561303i
$749$	46513.2			2.26910
$750$	8438.09	+	19336.6i	0.410820	+	0.941431i
$751$	−5126.43			−0.249090			−0.124545	−	0.992214i	$-0.539747\pi$
$751$	−5126.43			−0.249090			−0.124545	+	0.992214i	$0.539747\pi$
$752$	−43236.7	+	14048.5i	−2.09665	+	0.681243i
$753$	5839.75	+	8037.72i	0.282619	+	0.388992i
$754$	40517.4	−	29437.6i	1.95697	−	1.42182i
$755$	−21436.3	−	3834.42i	−1.03331	−	0.184833i
$756$	50298.3	+	36543.9i	2.41975	+	1.75805i
$757$			13009.2i			0.624607i	0.949982	+	0.312304i	$0.101101\pi$
$757$			13009.2i			0.624607i	−0.949982	+	0.312304i	$0.898899\pi$
$758$	13705.1	−	18863.4i	0.656715	−	0.903891i
$759$	−11.8981	+	36.6186i	−0.000569003	+	0.00175121i
$760$	55182.9	−	7616.50i	2.63381	−	0.363526i
$761$	2267.40	+	6978.35i	0.108007	+	0.332411i	0.990424	−	0.138056i	$-0.0440854\pi$
$761$	2267.40	+	6978.35i	0.108007	+	0.332411i	−0.882418	+	0.470467i	$0.844085\pi$
$762$	−21770.6	−	7073.70i	−1.03499	−	0.336290i
$763$	−39811.7	−	12935.6i	−1.88896	−	0.613762i
$764$	34.9186	+	107.468i	0.00165355	+	0.00508909i
$765$	−562.545	−	1160.66i	−0.0265868	−	0.0548544i
$766$	−3442.89	+	10596.1i	−0.162398	+	0.499809i
$767$	5524.44	−	7603.74i	0.260073	−	0.357960i
$768$		−	13556.8i		−	0.636966i
$769$	24506.0	+	17804.7i	1.14917	+	0.834920i	0.988370	−	0.152068i	$-0.0485932\pi$
$769$	24506.0	+	17804.7i	1.14917	+	0.834920i	0.160798	+	0.986987i	$0.448593\pi$
$770$	403.353	−	195.497i	0.0188777	−	0.00914962i
$771$	12513.0	−	9091.20i	0.584492	−	0.424658i
$772$	−53444.8	−	73560.4i	−2.49160	−	3.42940i
$773$	−10221.8	+	3321.26i	−0.475618	+	0.154538i	−0.537010	−	0.843576i	$-0.680446\pi$
$773$	−10221.8	+	3321.26i	−0.475618	+	0.154538i	0.0613918	+	0.998114i	$0.480446\pi$
$774$	−25120.9			−1.16660
$775$	16738.0	+	25081.5i	0.775803	+	1.16252i
$776$	−22960.1			−1.06214
$777$	−9809.27	+	3187.23i	−0.452903	+	0.147157i
$778$	36414.8	+	50120.7i	1.67807	+	2.30966i
$779$	−1673.76	+	1216.06i	−0.0769815	+	0.0559303i
$780$	−17925.2	−	18654.1i	−0.822853	−	0.856312i
$781$	9.14563	+	6.64469i	0.000419022	+	0.000304438i
$782$			1371.13i			0.0626999i
$783$	17898.0	−	24634.5i	0.816887	−	1.12435i
$784$	−12045.3	+	37071.7i	−0.548712	+	1.68876i
$785$	4357.70	−	24361.7i	0.198131	−	1.10765i
$786$	1438.36	+	4426.81i	0.0652729	+	0.200889i
$787$	12639.2	+	4106.72i	0.572475	+	0.186008i	0.580927	−	0.813956i	$-0.302690\pi$
$787$	12639.2	+	4106.72i	0.572475	+	0.186008i	−0.00845169	+	0.999964i	$0.502690\pi$
$788$	−94246.9	−	30622.7i	−4.26067	−	1.38437i
$789$	−5892.37	−	18134.8i	−0.265873	−	0.818273i
$790$	−12950.1	+	12444.1i	−0.583220	+	0.560431i
$791$	−7069.85	+	21758.8i	−0.317794	+	0.978068i
$792$	198.669	−	273.444i	0.00891337	−	0.0122682i
$793$			22503.4i			1.00772i
$794$	−25906.5	−	18822.2i	−1.15792	−	0.841276i
$795$	5770.94	−	10789.2i	0.257452	−	0.481325i
$796$	−31740.5	+	23060.8i	−1.41333	+	1.02685i
$797$	15064.9	+	20735.1i	0.669544	+	0.921549i	0.999750	−	0.0223604i	$-0.00711813\pi$
$797$	15064.9	+	20735.1i	0.669544	+	0.921549i	−0.330206	+	0.943909i	$0.607118\pi$
$798$	−30299.6	+	9844.92i	−1.34410	+	0.436725i
$799$	−1889.36			−0.0836556
$800$	−13566.5	+	36708.5i	−0.599561	+	1.62230i
$801$	8372.34			0.369316
$802$	−40108.3	+	13032.0i	−1.76593	+	0.573785i
$803$	150.865	+	207.648i	0.00663004	+	0.00912547i
$804$	2638.56	−	1917.02i	0.115740	−	0.0840899i
$805$	−1594.77	−	11554.4i	−0.0698238	−	0.505886i
$806$	−42417.1	−	30817.8i	−1.85370	−	1.34679i
$807$			8134.54i			0.354832i
$808$	−28487.5	+	39209.6i	−1.24033	+	1.70717i
$809$	6661.43	−	20501.8i	0.289497	−	0.890981i	−0.695517	−	0.718509i	$-0.744825\pi$
$809$	6661.43	−	20501.8i	0.289497	−	0.890981i	0.985015	−	0.172472i	$-0.0551753\pi$
$810$	6129.84	+	3278.74i	0.265902	+	0.142226i
$811$	−5826.23	−	17931.3i	−0.252265	−	0.776390i	−0.994356	−	0.106092i	$-0.966166\pi$
$811$	−5826.23	−	17931.3i	−0.252265	−	0.776390i	0.742092	−	0.670298i	$-0.233834\pi$
$812$	103104.	+	33500.6i	4.45597	+	1.44783i
$813$	19581.2	+	6362.32i	0.844702	+	0.274460i
$814$	72.9789	+	224.606i	0.00314240	+	0.00967130i
$815$	18882.3	+	10099.8i	0.811554	+	0.434086i
$816$	−828.601	+	2550.17i	−0.0355476	+	0.109404i
$817$	13080.6	−	18004.0i	0.560139	−	0.770966i
$818$		−	19315.9i		−	0.825629i
$819$	−15434.4	−	11213.8i	−0.658513	−	0.478438i
$820$	−705.050	−	5108.21i	−0.0300261	−	0.217544i
$821$	−16877.2	+	12262.0i	−0.717440	+	0.521250i	−0.885565	−	0.464515i	$-0.846229\pi$
$821$	−16877.2	+	12262.0i	−0.717440	+	0.521250i	0.168125	+	0.985766i	$0.446229\pi$
$822$	9258.17	+	12742.8i	0.392842	+	0.540700i
$823$	13391.3	−	4351.09i	0.567181	−	0.184288i	−0.0113686	−	0.999935i	$-0.503619\pi$
$823$	13391.3	−	4351.09i	0.567181	−	0.184288i	0.578550	+	0.815647i	$0.303619\pi$
$824$	16074.5			0.679591
$825$	−94.3257	+	62.9478i	−0.00398061	+	0.00265644i
$826$	28848.6			1.21522
$827$	41366.8	−	13440.9i	1.73938	−	0.565157i	0.744624	−	0.667484i	$-0.232629\pi$
$827$	41366.8	−	13440.9i	1.73938	−	0.565157i	0.994751	+	0.102327i	$0.0326287\pi$
$828$	−8882.38	−	12225.5i	−0.372807	−	0.513124i
$829$	−18143.6	+	13182.1i	−0.760136	+	0.552271i	−0.898952	−	0.438047i	$-0.855670\pi$
$829$	−18143.6	+	13182.1i	−0.760136	+	0.552271i	0.138816	+	0.990318i	$0.455670\pi$
$830$	−11637.7	+	21757.4i	−0.486686	+	0.909894i
$831$	−8276.47	−	6013.21i	−0.345496	−	0.251018i
$832$		−	18244.3i		−	0.760225i
$833$	−952.190	+	1310.58i	−0.0396056	+	0.0545124i
$834$	−14086.7	+	43354.3i	−0.584870	+	1.80005i
$835$	−8943.43	+	8593.98i	−0.370659	+	0.356176i
$836$	158.975	+	489.274i	0.00657686	+	0.0202415i
$837$	−30317.4	−	9850.73i	−1.25200	−	0.406799i
$838$	60749.0	+	19738.5i	2.50422	+	0.813671i
$839$	−271.837	−	836.629i	−0.0111858	−	0.0344263i	0.945308	−	0.326180i	$-0.105761\pi$
$839$	−271.837	−	836.629i	−0.0111858	−	0.0344263i	−0.956494	+	0.291753i	$0.905761\pi$
$840$	8137.92	−	45495.0i	0.334268	−	1.86872i
$841$	8870.91	−	27301.8i	0.363726	−	1.11943i
$842$	−16067.6	+	22115.1i	−0.657631	+	0.905151i
$843$			5276.37i			0.215573i
$844$	27236.8	+	19788.7i	1.11082	+	0.807055i
$845$	−3535.57	−	3679.34i	−0.143938	−	0.149791i
$846$	23887.7	−	17355.5i	0.970777	−	0.705311i
$847$	−19229.4	−	26467.0i	−0.780082	−	1.07369i
$848$	53595.8	−	17414.3i	2.17038	−	0.705201i
$849$	−2584.98			−0.104495
$850$	−2501.92	+	3169.90i	−0.100959	+	0.127914i
$851$	6145.48			0.247549
$852$	1904.67	−	618.866i	0.0765881	−	0.0248850i
$853$	12270.1	+	16888.3i	0.492521	+	0.677897i	0.980850	−	0.194763i	$-0.0623936\pi$
$853$	12270.1	+	16888.3i	0.492521	+	0.677897i	−0.488330	+	0.872659i	$0.662394\pi$
$854$	−55880.6	+	40599.6i	−2.23910	+	1.62680i
$855$	−16068.7	+	7788.18i	−0.642736	+	0.311520i
$856$	−88841.8	−	64547.4i	−3.54737	−	2.57732i
$857$			22343.7i			0.890602i	0.895381	+	0.445301i	$0.146903\pi$
$857$			22343.7i			0.890602i	−0.895381	+	0.445301i	$0.853097\pi$
$858$	115.899	−	159.521i	0.00461156	−	0.00634726i
$859$	−6263.44	+	19276.9i	−0.248784	+	0.765680i	0.746206	+	0.665715i	$0.231873\pi$
$859$	−6263.44	+	19276.9i	−0.248784	+	0.765680i	−0.994991	+	0.0999652i	$0.968127\pi$
$860$	24192.3	+	49914.2i	0.959247	+	1.97914i
$861$	530.417	+	1632.46i	0.0209949	+	0.0646155i
$862$	29999.9	+	9747.55i	1.18538	+	0.385154i
$863$	−26694.6	−	8673.61i	−1.05295	−	0.342124i	−0.269124	−	0.963105i	$-0.586734\pi$
$863$	−26694.6	−	8673.61i	−1.05295	−	0.342124i	−0.783825	+	0.620981i	$0.786734\pi$
$864$	−12784.8	−	39347.7i	−0.503414	−	1.54935i
$865$	19434.0	−	2682.34i	0.763904	−	0.105436i
$866$	−693.257	+	2133.62i	−0.0272030	+	0.0837223i
$867$	8302.62	−	11427.6i	0.325227	−	0.447637i
$868$		−	113493.i		−	4.43803i
$869$	−78.0994	−	56.7426i	−0.00304872	−	0.00221503i
$870$	−38283.6	−	6847.98i	−1.49188	−	0.266860i
$871$	−1984.79	+	1442.03i	−0.0772124	+	0.0560981i
$872$	58090.8	+	79955.1i	2.25597	+	3.10507i
$873$	6999.67	−	2274.33i	0.271366	−	0.0881723i
$874$	18982.6			0.734663
$875$	17396.5	−	29622.5i	0.672125	−	1.14449i
$876$	45470.4			1.75377
$877$	−7819.90	+	2540.84i	−0.301094	+	0.0978313i	−0.455668	−	0.890150i	$-0.650599\pi$
$877$	−7819.90	+	2540.84i	−0.301094	+	0.0978313i	0.154574	+	0.987981i	$0.450599\pi$
$878$	−13188.2	−	18152.0i	−0.506926	−	0.697723i
$879$	−6883.72	+	5001.32i	−0.264144	+	0.191912i
$880$	−514.133	−	91.9655i	−0.0196948	−	0.00352291i
$881$	−7414.26	−	5386.77i	−0.283533	−	0.205999i	0.436924	−	0.899498i	$-0.356068\pi$
$881$	−7414.26	−	5386.77i	−0.283533	−	0.205999i	−0.720457	+	0.693500i	$0.756068\pi$
$882$		−	25316.7i		−	0.966505i
$883$	−10297.7	+	14173.6i	−0.392464	+	0.540180i	−0.958833	−	0.283972i	$-0.908348\pi$
$883$	−10297.7	+	14173.6i	−0.392464	+	0.540180i	0.566369	+	0.824152i	$0.308348\pi$
$884$	1530.23	−	4709.55i	0.0582207	−	0.179185i
$885$	−7230.03	+	997.910i	−0.274616	+	0.0379032i
$886$	8589.05	+	26434.4i	0.325682	+	1.00235i
$887$	−3747.82	−	1217.74i	−0.141871	−	0.0460967i	0.237221	−	0.971456i	$-0.423764\pi$
$887$	−3747.82	−	1217.74i	−0.141871	−	0.0460967i	−0.379092	+	0.925359i	$0.623764\pi$
$888$	23159.1	+	7524.84i	0.875189	+	0.284366i
$889$	11518.1	+	35449.0i	0.434538	+	1.33737i
$890$	−11433.0	−	23588.8i	−0.430600	−	0.888424i
$891$	−11.5466	+	35.5367i	−0.000434147	+	0.00133617i
$892$	−34072.9	+	46897.4i	−1.27898	+	1.76036i
$893$			26157.3i			0.980203i
$894$	−33815.6	−	24568.4i	−1.26506	−	0.919118i
$895$	30597.7	−	14830.1i	1.14276	−	0.553871i
$896$	−4504.37	+	3272.61i	−0.167947	+	0.122021i
$897$	−3015.92	−	4151.05i	−0.112261	−	0.154515i
$898$	47840.9	−	15544.5i	1.77781	−	0.577645i
$899$	−55585.4			−2.06215
$900$	1773.00	−	44472.0i	0.0656667	−	1.64711i
$901$	2342.03			0.0865975
$902$	37.3789	−	12.1451i	0.00137980	−	0.000448325i
$903$	−10852.5	−	14937.2i	−0.399943	−	0.550475i
$904$	43698.8	−	31749.0i	1.60774	−	1.16809i
$905$	−3124.21	−	3251.24i	−0.114754	−	0.119420i
$906$	−23788.0	−	17283.0i	−0.872301	−	0.633764i
$907$			3369.04i			0.123337i	0.998097	+	0.0616687i	$0.0196422\pi$
$907$			3369.04i			0.123337i	−0.998097	+	0.0616687i	$0.980358\pi$
$908$	−1830.87	+	2519.97i	−0.0669157	+	0.0921015i
$909$	4800.82	−	14775.4i	0.175174	−	0.539130i
$910$	−10517.7	+	58799.0i	−0.383140	+	2.14194i
$911$	7871.66	+	24226.5i	0.286279	+	0.881075i	0.986012	+	0.166671i	$0.0533019\pi$
$911$	7871.66	+	24226.5i	0.286279	+	0.881075i	−0.699734	+	0.714404i	$0.746698\pi$
$912$	35305.9	+	11471.6i	1.28190	+	0.416516i
$913$	−126.135	−	40.9838i	−0.00457225	−	0.00148561i
$914$	11536.0	+	35504.1i	0.417480	+	1.28487i
$915$	12600.4	−	12108.0i	0.455252	−	0.437464i
$916$	−29872.8	+	91939.0i	−1.07754	+	3.31632i
$917$	4454.89	−	6131.63i	0.160429	−	0.220812i
$918$		−	4269.18i		−	0.153490i
$919$	−28138.2	−	20443.6i	−1.01000	−	0.733810i	−0.0457927	−	0.998951i	$-0.514581\pi$
$919$	−28138.2	−	20443.6i	−1.01000	−	0.733810i	−0.964210	+	0.265141i	$0.914581\pi$
$920$	−12988.2	+	24282.4i	−0.465444	+	0.870181i
$921$	2663.28	−	1934.99i	0.0952857	−	0.0692291i
$922$	−10691.2	−	14715.2i	−0.381882	−	0.525616i
$923$	−1432.74	+	465.526i	−0.0510935	+	0.0166013i
$924$	426.822			0.0151963
$925$	14207.7	+	11213.8i	0.505024	+	0.398601i
$926$	19878.1			0.705437
$927$	−4900.53	+	1592.28i	−0.173629	+	0.0564156i
$928$	−42404.0	−	58364.0i	−1.49998	−	2.06454i
$929$	44628.6	−	32424.6i	1.57612	−	1.14512i	0.655145	−	0.755503i	$-0.272608\pi$
$929$	44628.6	−	32424.6i	1.57612	−	1.14512i	0.920977	−	0.389616i	$-0.127392\pi$
$930$	5566.79	+	40332.4i	0.196282	+	1.42210i
$931$	18144.3	+	13182.6i	0.638729	+	0.464064i
$932$		−	71338.8i		−	2.50727i
$933$	−17945.5	+	24699.9i	−0.629700	+	0.866708i
$934$	28308.3	−	87124.0i	0.991730	−	3.05223i
$935$	−19.1402	−	10.2377i	−0.000669466	−	0.000358085i
$936$	13918.7	+	42837.4i	0.486055	+	1.49592i
$937$	−4352.37	−	1414.17i	−0.151746	−	0.0493051i	0.232159	−	0.972678i	$-0.425421\pi$
$937$	−4352.37	−	1414.17i	−0.151746	−	0.0493051i	−0.383905	+	0.923373i	$0.625421\pi$
$938$	−7161.73	−	2326.99i	−0.249295	−	0.0810009i
$939$	3895.73	+	11989.8i	0.135391	+	0.416691i
$940$	−57489.4	−	30750.1i	−1.99479	−	1.06697i
$941$	−13391.0	+	41213.3i	−0.463905	+	1.42775i	0.396450	+	0.918056i	$0.370242\pi$
$941$	−13391.0	+	41213.3i	−0.463905	+	1.42775i	−0.860355	+	0.509696i	$0.829758\pi$
$942$	19641.6	−	27034.4i	0.679362	−	0.935062i
$943$		−	1022.73i		−	0.0353178i
$944$	−27195.3	−	19758.5i	−0.937640	−	0.681235i
$945$	4965.52	+	35976.1i	0.170929	+	1.23841i
$946$	−342.021	+	248.493i	−0.0117548	+	0.00854039i
$947$	−13548.4	−	18647.8i	−0.464904	−	0.639885i	0.510613	−	0.859811i	$-0.329418\pi$
$947$	−13548.4	−	18647.8i	−0.464904	−	0.639885i	−0.975517	+	0.219926i	$0.929418\pi$
$948$	−16265.0	+	5284.83i	−0.557240	+	0.181058i
$949$	−34204.0			−1.16998
$950$	43885.8	+	34637.8i	1.49878	+	1.18295i
$951$	−916.172			−0.0312397
$952$	8413.49	−	2733.71i	0.286431	−	0.0930672i
$953$	−14314.9	−	19702.8i	−0.486574	−	0.669712i	0.493178	−	0.869929i	$-0.335835\pi$
$953$	−14314.9	−	19702.8i	−0.486574	−	0.669712i	−0.979752	+	0.200217i	$0.935835\pi$
$954$	−29611.0	+	21513.6i	−1.00492	+	0.730114i
$955$	−31.1323	+	58.2040i	−0.00105489	+	0.00197218i
$956$	11801.1	+	8574.02i	0.399242	+	0.290066i
$957$		−	209.044i		−	0.00706104i
$958$	−8493.21	+	11689.9i	−0.286433	+	0.394242i
$959$	7925.43	−	24392.0i	0.266867	−	0.821332i
$960$	−10215.6	+	9816.42i	−0.343444	+	0.330025i
$961$	8776.28	+	27010.6i	0.294595	+	0.906670i
$962$	−29931.4	−	9725.30i	−1.00315	−	0.325942i
$963$	33478.3	+	10877.8i	1.12027	+	0.363999i
$964$	4754.49	+	14632.8i	0.158850	+	0.488891i
$965$	9352.17	−	52283.3i	0.311976	−	1.74410i
$966$	4866.74	−	14978.3i	0.162096	−	0.498881i
$967$	−10816.4	+	14887.5i	−0.359701	+	0.495086i	−0.950065	−	0.312051i	$-0.898984\pi$
$967$	−10816.4	+	14887.5i	−0.359701	+	0.495086i	0.590364	+	0.807137i	$0.298984\pi$
$968$			77238.0i			2.56459i
$969$	1248.15	+	906.835i	0.0413792	+	0.0300637i
$970$	−15966.3	−	16615.6i	−0.528503	−	0.549993i
$971$	29739.6	−	21607.1i	0.982892	−	0.714113i	0.0245388	−	0.999699i	$-0.492188\pi$
$971$	29739.6	−	21607.1i	0.982892	−	0.714113i	0.958353	+	0.285586i	$0.0921883\pi$
$972$	44030.9	+	60603.3i	1.45298	+	1.99985i
$973$	70593.8	−	22937.3i	2.32593	−	0.755742i
$974$	83256.5			2.73892
$975$	602.004	−	15100.0i	0.0197739	−	0.495987i
$976$	80484.9			2.63961
$977$	−35305.5	+	11471.4i	−1.15611	+	0.375644i	−0.823443	−	0.567400i	$-0.807950\pi$
$977$	−35305.5	+	11471.4i	−1.15611	+	0.375644i	−0.332670	+	0.943043i	$0.607950\pi$
$978$	16995.0	+	23391.6i	0.555665	+	0.764808i
$979$	113.990	−	82.8184i	0.00372128	−	0.00270367i
$980$	−50303.3	+	24381.0i	−1.63967	+	0.794715i
$981$	−25629.7	−	18621.1i	−0.834142	−	0.606040i
$982$		−	65411.0i		−	2.12561i
$983$	5014.81	−	6902.29i	0.162714	−	0.223956i	−0.719873	−	0.694106i	$-0.755800\pi$
$983$	5014.81	−	6902.29i	0.162714	−	0.223956i	0.882587	+	0.470150i	$0.155800\pi$
$984$	1252.28	−	3854.13i	0.0405704	−	0.124863i
$985$	−25247.1	−	52090.4i	−0.816691	−	1.68501i
$986$	−2300.39	−	7079.87i	−0.0742995	−	0.228670i
$987$	20639.6	+	6706.20i	0.665617	+	0.216272i
$988$	−65201.5	−	21185.3i	−2.09953	−	0.682179i
$989$	3399.53	+	10462.7i	0.109301	+	0.336394i
$990$	336.037	−	46.3808i	0.0107878	−	0.00148897i
$991$	−4890.03	+	15050.0i	−0.156748	+	0.482420i	−0.998334	−	0.0577030i	$-0.981622\pi$
$991$	−4890.03	+	15050.0i	−0.156748	+	0.482420i	0.841586	+	0.540123i	$0.181622\pi$
$992$	−44392.2	+	61100.6i	−1.42082	+	1.95559i
$993$		−	1418.92i		−	0.0453456i
$994$	−3740.89	−	2717.91i	−0.119370	−	0.0867273i
$995$	−22559.7	−	4035.36i	−0.718784	−	0.128572i
$996$	−19008.4	+	13810.4i	−0.604723	+	0.439357i
$997$	12668.0	+	17436.1i	0.402408	+	0.553867i	0.961346	−	0.275342i	$-0.0887912\pi$
$997$	12668.0	+	17436.1i	0.402408	+	0.553867i	−0.558938	+	0.829209i	$0.688791\pi$
$998$	−3822.04	+	1241.86i	−0.121227	+	0.0393891i
$999$	−19134.8			−0.606003

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.e.a.19.1	yes	24
3.2	odd	2		225.4.m.a.19.6		24
5.2	odd	4		125.4.d.b.26.1		48
5.3	odd	4		125.4.d.b.26.12		48
5.4	even	2		125.4.e.a.99.6		24
25.2	odd	20		625.4.a.g.1.1		24
25.3	odd	20		125.4.d.b.101.12		48
25.4	even	10	inner	25.4.e.a.4.1	✓	24
25.21	even	5		125.4.e.a.24.6		24
25.22	odd	20		125.4.d.b.101.1		48
25.23	odd	20		625.4.a.g.1.24		24
75.29	odd	10		225.4.m.a.154.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.e.a.4.1	✓	24	25.4	even	10	inner
25.4.e.a.19.1	yes	24	1.1	even	1	trivial
125.4.d.b.26.1		48	5.2	odd	4
125.4.d.b.26.12		48	5.3	odd	4
125.4.d.b.101.1		48	25.22	odd	20
125.4.d.b.101.12		48	25.3	odd	20
125.4.e.a.24.6		24	25.21	even	5
125.4.e.a.99.6		24	5.4	even	2
225.4.m.a.19.6		24	3.2	odd	2
225.4.m.a.154.6		24	75.29	odd	10
625.4.a.g.1.1		24	25.2	odd	20
625.4.a.g.1.24		24	25.23	odd	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.95462 + 1.60985i) q^{2} +(-1.70326 - 2.34434i) q^{3} +(15.4845 - 11.2501i) q^{4} +(11.0057 + 1.96864i) q^{5} +(12.2131 + 8.87330i) q^{6} -24.5811i q^{7} +(-34.1117 + 46.9507i) q^{8} +(5.74864 - 17.6925i) q^{9} +O(q^{10})\)	\(q+(-4.95462 + 1.60985i) q^{2} +(-1.70326 - 2.34434i) q^{3} +(15.4845 - 11.2501i) q^{4} +(11.0057 + 1.96864i) q^{5} +(12.2131 + 8.87330i) q^{6} -24.5811i q^{7} +(-34.1117 + 46.9507i) q^{8} +(5.74864 - 17.6925i) q^{9} +(-57.6981 + 7.96365i) q^{10} +(-0.0967445 - 0.297749i) q^{11} +(-52.7483 - 17.1390i) q^{12} +(39.6785 + 12.8923i) q^{13} +(39.5719 + 121.790i) q^{14} +(-14.1304 - 29.1541i) q^{15} +(46.1103 - 141.913i) q^{16} +(3.64505 - 5.01698i) q^{17} +96.9140i q^{18} +(-69.4577 - 50.4640i) q^{19} +(192.564 - 93.3319i) q^{20} +(-57.6263 + 41.8680i) q^{21} +(0.958664 + 1.31949i) q^{22} +(40.3641 - 13.1151i) q^{23} +168.170 q^{24} +(117.249 + 43.3323i) q^{25} -217.347 q^{26} +(-125.679 + 40.8355i) q^{27} +(-276.540 - 380.625i) q^{28} +(-186.418 + 135.441i) q^{29} +(116.944 + 121.700i) q^{30} +(195.159 + 141.791i) q^{31} +313.081i q^{32} +(-0.533243 + 0.733946i) q^{33} +(-9.98322 + 30.7252i) q^{34} +(48.3912 - 270.531i) q^{35} +(-110.028 - 338.632i) q^{36} +(137.713 + 44.7455i) q^{37} +(425.376 + 138.213i) q^{38} +(-37.3589 - 114.979i) q^{39} +(-467.851 + 449.570i) q^{40} +(7.44654 - 22.9181i) q^{41} +(218.115 - 300.210i) q^{42} +259.208i q^{43} +(-4.84776 - 3.52210i) q^{44} +(98.0976 - 183.400i) q^{45} +(-178.875 + 129.961i) q^{46} +(-179.081 - 246.484i) q^{47} +(-411.230 + 133.617i) q^{48} -261.229 q^{49} +(-650.683 - 25.9413i) q^{50} -17.9700 q^{51} +(759.443 - 246.758i) q^{52} +(221.987 + 305.538i) q^{53} +(556.952 - 404.649i) q^{54} +(-0.478577 - 3.46738i) q^{55} +(1154.10 + 838.502i) q^{56} +248.786i q^{57} +(705.591 - 971.163i) q^{58} +(69.6150 - 214.253i) q^{59} +(-546.789 - 292.468i) q^{60} +(166.679 + 512.985i) q^{61} +(-1195.20 - 388.344i) q^{62} +(-434.900 - 141.308i) q^{63} +(-135.133 - 415.895i) q^{64} +(411.308 + 220.001i) q^{65} +(1.46047 - 4.49487i) q^{66} +(-34.5641 + 47.5735i) q^{67} -118.693i q^{68} +(-99.4968 - 72.2886i) q^{69} +(195.755 + 1418.28i) q^{70} +(-29.2126 + 21.2242i) q^{71} +(634.579 + 873.424i) q^{72} +(-779.711 + 253.343i) q^{73} -754.347 q^{74} +(-98.1201 - 348.677i) q^{75} -1643.24 q^{76} +(-7.31898 + 2.37808i) q^{77} +(370.198 + 509.534i) q^{78} +(249.462 - 181.245i) q^{79} +(786.850 - 1471.07i) q^{80} +(-96.5572 - 70.1529i) q^{81} +125.538i q^{82} +(249.003 - 342.723i) q^{83} +(-421.294 + 1296.61i) q^{84} +(49.9927 - 48.0393i) q^{85} +(-417.286 - 1284.28i) q^{86} +(635.037 + 206.336i) q^{87} +(17.2796 + 5.61450i) q^{88} +(139.074 + 428.027i) q^{89} +(-190.788 + 1066.60i) q^{90} +(316.907 - 975.341i) q^{91} +(477.471 - 657.182i) q^{92} -699.025i q^{93} +(1284.08 + 932.940i) q^{94} +(-665.082 - 692.126i) q^{95} +(733.969 - 533.260i) q^{96} +(232.545 + 320.071i) q^{97} +(1294.29 - 420.540i) q^{98} -5.82407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9 - 5 * q^10 + 83 * q^11 - 165 * q^12 - 5 * q^13 + 31 * q^14 - 225 * q^15 + 89 * q^16 - 165 * q^17 - 115 * q^19 + 395 * q^20 + 138 * q^21 + 30 * q^22 + 75 * q^23 + 640 * q^24 + 595 * q^25 - 822 * q^26 + 595 * q^27 + 675 * q^28 + 125 * q^29 - 965 * q^30 + 633 * q^31 - 1285 * q^33 - 779 * q^34 + 190 * q^35 - 531 * q^36 - 1510 * q^37 + 255 * q^38 - 1241 * q^39 - 2470 * q^40 - 117 * q^41 + 1745 * q^42 + 516 * q^44 + 1725 * q^45 + 1233 * q^46 - 95 * q^47 + 1410 * q^48 + 1148 * q^49 + 2165 * q^50 - 2022 * q^51 + 1740 * q^52 + 2580 * q^53 + 1745 * q^54 - 315 * q^55 + 3160 * q^56 - 4230 * q^58 - 1905 * q^59 + 560 * q^60 - 567 * q^61 - 6880 * q^62 - 1950 * q^63 - 3612 * q^64 - 3170 * q^65 - 2774 * q^66 + 4195 * q^67 + 539 * q^69 + 3630 * q^70 + 2473 * q^71 + 215 * q^72 - 845 * q^73 + 3596 * q^74 + 2045 * q^75 - 3280 * q^76 + 3870 * q^77 + 9295 * q^78 + 775 * q^79 - 3670 * q^80 + 3309 * q^81 - 4625 * q^83 - 5694 * q^84 - 1460 * q^85 - 3897 * q^86 - 8485 * q^87 - 1650 * q^88 - 2410 * q^89 - 8845 * q^90 - 382 * q^91 + 4090 * q^92 + 5401 * q^94 + 3545 * q^95 + 6488 * q^96 + 5185 * q^97 + 5180 * q^98 + 6024 * q^99

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