LMFDB - Embedded newform 25.4.e.a.14.5

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			14.5
Character	$\chi$	$=$	25.14
Dual form			25.4.e.a.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.81265 + 2.49489i) q^{2} +(3.16804 + 1.02936i) q^{3} +(-0.466674 + 1.43628i) q^{4} +(-10.8670 - 2.62823i) q^{5} +(3.17440 + 9.76980i) q^{6} +5.10302i q^{7} +(19.0341 - 6.18456i) q^{8} +(-12.8665 - 9.34809i) q^{9} +O(q^{10})$	\(q+(1.81265 + 2.49489i) q^{2} +(3.16804 + 1.02936i) q^{3} +(-0.466674 + 1.43628i) q^{4} +(-10.8670 - 2.62823i) q^{5} +(3.17440 + 9.76980i) q^{6} +5.10302i q^{7} +(19.0341 - 6.18456i) q^{8} +(-12.8665 - 9.34809i) q^{9} +(-13.1409 - 31.8762i) q^{10} +(-9.41641 + 6.84142i) q^{11} +(-2.95689 + 4.06981i) q^{12} +(27.9240 - 38.4341i) q^{13} +(-12.7315 + 9.24997i) q^{14} +(-31.7218 - 19.5124i) q^{15} +(59.7061 + 43.3790i) q^{16} +(-80.1567 + 26.0445i) q^{17} -49.0455i q^{18} +(32.9811 + 101.505i) q^{19} +(8.84623 - 14.3815i) q^{20} +(-5.25284 + 16.1666i) q^{21} +(-34.1372 - 11.0919i) q^{22} +(26.0076 + 35.7964i) q^{23} +66.6671 q^{24} +(111.185 + 57.1222i) q^{25} +146.505 q^{26} +(-84.0041 - 115.622i) q^{27} +(-7.32934 - 2.38145i) q^{28} +(-69.8341 + 214.927i) q^{29} +(-8.81900 - 114.512i) q^{30} +(-50.5937 - 155.711i) q^{31} +67.4821i q^{32} +(-36.8739 + 11.9810i) q^{33} +(-210.274 - 152.773i) q^{34} +(13.4119 - 55.4546i) q^{35} +(19.4309 - 14.1174i) q^{36} +(76.3255 - 105.053i) q^{37} +(-193.462 + 266.278i) q^{38} +(128.027 - 93.0171i) q^{39} +(-223.099 + 17.1817i) q^{40} +(-110.989 - 80.6385i) q^{41} +(-49.8554 + 16.1990i) q^{42} -414.866i q^{43} +(-5.43177 - 16.7173i) q^{44} +(115.252 + 135.402i) q^{45} +(-42.1657 + 129.773i) q^{46} +(510.490 + 165.868i) q^{47} +(144.499 + 198.886i) q^{48} +316.959 q^{49} +(59.0249 + 380.937i) q^{50} -280.749 q^{51} +(42.1706 + 58.0428i) q^{52} +(422.636 + 137.323i) q^{53} +(136.194 - 419.163i) q^{54} +(120.309 - 49.5974i) q^{55} +(31.5599 + 97.1315i) q^{56} +355.523i q^{57} +(-662.806 + 215.359i) q^{58} +(-654.183 - 475.292i) q^{59} +(42.8290 - 36.4553i) q^{60} +(-467.608 + 339.737i) q^{61} +(296.775 - 408.476i) q^{62} +(47.7035 - 65.6582i) q^{63} +(309.288 - 224.711i) q^{64} +(-404.465 + 344.274i) q^{65} +(-96.7307 - 70.2790i) q^{66} +(129.600 - 42.1095i) q^{67} -127.281i q^{68} +(45.5459 + 140.176i) q^{69} +(162.665 - 67.0584i) q^{70} +(179.051 - 551.063i) q^{71} +(-302.717 - 98.3588i) q^{72} +(-158.070 - 217.564i) q^{73} +400.447 q^{74} +(293.439 + 295.415i) q^{75} -161.181 q^{76} +(-34.9119 - 48.0521i) q^{77} +(464.136 + 150.807i) q^{78} +(-70.8764 + 218.135i) q^{79} +(-534.818 - 628.323i) q^{80} +(-14.4185 - 44.3755i) q^{81} -423.076i q^{82} +(-833.650 + 270.869i) q^{83} +(-20.7683 - 15.0890i) q^{84} +(939.516 - 72.3558i) q^{85} +(1035.05 - 752.006i) q^{86} +(-442.475 + 609.015i) q^{87} +(-136.922 + 188.457i) q^{88} +(-1246.69 + 905.776i) q^{89} +(-128.903 + 532.979i) q^{90} +(196.130 + 142.497i) q^{91} +(-63.5506 + 20.6489i) q^{92} -545.380i q^{93} +(511.514 + 1574.28i) q^{94} +(-91.6268 - 1189.74i) q^{95} +(-69.4633 + 213.786i) q^{96} +(3.24339 + 1.05384i) q^{97} +(574.535 + 790.780i) q^{98} +185.111 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 $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	1.81265	+	2.49489i	0.640868	+	0.882078i	0.998662	−	0.0517221i	$-0.0164710\pi$
$2$	1.81265	+	2.49489i	0.640868	+	0.882078i	−0.357794	+	0.933801i	$0.616471\pi$
$3$	3.16804	+	1.02936i	0.609690	+	0.198100i	0.597557	−	0.801826i	$-0.296138\pi$
$3$	3.16804	+	1.02936i	0.609690	+	0.198100i	0.0121326	+	0.999926i	$0.496138\pi$
$4$	−0.466674	+	1.43628i	−0.0583343	+	0.179534i
$5$	−10.8670	−	2.62823i	−0.971977	−	0.235076i
$5$	−10.8670	−	2.62823i	−0.971977	−	0.235076i
$6$	3.17440	+	9.76980i	0.215991	+	0.664751i
$7$			5.10302i			0.275537i	0.990464	+	0.137768i	$0.0439930\pi$
$7$			5.10302i			0.275537i	−0.990464	+	0.137768i	$0.956007\pi$
$8$	19.0341	−	6.18456i	0.841197	−	0.273322i
$9$	−12.8665	−	9.34809i	−0.476539	−	0.346226i
$10$	−13.1409	−	31.8762i	−0.415553	−	1.00801i
$11$	−9.41641	+	6.84142i	−0.258105	+	0.187524i	−0.709311	−	0.704896i	$-0.750994\pi$
$11$	−9.41641	+	6.84142i	−0.258105	+	0.187524i	0.451206	+	0.892420i	$0.350994\pi$
$12$	−2.95689	+	4.06981i	−0.0711316	+	0.0979043i
$13$	27.9240	−	38.4341i	0.595749	−	0.819978i	−0.399562	−	0.916706i	$-0.630838\pi$
$13$	27.9240	−	38.4341i	0.595749	−	0.819978i	0.995311	+	0.0967285i	$0.0308379\pi$
$14$	−12.7315	+	9.24997i	−0.243045	+	0.176583i
$15$	−31.7218	−	19.5124i	−0.546036	−	0.335873i
$16$	59.7061	+	43.3790i	0.932908	+	0.677798i
$17$	−80.1567	+	26.0445i	−1.14358	+	0.371571i	−0.818721	−	0.574191i	$-0.805317\pi$
$17$	−80.1567	+	26.0445i	−1.14358	+	0.371571i	−0.324858	+	0.945763i	$0.605317\pi$
$18$		−	49.0455i		−	0.642229i
$19$	32.9811	+	101.505i	0.398230	+	1.22563i	0.926417	+	0.376499i	$0.122872\pi$
$19$	32.9811	+	101.505i	0.398230	+	1.22563i	−0.528187	+	0.849128i	$0.677128\pi$
$20$	8.84623	−	14.3815i	0.0989038	−	0.160790i
$21$	−5.25284	+	16.1666i	−0.0545840	+	0.167992i
$22$	−34.1372	−	11.0919i	−0.330822	−	0.107491i
$23$	26.0076	+	35.7964i	0.235781	+	0.324525i	0.910468	−	0.413579i	$-0.135721\pi$
$23$	26.0076	+	35.7964i	0.235781	+	0.324525i	−0.674687	+	0.738104i	$0.735721\pi$
$24$	66.6671			0.567015
$25$	111.185	+	57.1222i	0.889478	+	0.456978i
$26$	146.505			1.10508
$27$	−84.0041	−	115.622i	−0.598763	−	0.824126i
$28$	−7.32934	−	2.38145i	−0.0494684	−	0.0160732i
$29$	−69.8341	+	214.927i	−0.447168	+	1.37624i	0.432921	+	0.901432i	$0.357483\pi$
$29$	−69.8341	+	214.927i	−0.447168	+	1.37624i	−0.880089	+	0.474809i	$0.842517\pi$
$30$	−8.81900	−	114.512i	−0.0536707	−	0.696896i
$31$	−50.5937	−	155.711i	−0.293126	−	0.902148i	−0.983845	−	0.179025i	$-0.942706\pi$
$31$	−50.5937	−	155.711i	−0.293126	−	0.902148i	0.690719	−	0.723123i	$-0.257294\pi$
$32$			67.4821i			0.372790i
$33$	−36.8739	+	11.9810i	−0.194513	+	0.0632010i
$34$	−210.274	−	152.773i	−1.06064	−	0.770598i
$35$	13.4119	−	55.4546i	0.0647722	−	0.267816i
$36$	19.4309	−	14.1174i	0.0899580	−	0.0653583i
$37$	76.3255	−	105.053i	0.339131	−	0.466773i	−0.605057	−	0.796182i	$-0.706850\pi$
$37$	76.3255	−	105.053i	0.339131	−	0.466773i	0.944187	+	0.329409i	$0.106850\pi$
$38$	−193.462	+	266.278i	−0.825886	+	1.13674i
$39$	128.027	−	93.0171i	0.525660	−	0.381914i
$40$	−223.099	+	17.1817i	−0.881876	+	0.0679167i
$41$	−110.989	−	80.6385i	−0.422771	−	0.307161i	0.355981	−	0.934493i	$-0.384147\pi$
$41$	−110.989	−	80.6385i	−0.422771	−	0.307161i	−0.778752	+	0.627332i	$0.784147\pi$
$42$	−49.8554	+	16.1990i	−0.183163	+	0.0595134i
$43$		−	414.866i		−	1.47131i	−0.677354	−	0.735657i	$-0.736874\pi$
$43$		−	414.866i		−	1.47131i	0.677354	−	0.735657i	$-0.263126\pi$
$44$	−5.43177	−	16.7173i	−0.0186107	−	0.0572778i
$45$	115.252	+	135.402i	0.381795	+	0.448546i
$46$	−42.1657	+	129.773i	−0.135152	+	0.415955i
$47$	510.490	+	165.868i	1.58431	+	0.514774i	0.963163	−	0.268919i	$-0.0866664\pi$
$47$	510.490	+	165.868i	1.58431	+	0.514774i	0.621148	+	0.783693i	$0.286666\pi$
$48$	144.499	+	198.886i	0.434513	+	0.598056i
$49$	316.959			0.924079
$50$	59.0249	+	380.937i	0.166948	+	1.07745i
$51$	−280.749			−0.770837
$52$	42.1706	+	58.0428i	0.112462	+	0.154790i
$53$	422.636	+	137.323i	1.09535	+	0.355901i	0.800311	−	0.599584i	$-0.204667\pi$
$53$	422.636	+	137.323i	1.09535	+	0.355901i	0.295039	+	0.955485i	$0.404667\pi$
$54$	136.194	−	419.163i	0.343216	−	1.05631i
$55$	120.309	−	49.5974i	0.294954	−	0.121595i
$56$	31.5599	+	97.1315i	0.0753102	+	0.231781i
$57$			355.523i			0.826142i
$58$	−662.806	+	215.359i	−1.50053	+	0.487551i
$59$	−654.183	−	475.292i	−1.44351	−	1.04877i	−0.987293	−	0.158908i	$-0.949203\pi$
$59$	−654.183	−	475.292i	−1.44351	−	1.04877i	−0.456221	−	0.889867i	$-0.650797\pi$
$60$	42.8290	−	36.4553i	0.0921533	−	0.0784394i
$61$	−467.608	+	339.737i	−0.981494	+	0.713097i	−0.958042	−	0.286628i	$-0.907466\pi$
$61$	−467.608	+	339.737i	−0.981494	+	0.713097i	−0.0234516	+	0.999725i	$0.507466\pi$
$62$	296.775	−	408.476i	0.607911	−	0.836718i
$63$	47.7035	−	65.6582i	0.0953980	−	0.131304i
$64$	309.288	−	224.711i	0.604079	−	0.438889i
$65$	−404.465	+	344.274i	−0.771811	+	0.656953i
$66$	−96.7307	−	70.2790i	−0.180405	−	0.131072i
$67$	129.600	−	42.1095i	0.236316	−	0.0767836i	−0.188465	−	0.982080i	$-0.560351\pi$
$67$	129.600	−	42.1095i	0.236316	−	0.0767836i	0.424781	+	0.905296i	$0.360351\pi$
$68$		−	127.281i		−	0.226987i
$69$	45.5459	+	140.176i	0.0794650	+	0.244568i
$70$	162.665	−	67.0584i	0.277745	−	0.114500i
$71$	179.051	−	551.063i	0.299288	−	0.921114i	−0.682459	−	0.730924i	$-0.739090\pi$
$71$	179.051	−	551.063i	0.299288	−	0.921114i	0.981747	−	0.190190i	$-0.0609105\pi$
$72$	−302.717	−	98.3588i	−0.495494	−	0.160996i
$73$	−158.070	−	217.564i	−0.253433	−	0.348821i	0.663277	−	0.748374i	$-0.269165\pi$
$73$	−158.070	−	217.564i	−0.253433	−	0.348821i	−0.916710	+	0.399553i	$0.869165\pi$
$74$	400.447			0.629068
$75$	293.439	+	295.415i	0.451779	+	0.454821i
$76$	−161.181			−0.243273
$77$	−34.9119	−	48.0521i	−0.0516698	−	0.0711174i
$78$	464.136	+	150.807i	0.673757	+	0.218917i
$79$	−70.8764	+	218.135i	−0.100940	+	0.310660i	−0.988756	−	0.149538i	$-0.952221\pi$
$79$	−70.8764	+	218.135i	−0.100940	+	0.310660i	0.887816	+	0.460198i	$0.152221\pi$
$80$	−534.818	−	628.323i	−0.747431	−	0.878108i
$81$	−14.4185	−	44.3755i	−0.0197784	−	0.0608718i
$82$		−	423.076i		−	0.569767i
$83$	−833.650	+	270.869i	−1.10247	+	0.358214i	−0.803053	−	0.595908i	$-0.796792\pi$
$83$	−833.650	+	270.869i	−1.10247	+	0.358214i	−0.299417	+	0.954122i	$0.596792\pi$
$84$	−20.7683	−	15.0890i	−0.0269763	−	0.0195994i
$85$	939.516	−	72.3558i	1.19888	−	0.0923304i
$86$	1035.05	−	752.006i	1.29781	−	0.942917i
$87$	−442.475	+	609.015i	−0.545268	+	0.750497i
$88$	−136.922	+	188.457i	−0.165863	+	0.228291i
$89$	−1246.69	+	905.776i	−1.48482	+	1.07879i	−0.508861	+	0.860849i	$0.669933\pi$
$89$	−1246.69	+	905.776i	−1.48482	+	1.07879i	−0.975962	+	0.217939i	$0.930067\pi$
$90$	−128.903	+	532.979i	−0.150973	+	0.624232i
$91$	196.130	+	142.497i	0.225934	+	0.164151i
$92$	−63.5506	+	20.6489i	−0.0720175	+	0.0233999i
$93$		−	545.380i		−	0.608099i
$94$	511.514	+	1574.28i	0.561263	+	1.72739i
$95$	−91.6268	−	1189.74i	−0.0989548	−	1.28490i
$96$	−69.4633	+	213.786i	−0.0738497	+	0.227286i
$97$	3.24339	+	1.05384i	0.00339502	+	0.00110311i	0.310714	−	0.950503i	$-0.399432\pi$
$97$	3.24339	+	1.05384i	0.00339502	+	0.00110311i	−0.307319	+	0.951607i	$0.599432\pi$
$98$	574.535	+	790.780i	0.592212	+	0.815111i
$99$	185.111			0.187923
$100$	−133.930	+	133.035i	−0.133930	+	0.133035i
$101$	370.211			0.364726			0.182363	−	0.983231i	$-0.441625\pi$
$101$	370.211			0.364726			0.182363	+	0.983231i	$0.441625\pi$
$102$	−508.899	−	700.439i	−0.494005	−	0.679939i
$103$	380.458	+	123.618i	0.363958	+	0.118257i	0.485286	−	0.874355i	$-0.338715\pi$
$103$	380.458	+	123.618i	0.363958	+	0.118257i	−0.121328	+	0.992612i	$0.538715\pi$
$104$	293.811	−	904.258i	0.277025	−	0.852594i
$105$	99.5723	−	161.877i	0.0925453	−	0.150453i
$106$	423.484	+	1303.35i	0.388042	+	1.19427i
$107$			20.2472i			0.0182932i	0.999958	+	0.00914659i	$0.00291149\pi$
$107$			20.2472i			0.0182932i	−0.999958	+	0.00914659i	$0.997089\pi$
$108$	205.267	−	66.6953i	0.182887	−	0.0594237i
$109$	344.066	+	249.979i	0.302345	+	0.219666i	0.728605	−	0.684934i	$-0.240169\pi$
$109$	344.066	+	249.979i	0.302345	+	0.219666i	−0.426260	+	0.904601i	$0.640169\pi$
$110$	341.819	+	210.256i	0.296283	+	0.182247i
$111$	349.940	−	254.246i	0.299232	−	0.217405i
$112$	−221.364	+	304.681i	−0.186758	+	0.257051i
$113$	602.735	−	829.594i	0.501775	−	0.690634i	−0.480731	−	0.876868i	$-0.659629\pi$
$113$	602.735	−	829.594i	0.501775	−	0.690634i	0.982505	+	0.186235i	$0.0596285\pi$
$114$	−886.991	+	644.437i	−0.728722	+	0.529448i
$115$	−188.544	−	457.355i	−0.152886	−	0.370857i
$116$	−276.105	−	200.602i	−0.220997	−	0.160564i
$117$	−718.571	+	233.478i	−0.567794	+	0.184488i
$118$		−	2493.65i		−	1.94542i
$119$	−132.905	−	409.041i	−0.102382	−	0.315098i
$120$	−724.473	−	175.217i	−0.551125	−	0.133292i
$121$	−369.438	+	1137.01i	−0.277564	+	0.854255i
$122$	−1695.22	−	550.810i	−1.25801	−	0.408754i
$123$	−268.613	−	369.714i	−0.196911	−	0.271024i
$124$	247.255			0.179066
$125$	−1058.12	−	912.968i	−0.757128	−	0.653267i
$126$	250.280			0.176958
$127$	1006.97	+	1385.98i	0.703577	+	0.968390i	0.999911	+	0.0133059i	$0.00423553\pi$
$127$	1006.97	+	1385.98i	0.703577	+	0.968390i	−0.296335	+	0.955084i	$0.595764\pi$
$128$	1634.70	+	531.145i	1.12881	+	0.366774i
$129$	427.046	−	1314.31i	0.291468	−	0.897045i
$130$	−1592.08	−	385.051i	−1.07411	−	0.259778i
$131$	−279.238	−	859.407i	−0.186238	−	0.573181i	0.813730	−	0.581244i	$-0.197434\pi$
$131$	−279.238	−	859.407i	−0.186238	−	0.573181i	−0.999967	+	0.00806241i	$0.997434\pi$
$132$		−	58.5523i		−	0.0386085i
$133$	−517.983	+	168.303i	−0.337706	+	0.109727i
$134$	339.978	+	247.008i	0.219176	+	0.159241i
$135$	608.994	+	1477.25i	0.388251	+	0.941787i
$136$	−1364.64	+	991.468i	−0.860417	+	0.625130i
$137$	−314.080	+	432.295i	−0.195866	+	0.269587i	−0.895642	−	0.444776i	$-0.853283\pi$
$137$	−314.080	+	432.295i	−0.195866	+	0.269587i	0.699775	+	0.714363i	$0.253283\pi$
$138$	−267.165	+	367.722i	−0.164802	+	0.226830i
$139$	−645.593	+	469.051i	−0.393946	+	0.286218i	−0.767071	−	0.641563i	$-0.778286\pi$
$139$	−645.593	+	469.051i	−0.393946	+	0.286218i	0.373125	+	0.927781i	$0.378286\pi$
$140$	73.3891	+	45.1425i	0.0443037	+	0.0272517i
$141$	1446.52	+	1050.96i	0.863962	+	0.627705i
$142$	1699.40	−	552.168i	1.00430	−	0.326316i
$143$			552.951i			0.323357i
$144$	−362.700	−	1116.28i	−0.209896	−	0.645994i
$145$	1323.77	−	2152.08i	0.758159	−	1.23256i
$146$	256.275	−	788.734i	0.145270	−	0.447096i
$147$	1004.14	+	326.265i	0.563402	+	0.183060i
$148$	115.266	+	158.650i	0.0640189	+	0.0881145i
$149$	−273.633			−0.150449			−0.0752244	−	0.997167i	$-0.523967\pi$
$149$	−273.633			−0.150449			−0.0752244	+	0.997167i	$0.523967\pi$
$150$	−205.127	+	1267.58i	−0.111657	+	0.689984i
$151$	−404.463			−0.217978			−0.108989	−	0.994043i	$-0.534761\pi$
$151$	−404.463			−0.217978			−0.108989	+	0.994043i	$0.534761\pi$
$152$	1255.53	+	1728.09i	0.669981	+	0.922150i
$153$	1274.81	+	414.209i	0.673607	+	0.218868i
$154$	56.6020	−	174.203i	0.0296176	−	0.0911537i
$155$	140.558	+	1825.09i	0.0728378	+	0.945774i
$156$	73.8512	+	227.291i	0.0379028	+	0.116653i
$157$		−	2125.74i		−	1.08059i	−0.841476	−	0.540294i	$-0.818313\pi$
$157$		−	2125.74i		−	1.08059i	0.841476	−	0.540294i	$-0.181687\pi$
$158$	−672.698	+	218.573i	−0.338715	+	0.110055i
$159$	1197.58	+	870.089i	0.597320	+	0.433978i
$160$	177.359	−	733.330i	0.0876340	−	0.362343i
$161$	−182.670	+	132.717i	−0.0894186	+	0.0649664i
$162$	84.5767	−	116.410i	0.0410183	−	0.0564569i
$163$	−1407.83	+	1937.71i	−0.676501	+	0.931124i	−0.999885	−	0.0151437i	$-0.995179\pi$
$163$	−1407.83	+	1937.71i	−0.676501	+	0.931124i	0.323384	+	0.946268i	$0.395179\pi$
$164$	167.615	−	121.779i	0.0798081	−	0.0579840i
$165$	432.198	−	33.2853i	0.203919	−	0.0157046i
$166$	−2186.90	−	1588.88i	−1.02251	−	0.742897i
$167$	201.561	−	65.4911i	0.0933967	−	0.0303464i	−0.261946	−	0.965083i	$-0.584364\pi$
$167$	201.561	−	65.4911i	0.0933967	−	0.0303464i	0.355343	+	0.934736i	$0.384364\pi$
$168$			340.203i			0.156234i
$169$	−18.5203	−	56.9996i	−0.00842981	−	0.0259443i
$170$	1883.53	+	2212.84i	0.849766	+	0.998335i
$171$	524.529	−	1614.33i	0.234571	−	0.721936i
$172$	595.862	+	193.607i	0.264151	+	0.0858280i
$173$	321.419	+	442.395i	0.141255	+	0.194420i	0.873783	−	0.486316i	$-0.161660\pi$
$173$	321.419	+	442.395i	0.141255	+	0.194420i	−0.732528	+	0.680737i	$0.761660\pi$
$174$	−2321.48			−1.01144
$175$	−291.495	+	567.378i	−0.125914	+	0.245084i
$176$	−858.992			−0.367892
$177$	−1583.23	−	2179.13i	−0.672334	−	0.925388i
$178$	−4519.63	−	1468.52i	−1.90315	−	0.618371i
$179$	627.379	−	1930.87i	0.261969	−	0.806258i	−0.730407	−	0.683012i	$-0.760670\pi$
$179$	627.379	−	1930.87i	0.261969	−	0.806258i	0.992376	−	0.123246i	$-0.0393304\pi$
$180$	−248.260	+	102.345i	−0.102801	+	0.0423798i
$181$	−1159.08	−	3567.27i	−0.475986	−	1.46494i	−0.844623	−	0.535362i	$-0.820175\pi$
$181$	−1159.08	−	3567.27i	−0.475986	−	1.46494i	0.368637	−	0.929574i	$-0.379825\pi$
$182$			747.620i			0.304491i
$183$	−1831.11	+	594.965i	−0.739672	+	0.240334i
$184$	716.418	+	520.508i	0.287038	+	0.208546i
$185$	−1105.54	+	941.013i	−0.439354	+	0.373971i
$186$	1360.66	−	988.581i	0.536391	−	0.389711i
$187$	576.606	−	793.631i	0.225485	−	0.310353i
$188$	−476.465	+	655.798i	−0.184839	+	0.254409i
$189$	590.019	−	428.674i	0.227077	−	0.164981i
$190$	2802.20	−	2385.18i	1.06996	−	0.910734i
$191$	1200.55	+	872.250i	0.454810	+	0.330439i	0.791492	−	0.611180i	$-0.209305\pi$
$191$	1200.55	+	872.250i	0.454810	+	0.330439i	−0.336682	+	0.941618i	$0.609305\pi$
$192$	1211.15	−	393.526i	0.455245	−	0.147918i
$193$			1353.74i			0.504894i	0.967611	+	0.252447i	$0.0812354\pi$
$193$			1353.74i			0.504894i	−0.967611	+	0.252447i	$0.918765\pi$
$194$	3.24990	+	10.0022i	0.00120273	+	0.00370162i
$195$	−1635.74	+	674.335i	−0.600708	+	0.247642i
$196$	−147.917	+	455.241i	−0.0539055	+	0.165904i
$197$	−1835.78	−	596.480i	−0.663928	−	0.215723i	−0.0423825	−	0.999101i	$-0.513495\pi$
$197$	−1835.78	−	596.480i	−0.663928	−	0.215723i	−0.621545	+	0.783378i	$0.713495\pi$
$198$	335.541	+	461.832i	0.120434	+	0.165763i
$199$	2682.83			0.955682			0.477841	−	0.878446i	$-0.341420\pi$
$199$	2682.83			0.955682			0.477841	+	0.878446i	$0.341420\pi$
$200$	2469.58	+	399.642i	0.873129	+	0.141295i
$201$	453.924			0.159290
$202$	671.061	+	923.637i	0.233741	+	0.321717i
$203$	−1096.78	−	356.365i	−0.379205	−	0.123211i
$204$	131.018	−	403.233i	0.0449662	−	0.138392i
$205$	994.188	+	1168.01i	0.338718	+	0.397937i
$206$	381.222	+	1173.28i	0.128937	+	0.396826i
$207$		−	703.698i		−	0.236282i
$208$	3334.47	−	1083.44i	1.11156	−	0.361167i
$209$	−1005.00	−	730.178i	−0.332620	−	0.241663i
$210$	584.355	−	45.0035i	0.192021	−	0.0147883i
$211$	−3406.49	+	2474.96i	−1.11143	+	0.807504i	−0.982889	−	0.184200i	$-0.941031\pi$
$211$	−3406.49	+	2474.96i	−1.11143	+	0.807504i	−0.128545	+	0.991704i	$0.541031\pi$
$212$	−394.467	+	542.937i	−0.127793	+	0.175892i
$213$	1134.48	−	1561.48i	0.364946	−	0.502305i
$214$	−50.5146	+	36.7010i	−0.0161360	+	0.0117235i
$215$	−1090.36	+	4508.36i	−0.345871	+	1.43008i
$216$	−2314.01	−	1681.23i	−0.728929	−	0.529598i
$217$	794.598	−	258.181i	0.248575	−	0.0807670i
$218$			1311.53i			0.407469i
$219$	−276.819	−	851.962i	−0.0854142	−	0.262878i
$220$	15.0903	+	195.943i	0.00462450	+	0.0600476i
$221$	−1237.30	+	3808.02i	−0.376605	+	1.15907i
$222$	1268.63	+	412.204i	0.383537	+	0.124619i
$223$	−483.501	−	665.483i	−0.145191	−	0.199839i	0.730227	−	0.683204i	$-0.239414\pi$
$223$	−483.501	−	665.483i	−0.145191	−	0.199839i	−0.875419	+	0.483366i	$0.839414\pi$
$224$	−344.362			−0.102717
$225$	−896.581	−	1774.33i	−0.265653	−	0.525728i
$226$	3162.29			0.930764
$227$	−675.321	−	929.500i	−0.197457	−	0.271776i	0.698795	−	0.715322i	$-0.253720\pi$
$227$	−675.321	−	929.500i	−0.197457	−	0.271776i	−0.896251	+	0.443547i	$0.853720\pi$
$228$	−510.628	−	165.913i	−0.148321	−	0.0481924i
$229$	−1663.18	+	5118.75i	−0.479939	+	1.47710i	0.359239	+	0.933245i	$0.383036\pi$
$229$	−1663.18	+	5118.75i	−0.479939	+	1.47710i	−0.839179	+	0.543856i	$0.816964\pi$
$230$	799.289	−	1299.42i	0.229146	−	0.372528i
$231$	−61.1395	−	188.168i	−0.0174142	−	0.0535954i
$232$			4522.85i			1.27991i
$233$	5148.08	−	1672.71i	1.44748	−	0.470313i	0.523256	−	0.852175i	$-0.324717\pi$
$233$	5148.08	−	1672.71i	1.44748	−	0.470313i	0.924219	+	0.381862i	$0.124717\pi$
$234$	−1885.02	−	1369.55i	−0.526614	−	0.382607i
$235$	−5111.57	−	3144.18i	−1.41890	−	0.872782i
$236$	987.940	−	717.780i	0.272497	−	0.197981i
$237$	−449.079	+	618.104i	−0.123084	+	0.169410i
$238$	779.603	−	1073.03i	0.212328	−	0.292245i
$239$	4738.35	−	3442.61i	1.28242	−	0.931733i	0.282797	−	0.959180i	$-0.408738\pi$
$239$	4738.35	−	3442.61i	1.28242	−	0.931733i	0.999623	+	0.0274464i	$0.00873756\pi$
$240$	−1047.56	−	2541.07i	−0.281748	−	0.683440i
$241$	4127.23	+	2998.61i	1.10315	+	0.801482i	0.981571	−	0.191100i	$-0.0612055\pi$
$241$	4127.23	+	2998.61i	1.10315	+	0.801482i	0.121575	+	0.992582i	$0.461206\pi$
$242$	−3506.39	+	1139.29i	−0.931402	+	0.302631i
$243$			3703.31i			0.977645i
$244$	−269.736	−	830.161i	−0.0707707	−	0.217810i
$245$	−3444.41	−	833.043i	−0.898184	−	0.217229i
$246$	435.497	−	1340.32i	0.112871	−	0.347382i
$247$	4822.23	+	1566.84i	1.24223	+	0.403626i
$248$	−1926.01	−	2650.93i	−0.493153	−	0.678767i
$249$	−2919.86			−0.743127
$250$	359.765	−	4294.78i	0.0910141	−	1.08650i
$251$	−1532.18			−0.385300			−0.192650	−	0.981268i	$-0.561708\pi$
$251$	−1532.18			−0.385300			−0.192650	+	0.981268i	$0.561708\pi$
$252$	72.0413	+	99.1563i	0.0180086	+	0.0247867i
$253$	−489.797	−	159.145i	−0.121713	−	0.0395468i
$254$	−1632.58	+	5024.57i	−0.403297	+	1.24122i
$255$	3050.91	+	737.873i	0.749236	+	0.181206i
$256$	692.875	+	2132.45i	0.169159	+	0.520618i
$257$		−	1882.30i		−	0.456867i	−0.973560	−	0.228434i	$-0.926640\pi$
$257$		−	1882.30i		−	0.456867i	0.973560	−	0.228434i	$-0.0733604\pi$
$258$	4053.16	−	1316.95i	0.978057	−	0.317790i
$259$	536.087	+	389.490i	0.128613	+	0.0934430i
$260$	−305.719	−	741.587i	−0.0729226	−	0.176890i
$261$	2907.68	−	2112.56i	0.689583	−	0.501011i
$262$	1637.97	−	2254.47i	0.386237	−	0.531610i
$263$	2968.12	−	4085.26i	0.695901	−	0.957825i	−0.304086	−	0.952645i	$-0.598351\pi$
$263$	2968.12	−	4085.26i	0.695901	−	0.957825i	0.999987	−	0.00518056i	$-0.00164903\pi$
$264$	−627.764	+	456.097i	−0.146349	+	0.106329i
$265$	−4231.89	−	2603.08i	−0.980991	−	0.603418i
$266$	−1358.82	−	987.240i	−0.313213	−	0.227562i
$267$	−4881.95	+	1586.24i	−1.11899	+	0.363582i
$268$			205.792i			0.0469059i
$269$	−137.326	−	422.645i	−0.0311260	−	0.0957960i	0.934287	−	0.356523i	$-0.116038\pi$
$269$	−137.326	−	422.645i	−0.0311260	−	0.0957960i	−0.965413	+	0.260727i	$0.916038\pi$
$270$	−2581.68	+	4197.10i	−0.581912	+	0.946028i
$271$	525.041	−	1615.91i	0.117690	−	0.362213i	−0.874809	−	0.484469i	$-0.839013\pi$
$271$	525.041	−	1615.91i	0.117690	−	0.362213i	0.992499	+	0.122256i	$0.0390129\pi$
$272$	−5915.63	−	1922.10i	−1.31870	−	0.428473i
$273$	474.668	+	653.324i	0.105231	+	0.144839i
$274$	−1647.85			−0.363321
$275$	−1437.76	+	222.776i	−0.315273	+	0.0488505i
$276$	−222.586			−0.0485439
$277$	−2844.45	−	3915.04i	−0.616990	−	0.849213i	0.380140	−	0.924929i	$-0.375876\pi$
$277$	−2844.45	−	3915.04i	−0.616990	−	0.849213i	−0.997129	+	0.0757156i	$0.975876\pi$
$278$	−2340.46	−	760.463i	−0.504934	−	0.164063i
$279$	−804.639	+	2476.42i	−0.172661	+	0.531396i
$280$	−87.6786	−	1138.48i	−0.0187136	−	0.242989i
$281$	1529.79	+	4708.21i	0.324768	+	0.999532i	0.971545	+	0.236854i	$0.0761162\pi$
$281$	1529.79	+	4708.21i	0.324768	+	0.999532i	−0.646778	+	0.762679i	$0.723884\pi$
$282$			5513.92i			1.16436i
$283$	−1855.70	+	602.954i	−0.389788	+	0.126650i	−0.497353	−	0.867548i	$-0.665695\pi$
$283$	−1855.70	+	602.954i	−0.389788	+	0.126650i	0.107565	+	0.994198i	$0.465695\pi$
$284$	707.919	+	514.333i	0.147913	+	0.107465i
$285$	934.396	−	3863.48i	0.194207	−	0.802991i
$286$	−1379.56	+	1002.31i	−0.285227	+	0.207229i
$287$	411.500	−	566.381i	0.0846343	−	0.116489i
$288$	630.829	−	868.262i	0.129069	−	0.177649i
$289$	1772.07	−	1287.49i	0.360691	−	0.262057i
$290$	7768.74	−	598.301i	1.57309	−	0.121150i
$291$	9.19043	+	6.67724i	0.00185138	+	0.00134511i
$292$	386.249	−	125.500i	0.0774092	−	0.0251518i
$293$			3881.00i			0.773825i	0.922116	+	0.386912i	$0.126458\pi$
$293$			3881.00i			0.773825i	−0.922116	+	0.386912i	$0.873542\pi$
$294$	1006.16	+	3096.63i	0.199592	+	0.614282i
$295$	5859.85	+	6884.35i	1.15652	+	1.35872i
$296$	803.082	−	2471.63i	0.157697	−	0.485340i
$297$	1582.03	+	514.034i	0.309087	+	0.100429i
$298$	−495.999	−	682.685i	−0.0964177	−	0.132708i
$299$	2102.04			0.406570
$300$	−561.237	+	283.597i	−0.108010	+	0.0545782i
$301$	2117.07			0.405401
$302$	−733.148	−	1009.09i	−0.139695	−	0.192274i
$303$	1172.84	+	381.080i	0.222370	+	0.0722524i
$304$	−2434.03	+	7491.18i	−0.459215	+	1.41332i
$305$	5974.42	−	2462.95i	1.12162	−	0.462388i
$306$	1277.36	+	3931.32i	0.238634	+	0.734440i
$307$		−	3856.45i		−	0.716935i	−0.933542	−	0.358468i	$-0.883299\pi$
$307$		−	3856.45i		−	0.716935i	0.933542	−	0.358468i	$-0.116701\pi$
$308$	85.3085	−	27.7184i	0.0157821	−	0.00512793i
$309$	1078.06	+	783.256i	0.198475	+	0.144200i
$310$	−4298.63	+	3658.93i	−0.787568	+	0.670365i
$311$	5403.16	−	3925.62i	0.985161	−	0.715761i	0.0263047	−	0.999654i	$-0.491626\pi$
$311$	5403.16	−	3925.62i	0.985161	−	0.715761i	0.958856	+	0.283893i	$0.0916260\pi$
$312$	1861.61	−	2562.29i	0.337798	−	0.464939i
$313$	−1831.22	+	2520.45i	−0.330691	+	0.455158i	−0.941694	−	0.336471i	$-0.890767\pi$
$313$	−1831.22	+	2520.45i	−0.330691	+	0.455158i	0.611002	+	0.791629i	$0.290767\pi$
$314$	5303.49	−	3853.21i	0.953163	−	0.692514i
$315$	−690.960	+	588.134i	−0.123591	+	0.105199i
$316$	−280.226	−	203.596i	−0.0498859	−	0.0362442i
$317$	−2805.55	+	911.579i	−0.497083	+	0.161512i	−0.546820	−	0.837250i	$-0.684162\pi$
$317$	−2805.55	+	911.579i	−0.497083	+	0.161512i	0.0497366	+	0.998762i	$0.484162\pi$
$318$			4564.99i			0.805006i
$319$	−812.822	−	2501.61i	−0.142662	−	0.439069i
$320$	−3951.64	+	1629.06i	−0.690323	+	0.284585i
$321$	−20.8417	+	64.1440i	−0.00362389	+	0.0111532i
$322$	−662.232	−	215.172i	−0.114611	−	0.0372394i
$323$	−5287.31	−	7277.35i	−0.910816	−	1.25363i
$324$	70.4642			0.0120823
$325$	5300.17	−	2678.21i	0.904617	−	0.457108i
$326$	−7386.28			−1.25487
$327$	832.698	+	1146.11i	0.140821	+	0.193823i
$328$	−2611.30	−	848.463i	−0.439588	−	0.142831i
$329$	−846.428	+	2605.04i	−0.141839	+	0.436536i
$330$	866.466	+	1017.96i	0.144538	+	0.169808i
$331$	−3398.42	−	10459.3i	−0.564332	−	1.73684i	−0.669927	−	0.742427i	$-0.733674\pi$
$331$	−3398.42	−	10459.3i	−0.564332	−	1.73684i	0.105594	−	0.994409i	$-0.466326\pi$
$332$		−	1323.76i		−	0.218827i
$333$	−1964.09	+	638.172i	−0.323218	+	0.105020i
$334$	528.752	+	384.161i	0.0866229	+	0.0629352i
$335$	−1519.04	+	116.987i	−0.247743	+	0.0190797i
$336$	−1014.92	+	737.380i	−0.164787	+	0.119724i
$337$	−4672.49	+	6431.13i	−0.755273	+	1.03954i	0.242320	+	0.970196i	$0.422092\pi$
$337$	−4672.49	+	6431.13i	−0.755273	+	1.03954i	−0.997593	+	0.0693472i	$0.977908\pi$
$338$	108.637	−	149.526i	0.0174825	−	0.0240626i
$339$	2763.44	−	2007.76i	0.442742	−	0.321671i
$340$	−334.525	+	1383.17i	−0.0533593	+	0.220626i
$341$	1541.70	+	1120.11i	0.244832	+	0.177881i
$342$	4978.38	−	1617.57i	0.787134	−	0.255755i
$343$			3367.78i			0.530155i
$344$	−2565.77	−	7896.61i	−0.402142	−	1.23767i
$345$	−126.534	−	1643.00i	−0.0197460	−	0.256395i
$346$	−521.111	+	1603.81i	−0.0809684	+	0.249195i
$347$	7073.15	+	2298.21i	1.09426	+	0.355545i	0.799889	−	0.600148i	$-0.204891\pi$
$347$	7073.15	+	2298.21i	1.09426	+	0.355545i	0.294366	+	0.955693i	$0.404891\pi$
$348$	−668.221	−	919.727i	−0.102932	−	0.141674i
$349$	−7527.08			−1.15449			−0.577243	−	0.816573i	$-0.695871\pi$
$349$	−7527.08			−1.15449			−0.577243	+	0.816573i	$0.695871\pi$
$350$	−1943.93	+	301.205i	−0.296878	+	0.0460003i
$351$	−6789.55			−1.03248
$352$	−461.673	−	635.439i	−0.0699070	−	0.0962188i
$353$	−3198.20	−	1039.16i	−0.482217	−	0.156682i	0.0578130	−	0.998327i	$-0.481587\pi$
$353$	−3198.20	−	1039.16i	−0.482217	−	0.156682i	−0.540030	+	0.841645i	$0.681587\pi$
$354$	2566.87	−	7900.00i	0.385388	−	1.18610i
$355$	−3394.07	+	5517.83i	−0.507433	+	0.824946i
$356$	−719.144	−	2213.30i	−0.107063	−	0.329507i
$357$		−	1432.67i		−	0.212394i
$358$	5954.54	−	1934.75i	0.879070	−	0.285627i
$359$	−3752.32	−	2726.22i	−0.551644	−	0.400793i	0.276747	−	0.960943i	$-0.410743\pi$
$359$	−3752.32	−	2726.22i	−0.551644	−	0.400793i	−0.828391	+	0.560150i	$0.810743\pi$
$360$	3031.13	+	1864.48i	0.443763	+	0.272963i
$361$	−3666.53	+	2663.89i	−0.534558	+	0.388379i
$362$	6798.97	−	9357.98i	0.987144	−	1.35869i
$363$	−2340.79	+	3221.82i	−0.338456	+	0.465845i
$364$	−296.193	+	215.197i	−0.0426504	+	0.0309873i
$365$	1145.94	+	2779.72i	0.164332	+	0.398622i
$366$	−4803.54	−	3489.98i	−0.686025	−	0.498426i
$367$	5102.38	−	1657.86i	0.725728	−	0.235803i	0.0772230	−	0.997014i	$-0.475395\pi$
$367$	5102.38	−	1657.86i	0.725728	−	0.235803i	0.648505	+	0.761211i	$0.275395\pi$
$368$			3265.45i			0.462564i
$369$	674.234	+	2075.08i	0.0951198	+	0.292749i
$370$	−4351.67	−	1052.47i	−0.611440	−	0.147879i
$371$	−700.761	+	2156.72i	−0.0980638	+	0.301809i
$372$	783.315	+	254.515i	0.109175	+	0.0354730i
$373$	5650.89	+	7777.78i	0.784429	+	1.07967i	0.994779	+	0.102048i	$0.0325395\pi$
$373$	5650.89	+	7777.78i	0.784429	+	1.07967i	−0.210350	+	0.977626i	$0.567460\pi$
$374$	3025.21			0.418262
$375$	−2412.39	−	3981.51i	−0.332201	−	0.548278i
$376$	10742.6			1.47342
$377$	6310.49	+	8685.65i	0.862087	+	1.18656i
$378$	2138.99	+	695.001i	0.291053	+	0.0945688i
$379$	4478.88	−	13784.6i	0.607030	−	1.86825i	0.124848	−	0.992176i	$-0.460156\pi$
$379$	4478.88	−	13784.6i	0.607030	−	1.86825i	0.482182	−	0.876071i	$-0.339844\pi$
$380$	1751.56	+	423.621i	0.236455	+	0.0571877i
$381$	1763.46	+	5427.37i	0.237125	+	0.729797i
$382$			4576.32i			0.612945i
$383$	−190.258	+	61.8186i	−0.0253831	+	0.00824747i	−0.321681	−	0.946848i	$-0.604248\pi$
$383$	−190.258	+	61.8186i	−0.0253831	+	0.00824747i	0.296298	+	0.955096i	$0.404248\pi$
$384$	4632.05	+	3365.38i	0.615568	+	0.447236i
$385$	253.096	+	613.940i	0.0335039	+	0.0812709i
$386$	−3377.45	+	2453.86i	−0.445356	+	0.323570i
$387$	−3878.21	+	5337.89i	−0.509407	+	0.701138i
$388$	−3.02722	+	4.16661i	−0.000396092	+	0.000545174i
$389$	−6933.50	+	5037.48i	−0.903708	+	0.656582i	−0.939416	−	0.342780i	$-0.888631\pi$
$389$	−6933.50	+	5037.48i	−0.903708	+	0.656582i	0.0357080	+	0.999362i	$0.488631\pi$
$390$	−4647.42	−	2858.68i	−0.603414	−	0.371166i
$391$	−3016.99	−	2191.97i	−0.390219	−	0.283510i
$392$	6033.04	−	1960.25i	0.777333	−	0.252571i
$393$		−	3010.07i		−	0.386357i
$394$	−1839.46	−	5661.28i	−0.235205	−	0.723886i
$395$	1343.53	−	2184.20i	0.171140	−	0.278226i
$396$	−86.3864	+	265.870i	−0.0109623	+	0.0337386i
$397$	2187.45	+	710.745i	0.276536	+	0.0898521i	0.444002	−	0.896026i	$-0.353558\pi$
$397$	2187.45	+	710.745i	0.276536	+	0.0898521i	−0.167466	+	0.985878i	$0.553558\pi$
$398$	4863.02	+	6693.38i	0.612466	+	0.842987i
$399$	−1814.24			−0.227633
$400$	4160.51	+	8233.63i	0.520063	+	1.02920i
$401$	−2215.03			−0.275844			−0.137922	−	0.990443i	$-0.544042\pi$
$401$	−2215.03			−0.275844			−0.137922	+	0.990443i	$0.544042\pi$
$402$	822.803	+	1132.49i	0.102084	+	0.140506i
$403$	−7397.41	−	2403.56i	−0.914371	−	0.297097i
$404$	−172.768	+	531.724i	−0.0212760	+	0.0654809i
$405$	40.0569	+	520.126i	0.00491468	+	0.0638154i
$406$	−1098.98	−	3382.31i	−0.134338	−	0.413451i
$407$			1511.40i			0.184072i
$408$	−5343.81	+	1736.31i	−0.648426	+	0.210686i
$409$	225.803	+	164.056i	0.0272989	+	0.0198338i	0.601351	−	0.798985i	$-0.294629\pi$
$409$	225.803	+	164.056i	0.0272989	+	0.0198338i	−0.574052	+	0.818819i	$0.694629\pi$
$410$	−1111.94	+	4597.58i	−0.133939	+	0.553801i
$411$	−1440.01	+	1046.23i	−0.172823	+	0.125563i
$412$	−355.100	+	488.753i	−0.0424624	+	0.0584445i
$413$	2425.42	−	3338.31i	0.288976	−	0.397742i
$414$	1755.65	−	1275.56i	0.208419	−	0.151426i
$415$	9771.21	−	752.519i	1.15578	−	0.0890113i
$416$	2593.62	+	1884.37i	0.305679	+	0.222089i
$417$	−2528.09	+	821.425i	−0.296885	+	0.0964637i
$418$		−	3830.93i		−	0.448271i
$419$	2297.09	+	7069.73i	0.267829	+	0.824293i	0.991028	+	0.133653i	$0.0426709\pi$
$419$	2297.09	+	7069.73i	0.267829	+	0.824293i	−0.723199	+	0.690640i	$0.757329\pi$
$420$	186.032	+	218.557i	0.0216129	+	0.0253916i
$421$	−1314.13	+	4044.48i	−0.152130	+	0.468209i	−0.997859	−	0.0654047i	$-0.979166\pi$
$421$	−1314.13	+	4044.48i	−0.152130	+	0.468209i	0.845729	+	0.533613i	$0.179166\pi$
$422$	−12349.5	−	4012.61i	−1.42456	−	0.462869i
$423$	−5017.69	−	6906.26i	−0.576758	−	0.793839i
$424$	8893.79			1.01868
$425$	−10399.9	−	1682.97i	−1.18699	−	0.192085i
$426$	5952.15			0.676954
$427$	−1733.68	−	2386.21i	−0.196485	−	0.270438i
$428$	−29.0806	−	9.44885i	−0.00328426	−	0.00106712i
$429$	−569.186	+	1751.77i	−0.0640572	+	0.197148i
$430$	−13224.3	+	5451.73i	−1.48310	+	0.611408i
$431$	−1333.15	−	4103.00i	−0.148992	−	0.458549i	0.848511	−	0.529178i	$-0.177499\pi$
$431$	−1333.15	−	4103.00i	−0.148992	−	0.458549i	−0.997503	+	0.0706286i	$0.977499\pi$
$432$		−	10547.3i		−	1.17467i
$433$	11993.5	−	3896.93i	1.33111	−	0.432505i	0.444816	−	0.895622i	$-0.353269\pi$
$433$	11993.5	−	3896.93i	1.33111	−	0.432505i	0.886297	+	0.463117i	$0.153269\pi$
$434$	2084.46	+	1514.45i	0.230547	+	0.167502i
$435$	6409.02	−	5455.25i	0.706412	−	0.601286i
$436$	−519.605	+	377.515i	−0.0570747	+	0.0414672i
$437$	−2775.77	+	3820.52i	−0.303851	+	0.418216i
$438$	1623.78	−	2234.94i	0.177140	−	0.243812i
$439$	−6675.61	+	4850.11i	−0.725762	+	0.527297i	−0.888220	−	0.459419i	$-0.848058\pi$
$439$	−6675.61	+	4850.11i	−0.725762	+	0.527297i	0.162458	+	0.986715i	$0.448058\pi$
$440$	1983.24	−	1688.10i	0.214880	−	0.182903i
$441$	−4078.17	−	2962.96i	−0.440360	−	0.319940i
$442$	−11743.4	+	3815.66i	−1.26375	+	0.410616i
$443$		−	8360.78i		−	0.896688i	−0.893861	−	0.448344i	$-0.852014\pi$
$443$		−	8360.78i		−	0.896688i	0.893861	−	0.448344i	$-0.147986\pi$
$444$	201.860	+	621.260i	0.0215762	+	0.0664047i
$445$	15928.5	−	6566.50i	1.69681	−	0.699510i
$446$	783.892	−	2412.57i	0.0832250	−	0.256140i
$447$	−866.880	−	281.666i	−0.0917271	−	0.0298039i
$448$	1146.70	+	1578.30i	0.120930	+	0.166446i
$449$	−4282.56			−0.450126			−0.225063	−	0.974344i	$-0.572259\pi$
$449$	−4282.56			−0.450126			−0.225063	+	0.974344i	$0.572259\pi$
$450$	2801.58	−	5453.11i	0.293484	−	0.571249i
$451$	1596.80			0.166720
$452$	910.244	+	1252.84i	0.0947218	+	0.130373i
$453$	−1281.35	−	416.337i	−0.132899	−	0.0431815i
$454$	1094.89	−	3369.71i	0.113184	−	0.348344i
$455$	−1756.84	−	2063.99i	−0.181015	−	0.212663i
$456$	2198.75	+	6767.06i	0.225803	+	0.694949i
$457$		−	12887.5i		−	1.31915i	−0.751639	−	0.659575i	$-0.770736\pi$
$457$		−	12887.5i		−	1.31915i	0.751639	−	0.659575i	$-0.229264\pi$
$458$	−15785.5	+	5129.02i	−1.61050	+	0.523282i
$459$	9744.79	+	7080.01i	0.990954	+	0.719970i
$460$	744.877	−	57.3659i	0.0755001	−	0.00581456i
$461$	9361.85	−	6801.78i	0.945824	−	0.687181i	−0.00399155	−	0.999992i	$-0.501271\pi$
$461$	9361.85	−	6801.78i	0.945824	−	0.687181i	0.949815	+	0.312811i	$0.101271\pi$
$462$	358.635	−	493.619i	0.0361152	−	0.0497083i
$463$	−4269.40	+	5876.33i	−0.428544	+	0.589841i	−0.967618	−	0.252418i	$-0.918774\pi$
$463$	−4269.40	+	5876.33i	−0.428544	+	0.589841i	0.539074	+	0.842258i	$0.318774\pi$
$464$	−13492.9	+	9803.14i	−1.34998	+	0.980818i
$465$	−1433.38	+	5926.66i	−0.142950	+	0.591058i
$466$	13504.9	+	9811.87i	1.34249	+	0.975378i
$467$	11244.0	−	3653.41i	1.11416	−	0.362012i	0.306623	−	0.951831i	$-0.400801\pi$
$467$	11244.0	−	3653.41i	1.11416	−	0.362012i	0.807536	+	0.589819i	$0.200801\pi$
$468$		−	1141.02i		−	0.112701i
$469$	214.886	+	661.350i	0.0211567	+	0.0651137i
$470$	−1421.07	−	18452.1i	−0.139466	−	1.81092i
$471$	2188.15	−	6734.43i	0.214065	−	0.658824i
$472$	−15391.3	−	5000.93i	−1.50093	−	0.487683i
$473$	2838.27	+	3906.55i	0.275907	+	0.379753i
$474$	−2356.13			−0.228313
$475$	−2131.21	+	13169.8i	−0.205867	+	1.27215i
$476$	649.519			0.0625433
$477$	−4154.16	−	5717.71i	−0.398755	−	0.548839i
$478$	17177.9	+	5581.45i	1.64372	+	0.534078i
$479$	−816.290	+	2512.28i	−0.0778648	+	0.239643i	−0.982411	−	0.186733i	$-0.940210\pi$
$479$	−816.290	+	2512.28i	−0.0778648	+	0.239643i	0.904546	+	0.426376i	$0.140210\pi$
$480$	1316.74	−	2140.66i	0.125210	−	0.203556i
$481$	−1906.31	−	5867.01i	−0.180707	−	0.556159i
$482$			15732.4i			1.48670i
$483$	−715.320	+	232.421i	−0.0673875	+	0.0218955i
$484$	−1460.66	−	1061.23i	−0.137177	−	0.0996646i
$485$	−32.4763	−	19.9765i	−0.00304057	−	0.00187028i
$486$	−9239.38	+	6712.80i	−0.862360	+	0.626541i
$487$	−9704.40	+	13357.0i	−0.902974	+	1.24284i	0.0665355	+	0.997784i	$0.478805\pi$
$487$	−9704.40	+	13357.0i	−0.902974	+	1.24284i	−0.969510	+	0.245053i	$0.921195\pi$
$488$	−6799.39	+	9358.56i	−0.630725	+	0.868119i
$489$	−6454.66	+	4689.59i	−0.596912	+	0.433682i
$490$	−4165.14	−	10103.4i	−0.384004	−	0.931484i
$491$	8269.60	+	6008.21i	0.760085	+	0.552234i	0.898936	−	0.438079i	$-0.144341\pi$
$491$	8269.60	+	6008.21i	0.760085	+	0.552234i	−0.138851	+	0.990313i	$0.544341\pi$
$492$	656.366	−	213.266i	0.0601449	−	0.0195422i
$493$		−	19046.6i		−	1.74000i
$494$	4831.91	+	14871.1i	0.440077	+	1.35442i
$495$	−2011.61	−	486.515i	−0.182656	−	0.0441762i
$496$	3733.86	−	11491.6i	0.338015	−	1.04030i
$497$	2812.08	+	913.701i	0.253801	+	0.0824649i
$498$	−5292.68	−	7284.75i	−0.476246	−	0.655496i
$499$	−1304.88			−0.117063			−0.0585317	−	0.998286i	$-0.518642\pi$
$499$	−1304.88			−0.117063			−0.0585317	+	0.998286i	$0.518642\pi$
$500$	1805.07	−	1093.69i	0.161450	−	0.0978226i
$501$	705.967			0.0629547
$502$	−2777.30	−	3822.62i	−0.246926	−	0.339865i
$503$	20548.1	+	6676.50i	1.82146	+	0.591830i	0.999760	+	0.0219153i	$0.00697643\pi$
$503$	20548.1	+	6676.50i	1.82146	+	0.591830i	0.821704	+	0.569914i	$0.193024\pi$
$504$	501.927	−	1544.77i	0.0443603	−	0.136527i
$505$	−4023.09	−	973.000i	−0.354505	−	0.0857385i
$506$	−490.780	−	1510.47i	−0.0431182	−	0.132704i
$507$		−	199.641i		−	0.0174879i
$508$	−2460.57	+	799.488i	−0.214902	+	0.0698259i
$509$	7739.84	+	5623.32i	0.673993	+	0.489684i	0.871359	−	0.490645i	$-0.163239\pi$
$509$	7739.84	+	5623.32i	0.673993	+	0.489684i	−0.197367	+	0.980330i	$0.563239\pi$
$510$	3689.30	+	8949.19i	0.320323	+	0.777014i
$511$	1110.23	−	806.631i	0.0961131	−	0.0698303i
$512$	4018.08	−	5530.41i	0.346828	−	0.477367i
$513$	8965.67	−	12340.2i	0.771626	−	1.06205i
$514$	4696.15	−	3411.95i	0.402993	−	0.292791i
$515$	−3809.55	−	2343.30i	−0.325959	−	0.200501i
$516$	1688.42	+	1226.71i	0.144048	+	0.104657i
$517$	−5941.76	+	1930.59i	−0.505451	+	0.164231i
$518$			2043.49i			0.173332i
$519$	562.885	+	1732.38i	0.0476068	+	0.146519i
$520$	−5569.46	+	9054.39i	−0.469686	+	0.763580i
$521$	−5503.70	+	16938.7i	−0.462806	+	1.42437i	0.398916	+	0.916987i	$0.369387\pi$
$521$	−5503.70	+	16938.7i	−0.462806	+	1.42437i	−0.861722	+	0.507382i	$0.830613\pi$
$522$	10541.2	+	3425.05i	0.883863	+	0.287184i
$523$	7737.13	+	10649.2i	0.646885	+	0.890361i	0.998959	−	0.0456108i	$-0.0145234\pi$
$523$	7737.13	+	10649.2i	0.646885	+	0.890361i	−0.352074	+	0.935972i	$0.614523\pi$
$524$	1364.66			0.113770
$525$	−1507.51	+	1497.42i	−0.125320	+	0.124482i
$526$	15572.4			1.29086
$527$	8110.85	+	11163.6i	0.670425	+	0.922761i
$528$	−2721.32	−	884.211i	−0.224300	−	0.0728794i
$529$	3154.82	−	9709.54i	0.259293	−	0.798023i
$530$	−1176.51	−	15276.6i	−0.0964231	−	1.25202i
$531$	3974.00	+	12230.7i	0.324778	+	0.999563i
$532$		−	822.509i		−	0.0670306i
$533$	−6198.54	+	2014.03i	−0.503731	+	0.163672i
$534$	−12806.8	−	9304.65i	−1.03783	−	0.754029i
$535$	53.2144	−	220.027i	0.00430030	−	0.0177806i
$536$	2206.39	−	1603.04i	0.177801	−	0.129180i
$537$	3975.12	−	5471.29i	0.319440	−	0.439671i
$538$	805.532	−	1108.72i	0.0645519	−	0.0888481i
$539$	−2984.62	+	2168.45i	−0.238509	+	0.173287i
$540$	−2405.94	+	185.290i	−0.191731	+	0.0147660i
$541$	−15137.2	−	10997.8i	−1.20295	−	0.873996i	−0.208380	−	0.978048i	$-0.566819\pi$
$541$	−15137.2	−	10997.8i	−1.20295	−	0.873996i	−0.994572	+	0.104052i	$0.966819\pi$
$542$	4983.24	−	1619.15i	0.394924	−	0.128318i
$543$		−	12494.4i		−	0.987450i
$544$	−1757.54	−	5409.14i	−0.138518	−	0.426314i
$545$	−3081.98	−	3620.81i	−0.242234	−	0.284585i
$546$	−769.570	+	2368.49i	−0.0603197	+	0.185645i
$547$	−810.927	−	263.486i	−0.0633871	−	0.0205957i	0.277152	−	0.960826i	$-0.410609\pi$
$547$	−810.927	−	263.486i	−0.0633871	−	0.0205957i	−0.340539	+	0.940230i	$0.610609\pi$
$548$	−474.321	−	652.847i	−0.0369744	−	0.0508909i
$549$	9192.40			0.714612
$550$	−3161.95	−	3183.24i	−0.245138	−	0.246789i
$551$	−24119.5			−1.86483
$552$	1733.85	+	2386.44i	0.133691	+	0.184010i
$553$	−1113.15	−	361.684i	−0.0855983	−	0.0278126i
$554$	4611.64	−	14193.2i	0.353664	−	1.08847i
$555$	−4471.02	+	1843.18i	−0.341954	+	0.140970i
$556$	−372.404	−	1146.14i	−0.0284055	−	0.0874232i
$557$		−	1602.08i		−	0.121872i	−0.998142	−	0.0609358i	$-0.980592\pi$
$557$		−	1602.08i		−	0.121872i	0.998142	−	0.0609358i	$-0.0194085\pi$
$558$	−7636.94	+	2481.39i	−0.579386	+	0.188254i
$559$	−15945.0	−	11584.7i	−1.20644	−	0.876533i
$560$	3206.34	−	2729.19i	0.241951	−	0.205945i
$561$	2643.65	−	1920.72i	0.198957	−	0.144551i
$562$	−8973.53	+	12351.0i	−0.673533	+	0.927038i
$563$	−3427.68	+	4717.80i	−0.256589	+	0.353164i	−0.917805	−	0.397031i	$-0.870041\pi$
$563$	−3427.68	+	4717.80i	−0.256589	+	0.353164i	0.661216	+	0.750195i	$0.270041\pi$
$564$	−2184.51	+	1587.14i	−0.163093	+	0.118494i
$565$	−8730.31	+	7431.09i	−0.650065	+	0.553325i
$566$	−4868.04	−	3536.84i	−0.361517	−	0.262658i
$567$	226.449	−	73.5778i	0.0167724	−	0.00544969i
$568$		−	11596.3i		−	0.856641i
$569$	−1655.75	−	5095.88i	−0.121991	−	0.375449i	0.871350	−	0.490662i	$-0.163245\pi$
$569$	−1655.75	−	5095.88i	−0.121991	−	0.375449i	−0.993341	+	0.115213i	$0.963245\pi$
$570$	11332.7	−	4671.90i	0.832762	−	0.343306i
$571$	−2999.90	+	9232.73i	−0.219863	+	0.676668i	0.778910	+	0.627136i	$0.215773\pi$
$571$	−2999.90	+	9232.73i	−0.219863	+	0.676668i	−0.998773	+	0.0495322i	$0.984227\pi$
$572$	−794.190	−	258.048i	−0.0580538	−	0.0188628i
$573$	2905.53	+	3999.12i	0.211833	+	0.291563i
$574$	2158.96			0.156992
$575$	846.882	+	5465.63i	0.0614216	+	0.396405i
$576$	−6080.09			−0.439822
$577$	−4372.38	−	6018.07i	−0.315467	−	0.434203i	0.621609	−	0.783327i	$-0.286479\pi$
$577$	−4372.38	−	6018.07i	−0.315467	−	0.434203i	−0.937077	+	0.349124i	$0.886479\pi$
$578$	6424.29	+	2087.38i	0.462310	+	0.150214i
$579$	−1393.49	+	4288.72i	−0.100020	+	0.307829i
$580$	2473.21	+	2905.62i	0.177060	+	0.208016i
$581$	−1382.25	−	4254.13i	−0.0987012	−	0.303771i
$582$			35.0326i			0.00249510i
$583$	−4919.20	+	1598.34i	−0.349455	+	0.113545i
$584$	−4354.25	−	3163.55i	−0.308528	−	0.224159i
$585$	8422.37	−	648.640i	0.595252	−	0.0458427i
$586$	−9682.70	+	7034.89i	−0.682574	+	0.495919i
$587$	12819.3	−	17644.3i	0.901380	−	1.24064i	−0.0686454	−	0.997641i	$-0.521868\pi$
$587$	12819.3	−	17644.3i	0.901380	−	1.24064i	0.970026	−	0.243002i	$-0.0781323\pi$
$588$	−937.213	+	1289.96i	−0.0657313	+	0.0904714i
$589$	14136.9	−	10271.1i	0.988966	−	0.718526i
$590$	−6553.90	+	27098.6i	−0.457322	+	1.89090i
$591$	−5201.83	−	3779.35i	−0.362055	−	0.263049i
$592$	9114.20	−	2961.38i	0.632756	−	0.205595i
$593$			506.827i			0.0350976i	0.999846	+	0.0175488i	$0.00558624\pi$
$593$			506.827i			0.0350976i	−0.999846	+	0.0175488i	$0.994414\pi$
$594$	1585.21	+	4878.77i	0.109498	+	0.337000i
$595$	369.233	+	4794.36i	0.0254404	+	0.330336i
$596$	127.697	−	393.012i	0.00877632	−	0.0270107i
$597$	8499.32	+	2761.60i	0.582670	+	0.189321i
$598$	3810.26	+	5244.38i	0.260557	+	0.358626i
$599$	11868.2			0.809554			0.404777	−	0.914415i	$-0.367349\pi$
$599$	11868.2			0.809554			0.404777	+	0.914415i	$0.367349\pi$
$600$	7412.36	+	3808.17i	0.504347	+	0.259113i
$601$	2856.11			0.193849			0.0969245	−	0.995292i	$-0.469099\pi$
$601$	2856.11			0.193849			0.0969245	+	0.995292i	$0.469099\pi$
$602$	3837.50	+	5281.86i	0.259809	+	0.357596i
$603$	−2061.15	−	669.707i	−0.139198	−	0.0452282i
$604$	188.752	−	580.920i	0.0127156	−	0.0391346i
$605$	7003.03	−	11385.0i	0.470601	−	0.765067i
$606$	1175.20	+	3616.88i	0.0787774	+	0.242452i
$607$			945.030i			0.0631921i	0.999501	+	0.0315960i	$0.0100590\pi$
$607$			945.030i			0.0631921i	−0.999501	+	0.0315960i	$0.989941\pi$
$608$	−6849.79	+	2225.63i	−0.456901	+	0.148456i
$609$	−3107.81	−	2257.96i	−0.206790	−	0.150241i
$610$	16974.3	+	10441.1i	1.12667	+	0.693029i
$611$	20629.9	−	14988.5i	1.36595	−	0.992424i
$612$	−1189.84	+	1637.67i	−0.0785888	+	0.108168i
$613$	−11343.3	+	15612.8i	−0.747396	+	1.02870i	0.250763	+	0.968048i	$0.419318\pi$
$613$	−11343.3	+	15612.8i	−0.747396	+	1.02870i	−0.998159	+	0.0606535i	$0.980682\pi$
$614$	9621.43	−	6990.38i	0.632393	−	0.459461i
$615$	1947.33	+	4723.67i	0.127681	+	0.309719i
$616$	−961.698	−	698.715i	−0.0629025	−	0.0457013i
$617$	−18285.2	+	5941.24i	−1.19309	+	0.387658i	−0.837214	−	0.546875i	$-0.815817\pi$
$617$	−18285.2	+	5941.24i	−1.19309	+	0.387658i	−0.355875	+	0.934533i	$0.615817\pi$
$618$			4109.41i			0.267484i
$619$	3394.88	+	10448.4i	0.220439	+	0.678442i	0.998723	+	0.0505291i	$0.0160908\pi$
$619$	3394.88	+	10448.4i	0.220439	+	0.678442i	−0.778283	+	0.627913i	$0.783909\pi$
$620$	−2686.93	−	649.844i	−0.174048	−	0.0420942i
$621$	1954.10	−	6014.10i	0.126273	−	0.388627i
$622$	19588.0	+	6364.54i	1.26272	+	0.410281i
$623$	−4622.19	−	6361.90i	−0.297246	−	0.409124i
$624$	11679.0			0.749253
$625$	9099.11	+	12702.2i	0.582343	+	0.812943i
$626$	−9607.61			−0.613414
$627$	−2432.28	−	3347.75i	−0.154922	−	0.213231i
$628$	3053.14	+	992.027i	0.194003	+	0.0630353i
$629$	−3381.94	+	10408.6i	−0.214383	+	0.659803i
$630$	−2719.80	−	657.794i	−0.171999	−	0.0415986i
$631$	1234.07	+	3798.08i	0.0778566	+	0.239618i	0.982408	−	0.186746i	$-0.0597942\pi$
$631$	1234.07	+	3798.08i	0.0778566	+	0.239618i	−0.904552	+	0.426364i	$0.859794\pi$
$632$			4590.35i			0.288915i
$633$	−13339.5	+	4334.28i	−0.837597	+	0.272152i
$634$	−7359.77	−	5347.18i	−0.461031	−	0.334959i
$635$	−7300.12	−	17708.0i	−0.456215	−	1.10665i
$636$	−1808.57	+	1314.00i	−0.112758	+	0.0819237i
$637$	8850.78	−	12182.0i	0.550519	−	0.757724i
$638$	4767.89	−	6562.44i	0.295866	−	0.407225i
$639$	−7455.15	+	5416.49i	−0.461536	+	0.335325i
$640$	−16368.3	−	10068.3i	−1.01096	−	0.621853i
$641$	−1089.23	−	791.370i	−0.0671168	−	0.0487632i	0.553721	−	0.832702i	$-0.313207\pi$
$641$	−1089.23	−	791.370i	−0.0671168	−	0.0487632i	−0.620838	+	0.783939i	$0.713207\pi$
$642$	−197.811	+	64.2727i	−0.0121604	+	0.00395116i
$643$			24552.6i			1.50585i	0.658106	+	0.752925i	$0.271358\pi$
$643$			24552.6i			1.50585i	−0.658106	+	0.752925i	$0.728642\pi$
$644$	−105.371	−	324.300i	−0.00644754	−	0.0198435i
$645$	−8095.05	+	13160.3i	−0.494174	+	0.803390i
$646$	8572.21	−	26382.5i	0.522088	−	1.60682i
$647$	−9643.56	−	3133.38i	−0.585977	−	0.190396i	0.000999200	−	1.00000i	$-0.499682\pi$
$647$	−9643.56	−	3133.38i	−0.585977	−	0.190396i	−0.586977	+	0.809604i	$0.699682\pi$
$648$	−548.887	−	755.478i	−0.0332752	−	0.0457993i
$649$	9411.72			0.569249
$650$	16289.2	+	8368.71i	0.982945	+	0.504997i
$651$	2783.08			0.167554
$652$	−2126.09	−	2926.31i	−0.127706	−	0.175772i
$653$	−15806.3	−	5135.77i	−0.947240	−	0.307777i	−0.205646	−	0.978626i	$-0.565930\pi$
$653$	−15806.3	−	5135.77i	−0.947240	−	0.307777i	−0.741594	+	0.670849i	$0.765930\pi$
$654$	−1350.04	+	4154.99i	−0.0807197	+	0.248430i
$655$	775.769	+	10073.1i	0.0462776	+	0.600899i
$656$	−3128.73	−	9629.23i	−0.186214	−	0.573107i
$657$			4276.95i			0.253972i
$658$	−8033.57	+	2610.27i	−0.475959	+	0.154649i
$659$	−13739.4	−	9982.29i	−0.812159	−	0.590068i	0.102297	−	0.994754i	$-0.467381\pi$
$659$	−13739.4	−	9982.29i	−0.812159	−	0.590068i	−0.914456	+	0.404686i	$0.867381\pi$
$660$	−153.889	+	636.289i	−0.00907594	+	0.0375266i
$661$	−2888.40	+	2098.55i	−0.169964	+	0.123486i	−0.669515	−	0.742798i	$-0.733498\pi$
$661$	−2888.40	+	2098.55i	−0.169964	+	0.123486i	0.499552	+	0.866284i	$0.333498\pi$
$662$	19934.6	−	27437.6i	1.17036	−	1.61087i
$663$	−7839.64	+	10790.3i	−0.459225	+	0.632069i
$664$	−14192.6	+	10311.5i	−0.829487	+	0.602658i
$665$	6071.28	−	467.573i	0.354036	−	0.0272657i
$666$	−5152.37	−	3743.42i	−0.299775	−	0.217800i
$667$	−9509.85	+	3089.94i	−0.552059	+	0.179375i
$668$			320.060i			0.0185382i
$669$	−846.732	−	2605.97i	−0.0489336	−	0.150602i
$670$	−3045.35	−	3577.79i	−0.175600	−	0.206301i
$671$	2078.90	−	6398.21i	0.119605	−	0.368108i
$672$	−1090.95	−	354.473i	−0.0626257	−	0.0203483i
$673$	3001.99	+	4131.88i	0.171944	+	0.236660i	0.886288	−	0.463134i	$-0.153275\pi$
$673$	3001.99	+	4131.88i	0.171944	+	0.236660i	−0.714345	+	0.699794i	$0.753275\pi$
$674$	−24514.6			−1.40099
$675$	−2735.41	−	17653.9i	−0.155979	−	1.00666i
$676$	90.5101			0.00514964
$677$	−4318.13	−	5943.39i	−0.245139	−	0.337405i	0.668662	−	0.743566i	$-0.266867\pi$
$677$	−4318.13	−	5943.39i	−0.245139	−	0.337405i	−0.913801	+	0.406161i	$0.866867\pi$
$678$	10018.3	+	3255.14i	0.567478	+	0.184385i
$679$	−5.37778	+	16.5511i	−0.000303947	+	0.000935453i
$680$	17435.4	−	7187.72i	0.983259	−	0.405348i
$681$	−1182.66	−	3639.84i	−0.0665485	−	0.204815i
$682$			5876.74i			0.329959i
$683$	−3679.04	+	1195.39i	−0.206112	+	0.0669700i	−0.410254	−	0.911971i	$-0.634560\pi$
$683$	−3679.04	+	1195.39i	−0.206112	+	0.0669700i	0.204141	+	0.978941i	$0.434560\pi$
$684$	2073.84	+	1506.73i	0.115929	+	0.0842273i
$685$	4549.29	−	3872.28i	0.253751	−	0.215989i
$686$	−8402.26	+	6104.60i	−0.467638	+	0.339759i
$687$	−10538.1	+	14504.4i	−0.585228	+	0.805498i
$688$	17996.5	−	24770.1i	0.997253	−	1.37260i
$689$	17079.6	−	12409.0i	0.944384	−	0.686135i
$690$	3869.75	−	3293.87i	0.213506	−	0.181733i
$691$	15195.8	+	11040.4i	0.836579	+	0.607810i	0.921413	−	0.388585i	$-0.127036\pi$
$691$	15195.8	+	11040.4i	0.836579	+	0.607810i	−0.0848342	+	0.996395i	$0.527036\pi$
$692$	−785.400	+	255.192i	−0.0431451	+	0.0140187i
$693$			944.624i			0.0517796i
$694$	7087.34	+	21812.6i	0.387654	+	1.19308i
$695$	8248.45	−	3400.42i	0.450189	−	0.185590i
$696$	−4655.64	+	14328.6i	−0.253551	+	0.780349i
$697$	10996.7	+	3573.05i	0.597605	+	0.194174i
$698$	−13643.9	−	18779.3i	−0.739872	−	1.01835i
$699$	18031.1			0.975681
$700$	−678.877	−	683.448i	−0.0366559	−	0.0369027i
$701$	4949.99			0.266702			0.133351	−	0.991069i	$-0.457426\pi$
$701$	4949.99			0.266702			0.133351	+	0.991069i	$0.457426\pi$
$702$	−12307.1	−	16939.2i	−0.661681	−	0.910726i
$703$	13180.7	+	4282.68i	0.707142	+	0.229764i
$704$	−1375.04	+	4231.94i	−0.0736134	+	0.226559i
$705$	−12957.2	−	15222.5i	−0.692192	−	0.813212i
$706$	−3204.61	−	9862.79i	−0.170832	−	0.525766i
$707$			1889.19i			0.100496i
$708$	3868.69	−	1257.01i	0.205359	−	0.0667252i
$709$	−14092.1	−	10238.5i	−0.746462	−	0.542337i	0.148266	−	0.988948i	$-0.452631\pi$
$709$	−14092.1	−	10238.5i	−0.746462	−	0.542337i	−0.894728	+	0.446611i	$0.852631\pi$
$710$	−19918.7	+	1534.01i	−1.05286	+	0.0810852i
$711$	2951.08	−	2144.09i	0.155660	−	0.113094i
$712$	−18127.9	+	24950.9i	−0.954174	+	1.31331i
$713$	4258.09	−	5860.76i	0.223656	−	0.307836i
$714$	3574.35	−	2596.92i	0.187348	−	0.136117i
$715$	1453.29	−	6008.94i	0.0760137	−	0.314296i
$716$	2480.48	+	1802.18i	0.129469	+	0.0940650i
$717$	18555.0	−	6028.88i	0.966456	−	0.314021i
$718$		−	14303.3i		−	0.743448i
$719$	−1752.06	−	5392.30i	−0.0908776	−	0.279692i	0.895280	−	0.445504i	$-0.146976\pi$
$719$	−1752.06	−	5392.30i	−0.0908776	−	0.279692i	−0.986157	+	0.165812i	$0.946976\pi$
$720$	1007.64	+	13083.9i	0.0521563	+	0.677232i
$721$	−630.826	+	1941.48i	−0.0325842	+	0.100284i
$722$	−13292.3	−	4318.92i	−0.685161	−	0.222622i
$723$	9988.59	+	13748.1i	0.513803	+	0.707189i
$724$	5664.50			0.290773
$725$	−20041.6	+	19907.6i	−1.02666	+	1.01979i
$726$	−12281.1			−0.627818
$727$	−9847.43	−	13553.8i	−0.502367	−	0.691449i	0.480242	−	0.877136i	$-0.340549\pi$
$727$	−9847.43	−	13553.8i	−0.502367	−	0.691449i	−0.982609	+	0.185687i	$0.940549\pi$
$728$	4614.44	+	1499.32i	0.234921	+	0.0763305i
$729$	−4201.34	+	12930.4i	−0.213450	+	0.656932i
$730$	−4857.93	+	7897.64i	−0.246301	+	0.400418i
$731$	10805.0	+	33254.3i	0.546698	+	1.68256i
$732$		−	2907.64i		−	0.146816i
$733$	13111.3	−	4260.11i	0.660677	−	0.214667i	0.0405608	−	0.999177i	$-0.487086\pi$
$733$	13111.3	−	4260.11i	0.660677	−	0.214667i	0.620116	+	0.784510i	$0.287086\pi$
$734$	13385.0	+	9724.78i	0.673092	+	0.489030i
$735$	−10054.5	−	6184.65i	−0.504581	−	0.310373i
$736$	−2415.62	+	1755.05i	−0.120980	+	0.0878968i
$737$	−932.276	+	1283.17i	−0.0465954	+	0.0641331i
$738$	−3954.95	+	5443.53i	−0.197268	+	0.271516i
$739$	7925.32	−	5758.08i	0.394503	−	0.286623i	−0.372795	−	0.927914i	$-0.621601\pi$
$739$	7925.32	−	5758.08i	0.394503	−	0.286623i	0.767298	+	0.641290i	$0.221601\pi$
$740$	−835.629	−	2027.00i	−0.0415113	−	0.100695i
$741$	13664.2	+	9927.62i	0.677418	+	0.492173i
$742$	−6651.02	+	2161.05i	−0.329066	+	0.106920i
$743$		−	31902.0i		−	1.57520i	−0.616190	−	0.787598i	$-0.711325\pi$
$743$		−	31902.0i		−	1.57520i	0.616190	−	0.787598i	$-0.288675\pi$
$744$	−3372.93	−	10380.8i	−0.166207	−	0.511532i
$745$	2973.58	+	719.170i	0.146233	+	0.0353669i
$746$	−9161.68	+	28196.8i	−0.449642	+	1.38386i
$747$	13258.3	+	4307.89i	0.649392	+	0.211000i
$748$	870.785	+	1198.53i	0.0425656	+	0.0585865i
$749$	−103.322			−0.00504045
$750$	5560.62	−	13235.7i	0.270727	−	0.644401i
$751$	20480.8			0.995145			0.497573	−	0.867422i	$-0.334225\pi$
$751$	20480.8			0.995145			0.497573	+	0.867422i	$0.334225\pi$
$752$	23284.2	+	32047.9i	1.12910	+	1.55408i
$753$	−4854.01	−	1577.16i	−0.234914	−	0.0763280i
$754$	−10231.1	+	31488.0i	−0.494157	+	1.52086i
$755$	4395.31	+	1063.02i	0.211870	+	0.0512415i
$756$	340.347	+	1047.48i	0.0163734	+	0.0503922i
$757$			19359.0i			0.929480i	0.885447	+	0.464740i	$0.153852\pi$
$757$			19359.0i			0.929480i	−0.885447	+	0.464740i	$0.846148\pi$
$758$	42509.7	−	13812.2i	2.03697	−	0.661850i
$759$	−1387.88	−	1008.35i	−0.0663727	−	0.0482226i
$760$	−9102.08	−	22079.1i	−0.434430	−	1.05380i
$761$	2385.67	−	1733.29i	0.113641	−	0.0825648i	−0.529513	−	0.848302i	$-0.677625\pi$
$761$	2385.67	−	1733.29i	0.113641	−	0.0825648i	0.643154	+	0.765737i	$0.277625\pi$
$762$	−10344.2	+	14237.5i	−0.491772	+	0.676866i
$763$	−1275.65	+	1755.78i	−0.0605262	+	0.0833071i
$764$	−1813.06	+	1317.26i	−0.0858561	+	0.0623781i
$765$	−12764.7	−	7851.71i	−0.603280	−	0.371084i
$766$	−499.102	−	362.618i	−0.0235421	−	0.0171044i
$767$	−36534.8	+	11870.9i	−1.71994	+	0.558843i
$768$			7468.91i			0.350926i
$769$	−5896.06	−	18146.2i	−0.276486	−	0.850936i	−0.988822	−	0.149098i	$-0.952363\pi$
$769$	−5896.06	−	18146.2i	−0.276486	−	0.850936i	0.712337	−	0.701838i	$-0.247637\pi$
$770$	−1072.94	+	1744.31i	−0.0502157	+	0.0816369i
$771$	1937.57	−	5963.22i	0.0905055	−	0.278547i
$772$	−1944.35	−	631.757i	−0.0906459	−	0.0294526i
$773$	2765.08	+	3805.80i	0.128658	+	0.177083i	0.868486	−	0.495713i	$-0.165093\pi$
$773$	2765.08	+	3805.80i	0.128658	+	0.177083i	−0.739828	+	0.672796i	$0.765093\pi$
$774$	−20347.3			−0.944921
$775$	3269.33	−	20202.8i	0.151533	−	0.936393i
$776$	68.2527			0.00315738
$777$	1297.42	+	1785.75i	0.0599031	+	0.0824496i
$778$	−25136.0	−	8167.17i	−1.15831	−	0.376359i
$779$	4524.69	−	13925.6i	0.208105	−	0.640481i
$780$	−205.171	−	2664.07i	−0.00941832	−	0.122294i
$781$	2084.03	+	6413.99i	0.0954834	+	0.293868i
$782$		−	11500.3i		−	0.525896i
$783$	30716.6	−	9980.43i	1.40194	−	0.455519i
$784$	18924.4	+	13749.4i	0.862081	+	0.626339i
$785$	−5586.93	+	23100.5i	−0.254021	+	1.05031i
$786$	7509.82	−	5456.20i	0.340797	−	0.247603i
$787$	17297.6	−	23808.1i	0.783472	−	1.07836i	−0.211419	−	0.977396i	$-0.567808\pi$
$787$	17297.6	−	23808.1i	0.783472	−	1.07836i	0.994890	−	0.100961i	$-0.0321916\pi$
$788$	1713.42	−	2358.32i	0.0774595	−	0.106614i
$789$	13608.3	−	9887.02i	0.614029	−	0.446118i
$790$	7884.70	−	607.231i	0.355095	−	0.0273472i
$791$	4233.43	+	3075.77i	0.190295	+	0.138257i
$792$	3523.42	−	1144.83i	0.158080	−	0.0513633i
$793$			27458.9i			1.22963i
$794$	2191.84	+	6745.78i	0.0979665	+	0.301510i
$795$	−10727.3	−	12602.8i	−0.478563	−	0.562233i
$796$	−1252.01	+	3853.28i	−0.0557490	+	0.171578i
$797$	−30359.9	−	9864.52i	−1.34931	−	0.438418i	−0.456852	−	0.889543i	$-0.651023\pi$
$797$	−30359.9	−	9864.52i	−1.34931	−	0.438418i	−0.892461	+	0.451125i	$0.851023\pi$
$798$	−3288.57	−	4526.33i	−0.145882	−	0.200790i
$799$	−45239.1			−2.00306
$800$	−3854.73	+	7502.98i	−0.170356	+	0.331588i
$801$	24507.9			1.08108
$802$	−4015.07	−	5526.26i	−0.176779	−	0.243316i
$803$	2976.89	+	967.251i	0.130825	+	0.0425075i
$804$	−211.834	+	651.959i	−0.00929207	+	0.0285981i
$805$	2333.89	−	962.145i	0.102185	−	0.0421257i
$806$	−7412.26	−	22812.6i	−0.323928	−	0.996946i
$807$		−	1480.32i		−	0.0645719i
$808$	7046.64	−	2289.59i	0.306807	−	0.0996875i
$809$	27466.7	+	19955.8i	1.19367	+	0.867252i	0.993647	−	0.112539i	$-0.0358983\pi$
$809$	27466.7	+	19955.8i	1.19367	+	0.867252i	0.200023	+	0.979791i	$0.435898\pi$
$810$	−1225.05	+	1042.74i	−0.0531406	+	0.0452324i
$811$	−25361.5	+	18426.2i	−1.09811	+	0.797821i	−0.980750	−	0.195269i	$-0.937442\pi$
$811$	−25361.5	+	18426.2i	−1.09811	+	0.797821i	−0.117356	+	0.993090i	$0.537442\pi$
$812$	1023.68	−	1408.97i	0.0442413	−	0.0608930i
$813$	3326.71	−	4578.82i	0.143509	−	0.197523i
$814$	−3770.78	+	2739.63i	−0.162366	+	0.117966i
$815$	20391.7	−	17357.1i	0.876429	−	0.746002i
$816$	−16762.4	−	12178.6i	−0.719121	−	0.522472i
$817$	42111.1	−	13682.7i	1.80328	−	0.585922i
$818$			860.730i			0.0367906i
$819$	−1191.44	−	3666.88i	−0.0508332	−	0.156448i
$820$	−2141.54	+	882.849i	−0.0912023	+	0.0375981i
$821$	−1161.59	+	3574.99i	−0.0493784	+	0.151971i	−0.972705	−	0.232044i	$-0.925459\pi$
$821$	−1161.59	+	3574.99i	−0.0493784	+	0.151971i	0.923327	+	0.384015i	$0.125459\pi$
$822$	−5220.45	−	1696.23i	−0.221513	−	0.0719741i
$823$	−17800.5	−	24500.3i	−0.753932	−	1.03770i	−0.997695	−	0.0678639i	$-0.978382\pi$
$823$	−17800.5	−	24500.3i	−0.753932	−	1.03770i	0.243762	−	0.969835i	$-0.421618\pi$
$824$	8006.21			0.338483
$825$	−4784.20	−	774.206i	−0.201896	−	0.0326720i
$826$	12725.2			0.536035
$827$	−9330.09	−	12841.8i	−0.392308	−	0.539966i	0.566484	−	0.824072i	$-0.308303\pi$
$827$	−9330.09	−	12841.8i	−0.392308	−	0.539966i	−0.958793	+	0.284106i	$0.908303\pi$
$828$	1010.70	+	328.398i	0.0424208	+	0.0137834i
$829$	2426.35	−	7467.53i	0.101653	−	0.312857i	−0.887277	−	0.461237i	$-0.847406\pi$
$829$	2426.35	−	7467.53i	0.101653	−	0.312857i	0.988930	+	0.148380i	$0.0474059\pi$
$830$	19589.2	+	23014.1i	0.819219	+	0.962447i
$831$	−4981.34	−	15331.0i	−0.207943	−	0.639983i
$832$		−	18162.1i		−	0.756798i
$833$	−25406.4	+	8255.04i	−1.05676	+	0.343361i
$834$	−6631.90	−	4818.36i	−0.275352	−	0.200055i
$835$	−2362.49	+	181.945i	−0.0979132	+	0.00754068i
$836$	1517.75	−	1102.71i	0.0627899	−	0.0456195i
$837$	−13753.5	+	18930.1i	−0.567971	+	0.781745i
$838$	−13474.4	+	18545.9i	−0.555448	+	0.764509i
$839$	−31973.0	+	23229.7i	−1.31565	+	0.955876i	−0.315674	+	0.948868i	$0.602231\pi$
$839$	−31973.0	+	23229.7i	−1.31565	+	0.955876i	−0.999975	+	0.00700798i	$0.997769\pi$
$840$	894.133	−	3697.00i	0.0367268	−	0.151855i
$841$	−21585.8	−	15683.0i	−0.885064	−	0.643037i
$842$	−12472.6	+	4052.59i	−0.510492	+	0.165869i
$843$			16490.5i			0.673741i
$844$	−1965.00	−	6047.66i	−0.0801401	−	0.246646i
$845$	51.4524	+	668.092i	0.00209469	+	0.0271989i
$846$	8135.09	−	25037.2i	0.330603	−	1.01749i
$847$	−5802.20	−	1885.25i	−0.235379	−	0.0764792i
$848$	19277.0	+	26532.6i	0.780633	+	1.07445i
$849$	−6499.60			−0.262739
$850$	−14652.5	−	28997.3i	−0.591268	−	1.17012i
$851$	5745.57			0.231440
$852$	1713.28	+	2358.13i	0.0688922	+	0.0948219i
$853$	−40911.5	−	13292.9i	−1.64218	−	0.533577i	−0.665158	−	0.746703i	$-0.731636\pi$
$853$	−40911.5	−	13292.9i	−1.64218	−	0.533577i	−0.977025	+	0.213125i	$0.931636\pi$
$854$	2810.79	−	8650.72i	0.112627	−	0.346630i
$855$	−9942.91	+	16164.4i	−0.397708	+	0.646563i
$856$	125.220	+	385.388i	0.00499992	+	0.0153882i
$857$			18154.4i			0.723622i	0.932251	+	0.361811i	$0.117841\pi$
$857$			18154.4i			0.723622i	−0.932251	+	0.361811i	$0.882159\pi$
$858$	−5402.22	+	1755.29i	−0.214952	+	0.0698422i
$859$	32675.5	+	23740.1i	1.29787	+	0.942960i	0.999932	−	0.0116239i	$-0.00370008\pi$
$859$	32675.5	+	23740.1i	1.29787	+	0.942960i	0.297941	+	0.954584i	$0.403700\pi$
$860$	−5966.41	−	3670.00i	−0.236573	−	0.145519i
$861$	1886.66	−	1370.74i	0.0746773	−	0.0542562i
$862$	7820.03	−	10763.4i	0.308992	−	0.425291i
$863$	1256.85	−	1729.91i	0.0495757	−	0.0682350i	−0.783509	−	0.621380i	$-0.786572\pi$
$863$	1256.85	−	1729.91i	0.0495757	−	0.0682350i	0.833085	+	0.553145i	$0.186572\pi$
$864$	7802.40	−	5668.77i	0.307226	−	0.223212i
$865$	−2330.15	−	5652.29i	−0.0915926	−	0.222178i
$866$	31462.5	+	22858.8i	1.23457	+	0.896968i
$867$	6939.29	−	2254.71i	0.271823	−	0.0883207i
$868$			1261.75i			0.0493393i
$869$	−824.954	−	2538.95i	−0.0322033	−	0.0991114i
$870$	25227.6	+	6101.39i	0.983098	+	0.237766i
$871$	2000.51	−	6156.92i	0.0778238	−	0.239517i
$872$	8095.01	+	2630.23i	0.314371	+	0.102145i
$873$	−31.8799	−	43.8789i	−0.00123593	−	0.00170112i
$874$	−14563.3			−0.563628
$875$	4658.89	−	5399.59i	0.179999	−	0.208617i
$876$	1352.84			0.0521782
$877$	24603.6	+	33863.9i	0.947325	+	1.30388i	0.952705	+	0.303896i	$0.0982875\pi$
$877$	24603.6	+	33863.9i	0.947325	+	1.30388i	−0.00538007	+	0.999986i	$0.501713\pi$
$878$	−24201.0	−	7863.40i	−0.930234	−	0.302251i
$879$	−3994.95	+	12295.2i	−0.153295	+	0.471793i
$880$	9334.69	+	2257.63i	0.357582	+	0.0864826i
$881$	−8792.97	−	27062.0i	−0.336257	−	1.03489i	−0.966099	−	0.258170i	$-0.916880\pi$
$881$	−8792.97	−	27062.0i	−0.336257	−	1.03489i	0.629842	−	0.776723i	$-0.283120\pi$
$882$		−	15545.4i		−	0.593471i
$883$	8961.80	−	2911.86i	0.341550	−	0.110976i	−0.133219	−	0.991087i	$-0.542532\pi$
$883$	8961.80	−	2911.86i	0.341550	−	0.110976i	0.474769	+	0.880110i	$0.342532\pi$
$884$	−4891.95	−	3554.21i	−0.186124	−	0.135227i
$885$	11477.8	+	27841.8i	0.435956	+	1.05751i
$886$	20859.3	−	15155.1i	0.790949	−	0.574658i
$887$	6421.32	−	8838.20i	0.243074	−	0.334563i	−0.669996	−	0.742364i	$-0.733704\pi$
$887$	6421.32	−	8838.20i	0.243074	−	0.334563i	0.913071	+	0.407801i	$0.133704\pi$
$888$	5088.40	−	7003.58i	0.192292	−	0.264667i
$889$	−7072.66	+	5138.59i	−0.266827	+	0.193861i
$890$	45255.4	+	27837.1i	1.70445	+	1.04843i
$891$	439.362	+	319.215i	0.0165198	+	0.0120024i
$892$	1181.45	−	383.878i	0.0443475	−	0.0144094i
$893$			57288.0i			2.14677i
$894$	−868.620	−	2673.34i	−0.0324955	−	0.100011i
$895$	−11892.5	+	19334.0i	−0.444160	+	0.722082i
$896$	−2710.44	+	8341.88i	−0.101060	+	0.311030i
$897$	6659.36	+	2163.76i	0.247881	+	0.0805416i
$898$	−7762.78	−	10684.5i	−0.288471	−	0.397047i
$899$	36999.8			1.37265
$900$	2966.84	−	459.702i	0.109883	−	0.0170260i
$901$	−37453.6			−1.38486
$902$	2894.44	+	3983.86i	0.106845	+	0.147060i
$903$	6706.96	+	2179.22i	0.247169	+	0.0803101i
$904$	6341.86	−	19518.2i	0.233326	−	0.718105i
$905$	3220.10	+	41812.0i	0.118276	+	1.53578i
$906$	−1283.93	−	3951.52i	−0.0470812	−	0.144901i
$907$		−	50736.1i		−	1.85740i	−0.370827	−	0.928702i	$-0.620926\pi$
$907$		−	50736.1i		−	1.85740i	0.370827	−	0.928702i	$-0.379074\pi$
$908$	1650.17	−	536.173i	0.0603116	−	0.0195964i
$909$	−4763.33	−	3460.76i	−0.173806	−	0.126278i
$910$	1964.92	−	8124.41i	0.0715785	−	0.295958i
$911$	−19614.0	+	14250.4i	−0.713328	+	0.518263i	−0.884246	−	0.467022i	$-0.845327\pi$
$911$	−19614.0	+	14250.4i	−0.713328	+	0.518263i	0.170917	+	0.985285i	$0.445327\pi$
$912$	−15422.2	+	21226.9i	−0.559957	+	0.770715i
$913$	5996.86	−	8253.97i	0.217379	−	0.299196i
$914$	32153.0	−	23360.5i	1.16359	−	0.845401i
$915$	21462.5	−	1652.91i	0.775440	−	0.0597197i
$916$	−6575.76	−	4777.57i	−0.237194	−	0.172331i
$917$	4385.57	−	1424.96i	0.157933	−	0.0513154i
$918$			37145.8i			1.33551i
$919$	−2469.43	−	7600.13i	−0.0886388	−	0.272802i	0.896905	−	0.442223i	$-0.145810\pi$
$919$	−2469.43	−	7600.13i	−0.0886388	−	0.272802i	−0.985544	+	0.169421i	$0.945810\pi$
$920$	−6417.32	−	7539.29i	−0.229970	−	0.270177i
$921$	3969.67	−	12217.4i	0.142025	−	0.437108i
$922$	33939.5	+	11027.6i	1.21230	+	0.393899i
$923$	−16179.8	−	22269.6i	−0.576992	−	0.794162i
$924$	298.793			0.0106381
$925$	14487.1	−	7320.42i	0.514954	−	0.260210i
$926$	−22399.7			−0.794926
$927$	−3739.59	−	5147.10i	−0.132496	−	0.182366i
$928$	−14503.7	−	4712.55i	−0.513048	−	0.166700i
$929$	2450.19	−	7540.92i	0.0865321	−	0.266318i	−0.898422	−	0.439132i	$-0.855286\pi$
$929$	2450.19	−	7540.92i	0.0865321	−	0.266318i	0.984954	+	0.172814i	$0.0552859\pi$
$930$	−17384.6	+	7166.79i	−0.612972	+	0.252697i
$931$	10453.7	+	32173.0i	0.367997	+	1.13258i
$932$			8174.67i			0.287307i
$933$	21158.3	−	6874.75i	0.742435	−	0.241232i
$934$	29496.4	+	21430.4i	1.03335	+	0.750774i
$935$	−8351.85	+	7108.95i	−0.292123	+	0.248650i
$936$	−12233.4	+	8888.10i	−0.427203	+	0.310381i
$937$	−9355.10	+	12876.2i	−0.326166	+	0.448929i	−0.940337	−	0.340244i	$-0.889490\pi$
$937$	−9355.10	+	12876.2i	−0.326166	+	0.448929i	0.614171	+	0.789173i	$0.289490\pi$
$938$	−1260.49	+	1734.91i	−0.0438767	+	0.0603911i
$939$	−8395.82	+	6099.92i	−0.291786	+	0.211995i
$940$	6901.35	−	5874.31i	0.239465	−	0.203829i
$941$	−15090.5	−	10963.9i	−0.522780	−	0.379822i	0.294870	−	0.955537i	$-0.404724\pi$
$941$	−15090.5	−	10963.9i	−0.522780	−	0.379822i	−0.817650	+	0.575715i	$0.804724\pi$
$942$	20768.0	−	6747.94i	0.718322	−	0.233397i
$943$		−	6070.24i		−	0.209623i
$944$	−18441.0	−	56755.7i	−0.635810	−	1.95682i
$945$	−7538.42	+	3107.71i	−0.259497	+	0.106978i
$946$	−4601.64	+	14162.4i	−0.158152	+	0.486743i
$947$	−52450.7	−	17042.3i	−1.79981	−	0.584793i	−0.799925	−	0.600100i	$-0.795127\pi$
$947$	−52450.7	−	17042.3i	−1.79981	−	0.584793i	−0.999883	+	0.0153071i	$0.995127\pi$
$948$	−678.194	−	933.455i	−0.0232350	−	0.0319802i
$949$	−12775.8			−0.437008
$950$	−36720.4	+	18555.0i	−1.25407	+	0.633690i
$951$	−9826.45			−0.335062
$952$	−5059.48	−	6963.77i	−0.172246	−	0.237077i
$953$	−17570.1	−	5708.86i	−0.597220	−	0.194048i	−0.00521959	−	0.999986i	$-0.501661\pi$
$953$	−17570.1	−	5708.86i	−0.597220	−	0.194048i	−0.592000	+	0.805938i	$0.701661\pi$
$954$	6735.06	−	20728.4i	0.228570	−	0.703466i
$955$	−10753.9	−	12634.1i	−0.364386	−	0.428094i
$956$	2733.28	+	8412.16i	0.0924691	+	0.284591i
$957$		−	8761.89i		−	0.295958i
$958$	−7747.53	+	2517.32i	−0.261285	+	0.0848967i
$959$	−2206.01	−	1602.76i	−0.0742812	−	0.0539684i
$960$	−14195.9	+	1093.28i	−0.477260	+	0.0367556i
$961$	2415.10	−	1754.67i	0.0810681	−	0.0588994i
$962$	11182.1	−	15390.8i	0.374767	−	0.515822i
$963$	189.273	−	260.512i	0.00633357	−	0.00871741i
$964$	−6232.89	+	4528.46i	−0.208245	+	0.151299i
$965$	3557.95	−	14711.2i	0.118689	−	0.490746i
$966$	−1876.49	−	1363.35i	−0.0625001	−	0.0454090i
$967$	29829.7	−	9692.26i	0.991995	−	0.322319i	0.232332	−	0.972636i	$-0.425364\pi$
$967$	29829.7	−	9692.26i	0.991995	−	0.322319i	0.759662	+	0.650318i	$0.225364\pi$
$968$			23926.9i			0.794461i
$969$	−9259.40	−	28497.5i	−0.306971	−	0.944759i
$970$	−9.02876	−	117.235i	−0.000298862	−	0.00388062i
$971$	−1350.42	+	4156.18i	−0.0446315	+	0.137362i	−0.970889	−	0.239529i	$-0.923007\pi$
$971$	−1350.42	+	4156.18i	−0.0446315	+	0.137362i	0.926258	+	0.376891i	$0.123007\pi$
$972$	−5318.98	−	1728.24i	−0.175521	−	0.0570302i
$973$	−2393.57	−	3294.47i	−0.0788638	−	0.108547i
$974$	−50914.9			−1.67497
$975$	19548.0	−	3028.90i	0.642089	−	0.0994897i
$976$	−42656.6			−1.39898
$977$	14803.8	+	20375.7i	0.484766	+	0.667224i	0.979412	−	0.201871i	$-0.0647021\pi$
$977$	14803.8	+	20375.7i	0.484766	+	0.667224i	−0.494646	+	0.869095i	$0.664702\pi$
$978$	−23400.1	−	7603.14i	−0.765083	−	0.248591i
$979$	5542.58	−	17058.3i	0.180941	−	0.556881i
$980$	2803.89	−	4558.36i	0.0913950	−	0.148583i
$981$	−2090.12	−	6432.72i	−0.0680248	−	0.209359i
$982$			31522.5i			1.02436i
$983$	38605.0	−	12543.5i	1.25260	−	0.406995i	0.393749	−	0.919218i	$-0.371178\pi$
$983$	38605.0	−	12543.5i	1.25260	−	0.406995i	0.858853	+	0.512223i	$0.171178\pi$
$984$	−7399.34	−	5375.93i	−0.239718	−	0.174165i
$985$	18381.8	+	11306.8i	0.594611	+	0.365752i
$986$	47519.4	−	34524.9i	1.53481	−	1.11511i
$987$	−5363.04	+	7381.60i	−0.172956	+	0.238053i
$988$	−4500.82	+	6194.85i	−0.144929	+	0.199478i
$989$	14850.7	−	10789.7i	0.477478	−	0.346908i
$990$	−2432.53	−	5900.62i	−0.0780918	−	0.189428i
$991$	−25117.4	−	18248.8i	−0.805125	−	0.584958i	0.107288	−	0.994228i	$-0.465783\pi$
$991$	−25117.4	−	18248.8i	−0.805125	−	0.584958i	−0.912413	+	0.409270i	$0.865783\pi$
$992$	10507.7	−	3414.17i	0.336311	−	0.109274i
$993$		−	36633.6i		−	1.17073i
$994$	2817.72	+	8672.06i	0.0899123	+	0.276721i
$995$	−29154.4	−	7051.10i	−0.928901	−	0.224658i
$996$	1362.62	−	4193.72i	0.0433498	−	0.133417i
$997$	46124.1	+	14986.6i	1.46516	+	0.476059i	0.929642	−	0.368465i	$-0.120116\pi$
$997$	46124.1	+	14986.6i	1.46516	+	0.476059i	0.535518	+	0.844524i	$0.320116\pi$
$998$	−2365.30	−	3255.55i	−0.0750222	−	0.103259i
$999$	−18558.1			−0.587739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.e.a.14.5	yes	24
3.2	odd	2		225.4.m.a.64.2		24
5.2	odd	4		125.4.d.b.51.4		48
5.3	odd	4		125.4.d.b.51.9		48
5.4	even	2		125.4.e.a.74.2		24
25.3	odd	20		625.4.a.g.1.7		24
25.9	even	10	inner	25.4.e.a.9.5	✓	24
25.12	odd	20		125.4.d.b.76.4		48
25.13	odd	20		125.4.d.b.76.9		48
25.16	even	5		125.4.e.a.49.2		24
25.22	odd	20		625.4.a.g.1.18		24
75.59	odd	10		225.4.m.a.109.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.e.a.9.5	✓	24	25.9	even	10	inner
25.4.e.a.14.5	yes	24	1.1	even	1	trivial
125.4.d.b.51.4		48	5.2	odd	4
125.4.d.b.51.9		48	5.3	odd	4
125.4.d.b.76.4		48	25.12	odd	20
125.4.d.b.76.9		48	25.13	odd	20
125.4.e.a.49.2		24	25.16	even	5
125.4.e.a.74.2		24	5.4	even	2
225.4.m.a.64.2		24	3.2	odd	2
225.4.m.a.109.2		24	75.59	odd	10
625.4.a.g.1.7		24	25.3	odd	20
625.4.a.g.1.18		24	25.22	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)

\(f(q)\)	\(=\)	\(q+(1.81265 + 2.49489i) q^{2} +(3.16804 + 1.02936i) q^{3} +(-0.466674 + 1.43628i) q^{4} +(-10.8670 - 2.62823i) q^{5} +(3.17440 + 9.76980i) q^{6} +5.10302i q^{7} +(19.0341 - 6.18456i) q^{8} +(-12.8665 - 9.34809i) q^{9} +O(q^{10})\)	\(q+(1.81265 + 2.49489i) q^{2} +(3.16804 + 1.02936i) q^{3} +(-0.466674 + 1.43628i) q^{4} +(-10.8670 - 2.62823i) q^{5} +(3.17440 + 9.76980i) q^{6} +5.10302i q^{7} +(19.0341 - 6.18456i) q^{8} +(-12.8665 - 9.34809i) q^{9} +(-13.1409 - 31.8762i) q^{10} +(-9.41641 + 6.84142i) q^{11} +(-2.95689 + 4.06981i) q^{12} +(27.9240 - 38.4341i) q^{13} +(-12.7315 + 9.24997i) q^{14} +(-31.7218 - 19.5124i) q^{15} +(59.7061 + 43.3790i) q^{16} +(-80.1567 + 26.0445i) q^{17} -49.0455i q^{18} +(32.9811 + 101.505i) q^{19} +(8.84623 - 14.3815i) q^{20} +(-5.25284 + 16.1666i) q^{21} +(-34.1372 - 11.0919i) q^{22} +(26.0076 + 35.7964i) q^{23} +66.6671 q^{24} +(111.185 + 57.1222i) q^{25} +146.505 q^{26} +(-84.0041 - 115.622i) q^{27} +(-7.32934 - 2.38145i) q^{28} +(-69.8341 + 214.927i) q^{29} +(-8.81900 - 114.512i) q^{30} +(-50.5937 - 155.711i) q^{31} +67.4821i q^{32} +(-36.8739 + 11.9810i) q^{33} +(-210.274 - 152.773i) q^{34} +(13.4119 - 55.4546i) q^{35} +(19.4309 - 14.1174i) q^{36} +(76.3255 - 105.053i) q^{37} +(-193.462 + 266.278i) q^{38} +(128.027 - 93.0171i) q^{39} +(-223.099 + 17.1817i) q^{40} +(-110.989 - 80.6385i) q^{41} +(-49.8554 + 16.1990i) q^{42} -414.866i q^{43} +(-5.43177 - 16.7173i) q^{44} +(115.252 + 135.402i) q^{45} +(-42.1657 + 129.773i) q^{46} +(510.490 + 165.868i) q^{47} +(144.499 + 198.886i) q^{48} +316.959 q^{49} +(59.0249 + 380.937i) q^{50} -280.749 q^{51} +(42.1706 + 58.0428i) q^{52} +(422.636 + 137.323i) q^{53} +(136.194 - 419.163i) q^{54} +(120.309 - 49.5974i) q^{55} +(31.5599 + 97.1315i) q^{56} +355.523i q^{57} +(-662.806 + 215.359i) q^{58} +(-654.183 - 475.292i) q^{59} +(42.8290 - 36.4553i) q^{60} +(-467.608 + 339.737i) q^{61} +(296.775 - 408.476i) q^{62} +(47.7035 - 65.6582i) q^{63} +(309.288 - 224.711i) q^{64} +(-404.465 + 344.274i) q^{65} +(-96.7307 - 70.2790i) q^{66} +(129.600 - 42.1095i) q^{67} -127.281i q^{68} +(45.5459 + 140.176i) q^{69} +(162.665 - 67.0584i) q^{70} +(179.051 - 551.063i) q^{71} +(-302.717 - 98.3588i) q^{72} +(-158.070 - 217.564i) q^{73} +400.447 q^{74} +(293.439 + 295.415i) q^{75} -161.181 q^{76} +(-34.9119 - 48.0521i) q^{77} +(464.136 + 150.807i) q^{78} +(-70.8764 + 218.135i) q^{79} +(-534.818 - 628.323i) q^{80} +(-14.4185 - 44.3755i) q^{81} -423.076i q^{82} +(-833.650 + 270.869i) q^{83} +(-20.7683 - 15.0890i) q^{84} +(939.516 - 72.3558i) q^{85} +(1035.05 - 752.006i) q^{86} +(-442.475 + 609.015i) q^{87} +(-136.922 + 188.457i) q^{88} +(-1246.69 + 905.776i) q^{89} +(-128.903 + 532.979i) q^{90} +(196.130 + 142.497i) q^{91} +(-63.5506 + 20.6489i) q^{92} -545.380i q^{93} +(511.514 + 1574.28i) q^{94} +(-91.6268 - 1189.74i) q^{95} +(-69.4633 + 213.786i) q^{96} +(3.24339 + 1.05384i) q^{97} +(574.535 + 790.780i) q^{98} +185.111 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more