LMFDB - Embedded newform 153.3.t.a.7.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(7,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([32, 33])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.t (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$34$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			7.10
Character	$\chi$	$=$	153.7
Dual form			153.3.t.a.22.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.11526 - 1.45343i) q^{2} +(2.99911 + 0.0730780i) q^{3} +(0.166611 - 0.621802i) q^{4} +(5.00581 - 4.38998i) q^{5} +(-3.23857 - 4.44050i) q^{6} +(-5.80360 - 5.08962i) q^{7} +(-7.85979 + 3.25563i) q^{8} +(8.98932 + 0.438338i) q^{9} +(-11.9633 - 2.37965i) q^{10} +(0.562772 + 8.58625i) q^{11} +(0.545125 - 1.85268i) q^{12} +(10.4255 + 2.79351i) q^{13} +(-0.924909 + 14.1114i) q^{14} +(15.3338 - 12.8002i) q^{15} +(11.2676 + 6.50533i) q^{16} +(-16.8018 - 2.58825i) q^{17} +(-9.38831 - 13.5542i) q^{18} +(9.10068 - 21.9710i) q^{19} +(-1.89567 - 3.84404i) q^{20} +(-17.0337 - 15.6885i) q^{21} +(11.8519 - 10.3938i) q^{22} +(-17.8117 + 36.1186i) q^{23} +(-23.8103 + 9.18962i) q^{24} +(2.52308 - 19.1647i) q^{25} +(-7.56697 - 18.2683i) q^{26} +(26.9279 + 1.97154i) q^{27} +(-4.13168 + 2.76070i) q^{28} +(8.39738 - 24.7379i) q^{29} +(-35.7054 - 8.01108i) q^{30} +(-0.474507 + 7.23958i) q^{31} +(1.33056 + 10.1066i) q^{32} +(1.06035 + 25.7922i) q^{33} +(14.9765 + 27.3069i) q^{34} -51.3951 q^{35} +(1.77028 - 5.51654i) q^{36} +(21.7695 - 32.5804i) q^{37} +(-42.0829 + 11.2761i) q^{38} +(31.0632 + 9.13992i) q^{39} +(-25.0525 + 50.8014i) q^{40} +(49.0386 - 16.6464i) q^{41} +(-3.80514 + 42.2540i) q^{42} +(15.9473 + 2.09950i) q^{43} +(5.43271 + 1.08063i) q^{44} +(46.9231 - 37.2687i) q^{45} +(72.3607 - 14.3934i) q^{46} +(15.4124 + 57.5200i) q^{47} +(33.3173 + 20.3336i) q^{48} +(1.38176 + 10.4955i) q^{49} +(-30.6684 + 17.7064i) q^{50} +(-50.2013 - 8.99029i) q^{51} +(3.47402 - 6.01718i) q^{52} +(-17.4706 + 42.1778i) q^{53} +(-27.1661 - 41.3367i) q^{54} +(40.5106 + 40.5106i) q^{55} +(62.1850 + 21.1090i) q^{56} +(28.8995 - 65.2284i) q^{57} +(-45.3201 + 15.3841i) q^{58} +(34.7410 + 26.6577i) q^{59} +(-5.40441 - 11.6672i) q^{60} +(-56.7700 + 64.7337i) q^{61} +(11.0514 - 7.38433i) q^{62} +(-49.9395 - 48.2962i) q^{63} +(50.0051 - 50.0051i) q^{64} +(64.4517 - 31.7840i) q^{65} +(36.3047 - 30.3061i) q^{66} +(0.708666 - 0.409148i) q^{67} +(-4.40875 + 10.0162i) q^{68} +(-56.0589 + 107.022i) q^{69} +(57.3187 + 74.6992i) q^{70} +(-46.3428 + 69.3569i) q^{71} +(-72.0812 + 25.8207i) q^{72} +(25.5163 + 128.279i) q^{73} +(-71.6321 + 4.69501i) q^{74} +(8.96750 - 57.2926i) q^{75} +(-12.1453 - 9.31943i) q^{76} +(40.4347 - 52.6955i) q^{77} +(-21.3592 - 55.3415i) q^{78} +(-2.96806 - 45.2838i) q^{79} +(84.9615 - 16.8999i) q^{80} +(80.6157 + 7.88072i) q^{81} +(-78.8851 - 52.7093i) q^{82} +(14.7523 - 11.3199i) q^{83} +(-12.5931 + 7.97771i) q^{84} +(-95.4691 + 60.8033i) q^{85} +(-14.7339 - 25.5198i) q^{86} +(26.9925 - 73.5780i) q^{87} +(-32.3769 - 65.6539i) q^{88} +(-21.9909 - 21.9909i) q^{89} +(-106.499 - 26.6354i) q^{90} +(-46.2877 - 69.2744i) q^{91} +(19.4910 + 17.0931i) q^{92} +(-1.95215 + 21.6776i) q^{93} +(66.4126 - 86.5505i) q^{94} +(-50.8959 - 149.934i) q^{95} +(3.25193 + 30.4081i) q^{96} +(24.1747 - 71.2163i) q^{97} +(13.7135 - 13.7135i) q^{98} +(1.29526 + 77.4312i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) $ 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.11526	−	1.45343i	−0.557629	−	0.726716i	0.426438	−	0.904517i	$-0.359768\pi$
$2$	−1.11526	−	1.45343i	−0.557629	−	0.726716i	−0.984066	+	0.177801i	$0.943102\pi$
$3$	2.99911	+	0.0730780i	0.999703	+	0.0243593i
$3$	2.99911	+	0.0730780i	0.999703	+	0.0243593i
$4$	0.166611	−	0.621802i	0.0416528	−	0.155450i
$5$	5.00581	−	4.38998i	1.00116	−	0.877996i	0.00862795	−	0.999963i	$-0.497254\pi$
$5$	5.00581	−	4.38998i	1.00116	−	0.877996i	0.992534	+	0.121967i	$0.0389203\pi$
$6$	−3.23857	−	4.44050i	−0.539761	−	0.740084i
$7$	−5.80360	−	5.08962i	−0.829086	−	0.727089i	0.135523	−	0.990774i	$-0.456729\pi$
$7$	−5.80360	−	5.08962i	−0.829086	−	0.727089i	−0.964609	+	0.263685i	$0.915062\pi$
$8$	−7.85979	+	3.25563i	−0.982474	+	0.406954i
$9$	8.98932	+	0.438338i	0.998813	+	0.0487042i
$10$	−11.9633	−	2.37965i	−1.19633	−	0.237965i
$11$	0.562772	+	8.58625i	0.0511611	+	0.780568i	0.943949	+	0.330091i	$0.107079\pi$
$11$	0.562772	+	8.58625i	0.0511611	+	0.780568i	−0.892788	+	0.450477i	$0.851254\pi$
$12$	0.545125	−	1.85268i	0.0454271	−	0.154390i
$13$	10.4255	+	2.79351i	0.801963	+	0.214885i	0.636446	−	0.771321i	$-0.280404\pi$
$13$	10.4255	+	2.79351i	0.801963	+	0.214885i	0.165518	+	0.986207i	$0.447071\pi$
$14$	−0.924909	+	14.1114i	−0.0660649	+	1.00796i
$15$	15.3338	−	12.8002i	1.02225	−	0.853347i
$16$	11.2676	+	6.50533i	0.704223	+	0.406583i
$17$	−16.8018	−	2.58825i	−0.988342	−	0.152250i
$17$	−16.8018	−	2.58825i	−0.988342	−	0.152250i
$18$	−9.38831	−	13.5542i	−0.521573	−	0.753012i
$19$	9.10068	−	21.9710i	0.478983	−	1.15637i	−0.481103	−	0.876664i	$-0.659764\pi$
$19$	9.10068	−	21.9710i	0.478983	−	1.15637i	0.960086	−	0.279704i	$-0.0902363\pi$
$20$	−1.89567	−	3.84404i	−0.0947836	−	0.192202i
$21$	−17.0337	−	15.6885i	−0.811129	−	0.747069i
$22$	11.8519	−	10.3938i	0.538722	−	0.472447i
$23$	−17.8117	+	36.1186i	−0.774424	+	1.57038i	0.0462170	+	0.998931i	$0.485283\pi$
$23$	−17.8117	+	36.1186i	−0.774424	+	1.57038i	−0.820641	+	0.571445i	$0.806383\pi$
$24$	−23.8103	+	9.18962i	−0.992095	+	0.382901i
$25$	2.52308	−	19.1647i	0.100923	−	0.766587i
$26$	−7.56697	−	18.2683i	−0.291037	−	0.702626i
$27$	26.9279	+	1.97154i	0.997330	+	0.0730202i
$28$	−4.13168	+	2.76070i	−0.147560	+	0.0985965i
$29$	8.39738	−	24.7379i	0.289565	−	0.853030i	−0.700653	−	0.713502i	$-0.747108\pi$
$29$	8.39738	−	24.7379i	0.289565	−	0.853030i	0.990218	−	0.139528i	$-0.0445587\pi$
$30$	−35.7054	−	8.01108i	−1.19018	−	0.267036i
$31$	−0.474507	+	7.23958i	−0.0153067	+	0.233535i	0.983350	+	0.181721i	$0.0581668\pi$
$31$	−0.474507	+	7.23958i	−0.0153067	+	0.233535i	−0.998657	+	0.0518136i	$0.983500\pi$
$32$	1.33056	+	10.1066i	0.0415801	+	0.315832i
$33$	1.06035	+	25.7922i	0.0321318	+	0.781582i
$34$	14.9765	+	27.3069i	0.440485	+	0.803143i
$35$	−51.3951			−1.46843
$36$	1.77028	−	5.51654i	0.0491745	−	0.153237i
$37$	21.7695	−	32.5804i	0.588366	−	0.880552i	−0.411153	−	0.911566i	$-0.634874\pi$
$37$	21.7695	−	32.5804i	0.588366	−	0.880552i	0.999519	+	0.0310145i	$0.00987380\pi$
$38$	−42.0829	+	11.2761i	−1.10745	+	0.296739i
$39$	31.0632	+	9.13992i	0.796491	+	0.234357i
$40$	−25.0525	+	50.8014i	−0.626312	+	1.27003i
$41$	49.0386	−	16.6464i	1.19606	−	0.406009i	0.348808	−	0.937194i	$-0.386586\pi$
$41$	49.0386	−	16.6464i	1.19606	−	0.406009i	0.847256	+	0.531185i	$0.178253\pi$
$42$	−3.80514	+	42.2540i	−0.0905985	+	1.00605i
$43$	15.9473	+	2.09950i	0.370868	+	0.0488257i	0.313657	−	0.949536i	$-0.398446\pi$
$43$	15.9473	+	2.09950i	0.370868	+	0.0488257i	0.0572110	+	0.998362i	$0.481779\pi$
$44$	5.43271	+	1.08063i	0.123471	+	0.0245598i
$45$	46.9231	−	37.2687i	1.04274	−	0.828193i
$46$	72.3607	−	14.3934i	1.57306	−	0.312901i
$47$	15.4124	+	57.5200i	0.327924	+	1.22383i	0.911339	+	0.411656i	$0.135049\pi$
$47$	15.4124	+	57.5200i	0.327924	+	1.22383i	−0.583415	+	0.812174i	$0.698284\pi$
$48$	33.3173	+	20.3336i	0.694109	+	0.423617i
$49$	1.38176	+	10.4955i	0.0281992	+	0.214194i
$50$	−30.6684	+	17.7064i	−0.613369	+	0.354128i
$51$	−50.2013	−	8.99029i	−0.984340	−	0.176280i
$52$	3.47402	−	6.01718i	0.0668081	−	0.115715i
$53$	−17.4706	+	42.1778i	−0.329635	+	0.795808i	0.668985	+	0.743276i	$0.266729\pi$
$53$	−17.4706	+	42.1778i	−0.329635	+	0.795808i	−0.998619	+	0.0525320i	$0.983271\pi$
$54$	−27.1661	−	41.3367i	−0.503075	−	0.765494i
$55$	40.5106	+	40.5106i	0.736556	+	0.736556i
$56$	62.1850	+	21.1090i	1.11045	+	0.376946i
$57$	28.8995	−	65.2284i	0.507010	−	1.14436i
$58$	−45.3201	+	15.3841i	−0.781380	+	0.265243i
$59$	34.7410	+	26.6577i	0.588830	+	0.451825i	0.859706	−	0.510789i	$-0.170647\pi$
$59$	34.7410	+	26.6577i	0.588830	+	0.451825i	−0.270876	+	0.962614i	$0.587313\pi$
$60$	−5.40441	−	11.6672i	−0.0900735	−	0.194454i
$61$	−56.7700	+	64.7337i	−0.930655	+	1.06121i	0.0673280	+	0.997731i	$0.478553\pi$
$61$	−56.7700	+	64.7337i	−0.930655	+	1.06121i	−0.997983	+	0.0634780i	$0.979781\pi$
$62$	11.0514	−	7.38433i	0.178249	−	0.119102i
$63$	−49.9395	−	48.2962i	−0.792690	−	0.766606i
$64$	50.0051	−	50.0051i	0.781329	−	0.781329i
$65$	64.4517	−	31.7840i	0.991564	−	0.488985i
$66$	36.3047	−	30.3061i	0.550071	−	0.459184i
$67$	0.708666	−	0.409148i	0.0105771	−	0.00610669i	−0.494702	−	0.869063i	$-0.664723\pi$
$67$	0.708666	−	0.409148i	0.0105771	−	0.00610669i	0.505279	+	0.862956i	$0.331390\pi$
$68$	−4.40875	+	10.0162i	−0.0648346	+	0.147297i
$69$	−56.0589	+	107.022i	−0.812447	+	1.55105i
$70$	57.3187	+	74.6992i	0.818839	+	1.06713i
$71$	−46.3428	+	69.3569i	−0.652715	+	0.976858i	0.346531	+	0.938039i	$0.387360\pi$
$71$	−46.3428	+	69.3569i	−0.652715	+	0.976858i	−0.999246	+	0.0388191i	$0.987640\pi$
$72$	−72.0812	+	25.8207i	−1.00113	+	0.358620i
$73$	25.5163	+	128.279i	0.349539	+	1.75725i	0.610610	+	0.791931i	$0.290924\pi$
$73$	25.5163	+	128.279i	0.349539	+	1.75725i	−0.261071	+	0.965320i	$0.584076\pi$
$74$	−71.6321	+	4.69501i	−0.968001	+	0.0634461i
$75$	8.96750	−	57.2926i	0.119567	−	0.763901i
$76$	−12.1453	−	9.31943i	−0.159807	−	0.122624i
$77$	40.4347	−	52.6955i	0.525125	−	0.684357i
$78$	−21.3592	−	55.3415i	−0.273835	−	0.709507i
$79$	−2.96806	−	45.2838i	−0.0375704	−	0.573213i	−0.974599	−	0.223959i	$-0.928102\pi$
$79$	−2.96806	−	45.2838i	−0.0375704	−	0.573213i	0.937028	−	0.349254i	$-0.113565\pi$
$80$	84.9615	−	16.8999i	1.06202	−	0.211249i
$81$	80.6157	+	7.88072i	0.995256	+	0.0972928i
$82$	−78.8851	−	52.7093i	−0.962013	−	0.642796i
$83$	14.7523	−	11.3199i	0.177739	−	0.136384i	−0.516061	−	0.856552i	$-0.672602\pi$
$83$	14.7523	−	11.3199i	0.177739	−	0.136384i	0.693800	+	0.720168i	$0.255935\pi$
$84$	−12.5931	+	7.97771i	−0.149918	+	0.0949728i
$85$	−95.4691	+	60.8033i	−1.12317	+	0.715333i
$86$	−14.7339	−	25.5198i	−0.171324	−	0.296742i
$87$	26.9925	−	73.5780i	0.310258	−	0.845724i
$88$	−32.3769	−	65.6539i	−0.367920	−	0.746067i
$89$	−21.9909	−	21.9909i	−0.247089	−	0.247089i	0.572686	−	0.819775i	$-0.305902\pi$
$89$	−21.9909	−	21.9909i	−0.247089	−	0.247089i	−0.819775	+	0.572686i	$0.805902\pi$
$90$	−106.499	−	26.6354i	−1.18332	−	0.295949i
$91$	−46.2877	−	69.2744i	−0.508656	−	0.761258i
$92$	19.4910	+	17.0931i	0.211859	+	0.185795i
$93$	−1.95215	+	21.6776i	−0.0209909	+	0.233093i
$94$	66.4126	−	86.5505i	0.706517	−	0.920750i
$95$	−50.8959	−	149.934i	−0.535746	−	1.57826i
$96$	3.25193	+	30.4081i	0.0338743	+	0.316751i
$97$	24.1747	−	71.2163i	0.249224	−	0.734189i	−0.748268	−	0.663397i	$-0.769114\pi$
$97$	24.1747	−	71.2163i	0.249224	−	0.734189i	0.997491	−	0.0707918i	$-0.0225526\pi$
$98$	13.7135	−	13.7135i	0.139934	−	0.139934i
$99$	1.29526	+	77.4312i	0.0130835	+	0.782133i
$100$	−11.4963	−	4.76190i	−0.114963	−	0.0476190i
$101$	−149.453	−	86.2868i	−1.47973	−	0.854325i	−0.479998	−	0.877270i	$-0.659363\pi$
$101$	−149.453	−	86.2868i	−1.47973	−	0.854325i	−0.999737	+	0.0229444i	$0.992696\pi$
$102$	42.9206	+	82.9907i	0.420791	+	0.813634i
$103$	21.9079	+	37.9457i	0.212698	+	0.368404i	0.952558	−	0.304357i	$-0.0984415\pi$
$103$	21.9079	+	37.9457i	0.212698	+	0.368404i	−0.739860	+	0.672761i	$0.765108\pi$
$104$	−91.0371	+	11.9853i	−0.875357	+	0.115243i
$105$	−154.139	−	3.75585i	−1.46800	−	0.0357700i
$106$	80.7869	−	21.6468i	0.762140	−	0.204215i
$107$	−30.6268	−	153.971i	−0.286231	−	1.43898i	−0.809653	−	0.586909i	$-0.800345\pi$
$107$	−30.6268	−	153.971i	−0.286231	−	1.43898i	0.523421	−	0.852074i	$-0.324655\pi$
$108$	5.71240	−	16.4153i	0.0528926	−	0.151994i
$109$	8.36116	−	42.0344i	0.0767079	−	0.385637i	−0.923291	−	0.384101i	$-0.874511\pi$
$109$	8.36116	−	42.0344i	0.0767079	−	0.385637i	0.999999	−	0.00153520i	$-0.000488671\pi$
$110$	13.6996	−	104.059i	0.124542	−	0.945991i
$111$	67.6702	−	96.1214i	0.609641	−	0.865958i
$112$	−32.2828	−	95.1020i	−0.288239	−	0.849125i
$113$	78.1391	+	38.5339i	0.691496	+	0.341008i	0.753851	−	0.657046i	$-0.228194\pi$
$113$	78.1391	+	38.5339i	0.691496	+	0.341008i	−0.0623544	+	0.998054i	$0.519861\pi$
$114$	−127.035	+	30.7429i	−1.11435	+	0.269675i
$115$	69.3978	+	258.996i	0.603459	+	2.25214i
$116$	−13.9830	−	9.34311i	−0.120543	−	0.0805441i
$117$	92.4939	+	29.6817i	0.790546	+	0.253689i
$118$		−	80.2238i		−	0.679863i
$119$	84.3379	+	100.536i	0.708721	+	0.844841i
$120$	−78.8476	+	150.528i	−0.657063	+	1.25440i
$121$	46.5579	−	6.12947i	0.384776	−	0.0506568i
$122$	157.399	+	10.3165i	1.29016	+	0.0845614i
$123$	148.289	−	46.3406i	1.20560	−	0.376753i
$124$	4.42253	+	1.50125i	0.0356655	+	0.0121068i
$125$	20.9733	+	31.3888i	0.167787	+	0.251111i
$126$	−14.4999	+	126.446i	−0.115078	+	1.00354i
$127$	−139.876	+	57.9384i	−1.10138	+	0.456208i	−0.857962	−	0.513713i	$-0.828270\pi$
$127$	−139.876	+	57.9384i	−1.10138	+	0.456208i	−0.243421	+	0.969921i	$0.578270\pi$
$128$	−88.0210	−	11.5882i	−0.687664	−	0.0905327i
$129$	47.6743	+	7.46204i	0.369568	+	0.0578453i
$130$	−118.076	−	58.2287i	−0.908278	−	0.447913i
$131$	48.5728	+	55.3866i	0.370785	+	0.422799i	0.906900	−	0.421346i	$-0.138442\pi$
$131$	48.5728	+	55.3866i	0.370785	+	0.422799i	−0.536115	+	0.844145i	$0.680109\pi$
$132$	16.2143	+	3.63795i	0.122836	+	0.0275602i
$133$	−164.641	+	81.1919i	−1.23790	+	0.610465i
$134$	−1.38501	−	0.573692i	−0.0103359	−	0.00428128i
$135$	143.451	−	108.344i	1.06260	−	0.802547i
$136$	140.485	−	34.3574i	1.03298	−	0.252628i
$137$	22.3003	−	38.6253i	0.162776	−	0.281937i	−0.773087	−	0.634300i	$-0.781288\pi$
$137$	22.3003	−	38.6253i	0.162776	−	0.281937i	0.935863	+	0.352363i	$0.114622\pi$
$138$	218.069	−	37.8795i	1.58021	−	0.274489i
$139$	−192.093	−	12.5904i	−1.38196	−	0.0905786i	−0.643796	−	0.765197i	$-0.722641\pi$
$139$	−192.093	−	12.5904i	−1.38196	−	0.0905786i	−0.738167	+	0.674618i	$0.764308\pi$
$140$	−8.56300	+	31.9575i	−0.0611643	+	0.228268i
$141$	42.0201	+	173.635i	0.298015	+	1.23145i
$142$	152.490	−	9.99470i	1.07387	−	0.0703852i
$143$	−18.1186	+	91.0882i	−0.126703	+	0.636981i
$144$	98.4362	+	63.4175i	0.683584	+	0.440399i
$145$	−66.5631	−	160.697i	−0.459056	−	1.10826i
$146$	157.988	−	180.151i	1.08211	−	1.23391i
$147$	3.37707	+	31.5782i	0.0229732	+	0.214818i
$148$	−16.6315	−	18.9646i	−0.112375	−	0.128139i
$149$	−94.6014	−	25.3484i	−0.634909	−	0.170123i	−0.0730126	−	0.997331i	$-0.523261\pi$
$149$	−94.6014	−	25.3484i	−0.634909	−	0.170123i	−0.561896	+	0.827208i	$0.689928\pi$
$150$	−93.2719	+	50.8623i	−0.621813	+	0.339082i
$151$	−8.65315	+	6.63980i	−0.0573056	+	0.0439722i	−0.637017	−	0.770850i	$-0.719832\pi$
$151$	−8.65315	+	6.63980i	−0.0573056	+	0.0439722i	0.579711	+	0.814822i	$0.303165\pi$
$152$			202.316i			1.33103i
$153$	−149.902	−	30.6315i	−0.979754	−	0.200206i
$154$	−121.684			−0.790158
$155$	29.4063	+	38.3230i	0.189718	+	0.247245i
$156$	10.8587	−	17.7923i	0.0696070	−	0.114053i
$157$	3.38326	−	12.6265i	0.0215494	−	0.0804236i	−0.954314	−	0.298806i	$-0.903411\pi$
$157$	3.38326	−	12.6265i	0.0215494	−	0.0804236i	0.975863	+	0.218383i	$0.0700782\pi$
$158$	−62.5068	+	54.8170i	−0.395613	+	0.346943i
$159$	−55.4786	+	125.219i	−0.348922	+	0.787542i
$160$	51.0284	+	44.7507i	0.318928	+	0.279692i
$161$	287.203	−	118.963i	1.78387	−	0.738902i
$162$	−78.4532	−	125.958i	−0.484279	−	0.777522i
$163$	−209.611	−	41.6941i	−1.28595	−	0.255792i	−0.495659	−	0.868517i	$-0.665073\pi$
$163$	−209.611	−	41.6941i	−1.28595	−	0.255792i	−0.790296	+	0.612725i	$0.790073\pi$
$164$	−2.18035	−	33.2658i	−0.0132948	−	0.202840i
$165$	118.535	+	124.456i	0.718395	+	0.754279i
$166$	−32.9053	−	8.81695i	−0.198225	−	0.0531142i
$167$	−14.6723	+	223.856i	−0.0878580	+	1.34045i	0.695340	+	0.718681i	$0.255254\pi$
$167$	−14.6723	+	223.856i	−0.0878580	+	1.34045i	−0.783198	+	0.621773i	$0.786413\pi$
$168$	184.957	+	67.8525i	1.10094	+	0.403884i
$169$	−45.4704	−	26.2524i	−0.269056	−	0.155339i
$170$	194.846	+	70.9464i	1.14615	+	0.417332i
$171$	91.4397	−	193.515i	0.534735	−	1.13167i
$172$	3.96248	−	9.56627i	0.0230377	−	0.0556178i
$173$	−86.1545	−	174.704i	−0.498003	−	1.00985i	−0.990238	−	0.139388i	$-0.955487\pi$
$173$	−86.1545	−	174.704i	−0.498003	−	1.00985i	0.492235	−	0.870462i	$-0.336180\pi$
$174$	−137.044	+	42.8267i	−0.787610	+	0.246130i
$175$	−112.184	+	98.3827i	−0.641051	+	0.562187i
$176$	−49.5153	+	100.407i	−0.281337	+	0.570495i
$177$	102.244	+	82.4881i	0.577649	+	0.466034i
$178$	−7.43677	+	56.4879i	−0.0417796	+	0.317348i
$179$	−18.8858	−	45.5943i	−0.105507	−	0.254717i	0.862306	−	0.506388i	$-0.169020\pi$
$179$	−18.8858	−	45.5943i	−0.105507	−	0.254717i	−0.967813	+	0.251672i	$0.919020\pi$
$180$	−15.3558	−	35.3863i	−0.0853100	−	0.196590i
$181$	263.775	−	176.249i	1.45732	−	0.973749i	0.461056	−	0.887371i	$-0.347471\pi$
$181$	263.775	−	176.249i	1.45732	−	0.973749i	0.996262	−	0.0863777i	$-0.0275292\pi$
$182$	−49.0630	+	144.535i	−0.269577	+	0.794148i
$183$	−174.990	+	189.995i	−0.956229	+	1.03822i
$184$	22.4076	−	341.873i	0.121780	−	1.85801i
$185$	−34.0531	−	258.659i	−0.184071	−	1.39816i
$186$	33.6841	−	21.3388i	0.181097	−	0.114725i
$187$	12.7678	−	145.721i	0.0682768	−	0.779257i
$188$	38.3339			0.203904
$189$	−146.245	−	148.495i	−0.773781	−	0.785688i
$190$	−161.157	+	241.189i	−0.848197	+	1.26942i
$191$	−100.808	+	27.0113i	−0.527788	+	0.141420i	−0.512867	−	0.858468i	$-0.671417\pi$
$191$	−100.808	+	27.0113i	−0.527788	+	0.141420i	−0.0149216	+	0.999889i	$0.504750\pi$
$192$	153.625	−	146.316i	0.800130	−	0.762065i
$193$	−101.654	+	206.133i	−0.526703	+	1.06805i	0.457203	+	0.889362i	$0.348851\pi$
$193$	−101.654	+	206.133i	−0.526703	+	1.06805i	−0.983906	+	0.178686i	$0.942815\pi$
$194$	−130.469	+	44.2883i	−0.672521	+	0.228290i
$195$	195.620	−	90.6138i	1.00318	−	0.464686i
$196$	6.75635	+	0.889491i	0.0344712	+	0.00453822i
$197$	−235.788	−	46.9012i	−1.19689	−	0.238077i	−0.443883	−	0.896085i	$-0.646400\pi$
$197$	−235.788	−	46.9012i	−1.19689	−	0.238077i	−0.753012	+	0.658007i	$0.771400\pi$
$198$	111.096	−	88.2383i	0.561093	−	0.445648i
$199$	−4.90692	+	0.976047i	−0.0246579	+	0.00490476i	−0.207404	−	0.978255i	$-0.566501\pi$
$199$	−4.90692	+	0.976047i	−0.0246579	+	0.00490476i	0.182746	+	0.983160i	$0.441501\pi$
$200$	42.5623	+	158.845i	0.212811	+	0.794223i
$201$	2.15527	−	1.17529i	0.0107227	−	0.00584723i
$202$	41.2668	+	313.452i	0.204291	+	1.55174i
$203$	−174.642	+	100.829i	−0.860303	+	0.496696i
$204$	−13.9543	+	29.7174i	−0.0684034	+	0.145673i
$205$	172.401	−	298.607i	0.840980	−	1.45662i
$206$	30.7184	−	74.1609i	0.149119	−	0.360004i
$207$	−175.948	+	316.874i	−0.849989	+	1.53079i
$208$	99.2975	+	99.2975i	0.477392	+	0.477392i
$209$	193.770	+	65.7760i	0.927129	+	0.314718i
$210$	166.446	+	228.220i	0.792602	+	1.08676i
$211$	−5.62798	+	1.91044i	−0.0266729	+	0.00905423i	−0.334744	−	0.942309i	$-0.608650\pi$
$211$	−5.62798	+	1.91044i	−0.0266729	+	0.00905423i	0.308071	+	0.951363i	$0.400317\pi$
$212$	23.3154	+	17.8906i	0.109979	+	0.0843895i
$213$	−144.056	+	204.622i	−0.676317	+	0.960668i
$214$	−189.630	+	216.231i	−0.886121	+	1.01043i
$215$	89.0460	−	59.4986i	0.414168	−	0.276738i
$216$	−218.066	+	72.1715i	−1.00957	+	0.334127i
$217$	39.6006	−	39.6006i	0.182491	−	0.182491i
$218$	−70.4190	+	34.7268i	−0.323023	+	0.159297i
$219$	67.1519	+	386.588i	0.306630	+	1.76524i
$220$	31.9390	−	18.4400i	0.145177	−	0.0838183i
$221$	−167.937	−	73.9199i	−0.759898	−	0.334479i
$222$	−215.176	+	8.84613i	−0.969259	+	0.0398474i
$223$	128.163	+	167.025i	0.574721	+	0.748990i	0.986762	−	0.162175i	$-0.0518508\pi$
$223$	128.163	+	167.025i	0.574721	+	0.748990i	−0.412041	+	0.911165i	$0.635184\pi$
$224$	43.7169	−	65.4269i	0.195165	−	0.292084i
$225$	31.0813	−	171.171i	0.138139	−	0.760762i
$226$	−31.1387	−	156.545i	−0.137782	−	0.692677i
$227$	−107.051	+	7.01649i	−0.471590	+	0.0309097i	−0.299346	−	0.954145i	$-0.596768\pi$
$227$	−107.051	+	7.01649i	−0.471590	+	0.0309097i	−0.172244	+	0.985054i	$0.555102\pi$
$228$	−35.7441	−	28.8376i	−0.156772	−	0.126481i
$229$	−37.1795	−	28.5289i	−0.162356	−	0.124580i	0.524388	−	0.851479i	$-0.324294\pi$
$229$	−37.1795	−	28.5289i	−0.162356	−	0.124580i	−0.686744	+	0.726899i	$0.740961\pi$
$230$	299.037	−	389.713i	1.30016	−	1.69440i
$231$	125.119	−	155.085i	0.541640	−	0.671362i
$232$	14.5358	+	221.773i	0.0626543	+	0.955919i
$233$	71.1737	−	14.1573i	0.305467	−	0.0607611i	−0.0399770	−	0.999201i	$-0.512728\pi$
$233$	71.1737	−	14.1573i	0.305467	−	0.0607611i	0.345444	+	0.938440i	$0.387728\pi$
$234$	−60.0142	−	167.536i	−0.256471	−	0.715967i
$235$	329.663	+	220.274i	1.40282	+	0.937336i
$236$	22.3640	−	17.1605i	0.0947628	−	0.0727140i
$237$	−5.59228	−	136.028i	−0.0235961	−	0.573958i
$238$	52.0639	−	234.703i	0.218756	−	0.986147i
$239$	−42.2877	−	73.2444i	−0.176936	−	0.306462i	0.763894	−	0.645342i	$-0.223285\pi$
$239$	−42.2877	−	73.2444i	−0.176936	−	0.306462i	−0.940830	+	0.338880i	$0.889952\pi$
$240$	256.044	−	44.4758i	1.06685	−	0.185316i
$241$	38.0077	+	77.0720i	0.157708	+	0.319801i	0.961358	−	0.275302i	$-0.0887779\pi$
$241$	38.0077	+	77.0720i	0.157708	+	0.319801i	−0.803649	+	0.595103i	$0.797111\pi$
$242$	−60.8328	−	60.8328i	−0.251375	−	0.251375i
$243$	241.199	+	29.5264i	0.992590	+	0.121508i
$244$	30.7930	+	46.0850i	0.126201	+	0.188873i
$245$	52.9920	+	46.4727i	0.216294	+	0.189685i
$246$	−232.733	−	163.846i	−0.946069	−	0.666040i
$247$	156.256	−	203.636i	0.632614	−	0.824438i
$248$	−19.8399	−	58.4464i	−0.0799995	−	0.235671i
$249$	45.0711	−	32.8715i	0.181009	−	0.132014i
$250$	22.2308	−	65.4900i	0.0889234	−	0.261960i
$251$	170.940	−	170.940i	0.681036	−	0.681036i	−0.279198	−	0.960234i	$-0.590069\pi$
$251$	170.940	−	170.940i	0.681036	−	0.681036i	0.960234	+	0.279198i	$0.0900685\pi$
$252$	−38.3511	+	23.0058i	−0.152187	+	0.0912927i
$253$	−320.148	−	132.609i	−1.26541	−	0.524148i
$254$	240.207	+	138.683i	0.945696	+	0.545998i
$255$	−290.766	+	175.379i	−1.14026	+	0.687761i
$256$	−60.1123	−	104.117i	−0.234814	−	0.406709i
$257$	−146.131	+	19.2385i	−0.568602	+	0.0748578i	−0.409345	−	0.912379i	$-0.634243\pi$
$257$	−146.131	+	19.2385i	−0.568602	+	0.0748578i	−0.159256	+	0.987237i	$0.550910\pi$
$258$	−42.3236	−	77.6135i	−0.164045	−	0.300827i
$259$	−292.164	+	78.2851i	−1.12805	+	0.302259i
$260$	−9.02500	−	45.3717i	−0.0347115	−	0.174507i
$261$	86.3303	−	218.696i	0.330767	−	0.837915i
$262$	26.3296	−	132.368i	0.100494	−	0.505220i
$263$	0.992679	−	7.54015i	0.00377445	−	0.0286698i	−0.989454	−	0.144847i	$-0.953731\pi$
$263$	0.992679	−	7.54015i	0.00377445	−	0.0286698i	0.993228	+	0.116178i	$0.0370642\pi$
$264$	−92.3041	−	199.269i	−0.349637	−	0.754808i
$265$	97.7051	+	287.830i	0.368698	+	1.08615i
$266$	301.624	+	148.744i	1.13392	+	0.559189i
$267$	−64.3462	−	67.5603i	−0.240997	−	0.253035i
$268$	−0.136337	−	0.508818i	−0.000508722	−	0.00189858i
$269$	−362.164	−	241.990i	−1.34633	−	0.899592i	−0.347066	−	0.937841i	$-0.612822\pi$
$269$	−362.164	−	241.990i	−1.34633	−	0.899592i	−0.999268	+	0.0382486i	$0.987822\pi$
$270$	−317.455	−	87.6652i	−1.17576	−	0.324686i
$271$			319.484i			1.17891i	0.807802	+	0.589455i	$0.200657\pi$
$271$			319.484i			1.17891i	−0.807802	+	0.589455i	$0.799343\pi$
$272$	−172.478	−	138.465i	−0.634110	−	0.509061i
$273$	−133.759	−	211.144i	−0.489961	−	0.773422i
$274$	−81.0099	+	10.6652i	−0.295657	+	0.0389239i
$275$	165.973	+	10.8784i	0.603536	+	0.0395579i
$276$	57.2065	+	52.6886i	0.207270	+	0.190901i
$277$	−344.959	−	117.098i	−1.24534	−	0.422735i	−0.380497	−	0.924782i	$-0.624247\pi$
$277$	−344.959	−	117.098i	−1.24534	−	0.422735i	−0.864840	+	0.502047i	$0.832580\pi$
$278$	195.934	+	293.235i	0.704797	+	1.05480i
$279$	−7.43888	+	64.8709i	−0.0266627	+	0.232512i
$280$	403.955	−	167.323i	1.44269	−	0.597584i
$281$	86.0731	+	11.3317i	0.306310	+	0.0403265i	0.282114	−	0.959381i	$-0.408964\pi$
$281$	86.0731	+	11.3317i	0.306310	+	0.0403265i	0.0241956	+	0.999707i	$0.492298\pi$
$282$	205.503	−	254.721i	0.728736	−	0.903267i
$283$	346.912	+	171.078i	1.22584	+	0.604517i	0.935811	−	0.352501i	$-0.114669\pi$
$283$	346.912	+	171.078i	1.22584	+	0.604517i	0.290028	+	0.957018i	$0.406335\pi$
$284$	35.4050	+	40.3717i	0.124665	+	0.142154i
$285$	−141.685	−	453.389i	−0.497142	−	1.59084i
$286$	152.597	−	75.2527i	0.533557	−	0.263121i
$287$	−369.325	−	152.979i	−1.28685	−	0.533029i
$288$	7.53073	+	91.4349i	0.0261484	+	0.317482i
$289$	275.602	+	86.9746i	0.953640	+	0.300950i
$290$	−159.328	+	275.964i	−0.549406	+	0.951600i
$291$	77.7069	−	211.819i	0.267034	−	0.727900i
$292$	84.0156	+	5.50667i	0.287725	+	0.0188585i
$293$	91.3054	−	340.756i	0.311622	−	1.16299i	−0.615471	−	0.788160i	$-0.711034\pi$
$293$	91.3054	−	340.756i	0.311622	−	1.16299i	0.927093	−	0.374831i	$-0.122299\pi$
$294$	42.1305	−	40.1262i	0.143301	−	0.136484i
$295$	290.933	−	19.0688i	0.986214	−	0.0646399i
$296$	−65.0342	+	326.949i	−0.219710	+	1.10456i
$297$	−1.77388	+	232.319i	−0.00597266	+	0.782220i
$298$	68.6628	+	165.767i	0.230412	+	0.556264i
$299$	−286.595	+	326.799i	−0.958510	+	1.09297i
$300$	−34.1305	−	15.1216i	−0.113768	−	0.0504053i
$301$	−81.8662	−	93.3505i	−0.271981	−	0.310135i
$302$	19.3010	+	5.17168i	0.0639105	+	0.0171248i
$303$	−441.921	−	269.705i	−1.45848	−	0.890117i
$304$	245.471	−	188.357i	0.807470	−	0.619594i
$305$			573.264i			1.87955i
$306$	122.659	+	252.035i	0.400846	+	0.823643i
$307$	−268.202			−0.873622			−0.436811	−	0.899553i	$-0.643892\pi$
$307$	−268.202			−0.873622			−0.436811	+	0.899553i	$0.643892\pi$
$308$	−26.0293	−	33.9220i	−0.0845106	−	0.110136i
$309$	62.9313	+	115.404i	0.203661	+	0.373476i
$310$	22.9043	−	85.4801i	0.0738849	−	0.275742i
$311$	−61.0277	+	53.5199i	−0.196231	+	0.172090i	−0.751823	−	0.659365i	$-0.770825\pi$
$311$	−61.0277	+	53.5199i	−0.196231	+	0.172090i	0.555592	+	0.831455i	$0.312492\pi$
$312$	−273.906	+	29.2923i	−0.877904	+	0.0938856i
$313$	−126.766	−	111.170i	−0.405002	−	0.355177i	0.432479	−	0.901644i	$-0.357639\pi$
$313$	−126.766	−	111.170i	−0.405002	−	0.355177i	−0.837481	+	0.546467i	$0.815972\pi$
$314$	−22.1250	+	9.16446i	−0.0704617	+	0.0291862i
$315$	−462.007	−	22.5284i	−1.46669	−	0.0715188i
$316$	−28.6521	−	5.69925i	−0.0906711	−	0.0180356i
$317$	−0.603224	−	9.20342i	−0.00190291	−	0.0290329i	0.996802	−	0.0799126i	$-0.0254641\pi$
$317$	−0.603224	−	9.20342i	−0.00190291	−	0.0290329i	−0.998705	+	0.0508798i	$0.983797\pi$
$318$	243.871	−	59.0173i	0.766889	−	0.185589i
$319$	217.131	+	58.1802i	0.680662	+	0.182383i
$320$	30.7947	−	469.837i	0.0962336	−	1.46824i
$321$	−80.6011	−	464.015i	−0.251094	−	1.44553i
$322$	−493.210	−	284.755i	−1.53171	−	0.884332i
$323$	−209.774	+	345.598i	−0.649456	+	1.06996i
$324$	18.3317	−	48.8140i	0.0565794	−	0.150660i
$325$	79.8411	−	192.754i	0.245665	−	0.593088i
$326$	173.170	+	351.154i	0.531197	+	1.07716i
$327$	28.1478	−	125.455i	0.0860790	−	0.383654i
$328$	−331.239	+	290.489i	−1.00987	+	0.885636i
$329$	203.307	−	412.267i	0.617956	−	1.25309i
$330$	48.6911	−	311.083i	0.147549	−	0.942677i
$331$	43.0652	−	327.112i	0.130106	−	0.988255i	−0.794482	−	0.607287i	$-0.792258\pi$
$331$	43.0652	−	327.112i	0.130106	−	0.988255i	0.924588	−	0.380968i	$-0.124409\pi$
$332$	−4.58081	−	11.0590i	−0.0137976	−	0.0333104i
$333$	209.975	−	283.333i	0.630554	−	0.850851i
$334$	341.723	−	228.332i	1.02312	−	0.683628i
$335$	1.75129	−	5.15915i	0.00522774	−	0.0154004i
$336$	−89.8697	−	287.580i	−0.267469	−	0.855894i
$337$	−20.6488	+	315.039i	−0.0612723	+	0.934835i	0.850978	+	0.525202i	$0.176010\pi$
$337$	−20.6488	+	315.039i	−0.0612723	+	0.934835i	−0.912250	+	0.409634i	$0.865657\pi$
$338$	12.5552	+	95.3663i	0.0371456	+	0.282149i
$339$	231.532	+	121.278i	0.682984	+	0.357751i
$340$	21.9014	+	69.4933i	0.0644158	+	0.204392i
$341$	−62.4279			−0.183073
$342$	−383.240	+	82.9178i	−1.12058	+	0.242450i
$343$	−164.740	+	246.551i	−0.480292	+	0.718808i
$344$	−132.178	+	35.4169i	−0.384238	+	0.102956i
$345$	189.205	+	781.830i	0.548420	+	2.26617i
$346$	−157.836	+	320.060i	−0.456173	+	0.925028i
$347$	−452.392	+	153.566i	−1.30372	+	0.442554i	−0.885013	−	0.465566i	$-0.845851\pi$
$347$	−452.392	+	153.566i	−1.30372	+	0.442554i	−0.418710	+	0.908120i	$0.637517\pi$
$348$	−41.2536	−	29.0429i	−0.118545	−	0.0834565i
$349$	660.589	+	86.9681i	1.89280	+	0.249192i	0.985298	−	0.170846i	$-0.0546501\pi$
$349$	660.589	+	86.9681i	1.89280	+	0.249192i	0.907506	+	0.420038i	$0.137983\pi$
$350$	268.106	+	53.3297i	0.766018	+	0.152371i
$351$	275.230	+	95.7778i	0.784132	+	0.272871i
$352$	−86.0292	+	17.1123i	−0.244401	+	0.0486144i
$353$	−87.2369	−	325.572i	−0.247130	−	0.922302i	−0.972301	−	0.233733i	$-0.924906\pi$
$353$	−87.2369	−	325.572i	−0.247130	−	0.922302i	0.725171	−	0.688569i	$-0.241761\pi$
$354$	5.86259	−	240.600i	0.0165610	−	0.679661i
$355$	72.4920	+	550.631i	0.204203	+	1.55107i
$356$	−17.3379	+	10.0101i	−0.0487021	+	0.0281182i
$357$	245.592	+	307.682i	0.687931	+	0.861854i
$358$	−45.2057	+	78.2985i	−0.126273	+	0.218711i
$359$	204.342	−	493.325i	0.569197	−	1.37416i	−0.333036	−	0.942914i	$-0.608073\pi$
$359$	204.342	−	493.325i	0.569197	−	1.37416i	0.902233	−	0.431249i	$-0.141927\pi$
$360$	−247.473	+	445.688i	−0.687424	+	1.23802i
$361$	−144.637	−	144.637i	−0.400655	−	0.400655i
$362$	−550.342	−	186.816i	−1.52028	−	0.516066i
$363$	140.080	−	14.9806i	0.385896	−	0.0412688i
$364$	−50.7870	+	17.2399i	−0.139525	+	0.0473623i
$365$	690.873	+	530.126i	1.89280	+	1.45240i
$366$	471.304	+	42.4427i	1.28771	+	0.115964i
$367$	−314.905	+	359.080i	−0.858050	+	0.978419i	−0.999934	−	0.0114643i	$-0.996351\pi$
$367$	−314.905	+	359.080i	−0.858050	+	0.978419i	0.141884	+	0.989883i	$0.454684\pi$
$368$	−435.659	+	291.098i	−1.18385	+	0.791027i
$369$	448.121	−	128.144i	1.21442	−	0.347274i
$370$	−337.966	+	337.966i	−0.913420	+	0.913420i
$371$	316.062	−	155.864i	0.851919	−	0.420120i
$372$	13.1539	+	4.82559i	0.0353600	+	0.0129720i
$373$	552.968	−	319.256i	1.48249	−	0.855915i	0.482686	−	0.875793i	$-0.339661\pi$
$373$	552.968	−	319.256i	1.48249	−	0.855915i	0.999802	+	0.0198782i	$0.00632785\pi$
$374$	−226.035	+	143.959i	−0.604372	+	0.384918i
$375$	60.6075	+	95.6712i	0.161620	+	0.255123i
$376$	−308.402	−	401.918i	−0.820219	−	1.06893i
$377$	156.653	−	234.447i	0.415524	−	0.621876i
$378$	−52.7271	+	378.167i	−0.139490	+	1.00044i
$379$	109.637	+	551.181i	0.289279	+	1.45430i	0.802812	+	0.596233i	$0.203336\pi$
$379$	109.637	+	551.181i	0.289279	+	1.45430i	−0.513533	+	0.858070i	$0.671664\pi$
$380$	−101.709	+	6.66638i	−0.267656	+	0.0175431i
$381$	−423.736	+	163.542i	−1.11217	+	0.429243i
$382$	151.686	+	116.392i	0.397083	+	0.304692i
$383$	−296.832	+	386.839i	−0.775018	+	1.01002i	0.224351	+	0.974508i	$0.427974\pi$
$383$	−296.832	+	386.839i	−0.775018	+	1.01002i	−0.999369	+	0.0355152i	$0.988693\pi$
$384$	−263.138	−	41.1866i	−0.685255	−	0.107257i
$385$	−28.9237	−	441.291i	−0.0751266	−	1.14621i
$386$	412.971	−	82.1450i	1.06987	−	0.212811i
$387$	142.435	+	25.8634i	0.368050	+	0.0668306i
$388$	−40.2547	−	26.8973i	−0.103749	−	0.0693229i
$389$	−88.7316	+	68.0862i	−0.228102	+	0.175029i	−0.716489	−	0.697598i	$-0.754252\pi$
$389$	−88.7316	+	68.0862i	−0.228102	+	0.175029i	0.488387	+	0.872627i	$0.337585\pi$
$390$	−349.868	−	183.263i	−0.897098	−	0.469905i
$391$	392.754	−	560.758i	1.00449	−	1.43416i
$392$	−45.0299	−	77.9941i	−0.114872	−	0.198965i
$393$	141.628	+	169.660i	0.360376	+	0.431705i
$394$	194.797	+	395.009i	0.494409	+	1.00256i
$395$	−213.653	−	213.653i	−0.540892	−	0.540892i
$396$	48.3626	+	12.0955i	0.122128	+	0.0305442i
$397$	−315.611	−	472.346i	−0.794991	−	1.18979i	−0.978394	−	0.206750i	$-0.933711\pi$
$397$	−315.611	−	472.346i	−0.794991	−	1.18979i	0.183403	−	0.983038i	$-0.441289\pi$
$398$	6.89110	+	6.04333i	0.0173143	+	0.0151842i
$399$	−499.709	+	231.472i	−1.25240	+	0.580130i
$400$	153.101	−	199.526i	0.382754	−	0.498814i
$401$	223.410	+	658.144i	0.557132	+	1.64126i	0.751055	+	0.660240i	$0.229545\pi$
$401$	223.410	+	658.144i	0.557132	+	1.64126i	−0.193923	+	0.981017i	$0.562121\pi$
$402$	−4.11188	−	1.82178i	−0.0102286	−	0.00453179i
$403$	−25.1708	+	74.1509i	−0.0624587	+	0.183997i
$404$	−78.5539	+	78.5539i	−0.194440	+	0.194440i
$405$	438.143	−	314.452i	1.08184	−	0.776424i
$406$	341.319	+	141.379i	0.840687	+	0.348224i
$407$	291.995	+	168.583i	0.717432	+	0.414209i
$408$	423.841	−	92.7753i	1.03883	−	0.227390i
$409$	−1.12546	−	1.94935i	−0.00275173	−	0.00476613i	0.864646	−	0.502381i	$-0.167543\pi$
$409$	−1.12546	−	1.94935i	−0.00275173	−	0.00476613i	−0.867398	+	0.497615i	$0.834209\pi$
$410$	−626.276	+	82.4508i	−1.52750	+	0.201100i
$411$	69.7039	−	114.212i	0.169596	−	0.277888i
$412$	27.2448	−	7.30022i	0.0661281	−	0.0177190i
$413$	−65.9452	−	331.529i	−0.159674	−	0.802734i
$414$	656.782	−	97.6687i	1.58643	−	0.235915i
$415$	24.1534	−	121.428i	0.0582011	−	0.292597i
$416$	−14.3612	+	109.084i	−0.0345220	+	0.262221i
$417$	−575.187	−	51.7978i	−1.37935	−	0.124215i
$418$	−120.502	−	354.989i	−0.288283	−	0.849255i
$419$	−299.842	−	147.866i	−0.715614	−	0.352902i	0.0477596	−	0.998859i	$-0.484792\pi$
$419$	−299.842	−	147.866i	−0.715614	−	0.352902i	−0.763374	+	0.645957i	$0.776459\pi$
$420$	−28.0168	+	95.2184i	−0.0667066	+	0.226711i
$421$	36.0880	+	134.682i	0.0857197	+	0.319910i	0.995450	−	0.0952906i	$-0.0303780\pi$
$421$	36.0880	+	134.682i	0.0857197	+	0.319910i	−0.909730	+	0.415201i	$0.863711\pi$
$422$	9.05335	+	6.04925i	0.0214534	+	0.0143347i
$423$	113.334	+	523.821i	0.267929	+	1.23835i
$424$		−	388.387i		−	0.916007i
$425$	−91.9952	+	315.471i	−0.216459	+	0.742284i
$426$	458.064	−	18.8316i	1.07527	−	0.0442056i
$427$	658.941	−	86.7512i	1.54319	−	0.203164i
$428$	−100.842	−	6.60955i	−0.235613	−	0.0154429i
$429$	−60.9961	+	271.860i	−0.142182	+	0.633705i
$430$	−185.786	−	63.0660i	−0.432062	−	0.146665i
$431$	306.622	+	458.892i	0.711419	+	1.06471i	0.994410	+	0.105591i	$0.0336734\pi$
$431$	306.622	+	458.892i	0.711419	+	1.06471i	−0.282991	+	0.959123i	$0.591327\pi$
$432$	290.586	+	197.389i	0.672654	+	0.456920i
$433$	−233.620	+	96.7684i	−0.539537	+	0.223484i	−0.635775	−	0.771875i	$-0.719319\pi$
$433$	−233.620	+	96.7684i	−0.539537	+	0.223484i	0.0962373	+	0.995358i	$0.469319\pi$
$434$	−101.722	−	13.3919i	−0.234382	−	0.0308569i
$435$	−187.886	−	486.814i	−0.431923	−	1.11911i
$436$	−24.7440	−	12.2024i	−0.0567523	−	0.0279871i
$437$	631.463	+	720.046i	1.44500	+	1.64770i
$438$	486.988	−	528.746i	1.11185	−	1.20718i
$439$	315.857	−	155.764i	0.719493	−	0.354814i	−0.0454030	−	0.998969i	$-0.514457\pi$
$439$	315.857	−	155.764i	0.719493	−	0.354814i	0.764896	+	0.644154i	$0.222791\pi$
$440$	−450.292	−	186.517i	−1.02339	−	0.423902i
$441$	7.82052	+	94.9533i	0.0177336	+	0.215314i
$442$	79.8559	+	326.525i	0.180669	+	0.738745i
$443$	192.337	−	333.137i	0.434169	−	0.752002i	−0.563059	−	0.826417i	$-0.690376\pi$
$443$	192.337	−	333.137i	0.434169	−	0.752002i	0.997227	+	0.0744147i	$0.0237089\pi$
$444$	−48.4938	−	58.0923i	−0.109220	−	0.130839i
$445$	−206.622	−	13.5427i	−0.464320	−	0.0304331i
$446$	99.8249	−	372.551i	0.223823	−	0.835317i
$447$	−281.868	−	82.9358i	−0.630576	−	0.185539i
$448$	−544.717	+	35.7026i	−1.21589	+	0.0796933i
$449$	−11.4207	+	57.4159i	−0.0254359	+	0.127875i	−0.991417	−	0.130738i	$-0.958265\pi$
$449$	−11.4207	+	57.4159i	−0.0254359	+	0.127875i	0.965981	+	0.258613i	$0.0832654\pi$
$450$	−283.450	+	145.726i	−0.629888	+	0.323835i
$451$	170.527	+	411.690i	0.378110	+	0.912837i
$452$	36.9793	−	42.1668i	0.0818126	−	0.0932894i
$453$	−26.4370	+	19.2811i	−0.0583598	+	0.0425632i
$454$	129.587	+	147.766i	0.285435	+	0.325476i
$455$	−535.821	−	143.573i	−1.17763	−	0.315544i
$456$	−14.7848	+	606.767i	−0.0324229	+	1.33063i
$457$	200.831	−	154.103i	0.439454	−	0.337205i	−0.365220	−	0.930921i	$-0.619006\pi$
$457$	200.831	−	154.103i	0.439454	−	0.337205i	0.804675	+	0.593716i	$0.202340\pi$
$458$			85.8549i			0.187456i
$459$	−447.335	−	102.822i	−0.974586	−	0.224012i
$460$	172.607			0.375232
$461$	336.351	+	438.341i	0.729612	+	0.950849i	0.999929	−	0.0119223i	$-0.00379506\pi$
$461$	336.351	+	438.341i	0.729612	+	0.950849i	−0.270317	+	0.962771i	$0.587128\pi$
$462$	−364.945	−	8.89245i	−0.789924	−	0.0192477i
$463$	152.711	−	569.924i	0.329828	−	1.23094i	−0.579540	−	0.814944i	$-0.696768\pi$
$463$	152.711	−	569.924i	0.329828	−	1.23094i	0.909368	−	0.415992i	$-0.136566\pi$
$464$	255.546	−	224.108i	0.550746	−	0.482991i
$465$	85.3922	+	117.084i	0.183639	+	0.251794i
$466$	−99.9537	−	87.6571i	−0.214493	−	0.188105i
$467$	347.068	−	143.760i	0.743187	−	0.307838i	0.0212286	−	0.999775i	$-0.493242\pi$
$467$	347.068	−	143.760i	0.743187	−	0.307838i	0.721958	+	0.691937i	$0.243242\pi$
$468$	33.8666	−	52.5675i	0.0723646	−	0.112324i
$469$	−6.19523	−	1.23231i	−0.0132094	−	0.00262752i
$470$	−47.5062	−	724.805i	−0.101077	−	1.54214i
$471$	11.0695	−	37.6210i	0.0235021	−	0.0798748i
$472$	−359.844	−	96.4200i	−0.762382	−	0.204280i
$473$	−9.05215	+	138.109i	−0.0191377	+	0.291985i
$474$	−191.471	+	159.834i	−0.403947	+	0.337203i
$475$	−398.105	−	229.846i	−0.838116	−	0.483887i
$476$	76.5651	−	35.6910i	0.160851	−	0.0749810i
$477$	−175.537	+	371.492i	−0.368003	+	0.778809i
$478$	−59.2941	+	143.149i	−0.124046	+	0.299474i
$479$	−272.230	−	552.028i	−0.568330	−	1.15246i	−0.971435	−	0.237305i	$-0.923736\pi$
$479$	−272.230	−	552.028i	−0.568330	−	1.15246i	0.403106	−	0.915153i	$-0.367931\pi$
$480$	149.770	+	137.941i	0.312020	+	0.287378i
$481$	317.973	−	278.855i	0.661066	−	0.579739i
$482$	69.6305	−	141.197i	0.144462	−	0.292939i
$483$	870.046	−	335.796i	1.80134	−	0.695229i
$484$	3.94576	−	29.9710i	0.00815240	−	0.0619236i
$485$	−191.624	−	462.622i	−0.395101	−	0.953859i
$486$	−226.085	−	383.497i	−0.465195	−	0.789088i
$487$	−281.762	+	188.267i	−0.578566	+	0.386585i	−0.810144	−	0.586231i	$-0.800611\pi$
$487$	−281.762	+	188.267i	−0.578566	+	0.386585i	0.231578	+	0.972816i	$0.425611\pi$
$488$	235.451	−	693.616i	0.482481	−	1.42134i
$489$	−625.598	−	140.363i	−1.27934	−	0.287041i
$490$	8.44523	−	128.849i	0.0172352	−	0.262958i
$491$	−7.66237	−	58.2015i	−0.0156056	−	0.118537i	0.981869	−	0.189561i	$-0.0607065\pi$
$491$	−7.66237	−	58.2015i	−0.0156056	−	0.118537i	−0.997475	+	0.0710245i	$0.977373\pi$
$492$	−4.10812	−	99.9270i	−0.00834985	−	0.203104i
$493$	−205.119	+	393.907i	−0.416063	+	0.798999i
$494$	−470.237			−0.951896
$495$	346.405	+	381.920i	0.699808	+	0.771555i
$496$	−52.4424	+	78.4856i	−0.105731	+	0.158237i
$497$	621.956	−	166.653i	1.25142	−	0.335317i
$498$	−98.0423	−	28.8477i	−0.196872	−	0.0579270i
$499$	−75.9480	+	154.007i	−0.152200	+	0.308632i	−0.959597	−	0.281377i	$-0.909209\pi$
$499$	−75.9480	+	154.007i	−0.152200	+	0.308632i	0.807397	+	0.590009i	$0.200876\pi$
$500$	23.0120	−	7.81153i	0.0460240	−	0.0156231i
$501$	−60.3627	+	670.296i	−0.120485	+	1.33792i
$502$	−439.092	−	57.8075i	−0.874685	−	0.115154i
$503$	−13.3014	−	2.64581i	−0.0264441	−	0.00526005i	0.181851	−	0.983326i	$-0.441791\pi$
$503$	−13.3014	−	2.64581i	−0.0264441	−	0.00526005i	−0.208295	+	0.978066i	$0.566791\pi$
$504$	549.748	+	217.013i	1.09077	+	0.430582i
$505$	−1126.93	+	224.161i	−2.23155	+	0.443882i
$506$	164.308	+	613.206i	0.324720	+	1.21187i
$507$	−134.452	−	82.0566i	−0.265192	−	0.161847i
$508$	12.7213	+	96.6281i	0.0250420	+	0.190213i
$509$	38.7169	−	22.3532i	0.0760646	−	0.0439159i	−0.461485	−	0.887148i	$-0.652683\pi$
$509$	38.7169	−	22.3532i	0.0760646	−	0.0439159i	0.537550	+	0.843232i	$0.319350\pi$
$510$	579.180	+	227.015i	1.13565	+	0.445128i
$511$	504.807	−	874.351i	0.987880	−	1.71106i
$512$	−220.186	+	531.577i	−0.430051	+	1.03824i
$513$	288.379	−	573.691i	0.562143	−	1.11831i
$514$	190.935	+	190.935i	0.371469	+	0.371469i
$515$	276.248	+	93.7734i	0.536403	+	0.182084i
$516$	12.5830	−	28.4007i	0.0243856	−	0.0550401i
$517$	−485.207	+	164.706i	−0.938505	+	0.318580i
$518$	439.620	+	337.332i	0.848687	+	0.651221i
$519$	−245.620	−	530.253i	−0.473256	−	1.02168i
$520$	−403.099	+	459.647i	−0.775191	+	0.883936i
$521$	−369.540	+	246.919i	−0.709290	+	0.473933i	−0.857144	−	0.515077i	$-0.827763\pi$
$521$	−369.540	+	246.919i	−0.709290	+	0.473933i	0.147854	+	0.989009i	$0.452763\pi$
$522$	−414.140	+	118.427i	−0.793372	+	0.226872i
$523$	−268.020	+	268.020i	−0.512466	+	0.512466i	−0.915281	−	0.402815i	$-0.868032\pi$
$523$	−268.020	+	268.020i	−0.512466	+	0.512466i	0.402815	+	0.915281i	$0.368032\pi$
$524$	42.5323	−	20.9746i	0.0811685	−	0.0400279i
$525$	−343.641	+	286.862i	−0.654555	+	0.546404i
$526$	−12.0662	+	6.96641i	−0.0229395	+	0.0132441i
$527$	26.7104	−	120.410i	0.0506839	−	0.228482i
$528$	−155.839	+	297.513i	−0.295150	+	0.563472i
$529$	−665.264	−	866.988i	−1.25759	−	1.63892i
$530$	309.375	−	463.012i	0.583726	−	0.873608i
$531$	300.612	+	254.863i	0.566125	+	0.479967i
$532$	23.0542	+	115.901i	0.0433350	+	0.217860i
$533$	557.755	−	36.5572i	1.04645	−	0.0685876i
$534$	−26.4317	+	168.870i	−0.0494976	+	0.316236i
$535$	−829.242	−	636.300i	−1.54998	−	1.18935i
$536$	−4.23793	+	5.52297i	−0.00790658	+	0.0103041i
$537$	−53.3085	−	138.122i	−0.0992710	−	0.257211i
$538$	52.1898	+	796.262i	0.0970070	+	1.48004i
$539$	−89.3396	+	17.7707i	−0.165751	+	0.0329698i
$540$	−43.4678	−	107.249i	−0.0804959	−	0.198610i
$541$	−373.928	−	249.851i	−0.691179	−	0.461831i	0.159719	−	0.987163i	$-0.448941\pi$
$541$	−373.928	−	249.851i	−0.691179	−	0.461831i	−0.850898	+	0.525332i	$0.823941\pi$
$542$	464.349	−	356.307i	0.856732	−	0.657394i
$543$	803.969	−	509.313i	1.48061	−	0.937961i
$544$	3.80261	−	173.253i	0.00699010	−	0.318481i
$545$	−142.676	−	247.121i	−0.261790	−	0.453434i
$546$	−157.708	+	429.890i	−0.288842	+	0.787345i
$547$	−32.2588	−	65.4145i	−0.0589741	−	0.119588i	0.865390	−	0.501099i	$-0.167071\pi$
$547$	−32.2588	−	65.4145i	−0.0589741	−	0.119588i	−0.924364	+	0.381511i	$0.875404\pi$
$548$	−20.3018	−	20.3018i	−0.0370471	−	0.0370471i
$549$	−538.699	+	557.028i	−0.981236	+	1.01462i
$550$	−169.291	−	253.362i	−0.307802	−	0.460658i
$551$	−467.094	−	409.630i	−0.847720	−	0.743431i
$552$	92.1862	−	1023.68i	0.167004	−	1.85449i
$553$	−213.252	+	277.916i	−0.385628	+	0.502560i
$554$	214.524	+	631.968i	0.387228	+	1.14074i
$555$	−83.2268	−	778.236i	−0.149958	−	1.40223i
$556$	−39.8336	+	117.346i	−0.0716431	+	0.211054i
$557$	185.132	−	185.132i	0.332373	−	0.332373i	−0.521114	−	0.853487i	$-0.674483\pi$
$557$	185.132	−	185.132i	0.332373	−	0.332373i	0.853487	+	0.521114i	$0.174483\pi$
$558$	102.582	−	61.5359i	0.183838	−	0.110279i
$559$	160.394	+	66.4374i	0.286931	+	0.118851i
$560$	−579.097	−	334.342i	−1.03410	−	0.597039i
$561$	48.9409	−	436.101i	0.0872387	−	0.777363i
$562$	−79.5238	−	137.739i	−0.141501	−	0.245088i
$563$	521.535	−	68.6614i	0.926349	−	0.121956i	0.347768	−	0.937581i	$-0.386940\pi$
$563$	521.535	−	68.6614i	0.926349	−	0.121956i	0.578582	+	0.815624i	$0.303606\pi$
$564$	114.968	+	2.80137i	0.203843	+	0.00496696i
$565$	560.312	−	150.135i	0.991703	−	0.265726i
$566$	−138.246	−	695.010i	−0.244251	−	1.22793i
$567$	−427.752	−	456.040i	−0.754412	−	0.804304i
$568$	138.444	−	696.006i	0.243740	−	1.22536i
$569$	74.5125	−	565.979i	0.130953	−	0.994690i	−0.792201	−	0.610260i	$-0.791065\pi$
$569$	74.5125	−	565.979i	0.130953	−	0.994690i	0.923154	−	0.384430i	$-0.125602\pi$
$570$	−500.955	+	711.576i	−0.878868	+	1.24838i
$571$	76.1637	+	224.371i	0.133387	+	0.392944i	0.993017	−	0.117972i	$-0.0376395\pi$
$571$	76.1637	+	224.371i	0.133387	+	0.392944i	−0.859630	+	0.510917i	$0.829306\pi$
$572$	53.6201	+	26.4425i	0.0937414	+	0.0462281i
$573$	−304.307	+	73.6431i	−0.531077	+	0.128522i
$574$	189.547	+	707.399i	0.330221	+	1.23240i
$575$	647.262	+	432.486i	1.12567	+	0.752150i
$576$	471.431	−	427.592i	0.818456	−	0.742348i
$577$			356.537i			0.617916i	0.951076	+	0.308958i	$0.0999802\pi$
$577$			356.537i			0.617916i	−0.951076	+	0.308958i	$0.900020\pi$
$578$	−180.955	−	497.568i	−0.313072	−	0.860844i
$579$	−319.934	+	610.788i	−0.552564	+	1.05490i
$580$	−111.012	+	14.6150i	−0.191400	+	0.0251983i
$581$	−143.231	−	9.38783i	−0.246524	−	0.0161581i
$582$	−394.528	+	123.291i	−0.677882	+	0.211840i
$583$	−371.981	−	126.271i	−0.638047	−	0.216588i
$584$	−618.183	−	925.177i	−1.05853	−	1.58421i
$585$	593.309	−	257.465i	1.01420	−	0.440112i
$586$	−597.095	+	247.325i	−1.01893	+	0.422056i
$587$	118.988	+	15.6651i	0.202705	+	0.0266866i	0.231195	−	0.972907i	$-0.425736\pi$
$587$	118.988	+	15.6651i	0.202705	+	0.0266866i	−0.0284898	+	0.999594i	$0.509070\pi$
$588$	20.1980	+	3.16142i	0.0343504	+	0.00537657i
$589$	154.742	+	76.3105i	0.262721	+	0.129559i
$590$	−352.181	−	401.585i	−0.596916	−	0.680653i
$591$	−703.728	−	157.893i	−1.19074	−	0.267162i
$592$	457.236	−	225.484i	0.772358	−	0.380885i
$593$	673.990	+	279.176i	1.13658	+	0.470785i	0.870011	−	0.493032i	$-0.164111\pi$
$593$	673.990	+	279.176i	1.13658	+	0.470785i	0.266565	+	0.963817i	$0.414111\pi$
$594$	339.639	−	256.518i	0.571782	−	0.431848i
$595$	863.531	+	133.023i	1.45131	+	0.223569i
$596$	−31.5233	+	54.6000i	−0.0528915	+	0.0916107i
$597$	−14.7877	+	2.56868i	−0.0247701	+	0.00430265i
$598$	794.606	+	52.0812i	1.32877	+	0.0870924i
$599$	185.625	−	692.762i	0.309892	−	1.15653i	−0.618760	−	0.785580i	$-0.712365\pi$
$599$	185.625	−	692.762i	0.309892	−	1.15653i	0.928652	−	0.370952i	$-0.120968\pi$
$600$	116.041	+	479.502i	0.193401	+	0.799171i
$601$	−716.810	+	46.9822i	−1.19270	+	0.0781734i	−0.648786	−	0.760971i	$-0.724723\pi$
$601$	−716.810	+	46.9822i	−1.19270	+	0.0781734i	−0.543909	+	0.839144i	$0.683056\pi$
$602$	−44.3767	+	223.097i	−0.0737155	+	0.370593i
$603$	6.54977	−	3.36733i	0.0108620	−	0.00558429i
$604$	2.68692	+	6.48681i	0.00444855	+	0.0107397i
$605$	206.152	−	235.071i	0.340747	−	0.388547i
$606$	100.857	+	943.093i	0.166431	+	1.55626i
$607$	147.256	+	167.913i	0.242596	+	0.276627i	0.860306	−	0.509779i	$-0.170273\pi$
$607$	147.256	+	167.913i	0.242596	+	0.276627i	−0.617710	+	0.786406i	$0.711939\pi$
$608$	234.162	+	62.7434i	0.385134	+	0.103196i
$609$	−531.138	+	289.636i	−0.872147	+	0.475593i
$610$	833.200	−	639.337i	1.36590	−	1.04809i
$611$			642.731i			1.05193i
$612$	−44.0221	+	88.1060i	−0.0719316	+	0.143964i
$613$	235.579			0.384305			0.192152	−	0.981365i	$-0.438453\pi$
$613$	235.579			0.384305			0.192152	+	0.981365i	$0.438453\pi$
$614$	299.114	+	389.813i	0.487157	+	0.634875i
$615$	538.871	−	882.957i	0.876213	−	1.43570i
$616$	−146.251	+	545.816i	−0.237420	+	0.886064i
$617$	874.053	−	766.524i	1.41662	−	1.24234i	0.487209	−	0.873285i	$-0.338015\pi$
$617$	874.053	−	766.524i	1.41662	−	1.24234i	0.929408	−	0.369055i	$-0.120319\pi$
$618$	97.5475	−	220.172i	0.157844	−	0.356265i
$619$	759.906	+	666.420i	1.22764	+	1.07661i	0.994562	+	0.104148i	$0.0332115\pi$
$619$	759.906	+	666.420i	1.22764	+	1.07661i	0.233073	+	0.972459i	$0.425122\pi$
$620$	28.7288	−	11.8998i	0.0463367	−	0.0191933i
$621$	−550.843	+	937.483i	−0.887025	+	1.50964i
$622$	145.849	+	29.0112i	0.234484	+	0.0466418i
$623$	15.7011	+	239.552i	0.0252024	+	0.384514i
$624$	290.548	+	305.061i	0.465621	+	0.488879i
$625$	709.570	+	190.129i	1.13531	+	0.304206i
$626$	−20.2024	+	308.229i	−0.0322722	+	0.492378i
$627$	576.331	+	211.430i	0.919187	+	0.337209i
$628$	−7.28749	−	4.20744i	−0.0116043	−	0.00669974i
$629$	−450.094	+	491.065i	−0.715571	+	0.780708i
$630$	482.513	+	696.620i	0.765894	+	1.10575i
$631$	154.017	−	371.831i	0.244085	−	0.589273i	−0.753596	−	0.657338i	$-0.771683\pi$
$631$	154.017	−	371.831i	0.244085	−	0.589273i	0.997681	+	0.0680650i	$0.0216825\pi$
$632$	170.756	+	346.258i	0.270183	+	0.547877i
$633$	−17.0185	+	5.31834i	−0.0268855	+	0.00840181i
$634$	−12.7038	+	11.1409i	−0.0200375	+	0.0175724i
$635$	−445.843	+	904.079i	−0.702114	+	1.42375i
$636$	68.6182	+	55.3596i	0.107890	+	0.0870434i
$637$	−14.9138	+	113.281i	−0.0234125	+	0.177836i
$638$	−157.596	−	380.471i	−0.247016	−	0.596350i
$639$	−446.992	+	603.157i	−0.699518	+	0.943908i
$640$	−491.488	+	328.402i	−0.767950	+	0.513128i
$641$	−23.7229	+	69.8855i	−0.0370092	+	0.109026i	−0.963864	−	0.266394i	$-0.914168\pi$
$641$	−23.7229	+	69.8855i	−0.0370092	+	0.109026i	0.926855	+	0.375419i	$0.122501\pi$
$642$	−584.523	+	634.644i	−0.910471	+	0.988542i
$643$	40.6003	−	619.441i	0.0631420	−	0.963361i	−0.842332	−	0.538959i	$-0.818818\pi$
$643$	40.6003	−	619.441i	0.0631420	−	0.963361i	0.905474	−	0.424402i	$-0.139516\pi$
$644$	−26.1203	−	198.404i	−0.0405595	−	0.308080i
$645$	271.407	−	171.936i	0.420786	−	0.266567i
$646$	736.255	−	80.5376i	1.13971	−	0.124671i
$647$	394.639			0.609952			0.304976	−	0.952360i	$-0.401352\pi$
$647$	394.639			0.609952			0.304976	+	0.952360i	$0.401352\pi$
$648$	−659.279	+	200.514i	−1.01741	+	0.309436i
$649$	−209.338	+	313.297i	−0.322555	+	0.482737i
$650$	−369.198	+	98.9262i	−0.567996	+	0.152194i
$651$	121.660	−	115.873i	0.186882	−	0.177992i
$652$	−60.8490	+	123.390i	−0.0933267	+	0.189248i
$653$	−412.923	+	140.168i	−0.632347	+	0.214653i	−0.619166	−	0.785260i	$-0.712529\pi$
$653$	−412.923	+	140.168i	−0.632347	+	0.214653i	−0.0131812	+	0.999913i	$0.504196\pi$
$654$	−213.732	+	99.0034i	−0.326807	+	0.151381i
$655$	486.292	+	64.0216i	0.742431	+	0.0977429i
$656$	660.836	+	131.448i	1.00737	+	0.200379i
$657$	173.145	+	1164.33i	0.263539	+	1.77219i
$658$	−825.942	+	164.290i	−1.25523	+	0.249681i
$659$	−88.6787	−	330.953i	−0.134566	−	0.502206i	−0.999999	−	0.00118213i	$-0.999624\pi$
$659$	−88.6787	−	330.953i	−0.134566	−	0.502206i	0.865434	−	0.501023i	$-0.167043\pi$
$660$	97.1363	−	52.9696i	0.147176	−	0.0802570i
$661$	−37.6386	−	285.894i	−0.0569420	−	0.432517i	−0.996043	−	0.0888754i	$-0.971673\pi$
$661$	−37.6386	−	285.894i	−0.0569420	−	0.432517i	0.939101	−	0.343642i	$-0.111661\pi$
$662$	−523.464	+	302.222i	−0.790732	+	0.456529i
$663$	−498.261	−	233.966i	−0.751525	−	0.352891i
$664$	−79.0970	+	137.000i	−0.119122	+	0.206325i
$665$	−467.730	+	1129.20i	−0.703354	+	1.69805i
$666$	−645.981	+	10.8059i	−0.969942	+	0.0162251i
$667$	743.927	+	743.927i	1.11533	+	1.11533i
$668$	136.749	+	46.4202i	0.204715	+	0.0694913i
$669$	372.168	+	510.292i	0.556305	+	0.762768i
$670$	−9.45161	+	3.20839i	−0.0141069	+	0.00478864i
$671$	−587.768	−	451.011i	−0.875959	−	0.672147i
$672$	135.893	−	193.028i	0.202222	−	0.287244i
$673$	−441.896	+	503.886i	−0.656606	+	0.748716i	−0.980315	−	0.197441i	$-0.936737\pi$
$673$	−441.896	+	503.886i	−0.656606	+	0.748716i	0.323709	+	0.946157i	$0.395070\pi$
$674$	480.917	−	321.339i	0.713527	−	0.476763i
$675$	105.725	−	511.090i	0.156630	−	0.757171i
$676$	−23.8996	+	23.8996i	−0.0353545	+	0.0353545i
$677$	−1075.66	+	530.459i	−1.58887	+	0.783543i	−0.999701	−	0.0244683i	$-0.992211\pi$
$677$	−1075.66	+	530.459i	−1.58887	+	0.783543i	−0.589167	+	0.808011i	$0.700544\pi$
$678$	−81.9485	−	471.771i	−0.120868	−	0.695828i
$679$	−502.765	+	290.271i	−0.740449	+	0.427498i
$680$	552.414	−	788.713i	0.812373	−	1.15987i
$681$	−321.570	+	13.2202i	−0.472203	+	0.0194129i
$682$	69.6231	+	90.7346i	0.102087	+	0.133042i
$683$	460.495	−	689.179i	0.674224	−	1.00905i	−0.323795	−	0.946127i	$-0.604959\pi$
$683$	460.495	−	689.179i	0.674224	−	1.00905i	0.998019	−	0.0629199i	$-0.0200413\pi$
$684$	−105.093	−	89.0991i	−0.153645	−	0.130262i
$685$	−57.9331	−	291.249i	−0.0845738	−	0.425181i
$686$	542.073	−	35.5294i	0.790194	−	0.0517921i
$687$	−109.421	−	88.2782i	−0.159273	−	0.128498i
$688$	166.029	+	127.399i	0.241322	+	0.185173i
$689$	−299.965	+	390.922i	−0.435362	+	0.567375i
$690$	925.324	−	1146.94i	1.34105	−	1.66223i
$691$	−66.5124	−	1014.78i	−0.0962553	−	1.46857i	−0.723810	−	0.690000i	$-0.757611\pi$
$691$	−66.5124	−	1014.78i	−0.0962553	−	1.46857i	0.627554	−	0.778573i	$-0.284056\pi$
$692$	−122.986	+	24.4634i	−0.177725	+	0.0353517i
$693$	386.578	−	455.972i	0.557833	−	0.657969i
$694$	727.732	+	486.255i	1.04860	+	0.700655i
$695$	−1016.85	+	780.258i	−1.46310	+	1.12267i
$696$	27.3877	+	666.185i	0.0393501	+	0.957162i
$697$	−867.023	+	152.765i	−1.24394	+	0.219175i
$698$	−610.324	−	1057.11i	−0.874390	−	1.51449i
$699$	214.492	−	37.2582i	0.306856	−	0.0533021i
$700$	42.4834	+	86.1478i	0.0606906	+	0.123068i
$701$	634.377	+	634.377i	0.904959	+	0.904959i	0.995860	−	0.0909006i	$-0.0289746\pi$
$701$	634.377	+	634.377i	0.904959	+	0.904959i	−0.0909006	+	0.995860i	$0.528975\pi$
$702$	−167.746	−	506.845i	−0.238954	−	0.722002i
$703$	−517.706	−	774.802i	−0.736425	−	1.10214i
$704$	457.497	+	401.214i	0.649854	+	0.569907i
$705$	972.599	+	684.717i	1.37957	+	0.971229i
$706$	−375.906	+	489.890i	−0.532444	+	0.693895i
$707$	428.200	+	1261.44i	0.605657	+	1.78421i
$708$	68.3262	−	49.8320i	0.0965059	−	0.0703841i
$709$	314.301	−	925.902i	0.443302	−	1.30593i	−0.464145	−	0.885759i	$-0.653638\pi$
$709$	314.301	−	925.902i	0.443302	−	1.30593i	0.907447	−	0.420167i	$-0.138028\pi$
$710$	719.458	−	719.458i	1.01332	−	1.01332i
$711$	−6.83121	−	408.372i	−0.00960789	−	0.574363i
$712$	244.439	+	101.250i	0.343313	+	0.142205i
$713$	−253.032	−	146.088i	−0.354884	−	0.204892i
$714$	173.297	−	700.095i	0.242713	−	0.980526i
$715$	309.177	+	535.511i	0.432416	+	0.748966i
$716$	−31.4972	+	4.14668i	−0.0439905	+	0.00579145i
$717$	−121.473	−	222.758i	−0.169418	−	0.310681i
$718$	−944.907	+	253.187i	−1.31603	+	0.352628i
$719$	101.002	+	507.774i	0.140476	+	0.706222i	0.985253	+	0.171103i	$0.0547331\pi$
$719$	101.002	+	507.774i	0.140476	+	0.706222i	−0.844777	+	0.535119i	$0.820267\pi$
$720$	771.154	−	114.677i	1.07105	−	0.159273i
$721$	65.9841	−	331.725i	0.0915175	−	0.460090i
$722$	−48.9124	+	371.526i	−0.0677456	+	0.514579i
$723$	108.357	+	233.925i	0.149871	+	0.323548i
$724$	−65.6438	−	193.380i	−0.0906683	−	0.267100i
$725$	−452.906	−	223.349i	−0.624698	−	0.308067i
$726$	−177.999	−	186.890i	−0.245177	−	0.257424i
$727$	66.2333	+	247.186i	0.0911050	+	0.340008i	0.996400	−	0.0847746i	$-0.0270170\pi$
$727$	66.2333	+	247.186i	0.0911050	+	0.340008i	−0.905295	+	0.424783i	$0.860350\pi$
$728$	589.344	+	393.787i	0.809538	+	0.540916i
$729$	721.226	+	106.179i	0.989336	+	0.145650i
$730$		−	1595.36i		−	2.18543i
$731$	−262.510	−	76.5511i	−0.359111	−	0.104721i
$732$	88.9839	+	140.464i	0.121563	+	0.191891i
$733$	−184.121	+	24.2400i	−0.251188	+	0.0330695i	−0.255069	−	0.966923i	$-0.582098\pi$
$733$	−184.121	+	24.2400i	−0.251188	+	0.0330695i	0.00388059	+	0.999992i	$0.498765\pi$
$734$	873.098	+	57.2258i	1.18951	+	0.0779644i
$735$	155.533	+	143.249i	0.211609	+	0.194897i
$736$	−388.737	−	131.959i	−0.528176	−	0.179291i
$737$	3.91187	+	5.85452i	0.00530782	+	0.00794372i
$738$	−686.018	−	508.399i	−0.929564	−	0.688888i
$739$	97.5858	−	40.4214i	0.132051	−	0.0546974i	−0.315679	−	0.948866i	$-0.602232\pi$
$739$	97.5858	−	40.4214i	0.132051	−	0.0546974i	0.447731	+	0.894169i	$0.352232\pi$
$740$	−166.508	−	21.9212i	−0.225011	−	0.0296233i
$741$	483.509	−	599.309i	0.652509	−	0.808784i
$742$	−579.029	−	285.545i	−0.780362	−	0.384832i
$743$	−633.680	−	722.574i	−0.852867	−	0.972509i	0.146995	−	0.989137i	$-0.453040\pi$
$743$	−633.680	−	722.574i	−0.852867	−	0.972509i	−0.999862	+	0.0166288i	$0.994707\pi$
$744$	−55.2308	−	176.737i	−0.0742350	−	0.237550i
$745$	−584.836	+	288.409i	−0.785014	+	0.387126i
$746$	−1080.72	−	447.649i	−1.44869	−	0.600065i
$747$	137.575	−	95.2914i	0.184171	−	0.127565i
$748$	−88.4824	−	32.2178i	−0.118292	−	0.0430719i
$749$	−605.910	+	1049.47i	−0.808958	+	1.40116i
$750$	71.4586	−	194.787i	0.0952782	−	0.259716i
$751$	−293.728	−	19.2520i	−0.391116	−	0.0256351i	−0.131423	−	0.991326i	$-0.541955\pi$
$751$	−293.728	−	19.2520i	−0.391116	−	0.0256351i	−0.259693	+	0.965691i	$0.583621\pi$
$752$	−200.526	+	748.373i	−0.266657	+	0.995177i
$753$	525.160	−	500.176i	0.697423	−	0.664244i
$754$	−515.461	+	33.7851i	−0.683635	+	0.0448078i
$755$	−14.1675	+	71.2247i	−0.0187649	+	0.0943373i
$756$	−116.700	+	66.1942i	−0.154366	+	0.0875584i
$757$	−15.9800	−	38.5791i	−0.0211096	−	0.0509631i	0.912973	−	0.408019i	$-0.133780\pi$
$757$	−15.9800	−	38.5791i	−0.0211096	−	0.0509631i	−0.934083	+	0.357056i	$0.883780\pi$
$758$	678.830	−	774.058i	0.895555	−	1.02118i
$759$	−950.467	−	421.106i	−1.25226	−	0.554817i
$760$	888.162	+	1012.75i	1.16863	+	1.33257i
$761$	830.487	+	222.528i	1.09131	+	0.292416i	0.759221	−	0.650833i	$-0.225580\pi$
$761$	830.487	+	222.528i	1.09131	+	0.292416i	0.332089	+	0.943248i	$0.392247\pi$
$762$	710.272	+	433.481i	0.932115	+	0.568872i
$763$	−262.464	+	201.396i	−0.343990	+	0.263952i
$764$			67.1827i			0.0879355i
$765$	−884.854	+	504.733i	−1.15667	+	0.659781i
$766$	893.288			1.16617
$767$	287.724	+	374.969i	0.375129	+	0.488878i
$768$	−172.675	−	316.653i	−0.224837	−	0.412308i
$769$	−166.390	+	620.974i	−0.216371	+	0.807509i	0.769308	+	0.638878i	$0.220601\pi$
$769$	−166.390	+	620.974i	−0.216371	+	0.807509i	−0.985679	+	0.168631i	$0.946065\pi$
$770$	−609.129	+	534.192i	−0.791076	+	0.693755i
$771$	−439.668	+	47.0193i	−0.570256	+	0.0609849i
$772$	111.237	+	97.5525i	0.144090	+	0.126363i
$773$	−144.391	+	59.8087i	−0.186793	+	0.0773722i	−0.474119	−	0.880461i	$-0.657234\pi$
$773$	−144.391	+	59.8087i	−0.186793	+	0.0773722i	0.287327	+	0.957833i	$0.407234\pi$
$774$	−121.261	−	235.864i	−0.156668	−	0.304734i
$775$	137.547	+	27.3598i	0.177480	+	0.0353030i
$776$	41.8462	+	638.449i	0.0539255	+	0.822744i
$777$	−881.952	+	213.435i	−1.13507	+	0.274691i
$778$	197.917	+	53.0318i	0.254392	+	0.0681642i
$779$	80.5477	−	1228.92i	0.103399	−	1.57756i
$780$	−23.7513	−	136.734i	−0.0304504	−	0.175300i
$781$	−621.596	−	358.878i	−0.795897	−	0.459512i
$782$	−1253.04	+	54.5482i	−1.60236	+	0.0697548i
$783$	274.896	−	649.584i	0.351080	−	0.829609i
$784$	−52.7078	+	127.248i	−0.0672293	+	0.162306i
$785$	−38.4941	−	78.0583i	−0.0490371	−	0.0994374i
$786$	88.6384	−	395.061i	0.112771	−	0.502622i
$787$	837.607	−	734.562i	1.06430	−	0.933369i	0.0663811	−	0.997794i	$-0.478855\pi$
$787$	837.607	−	734.562i	1.06430	−	0.933369i	0.997923	+	0.0644251i	$0.0205214\pi$
$788$	−68.4482	+	138.799i	−0.0868632	+	0.176141i
$789$	3.52817	−	22.5412i	0.00447170	−	0.0285693i
$790$	−72.2518	+	548.807i	−0.0914580	+	0.694692i
$791$	−257.365	−	621.334i	−0.325367	−	0.785505i
$792$	−262.268	−	604.376i	−0.331146	−	0.763101i
$793$	−772.691	+	516.296i	−0.974390	+	0.651066i
$794$	−334.534	+	985.507i	−0.421328	+	1.24119i
$795$	271.994	+	870.374i	0.342131	+	1.09481i
$796$	−0.210640	+	3.21375i	−0.000264624	+	0.00403738i
$797$	−119.151	−	905.040i	−0.149499	−	1.13556i	−0.887516	−	0.460776i	$-0.847571\pi$
$797$	−119.151	−	905.040i	−0.149499	−	1.13556i	0.738017	−	0.674782i	$-0.235762\pi$
$798$	893.733	+	468.143i	1.11997	+	0.586645i
$799$	−110.081	−	1006.33i	−0.137773	−	1.25949i
$800$	197.047			0.246309
$801$	−188.044	−	207.323i	−0.234762	−	0.258830i
$802$	707.408	−	1058.71i	0.882055	−	1.32009i
$803$	−1087.08	+	291.282i	−1.35377	+	0.362742i
$804$	−0.371707	−	1.53596i	−0.000462323	−	0.00191040i
$805$	915.436	−	1856.32i	1.13719	−	2.30599i
$806$	135.845	−	46.1132i	0.168542	−	0.0572125i
$807$	−1068.49	−	752.222i	−1.32402	−	0.932121i
$808$	1455.59	+	191.632i	1.80147	+	0.237168i
$809$	1165.85	+	231.902i	1.44110	+	0.286652i	0.852904	−	0.522067i	$-0.174839\pi$
$809$	1165.85	+	231.902i	1.44110	+	0.286652i	0.588195	+	0.808719i	$0.299839\pi$
$810$	−945.677	−	286.116i	−1.16750	−	0.353230i
$811$	1166.04	−	231.940i	1.43778	−	0.285993i	0.586181	−	0.810180i	$-0.300631\pi$
$811$	1166.04	−	231.940i	1.43778	−	0.285993i	0.851603	+	0.524187i	$0.175631\pi$
$812$	33.5986	+	125.392i	0.0413776	+	0.154423i
$813$	−23.3473	+	958.169i	−0.0287174	+	1.17856i
$814$	−80.6251	−	612.408i	−0.0990480	−	0.752344i
$815$	−1232.31	+	711.473i	−1.51203	+	0.872973i
$816$	−507.162	−	427.875i	−0.621522	−	0.524356i
$817$	191.260	−	331.271i	0.234100	−	0.405473i
$818$	−1.57807	+	3.80980i	−0.00192918	+	0.00465746i
$819$	−385.729	−	643.020i	−0.470976	−	0.785128i
$820$	−156.950	−	156.950i	−0.191403	−	0.191403i
$821$	472.803	+	160.495i	0.575887	+	0.195487i	0.594162	−	0.804346i	$-0.297484\pi$
$821$	472.803	+	160.495i	0.575887	+	0.195487i	−0.0182745	+	0.999833i	$0.505817\pi$
$822$	−243.737	+	26.0659i	−0.296517	+	0.0317104i
$823$	−838.262	+	284.551i	−1.01854	+	0.345749i	−0.780266	−	0.625448i	$-0.784916\pi$
$823$	−838.262	+	284.551i	−1.01854	+	0.345749i	−0.238278	+	0.971197i	$0.576583\pi$
$824$	−295.729	−	226.921i	−0.358894	−	0.275389i
$825$	496.975	+	44.7545i	0.602394	+	0.0542479i
$826$	−408.309	+	465.587i	−0.494321	+	0.563665i
$827$	−796.390	+	532.131i	−0.962987	+	0.643447i	−0.934431	−	0.356145i	$-0.884091\pi$
$827$	−796.390	+	532.131i	−0.962987	+	0.643447i	−0.0285564	+	0.999592i	$0.509091\pi$
$828$	167.718	+	162.199i	0.202558	+	0.195893i
$829$	178.837	−	178.837i	0.215726	−	0.215726i	−0.590969	−	0.806695i	$-0.701254\pi$
$829$	178.837	−	178.837i	0.215726	−	0.215726i	0.806695	+	0.590969i	$0.201254\pi$
$830$	−203.424	+	100.318i	−0.245089	+	0.120865i
$831$	−1026.01	−	376.398i	−1.23467	−	0.452945i
$832$	661.019	−	381.639i	0.794494	−	0.458701i
$833$	3.94894	−	179.920i	0.00474062	−	0.215991i
$834$	566.197	+	893.764i	0.678894	+	1.07166i
$835$	909.276	+	1184.99i	1.08895	+	1.41915i
$836$	73.1839	−	109.527i	0.0875405	−	0.131014i
$837$	−27.0507	+	194.011i	−0.0323186	+	0.231794i
$838$	119.488	+	600.709i	0.142588	+	0.716837i
$839$	−952.691	+	62.4426i	−1.13551	+	0.0744251i	−0.621538	−	0.783384i	$-0.713492\pi$
$839$	−952.691	+	62.4426i	−1.13551	+	0.0744251i	−0.513969	+	0.857809i	$0.671825\pi$
$840$	1223.73	−	472.301i	1.45682	−	0.562263i
$841$	125.763	+	96.5017i	0.149540	+	0.114746i
$842$	155.504	−	202.657i	0.184684	−	0.240685i
$843$	257.315	+	40.2752i	0.305237	+	0.0477760i
$844$	0.250231	+	3.81779i	0.000296482	+	0.00452345i
$845$	−342.864	+	68.1998i	−0.405756	+	0.0807098i
$846$	634.942	−	748.919i	0.750522	−	0.885247i
$847$	−301.400	−	201.389i	−0.355845	−	0.237768i
$848$	−471.232	+	361.589i	−0.555698	+	0.426402i
$849$	1027.93	+	538.434i	1.21075	+	0.634198i
$850$	561.114	−	218.122i	0.660134	−	0.256615i
$851$	789.007	+	1366.60i	0.927153	+	1.60588i
$852$	103.233	+	123.666i	0.121166	+	0.145148i
$853$	586.499	+	1189.30i	0.687573	+	1.39426i	0.908048	+	0.418867i	$0.137573\pi$
$853$	586.499	+	1189.30i	0.687573	+	1.39426i	−0.220475	+	0.975393i	$0.570761\pi$
$854$	−860.976	−	860.976i	−1.00817	−	1.00817i
$855$	−391.797	−	1370.12i	−0.458243	−	1.60248i
$856$	741.993	+	1110.47i	0.866815	+	1.29728i
$857$	9.13186	+	8.00842i	0.0106556	+	0.00934472i	0.664657	−	0.747149i	$-0.268578\pi$
$857$	9.13186	+	8.00842i	0.0106556	+	0.00934472i	−0.654001	+	0.756493i	$0.726911\pi$
$858$	463.156	−	214.540i	0.539809	−	0.250046i
$859$	−264.340	+	344.495i	−0.307730	+	0.401042i	−0.921459	−	0.388475i	$-0.873002\pi$
$859$	−264.340	+	344.495i	−0.307730	+	0.401042i	0.613729	+	0.789517i	$0.289669\pi$
$860$	−22.1603	−	65.2821i	−0.0257678	−	0.0759094i
$861$	−1096.47	−	485.791i	−1.27348	−	0.564217i
$862$	325.006	−	957.436i	0.377037	−	1.11071i
$863$	196.772	−	196.772i	0.228010	−	0.228010i	−0.583851	−	0.811861i	$-0.698455\pi$
$863$	196.772	−	196.772i	0.228010	−	0.228010i	0.811861	+	0.583851i	$0.198455\pi$
$864$	15.9036	+	274.774i	0.0184070	+	0.318025i
$865$	−1198.22	−	496.319i	−1.38523	−	0.573779i
$866$	401.192	+	231.629i	0.463271	+	0.267469i
$867$	820.204	+	280.987i	0.946026	+	0.324091i
$868$	−18.0258	−	31.2216i	−0.0207671	−	0.0359696i
$869$	387.148	−	50.9690i	0.445509	−	0.0586524i
$870$	−498.009	+	816.003i	−0.572424	+	0.937934i
$871$	8.53117	−	2.28592i	0.00979469	−	0.00262448i
$872$	71.1315	+	357.602i	0.0815728	+	0.410094i
$873$	248.531	−	629.590i	0.284686	−	0.721179i
$874$	342.294	−	1720.83i	0.391640	−	1.96891i
$875$	38.0364	−	288.915i	0.0434701	−	0.330188i
$876$	251.570	+	22.6548i	0.287180	+	0.0258617i
$877$	144.436	+	425.496i	0.164694	+	0.485172i	0.997677	−	0.0681266i	$-0.0217022\pi$
$877$	144.436	+	425.496i	0.164694	+	0.485172i	−0.832983	+	0.553299i	$0.813369\pi$
$878$	−578.654	−	285.361i	−0.659059	−	0.325012i
$879$	298.737	−	1015.29i	0.339860	−	1.15505i
$880$	192.921	+	719.990i	0.219228	+	0.818170i
$881$	−335.670	−	224.288i	−0.381010	−	0.254583i	0.350286	−	0.936643i	$-0.386084\pi$
$881$	−335.670	−	224.288i	−0.381010	−	0.254583i	−0.731296	+	0.682060i	$0.761084\pi$
$882$	129.286	−	117.264i	0.146583	−	0.132952i
$883$		−	1112.35i		−	1.25974i	−0.776701	−	0.629870i	$-0.783108\pi$
$883$		−	1112.35i		−	1.25974i	0.776701	−	0.629870i	$-0.216892\pi$
$884$	−73.9438	+	92.1079i	−0.0836468	+	0.104194i
$885$	873.934	−	35.9285i	0.987496	−	0.0405972i
$886$	−698.697	+	91.9852i	−0.788597	+	0.103821i
$887$	1589.56	+	104.185i	1.79206	+	0.117458i	0.924814	−	0.380419i	$-0.124220\pi$
$887$	1589.56	+	104.185i	1.79206	+	0.117458i	0.867248	+	0.497877i	$0.165887\pi$
$888$	−218.937	+	975.803i	−0.246551	+	1.09888i
$889$	1106.67	+	375.663i	1.24484	+	0.422568i
$890$	210.754	+	315.415i	0.236802	+	0.354399i
$891$	−22.2975	+	696.621i	−0.0250252	+	0.781842i
$892$	125.210	−	51.8636i	0.140370	−	0.0581430i
$893$	1404.03	+	184.845i	1.57227	+	0.206993i
$894$	193.813	+	502.170i	0.216794	+	0.561712i
$895$	−294.696	−	145.328i	−0.329270	−	0.162378i
$896$	451.859	+	515.247i	0.504307	+	0.575052i
$897$	−883.411	+	959.161i	−0.984850	+	1.06930i
$898$	96.1871	−	47.4342i	0.107113	−	0.0528221i
$899$	175.107	+	72.5318i	0.194780	+	0.0806805i
$900$	−101.256	−	47.8455i	−0.112507	−	0.0531617i
$901$	402.705	−	663.446i	0.446953	−	0.736344i
$902$	408.181	−	706.990i	0.452529	−	0.783802i
$903$	−238.704	−	285.951i	−0.264345	−	0.316668i
$904$	−739.609	−	48.4765i	−0.818151	−	0.0536245i
$905$	546.678	−	2040.23i	0.604064	−	2.25440i
$906$	57.5078	+	16.9209i	0.0634744	+	0.0186765i
$907$	497.861	−	32.6315i	0.548909	−	0.0359774i	0.211574	−	0.977362i	$-0.432141\pi$
$907$	497.861	−	32.6315i	0.548909	−	0.0359774i	0.337335	+	0.941385i	$0.390474\pi$
$908$	−13.4730	+	67.7335i	−0.0148381	+	0.0745964i
$909$	−1305.66	−	841.171i	−1.43637	−	0.925381i
$910$	388.905	+	938.899i	0.427368	+	1.03176i
$911$	−344.468	+	392.791i	−0.378121	+	0.431164i	−0.909330	−	0.416077i	$-0.863405\pi$
$911$	−344.468	+	392.791i	−0.378121	+	0.431164i	0.531208	+	0.847241i	$0.321738\pi$
$912$	749.959	−	546.963i	0.822324	−	0.599741i
$913$	105.497	+	120.297i	0.115550	+	0.131760i
$914$	−447.956	−	120.029i	−0.490105	−	0.131323i
$915$	−41.8930	+	1719.28i	−0.0457847	+	1.87900i
$916$	−23.9338	+	18.3651i	−0.0261286	+	0.0200492i
$917$		−	568.659i		−	0.620130i
$918$	349.449	+	764.844i	0.380664	+	0.833163i
$919$	−201.084			−0.218807			−0.109403	−	0.993997i	$-0.534894\pi$
$919$	−201.084			−0.218807			−0.109403	+	0.993997i	$0.534894\pi$
$920$	−1388.65	−	1809.72i	−1.50940	−	1.96709i
$921$	−804.367	−	19.5997i	−0.873363	−	0.0212808i
$922$	261.981	−	977.727i	0.284145	−	1.06044i
$923$	−676.897	+	593.623i	−0.733366	+	0.643145i
$924$	−75.5857	−	103.638i	−0.0818027	−	0.112162i
$925$	−569.467	−	499.409i	−0.615640	−	0.539902i
$926$	−998.657	+	413.657i	−1.07846	+	0.446714i
$927$	180.304	+	350.709i	0.194503	+	0.378326i
$928$	261.190	+	51.9539i	0.281454	+	0.0559848i
$929$	−27.3405	−	417.135i	−0.0294300	−	0.449015i	−0.986990	−	0.160781i	$-0.948599\pi$
$929$	−27.3405	−	417.135i	−0.0294300	−	0.449015i	0.957560	−	0.288234i	$-0.0930680\pi$
$930$	74.9393	−	254.690i	0.0805799	−	0.273861i
$931$	243.172	+	65.1578i	0.261195	+	0.0699869i
$932$	3.05529	−	46.6147i	0.00327821	−	0.0500158i
$933$	−186.940	+	156.052i	−0.200364	+	0.167258i
$934$	−596.017	−	344.110i	−0.638133	−	0.368426i
$935$	−575.799	−	785.502i	−0.615828	−	0.840109i
$936$	−823.615	+	67.8343i	−0.879931	+	0.0724726i
$937$	326.929	−	789.275i	0.348910	−	0.842343i	−0.647839	−	0.761777i	$-0.724327\pi$
$937$	326.929	−	789.275i	0.348910	−	0.842343i	0.996749	−	0.0805659i	$-0.0256728\pi$
$938$	5.11820	+	10.3787i	0.00545650	+	0.0110647i
$939$	−372.060	−	342.676i	−0.396230	−	0.364937i
$940$	191.892	−	168.285i	0.204141	−	0.179027i
$941$	−144.819	+	293.663i	−0.153899	+	0.312076i	−0.960144	−	0.279505i	$-0.909829\pi$
$941$	−144.819	+	293.663i	−0.153899	+	0.312076i	0.806245	+	0.591581i	$0.201496\pi$
$942$	−67.0249	+	25.8684i	−0.0711517	+	0.0274611i
$943$	−272.219	+	2067.71i	−0.288674	+	2.19269i
$944$	218.029	+	526.368i	0.230963	+	0.557594i
$945$	−1383.96	−	101.328i	−1.46451	−	0.107225i
$946$	210.828	−	140.871i	0.222862	−	0.148912i
$947$	423.310	−	1247.03i	0.447001	−	1.31682i	−0.457066	−	0.889433i	$-0.651100\pi$
$947$	423.310	−	1247.03i	0.447001	−	1.31682i	0.904067	−	0.427391i	$-0.140567\pi$
$948$	−85.5142	−	19.1865i	−0.0902049	−	0.0202389i
$949$	−92.3284	+	1408.66i	−0.0972902	+	1.48436i
$950$	109.924	+	834.956i	0.115710	+	0.878901i
$951$	−1.13657	−	27.6461i	−0.00119513	−	0.0290706i
$952$	−990.186	−	515.620i	−1.04011	−	0.541617i
$953$	93.9758			0.0986105			0.0493052	−	0.998784i	$-0.484299\pi$
$953$	93.9758			0.0986105			0.0493052	+	0.998784i	$0.484299\pi$
$954$	735.707	−	159.178i	0.771182	−	0.166853i
$955$	−386.045	+	577.757i	−0.404235	+	0.604981i
$956$	−52.5891	+	14.0912i	−0.0550095	+	0.0147398i
$957$	646.949	+	190.356i	0.676018	+	0.198909i
$958$	−498.728	+	1011.32i	−0.520593	+	1.05566i
$959$	−326.011	+	110.666i	−0.339949	+	0.115397i
$960$	126.692	−	1406.84i	0.131970	−	1.46546i
$961$	900.592	+	118.565i	0.937141	+	0.123377i
$962$	−759.917	−	151.157i	−0.789935	−	0.157128i
$963$	−207.822	−	1397.52i	−0.215807	−	1.45122i
$964$	54.2560	−	10.7922i	0.0562822	−	0.0111952i
$965$	396.061	+	1478.12i	0.410426	+	1.53173i
$966$	−1458.38	−	890.054i	−1.50971	−	0.921381i
$967$	144.465	+	1097.32i	0.149395	+	1.13477i	0.887740	+	0.460345i	$0.152274\pi$
$967$	144.465	+	1097.32i	0.149395	+	1.13477i	−0.738345	+	0.674423i	$0.764392\pi$
$968$	−345.980	+	199.752i	−0.357418	+	0.206355i
$969$	−654.392	+	1021.16i	−0.675327	+	1.05382i
$970$	−458.679	+	794.455i	−0.472865	+	0.819026i
$971$	242.902	−	586.418i	0.250157	−	0.603932i	−0.748060	−	0.663632i	$-0.769014\pi$
$971$	242.902	−	586.418i	0.250157	−	0.603932i	0.998216	+	0.0596996i	$0.0190143\pi$
$972$	58.5461	−	145.059i	0.0602326	−	0.149237i
$973$	1050.75	+	1050.75i	1.07991	+	1.07991i
$974$	587.870	+	199.555i	0.603563	+	0.204882i
$975$	253.538	−	572.254i	0.260039	−	0.586928i
$976$	−1060.77	+	360.084i	−1.08686	+	0.368939i
$977$	263.252	+	202.001i	0.269450	+	0.206756i	0.734644	−	0.678452i	$-0.237349\pi$
$977$	263.252	+	202.001i	0.269450	+	0.206756i	−0.465195	+	0.885208i	$0.654016\pi$
$978$	493.695	+	1065.81i	0.504800	+	1.08978i
$979$	176.444	−	201.195i	0.180229	−	0.205511i
$980$	37.7259	−	25.2076i	0.0384958	−	0.0257221i
$981$	93.5864	−	374.195i	0.0953990	−	0.381443i
$982$	−76.0463	+	76.0463i	−0.0774403	+	0.0774403i
$983$	−503.847	+	248.470i	−0.512560	+	0.252767i	−0.680127	−	0.733094i	$-0.738076\pi$
$983$	−503.847	+	248.470i	−0.512560	+	0.252767i	0.167567	+	0.985861i	$0.446409\pi$
$984$	−1014.65	+	847.001i	−1.03115	+	0.860774i
$985$	−1386.21	+	800.327i	−1.40732	+	0.812515i
$986$	801.277	−	141.181i	0.812654	−	0.143186i
$987$	639.869	−	1221.58i	0.648297	−	1.23767i
$988$	−100.587	−	131.088i	−0.101809	−	0.132680i
$989$	−359.881	+	538.600i	−0.363883	+	0.544590i
$990$	168.763	−	929.415i	0.170468	−	0.938803i
$991$	−3.64993	−	18.3494i	−0.00368308	−	0.0185161i	0.978900	−	0.204340i	$-0.0655047\pi$
$991$	−3.64993	−	18.3494i	−0.00368308	−	0.0185161i	−0.982583	+	0.185824i	$0.940505\pi$
$992$	−73.7991	+	4.83705i	−0.0743943	+	0.00487606i
$993$	153.062	−	977.899i	0.154141	−	0.984793i
$994$	−935.859	−	718.110i	−0.941508	−	0.722444i
$995$	−20.2783	+	26.4272i	−0.0203802	+	0.0265600i
$996$	−12.9302	−	33.5020i	−0.0129821	−	0.0336366i
$997$	−60.0295	−	915.874i	−0.0602102	−	0.918630i	−0.915968	−	0.401252i	$-0.868575\pi$
$997$	−60.0295	−	915.874i	−0.0602102	−	0.918630i	0.855757	−	0.517377i	$-0.173092\pi$
$998$	308.541	−	61.3726i	0.309159	−	0.0614956i
$999$	650.442	−	834.403i	0.651093	−	0.835239i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.t.a.7.10	✓	544
9.4	even	3	inner	153.3.t.a.58.25	yes	544
17.5	odd	16	inner	153.3.t.a.124.25	yes	544
153.22	odd	48	inner	153.3.t.a.22.10	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.t.a.7.10	✓	544	1.1	even	1	trivial
153.3.t.a.22.10	yes	544	153.22	odd	48	inner
153.3.t.a.58.25	yes	544	9.4	even	3	inner
153.3.t.a.124.25	yes	544	17.5	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.t (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11526 - 1.45343i) q^{2} +(2.99911 + 0.0730780i) q^{3} +(0.166611 - 0.621802i) q^{4} +(5.00581 - 4.38998i) q^{5} +(-3.23857 - 4.44050i) q^{6} +(-5.80360 - 5.08962i) q^{7} +(-7.85979 + 3.25563i) q^{8} +(8.98932 + 0.438338i) q^{9} +(-11.9633 - 2.37965i) q^{10} +(0.562772 + 8.58625i) q^{11} +(0.545125 - 1.85268i) q^{12} +(10.4255 + 2.79351i) q^{13} +(-0.924909 + 14.1114i) q^{14} +(15.3338 - 12.8002i) q^{15} +(11.2676 + 6.50533i) q^{16} +(-16.8018 - 2.58825i) q^{17} +(-9.38831 - 13.5542i) q^{18} +(9.10068 - 21.9710i) q^{19} +(-1.89567 - 3.84404i) q^{20} +(-17.0337 - 15.6885i) q^{21} +(11.8519 - 10.3938i) q^{22} +(-17.8117 + 36.1186i) q^{23} +(-23.8103 + 9.18962i) q^{24} +(2.52308 - 19.1647i) q^{25} +(-7.56697 - 18.2683i) q^{26} +(26.9279 + 1.97154i) q^{27} +(-4.13168 + 2.76070i) q^{28} +(8.39738 - 24.7379i) q^{29} +(-35.7054 - 8.01108i) q^{30} +(-0.474507 + 7.23958i) q^{31} +(1.33056 + 10.1066i) q^{32} +(1.06035 + 25.7922i) q^{33} +(14.9765 + 27.3069i) q^{34} -51.3951 q^{35} +(1.77028 - 5.51654i) q^{36} +(21.7695 - 32.5804i) q^{37} +(-42.0829 + 11.2761i) q^{38} +(31.0632 + 9.13992i) q^{39} +(-25.0525 + 50.8014i) q^{40} +(49.0386 - 16.6464i) q^{41} +(-3.80514 + 42.2540i) q^{42} +(15.9473 + 2.09950i) q^{43} +(5.43271 + 1.08063i) q^{44} +(46.9231 - 37.2687i) q^{45} +(72.3607 - 14.3934i) q^{46} +(15.4124 + 57.5200i) q^{47} +(33.3173 + 20.3336i) q^{48} +(1.38176 + 10.4955i) q^{49} +(-30.6684 + 17.7064i) q^{50} +(-50.2013 - 8.99029i) q^{51} +(3.47402 - 6.01718i) q^{52} +(-17.4706 + 42.1778i) q^{53} +(-27.1661 - 41.3367i) q^{54} +(40.5106 + 40.5106i) q^{55} +(62.1850 + 21.1090i) q^{56} +(28.8995 - 65.2284i) q^{57} +(-45.3201 + 15.3841i) q^{58} +(34.7410 + 26.6577i) q^{59} +(-5.40441 - 11.6672i) q^{60} +(-56.7700 + 64.7337i) q^{61} +(11.0514 - 7.38433i) q^{62} +(-49.9395 - 48.2962i) q^{63} +(50.0051 - 50.0051i) q^{64} +(64.4517 - 31.7840i) q^{65} +(36.3047 - 30.3061i) q^{66} +(0.708666 - 0.409148i) q^{67} +(-4.40875 + 10.0162i) q^{68} +(-56.0589 + 107.022i) q^{69} +(57.3187 + 74.6992i) q^{70} +(-46.3428 + 69.3569i) q^{71} +(-72.0812 + 25.8207i) q^{72} +(25.5163 + 128.279i) q^{73} +(-71.6321 + 4.69501i) q^{74} +(8.96750 - 57.2926i) q^{75} +(-12.1453 - 9.31943i) q^{76} +(40.4347 - 52.6955i) q^{77} +(-21.3592 - 55.3415i) q^{78} +(-2.96806 - 45.2838i) q^{79} +(84.9615 - 16.8999i) q^{80} +(80.6157 + 7.88072i) q^{81} +(-78.8851 - 52.7093i) q^{82} +(14.7523 - 11.3199i) q^{83} +(-12.5931 + 7.97771i) q^{84} +(-95.4691 + 60.8033i) q^{85} +(-14.7339 - 25.5198i) q^{86} +(26.9925 - 73.5780i) q^{87} +(-32.3769 - 65.6539i) q^{88} +(-21.9909 - 21.9909i) q^{89} +(-106.499 - 26.6354i) q^{90} +(-46.2877 - 69.2744i) q^{91} +(19.4910 + 17.0931i) q^{92} +(-1.95215 + 21.6776i) q^{93} +(66.4126 - 86.5505i) q^{94} +(-50.8959 - 149.934i) q^{95} +(3.25193 + 30.4081i) q^{96} +(24.1747 - 71.2163i) q^{97} +(13.7135 - 13.7135i) q^{98} +(1.29526 + 77.4312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) \) 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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