LMFDB - Embedded newform 153.3.t.a.58.15

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			58.15
Character	$\chi$	$=$	153.58
Dual form			153.3.t.a.124.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707508 + 0.0931452i) q^{2} +(-2.22368 - 2.01376i) q^{3} +(-3.37181 + 0.903474i) q^{4} +(-2.15087 - 0.730123i) q^{5} +(1.76084 + 1.21763i) q^{6} +(1.07898 - 0.366265i) q^{7} +(4.93860 - 2.04563i) q^{8} +(0.889516 + 8.95593i) q^{9} +(1.58977 + 0.316224i) q^{10} +(6.69905 + 3.30361i) q^{11} +(9.31722 + 4.78099i) q^{12} +(1.56021 + 5.82278i) q^{13} +(-0.729271 + 0.359637i) q^{14} +(3.31256 + 5.95491i) q^{15} +(8.78878 - 5.07421i) q^{16} +(14.4664 + 8.92882i) q^{17} +(-1.46354 - 6.25354i) q^{18} +(-7.99196 + 19.2943i) q^{19} +(7.91198 + 0.518579i) q^{20} +(-3.13688 - 1.35836i) q^{21} +(-5.04735 - 1.71334i) q^{22} +(17.6274 - 1.15536i) q^{23} +(-15.1013 - 5.39633i) q^{24} +(-15.7407 - 12.0782i) q^{25} +(-1.64622 - 3.97434i) q^{26} +(16.0571 - 21.7064i) q^{27} +(-3.30721 + 2.20981i) q^{28} +(18.8464 + 21.4902i) q^{29} +(-2.89833 - 3.90459i) q^{30} +(-11.8236 + 5.83077i) q^{31} +(-22.7090 + 17.4252i) q^{32} +(-8.24387 - 20.8365i) q^{33} +(-11.0668 - 4.96973i) q^{34} -2.58817 q^{35} +(-11.0907 - 29.3941i) q^{36} +(-30.4113 + 45.5137i) q^{37} +(3.85720 - 14.3953i) q^{38} +(8.25629 - 16.0899i) q^{39} +(-12.1159 + 0.794115i) q^{40} +(18.2158 + 15.9748i) q^{41} +(2.34589 + 0.668862i) q^{42} +(14.9971 - 19.5447i) q^{43} +(-25.5727 - 5.08672i) q^{44} +(4.62570 - 19.9125i) q^{45} +(-12.3639 + 2.45934i) q^{46} +(39.7995 + 10.6642i) q^{47} +(-29.7617 - 6.41511i) q^{48} +(-37.8443 + 29.0389i) q^{49} +(12.2617 + 7.07928i) q^{50} +(-14.1881 - 48.9867i) q^{51} +(-10.5215 - 18.2237i) q^{52} +(6.58082 - 15.8875i) q^{53} +(-9.33870 + 16.8531i) q^{54} +(-11.9968 - 11.9968i) q^{55} +(4.57941 - 4.01603i) q^{56} +(56.6257 - 26.8105i) q^{57} +(-15.3357 - 13.4491i) q^{58} +(0.665981 - 5.05863i) q^{59} +(-16.5494 - 17.0860i) q^{60} +(-17.8989 - 52.7283i) q^{61} +(7.82220 - 5.22663i) q^{62} +(4.24001 + 9.33748i) q^{63} +(-14.2603 + 14.2603i) q^{64} +(0.895534 - 13.6632i) q^{65} +(7.77342 + 13.9741i) q^{66} +(37.7144 + 21.7744i) q^{67} +(-56.8449 - 17.0363i) q^{68} +(-41.5245 - 32.9283i) q^{69} +(1.83115 - 0.241075i) q^{70} +(12.5470 - 18.7780i) q^{71} +(22.7135 + 42.4101i) q^{72} +(15.7033 + 78.9458i) q^{73} +(17.2768 - 35.0340i) q^{74} +(10.6795 + 58.5561i) q^{75} +(9.51549 - 72.2773i) q^{76} +(8.43814 + 1.11090i) q^{77} +(-4.34270 + 12.1528i) q^{78} +(104.764 + 51.6638i) q^{79} +(-22.6083 + 4.49708i) q^{80} +(-79.4175 + 15.9329i) q^{81} +(-14.3758 - 9.60560i) q^{82} +(15.7020 + 119.269i) q^{83} +(11.8042 + 1.74603i) q^{84} +(-24.5962 - 29.7670i) q^{85} +(-8.79010 + 15.2249i) q^{86} +(1.36779 - 85.7397i) q^{87} +(39.8419 + 2.61138i) q^{88} +(-39.2771 - 39.2771i) q^{89} +(-1.41796 + 14.5191i) q^{90} +(3.81611 + 5.71122i) q^{91} +(-58.3926 + 19.8216i) q^{92} +(38.0338 + 10.8442i) q^{93} +(-29.1518 - 3.83790i) q^{94} +(31.2769 - 35.6645i) q^{95} +(85.5878 + 6.98239i) q^{96} +(69.2181 + 78.9281i) q^{97} +(24.0703 - 24.0703i) q^{98} +(-23.6280 + 62.9349i) 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 $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.707508	+	0.0931452i	−0.353754	+	0.0465726i	−0.305309	−	0.952253i	$-0.598760\pi$
$2$	−0.707508	+	0.0931452i	−0.353754	+	0.0465726i	−0.0484447	+	0.998826i	$0.515426\pi$
$3$	−2.22368	−	2.01376i	−0.741227	−	0.671254i
$3$	−2.22368	−	2.01376i	−0.741227	−	0.671254i
$4$	−3.37181	+	0.903474i	−0.842953	+	0.225869i
$5$	−2.15087	−	0.730123i	−0.430174	−	0.146025i	0.0979504	−	0.995191i	$-0.468771\pi$
$5$	−2.15087	−	0.730123i	−0.430174	−	0.146025i	−0.528125	+	0.849167i	$0.677105\pi$
$6$	1.76084	+	1.21763i	0.293474	+	0.202938i
$7$	1.07898	−	0.366265i	0.154140	−	0.0523235i	−0.243303	−	0.969950i	$-0.578231\pi$
$7$	1.07898	−	0.366265i	0.154140	−	0.0523235i	0.397443	+	0.917627i	$0.369898\pi$
$8$	4.93860	−	2.04563i	0.617325	−	0.255704i
$9$	0.889516	+	8.95593i	0.0988351	+	0.995104i
$10$	1.58977	+	0.316224i	0.158977	+	0.0316224i
$11$	6.69905	+	3.30361i	0.609005	+	0.300328i	0.720519	−	0.693435i	$-0.243903\pi$
$11$	6.69905	+	3.30361i	0.609005	+	0.300328i	−0.111515	+	0.993763i	$0.535570\pi$
$12$	9.31722	+	4.78099i	0.776435	+	0.398416i
$13$	1.56021	+	5.82278i	0.120016	+	0.447906i	0.999613	−	0.0278133i	$-0.00885438\pi$
$13$	1.56021	+	5.82278i	0.120016	+	0.447906i	−0.879597	+	0.475720i	$0.842188\pi$
$14$	−0.729271	+	0.359637i	−0.0520908	+	0.0256883i
$15$	3.31256	+	5.95491i	0.220837	+	0.396994i
$16$	8.78878	−	5.07421i	0.549299	−	0.317138i
$17$	14.4664	+	8.92882i	0.850964	+	0.525225i
$17$	14.4664	+	8.92882i	0.850964	+	0.525225i
$18$	−1.46354	−	6.25354i	−0.0813078	−	0.347419i
$19$	−7.99196	+	19.2943i	−0.420630	+	1.01549i	0.561533	+	0.827455i	$0.310212\pi$
$19$	−7.99196	+	19.2943i	−0.420630	+	1.01549i	−0.982162	+	0.188035i	$0.939788\pi$
$20$	7.91198	+	0.518579i	0.395599	+	0.0259289i
$21$	−3.13688	−	1.35836i	−0.149375	−	0.0646836i
$22$	−5.04735	−	1.71334i	−0.229425	−	0.0778792i
$23$	17.6274	−	1.15536i	0.766411	−	0.0502332i	0.322817	−	0.946461i	$-0.395370\pi$
$23$	17.6274	−	1.15536i	0.766411	−	0.0502332i	0.443594	+	0.896228i	$0.353703\pi$
$24$	−15.1013	−	5.39633i	−0.629220	−	0.224847i
$25$	−15.7407	−	12.0782i	−0.629626	−	0.483129i
$26$	−1.64622	−	3.97434i	−0.0633163	−	0.152859i
$27$	16.0571	−	21.7064i	0.594709	−	0.803941i
$28$	−3.30721	+	2.20981i	−0.118115	+	0.0789217i
$29$	18.8464	+	21.4902i	0.649877	+	0.741043i	0.979138	−	0.203196i	$-0.0651329\pi$
$29$	18.8464	+	21.4902i	0.649877	+	0.741043i	−0.329261	+	0.944239i	$0.606800\pi$
$30$	−2.89833	−	3.90459i	−0.0966111	−	0.130153i
$31$	−11.8236	+	5.83077i	−0.381407	+	0.188089i	−0.622878	−	0.782319i	$-0.714037\pi$
$31$	−11.8236	+	5.83077i	−0.381407	+	0.188089i	0.241471	+	0.970408i	$0.422370\pi$
$32$	−22.7090	+	17.4252i	−0.709655	+	0.544538i
$33$	−8.24387	−	20.8365i	−0.249814	−	0.631408i
$34$	−11.0668	−	4.96973i	−0.325493	−	0.146169i
$35$	−2.58817			−0.0739476
$36$	−11.0907	−	29.3941i	−0.308076	−	0.816502i
$37$	−30.4113	+	45.5137i	−0.821927	+	1.23010i	0.148550	+	0.988905i	$0.452539\pi$
$37$	−30.4113	+	45.5137i	−0.821927	+	1.23010i	−0.970477	+	0.241195i	$0.922461\pi$
$38$	3.85720	−	14.3953i	0.101505	−	0.378823i
$39$	8.25629	−	16.0899i	0.211700	−	0.412562i
$40$	−12.1159	+	0.794115i	−0.302896	+	0.0198529i
$41$	18.2158	+	15.9748i	0.444288	+	0.389630i	0.852052	−	0.523457i	$-0.175358\pi$
$41$	18.2158	+	15.9748i	0.444288	+	0.389630i	−0.407764	+	0.913087i	$0.633691\pi$
$42$	2.34589	+	0.668862i	0.0558545	+	0.0159253i
$43$	14.9971	−	19.5447i	0.348771	−	0.454527i	−0.585720	−	0.810513i	$-0.699188\pi$
$43$	14.9971	−	19.5447i	0.348771	−	0.454527i	0.934491	+	0.355986i	$0.115855\pi$
$44$	−25.5727	−	5.08672i	−0.581197	−	0.115607i
$45$	4.62570	−	19.9125i	0.102793	−	0.442501i
$46$	−12.3639	+	2.45934i	−0.268781	+	0.0534639i
$47$	39.7995	+	10.6642i	0.846798	+	0.226899i	0.656028	−	0.754736i	$-0.272235\pi$
$47$	39.7995	+	10.6642i	0.846798	+	0.226899i	0.190769	+	0.981635i	$0.438902\pi$
$48$	−29.7617	−	6.41511i	−0.620035	−	0.133648i
$49$	−37.8443	+	29.0389i	−0.772332	+	0.592631i
$50$	12.2617	+	7.07928i	0.245233	+	0.141586i
$51$	−14.1881	−	48.9867i	−0.278198	−	0.960524i
$52$	−10.5215	−	18.2237i	−0.202336	−	0.350456i
$53$	6.58082	−	15.8875i	0.124166	−	0.299764i	−0.849558	−	0.527496i	$-0.823131\pi$
$53$	6.58082	−	15.8875i	0.124166	−	0.299764i	0.973724	+	0.227732i	$0.0731310\pi$
$54$	−9.33870	+	16.8531i	−0.172939	+	0.312094i
$55$	−11.9968	−	11.9968i	−0.218123	−	0.218123i
$56$	4.57941	−	4.01603i	0.0817751	−	0.0717149i
$57$	56.6257	−	26.8105i	0.993434	−	0.470359i
$58$	−15.3357	−	13.4491i	−0.264409	−	0.231880i
$59$	0.665981	−	5.05863i	0.0112878	−	0.0857395i	−0.984874	−	0.173274i	$-0.944565\pi$
$59$	0.665981	−	5.05863i	0.0112878	−	0.0857395i	0.996162	+	0.0875344i	$0.0278988\pi$
$60$	−16.5494	−	17.0860i	−0.275824	−	0.284767i
$61$	−17.8989	−	52.7283i	−0.293424	−	0.864399i	−0.989256	−	0.146194i	$-0.953298\pi$
$61$	−17.8989	−	52.7283i	−0.293424	−	0.864399i	0.695832	−	0.718205i	$-0.255036\pi$
$62$	7.82220	−	5.22663i	0.126165	−	0.0843005i
$63$	4.24001	+	9.33748i	0.0673018	+	0.148214i
$64$	−14.2603	+	14.2603i	−0.222818	+	0.222818i
$65$	0.895534	−	13.6632i	0.0137774	−	0.210203i
$66$	7.77342	+	13.9741i	0.117779	+	0.211729i
$67$	37.7144	+	21.7744i	0.562901	+	0.324991i	0.754309	−	0.656519i	$-0.227972\pi$
$67$	37.7144	+	21.7744i	0.562901	+	0.324991i	−0.191408	+	0.981511i	$0.561305\pi$
$68$	−56.8449	−	17.0363i	−0.835954	−	0.250534i
$69$	−41.5245	−	32.9283i	−0.601804	−	0.477222i
$70$	1.83115	−	0.241075i	0.0261593	−	0.00344393i
$71$	12.5470	−	18.7780i	0.176719	−	0.264479i	−0.732527	−	0.680738i	$-0.761659\pi$
$71$	12.5470	−	18.7780i	0.176719	−	0.264479i	0.909246	+	0.416259i	$0.136659\pi$
$72$	22.7135	+	42.4101i	0.315466	+	0.589030i
$73$	15.7033	+	78.9458i	0.215114	+	1.08145i	0.925821	+	0.377962i	$0.123375\pi$
$73$	15.7033	+	78.9458i	0.215114	+	1.08145i	−0.710707	+	0.703488i	$0.751625\pi$
$74$	17.2768	−	35.0340i	0.233471	−	0.473432i
$75$	10.6795	+	58.5561i	0.142393	+	0.780748i
$76$	9.51549	−	72.2773i	0.125204	−	0.951017i
$77$	8.43814	+	1.11090i	0.109586	+	0.0144273i
$78$	−4.34270	+	12.1528i	−0.0556756	+	0.155805i
$79$	104.764	+	51.6638i	1.32612	+	0.653972i	0.960886	−	0.276943i	$-0.0893213\pi$
$79$	104.764	+	51.6638i	1.32612	+	0.653972i	0.365237	+	0.930915i	$0.380988\pi$
$80$	−22.6083	+	4.49708i	−0.282604	+	0.0562135i
$81$	−79.4175	+	15.9329i	−0.980463	+	0.196702i
$82$	−14.3758	−	9.60560i	−0.175315	−	0.117141i
$83$	15.7020	+	119.269i	0.189181	+	1.43697i	0.777775	+	0.628543i	$0.216348\pi$
$83$	15.7020	+	119.269i	0.189181	+	1.43697i	−0.588594	+	0.808429i	$0.700318\pi$
$84$	11.8042	+	1.74603i	0.140526	+	0.0207861i
$85$	−24.5962	−	29.7670i	−0.289367	−	0.350200i
$86$	−8.79010	+	15.2249i	−0.102210	+	0.177034i
$87$	1.36779	−	85.7397i	0.0157217	−	0.985514i
$88$	39.8419	+	2.61138i	0.452749	+	0.0296747i
$89$	−39.2771	−	39.2771i	−0.441316	−	0.441316i	0.451138	−	0.892454i	$-0.351018\pi$
$89$	−39.2771	−	39.2771i	−0.441316	−	0.441316i	−0.892454	+	0.451138i	$0.851018\pi$
$90$	−1.41796	+	14.5191i	−0.0157551	+	0.161324i
$91$	3.81611	+	5.71122i	0.0419353	+	0.0627606i
$92$	−58.3926	+	19.8216i	−0.634702	+	0.215452i
$93$	38.0338	+	10.8442i	0.408965	+	0.116605i
$94$	−29.1518	−	3.83790i	−0.310125	−	0.0408288i
$95$	31.2769	−	35.6645i	0.329231	−	0.375415i
$96$	85.5878	+	6.98239i	0.891539	+	0.0727332i
$97$	69.2181	+	78.9281i	0.713589	+	0.813692i	0.989044	−	0.147622i	$-0.0471619\pi$
$97$	69.2181	+	78.9281i	0.713589	+	0.813692i	−0.275455	+	0.961314i	$0.588829\pi$
$98$	24.0703	−	24.0703i	0.245615	−	0.245615i
$99$	−23.6280	+	62.9349i	−0.238666	+	0.635706i
$100$	63.9869	+	26.5043i	0.639869	+	0.265043i
$101$	−88.0649	+	50.8443i	−0.871930	+	0.503409i	−0.867989	−	0.496583i	$-0.834588\pi$
$101$	−88.0649	+	50.8443i	−0.871930	+	0.503409i	−0.00394092	+	0.999992i	$0.501254\pi$
$102$	14.6011	+	33.3369i	0.143148	+	0.326833i
$103$	11.9203	−	20.6465i	0.115731	−	0.200452i	−0.802341	−	0.596866i	$-0.796412\pi$
$103$	11.9203	−	20.6465i	0.115731	−	0.200452i	0.918072	+	0.396414i	$0.129746\pi$
$104$	19.6165	+	25.5648i	0.188620	+	0.245815i
$105$	5.75526	+	5.21196i	0.0548120	+	0.0496377i
$106$	−3.17614	+	11.8535i	−0.0299635	+	0.111825i
$107$	32.0208	+	160.980i	0.299260	+	1.50448i	0.778973	+	0.627057i	$0.215741\pi$
$107$	32.0208	+	160.980i	0.299260	+	1.50448i	−0.479713	+	0.877425i	$0.659259\pi$
$108$	−34.5304	+	87.6972i	−0.319726	+	0.812011i
$109$	−7.12601	+	35.8249i	−0.0653763	+	0.328669i	−0.999608	−	0.0279980i	$-0.991087\pi$
$109$	−7.12601	+	35.8249i	−0.0653763	+	0.328669i	0.934232	+	0.356667i	$0.116087\pi$
$110$	9.60525	+	7.37036i	0.0873204	+	0.0670033i
$111$	159.279	−	39.9668i	1.43494	−	0.360062i
$112$	7.62442	−	8.69399i	0.0680752	−	0.0776249i
$113$	−9.49591	−	144.880i	−0.0840346	−	1.28212i	−0.806716	−	0.590939i	$-0.798757\pi$
$113$	−9.49591	−	144.880i	−0.0840346	−	1.28212i	0.722682	−	0.691181i	$-0.242909\pi$
$114$	−37.5659	+	24.2430i	−0.329525	+	0.212658i
$115$	−38.7579	−	10.3852i	−0.337026	−	0.0903057i
$116$	−82.9625	−	55.4338i	−0.715194	−	0.477877i
$117$	−50.7606	+	19.1526i	−0.433851	+	0.163697i
$118$			3.64105i			0.0308564i
$119$	18.8793	+	4.33550i	0.158649	+	0.0364327i
$120$	28.5410	+	22.6326i	0.237841	+	0.188605i
$121$	−39.6966	−	51.7337i	−0.328071	−	0.427551i
$122$	17.5750	+	35.6385i	0.144057	+	0.292119i
$123$	−8.33661	−	72.2052i	−0.0677773	−	0.587034i
$124$	34.5991	−	30.3426i	0.279025	−	0.244698i
$125$	56.5858	+	84.6867i	0.452687	+	0.677493i
$126$	−3.86958	−	6.21140i	−0.0307110	−	0.0492968i
$127$	141.039	−	58.4203i	1.11054	−	0.460002i	0.249419	−	0.968396i	$-0.419760\pi$
$127$	141.039	−	58.4203i	1.11054	−	0.460002i	0.861125	+	0.508393i	$0.169760\pi$
$128$	78.4618	−	102.253i	0.612983	−	0.798855i
$129$	−72.7072	+	13.2604i	−0.563621	+	0.102794i
$130$	0.639064	+	9.75024i	0.00491588	+	0.0750018i
$131$	11.6986	−	34.4630i	0.0893024	−	0.263076i	−0.893098	−	0.449861i	$-0.851473\pi$
$131$	11.6986	−	34.4630i	0.0893024	−	0.263076i	0.982401	+	0.186785i	$0.0598067\pi$
$132$	46.6220	+	62.8085i	0.353197	+	0.475822i
$133$	−1.55635	+	23.7453i	−0.0117019	+	0.178536i
$134$	−28.7114	−	11.8926i	−0.214264	−	0.0887511i
$135$	−50.3852	+	34.9641i	−0.373224	+	0.258993i
$136$	89.7087	+	14.5029i	0.659623	+	0.106639i
$137$	−69.5887	−	120.531i	−0.507947	−	0.879789i	−0.999958	−	0.00920030i	$-0.997071\pi$
$137$	−69.5887	−	120.531i	−0.507947	−	0.879789i	0.492011	−	0.870589i	$-0.336262\pi$
$138$	32.4460	+	19.4293i	0.235116	+	0.140792i
$139$	6.80287	+	13.7949i	0.0489415	+	0.0992435i	0.919970	−	0.391989i	$-0.128213\pi$
$139$	6.80287	+	13.7949i	0.0489415	+	0.0992435i	−0.871028	+	0.491233i	$0.836546\pi$
$140$	8.72681	−	2.33834i	0.0623344	−	0.0167024i
$141$	−67.0261	−	103.861i	−0.475363	−	0.736600i
$142$	−7.12805	+	14.4543i	−0.0501976	+	0.101791i
$143$	−8.78426	+	44.1614i	−0.0614284	+	0.308821i
$144$	53.2620	+	74.1982i	0.369875	+	0.515265i
$145$	−24.8458	−	59.9830i	−0.171350	−	0.413676i
$146$	−18.4636	−	54.3921i	−0.126463	−	0.372549i
$147$	142.631	+	11.6361i	0.970280	+	0.0791570i
$148$	61.4207	−	180.939i	0.415005	−	1.22256i
$149$	6.45730	+	24.0990i	0.0433376	+	0.161738i	0.984203	−	0.177041i	$-0.0566526\pi$
$149$	6.45730	+	24.0990i	0.0433376	+	0.161738i	−0.940866	+	0.338779i	$0.889986\pi$
$150$	−13.0101	−	40.4342i	−0.0867337	−	0.269561i
$151$	−12.7021	−	96.4824i	−0.0841202	−	0.638956i	−0.980621	−	0.195914i	$-0.937233\pi$
$151$	−12.7021	−	96.4824i	−0.0841202	−	0.638956i	0.896501	−	0.443042i	$-0.146101\pi$
$152$			111.635i			0.734444i
$153$	−67.0978	+	137.502i	−0.438548	+	0.898708i
$154$	−6.07352			−0.0394385
$155$	29.6883	−	3.90854i	0.191537	−	0.0252164i
$156$	−13.3019	+	61.7115i	−0.0852683	+	0.395586i
$157$	−299.975	+	80.3780i	−1.91067	+	0.511962i	−0.917111	+	0.398633i	$0.869485\pi$
$157$	−299.975	+	80.3780i	−1.91067	+	0.511962i	−0.993557	+	0.113329i	$0.963848\pi$
$158$	−78.9334	−	26.7943i	−0.499578	−	0.169584i
$159$	−46.6273	+	22.0765i	−0.293253	+	0.138846i
$160$	61.5666	−	20.8991i	0.384791	−	0.130619i
$161$	18.5965	−	7.70292i	0.115506	−	0.0478442i
$162$	54.7044	−	18.6700i	0.337682	−	0.115247i
$163$	−180.883	−	35.9799i	−1.10971	−	0.220736i	−0.393986	−	0.919116i	$-0.628904\pi$
$163$	−180.883	−	35.9799i	−1.10971	−	0.220736i	−0.715726	+	0.698381i	$0.753904\pi$
$164$	−75.8531	−	37.4066i	−0.462519	−	0.228089i
$165$	2.51834	+	50.8356i	0.0152627	+	0.308095i
$166$	−22.2186	−	82.9209i	−0.133847	−	0.499524i
$167$	−66.6469	+	32.8666i	−0.399083	+	0.196806i	−0.630745	−	0.775990i	$-0.717251\pi$
$167$	−66.6469	+	32.8666i	−0.399083	+	0.196806i	0.231661	+	0.972796i	$0.425584\pi$
$168$	−18.2705	−	0.291466i	−0.108753	−	0.00173492i
$169$	114.888	−	66.3305i	0.679809	−	0.392488i
$170$	20.1747	+	18.7693i	0.118674	+	0.110408i
$171$	−179.908	−	54.4129i	−1.05209	−	0.318204i
$172$	−32.9094	+	79.4504i	−0.191334	+	0.461921i
$173$	−222.071	−	14.5553i	−1.28364	−	0.0841345i	−0.591743	−	0.806126i	$-0.701560\pi$
$173$	−222.071	−	14.5553i	−1.28364	−	0.0841345i	−0.691901	+	0.721992i	$0.743227\pi$
$174$	7.01851	+	60.7889i	0.0403363	+	0.349361i
$175$	−21.4077	−	7.26693i	−0.122330	−	0.0415253i
$176$	75.6397	−	4.95769i	0.429771	−	0.0281687i
$177$	−11.6678	+	9.90765i	−0.0659199	+	0.0559754i
$178$	31.4473	+	24.1304i	0.176670	+	0.135564i
$179$	−134.059	−	323.646i	−0.748931	−	1.80808i	−0.564899	−	0.825160i	$-0.691085\pi$
$179$	−134.059	−	323.646i	−0.748931	−	1.80808i	−0.184033	−	0.982920i	$-0.558915\pi$
$180$	2.39348	+	71.3205i	0.0132971	+	0.396225i
$181$	95.5047	−	63.8142i	0.527650	−	0.352565i	−0.263036	−	0.964786i	$-0.584724\pi$
$181$	95.5047	−	63.8142i	0.527650	−	0.352565i	0.790687	+	0.612221i	$0.209724\pi$
$182$	−3.23190	−	3.68528i	−0.0177577	−	0.0202488i
$183$	−66.3810	+	153.295i	−0.362738	+	0.837678i
$184$	84.6914	−	41.7652i	0.460279	−	0.226985i
$185$	98.6414	−	75.6902i	0.533197	−	0.409136i
$186$	−27.9193	−	4.12971i	−0.150104	−	0.0222027i
$187$	67.4138	+	107.606i	0.360501	+	0.575432i
$188$	−143.831			−0.765060
$189$	9.37504	−	29.3020i	0.0496034	−	0.155037i
$190$	−18.8067	+	28.1462i	−0.0989825	+	0.148138i
$191$	60.5352	−	225.921i	0.316938	−	1.18283i	−0.605233	−	0.796049i	$-0.706920\pi$
$191$	60.5352	−	225.921i	0.316938	−	1.18283i	0.922171	−	0.386782i	$-0.126413\pi$
$192$	60.4274	−	2.99350i	0.314726	−	0.0155912i
$193$	−163.806	+	10.7364i	−0.848737	+	0.0556291i	−0.483562	−	0.875310i	$-0.660657\pi$
$193$	−163.806	+	10.7364i	−0.848737	+	0.0556291i	−0.365174	+	0.930939i	$0.618991\pi$
$194$	−56.3241	−	49.3949i	−0.290330	−	0.254613i
$195$	−29.5058	+	28.5792i	−0.151312	+	0.146560i
$196$	101.368	−	132.105i	0.517183	−	0.674006i
$197$	137.401	+	27.3309i	0.697469	+	0.138735i	0.531076	−	0.847324i	$-0.321788\pi$
$197$	137.401	+	27.3309i	0.697469	+	0.138735i	0.166393	+	0.986059i	$0.446788\pi$
$198$	10.8549	−	46.7277i	0.0548227	−	0.235999i
$199$	37.8302	−	7.52489i	0.190101	−	0.0378135i	−0.0991214	−	0.995075i	$-0.531603\pi$
$199$	37.8302	−	7.52489i	0.190101	−	0.0378135i	0.289223	+	0.957262i	$0.406603\pi$
$200$	−102.444	−	27.4499i	−0.512222	−	0.137250i
$201$	−40.0162	−	124.367i	−0.199086	−	0.618742i
$202$	57.5707	−	44.1756i	0.285004	−	0.218691i
$203$	28.2060	+	16.2848i	0.138946	+	0.0802205i
$204$	92.0978	+	152.355i	0.451460	+	0.746840i
$205$	−27.5163	−	47.6596i	−0.134226	−	0.232486i
$206$	−6.51056	+	15.7179i	−0.0316047	+	0.0763004i
$207$	26.0273	+	156.843i	0.125736	+	0.757694i
$208$	43.2583	+	43.2583i	0.207973	+	0.207973i
$209$	−117.279	+	102.851i	−0.561145	+	0.492111i
$210$	−4.55736	−	3.15142i	−0.0217017	−	0.0150068i
$211$	97.7036	+	85.6837i	0.463050	+	0.406084i	0.858829	−	0.512262i	$-0.171192\pi$
$211$	97.7036	+	85.6837i	0.463050	+	0.406084i	−0.395779	+	0.918346i	$0.629526\pi$
$212$	−7.83533	+	59.5153i	−0.0369591	+	0.280732i
$213$	−65.7150	+	16.4895i	−0.308521	+	0.0774153i
$214$	−37.6495	−	110.912i	−0.175932	−	0.518279i
$215$	−46.5269	+	31.0883i	−0.216404	+	0.144597i
$216$	34.8963	−	140.046i	0.161557	−	0.648362i
$217$	−10.6219	+	10.6219i	−0.0489487	+	0.0489487i
$218$	1.70479	−	26.0101i	0.00782016	−	0.119313i
$219$	124.059	−	207.173i	0.566480	−	0.945996i
$220$	51.2896	+	29.6121i	0.233135	+	0.134600i
$221$	−29.4200	+	98.1654i	−0.133122	+	0.444187i
$222$	−108.968	+	43.1129i	−0.490848	+	0.194202i
$223$	362.763	−	47.7586i	1.62674	−	0.214164i	0.738733	−	0.673998i	$-0.235424\pi$
$223$	362.763	−	47.7586i	1.62674	−	0.214164i	0.888005	+	0.459834i	$0.152091\pi$
$224$	−18.1203	+	27.1189i	−0.0808942	+	0.121067i
$225$	94.1703	−	151.716i	0.418535	−	0.674294i
$226$	20.2133	+	101.619i	0.0894392	+	0.449641i
$227$	−84.3235	+	170.991i	−0.371469	+	0.753265i	−0.999693	−	0.0247677i	$-0.992115\pi$
$227$	−84.3235	+	170.991i	−0.371469	+	0.753265i	0.628224	+	0.778032i	$0.283782\pi$
$228$	−166.709	+	141.560i	−0.731179	+	0.620876i
$229$	−2.30441	+	17.5038i	−0.0100629	+	0.0764356i	−0.995739	−	0.0922114i	$-0.970606\pi$
$229$	−2.30441	+	17.5038i	−0.0100629	+	0.0764356i	0.985677	+	0.168647i	$0.0539398\pi$
$230$	28.3889	+	3.73747i	0.123430	+	0.0162499i
$231$	−16.5266	−	19.4627i	−0.0715439	−	0.0842542i
$232$	137.036	+	67.5787i	0.590673	+	0.291288i
$233$	298.526	−	59.3806i	1.28123	−	0.254852i	0.492889	−	0.870092i	$-0.335941\pi$
$233$	298.526	−	59.3806i	1.28123	−	0.254852i	0.788340	+	0.615240i	$0.210941\pi$
$234$	34.1296	−	18.2787i	0.145853	−	0.0781142i
$235$	−77.8174	−	51.9959i	−0.331138	−	0.221259i
$236$	2.32478	+	17.6584i	0.00985076	+	0.0748239i
$237$	−128.923	−	325.853i	−0.543977	−	1.37491i
$238$	−13.7610	−	1.30889i	−0.0578195	−	0.00549952i
$239$	−117.060	+	202.754i	−0.489792	+	0.848344i	−0.999931	−	0.0117474i	$-0.996261\pi$
$239$	−117.060	+	202.754i	−0.489792	+	0.848344i	0.510139	+	0.860092i	$0.329594\pi$
$240$	59.3298	+	35.5278i	0.247207	+	0.148032i
$241$	−471.001	−	30.8710i	−1.95436	−	0.128095i	−0.963934	−	0.266142i	$-0.914251\pi$
$241$	−471.001	−	30.8710i	−1.95436	−	0.128095i	−0.990426	+	0.138046i	$0.955918\pi$
$242$	32.9044	+	32.9044i	0.135969	+	0.135969i
$243$	208.684	+	124.498i	0.858783	+	0.512339i
$244$	107.990	+	161.619i	0.442583	+	0.662373i
$245$	102.600	−	34.8281i	0.418776	−	0.142155i
$246$	12.6238	+	50.3092i	0.0513162	+	0.204509i
$247$	−124.816	−	16.4323i	−0.505327	−	0.0665275i
$248$	−46.4645	+	52.9826i	−0.187357	+	0.213640i
$249$	205.263	−	296.836i	0.824348	−	1.19211i
$250$	−47.9231	−	54.6458i	−0.191692	−	0.218583i
$251$	204.162	−	204.162i	0.813395	−	0.813395i	−0.171746	−	0.985141i	$-0.554941\pi$
$251$	204.162	−	204.162i	0.813395	−	0.813395i	0.985141	+	0.171746i	$0.0549409\pi$
$252$	−22.7327	−	27.6535i	−0.0902091	−	0.109736i
$253$	121.904	+	50.4943i	0.481834	+	0.199582i
$254$	−94.3447	+	54.4699i	−0.371436	+	0.214448i
$255$	−5.24952	+	115.723i	−0.0205864	+	0.453816i
$256$	−5.65361	+	9.79234i	−0.0220844	+	0.0382513i
$257$	35.3652	+	46.0889i	0.137608	+	0.179334i	0.857074	−	0.515194i	$-0.172280\pi$
$257$	35.3652	+	46.0889i	0.137608	+	0.179334i	−0.719466	+	0.694528i	$0.755613\pi$
$258$	50.2057	−	16.1541i	0.194596	−	0.0626130i
$259$	−16.1431	+	60.2470i	−0.0623287	+	0.232614i
$260$	9.32478	+	46.8788i	0.0358645	+	0.180303i
$261$	−175.701	+	187.903i	−0.673184	+	0.719936i
$262$	−5.06680	+	25.4725i	−0.0193389	+	0.0972234i
$263$	335.464	+	257.410i	1.27553	+	0.978747i	0.999847	+	0.0174976i	$0.00556994\pi$
$263$	335.464	+	257.410i	1.27553	+	0.978747i	0.275681	+	0.961249i	$0.411097\pi$
$264$	−83.3370	−	86.0390i	−0.315670	−	0.325905i
$265$	−25.7543	+	29.3672i	−0.0971861	+	0.110820i
$266$	−1.11063	−	16.9450i	−0.00417531	−	0.0637029i
$267$	8.24498	+	166.435i	0.0308801	+	0.623351i
$268$	−146.838	−	39.3452i	−0.547904	−	0.146811i
$269$	−7.13264	−	4.76588i	−0.0265154	−	0.0177170i	0.542242	−	0.840222i	$-0.317576\pi$
$269$	−7.13264	−	4.76588i	−0.0265154	−	0.0177170i	−0.568757	+	0.822505i	$0.692576\pi$
$270$	32.3912	−	29.4305i	0.119967	−	0.109002i
$271$			2.78945i			0.0102932i	0.999987	+	0.00514658i	$0.00163822\pi$
$271$			2.78945i			0.0102932i	−0.999987	+	0.00514658i	$0.998362\pi$
$272$	172.449	+	5.06803i	0.634002	+	0.0186325i
$273$	3.01522	−	20.3847i	0.0110448	−	0.0746692i
$274$	60.4614	+	78.7948i	0.220662	+	0.287572i
$275$	−65.5458	−	132.914i	−0.238348	−	0.483323i
$276$	169.763	+	73.5119i	0.615082	+	0.266348i
$277$	−285.035	+	249.969i	−1.02901	+	0.902414i	−0.995283	−	0.0970176i	$-0.969070\pi$
$277$	−285.035	+	249.969i	−1.02901	+	0.902414i	−0.0337228	+	0.999431i	$0.510736\pi$
$278$	−6.09800	−	9.12631i	−0.0219353	−	0.0328284i
$279$	−62.7373	−	100.705i	−0.224865	−	0.360950i
$280$	−12.7819	+	5.29444i	−0.0456497	+	0.0189087i
$281$	87.9412	−	114.607i	0.312958	−	0.407855i	−0.610217	−	0.792234i	$-0.708918\pi$
$281$	87.9412	−	114.607i	0.312958	−	0.407855i	0.923175	+	0.384379i	$0.125585\pi$
$282$	57.0956	+	67.2390i	0.202467	+	0.238436i
$283$	21.7613	+	332.013i	0.0768949	+	1.17319i	0.845683	+	0.533686i	$0.179194\pi$
$283$	21.7613	+	332.013i	0.0768949	+	1.17319i	−0.768788	+	0.639504i	$0.779140\pi$
$284$	−25.3409	+	74.6518i	−0.0892284	+	0.262858i
$285$	−141.370	+	16.3221i	−0.496034	+	0.0572707i
$286$	2.10150	−	32.0628i	0.00734792	−	0.112108i
$287$	25.5055	+	10.5647i	0.0888694	+	0.0368109i
$288$	−176.259	−	187.880i	−0.612010	−	0.652361i
$289$	129.552	+	258.335i	0.448278	+	0.893894i
$290$	23.1657	+	40.1241i	0.0798817	+	0.138359i
$291$	5.02354	−	314.900i	0.0172630	−	1.08213i
$292$	−124.274	−	252.003i	−0.425596	−	0.863024i
$293$	30.4366	−	8.15547i	0.103879	−	0.0278344i	−0.206505	−	0.978446i	$-0.566209\pi$
$293$	30.4366	−	8.15547i	0.103879	−	0.0278344i	0.310384	+	0.950611i	$0.399542\pi$
$294$	−101.996	+	5.05278i	−0.346927	+	0.0171863i
$295$	−5.12586	+	10.3942i	−0.0173758	+	0.0352346i
$296$	−57.0847	+	286.984i	−0.192854	+	0.969541i
$297$	179.277	−	92.3660i	0.603626	−	0.310997i
$298$	−6.81329	−	16.4487i	−0.0228634	−	0.0551971i
$299$	34.2299	+	100.838i	0.114481	+	0.337251i
$300$	−88.9132	−	187.792i	−0.296377	−	0.625972i
$301$	9.02311	−	26.5812i	0.0299771	−	0.0883097i
$302$	17.9737	+	67.0789i	0.0595157	+	0.222116i
$303$	298.217	+	64.2804i	0.984214	+	0.212146i
$304$	27.6637	+	210.126i	0.0909988	+	0.691205i
$305$			126.480i			0.414689i
$306$	34.6646	−	103.534i	0.113283	−	0.338346i
$307$	−195.690			−0.637428			−0.318714	−	0.947851i	$-0.603251\pi$
$307$	−195.690			−0.637428			−0.318714	+	0.947851i	$0.603251\pi$
$308$	−29.4555	+	3.87789i	−0.0956347	+	0.0125906i
$309$	−68.0841	+	21.9067i	−0.220337	+	0.0708954i
$310$	−20.6406	+	5.53064i	−0.0665827	+	0.0178408i
$311$	77.1365	+	26.1843i	0.248027	+	0.0841939i	0.442685	−	0.896677i	$-0.354026\pi$
$311$	77.1365	+	26.1843i	0.248027	+	0.0841939i	−0.194657	+	0.980871i	$0.562359\pi$
$312$	7.86046	−	96.3509i	0.0251938	−	0.308817i
$313$	75.0879	−	25.4889i	0.239897	−	0.0814342i	−0.198901	−	0.980019i	$-0.563737\pi$
$313$	75.0879	−	25.4889i	0.239897	−	0.0814342i	0.438799	+	0.898585i	$0.355404\pi$
$314$	204.748	−	84.8093i	0.652063	−	0.270093i
$315$	−2.30222	−	23.1795i	−0.00730862	−	0.0735856i
$316$	−399.921	−	79.5491i	−1.26557	−	0.251738i
$317$	445.882	+	219.885i	1.40657	+	0.693642i	0.977755	−	0.209751i	$-0.0672653\pi$
$317$	445.882	+	219.885i	1.40657	+	0.693642i	0.428813	+	0.903393i	$0.358932\pi$
$318$	30.9328	−	19.9624i	0.0972731	−	0.0627749i
$319$	55.2579	+	206.225i	0.173222	+	0.646475i
$320$	41.0840	−	20.2604i	0.128387	−	0.0633137i
$321$	252.971	−	422.450i	0.788071	−	1.31604i
$322$	−12.4397	+	7.18205i	−0.0386325	+	0.0223045i
$323$	−287.890	+	207.760i	−0.891301	+	0.643220i
$324$	253.386	−	125.474i	0.782056	−	0.387267i
$325$	45.7702	−	110.499i	0.140831	−	0.339997i
$326$	131.328	+	8.60766i	0.402845	+	0.0264039i
$327$	87.9888	−	65.3130i	0.269079	−	0.199734i
$328$	122.639	+	41.6304i	0.373900	+	0.126922i
$329$	46.8488	−	3.07063i	0.142398	−	0.00933323i
$330$	−6.51684	−	35.7320i	−0.0197480	−	0.108279i
$331$	−426.549	−	327.302i	−1.28867	−	0.988829i	−0.999502	−	0.0315496i	$-0.989956\pi$
$331$	−426.549	−	327.302i	−1.28867	−	0.988829i	−0.289165	−	0.957279i	$-0.593378\pi$
$332$	−160.700	−	387.965i	−0.484037	−	1.16857i
$333$	−434.669	−	231.876i	−1.30531	−	0.696325i
$334$	44.0919	−	29.4612i	0.132012	−	0.0882073i
$335$	−65.2208	−	74.3701i	−0.194689	−	0.222000i
$336$	−34.4619	+	3.97888i	−0.102565	+	0.0118419i
$337$	142.460	−	70.2535i	0.422730	−	0.208467i	−0.218466	−	0.975845i	$-0.570105\pi$
$337$	142.460	−	70.2535i	0.422730	−	0.208467i	0.641196	+	0.767377i	$0.278439\pi$
$338$	−75.1056	+	57.6306i	−0.222206	+	0.170505i
$339$	−270.637	+	341.288i	−0.798340	+	1.00675i
$340$	109.827	+	78.1466i	0.323022	+	0.229843i
$341$	−98.4697			−0.288767
$342$	132.354	+	21.7400i	0.387001	+	0.0635673i
$343$	−61.2165	+	91.6170i	−0.178474	+	0.267105i
$344$	34.0836	−	127.202i	0.0990803	−	0.369773i
$345$	65.2721	+	101.143i	0.189194	+	0.293167i
$346$	158.472	−	10.3868i	0.458013	−	0.0300197i
$347$	140.795	+	123.474i	0.405749	+	0.355832i	0.837762	−	0.546035i	$-0.183863\pi$
$347$	140.795	+	123.474i	0.405749	+	0.355832i	−0.432014	+	0.901867i	$0.642197\pi$
$348$	72.8517	+	290.334i	0.209344	+	0.834293i
$349$	−207.800	+	270.810i	−0.595415	+	0.775960i	−0.989720	−	0.143020i	$-0.954319\pi$
$349$	−207.800	+	270.810i	−0.595415	+	0.775960i	0.394305	+	0.918980i	$0.370985\pi$
$350$	15.8230	+	3.14739i	0.0452085	+	0.00899254i
$351$	151.444	+	59.6306i	0.431465	+	0.169888i
$352$	−209.695	+	41.7109i	−0.595723	+	0.118497i
$353$	205.107	+	54.9582i	0.581039	+	0.155689i	0.537355	−	0.843356i	$-0.319424\pi$
$353$	205.107	+	54.9582i	0.581039	+	0.155689i	0.0436845	+	0.999045i	$0.486090\pi$
$354$	7.33222	−	8.09654i	0.0207125	−	0.0228716i
$355$	−40.6973	+	31.2282i	−0.114640	+	0.0879666i
$356$	167.921	+	96.9492i	0.471688	+	0.272329i
$357$	−33.2508	−	47.6591i	−0.0931394	−	0.133499i
$358$	124.994	+	216.495i	0.349144	+	0.604736i
$359$	62.1499	−	150.043i	0.173119	−	0.417947i	−0.813375	−	0.581739i	$-0.802372\pi$
$359$	62.1499	−	150.043i	0.173119	−	0.417947i	0.986495	+	0.163792i	$0.0523725\pi$
$360$	−17.8893	−	107.802i	−0.0496925	−	0.299451i
$361$	−53.1332	−	53.1332i	−0.147183	−	0.147183i
$362$	−61.6263	+	54.0449i	−0.170239	+	0.149295i
$363$	−15.9067	+	194.979i	−0.0438201	+	0.537132i
$364$	−18.0272	−	15.8094i	−0.0495252	−	0.0434324i
$365$	23.8643	−	181.268i	0.0653818	−	0.496624i
$366$	32.6864	−	114.641i	0.0893071	−	0.313225i
$367$	−142.545	−	419.923i	−0.388405	−	1.14420i	−0.948773	−	0.315960i	$-0.897673\pi$
$367$	−142.545	−	419.923i	−0.388405	−	1.14420i	0.560368	−	0.828244i	$-0.310660\pi$
$368$	149.061	−	99.5995i	0.405058	−	0.270651i
$369$	−126.866	+	177.349i	−0.343811	+	0.480622i
$370$	−62.7393	+	62.7393i	−0.169566	+	0.169566i
$371$	1.28155	−	19.5526i	0.00345430	−	0.0527025i
$372$	−138.040	−	2.20213i	−0.371076	−	0.00591971i
$373$	572.285	+	330.409i	1.53428	+	0.885815i	0.999158	+	0.0410382i	$0.0130665\pi$
$373$	572.285	+	330.409i	1.53428	+	0.885815i	0.535119	+	0.844777i	$0.320267\pi$
$374$	−57.7187	−	69.8527i	−0.154328	−	0.186772i
$375$	44.7101	−	302.267i	0.119227	−	0.806044i
$376$	218.369	−	28.7488i	0.580768	−	0.0764596i
$377$	−95.7286	+	143.268i	−0.253922	+	0.380021i
$378$	−3.90358	+	21.6046i	−0.0103269	+	0.0571550i
$379$	−87.5798	−	440.293i	−0.231081	−	1.16172i	−0.905819	−	0.423666i	$-0.860743\pi$
$379$	−87.5798	−	440.293i	−0.231081	−	1.16172i	0.674737	−	0.738058i	$-0.264257\pi$
$380$	−73.2379	+	148.512i	−0.192731	+	0.390820i
$381$	−431.271	−	154.111i	−1.13194	−	0.404491i
$382$	−21.7857	+	165.479i	−0.0570307	+	0.433191i
$383$	−338.122	−	44.5146i	−0.882826	−	0.116226i	−0.324537	−	0.945873i	$-0.605208\pi$
$383$	−338.122	−	44.5146i	−0.882826	−	0.116226i	−0.558289	+	0.829647i	$0.688542\pi$
$384$	−380.388	+	69.3755i	−0.990595	+	0.180665i
$385$	−17.3383	−	8.55029i	−0.0450345	−	0.0222085i
$386$	114.894	−	22.8539i	0.297653	−	0.0592069i
$387$	188.381	+	116.928i	0.486772	+	0.302140i
$388$	−304.700	−	203.594i	−0.785309	−	0.524727i
$389$	−17.1040	−	129.918i	−0.0439691	−	0.333978i	−0.999265	−	0.0383278i	$-0.987797\pi$
$389$	−17.1040	−	129.918i	−0.0439691	−	0.333978i	0.955296	−	0.295651i	$-0.0955364\pi$
$390$	18.2136	−	22.9683i	0.0467015	−	0.0588932i
$391$	265.321	+	140.678i	0.678571	+	0.359791i
$392$	−127.495	+	220.827i	−0.325241	+	0.563334i
$393$	−95.4144	+	53.0765i	−0.242785	+	0.135055i
$394$	−99.7583	−	6.53851i	−0.253194	−	0.0165952i
$395$	−187.613	−	187.613i	−0.474968	−	0.474968i
$396$	22.8090	−	233.552i	0.0575986	−	0.589778i
$397$	−303.849	−	454.742i	−0.765362	−	1.14545i	−0.985450	−	0.169966i	$-0.945634\pi$
$397$	−303.849	−	454.742i	−0.765362	−	1.14545i	0.220087	−	0.975480i	$-0.429366\pi$
$398$	−26.0642	+	8.84761i	−0.0654880	+	0.0222302i
$399$	51.2783	−	49.6680i	0.128517	−	0.124481i
$400$	−199.629	−	26.2816i	−0.499072	−	0.0657040i
$401$	392.629	−	447.708i	0.979125	−	1.11648i	−0.0140562	−	0.999901i	$-0.504474\pi$
$401$	392.629	−	447.708i	0.979125	−	1.11648i	0.993182	−	0.116577i	$-0.0371923\pi$
$402$	39.8960	+	84.2634i	0.0992438	+	0.209610i
$403$	−52.3986	−	59.7492i	−0.130021	−	0.148261i
$404$	251.002	−	251.002i	0.621292	−	0.621292i
$405$	182.450	+	23.7149i	0.450494	+	0.0585554i
$406$	−21.4728	−	8.89434i	−0.0528888	−	0.0219072i
$407$	−354.086	+	204.432i	−0.869991	+	0.502289i
$408$	−170.278	−	212.902i	−0.417349	−	0.521819i
$409$	−40.7262	+	70.5398i	−0.0995750	+	0.172469i	−0.911509	−	0.411281i	$-0.865082\pi$
$409$	−40.7262	+	70.5398i	−0.0995750	+	0.172469i	0.811934	+	0.583749i	$0.198415\pi$
$410$	23.9072	+	31.1565i	0.0583103	+	0.0759915i
$411$	−87.9781	+	408.158i	−0.214059	+	0.993085i
$412$	−21.5393	+	80.3859i	−0.0522799	+	0.195111i
$413$	−1.13422	−	5.70209i	−0.00274629	−	0.0138065i
$414$	−33.0236	−	108.543i	−0.0797672	−	0.262181i
$415$	53.3077	−	267.996i	0.128452	−	0.645774i
$416$	−136.894	−	105.042i	−0.329072	−	0.252506i
$417$	12.6522	−	44.3747i	0.0303409	−	0.106414i
$418$	73.3960	−	83.6921i	0.175588	−	0.200220i
$419$	11.4572	+	174.804i	0.0273443	+	0.417193i	0.989485	+	0.144638i	$0.0462018\pi$
$419$	11.4572	+	174.804i	0.0273443	+	0.417193i	−0.962140	+	0.272555i	$0.912131\pi$
$420$	−24.1145	−	12.3740i	−0.0574155	−	0.0294619i
$421$	−580.339	−	155.501i	−1.37848	−	0.369362i	−0.507909	−	0.861410i	$-0.669582\pi$
$421$	−580.339	−	155.501i	−1.37848	−	0.369362i	−0.870568	+	0.492049i	$0.836248\pi$
$422$	−77.1071	−	51.5213i	−0.182718	−	0.122088i
$423$	−60.1060	+	365.928i	−0.142094	+	0.865077i
$424$		−	91.9239i		−	0.216802i
$425$	−119.866	−	315.274i	−0.282038	−	0.741821i
$426$	44.9580	−	17.7875i	0.105535	−	0.0417546i
$427$	−38.6250	−	50.3371i	−0.0904568	−	0.117886i
$428$	−253.409	−	513.863i	−0.592078	−	1.20061i
$429$	108.464	−	80.5116i	0.252830	−	0.187673i
$430$	30.0224	−	26.3290i	0.0698196	−	0.0612302i
$431$	114.651	+	171.588i	0.266012	+	0.398116i	0.940297	−	0.340356i	$-0.110548\pi$
$431$	114.651	+	171.588i	0.266012	+	0.398116i	−0.674284	+	0.738472i	$0.735548\pi$
$432$	30.9798	−	272.250i	0.0717125	−	0.630209i
$433$	330.769	−	137.009i	0.763900	−	0.316418i	0.0335014	−	0.999439i	$-0.489334\pi$
$433$	330.769	−	137.009i	0.763900	−	0.316418i	0.730399	+	0.683021i	$0.239334\pi$
$434$	6.52567	−	8.50442i	0.0150361	−	0.0195954i
$435$	−65.5424	+	183.416i	−0.150672	+	0.421647i
$436$	−8.33929	−	127.233i	−0.0191268	−	0.291819i
$437$	−118.586	+	349.343i	−0.271364	+	0.799412i
$438$	−68.4756	+	158.132i	−0.156337	+	0.361032i
$439$	−15.0587	+	229.752i	−0.0343023	+	0.523353i	0.945786	+	0.324791i	$0.105294\pi$
$439$	−15.0587	+	229.752i	−0.0343023	+	0.523353i	−0.980088	+	0.198562i	$0.936373\pi$
$440$	−83.7882	−	34.7062i	−0.190428	−	0.0788777i
$441$	−293.734	−	313.100i	−0.666063	−	0.709978i
$442$	11.6712	−	72.1931i	0.0264055	−	0.163333i
$443$	−371.999	−	644.321i	−0.839727	−	1.45445i	−0.890123	−	0.455720i	$-0.849382\pi$
$443$	−371.999	−	644.321i	−0.839727	−	1.45445i	0.0503961	−	0.998729i	$-0.483952\pi$
$444$	−500.949	+	278.665i	−1.12826	+	0.627624i
$445$	55.8030	+	113.157i	0.125400	+	0.254286i
$446$	−252.209	+	67.5792i	−0.565491	+	0.151523i
$447$	34.1706	−	66.5919i	0.0764444	−	0.148975i
$448$	−10.1636	+	20.6097i	−0.0226865	+	0.0460038i
$449$	−62.9246	+	316.343i	−0.140144	+	0.704551i	0.845265	+	0.534347i	$0.179443\pi$
$449$	−62.9246	+	316.343i	−0.140144	+	0.704551i	−0.985409	+	0.170204i	$0.945557\pi$
$450$	−52.4946	+	116.112i	−0.116655	+	0.258026i
$451$	69.2540	+	167.194i	0.153557	+	0.370719i
$452$	162.913	+	479.927i	0.360428	+	1.06179i
$453$	−166.047	+	240.125i	−0.366550	+	0.530078i
$454$	43.7325	−	128.832i	0.0963271	−	0.283771i
$455$	−4.03808	−	15.0703i	−0.00887491	−	0.0331216i
$456$	224.807	−	248.242i	0.492999	−	0.544390i
$457$	74.7694	+	567.930i	0.163609	+	1.24273i	0.854375	+	0.519657i	$0.173940\pi$
$457$	74.7694	+	567.930i	0.163609	+	1.24273i	−0.690766	+	0.723078i	$0.742727\pi$
$458$		−	12.5987i		−	0.0275081i
$459$	426.101	−	170.642i	0.928325	−	0.371769i
$460$	140.067			0.304494
$461$	−169.822	+	22.3574i	−0.368377	+	0.0484977i	−0.312442	−	0.949937i	$-0.601147\pi$
$461$	−169.822	+	22.3574i	−0.368377	+	0.0484977i	−0.0559344	+	0.998434i	$0.517814\pi$
$462$	13.5056	+	12.2306i	0.0292329	+	0.0264732i
$463$	591.798	−	158.572i	1.27818	−	0.342488i	0.445021	−	0.895520i	$-0.353196\pi$
$463$	591.798	−	158.572i	1.27818	−	0.342488i	0.833160	+	0.553032i	$0.186529\pi$
$464$	274.683	+	93.2423i	0.591989	+	0.200953i
$465$	−73.8882	−	51.0939i	−0.158899	−	0.109879i
$466$	−205.679	+	69.8185i	−0.441371	+	0.149825i
$467$	−419.399	+	173.721i	−0.898070	+	0.371993i	−0.783478	−	0.621420i	$-0.786556\pi$
$467$	−419.399	+	173.721i	−0.898070	+	0.371993i	−0.114592	+	0.993413i	$0.536556\pi$
$468$	153.851	−	110.440i	0.328742	−	0.235983i
$469$	48.6683	+	9.68072i	0.103770	+	0.0206412i
$470$	59.8996	+	29.5392i	0.127446	+	0.0628494i
$471$	828.911	+	425.343i	1.75990	+	0.903064i
$472$	−7.05909	−	26.3449i	−0.0149557	−	0.0558155i
$473$	165.034	−	81.3860i	0.348910	−	0.172063i
$474$	121.565	+	218.535i	0.256467	+	0.461044i
$475$	358.840	−	207.176i	0.755452	−	0.436161i
$476$	−67.5743	+	2.43844i	−0.141963	+	0.00512277i
$477$	148.141	+	44.8052i	0.310568	+	0.0939312i
$478$	63.9355	−	154.354i	0.133756	−	0.322916i
$479$	744.752	+	48.8136i	1.55481	+	0.101907i	0.818407	−	0.574640i	$-0.194858\pi$
$479$	744.752	+	48.8136i	1.55481	+	0.101907i	0.736399	+	0.676547i	$0.236524\pi$
$480$	−178.990	−	77.5078i	−0.372896	−	0.161475i
$481$	−312.464	−	106.067i	−0.649614	−	0.220514i
$482$	336.112	−	22.0299i	0.697328	−	0.0457053i
$483$	−56.8646	−	20.3201i	−0.117732	−	0.0420706i
$484$	180.590	+	138.571i	0.373119	+	0.286304i
$485$	−91.2521	−	220.302i	−0.188149	−	0.454231i
$486$	−159.242	−	68.6456i	−0.327659	−	0.141246i
$487$	348.753	−	233.029i	0.716125	−	0.478500i	−0.143353	−	0.989672i	$-0.545788\pi$
$487$	348.753	−	233.029i	0.716125	−	0.478500i	0.859478	+	0.511172i	$0.170788\pi$
$488$	−196.258	−	223.790i	−0.402168	−	0.458585i
$489$	329.772	+	444.264i	0.674379	+	0.908515i
$490$	−69.3463	+	34.1978i	−0.141523	+	0.0697915i
$491$	31.7954	−	24.3975i	0.0647564	−	0.0496893i	−0.575876	−	0.817537i	$-0.695339\pi$
$491$	31.7954	−	24.3975i	0.0647564	−	0.0496893i	0.640632	+	0.767848i	$0.278672\pi$
$492$	93.3451	+	235.931i	0.189726	+	0.479534i
$493$	80.7573	+	479.162i	0.163808	+	0.971932i
$494$	89.8386			0.181860
$495$	96.7709	−	118.114i	0.195497	−	0.238613i
$496$	−74.3288	+	111.241i	−0.149856	+	0.224276i
$497$	6.66031	−	24.8566i	0.0134010	−	0.0500133i
$498$	−117.576	+	229.133i	−0.236096	+	0.460106i
$499$	628.085	−	41.1669i	1.25869	−	0.0824987i	0.578589	−	0.815619i	$-0.303604\pi$
$499$	628.085	−	41.1669i	1.25869	−	0.0824987i	0.680099	+	0.733121i	$0.261937\pi$
$500$	−267.309	−	234.424i	−0.534618	−	0.468847i
$501$	214.387	+	61.1262i	0.427919	+	0.122008i
$502$	−125.430	+	163.463i	−0.249860	+	0.325624i
$503$	944.979	+	187.968i	1.87869	+	0.373694i	0.995454	−	0.0952420i	$-0.0303625\pi$
$503$	944.979	+	187.968i	1.87869	+	0.373694i	0.883232	+	0.468936i	$0.155362\pi$
$504$	40.0408	+	37.4405i	0.0794460	+	0.0742868i
$505$	226.539	−	45.0614i	0.448592	−	0.0892305i
$506$	−90.9514	−	24.3703i	−0.179746	−	0.0481627i
$507$	−389.048	−	83.8589i	−0.767352	−	0.165402i
$508$	−422.776	+	324.407i	−0.832236	+	0.638597i
$509$	454.759	+	262.555i	0.893436	+	0.515825i	0.875065	−	0.484006i	$-0.160819\pi$
$509$	454.759	+	262.555i	0.893436	+	0.515825i	0.0183710	+	0.999831i	$0.494152\pi$
$510$	−7.06498	−	82.3640i	−0.0138529	−	0.161498i
$511$	45.8586	+	79.4294i	0.0897429	+	0.155439i
$512$	−194.205	+	468.852i	−0.379306	+	0.915727i
$513$	290.482	+	483.288i	0.566242	+	0.942082i
$514$	−29.3141	−	29.3141i	−0.0570314	−	0.0570314i
$515$	−40.7135	+	35.7048i	−0.0790553	+	0.0693297i
$516$	233.174	−	110.401i	0.451888	−	0.213955i
$517$	231.388	+	202.922i	0.447560	+	0.392499i
$518$	5.80967	−	44.1288i	0.0112156	−	0.0851908i
$519$	464.503	+	479.564i	0.894997	+	0.924015i
$520$	−23.5272	−	69.3090i	−0.0452447	−	0.133287i
$521$	−671.218	+	448.494i	−1.28833	+	0.860832i	−0.995447	−	0.0953174i	$-0.969613\pi$
$521$	−671.218	+	448.494i	−1.28833	+	0.860832i	−0.292879	+	0.956149i	$0.594613\pi$
$522$	106.807	−	149.309i	0.204612	−	0.286032i
$523$	357.329	−	357.329i	0.683229	−	0.683229i	−0.277497	−	0.960726i	$-0.589505\pi$
$523$	357.329	−	357.329i	0.683229	−	0.683229i	0.960726	+	0.277497i	$0.0895049\pi$
$524$	−8.30909	+	126.772i	−0.0158570	+	0.241932i
$525$	32.9700	+	59.2694i	0.0628000	+	0.112894i
$526$	−261.320	−	150.873i	−0.496806	−	0.286831i
$527$	−223.107	−	21.2209i	−0.423353	−	0.0402674i
$528$	−178.182	−	141.296i	−0.337466	−	0.267606i
$529$	−215.082	+	28.3161i	−0.406583	+	0.0535276i
$530$	15.4860	−	23.1764i	0.0292188	−	0.0437290i
$531$	45.8972	+	1.46475i	0.0864353	+	0.00275848i
$532$	−16.2056	−	81.4710i	−0.0304616	−	0.153141i
$533$	−64.5975	+	130.991i	−0.121196	+	0.245761i
$534$	−21.3360	−	116.986i	−0.0399550	−	0.219075i
$535$	48.6622	−	369.626i	0.0909573	−	0.690889i
$536$	230.799	+	30.3852i	0.430594	+	0.0566888i
$537$	−353.643	+	989.649i	−0.658554	+	1.84292i
$538$	5.49032	+	2.70753i	0.0102051	+	0.00503258i
$539$	−349.454	+	69.5107i	−0.648338	+	0.128962i
$540$	138.300	−	163.414i	0.256112	−	0.302618i
$541$	664.116	+	443.748i	1.22757	+	0.820237i	0.988567	−	0.150782i	$-0.0481792\pi$
$541$	664.116	+	443.748i	1.22757	+	0.820237i	0.239004	+	0.971019i	$0.423179\pi$
$542$	−0.259824	−	1.97356i	−0.000479379	−	0.00364125i
$543$	−340.879	−	50.4214i	−0.627769	−	0.0928571i
$544$	−484.103	+	49.3155i	−0.889896	+	0.0906534i
$545$	41.4837	−	71.8519i	0.0761169	−	0.131838i
$546$	−0.234557	+	14.7032i	−0.000429592	+	0.0269289i
$547$	−447.609	−	29.3378i	−0.818298	−	0.0536341i	−0.349496	−	0.936938i	$-0.613647\pi$
$547$	−447.609	−	29.3378i	−0.818298	−	0.0536341i	−0.468801	+	0.883304i	$0.655314\pi$
$548$	343.537	+	343.537i	0.626892	+	0.626892i
$549$	456.310	−	207.204i	0.831166	−	0.377420i
$550$	58.7544	+	87.9322i	0.106826	+	0.159877i
$551$	−565.259	+	191.880i	−1.02588	+	0.348239i
$552$	−272.432	−	77.6760i	−0.493536	−	0.140717i
$553$	131.961	+	17.3729i	0.238627	+	0.0314158i
$554$	178.381	−	203.404i	0.321987	−	0.367156i
$555$	−371.769	−	30.3295i	−0.669854	−	0.0546478i
$556$	−35.4013	−	40.3674i	−0.0636714	−	0.0726033i
$557$	686.583	−	686.583i	1.23264	−	1.23264i	0.269700	−	0.962944i	$-0.413076\pi$
$557$	686.583	−	686.583i	1.23264	−	1.23264i	0.962944	−	0.269700i	$-0.0869245\pi$
$558$	53.7673	+	65.4060i	0.0963572	+	0.117215i
$559$	137.203	+	56.8313i	0.245444	+	0.101666i
$560$	−22.7468	+	13.1329i	−0.0406193	+	0.0234516i
$561$	66.7860	−	375.036i	0.119048	−	0.668514i
$562$	−51.5440	+	89.2768i	−0.0917152	+	0.158855i
$563$	−564.994	−	736.314i	−1.00354	−	1.30784i	−0.950990	−	0.309223i	$-0.899931\pi$
$563$	−564.994	−	736.314i	−1.00354	−	1.30784i	−0.0525518	−	0.998618i	$-0.516735\pi$
$564$	319.835	+	289.642i	0.567083	+	0.513550i
$565$	−85.3553	+	318.550i	−0.151071	+	0.563806i
$566$	−46.3216	−	232.875i	−0.0818403	−	0.411439i
$567$	−79.8543	+	46.2791i	−0.140837	+	0.0816210i
$568$	23.5519	−	118.404i	0.0414647	−	0.208457i
$569$	−355.624	−	272.880i	−0.624998	−	0.479578i	0.247047	−	0.969004i	$-0.420540\pi$
$569$	−355.624	−	272.880i	−0.624998	−	0.479578i	−0.872045	+	0.489426i	$0.837206\pi$
$570$	98.4998	−	24.7159i	0.172807	−	0.0433613i
$571$	508.119	−	579.399i	0.889876	−	1.01471i	−0.109908	−	0.993942i	$-0.535056\pi$
$571$	508.119	−	579.399i	0.889876	−	1.01471i	0.999784	−	0.0207676i	$-0.00661101\pi$
$572$	−10.2799	−	156.840i	−0.0179718	−	0.274197i
$573$	−589.562	+	380.472i	−1.02890	+	0.664000i
$574$	−19.0294	−	5.09891i	−0.0331523	−	0.00888312i
$575$	−291.422	−	194.722i	−0.506822	−	0.338647i
$576$	−140.399	−	115.030i	−0.243749	−	0.199705i
$577$		−	843.017i		−	1.46104i	−0.682894	−	0.730518i	$-0.739279\pi$
$577$		−	843.017i		−	1.46104i	0.682894	−	0.730518i	$-0.260721\pi$
$578$	−115.722	−	170.707i	−0.200211	−	0.295341i
$579$	385.873	+	305.992i	0.666448	+	0.528484i
$580$	137.968	+	179.804i	0.237876	+	0.310007i
$581$	60.6260	+	122.937i	0.104348	+	0.211596i
$582$	25.7772	+	223.262i	0.0442907	+	0.383612i
$583$	96.5713	−	84.6907i	0.165645	−	0.145267i
$584$	239.047	+	357.758i	0.409326	+	0.612600i
$585$	123.163	−	4.13330i	0.210536	−	0.00706547i
$586$	−20.7745	+	8.60508i	−0.0354514	+	0.0146844i
$587$	−58.6553	+	76.4410i	−0.0999238	+	0.130223i	−0.840639	−	0.541596i	$-0.817820\pi$
$587$	−58.6553	+	76.4410i	−0.0999238	+	0.130223i	0.740715	+	0.671819i	$0.234487\pi$
$588$	−491.438	+	89.6289i	−0.835779	+	0.152430i
$589$	−18.0066	−	274.728i	−0.0305715	−	0.466431i
$590$	2.65842	−	7.83144i	0.00450579	−	0.0132736i
$591$	−250.499	−	337.469i	−0.423857	−	0.571014i
$592$	−36.3323	+	554.323i	−0.0613720	+	0.936356i
$593$	−712.341	−	295.061i	−1.20125	−	0.497574i	−0.309847	−	0.950786i	$-0.600278\pi$
$593$	−712.341	−	295.061i	−1.20125	−	0.497574i	−0.891403	+	0.453212i	$0.850278\pi$
$594$	−118.236	+	82.0484i	−0.199051	+	0.138129i
$595$	−37.4414	−	23.1093i	−0.0629267	−	0.0388391i
$596$	−43.5456	−	75.4232i	−0.0730631	−	0.126549i
$597$	−99.2755	−	59.4480i	−0.166291	−	0.0995779i
$598$	−33.6105	−	68.1554i	−0.0562049	−	0.113972i
$599$	−1106.83	+	296.575i	−1.84780	+	0.495117i	−0.999413	−	0.0342595i	$-0.989093\pi$
$599$	−1106.83	+	296.575i	−1.84780	+	0.495117i	−0.848387	+	0.529376i	$0.822426\pi$
$600$	172.526	+	267.339i	0.287544	+	0.445564i
$601$	214.812	−	435.595i	0.357424	−	0.724783i	−0.641686	−	0.766967i	$-0.721765\pi$
$601$	214.812	−	435.595i	0.357424	−	0.724783i	0.999110	+	0.0421839i	$0.0134316\pi$
$602$	−3.90801	+	19.6469i	−0.00649170	+	0.0326360i
$603$	−161.463	+	357.136i	−0.267765	+	0.592266i
$604$	129.999	+	313.844i	0.215230	+	0.519610i
$605$	47.6105	+	140.256i	0.0786950	+	0.231828i
$606$	−216.978	−	17.7014i	−0.358050	−	0.0292103i
$607$	−58.3125	+	171.783i	−0.0960667	+	0.283004i	−0.984331	−	0.176329i	$-0.943578\pi$
$607$	−58.3125	+	171.783i	−0.0960667	+	0.283004i	0.888265	+	0.459332i	$0.151911\pi$
$608$	−154.718	−	577.415i	−0.254470	−	0.949696i
$609$	−29.9276	−	93.0124i	−0.0491422	−	0.152730i
$610$	−11.7810	−	89.4858i	−0.0193132	−	0.146698i
$611$			248.382i			0.406517i
$612$	102.011	−	524.253i	0.166685	−	0.856623i
$613$	393.271			0.641552			0.320776	−	0.947155i	$-0.396056\pi$
$613$	393.271			0.641552			0.320776	+	0.947155i	$0.396056\pi$
$614$	138.452	−	18.2276i	0.225493	−	0.0296867i
$615$	−34.7877	+	161.391i	−0.0565653	+	0.262424i
$616$	43.9451	−	11.7750i	0.0713394	−	0.0191153i
$617$	−110.656	−	37.5626i	−0.179345	−	0.0608794i	0.230322	−	0.973114i	$-0.426022\pi$
$617$	−110.656	−	37.5626i	−0.179345	−	0.0608794i	−0.409667	+	0.912235i	$0.634355\pi$
$618$	46.1295	−	21.8408i	0.0746433	−	0.0353412i
$619$	784.955	−	266.456i	1.26810	−	0.430462i	0.395306	−	0.918549i	$-0.370639\pi$
$619$	784.955	−	266.456i	1.26810	−	0.430462i	0.872795	+	0.488087i	$0.162305\pi$
$620$	−96.5721	+	40.0015i	−0.155761	+	0.0645185i
$621$	257.967	−	401.181i	0.415406	−	0.646023i
$622$	−57.0136	−	11.3407i	−0.0916617	−	0.0182326i
$623$	−56.7651	−	27.9934i	−0.0911157	−	0.0449333i
$624$	−9.08070	−	183.305i	−0.0145524	−	0.293758i
$625$	68.5014	+	255.651i	0.109602	+	0.409041i
$626$	−50.7511	+	25.0277i	−0.0810720	+	0.0399803i
$627$	467.910	+	7.46449i	0.746268	+	0.0119051i
$628$	938.840	−	542.039i	1.49497	−	0.863120i
$629$	−846.325	+	386.882i	−1.34551	+	0.615074i
$630$	3.78789	+	16.1852i	0.00601252	+	0.0256908i
$631$	70.7952	−	170.915i	0.112195	−	0.270863i	−0.857802	−	0.513981i	$-0.828170\pi$
$631$	70.7952	−	170.915i	0.112195	−	0.270863i	0.969997	+	0.243118i	$0.0781702\pi$
$632$	623.071	+	40.8382i	0.985872	+	0.0646175i
$633$	−44.7149	−	387.285i	−0.0706396	−	0.611825i
$634$	−335.946	−	114.038i	−0.529883	−	0.179871i
$635$	−346.011	+	22.6788i	−0.544899	+	0.0357146i
$636$	137.273	−	116.564i	0.215838	−	0.183277i
$637$	−228.132	−	175.052i	−0.358135	−	0.274807i
$638$	−58.3043	−	140.759i	−0.0913861	−	0.220626i
$639$	179.335	+	95.6672i	0.280650	+	0.149714i
$640$	−243.419	+	162.647i	−0.380342	+	0.254137i
$641$	77.3455	+	88.1956i	0.120664	+	0.137591i	0.809018	−	0.587784i	$-0.200000\pi$
$641$	77.3455	+	88.1956i	0.120664	+	0.137591i	−0.688354	+	0.725375i	$0.741666\pi$
$642$	−139.630	+	322.449i	−0.217492	+	0.502258i
$643$	−152.318	+	75.1149i	−0.236886	+	0.116819i	−0.556858	−	0.830608i	$-0.687993\pi$
$643$	−152.318	+	75.1149i	−0.236886	+	0.116819i	0.319972	+	0.947427i	$0.396327\pi$
$644$	−55.7445	+	42.7743i	−0.0865598	+	0.0664197i
$645$	166.066	+	24.5637i	0.257466	+	0.0380833i
$646$	184.333	−	173.807i	0.285345	−	0.269052i
$647$	−371.295			−0.573872			−0.286936	−	0.957950i	$-0.592637\pi$
$647$	−371.295			−0.573872			−0.286936	+	0.957950i	$0.592637\pi$
$648$	−359.618	+	241.145i	−0.554967	+	0.372138i
$649$	21.1732	−	31.6879i	0.0326243	−	0.0488257i
$650$	−22.0903	+	82.4422i	−0.0339851	+	0.126834i
$651$	45.0096	−	2.22972i	0.0691391	−	0.00342507i
$652$	642.411	−	42.1058i	0.985293	−	0.0645795i
$653$	699.727	+	613.644i	1.07156	+	0.939731i	0.998341	−	0.0575849i	$-0.0183400\pi$
$653$	699.727	+	613.644i	1.07156	+	0.939731i	0.0732173	+	0.997316i	$0.476673\pi$
$654$	−56.1692	+	54.4052i	−0.0858856	+	0.0831884i
$655$	−50.3245	+	65.5841i	−0.0768312	+	0.100128i
$656$	241.154	+	47.9686i	0.367613	+	0.0731228i
$657$	−693.065	+	210.861i	−1.05489	+	0.320946i
$658$	−32.8599	+	6.53623i	−0.0499390	+	0.00993349i
$659$	−766.150	−	205.289i	−1.16259	−	0.311516i	−0.374593	−	0.927189i	$-0.622218\pi$
$659$	−766.150	−	205.289i	−1.16259	−	0.311516i	−0.788002	+	0.615673i	$0.788884\pi$
$660$	−54.4201	−	169.133i	−0.0824546	−	0.256262i
$661$	−824.614	+	632.749i	−1.24752	+	0.957260i	−0.999933	−	0.0116047i	$-0.996306\pi$
$661$	−824.614	+	632.749i	−1.24752	+	0.957260i	−0.247592	+	0.968864i	$0.579639\pi$
$662$	332.273	+	191.838i	0.501923	+	0.289786i
$663$	263.103	−	159.044i	0.396836	−	0.239885i
$664$	321.526	+	556.899i	0.484226	+	0.838704i
$665$	20.6845	−	49.9369i	0.0311046	−	0.0750931i
$666$	329.130	+	123.567i	0.494189	+	0.185536i
$667$	357.044	+	357.044i	0.535298	+	0.535298i
$668$	195.027	−	171.034i	0.291956	−	0.256039i
$669$	−902.843	−	624.318i	−1.34954	−	0.933211i
$670$	53.0714	+	46.5424i	0.0792111	+	0.0694663i
$671$	54.2883	−	412.361i	0.0809066	−	0.614547i
$672$	94.9049	−	23.8139i	0.141228	−	0.0354374i
$673$	−188.416	−	555.056i	−0.279965	−	0.824749i	−0.992405	−	0.123016i	$-0.960743\pi$
$673$	−188.416	−	555.056i	−0.279965	−	0.824749i	0.712440	−	0.701733i	$-0.247590\pi$
$674$	−94.2478	+	62.9744i	−0.139834	+	0.0934338i
$675$	−514.925	+	147.732i	−0.762852	+	0.218862i
$676$	−327.452	+	327.452i	−0.484397	+	0.484397i
$677$	38.7236	−	590.808i	0.0571988	−	0.872685i	−0.868801	−	0.495161i	$-0.835109\pi$
$677$	38.7236	−	590.808i	0.0571988	−	0.872685i	0.926000	−	0.377524i	$-0.123224\pi$
$678$	159.689	−	266.673i	0.235529	−	0.393323i
$679$	103.594	+	59.8097i	0.152568	+	0.0880850i
$680$	−182.363	−	96.6923i	−0.268181	−	0.142195i
$681$	531.844	−	210.422i	0.780975	−	0.308990i
$682$	69.6681	−	9.17198i	0.102153	−	0.0134486i
$683$	477.510	−	714.645i	0.699136	−	1.04633i	−0.296682	−	0.954976i	$-0.595880\pi$
$683$	477.510	−	714.645i	0.699136	−	1.04633i	0.995818	−	0.0913553i	$-0.0291199\pi$
$684$	655.775	+	20.9283i	0.958735	+	0.0305969i
$685$	61.6738	+	310.055i	0.0900348	+	0.452635i
$686$	34.7775	−	70.5217i	0.0506960	−	0.102801i
$687$	40.3727	−	34.2822i	0.0587667	−	0.0499014i
$688$	32.6330	−	247.872i	0.0474317	−	0.360279i
$689$	102.777	+	13.5308i	0.149168	+	0.0196384i
$690$	−55.6014	−	65.4794i	−0.0805818	−	0.0948977i
$691$	−673.181	−	331.976i	−0.974213	−	0.480429i	−0.115736	−	0.993280i	$-0.536923\pi$
$691$	−673.181	−	331.976i	−0.974213	−	0.480429i	−0.858478	+	0.512851i	$0.828589\pi$
$692$	761.930	−	151.557i	1.10106	−	0.219014i
$693$	−2.44331	+	76.5596i	−0.00352570	+	0.110476i
$694$	−111.114	−	74.2443i	−0.160107	−	0.106980i
$695$	−4.56016	−	34.6379i	−0.00656139	−	0.0498387i
$696$	−168.637	−	426.232i	−0.242295	−	0.612402i
$697$	120.880	+	393.744i	0.173430	+	0.564912i
$698$	121.795	−	210.956i	0.174492	−	0.302229i
$699$	−783.406	−	469.118i	−1.12075	−	0.671127i
$700$	78.7482	+	5.16143i	0.112497	+	0.00737347i
$701$	−119.189	−	119.189i	−0.170027	−	0.170027i	0.616964	−	0.786991i	$-0.288362\pi$
$701$	−119.189	−	119.189i	−0.170027	−	0.170027i	−0.786991	+	0.616964i	$0.788362\pi$
$702$	−112.702	−	28.0828i	−0.160545	−	0.0400040i
$703$	−635.109	−	950.508i	−0.903427	−	1.35207i
$704$	−142.641	+	48.4202i	−0.202616	+	0.0687787i
$705$	68.3336	+	272.328i	0.0969271	+	0.386281i
$706$	−150.234	−	19.7786i	−0.212796	−	0.0280151i
$707$	−76.3979	+	87.1151i	−0.108059	+	0.123218i
$708$	30.3904	−	43.9483i	0.0429242	−	0.0620739i
$709$	−552.953	−	630.522i	−0.779906	−	0.889312i	0.216301	−	0.976327i	$-0.430601\pi$
$709$	−552.953	−	630.522i	−0.779906	−	0.889312i	−0.996207	+	0.0870143i	$0.972267\pi$
$710$	25.8849	−	25.8849i	0.0364576	−	0.0364576i
$711$	−369.508	+	984.213i	−0.519702	+	1.38427i
$712$	−274.321	−	113.627i	−0.385282	−	0.159589i
$713$	−201.684	+	116.442i	−0.282866	+	0.163313i
$714$	27.9644	+	30.6220i	0.0391658	+	0.0428880i
$715$	51.1371	−	88.5720i	0.0715204	−	0.123877i
$716$	744.427	+	970.156i	1.03970	+	1.35497i
$717$	668.604	−	215.129i	0.932502	−	0.300041i
$718$	−29.9957	+	111.946i	−0.0417768	+	0.155913i
$719$	−172.497	−	867.200i	−0.239912	−	1.20612i	−0.893428	−	0.449206i	$-0.851707\pi$
$719$	−172.497	−	867.200i	−0.239912	−	1.20612i	0.653516	−	0.756913i	$-0.273293\pi$
$720$	−60.3860	−	198.479i	−0.0838695	−	0.275665i
$721$	5.29966	−	26.6432i	0.00735042	−	0.0369531i
$722$	42.5412	+	32.6430i	0.0589214	+	0.0452119i
$723$	985.188	+	1017.13i	1.36264	+	1.40682i
$724$	−264.370	+	301.456i	−0.365151	+	0.416375i
$725$	−37.0912	−	565.902i	−0.0511603	−	0.780555i
$726$	−6.90723	−	139.431i	−0.00951409	−	0.192053i
$727$	−901.938	−	241.674i	−1.24063	−	0.332426i	−0.421920	−	0.906633i	$-0.638644\pi$
$727$	−901.938	−	241.674i	−1.24063	−	0.332426i	−0.818710	+	0.574207i	$0.805310\pi$
$728$	30.5293	+	20.3990i	0.0419359	+	0.0280207i
$729$	−213.337	−	697.086i	−0.292643	−	0.956222i
$730$			130.471i			0.178728i
$731$	391.465	−	148.834i	0.535520	−	0.203603i
$732$	85.3262	−	576.856i	0.116566	−	0.788054i
$733$	−66.2830	−	86.3817i	−0.0904270	−	0.117847i	0.745949	−	0.666003i	$-0.231996\pi$
$733$	−66.2830	−	86.3817i	−0.0904270	−	0.117847i	−0.836376	+	0.548157i	$0.815330\pi$
$734$	139.965	+	283.821i	0.190688	+	0.386677i
$735$	−298.285	−	129.166i	−0.405831	−	0.175736i
$736$	−380.169	+	333.399i	−0.516534	+	0.452988i
$737$	180.716	+	270.461i	0.245206	+	0.366976i
$738$	73.2396	−	137.293i	0.0992407	−	0.186034i
$739$	−1198.60	+	496.476i	−1.62192	+	0.671822i	−0.994292	−	0.106690i	$-0.965975\pi$
$739$	−1198.60	+	496.476i	−1.62192	+	0.671822i	−0.627629	+	0.778512i	$0.715975\pi$
$740$	−264.216	+	344.333i	−0.357049	+	0.465315i
$741$	244.459	+	287.889i	0.329905	+	0.388515i
$742$	0.914528	+	13.9530i	0.00123252	+	0.0188046i
$743$	45.5932	−	134.313i	0.0613637	−	0.180772i	−0.911925	−	0.410358i	$-0.865404\pi$
$743$	45.5932	−	134.313i	0.0613637	−	0.180772i	0.973288	+	0.229586i	$0.0737372\pi$
$744$	210.017	−	24.2479i	0.282281	−	0.0325913i
$745$	3.70638	−	56.5484i	0.00497501	−	0.0759039i
$746$	−435.672	−	180.461i	−0.584011	−	0.241905i
$747$	−1054.20	+	246.718i	−1.41124	+	0.330278i
$748$	−324.526	−	301.920i	−0.433858	−	0.403637i
$749$	93.5110	+	161.966i	0.124848	+	0.216243i
$750$	−3.47804	+	218.021i	−0.00463739	+	0.290694i
$751$	−368.676	−	747.600i	−0.490913	−	0.995473i	−0.991539	−	0.129809i	$-0.958563\pi$
$751$	−368.676	−	747.600i	−0.490913	−	0.995473i	0.500626	−	0.865664i	$-0.333103\pi$
$752$	403.902	−	108.225i	0.537103	−	0.143916i
$753$	−865.126	+	42.8573i	−1.14891	+	0.0569154i
$754$	54.3840	−	110.280i	0.0721273	−	0.146260i
$755$	−43.1233	+	216.795i	−0.0571169	+	0.287146i
$756$	−5.13731	+	107.271i	−0.00679538	+	0.141893i
$757$	509.672	+	1230.46i	0.673279	+	1.62544i	0.776003	+	0.630729i	$0.217244\pi$
$757$	509.672	+	1230.46i	0.673279	+	1.62544i	−0.102724	+	0.994710i	$0.532756\pi$
$758$	102.975	+	303.353i	0.135850	+	0.400202i
$759$	−169.392	−	357.769i	−0.223178	−	0.471369i
$760$	81.5076	−	240.114i	0.107247	−	0.315939i
$761$	391.553	+	1461.30i	0.514524	+	1.92023i	0.363050	+	0.931770i	$0.381735\pi$
$761$	391.553	+	1461.30i	0.514524	+	1.92023i	0.151474	+	0.988461i	$0.451598\pi$
$762$	319.482	+	68.8641i	0.419268	+	0.0903728i
$763$	5.43256	+	41.2644i	0.00711999	+	0.0540817i
$764$			816.454i			1.06866i
$765$	244.712	−	246.760i	0.319885	−	0.322562i
$766$	243.370			0.317716
$767$	30.4944	−	4.01466i	0.0397580	−	0.00523424i
$768$	32.2913	−	10.3900i	0.0420459	−	0.0135287i
$769$	−813.046	+	217.855i	−1.05728	+	0.283297i	−0.745256	−	0.666778i	$-0.767673\pi$
$769$	−813.046	+	217.855i	−1.05728	+	0.283297i	−0.312021	+	0.950075i	$0.601006\pi$
$770$	13.0634	+	4.43442i	0.0169654	+	0.00575898i
$771$	14.1711	−	173.704i	0.0183801	−	0.225297i
$772$	542.624	−	184.196i	0.702880	−	0.238596i
$773$	915.550	−	379.233i	1.18441	−	0.490600i	0.298481	−	0.954416i	$-0.403520\pi$
$773$	915.550	−	379.233i	1.18441	−	0.490600i	0.885931	+	0.463816i	$0.153520\pi$
$774$	−144.172	−	65.1808i	−0.186269	−	0.0842129i
$775$	256.537	+	51.0284i	0.331016	+	0.0658431i
$776$	503.298	+	248.199i	0.648580	+	0.319844i
$777$	157.220	−	101.462i	0.202343	−	0.130581i
$778$	24.2024	+	90.3245i	0.0311085	+	0.116098i
$779$	−453.803	+	223.791i	−0.582546	+	0.287280i
$780$	73.6676	−	123.022i	0.0944456	−	0.157720i
$781$	146.088	−	84.3442i	0.187053	−	0.107995i
$782$	−200.820	−	74.8176i	−0.256804	−	0.0956747i
$783$	769.096	−	64.0170i	0.982242	−	0.0817586i
$784$	−185.256	+	447.246i	−0.236295	+	0.570467i
$785$	703.893	+	46.1356i	0.896680	+	0.0587715i
$786$	62.5626	−	46.4394i	0.0795961	−	0.0590832i
$787$	−212.089	−	71.9944i	−0.269490	−	0.0914796i	0.183423	−	0.983034i	$-0.441282\pi$
$787$	−212.089	−	71.9944i	−0.269490	−	0.0914796i	−0.452914	+	0.891554i	$0.649615\pi$
$788$	−487.985	+	31.9842i	−0.619270	+	0.0405891i
$789$	−227.601	−	1247.94i	−0.288468	−	1.58168i
$790$	150.213	+	115.262i	0.190142	+	0.145901i
$791$	−63.3101	−	152.844i	−0.0800381	−	0.193229i
$792$	12.0527	+	359.144i	0.0152180	+	0.453465i
$793$	279.100	−	186.488i	0.351954	−	0.235168i
$794$	257.332	+	293.431i	0.324096	+	0.369561i
$795$	116.408	−	13.4401i	0.146425	−	0.0169058i
$796$	−120.758	+	59.5511i	−0.151706	+	0.0748129i
$797$	579.774	−	444.876i	0.727446	−	0.558189i	−0.177292	−	0.984158i	$-0.556734\pi$
$797$	579.774	−	444.876i	0.727446	−	0.558189i	0.904737	+	0.425970i	$0.140067\pi$
$798$	−31.6535	+	39.9168i	−0.0396660	+	0.0500210i
$799$	480.536	+	509.635i	0.601421	+	0.637841i
$800$	567.920			0.709900
$801$	316.826	−	386.701i	0.395538	−	0.482773i
$802$	−236.086	+	353.328i	−0.294372	+	0.440559i
$803$	−155.609	+	580.740i	−0.193784	+	0.723213i
$804$	247.290	+	383.189i	0.307574	+	0.476603i
$805$	−45.6228	+	2.99028i	−0.0566743	+	0.00371463i
$806$	42.6378	+	37.3923i	0.0529005	+	0.0463925i
$807$	6.26337	+	24.9613i	0.00776130	+	0.0309309i
$808$	−330.908	+	431.248i	−0.409540	+	0.533723i
$809$	1348.01	+	268.136i	1.66627	+	0.331441i	0.936075	−	0.351799i	$-0.114430\pi$
$809$	1348.01	+	268.136i	1.66627	+	0.331441i	0.730193	+	0.683241i	$0.239430\pi$
$810$	−131.294	+	0.215837i	−0.162091	+	0.000266465i
$811$	−1211.22	+	240.926i	−1.49349	+	0.297073i	−0.873223	−	0.487322i	$-0.837974\pi$
$811$	−1211.22	+	240.926i	−1.49349	+	0.297073i	−0.620263	+	0.784394i	$0.712974\pi$
$812$	−109.818	−	29.4257i	−0.135244	−	0.0362386i
$813$	5.61729	−	6.20284i	0.00690933	−	0.00762957i
$814$	231.477	−	177.618i	0.284370	−	0.218204i
$815$	362.787	+	209.455i	0.445137	+	0.257000i
$816$	−373.265	−	358.540i	−0.457432	−	0.439387i
$817$	257.244	+	445.559i	0.314864	+	0.545360i
$818$	22.2436	−	53.7009i	0.0271927	−	0.0656490i
$819$	−47.7548	+	39.2571i	−0.0583087	+	0.0479330i
$820$	135.839	+	135.839i	0.165657	+	0.165657i
$821$	666.912	−	584.866i	0.812317	−	0.712383i	−0.148697	−	0.988883i	$-0.547508\pi$
$821$	666.912	−	584.866i	0.812317	−	0.712383i	0.961014	+	0.276500i	$0.0891746\pi$
$822$	24.2273	−	296.970i	0.0294735	−	0.361277i
$823$	517.879	+	454.168i	0.629258	+	0.551844i	0.913464	−	0.406919i	$-0.133397\pi$
$823$	517.879	+	454.168i	0.629258	+	0.551844i	−0.284207	+	0.958763i	$0.591730\pi$
$824$	16.6342	−	126.349i	0.0201872	−	0.153337i
$825$	−121.904	+	427.551i	−0.147762	+	0.518244i
$826$	1.33359	+	3.92862i	0.00161451	+	0.00475620i
$827$	−993.699	+	663.969i	−1.20157	+	0.802864i	−0.984857	−	0.173371i	$-0.944534\pi$
$827$	−993.699	+	663.969i	−1.20157	+	0.802864i	−0.216715	+	0.976235i	$0.569534\pi$
$828$	−229.462	−	505.329i	−0.277128	−	0.610300i
$829$	−415.809	+	415.809i	−0.501579	+	0.501579i	−0.911928	−	0.410349i	$-0.865407\pi$
$829$	−415.809	+	415.809i	−0.501579	+	0.501579i	0.410349	+	0.911928i	$0.365407\pi$
$830$	−12.7531	+	194.575i	−0.0153652	+	0.234427i
$831$	1137.20	+	18.1416i	1.36848	+	0.0218311i
$832$	−105.284	−	60.7857i	−0.126543	−	0.0730598i
$833$	−806.753	+	82.1837i	−0.968491	+	0.0986599i
$834$	−4.81821	+	32.5739i	−0.00577723	+	0.0390575i
$835$	167.346	−	22.0315i	0.200414	−	0.0263850i
$836$	302.521	−	452.754i	0.361867	−	0.541572i
$837$	−63.2885	+	350.274i	−0.0756135	+	0.418488i
$838$	−24.3882	−	122.608i	−0.0291029	−	0.146310i
$839$	48.9886	−	99.3391i	0.0583893	−	0.118402i	−0.865722	−	0.500525i	$-0.833140\pi$
$839$	48.9886	−	99.3391i	0.0583893	−	0.118402i	0.924111	+	0.382123i	$0.124807\pi$
$840$	39.0847	+	13.9666i	0.0465294	+	0.0166269i
$841$	3.13023	−	23.7764i	0.00372203	−	0.0282716i
$842$	425.078	+	55.9626i	0.504844	+	0.0664639i
$843$	−426.345	+	77.7571i	−0.505747	+	0.0922386i
$844$	−406.851	−	200.637i	−0.482051	−	0.237721i
$845$	−295.538	+	58.7862i	−0.349749	+	0.0695695i
$846$	8.44104	−	264.495i	0.00997759	−	0.312642i
$847$	−61.7801	−	41.2802i	−0.0729399	−	0.0487369i
$848$	−22.7791	−	173.024i	−0.0268621	−	0.204038i
$849$	620.205	−	782.112i	0.730512	−	0.921216i
$850$	114.172	+	211.894i	0.134320	+	0.249287i
$851$	−483.488	+	837.426i	−0.568141	+	0.984050i
$852$	206.681	−	114.971i	0.242583	−	0.134943i
$853$	402.656	+	26.3915i	0.472047	+	0.0309396i	0.299571	−	0.954074i	$-0.403156\pi$
$853$	402.656	+	26.3915i	0.472047	+	0.0309396i	0.172476	+	0.985014i	$0.444823\pi$
$854$	32.0162	+	32.0162i	0.0374897	+	0.0374897i
$855$	347.230	+	248.390i	0.406117	+	0.290514i
$856$	487.443	+	729.511i	0.569443	+	0.852232i
$857$	744.039	−	252.567i	0.868190	−	0.294711i	0.148421	−	0.988924i	$-0.452581\pi$
$857$	744.039	−	252.567i	0.868190	−	0.294711i	0.719769	+	0.694213i	$0.244248\pi$
$858$	−69.2399	+	67.0654i	−0.0806992	+	0.0781649i
$859$	−476.064	−	62.6750i	−0.554207	−	0.0729627i	−0.151779	−	0.988414i	$-0.548500\pi$
$859$	−476.064	−	62.6750i	−0.554207	−	0.0729627i	−0.402428	+	0.915452i	$0.631834\pi$
$860$	128.793	−	146.860i	0.149759	−	0.170767i
$861$	−35.4413	−	74.8546i	−0.0411629	−	0.0869392i
$862$	−97.0993	−	110.721i	−0.112644	−	0.128446i
$863$	563.282	−	563.282i	0.652702	−	0.652702i	−0.300941	−	0.953643i	$-0.597301\pi$
$863$	563.282	−	563.282i	0.652702	−	0.652702i	0.953643	+	0.300941i	$0.0973007\pi$
$864$	13.5979	+	772.729i	0.0157383	+	0.894363i
$865$	467.018	+	193.445i	0.539905	+	0.223636i
$866$	−221.260	+	127.744i	−0.255496	+	0.147511i
$867$	232.143	−	835.343i	0.267754	−	0.963487i
$868$	26.2183	−	45.4115i	0.0302055	−	0.0523174i
$869$	531.141	+	692.196i	0.611209	+	0.796544i
$870$	29.2874	−	135.874i	0.0336637	−	0.156176i
$871$	−67.9453	+	253.575i	−0.0780083	+	0.291131i
$872$	38.0921	+	191.502i	0.0436836	+	0.219612i
$873$	−645.304	+	690.120i	−0.739180	+	0.790516i
$874$	51.3609	−	258.209i	0.0587653	−	0.295433i
$875$	92.0727	+	70.6499i	0.105226	+	0.0807427i
$876$	−231.128	+	810.633i	−0.263845	+	0.925380i
$877$	951.879	−	1085.41i	1.08538	−	1.23764i	0.115694	−	0.993285i	$-0.463091\pi$
$877$	951.879	−	1085.41i	1.08538	−	1.23764i	0.969686	−	0.244354i	$-0.0785759\pi$
$878$	−10.7461	−	163.954i	−0.0122393	−	0.186736i
$879$	−84.1045	−	43.1570i	−0.0956821	−	0.0490978i
$880$	−166.311	−	44.5629i	−0.188990	−	0.0506397i
$881$	1119.17	+	747.806i	1.27034	+	0.848815i	0.993691	−	0.112155i	$-0.0357754\pi$
$881$	1119.17	+	747.806i	1.27034	+	0.848815i	0.276651	+	0.960970i	$0.410775\pi$
$882$	236.983	+	194.161i	0.268688	+	0.220137i
$883$		−	249.005i		−	0.281999i	−0.990010	−	0.141000i	$-0.954968\pi$
$883$		−	249.005i		−	0.281999i	0.990010	−	0.141000i	$-0.0450317\pi$
$884$	10.5087	−	357.576i	0.0118876	−	0.404497i
$885$	32.3298	−	12.7912i	0.0365308	−	0.0144533i
$886$	323.208	+	421.212i	0.364794	+	0.475409i
$887$	−685.580	−	1390.22i	−0.772919	−	1.56733i	−0.822640	−	0.568562i	$-0.807500\pi$
$887$	−685.580	−	1390.22i	−0.772919	−	1.56733i	0.0497208	−	0.998763i	$-0.484167\pi$
$888$	704.856	−	523.206i	0.793757	−	0.589196i
$889$	130.781	−	114.692i	0.147110	−	0.129012i
$890$	−50.0211	−	74.8618i	−0.0562034	−	0.0841144i
$891$	−584.658	−	155.629i	−0.656182	−	0.174668i
$892$	−1180.02	+	488.780i	−1.32289	+	0.547959i
$893$	−523.835	+	682.675i	−0.586601	+	0.764474i
$894$	−17.9733	+	50.2971i	−0.0201043	+	0.0562608i
$895$	52.0416	+	794.001i	0.0581470	+	0.887152i
$896$	47.2070	−	139.067i	0.0526864	−	0.155209i
$897$	126.948	−	293.163i	0.141525	−	0.326826i
$898$	15.0538	−	229.676i	0.0167637	−	0.255764i
$899$	−348.138	−	144.203i	−0.387250	−	0.160404i
$900$	−180.453	+	596.639i	−0.200503	+	0.662932i
$901$	237.057	−	171.076i	0.263105	−	0.189873i
$902$	−64.5711	−	111.840i	−0.0715866	−	0.123992i
$903$	−73.5928	+	40.9378i	−0.0814981	+	0.0453353i
$904$	−343.267	−	696.076i	−0.379720	−	0.769996i
$905$	−252.011	+	67.5261i	−0.278465	+	0.0746144i
$906$	95.1131	−	185.357i	0.104981	−	0.204588i
$907$	277.634	−	562.987i	0.306102	−	0.620713i	−0.688412	−	0.725320i	$-0.741692\pi$
$907$	277.634	−	562.987i	0.306102	−	0.620713i	0.994514	+	0.104607i	$0.0333584\pi$
$908$	129.837	−	652.734i	0.142992	−	0.718870i
$909$	−533.694	−	743.477i	−0.587122	−	0.817906i
$910$	4.26070	+	10.2862i	0.00468209	+	0.0113036i
$911$	532.892	+	1569.85i	0.584953	+	1.72322i	0.685298	+	0.728263i	$0.259672\pi$
$911$	532.892	+	1569.85i	0.584953	+	1.72322i	−0.100345	+	0.994953i	$0.531995\pi$
$912$	361.629	−	522.962i	0.396523	−	0.573423i
$913$	−288.828	+	850.860i	−0.316351	+	0.931939i
$914$	−105.800	−	394.850i	−0.115755	−	0.432003i
$915$	254.701	−	281.252i	0.278362	−	0.307379i
$916$	−8.04415	−	61.1014i	−0.00878182	−	0.0667045i
$917$		−	41.4697i		−	0.0452232i
$918$	−285.575	+	160.420i	−0.311084	+	0.174749i
$919$	83.4376			0.0907917			0.0453959	−	0.998969i	$-0.485545\pi$
$919$	83.4376			0.0907917			0.0453959	+	0.998969i	$0.485545\pi$
$920$	−212.654	+	27.9964i	−0.231146	+	0.0304309i
$921$	435.153	+	394.074i	0.472479	+	0.427876i
$922$	118.068	−	31.6361i	0.128056	−	0.0343125i
$923$	128.916	+	43.7611i	0.139671	+	0.0474118i
$924$	73.3088	+	50.6932i	0.0793385	+	0.0548628i
$925$	1028.42	−	349.101i	1.11180	−	0.377407i
$926$	−403.931	+	167.314i	−0.436211	+	0.180685i
$927$	195.512	+	88.3918i	0.210909	+	0.0953525i
$928$	−802.455	−	159.618i	−0.864714	−	0.172002i
$929$	−625.214	−	308.322i	−0.672997	−	0.331885i	0.0734798	−	0.997297i	$-0.476590\pi$
$929$	−625.214	−	308.322i	−0.672997	−	0.331885i	−0.746477	+	0.665411i	$0.768256\pi$
$930$	57.0356	+	29.2670i	0.0613286	+	0.0314699i
$931$	−257.836	−	962.257i	−0.276945	−	1.03357i
$932$	−952.926	+	469.931i	−1.02245	+	0.504218i
$933$	−118.798	−	213.560i	−0.127329	−	0.228896i
$934$	280.546	−	161.974i	0.300371	−	0.173419i
$935$	−66.4329	−	280.667i	−0.0710512	−	0.300178i
$936$	−211.507	+	198.425i	−0.225969	+	0.211992i
$937$	−296.558	+	715.955i	−0.316498	+	0.764093i	0.682937	+	0.730477i	$0.260702\pi$
$937$	−296.558	+	715.955i	−0.316498	+	0.764093i	−0.999435	+	0.0336161i	$0.989298\pi$
$938$	−35.3349	−	2.31597i	−0.0376704	−	0.00246905i
$939$	−218.300	−	94.5300i	−0.232482	−	0.100671i
$940$	309.363	+	105.014i	0.329109	+	0.111718i
$941$	135.907	−	8.90784i	0.144429	−	0.00946636i	0.00698273	−	0.999976i	$-0.497777\pi$
$941$	135.907	−	8.90784i	0.144429	−	0.00946636i	0.137446	+	0.990509i	$0.456111\pi$
$942$	−626.079	−	223.725i	−0.664628	−	0.237500i
$943$	339.555	+	260.550i	0.360079	+	0.276299i
$944$	−19.8154	−	47.8385i	−0.0209909	−	0.0506764i
$945$	−41.5585	+	56.1798i	−0.0439773	+	0.0594496i
$946$	−109.182	+	72.9534i	−0.115415	+	0.0771177i
$947$	−111.036	−	126.612i	−0.117250	−	0.133698i	0.690237	−	0.723583i	$-0.257506\pi$
$947$	−111.036	−	126.612i	−0.117250	−	0.133698i	−0.807487	+	0.589885i	$0.799173\pi$
$948$	729.103	+	982.237i	0.769096	+	1.03612i
$949$	−435.184	+	214.609i	−0.458571	+	0.226142i
$950$	−234.585	+	180.003i	−0.246931	+	0.189477i
$951$	−548.704	−	1386.85i	−0.576976	−	1.45831i
$952$	102.106	−	17.2088i	0.107254	−	0.0180764i
$953$	−132.763			−0.139311			−0.0696553	−	0.997571i	$-0.522190\pi$
$953$	−132.763			−0.139311			−0.0696553	+	0.997571i	$0.522190\pi$
$954$	−108.984	−	17.9014i	−0.114239	−	0.0187646i
$955$	−295.153	+	441.728i	−0.309061	+	0.462543i
$956$	211.522	−	789.410i	0.221257	−	0.825743i
$957$	292.413	−	569.856i	0.305552	−	0.595461i
$958$	−531.465	+	34.8340i	−0.554765	+	0.0363612i
$959$	−119.231	−	104.563i	−0.124329	−	0.109033i
$960$	−132.157	−	37.6808i	−0.137664	−	0.0392508i
$961$	−479.219	+	624.531i	−0.498667	+	0.649876i
$962$	230.951	+	45.9389i	0.240073	+	0.0477536i
$963$	−1413.24	+	429.971i	−1.46754	+	0.446491i
$964$	1616.02	−	321.446i	1.67637	−	0.333450i
$965$	360.165	+	96.5059i	0.373228	+	0.100006i
$966$	42.1248	+	9.07997i	0.0436075	+	0.00939956i
$967$	892.864	−	685.118i	0.923334	−	0.708499i	−0.0334068	−	0.999442i	$-0.510636\pi$
$967$	892.864	−	685.118i	0.923334	−	0.708499i	0.956740	+	0.290943i	$0.0939690\pi$
$968$	−301.874	−	174.287i	−0.311853	−	0.180049i
$969$	1058.56	+	117.750i	1.09242	+	0.121517i
$970$	85.0816	+	147.366i	0.0877130	+	0.151923i
$971$	−249.313	+	601.894i	−0.256759	+	0.619871i	−0.998720	−	0.0505717i	$-0.983896\pi$
$971$	−249.313	+	601.894i	−0.256759	+	0.619871i	0.741962	+	0.670442i	$0.233896\pi$
$972$	−816.125	−	231.244i	−0.839635	−	0.237906i
$973$	12.3927	+	12.3927i	0.0127366	+	0.0127366i
$974$	−225.040	+	197.355i	−0.231047	+	0.202623i
$975$	−324.297	+	153.544i	−0.332612	+	0.157481i
$976$	−424.864	−	372.595i	−0.435311	−	0.381758i
$977$	−72.1092	+	547.724i	−0.0738068	+	0.560618i	0.914091	+	0.405510i	$0.132906\pi$
$977$	−72.1092	+	547.724i	−0.0738068	+	0.560618i	−0.987897	+	0.155108i	$0.950427\pi$
$978$	−274.697	−	283.603i	−0.280876	−	0.289983i
$979$	−133.363	−	392.876i	−0.136224	−	0.401303i
$980$	−314.482	+	210.130i	−0.320900	+	0.214419i
$981$	−327.184	−	31.9533i	−0.333521	−	0.0325722i
$982$	−20.2230	+	20.2230i	−0.0205937	+	0.0205937i
$983$	66.0663	−	1007.98i	0.0672088	−	1.02541i	−0.822466	−	0.568814i	$-0.807402\pi$
$983$	66.0663	−	1007.98i	0.0672088	−	1.02541i	0.889675	−	0.456594i	$-0.150931\pi$
$984$	−188.877	−	339.539i	−0.191948	−	0.345060i
$985$	−275.578	−	159.105i	−0.279775	−	0.161528i
$986$	−101.768	−	331.489i	−0.103213	−	0.336196i
$987$	−110.360	−	87.5143i	−0.111814	−	0.0886670i
$988$	435.701	−	57.3611i	0.440993	−	0.0580578i
$989$	241.780	−	361.850i	0.244469	−	0.365874i
$990$	−57.4645	+	92.5800i	−0.0580449	+	0.0935152i
$991$	−44.7221	−	224.833i	−0.0451282	−	0.226875i	0.951639	−	0.307218i	$-0.0993982\pi$
$991$	−44.7221	−	224.833i	−0.0451282	−	0.226875i	−0.996767	+	0.0803436i	$0.974398\pi$
$992$	166.900	−	338.440i	0.168246	−	0.341169i
$993$	289.399	+	1586.78i	0.291439	+	1.59797i
$994$	−2.39695	+	18.2066i	−0.00241142	+	0.0183165i
$995$	−86.8619	−	11.4356i	−0.0872984	−	0.0114931i
$996$	−423.923	+	1186.32i	−0.425626	+	1.19109i
$997$	47.2751	+	23.3135i	0.0474174	+	0.0233837i	0.465843	−	0.884867i	$-0.345751\pi$
$997$	47.2751	+	23.3135i	0.0474174	+	0.0233837i	−0.418425	+	0.908251i	$0.637418\pi$
$998$	−440.540	+	87.6289i	−0.441423	+	0.0878046i
$999$	499.621	+	1390.94i	0.500122	+	1.39233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.t.a.58.15	yes	544
9.7	even	3	inner	153.3.t.a.7.20	✓	544
17.5	odd	16	inner	153.3.t.a.22.20	yes	544
153.124	odd	48	inner	153.3.t.a.124.15	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.t.a.7.20	✓	544	9.7	even	3	inner
153.3.t.a.22.20	yes	544	17.5	odd	16	inner
153.3.t.a.58.15	yes	544	1.1	even	1	trivial
153.3.t.a.124.15	yes	544	153.124	odd	48	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+(-0.707508 + 0.0931452i) q^{2} +(-2.22368 - 2.01376i) q^{3} +(-3.37181 + 0.903474i) q^{4} +(-2.15087 - 0.730123i) q^{5} +(1.76084 + 1.21763i) q^{6} +(1.07898 - 0.366265i) q^{7} +(4.93860 - 2.04563i) q^{8} +(0.889516 + 8.95593i) q^{9} +(1.58977 + 0.316224i) q^{10} +(6.69905 + 3.30361i) q^{11} +(9.31722 + 4.78099i) q^{12} +(1.56021 + 5.82278i) q^{13} +(-0.729271 + 0.359637i) q^{14} +(3.31256 + 5.95491i) q^{15} +(8.78878 - 5.07421i) q^{16} +(14.4664 + 8.92882i) q^{17} +(-1.46354 - 6.25354i) q^{18} +(-7.99196 + 19.2943i) q^{19} +(7.91198 + 0.518579i) q^{20} +(-3.13688 - 1.35836i) q^{21} +(-5.04735 - 1.71334i) q^{22} +(17.6274 - 1.15536i) q^{23} +(-15.1013 - 5.39633i) q^{24} +(-15.7407 - 12.0782i) q^{25} +(-1.64622 - 3.97434i) q^{26} +(16.0571 - 21.7064i) q^{27} +(-3.30721 + 2.20981i) q^{28} +(18.8464 + 21.4902i) q^{29} +(-2.89833 - 3.90459i) q^{30} +(-11.8236 + 5.83077i) q^{31} +(-22.7090 + 17.4252i) q^{32} +(-8.24387 - 20.8365i) q^{33} +(-11.0668 - 4.96973i) q^{34} -2.58817 q^{35} +(-11.0907 - 29.3941i) q^{36} +(-30.4113 + 45.5137i) q^{37} +(3.85720 - 14.3953i) q^{38} +(8.25629 - 16.0899i) q^{39} +(-12.1159 + 0.794115i) q^{40} +(18.2158 + 15.9748i) q^{41} +(2.34589 + 0.668862i) q^{42} +(14.9971 - 19.5447i) q^{43} +(-25.5727 - 5.08672i) q^{44} +(4.62570 - 19.9125i) q^{45} +(-12.3639 + 2.45934i) q^{46} +(39.7995 + 10.6642i) q^{47} +(-29.7617 - 6.41511i) q^{48} +(-37.8443 + 29.0389i) q^{49} +(12.2617 + 7.07928i) q^{50} +(-14.1881 - 48.9867i) q^{51} +(-10.5215 - 18.2237i) q^{52} +(6.58082 - 15.8875i) q^{53} +(-9.33870 + 16.8531i) q^{54} +(-11.9968 - 11.9968i) q^{55} +(4.57941 - 4.01603i) q^{56} +(56.6257 - 26.8105i) q^{57} +(-15.3357 - 13.4491i) q^{58} +(0.665981 - 5.05863i) q^{59} +(-16.5494 - 17.0860i) q^{60} +(-17.8989 - 52.7283i) q^{61} +(7.82220 - 5.22663i) q^{62} +(4.24001 + 9.33748i) q^{63} +(-14.2603 + 14.2603i) q^{64} +(0.895534 - 13.6632i) q^{65} +(7.77342 + 13.9741i) q^{66} +(37.7144 + 21.7744i) q^{67} +(-56.8449 - 17.0363i) q^{68} +(-41.5245 - 32.9283i) q^{69} +(1.83115 - 0.241075i) q^{70} +(12.5470 - 18.7780i) q^{71} +(22.7135 + 42.4101i) q^{72} +(15.7033 + 78.9458i) q^{73} +(17.2768 - 35.0340i) q^{74} +(10.6795 + 58.5561i) q^{75} +(9.51549 - 72.2773i) q^{76} +(8.43814 + 1.11090i) q^{77} +(-4.34270 + 12.1528i) q^{78} +(104.764 + 51.6638i) q^{79} +(-22.6083 + 4.49708i) q^{80} +(-79.4175 + 15.9329i) q^{81} +(-14.3758 - 9.60560i) q^{82} +(15.7020 + 119.269i) q^{83} +(11.8042 + 1.74603i) q^{84} +(-24.5962 - 29.7670i) q^{85} +(-8.79010 + 15.2249i) q^{86} +(1.36779 - 85.7397i) q^{87} +(39.8419 + 2.61138i) q^{88} +(-39.2771 - 39.2771i) q^{89} +(-1.41796 + 14.5191i) q^{90} +(3.81611 + 5.71122i) q^{91} +(-58.3926 + 19.8216i) q^{92} +(38.0338 + 10.8442i) q^{93} +(-29.1518 - 3.83790i) q^{94} +(31.2769 - 35.6645i) q^{95} +(85.5878 + 6.98239i) q^{96} +(69.2181 + 78.9281i) q^{97} +(24.0703 - 24.0703i) q^{98} +(-23.6280 + 62.9349i) 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

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Representations

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Database

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