LMFDB - Embedded newform 152.2.o.c.27.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(27,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.27"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-3,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.4
Character	$\chi$	$=$	152.27
Dual form			152.2.o.c.107.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.861662 + 1.12140i) q^{2} +(2.07624 + 1.19872i) q^{3} +(-0.515076 - 1.93254i) q^{4} +(0.418341 + 0.241529i) q^{5} +(-3.13326 + 1.29541i) q^{6} +1.56686i q^{7} +(2.61097 + 1.08759i) q^{8} +(1.37385 + 2.37958i) q^{9} +(-0.631319 + 0.261011i) q^{10} +1.24363 q^{11} +(1.24714 - 4.62984i) q^{12} +(-1.80015 - 3.11796i) q^{13} +(-1.75708 - 1.35010i) q^{14} +(0.579050 + 1.00294i) q^{15} +(-3.46939 + 1.99081i) q^{16} +(-1.35570 + 2.34815i) q^{17} +(-3.85225 - 0.509757i) q^{18} +(-4.25703 + 0.936862i) q^{19} +(0.251286 - 0.932864i) q^{20} +(-1.87822 + 3.25318i) q^{21} +(-1.07159 + 1.39460i) q^{22} +(5.52533 - 3.19005i) q^{23} +(4.11729 + 5.38791i) q^{24} +(-2.38333 - 4.12804i) q^{25} +(5.04760 + 0.667934i) q^{26} -0.604878i q^{27} +(3.02801 - 0.807052i) q^{28} +(0.695157 + 1.20405i) q^{29} +(-1.62365 - 0.214852i) q^{30} +4.86016 q^{31} +(0.756953 - 5.60598i) q^{32} +(2.58207 + 1.49076i) q^{33} +(-1.46506 - 3.54360i) q^{34} +(-0.378442 + 0.655481i) q^{35} +(3.89098 - 3.88068i) q^{36} -10.9720 q^{37} +(2.61752 - 5.58109i) q^{38} -8.63150i q^{39} +(0.829590 + 1.08561i) q^{40} +(1.10008 + 0.635132i) q^{41} +(-2.02972 - 4.90938i) q^{42} +(4.78175 - 8.28223i) q^{43} +(-0.640562 - 2.40335i) q^{44} +1.32730i q^{45} +(-1.18364 + 8.94485i) q^{46} +(7.26763 - 4.19597i) q^{47} +(-9.58971 - 0.0254286i) q^{48} +4.54495 q^{49} +(6.68281 + 0.884316i) q^{50} +(-5.62954 + 3.25022i) q^{51} +(-5.09835 + 5.08485i) q^{52} +(-1.50024 - 2.59849i) q^{53} +(0.678311 + 0.521201i) q^{54} +(0.520259 + 0.300372i) q^{55} +(-1.70410 + 4.09102i) q^{56} +(-9.96165 - 3.15782i) q^{57} +(-1.94921 - 0.257933i) q^{58} +(4.43723 + 2.56184i) q^{59} +(1.63997 - 1.63563i) q^{60} +(-9.42313 + 5.44044i) q^{61} +(-4.18781 + 5.45018i) q^{62} +(-3.72846 + 2.15263i) q^{63} +(5.63431 + 5.67931i) q^{64} -1.73916i q^{65} +(-3.89660 + 1.61100i) q^{66} +(-3.22460 + 1.86172i) q^{67} +(5.23618 + 1.41047i) q^{68} +15.2959 q^{69} +(-0.408967 - 0.989188i) q^{70} +(-6.62670 + 11.4778i) q^{71} +(0.999080 + 7.70718i) q^{72} +(-0.494526 + 0.856544i) q^{73} +(9.45417 - 12.3040i) q^{74} -11.4277i q^{75} +(4.00322 + 7.74431i) q^{76} +1.94859i q^{77} +(9.67937 + 7.43744i) q^{78} +(-5.81311 + 10.0686i) q^{79} +(-1.93223 - 0.00512359i) q^{80} +(4.84663 - 8.39460i) q^{81} +(-1.66013 + 0.686361i) q^{82} -12.1949 q^{83} +(7.25431 + 1.95410i) q^{84} +(-1.13429 + 0.654884i) q^{85} +(5.16744 + 12.4987i) q^{86} +3.33319i q^{87} +(3.24707 + 1.35255i) q^{88} +(-11.1625 + 6.44469i) q^{89} +(-1.48843 - 1.14368i) q^{90} +(4.88540 - 2.82059i) q^{91} +(-9.01085 - 9.03478i) q^{92} +(10.0909 + 5.82596i) q^{93} +(-1.55688 + 11.7654i) q^{94} +(-2.00717 - 0.636268i) q^{95} +(8.29161 - 10.7320i) q^{96} +(2.42717 + 1.40133i) q^{97} +(-3.91621 + 5.09671i) q^{98} +(1.70855 + 2.95930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) $ 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.861662	+	1.12140i	−0.609287	+	0.792950i
$2$	−0.861662	+	1.12140i	−0.609287	+	0.792950i
$3$	2.07624	+	1.19872i	1.19872	+	0.692080i	0.960269	−	0.279075i	$-0.0900278\pi$
$3$	2.07624	+	1.19872i	1.19872	+	0.692080i	0.238449	+	0.971155i	$0.423361\pi$
$4$	−0.515076	−	1.93254i	−0.257538	−	0.966268i
$5$	0.418341	+	0.241529i	0.187088	+	0.108015i	0.590618	−	0.806951i	$-0.298884\pi$
$5$	0.418341	+	0.241529i	0.187088	+	0.108015i	−0.403531	+	0.914966i	$0.632217\pi$
$6$	−3.13326	+	1.29541i	−1.27915	+	0.528847i
$7$			1.56686i			0.592217i	0.955154	+	0.296109i	$0.0956891\pi$
$7$			1.56686i			0.592217i	−0.955154	+	0.296109i	$0.904311\pi$
$8$	2.61097	+	1.08759i	0.923117	+	0.384520i
$9$	1.37385	+	2.37958i	0.457950	+	0.793192i
$10$	−0.631319	+	0.261011i	−0.199641	+	0.0825388i
$11$	1.24363			0.374967			0.187484	−	0.982268i	$-0.439967\pi$
$11$	1.24363			0.374967			0.187484	+	0.982268i	$0.439967\pi$
$12$	1.24714	−	4.62984i	0.360019	−	1.33652i
$13$	−1.80015	−	3.11796i	−0.499273	−	0.864766i	0.500727	−	0.865605i	$-0.333066\pi$
$13$	−1.80015	−	3.11796i	−0.499273	−	0.864766i	−1.00000		0.000839577i	$0.999733\pi$
$14$	−1.75708	−	1.35010i	−0.469598	−	0.360830i
$15$	0.579050	+	1.00294i	0.149510	+	0.258959i
$16$	−3.46939	+	1.99081i	−0.867348	+	0.497702i
$17$	−1.35570	+	2.34815i	−0.328807	+	0.569510i	−0.982275	−	0.187444i	$-0.939980\pi$
$17$	−1.35570	+	2.34815i	−0.328807	+	0.569510i	0.653469	+	0.756954i	$0.273313\pi$
$18$	−3.85225	−	0.509757i	−0.907984	−	0.120151i
$19$	−4.25703	+	0.936862i	−0.976629	+	0.214931i
$19$	−4.25703	+	0.936862i	−0.976629	+	0.214931i
$20$	0.251286	−	0.932864i	0.0561893	−	0.208595i
$21$	−1.87822	+	3.25318i	−0.409862	+	0.709901i
$22$	−1.07159	+	1.39460i	−0.228463	+	0.297330i
$23$	5.52533	−	3.19005i	1.15211	−	0.665171i	0.202710	−	0.979239i	$-0.435025\pi$
$23$	5.52533	−	3.19005i	1.15211	−	0.665171i	0.949401	+	0.314068i	$0.101692\pi$
$24$	4.11729	+	5.38791i	0.840438	+	1.09980i
$25$	−2.38333	−	4.12804i	−0.476665	−	0.825609i
$26$	5.04760	+	0.667934i	0.989916	+	0.130993i
$27$		−	0.604878i		−	0.116409i
$28$	3.02801	−	0.807052i	0.572241	−	0.152519i
$29$	0.695157	+	1.20405i	0.129087	+	0.223586i	0.923323	−	0.384024i	$-0.125462\pi$
$29$	0.695157	+	1.20405i	0.129087	+	0.223586i	−0.794236	+	0.607610i	$0.792129\pi$
$30$	−1.62365	−	0.214852i	−0.296436	−	0.0392265i
$31$	4.86016			0.872910			0.436455	−	0.899726i	$-0.356234\pi$
$31$	4.86016			0.872910			0.436455	+	0.899726i	$0.356234\pi$
$32$	0.756953	−	5.60598i	0.133812	−	0.991007i
$33$	2.58207	+	1.49076i	0.449480	+	0.259507i
$34$	−1.46506	−	3.54360i	−0.251255	−	0.607722i
$35$	−0.378442	+	0.655481i	−0.0639684	+	0.110797i
$36$	3.89098	−	3.88068i	0.648497	−	0.646779i
$37$	−10.9720			−1.80379			−0.901894	−	0.431957i	$-0.857823\pi$
$37$	−10.9720			−1.80379			−0.901894	+	0.431957i	$0.857823\pi$
$38$	2.61752	−	5.58109i	0.424618	−	0.905372i
$39$		−	8.63150i		−	1.38215i
$40$	0.829590	+	1.08561i	0.131170	+	0.171649i
$41$	1.10008	+	0.635132i	0.171804	+	0.0991909i	0.583436	−	0.812159i	$-0.301708\pi$
$41$	1.10008	+	0.635132i	0.171804	+	0.0991909i	−0.411632	+	0.911350i	$0.635041\pi$
$42$	−2.02972	−	4.90938i	−0.313193	−	0.757534i
$43$	4.78175	−	8.28223i	0.729210	−	1.26303i	−0.228008	−	0.973659i	$-0.573221\pi$
$43$	4.78175	−	8.28223i	0.729210	−	1.26303i	0.957218	−	0.289369i	$-0.0934455\pi$
$44$	−0.640562	−	2.40335i	−0.0965684	−	0.362319i
$45$			1.32730i			0.197862i
$46$	−1.18364	+	8.94485i	−0.174519	+	1.31885i
$47$	7.26763	−	4.19597i	1.06009	−	0.612045i	0.134635	−	0.990895i	$-0.457014\pi$
$47$	7.26763	−	4.19597i	1.06009	−	0.612045i	0.925458	+	0.378850i	$0.123680\pi$
$48$	−9.58971	−	0.0254286i	−1.38416	−	0.00367030i
$49$	4.54495			0.649279
$50$	6.68281	+	0.884316i	0.945092	+	0.125061i
$51$	−5.62954	+	3.25022i	−0.788293	+	0.455121i
$52$	−5.09835	+	5.08485i	−0.707014	+	0.705142i
$53$	−1.50024	−	2.59849i	−0.206074	−	0.356930i	0.744400	−	0.667733i	$-0.232735\pi$
$53$	−1.50024	−	2.59849i	−0.206074	−	0.356930i	−0.950474	+	0.310803i	$0.899402\pi$
$54$	0.678311	+	0.521201i	0.0923064	+	0.0709265i
$55$	0.520259	+	0.300372i	0.0701517	+	0.0405021i
$56$	−1.70410	+	4.09102i	−0.227719	+	0.546686i
$57$	−9.96165	−	3.15782i	−1.31945	−	0.418264i
$58$	−1.94921	−	0.257933i	−0.255944	−	0.0338682i
$59$	4.43723	+	2.56184i	0.577678	+	0.333523i	0.760210	−	0.649677i	$-0.225096\pi$
$59$	4.43723	+	2.56184i	0.577678	+	0.333523i	−0.182532	+	0.983200i	$0.558429\pi$
$60$	1.63997	−	1.63563i	0.211719	−	0.211159i
$61$	−9.42313	+	5.44044i	−1.20651	+	0.696578i	−0.961995	−	0.273068i	$-0.911961\pi$
$61$	−9.42313	+	5.44044i	−1.20651	+	0.696578i	−0.244513	+	0.969646i	$0.578628\pi$
$62$	−4.18781	+	5.45018i	−0.531853	+	0.692174i
$63$	−3.72846	+	2.15263i	−0.469742	+	0.271206i
$64$	5.63431	+	5.67931i	0.704289	+	0.709914i
$65$		−	1.73916i		−	0.215716i
$66$	−3.89660	+	1.61100i	−0.479639	+	0.198300i
$67$	−3.22460	+	1.86172i	−0.393947	+	0.227446i	−0.683869	−	0.729605i	$-0.739704\pi$
$67$	−3.22460	+	1.86172i	−0.393947	+	0.227446i	0.289922	+	0.957050i	$0.406371\pi$
$68$	5.23618	+	1.41047i	0.634980	+	0.171045i
$69$	15.2959			1.84141
$70$	−0.408967	−	0.989188i	−0.0488809	−	0.118231i
$71$	−6.62670	+	11.4778i	−0.786444	+	1.36216i	0.141688	+	0.989911i	$0.454747\pi$
$71$	−6.62670	+	11.4778i	−0.786444	+	1.36216i	−0.928132	+	0.372250i	$0.878586\pi$
$72$	0.999080	+	7.70718i	0.117743	+	0.908300i
$73$	−0.494526	+	0.856544i	−0.0578799	+	0.100251i	−0.893514	−	0.449036i	$-0.851767\pi$
$73$	−0.494526	+	0.856544i	−0.0578799	+	0.100251i	0.835634	+	0.549287i	$0.185101\pi$
$74$	9.45417	−	12.3040i	1.09902	−	1.43031i
$75$		−	11.4277i		−	1.31956i
$76$	4.00322	+	7.74431i	0.459200	+	0.888333i
$77$			1.94859i			0.222062i
$78$	9.67937	+	7.43744i	1.09597	+	0.842124i
$79$	−5.81311	+	10.0686i	−0.654026	+	1.13281i	0.328111	+	0.944639i	$0.393588\pi$
$79$	−5.81311	+	10.0686i	−0.654026	+	1.13281i	−0.982137	+	0.188168i	$0.939745\pi$
$80$	−1.93223	−	0.00512359i	−0.216029	−	0.000572835i
$81$	4.84663	−	8.39460i	0.538514	−	0.932733i
$82$	−1.66013	+	0.686361i	−0.183331	+	0.0757959i
$83$	−12.1949			−1.33856			−0.669280	−	0.743010i	$-0.733397\pi$
$83$	−12.1949			−1.33856			−0.669280	+	0.743010i	$0.733397\pi$
$84$	7.25431	+	1.95410i	0.791510	+	0.213210i
$85$	−1.13429	+	0.654884i	−0.123031	+	0.0710322i
$86$	5.16744	+	12.4987i	0.557220	+	1.34777i
$87$			3.33319i			0.357355i
$88$	3.24707	+	1.35255i	0.346139	+	0.144182i
$89$	−11.1625	+	6.44469i	−1.18323	+	0.683136i	−0.956759	−	0.290883i	$-0.906051\pi$
$89$	−11.1625	+	6.44469i	−1.18323	+	0.683136i	−0.226467	+	0.974019i	$0.572718\pi$
$90$	−1.48843	−	1.14368i	−0.156894	−	0.120555i
$91$	4.88540	−	2.82059i	0.512129	−	0.295678i
$92$	−9.01085	−	9.03478i	−0.939446	−	0.941941i
$93$	10.0909	+	5.82596i	1.04637	+	0.604124i
$94$	−1.55688	+	11.7654i	−0.160580	+	1.21351i
$95$	−2.00717	−	0.636268i	−0.205931	−	0.0652798i
$96$	8.29161	−	10.7320i	0.846258	−	1.09533i
$97$	2.42717	+	1.40133i	0.246442	+	0.142283i	0.618134	−	0.786073i	$-0.287889\pi$
$97$	2.42717	+	1.40133i	0.246442	+	0.142283i	−0.371692	+	0.928356i	$0.621222\pi$
$98$	−3.91621	+	5.09671i	−0.395597	+	0.514845i
$99$	1.70855	+	2.95930i	0.171716	+	0.297421i
$100$	−6.75000	+	6.73212i	−0.675000	+	0.673212i
$101$	0.655955	−	0.378716i	0.0652700	−	0.0376837i	−0.467010	−	0.884252i	$-0.654669\pi$
$101$	0.655955	−	0.378716i	0.0652700	−	0.0376837i	0.532280	+	0.846568i	$0.321335\pi$
$102$	1.20597	−	9.11355i	0.119409	−	0.902376i
$103$	−4.06152			−0.400193			−0.200097	−	0.979776i	$-0.564126\pi$
$103$	−4.06152			−0.400193			−0.200097	+	0.979776i	$0.564126\pi$
$104$	−1.30909	−	10.0987i	−0.128367	−	0.990260i
$105$	−1.57147	+	0.907291i	−0.153360	+	0.0885425i
$106$	4.20665	+	0.556653i	0.408586	+	0.0540670i
$107$			4.15320i			0.401505i	0.979642	+	0.200753i	$0.0643388\pi$
$107$			4.15320i			0.401505i	−0.979642	+	0.200753i	$0.935661\pi$
$108$	−1.16895	+	0.311559i	−0.112482	+	0.0299797i
$109$	9.07011	−	15.7099i	0.868759	−	1.50473i	0.00549325	−	0.999985i	$-0.498251\pi$
$109$	9.07011	−	15.7099i	0.868759	−	1.50473i	0.863266	−	0.504750i	$-0.168415\pi$
$110$	−0.785125	+	0.324600i	−0.0748587	+	0.0309494i
$111$	−22.7805	−	13.1523i	−2.16223	−	1.24837i
$112$	−3.11932	−	5.43605i	−0.294748	−	0.513659i
$113$		−	7.00334i		−	0.658819i	−0.944187	−	0.329409i	$-0.893150\pi$
$113$		−	7.00334i		−	0.658819i	0.944187	−	0.329409i	$-0.106850\pi$
$114$	12.1248	−	8.45001i	1.13559	−	0.791416i
$115$	3.08196			0.287394
$116$	1.96881	−	1.96359i	0.182799	−	0.182315i
$117$	4.94628	−	8.56720i	0.457284	−	0.792038i
$118$	−6.69624	+	2.76847i	−0.616439	+	0.254859i
$119$	−3.67922	−	2.12420i	−0.337274	−	0.194725i
$120$	0.421093	+	3.24842i	0.0384403	+	0.296539i
$121$	−9.45340			−0.859400
$122$	2.01864	−	15.2549i	0.182759	−	1.38112i
$123$	1.52269	+	2.63737i	0.137296	+	0.237804i
$124$	−2.50335	−	9.39243i	−0.224808	−	0.843465i
$125$		−	4.71786i		−	0.421978i
$126$	0.798717	−	6.03594i	0.0711554	−	0.537724i
$127$	7.61514	+	13.1898i	0.675734	+	1.17041i	0.976254	+	0.216630i	$0.0695065\pi$
$127$	7.61514	+	13.1898i	0.675734	+	1.17041i	−0.300520	+	0.953776i	$0.597160\pi$
$128$	−11.2236	+	1.42467i	−0.992040	+	0.125924i
$129$	19.8561	−	11.4639i	1.74823	−	1.00934i
$130$	1.95029	+	1.49857i	0.171052	+	0.131433i
$131$	−4.14342	+	7.17662i	−0.362012	+	0.627024i	−0.988292	−	0.152575i	$-0.951244\pi$
$131$	−4.14342	+	7.17662i	−0.362012	+	0.627024i	0.626279	+	0.779599i	$0.284577\pi$
$132$	1.55098	−	5.75779i	0.134995	−	0.501151i
$133$	−1.46793	−	6.67017i	−0.127286	−	0.578377i
$134$	0.690778	−	5.22024i	0.0596742	−	0.450960i
$135$	0.146096	−	0.253045i	0.0125739	−	0.0217787i
$136$	−6.09352	+	4.65650i	−0.522515	+	0.399291i
$137$	8.90976	+	15.4322i	0.761212	+	1.31846i	0.942226	+	0.334978i	$0.108729\pi$
$137$	8.90976	+	15.4322i	0.761212	+	1.31846i	−0.181013	+	0.983481i	$0.557938\pi$
$138$	−13.1799	+	17.1528i	−1.12195	+	1.46014i
$139$	4.16150	+	7.20793i	0.352974	+	0.611368i	0.986769	−	0.162132i	$-0.0518372\pi$
$139$	4.16150	+	7.20793i	0.352974	+	0.611368i	−0.633795	+	0.773501i	$0.718504\pi$
$140$	1.46167	+	0.393730i	0.123533	+	0.0332763i
$141$	20.1191			1.69434
$142$	−7.16121	−	17.3211i	−0.600955	−	1.45356i
$143$	−2.23872	−	3.87757i	−0.187211	−	0.324259i
$144$	−9.50370	−	5.52062i	−0.791975	−	0.460051i
$145$			0.671602i			0.0557735i
$146$	−0.534414	−	1.29261i	−0.0442285	−	0.106977i
$147$	9.43641	+	5.44811i	0.778302	+	0.449353i
$148$	5.65142	+	21.2038i	0.464544	+	1.74294i
$149$	16.0928	+	9.29117i	1.31837	+	0.761162i	0.983467	−	0.181090i	$-0.0579625\pi$
$149$	16.0928	+	9.29117i	1.31837	+	0.761162i	0.334905	+	0.942252i	$0.391296\pi$
$150$	12.8151	+	9.84686i	1.04635	+	0.803993i
$151$	4.56745			0.371694			0.185847	−	0.982579i	$-0.440497\pi$
$151$	4.56745			0.371694			0.185847	+	0.982579i	$0.440497\pi$
$152$	−12.1339	−	2.18377i	−0.984188	−	0.177127i
$153$	−7.45013			−0.602308
$154$	−2.18515	−	1.67902i	−0.176084	−	0.135300i
$155$	2.03320	+	1.17387i	0.163311	+	0.0942875i
$156$	−16.6807	+	4.44588i	−1.33552	+	0.355956i
$157$	−16.0994	−	9.29499i	−1.28487	−	0.741821i	−0.307137	−	0.951665i	$-0.599371\pi$
$157$	−16.0994	−	9.29499i	−1.28487	−	0.741821i	−0.977735	+	0.209844i	$0.932704\pi$
$158$	−6.28200	−	15.1946i	−0.499769	−	1.20881i
$159$		−	7.19346i		−	0.570479i
$160$	1.67067	−	2.16238i	0.132078	−	0.170951i
$161$	4.99836	+	8.65741i	0.393926	+	0.682300i
$162$	5.23755	+	12.6683i	0.411501	+	0.995317i
$163$	13.2618			1.03874			0.519370	−	0.854549i	$-0.326167\pi$
$163$	13.2618			1.03874			0.519370	+	0.854549i	$0.326167\pi$
$164$	0.660790	−	2.45309i	0.0515990	−	0.191554i
$165$	0.720122	+	1.24729i	0.0560614	+	0.0971012i
$166$	10.5079	−	13.6753i	0.815568	−	1.06141i
$167$	5.01139	+	8.67998i	0.387793	+	0.671677i	0.992152	−	0.125035i	$-0.0399042\pi$
$167$	5.01139	+	8.67998i	0.387793	+	0.671677i	−0.604359	+	0.796712i	$0.706571\pi$
$168$	−8.44209	+	6.45121i	−0.651322	+	0.497722i
$169$	0.0188953	−	0.0327276i	0.00145348	−	0.00251751i
$170$	0.242990	−	1.83629i	0.0186365	−	0.140837i
$171$	−8.07785	−	8.84281i	−0.617729	−	0.676227i
$172$	−18.4687	−	4.97492i	−1.40822	−	0.379334i
$173$	−7.75097	+	13.4251i	−0.589296	+	1.02069i	0.405029	+	0.914304i	$0.367261\pi$
$173$	−7.75097	+	13.4251i	−0.589296	+	1.02069i	−0.994325	+	0.106386i	$0.966072\pi$
$174$	−3.73784	−	2.87208i	−0.283365	−	0.217732i
$175$	6.46807	−	3.73434i	0.488940	−	0.282290i
$176$	−4.31463	+	2.47582i	−0.325227	+	0.186622i
$177$	6.14184	+	10.6380i	0.461649	+	0.799599i
$178$	2.39126	−	18.0708i	0.179232	−	1.35446i
$179$			2.86093i			0.213836i	0.994268	+	0.106918i	$0.0340982\pi$
$179$			2.86093i			0.213836i	−0.994268	+	0.106918i	$0.965902\pi$
$180$	2.56505	−	0.683660i	0.191188	−	0.0509570i
$181$	0.305140	+	0.528519i	0.0226809	+	0.0392845i	0.877143	−	0.480229i	$-0.159446\pi$
$181$	0.305140	+	0.528519i	0.0226809	+	0.0392845i	−0.854462	+	0.519514i	$0.826113\pi$
$182$	−1.04656	+	7.90888i	−0.0775761	+	0.586245i
$183$	−26.0862			−1.92835
$184$	17.8959	−	2.31984i	1.31930	−	0.171021i
$185$	−4.59004	−	2.65006i	−0.337466	−	0.194836i
$186$	−15.2281	+	6.29588i	−1.11658	+	0.461636i
$187$	−1.68599	+	2.92022i	−0.123292	+	0.213548i
$188$	−11.8523	−	11.8837i	−0.864414	−	0.866710i
$189$	0.947760			0.0689394
$190$	2.44301	−	1.70259i	0.177235	−	0.123519i
$191$		−	21.9035i		−	1.58488i	−0.609947	−	0.792442i	$-0.708809\pi$
$191$		−	21.9035i		−	1.58488i	0.609947	−	0.792442i	$-0.291191\pi$
$192$	4.89029	+	18.5456i	0.352926	+	1.33841i
$193$	4.60435	+	2.65832i	0.331428	+	0.191350i	0.656475	−	0.754348i	$-0.272047\pi$
$193$	4.60435	+	2.65832i	0.331428	+	0.191350i	−0.325047	+	0.945698i	$0.605380\pi$
$194$	−3.66285	+	1.51436i	−0.262977	+	0.108725i
$195$	2.08476	−	3.61091i	0.149293	−	0.258583i
$196$	−2.34100	−	8.78328i	−0.167214	−	0.627377i
$197$			0.913518i			0.0650855i	0.999470	+	0.0325427i	$0.0103605\pi$
$197$			0.913518i			0.0650855i	−0.999470	+	0.0325427i	$0.989639\pi$
$198$	−4.79076	−	0.633946i	−0.340464	−	0.0450526i
$199$	17.3763	−	10.0322i	1.23177	−	0.711164i	0.264373	−	0.964421i	$-0.414835\pi$
$199$	17.3763	−	10.0322i	1.23177	−	0.711164i	0.967399	+	0.253257i	$0.0815017\pi$
$200$	−1.73319	−	13.3703i	−0.122555	−	0.945421i
$201$	−8.92672			−0.629642
$202$	−0.140520	+	1.06191i	−0.00988694	+	0.0747160i
$203$	−1.88657	+	1.08921i	−0.132411	+	0.0764478i
$204$	9.18080	+	9.20518i	0.642785	+	0.644491i
$205$	0.306806	+	0.531403i	0.0214282	+	0.0371148i
$206$	3.49966	−	4.55458i	0.243833	−	0.317333i
$207$	15.1819	+	8.76529i	1.05522	+	0.609230i
$208$	12.4527	+	7.23366i	0.863439	+	0.501564i
$209$	−5.29415	+	1.16511i	−0.366204	+	0.0805921i
$210$	0.336644	−	2.54403i	0.0232306	−	0.175555i
$211$	−21.5716	−	12.4544i	−1.48505	−	0.857394i	−0.485194	−	0.874406i	$-0.661251\pi$
$211$	−21.5716	−	12.4544i	−1.48505	−	0.857394i	−0.999855	+	0.0170124i	$0.994585\pi$
$212$	−4.24894	+	4.23769i	−0.291819	+	0.291046i
$213$	−27.5172	+	15.8871i	−1.88545	+	1.08856i
$214$	−4.65740	−	3.57866i	−0.318374	−	0.244632i
$215$	4.00080	−	2.30986i	0.272852	−	0.157531i
$216$	0.657858	−	1.57932i	0.0447616	−	0.107459i
$217$			7.61519i			0.516953i
$218$	9.80170	+	23.7078i	0.663855	+	1.60570i
$219$	−2.05351	+	1.18559i	−0.138763	+	0.0801151i
$220$	0.312506	−	1.16013i	0.0210692	−	0.0782162i
$221$	9.76191			0.656657
$222$	34.3782	−	14.2132i	2.30731	−	0.953928i
$223$	−1.75003	+	3.03114i	−0.117191	+	0.202980i	−0.918653	−	0.395065i	$-0.870722\pi$
$223$	−1.75003	+	3.03114i	−0.117191	+	0.202980i	0.801463	+	0.598045i	$0.204056\pi$
$224$	8.78379	+	1.18604i	0.586891	+	0.0792456i
$225$	6.54866	−	11.3426i	0.436578	−	0.756175i
$226$	7.85355	+	6.03451i	0.522410	+	0.401410i
$227$			5.29383i			0.351364i	0.984447	+	0.175682i	$0.0562130\pi$
$227$			5.29383i			0.351364i	−0.984447	+	0.175682i	$0.943787\pi$
$228$	−0.971601	+	20.8778i	−0.0643458	+	1.38266i
$229$		−	1.20868i		−	0.0798721i	−0.999202	−	0.0399360i	$-0.987285\pi$
$229$		−	1.20868i		−	0.0798721i	0.999202	−	0.0399360i	$-0.0127154\pi$
$230$	−2.65561	+	3.45611i	−0.175106	+	0.227889i
$231$	−2.33581	+	4.04573i	−0.153685	+	0.266190i
$232$	0.505527	+	3.89977i	0.0331895	+	0.256033i
$233$	5.58944	−	9.68119i	0.366176	−	0.634236i	−0.622788	−	0.782391i	$-0.714000\pi$
$233$	5.58944	−	9.68119i	0.366176	−	0.634236i	0.988964	+	0.148155i	$0.0473334\pi$
$234$	5.34524	+	12.9288i	0.349429	+	0.845182i
$235$	4.05380			0.264440
$236$	2.66533	−	9.89465i	0.173498	−	0.644087i
$237$	−24.1388	+	13.9366i	−1.56799	+	0.905277i
$238$	5.55232	−	2.29554i	0.359904	−	0.148798i
$239$			20.3237i			1.31463i	0.753615	+	0.657317i	$0.228309\pi$
$239$			20.3237i			1.31463i	−0.753615	+	0.657317i	$0.771691\pi$
$240$	−4.00562	−	2.32683i	−0.258562	−	0.150196i
$241$	5.48096	−	3.16443i	0.353060	−	0.203839i	−0.312972	−	0.949762i	$-0.601325\pi$
$241$	5.48096	−	3.16443i	0.353060	−	0.203839i	0.666032	+	0.745923i	$0.267991\pi$
$242$	8.14563	−	10.6010i	0.523621	−	0.681461i
$243$	18.5540	−	10.7122i	1.19024	−	0.687185i
$244$	15.3675	+	15.4083i	0.983803	+	0.986415i
$245$	1.90134	+	1.09774i	0.121472	+	0.0701319i
$246$	−4.26959	−	0.564982i	−0.272219	−	0.0360219i
$247$	10.5844	+	11.5867i	0.673469	+	0.737246i
$248$	12.6897	+	5.28584i	0.805798	+	0.335651i
$249$	−25.3195	−	14.6182i	−1.60456	−	0.926391i
$250$	5.29061	+	4.06520i	0.334608	+	0.257106i
$251$	12.1536	+	21.0507i	0.767131	+	1.32871i	0.939113	+	0.343609i	$0.111650\pi$
$251$	12.1536	+	21.0507i	0.767131	+	1.32871i	−0.171982	+	0.985100i	$0.555017\pi$
$252$	6.08048	+	6.09662i	0.383034	+	0.384051i
$253$	6.87144	−	3.96723i	0.432004	−	0.249417i
$254$	−21.3527	−	2.82554i	−1.33979	−	0.177290i
$255$	−3.14009			−0.196640
$256$	8.07337	−	13.8138i	0.504586	−	0.863362i
$257$	7.08286	−	4.08929i	0.441817	−	0.255083i	−0.262551	−	0.964918i	$-0.584564\pi$
$257$	7.08286	−	4.08929i	0.441817	−	0.255083i	0.704368	+	0.709835i	$0.251231\pi$
$258$	−4.25361	+	32.1447i	−0.264818	+	2.00124i
$259$		−	17.1916i		−	1.06823i
$260$	−3.36098	+	0.895799i	−0.208439	+	0.0555551i
$261$	−1.91008	+	3.30836i	−0.118231	+	0.204782i
$262$	−4.47763	−	10.8303i	−0.276629	−	0.669095i
$263$	−19.0322	−	10.9882i	−1.17358	−	0.677564i	−0.219056	−	0.975712i	$-0.570298\pi$
$263$	−19.0322	−	10.9882i	−1.17358	−	0.677564i	−0.954520	+	0.298148i	$0.903631\pi$
$264$	5.12036	+	6.70054i	0.315137	+	0.412390i
$265$		−	1.44941i		−	0.0890364i
$266$	8.74479	+	4.10129i	0.536177	+	0.251466i
$267$	−30.9015			−1.89114
$268$	5.25876	+	5.27272i	0.321230	+	0.322083i
$269$	−1.94226	+	3.36410i	−0.118422	+	0.205113i	−0.919142	−	0.393925i	$-0.871117\pi$
$269$	−1.94226	+	3.36410i	−0.118422	+	0.205113i	0.800721	+	0.599038i	$0.204450\pi$
$270$	0.157880	+	0.381871i	0.00960826	+	0.0232399i
$271$	1.81233	+	1.04635i	0.110091	+	0.0635611i	0.554035	−	0.832494i	$-0.313088\pi$
$271$	1.81233	+	1.04635i	0.110091	+	0.0635611i	−0.443943	+	0.896055i	$0.646421\pi$
$272$	0.0287587	−	10.8456i	0.00174376	−	0.657611i
$273$	13.5244			0.818531
$274$	−24.9828	−	3.30590i	−1.50927	−	0.199717i
$275$	−2.96397	−	5.13374i	−0.178734	−	0.309576i
$276$	−7.87854	−	29.5598i	−0.474233	−	1.77929i
$277$		−	27.8262i		−	1.67191i	−0.548797	−	0.835956i	$-0.684914\pi$
$277$		−	27.8262i		−	1.67191i	0.548797	−	0.835956i	$-0.315086\pi$
$278$	−11.6688	−	1.54409i	−0.699847	−	0.0926086i
$279$	6.67712	+	11.5651i	0.399749	+	0.692385i
$280$	−1.70099	+	1.29985i	−0.101654	+	0.0776810i
$281$	−20.0761	+	11.5910i	−1.19764	+	0.691458i	−0.960029	−	0.279902i	$-0.909698\pi$
$281$	−20.0761	+	11.5910i	−1.19764	+	0.691458i	−0.237612	+	0.971360i	$0.576365\pi$
$282$	−17.3359	+	22.5616i	−1.03234	+	1.34352i
$283$	1.40718	−	2.43730i	0.0836480	−	0.144883i	−0.821166	−	0.570689i	$-0.806676\pi$
$283$	1.40718	−	2.43730i	0.0836480	−	0.144883i	0.904814	+	0.425806i	$0.140010\pi$
$284$	25.5945	+	6.89440i	1.51875	+	0.409108i
$285$	−3.40466	−	3.72707i	−0.201674	−	0.220773i
$286$	6.27733	+	0.830660i	0.371186	+	0.0491179i
$287$	−0.995162	+	1.72367i	−0.0587426	+	0.101745i
$288$	14.3798	−	5.90054i	0.847338	−	0.347693i
$289$	4.82413	+	8.35564i	0.283772	+	0.491508i
$290$	−0.753135	−	0.578694i	−0.0442256	−	0.0339821i
$291$	3.35959	+	5.81899i	0.196943	+	0.341115i
$292$	1.91002	+	0.514504i	0.111776	+	0.0301091i
$293$	8.65633			0.505708			0.252854	−	0.967504i	$-0.418631\pi$
$293$	8.65633			0.505708			0.252854	+	0.967504i	$0.418631\pi$
$294$	−14.2405	+	5.88756i	−0.830524	+	0.343369i
$295$	1.23752	+	2.14344i	0.0720510	+	0.124796i
$296$	−28.6476	−	11.9330i	−1.66511	−	0.693593i
$297$		−	0.752242i		−	0.0436495i
$298$	−24.2856	+	10.0406i	−1.40683	+	0.581636i
$299$	−19.8929	−	11.4852i	−1.15043	−	0.664204i
$300$	−22.0845	+	5.88616i	−1.27505	+	0.339838i
$301$	12.9771	+	7.49233i	0.747987	+	0.431851i
$302$	−3.93560	+	5.12194i	−0.226468	+	0.294734i
$303$	1.81589			0.104320
$304$	12.9042	−	11.7253i	0.740106	−	0.672490i
$305$	−5.25610			−0.300964
$306$	6.41950	−	8.35458i	0.366978	−	0.477600i
$307$	8.98393	+	5.18688i	0.512740	+	0.296031i	0.733959	−	0.679194i	$-0.237670\pi$
$307$	8.98393	+	5.18688i	0.512740	+	0.296031i	−0.221219	+	0.975224i	$0.571004\pi$
$308$	3.76571	−	1.00367i	0.214572	−	0.0571895i
$309$	−8.43268	−	4.86861i	−0.479719	−	0.276966i
$310$	−3.06831	+	1.26855i	−0.174268	+	0.0720490i
$311$		−	20.7808i		−	1.17837i	−0.807997	−	0.589186i	$-0.799449\pi$
$311$		−	20.7808i		−	1.17837i	0.807997	−	0.589186i	$-0.200551\pi$
$312$	9.38751	−	22.5366i	0.531463	−	1.27588i
$313$	−11.9901	−	20.7674i	−0.677720	−	1.17384i	−0.975666	−	0.219262i	$-0.929635\pi$
$313$	−11.9901	−	20.7674i	−0.677720	−	1.17384i	0.297946	−	0.954583i	$-0.403698\pi$
$314$	24.2956	−	10.0447i	1.37108	−	0.566856i
$315$	−2.07969			−0.117177
$316$	22.4521	+	6.04795i	1.26303	+	0.340224i
$317$	−9.45498	−	16.3765i	−0.531045	−	0.919797i	−0.999344	−	0.0362265i	$-0.988466\pi$
$317$	−9.45498	−	16.3765i	−0.531045	−	0.919797i	0.468299	−	0.883570i	$-0.344867\pi$
$318$	8.06675	+	6.19833i	0.452361	+	0.347585i
$319$	0.864515	+	1.49738i	0.0484035	+	0.0838374i
$320$	0.985342	+	3.73674i	0.0550823	+	0.208890i
$321$	−4.97852	+	8.62305i	−0.277874	+	0.481292i
$322$	−14.0153	−	1.85461i	−0.781043	−	0.103353i
$323$	3.57138	−	11.2662i	0.198717	−	0.626871i
$324$	−18.7193	−	5.04242i	−1.03996	−	0.280134i
$325$	−8.58071	+	14.8622i	−0.475972	+	0.824408i
$326$	−11.4272	+	14.8717i	−0.632891	+	0.823669i
$327$	37.6635	−	21.7450i	2.08279	−	1.20250i
$328$	2.18151	+	2.85474i	0.120454	+	0.157627i
$329$	6.57450	+	11.3874i	0.362464	+	0.627806i
$330$	−2.01921	−	0.267196i	−0.111154	−	0.0147087i
$331$			15.9594i			0.877208i	0.898680	+	0.438604i	$0.144527\pi$
$331$			15.9594i			0.877208i	−0.898680	+	0.438604i	$0.855473\pi$
$332$	6.28129	+	23.5670i	0.344730	+	1.29341i
$333$	−15.0739	−	26.1087i	−0.826044	−	1.43075i
$334$	−14.0519	−	1.85944i	−0.768883	−	0.101744i
$335$	−1.79864			−0.0982702
$336$	0.0398430	−	15.0257i	0.00217361	−	0.819721i
$337$	−21.3485	−	12.3256i	−1.16293	−	0.671418i	−0.210925	−	0.977502i	$-0.567648\pi$
$337$	−21.3485	−	12.3256i	−1.16293	−	0.671418i	−0.952004	+	0.306085i	$0.900981\pi$
$338$	0.0204194	+	0.0493893i	0.00111067	+	0.00268643i
$339$	8.39503	−	14.5406i	0.455955	−	0.789738i
$340$	1.84984	+	1.85475i	0.100321	+	0.100588i
$341$	6.04422			0.327313
$342$	16.8767	−	1.43898i	0.912588	−	0.0778112i
$343$			18.0893i			0.976731i
$344$	21.4926	−	16.4241i	1.15881	−	0.885527i
$345$	6.39889	+	3.69440i	0.344504	+	0.198900i
$346$	−8.37616	−	20.2598i	−0.450305	−	1.08917i
$347$	4.57443	−	7.92314i	0.245568	−	0.425336i	−0.716723	−	0.697358i	$-0.754359\pi$
$347$	4.57443	−	7.92314i	0.245568	−	0.425336i	0.962291	+	0.272022i	$0.0876922\pi$
$348$	6.44150	−	1.71685i	0.345301	−	0.0920326i
$349$			17.8070i			0.953189i	0.879123	+	0.476595i	$0.158129\pi$
$349$			17.8070i			0.953189i	−0.879123	+	0.476595i	$0.841871\pi$
$350$	−1.38560	+	10.4710i	−0.0740634	+	0.559700i
$351$	−1.88599	+	1.08887i	−0.100666	+	0.0581198i
$352$	0.941366	−	6.97174i	0.0501750	−	0.371595i
$353$	23.3856			1.24469			0.622344	−	0.782744i	$-0.286181\pi$
$353$	23.3856			1.24469			0.622344	+	0.782744i	$0.286181\pi$
$354$	−17.2216	−	2.27888i	−0.915319	−	0.121121i
$355$	−5.54443	+	3.20108i	−0.294268	+	0.169896i
$356$	18.2042	+	18.2525i	0.964818	+	0.967380i
$357$	−5.09263	−	8.82070i	−0.269531	−	0.466841i
$358$	−3.20824	−	2.46515i	−0.169561	−	0.130287i
$359$	−11.4051	−	6.58476i	−0.601940	−	0.347530i	0.167864	−	0.985810i	$-0.446313\pi$
$359$	−11.4051	−	6.58476i	−0.601940	−	0.347530i	−0.769805	+	0.638280i	$0.779646\pi$
$360$	−1.44355	+	3.46553i	−0.0760818	+	0.182650i
$361$	17.2446	−	7.97650i	0.907609	−	0.419816i
$362$	−0.855609	−	0.113220i	−0.0449698	−	0.00595072i
$363$	−19.6275	−	11.3320i	−1.03018	−	0.594773i
$364$	−7.96724	−	7.98840i	−0.417597	−	0.418706i
$365$	−0.413761	+	0.238885i	−0.0216572	+	0.0125038i
$366$	22.4775	−	29.2531i	1.17492	−	1.52908i
$367$	13.2710	−	7.66199i	0.692738	−	0.399953i	−0.111899	−	0.993720i	$-0.535693\pi$
$367$	13.2710	−	7.66199i	0.692738	−	0.399953i	0.804637	+	0.593767i	$0.202360\pi$
$368$	−12.8188	+	22.0674i	−0.668224	+	1.15034i
$369$			3.49030i			0.181698i
$370$	6.92684	−	2.86381i	0.360109	−	0.148883i
$371$	4.07147	−	2.35067i	0.211380	−	0.122041i
$372$	6.06131	−	22.5018i	0.314265	−	1.16666i
$373$	8.33115			0.431370			0.215685	−	0.976463i	$-0.430801\pi$
$373$	8.33115			0.431370			0.215685	+	0.976463i	$0.430801\pi$
$374$	−1.82198	−	4.40691i	−0.0942124	−	0.227876i
$375$	5.65539	−	9.79541i	0.292043	−	0.505833i
$376$	23.5390	−	3.05136i	1.21393	−	0.157362i
$377$	2.50278	−	4.33494i	0.128900	−	0.223261i
$378$	−0.816649	+	1.06282i	−0.0420039	+	0.0546655i
$379$			10.4481i			0.536682i	0.963324	+	0.268341i	$0.0864754\pi$
$379$			10.4481i			0.536682i	−0.963324	+	0.268341i	$0.913525\pi$
$380$	−0.195767	+	4.20665i	−0.0100427	+	0.215797i
$381$			36.5136i			1.87065i
$382$	24.5626	+	18.8735i	1.25673	+	0.965650i
$383$	−4.22512	+	7.31812i	−0.215893	+	0.373938i	−0.953549	−	0.301239i	$-0.902600\pi$
$383$	−4.22512	+	7.31812i	−0.215893	+	0.373938i	0.737655	+	0.675178i	$0.235933\pi$
$384$	−25.0108	−	10.4960i	−1.27633	−	0.535624i
$385$	−0.470640	+	0.815173i	−0.0239861	+	0.0415451i
$386$	−6.94843	+	2.87274i	−0.353666	+	0.146219i
$387$	26.2776			1.33577
$388$	1.45794	−	5.41239i	0.0740156	−	0.274772i
$389$	−5.29150	+	3.05505i	−0.268290	+	0.154897i	−0.628110	−	0.778124i	$-0.716171\pi$
$389$	−5.29150	+	3.05505i	−0.268290	+	0.154897i	0.359820	+	0.933022i	$0.382838\pi$
$390$	2.25292	+	5.44923i	0.114081	+	0.275933i
$391$			17.2991i			0.874851i
$392$	11.8667	+	4.94303i	0.599360	+	0.249661i
$393$	−17.2055	+	9.93359i	−0.867902	+	0.501083i
$394$	−1.02442	−	0.787144i	−0.0516095	−	0.0396557i
$395$	−4.86372	+	2.80807i	−0.244720	+	0.141289i
$396$	4.83892	−	4.82611i	0.243165	−	0.242521i
$397$	−19.5160	−	11.2676i	−0.979481	−	0.565504i	−0.0773678	−	0.997003i	$-0.524652\pi$
$397$	−19.5160	−	11.2676i	−0.979481	−	0.565504i	−0.902113	+	0.431499i	$0.857985\pi$
$398$	−3.72238	+	28.1301i	−0.186586	+	1.41004i
$399$	4.94787	−	15.6085i	0.247703	−	0.781403i
$400$	16.4868	+	9.57706i	0.824342	+	0.478853i
$401$	−1.59335	−	0.919919i	−0.0795679	−	0.0459386i	0.459688	−	0.888080i	$-0.347961\pi$
$401$	−1.59335	−	0.919919i	−0.0795679	−	0.0459386i	−0.539256	+	0.842142i	$0.681295\pi$
$402$	7.69182	−	10.0104i	0.383633	−	0.499275i
$403$	−8.74903	−	15.1538i	−0.435820	−	0.754863i
$404$	−1.06975	−	1.07259i	−0.0532220	−	0.0533633i
$405$	4.05508	−	2.34120i	0.201499	−	0.116335i
$406$	0.404145	−	3.05414i	0.0200574	−	0.151574i
$407$	−13.6451			−0.676361
$408$	−18.2334	+	2.36360i	−0.902690	+	0.117015i
$409$	−31.6805	+	18.2907i	−1.56650	+	0.904418i	−0.569925	+	0.821696i	$0.693028\pi$
$409$	−31.6805	+	18.2907i	−1.56650	+	0.904418i	−0.996573	+	0.0827216i	$0.973639\pi$
$410$	−0.860278	−	0.113838i	−0.0424861	−	0.00562206i
$411$			42.7212i			2.10728i
$412$	2.09199	+	7.84903i	0.103065	+	0.386694i
$413$	−4.01404	+	6.95252i	−0.197518	+	0.342111i
$414$	−22.9111	+	9.47230i	−1.12602	+	0.465538i
$415$	−5.10161	−	2.94542i	−0.250428	−	0.144585i
$416$	−18.8418	+	7.73148i	−0.923797	+	0.379067i
$417$			19.9539i			0.977144i
$418$	3.25522	−	6.94079i	0.159218	−	0.339485i
$419$	4.03779			0.197259			0.0986294	−	0.995124i	$-0.468554\pi$
$419$	4.03779			0.197259			0.0986294	+	0.995124i	$0.468554\pi$
$420$	2.56280	+	2.56961i	0.125052	+	0.125384i
$421$	3.23520	−	5.60354i	0.157674	−	0.273100i	−0.776355	−	0.630295i	$-0.782934\pi$
$421$	3.23520	−	5.60354i	0.157674	−	0.273100i	0.934030	+	0.357196i	$0.116267\pi$
$422$	32.5538	−	13.4589i	1.58469	−	0.655170i
$423$	19.9693	+	11.5293i	0.970939	+	0.560572i
$424$	−1.09099	−	8.41622i	−0.0529833	−	0.408728i
$425$	12.9244			0.626923
$426$	5.89479	−	44.5471i	0.285603	−	2.15832i
$427$	−8.52441	−	14.7647i	−0.412525	−	0.714515i
$428$	8.02622	−	2.13922i	0.387962	−	0.103403i
$429$		−	10.7344i		−	0.518260i
$430$	−0.857058	+	6.47682i	−0.0413310	+	0.312340i
$431$	−3.17434	−	5.49811i	−0.152902	−	0.264835i	0.779391	−	0.626538i	$-0.215529\pi$
$431$	−3.17434	−	5.49811i	−0.152902	−	0.264835i	−0.932293	+	0.361703i	$0.882195\pi$
$432$	1.20420	+	2.09856i	0.0579369	+	0.100967i
$433$	20.1286	−	11.6213i	0.967320	−	0.558482i	0.0689019	−	0.997623i	$-0.478050\pi$
$433$	20.1286	−	11.6213i	0.967320	−	0.558482i	0.898418	+	0.439141i	$0.144717\pi$
$434$	−8.53967	−	6.56172i	−0.409917	−	0.314973i
$435$	−0.805062	+	1.39441i	−0.0385997	+	0.0668567i
$436$	−35.0317	−	9.43652i	−1.67772	−	0.451927i
$437$	−20.5328	+	18.7566i	−0.982219	+	0.897250i
$438$	0.439906	−	3.32439i	0.0210195	−	0.158845i
$439$	5.22682	−	9.05312i	0.249462	−	0.432082i	−0.713914	−	0.700233i	$-0.753079\pi$
$439$	5.22682	−	9.05312i	0.249462	−	0.432082i	0.963377	+	0.268151i	$0.0864127\pi$
$440$	1.03170	+	1.35009i	0.0491843	+	0.0643629i
$441$	6.24408	+	10.8151i	0.297337	+	0.515003i
$442$	−8.41147	+	10.9470i	−0.400093	+	0.520696i
$443$	7.15226	+	12.3881i	0.339814	+	0.588575i	0.984398	−	0.175959i	$-0.0563026\pi$
$443$	7.15226	+	12.3881i	0.339814	+	0.588575i	−0.644584	+	0.764534i	$0.722969\pi$
$444$	−13.6837	+	50.7987i	−0.649398	+	2.41080i
$445$	−6.22632			−0.295156
$446$	−1.89119	−	4.57431i	−0.0895503	−	0.216600i
$447$	22.2750	+	38.5814i	1.05357	+	1.82484i
$448$	−8.89868	+	8.82817i	−0.420423	+	0.417092i
$449$		−	35.1956i		−	1.66098i	−0.557030	−	0.830492i	$-0.688059\pi$
$449$		−	35.1956i		−	1.66098i	0.557030	−	0.830492i	$-0.311941\pi$
$450$	7.07688	+	17.1172i	0.333607	+	0.806911i
$451$	1.36809	+	0.789866i	0.0644208	+	0.0371933i
$452$	−13.5342	+	3.60725i	−0.636596	+	0.169671i
$453$	9.48312	+	5.47508i	0.445556	+	0.257242i
$454$	−5.93650	−	4.56149i	−0.278614	−	0.214081i
$455$	2.72502			0.127751
$456$	−22.5751	−	19.0791i	−1.05718	−	0.893462i
$457$	5.76335			0.269598			0.134799	−	0.990873i	$-0.456961\pi$
$457$	5.76335			0.269598			0.134799	+	0.990873i	$0.456961\pi$
$458$	1.35542	+	1.04148i	0.0633345	+	0.0486650i
$459$	1.42035	+	0.820037i	0.0662960	+	0.0382760i
$460$	−1.58744	−	5.95600i	−0.0740150	−	0.277700i
$461$	23.7050	+	13.6861i	1.10405	+	0.637424i	0.937282	−	0.348572i	$-0.113333\pi$
$461$	23.7050	+	13.6861i	1.10405	+	0.637424i	0.166769	+	0.985996i	$0.446667\pi$
$462$	−2.52421	−	6.10543i	−0.117437	−	0.284050i
$463$		−	9.63243i		−	0.447657i	−0.974629	−	0.223828i	$-0.928144\pi$
$463$		−	9.63243i		−	0.447657i	0.974629	−	0.223828i	$-0.0718555\pi$
$464$	−4.80880	−	2.79339i	−0.223243	−	0.129680i
$465$	2.81428	+	4.87447i	0.130509	+	0.226048i
$466$	6.04028	+	14.6099i	0.279811	+	0.676791i
$467$	14.1545			0.654992			0.327496	−	0.944853i	$-0.393795\pi$
$467$	14.1545			0.654992			0.327496	+	0.944853i	$0.393795\pi$
$468$	−19.1041	−	5.14610i	−0.883089	−	0.237878i
$469$	−2.91706	−	5.05249i	−0.134697	−	0.233302i
$470$	−3.49300	+	4.54593i	−0.161120	+	0.209688i
$471$	−22.2841	−	38.5973i	−1.02680	−	1.77847i
$472$	8.79925	+	11.5147i	0.405018	+	0.530009i
$473$	5.94671	−	10.3000i	0.273430	−	0.473594i
$474$	5.17106	−	39.0779i	0.237515	−	1.79491i
$475$	14.0133	+	15.3404i	0.642974	+	0.703864i
$476$	−2.21001	+	8.20435i	−0.101296	+	0.376046i
$477$	4.12221	−	7.13987i	0.188743	−	0.326912i
$478$	−22.7910	−	17.5122i	−1.04244	−	0.800989i
$479$	20.5947	−	11.8903i	0.940995	−	0.543284i	0.0507227	−	0.998713i	$-0.483848\pi$
$479$	20.5947	−	11.8903i	0.940995	−	0.543284i	0.890272	+	0.455429i	$0.150514\pi$
$480$	6.06080	−	2.48696i	0.276637	−	0.113514i
$481$	19.7513	+	34.2103i	0.900582	+	1.55985i
$482$	−1.17414	+	8.87302i	−0.0534806	+	0.404155i
$483$			23.9665i			1.09051i
$484$	4.86922	+	18.2690i	0.221328	+	0.830410i
$485$	0.676923	+	1.17246i	0.0307375	+	0.0532389i
$486$	−3.97467	+	30.0367i	−0.180295	+	1.36249i
$487$	−7.31176			−0.331327			−0.165664	−	0.986182i	$-0.552977\pi$
$487$	−7.31176			−0.331327			−0.165664	+	0.986182i	$0.552977\pi$
$488$	−30.5204	+	3.95636i	−1.38160	+	0.179096i
$489$	27.5346	+	15.8971i	1.24516	+	0.718892i
$490$	−2.86931	+	1.18628i	−0.129622	+	0.0535907i
$491$	7.42662	−	12.8633i	0.335159	−	0.580512i	−0.648357	−	0.761337i	$-0.724543\pi$
$491$	7.42662	−	12.8633i	0.335159	−	0.580512i	0.983515	+	0.180825i	$0.0578768\pi$
$492$	4.31252	−	4.30110i	0.194423	−	0.193908i
$493$	−3.76971			−0.169779
$494$	−22.1135	+	1.88550i	−0.994935	+	0.0848325i
$495$			1.65066i			0.0741917i
$496$	−16.8618	+	9.67564i	−0.757117	+	0.434449i
$497$	−17.9841	−	10.3831i	−0.806696	−	0.465746i
$498$	38.2097	−	15.7973i	1.71222	−	0.707894i
$499$	−1.07280	+	1.85814i	−0.0480251	+	0.0831819i	−0.889039	−	0.457832i	$-0.848626\pi$
$499$	−1.07280	+	1.85814i	−0.0480251	+	0.0831819i	0.841014	+	0.541014i	$0.181959\pi$
$500$	−9.11744	+	2.43006i	−0.407744	+	0.108676i
$501$			24.0290i			1.07353i
$502$	−34.0786	−	4.50952i	−1.52100	−	0.201270i
$503$	−17.1288	+	9.88932i	−0.763736	+	0.440943i	−0.830635	−	0.556817i	$-0.812023\pi$
$503$	−17.1288	+	9.88932i	−0.763736	+	0.440943i	0.0668997	+	0.997760i	$0.478689\pi$
$504$	−12.0761	+	1.56542i	−0.537911	+	0.0697293i
$505$	0.365884			0.0162816
$506$	−1.47201	+	11.1240i	−0.0654389	+	0.494524i
$507$	0.0784624	−	0.0453003i	0.00348464	−	0.00201186i
$508$	21.5674	−	21.5103i	0.956898	−	0.954364i
$509$	7.29492	+	12.6352i	0.323342	+	0.560044i	0.981175	−	0.193119i	$-0.0618603\pi$
$509$	7.29492	+	12.6352i	0.323342	+	0.560044i	−0.657834	+	0.753163i	$0.728527\pi$
$510$	2.70569	−	3.52129i	0.119810	−	0.155925i
$511$	−1.34208	−	0.774853i	−0.0593703	−	0.0342775i
$512$	8.53426	+	20.9563i	0.377165	+	0.926146i
$513$	0.566688	+	2.57498i	0.0250199	+	0.113688i
$514$	−1.51730	+	11.4663i	−0.0669253	+	0.505757i
$515$	−1.69910	−	0.980974i	−0.0748712	−	0.0432269i
$516$	−32.3819	−	32.4679i	−1.42553	−	1.42932i
$517$	9.03822	−	5.21822i	0.397500	−	0.229497i
$518$	19.2787	+	14.8134i	0.847056	+	0.650862i
$519$	−32.1858	+	18.5825i	−1.41280	+	0.815679i
$520$	1.89148	−	4.54088i	0.0829471	−	0.199131i
$521$			27.1524i			1.18957i	0.803885	+	0.594784i	$0.202763\pi$
$521$			27.1524i			1.18957i	−0.803885	+	0.594784i	$0.797237\pi$
$522$	−2.06415	−	4.99265i	−0.0903453	−	0.218522i
$523$	1.66719	−	0.962550i	0.0729009	−	0.0420894i	−0.463106	−	0.886303i	$-0.653265\pi$
$523$	1.66719	−	0.962550i	0.0729009	−	0.0420894i	0.536007	+	0.844213i	$0.319932\pi$
$524$	16.0033	+	4.31081i	0.699105	+	0.188319i
$525$	17.9057			0.781468
$526$	28.7215	−	11.8746i	1.25232	−	0.517755i
$527$	−6.58894	+	11.4124i	−0.287019	+	0.497131i
$528$	−11.9260	−	0.0316236i	−0.519013	−	0.00137624i
$529$	8.85283	−	15.3336i	0.384906	−	0.666676i
$530$	1.62536	+	1.24890i	0.0706013	+	0.0542487i
$531$			14.0783i			0.610947i
$532$	−12.1342	+	6.27248i	−0.526086	+	0.271946i
$533$		−	4.57334i		−	0.198093i
$534$	26.6266	−	34.6529i	1.15225	−	1.49958i
$535$	−1.00312	+	1.73745i	−0.0433686	+	0.0751167i
$536$	−10.4441	+	1.35387i	−0.451117	+	0.0584782i
$537$	−3.42944	+	5.93997i	−0.147991	+	0.256329i
$538$	−2.09892	−	5.07677i	−0.0904911	−	0.218875i
$539$	5.65222			0.243458
$540$	−0.564270	−	0.151998i	−0.0242823	−	0.00654094i
$541$	30.5146	−	17.6176i	1.31193	−	0.757441i	0.329511	−	0.944152i	$-0.393116\pi$
$541$	30.5146	−	17.6176i	1.31193	−	0.757441i	0.982415	+	0.186711i	$0.0597828\pi$
$542$	−2.73499	+	1.13075i	−0.117478	+	0.0485697i
$543$			1.46311i			0.0627880i
$544$	12.1375	+	9.37750i	0.520390	+	0.402057i
$545$	7.58879	−	4.38139i	0.325068	−	0.187678i
$546$	−11.6534	+	15.1662i	−0.498721	+	0.649054i
$547$	−7.93165	+	4.57934i	−0.339133	+	0.195798i	−0.659888	−	0.751364i	$-0.729396\pi$
$547$	−7.93165	+	4.57934i	−0.339133	+	0.195798i	0.320756	+	0.947162i	$0.396063\pi$
$548$	25.2340	−	25.1672i	1.07794	−	1.07509i
$549$	−25.8919	−	14.9487i	−1.10504	−	0.637995i
$550$	8.31092	+	1.09976i	0.354379	+	0.0468939i
$551$	−4.08733	−	4.47439i	−0.174126	−	0.190616i
$552$	39.9370	+	16.6356i	1.69983	+	0.708058i
$553$	−15.7761	−	9.10833i	−0.670868	−	0.387326i
$554$	31.2043	+	23.9767i	1.32574	+	1.01867i
$555$	−6.35335	−	11.0043i	−0.269685	−	0.467108i
$556$	11.7861	−	11.7549i	0.499842	−	0.498518i
$557$	26.0361	−	15.0319i	1.10318	−	0.636924i	0.166129	−	0.986104i	$-0.446873\pi$
$557$	26.0361	−	15.0319i	1.10318	−	0.636924i	0.937056	+	0.349180i	$0.113540\pi$
$558$	−18.7225	−	2.47750i	−0.792589	−	0.104881i
$559$	−34.4315			−1.45630
$560$	0.00802794	−	3.02753i	0.000339243	−	0.127936i
$561$	−7.00104	+	4.04205i	−0.295584	+	0.170656i
$562$	4.30074	−	32.5009i	0.181416	−	1.37097i
$563$		−	35.3632i		−	1.49038i	−0.666851	−	0.745191i	$-0.732358\pi$
$563$		−	35.3632i		−	1.49038i	0.666851	−	0.745191i	$-0.267642\pi$
$564$	−10.3629	−	38.8810i	−0.436357	−	1.63718i
$565$	1.69151	−	2.92978i	0.0711624	−	0.123257i
$566$	1.52068	+	3.67814i	0.0639189	+	0.154604i
$567$	13.1532	+	7.59398i	0.552381	+	0.318917i
$568$	−29.7852	+	22.7610i	−1.24976	+	0.955030i
$569$		−	24.5320i		−	1.02844i	−0.857660	−	0.514218i	$-0.828082\pi$
$569$		−	24.5320i		−	1.02844i	0.857660	−	0.514218i	$-0.171918\pi$
$570$	7.11320	−	0.606502i	0.297939	−	0.0254036i
$571$	16.3080			0.682467			0.341233	−	0.939979i	$-0.389155\pi$
$571$	16.3080			0.682467			0.341233	+	0.939979i	$0.389155\pi$
$572$	−6.34044	+	6.32365i	−0.265107	+	0.264405i
$573$	26.2562	−	45.4770i	1.09687	−	1.89983i
$574$	−1.07543	−	2.60120i	−0.0448877	−	0.108572i
$575$	−26.3373	−	15.2059i	−1.09834	−	0.634128i
$576$	−5.77366	+	21.2098i	−0.240569	+	0.883741i
$577$	−13.0747			−0.544305			−0.272153	−	0.962254i	$-0.587736\pi$
$577$	−13.0747			−0.544305			−0.272153	+	0.962254i	$0.587736\pi$
$578$	−13.5268	−	1.78996i	−0.562640	−	0.0744524i
$579$	6.37315	+	11.0386i	0.264859	+	0.458750i
$580$	1.29790	−	0.345926i	0.0538922	−	0.0143638i
$581$		−	19.1076i		−	0.792719i
$582$	−9.42025	−	1.24655i	−0.390482	−	0.0516713i
$583$	−1.86574	−	3.23155i	−0.0772710	−	0.133837i
$584$	−2.22276	+	1.69857i	−0.0919784	+	0.0702873i
$585$	4.13846	−	2.38934i	0.171104	−	0.0987870i
$586$	−7.45884	+	9.70721i	−0.308122	+	0.401001i
$587$	8.90580	−	15.4253i	0.367582	−	0.636671i	−0.621605	−	0.783331i	$-0.713519\pi$
$587$	8.90580	−	15.4253i	0.367582	−	0.636671i	0.989187	+	0.146660i	$0.0468524\pi$
$588$	5.66821	−	21.0424i	0.233753	−	0.867774i
$589$	−20.6898	+	4.55330i	−0.852510	+	0.187615i
$590$	−3.46998	−	0.459171i	−0.142857	−	0.0189038i
$591$	−1.09505	+	1.89668i	−0.0450443	+	0.0780191i
$592$	38.0662	−	21.8432i	1.56451	−	0.897749i
$593$	−14.1110	−	24.4410i	−0.579471	−	1.00367i	−0.995540	−	0.0943399i	$-0.969926\pi$
$593$	−14.1110	−	24.4410i	−0.579471	−	1.00367i	0.416069	−	0.909333i	$-0.363407\pi$
$594$	0.843565	+	0.648179i	0.0346119	+	0.0265951i
$595$	−1.02611	−	1.77728i	−0.0420665	−	0.0728613i
$596$	9.66651	−	35.8855i	0.395956	−	1.46993i
$597$	48.1031			1.96873
$598$	30.0204	−	12.4115i	1.22763	−	0.507546i
$599$	18.3746	+	31.8258i	0.750766	+	1.30037i	0.947452	+	0.319899i	$0.103649\pi$
$599$	18.3746	+	31.8258i	0.750766	+	1.30037i	−0.196685	+	0.980467i	$0.563018\pi$
$600$	12.4287	−	29.8375i	0.507398	−	1.21811i
$601$			13.0119i			0.530767i	0.964143	+	0.265384i	$0.0854986\pi$
$601$			13.0119i			0.530767i	−0.964143	+	0.265384i	$0.914501\pi$
$602$	−19.5838	+	8.09666i	−0.798175	+	0.329995i
$603$	−8.86022	−	5.11545i	−0.360816	−	0.208317i
$604$	−2.35259	−	8.82676i	−0.0957253	−	0.359156i
$605$	−3.95474	−	2.28327i	−0.160783	−	0.0928281i
$606$	−1.56469	+	2.03634i	−0.0635611	+	0.0827208i
$607$	−28.9061			−1.17326			−0.586631	−	0.809854i	$-0.699546\pi$
$607$	−28.9061			−1.17326			−0.586631	+	0.809854i	$0.699546\pi$
$608$	2.02966	+	24.5740i	0.0823137	+	0.996606i
$609$	−5.22264			−0.211632
$610$	4.52898	−	5.89419i	0.183373	−	0.238649i
$611$	−26.1657	−	15.1068i	−1.05855	−	0.611155i
$612$	3.83739	+	14.3977i	0.155117	+	0.581991i
$613$	25.3842	+	14.6556i	1.02526	+	0.591934i	0.915623	−	0.402038i	$-0.131698\pi$
$613$	25.3842	+	14.6556i	1.02526	+	0.591934i	0.109636	+	0.993972i	$0.465031\pi$
$614$	−13.5577	+	5.60525i	−0.547143	+	0.226209i
$615$			1.47109i			0.0593202i
$616$	−2.11926	+	5.08770i	−0.0853873	+	0.204989i
$617$	−2.44550	−	4.23572i	−0.0984519	−	0.170524i	0.812592	−	0.582833i	$-0.198056\pi$
$617$	−2.44550	−	4.23572i	−0.0984519	−	0.170524i	−0.911044	+	0.412309i	$0.864722\pi$
$618$	12.7258	−	5.26131i	0.511906	−	0.211641i
$619$	−31.8807			−1.28139			−0.640696	−	0.767795i	$-0.721354\pi$
$619$	−31.8807			−1.28139			−0.640696	+	0.767795i	$0.721354\pi$
$620$	1.22129	−	4.53387i	0.0490482	−	0.182085i
$621$	−1.92959	−	3.34215i	−0.0774319	−	0.134116i
$622$	23.3036	+	17.9060i	0.934389	+	0.717967i
$623$	−10.0979	−	17.4901i	−0.404565	−	0.700727i
$624$	17.1837	+	29.9461i	0.687897	+	1.19880i
$625$	−10.7771	+	18.6665i	−0.431085	+	0.746662i
$626$	33.6200	+	4.44883i	1.34373	+	0.177811i
$627$	−12.3886	−	3.92715i	−0.494751	−	0.156835i
$628$	−9.67049	+	35.9003i	−0.385894	+	1.43258i
$629$	14.8748	−	25.7639i	0.593098	−	1.02728i
$630$	1.79199	−	2.33216i	0.0713946	−	0.0929156i
$631$	−7.83877	+	4.52572i	−0.312057	+	0.180166i	−0.647846	−	0.761771i	$-0.724330\pi$
$631$	−7.83877	+	4.52572i	−0.312057	+	0.180166i	0.335790	+	0.941937i	$0.390997\pi$
$632$	−26.1283	+	19.9665i	−1.03933	+	0.794227i
$633$	−29.8585	−	51.7165i	−1.18677	−	2.05555i
$634$	26.5116	+	3.50820i	1.05291	+	0.139329i
$635$			7.35711i			0.291958i
$636$	−13.9016	+	3.70518i	−0.551235	+	0.146920i
$637$	−8.18161	−	14.1710i	−0.324167	−	0.561474i
$638$	−2.42409	−	0.320772i	−0.0959705	−	0.0126995i
$639$	−36.4163			−1.44061
$640$	−5.03941	−	2.11484i	−0.199200	−	0.0835964i
$641$	−33.2407	−	19.1916i	−1.31293	−	0.758021i	−0.330350	−	0.943859i	$-0.607167\pi$
$641$	−33.2407	−	19.1916i	−1.31293	−	0.758021i	−0.982580	+	0.185838i	$0.940500\pi$
$642$	−5.38009	−	13.0131i	−0.212335	−	0.513585i
$643$	−14.9780	+	25.9427i	−0.590677	+	1.02308i	0.403465	+	0.914995i	$0.367806\pi$
$643$	−14.9780	+	25.9427i	−0.590677	+	1.02308i	−0.994141	+	0.108087i	$0.965528\pi$
$644$	14.1562	−	14.1187i	0.557834	−	0.556356i
$645$	11.0755			0.436097
$646$	9.55665	+	13.7126i	0.376001	+	0.539517i
$647$			14.7012i			0.577963i	0.957335	+	0.288982i	$0.0933167\pi$
$647$			14.7012i			0.577963i	−0.957335	+	0.288982i	$0.906683\pi$
$648$	21.7842	−	16.6469i	0.855766	−	0.653952i
$649$	5.51826	+	3.18597i	0.216610	+	0.125060i
$650$	−9.27283	−	22.4286i	−0.363710	−	0.879723i
$651$	−9.12846	+	15.8110i	−0.357773	+	0.619680i
$652$	−6.83082	−	25.6288i	−0.267515	−	1.00370i
$653$			12.1042i			0.473673i	0.971550	+	0.236836i	$0.0761105\pi$
$653$			12.1042i			0.473673i	−0.971550	+	0.236836i	$0.923889\pi$
$654$	−8.06833	+	60.9726i	−0.315496	+	2.38422i
$655$	−3.46672	+	2.00151i	−0.135456	+	0.0782056i
$656$	−5.08104	−	0.0134731i	−0.198381	−	0.000526037i
$657$	−2.71762			−0.106024
$658$	−18.4348	−	2.43942i	−0.718663	−	0.0950985i
$659$	−8.35717	+	4.82502i	−0.325549	+	0.187956i	−0.653863	−	0.756613i	$-0.726853\pi$
$659$	−8.35717	+	4.82502i	−0.325549	+	0.187956i	0.328314	+	0.944569i	$0.393520\pi$
$660$	2.03951	−	2.03411i	0.0793879	−	0.0791776i
$661$	18.5479	+	32.1258i	0.721428	+	1.24955i	0.960427	+	0.278530i	$0.0898473\pi$
$661$	18.5479	+	32.1258i	0.721428	+	1.24955i	−0.238999	+	0.971020i	$0.576819\pi$
$662$	−17.8969	−	13.7516i	−0.695582	−	0.534472i
$663$	20.2681	+	11.7018i	0.787146	+	0.454459i
$664$	−31.8404	−	13.2630i	−1.23565	−	0.514703i
$665$	0.996943	−	3.14495i	0.0386598	−	0.121956i
$666$	42.2669	+	5.59306i	1.63781	+	0.216727i
$667$	7.68194	+	4.43517i	0.297446	+	0.171730i
$668$	14.1931	−	14.1555i	0.549149	−	0.547694i
$669$	−7.26697	+	4.19559i	−0.280957	+	0.162211i
$670$	1.54982	−	2.01700i	0.0598748	−	0.0779233i
$671$	−11.7188	+	6.76588i	−0.452401	+	0.261194i
$672$	16.8155	+	12.9918i	0.648673	+	0.501169i
$673$		−	10.8787i		−	0.419342i	−0.977772	−	0.209671i	$-0.932761\pi$
$673$		−	10.8787i		−	0.419342i	0.977772	−	0.209671i	$-0.0672392\pi$
$674$	32.2171	−	13.3198i	1.24096	−	0.513058i
$675$	−2.49697	+	1.44162i	−0.0961082	+	0.0554881i
$676$	−0.0729798	−	0.0196586i	−0.00280692	−	0.000756101i
$677$	−37.4698			−1.44008			−0.720040	−	0.693932i	$-0.755877\pi$
$677$	−37.4698			−1.44008			−0.720040	+	0.693932i	$0.755877\pi$
$678$	9.07217	+	21.9433i	0.348415	+	0.842727i
$679$	−2.19568	+	3.80304i	−0.0842626	+	0.145947i
$680$	−3.67385	+	0.476240i	−0.140886	+	0.0182630i
$681$	−6.34580	+	10.9913i	−0.243172	+	0.421186i
$682$	−5.20807	+	6.77799i	−0.199427	+	0.259542i
$683$		−	51.9840i		−	1.98911i	−0.104201	−	0.994556i	$-0.533229\pi$
$683$		−	51.9840i		−	1.98911i	0.104201	−	0.994556i	$-0.466771\pi$
$684$	−12.9284	+	20.1655i	−0.494328	+	0.771046i
$685$			8.60787i			0.328890i
$686$	−20.2854	−	15.5869i	−0.774499	−	0.595110i
$687$	1.44887	−	2.50952i	0.0552779	−	0.0957441i
$688$	−0.101436	+	38.2539i	−0.00386721	+	1.45841i
$689$	−5.40133	+	9.35537i	−0.205774	+	0.356411i
$690$	−9.65658	+	3.99239i	−0.367620	+	0.151988i
$691$	−7.12137			−0.270910			−0.135455	−	0.990784i	$-0.543250\pi$
$691$	−7.12137			−0.270910			−0.135455	+	0.990784i	$0.543250\pi$
$692$	29.9368	+	8.06410i	1.13803	+	0.306551i
$693$	−4.63681	+	2.67706i	−0.176138	+	0.101693i
$694$	4.94340	+	11.9568i	0.187649	+	0.453875i
$695$			4.02049i			0.152506i
$696$	−3.62513	+	8.70285i	−0.137410	+	0.329881i
$697$	−2.98277	+	1.72210i	−0.112980	+	0.0652293i
$698$	−19.9688	−	15.3437i	−0.755831	−	0.580766i
$699$	23.2100	−	13.4003i	0.877884	−	0.506847i
$700$	−10.5483	−	10.5763i	−0.398688	−	0.399747i
$701$	−6.27811	−	3.62467i	−0.237121	−	0.136902i	0.376732	−	0.926322i	$-0.377048\pi$
$701$	−6.27811	−	3.62467i	−0.237121	−	0.136902i	−0.613853	+	0.789421i	$0.710381\pi$
$702$	0.404019	−	3.05319i	0.0152487	−	0.115235i
$703$	46.7082	−	10.2793i	1.76163	−	0.387690i
$704$	7.00697	+	7.06293i	0.264085	+	0.266194i
$705$	8.41665	+	4.85936i	0.316990	+	0.183014i
$706$	−20.1504	+	26.2246i	−0.758372	+	0.986974i
$707$	0.593395	+	1.02779i	0.0223169	+	0.0386540i
$708$	17.3948	−	17.3487i	0.653735	−	0.652004i
$709$	−16.8968	+	9.75535i	−0.634571	+	0.366370i	−0.782520	−	0.622625i	$-0.786066\pi$
$709$	−16.8968	+	9.75535i	−0.634571	+	0.366370i	0.147949	+	0.988995i	$0.452733\pi$
$710$	1.18774	−	8.97578i	0.0445750	−	0.336855i
$711$	−31.9454			−1.19804
$712$	−36.1542	+	4.68666i	−1.35494	+	0.175640i
$713$	26.8540	−	15.5041i	1.00569	−	0.580635i
$714$	14.2797	+	1.88958i	0.534403	+	0.0707159i
$715$		−	2.16286i		−	0.0808864i
$716$	5.52885	−	1.47360i	0.206623	−	0.0550709i
$717$	−24.3624	+	42.1970i	−0.909831	+	1.57587i
$718$	17.2115	−	7.11589i	0.642329	−	0.265563i
$719$	37.0563	+	21.3944i	1.38197	+	0.797878i	0.992392	−	0.123117i	$-0.0392891\pi$
$719$	37.0563	+	21.3944i	1.38197	+	0.797878i	0.389573	+	0.920995i	$0.372622\pi$
$720$	−2.64239	−	4.60492i	−0.0984762	−	0.171615i
$721$		−	6.36383i		−	0.237001i
$722$	−5.91415	+	26.2111i	−0.220102	+	0.975477i
$723$	15.1731			0.564292
$724$	0.864211	−	0.861922i	0.0321181	−	0.0320331i
$725$	3.31357	−	5.73928i	0.123063	−	0.213151i
$726$	29.6199	−	12.2460i	1.09930	−	0.454491i
$727$	−21.7487	−	12.5566i	−0.806614	−	0.465699i	0.0391646	−	0.999233i	$-0.487530\pi$
$727$	−21.7487	−	12.5566i	−0.806614	−	0.465699i	−0.845779	+	0.533534i	$0.820864\pi$
$728$	15.8233	−	2.05117i	0.586449	−	0.0760213i
$729$	22.2837			0.825320
$730$	0.0886365	−	0.669829i	0.00328058	−	0.0247915i
$731$	12.9653	+	22.4565i	0.479538	+	0.830585i
$732$	13.4364	+	50.4126i	0.496624	+	1.86330i
$733$			0.990917i			0.0366004i	0.999833	+	0.0183002i	$0.00582545\pi$
$733$			0.990917i			0.0366004i	−0.999833	+	0.0183002i	$0.994175\pi$
$734$	−2.84293	+	21.4841i	−0.104934	+	0.792993i
$735$	2.63176	+	4.55833i	0.0970738	+	0.168137i
$736$	−13.7009	−	33.3896i	−0.505023	−	1.23076i
$737$	−4.01019	+	2.31529i	−0.147717	+	0.0852846i
$738$	−3.91402	−	3.00746i	−0.144077	−	0.110706i
$739$	−8.15940	+	14.1325i	−0.300149	+	0.519872i	−0.976169	−	0.217010i	$-0.930370\pi$
$739$	−8.15940	+	14.1325i	−0.300149	+	0.519872i	0.676021	+	0.736882i	$0.263703\pi$
$740$	−2.75712	+	10.2354i	−0.101354	+	0.376261i
$741$	8.08653	+	36.7446i	0.297066	+	1.34984i
$742$	−0.872198	+	6.59123i	−0.0320194	+	0.241972i
$743$	21.4854	−	37.2138i	0.788223	−	1.36524i	−0.138832	−	0.990316i	$-0.544335\pi$
$743$	21.4854	−	37.2138i	0.788223	−	1.36524i	0.927055	−	0.374926i	$-0.122332\pi$
$744$	20.0107	+	26.1861i	0.733627	+	0.960028i
$745$	4.48817	+	7.77374i	0.164434	+	0.284808i
$746$	−7.17864	+	9.34255i	−0.262829	+	0.342055i
$747$	−16.7539	−	29.0186i	−0.612993	−	1.06174i
$748$	6.51184	+	1.75410i	0.238097	+	0.0641362i
$749$	−6.50749			−0.237778
$750$	6.11155	+	14.7823i	0.223162	+	0.539773i
$751$	10.3838	+	17.9853i	0.378910	+	0.656292i	0.990904	−	0.134571i	$-0.0429656\pi$
$751$	10.3838	+	17.9853i	0.378910	+	0.656292i	−0.611994	+	0.790863i	$0.709632\pi$
$752$	−16.8609	+	29.0259i	−0.614854	+	1.05847i
$753$			58.2751i			2.12366i
$754$	2.70465	+	6.54187i	0.0984976	+	0.238241i
$755$	1.91075	+	1.10317i	0.0695393	+	0.0401485i
$756$	−0.488169	−	1.83158i	−0.0177545	−	0.0666139i
$757$	−10.7348	−	6.19774i	−0.390163	−	0.225261i	0.292068	−	0.956398i	$-0.405657\pi$
$757$	−10.7348	−	6.19774i	−0.390163	−	0.225261i	−0.682231	+	0.731137i	$0.738990\pi$
$758$	−11.7165	−	9.00272i	−0.425562	−	0.326993i
$759$	19.0223			0.690467
$760$	−4.54865	−	3.84425i	−0.164997	−	0.139445i
$761$	46.1918			1.67445			0.837226	−	0.546858i	$-0.184176\pi$
$761$	46.1918			1.67445			0.837226	+	0.546858i	$0.184176\pi$
$762$	−40.9463	−	31.4624i	−1.48333	−	1.13976i
$763$	24.6152	+	14.2116i	0.891130	+	0.514494i
$764$	−42.3294	+	11.2820i	−1.53142	+	0.408168i
$765$	−3.11669	−	1.79942i	−0.112684	−	0.0650583i
$766$	−4.56591	−	11.0438i	−0.164973	−	0.399029i
$767$		−	18.4468i		−	0.666075i
$768$	33.3211	−	19.0030i	1.20237	−	0.685713i
$769$	7.84569	+	13.5891i	0.282923	+	0.490037i	0.972103	−	0.234553i	$-0.0753627\pi$
$769$	7.84569	+	13.5891i	0.282923	+	0.490037i	−0.689181	+	0.724590i	$0.742029\pi$
$770$	−0.508602	−	1.23018i	−0.0183287	−	0.0443326i
$771$	19.6076			0.706151
$772$	2.76571	−	10.2673i	0.0995401	−	0.369528i
$773$	−2.97659	−	5.15560i	−0.107060	−	0.185434i	0.807518	−	0.589843i	$-0.200810\pi$
$773$	−2.97659	−	5.15560i	−0.107060	−	0.185434i	−0.914578	+	0.404409i	$0.867477\pi$
$774$	−22.6424	+	29.4677i	−0.813865	+	1.05919i
$775$	−11.5833	−	20.0629i	−0.416086	−	0.720682i
$776$	4.81320	+	6.29858i	0.172784	+	0.226106i
$777$	20.6079	−	35.6939i	0.739304	−	1.28051i
$778$	1.13355	−	8.56632i	0.0406399	−	0.307117i
$779$	−5.27810	−	1.67315i	−0.189108	−	0.0599468i
$780$	−8.05202	−	2.16898i	−0.288309	−	0.0776619i
$781$	−8.24113	+	14.2741i	−0.294891	+	0.510766i
$782$	−19.3992	−	14.9059i	−0.693713	−	0.533036i
$783$	0.728302	−	0.420485i	0.0260274	−	0.0150269i
$784$	−15.7682	+	9.04812i	−0.563151	+	0.323147i
$785$	−4.49002	−	7.77694i	−0.160256	−	0.277571i
$786$	3.68579	−	27.8536i	0.131468	−	0.993506i
$787$		−	5.02671i		−	0.179183i	−0.995979	−	0.0895915i	$-0.971444\pi$
$787$		−	5.02671i		−	0.179183i	0.995979	−	0.0895915i	$-0.0285561\pi$
$788$	1.76541	−	0.470531i	0.0628900	−	0.0167620i
$789$	−26.3436	−	45.6285i	−0.937857	−	1.62442i
$790$	1.04191	−	7.87379i	0.0370697	−	0.280137i
$791$	10.9733			0.390164
$792$	1.24248	+	9.58484i	0.0441497	+	0.340583i
$793$	33.9261	+	19.5873i	1.20475	+	0.695564i
$794$	29.4517	−	12.1764i	1.04520	−	0.432125i
$795$	1.73743	−	3.00932i	0.0616203	−	0.106729i
$796$	−28.3377	−	28.4129i	−1.00440	−	1.00707i
$797$	23.2783			0.824558			0.412279	−	0.911058i	$-0.364733\pi$
$797$	23.2783			0.824558			0.412279	+	0.911058i	$0.364733\pi$
$798$	13.2400	+	18.9978i	0.468690	+	0.672515i
$799$			22.7540i			0.804978i
$800$	−24.9458	+	10.2362i	−0.881967	+	0.361903i
$801$	−30.6713	−	17.7081i	−1.08372	−	0.625684i
$802$	2.40452	−	0.994120i	0.0849067	−	0.0351036i
$803$	−0.615005	+	1.06522i	−0.0217031	+	0.0375908i
$804$	4.59794	+	17.2512i	0.162157	+	0.608403i
$805$			4.82900i			0.170200i
$806$	24.5321	+	3.24626i	0.864108	+	0.114345i
$807$	−8.06521	+	4.65645i	−0.283909	+	0.163915i
$808$	2.12457	−	0.275407i	0.0747419	−	0.00968879i
$809$	−38.1510			−1.34132			−0.670659	−	0.741766i	$-0.733989\pi$
$809$	−38.1510			−1.34132			−0.670659	+	0.741766i	$0.733989\pi$
$810$	−0.868686	+	6.56469i	−0.0305225	+	0.230660i
$811$	43.8993	−	25.3453i	1.54151	−	0.889993i	0.542770	−	0.839881i	$-0.317375\pi$
$811$	43.8993	−	25.3453i	1.54151	−	0.889993i	0.998744	−	0.0501122i	$-0.0159579\pi$
$812$	3.07667	+	3.08484i	0.107970	+	0.108257i
$813$	2.50855	+	4.34494i	0.0879788	+	0.152384i
$814$	11.7574	−	15.3016i	0.412098	−	0.536321i
$815$	5.54793	+	3.20310i	0.194336	+	0.112200i
$816$	13.0605	−	22.4836i	0.457210	−	0.787083i
$817$	−12.5967	+	39.7375i	−0.440704	+	1.39024i
$818$	6.78664	−	51.2869i	0.237289	−	1.79320i
$819$	13.4236	+	7.75012i	0.469059	+	0.270811i
$820$	0.868927	−	0.866626i	0.0303442	−	0.0302639i
$821$	−17.8048	+	10.2796i	−0.621391	+	0.358760i	−0.777410	−	0.628994i	$-0.783467\pi$
$821$	−17.8048	+	10.2796i	−0.621391	+	0.358760i	0.156019	+	0.987754i	$0.450134\pi$
$822$	−47.9075	−	36.8112i	−1.67097	−	1.28394i
$823$	16.8787	−	9.74491i	0.588354	−	0.339686i	−0.176093	−	0.984374i	$-0.556346\pi$
$823$	16.8787	−	9.74491i	0.588354	−	0.339686i	0.764446	+	0.644687i	$0.223012\pi$
$824$	−10.6045	−	4.41725i	−0.369425	−	0.153882i
$825$		−	14.2118i		−	0.494793i
$826$	−4.33781	−	10.4921i	−0.150932	−	0.365066i
$827$	12.7206	−	7.34424i	0.442338	−	0.255384i	−0.262251	−	0.965000i	$-0.584465\pi$
$827$	12.7206	−	7.34424i	0.442338	−	0.255384i	0.704589	+	0.709616i	$0.251131\pi$
$828$	9.11939	−	33.8544i	0.316921	−	1.17652i
$829$	−35.2405			−1.22395			−0.611976	−	0.790876i	$-0.709625\pi$
$829$	−35.2405			−1.22395			−0.611976	+	0.790876i	$0.709625\pi$
$830$	7.69885	−	3.18299i	0.267231	−	0.110483i
$831$	33.3557	−	57.7738i	1.15710	−	2.00415i
$832$	7.56522	−	27.7912i	0.262277	−	0.963485i
$833$	−6.16161	+	10.6722i	−0.213487	+	0.369771i
$834$	−22.3763	−	17.1935i	−0.774826	−	0.595362i
$835$			4.84158i			0.167550i
$836$	4.97850	+	9.63102i	0.172185	+	0.333096i
$837$		−	2.93981i		−	0.101615i
$838$	−3.47921	+	4.52798i	−0.120187	+	0.156416i
$839$	3.11351	−	5.39276i	0.107490	−	0.186179i	−0.807263	−	0.590192i	$-0.799052\pi$
$839$	3.11351	−	5.39276i	0.107490	−	0.186179i	0.914753	+	0.404014i	$0.132385\pi$
$840$	−5.08983	+	0.659793i	−0.175616	+	0.0227650i
$841$	13.5335	−	23.4407i	0.466673	−	0.808301i
$842$	3.49615	+	8.45632i	0.120485	+	0.291424i
$843$	−55.5771			−1.91418
$844$	−12.9575	+	48.1028i	−0.446015	+	1.65577i
$845$	0.0158093	−	0.00912753i	0.000543858	−	0.000313997i
$846$	−30.1357	+	12.4592i	−1.03609	+	0.428356i
$847$		−	14.8121i		−	0.508951i
$848$	10.3780	+	6.02850i	0.356383	+	0.207020i
$849$	5.84328	−	3.37362i	0.200541	−	0.115782i
$850$	−11.1364	+	14.4934i	−0.381976	+	0.497119i
$851$	−60.6240	+	35.0013i	−2.07816	+	1.19983i
$852$	44.8758	+	44.9950i	1.53742	+	1.54150i
$853$	−28.3047	−	16.3417i	−0.969134	−	0.559530i	−0.0701616	−	0.997536i	$-0.522351\pi$
$853$	−28.3047	−	16.3417i	−0.969134	−	0.559530i	−0.898972	+	0.438006i	$0.855685\pi$
$854$	23.9023	+	3.16292i	0.817921	+	0.108233i
$855$	−1.24350	−	5.65034i	−0.0425266	−	0.193238i
$856$	−4.51697	+	10.8439i	−0.154387	+	0.370636i
$857$	45.5110	+	26.2758i	1.55463	+	0.897564i	0.997755	+	0.0669647i	$0.0213315\pi$
$857$	45.5110	+	26.2758i	1.55463	+	0.897564i	0.556871	+	0.830599i	$0.312002\pi$
$858$	12.0375	+	9.24939i	0.410954	+	0.315769i
$859$	12.3600	+	21.4082i	0.421718	+	0.730437i	0.996108	−	0.0881450i	$-0.0280939\pi$
$859$	12.3600	+	21.4082i	0.421718	+	0.730437i	−0.574390	+	0.818582i	$0.694761\pi$
$860$	−6.52461	−	6.54193i	−0.222487	−	0.223078i
$861$	−4.13239	+	2.38584i	−0.140832	+	0.0813091i
$862$	8.90079	+	1.17781i	0.303162	+	0.0401165i
$863$	25.0075			0.851266			0.425633	−	0.904896i	$-0.360051\pi$
$863$	25.0075			0.851266			0.425633	+	0.904896i	$0.360051\pi$
$864$	−3.39094	−	0.457865i	−0.115362	−	0.0155769i
$865$	−6.48509	+	3.74417i	−0.220500	+	0.127306i
$866$	−4.31199	+	32.5859i	−0.146527	+	1.10731i
$867$			23.1311i			0.785572i
$868$	14.7166	−	3.92240i	0.499515	−	0.133135i
$869$	−7.22934	+	12.5216i	−0.245238	+	0.424765i
$870$	−0.869998	−	2.10430i	−0.0294957	−	0.0713426i
$871$	11.6095	+	6.70277i	0.393374	+	0.227115i
$872$	40.7676	−	31.1535i	1.38057	−	1.05499i
$873$			7.70085i			0.260634i
$874$	−3.34128	−	39.1874i	−0.113021	−	1.32553i
$875$	7.39223			0.249903
$876$	3.34892	+	3.35781i	0.113149	+	0.113450i
$877$	−1.76754	+	3.06146i	−0.0596855	+	0.103378i	−0.894324	−	0.447419i	$-0.852343\pi$
$877$	−1.76754	+	3.06146i	−0.0596855	+	0.103378i	0.834639	+	0.550798i	$0.185676\pi$
$878$	5.64841	+	13.6621i	0.190625	+	0.461073i
$879$	17.9726	+	10.3765i	0.606202	+	0.349991i
$880$	−2.40297	−	0.00637183i	−0.0810039	−	0.000214794i
$881$	−5.22599			−0.176068			−0.0880341	−	0.996117i	$-0.528058\pi$
$881$	−5.22599			−0.176068			−0.0880341	+	0.996117i	$0.528058\pi$
$882$	−17.5083	−	2.31682i	−0.589535	−	0.0780113i
$883$	−2.22587	−	3.85532i	−0.0749066	−	0.129742i	0.826139	−	0.563466i	$-0.190533\pi$
$883$	−2.22587	−	3.85532i	−0.0749066	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$884$	−5.02813	−	18.8652i	−0.169114	−	0.634507i
$885$			5.93373i			0.199460i
$886$	−20.0548	−	2.65379i	−0.673755	−	0.0891559i
$887$	23.1207	+	40.0463i	0.776318	+	1.34462i	0.934051	+	0.357141i	$0.116248\pi$
$887$	23.1207	+	40.0463i	0.776318	+	1.34462i	−0.157732	+	0.987482i	$0.550418\pi$
$888$	−45.1749	−	59.1162i	−1.51597	−	1.98381i
$889$	−20.6666	+	11.9318i	−0.693134	+	0.400181i
$890$	5.36499	−	6.98220i	0.179835	−	0.234044i
$891$	6.02739	−	10.4397i	0.201925	−	0.349744i
$892$	6.75919	+	1.82073i	0.226314	+	0.0609625i
$893$	−27.0075	+	24.6711i	−0.903771	+	0.825588i
$894$	−62.4587	−	8.26497i	−2.08893	−	0.276422i
$895$	−0.690997	+	1.19684i	−0.0230975	+	0.0400060i
$896$	−2.23226	−	17.5859i	−0.0745744	−	0.587503i
$897$	−27.5349	−	47.6919i	−0.919364	−	1.59239i
$898$	39.4684	+	30.3268i	1.31708	+	1.01202i
$899$	3.37857	+	5.85186i	0.112682	+	0.195170i
$900$	−25.2931	−	6.81322i	−0.843103	−	0.227107i
$901$	8.13553			0.271034
$902$	−2.06459	+	0.853576i	−0.0687432	+	0.0284210i
$903$	17.9624	+	31.1118i	0.597751	+	1.03533i
$904$	7.61674	−	18.2855i	0.253329	−	0.608167i
$905$			0.294801i			0.00979952i
$906$	−14.3110	+	5.91670i	−0.475451	+	0.196569i
$907$	1.48781	+	0.858985i	0.0494018	+	0.0285221i	0.524497	−	0.851412i	$-0.324253\pi$
$907$	1.48781	+	0.858985i	0.0494018	+	0.0285221i	−0.475096	+	0.879934i	$0.657587\pi$
$908$	10.2305	−	2.72672i	0.339511	−	0.0904895i
$909$	1.80237	+	1.04060i	0.0597807	+	0.0345144i
$910$	−2.34804	+	3.05583i	−0.0778369	+	0.101300i
$911$	0.307661			0.0101933			0.00509664	−	0.999987i	$-0.498378\pi$
$911$	0.307661			0.0101933			0.00509664	+	0.999987i	$0.498378\pi$
$912$	40.8475	−	8.87599i	1.35260	−	0.293913i
$913$	−15.1659			−0.501916
$914$	−4.96606	+	6.46302i	−0.164263	+	0.213778i
$915$	−10.9129	−	6.30058i	−0.360770	−	0.208291i
$916$	−2.33583	+	0.622565i	−0.0771779	+	0.0205701i
$917$	−11.2448	−	6.49216i	−0.371334	−	0.214390i
$918$	−2.14345	+	0.886181i	−0.0707443	+	0.0292483i
$919$		−	28.6229i		−	0.944183i	−0.881550	−	0.472091i	$-0.843499\pi$
$919$		−	28.6229i		−	0.944183i	0.881550	−	0.472091i	$-0.156501\pi$
$920$	8.04690	+	3.35190i	0.265298	+	0.110509i
$921$	12.4352	+	21.5384i	0.409754	+	0.709714i
$922$	−35.7732	+	14.7900i	−1.17813	+	0.487082i
$923$	47.7163			1.57060
$924$	9.02165	+	2.43017i	0.296790	+	0.0799466i
$925$	26.1499	+	45.2930i	0.859803	+	1.48922i
$926$	10.8018	+	8.29990i	0.354969	+	0.272752i
$927$	−5.57991	−	9.66469i	−0.183268	−	0.317430i
$928$	7.27606	−	2.98563i	0.238849	−	0.0980081i
$929$	−30.2173	+	52.3378i	−0.991396	+	1.71715i	−0.382337	+	0.924023i	$0.624881\pi$
$929$	−30.2173	+	52.3378i	−0.991396	+	1.71715i	−0.609059	+	0.793125i	$0.708453\pi$
$930$	−7.89119	−	1.04422i	−0.258762	−	0.0342412i
$931$	−19.3480	+	4.25799i	−0.634105	+	0.139550i
$932$	−21.5882	−	5.81524i	−0.707146	−	0.190485i
$933$	24.9103	−	43.1460i	0.815528	−	1.41254i
$934$	−12.1964	+	15.8729i	−0.399078	+	0.519376i
$935$	−1.41064	+	0.814431i	−0.0461327	+	0.0266347i
$936$	22.2322	−	16.9892i	0.726681	−	0.555309i
$937$	−10.5175	−	18.2168i	−0.343592	−	0.595118i	0.641505	−	0.767119i	$-0.278310\pi$
$937$	−10.5175	−	18.2168i	−0.343592	−	0.595118i	−0.985097	+	0.172000i	$0.944977\pi$
$938$	8.17938	+	1.08235i	0.267066	+	0.0353401i
$939$		−	57.4909i		−	1.87614i
$940$	−2.08801	−	7.83411i	−0.0681035	−	0.255520i
$941$	−17.6157	−	30.5113i	−0.574256	−	0.994641i	−0.996122	−	0.0879826i	$-0.971958\pi$
$941$	−17.6157	−	30.5113i	−0.574256	−	0.994641i	0.421866	−	0.906658i	$-0.361375\pi$
$942$	62.4844	+	8.26837i	2.03585	+	0.269398i
$943$	8.10441			0.263916
$944$	−20.4946	−	0.0543446i	−0.667043	−	0.00176877i
$945$	0.396486	+	0.228912i	0.0128977	+	0.00744649i
$946$	6.42636	+	15.5438i	0.208939	+	0.505371i
$947$	−8.10653	+	14.0409i	−0.263427	+	0.456268i	−0.967150	−	0.254205i	$-0.918186\pi$
$947$	−8.10653	+	14.0409i	−0.263427	+	0.456268i	0.703724	+	0.710474i	$0.251519\pi$
$948$	39.3663	+	39.4708i	1.27856	+	1.28195i
$949$	3.56089			0.115591
$950$	−29.2774	+	2.49632i	−0.949884	+	0.0809912i
$951$		−	45.3354i		−	1.47010i
$952$	−7.29608	−	9.54769i	−0.236467	−	0.309442i
$953$	32.1131	+	18.5405i	1.04024	+	0.600585i	0.919902	−	0.392148i	$-0.128268\pi$
$953$	32.1131	+	18.5405i	1.04024	+	0.600585i	0.120341	+	0.992733i	$0.461601\pi$
$954$	4.45470	+	10.7748i	0.144226	+	0.348847i
$955$	5.29034	−	9.16314i	0.171191	−	0.296512i
$956$	39.2764	−	10.4683i	1.27029	−	0.338568i
$957$			4.14524i			0.133996i
$958$	−4.41182	+	33.3403i	−0.142540	+	1.07718i
$959$	−24.1800	+	13.9603i	−0.780814	+	0.450803i
$960$	−2.43348	+	8.93951i	−0.0785404	+	0.288521i
$961$	−7.37886			−0.238028
$962$	−55.3824	−	7.32858i	−1.78560	−	0.236283i
$963$	−9.88286	+	5.70587i	−0.318471	+	0.183869i
$964$	−8.93850	−	8.96223i	−0.287890	−	0.288654i
$965$	1.28412	+	2.22417i	0.0413374	+	0.0715985i
$966$	−26.8760	−	20.6510i	−0.864722	−	0.664436i
$967$	−0.859439	−	0.496197i	−0.0276377	−	0.0159566i	0.486117	−	0.873893i	$-0.338413\pi$
$967$	−0.859439	−	0.496197i	−0.0276377	−	0.0159566i	−0.513755	+	0.857937i	$0.671746\pi$
$968$	−24.6825	−	10.2814i	−0.793326	−	0.330456i
$969$	20.9201	−	19.1104i	0.672050	−	0.613913i
$970$	−1.89808	−	0.251167i	−0.0609437	−	0.00806450i
$971$	31.4894	+	18.1804i	1.01054	+	0.583437i	0.911351	−	0.411631i	$-0.135041\pi$
$971$	31.4894	+	18.1804i	1.01054	+	0.583437i	0.0991922	+	0.995068i	$0.468374\pi$
$972$	−30.2584	−	30.3387i	−0.970537	−	0.973114i
$973$	−11.2938	+	6.52049i	−0.362063	+	0.209037i
$974$	6.30027	−	8.19941i	0.201874	−	0.262726i
$975$	−35.6312	+	20.5717i	−1.14111	+	0.658822i
$976$	21.8616	−	37.6347i	0.699774	−	1.20466i
$977$		−	39.6271i		−	1.26778i	−0.773421	−	0.633892i	$-0.781456\pi$
$977$		−	39.6271i		−	1.26778i	0.773421	−	0.633892i	$-0.218544\pi$
$978$	−41.5525	+	17.1794i	−1.32870	+	0.549335i
$979$	−13.8820	+	8.01478i	−0.443671	+	0.256154i
$980$	1.14208	−	4.23982i	0.0364825	−	0.135436i
$981$	49.8438			1.59139
$982$	8.02565	+	19.4120i	0.256109	+	0.619462i
$983$	21.5716	−	37.3631i	0.688027	−	1.19170i	−0.284448	−	0.958691i	$-0.591810\pi$
$983$	21.5716	−	37.3631i	0.688027	−	1.19170i	0.972475	−	0.233007i	$-0.0748564\pi$
$984$	1.10732	+	8.54215i	0.0353000	+	0.272314i
$985$	−0.220641	+	0.382162i	−0.00703021	+	0.0121767i
$986$	3.24822	−	4.22735i	0.103444	−	0.134626i
$987$			31.5239i			1.00342i
$988$	16.9400	−	26.4228i	0.538934	−	0.840621i
$989$		−	61.0161i		−	1.94020i
$990$	−1.85105	−	1.42231i	−0.0588303	−	0.0452041i
$991$	4.38682	−	7.59820i	0.139352	−	0.241365i	−0.787899	−	0.615804i	$-0.788831\pi$
$991$	4.38682	−	7.59820i	0.139352	−	0.241365i	0.927252	+	0.374439i	$0.122165\pi$
$992$	3.67891	−	27.2460i	0.116806	−	0.865060i
$993$	−19.1308	+	33.1356i	−0.607098	+	1.05153i
$994$	27.1398	−	11.2206i	0.860822	−	0.355896i
$995$	9.69227			0.307266
$996$	−15.2088	+	56.4603i	−0.481908	+	1.78901i
$997$	15.8403	−	9.14540i	0.501667	−	0.289638i	−0.227734	−	0.973723i	$-0.573132\pi$
$997$	15.8403	−	9.14540i	0.501667	−	0.289638i	0.729402	+	0.684085i	$0.239798\pi$
$998$	−1.15933	−	2.80413i	−0.0366980	−	0.0887632i
$999$			6.63673i			0.209977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.27.4	✓	28
4.3	odd	2		608.2.s.c.559.2		28
8.3	odd	2	inner	152.2.o.c.27.10	yes	28
8.5	even	2		608.2.s.c.559.1		28
19.12	odd	6	inner	152.2.o.c.107.10	yes	28
76.31	even	6		608.2.s.c.335.1		28
152.69	odd	6		608.2.s.c.335.2		28
152.107	even	6	inner	152.2.o.c.107.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.4	✓	28	1.1	even	1	trivial
152.2.o.c.27.10	yes	28	8.3	odd	2	inner
152.2.o.c.107.4	yes	28	152.107	even	6	inner
152.2.o.c.107.10	yes	28	19.12	odd	6	inner
608.2.s.c.335.1		28	76.31	even	6
608.2.s.c.335.2		28	152.69	odd	6
608.2.s.c.559.1		28	8.5	even	2
608.2.s.c.559.2		28	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.861662 + 1.12140i) q^{2} +(2.07624 + 1.19872i) q^{3} +(-0.515076 - 1.93254i) q^{4} +(0.418341 + 0.241529i) q^{5} +(-3.13326 + 1.29541i) q^{6} +1.56686i q^{7} +(2.61097 + 1.08759i) q^{8} +(1.37385 + 2.37958i) q^{9} +(-0.631319 + 0.261011i) q^{10} +1.24363 q^{11} +(1.24714 - 4.62984i) q^{12} +(-1.80015 - 3.11796i) q^{13} +(-1.75708 - 1.35010i) q^{14} +(0.579050 + 1.00294i) q^{15} +(-3.46939 + 1.99081i) q^{16} +(-1.35570 + 2.34815i) q^{17} +(-3.85225 - 0.509757i) q^{18} +(-4.25703 + 0.936862i) q^{19} +(0.251286 - 0.932864i) q^{20} +(-1.87822 + 3.25318i) q^{21} +(-1.07159 + 1.39460i) q^{22} +(5.52533 - 3.19005i) q^{23} +(4.11729 + 5.38791i) q^{24} +(-2.38333 - 4.12804i) q^{25} +(5.04760 + 0.667934i) q^{26} -0.604878i q^{27} +(3.02801 - 0.807052i) q^{28} +(0.695157 + 1.20405i) q^{29} +(-1.62365 - 0.214852i) q^{30} +4.86016 q^{31} +(0.756953 - 5.60598i) q^{32} +(2.58207 + 1.49076i) q^{33} +(-1.46506 - 3.54360i) q^{34} +(-0.378442 + 0.655481i) q^{35} +(3.89098 - 3.88068i) q^{36} -10.9720 q^{37} +(2.61752 - 5.58109i) q^{38} -8.63150i q^{39} +(0.829590 + 1.08561i) q^{40} +(1.10008 + 0.635132i) q^{41} +(-2.02972 - 4.90938i) q^{42} +(4.78175 - 8.28223i) q^{43} +(-0.640562 - 2.40335i) q^{44} +1.32730i q^{45} +(-1.18364 + 8.94485i) q^{46} +(7.26763 - 4.19597i) q^{47} +(-9.58971 - 0.0254286i) q^{48} +4.54495 q^{49} +(6.68281 + 0.884316i) q^{50} +(-5.62954 + 3.25022i) q^{51} +(-5.09835 + 5.08485i) q^{52} +(-1.50024 - 2.59849i) q^{53} +(0.678311 + 0.521201i) q^{54} +(0.520259 + 0.300372i) q^{55} +(-1.70410 + 4.09102i) q^{56} +(-9.96165 - 3.15782i) q^{57} +(-1.94921 - 0.257933i) q^{58} +(4.43723 + 2.56184i) q^{59} +(1.63997 - 1.63563i) q^{60} +(-9.42313 + 5.44044i) q^{61} +(-4.18781 + 5.45018i) q^{62} +(-3.72846 + 2.15263i) q^{63} +(5.63431 + 5.67931i) q^{64} -1.73916i q^{65} +(-3.89660 + 1.61100i) q^{66} +(-3.22460 + 1.86172i) q^{67} +(5.23618 + 1.41047i) q^{68} +15.2959 q^{69} +(-0.408967 - 0.989188i) q^{70} +(-6.62670 + 11.4778i) q^{71} +(0.999080 + 7.70718i) q^{72} +(-0.494526 + 0.856544i) q^{73} +(9.45417 - 12.3040i) q^{74} -11.4277i q^{75} +(4.00322 + 7.74431i) q^{76} +1.94859i q^{77} +(9.67937 + 7.43744i) q^{78} +(-5.81311 + 10.0686i) q^{79} +(-1.93223 - 0.00512359i) q^{80} +(4.84663 - 8.39460i) q^{81} +(-1.66013 + 0.686361i) q^{82} -12.1949 q^{83} +(7.25431 + 1.95410i) q^{84} +(-1.13429 + 0.654884i) q^{85} +(5.16744 + 12.4987i) q^{86} +3.33319i q^{87} +(3.24707 + 1.35255i) q^{88} +(-11.1625 + 6.44469i) q^{89} +(-1.48843 - 1.14368i) q^{90} +(4.88540 - 2.82059i) q^{91} +(-9.01085 - 9.03478i) q^{92} +(10.0909 + 5.82596i) q^{93} +(-1.55688 + 11.7654i) q^{94} +(-2.00717 - 0.636268i) q^{95} +(8.29161 - 10.7320i) q^{96} +(2.42717 + 1.40133i) q^{97} +(-3.91621 + 5.09671i) q^{98} +(1.70855 + 2.95930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

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