LMFDB - Embedded newform 43.7.d.a.37.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.13
Character	$\chi$	$=$	43.37
Dual form			43.7.d.a.7.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.64495i q^{2} +(-0.554504 - 0.320143i) q^{3} +57.0043 q^{4} +(14.6929 + 8.48295i) q^{5} +(0.846761 - 1.46663i) q^{6} +(131.768 - 76.0760i) q^{7} +320.050i q^{8} +(-364.295 - 630.977i) q^{9} +O(q^{10})$	\(q+2.64495i q^{2} +(-0.554504 - 0.320143i) q^{3} +57.0043 q^{4} +(14.6929 + 8.48295i) q^{5} +(0.846761 - 1.46663i) q^{6} +(131.768 - 76.0760i) q^{7} +320.050i q^{8} +(-364.295 - 630.977i) q^{9} +(-22.4370 + 38.8619i) q^{10} +1691.94 q^{11} +(-31.6091 - 18.2495i) q^{12} +(892.086 + 1545.14i) q^{13} +(201.217 + 348.518i) q^{14} +(-5.43151 - 9.40766i) q^{15} +2801.76 q^{16} +(1210.07 + 2095.91i) q^{17} +(1668.90 - 963.541i) q^{18} +(8142.05 + 4700.81i) q^{19} +(837.558 + 483.564i) q^{20} -97.4208 q^{21} +4475.08i q^{22} +(-2997.75 + 5192.26i) q^{23} +(102.462 - 177.469i) q^{24} +(-7668.58 - 13282.4i) q^{25} +(-4086.81 + 2359.52i) q^{26} +933.274i q^{27} +(7511.31 - 4336.66i) q^{28} +(3630.94 - 2096.33i) q^{29} +(24.8827 - 14.3661i) q^{30} +(11760.7 - 20370.1i) q^{31} +27893.7i q^{32} +(-938.184 - 541.661i) q^{33} +(-5543.56 + 3200.58i) q^{34} +2581.40 q^{35} +(-20766.4 - 35968.4i) q^{36} +(-44165.0 - 25498.7i) q^{37} +(-12433.4 + 21535.3i) q^{38} -1142.38i q^{39} +(-2714.97 + 4702.46i) q^{40} -68362.2 q^{41} -257.673i q^{42} +(-38156.7 - 69752.6i) q^{43} +96447.5 q^{44} -12361.2i q^{45} +(-13733.2 - 7928.89i) q^{46} -143367. q^{47} +(-1553.59 - 896.963i) q^{48} +(-47249.4 + 81838.3i) q^{49} +(35131.1 - 20283.0i) q^{50} -1549.58i q^{51} +(50852.7 + 88079.5i) q^{52} +(4028.49 - 6977.56i) q^{53} -2468.46 q^{54} +(24859.4 + 14352.6i) q^{55} +(24348.1 + 42172.2i) q^{56} +(-3009.86 - 5213.23i) q^{57} +(5544.67 + 9603.65i) q^{58} +270265. q^{59} +(-309.619 - 536.276i) q^{60} +(195636. - 112951. i) q^{61} +(53877.8 + 31106.4i) q^{62} +(-96004.5 - 55428.2i) q^{63} +105535. q^{64} +30270.1i q^{65} +(1432.66 - 2481.45i) q^{66} +(-69735.4 + 120785. i) q^{67} +(68979.3 + 119476. i) q^{68} +(3324.53 - 1919.42i) q^{69} +6827.66i q^{70} +(-501487. + 289534. i) q^{71} +(201944. - 116593. i) q^{72} +(357004. - 206116. i) q^{73} +(67442.7 - 116814. i) q^{74} +9820.16i q^{75} +(464131. + 267966. i) q^{76} +(222942. - 128716. i) q^{77} +3021.53 q^{78} +(-387632. - 671399. i) q^{79} +(41166.0 + 23767.2i) q^{80} +(-265272. + 459465. i) q^{81} -180814. i q^{82} +(-234913. + 406881. i) q^{83} -5553.40 q^{84} +41059.9i q^{85} +(184492. - 100922. i) q^{86} -2684.49 q^{87} +541504. i q^{88} +(-511098. - 295082. i) q^{89} +32694.7 q^{90} +(235096. + 135733. i) q^{91} +(-170885. + 295981. i) q^{92} +(-13042.7 + 7530.20i) q^{93} -379198. i q^{94} +(79753.5 + 138137. i) q^{95} +(8929.96 - 15467.1i) q^{96} -1.06433e6 q^{97} +(-216458. - 124972. i) q^{98} +(-616364. - 1.06757e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) $ 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			2.64495i			0.330618i	0.986242	+	0.165309i	$0.0528622\pi$
$2$			2.64495i			0.330618i	−0.986242	+	0.165309i	$0.947138\pi$
$3$	−0.554504	−	0.320143i	−0.0205372	−	0.0118571i	0.489696	−	0.871893i	$-0.337108\pi$
$3$	−0.554504	−	0.320143i	−0.0205372	−	0.0118571i	−0.510233	+	0.860036i	$0.670441\pi$
$4$	57.0043			0.890692
$5$	14.6929	+	8.48295i	0.117543	+	0.0678636i	0.557619	−	0.830097i	$-0.311715\pi$
$5$	14.6929	+	8.48295i	0.117543	+	0.0678636i	−0.440076	+	0.897961i	$0.645048\pi$
$6$	0.846761	−	1.46663i	0.00392019	−	0.00678996i
$7$	131.768	−	76.0760i	0.384162	−	0.221796i	−0.295466	−	0.955353i	$-0.595475\pi$
$7$	131.768	−	76.0760i	0.384162	−	0.221796i	0.679627	+	0.733557i	$0.262141\pi$
$8$			320.050i			0.625097i
$9$	−364.295	−	630.977i	−0.499719	−	0.865538i
$10$	−22.4370	+	38.8619i	−0.0224370	+	0.0388619i
$11$	1691.94			1.27118			0.635588	−	0.772028i	$-0.280758\pi$
$11$	1691.94			1.27118			0.635588	+	0.772028i	$0.280758\pi$
$12$	−31.6091	−	18.2495i	−0.0182923	−	0.0105611i
$13$	892.086	+	1545.14i	0.406047	+	0.703295i	0.994443	−	0.105279i	$-0.0335734\pi$
$13$	892.086	+	1545.14i	0.406047	+	0.703295i	−0.588395	+	0.808573i	$0.700240\pi$
$14$	201.217	+	348.518i	0.0733298	+	0.127011i
$15$	−5.43151	−	9.40766i	−0.00160934	−	0.00278745i
$16$	2801.76			0.684023
$17$	1210.07	+	2095.91i	0.246300	+	0.426604i	0.962496	−	0.271295i	$-0.0874518\pi$
$17$	1210.07	+	2095.91i	0.246300	+	0.426604i	−0.716196	+	0.697899i	$0.754118\pi$
$18$	1668.90	−	963.541i	0.286163	−	0.165216i
$19$	8142.05	+	4700.81i	1.18706	+	0.685349i	0.957637	−	0.287977i	$-0.0929828\pi$
$19$	8142.05	+	4700.81i	1.18706	+	0.685349i	0.229423	+	0.973327i	$0.426316\pi$
$20$	837.558	+	483.564i	0.104695	+	0.0604455i
$21$	−97.4208			−0.0105195
$22$			4475.08i			0.420274i
$23$	−2997.75	+	5192.26i	−0.246384	+	0.426749i	−0.962520	−	0.271212i	$-0.912576\pi$
$23$	−2997.75	+	5192.26i	−0.246384	+	0.426749i	0.716136	+	0.697961i	$0.245909\pi$
$24$	102.462	−	177.469i	0.00741187	−	0.0128377i
$25$	−7668.58	−	13282.4i	−0.490789	−	0.850072i
$26$	−4086.81	+	2359.52i	−0.232522	+	0.134247i
$27$			933.274i			0.0474152i
$28$	7511.31	−	4336.66i	0.342170	−	0.197552i
$29$	3630.94	−	2096.33i	0.148876	−	0.0859537i	−0.423711	−	0.905797i	$-0.639273\pi$
$29$	3630.94	−	2096.33i	0.148876	−	0.0859537i	0.572588	+	0.819843i	$0.305940\pi$
$30$	24.8827	−	14.3661i	0.000921583	−	0.000532076i
$31$	11760.7	−	20370.1i	0.394773	−	0.683767i	−0.598299	−	0.801273i	$-0.704157\pi$
$31$	11760.7	−	20370.1i	0.394773	−	0.683767i	0.993072	+	0.117506i	$0.0374899\pi$
$32$			27893.7i			0.851248i
$33$	−938.184	−	541.661i	−0.0261064	−	0.0150725i
$34$	−5543.56	+	3200.58i	−0.141043	+	0.0814313i
$35$	2581.40			0.0602075
$36$	−20766.4	−	35968.4i	−0.445095	−	0.770928i
$37$	−44165.0	−	25498.7i	−0.871914	−	0.503399i	−0.00392986	−	0.999992i	$-0.501251\pi$
$37$	−44165.0	−	25498.7i	−0.871914	−	0.503399i	−0.867984	+	0.496593i	$0.834584\pi$
$38$	−12433.4	+	21535.3i	−0.226589	+	0.392464i
$39$		−	1142.38i		−	0.0192583i
$40$	−2714.97	+	4702.46i	−0.0424214	+	0.0734759i
$41$	−68362.2			−0.991892			−0.495946	−	0.868353i	$-0.665179\pi$
$41$	−68362.2			−0.991892			−0.495946	+	0.868353i	$0.665179\pi$
$42$		−	257.673i		−	0.00347793i
$43$	−38156.7	−	69752.6i	−0.479916	−	0.877314i
$43$	−38156.7	−	69752.6i	−0.479916	−	0.877314i
$44$	96447.5			1.13223
$45$		−	12361.2i		−	0.135651i
$46$	−13733.2	−	7928.89i	−0.141091	−	0.0814590i
$47$	−143367.			−1.38088			−0.690440	−	0.723389i	$-0.742583\pi$
$47$	−143367.			−1.38088			−0.690440	+	0.723389i	$0.742583\pi$
$48$	−1553.59	−	896.963i	−0.0140479	−	0.00811056i
$49$	−47249.4	+	81838.3i	−0.401613	+	0.695614i
$50$	35131.1	−	20283.0i	0.281049	−	0.162264i
$51$		−	1549.58i		−	0.0116817i
$52$	50852.7	+	88079.5i	0.361663	+	0.626419i
$53$	4028.49	−	6977.56i	0.0270592	−	0.0468679i	−0.852179	−	0.523251i	$-0.824719\pi$
$53$	4028.49	−	6977.56i	0.0270592	−	0.0468679i	0.879238	+	0.476383i	$0.158052\pi$
$54$	−2468.46			−0.0156763
$55$	24859.4	+	14352.6i	0.149418	+	0.0862666i
$56$	24348.1	+	42172.2i	0.138644	+	0.240138i
$57$	−3009.86	−	5213.23i	−0.0162526	−	0.0281503i
$58$	5544.67	+	9603.65i	0.0284179	+	0.0492212i
$59$	270265.			1.31593			0.657966	−	0.753048i	$-0.271417\pi$
$59$	270265.			1.31593			0.657966	+	0.753048i	$0.271417\pi$
$60$	−309.619	−	536.276i	−0.00143342	−	0.00248276i
$61$	195636.	−	112951.i	0.861906	−	0.497621i	−0.00274431	−	0.999996i	$-0.500874\pi$
$61$	195636.	−	112951.i	0.861906	−	0.497621i	0.864650	+	0.502375i	$0.167540\pi$
$62$	53877.8	+	31106.4i	0.226066	+	0.130519i
$63$	−96004.5	−	55428.2i	−0.383946	−	0.221671i
$64$	105535.			0.402585
$65$			30270.1i			0.110223i
$66$	1432.66	−	2481.45i	0.00498325	−	0.00863124i
$67$	−69735.4	+	120785.i	−0.231862	+	0.401596i	−0.958356	−	0.285576i	$-0.907815\pi$
$67$	−69735.4	+	120785.i	−0.231862	+	0.401596i	0.726494	+	0.687172i	$0.241148\pi$
$68$	68979.3	+	119476.i	0.219377	+	0.379973i
$69$	3324.53	−	1919.42i	0.0101201	−	0.00584281i
$70$			6827.66i			0.0199057i
$71$	−501487.	+	289534.i	−1.40115	+	0.808954i	−0.994511	−	0.104634i	$-0.966633\pi$
$71$	−501487.	+	289534.i	−1.40115	+	0.808954i	−0.406639	+	0.913589i	$0.633299\pi$
$72$	201944.	−	116593.i	0.541046	−	0.312373i
$73$	357004.	−	206116.i	0.917707	−	0.529838i	0.0348041	−	0.999394i	$-0.488919\pi$
$73$	357004.	−	206116.i	0.917707	−	0.529838i	0.882903	+	0.469556i	$0.155586\pi$
$74$	67442.7	−	116814.i	0.166433	−	0.288271i
$75$			9820.16i			0.0232774i
$76$	464131.	+	267966.i	1.05730	+	0.610435i
$77$	222942.	−	128716.i	0.488337	−	0.281942i
$78$	3021.53			0.00636713
$79$	−387632.	−	671399.i	−0.786210	−	1.36176i	−0.928273	−	0.371898i	$-0.878707\pi$
$79$	−387632.	−	671399.i	−0.786210	−	1.36176i	0.142063	−	0.989858i	$-0.454626\pi$
$80$	41166.0	+	23767.2i	0.0804023	+	0.0464203i
$81$	−265272.	+	459465.i	−0.499157	+	0.864565i
$82$		−	180814.i		−	0.327938i
$83$	−234913.	+	406881.i	−0.410840	+	0.711596i	−0.994982	−	0.100056i	$-0.968098\pi$
$83$	−234913.	+	406881.i	−0.410840	+	0.711596i	0.584142	+	0.811652i	$0.301431\pi$
$84$	−5553.40			−0.00936960
$85$			41059.9i			0.0668593i
$86$	184492.	−	100922.i	0.290056	−	0.158669i
$87$	−2684.49			−0.00407666
$88$			541504.i			0.794609i
$89$	−511098.	−	295082.i	−0.724993	−	0.418575i	0.0915945	−	0.995796i	$-0.470804\pi$
$89$	−511098.	−	295082.i	−0.724993	−	0.418575i	−0.816588	+	0.577221i	$0.804137\pi$
$90$	32694.7			0.0448487
$91$	235096.	+	135733.i	0.311976	+	0.180119i
$92$	−170885.	+	295981.i	−0.219452	+	0.380102i
$93$	−13042.7	+	7530.20i	−0.0162150	+	0.00936176i
$94$		−	379198.i		−	0.456544i
$95$	79753.5	+	138137.i	0.0930206	+	0.161116i
$96$	8929.96	−	15467.1i	0.0100934	−	0.0174822i
$97$	−1.06433e6			−1.16617			−0.583087	−	0.812410i	$-0.698155\pi$
$97$	−1.06433e6			−1.16617			−0.583087	+	0.812410i	$0.698155\pi$
$98$	−216458.	−	124972.i	−0.229983	−	0.132781i
$99$	−616364.	−	1.06757e6i	−0.635231	−	1.10025i
$100$	−437142.	−	757152.i	−0.437142	−	0.757152i
$101$	−192136.	−	332789.i	−0.186485	−	0.323002i	0.757591	−	0.652730i	$-0.226376\pi$
$101$	−192136.	−	332789.i	−0.186485	−	0.323002i	−0.944076	+	0.329728i	$0.893043\pi$
$102$	4098.57			0.00386217
$103$	−215586.	−	373405.i	−0.197291	−	0.341719i	0.750358	−	0.661032i	$-0.229881\pi$
$103$	−215586.	−	373405.i	−0.197291	−	0.341719i	−0.947649	+	0.319313i	$0.896548\pi$
$104$	−494521.	+	285512.i	−0.439628	+	0.253819i
$105$	−1431.39	−	826.416i	−0.00123649	−	0.000713889i
$106$	18455.3	+	10655.2i	0.0154954	+	0.00894627i
$107$	810838.			0.661885			0.330943	−	0.943651i	$-0.392633\pi$
$107$	810838.			0.661885			0.330943	+	0.943651i	$0.392633\pi$
$108$			53200.6i			0.0422323i
$109$	−517362.	+	896097.i	−0.399498	+	0.691951i	−0.993664	−	0.112392i	$-0.964149\pi$
$109$	−517362.	+	896097.i	−0.399498	+	0.691951i	0.594166	+	0.804343i	$0.297482\pi$
$110$	−37961.9	+	65751.9i	−0.0285213	+	0.0494004i
$111$	16326.4	+	28278.2i	0.0119378	+	0.0206768i
$112$	369181.	−	213147.i	0.262776	−	0.151714i
$113$			555376.i			0.384903i	0.981306	+	0.192452i	$0.0616439\pi$
$113$			555376.i			0.384903i	−0.981306	+	0.192452i	$0.938356\pi$
$114$	13788.7	−	7960.92i	0.00930700	−	0.00537340i
$115$	−88091.3	+	50859.6i	−0.0579215	+	0.0334410i
$116$	206979.	−	119499.i	0.132603	−	0.0765583i
$117$	649965.	−	1.12577e6i	0.405819	−	0.702899i
$118$			714835.i			0.435071i
$119$	318896.	+	184115.i	0.189238	+	0.109257i
$120$	3010.92	−	1738.35i	0.00174243	−	0.00100599i
$121$	1.09108e6			0.615889
$122$	298748.	+	517447.i	0.164523	+	0.284962i
$123$	37907.1	+	21885.7i	0.0203707	+	0.0117610i
$124$	670409.	−	1.16118e6i	0.351621	−	0.609025i
$125$		−	525301.i		−	0.268954i
$126$	146605.	−	253927.i	0.0732886	−	0.126940i
$127$	841586.			0.410854			0.205427	−	0.978672i	$-0.434142\pi$
$127$	841586.			0.410854			0.205427	+	0.978672i	$0.434142\pi$
$128$			2.06433e6i			0.984350i
$129$	−1172.79	+	50893.7i	−0.000546327	+	0.0237080i
$130$	−80062.8			−0.0364419
$131$		−	297380.i		−	0.132281i	−0.997810	−	0.0661405i	$-0.978931\pi$
$131$		−	297380.i		−	0.132281i	0.997810	−	0.0661405i	$-0.0210685\pi$
$132$	−53480.5	−	30877.0i	−0.0232527	−	0.0134250i
$133$	1.43048e6			0.608031
$134$	−319470.	−	184446.i	−0.132775	−	0.0766577i
$135$	−7916.92	+	13712.5i	−0.00321777	+	0.00557334i
$136$	−670794.	+	387283.i	−0.266669	+	0.153961i
$137$			4.08224e6i			1.58758i	0.608189	+	0.793792i	$0.291896\pi$
$137$			4.08224e6i			1.58758i	−0.608189	+	0.793792i	$0.708104\pi$
$138$	5076.75	+	8793.20i	0.00193174	+	0.00334587i
$139$	392933.	−	680580.i	0.146310	−	0.253417i	−0.783551	−	0.621328i	$-0.786594\pi$
$139$	392933.	−	680580.i	0.146310	−	0.253417i	0.929861	+	0.367911i	$0.119927\pi$
$140$	147151.			0.0536263
$141$	79497.6	+	45898.0i	0.0283594	+	0.0163733i
$142$	−765801.	−	1.32641e6i	−0.267455	−	0.463246i
$143$	1.50935e6	+	2.61428e6i	0.516158	+	0.894012i
$144$	−1.02067e6	−	1.76785e6i	−0.341819	−	0.592048i
$145$	71132.1			0.0233325
$146$	545166.	+	944255.i	0.175174	+	0.303411i
$147$	52399.9	−	30253.1i	0.0164960	−	0.00952397i
$148$	−2.51760e6	−	1.45353e6i	−0.776606	−	0.448374i
$149$	4.99758e6	+	2.88535e6i	1.51078	+	0.872248i	0.999921	+	0.0125828i	$0.00400535\pi$
$149$	4.99758e6	+	2.88535e6i	1.51078	+	0.872248i	0.510857	+	0.859665i	$0.329328\pi$
$150$	−25973.8			−0.00769594
$151$		−	3.18513e6i		−	0.925116i	−0.886589	−	0.462558i	$-0.846932\pi$
$151$		−	3.18513e6i		−	0.925116i	0.886589	−	0.462558i	$-0.153068\pi$
$152$	−1.50449e6	+	2.60586e6i	−0.428410	+	0.742028i
$153$	881647.	−	1.52706e6i	0.246162	−	0.426364i
$154$	340446.	+	589670.i	0.0932151	+	0.161453i
$155$	345597.	−	199531.i	0.0928058	−	0.0535814i
$156$		−	65120.5i		−	0.0171532i
$157$	5.14816e6	−	2.97229e6i	1.33031	−	0.768055i	0.344963	−	0.938616i	$-0.387892\pi$
$157$	5.14816e6	−	2.97229e6i	1.33031	−	0.768055i	0.985347	+	0.170562i	$0.0545583\pi$
$158$	1.77581e6	−	1.02527e6i	0.450221	−	0.259935i
$159$	−4467.63	+	2579.39i	−0.00111144	+	0.000641690i
$160$	−236621.	+	409839.i	−0.0577687	+	0.100058i
$161$			912228.i			0.218588i
$162$	−1.21526e6	−	701631.i	−0.285841	−	0.165030i
$163$	−5.84870e6	+	3.37675e6i	−1.35051	+	0.779715i	−0.988320	−	0.152391i	$-0.951303\pi$
$163$	−5.84870e6	+	3.37675e6i	−1.35051	+	0.779715i	−0.362185	+	0.932106i	$0.617969\pi$
$164$	−3.89694e6			−0.883470
$165$	−9189.77	−	15917.1i	−0.00204575	−	0.00354334i
$166$	−1.07618e6	−	621332.i	−0.235267	−	0.135831i
$167$	−2.47160e6	+	4.28093e6i	−0.530674	+	0.919155i	0.468685	+	0.883365i	$0.344728\pi$
$167$	−2.47160e6	+	4.28093e6i	−0.530674	+	0.919155i	−0.999359	+	0.0357896i	$0.988605\pi$
$168$		−	31179.5i		−	0.00657569i
$169$	821768.	−	1.42334e6i	0.170251	−	0.294883i
$170$	−108601.			−0.0221049
$171$		−	6.84993e6i		−	1.36993i
$172$	−2.17509e6	−	3.97620e6i	−0.427457	−	0.781417i
$173$	−2.70120e6			−0.521697			−0.260848	−	0.965380i	$-0.584002\pi$
$173$	−2.70120e6			−0.521697			−0.260848	+	0.965380i	$0.584002\pi$
$174$		−	7100.34i		−	0.00134782i
$175$	−2.02094e6	−	1.16679e6i	−0.377085	−	0.217710i
$176$	4.74039e6			0.869514
$177$	−149863.	−	86523.3i	−0.0270255	−	0.0156032i
$178$	780477.	−	1.35183e6i	0.138389	−	0.239696i
$179$	−2.84429e6	+	1.64215e6i	−0.495924	+	0.286322i	−0.727029	−	0.686607i	$-0.759099\pi$
$179$	−2.84429e6	+	1.64215e6i	−0.495924	+	0.286322i	0.231105	+	0.972929i	$0.425766\pi$
$180$		−	704640.i		−	0.120823i
$181$	−1.67543e6	−	2.90193e6i	−0.282547	−	0.489385i	0.689465	−	0.724319i	$-0.257846\pi$
$181$	−1.67543e6	−	2.90193e6i	−0.282547	−	0.489385i	−0.972011	+	0.234934i	$0.924513\pi$
$182$	−359006.	+	621816.i	−0.0595508	+	0.103145i
$183$	−144641.			−0.0236015
$184$	−1.66178e6	−	959429.i	−0.266760	−	0.154014i
$185$	−432608.	−	749300.i	−0.0683250	−	0.118342i
$186$	−19917.0	−	34497.2i	−0.00309517	−	0.00536099i
$187$	2.04736e6	+	3.54614e6i	0.313091	+	0.542289i
$188$	−8.17254e6			−1.22994
$189$	70999.8	+	122975.i	0.0105165	+	0.0182151i
$190$	−365365.	+	210944.i	−0.0532680	+	0.0307543i
$191$	−950199.	−	548598.i	−0.136369	−	0.0787324i	0.430264	−	0.902703i	$-0.358421\pi$
$191$	−950199.	−	548598.i	−0.136369	−	0.0787324i	−0.566632	+	0.823971i	$0.691754\pi$
$192$	−58519.7	−	33786.3i	−0.00826796	−	0.00477351i
$193$	−3.58054e6			−0.498054			−0.249027	−	0.968497i	$-0.580111\pi$
$193$	−3.58054e6			−0.498054			−0.249027	+	0.968497i	$0.580111\pi$
$194$		−	2.81511e6i		−	0.385558i
$195$	9690.76	−	16784.9i	0.00130693	−	0.00226368i
$196$	−2.69342e6	+	4.66513e6i	−0.357713	+	0.619578i
$197$	3.35427e6	+	5.80976e6i	0.438731	+	0.759905i	0.997592	−	0.0693566i	$-0.0220946\pi$
$197$	3.35427e6	+	5.80976e6i	0.438731	+	0.759905i	−0.558861	+	0.829262i	$0.688761\pi$
$198$	2.82367e6	−	1.63025e6i	0.363763	−	0.210019i
$199$			1.46542e6i			0.185953i	0.995668	+	0.0929767i	$0.0296382\pi$
$199$			1.46542e6i			0.185953i	−0.995668	+	0.0929767i	$0.970362\pi$
$200$	4.25102e6	−	2.45433e6i	0.531377	−	0.306791i
$201$	77337.0	−	44650.6i	0.00952356	−	0.00549843i
$202$	880209.	−	508189.i	0.106790	−	0.0616554i
$203$	318960.	−	552455.i	0.0381284	−	0.0660403i
$204$		−	88332.9i		−	0.0104048i
$205$	−1.00444e6	−	579913.i	−0.116590	−	0.0673134i
$206$	987637.	−	570212.i	0.112978	−	0.0652281i
$207$	4.36826e6			0.492490
$208$	2.49941e6	+	4.32911e6i	0.277746	+	0.481070i
$209$	1.37758e7	+	7.95347e6i	1.50896	+	0.871200i
$210$	2185.82	−	3785.96i	0.000236025	−	0.000408807i
$211$			1.02849e6i			0.109484i	0.998501	+	0.0547420i	$0.0174336\pi$
$211$			1.02849e6i			0.109484i	−0.998501	+	0.0547420i	$0.982566\pi$
$212$	229641.	−	397750.i	0.0241014	−	0.0417449i
$213$	370769.			0.0383675
$214$			2.14462e6i			0.218831i
$215$	31076.0	−	1.34855e6i	0.00312687	−	0.135691i
$216$	−298694.			−0.0296391
$217$		−	3.57882e6i		−	0.350236i
$218$	−2.37013e6	−	1.36839e6i	−0.228772	−	0.132081i
$219$	−263946.			−0.0251295
$220$	1.41709e6	+	818160.i	0.133085	+	0.0768369i
$221$	−2.15898e6	+	3.73946e6i	−0.200019	+	0.346443i
$222$	−74794.4	+	43182.6i	−0.00683613	+	0.00394684i
$223$		−	1.73589e7i		−	1.56534i	−0.622440	−	0.782668i	$-0.713858\pi$
$223$		−	1.73589e7i		−	1.56534i	0.622440	−	0.782668i	$-0.286142\pi$
$224$	2.12204e6	+	3.67548e6i	0.188803	+	0.327017i
$225$	−5.58725e6	+	9.67740e6i	−0.490513	+	0.849594i
$226$	−1.46894e6			−0.127256
$227$	−8.99921e6	−	5.19570e6i	−0.769355	−	0.444187i	0.0632893	−	0.997995i	$-0.479841\pi$
$227$	−8.99921e6	−	5.19570e6i	−0.769355	−	0.444187i	−0.832645	+	0.553808i	$0.813174\pi$
$228$	−171575.	−	297177.i	−0.0144760	−	0.0250732i
$229$	5.92972e6	+	1.02706e7i	0.493774	+	0.855241i	0.999974	−	0.00717446i	$-0.00228372\pi$
$229$	5.92972e6	+	1.02706e7i	0.493774	+	0.855241i	−0.506200	+	0.862416i	$0.668950\pi$
$230$	−134521.	−	232997.i	−0.0110562	−	0.0191499i
$231$	−164830.			−0.0133721
$232$	670928.	+	1.16208e6i	0.0537294	+	0.0930621i
$233$	1.43862e7	−	8.30586e6i	1.13731	−	0.656624i	0.191544	−	0.981484i	$-0.438650\pi$
$233$	1.43862e7	−	8.30586e6i	1.13731	−	0.656624i	0.945762	+	0.324860i	$0.105317\pi$
$234$	2.97761e6	+	1.71912e6i	0.232391	+	0.134171i
$235$	−2.10648e6	−	1.21618e6i	−0.162313	−	0.0937115i
$236$	1.54062e7			1.17209
$237$			496391.i			0.0372888i
$238$	−486974.	+	843464.i	−0.0361223	+	0.0625656i
$239$	−5.71300e6	+	9.89520e6i	−0.418476	+	0.724821i	−0.995786	−	0.0917032i	$-0.970769\pi$
$239$	−5.71300e6	+	9.89520e6i	−0.418476	+	0.724821i	0.577311	+	0.816525i	$0.304102\pi$
$240$	−15217.8	−	26358.0i	−0.00110082	−	0.00190668i
$241$	1.47261e7	−	8.50213e6i	1.05205	−	0.607403i	0.128829	−	0.991667i	$-0.458878\pi$
$241$	1.47261e7	−	8.50213e6i	1.05205	−	0.607403i	0.923223	+	0.384264i	$0.125545\pi$
$242$			2.88586e6i			0.203624i
$243$	883395.	−	510028.i	0.0615653	−	0.0355448i
$244$	1.11521e7	−	6.43867e6i	0.767692	−	0.443227i
$245$	−1.38846e6	+	801628.i	−0.0944138	+	0.0545098i
$246$	−57886.4	+	100262.i	−0.00388840	+	0.00673491i
$247$			1.67741e7i			1.11314i
$248$	6.51945e6	+	3.76400e6i	0.427421	+	0.246771i
$249$	260520.	−	150411.i	0.0168750	−	0.00974278i
$250$	1.38939e6			0.0889211
$251$	−1.39856e7	−	2.42238e7i	−0.884423	−	1.53186i	−0.846374	−	0.532589i	$-0.821219\pi$
$251$	−1.39856e7	−	2.42238e7i	−0.884423	−	1.53186i	−0.0380487	−	0.999276i	$-0.512114\pi$
$252$	−5.47267e6	−	3.15964e6i	−0.341977	−	0.197441i
$253$	−5.07200e6	+	8.78496e6i	−0.313197	+	0.542473i
$254$			2.22595e6i			0.135836i
$255$	13145.0	−	22767.9i	0.000792760	−	0.00137310i
$256$	1.29421e6			0.0771410
$257$			4.50581e6i			0.265444i	0.991153	+	0.132722i	$0.0423718\pi$
$257$			4.50581e6i			0.265444i	−0.991153	+	0.132722i	$0.957628\pi$
$258$	−134611.	−	3101.98i	−0.00783829	−	0.000180626i
$259$	−7.75936e6			−0.446608
$260$			1.72552e6i			0.0981751i
$261$	−2.64547e6	−	1.52736e6i	−0.148792	−	0.0859054i
$262$	786553.			0.0437345
$263$	−1.82591e7	−	1.05419e7i	−1.00372	−	0.579496i	−0.0943709	−	0.995537i	$-0.530084\pi$
$263$	−1.82591e7	−	1.05419e7i	−1.00372	−	0.579496i	−0.909346	+	0.416041i	$0.863417\pi$
$264$	173358.	−	300266.i	0.00942179	−	0.0163190i
$265$	118381.	−	68347.0i	0.00636125	−	0.00367267i
$266$			3.78353e6i			0.201026i
$267$	188937.	+	327249.i	0.00992621	+	0.0171927i
$268$	−3.97521e6	+	6.88527e6i	−0.206517	+	0.357698i
$269$	−1.10670e6			−0.0568553			−0.0284277	−	0.999596i	$-0.509050\pi$
$269$	−1.10670e6			−0.0568553			−0.0284277	+	0.999596i	$0.509050\pi$
$270$	−36268.8	−	20939.8i	−0.00184265	−	0.00106385i
$271$	−4.25696e6	−	7.37327e6i	−0.213891	−	0.370469i	0.739038	−	0.673663i	$-0.235280\pi$
$271$	−4.25696e6	−	7.37327e6i	−0.213891	−	0.370469i	−0.952929	+	0.303194i	$0.901947\pi$
$272$	3.39033e6	+	5.87222e6i	0.168475	+	0.291807i
$273$	−86907.7	−	150529.i	−0.00427140	−	0.00739829i
$274$	−1.07973e7			−0.524884
$275$	−1.29747e7	−	2.24729e7i	−0.623879	−	1.08059i
$276$	189512.	−	109415.i	0.00901384	−	0.00520414i
$277$	−5.00837e6	−	2.89159e6i	−0.235644	−	0.136049i	0.377529	−	0.925998i	$-0.376774\pi$
$277$	−5.00837e6	−	2.89159e6i	−0.235644	−	0.136049i	−0.613173	+	0.789948i	$0.710107\pi$
$278$	1.80010e6	+	1.03929e6i	0.0837841	+	0.0483728i
$279$	−1.71374e7			−0.789102
$280$			826175.i			0.0376355i
$281$	481566.	−	834097.i	0.0217038	−	0.0375922i	−0.854969	−	0.518678i	$-0.826424\pi$
$281$	481566.	−	834097.i	0.0217038	−	0.0375922i	0.876673	+	0.481086i	$0.159758\pi$
$282$	−121398.	+	210267.i	−0.00541331	+	0.00937613i
$283$	−1.99440e6	−	3.45439e6i	−0.0879938	−	0.152410i	0.818669	−	0.574265i	$-0.194712\pi$
$283$	−1.99440e6	−	3.45439e6i	−0.0879938	−	0.152410i	−0.906663	+	0.421856i	$0.861379\pi$
$284$	−2.85869e7	+	1.65047e7i	−1.24799	+	0.720529i
$285$		−	102130.i		−	0.00441183i
$286$	−6.91462e6	+	3.99216e6i	−0.295577	+	0.170651i
$287$	−9.00792e6	+	5.20072e6i	−0.381047	+	0.219998i
$288$	1.76003e7	−	1.01615e7i	0.736788	−	0.425384i
$289$	9.14023e6	−	1.58313e7i	0.378673	−	0.655880i
$290$			188141.i			0.00771416i
$291$	590178.	+	340739.i	0.0239499	+	0.0138275i
$292$	2.03507e7	−	1.17495e7i	0.817394	−	0.471923i
$293$	−1.67538e7			−0.666057			−0.333028	−	0.942917i	$-0.608070\pi$
$293$	−1.67538e7			−0.666057			−0.333028	+	0.942917i	$0.608070\pi$
$294$	80017.8	+	138595.i	0.00314880	+	0.00545388i
$295$	3.97097e6	+	2.29264e6i	0.154679	+	0.0893039i
$296$	8.16085e6	−	1.41350e7i	0.314674	−	0.545031i
$297$			1.57904e6i			0.0602731i
$298$	−7.63160e6	+	1.32183e7i	−0.288381	+	0.499491i
$299$	−1.06970e7			−0.400174
$300$			559791.i			0.0207330i
$301$	−1.03343e7	−	6.28833e6i	−0.378950	−	0.230587i
$302$	8.42450e6			0.305860
$303$			246043.i			0.00884472i
$304$	2.28120e7	+	1.31705e7i	0.811976	+	0.468795i
$305$	3.83262e6			0.135082
$306$	4.03898e6	+	2.33191e6i	0.140964	+	0.0813855i
$307$	−2.23703e7	+	3.87464e7i	−0.773136	+	1.33911i	0.162701	+	0.986676i	$0.447980\pi$
$307$	−2.23703e7	+	3.87464e7i	−0.773136	+	1.33911i	−0.935836	+	0.352435i	$0.885354\pi$
$308$	1.27087e7	−	7.33734e6i	0.434958	−	0.251123i
$309$			276073.i			0.00935725i
$310$	527748.	+	914086.i	0.0177150	+	0.0306833i
$311$	1.69588e7	−	2.93735e7i	0.563785	−	0.976504i	−0.433377	−	0.901213i	$-0.642678\pi$
$311$	1.69588e7	−	2.93735e7i	0.563785	−	0.976504i	0.997162	−	0.0752913i	$-0.0239887\pi$
$312$	365618.			0.0120383
$313$	1.13215e7	+	6.53648e6i	0.369208	+	0.213162i	0.673112	−	0.739540i	$-0.264957\pi$
$313$	1.13215e7	+	6.53648e6i	0.369208	+	0.213162i	−0.303904	+	0.952703i	$0.598290\pi$
$314$	7.86154e6	+	1.36166e7i	0.253933	+	0.439825i
$315$	−940390.	−	1.62880e6i	−0.0300868	−	0.0521119i
$316$	−2.20967e7	−	3.82726e7i	−0.700271	−	1.21290i
$317$	5.50253e7			1.72737			0.863684	−	0.504033i	$-0.168151\pi$
$317$	5.50253e7			1.72737			0.863684	+	0.504033i	$0.168151\pi$
$318$	−6822.34	−	11816.6i	−0.000212154	−	0.000367462i
$319$	6.14332e6	−	3.54685e6i	0.189248	−	0.109262i
$320$	1.55062e6	+	895250.i	0.0473211	+	0.0273209i
$321$	−449612.	−	259584.i	−0.0135932	−	0.00784806i
$322$	−2.41279e6			−0.0722691
$323$			2.27533e7i			0.675207i
$324$	−1.51217e7	+	2.61915e7i	−0.444595	+	0.770060i
$325$	1.36821e7	−	2.36980e7i	0.398567	−	0.690339i
$326$	−8.93131e6	−	1.54695e7i	−0.257788	−	0.446502i
$327$	573758.	−	331259.i	0.0164091	−	0.00947381i
$328$		−	2.18793e7i		−	0.620029i
$329$	−1.88911e7	+	1.09068e7i	−0.530482	+	0.306274i
$330$	42100.0	−	24306.4i	0.00117149	−	0.000676363i
$331$	1.60706e7	−	9.27836e6i	0.443147	−	0.255851i	−0.261785	−	0.965126i	$-0.584311\pi$
$331$	1.60706e7	−	9.27836e6i	0.443147	−	0.255851i	0.704932	+	0.709275i	$0.250978\pi$
$332$	−1.33910e7	+	2.31940e7i	−0.365932	+	0.633812i
$333$			3.71562e7i			1.00623i
$334$	−1.13228e7	−	6.53724e6i	−0.303889	−	0.175451i
$335$	−2.04923e6	+	1.18312e6i	−0.0545075	+	0.0314699i
$336$	−272949.			−0.00719556
$337$	1.47117e7	+	2.54814e7i	0.384392	+	0.665786i	0.991685	−	0.128692i	$-0.0410779\pi$
$337$	1.47117e7	+	2.54814e7i	0.384392	+	0.665786i	−0.607293	+	0.794478i	$0.707745\pi$
$338$	3.76467e6	+	2.17353e6i	0.0974938	+	0.0562880i
$339$	177800.	−	307958.i	0.00456385	−	0.00790483i
$340$			2.34059e6i			0.0595510i
$341$	1.98983e7	−	3.44649e7i	0.501826	−	0.869188i
$342$	1.81177e7			0.452923
$343$			3.22787e7i			0.799897i
$344$	2.23243e7	−	1.22120e7i	0.548407	−	0.299994i
$345$	65129.3			0.00158606
$346$		−	7.14452e6i		−	0.172482i
$347$	1.77642e7	+	1.02561e7i	0.425164	+	0.245468i	0.697284	−	0.716795i	$-0.254392\pi$
$347$	1.77642e7	+	1.02561e7i	0.425164	+	0.245468i	−0.272120	+	0.962263i	$0.587725\pi$
$348$	−153028.			−0.00363105
$349$	5.54397e7	+	3.20081e7i	1.30420	+	0.752980i	0.981122	−	0.193392i	$-0.0619489\pi$
$349$	5.54397e7	+	3.20081e7i	1.30420	+	0.752980i	0.323078	+	0.946372i	$0.395282\pi$
$350$	3.08610e6	−	5.34528e6i	0.0719789	−	0.124671i
$351$	−1.44204e6	+	832561.i	−0.0333469	+	0.0192528i
$352$			4.71943e7i			1.08209i
$353$	−2.16461e7	−	3.74921e7i	−0.492103	−	0.852347i	0.507856	−	0.861442i	$-0.330438\pi$
$353$	−2.16461e7	−	3.74921e7i	−0.492103	−	0.852347i	−0.999959	+	0.00909535i	$0.997105\pi$
$354$	228849.	−	396379.i	0.00515870	−	0.00893513i
$355$	−9.82440e6			−0.219594
$356$	−2.91347e7	−	1.68210e7i	−0.645745	−	0.372821i
$357$	−117886.	−	204185.i	−0.00259095	−	0.00448765i
$358$	−4.34340e6	−	7.52299e6i	−0.0946631	−	0.163961i
$359$	−2.44464e7	−	4.23424e7i	−0.528361	−	0.915149i	−0.999453	−	0.0330645i	$-0.989473\pi$
$359$	−2.44464e7	−	4.23424e7i	−0.528361	−	0.915149i	0.471092	−	0.882084i	$-0.343860\pi$
$360$	3.95620e6			0.0847950
$361$	2.06723e7	+	3.58055e7i	0.439408	+	0.761077i
$362$	7.67544e6	−	4.43142e6i	0.161800	−	0.0934151i
$363$	−605010.	−	349303.i	−0.0126486	−	0.00730268i
$364$	1.34015e7	+	7.73734e6i	0.277874	+	0.160431i
$365$	6.99389e6			0.143827
$366$		−	382569.i		−	0.00780308i
$367$	−2.11258e6	+	3.65909e6i	−0.0427380	+	0.0740244i	−0.886603	−	0.462531i	$-0.846941\pi$
$367$	−2.11258e6	+	3.65909e6i	−0.0427380	+	0.0740244i	0.843865	+	0.536555i	$0.180275\pi$
$368$	−8.39897e6	+	1.45474e7i	−0.168532	+	0.291906i
$369$	2.49040e7	+	4.31350e7i	0.495667	+	0.858521i
$370$	1.98186e6	−	1.14423e6i	0.0391262	−	0.0225895i
$371$		−	1.22589e6i		−	0.0240065i
$372$	−743488.	+	429253.i	−0.0144426	+	0.00833844i
$373$	−4.87230e7	+	2.81303e7i	−0.938875	+	0.542060i	−0.889607	−	0.456726i	$-0.849022\pi$
$373$	−4.87230e7	+	2.81303e7i	−0.938875	+	0.542060i	−0.0492675	+	0.998786i	$0.515689\pi$
$374$	−9.37935e6	+	5.41517e6i	−0.179291	+	0.103514i
$375$	−168171.	+	291281.i	−0.00318903	+	0.00552356i
$376$		−	4.58846e7i		−	0.863184i
$377$	6.47823e6	+	3.74021e6i	0.120902	+	0.0698026i
$378$	−325263.	+	187791.i	−0.00602225	+	0.00347695i
$379$	3.20334e7			0.588417			0.294209	−	0.955741i	$-0.404944\pi$
$379$	3.20334e7			0.588417			0.294209	+	0.955741i	$0.404944\pi$
$380$	4.54629e6	+	7.87441e6i	0.0828527	+	0.143505i
$381$	−466663.	−	269428.i	−0.00843778	−	0.00487155i
$382$	1.45101e6	−	2.51322e6i	0.0260304	−	0.0450859i
$383$		−	6.33025e7i		−	1.12674i	−0.826204	−	0.563372i	$-0.809504\pi$
$383$		−	6.33025e7i		−	1.12674i	0.826204	−	0.563372i	$-0.190496\pi$
$384$	660881.	−	1.14468e6i	0.0116716	−	0.0202158i
$385$	4.36756e6			0.0765343
$386$		−	9.47032e6i		−	0.164666i
$387$	−3.01121e7	+	4.94865e7i	−0.519526	+	0.853796i
$388$	−6.06716e7			−1.03870
$389$		−	7.03747e7i		−	1.19555i	−0.801664	−	0.597775i	$-0.796052\pi$
$389$		−	7.03747e7i		−	1.19555i	0.801664	−	0.597775i	$-0.203948\pi$
$390$	44395.1	+	25631.5i	0.000748413	+	0.000432096i
$391$	−1.45100e7			−0.242737
$392$	−2.61923e7	−	1.51222e7i	−0.434827	−	0.251047i
$393$	−95203.9	+	164898.i	−0.00156847	+	0.00271668i
$394$	−1.53665e7	+	8.87185e6i	−0.251239	+	0.145053i
$395$		−	1.31531e7i		−	0.213420i
$396$	−3.51354e7	−	6.08562e7i	−0.565795	−	0.979985i
$397$	−2.88012e7	+	4.98851e7i	−0.460297	+	0.797259i	−0.998976	−	0.0452531i	$-0.985591\pi$
$397$	−2.88012e7	+	4.98851e7i	−0.460297	+	0.797259i	0.538678	+	0.842512i	$0.318924\pi$
$398$	−3.87597e6			−0.0614796
$399$	−793204.	−	457957.i	−0.0124872	−	0.00720951i
$400$	−2.14855e7	−	3.72140e7i	−0.335711	−	0.581469i
$401$	−1.94172e7	−	3.36316e7i	−0.301130	−	0.521572i	0.675262	−	0.737578i	$-0.264030\pi$
$401$	−1.94172e7	−	3.36316e7i	−0.301130	−	0.521572i	−0.976392	+	0.216005i	$0.930697\pi$
$402$	118098.	+	204552.i	0.00181788	+	0.00314866i
$403$	4.19662e7			0.641186
$404$	−1.09526e7	−	1.89704e7i	−0.166101	−	0.287695i
$405$	−7.79524e6	+	4.50058e6i	−0.117345	+	0.0677491i
$406$	1.46121e6	+	843632.i	0.0218341	+	0.0126059i
$407$	−7.47244e7	−	4.31421e7i	−1.10836	−	0.639909i
$408$	495944.			0.00730217
$409$			7.57717e7i			1.10748i	0.832689	+	0.553741i	$0.186800\pi$
$409$			7.57717e7i			1.10748i	−0.832689	+	0.553741i	$0.813200\pi$
$410$	1.53384e6	−	2.65669e6i	0.0222550	−	0.0385469i
$411$	1.30690e6	−	2.26362e6i	0.0188242	−	0.0326045i
$412$	−1.22893e7	−	2.12857e7i	−0.175726	−	0.304366i
$413$	3.56121e7	−	2.05607e7i	0.505531	−	0.291868i
$414$			1.15538e7i			0.162826i
$415$	−6.90311e6	+	3.98551e6i	−0.0965829	+	0.0557622i
$416$	−4.30996e7	+	2.48836e7i	−0.598678	+	0.345647i
$417$	−435766.	+	251589.i	−0.00600959	+	0.00346964i
$418$	−2.10365e7	+	3.64363e7i	−0.288035	+	0.498891i
$419$		−	6.85238e7i		−	0.931536i	−0.884907	−	0.465768i	$-0.845778\pi$
$419$		−	6.85238e7i		−	0.931536i	0.884907	−	0.465768i	$-0.154222\pi$
$420$	−81595.5	−	47109.2i	−0.00110133	−	0.000635855i
$421$	3.22707e7	−	1.86315e7i	0.432477	−	0.249691i	−0.267925	−	0.963440i	$-0.586338\pi$
$421$	3.22707e7	−	1.86315e7i	0.432477	−	0.249691i	0.700401	+	0.713749i	$0.253004\pi$
$422$	−2.72029e6			−0.0361974
$423$	5.22279e7	+	9.04614e7i	0.690052	+	1.19520i
$424$	2.23317e6	+	1.28932e6i	0.0292970	+	0.0169146i
$425$	1.85591e7	−	3.21453e7i	0.241763	−	0.418745i
$426$			980663.i			0.0126850i
$427$	1.71857e7	−	2.97664e7i	0.220741	−	0.382334i
$428$	4.62212e7			0.589535
$429$		−	1.93283e6i		−	0.0244806i
$430$	3.56684e6	+	82194.3i	0.0448620	+	0.00103380i
$431$	−4.56323e7			−0.569955			−0.284978	−	0.958534i	$-0.591986\pi$
$431$	−4.56323e7			−0.569955			−0.284978	+	0.958534i	$0.591986\pi$
$432$			2.61481e6i			0.0324331i
$433$	6.35332e7	+	3.66809e7i	0.782594	+	0.451831i	0.837349	−	0.546669i	$-0.184104\pi$
$433$	6.35332e7	+	3.66809e7i	0.782594	+	0.451831i	−0.0547545	+	0.998500i	$0.517438\pi$
$434$	9.46580e6			0.115794
$435$	−39443.0	−	22772.4i	−0.000479184	−	0.000276657i
$436$	−2.94918e7	+	5.10813e7i	−0.355830	+	0.616315i
$437$	−4.88156e7	+	2.81837e7i	−0.584945	+	0.337718i
$438$		−	698124.i		−	0.00830826i
$439$	−6.69897e7	−	1.16029e8i	−0.791798	−	1.37143i	−0.924853	−	0.380325i	$-0.875812\pi$
$439$	−6.69897e7	−	1.16029e8i	−0.791798	−	1.37143i	0.133055	−	0.991109i	$-0.457521\pi$
$440$	−4.59355e6	+	7.95626e6i	−0.0539250	+	0.0934009i
$441$	6.88509e7			0.802775
$442$	−9.89067e6	−	5.71038e6i	−0.114540	−	0.0661300i
$443$	7.12177e7	+	1.23353e8i	0.819175	+	1.41885i	0.906291	+	0.422655i	$0.138902\pi$
$443$	7.12177e7	+	1.23353e8i	0.819175	+	1.41885i	−0.0871157	+	0.996198i	$0.527765\pi$
$444$	930677.	+	1.61198e6i	0.0106329	+	0.0184167i
$445$	−5.00634e6	−	8.67123e6i	−0.0568120	−	0.0984013i
$446$	4.59133e7			0.517529
$447$	−1.84745e6	−	3.19988e6i	−0.0206847	−	0.0358270i
$448$	1.39061e7	−	8.02870e6i	0.154658	−	0.0892917i
$449$	7.36710e7	+	4.25340e7i	0.813875	+	0.469891i	0.848300	−	0.529517i	$-0.177627\pi$
$449$	7.36710e7	+	4.25340e7i	0.813875	+	0.469891i	−0.0344249	+	0.999407i	$0.510960\pi$
$450$	−2.55962e7	−	1.47780e7i	−0.280891	−	0.162173i
$451$	−1.15664e8			−1.26087
$452$			3.16588e7i			0.342830i
$453$	−1.01970e6	+	1.76617e6i	−0.0109692	+	0.0189993i
$454$	1.37423e7	−	2.38024e7i	0.146856	−	0.254363i
$455$	2.30283e6	+	3.98862e6i	0.0244471	+	0.0423436i
$456$	1.66849e6	−	963306.i	0.0175967	−	0.0101594i
$457$			3.60796e6i			0.0378018i	0.999821	+	0.0189009i	$0.00601671\pi$
$457$			3.60796e6i			0.0378018i	−0.999821	+	0.0189009i	$0.993983\pi$
$458$	−2.71651e7	+	1.56838e7i	−0.282758	+	0.163251i
$459$	−1.95606e6	+	1.12933e6i	−0.0202275	+	0.0116784i
$460$	−5.02158e6	+	2.89921e6i	−0.0515902	+	0.0297856i
$461$	1.97365e7	−	3.41846e7i	0.201450	−	0.348922i	−0.747546	−	0.664210i	$-0.768768\pi$
$461$	1.97365e7	−	3.41846e7i	0.201450	−	0.348922i	0.948996	+	0.315289i	$0.102101\pi$
$462$		−	435965.i		−	0.00442106i
$463$	4.58515e7	+	2.64724e7i	0.461967	+	0.266717i	0.712871	−	0.701295i	$-0.247394\pi$
$463$	4.58515e7	+	2.64724e7i	0.461967	+	0.266717i	−0.250904	+	0.968012i	$0.580728\pi$
$464$	1.01730e7	−	5.87340e6i	0.101835	−	0.0587943i
$465$	−255513.			−0.00254129
$466$	2.19686e7	+	3.80507e7i	0.217092	+	0.376014i
$467$	1.57817e8	+	9.11159e7i	1.54955	+	0.894630i	0.998176	+	0.0603692i	$0.0192278\pi$
$467$	1.57817e8	+	9.11159e7i	1.54955	+	0.894630i	0.551369	+	0.834261i	$0.314106\pi$
$468$	3.70508e7	−	6.41738e7i	0.361460	−	0.626067i
$469$			2.12208e7i			0.205704i
$470$	3.21672e6	−	5.57153e6i	0.0309827	−	0.0536637i
$471$	−3.80623e6			−0.0364277
$472$			8.64981e7i			0.822585i
$473$	−6.45586e7	−	1.18017e8i	−0.610058	−	1.11522i
$474$	−1.31293e6			−0.0123284
$475$		−	1.44194e8i		−	1.34545i
$476$	1.81785e7	+	1.04953e7i	0.168553	+	0.0973141i
$477$	−5.87024e6			−0.0540880
$478$	−2.61723e7	−	1.51106e7i	−0.239639	−	0.138356i
$479$	−8.31696e7	+	1.44054e8i	−0.756760	+	1.31075i	0.187735	+	0.982220i	$0.439885\pi$
$479$	−8.31696e7	+	1.44054e8i	−0.756760	+	1.31075i	−0.944495	+	0.328526i	$0.893448\pi$
$480$	262414.	−	151505.i	0.00237281	−	0.00136994i
$481$		−	9.09881e7i		−	0.817616i
$482$	2.24877e7	+	3.89498e7i	0.200818	+	0.347828i
$483$	292043.	−	505834.i	0.00259182	−	0.00448917i
$484$	6.21965e7			0.548567
$485$	−1.56382e7	−	9.02870e6i	−0.137076	−	0.0791407i
$486$	1.34900e6	+	2.33653e6i	0.0117517	+	0.0203546i
$487$	8.56164e7	+	1.48292e8i	0.741259	+	1.28390i	0.951922	+	0.306339i	$0.0991042\pi$
$487$	8.56164e7	+	1.48292e8i	0.741259	+	1.28390i	−0.210664	+	0.977559i	$0.567562\pi$
$488$	3.61498e7	+	6.26133e7i	0.311062	+	0.538775i
$489$	4.32417e6			0.0369808
$490$	−2.12026e6	−	3.67241e6i	−0.0180219	−	0.0312149i
$491$	1.35259e8	−	7.80921e7i	1.14268	−	0.659724i	0.195584	−	0.980687i	$-0.437340\pi$
$491$	1.35259e8	−	7.80921e7i	1.14268	−	0.659724i	0.947092	+	0.320963i	$0.104006\pi$
$492$	2.16087e6	+	1.24758e6i	0.0181440	+	0.0104754i
$493$	8.78741e6	+	5.07341e6i	0.0733365	+	0.0423408i
$494$	−4.43666e7			−0.368024
$495$		−	2.09143e7i		−	0.172436i
$496$	3.29506e7	−	5.70721e7i	0.270034	−	0.467712i
$497$	−4.40531e7	+	7.63023e7i	−0.358846	+	0.621539i
$498$	397830.	+	689062.i	0.00322114	+	0.00557918i
$499$	−5.27018e7	+	3.04274e7i	−0.424154	+	0.244886i	−0.696853	−	0.717214i	$-0.745417\pi$
$499$	−5.27018e7	+	3.04274e7i	−0.424154	+	0.244886i	0.272699	+	0.962099i	$0.412084\pi$
$500$		−	2.99444e7i		−	0.239555i
$501$	2.74102e6	−	1.58253e6i	0.0217971	−	0.0125846i
$502$	6.40706e7	−	3.69912e7i	0.506463	−	0.292406i
$503$	7.31714e7	−	4.22455e7i	0.574959	−	0.331953i	−0.184168	−	0.982895i	$-0.558959\pi$
$503$	7.31714e7	−	4.22455e7i	0.574959	−	0.331953i	0.759128	+	0.650942i	$0.225626\pi$
$504$	1.77398e7	−	3.07262e7i	0.138566	−	0.240003i
$505$		−	6.51951e6i		−	0.0506222i
$506$	−2.32358e7	−	1.34152e7i	−0.179352	−	0.103549i
$507$	−911347.	+	526167.i	−0.00699294	+	0.00403738i
$508$	4.79740e7			0.365944
$509$	2.51380e7	+	4.35403e7i	0.190624	+	0.330170i	0.945457	−	0.325746i	$-0.105616\pi$
$509$	2.51380e7	+	4.35403e7i	0.190624	+	0.330170i	−0.754833	+	0.655917i	$0.772282\pi$
$510$	60219.8	+	34767.9i	0.000453972	+	0.000262101i
$511$	3.13610e7	−	5.43188e7i	0.235032	−	0.407087i
$512$			1.35540e8i			1.00985i
$513$	−4.38715e6	+	7.59876e6i	−0.0324960	+	0.0562847i
$514$	−1.19176e7			−0.0877608
$515$		−	7.31521e6i		−	0.0535556i
$516$	−66854.2	+	2.90116e6i	−0.000486609	+	0.0211165i
$517$	−2.42568e8			−1.75534
$518$		−	2.05231e7i		−	0.147657i
$519$	1.49782e6	+	864769.i	0.0107142	+	0.00618583i
$520$	−9.68794e6			−0.0689003
$521$	−2.44211e8	−	1.40995e8i	−1.72684	−	0.996989i	−0.902187	−	0.431345i	$-0.858039\pi$
$521$	−2.44211e8	−	1.40995e8i	−1.72684	−	0.996989i	−0.824649	−	0.565645i	$-0.808627\pi$
$522$	4.03979e6	−	6.99712e6i	0.0284019	−	0.0491935i
$523$	−3.96187e7	+	2.28739e7i	−0.276946	+	0.159895i	−0.632040	−	0.774936i	$-0.717782\pi$
$523$	−3.96187e7	+	2.28739e7i	−0.276946	+	0.159895i	0.355094	+	0.934831i	$0.384449\pi$
$524$		−	1.69519e7i		−	0.117821i
$525$	747079.	+	1.29398e6i	0.00516284	+	0.00894230i
$526$	2.78827e7	−	4.82942e7i	0.191592	−	0.331847i
$527$	5.69251e7			0.388931
$528$	−2.62857e6	−	1.51760e6i	−0.0178574	−	0.0103099i
$529$	5.60449e7	+	9.70727e7i	0.378590	+	0.655737i
$530$	180774.	+	313110.i	0.00121425	+	0.00210315i
$531$	−9.84561e7	−	1.70531e8i	−0.657596	−	1.13899i
$532$	8.15432e7			0.541568
$533$	−6.09850e7	−	1.05629e8i	−0.402755	−	0.697593i
$534$	−865555.	+	499728.i	−0.00568422	+	0.00328179i
$535$	1.19136e7	+	6.87830e6i	0.0778001	+	0.0449179i
$536$	−3.86573e7	−	2.23188e7i	−0.251036	−	0.144936i
$537$	2.10289e6			0.0135798
$538$		−	2.92715e6i		−	0.0187974i
$539$	−7.99429e7	+	1.38465e8i	−0.510521	+	0.884248i
$540$	−451298.	+	781671.i	−0.00286604	+	0.00496413i
$541$	−7.93433e7	−	1.37427e8i	−0.501093	−	0.867919i	−0.999999	−	0.00126265i	$-0.999598\pi$
$541$	−7.93433e7	−	1.37427e8i	−0.501093	−	0.867919i	0.498906	−	0.866656i	$-0.333735\pi$
$542$	1.95019e7	−	1.12594e7i	0.122484	−	0.0707161i
$543$			2.14551e6i			0.0134008i
$544$	−5.84626e7	+	3.37534e7i	−0.363146	+	0.209662i
$545$	−1.52031e7	+	8.77751e6i	−0.0939166	+	0.0542228i
$546$	398140.	−	229866.i	0.00244601	−	0.00141220i
$547$	−8.78352e7	+	1.52135e8i	−0.536669	+	0.929538i	0.462411	+	0.886665i	$0.346984\pi$
$547$	−8.78352e7	+	1.52135e8i	−0.536669	+	0.929538i	−0.999081	+	0.0428726i	$0.986349\pi$
$548$			2.32705e8i			1.41405i
$549$	−1.42539e8	−	8.22947e7i	−0.861421	−	0.497342i
$550$	5.94396e7	−	3.43175e7i	0.357263	−	0.206266i
$551$	3.94177e7			0.235633
$552$	614309.	+	1.06401e6i	0.00365233	+	0.00632601i
$553$	−1.02155e8	−	5.89790e7i	−0.604064	−	0.348757i
$554$	7.64809e6	−	1.32469e7i	0.0449804	−	0.0779084i
$555$			553986.i			0.00324056i
$556$	2.23989e7	−	3.87960e7i	0.130317	−	0.225716i
$557$	−8.90236e7			−0.515157			−0.257578	−	0.966257i	$-0.582925\pi$
$557$	−8.90236e7			−0.515157			−0.257578	+	0.966257i	$0.582925\pi$
$558$		−	4.53276e7i		−	0.260892i
$559$	7.37385e7	−	1.21183e8i	0.422142	−	0.693754i
$560$	7.23245e6			0.0411833
$561$		−	2.62180e6i		−	0.0148494i
$562$	2.20614e6	+	1.27372e6i	0.0124287	+	0.00717569i
$563$	−5.61396e7			−0.314589			−0.157295	−	0.987552i	$-0.550277\pi$
$563$	−5.61396e7			−0.314589			−0.157295	+	0.987552i	$0.550277\pi$
$564$	4.53170e6	+	2.61638e6i	0.0252595	+	0.0145836i
$565$	−4.71123e6	+	8.16009e6i	−0.0261209	+	0.0452428i
$566$	9.13669e6	−	5.27507e6i	0.0503894	−	0.0290924i
$567$			8.07234e7i			0.442844i
$568$	−9.26652e7	−	1.60501e8i	−0.505675	−	0.875855i
$569$	−1.74972e8	+	3.03061e8i	−0.949800	+	1.64510i	−0.203958	+	0.978980i	$0.565381\pi$
$569$	−1.74972e8	+	3.03061e8i	−0.949800	+	1.64510i	−0.745842	+	0.666123i	$0.767953\pi$
$570$	270129.			0.00145863
$571$	−2.20836e8	−	1.27500e8i	−1.18621	−	0.684860i	−0.228769	−	0.973481i	$-0.573470\pi$
$571$	−2.20836e8	−	1.27500e8i	−1.18621	−	0.684860i	−0.957443	+	0.288621i	$0.906803\pi$
$572$	8.60395e7	+	1.49025e8i	0.459737	+	0.796289i
$573$	351259.	+	608399.i	0.00186708	+	0.00323388i
$574$	−1.37556e7	−	2.38255e7i	−0.0727353	−	0.125981i
$575$	9.19540e7			0.483690
$576$	−3.84460e7	−	6.65904e7i	−0.201179	−	0.348453i
$577$	2.67246e8	−	1.54295e8i	1.39118	−	0.803200i	0.397737	−	0.917499i	$-0.369796\pi$
$577$	2.67246e8	−	1.54295e8i	1.39118	−	0.803200i	0.993446	+	0.114299i	$0.0364622\pi$
$578$	4.18731e7	+	2.41754e7i	0.216846	+	0.125196i
$579$	1.98542e6	+	1.14628e6i	0.0102286	+	0.00590549i
$580$	4.05483e6			0.0207821
$581$			7.14850e7i			0.364491i
$582$	−901237.	+	1.56099e6i	−0.00457162	+	0.00791827i
$583$	6.81595e6	−	1.18056e7i	0.0343970	−	0.0595774i
$584$	6.59674e7	+	1.14259e8i	0.331200	+	0.573656i
$585$	1.90998e7	−	1.10272e7i	0.0954026	−	0.0550807i
$586$		−	4.43130e7i		−	0.220210i
$587$	1.99940e7	−	1.15435e7i	0.0988518	−	0.0570721i	−0.449759	−	0.893150i	$-0.648490\pi$
$587$	1.99940e7	−	1.15435e7i	0.0988518	−	0.0570721i	0.548611	+	0.836078i	$0.315157\pi$
$588$	2.98702e6	−	1.72456e6i	0.0146928	−	0.00848292i
$589$	1.91512e8	−	1.10570e8i	0.937239	−	0.541115i
$590$	−6.06391e6	+	1.05030e7i	−0.0295255	+	0.0511396i
$591$		−	4.29538e6i		−	0.0208084i
$592$	−1.23740e8	−	7.14412e7i	−0.596409	−	0.344337i
$593$	3.23510e8	−	1.86779e8i	1.55140	−	0.895701i	0.553371	−	0.832935i	$-0.313341\pi$
$593$	3.23510e8	−	1.86779e8i	1.55140	−	0.895701i	0.998028	−	0.0627658i	$-0.0199921\pi$
$594$	−4.17647e6			−0.0199274
$595$	3.12368e6	+	5.41037e6i	0.0148291	+	0.0256848i
$596$	2.84883e8	+	1.64477e8i	1.34564	+	0.776904i
$597$	469145.	−	812583.i	0.00220488	−	0.00381896i
$598$		−	2.82930e7i		−	0.132305i
$599$	−8.55309e7	+	1.48144e8i	−0.397963	+	0.689292i	−0.993474	−	0.114055i	$-0.963616\pi$
$599$	−8.55309e7	+	1.48144e8i	−0.397963	+	0.689292i	0.595512	+	0.803347i	$0.296949\pi$
$600$	−3.14294e6			−0.0145507
$601$			4.18374e8i			1.92726i	0.267231	+	0.963632i	$0.413891\pi$
$601$			4.18374e8i			1.92726i	−0.267231	+	0.963632i	$0.586109\pi$
$602$	1.66323e7	−	2.73337e7i	0.0762364	−	0.125288i
$603$	1.01617e8			0.463462
$604$		−	1.81566e8i		−	0.823993i
$605$	1.60312e7	+	9.25562e6i	0.0723935	+	0.0417964i
$606$	−650772.			−0.00292423
$607$	1.81315e8	+	1.04682e8i	0.810715	+	0.468067i	0.847204	−	0.531267i	$-0.178284\pi$
$607$	1.81315e8	+	1.04682e8i	0.810715	+	0.468067i	−0.0364889	+	0.999334i	$0.511617\pi$
$608$	−1.31123e8	+	2.27112e8i	−0.583402	+	1.01048i
$609$	−353729.	+	204226.i	−0.00156610	+	0.000904187i
$610$			1.01371e7i			0.0446604i
$611$	−1.27896e8	−	2.21522e8i	−0.560703	−	0.971166i
$612$	5.02576e7	−	8.70487e7i	0.219254	−	0.379759i
$613$	−3.59742e8			−1.56174			−0.780872	−	0.624691i	$-0.785225\pi$
$613$	−3.59742e8			−1.56174			−0.780872	+	0.624691i	$0.785225\pi$
$614$	−1.02482e8	−	5.91681e7i	−0.442734	−	0.255613i
$615$	371310.	+	643128.i	0.00159629	+	0.00276485i
$616$	4.11954e7	+	7.13526e7i	0.176241	+	0.305258i
$617$	−1.69186e8	−	2.93039e8i	−0.720292	−	1.24758i	−0.960883	−	0.276956i	$-0.910674\pi$
$617$	−1.69186e8	−	2.93039e8i	−0.720292	−	1.24758i	0.240590	−	0.970627i	$-0.422659\pi$
$618$	−730198.			−0.00309368
$619$	7.46156e7	+	1.29238e8i	0.314599	+	0.544902i	0.979352	−	0.202161i	$-0.0647965\pi$
$619$	7.46156e7	+	1.29238e8i	0.314599	+	0.544902i	−0.664753	+	0.747063i	$0.731463\pi$
$620$	1.97005e7	−	1.13741e7i	0.0826613	−	0.0477245i
$621$	−4.84580e6	−	2.79772e6i	−0.0202344	−	0.0116823i
$622$	7.76913e7	+	4.48551e7i	0.322850	+	0.186398i
$623$	−8.97948e7			−0.371353
$624$		−	3.20067e6i		−	0.0131731i
$625$	−1.15365e8	+	1.99819e8i	−0.472537	+	0.818458i
$626$	−1.72886e7	+	2.99448e7i	−0.0704754	+	0.122067i
$627$	−5.09249e6	−	8.82046e6i	−0.0206599	−	0.0357840i
$628$	2.93467e8	−	1.69433e8i	1.18490	−	0.684100i
$629$		−	1.23421e8i		−	0.495949i
$630$	4.30810e6	−	2.48728e6i	0.0172291	−	0.00994725i
$631$	2.88097e8	−	1.66333e8i	1.14670	−	0.662048i	0.198620	−	0.980077i	$-0.436354\pi$
$631$	2.88097e8	−	1.66333e8i	1.14670	−	0.662048i	0.948081	+	0.318028i	$0.103021\pi$
$632$	2.14881e8	−	1.24062e8i	0.851230	−	0.491458i
$633$	329262.	−	570299.i	0.00129817	−	0.00224849i
$634$			1.45539e8i			0.571100i
$635$	1.23653e7	+	7.13914e6i	0.0482931	+	0.0278820i
$636$	−254674.	+	147036.i	−0.000989950	+	0.000571548i
$637$	−1.68602e8			−0.652296
$638$	9.38122e6	+	1.62487e7i	0.0361241	+	0.0625688i
$639$	3.65378e8	+	2.10951e8i	1.40036	+	0.808499i
$640$	−1.75116e7	+	3.03310e7i	−0.0668015	+	0.115704i
$641$		−	4.49116e7i		−	0.170524i	−0.996359	−	0.0852618i	$-0.972827\pi$
$641$		−	4.49116e7i		−	0.170524i	0.996359	−	0.0852618i	$-0.0271727\pi$
$642$	686585.	−	1.18920e6i	0.00259471	−	0.00449418i
$643$	4.64966e8			1.74900			0.874498	−	0.485030i	$-0.161191\pi$
$643$	4.64966e8			1.74900			0.874498	+	0.485030i	$0.161191\pi$
$644$			5.20009e7i			0.194694i
$645$	−448960.	+	737827.i	−0.00167313	+	0.00274964i
$646$	−6.01812e7			−0.223236
$647$			8.86037e7i			0.327144i	0.986531	+	0.163572i	$0.0523016\pi$
$647$			8.86037e7i			0.327144i	−0.986531	+	0.163572i	$0.947698\pi$
$648$	−1.47052e8	−	8.49003e7i	−0.540437	−	0.312021i
$649$	4.57270e8			1.67278
$650$	6.26800e7	+	3.61883e7i	0.228239	+	0.131774i
$651$	−1.14573e6	+	1.98447e6i	−0.00415280	+	0.00719286i
$652$	−3.33401e8	+	1.92489e8i	−1.20288	+	0.694485i
$653$			2.34811e8i			0.843293i	0.906760	+	0.421647i	$0.138548\pi$
$653$			2.34811e8i			0.843293i	−0.906760	+	0.421647i	$0.861452\pi$
$654$	876163.	+	1.51756e6i	0.00313221	+	0.00542516i
$655$	2.52266e6	−	4.36937e6i	0.00897706	−	0.0155487i
$656$	−1.91534e8			−0.678477
$657$	−2.60109e8	−	1.50174e8i	−0.917191	−	0.529540i
$658$	−2.88479e7	−	4.99660e7i	−0.101260	−	0.175387i
$659$	1.39292e8	+	2.41261e8i	0.486710	+	0.843007i	0.999883	−	0.0152783i	$-0.00486343\pi$
$659$	1.39292e8	+	2.41261e8i	0.486710	+	0.843007i	−0.513173	+	0.858285i	$0.671530\pi$
$660$	−523856.	−	907345.i	−0.00182213	−	0.00315603i
$661$	3.76809e7			0.130472			0.0652360	−	0.997870i	$-0.479220\pi$
$661$	3.76809e7			0.130472			0.0652360	+	0.997870i	$0.479220\pi$
$662$	2.45408e7	+	4.25059e7i	0.0845890	+	0.146513i
$663$	2.39432e6	−	1.38236e6i	0.00821565	−	0.00474331i
$664$	−1.30222e8	−	7.51838e7i	−0.444816	−	0.256815i
$665$	2.10178e7	+	1.21347e7i	0.0714699	+	0.0412632i
$666$	−9.82761e7			−0.332679
$667$			2.51370e7i			0.0847104i
$668$	−1.40892e8	+	2.44031e8i	−0.472667	+	0.818684i
$669$	−5.55733e6	+	9.62557e6i	−0.0185604	+	0.0321476i
$670$	−3.12930e6	−	5.42010e6i	−0.0104045	−	0.0180212i
$671$	3.31004e8	−	1.91105e8i	1.09563	−	0.632565i
$672$		−	2.71742e6i		−	0.00895467i
$673$	−1.83395e8	+	1.05883e8i	−0.601648	+	0.347362i	−0.769690	−	0.638418i	$-0.779589\pi$
$673$	−1.83395e8	+	1.05883e8i	−0.601648	+	0.347362i	0.168042	+	0.985780i	$0.446256\pi$
$674$	−6.73971e7	+	3.89117e7i	−0.220121	+	0.127087i
$675$	1.23961e7	−	7.15689e6i	0.0403063	−	0.0232709i
$676$	4.68443e7	−	8.11367e7i	0.151641	−	0.262650i
$677$		−	4.10967e7i		−	0.132447i	−0.997805	−	0.0662233i	$-0.978905\pi$
$677$		−	4.10967e7i		−	0.132447i	0.997805	−	0.0662233i	$-0.0210950\pi$
$678$	814532.	+	470271.i	0.00261348	+	0.00150889i
$679$	−1.40245e8	+	8.09704e7i	−0.447999	+	0.258653i
$680$	−1.31412e7			−0.0417935
$681$	3.32673e6	+	5.76207e6i	0.0105336	+	0.0182447i
$682$	9.11578e7	+	5.26300e7i	0.287369	+	0.165913i
$683$	6.45063e7	−	1.11728e8i	0.202461	−	0.350672i	−0.746860	−	0.664981i	$-0.768440\pi$
$683$	6.45063e7	−	1.11728e8i	0.202461	−	0.350672i	0.949321	+	0.314309i	$0.101773\pi$
$684$		−	3.90475e8i		−	1.22018i
$685$	−3.46294e7	+	5.99799e7i	−0.107739	+	0.186610i
$686$	−8.53755e7			−0.264460
$687$		−	7.59344e6i		−	0.0234190i
$688$	−1.06906e8	−	1.95430e8i	−0.328274	−	0.600103i
$689$	1.43751e7			0.0439493
$690$			172263.i			0.000524380i
$691$	5.46960e7	+	3.15788e7i	0.165776	+	0.0957108i	0.580593	−	0.814194i	$-0.302821\pi$
$691$	5.46960e7	+	3.15788e7i	0.165776	+	0.0957108i	−0.414817	+	0.909905i	$0.636154\pi$
$692$	−1.53980e8			−0.464671
$693$	−1.62433e8	−	9.37810e7i	−0.488063	−	0.281783i
$694$	−2.71269e7	+	4.69852e7i	−0.0811563	+	0.140567i
$695$	1.15467e7	−	6.66647e6i	0.0343955	−	0.0198583i
$696$		−	859172.i		−	0.00254831i
$697$	−8.27232e7	−	1.43281e8i	−0.244303	−	0.423146i
$698$	−8.46597e7	+	1.46635e8i	−0.248949	+	0.431192i
$699$	−1.06362e7			−0.0311428
$700$	−1.15202e8	−	6.65120e7i	−0.335866	−	0.193913i
$701$	−9.31980e7	−	1.61424e8i	−0.270553	−	0.468612i	0.698450	−	0.715658i	$-0.253873\pi$
$701$	−9.31980e7	−	1.61424e8i	−0.270553	−	0.468612i	−0.969004	+	0.247047i	$0.920540\pi$
$702$	−2.20208e6	−	3.81411e6i	−0.00636534	−	0.0110251i
$703$	−2.39729e8	−	4.15223e8i	−0.690009	−	1.19513i
$704$	1.78559e8			0.511756
$705$	778700.	+	1.34875e6i	0.00222230	+	0.00384914i
$706$	9.91647e7	−	5.72528e7i	0.281801	−	0.162698i
$707$	−5.06345e7	−	2.92338e7i	−0.143281	−	0.0827233i
$708$	−8.54281e6	−	4.93220e6i	−0.0240714	−	0.0138976i
$709$	−5.82949e8			−1.63565			−0.817827	−	0.575464i	$-0.804822\pi$
$709$	−5.82949e8			−1.63565			−0.817827	+	0.575464i	$0.804822\pi$
$710$		−	2.59850e7i		−	0.0726019i
$711$	−2.82425e8	+	4.89175e8i	−0.785768	+	1.36099i
$712$	9.44410e7	−	1.63577e8i	0.261650	−	0.453191i
$713$	7.05112e7	+	1.22129e8i	0.194531	+	0.336938i
$714$	540058.	−	311803.i	0.00148370	−	0.000856614i
$715$			5.12151e7i			0.140113i
$716$	−1.62137e8	+	9.36096e7i	−0.441715	+	0.255024i
$717$	6.33576e6	−	3.65795e6i	0.0171886	−	0.00992385i
$718$	1.11993e8	−	6.46593e7i	0.302565	−	0.174686i
$719$	4.40297e7	−	7.62617e7i	0.118457	−	0.205173i	−0.800700	−	0.599066i	$-0.795539\pi$
$719$	4.40297e7	−	7.62617e7i	0.118457	−	0.205173i	0.919156	+	0.393893i	$0.128872\pi$
$720$		−	3.46331e7i		−	0.0927883i
$721$	−5.68144e7	−	3.28018e7i	−0.151584	−	0.0875169i
$722$	−9.47037e7	+	5.46772e7i	−0.251626	+	0.145276i
$723$	−1.08876e7			−0.0288082
$724$	−9.55066e7	−	1.65422e8i	−0.251662	−	0.435891i
$725$	−5.56883e7	−	3.21517e7i	−0.146134	−	0.0843703i
$726$	923887.	−	1.60022e6i	0.00241440	−	0.00418186i
$727$			1.49064e8i			0.387944i	0.981007	+	0.193972i	$0.0621371\pi$
$727$			1.49064e8i			0.387944i	−0.981007	+	0.193972i	$0.937863\pi$
$728$	−4.34412e7	+	7.52424e7i	−0.112592	+	0.195015i
$729$	3.86114e8			0.996627
$730$			1.84985e7i			0.0475518i
$731$	1.00023e8	−	1.64379e8i	0.256063	−	0.420817i
$732$	−8.24517e6			−0.0210216
$733$		−	6.87787e8i		−	1.74639i	−0.487369	−	0.873196i	$-0.662043\pi$
$733$		−	6.87787e8i		−	1.74639i	0.487369	−	0.873196i	$-0.337957\pi$
$734$	−9.67810e6	−	5.58765e6i	−0.0244738	−	0.0141300i
$735$	1.02654e6			0.00258532
$736$	−1.44831e8	−	8.36183e7i	−0.363269	−	0.209734i
$737$	−1.17988e8	+	2.04361e8i	−0.294737	+	0.510499i
$738$	−1.14090e8	+	6.58698e7i	−0.283843	+	0.163877i
$739$			5.13587e8i			1.27257i	0.771455	+	0.636284i	$0.219529\pi$
$739$			5.13587e8i			1.27257i	−0.771455	+	0.636284i	$0.780471\pi$
$740$	−2.46605e7	−	4.27133e7i	−0.0608565	−	0.105407i
$741$	5.37011e6	−	9.30131e6i	0.0131986	−	0.0228607i
$742$	3.24241e6			0.00793699
$743$	−1.44913e8	−	8.36657e7i	−0.353298	−	0.203977i	0.312839	−	0.949806i	$-0.398720\pi$
$743$	−1.44913e8	−	8.36657e7i	−0.353298	−	0.203977i	−0.666137	+	0.745829i	$0.732053\pi$
$744$	−2.41004e6	−	4.17431e6i	−0.00585201	−	0.0101360i
$745$	4.89526e7	+	8.47884e7i	0.118388	+	0.205054i
$746$	−7.44030e7	−	1.28870e8i	−0.179215	−	0.310409i
$747$	3.42310e8			0.821218
$748$	1.16708e8	+	2.02145e8i	0.278867	+	0.483012i
$749$	1.06842e8	−	6.16853e7i	0.254271	−	0.146803i
$750$	−770423.	−	444804.i	−0.00182619	−	0.00105435i
$751$	2.31638e8	+	1.33736e8i	0.546878	+	0.315740i	0.747862	−	0.663854i	$-0.231080\pi$
$751$	2.31638e8	+	1.33736e8i	0.546878	+	0.315740i	−0.200984	+	0.979595i	$0.564414\pi$
$752$	−4.01680e8			−0.944554
$753$			1.79096e7i			0.0419469i
$754$	−9.89264e6	+	1.71346e7i	−0.0230780	+	0.0399723i
$755$	2.70193e7	−	4.67988e7i	0.0627817	−	0.108741i
$756$	4.04729e6	+	7.01011e6i	0.00936696	+	0.0162241i
$757$	6.90604e8	−	3.98720e8i	1.59199	−	0.919138i	0.599029	−	0.800727i	$-0.295553\pi$
$757$	6.90604e8	−	3.98720e8i	1.59199	−	0.919138i	0.992965	−	0.118411i	$-0.0377800\pi$
$758$			8.47266e7i			0.194542i
$759$	5.62489e6	−	3.24753e6i	0.0128644	−	0.00742725i
$760$	−4.42108e7	+	2.55251e7i	−0.100713	+	0.0581469i
$761$	7.23998e8	−	4.18000e8i	1.64279	−	0.948468i	0.662961	−	0.748654i	$-0.269299\pi$
$761$	7.23998e8	−	4.18000e8i	1.64279	−	0.948468i	0.979834	−	0.199814i	$-0.0640339\pi$
$762$	712622.	−	1.23430e6i	0.00161062	−	0.00278968i
$763$			1.57435e8i			0.354428i
$764$	−5.41654e7	−	3.12724e7i	−0.121462	−	0.0701263i
$765$	2.59079e7	−	1.49579e7i	0.0578693	−	0.0334108i
$766$	1.67432e8			0.372522
$767$	2.41099e8	+	4.17596e8i	0.534331	+	0.925488i
$768$	−717645.	−	414332.i	−0.00158426	−	0.000914672i
$769$	9.50262e7	−	1.64590e8i	0.208961	−	0.361930i	−0.742427	−	0.669927i	$-0.766325\pi$
$769$	9.50262e7	−	1.64590e8i	0.208961	−	0.361930i	0.951387	+	0.307997i	$0.0996586\pi$
$770$			1.15520e7i			0.0253037i
$771$	1.44250e6	−	2.49849e6i	0.00314741	−	0.00545148i
$772$	−2.04106e8			−0.443612
$773$			4.56501e8i			0.988333i	0.869367	+	0.494167i	$0.164527\pi$
$773$			4.56501e8i			0.988333i	−0.869367	+	0.494167i	$0.835473\pi$
$774$	−1.30889e8	−	7.96448e7i	−0.282281	−	0.171765i
$775$	−3.60751e8			−0.775001
$776$		−	3.40640e8i		−	0.728972i
$777$	4.30259e6	+	2.48410e6i	0.00917206	+	0.00529549i
$778$	1.86137e8			0.395270
$779$	−5.56608e8	−	3.21358e8i	−1.17744	−	0.679793i
$780$	552414.	−	956810.i	0.00116408	−	0.00201624i
$781$	−8.48484e8	+	4.89872e8i	−1.78111	+	1.02832i
$782$		−	3.83781e7i		−	0.0802534i
$783$	1.95645e6	+	3.38866e6i	0.00407552	+	0.00705900i
$784$	−1.32381e8	+	2.29291e8i	−0.274713	+	0.475816i
$785$	1.00855e8			0.208492
$786$	−436146.	−	251809.i	−0.000898183	−	0.000518566i
$787$	1.70805e8	+	2.95843e8i	0.350410	+	0.606927i	0.986321	−	0.164835i	$-0.0527091\pi$
$787$	1.70805e8	+	2.95843e8i	0.350410	+	0.606927i	−0.635912	+	0.771762i	$0.719376\pi$
$788$	1.91207e8	+	3.31181e8i	0.390774	+	0.676841i
$789$	6.74981e6	+	1.16910e7i	0.0137423	+	0.0238024i
$790$	3.47891e7			0.0705606
$791$	4.22508e7	+	7.31805e7i	0.0853700	+	0.147865i
$792$	3.41677e8	−	1.97267e8i	0.687764	−	0.397081i
$793$	3.49049e8	+	2.01523e8i	0.699949	+	0.404116i
$794$	−1.31943e8	−	7.61775e7i	−0.263588	−	0.152183i
$795$	−87523.3			−0.000174190
$796$			8.35355e7i			0.165627i
$797$	−4.46931e8	+	7.74107e8i	−0.882807	+	1.52907i	−0.0345997	+	0.999401i	$0.511016\pi$
$797$	−4.46931e8	+	7.74107e8i	−0.882807	+	1.52907i	−0.848207	+	0.529665i	$0.822318\pi$
$798$	1.21127e6	−	2.09798e6i	0.00238360	−	0.00412851i
$799$	−1.73485e8	−	3.00484e8i	−0.340111	−	0.589089i
$800$	3.70494e8	−	2.13905e8i	0.723621	−	0.417783i
$801$			4.29988e8i			0.836679i
$802$	8.89538e7	−	5.13575e7i	0.172441	−	0.0995591i
$803$	6.04027e8	−	3.48735e8i	1.16657	−	0.673518i
$804$	4.40854e6	−	2.54527e6i	0.00848255	−	0.00489740i
$805$	−7.73838e6	+	1.34033e7i	−0.0148341	+	0.0256935i
$806$			1.10998e8i			0.211988i
$807$	613667.	+	354301.i	0.00116765	+	0.000674142i
$808$	1.06509e8	−	6.14930e7i	0.201907	−	0.116571i
$809$	4.90399e8			0.926199			0.463099	−	0.886306i	$-0.346737\pi$
$809$	4.90399e8			0.926199			0.463099	+	0.886306i	$0.346737\pi$
$810$	−1.19038e7	−	2.06180e7i	−0.0223991	−	0.0387964i
$811$	7.60096e8	+	4.38842e8i	1.42497	+	0.822708i	0.996718	−	0.0809513i	$-0.0257958\pi$
$811$	7.60096e8	+	4.38842e8i	1.42497	+	0.822708i	0.428253	+	0.903659i	$0.359129\pi$
$812$	1.81821e7	−	3.14923e7i	0.0339606	−	0.0588215i
$813$			5.45134e6i			0.0101445i
$814$	1.14109e8	−	1.97642e8i	0.211566	−	0.366443i
$815$	−1.14579e8			−0.211657
$816$		−	4.34156e6i		−	0.00799052i
$817$	1.72207e7	−	7.47297e8i	0.0315780	−	1.37034i
$818$	−2.00412e8			−0.366154
$819$		−	1.97787e8i		−	0.360036i
$820$	−5.72573e7	−	3.30575e7i	−0.103846	−	0.0599555i
$821$	7.05864e7			0.127553			0.0637766	−	0.997964i	$-0.479685\pi$
$821$	7.05864e7			0.127553			0.0637766	+	0.997964i	$0.479685\pi$
$822$	5.98714e6	+	3.45668e6i	0.0107796	+	0.00622363i
$823$	−4.63268e8	+	8.02404e8i	−0.831062	+	1.43944i	0.0661357	+	0.997811i	$0.478933\pi$
$823$	−4.63268e8	+	8.02404e8i	−0.831062	+	1.43944i	−0.897197	+	0.441630i	$0.854400\pi$
$824$	1.19508e8	−	6.89981e7i	0.213607	−	0.123326i
$825$			1.66151e7i			0.0295897i
$826$	5.43818e7	+	9.41921e7i	0.0964970	+	0.167138i
$827$	2.07224e8	−	3.58923e8i	0.366374	−	0.634578i	−0.622622	−	0.782523i	$-0.713932\pi$
$827$	2.07224e8	−	3.58923e8i	0.366374	−	0.634578i	0.988996	+	0.147945i	$0.0472658\pi$
$828$	2.49010e8			0.438657
$829$	−5.02043e8	−	2.89855e8i	−0.881206	−	0.508764i	−0.0101500	−	0.999948i	$-0.503231\pi$
$829$	−5.02043e8	−	2.89855e8i	−0.881206	−	0.508764i	−0.871056	+	0.491184i	$0.836564\pi$
$830$	−1.05415e7	−	1.82583e7i	−0.0184360	−	0.0319321i
$831$	1.85144e6	+	3.20679e6i	0.00322631	+	0.00558814i
$832$	9.41465e7	+	1.63067e8i	0.163469	+	0.283136i
$833$	−2.28701e8			−0.395669
$834$	−665441.	−	1.15258e6i	−0.00114713	−	0.00198688i
$835$	−7.26299e7	+	4.19329e7i	−0.124754	+	0.0720270i
$836$	7.85280e8	+	4.53382e8i	1.34402	+	0.775970i
$837$	1.90109e7	+	1.09759e7i	0.0324210	+	0.0187183i
$838$	1.81242e8			0.307983
$839$		−	1.11031e9i		−	1.88001i	−0.341164	−	0.940004i	$-0.610821\pi$
$839$		−	1.11031e9i		−	1.88001i	0.341164	−	0.940004i	$-0.389179\pi$
$840$	264494.	−	458117.i	0.000446250	−	0.000772928i
$841$	−2.88623e8	+	4.99909e8i	−0.485224	+	0.840432i
$842$	4.92794e7	+	8.53544e7i	0.0825522	+	0.142985i
$843$	−534060.	+	308340.i	−0.000891471	+	0.000514691i
$844$			5.86281e7i			0.0975165i
$845$	2.41483e7	−	1.39420e7i	0.0400237	−	0.0231077i
$846$	−2.39266e8	+	1.38140e8i	−0.395157	+	0.228144i
$847$	1.43769e8	−	8.30054e7i	0.236601	−	0.136602i
$848$	1.12869e7	−	1.95494e7i	0.0185091	−	0.0320587i
$849$			2.55397e6i			0.00417342i
$850$	8.50225e7	+	4.90877e7i	0.138445	+	0.0799312i
$851$	2.64792e8	−	1.52877e8i	0.429651	−	0.248059i
$852$	2.11354e7			0.0341736
$853$	2.38180e8	+	4.12539e8i	0.383758	+	0.664688i	0.991596	−	0.129373i	$-0.0412963\pi$
$853$	2.38180e8	+	4.12539e8i	0.383758	+	0.664688i	−0.607838	+	0.794061i	$0.707963\pi$
$854$	7.87306e7	+	4.54552e7i	0.126407	+	0.0729810i
$855$	5.81076e7	−	1.00645e8i	0.0929683	−	0.161026i
$856$			2.59508e8i			0.413742i
$857$	−1.73295e8	+	3.00155e8i	−0.275323	+	0.476874i	−0.970217	−	0.242239i	$-0.922118\pi$
$857$	−1.73295e8	+	3.00155e8i	−0.275323	+	0.476874i	0.694893	+	0.719113i	$0.255452\pi$
$858$	5.11224e6			0.00809374
$859$			8.47499e8i			1.33709i	0.743673	+	0.668544i	$0.233082\pi$
$859$			8.47499e8i			1.33709i	−0.743673	+	0.668544i	$0.766918\pi$
$860$	1.77146e6	−	7.68731e7i	0.00278507	−	0.120859i
$861$	6.65990e6			0.0104342
$862$		−	1.20695e8i		−	0.188438i
$863$	−7.89728e8	−	4.55950e8i	−1.22870	−	0.709389i	−0.261941	−	0.965084i	$-0.584362\pi$
$863$	−7.89728e8	−	4.55950e8i	−1.22870	−	0.709389i	−0.966758	+	0.255695i	$0.917696\pi$
$864$	−2.60324e7			−0.0403621
$865$	−3.96884e7	−	2.29141e7i	−0.0613219	−	0.0354042i
$866$	−9.70190e7	+	1.68042e8i	−0.149384	+	0.258740i
$867$	−1.01366e7	+	5.85236e6i	−0.0155537	+	0.00897995i
$868$		−	2.04008e8i		−	0.311952i
$869$	−6.55849e8	−	1.13596e9i	−0.999412	−	1.73103i
$870$	60231.9	−	104325.i	9.14679e−5	−	0.000158427i
$871$	−2.48840e8			−0.376587
$872$	−2.86795e8	−	1.65581e8i	−0.432537	−	0.249725i
$873$	3.87732e8	+	6.71571e8i	0.582759	+	1.00937i
$874$	−7.45444e7	−	1.29115e8i	−0.111656	−	0.193393i
$875$	−3.99628e7	−	6.92176e7i	−0.0596529	−	0.103322i
$876$	−1.50461e7			−0.0223826
$877$	−4.29965e8	−	7.44722e8i	−0.637433	−	1.10407i	−0.985994	−	0.166780i	$-0.946663\pi$
$877$	−4.29965e8	−	7.44722e8i	−0.637433	−	1.10407i	0.348561	−	0.937286i	$-0.386670\pi$
$878$	3.06892e8	−	1.77184e8i	0.453421	−	0.261783i
$879$	9.29006e6	+	5.36362e6i	0.0136789	+	0.00789753i
$880$	6.96502e7	+	4.02125e7i	0.102205	+	0.0590083i
$881$	−4.18104e7			−0.0611444			−0.0305722	−	0.999533i	$-0.509733\pi$
$881$	−4.18104e7			−0.0611444			−0.0305722	+	0.999533i	$0.509733\pi$
$882$			1.82107e8i			0.265412i
$883$	2.83339e8	−	4.90758e8i	0.411552	−	0.712829i	−0.583508	−	0.812108i	$-0.698320\pi$
$883$	2.83339e8	−	4.90758e8i	0.411552	−	0.712829i	0.995060	+	0.0992787i	$0.0316535\pi$
$884$	−1.23071e8	+	2.13165e8i	−0.178155	+	0.308574i
$885$	−1.46795e6	−	2.54256e6i	−0.00211778	−	0.00366810i
$886$	−3.26261e8	+	1.88367e8i	−0.469099	+	0.270834i
$887$		−	1.34051e9i		−	1.92088i	−0.278486	−	0.960440i	$-0.589833\pi$
$887$		−	1.34051e9i		−	1.92088i	0.278486	−	0.960440i	$-0.410167\pi$
$888$	−9.05044e6	+	5.22528e6i	−0.0129250	+	0.00746226i
$889$	1.10894e8	−	6.40245e7i	0.157834	−	0.0911257i
$890$	2.29349e7	−	1.32415e7i	0.0325333	−	0.0187831i
$891$	−4.48824e8	+	7.77385e8i	−0.634516	+	1.09901i
$892$		−	9.89531e8i		−	1.39423i
$893$	−1.16730e9	−	6.73942e8i	−1.63919	−	0.946386i
$894$	8.46350e6	−	4.88641e6i	0.0118451	−	0.00683875i
$895$	−5.57212e7			−0.0777233
$896$	1.57046e8	+	2.72012e8i	0.218325	+	0.378150i
$897$	5.93153e6	+	3.42457e6i	0.00821844	+	0.00474492i
$898$	−1.12500e8	+	1.94856e8i	−0.155354	+	0.269082i
$899$		−	9.86169e7i		−	0.135729i
$900$	−3.18497e8	+	5.51653e8i	−0.436896	+	0.756726i
$901$	1.94991e7			0.0266587
$902$		−	3.05926e8i		−	0.416867i
$903$	3.71725e6	+	6.79536e6i	0.00504846	+	0.00922888i
$904$	−1.77748e8			−0.240602
$905$		−	5.68503e7i		−	0.0766985i
$906$	−4.67141e6	−	2.69704e6i	−0.00628151	−	0.00362663i
$907$	−3.63373e8			−0.487002			−0.243501	−	0.969901i	$-0.578296\pi$
$907$	−3.63373e8			−0.487002			−0.243501	+	0.969901i	$0.578296\pi$
$908$	−5.12993e8	−	2.96177e8i	−0.685258	−	0.395634i
$909$	−1.39988e8	+	2.42467e8i	−0.186380	+	0.322820i
$910$	−1.05497e7	+	6.09086e6i	−0.0139996	+	0.00808266i
$911$			4.11096e8i			0.543736i	0.962334	+	0.271868i	$0.0876415\pi$
$911$			4.11096e8i			0.543736i	−0.962334	+	0.271868i	$0.912359\pi$
$912$	−8.43291e6	−	1.46062e7i	−0.0111171	−	0.0192554i
$913$	−3.97458e8	+	6.88417e8i	−0.522250	+	0.904563i
$914$	−9.54286e6			−0.0124980
$915$	−2.12520e6	−	1.22699e6i	−0.00277419	−	0.00160168i
$916$	3.38020e8	+	5.85467e8i	0.439800	+	0.761756i
$917$	−2.26234e7	−	3.91850e7i	−0.0293394	−	0.0508173i
$918$	−2.98701e6	−	5.17366e6i	−0.00386108	−	0.00668759i
$919$	7.87128e8			1.01414			0.507071	−	0.861904i	$-0.330728\pi$
$919$	7.87128e8			1.01414			0.507071	+	0.861904i	$0.330728\pi$
$920$	−1.62776e7	−	2.81936e7i	−0.0209039	−	0.0362066i
$921$	2.48088e7	−	1.43234e7i	0.0317560	−	0.0183344i
$922$	9.04164e7	+	5.22020e7i	0.115360	+	0.0666030i
$923$	−8.94739e8	−	5.16578e8i	−1.13787	−	0.656948i
$924$	−9.39599e6			−0.0119104
$925$			7.82155e8i			0.988252i
$926$	−7.00181e7	+	1.21275e8i	−0.0881815	+	0.152735i
$927$	−1.57074e8	+	2.72059e8i	−0.197180	+	0.341527i
$928$	5.84742e7	+	1.01280e8i	0.0731679	+	0.126731i
$929$	5.70995e8	−	3.29664e8i	0.712172	−	0.411173i	−0.0996927	−	0.995018i	$-0.531786\pi$
$929$	5.70995e8	−	3.29664e8i	0.712172	−	0.411173i	0.811865	+	0.583846i	$0.198453\pi$
$930$		−	675819.i		−	0.000840197i
$931$	−7.69413e8	+	4.44221e8i	−0.953478	+	0.550491i
$932$	8.20073e8	−	4.73470e8i	1.01299	−	0.584850i
$933$	−1.88074e7	+	1.08585e7i	−0.0231571	+	0.0133698i
$934$	−2.40997e8	+	4.17419e8i	−0.295781	+	0.512308i
$935$			6.94708e7i			0.0849899i
$936$	3.60303e8	+	2.08021e8i	0.439380	+	0.253676i
$937$	9.54000e8	−	5.50792e8i	1.15966	−	0.669528i	0.208435	−	0.978036i	$-0.433163\pi$
$937$	9.54000e8	−	5.50792e8i	1.15966	−	0.669528i	0.951222	+	0.308508i	$0.0998297\pi$
$938$	−5.61278e7			−0.0680094
$939$	−4.18521e6	−	7.24900e6i	−0.00505499	−	0.00875551i
$940$	−1.20078e8	−	6.93272e7i	−0.144571	−	0.0834681i
$941$	4.29023e8	−	7.43089e8i	0.514886	−	0.891809i	−0.484965	−	0.874534i	$-0.661168\pi$
$941$	4.29023e8	−	7.43089e8i	0.514886	−	0.891809i	0.999851	−	0.0172752i	$-0.00549915\pi$
$942$		−	1.00673e7i		−	0.0120437i
$943$	2.04933e8	−	3.54954e8i	0.244386	−	0.423289i
$944$	7.57216e8			0.900127
$945$			2.40915e6i			0.00285475i
$946$	3.12149e8	−	1.70754e8i	0.368713	−	0.201696i
$947$	−1.30277e9			−1.53397			−0.766986	−	0.641663i	$-0.778245\pi$
$947$	−1.30277e9			−1.53397			−0.766986	+	0.641663i	$0.778245\pi$
$948$			2.82964e7i			0.0332128i
$949$	6.36956e8	+	3.67747e8i	0.745265	+	0.430279i
$950$	3.81386e8			0.444830
$951$	−3.05118e7	−	1.76160e7i	−0.0354753	−	0.0204817i
$952$	−5.89260e7	+	1.02063e8i	−0.0682961	+	0.118292i
$953$	−3.44188e8	+	1.98717e8i	−0.397665	+	0.229592i	−0.685476	−	0.728095i	$-0.740406\pi$
$953$	−3.44188e8	+	1.98717e8i	−0.397665	+	0.229592i	0.287811	+	0.957687i	$0.407073\pi$
$954$		−	1.55265e7i		−	0.0178825i
$955$	−9.30745e6	−	1.61210e7i	−0.0106861	−	0.0185089i
$956$	−3.25665e8	+	5.64069e8i	−0.372733	+	0.645592i
$957$	−4.54199e6			−0.00518216
$958$	−3.81015e8	−	2.19979e8i	−0.433357	−	0.250199i
$959$	3.10560e8	+	5.37906e8i	0.352120	+	0.609889i
$960$	−573216.	−	992839.i	−0.000647895	−	0.00112219i
$961$	1.67125e8	+	2.89468e8i	0.188309	+	0.326160i
$962$	2.40659e8			0.270319
$963$	−2.95384e8	−	5.11620e8i	−0.330756	−	0.572887i
$964$	8.39452e8	−	4.84658e8i	0.937054	−	0.541008i
$965$	−5.26085e7	−	3.03735e7i	−0.0585428	−	0.0337997i
$966$	1.33790e6	+	772438.i	0.00148420	+	0.000856905i
$967$	−1.00383e9			−1.11015			−0.555075	−	0.831800i	$-0.687311\pi$
$967$	−1.00383e9			−1.11015			−0.555075	+	0.831800i	$0.687311\pi$
$968$			3.49201e8i			0.384990i
$969$	7.28430e6	−	1.26168e7i	0.00800602	−	0.0138668i
$970$	2.38804e7	−	4.13621e7i	0.0261654	−	0.0453198i
$971$	−1.89341e8	−	3.27949e8i	−0.206818	−	0.358219i	0.743893	−	0.668299i	$-0.232977\pi$
$971$	−1.89341e8	−	3.27949e8i	−0.206818	−	0.358219i	−0.950710	+	0.310080i	$0.899644\pi$
$972$	5.03573e7	−	2.90738e7i	0.0548357	−	0.0316594i
$973$		−	1.19571e8i		−	0.129804i
$974$	−3.92224e8	+	2.26451e8i	−0.424480	+	0.245074i
$975$	−1.51735e7	+	8.76043e6i	−0.0163709	+	0.00945174i
$976$	5.48125e8	−	3.16460e8i	0.589563	−	0.340385i
$977$	2.40955e7	−	4.17347e7i	0.0258377	−	0.0447521i	−0.852817	−	0.522209i	$-0.825108\pi$
$977$	2.40955e7	−	4.17347e7i	0.0258377	−	0.0447521i	0.878655	+	0.477457i	$0.158441\pi$
$978$			1.14372e7i			0.0122265i
$979$	−8.64744e8	−	4.99260e8i	−0.921594	−	0.532083i
$980$	−7.91482e7	+	4.56962e7i	−0.0840936	+	0.0485514i
$981$	7.53889e8			0.798547
$982$	2.06549e8	+	3.57754e8i	0.218117	+	0.377790i
$983$	1.10591e9	+	6.38498e8i	1.16429	+	0.672201i	0.952327	−	0.305078i	$-0.0986825\pi$
$983$	1.10591e9	+	6.38498e8i	1.16429	+	0.672201i	0.211959	+	0.977279i	$0.432016\pi$
$984$	−7.00450e6	+	1.21322e7i	−0.00735177	+	0.0127336i
$985$			1.13816e8i			0.119096i
$986$	−1.34189e7	+	2.32422e7i	−0.0139986	+	0.0242464i
$987$	1.39669e7			0.0145261
$988$			9.56196e8i			0.991462i
$989$	4.76558e8	+	1.09818e7i	0.492637	+	0.0113523i
$990$	5.53173e7			0.0570106
$991$		−	2.64106e8i		−	0.271367i	−0.990752	−	0.135683i	$-0.956677\pi$
$991$		−	2.64106e8i		−	0.271367i	0.990752	−	0.135683i	$-0.0433230\pi$
$992$	5.68197e8	+	3.28049e8i	0.582055	+	0.336050i
$993$	−1.18816e7			−0.0121347
$994$	−2.01815e8	−	1.16518e8i	−0.205492	−	0.118641i
$995$	−1.24311e7	+	2.15313e7i	−0.0126195	+	0.0218576i
$996$	1.48508e7	−	8.57409e6i	0.0150304	−	0.00867781i
$997$		−	1.59148e7i		−	0.0160589i	−0.999968	−	0.00802946i	$-0.997444\pi$
$997$		−	1.59148e7i		−	0.0160589i	0.999968	−	0.00802946i	$-0.00255588\pi$
$998$	−8.04789e7	−	1.39394e8i	−0.0809637	−	0.140233i
$999$	2.37973e7	−	4.12181e7i	0.0238688	−	0.0413420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.d.a.37.13	yes	42
43.7	odd	6	inner	43.7.d.a.7.9	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.d.a.7.9	✓	42	43.7	odd	6	inner
43.7.d.a.37.13	yes	42	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.64495i q^{2} +(-0.554504 - 0.320143i) q^{3} +57.0043 q^{4} +(14.6929 + 8.48295i) q^{5} +(0.846761 - 1.46663i) q^{6} +(131.768 - 76.0760i) q^{7} +320.050i q^{8} +(-364.295 - 630.977i) q^{9} +O(q^{10})\)	\(q+2.64495i q^{2} +(-0.554504 - 0.320143i) q^{3} +57.0043 q^{4} +(14.6929 + 8.48295i) q^{5} +(0.846761 - 1.46663i) q^{6} +(131.768 - 76.0760i) q^{7} +320.050i q^{8} +(-364.295 - 630.977i) q^{9} +(-22.4370 + 38.8619i) q^{10} +1691.94 q^{11} +(-31.6091 - 18.2495i) q^{12} +(892.086 + 1545.14i) q^{13} +(201.217 + 348.518i) q^{14} +(-5.43151 - 9.40766i) q^{15} +2801.76 q^{16} +(1210.07 + 2095.91i) q^{17} +(1668.90 - 963.541i) q^{18} +(8142.05 + 4700.81i) q^{19} +(837.558 + 483.564i) q^{20} -97.4208 q^{21} +4475.08i q^{22} +(-2997.75 + 5192.26i) q^{23} +(102.462 - 177.469i) q^{24} +(-7668.58 - 13282.4i) q^{25} +(-4086.81 + 2359.52i) q^{26} +933.274i q^{27} +(7511.31 - 4336.66i) q^{28} +(3630.94 - 2096.33i) q^{29} +(24.8827 - 14.3661i) q^{30} +(11760.7 - 20370.1i) q^{31} +27893.7i q^{32} +(-938.184 - 541.661i) q^{33} +(-5543.56 + 3200.58i) q^{34} +2581.40 q^{35} +(-20766.4 - 35968.4i) q^{36} +(-44165.0 - 25498.7i) q^{37} +(-12433.4 + 21535.3i) q^{38} -1142.38i q^{39} +(-2714.97 + 4702.46i) q^{40} -68362.2 q^{41} -257.673i q^{42} +(-38156.7 - 69752.6i) q^{43} +96447.5 q^{44} -12361.2i q^{45} +(-13733.2 - 7928.89i) q^{46} -143367. q^{47} +(-1553.59 - 896.963i) q^{48} +(-47249.4 + 81838.3i) q^{49} +(35131.1 - 20283.0i) q^{50} -1549.58i q^{51} +(50852.7 + 88079.5i) q^{52} +(4028.49 - 6977.56i) q^{53} -2468.46 q^{54} +(24859.4 + 14352.6i) q^{55} +(24348.1 + 42172.2i) q^{56} +(-3009.86 - 5213.23i) q^{57} +(5544.67 + 9603.65i) q^{58} +270265. q^{59} +(-309.619 - 536.276i) q^{60} +(195636. - 112951. i) q^{61} +(53877.8 + 31106.4i) q^{62} +(-96004.5 - 55428.2i) q^{63} +105535. q^{64} +30270.1i q^{65} +(1432.66 - 2481.45i) q^{66} +(-69735.4 + 120785. i) q^{67} +(68979.3 + 119476. i) q^{68} +(3324.53 - 1919.42i) q^{69} +6827.66i q^{70} +(-501487. + 289534. i) q^{71} +(201944. - 116593. i) q^{72} +(357004. - 206116. i) q^{73} +(67442.7 - 116814. i) q^{74} +9820.16i q^{75} +(464131. + 267966. i) q^{76} +(222942. - 128716. i) q^{77} +3021.53 q^{78} +(-387632. - 671399. i) q^{79} +(41166.0 + 23767.2i) q^{80} +(-265272. + 459465. i) q^{81} -180814. i q^{82} +(-234913. + 406881. i) q^{83} -5553.40 q^{84} +41059.9i q^{85} +(184492. - 100922. i) q^{86} -2684.49 q^{87} +541504. i q^{88} +(-511098. - 295082. i) q^{89} +32694.7 q^{90} +(235096. + 135733. i) q^{91} +(-170885. + 295981. i) q^{92} +(-13042.7 + 7530.20i) q^{93} -379198. i q^{94} +(79753.5 + 138137. i) q^{95} +(8929.96 - 15467.1i) q^{96} -1.06433e6 q^{97} +(-216458. - 124972. i) q^{98} +(-616364. - 1.06757e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Introduction

L-functions

Modular forms

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