LMFDB - Embedded newform 48.6.j.a.13.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,6,Mod(13,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, 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:	$7.69842335102$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.17
Character	$\chi$	$=$	48.13
Dual form			48.6.j.a.37.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.81279 + 2.97273i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(14.3258 + 28.6142i) q^{4} +(-30.6986 + 30.6986i) q^{5} +(-11.7101 - 49.5467i) q^{6} +92.2922i q^{7} +(-16.1150 + 180.301i) q^{8} +81.0000i q^{9} +O(q^{10})$	\(q+(4.81279 + 2.97273i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(14.3258 + 28.6142i) q^{4} +(-30.6986 + 30.6986i) q^{5} +(-11.7101 - 49.5467i) q^{6} +92.2922i q^{7} +(-16.1150 + 180.301i) q^{8} +81.0000i q^{9} +(-239.005 + 56.4873i) q^{10} +(-246.823 + 246.823i) q^{11} +(90.9306 - 273.268i) q^{12} +(296.592 + 296.592i) q^{13} +(-274.359 + 444.182i) q^{14} +390.730 q^{15} +(-613.542 + 819.843i) q^{16} +554.315 q^{17} +(-240.791 + 389.836i) q^{18} +(-574.858 - 574.858i) q^{19} +(-1318.20 - 438.633i) q^{20} +(587.344 - 587.344i) q^{21} +(-1921.64 + 454.169i) q^{22} -4121.02i q^{23} +(1249.98 - 1044.87i) q^{24} +1240.19i q^{25} +(545.747 + 2309.12i) q^{26} +(515.481 - 515.481i) q^{27} +(-2640.86 + 1322.16i) q^{28} +(1672.84 + 1672.84i) q^{29} +(1880.50 + 1161.53i) q^{30} +10212.1 q^{31} +(-5390.01 + 2121.83i) q^{32} +3141.54 q^{33} +(2667.80 + 1647.83i) q^{34} +(-2833.24 - 2833.24i) q^{35} +(-2317.75 + 1160.39i) q^{36} +(235.481 - 235.481i) q^{37} +(-1057.77 - 4475.56i) q^{38} -3775.00i q^{39} +(-5040.27 - 6029.69i) q^{40} +542.980i q^{41} +(4572.77 - 1080.75i) q^{42} +(10422.1 - 10422.1i) q^{43} +(-10598.6 - 3526.69i) q^{44} +(-2486.59 - 2486.59i) q^{45} +(12250.7 - 19833.6i) q^{46} -4005.66 q^{47} +(9122.01 - 1312.89i) q^{48} +8289.16 q^{49} +(-3686.74 + 5968.76i) q^{50} +(-3527.64 - 3527.64i) q^{51} +(-4237.82 + 12735.7i) q^{52} +(-19966.8 + 19966.8i) q^{53} +(4013.28 - 948.516i) q^{54} -15154.2i q^{55} +(-16640.3 - 1487.29i) q^{56} +7316.75i q^{57} +(3078.13 + 13023.9i) q^{58} +(-29969.7 + 29969.7i) q^{59} +(5597.52 + 11180.4i) q^{60} +(15383.3 + 15383.3i) q^{61} +(49148.8 + 30357.9i) q^{62} -7475.66 q^{63} +(-32248.6 - 5811.10i) q^{64} -18209.9 q^{65} +(15119.6 + 9338.94i) q^{66} +(5107.14 + 5107.14i) q^{67} +(7941.02 + 15861.3i) q^{68} +(-26226.0 + 26226.0i) q^{69} +(-5213.34 - 22058.2i) q^{70} -54221.0i q^{71} +(-14604.3 - 1305.32i) q^{72} +83035.8i q^{73} +(1833.34 - 433.300i) q^{74} +(7892.51 - 7892.51i) q^{75} +(8213.78 - 24684.4i) q^{76} +(-22779.8 - 22779.8i) q^{77} +(11222.0 - 18168.3i) q^{78} +14255.0 q^{79} +(-6333.14 - 44003.0i) q^{80} -6561.00 q^{81} +(-1614.13 + 2613.25i) q^{82} +(-28755.5 - 28755.5i) q^{83} +(25220.5 + 8392.18i) q^{84} +(-17016.7 + 17016.7i) q^{85} +(81141.7 - 19177.4i) q^{86} -21291.8i q^{87} +(-40524.7 - 48479.8i) q^{88} +48613.0i q^{89} +(-4575.47 - 19359.4i) q^{90} +(-27373.1 + 27373.1i) q^{91} +(117920. - 59036.9i) q^{92} +(-64989.6 - 64989.6i) q^{93} +(-19278.4 - 11907.7i) q^{94} +35294.7 q^{95} +(47805.1 + 20798.6i) q^{96} +132198. q^{97} +(39893.9 + 24641.4i) q^{98} +(-19992.6 - 19992.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 492 q^{8}+O(q^{10}) $ 40 * q + 44 * q^4 - 492 * q^8	\( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 492 * q^8 + 968 * q^10 + 1208 * q^11 - 792 * q^12 + 324 * q^14 - 1800 * q^15 - 384 * q^16 - 324 * q^18 + 2360 * q^19 - 7600 * q^20 - 1024 * q^22 + 5220 * q^24 - 12980 * q^26 + 10472 * q^28 - 8144 * q^29 - 1368 * q^30 + 23064 * q^31 + 44160 * q^32 + 4864 * q^34 - 4776 * q^35 - 1620 * q^36 + 21296 * q^37 - 72088 * q^38 - 90864 * q^40 - 14220 * q^42 + 31416 * q^43 + 43768 * q^44 + 90664 * q^46 + 44784 * q^48 - 96040 * q^49 + 106212 * q^50 + 10440 * q^51 - 116432 * q^52 - 49456 * q^53 - 14580 * q^54 - 158592 * q^56 - 111472 * q^58 + 28960 * q^59 + 49464 * q^60 + 48080 * q^61 + 191100 * q^62 + 31752 * q^63 + 369032 * q^64 - 55376 * q^65 + 63720 * q^66 + 101488 * q^67 - 122336 * q^68 - 22320 * q^69 - 460192 * q^70 - 28836 * q^72 - 94996 * q^74 - 96624 * q^75 + 211304 * q^76 - 14896 * q^77 + 200124 * q^78 - 71960 * q^79 + 623368 * q^80 - 262440 * q^81 + 33880 * q^82 - 126440 * q^83 - 116856 * q^84 + 132400 * q^85 - 581168 * q^86 - 466400 * q^88 - 46008 * q^90 + 429496 * q^91 - 12752 * q^92 + 524120 * q^94 - 76848 * q^95 + 51840 * q^96 + 477736 * q^98 + 97848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	4.81279	+	2.97273i	0.850788	+	0.525509i
$2$	4.81279	+	2.97273i	0.850788	+	0.525509i
$3$	−6.36396	−	6.36396i	−0.408248	−	0.408248i
$3$	−6.36396	−	6.36396i	−0.408248	−	0.408248i
$4$	14.3258	+	28.6142i	0.447682	+	0.894193i
$5$	−30.6986	+	30.6986i	−0.549154	+	0.549154i	−0.926196	−	0.377042i	$-0.876941\pi$
$5$	−30.6986	+	30.6986i	−0.549154	+	0.549154i	0.377042	+	0.926196i	$0.376941\pi$
$6$	−11.7101	−	49.5467i	−0.132795	−	0.561871i
$7$			92.2922i			0.711901i	0.934505	+	0.355951i	$0.115843\pi$
$7$			92.2922i			0.711901i	−0.934505	+	0.355951i	$0.884157\pi$
$8$	−16.1150	+	180.301i	−0.0890238	+	0.996029i
$9$			81.0000i			0.333333i
$10$	−239.005	+	56.4873i	−0.755799	+	0.178629i
$11$	−246.823	+	246.823i	−0.615040	+	0.615040i	−0.944255	−	0.329215i	$-0.893216\pi$
$11$	−246.823	+	246.823i	−0.615040	+	0.615040i	0.329215	+	0.944255i	$0.393216\pi$
$12$	90.9306	−	273.268i	0.182288	−	0.547818i
$13$	296.592	+	296.592i	0.486745	+	0.486745i	0.907277	−	0.420533i	$-0.138157\pi$
$13$	296.592	+	296.592i	0.486745	+	0.486745i	−0.420533	+	0.907277i	$0.638157\pi$
$14$	−274.359	+	444.182i	−0.374110	+	0.605677i
$15$	390.730			0.448382
$16$	−613.542	+	819.843i	−0.599162	+	0.800628i
$17$	554.315			0.465195			0.232597	−	0.972573i	$-0.425278\pi$
$17$	554.315			0.465195			0.232597	+	0.972573i	$0.425278\pi$
$18$	−240.791	+	389.836i	−0.175170	+	0.283596i
$19$	−574.858	−	574.858i	−0.365323	−	0.365323i	0.500445	−	0.865768i	$-0.333170\pi$
$19$	−574.858	−	574.858i	−0.365323	−	0.365323i	−0.865768	+	0.500445i	$0.833170\pi$
$20$	−1318.20	−	438.633i	−0.736896	−	0.245203i
$21$	587.344	−	587.344i	0.290632	−	0.290632i
$22$	−1921.64	+	454.169i	−0.846478	+	0.200060i
$23$		−	4121.02i		−	1.62437i	−0.583400	−	0.812185i	$-0.698278\pi$
$23$		−	4121.02i		−	1.62437i	0.583400	−	0.812185i	$-0.301722\pi$
$24$	1249.98	−	1044.87i	0.442971	−	0.370284i
$25$			1240.19i			0.396860i
$26$	545.747	+	2309.12i	0.158328	+	0.669905i
$27$	515.481	−	515.481i	0.136083	−	0.136083i
$28$	−2640.86	+	1322.16i	−0.636577	+	0.318705i
$29$	1672.84	+	1672.84i	0.369369	+	0.369369i	0.867247	−	0.497878i	$-0.165887\pi$
$29$	1672.84	+	1672.84i	0.369369	+	0.369369i	−0.497878	+	0.867247i	$0.665887\pi$
$30$	1880.50	+	1161.53i	0.381478	+	0.235629i
$31$	10212.1			1.90859			0.954294	−	0.298869i	$-0.0966094\pi$
$31$	10212.1			1.90859			0.954294	+	0.298869i	$0.0966094\pi$
$32$	−5390.01	+	2121.83i	−0.930497	+	0.366300i
$33$	3141.54			0.502178
$34$	2667.80	+	1647.83i	0.395782	+	0.244464i
$35$	−2833.24	−	2833.24i	−0.390943	−	0.390943i
$36$	−2317.75	+	1160.39i	−0.298064	+	0.149227i
$37$	235.481	−	235.481i	0.0282782	−	0.0282782i	−0.692826	−	0.721105i	$-0.743635\pi$
$37$	235.481	−	235.481i	0.0282782	−	0.0282782i	0.721105	+	0.692826i	$0.243635\pi$
$38$	−1057.77	−	4475.56i	−0.118832	−	0.502792i
$39$		−	3775.00i		−	0.397425i
$40$	−5040.27	−	6029.69i	−0.498086	−	0.595861i
$41$			542.980i			0.0504457i	0.999682	+	0.0252229i	$0.00802953\pi$
$41$			542.980i			0.0504457i	−0.999682	+	0.0252229i	$0.991970\pi$
$42$	4572.77	−	1080.75i	0.399996	−	0.0945369i
$43$	10422.1	−	10422.1i	0.859579	−	0.859579i	−0.131710	−	0.991288i	$-0.542047\pi$
$43$	10422.1	−	10422.1i	0.859579	−	0.859579i	0.991288	+	0.131710i	$0.0420466\pi$
$44$	−10598.6	−	3526.69i	−0.825307	−	0.274622i
$45$	−2486.59	−	2486.59i	−0.183051	−	0.183051i
$46$	12250.7	−	19833.6i	0.853620	−	1.38199i
$47$	−4005.66			−0.264503			−0.132251	−	0.991216i	$-0.542221\pi$
$47$	−4005.66			−0.264503			−0.132251	+	0.991216i	$0.542221\pi$
$48$	9122.01	−	1312.89i	0.571462	−	0.0822478i
$49$	8289.16			0.493197
$50$	−3686.74	+	5968.76i	−0.208553	+	0.337644i
$51$	−3527.64	−	3527.64i	−0.189915	−	0.189915i
$52$	−4237.82	+	12735.7i	−0.217337	+	0.653150i
$53$	−19966.8	+	19966.8i	−0.976378	+	0.976378i	−0.999727	−	0.0233497i	$-0.992567\pi$
$53$	−19966.8	+	19966.8i	−0.976378	+	0.976378i	0.0233497	+	0.999727i	$0.492567\pi$
$54$	4013.28	−	948.516i	0.187290	−	0.0442650i
$55$		−	15154.2i		−	0.675503i
$56$	−16640.3	−	1487.29i	−0.709075	−	0.0633762i
$57$			7316.75i			0.298285i
$58$	3078.13	+	13023.9i	0.120148	+	0.508361i
$59$	−29969.7	+	29969.7i	−1.12086	+	1.12086i	−0.129249	+	0.991612i	$0.541257\pi$
$59$	−29969.7	+	29969.7i	−1.12086	+	1.12086i	−0.991612	+	0.129249i	$0.958743\pi$
$60$	5597.52	+	11180.4i	0.200732	+	0.400940i
$61$	15383.3	+	15383.3i	0.529328	+	0.529328i	0.920372	−	0.391044i	$-0.127886\pi$
$61$	15383.3	+	15383.3i	0.529328	+	0.529328i	−0.391044	+	0.920372i	$0.627886\pi$
$62$	49148.8	+	30357.9i	1.62380	+	1.00298i
$63$	−7475.66			−0.237300
$64$	−32248.6	−	5811.10i	−0.984150	−	0.177341i
$65$	−18209.9			−0.534595
$66$	15119.6	+	9338.94i	0.427247	+	0.263899i
$67$	5107.14	+	5107.14i	0.138992	+	0.138992i	0.773180	−	0.634187i	$-0.218665\pi$
$67$	5107.14	+	5107.14i	0.138992	+	0.138992i	−0.634187	+	0.773180i	$0.718665\pi$
$68$	7941.02	+	15861.3i	0.208259	+	0.415974i
$69$	−26226.0	+	26226.0i	−0.663146	+	0.663146i
$70$	−5213.34	−	22058.2i	−0.127166	−	0.538054i
$71$		−	54221.0i		−	1.27650i	−0.769828	−	0.638252i	$-0.779658\pi$
$71$		−	54221.0i		−	1.27650i	0.769828	−	0.638252i	$-0.220342\pi$
$72$	−14604.3	−	1305.32i	−0.332010	−	0.0296746i
$73$			83035.8i			1.82372i	0.410501	+	0.911860i	$0.365354\pi$
$73$			83035.8i			1.82372i	−0.410501	+	0.911860i	$0.634646\pi$
$74$	1833.34	−	433.300i	0.0389192	−	0.00919833i
$75$	7892.51	−	7892.51i	0.162017	−	0.162017i
$76$	8213.78	−	24684.4i	0.163121	−	0.490217i
$77$	−22779.8	−	22779.8i	−0.437848	−	0.437848i
$78$	11222.0	−	18168.3i	0.208850	−	0.338125i
$79$	14255.0			0.256981			0.128490	−	0.991711i	$-0.458987\pi$
$79$	14255.0			0.256981			0.128490	+	0.991711i	$0.458987\pi$
$80$	−6333.14	−	44003.0i	−0.110635	−	0.768700i
$81$	−6561.00			−0.111111
$82$	−1614.13	+	2613.25i	−0.0265096	+	0.0429186i
$83$	−28755.5	−	28755.5i	−0.458169	−	0.458169i	0.439885	−	0.898054i	$-0.355019\pi$
$83$	−28755.5	−	28755.5i	−0.458169	−	0.458169i	−0.898054	+	0.439885i	$0.855019\pi$
$84$	25220.5	+	8392.18i	0.389992	+	0.129771i
$85$	−17016.7	+	17016.7i	−0.255463	+	0.255463i
$86$	81141.7	−	19177.4i	1.18304	−	0.279604i
$87$		−	21291.8i		−	0.301588i
$88$	−40524.7	−	48479.8i	−0.557845	−	0.667351i
$89$			48613.0i			0.650545i	0.945620	+	0.325272i	$0.105456\pi$
$89$			48613.0i			0.650545i	−0.945620	+	0.325272i	$0.894544\pi$
$90$	−4575.47	−	19359.4i	−0.0595429	−	0.251933i
$91$	−27373.1	+	27373.1i	−0.346514	+	0.346514i
$92$	117920.	−	59036.9i	1.45250	−	0.727200i
$93$	−64989.6	−	64989.6i	−0.779178	−	0.779178i
$94$	−19278.4	−	11907.7i	−0.225036	−	0.138998i
$95$	35294.7			0.401237
$96$	47805.1	+	20798.6i	0.529415	+	0.230333i
$97$	132198.			1.42658			0.713289	−	0.700870i	$-0.247205\pi$
$97$	132198.			1.42658			0.713289	+	0.700870i	$0.247205\pi$
$98$	39893.9	+	24641.4i	0.419606	+	0.259179i
$99$	−19992.6	−	19992.6i	−0.205013	−	0.205013i
$100$	−35487.0	+	17766.7i	−0.354870	+	0.177667i
$101$	104990.	−	104990.i	1.02410	−	1.02410i	0.0244019	−	0.999702i	$-0.492232\pi$
$101$	104990.	−	104990.i	1.02410	−	1.02410i	0.999702	−	0.0244019i	$-0.00776813\pi$
$102$	−6491.07	−	27464.5i	−0.0617755	−	0.261379i
$103$		−	91609.4i		−	0.850838i	−0.904996	−	0.425419i	$-0.860127\pi$
$103$		−	91609.4i		−	0.850838i	0.904996	−	0.425419i	$-0.139873\pi$
$104$	−58255.3	+	48696.1i	−0.528144	+	0.441480i
$105$			36061.3i			0.319204i
$106$	−155451.	+	36740.0i	−1.34379	+	0.317596i
$107$	−83886.5	+	83886.5i	−0.708325	+	0.708325i	−0.966183	−	0.257858i	$-0.916983\pi$
$107$	−83886.5	+	83886.5i	−0.708325	+	0.708325i	0.257858	+	0.966183i	$0.416983\pi$
$108$	22134.7	+	7365.38i	0.182606	+	0.0607625i
$109$	−118359.	−	118359.i	−0.954192	−	0.954192i	0.0448042	−	0.998996i	$-0.485734\pi$
$109$	−118359.	−	118359.i	−0.954192	−	0.954192i	−0.998996	+	0.0448042i	$0.985734\pi$
$110$	45049.4	−	72934.1i	0.354983	−	0.574710i
$111$	−2997.19			−0.0230891
$112$	−75665.0	−	56625.1i	−0.569968	−	0.426544i
$113$	257693.			1.89848			0.949241	−	0.314550i	$-0.101854\pi$
$113$	257693.			1.89848			0.949241	+	0.314550i	$0.101854\pi$
$114$	−21750.7	+	35213.9i	−0.156751	+	0.253777i
$115$	126510.	+	126510.i	0.892029	+	0.892029i
$116$	−23902.2	+	71831.8i	−0.164927	+	0.495646i
$117$	−24024.0	+	24024.0i	−0.162248	+	0.162248i
$118$	−233329.	+	55146.0i	−1.54264	+	0.364594i
$119$			51159.0i			0.331173i
$120$	−6296.62	+	70448.8i	−0.0399167	+	0.446602i
$121$			39208.1i			0.243451i
$122$	28306.2	+	119767.i	0.172180	+	0.728512i
$123$	3455.50	−	3455.50i	0.0205944	−	0.0205944i
$124$	146297.	+	292212.i	0.854440	+	1.70665i
$125$	−134005.	−	134005.i	−0.767091	−	0.767091i
$126$	−35978.8	−	22223.1i	−0.201892	−	0.124703i
$127$	300733.			1.65452			0.827260	−	0.561820i	$-0.189899\pi$
$127$	300733.			1.65452			0.827260	+	0.561820i	$0.189899\pi$
$128$	−137931.	−	123834.i	−0.744109	−	0.668058i
$129$	−132652.			−0.701843
$130$	−87640.6	−	54133.2i	−0.454828	−	0.280934i
$131$	125326.	+	125326.i	0.638060	+	0.638060i	0.950077	−	0.312017i	$-0.101005\pi$
$131$	125326.	+	125326.i	0.638060	+	0.638060i	−0.312017	+	0.950077i	$0.601005\pi$
$132$	45005.1	+	89892.6i	0.224816	+	0.449044i
$133$	53054.9	−	53054.9i	0.260074	−	0.260074i
$134$	9397.45	+	39761.7i	0.0452114	+	0.191295i
$135$			31649.1i			0.149461i
$136$	−8932.81	+	99943.4i	−0.0414134	+	0.463347i
$137$		−	293628.i		−	1.33658i	−0.743900	−	0.668291i	$-0.767026\pi$
$137$		−	293628.i		−	1.33658i	0.743900	−	0.668291i	$-0.232974\pi$
$138$	−204183.	+	48257.4i	−0.912686	+	0.215708i
$139$	−144609.	+	144609.i	−0.634829	+	0.634829i	−0.949275	−	0.314446i	$-0.898181\pi$
$139$	−144609.	+	144609.i	−0.634829	+	0.634829i	0.314446	+	0.949275i	$0.398181\pi$
$140$	40482.4	−	121659.i	0.174561	−	0.524597i
$141$	25491.9	+	25491.9i	0.107983	+	0.107983i
$142$	161184.	−	260954.i	0.670813	−	1.08603i
$143$	−146411.			−0.598735
$144$	−66407.2	−	49696.9i	−0.266876	−	0.199721i
$145$	−102708.			−0.405680
$146$	−246843.	+	399633.i	−0.958380	+	1.55160i
$147$	−52751.9	−	52751.9i	−0.201347	−	0.201347i
$148$	10111.6	+	3364.64i	0.0379458	+	0.0126265i
$149$	39456.3	−	39456.3i	0.145596	−	0.145596i	−0.630551	−	0.776148i	$-0.717171\pi$
$149$	39456.3	−	39456.3i	0.145596	−	0.145596i	0.776148	+	0.630551i	$0.217171\pi$
$150$	61447.2	−	14522.7i	0.222984	−	0.0527010i
$151$		−	278028.i		−	0.992308i	−0.868234	−	0.496154i	$-0.834745\pi$
$151$		−	278028.i		−	0.992308i	0.868234	−	0.496154i	$-0.165255\pi$
$152$	112911.	−	94383.4i	0.396394	−	0.331350i
$153$			44899.5i			0.155065i
$154$	−41916.2	−	177352.i	−0.142423	−	0.602609i
$155$	−313499.	+	313499.i	−1.04811	+	1.04811i
$156$	108019.	−	54080.0i	0.355375	−	0.177920i
$157$	41816.8	+	41816.8i	0.135395	+	0.135395i	0.771556	−	0.636161i	$-0.219479\pi$
$157$	41816.8	+	41816.8i	0.135395	+	0.135395i	−0.636161	+	0.771556i	$0.719479\pi$
$158$	68606.4	+	42376.3i	0.218636	+	0.135045i
$159$	254135.			0.797209
$160$	100329.	−	230603.i	0.309831	−	0.712141i
$161$	380338.			1.15639
$162$	−31576.7	−	19504.0i	−0.0945320	−	0.0583898i
$163$	145825.	+	145825.i	0.429895	+	0.429895i	0.888592	−	0.458698i	$-0.151684\pi$
$163$	145825.	+	145825.i	0.429895	+	0.429895i	−0.458698	+	0.888592i	$0.651684\pi$
$164$	−15536.9	+	7778.63i	−0.0451082	+	0.0225836i
$165$	−96441.0	+	96441.0i	−0.275773	+	0.275773i
$166$	−52911.9	−	223876.i	−0.149033	−	0.630577i
$167$			466171.i			1.29346i	0.762718	+	0.646731i	$0.223864\pi$
$167$			466171.i			1.29346i	−0.762718	+	0.646731i	$0.776136\pi$
$168$	96433.4	+	115363.i	0.263605	+	0.315352i
$169$		−	195359.i		−	0.526159i
$170$	−132484.	+	31311.8i	−0.351593	+	0.0830971i
$171$	46563.5	−	46563.5i	0.121774	−	0.121774i
$172$	447526.	+	148915.i	1.15345	+	0.383812i
$173$	−206670.	−	206670.i	−0.525003	−	0.525003i	0.394075	−	0.919078i	$-0.371065\pi$
$173$	−206670.	−	206670.i	−0.525003	−	0.525003i	−0.919078	+	0.394075i	$0.871065\pi$
$174$	63294.7	−	102473.i	0.158487	−	0.256588i
$175$	−114460.			−0.282525
$176$	−50919.6	−	353792.i	−0.123909	−	0.860927i
$177$	381452.			0.915179
$178$	−144513.	+	233964.i	−0.341867	+	0.553476i
$179$	−333727.	−	333727.i	−0.778501	−	0.778501i	0.201075	−	0.979576i	$-0.435557\pi$
$179$	−333727.	−	333727.i	−0.778501	−	0.778501i	−0.979576	+	0.201075i	$0.935557\pi$
$180$	35529.3	−	106774.i	0.0817345	−	0.245632i
$181$	−87758.3	+	87758.3i	−0.199110	+	0.199110i	−0.799618	−	0.600509i	$-0.794965\pi$
$181$	−87758.3	+	87758.3i	−0.199110	+	0.199110i	0.600509	+	0.799618i	$0.294965\pi$
$182$	−213114.	+	50368.2i	−0.476906	+	0.112714i
$183$		−	195797.i		−	0.432194i
$184$	743022.	+	66410.3i	1.61792	+	0.144608i
$185$			14457.9i			0.0310582i
$186$	−119585.	−	505977.i	−0.253451	−	1.07238i
$187$	−136818.	+	136818.i	−0.286113	+	0.286113i
$188$	−57384.4	−	114619.i	−0.118413	−	0.236516i
$189$	47574.8	+	47574.8i	0.0968775	+	0.0968775i
$190$	169866.	+	104921.i	0.341367	+	0.210853i
$191$	−322332.			−0.639322			−0.319661	−	0.947532i	$-0.603569\pi$
$191$	−322332.			−0.639322			−0.319661	+	0.947532i	$0.603569\pi$
$192$	168247.	+	242211.i	0.329378	+	0.474176i
$193$	−968599.			−1.87176			−0.935882	−	0.352315i	$-0.885395\pi$
$193$	−968599.			−1.87176			−0.935882	+	0.352315i	$0.885395\pi$
$194$	636241.	+	392988.i	1.21372	+	0.749679i
$195$	115887.	+	115887.i	0.218248	+	0.218248i
$196$	118749.	+	237187.i	0.220795	+	0.441013i
$197$	152352.	−	152352.i	0.279693	−	0.279693i	−0.553293	−	0.832986i	$-0.686629\pi$
$197$	152352.	−	152352.i	0.279693	−	0.279693i	0.832986	+	0.553293i	$0.186629\pi$
$198$	−36787.7	−	155653.i	−0.0666867	−	0.282159i
$199$		−	505112.i		−	0.904180i	−0.891972	−	0.452090i	$-0.850679\pi$
$199$		−	505112.i		−	0.904180i	0.891972	−	0.452090i	$-0.149321\pi$
$200$	−223607.	−	19985.7i	−0.395284	−	0.0353300i
$201$		−	65003.3i		−	0.113487i
$202$	817400.	−	193188.i	1.40947	−	0.333120i
$203$	−154390.	+	154390.i	−0.262954	+	0.262954i
$204$	50404.2	−	151477.i	0.0847992	−	0.254842i
$205$	−16668.7	−	16668.7i	−0.0277025	−	0.0277025i
$206$	272330.	−	440897.i	0.447123	−	0.723883i
$207$	333802.			0.541457
$208$	−425131.	+	61187.0i	−0.681340	+	0.0980621i
$209$	283776.			0.449376
$210$	−107200.	+	173555.i	−0.167744	+	0.271575i
$211$	−282708.	−	282708.i	−0.437151	−	0.437151i	0.453901	−	0.891052i	$-0.350032\pi$
$211$	−282708.	−	282708.i	−0.437151	−	0.437151i	−0.891052	+	0.453901i	$0.850032\pi$
$212$	−857372.	−	285292.i	−1.31018	−	0.435964i
$213$	−345061.	+	345061.i	−0.521130	+	0.521130i
$214$	−653099.	+	154356.i	−0.974865	+	0.230404i
$215$			639891.i			0.944082i
$216$	84634.5	+	101248.i	0.123428	+	0.147657i
$217$			942500.i			1.35873i
$218$	−217788.	−	921486.i	−0.310379	−	1.31325i
$219$	528436.	−	528436.i	0.744531	−	0.744531i
$220$	433626.	−	217097.i	0.604030	−	0.302410i
$221$	164406.	+	164406.i	0.226431	+	0.226431i
$222$	−14424.8	−	8909.81i	−0.0196439	−	0.0121335i
$223$	−474777.			−0.639334			−0.319667	−	0.947530i	$-0.603571\pi$
$223$	−474777.			−0.639334			−0.319667	+	0.947530i	$0.603571\pi$
$224$	−195829.	−	497456.i	−0.260769	−	0.662422i
$225$	−100455.			−0.132287
$226$	1.24022e6	+	766050.i	1.61521	+	0.997668i
$227$	86384.2	+	86384.2i	0.111268	+	0.111268i	0.760549	−	0.649281i	$-0.224930\pi$
$227$	86384.2	+	86384.2i	0.111268	+	0.111268i	−0.649281	+	0.760549i	$0.724930\pi$
$228$	−209363.	+	104818.i	−0.266724	+	0.133537i
$229$	78901.8	−	78901.8i	0.0994256	−	0.0994256i	−0.655644	−	0.755070i	$-0.727603\pi$
$229$	78901.8	−	78901.8i	0.0994256	−	0.0994256i	0.755070	+	0.655644i	$0.227603\pi$
$230$	232785.	+	984942.i	0.290159	+	1.22770i
$231$			289940.i			0.357501i
$232$	−328572.	+	274657.i	−0.400785	+	0.335019i
$233$			536650.i			0.647592i	0.946127	+	0.323796i	$0.104959\pi$
$233$			536650.i			0.647592i	−0.946127	+	0.323796i	$0.895041\pi$
$234$	−187039.	+	44205.5i	−0.223302	+	0.0527761i
$235$	122968.	−	122968.i	0.145253	−	0.145253i
$236$	−1.28690e6	−	428218.i	−1.50406	−	0.500477i
$237$	−90718.4	−	90718.4i	−0.104912	−	0.104912i
$238$	−152082.	+	246217.i	−0.174034	+	0.281758i
$239$	15916.3			0.0180238			0.00901189	−	0.999959i	$-0.497131\pi$
$239$	15916.3			0.0180238			0.00901189	+	0.999959i	$0.497131\pi$
$240$	−239729.	+	320337.i	−0.268654	+	0.358987i
$241$	−1.18340e6			−1.31247			−0.656236	−	0.754555i	$-0.727853\pi$
$241$	−1.18340e6			−1.31247			−0.656236	+	0.754555i	$0.727853\pi$
$242$	−116555.	+	188700.i	−0.127936	+	0.207125i
$243$	41753.9	+	41753.9i	0.0453609	+	0.0453609i
$244$	−219802.	+	660558.i	−0.236351	+	0.710291i
$245$	−254466.	+	254466.i	−0.270841	+	0.270841i
$246$	26902.9	−	6358.34i	0.0283440	−	0.00669893i
$247$		−	340997.i		−	0.355638i
$248$	−164569.	+	1.84125e6i	−0.169910	+	1.90101i
$249$			365998.i			0.374094i
$250$	−246578.	−	1.04330e6i	−0.249519	−	1.05575i
$251$	1.12562e6	−	1.12562e6i	1.12773	−	1.12773i	0.137188	−	0.990545i	$-0.456193\pi$
$251$	1.12562e6	−	1.12562e6i	1.12773	−	1.12773i	0.990545	−	0.137188i	$-0.0438066\pi$
$252$	−107095.	−	213910.i	−0.106235	−	0.212192i
$253$	1.01716e6	+	1.01716e6i	0.999053	+	0.999053i
$254$	1.44736e6	+	893997.i	1.40765	+	0.869464i
$255$	216588.			0.208585
$256$	−295708.	−	1.00602e6i	−0.282009	−	0.959412i
$257$	710021.			0.670561			0.335280	−	0.942118i	$-0.391169\pi$
$257$	710021.			0.670561			0.335280	+	0.942118i	$0.391169\pi$
$258$	−638426.	−	394338.i	−0.597120	−	0.368825i
$259$	21733.1	+	21733.1i	0.0201313	+	0.0201313i
$260$	−260872.	−	521063.i	−0.239329	−	0.478032i
$261$	−135500.	+	135500.i	−0.123123	+	0.123123i
$262$	230607.	+	975723.i	0.207548	+	0.878160i
$263$		−	457225.i		−	0.407606i	−0.979012	−	0.203803i	$-0.934670\pi$
$263$		−	457225.i		−	0.407606i	0.979012	−	0.203803i	$-0.0653303\pi$
$264$	−50626.0	+	566422.i	−0.0447058	+	0.500184i
$265$		−	1.22590e6i		−	1.07236i
$266$	413059.	−	97624.2i	0.357938	−	0.0845967i
$267$	309371.	−	309371.i	0.265584	−	0.265584i
$268$	−72972.7	+	219301.i	−0.0620617	+	0.186510i
$269$	988102.	+	988102.i	0.832571	+	0.832571i	0.987868	−	0.155297i	$-0.0496334\pi$
$269$	988102.	+	988102.i	0.832571	+	0.832571i	−0.155297	+	0.987868i	$0.549633\pi$
$270$	−94084.1	+	152320.i	−0.0785429	+	0.127159i
$271$	−645877.			−0.534228			−0.267114	−	0.963665i	$-0.586070\pi$
$271$	−645877.			−0.534228			−0.267114	+	0.963665i	$0.586070\pi$
$272$	−340096.	+	454451.i	−0.278727	+	0.372448i
$273$	348403.			0.282928
$274$	872874.	−	1.41317e6i	0.702385	−	1.13715i
$275$	−306107.	−	306107.i	−0.244085	−	0.244085i
$276$	−1.12614e6	−	374727.i	−0.889859	−	0.296102i
$277$	1.00491e6	−	1.00491e6i	0.786916	−	0.786916i	−0.194071	−	0.980987i	$-0.562169\pi$
$277$	1.00491e6	−	1.00491e6i	0.786916	−	0.786916i	0.980987	+	0.194071i	$0.0621693\pi$
$278$	−1.12585e6	+	266088.i	−0.873713	+	0.206497i
$279$			827183.i			0.636196i
$280$	556493.	−	465178.i	0.424194	−	0.354588i
$281$		−	2.03557e6i		−	1.53787i	−0.639327	−	0.768935i	$-0.720787\pi$
$281$		−	2.03557e6i		−	1.53787i	0.639327	−	0.768935i	$-0.279213\pi$
$282$	46906.6	+	198467.i	0.0351246	+	0.148616i
$283$	1.63741e6	−	1.63741e6i	1.21532	−	1.21532i	0.246071	−	0.969252i	$-0.420860\pi$
$283$	1.63741e6	−	1.63741e6i	1.21532	−	1.21532i	0.969252	−	0.246071i	$-0.0791396\pi$
$284$	1.55149e6	−	776760.i	1.14144	−	0.571467i
$285$	−224614.	−	224614.i	−0.163804	−	0.163804i
$286$	−704647.	−	435241.i	−0.509397	−	0.314640i
$287$	−50112.8			−0.0359124
$288$	−171869.	−	436591.i	−0.122100	−	0.310166i
$289$	−1.11259e6			−0.783594
$290$	−494311.	−	305322.i	−0.345148	−	0.213188i
$291$	−841303.	−	841303.i	−0.582398	−	0.582398i
$292$	−2.37600e6	+	1.18955e6i	−1.63076	+	0.816446i
$293$	795528.	−	795528.i	0.541360	−	0.541360i	−0.382567	−	0.923928i	$-0.624960\pi$
$293$	795528.	−	795528.i	0.541360	−	0.541360i	0.923928	+	0.382567i	$0.124960\pi$
$294$	−97066.6	−	410700.i	−0.0654940	−	0.277113i
$295$		−	1.84006e6i		−	1.23105i
$296$	38662.6	+	46252.2i	0.0256485	+	0.0306834i
$297$			254465.i			0.167393i
$298$	307187.	−	72602.0i	0.200384	−	0.0473596i
$299$	1.22226e6	−	1.22226e6i	0.790653	−	0.790653i
$300$	338904.	+	112771.i	0.217407	+	0.0723427i
$301$	961882.	+	961882.i	0.611935	+	0.611935i
$302$	826502.	−	1.33809e6i	0.521466	−	0.844244i
$303$	−1.33630e6			−0.836178
$304$	823993.	−	118593.i	0.511375	−	0.0735997i
$305$	−944492.			−0.581365
$306$	−133474.	+	216092.i	−0.0814879	+	0.131927i
$307$	1.46689e6	+	1.46689e6i	0.888281	+	0.888281i	0.994358	−	0.106077i	$-0.0338289\pi$
$307$	1.46689e6	+	1.46689e6i	0.888281	+	0.888281i	−0.106077	+	0.994358i	$0.533829\pi$
$308$	325486.	−	978164.i	0.195504	−	0.587537i
$309$	−582999.	+	582999.i	−0.347353	+	0.347353i
$310$	−2.44075e6	+	576856.i	−1.44251	+	0.340929i
$311$			1.79049e6i			1.04971i	0.851191	+	0.524856i	$0.175881\pi$
$311$			1.79049e6i			1.04971i	−0.851191	+	0.524856i	$0.824119\pi$
$312$	680635.	+	60834.3i	0.395847	+	0.0353803i
$313$			1.73892e6i			1.00327i	0.865079	+	0.501636i	$0.167268\pi$
$313$			1.73892e6i			1.00327i	−0.865079	+	0.501636i	$0.832732\pi$
$314$	76945.5	+	325565.i	0.0440412	+	0.186343i
$315$	229493.	−	229493.i	0.130314	−	0.130314i
$316$	204215.	+	407896.i	0.115045	+	0.229790i
$317$	1.12277e6	+	1.12277e6i	0.627540	+	0.627540i	0.947449	−	0.319908i	$-0.103652\pi$
$317$	1.12277e6	+	1.12277e6i	0.627540	+	0.627540i	−0.319908	+	0.947449i	$0.603652\pi$
$318$	1.22310e6	+	755474.i	0.678256	+	0.418940i
$319$	−825791.			−0.454353
$320$	1.16838e6	−	811595.i	0.637837	−	0.443062i
$321$	1.06770e6			0.578345
$322$	1.83048e6	+	1.13064e6i	0.983844	+	0.607693i
$323$	−318653.	−	318653.i	−0.169946	−	0.169946i
$324$	−93991.6	−	187738.i	−0.0497424	−	0.0993548i
$325$	−367830.	+	367830.i	−0.193170	+	0.193170i
$326$	268326.	+	1.13532e6i	0.139836	+	0.591663i
$327$			1.50647e6i			0.779094i
$328$	−97899.6	−	8750.14i	−0.0502454	−	0.00449087i
$329$		−	369691.i		−	0.188300i
$330$	−750842.	+	177457.i	−0.379546	+	0.0897034i
$331$	−2.29950e6	+	2.29950e6i	−1.15362	+	1.15362i	−0.167799	+	0.985821i	$0.553666\pi$
$331$	−2.29950e6	+	2.29950e6i	−1.15362	+	1.15362i	−0.985821	+	0.167799i	$0.946334\pi$
$332$	410869.	−	1.23476e6i	0.204578	−	0.614806i
$333$	19074.0	+	19074.0i	0.00942607	+	0.00942607i
$334$	−1.38580e6	+	2.24358e6i	−0.679725	+	1.10046i
$335$	−313565.			−0.152656
$336$	121169.	+	841890.i	0.0585523	+	0.406824i
$337$	−2.22374e6			−1.06662			−0.533309	−	0.845920i	$-0.679052\pi$
$337$	−2.22374e6			−1.06662			−0.533309	+	0.845920i	$0.679052\pi$
$338$	580749.	−	940222.i	0.276501	−	0.447650i
$339$	−1.63995e6	−	1.63995e6i	−0.775052	−	0.775052i
$340$	−730698.	−	243141.i	−0.342800	−	0.114067i
$341$	−2.52059e6	+	2.52059e6i	−1.17386	+	1.17386i
$342$	362521.	−	85679.6i	0.167597	−	0.0396107i
$343$			2.31618e6i			1.06301i
$344$	1.71116e6	+	2.04707e6i	0.779643	+	0.932689i
$345$		−	1.61020e6i		−	0.728338i
$346$	−380285.	−	1.60903e6i	−0.170773	−	0.722560i
$347$	−1.06667e6	+	1.06667e6i	−0.475563	+	0.475563i	−0.903710	−	0.428146i	$-0.859167\pi$
$347$	−1.06667e6	+	1.06667e6i	−0.475563	+	0.475563i	0.428146	+	0.903710i	$0.359167\pi$
$348$	609247.	−	305022.i	0.269678	−	0.135015i
$349$	−385591.	−	385591.i	−0.169458	−	0.169458i	0.617283	−	0.786741i	$-0.288233\pi$
$349$	−385591.	−	385591.i	−0.169458	−	0.169458i	−0.786741	+	0.617283i	$0.788233\pi$
$350$	−550870.	−	340257.i	−0.240369	−	0.148469i
$351$	305775.			0.132475
$352$	806661.	−	1.85409e6i	0.347004	−	0.797582i
$353$	−1.09057e6			−0.465820			−0.232910	−	0.972498i	$-0.574825\pi$
$353$	−1.09057e6			−0.465820			−0.232910	+	0.972498i	$0.574825\pi$
$354$	1.83584e6	+	1.13395e6i	0.778624	+	0.480935i
$355$	1.66451e6	+	1.66451e6i	0.700997	+	0.700997i
$356$	−1.39102e6	+	696421.i	−0.581713	+	0.291237i
$357$	325574.	−	325574.i	0.135201	−	0.135201i
$358$	−614078.	−	2.59824e6i	−0.253231	−	1.07145i
$359$			1.42859e6i			0.585022i	0.956262	+	0.292511i	$0.0944908\pi$
$359$			1.42859e6i			0.585022i	−0.956262	+	0.292511i	$0.905509\pi$
$360$	488405.	−	408262.i	0.198620	−	0.166029i
$361$		−	1.81518e6i		−	0.733079i
$362$	−683244.	+	161481.i	−0.274034	+	0.0647663i
$363$	249519.	−	249519.i	0.0993886	−	0.0993886i
$364$	−1.17540e6	−	391117.i	−0.464979	−	0.154723i
$365$	−2.54908e6	−	2.54908e6i	−1.00150	−	1.00150i
$366$	582051.	−	942330.i	0.227122	−	0.367706i
$367$	645209.			0.250055			0.125027	−	0.992153i	$-0.460098\pi$
$367$	645209.			0.250055			0.125027	+	0.992153i	$0.460098\pi$
$368$	3.37859e6	+	2.52842e6i	1.30052	+	0.973261i
$369$	−43981.4			−0.0168152
$370$	−42979.4	+	69582.8i	−0.0163213	+	0.0264239i
$371$	−1.84277e6	−	1.84277e6i	−0.695084	−	0.695084i
$372$	928596.	−	2.79065e6i	0.347912	−	1.04556i
$373$	3.17417e6	−	3.17417e6i	1.18130	−	1.18130i	0.201886	−	0.979409i	$-0.435293\pi$
$373$	3.17417e6	−	3.17417e6i	1.18130	−	1.18130i	0.979409	−	0.201886i	$-0.0647072\pi$
$374$	−1.06520e6	+	251753.i	−0.393777	+	0.0930669i
$375$			1.70561e6i			0.626327i
$376$	64551.4	−	722223.i	0.0235470	−	0.263452i
$377$			992304.i			0.359576i
$378$	87540.6	+	370394.i	0.0315123	+	0.133332i
$379$	−2.03555e6	+	2.03555e6i	−0.727920	+	0.727920i	−0.970205	−	0.242285i	$-0.922103\pi$
$379$	−2.03555e6	+	2.03555e6i	−0.727920	+	0.727920i	0.242285	+	0.970205i	$0.422103\pi$
$380$	505625.	+	1.00993e6i	0.179626	+	0.358783i
$381$	−1.91385e6	−	1.91385e6i	−0.675455	−	0.675455i
$382$	−1.55131e6	−	958204.i	−0.543928	−	0.335969i
$383$	2.26887e6			0.790339			0.395170	−	0.918608i	$-0.370686\pi$
$383$	2.26887e6			0.790339			0.395170	+	0.918608i	$0.370686\pi$
$384$	89712.9	+	1.66586e6i	0.0310475	+	0.576515i
$385$	1.39862e6			0.480892
$386$	−4.66166e6	−	2.87938e6i	−1.59247	−	0.983627i
$387$	844193.	+	844193.i	0.286526	+	0.286526i
$388$	1.89384e6	+	3.78274e6i	0.638653	+	1.27564i
$389$	−484484.	+	484484.i	−0.162332	+	0.162332i	−0.783599	−	0.621267i	$-0.786618\pi$
$389$	−484484.	+	484484.i	−0.162332	+	0.162332i	0.621267	+	0.783599i	$0.286618\pi$
$390$	213240.	+	902242.i	0.0709916	+	0.300374i
$391$		−	2.28434e6i		−	0.755648i
$392$	−133580.	+	1.49454e6i	−0.0439063	+	0.491239i
$393$		−	1.59513e6i		−	0.520974i
$394$	1.18614e6	−	280336.i	0.384941	−	0.0909785i
$395$	−437610.	+	437610.i	−0.141122	+	0.141122i
$396$	285662.	−	858484.i	0.0915408	−	0.275102i
$397$	3.90917e6	+	3.90917e6i	1.24483	+	1.24483i	0.957976	+	0.286850i	$0.0926081\pi$
$397$	3.90917e6	+	3.90917e6i	1.24483	+	1.24483i	0.286850	+	0.957976i	$0.407392\pi$
$398$	1.50156e6	−	2.43100e6i	0.475154	−	0.769266i
$399$	−675278.			−0.212349
$400$	−1.01676e6	−	760908.i	−0.317737	−	0.237784i
$401$	−2.70721e6			−0.840738			−0.420369	−	0.907353i	$-0.638099\pi$
$401$	−2.70721e6			−0.840738			−0.420369	+	0.907353i	$0.638099\pi$
$402$	193237.	−	312847.i	0.0596383	−	0.0965532i
$403$	3.02884e6	+	3.02884e6i	0.928995	+	0.928995i
$404$	4.50827e6	+	1.50013e6i	1.37422	+	0.457274i
$405$	201414.	−	201414.i	0.0610171	−	0.0610171i
$406$	−1.20201e6	+	284087.i	−0.361903	+	0.0855336i
$407$			116244.i			0.0347845i
$408$	692884.	−	579188.i	0.206068	−	0.172254i
$409$		−	3.59980e6i		−	1.06407i	−0.846723	−	0.532034i	$-0.821428\pi$
$409$		−	3.59980e6i		−	1.06407i	0.846723	−	0.532034i	$-0.178572\pi$
$410$	−30671.5	−	129775.i	−0.00901105	−	0.0381268i
$411$	−1.86863e6	+	1.86863e6i	−0.545657	+	0.545657i
$412$	2.62133e6	−	1.31238e6i	0.760814	−	0.380905i
$413$	−2.76597e6	−	2.76597e6i	−0.797942	−	0.797942i
$414$	1.60652e6	+	992303.i	0.460665	+	0.284540i
$415$	1.76551e6			0.503211
$416$	−2.22796e6	−	969317.i	−0.631209	−	0.274620i
$417$	1.84057e6			0.518336
$418$	1.36575e6	+	843588.i	0.382324	+	0.236151i
$419$	−776229.	−	776229.i	−0.216001	−	0.216001i	0.590810	−	0.806811i	$-0.298808\pi$
$419$	−776229.	−	776229.i	−0.216001	−	0.216001i	−0.806811	+	0.590810i	$0.798808\pi$
$420$	−1.03186e6	+	516607.i	−0.285430	+	0.142902i
$421$	4.66408e6	−	4.66408e6i	1.28251	−	1.28251i	0.343276	−	0.939234i	$-0.388463\pi$
$421$	4.66408e6	−	4.66408e6i	1.28251	−	1.28251i	0.939234	−	0.343276i	$-0.111537\pi$
$422$	−520199.	−	2.20102e6i	−0.142196	−	0.601650i
$423$		−	324459.i		−	0.0881675i
$424$	−3.27825e6	−	3.92178e6i	−0.885580	−	1.05942i
$425$			687455.i			0.184617i
$426$	−2.68647e6	+	634932.i	−0.717230	+	0.169513i
$427$	−1.41976e6	+	1.41976e6i	−0.376829	+	0.376829i
$428$	−3.60208e6	−	1.19860e6i	−0.950483	−	0.316275i
$429$	931756.	+	931756.i	0.244433	+	0.244433i
$430$	−1.90222e6	+	3.07966e6i	−0.496123	+	0.803214i
$431$	−1.94067e6			−0.503220			−0.251610	−	0.967829i	$-0.580960\pi$
$431$	−1.94067e6			−0.503220			−0.251610	+	0.967829i	$0.580960\pi$
$432$	106344.	+	738882.i	0.0274159	+	0.190487i
$433$	1.72882e6			0.443129			0.221564	−	0.975146i	$-0.428884\pi$
$433$	1.72882e6			0.443129			0.221564	+	0.975146i	$0.428884\pi$
$434$	−2.80179e6	+	4.53605e6i	−0.714022	+	1.15599i
$435$	653629.	+	653629.i	0.165618	+	0.165618i
$436$	1.69116e6	−	5.08234e6i	0.426057	−	1.28041i
$437$	−2.36900e6	+	2.36900e6i	−0.593419	+	0.593419i
$438$	4.11415e6	−	972355.i	1.02470	−	0.242181i
$439$		−	3.28558e6i		−	0.813675i	−0.913501	−	0.406838i	$-0.866632\pi$
$439$		−	3.28558e6i		−	0.813675i	0.913501	−	0.406838i	$-0.133368\pi$
$440$	2.73232e6	+	244211.i	0.672821	+	0.0601359i
$441$			671422.i			0.164399i
$442$	302516.	+	1.27998e6i	0.0736534	+	0.311636i
$443$	4.91113e6	−	4.91113e6i	1.18897	−	1.18897i	0.211620	−	0.977352i	$-0.432126\pi$
$443$	4.91113e6	−	4.91113e6i	1.18897	−	1.18897i	0.977352	−	0.211620i	$-0.0678741\pi$
$444$	−42937.1	−	85762.0i	−0.0103365	−	0.0206461i
$445$	−1.49235e6	−	1.49235e6i	−0.357249	−	0.357249i
$446$	−2.28500e6	−	1.41138e6i	−0.543938	−	0.335975i
$447$	−502197.			−0.118879
$448$	536319.	−	2.97629e6i	0.126249	−	0.700617i
$449$	5.42005e6			1.26878			0.634391	−	0.773012i	$-0.281251\pi$
$449$	5.42005e6			1.26878			0.634391	+	0.773012i	$0.281251\pi$
$450$	−483469.	−	298626.i	−0.112548	−	0.0695178i
$451$	−134020.	−	134020.i	−0.0310261	−	0.0310261i
$452$	3.69166e6	+	7.37367e6i	0.849915	+	1.69761i
$453$	−1.76936e6	+	1.76936e6i	−0.405108	+	0.405108i
$454$	158952.	+	672545.i	0.0361932	+	0.153138i
$455$		−	1.68064e6i		−	0.380579i
$456$	−1.31921e6	−	117910.i	−0.297100	−	0.0265544i
$457$			3.98596e6i			0.892776i	0.894840	+	0.446388i	$0.147290\pi$
$457$			3.98596e6i			0.892776i	−0.894840	+	0.446388i	$0.852710\pi$
$458$	614291.	−	145184.i	0.136839	−	0.0323411i
$459$	285739.	−	285739.i	0.0633050	−	0.0633050i
$460$	−1.80762e6	+	5.43232e6i	−0.398301	+	1.19699i
$461$	−1.52531e6	−	1.52531e6i	−0.334277	−	0.334277i	0.519931	−	0.854208i	$-0.325958\pi$
$461$	−1.52531e6	−	1.52531e6i	−0.334277	−	0.334277i	−0.854208	+	0.519931i	$0.825958\pi$
$462$	−861911.	+	1.39542e6i	−0.187870	+	0.304158i
$463$	565434.			0.122583			0.0612914	−	0.998120i	$-0.480478\pi$
$463$	565434.			0.122583			0.0612914	+	0.998120i	$0.480478\pi$
$464$	−2.39783e6	+	345108.i	−0.517038	+	0.0744149i
$465$	3.99018e6			0.855777
$466$	−1.59531e6	+	2.58278e6i	−0.340315	+	0.550963i
$467$	2.47619e6	+	2.47619e6i	0.525403	+	0.525403i	0.919198	−	0.393795i	$-0.128838\pi$
$467$	2.47619e6	+	2.47619e6i	0.525403	+	0.525403i	−0.393795	+	0.919198i	$0.628838\pi$
$468$	−1.03159e6	−	343263.i	−0.217717	−	0.0724457i
$469$	−471349.	+	471349.i	−0.0989488	+	0.0989488i
$470$	957372.	−	226269.i	0.199911	−	0.0472477i
$471$		−	532241.i		−	0.110549i
$472$	−4.92059e6	−	5.88651e6i	−1.01663	−	1.21619i
$473$			5.14484e6i			1.05735i
$474$	−166927.	−	706289.i	−0.0341257	−	0.144390i
$475$	712932.	−	712932.i	0.144982	−	0.144982i
$476$	−1.46387e6	+	732893.i	−0.296132	+	0.148260i
$477$	−1.61731e6	−	1.61731e6i	−0.325459	−	0.325459i
$478$	76601.5	+	47314.6i	0.0153344	+	0.00947165i
$479$	4.19375e6			0.835148			0.417574	−	0.908643i	$-0.362880\pi$
$479$	4.19375e6			0.835148			0.417574	+	0.908643i	$0.362880\pi$
$480$	−2.10604e6	+	829064.i	−0.417218	+	0.164242i
$481$	139684.			0.0275285
$482$	−5.69547e6	−	3.51793e6i	−1.11664	−	0.689716i
$483$	−2.42045e6	−	2.42045e6i	−0.472094	−	0.472094i
$484$	−1.12191e6	+	561687.i	−0.217692	+	0.108989i
$485$	−4.05830e6	+	4.05830e6i	−0.783411	+	0.783411i
$486$	76829.8	+	325076.i	0.0147550	+	0.0624301i
$487$		−	2.43169e6i		−	0.464607i	−0.972643	−	0.232303i	$-0.925374\pi$
$487$		−	2.43169e6i		−	0.464607i	0.972643	−	0.232303i	$-0.0746262\pi$
$488$	−3.02152e6	+	2.52571e6i	−0.574349	+	0.480103i
$489$		−	1.85605e6i		−	0.351008i
$490$	−1.98115e6	+	468232.i	−0.372757	+	0.0880991i
$491$	1.44758e6	−	1.44758e6i	0.270980	−	0.270980i	−0.558515	−	0.829495i	$-0.688628\pi$
$491$	1.44758e6	−	1.44758e6i	0.270980	−	0.270980i	0.829495	+	0.558515i	$0.188628\pi$
$492$	148379.	+	49373.5i	0.0276351	+	0.00919562i
$493$	927282.	+	927282.i	0.171828	+	0.171828i
$494$	1.01369e6	−	1.64114e6i	0.186891	−	0.302572i
$495$	1.22749e6			0.225168
$496$	−6.26558e6	+	8.37234e6i	−1.14355	+	1.52807i
$497$	5.00418e6			0.908744
$498$	−1.08801e6	+	1.76147e6i	−0.196589	+	0.318274i
$499$	−1.83485e6	−	1.83485e6i	−0.329876	−	0.329876i	0.522663	−	0.852539i	$-0.324938\pi$
$499$	−1.83485e6	−	1.83485e6i	−0.329876	−	0.329876i	−0.852539	+	0.522663i	$0.824938\pi$
$500$	1.91472e6	−	5.75419e6i	0.342515	−	1.02934i
$501$	2.96669e6	−	2.96669e6i	0.528054	−	0.528054i
$502$	8.76351e6	−	2.07120e6i	1.55210	−	0.366829i
$503$		−	6.44170e6i		−	1.13522i	−0.823297	−	0.567611i	$-0.807868\pi$
$503$		−	6.44170e6i		−	1.13522i	0.823297	−	0.567611i	$-0.192132\pi$
$504$	120471.	−	1.34787e6i	0.0211254	−	0.236358i
$505$			6.44609e6i			1.12478i
$506$	1.87164e6	+	7.91912e6i	0.324972	+	1.37499i
$507$	−1.24326e6	+	1.24326e6i	−0.214804	+	0.214804i
$508$	4.30824e6	+	8.60523e6i	0.740698	+	1.47946i
$509$	−3.85964e6	−	3.85964e6i	−0.660316	−	0.660316i	0.295138	−	0.955454i	$-0.404634\pi$
$509$	−3.85964e6	−	3.85964e6i	−0.660316	−	0.660316i	−0.955454	+	0.295138i	$0.904634\pi$
$510$	1.04239e6	+	643855.i	0.177462	+	0.109613i
$511$	−7.66355e6			−1.29831
$512$	1.56743e6	−	5.72080e6i	0.264249	−	0.964454i
$513$	−592657.			−0.0994282
$514$	3.41718e6	+	2.11070e6i	0.570505	+	0.352385i
$515$	2.81228e6	+	2.81228e6i	0.467241	+	0.467241i
$516$	−1.90035e6	−	3.79573e6i	−0.314202	−	0.627583i
$517$	988689.	−	988689.i	0.162680	−	0.162680i
$518$	39990.2	+	169203.i	0.00654830	+	0.0277066i
$519$			2.63048e6i			0.428663i
$520$	293454.	−	3.28326e6i	0.0475917	−	0.532473i
$521$			5.58015e6i			0.900641i	0.892867	+	0.450321i	$0.148690\pi$
$521$			5.58015e6i			0.900641i	−0.892867	+	0.450321i	$0.851310\pi$
$522$	−1.05494e6	+	249329.i	−0.169454	+	0.0400494i
$523$	−7.14866e6	+	7.14866e6i	−1.14280	+	1.14280i	−0.154864	+	0.987936i	$0.549494\pi$
$523$	−7.14866e6	+	7.14866e6i	−1.14280	+	1.14280i	−0.987936	+	0.154864i	$0.950506\pi$
$524$	−1.79070e6	+	5.38148e6i	−0.284901	+	0.856196i
$525$	728417.	+	728417.i	0.115340	+	0.115340i
$526$	1.35921e6	−	2.20053e6i	0.214201	−	0.346787i
$527$	5.66074e6			0.887865
$528$	−1.92747e6	+	2.57557e6i	−0.300886	+	0.402058i
$529$	−1.05464e7			−1.63858
$530$	3.64428e6	−	5.90001e6i	0.563536	−	0.912354i
$531$	−2.42754e6	−	2.42754e6i	−0.373620	−	0.373620i
$532$	2.27818e6	+	758068.i	0.348986	+	0.116126i
$533$	−161044.	+	161044.i	−0.0245542	+	0.0245542i
$534$	2.40861e6	−	569262.i	0.365522	−	0.0863891i
$535$		−	5.15040e6i		−	0.777959i
$536$	−1.00312e6	+	838519.i	−0.150814	+	0.126067i
$537$			4.24766e6i			0.635643i
$538$	1.81817e6	+	7.69288e6i	0.270819	+	1.14586i
$539$	−2.04595e6	+	2.04595e6i	−0.303336	+	0.303336i
$540$	−905613.	+	453399.i	−0.133647	+	0.0669108i
$541$	−5.75392e6	−	5.75392e6i	−0.845222	−	0.845222i	0.144311	−	0.989532i	$-0.453904\pi$
$541$	−5.75392e6	−	5.75392e6i	−0.845222	−	0.845222i	−0.989532	+	0.144311i	$0.953904\pi$
$542$	−3.10847e6	−	1.92001e6i	−0.454515	−	0.280741i
$543$	1.11698e6			0.162572
$544$	−2.98777e6	+	1.17616e6i	−0.432862	+	0.170401i
$545$	7.26693e6			1.04800
$546$	1.67679e6	+	1.03571e6i	0.240711	+	0.148681i
$547$	−315098.	−	315098.i	−0.0450275	−	0.0450275i	0.684235	−	0.729262i	$-0.260136\pi$
$547$	−315098.	−	315098.i	−0.0450275	−	0.0450275i	−0.729262	+	0.684235i	$0.760136\pi$
$548$	8.40191e6	−	4.20645e6i	1.19516	−	0.598363i
$549$	−1.24605e6	+	1.24605e6i	−0.176443	+	0.176443i
$550$	−563255.	−	2.38320e6i	−0.0793959	−	0.335933i
$551$		−	1.92329e6i		−	0.269877i
$552$	−4.30593e6	−	5.15120e6i	−0.601477	−	0.719549i
$553$			1.31563e6i			0.182945i
$554$	7.82375e6	−	1.84910e6i	1.08303	−	0.255968i
$555$	92009.5	−	92009.5i	0.0126794	−	0.0126794i
$556$	−6.20949e6	−	2.06622e6i	−0.851861	−	0.283458i
$557$	7.02215e6	+	7.02215e6i	0.959030	+	0.959030i	0.999193	−	0.0401635i	$-0.0127879\pi$
$557$	7.02215e6	+	7.02215e6i	0.959030	+	0.959030i	−0.0401635	+	0.999193i	$0.512788\pi$
$558$	−2.45899e6	+	3.98105e6i	−0.334326	+	0.541268i
$559$	6.18225e6			0.836791
$560$	4.06113e6	−	584499.i	0.547238	−	0.0787614i
$561$	1.74140e6			0.233611
$562$	6.05118e6	−	9.79674e6i	0.808163	−	1.30840i
$563$	−6.55715e6	−	6.55715e6i	−0.871855	−	0.871855i	0.120820	−	0.992674i	$-0.461448\pi$
$563$	−6.55715e6	−	6.55715e6i	−0.871855	−	0.871855i	−0.992674	+	0.120820i	$0.961448\pi$
$564$	−364237.	+	1.09462e6i	−0.0482155	+	0.144899i
$565$	−7.91082e6	+	7.91082e6i	−1.04256	+	1.04256i
$566$	1.27481e7	−	3.01293e6i	1.67264	−	0.395320i
$567$		−	605529.i		−	0.0791001i
$568$	9.77608e6	+	873774.i	1.27143	+	0.113639i
$569$		−	1.51685e6i		−	0.196410i	−0.995166	−	0.0982049i	$-0.968690\pi$
$569$		−	1.51685e6i		−	0.196410i	0.995166	−	0.0982049i	$-0.0313100\pi$
$570$	−413304.	−	1.74874e6i	−0.0532822	−	0.225443i
$571$	−5.23365e6	+	5.23365e6i	−0.671760	+	0.671760i	−0.958122	−	0.286362i	$-0.907554\pi$
$571$	−5.23365e6	+	5.23365e6i	−0.671760	+	0.671760i	0.286362	+	0.958122i	$0.407554\pi$
$572$	−2.09746e6	−	4.18944e6i	−0.268043	−	0.535385i
$573$	2.05131e6	+	2.05131e6i	0.261002	+	0.261002i
$574$	−241182.	−	148972.i	−0.0305538	−	0.0188722i
$575$	5.11084e6			0.644648
$576$	470699.	−	2.61214e6i	0.0591136	−	0.328050i
$577$	2.93421e6			0.366903			0.183452	−	0.983029i	$-0.441273\pi$
$577$	2.93421e6			0.366903			0.183452	+	0.983029i	$0.441273\pi$
$578$	−5.35466e6	−	3.30743e6i	−0.666673	−	0.411785i
$579$	6.16413e6	+	6.16413e6i	0.764144	+	0.764144i
$580$	−1.47137e6	−	2.93890e6i	−0.181616	−	0.362757i
$581$	2.65391e6	−	2.65391e6i	0.326171	−	0.326171i
$582$	−1.54805e6	−	6.54997e6i	−0.189442	−	0.801553i
$583$		−	9.85650e6i		−	1.20102i
$584$	−1.49714e7	−	1.33812e6i	−1.81648	−	0.162354i
$585$		−	1.47501e6i		−	0.178198i
$586$	6.19359e6	−	1.46382e6i	0.745073	−	0.176094i
$587$	858576.	−	858576.i	0.102845	−	0.102845i	−0.653812	−	0.756657i	$-0.726831\pi$
$587$	858576.	−	858576.i	0.102845	−	0.102845i	0.756657	+	0.653812i	$0.226831\pi$
$588$	753738.	−	2.26517e6i	0.0899036	−	0.270182i
$589$	−5.87053e6	−	5.87053e6i	−0.697250	−	0.697250i
$590$	5.46998e6	−	8.85579e6i	0.646928	−	1.04736i
$591$	−1.93912e6			−0.228368
$592$	48579.8	+	337535.i	0.00569707	+	0.0395836i
$593$	−1.38842e7			−1.62138			−0.810690	−	0.585475i	$-0.800908\pi$
$593$	−1.38842e7			−1.62138			−0.810690	+	0.585475i	$0.800908\pi$
$594$	−756454.	+	1.22468e6i	−0.0879663	+	0.142416i
$595$	−1.57051e6	−	1.57051e6i	−0.181865	−	0.181865i
$596$	1.69425e6	+	563766.i	0.195372	+	0.0650105i
$597$	−3.21451e6	+	3.21451e6i	−0.369130	+	0.369130i
$598$	9.51593e6	−	2.24903e6i	1.08817	−	0.257184i
$599$		−	4.69746e6i		−	0.534929i	−0.963568	−	0.267465i	$-0.913814\pi$
$599$		−	4.69746e6i		−	0.534929i	0.963568	−	0.267465i	$-0.0861858\pi$
$600$	1.29584e6	+	1.55021e6i	0.146951	+	0.175798i
$601$		−	531207.i		−	0.0599898i	−0.999550	−	0.0299949i	$-0.990451\pi$
$601$		−	531207.i		−	0.0599898i	0.999550	−	0.0299949i	$-0.00954911\pi$
$602$	1.76992e6	+	7.48874e6i	0.199050	+	0.842204i
$603$	−413678.	+	413678.i	−0.0463308	+	0.0463308i
$604$	7.95555e6	−	3.98298e6i	0.887315	−	0.444238i
$605$	−1.20363e6	−	1.20363e6i	−0.133692	−	0.133692i
$606$	−6.43134e6	−	3.97246e6i	−0.711410	−	0.439418i
$607$	−448068.			−0.0493597			−0.0246799	−	0.999695i	$-0.507857\pi$
$607$	−448068.			−0.0493597			−0.0246799	+	0.999695i	$0.507857\pi$
$608$	4.31825e6	+	1.87874e6i	0.473749	+	0.206114i
$609$	1.96507e6			0.214701
$610$	−4.54564e6	−	2.80771e6i	−0.494618	−	0.305512i
$611$	−1.18805e6	−	1.18805e6i	−0.128745	−	0.128745i
$612$	−1.28476e6	+	643222.i	−0.138658	+	0.0694197i
$613$	−2.91493e6	+	2.91493e6i	−0.313312	+	0.313312i	−0.846191	−	0.532879i	$-0.821110\pi$
$613$	−2.91493e6	+	2.91493e6i	−0.313312	+	0.313312i	0.532879	+	0.846191i	$0.321110\pi$
$614$	2.69916e6	+	1.14205e7i	0.288940	+	1.22254i
$615$			212158.i			0.0226190i
$616$	4.47431e6	−	3.74011e6i	0.475088	−	0.397130i
$617$		−	1.88993e6i		−	0.199864i	−0.994994	−	0.0999318i	$-0.968138\pi$
$617$		−	1.88993e6i		−	0.199864i	0.994994	−	0.0999318i	$-0.0318625\pi$
$618$	−4.53894e6	+	1.07275e6i	−0.478061	+	0.112987i
$619$	8.87703e6	−	8.87703e6i	0.931196	−	0.931196i	−0.0665849	−	0.997781i	$-0.521210\pi$
$619$	8.87703e6	−	8.87703e6i	0.931196	−	0.931196i	0.997781	+	0.0665849i	$0.0212103\pi$
$620$	−1.34616e7	−	4.47938e6i	−1.40643	−	0.467992i
$621$	−2.12431e6	−	2.12431e6i	−0.221049	−	0.221049i
$622$	−5.32262e6	+	8.61723e6i	−0.551632	+	0.893083i
$623$	−4.48660e6			−0.463124
$624$	3.09491e6	+	2.31612e6i	0.318190	+	0.238122i
$625$	4.35197e6			0.445642
$626$	−5.16933e6	+	8.36904e6i	−0.527228	+	0.853572i
$627$	−1.80594e6	−	1.80594e6i	−0.183457	−	0.183457i
$628$	−597494.	+	1.79561e6i	−0.0604553	+	0.181683i
$629$	130531.	−	130531.i	0.0131549	−	0.0131549i
$630$	1.78672e6	−	422280.i	0.179351	−	0.0423886i
$631$			1.05967e7i			1.05949i	0.848157	+	0.529744i	$0.177712\pi$
$631$			1.05967e7i			1.05949i	−0.848157	+	0.529744i	$0.822288\pi$
$632$	−229720.	+	2.57019e6i	−0.0228774	+	0.255960i
$633$			3.59828e6i			0.356932i
$634$	2.06596e6	+	8.74132e6i	0.204126	+	0.863682i
$635$	−9.23209e6	+	9.23209e6i	−0.908586	+	0.908586i
$636$	3.64069e6	+	7.27187e6i	0.356896	+	0.712859i
$637$	2.45850e6	+	2.45850e6i	0.240061	+	0.240061i
$638$	−3.97435e6	−	2.45485e6i	−0.386558	−	0.238766i
$639$	4.39190e6			0.425501
$640$	8.03582e6	−	432759.i	0.775497	−	0.0417634i
$641$	6.35478e6			0.610880			0.305440	−	0.952211i	$-0.401197\pi$
$641$	6.35478e6			0.610880			0.305440	+	0.952211i	$0.401197\pi$
$642$	5.13861e6	+	3.17398e6i	0.492049	+	0.303925i
$643$	−2.65490e6	−	2.65490e6i	−0.253234	−	0.253234i	0.569061	−	0.822295i	$-0.307307\pi$
$643$	−2.65490e6	−	2.65490e6i	−0.253234	−	0.253234i	−0.822295	+	0.569061i	$0.807307\pi$
$644$	5.44864e6	+	1.08830e7i	0.517695	+	1.03404i
$645$	4.07224e6	−	4.07224e6i	0.385420	−	0.385420i
$646$	−586340.	−	2.48087e6i	−0.0552800	−	0.233896i
$647$			1.99429e7i			1.87296i	0.350721	+	0.936480i	$0.385937\pi$
$647$			1.99429e7i			1.87296i	−0.350721	+	0.936480i	$0.614063\pi$
$648$	105731.	−	1.18295e6i	0.00989153	−	0.110670i
$649$		−	1.47944e7i		−	1.37875i
$650$	−2.86374e6	+	676829.i	−0.265859	+	0.0628342i
$651$	5.99803e6	−	5.99803e6i	0.554698	−	0.554698i
$652$	−2.08360e6	+	6.26171e6i	−0.191953	+	0.576865i
$653$	7.98917e6	+	7.98917e6i	0.733193	+	0.733193i	0.971251	−	0.238058i	$-0.0765107\pi$
$653$	7.98917e6	+	7.98917e6i	0.733193	+	0.733193i	−0.238058	+	0.971251i	$0.576511\pi$
$654$	−4.47831e6	+	7.25030e6i	−0.409421	+	0.662844i
$655$	−7.69464e6			−0.700786
$656$	−445158.	−	333141.i	−0.0403882	−	0.0302252i
$657$	−6.72590e6			−0.607907
$658$	1.09899e6	−	1.77924e6i	0.0989531	−	0.160203i
$659$	3.27519e6	+	3.27519e6i	0.293780	+	0.293780i	0.838572	−	0.544791i	$-0.183391\pi$
$659$	3.27519e6	+	3.27519e6i	0.293780	+	0.293780i	−0.544791	+	0.838572i	$0.683391\pi$
$660$	−4.14118e6	−	1.37798e6i	−0.370053	−	0.123136i
$661$	−6.03747e6	+	6.03747e6i	−0.537467	+	0.537467i	−0.922784	−	0.385317i	$-0.874092\pi$
$661$	−6.03747e6	+	6.03747e6i	−0.537467	+	0.537467i	0.385317	+	0.922784i	$0.374092\pi$
$662$	−1.79028e7	+	4.23121e6i	−1.58772	+	0.375249i
$663$		−	2.09254e6i		−	0.184880i
$664$	5.64803e6	−	4.72124e6i	0.497138	−	0.415562i
$665$			3.25742e6i			0.285641i
$666$	35097.3	+	148501.i	0.00306611	+	0.0129731i
$667$	6.89381e6	−	6.89381e6i	0.599991	−	0.599991i
$668$	−1.33391e7	+	6.67827e6i	−1.15660	+	0.579059i
$669$	3.02146e6	+	3.02146e6i	0.261007	+	0.261007i
$670$	−1.50912e6	−	932141.i	−0.129878	−	0.0802222i
$671$	−7.59389e6			−0.651115
$672$	−1.91955e6	+	4.41204e6i	−0.163974	+	0.376891i
$673$	7.43637e6			0.632883			0.316441	−	0.948612i	$-0.397512\pi$
$673$	7.43637e6			0.632883			0.316441	+	0.948612i	$0.397512\pi$
$674$	−1.07024e7	−	6.61057e6i	−0.907467	−	0.560517i
$675$	639293.	+	639293.i	0.0540058	+	0.0540058i
$676$	5.59004e6	−	2.79868e6i	0.470488	−	0.235552i
$677$	1.36583e7	−	1.36583e7i	1.14532	−	1.14532i	0.157853	−	0.987463i	$-0.449543\pi$
$677$	1.36583e7	−	1.36583e7i	1.14532	−	1.14532i	0.987463	−	0.157853i	$-0.0504573\pi$
$678$	−3.01760e6	−	1.27678e7i	−0.252109	−	1.06670i
$679$			1.22008e7i			1.01558i
$680$	−2.79390e6	−	3.34235e6i	−0.231707	−	0.277191i
$681$		−	1.09949e6i		−	0.0908498i
$682$	−1.96241e7	+	4.63803e6i	−1.61558	+	0.381832i
$683$	−6.82078e6	+	6.82078e6i	−0.559477	+	0.559477i	−0.929159	−	0.369681i	$-0.879467\pi$
$683$	−6.82078e6	+	6.82078e6i	−0.559477	+	0.559477i	0.369681	+	0.929159i	$0.379467\pi$
$684$	1.99944e6	+	665316.i	0.163406	+	0.0543736i
$685$	9.01397e6	+	9.01397e6i	0.733989	+	0.733989i
$686$	−6.88536e6	+	1.11473e7i	−0.558620	+	0.904395i
$687$	−1.00426e6			−0.0811807
$688$	2.15009e6	+	1.49389e7i	0.173175	+	1.20323i
$689$	−1.18440e7			−0.950493
$690$	4.78669e6	−	7.74957e6i	0.382748	−	0.619662i
$691$	3.13336e6	+	3.13336e6i	0.249641	+	0.249641i	0.820823	−	0.571182i	$-0.193515\pi$
$691$	3.13336e6	+	3.13336e6i	0.249641	+	0.249641i	−0.571182	+	0.820823i	$0.693515\pi$
$692$	2.95297e6	−	8.87440e6i	0.234420	−	0.704488i
$693$	1.84516e6	−	1.84516e6i	0.145949	−	0.145949i
$694$	−8.30461e6	+	1.96275e6i	−0.654516	+	0.154691i
$695$		−	8.87857e6i		−	0.697238i
$696$	3.83892e6	+	343118.i	0.300391	+	0.0268485i
$697$			300982.i			0.0234671i
$698$	−709510.	−	3.00202e6i	−0.0551214	−	0.233225i
$699$	3.41522e6	−	3.41522e6i	0.264378	−	0.264378i
$700$	−1.63973e6	−	3.27517e6i	−0.126481	−	0.252632i
$701$	1.47680e6	+	1.47680e6i	0.113508	+	0.113508i	0.761579	−	0.648072i	$-0.224424\pi$
$701$	1.47680e6	+	1.47680e6i	0.113508	+	0.113508i	−0.648072	+	0.761579i	$0.724424\pi$
$702$	1.47163e6	+	908985.i	0.112708	+	0.0696168i
$703$	−270736.			−0.0206613
$704$	9.39400e6	−	6.52538e6i	0.714363	−	0.496220i
$705$	−1.56513e6			−0.118598
$706$	−5.24870e6	−	3.24198e6i	−0.396315	−	0.244793i
$707$	9.68974e6	+	9.68974e6i	0.729061	+	0.729061i
$708$	5.46460e6	+	1.09149e7i	0.409709	+	0.818347i
$709$	1.65383e7	−	1.65383e7i	1.23559	−	1.23559i	0.273812	−	0.961783i	$-0.411715\pi$
$709$	1.65383e7	−	1.65383e7i	1.23559	−	1.23559i	0.961783	−	0.273812i	$-0.0882845\pi$
$710$	3.06280e6	+	1.29591e7i	0.228020	+	0.964779i
$711$			1.15466e6i			0.0856602i
$712$	−8.76495e6	−	783400.i	−0.647962	−	0.0579140i
$713$		−	4.20844e7i		−	3.10025i
$714$	2.53476e6	−	599075.i	0.186076	−	0.0439780i
$715$	4.49463e6	−	4.49463e6i	0.328798	−	0.328798i
$716$	4.76842e6	−	1.43302e7i	0.347610	−	1.04465i
$717$	−101290.	−	101290.i	−0.00735818	−	0.00735818i
$718$	−4.24681e6	+	6.87550e6i	−0.307434	+	0.497730i
$719$	−8.45418e6			−0.609887			−0.304944	−	0.952370i	$-0.598638\pi$
$719$	−8.45418e6			−0.609887			−0.304944	+	0.952370i	$0.598638\pi$
$720$	3.56424e6	−	512984.i	0.256233	−	0.0368784i
$721$	8.45483e6			0.605713
$722$	5.39602e6	−	8.73605e6i	0.385239	−	0.623695i
$723$	7.53113e6	+	7.53113e6i	0.535815	+	0.535815i
$724$	−3.76834e6	−	1.25392e6i	−0.267180	−	0.0889047i
$725$	−2.07464e6	+	2.07464e6i	−0.146588	+	0.146588i
$726$	1.94263e6	−	459129.i	0.136788	−	0.0323291i
$727$			1.28702e7i			0.903129i	0.892238	+	0.451564i	$0.149134\pi$
$727$			1.28702e7i			0.903129i	−0.892238	+	0.451564i	$0.850866\pi$
$728$	−4.49427e6	−	5.37651e6i	−0.314290	−	0.375986i
$729$		−	531441.i		−	0.0370370i
$730$	−4.69047e6	−	1.98459e7i	−0.325769	−	1.37837i
$731$	5.77715e6	−	5.77715e6i	0.399871	−	0.399871i
$732$	5.60258e6	−	2.80495e6i	0.386465	−	0.193485i
$733$	−1.13526e7	−	1.13526e7i	−0.780432	−	0.780432i	0.199472	−	0.979904i	$-0.436077\pi$
$733$	−1.13526e7	−	1.13526e7i	−0.780432	−	0.780432i	−0.979904	+	0.199472i	$0.936077\pi$
$734$	3.10525e6	+	1.91803e6i	0.212744	+	0.131406i
$735$	3.23882e6			0.221141
$736$	8.74411e6	+	2.22123e7i	0.595006	+	1.51147i
$737$	−2.52112e6			−0.170972
$738$	−211673.	−	130745.i	−0.0143062	−	0.00883655i
$739$	−1.33090e7	−	1.33090e7i	−0.896468	−	0.896468i	0.0986542	−	0.995122i	$-0.468546\pi$
$739$	−1.33090e7	−	1.33090e7i	−0.896468	−	0.896468i	−0.995122	+	0.0986542i	$0.968546\pi$
$740$	−413701.	+	207121.i	−0.0277720	+	0.0139042i
$741$	−2.17009e6	+	2.17009e6i	−0.145188	+	0.145188i
$742$	−3.39082e6	−	1.43469e7i	−0.226097	−	0.956642i
$743$			9.27529e6i			0.616390i	0.951323	+	0.308195i	$0.0997249\pi$
$743$			9.27529e6i			0.616390i	−0.951323	+	0.308195i	$0.900275\pi$
$744$	1.27650e7	−	1.06704e7i	0.845450	−	0.706719i
$745$			2.42251e6i			0.159910i
$746$	2.47126e7	−	5.84067e6i	1.62581	−	0.384252i
$747$	2.32920e6	−	2.32920e6i	0.152723	−	0.152723i
$748$	−5.87495e6	−	1.95490e6i	−0.383928	−	0.127753i
$749$	−7.74206e6	−	7.74206e6i	−0.504257	−	0.504257i
$750$	−5.07031e6	+	8.20873e6i	−0.329140	+	0.532872i
$751$	1.96984e7			1.27447			0.637237	−	0.770668i	$-0.280077\pi$
$751$	1.96984e7			1.27447			0.637237	+	0.770668i	$0.280077\pi$
$752$	2.45764e6	−	3.28401e6i	0.158480	−	0.211768i
$753$	−1.43268e7			−0.920790
$754$	−2.94985e6	+	4.77574e6i	−0.188960	+	0.305923i
$755$	8.53509e6	+	8.53509e6i	0.544930	+	0.544930i
$756$	−679767.	+	2.04286e6i	−0.0432569	+	0.129997i
$757$	−4.76671e6	+	4.76671e6i	−0.302329	+	0.302329i	−0.841924	−	0.539596i	$-0.818577\pi$
$757$	−4.76671e6	+	4.76671e6i	−0.302329	+	0.302329i	0.539596	+	0.841924i	$0.318577\pi$
$758$	−1.58478e7	+	3.74554e6i	−1.00183	+	0.236778i
$759$		−	1.29463e7i		−	0.815723i
$760$	−568775.	+	6.36366e6i	−0.0357196	+	0.399643i
$761$			4.84608e6i			0.303339i	0.988431	+	0.151670i	$0.0484650\pi$
$761$			4.84608e6i			0.303339i	−0.988431	+	0.151670i	$0.951535\pi$
$762$	−3.52161e6	−	1.49003e7i	−0.219712	−	0.929626i
$763$	1.09236e7	−	1.09236e7i	0.679290	−	0.679290i
$764$	−4.61766e6	−	9.22326e6i	−0.286213	−	0.571677i
$765$	−1.37835e6	−	1.37835e6i	−0.0851544	−	0.0851544i
$766$	1.09196e7	+	6.74474e6i	0.672412	+	0.415330i
$767$	−1.77775e7			−1.09115
$768$	−4.52038e6	+	8.28412e6i	−0.276549	+	0.506808i
$769$	−9.50560e6			−0.579647			−0.289824	−	0.957080i	$-0.593597\pi$
$769$	−9.50560e6			−0.579647			−0.289824	+	0.957080i	$0.593597\pi$
$770$	6.73125e6	+	4.15771e6i	0.409137	+	0.252713i
$771$	−4.51854e6	−	4.51854e6i	−0.273755	−	0.273755i
$772$	−1.38760e7	−	2.77157e7i	−0.837954	−	1.67372i
$773$	1.74973e7	−	1.74973e7i	1.05323	−	1.05323i	0.0547282	−	0.998501i	$-0.482571\pi$
$773$	1.74973e7	−	1.74973e7i	1.05323	−	1.05323i	0.998501	−	0.0547282i	$-0.0174292\pi$
$774$	1.55337e6	+	6.57247e6i	0.0932012	+	0.394345i
$775$			1.26650e7i			0.757443i
$776$	−2.13037e6	+	2.38354e7i	−0.126999	+	1.42091i
$777$		−	276617.i		−	0.0164371i
$778$	−3.77195e6	+	891479.i	−0.223417	+	0.0528034i
$779$	312136.	−	312136.i	0.0184290	−	0.0184290i
$780$	−1.65584e6	+	4.97620e6i	−0.0974501	+	0.292861i
$781$	1.33830e7	+	1.33830e7i	0.785101	+	0.785101i
$782$	6.79072e6	−	1.09941e7i	0.397099	−	0.642896i
$783$	1.72464e6			0.100529
$784$	−5.08575e6	+	6.79580e6i	−0.295505	+	0.394867i
$785$	−2.56744e6			−0.148705
$786$	4.74189e6	−	7.67704e6i	0.273776	−	0.443238i
$787$	1.81543e7	+	1.81543e7i	1.04482	+	1.04482i	0.998947	+	0.0458772i	$0.0146083\pi$
$787$	1.81543e7	+	1.81543e7i	1.04482	+	1.04482i	0.0458772	+	0.998947i	$0.485392\pi$
$788$	6.54198e6	+	2.17686e6i	0.375313	+	0.124886i
$789$	−2.90976e6	+	2.90976e6i	−0.166405	+	0.166405i
$790$	−3.40702e6	+	805228.i	−0.194226	+	0.0459041i
$791$			2.37830e7i			1.35153i
$792$	3.92687e6	−	3.28250e6i	0.222450	−	0.185948i
$793$			9.12512e6i			0.515295i
$794$	7.19311e6	+	3.04349e7i	0.404917	+	1.71325i
$795$	−7.80161e6	+	7.80161e6i	−0.437790	+	0.437790i
$796$	1.44534e7	−	7.23614e6i	0.808512	−	0.404785i
$797$	6.65409e6	+	6.65409e6i	0.371059	+	0.371059i	0.867863	−	0.496804i	$-0.165493\pi$
$797$	6.65409e6	+	6.65409e6i	0.371059	+	0.371059i	−0.496804	+	0.867863i	$0.665493\pi$
$798$	−3.24997e6	−	2.00742e6i	−0.180664	−	0.111591i
$799$	−2.22040e6			−0.123045
$800$	−2.63147e6	−	6.68463e6i	−0.145370	−	0.369277i
$801$	−3.93765e6			−0.216848
$802$	−1.30292e7	−	8.04778e6i	−0.715290	−	0.441815i
$803$	−2.04951e7	−	2.04951e7i	−1.12166	−	1.12166i
$804$	1.86002e6	−	931225.i	0.101479	−	0.0508059i
$805$	−1.16758e7	+	1.16758e7i	−0.635036	+	0.635036i
$806$	5.57325e6	+	2.35811e7i	0.302183	+	1.27857i
$807$		−	1.25765e7i		−	0.679791i
$808$	1.72378e7	+	2.06217e7i	0.928868	+	1.11121i
$809$		−	2.81860e6i		−	0.151412i	−0.997130	−	0.0757062i	$-0.975879\pi$
$809$		−	2.81860e6i		−	0.151412i	0.997130	−	0.0757062i	$-0.0241211\pi$
$810$	1.56811e6	−	370613.i	0.0839776	−	0.0198476i
$811$	1.87385e7	−	1.87385e7i	1.00042	−	1.00042i	0.000423338	−	1.00000i	$-0.499865\pi$
$811$	1.87385e7	−	1.87385e7i	1.00042	−	1.00042i	1.00000		0.000423338i	$-0.000134753\pi$
$812$	−6.62951e6	−	2.20598e6i	−0.352851	−	0.117412i
$813$	4.11034e6	+	4.11034e6i	0.218098	+	0.218098i
$814$	−345562.	+	559459.i	−0.0182795	+	0.0295942i
$815$	−8.95324e6			−0.472157
$816$	5.05647e6	−	727753.i	0.265841	−	0.0382612i
$817$	−1.19825e7			−0.628047
$818$	1.07012e7	−	1.73250e7i	0.559177	−	0.905297i
$819$	−2.21722e6	−	2.21722e6i	−0.115505	−	0.115505i
$820$	238169.	−	715756.i	0.0123695	−	0.0371732i
$821$	2.16554e6	−	2.16554e6i	0.112126	−	0.112126i	−0.648818	−	0.760944i	$-0.724736\pi$
$821$	2.16554e6	−	2.16554e6i	0.112126	−	0.112126i	0.760944	+	0.648818i	$0.224736\pi$
$822$	−1.45483e7	+	3.43840e6i	−0.750986	+	0.177491i
$823$			3.03763e7i			1.56328i	0.623733	+	0.781638i	$0.285615\pi$
$823$			3.03763e7i			1.56328i	−0.623733	+	0.781638i	$0.714385\pi$
$824$	1.65172e7	+	1.47629e6i	0.847460	+	0.0757449i
$825$			3.89610e6i			0.199295i
$826$	−5.08954e6	−	2.15345e7i	−0.259555	−	1.09821i
$827$	−1.72863e7	+	1.72863e7i	−0.878897	+	0.878897i	−0.993421	−	0.114524i	$-0.963466\pi$
$827$	−1.72863e7	+	1.72863e7i	−0.878897	+	0.878897i	0.114524	+	0.993421i	$0.463466\pi$
$828$	4.78199e6	+	9.55148e6i	0.242400	+	0.484167i
$829$	−6.02439e6	−	6.02439e6i	−0.304458	−	0.304458i	0.538297	−	0.842755i	$-0.319068\pi$
$829$	−6.02439e6	−	6.02439e6i	−0.304458	−	0.304458i	−0.842755	+	0.538297i	$0.819068\pi$
$830$	8.49702e6	+	5.24838e6i	0.428126	+	0.264442i
$831$	−1.27904e7			−0.642514
$832$	−7.84116e6	−	1.12882e7i	−0.392710	−	0.565349i
$833$	4.59481e6			0.229432
$834$	8.85825e6	+	5.47150e6i	0.440994	+	0.272390i
$835$	−1.43108e7	−	1.43108e7i	−0.710310	−	0.710310i
$836$	4.06532e6	+	8.12002e6i	0.201177	+	0.401829i
$837$	5.26416e6	−	5.26416e6i	0.259726	−	0.259726i
$838$	−1.42831e6	−	6.04334e6i	−0.0702606	−	0.297281i
$839$		−	1.97485e7i		−	0.968567i	−0.874911	−	0.484283i	$-0.839080\pi$
$839$		−	1.97485e7i		−	0.968567i	0.874911	−	0.484283i	$-0.160920\pi$
$840$	−6.50187e6	−	581129.i	−0.317936	−	0.0284167i
$841$		−	1.49143e7i		−	0.727134i
$842$	3.63123e7	−	8.58219e6i	1.76512	−	0.417175i
$843$	−1.29543e7	+	1.29543e7i	−0.627833	+	0.627833i
$844$	4.03943e6	−	1.21395e7i	0.195193	−	0.586602i
$845$	5.99726e6	+	5.99726e6i	0.288942	+	0.288942i
$846$	964527.	−	1.56155e6i	0.0463328	−	0.0750119i
$847$	−3.61860e6			−0.173313
$848$	−4.11915e6	−	2.86200e7i	−0.196706	−	1.36672i
$849$	−2.08408e7			−0.992307
$850$	−2.04362e6	+	3.30857e6i	−0.0970179	+	0.157070i
$851$	−970422.	−	970422.i	−0.0459343	−	0.0459343i
$852$	−1.48169e7	−	4.93035e6i	−0.699291	−	0.232691i
$853$	−1.49811e7	+	1.49811e7i	−0.704970	+	0.704970i	−0.965473	−	0.260503i	$-0.916112\pi$
$853$	−1.49811e7	+	1.49811e7i	−0.704970	+	0.704970i	0.260503	+	0.965473i	$0.416112\pi$
$854$	−1.10535e7	+	2.61244e6i	−0.518628	+	0.122575i
$855$			2.85887e6i			0.133746i
$856$	−1.37729e7	−	1.64766e7i	−0.642455	−	0.768570i
$857$			2.85631e7i			1.32847i	0.747522	+	0.664237i	$0.231243\pi$
$857$			2.85631e7i			1.32847i	−0.747522	+	0.664237i	$0.768757\pi$
$858$	1.71449e6	+	7.25420e6i	0.0795090	+	0.336412i
$859$	6.41005e6	−	6.41005e6i	0.296400	−	0.296400i	−0.543202	−	0.839602i	$-0.682788\pi$
$859$	6.41005e6	−	6.41005e6i	0.296400	−	0.296400i	0.839602	+	0.543202i	$0.182788\pi$
$860$	−1.83099e7	+	9.16695e6i	−0.844191	+	0.422648i
$861$	318916.	+	318916.i	0.0146612	+	0.0146612i
$862$	−9.34001e6	−	5.76907e6i	−0.428134	−	0.264446i
$863$	−3.48213e7			−1.59154			−0.795770	−	0.605599i	$-0.792934\pi$
$863$	−3.48213e7			−1.59154			−0.795770	+	0.605599i	$0.792934\pi$
$864$	−1.68468e6	+	3.87221e6i	−0.0767775	+	0.176472i
$865$	1.26890e7			0.576615
$866$	8.32044e6	+	5.13931e6i	0.377009	+	0.232868i
$867$	7.08049e6	+	7.08049e6i	0.319901	+	0.319901i
$868$	−2.69689e7	+	1.35021e7i	−1.21496	+	0.608277i
$869$	−3.51846e6	+	3.51846e6i	−0.158053	+	0.158053i
$870$	1.20272e6	+	5.08884e6i	0.0538723	+	0.227940i
$871$			3.02948e6i			0.135308i
$872$	2.32476e7	−	1.94329e7i	1.03535	−	0.865457i
$873$			1.07080e7i			0.475526i
$874$	−1.84439e7	+	4.35910e6i	−0.816721	+	0.193027i
$875$	1.23676e7	−	1.23676e7i	0.546093	−	0.546093i
$876$	2.26911e7	+	7.55049e6i	0.999067	+	0.332441i
$877$	8.34862e6	+	8.34862e6i	0.366535	+	0.366535i	0.866212	−	0.499677i	$-0.166548\pi$
$877$	8.34862e6	+	8.34862e6i	0.366535	+	0.366535i	−0.499677	+	0.866212i	$0.666548\pi$
$878$	9.76713e6	−	1.58128e7i	0.427593	−	0.692265i
$879$	−1.01254e7			−0.442019
$880$	1.24241e7	+	9.29777e6i	0.540827	+	0.404736i
$881$	1.08631e7			0.471534			0.235767	−	0.971810i	$-0.424240\pi$
$881$	1.08631e7			0.471534			0.235767	+	0.971810i	$0.424240\pi$
$882$	−1.99595e6	+	3.23141e6i	−0.0863930	+	0.139869i
$883$	−1.91765e7	−	1.91765e7i	−0.827691	−	0.827691i	0.159506	−	0.987197i	$-0.449010\pi$
$883$	−1.91765e7	−	1.91765e7i	−0.827691	−	0.827691i	−0.987197	+	0.159506i	$0.949010\pi$
$884$	−2.34909e6	+	7.05957e6i	−0.101104	+	0.303842i
$885$	−1.17100e7	+	1.17100e7i	−0.502574	+	0.502574i
$886$	3.82356e7	−	9.03677e6i	1.63638	−	0.386749i
$887$		−	9.50504e6i		−	0.405644i	−0.979216	−	0.202822i	$-0.934989\pi$
$887$		−	9.50504e6i		−	0.405644i	0.979216	−	0.202822i	$-0.0650112\pi$
$888$	48299.8	−	540394.i	0.00205548	−	0.0229974i
$889$			2.77553e7i			1.17785i
$890$	−2.74602e6	−	1.16187e7i	−0.116206	−	0.491681i
$891$	1.61940e6	−	1.61940e6i	0.0683378	−	0.0683378i
$892$	−6.80157e6	−	1.35854e7i	−0.286218	−	0.571688i
$893$	2.30269e6	+	2.30269e6i	0.0966287	+	0.0966287i
$894$	−2.41696e6	−	1.49289e6i	−0.101141	−	0.0624719i
$895$	2.04899e7			0.855034
$896$	1.14289e7	−	1.27299e7i	0.475592	−	0.529732i
$897$	−1.55568e7			−0.645566
$898$	2.60855e7	+	1.61123e7i	1.07947	+	0.666756i
$899$	1.70833e7	+	1.70833e7i	0.704973	+	0.704973i
$900$	−1.43910e6	−	2.87444e6i	−0.0592223	−	0.118290i
$901$	−1.10679e7	+	1.10679e7i	−0.454206	+	0.454206i
$902$	−246605.	−	1.04341e6i	−0.0100922	−	0.0427012i
$903$		−	1.22428e7i		−	0.499643i
$904$	−4.15273e6	+	4.64622e7i	−0.169010	+	1.89094i
$905$		−	5.38812e6i		−	0.218683i
$906$	−1.37754e7	+	3.25573e6i	−0.557549	+	0.131773i
$907$	−5.68941e6	+	5.68941e6i	−0.229641	+	0.229641i	−0.812543	−	0.582902i	$-0.801917\pi$
$907$	−5.68941e6	+	5.68941e6i	−0.229641	+	0.229641i	0.582902	+	0.812543i	$0.301917\pi$
$908$	−1.23429e6	+	3.70933e6i	−0.0496823	+	0.149307i
$909$	8.50418e6	+	8.50418e6i	0.341368	+	0.341368i
$910$	4.99607e6	−	8.08854e6i	0.199998	−	0.323792i
$911$	3.62810e7			1.44838			0.724191	−	0.689600i	$-0.242213\pi$
$911$	3.62810e7			1.44838			0.724191	+	0.689600i	$0.242213\pi$
$912$	−5.99858e6	−	4.48913e6i	−0.238815	−	0.178721i
$913$	1.41950e7			0.563585
$914$	−1.18492e7	+	1.91836e7i	−0.469161	+	0.759563i
$915$	6.01071e6	+	6.01071e6i	0.237341	+	0.237341i
$916$	3.38804e6	+	1.12738e6i	0.133417	+	0.0443947i
$917$	−1.15666e7	+	1.15666e7i	−0.454235	+	0.454235i
$918$	2.22462e6	−	525777.i	0.0871264	−	0.0205918i
$919$		−	3.35577e7i		−	1.31070i	−0.755325	−	0.655351i	$-0.772521\pi$
$919$		−	3.35577e7i		−	1.31070i	0.755325	−	0.655351i	$-0.227479\pi$
$920$	−2.48485e7	+	2.07710e7i	−0.967899	+	0.809075i
$921$		−	1.86704e7i		−	0.725279i
$922$	−2.80667e6	−	1.18753e7i	−0.108733	−	0.460064i
$923$	1.60815e7	−	1.60815e7i	0.621331	−	0.621331i
$924$	−8.29638e6	+	4.15362e6i	−0.319675	+	0.160047i
$925$	292041.	+	292041.i	0.0112225	+	0.0112225i
$926$	2.72131e6	+	1.68088e6i	0.104292	+	0.0644183i
$927$	7.42036e6			0.283613
$928$	−1.25661e7	−	5.46715e6i	−0.478996	−	0.208397i
$929$	−2.30983e7			−0.878093			−0.439047	−	0.898464i	$-0.644684\pi$
$929$	−2.30983e7			−0.878093			−0.439047	+	0.898464i	$0.644684\pi$
$930$	1.92039e7	+	1.18617e7i	0.728085	+	0.449718i
$931$	−4.76509e6	−	4.76509e6i	−0.180176	−	0.180176i
$932$	−1.53558e7	+	7.68794e6i	−0.579072	+	0.289915i
$933$	1.13946e7	−	1.13946e7i	0.428543	−	0.428543i
$934$	4.55635e6	+	1.92784e7i	0.170903	+	0.723110i
$935$		−	8.40023e6i		−	0.314240i
$936$	−3.94439e6	−	4.71868e6i	−0.147160	−	0.176048i
$937$		−	4.37450e7i		−	1.62772i	−0.581062	−	0.813859i	$-0.697363\pi$
$937$		−	4.37450e7i		−	1.62772i	0.581062	−	0.813859i	$-0.302637\pi$
$938$	−3.66969e6	+	867311.i	−0.136183	+	0.0321861i
$939$	1.10664e7	−	1.10664e7i	0.409584	−	0.409584i
$940$	5.28026e6	+	1.75702e6i	0.194911	+	0.0648569i
$941$	3.09201e7	+	3.09201e7i	1.13833	+	1.13833i	0.988750	+	0.149575i	$0.0477907\pi$
$941$	3.09201e7	+	3.09201e7i	1.13833	+	1.13833i	0.149575	+	0.988750i	$0.452209\pi$
$942$	1.58221e6	−	2.56156e6i	0.0580946	−	0.0940541i
$943$	2.23763e6			0.0819425
$944$	−6.18275e6	−	4.29581e7i	−0.225814	−	1.56897i
$945$	−2.92096e6			−0.106401
$946$	−1.52942e7	+	2.47610e7i	−0.555647	+	0.899582i
$947$	−1.45245e7	−	1.45245e7i	−0.526291	−	0.526291i	0.393174	−	0.919464i	$-0.371377\pi$
$947$	−1.45245e7	−	1.45245e7i	−0.526291	−	0.526291i	−0.919464	+	0.393174i	$0.871377\pi$
$948$	1.29622e6	−	3.89545e6i	0.0468443	−	0.140779i
$949$	−2.46278e7	+	2.46278e7i	−0.887686	+	0.887686i
$950$	5.55054e6	−	1.31184e6i	0.199538	−	0.0471597i
$951$		−	1.42905e7i		−	0.512385i
$952$	−9.22399e6	−	824428.i	−0.329858	−	0.0294822i
$953$			1.25116e7i			0.446251i	0.974790	+	0.223126i	$0.0716260\pi$
$953$			1.25116e7i			0.446251i	−0.974790	+	0.223126i	$0.928374\pi$
$954$	−2.97594e6	−	1.25916e7i	−0.105865	−	0.447929i
$955$	9.89514e6	−	9.89514e6i	0.351086	−	0.351086i
$956$	228013.	+	455430.i	0.00806892	+	0.0161167i
$957$	5.25530e6	+	5.25530e6i	0.185489	+	0.185489i
$958$	2.01836e7	+	1.24669e7i	0.710535	+	0.438878i
$959$	2.70995e7			0.951514
$960$	−1.26005e7	−	2.27057e6i	−0.441275	−	0.0795164i
$961$	7.56585e7			2.64271
$962$	672268.	+	415241.i	0.0234210	+	0.0144665i
$963$	−6.79480e6	−	6.79480e6i	−0.236108	−	0.236108i
$964$	−1.69532e7	−	3.38621e7i	−0.587570	−	1.17360i
$965$	2.97347e7	−	2.97347e7i	1.02789	−	1.02789i
$966$	−4.45378e6	−	1.88445e7i	−0.153563	−	0.649742i
$967$			3.53145e6i			0.121447i	0.998155	+	0.0607236i	$0.0193408\pi$
$967$			3.53145e6i			0.121447i	−0.998155	+	0.0607236i	$0.980659\pi$
$968$	−7.06924e6	−	631839.i	−0.242485	−	0.0216730i
$969$			4.05578e6i			0.138760i
$970$	−3.15959e7	+	7.46751e6i	−1.07821	+	0.254828i
$971$	−5.24102e6	+	5.24102e6i	−0.178389	+	0.178389i	−0.790653	−	0.612264i	$-0.790259\pi$
$971$	−5.24102e6	+	5.24102e6i	−0.178389	+	0.178389i	0.612264	+	0.790653i	$0.290259\pi$
$972$	−596596.	+	1.79291e6i	−0.0202542	+	0.0608687i
$973$	−1.33462e7	−	1.33462e7i	−0.451936	−	0.451936i
$974$	7.22874e6	−	1.17032e7i	0.244155	−	0.395282i
$975$	4.68171e6			0.157722
$976$	−2.20502e7	+	3.17358e6i	−0.740947	+	0.106641i
$977$	−1.49681e7			−0.501686			−0.250843	−	0.968028i	$-0.580708\pi$
$977$	−1.49681e7			−0.501686			−0.250843	+	0.968028i	$0.580708\pi$
$978$	5.51751e6	−	8.93275e6i	0.184457	−	0.298633i
$979$	−1.19988e7	−	1.19988e7i	−0.400111	−	0.400111i
$980$	−1.09268e7	−	3.63590e6i	−0.363435	−	0.120934i
$981$	9.58709e6	−	9.58709e6i	0.318064	−	0.318064i
$982$	1.12701e7	−	2.66363e6i	0.372949	−	0.0881444i
$983$		−	3.51865e7i		−	1.16143i	−0.814107	−	0.580715i	$-0.802773\pi$
$983$		−	3.51865e7i		−	1.16143i	0.814107	−	0.580715i	$-0.197227\pi$
$984$	567344.	+	678715.i	0.0186792	+	0.0223460i
$985$			9.35398e6i			0.307189i
$986$	1.70625e6	+	7.21936e6i	0.0558923	+	0.236487i
$987$	−2.35270e6	+	2.35270e6i	−0.0768730	+	0.0768730i
$988$	9.75734e6	−	4.88505e6i	0.318009	−	0.159212i
$989$	−4.29498e7	−	4.29498e7i	−1.39627	−	1.39627i
$990$	5.90766e6	+	3.64900e6i	0.191570	+	0.118328i
$991$	−1.02447e7			−0.331370			−0.165685	−	0.986179i	$-0.552983\pi$
$991$	−1.02447e7			−0.331370			−0.165685	+	0.986179i	$0.552983\pi$
$992$	−5.50435e7	+	2.16685e7i	−1.77594	+	0.699115i
$993$	2.92678e7			0.941927
$994$	2.40840e7	+	1.48760e7i	0.773149	+	0.477553i
$995$	1.55062e7	+	1.55062e7i	0.496534	+	0.496534i
$996$	−1.04727e7	+	5.24322e6i	−0.334512	+	0.167475i
$997$	1.08282e7	−	1.08282e7i	0.345000	−	0.345000i	−0.513243	−	0.858243i	$-0.671556\pi$
$997$	1.08282e7	−	1.08282e7i	0.345000	−	0.345000i	0.858243	+	0.513243i	$0.171556\pi$
$998$	−3.37624e6	−	1.42853e7i	−0.107302	−	0.454007i
$999$		−	242772.i		−	0.00769635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.j.a.13.17	✓	40
3.2	odd	2		144.6.k.c.109.4		40
4.3	odd	2		192.6.j.a.145.15		40
8.3	odd	2		384.6.j.b.289.6		40
8.5	even	2		384.6.j.a.289.15		40
12.11	even	2		576.6.k.c.145.15		40
16.3	odd	4		384.6.j.b.97.6		40
16.5	even	4	inner	48.6.j.a.37.17	yes	40
16.11	odd	4		192.6.j.a.49.15		40
16.13	even	4		384.6.j.a.97.15		40
48.5	odd	4		144.6.k.c.37.4		40
48.11	even	4		576.6.k.c.433.15		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.j.a.13.17	✓	40	1.1	even	1	trivial
48.6.j.a.37.17	yes	40	16.5	even	4	inner
144.6.k.c.37.4		40	48.5	odd	4
144.6.k.c.109.4		40	3.2	odd	2
192.6.j.a.49.15		40	16.11	odd	4
192.6.j.a.145.15		40	4.3	odd	2
384.6.j.a.97.15		40	16.13	even	4
384.6.j.a.289.15		40	8.5	even	2
384.6.j.b.97.6		40	16.3	odd	4
384.6.j.b.289.6		40	8.3	odd	2
576.6.k.c.145.15		40	12.11	even	2
576.6.k.c.433.15		40	48.11	even	4

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.81279 + 2.97273i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(14.3258 + 28.6142i) q^{4} +(-30.6986 + 30.6986i) q^{5} +(-11.7101 - 49.5467i) q^{6} +92.2922i q^{7} +(-16.1150 + 180.301i) q^{8} +81.0000i q^{9} +O(q^{10})\)	\(q+(4.81279 + 2.97273i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(14.3258 + 28.6142i) q^{4} +(-30.6986 + 30.6986i) q^{5} +(-11.7101 - 49.5467i) q^{6} +92.2922i q^{7} +(-16.1150 + 180.301i) q^{8} +81.0000i q^{9} +(-239.005 + 56.4873i) q^{10} +(-246.823 + 246.823i) q^{11} +(90.9306 - 273.268i) q^{12} +(296.592 + 296.592i) q^{13} +(-274.359 + 444.182i) q^{14} +390.730 q^{15} +(-613.542 + 819.843i) q^{16} +554.315 q^{17} +(-240.791 + 389.836i) q^{18} +(-574.858 - 574.858i) q^{19} +(-1318.20 - 438.633i) q^{20} +(587.344 - 587.344i) q^{21} +(-1921.64 + 454.169i) q^{22} -4121.02i q^{23} +(1249.98 - 1044.87i) q^{24} +1240.19i q^{25} +(545.747 + 2309.12i) q^{26} +(515.481 - 515.481i) q^{27} +(-2640.86 + 1322.16i) q^{28} +(1672.84 + 1672.84i) q^{29} +(1880.50 + 1161.53i) q^{30} +10212.1 q^{31} +(-5390.01 + 2121.83i) q^{32} +3141.54 q^{33} +(2667.80 + 1647.83i) q^{34} +(-2833.24 - 2833.24i) q^{35} +(-2317.75 + 1160.39i) q^{36} +(235.481 - 235.481i) q^{37} +(-1057.77 - 4475.56i) q^{38} -3775.00i q^{39} +(-5040.27 - 6029.69i) q^{40} +542.980i q^{41} +(4572.77 - 1080.75i) q^{42} +(10422.1 - 10422.1i) q^{43} +(-10598.6 - 3526.69i) q^{44} +(-2486.59 - 2486.59i) q^{45} +(12250.7 - 19833.6i) q^{46} -4005.66 q^{47} +(9122.01 - 1312.89i) q^{48} +8289.16 q^{49} +(-3686.74 + 5968.76i) q^{50} +(-3527.64 - 3527.64i) q^{51} +(-4237.82 + 12735.7i) q^{52} +(-19966.8 + 19966.8i) q^{53} +(4013.28 - 948.516i) q^{54} -15154.2i q^{55} +(-16640.3 - 1487.29i) q^{56} +7316.75i q^{57} +(3078.13 + 13023.9i) q^{58} +(-29969.7 + 29969.7i) q^{59} +(5597.52 + 11180.4i) q^{60} +(15383.3 + 15383.3i) q^{61} +(49148.8 + 30357.9i) q^{62} -7475.66 q^{63} +(-32248.6 - 5811.10i) q^{64} -18209.9 q^{65} +(15119.6 + 9338.94i) q^{66} +(5107.14 + 5107.14i) q^{67} +(7941.02 + 15861.3i) q^{68} +(-26226.0 + 26226.0i) q^{69} +(-5213.34 - 22058.2i) q^{70} -54221.0i q^{71} +(-14604.3 - 1305.32i) q^{72} +83035.8i q^{73} +(1833.34 - 433.300i) q^{74} +(7892.51 - 7892.51i) q^{75} +(8213.78 - 24684.4i) q^{76} +(-22779.8 - 22779.8i) q^{77} +(11222.0 - 18168.3i) q^{78} +14255.0 q^{79} +(-6333.14 - 44003.0i) q^{80} -6561.00 q^{81} +(-1614.13 + 2613.25i) q^{82} +(-28755.5 - 28755.5i) q^{83} +(25220.5 + 8392.18i) q^{84} +(-17016.7 + 17016.7i) q^{85} +(81141.7 - 19177.4i) q^{86} -21291.8i q^{87} +(-40524.7 - 48479.8i) q^{88} +48613.0i q^{89} +(-4575.47 - 19359.4i) q^{90} +(-27373.1 + 27373.1i) q^{91} +(117920. - 59036.9i) q^{92} +(-64989.6 - 64989.6i) q^{93} +(-19278.4 - 11907.7i) q^{94} +35294.7 q^{95} +(47805.1 + 20798.6i) q^{96} +132198. q^{97} +(39893.9 + 24641.4i) q^{98} +(-19992.6 - 19992.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 492 q^{8}+O(q^{10}) \) 40 * q + 44 * q^4 - 492 * q^8	\( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 492 * q^8 + 968 * q^10 + 1208 * q^11 - 792 * q^12 + 324 * q^14 - 1800 * q^15 - 384 * q^16 - 324 * q^18 + 2360 * q^19 - 7600 * q^20 - 1024 * q^22 + 5220 * q^24 - 12980 * q^26 + 10472 * q^28 - 8144 * q^29 - 1368 * q^30 + 23064 * q^31 + 44160 * q^32 + 4864 * q^34 - 4776 * q^35 - 1620 * q^36 + 21296 * q^37 - 72088 * q^38 - 90864 * q^40 - 14220 * q^42 + 31416 * q^43 + 43768 * q^44 + 90664 * q^46 + 44784 * q^48 - 96040 * q^49 + 106212 * q^50 + 10440 * q^51 - 116432 * q^52 - 49456 * q^53 - 14580 * q^54 - 158592 * q^56 - 111472 * q^58 + 28960 * q^59 + 49464 * q^60 + 48080 * q^61 + 191100 * q^62 + 31752 * q^63 + 369032 * q^64 - 55376 * q^65 + 63720 * q^66 + 101488 * q^67 - 122336 * q^68 - 22320 * q^69 - 460192 * q^70 - 28836 * q^72 - 94996 * q^74 - 96624 * q^75 + 211304 * q^76 - 14896 * q^77 + 200124 * q^78 - 71960 * q^79 + 623368 * q^80 - 262440 * q^81 + 33880 * q^82 - 126440 * q^83 - 116856 * q^84 + 132400 * q^85 - 581168 * q^86 - 466400 * q^88 - 46008 * q^90 + 429496 * q^91 - 12752 * q^92 + 524120 * q^94 - 76848 * q^95 + 51840 * q^96 + 477736 * q^98 + 97848 * q^99

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