LMFDB - Embedded newform 40.6.f.a.29.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(29,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("40.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.f (of order $2$, degree $1$, 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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.18
Character	$\chi$	$=$	40.29
Dual form			40.6.f.a.29.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.42014 + 5.47569i) q^{2} -7.17847 q^{3} +(-27.9664 + 15.5525i) q^{4} +(-1.28331 + 55.8870i) q^{5} +(-10.1944 - 39.3071i) q^{6} -146.905i q^{7} +(-124.877 - 131.049i) q^{8} -191.470 q^{9} +(-307.842 + 72.3401i) q^{10} +42.4351i q^{11} +(200.756 - 111.643i) q^{12} -605.383 q^{13} +(804.405 - 208.625i) q^{14} +(9.21223 - 401.183i) q^{15} +(540.241 - 869.894i) q^{16} -409.138i q^{17} +(-271.913 - 1048.43i) q^{18} +2096.86i q^{19} +(-833.291 - 1582.92i) q^{20} +1054.55i q^{21} +(-232.362 + 60.2637i) q^{22} +3048.59i q^{23} +(896.424 + 940.730i) q^{24} +(-3121.71 - 143.441i) q^{25} +(-859.728 - 3314.89i) q^{26} +3118.83 q^{27} +(2284.73 + 4108.40i) q^{28} +4594.96i q^{29} +(2209.84 - 519.291i) q^{30} -5118.83 q^{31} +(5530.49 + 1722.83i) q^{32} -304.619i q^{33} +(2240.32 - 581.033i) q^{34} +(8210.06 + 188.525i) q^{35} +(5354.72 - 2977.82i) q^{36} -11248.5 q^{37} +(-11481.8 + 2977.83i) q^{38} +4345.73 q^{39} +(7484.18 - 6810.80i) q^{40} +11002.0 q^{41} +(-5774.40 + 1497.61i) q^{42} +8413.16 q^{43} +(-659.971 - 1186.76i) q^{44} +(245.715 - 10700.7i) q^{45} +(-16693.2 + 4329.42i) q^{46} -3975.72i q^{47} +(-3878.11 + 6244.51i) q^{48} -4774.02 q^{49} +(-3647.81 - 17297.2i) q^{50} +2936.99i q^{51} +(16930.4 - 9415.21i) q^{52} -38273.5 q^{53} +(4429.16 + 17077.7i) q^{54} +(-2371.57 - 54.4575i) q^{55} +(-19251.7 + 18345.0i) q^{56} -15052.2i q^{57} +(-25160.6 + 6525.47i) q^{58} -36611.0i q^{59} +(5981.75 + 11362.9i) q^{60} -3181.32i q^{61} +(-7269.44 - 28029.1i) q^{62} +28127.8i q^{63} +(-1579.62 + 32729.9i) q^{64} +(776.897 - 33833.0i) q^{65} +(1668.00 - 432.601i) q^{66} +41894.6 q^{67} +(6363.11 + 11442.1i) q^{68} -21884.2i q^{69} +(10627.1 + 45223.5i) q^{70} +72161.6 q^{71} +(23910.1 + 25091.9i) q^{72} +48275.5i q^{73} +(-15974.4 - 61593.2i) q^{74} +(22409.1 + 1029.69i) q^{75} +(-32611.3 - 58641.7i) q^{76} +6233.92 q^{77} +(6171.53 + 23795.9i) q^{78} -39428.9 q^{79} +(47922.4 + 31308.8i) q^{80} +24138.7 q^{81} +(15624.4 + 60243.7i) q^{82} -46504.5 q^{83} +(-16400.9 - 29492.0i) q^{84} +(22865.5 + 525.053i) q^{85} +(11947.8 + 46067.9i) q^{86} -32984.8i q^{87} +(5561.07 - 5299.16i) q^{88} -38217.3 q^{89} +(58942.4 - 13850.9i) q^{90} +88933.7i q^{91} +(-47413.2 - 85258.2i) q^{92} +36745.3 q^{93} +(21769.8 - 5646.07i) q^{94} +(-117187. - 2690.93i) q^{95} +(-39700.4 - 12367.3i) q^{96} +95979.0i q^{97} +(-6779.76 - 26141.1i) q^{98} -8125.03i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9} - 16 q^{10} - 692 q^{14} - 488 q^{15} + 1560 q^{16} + 2732 q^{20} - 2224 q^{24} + 1556 q^{25} - 9976 q^{26} - 15012 q^{30} + 4368 q^{31} + 13016 q^{34} - 34116 q^{36}+ \cdots - 236176 q^{96}+O(q^{100}) $ 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9 - 16 * q^10 - 692 * q^14 - 488 * q^15 + 1560 * q^16 + 2732 * q^20 - 2224 * q^24 + 1556 * q^25 - 9976 * q^26 - 15012 * q^30 + 4368 * q^31 + 13016 * q^34 - 34116 * q^36 + 23360 * q^39 - 22496 * q^40 - 2480 * q^41 + 10712 * q^44 + 58372 * q^46 - 38420 * q^49 + 45624 * q^50 - 3568 * q^54 - 48776 * q^55 + 110944 * q^56 + 111688 * q^60 - 46944 * q^64 + 37200 * q^65 - 136120 * q^66 - 112852 * q^70 - 69232 * q^71 + 34176 * q^74 - 13944 * q^76 - 35984 * q^79 - 47064 * q^80 + 122596 * q^81 - 165688 * q^84 - 73676 * q^86 - 178744 * q^89 + 51496 * q^90 + 314740 * q^94 + 89416 * q^95 - 236176 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.42014	+	5.47569i	0.251047	+	0.967975i
$2$	1.42014	+	5.47569i	0.251047	+	0.967975i
$3$	−7.17847			−0.460499			−0.230250	−	0.973132i	$-0.573954\pi$
$3$	−7.17847			−0.460499			−0.230250	+	0.973132i	$0.573954\pi$
$4$	−27.9664	+	15.5525i	−0.873951	+	0.486015i
$5$	−1.28331	+	55.8870i	−0.0229566	+	0.999736i
$5$	−1.28331	+	55.8870i	−0.0229566	+	0.999736i
$6$	−10.1944	−	39.3071i	−0.115607	−	0.445751i
$7$		−	146.905i		−	1.13316i	−0.824007	−	0.566580i	$-0.808266\pi$
$7$		−	146.905i		−	1.13316i	0.824007	−	0.566580i	$-0.191734\pi$
$8$	−124.877	−	131.049i	−0.689853	−	0.723950i
$9$	−191.470			−0.787941
$10$	−307.842	+	72.3401i	−0.973483	+	0.228760i
$11$			42.4351i			0.105741i	0.998601	+	0.0528705i	$0.0168371\pi$
$11$			42.4351i			0.105741i	−0.998601	+	0.0528705i	$0.983163\pi$
$12$	200.756	−	111.643i	0.402453	−	0.223809i
$13$	−605.383			−0.993510			−0.496755	−	0.867891i	$-0.665475\pi$
$13$	−605.383			−0.993510			−0.496755	+	0.867891i	$0.665475\pi$
$14$	804.405	−	208.625i	1.09687	−	0.284476i
$15$	9.21223	−	401.183i	0.0105715	−	0.460378i
$16$	540.241	−	869.894i	0.527579	−	0.849506i
$17$		−	409.138i		−	0.343359i	−0.985153	−	0.171679i	$-0.945081\pi$
$17$		−	409.138i		−	0.343359i	0.985153	−	0.171679i	$-0.0549193\pi$
$18$	−271.913	−	1048.43i	−0.197810	−	0.762707i
$19$			2096.86i			1.33256i	0.745704	+	0.666278i	$0.232114\pi$
$19$			2096.86i			1.33256i	−0.745704	+	0.666278i	$0.767886\pi$
$20$	−833.291	−	1582.92i	−0.465824	−	0.884878i
$21$			1054.55i			0.521819i
$22$	−232.362	+	60.2637i	−0.102355	+	0.0265460i
$23$			3048.59i			1.20166i	0.799379	+	0.600828i	$0.205162\pi$
$23$			3048.59i			1.20166i	−0.799379	+	0.600828i	$0.794838\pi$
$24$	896.424	+	940.730i	0.317677	+	0.333378i
$25$	−3121.71	−	143.441i	−0.998946	−	0.0459011i
$26$	−859.728	−	3314.89i	−0.249418	−	0.961693i
$27$	3118.83			0.823345
$28$	2284.73	+	4108.40i	0.550732	+	0.990325i
$29$			4594.96i			1.01458i	0.861775	+	0.507290i	$0.169353\pi$
$29$			4594.96i			1.01458i	−0.861775	+	0.507290i	$0.830647\pi$
$30$	2209.84	−	519.291i	0.448288	−	0.105344i
$31$	−5118.83			−0.956679			−0.478339	−	0.878175i	$-0.658761\pi$
$31$	−5118.83			−0.956679			−0.478339	+	0.878175i	$0.658761\pi$
$32$	5530.49	+	1722.83i	0.954747	+	0.297418i
$33$		−	304.619i		−	0.0486937i
$34$	2240.32	−	581.033i	0.332363	−	0.0861992i
$35$	8210.06	+	188.525i	1.13286	+	0.0260135i
$36$	5354.72	−	2977.82i	0.688621	−	0.382951i
$37$	−11248.5			−1.35080			−0.675398	−	0.737454i	$-0.736028\pi$
$37$	−11248.5			−1.35080			−0.675398	+	0.737454i	$0.736028\pi$
$38$	−11481.8	+	2977.83i	−1.28988	+	0.334534i
$39$	4345.73			0.457510
$40$	7484.18	−	6810.80i	0.739596	−	0.673052i
$41$	11002.0			1.02215			0.511073	−	0.859537i	$-0.329248\pi$
$41$	11002.0			1.02215			0.511073	+	0.859537i	$0.329248\pi$
$42$	−5774.40	+	1497.61i	−0.505107	+	0.131001i
$43$	8413.16			0.693886			0.346943	−	0.937886i	$-0.387220\pi$
$43$	8413.16			0.693886			0.346943	+	0.937886i	$0.387220\pi$
$44$	−659.971	−	1186.76i	−0.0513917	−	0.0924125i
$45$	245.715	−	10700.7i	0.0180884	−	0.787733i
$46$	−16693.2	+	4329.42i	−1.16317	+	0.301672i
$47$		−	3975.72i		−	0.262525i	−0.991348	−	0.131263i	$-0.958097\pi$
$47$		−	3975.72i		−	0.262525i	0.991348	−	0.131263i	$-0.0419031\pi$
$48$	−3878.11	+	6244.51i	−0.242950	+	0.391197i
$49$	−4774.02			−0.284049
$50$	−3647.81	−	17297.2i	−0.206351	−	0.978478i
$51$			2936.99i			0.158116i
$52$	16930.4	−	9415.21i	0.868279	−	0.482860i
$53$	−38273.5			−1.87158			−0.935790	−	0.352558i	$-0.885312\pi$
$53$	−38273.5			−1.87158			−0.935790	+	0.352558i	$0.885312\pi$
$54$	4429.16	+	17077.7i	0.206698	+	0.796977i
$55$	−2371.57	−	54.4575i	−0.105713	−	0.00242746i
$56$	−19251.7	+	18345.0i	−0.820350	+	0.781713i
$57$		−	15052.2i		−	0.613641i
$58$	−25160.6	+	6525.47i	−0.982088	+	0.254707i
$59$		−	36611.0i		−	1.36924i	−0.728898	−	0.684622i	$-0.759967\pi$
$59$		−	36611.0i		−	1.36924i	0.728898	−	0.684622i	$-0.240033\pi$
$60$	5981.75	+	11362.9i	0.214511	+	0.407485i
$61$		−	3181.32i		−	0.109467i	−0.998501	−	0.0547335i	$-0.982569\pi$
$61$		−	3181.32i		−	0.109467i	0.998501	−	0.0547335i	$-0.0174309\pi$
$62$	−7269.44	−	28029.1i	−0.240172	−	0.926041i
$63$			28127.8i			0.892862i
$64$	−1579.62	+	32729.9i	−0.0482062	+	0.998837i
$65$	776.897	−	33833.0i	0.0228076	−	0.993248i
$66$	1668.00	−	432.601i	0.0471342	−	0.0122244i
$67$	41894.6			1.14017			0.570087	−	0.821584i	$-0.306909\pi$
$67$	41894.6			1.14017			0.570087	+	0.821584i	$0.306909\pi$
$68$	6363.11	+	11442.1i	0.166877	+	0.300079i
$69$		−	21884.2i		−	0.553361i
$70$	10627.1	+	45223.5i	0.259221	+	1.10311i
$71$	72161.6			1.69887			0.849435	−	0.527693i	$-0.176943\pi$
$71$	72161.6			1.69887			0.849435	+	0.527693i	$0.176943\pi$
$72$	23910.1	+	25091.9i	0.543563	+	0.570429i
$73$			48275.5i			1.06028i	0.847911	+	0.530138i	$0.177860\pi$
$73$			48275.5i			1.06028i	−0.847911	+	0.530138i	$0.822140\pi$
$74$	−15974.4	−	61593.2i	−0.339113	−	1.30754i
$75$	22409.1	+	1029.69i	0.460014	+	0.0211374i
$76$	−32611.3	−	58641.7i	−0.647642	−	1.16459i
$77$	6233.92			0.119821
$78$	6171.53	+	23795.9i	0.114857	+	0.442859i
$79$	−39428.9			−0.710798			−0.355399	−	0.934715i	$-0.615655\pi$
$79$	−39428.9			−0.710798			−0.355399	+	0.934715i	$0.615655\pi$
$80$	47922.4	+	31308.8i	0.837170	+	0.546942i
$81$	24138.7			0.408791
$82$	15624.4	+	60243.7i	0.256607	+	0.989412i
$83$	−46504.5			−0.740968			−0.370484	−	0.928839i	$-0.620808\pi$
$83$	−46504.5			−0.740968			−0.370484	+	0.928839i	$0.620808\pi$
$84$	−16400.9	−	29492.0i	−0.253612	−	0.456044i
$85$	22865.5	+	525.053i	0.343268	+	0.00788235i
$86$	11947.8	+	46067.9i	0.174198	+	0.671664i
$87$		−	32984.8i		−	0.467213i
$88$	5561.07	−	5299.16i	0.0765512	−	0.0729458i
$89$	−38217.3			−0.511428			−0.255714	−	0.966752i	$-0.582311\pi$
$89$	−38217.3			−0.511428			−0.255714	+	0.966752i	$0.582311\pi$
$90$	58942.4	−	13850.9i	0.767047	−	0.180249i
$91$			88933.7i			1.12580i
$92$	−47413.2	−	85258.2i	−0.584022	−	1.05019i
$93$	36745.3			0.440550
$94$	21769.8	−	5646.07i	0.254118	−	0.0659062i
$95$	−117187.	−	2690.93i	−1.33220	−	0.0305910i
$96$	−39700.4	−	12367.3i	−0.439660	−	0.136961i
$97$			95979.0i			1.03573i	0.855462	+	0.517865i	$0.173273\pi$
$97$			95979.0i			1.03573i	−0.855462	+	0.517865i	$0.826727\pi$
$98$	−6779.76	−	26141.1i	−0.0713098	−	0.274953i
$99$		−	8125.03i		−	0.0833177i
$100$	89533.8	−	44538.7i	0.895338	−	0.445387i
$101$			83900.0i			0.818386i	0.912448	+	0.409193i	$0.134190\pi$
$101$			83900.0i			0.818386i	−0.912448	+	0.409193i	$0.865810\pi$
$102$	−16082.0	+	4170.93i	−0.153053	+	0.0396947i
$103$		−	10693.4i		−	0.0993165i	−0.998766	−	0.0496583i	$-0.984187\pi$
$103$		−	10693.4i		−	0.0993165i	0.998766	−	0.0496583i	$-0.0158132\pi$
$104$	75598.3	+	79334.8i	0.685376	+	0.719251i
$105$	−58935.7	−	1353.32i	−0.521681	−	0.0119792i
$106$	−54353.6	−	209574.i	−0.469855	−	1.81164i
$107$	−109794.			−0.927081			−0.463540	−	0.886076i	$-0.653421\pi$
$107$	−109794.			−0.927081			−0.463540	+	0.886076i	$0.653421\pi$
$108$	−87222.4	+	48505.5i	−0.719563	+	0.400158i
$109$			135615.i			1.09330i	0.837361	+	0.546651i	$0.184097\pi$
$109$			135615.i			1.09330i	−0.837361	+	0.546651i	$0.815903\pi$
$110$	−3069.76	−	13063.3i	−0.0241893	−	0.102937i
$111$	80746.9			0.622040
$112$	−127792.	−	79364.0i	−0.962625	−	0.597831i
$113$		−	195440.i		−	1.43985i	−0.694050	−	0.719927i	$-0.744175\pi$
$113$		−	195440.i		−	1.43985i	0.694050	−	0.719927i	$-0.255825\pi$
$114$	82421.5	−	21376.3i	0.593989	−	0.154053i
$115$	−170377.	−	3912.30i	−1.20134	−	0.0275859i
$116$	−71462.9	−	128504.i	−0.493101	−	0.886693i
$117$	115913.			0.782827
$118$	200470.	−	51992.6i	1.32539	−	0.343745i
$119$	−60104.4			−0.389080
$120$	−53725.0	+	48891.1i	−0.340583	+	0.309940i
$121$	159250.			0.988819
$122$	17420.0	−	4517.92i	0.105961	−	0.0274814i
$123$	−78977.7			−0.470697
$124$	143155.	−	79610.4i	0.836090	−	0.464960i
$125$	12022.6	−	174279.i	0.0688214	−	0.997629i
$126$	−154019.	+	39945.3i	−0.864268	+	0.224150i
$127$		−	171245.i		−	0.942126i	−0.882100	−	0.471063i	$-0.843870\pi$
$127$		−	171245.i		−	0.942126i	0.882100	−	0.471063i	$-0.156130\pi$
$128$	−181462.	+	37831.4i	−0.978952	+	0.204093i
$129$	−60393.6			−0.319534
$130$	186363.	−	43793.5i	0.967165	−	0.227275i
$131$			111420.i			0.567265i	0.958933	+	0.283632i	$0.0915395\pi$
$131$			111420.i			0.567265i	−0.958933	+	0.283632i	$0.908460\pi$
$132$	4737.58	+	8519.11i	0.0236658	+	0.0425559i
$133$	308039.			1.51000
$134$	59496.1	+	229402.i	0.286238	+	1.10366i
$135$	−4002.43	+	174302.i	−0.0189012	+	0.823128i
$136$	−53617.1	+	51091.9i	−0.248574	+	0.236867i
$137$			282243.i			1.28476i	0.766387	+	0.642379i	$0.222052\pi$
$137$			282243.i			1.28476i	−0.766387	+	0.642379i	$0.777948\pi$
$138$	119831.	−	31078.6i	0.535640	−	0.138920i
$139$		−	44060.1i		−	0.193423i	−0.995312	−	0.0967117i	$-0.969168\pi$
$139$		−	44060.1i		−	0.193423i	0.995312	−	0.0967117i	$-0.0308325\pi$
$140$	−232538.	+	122414.i	−1.00271	+	0.527852i
$141$			28539.6i			0.120893i
$142$	102479.	+	395135.i	0.426496	+	1.64446i
$143$		−	25689.5i		−	0.105055i
$144$	−103440.	+	166558.i	−0.415701	+	0.669360i
$145$	−256798.	−	5896.77i	−1.01431	−	0.0232913i
$146$	−264342.	+	68557.8i	−1.02632	+	0.266180i
$147$	34270.1			0.130804
$148$	314580.	−	174942.i	1.18053	−	0.656506i
$149$		−	251552.i		−	0.928244i	−0.885771	−	0.464122i	$-0.846370\pi$
$149$		−	251552.i		−	0.928244i	0.885771	−	0.464122i	$-0.153630\pi$
$150$	26185.7	+	124167.i	0.0950246	+	0.450588i
$151$	95790.0			0.341883			0.170942	−	0.985281i	$-0.445319\pi$
$151$	95790.0			0.341883			0.170942	+	0.985281i	$0.445319\pi$
$152$	274791.	−	261849.i	0.964703	−	0.919267i
$153$			78337.6i			0.270546i
$154$	8853.02	+	34135.0i	0.0300808	+	0.115984i
$155$	6569.06	−	286076.i	0.0219621	−	0.956427i
$156$	−121534.	+	67586.8i	−0.399841	+	0.222357i
$157$	−178462.			−0.577824			−0.288912	−	0.957356i	$-0.593294\pi$
$157$	−178462.			−0.577824			−0.288912	+	0.957356i	$0.593294\pi$
$158$	−55994.4	−	215900.i	−0.178444	−	0.688035i
$159$	274745.			0.861861
$160$	−103381.	+	306871.i	−0.319257	+	0.947668i
$161$	447853.			1.36167
$162$	34280.3	+	132176.i	0.102626	+	0.395699i
$163$	147330.			0.434332			0.217166	−	0.976135i	$-0.430319\pi$
$163$	147330.			0.434332			0.217166	+	0.976135i	$0.430319\pi$
$164$	−307687.	+	171109.i	−0.893305	+	0.496778i
$165$	17024.2	+	390.922i	0.0486808	+	0.00111784i
$166$	−66042.7	−	254644.i	−0.186018	−	0.717239i
$167$		−	310989.i		−	0.862888i	−0.902140	−	0.431444i	$-0.858004\pi$
$167$		−	310989.i		−	0.862888i	0.902140	−	0.431444i	$-0.141996\pi$
$168$	138198.	−	131689.i	0.377770	−	0.359978i
$169$	−4803.84			−0.0129381
$170$	29597.1	+	125950.i	0.0785466	+	0.334254i
$171$		−	401485.i		−	1.04997i
$172$	−235286.	+	130845.i	−0.606422	+	0.337239i
$173$	−120278.			−0.305542			−0.152771	−	0.988262i	$-0.548820\pi$
$173$	−120278.			−0.305542			−0.152771	+	0.988262i	$0.548820\pi$
$174$	180614.	−	46842.9i	0.452251	−	0.117293i
$175$	−21072.2	+	458594.i	−0.0520133	+	1.13196i
$176$	36914.0	+	22925.2i	0.0898276	+	0.0557868i
$177$			262811.i			0.630536i
$178$	−54273.8	−	209266.i	−0.128393	−	0.495050i
$179$			180544.i			0.421162i	0.977576	+	0.210581i	$0.0675356\pi$
$179$			180544.i			0.421162i	−0.977576	+	0.210581i	$0.932464\pi$
$180$	159550.	+	303080.i	0.367041	+	0.697231i
$181$			149699.i			0.339643i	0.985475	+	0.169821i	$0.0543191\pi$
$181$			149699.i			0.339643i	−0.985475	+	0.169821i	$0.945681\pi$
$182$	−486974.	+	126298.i	−1.08975	+	0.282630i
$183$			22837.0i			0.0504095i
$184$	399515.	−	380698.i	0.869938	−	0.828965i
$185$	14435.3	−	628643.i	0.0310097	−	1.35044i
$186$	52183.4	+	201206.i	0.110599	+	0.426441i
$187$	17361.8			0.0363071
$188$	61832.2	+	111187.i	0.127591	+	0.229434i
$189$		−	458171.i		−	0.932981i
$190$	−151687.	−	645502.i	−0.304835	−	1.29722i
$191$	213909.			0.424273			0.212136	−	0.977240i	$-0.431958\pi$
$191$	213909.			0.424273			0.212136	+	0.977240i	$0.431958\pi$
$192$	11339.3	−	234951.i	0.0221989	−	0.459964i
$193$		−	729587.i		−	1.40988i	−0.709265	−	0.704942i	$-0.750973\pi$
$193$		−	729587.i		−	1.40988i	0.709265	−	0.704942i	$-0.249027\pi$
$194$	−525551.	+	136303.i	−1.00256	+	0.260017i
$195$	−5576.93	+	242869.i	−0.0105029	+	0.457390i
$196$	133512.	−	74247.8i	0.248245	−	0.138052i
$197$	−922110.			−1.69285			−0.846423	−	0.532512i	$-0.821248\pi$
$197$	−922110.			−1.69285			−0.846423	+	0.532512i	$0.821248\pi$
$198$	44490.2	−	11538.7i	0.0806494	−	0.0209167i
$199$	−985328.			−1.76379			−0.881897	−	0.471442i	$-0.843734\pi$
$199$	−985328.			−1.76379			−0.881897	+	0.471442i	$0.843734\pi$
$200$	371031.	+	427009.i	0.655896	+	0.754852i
$201$	−300739.			−0.525049
$202$	−459410.	+	119149.i	−0.792177	+	0.205454i
$203$	675021.			1.14968
$204$	−45677.4	−	82137.0i	−0.0768469	−	0.138186i
$205$	−14119.0	+	614870.i	−0.0234650	+	1.02188i
$206$	58553.6	−	15186.0i	0.0961359	−	0.0249331i
$207$		−	583713.i		−	0.946833i
$208$	−327053.	+	526619.i	−0.524155	+	0.843992i
$209$	−88980.5			−0.140906
$210$	−76286.4	−	324636.i	−0.119371	−	0.507982i
$211$			932526.i			1.44197i	0.692953	+	0.720983i	$0.256309\pi$
$211$			932526.i			1.44197i	−0.692953	+	0.720983i	$0.743691\pi$
$212$	1.07037e6	−	595247.i	1.63567	−	0.909615i
$213$	−518010.			−0.782328
$214$	−155922.	−	601196.i	−0.232741	−	0.897391i
$215$	−10796.7	+	470186.i	−0.0159293	+	0.693703i
$216$	−389469.	−	408719.i	−0.567987	−	0.596060i
$217$			751980.i			1.08407i
$218$	−742584.	+	192591.i	−1.05829	+	0.274470i
$219$		−	346544.i		−	0.488257i
$220$	67171.3	−	35360.8i	0.0935679	−	0.0492567i
$221$			247686.i			0.341130i
$222$	114672.	+	442145.i	0.156161	+	0.602119i
$223$			748564.i			1.00801i	0.863699	+	0.504007i	$0.168142\pi$
$223$			748564.i			1.00801i	−0.863699	+	0.504007i	$0.831858\pi$
$224$	253092.	−	812455.i	0.337022	−	1.08188i
$225$	597712.	+	27464.6i	0.787110	+	0.0361674i
$226$	1.07017e6	−	277552.i	1.39374	−	0.361471i
$227$	1.47117e6			1.89495			0.947475	−	0.319829i	$-0.103626\pi$
$227$	1.47117e6			1.89495			0.947475	+	0.319829i	$0.103626\pi$
$228$	234100.	+	420957.i	0.298238	+	0.536292i
$229$			835029.i			1.05223i	0.850412	+	0.526117i	$0.176353\pi$
$229$			835029.i			1.05223i	−0.850412	+	0.526117i	$0.823647\pi$
$230$	−220536.	−	938486.i	−0.274890	−	1.16979i
$231$	−44750.0			−0.0551777
$232$	602164.	−	573803.i	0.734505	−	0.699911i
$233$			284718.i			0.343577i	0.985134	+	0.171789i	$0.0549546\pi$
$233$			284718.i			0.343577i	−0.985134	+	0.171789i	$0.945045\pi$
$234$	164612.	+	634701.i	0.196526	+	0.757757i
$235$	222191.	+	5102.09i	0.262456	+	0.00602669i
$236$	569391.	+	1.02388e6i	0.665473	+	1.19665i
$237$	283039.			0.327322
$238$	−85356.5	−	329113.i	−0.0976774	−	0.376620i
$239$	800635.			0.906650			0.453325	−	0.891345i	$-0.350238\pi$
$239$	800635.			0.906650			0.453325	+	0.891345i	$0.350238\pi$
$240$	−344010.	−	224749.i	−0.385516	−	0.251866i
$241$	−1.50596e6			−1.67021			−0.835107	−	0.550088i	$-0.814594\pi$
$241$	−1.50596e6			−1.67021			−0.835107	+	0.550088i	$0.814594\pi$
$242$	226157.	+	872005.i	0.248240	+	0.957152i
$243$	−931154.			−1.01159
$244$	49477.4	+	88970.2i	0.0532026	+	0.0956688i
$245$	6126.56	−	266805.i	0.00652081	−	0.283975i
$246$	−112159.	−	432458.i	−0.118167	−	0.455623i
$247$		−	1.26940e6i		−	1.32391i
$248$	639222.	+	670817.i	0.659968	+	0.692587i
$249$	333831.			0.341215
$250$	971370.	−	181667.i	0.982957	−	0.183835i
$251$		−	1.10255e6i		−	1.10463i	−0.833637	−	0.552313i	$-0.813745\pi$
$251$		−	1.10255e6i		−	1.10463i	0.833637	−	0.552313i	$-0.186255\pi$
$252$	−437457.	−	786634.i	−0.433944	−	0.780317i
$253$	−129367.			−0.127064
$254$	937686.	−	243192.i	0.911955	−	0.236518i
$255$	−164139.	−	3769.08i	−0.158075	−	0.00362981i
$256$	−464854.	−	939905.i	−0.443320	−	0.896364i
$257$			1.41038e6i			1.33200i	0.745953	+	0.665999i	$0.231994\pi$
$257$			1.41038e6i			1.33200i	−0.745953	+	0.665999i	$0.768006\pi$
$258$	−85767.2	−	330697.i	−0.0802181	−	0.309301i
$259$			1.65246e6i			1.53067i
$260$	504460.	+	958272.i	0.462800	+	0.879135i
$261$		−	879794.i		−	0.799429i
$262$	−610103.	+	158232.i	−0.549098	+	0.142410i
$263$			1.68879e6i			1.50552i	0.658298	+	0.752758i	$0.271277\pi$
$263$			1.68879e6i			1.50552i	−0.658298	+	0.752758i	$0.728723\pi$
$264$	−39920.0	+	38039.8i	−0.0352518	+	0.0335915i
$265$	49116.9	−	2.13899e6i	0.0429651	−	1.87109i
$266$	437457.	+	1.68673e6i	0.379081	+	1.46164i
$267$	274342.			0.235512
$268$	−1.17164e6	+	651565.i	−0.996456	+	0.554141i
$269$		−	305848.i		−	0.257706i	−0.991664	−	0.128853i	$-0.958870\pi$
$269$		−	305848.i		−	0.257706i	0.991664	−	0.128853i	$-0.0411295\pi$
$270$	−960107.	+	225616.i	−0.801512	+	0.188348i
$271$	−1.25325e6			−1.03661			−0.518306	−	0.855195i	$-0.673437\pi$
$271$	−1.25325e6			−1.03661			−0.518306	+	0.855195i	$0.673437\pi$
$272$	−355907.	−	221034.i	−0.291685	−	0.181149i
$273$		−	638408.i		−	0.518432i
$274$	−1.54547e6	+	400823.i	−1.24361	+	0.322535i
$275$	6086.93	−	132470.i	0.00485363	−	0.105630i
$276$	340354.	+	612024.i	0.268942	+	0.483610i
$277$	483396.			0.378533			0.189267	−	0.981926i	$-0.439389\pi$
$277$	483396.			0.378533			0.189267	+	0.981926i	$0.439389\pi$
$278$	241260.	−	62571.4i	0.187229	−	0.0485584i
$279$	980100.			0.753806
$280$	−1.00054e6	−	1.09946e6i	−0.762674	−	0.838079i
$281$	88721.8			0.0670293			0.0335147	−	0.999438i	$-0.489330\pi$
$281$	88721.8			0.0670293			0.0335147	+	0.999438i	$0.489330\pi$
$282$	−156274.	+	40530.1i	−0.117021	+	0.0303497i
$283$	−1.76445e6			−1.30961			−0.654807	−	0.755796i	$-0.727250\pi$
$283$	−1.76445e6			−1.30961			−0.654807	+	0.755796i	$0.727250\pi$
$284$	−2.01810e6	+	1.12229e6i	−1.48473	+	0.825676i
$285$	841224.	+	19316.7i	0.613479	+	0.0140871i
$286$	140668.	−	36482.6i	0.101690	−	0.0263737i
$287$		−	1.61625e6i		−	1.15825i
$288$	−1.05892e6	−	329869.i	−0.752284	−	0.234347i
$289$	1.25246e6			0.882105
$290$	−332400.	−	1.41452e6i	−0.232095	−	0.987677i
$291$		−	688982.i		−	0.476953i
$292$	−750803.	−	1.35009e6i	−0.515310	−	0.926630i
$293$	−9124.96			−0.00620957			−0.00310479	−	0.999995i	$-0.500988\pi$
$293$	−9124.96			−0.00620957			−0.00310479	+	0.999995i	$0.500988\pi$
$294$	48668.3	+	187653.i	0.0328381	+	0.126615i
$295$	2.04608e6	+	46983.3i	1.36888	+	0.0314332i
$296$	1.40467e6	+	1.47410e6i	0.931850	+	0.977908i
$297$			132348.i			0.0870614i
$298$	1.37742e6	−	357238.i	0.898517	−	0.233033i
$299$		−	1.84557e6i		−	1.19386i
$300$	−642716.	+	319720.i	−0.412302	+	0.205100i
$301$		−	1.23593e6i		−	0.786283i
$302$	136035.	+	524516.i	0.0858288	+	0.330934i
$303$		−	602273.i		−	0.376866i
$304$	1.82405e6	+	1.13281e6i	1.13201	+	0.703029i
$305$	177795.	+	4082.64i	0.109438	+	0.00251299i
$306$	−428952.	+	111250.i	−0.261882	+	0.0679199i
$307$	−2.64214e6			−1.59996			−0.799980	−	0.600026i	$-0.795157\pi$
$307$	−2.64214e6			−1.59996			−0.799980	+	0.600026i	$0.795157\pi$
$308$	−174340.	+	96952.9i	−0.104718	+	0.0582350i
$309$			76762.0i			0.0457352i
$310$	1.57579e6	−	370297.i	0.931311	−	0.218849i
$311$	−1.40253e6			−0.822262			−0.411131	−	0.911576i	$-0.634866\pi$
$311$	−1.40253e6			−0.822262			−0.411131	+	0.911576i	$0.634866\pi$
$312$	−542680.	−	569503.i	−0.315615	−	0.331214i
$313$			1.35907e6i			0.784115i	0.919941	+	0.392058i	$0.128237\pi$
$313$			1.35907e6i			0.784115i	−0.919941	+	0.392058i	$0.871763\pi$
$314$	−253440.	−	977201.i	−0.145061	−	0.559319i
$315$	−1.57198e6	−	36096.8i	−0.892627	−	0.0204971i
$316$	1.10268e6	−	613216.i	0.621203	−	0.345458i
$317$	300344.			0.167869			0.0839344	−	0.996471i	$-0.473251\pi$
$317$	300344.			0.167869			0.0839344	+	0.996471i	$0.473251\pi$
$318$	390176.	+	1.50442e6i	0.216368	+	0.834259i
$319$	−194987.			−0.107283
$320$	−1.82715e6	−	130283.i	−0.997468	−	0.0711234i
$321$	788150.			0.426920
$322$	636013.	+	2.45231e6i	0.341842	+	1.31806i
$323$	857906.			0.457545
$324$	−675073.	+	375416.i	−0.357263	+	0.198678i
$325$	1.88983e6	+	86836.8i	0.992463	+	0.0456032i
$326$	209228.	+	806732.i	0.109038	+	0.420422i
$327$		−	973505.i		−	0.503464i
$328$	−1.37390e6	−	1.44180e6i	−0.705130	−	0.739982i
$329$	−584052.			−0.297483
$330$	22036.2	+	93774.7i	0.0111391	+	0.0474024i
$331$		−	2.37543e6i		−	1.19172i	−0.803090	−	0.595858i	$-0.796812\pi$
$331$		−	2.37543e6i		−	1.19172i	0.803090	−	0.595858i	$-0.203188\pi$
$332$	1.30056e6	−	723259.i	0.647570	−	0.360121i
$333$	2.15374e6			1.06435
$334$	1.70288e6	−	441647.i	0.835253	−	0.216625i
$335$	−53763.9	+	2.34136e6i	−0.0261745	+	1.13987i
$336$	917348.	+	569712.i	0.443288	+	0.275301i
$337$			3.69929e6i			1.77437i	0.461416	+	0.887184i	$0.347341\pi$
$337$			3.69929e6i			1.77437i	−0.461416	+	0.887184i	$0.652659\pi$
$338$	−6822.11	−	26304.4i	−0.00324808	−	0.0125238i
$339$			1.40296e6i			0.663051i
$340$	−647632.	+	340931.i	−0.303830	+	0.159945i
$341$		−	217218.i		−	0.101160i
$342$	2.19841e6	−	570164.i	1.01635	−	0.263593i
$343$		−	1.76770e6i		−	0.811286i
$344$	−1.05061e6	−	1.10254e6i	−0.478679	−	0.502339i
$345$	1.22304e6	+	28084.3i	0.553215	+	0.0127033i
$346$	−170811.	−	658605.i	−0.0767054	−	0.295757i
$347$	1.98355e6			0.884339			0.442170	−	0.896931i	$-0.354209\pi$
$347$	1.98355e6			0.884339			0.442170	+	0.896931i	$0.354209\pi$
$348$	512994.	+	922466.i	0.227072	+	0.408321i
$349$			1.51829e6i			0.667256i	0.942705	+	0.333628i	$0.108273\pi$
$349$			1.51829e6i			0.667256i	−0.942705	+	0.333628i	$0.891727\pi$
$350$	−2.54104e6	+	535881.i	−1.10877	+	0.233829i
$351$	−1.88809e6			−0.818001
$352$	−73108.4	+	234687.i	−0.0314493	+	0.100956i
$353$		−	2.06194e6i		−	0.880724i	−0.897820	−	0.440362i	$-0.854850\pi$
$353$		−	2.06194e6i		−	0.880724i	0.897820	−	0.440362i	$-0.145150\pi$
$354$	−1.43907e6	+	373227.i	−0.610343	+	0.158294i
$355$	−92605.9	+	4.03289e6i	−0.0390003	+	1.69842i
$356$	1.06880e6	−	594373.i	0.446963	−	0.248562i
$357$	431458.			0.179171
$358$	−988602.	+	256397.i	−0.407675	+	0.105732i
$359$	1.33255e6			0.545691			0.272846	−	0.962058i	$-0.412035\pi$
$359$	1.33255e6			0.545691			0.272846	+	0.962058i	$0.412035\pi$
$360$	−1.43299e6	+	1.30406e6i	−0.582757	+	0.530325i
$361$	−1.92072e6			−0.775705
$362$	−819705.	+	212593.i	−0.328766	+	0.0852663i
$363$	−1.14317e6			−0.455350
$364$	−1.38314e6	−	2.48716e6i	−0.547158	−	0.983898i
$365$	−2.69797e6	−	61952.6i	−1.06000	−	0.0243404i
$366$	−125049.	+	32431.7i	−0.0487951	+	0.0126552i
$367$			313330.i			0.121433i	0.998155	+	0.0607166i	$0.0193386\pi$
$367$			313330.i			0.121433i	−0.998155	+	0.0607166i	$0.980661\pi$
$368$	2.65195e6	+	1.64698e6i	1.02081	+	0.633969i
$369$	−2.10655e6			−0.805390
$370$	3.46276e6	−	813716.i	1.31498	−	0.309007i
$371$			5.62256e6i			2.12080i
$372$	−1.02764e6	+	571481.i	−0.385019	+	0.214114i
$373$	2.93069e6			1.09068			0.545341	−	0.838215i	$-0.316400\pi$
$373$	2.93069e6			1.09068			0.545341	+	0.838215i	$0.316400\pi$
$374$	24656.2	+	95068.1i	0.00911480	+	0.0351444i
$375$	−86303.9	+	1.25105e6i	−0.0316922	+	0.459407i
$376$	−521014.	+	496475.i	−0.190055	+	0.181104i
$377$		−	2.78171e6i		−	1.00800i
$378$	2.50880e6	−	650665.i	0.903102	−	0.234222i
$379$		−	4.10811e6i		−	1.46907i	−0.678569	−	0.734537i	$-0.737399\pi$
$379$		−	4.10811e6i		−	1.46907i	0.678569	−	0.734537i	$-0.262601\pi$
$380$	3.31916e6	−	1.74729e6i	1.17915	−	0.620736i
$381$			1.22928e6i			0.433848i
$382$	303780.	+	1.17130e6i	0.106512	+	0.410685i
$383$			958991.i			0.334055i	0.985952	+	0.167027i	$0.0534168\pi$
$383$			958991.i			0.334055i	−0.985952	+	0.167027i	$0.946583\pi$
$384$	1.30262e6	−	271572.i	0.450806	−	0.0939846i
$385$	−8000.07	+	348395.i	−0.00275069	+	0.119790i
$386$	3.99499e6	−	1.03611e6i	1.36473	−	0.353948i
$387$	−1.61086e6			−0.546741
$388$	−1.49271e6	−	2.68419e6i	−0.503380	−	0.905178i
$389$			647634.i			0.216998i	0.994097	+	0.108499i	$0.0346044\pi$
$389$			647634.i			0.216998i	−0.994097	+	0.108499i	$0.965396\pi$
$390$	−1.33780e6	+	314370.i	−0.445379	+	0.104660i
$391$	1.24730e6			0.412599
$392$	596164.	+	625630.i	0.195952	+	0.205637i
$393$		−	799827.i		−	0.261225i
$394$	−1.30952e6	−	5.04919e6i	−0.424984	−	1.63863i
$395$	50599.6	−	2.20356e6i	0.0163175	−	0.710611i
$396$	126364.	+	227228.i	0.0404936	+	0.0728155i
$397$	−2.06284e6			−0.656885			−0.328443	−	0.944524i	$-0.606524\pi$
$397$	−2.06284e6			−0.656885			−0.328443	+	0.944524i	$0.606524\pi$
$398$	−1.39930e6	−	5.39535e6i	−0.442796	−	1.70731i
$399$	−2.21125e6			−0.695352
$400$	−1.81125e6	+	2.63806e6i	−0.566017	+	0.824394i
$401$	−1.92225e6			−0.596964			−0.298482	−	0.954415i	$-0.596480\pi$
$401$	−1.92225e6			−0.596964			−0.298482	+	0.954415i	$0.596480\pi$
$402$	−427091.	−	1.64676e6i	−0.131812	−	0.508234i
$403$	3.09885e6			0.950470
$404$	−1.30485e6	−	2.34638e6i	−0.397748	−	0.715229i
$405$	−30977.5	+	1.34904e6i	−0.00938446	+	0.408683i
$406$	958623.	+	3.69621e6i	0.288624	+	1.11286i
$407$		−	477330.i		−	0.142834i
$408$	384889.	−	366761.i	0.114468	−	0.109077i
$409$	1.40471e6			0.415221			0.207610	−	0.978212i	$-0.433431\pi$
$409$	1.40471e6			0.415221			0.207610	+	0.978212i	$0.433431\pi$
$410$	−3.38689e6	+	795888.i	−0.995042	+	0.233826i
$411$		−	2.02607e6i		−	0.591630i
$412$	166308.	+	299055.i	0.0482693	+	0.0867977i
$413$	−5.37833e6			−1.55157
$414$	3.19623e6	−	828952.i	0.916511	−	0.237700i
$415$	59679.8	−	2.59899e6i	0.0170101	−	0.740773i
$416$	−3.34807e6	−	1.04297e6i	−0.948551	−	0.295487i
$417$			316284.i			0.0890712i
$418$	−126364.	−	487230.i	−0.0353740	−	0.136393i
$419$			4.03594e6i			1.12308i	0.827451	+	0.561538i	$0.189790\pi$
$419$			4.03594e6i			1.12308i	−0.827451	+	0.561538i	$0.810210\pi$
$420$	1.66927e6	−	878748.i	0.461746	−	0.243075i
$421$			594910.i			0.163586i	0.996649	+	0.0817929i	$0.0260646\pi$
$421$			594910.i			0.163586i	−0.996649	+	0.0817929i	$0.973935\pi$
$422$	−5.10623e6	+	1.32432e6i	−1.39579	+	0.362001i
$423$			761229.i			0.206854i
$424$	4.77947e6	+	5.01570e6i	1.29111	+	1.35493i
$425$	−58687.2	+	1.27721e6i	−0.0157605	+	0.342997i
$426$	−735645.	−	2.83646e6i	−0.196401	−	0.757274i
$427$	−467352.			−0.124044
$428$	3.07053e6	−	1.70756e6i	0.810223	−	0.450575i
$429$			184411.i			0.0483776i
$430$	−2.58993e6	+	608609.i	−0.675486	+	0.158733i
$431$	4.15801e6			1.07818			0.539091	−	0.842247i	$-0.318768\pi$
$431$	4.15801e6			1.07818			0.539091	+	0.842247i	$0.318768\pi$
$432$	1.68492e6	−	2.71305e6i	0.434380	−	0.699436i
$433$		−	2.27636e6i		−	0.583474i	−0.956499	−	0.291737i	$-0.905767\pi$
$433$		−	2.27636e6i		−	0.583474i	0.956499	−	0.291737i	$-0.0942333\pi$
$434$	−4.11761e6	+	1.06792e6i	−1.04935	+	0.272153i
$435$	1.84342e6	+	42329.8i	0.467090	+	0.0107256i
$436$	−2.10914e6	−	3.79265e6i	−0.531361	−	0.955492i
$437$	−6.39247e6			−1.60127
$438$	1.89757e6	−	492140.i	0.472620	−	0.122575i
$439$	−1.28126e6			−0.317305			−0.158653	−	0.987334i	$-0.550715\pi$
$439$	−1.28126e6			−0.317305			−0.158653	+	0.987334i	$0.550715\pi$
$440$	289017.	+	317592.i	0.0711692	+	0.0782056i
$441$	914079.			0.223814
$442$	−1.35625e6	+	351748.i	−0.330205	+	0.0856398i
$443$	6.01266e6			1.45565			0.727825	−	0.685763i	$-0.240531\pi$
$443$	6.01266e6			1.45565			0.727825	+	0.685763i	$0.240531\pi$
$444$	−2.25820e6	+	1.25581e6i	−0.543632	+	0.302320i
$445$	49044.7	−	2.13585e6i	0.0117407	−	0.511294i
$446$	−4.09891e6	+	1.06306e6i	−0.975733	+	0.253059i
$447$			1.80576e6i			0.427455i
$448$	4.80818e6	+	232054.i	1.13184	+	0.0546253i
$449$	2.11543e6			0.495202			0.247601	−	0.968862i	$-0.420358\pi$
$449$	2.11543e6			0.495202			0.247601	+	0.968862i	$0.420358\pi$
$450$	698445.	+	3.31189e6i	0.162593	+	0.770983i
$451$			466872.i			0.108083i
$452$	3.03958e6	+	5.46577e6i	0.699790	+	1.25836i
$453$	−687625.			−0.157437
$454$	2.08926e6	+	8.05567e6i	0.475722	+	1.83426i
$455$	−4.97024e6	−	114130.i	−1.12551	−	0.0258447i
$456$	−1.97258e6	+	1.87967e6i	−0.444245	+	0.423322i
$457$			1.35964e6i			0.304533i	0.988339	+	0.152267i	$0.0486573\pi$
$457$			1.35964e6i			0.304533i	−0.988339	+	0.152267i	$0.951343\pi$
$458$	−4.57236e6	+	1.18586e6i	−1.01854	+	0.264161i
$459$		−	1.27603e6i		−	0.282703i
$460$	4.82567e6	−	2.54036e6i	1.06332	−	0.559759i
$461$		−	2.06438e6i		−	0.452415i	−0.974079	−	0.226208i	$-0.927367\pi$
$461$		−	2.06438e6i		−	0.452415i	0.974079	−	0.226208i	$-0.0726328\pi$
$462$	−63551.2	−	245037.i	−0.0138522	−	0.0534106i
$463$		−	1.48917e6i		−	0.322843i	−0.986886	−	0.161421i	$-0.948392\pi$
$463$		−	1.48917e6i		−	0.322843i	0.986886	−	0.161421i	$-0.0516078\pi$
$464$	3.99712e6	+	2.48239e6i	0.861892	+	0.535272i
$465$	−47155.8	+	2.05359e6i	−0.0101135	+	0.440434i
$466$	−1.55903e6	+	404338.i	−0.332574	+	0.0862541i
$467$	7.05856e6			1.49770			0.748849	−	0.662741i	$-0.230607\pi$
$467$	7.05856e6			1.49770			0.748849	+	0.662741i	$0.230607\pi$
$468$	−3.24166e6	+	1.80273e6i	−0.684152	+	0.380465i
$469$		−	6.15452e6i		−	1.29200i
$470$	287604.	+	1.22389e6i	0.0600552	+	0.255564i
$471$	1.28108e6			0.266087
$472$	−4.79783e6	+	4.57186e6i	−0.991264	+	0.944577i
$473$			357014.i			0.0733722i
$474$	401954.	+	1.54983e6i	0.0821732	+	0.316839i
$475$	300776.	−	6.54578e6i	0.0611658	−	1.33115i
$476$	1.68090e6	−	934772.i	0.340037	−	0.189099i
$477$	7.32821e6			1.47469
$478$	1.13701e6	+	4.38403e6i	0.227612	+	0.877614i
$479$	1.47482e6			0.293697			0.146849	−	0.989159i	$-0.453087\pi$
$479$	1.47482e6			0.293697			0.146849	+	0.989159i	$0.453087\pi$
$480$	742117.	−	2.20287e6i	0.147018	−	0.436400i
$481$	6.80964e6			1.34203
$482$	−2.13867e6	−	8.24619e6i	−0.419302	−	1.61672i
$483$	−3.21490e6			−0.627046
$484$	−4.45366e6	+	2.47673e6i	−0.864179	+	0.480580i
$485$	−5.36397e6	−	123171.i	−1.03546	−	0.0237769i
$486$	−1.32237e6	−	5.09871e6i	−0.253958	−	0.979196i
$487$			9.13416e6i			1.74520i	0.488433	+	0.872602i	$0.337569\pi$
$487$			9.13416e6i			1.74520i	−0.488433	+	0.872602i	$0.662431\pi$
$488$	−416909.	+	397273.i	−0.0792486	+	0.0755161i
$489$	−1.05760e6			−0.200009
$490$	1.46964e6	−	345353.i	0.276517	−	0.0649790i
$491$		−	4.74188e6i		−	0.887660i	−0.896111	−	0.443830i	$-0.853619\pi$
$491$		−	4.74188e6i		−	0.887660i	0.896111	−	0.443830i	$-0.146381\pi$
$492$	2.20872e6	−	1.22830e6i	0.411366	−	0.228766i
$493$	1.87997e6			0.348365
$494$	6.95087e6	−	1.80273e6i	1.28151	−	0.332363i
$495$	454083.	+	10427.0i	0.0832957	+	0.00191269i
$496$	−2.76540e6	+	4.45284e6i	−0.504724	+	0.812704i
$497$		−	1.06009e7i		−	1.92509i
$498$	474086.	+	1.82796e6i	0.0856611	+	0.330288i
$499$			539009.i			0.0969046i	0.998825	+	0.0484523i	$0.0154289\pi$
$499$			539009.i			0.0969046i	−0.998825	+	0.0484523i	$0.984571\pi$
$500$	2.37423e6	+	5.06093e6i	0.424716	+	0.905327i
$501$			2.23243e6i			0.397359i
$502$	6.03724e6	−	1.56578e6i	1.06925	−	0.277313i
$503$		−	2.21657e6i		−	0.390627i	−0.980741	−	0.195313i	$-0.937428\pi$
$503$		−	2.21657e6i		−	0.390627i	0.980741	−	0.195313i	$-0.0625724\pi$
$504$	3.68612e6	−	3.51251e6i	0.646387	−	0.615943i
$505$	−4.68891e6	−	107670.i	−0.818171	−	0.0187874i
$506$	−183719.	−	708376.i	−0.0318991	−	0.122995i
$507$	34484.2			0.00595800
$508$	2.66329e6	+	4.78912e6i	0.457887	+	0.823372i
$509$			3.35132e6i			0.573352i	0.958028	+	0.286676i	$0.0925503\pi$
$509$			3.35132e6i			0.573352i	−0.958028	+	0.286676i	$0.907450\pi$
$510$	−212462.	−	904129.i	−0.0361706	−	0.153924i
$511$	7.09190e6			1.20146
$512$	4.48648e6	−	3.88019e6i	0.756363	−	0.654152i
$513$			6.53974e6i			1.09715i
$514$	−7.72281e6	+	2.00293e6i	−1.28934	+	0.334394i
$515$	597620.	+	13722.9i	0.0992903	+	0.00227997i
$516$	1.68899e6	−	939270.i	0.279257	−	0.155298i
$517$	168710.			0.0277597
$518$	−9.04834e6	+	2.34671e6i	−1.48165	+	0.384269i
$519$	863411.			0.140702
$520$	−4.53080e6	+	4.12315e6i	−0.734795	+	0.668683i
$521$	5.01924e6			0.810109			0.405054	−	0.914293i	$-0.367253\pi$
$521$	5.01924e6			0.810109			0.405054	+	0.914293i	$0.367253\pi$
$522$	4.81748e6	−	1.24943e6i	0.773827	−	0.200694i
$523$	−3.44581e6			−0.550855			−0.275428	−	0.961322i	$-0.588819\pi$
$523$	−3.44581e6			−0.550855			−0.275428	+	0.961322i	$0.588819\pi$
$524$	−1.73286e6	−	3.11602e6i	−0.275699	−	0.495761i
$525$	151266.	−	3.29200e6i	0.0239521	−	0.521269i
$526$	−9.24727e6	+	2.39831e6i	−1.45730	+	0.377955i
$527$			2.09431e6i			0.328484i
$528$	−264986.	−	164568.i	−0.0413655	−	0.0256898i
$529$	−2.85758e6			−0.443975
$530$	1.17822e7	−	2.76871e6i	1.82195	−	0.428142i
$531$			7.00988e6i			1.07888i
$532$	−8.61474e6	+	4.79076e6i	−1.31966	+	0.733881i
$533$	−6.66044e6			−1.01551
$534$	389603.	+	1.50221e6i	0.0591247	+	0.227970i
$535$	140900.	−	6.13603e6i	0.0212826	−	0.926836i
$536$	−5.23166e6	−	5.49024e6i	−0.786552	−	0.825429i
$537$		−	1.29603e6i		−	0.193945i
$538$	1.67473e6	−	434346.i	0.249453	−	0.0646963i
$539$		−	202586.i		−	0.0300357i
$540$	−2.59889e6	−	4.93684e6i	−0.383534	−	0.728559i
$541$			3.97667e6i			0.584153i	0.956395	+	0.292076i	$0.0943461\pi$
$541$			3.97667e6i			0.584153i	−0.956395	+	0.292076i	$0.905654\pi$
$542$	−1.77979e6	−	6.86244e6i	−0.260238	−	1.00341i
$543$		−	1.07461e6i		−	0.156405i
$544$	704875.	−	2.26274e6i	0.102121	−	0.327821i
$545$	−7.57908e6	−	174036.i	−1.09301	−	0.0250985i
$546$	3.49573e6	−	906627.i	0.501829	−	0.130151i
$547$	−9.20664e6			−1.31563			−0.657814	−	0.753181i	$-0.728519\pi$
$547$	−9.20664e6			−1.31563			−0.657814	+	0.753181i	$0.728519\pi$
$548$	−4.38957e6	−	7.89332e6i	−0.624411	−	1.12281i
$549$			609127.i			0.0862535i
$550$	734009.	−	154795.i	0.103465	−	0.0218198i
$551$	−9.63498e6			−1.35198
$552$	−2.86790e6	+	2.73283e6i	−0.400606	+	0.381738i
$553$			5.79229e6i			0.805448i
$554$	686489.	+	2.64693e6i	0.0950296	+	0.366410i
$555$	−103624.	+	4.51270e6i	−0.0142799	+	0.621876i
$556$	685244.	+	1.23220e6i	0.0940066	+	0.169042i
$557$	6.00805e6			0.820531			0.410266	−	0.911966i	$-0.365436\pi$
$557$	6.00805e6			0.820531			0.410266	+	0.911966i	$0.365436\pi$
$558$	1.39188e6	+	5.36672e6i	0.189241	+	0.729665i
$559$	−5.09319e6			−0.689383
$560$	4.59941e6	−	7.04003e6i	0.619773	−	0.948647i
$561$	−124631.			−0.0167194
$562$	125997.	+	485814.i	0.0168275	+	0.0648827i
$563$	−3.22469e6			−0.428763			−0.214381	−	0.976750i	$-0.568774\pi$
$563$	−3.22469e6			−0.428763			−0.214381	+	0.976750i	$0.568774\pi$
$564$	−443861.	−	798150.i	−0.0587556	−	0.105654i
$565$	1.09226e7	+	250811.i	1.43947	+	0.0330542i
$566$	−2.50576e6	−	9.66158e6i	−0.328775	−	1.26767i
$567$		−	3.54609e6i		−	0.463225i
$568$	−9.01130e6	−	9.45669e6i	−1.17197	−	1.22990i
$569$	−3.74802e6			−0.485312			−0.242656	−	0.970112i	$-0.578019\pi$
$569$	−3.74802e6			−0.485312			−0.242656	+	0.970112i	$0.578019\pi$
$570$	1.08888e6	+	4.63372e6i	0.140376	+	0.597369i
$571$			4.37966e6i			0.562148i	0.959686	+	0.281074i	$0.0906906\pi$
$571$			4.37966e6i			0.562148i	−0.959686	+	0.281074i	$0.909309\pi$
$572$	399535.	+	718444.i	0.0510582	+	0.0918127i
$573$	−1.53554e6			−0.195377
$574$	8.85009e6	−	2.29530e6i	1.12116	−	0.290776i
$575$	437293.	−	9.51681e6i	0.0551573	−	1.20039i
$576$	302449.	−	6.26678e6i	0.0379836	−	0.787025i
$577$		−	1.03145e7i		−	1.28976i	−0.764284	−	0.644880i	$-0.776907\pi$
$577$		−	1.03145e7i		−	1.28976i	0.764284	−	0.644880i	$-0.223093\pi$
$578$	1.77867e6	+	6.85810e6i	0.221450	+	0.853855i
$579$			5.23732e6i			0.649251i
$580$	7.27344e6	−	3.82893e6i	0.897779	−	0.472615i
$581$			6.83173e6i			0.839635i
$582$	3.77266e6	−	978449.i	0.461679	−	0.119738i
$583$		−	1.62414e6i		−	0.197903i
$584$	6.32645e6	−	6.02848e6i	0.767587	−	0.731435i
$585$	−148752.	+	6.47800e6i	−0.0179710	+	0.782620i
$586$	−12958.7	−	49965.5i	−0.00155890	−	0.00601071i
$587$	−5.88489e6			−0.704925			−0.352463	−	0.935826i	$-0.614656\pi$
$587$	−5.88489e6			−0.704925			−0.352463	+	0.935826i	$0.614656\pi$
$588$	−958413.	+	532985.i	−0.114317	+	0.0635729i
$589$		−	1.07335e7i		−	1.27483i
$590$	2.64844e6	+	1.12704e7i	0.313228	+	1.33294i
$591$	6.61934e6			0.779554
$592$	−6.07689e6	+	9.78498e6i	−0.712652	+	1.14751i
$593$			1.07458e7i			1.25488i	0.778664	+	0.627442i	$0.215898\pi$
$593$			1.07458e7i			1.25488i	−0.778664	+	0.627442i	$0.784102\pi$
$594$	−724696.	+	187952.i	−0.0842732	+	0.0218565i
$595$	77132.8	−	3.35905e6i	0.00893196	−	0.388977i
$596$	3.91226e6	+	7.03501e6i	0.451140	+	0.811239i
$597$	7.07314e6			0.812226
$598$	1.01058e7	−	2.62096e6i	1.15562	−	0.299714i
$599$	1.01249e6			0.115299			0.0576493	−	0.998337i	$-0.481639\pi$
$599$	1.01249e6			0.115299			0.0576493	+	0.998337i	$0.481639\pi$
$600$	−2.66343e6	−	3.06527e6i	−0.302039	−	0.347608i
$601$	7.16049e6			0.808643			0.404321	−	0.914617i	$-0.367508\pi$
$601$	7.16049e6			0.808643			0.404321	+	0.914617i	$0.367508\pi$
$602$	6.76759e6	−	1.75520e6i	0.761102	−	0.197394i
$603$	−8.02154e6			−0.898390
$604$	−2.67890e6	+	1.48977e6i	−0.298789	+	0.166160i
$605$	−204368.	+	8.90001e6i	−0.0226999	+	0.988558i
$606$	3.29786e6	−	855311.i	0.364797	−	0.0946112i
$607$			1.22036e7i			1.34437i	0.740385	+	0.672183i	$0.234643\pi$
$607$			1.22036e7i			1.34437i	−0.740385	+	0.672183i	$0.765357\pi$
$608$	−3.61253e6	+	1.15967e7i	−0.396326	+	1.27225i
$609$	−4.84562e6			−0.529427
$610$	230137.	+	979346.i	0.0250416	+	0.106564i
$611$			2.40683e6i			0.260821i
$612$	−1.21834e6	−	2.19082e6i	−0.131489	−	0.236444i
$613$	1.15888e7			1.24563			0.622815	−	0.782369i	$-0.285989\pi$
$613$	1.15888e7			1.24563			0.622815	+	0.782369i	$0.285989\pi$
$614$	−3.75220e6	−	1.44675e7i	−0.401666	−	1.54872i
$615$	101353.	−	4.41382e6i	0.0108056	−	0.470573i
$616$	−778471.	−	816948.i	−0.0826591	−	0.0867447i
$617$		−	1.47499e6i		−	0.155983i	−0.996954	−	0.0779915i	$-0.975149\pi$
$617$		−	1.47499e6i		−	0.155983i	0.996954	−	0.0779915i	$-0.0248507\pi$
$618$	−420325.	+	109013.i	−0.0442705	+	0.0114817i
$619$		−	6.94510e6i		−	0.728537i	−0.931294	−	0.364269i	$-0.881319\pi$
$619$		−	6.94510e6i		−	0.728537i	0.931294	−	0.364269i	$-0.118681\pi$
$620$	4.26547e6	+	8.10268e6i	0.445644	+	0.846544i
$621$			9.50803e6i			0.989377i
$622$	−1.99178e6	−	7.67981e6i	−0.206427	−	0.795929i
$623$			5.61430e6i			0.579530i
$624$	2.34774e6	−	3.78032e6i	0.241373	−	0.388658i
$625$	9.72447e6	+	895561.i	0.995786	+	0.0917055i
$626$	−7.44183e6	+	1.93006e6i	−0.759004	+	0.196850i
$627$	638744.			0.0648870
$628$	4.99093e6	−	2.77552e6i	0.504990	−	0.280831i
$629$			4.60218e6i			0.463807i
$630$	−2.03477e6	−	8.65893e6i	−0.204251	−	0.869186i
$631$	3.38551e6			0.338494			0.169247	−	0.985574i	$-0.445867\pi$
$631$	3.38551e6			0.338494			0.169247	+	0.985574i	$0.445867\pi$
$632$	4.92374e6	+	5.16711e6i	0.490346	+	0.514582i
$633$		−	6.69411e6i		−	0.664024i
$634$	426529.	+	1.64459e6i	0.0421430	+	0.162493i
$635$	9.57037e6	+	219761.i	0.941878	+	0.0216280i
$636$	−7.68364e6	+	4.27296e6i	−0.753224	+	0.418877i
$637$	2.89011e6			0.282206
$638$	−276909.	−	1.06769e6i	−0.0269330	−	0.103847i
$639$	−1.38167e7			−1.33861
$640$	−1.88141e6	−	1.01899e7i	−0.181566	−	0.983379i
$641$	−6.43478e6			−0.618570			−0.309285	−	0.950969i	$-0.600090\pi$
$641$	−6.43478e6			−0.618570			−0.309285	+	0.950969i	$0.600090\pi$
$642$	1.11928e6	+	4.31567e6i	0.107177	+	0.413248i
$643$	819506.			0.0781672			0.0390836	−	0.999236i	$-0.487556\pi$
$643$	819506.			0.0781672			0.0390836	+	0.999236i	$0.487556\pi$
$644$	−1.25248e7	+	6.96522e6i	−1.19003	+	0.661790i
$645$	77504.0	−	3.37522e6i	0.00733541	−	0.319450i
$646$	1.21834e6	+	4.69763e6i	0.114865	+	0.442892i
$647$			1.00673e7i			0.945482i	0.881201	+	0.472741i	$0.156735\pi$
$647$			1.00673e7i			0.945482i	−0.881201	+	0.472741i	$0.843265\pi$
$648$	−3.01436e6	−	3.16335e6i	−0.282006	−	0.295944i
$649$	1.55359e6			0.144785
$650$	2.20833e6	+	1.04714e7i	0.205012	+	0.972127i
$651$		−	5.39807e6i		−	0.499213i
$652$	−4.12029e6	+	2.29134e6i	−0.379584	+	0.211092i
$653$	3.73524e6			0.342796			0.171398	−	0.985202i	$-0.445172\pi$
$653$	3.73524e6			0.342796			0.171398	+	0.985202i	$0.445172\pi$
$654$	5.33061e6	−	1.38251e6i	0.487341	−	0.126393i
$655$	−6.22694e6	−	142987.i	−0.567115	−	0.0130225i
$656$	5.94375e6	−	9.57059e6i	0.539263	−	0.868319i
$657$		−	9.24328e6i		−	0.835435i
$658$	−829434.	−	3.19809e6i	−0.0746822	−	0.287956i
$659$			2.11585e6i			0.189789i	0.995487	+	0.0948947i	$0.0302514\pi$
$659$			2.11585e6i			0.189789i	−0.995487	+	0.0948947i	$0.969749\pi$
$660$	−482187.	+	253836.i	−0.0430879	+	0.0226827i
$661$		−	1.89096e7i		−	1.68337i	−0.539970	−	0.841684i	$-0.681565\pi$
$661$		−	1.89096e7i		−	1.68337i	0.539970	−	0.841684i	$-0.318435\pi$
$662$	1.30071e7	−	3.37344e6i	1.15355	−	0.299177i
$663$		−	1.77800e6i		−	0.157090i
$664$	5.80733e6	+	6.09436e6i	0.511159	+	0.536424i
$665$	−395310.	+	1.72154e7i	−0.0346644	+	1.50960i
$666$	3.05861e6	+	1.17932e7i	0.267201	+	1.03026i
$667$	−1.40082e7			−1.21918
$668$	4.83665e6	+	8.69726e6i	0.419376	+	0.754121i
$669$		−	5.37355e6i		−	0.464190i
$670$	−1.28969e7	+	3.03066e6i	−1.10994	+	0.260826i
$671$	135000.			0.0115752
$672$	−1.81681e6	+	5.83218e6i	−0.155198	+	0.498205i
$673$			2.10683e6i			0.179304i	0.995973	+	0.0896522i	$0.0285755\pi$
$673$			2.10683e6i			0.179304i	−0.995973	+	0.0896522i	$0.971424\pi$
$674$	−2.02562e7	+	5.25350e6i	−1.71754	+	0.445450i
$675$	−9.73606e6	−	447368.i	−0.822477	−	0.0377925i
$676$	134346.	−	74711.6i	0.0113073	−	0.00628813i
$677$	−5.17934e6			−0.434313			−0.217156	−	0.976137i	$-0.569678\pi$
$677$	−5.17934e6			−0.434313			−0.217156	+	0.976137i	$0.569678\pi$
$678$	−7.68220e6	+	1.99240e6i	−0.641817	+	0.166457i
$679$	1.40998e7			1.17365
$680$	−2.78656e6	−	3.06207e6i	−0.231098	−	0.253947i
$681$	−1.05607e7			−0.872623
$682$	1.18942e6	−	308479.i	0.0979206	−	0.0253960i
$683$	8.80956e6			0.722608			0.361304	−	0.932448i	$-0.382332\pi$
$683$	8.80956e6			0.722608			0.361304	+	0.932448i	$0.382332\pi$
$684$	6.24408e6	+	1.12281e7i	0.510303	+	0.917626i
$685$	−1.57737e7	−	362206.i	−1.28442	−	0.0294937i
$686$	9.67940e6	−	2.51038e6i	0.785304	−	0.203671i
$687$		−	5.99423e6i		−	0.484553i
$688$	4.54514e6	−	7.31856e6i	0.366080	−	0.589460i
$689$	2.31701e7			1.85943
$690$	1.58311e6	+	6.73689e6i	0.126587	+	0.538688i
$691$		−	5.78539e6i		−	0.460933i	−0.973080	−	0.230466i	$-0.925975\pi$
$691$		−	5.78539e6i		−	0.460933i	0.973080	−	0.230466i	$-0.0740252\pi$
$692$	3.36374e6	−	1.87062e6i	0.267028	−	0.148498i
$693$	−1.19361e6			−0.0944122
$694$	2.81691e6	+	1.08613e7i	0.222011	+	0.856018i
$695$	2.46239e6	+	56543.0i	0.193372	+	0.00444034i
$696$	−4.32262e6	+	4.11903e6i	−0.338239	+	0.322308i
$697$		−	4.50135e6i		−	0.350963i
$698$	−8.31371e6	+	2.15619e6i	−0.645887	+	0.167513i
$699$		−	2.04384e6i		−	0.158217i
$700$	−6.54295e6	−	1.31529e7i	−0.504694	−	1.01456i
$701$		−	2.01716e7i		−	1.55041i	−0.631711	−	0.775204i	$-0.717647\pi$
$701$		−	2.01716e7i		−	1.55041i	0.631711	−	0.775204i	$-0.282353\pi$
$702$	−2.68134e6	−	1.03386e7i	−0.205357	−	0.791805i
$703$		−	2.35865e7i		−	1.80001i
$704$	−1.38890e6	−	67031.4i	−0.105618	−	0.00509738i
$705$	−1.59499e6	−	36625.2i	−0.120861	−	0.00277528i
$706$	1.12906e7	−	2.92824e6i	0.852519	−	0.221103i
$707$	1.23253e7			0.927362
$708$	−4.08735e6	−	7.34987e6i	−0.306450	−	0.551057i
$709$			1.71661e7i			1.28250i	0.767334	+	0.641248i	$0.221583\pi$
$709$			1.71661e7i			1.28250i	−0.767334	+	0.641248i	$0.778417\pi$
$710$	−2.22144e7	+	5.22018e6i	−1.65382	+	0.388633i
$711$	7.54943e6			0.560067
$712$	4.77245e6	+	5.00833e6i	0.352810	+	0.370248i
$713$		−	1.56052e7i		−	1.14960i
$714$	612729.	+	2.36253e6i	0.0449804	+	0.173433i
$715$	1.43571e6	+	32967.7i	0.105027	+	0.00241170i
$716$	−2.80790e6	−	5.04916e6i	−0.204691	−	0.368075i
$717$	−5.74733e6			−0.417511
$718$	1.89240e6	+	7.29663e6i	0.136994	+	0.528215i
$719$	1.37927e7			0.995009			0.497505	−	0.867461i	$-0.334250\pi$
$719$	1.37927e7			0.995009			0.497505	+	0.867461i	$0.334250\pi$
$720$	−9.17569e6	−	5.99468e6i	−0.659641	−	0.430958i
$721$	−1.57091e6			−0.112541
$722$	−2.72769e6	−	1.05173e7i	−0.194739	−	0.750863i
$723$	1.08105e7			0.769132
$724$	−2.32819e6	−	4.18654e6i	−0.165071	−	0.296831i
$725$	659105.	−	1.43441e7i	0.0465704	−	1.01351i
$726$	−1.62346e6	−	6.25966e6i	−0.114314	−	0.440767i
$727$			9.10175e6i			0.638688i	0.947639	+	0.319344i	$0.103463\pi$
$727$			9.10175e6i			0.638688i	−0.947639	+	0.319344i	$0.896537\pi$
$728$	1.16547e7	−	1.11058e7i	0.815026	−	0.776640i
$729$	818554.			0.0570465
$730$	−3.49225e6	−	1.48612e7i	−0.242549	−	1.03216i
$731$		−	3.44215e6i		−	0.238252i
$732$	−355172.	−	638670.i	−0.0244997	−	0.0440554i
$733$	−1.79637e7			−1.23491			−0.617456	−	0.786605i	$-0.711837\pi$
$733$	−1.79637e7			−1.23491			−0.617456	+	0.786605i	$0.711837\pi$
$734$	−1.71570e6	+	444972.i	−0.117544	+	0.0304855i
$735$	−43979.3	+	1.91525e6i	−0.00300283	+	0.130770i
$736$	−5.25220e6	+	1.68602e7i	−0.357394	+	1.14728i
$737$			1.77780e6i			0.120563i
$738$	−2.99159e6	−	1.15348e7i	−0.202191	−	0.779598i
$739$		−	1.38839e7i		−	0.935192i	−0.883942	−	0.467596i	$-0.845120\pi$
$739$		−	1.38839e7i		−	0.935192i	0.883942	−	0.467596i	$-0.154880\pi$
$740$	9.37325e6	+	1.78054e7i	0.629232	+	1.19529i
$741$			9.11238e6i			0.609658i
$742$	−3.07874e7	+	7.98480e6i	−2.05288	+	0.532420i
$743$		−	2.37521e6i		−	0.157845i	−0.996881	−	0.0789225i	$-0.974852\pi$
$743$		−	2.37521e6i		−	0.157845i	0.996881	−	0.0789225i	$-0.0251480\pi$
$744$	−4.58864e6	−	4.81544e6i	−0.303914	−	0.318936i
$745$	1.40585e7	+	322820.i	0.927999	+	0.0213093i
$746$	4.16198e6	+	1.60476e7i	0.273812	+	1.05575i
$747$	8.90419e6			0.583839
$748$	−485548.	+	270019.i	−0.0317306	+	0.0176458i
$749$			1.61292e7i			1.05053i
$750$	−6.97295e6	+	1.30409e6i	−0.452651	+	0.0846556i
$751$	−1.99260e7			−1.28920			−0.644600	−	0.764520i	$-0.722976\pi$
$751$	−1.99260e7			−1.28920			−0.644600	+	0.764520i	$0.722976\pi$
$752$	−3.45845e6	−	2.14785e6i	−0.223017	−	0.138503i
$753$			7.91465e6i			0.508679i
$754$	1.52318e7	−	3.95041e6i	0.975714	−	0.253054i
$755$	−122929.	+	5.35341e6i	−0.00784848	+	0.341793i
$756$	7.12568e6	+	1.28134e7i	0.453442	+	0.815379i
$757$	−1.30771e7			−0.829413			−0.414707	−	0.909955i	$-0.636116\pi$
$757$	−1.30771e7			−0.829413			−0.414707	+	0.909955i	$0.636116\pi$
$758$	2.24947e7	−	5.83407e6i	1.42203	−	0.368807i
$759$	928660.			0.0585130
$760$	1.42813e7	+	1.56933e7i	0.896879	+	0.985552i
$761$	−1.75251e7			−1.09698			−0.548492	−	0.836156i	$-0.684798\pi$
$761$	−1.75251e7			−1.09698			−0.548492	+	0.836156i	$0.684798\pi$
$762$	−6.73115e6	+	1.74574e6i	−0.419954	+	0.108916i
$763$	1.99224e7			1.23888
$764$	−5.98226e6	+	3.32681e6i	−0.370794	+	0.206203i
$765$	−4.37805e6	−	100532.i	−0.270475	−	0.00621082i
$766$	−5.25114e6	+	1.36190e6i	−0.323356	+	0.0838634i
$767$			2.21637e7i			1.36036i
$768$	3.33694e6	+	6.74708e6i	0.204148	+	0.412775i
$769$	−3.13820e7			−1.91366			−0.956830	−	0.290647i	$-0.906129\pi$
$769$	−3.13820e7			−1.91366			−0.956830	+	0.290647i	$0.906129\pi$
$770$	−1.91906e6	+	450963.i	−0.116644	+	0.0274103i
$771$		−	1.01244e7i		−	0.613384i
$772$	1.13469e7	+	2.04039e7i	0.685225	+	1.23217i
$773$	103265.			0.00621590			0.00310795	−	0.999995i	$-0.499011\pi$
$773$	103265.			0.00621590			0.00310795	+	0.999995i	$0.499011\pi$
$774$	−2.28765e6	−	8.82060e6i	−0.137258	−	0.529232i
$775$	1.59795e7	+	734250.i	0.955671	+	0.0439126i
$776$	1.25779e7	−	1.19855e7i	0.749817	−	0.714502i
$777$		−	1.18621e7i		−	0.704870i
$778$	−3.54625e6	+	919729.i	−0.210049	+	0.0544767i
$779$			2.30697e7i			1.36207i
$780$	−3.62125e6	−	6.87893e6i	−0.213119	−	0.404841i
$781$			3.06218e6i			0.179640i
$782$	1.77133e6	+	6.82981e6i	0.103582	+	0.399385i
$783$			1.43309e7i			0.835350i
$784$	−2.57912e6	+	4.15289e6i	−0.149859	+	0.241302i
$785$	229022.	−	9.97368e6i	0.0132649	−	0.577672i
$786$	4.37960e6	−	1.13586e6i	0.252859	−	0.0655798i
$787$	5.01823e6			0.288811			0.144405	−	0.989519i	$-0.453873\pi$
$787$	5.01823e6			0.288811			0.144405	+	0.989519i	$0.453873\pi$
$788$	2.57881e7	−	1.43411e7i	1.47946	−	0.822748i
$789$		−	1.21229e7i		−	0.693288i
$790$	1.21379e7	−	2.85229e6i	0.691950	−	0.162602i
$791$	−2.87111e7			−1.63158
$792$	−1.06478e6	+	1.01463e6i	−0.0603178	+	0.0574769i
$793$			1.92592e6i			0.108757i
$794$	−2.92952e6	−	1.12955e7i	−0.164909	−	0.635849i
$795$	−352584.	+	1.53547e7i	−0.0197854	+	0.861634i
$796$	2.75561e7	−	1.53243e7i	1.54147	−	0.857230i
$797$	9.61578e6			0.536215			0.268107	−	0.963389i	$-0.413602\pi$
$797$	9.61578e6			0.536215			0.268107	+	0.963389i	$0.413602\pi$
$798$	−3.14027e6	−	1.21081e7i	−0.174566	−	0.673084i
$799$	−1.62662e6			−0.0901403
$800$	−1.70174e7	−	6.17146e6i	−0.940089	−	0.340928i
$801$	7.31745e6			0.402975
$802$	−2.72985e6	−	1.05256e7i	−0.149866	−	0.577846i
$803$	−2.04857e6			−0.112115
$804$	8.41060e6	−	4.67724e6i	0.458867	−	0.255182i
$805$	−574736.	+	2.50291e7i	−0.0312592	+	1.36131i
$806$	4.40080e6	+	1.69684e7i	0.238613	+	0.920031i
$807$			2.19552e6i			0.118673i
$808$	1.09950e7	−	1.04771e7i	0.592470	−	0.564566i
$809$	2.06325e7			1.10836			0.554181	−	0.832396i	$-0.313032\pi$
$809$	2.06325e7			1.10836			0.554181	+	0.832396i	$0.313032\pi$
$810$	−7.43092e6	+	1.74620e6i	−0.397951	+	0.0935149i
$811$			3.18795e7i			1.70200i	0.525164	+	0.851001i	$0.324004\pi$
$811$			3.18795e7i			1.70200i	−0.525164	+	0.851001i	$0.675996\pi$
$812$	−1.88779e7	+	1.04982e7i	−1.00476	+	0.558762i
$813$	8.99645e6			0.477359
$814$	2.61371e6	−	677875.i	0.138260	−	0.0358582i
$815$	−189070.	+	8.23381e6i	−0.00997078	+	0.434217i
$816$	2.55487e6	+	1.58668e6i	0.134321	+	0.0834189i
$817$			1.76412e7i			0.924642i
$818$	1.99488e6	+	7.69177e6i	0.104240	+	0.401923i
$819$		−	1.70281e7i		−	0.887067i
$820$	−9.16788e6	−	1.74153e7i	−0.476140	−	0.904474i
$821$		−	7.88522e6i		−	0.408278i	−0.978942	−	0.204139i	$-0.934561\pi$
$821$		−	7.88522e6i		−	0.408278i	0.978942	−	0.204139i	$-0.0654394\pi$
$822$	1.10941e7	−	2.87730e6i	0.572683	−	0.148527i
$823$		−	51764.9i		−	0.00266401i	−0.999999	−	0.00133200i	$-0.999576\pi$
$823$		−	51764.9i		−	0.00266401i	0.999999	−	0.00133200i	$-0.000423990\pi$
$824$	−1.40135e6	+	1.33535e6i	−0.0719002	+	0.0685138i
$825$	−43694.9	+	950932.i	−0.00223509	+	0.0486423i
$826$	−7.63796e6	−	2.94501e7i	−0.389518	−	1.50188i
$827$	5.24793e6			0.266824			0.133412	−	0.991061i	$-0.457407\pi$
$827$	5.24793e6			0.266824			0.133412	+	0.991061i	$0.457407\pi$
$828$	9.07818e6	+	1.63244e7i	0.460175	+	0.827485i
$829$			6.76109e6i			0.341689i	0.985298	+	0.170844i	$0.0546495\pi$
$829$			6.76109e6i			0.341689i	−0.985298	+	0.170844i	$0.945350\pi$
$830$	1.43160e7	−	3.36414e6i	0.721320	−	0.169504i
$831$	−3.47004e6			−0.174314
$832$	956277.	−	1.98141e7i	0.0478934	−	0.992355i
$833$			1.95323e6i			0.0975308i
$834$	−1.73188e6	+	449167.i	−0.0862187	+	0.0223611i
$835$	1.73802e7	+	399097.i	0.862660	+	0.0198090i
$836$	2.48847e6	−	1.38387e6i	0.123145	−	0.0684823i
$837$	−1.59647e7			−0.787677
$838$	−2.20995e7	+	5.73158e6i	−1.08711	+	0.281945i
$839$	−5.32681e6			−0.261254			−0.130627	−	0.991432i	$-0.541699\pi$
$839$	−5.32681e6			−0.261254			−0.130627	+	0.991432i	$0.541699\pi$
$840$	7.18234e6	+	7.89245e6i	0.351211	+	0.385935i
$841$	−602476.			−0.0293731
$842$	−3.25754e6	+	844853.i	−0.158347	+	0.0410678i
$843$	−636887.			−0.0308669
$844$	−1.45031e7	−	2.60794e7i	−0.700816	−	1.26021i
$845$	6164.83	−	268472.i	0.000297016	−	0.0129347i
$846$	−4.16826e6	+	1.08105e6i	−0.200230	+	0.0519302i
$847$		−	2.33946e7i		−	1.12049i
$848$	−2.06769e7	+	3.32939e7i	−0.987407	+	1.58992i
$849$	1.26660e7			0.603076
$850$	−7.07695e6	+	1.49246e6i	−0.335969	+	0.0708525i
$851$		−	3.42920e7i		−	1.62319i
$852$	1.44869e7	−	8.05633e6i	0.683716	−	0.380223i
$853$	−8.20548e6			−0.386128			−0.193064	−	0.981186i	$-0.561843\pi$
$853$	−8.20548e6			−0.386128			−0.193064	+	0.981186i	$0.561843\pi$
$854$	−663704.	−	2.55907e6i	−0.0311408	−	0.120071i
$855$	2.24378e7	+	515231.i	1.04970	+	0.0241039i
$856$	1.37107e7	+	1.43883e7i	0.639549	+	0.671160i
$857$			5.45868e6i			0.253884i	0.991910	+	0.126942i	$0.0405162\pi$
$857$			5.45868e6i			0.253884i	−0.991910	+	0.126942i	$0.959484\pi$
$858$	−1.00978e6	+	261889.i	−0.0468283	+	0.0121451i
$859$			3.18230e7i			1.47149i	0.677257	+	0.735747i	$0.263169\pi$
$859$			3.18230e7i			1.47149i	−0.677257	+	0.735747i	$0.736831\pi$
$860$	−7.01061e6	−	1.33173e7i	−0.323229	−	0.614004i
$861$			1.16022e7i			0.533375i
$862$	5.90494e6	+	2.27680e7i	0.270675	+	1.04365i
$863$		−	9.28914e6i		−	0.424569i	−0.977208	−	0.212285i	$-0.931910\pi$
$863$		−	9.28914e6i		−	0.424569i	0.977208	−	0.212285i	$-0.0680904\pi$
$864$	1.72486e7	+	5.37320e6i	0.786086	+	0.244877i
$865$	154354.	−	6.72196e6i	0.00701420	−	0.305461i
$866$	1.24647e7	−	3.23275e6i	0.564789	−	0.146480i
$867$	−8.99077e6			−0.406208
$868$	−1.16951e7	−	2.10302e7i	−0.526874	−	0.947423i
$869$		−	1.67317e6i		−	0.0751606i
$870$	2.38612e6	+	1.01541e7i	0.106880	+	0.454824i
$871$	−2.53623e7			−1.13277
$872$	1.77721e7	−	1.69351e7i	0.791495	−	0.754217i
$873$		−	1.83771e7i		−	0.816094i
$874$	−9.07819e6	−	3.50032e7i	−0.401995	−	1.54999i
$875$	−2.56024e7	−	1.76618e6i	−1.13047	−	0.0779856i
$876$	5.38961e6	+	9.69159e6i	0.237300	+	0.426712i
$877$	1.60806e7			0.705997			0.352999	−	0.935624i	$-0.385162\pi$
$877$	1.60806e7			0.705997			0.352999	+	0.935624i	$0.385162\pi$
$878$	−1.81957e6	−	7.01580e6i	−0.0796585	−	0.307143i
$879$	65503.2			0.00285950
$880$	−1.32859e6	+	2.03359e6i	−0.0578342	+	0.0885233i
$881$	−1.74471e7			−0.757327			−0.378663	−	0.925535i	$-0.623616\pi$
$881$	−1.74471e7			−0.757327			−0.378663	+	0.925535i	$0.623616\pi$
$882$	1.29812e6	+	5.00522e6i	0.0561879	+	0.216646i
$883$	−2.18862e7			−0.944645			−0.472323	−	0.881426i	$-0.656584\pi$
$883$	−2.18862e7			−0.944645			−0.472323	+	0.881426i	$0.656584\pi$
$884$	−3.85212e6	−	6.92688e6i	−0.165794	−	0.298131i
$885$	−1.46877e7	−	337268.i	−0.630370	−	0.0144750i
$886$	8.53880e6	+	3.29235e7i	0.365437	+	1.40903i
$887$		−	4.00556e7i		−	1.70944i	−0.519088	−	0.854721i	$-0.673728\pi$
$887$		−	4.00556e7i		−	1.70944i	0.519088	−	0.854721i	$-0.326272\pi$
$888$	−1.00834e7	−	1.05818e7i	−0.429116	−	0.450326i
$889$	−2.51567e7			−1.06758
$890$	1.17649e7	−	2.76464e6i	0.497867	−	0.116994i
$891$			1.02433e6i			0.0432260i
$892$	−1.16420e7	−	2.09347e7i	−0.489910	−	0.880955i
$893$	8.33653e6			0.349830
$894$	−9.88778e6	+	2.56442e6i	−0.413766	+	0.107311i
$895$	−1.00900e7	−	231694.i	−0.421051	−	0.00966846i
$896$	5.55762e6	+	2.66577e7i	0.231270	+	1.10931i
$897$			1.32484e7i			0.549770i
$898$	3.00420e6	+	1.15834e7i	0.124319	+	0.479343i
$899$		−	2.35208e7i		−	0.970628i
$900$	−1.71430e7	+	8.52781e6i	−0.705473	+	0.350939i
$901$			1.56592e7i			0.642623i
$902$	−2.55645e6	+	663022.i	−0.104621	+	0.0271339i
$903$			8.87211e6i			0.362083i
$904$	−2.56123e7	+	2.44060e7i	−1.04238	+	0.993287i
$905$	−8.36622e6	−	192111.i	−0.339553	−	0.00779704i
$906$	−976522.	−	3.76523e6i	−0.0395241	−	0.152395i
$907$	1.61797e7			0.653060			0.326530	−	0.945187i	$-0.394121\pi$
$907$	1.61797e7			0.653060			0.326530	+	0.945187i	$0.394121\pi$
$908$	−4.11433e7	+	2.28803e7i	−1.65609	+	0.920974i
$909$		−	1.60643e7i		−	0.644840i
$910$	−6.43348e6	−	2.73776e7i	−0.257539	−	1.09595i
$911$	3.81429e7			1.52271			0.761356	−	0.648334i	$-0.224534\pi$
$911$	3.81429e7			1.52271			0.761356	+	0.648334i	$0.224534\pi$
$912$	−1.30939e7	−	8.13185e6i	−0.521291	−	0.323744i
$913$		−	1.97342e6i		−	0.0783508i
$914$	−7.44500e6	+	1.93088e6i	−0.294781	+	0.0764523i
$915$	−1.27629e6	−	29307.1i	−0.0503962	−	0.00115723i
$916$	−1.29868e7	−	2.33528e7i	−0.511402	−	0.919601i
$917$	1.63682e7			0.642801
$918$	6.98716e6	−	1.81214e6i	0.273649	−	0.0709717i
$919$	−5.75041e6			−0.224600			−0.112300	−	0.993674i	$-0.535822\pi$
$919$	−5.75041e6			−0.224600			−0.112300	+	0.993674i	$0.535822\pi$
$920$	2.07634e7	+	2.28162e7i	0.808776	+	0.888739i
$921$	1.89665e7			0.736780
$922$	1.13039e7	−	2.93170e6i	0.437927	−	0.113578i
$923$	−4.36854e7			−1.68784
$924$	1.25150e6	−	695973.i	0.0482225	−	0.0268171i
$925$	3.51144e7	+	1.61349e6i	1.34937	+	0.0620030i
$926$	8.15422e6	−	2.11482e6i	0.312504	−	0.0810487i
$927$			2.04745e6i			0.0782555i
$928$	−7.91632e6	+	2.54124e7i	−0.301754	+	0.968668i
$929$	1.58033e7			0.600771			0.300386	−	0.953818i	$-0.402885\pi$
$929$	1.58033e7			0.600771			0.300386	+	0.953818i	$0.402885\pi$
$930$	−1.13118e7	+	2.65816e6i	−0.428868	+	0.100780i
$931$		−	1.00104e7i		−	0.378512i
$932$	−4.42806e6	−	7.96254e6i	−0.166984	−	0.300270i
$933$	1.00680e7			0.378651
$934$	1.00241e7	+	3.86505e7i	0.375993	+	1.44973i
$935$	−22280.7	+	970300.i	−0.000833488	+	0.0362975i
$936$	−1.44748e7	−	1.51902e7i	−0.540035	−	0.566727i
$937$			1.61564e7i			0.601167i	0.953756	+	0.300583i	$0.0971814\pi$
$937$			1.61564e7i			0.601167i	−0.953756	+	0.300583i	$0.902819\pi$
$938$	3.37003e7	−	8.74026e6i	1.25062	−	0.324353i
$939$		−	9.75602e6i		−	0.361084i
$940$	−6.29323e6	+	3.31293e6i	−0.232303	+	0.122290i
$941$		−	4.39614e7i		−	1.61844i	−0.587504	−	0.809221i	$-0.699889\pi$
$941$		−	4.39614e7i		−	1.61844i	0.587504	−	0.809221i	$-0.300111\pi$
$942$	1.81931e6	+	7.01481e6i	0.0668005	+	0.257566i
$943$			3.35407e7i			1.22827i
$944$	−3.18476e7	−	1.97788e7i	−1.16318	−	0.722385i
$945$	2.56058e7	+	587976.i	0.932735	+	0.0214181i
$946$	−1.95490e6	+	507008.i	−0.0710225	+	0.0184199i
$947$	−4.52665e7			−1.64022			−0.820111	−	0.572205i	$-0.806088\pi$
$947$	−4.52665e7			−1.64022			−0.820111	+	0.572205i	$0.806088\pi$
$948$	−7.91558e6	+	4.40195e6i	−0.286063	+	0.159083i
$949$		−	2.92252e7i		−	1.05340i
$950$	3.62698e7	−	7.64895e6i	1.30388	−	0.274975i
$951$	−2.15601e6			−0.0773035
$952$	7.50564e6	+	7.87661e6i	0.268408	+	0.281674i
$953$			3.21216e6i			0.114569i	0.998358	+	0.0572843i	$0.0182441\pi$
$953$			3.21216e6i			0.114569i	−0.998358	+	0.0572843i	$0.981756\pi$
$954$	1.04071e7	+	4.01270e7i	0.370218	+	1.42747i
$955$	−274512.	+	1.19547e7i	−0.00973986	+	0.424161i
$956$	−2.23909e7	+	1.24518e7i	−0.792367	+	0.440645i
$957$	1.39971e6			0.0494036
$958$	2.09444e6	+	8.07565e6i	0.0737318	+	0.284292i
$959$	4.14628e7			1.45583
$960$	1.31161e7	+	935232.i	0.459333	+	0.0327523i
$961$	−2.42676e6			−0.0847654
$962$	9.67063e6	+	3.72875e7i	0.336912	+	1.29905i
$963$	2.10221e7			0.730485
$964$	4.21164e7	−	2.34215e7i	1.45968	−	0.811748i
$965$	4.07744e7	+	936288.i	1.40951	+	0.0323662i
$966$	−4.56560e6	−	1.76038e7i	−0.157418	−	0.606965i
$967$		−	4.06241e6i		−	0.139707i	−0.997557	−	0.0698533i	$-0.977747\pi$
$967$		−	4.06241e6i		−	0.139707i	0.997557	−	0.0698533i	$-0.0222531\pi$
$968$	−1.98866e7	−	2.08696e7i	−0.682139	−	0.715855i
$969$	−6.15845e6			−0.210699
$970$	−6.94313e6	−	2.95464e7i	−0.236933	−	1.00827i
$971$			2.41409e7i			0.821685i	0.911706	+	0.410842i	$0.134765\pi$
$971$			2.41409e7i			0.821685i	−0.911706	+	0.410842i	$0.865235\pi$
$972$	2.60410e7	−	1.44817e7i	0.884082	−	0.491649i
$973$	−6.47264e6			−0.219179
$974$	−5.00158e7	+	1.29718e7i	−1.68931	+	0.438128i
$975$	−1.35661e7	−	623355.i	−0.457028	−	0.0210002i
$976$	−2.76741e6	−	1.71868e6i	−0.0929928	−	0.0577526i
$977$			1.48416e7i			0.497443i	0.968575	+	0.248722i	$0.0800104\pi$
$977$			1.48416e7i			0.497443i	−0.968575	+	0.248722i	$0.919990\pi$
$978$	−1.50194e6	−	5.79110e6i	−0.0502118	−	0.193604i
$979$		−	1.62175e6i		−	0.0540790i
$980$	3.97814e6	+	7.55687e6i	0.132317	+	0.251349i
$981$		−	2.59661e7i		−	0.861457i
$982$	2.59651e7	−	6.73412e6i	0.859233	−	0.222845i
$983$			3.34107e7i			1.10281i	0.834237	+	0.551406i	$0.185908\pi$
$983$			3.34107e7i			1.10281i	−0.834237	+	0.551406i	$0.814092\pi$
$984$	9.86247e6	+	1.03499e7i	0.324712	+	0.340761i
$985$	1.18336e6	−	5.15339e7i	0.0388620	−	1.69240i
$986$	2.66982e6	+	1.02942e7i	0.0874560	+	0.337208i
$987$	4.19260e6			0.136991
$988$	1.97424e7	+	3.55007e7i	0.643438	+	1.15703i
$989$			2.56483e7i			0.833812i
$990$	587766.	+	2.50123e6i	0.0190597	+	0.0811083i
$991$	5.15057e7			1.66599			0.832993	−	0.553284i	$-0.186626\pi$
$991$	5.15057e7			1.66599			0.832993	+	0.553284i	$0.186626\pi$
$992$	−2.83096e7	−	8.81886e6i	−0.913387	−	0.284533i
$993$			1.70520e7i			0.548784i
$994$	5.80472e7	−	1.50547e7i	1.86344	−	0.483288i
$995$	1.26448e6	−	5.50670e7i	0.0404907	−	1.76333i
$996$	−9.33606e6	+	5.19190e6i	−0.298205	+	0.165836i
$997$	−1.18985e7			−0.379102			−0.189551	−	0.981871i	$-0.560703\pi$
$997$	−1.18985e7			−0.379102			−0.189551	+	0.981871i	$0.560703\pi$
$998$	−2.95144e6	+	765466.i	−0.0938012	+	0.0243276i
$999$	−3.50821e7			−1.11217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.f.a.29.18	yes	28
4.3	odd	2		160.6.f.a.49.18		28
5.2	odd	4		200.6.d.e.101.4		28
5.3	odd	4		200.6.d.e.101.25		28
5.4	even	2	inner	40.6.f.a.29.11	✓	28
8.3	odd	2		160.6.f.a.49.12		28
8.5	even	2	inner	40.6.f.a.29.12	yes	28
20.3	even	4		800.6.d.e.401.22		28
20.7	even	4		800.6.d.e.401.7		28
20.19	odd	2		160.6.f.a.49.11		28
40.3	even	4		800.6.d.e.401.21		28
40.13	odd	4		200.6.d.e.101.26		28
40.19	odd	2		160.6.f.a.49.17		28
40.27	even	4		800.6.d.e.401.8		28
40.29	even	2	inner	40.6.f.a.29.17	yes	28
40.37	odd	4		200.6.d.e.101.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.f.a.29.11	✓	28	5.4	even	2	inner
40.6.f.a.29.12	yes	28	8.5	even	2	inner
40.6.f.a.29.17	yes	28	40.29	even	2	inner
40.6.f.a.29.18	yes	28	1.1	even	1	trivial
160.6.f.a.49.11		28	20.19	odd	2
160.6.f.a.49.12		28	8.3	odd	2
160.6.f.a.49.17		28	40.19	odd	2
160.6.f.a.49.18		28	4.3	odd	2
200.6.d.e.101.3		28	40.37	odd	4
200.6.d.e.101.4		28	5.2	odd	4
200.6.d.e.101.25		28	5.3	odd	4
200.6.d.e.101.26		28	40.13	odd	4
800.6.d.e.401.7		28	20.7	even	4
800.6.d.e.401.8		28	40.27	even	4
800.6.d.e.401.21		28	40.3	even	4
800.6.d.e.401.22		28	20.3	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42014 + 5.47569i) q^{2} -7.17847 q^{3} +(-27.9664 + 15.5525i) q^{4} +(-1.28331 + 55.8870i) q^{5} +(-10.1944 - 39.3071i) q^{6} -146.905i q^{7} +(-124.877 - 131.049i) q^{8} -191.470 q^{9} +(-307.842 + 72.3401i) q^{10} +42.4351i q^{11} +(200.756 - 111.643i) q^{12} -605.383 q^{13} +(804.405 - 208.625i) q^{14} +(9.21223 - 401.183i) q^{15} +(540.241 - 869.894i) q^{16} -409.138i q^{17} +(-271.913 - 1048.43i) q^{18} +2096.86i q^{19} +(-833.291 - 1582.92i) q^{20} +1054.55i q^{21} +(-232.362 + 60.2637i) q^{22} +3048.59i q^{23} +(896.424 + 940.730i) q^{24} +(-3121.71 - 143.441i) q^{25} +(-859.728 - 3314.89i) q^{26} +3118.83 q^{27} +(2284.73 + 4108.40i) q^{28} +4594.96i q^{29} +(2209.84 - 519.291i) q^{30} -5118.83 q^{31} +(5530.49 + 1722.83i) q^{32} -304.619i q^{33} +(2240.32 - 581.033i) q^{34} +(8210.06 + 188.525i) q^{35} +(5354.72 - 2977.82i) q^{36} -11248.5 q^{37} +(-11481.8 + 2977.83i) q^{38} +4345.73 q^{39} +(7484.18 - 6810.80i) q^{40} +11002.0 q^{41} +(-5774.40 + 1497.61i) q^{42} +8413.16 q^{43} +(-659.971 - 1186.76i) q^{44} +(245.715 - 10700.7i) q^{45} +(-16693.2 + 4329.42i) q^{46} -3975.72i q^{47} +(-3878.11 + 6244.51i) q^{48} -4774.02 q^{49} +(-3647.81 - 17297.2i) q^{50} +2936.99i q^{51} +(16930.4 - 9415.21i) q^{52} -38273.5 q^{53} +(4429.16 + 17077.7i) q^{54} +(-2371.57 - 54.4575i) q^{55} +(-19251.7 + 18345.0i) q^{56} -15052.2i q^{57} +(-25160.6 + 6525.47i) q^{58} -36611.0i q^{59} +(5981.75 + 11362.9i) q^{60} -3181.32i q^{61} +(-7269.44 - 28029.1i) q^{62} +28127.8i q^{63} +(-1579.62 + 32729.9i) q^{64} +(776.897 - 33833.0i) q^{65} +(1668.00 - 432.601i) q^{66} +41894.6 q^{67} +(6363.11 + 11442.1i) q^{68} -21884.2i q^{69} +(10627.1 + 45223.5i) q^{70} +72161.6 q^{71} +(23910.1 + 25091.9i) q^{72} +48275.5i q^{73} +(-15974.4 - 61593.2i) q^{74} +(22409.1 + 1029.69i) q^{75} +(-32611.3 - 58641.7i) q^{76} +6233.92 q^{77} +(6171.53 + 23795.9i) q^{78} -39428.9 q^{79} +(47922.4 + 31308.8i) q^{80} +24138.7 q^{81} +(15624.4 + 60243.7i) q^{82} -46504.5 q^{83} +(-16400.9 - 29492.0i) q^{84} +(22865.5 + 525.053i) q^{85} +(11947.8 + 46067.9i) q^{86} -32984.8i q^{87} +(5561.07 - 5299.16i) q^{88} -38217.3 q^{89} +(58942.4 - 13850.9i) q^{90} +88933.7i q^{91} +(-47413.2 - 85258.2i) q^{92} +36745.3 q^{93} +(21769.8 - 5646.07i) q^{94} +(-117187. - 2690.93i) q^{95} +(-39700.4 - 12367.3i) q^{96} +95979.0i q^{97} +(-6779.76 - 26141.1i) q^{98} -8125.03i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9} - 16 q^{10} - 692 q^{14} - 488 q^{15} + 1560 q^{16} + 2732 q^{20} - 2224 q^{24} + 1556 q^{25} - 9976 q^{26} - 15012 q^{30} + 4368 q^{31} + 13016 q^{34} - 34116 q^{36}+ \cdots - 236176 q^{96}+O(q^{100}) \) 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9 - 16 * q^10 - 692 * q^14 - 488 * q^15 + 1560 * q^16 + 2732 * q^20 - 2224 * q^24 + 1556 * q^25 - 9976 * q^26 - 15012 * q^30 + 4368 * q^31 + 13016 * q^34 - 34116 * q^36 + 23360 * q^39 - 22496 * q^40 - 2480 * q^41 + 10712 * q^44 + 58372 * q^46 - 38420 * q^49 + 45624 * q^50 - 3568 * q^54 - 48776 * q^55 + 110944 * q^56 + 111688 * q^60 - 46944 * q^64 + 37200 * q^65 - 136120 * q^66 - 112852 * q^70 - 69232 * q^71 + 34176 * q^74 - 13944 * q^76 - 35984 * q^79 - 47064 * q^80 + 122596 * q^81 - 165688 * q^84 - 73676 * q^86 - 178744 * q^89 + 51496 * q^90 + 314740 * q^94 + 89416 * q^95 - 236176 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more