LMFDB - Embedded newform 84.6.e.a.71.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,6,Mod(71,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("84.71");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	84.e (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:	$13.4722408643$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.28
Character	$\chi$	$=$	84.71
Dual form			84.6.e.a.71.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03887 + 5.56064i) q^{2} +(13.7520 + 7.34039i) q^{3} +(-29.8415 - 11.5536i) q^{4} -59.1709i q^{5} +(-55.1039 + 68.8445i) q^{6} -49.0000i q^{7} +(95.2469 - 153.935i) q^{8} +(135.237 + 201.891i) q^{9} +(329.028 + 61.4710i) q^{10} +242.318 q^{11} +(-325.573 - 377.934i) q^{12} +886.271 q^{13} +(272.471 + 50.9048i) q^{14} +(434.338 - 813.721i) q^{15} +(757.029 + 689.553i) q^{16} +988.260i q^{17} +(-1263.14 + 542.267i) q^{18} -2556.36i q^{19} +(-683.637 + 1765.75i) q^{20} +(359.679 - 673.850i) q^{21} +(-251.737 + 1347.44i) q^{22} +27.1924 q^{23} +(2439.78 - 1417.77i) q^{24} -376.197 q^{25} +(-920.723 + 4928.24i) q^{26} +(377.831 + 3769.10i) q^{27} +(-566.126 + 1462.23i) q^{28} -924.401i q^{29} +(4073.59 + 3260.55i) q^{30} +30.5693i q^{31} +(-4620.81 + 3493.21i) q^{32} +(3332.36 + 1778.71i) q^{33} +(-5495.36 - 1026.68i) q^{34} -2899.37 q^{35} +(-1703.12 - 7587.20i) q^{36} +13281.5 q^{37} +(14215.0 + 2655.74i) q^{38} +(12188.0 + 6505.58i) q^{39} +(-9108.48 - 5635.85i) q^{40} +9496.50i q^{41} +(3373.38 + 2700.09i) q^{42} -9136.93i q^{43} +(-7231.12 - 2799.64i) q^{44} +(11946.1 - 8002.11i) q^{45} +(-28.2495 + 151.207i) q^{46} -17244.2 q^{47} +(5349.10 + 15039.7i) q^{48} -2401.00 q^{49} +(390.821 - 2091.90i) q^{50} +(-7254.22 + 13590.6i) q^{51} +(-26447.7 - 10239.6i) q^{52} -17877.9i q^{53} +(-21351.2 - 1814.64i) q^{54} -14338.2i q^{55} +(-7542.82 - 4667.10i) q^{56} +(18764.7 - 35155.2i) q^{57} +(5140.26 + 960.335i) q^{58} -38990.5 q^{59} +(-22362.7 + 19264.5i) q^{60} +32882.7 q^{61} +(-169.985 - 31.7576i) q^{62} +(9892.65 - 6626.63i) q^{63} +(-14624.0 - 29323.7i) q^{64} -52441.5i q^{65} +(-13352.7 + 16682.2i) q^{66} -36063.7i q^{67} +(11418.0 - 29491.2i) q^{68} +(373.951 + 199.603i) q^{69} +(3012.08 - 16122.4i) q^{70} +58398.1 q^{71} +(43959.0 - 1588.29i) q^{72} -73802.4 q^{73} +(-13797.7 + 73853.4i) q^{74} +(-5173.48 - 2761.43i) q^{75} +(-29535.2 + 76285.7i) q^{76} -11873.6i q^{77} +(-48837.0 + 61014.9i) q^{78} +65539.0i q^{79} +(40801.5 - 44794.1i) q^{80} +(-22470.8 + 54606.3i) q^{81} +(-52806.6 - 9865.65i) q^{82} +61273.6 q^{83} +(-18518.8 + 15953.1i) q^{84} +58476.3 q^{85} +(50807.2 + 9492.11i) q^{86} +(6785.47 - 12712.4i) q^{87} +(23080.0 - 37301.2i) q^{88} +41863.3i q^{89} +(32086.5 + 74740.9i) q^{90} -43427.3i q^{91} +(-811.462 - 314.170i) q^{92} +(-224.391 + 420.391i) q^{93} +(17914.5 - 95888.8i) q^{94} -151262. q^{95} +(-89187.2 + 14120.2i) q^{96} +38533.2 q^{97} +(2494.33 - 13351.1i) q^{98} +(32770.4 + 48921.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 20 q^{4} - 114 q^{6} + 44 q^{9} + 668 q^{10} + 786 q^{12} - 3004 q^{16} - 3320 q^{18} + 7120 q^{22} + 16466 q^{24} - 37500 q^{25} - 7448 q^{28} - 35236 q^{30} - 9424 q^{33} + 43360 q^{34} + 50524 q^{36}+ \cdots + 232584 q^{97}+O(q^{100}) $ 60 * q - 20 * q^4 - 114 * q^6 + 44 * q^9 + 668 * q^10 + 786 * q^12 - 3004 * q^16 - 3320 * q^18 + 7120 * q^22 + 16466 * q^24 - 37500 * q^25 - 7448 * q^28 - 35236 * q^30 - 9424 * q^33 + 43360 * q^34 + 50524 * q^36 - 15056 * q^37 - 35468 * q^40 - 20090 * q^42 + 36024 * q^45 + 124416 * q^46 + 88654 * q^48 - 144060 * q^49 - 140108 * q^52 + 19486 * q^54 - 65072 * q^57 + 115616 * q^58 + 164908 * q^60 - 169424 * q^61 + 20116 * q^64 - 98484 * q^66 + 142536 * q^69 + 35868 * q^70 + 121312 * q^72 + 107256 * q^73 + 214836 * q^76 + 263708 * q^78 - 114932 * q^81 - 479624 * q^82 + 40474 * q^84 - 383992 * q^85 - 107320 * q^88 + 423760 * q^90 + 545208 * q^93 - 448512 * q^94 - 751618 * q^96 + 232584 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.03887	+	5.56064i	−0.183648	+	0.982992i
$2$	−1.03887	+	5.56064i	−0.183648	+	0.982992i
$3$	13.7520	+	7.34039i	0.882194	+	0.470886i
$3$	13.7520	+	7.34039i	0.882194	+	0.470886i
$4$	−29.8415	−	11.5536i	−0.932546	−	0.361050i
$5$		−	59.1709i		−	1.05848i	−0.848472	−	0.529241i	$-0.822477\pi$
$5$		−	59.1709i		−	1.05848i	0.848472	−	0.529241i	$-0.177523\pi$
$6$	−55.1039	+	68.8445i	−0.624891	+	0.780712i
$7$		−	49.0000i		−	0.377964i
$7$		−	49.0000i		−	0.377964i
$8$	95.2469	−	153.935i	0.526170	−	0.850379i
$9$	135.237	+	201.891i	0.556532	+	0.830826i
$10$	329.028	+	61.4710i	1.04048	+	0.194388i
$11$	242.318			0.603814			0.301907	−	0.953337i	$-0.402377\pi$
$11$	242.318			0.603814			0.301907	+	0.953337i	$0.402377\pi$
$12$	−325.573	−	377.934i	−0.652673	−	0.757639i
$13$	886.271			1.45448			0.727241	−	0.686382i	$-0.240802\pi$
$13$	886.271			1.45448			0.727241	+	0.686382i	$0.240802\pi$
$14$	272.471	+	50.9048i	0.371536	+	0.0694126i
$15$	434.338	−	813.721i	0.498425	−	0.933786i
$16$	757.029	+	689.553i	0.739286	+	0.673392i
$17$			988.260i			0.829371i	0.909965	+	0.414686i	$0.136108\pi$
$17$			988.260i			0.829371i	−0.909965	+	0.414686i	$0.863892\pi$
$18$	−1263.14	+	542.267i	−0.918902	+	0.394487i
$19$		−	2556.36i		−	1.62457i	−0.583260	−	0.812285i	$-0.698223\pi$
$19$		−	2556.36i		−	1.62457i	0.583260	−	0.812285i	$-0.301777\pi$
$20$	−683.637	+	1765.75i	−0.382165	+	0.987083i
$21$	359.679	−	673.850i	0.177978	−	0.333438i
$22$	−251.737	+	1347.44i	−0.110890	+	0.593545i
$23$	27.1924			0.0107184			0.00535918	−	0.999986i	$-0.498294\pi$
$23$	27.1924			0.0107184			0.00535918	+	0.999986i	$0.498294\pi$
$24$	2439.78	−	1417.77i	0.864616	−	0.502433i
$25$	−376.197			−0.120383
$26$	−920.723	+	4928.24i	−0.267113	+	1.42974i
$27$	377.831	+	3769.10i	0.0997444	+	0.995013i
$28$	−566.126	+	1462.23i	−0.136464	+	0.352469i
$29$		−	924.401i		−	0.204111i	−0.994779	−	0.102055i	$-0.967458\pi$
$29$		−	924.401i		−	0.204111i	0.994779	−	0.102055i	$-0.0325419\pi$
$30$	4073.59	+	3260.55i	0.826369	+	0.661436i
$31$			30.5693i			0.00571323i	0.999996	+	0.00285661i	$0.000909290\pi$
$31$			30.5693i			0.00571323i	−0.999996	+	0.00285661i	$0.999091\pi$
$32$	−4620.81	+	3493.21i	−0.797707	+	0.603045i
$33$	3332.36	+	1778.71i	0.532681	+	0.284328i
$34$	−5495.36	−	1026.68i	−0.815265	−	0.152313i
$35$	−2899.37			−0.400068
$36$	−1703.12	−	7587.20i	−0.219022	−	0.975720i
$37$	13281.5			1.59493			0.797464	−	0.603366i	$-0.206174\pi$
$37$	13281.5			1.59493			0.797464	+	0.603366i	$0.206174\pi$
$38$	14215.0	+	2655.74i	1.59694	+	0.298350i
$39$	12188.0	+	6505.58i	1.28314	+	0.684896i
$40$	−9108.48	−	5635.85i	−0.900111	−	0.556941i
$41$			9496.50i			0.882275i	0.897440	+	0.441137i	$0.145425\pi$
$41$			9496.50i			0.882275i	−0.897440	+	0.441137i	$0.854575\pi$
$42$	3373.38	+	2700.09i	0.295081	+	0.236187i
$43$		−	9136.93i		−	0.753580i	−0.926299	−	0.376790i	$-0.877028\pi$
$43$		−	9136.93i		−	0.753580i	0.926299	−	0.376790i	$-0.122972\pi$
$44$	−7231.12	−	2799.64i	−0.563085	−	0.218007i
$45$	11946.1	−	8002.11i	0.879414	−	0.589079i
$46$	−28.2495	+	151.207i	−0.00196841	+	0.0105361i
$47$	−17244.2			−1.13867			−0.569335	−	0.822105i	$-0.692799\pi$
$47$	−17244.2			−1.13867			−0.569335	+	0.822105i	$0.692799\pi$
$48$	5349.10	+	15039.7i	0.335102	+	0.942182i
$49$	−2401.00			−0.142857
$50$	390.821	−	2091.90i	0.0221082	−	0.118336i
$51$	−7254.22	+	13590.6i	−0.390540	+	0.731666i
$52$	−26447.7	−	10239.6i	−1.35637	−	0.525141i
$53$		−	17877.9i		−	0.874233i	−0.899405	−	0.437117i	$-0.856000\pi$
$53$		−	17877.9i		−	0.874233i	0.899405	−	0.437117i	$-0.144000\pi$
$54$	−21351.2	−	1814.64i	−0.996408	−	0.0846847i
$55$		−	14338.2i		−	0.639126i
$56$	−7542.82	−	4667.10i	−0.321413	−	0.198874i
$57$	18764.7	−	35155.2i	0.764988	−	1.43319i
$58$	5140.26	+	960.335i	0.200639	+	0.0374846i
$59$	−38990.5			−1.45824			−0.729120	−	0.684386i	$-0.760070\pi$
$59$	−38990.5			−1.45824			−0.729120	+	0.684386i	$0.760070\pi$
$60$	−22362.7	+	19264.5i	−0.801947	+	0.690843i
$61$	32882.7			1.13147			0.565736	−	0.824587i	$-0.308592\pi$
$61$	32882.7			1.13147			0.565736	+	0.824587i	$0.308592\pi$
$62$	−169.985	−	31.7576i	−0.00561606	−	0.00104923i
$63$	9892.65	−	6626.63i	0.314023	−	0.210349i
$64$	−14624.0	−	29323.7i	−0.446290	−	0.894888i
$65$		−	52441.5i		−	1.53954i
$66$	−13352.7	+	16682.2i	−0.377318	+	0.471405i
$67$		−	36063.7i		−	0.981484i	−0.871305	−	0.490742i	$-0.836726\pi$
$67$		−	36063.7i		−	0.981484i	0.871305	−	0.490742i	$-0.163274\pi$
$68$	11418.0	−	29491.2i	0.299444	−	0.773427i
$69$	373.951	+	199.603i	0.00945567	+	0.00504713i
$70$	3012.08	−	16122.4i	0.0734719	−	0.393264i
$71$	58398.1			1.37484			0.687422	−	0.726259i	$-0.258742\pi$
$71$	58398.1			1.37484			0.687422	+	0.726259i	$0.258742\pi$
$72$	43959.0	−	1588.29i	0.999348	−	0.0361076i
$73$	−73802.4			−1.62093			−0.810463	−	0.585789i	$-0.800785\pi$
$73$	−73802.4			−1.62093			−0.810463	+	0.585789i	$0.800785\pi$
$74$	−13797.7	+	73853.4i	−0.292906	+	1.56780i
$75$	−5173.48	−	2761.43i	−0.106201	−	0.0566867i
$76$	−29535.2	+	76285.7i	−0.586551	+	1.51499i
$77$		−	11873.6i		−	0.228220i
$78$	−48837.0	+	61014.9i	−0.908893	+	1.13553i
$79$			65539.0i			1.18150i	0.806856	+	0.590748i	$0.201167\pi$
$79$			65539.0i			1.18150i	−0.806856	+	0.590748i	$0.798833\pi$
$80$	40801.5	−	44794.1i	0.712773	−	0.782520i
$81$	−22470.8	+	54606.3i	−0.380544	+	0.924763i
$82$	−52806.6	−	9865.65i	−0.867269	−	0.162028i
$83$	61273.6			0.976289			0.488144	−	0.872763i	$-0.337674\pi$
$83$	61273.6			0.976289			0.488144	+	0.872763i	$0.337674\pi$
$84$	−18518.8	+	15953.1i	−0.286361	+	0.246687i
$85$	58476.3			0.877874
$86$	50807.2	+	9492.11i	0.740763	+	0.138394i
$87$	6785.47	−	12712.4i	0.0961129	−	0.180065i
$88$	23080.0	−	37301.2i	0.317709	−	0.513471i
$89$			41863.3i			0.560219i	0.959968	+	0.280110i	$0.0903708\pi$
$89$			41863.3i			0.560219i	−0.959968	+	0.280110i	$0.909629\pi$
$90$	32086.5	+	74740.9i	0.417557	+	0.972640i
$91$		−	43427.3i		−	0.549743i
$92$	−811.462	−	314.170i	−0.00999537	−	0.00386986i
$93$	−224.391	+	420.391i	−0.00269028	+	0.00504017i
$94$	17914.5	−	95888.8i	0.209115	−	1.11930i
$95$	−151262.			−1.71958
$96$	−89187.2	+	14120.2i	−0.987698	+	0.156373i
$97$	38533.2			0.415821			0.207910	−	0.978148i	$-0.433334\pi$
$97$	38533.2			0.415821			0.207910	+	0.978148i	$0.433334\pi$
$98$	2494.33	−	13351.1i	0.0262355	−	0.140427i
$99$	32770.4	+	48921.7i	0.336042	+	0.501665i
$100$	11226.3	+	4346.43i	0.112263	+	0.0434643i
$101$			66057.6i			0.644347i	0.946681	+	0.322173i	$0.104413\pi$
$101$			66057.6i			0.644347i	−0.946681	+	0.322173i	$0.895587\pi$
$102$	−68036.2	−	54457.0i	−0.647500	−	0.518267i
$103$		−	65469.3i		−	0.608058i	−0.952663	−	0.304029i	$-0.901668\pi$
$103$		−	65469.3i		−	0.608058i	0.952663	−	0.304029i	$-0.0983319\pi$
$104$	84414.6	−	136428.i	0.765305	−	1.23686i
$105$	−39872.3	−	21282.5i	−0.352938	−	0.188387i
$106$	99412.7	+	18572.9i	0.859364	+	0.160552i
$107$	−101283.			−0.855216			−0.427608	−	0.903964i	$-0.640644\pi$
$107$	−101283.			−0.855216			−0.427608	+	0.903964i	$0.640644\pi$
$108$	32271.7	−	116841.i	0.266233	−	0.963909i
$109$	−134833.			−1.08700			−0.543499	−	0.839410i	$-0.682901\pi$
$109$	−134833.			−1.08700			−0.543499	+	0.839410i	$0.682901\pi$
$110$	79729.4	+	14895.5i	0.628256	+	0.117375i
$111$	182647.	+	97491.1i	1.40704	+	0.751030i
$112$	33788.1	−	37094.4i	0.254518	−	0.279424i
$113$			235631.i			1.73595i	0.496610	+	0.867974i	$0.334578\pi$
$113$			235631.i			1.73595i	−0.496610	+	0.867974i	$0.665422\pi$
$114$	175991.	+	140866.i	1.26832	+	1.01518i
$115$		−	1609.00i		−	0.0113452i
$116$	−10680.2	+	27585.5i	−0.0736941	+	0.190343i
$117$	119857.	+	178930.i	0.809466	+	1.20842i
$118$	40506.2	−	216812.i	0.267803	−	1.43344i
$119$	48424.7			0.313473
$120$	−83890.9	−	144364.i	−0.531816	−	0.915180i
$121$	−102333.			−0.635408
$122$	−34161.0	+	182849.i	−0.207793	+	1.11223i
$123$	−69708.0	+	130596.i	−0.415451	+	0.778338i
$124$	353.186	−	912.234i	0.00206276	−	0.00532785i
$125$		−	162649.i		−	0.931058i
$126$	26571.1	+	61893.7i	0.149102	+	0.347312i
$127$			49051.3i			0.269862i	0.990855	+	0.134931i	$0.0430812\pi$
$127$			49051.3i			0.269862i	−0.990855	+	0.134931i	$0.956919\pi$
$128$	178251.	−	50855.5i	0.961628	−	0.274355i
$129$	67068.7	−	125651.i	0.354851	−	0.664804i
$130$	291608.	+	54480.0i	1.51336	+	0.282735i
$131$	−228873.			−1.16524			−0.582620	−	0.812744i	$-0.697973\pi$
$131$	−228873.			−1.16524			−0.582620	+	0.812744i	$0.697973\pi$
$132$	−78892.2	−	91580.1i	−0.394094	−	0.457474i
$133$	−125262.			−0.614030
$134$	200537.	+	37465.6i	0.964791	+	0.180248i
$135$	223021.	−	22356.6i	1.05320	−	0.105578i
$136$	152128.	+	94128.7i	0.705280	+	0.436390i
$137$		−	13195.3i		−	0.0600646i	−0.999549	−	0.0300323i	$-0.990439\pi$
$137$		−	13195.3i		−	0.0600646i	0.999549	−	0.0300323i	$-0.00956102\pi$
$138$	−1498.41	+	1872.05i	−0.00669781	+	0.00836795i
$139$		−	327394.i		−	1.43725i	−0.695396	−	0.718627i	$-0.744771\pi$
$139$		−	327394.i		−	1.43725i	0.695396	−	0.718627i	$-0.255229\pi$
$140$	86521.7	+	33498.2i	0.373082	+	0.144445i
$141$	−237143.	−	126579.i	−1.00453	−	0.536185i
$142$	−60668.2	+	324731.i	−0.252488	+	1.35146i
$143$	214759.			0.878237
$144$	−36835.9	+	246090.i	−0.148035	+	0.988982i
$145$	−54697.6			−0.216047
$146$	76671.3	−	410389.i	0.297681	−	1.59336i
$147$	−33018.7	−	17624.3i	−0.126028	−	0.0672695i
$148$	−396338.	−	153449.i	−1.48735	−	0.575849i
$149$			242751.i			0.895767i	0.894092	+	0.447883i	$0.147822\pi$
$149$			242751.i			0.895767i	−0.894092	+	0.447883i	$0.852178\pi$
$150$	20729.9	−	25899.1i	0.0752263	−	0.0939845i
$151$			398555.i			1.42248i	0.702949	+	0.711240i	$0.251866\pi$
$151$			398555.i			1.42248i	−0.702949	+	0.711240i	$0.748134\pi$
$152$	−393514.	−	243486.i	−1.38150	−	0.854800i
$153$	−199521.	+	133650.i	−0.689063	+	0.461572i
$154$	66024.7	+	12335.1i	0.224339	+	0.0419123i
$155$	1808.81			0.00604735
$156$	−288546.	−	334952.i	−0.949302	−	1.10197i
$157$	−436664.			−1.41383			−0.706917	−	0.707296i	$-0.749915\pi$
$157$	−436664.			−1.41383			−0.706917	+	0.707296i	$0.749915\pi$
$158$	−364439.	−	68086.7i	−1.16140	−	0.216980i
$159$	131231.	−	245858.i	0.411665	−	0.771243i
$160$	206696.	+	273418.i	0.638312	+	0.844358i
$161$		−	1332.43i		−	0.00405116i
$162$	−280302.	−	181681.i	−0.839148	−	0.543903i
$163$			86055.8i			0.253695i	0.991922	+	0.126847i	$0.0404858\pi$
$163$			86055.8i			0.253695i	−0.991922	+	0.126847i	$0.959514\pi$
$164$	109719.	−	283390.i	0.318545	−	0.822762i
$165$	105248.	−	197179.i	0.300956	−	0.563833i
$166$	−63655.5	+	340721.i	−0.179294	+	0.959684i
$167$	−638491.			−1.77159			−0.885796	−	0.464075i	$-0.846387\pi$
$167$	−638491.			−1.77159			−0.885796	+	0.464075i	$0.846387\pi$
$168$	−69470.8	−	119549.i	−0.189902	−	0.326794i
$169$	414184.			1.11552
$170$	−60749.4	+	325166.i	−0.161220	+	0.862943i
$171$	516106.	−	345716.i	1.34974	−	0.904125i
$172$	−105564.	+	272660.i	−0.272080	+	0.702748i
$173$			458953.i			1.16588i	0.812516	+	0.582939i	$0.198097\pi$
$173$			458953.i			1.16588i	−0.812516	+	0.582939i	$0.801903\pi$
$174$	63639.9	+	50938.1i	0.159352	+	0.127547i
$175$			18433.7i			0.0455005i
$176$	183442.	+	167091.i	0.446392	+	0.406604i
$177$	−536199.	−	286206.i	−1.28645	−	0.686665i
$178$	−232787.	−	43490.6i	−0.550691	−	0.102883i
$179$	−711126.			−1.65888			−0.829438	−	0.558599i	$-0.811339\pi$
$179$	−711126.			−1.65888			−0.829438	+	0.558599i	$0.811339\pi$
$180$	−448941.	+	100775.i	−1.03278	+	0.231831i
$181$	390406.			0.885767			0.442884	−	0.896579i	$-0.353955\pi$
$181$	390406.			0.885767			0.442884	+	0.896579i	$0.353955\pi$
$182$	241484.	+	45115.4i	0.540393	+	0.100959i
$183$	452205.	+	241372.i	0.998177	+	0.532794i
$184$	2589.99	−	4185.87i	0.00563968	−	0.00911467i
$185$		−	785876.i		−	1.68820i
$186$	−2104.53	−	1684.49i	−0.00446038	−	0.00357015i
$187$			239473.i			0.500786i
$188$	514592.	+	199232.i	1.06186	+	0.411117i
$189$	184686.	−	18513.7i	0.376080	−	0.0376998i
$190$	157142.	−	841116.i	0.315798	−	1.69033i
$191$	−243302.			−0.482571			−0.241286	−	0.970454i	$-0.577569\pi$
$191$	−243302.			−0.482571			−0.241286	+	0.970454i	$0.577569\pi$
$192$	14137.0	−	510607.i	0.0276760	−	0.999617i
$193$	314904.			0.608534			0.304267	−	0.952587i	$-0.401589\pi$
$193$	314904.			0.608534			0.304267	+	0.952587i	$0.401589\pi$
$194$	−40031.1	+	214269.i	−0.0763648	+	0.408748i
$195$	384941.	−	721178.i	0.724950	−	1.35817i
$196$	71649.4	+	27740.2i	0.133221	+	0.0515786i
$197$		−	312556.i		−	0.573802i	−0.957960	−	0.286901i	$-0.907375\pi$
$197$		−	312556.i		−	0.573802i	0.957960	−	0.286901i	$-0.0926251\pi$
$198$	−306080.	+	131401.i	−0.554846	+	0.238197i
$199$			560445.i			1.00323i	0.865091	+	0.501615i	$0.167261\pi$
$199$			560445.i			1.00323i	−0.865091	+	0.501615i	$0.832739\pi$
$200$	−35831.6	+	57909.9i	−0.0633419	+	0.102371i
$201$	264722.	−	495949.i	0.462167	−	0.865859i
$202$	−367323.	−	68625.5i	−0.633388	−	0.118333i
$203$	−45295.6			−0.0771465
$204$	373497.	−	321751.i	0.628364	−	0.541308i
$205$	561917.			0.933872
$206$	364051.	+	68014.3i	0.597716	+	0.111669i
$207$	3677.43	+	5489.90i	0.00596511	+	0.00890509i
$208$	670933.	+	611131.i	1.07528	+	0.979436i
$209$		−	619452.i		−	0.980939i
$210$	159767.	−	199606.i	0.249999	−	0.312338i
$211$			476519.i			0.736841i	0.929659	+	0.368421i	$0.120101\pi$
$211$			476519.i			0.736841i	−0.929659	+	0.368421i	$0.879899\pi$
$212$	−206554.	+	533504.i	−0.315642	+	0.815263i
$213$	803094.	+	428665.i	1.21288	+	0.647395i
$214$	105220.	−	563197.i	0.157059	−	0.840671i
$215$	−540641.			−0.797650
$216$	616185.	+	300834.i	0.898621	+	0.438725i
$217$	1497.90			0.00215940
$218$	140074.	−	749756.i	0.199626	−	1.06851i
$219$	−1.01493e6	−	541739.i	−1.42997	−	0.763272i
$220$	−165657.	+	427872.i	−0.230757	+	0.596015i
$221$			875867.i			1.20631i
$222$	−731860.	+	914354.i	−0.996657	+	1.24518i
$223$		−	166322.i		−	0.223968i	−0.993710	−	0.111984i	$-0.964279\pi$
$223$		−	166322.i		−	0.223968i	0.993710	−	0.111984i	$-0.0357206\pi$
$224$	171167.	+	226420.i	0.227929	+	0.301505i
$225$	−50875.9	−	75950.7i	−0.0669970	−	0.100017i
$226$	−1.31026e6	−	244791.i	−1.70642	−	0.318804i
$227$	830034.			1.06913			0.534566	−	0.845127i	$-0.320475\pi$
$227$	830034.			1.06913			0.534566	+	0.845127i	$0.320475\pi$
$228$	−966136.	+	832284.i	−1.23084	+	1.06031i
$229$	669986.			0.844262			0.422131	−	0.906535i	$-0.361282\pi$
$229$	669986.			0.844262			0.422131	+	0.906535i	$0.361282\pi$
$230$	8947.07	+	1671.55i	0.0111522	+	0.00208353i
$231$	87156.7	−	163286.i	0.107466	−	0.201335i
$232$	−142298.	−	88046.4i	−0.173571	−	0.107397i
$233$			431808.i			0.521076i	0.965464	+	0.260538i	$0.0839000\pi$
$233$			431808.i			0.521076i	−0.965464	+	0.260538i	$0.916100\pi$
$234$	−1.11948e6	+	480596.i	−1.33653	+	0.573774i
$235$			1.02035e6i			1.20526i
$236$	1.16353e6	+	450481.i	1.35988	+	0.526497i
$237$	−481082.	+	901295.i	−0.556350	+	1.04231i
$238$	−50307.1	+	269273.i	−0.0575688	+	0.308141i
$239$	1.03478e6			1.17180			0.585902	−	0.810382i	$-0.300740\pi$
$239$	1.03478e6			1.17180			0.585902	+	0.810382i	$0.300740\pi$
$240$	889910.	−	316511.i	0.997282	−	0.354700i
$241$	427091.			0.473672			0.236836	−	0.971550i	$-0.423890\pi$
$241$	427091.			0.473672			0.236836	+	0.971550i	$0.423890\pi$
$242$	106311.	−	569038.i	0.116692	−	0.624601i
$243$	−709851.	+	586004.i	−0.771172	+	0.636627i
$244$	−981270.	−	379914.i	−1.05515	−	0.408518i
$245$			142069.i			0.151212i
$246$	−653781.	−	523294.i	−0.688803	−	0.551326i
$247$		−	2.26563e6i		−	2.36291i
$248$	4705.69	+	2911.63i	0.00485841	+	0.00300613i
$249$	842637.	+	449772.i	0.861276	+	0.459721i
$250$	904434.	+	168972.i	0.915223	+	0.170987i
$251$	900539.			0.902232			0.451116	−	0.892465i	$-0.351026\pi$
$251$	900539.			0.902232			0.451116	+	0.892465i	$0.351026\pi$
$252$	−371773.	+	83452.7i	−0.368787	+	0.0827826i
$253$	6589.21			0.00647190
$254$	−272757.	−	50958.1i	−0.265272	−	0.0495597i
$255$	804168.	+	429239.i	0.774455	+	0.413379i
$256$	97609.1	+	1.04402e6i	0.0930873	+	0.995658i
$257$		−	303145.i		−	0.286297i	−0.989701	−	0.143149i	$-0.954277\pi$
$257$		−	303145.i		−	0.286297i	0.989701	−	0.143149i	$-0.0457227\pi$
$258$	629027.	+	503481.i	0.588329	+	0.470905i
$259$		−	650791.i		−	0.602826i
$260$	−605888.	+	1.56493e6i	−0.555852	+	1.43569i
$261$	186628.	−	125013.i	0.169580	−	0.113594i
$262$	237770.	−	1.27268e6i	0.213995	−	1.14542i
$263$	−644021.			−0.574131			−0.287065	−	0.957911i	$-0.592680\pi$
$263$	−644021.			−0.574131			−0.287065	+	0.957911i	$0.592680\pi$
$264$	591203.	−	343551.i	0.522068	−	0.303376i
$265$	−1.05785e6			−0.925360
$266$	130131.	−	696536.i	0.112766	−	0.603586i
$267$	−307293.	+	575705.i	−0.263800	+	0.494222i
$268$	−416665.	+	1.07619e6i	−0.354365	+	0.915280i
$269$			85711.5i			0.0722202i	0.999348	+	0.0361101i	$0.0114967\pi$
$269$			85711.5i			0.0722202i	−0.999348	+	0.0361101i	$0.988503\pi$
$270$	−107374.	+	1.26337e6i	−0.0896372	+	1.05468i
$271$		−	1.68186e6i		−	1.39113i	−0.718464	−	0.695565i	$-0.755154\pi$
$271$		−	1.68186e6i		−	1.39113i	0.718464	−	0.695565i	$-0.244846\pi$
$272$	−681458.	+	748141.i	−0.558492	+	0.613142i
$273$	318773.	−	597214.i	0.258866	−	0.484980i
$274$	73374.5	+	13708.3i	0.0590430	+	0.0110308i
$275$	−91159.2			−0.0726890
$276$	−8853.13	−	10276.9i	−0.00699558	−	0.00812065i
$277$	−115110.			−0.0901388			−0.0450694	−	0.998984i	$-0.514351\pi$
$277$	−115110.			−0.0901388			−0.0450694	+	0.998984i	$0.514351\pi$
$278$	1.82052e6	+	340120.i	1.41281	+	0.263949i
$279$	−6171.66	+	4134.11i	−0.00474670	+	0.00317959i
$280$	−276157.	+	446316.i	−0.210504	+	0.340210i
$281$		−	974793.i		−	0.736456i	−0.929736	−	0.368228i	$-0.879965\pi$
$281$		−	974793.i		−	0.736456i	0.929736	−	0.368228i	$-0.120035\pi$
$282$	950222.	−	1.18717e6i	0.711545	−	0.888974i
$283$			909235.i			0.674854i	0.941352	+	0.337427i	$0.109557\pi$
$283$			909235.i			0.674854i	−0.941352	+	0.337427i	$0.890443\pi$
$284$	−1.74269e6	−	674709.i	−1.28211	−	0.496387i
$285$	−2.08017e6	−	1.11032e6i	−1.51700	−	0.809726i
$286$	−223108.	+	1.19420e6i	−0.161287	+	0.863300i
$287$	465329.			0.333469
$288$	−1.33015e6	−	460488.i	−0.944975	−	0.327142i
$289$	443199.			0.312143
$290$	56823.9	−	304154.i	0.0396767	−	0.212373i
$291$	529910.	+	282849.i	0.366834	+	0.195804i
$292$	2.20237e6	+	852683.i	1.51159	+	0.585236i
$293$			249224.i			0.169598i	0.996398	+	0.0847991i	$0.0270248\pi$
$293$			249224.i			0.169598i	−0.996398	+	0.0847991i	$0.972975\pi$
$294$	132305.	−	165296.i	0.0892702	−	0.111530i
$295$			2.30710e6i			1.54352i
$296$	1.26502e6	−	2.04448e6i	0.839203	−	1.35629i
$297$	91555.2	+	913321.i	0.0602271	+	0.600803i
$298$	−1.34985e6	−	252187.i	−0.880532	−	0.164506i
$299$	24099.9			0.0155897
$300$	122480.	+	142178.i	0.0785708	+	0.0912069i
$301$	−447710.			−0.284826
$302$	−2.21622e6	−	414048.i	−1.39829	−	0.261236i
$303$	−484889.	+	908427.i	−0.303414	+	0.568439i
$304$	1.76275e6	−	1.93524e6i	1.09397	−	1.20102i
$305$		−	1.94570e6i		−	1.19764i
$306$	−535901.	−	1.24831e6i	−0.327176	−	0.762111i
$307$		−	2.54784e6i		−	1.54286i	−0.636315	−	0.771429i	$-0.719542\pi$
$307$		−	2.54784e6i		−	1.54286i	0.636315	−	0.771429i	$-0.280458\pi$
$308$	−137182.	+	354325.i	−0.0823990	+	0.212826i
$309$	480571.	−	900337.i	0.286326	−	0.536425i
$310$	−1879.13	+	10058.2i	−0.00111059	+	0.00594449i
$311$	−2.29008e6			−1.34261			−0.671305	−	0.741182i	$-0.734266\pi$
$311$	−2.29008e6			−1.34261			−0.671305	+	0.741182i	$0.734266\pi$
$312$	2.16231e6	−	1.25653e6i	1.25757	−	0.730780i
$313$	−2.93022e6			−1.69060			−0.845298	−	0.534295i	$-0.820577\pi$
$313$	−2.93022e6			−1.69060			−0.845298	+	0.534295i	$0.820577\pi$
$314$	453638.	−	2.42813e6i	0.259648	−	1.38979i
$315$	−392104.	−	585357.i	−0.222651	−	0.332387i
$316$	757211.	−	1.95578e6i	0.426579	−	1.10180i
$317$			1.34286e6i			0.750555i	0.926913	+	0.375277i	$0.122453\pi$
$317$			1.34286e6i			0.750555i	−0.926913	+	0.375277i	$0.877547\pi$
$318$	1.23080e6	+	985144.i	0.682524	+	0.546301i
$319$		−	223999.i		−	0.123245i
$320$	−1.73511e6	+	865318.i	−0.947223	+	0.472390i
$321$	−1.39284e6	−	743455.i	−0.754466	−	0.402710i
$322$	7409.16	+	1384.22i	0.00398226	+	0.000743989i
$323$	2.52635e6			1.34737
$324$	1.30146e6	−	1.36992e6i	0.688761	−	0.724989i
$325$	−333413.			−0.175095
$326$	−478526.	−	89401.0i	−0.249380	−	0.0465906i
$327$	−1.85422e6	−	989725.i	−0.958943	−	0.511853i
$328$	1.46184e6	+	904512.i	0.750268	+	0.464227i
$329$			844965.i			0.430377i
$330$	987103.	+	790089.i	0.498974	+	0.399384i
$331$			2.36598e6i			1.18697i	0.804844	+	0.593487i	$0.202249\pi$
$331$			2.36598e6i			1.18697i	−0.804844	+	0.593487i	$0.797751\pi$
$332$	−1.82850e6	−	707931.i	−0.910435	−	0.352489i
$333$	1.79615e6	+	2.68140e6i	0.887629	+	1.32511i
$334$	663311.	−	3.55042e6i	0.325350	−	1.74146i
$335$	−2.13392e6			−1.03888
$336$	736943.	−	262106.i	0.356111	−	0.126657i
$337$	−1.04998e6			−0.503626			−0.251813	−	0.967776i	$-0.581027\pi$
$337$	−1.04998e6			−0.503626			−0.251813	+	0.967776i	$0.581027\pi$
$338$	−430284.	+	2.30313e6i	−0.204863	+	1.09655i
$339$	−1.72963e6	+	3.24041e6i	−0.817434	+	1.53144i
$340$	−1.74502e6	−	675611.i	−0.818658	−	0.316956i
$341$			7407.49i			0.00344973i
$342$	1.38623e6	+	3.22904e6i	0.640871	+	1.49282i
$343$			117649.i			0.0539949i
$344$	−1.40650e6	−	870265.i	−0.640829	−	0.396511i
$345$	11810.7	−	22127.0i	0.00534229	−	0.0100086i
$346$	−2.55208e6	−	476794.i	−1.14605	−	0.214112i
$347$	4.25431e6			1.89673			0.948365	−	0.317181i	$-0.102736\pi$
$347$	4.25431e6			1.89673			0.948365	+	0.317181i	$0.102736\pi$
$348$	−349362.	+	300960.i	−0.154642	+	0.133217i
$349$	729310.			0.320515			0.160258	−	0.987075i	$-0.448767\pi$
$349$	729310.			0.320515			0.160258	+	0.987075i	$0.448767\pi$
$350$	−102503.	−	19150.2i	−0.0447266	−	0.00835610i
$351$	334861.	+	3.34045e6i	0.145076	+	1.44723i
$352$	−1.11971e6	+	846466.i	−0.481667	+	0.364127i
$353$		−	195287.i		−	0.0834136i	−0.999130	−	0.0417068i	$-0.986720\pi$
$353$		−	195287.i		−	0.0834136i	0.999130	−	0.0417068i	$-0.0132795\pi$
$354$	2.14853e6	−	2.68428e6i	0.911241	−	1.13846i
$355$		−	3.45547e6i		−	1.45525i
$356$	483671.	−	1.24926e6i	0.202267	−	0.522431i
$357$	665939.	+	355457.i	0.276544	+	0.147610i
$358$	738769.	−	3.95431e6i	0.304650	−	1.63066i
$359$	427696.			0.175146			0.0875729	−	0.996158i	$-0.472089\pi$
$359$	427696.			0.175146			0.0875729	+	0.996158i	$0.472089\pi$
$360$	−93980.7	−	2.60110e6i	−0.0382193	−	1.05779i
$361$	−4.05889e6			−1.63923
$362$	−405582.	+	2.17091e6i	−0.162670	+	0.870702i
$363$	−1.40729e6	−	751165.i	−0.560553	−	0.299205i
$364$	−501742.	+	1.29594e6i	−0.198485	+	0.512660i
$365$			4.36696e6i			1.71572i
$366$	−1.81197e6	+	2.26379e6i	−0.707046	+	0.883353i
$367$			45114.1i			0.0174842i	0.999962	+	0.00874212i	$0.00278274\pi$
$367$			45114.1i			0.0174842i	−0.999962	+	0.00874212i	$0.997217\pi$
$368$	20585.4	+	18750.6i	0.00792393	+	0.00721765i
$369$	−1.91726e6	+	1.28428e6i	−0.733017	+	0.491014i
$370$	4.36997e6	+	816425.i	1.65949	+	0.310036i
$371$	−876018.			−0.330429
$372$	11553.2	−	9952.56i	0.00432857	−	0.00372887i
$373$	−466820.			−0.173731			−0.0868656	−	0.996220i	$-0.527685\pi$
$373$	−466820.			−0.173731			−0.0868656	+	0.996220i	$0.527685\pi$
$374$	−1.33162e6	−	248782.i	−0.492269	−	0.0919686i
$375$	1.19391e6	−	2.23676e6i	0.438423	−	0.821374i
$376$	−1.64246e6	+	2.65449e6i	−0.599134	+	0.968302i
$377$		−	819270.i		−	0.296875i
$378$	−88917.2	+	1.04621e6i	−0.0320078	+	0.376607i
$379$			3.53522e6i			1.26421i	0.774883	+	0.632104i	$0.217809\pi$
$379$			3.53522e6i			1.26421i	−0.774883	+	0.632104i	$0.782191\pi$
$380$	4.51389e6	+	1.74762e6i	1.60359	+	0.620853i
$381$	−360056.	+	674556.i	−0.127074	+	0.238070i
$382$	252759.	−	1.35291e6i	0.0886235	−	0.474364i
$383$	760513.			0.264917			0.132458	−	0.991189i	$-0.457713\pi$
$383$	760513.			0.264917			0.132458	+	0.991189i	$0.457713\pi$
$384$	2.82462e6	+	609066.i	0.977533	+	0.210783i
$385$	−702570.			−0.241567
$386$	−327145.	+	1.75107e6i	−0.111756	+	0.598184i
$387$	1.84466e6	−	1.23565e6i	0.626094	−	0.419391i
$388$	−1.14989e6	−	445197.i	−0.387772	−	0.150132i
$389$		−	313315.i		−	0.104980i	−0.998621	−	0.0524900i	$-0.983284\pi$
$389$		−	313315.i		−	0.104980i	0.998621	−	0.0524900i	$-0.0167158\pi$
$390$	3.61031e6	+	2.88973e6i	1.20194	+	0.962046i
$391$			26873.2i			0.00888950i
$392$	−228688.	+	369598.i	−0.0751671	+	0.121483i
$393$	−3.14747e6	−	1.68002e6i	−1.02797	−	0.548696i
$394$	1.73801e6	+	324706.i	0.564043	+	0.105378i
$395$	3.87800e6			1.25059
$396$	−412695.	−	1.83851e6i	−0.132249	−	0.589154i
$397$	3.20546e6			1.02074			0.510369	−	0.859956i	$-0.329509\pi$
$397$	3.20546e6			1.02074			0.510369	+	0.859956i	$0.329509\pi$
$398$	−3.11644e6	−	582231.i	−0.986167	−	0.184242i
$399$	−1.72261e6	−	919471.i	−0.541693	−	0.289138i
$400$	−284792.	−	259408.i	−0.0889975	−	0.0810649i
$401$		−	2.26595e6i		−	0.703703i	−0.936056	−	0.351852i	$-0.885552\pi$
$401$		−	2.26595e6i		−	0.703703i	0.936056	−	0.351852i	$-0.114448\pi$
$402$	2.48279e6	+	1.98725e6i	0.766256	+	0.613321i
$403$			27092.7i			0.00830979i
$404$	763203.	−	1.97126e6i	0.232641	−	0.600883i
$405$	3.23111e6	+	1.32962e6i	0.978844	+	0.402799i
$406$	47056.4	−	251873.i	0.0141678	−	0.0758344i
$407$	3.21833e6			0.963041
$408$	1.40113e6	+	2.41114e6i	0.416704	+	0.717088i
$409$	679008.			0.200709			0.100354	−	0.994952i	$-0.468002\pi$
$409$	679008.			0.200709			0.100354	+	0.994952i	$0.468002\pi$
$410$	−583760.	+	3.12462e6i	−0.171504	+	0.917988i
$411$	96858.9	−	181463.i	0.0282836	−	0.0529886i
$412$	−756406.	+	1.95370e6i	−0.219539	+	0.567042i
$413$			1.91053e6i			0.551163i
$414$	−34347.7	+	14745.6i	−0.00984912	+	0.00422825i
$415$		−	3.62562e6i		−	1.03338i
$416$	−4.09530e6	+	3.09593e6i	−1.16025	+	0.877118i
$417$	2.40320e6	−	4.50233e6i	0.676783	−	1.26794i
$418$	3.44455e6	+	643532.i	0.964255	+	0.180148i
$419$	−5.00575e6			−1.39294			−0.696472	−	0.717584i	$-0.745248\pi$
$419$	−5.00575e6			−1.39294			−0.696472	+	0.717584i	$0.745248\pi$
$420$	943959.	+	1.09577e6i	0.261114	+	0.303108i
$421$	6.42332e6			1.76626			0.883130	−	0.469129i	$-0.155432\pi$
$421$	6.42332e6			1.76626			0.883130	+	0.469129i	$0.155432\pi$
$422$	−2.64975e6	−	495042.i	−0.724309	−	0.135320i
$423$	−2.33206e6	−	3.48144e6i	−0.633707	−	0.946037i
$424$	−2.75204e6	−	1.70282e6i	−0.743430	−	0.459995i
$425$		−	371780.i		−	0.0998422i
$426$	−3.21797e6	+	4.02039e6i	−0.859127	+	1.07336i
$427$		−	1.61125e6i		−	0.427656i
$428$	3.02243e6	+	1.17018e6i	0.797529	+	0.308776i
$429$	2.95338e6	+	1.57642e6i	0.774776	+	0.413550i
$430$	561657.	−	3.00631e6i	0.146487	−	0.784084i
$431$	4.18651e6			1.08557			0.542787	−	0.839870i	$-0.317369\pi$
$431$	4.18651e6			1.08557			0.542787	+	0.839870i	$0.317369\pi$
$432$	−2.31297e6	+	3.11386e6i	−0.596294	+	0.802766i
$433$	2.71085e6			0.694842			0.347421	−	0.937709i	$-0.387057\pi$
$433$	2.71085e6			0.694842			0.347421	+	0.937709i	$0.387057\pi$
$434$	−1556.12	+	8329.27i	−0.000396570	+	0.00212267i
$435$	−752204.	−	401502.i	−0.190596	−	0.101734i
$436$	4.02361e6	+	1.55780e6i	1.01368	+	0.392461i
$437$		−	69513.7i		−	0.0174127i
$438$	4.06680e6	−	5.08089e6i	1.01290	−	1.26548i
$439$		−	4.55090e6i		−	1.12703i	−0.826106	−	0.563515i	$-0.809449\pi$
$439$		−	4.55090e6i		−	1.12703i	0.826106	−	0.563515i	$-0.190551\pi$
$440$	−2.20715e6	−	1.36567e6i	−0.543500	−	0.336289i
$441$	−324705.	−	484740.i	−0.0795046	−	0.118689i
$442$	−4.87038e6	−	909914.i	−1.18579	−	0.221536i
$443$	3.38222e6			0.818827			0.409413	−	0.912349i	$-0.365733\pi$
$443$	3.38222e6			0.818827			0.409413	+	0.912349i	$0.365733\pi$
$444$	−4.32409e6	−	5.01951e6i	−1.04097	−	1.20838i
$445$	2.47709e6			0.592982
$446$	924854.	+	172787.i	0.220159	+	0.0411314i
$447$	−1.78189e6	+	3.33832e6i	−0.421804	+	0.790240i
$448$	−1.43686e6	+	716578.i	−0.338236	+	0.168682i
$449$		−	3.15731e6i		−	0.739097i	−0.929211	−	0.369548i	$-0.879512\pi$
$449$		−	3.15731e6i		−	0.739097i	0.929211	−	0.369548i	$-0.120488\pi$
$450$	475188.	−	203999.i	0.110620	−	0.0474895i
$451$			2.30117e6i			0.532730i
$452$	2.72239e6	−	7.03158e6i	0.626764	−	1.61885i
$453$	−2.92555e6	+	5.48095e6i	−0.669827	+	1.25490i
$454$	−862300.	+	4.61552e6i	−0.196344	+	1.05095i
$455$	−2.56963e6			−0.581892
$456$	−3.62434e6	−	6.23697e6i	−0.816238	−	1.40463i
$457$	−6.41403e6			−1.43662			−0.718308	−	0.695726i	$-0.755083\pi$
$457$	−6.41403e6			−1.43662			−0.718308	+	0.695726i	$0.755083\pi$
$458$	−696030.	+	3.72555e6i	−0.155047	+	0.829903i
$459$	−3.72486e6	+	373395.i	−0.825235	+	0.0827251i
$460$	−18589.7	+	48015.0i	−0.00409618	+	0.0105799i
$461$		−	306524.i		−	0.0671756i	−0.999436	−	0.0335878i	$-0.989307\pi$
$461$		−	306524.i		−	0.0671756i	0.999436	−	0.0335878i	$-0.0106933\pi$
$462$	817429.	+	654280.i	0.178174	+	0.142613i
$463$			8.39434e6i			1.81984i	0.414779	+	0.909922i	$0.363859\pi$
$463$			8.39434e6i			1.81984i	−0.414779	+	0.909922i	$0.636141\pi$
$464$	637424.	−	699798.i	0.137446	−	0.150896i
$465$	24874.9	+	13277.4i	0.00533493	+	0.00284761i
$466$	−2.40113e6	−	448594.i	−0.512214	−	0.0956948i
$467$	−272126.			−0.0577402			−0.0288701	−	0.999583i	$-0.509191\pi$
$467$	−272126.			−0.0577402			−0.0288701	+	0.999583i	$0.509191\pi$
$468$	−1.50942e6	−	6.72432e6i	−0.318564	−	1.41917i
$469$	−1.76712e6			−0.370966
$470$	−5.67383e6	−	1.06002e6i	−1.18476	−	0.221344i
$471$	−6.00502e6	−	3.20529e6i	−1.24728	−	0.665755i
$472$	−3.71373e6	+	6.00201e6i	−0.767282	+	1.24006i
$473$		−	2.21404e6i		−	0.455023i
$474$	−4.51200e6	−	3.61145e6i	−0.922407	−	0.738306i
$475$			961696.i			0.195571i
$476$	−1.44507e6	−	559480.i	−0.292328	−	0.113179i
$477$	3.60939e6	−	2.41776e6i	0.726336	−	0.486539i
$478$	−1.07501e6	+	5.75406e6i	−0.215200	+	1.15187i
$479$	2.17808e6			0.433746			0.216873	−	0.976200i	$-0.430414\pi$
$479$	2.17808e6			0.433746			0.216873	+	0.976200i	$0.430414\pi$
$480$	835502.	+	5.27729e6i	0.165518	+	1.04546i
$481$	1.17710e7			2.31980
$482$	−443693.	+	2.37490e6i	−0.0869891	+	0.465616i
$483$	9780.55	−	18323.6i	0.00190764	−	0.00357391i
$484$	3.05377e6	+	1.18232e6i	0.592548	+	0.229414i
$485$		−	2.28005e6i		−	0.440138i
$486$	−2.52111e6	−	4.55601e6i	−0.484175	−	0.874971i
$487$		−	519090.i		−	0.0991792i	−0.998770	−	0.0495896i	$-0.984209\pi$
$487$		−	519090.i		−	0.0991792i	0.998770	−	0.0495896i	$-0.0157913\pi$
$488$	3.13198e6	−	5.06181e6i	0.595346	−	0.962180i
$489$	−631684.	+	1.18344e6i	−0.119461	+	0.223808i
$490$	−789997.	−	147592.i	−0.148640	−	0.0277698i
$491$	−2.68333e6			−0.502309			−0.251155	−	0.967947i	$-0.580810\pi$
$491$	−2.68333e6			−0.502309			−0.251155	+	0.967947i	$0.580810\pi$
$492$	3.58905e6	−	3.09181e6i	0.668446	−	0.575837i
$493$	913549.			0.169283
$494$	1.25984e7	+	2.35370e6i	2.32272	+	0.433945i
$495$	2.89474e6	−	1.93905e6i	0.531003	−	0.355694i
$496$	−21079.2	+	23141.9i	−0.00384724	+	0.00422371i
$497$		−	2.86151e6i		−	0.519642i
$498$	−3.37642e6	+	4.21835e6i	−0.610074	+	0.762200i
$499$			4.91831e6i			0.884228i	0.896959	+	0.442114i	$0.145771\pi$
$499$			4.91831e6i			0.884228i	−0.896959	+	0.442114i	$0.854229\pi$
$500$	−1.87918e6	+	4.85369e6i	−0.336159	+	0.868255i
$501$	−8.78056e6	−	4.68678e6i	−1.56289	−	0.834218i
$502$	−935545.	+	5.00757e6i	−0.165693	+	0.886886i
$503$	3.79230e6			0.668317			0.334159	−	0.942517i	$-0.391548\pi$
$503$	3.79230e6			0.668317			0.334159	+	0.942517i	$0.391548\pi$
$504$	−77826.3	−	2.15399e6i	−0.0136474	−	0.377718i
$505$	3.90869e6			0.682029
$506$	−6845.34	+	36640.2i	−0.00118855	+	0.00636182i
$507$	5.69588e6	+	3.04027e6i	0.984103	+	0.525282i
$508$	566719.	−	1.46376e6i	0.0974336	−	0.251659i
$509$		−	6.08584e6i		−	1.04118i	−0.853807	−	0.520590i	$-0.825712\pi$
$509$		−	6.08584e6i		−	1.04118i	0.853807	−	0.520590i	$-0.174288\pi$
$510$	−3.22227e6	+	4.02577e6i	−0.548576	+	0.685367i
$511$			3.61632e6i			0.612653i
$512$	−5.90684e6	−	541838.i	−0.995819	−	0.0913470i
$513$	9.63520e6	−	965874.i	1.61647	−	0.162042i
$514$	1.68568e6	+	314929.i	0.281428	+	0.0525781i
$515$	−3.87388e6			−0.643618
$516$	−3.45316e6	+	2.97474e6i	−0.570942	+	0.491842i
$517$	−4.17857e6			−0.687546
$518$	3.61882e6	+	676089.i	0.592573	+	0.110708i
$519$	−3.36890e6	+	6.31154e6i	−0.548996	+	1.02853i
$520$	−8.07259e6	−	4.99489e6i	−1.30920	−	0.810061i
$521$		−	1.08633e7i		−	1.75335i	−0.481082	−	0.876676i	$-0.659756\pi$
$521$		−	1.08633e7i		−	1.75335i	0.481082	−	0.876676i	$-0.340244\pi$
$522$	501272.	+	1.16764e6i	0.0805189	+	0.187558i
$523$		−	5.64070e6i		−	0.901735i	−0.892591	−	0.450867i	$-0.851115\pi$
$523$		−	5.64070e6i		−	0.901735i	0.892591	−	0.450867i	$-0.148885\pi$
$524$	6.82990e6	+	2.64430e6i	1.08664	+	0.420710i
$525$	−135310.	+	253500.i	−0.0214256	+	0.0401403i
$526$	669056.	−	3.58117e6i	0.105438	−	0.564366i
$527$	−30210.4			−0.00473839
$528$	1.29618e6	+	3.64437e6i	0.202340	+	0.568903i
$529$	−6.43560e6			−0.999885
$530$	1.09897e6	−	5.88234e6i	0.169941	−	0.909621i
$531$	−5.27297e6	−	7.87182e6i	−0.811557	−	1.21154i
$532$	3.73800e6	+	1.44722e6i	0.572611	+	0.221695i
$533$			8.41648e6i			1.28325i
$534$	−2.88205e6	−	2.30683e6i	−0.437370	−	0.350076i
$535$			5.99299e6i			0.905230i
$536$	−5.55147e6	−	3.43496e6i	−0.834634	−	0.516427i
$537$	−9.77943e6	−	5.21994e6i	−1.46345	−	0.781142i
$538$	−476611.	−	89043.3i	−0.0709918	−	0.0132631i
$539$	−581805.			−0.0862592
$540$	−6.91359e6	−	1.90954e6i	−1.02028	−	0.281803i
$541$	−1.08245e7			−1.59006			−0.795032	−	0.606568i	$-0.792546\pi$
$541$	−1.08245e7			−1.59006			−0.795032	+	0.606568i	$0.792546\pi$
$542$	9.35224e6	+	1.74724e6i	1.36747	+	0.255479i
$543$	5.36888e6	+	2.86573e6i	0.781419	+	0.417096i
$544$	−3.45220e6	−	4.56657e6i	−0.500148	−	0.661596i
$545$			7.97817e6i			1.15057i
$546$	2.98973e6	+	2.39301e6i	0.429191	+	0.343529i
$547$		−	3.31590e6i		−	0.473841i	−0.971529	−	0.236921i	$-0.923862\pi$
$547$		−	3.31590e6i		−	0.473841i	0.971529	−	0.236921i	$-0.0761381\pi$
$548$	−152453.	+	393768.i	−0.0216863	+	0.0560130i
$549$	4.44697e6	+	6.63872e6i	0.629700	+	0.940056i
$550$	94702.8	−	506904.i	0.0133492	−	0.0714527i
$551$	−2.36310e6			−0.331592
$552$	66343.6	−	38552.7i	0.00926726	−	0.00538526i
$553$	3.21141e6			0.446563
$554$	119584.	−	640083.i	0.0165539	−	0.0886057i
$555$	5.76864e6	−	1.08074e7i	0.794952	−	1.48932i
$556$	−3.78258e6	+	9.76992e6i	−0.518920	+	1.34031i
$557$			1.19243e7i			1.62853i	0.580496	+	0.814263i	$0.302859\pi$
$557$			1.19243e7i			1.62853i	−0.580496	+	0.814263i	$0.697141\pi$
$558$	−16576.7	−	38613.2i	−0.00225379	−	0.00524989i
$559$		−	8.09780e6i		−	1.09607i
$560$	−2.19491e6	−	1.99927e6i	−0.295765	−	0.269403i
$561$	−1.75783e6	+	3.29324e6i	−0.235813	+	0.441791i
$562$	5.42048e6	+	1.01269e6i	0.723930	+	0.135249i
$563$	−9.39928e6			−1.24975			−0.624876	−	0.780724i	$-0.714850\pi$
$563$	−9.39928e6			−1.24975			−0.624876	+	0.780724i	$0.714850\pi$
$564$	5.61425e6	+	6.51716e6i	0.743180	+	0.862702i
$565$	1.39425e7			1.83747
$566$	−5.05593e6	−	944579.i	−0.663376	−	0.123936i
$567$	2.67571e6	+	1.10107e6i	0.349527	+	0.143832i
$568$	5.56224e6	−	8.98953e6i	0.723401	−	1.16914i
$569$		−	1.21681e7i		−	1.57559i	−0.615939	−	0.787794i	$-0.711223\pi$
$569$		−	1.21681e7i		−	1.57559i	0.615939	−	0.787794i	$-0.288777\pi$
$570$	8.33515e6	−	1.04136e7i	1.07455	−	1.34249i
$571$			2.91544e6i			0.374208i	0.982340	+	0.187104i	$0.0599101\pi$
$571$			2.91544e6i			0.374208i	−0.982340	+	0.187104i	$0.940090\pi$
$572$	−6.40874e6	−	2.48124e6i	−0.818997	−	0.317088i
$573$	−3.34589e6	−	1.78593e6i	−0.425721	−	0.227236i
$574$	−483417.	+	2.58753e6i	−0.0612410	+	0.327797i
$575$	−10229.7			−0.00129031
$576$	3.94247e6	−	6.91812e6i	0.495122	−	0.868824i
$577$	−6.61930e6			−0.827699			−0.413850	−	0.910345i	$-0.635816\pi$
$577$	−6.61930e6			−0.827699			−0.413850	+	0.910345i	$0.635816\pi$
$578$	−460427.	+	2.46447e6i	−0.0573247	+	0.306834i
$579$	4.33057e6	+	2.31152e6i	0.536845	+	0.286550i
$580$	1.63226e6	+	631955.i	0.201474	+	0.0780038i
$581$		−	3.00241e6i		−	0.369003i
$582$	−2.12333e6	+	2.65280e6i	−0.259843	+	0.324636i
$583$		−	4.33214e6i		−	0.527875i
$584$	−7.02945e6	+	1.13608e7i	−0.852883	+	1.37840i
$585$	1.05875e7	−	7.09204e6i	1.27909	−	0.856805i
$586$	−1.38585e6	−	258912.i	−0.166714	−	0.0311464i
$587$	−3.72762e6			−0.446516			−0.223258	−	0.974759i	$-0.571669\pi$
$587$	−3.72762e6			−0.446516			−0.223258	+	0.974759i	$0.571669\pi$
$588$	781702.	+	907419.i	0.0932390	+	0.108234i
$589$	78146.3			0.00928154
$590$	−1.28290e7	−	2.39679e6i	−1.51727	−	0.283465i
$591$	2.29428e6	−	4.29828e6i	0.270196	−	0.506205i
$592$	1.00544e7	+	9.15827e6i	1.17911	+	1.07401i
$593$			1.55995e7i			1.82168i	0.412755	+	0.910842i	$0.364567\pi$
$593$			1.55995e7i			1.82168i	−0.412755	+	0.910842i	$0.635433\pi$
$594$	−5.17377e6	−	439718.i	−0.601645	−	0.0511339i
$595$		−	2.86534e6i		−	0.331805i
$596$	2.80465e6	−	7.24405e6i	0.323417	−	0.835344i
$597$	−4.11389e6	+	7.70727e6i	−0.472407	+	0.885044i
$598$	−25036.7	+	134011.i	−0.00286302	+	0.0153245i
$599$	1.24739e7			1.42048			0.710239	−	0.703960i	$-0.248587\pi$
$599$	1.24739e7			1.42048			0.710239	+	0.703960i	$0.248587\pi$
$600$	−917839.	+	533362.i	−0.104085	+	0.0604844i
$601$	3.14288e6			0.354929			0.177465	−	0.984127i	$-0.443210\pi$
$601$	3.14288e6			0.354929			0.177465	+	0.984127i	$0.443210\pi$
$602$	465113.	−	2.48955e6i	0.0523079	−	0.279982i
$603$	7.28093e6	−	4.87716e6i	0.815443	−	0.546227i
$604$	4.60475e6	−	1.18935e7i	0.513587	−	1.32653i
$605$			6.05514e6i			0.672568i
$606$	−4.54770e6	−	3.64003e6i	−0.503049	−	0.402646i
$607$			3.72328e6i			0.410161i	0.978745	+	0.205080i	$0.0657456\pi$
$607$			3.72328e6i			0.410161i	−0.978745	+	0.205080i	$0.934254\pi$
$608$	8.92991e6	+	1.18125e7i	0.979689	+	1.29593i
$609$	−622908.	−	332488.i	−0.0680582	−	0.0363273i
$610$	1.08194e7	+	2.02134e6i	1.17727	+	0.219945i
$611$	−1.52830e7			−1.65618
$612$	7.49812e6	−	1.68312e6i	0.809234	−	0.181651i
$613$	152209.			0.0163602			0.00818011	−	0.999967i	$-0.497396\pi$
$613$	152209.			0.0163602			0.00818011	+	0.999967i	$0.497396\pi$
$614$	1.41676e7	+	2.64688e6i	1.51662	+	0.283344i
$615$	7.72750e6	+	4.12469e6i	0.823856	+	0.439747i
$616$	−1.82776e6	−	1.13092e6i	−0.194074	−	0.120083i
$617$			2.60244e6i			0.275213i	0.990487	+	0.137606i	$0.0439409\pi$
$617$			2.60244e6i			0.275213i	−0.990487	+	0.137606i	$0.956059\pi$
$618$	4.50720e6	+	3.60762e6i	0.474718	+	0.379970i
$619$			1.74135e7i			1.82667i	0.407213	+	0.913333i	$0.366501\pi$
$619$			1.74135e7i			1.82667i	−0.407213	+	0.913333i	$0.633499\pi$
$620$	−53977.7	−	20898.3i	−0.00563943	−	0.00218339i
$621$	10274.1	+	102491.i	0.00106910	+	0.0106649i
$622$	2.37910e6	−	1.27343e7i	0.246568	−	1.31977i
$623$	2.05130e6			0.211743
$624$	4.74075e6	+	1.33292e7i	0.487401	+	1.37039i
$625$	−1.07997e7			−1.10589
$626$	3.04413e6	−	1.62939e7i	0.310475	−	1.66184i
$627$	4.54702e6	−	8.51873e6i	0.461911	−	0.865378i
$628$	1.30307e7	+	5.04504e6i	1.31847	+	0.510465i
$629$			1.31255e7i			1.32279i
$630$	3.66231e6	−	1.57224e6i	0.367624	−	0.157822i
$631$		−	1.50006e7i		−	1.49981i	−0.661547	−	0.749903i	$-0.730100\pi$
$631$		−	1.50006e7i		−	1.49981i	0.661547	−	0.749903i	$-0.269900\pi$
$632$	1.00888e7	+	6.24239e6i	1.00472	+	0.621667i
$633$	−3.49783e6	+	6.55310e6i	−0.346968	+	0.650037i
$634$	−7.46716e6	−	1.39506e6i	−0.737789	−	0.137838i
$635$	2.90241e6			0.285644
$636$	−6.75667e6	+	5.82058e6i	−0.662354	+	0.570589i
$637$	−2.12794e6			−0.207783
$638$	1.24558e6	+	232706.i	0.121149	+	0.0226337i
$639$	7.89761e6	+	1.17900e7i	0.765144	+	1.14226i
$640$	−3.00917e6	−	1.05473e7i	−0.290400	−	1.01787i
$641$			4.13438e6i			0.397435i	0.980057	+	0.198717i	$0.0636776\pi$
$641$			4.13438e6i			0.397435i	−0.980057	+	0.198717i	$0.936322\pi$
$642$	5.58107e6	−	6.97275e6i	0.534417	−	0.667677i
$643$			8.44865e6i			0.805861i	0.915231	+	0.402930i	$0.132008\pi$
$643$			8.44865e6i			0.805861i	−0.915231	+	0.402930i	$0.867992\pi$
$644$	−15394.3	+	39761.6i	−0.00146267	+	0.00377789i
$645$	−7.43491e6	−	3.96852e6i	−0.703682	−	0.375603i
$646$	−2.62456e6	+	1.40481e7i	−0.247443	+	1.32446i
$647$	−7.57482e6			−0.711397			−0.355698	−	0.934601i	$-0.615757\pi$
$647$	−7.57482e6			−0.711397			−0.355698	+	0.934601i	$0.615757\pi$
$648$	6.26556e6	+	8.66012e6i	0.586168	+	0.810189i
$649$	−9.44809e6			−0.880506
$650$	346373.	−	1.85399e6i	0.0321559	−	0.172117i
$651$	20599.1	+	10995.1i	0.00190501	+	0.00101683i
$652$	994254.	−	2.56803e6i	0.0915964	−	0.236582i
$653$			1.32696e7i			1.21779i	0.793250	+	0.608896i	$0.208387\pi$
$653$			1.32696e7i			1.21779i	−0.793250	+	0.608896i	$0.791613\pi$
$654$	7.42981e6	−	9.28248e6i	0.679256	−	0.848633i
$655$			1.35426e7i			1.23339i
$656$	−6.54834e6	+	7.18912e6i	−0.594117	+	0.652253i
$657$	−9.98084e6	−	1.49000e7i	−0.902098	−	1.34671i
$658$	−4.69855e6	−	877811.i	−0.423057	−	0.0790381i
$659$	−9.77129e6			−0.876472			−0.438236	−	0.898860i	$-0.644397\pi$
$659$	−9.77129e6			−0.876472			−0.438236	+	0.898860i	$0.644397\pi$
$660$	−5.41888e6	+	4.66812e6i	−0.484227	+	0.417141i
$661$	−5.63822e6			−0.501925			−0.250962	−	0.967997i	$-0.580747\pi$
$661$	−5.63822e6			−0.501925			−0.250962	+	0.967997i	$0.580747\pi$
$662$	−1.31564e7	−	2.45795e6i	−1.16679	−	0.217986i
$663$	−6.42921e6	+	1.20450e7i	−0.568033	+	1.06420i
$664$	5.83612e6	−	9.43216e6i	0.513694	−	0.830216i
$665$			7.41185e6i			0.649939i
$666$	−1.67763e7	+	7.20210e6i	−1.46558	+	0.629178i
$667$		−	25136.7i		−	0.00218773i
$668$	1.90535e7	+	7.37687e6i	1.65209	+	0.639633i
$669$	1.22087e6	−	2.28726e6i	0.105464	−	0.197583i
$670$	2.21687e6	−	1.18660e7i	0.190789	−	1.02121i
$671$	7.96807e6			0.683199
$672$	691887.	+	4.37017e6i	0.0591034	+	0.373315i
$673$	−74337.5			−0.00632660			−0.00316330	−	0.999995i	$-0.501007\pi$
$673$	−74337.5			−0.00632660			−0.00316330	+	0.999995i	$0.501007\pi$
$674$	1.09080e6	−	5.83859e6i	0.0924901	−	0.495060i
$675$	−142139.	−	1.41793e6i	−0.0120075	−	0.119783i
$676$	−1.23599e7	−	4.78532e6i	−1.04027	−	0.402758i
$677$		−	1.41229e7i		−	1.18427i	−0.805837	−	0.592137i	$-0.798284\pi$
$677$		−	1.41229e7i		−	1.18427i	0.805837	−	0.592137i	$-0.201716\pi$
$678$	−1.62219e7	−	1.29842e7i	−1.35527	−	1.08478i
$679$		−	1.88813e6i		−	0.157165i
$680$	5.56968e6	−	9.00155e6i	0.461911	−	0.746526i
$681$	1.14147e7	+	6.09278e6i	0.943182	+	0.503440i
$682$	−41190.4	−	7695.44i	−0.00339106	−	0.000633538i
$683$	−1.25021e7			−1.02549			−0.512746	−	0.858540i	$-0.671372\pi$
$683$	−1.25021e7			−1.02549			−0.512746	+	0.858540i	$0.671372\pi$
$684$	−1.93956e7	+	4.35378e6i	−1.58513	+	0.355817i
$685$	−780779.			−0.0635773
$686$	−654204.	−	122222.i	−0.0530766	−	0.00991608i
$687$	9.21368e6	+	4.91796e6i	0.744803	+	0.397551i
$688$	6.30040e6	−	6.91692e6i	0.507455	−	0.557111i
$689$		−	1.58447e7i		−	1.27156i
$690$	110771.	+	88662.2i	0.00885732	+	0.00708950i
$691$			9.16300e6i			0.730033i	0.931001	+	0.365017i	$0.118937\pi$
$691$			9.16300e6i			0.730033i	−0.931001	+	0.365017i	$0.881063\pi$
$692$	5.30256e6	−	1.36958e7i	0.420940	−	1.08724i
$693$	2.39716e6	−	1.60575e6i	0.189612	−	0.127012i
$694$	−4.41969e6	+	2.36567e7i	−0.348332	+	1.86447i
$695$	−1.93722e7			−1.52131
$696$	−1.31059e6	−	2.25534e6i	−0.102552	−	0.176477i
$697$	−9.38501e6			−0.731733
$698$	−757660.	+	4.05543e6i	−0.0588621	+	0.315064i
$699$	−3.16964e6	+	5.93825e6i	−0.245368	+	0.459690i
$700$	212975.	−	550088.i	0.0164280	−	0.0424313i
$701$		−	2.25538e7i		−	1.73350i	−0.498741	−	0.866751i	$-0.666204\pi$
$701$		−	2.25538e7i		−	1.73350i	0.498741	−	0.866751i	$-0.333796\pi$
$702$	−1.89229e7	−	1.60826e6i	−1.44926	−	0.123172i
$703$		−	3.39522e7i		−	2.59107i
$704$	−3.54367e6	−	7.10565e6i	−0.269477	−	0.540346i
$705$	−7.48980e6	+	1.40320e7i	−0.567541	+	1.06327i
$706$	1.08592e6	+	202878.i	0.0819949	+	0.0153188i
$707$	3.23682e6			0.243540
$708$	1.26943e7	+	1.47358e7i	0.951754	+	1.10482i
$709$	3.00355e6			0.224398			0.112199	−	0.993686i	$-0.464211\pi$
$709$	3.00355e6			0.224398			0.112199	+	0.993686i	$0.464211\pi$
$710$	1.92146e7	+	3.58979e6i	1.43050	+	0.267254i
$711$	−1.32317e7	+	8.86331e6i	−0.981617	+	0.657540i
$712$	6.44423e6	+	3.98735e6i	0.476399	+	0.294771i
$713$			831.254i			6.12364e-5i
$714$	−2.66839e6	+	3.33377e6i	−0.195886	+	0.244732i
$715$		−	1.27075e7i		−	0.929598i
$716$	2.12210e7	+	8.21606e6i	1.54698	+	0.598937i
$717$	1.42304e7	+	7.59572e6i	1.03376	+	0.551786i
$718$	−444322.	+	2.37827e6i	−0.0321652	+	0.172167i
$719$	−8.83880e6			−0.637633			−0.318817	−	0.947816i	$-0.603285\pi$
$719$	−8.83880e6			−0.637633			−0.318817	+	0.947816i	$0.603285\pi$
$720$	1.45614e7	+	2.17961e6i	1.04682	+	0.156693i
$721$	−3.20800e6			−0.229824
$722$	4.21667e6	−	2.25701e7i	0.301042	−	1.61135i
$723$	5.87337e6	+	3.13501e6i	0.417870	+	0.223046i
$724$	−1.16503e7	−	4.51059e6i	−0.826019	−	0.319806i
$725$			347757.i			0.0245714i
$726$	5.63895e6	−	7.04507e6i	0.397061	−	0.496071i
$727$		−	5.13842e6i		−	0.360573i	−0.983614	−	0.180287i	$-0.942297\pi$
$727$		−	5.13842e6i		−	0.360573i	0.983614	−	0.180287i	$-0.0577025\pi$
$728$	−6.68499e6	−	4.13632e6i	−0.467490	−	0.289258i
$729$	−1.40634e7	+	2.84817e6i	−0.980102	+	0.198494i
$730$	−2.42831e7	−	4.53671e6i	−1.68654	−	0.315090i
$731$	9.02967e6			0.624998
$732$	−1.07057e7	−	1.24275e7i	−0.738481	−	0.857247i
$733$	9.76352e6			0.671191			0.335596	−	0.942006i	$-0.391062\pi$
$733$	9.76352e6			0.671191			0.335596	+	0.942006i	$0.391062\pi$
$734$	−250863.	−	46867.8i	−0.0171869	−	0.00321095i
$735$	−1.04284e6	+	1.95374e6i	−0.0712035	+	0.133398i
$736$	−125651.	+	94988.8i	−0.00855011	+	0.00646365i
$737$		−	8.73887e6i		−	0.592634i
$738$	−5.14964e6	−	1.19954e7i	−0.348046	−	0.810724i
$739$		−	2.86509e7i		−	1.92987i	−0.262491	−	0.964934i	$-0.584544\pi$
$739$		−	2.86509e7i		−	1.92987i	0.262491	−	0.964934i	$-0.415456\pi$
$740$	−9.07969e6	+	2.34517e7i	−0.609525	+	1.57433i
$741$	1.66306e7	−	3.11571e7i	1.11266	−	2.08454i
$742$	910071.	−	4.87122e6i	0.0606828	−	0.324809i
$743$	1.42147e7			0.944636			0.472318	−	0.881428i	$-0.343417\pi$
$743$	1.42147e7			0.944636			0.472318	+	0.881428i	$0.343417\pi$
$744$	43340.3	+	74582.5i	0.00287052	+	0.00493975i
$745$	1.43638e7			0.948153
$746$	484967.	−	2.59582e6i	0.0319055	−	0.170776i
$747$	8.28648e6	+	1.23706e7i	0.543336	+	0.811126i
$748$	2.76677e6	−	7.14623e6i	0.180809	−	0.467007i
$749$			4.96285e6i			0.323241i
$750$	1.11975e7	+	8.96261e6i	0.726888	+	0.581810i
$751$			8.51671e6i			0.551026i	0.961297	+	0.275513i	$0.0888477\pi$
$751$			8.51671e6i			0.551026i	−0.961297	+	0.275513i	$0.911152\pi$
$752$	−1.30543e7	−	1.18908e7i	−0.841803	−	0.766771i
$753$	1.23842e7	+	6.61031e6i	0.795943	+	0.424849i
$754$	4.55567e6	+	851117.i	0.291826	+	0.0545207i
$755$	2.35829e7			1.50567
$756$	−5.72521e6	−	1.58131e6i	−0.364323	−	0.100627i
$757$	−1.66723e7			−1.05744			−0.528719	−	0.848797i	$-0.677327\pi$
$757$	−1.66723e7			−1.05744			−0.528719	+	0.848797i	$0.677327\pi$
$758$	−1.96581e7	−	3.67265e6i	−1.24271	−	0.232170i
$759$	90615.0	+	48367.4i	0.00570947	+	0.00304753i
$760$	−1.44073e7	+	2.32846e7i	−0.904790	+	1.46229i
$761$		−	1.10023e7i		−	0.688687i	−0.938844	−	0.344343i	$-0.888102\pi$
$761$		−	1.10023e7i		−	0.688687i	0.938844	−	0.344343i	$-0.111898\pi$
$762$	−3.37691e6	−	2.70292e6i	−0.210684	−	0.168634i
$763$			6.60680e6i			0.410847i
$764$	7.26048e6	+	2.81101e6i	0.450020	+	0.174232i
$765$	7.90817e6	+	1.18058e7i	0.488565	+	0.729361i
$766$	−790076.	+	4.22894e6i	−0.0486516	+	0.260411i
$767$	−3.45562e7			−2.12098
$768$	−6.32121e6	+	1.50739e7i	−0.386721	+	0.922197i
$769$	6.75356e6			0.411829			0.205915	−	0.978570i	$-0.433983\pi$
$769$	6.75356e6			0.411829			0.205915	+	0.978570i	$0.433983\pi$
$770$	729881.	−	3.90674e6i	0.0443634	−	0.237459i
$771$	2.22520e6	−	4.16886e6i	0.134814	−	0.252570i
$772$	−9.39720e6	−	3.63827e6i	−0.567486	−	0.219711i
$773$		−	2.03339e7i		−	1.22397i	−0.790869	−	0.611985i	$-0.790371\pi$
$773$		−	2.03339e7i		−	1.22397i	0.790869	−	0.611985i	$-0.209629\pi$
$774$	4.95466e6	+	1.15412e7i	0.297277	+	0.692466i
$775$		−	11500.1i		−	0.000687776i
$776$	3.67017e6	−	5.93162e6i	0.218792	−	0.353605i
$777$	4.77706e6	−	8.94971e6i	0.283863	−	0.531810i
$778$	1.74223e6	+	325494.i	0.103195	+	0.0192794i
$779$	2.42765e7			1.43332
$780$	−1.98194e7	+	1.70736e7i	−1.16642	+	1.00482i
$781$	1.41509e7			0.830150
$782$	−149432.	−	27917.8i	−0.00873830	−	0.00163254i
$783$	3.48416e6	−	349267.i	0.203093	−	0.0203589i
$784$	−1.81763e6	−	1.65562e6i	−0.105612	−	0.0961988i
$785$			2.58378e7i			1.49652i
$786$	1.26118e7	−	1.57566e7i	0.728149	−	0.909717i
$787$		−	9.45511e6i		−	0.544164i	−0.962274	−	0.272082i	$-0.912288\pi$
$787$		−	9.45511e6i		−	0.544164i	0.962274	−	0.272082i	$-0.0877122\pi$
$788$	−3.61114e6	+	9.32713e6i	−0.207171	+	0.535097i
$789$	−8.85660e6	−	4.72737e6i	−0.506494	−	0.270350i
$790$	−4.02875e6	+	2.15642e7i	−0.229669	+	1.22932i
$791$	1.15459e7			0.656126
$792$	1.06520e7	−	384871.i	0.603421	−	0.0218023i
$793$	2.91430e7			1.64570
$794$	−3.33006e6	+	1.78244e7i	−0.187457	+	1.00338i
$795$	−1.45476e7	−	7.76506e6i	−0.816347	−	0.435739i
$796$	6.47516e6	−	1.67245e7i	0.362216	−	0.935559i
$797$		−	569598.i		−	0.0317631i	−0.999874	−	0.0158815i	$-0.994945\pi$
$797$		−	569598.i		−	0.0317631i	0.999874	−	0.0158815i	$-0.00505547\pi$
$798$	6.90242e6	−	8.62358e6i	0.383702	−	0.479380i
$799$		−	1.70417e7i		−	0.944381i
$800$	1.73834e6	−	1.31413e6i	0.0960304	−	0.0725964i
$801$	−8.45181e6	+	5.66147e6i	−0.465445	+	0.311780i
$802$	1.26001e7	+	2.35403e6i	0.691735	+	0.129234i
$803$	−1.78836e7			−0.978739
$804$	−1.36297e7	+	1.17414e7i	−0.743611	+	0.640588i
$805$	−78841.0			−0.00428808
$806$	−150653.	−	28145.9i	−0.00816845	−	0.00152608i
$807$	−629156.	+	1.17871e6i	−0.0340075	+	0.0637122i
$808$	1.01686e7	+	6.29179e6i	0.547939	+	0.339036i
$809$			1.48080e7i			0.795472i	0.917500	+	0.397736i	$0.130204\pi$
$809$			1.48080e7i			0.795472i	−0.917500	+	0.397736i	$0.869796\pi$
$810$	−1.07502e7	+	1.65857e7i	−0.575711	+	0.888223i
$811$			2.06457e6i			0.110224i	0.998480	+	0.0551121i	$0.0175516\pi$
$811$			2.06457e6i			0.110224i	−0.998480	+	0.0551121i	$0.982448\pi$
$812$	1.35169e6	+	523328.i	0.0719427	+	0.0278537i
$813$	1.23455e7	−	2.31291e7i	0.655064	−	1.22725i
$814$	−3.34344e6	+	1.78960e7i	−0.176861	+	0.946662i
$815$	5.09200e6			0.268531
$816$	−1.48631e7	+	5.28630e6i	−0.781418	+	0.277924i
$817$	−2.33573e7			−1.22424
$818$	−705402.	+	3.77572e6i	−0.0368599	+	0.197295i
$819$	8.76757e6	−	5.87299e6i	0.456741	−	0.305949i
$820$	−1.67684e7	−	6.49216e6i	−0.870879	−	0.337174i
$821$		−	1.59219e7i		−	0.824399i	−0.911094	−	0.412199i	$-0.864761\pi$
$821$		−	1.59219e7i		−	0.824399i	0.911094	−	0.412199i	$-0.135239\pi$
$822$	908425.	+	727114.i	0.0468932	+	0.0375338i
$823$			1.52891e7i			0.786833i	0.919360	+	0.393416i	$0.128707\pi$
$823$			1.52891e7i			0.786833i	−0.919360	+	0.393416i	$0.871293\pi$
$824$	−1.00780e7	−	6.23575e6i	−0.517080	−	0.319942i
$825$	−1.25363e6	−	669144.i	−0.0641258	−	0.0342283i
$826$	−1.06238e7	−	1.98480e6i	−0.541788	−	0.101220i
$827$	−2.76297e7			−1.40479			−0.702397	−	0.711785i	$-0.747887\pi$
$827$	−2.76297e7			−1.40479			−0.702397	+	0.711785i	$0.747887\pi$
$828$	−46311.9	−	206314.i	−0.00234756	−	0.0104581i
$829$	−2.02054e7			−1.02113			−0.510565	−	0.859839i	$-0.670564\pi$
$829$	−2.02054e7			−1.02113			−0.510565	+	0.859839i	$0.670564\pi$
$830$	2.01608e7	+	3.76655e6i	1.01581	+	0.189779i
$831$	−1.58299e6	−	844949.i	−0.0795199	−	0.0424451i
$832$	−1.29609e7	−	2.59888e7i	−0.649121	−	1.30160i
$833$		−	2.37281e6i		−	0.118482i
$834$	2.25392e7	+	1.80407e7i	1.12208	+	0.898127i
$835$			3.77801e7i			1.87520i
$836$	−7.15690e6	+	1.84854e7i	−0.354168	+	0.914771i
$837$	−115219.	+	11550.0i	−0.00568474	+	0.000569862i
$838$	5.20033e6	−	2.78352e7i	0.255812	−	1.36925i
$839$	−4.57718e6			−0.224488			−0.112244	−	0.993681i	$-0.535804\pi$
$839$	−4.57718e6			−0.224488			−0.112244	+	0.993681i	$0.535804\pi$
$840$	−7.07385e6	+	4.11065e6i	−0.345906	+	0.201008i
$841$	1.96566e7			0.958339
$842$	−6.67301e6	+	3.57178e7i	−0.324371	+	1.73622i
$843$	7.15536e6	−	1.34054e7i	0.346787	−	0.649697i
$844$	5.50551e6	−	1.42200e7i	0.266036	−	0.687138i
$845$		−	2.45077e7i		−	1.18076i
$846$	2.17818e7	−	9.35096e6i	1.04633	−	0.449190i
$847$			5.01432e6i			0.240162i
$848$	1.23278e7	−	1.35341e7i	0.588702	−	0.646308i
$849$	−6.67414e6	+	1.25038e7i	−0.317780	+	0.595352i
$850$	2.06734e6	+	386233.i	0.0981441	+	0.0183359i
$851$	361155.			0.0170950
$852$	−1.90129e7	−	2.20706e7i	−0.897323	−	1.04164i
$853$	4.05616e6			0.190872			0.0954360	−	0.995436i	$-0.469575\pi$
$853$	4.05616e6			0.190872			0.0954360	+	0.995436i	$0.469575\pi$
$854$	8.95961e6	+	1.67389e6i	0.420382	+	0.0785384i
$855$	−2.04563e7	−	3.05385e7i	−0.957000	−	1.42867i
$856$	−9.64687e6	+	1.55910e7i	−0.449989	+	0.727258i
$857$			1.31705e7i			0.612561i	0.951941	+	0.306280i	$0.0990845\pi$
$857$			1.31705e7i			0.612561i	−0.951941	+	0.306280i	$0.900916\pi$
$858$	−1.18341e7	+	1.47850e7i	−0.548803	+	0.685650i
$859$			1.81439e7i			0.838971i	0.907762	+	0.419485i	$0.137789\pi$
$859$			1.81439e7i			0.838971i	−0.907762	+	0.419485i	$0.862211\pi$
$860$	1.61335e7	+	6.24635e6i	0.743846	+	0.287992i
$861$	6.39922e6	+	3.41569e6i	0.294184	+	0.157026i
$862$	−4.34925e6	+	2.32797e7i	−0.199364	+	1.06711i
$863$	3.18985e7			1.45795			0.728975	−	0.684540i	$-0.239997\pi$
$863$	3.18985e7			1.45795			0.728975	+	0.684540i	$0.239997\pi$
$864$	−1.49122e7	−	1.60965e7i	−0.679604	−	0.733579i
$865$	2.71567e7			1.23406
$866$	−2.81623e6	+	1.50741e7i	−0.127607	+	0.683024i
$867$	6.09489e6	+	3.25325e6i	0.275371	+	0.146984i
$868$	−44699.5	−	17306.1i	−0.00201374	−	0.000779650i
$869$			1.58813e7i			0.713404i
$870$	3.01405e6	−	3.76563e6i	0.135006	−	0.168671i
$871$		−	3.19622e7i		−	1.42755i
$872$	−1.28424e7	+	2.07555e7i	−0.571946	+	0.924361i
$873$	5.21113e6	+	7.77950e6i	0.231417	+	0.345475i
$874$	386541.	+	72215.9i	0.0171166	+	0.00319782i
$875$	−7.96981e6			−0.351907
$876$	2.40281e7	+	2.78924e7i	1.05794	+	1.22808i
$877$	1.94937e7			0.855845			0.427923	−	0.903815i	$-0.359246\pi$
$877$	1.94937e7			0.855845			0.427923	+	0.903815i	$0.359246\pi$
$878$	2.53059e7	+	4.72780e6i	1.10786	+	0.206977i
$879$	−1.82940e6	+	3.42734e6i	−0.0798615	+	0.149618i
$880$	9.88692e6	−	1.08544e7i	0.430382	−	0.472497i
$881$			1.28853e7i			0.559314i	0.960100	+	0.279657i	$0.0902208\pi$
$881$			1.28853e7i			0.559314i	−0.960100	+	0.279657i	$0.909779\pi$
$882$	3.03279e6	−	1.30198e6i	0.131272	−	0.0563552i
$883$			6.36053e6i			0.274531i	0.990534	+	0.137266i	$0.0438314\pi$
$883$			6.36053e6i			0.274531i	−0.990534	+	0.137266i	$0.956169\pi$
$884$	1.01194e7	−	2.61372e7i	0.435537	−	1.12494i
$885$	−1.69350e7	+	3.17274e7i	−0.726822	+	1.36168i
$886$	−3.51369e6	+	1.88073e7i	−0.150376	+	0.804900i
$887$	1.04177e7			0.444593			0.222296	−	0.974979i	$-0.428645\pi$
$887$	1.04177e7			0.444593			0.222296	+	0.974979i	$0.428645\pi$
$888$	3.24039e7	−	1.88301e7i	1.37900	−	0.801345i
$889$	2.40351e6			0.101998
$890$	−2.57338e6	+	1.37742e7i	−0.108900	+	0.582896i
$891$	−5.44506e6	+	1.32321e7i	−0.229778	+	0.558385i
$892$	−1.92161e6	+	4.96328e6i	−0.0808637	+	0.208861i
$893$			4.40824e7i			1.84985i
$894$	−1.67120e7	−	1.33765e7i	−0.699336	−	0.559757i
$895$			4.20779e7i			1.75589i
$896$	−2.49192e6	−	8.73430e6i	−0.103696	−	0.363461i
$897$	331422.	+	176902.i	0.0137531	+	0.00734096i
$898$	1.75567e7	+	3.28004e6i	0.726526	+	0.135734i
$899$	28258.3			0.00116613
$900$	640707.	+	2.85428e6i	0.0263666	+	0.117460i
$901$	1.76680e7			0.725064
$902$	−1.27960e7	−	2.39062e6i	−0.523670	−	0.0978351i
$903$	−6.15692e6	−	3.28637e6i	−0.251272	−	0.134121i
$904$	3.62719e7	+	2.24431e7i	1.47621	+	0.913403i
$905$		−	2.31007e7i		−	0.937568i
$906$	−2.74383e7	−	2.19620e7i	−1.11055	−	0.888896i
$907$			2.81364e7i			1.13567i	0.823144	+	0.567833i	$0.192218\pi$
$907$			2.81364e7i			1.13567i	−0.823144	+	0.567833i	$0.807782\pi$
$908$	−2.47695e7	−	9.58988e6i	−0.997015	−	0.386010i
$909$	−1.33364e7	+	8.93345e6i	−0.535340	+	0.358600i
$910$	2.66952e6	−	1.42888e7i	0.106864	−	0.571995i
$911$	−2.57137e7			−1.02652			−0.513262	−	0.858232i	$-0.671563\pi$
$911$	−2.57137e7			−1.02652			−0.513262	+	0.858232i	$0.671563\pi$
$912$	3.84468e7	−	1.36742e7i	1.53064	−	0.544398i
$913$	1.48477e7			0.589497
$914$	6.66336e6	−	3.56661e7i	0.263832	−	1.41218i
$915$	1.42822e7	−	2.67574e7i	0.563953	−	1.05655i
$916$	−1.99934e7	−	7.74075e6i	−0.787313	−	0.304821i
$917$			1.12148e7i			0.440420i
$918$	1.79333e6	−	2.11005e7i	0.0702351	−	0.826392i
$919$		−	1.05907e7i		−	0.413651i	−0.978378	−	0.206826i	$-0.933687\pi$
$919$		−	1.05907e7i		−	0.413651i	0.978378	−	0.206826i	$-0.0663133\pi$
$920$	−247682.	−	153252.i	−0.00964771	−	0.00596949i
$921$	1.87021e7	−	3.50380e7i	0.726511	−	1.36110i
$922$	1.70447e6	+	318439.i	0.0660331	+	0.0123367i
$923$	5.17566e7			1.99968
$924$	−4.48742e6	+	3.86572e6i	−0.172909	+	0.148953i
$925$	−4.99644e6			−0.192002
$926$	−4.66779e7	−	8.72065e6i	−1.78889	−	0.334212i
$927$	1.32177e7	−	8.85389e6i	0.505190	−	0.338404i
$928$	3.22913e6	+	4.27149e6i	0.123088	+	0.162820i
$929$			2.80909e7i			1.06789i	0.845520	+	0.533944i	$0.179291\pi$
$929$			2.80909e7i			1.06789i	−0.845520	+	0.533944i	$0.820709\pi$
$930$	−99672.8	+	124527.i	−0.00377893	+	0.00472123i
$931$			6.13783e6i			0.232081i
$932$	4.98894e6	−	1.28858e7i	0.188135	−	0.485928i
$933$	−3.14933e7	−	1.68101e7i	−1.18444	−	0.632216i
$934$	282705.	−	1.51320e6i	0.0106039	−	0.0567582i
$935$	1.41698e7			0.530073
$936$	3.89596e7	−	1.40766e6i	1.45353	−	0.0525179i
$937$	−9.64582e6			−0.358914			−0.179457	−	0.983766i	$-0.557434\pi$
$937$	−9.64582e6			−0.358914			−0.179457	+	0.983766i	$0.557434\pi$
$938$	1.83581e6	−	9.82633e6i	0.0681274	−	0.364657i
$939$	−4.02965e7	−	2.15090e7i	−1.49143	−	0.796079i
$940$	1.17888e7	−	3.04489e7i	0.435160	−	1.12396i
$941$		−	5.28771e7i		−	1.94668i	−0.229376	−	0.973338i	$-0.573668\pi$
$941$		−	5.28771e7i		−	1.94668i	0.229376	−	0.973338i	$-0.426332\pi$
$942$	2.40619e7	−	3.00619e7i	0.883492	−	1.10380i
$943$			258233.i			0.00945654i
$944$	−2.95169e7	−	2.68860e7i	−1.07806	−	0.981966i
$945$	−1.09547e6	−	1.09280e7i	−0.0399046	−	0.398073i
$946$	1.23115e7	+	2.30011e6i	0.447283	+	0.0835642i
$947$	−1.59694e7			−0.578645			−0.289323	−	0.957232i	$-0.593430\pi$
$947$	−1.59694e7			−0.578645			−0.289323	+	0.957232i	$0.593430\pi$
$948$	2.47694e7	−	2.13378e7i	0.895147	−	0.771130i
$949$	−6.54090e7			−2.35761
$950$	−5.34765e6	−	999080.i	−0.192244	−	0.0359163i
$951$	−9.85711e6	+	1.84671e7i	−0.353426	+	0.662135i
$952$	4.61231e6	−	7.45427e6i	0.164940	−	0.266571i
$953$			8.01671e6i			0.285933i	0.989728	+	0.142966i	$0.0456641\pi$
$953$			8.01671e6i			0.285933i	−0.989728	+	0.142966i	$0.954336\pi$
$954$	9.69461e6	+	2.25823e7i	0.344873	+	0.803335i
$955$			1.43964e7i			0.510793i
$956$	−3.08795e7	−	1.19555e7i	−1.09276	−	0.423080i
$957$	1.64424e6	−	3.08044e6i	0.0580343	−	0.108726i
$958$	−2.26275e6	+	1.21115e7i	−0.0796567	+	0.426369i
$959$	−646571.			−0.0227023
$960$	−3.02131e7	−	836497.i	−1.05808	−	0.0292945i
$961$	2.86282e7			0.999967
$962$	−1.22285e7	+	6.54542e7i	−0.426027	+	2.28034i
$963$	−1.36972e7	−	2.04480e7i	−0.475955	−	0.710536i
$964$	−1.27450e7	−	4.93443e6i	−0.441721	−	0.171019i
$965$		−	1.86331e7i		−	0.644122i
$966$	91730.3	+	73422.0i	0.00316279	+	0.00253153i
$967$		−	3.33971e7i		−	1.14853i	−0.818669	−	0.574266i	$-0.805287\pi$
$967$		−	3.33971e7i		−	1.14853i	0.818669	−	0.574266i	$-0.194713\pi$
$968$	−9.74691e6	+	1.57527e7i	−0.334333	+	0.540338i
$969$	3.47425e7	+	1.85444e7i	1.18864	+	0.634459i
$970$	1.26785e7	+	2.36868e6i	0.432652	+	0.0808307i
$971$	3.85814e7			1.31320			0.656599	−	0.754240i	$-0.271995\pi$
$971$	3.85814e7			1.31320			0.656599	+	0.754240i	$0.271995\pi$
$972$	2.79535e7	−	9.28590e6i	0.949008	−	0.315253i
$973$	−1.60423e7			−0.543231
$974$	2.88648e6	+	539269.i	0.0974924	+	0.0182141i
$975$	−4.58510e6	−	2.44738e6i	−0.154468	−	0.0824498i
$976$	2.48932e7	+	2.26744e7i	0.836481	+	0.761923i
$977$			1.00246e7i			0.335992i	0.985788	+	0.167996i	$0.0537296\pi$
$977$			1.00246e7i			0.335992i	−0.985788	+	0.167996i	$0.946270\pi$
$978$	−5.92447e6	−	4.74201e6i	−0.198062	−	0.158532i
$979$			1.01442e7i			0.338269i
$980$	1.64141e6	−	4.23956e6i	0.0545950	−	0.141012i
$981$	−1.82344e7	−	2.72215e7i	−0.604949	−	0.903107i
$982$	2.78764e6	−	1.49211e7i	0.0922483	−	0.493766i
$983$	−3.70376e7			−1.22253			−0.611264	−	0.791426i	$-0.709339\pi$
$983$	−3.70376e7			−1.22253			−0.611264	+	0.791426i	$0.709339\pi$
$984$	1.34639e7	+	2.31694e7i	0.443284	+	0.762829i
$985$	−1.84942e7			−0.607359
$986$	−949061.	+	5.07992e6i	−0.0310886	+	0.166404i
$987$	−6.20238e6	+	1.16200e7i	−0.202659	+	0.379676i
$988$	−2.61762e7	+	6.76098e7i	−0.853128	+	2.20352i
$989$		−	248455.i		−	0.00807714i
$990$	7.77512e6	+	1.81111e7i	0.252127	+	0.587294i
$991$		−	3.61745e7i		−	1.17009i	−0.811001	−	0.585044i	$-0.801077\pi$
$991$		−	3.61745e7i		−	1.17009i	0.811001	−	0.585044i	$-0.198923\pi$
$992$	−106785.	−	141255.i	−0.00344533	−	0.00455748i
$993$	−1.73672e7	+	3.25370e7i	−0.558930	+	1.04714i
$994$	1.59118e7	+	2.97274e6i	0.510804	+	0.0954314i
$995$	3.31621e7			1.06190
$996$	−1.99491e7	−	2.31574e7i	−0.637198	−	0.739675i
$997$	−3.59902e7			−1.14669			−0.573346	−	0.819313i	$-0.694355\pi$
$997$	−3.59902e7			−1.14669			−0.573346	+	0.819313i	$0.694355\pi$
$998$	−2.73490e7	−	5.10950e6i	−0.869189	−	0.162387i
$999$	5.01815e6	+	5.00592e7i	0.159085	+	1.58697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.6.e.a.71.28	yes	60
3.2	odd	2	inner	84.6.e.a.71.33	yes	60
4.3	odd	2	inner	84.6.e.a.71.34	yes	60
12.11	even	2	inner	84.6.e.a.71.27	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.6.e.a.71.27	✓	60	12.11	even	2	inner
84.6.e.a.71.28	yes	60	1.1	even	1	trivial
84.6.e.a.71.33	yes	60	3.2	odd	2	inner
84.6.e.a.71.34	yes	60	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	84.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03887 + 5.56064i) q^{2} +(13.7520 + 7.34039i) q^{3} +(-29.8415 - 11.5536i) q^{4} -59.1709i q^{5} +(-55.1039 + 68.8445i) q^{6} -49.0000i q^{7} +(95.2469 - 153.935i) q^{8} +(135.237 + 201.891i) q^{9} +(329.028 + 61.4710i) q^{10} +242.318 q^{11} +(-325.573 - 377.934i) q^{12} +886.271 q^{13} +(272.471 + 50.9048i) q^{14} +(434.338 - 813.721i) q^{15} +(757.029 + 689.553i) q^{16} +988.260i q^{17} +(-1263.14 + 542.267i) q^{18} -2556.36i q^{19} +(-683.637 + 1765.75i) q^{20} +(359.679 - 673.850i) q^{21} +(-251.737 + 1347.44i) q^{22} +27.1924 q^{23} +(2439.78 - 1417.77i) q^{24} -376.197 q^{25} +(-920.723 + 4928.24i) q^{26} +(377.831 + 3769.10i) q^{27} +(-566.126 + 1462.23i) q^{28} -924.401i q^{29} +(4073.59 + 3260.55i) q^{30} +30.5693i q^{31} +(-4620.81 + 3493.21i) q^{32} +(3332.36 + 1778.71i) q^{33} +(-5495.36 - 1026.68i) q^{34} -2899.37 q^{35} +(-1703.12 - 7587.20i) q^{36} +13281.5 q^{37} +(14215.0 + 2655.74i) q^{38} +(12188.0 + 6505.58i) q^{39} +(-9108.48 - 5635.85i) q^{40} +9496.50i q^{41} +(3373.38 + 2700.09i) q^{42} -9136.93i q^{43} +(-7231.12 - 2799.64i) q^{44} +(11946.1 - 8002.11i) q^{45} +(-28.2495 + 151.207i) q^{46} -17244.2 q^{47} +(5349.10 + 15039.7i) q^{48} -2401.00 q^{49} +(390.821 - 2091.90i) q^{50} +(-7254.22 + 13590.6i) q^{51} +(-26447.7 - 10239.6i) q^{52} -17877.9i q^{53} +(-21351.2 - 1814.64i) q^{54} -14338.2i q^{55} +(-7542.82 - 4667.10i) q^{56} +(18764.7 - 35155.2i) q^{57} +(5140.26 + 960.335i) q^{58} -38990.5 q^{59} +(-22362.7 + 19264.5i) q^{60} +32882.7 q^{61} +(-169.985 - 31.7576i) q^{62} +(9892.65 - 6626.63i) q^{63} +(-14624.0 - 29323.7i) q^{64} -52441.5i q^{65} +(-13352.7 + 16682.2i) q^{66} -36063.7i q^{67} +(11418.0 - 29491.2i) q^{68} +(373.951 + 199.603i) q^{69} +(3012.08 - 16122.4i) q^{70} +58398.1 q^{71} +(43959.0 - 1588.29i) q^{72} -73802.4 q^{73} +(-13797.7 + 73853.4i) q^{74} +(-5173.48 - 2761.43i) q^{75} +(-29535.2 + 76285.7i) q^{76} -11873.6i q^{77} +(-48837.0 + 61014.9i) q^{78} +65539.0i q^{79} +(40801.5 - 44794.1i) q^{80} +(-22470.8 + 54606.3i) q^{81} +(-52806.6 - 9865.65i) q^{82} +61273.6 q^{83} +(-18518.8 + 15953.1i) q^{84} +58476.3 q^{85} +(50807.2 + 9492.11i) q^{86} +(6785.47 - 12712.4i) q^{87} +(23080.0 - 37301.2i) q^{88} +41863.3i q^{89} +(32086.5 + 74740.9i) q^{90} -43427.3i q^{91} +(-811.462 - 314.170i) q^{92} +(-224.391 + 420.391i) q^{93} +(17914.5 - 95888.8i) q^{94} -151262. q^{95} +(-89187.2 + 14120.2i) q^{96} +38533.2 q^{97} +(2494.33 - 13351.1i) q^{98} +(32770.4 + 48921.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 20 q^{4} - 114 q^{6} + 44 q^{9} + 668 q^{10} + 786 q^{12} - 3004 q^{16} - 3320 q^{18} + 7120 q^{22} + 16466 q^{24} - 37500 q^{25} - 7448 q^{28} - 35236 q^{30} - 9424 q^{33} + 43360 q^{34} + 50524 q^{36}+ \cdots + 232584 q^{97}+O(q^{100}) \) 60 * q - 20 * q^4 - 114 * q^6 + 44 * q^9 + 668 * q^10 + 786 * q^12 - 3004 * q^16 - 3320 * q^18 + 7120 * q^22 + 16466 * q^24 - 37500 * q^25 - 7448 * q^28 - 35236 * q^30 - 9424 * q^33 + 43360 * q^34 + 50524 * q^36 - 15056 * q^37 - 35468 * q^40 - 20090 * q^42 + 36024 * q^45 + 124416 * q^46 + 88654 * q^48 - 144060 * q^49 - 140108 * q^52 + 19486 * q^54 - 65072 * q^57 + 115616 * q^58 + 164908 * q^60 - 169424 * q^61 + 20116 * q^64 - 98484 * q^66 + 142536 * q^69 + 35868 * q^70 + 121312 * q^72 + 107256 * q^73 + 214836 * q^76 + 263708 * q^78 - 114932 * q^81 - 479624 * q^82 + 40474 * q^84 - 383992 * q^85 - 107320 * q^88 + 423760 * q^90 + 545208 * q^93 - 448512 * q^94 - 751618 * q^96 + 232584 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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