LMFDB - Embedded newform 76.5.g.a.7.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(7,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("76.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.11
Character	$\chi$	$=$	76.7
Dual form			76.5.g.a.11.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.87075 + 2.78547i) q^{2} +(2.38822 - 1.37884i) q^{3} +(0.482361 - 15.9927i) q^{4} +(-16.6192 - 28.7853i) q^{5} +(-3.01526 + 10.6106i) q^{6} +28.7543i q^{7} +(43.1625 + 47.2547i) q^{8} +(-36.6976 + 63.5621i) q^{9} +O(q^{10})$	\(q+(-2.87075 + 2.78547i) q^{2} +(2.38822 - 1.37884i) q^{3} +(0.482361 - 15.9927i) q^{4} +(-16.6192 - 28.7853i) q^{5} +(-3.01526 + 10.6106i) q^{6} +28.7543i q^{7} +(43.1625 + 47.2547i) q^{8} +(-36.6976 + 63.5621i) q^{9} +(127.890 + 36.3431i) q^{10} +156.718i q^{11} +(-20.8994 - 38.8592i) q^{12} +(26.2442 - 45.4563i) q^{13} +(-80.0940 - 82.5461i) q^{14} +(-79.3805 - 45.8304i) q^{15} +(-255.535 - 15.4285i) q^{16} +(124.557 + 215.739i) q^{17} +(-71.7006 - 284.691i) q^{18} +(-181.417 + 312.104i) q^{19} +(-468.372 + 251.902i) q^{20} +(39.6474 + 68.6714i) q^{21} +(-436.532 - 449.897i) q^{22} +(-263.704 - 152.250i) q^{23} +(168.238 + 53.3403i) q^{24} +(-239.896 + 415.512i) q^{25} +(51.2765 + 203.596i) q^{26} +425.772i q^{27} +(459.859 + 13.8699i) q^{28} +(-691.626 + 1197.93i) q^{29} +(355.540 - 89.5444i) q^{30} -1041.75i q^{31} +(776.551 - 667.492i) q^{32} +(216.089 + 374.276i) q^{33} +(-958.505 - 272.383i) q^{34} +(827.700 - 477.873i) q^{35} +(998.830 + 617.555i) q^{36} +1409.13 q^{37} +(-348.555 - 1401.30i) q^{38} -144.746i q^{39} +(642.914 - 2027.78i) q^{40} +(-224.809 - 389.381i) q^{41} +(-305.100 - 86.7015i) q^{42} +(-1642.67 + 948.395i) q^{43} +(2506.35 + 75.5946i) q^{44} +2439.54 q^{45} +(1181.11 - 297.469i) q^{46} +(-234.559 - 135.423i) q^{47} +(-631.546 + 315.494i) q^{48} +1574.19 q^{49} +(-468.714 - 1861.05i) q^{50} +(594.938 + 343.488i) q^{51} +(-714.311 - 441.643i) q^{52} +(-2540.48 + 4400.24i) q^{53} +(-1185.97 - 1222.28i) q^{54} +(4511.17 - 2604.53i) q^{55} +(-1358.77 + 1241.10i) q^{56} +(-2.92104 + 995.517i) q^{57} +(-1351.31 - 5365.46i) q^{58} +(-1961.37 + 1132.40i) q^{59} +(-771.243 + 1247.40i) q^{60} +(1343.04 - 2326.22i) q^{61} +(2901.77 + 2990.61i) q^{62} +(-1827.68 - 1055.21i) q^{63} +(-370.004 + 4079.25i) q^{64} -1744.63 q^{65} +(-1662.87 - 472.545i) q^{66} +(-1551.55 - 895.788i) q^{67} +(3510.34 - 1887.94i) q^{68} -839.710 q^{69} +(-1045.02 + 3677.38i) q^{70} +(-4168.48 + 2406.67i) q^{71} +(-4587.57 + 1009.36i) q^{72} +(-4556.11 - 7891.41i) q^{73} +(-4045.25 + 3925.08i) q^{74} +1323.11i q^{75} +(4903.89 + 3051.89i) q^{76} -4506.31 q^{77} +(403.185 + 415.529i) q^{78} +(6945.24 - 4009.83i) q^{79} +(3802.67 + 7612.05i) q^{80} +(-2385.44 - 4131.70i) q^{81} +(1729.98 + 491.615i) q^{82} +8665.43i q^{83} +(1117.37 - 600.946i) q^{84} +(4140.07 - 7170.82i) q^{85} +(2073.96 - 7298.19i) q^{86} +3814.56i q^{87} +(-7405.65 + 6764.33i) q^{88} +(482.886 - 836.384i) q^{89} +(-7003.30 + 6795.26i) q^{90} +(1307.06 + 754.633i) q^{91} +(-2562.09 + 4143.91i) q^{92} +(-1436.41 - 2487.94i) q^{93} +(1050.58 - 264.592i) q^{94} +(11999.0 + 35.2075i) q^{95} +(934.209 - 2664.85i) q^{96} +(4225.04 + 7317.98i) q^{97} +(-4519.11 + 4384.86i) q^{98} +(-9961.32 - 5751.17i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - q^{2} + 13 q^{4} - 2 q^{5} - 15 q^{6} - 94 q^{8} + 972 q^{9}+O(q^{10}) $ 76 * q - q^2 + 13 * q^4 - 2 * q^5 - 15 * q^6 - 94 * q^8 + 972 * q^9	$ 76 q - q^{2} + 13 q^{4} - 2 q^{5} - 15 q^{6} - 94 q^{8} + 972 q^{9} + 180 q^{10} - 166 q^{12} - 178 q^{13} - 30 q^{14} + 237 q^{16} - 50 q^{17} + 356 q^{18} + 2212 q^{20} + 304 q^{21} - 1035 q^{22} + 1697 q^{24} - 3752 q^{25} + 3952 q^{26} + 990 q^{28} - 2 q^{29} + 408 q^{30} - 181 q^{32} - 3000 q^{33} + 2712 q^{34} + 1078 q^{36} - 2088 q^{37} - 3198 q^{38} - 6562 q^{40} - 2138 q^{41} - 2698 q^{42} - 8631 q^{44} + 2168 q^{45} - 9380 q^{46} + 10159 q^{48} - 19380 q^{49} + 9354 q^{50} + 4706 q^{52} - 818 q^{53} + 6431 q^{54} + 1476 q^{56} - 6 q^{57} - 13080 q^{58} + 5626 q^{60} + 5470 q^{61} + 8892 q^{62} - 30890 q^{64} + 16316 q^{65} - 14001 q^{66} - 3284 q^{68} + 38836 q^{69} + 8532 q^{70} - 2766 q^{72} + 7222 q^{73} - 10328 q^{74} - 29613 q^{76} + 16320 q^{77} + 19028 q^{78} + 12778 q^{80} - 25574 q^{81} + 30563 q^{82} + 65132 q^{84} - 21006 q^{85} - 8430 q^{86} + 44242 q^{88} + 12910 q^{89} - 48688 q^{90} - 14052 q^{92} - 4304 q^{93} - 39664 q^{94} + 15670 q^{96} + 1174 q^{97} + 2783 q^{98}+O(q^{100}) $ 76 * q - q^2 + 13 * q^4 - 2 * q^5 - 15 * q^6 - 94 * q^8 + 972 * q^9 + 180 * q^10 - 166 * q^12 - 178 * q^13 - 30 * q^14 + 237 * q^16 - 50 * q^17 + 356 * q^18 + 2212 * q^20 + 304 * q^21 - 1035 * q^22 + 1697 * q^24 - 3752 * q^25 + 3952 * q^26 + 990 * q^28 - 2 * q^29 + 408 * q^30 - 181 * q^32 - 3000 * q^33 + 2712 * q^34 + 1078 * q^36 - 2088 * q^37 - 3198 * q^38 - 6562 * q^40 - 2138 * q^41 - 2698 * q^42 - 8631 * q^44 + 2168 * q^45 - 9380 * q^46 + 10159 * q^48 - 19380 * q^49 + 9354 * q^50 + 4706 * q^52 - 818 * q^53 + 6431 * q^54 + 1476 * q^56 - 6 * q^57 - 13080 * q^58 + 5626 * q^60 + 5470 * q^61 + 8892 * q^62 - 30890 * q^64 + 16316 * q^65 - 14001 * q^66 - 3284 * q^68 + 38836 * q^69 + 8532 * q^70 - 2766 * q^72 + 7222 * q^73 - 10328 * q^74 - 29613 * q^76 + 16320 * q^77 + 19028 * q^78 + 12778 * q^80 - 25574 * q^81 + 30563 * q^82 + 65132 * q^84 - 21006 * q^85 - 8430 * q^86 + 44242 * q^88 + 12910 * q^89 - 48688 * q^90 - 14052 * q^92 - 4304 * q^93 - 39664 * q^94 + 15670 * q^96 + 1174 * q^97 + 2783 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−2.87075	+	2.78547i	−0.717686	+	0.696366i
$2$	−2.87075	+	2.78547i	−0.717686	+	0.696366i
$3$	2.38822	−	1.37884i	0.265357	−	0.153204i	−0.361419	−	0.932404i	$-0.617707\pi$
$3$	2.38822	−	1.37884i	0.265357	−	0.153204i	0.626776	+	0.779199i	$0.284374\pi$
$4$	0.482361	−	15.9927i	0.0301476	−	0.999545i
$5$	−16.6192	−	28.7853i	−0.664768	−	1.15141i	−0.979348	−	0.202181i	$-0.935197\pi$
$5$	−16.6192	−	28.7853i	−0.664768	−	1.15141i	0.314580	−	0.949231i	$-0.398136\pi$
$6$	−3.01526	+	10.6106i	−0.0837572	+	0.294739i
$7$			28.7543i			0.586821i	0.955986	+	0.293411i	$0.0947903\pi$
$7$			28.7543i			0.586821i	−0.955986	+	0.293411i	$0.905210\pi$
$8$	43.1625	+	47.2547i	0.674413	+	0.738354i
$9$	−36.6976	+	63.5621i	−0.453057	+	0.784718i
$10$	127.890	+	36.3431i	1.27890	+	0.363431i
$11$			156.718i			1.29519i	0.761985	+	0.647595i	$0.224225\pi$
$11$			156.718i			1.29519i	−0.761985	+	0.647595i	$0.775775\pi$
$12$	−20.8994	−	38.8592i	−0.145135	−	0.269856i
$13$	26.2442	−	45.4563i	0.155291	−	0.268972i	−0.777874	−	0.628421i	$-0.783702\pi$
$13$	26.2442	−	45.4563i	0.155291	−	0.268972i	0.933165	+	0.359448i	$0.117035\pi$
$14$	−80.0940	−	82.5461i	−0.408643	−	0.421154i
$15$	−79.3805	−	45.8304i	−0.352802	−	0.203691i
$16$	−255.535	−	15.4285i	−0.998182	−	0.0602677i
$17$	124.557	+	215.739i	0.430993	+	0.746501i	0.996959	−	0.0779269i	$-0.0248301\pi$
$17$	124.557	+	215.739i	0.430993	+	0.746501i	−0.565966	+	0.824428i	$0.691497\pi$
$18$	−71.7006	−	284.691i	−0.221298	−	0.878675i
$19$	−181.417	+	312.104i	−0.502539	+	0.864555i
$19$	−181.417	+	312.104i	−0.502539	+	0.864555i
$20$	−468.372	+	251.902i	−1.17093	+	0.629754i
$21$	39.6474	+	68.6714i	0.0899035	+	0.155717i
$22$	−436.532	−	449.897i	−0.901926	−	0.929540i
$23$	−263.704	−	152.250i	−0.498495	−	0.287806i	0.229597	−	0.973286i	$-0.426259\pi$
$23$	−263.704	−	152.250i	−0.498495	−	0.287806i	−0.728092	+	0.685479i	$0.759593\pi$
$24$	168.238	+	53.3403i	0.292080	+	0.0926047i
$25$	−239.896	+	415.512i	−0.383834	+	0.664819i
$26$	51.2765	+	203.596i	0.0758529	+	0.301177i
$27$			425.772i			0.584049i
$28$	459.859	+	13.8699i	0.586555	+	0.0176912i
$29$	−691.626	+	1197.93i	−0.822385	+	1.42441i	0.0815163	+	0.996672i	$0.474024\pi$
$29$	−691.626	+	1197.93i	−0.822385	+	1.42441i	−0.903901	+	0.427741i	$0.859310\pi$
$30$	355.540	−	89.5444i	0.395045	−	0.0994938i
$31$		−	1041.75i		−	1.08403i	−0.840368	−	0.542016i	$-0.817661\pi$
$31$		−	1041.75i		−	1.08403i	0.840368	−	0.542016i	$-0.182339\pi$
$32$	776.551	−	667.492i	0.758350	−	0.651847i
$33$	216.089	+	374.276i	0.198428	+	0.343688i
$34$	−958.505	−	272.383i	−0.829156	−	0.235625i
$35$	827.700	−	477.873i	0.675673	−	0.390100i
$36$	998.830	+	617.555i	0.770702	+	0.476508i
$37$	1409.13			1.02931			0.514656	−	0.857396i	$-0.327919\pi$
$37$	1409.13			1.02931			0.514656	+	0.857396i	$0.327919\pi$
$38$	−348.555	−	1401.30i	−0.241381	−	0.970430i
$39$		−	144.746i		−	0.0951651i
$40$	642.914	−	2027.78i	0.401821	−	1.26736i
$41$	−224.809	−	389.381i	−0.133735	−	0.231636i	0.791378	−	0.611327i	$-0.209364\pi$
$41$	−224.809	−	389.381i	−0.133735	−	0.231636i	−0.925114	+	0.379690i	$0.876031\pi$
$42$	−305.100	−	86.7015i	−0.172959	−	0.0491505i
$43$	−1642.67	+	948.395i	−0.888409	+	0.512923i	−0.873422	−	0.486965i	$-0.838104\pi$
$43$	−1642.67	+	948.395i	−0.888409	+	0.512923i	−0.0149870	+	0.999888i	$0.504771\pi$
$44$	2506.35	+	75.5946i	1.29460	+	0.0390468i
$45$	2439.54			1.20471
$46$	1181.11	−	297.469i	0.558182	−	0.140581i
$47$	−234.559	−	135.423i	−0.106183	−	0.0613050i	0.445968	−	0.895049i	$-0.352860\pi$
$47$	−234.559	−	135.423i	−0.106183	−	0.0613050i	−0.552151	+	0.833744i	$0.686193\pi$
$48$	−631.546	+	315.494i	−0.274108	+	0.136933i
$49$	1574.19			0.655641
$50$	−468.714	−	1861.05i	−0.187486	−	0.744421i
$51$	594.938	+	343.488i	0.228734	+	0.132060i
$52$	−714.311	−	441.643i	−0.264168	−	0.163329i
$53$	−2540.48	+	4400.24i	−0.904408	+	1.56648i	−0.0826979	+	0.996575i	$0.526354\pi$
$53$	−2540.48	+	4400.24i	−0.904408	+	1.56648i	−0.821710	+	0.569906i	$0.806980\pi$
$54$	−1185.97	−	1222.28i	−0.406712	−	0.419164i
$55$	4511.17	−	2604.53i	1.49130	−	0.861001i
$56$	−1358.77	+	1241.10i	−0.433282	+	0.395760i
$57$	−2.92104	+	995.517i	−0.000899059	+	0.306407i
$58$	−1351.31	−	5365.46i	−0.401699	−	1.59496i
$59$	−1961.37	+	1132.40i	−0.563450	+	0.325308i	−0.754529	−	0.656267i	$-0.772135\pi$
$59$	−1961.37	+	1132.40i	−0.563450	+	0.325308i	0.191079	+	0.981575i	$0.438801\pi$
$60$	−771.243	+	1247.40i	−0.214234	+	0.346501i
$61$	1343.04	−	2326.22i	0.360936	−	0.625159i	−0.627179	−	0.778875i	$-0.715791\pi$
$61$	1343.04	−	2326.22i	0.360936	−	0.625159i	0.988115	+	0.153716i	$0.0491241\pi$
$62$	2901.77	+	2990.61i	0.754883	+	0.777995i
$63$	−1827.68	−	1055.21i	−0.460489	−	0.265864i
$64$	−370.004	+	4079.25i	−0.0903331	+	0.995912i
$65$	−1744.63			−0.412931
$66$	−1662.87	−	472.545i	−0.381742	−	0.108481i
$67$	−1551.55	−	895.788i	−0.345634	−	0.199552i	0.317127	−	0.948383i	$-0.397282\pi$
$67$	−1551.55	−	895.788i	−0.345634	−	0.199552i	−0.662761	+	0.748831i	$0.730615\pi$
$68$	3510.34	−	1887.94i	0.759156	−	0.408292i
$69$	−839.710			−0.176373
$70$	−1045.02	+	3677.38i	−0.213269	+	0.750486i
$71$	−4168.48	+	2406.67i	−0.826915	+	0.477419i	−0.852795	−	0.522246i	$-0.825094\pi$
$71$	−4168.48	+	2406.67i	−0.826915	+	0.477419i	0.0258804	+	0.999665i	$0.491761\pi$
$72$	−4587.57	+	1009.36i	−0.884947	+	0.194708i
$73$	−4556.11	−	7891.41i	−0.854965	−	1.48084i	−0.876677	−	0.481079i	$-0.840245\pi$
$73$	−4556.11	−	7891.41i	−0.854965	−	1.48084i	0.0217123	−	0.999764i	$-0.493088\pi$
$74$	−4045.25	+	3925.08i	−0.738724	+	0.716779i
$75$			1323.11i			0.235220i
$76$	4903.89	+	3051.89i	0.849011	+	0.528375i
$77$	−4506.31			−0.760045
$78$	403.185	+	415.529i	0.0662698	+	0.0682987i
$79$	6945.24	−	4009.83i	1.11284	−	0.642499i	0.173277	−	0.984873i	$-0.444564\pi$
$79$	6945.24	−	4009.83i	1.11284	−	0.642499i	0.939564	+	0.342374i	$0.111231\pi$
$80$	3802.67	+	7612.05i	0.594167	+	1.18938i
$81$	−2385.44	−	4131.70i	−0.363578	−	0.629736i
$82$	1729.98	+	491.615i	0.257284	+	0.0731135i
$83$			8665.43i			1.25787i	0.777460	+	0.628933i	$0.216508\pi$
$83$			8665.43i			1.25787i	−0.777460	+	0.628933i	$0.783492\pi$
$84$	1117.37	−	600.946i	0.158357	−	0.0851681i
$85$	4140.07	−	7170.82i	0.573021	−	0.992501i
$86$	2073.96	−	7298.19i	0.280416	−	0.986776i
$87$			3814.56i			0.503971i
$88$	−7405.65	+	6764.33i	−0.956308	+	0.873493i
$89$	482.886	−	836.384i	0.0609628	−	0.105591i	−0.833933	−	0.551865i	$-0.813916\pi$
$89$	482.886	−	836.384i	0.0609628	−	0.105591i	0.894896	+	0.446275i	$0.147250\pi$
$90$	−7003.30	+	6795.26i	−0.864605	+	0.838921i
$91$	1307.06	+	754.633i	0.157839	+	0.0911282i
$92$	−2562.09	+	4143.91i	−0.302704	+	0.489592i
$93$	−1436.41	−	2487.94i	−0.166078	−	0.287656i
$94$	1050.58	−	264.592i	0.118897	−	0.0299448i
$95$	11999.0	+	35.2075i	1.32953	+	0.00390110i
$96$	934.209	−	2664.85i	0.101368	−	0.289155i
$97$	4225.04	+	7317.98i	0.449042	+	0.777764i	0.998324	−	0.0578735i	$-0.0184320\pi$
$97$	4225.04	+	7317.98i	0.449042	+	0.777764i	−0.549282	+	0.835637i	$0.685099\pi$
$98$	−4519.11	+	4384.86i	−0.470544	+	0.456566i
$99$	−9961.32	−	5751.17i	−1.01636	−	0.586794i
$100$	6529.46	+	4037.02i	0.652946	+	0.403702i
$101$	5818.72	−	10078.3i	0.570407	−	0.987973i	−0.426117	−	0.904668i	$-0.640119\pi$
$101$	5818.72	−	10078.3i	0.570407	−	0.987973i	0.996524	−	0.0833055i	$-0.0265477\pi$
$102$	−2664.69	+	671.114i	−0.256122	+	0.0645054i
$103$			7666.96i			0.722685i	0.932433	+	0.361342i	$0.117681\pi$
$103$			7666.96i			0.722685i	−0.932433	+	0.361342i	$0.882319\pi$
$104$	3280.79	−	721.845i	0.303327	−	0.0667386i
$105$	1317.82	−	2282.53i	0.119530	−	0.207032i
$106$	−4963.65	−	19708.4i	−0.441763	−	1.75404i
$107$		−	14758.3i		−	1.28905i	−0.764584	−	0.644524i	$-0.777056\pi$
$107$		−	14758.3i		−	1.28905i	0.764584	−	0.644524i	$-0.222944\pi$
$108$	6809.25	+	205.376i	0.583784	+	0.0176077i
$109$	−325.934	−	564.535i	−0.0274332	−	0.0475158i	0.851983	−	0.523570i	$-0.175400\pi$
$109$	−325.934	−	564.535i	−0.0274332	−	0.0475158i	−0.879416	+	0.476054i	$0.842067\pi$
$110$	−5695.61	+	20042.7i	−0.470712	+	1.65642i
$111$	3365.31	−	1942.96i	0.273136	−	0.157695i
$112$	443.636	−	7347.71i	0.0353664	−	0.585755i
$113$	269.979			0.0211433			0.0105717	−	0.999944i	$-0.496635\pi$
$113$	269.979			0.0211433			0.0105717	+	0.999944i	$0.496635\pi$
$114$	−2764.59	−	2866.01i	−0.212726	−	0.220530i
$115$			10121.1i			0.765298i
$116$	18824.6	+	11638.8i	1.39897	+	0.864954i
$117$	1926.20	+	3336.28i	0.140712	+	0.243720i
$118$	2476.34	−	8714.15i	0.177847	−	0.625836i
$119$	−6203.41	+	3581.54i	−0.438063	+	0.252916i
$120$	−1260.56	−	5729.25i	−0.0875390	−	0.397865i
$121$	−9919.50			−0.677515
$122$	2624.07	+	10419.0i	0.176301	+	0.700012i
$123$	−1073.79	−	619.951i	−0.0709754	−	0.0409776i
$124$	−16660.5	−	502.502i	−1.08354	−	0.0326809i
$125$	−4826.48			−0.308895
$126$	8186.07	−	2061.70i	0.515625	−	0.129863i
$127$	−20378.7	−	11765.6i	−1.26348	−	0.729470i	−0.289733	−	0.957107i	$-0.593567\pi$
$127$	−20378.7	−	11765.6i	−1.26348	−	0.729470i	−0.973746	+	0.227637i	$0.926900\pi$
$128$	−10300.4	−	12741.1i	−0.628689	−	0.777657i
$129$	−2615.36	+	4529.94i	−0.157164	+	0.272216i
$130$	5008.39	−	4859.61i	0.296355	−	0.287551i
$131$	26395.9	−	15239.7i	1.53813	−	0.888042i	0.539186	−	0.842187i	$-0.318732\pi$
$131$	26395.9	−	15239.7i	1.53813	−	0.888042i	0.998948	−	0.0458558i	$-0.0146015\pi$
$132$	6089.93	−	3275.31i	0.349514	−	0.187977i
$133$	−8974.32	−	5216.50i	−0.507339	−	0.294901i
$134$	6949.30	−	1750.21i	0.387018	−	0.0974723i
$135$	12256.0	−	7075.99i	0.672482	−	0.388257i
$136$	−4818.48	+	15197.7i	−0.260515	+	0.821676i
$137$	−10299.1	+	17838.5i	−0.548728	+	0.950425i	0.449634	+	0.893213i	$0.351555\pi$
$137$	−10299.1	+	17838.5i	−0.548728	+	0.950425i	−0.998362	+	0.0572124i	$0.981779\pi$
$138$	2410.59	−	2338.98i	0.126580	−	0.122820i
$139$	−16496.8	−	9524.46i	−0.853830	−	0.492959i	0.00811149	−	0.999967i	$-0.497418\pi$
$139$	−16496.8	−	9524.46i	−0.853830	−	0.492959i	−0.861941	+	0.507008i	$0.830751\pi$
$140$	−7243.24	−	13467.7i	−0.369553	−	0.687127i
$141$	−746.904			−0.0375688
$142$	5262.94	−	18520.1i	0.261007	−	0.918473i
$143$	7123.82	+	4112.94i	0.348370	+	0.201131i
$144$	10358.2	−	15676.1i	0.499527	−	0.755987i
$145$	45977.1			2.18678
$146$	35060.7	+	9963.35i	1.64481	+	0.467412i
$147$	3759.51	−	2170.56i	0.173979	−	0.100447i
$148$	679.709	−	22535.8i	0.0310313	−	1.02885i
$149$	13040.8	+	22587.4i	0.587399	+	1.01740i	0.994572	+	0.104054i	$0.0331814\pi$
$149$	13040.8	+	22587.4i	0.587399	+	1.01740i	−0.407173	+	0.913351i	$0.633485\pi$
$150$	−3685.48	−	3798.31i	−0.163799	−	0.168814i
$151$			2397.42i			0.105146i	0.998617	+	0.0525728i	$0.0167422\pi$
$151$			2397.42i			0.105146i	−0.998617	+	0.0525728i	$0.983258\pi$
$152$	−22578.8	+	4898.41i	−0.977266	+	0.212016i
$153$	−18283.8			−0.781057
$154$	12936.5	−	12552.2i	0.545474	−	0.529270i
$155$	−29987.2	+	17313.1i	−1.24817	+	0.720630i
$156$	−2314.88	−	69.8198i	−0.0951218	−	0.00286899i
$157$	12006.7	+	20796.3i	0.487108	+	0.843696i	0.999890	−	0.0148228i	$-0.00471843\pi$
$157$	12006.7	+	20796.3i	0.487108	+	0.843696i	−0.512782	+	0.858519i	$0.671385\pi$
$158$	−8768.75	+	30856.9i	−0.351256	+	1.23606i
$159$			14011.6i			0.554236i
$160$	−32119.6	−	11260.1i	−1.25467	−	0.439846i
$161$	4377.82	−	7582.61i	0.168891	−	0.292528i
$162$	18356.7	+	5216.50i	0.699462	+	0.198769i
$163$			1871.77i			0.0704495i	0.999379	+	0.0352247i	$0.0112147\pi$
$163$			1871.77i			0.0704495i	−0.999379	+	0.0352247i	$0.988785\pi$
$164$	−6335.70	+	3407.49i	−0.235563	+	0.126691i
$165$	7182.44	−	12440.4i	0.263818	−	0.456946i
$166$	−24137.3	−	24876.3i	−0.875935	−	0.902753i
$167$	42367.9	+	24461.1i	1.51916	+	0.877087i	0.999745	+	0.0225651i	$0.00718332\pi$
$167$	42367.9	+	24461.1i	1.51916	+	0.877087i	0.519415	+	0.854522i	$0.326150\pi$
$168$	−1533.76	+	4837.55i	−0.0543425	+	0.171399i
$169$	12903.0	+	22348.6i	0.451769	+	0.782487i
$170$	8088.97	+	32117.6i	0.279895	+	1.11134i
$171$	−13180.5	−	22984.7i	−0.450752	−	0.786044i
$172$	14375.1	+	26728.2i	0.485906	+	0.903468i
$173$	5991.35	+	10377.3i	0.200185	+	0.346731i	0.948588	−	0.316513i	$-0.102512\pi$
$173$	5991.35	+	10377.3i	0.200185	+	0.346731i	−0.748403	+	0.663245i	$0.769179\pi$
$174$	−10625.3	−	10950.6i	−0.350949	−	0.361693i
$175$	−11947.7	−	6898.03i	−0.390130	−	0.225242i
$176$	2417.93	−	40046.9i	0.0780581	−	1.29283i
$177$	−3122.78	+	5408.82i	−0.0996770	+	0.172646i
$178$	943.475	+	3746.11i	0.0297776	+	0.118233i
$179$			34384.1i			1.07313i	0.843859	+	0.536564i	$0.180278\pi$
$179$			34384.1i			1.07313i	−0.843859	+	0.536564i	$0.819722\pi$
$180$	1176.74	−	39014.9i	0.0363191	−	1.20416i
$181$	−14984.5	+	25953.9i	−0.457389	+	0.792221i	−0.998822	−	0.0485230i	$-0.984549\pi$
$181$	−14984.5	+	25953.9i	−0.457389	+	0.792221i	0.541433	+	0.840744i	$0.317882\pi$
$182$	−5854.25	+	1474.42i	−0.176737	+	0.0445121i
$183$		−	7407.35i		−	0.221187i
$184$	−4187.61	−	19032.7i	−0.123689	−	0.562167i
$185$	−23418.6	−	40562.2i	−0.684255	−	1.18516i
$186$	11053.6	+	3141.16i	0.319506	+	0.0907954i
$187$	−33810.1	+	19520.3i	−0.966861	+	0.558217i
$188$	−2278.92	+	3685.92i	−0.0644783	+	0.104287i
$189$	−12242.8			−0.342733
$190$	−34544.2	+	33321.8i	−0.956903	+	0.923041i
$191$			4129.81i			0.113204i	0.998397	+	0.0566022i	$0.0180267\pi$
$191$			4129.81i			0.113204i	−0.998397	+	0.0566022i	$0.981973\pi$
$192$	4740.98	+	10252.3i	0.128607	+	0.278112i
$193$	12953.2	+	22435.6i	0.347747	+	0.602315i	0.985849	−	0.167637i	$-0.0536135\pi$
$193$	12953.2	+	22435.6i	0.347747	+	0.602315i	−0.638102	+	0.769952i	$0.720280\pi$
$194$	−32513.0	−	9239.36i	−0.863880	−	0.245493i
$195$	−4166.56	+	2405.56i	−0.109574	+	0.0632627i
$196$	759.329	−	25175.6i	0.0197660	−	0.655343i
$197$	−28207.1			−0.726820			−0.363410	−	0.931629i	$-0.618388\pi$
$197$	−28207.1			−0.726820			−0.363410	+	0.931629i	$0.618388\pi$
$198$	44616.1	−	11236.8i	1.13805	−	0.286623i
$199$	−18905.1	−	10914.9i	−0.477391	−	0.275622i	0.241938	−	0.970292i	$-0.422217\pi$
$199$	−18905.1	−	10914.9i	−0.477391	−	0.275622i	−0.719328	+	0.694670i	$0.755550\pi$
$200$	−29989.4	+	6598.32i	−0.749735	+	0.164958i
$201$	−4940.59			−0.122289
$202$	11368.7	+	45140.1i	0.278618	+	1.10627i
$203$	−34445.6	−	19887.2i	−0.835876	−	0.482593i
$204$	5780.28	−	9349.00i	0.138896	−	0.224649i
$205$	−7472.30	+	12942.4i	−0.177806	+	0.307969i
$206$	−21356.1	−	22009.9i	−0.503253	−	0.518661i
$207$	19354.6	−	11174.4i	0.451694	−	0.260785i
$208$	−7407.63	+	11210.8i	−0.171219	+	0.259124i
$209$	−48912.3	−	28431.2i	−1.11976	−	0.650883i
$210$	2574.78	+	10223.3i	0.0583851	+	0.231821i
$211$	14853.8	−	8575.86i	0.333636	−	0.192625i	−0.323818	−	0.946119i	$-0.604967\pi$
$211$	14853.8	−	8575.86i	0.333636	−	0.192625i	0.657454	+	0.753494i	$0.271633\pi$
$212$	69146.5	+	42751.7i	1.53850	+	0.951222i
$213$	−6636.82	+	11495.3i	−0.146285	+	0.253374i
$214$	41108.8	+	42367.3i	0.897650	+	0.925132i
$215$	54599.7	+	31523.1i	1.18117	+	0.681950i
$216$	−20119.7	+	18377.4i	−0.431235	+	0.393891i
$217$	29954.9			0.636133
$218$	2508.17	+	712.757i	0.0527768	+	0.0149978i
$219$	−21762.0	−	12564.3i	−0.453743	−	0.261968i
$220$	−39477.5	−	73402.3i	−0.815650	−	1.51658i
$221$	13075.6			0.267718
$222$	−4248.89	+	14951.7i	−0.0862123	+	0.303378i
$223$	55014.0	−	31762.3i	1.10628	−	0.638709i	0.168413	−	0.985716i	$-0.446136\pi$
$223$	55014.0	−	31762.3i	1.10628	−	0.638709i	0.937862	+	0.347008i	$0.112802\pi$
$224$	19193.2	+	22329.1i	0.382518	+	0.445016i
$225$	−17607.2	−	30496.6i	−0.347797	−	0.602402i
$226$	−775.041	+	752.018i	−0.0151743	+	0.0147235i
$227$			64608.0i			1.25382i	0.779093	+	0.626909i	$0.215680\pi$
$227$			64608.0i			1.25382i	−0.779093	+	0.626909i	$0.784320\pi$
$228$	15919.6	+	526.914i	0.306241	+	0.0101361i
$229$	74766.6			1.42573			0.712864	−	0.701303i	$-0.247398\pi$
$229$	74766.6			1.42573			0.712864	+	0.701303i	$0.247398\pi$
$230$	−28191.9	−	29055.0i	−0.532928	−	0.549244i
$231$	−10762.0	+	6213.46i	−0.201684	+	0.116442i
$232$	−86460.1	+	19023.1i	−1.60635	+	0.353432i
$233$	−2367.82	−	4101.19i	−0.0436152	−	0.0755437i	0.843394	−	0.537296i	$-0.180554\pi$
$233$	−2367.82	−	4101.19i	−0.0436152	−	0.0755437i	−0.887009	+	0.461752i	$0.847221\pi$
$234$	−14822.7	−	4212.24i	−0.270705	−	0.0769274i
$235$			9002.48i			0.163015i
$236$	17164.0	+	31913.8i	0.308173	+	0.573001i
$237$	11057.8	−	19152.7i	0.196867	−	0.340984i
$238$	7832.16	−	27561.1i	0.138270	−	0.486567i
$239$		−	66308.2i		−	1.16084i	−0.814318	−	0.580419i	$-0.802889\pi$
$239$		−	66308.2i		−	1.16084i	0.814318	−	0.580419i	$-0.197111\pi$
$240$	19577.4	+	12936.0i	0.339885	+	0.224583i
$241$	5305.79	−	9189.90i	0.0913515	−	0.158226i	−0.816729	−	0.577022i	$-0.804215\pi$
$241$	5305.79	−	9189.90i	0.0913515	−	0.158226i	0.908080	+	0.418797i	$0.137548\pi$
$242$	28476.3	−	27630.4i	0.486243	−	0.471799i
$243$	−41261.0	−	23822.0i	−0.698758	−	0.403428i
$244$	−36554.7	−	22601.0i	−0.613993	−	0.379619i
$245$	−26161.8	−	45313.6i	−0.435849	−	0.754913i
$246$	4809.42	−	1211.27i	0.0794735	−	0.0200158i
$247$	9425.97	+	16437.5i	0.154501	+	0.269427i
$248$	49227.8	−	44964.7i	0.800399	−	0.731086i
$249$	11948.2	+	20694.9i	0.192710	+	0.333784i
$250$	13855.6	−	13444.0i	0.221690	−	0.215104i
$251$	−27638.6	−	15957.2i	−0.438701	−	0.253284i	0.264345	−	0.964428i	$-0.414844\pi$
$251$	−27638.6	−	15957.2i	−0.438701	−	0.253284i	−0.703047	+	0.711144i	$0.748178\pi$
$252$	−17757.3	+	28720.6i	−0.279625	+	0.452265i
$253$	23860.2	−	41327.1i	0.372764	−	0.645646i
$254$	91274.7	−	22987.9i	1.41476	−	0.356314i
$255$		−	22834.0i		−	0.351157i
$256$	65059.9	+	7885.05i	0.992736	+	0.120316i
$257$	2822.78	−	4889.20i	0.0427377	−	0.0740239i	−0.843865	−	0.536555i	$-0.819725\pi$
$257$	2822.78	−	4889.20i	0.0427377	−	0.0740239i	0.886603	+	0.462531i	$0.153059\pi$
$258$	−5109.96	−	20289.3i	−0.0767676	−	0.304809i
$259$			40518.5i			0.604023i
$260$	−841.542	+	27901.4i	−0.0124488	+	0.412743i
$261$	−50762.0	−	87922.4i	−0.745175	−	1.29068i
$262$	−33326.3	+	117274.i	−0.485495	+	1.70844i
$263$	104778.	−	60493.8i	1.51482	−	0.874579i	0.514966	−	0.857210i	$-0.327804\pi$
$263$	104778.	−	60493.8i	1.51482	−	0.874579i	0.999849	−	0.0173688i	$-0.00552894\pi$
$264$	−8359.38	+	26365.9i	−0.119941	+	0.378298i
$265$	168883.			2.40489
$266$	40293.4	−	10022.4i	0.569469	−	0.141648i
$267$		−	2663.29i		−	0.0373590i
$268$	−15074.5	+	24381.4i	−0.209881	+	0.339461i
$269$	−17194.0	−	29781.0i	−0.237615	−	0.411561i	0.722415	−	0.691460i	$-0.243032\pi$
$269$	−17194.0	−	29781.0i	−0.237615	−	0.411561i	−0.960029	+	0.279899i	$0.909699\pi$
$270$	−15473.9	+	54452.0i	−0.212261	+	0.746941i
$271$	54648.7	−	31551.5i	0.744117	−	0.429616i	−0.0794471	−	0.996839i	$-0.525315\pi$
$271$	54648.7	−	31551.5i	0.744117	−	0.429616i	0.823564	+	0.567223i	$0.191982\pi$
$272$	−28500.1	−	57050.5i	−0.385219	−	0.771119i
$273$	4162.06			0.0558449
$274$	−20122.6	−	79897.6i	−0.268029	−	1.06422i
$275$	−65118.2	−	37596.0i	−0.861067	−	0.497137i
$276$	−405.043	+	13429.3i	−0.00531720	+	0.176292i
$277$	−133958.			−1.74586			−0.872930	−	0.487845i	$-0.837783\pi$
$277$	−133958.			−1.74586			−0.872930	+	0.487845i	$0.837783\pi$
$278$	73888.3	−	18609.1i	0.956062	−	0.240789i
$279$	66216.1	+	38229.9i	0.850659	+	0.491128i
$280$	58307.3	+	18486.5i	0.743715	+	0.235797i
$281$	−41710.6	+	72244.8i	−0.528243	+	0.914943i	0.471215	+	0.882018i	$0.343815\pi$
$281$	−41710.6	+	72244.8i	−0.528243	+	0.914943i	−0.999458	+	0.0329247i	$0.989518\pi$
$282$	2144.17	−	2080.48i	0.0269626	−	0.0261616i
$283$	−12837.6	+	7411.81i	−0.160292	+	0.0925447i	−0.578000	−	0.816037i	$-0.696167\pi$
$283$	−12837.6	+	7411.81i	−0.160292	+	0.0925447i	0.417708	+	0.908581i	$0.362833\pi$
$284$	36478.5	+	67826.2i	0.452273	+	0.840932i
$285$	28704.8	−	16460.6i	0.353399	−	0.202655i
$286$	−31907.1	+	8035.95i	−0.390082	+	0.0982438i
$287$	11196.4	−	6464.22i	0.135929	−	0.0784788i
$288$	13929.6	+	73854.6i	0.167940	+	0.890415i
$289$	10731.6	−	18587.8i	0.128490	−	0.222552i
$290$	−131989.	+	128068.i	−1.56942	+	1.52280i
$291$	20180.6	+	11651.3i	0.238313	+	0.137590i
$292$	−128403.	+	69058.1i	−1.50594	+	0.809933i
$293$	15084.1			0.175705			0.0878527	−	0.996133i	$-0.472000\pi$
$293$	15084.1			0.175705			0.0878527	+	0.996133i	$0.472000\pi$
$294$	−4746.60	+	16703.1i	−0.0549146	+	0.193243i
$295$	65192.8	+	37639.1i	0.749127	+	0.432509i
$296$	60821.5	+	66587.9i	0.694182	+	0.759997i
$297$	−66726.1			−0.756454
$298$	−100353.	−	28517.9i	−1.13005	−	0.321133i
$299$	−13841.4	+	7991.34i	−0.154824	+	0.0893876i
$300$	21160.2	+	638.217i	0.235113	+	0.00709130i
$301$	−27270.4	−	47233.7i	−0.300994	−	0.521337i
$302$	−6677.94	−	6882.40i	−0.0732199	−	0.0754616i
$303$		−	32092.3i		−	0.349555i
$304$	51173.5	−	76954.4i	0.553730	−	0.832696i
$305$	−89281.1			−0.959754
$306$	52488.0	−	50928.8i	0.560554	−	0.543902i
$307$	−119432.	+	68954.0i	−1.26720	+	0.731616i	−0.974456	−	0.224577i	$-0.927900\pi$
$307$	−119432.	+	68954.0i	−1.26720	+	0.731616i	−0.292739	+	0.956192i	$0.594567\pi$
$308$	−2173.67	+	72068.1i	−0.0229135	+	0.759699i
$309$	10571.5	+	18310.4i	0.110718	+	0.191770i
$310$	37860.6	−	133230.i	0.393971	−	1.38637i
$311$		−	76041.4i		−	0.786193i	−0.919497	−	0.393097i	$-0.871404\pi$
$311$		−	76041.4i		−	0.786193i	0.919497	−	0.393097i	$-0.128596\pi$
$312$	6839.92	−	6247.60i	0.0702655	−	0.0641806i
$313$	2842.39	−	4923.16i	0.0290131	−	0.0502522i	−0.851154	−	0.524916i	$-0.824097\pi$
$313$	2842.39	−	4923.16i	0.0290131	−	0.0502522i	0.880167	+	0.474663i	$0.157430\pi$
$314$	−92395.5	−	26256.5i	−0.937112	−	0.266303i
$315$			70147.2i			0.706951i
$316$	−60778.1	−	113007.i	−0.608657	−	1.13170i
$317$	−26278.9	+	45516.3i	−0.261510	+	0.452949i	−0.966643	−	0.256126i	$-0.917554\pi$
$317$	−26278.9	+	45516.3i	−0.261510	+	0.452949i	0.705133	+	0.709075i	$0.250887\pi$
$318$	−39029.0	−	40223.9i	−0.385952	−	0.397768i
$319$	−187737.	−	108390.i	−1.84488	−	1.06514i
$320$	123572.	−	57143.3i	1.20676	−	0.558040i
$321$	−20349.3	−	35246.0i	−0.197488	−	0.342058i
$322$	8553.49	+	33962.0i	0.0824958	+	0.327553i
$323$	−89929.7	−	263.871i	−0.861982	−	0.00252922i
$324$	−67227.7	+	36156.7i	−0.640411	+	0.344428i
$325$	12591.8	+	21809.6i	0.119212	+	0.206481i
$326$	−5213.76	−	5373.38i	−0.0490586	−	0.0505606i
$327$	−1556.80	−	898.821i	−0.0145592	−	0.00840577i
$328$	8696.74	−	27429.9i	0.0808368	−	0.254963i
$329$	3893.98	−	6744.58i	0.0359751	−	0.0623107i
$330$	14033.2	+	55719.5i	0.128863	+	0.511658i
$331$			200313.i			1.82832i	0.405352	+	0.914161i	$0.367149\pi$
$331$			200313.i			1.82832i	−0.405352	+	0.914161i	$0.632851\pi$
$332$	138584.	+	4179.87i	1.25729	+	0.0379216i
$333$	−51711.7	+	89567.3i	−0.466337	+	0.807720i
$334$	−189763.	+	47792.6i	−1.70105	+	0.428418i
$335$			59549.2i			0.530623i
$336$	−9071.80	−	18159.6i	−0.0803554	−	0.160853i
$337$	54570.5	+	94518.9i	0.480505	+	0.832259i	0.999750	−	0.0223663i	$-0.00712002\pi$
$337$	54570.5	+	94518.9i	0.480505	+	0.832259i	−0.519245	+	0.854626i	$0.673787\pi$
$338$	−99292.5	−	28216.4i	−0.869127	−	0.246984i
$339$	644.769	−	372.257i	0.00561054	−	0.00323925i
$340$	−112684.	−	69670.0i	−0.974775	−	0.602682i
$341$	163262.			1.40403
$342$	101861.	+	29269.5i	0.870873	+	0.250244i
$343$			114304.i			0.971565i
$344$	−115718.	−	36688.6i	−0.977873	−	0.310038i
$345$	13955.3	+	24171.3i	0.117247	+	0.203078i
$346$	−46105.3	−	13102.0i	−0.385122	−	0.109442i
$347$	77079.8	−	44502.1i	0.640150	−	0.369591i	−0.144522	−	0.989502i	$-0.546165\pi$
$347$	77079.8	−	44502.1i	0.640150	−	0.369591i	0.784672	+	0.619911i	$0.212831\pi$
$348$	61005.2	+	1839.99i	0.503742	+	0.0151935i
$349$	235806.			1.93599			0.967996	−	0.250964i	$-0.0807475\pi$
$349$	235806.			1.93599			0.967996	+	0.250964i	$0.0807475\pi$
$350$	53513.2	−	13477.5i	0.436842	−	0.110021i
$351$	19354.0	+	11174.0i	0.157093	+	0.0906977i
$352$	104608.	+	121699.i	0.844266	+	0.982207i
$353$	−34560.9			−0.277355			−0.138677	−	0.990338i	$-0.544285\pi$
$353$	−34560.9			−0.277355			−0.138677	+	0.990338i	$0.544285\pi$
$354$	−6101.36	−	24225.7i	−0.0486878	−	0.193317i
$355$	138554.	+	79993.9i	1.09941	+	0.634747i
$356$	−13143.1	−	8126.11i	−0.103705	−	0.0641184i
$357$	−9876.73	+	17107.0i	−0.0774955	+	0.134226i
$358$	−95775.8	−	98708.0i	−0.747291	−	0.770170i
$359$	85412.3	−	49312.8i	0.662723	−	0.382623i	−0.130591	−	0.991436i	$-0.541687\pi$
$359$	85412.3	−	49312.8i	0.662723	−	0.382623i	0.793314	+	0.608813i	$0.208354\pi$
$360$	105297.	+	115280.i	0.812474	+	0.889503i
$361$	−64497.1	−	113242.i	−0.494909	−	0.868945i
$362$	−29277.1	−	116246.i	−0.223414	−	0.887076i
$363$	−23689.9	+	13677.4i	−0.179784	+	0.103798i
$364$	12699.1	−	20539.5i	0.0958452	−	0.155020i
$365$	−151438.	+	262298.i	−1.13671	+	1.96883i
$366$	20632.9	+	21264.6i	0.154028	+	0.158743i
$367$	176919.	+	102144.i	1.31353	+	0.758369i	0.982680	−	0.185312i	$-0.0593297\pi$
$367$	176919.	+	102144.i	1.31353	+	0.758369i	0.330855	+	0.943682i	$0.392663\pi$
$368$	65036.5	+	42973.6i	0.480244	+	0.317326i
$369$	32999.8			0.242359
$370$	180214.	+	51212.1i	1.31639	+	0.374084i
$371$	−126526.	−	73049.7i	−0.919244	−	0.530726i
$372$	−40481.8	+	21772.0i	−0.292532	+	0.157331i
$373$	−28242.3			−0.202994			−0.101497	−	0.994836i	$-0.532363\pi$
$373$	−28242.3			−0.202994			−0.101497	+	0.994836i	$0.532363\pi$
$374$	42687.2	−	150215.i	0.305179	−	1.07391i
$375$	−11526.7	+	6654.93i	−0.0819675	+	0.0473240i
$376$	−3724.79	−	16929.2i	−0.0263467	−	0.119746i
$377$	36302.4	+	62877.5i	0.255418	+	0.442398i
$378$	35145.8	−	34101.8i	0.245975	−	0.238668i
$379$		−	203220.i		−	1.41478i	−0.706825	−	0.707388i	$-0.749873\pi$
$379$		−	203220.i		−	1.41478i	0.706825	−	0.707388i	$-0.250127\pi$
$380$	6350.92	−	191880.i	0.0439814	−	1.32881i
$381$	−64891.5			−0.447031
$382$	−11503.5	−	11855.6i	−0.0788318	−	0.0812453i
$383$	−133061.	+	76822.6i	−0.907094	+	0.523711i	−0.879495	−	0.475908i	$-0.842119\pi$
$383$	−133061.	+	76822.6i	−0.907094	+	0.523711i	−0.0275987	+	0.999619i	$0.508786\pi$
$384$	−42167.6	−	16226.0i	−0.285968	−	0.110039i
$385$	74891.2	+	129715.i	0.505254	+	0.875125i
$386$	−99679.1	−	28326.3i	−0.669005	−	0.190114i
$387$		−	139215.i		−	0.929533i
$388$	119072.	−	64039.9i	0.790948	−	0.425390i
$389$	94199.0	−	163157.i	0.622511	−	1.07822i	−0.366506	−	0.930416i	$-0.619446\pi$
$389$	94199.0	−	163157.i	0.622511	−	1.07822i	0.989017	−	0.147805i	$-0.0472207\pi$
$390$	5260.52	−	18511.6i	0.0345859	−	0.121707i
$391$		−	75855.0i		−	0.496170i
$392$	67946.0	+	74387.9i	0.442173	+	0.484095i
$393$	42026.1	−	72791.4i	0.272104	−	0.471297i
$394$	80975.5	−	78570.0i	0.521629	−	0.506133i
$395$	−230849.	−	133281.i	−1.47956	−	0.854226i
$396$	−96781.9	+	156535.i	−0.617168	+	0.998205i
$397$	14251.3	+	24684.0i	0.0904221	+	0.156616i	0.907689	−	0.419644i	$-0.137845\pi$
$397$	14251.3	+	24684.0i	0.0904221	+	0.156616i	−0.817267	+	0.576260i	$0.804512\pi$
$398$	84674.9	−	21325.8i	0.534550	−	0.134629i
$399$	−28625.3	−	83.9924i	−0.179806	−	0.000527587i
$400$	67712.5	−	102477.i	0.423203	−	0.640478i
$401$	−47479.3	−	82236.5i	−0.295267	−	0.511418i	0.679780	−	0.733416i	$-0.262075\pi$
$401$	−47479.3	−	82236.5i	−0.295267	−	0.511418i	−0.975047	+	0.221998i	$0.928742\pi$
$402$	14183.2	−	13761.8i	0.0877650	−	0.0851578i
$403$	−47354.3	−	27340.0i	−0.291575	−	0.168341i
$404$	−158373.	−	97918.6i	−0.970328	−	0.599932i
$405$	−79288.1	+	137331.i	−0.483390	+	0.837257i
$406$	154280.	−	38856.0i	0.935959	−	0.235725i
$407$			220836.i			1.33315i
$408$	9447.60	+	42939.4i	0.0567546	+	0.257950i
$409$	−62470.7	+	108202.i	−0.373447	+	0.646830i	−0.990093	−	0.140411i	$-0.955158\pi$
$409$	−62470.7	+	108202.i	−0.373447	+	0.646830i	0.616646	+	0.787241i	$0.288491\pi$
$410$	−14599.6	−	57968.2i	−0.0868504	−	0.344843i
$411$			56803.1i			0.336270i
$412$	122616.	+	3698.24i	0.722356	+	0.0217872i
$413$	−32561.2	−	56397.7i	−0.190898	−	0.330644i
$414$	−24436.3	+	85990.5i	−0.142572	+	0.501706i
$415$	249437.	−	144013.i	1.44832	−	0.836189i
$416$	−9961.75	−	52816.9i	−0.0575637	−	0.305201i
$417$	−52530.7			−0.302093
$418$	219609.	−	54624.8i	1.25689	−	0.312635i
$419$		−	304961.i		−	1.73706i	−0.495634	−	0.868532i	$-0.665064\pi$
$419$		−	304961.i		−	1.73706i	0.495634	−	0.868532i	$-0.334936\pi$
$420$	−35868.2	−	22176.5i	−0.203334	−	0.125717i
$421$	148628.	+	257432.i	0.838567	+	1.45244i	0.891093	+	0.453821i	$0.149940\pi$
$421$	148628.	+	257432.i	0.838567	+	1.45244i	−0.0525256	+	0.998620i	$0.516727\pi$
$422$	−18753.8	+	65993.9i	−0.105309	+	0.370578i
$423$	17215.5	−	9939.39i	0.0962143	−	0.0555494i
$424$	−317585.	+	69875.8i	−1.76656	+	0.388682i
$425$	−119523.			−0.661718
$426$	−12967.2	−	51486.7i	−0.0714539	−	0.283711i
$427$	66888.6	+	38618.2i	0.366857	+	0.211805i
$428$	−236026.	−	7118.83i	−1.28846	−	0.0388616i
$429$	22684.3			0.123257
$430$	−244548.	+	61590.6i	−1.32260	+	0.333102i
$431$	−125198.	−	72282.9i	−0.673971	−	0.389118i	0.123608	−	0.992331i	$-0.460553\pi$
$431$	−125198.	−	72282.9i	−0.673971	−	0.389118i	−0.797580	+	0.603213i	$0.793887\pi$
$432$	6569.03	−	108799.i	0.0351993	−	0.582988i
$433$	67072.3	−	116173.i	0.357740	−	0.619624i	−0.629843	−	0.776723i	$-0.716881\pi$
$433$	67072.3	−	116173.i	0.357740	−	0.619624i	0.987583	+	0.157099i	$0.0502141\pi$
$434$	−85992.8	+	83438.3i	−0.456544	+	0.442982i
$435$	109803.	−	63395.0i	0.580279	−	0.335024i
$436$	−9185.67	+	4940.27i	−0.0483212	+	0.0259883i
$437$	95358.0	−	54682.6i	0.499338	−	0.286343i
$438$	97470.4	−	24548.4i	0.508071	−	0.127960i
$439$	−204075.	+	117823.i	−1.05891	+	0.611364i	−0.925132	−	0.379646i	$-0.876046\pi$
$439$	−204075.	+	117823.i	−1.05891	+	0.611364i	−0.133783	+	0.991011i	$0.542712\pi$
$440$	317789.	+	100756.i	1.64147	+	0.520434i
$441$	−57769.1	+	100059.i	−0.297043	+	0.514493i
$442$	−37536.7	+	36421.6i	−0.192137	+	0.186430i
$443$	218042.	+	125887.i	1.11105	+	0.641465i	0.939101	−	0.343641i	$-0.111660\pi$
$443$	218042.	+	125887.i	1.11105	+	0.641465i	0.171949	+	0.985106i	$0.444994\pi$
$444$	−29449.9	−	54757.6i	−0.149389	−	0.277766i
$445$	−32100.8			−0.162105
$446$	−69458.2	+	244421.i	−0.349184	+	1.22877i
$447$	62288.7	+	35962.4i	0.311741	+	0.179984i
$448$	−117296.	−	10639.2i	−0.584422	−	0.0530094i
$449$	319076.			1.58271			0.791355	−	0.611357i	$-0.209376\pi$
$449$	319076.			1.58271			0.791355	+	0.611357i	$0.209376\pi$
$450$	135493.	+	38503.7i	0.669102	+	0.190142i
$451$	61023.0	−	35231.6i	0.300013	−	0.173213i
$452$	130.227	−	4317.70i	0.000637420	−	0.0211337i
$453$	3305.66	+	5725.57i	0.0161087	+	0.0279012i
$454$	−179963.	−	185473.i	−0.873117	−	0.899848i
$455$		−	50165.6i		−	0.242317i
$456$	−47168.9	+	42830.9i	−0.226843	+	0.205981i
$457$	124192.			0.594649			0.297325	−	0.954776i	$-0.403906\pi$
$457$	124192.			0.594649			0.297325	+	0.954776i	$0.403906\pi$
$458$	−214636.	+	208260.i	−1.02322	+	0.992829i
$459$	−91855.6	+	53032.8i	−0.435994	+	0.251721i
$460$	161864.	+	4882.01i	0.764951	+	0.0230719i
$461$	−57803.9	−	100119.i	−0.271991	−	0.471103i	0.697380	−	0.716701i	$-0.254349\pi$
$461$	−57803.9	−	100119.i	−0.271991	−	0.471103i	−0.969372	+	0.245599i	$0.921016\pi$
$462$	13587.7	−	47814.6i	0.0636592	−	0.224015i
$463$		−	120840.i		−	0.563699i	−0.959459	−	0.281849i	$-0.909052\pi$
$463$		−	120840.i		−	0.563699i	0.959459	−	0.281849i	$-0.0909478\pi$
$464$	195217.	−	295442.i	0.906736	−	1.37226i
$465$	−47744.0	+	82695.1i	−0.220807	+	0.382449i
$466$	18221.1	+	5177.98i	0.0839081	+	0.0238445i
$467$			323875.i			1.48506i	0.669815	+	0.742528i	$0.266374\pi$
$467$			323875.i			1.48506i	−0.669815	+	0.742528i	$0.733626\pi$
$468$	54285.3	−	29195.9i	0.247851	−	0.133300i
$469$	25757.7	−	44613.7i	0.117101	−	0.202825i
$470$	−25076.1	−	25843.8i	−0.113518	−	0.116993i
$471$	57349.3	+	33110.7i	0.258516	+	0.149254i
$472$	−138168.	−	43806.8i	−0.620190	−	0.196633i
$473$	−148630.	−	257435.i	−0.664332	−	1.15066i
$474$	21605.0	+	85783.8i	0.0961608	+	0.381811i
$475$	−86162.0	−	150253.i	−0.381881	−	0.665943i
$476$	54286.3	+	100937.i	0.239594	+	0.445489i
$477$	−186459.	−	322957.i	−0.819497	−	1.41941i
$478$	184699.	+	190354.i	0.808368	+	0.833117i
$479$	128662.	+	74282.8i	0.560761	+	0.323755i	0.753451	−	0.657504i	$-0.228388\pi$
$479$	128662.	+	74282.8i	0.560761	+	0.323755i	−0.192690	+	0.981260i	$0.561721\pi$
$480$	−92234.4	+	17396.2i	−0.400323	+	0.0755045i
$481$	36981.5	−	64053.8i	0.159843	−	0.276857i
$482$	10366.6	+	41160.9i	0.0446212	+	0.177170i
$483$		−	24145.2i		−	0.103499i
$484$	−4784.78	+	158640.i	−0.0204254	+	0.677207i
$485$	140434.	−	243238.i	0.597018	−	1.03407i
$486$	184805.	−	46544.0i	0.782423	−	0.197057i
$487$			76901.9i			0.324249i	0.986770	+	0.162125i	$0.0518347\pi$
$487$			76901.9i			0.324249i	−0.986770	+	0.162125i	$0.948165\pi$
$488$	167894.	−	36940.3i	0.705008	−	0.155117i
$489$	2580.87	+	4470.20i	0.0107932	+	0.0186943i
$490$	201324.	+	57211.0i	0.838499	+	0.238280i
$491$	−244126.	+	140946.i	−1.01263	+	0.584643i	−0.911961	−	0.410276i	$-0.865432\pi$
$491$	−244126.	+	140946.i	−1.01263	+	0.584643i	−0.100671	+	0.994920i	$0.532099\pi$
$492$	−10432.7	+	16873.7i	−0.0430988	+	0.0697077i
$493$	−344587.			−1.41777
$494$	−72845.5	−	20932.0i	−0.298503	−	0.0857744i
$495$			382320.i			1.56033i
$496$	−16072.7	+	266204.i	−0.0653321	+	1.08206i
$497$	−69202.0	−	119861.i	−0.280160	−	0.485251i
$498$	−91945.4	−	26128.5i	−0.370741	−	0.105355i
$499$	−117073.	+	67591.9i	−0.470169	+	0.271452i	−0.716310	−	0.697782i	$-0.754171\pi$
$499$	−117073.	+	67591.9i	−0.470169	+	0.271452i	0.246141	+	0.969234i	$0.420837\pi$
$500$	−2328.10	+	77188.6i	−0.00931242	+	0.308754i
$501$	134912.			0.537494
$502$	123792.	−	31177.5i	0.491229	−	0.123718i
$503$	−187283.	−	108128.i	−0.740223	−	0.427368i	0.0819274	−	0.996638i	$-0.473892\pi$
$503$	−187283.	−	108128.i	−0.740223	−	0.427368i	−0.822150	+	0.569270i	$0.807226\pi$
$504$	−29023.5	−	131912.i	−0.114259	−	0.519306i
$505$	−386810.			−1.51675
$506$	46618.7	+	185102.i	0.182079	+	0.722952i
$507$	61630.2	+	35582.2i	0.239761	+	0.138426i
$508$	−197994.	+	320235.i	−0.767229	+	1.24091i
$509$	87635.9	−	151790.i	0.338257	−	0.585878i	−0.645848	−	0.763466i	$-0.723496\pi$
$509$	87635.9	−	151790.i	0.338257	−	0.585878i	0.984105	+	0.177588i	$0.0568295\pi$
$510$	63603.2	+	65550.5i	0.244534	+	0.252020i
$511$	226912.	−	131008.i	0.868990	−	0.501712i
$512$	−208734.	+	158586.i	−0.796257	+	0.604958i
$513$	−132885.	−	77242.1i	−0.504942	−	0.293507i
$514$	5515.22	+	21898.4i	0.0208755	+	0.0828871i
$515$	220696.	−	127419.i	0.832108	−	0.480418i
$516$	71184.6	+	44011.9i	0.267354	+	0.165299i
$517$	21223.2	−	36759.6i	0.0794016	−	0.137528i
$518$	−112863.	−	116318.i	−0.420621	−	0.433499i
$519$	28617.3	+	16522.2i	0.106241	+	0.0613385i
$520$	−75302.6	−	82442.0i	−0.278486	−	0.304889i
$521$	−53699.6			−0.197831			−0.0989157	−	0.995096i	$-0.531537\pi$
$521$	−53699.6			−0.197831			−0.0989157	+	0.995096i	$0.531537\pi$
$522$	390630.	+	111007.i	1.43359	+	0.407389i
$523$	287581.	+	166035.i	1.05137	+	0.607010i	0.923033	−	0.384720i	$-0.125702\pi$
$523$	287581.	+	166035.i	1.05137	+	0.607010i	0.128339	+	0.991730i	$0.459035\pi$
$524$	−230992.	−	429494.i	−0.841268	−	1.56421i
$525$	−38045.1			−0.138032
$526$	−132288.	+	465519.i	−0.478135	+	1.68254i
$527$	224747.	−	129758.i	0.809231	−	0.467210i
$528$	−49443.6	−	98974.5i	−0.177354	−	0.355022i
$529$	−93560.6	−	162052.i	−0.334335	−	0.579085i
$530$	−484821.	+	470418.i	−1.72595	+	1.67468i
$531$		−	166225.i		−	0.589532i
$532$	−87754.9	+	141008.i	−0.310062	+	0.498218i
$533$	−23599.8			−0.0830717
$534$	7418.50	+	7645.62i	0.0260156	+	0.0268121i
$535$	−424822.	+	245271.i	−1.48423	+	0.856918i
$536$	−24638.6	−	111982.i	−0.0857603	−	0.389781i
$537$	47410.1	+	82116.7i	0.164408	+	0.284763i
$538$	132314.	+	37600.1i	0.457130	+	0.129905i
$539$			246704.i			0.849179i
$540$	−107253.	−	199420.i	−0.367807	−	0.683881i
$541$	122157.	−	211583.i	0.417373	−	0.722912i	−0.578301	−	0.815824i	$-0.696284\pi$
$541$	122157.	−	211583.i	0.417373	−	0.722912i	0.995674	+	0.0929115i	$0.0296174\pi$
$542$	−68997.1	+	242798.i	−0.234872	+	0.826508i
$543$			82644.9i			0.280296i
$544$	240729.	+	84391.5i	0.813448	+	0.285168i
$545$	−10833.5	+	18764.2i	−0.0364735	+	0.0631739i
$546$	−11948.2	+	11593.3i	−0.0400791	+	0.0388885i
$547$	−15475.8	−	8934.95i	−0.0517223	−	0.0298619i	0.473916	−	0.880570i	$-0.342840\pi$
$547$	−15475.8	−	8934.95i	−0.0517223	−	0.0298619i	−0.525638	+	0.850708i	$0.676173\pi$
$548$	280319.	+	173315.i	0.933451	+	0.577132i
$549$	98572.8	+	170733.i	0.327049	+	0.566465i
$550$	291660.	−	73455.9i	0.964166	−	0.242829i
$551$	−248407.	−	433184.i	−0.818202	−	1.42682i
$552$	−36244.0	−	39680.2i	−0.118948	−	0.130225i
$553$	115300.	+	199705.i	0.377032	+	0.653039i
$554$	384560.	−	373136.i	1.25298	−	1.21576i
$555$	−111857.	−	64580.9i	−0.363144	−	0.209661i
$556$	−160279.	+	259235.i	−0.518476	+	0.838580i
$557$	−177197.	+	306914.i	−0.571144	+	0.989250i	0.425305	+	0.905050i	$0.360167\pi$
$557$	−177197.	+	306914.i	−0.571144	+	0.989250i	−0.996449	+	0.0842002i	$0.973166\pi$
$558$	−296578.	+	74694.5i	−0.952512	+	0.239894i
$559$			99559.5i			0.318610i
$560$	−218879.	+	109343.i	−0.697956	+	0.348670i
$561$	−53830.6	+	93237.4i	−0.171042	+	0.296254i
$562$	−81495.0	−	323580.i	−0.258023	−	1.02449i
$563$		−	569773.i		−	1.79757i	−0.438393	−	0.898783i	$-0.644452\pi$
$563$		−	569773.i		−	1.79757i	0.438393	−	0.898783i	$-0.355548\pi$
$564$	−360.277	+	11945.0i	−0.00113261	+	0.0375517i
$565$	−4486.84	−	7771.43i	−0.0140554	−	0.0243447i
$566$	16208.2	−	57036.2i	0.0505945	−	0.178040i
$567$	118804.	−	68591.4i	0.369543	−	0.213355i
$568$	−293648.	−	93102.1i	−0.910187	−	0.288578i
$569$	587884.			1.81580			0.907898	−	0.419190i	$-0.137686\pi$
$569$	587884.			1.81580			0.907898	+	0.419190i	$0.137686\pi$
$570$	−36553.7	+	127210.i	−0.112508	+	0.391537i
$571$			425660.i			1.30554i	0.757556	+	0.652770i	$0.226393\pi$
$571$			425660.i			1.30554i	−0.757556	+	0.652770i	$0.773607\pi$
$572$	69213.3	−	111945.i	0.211543	−	0.342148i
$573$	5694.34	+	9862.89i	0.0173434	+	0.0300397i
$574$	−14136.0	+	49744.2i	−0.0429046	+	0.150980i
$575$	126523.	−	73048.2i	0.382679	−	0.220940i
$576$	−245708.	−	173217.i	−0.740583	−	0.522091i
$577$	−68230.5			−0.204940			−0.102470	−	0.994736i	$-0.532675\pi$
$577$	−68230.5			−0.204940			−0.102470	+	0.994736i	$0.532675\pi$
$578$	20967.7	+	83253.3i	0.0627619	+	0.249199i
$579$	61870.2	+	35720.8i	0.184554	+	0.106553i
$580$	22177.5	−	735299.i	0.0659261	−	2.18579i
$581$	−249168.			−0.738142
$582$	−90387.6	+	22764.5i	−0.266847	+	0.0672067i
$583$	−689597.	−	398139.i	−2.02889	−	1.17138i
$584$	176253.	−	555910.i	0.516786	−	1.62997i
$585$	64023.8	−	110893.i	0.187081	−	0.324034i
$586$	−43302.7	+	42016.3i	−0.126101	+	0.122355i
$587$	406224.	−	234534.i	1.17893	−	0.680658i	0.223166	−	0.974780i	$-0.428361\pi$
$587$	406224.	−	234534.i	1.17893	−	0.680658i	0.955768	+	0.294123i	$0.0950274\pi$
$588$	−32899.7	−	61171.9i	−0.0951562	−	0.176928i
$589$	325136.	+	188992.i	0.937205	+	0.544768i
$590$	−291994.	+	73540.0i	−0.838823	+	0.211261i
$591$	−67364.8	+	38893.1i	−0.192867	+	0.111352i
$592$	−360081.	−	21740.8i	−1.02744	−	0.0620343i
$593$	52738.2	−	91345.3i	0.149974	−	0.259763i	−0.781244	−	0.624226i	$-0.785414\pi$
$593$	52738.2	−	91345.3i	0.149974	−	0.259763i	0.931218	+	0.364464i	$0.118748\pi$
$594$	191554.	−	185863.i	0.542897	−	0.526769i
$595$	206192.	+	119045.i	0.582421	+	0.336261i
$596$	367525.	−	197663.i	1.03465	−	0.556460i
$597$	−60199.4			−0.168906
$598$	17475.6	−	61495.9i	0.0488685	−	0.171966i
$599$	164584.	+	95022.8i	0.458706	+	0.264834i	0.711500	−	0.702686i	$-0.248016\pi$
$599$	164584.	+	95022.8i	0.458706	+	0.264834i	−0.252794	+	0.967520i	$0.581349\pi$
$600$	−62523.1	+	57108.7i	−0.173675	+	0.158635i
$601$	33085.5			0.0915986			0.0457993	−	0.998951i	$-0.485417\pi$
$601$	33085.5			0.0915986			0.0457993	+	0.998951i	$0.485417\pi$
$602$	209854.	+	59635.2i	0.579061	+	0.164554i
$603$	113876.	−	65746.6i	0.313184	−	0.180817i
$604$	38341.4	+	1156.42i	0.105098	+	0.00316988i
$605$	164854.	+	285536.i	0.450390	+	0.780099i
$606$	89391.9	+	92128.8i	0.243418	+	0.250871i
$607$		−	406303.i		−	1.10274i	−0.834261	−	0.551370i	$-0.814105\pi$
$607$		−	406303.i		−	1.10274i	0.834261	−	0.551370i	$-0.185895\pi$
$608$	67447.8	+	363459.i	0.182457	+	0.983214i
$609$	−109685.			−0.295741
$610$	256303.	−	248690.i	0.688803	−	0.668341i
$611$	−12311.6	+	7108.13i	−0.0329787	+	0.0190403i
$612$	−8819.37	+	292407.i	−0.0235470	+	0.780702i
$613$	−159656.	−	276532.i	−0.424878	−	0.735909i	0.571531	−	0.820580i	$-0.306350\pi$
$613$	−159656.	−	276532.i	−0.424878	−	0.735909i	−0.996409	+	0.0846707i	$0.973016\pi$
$614$	150789.	−	530623.i	0.399976	−	1.40750i
$615$			41212.4i			0.108963i
$616$	−194503.	−	212944.i	−0.512584	−	0.561182i
$617$	−94279.0	+	163296.i	−0.247654	+	0.428949i	−0.962874	−	0.269950i	$-0.912993\pi$
$617$	−94279.0	+	163296.i	−0.247654	+	0.428949i	0.715221	+	0.698899i	$0.246326\pi$
$618$	−81351.0	−	23117.9i	−0.213003	−	0.0605300i
$619$			590884.i			1.54213i	0.636756	+	0.771065i	$0.280276\pi$
$619$			590884.i			1.54213i	−0.636756	+	0.771065i	$0.719724\pi$
$620$	262420.	+	487929.i	0.682673	+	1.26933i
$621$	64823.6	−	112278.i	0.168093	−	0.291146i
$622$	211811.	+	218296.i	0.547479	+	0.564240i
$623$	24049.6	+	13885.0i	0.0619629	+	0.0357743i
$624$	−2233.22	+	36987.6i	−0.00573538	+	0.0949921i
$625$	230147.	+	398627.i	0.589177	+	1.02048i
$626$	5553.52	+	22050.5i	0.0141716	+	0.0562691i
$627$	−156015.	−	457.779i	−0.396855	−	0.00116445i
$628$	338381.	−	181989.i	0.857998	−	0.461451i
$629$	175517.	+	304004.i	0.443626	+	0.768384i
$630$	−195393.	−	201375.i	−0.492297	−	0.507369i
$631$	−103217.	−	59592.4i	−0.259235	−	0.149669i	0.364751	−	0.931105i	$-0.381154\pi$
$631$	−103217.	−	59592.4i	−0.259235	−	0.149669i	−0.623985	+	0.781436i	$0.714488\pi$
$632$	489257.	+	155120.i	1.22491	+	0.388360i
$633$	23649.4	−	40962.0i	0.0590219	−	0.102229i
$634$	−51344.3	−	203865.i	−0.127736	−	0.507182i
$635$			782141.i			1.93971i
$636$	224084.	+	6758.67i	0.553984	+	0.0167089i
$637$	41313.5	−	71557.0i	0.101815	−	0.176349i
$638$	840863.	−	211775.i	2.06578	−	0.520276i
$639$		−	353276.i		−	0.865193i
$640$	−195572.	+	508249.i	−0.477472	+	1.24084i
$641$	90305.1	+	156413.i	0.219784	+	0.380677i	0.954742	−	0.297436i	$-0.0961314\pi$
$641$	90305.1	+	156413.i	0.219784	+	0.380677i	−0.734958	+	0.678113i	$0.762798\pi$
$642$	156594.	+	44500.1i	0.379932	+	0.107967i
$643$	583091.	−	336648.i	1.41031	−	0.814243i	0.414892	−	0.909871i	$-0.363819\pi$
$643$	583091.	−	336648.i	1.41031	−	0.814243i	0.995417	+	0.0956280i	$0.0304859\pi$
$644$	−119155.	−	73670.9i	−0.287303	−	0.177633i
$645$	173861.			0.417910
$646$	258900.	−	249739.i	0.620394	−	0.598440i
$647$			291577.i			0.696539i	0.937394	+	0.348269i	$0.113231\pi$
$647$			291577.i			0.696539i	−0.937394	+	0.348269i	$0.886769\pi$
$648$	92280.6	−	291057.i	0.219766	−	0.693152i
$649$	−177467.	−	307381.i	−0.421335	−	0.729774i
$650$	−96897.6	−	27535.8i	−0.229343	−	0.0651735i
$651$	71538.7	−	41302.9i	0.168803	−	0.0974583i
$652$	29934.7	+	902.869i	0.0704174	+	0.00212388i
$653$	−360314.			−0.844997			−0.422498	−	0.906364i	$-0.638847\pi$
$653$	−360314.			−0.844997			−0.422498	+	0.906364i	$0.638847\pi$
$654$	6972.82	−	1756.14i	0.0163025	−	0.00410585i
$655$	−877359.	−	506543.i	−2.04501	−	1.18068i
$656$	51439.0	+	102969.i	0.119532	+	0.239275i
$657$	668793.			1.54939
$658$	7608.15	+	30208.5i	0.0175722	+	0.0697714i
$659$	−474220.	−	273791.i	−1.09197	−	0.630447i	−0.157867	−	0.987460i	$-0.550462\pi$
$659$	−474220.	−	273791.i	−1.09197	−	0.630447i	−0.934099	+	0.357013i	$0.883795\pi$
$660$	−195491.	−	120868.i	−0.448785	−	0.277474i
$661$	−355909.	+	616453.i	−0.814584	+	1.41090i	0.0950415	+	0.995473i	$0.469702\pi$
$661$	−355909.	+	616453.i	−0.814584	+	1.41090i	−0.909626	+	0.415428i	$0.863632\pi$
$662$	−557964.	−	575047.i	−1.27318	−	1.31216i
$663$	31227.4	−	18029.1i	0.0710409	−	0.0410155i
$664$	−409482.	+	374021.i	−0.928750	+	0.848321i
$665$	−1012.36	+	345023.i	−0.00228925	+	0.780197i
$666$	−101035.	−	401166.i	−0.227785	−	0.904431i
$667$	364769.	−	210600.i	0.819911	−	0.473376i
$668$	411636.	−	665778.i	0.922488	−	1.49203i
$669$	87590.2	−	151711.i	0.195706	−	0.338972i
$670$	−165872.	−	170951.i	−0.369508	−	0.380821i
$671$	364560.	+	210479.i	0.809699	+	0.467480i
$672$	76625.8	+	26862.5i	0.169682	+	0.0594850i
$673$	−765884.			−1.69096			−0.845479	−	0.534009i	$-0.820685\pi$
$673$	−765884.			−1.69096			−0.845479	+	0.534009i	$0.820685\pi$
$674$	−419937.	−	119335.i	−0.924409	−	0.262694i
$675$	−176913.	−	102141.i	−0.388287	−	0.224178i
$676$	363639.	−	195574.i	0.795751	−	0.427974i
$677$	−746496.			−1.62873			−0.814367	−	0.580350i	$-0.802916\pi$
$677$	−746496.			−1.62873			−0.814367	+	0.580350i	$0.802916\pi$
$678$	−814.057	+	2864.64i	−0.00177091	+	0.00623175i
$679$	−210423.	+	121488.i	−0.456408	+	0.263507i
$680$	517550.	−	113872.i	1.11927	−	0.246264i
$681$	89083.9	+	154298.i	0.192090	+	0.332710i
$682$	−468683.	+	454760.i	−1.00765	+	0.977717i
$683$			445604.i			0.955229i	0.878570	+	0.477614i	$0.158498\pi$
$683$			445604.i			0.955229i	−0.878570	+	0.477614i	$0.841502\pi$
$684$	−373946.	+	199704.i	−0.799275	+	0.426850i
$685$	684650.			1.45911
$686$	−318389.	−	328137.i	−0.676566	−	0.697279i
$687$	178559.	−	103091.i	0.378327	−	0.218427i
$688$	434391.	−	217004.i	0.917706	−	0.458448i
$689$	133346.	+	230962.i	0.280893	+	0.486521i
$690$	−107391.	−	30517.6i	−0.225563	−	0.0640992i
$691$		−	346370.i		−	0.725411i	−0.931904	−	0.362706i	$-0.881853\pi$
$691$		−	346370.i		−	0.725411i	0.931904	−	0.362706i	$-0.118147\pi$
$692$	168852.	−	90812.4i	0.352609	−	0.189641i
$693$	165371.	−	286430.i	0.344344	−	0.596421i
$694$	−97317.6	+	342457.i	−0.202056	+	0.711029i
$695$			633156.i			1.31081i
$696$	−180256.	+	164646.i	−0.372109	+	0.339885i
$697$	56003.1	−	97000.2i	0.115278	−	0.199667i
$698$	−676939.	+	656829.i	−1.38944	+	1.34816i
$699$	−11309.8	−	6529.69i	−0.0231472	−	0.0133640i
$700$	−116081.	+	187750.i	−0.236901	+	0.383162i
$701$	390684.	+	676684.i	0.795040	+	1.37705i	0.922814	+	0.385247i	$0.125884\pi$
$701$	390684.	+	676684.i	0.795040	+	1.37705i	−0.127773	+	0.991803i	$0.540783\pi$
$702$	−86685.4	+	21832.1i	−0.175902	+	0.0443018i
$703$	−255639.	+	439795.i	−0.517270	+	0.889897i
$704$	−639292.	−	57986.3i	−1.28989	−	0.116998i
$705$	12413.0	+	21499.9i	0.0249745	+	0.0432571i
$706$	99215.6	−	96268.2i	0.199054	−	0.193141i
$707$	289794.	+	167313.i	0.579764	+	0.334727i
$708$	84995.4	+	52550.8i	0.169562	+	0.104837i
$709$	−128840.	+	223158.i	−0.256307	+	0.443936i	−0.965250	−	0.261330i	$-0.915839\pi$
$709$	−128840.	+	223158.i	−0.256307	+	0.443936i	0.708943	+	0.705266i	$0.249172\pi$
$710$	−620572.	+	156294.i	−1.23105	+	0.310046i
$711$			588605.i			1.16435i
$712$	60365.6	−	13281.8i	0.119077	−	0.0261996i
$713$	−158607.	+	274715.i	−0.311991	+	0.540385i
$714$	−19297.4	−	76621.1i	−0.0378531	−	0.150298i
$715$		−	273415.i		−	0.534823i
$716$	549896.	+	16585.5i	1.07264	+	0.0323522i
$717$	−91428.2	−	158358.i	−0.177845	−	0.308037i
$718$	−107838.	+	379478.i	−0.209181	+	0.736101i
$719$	−292091.	+	168639.i	−0.565016	+	0.326212i	−0.755156	−	0.655545i	$-0.772439\pi$
$719$	−292091.	+	168639.i	−0.565016	+	0.326212i	0.190141	+	0.981757i	$0.439106\pi$
$720$	−623387.	−	37638.5i	−1.20252	−	0.0726052i
$721$	−220458.			−0.424087
$722$	500586.	+	145434.i	0.960294	+	0.278992i
$723$		−	29263.3i		−	0.0559818i
$724$	407846.	+	252162.i	0.778072	+	0.481064i
$725$	−331837.	−	574758.i	−0.631318	−	1.09348i
$726$	29909.8	−	105252.i	0.0567467	−	0.199690i
$727$	−340136.	+	196377.i	−0.643551	+	0.371555i	−0.785981	−	0.618250i	$-0.787842\pi$
$727$	−340136.	+	196377.i	−0.643551	+	0.371555i	0.142430	+	0.989805i	$0.454508\pi$
$728$	20756.1	+	94336.6i	0.0391637	+	0.177999i
$729$	255054.			0.479929
$730$	−295883.	−	1.17482e6i	−0.555231	−	2.20457i
$731$	−409211.	−	236258.i	−0.765795	−	0.442132i
$732$	−118464.	−	3573.01i	−0.221087	−	0.00666826i
$733$	−66453.3			−0.123683			−0.0618413	−	0.998086i	$-0.519697\pi$
$733$	−66453.3			−0.123683			−0.0618413	+	0.998086i	$0.519697\pi$
$734$	−792407.	+	199571.i	−1.47081	+	0.370430i
$735$	−124960.	−	72145.9i	−0.231312	−	0.133548i
$736$	−306405.	+	57790.7i	−0.565640	+	0.106685i
$737$	140386.	−	243156.i	0.258457	−	0.447661i
$738$	−94734.2	+	91919.9i	−0.173938	+	0.168771i
$739$	858977.	−	495930.i	1.57287	−	0.908096i	0.577053	−	0.816706i	$-0.304202\pi$
$739$	858977.	−	495930.i	1.57287	−	0.908096i	0.995815	−	0.0913896i	$-0.0291309\pi$
$740$	−659997.	+	354962.i	−1.20525	+	0.648214i
$741$	45175.9	+	26259.3i	0.0822754	+	0.0478241i
$742$	566700.	−	142726.i	1.02931	−	0.259236i
$743$	−239997.	+	138562.i	−0.434738	+	0.250996i	−0.701363	−	0.712804i	$-0.747425\pi$
$743$	−239997.	+	138562.i	−0.434738	+	0.250996i	0.266625	+	0.963800i	$0.414091\pi$
$744$	55567.5	−	175263.i	0.100387	−	0.316624i
$745$	433457.	−	750770.i	0.780968	−	1.35268i
$746$	81076.5	−	78668.0i	0.145686	−	0.141358i
$747$	−550793.	−	318001.i	−0.987069	−	0.569885i
$748$	295874.	+	550132.i	0.528815	+	0.983250i
$749$	424364.			0.756441
$750$	14553.1	−	51211.8i	0.0258721	−	0.0910432i
$751$	225785.	+	130357.i	0.400328	+	0.231129i	0.686625	−	0.727011i	$-0.259091\pi$
$751$	225785.	+	130357.i	0.400328	+	0.231129i	−0.286298	+	0.958141i	$0.592425\pi$
$752$	57848.6	+	38224.1i	0.102296	+	0.0675930i
$753$	−88009.4			−0.155217
$754$	−279358.	−	79386.4i	−0.491381	−	0.139638i
$755$	69010.6	−	39843.3i	0.121066	−	0.0698975i
$756$	−5905.42	+	195795.i	−0.0103325	+	0.342577i
$757$	−281034.	−	486766.i	−0.490420	−	0.849432i	0.509520	−	0.860459i	$-0.329823\pi$
$757$	−281034.	−	486766.i	−0.490420	−	0.849432i	−0.999939	+	0.0110275i	$0.996490\pi$
$758$	566062.	+	583393.i	0.985203	+	1.01537i
$759$		−	131598.i		−	0.228436i
$760$	516243.	+	568529.i	0.893773	+	0.984295i
$761$	−990243.			−1.70991			−0.854953	−	0.518705i	$-0.826414\pi$
$761$	−990243.			−1.70991			−0.854953	+	0.518705i	$0.826414\pi$
$762$	186287.	−	180753.i	0.320828	−	0.311298i
$763$	16232.8	−	9372.00i	0.0278833	−	0.0160984i
$764$	66047.0	+	1992.06i	0.113153	+	0.00341284i
$765$	303862.	+	526304.i	0.519222	+	0.899319i
$766$	167997.	−	591174.i	0.286314	−	1.00753i
$767$			118875.i			0.202070i
$768$	166249.	−	70875.9i	0.281863	−	0.120164i
$769$	−390045.	+	675577.i	−0.659571	+	1.14241i	0.321156	+	0.947026i	$0.395929\pi$
$769$	−390045.	+	675577.i	−0.659571	+	1.14241i	−0.980727	+	0.195384i	$0.937405\pi$
$770$	−576311.	−	163773.i	−0.972021	−	0.276224i
$771$		−	15568.6i		−	0.0261904i
$772$	365055.	−	196335.i	0.612525	−	0.329430i
$773$	10270.9	−	17789.7i	0.0171890	−	0.0297721i	−0.857303	−	0.514812i	$-0.827862\pi$
$773$	10270.9	−	17789.7i	0.0171890	−	0.0297721i	0.874492	+	0.485040i	$0.161195\pi$
$774$	387779.	+	399652.i	0.647296	+	0.667113i
$775$	432862.	+	249913.i	0.720686	+	0.416088i
$776$	−163446.	+	515515.i	−0.271425	+	0.856086i
$777$	55868.4	+	96766.9i	0.0925388	+	0.160282i
$778$	184048.	+	730771.i	0.304069	+	1.20732i
$779$	162312.	+	476.254i	0.267470	+	0.000784809i
$780$	36461.8	+	67795.0i	0.0599306	+	0.111432i
$781$	−377168.	−	653275.i	−0.618348	−	1.07101i
$782$	211291.	+	217760.i	0.345516	+	0.356095i
$783$	−510045.	−	294475.i	−0.831927	−	0.480313i
$784$	−402261.	−	24287.5i	−0.654449	−	0.0395139i
$785$	399085.	−	691235.i	0.647628	−	1.12172i
$786$	82111.6	+	326028.i	0.132911	+	0.527727i
$787$			409678.i			0.661444i	0.943728	+	0.330722i	$0.107292\pi$
$787$			409678.i			0.661444i	−0.943728	+	0.330722i	$0.892708\pi$
$788$	−13606.0	+	451109.i	−0.0219118	+	0.726489i
$789$	166822.	−	288944.i	0.267978	−	0.464152i
$790$	1.03396e6	−	260407.i	1.65672	−	0.417251i
$791$			7763.05i			0.0124074i
$792$	−158186.	−	718954.i	−0.252183	−	1.14617i
$793$	−70494.1	−	122099.i	−0.112100	−	0.194163i
$794$	−109669.	−	31165.0i	−0.173957	−	0.0494340i
$795$	403330.	−	232862.i	0.638155	−	0.368439i
$796$	−183678.	+	297080.i	−0.289888	+	0.468864i
$797$	−1.17596e6			−1.85129			−0.925647	−	0.378388i	$-0.876478\pi$
$797$	−1.17596e6			−1.85129			−0.925647	+	0.378388i	$0.876478\pi$
$798$	82410.0	−	79493.8i	0.129412	−	0.124832i
$799$		−	67471.4i		−	0.105688i
$800$	91059.5	+	482795.i	0.142280	+	0.754367i
$801$	35441.6	+	61386.6i	0.0552393	+	0.0956772i
$802$	365368.	+	103828.i	0.568044	+	0.161423i
$803$	1.23673e6	−	714024.i	1.91797	−	1.10734i
$804$	−2383.15	+	79013.5i	−0.00368671	+	0.122233i
$805$	−291024.			−0.449094
$806$	212097.	−	53417.6i	0.326486	−	0.0822269i
$807$	−82126.2	−	47415.6i	−0.126106	−	0.0728071i
$808$	727398.	−	160043.i	1.11416	−	0.245140i
$809$	994465.			1.51947			0.759736	−	0.650232i	$-0.225328\pi$
$809$	994465.			1.51947			0.759736	+	0.650232i	$0.225328\pi$
$810$	−154915.	−	615097.i	−0.236115	−	0.937505i
$811$	713602.	+	411998.i	1.08496	+	0.626403i	0.932231	−	0.361865i	$-0.117860\pi$
$811$	713602.	+	411998.i	1.08496	+	0.626403i	0.152731	+	0.988268i	$0.451193\pi$
$812$	−334666.	+	541287.i	−0.507573	+	0.820947i
$813$	87008.7	−	150703.i	0.131638	−	0.228004i
$814$	−615130.	−	633963.i	−0.928364	−	0.956787i
$815$	53879.5	−	31107.4i	0.0811164	−	0.0468326i
$816$	−146728.	−	96952.0i	−0.220360	−	0.145605i
$817$	2009.16	−	684738.i	0.00301002	−	1.02584i
$818$	−122057.	−	484631.i	−0.182413	−	0.724277i
$819$	−95932.1	+	55386.4i	−0.143020	+	0.0825725i
$820$	203380.	+	125745.i	0.302469	+	0.187010i
$821$	284611.	−	492961.i	0.422246	−	0.731352i	−0.573913	−	0.818916i	$-0.694575\pi$
$821$	284611.	−	492961.i	0.422246	−	0.731352i	0.996159	+	0.0875648i	$0.0279085\pi$
$822$	−158223.	−	163067.i	−0.234167	−	0.241336i
$823$	71888.6	+	41504.9i	0.106135	+	0.0612773i	0.552128	−	0.833759i	$-0.313816\pi$
$823$	71888.6	+	41504.9i	0.106135	+	0.0612773i	−0.445993	+	0.895037i	$0.647149\pi$
$824$	−362300.	+	330925.i	−0.533597	+	0.487388i
$825$	−207355.			−0.304654
$826$	250569.	+	71205.2i	0.367254	+	0.104364i
$827$	627548.	+	362315.i	0.917564	+	0.529756i	0.882857	−	0.469642i	$-0.155617\pi$
$827$	627548.	+	362315.i	0.917564	+	0.529756i	0.0347067	+	0.999398i	$0.488950\pi$
$828$	−169373.	−	314923.i	−0.247049	−	0.459350i
$829$	60348.9			0.0878132			0.0439066	−	0.999036i	$-0.486020\pi$
$829$	60348.9			0.0878132			0.0439066	+	0.999036i	$0.486020\pi$
$830$	−314929.	+	1.10822e6i	−0.457147	+	1.60868i
$831$	−319921.	+	184707.i	−0.463277	+	0.267473i
$832$	175717.	+	123876.i	0.253845	+	0.178953i
$833$	196077.	+	339615.i	0.282576	+	0.489437i
$834$	150802.	−	146323.i	0.216808	−	0.210368i
$835$		−	1.62610e6i		−	2.33224i
$836$	−478286.	+	768527.i	−0.684345	+	1.09963i
$837$	443550.			0.633128
$838$	849457.	+	875464.i	1.20963	+	1.24667i
$839$	−940359.	+	542917.i	−1.33589	+	0.771275i	−0.986195	−	0.165589i	$-0.947047\pi$
$839$	−940359.	+	542917.i	−1.33589	+	0.771275i	−0.349693	+	0.936864i	$0.613714\pi$
$840$	164740.	−	36246.5i	0.233476	−	0.0513697i
$841$	−603052.	−	1.04452e6i	−0.852635	−	1.47681i
$842$	−1.14374e6	−	325022.i	−1.61326	−	0.458447i
$843$			230048.i			0.323716i
$844$	−129986.	−	241690.i	−0.182479	−	0.339292i
$845$	428875.	−	742833.i	0.600644	−	1.04035i
$846$	−21735.6	+	76486.7i	−0.0303690	+	0.106867i
$847$		−	285228.i		−	0.397580i
$848$	717070.	−	1.08522e6i	0.997172	−	1.50913i
$849$	−20439.4	+	35402.0i	−0.0283565	+	0.0491149i
$850$	343120.	−	332927.i	0.474906	−	0.460798i
$851$	−371593.	−	214539.i	−0.513108	−	0.296243i
$852$	180640.	+	111686.i	0.248848	+	0.153857i
$853$	48056.3	+	83236.0i	0.0660469	+	0.114397i	0.897158	−	0.441710i	$-0.145628\pi$
$853$	48056.3	+	83236.0i	0.0660469	+	0.114397i	−0.831111	+	0.556107i	$0.812295\pi$
$854$	−299590.	+	75453.0i	−0.410782	+	0.103457i
$855$	−442573.	+	761391.i	−0.605414	+	1.04154i
$856$	697399.	−	637005.i	0.951773	−	0.869351i
$857$	503671.	+	872385.i	0.685781	+	1.18781i	0.973191	+	0.230000i	$0.0738727\pi$
$857$	503671.	+	872385.i	0.685781	+	1.18781i	−0.287409	+	0.957808i	$0.592794\pi$
$858$	−65120.8	+	63186.3i	−0.0884597	+	0.0858319i
$859$	53419.3	+	30841.6i	0.0723955	+	0.0417976i	0.535761	−	0.844370i	$-0.320025\pi$
$859$	53419.3	+	30841.6i	0.0723955	+	0.0417976i	−0.463365	+	0.886167i	$0.653358\pi$
$860$	530478.	−	857992.i	0.717249	−	1.16008i
$861$	17826.2	−	30875.9i	0.0240466	−	0.0416499i
$862$	560752.	−	141228.i	0.754669	−	0.190067i
$863$		−	380618.i		−	0.511056i	−0.966802	−	0.255528i	$-0.917751\pi$
$863$		−	380618.i		−	0.511056i	0.966802	−	0.255528i	$-0.0822493\pi$
$864$	284199.	+	330633.i	0.380711	+	0.442914i
$865$	199143.	−	344926.i	0.266154	−	0.460992i
$866$	131047.	+	520330.i	0.174740	+	0.693814i
$867$		−	59188.8i		−	0.0787411i
$868$	14449.1	−	479060.i	0.0191779	−	0.635844i
$869$	628413.	+	1.08844e6i	0.832157	+	1.44134i
$870$	−138633.	+	487844.i	−0.183159	+	0.644529i
$871$	−81438.5	+	47018.5i	−0.107348	+	0.0619773i
$872$	12608.8	−	39768.6i	0.0165821	−	0.0523007i
$873$	−620195.			−0.813766
$874$	−121432.	+	422596.i	−0.158969	+	0.553226i
$875$		−	138782.i		−	0.181266i
$876$	−211434.	+	341972.i	−0.275529	+	0.445639i
$877$	−22993.1	−	39825.1i	−0.0298949	−	0.0517795i	0.850691	−	0.525666i	$-0.176184\pi$
$877$	−22993.1	−	39825.1i	−0.0298949	−	0.0517795i	−0.880586	+	0.473887i	$0.842851\pi$
$878$	257656.	−	906683.i	0.334235	−	1.17616i
$879$	36024.2	−	20798.6i	0.0466247	−	0.0269188i
$880$	−1.19295e6	+	595946.i	−1.54048	+	0.769559i
$881$	−57124.3			−0.0735985			−0.0367993	−	0.999323i	$-0.511716\pi$
$881$	−57124.3			−0.0735985			−0.0367993	+	0.999323i	$0.511716\pi$
$882$	−112871.	−	448158.i	−0.145092	−	0.576095i
$883$	−766379.	−	442469.i	−0.982929	−	0.567494i	−0.0797758	−	0.996813i	$-0.525420\pi$
$883$	−766379.	−	442469.i	−0.982929	−	0.567494i	−0.903153	+	0.429319i	$0.858754\pi$
$884$	6307.15	−	209114.i	0.00807103	−	0.267596i
$885$	207593.			0.265049
$886$	−976598.	+	245961.i	−1.24408	+	0.313327i
$887$	−295744.	−	170748.i	−0.375896	−	0.217024i	0.300135	−	0.953897i	$-0.402968\pi$
$887$	−295744.	−	170748.i	−0.375896	−	0.217024i	−0.676031	+	0.736873i	$0.736302\pi$
$888$	237069.	+	75163.4i	0.300641	+	0.0953193i
$889$	338312.	−	585973.i	0.428069	−	0.741437i
$890$	92153.1	−	89415.6i	0.116340	−	0.112884i
$891$	647511.	−	373841.i	0.815627	−	0.470902i
$892$	−481430.	−	895144.i	−0.605067	−	1.12503i
$893$	84819.0	−	48639.0i	0.106363	−	0.0609932i
$894$	−278987.	+	70264.2i	−0.349067	+	0.0879142i
$895$	989757.	−	571437.i	1.23561	−	0.713382i
$896$	366362.	−	296181.i	0.456346	−	0.368928i
$897$	−22037.5	+	38170.1i	−0.0273891	+	0.0474393i
$898$	−915986.	+	888775.i	−1.13589	+	1.10215i
$899$	1.24795e6	+	720505.i	1.54411	+	0.891492i
$900$	−496217.	+	266877.i	−0.612614	+	0.329478i
$901$	−1.26574e6			−1.55917
$902$	−77044.9	+	271118.i	−0.0946958	+	0.333231i
$903$	−130255.	−	75202.8i	−0.159742	−	0.0922271i
$904$	11653.0	+	12757.8i	0.0142593	+	0.0156113i
$905$	996123.			1.21623
$906$	−25438.1	−	7228.85i	−0.0309905	−	0.00880670i
$907$	−1.00650e6	+	581106.i	−1.22349	+	0.706384i	−0.965661	−	0.259806i	$-0.916341\pi$
$907$	−1.00650e6	+	581106.i	−1.22349	+	0.706384i	−0.257832	+	0.966190i	$0.583008\pi$
$908$	1.03326e6	+	31164.4i	1.25325	+	0.0377995i
$909$	427066.	+	739700.i	0.516853	+	0.895216i
$910$	139735.	+	144013.i	0.168741	+	0.173907i
$911$		−	536830.i		−	0.646845i	−0.946255	−	0.323422i	$-0.895167\pi$
$911$		−	536830.i		−	0.646845i	0.946255	−	0.323422i	$-0.104833\pi$
$912$	16105.8	−	254344.i	0.0193639	−	0.305796i
$913$	−1.35803e6			−1.62917
$914$	−356523.	+	345932.i	−0.426772	+	0.414094i
$915$	−213223.	+	123104.i	−0.254678	+	0.147038i
$916$	36064.5	−	1.19572e6i	0.0429822	−	1.42508i
$917$	438206.	+	758995.i	0.521122	+	0.902610i
$918$	115973.	−	408104.i	0.137617	−	0.484268i
$919$		−	678925.i		−	0.803880i	−0.915666	−	0.401940i	$-0.868336\pi$
$919$		−	678925.i		−	0.803880i	0.915666	−	0.401940i	$-0.131664\pi$
$920$	−478268.	+	436850.i	−0.565061	+	0.516128i
$921$	−190153.	+	329354.i	−0.224173	+	0.388279i
$922$	444819.	+	126406.i	0.523265	+	0.148698i
$923$			252645.i			0.296556i
$924$	94179.0	+	175111.i	0.110309	+	0.205102i
$925$	−338045.	+	585510.i	−0.395085	+	0.684307i
$926$	336594.	+	346900.i	0.392541	+	0.404559i
$927$	−487328.	−	281359.i	−0.567103	−	0.327417i
$928$	262527.	+	1.39191e6i	0.304844	+	1.61627i
$929$	−288227.	−	499223.i	−0.333966	−	0.578446i	0.649319	−	0.760516i	$-0.275054\pi$
$929$	−288227.	−	499223.i	−0.333966	−	0.578446i	−0.983286	+	0.182069i	$0.941720\pi$
$930$	−93283.3	−	370386.i	−0.107854	−	0.428241i
$931$	−285585.	+	491312.i	−0.329485	+	0.566837i
$932$	−66731.4	+	35889.7i	−0.0768242	+	0.0413179i
$933$	−104849.	−	181603.i	−0.120448	−	0.208622i
$934$	−902141.	−	929761.i	−1.03414	−	1.06581i
$935$	1.12380e6	+	648824.i	1.28548	+	0.742170i
$936$	−74515.0	+	235024.i	−0.0850535	+	0.268263i
$937$	−556901.	+	964580.i	−0.634306	+	1.09865i	0.352356	+	0.935866i	$0.385381\pi$
$937$	−556901.	+	964580.i	−0.634306	+	1.09865i	−0.986662	+	0.162784i	$0.947953\pi$
$938$	50326.0	+	199822.i	0.0571988	+	0.227111i
$939$		−	15676.8i		−	0.0177797i
$940$	143974.	+	4342.44i	0.162940	+	0.00491449i
$941$	118454.	−	205168.i	0.133774	−	0.231703i	−0.791355	−	0.611357i	$-0.790624\pi$
$941$	118454.	−	205168.i	0.133774	−	0.231703i	0.925128	+	0.379655i	$0.123957\pi$
$942$	−256864.	+	64692.4i	−0.289469	+	0.0729040i
$943$			136908.i			0.153960i
$944$	518669.	−	259105.i	0.582031	−	0.290759i
$945$	203465.	+	352411.i	0.227838	+	0.394627i
$946$	1.14376e6	+	325027.i	1.27806	+	0.363192i
$947$	−552854.	+	319191.i	−0.616468	+	0.355918i	−0.775493	−	0.631356i	$-0.782498\pi$
$947$	−552854.	+	319191.i	−0.616468	+	0.355918i	0.159024	+	0.987275i	$0.449165\pi$
$948$	−300970.	−	186083.i	−0.334894	−	0.207057i
$949$	−478286.			−0.531074
$950$	665875.	+	191338.i	0.737811	+	0.212009i
$951$			144937.i			0.160258i
$952$	−436999.	−	138552.i	−0.482177	−	0.152876i
$953$	−751822.	−	1.30219e6i	−0.827807	−	1.43380i	−0.899755	−	0.436395i	$-0.856255\pi$
$953$	−751822.	−	1.30219e6i	−0.827807	−	1.43380i	0.0719483	−	0.997408i	$-0.477078\pi$
$954$	1.43486e6	+	407751.i	1.57657	+	0.448021i
$955$	118878.	−	68634.2i	0.130345	−	0.0752548i
$956$	−1.06045e6	−	31984.5i	−1.16031	−	0.0349964i
$957$	−597810.			−0.652738
$958$	−576267.	+	145135.i	−0.627903	+	0.158140i
$959$	−512934.	−	296142.i	−0.557730	−	0.322006i
$960$	216325.	−	306856.i	0.234728	−	0.332960i
$961$	−161732.			−0.175125
$962$	72255.3	+	286893.i	0.0780763	+	0.310006i
$963$	938069.	+	541595.i	1.01154	+	0.584012i
$964$	−144412.	−	89286.9i	−0.155400	−	0.0960801i
$965$	430545.	−	745725.i	0.462342	−	0.800800i
$966$	67255.7	+	69314.8i	0.0720734	+	0.0742800i
$967$	−677820.	+	391340.i	−0.724872	+	0.418505i	−0.816543	−	0.577284i	$-0.804113\pi$
$967$	−677820.	+	391340.i	−0.724872	+	0.418505i	0.0916710	+	0.995789i	$0.470779\pi$
$968$	−428150.	−	468742.i	−0.456925	−	0.500246i
$969$	−215136.	+	123368.i	−0.229121	+	0.131388i
$970$	274382.	+	1.08945e6i	0.291617	+	1.15788i
$971$	−546036.	+	315254.i	−0.579139	+	0.334366i	−0.760791	−	0.648997i	$-0.775189\pi$
$971$	−546036.	+	315254.i	−0.579139	+	0.334366i	0.181652	+	0.983363i	$0.441856\pi$
$972$	−400882.	+	648384.i	−0.424310	+	0.686278i
$973$	273869.	−	474354.i	0.289279	−	0.501046i
$974$	−214208.	−	220766.i	−0.225796	−	0.232709i
$975$	60143.7	+	34724.0i	0.0632676	+	0.0365276i
$976$	−379084.	+	573708.i	−0.397956	+	0.602270i
$977$	704373.			0.737928			0.368964	−	0.929444i	$-0.379713\pi$
$977$	704373.			0.737928			0.368964	+	0.929444i	$0.379713\pi$
$978$	−19860.6	−	5643.87i	−0.0207642	−	0.00590065i
$979$	131076.	+	75676.9i	0.136760	+	0.0789584i
$980$	−737308.	+	396542.i	−0.767709	+	0.412892i
$981$	47844.0			0.0497153
$982$	308223.	−	1.08463e6i	0.319626	−	1.12475i
$983$	−94520.9	+	54571.7i	−0.0978185	+	0.0564755i	−0.548111	−	0.836405i	$-0.684653\pi$
$983$	−94520.9	+	54571.7i	−0.0978185	+	0.0564755i	0.450293	+	0.892881i	$0.351320\pi$
$984$	−17051.7	−	77500.0i	−0.0176107	−	0.0800408i
$985$	468780.	+	811951.i	0.483167	+	0.836869i
$986$	989222.	−	959836.i	1.01751	−	0.987286i
$987$		−	21476.7i		−	0.0220462i
$988$	267426.	−	142818.i	0.273962	−	0.146309i
$989$	577571.			0.590490
$990$	−1.06494e6	−	1.09754e6i	−1.08656	−	1.11983i
$991$	−91159.1	+	52630.7i	−0.0928224	+	0.0535910i	−0.545693	−	0.837985i	$-0.683733\pi$
$991$	−91159.1	+	52630.7i	−0.0928224	+	0.0535910i	0.452870	+	0.891576i	$0.350400\pi$
$992$	−695363.	−	808975.i	−0.706623	−	0.822076i
$993$	276199.	+	478390.i	0.280106	+	0.485159i
$994$	532531.	+	151332.i	0.538980	+	0.153164i
$995$			725587.i			0.732898i
$996$	336732.	−	181102.i	0.339442	−	0.182560i
$997$	417999.	−	723995.i	0.420518	−	0.728359i	−0.575472	−	0.817822i	$-0.695182\pi$
$997$	417999.	−	723995.i	0.420518	−	0.728359i	0.995990	+	0.0894626i	$0.0285150\pi$
$998$	147811.	−	520141.i	0.148404	−	0.522228i
$999$			599968.i			0.601169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.g.a.7.11	✓	76
4.3	odd	2	inner	76.5.g.a.7.36	yes	76
19.11	even	3	inner	76.5.g.a.11.36	yes	76
76.11	odd	6	inner	76.5.g.a.11.11	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.g.a.7.11	✓	76	1.1	even	1	trivial
76.5.g.a.7.36	yes	76	4.3	odd	2	inner
76.5.g.a.11.11	yes	76	76.11	odd	6	inner
76.5.g.a.11.36	yes	76	19.11	even	3	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.87075 + 2.78547i) q^{2} +(2.38822 - 1.37884i) q^{3} +(0.482361 - 15.9927i) q^{4} +(-16.6192 - 28.7853i) q^{5} +(-3.01526 + 10.6106i) q^{6} +28.7543i q^{7} +(43.1625 + 47.2547i) q^{8} +(-36.6976 + 63.5621i) q^{9} +O(q^{10})\)	\(q+(-2.87075 + 2.78547i) q^{2} +(2.38822 - 1.37884i) q^{3} +(0.482361 - 15.9927i) q^{4} +(-16.6192 - 28.7853i) q^{5} +(-3.01526 + 10.6106i) q^{6} +28.7543i q^{7} +(43.1625 + 47.2547i) q^{8} +(-36.6976 + 63.5621i) q^{9} +(127.890 + 36.3431i) q^{10} +156.718i q^{11} +(-20.8994 - 38.8592i) q^{12} +(26.2442 - 45.4563i) q^{13} +(-80.0940 - 82.5461i) q^{14} +(-79.3805 - 45.8304i) q^{15} +(-255.535 - 15.4285i) q^{16} +(124.557 + 215.739i) q^{17} +(-71.7006 - 284.691i) q^{18} +(-181.417 + 312.104i) q^{19} +(-468.372 + 251.902i) q^{20} +(39.6474 + 68.6714i) q^{21} +(-436.532 - 449.897i) q^{22} +(-263.704 - 152.250i) q^{23} +(168.238 + 53.3403i) q^{24} +(-239.896 + 415.512i) q^{25} +(51.2765 + 203.596i) q^{26} +425.772i q^{27} +(459.859 + 13.8699i) q^{28} +(-691.626 + 1197.93i) q^{29} +(355.540 - 89.5444i) q^{30} -1041.75i q^{31} +(776.551 - 667.492i) q^{32} +(216.089 + 374.276i) q^{33} +(-958.505 - 272.383i) q^{34} +(827.700 - 477.873i) q^{35} +(998.830 + 617.555i) q^{36} +1409.13 q^{37} +(-348.555 - 1401.30i) q^{38} -144.746i q^{39} +(642.914 - 2027.78i) q^{40} +(-224.809 - 389.381i) q^{41} +(-305.100 - 86.7015i) q^{42} +(-1642.67 + 948.395i) q^{43} +(2506.35 + 75.5946i) q^{44} +2439.54 q^{45} +(1181.11 - 297.469i) q^{46} +(-234.559 - 135.423i) q^{47} +(-631.546 + 315.494i) q^{48} +1574.19 q^{49} +(-468.714 - 1861.05i) q^{50} +(594.938 + 343.488i) q^{51} +(-714.311 - 441.643i) q^{52} +(-2540.48 + 4400.24i) q^{53} +(-1185.97 - 1222.28i) q^{54} +(4511.17 - 2604.53i) q^{55} +(-1358.77 + 1241.10i) q^{56} +(-2.92104 + 995.517i) q^{57} +(-1351.31 - 5365.46i) q^{58} +(-1961.37 + 1132.40i) q^{59} +(-771.243 + 1247.40i) q^{60} +(1343.04 - 2326.22i) q^{61} +(2901.77 + 2990.61i) q^{62} +(-1827.68 - 1055.21i) q^{63} +(-370.004 + 4079.25i) q^{64} -1744.63 q^{65} +(-1662.87 - 472.545i) q^{66} +(-1551.55 - 895.788i) q^{67} +(3510.34 - 1887.94i) q^{68} -839.710 q^{69} +(-1045.02 + 3677.38i) q^{70} +(-4168.48 + 2406.67i) q^{71} +(-4587.57 + 1009.36i) q^{72} +(-4556.11 - 7891.41i) q^{73} +(-4045.25 + 3925.08i) q^{74} +1323.11i q^{75} +(4903.89 + 3051.89i) q^{76} -4506.31 q^{77} +(403.185 + 415.529i) q^{78} +(6945.24 - 4009.83i) q^{79} +(3802.67 + 7612.05i) q^{80} +(-2385.44 - 4131.70i) q^{81} +(1729.98 + 491.615i) q^{82} +8665.43i q^{83} +(1117.37 - 600.946i) q^{84} +(4140.07 - 7170.82i) q^{85} +(2073.96 - 7298.19i) q^{86} +3814.56i q^{87} +(-7405.65 + 6764.33i) q^{88} +(482.886 - 836.384i) q^{89} +(-7003.30 + 6795.26i) q^{90} +(1307.06 + 754.633i) q^{91} +(-2562.09 + 4143.91i) q^{92} +(-1436.41 - 2487.94i) q^{93} +(1050.58 - 264.592i) q^{94} +(11999.0 + 35.2075i) q^{95} +(934.209 - 2664.85i) q^{96} +(4225.04 + 7317.98i) q^{97} +(-4519.11 + 4384.86i) q^{98} +(-9961.32 - 5751.17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - q^{2} + 13 q^{4} - 2 q^{5} - 15 q^{6} - 94 q^{8} + 972 q^{9}+O(q^{10}) \) 76 * q - q^2 + 13 * q^4 - 2 * q^5 - 15 * q^6 - 94 * q^8 + 972 * q^9	\( 76 q - q^{2} + 13 q^{4} - 2 q^{5} - 15 q^{6} - 94 q^{8} + 972 q^{9} + 180 q^{10} - 166 q^{12} - 178 q^{13} - 30 q^{14} + 237 q^{16} - 50 q^{17} + 356 q^{18} + 2212 q^{20} + 304 q^{21} - 1035 q^{22} + 1697 q^{24} - 3752 q^{25} + 3952 q^{26} + 990 q^{28} - 2 q^{29} + 408 q^{30} - 181 q^{32} - 3000 q^{33} + 2712 q^{34} + 1078 q^{36} - 2088 q^{37} - 3198 q^{38} - 6562 q^{40} - 2138 q^{41} - 2698 q^{42} - 8631 q^{44} + 2168 q^{45} - 9380 q^{46} + 10159 q^{48} - 19380 q^{49} + 9354 q^{50} + 4706 q^{52} - 818 q^{53} + 6431 q^{54} + 1476 q^{56} - 6 q^{57} - 13080 q^{58} + 5626 q^{60} + 5470 q^{61} + 8892 q^{62} - 30890 q^{64} + 16316 q^{65} - 14001 q^{66} - 3284 q^{68} + 38836 q^{69} + 8532 q^{70} - 2766 q^{72} + 7222 q^{73} - 10328 q^{74} - 29613 q^{76} + 16320 q^{77} + 19028 q^{78} + 12778 q^{80} - 25574 q^{81} + 30563 q^{82} + 65132 q^{84} - 21006 q^{85} - 8430 q^{86} + 44242 q^{88} + 12910 q^{89} - 48688 q^{90} - 14052 q^{92} - 4304 q^{93} - 39664 q^{94} + 15670 q^{96} + 1174 q^{97} + 2783 q^{98}+O(q^{100}) \) 76 * q - q^2 + 13 * q^4 - 2 * q^5 - 15 * q^6 - 94 * q^8 + 972 * q^9 + 180 * q^10 - 166 * q^12 - 178 * q^13 - 30 * q^14 + 237 * q^16 - 50 * q^17 + 356 * q^18 + 2212 * q^20 + 304 * q^21 - 1035 * q^22 + 1697 * q^24 - 3752 * q^25 + 3952 * q^26 + 990 * q^28 - 2 * q^29 + 408 * q^30 - 181 * q^32 - 3000 * q^33 + 2712 * q^34 + 1078 * q^36 - 2088 * q^37 - 3198 * q^38 - 6562 * q^40 - 2138 * q^41 - 2698 * q^42 - 8631 * q^44 + 2168 * q^45 - 9380 * q^46 + 10159 * q^48 - 19380 * q^49 + 9354 * q^50 + 4706 * q^52 - 818 * q^53 + 6431 * q^54 + 1476 * q^56 - 6 * q^57 - 13080 * q^58 + 5626 * q^60 + 5470 * q^61 + 8892 * q^62 - 30890 * q^64 + 16316 * q^65 - 14001 * q^66 - 3284 * q^68 + 38836 * q^69 + 8532 * q^70 - 2766 * q^72 + 7222 * q^73 - 10328 * q^74 - 29613 * q^76 + 16320 * q^77 + 19028 * q^78 + 12778 * q^80 - 25574 * q^81 + 30563 * q^82 + 65132 * q^84 - 21006 * q^85 - 8430 * q^86 + 44242 * q^88 + 12910 * q^89 - 48688 * q^90 - 14052 * q^92 - 4304 * q^93 - 39664 * q^94 + 15670 * q^96 + 1174 * q^97 + 2783 * q^98

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