LMFDB - Embedded newform 62.6.g.b.45.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			45.7
Character	$\chi$	$=$	62.45
Dual form			62.6.g.b.51.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23607 + 3.80423i) q^{2} +(18.0092 - 20.0013i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(24.3476 - 42.1713i) q^{5} +(53.8287 + 93.2340i) q^{6} +(-3.21782 + 30.6155i) q^{7} +(51.7771 - 37.6183i) q^{8} +(-50.3181 - 478.745i) q^{9} +(130.334 + 144.750i) q^{10} +(26.3145 - 11.7160i) q^{11} +(-421.219 + 89.5329i) q^{12} +(-816.653 - 173.585i) q^{13} +(-112.491 - 50.0841i) q^{14} +(-404.997 - 1246.45i) q^{15} +(79.1084 + 243.470i) q^{16} +(-899.956 - 400.686i) q^{17} +(1883.45 + 400.340i) q^{18} +(2808.79 - 597.027i) q^{19} +(-711.764 + 316.898i) q^{20} +(554.398 + 615.721i) q^{21} +(12.0437 + 114.588i) q^{22} +(1310.09 - 951.838i) q^{23} +(180.052 - 1713.08i) q^{24} +(376.889 + 652.791i) q^{25} +(1669.79 - 2892.17i) q^{26} +(-5190.57 - 3771.17i) q^{27} +(329.578 - 366.033i) q^{28} +(1171.67 - 3606.02i) q^{29} +5242.40 q^{30} +(3007.57 + 4425.34i) q^{31} -1024.00 q^{32} +(239.570 - 737.320i) q^{33} +(2636.71 - 2928.36i) q^{34} +(1212.75 + 881.113i) q^{35} +(-3851.06 + 6670.23i) q^{36} +(-1970.22 - 3412.52i) q^{37} +(-1200.63 + 11423.2i) q^{38} +(-18179.2 + 13208.0i) q^{39} +(-325.762 - 3099.42i) q^{40} +(4695.39 + 5214.76i) q^{41} +(-3027.62 + 1347.98i) q^{42} +(-14937.7 + 3175.10i) q^{43} +(-450.806 - 95.8219i) q^{44} +(-21414.4 - 9534.31i) q^{45} +(2001.64 + 6160.43i) q^{46} +(2213.49 + 6812.42i) q^{47} +(6294.40 + 2802.45i) q^{48} +(15512.8 + 3297.34i) q^{49} +(-2949.23 + 626.877i) q^{50} +(-24221.7 + 10784.2i) q^{51} +(8938.48 + 9927.19i) q^{52} +(2310.83 + 21986.1i) q^{53} +(20762.3 - 15084.7i) q^{54} +(146.618 - 1394.97i) q^{55} +(985.092 + 1706.23i) q^{56} +(38642.8 - 66931.4i) q^{57} +(12269.8 + 8914.56i) q^{58} +(21532.0 - 23913.7i) q^{59} +(-6479.96 + 19943.3i) q^{60} +12679.0 q^{61} +(-20552.6 + 5971.47i) q^{62} +14818.9 q^{63} +(1265.73 - 3895.53i) q^{64} +(-27203.8 + 30212.9i) q^{65} +(2508.81 + 1822.75i) q^{66} +(8516.46 - 14750.9i) q^{67} +(7880.99 + 13650.3i) q^{68} +(4555.78 - 43345.4i) q^{69} +(-4850.99 + 3524.45i) q^{70} +(6335.66 + 60279.8i) q^{71} +(-20614.9 - 22895.1i) q^{72} +(-8949.35 + 3984.51i) q^{73} +(15417.3 - 3277.05i) q^{74} +(19844.1 + 4218.00i) q^{75} +(-41972.6 - 18687.4i) q^{76} +(274.015 + 843.332i) q^{77} +(-27775.3 - 85483.7i) q^{78} +(-94925.0 - 42263.3i) q^{79} +(12193.6 + 2591.82i) q^{80} +(-54486.7 + 11581.5i) q^{81} +(-25641.9 + 11416.5i) q^{82} +(71420.1 + 79320.1i) q^{83} +(-1385.69 - 13183.9i) q^{84} +(-38809.2 + 28196.5i) q^{85} +(6385.18 - 60750.9i) q^{86} +(-51024.1 - 88376.3i) q^{87} +(921.755 - 1596.53i) q^{88} +(113238. + 82272.2i) q^{89} +(62740.4 - 69680.2i) q^{90} +(7942.22 - 24443.6i) q^{91} -25909.8 q^{92} +(142676. + 19541.7i) q^{93} -28652.0 q^{94} +(43209.9 - 132987. i) q^{95} +(-18441.4 + 20481.3i) q^{96} +(73932.7 + 53715.3i) q^{97} +(-31718.7 + 54938.4i) q^{98} +(-6933.07 - 12008.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 7 q^{3} - 224 q^{4} + 91 q^{5} - 152 q^{6} - 94 q^{7} + 896 q^{8} + 896 q^{9} - 944 q^{10} - 31 q^{11} - 112 q^{12} - 1244 q^{13} + 856 q^{14} + 518 q^{15} - 3584 q^{16} + 1064 q^{17}+ \cdots - 625437 q^{99}+O(q^{100}) $ 56 * q + 56 * q^2 - 7 * q^3 - 224 * q^4 + 91 * q^5 - 152 * q^6 - 94 * q^7 + 896 * q^8 + 896 * q^9 - 944 * q^10 - 31 * q^11 - 112 * q^12 - 1244 * q^13 + 856 * q^14 + 518 * q^15 - 3584 * q^16 + 1064 * q^17 - 1724 * q^18 + 619 * q^19 - 1024 * q^20 + 9541 * q^21 + 124 * q^22 - 1717 * q^23 + 768 * q^24 - 24033 * q^25 - 1344 * q^26 + 22754 * q^27 + 1776 * q^28 + 11733 * q^29 + 13928 * q^30 + 57065 * q^31 - 57344 * q^32 - 11248 * q^33 - 10456 * q^34 - 7296 * q^35 - 42464 * q^36 - 1504 * q^37 - 29736 * q^38 - 19566 * q^39 + 4096 * q^40 + 35891 * q^41 + 40636 * q^42 + 66400 * q^43 + 23344 * q^44 - 27014 * q^45 - 7612 * q^46 + 36521 * q^47 - 3072 * q^48 + 121465 * q^49 - 13108 * q^50 - 236890 * q^51 - 19904 * q^52 - 143661 * q^53 - 91016 * q^54 + 106359 * q^55 + 5056 * q^56 + 13060 * q^57 + 59468 * q^58 + 230112 * q^59 + 8288 * q^60 - 49860 * q^61 + 26740 * q^62 + 66726 * q^63 - 57344 * q^64 + 201094 * q^65 - 30508 * q^66 + 74372 * q^67 - 4656 * q^68 - 599733 * q^69 + 29184 * q^70 + 23383 * q^71 - 27584 * q^72 - 66915 * q^73 + 186916 * q^74 + 553648 * q^75 - 152736 * q^76 + 120895 * q^77 + 142024 * q^78 - 452529 * q^79 - 50944 * q^80 - 365276 * q^81 - 14324 * q^82 - 469160 * q^83 - 50464 * q^84 - 127377 * q^85 + 215540 * q^86 + 217461 * q^87 + 39744 * q^88 - 155746 * q^89 + 820796 * q^90 - 142152 * q^91 - 5952 * q^92 + 342224 * q^93 + 29656 * q^94 + 756444 * q^95 + 7168 * q^96 + 325303 * q^97 + 533540 * q^98 - 625437 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

Coefficient data

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

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

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

$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$3$	18.0092	−	20.0013i	1.15529	−	1.28308i	0.202559	−	0.979270i	$-0.435074\pi$
$3$	18.0092	−	20.0013i	1.15529	−	1.28308i	0.952732	−	0.303811i	$-0.0982593\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	24.3476	−	42.1713i	0.435543	−	0.754383i	−0.561797	−	0.827275i	$-0.689890\pi$
$5$	24.3476	−	42.1713i	0.435543	−	0.754383i	0.997340	+	0.0728926i	$0.0232230\pi$
$6$	53.8287	+	93.2340i	0.610430	+	1.05730i
$7$	−3.21782	+	30.6155i	−0.0248208	+	0.236154i	0.975077	+	0.221866i	$0.0712149\pi$
$7$	−3.21782	+	30.6155i	−0.0248208	+	0.236154i	−0.999898	+	0.0142881i	$0.995452\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	−50.3181	−	478.745i	−0.207071	−	1.97014i
$10$	130.334	+	144.750i	0.412152	+	0.457741i
$11$	26.3145	−	11.7160i	0.0655714	−	0.0291942i	−0.373689	−	0.927554i	$-0.621907\pi$
$11$	26.3145	−	11.7160i	0.0655714	−	0.0291942i	0.439260	+	0.898360i	$0.355241\pi$
$12$	−421.219	+	89.5329i	−0.844413	+	0.179486i
$13$	−816.653	−	173.585i	−1.34023	−	0.284874i	−0.518658	−	0.854982i	$-0.673568\pi$
$13$	−816.653	−	173.585i	−1.34023	−	0.284874i	−0.821570	+	0.570107i	$0.806902\pi$
$14$	−112.491	−	50.0841i	−0.153390	−	0.0682936i
$15$	−404.997	−	1246.45i	−0.464755	−	1.43037i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	−899.956	−	400.686i	−0.755264	−	0.336265i	−0.00727254	−	0.999974i	$-0.502315\pi$
$17$	−899.956	−	400.686i	−0.755264	−	0.336265i	−0.747991	+	0.663708i	$0.768982\pi$
$18$	1883.45	+	400.340i	1.37017	+	0.291238i
$19$	2808.79	−	597.027i	1.78499	−	0.379411i	0.807412	−	0.589988i	$-0.200868\pi$
$19$	2808.79	−	597.027i	1.78499	−	0.379411i	0.977577	+	0.210577i	$0.0675342\pi$
$20$	−711.764	+	316.898i	−0.397888	+	0.177151i
$21$	554.398	+	615.721i	0.274330	+	0.304674i
$22$	12.0437	+	114.588i	0.00530522	+	0.0504758i
$23$	1310.09	−	951.838i	0.516396	−	0.375183i	−0.298849	−	0.954301i	$-0.596603\pi$
$23$	1310.09	−	951.838i	0.516396	−	0.375183i	0.815244	+	0.579117i	$0.196603\pi$
$24$	180.052	−	1713.08i	0.0638073	−	0.607086i
$25$	376.889	+	652.791i	0.120605	+	0.208893i
$26$	1669.79	−	2892.17i	0.484428	−	0.839054i
$27$	−5190.57	−	3771.17i	−1.37027	−	0.995559i
$28$	329.578	−	366.033i	0.0794443	−	0.0882318i
$29$	1171.67	−	3606.02i	0.258707	−	0.796219i	−0.734369	−	0.678750i	$-0.762522\pi$
$29$	1171.67	−	3606.02i	0.258707	−	0.796219i	0.993077	−	0.117469i	$-0.0374781\pi$
$30$	5242.40			1.06347
$31$	3007.57	+	4425.34i	0.562098	+	0.827071i
$31$	3007.57	+	4425.34i	0.562098	+	0.827071i
$32$	−1024.00			−0.176777
$33$	239.570	−	737.320i	0.0382954	−	0.117861i
$34$	2636.71	−	2928.36i	0.391169	−	0.434437i
$35$	1212.75	+	881.113i	0.167340	+	0.121580i
$36$	−3851.06	+	6670.23i	−0.495249	+	0.857797i
$37$	−1970.22	−	3412.52i	−0.236598	−	0.409799i	0.723138	−	0.690703i	$-0.242699\pi$
$37$	−1970.22	−	3412.52i	−0.236598	−	0.409799i	−0.959736	+	0.280904i	$0.909366\pi$
$38$	−1200.63	+	11423.2i	−0.134881	+	1.28331i
$39$	−18179.2	+	13208.0i	−1.91387	+	1.39051i
$40$	−325.762	−	3099.42i	−0.0321922	−	0.306288i
$41$	4695.39	+	5214.76i	0.436227	+	0.484479i	0.920669	−	0.390345i	$-0.127644\pi$
$41$	4695.39	+	5214.76i	0.436227	+	0.484479i	−0.484442	+	0.874823i	$0.660977\pi$
$42$	−3027.62	+	1347.98i	−0.264836	+	0.117913i
$43$	−14937.7	+	3175.10i	−1.23200	+	0.261870i	−0.777505	−	0.628877i	$-0.783515\pi$
$43$	−14937.7	+	3175.10i	−1.23200	+	0.261870i	−0.454499	+	0.890747i	$0.650182\pi$
$44$	−450.806	−	95.8219i	−0.0351041	−	0.00746162i
$45$	−21414.4	−	9534.31i	−1.57643	−	0.701872i
$46$	2001.64	+	6160.43i	0.139474	+	0.429256i
$47$	2213.49	+	6812.42i	0.146161	+	0.449839i	0.997159	−	0.0753318i	$-0.0240016\pi$
$47$	2213.49	+	6812.42i	0.146161	+	0.449839i	−0.850997	+	0.525170i	$0.824002\pi$
$48$	6294.40	+	2802.45i	0.394322	+	0.175563i
$49$	15512.8	+	3297.34i	0.922995	+	0.196189i
$50$	−2949.23	+	626.877i	−0.166833	+	0.0354615i
$51$	−24221.7	+	10784.2i	−1.30401	+	0.580581i
$52$	8938.48	+	9927.19i	0.458411	+	0.509117i
$53$	2310.83	+	21986.1i	0.113000	+	1.07513i	0.893220	+	0.449620i	$0.148440\pi$
$53$	2310.83	+	21986.1i	0.113000	+	1.07513i	−0.780220	+	0.625505i	$0.784893\pi$
$54$	20762.3	−	15084.7i	0.968927	−	0.703966i
$55$	146.618	−	1394.97i	0.00653551	−	0.0621812i
$56$	985.092	+	1706.23i	0.0419765	+	0.0727055i
$57$	38642.8	−	66931.4i	1.57537	−	2.72862i
$58$	12269.8	+	8914.56i	0.478927	+	0.347961i
$59$	21532.0	−	23913.7i	0.805293	−	0.894368i	−0.190894	−	0.981611i	$-0.561139\pi$
$59$	21532.0	−	23913.7i	0.805293	−	0.894368i	0.996187	+	0.0872424i	$0.0278055\pi$
$60$	−6479.96	+	19943.3i	−0.232378	+	0.715185i
$61$	12679.0			0.436276			0.218138	−	0.975918i	$-0.430002\pi$
$61$	12679.0			0.436276			0.218138	+	0.975918i	$0.430002\pi$
$62$	−20552.6	+	5971.47i	−0.679027	+	0.197289i
$63$	14818.9			0.470398
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	−27203.8	+	30212.9i	−0.798632	+	0.886970i
$66$	2508.81	+	1822.75i	0.0708937	+	0.0515073i
$67$	8516.46	−	14750.9i	0.231778	−	0.401451i	−0.726553	−	0.687110i	$-0.758879\pi$
$67$	8516.46	−	14750.9i	0.231778	−	0.401451i	0.958331	+	0.285659i	$0.0922124\pi$
$68$	7880.99	+	13650.3i	0.206685	+	0.357989i
$69$	4555.78	−	43345.4i	0.115197	−	1.09602i
$70$	−4850.99	+	3524.45i	−0.118327	+	0.0859699i
$71$	6335.66	+	60279.8i	0.149158	+	1.41914i	0.771417	+	0.636331i	$0.219549\pi$
$71$	6335.66	+	60279.8i	0.149158	+	1.41914i	−0.622259	+	0.782812i	$0.713785\pi$
$72$	−20614.9	−	22895.1i	−0.468651	−	0.520490i
$73$	−8949.35	+	3984.51i	−0.196555	+	0.0875120i	−0.502654	−	0.864488i	$-0.667643\pi$
$73$	−8949.35	+	3984.51i	−0.196555	+	0.0875120i	0.306099	+	0.952000i	$0.400976\pi$
$74$	15417.3	−	3277.05i	0.327288	−	0.0695671i
$75$	19844.1	+	4218.00i	0.407360	+	0.0865871i
$76$	−41972.6	−	18687.4i	−0.833550	−	0.371120i
$77$	274.015	+	843.332i	0.00526681	+	0.0162096i
$78$	−27775.3	−	85483.7i	−0.516919	−	1.59091i
$79$	−94925.0	−	42263.3i	−1.71125	−	0.761896i	−0.998148	−	0.0608328i	$-0.980624\pi$
$79$	−94925.0	−	42263.3i	−1.71125	−	0.761896i	−0.713099	−	0.701063i	$-0.752709\pi$
$80$	12193.6	+	2591.82i	0.213013	+	0.0452772i
$81$	−54486.7	+	11581.5i	−0.922737	+	0.196134i
$82$	−25641.9	+	11416.5i	−0.421130	+	0.187499i
$83$	71420.1	+	79320.1i	1.13796	+	1.26383i	0.960065	+	0.279777i	$0.0902606\pi$
$83$	71420.1	+	79320.1i	1.13796	+	1.26383i	0.177891	+	0.984050i	$0.443073\pi$
$84$	−1385.69	−	13183.9i	−0.0214273	−	0.203867i
$85$	−38809.2	+	28196.5i	−0.582623	+	0.423300i
$86$	6385.18	−	60750.9i	0.0930952	−	0.885741i
$87$	−51024.1	−	88376.3i	−0.722732	−	1.25181i
$88$	921.755	−	1596.53i	0.0126885	−	0.0219771i
$89$	113238.	+	82272.2i	1.51536	+	1.10098i	0.963726	+	0.266893i	$0.0859970\pi$
$89$	113238.	+	82272.2i	1.51536	+	1.10098i	0.551638	+	0.834084i	$0.314003\pi$
$90$	62740.4	−	69680.2i	0.816471	−	0.906783i
$91$	7942.22	−	24443.6i	0.100540	−	0.309430i
$92$	−25909.8			−0.319150
$93$	142676.	+	19541.7i	1.71059	+	0.234290i
$94$	−28652.0			−0.334453
$95$	43209.9	−	132987.i	0.491218	−	1.51181i
$96$	−18441.4	+	20481.3i	−0.204229	+	0.226819i
$97$	73932.7	+	53715.3i	0.797824	+	0.579653i	0.910275	−	0.414004i	$-0.135870\pi$
$97$	73932.7	+	53715.3i	0.797824	+	0.579653i	−0.112451	+	0.993657i	$0.535870\pi$
$98$	−31718.7	+	54938.4i	−0.333618	+	0.577844i
$99$	−6933.07	−	12008.4i	−0.0710948	−	0.123140i
$100$	1260.66	−	11994.4i	0.0126066	−	0.119944i
$101$	−24769.1	+	17995.8i	−0.241606	+	0.175537i	−0.701998	−	0.712179i	$-0.747709\pi$
$101$	−24769.1	+	17995.8i	−0.241606	+	0.175537i	0.460393	+	0.887715i	$0.347709\pi$
$102$	−11085.9	−	105475.i	−0.105504	−	1.00380i
$103$	37731.7	+	41905.3i	0.350440	+	0.389203i	0.892433	−	0.451180i	$-0.148997\pi$
$103$	37731.7	+	41905.3i	0.350440	+	0.389203i	−0.541993	+	0.840383i	$0.682330\pi$
$104$	−48813.8	+	21733.3i	−0.442547	+	0.197035i
$105$	39464.0	−	8388.33i	0.349324	−	0.0742510i
$106$	−86496.5	−	18385.4i	−0.747711	−	0.158931i
$107$	23245.5	+	10349.6i	0.196281	+	0.0873901i	0.502523	−	0.864564i	$-0.332405\pi$
$107$	23245.5	+	10349.6i	0.196281	+	0.0873901i	−0.306242	+	0.951954i	$0.599072\pi$
$108$	31722.0	+	97630.2i	0.261698	+	0.805424i
$109$	−64993.3	−	200029.i	−0.523965	−	1.61260i	−0.766353	−	0.642420i	$-0.777931\pi$
$109$	−64993.3	−	200029.i	−0.523965	−	1.61260i	0.242388	−	0.970179i	$-0.422069\pi$
$110$	5125.57	+	2282.05i	0.0403887	+	0.0179822i
$111$	−103737.	−	22049.9i	−0.799145	−	0.169863i
$112$	−7708.52	+	1638.50i	−0.0580665	+	0.0123424i
$113$	−81330.5	+	36210.7i	−0.599180	+	0.266772i	−0.683833	−	0.729638i	$-0.739688\pi$
$113$	−81330.5	+	36210.7i	−0.599180	+	0.266772i	0.0846532	+	0.996410i	$0.473022\pi$
$114$	206857.	+	229738.i	1.49076	+	1.65566i
$115$	−8242.62	−	78423.3i	−0.0581193	−	0.552968i
$116$	−49079.4	+	35658.2i	−0.338652	+	0.246045i
$117$	−42010.5	+	399703.i	−0.283722	+	2.69943i
$118$	64358.1	+	111471.i	0.425498	+	0.736985i
$119$	15163.1	−	26263.2i	0.0981568	−	0.170013i
$120$	−67859.0	−	49302.5i	−0.430184	−	0.312547i
$121$	−107209.	+	119068.i	−0.665683	+	0.739316i
$122$	−15672.2	+	48233.9i	−0.0953299	+	0.293395i
$123$	188862.			1.12559
$124$	2687.55	−	85567.7i	0.0156965	−	0.499754i
$125$	188878.			1.08120
$126$	−18317.2	+	56374.5i	−0.102786	+	0.316342i
$127$	−12580.7	+	13972.2i	−0.0692140	+	0.0768699i	−0.776757	−	0.629800i	$-0.783137\pi$
$127$	−12580.7	+	13972.2i	−0.0692140	+	0.0768699i	0.707543	+	0.706670i	$0.249803\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	−205510.	+	355953.i	−1.08732	+	1.88330i
$130$	−81310.9	−	140835.i	−0.421979	−	0.730889i
$131$	39869.4	−	379332.i	0.202984	−	1.93126i	−0.136484	−	0.990642i	$-0.543580\pi$
$131$	39869.4	−	379332.i	0.202984	−	1.93126i	0.339467	−	0.940618i	$-0.389753\pi$
$132$	−10035.2	+	7291.02i	−0.0501294	+	0.0364211i
$133$	9240.10	+	87913.7i	0.0452947	+	0.430950i
$134$	45589.0	+	50631.7i	0.219330	+	0.243591i
$135$	−285413.	+	127074.i	−1.34784	+	0.600099i
$136$	−61670.2	+	13108.4i	−0.285909	+	0.0607719i
$137$	−159315.	−	33863.4i	−0.725196	−	0.154145i	−0.169499	−	0.985530i	$-0.554215\pi$
$137$	−159315.	−	33863.4i	−0.725196	−	0.154145i	−0.555696	+	0.831385i	$0.687548\pi$
$138$	159264.	+	70909.1i	0.711903	+	0.316960i
$139$	−87480.9	−	269239.i	−0.384040	−	1.18195i	−0.937174	−	0.348861i	$-0.886568\pi$
$139$	−87480.9	−	269239.i	−0.384040	−	1.18195i	0.553135	−	0.833092i	$-0.313432\pi$
$140$	−7411.65	−	22810.7i	−0.0319591	−	0.0983601i
$141$	176120.	+	78413.7i	0.746039	+	0.332158i
$142$	−237149.	−	50407.6i	−0.986963	−	0.209786i
$143$	−23523.6	+	5000.09i	−0.0961973	+	0.0204474i
$144$	112580.	−	50123.7i	0.452433	−	0.201436i
$145$	−123543.	−	137208.i	−0.487976	−	0.541952i
$146$	−4095.96	−	38970.5i	−0.0159028	−	0.151305i
$147$	345324.	−	250892.i	1.31805	−	0.957622i
$148$	−6590.21	+	62701.6i	−0.0247312	+	0.235301i
$149$	37958.5	+	65746.0i	0.140069	+	0.242607i	0.927523	−	0.373767i	$-0.121934\pi$
$149$	37958.5	+	65746.0i	0.140069	+	0.242607i	−0.787453	+	0.616374i	$0.788601\pi$
$150$	−40574.9	+	70277.8i	−0.147241	+	0.255029i
$151$	−330953.	−	240451.i	−1.18120	−	0.858192i	−0.188893	−	0.981998i	$-0.560490\pi$
$151$	−330953.	−	240451.i	−1.18120	−	0.858192i	−0.992306	+	0.123806i	$0.960490\pi$
$152$	122972.	−	136574.i	0.431715	−	0.479468i
$153$	−146542.	+	451011.i	−0.506098	+	1.55761i
$154$	−3546.93			−0.0120518
$155$	259849.	−	19086.8i	0.868746	−	0.0638122i
$156$	359531.			1.18284
$157$	−14657.2	+	45110.1i	−0.0474571	+	0.146058i	−0.971977	−	0.235076i	$-0.924466\pi$
$157$	−14657.2	+	45110.1i	−0.0474571	+	0.146058i	0.924520	+	0.381134i	$0.124466\pi$
$158$	278113.	−	308876.i	0.886295	−	0.984331i
$159$	481366.	+	349733.i	1.51002	+	1.09709i
$160$	−24931.9	+	43183.4i	−0.0769939	+	0.133357i
$161$	24925.4	+	43172.0i	0.0757838	+	0.131261i
$162$	23290.6	−	221595.i	0.0697257	−	0.663396i
$163$	−75804.6	+	55075.3i	−0.223474	+	0.162363i	−0.693889	−	0.720082i	$-0.744104\pi$
$163$	−75804.6	+	55075.3i	−0.223474	+	0.162363i	0.470415	+	0.882445i	$0.344104\pi$
$164$	−11735.9	−	111659.i	−0.0340726	−	0.324180i
$165$	−25260.8	−	28054.9i	−0.0722332	−	0.0802231i
$166$	−390032.	+	173653.i	−1.09857	+	0.489117i
$167$	−592908.	+	126026.i	−1.64511	+	0.349680i	−0.935066	−	0.354474i	$-0.884660\pi$
$167$	−592908.	+	126026.i	−1.64511	+	0.349680i	−0.710048	+	0.704153i	$0.751327\pi$
$168$	51867.5	+	11024.8i	0.141782	+	0.0301367i
$169$	297597.	+	132499.i	0.801514	+	0.356857i
$170$	−59295.2	−	182492.i	−0.157361	−	0.484307i
$171$	−427157.	−	1.31465e6i	−1.11711	−	3.43812i
$172$	223218.	+	99383.0i	0.575318	+	0.256148i
$173$	82370.1	+	17508.3i	0.209245	+	0.0444763i	0.311341	−	0.950298i	$-0.399222\pi$
$173$	82370.1	+	17508.3i	0.209245	+	0.0444763i	−0.102097	+	0.994774i	$0.532555\pi$
$174$	399273.	−	84868.0i	0.999762	−	0.212506i
$175$	−21198.3	+	9438.08i	−0.0523245	+	0.0232964i
$176$	4934.20	+	5479.98i	0.0120070	+	0.0133351i
$177$	−90529.8	−	861333.i	−0.217199	−	2.06651i
$178$	−452952.	+	329089.i	−1.07152	+	0.778508i
$179$	−31105.0	+	295944.i	−0.0725601	+	0.690363i	0.896417	+	0.443212i	$0.146161\pi$
$179$	−31105.0	+	295944.i	−0.0725601	+	0.690363i	−0.968977	+	0.247151i	$0.920506\pi$
$180$	187528.	+	324808.i	0.431405	+	0.747215i
$181$	−50255.2	+	87044.5i	−0.114021	+	0.197490i	−0.917388	−	0.397994i	$-0.869706\pi$
$181$	−50255.2	+	87044.5i	−0.114021	+	0.197490i	0.803367	+	0.595484i	$0.203040\pi$
$182$	83172.0	+	60428.0i	0.186122	+	0.135226i
$183$	228340.	−	253597.i	0.504027	−	0.559778i
$184$	32026.3	−	98566.8i	0.0697369	−	0.214628i
$185$	−191880.			−0.412194
$186$	−250699.	+	518619.i	−0.531337	+	1.09917i
$187$	−28376.4			−0.0593407
$188$	35415.8	−	108999.i	0.0730807	−	0.224919i
$189$	132159.	−	146777.i	0.269117	−	0.298884i
$190$	452500.	+	328761.i	0.909358	+	0.660687i
$191$	61230.8	−	106055.i	0.121447	−	0.210352i	−0.798892	−	0.601475i	$-0.794580\pi$
$191$	61230.8	−	106055.i	0.121447	−	0.210352i	0.920339	+	0.391123i	$0.127913\pi$
$192$	−55120.6	−	95471.7i	−0.107910	−	0.186905i
$193$	86052.7	−	818737.i	0.166292	−	1.58216i	−0.519568	−	0.854429i	$-0.673907\pi$
$193$	86052.7	−	818737.i	0.166292	−	1.58216i	0.685860	−	0.727733i	$-0.259426\pi$
$194$	−295731.	+	214861.i	−0.564147	+	0.409877i
$195$	114377.	+	1.08822e6i	0.215403	+	2.04942i
$196$	−169791.	−	188573.i	−0.315701	−	0.350621i
$197$	374575.	−	166771.i	0.687659	−	0.306165i	−0.0329999	−	0.999455i	$-0.510506\pi$
$197$	374575.	−	166771.i	0.687659	−	0.306165i	0.720659	+	0.693290i	$0.243839\pi$
$198$	54252.5	−	11531.7i	0.0983461	−	0.0209041i
$199$	−802946.	−	170671.i	−1.43732	−	0.305512i	−0.577618	−	0.816307i	$-0.696018\pi$
$199$	−802946.	−	170671.i	−1.43732	−	0.305512i	−0.859703	+	0.510795i	$0.829351\pi$
$200$	44071.1	+	19621.7i	0.0779074	+	0.0346866i
$201$	−141663.	−	435993.i	−0.247324	−	0.761183i
$202$	−37843.8	−	116471.i	−0.0652554	−	0.200836i
$203$	106630.	+	47474.6i	0.181609	+	0.0808577i
$204$	414953.	+	88201.0i	0.698110	+	0.148388i
$205$	334235.	−	71043.7i	0.555478	−	0.118070i
$206$	−206056.	+	91742.2i	−0.338312	+	0.150626i
$207$	−521609.	−	579306.i	−0.846096	−	0.939685i
$208$	−22341.2	−	212563.i	−0.0358054	−	0.340666i
$209$	66917.3	−	48618.3i	0.105968	−	0.0769899i
$210$	−16869.1	+	160499.i	−0.0263963	+	0.251144i
$211$	476920.	+	826049.i	0.737461	+	1.27732i	0.953635	+	0.300965i	$0.0973089\pi$
$211$	476920.	+	826049.i	0.737461	+	1.27732i	−0.216174	+	0.976355i	$0.569358\pi$
$212$	176858.	−	306327.i	0.270262	−	0.468107i
$213$	1.31977e6	+	958871.i	1.99320	+	1.44814i
$214$	−68105.1	+	75638.3i	−0.101659	+	0.112904i
$215$	−229798.	+	707247.i	−0.339040	+	1.04346i
$216$	−410618.			−0.598830
$217$	−145162.	+	77838.4i	−0.209268	+	0.112213i
$218$	841291.			1.19896
$219$	−81475.6	+	250756.i	−0.114794	+	0.353298i
$220$	−15017.0	+	16678.0i	−0.0209183	+	0.0232321i
$221$	665398.	+	483440.i	0.916433	+	0.665828i
$222$	212109.	−	367383.i	0.288852	−	0.500307i
$223$	79169.1	+	137125.i	0.106609	+	0.184652i	0.914394	−	0.404824i	$-0.132667\pi$
$223$	79169.1	+	137125.i	0.106609	+	0.184652i	−0.807785	+	0.589477i	$0.799334\pi$
$224$	3295.04	−	31350.3i	0.00438774	−	0.0417466i
$225$	293556.	−	213281.i	0.386576	−	0.280864i
$226$	−37223.6	−	354158.i	−0.0484782	−	0.461240i
$227$	−679975.	−	755188.i	−0.875847	−	0.972726i	0.123962	−	0.992287i	$-0.460440\pi$
$227$	−679975.	−	755188.i	−0.875847	−	0.972726i	−0.999809	+	0.0195607i	$0.993773\pi$
$228$	−1.12966e6	+	502959.i	−1.43917	+	0.640760i
$229$	−550426.	+	116997.i	−0.693602	+	0.147430i	−0.541206	−	0.840890i	$-0.682032\pi$
$229$	−550426.	+	116997.i	−0.693602	+	0.147430i	−0.152396	+	0.988320i	$0.548699\pi$
$230$	308528.	+	65579.7i	0.384570	+	0.0817429i
$231$	21802.5	+	9707.10i	0.0268829	+	0.0119690i
$232$	−74986.6	−	230785.i	−0.0914668	−	0.281506i
$233$	−16341.4	−	50293.5i	−0.0197196	−	0.0606907i	0.940712	−	0.339205i	$-0.110158\pi$
$233$	−16341.4	−	50293.5i	−0.0197196	−	0.0606907i	−0.960432	+	0.278514i	$0.910158\pi$
$234$	−1.46863e6	−	653877.i	−1.75337	−	0.780650i
$235$	341182.	+	72520.4i	0.403010	+	0.0856624i
$236$	−503613.	+	107046.i	−0.588596	+	0.125110i
$237$	−2.55484e6	+	1.13749e6i	−2.95456	+	1.31546i
$238$	81168.7	+	90147.0i	0.0928851	+	0.103159i
$239$	153329.	+	1.45883e6i	0.173632	+	1.65200i	0.640713	+	0.767781i	$0.278639\pi$
$239$	153329.	+	1.45883e6i	0.173632	+	1.65200i	−0.467081	+	0.884214i	$0.654694\pi$
$240$	271436.	−	197210.i	0.304186	−	0.221004i
$241$	−110778.	+	1.05398e6i	−0.122860	+	1.16893i	0.743226	+	0.669040i	$0.233295\pi$
$241$	−110778.	+	1.05398e6i	−0.122860	+	1.16893i	−0.866086	+	0.499895i	$0.833372\pi$
$242$	−320443.	−	555023.i	−0.351732	−	0.609218i
$243$	29914.4	−	51813.3i	0.0324986	−	0.0562893i
$244$	−164121.	−	119241.i	−0.176478	−	0.128218i
$245$	516752.	−	573911.i	0.550005	−	0.610843i
$246$	−233446.	+	718474.i	−0.245951	+	0.756961i
$247$	−2.39744e6			−2.50038
$248$	322197.	+	115992.i	0.332654	+	0.119756i
$249$	2.87272e6			2.93626
$250$	−233466.	+	718534.i	−0.236251	+	0.727105i
$251$	479137.	−	532136.i	0.480038	−	0.533136i	−0.453671	−	0.891169i	$-0.649886\pi$
$251$	479137.	−	532136.i	0.480038	−	0.533136i	0.933709	+	0.358033i	$0.116552\pi$
$252$	−191820.	−	139366.i	−0.190280	−	0.138246i
$253$	23322.8	−	40396.2i	0.0229076	−	0.0396771i
$254$	−37603.0	−	65130.3i	−0.0365711	−	0.0633430i
$255$	−134957.	+	1.28403e6i	−0.129971	+	1.23659i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	−18654.9	−	177490.i	−0.0176181	−	0.167625i	0.982175	−	0.187969i	$-0.0601906\pi$
$257$	−18654.9	−	177490.i	−0.0176181	−	0.167625i	−0.999793	+	0.0203439i	$0.993524\pi$
$258$	−1.10010e6	−	1.22179e6i	−1.02893	−	1.14274i
$259$	110816.	−	49338.3i	0.102648	−	0.0457020i
$260$	636273.	−	135244.i	0.583727	−	0.124075i
$261$	−1.78532e6	−	379481.i	−1.62224	−	0.344817i
$262$	1.39378e6	+	620552.i	1.25442	+	0.558502i
$263$	384680.	+	1.18392e6i	0.342933	+	1.05544i	0.962681	+	0.270639i	$0.0872351\pi$
$263$	384680.	+	1.18392e6i	0.342933	+	1.05544i	−0.619747	+	0.784801i	$0.712765\pi$
$264$	−15332.5	−	47188.5i	−0.0135395	−	0.0416702i
$265$	983446.	+	437858.i	0.860272	+	0.383018i
$266$	−345865.	−	73515.8i	−0.299711	−	0.0637055i
$267$	3.68487e6	−	783244.i	3.16333	−	0.672387i
$268$	−248966.	+	110847.i	−0.211740	+	0.0942726i
$269$	514282.	+	571169.i	0.433332	+	0.481264i	0.919774	−	0.392449i	$-0.128372\pi$
$269$	514282.	+	571169.i	0.433332	+	0.481264i	−0.486442	+	0.873713i	$0.661705\pi$
$270$	−130629.	−	1.24285e6i	−0.109051	−	1.03755i
$271$	765260.	−	555994.i	0.632974	−	0.459883i	−0.224455	−	0.974484i	$-0.572060\pi$
$271$	765260.	−	555994.i	0.632974	−	0.459883i	0.857429	+	0.514602i	$0.172060\pi$
$272$	26361.2	−	250810.i	0.0216044	−	0.205553i
$273$	−345870.	−	599065.i	−0.280871	−	0.486483i
$274$	325748.	−	564213.i	0.262123	−	0.454011i
$275$	17565.8	+	12762.3i	0.0140067	+	0.0101764i
$276$	−466616.	+	518229.i	−0.368711	+	0.409496i
$277$	−208843.	+	642754.i	−0.163539	+	0.503321i	−0.998926	−	0.0463416i	$-0.985244\pi$
$277$	−208843.	+	642754.i	−0.163539	+	0.503321i	0.835387	+	0.549663i	$0.185244\pi$
$278$	1.13238e6			0.878778
$279$	1.96728e6	−	1.66254e6i	1.51305	−	1.27868i
$280$	95938.5			0.0731304
$281$	−79955.5	+	246078.i	−0.0604063	+	0.185912i	−0.976706	−	0.214582i	$-0.931161\pi$
$281$	−79955.5	+	246078.i	−0.0604063	+	0.185912i	0.916300	+	0.400493i	$0.131161\pi$
$282$	−516000.	+	573076.i	−0.386391	+	0.429131i
$283$	−550774.	−	400161.i	−0.408797	−	0.297008i	0.364318	−	0.931275i	$-0.381302\pi$
$283$	−550774.	−	400161.i	−0.408797	−	0.297008i	−0.773115	+	0.634266i	$0.781302\pi$
$284$	484895.	−	839862.i	0.356740	−	0.617891i
$285$	−1.88172e6	−	3.25924e6i	−1.37228	−	2.37686i
$286$	10055.3	−	95669.4i	0.00726906	−	0.0691605i
$287$	−174761.	+	126972.i	−0.125239	+	0.0909916i
$288$	51525.8	+	490235.i	0.0366052	+	0.348276i
$289$	−300699.	−	333960.i	−0.211781	−	0.235207i
$290$	674680.	−	300387.i	0.471089	−	0.209742i
$291$	2.40584e6	−	511378.i	1.66546	−	0.354005i
$292$	153315.	+	32588.2i	0.105227	+	0.0223668i
$293$	−1.96208e6	−	873576.i	−1.33521	−	0.594473i	−0.389961	−	0.920831i	$-0.627512\pi$
$293$	−1.96208e6	−	873576.i	−1.33521	−	0.594473i	−0.945246	+	0.326359i	$0.894178\pi$
$294$	527608.	+	1.62381e6i	0.355994	+	1.09564i
$295$	−484218.	−	1.49027e6i	−0.323956	−	0.997035i
$296$	−230385.	−	102574.i	−0.152836	−	0.0680469i
$297$	−180771.	−	38424.0i	−0.118915	−	0.0252762i
$298$	−297032.	+	63136.1i	−0.193759	+	0.0411848i
$299$	−1.23512e6	+	549909.i	−0.798968	+	0.355724i
$300$	−217199.	−	241224.i	−0.139333	−	0.154745i
$301$	−49140.5	−	467541.i	−0.0312625	−	0.297443i
$302$	1.32381e6	−	961804.i	0.835234	−	0.606833i
$303$	−86133.3	+	819504.i	−0.0538970	+	0.512796i
$304$	367557.	+	636628.i	0.228108	+	0.395095i
$305$	308704.	−	534691.i	0.190017	−	0.329119i
$306$	−1.53461e6	−	1.11496e6i	−0.936904	−	0.680700i
$307$	716280.	−	795509.i	0.433747	−	0.481725i	−0.486155	−	0.873873i	$-0.661601\pi$
$307$	716280.	−	795509.i	0.433747	−	0.481725i	0.919902	+	0.392147i	$0.128268\pi$
$308$	4384.24	−	13493.3i	0.00263341	−	0.00810479i
$309$	1.51768e6			0.904239
$310$	−248581.	+	1.01212e6i	−0.146914	+	0.598174i
$311$	−178101.			−0.104415			−0.0522077	−	0.998636i	$-0.516626\pi$
$311$	−178101.			−0.104415			−0.0522077	+	0.998636i	$0.516626\pi$
$312$	−444405.	+	1.36774e6i	−0.258460	+	0.795457i
$313$	−297382.	+	330276.i	−0.171575	+	0.190553i	−0.822799	−	0.568332i	$-0.807589\pi$
$313$	−297382.	+	330276.i	−0.171575	+	0.190553i	0.651224	+	0.758885i	$0.274256\pi$
$314$	−153492.	−	111518.i	−0.0878539	−	0.0638296i
$315$	360805.	−	624933.i	0.204879	−	0.354860i
$316$	831266.	+	1.43980e6i	0.468298	+	0.811116i
$317$	−325720.	+	3.09902e6i	−0.182052	+	1.73211i	0.397870	+	0.917442i	$0.369750\pi$
$317$	−325720.	+	3.09902e6i	−0.182052	+	1.73211i	−0.579922	+	0.814672i	$0.696917\pi$
$318$	−1.92547e6	+	1.39893e6i	−1.06775	+	0.775763i
$319$	−11416.2	−	108618.i	−0.00628123	−	0.0597619i
$320$	−133462.	−	148224.i	−0.0728588	−	0.0809179i
$321$	625637.	−	278552.i	0.338891	−	0.150884i
$322$	−195045.	+	41458.2i	−0.104833	+	0.0222828i
$323$	−2.76701e6	−	588146.i	−1.47572	−	0.313674i
$324$	814209.	+	362509.i	0.430897	+	0.191848i
$325$	−194473.	−	598526.i	−0.102129	−	0.314322i
$326$	−115819.	−	356455.i	−0.0603582	−	0.185763i
$327$	−5.17131e6	−	2.30241e6i	−2.67443	−	1.19073i
$328$	439284.	+	93372.7i	0.225455	+	0.0479220i
$329$	−215688.	+	45845.9i	−0.109859	+	0.0233513i
$330$	137951.	−	61419.9i	0.0697334	−	0.0310473i
$331$	−1.35228e6	−	1.50185e6i	−0.678415	−	0.753456i	0.301371	−	0.953507i	$-0.402556\pi$
$331$	−1.35228e6	−	1.50185e6i	−0.678415	−	0.753456i	−0.979785	+	0.200051i	$0.935889\pi$
$332$	−178511.	−	1.69842e6i	−0.0888830	−	0.845666i
$333$	−1.53459e6	+	1.11494e6i	−0.758371	+	0.550989i
$334$	253441.	−	2.41133e6i	0.124311	−	1.18274i
$335$	−414711.	−	718300.i	−0.201899	−	0.349699i
$336$	−106052.	+	183688.i	−0.0512475	+	0.0887632i
$337$	2.00572e6	+	1.45724e6i	0.962044	+	0.698966i	0.953625	−	0.300998i	$-0.0973199\pi$
$337$	2.00572e6	+	1.45724e6i	0.962044	+	0.698966i	0.00841973	+	0.999965i	$0.497320\pi$
$338$	−871904.	+	968347.i	−0.415123	+	0.461041i
$339$	−740439.	+	2.27884e6i	−0.349937	+	1.07700i
$340$	767533.			0.360081
$341$	130990.	+	81214.1i	0.0610032	+	0.0378221i
$342$	5.52924e6			2.55623
$343$	−310749.	+	956387.i	−0.142618	+	0.438933i
$344$	−653988.	+	726327.i	−0.297971	+	0.330930i
$345$	−1.71701e6	−	1.24748e6i	−0.776648	−	0.564268i
$346$	−168421.	+	291713.i	−0.0756319	+	0.130998i
$347$	−296869.	−	514193.i	−0.132355	−	0.229246i	0.792229	−	0.610224i	$-0.208921\pi$
$347$	−296869.	−	514193.i	−0.132355	−	0.229246i	−0.924584	+	0.380978i	$0.875587\pi$
$348$	−170671.	+	1.62383e6i	−0.0755460	+	0.718772i
$349$	269477.	−	195786.i	0.118429	−	0.0860437i	−0.526994	−	0.849869i	$-0.676681\pi$
$349$	269477.	−	195786.i	0.118429	−	0.0860437i	0.645423	+	0.763825i	$0.276681\pi$
$350$	−9702.08	−	92309.1i	−0.00423345	−	0.0402786i
$351$	3.58428e6	+	3.98074e6i	1.55286	+	1.72463i
$352$	−26946.1	+	11997.2i	−0.0115915	+	0.00516086i
$353$	−2.75164e6	+	584879.i	−1.17532	+	0.249821i	−0.753865	−	0.657029i	$-0.771813\pi$
$353$	−2.75164e6	+	584879.i	−1.17532	+	0.249821i	−0.421452	+	0.906851i	$0.638479\pi$
$354$	3.38861e6	+	720271.i	1.43719	+	0.305483i
$355$	2.69633e6	+	1.20049e6i	1.13554	+	0.505575i
$356$	−692049.	−	2.12991e6i	−0.289409	−	0.890709i
$357$	−252223.	−	776261.i	−0.104740	−	0.322357i
$358$	−1.08739e6	−	484138.i	−0.448413	−	0.199646i
$359$	3.69952e6	+	786357.i	1.51499	+	0.322021i	0.889035	−	0.457839i	$-0.151377\pi$
$359$	3.69952e6	+	786357.i	1.51499	+	0.322021i	0.625954	+	0.779860i	$0.284710\pi$
$360$	−1.46744e6	+	311914.i	−0.596766	+	0.126847i
$361$	5.27084e6	−	2.34673e6i	2.12869	−	0.947753i
$362$	−269018.	−	298775.i	−0.107897	−	0.119832i
$363$	450753.	+	4.28863e6i	0.179544	+	1.70825i
$364$	−332688.	+	241712.i	−0.131608	+	0.0956191i
$365$	−49863.4	+	474419.i	−0.0195907	+	0.186393i
$366$	682496.	+	1.18212e6i	0.266316	+	0.461273i
$367$	−1.56587e6	+	2.71216e6i	−0.606862	+	1.05112i	0.384892	+	0.922961i	$0.374239\pi$
$367$	−1.56587e6	+	2.71216e6i	−0.606862	+	1.05112i	−0.991754	+	0.128154i	$0.959095\pi$
$368$	335384.	+	243671.i	0.129099	+	0.0937959i
$369$	2.26028e6	−	2.51029e6i	0.864163	−	0.959751i
$370$	237177.	−	729956.i	0.0900676	−	0.277200i
$371$	−680552.			−0.256700
$372$	−1.66306e6	−	1.59476e6i	−0.623090	−	0.597501i
$373$	−4.88526e6			−1.81809			−0.909046	−	0.416697i	$-0.863188\pi$
$373$	−4.88526e6			−1.81809			−0.909046	+	0.416697i	$0.863188\pi$
$374$	35075.1	−	107950.i	0.0129664	−	0.0399065i
$375$	3.40154e6	−	3.77779e6i	1.24910	−	1.38727i
$376$	370879.	+	269460.i	0.135289	+	0.0982933i
$377$	−1.58279e6	+	2.74148e6i	−0.573549	+	0.993417i
$378$	395016.	+	684187.i	0.142195	+	0.246289i
$379$	426074.	−	4.05382e6i	0.152366	−	1.44966i	−0.604768	−	0.796401i	$-0.706734\pi$
$379$	426074.	−	4.05382e6i	0.152366	−	1.44966i	0.757134	−	0.653260i	$-0.226599\pi$
$380$	−1.81000e6	+	1.31504e6i	−0.643013	+	0.467177i
$381$	52894.5	+	503258.i	0.0186680	+	0.177614i
$382$	327771.	+	364027.i	0.114924	+	0.127637i
$383$	363108.	−	161666.i	0.126485	−	0.0563148i	−0.342518	−	0.939511i	$-0.611280\pi$
$383$	363108.	−	161666.i	0.126485	−	0.0563148i	0.469003	+	0.883196i	$0.344613\pi$
$384$	431329.	−	91681.7i	0.149273	−	0.0317289i
$385$	42236.0	+	8977.54i	0.0145222	+	0.00308678i
$386$	3.00829e6	+	1.33938e6i	1.02767	+	0.457546i
$387$	2.27170e6	+	6.99157e6i	0.771034	+	2.37300i
$388$	−451837.	−	1.39061e6i	−0.152371	−	0.468949i
$389$	77843.9	+	34658.3i	0.0260826	+	0.0116127i	0.419736	−	0.907646i	$-0.362122\pi$
$389$	77843.9	+	34658.3i	0.0260826	+	0.0116127i	−0.393654	+	0.919259i	$0.628789\pi$
$390$	−4.28122e6	−	910001.i	−1.42530	−	0.302956i
$391$	−1.56041e6	+	331676.i	−0.516176	+	0.109717i
$392$	927246.	−	412837.i	0.304775	−	0.135695i
$393$	−6.86909e6	−	7.62890e6i	−2.24346	−	2.49161i
$394$	171436.	+	1.63111e6i	0.0556368	+	0.529349i
$395$	−4.09349e6	+	2.97410e6i	−1.32008	+	0.959096i
$396$	−23190.5	+	220643.i	−0.00743143	+	0.0707053i
$397$	1.91400e6	+	3.31514e6i	0.609488	+	1.05566i	0.991325	+	0.131434i	$0.0419582\pi$
$397$	1.91400e6	+	3.31514e6i	0.609488	+	1.05566i	−0.381837	+	0.924230i	$0.624708\pi$
$398$	1.64177e6	−	2.84363e6i	0.519523	−	0.899839i
$399$	1.92479e6	+	1.39844e6i	0.605273	+	0.439757i
$400$	−129120.	+	143403.i	−0.0403501	+	0.0448133i
$401$	−87798.9	+	270217.i	−0.0272664	+	0.0839175i	−0.963764	−	0.266757i	$-0.914048\pi$
$401$	−87798.9	+	270217.i	−0.0272664	+	0.0839175i	0.936497	+	0.350675i	$0.114048\pi$
$402$	1.83372e6			0.565937
$403$	−1.68797e6	−	4.13604e6i	−0.517729	−	1.26859i
$404$	489861.			0.149320
$405$	−838213.	+	2.57975e6i	−0.253932	+	0.781521i
$406$	−312406.	+	346962.i	−0.0940598	+	0.104464i
$407$	−91826.5	−	66715.8i	−0.0274778	−	0.0199638i
$408$	−848447.	+	1.46955e6i	−0.252333	+	0.437054i
$409$	−1.25933e6	−	2.18122e6i	−0.372246	−	0.644749i	0.617665	−	0.786441i	$-0.288079\pi$
$409$	−1.25933e6	−	2.18122e6i	−0.372246	−	0.644749i	−0.989911	+	0.141693i	$0.954746\pi$
$410$	−142870.	+	1.35932e6i	−0.0419741	+	0.399357i
$411$	−3.54645e6	+	2.57665e6i	−1.03559	+	0.752402i
$412$	−94308.4	−	897284.i	−0.0273720	−	0.260428i
$413$	662843.	+	736161.i	0.191221	+	0.212372i
$414$	2.84856e6	−	1.26826e6i	0.816815	−	0.363670i
$415$	5.08394e6	−	1.08062e6i	1.44904	−	0.308003i
$416$	836252.	+	177751.i	0.236921	+	0.0503592i
$417$	−6.96057e6	−	3.09905e6i	−1.96022	−	0.872746i
$418$	102241.	+	314664.i	0.0286209	+	0.0880859i
$419$	89142.5	+	274352.i	0.0248056	+	0.0763438i	0.962693	−	0.270596i	$-0.0872208\pi$
$419$	89142.5	+	274352.i	0.0248056	+	0.0763438i	−0.937887	+	0.346940i	$0.887221\pi$
$420$	−589721.	−	262561.i	−0.163126	−	0.0726284i
$421$	4.52109e6	+	960987.i	1.24319	+	0.264248i	0.782127	−	0.623119i	$-0.214135\pi$
$421$	4.52109e6	+	960987.i	1.24319	+	0.264248i	0.461064	+	0.887367i	$0.347468\pi$
$422$	−3.73198e6	+	793258.i	−1.02014	+	0.216837i
$423$	3.15003e6	−	1.40249e6i	0.855981	−	0.381107i
$424$	946728.	+	1.05145e6i	0.255747	+	0.284036i
$425$	−77619.2	−	738497.i	−0.0208448	−	0.198325i
$426$	−5.27909e6	+	3.83548e6i	−1.40940	+	1.02399i
$427$	−40798.8	+	388175.i	−0.0108287	+	0.103029i
$428$	−203563.	−	352581.i	−0.0537142	−	0.0930357i
$429$	−323633.	+	560548.i	−0.0849003	+	0.147052i
$430$	−2.40648e6	−	1.74841e6i	−0.627641	−	0.456008i
$431$	−2.69464e6	+	2.99270e6i	−0.698728	+	0.776016i	−0.983173	−	0.182676i	$-0.941524\pi$
$431$	−2.69464e6	+	2.99270e6i	−0.698728	+	0.776016i	0.284445	+	0.958692i	$0.408191\pi$
$432$	507551.	−	1.56208e6i	0.130849	−	0.402712i
$433$	4.85913e6			1.24549			0.622743	−	0.782427i	$-0.286018\pi$
$433$	4.85913e6			1.24549			0.622743	+	0.782427i	$0.286018\pi$
$434$	−116685.	−	648442.i	−0.0297366	−	0.165252i
$435$	−4.96926e6			−1.25912
$436$	−1.03989e6	+	3.20046e6i	−0.261983	+	0.806300i
$437$	3.11151e6	−	3.45568e6i	0.779412	−	0.865625i
$438$	−853224.	−	619904.i	−0.212509	−	0.154397i
$439$	1.08432e6	−	1.87809e6i	0.268531	−	0.465110i	−0.699951	−	0.714191i	$-0.746795\pi$
$439$	1.08432e6	−	1.87809e6i	0.268531	−	0.465110i	0.968483	+	0.249080i	$0.0801283\pi$
$440$	−44885.1	−	77743.2i	−0.0110527	−	0.0191439i
$441$	798012.	−	7.59258e6i	0.195395	−	1.85906i
$442$	−2.66159e6	+	1.93376e6i	−0.648016	+	0.470811i
$443$	−420852.	−	4.00414e6i	−0.101887	−	0.969392i	−0.919358	−	0.393422i	$-0.871291\pi$
$443$	−420852.	−	4.00414e6i	−0.101887	−	0.969392i	0.817471	−	0.575970i	$-0.195376\pi$
$444$	1.13543e6	+	1.26102e6i	0.273339	+	0.303574i
$445$	6.22660e6	−	2.77226e6i	1.49056	−	0.663642i
$446$	−619513.	+	131681.i	−0.147473	+	0.0313464i
$447$	1.99861e6	+	424817.i	0.473106	+	0.100562i
$448$	115191.	+	51286.1i	0.0271158	+	0.0120727i
$449$	−635771.	−	1.95670e6i	−0.148828	−	0.458046i	0.848655	−	0.528946i	$-0.177413\pi$
$449$	−635771.	−	1.95670e6i	−0.148828	−	0.458046i	−0.997483	+	0.0709004i	$0.977413\pi$
$450$	448514.	+	1.38038e6i	0.104411	+	0.321343i
$451$	184653.	+	82212.9i	0.0427480	+	0.0190326i
$452$	1.39331e6	+	296157.i	0.320776	+	0.0681830i
$453$	−1.07695e7	+	2.28913e6i	−2.46576	+	0.524114i
$454$	3.71340e6	−	1.65331e6i	0.845536	−	0.376457i
$455$	−837446.	−	930078.i	−0.189639	−	0.210616i
$456$	−517028.	−	4.91919e6i	−0.116440	−	1.10785i
$457$	5.89529e6	−	4.28318e6i	1.32043	−	0.959347i	0.320502	−	0.947248i	$-0.396149\pi$
$457$	5.89529e6	−	4.28318e6i	1.32043	−	0.959347i	0.999927	−	0.0120993i	$-0.00385143\pi$
$458$	235282.	−	2.23856e6i	0.0524113	−	0.498661i
$459$	3.16023e6	+	5.47368e6i	0.700143	+	1.21268i
$460$	−630842.	+	1.09265e6i	−0.139004	+	0.240761i
$461$	5.02771e6	+	3.65285e6i	1.10184	+	0.800533i	0.981359	−	0.192183i	$-0.0615566\pi$
$461$	5.02771e6	+	3.65285e6i	1.10184	+	0.800533i	0.120480	+	0.992716i	$0.461557\pi$
$462$	−63877.4	+	70943.0i	−0.0139233	+	0.0154634i
$463$	1.31019e6	−	4.03235e6i	0.284041	−	0.874189i	−0.702643	−	0.711543i	$-0.747997\pi$
$463$	1.31019e6	−	4.03235e6i	0.284041	−	0.874189i	0.986684	−	0.162647i	$-0.0520031\pi$
$464$	970647.			0.209299
$465$	4.29793e6	−	5.54106e6i	0.921778	−	1.18839i
$466$	211527.			0.0451233
$467$	−502968.	+	1.54797e6i	−0.106720	+	0.328452i	−0.990130	−	0.140149i	$-0.955242\pi$
$467$	−502968.	+	1.54797e6i	−0.106720	+	0.328452i	0.883410	+	0.468601i	$0.155242\pi$
$468$	4.30283e6	−	4.77877e6i	0.908111	−	1.00856i
$469$	424203.	+	308201.i	0.0890516	+	0.0646997i
$470$	−697607.	+	1.20829e6i	−0.145669	+	0.252306i
$471$	638295.	+	1.10556e6i	0.132577	+	0.229631i
$472$	215272.	−	2.04818e6i	0.0444767	−	0.423167i
$473$	−355879.	+	258561.i	−0.0731390	+	0.0531386i
$474$	−1.16931e6	−	1.11252e7i	−0.239047	−	2.27438i
$475$	1.44834e6	+	1.60854e6i	0.294534	+	0.327113i
$476$	−443269.	+	197356.i	−0.0896707	+	0.0399240i
$477$	1.04095e7	−	2.21260e6i	2.09475	−	0.445253i
$478$	−5.73923e6	−	1.21991e6i	−1.14890	−	0.244207i
$479$	−4.78748e6	−	2.13152e6i	−0.953385	−	0.424475i	−0.129720	−	0.991551i	$-0.541408\pi$
$479$	−4.78748e6	−	2.13152e6i	−0.953385	−	0.424475i	−0.823665	+	0.567076i	$0.808075\pi$
$480$	414717.	+	1.27637e6i	0.0821579	+	0.252856i
$481$	1.01662e6	+	3.12884e6i	0.200354	+	0.616625i
$482$	−3.87265e6	−	1.72422e6i	−0.759261	−	0.338045i
$483$	1.31238e6	+	278955.i	0.255972	+	0.0544084i
$484$	2.50752e6	−	532990.i	0.486554	−	0.103420i
$485$	4.06532e6	−	1.81000e6i	0.784767	−	0.349401i
$486$	160133.	+	177846.i	0.0307532	+	0.0341549i
$487$	616799.	+	5.86845e6i	0.117848	+	1.12125i	0.880371	+	0.474285i	$0.157293\pi$
$487$	616799.	+	5.86845e6i	0.117848	+	1.12125i	−0.762524	+	0.646960i	$0.776040\pi$
$488$	656484.	−	476963.i	0.124788	−	0.0906641i
$489$	−263607.	+	2.50805e6i	−0.0498522	+	0.474312i
$490$	1.54455e6	+	2.67523e6i	0.290610	+	0.503352i
$491$	−2.67921e6	+	4.64053e6i	−0.501537	+	0.868688i	0.498461	+	0.866912i	$0.333899\pi$
$491$	−2.67921e6	+	4.64053e6i	−0.501537	+	0.868688i	−0.999998	+	0.00177597i	$0.999435\pi$
$492$	−2.44468e6	−	1.77617e6i	−0.455313	−	0.330804i
$493$	−2.49933e6	+	2.77578e6i	−0.463133	+	0.514361i
$494$	2.96340e6	−	9.12041e6i	0.546353	−	1.68150i
$495$	−675215.			−0.123859
$496$	−839516.	+	1.08234e6i	−0.153223	+	0.197541i
$497$	−1.86588e6			−0.338839
$498$	−3.55088e6	+	1.09285e7i	−0.641597	+	1.97463i
$499$	−5.88640e6	+	6.53751e6i	−1.05827	+	1.17533i	−0.0742611	+	0.997239i	$0.523660\pi$
$499$	−5.88640e6	+	6.53751e6i	−1.05827	+	1.17533i	−0.984013	+	0.178094i	$0.943007\pi$
$500$	−2.44489e6	−	1.77631e6i	−0.437355	−	0.317757i
$501$	−8.15712e6	+	1.41285e7i	−1.45192	+	2.51480i
$502$	1.43212e6	+	2.48050e6i	0.253641	+	0.439319i
$503$	−877352.	+	8.34744e6i	−0.154616	+	1.47107i	0.592066	+	0.805889i	$0.298312\pi$
$503$	−877352.	+	8.34744e6i	−0.154616	+	1.47107i	−0.746682	+	0.665181i	$0.768354\pi$
$504$	767281.	−	557462.i	0.134548	−	0.0977550i
$505$	155838.	+	1.48270e6i	0.0271922	+	0.258717i
$506$	124848.	+	138658.i	0.0216773	+	0.0240751i
$507$	8.00962e6	−	3.56611e6i	1.38386	−	0.616134i
$508$	294250.	−	62544.8i	0.0505892	−	0.0107531i
$509$	5.12159e6	+	1.08863e6i	0.876214	+	0.186245i	0.623998	−	0.781426i	$-0.285507\pi$
$509$	5.12159e6	+	1.08863e6i	0.876214	+	0.186245i	0.252216	+	0.967671i	$0.418841\pi$
$510$	−4.71793e6	−	2.10056e6i	−0.803204	−	0.357609i
$511$	−93190.3	−	286810.i	−0.0157877	−	0.0485895i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	−1.68307e7	−	7.49353e6i	−2.82364	−	1.25717i
$514$	698269.	+	148422.i	0.116578	+	0.0247793i
$515$	2.68588e6	−	570901.i	0.446240	−	0.0948512i
$516$	6.00776e6	−	2.67483e6i	0.993318	−	0.442254i
$517$	138061.	+	153332.i	0.0227167	+	0.0252295i
$518$	50718.4	+	482554.i	0.00830503	+	0.0790171i
$519$	1.83361e6	−	1.33219e6i	0.298805	−	0.217095i
$520$	−271978.	+	2.58770e6i	−0.0441088	+	0.419667i
$521$	4.25930e6	+	7.37732e6i	0.687454	+	1.19070i	0.972659	+	0.232238i	$0.0746049\pi$
$521$	4.25930e6	+	7.37732e6i	0.687454	+	1.19070i	−0.285205	+	0.958466i	$0.592062\pi$
$522$	3.65041e6	−	6.32269e6i	0.586361	−	1.01561i
$523$	4.77154e6	+	3.46673e6i	0.762789	+	0.554198i	0.899764	−	0.436376i	$-0.143738\pi$
$523$	4.77154e6	+	3.46673e6i	0.762789	+	0.554198i	−0.136976	+	0.990574i	$0.543738\pi$
$524$	−4.08353e6	+	4.53522e6i	−0.649692	+	0.721556i
$525$	−192991.	+	593965.i	−0.0305589	+	0.0940508i
$526$	−4.97940e6			−0.784716
$527$	−933510.	−	5.18770e6i	−0.146417	−	0.813671i
$528$	198468.			0.0309817
$529$	−1.17859e6	+	3.62733e6i	−0.183115	+	0.563570i
$530$	−2.88132e6	+	3.20003e6i	−0.445555	+	0.494839i
$531$	−1.25320e7	−	9.10503e6i	−1.92879	−	1.40135i
$532$	707183.	−	1.22488e6i	0.108331	−	0.187635i
$533$	−2.92930e6	−	5.07370e6i	−0.446628	−	0.773582i
$534$	−1.57512e6	+	1.49862e7i	−0.239034	+	2.27426i
$535$	1.00243e6	−	728305.i	0.151415	−	0.110009i
$536$	−113947.	−	1.08414e6i	−0.0171314	−	0.162994i
$537$	5.35908e6	+	5.95186e6i	0.801964	+	0.890671i
$538$	−2.80854e6	+	1.25044e6i	−0.418336	+	0.186255i
$539$	446843.	−	94979.5i	0.0662496	−	0.0140818i
$540$	4.88954e6	+	1.03930e6i	0.721579	+	0.153376i
$541$	−6.85348e6	−	3.05137e6i	−1.00674	−	0.448230i	−0.163949	−	0.986469i	$-0.552423\pi$
$541$	−6.85348e6	−	3.05137e6i	−1.00674	−	0.448230i	−0.842793	+	0.538239i	$0.819090\pi$
$542$	1.16921e6	+	3.59847e6i	0.170960	+	0.526162i
$543$	835944.	+	2.57277e6i	0.121668	+	0.374457i
$544$	921555.	+	410303.i	0.133513	+	0.0594438i
$545$	−1.00179e7	−	2.12937e6i	−1.44473	−	0.307086i
$546$	2.70650e6	−	575284.i	0.388532	−	0.0825849i
$547$	−4.61908e6	+	2.05655e6i	−0.660065	+	0.293880i	−0.709300	−	0.704907i	$-0.750989\pi$
$547$	−4.61908e6	+	2.05655e6i	−0.660065	+	0.293880i	0.0492341	+	0.998787i	$0.484322\pi$
$548$	1.74375e6	+	1.93663e6i	0.248046	+	0.275483i
$549$	−637986.	−	6.07003e6i	−0.0903400	−	0.859528i
$550$	−70263.0	+	51049.1i	−0.00990422	+	0.00719584i
$551$	1.13808e6	−	1.08281e7i	0.159695	−	1.51940i
$552$	−1.39469e6	−	2.41568e6i	−0.194819	−	0.337436i
$553$	1.59936e6	−	2.77018e6i	0.222400	−	0.385208i
$554$	−2.18704e6	−	1.58897e6i	−0.302748	−	0.219959i
$555$	−3.45562e6	+	3.83785e6i	−0.476204	+	0.528878i
$556$	−1.39969e6	+	4.30782e6i	−0.192020	+	0.590977i
$557$	932601.			0.127367			0.0636836	−	0.997970i	$-0.479715\pi$
$557$	932601.			0.127367			0.0636836	+	0.997970i	$0.479715\pi$
$558$	3.89298e6	+	9.53897e6i	0.529293	+	1.29693i
$559$	1.27500e7			1.72577
$560$	−118586.	+	364972.i	−0.0159796	+	0.0491801i
$561$	−511036.	+	567563.i	−0.0685558	+	0.0761389i
$562$	−837305.	−	608338.i	−0.111826	−	0.0812463i
$563$	2.92329e6	−	5.06329e6i	0.388688	−	0.673228i	−0.603585	−	0.797299i	$-0.706262\pi$
$563$	2.92329e6	−	5.06329e6i	0.388688	−	0.673228i	0.992273	+	0.124071i	$0.0395949\pi$
$564$	−1.54230e6	−	2.67134e6i	−0.204160	−	0.353616i
$565$	−453152.	+	4.31145e6i	−0.0597204	+	0.568202i
$566$	2.20310e6	−	1.60064e6i	0.289063	−	0.210017i
$567$	−179245.	−	1.70540e6i	−0.0234147	−	0.222776i
$568$	2.59566e6	+	2.88278e6i	0.337581	+	0.374921i
$569$	1.17150e7	−	5.21584e6i	1.51691	−	0.675372i	0.531734	−	0.846912i	$-0.321541\pi$
$569$	1.17150e7	−	5.21584e6i	1.51691	−	0.675372i	0.985177	+	0.171539i	$0.0548740\pi$
$570$	1.47248e7	−	3.12985e6i	1.89829	−	0.403494i
$571$	7.42695e6	+	1.57865e6i	0.953280	+	0.202626i	0.658197	−	0.752846i	$-0.271319\pi$
$571$	7.42695e6	+	1.57865e6i	0.953280	+	0.202626i	0.295083	+	0.955472i	$0.404653\pi$
$572$	351519.	+	156506.i	0.0449220	+	0.0200005i
$573$	−1.01851e6	−	3.13466e6i	−0.129592	−	0.398845i
$574$	−267011.	−	821777.i	−0.0338260	−	0.104106i
$575$	1.11511e6	+	496480.i	0.140653	+	0.0626227i
$576$	−1.92865e6	−	409948.i	−0.242213	−	0.0514840i
$577$	−9.18996e6	+	1.95339e6i	−1.14914	+	0.244258i	−0.742833	−	0.669477i	$-0.766518\pi$
$577$	−9.18996e6	+	1.95339e6i	−1.14914	+	0.244258i	−0.406311	+	0.913735i	$0.633185\pi$
$578$	1.64214e6	−	731130.i	0.204452	−	0.0910280i
$579$	−1.48260e7	−	1.64660e7i	−1.83793	−	2.04122i
$580$	308789.	+	2.93793e6i	0.0381147	+	0.362637i
$581$	−2.65824e6	+	1.93132e6i	−0.326703	+	0.237364i
$582$	−1.02839e6	+	9.78447e6i	−0.125849	+	1.19737i
$583$	318398.	+	551481.i	0.0387970	+	0.0671985i
$584$	−313481.	+	542965.i	−0.0380346	+	0.0658779i
$585$	1.58331e7	+	1.15034e7i	1.91283	+	1.38975i
$586$	5.74855e6	−	6.38441e6i	0.691535	−	0.768028i
$587$	−3.71732e6	+	1.14407e7i	−0.445281	+	1.37044i	0.436894	+	0.899513i	$0.356079\pi$
$587$	−3.71732e6	+	1.14407e7i	−0.445281	+	1.37044i	−0.882175	+	0.470922i	$0.843921\pi$
$588$	−6.82950e6			−0.814602
$589$	1.10897e7	+	1.06343e7i	1.31714	+	1.26305i
$590$	6.26786e6			0.741291
$591$	3.41016e6	−	1.04954e7i	0.401611	−	1.23603i
$592$	674987.	−	749649.i	0.0791573	−	0.0879131i
$593$	−3.29339e6	−	2.39278e6i	−0.384597	−	0.279426i	0.378641	−	0.925544i	$-0.376392\pi$
$593$	−3.29339e6	−	2.39278e6i	−0.384597	−	0.279426i	−0.763238	+	0.646118i	$0.776392\pi$
$594$	369618.	−	640198.i	0.0429821	−	0.0744471i
$595$	−738369.	−	1.27889e6i	−0.0855030	−	0.148096i
$596$	126968.	−	1.20802e6i	0.0146412	−	0.139302i
$597$	−1.78741e7	+	1.29863e7i	−2.05252	+	1.49124i
$598$	−565291.	−	5.37838e6i	−0.0646426	−	0.615034i
$599$	−6.31784e6	−	7.01667e6i	−0.719452	−	0.799032i	0.266893	−	0.963726i	$-0.414003\pi$
$599$	−6.31784e6	−	7.01667e6i	−0.719452	−	0.799032i	−0.986345	+	0.164694i	$0.947336\pi$
$600$	1.18614e6	−	528106.i	0.134512	−	0.0598884i
$601$	−9.10460e6	+	1.93524e6i	−1.02819	+	0.218549i	−0.690976	−	0.722878i	$-0.742819\pi$
$601$	−9.10460e6	+	1.93524e6i	−1.02819	+	0.218549i	−0.337217	+	0.941427i	$0.609486\pi$
$602$	1.83937e6	+	390971.i	0.206861	+	0.0439697i
$603$	−7.49048e6	−	3.33498e6i	−0.838912	−	0.373507i
$604$	2.02260e6	+	6.22493e6i	0.225589	+	0.694292i
$605$	2.41095e6	+	7.42015e6i	0.267794	+	0.824184i
$606$	−3.01111e6	−	1.34063e6i	−0.333077	−	0.148296i
$607$	−6.07123e6	−	1.29048e6i	−0.668814	−	0.142161i	−0.139023	−	0.990289i	$-0.544396\pi$
$607$	−6.07123e6	−	1.29048e6i	−0.668814	−	0.142161i	−0.529791	+	0.848128i	$0.677730\pi$
$608$	−2.87620e6	+	611356.i	−0.315545	+	0.0670711i
$609$	2.86987e6	−	1.27775e6i	0.313559	−	0.139605i
$610$	1.65251e6	+	1.83529e6i	0.179812	+	0.199701i
$611$	−625119.	−	5.94761e6i	−0.0677422	−	0.644524i
$612$	6.13845e6	−	4.45984e6i	0.662491	−	0.481328i
$613$	1.11105e6	−	1.05709e7i	0.119422	−	1.13622i	−0.756576	−	0.653905i	$-0.773129\pi$
$613$	1.11105e6	−	1.05709e7i	0.119422	−	1.13622i	0.875998	−	0.482315i	$-0.160204\pi$
$614$	2.14093e6	+	3.70819e6i	0.229182	+	0.396955i
$615$	4.59834e6	−	7.96455e6i	0.490245	−	0.849129i
$616$	45912.4	+	33357.3i	0.00487504	+	0.00354192i
$617$	9.38774e6	−	1.04261e7i	0.992768	−	1.10258i	−0.00195601	−	0.999998i	$-0.500623\pi$
$617$	9.38774e6	−	1.04261e7i	0.992768	−	1.10258i	0.994724	−	0.102583i	$-0.0327107\pi$
$618$	−1.87595e6	+	5.77359e6i	−0.197584	+	0.608100i
$619$	−1.43195e7			−1.50210			−0.751052	−	0.660243i	$-0.770453\pi$
$619$	−1.43195e7			−1.50210			−0.751052	+	0.660243i	$0.770453\pi$
$620$	−3.54307e6	−	2.19671e6i	−0.370169	−	0.229505i
$621$	−1.03897e7			−1.08112
$622$	220145.	−	677535.i	0.0228156	−	0.0702192i
$623$	−2.88318e6	+	3.20210e6i	−0.297613	+	0.330533i
$624$	−4.65387e6	−	3.38124e6i	−0.478468	−	0.347627i
$625$	3.42094e6	−	5.92525e6i	0.350305	−	0.606745i
$626$	−888861.	−	1.53955e6i	−0.0906563	−	0.157021i
$627$	232702.	−	2.21401e6i	0.0236391	−	0.224911i
$628$	613967.	−	446073.i	0.0621221	−	0.0451344i
$629$	405761.	+	3.86056e6i	0.0408925	+	0.389066i
$630$	1.93141e6	+	2.14504e6i	0.193875	+	0.215320i
$631$	1.13182e6	−	503919.i	0.113163	−	0.0503834i	−0.349374	−	0.936983i	$-0.613606\pi$
$631$	1.13182e6	−	503919.i	0.113163	−	0.0503834i	0.462537	+	0.886600i	$0.346939\pi$
$632$	−6.50481e6	+	1.38264e6i	−0.647801	+	0.137694i
$633$	2.51110e7	+	5.33750e6i	2.49089	+	0.529455i
$634$	−1.13868e7	−	5.06971e6i	−1.12506	−	0.500911i
$635$	282918.	+	870733.i	0.0278437	+	0.0856940i
$636$	−2.94185e6	−	9.05408e6i	−0.288388	−	0.887568i
$637$	−1.20962e7	−	5.38556e6i	−1.18114	−	0.525875i
$638$	427318.	+	90829.3i	0.0415623	+	0.00883434i
$639$	2.85399e7	−	6.06633e6i	2.76503	−	0.587725i
$640$	728847.	−	324503.i	0.0703374	−	0.0313162i
$641$	−1.32795e6	−	1.47484e6i	−0.127655	−	0.141775i	0.675929	−	0.736967i	$-0.263743\pi$
$641$	−1.32795e6	−	1.47484e6i	−0.127655	−	0.141775i	−0.803584	+	0.595192i	$0.797076\pi$
$642$	286343.	+	2.72437e6i	0.0274189	+	0.260873i
$643$	1.30599e6	−	948858.i	0.124570	−	0.0905053i	−0.523756	−	0.851868i	$-0.675470\pi$
$643$	1.30599e6	−	948858.i	0.124570	−	0.0905053i	0.648326	+	0.761363i	$0.275470\pi$
$644$	83373.1	−	793242.i	0.00792157	−	0.0753687i
$645$	1.00073e7	+	1.73332e7i	0.947151	+	1.64051i
$646$	5.65765e6	−	9.79934e6i	0.533402	−	0.923880i
$647$	321603.	+	233658.i	0.0302037	+	0.0219443i	0.602785	−	0.797904i	$-0.294058\pi$
$647$	321603.	+	233658.i	0.0302037	+	0.0219443i	−0.572581	+	0.819848i	$0.694058\pi$
$648$	−2.38549e6	+	2.64935e6i	−0.223172	+	0.247857i
$649$	286432.	−	881546.i	0.0266937	−	0.0821548i
$650$	2.51731e6			0.233697
$651$	−1.05738e6	+	4.30523e6i	−0.0977868	+	0.398147i
$652$	1.49919e6			0.138114
$653$	−4.17982e6	+	1.28642e7i	−0.383597	+	1.18059i	0.553896	+	0.832586i	$0.313140\pi$
$653$	−4.17982e6	+	1.28642e7i	−0.383597	+	1.18059i	−0.937493	+	0.348004i	$0.886860\pi$
$654$	1.51510e7	−	1.68269e7i	1.38515	−	1.53836i
$655$	−1.50262e7	−	1.09172e7i	−1.36850	−	0.994274i
$656$	−898195.	+	1.55572e6i	−0.0814913	+	0.141147i
$657$	2.35788e6	+	4.08397e6i	0.213112	+	0.369121i
$658$	92196.9	−	877195.i	0.00830140	−	0.0789826i
$659$	5.34035e6	−	3.87999e6i	0.479023	−	0.348030i	−0.321924	−	0.946765i	$-0.604330\pi$
$659$	5.34035e6	−	3.87999e6i	0.479023	−	0.348030i	0.800947	+	0.598735i	$0.204330\pi$
$660$	63137.9	+	600717.i	0.00564196	+	0.0536797i
$661$	−7.43952e6	−	8.26242e6i	−0.662279	−	0.735536i	0.314624	−	0.949216i	$-0.398122\pi$
$661$	−7.43952e6	−	8.26242e6i	−0.662279	−	0.735536i	−0.976904	+	0.213681i	$0.931455\pi$
$662$	7.38490e6	−	3.28797e6i	0.654937	−	0.291597i
$663$	2.16527e7	−	4.60242e6i	1.91306	−	0.406633i
$664$	6.68181e6	+	1.42026e6i	0.588131	+	0.125011i
$665$	3.93240e6	+	1.75082e6i	0.344829	+	0.153528i
$666$	−2.34464e6	−	7.21607e6i	−0.204829	−	0.630399i
$667$	−1.89735e6	−	5.83945e6i	−0.165133	−	0.508227i
$668$	8.85998e6	+	3.94472e6i	0.768231	+	0.342038i
$669$	4.16844e6	+	886030.i	0.360088	+	0.0765391i
$670$	3.24519e6	−	689786.i	0.279288	−	0.0593646i
$671$	333643.	−	148547.i	0.0286072	−	0.0127368i
$672$	−567703.	−	630498.i	−0.0484951	−	0.0538593i
$673$	1.68343e6	+	1.60168e7i	0.143271	+	1.36313i	0.795887	+	0.605445i	$0.207005\pi$
$673$	1.68343e6	+	1.60168e7i	0.143271	+	1.36313i	−0.652616	+	0.757688i	$0.726329\pi$
$674$	−8.02287e6	+	5.82896e6i	−0.680268	+	0.494244i
$675$	505517.	−	4.80967e6i	0.0427048	−	0.406309i
$676$	−2.60608e6	−	4.51386e6i	−0.219342	−	0.379911i
$677$	574218.	−	994575.i	0.0481510	−	0.0834000i	−0.840945	−	0.541120i	$-0.818000\pi$
$677$	574218.	−	994575.i	0.0481510	−	0.0834000i	0.889096	+	0.457720i	$0.151334\pi$
$678$	−7.75398e6	−	5.63360e6i	−0.647814	−	0.470665i
$679$	−1.88242e6	+	2.09064e6i	−0.156690	+	0.174022i
$680$	−948723.	+	2.91987e6i	−0.0786805	+	0.242154i
$681$	−2.73505e7			−2.25995
$682$	−470870.	+	397930.i	−0.0387650	+	0.0327601i
$683$	5.12080e6			0.420036			0.210018	−	0.977698i	$-0.432648\pi$
$683$	5.12080e6			0.420036			0.210018	+	0.977698i	$0.432648\pi$
$684$	−6.83451e6	+	2.10345e7i	−0.558557	+	1.71906i
$685$	−5.30700e6	+	5.89402e6i	−0.432138	+	0.479938i
$686$	−3.25420e6	−	2.36432e6i	−0.264019	−	0.191821i
$687$	−7.57266e6	+	1.31162e7i	−0.612148	+	1.06027i
$688$	−1.95474e6	−	3.38571e6i	−0.157441	−	0.272696i
$689$	1.92931e6	−	1.83561e7i	0.154830	−	1.47310i
$690$	6.86803e6	−	4.98992e6i	0.549173	−	0.398998i
$691$	−1.50861e6	−	1.43535e7i	−0.120194	−	1.14357i	−0.873815	−	0.486258i	$-0.838361\pi$
$691$	−1.50861e6	−	1.43535e7i	−0.120194	−	1.14357i	0.753621	−	0.657309i	$-0.228305\pi$
$692$	−901563.	−	1.00129e6i	−0.0715700	−	0.0794865i
$693$	389953.	−	173618.i	0.0308446	−	0.0137329i
$694$	2.32306e6	−	493781.i	0.183089	−	0.0389167i
$695$	−1.34841e7	−	2.86613e6i	−1.05891	−	0.225078i
$696$	−5.96644e6	−	2.65643e6i	−0.466866	−	0.207862i
$697$	−2.13616e6	−	6.57443e6i	−0.166553	−	0.512597i
$698$	411724.	+	1.26716e6i	0.0319866	+	0.0984446i
$699$	−1.30023e6	−	578899.i	−0.100653	−	0.0448136i
$700$	363157.	+	77191.5i	0.0280124	+	0.00595421i
$701$	1.24474e7	−	2.64578e6i	0.956719	−	0.203357i	0.297007	−	0.954875i	$-0.404012\pi$
$701$	1.24474e7	−	2.64578e6i	0.956719	−	0.203357i	0.659712	+	0.751519i	$0.270678\pi$
$702$	−1.95741e7	+	8.71493e6i	−1.49913	+	0.667454i
$703$	−7.57130e6	−	8.40879e6i	−0.577806	−	0.641719i
$704$	−12332.8	−	117338.i	−0.000937840	−	0.00892295i
$705$	7.59491e6	−	5.51803e6i	0.575506	−	0.418130i
$706$	1.17620e6	−	1.11908e7i	0.0888117	−	0.844987i
$707$	−471248.	−	816225.i	−0.0354569	−	0.0614132i
$708$	−6.92862e6	+	1.20007e7i	−0.519474	+	0.899755i
$709$	1.36705e6	+	993221.i	0.102134	+	0.0742045i	0.637680	−	0.770301i	$-0.279894\pi$
$709$	1.36705e6	+	993221.i	0.102134	+	0.0742045i	−0.535546	+	0.844506i	$0.679894\pi$
$710$	−7.89977e6	+	8.77358e6i	−0.588124	+	0.653177i
$711$	−1.54569e7	+	4.75715e7i	−1.14670	+	3.52917i
$712$	8.95807e6			0.662238
$713$	8.15241e6	+	2.93489e6i	0.600568	+	0.216206i
$714$	3.26484e6			0.239671
$715$	−361882.	+	1.11376e6i	−0.0264729	+	0.0814753i
$716$	3.18586e6	−	3.53825e6i	0.232244	−	0.257933i
$717$	3.19397e7	+	2.32055e7i	2.32024	+	1.68575i
$718$	−7.56434e6	+	1.31018e7i	−0.547596	+	0.948463i
$719$	−5.69291e6	−	9.86041e6i	−0.410688	−	0.711332i	0.584277	−	0.811554i	$-0.301378\pi$
$719$	−5.69291e6	−	9.86041e6i	−0.410688	−	0.711332i	−0.994965	+	0.100222i	$0.968045\pi$
$720$	627264.	−	5.96802e6i	0.0450941	−	0.429041i
$721$	−1.40437e6	+	1.02033e6i	−0.100610	+	0.0730976i
$722$	2.41237e6	+	2.29522e7i	0.172227	+	1.63863i
$723$	1.90859e7	+	2.11971e7i	1.35790	+	1.50810i
$724$	1.46913e6	−	654100.i	0.104163	−	0.0463765i
$725$	2.79556e6	−	594215.i	0.197526	−	0.0419855i
$726$	−1.68721e7	−	3.58627e6i	−1.18803	−	0.252523i
$727$	5.37128e6	+	2.39145e6i	0.376913	+	0.167813i	0.586445	−	0.809989i	$-0.300527\pi$
$727$	5.37128e6	+	2.39145e6i	0.376913	+	0.167813i	−0.209531	+	0.977802i	$0.567194\pi$
$728$	−508302.	−	1.56439e6i	−0.0355462	−	0.109400i
$729$	−4.68047e6	−	1.44050e7i	−0.326190	−	1.00391i
$730$	−1.74316e6	−	776106.i	−0.121068	−	0.0539031i
$731$	1.47155e7	+	3.12787e6i	1.01855	+	0.216499i
$732$	−5.34066e6	+	1.13519e6i	−0.368398	+	0.0783053i
$733$	−1.10264e7	+	4.90928e6i	−0.758009	+	0.337487i	−0.749086	−	0.662473i	$-0.769507\pi$
$733$	−1.10264e7	+	4.90928e6i	−0.758009	+	0.337487i	−0.00892309	+	0.999960i	$0.502840\pi$
$734$	−8.38216e6	−	9.30933e6i	−0.574270	−	0.637791i
$735$	−2.17265e6	−	2.06714e7i	−0.148344	−	1.41140i
$736$	−1.34154e6	+	974683.i	−0.0912867	+	0.0663237i
$737$	51284.9	−	487943.i	0.00347793	−	0.0330903i
$738$	6.75586e6	+	1.17015e7i	0.456604	+	0.790862i
$739$	−3.93308e6	+	6.81229e6i	−0.264924	+	0.458862i	−0.967544	−	0.252704i	$-0.918680\pi$
$739$	−3.93308e6	+	6.81229e6i	−0.264924	+	0.458862i	0.702620	+	0.711566i	$0.252014\pi$
$740$	2.48375e6	+	1.80455e6i	0.166736	+	0.121141i
$741$	−4.31761e7	+	4.79519e7i	−2.88867	+	3.20819i
$742$	841208.	−	2.58897e6i	0.0560911	−	0.172631i
$743$	−7.62690e6			−0.506846			−0.253423	−	0.967356i	$-0.581556\pi$
$743$	−7.62690e6			−0.506846			−0.253423	+	0.967356i	$0.581556\pi$
$744$	8.12249e6	−	4.35543e6i	0.537969	−	0.288469i
$745$	3.69679e6			0.244025
$746$	6.03851e6	−	1.85846e7i	0.397267	−	1.22266i
$747$	3.43804e7	−	3.81833e7i	2.25429	−	2.50364i
$748$	367311.	+	266867.i	0.0240038	+	0.0174398i
$749$	−391656.	+	678369.i	−0.0255094	+	0.0441836i
$750$	1.01670e7	+	1.76098e7i	0.659997	+	1.14315i
$751$	−254470.	+	2.42112e6i	−0.0164641	+	0.156645i	−0.999665	−	0.0258812i	$-0.991761\pi$
$751$	−254470.	+	2.42112e6i	−0.0164641	+	0.156645i	0.983201	+	0.182526i	$0.0584275\pi$
$752$	−1.48352e6	+	1.07784e6i	−0.0956639	+	0.0695039i
$753$	−2.01450e6	−	1.91667e7i	−0.129473	−	1.23186i
$754$	−8.47276e6	−	9.40996e6i	−0.542746	−	0.602781i
$755$	−1.81980e7	+	8.10228e6i	−1.16187	+	0.517297i
$756$	−3.09107e6	+	657027.i	−0.196700	+	0.0418099i
$757$	−1.91118e7	−	4.06235e6i	−1.21217	−	0.257654i	−0.442895	−	0.896574i	$-0.646048\pi$
$757$	−1.91118e7	−	4.06235e6i	−1.21217	−	0.257654i	−0.769274	+	0.638919i	$0.779382\pi$
$758$	1.48950e7	+	6.63168e6i	0.941602	+	0.419228i
$759$	−387951.	−	1.19399e6i	−0.0244440	−	0.0752309i
$760$	−2.76544e6	−	8.51114e6i	−0.173672	−	0.534507i
$761$	2.28908e7	+	1.01916e7i	1.43284	+	0.637943i	0.968794	−	0.247866i	$-0.0797293\pi$
$761$	2.28908e7	+	1.01916e7i	1.43284	+	0.637943i	0.464050	+	0.885809i	$0.346396\pi$
$762$	−1.97989e6	−	420838.i	−0.123525	−	0.0262559i
$763$	6.33312e6	−	1.34615e6i	0.393828	−	0.0837106i
$764$	−1.78999e6	+	796954.i	−0.110947	+	0.0493969i
$765$	1.54518e7	+	1.71609e7i	0.954606	+	1.06020i
$766$	166188.	+	1.58118e6i	0.0102336	+	0.0973662i
$767$	−2.17352e7	+	1.57915e7i	−1.33406	+	0.969251i
$768$	−184373.	+	1.75420e6i	−0.0112796	+	0.107319i
$769$	−178434.	−	309057.i	−0.0108808	−	0.0188461i	0.860534	−	0.509393i	$-0.170130\pi$
$769$	−178434.	−	309057.i	−0.0108808	−	0.0188461i	−0.871415	+	0.490547i	$0.836797\pi$
$770$	−86359.2	+	149578.i	−0.00524906	+	0.00909164i
$771$	−3.88597e6	−	2.82333e6i	−0.235431	−	0.171051i
$772$	−8.81375e6	+	9.78866e6i	−0.532252	+	0.591126i
$773$	39973.1	−	123025.i	0.00240613	−	0.00740531i	−0.949846	−	0.312717i	$-0.898761\pi$
$773$	39973.1	−	123025.i	0.00240613	−	0.00740531i	0.952252	+	0.305312i	$0.0987608\pi$
$774$	−2.94055e7			−1.76432
$775$	−1.75530e6	+	3.63118e6i	−0.104978	+	0.217167i
$776$	5.84869e6			0.348662
$777$	1.00888e6	−	3.10500e6i	0.0599494	−	0.184505i
$778$	−228068.	+	253296.i	−0.0135088	+	0.0150030i
$779$	1.63017e7	+	1.18439e7i	0.962476	+	0.699280i
$780$	8.75372e6	−	1.51619e7i	0.515177	−	0.892312i
$781$	872958.	+	1.51201e6i	0.0512113	+	0.0887005i
$782$	667006.	−	6.34614e6i	0.0390044	−	0.371102i
$783$	−1.96805e7	+	1.42987e7i	−1.14718	+	0.833476i
$784$	424385.	+	4.03775e6i	0.0246587	+	0.234611i
$785$	1.54548e6	+	1.71643e6i	0.0895139	+	0.0994153i
$786$	3.75127e7	−	1.67017e7i	2.16582	−	0.964285i
$787$	1.10122e7	−	2.34072e6i	0.633780	−	0.134714i	0.120191	−	0.992751i	$-0.461649\pi$
$787$	1.10122e7	−	2.34072e6i	0.633780	−	0.134714i	0.513588	+	0.858037i	$0.328316\pi$
$788$	−6.41701e6	−	1.36398e6i	−0.368144	−	0.0782514i
$789$	3.06077e7	+	1.36274e7i	1.75040	+	0.779330i
$790$	−6.25430e6	−	1.92488e7i	−0.356542	−	1.09732i
$791$	−846900.	−	2.60649e6i	−0.0481273	−	0.148120i
$792$	−810711.	−	360952.i	−0.0459254	−	0.0204473i
$793$	−1.03544e7	−	2.20089e6i	−0.584710	−	0.124284i
$794$	−1.49774e7	+	3.18354e6i	−0.843110	+	0.179209i
$795$	2.64688e7	−	1.17847e7i	1.48531	−	0.661302i
$796$	8.78846e6	+	9.76058e6i	0.491621	+	0.546000i
$797$	−1.81559e6	−	1.72742e7i	−0.101245	−	0.963279i	−0.920736	−	0.390187i	$-0.872410\pi$
$797$	−1.81559e6	−	1.72742e7i	−0.101245	−	0.963279i	0.819491	−	0.573092i	$-0.194256\pi$
$798$	−7.69916e6	+	5.59377e6i	−0.427993	+	0.310955i
$799$	737599.	−	7.01779e6i	0.0408746	−	0.388896i
$800$	−385934.	−	668458.i	−0.0213201	−	0.0369274i
$801$	3.36895e7	−	5.83519e7i	1.85530	−	3.21347i
$802$	−919442.	−	668014.i	−0.0504764	−	0.0366733i
$803$	−188816.	+	209701.i	−0.0103335	+	0.0114766i
$804$	−2.26660e6	+	6.97589e6i	−0.123662	+	0.380592i
$805$	2.42749e6			0.132028
$806$	1.78209e7	−	1.30900e6i	0.966254	−	0.0709745i
$807$	2.06859e7			1.11813
$808$	−605501.	+	1.86354e6i	−0.0326277	+	0.100418i
$809$	1.01549e6	−	1.12782e6i	0.0545513	−	0.0605854i	−0.715252	−	0.698867i	$-0.753688\pi$
$809$	1.01549e6	−	1.12782e6i	0.0545513	−	0.0605854i	0.769803	+	0.638282i	$0.220355\pi$
$810$	−8.77788e6	−	6.37750e6i	−0.470086	−	0.341537i
$811$	−1.32276e7	+	2.29108e7i	−0.706200	+	1.22317i	0.260056	+	0.965593i	$0.416259\pi$
$811$	−1.32276e7	+	2.29108e7i	−0.706200	+	1.22317i	−0.966257	+	0.257581i	$0.917074\pi$
$812$	−933766.	−	1.61733e6i	−0.0496990	−	0.0860813i
$813$	2.66115e6	−	2.53192e7i	0.141203	−	1.34346i
$814$	367306.	−	266863.i	0.0194297	−	0.0141165i
$815$	476934.	+	4.53773e6i	0.0251515	+	0.239301i
$816$	−4.54178e6	−	5.04415e6i	−0.238781	−	0.265193i
$817$	−4.00612e7	+	1.78364e7i	−2.09976	+	0.934872i
$818$	9.85445e6	−	2.09463e6i	0.514931	−	0.109452i
$819$	−1.21019e7	−	2.57234e6i	−0.630441	−	0.134004i
$820$	−4.99456e6	−	2.22372e6i	−0.259396	−	0.115490i
$821$	1.84552e6	+	5.67994e6i	0.0955568	+	0.294094i	0.987398	−	0.158254i	$-0.0505866\pi$
$821$	1.84552e6	+	5.67994e6i	0.0955568	+	0.294094i	−0.891842	+	0.452348i	$0.850587\pi$
$822$	−5.41849e6	−	1.66764e7i	−0.279704	−	0.860841i
$823$	9.89630e6	+	4.40612e6i	0.509300	+	0.226755i	0.645265	−	0.763959i	$-0.276747\pi$
$823$	9.89630e6	+	4.40612e6i	0.509300	+	0.226755i	−0.135965	+	0.990714i	$0.543414\pi$
$824$	3.53004e6	+	750334.i	0.181118	+	0.0384979i
$825$	571607.	−	121499.i	0.0292390	−	0.00621494i
$826$	−3.61984e6	+	1.61166e6i	−0.184603	+	0.0821907i
$827$	−448887.	−	498539.i	−0.0228230	−	0.0253475i	0.731625	−	0.681707i	$-0.238762\pi$
$827$	−448887.	−	498539.i	−0.0228230	−	0.0253475i	−0.754448	+	0.656360i	$0.772095\pi$
$828$	1.30373e6	+	1.24042e7i	0.0660866	+	0.628772i
$829$	3.55496e6	−	2.58283e6i	0.179659	−	0.130530i	−0.494321	−	0.869279i	$-0.664583\pi$
$829$	3.55496e6	−	2.58283e6i	0.179659	−	0.130530i	0.673980	+	0.738750i	$0.264583\pi$
$830$	−2.17315e6	+	2.06762e7i	−0.109495	+	1.04178i
$831$	9.09478e6	+	1.57526e7i	0.456867	+	0.791316i
$832$	−1.70987e6	+	2.96158e6i	−0.0856356	+	0.148325i
$833$	−1.26396e7	−	9.18321e6i	−0.631133	−	0.458545i
$834$	2.03932e7	−	2.26490e7i	1.01524	−	1.12754i
$835$	−9.12118e6	+	2.80721e7i	−0.452726	+	1.39335i
$836$	−1.32343e6			−0.0654915
$837$	1.07769e6	−	3.43121e7i	0.0531718	−	1.69291i
$838$	−1.15388e6			−0.0567613
$839$	−6.04778e6	+	1.86132e7i	−0.296614	+	0.912884i	0.686061	+	0.727544i	$0.259338\pi$
$839$	−6.04778e6	+	1.86132e7i	−0.296614	+	0.912884i	−0.982675	+	0.185339i	$0.940662\pi$
$840$	1.72778e6	−	1.91889e6i	0.0844869	−	0.0938322i
$841$	4.96332e6	+	3.60606e6i	0.241981	+	0.175810i
$842$	−9.24419e6	+	1.60114e7i	−0.449354	+	0.778304i
$843$	3.48193e6	+	6.03088e6i	0.168753	+	0.292288i
$844$	1.59525e6	−	1.51778e7i	0.0770857	−	0.733421i
$845$	1.28334e7	−	9.32401e6i	0.618301	−	0.449222i
$846$	1.44172e6	+	1.37170e7i	0.0692554	+	0.658921i
$847$	−3.30033e6	−	3.66539e6i	−0.158070	−	0.175554i
$848$	−5.17017e6	+	2.30191e6i	−0.246896	+	0.109925i
$849$	−1.79227e7	+	3.80960e6i	−0.853366	+	0.181388i
$850$	2.90535e6	+	617552.i	0.137928	+	0.0293174i
$851$	−5.82934e6	−	2.59539e6i	−0.275928	−	0.122851i
$852$	−8.06573e6	−	2.48238e7i	−0.380667	−	1.17157i
$853$	−4.72705e6	−	1.45484e7i	−0.222442	−	0.684607i	−0.998541	−	0.0539960i	$-0.982804\pi$
$853$	−4.72705e6	−	1.45484e7i	−0.222442	−	0.684607i	0.776099	−	0.630611i	$-0.217196\pi$
$854$	−1.42627e6	−	635018.i	−0.0669204	−	0.0297949i
$855$	−6.58409e7	−	1.39949e7i	−3.08021	−	0.654719i
$856$	1.59292e6	−	338585.i	0.0743034	−	0.0157937i
$857$	3.01185e7	−	1.34096e7i	1.40082	−	0.623683i	0.439277	−	0.898352i	$-0.355235\pi$
$857$	3.01185e7	−	1.34096e7i	1.40082	−	0.623683i	0.961539	+	0.274668i	$0.0885681\pi$
$858$	−1.73242e6	−	1.92405e6i	−0.0803406	−	0.0892273i
$859$	−1.17729e6	−	1.12012e7i	−0.0544378	−	0.517941i	−0.987431	−	0.158048i	$-0.949480\pi$
$859$	−1.17729e6	−	1.12012e7i	−0.0544378	−	0.517941i	0.932994	−	0.359893i	$-0.117187\pi$
$860$	9.62592e6	−	6.99364e6i	0.443809	−	0.322446i
$861$	−607724.	+	5.78210e6i	−0.0279382	+	0.265814i
$862$	−8.05416e6	−	1.39502e7i	−0.369192	−	0.639459i
$863$	1.17016e7	−	2.02677e7i	0.534832	−	0.926356i	−0.464340	−	0.885657i	$-0.653708\pi$
$863$	1.17016e7	−	2.02677e7i	0.534832	−	0.926356i	0.999171	−	0.0406988i	$-0.0129584\pi$
$864$	5.31515e6	+	3.86168e6i	0.242232	+	0.175992i
$865$	2.74386e6	−	3.04737e6i	0.124687	−	0.138479i
$866$	−6.00621e6	+	1.84852e7i	−0.272148	+	0.837587i
$867$	−1.20950e7			−0.546459
$868$	2.61105e6	+	357622.i	0.117629	+	0.0161111i
$869$	−2.99306e6			−0.134452
$870$	6.14234e6	−	1.89042e7i	0.275128	−	0.846758i
$871$	−9.51553e6	+	1.05681e7i	−0.424999	+	0.472009i
$872$	−1.08899e7	−	7.91198e6i	−0.484990	−	0.352366i
$873$	2.19958e7	−	3.80978e7i	0.976795	−	1.69186i
$874$	9.30015e6	+	1.61083e7i	0.411824	+	0.713299i
$875$	−607774.	+	5.78259e6i	−0.0268363	+	0.255330i
$876$	3.41290e6	−	2.47961e6i	0.150267	−	0.109175i
$877$	853244.	+	8.11807e6i	0.0374605	+	0.356413i	0.997156	+	0.0753700i	$0.0240138\pi$
$877$	853244.	+	8.11807e6i	0.0374605	+	0.356413i	−0.959695	+	0.281043i	$0.909320\pi$
$878$	5.80440e6	+	6.44644e6i	0.254110	+	0.282217i
$879$	−5.28082e7	+	2.35117e7i	−2.30531	+	1.02639i
$880$	351234.	−	74657.0i	0.0152894	−	0.00324985i
$881$	−2.84224e7	−	6.04136e6i	−1.23373	−	0.262238i	−0.455512	−	0.890230i	$-0.650544\pi$
$881$	−2.84224e7	−	6.04136e6i	−1.23373	−	0.262238i	−0.778220	+	0.627992i	$0.783877\pi$
$882$	2.78975e7	+	1.24208e7i	1.20752	+	0.537622i
$883$	424548.	+	1.30663e6i	0.0183242	+	0.0563961i	0.959801	−	0.280683i	$-0.0905610\pi$
$883$	424548.	+	1.30663e6i	0.0183242	+	0.0563961i	−0.941476	+	0.337079i	$0.890561\pi$
$884$	−4.06655e6	−	1.25156e7i	−0.175023	−	0.538666i
$885$	−3.85277e7	−	1.71536e7i	−1.65354	−	0.736204i
$886$	1.57528e7	+	3.34837e6i	0.674178	+	0.143301i
$887$	1.70914e7	−	3.63290e6i	0.729407	−	0.155040i	0.171784	−	0.985135i	$-0.445047\pi$
$887$	1.70914e7	−	3.63290e6i	0.729407	−	0.155040i	0.557623	+	0.830094i	$0.311714\pi$
$888$	−6.20067e6	+	2.76072e6i	−0.263880	+	0.117487i
$889$	−387284.	−	430123.i	−0.0164352	−	0.0182532i
$890$	2.84980e6	+	2.71141e7i	0.120598	+	1.14741i
$891$	−1.29810e6	+	943127.i	−0.0547791	+	0.0397994i
$892$	264814.	−	2.51953e6i	0.0111437	−	0.106025i
$893$	1.02844e7	+	1.78132e7i	0.431570	+	0.747502i
$894$	−4.08651e6	+	7.07804e6i	−0.171005	+	0.296189i
$895$	1.17230e7	+	8.51727e6i	0.489195	+	0.355421i
$896$	−337487.	+	374818.i	−0.0140439	+	0.0155973i
$897$	−1.12446e7	+	3.46073e7i	−0.466619	+	1.43611i
$898$	8.22960e6			0.340555
$899$	1.94817e7	−	5.66034e6i	0.803948	−	0.233584i
$900$	−5.80569e6			−0.238917
$901$	6.72988e6	−	2.07125e7i	0.276182	−	0.850001i
$902$	−541000.	+	600842.i	−0.0221402	+	0.0245892i
$903$	−1.02364e7	−	7.43717e6i	−0.417761	−	0.303521i
$904$	−2.84887e6	+	4.93439e6i	−0.115945	+	0.200823i
$905$	2.44719e6	+	4.23865e6i	0.0993220	+	0.172031i
$906$	4.60348e6	−	4.37992e7i	0.186323	−	1.77274i
$907$	1.62939e7	−	1.18382e7i	0.657667	−	0.477823i	−0.208207	−	0.978085i	$-0.566763\pi$
$907$	1.62939e7	−	1.18382e7i	0.657667	−	0.477823i	0.865874	+	0.500262i	$0.166763\pi$
$908$	1.69956e6	+	1.61702e7i	0.0684103	+	0.650881i
$909$	9.86174e6	+	1.09526e7i	0.395862	+	0.439649i
$910$	4.57336e6	−	2.03619e6i	0.183076	−	0.0815109i
$911$	−2.20199e7	+	4.68048e6i	−0.879062	+	0.186850i	−0.625270	−	0.780408i	$-0.715011\pi$
$911$	−2.20199e7	+	4.68048e6i	−0.879062	+	0.186850i	−0.253792	+	0.967259i	$0.581678\pi$
$912$	1.93528e7	+	4.11356e6i	0.770471	+	0.163769i
$913$	2.80870e6	+	1.25051e6i	0.111514	+	0.0496491i
$914$	9.00720e6	+	2.77213e7i	0.356635	+	1.09761i
$915$	−5.13498e6	−	1.58038e7i	−0.202762	−	0.624036i
$916$	8.22516e6	+	3.66208e6i	0.323896	+	0.144208i
$917$	1.14851e7	+	2.44124e6i	0.451037	+	0.0958709i
$918$	−2.47294e7	+	5.25639e6i	−0.968515	+	0.205864i
$919$	1.49707e7	−	6.66541e6i	0.584729	−	0.260338i	−0.0929804	−	0.995668i	$-0.529639\pi$
$919$	1.49707e7	−	6.66541e6i	0.584729	−	0.260338i	0.677709	+	0.735330i	$0.262973\pi$
$920$	−3.37693e6	−	3.75046e6i	−0.131538	−	0.146088i
$921$	−3.01155e6	−	2.86530e7i	−0.116988	−	1.11307i
$922$	−2.01109e7	+	1.46114e7i	−0.779118	+	0.566062i
$923$	5.28963e6	−	5.03274e7i	0.204372	−	1.94447i
$924$	−190927.	−	330694.i	−0.00735676	−	0.0127423i
$925$	1.48511e6	−	2.57228e6i	0.0570695	−	0.0988472i
$926$	1.37205e7	+	9.96851e6i	0.525826	+	0.382035i
$927$	1.81634e7	−	2.01725e7i	0.694220	−	0.771010i
$928$	−1.19979e6	+	3.69256e6i	−0.0457334	+	0.140753i
$929$	2.26322e7			0.860375			0.430188	−	0.902739i	$-0.358447\pi$
$929$	2.26322e7			0.860375			0.430188	+	0.902739i	$0.358447\pi$
$930$	1.57669e7	+	2.31994e7i	0.597777	+	0.879568i
$931$	4.55408e7			1.72197
$932$	−261462.	+	804697.i	−0.00985981	+	0.0303454i
$933$	−3.20745e6	+	3.56224e6i	−0.120630	+	0.133973i
$934$	−5.26714e6	−	3.82680e6i	−0.197564	−	0.143539i
$935$	−690896.	+	1.19667e6i	−0.0258454	+	0.0447656i
$936$	1.28609e7	+	2.22758e7i	0.479825	+	0.831082i
$937$	−3.27468e6	+	3.11565e7i	−0.121848	+	1.15931i	0.747205	+	0.664593i	$0.231395\pi$
$937$	−3.27468e6	+	3.11565e7i	−0.121848	+	1.15931i	−0.869054	+	0.494718i	$0.835272\pi$
$938$	−1.69681e6	+	1.23281e6i	−0.0629690	+	0.0457496i
$939$	1.25032e6	+	1.18960e7i	0.0462763	+	0.440289i
$940$	−3.73432e6	−	4.14739e6i	−0.137845	−	0.153093i
$941$	3.95040e6	−	1.75883e6i	0.145434	−	0.0647516i	−0.332729	−	0.943023i	$-0.607969\pi$
$941$	3.95040e6	−	1.75883e6i	0.145434	−	0.0647516i	0.478163	+	0.878271i	$0.341303\pi$
$942$	−4.99478e6	+	1.06167e6i	−0.183396	+	0.0389819i
$943$	1.11150e7	+	2.36257e6i	0.407034	+	0.0865177i
$944$	7.52563e6	+	3.35063e6i	0.274861	+	0.122376i
$945$	−2.97203e6	−	9.14696e6i	−0.108261	−	0.333194i
$946$	−543734.	−	1.67344e6i	−0.0197542	−	0.0607971i
$947$	−9.17346e6	−	4.08429e6i	−0.332398	−	0.147993i	0.233750	−	0.972297i	$-0.424900\pi$
$947$	−9.17346e6	−	4.08429e6i	−0.332398	−	0.147993i	−0.566148	+	0.824304i	$0.691567\pi$
$948$	4.37682e7	+	9.30321e6i	1.58175	+	0.336211i
$949$	8.00016e6	−	1.70049e6i	0.288359	−	0.0612926i
$950$	−7.90950e6	+	3.52154e6i	−0.284341	+	0.126597i
$951$	5.61184e7	+	6.23258e7i	2.01212	+	2.23468i
$952$	−202877.	−	1.93024e6i	−0.00725504	−	0.0690271i
$953$	1.21723e7	−	8.84367e6i	0.434149	−	0.315428i	−0.349157	−	0.937064i	$-0.613532\pi$
$953$	1.21723e7	−	8.84367e6i	0.434149	−	0.315428i	0.783306	+	0.621637i	$0.213532\pi$
$954$	−4.44958e6	+	4.23349e7i	−0.158288	+	1.50601i
$955$	−2.98165e6	−	5.16436e6i	−0.105791	−	0.183235i
$956$	1.17349e7	−	2.03254e7i	0.415274	−	0.719275i
$957$	−2.37809e6	−	1.72778e6i	−0.0839361	−	0.0609831i
$958$	1.40265e7	−	1.55780e7i	0.493781	−	0.548399i
$959$	1.54939e6	−	4.76854e6i	0.0544020	−	0.167432i
$960$	−5.36822e6			−0.187997
$961$	−1.05381e7	+	2.66191e7i	−0.368092	+	0.929790i
$962$	−1.31594e7			−0.458458
$963$	3.78513e6	−	1.16494e7i	0.131527	−	0.404799i
$964$	1.13462e7	−	1.26012e7i	0.393239	−	0.436736i
$965$	−3.24320e7	−	2.35632e7i	−1.12113	−	0.814547i
$966$	−2.68340e6	+	4.64778e6i	−0.0925214	+	0.160252i
$967$	−2.10124e7	−	3.63946e7i	−0.722620	−	1.25161i	−0.959946	−	0.280184i	$-0.909604\pi$
$967$	−2.10124e7	−	3.63946e7i	−0.722620	−	1.25161i	0.237327	−	0.971430i	$-0.423729\pi$
$968$	−1.07185e6	+	1.01980e7i	−0.0367660	+	0.349805i
$969$	−6.15953e7	+	4.47516e7i	−2.10736	+	1.53108i
$970$	1.86063e6	+	1.77027e7i	0.0634936	+	0.604102i
$971$	1.20278e7	+	1.33583e7i	0.409392	+	0.454676i	0.912214	−	0.409714i	$-0.134371\pi$
$971$	1.20278e7	+	1.33583e7i	0.409392	+	0.454676i	−0.502822	+	0.864390i	$0.667705\pi$
$972$	−874502.	+	389353.i	−0.0296890	+	0.0132184i
$973$	8.52437e6	−	1.81191e6i	0.288656	−	0.0613556i
$974$	−2.30873e7	−	4.90736e6i	−0.779787	−	0.165749i
$975$	−1.54736e7	−	6.88928e6i	−0.521290	−	0.232093i
$976$	1.00302e6	+	3.08697e6i	0.0337042	+	0.103731i
$977$	458593.	+	1.41140e6i	0.0153706	+	0.0473059i	0.958448	−	0.285268i	$-0.0920828\pi$
$977$	458593.	+	1.41140e6i	0.0153706	+	0.0473059i	−0.943077	+	0.332574i	$0.892083\pi$
$978$	−9.21535e6	−	4.10294e6i	−0.308081	−	0.137166i
$979$	3.94371e6	+	838260.i	0.131507	+	0.0279526i
$980$	−1.20864e7	+	2.56904e6i	−0.402004	+	0.0854486i
$981$	−9.24925e7	+	4.11803e7i	−3.06856	+	1.36621i
$982$	−1.43419e7	−	1.59283e7i	−0.474601	−	0.527098i
$983$	−1.31737e6	−	1.25340e7i	−0.0434835	−	0.413718i	−0.994513	−	0.104617i	$-0.966638\pi$
$983$	−1.31737e6	−	1.25340e7i	−0.0434835	−	0.413718i	0.951029	−	0.309101i	$-0.100028\pi$
$984$	9.77873e6	−	7.10466e6i	0.321955	−	0.233914i
$985$	2.08703e6	−	1.98568e7i	0.0685391	−	0.652106i
$986$	−7.47037e6	−	1.29391e7i	−0.244709	−	0.423848i
$987$	−2.96740e6	+	5.13968e6i	−0.0969578	+	0.167936i
$988$	3.10331e7	+	2.25469e7i	1.01142	+	0.734843i
$989$	−1.65476e7	+	1.83779e7i	−0.537952	+	0.597456i
$990$	834611.	−	2.56867e6i	0.0270643	−	0.0832952i
$991$	2.66175e7			0.860962			0.430481	−	0.902600i	$-0.358344\pi$
$991$	2.66175e7			0.860962			0.430481	+	0.902600i	$0.358344\pi$
$992$	−3.07976e6	−	4.53155e6i	−0.0993658	−	0.146207i
$993$	−5.43924e7			−1.75051
$994$	2.30636e6	−	7.09824e6i	0.0740390	−	0.227869i
$995$	−2.67472e7	+	2.97058e7i	−0.856488	+	0.951226i
$996$	−3.71853e7	−	2.70167e7i	−1.18774	−	0.862946i
$997$	−1.42716e7	+	2.47191e7i	−0.454709	+	0.787579i	−0.998671	−	0.0515306i	$-0.983590\pi$
$997$	−1.42716e7	+	2.47191e7i	−0.454709	+	0.787579i	0.543963	+	0.839109i	$0.316923\pi$
$998$	−1.75942e7	−	3.04740e7i	−0.559168	−	0.968508i
$999$	−2.64263e6	+	2.51430e7i	−0.0837767	+	0.797082i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.g.b.45.7	✓	56
31.20	even	15	inner	62.6.g.b.51.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.g.b.45.7	✓	56	1.1	even	1	trivial
62.6.g.b.51.7	yes	56	31.20	even	15	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(18.0092 - 20.0013i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(24.3476 - 42.1713i) q^{5} +(53.8287 + 93.2340i) q^{6} +(-3.21782 + 30.6155i) q^{7} +(51.7771 - 37.6183i) q^{8} +(-50.3181 - 478.745i) q^{9} +(130.334 + 144.750i) q^{10} +(26.3145 - 11.7160i) q^{11} +(-421.219 + 89.5329i) q^{12} +(-816.653 - 173.585i) q^{13} +(-112.491 - 50.0841i) q^{14} +(-404.997 - 1246.45i) q^{15} +(79.1084 + 243.470i) q^{16} +(-899.956 - 400.686i) q^{17} +(1883.45 + 400.340i) q^{18} +(2808.79 - 597.027i) q^{19} +(-711.764 + 316.898i) q^{20} +(554.398 + 615.721i) q^{21} +(12.0437 + 114.588i) q^{22} +(1310.09 - 951.838i) q^{23} +(180.052 - 1713.08i) q^{24} +(376.889 + 652.791i) q^{25} +(1669.79 - 2892.17i) q^{26} +(-5190.57 - 3771.17i) q^{27} +(329.578 - 366.033i) q^{28} +(1171.67 - 3606.02i) q^{29} +5242.40 q^{30} +(3007.57 + 4425.34i) q^{31} -1024.00 q^{32} +(239.570 - 737.320i) q^{33} +(2636.71 - 2928.36i) q^{34} +(1212.75 + 881.113i) q^{35} +(-3851.06 + 6670.23i) q^{36} +(-1970.22 - 3412.52i) q^{37} +(-1200.63 + 11423.2i) q^{38} +(-18179.2 + 13208.0i) q^{39} +(-325.762 - 3099.42i) q^{40} +(4695.39 + 5214.76i) q^{41} +(-3027.62 + 1347.98i) q^{42} +(-14937.7 + 3175.10i) q^{43} +(-450.806 - 95.8219i) q^{44} +(-21414.4 - 9534.31i) q^{45} +(2001.64 + 6160.43i) q^{46} +(2213.49 + 6812.42i) q^{47} +(6294.40 + 2802.45i) q^{48} +(15512.8 + 3297.34i) q^{49} +(-2949.23 + 626.877i) q^{50} +(-24221.7 + 10784.2i) q^{51} +(8938.48 + 9927.19i) q^{52} +(2310.83 + 21986.1i) q^{53} +(20762.3 - 15084.7i) q^{54} +(146.618 - 1394.97i) q^{55} +(985.092 + 1706.23i) q^{56} +(38642.8 - 66931.4i) q^{57} +(12269.8 + 8914.56i) q^{58} +(21532.0 - 23913.7i) q^{59} +(-6479.96 + 19943.3i) q^{60} +12679.0 q^{61} +(-20552.6 + 5971.47i) q^{62} +14818.9 q^{63} +(1265.73 - 3895.53i) q^{64} +(-27203.8 + 30212.9i) q^{65} +(2508.81 + 1822.75i) q^{66} +(8516.46 - 14750.9i) q^{67} +(7880.99 + 13650.3i) q^{68} +(4555.78 - 43345.4i) q^{69} +(-4850.99 + 3524.45i) q^{70} +(6335.66 + 60279.8i) q^{71} +(-20614.9 - 22895.1i) q^{72} +(-8949.35 + 3984.51i) q^{73} +(15417.3 - 3277.05i) q^{74} +(19844.1 + 4218.00i) q^{75} +(-41972.6 - 18687.4i) q^{76} +(274.015 + 843.332i) q^{77} +(-27775.3 - 85483.7i) q^{78} +(-94925.0 - 42263.3i) q^{79} +(12193.6 + 2591.82i) q^{80} +(-54486.7 + 11581.5i) q^{81} +(-25641.9 + 11416.5i) q^{82} +(71420.1 + 79320.1i) q^{83} +(-1385.69 - 13183.9i) q^{84} +(-38809.2 + 28196.5i) q^{85} +(6385.18 - 60750.9i) q^{86} +(-51024.1 - 88376.3i) q^{87} +(921.755 - 1596.53i) q^{88} +(113238. + 82272.2i) q^{89} +(62740.4 - 69680.2i) q^{90} +(7942.22 - 24443.6i) q^{91} -25909.8 q^{92} +(142676. + 19541.7i) q^{93} -28652.0 q^{94} +(43209.9 - 132987. i) q^{95} +(-18441.4 + 20481.3i) q^{96} +(73932.7 + 53715.3i) q^{97} +(-31718.7 + 54938.4i) q^{98} +(-6933.07 - 12008.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 7 q^{3} - 224 q^{4} + 91 q^{5} - 152 q^{6} - 94 q^{7} + 896 q^{8} + 896 q^{9} - 944 q^{10} - 31 q^{11} - 112 q^{12} - 1244 q^{13} + 856 q^{14} + 518 q^{15} - 3584 q^{16} + 1064 q^{17}+ \cdots - 625437 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 7 * q^3 - 224 * q^4 + 91 * q^5 - 152 * q^6 - 94 * q^7 + 896 * q^8 + 896 * q^9 - 944 * q^10 - 31 * q^11 - 112 * q^12 - 1244 * q^13 + 856 * q^14 + 518 * q^15 - 3584 * q^16 + 1064 * q^17 - 1724 * q^18 + 619 * q^19 - 1024 * q^20 + 9541 * q^21 + 124 * q^22 - 1717 * q^23 + 768 * q^24 - 24033 * q^25 - 1344 * q^26 + 22754 * q^27 + 1776 * q^28 + 11733 * q^29 + 13928 * q^30 + 57065 * q^31 - 57344 * q^32 - 11248 * q^33 - 10456 * q^34 - 7296 * q^35 - 42464 * q^36 - 1504 * q^37 - 29736 * q^38 - 19566 * q^39 + 4096 * q^40 + 35891 * q^41 + 40636 * q^42 + 66400 * q^43 + 23344 * q^44 - 27014 * q^45 - 7612 * q^46 + 36521 * q^47 - 3072 * q^48 + 121465 * q^49 - 13108 * q^50 - 236890 * q^51 - 19904 * q^52 - 143661 * q^53 - 91016 * q^54 + 106359 * q^55 + 5056 * q^56 + 13060 * q^57 + 59468 * q^58 + 230112 * q^59 + 8288 * q^60 - 49860 * q^61 + 26740 * q^62 + 66726 * q^63 - 57344 * q^64 + 201094 * q^65 - 30508 * q^66 + 74372 * q^67 - 4656 * q^68 - 599733 * q^69 + 29184 * q^70 + 23383 * q^71 - 27584 * q^72 - 66915 * q^73 + 186916 * q^74 + 553648 * q^75 - 152736 * q^76 + 120895 * q^77 + 142024 * q^78 - 452529 * q^79 - 50944 * q^80 - 365276 * q^81 - 14324 * q^82 - 469160 * q^83 - 50464 * q^84 - 127377 * q^85 + 215540 * q^86 + 217461 * q^87 + 39744 * q^88 - 155746 * q^89 + 820796 * q^90 - 142152 * q^91 - 5952 * q^92 + 342224 * q^93 + 29656 * q^94 + 756444 * q^95 + 7168 * q^96 + 325303 * q^97 + 533540 * q^98 - 625437 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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