LMFDB - Embedded newform 76.6.k.a.3.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.6
Character	$\chi$	$=$	76.3
Dual form			76.6.k.a.51.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.42730 + 1.59511i) q^{2} +(17.0177 - 6.19395i) q^{3} +(26.9112 - 17.3143i) q^{4} +(1.86638 - 10.5848i) q^{5} +(-82.4803 + 60.7617i) q^{6} +(-201.097 + 116.103i) q^{7} +(-118.437 + 136.897i) q^{8} +(65.0895 - 54.6166i) q^{9} +O(q^{10})$	\(q+(-5.42730 + 1.59511i) q^{2} +(17.0177 - 6.19395i) q^{3} +(26.9112 - 17.3143i) q^{4} +(1.86638 - 10.5848i) q^{5} +(-82.4803 + 60.7617i) q^{6} +(-201.097 + 116.103i) q^{7} +(-118.437 + 136.897i) q^{8} +(65.0895 - 54.6166i) q^{9} +(6.75451 + 60.4239i) q^{10} +(172.811 + 99.7726i) q^{11} +(350.724 - 461.338i) q^{12} +(-209.739 + 576.252i) q^{13} +(906.215 - 950.900i) q^{14} +(-33.8000 - 191.689i) q^{15} +(424.428 - 931.900i) q^{16} +(377.298 + 316.591i) q^{17} +(-266.141 + 400.246i) q^{18} +(1167.38 + 1055.14i) q^{19} +(-133.042 - 317.164i) q^{20} +(-2703.08 + 3221.40i) q^{21} +(-1097.05 - 265.842i) q^{22} +(-3835.55 + 676.311i) q^{23} +(-1167.60 + 3063.26i) q^{24} +(2827.99 + 1029.30i) q^{25} +(219.127 - 3462.05i) q^{26} +(-1430.97 + 2478.51i) q^{27} +(-3401.51 + 6606.34i) q^{28} +(1519.29 + 1810.62i) q^{29} +(489.209 + 986.440i) q^{30} +(-1767.13 - 3060.76i) q^{31} +(-817.010 + 5734.71i) q^{32} +(3558.84 + 627.520i) q^{33} +(-2552.71 - 1116.40i) q^{34} +(853.604 + 2345.26i) q^{35} +(805.989 - 2596.78i) q^{36} -6372.56i q^{37} +(-8018.78 - 3864.49i) q^{38} +11105.6i q^{39} +(1227.97 + 1509.13i) q^{40} +(6177.25 + 16971.9i) q^{41} +(9531.91 - 21795.2i) q^{42} +(-21090.8 - 3718.88i) q^{43} +(6378.05 - 307.109i) q^{44} +(-456.623 - 790.894i) q^{45} +(19737.9 - 9788.69i) q^{46} +(1919.36 + 2287.40i) q^{47} +(1450.66 - 18487.7i) q^{48} +(18556.5 - 32140.7i) q^{49} +(-16990.2 - 1075.38i) q^{50} +(8381.71 + 3050.69i) q^{51} +(4333.10 + 19139.1i) q^{52} +(-10633.1 + 1874.89i) q^{53} +(3812.79 - 15734.2i) q^{54} +(1378.60 - 1642.95i) q^{55} +(7923.15 - 41280.4i) q^{56} +(26401.6 + 10725.5i) q^{57} +(-11133.8 - 7403.35i) q^{58} +(12191.1 + 10229.5i) q^{59} +(-4228.57 - 4573.37i) q^{60} +(-4248.83 - 24096.3i) q^{61} +(14473.0 + 13792.9i) q^{62} +(-6748.13 + 18540.3i) q^{63} +(-4713.36 - 32427.2i) q^{64} +(5708.05 + 3295.54i) q^{65} +(-20315.9 + 2271.02i) q^{66} +(-20462.8 + 17170.4i) q^{67} +(15635.1 + 1987.18i) q^{68} +(-61083.4 + 35266.5i) q^{69} +(-8373.72 - 11366.8i) q^{70} +(-1137.40 + 6450.53i) q^{71} +(-232.180 + 15379.2i) q^{72} +(20612.3 - 7502.27i) q^{73} +(10165.0 + 34585.8i) q^{74} +54501.4 q^{75} +(49684.7 + 8182.87i) q^{76} -46335.7 q^{77} +(-17714.7 - 60273.6i) q^{78} +(-31298.1 + 11391.6i) q^{79} +(-9071.81 - 6231.75i) q^{80} +(-12585.4 + 71375.6i) q^{81} +(-60597.9 - 82258.0i) q^{82} +(-28682.7 + 16560.0i) q^{83} +(-16966.7 + 133494. i) q^{84} +(4055.22 - 3402.74i) q^{85} +(120398. - 13458.8i) q^{86} +(37069.9 + 21402.3i) q^{87} +(-34125.8 + 11840.5i) q^{88} +(-8809.94 + 24205.1i) q^{89} +(3739.80 + 3564.05i) q^{90} +(-24727.0 - 140234. i) q^{91} +(-91509.5 + 84610.4i) q^{92} +(-49030.8 - 41141.7i) q^{93} +(-14065.6 - 9352.84i) q^{94} +(13347.2 - 10387.1i) q^{95} +(21616.9 + 102652. i) q^{96} +(99349.4 - 118400. i) q^{97} +(-49443.4 + 204037. i) q^{98} +(16697.4 - 2944.21i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) $ 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9 - 657 * q^10 - 9 * q^12 + 336 * q^13 - 2163 * q^14 + 1824 * q^16 - 12 * q^17 - 10242 * q^20 - 7842 * q^21 - 102 * q^22 - 11856 * q^24 - 12 * q^25 + 1317 * q^26 + 6660 * q^28 - 12 * q^29 - 40692 * q^30 - 3351 * q^32 - 8604 * q^33 - 15756 * q^34 + 81783 * q^36 + 50400 * q^38 + 39246 * q^40 - 29082 * q^41 - 123081 * q^42 - 39651 * q^44 - 6 * q^45 - 112554 * q^46 - 68403 * q^48 + 259302 * q^49 + 154188 * q^50 - 36867 * q^52 - 26280 * q^53 + 172605 * q^54 - 12 * q^57 + 229740 * q^58 - 136062 * q^60 + 169296 * q^61 + 35076 * q^62 + 63795 * q^64 - 189918 * q^65 + 73644 * q^66 + 59706 * q^68 - 200898 * q^69 - 177831 * q^70 - 188502 * q^72 + 397428 * q^73 - 530703 * q^74 - 53022 * q^76 + 159804 * q^77 - 618237 * q^78 + 18045 * q^80 - 110160 * q^81 + 155859 * q^82 + 733851 * q^84 - 645108 * q^85 + 616836 * q^86 + 598383 * q^88 - 226320 * q^89 + 546366 * q^90 - 754308 * q^92 + 558942 * q^93 - 454530 * q^96 - 177198 * q^97 - 76791 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	−5.42730	+	1.59511i	−0.959421	+	0.281979i
$2$	−5.42730	+	1.59511i	−0.959421	+	0.281979i
$3$	17.0177	−	6.19395i	1.09169	−	0.397342i	0.267442	−	0.963574i	$-0.413822\pi$
$3$	17.0177	−	6.19395i	1.09169	−	0.397342i	0.824246	+	0.566232i	$0.191599\pi$
$4$	26.9112	−	17.3143i	0.840976	−	0.541073i
$5$	1.86638	−	10.5848i	0.0333869	−	0.189346i	−0.963553	−	0.267517i	$-0.913797\pi$
$5$	1.86638	−	10.5848i	0.0333869	−	0.189346i	0.996940	+	0.0781708i	$0.0249079\pi$
$6$	−82.4803	+	60.7617i	−0.935346	+	0.689051i
$7$	−201.097	+	116.103i	−1.55117	+	0.895570i	−0.553126	+	0.833097i	$0.686565\pi$
$7$	−201.097	+	116.103i	−1.55117	+	0.895570i	−0.998047	+	0.0624727i	$0.980101\pi$
$8$	−118.437	+	136.897i	−0.654278	+	0.756254i
$9$	65.0895	−	54.6166i	0.267858	−	0.224760i
$10$	6.75451	+	60.4239i	0.0213596	+	0.191077i
$11$	172.811	+	99.7726i	0.430616	+	0.248616i	0.699609	−	0.714526i	$-0.253358\pi$
$11$	172.811	+	99.7726i	0.430616	+	0.248616i	−0.268993	+	0.963142i	$0.586691\pi$
$12$	350.724	−	461.338i	0.703092	−	0.924838i
$13$	−209.739	+	576.252i	−0.344207	+	0.945702i	0.639952	+	0.768415i	$0.278954\pi$
$13$	−209.739	+	576.252i	−0.344207	+	0.945702i	−0.984159	+	0.177287i	$0.943268\pi$
$14$	906.215	−	950.900i	1.23570	−	1.29663i
$15$	−33.8000	−	191.689i	−0.0387872	−	0.219973i
$16$	424.428	−	931.900i	0.414480	−	0.910058i
$17$	377.298	+	316.591i	0.316638	+	0.265690i	0.787229	−	0.616661i	$-0.211515\pi$
$17$	377.298	+	316.591i	0.316638	+	0.265690i	−0.470591	+	0.882351i	$0.655959\pi$
$18$	−266.141	+	400.246i	−0.193611	+	0.291170i
$19$	1167.38	+	1055.14i	0.741869	+	0.670545i
$19$	1167.38	+	1055.14i	0.741869	+	0.670545i
$20$	−133.042	−	317.164i	−0.0743726	−	0.177300i
$21$	−2703.08	+	3221.40i	−1.33755	+	1.59403i
$22$	−1097.05	−	265.842i	−0.483246	−	0.117103i
$23$	−3835.55	+	676.311i	−1.51185	+	0.266580i	−0.867223	−	0.497919i	$-0.834098\pi$
$23$	−3835.55	+	676.311i	−1.51185	+	0.266580i	−0.644625	+	0.764499i	$0.722986\pi$
$24$	−1167.60	+	3063.26i	−0.413776	+	1.08557i
$25$	2827.99	+	1029.30i	0.904955	+	0.329377i
$26$	219.127	−	3462.05i	0.0635715	−	1.00439i
$27$	−1430.97	+	2478.51i	−0.377764	+	0.654306i
$28$	−3401.51	+	6606.34i	−0.819930	+	1.59245i
$29$	1519.29	+	1810.62i	0.335465	+	0.399791i	0.907236	−	0.420622i	$-0.138188\pi$
$29$	1519.29	+	1810.62i	0.335465	+	0.399791i	−0.571771	+	0.820413i	$0.693744\pi$
$30$	489.209	+	986.440i	0.0992410	+	0.200110i
$31$	−1767.13	−	3060.76i	−0.330266	−	0.572038i	0.652298	−	0.757963i	$-0.273805\pi$
$31$	−1767.13	−	3060.76i	−0.330266	−	0.572038i	−0.982564	+	0.185925i	$0.940472\pi$
$32$	−817.010	+	5734.71i	−0.141043	+	0.990003i
$33$	3558.84	+	627.520i	0.568884	+	0.100310i
$34$	−2552.71	−	1116.40i	−0.378708	−	0.165624i
$35$	853.604	+	2345.26i	0.117784	+	0.323609i
$36$	805.989	−	2596.78i	0.103651	−	0.333948i
$37$		−	6372.56i		−	0.765261i	−0.923901	−	0.382631i	$-0.875018\pi$
$37$		−	6372.56i		−	0.765261i	0.923901	−	0.382631i	$-0.124982\pi$
$38$	−8018.78	−	3864.49i	−0.900844	−	0.434143i
$39$			11105.6i			1.16918i
$40$	1227.97	+	1509.13i	0.121350	+	0.149134i
$41$	6177.25	+	16971.9i	0.573900	+	1.57678i	0.798288	+	0.602276i	$0.205739\pi$
$41$	6177.25	+	16971.9i	0.573900	+	1.57678i	−0.224388	+	0.974500i	$0.572038\pi$
$42$	9531.91	−	21795.2i	0.833790	−	1.90651i
$43$	−21090.8	−	3718.88i	−1.73949	−	0.306720i	−0.788294	−	0.615298i	$-0.789036\pi$
$43$	−21090.8	−	3718.88i	−1.73949	−	0.306720i	−0.951199	+	0.308579i	$0.900147\pi$
$44$	6378.05	−	307.109i	0.496657	−	0.0239145i
$45$	−456.623	−	790.894i	−0.0336145	−	0.0582220i
$46$	19737.9	−	9788.69i	1.37533	−	0.682072i
$47$	1919.36	+	2287.40i	0.126739	+	0.151042i	0.825682	−	0.564135i	$-0.190790\pi$
$47$	1919.36	+	2287.40i	0.126739	+	0.151042i	−0.698943	+	0.715177i	$0.746346\pi$
$48$	1450.66	−	18487.7i	0.0908785	−	1.15819i
$49$	18556.5	−	32140.7i	1.10409	−	1.91234i
$50$	−16990.2	−	1075.38i	−0.961110	−	0.0608324i
$51$	8381.71	+	3050.69i	0.451239	+	0.164238i
$52$	4333.10	+	19139.1i	0.222224	+	0.981554i
$53$	−10633.1	+	1874.89i	−0.519958	+	0.0916827i	−0.427467	−	0.904031i	$-0.640594\pi$
$53$	−10633.1	+	1874.89i	−0.519958	+	0.0916827i	−0.0924910	+	0.995714i	$0.529483\pi$
$54$	3812.79	−	15734.2i	0.177934	−	0.734277i
$55$	1378.60	−	1642.95i	0.0614514	−	0.0732350i
$56$	7923.15	−	41280.4i	0.337620	−	1.75903i
$57$	26401.6	+	10725.5i	1.07633	+	0.437251i
$58$	−11133.8	−	7403.35i	−0.434584	−	0.288974i
$59$	12191.1	+	10229.5i	0.455944	+	0.382582i	0.841636	−	0.540045i	$-0.181593\pi$
$59$	12191.1	+	10229.5i	0.455944	+	0.382582i	−0.385692	+	0.922627i	$0.626037\pi$
$60$	−4228.57	−	4573.37i	−0.151641	−	0.164005i
$61$	−4248.83	−	24096.3i	−0.146199	−	0.829136i	−0.966397	−	0.257056i	$-0.917248\pi$
$61$	−4248.83	−	24096.3i	−0.146199	−	0.829136i	0.820198	−	0.572080i	$-0.193863\pi$
$62$	14473.0	+	13792.9i	0.478167	+	0.455697i
$63$	−6748.13	+	18540.3i	−0.214206	+	0.588527i
$64$	−4713.36	−	32427.2i	−0.143840	−	0.989601i
$65$	5708.05	+	3295.54i	0.167573	+	0.0967484i
$66$	−20315.9	+	2271.02i	−0.574084	+	0.0641743i
$67$	−20462.8	+	17170.4i	−0.556902	+	0.467296i	−0.877270	−	0.479997i	$-0.840638\pi$
$67$	−20462.8	+	17170.4i	−0.556902	+	0.467296i	0.320368	+	0.947293i	$0.396193\pi$
$68$	15635.1	+	1987.18i	0.410042	+	0.0521152i
$69$	−61083.4	+	35266.5i	−1.54454	+	0.891743i
$70$	−8373.72	−	11366.8i	−0.204255	−	0.277265i
$71$	−1137.40	+	6450.53i	−0.0267774	+	0.151862i	−0.995265	−	0.0972002i	$-0.969011\pi$
$71$	−1137.40	+	6450.53i	−0.0267774	+	0.151862i	0.968487	+	0.249062i	$0.0801224\pi$
$72$	−232.180	+	15379.2i	−0.00527829	+	0.349624i
$73$	20612.3	−	7502.27i	0.452710	−	0.164773i	−0.105594	−	0.994409i	$-0.533674\pi$
$73$	20612.3	−	7502.27i	0.452710	−	0.164773i	0.558304	+	0.829636i	$0.311452\pi$
$74$	10165.0	+	34585.8i	0.215788	+	0.734208i
$75$	54501.4			1.11880
$76$	49684.7	+	8182.87i	0.986707	+	0.162507i
$77$	−46335.7			−0.890613
$78$	−17714.7	−	60273.6i	−0.329684	−	1.12174i
$79$	−31298.1	+	11391.6i	−0.564223	+	0.205360i	−0.608355	−	0.793665i	$-0.708170\pi$
$79$	−31298.1	+	11391.6i	−0.564223	+	0.205360i	0.0441317	+	0.999026i	$0.485948\pi$
$80$	−9071.81	−	6231.75i	−0.158478	−	0.108864i
$81$	−12585.4	+	71375.6i	−0.213136	+	1.20875i
$82$	−60597.9	−	82258.0i	−0.995229	−	1.35096i
$83$	−28682.7	+	16560.0i	−0.457009	+	0.263854i	−0.710786	−	0.703409i	$-0.751660\pi$
$83$	−28682.7	+	16560.0i	−0.457009	+	0.263854i	0.253777	+	0.967263i	$0.418327\pi$
$84$	−16966.7	+	133494.i	−0.262360	+	2.06425i
$85$	4055.22	−	3402.74i	0.0608790	−	0.0510836i
$86$	120398.	−	13458.8i	1.75539	−	0.196228i
$87$	37069.9	+	21402.3i	0.525077	+	0.303153i
$88$	−34125.8	+	11840.5i	−0.469760	+	0.162991i
$89$	−8809.94	+	24205.1i	−0.117896	+	0.323916i	−0.984578	−	0.174944i	$-0.944026\pi$
$89$	−8809.94	+	24205.1i	−0.117896	+	0.323916i	0.866683	+	0.498860i	$0.166248\pi$
$90$	3739.80	+	3564.05i	0.0486678	+	0.0463808i
$91$	−24727.0	−	140234.i	−0.313017	−	1.77521i
$92$	−91509.5	+	84610.4i	−1.12719	+	1.04221i
$93$	−49030.8	−	41141.7i	−0.587843	−	0.493259i
$94$	−14065.6	−	9352.84i	−0.164187	−	0.109175i
$95$	13347.2	−	10387.1i	0.151734	−	0.118083i
$96$	21616.9	+	102652.i	0.239395	+	1.13682i
$97$	99349.4	−	118400.i	1.07210	−	1.27768i	0.113314	−	0.993559i	$-0.463853\pi$
$97$	99349.4	−	118400.i	1.07210	−	1.27768i	0.958788	−	0.284122i	$-0.0917021\pi$
$98$	−49443.4	+	204037.i	−0.520048	+	2.14607i
$99$	16697.4	−	2944.21i	0.171223	−	0.0301912i
$100$	93926.2	−	21264.9i	0.939262	−	0.212649i
$101$	143219.	+	52127.6i	1.39701	+	0.508469i	0.927289	−	0.374347i	$-0.122133\pi$
$101$	143219.	+	52127.6i	1.39701	+	0.508469i	0.469718	+	0.882816i	$0.344355\pi$
$102$	−50356.3	−	3187.25i	−0.479240	−	0.0303330i
$103$	52999.5	−	91797.8i	0.492242	−	0.852588i	−0.507718	−	0.861523i	$-0.669511\pi$
$103$	52999.5	−	91797.8i	0.492242	−	0.852588i	0.999960	+	0.00893552i	$0.00284430\pi$
$104$	−54046.2	−	96962.1i	−0.489984	−	0.879060i
$105$	29052.8	+	34623.8i	0.257167	+	0.306480i
$106$	54718.1	−	27136.6i	0.473006	−	0.234580i
$107$	−73715.4	−	127679.i	−0.622442	−	1.07810i	−0.989030	−	0.147717i	$-0.952807\pi$
$107$	−73715.4	−	127679.i	−0.622442	−	1.07810i	0.366588	−	0.930383i	$-0.380526\pi$
$108$	4404.65	+	91476.0i	0.0363372	+	0.754654i
$109$	−39741.1	−	7007.43i	−0.320386	−	0.0564927i	0.0111424	−	0.999938i	$-0.496453\pi$
$109$	−39741.1	−	7007.43i	−0.320386	−	0.0564927i	−0.331528	+	0.943445i	$0.607564\pi$
$110$	−4861.39	+	11115.8i	−0.0383071	+	0.0875912i
$111$	−39471.3	−	108447.i	−0.304071	−	0.835427i
$112$	22845.6	+	236680.i	0.172091	+	1.78285i
$113$		−	75101.1i		−	0.553286i	−0.960973	−	0.276643i	$-0.910778\pi$
$113$		−	75101.1i		−	0.553286i	0.960973	−	0.276643i	$-0.0892220\pi$
$114$	−160398.	−	16096.9i	−1.15594	−	0.116006i
$115$			41860.7i			0.295163i
$116$	72235.8	+	22420.5i	0.498434	+	0.154704i
$117$	17821.2	+	48963.2i	0.120357	+	0.330678i
$118$	−82481.7	−	36072.5i	−0.545322	−	0.238491i
$119$	−112631.	−	19859.8i	−0.729104	−	0.128561i
$120$	30244.8	+	18076.0i	0.191733	+	0.114591i
$121$	−60616.4	−	104991.i	−0.376380	−	0.651909i
$122$	61496.0	+	124001.i	0.374065	+	0.754265i
$123$	210246.	+	250561.i	1.25304	+	1.49331i
$124$	−100551.	−	51772.1i	−0.587261	−	0.302372i
$125$	32966.9	−	57100.3i	0.188713	−	0.326861i
$126$	7050.19	−	111388.i	0.0395617	−	0.625047i
$127$	193737.	+	70514.6i	1.06587	+	0.387945i	0.814630	−	0.579981i	$-0.196940\pi$
$127$	193737.	+	70514.6i	1.06587	+	0.387945i	0.251239	+	0.967925i	$0.419162\pi$
$128$	77306.0	+	168474.i	0.417050	+	0.908883i
$129$	−381953.	+	67348.6i	−2.02086	+	0.356332i
$130$	−36236.1	−	8780.92i	−0.188054	−	0.0455703i
$131$	132768.	−	158227.i	0.675953	−	0.805570i	−0.313628	−	0.949546i	$-0.601544\pi$
$131$	132768.	−	158227.i	0.675953	−	0.805570i	0.989581	+	0.143976i	$0.0459889\pi$
$132$	106638.	−	44731.6i	0.532692	−	0.223450i
$133$	−357262.	−	76649.9i	−1.75129	−	0.375736i
$134$	83669.3	−	125829.i	0.402535	−	0.605368i
$135$	23563.7	+	19772.3i	0.111278	+	0.0933734i
$136$	−88026.3	+	14154.8i	−0.408098	+	0.0656230i
$137$	35330.4	+	200369.i	0.160823	+	0.912071i	0.953268	+	0.302127i	$0.0976968\pi$
$137$	35330.4	+	200369.i	0.160823	+	0.912071i	−0.792445	+	0.609944i	$0.791192\pi$
$138$	275264.	−	288837.i	1.23041	−	1.29109i
$139$	−102815.	+	282483.i	−0.451358	+	1.24010i	0.480411	+	0.877044i	$0.340488\pi$
$139$	−102815.	+	282483.i	−0.451358	+	1.24010i	−0.931769	+	0.363052i	$0.881735\pi$
$140$	63578.1	+	48334.2i	0.274150	+	0.208418i
$141$	46831.2	+	27038.0i	0.198375	+	0.114532i
$142$	−4116.30	−	36823.2i	−0.0171312	−	0.153250i
$143$	−93739.4	+	78656.7i	−0.383338	+	0.321659i
$144$	−23271.4	−	83837.7i	−0.0935226	−	0.336925i
$145$	22000.6	−	12702.1i	0.0868991	−	0.0501712i
$146$	−99902.3	+	73596.1i	−0.387877	+	0.285741i
$147$	116711.	−	661901.i	0.445470	−	2.52638i
$148$	−110337.	−	171493.i	−0.414062	−	0.643566i
$149$	−122508.	+	44589.1i	−0.452061	+	0.164537i	−0.558009	−	0.829835i	$-0.688435\pi$
$149$	−122508.	+	44589.1i	−0.452061	+	0.164537i	0.105948	+	0.994372i	$0.466212\pi$
$150$	−295795.	+	86935.9i	−1.07340	+	0.315479i
$151$	113702.			0.405813			0.202906	−	0.979198i	$-0.434961\pi$
$151$	113702.			0.405813			0.202906	+	0.979198i	$0.434961\pi$
$152$	−282706.	+	34841.8i	−0.992491	+	0.122318i
$153$	41849.3			0.144530
$154$	251478.	−	73910.8i	0.854472	−	0.251134i
$155$	−35695.6	+	12992.1i	−0.119340	+	0.0434362i
$156$	192286.	+	298866.i	0.632612	+	0.983252i
$157$	29298.8	−	166162.i	0.0948637	−	0.537999i	−0.899925	−	0.436044i	$-0.856379\pi$
$157$	29298.8	−	166162.i	0.0948637	−	0.537999i	0.994789	−	0.101955i	$-0.0325097\pi$
$158$	151694.	−	111750.i	0.483420	−	0.356126i
$159$	−169338.	+	97767.1i	−0.531203	+	0.306690i
$160$	59175.8	+	19351.0i	0.182744	+	0.0597591i
$161$	692795.	−	581324.i	2.10640	−	1.76748i
$162$	−45547.2	−	407452.i	−0.136356	−	1.21980i
$163$	443910.	+	256291.i	1.30866	+	0.755553i	0.981872	−	0.189546i	$-0.0607016\pi$
$163$	443910.	+	256291.i	1.30866	+	0.755553i	0.326784	+	0.945099i	$0.394035\pi$
$164$	460094.	+	349779.i	1.33579	+	1.01551i
$165$	13284.3	−	36498.3i	0.0379865	−	0.104367i
$166$	129255.	−	135628.i	0.364062	−	0.382014i
$167$	−52361.9	−	296959.i	−0.145286	−	0.823958i	−0.967137	−	0.254256i	$-0.918169\pi$
$167$	−52361.9	−	296959.i	−0.145286	−	0.823958i	0.821851	−	0.569703i	$-0.192942\pi$
$168$	−120855.	−	751575.i	−0.330362	−	2.05447i
$169$	−3649.48	−	3062.28i	−0.00982911	−	0.00824760i
$170$	−16581.2	+	24936.2i	−0.0440041	+	0.0661772i
$171$	133612.	+	4920.71i	0.349427	+	0.0128688i
$172$	−631970.	+	265094.i	−1.62883	+	0.683249i
$173$	−213065.	+	253921.i	−0.541249	+	0.645036i	−0.965467	−	0.260524i	$-0.916105\pi$
$173$	−213065.	+	253921.i	−0.541249	+	0.645036i	0.424218	+	0.905560i	$0.360549\pi$
$174$	−235328.	−	57026.0i	−0.589252	−	0.142791i
$175$	−688204.	+	121349.i	−1.69872	+	0.299531i
$176$	166324.	−	118696.i	0.404737	−	0.288839i
$177$	270825.	+	98572.3i	0.649764	+	0.236495i
$178$	9204.29	−	145421.i	0.0217741	−	0.344016i
$179$	−336437.	+	582727.i	−0.784823	+	1.35935i	0.144282	+	0.989537i	$0.453913\pi$
$179$	−336437.	+	582727.i	−0.784823	+	1.35935i	−0.929105	+	0.369816i	$0.879421\pi$
$180$	−25982.1	−	13377.8i	−0.0597713	−	0.0307754i
$181$	229772.	+	273831.i	0.521315	+	0.621279i	0.960891	−	0.276927i	$-0.0893159\pi$
$181$	229772.	+	273831.i	0.521315	+	0.621279i	−0.439576	+	0.898205i	$0.644871\pi$
$182$	357890.	+	721649.i	0.800887	+	1.61491i
$183$	−221557.	−	383747.i	−0.489054	−	0.847067i
$184$	361686.	−	605174.i	0.787567	−	1.31776i
$185$	−67452.2	−	11893.6i	−0.144899	−	0.0255497i
$186$	331731.	+	145079.i	0.703077	+	0.307483i
$187$	33614.3	+	92354.4i	0.0702942	+	0.193132i
$188$	91257.2	+	28324.4i	0.188310	+	0.0584475i
$189$		−	664561.i		−	1.35326i
$190$	−55870.9	+	77664.4i	−0.112280	+	0.156077i
$191$			727306.i			1.44256i	0.692644	+	0.721279i	$0.256446\pi$
$191$			727306.i			1.44256i	−0.692644	+	0.721279i	$0.743554\pi$
$192$	−281064.	−	522644.i	−0.550239	−	1.02318i
$193$	8021.78	+	22039.7i	0.0155016	+	0.0425904i	0.947202	−	0.320637i	$-0.103897\pi$
$193$	8021.78	+	22039.7i	0.0155016	+	0.0425904i	−0.931700	+	0.363228i	$0.881675\pi$
$194$	−350338.	+	801067.i	−0.668317	+	1.52814i
$195$	117551.	+	20727.3i	0.221380	+	0.0390352i
$196$	−57118.5	−	1.18624e6i	−0.106203	−	2.20563i
$197$	352877.	+	611201.i	0.647825	+	1.12207i	0.983641	+	0.180138i	$0.0576544\pi$
$197$	352877.	+	611201.i	0.647825	+	1.12207i	−0.335817	+	0.941927i	$0.609012\pi$
$198$	−85925.7	+	42613.4i	−0.155761	+	0.0772474i
$199$	351281.	+	418640.i	0.628813	+	0.749390i	0.982559	−	0.185951i	$-0.0595367\pi$
$199$	351281.	+	418640.i	0.628813	+	0.749390i	−0.353746	+	0.935342i	$0.615092\pi$
$200$	−475846.	+	265234.i	−0.841185	+	0.468872i
$201$	−241879.	+	418946.i	−0.422287	+	0.731422i
$202$	−860445.	−	54460.9i	−1.48369	−	0.0939089i
$203$	−515745.	−	187716.i	−0.878405	−	0.319713i
$204$	278383.	−	63025.9i	0.468346	−	0.106034i
$205$	191173.	−	33708.9i	0.317717	−	0.0560221i
$206$	−141216.	+	582754.i	−0.231855	+	0.956792i
$207$	−212716.	+	253506.i	−0.345045	+	0.411208i
$208$	447991.	+	440033.i	0.717977	+	0.705223i
$209$	96461.2	+	298813.i	0.152752	+	0.473188i
$210$	−212907.	−	141571.i	−0.333152	−	0.221527i
$211$	−974798.	−	817953.i	−1.50733	−	1.26480i	−0.868754	−	0.495243i	$-0.835079\pi$
$211$	−974798.	−	817953.i	−1.50733	−	1.26480i	−0.638577	−	0.769558i	$-0.720477\pi$
$212$	−253686.	+	234560.i	−0.387665	+	0.358438i
$213$	20598.2	+	116818.i	0.0311086	+	0.176426i
$214$	603738.	+	575367.i	0.901185	+	0.858836i
$215$	−78727.1	+	216301.i	−0.116152	+	0.319126i
$216$	−169820.	−	489442.i	−0.247659	−	0.713784i
$217$	710729.	+	410340.i	1.02460	+	0.591554i
$218$	226865.	−	25360.2i	0.323315	−	0.0361419i
$219$	304306.	−	255343.i	0.428747	−	0.359761i
$220$	8653.20	−	68083.5i	0.0120537	−	0.0948386i
$221$	−261570.	+	151018.i	−0.360253	+	0.207992i
$222$	387208.	+	525611.i	0.527304	+	0.715784i
$223$	37257.4	−	211297.i	0.0501708	−	0.284532i	−0.949392	−	0.314093i	$-0.898300\pi$
$223$	37257.4	−	211297.i	0.0501708	−	0.284532i	0.999563	+	0.0295605i	$0.00941076\pi$
$224$	−501521.	−	1.24809e6i	−0.667835	−	1.66198i
$225$	240289.	−	87458.2i	0.316430	−	0.115171i
$226$	119795.	+	407596.i	0.156015	+	0.530834i
$227$	1.10070e6			1.41777			0.708885	−	0.705324i	$-0.249198\pi$
$227$	1.10070e6			1.41777			0.708885	+	0.705324i	$0.249198\pi$
$228$	896205.	−	168490.i	1.14175	−	0.214653i
$229$	−177106.			−0.223174			−0.111587	−	0.993755i	$-0.535593\pi$
$229$	−177106.			−0.223174			−0.111587	+	0.993755i	$0.535593\pi$
$230$	−66772.6	−	227191.i	−0.0832298	−	0.283185i
$231$	−788529.	+	287001.i	−0.972272	+	0.353878i
$232$	−427809.	−	6458.64i	−0.521831	−	0.00787809i
$233$	−224401.	+	1.27264e6i	−0.270791	+	1.53573i	0.481231	+	0.876594i	$0.340190\pi$
$233$	−224401.	+	1.27264e6i	−0.270791	+	1.53573i	−0.752022	+	0.659138i	$0.770921\pi$
$234$	−174823.	−	237311.i	−0.208717	−	0.283321i
$235$	27793.9	−	16046.8i	0.0328307	−	0.0189548i
$236$	505193.	+	64208.5i	0.590442	+	0.0750434i
$237$	−462064.	+	387718.i	−0.534357	+	0.448379i
$238$	642960.	−	71873.6i	0.735769	−	0.0822483i
$239$	−81832.2	−	47245.8i	−0.0926679	−	0.0535019i	0.452950	−	0.891536i	$-0.350372\pi$
$239$	−81832.2	−	47245.8i	−0.0926679	−	0.0535019i	−0.545618	+	0.838034i	$0.683705\pi$
$240$	−192981.	−	49860.0i	−0.216265	−	0.0558758i
$241$	126000.	−	346182.i	0.139742	−	0.383939i	−0.850004	−	0.526776i	$-0.823401\pi$
$241$	126000.	−	346182.i	0.139742	−	0.383939i	0.989746	+	0.142838i	$0.0456227\pi$
$242$	496455.	+	473126.i	0.544931	+	0.519324i
$243$	107157.	+	607720.i	0.116414	+	0.660218i
$244$	−531553.	−	574895.i	−0.571573	−	0.618179i
$245$	−305569.	−	256403.i	−0.325233	−	0.272903i
$246$	−1.54074e6	−	1.02451e6i	−1.62327	−	1.07938i
$247$	−852874.	+	451399.i	−0.889493	+	0.470780i
$248$	628301.	+	120593.i	0.648692	+	0.124507i
$249$	−385543.	+	459472.i	−0.394071	+	0.469635i
$250$	−87839.7	+	362487.i	−0.0888875	+	0.366811i
$251$	1.02380e6	−	180524.i	1.02573	−	0.180863i	0.364621	−	0.931156i	$-0.381198\pi$
$251$	1.02380e6	−	180524.i	1.02573	−	0.180863i	0.661106	+	0.750293i	$0.270087\pi$
$252$	139413.	+	615783.i	0.138294	+	0.610838i
$253$	−730303.	−	265809.i	−0.717302	−	0.261077i
$254$	−1.16395e6	−	73670.9i	−1.13201	−	0.0716493i
$255$	47934.4	−	83024.7i	0.0461633	−	0.0799571i
$256$	−688299.	−	791048.i	−0.656413	−	0.754402i
$257$	−649947.	−	774577.i	−0.613826	−	0.731529i	0.366170	−	0.930548i	$-0.380669\pi$
$257$	−649947.	−	774577.i	−0.613826	−	0.731529i	−0.979996	+	0.199019i	$0.936224\pi$
$258$	1.96555e6	−	974780.i	1.83837	−	0.911711i
$259$	739876.	+	1.28150e6i	0.685345	+	1.18705i
$260$	210671.	−	10144.0i	0.193273	−	0.00930626i
$261$	197780.	+	34874.0i	0.179714	+	0.0316884i
$262$	−468184.	+	1.07053e6i	−0.421370	+	0.963485i
$263$	−91054.6	−	250170.i	−0.0811732	−	0.223021i	0.892466	−	0.451114i	$-0.148973\pi$
$263$	−91054.6	−	250170.i	−0.0811732	−	0.223021i	−0.973639	+	0.228093i	$0.926751\pi$
$264$	−507404.	+	412872.i	−0.448068	+	0.364590i
$265$			116048.i			0.101513i
$266$	2.06123e6	−	153871.i	1.78617	−	0.133337i
$267$			466485.i			0.400460i
$268$	−253386.	+	816376.i	−0.215500	+	0.694309i
$269$	−357230.	−	981482.i	−0.301001	−	0.826992i	−0.994327	−	0.106369i	$-0.966078\pi$
$269$	−357230.	−	981482.i	−0.301001	−	0.826992i	0.693326	−	0.720624i	$-0.256145\pi$
$270$	−159427.	−	69723.5i	−0.133092	−	0.0582063i
$271$	1.25247e6	+	220844.i	1.03596	+	0.182668i	0.665669	−	0.746247i	$-0.268146\pi$
$271$	1.25247e6	+	220844.i	1.03596	+	0.182668i	0.370292	+	0.928915i	$0.379257\pi$
$272$	455167.	−	217234.i	0.373034	−	0.178035i
$273$	−1.28940e6	−	2.23331e6i	−1.04708	−	1.81360i
$274$	−511360.	−	1.03111e6i	−0.411482	−	0.829711i
$275$	386011.	+	460030.i	0.307800	+	0.366821i
$276$	−1.03321e6	+	2.00668e6i	−0.816426	+	1.58564i
$277$	227565.	−	394154.i	0.178199	−	0.308650i	−0.763064	−	0.646322i	$-0.776306\pi$
$277$	227565.	−	394154.i	0.178199	−	0.308650i	0.941264	+	0.337672i	$0.109639\pi$
$278$	107418.	−	1.69712e6i	0.0833611	−	1.31705i
$279$	−282190.	−	102709.i	−0.217036	−	0.0789946i
$280$	−422156.	−	160910.i	−0.321794	−	0.122656i
$281$	1.93634e6	−	341428.i	1.46290	−	0.257949i	0.615178	−	0.788388i	$-0.289084\pi$
$281$	1.93634e6	−	341428.i	1.46290	−	0.257949i	0.847723	+	0.530439i	$0.177973\pi$
$282$	−297296.	−	72042.4i	−0.222621	−	0.0539467i
$283$	1.10840e6	−	1.32094e6i	0.822681	−	0.980433i	−0.177312	−	0.984155i	$-0.556740\pi$
$283$	1.10840e6	−	1.32094e6i	0.822681	−	0.980433i	0.999993	+	0.00372182i	$0.00118469\pi$
$284$	81077.7	+	193285.i	0.0596493	+	0.142201i
$285$	162803.	−	259437.i	0.118727	−	0.189200i
$286$	383285.	−	576418.i	0.277081	−	0.416699i
$287$	−3.21272e6	−	2.69579e6i	−2.30233	−	1.93188i
$288$	260032.	+	417892.i	0.184733	+	0.296881i
$289$	−204431.	−	1.15939e6i	−0.143980	−	0.816553i
$290$	−99142.8	+	104031.i	−0.0692255	+	0.0726390i
$291$	957339.	−	2.63027e6i	0.662725	−	1.82082i
$292$	424806.	−	558784.i	0.291564	−	0.383519i
$293$	1.17479e6	+	678266.i	0.799451	+	0.461563i	0.843279	−	0.537476i	$-0.180622\pi$
$293$	1.17479e6	+	678266.i	0.799451	+	0.461563i	−0.0438283	+	0.999039i	$0.513955\pi$
$294$	422382.	+	3.77850e6i	0.284995	+	2.54948i
$295$	131030.	−	109947.i	0.0876630	−	0.0735580i
$296$	872382.	+	754747.i	0.578732	+	0.500694i
$297$	−494575.	+	285543.i	−0.325342	+	0.187836i
$298$	593761.	−	437412.i	0.387321	−	0.285332i
$299$	414738.	−	2.35209e6i	0.268284	−	1.52152i
$300$	1.46670e6	−	943655.i	0.940887	−	0.605355i
$301$	4.67308e6	−	1.70086e6i	2.97294	−	1.08206i
$302$	−617095.	+	181368.i	−0.389345	+	0.114431i
$303$	2.76015e6			1.72713
$304$	1.47876e6	−	640046.i	0.917725	−	0.397216i
$305$	−262984.			−0.161875
$306$	−227129.	+	66754.4i	−0.138666	+	0.0407546i
$307$	−308565.	+	112309.i	−0.186853	+	0.0680091i	−0.433752	−	0.901032i	$-0.642811\pi$
$307$	−308565.	+	112309.i	−0.186853	+	0.0680091i	0.246899	+	0.969041i	$0.420588\pi$
$308$	−1.24695e6	+	802272.i	−0.748984	+	0.481887i
$309$	333340.	−	1.89047e6i	0.198606	−	1.12635i
$310$	173007.	−	127451.i	0.102249	−	0.0753249i
$311$	−765892.	+	442188.i	−0.449021	+	0.259242i	−0.707417	−	0.706797i	$-0.750139\pi$
$311$	−765892.	+	442188.i	−0.449021	+	0.259242i	0.258396	+	0.966039i	$0.416806\pi$
$312$	−1.52032e6	−	1.31532e6i	−0.884197	−	0.764969i
$313$	−2.03676e6	+	1.70904e6i	−1.17511	+	0.986035i	−0.175112	+	0.984549i	$0.556029\pi$
$313$	−2.03676e6	+	1.70904e6i	−1.17511	+	0.986035i	−0.999999	+	0.00148639i	$0.999527\pi$
$314$	106033.	+	948544.i	0.0606902	+	0.542917i
$315$	183651.	+	106031.i	0.104284	+	0.0602082i
$316$	−645033.	+	848468.i	−0.363383	+	0.477989i
$317$	−900152.	+	2.47315e6i	−0.503116	+	1.38230i	0.385101	+	0.922874i	$0.374167\pi$
$317$	−900152.	+	2.47315e6i	−0.503116	+	1.38230i	−0.888217	+	0.459425i	$0.848056\pi$
$318$	763096.	−	800724.i	0.423167	−	0.444033i
$319$	81900.3	+	464480.i	0.0450618	+	0.255558i
$320$	−352032.	−	10631.7i	−0.192180	−	0.00580400i
$321$	−2.04531e6	−	1.71621e6i	−1.10789	−	0.929628i
$322$	−2.83273e6	+	4.26011e6i	−1.52253	+	2.28971i
$323$	106400.	+	767685.i	0.0567461	+	0.409427i
$324$	897132.	+	2.13871e6i	0.474781	+	1.13185i
$325$	−1.18628e6	+	1.41375e6i	−0.622985	+	0.742444i
$326$	−2.81805e6	−	682884.i	−1.46860	−	0.355879i
$327$	−719707.	+	126904.i	−0.372209	+	0.0656304i
$328$	−3.05501e6	−	1.16445e6i	−1.56793	−	0.597636i
$329$	−651553.	−	237146.i	−0.331864	−	0.120789i
$330$	−13878.9	+	219278.i	−0.00701570	+	0.110843i
$331$	23808.5	−	41237.6i	0.0119444	−	0.0206882i	−0.859991	−	0.510308i	$-0.829531\pi$
$331$	23808.5	−	41237.6i	0.0119444	−	0.0206882i	0.871936	+	0.489620i	$0.162865\pi$
$332$	−485161.	+	942270.i	−0.241569	+	0.469170i
$333$	−348048.	−	414787.i	−0.172000	−	0.204982i
$334$	757867.	+	1.52816e6i	0.371729	+	0.749555i
$335$	143553.	+	248641.i	0.0698876	+	0.121049i
$336$	1.85476e6	+	3.88625e6i	0.896273	+	1.87794i
$337$	−3.73857e6	−	659211.i	−1.79321	−	0.316191i	−0.824774	−	0.565462i	$-0.808698\pi$
$337$	−3.73857e6	−	659211.i	−1.79321	−	0.316191i	−0.968434	+	0.249271i	$0.919809\pi$
$338$	24691.5	+	10798.6i	0.0117559	+	0.00514132i
$339$	−465172.	−	1.27805e6i	−0.219844	−	0.604016i
$340$	50214.9	−	161785.i	0.0235578	−	0.0759000i
$341$		−	705245.i		−	0.328438i
$342$	−733004.	+	186421.i	−0.338876	+	0.0861846i
$343$			4.71517e6i			2.16403i
$344$	3.00704e6	−	2.44681e6i	1.37007	−	1.11482i
$345$	259283.	+	712374.i	0.117281	+	0.322226i
$346$	751336.	−	1.71797e6i	0.337399	−	0.771481i
$347$	2.95115e6	+	520367.i	1.31573	+	0.231999i	0.787086	−	0.616844i	$-0.211589\pi$
$347$	2.95115e6	+	520367.i	1.31573	+	0.231999i	0.528646	+	0.848843i	$0.322700\pi$
$348$	1.36816e6	−	65878.2i	0.605605	−	0.0291604i
$349$	2.13061e6	+	3.69032e6i	0.936353	+	1.62181i	0.772204	+	0.635374i	$0.219154\pi$
$349$	2.13061e6	+	3.69032e6i	0.936353	+	1.62181i	0.164148	+	0.986436i	$0.447512\pi$
$350$	3.54153e6	−	1.75636e6i	1.54533	−	0.766380i
$351$	−1.12812e6	−	1.34444e6i	−0.488750	−	0.582469i
$352$	−713355.	+	909507.i	−0.306866	+	0.391246i
$353$	−858924.	+	1.48770e6i	−0.366875	+	0.635446i	−0.989075	−	0.147412i	$-0.952906\pi$
$353$	−858924.	+	1.48770e6i	−0.366875	+	0.635446i	0.622200	+	0.782858i	$0.286239\pi$
$354$	−1.62708e6	−	102985.i	−0.690084	−	0.0436781i
$355$	66154.6	+	24078.3i	0.0278605	+	0.0101404i
$356$	182009.	+	803928.i	0.0761147	+	0.336196i
$357$	−2.03973e6	+	359660.i	−0.847037	+	0.149355i
$358$	896432.	−	3.69929e6i	0.369666	−	1.52549i
$359$	−800247.	+	953698.i	−0.327709	+	0.390548i	−0.904592	−	0.426279i	$-0.859824\pi$
$359$	−800247.	+	953698.i	−0.327709	+	0.390548i	0.576883	+	0.816827i	$0.304269\pi$
$360$	162352.	+	31161.0i	0.0660238	+	0.0126723i
$361$	249439.	+	2.46350e6i	0.100739	+	0.994913i
$362$	−1.68383e6	−	1.11965e6i	−0.675348	−	0.449068i
$363$	−1.68186e6	−	1.41125e6i	−0.669921	−	0.562130i
$364$	−3.09349e6	−	3.34573e6i	−1.22376	−	1.32354i
$365$	−40939.4	−	232179.i	−0.0160846	−	0.0912201i
$366$	1.81458e6	+	1.72931e6i	0.708064	+	0.674791i
$367$	−1.03840e6	+	2.85297e6i	−0.402437	+	1.10569i	0.558640	+	0.829410i	$0.311323\pi$
$367$	−1.03840e6	+	2.85297e6i	−0.402437	+	1.10569i	−0.961078	+	0.276278i	$0.910899\pi$
$368$	−997659.	+	3.86139e6i	−0.384028	+	1.48636i
$369$	1.32902e6	+	767310.i	0.508119	+	0.293363i
$370$	385055.	−	43043.6i	0.146224	−	0.0163457i
$371$	1.92059e6	−	1.61157e6i	0.724437	−	0.607875i
$372$	−2.03182e6	−	258238.i	−0.761251	−	0.0967527i
$373$	2.38199e6	−	1.37524e6i	0.886477	−	0.511808i	0.0136886	−	0.999906i	$-0.495643\pi$
$373$	2.38199e6	−	1.37524e6i	0.886477	−	0.511808i	0.872789	+	0.488098i	$0.162309\pi$
$374$	−329751.	−	447617.i	−0.121901	−	0.165473i
$375$	207345.	−	1.17591e6i	0.0761405	−	0.431814i
$376$	−540461.	−	8159.36i	−0.197149	−	0.00297637i
$377$	−1.36203e6	+	495739.i	−0.493553	+	0.179638i
$378$	1.06005e6	+	3.60677e6i	0.381590	+	1.29834i
$379$	1.11526e6			0.398820			0.199410	−	0.979916i	$-0.436097\pi$
$379$	1.11526e6			0.398820			0.199410	+	0.979916i	$0.436097\pi$
$380$	179344.	−	510629.i	0.0637131	−	0.181404i
$381$	3.73373e6			1.31774
$382$	−1.16014e6	−	3.94731e6i	−0.406771	−	1.38402i
$383$	−907099.	+	330157.i	−0.315979	+	0.115007i	−0.495141	−	0.868813i	$-0.664884\pi$
$383$	−907099.	+	330157.i	−0.315979	+	0.115007i	0.179162	+	0.983820i	$0.442661\pi$
$384$	2.35909e6	+	2.38822e6i	0.816426	+	0.826506i
$385$	−86480.1	+	490453.i	−0.0297348	+	0.168634i
$386$	−78692.4	−	106820.i	−0.0268822	−	0.0364910i
$387$	−1.57591e6	+	909850.i	−0.534876	+	0.308811i
$388$	623596.	−	4.90646e6i	0.210293	−	1.65458i
$389$	629363.	−	528098.i	0.210876	−	0.176946i	−0.531232	−	0.847227i	$-0.678271\pi$
$389$	629363.	−	528098.i	0.210876	−	0.176946i	0.742108	+	0.670280i	$0.233826\pi$
$390$	−671045.	+	75013.1i	−0.223403	+	0.0249733i
$391$	−1.66126e6	−	959129.i	−0.549536	−	0.317274i
$392$	2.20219e6	+	6.34697e6i	0.723834	+	2.08618i
$393$	1.27937e6	−	3.51503e6i	0.417843	−	1.14802i
$394$	−2.89010e6	−	2.75429e6i	−0.937935	−	0.893860i
$395$	62163.2	+	352545.i	0.0200466	+	0.113690i
$396$	398371.	−	368337.i	0.127659	−	0.118034i
$397$	2.80138e6	+	2.35064e6i	0.892064	+	0.748531i	0.968623	−	0.248534i	$-0.0799489\pi$
$397$	2.80138e6	+	2.35064e6i	0.892064	+	0.748531i	−0.0765588	+	0.997065i	$0.524393\pi$
$398$	−2.57428e6	−	1.71175e6i	−0.814608	−	0.541668i
$399$	−6.55455e6	+	908452.i	−2.06116	+	0.285673i
$400$	2.15948e6	−	2.19853e6i	0.674838	−	0.687042i
$401$	1.51712e6	−	1.80803e6i	0.471150	−	0.561494i	−0.477170	−	0.878811i	$-0.658337\pi$
$401$	1.51712e6	−	1.80803e6i	0.471150	−	0.561494i	0.948320	+	0.317317i	$0.102782\pi$
$402$	644482.	−	2.65957e6i	0.198905	−	0.820818i
$403$	2.13441e6	−	376353.i	0.654658	−	0.115434i
$404$	4.75677e6	−	1.07693e6i	1.44997	−	0.328273i
$405$	732006.	+	266428.i	0.221757	+	0.0807129i
$406$	3.09853e6	+	196118.i	0.932912	+	0.0590476i
$407$	635807.	−	1.10125e6i	0.190256	−	0.329534i
$408$	−1.41033e6	+	786113.i	−0.419442	+	0.233795i
$409$	719222.	+	857136.i	0.212596	+	0.253362i	0.861795	−	0.507256i	$-0.169340\pi$
$409$	719222.	+	857136.i	0.212596	+	0.253362i	−0.649199	+	0.760618i	$0.724896\pi$
$410$	−983782.	+	487890.i	−0.289027	+	0.143338i
$411$	1.84232e6	+	3.19099e6i	0.537972	+	0.931796i
$412$	−163137.	−	3.38804e6i	−0.0473489	−	0.983344i
$413$	−3.63926e6	−	641700.i	−1.04988	−	0.185122i
$414$	750106.	−	1.71516e6i	0.215091	−	0.491817i
$415$	121751.	+	334507.i	0.0347017	+	0.0953421i
$416$	−3.13328e6	−	1.67359e6i	−0.887700	−	0.474151i
$417$			5.44405e6i			1.53314i
$418$	−1.00017e6	−	1.46788e6i	−0.279983	−	0.410913i
$419$		−	2.83956e6i		−	0.790161i	−0.918647	−	0.395080i	$-0.870717\pi$
$419$		−	2.83956e6i		−	0.790161i	0.918647	−	0.395080i	$-0.129283\pi$
$420$	1.38134e6	+	428739.i	0.382099	+	0.118596i
$421$	−1.51508e6	−	4.16266e6i	−0.416612	−	1.14463i	−0.953609	−	0.301048i	$-0.902664\pi$
$421$	−1.51508e6	−	4.16266e6i	−0.416612	−	1.14463i	0.536997	−	0.843584i	$-0.319559\pi$
$422$	6.59525e6	+	2.88436e6i	1.80281	+	0.788440i
$423$	249861.	+	44057.2i	0.0678964	+	0.0119720i
$424$	1.00268e6	−	1.67769e6i	0.270862	−	0.453207i
$425$	741126.	+	1.28367e6i	0.199031	+	0.344731i
$426$	−298132.	−	601152.i	−0.0795947	−	0.160495i
$427$	3.65209e6	+	4.35239e6i	0.969330	+	1.15520i
$428$	−4.19444e6	−	2.15966e6i	−1.10679	−	0.569870i
$429$	−1.10804e6	+	1.91918e6i	−0.290677	+	0.503467i
$430$	82251.0	−	1.29951e6i	0.0214521	−	0.338929i
$431$	−3.67846e6	−	1.33885e6i	−0.953835	−	0.347168i	−0.182220	−	0.983258i	$-0.558328\pi$
$431$	−3.67846e6	−	1.33885e6i	−0.953835	−	0.347168i	−0.771615	+	0.636090i	$0.780551\pi$
$432$	1.70238e6	+	2.38547e6i	0.438881	+	0.614984i
$433$	2.25924e6	−	398366.i	0.579086	−	0.102109i	0.123570	−	0.992336i	$-0.460566\pi$
$433$	2.25924e6	−	398366.i	0.579086	−	0.102109i	0.455516	+	0.890227i	$0.349455\pi$
$434$	−4.51188e6	−	1.09334e6i	−1.14983	−	0.278633i
$435$	295725.	−	352431.i	0.0749316	−	0.0893000i
$436$	−1.19081e6	+	499512.i	−0.300003	+	0.125843i
$437$	−5.19114e6	−	3.25755e6i	−1.30035	−	0.815995i
$438$	−1.24426e6	+	1.87123e6i	−0.309903	+	0.466060i
$439$	1.09456e6	+	918442.i	0.271067	+	0.227452i	0.768181	−	0.640233i	$-0.221162\pi$
$439$	1.09456e6	+	918442.i	0.271067	+	0.227452i	−0.497113	+	0.867686i	$0.665607\pi$
$440$	61637.4	+	383312.i	0.0151779	+	0.0943890i
$441$	−547587.	−	3.10552e6i	−0.134078	−	0.760392i
$442$	1.17873e6	−	1.23685e6i	0.286985	−	0.301136i
$443$	−1.26797e6	+	3.48372e6i	−0.306973	+	0.843402i	0.686270	+	0.727347i	$0.259247\pi$
$443$	−1.26797e6	+	3.48372e6i	−0.306973	+	0.843402i	−0.993243	+	0.116055i	$0.962975\pi$
$444$	−2.93990e6	−	2.23501e6i	−0.707743	−	0.538049i
$445$	239763.	+	138427.i	0.0573961	+	0.0331376i
$446$	134836.	+	1.20620e6i	0.0320973	+	0.287133i
$447$	−1.80862e6	+	1.51761e6i	−0.428132	+	0.359246i
$448$	4.71275e6	+	5.97378e6i	1.10938	+	1.40622i
$449$	5.89329e6	−	3.40249e6i	1.37956	−	0.796491i	0.387457	−	0.921888i	$-0.373354\pi$
$449$	5.89329e6	−	3.40249e6i	1.37956	−	0.796491i	0.992107	+	0.125396i	$0.0400203\pi$
$450$	−1.16462e6	+	857951.i	−0.271114	+	0.199724i
$451$	−625828.	+	3.54925e6i	−0.144882	+	0.821665i
$452$	−1.30033e6	−	2.02106e6i	−0.299368	−	0.465300i
$453$	1.93495e6	−	704265.i	0.443021	−	0.161247i
$454$	−5.97385e6	+	1.75575e6i	−1.36024	+	0.399782i
$455$	−1.53049e6			−0.346580
$456$	−4.59521e6	+	2.34400e6i	−1.03489	+	0.527892i
$457$	551503.			0.123526			0.0617629	−	0.998091i	$-0.480328\pi$
$457$	551503.			0.123526			0.0617629	+	0.998091i	$0.480328\pi$
$458$	961208.	−	282504.i	0.214118	−	0.0629305i
$459$	−1.32457e6	+	482106.i	−0.293457	+	0.106810i
$460$	724790.	+	1.12652e6i	0.159705	+	0.248225i
$461$	−1.53615e6	+	8.71196e6i	−0.336653	+	1.90925i	0.0736102	+	0.997287i	$0.476548\pi$
$461$	−1.53615e6	+	8.71196e6i	−0.336653	+	1.90925i	−0.410263	+	0.911967i	$0.634563\pi$
$462$	3.82178e6	−	2.81544e6i	0.833031	−	0.613678i
$463$	−6.52005e6	+	3.76435e6i	−1.41351	+	0.816089i	−0.995717	−	0.0924544i	$-0.970529\pi$
$463$	−6.52005e6	+	3.76435e6i	−1.41351	+	0.816089i	−0.417791	+	0.908543i	$0.637195\pi$
$464$	2.33215e6	−	647351.i	0.502877	−	0.139587i
$465$	−526986.	+	442194.i	−0.113023	+	0.0948375i
$466$	−812115.	−	7.26494e6i	−0.173242	−	1.54977i
$467$	244216.	+	140998.i	0.0518183	+	0.0299173i	0.525685	−	0.850679i	$-0.323809\pi$
$467$	244216.	+	140998.i	0.0518183	+	0.0299173i	−0.473867	+	0.880596i	$0.657142\pi$
$468$	1.32735e6	+	1.00910e6i	0.280138	+	0.212970i
$469$	2.12148e6	−	5.82871e6i	0.445355	−	1.22360i
$470$	−125250.	+	131426.i	−0.0261536	+	0.0274432i
$471$	−530598.	−	3.00917e6i	−0.110208	−	0.625021i
$472$	−2.84426e6	+	457362.i	−0.587643	+	0.0944941i
$473$	−3.27369e6	−	2.74695e6i	−0.672798	−	0.564544i
$474$	1.88931e6	−	2.84131e6i	0.386240	−	0.580861i
$475$	2.21526e6	+	4.18552e6i	0.450496	+	0.851168i
$476$	−3.37489e6	+	1.41567e6i	−0.682719	+	0.286382i
$477$	−589700.	+	702778.i	−0.118669	+	0.141424i
$478$	519491.	+	125886.i	0.103994	+	0.0252004i
$479$	8.06202e6	−	1.42155e6i	1.60548	−	0.283090i	0.702149	−	0.712030i	$-0.252224\pi$
$479$	8.06202e6	−	1.42155e6i	1.60548	−	0.283090i	0.903333	+	0.428941i	$0.141113\pi$
$480$	1.12690e6	−	37221.3i	0.223245	−	0.00737374i
$481$	3.67220e6	+	1.33657e6i	0.723709	+	0.263409i
$482$	−131640.	+	2.07982e6i	−0.0258089	+	0.407763i
$483$	8.18912e6	−	1.41840e7i	1.59724	−	2.76649i
$484$	−3.44910e6	−	1.77589e6i	−0.669257	−	0.344591i
$485$	−1.06781e6	−	1.27257e6i	−0.206130	−	0.245656i
$486$	−1.55096e6	−	3.12735e6i	−0.297858	−	0.600601i
$487$	−1.83810e6	−	3.18368e6i	−0.351193	−	0.608284i	0.635266	−	0.772294i	$-0.280891\pi$
$487$	−1.83810e6	−	3.18368e6i	−0.351193	−	0.608284i	−0.986459	+	0.164009i	$0.947557\pi$
$488$	3.80192e6	+	2.27224e6i	0.722692	+	0.431922i
$489$	9.14179e6	+	1.61194e6i	1.72886	+	0.304844i
$490$	2.06741e6	+	904159.i	0.388988	+	0.170120i
$491$	−2.92248e6	−	8.02946e6i	−0.547077	−	1.50308i	−0.837639	−	0.546225i	$-0.816064\pi$
$491$	−2.92248e6	−	8.02946e6i	−0.547077	−	1.50308i	0.290562	−	0.956856i	$-0.406158\pi$
$492$	9.99627e6	+	3.10264e6i	1.86177	+	0.577855i
$493$			1.16414e6i			0.215719i
$494$	3.90877e6	−	3.81031e6i	0.720647	−	0.702494i
$495$		−	182234.i		−	0.0334284i
$496$	−3.60234e6	+	347718.i	−0.657477	+	0.0634634i
$497$	−520200.	−	1.42924e6i	−0.0944668	−	0.259545i
$498$	1.35955e6	−	3.10868e6i	0.245652	−	0.561697i
$499$	967200.	+	170544.i	0.173886	+	0.0306608i	0.259913	−	0.965632i	$-0.416306\pi$
$499$	967200.	+	170544.i	0.173886	+	0.0306608i	−0.0860271	+	0.996293i	$0.527417\pi$
$500$	−101475.	−	2.10744e6i	−0.0181524	−	0.376990i
$501$	−2.73043e6	−	4.72924e6i	−0.486000	−	0.841778i
$502$	−5.26853e6	+	2.61284e6i	−0.933104	+	0.462758i
$503$	5.38928e6	+	6.42269e6i	0.949752	+	1.13187i	0.991152	+	0.132728i	$0.0423737\pi$
$503$	5.38928e6	+	6.42269e6i	0.949752	+	1.13187i	−0.0414000	+	0.999143i	$0.513182\pi$
$504$	−1.73888e6	−	3.11966e6i	−0.304925	−	0.547055i
$505$	819061.	−	1.41866e6i	0.142918	−	0.247542i
$506$	4.38757e6	+	277707.i	0.761812	+	0.0482181i
$507$	−81073.5	−	29508.3i	−0.0140074	−	0.00509829i
$508$	6.43462e6	−	1.45680e6i	1.10628	−	0.250461i
$509$	−7.06504e6	+	1.24576e6i	−1.20870	+	0.213127i	−0.741457	−	0.671000i	$-0.765865\pi$
$509$	−7.06504e6	+	1.24576e6i	−1.20870	+	0.213127i	−0.467247	+	0.884127i	$0.654754\pi$
$510$	−127720.	+	527061.i	−0.0217438	+	0.0897296i
$511$	−3.27404e6	+	3.90184e6i	−0.554665	+	0.661025i
$512$	4.99742e6	+	3.19534e6i	0.842501	+	0.538694i
$513$	−4.28567e6	+	1.38348e6i	−0.718993	+	0.232102i
$514$	4.76300e6	+	3.16712e6i	0.795193	+	0.528758i
$515$	−872741.	−	732317.i	−0.145000	−	0.121669i
$516$	−9.11272e6	+	8.42569e6i	−1.50669	+	1.39310i
$517$	103467.	+	586789.i	0.0170245	+	0.0965507i
$518$	−6.05967e6	−	5.77491e6i	−0.992258	−	0.945630i
$519$	−2.05311e6	+	5.64088e6i	−0.334576	+	0.919239i
$520$	−1.12719e6	+	391098.i	−0.182806	+	0.0634275i
$521$	2.48614e6	+	1.43537e6i	0.401265	+	0.231670i	0.687030	−	0.726629i	$-0.258914\pi$
$521$	2.48614e6	+	1.43537e6i	0.401265	+	0.231670i	−0.285765	+	0.958300i	$0.592248\pi$
$522$	−1.12904e6	+	126210.i	−0.181357	+	0.0202730i
$523$	−5.53326e6	+	4.64296e6i	−0.884559	+	0.742233i	−0.967111	−	0.254353i	$-0.918137\pi$
$523$	−5.53326e6	+	4.64296e6i	−0.884559	+	0.742233i	0.0825521	+	0.996587i	$0.473693\pi$
$524$	833361.	−	6.55689e6i	0.132588	−	1.04320i
$525$	−1.09601e7	+	6.32779e6i	−1.73546	+	1.00197i
$526$	893231.	+	1.21251e6i	0.140767	+	0.191082i
$527$	302273.	−	1.71428e6i	0.0474103	−	0.268877i
$528$	2.09526e6	−	3.05015e6i	0.327079	−	0.476141i
$529$	8.20587e6	−	2.98669e6i	1.27493	−	0.464036i
$530$	−185110.	−	629827.i	−0.0286246	−	0.0973938i
$531$	1.35221e6			0.208117
$532$	−1.09415e7	+	4.12300e6i	−1.67609	+	0.631589i
$533$	−1.10757e7			−1.68870
$534$	−744096.	−	2.53175e6i	−0.112921	−	0.384210i
$535$	−1.48903e6	+	541964.i	−0.224916	+	0.0818626i
$536$	72992.6	−	4.83490e6i	0.0109740	−	0.726901i
$537$	−2.11602e6	+	1.20006e7i	−0.316654	+	1.79583i
$538$	3.50437e6	+	4.75698e6i	0.521981	+	0.708558i
$539$	6.41353e6	−	3.70285e6i	0.950879	−	0.548990i
$540$	976474.	+	124107.i	0.144104	+	0.0183152i
$541$	1.23457e6	−	1.03593e6i	0.181352	−	0.152173i	−0.547593	−	0.836745i	$-0.684456\pi$
$541$	1.23457e6	−	1.03593e6i	0.181352	−	0.152173i	0.728945	+	0.684573i	$0.240011\pi$
$542$	−7.14980e6	+	799243.i	−1.04543	+	0.116864i
$543$	5.60629e6	+	3.23679e6i	0.815973	+	0.471102i
$544$	−2.12381e6	+	1.90504e6i	−0.307694	+	0.275998i
$545$	−148344.	+	407572.i	−0.0213934	+	0.0587778i
$546$	1.05603e7	+	1.00641e7i	1.51599	+	1.44475i
$547$	146682.	+	831873.i	0.0209608	+	0.118875i	0.993493	−	0.113894i	$-0.0363325\pi$
$547$	146682.	+	831873.i	0.0209608	+	0.118875i	−0.972532	+	0.232769i	$0.925221\pi$
$548$	4.42004e6	+	4.78045e6i	0.628745	+	0.680013i
$549$	−1.59261e6	−	1.33636e6i	−0.225517	−	0.189231i
$550$	−2.82880e6	−	1.88099e6i	−0.398745	−	0.265143i
$551$	−136882.	+	3.71675e6i	−0.0192073	+	0.521537i
$552$	2.40666e6	−	1.25390e7i	0.336177	−	1.75152i
$553$	4.97135e6	−	5.92463e6i	0.691293	−	0.823850i
$554$	−606343.	+	2.50219e6i	−0.0839352	+	0.346374i
$555$	−1.22155e6	+	215392.i	−0.168337	+	0.0296823i
$556$	2.12412e6	+	9.38214e6i	0.291401	+	1.28711i
$557$	−4.39950e6	−	1.60129e6i	−0.600849	−	0.218691i	0.0236455	−	0.999720i	$-0.492473\pi$
$557$	−4.39950e6	−	1.60129e6i	−0.600849	−	0.218691i	−0.624494	+	0.781029i	$0.714695\pi$
$558$	1.69536e6	+	107306.i	0.230503	+	0.0145895i
$559$	6.56658e6	−	1.13737e7i	0.888812	−	1.53947i
$560$	2.54784e6	+	199919.i	0.343322	+	0.0269391i
$561$	1.14408e6	+	1.36346e6i	0.153479	+	0.182909i
$562$	−9.96446e6	+	4.94171e6i	−1.33080	+	0.659989i
$563$	761305.	+	1.31862e6i	0.101225	+	0.175327i	0.912190	−	0.409768i	$-0.134390\pi$
$563$	761305.	+	1.31862e6i	0.101225	+	0.175327i	−0.810965	+	0.585095i	$0.801057\pi$
$564$	1.72843e6	−	83225.5i	0.228799	−	0.0110169i
$565$	−794928.	−	140167.i	−0.104763	−	0.0184725i
$566$	−3.90858e6	+	8.93718e6i	−0.512835	+	1.17263i
$567$	−5.75605e6	−	1.58146e7i	−0.751912	−	2.06586i
$568$	−748345.	−	919687.i	−0.0973265	−	0.119611i
$569$			357338.i			0.0462699i	0.999732	+	0.0231349i	$0.00736474\pi$
$569$			357338.i			0.0462699i	−0.999732	+	0.0231349i	$0.992635\pi$
$570$	−469746.	+	1.66773e6i	−0.0605586	+	0.215001i
$571$		−	3.64716e6i		−	0.468128i	−0.972221	−	0.234064i	$-0.924797\pi$
$571$		−	3.64716e6i		−	0.468128i	0.972221	−	0.234064i	$-0.0752026\pi$
$572$	−1.16075e6	+	3.73978e6i	−0.148337	+	0.477921i
$573$	4.50489e6	+	1.23771e7i	0.573189	+	1.57482i
$574$	2.17365e7	+	9.50621e6i	2.75365	+	1.20428i
$575$	−1.15430e7	−	2.03534e6i	−1.45596	−	0.256725i
$576$	−2.07786e6	−	1.85325e6i	−0.260951	−	0.232743i
$577$	−709937.	−	1.22965e6i	−0.0887728	−	0.153759i	0.818220	−	0.574905i	$-0.194961\pi$
$577$	−709937.	−	1.22965e6i	−0.0887728	−	0.153759i	−0.906993	+	0.421146i	$0.861628\pi$
$578$	2.95887e6	+	5.96626e6i	0.368388	+	0.742818i
$579$	273025.	+	325379.i	0.0338459	+	0.0403360i
$580$	372136.	−	722754.i	0.0459337	−	0.0892115i
$581$	3.84533e6	−	6.66031e6i	0.472600	−	0.818567i
$582$	−1.00019e6	+	1.58023e7i	−0.122398	+	1.93381i
$583$	−2.02457e6	−	736885.i	−0.246696	−	0.0897900i
$584$	−1.41423e6	+	3.71030e6i	−0.171588	+	0.450171i
$585$	551526.	−	97248.9i	0.0666310	−	0.0117488i
$586$	−7.45786e6	−	1.80723e6i	−0.897161	−	0.217405i
$587$	5.95880e6	−	7.10142e6i	0.713778	−	0.850648i	−0.280232	−	0.959932i	$-0.590412\pi$
$587$	5.95880e6	−	7.10142e6i	0.713778	−	0.850648i	0.994011	+	0.109285i	$0.0348560\pi$
$588$	−8.31954e6	−	1.98333e7i	−0.992329	−	2.36566i
$589$	1.16664e6	−	5.43764e6i	0.138563	−	0.645836i
$590$	−535762.	+	805726.i	−0.0633639	+	0.0952922i
$591$	9.79091e6	+	8.21555e6i	1.15307	+	0.967538i
$592$	−5.93859e6	−	2.70469e6i	−0.696433	−	0.317186i
$593$	−1.33892e6	−	7.59341e6i	−0.156358	−	0.886748i	−0.957534	−	0.288320i	$-0.906903\pi$
$593$	−1.33892e6	−	7.59341e6i	−0.156358	−	0.886748i	0.801176	−	0.598428i	$-0.204208\pi$
$594$	2.22873e6	−	2.33863e6i	0.259174	−	0.271954i
$595$	−420424.	+	1.15510e6i	−0.0486850	+	0.133761i
$596$	−2.52480e6	+	3.32108e6i	−0.291146	+	0.382969i
$597$	8.57104e6	+	4.94849e6i	0.984232	+	0.568247i
$598$	1.50095e6	+	1.34271e7i	0.171638	+	1.53542i
$599$	1.99954e6	−	1.67781e6i	0.227700	−	0.191063i	−0.521799	−	0.853068i	$-0.674739\pi$
$599$	1.99954e6	−	1.67781e6i	0.227700	−	0.191063i	0.749499	+	0.662005i	$0.230294\pi$
$600$	−6.45498e6	+	7.46105e6i	−0.732009	+	0.846100i
$601$	−1.20505e7	+	6.95738e6i	−1.36088	+	0.785705i	−0.989741	−	0.142873i	$-0.954366\pi$
$601$	−1.20505e7	+	6.95738e6i	−1.36088	+	0.785705i	−0.371139	+	0.928577i	$0.621033\pi$
$602$	−2.26491e7	+	1.66852e7i	−2.54718	+	1.87646i
$603$	−394130.	+	2.23522e6i	−0.0441414	+	0.250338i
$604$	3.05986e6	−	1.96868e6i	0.341279	−	0.219574i
$605$	−1.22444e6	+	445658.i	−0.136003	+	0.0495009i
$606$	−1.49801e7	+	4.40275e6i	−1.65705	+	0.487015i
$607$	−2.64462e6			−0.291334			−0.145667	−	0.989334i	$-0.546533\pi$
$607$	−2.64462e6			−0.291334			−0.145667	+	0.989334i	$0.546533\pi$
$608$	−7.00471e6	+	5.83251e6i	−0.768478	+	0.639877i
$609$	−9.93951e6			−1.08598
$610$	1.42729e6	−	419489.i	0.155306	−	0.0456453i
$611$	−1.72069e6	+	626279.i	−0.186466	+	0.0678679i
$612$	1.12622e6	−	724593.i	0.121547	−	0.0782015i
$613$	1.47744e6	−	8.37898e6i	0.158803	−	0.900617i	−0.796423	−	0.604740i	$-0.793277\pi$
$613$	1.47744e6	−	8.37898e6i	0.158803	−	0.900617i	0.955226	−	0.295877i	$-0.0956119\pi$
$614$	1.49553e6	−	1.10173e6i	0.160094	−	0.117938i
$615$	3.04453e6	−	1.75776e6i	0.324588	−	0.187401i
$616$	5.48786e6	−	6.34320e6i	0.582708	−	0.673530i
$617$	1.19038e7	−	9.98844e6i	1.25884	−	1.05629i	0.263038	−	0.964785i	$-0.415275\pi$
$617$	1.19038e7	−	9.98844e6i	1.25884	−	1.05629i	0.995804	−	0.0915090i	$-0.0291690\pi$
$618$	1.20637e6	+	1.07918e7i	0.127060	+	1.13664i
$619$	−4.93393e6	−	2.84861e6i	−0.517567	−	0.298817i	0.218372	−	0.975866i	$-0.429925\pi$
$619$	−4.93393e6	−	2.84861e6i	−0.517567	−	0.298817i	−0.735938	+	0.677048i	$0.763259\pi$
$620$	−735662.	+	967680.i	−0.0768598	+	0.101100i
$621$	3.81231e6	−	1.04742e7i	0.396697	−	1.08992i
$622$	3.45139e6	−	3.62157e6i	0.357699	−	0.375337i
$623$	−1.03864e6	−	5.89044e6i	−0.107213	−	0.608033i
$624$	1.03493e7	+	4.71353e6i	1.06402	+	0.484602i
$625$	6.66149e6	+	5.58966e6i	0.682137	+	0.572381i
$626$	8.32799e6	−	1.25244e7i	0.849384	−	1.27738i
$627$	3.49238e6	+	4.48764e6i	0.354775	+	0.455879i
$628$	−2.08851e6	−	4.97890e6i	−0.211319	−	0.503772i
$629$	2.01749e6	−	2.40436e6i	0.203323	−	0.242310i
$630$	−1.16586e6	−	282517.i	−0.117029	−	0.0283592i
$631$	3.86877e6	−	682169.i	0.386812	−	0.0682054i	0.0231395	−	0.999732i	$-0.492634\pi$
$631$	3.86877e6	−	682169.i	0.386812	−	0.0682054i	0.363673	+	0.931527i	$0.381523\pi$
$632$	2.14739e6	−	5.63379e6i	0.213854	−	0.561059i
$633$	−2.16552e7	−	7.88186e6i	−2.14809	−	0.781842i
$634$	940444.	−	1.48584e7i	0.0929202	−	1.46807i
$635$	1.10797e6	−	1.91906e6i	0.109042	−	0.188866i
$636$	−2.86431e6	+	5.56300e6i	−0.280787	+	0.545339i
$637$	1.46292e7	+	1.74344e7i	1.42847	+	1.70238i
$638$	−1.18540e6	−	2.39023e6i	−0.115295	−	0.232481i
$639$	278273.	+	481983.i	0.0269599	+	0.0466960i
$640$	1.92754e6	−	503830.i	0.186018	−	0.0486221i
$641$	−6.19119e6	−	1.09167e6i	−0.595153	−	0.104942i	−0.132046	−	0.991244i	$-0.542155\pi$
$641$	−6.19119e6	−	1.09167e6i	−0.595153	−	0.104942i	−0.463108	+	0.886302i	$0.653266\pi$
$642$	1.38380e7	+	6.05192e6i	1.32507	+	0.579503i
$643$	418591.	+	1.15007e6i	0.0399266	+	0.109697i	0.958054	−	0.286588i	$-0.0925212\pi$
$643$	418591.	+	1.15007e6i	0.0399266	+	0.109697i	−0.918127	+	0.396286i	$0.870299\pi$
$644$	8.57872e6	−	2.76394e7i	0.815095	−	2.62612i
$645$			4.16858e6i			0.394538i
$646$	−1.80201e6	−	3.99674e6i	−0.169893	−	0.376812i
$647$		−	1.18931e6i		−	0.111695i	−0.998439	−	0.0558477i	$-0.982214\pi$
$647$		−	1.18931e6i		−	0.111695i	0.998439	−	0.0558477i	$-0.0177861\pi$
$648$	−8.28050e6	−	1.01764e7i	−0.774674	−	0.952045i
$649$	1.08613e6	+	2.98410e6i	0.101220	+	0.278101i
$650$	4.18319e6	−	9.56509e6i	0.388351	−	0.887985i
$651$	1.46366e7	+	2.58083e6i	1.35359	+	0.238675i
$652$	1.63837e7	−	788888.i	1.50936	−	0.0726769i
$653$	−2.11998e6	−	3.67191e6i	−0.194557	−	0.336983i	0.752198	−	0.658937i	$-0.228994\pi$
$653$	−2.11998e6	−	3.67191e6i	−0.194557	−	0.336983i	−0.946755	+	0.321954i	$0.895660\pi$
$654$	3.70364e6	−	1.83676e6i	0.338598	−	0.167922i
$655$	−1.42700e6	−	1.70064e6i	−0.129964	−	0.154885i
$656$	1.84379e7	+	1.44675e6i	1.67283	+	0.131260i
$657$	931898.	−	1.61410e6i	0.0842277	−	0.145887i
$658$	3.91445e6	+	247761.i	0.352457	+	0.0223084i
$659$	−3.27078e6	−	1.19047e6i	−0.293385	−	0.106783i	0.191135	−	0.981564i	$-0.438783\pi$
$659$	−3.27078e6	−	1.19047e6i	−0.293385	−	0.106783i	−0.484519	+	0.874781i	$0.661005\pi$
$660$	−274448.	−	1.21222e6i	−0.0245245	−	0.108324i
$661$	−5.90396e6	+	1.04103e6i	−0.525582	+	0.0926742i	−0.430142	−	0.902761i	$-0.641537\pi$
$661$	−5.90396e6	+	1.04103e6i	−0.525582	+	0.0926742i	−0.0954391	+	0.995435i	$0.530426\pi$
$662$	−63437.4	+	261786.i	−0.00562601	+	0.0232168i
$663$	−3.51594e6	+	4.19013e6i	−0.310640	+	0.370206i
$664$	1.13009e6	−	5.88787e6i	0.0994700	−	0.518249i
$665$	−1.47811e6	+	3.63848e6i	−0.129614	+	0.319055i
$666$	2.55059e6	+	1.69600e6i	0.222821	+	0.148163i
$667$	−7.05187e6	−	5.91722e6i	−0.613748	−	0.514996i
$668$	−6.55077e6	−	7.08492e6i	−0.568004	−	0.614319i
$669$	−674728.	−	3.82657e6i	−0.0582859	−	0.330556i
$670$	−1.17572e6	−	1.12047e6i	−0.101185	−	0.0964299i
$671$	1.66990e6	−	4.58803e6i	0.143181	−	0.393387i
$672$	−1.62654e7	−	1.81333e7i	−1.38944	−	1.54901i
$673$	−1.36500e7	−	7.88084e6i	−1.16170	−	0.670710i	−0.209992	−	0.977703i	$-0.567344\pi$
$673$	−1.36500e7	−	7.88084e6i	−1.16170	−	0.670710i	−0.951712	+	0.306993i	$0.900677\pi$
$674$	2.13419e7	−	2.38571e6i	1.80960	−	0.202287i
$675$	−6.59789e6	+	5.53629e6i	−0.557373	+	0.467691i
$676$	−151233.	−	19221.3i	−0.0127286	−	0.00161777i
$677$	1.64191e7	−	9.47955e6i	1.37682	−	0.794907i	0.385044	−	0.922898i	$-0.374186\pi$
$677$	1.64191e7	−	9.47955e6i	1.37682	−	0.794907i	0.991775	+	0.127991i	$0.0408530\pi$
$678$	4.56327e6	+	6.19436e6i	0.381243	+	0.517514i
$679$	−6.23222e6	+	3.53447e7i	−0.518762	+	2.94205i
$680$	−14465.3	+	958156.i	−0.00119965	+	0.0794629i
$681$	1.87315e7	−	6.81771e6i	1.54776	−	0.563340i
$682$	1.12495e6	+	3.82758e6i	0.0926127	+	0.315111i
$683$	5.74311e6			0.471081			0.235540	−	0.971865i	$-0.424314\pi$
$683$	5.74311e6			0.471081			0.235540	+	0.971865i	$0.424314\pi$
$684$	3.68087e6	−	2.18099e6i	0.300823	−	0.178243i
$685$	2.18680e6			0.178067
$686$	−7.52124e6	−	2.55907e7i	−0.610210	−	2.07621i
$687$	−3.01394e6	+	1.09699e6i	−0.243637	+	0.0886766i
$688$	−1.24172e7	+	1.80762e7i	−1.00012	+	1.45591i
$689$	1.14975e6	−	6.52056e6i	0.0922690	−	0.523283i
$690$	−2.54353e6	−	3.45269e6i	−0.203382	−	0.276080i
$691$	6.45291e6	−	3.72559e6i	0.514115	−	0.296824i	−0.220409	−	0.975408i	$-0.570739\pi$
$691$	6.45291e6	−	3.72559e6i	0.514115	−	0.296824i	0.734523	+	0.678583i	$0.237406\pi$
$692$	−1.33737e6	+	1.05224e7i	−0.106166	+	0.835315i
$693$	−3.01597e6	+	2.53070e6i	−0.238558	+	0.200174i
$694$	−1.68468e7	+	1.88323e6i	−1.32776	+	0.148424i
$695$	2.79813e6	+	1.61550e6i	0.219738	+	0.126866i
$696$	−7.32034e6	+	2.53991e6i	−0.572807	+	0.198745i
$697$	−3.04247e6	+	8.35912e6i	−0.237216	+	0.651746i
$698$	−1.74499e7	−	1.66299e7i	−1.35567	−	1.29197i
$699$	4.06387e6	+	2.30474e7i	0.314592	+	1.78414i
$700$	−1.64193e7	+	1.51815e7i	−1.26652	+	1.17103i
$701$	−3.96715e6	−	3.32883e6i	−0.304918	−	0.255857i	0.477470	−	0.878648i	$-0.341554\pi$
$701$	−3.96715e6	−	3.32883e6i	−0.304918	−	0.255857i	−0.782388	+	0.622791i	$0.785999\pi$
$702$	8.26717e6	+	5.49720e6i	0.633161	+	0.421016i
$703$	6.72398e6	−	7.43918e6i	0.513142	−	0.567724i
$704$	2.42083e6	−	6.07405e6i	0.184091	−	0.461899i
$705$	373596.	−	445235.i	0.0283094	−	0.0337378i
$706$	2.28859e6	−	9.44428e6i	0.172805	−	0.713111i
$707$	−3.48532e7	+	6.14555e6i	−2.62237	+	0.462394i
$708$	8.99495e6	−	2.03646e6i	0.674397	−	0.152683i
$709$	−542045.	−	197288.i	−0.0404967	−	0.0147396i	0.321692	−	0.946844i	$-0.395748\pi$
$709$	−542045.	−	197288.i	−0.0404967	−	0.0147396i	−0.362189	+	0.932105i	$0.617971\pi$
$710$	−397448.	−	25156.1i	−0.0295893	−	0.00187282i
$711$	−1.41501e6	+	2.45087e6i	−0.104975	+	0.181822i
$712$	−2.27018e6	−	4.07283e6i	−0.167826	−	0.301090i
$713$	8.84795e6	+	1.05446e7i	0.651807	+	0.776793i
$714$	1.04965e7	−	5.20559e6i	0.770549	−	0.382141i
$715$	657610.	+	1.13901e6i	0.0481064	+	0.0833228i
$716$	1.03558e6	+	2.15071e7i	0.0754924	+	1.56783i
$717$	−1.68524e6	−	297153.i	−0.122423	−	0.0215865i
$718$	2.82193e6	−	6.45249e6i	0.204284	−	0.467107i
$719$	−6.45885e6	−	1.77455e7i	−0.465943	−	1.28017i	−0.920950	−	0.389680i	$-0.872586\pi$
$719$	−6.45885e6	−	1.77455e7i	−0.465943	−	1.28017i	0.455007	−	0.890488i	$-0.349637\pi$
$720$	−930837.	+	89849.6i	−0.0669179	+	0.00645929i
$721$			2.46137e7i			1.76335i
$722$	−5.28335e6	−	1.29723e7i	−0.377195	−	0.926134i
$723$		−	6.67167e6i		−	0.474667i
$724$	1.09246e7	+	3.39079e6i	0.774570	+	0.240411i
$725$	2.43286e6	+	6.68423e6i	0.171899	+	0.472287i
$726$	1.13791e7	+	4.97651e6i	0.801245	+	0.350416i
$727$	2.23181e7	+	3.93529e6i	1.56611	+	0.276147i	0.888360	−	0.459148i	$-0.151845\pi$
$727$	2.23181e7	+	3.93529e6i	1.56611	+	0.276147i	0.677747	+	0.735295i	$0.262956\pi$
$728$	2.21261e7	+	1.32238e7i	1.54731	+	0.924760i
$729$	−3.21816e6	−	5.57401e6i	−0.224279	−	0.388462i
$730$	592543.	+	1.19480e6i	0.0411540	+	0.0829830i
$731$	−6.78017e6	−	8.08029e6i	−0.469296	−	0.559286i
$732$	−1.26067e7	−	6.49101e6i	−0.869608	−	0.447749i
$733$	203144.	−	351856.i	0.0139651	−	0.0241883i	−0.858958	−	0.512045i	$-0.828888\pi$
$733$	203144.	−	351856.i	0.0139651	−	0.0241883i	0.872924	+	0.487857i	$0.162221\pi$
$734$	1.08488e6	−	1.71403e7i	0.0743260	−	1.17430i
$735$	−6.78824e6	−	2.47072e6i	−0.463489	−	0.168696i
$736$	−744768.	−	2.25483e7i	−0.0506788	−	1.53433i
$737$	−5.24934e6	+	925600.i	−0.355988	+	0.0627703i
$738$	−8.43695e6	−	2.04449e6i	−0.570222	−	0.138179i
$739$	−1.60027e7	+	1.90712e7i	−1.07791	+	1.28460i	−0.121489	+	0.992593i	$0.538767\pi$
$739$	−1.60027e7	+	1.90712e7i	−1.07791	+	1.28460i	−0.956417	+	0.292006i	$0.905677\pi$
$740$	−2.02115e6	+	847817.i	−0.135681	+	0.0569145i
$741$	−1.17180e7	+	1.29644e7i	−0.783988	+	0.867378i
$742$	−7.85300e6	+	1.18100e7i	−0.523632	+	0.787484i
$743$	1.85651e7	+	1.55780e7i	1.23375	+	1.03524i	0.997987	+	0.0634264i	$0.0202028\pi$
$743$	1.85651e7	+	1.55780e7i	1.23375	+	1.03524i	0.235761	+	0.971811i	$0.424242\pi$
$744$	1.14392e7	−	1.83945e6i	0.757642	−	0.121830i
$745$	243320.	+	1.37994e6i	0.0160615	+	0.0910894i
$746$	−1.07341e7	+	1.12634e7i	−0.706185	+	0.741007i
$747$	−962494.	+	2.64443e6i	−0.0631098	+	0.173393i
$748$	2.50366e6	+	1.90336e6i	0.163614	+	0.124385i
$749$	2.96479e7	+	1.71172e7i	1.93103	+	1.11488i
$750$	750391.	+	6.71278e6i	0.0487118	+	0.435762i
$751$	1.15872e7	−	9.72282e6i	0.749685	−	0.629060i	−0.185735	−	0.982600i	$-0.559466\pi$
$751$	1.15872e7	−	9.72282e6i	0.749685	−	0.629060i	0.935420	+	0.353540i	$0.115022\pi$
$752$	2.94626e6	−	817814.i	0.189988	−	0.0527363i
$753$	1.63046e7	−	9.41349e6i	1.04791	−	0.605011i
$754$	6.60139e6	−	4.86312e6i	0.422870	−	0.311520i
$755$	212211.	−	1.20351e6i	0.0135488	−	0.0768391i
$756$	−1.15064e7	−	1.78841e7i	−0.732211	−	1.13806i
$757$	−6.00037e6	+	2.18396e6i	−0.380573	+	0.138517i	−0.525221	−	0.850966i	$-0.676017\pi$
$757$	−6.00037e6	+	2.18396e6i	−0.380573	+	0.138517i	0.144648	+	0.989483i	$0.453795\pi$
$758$	−6.05284e6	+	1.77896e6i	−0.382636	+	0.112459i
$759$	−1.40745e7			−0.886807
$760$	−158845.	+	3.05741e6i	−0.00997563	+	0.192008i
$761$	−3.05006e7			−1.90918			−0.954589	−	0.297927i	$-0.903705\pi$
$761$	−3.05006e7			−1.90918			−0.954589	+	0.297927i	$0.903705\pi$
$762$	−2.02641e7	+	5.95573e6i	−1.26427	+	0.371576i
$763$	8.80539e6	−	3.20490e6i	0.547567	−	0.199298i
$764$	1.25928e7	+	1.95727e7i	0.780530	+	1.21316i
$765$	78106.7	−	442965.i	0.00482542	−	0.0273663i
$766$	4.39646e6	−	3.23879e6i	0.270727	−	0.199439i
$767$	−8.45171e6	+	4.87960e6i	−0.518748	+	0.299499i
$768$	−1.66130e7	−	9.19856e6i	−1.01635	−	0.562752i
$769$	−1.50585e7	+	1.26356e7i	−0.918260	+	0.770512i	−0.973672	−	0.227952i	$-0.926797\pi$
$769$	−1.50585e7	+	1.26356e7i	−0.918260	+	0.770512i	0.0554124	+	0.998464i	$0.482353\pi$
$770$	−312975.	−	2.79978e6i	−0.0190232	−	0.170176i
$771$	−1.58583e7	−	9.15580e6i	−0.960774	−	0.554703i
$772$	597478.	+	454222.i	0.0360810	+	0.0274300i
$773$	6.54092e6	−	1.79710e7i	0.393722	−	1.08174i	−0.571566	−	0.820556i	$-0.693664\pi$
$773$	6.54092e6	−	1.79710e7i	0.393722	−	1.08174i	0.965288	−	0.261187i	$-0.0841139\pi$
$774$	7.10160e6	−	7.45178e6i	0.426093	−	0.447103i
$775$	−1.84697e6	−	1.04747e7i	−0.110460	−	0.626451i
$776$	4.44192e6	+	2.76235e7i	0.264799	+	1.64674i
$777$	2.05286e7	+	1.72255e7i	1.21985	+	1.02358i
$778$	−2.57337e6	+	3.87006e6i	−0.152424	+	0.229228i
$779$	−1.06966e7	+	2.63305e7i	−0.631541	+	1.55459i
$780$	3.52231e6	−	1.47751e6i	0.207296	−	0.0869550i
$781$	−840141.	+	1.00124e6i	−0.0492861	+	0.0587369i
$782$	1.05461e7	+	2.55558e6i	0.616700	+	0.149442i
$783$	−6.66171e6	+	1.17464e6i	−0.388312	+	0.0684700i
$784$	−2.20761e7	−	3.09342e7i	−1.28272	−	1.79742i
$785$	−1.70410e6	−	620242.i	−0.0987009	−	0.0359242i
$786$	−1.33663e6	+	2.11179e7i	−0.0771713	+	1.21925i
$787$	7.20634e6	−	1.24818e7i	0.414742	−	0.718354i	−0.580659	−	0.814147i	$-0.697205\pi$
$787$	7.20634e6	−	1.24818e7i	0.414742	−	0.718354i	0.995401	+	0.0957923i	$0.0305385\pi$
$788$	2.00789e7	+	1.03383e7i	1.15192	+	0.593109i
$789$	−3.09909e6	−	3.69335e6i	−0.177232	−	0.211216i
$790$	−899727.	−	1.81421e6i	−0.0512912	−	0.103424i
$791$	8.71948e6	+	1.51026e7i	0.495507	+	0.858243i
$792$	−1.57454e6	+	2.63453e6i	−0.0891952	+	0.149241i
$793$	1.47767e7	+	2.60553e6i	0.834438	+	0.147134i
$794$	−1.89535e7	−	8.28910e6i	−1.06693	−	0.466612i
$795$	718794.	+	1.97487e6i	0.0403354	+	0.110821i
$796$	1.67019e7	+	5.18392e6i	0.934291	+	0.289985i
$797$			2.18360e7i			1.21766i	0.793300	+	0.608831i	$0.208361\pi$
$797$			2.18360e7i			1.21766i	−0.793300	+	0.608831i	$0.791639\pi$
$798$	3.41244e7	−	1.53857e7i	1.89696	−	0.855284i
$799$			1.47069e6i			0.0814991i
$800$	−8.21324e6	+	1.53767e7i	−0.453722	+	0.849453i
$801$	748566.	+	2.05667e6i	0.0412239	+	0.113262i
$802$	−5.34985e6	+	1.22327e7i	−0.293701	+	0.671563i
$803$	4.31056e6	+	760068.i	0.235909	+	0.0415972i
$804$	744525.	+	1.54623e7i	0.0406199	+	0.843596i
$805$	−4.86017e6	−	8.41806e6i	−0.264339	−	0.457849i
$806$	−1.09837e7	+	5.44721e6i	−0.595542	+	0.295349i
$807$	−1.21585e7	−	1.44899e7i	−0.657198	−	0.783218i
$808$	−2.40986e7	+	1.34324e7i	−1.29856	+	0.723812i
$809$	−1.76114e6	+	3.05038e6i	−0.0946066	+	0.163863i	−0.909444	−	0.415826i	$-0.863493\pi$
$809$	−1.76114e6	+	3.05038e6i	−0.0946066	+	0.163863i	0.814838	+	0.579689i	$0.196826\pi$
$810$	−4.39780e6	−	278354.i	−0.235517	−	0.0149068i
$811$	−1.53400e7	−	5.58331e6i	−0.818980	−	0.298085i	−0.101652	−	0.994820i	$-0.532413\pi$
$811$	−1.53400e7	−	5.58331e6i	−0.818980	−	0.298085i	−0.717328	+	0.696735i	$0.754635\pi$
$812$	−1.71295e7	+	3.87812e6i	−0.911705	+	0.206410i
$813$	2.26821e7	−	3.99946e6i	1.20353	−	0.212215i
$814$	−1.69410e6	+	6.99100e6i	−0.0896143	+	0.369810i
$815$	3.54129e6	−	4.22035e6i	0.186753	−	0.222564i
$816$	6.40037e6	−	6.51611e6i	0.336496	−	0.342581i
$817$	−2.06970e7	−	2.65952e7i	−1.08481	−	1.39395i
$818$	−5.27067e6	−	3.50469e6i	−0.275412	−	0.183133i
$819$	−9.26857e6	−	7.77726e6i	−0.482840	−	0.405151i
$820$	4.56104e6	−	4.21717e6i	0.236880	−	0.219022i
$821$	777482.	+	4.40932e6i	0.0402562	+	0.228304i	0.998298	−	0.0583257i	$-0.0185762\pi$
$821$	777482.	+	4.40932e6i	0.0402562	+	0.228304i	−0.958041	+	0.286630i	$0.907465\pi$
$822$	−1.50888e7	−	1.43798e7i	−0.778889	−	0.742287i
$823$	7.50526e6	−	2.06205e7i	0.386248	−	1.06121i	−0.582429	−	0.812882i	$-0.697898\pi$
$823$	7.50526e6	−	2.06205e7i	0.386248	−	1.06121i	0.968677	−	0.248325i	$-0.0798802\pi$
$824$	6.28971e6	+	1.81277e7i	0.322710	+	0.930089i
$825$	9.41844e6	+	5.43774e6i	0.481775	+	0.278153i
$826$	2.07750e7	−	2.32234e6i	1.05947	−	0.118434i
$827$	−2.89826e6	+	2.43193e6i	−0.147358	+	0.123648i	−0.713487	−	0.700669i	$-0.752885\pi$
$827$	−2.89826e6	+	2.43193e6i	−0.147358	+	0.123648i	0.566129	+	0.824317i	$0.308441\pi$
$828$	−1.33518e6	+	1.05052e7i	−0.0676805	+	0.532510i
$829$	1.16440e7	−	6.72264e6i	0.588457	−	0.339746i	−0.176030	−	0.984385i	$-0.556326\pi$
$829$	1.16440e7	−	6.72264e6i	0.588457	−	0.339746i	0.764487	+	0.644639i	$0.222992\pi$
$830$	−1.19435e6	−	1.62126e6i	−0.0601780	−	0.0816880i
$831$	1.43127e6	−	8.11714e6i	0.0718984	−	0.407756i
$832$	1.96748e7	+	4.08516e6i	0.985378	+	0.204598i
$833$	1.71768e7	−	6.25184e6i	0.857688	−	0.312173i
$834$	−8.68389e6	−	2.95465e7i	−0.432314	−	1.47093i
$835$	−3.24097e6			−0.160864
$836$	7.76964e6	+	6.37126e6i	0.384490	+	0.315289i
$837$	1.01148e7			0.499051
$838$	4.52942e6	+	1.54111e7i	0.222809	+	0.758096i
$839$	3.78638e6	−	1.37813e6i	0.185703	−	0.0675905i	−0.247495	−	0.968889i	$-0.579607\pi$
$839$	3.78638e6	−	1.37813e6i	0.185703	−	0.0675905i	0.433198	+	0.901299i	$0.357385\pi$
$840$	−8.18081e6	−	123506.i	−0.400035	−	0.00603934i
$841$	2.59162e6	−	1.46978e7i	0.126352	−	0.716576i
$842$	1.48627e7	+	2.01753e7i	0.722468	+	0.980707i
$843$	3.08373e7	−	1.78039e7i	1.49454	−	0.862872i
$844$	−4.03953e7	−	5.13413e6i	−1.95198	−	0.248091i
$845$	−39224.8	+	32913.5i	−0.00188982	+	0.00158574i
$846$	−1.42635e6	+	159445.i	−0.0685171	+	0.00765921i
$847$	2.43795e7	+	1.40755e7i	1.16766	+	0.674149i
$848$	−2.76575e6	+	1.07047e7i	−0.132076	+	0.511193i
$849$	1.06806e7	−	2.93448e7i	0.508544	−	1.39721i
$850$	−6.06991e6	−	5.78467e6i	−0.288161	−	0.274620i
$851$	4.30984e6	+	2.44423e7i	0.204003	+	1.15696i
$852$	2.57696e6	+	2.78708e6i	0.121621	+	0.131538i
$853$	8.50800e6	+	7.13906e6i	0.400364	+	0.335945i	0.820634	−	0.571454i	$-0.193620\pi$
$853$	8.50800e6	+	7.13906e6i	0.400364	+	0.335945i	−0.420270	+	0.907399i	$0.638065\pi$
$854$	−2.67635e7	−	1.77962e7i	−1.25574	−	0.834994i
$855$	301457.	−	1.40507e6i	0.0141029	−	0.0657331i
$856$	2.62094e7	+	5.03050e6i	1.22257	+	0.234654i
$857$	−1.58146e7	+	1.88471e7i	−0.735539	+	0.876582i	−0.996041	−	0.0888918i	$-0.971667\pi$
$857$	−1.58146e7	+	1.88471e7i	−0.735539	+	0.876582i	0.260502	+	0.965473i	$0.416112\pi$
$858$	2.95234e6	−	1.21834e7i	0.136914	−	0.565002i
$859$	−2.19020e7	+	3.86192e6i	−1.01275	+	0.178575i	−0.655308	−	0.755362i	$-0.727461\pi$
$859$	−2.19020e7	+	3.86192e6i	−1.01275	+	0.178575i	−0.357439	+	0.933936i	$0.616350\pi$
$860$	1.62647e6	+	7.18403e6i	0.0749892	+	0.331224i
$861$	−7.13708e7	−	2.59768e7i	−3.28105	−	1.19420i
$862$	2.20998e7	+	1.39878e6i	1.01302	+	0.0641182i
$863$	−9.49623e6	+	1.64480e7i	−0.434034	+	0.751770i	−0.997216	−	0.0745633i	$-0.976244\pi$
$863$	−9.49623e6	+	1.64480e7i	−0.434034	+	0.751770i	0.563182	+	0.826333i	$0.309577\pi$
$864$	−1.30444e7	−	1.02312e7i	−0.594485	−	0.466273i
$865$	2.29004e6	+	2.72916e6i	0.104064	+	0.124019i
$866$	−1.16262e7	+	5.76580e6i	−0.526795	+	0.261255i
$867$	−1.06602e7	−	1.84639e7i	−0.481632	−	0.834212i
$868$	2.62313e7	−	1.26306e6i	1.18174	−	0.0569017i
$869$	−6.54523e6	−	1.15410e6i	−0.294019	−	0.0518435i
$870$	−1.04282e6	+	2.38447e6i	−0.0467102	+	0.106805i
$871$	−5.60261e6	−	1.53930e7i	−0.250233	−	0.687510i
$872$	5.66611e6	−	4.61048e6i	0.252344	−	0.205331i
$873$		−	1.31327e7i		−	0.583203i
$874$	3.33701e7	+	9.39925e6i	1.47767	+	0.416212i
$875$			1.53103e7i			0.676025i
$876$	3.76816e6	−	1.21405e7i	0.165908	−	0.534534i
$877$	−7.74151e6	−	2.12696e7i	−0.339881	−	0.933815i	−0.985428	−	0.170095i	$-0.945593\pi$
$877$	−7.74151e6	−	2.12696e7i	−0.339881	−	0.933815i	0.645547	−	0.763721i	$-0.276630\pi$
$878$	−7.40551e6	−	3.23872e6i	−0.324204	−	0.141787i
$879$	2.41934e7	+	4.26596e6i	1.05615	+	0.186228i
$880$	−945952.	−	1.98203e6i	−0.0411777	−	0.0862788i
$881$	2.12774e7	+	3.68535e7i	0.923588	+	1.59970i	0.793817	+	0.608157i	$0.208091\pi$
$881$	2.12774e7	+	3.68535e7i	0.923588	+	1.59970i	0.129771	+	0.991544i	$0.458576\pi$
$882$	7.92558e6	+	1.59811e7i	0.343051	+	0.691729i
$883$	−1.61402e7	−	1.92351e7i	−0.696636	−	0.830218i	0.295505	−	0.955341i	$-0.404512\pi$
$883$	−1.61402e7	−	1.92351e7i	−0.696636	−	0.830218i	−0.992141	+	0.125123i	$0.960068\pi$
$884$	−4.42440e6	+	8.59298e6i	−0.190425	+	0.369839i
$885$	1.54883e6	−	2.68265e6i	0.0664730	−	0.115135i
$886$	1.32473e6	−	2.09298e7i	0.0566947	−	0.895737i
$887$	2.88133e7	+	1.04872e7i	1.22966	+	0.447558i	0.873479	−	0.486861i	$-0.161858\pi$
$887$	2.88133e7	+	1.04872e7i	1.22966	+	0.447558i	0.356176	+	0.934419i	$0.384080\pi$
$888$	1.95208e7	+	7.44059e6i	0.830742	+	0.316647i
$889$	−4.71469e7	+	8.31328e6i	−2.00078	+	0.352791i
$890$	−1.52207e6	−	368837.i	−0.0644111	−	0.0156084i
$891$	−9.29623e6	+	1.10788e7i	−0.392295	+	0.467519i
$892$	−2.65583e6	−	6.33136e6i	−0.111760	−	0.266431i
$893$	−172926.	+	4.69547e6i	−0.00725657	+	0.197038i
$894$	7.39516e6	−	1.11215e7i	0.309459	−	0.465392i
$895$	5.54011e6	+	4.64870e6i	0.231186	+	0.193988i
$896$	−3.51064e7	−	2.49041e7i	−1.46089	−	1.03634i
$897$	−7.51086e6	−	4.25962e7i	−0.311680	−	1.76762i
$898$	−2.65573e7	+	2.78668e7i	−1.09899	+	1.15318i
$899$	2.85709e6	−	7.84980e6i	0.117903	−	0.323936i
$900$	4.95220e6	−	6.51406e6i	0.203794	−	0.268068i
$901$	−4.60541e6	−	2.65893e6i	−0.188997	−	0.109118i
$902$	−2.26490e6	−	2.02611e7i	−0.0926899	−	0.829176i
$903$	6.89901e7	−	5.78896e7i	2.81558	−	2.36255i
$904$	1.02811e7	+	8.89474e6i	0.418425	+	0.362003i
$905$	3.32728e6	−	1.92101e6i	0.135042	−	0.0779664i
$906$	−9.37818e6	+	6.90873e6i	−0.379575	+	0.279626i
$907$	326354.	−	1.85084e6i	0.0131726	−	0.0747053i	−0.977513	−	0.210876i	$-0.932368\pi$
$907$	326354.	−	1.85084e6i	0.0131726	−	0.0747053i	0.990685	+	0.136171i	$0.0434795\pi$
$908$	2.96213e7	−	1.90580e7i	1.19231	−	0.767117i
$909$	1.21691e7	−	4.42920e6i	0.488483	−	0.177793i
$910$	8.30646e6	−	2.44131e6i	0.332516	−	0.0977283i
$911$	4.83681e7			1.93091			0.965457	−	0.260563i	$-0.0839082\pi$
$911$	4.83681e7			1.93091			0.965457	+	0.260563i	$0.0839082\pi$
$912$	2.12007e7	−	2.00515e7i	0.844039	−	0.798287i
$913$	−6.60891e6			−0.262394
$914$	−2.99318e6	+	879711.i	−0.118513	+	0.0348317i
$915$	−4.47539e6	+	1.62891e6i	−0.176717	+	0.0643197i
$916$	−4.76614e6	+	3.06647e6i	−0.187684	+	0.120754i
$917$	−8.32860e6	+	4.72339e7i	−0.327076	+	1.85494i
$918$	6.41985e6	−	4.72938e6i	0.251431	−	0.185224i
$919$	−2.79250e7	+	1.61225e7i	−1.09070	+	0.629716i	−0.933763	−	0.357893i	$-0.883495\pi$
$919$	−2.79250e7	+	1.61225e7i	−1.09070	+	0.629716i	−0.156937	+	0.987609i	$0.550162\pi$
$920$	−5.73059e6	−	4.95786e6i	−0.223218	−	0.193119i
$921$	−4.55545e6	+	3.82247e6i	−0.176963	+	0.148489i
$922$	−5.55941e6	−	4.97328e7i	−0.215378	−	1.92671i
$923$	−3.47857e6	−	2.00836e6i	−0.134399	−	0.0775955i
$924$	−1.62510e7	+	2.13764e7i	−0.626183	+	0.823673i
$925$	6.55929e6	−	1.80215e7i	0.252059	−	0.692527i
$926$	2.93817e7	−	3.08305e7i	1.12603	−	1.18155i
$927$	−1.56397e6	−	8.86973e6i	−0.0597764	−	0.339009i
$928$	−1.16247e7	+	7.23342e6i	−0.443110	+	0.275723i
$929$	−1.35134e7	−	1.13391e7i	−0.513719	−	0.431062i	0.348716	−	0.937228i	$-0.386618\pi$
$929$	−1.35134e7	−	1.13391e7i	−0.513719	−	0.431062i	−0.862436	+	0.506167i	$0.831062\pi$
$930$	2.15476e6	−	3.24052e6i	0.0816943	−	0.122859i
$931$	5.55755e7	−	1.79406e7i	2.10140	−	0.678364i
$932$	1.59960e7	+	3.81336e7i	0.603214	+	1.43803i
$933$	−1.02949e7	+	1.22689e7i	−0.387183	+	0.461427i
$934$	−1.55035e6	−	375688.i	−0.0581515	−	0.0140916i
$935$	1.04029e6	−	183431.i	0.0389157	−	0.00686188i
$936$	−8.81358e6	−	3.35940e6i	−0.328824	−	0.125335i
$937$	−7.32969e6	−	2.66779e6i	−0.272732	−	0.0992664i	0.202033	−	0.979379i	$-0.435245\pi$
$937$	−7.32969e6	−	2.66779e6i	−0.272732	−	0.0992664i	−0.474766	+	0.880112i	$0.657467\pi$
$938$	−2.21644e6	+	3.50182e7i	−0.0822523	+	1.29953i
$939$	−2.40753e7	+	4.16996e7i	−0.891061	+	1.54336i
$940$	470128.	−	913073.i	0.0173539	−	0.0337044i
$941$	−1.57148e7	−	1.87282e7i	−0.578542	−	0.689479i	0.394819	−	0.918759i	$-0.370807\pi$
$941$	−1.57148e7	−	1.87282e7i	−0.578542	−	0.689479i	−0.973361	+	0.229280i	$0.926363\pi$
$942$	7.67968e6	+	1.54853e7i	0.281979	+	0.568581i
$943$	−3.51714e7	−	6.09187e7i	−1.28799	−	2.23086i
$944$	1.47071e7	−	7.01915e6i	0.537152	−	0.256363i
$945$	−7.03423e6	−	1.24032e6i	−0.256234	−	0.0451810i
$946$	2.21490e7	+	9.68663e6i	0.804686	+	0.351921i
$947$	3.91755e6	+	1.07634e7i	0.141951	+	0.390008i	0.990212	−	0.139571i	$-0.0445723\pi$
$947$	3.91755e6	+	1.07634e7i	0.141951	+	0.390008i	−0.848261	+	0.529579i	$0.822350\pi$
$948$	−5.72164e6	+	1.84343e7i	−0.206776	+	0.666202i
$949$			1.34514e7i			0.484845i
$950$	−1.86993e7	−	1.91825e7i	−0.672227	−	0.689597i
$951$			4.76629e7i			1.70895i
$952$	1.60584e7	−	1.30666e7i	0.574261	−	0.467273i
$953$	1.03558e7	+	2.84524e7i	0.369363	+	1.01482i	0.975605	+	0.219535i	$0.0704541\pi$
$953$	1.03558e7	+	2.84524e7i	0.369363	+	1.01482i	−0.606242	+	0.795280i	$0.707324\pi$
$954$	2.07947e6	−	4.75483e6i	0.0739745	−	0.169147i
$955$	7.69837e6	+	1.35743e6i	0.273143	+	0.0481625i
$956$	−3.02023e6	+	145427.i	−0.106880	+	0.00514636i
$957$	4.27072e6	+	7.39711e6i	0.150738	+	0.261085i
$958$	−4.14875e7	+	2.05750e7i	−1.46051	+	0.724314i
$959$	−3.03683e7	−	3.61916e7i	−1.06629	−	1.27075i
$960$	−6.05664e6	+	1.99954e6i	−0.212106	+	0.0700249i
$961$	8.06907e6	−	1.39760e7i	0.281848	−	0.488175i
$962$	−2.20621e7	−	1.39640e6i	−0.768617	−	0.0486488i
$963$	−1.17715e7	−	4.28447e6i	−0.409040	−	0.148878i
$964$	−2.60310e6	−	1.14978e7i	−0.0902190	−	0.398494i
$965$	248257.	−	43774.3i	0.00858188	−	0.00151322i
$966$	−2.18198e7	+	9.00432e7i	−0.752328	+	3.10462i
$967$	3.39399e6	−	4.04480e6i	0.116720	−	0.139101i	−0.704521	−	0.709683i	$-0.748838\pi$
$967$	3.39399e6	−	4.04480e6i	0.116720	−	0.139101i	0.821241	+	0.570582i	$0.193282\pi$
$968$	2.15521e7	+	4.13660e6i	0.739266	+	0.141891i
$969$	6.56569e6	+	1.24052e7i	0.224632	+	0.424419i
$970$	7.82525e6	+	5.20334e6i	0.267035	+	0.177563i
$971$	4.27943e6	+	3.59087e6i	0.145659	+	0.122223i	0.712706	−	0.701463i	$-0.247470\pi$
$971$	4.27943e6	+	3.59087e6i	0.145659	+	0.122223i	−0.567046	+	0.823686i	$0.691914\pi$
$972$	1.34060e7	+	1.44991e7i	0.455128	+	0.492239i
$973$	−1.21214e7	−	6.87436e7i	−0.410458	−	2.32783i
$974$	1.50542e7	+	1.43468e7i	0.508465	+	0.484571i
$975$	−1.14310e7	+	3.14065e7i	−0.385101	+	1.05806i
$976$	−2.42587e7	−	6.26765e6i	−0.815159	−	0.210611i
$977$	−1.91939e7	−	1.10816e7i	−0.643319	−	0.371420i	0.142573	−	0.989784i	$-0.454462\pi$
$977$	−1.91939e7	−	1.10816e7i	−0.643319	−	0.371420i	−0.785892	+	0.618364i	$0.787796\pi$
$978$	−5.21865e7	+	5.83369e6i	−1.74466	+	0.195028i
$979$	−3.93746e6	+	3.30392e6i	−0.131298	+	0.110173i
$980$	−1.26627e7	−	1.60939e6i	−0.421173	−	0.0535298i
$981$	−2.96945e6	+	1.71441e6i	−0.0985153	+	0.0568778i
$982$	2.86691e7	+	3.89166e7i	0.948714	+	1.28782i
$983$	1.76872e6	−	1.00309e7i	0.0583816	−	0.331099i	−0.941603	−	0.336726i	$-0.890680\pi$
$983$	1.76872e6	−	1.00309e7i	0.0583816	−	0.331099i	0.999984	+	0.00562773i	$0.00179137\pi$
$984$	−5.92019e7	−	893772.i	−1.94916	−	0.0294265i
$985$	7.12802e6	−	2.59439e6i	0.234088	−	0.0852010i
$986$	−1.85694e6	−	6.31814e6i	−0.0608281	−	0.206965i
$987$	−1.25568e7			−0.410286
$988$	−1.51362e7	+	2.69146e7i	−0.493315	+	0.877195i
$989$	8.34101e7			2.71161
$990$	290684.	+	989037.i	0.00942611	+	0.0320719i
$991$	4.37341e7	−	1.59179e7i	1.41461	−	0.514876i	0.482130	−	0.876100i	$-0.339863\pi$
$991$	4.37341e7	−	1.59179e7i	1.41461	−	0.514876i	0.932479	+	0.361224i	$0.117641\pi$
$992$	1.89963e7	−	7.63332e6i	0.612902	−	0.246283i
$993$	149744.	−	849239.i	0.00481921	−	0.0273311i
$994$	5.10308e6	+	6.92712e6i	0.163820	+	0.222376i
$995$	5.08683e6	−	2.93688e6i	0.162888	−	0.0940436i
$996$	−2.41997e6	+	1.90404e7i	−0.0772969	+	0.608173i
$997$	1.89269e7	−	1.58815e7i	0.603033	−	0.506005i	−0.289386	−	0.957212i	$-0.593451\pi$
$997$	1.89269e7	−	1.58815e7i	0.603033	−	0.506005i	0.892419	+	0.451208i	$0.149007\pi$
$998$	−5.52132e6	+	617204.i	−0.175476	+	0.0196156i
$999$	1.57945e7	+	9.11893e6i	0.500715	+	0.289088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.k.a.3.6	✓	288
4.3	odd	2	inner	76.6.k.a.3.23	yes	288
19.13	odd	18	inner	76.6.k.a.51.23	yes	288
76.51	even	18	inner	76.6.k.a.51.6	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.k.a.3.6	✓	288	1.1	even	1	trivial
76.6.k.a.3.23	yes	288	4.3	odd	2	inner
76.6.k.a.51.6	yes	288	76.51	even	18	inner
76.6.k.a.51.23	yes	288	19.13	odd	18	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.42730 + 1.59511i) q^{2} +(17.0177 - 6.19395i) q^{3} +(26.9112 - 17.3143i) q^{4} +(1.86638 - 10.5848i) q^{5} +(-82.4803 + 60.7617i) q^{6} +(-201.097 + 116.103i) q^{7} +(-118.437 + 136.897i) q^{8} +(65.0895 - 54.6166i) q^{9} +O(q^{10})\)	\(q+(-5.42730 + 1.59511i) q^{2} +(17.0177 - 6.19395i) q^{3} +(26.9112 - 17.3143i) q^{4} +(1.86638 - 10.5848i) q^{5} +(-82.4803 + 60.7617i) q^{6} +(-201.097 + 116.103i) q^{7} +(-118.437 + 136.897i) q^{8} +(65.0895 - 54.6166i) q^{9} +(6.75451 + 60.4239i) q^{10} +(172.811 + 99.7726i) q^{11} +(350.724 - 461.338i) q^{12} +(-209.739 + 576.252i) q^{13} +(906.215 - 950.900i) q^{14} +(-33.8000 - 191.689i) q^{15} +(424.428 - 931.900i) q^{16} +(377.298 + 316.591i) q^{17} +(-266.141 + 400.246i) q^{18} +(1167.38 + 1055.14i) q^{19} +(-133.042 - 317.164i) q^{20} +(-2703.08 + 3221.40i) q^{21} +(-1097.05 - 265.842i) q^{22} +(-3835.55 + 676.311i) q^{23} +(-1167.60 + 3063.26i) q^{24} +(2827.99 + 1029.30i) q^{25} +(219.127 - 3462.05i) q^{26} +(-1430.97 + 2478.51i) q^{27} +(-3401.51 + 6606.34i) q^{28} +(1519.29 + 1810.62i) q^{29} +(489.209 + 986.440i) q^{30} +(-1767.13 - 3060.76i) q^{31} +(-817.010 + 5734.71i) q^{32} +(3558.84 + 627.520i) q^{33} +(-2552.71 - 1116.40i) q^{34} +(853.604 + 2345.26i) q^{35} +(805.989 - 2596.78i) q^{36} -6372.56i q^{37} +(-8018.78 - 3864.49i) q^{38} +11105.6i q^{39} +(1227.97 + 1509.13i) q^{40} +(6177.25 + 16971.9i) q^{41} +(9531.91 - 21795.2i) q^{42} +(-21090.8 - 3718.88i) q^{43} +(6378.05 - 307.109i) q^{44} +(-456.623 - 790.894i) q^{45} +(19737.9 - 9788.69i) q^{46} +(1919.36 + 2287.40i) q^{47} +(1450.66 - 18487.7i) q^{48} +(18556.5 - 32140.7i) q^{49} +(-16990.2 - 1075.38i) q^{50} +(8381.71 + 3050.69i) q^{51} +(4333.10 + 19139.1i) q^{52} +(-10633.1 + 1874.89i) q^{53} +(3812.79 - 15734.2i) q^{54} +(1378.60 - 1642.95i) q^{55} +(7923.15 - 41280.4i) q^{56} +(26401.6 + 10725.5i) q^{57} +(-11133.8 - 7403.35i) q^{58} +(12191.1 + 10229.5i) q^{59} +(-4228.57 - 4573.37i) q^{60} +(-4248.83 - 24096.3i) q^{61} +(14473.0 + 13792.9i) q^{62} +(-6748.13 + 18540.3i) q^{63} +(-4713.36 - 32427.2i) q^{64} +(5708.05 + 3295.54i) q^{65} +(-20315.9 + 2271.02i) q^{66} +(-20462.8 + 17170.4i) q^{67} +(15635.1 + 1987.18i) q^{68} +(-61083.4 + 35266.5i) q^{69} +(-8373.72 - 11366.8i) q^{70} +(-1137.40 + 6450.53i) q^{71} +(-232.180 + 15379.2i) q^{72} +(20612.3 - 7502.27i) q^{73} +(10165.0 + 34585.8i) q^{74} +54501.4 q^{75} +(49684.7 + 8182.87i) q^{76} -46335.7 q^{77} +(-17714.7 - 60273.6i) q^{78} +(-31298.1 + 11391.6i) q^{79} +(-9071.81 - 6231.75i) q^{80} +(-12585.4 + 71375.6i) q^{81} +(-60597.9 - 82258.0i) q^{82} +(-28682.7 + 16560.0i) q^{83} +(-16966.7 + 133494. i) q^{84} +(4055.22 - 3402.74i) q^{85} +(120398. - 13458.8i) q^{86} +(37069.9 + 21402.3i) q^{87} +(-34125.8 + 11840.5i) q^{88} +(-8809.94 + 24205.1i) q^{89} +(3739.80 + 3564.05i) q^{90} +(-24727.0 - 140234. i) q^{91} +(-91509.5 + 84610.4i) q^{92} +(-49030.8 - 41141.7i) q^{93} +(-14065.6 - 9352.84i) q^{94} +(13347.2 - 10387.1i) q^{95} +(21616.9 + 102652. i) q^{96} +(99349.4 - 118400. i) q^{97} +(-49443.4 + 204037. i) q^{98} +(16697.4 - 2944.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9 - 657 * q^10 - 9 * q^12 + 336 * q^13 - 2163 * q^14 + 1824 * q^16 - 12 * q^17 - 10242 * q^20 - 7842 * q^21 - 102 * q^22 - 11856 * q^24 - 12 * q^25 + 1317 * q^26 + 6660 * q^28 - 12 * q^29 - 40692 * q^30 - 3351 * q^32 - 8604 * q^33 - 15756 * q^34 + 81783 * q^36 + 50400 * q^38 + 39246 * q^40 - 29082 * q^41 - 123081 * q^42 - 39651 * q^44 - 6 * q^45 - 112554 * q^46 - 68403 * q^48 + 259302 * q^49 + 154188 * q^50 - 36867 * q^52 - 26280 * q^53 + 172605 * q^54 - 12 * q^57 + 229740 * q^58 - 136062 * q^60 + 169296 * q^61 + 35076 * q^62 + 63795 * q^64 - 189918 * q^65 + 73644 * q^66 + 59706 * q^68 - 200898 * q^69 - 177831 * q^70 - 188502 * q^72 + 397428 * q^73 - 530703 * q^74 - 53022 * q^76 + 159804 * q^77 - 618237 * q^78 + 18045 * q^80 - 110160 * q^81 + 155859 * q^82 + 733851 * q^84 - 645108 * q^85 + 616836 * q^86 + 598383 * q^88 - 226320 * q^89 + 546366 * q^90 - 754308 * q^92 + 558942 * q^93 - 454530 * q^96 - 177198 * q^97 - 76791 * q^98

Introduction

L-functions

Modular forms

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