LMFDB - Embedded newform 76.6.i.a.9.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(5,76)]

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([0, 16]))

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

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, 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:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.7
Character	$\chi$	$=$	76.9
Dual form			76.6.i.a.17.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(14.0139 - 11.7590i) q^{3} +(57.8858 + 21.0687i) q^{5} +(68.1093 - 117.969i) q^{7} +(15.9173 - 90.2714i) q^{9} +O(q^{10})$	\(q+(14.0139 - 11.7590i) q^{3} +(57.8858 + 21.0687i) q^{5} +(68.1093 - 117.969i) q^{7} +(15.9173 - 90.2714i) q^{9} +(211.696 + 366.668i) q^{11} +(1.68328 + 1.41244i) q^{13} +(1058.95 - 385.427i) q^{15} +(-204.924 - 1162.18i) q^{17} +(-1573.13 - 36.6809i) q^{19} +(-432.724 - 2454.10i) q^{21} +(4190.40 - 1525.18i) q^{23} +(512.983 + 430.444i) q^{25} +(1384.26 + 2397.60i) q^{27} +(153.099 - 868.267i) q^{29} +(1290.90 - 2235.91i) q^{31} +(7278.34 + 2649.10i) q^{33} +(6428.00 - 5393.73i) q^{35} -3292.15 q^{37} +40.1983 q^{39} +(-4058.46 + 3405.46i) q^{41} +(-12737.4 - 4636.02i) q^{43} +(2823.28 - 4890.07i) q^{45} +(-3523.80 + 19984.5i) q^{47} +(-874.240 - 1514.23i) q^{49} +(-16537.9 - 13876.9i) q^{51} +(-24125.0 + 8780.77i) q^{53} +(4528.95 + 25685.0i) q^{55} +(-22477.1 + 17984.5i) q^{57} +(3323.41 + 18848.0i) q^{59} +(-4671.05 + 1700.12i) q^{61} +(-9565.08 - 8026.06i) q^{63} +(67.6799 + 117.225i) q^{65} +(-8528.83 + 48369.4i) q^{67} +(40789.1 - 70648.8i) q^{69} +(-24515.1 - 8922.76i) q^{71} +(49952.2 - 41914.9i) q^{73} +12250.5 q^{75} +57673.7 q^{77} +(-68702.5 + 57648.3i) q^{79} +(68523.4 + 24940.5i) q^{81} +(-28697.2 + 49704.9i) q^{83} +(12623.5 - 71591.2i) q^{85} +(-8064.48 - 13968.1i) q^{87} +(-28715.4 - 24095.1i) q^{89} +(281.271 - 102.374i) q^{91} +(-8201.60 - 46513.6i) q^{93} +(-90289.3 - 35267.2i) q^{95} +(2607.80 + 14789.5i) q^{97} +(36469.2 - 13273.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) $ 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9	$ 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) $ 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9 - 237 * q^11 + 2049 * q^13 + 2085 * q^15 - 609 * q^17 - 6012 * q^19 + 3591 * q^21 + 14100 * q^23 + 11802 * q^25 - 861 * q^27 - 10575 * q^29 - 6546 * q^31 - 21234 * q^33 - 231 * q^35 + 20052 * q^37 + 72204 * q^39 - 3249 * q^41 - 34677 * q^43 - 34956 * q^45 + 4461 * q^47 - 41139 * q^49 + 12099 * q^51 - 24291 * q^53 - 61767 * q^55 - 64470 * q^57 - 20100 * q^59 + 95490 * q^61 + 86403 * q^63 - 57915 * q^65 - 64452 * q^67 - 99315 * q^69 - 115536 * q^71 - 16362 * q^73 + 236250 * q^75 + 26688 * q^77 + 29799 * q^79 + 180327 * q^81 + 52347 * q^83 + 204618 * q^85 + 69414 * q^87 + 47394 * q^89 - 249384 * q^91 - 462126 * q^93 + 412869 * q^95 - 229974 * q^97 - 692274 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	14.0139	−	11.7590i	0.898991	−	0.754343i	−0.0710020	−	0.997476i	$-0.522620\pi$
$3$	14.0139	−	11.7590i	0.898991	−	0.754343i	0.969993	+	0.243133i	$0.0781752\pi$
$4$		0			0
$5$	57.8858	+	21.0687i	1.03549	+	0.376888i	0.803170	−	0.595751i	$-0.203145\pi$
$5$	57.8858	+	21.0687i	1.03549	+	0.376888i	0.232323	+	0.972639i	$0.425368\pi$
$6$		0			0
$7$	68.1093	−	117.969i	0.525365	−	0.909959i	−0.474199	−	0.880418i	$-0.657262\pi$
$7$	68.1093	−	117.969i	0.525365	−	0.909959i	0.999564	−	0.0295408i	$-0.00940449\pi$
$8$		0			0
$9$	15.9173	−	90.2714i	0.0655032	−	0.371487i
$10$		0			0
$11$	211.696	+	366.668i	0.527509	+	0.913673i	0.999486	+	0.0320618i	$0.0102073\pi$
$11$	211.696	+	366.668i	0.527509	+	0.913673i	−0.471977	+	0.881611i	$0.656459\pi$
$12$		0			0
$13$	1.68328	+	1.41244i	0.00276248	+	0.00231800i	0.644168	−	0.764884i	$-0.277204\pi$
$13$	1.68328	+	1.41244i	0.00276248	+	0.00231800i	−0.641405	+	0.767202i	$0.721648\pi$
$14$		0			0
$15$	1058.95	−	385.427i	1.21520	−	0.442297i
$16$		0			0
$17$	−204.924	−	1162.18i	−0.171977	−	0.975329i	−0.941576	−	0.336801i	$-0.890655\pi$
$17$	−204.924	−	1162.18i	−0.171977	−	0.975329i	0.769599	−	0.638528i	$-0.220456\pi$
$18$		0			0
$19$	−1573.13	−	36.6809i	−0.999728	−	0.0233107i
$19$	−1573.13	−	36.6809i	−0.999728	−	0.0233107i
$20$		0			0
$21$	−432.724	−	2454.10i	−0.214123	−	1.21435i
$22$		0			0
$23$	4190.40	−	1525.18i	1.65172	−	0.601176i	0.662689	−	0.748895i	$-0.269415\pi$
$23$	4190.40	−	1525.18i	1.65172	−	0.601176i	0.989029	+	0.147718i	$0.0471929\pi$
$24$		0			0
$25$	512.983	+	430.444i	0.164155	+	0.137742i
$26$		0			0
$27$	1384.26	+	2397.60i	0.365433	+	0.632948i
$28$		0			0
$29$	153.099	−	868.267i	0.0338047	−	0.191716i	−0.963229	−	0.268682i	$-0.913412\pi$
$29$	153.099	−	868.267i	0.0338047	−	0.191716i	0.997034	+	0.0769656i	$0.0245232\pi$
$30$		0			0
$31$	1290.90	−	2235.91i	0.241262	−	0.417879i	−0.719812	−	0.694169i	$-0.755772\pi$
$31$	1290.90	−	2235.91i	0.241262	−	0.417879i	0.961074	+	0.276291i	$0.0891052\pi$
$32$		0			0
$33$	7278.34	+	2649.10i	1.16345	+	0.423461i
$34$		0			0
$35$	6428.00	−	5393.73i	0.886964	−	0.744251i
$36$		0			0
$37$	−3292.15			−0.395344			−0.197672	−	0.980268i	$-0.563338\pi$
$37$	−3292.15			−0.395344			−0.197672	+	0.980268i	$0.563338\pi$
$38$		0			0
$39$	40.1983			0.00423201
$40$		0			0
$41$	−4058.46	+	3405.46i	−0.377053	+	0.316385i	−0.811544	−	0.584291i	$-0.801373\pi$
$41$	−4058.46	+	3405.46i	−0.377053	+	0.316385i	0.434491	+	0.900676i	$0.356928\pi$
$42$		0			0
$43$	−12737.4	−	4636.02i	−1.05053	−	0.382361i	−0.241667	−	0.970359i	$-0.577694\pi$
$43$	−12737.4	−	4636.02i	−1.05053	−	0.382361i	−0.808862	+	0.587998i	$0.799916\pi$
$44$		0			0
$45$	2823.28	−	4890.07i	0.207837	−	0.359985i
$46$		0			0
$47$	−3523.80	+	19984.5i	−0.232684	+	1.31962i	0.614752	+	0.788721i	$0.289256\pi$
$47$	−3523.80	+	19984.5i	−0.232684	+	1.31962i	−0.847436	+	0.530897i	$0.821855\pi$
$48$		0			0
$49$	−874.240	−	1514.23i	−0.0520164	−	0.0900951i
$50$		0			0
$51$	−16537.9	−	13876.9i	−0.890338	−	0.747082i
$52$		0			0
$53$	−24125.0	+	8780.77i	−1.17971	+	0.429381i	−0.856101	−	0.516808i	$-0.827120\pi$
$53$	−24125.0	+	8780.77i	−1.17971	+	0.429381i	−0.323614	+	0.946189i	$0.604898\pi$
$54$		0			0
$55$	4528.95	+	25685.0i	0.201879	+	1.14491i
$56$		0			0
$57$	−22477.1	+	17984.5i	−0.916331	+	0.733182i
$58$		0			0
$59$	3323.41	+	18848.0i	0.124295	+	0.704912i	0.981724	+	0.190310i	$0.0609492\pi$
$59$	3323.41	+	18848.0i	0.124295	+	0.704912i	−0.857429	+	0.514602i	$0.827940\pi$
$60$		0			0
$61$	−4671.05	+	1700.12i	−0.160727	+	0.0585000i	−0.421131	−	0.907000i	$-0.638367\pi$
$61$	−4671.05	+	1700.12i	−0.160727	+	0.0585000i	0.260403	+	0.965500i	$0.416144\pi$
$62$		0			0
$63$	−9565.08	−	8026.06i	−0.303625	−	0.254772i
$64$		0			0
$65$	67.6799	+	117.225i	0.00198690	+	0.00344141i
$66$		0			0
$67$	−8528.83	+	48369.4i	−0.232115	+	1.31639i	0.616491	+	0.787362i	$0.288554\pi$
$67$	−8528.83	+	48369.4i	−0.232115	+	1.31639i	−0.848606	+	0.529026i	$0.822557\pi$
$68$		0			0
$69$	40789.1	−	70648.8i	1.03139	−	1.78641i
$70$		0			0
$71$	−24515.1	−	8922.76i	−0.577148	−	0.210065i	0.0369192	−	0.999318i	$-0.488246\pi$
$71$	−24515.1	−	8922.76i	−0.577148	−	0.210065i	−0.614068	+	0.789253i	$0.710468\pi$
$72$		0			0
$73$	49952.2	−	41914.9i	1.09710	−	0.920579i	0.0998767	−	0.995000i	$-0.468155\pi$
$73$	49952.2	−	41914.9i	1.09710	−	0.920579i	0.997227	+	0.0744206i	$0.0237107\pi$
$74$		0			0
$75$	12250.5			0.251478
$76$		0			0
$77$	57673.7			1.10854
$78$		0			0
$79$	−68702.5	+	57648.3i	−1.23853	+	1.03925i	−0.240888	+	0.970553i	$0.577439\pi$
$79$	−68702.5	+	57648.3i	−1.23853	+	1.03925i	−0.997638	+	0.0686934i	$0.978117\pi$
$80$		0			0
$81$	68523.4	+	24940.5i	1.16045	+	0.422369i
$82$		0			0
$83$	−28697.2	+	49704.9i	−0.457239	+	0.791962i	−0.998814	−	0.0486909i	$-0.984495\pi$
$83$	−28697.2	+	49704.9i	−0.457239	+	0.791962i	0.541575	+	0.840653i	$0.317828\pi$
$84$		0			0
$85$	12623.5	−	71591.2i	0.189509	−	1.07476i
$86$		0			0
$87$	−8064.48	−	13968.1i	−0.114230	−	0.197851i
$88$		0			0
$89$	−28715.4	−	24095.1i	−0.384273	−	0.322444i	0.430104	−	0.902779i	$-0.358477\pi$
$89$	−28715.4	−	24095.1i	−0.384273	−	0.322444i	−0.814377	+	0.580336i	$0.802921\pi$
$90$		0			0
$91$	281.271	−	102.374i	0.00356059	−	0.00129595i
$92$		0			0
$93$	−8201.60	−	46513.6i	−0.0983312	−	0.557664i
$94$		0			0
$95$	−90289.3	−	35267.2i	−1.02643	−	0.400924i
$96$		0			0
$97$	2607.80	+	14789.5i	0.0281413	+	0.159597i	0.995640	−	0.0932785i	$-0.0297347\pi$
$97$	2607.80	+	14789.5i	0.0281413	+	0.159597i	−0.967499	+	0.252876i	$0.918624\pi$
$98$		0			0
$99$	36469.2	−	13273.7i	0.373971	−	0.136114i
$100$		0			0
$101$	−32534.1	−	27299.4i	−0.317348	−	0.266287i	0.470173	−	0.882574i	$-0.344191\pi$
$101$	−32534.1	−	27299.4i	−0.317348	−	0.266287i	−0.787521	+	0.616288i	$0.788636\pi$
$102$		0			0
$103$	72718.1	+	125951.i	0.675382	+	1.16980i	0.976357	+	0.216163i	$0.0693544\pi$
$103$	72718.1	+	125951.i	0.675382	+	1.16980i	−0.300976	+	0.953632i	$0.597312\pi$
$104$		0			0
$105$	26656.1	−	151174.i	0.235952	−	1.33815i
$106$		0			0
$107$	91415.7	−	158337.i	0.771900	−	1.33697i	−0.164620	−	0.986357i	$-0.552640\pi$
$107$	91415.7	−	158337.i	0.771900	−	1.33697i	0.936520	−	0.350614i	$-0.114027\pi$
$108$		0			0
$109$	56750.7	+	20655.5i	0.457514	+	0.166522i	0.560488	−	0.828162i	$-0.310614\pi$
$109$	56750.7	+	20655.5i	0.457514	+	0.166522i	−0.102974	+	0.994684i	$0.532836\pi$
$110$		0			0
$111$	−46135.8	+	38712.5i	−0.355410	+	0.298225i
$112$		0			0
$113$	201386.			1.48365			0.741826	−	0.670592i	$-0.233960\pi$
$113$	201386.			1.48365			0.741826	+	0.670592i	$0.233960\pi$
$114$		0			0
$115$	274698.			1.93692
$116$		0			0
$117$	154.297	−	129.470i	0.00104206	−	0.000874390i
$118$		0			0
$119$	−151058.	−	54980.6i	−0.977859	−	0.355912i
$120$		0			0
$121$	−9104.54	+	15769.5i	−0.0565320	+	0.0979164i
$122$		0			0
$123$	−16829.9	+	95447.3i	−0.100304	+	0.568854i
$124$		0			0
$125$	−75625.6	−	130987.i	−0.432906	−	0.749816i
$126$		0			0
$127$	142333.	+	119432.i	0.783065	+	0.657069i	0.944018	−	0.329893i	$-0.107013\pi$
$127$	142333.	+	119432.i	0.783065	+	0.657069i	−0.160954	+	0.986962i	$0.551457\pi$
$128$		0			0
$129$	−233015.	+	84810.5i	−1.23285	+	0.448720i
$130$		0			0
$131$	−35835.5	−	203233.i	−0.182447	−	1.03471i	−0.929192	−	0.369596i	$-0.879496\pi$
$131$	−35835.5	−	203233.i	−0.182447	−	1.03471i	0.746746	−	0.665110i	$-0.231615\pi$
$132$		0			0
$133$	−111472.	+	183082.i	−0.546434	+	0.897465i
$134$		0			0
$135$	29614.4	+	167952.i	0.139852	+	0.793140i
$136$		0			0
$137$	−272793.	+	99288.5i	−1.24174	+	0.451957i	−0.877604	−	0.479387i	$-0.840859\pi$
$137$	−272793.	+	99288.5i	−1.24174	+	0.451957i	−0.364139	+	0.931344i	$0.618637\pi$
$138$		0			0
$139$	−126522.	−	106164.i	−0.555428	−	0.466060i	0.321346	−	0.946962i	$-0.395865\pi$
$139$	−126522.	−	106164.i	−0.555428	−	0.466060i	−0.876774	+	0.480902i	$0.840309\pi$
$140$		0			0
$141$	185616.	+	321497.i	0.786264	+	1.36185i
$142$		0			0
$143$	−161.553	+	916.214i	−0.000660656	+	0.00374677i
$144$		0			0
$145$	27155.5	−	47034.7i	0.107260	−	0.185780i
$146$		0			0
$147$	−30057.4	−	10940.0i	−0.114725	−	0.0417565i
$148$		0			0
$149$	−44919.5	+	37691.9i	−0.165756	+	0.139086i	−0.721893	−	0.692005i	$-0.756728\pi$
$149$	−44919.5	+	37691.9i	−0.165756	+	0.139086i	0.556137	+	0.831091i	$0.312283\pi$
$150$		0			0
$151$	−358737.			−1.28037			−0.640183	−	0.768222i	$-0.721142\pi$
$151$	−358737.			−1.28037			−0.640183	+	0.768222i	$0.721142\pi$
$152$		0			0
$153$	−108173.			−0.373587
$154$		0			0
$155$	121833.	−	102230.i	0.407319	−	0.341781i
$156$		0			0
$157$	−433143.	−	157651.i	−1.40243	−	0.510444i	−0.473534	−	0.880775i	$-0.657022\pi$
$157$	−433143.	−	157651.i	−1.40243	−	0.510444i	−0.928900	+	0.370331i	$0.879244\pi$
$158$		0			0
$159$	−234831.	+	406739.i	−0.736652	+	1.27592i
$160$		0			0
$161$	105481.	−	598215.i	0.320709	−	1.81883i
$162$		0			0
$163$	175835.	+	304556.i	0.518367	+	0.897837i	0.999772	+	0.0213394i	$0.00679306\pi$
$163$	175835.	+	304556.i	0.518367	+	0.897837i	−0.481406	+	0.876498i	$0.659874\pi$
$164$		0			0
$165$	365499.	+	306690.i	1.04514	+	0.876980i
$166$		0			0
$167$	−338897.	+	123348.i	−0.940321	+	0.342249i	−0.766293	−	0.642492i	$-0.777901\pi$
$167$	−338897.	+	123348.i	−0.940321	+	0.342249i	−0.174028	+	0.984741i	$0.555678\pi$
$168$		0			0
$169$	−64473.5	−	365647.i	−0.173646	−	0.984795i
$170$		0			0
$171$	−28351.3	+	141425.i	−0.0741451	+	0.369859i
$172$		0			0
$173$	13236.1	+	75065.7i	0.0336236	+	0.190689i	0.996993	−	0.0774879i	$-0.0246899\pi$
$173$	13236.1	+	75065.7i	0.0336236	+	0.190689i	−0.963370	+	0.268177i	$0.913579\pi$
$174$		0			0
$175$	85717.8	−	31198.7i	0.211581	−	0.0770090i
$176$		0			0
$177$	268208.	+	225053.i	0.643485	+	0.539948i
$178$		0			0
$179$	−163793.	−	283697.i	−0.382087	−	0.661794i	0.609273	−	0.792960i	$-0.291461\pi$
$179$	−163793.	−	283697.i	−0.382087	−	0.661794i	−0.991360	+	0.131166i	$0.958128\pi$
$180$		0			0
$181$	−108815.	+	617120.i	−0.246883	+	1.40014i	0.569195	+	0.822203i	$0.307255\pi$
$181$	−108815.	+	617120.i	−0.246883	+	1.40014i	−0.816078	+	0.577942i	$0.803856\pi$
$182$		0			0
$183$	−45467.7	+	78752.4i	−0.100363	+	0.173834i
$184$		0			0
$185$	−190568.	−	69361.2i	−0.409375	−	0.149000i
$186$		0			0
$187$	382752.	−	321167.i	0.800412	−	0.671626i
$188$		0			0
$189$	377123.			0.767942
$190$		0			0
$191$	716257.			1.42065			0.710323	−	0.703876i	$-0.248549\pi$
$191$	716257.			1.42065			0.710323	+	0.703876i	$0.248549\pi$
$192$		0			0
$193$	591699.	−	496494.i	1.14342	−	0.959447i	0.143879	−	0.989595i	$-0.454042\pi$
$193$	591699.	−	496494.i	1.14342	−	0.959447i	0.999545	+	0.0301479i	$0.00959782\pi$
$194$		0			0
$195$	2326.91	+	846.927i	0.00438221	+	0.00159499i
$196$		0			0
$197$	63749.7	−	110418.i	0.117034	−	0.202709i	−0.801557	−	0.597918i	$-0.795995\pi$
$197$	63749.7	−	110418.i	0.117034	−	0.202709i	0.918591	+	0.395209i	$0.129328\pi$
$198$		0			0
$199$	152748.	−	866277.i	0.273428	−	1.55069i	−0.470483	−	0.882409i	$-0.655920\pi$
$199$	152748.	−	866277.i	0.273428	−	1.55069i	0.743911	−	0.668278i	$-0.232969\pi$
$200$		0			0
$201$	449256.	+	778134.i	0.784339	+	1.35851i
$202$		0			0
$203$	−92000.9	−	77197.9i	−0.156694	−	0.131482i
$204$		0			0
$205$	−306676.	+	111621.i	−0.509677	+	0.185507i
$206$		0			0
$207$	−70980.5	−	402550.i	−0.115136	−	0.652971i
$208$		0			0
$209$	−319576.	−	584583.i	−0.506068	−	0.925721i
$210$		0			0
$211$	85785.8	+	486516.i	0.132651	+	0.752299i	0.976467	+	0.215667i	$0.0691926\pi$
$211$	85785.8	+	486516.i	0.132651	+	0.752299i	−0.843816	+	0.536632i	$0.819696\pi$
$212$		0			0
$213$	−448475.	+	163231.i	−0.677312	+	0.246521i
$214$		0			0
$215$	−639637.	−	536719.i	−0.943707	−	0.791864i
$216$		0			0
$217$	−175845.	−	304572.i	−0.253502	−	0.439078i
$218$		0			0
$219$	207146.	−	1.17478e6i	0.291854	−	1.65518i
$220$		0			0
$221$	1296.57	−	2245.72i	0.00178573	−	0.00309297i
$222$		0			0
$223$	1.24968e6	+	454848.i	1.68282	+	0.612497i	0.993692	−	0.112142i	$-0.0357711\pi$
$223$	1.24968e6	+	454848.i	1.68282	+	0.612497i	0.689129	+	0.724639i	$0.257993\pi$
$224$		0			0
$225$	47022.1	−	39456.2i	0.0619221	−	0.0519588i
$226$		0			0
$227$	−513229.			−0.661069			−0.330534	−	0.943794i	$-0.607229\pi$
$227$	−513229.			−0.661069			−0.330534	+	0.943794i	$0.607229\pi$
$228$		0			0
$229$	−180910.			−0.227968			−0.113984	−	0.993483i	$-0.536361\pi$
$229$	−180910.			−0.227968			−0.113984	+	0.993483i	$0.536361\pi$
$230$		0			0
$231$	808233.	−	678188.i	0.996567	−	0.836219i
$232$		0			0
$233$	−25218.0	−	9178.60i	−0.0304313	−	0.0110761i	0.326760	−	0.945107i	$-0.394043\pi$
$233$	−25218.0	−	9178.60i	−0.0304313	−	0.0110761i	−0.357191	+	0.934031i	$0.616265\pi$
$234$		0			0
$235$	−625025.	+	1.08258e6i	−0.738291	+	1.27876i
$236$		0			0
$237$	−284901.	+	1.61575e6i	−0.329475	+	1.86855i
$238$		0			0
$239$	−227347.	−	393777.i	−0.257451	−	0.445918i	0.708107	−	0.706105i	$-0.249549\pi$
$239$	−227347.	−	393777.i	−0.257451	−	0.445918i	−0.965558	+	0.260186i	$0.916216\pi$
$240$		0			0
$241$	107884.	+	90525.7i	0.119651	+	0.100399i	0.700650	−	0.713505i	$-0.252894\pi$
$241$	107884.	+	90525.7i	0.119651	+	0.100399i	−0.580999	+	0.813904i	$0.697338\pi$
$242$		0			0
$243$	621377.	−	226163.i	0.675056	−	0.245700i
$244$		0			0
$245$	−18703.2	−	106071.i	−0.0199068	−	0.112897i
$246$		0			0
$247$	−2596.22	−	2283.71i	−0.00270770	−	0.00238176i
$248$		0			0
$249$	182324.	+	1.03401e6i	0.186357	+	1.05688i
$250$		0			0
$251$	−56535.9	+	20577.4i	−0.0566422	+	0.0206161i	−0.370186	−	0.928958i	$-0.620706\pi$
$251$	−56535.9	+	20577.4i	−0.0566422	+	0.0206161i	0.313544	+	0.949574i	$0.398484\pi$
$252$		0			0
$253$	1.44632e6	+	1.21361e6i	1.42058	+	1.19200i
$254$		0			0
$255$	−664940.	−	1.15171e6i	−0.640371	−	1.10916i
$256$		0			0
$257$	353714.	−	2.00601e6i	0.334056	−	1.89453i	−0.102304	−	0.994753i	$-0.532621\pi$
$257$	353714.	−	2.00601e6i	0.334056	−	1.89453i	0.436360	−	0.899772i	$-0.356268\pi$
$258$		0			0
$259$	−224226.	+	388370.i	−0.207700	+	0.359746i
$260$		0			0
$261$	−75942.8	−	27640.9i	−0.0690058	−	0.0251160i
$262$		0			0
$263$	452104.	−	379361.i	0.403041	−	0.338192i	−0.418627	−	0.908158i	$-0.637488\pi$
$263$	452104.	−	379361.i	0.403041	−	0.338192i	0.821668	+	0.569967i	$0.193044\pi$
$264$		0			0
$265$	−1.58149e6			−1.38341
$266$		0			0
$267$	−685750.			−0.588691
$268$		0			0
$269$	−416672.	+	349630.i	−0.351086	+	0.294596i	−0.801226	−	0.598362i	$-0.795819\pi$
$269$	−416672.	+	349630.i	−0.351086	+	0.294596i	0.450140	+	0.892958i	$0.351374\pi$
$270$		0			0
$271$	1.78600e6	+	650051.i	1.47727	+	0.537681i	0.950063	−	0.312059i	$-0.101019\pi$
$271$	1.78600e6	+	650051.i	1.47727	+	0.537681i	0.527202	+	0.849740i	$0.323241\pi$
$272$		0			0
$273$	2737.88	−	4742.14i	0.00222335	−	0.00385095i
$274$		0			0
$275$	−49233.5	+	279217.i	−0.0392581	+	0.222644i
$276$		0			0
$277$	231893.	+	401650.i	0.181588	+	0.314520i	0.942422	−	0.334427i	$-0.108543\pi$
$277$	231893.	+	401650.i	0.181588	+	0.314520i	−0.760833	+	0.648948i	$0.775209\pi$
$278$		0			0
$279$	−181291.	−	152121.i	−0.139433	−	0.116998i
$280$		0			0
$281$	−1.77366e6	+	645558.i	−1.34000	+	0.487719i	−0.909811	−	0.415022i	$-0.863774\pi$
$281$	−1.77366e6	+	645558.i	−1.34000	+	0.487719i	−0.430185	+	0.902741i	$0.641552\pi$
$282$		0			0
$283$	−41588.2	−	235858.i	−0.0308677	−	0.175059i	0.965476	−	0.260491i	$-0.0838843\pi$
$283$	−41588.2	−	235858.i	−0.0308677	−	0.175059i	−0.996344	+	0.0854313i	$0.972773\pi$
$284$		0			0
$285$	−1.68001e6	+	567485.i	−1.22518	+	0.413850i
$286$		0			0
$287$	125318.	+	710715.i	0.0898068	+	0.509320i
$288$		0			0
$289$	25560.5	−	9303.27i	0.0180022	−	0.00655226i
$290$		0			0
$291$	210456.	+	176594.i	0.145690	+	0.122248i
$292$		0			0
$293$	−519067.	−	899050.i	−0.353227	−	0.611808i	0.633586	−	0.773673i	$-0.281582\pi$
$293$	−519067.	−	899050.i	−0.353227	−	0.611808i	−0.986813	+	0.161865i	$0.948249\pi$
$294$		0			0
$295$	−204724.	+	1.16105e6i	−0.136966	+	0.776776i
$296$		0			0
$297$	−586082.	+	1.01512e6i	−0.385538	+	0.667772i
$298$		0			0
$299$	9207.87	+	3351.39i	0.00595636	+	0.00216794i
$300$		0			0
$301$	−1.41444e6	+	1.18685e6i	−0.899844	+	0.755059i
$302$		0			0
$303$	−776944.			−0.486164
$304$		0			0
$305$	−306206.			−0.188480
$306$		0			0
$307$	−1.79518e6	+	1.50633e6i	−1.08708	+	0.912169i	−0.996489	−	0.0837189i	$-0.973320\pi$
$307$	−1.79518e6	+	1.50633e6i	−1.08708	+	0.912169i	−0.0905916	+	0.995888i	$0.528876\pi$
$308$		0			0
$309$	2.50013e6	+	909973.i	1.48959	+	0.542166i
$310$		0			0
$311$	549397.	−	951583.i	0.322096	−	0.557886i	−0.658825	−	0.752297i	$-0.728946\pi$
$311$	549397.	−	951583.i	0.322096	−	0.557886i	0.980920	+	0.194410i	$0.0622794\pi$
$312$		0			0
$313$	55871.8	−	316865.i	0.0322353	−	0.182816i	−0.964439	−	0.264306i	$-0.914857\pi$
$313$	55871.8	−	316865.i	0.0322353	−	0.182816i	0.996674	+	0.0814907i	$0.0259681\pi$
$314$		0			0
$315$	−384584.	−	666118.i	−0.218381	−	0.378247i
$316$		0			0
$317$	−2.69752e6	−	2.26349e6i	−1.50770	−	1.26511i	−0.868078	−	0.496427i	$-0.834645\pi$
$317$	−2.69752e6	−	2.26349e6i	−1.50770	−	1.26511i	−0.639626	−	0.768686i	$-0.720911\pi$
$318$		0			0
$319$	350776.	−	127672.i	0.192998	−	0.0702456i
$320$		0			0
$321$	−580798.	−	3.29387e6i	−0.314603	−	1.78420i
$322$		0			0
$323$	279743.	+	1.83578e6i	0.149194	+	0.979073i
$324$		0			0
$325$	255.519	+	1449.12i	0.000134188	+	0.000761019i
$326$		0			0
$327$	1.03819e6	−	377869.i	0.536916	−	0.195421i
$328$		0			0
$329$	2.11754e6	+	1.77683e6i	1.07855	+	0.905014i
$330$		0			0
$331$	−1.49043e6	−	2.58151e6i	−0.747726	−	1.29510i	−0.948910	−	0.315546i	$-0.897812\pi$
$331$	−1.49043e6	−	2.58151e6i	−0.747726	−	1.29510i	0.201184	−	0.979553i	$-0.435521\pi$
$332$		0			0
$333$	−52402.0	+	297187.i	−0.0258963	+	0.146865i
$334$		0			0
$335$	−1.51278e6	+	2.62021e6i	−0.736484	+	1.27563i
$336$		0			0
$337$	3.09604e6	+	1.12687e6i	1.48502	+	0.540503i	0.952133	−	0.305684i	$-0.0988852\pi$
$337$	3.09604e6	+	1.12687e6i	1.48502	+	0.540503i	0.532886	+	0.846187i	$0.321107\pi$
$338$		0			0
$339$	2.82219e6	−	2.36810e6i	1.33379	−	1.11918i
$340$		0			0
$341$	1.09311e6			0.509073
$342$		0			0
$343$	2.05125e6			0.941419
$344$		0			0
$345$	3.84959e6	−	3.23019e6i	1.74127	−	1.46110i
$346$		0			0
$347$	3.12374e6	+	1.13695e6i	1.39268	+	0.506894i	0.925997	−	0.377531i	$-0.123227\pi$
$347$	3.12374e6	+	1.13695e6i	1.39268	+	0.506894i	0.466682	+	0.884425i	$0.345449\pi$
$348$		0			0
$349$	520699.	−	901877.i	0.228835	−	0.396354i	−0.728628	−	0.684910i	$-0.759842\pi$
$349$	520699.	−	901877.i	0.228835	−	0.396354i	0.957463	+	0.288555i	$0.0931749\pi$
$350$		0			0
$351$	−1056.38	+	5991.03i	−0.000457670	+	0.00259558i
$352$		0			0
$353$	−1.57419e6	−	2.72658e6i	−0.672390	−	1.16461i	−0.977225	−	0.212208i	$-0.931935\pi$
$353$	−1.57419e6	−	2.72658e6i	−0.672390	−	1.16461i	0.304835	−	0.952405i	$-0.401399\pi$
$354$		0			0
$355$	−1.23108e6	−	1.03300e6i	−0.518462	−	0.435041i
$356$		0			0
$357$	−2.76343e6	+	1.00581e6i	−1.14757	+	0.417680i
$358$		0			0
$359$	−77347.2	−	438657.i	−0.0316744	−	0.179634i	0.964866	−	0.262742i	$-0.0846267\pi$
$359$	−77347.2	−	438657.i	−0.0316744	−	0.179634i	−0.996541	+	0.0831073i	$0.973516\pi$
$360$		0			0
$361$	2.47341e6	+	115408.i	0.998913	+	0.0466088i
$362$		0			0
$363$	57844.6	+	328053.i	0.0230407	+	0.130670i
$364$		0			0
$365$	3.77461e6	−	1.37385e6i	1.48300	−	0.539767i
$366$		0			0
$367$	−1.49789e6	−	1.25688e6i	−0.580517	−	0.487111i	0.304600	−	0.952480i	$-0.401477\pi$
$367$	−1.49789e6	−	1.25688e6i	−0.580517	−	0.487111i	−0.885117	+	0.465369i	$0.845922\pi$
$368$		0			0
$369$	242816.	+	420569.i	0.0928347	+	0.160794i
$370$		0			0
$371$	−607278.	+	3.44404e6i	−0.229062	+	1.29907i
$372$		0			0
$373$	−879442.	+	1.52324e6i	−0.327292	+	0.566886i	−0.981974	−	0.189019i	$-0.939469\pi$
$373$	−879442.	+	1.52324e6i	−0.327292	+	0.566886i	0.654682	+	0.755905i	$0.272803\pi$
$374$		0			0
$375$	−2.60010e6	−	946358.i	−0.954797	−	0.347518i
$376$		0			0
$377$	1484.09	−	1245.30i	0.000537782	−	0.000451253i
$378$		0			0
$379$	−1.92804e6			−0.689474			−0.344737	−	0.938699i	$-0.612032\pi$
$379$	−1.92804e6			−0.689474			−0.344737	+	0.938699i	$0.612032\pi$
$380$		0			0
$381$	3.39905e6			1.19962
$382$		0			0
$383$	1.57341e6	−	1.32025e6i	0.548082	−	0.459896i	−0.326209	−	0.945298i	$-0.605771\pi$
$383$	1.57341e6	−	1.32025e6i	0.548082	−	0.459896i	0.874291	+	0.485402i	$0.161327\pi$
$384$		0			0
$385$	3.33849e6	+	1.21511e6i	1.14788	+	0.417795i
$386$		0			0
$387$	−621244.	+	1.07603e6i	−0.210855	+	0.365212i
$388$		0			0
$389$	−894382.	+	5.07229e6i	−0.299674	+	1.69954i	0.347898	+	0.937532i	$0.386895\pi$
$389$	−894382.	+	5.07229e6i	−0.299674	+	1.69954i	−0.647572	+	0.762004i	$0.724216\pi$
$390$		0			0
$391$	−2.63125e6	−	4.55745e6i	−0.870402	−	1.50758i
$392$		0			0
$393$	−2.89203e6	−	2.42670e6i	−0.944541	−	0.792564i
$394$		0			0
$395$	−5.19147e6	+	1.88954e6i	−1.67416	+	0.609346i
$396$		0			0
$397$	−1.04913e6	−	5.94992e6i	−0.334083	−	1.89468i	−0.436108	−	0.899894i	$-0.643643\pi$
$397$	−1.04913e6	−	5.94992e6i	−0.334083	−	1.89468i	0.102026	−	0.994782i	$-0.467468\pi$
$398$		0			0
$399$	590714.	+	3.87650e6i	0.185757	+	1.21901i
$400$		0			0
$401$	−908480.	−	5.15225e6i	−0.282133	−	1.60006i	−0.715349	−	0.698768i	$-0.753732\pi$
$401$	−908480.	−	5.15225e6i	−0.282133	−	1.60006i	0.433215	−	0.901290i	$-0.357379\pi$
$402$		0			0
$403$	5331.06	−	1940.35i	0.00163512	−	0.000595136i
$404$		0			0
$405$	3.44107e6	+	2.88740e6i	1.04245	+	0.874720i
$406$		0			0
$407$	−696933.	−	1.20712e6i	−0.208548	−	0.361215i
$408$		0			0
$409$	1.03813e6	−	5.88754e6i	0.306863	−	1.74031i	−0.307741	−	0.951470i	$-0.599573\pi$
$409$	1.03813e6	−	5.88754e6i	0.306863	−	1.74031i	0.614604	−	0.788836i	$-0.289316\pi$
$410$		0			0
$411$	−2.65535e6	+	4.59920e6i	−0.775385	+	1.34301i
$412$		0			0
$413$	2.44983e6	+	891663.i	0.706741	+	0.257233i
$414$		0			0
$415$	−2.70837e6	+	2.27260e6i	−0.771949	+	0.647742i
$416$		0			0
$417$	−3.02145e6			−0.850894
$418$		0			0
$419$	6.41810e6			1.78596			0.892980	−	0.450097i	$-0.148611\pi$
$419$	6.41810e6			1.78596			0.892980	+	0.450097i	$0.148611\pi$
$420$		0			0
$421$	−645818.	+	541906.i	−0.177584	+	0.149011i	−0.727247	−	0.686376i	$-0.759201\pi$
$421$	−645818.	+	541906.i	−0.177584	+	0.149011i	0.549663	+	0.835387i	$0.314756\pi$
$422$		0			0
$423$	1.74794e6	+	636197.i	0.474980	+	0.172878i
$424$		0			0
$425$	395131.	−	684387.i	0.106113	−	0.183793i
$426$		0			0
$427$	−117580.	+	666831.i	−0.0312079	+	0.176989i
$428$		0			0
$429$	8509.81	+	14739.4i	0.00223242	+	0.00386667i
$430$		0			0
$431$	1.35621e6	+	1.13799e6i	0.351668	+	0.295085i	0.801460	−	0.598049i	$-0.204057\pi$
$431$	1.35621e6	+	1.13799e6i	0.351668	+	0.295085i	−0.449791	+	0.893134i	$0.648502\pi$
$432$		0			0
$433$	1.45795e6	−	530650.i	0.373700	−	0.136016i	−0.148341	−	0.988936i	$-0.547393\pi$
$433$	1.45795e6	−	530650.i	0.373700	−	0.136016i	0.522040	+	0.852921i	$0.325171\pi$
$434$		0			0
$435$	−172529.	−	978462.i	−0.0437159	−	0.247925i
$436$		0			0
$437$	−6.64801e6	+	2.24561e6i	−1.66528	+	0.562510i
$438$		0			0
$439$	930676.	+	5.27813e6i	0.230482	+	1.30713i	0.851922	+	0.523668i	$0.175437\pi$
$439$	930676.	+	5.27813e6i	0.230482	+	1.30713i	−0.621440	+	0.783462i	$0.713452\pi$
$440$		0			0
$441$	−150607.	+	54816.5i	−0.0368764	+	0.0134219i
$442$		0			0
$443$	3.58218e6	+	3.00581e6i	0.867238	+	0.727699i	0.963515	−	0.267656i	$-0.0862490\pi$
$443$	3.58218e6	+	3.00581e6i	0.867238	+	0.727699i	−0.0962770	+	0.995355i	$0.530693\pi$
$444$		0			0
$445$	−1.15456e6	−	1.99976e6i	−0.276387	−	0.478716i
$446$		0			0
$447$	−186275.	+	1.05642e6i	−0.0440947	+	0.250074i
$448$		0			0
$449$	−637696.	+	1.10452e6i	−0.149279	+	0.258558i	−0.930961	−	0.365119i	$-0.881028\pi$
$449$	−637696.	+	1.10452e6i	−0.149279	+	0.258558i	0.781682	+	0.623677i	$0.214362\pi$
$450$		0			0
$451$	−2.10783e6	−	767187.i	−0.487971	−	0.177607i
$452$		0			0
$453$	−5.02730e6	+	4.21841e6i	−1.15104	+	0.965835i
$454$		0			0
$455$	18438.5			0.00417539
$456$		0			0
$457$	−7.25630e6			−1.62527			−0.812633	−	0.582775i	$-0.801967\pi$
$457$	−7.25630e6			−1.62527			−0.812633	+	0.582775i	$0.801967\pi$
$458$		0			0
$459$	2.50278e6	−	2.10008e6i	0.554487	−	0.465269i
$460$		0			0
$461$	4.05785e6	+	1.47694e6i	0.889290	+	0.323675i	0.745953	−	0.665999i	$-0.231994\pi$
$461$	4.05785e6	+	1.47694e6i	0.889290	+	0.323675i	0.143337	+	0.989674i	$0.454217\pi$
$462$		0			0
$463$	−2.06641e6	+	3.57912e6i	−0.447985	+	0.775932i	−0.998255	−	0.0590545i	$-0.981191\pi$
$463$	−2.06641e6	+	3.57912e6i	−0.447985	+	0.775932i	0.550270	+	0.834987i	$0.314525\pi$
$464$		0			0
$465$	505225.	−	2.86527e6i	0.108356	−	0.614516i
$466$		0			0
$467$	201749.	+	349440.i	0.0428075	+	0.0741447i	0.886635	−	0.462469i	$-0.153036\pi$
$467$	201749.	+	349440.i	0.0428075	+	0.0741447i	−0.843828	+	0.536614i	$0.819703\pi$
$468$		0			0
$469$	5.12518e6	+	4.30054e6i	1.07591	+	0.902799i
$470$		0			0
$471$	−7.92385e6	+	2.88404e6i	−1.64583	+	0.599031i
$472$		0			0
$473$	−996564.	−	5.65180e6i	−0.204811	−	1.16154i
$474$		0			0
$475$	−791202.	−	695963.i	−0.160899	−	0.141531i
$476$		0			0
$477$	408649.	+	2.31756e6i	0.0822345	+	0.466375i
$478$		0			0
$479$	4.94268e6	−	1.79899e6i	0.984292	−	0.358253i	0.200785	−	0.979635i	$-0.435651\pi$
$479$	4.94268e6	−	1.79899e6i	0.984292	−	0.358253i	0.783507	+	0.621382i	$0.213429\pi$
$480$		0			0
$481$	−5541.62	−	4649.97i	−0.00109213	−	0.000916405i
$482$		0			0
$483$	−5.55623e6	−	9.62368e6i	−1.08371	−	1.87704i
$484$		0			0
$485$	−160642.	+	911047.i	−0.0310102	+	0.175868i
$486$		0			0
$487$	−1.17985e6	+	2.04355e6i	−0.225425	+	0.390448i	−0.956447	−	0.291906i	$-0.905710\pi$
$487$	−1.17985e6	+	2.04355e6i	−0.225425	+	0.390448i	0.731022	+	0.682354i	$0.239044\pi$
$488$		0			0
$489$	6.04542e6	+	2.20035e6i	1.14328	+	0.416121i
$490$		0			0
$491$	2.08180e6	−	1.74684e6i	0.389705	−	0.327001i	−0.426793	−	0.904349i	$-0.640357\pi$
$491$	2.08180e6	−	1.74684e6i	0.389705	−	0.327001i	0.816498	+	0.577348i	$0.195912\pi$
$492$		0			0
$493$	−1.04046e6			−0.192800
$494$		0			0
$495$	2.39071e6			0.438544
$496$		0			0
$497$	−2.72231e6	+	2.28429e6i	−0.494364	+	0.414821i
$498$		0			0
$499$	6.44257e6	+	2.34490e6i	1.15827	+	0.421574i	0.848477	−	0.529232i	$-0.177520\pi$
$499$	6.44257e6	+	2.34490e6i	1.15827	+	0.421574i	0.309788	+	0.950806i	$0.399742\pi$
$500$		0			0
$501$	−3.29880e6	+	5.71369e6i	−0.587167	+	1.01700i
$502$		0			0
$503$	77043.5	−	436935.i	0.0135774	−	0.0770011i	−0.977266	−	0.212016i	$-0.931997\pi$
$503$	77043.5	−	436935.i	0.0135774	−	0.0770011i	0.990844	+	0.135015i	$0.0431082\pi$
$504$		0			0
$505$	−1.30810e6	−	2.26570e6i	−0.228251	−	0.395342i
$506$		0			0
$507$	−5.20319e6	−	4.36599e6i	−0.898979	−	0.754333i
$508$		0			0
$509$	−1.42478e6	+	518576.i	−0.243754	+	0.0887192i	−0.461008	−	0.887396i	$-0.652512\pi$
$509$	−1.42478e6	+	518576.i	−0.243754	+	0.0887192i	0.217254	+	0.976115i	$0.430290\pi$
$510$		0			0
$511$	−1.54244e6	−	8.74759e6i	−0.261309	−	1.48196i
$512$		0			0
$513$	−2.08968e6	−	3.82253e6i	−0.350579	−	0.641294i
$514$		0			0
$515$	1.55571e6	+	8.82287e6i	0.258470	+	1.46586i
$516$		0			0
$517$	−8.07363e6	+	2.93856e6i	−1.32844	+	0.483513i
$518$		0			0
$519$	1.06819e6	+	896317.i	0.174072	+	0.146064i
$520$		0			0
$521$	1.98540e6	+	3.43882e6i	0.320446	+	0.555028i	0.980580	−	0.196119i	$-0.0628339\pi$
$521$	1.98540e6	+	3.43882e6i	0.320446	+	0.555028i	−0.660134	+	0.751148i	$0.729501\pi$
$522$		0			0
$523$	1.81026e6	−	1.02665e7i	0.289392	−	1.64122i	−0.399771	−	0.916615i	$-0.630910\pi$
$523$	1.81026e6	−	1.02665e7i	0.289392	−	1.64122i	0.689163	−	0.724607i	$-0.257979\pi$
$524$		0			0
$525$	834372.	−	1.44517e6i	0.132118	−	0.228835i
$526$		0			0
$527$	−2.86307e6	−	1.04207e6i	−0.449061	−	0.163445i
$528$		0			0
$529$	1.03028e7	−	8.64504e6i	1.60072	−	1.34316i
$530$		0			0
$531$	1.75433e6			0.270007
$532$		0			0
$533$	−11641.6			−0.00177498
$534$		0			0
$535$	8.62761e6	−	7.23943e6i	1.30319	−	1.09350i
$536$		0			0
$537$	−5.63138e6	−	2.04966e6i	−0.842712	−	0.306722i
$538$		0			0
$539$	370146.	−	641111.i	0.0548783	−	0.0950520i
$540$		0			0
$541$	−44626.6	+	253090.i	−0.00655543	+	0.0371777i	−0.987910	−	0.155028i	$-0.950453\pi$
$541$	−44626.6	+	253090.i	−0.00655543	+	0.0371777i	0.981355	+	0.192206i	$0.0615642\pi$
$542$		0			0
$543$	5.73182e6	+	9.92780e6i	0.834243	+	1.44495i
$544$		0			0
$545$	2.84987e6	+	2.39132e6i	0.410992	+	0.344864i
$546$		0			0
$547$	−2.45126e6	+	892185.i	−0.350285	+	0.127493i	−0.511169	−	0.859480i	$-0.670787\pi$
$547$	−2.45126e6	+	892185.i	−0.350285	+	0.127493i	0.160885	+	0.986973i	$0.448565\pi$
$548$		0			0
$549$	79122.0	+	448723.i	0.0112038	+	0.0635401i
$550$		0			0
$551$	−272694.	+	1.36029e6i	−0.0382646	+	0.190876i
$552$		0			0
$553$	2.12141e6	+	1.20311e7i	0.294993	+	1.67299i
$554$		0			0
$555$	−3.48623e6	+	1.26888e6i	−0.480422	+	0.174859i
$556$		0			0
$557$	1.24048e6	+	1.04089e6i	0.169415	+	0.142156i	0.723553	−	0.690268i	$-0.242508\pi$
$557$	1.24048e6	+	1.04089e6i	0.169415	+	0.142156i	−0.554138	+	0.832425i	$0.686952\pi$
$558$		0			0
$559$	−14892.5	−	25794.5i	−0.00201575	−	0.00349139i
$560$		0			0
$561$	1.58722e6	−	9.00160e6i	0.212927	−	1.20757i
$562$		0			0
$563$	4.00301e6	−	6.93341e6i	0.532249	−	0.921883i	−0.467042	−	0.884235i	$-0.654680\pi$
$563$	4.00301e6	−	6.93341e6i	0.532249	−	0.921883i	0.999291	−	0.0376477i	$-0.0119865\pi$
$564$		0			0
$565$	1.16574e7	+	4.24293e6i	1.53631	+	0.559171i
$566$		0			0
$567$	7.60927e6	−	6.38494e6i	0.993998	−	0.834063i
$568$		0			0
$569$	−3.04285e6			−0.394004			−0.197002	−	0.980403i	$-0.563121\pi$
$569$	−3.04285e6			−0.394004			−0.197002	+	0.980403i	$0.563121\pi$
$570$		0			0
$571$	1.38313e7			1.77531			0.887653	−	0.460512i	$-0.152334\pi$
$571$	1.38313e7			1.77531			0.887653	+	0.460512i	$0.152334\pi$
$572$		0			0
$573$	1.00375e7	−	8.42250e6i	1.27715	−	1.07165i
$574$		0			0
$575$	2.80611e6	+	1.02134e6i	0.353944	+	0.128825i
$576$		0			0
$577$	−1.57631e6	+	2.73025e6i	−0.197107	+	0.341399i	−0.947589	−	0.319491i	$-0.896488\pi$
$577$	−1.57631e6	+	2.73025e6i	−0.197107	+	0.341399i	0.750482	+	0.660891i	$0.229821\pi$
$578$		0			0
$579$	2.45370e6	−	1.39156e7i	0.304176	−	1.72507i
$580$		0			0
$581$	3.90908e6	+	6.77073e6i	0.480435	+	0.832138i
$582$		0			0
$583$	−8.32677e6	−	6.98699e6i	−1.01462	−	0.851371i
$584$		0			0
$585$	11659.3	−	4243.65i	0.00140859	−	0.000512685i
$586$		0			0
$587$	736966.	+	4.17954e6i	0.0882780	+	0.500649i	0.996601	+	0.0823799i	$0.0262521\pi$
$587$	736966.	+	4.17954e6i	0.0882780	+	0.500649i	−0.908323	+	0.418269i	$0.862637\pi$
$588$		0			0
$589$	−2.11278e6	+	3.47004e6i	−0.250938	+	0.412141i
$590$		0			0
$591$	−405026.	−	2.29702e6i	−0.0476995	−	0.270518i
$592$		0			0
$593$	−3.79321e6	+	1.38062e6i	−0.442966	+	0.161226i	−0.553867	−	0.832605i	$-0.686848\pi$
$593$	−3.79321e6	+	1.38062e6i	−0.442966	+	0.161226i	0.110901	+	0.993831i	$0.464626\pi$
$594$		0			0
$595$	−7.58574e6	−	6.36519e6i	−0.878427	−	0.737088i
$596$		0			0
$597$	−8.04600e6	−	1.39361e7i	−0.923941	−	1.60031i
$598$		0			0
$599$	−1.46041e6	+	8.28241e6i	−0.166306	+	0.943169i	0.781401	+	0.624029i	$0.214505\pi$
$599$	−1.46041e6	+	8.28241e6i	−0.166306	+	0.943169i	−0.947708	+	0.319140i	$0.896606\pi$
$600$		0			0
$601$	−1.08247e6	+	1.87490e6i	−0.122245	+	0.211735i	−0.920653	−	0.390383i	$-0.872343\pi$
$601$	−1.08247e6	+	1.87490e6i	−0.122245	+	0.211735i	0.798408	+	0.602117i	$0.205676\pi$
$602$		0			0
$603$	4.23062e6	+	1.53982e6i	0.473817	+	0.172455i
$604$		0			0
$605$	−859267.	+	721011.i	−0.0954420	+	0.0800854i
$606$		0			0
$607$	−1.68378e7			−1.85487			−0.927434	−	0.373988i	$-0.877990\pi$
$607$	−1.68378e7			−1.85487			−0.927434	+	0.373988i	$0.877990\pi$
$608$		0			0
$609$	−2.19706e6			−0.240049
$610$		0			0
$611$	−34158.5	+	28662.4i	−0.00370166	+	0.00310606i
$612$		0			0
$613$	−1.24410e7	−	4.52816e6i	−1.33722	−	0.486710i	−0.428287	−	0.903643i	$-0.640883\pi$
$613$	−1.24410e7	−	4.52816e6i	−1.33722	−	0.486710i	−0.908937	+	0.416933i	$0.863105\pi$
$614$		0			0
$615$	−2.98516e6	+	5.17046e6i	−0.318259	+	0.551240i
$616$		0			0
$617$	−1.26988e6	+	7.20183e6i	−0.134292	+	0.761606i	0.841059	+	0.540944i	$0.181933\pi$
$617$	−1.26988e6	+	7.20183e6i	−0.134292	+	0.761606i	−0.975350	+	0.220662i	$0.929178\pi$
$618$		0			0
$619$	7.55238e6	+	1.30811e7i	0.792240	+	1.37220i	0.924577	+	0.380996i	$0.124419\pi$
$619$	7.55238e6	+	1.30811e7i	0.792240	+	1.37220i	−0.132336	+	0.991205i	$0.542248\pi$
$620$		0			0
$621$	9.45737e6	+	7.93568e6i	0.984105	+	0.825762i
$622$		0			0
$623$	−4.79825e6	+	1.74642e6i	−0.495294	+	0.180272i
$624$		0			0
$625$	−1.98130e6	−	1.12365e7i	−0.202885	−	1.15062i
$626$		0			0
$627$	−1.13526e7	−	4.43436e6i	−1.15326	−	0.450466i
$628$		0			0
$629$	674639.	+	3.82607e6i	0.0679900	+	0.385590i
$630$		0			0
$631$	−1.68352e7	+	6.12752e6i	−1.68324	+	0.612648i	−0.993748	−	0.111647i	$-0.964387\pi$
$631$	−1.68352e7	+	6.12752e6i	−1.68324	+	0.612648i	−0.689490	+	0.724295i	$0.742165\pi$
$632$		0			0
$633$	6.92315e6	+	5.80921e6i	0.686743	+	0.576246i
$634$		0			0
$635$	5.72280e6	+	9.91219e6i	0.563215	+	0.975518i
$636$		0			0
$637$	667.167	−	3783.69i	6.51457e−5	−	0.000369460i
$638$		0			0
$639$	−1.19568e6	+	2.07099e6i	−0.115842	+	0.200643i
$640$		0			0
$641$	4.16727e6	+	1.51676e6i	0.400596	+	0.145805i	0.534458	−	0.845195i	$-0.320516\pi$
$641$	4.16727e6	+	1.51676e6i	0.400596	+	0.145805i	−0.133862	+	0.991000i	$0.542738\pi$
$642$		0			0
$643$	859234.	−	720983.i	0.0819566	−	0.0687698i	−0.600889	−	0.799333i	$-0.705187\pi$
$643$	859234.	−	720983.i	0.0819566	−	0.0687698i	0.682846	+	0.730563i	$0.260742\pi$
$644$		0			0
$645$	−1.52751e7			−1.44572
$646$		0			0
$647$	1.21455e7			1.14065			0.570326	−	0.821418i	$-0.306817\pi$
$647$	1.21455e7			1.14065			0.570326	+	0.821418i	$0.306817\pi$
$648$		0			0
$649$	−6.20739e6	+	5.20862e6i	−0.578492	+	0.485412i
$650$		0			0
$651$	−6.04575e6	−	2.20047e6i	−0.559111	−	0.203500i
$652$		0			0
$653$	−6.51852e6	+	1.12904e7i	−0.598227	+	1.03616i	0.394856	+	0.918743i	$0.370795\pi$
$653$	−6.51852e6	+	1.12904e7i	−0.598227	+	1.03616i	−0.993083	+	0.117416i	$0.962539\pi$
$654$		0			0
$655$	2.20750e6	−	1.25193e7i	0.201047	−	1.14019i
$656$		0			0
$657$	−2.98861e6	−	5.17643e6i	−0.270120	−	0.467861i
$658$		0			0
$659$	1.86519e6	+	1.56508e6i	0.167305	+	0.140386i	0.722596	−	0.691270i	$-0.242949\pi$
$659$	1.86519e6	+	1.56508e6i	0.167305	+	0.140386i	−0.555291	+	0.831656i	$0.687393\pi$
$660$		0			0
$661$	−5.63903e6	+	2.05244e6i	−0.501997	+	0.182712i	−0.580592	−	0.814195i	$-0.697179\pi$
$661$	−5.63903e6	+	2.05244e6i	−0.501997	+	0.182712i	0.0785951	+	0.996907i	$0.474957\pi$
$662$		0			0
$663$	−8237.59	−	46717.7i	−0.000727807	−	0.00412760i
$664$		0			0
$665$	−1.03100e7	+	8.24929e6i	−0.904072	+	0.723373i
$666$		0			0
$667$	−682719.	−	3.87189e6i	−0.0594193	−	0.336984i
$668$		0			0
$669$	2.28615e7	−	8.32090e6i	1.97487	−	0.718795i
$670$		0			0
$671$	−1.61222e6	−	1.35281e6i	−0.138235	−	0.115993i
$672$		0			0
$673$	9.87086e6	+	1.70968e7i	0.840074	+	1.45505i	0.889831	+	0.456290i	$0.150822\pi$
$673$	9.87086e6	+	1.70968e7i	0.840074	+	1.45505i	−0.0497574	+	0.998761i	$0.515845\pi$
$674$		0			0
$675$	−321933.	+	1.82577e6i	−0.0271961	+	0.154237i
$676$		0			0
$677$	4.80547e6	−	8.32332e6i	0.402962	−	0.697951i	−0.591120	−	0.806584i	$-0.701314\pi$
$677$	4.80547e6	−	8.32332e6i	0.402962	−	0.697951i	0.994082	+	0.108633i	$0.0346473\pi$
$678$		0			0
$679$	1.92232e6	+	699666.i	0.160011	+	0.0582394i
$680$		0			0
$681$	−7.19233e6	+	6.03508e6i	−0.594295	+	0.498673i
$682$		0			0
$683$	1.51324e7			1.24124			0.620619	−	0.784112i	$-0.286881\pi$
$683$	1.51324e7			1.24124			0.620619	+	0.784112i	$0.286881\pi$
$684$		0			0
$685$	−1.78827e7			−1.45615
$686$		0			0
$687$	−2.53526e6	+	2.12733e6i	−0.204942	+	0.171966i
$688$		0			0
$689$	−53011.5	−	19294.6i	−0.00425424	−	0.00154842i
$690$		0			0
$691$	3.58032e6	−	6.20130e6i	0.285251	−	0.494069i	−0.687419	−	0.726261i	$-0.741256\pi$
$691$	3.58032e6	−	6.20130e6i	0.285251	−	0.494069i	0.972670	+	0.232192i	$0.0745897\pi$
$692$		0			0
$693$	918009.	−	5.20629e6i	0.0726129	−	0.411808i
$694$		0			0
$695$	−5.08706e6	−	8.81105e6i	−0.399489	−	0.691935i
$696$		0			0
$697$	4.78943e6	+	4.01881e6i	0.373424	+	0.313340i
$698$		0			0
$699$	−461334.	+	167912.i	−0.0357127	+	0.0129983i
$700$		0			0
$701$	−3.33438e6	−	1.89102e7i	−0.256283	−	1.45345i	−0.792758	−	0.609536i	$-0.791356\pi$
$701$	−3.33438e6	−	1.89102e7i	−0.256283	−	1.45345i	0.536475	−	0.843916i	$-0.319755\pi$
$702$		0			0
$703$	5.17899e6	+	120759.i	0.395236	+	0.00921575i
$704$		0			0
$705$	3.97102e6	+	2.25208e7i	0.300905	+	1.70652i
$706$		0			0
$707$	−5.43635e6	+	1.97867e6i	−0.409033	+	0.148876i
$708$		0			0
$709$	−1.52348e6	−	1.27835e6i	−0.113821	−	0.0955068i	0.584101	−	0.811681i	$-0.301447\pi$
$709$	−1.52348e6	−	1.27835e6i	−0.113821	−	0.0955068i	−0.697922	+	0.716174i	$0.745892\pi$
$710$		0			0
$711$	4.11043e6	+	7.11948e6i	0.304939	+	0.528170i
$712$		0			0
$713$	1.99924e6	−	1.13382e7i	0.147279	−	0.835259i
$714$		0			0
$715$	−28655.1	+	49632.0i	−0.00209622	+	0.00363075i
$716$		0			0
$717$	−7.81646e6	−	2.84496e6i	−0.567822	−	0.206670i
$718$		0			0
$719$	8.71628e6	−	7.31383e6i	0.628795	−	0.527622i	−0.271759	−	0.962365i	$-0.587605\pi$
$719$	8.71628e6	−	7.31383e6i	0.628795	−	0.527622i	0.900554	+	0.434744i	$0.143161\pi$
$720$		0			0
$721$	1.98111e7			1.41929
$722$		0			0
$723$	2.57637e6			0.183300
$724$		0			0
$725$	452278.	−	379506.i	0.0319566	−	0.0268147i
$726$		0			0
$727$	−1.27015e6	−	462295.i	−0.0891287	−	0.0324402i	0.297071	−	0.954855i	$-0.403990\pi$
$727$	−1.27015e6	−	462295.i	−0.0891287	−	0.0324402i	−0.386200	+	0.922415i	$0.626212\pi$
$728$		0			0
$729$	−2.81146e6	+	4.86959e6i	−0.195935	+	0.339370i
$730$		0			0
$731$	−2.77770e6	+	1.57531e7i	−0.192261	+	1.09037i
$732$		0			0
$733$	7.62865e6	+	1.32132e7i	0.524430	+	0.908340i	0.999595	+	0.0284434i	$0.00905505\pi$
$733$	7.62865e6	+	1.32132e7i	0.524430	+	0.908340i	−0.475165	+	0.879897i	$0.657612\pi$
$734$		0			0
$735$	−1.50940e6	−	1.26654e6i	−0.103059	−	0.0864770i
$736$		0			0
$737$	−1.95410e7	+	7.11235e6i	−1.32519	+	0.482330i
$738$		0			0
$739$	−42375.2	−	240322.i	−0.00285430	−	0.0161876i	0.983347	−	0.181736i	$-0.0581717\pi$
$739$	−42375.2	−	240322.i	−0.00285430	−	0.0161876i	−0.986202	+	0.165549i	$0.947061\pi$
$740$		0			0
$741$	−63237.4	−	1474.51i	−0.00423086	−	9.86512e-5i
$742$		0			0
$743$	−3.22082e6	−	1.82662e7i	−0.214040	−	1.21388i	−0.882565	−	0.470190i	$-0.844185\pi$
$743$	−3.22082e6	−	1.82662e7i	−0.214040	−	1.21388i	0.668526	−	0.743689i	$-0.266926\pi$
$744$		0			0
$745$	−3.39432e6	+	1.23543e6i	−0.224059	+	0.0815507i
$746$		0			0
$747$	4.03015e6	+	3.38170e6i	0.264253	+	0.221735i
$748$		0			0
$749$	−1.24525e7	−	2.15684e7i	−0.811059	−	1.40479i
$750$		0			0
$751$	−1.41638e6	+	8.03269e6i	−0.0916389	+	0.519710i	0.904087	+	0.427349i	$0.140552\pi$
$751$	−1.41638e6	+	8.03269e6i	−0.0916389	+	0.519710i	−0.995726	+	0.0923609i	$0.970559\pi$
$752$		0			0
$753$	−550317.	+	953178.i	−0.0353692	+	0.0612613i
$754$		0			0
$755$	−2.07658e7	−	7.55813e6i	−1.32581	−	0.482555i
$756$		0			0
$757$	−2.17286e6	+	1.82324e6i	−0.137813	+	0.115639i	−0.709089	−	0.705119i	$-0.750893\pi$
$757$	−2.17286e6	+	1.82324e6i	−0.137813	+	0.115639i	0.571275	+	0.820759i	$0.306449\pi$
$758$		0			0
$759$	3.45395e7			2.17626
$760$		0			0
$761$	1.28986e7			0.807385			0.403693	−	0.914895i	$-0.367727\pi$
$761$	1.28986e7			0.807385			0.403693	+	0.914895i	$0.367727\pi$
$762$		0			0
$763$	6.30195e6	−	5.28797e6i	0.391890	−	0.328834i
$764$		0			0
$765$	−6.26170e6	−	2.27907e6i	−0.386847	−	0.140801i
$766$		0			0
$767$	−21027.5	+	36420.6i	−0.00129062	+	0.00223542i
$768$		0			0
$769$	493403.	−	2.79823e6i	0.0300875	−	0.170635i	−0.966061	−	0.258313i	$-0.916834\pi$
$769$	493403.	−	2.79823e6i	0.0300875	−	0.170635i	0.996149	+	0.0876779i	$0.0279446\pi$
$770$		0			0
$771$	−1.86319e7	−	3.22713e7i	−1.12881	−	1.95515i
$772$		0			0
$773$	1.81120e7	+	1.51978e7i	1.09023	+	0.914813i	0.996730	−	0.0808066i	$-0.0257496\pi$
$773$	1.81120e7	+	1.51978e7i	1.09023	+	0.914813i	0.0935014	+	0.995619i	$0.470194\pi$
$774$		0			0
$775$	1.62465e6	−	591323.i	0.0971638	−	0.0353647i
$776$		0			0
$777$	1.42459e6	+	8.07925e6i	0.0846521	+	0.480086i
$778$		0			0
$779$	6.50943e6	−	5.20837e6i	0.384325	−	0.307509i
$780$		0			0
$781$	−1.91805e6	−	1.08778e7i	−0.112521	−	0.638136i
$782$		0			0
$783$	2.29369e6	−	834835.i	0.133700	−	0.0486627i
$784$		0			0
$785$	−2.17513e7	−	1.82515e7i	−1.25983	−	1.05712i
$786$		0			0
$787$	9.54290e6	+	1.65288e7i	0.549216	+	0.951270i	0.998328	+	0.0577950i	$0.0184070\pi$
$787$	9.54290e6	+	1.65288e7i	0.549216	+	0.951270i	−0.449112	+	0.893475i	$0.648260\pi$
$788$		0			0
$789$	1.87482e6	−	1.06326e7i	0.107218	−	0.608063i
$790$		0			0
$791$	1.37162e7	−	2.37572e7i	0.779459	−	1.35006i
$792$		0			0
$793$	−10264.0	−	3735.80i	−0.000579609	−	0.000210960i
$794$		0			0
$795$	−2.21628e7	+	1.85968e7i	−1.24368	+	1.04357i
$796$		0			0
$797$	−5.86429e6			−0.327017			−0.163508	−	0.986542i	$-0.552281\pi$
$797$	−5.86429e6			−0.327017			−0.163508	+	0.986542i	$0.552281\pi$
$798$		0			0
$799$	2.39477e7			1.32708
$800$		0			0
$801$	−2.63217e6	+	2.20865e6i	−0.144955	+	0.121632i
$802$		0			0
$803$	2.59435e7	+	9.44266e6i	1.41984	+	0.516780i
$804$		0			0
$805$	1.87095e7	−	3.24058e7i	1.01759	−	1.76251i
$806$		0			0
$807$	−1.72789e6	+	9.79933e6i	−0.0933967	+	0.529679i
$808$		0			0
$809$	−1.48758e7	−	2.57657e7i	−0.799115	−	1.38411i	−0.920193	−	0.391465i	$-0.871968\pi$
$809$	−1.48758e7	−	2.57657e7i	−0.799115	−	1.38411i	0.121077	−	0.992643i	$-0.461365\pi$
$810$		0			0
$811$	−1.54853e7	−	1.29937e7i	−0.826735	−	0.693713i	0.127804	−	0.991799i	$-0.459207\pi$
$811$	−1.54853e7	−	1.29937e7i	−0.826735	−	0.693713i	−0.954539	+	0.298087i	$0.903652\pi$
$812$		0			0
$813$	3.26728e7	−	1.18919e7i	1.73364	−	0.630995i
$814$		0			0
$815$	3.76177e6	+	2.13341e7i	0.198380	+	1.12507i
$816$		0			0
$817$	1.98675e7	+	7.76030e6i	1.04133	+	0.406746i
$818$		0			0
$819$	−4764.40	−	27020.3i	−0.000248198	−	0.00140760i
$820$		0			0
$821$	3.14908e7	−	1.14617e7i	1.63052	−	0.593461i	0.645175	−	0.764035i	$-0.276785\pi$
$821$	3.14908e7	−	1.14617e7i	1.63052	−	0.593461i	0.985345	+	0.170575i	$0.0545624\pi$
$822$		0			0
$823$	9.73753e6	+	8.17076e6i	0.501129	+	0.420497i	0.857995	−	0.513659i	$-0.171710\pi$
$823$	9.73753e6	+	8.17076e6i	0.501129	+	0.420497i	−0.356866	+	0.934156i	$0.616155\pi$
$824$		0			0
$825$	2.59337e6	+	4.49186e6i	0.132657	+	0.229769i
$826$		0			0
$827$	−5.58355e6	+	3.16659e7i	−0.283888	+	1.61001i	0.425343	+	0.905032i	$0.360153\pi$
$827$	−5.58355e6	+	3.16659e7i	−0.283888	+	1.61001i	−0.709231	+	0.704976i	$0.750958\pi$
$828$		0			0
$829$	−3.11494e6	+	5.39523e6i	−0.157421	+	0.272662i	−0.933938	−	0.357435i	$-0.883651\pi$
$829$	−3.11494e6	+	5.39523e6i	−0.157421	+	0.272662i	0.776517	+	0.630097i	$0.216985\pi$
$830$		0			0
$831$	7.97275e6	+	2.90184e6i	0.400503	+	0.145771i
$832$		0			0
$833$	−1.58065e6	+	1.32633e6i	−0.0789267	+	0.0662274i
$834$		0			0
$835$	−2.22161e7			−1.10268
$836$		0			0
$837$	7.14777e6			0.352661
$838$		0			0
$839$	−1.67294e7	+	1.40376e7i	−0.820493	+	0.688475i	−0.953088	−	0.302695i	$-0.902114\pi$
$839$	−1.67294e7	+	1.40376e7i	−0.820493	+	0.688475i	0.132594	+	0.991170i	$0.457669\pi$
$840$		0			0
$841$	1.85437e7	+	6.74936e6i	0.904080	+	0.329058i
$842$		0			0
$843$	−1.72647e7	+	2.99033e7i	−0.836737	+	1.44927i
$844$		0			0
$845$	3.97162e6	−	2.25242e7i	0.191349	−	1.08519i
$846$		0			0
$847$	1.24021e6	+	2.14810e6i	0.0593999	+	0.102884i
$848$		0			0
$849$	−3.35628e6	−	2.81625e6i	−0.159804	−	0.134092i
$850$		0			0
$851$	−1.37954e7	+	5.02112e6i	−0.652997	+	0.237671i
$852$		0			0
$853$	2.03319e6	+	1.15308e7i	0.0956765	+	0.542608i	0.994538	+	0.104375i	$0.0332843\pi$
$853$	2.03319e6	+	1.15308e7i	0.0956765	+	0.542608i	−0.898862	+	0.438233i	$0.855605\pi$
$854$		0			0
$855$	−4.62078e6	+	7.58918e6i	−0.216172	+	0.355042i
$856$		0			0
$857$	−4.60283e6	−	2.61039e7i	−0.214078	−	1.21410i	−0.882499	−	0.470315i	$-0.844140\pi$
$857$	−4.60283e6	−	2.61039e7i	−0.214078	−	1.21410i	0.668420	−	0.743784i	$-0.266971\pi$
$858$		0			0
$859$	−2.53894e7	+	9.24098e6i	−1.17400	+	0.427302i	−0.854080	−	0.520141i	$-0.825879\pi$
$859$	−2.53894e7	+	9.24098e6i	−1.17400	+	0.427302i	−0.319923	+	0.947444i	$0.603657\pi$
$860$		0			0
$861$	1.01135e7	+	8.48625e6i	0.464937	+	0.390129i
$862$		0			0
$863$	−6.64699e6	−	1.15129e7i	−0.303807	−	0.526210i	0.673188	−	0.739472i	$-0.264925\pi$
$863$	−6.64699e6	−	1.15129e7i	−0.303807	−	0.526210i	−0.976995	+	0.213262i	$0.931591\pi$
$864$		0			0
$865$	−815354.	+	4.62410e6i	−0.0370515	+	0.210129i
$866$		0			0
$867$	248805.	−	430942.i	0.0112411	−	0.0194702i
$868$		0			0
$869$	−3.56818e7	−	1.29871e7i	−1.60286	−	0.583395i
$870$		0			0
$871$	−82675.5	+	69373.0i	−0.00369259	+	0.00309845i
$872$		0			0
$873$	1.37658e6			0.0611317
$874$		0			0
$875$	−2.06032e7			−0.909735
$876$		0			0
$877$	−2.01478e7	+	1.69060e7i	−0.884563	+	0.742237i	−0.967112	−	0.254350i	$-0.918138\pi$
$877$	−2.01478e7	+	1.69060e7i	−0.884563	+	0.742237i	0.0825488	+	0.996587i	$0.473694\pi$
$878$		0			0
$879$	−1.78461e7	−	6.49545e6i	−0.779061	−	0.283555i
$880$		0			0
$881$	6.55837e6	−	1.13594e7i	0.284679	−	0.493079i	−0.687852	−	0.725851i	$-0.741446\pi$
$881$	6.55837e6	−	1.13594e7i	0.284679	−	0.493079i	0.972531	+	0.232772i	$0.0747795\pi$
$882$		0			0
$883$	−1.65400e6	+	9.38029e6i	−0.0713893	+	0.404869i	0.928083	+	0.372374i	$0.121456\pi$
$883$	−1.65400e6	+	9.38029e6i	−0.0713893	+	0.404869i	−0.999472	+	0.0324946i	$0.989655\pi$
$884$		0			0
$885$	1.07838e7	+	1.86782e7i	0.462824	+	0.801634i
$886$		0			0
$887$	−2.44080e7	−	2.04807e7i	−1.04165	−	0.874050i	−0.0494613	−	0.998776i	$-0.515750\pi$
$887$	−2.44080e7	−	2.04807e7i	−1.04165	−	0.874050i	−0.992191	+	0.124726i	$0.960195\pi$
$888$		0			0
$889$	2.37834e7	−	8.65647e6i	1.00930	−	0.367355i
$890$		0			0
$891$	5.36124e6	+	3.04051e7i	0.226241	+	1.28307i
$892$		0			0
$893$	6.27647e6	−	3.13090e7i	0.263382	−	1.31384i
$894$		0			0
$895$	−3.50414e6	−	1.98729e7i	−0.146226	−	0.829287i
$896$		0			0
$897$	168447.	−	61309.8i	0.00699009	−	0.00254418i
$898$		0			0
$899$	−1.74373e6	−	1.46317e6i	−0.0719583	−	0.0603801i
$900$		0			0
$901$	1.51486e7	+	2.62382e7i	0.621671	+	1.07677i
$902$		0			0
$903$	−5.86549e6	+	3.32648e7i	−0.239378	+	1.35758i
$904$		0			0
$905$	−1.93007e7	+	3.34299e7i	−0.783344	+	1.35679i
$906$		0			0
$907$	−9.72441e6	−	3.53940e6i	−0.392505	−	0.142860i	0.138226	−	0.990401i	$-0.455860\pi$
$907$	−9.72441e6	−	3.53940e6i	−0.392505	−	0.142860i	−0.530730	+	0.847541i	$0.678082\pi$
$908$		0			0
$909$	−2.98221e6	+	2.50237e6i	−0.119709	+	0.100448i
$910$		0			0
$911$	−1.32981e7			−0.530878			−0.265439	−	0.964128i	$-0.585517\pi$
$911$	−1.32981e7			−0.530878			−0.265439	+	0.964128i	$0.585517\pi$
$912$		0			0
$913$	−2.43002e7			−0.964792
$914$		0			0
$915$	−4.29114e6	+	3.60070e6i	−0.169442	+	0.142178i
$916$		0			0
$917$	−2.64159e7	−	9.61461e6i	−1.03739	−	0.377579i
$918$		0			0
$919$	1.88799e7	−	3.27010e7i	0.737414	−	1.27724i	−0.216243	−	0.976340i	$-0.569380\pi$
$919$	1.88799e7	−	3.27010e7i	0.737414	−	1.27724i	0.953656	−	0.300898i	$-0.0972865\pi$
$920$		0			0
$921$	−7.44438e6	+	4.22192e7i	−0.289187	+	1.64006i
$922$		0			0
$923$	−28663.0	−	49645.7i	−0.00110743	−	0.00191813i
$924$		0			0
$925$	−1.68882e6	−	1.41708e6i	−0.0648975	−	0.0544555i
$926$		0			0
$927$	1.25273e7	−	4.55956e6i	0.478804	−	0.174270i
$928$		0			0
$929$	2.66656e6	+	1.51228e7i	0.101371	+	0.574901i	0.992608	+	0.121364i	$0.0387269\pi$
$929$	2.66656e6	+	1.51228e7i	0.101371	+	0.574901i	−0.891237	+	0.453537i	$0.850162\pi$
$930$		0			0
$931$	1.31975e6	+	2.41415e6i	0.0499021	+	0.0912832i
$932$		0			0
$933$	−3.49052e6	−	1.97957e7i	−0.131276	−	0.744505i
$934$		0			0
$935$	2.89225e7	−	1.05269e7i	1.08195	−	0.393797i
$936$		0			0
$937$	−1.81000e7	−	1.51877e7i	−0.673488	−	0.565123i	0.240608	−	0.970622i	$-0.422653\pi$
$937$	−1.81000e7	−	1.51877e7i	−0.673488	−	0.565123i	−0.914095	+	0.405499i	$0.867098\pi$
$938$		0			0
$939$	−2.94305e6	−	5.09751e6i	−0.108926	−	0.188666i
$940$		0			0
$941$	2.12714e6	−	1.20636e7i	0.0783110	−	0.444124i	−0.920290	−	0.391238i	$-0.872047\pi$
$941$	2.12714e6	−	1.20636e7i	0.0783110	−	0.444124i	0.998601	−	0.0528858i	$-0.0168419\pi$
$942$		0			0
$943$	−1.18127e7	+	2.04601e7i	−0.432582	+	0.749254i
$944$		0			0
$945$	2.18300e7	+	7.94549e6i	0.795198	+	0.289428i
$946$		0			0
$947$	2.12924e6	−	1.78664e6i	0.0771523	−	0.0647385i	−0.603396	−	0.797442i	$-0.706186\pi$
$947$	2.12924e6	−	1.78664e6i	0.0771523	−	0.0647385i	0.680548	+	0.732703i	$0.261742\pi$
$948$		0			0
$949$	143286.			0.00516463
$950$		0			0
$951$	−6.44191e7			−2.30974
$952$		0			0
$953$	2.78322e6	−	2.33540e6i	0.0992694	−	0.0832969i	−0.591802	−	0.806083i	$-0.701583\pi$
$953$	2.78322e6	−	2.33540e6i	0.0992694	−	0.0832969i	0.691072	+	0.722786i	$0.257139\pi$
$954$		0			0
$955$	4.14611e7	+	1.50906e7i	1.47107	+	0.535424i
$956$		0			0
$957$	3.41443e6	−	5.91397e6i	0.120514	−	0.208737i
$958$		0			0
$959$	−6.86679e6	+	3.89435e7i	−0.241105	+	1.36738i
$960$		0			0
$961$	1.09817e7	+	1.90209e7i	0.383585	+	0.664389i
$962$		0			0
$963$	−1.28382e7	−	1.07725e7i	−0.446106	−	0.374327i
$964$		0			0
$965$	4.47114e7	−	1.62736e7i	1.54561	−	0.562557i
$966$		0			0
$967$	−2.44295e6	−	1.38547e7i	−0.0840134	−	0.476464i	−0.997565	−	0.0697411i	$-0.977783\pi$
$967$	−2.44295e6	−	1.38547e7i	−0.0840134	−	0.476464i	0.913552	−	0.406723i	$-0.133328\pi$
$968$		0			0
$969$	2.55073e7	+	2.24369e7i	0.872681	+	0.767634i
$970$		0			0
$971$	−3088.46	−	17515.5i	−0.000105122	−	0.000596176i	0.984755	−	0.173946i	$-0.0556519\pi$
$971$	−3088.46	−	17515.5i	−0.000105122	−	0.000596176i	−0.984860	+	0.173350i	$0.944541\pi$
$972$		0			0
$973$	−2.11414e7	+	7.69482e6i	−0.715897	+	0.260565i
$974$		0			0
$975$	20621.1	+	17303.1i	0.000694704	+	0.000582925i
$976$		0			0
$977$	−4.81182e6	−	8.33432e6i	−0.161277	−	0.279341i	0.774050	−	0.633125i	$-0.218228\pi$
$977$	−4.81182e6	−	8.33432e6i	−0.161277	−	0.279341i	−0.935327	+	0.353784i	$0.884895\pi$
$978$		0			0
$979$	2.75596e6	−	1.56298e7i	0.0919002	−	0.521192i
$980$		0			0
$981$	2.76792e6	−	4.79418e6i	0.0918293	−	0.159053i
$982$		0			0
$983$	5.37821e7	+	1.95751e7i	1.77523	+	0.646130i	0.999894	+	0.0145776i	$0.00464035\pi$
$983$	5.37821e7	+	1.95751e7i	1.77523	+	0.646130i	0.775333	+	0.631552i	$0.217582\pi$
$984$		0			0
$985$	6.01656e6	−	5.04849e6i	0.197587	−	0.165795i
$986$		0			0
$987$	5.05687e7			1.65230
$988$		0			0
$989$	−6.04454e7			−1.96504
$990$		0			0
$991$	−3.80215e7	+	3.19039e7i	−1.22983	+	1.03195i	−0.231582	+	0.972815i	$0.574390\pi$
$991$	−3.80215e7	+	3.19039e7i	−1.22983	+	1.03195i	−0.998250	+	0.0591358i	$0.981166\pi$
$992$		0			0
$993$	−5.12428e7	−	1.86508e7i	−1.64915	−	0.600241i
$994$		0			0
$995$	2.70933e7	−	4.69269e7i	0.867568	−	1.50267i
$996$		0			0
$997$	2.73232e6	−	1.54957e7i	0.0870548	−	0.493713i	−0.909839	−	0.414961i	$-0.863795\pi$
$997$	2.73232e6	−	1.54957e7i	0.0870548	−	0.493713i	0.996894	−	0.0787520i	$-0.0250935\pi$
$998$		0			0
$999$	−4.55718e6	−	7.89326e6i	−0.144472	−	0.250232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.i.a.9.7	✓	48
19.17	even	9	inner	76.6.i.a.17.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.i.a.9.7	✓	48	1.1	even	1	trivial
76.6.i.a.17.7	yes	48	19.17	even	9	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.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(14.0139 - 11.7590i) q^{3} +(57.8858 + 21.0687i) q^{5} +(68.1093 - 117.969i) q^{7} +(15.9173 - 90.2714i) q^{9} +O(q^{10})\)	\(q+(14.0139 - 11.7590i) q^{3} +(57.8858 + 21.0687i) q^{5} +(68.1093 - 117.969i) q^{7} +(15.9173 - 90.2714i) q^{9} +(211.696 + 366.668i) q^{11} +(1.68328 + 1.41244i) q^{13} +(1058.95 - 385.427i) q^{15} +(-204.924 - 1162.18i) q^{17} +(-1573.13 - 36.6809i) q^{19} +(-432.724 - 2454.10i) q^{21} +(4190.40 - 1525.18i) q^{23} +(512.983 + 430.444i) q^{25} +(1384.26 + 2397.60i) q^{27} +(153.099 - 868.267i) q^{29} +(1290.90 - 2235.91i) q^{31} +(7278.34 + 2649.10i) q^{33} +(6428.00 - 5393.73i) q^{35} -3292.15 q^{37} +40.1983 q^{39} +(-4058.46 + 3405.46i) q^{41} +(-12737.4 - 4636.02i) q^{43} +(2823.28 - 4890.07i) q^{45} +(-3523.80 + 19984.5i) q^{47} +(-874.240 - 1514.23i) q^{49} +(-16537.9 - 13876.9i) q^{51} +(-24125.0 + 8780.77i) q^{53} +(4528.95 + 25685.0i) q^{55} +(-22477.1 + 17984.5i) q^{57} +(3323.41 + 18848.0i) q^{59} +(-4671.05 + 1700.12i) q^{61} +(-9565.08 - 8026.06i) q^{63} +(67.6799 + 117.225i) q^{65} +(-8528.83 + 48369.4i) q^{67} +(40789.1 - 70648.8i) q^{69} +(-24515.1 - 8922.76i) q^{71} +(49952.2 - 41914.9i) q^{73} +12250.5 q^{75} +57673.7 q^{77} +(-68702.5 + 57648.3i) q^{79} +(68523.4 + 24940.5i) q^{81} +(-28697.2 + 49704.9i) q^{83} +(12623.5 - 71591.2i) q^{85} +(-8064.48 - 13968.1i) q^{87} +(-28715.4 - 24095.1i) q^{89} +(281.271 - 102.374i) q^{91} +(-8201.60 - 46513.6i) q^{93} +(-90289.3 - 35267.2i) q^{95} +(2607.80 + 14789.5i) q^{97} +(36469.2 - 13273.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) \) 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) \) 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9 - 237 * q^11 + 2049 * q^13 + 2085 * q^15 - 609 * q^17 - 6012 * q^19 + 3591 * q^21 + 14100 * q^23 + 11802 * q^25 - 861 * q^27 - 10575 * q^29 - 6546 * q^31 - 21234 * q^33 - 231 * q^35 + 20052 * q^37 + 72204 * q^39 - 3249 * q^41 - 34677 * q^43 - 34956 * q^45 + 4461 * q^47 - 41139 * q^49 + 12099 * q^51 - 24291 * q^53 - 61767 * q^55 - 64470 * q^57 - 20100 * q^59 + 95490 * q^61 + 86403 * q^63 - 57915 * q^65 - 64452 * q^67 - 99315 * q^69 - 115536 * q^71 - 16362 * q^73 + 236250 * q^75 + 26688 * q^77 + 29799 * q^79 + 180327 * q^81 + 52347 * q^83 + 204618 * q^85 + 69414 * q^87 + 47394 * q^89 - 249384 * q^91 - 462126 * q^93 + 412869 * q^95 - 229974 * q^97 - 692274 * q^99

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