LMFDB - Embedded newform 76.6.i.a.5.7

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			5.7
Character	$\chi$	$=$	76.5
Dual form			76.6.i.a.61.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.64287 - 20.6597i) q^{3} +(83.5459 + 70.1033i) q^{5} +(58.2786 + 100.941i) q^{7} +(-185.208 - 67.4103i) q^{9} +O(q^{10})$	\(q+(3.64287 - 20.6597i) q^{3} +(83.5459 + 70.1033i) q^{5} +(58.2786 + 100.941i) q^{7} +(-185.208 - 67.4103i) q^{9} +(-313.273 + 542.605i) q^{11} +(117.360 + 665.581i) q^{13} +(1752.66 - 1470.66i) q^{15} +(735.035 - 267.531i) q^{17} +(-229.227 - 1556.78i) q^{19} +(2297.72 - 836.303i) q^{21} +(1883.53 - 1580.47i) q^{23} +(1522.79 + 8636.17i) q^{25} +(481.513 - 834.005i) q^{27} +(-1421.36 - 517.334i) q^{29} +(-3992.33 - 6914.92i) q^{31} +(10068.8 + 8448.77i) q^{33} +(-2207.40 + 12518.8i) q^{35} -9182.79 q^{37} +14178.2 q^{39} +(1150.76 - 6526.29i) q^{41} +(-4762.40 - 3996.13i) q^{43} +(-10747.7 - 18615.6i) q^{45} +(3390.72 + 1234.12i) q^{47} +(1610.71 - 2789.84i) q^{49} +(-2849.48 - 16160.2i) q^{51} +(15994.4 - 13420.9i) q^{53} +(-64211.1 + 23370.9i) q^{55} +(-32997.6 - 935.355i) q^{57} +(6177.95 - 2248.59i) q^{59} +(-9460.05 + 7937.92i) q^{61} +(-3989.18 - 22623.8i) q^{63} +(-36854.5 + 63833.9i) q^{65} +(55339.9 + 20142.1i) q^{67} +(-25790.6 - 44670.6i) q^{69} +(-9796.94 - 8220.61i) q^{71} +(-7770.94 + 44071.2i) q^{73} +183968. q^{75} -73028.4 q^{77} +(8073.99 - 45789.9i) q^{79} +(-52165.1 - 43771.7i) q^{81} +(-2592.40 - 4490.17i) q^{83} +(80163.9 + 29177.3i) q^{85} +(-15865.8 + 27480.4i) q^{87} +(12681.3 + 71919.5i) q^{89} +(-60345.1 + 50635.6i) q^{91} +(-157404. + 57290.3i) q^{93} +(89984.2 - 146132. i) q^{95} +(118356. - 43077.9i) q^{97} +(94597.8 - 79377.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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
$3$	3.64287	−	20.6597i	0.233690	−	1.32532i	−0.611665	−	0.791117i	$-0.709500\pi$
$3$	3.64287	−	20.6597i	0.233690	−	1.32532i	0.845355	−	0.534205i	$-0.179389\pi$
$4$		0			0
$5$	83.5459	+	70.1033i	1.49451	+	1.25405i	0.888741	+	0.458410i	$0.151581\pi$
$5$	83.5459	+	70.1033i	1.49451	+	1.25405i	0.605774	+	0.795637i	$0.292864\pi$
$6$		0			0
$7$	58.2786	+	100.941i	0.449535	+	0.778618i	0.998356	−	0.0573222i	$-0.0182562\pi$
$7$	58.2786	+	100.941i	0.449535	+	0.778618i	−0.548820	+	0.835940i	$0.684923\pi$
$8$		0			0
$9$	−185.208	−	67.4103i	−0.762174	−	0.277409i
$10$		0			0
$11$	−313.273	+	542.605i	−0.780622	+	1.35208i	0.150957	+	0.988540i	$0.451764\pi$
$11$	−313.273	+	542.605i	−0.780622	+	1.35208i	−0.931580	+	0.363538i	$0.881569\pi$
$12$		0			0
$13$	117.360	+	665.581i	0.192602	+	1.09230i	0.915792	+	0.401652i	$0.131564\pi$
$13$	117.360	+	665.581i	0.192602	+	1.09230i	−0.723190	+	0.690649i	$0.757325\pi$
$14$		0			0
$15$	1752.66	−	1470.66i	2.01127	−	1.68765i
$16$		0			0
$17$	735.035	−	267.531i	0.616858	−	0.224518i	−0.0146431	−	0.999893i	$-0.504661\pi$
$17$	735.035	−	267.531i	0.616858	−	0.224518i	0.631501	+	0.775375i	$0.282439\pi$
$18$		0			0
$19$	−229.227	−	1556.78i	−0.145674	−	0.989333i
$19$	−229.227	−	1556.78i	−0.145674	−	0.989333i
$20$		0			0
$21$	2297.72	−	836.303i	1.13697	−	0.413824i
$22$		0			0
$23$	1883.53	−	1580.47i	0.742426	−	0.622969i	−0.191062	−	0.981578i	$-0.561193\pi$
$23$	1883.53	−	1580.47i	0.742426	−	0.622969i	0.933488	+	0.358609i	$0.116749\pi$
$24$		0			0
$25$	1522.79	+	8636.17i	0.487293	+	2.76358i
$26$		0			0
$27$	481.513	−	834.005i	0.127115	−	0.220170i
$28$		0			0
$29$	−1421.36	−	517.334i	−0.313841	−	0.114229i	0.180297	−	0.983612i	$-0.442294\pi$
$29$	−1421.36	−	517.334i	−0.313841	−	0.114229i	−0.494138	+	0.869383i	$0.664516\pi$
$30$		0			0
$31$	−3992.33	−	6914.92i	−0.746143	−	1.29236i	−0.949659	−	0.313286i	$-0.898570\pi$
$31$	−3992.33	−	6914.92i	−0.746143	−	1.29236i	0.203515	−	0.979072i	$-0.434763\pi$
$32$		0			0
$33$	10068.8	+	8448.77i	1.60951	+	1.35054i
$34$		0			0
$35$	−2207.40	+	12518.8i	−0.304586	+	1.72739i
$36$		0			0
$37$	−9182.79			−1.10273			−0.551366	−	0.834263i	$-0.685893\pi$
$37$	−9182.79			−1.10273			−0.551366	+	0.834263i	$0.685893\pi$
$38$		0			0
$39$	14178.2			1.49266
$40$		0			0
$41$	1150.76	−	6526.29i	0.106912	−	0.606327i	−0.883528	−	0.468379i	$-0.844838\pi$
$41$	1150.76	−	6526.29i	0.106912	−	0.606327i	0.990439	−	0.137948i	$-0.0440507\pi$
$42$		0			0
$43$	−4762.40	−	3996.13i	−0.392785	−	0.329585i	0.424912	−	0.905235i	$-0.360305\pi$
$43$	−4762.40	−	3996.13i	−0.392785	−	0.329585i	−0.817697	+	0.575649i	$0.804749\pi$
$44$		0			0
$45$	−10747.7	−	18615.6i	−0.791197	−	1.37039i
$46$		0			0
$47$	3390.72	+	1234.12i	0.223897	+	0.0814917i	0.451533	−	0.892255i	$-0.350877\pi$
$47$	3390.72	+	1234.12i	0.223897	+	0.0814917i	−0.227636	+	0.973746i	$0.573100\pi$
$48$		0			0
$49$	1610.71	−	2789.84i	0.0958359	−	0.165993i
$50$		0			0
$51$	−2849.48	−	16160.2i	−0.153405	−	0.870003i
$52$		0			0
$53$	15994.4	−	13420.9i	0.782129	−	0.656284i	−0.161655	−	0.986847i	$-0.551683\pi$
$53$	15994.4	−	13420.9i	0.782129	−	0.656284i	0.943784	+	0.330563i	$0.107239\pi$
$54$		0			0
$55$	−64211.1	+	23370.9i	−2.86222	+	1.04176i
$56$		0			0
$57$	−32997.6	−	935.355i	−1.34523	−	0.0381320i
$58$		0			0
$59$	6177.95	−	2248.59i	0.231055	−	0.0840970i	−0.223898	−	0.974613i	$-0.571878\pi$
$59$	6177.95	−	2248.59i	0.231055	−	0.0840970i	0.454953	+	0.890516i	$0.349656\pi$
$60$		0			0
$61$	−9460.05	+	7937.92i	−0.325513	+	0.273138i	−0.790869	−	0.611986i	$-0.790371\pi$
$61$	−9460.05	+	7937.92i	−0.325513	+	0.273138i	0.465355	+	0.885124i	$0.345926\pi$
$62$		0			0
$63$	−3989.18	−	22623.8i	−0.126629	−	0.718147i
$64$		0			0
$65$	−36854.5	+	63833.9i	−1.08195	+	1.87399i
$66$		0			0
$67$	55339.9	+	20142.1i	1.50609	+	0.548173i	0.957630	−	0.288002i	$-0.0929910\pi$
$67$	55339.9	+	20142.1i	1.50609	+	0.548173i	0.548463	+	0.836175i	$0.315213\pi$
$68$		0			0
$69$	−25790.6	−	44670.6i	−0.652137	−	1.12953i
$70$		0			0
$71$	−9796.94	−	8220.61i	−0.230645	−	0.193534i	0.520139	−	0.854081i	$-0.325880\pi$
$71$	−9796.94	−	8220.61i	−0.230645	−	0.193534i	−0.750785	+	0.660547i	$0.770324\pi$
$72$		0			0
$73$	−7770.94	+	44071.2i	−0.170674	+	0.967938i	0.772346	+	0.635202i	$0.219083\pi$
$73$	−7770.94	+	44071.2i	−0.170674	+	0.967938i	−0.943020	+	0.332736i	$0.892028\pi$
$74$		0			0
$75$	183968.			3.77650
$76$		0			0
$77$	−73028.4			−1.40367
$78$		0			0
$79$	8073.99	−	45789.9i	0.145553	−	0.825471i	−0.821369	−	0.570397i	$-0.806789\pi$
$79$	8073.99	−	45789.9i	0.145553	−	0.825471i	0.966922	−	0.255073i	$-0.0820996\pi$
$80$		0			0
$81$	−52165.1	−	43771.7i	−0.883421	−	0.741278i
$82$		0			0
$83$	−2592.40	−	4490.17i	−0.0413054	−	0.0715430i	0.844634	−	0.535345i	$-0.179818\pi$
$83$	−2592.40	−	4490.17i	−0.0413054	−	0.0715430i	−0.885939	+	0.463802i	$0.846485\pi$
$84$		0			0
$85$	80163.9	+	29177.3i	1.20346	+	0.438024i
$86$		0			0
$87$	−15865.8	+	27480.4i	−0.224732	+	0.389247i
$88$		0			0
$89$	12681.3	+	71919.5i	0.169703	+	0.962435i	0.944082	+	0.329712i	$0.106952\pi$
$89$	12681.3	+	71919.5i	0.169703	+	0.962435i	−0.774378	+	0.632723i	$0.781937\pi$
$90$		0			0
$91$	−60345.1	+	50635.6i	−0.763904	+	0.640992i
$92$		0			0
$93$	−157404.	+	57290.3i	−1.88716	+	0.686869i
$94$		0			0
$95$	89984.2	−	146132.i	1.02296	−	1.66125i
$96$		0			0
$97$	118356.	−	43077.9i	1.27720	−	0.464863i	0.387696	−	0.921787i	$-0.373271\pi$
$97$	118356.	−	43077.9i	1.27720	−	0.464863i	0.889506	+	0.456924i	$0.151049\pi$
$98$		0			0
$99$	94597.8	−	79377.0i	0.970048	−	0.813967i
$100$		0			0
$101$	−28346.6	−	160762.i	−0.276502	−	1.56812i	−0.734151	−	0.678986i	$-0.762420\pi$
$101$	−28346.6	−	160762.i	−0.276502	−	1.56812i	0.457649	−	0.889133i	$-0.348692\pi$
$102$		0			0
$103$	−12256.8	+	21229.3i	−0.113837	+	0.197171i	−0.917314	−	0.398164i	$-0.869647\pi$
$103$	−12256.8	+	21229.3i	−0.113837	+	0.197171i	0.803477	+	0.595335i	$0.202981\pi$
$104$		0			0
$105$	250593.	+	91208.4i	2.21817	+	0.807350i
$106$		0			0
$107$	−12144.6	−	21035.1i	−0.102547	−	0.177617i	0.810186	−	0.586173i	$-0.199366\pi$
$107$	−12144.6	−	21035.1i	−0.102547	−	0.177617i	−0.912733	+	0.408556i	$0.866033\pi$
$108$		0			0
$109$	133475.	+	111999.i	1.07605	+	0.902914i	0.995587	−	0.0938431i	$-0.0299152\pi$
$109$	133475.	+	111999.i	1.07605	+	0.902914i	0.0804645	+	0.996757i	$0.474360\pi$
$110$		0			0
$111$	−33451.7	+	189714.i	−0.257698	+	1.46148i
$112$		0			0
$113$	−120624.			−0.888663			−0.444332	−	0.895862i	$-0.646559\pi$
$113$	−120624.			−0.888663			−0.444332	+	0.895862i	$0.646559\pi$
$114$		0			0
$115$	268157.			1.89080
$116$		0			0
$117$	23131.0	−	131182.i	0.156217	−	0.885953i
$118$		0			0
$119$	69841.7	+	58604.2i	0.452113	+	0.379368i
$120$		0			0
$121$	−115754.	−	200492.i	−0.718743	−	1.24490i
$122$		0			0
$123$	−130639.	−	47548.8i	−0.778594	−	0.283385i
$124$		0			0
$125$	−307793.	+	533113.i	−1.76191	+	3.05172i
$126$		0			0
$127$	−18386.4	−	104275.i	−0.101155	−	0.573680i	−0.992687	−	0.120721i	$-0.961479\pi$
$127$	−18386.4	−	104275.i	−0.101155	−	0.573680i	0.891531	−	0.452959i	$-0.149632\pi$
$128$		0			0
$129$	−99907.6	+	83832.4i	−0.528596	+	0.443545i
$130$		0			0
$131$	−263995.	+	96086.4i	−1.34406	+	0.489197i	−0.911088	−	0.412212i	$-0.864756\pi$
$131$	−263995.	+	96086.4i	−1.34406	+	0.489197i	−0.432969	+	0.901409i	$0.642534\pi$
$132$		0			0
$133$	143784.	−	113865.i	0.704827	−	0.558165i
$134$		0			0
$135$	98694.9	−	35922.0i	0.466080	−	0.169639i
$136$		0			0
$137$	−902.240	+	757.070i	−0.00410696	+	0.00344615i	−0.644839	−	0.764319i	$-0.723075\pi$
$137$	−902.240	+	757.070i	−0.00410696	+	0.00344615i	0.640732	+	0.767765i	$0.278631\pi$
$138$		0			0
$139$	48880.8	+	277217.i	0.214586	+	1.21698i	0.881623	+	0.471953i	$0.156451\pi$
$139$	48880.8	+	277217.i	0.214586	+	1.21698i	−0.667038	+	0.745024i	$0.732438\pi$
$140$		0			0
$141$	37848.6	−	65555.6i	0.160325	−	0.277691i
$142$		0			0
$143$	−397913.	−	144828.i	−1.62723	−	0.592262i
$144$		0			0
$145$	−82482.3	−	142864.i	−0.325792	−	0.564289i
$146$		0			0
$147$	−51769.6	−	43439.9i	−0.197598	−	0.165804i
$148$		0			0
$149$	80707.5	−	457715.i	0.297816	−	1.68900i	−0.357714	−	0.933831i	$-0.616444\pi$
$149$	80707.5	−	457715.i	0.297816	−	1.68900i	0.655531	−	0.755169i	$-0.272445\pi$
$150$		0			0
$151$	−41934.9			−0.149669			−0.0748347	−	0.997196i	$-0.523843\pi$
$151$	−41934.9			−0.149669			−0.0748347	+	0.997196i	$0.523843\pi$
$152$		0			0
$153$	−154169.			−0.532436
$154$		0			0
$155$	151216.	−	857589.i	0.505555	−	2.86715i
$156$		0			0
$157$	−100744.	−	84534.5i	−0.326191	−	0.273706i	0.464955	−	0.885334i	$-0.346071\pi$
$157$	−100744.	−	84534.5i	−0.326191	−	0.273706i	−0.791146	+	0.611628i	$0.790515\pi$
$158$		0			0
$159$	−219007.	−	379331.i	−0.687012	−	1.18994i
$160$		0			0
$161$	269304.	+	98018.8i	0.818802	+	0.298019i
$162$		0			0
$163$	82669.6	−	143188.i	0.243712	−	0.422121i	−0.718057	−	0.695985i	$-0.754968\pi$
$163$	82669.6	−	143188.i	0.243712	−	0.422121i	0.961769	+	0.273863i	$0.0883015\pi$
$164$		0			0
$165$	248924.	+	1.41172e6i	0.711799	+	4.03681i
$166$		0			0
$167$	118884.	−	99755.3i	0.329861	−	0.276786i	−0.462782	−	0.886472i	$-0.653149\pi$
$167$	118884.	−	99755.3i	0.329861	−	0.276786i	0.792643	+	0.609686i	$0.208704\pi$
$168$		0			0
$169$	−80323.2	+	29235.2i	−0.216334	+	0.0787390i
$170$		0			0
$171$	−62488.0	+	303780.i	−0.163420	+	0.794455i
$172$		0			0
$173$	−306799.	+	111666.i	−0.779360	+	0.283664i	−0.700906	−	0.713254i	$-0.747221\pi$
$173$	−306799.	+	111666.i	−0.779360	+	0.283664i	−0.0784541	+	0.996918i	$0.524998\pi$
$174$		0			0
$175$	−783002.	+	657017.i	−1.93271	+	1.62174i
$176$		0			0
$177$	−23949.8	−	135826.i	−0.0574604	−	0.325874i
$178$		0			0
$179$	180975.	−	313457.i	0.422168	−	0.731216i	−0.573983	−	0.818867i	$-0.694603\pi$
$179$	180975.	−	313457.i	0.422168	−	0.731216i	0.996151	+	0.0876507i	$0.0279359\pi$
$180$		0			0
$181$	−36051.7	−	13121.8i	−0.0817955	−	0.0297711i	0.300798	−	0.953688i	$-0.402747\pi$
$181$	−36051.7	−	13121.8i	−0.0817955	−	0.0297711i	−0.382594	+	0.923917i	$0.624969\pi$
$182$		0			0
$183$	129534.	+	224359.i	0.285927	+	0.495239i
$184$		0			0
$185$	−767185.	−	643744.i	−1.64805	−	1.38288i
$186$		0			0
$187$	−85103.0	+	482643.i	−0.177968	+	1.00930i
$188$		0			0
$189$	112248.			0.228572
$190$		0			0
$191$	386666.			0.766925			0.383462	−	0.923557i	$-0.374732\pi$
$191$	386666.			0.766925			0.383462	+	0.923557i	$0.374732\pi$
$192$		0			0
$193$	19595.0	−	111129.i	0.0378661	−	0.214750i	−0.960004	−	0.279988i	$-0.909670\pi$
$193$	19595.0	−	111129.i	0.0378661	−	0.214750i	0.997870	+	0.0652382i	$0.0207807\pi$
$194$		0			0
$195$	1.18453e6	+	993942.i	2.23080	+	1.87186i
$196$		0			0
$197$	81454.5	+	141083.i	0.149537	+	0.259006i	0.931057	−	0.364875i	$-0.118888\pi$
$197$	81454.5	+	141083.i	0.149537	+	0.259006i	−0.781519	+	0.623881i	$0.785555\pi$
$198$		0			0
$199$	450455.	+	163952.i	0.806340	+	0.293484i	0.712111	−	0.702067i	$-0.247739\pi$
$199$	450455.	+	163952.i	0.806340	+	0.293484i	0.0942290	+	0.995551i	$0.469961\pi$
$200$		0			0
$201$	617726.	−	1.06993e6i	1.07846	−	1.86795i
$202$		0			0
$203$	−30614.6	−	173624.i	−0.0521421	−	0.295713i
$204$		0			0
$205$	553656.	−	464573.i	0.920144	−	0.772092i
$206$		0			0
$207$	−455385.	+	165747.i	−0.738674	+	0.268855i
$208$		0			0
$209$	916525.	+	363316.i	1.45137	+	0.575332i
$210$		0			0
$211$	−373830.	+	136063.i	−0.578053	+	0.210394i	−0.614467	−	0.788943i	$-0.710629\pi$
$211$	−373830.	+	136063.i	−0.578053	+	0.210394i	0.0364139	+	0.999337i	$0.488407\pi$
$212$		0			0
$213$	−205524.	+	172455.i	−0.310395	+	0.260452i
$214$		0			0
$215$	−117737.	−	667720.i	−0.173707	−	0.985140i
$216$		0			0
$217$	465335.	−	805983.i	0.670836	−	1.16192i
$218$		0			0
$219$	882190.	+	321091.i	1.24294	+	0.452395i
$220$		0			0
$221$	264327.	+	457827.i	0.364050	+	0.630552i
$222$		0			0
$223$	−345642.	−	290028.i	−0.465441	−	0.390551i	0.379688	−	0.925115i	$-0.376031\pi$
$223$	−345642.	−	290028.i	−0.465441	−	0.390551i	−0.845128	+	0.534564i	$0.820476\pi$
$224$		0			0
$225$	300134.	−	1.70214e6i	0.395238	−	2.24150i
$226$		0			0
$227$	−1.42560e6			−1.83626			−0.918128	−	0.396284i	$-0.870300\pi$
$227$	−1.42560e6			−1.83626			−0.918128	+	0.396284i	$0.870300\pi$
$228$		0			0
$229$	1.04505e6			1.31689			0.658445	−	0.752629i	$-0.271215\pi$
$229$	1.04505e6			1.31689			0.658445	+	0.752629i	$0.271215\pi$
$230$		0			0
$231$	−266033.	+	1.50875e6i	−0.328024	+	1.86031i
$232$		0			0
$233$	−397556.	−	333589.i	−0.479742	−	0.402552i	0.370591	−	0.928796i	$-0.379155\pi$
$233$	−397556.	−	333589.i	−0.479742	−	0.402552i	−0.850333	+	0.526245i	$0.823600\pi$
$234$		0			0
$235$	196765.	+	340807.i	0.232422	+	0.402567i
$236$		0			0
$237$	−916593.	−	333613.i	−1.06000	−	0.385808i
$238$		0			0
$239$	20846.7	−	36107.6i	0.0236071	−	0.0408888i	−0.853980	−	0.520305i	$-0.825818\pi$
$239$	20846.7	−	36107.6i	0.0236071	−	0.0408888i	0.877588	+	0.479416i	$0.159152\pi$
$240$		0			0
$241$	183624.	+	1.04139e6i	0.203652	+	1.15497i	0.899547	+	0.436823i	$0.143896\pi$
$241$	183624.	+	1.04139e6i	0.203652	+	1.15497i	−0.695896	+	0.718143i	$0.744992\pi$
$242$		0			0
$243$	−915076.	+	767840.i	−0.994126	+	0.834171i
$244$		0			0
$245$	330145.	−	120163.i	0.351391	−	0.127896i
$246$		0			0
$247$	1.00926e6	−	335272.i	1.05259	−	0.349668i
$248$		0			0
$249$	−102209.	+	37201.2i	−0.104470	+	0.0380240i
$250$		0			0
$251$	−1.16363e6	+	976405.i	−1.16582	+	0.978240i	−0.999969	−	0.00791005i	$-0.997482\pi$
$251$	−1.16363e6	+	976405.i	−1.16582	+	0.978240i	−0.165853	+	0.986151i	$0.553038\pi$
$252$		0			0
$253$	267511.	+	1.51713e6i	0.262749	+	1.49012i
$254$		0			0
$255$	894821.	−	1.54988e6i	0.861759	−	1.49261i
$256$		0			0
$257$	−1.52832e6	−	556263.i	−1.44338	−	0.525348i	−0.502648	−	0.864491i	$-0.667641\pi$
$257$	−1.52832e6	−	556263.i	−1.44338	−	0.525348i	−0.940735	+	0.339143i	$0.889863\pi$
$258$		0			0
$259$	−535160.	−	926924.i	−0.495718	−	0.858608i
$260$		0			0
$261$	228375.	+	191629.i	0.207514	+	0.174125i
$262$		0			0
$263$	−165070.	+	936156.i	−0.147156	+	0.834563i	0.818455	+	0.574571i	$0.194831\pi$
$263$	−165070.	+	936156.i	−0.147156	+	0.834563i	−0.965611	+	0.259992i	$0.916280\pi$
$264$		0			0
$265$	2.27712e6			1.99191
$266$		0			0
$267$	1.53203e6			1.31519
$268$		0			0
$269$	−119930.	+	680156.i	−0.101052	+	0.573097i	0.891671	+	0.452683i	$0.149533\pi$
$269$	−119930.	+	680156.i	−0.101052	+	0.573097i	−0.992724	+	0.120414i	$0.961578\pi$
$270$		0			0
$271$	−1.39367e6	−	1.16943e6i	−1.15276	−	0.967277i	−0.152975	−	0.988230i	$-0.548886\pi$
$271$	−1.39367e6	−	1.16943e6i	−1.15276	−	0.967277i	−0.999780	+	0.0209530i	$0.993330\pi$
$272$		0			0
$273$	826288.	+	1.43117e6i	0.671003	+	1.16221i
$274$		0			0
$275$	−5.16308e6	−	1.87921e6i	−4.11696	−	1.49845i
$276$		0			0
$277$	−547056.	+	947529.i	−0.428383	+	0.741982i	−0.996730	−	0.0808077i	$-0.974250\pi$
$277$	−547056.	+	947529.i	−0.428383	+	0.741982i	0.568346	+	0.822789i	$0.307583\pi$
$278$		0			0
$279$	273276.	+	1.54982e6i	0.210180	+	1.19199i
$280$		0			0
$281$	623950.	−	523556.i	0.471394	−	0.395547i	−0.375909	−	0.926657i	$-0.622669\pi$
$281$	623950.	−	523556.i	0.471394	−	0.395547i	0.847303	+	0.531110i	$0.178225\pi$
$282$		0			0
$283$	1.58332e6	−	576281.i	1.17517	−	0.427729i	0.320679	−	0.947188i	$-0.396089\pi$
$283$	1.58332e6	−	576281.i	1.17517	−	0.427729i	0.854495	+	0.519459i	$0.173867\pi$
$284$		0			0
$285$	−2.69124e6	−	2.39139e6i	−1.96264	−	1.74397i
$286$		0			0
$287$	725838.	−	264184.i	0.520158	−	0.189322i
$288$		0			0
$289$	−618970.	+	519378.i	−0.435939	+	0.365796i
$290$		0			0
$291$	−458824.	−	2.60212e6i	−0.317624	−	1.80134i
$292$		0			0
$293$	−447358.	+	774847.i	−0.304429	+	0.527287i	−0.977134	−	0.212624i	$-0.931799\pi$
$293$	−447358.	+	774847.i	−0.304429	+	0.527287i	0.672705	+	0.739911i	$0.265132\pi$
$294$		0			0
$295$	673776.	+	245235.i	0.450776	+	0.164069i
$296$		0			0
$297$	301690.	+	522542.i	0.198458	+	0.343740i
$298$		0			0
$299$	1.27298e6	+	1.06816e6i	0.823463	+	0.690967i
$300$		0			0
$301$	125829.	−	713612.i	0.0800506	−	0.453989i
$302$		0			0
$303$	−3.42455e6			−2.14288
$304$		0			0
$305$	−1.34682e6			−0.829012
$306$		0			0
$307$	−103757.	+	588436.i	−0.0628307	+	0.356331i	0.937142	+	0.348948i	$0.113461\pi$
$307$	−103757.	+	588436.i	−0.0628307	+	0.356331i	−0.999973	+	0.00738246i	$0.997650\pi$
$308$		0			0
$309$	393942.	+	330557.i	0.234713	+	0.196947i
$310$		0			0
$311$	−466481.	−	807970.i	−0.273485	−	0.473690i	0.696267	−	0.717783i	$-0.254843\pi$
$311$	−466481.	−	807970.i	−0.273485	−	0.473690i	−0.969752	+	0.244093i	$0.921510\pi$
$312$		0			0
$313$	1.12996e6	+	411273.i	0.651934	+	0.237285i	0.646750	−	0.762702i	$-0.276128\pi$
$313$	1.12996e6	+	411273.i	0.651934	+	0.237285i	0.00518417	+	0.999987i	$0.498350\pi$
$314$		0			0
$315$	1.25272e6	−	2.16978e6i	0.711342	−	1.23208i
$316$		0			0
$317$	−321492.	−	1.82327e6i	−0.179689	−	1.01907i	−0.932591	−	0.360935i	$-0.882458\pi$
$317$	−321492.	−	1.82327e6i	−0.179689	−	1.01907i	0.752902	−	0.658133i	$-0.228653\pi$
$318$		0			0
$319$	725983.	−	609172.i	0.399438	−	0.335168i
$320$		0			0
$321$	−478820.	+	174276.i	−0.259364	+	0.0944007i
$322$		0			0
$323$	−584976.	−	1.08296e6i	−0.311983	−	0.577572i
$324$		0			0
$325$	−5.56936e6	+	2.02708e6i	−2.92480	+	1.06454i
$326$		0			0
$327$	2.80009e6	−	2.34956e6i	1.44811	−	1.21511i
$328$		0			0
$329$	73032.4	+	414187.i	0.0371985	+	0.210963i
$330$		0			0
$331$	−1.40598e6	+	2.43523e6i	−0.705357	+	1.22171i	0.261205	+	0.965283i	$0.415880\pi$
$331$	−1.40598e6	+	2.43523e6i	−0.705357	+	1.22171i	−0.966562	+	0.256431i	$0.917453\pi$
$332$		0			0
$333$	1.70073e6	+	619015.i	0.840474	+	0.305908i
$334$		0			0
$335$	3.21140e6	+	5.56230e6i	1.56344	+	2.70796i
$336$		0			0
$337$	2.46777e6	+	2.07071e6i	1.18367	+	0.993217i	0.999948	+	0.0102388i	$0.00325918\pi$
$337$	2.46777e6	+	2.07071e6i	1.18367	+	0.993217i	0.183722	+	0.982978i	$0.441185\pi$
$338$		0			0
$339$	−439417.	+	2.49206e6i	−0.207672	+	1.17776i
$340$		0			0
$341$	5.00276e6			2.32983
$342$		0			0
$343$	2.33446e6			1.07140
$344$		0			0
$345$	976862.	−	5.54006e6i	0.441861	−	2.50592i
$346$		0			0
$347$	−176100.	−	147766.i	−0.0785120	−	0.0658794i	0.602687	−	0.797978i	$-0.294097\pi$
$347$	−176100.	−	147766.i	−0.0785120	−	0.0658794i	−0.681199	+	0.732098i	$0.738541\pi$
$348$		0			0
$349$	1.24243e6	+	2.15195e6i	0.546019	+	0.945733i	0.998542	+	0.0539804i	$0.0171908\pi$
$349$	1.24243e6	+	2.15195e6i	0.546019	+	0.945733i	−0.452523	+	0.891753i	$0.649476\pi$
$350$		0			0
$351$	611608.	+	222607.i	0.264975	+	0.0964431i
$352$		0			0
$353$	2.15412e6	−	3.73104e6i	0.920095	−	1.59365i	0.120829	−	0.992673i	$-0.461445\pi$
$353$	2.15412e6	−	3.73104e6i	0.920095	−	1.59365i	0.799266	−	0.600978i	$-0.205222\pi$
$354$		0			0
$355$	−242202.	−	1.37360e6i	−0.102002	−	0.578480i
$356$		0			0
$357$	1.46517e6	−	1.22942e6i	0.608439	−	0.510541i
$358$		0			0
$359$	−1.67437e6	+	609421.i	−0.685671	+	0.249564i	−0.661280	−	0.750139i	$-0.729987\pi$
$359$	−1.67437e6	+	609421.i	−0.685671	+	0.249564i	−0.0243902	+	0.999703i	$0.507764\pi$
$360$		0			0
$361$	−2.37101e6	+	713712.i	−0.957558	+	0.288240i
$362$		0			0
$363$	−4.56379e6	+	1.66108e6i	−1.81786	+	0.661645i
$364$		0			0
$365$	−3.73877e6	+	3.13720e6i	−1.46891	+	1.23257i
$366$		0			0
$367$	−676217.	−	3.83502e6i	−0.262072	−	1.48628i	−0.777245	−	0.629198i	$-0.783383\pi$
$367$	−676217.	−	3.83502e6i	−0.262072	−	1.48628i	0.515173	−	0.857086i	$-0.327728\pi$
$368$		0			0
$369$	−653070.	+	1.13115e6i	−0.249686	+	0.432468i
$370$		0			0
$371$	2.28686e6	+	832348.i	0.862590	+	0.313957i
$372$		0			0
$373$	−276825.	−	479476.i	−0.103023	−	0.178441i	0.809906	−	0.586560i	$-0.199518\pi$
$373$	−276825.	−	479476.i	−0.103023	−	0.178441i	−0.912929	+	0.408119i	$0.866185\pi$
$374$		0			0
$375$	9.89272e6	+	8.30098e6i	3.63277	+	3.04825i
$376$		0			0
$377$	177517.	−	1.00675e6i	0.0643259	−	0.364810i
$378$		0			0
$379$	−210939.			−0.0754326			−0.0377163	−	0.999288i	$-0.512008\pi$
$379$	−210939.			−0.0754326			−0.0377163	+	0.999288i	$0.512008\pi$
$380$		0			0
$381$	−2.22127e6			−0.783949
$382$		0			0
$383$	−199189.	+	1.12966e6i	−0.0693854	+	0.393504i	0.930261	+	0.366899i	$0.119581\pi$
$383$	−199189.	+	1.12966e6i	−0.0693854	+	0.393504i	−0.999646	+	0.0266047i	$0.991530\pi$
$384$		0			0
$385$	−6.10122e6	−	5.11953e6i	−2.09781	−	1.76027i
$386$		0			0
$387$	612655.	+	1.06115e6i	0.207940	+	0.360163i
$388$		0			0
$389$	784886.	+	285675.i	0.262986	+	0.0957191i	0.470148	−	0.882588i	$-0.344200\pi$
$389$	784886.	+	285675.i	0.262986	+	0.0957191i	−0.207162	+	0.978307i	$0.566423\pi$
$390$		0			0
$391$	961636.	−	1.66560e6i	0.318104	−	0.550972i
$392$		0			0
$393$	1.02342e6	+	5.80410e6i	0.334250	+	1.89563i
$394$		0			0
$395$	3.88457e6	−	3.25954e6i	1.25271	−	1.05115i
$396$		0			0
$397$	−1.91510e6	+	697041.i	−0.609840	+	0.221964i	−0.628433	−	0.777863i	$-0.716304\pi$
$397$	−1.91510e6	+	697041.i	−0.609840	+	0.221964i	0.0185931	+	0.999827i	$0.494081\pi$
$398$		0			0
$399$	−1.82864e6	−	3.38534e6i	−0.575037	−	1.06456i
$400$		0			0
$401$	317357.	−	115509.i	0.0985570	−	0.0358718i	−0.292271	−	0.956336i	$-0.594411\pi$
$401$	317357.	−	115509.i	0.0985570	−	0.0358718i	0.390828	+	0.920464i	$0.372189\pi$
$402$		0			0
$403$	4.13390e6	−	3.46875e6i	1.26794	−	1.06392i
$404$		0			0
$405$	−1.28964e6	−	7.31390e6i	−0.390688	−	2.21570i
$406$		0			0
$407$	2.87672e6	−	4.98262e6i	0.860818	−	1.49098i
$408$		0			0
$409$	−5.39634e6	−	1.96411e6i	−1.59511	−	0.580573i	−0.616693	−	0.787204i	$-0.711528\pi$
$409$	−5.39634e6	−	1.96411e6i	−1.59511	−	0.580573i	−0.978419	+	0.206631i	$0.933750\pi$
$410$		0			0
$411$	12354.1	+	21397.9i	0.00360750	+	0.00624838i
$412$		0			0
$413$	587018.	+	492567.i	0.169347	+	0.142099i
$414$		0			0
$415$	98191.4	−	556871.i	0.0279868	−	0.158721i
$416$		0			0
$417$	5.90529e6			1.66303
$418$		0			0
$419$	524284.			0.145892			0.0729460	−	0.997336i	$-0.476760\pi$
$419$	524284.			0.145892			0.0729460	+	0.997336i	$0.476760\pi$
$420$		0			0
$421$	−579910.	+	3.28883e6i	−0.159461	+	0.904350i	0.795132	+	0.606437i	$0.207402\pi$
$421$	−579910.	+	3.28883e6i	−0.159461	+	0.904350i	−0.954593	+	0.297913i	$0.903709\pi$
$422$		0			0
$423$	−544797.	−	457139.i	−0.148042	−	0.124222i
$424$		0			0
$425$	3.42974e6	+	5.94049e6i	0.921063	+	1.59533i
$426$		0			0
$427$	−1.35258e6	−	492300.i	−0.359000	−	0.130665i
$428$		0			0
$429$	−4.44166e6	+	7.69318e6i	−1.16520	+	2.01819i
$430$		0			0
$431$	−308494.	−	1.74956e6i	−0.0799933	−	0.453664i	−0.998325	−	0.0578530i	$-0.981575\pi$
$431$	−308494.	−	1.74956e6i	−0.0799933	−	0.453664i	0.918332	−	0.395811i	$-0.129537\pi$
$432$		0			0
$433$	2.70044e6	−	2.26594e6i	0.692174	−	0.580803i	−0.227362	−	0.973810i	$-0.573010\pi$
$433$	2.70044e6	−	2.26594e6i	0.692174	−	0.580803i	0.919535	+	0.393008i	$0.128565\pi$
$434$		0			0
$435$	−3.25199e6	+	1.18363e6i	−0.823998	+	0.299911i
$436$		0			0
$437$	−2.89219e6	−	2.56995e6i	−0.724476	−	0.643755i
$438$		0			0
$439$	−6.02098e6	+	2.19146e6i	−1.49110	+	0.542715i	−0.953738	−	0.300638i	$-0.902800\pi$
$439$	−6.02098e6	+	2.19146e6i	−1.49110	+	0.542715i	−0.537360	+	0.843353i	$0.680578\pi$
$440$		0			0
$441$	−486381.	+	408122.i	−0.119091	+	0.0999295i
$442$		0			0
$443$	361711.	+	2.05137e6i	0.0875695	+	0.496631i	0.996773	+	0.0802781i	$0.0255808\pi$
$443$	361711.	+	2.05137e6i	0.0875695	+	0.496631i	−0.909203	+	0.416353i	$0.863308\pi$
$444$		0			0
$445$	−3.98232e6	+	6.89758e6i	−0.953314	+	1.65119i
$446$		0			0
$447$	−9.16226e6	−	3.33479e6i	−2.16887	−	0.789404i
$448$		0			0
$449$	−442184.	−	765885.i	−0.103511	−	0.179287i	0.809618	−	0.586957i	$-0.199674\pi$
$449$	−442184.	−	765885.i	−0.103511	−	0.179287i	−0.913129	+	0.407671i	$0.866341\pi$
$450$		0			0
$451$	3.18069e6	+	2.66892e6i	0.736343	+	0.617866i
$452$		0			0
$453$	−152763.	+	866363.i	−0.0349762	+	0.198360i
$454$		0			0
$455$	−8.59131e6			−1.94550
$456$		0			0
$457$	3.93004e6			0.880250			0.440125	−	0.897937i	$-0.354934\pi$
$457$	3.93004e6			0.880250			0.440125	+	0.897937i	$0.354934\pi$
$458$		0			0
$459$	130807.	−	741842.i	0.0289800	−	0.164354i
$460$		0			0
$461$	2.43535e6	+	2.04350e6i	0.533714	+	0.447839i	0.869382	−	0.494141i	$-0.164517\pi$
$461$	2.43535e6	+	2.04350e6i	0.533714	+	0.447839i	−0.335668	+	0.941981i	$0.608962\pi$
$462$		0			0
$463$	1.27049e6	+	2.20055e6i	0.275435	+	0.477067i	0.970245	−	0.242126i	$-0.0778448\pi$
$463$	1.27049e6	+	2.20055e6i	0.275435	+	0.477067i	−0.694810	+	0.719194i	$0.744511\pi$
$464$		0			0
$465$	−1.71667e7	−	6.24816e6i	−3.68175	−	1.34005i
$466$		0			0
$467$	−388946.	+	673674.i	−0.0825272	+	0.142941i	−0.904335	−	0.426824i	$-0.859632\pi$
$467$	−388946.	+	673674.i	−0.0825272	+	0.142941i	0.821808	+	0.569765i	$0.192966\pi$
$468$		0			0
$469$	1.19196e6	+	6.75995e6i	0.250225	+	1.41909i
$470$		0			0
$471$	−2.11346e6	+	1.77340e6i	−0.438976	+	0.368345i
$472$		0			0
$473$	3.66025e6	−	1.33222e6i	0.752242	−	0.273794i
$474$		0			0
$475$	1.30955e7	−	4.35029e6i	2.66311	−	0.884676i
$476$		0			0
$477$	−3.86700e6	+	1.40747e6i	−0.778177	+	0.283233i
$478$		0			0
$479$	−1.80878e6	+	1.51775e6i	−0.360203	+	0.302246i	−0.804871	−	0.593449i	$-0.797766\pi$
$479$	−1.80878e6	+	1.51775e6i	−0.360203	+	0.302246i	0.444669	+	0.895695i	$0.353321\pi$
$480$		0			0
$481$	−1.07769e6	−	6.11189e6i	−0.212389	−	1.20452i
$482$		0			0
$483$	3.00608e6	−	5.20668e6i	0.586317	−	1.01553i
$484$		0			0
$485$	1.29080e7	+	4.69814e6i	2.49176	+	0.906925i
$486$		0			0
$487$	−4.92687e6	−	8.53359e6i	−0.941345	−	1.63046i	−0.762910	−	0.646505i	$-0.776230\pi$
$487$	−4.92687e6	−	8.53359e6i	−0.941345	−	1.63046i	−0.178435	−	0.983952i	$-0.557103\pi$
$488$		0			0
$489$	−2.65707e6	−	2.22954e6i	−0.502493	−	0.421642i
$490$		0			0
$491$	−159454.	+	904310.i	−0.0298492	+	0.169283i	−0.996088	−	0.0883640i	$-0.971836\pi$
$491$	−159454.	+	904310.i	−0.0298492	+	0.169283i	0.966239	+	0.257647i	$0.0829472\pi$
$492$		0			0
$493$	−1.18315e6			−0.219242
$494$		0			0
$495$	1.34679e7			2.47050
$496$		0			0
$497$	258848.	−	1.46800e6i	0.0470061	−	0.266585i
$498$		0			0
$499$	−541930.	−	454733.i	−0.0974298	−	0.0817533i	0.592772	−	0.805371i	$-0.298034\pi$
$499$	−541930.	−	454733.i	−0.0974298	−	0.0817533i	−0.690201	+	0.723617i	$0.742478\pi$
$500$		0			0
$501$	−1.62784e6	−	2.81950e6i	−0.289746	−	0.501855i
$502$		0			0
$503$	−4.10617e6	−	1.49452e6i	−0.723631	−	0.263380i	−0.0461643	−	0.998934i	$-0.514700\pi$
$503$	−4.10617e6	−	1.49452e6i	−0.723631	−	0.263380i	−0.677466	+	0.735554i	$0.736922\pi$
$504$		0			0
$505$	8.90169e6	−	1.54182e7i	1.55326	−	2.69032i
$506$		0			0
$507$	311385.	+	1.76595e6i	0.0537995	+	0.305112i
$508$		0			0
$509$	−3.36251e6	+	2.82148e6i	−0.575267	+	0.482706i	−0.883389	−	0.468641i	$-0.844744\pi$
$509$	−3.36251e6	+	2.82148e6i	−0.575267	+	0.482706i	0.308122	+	0.951347i	$0.400299\pi$
$510$		0			0
$511$	−4.90149e6	+	1.78400e6i	−0.830378	+	0.302233i
$512$		0			0
$513$	−1.40873e6	−	558431.i	−0.236339	−	0.0936863i
$514$		0			0
$515$	−2.51225e6	+	914384.i	−0.417392	+	0.151918i
$516$		0			0
$517$	−1.73186e6	+	1.45320e6i	−0.284962	+	0.239111i
$518$		0			0
$519$	1.18935e6	+	6.74515e6i	0.193817	+	1.09919i
$520$		0			0
$521$	4.30208e6	−	7.45141e6i	0.694358	−	1.20266i	−0.276038	−	0.961147i	$-0.589022\pi$
$521$	4.30208e6	−	7.45141e6i	0.694358	−	1.20266i	0.970397	−	0.241517i	$-0.0776451\pi$
$522$		0			0
$523$	−666456.	−	242570.i	−0.106541	−	0.0387778i	0.288200	−	0.957570i	$-0.406943\pi$
$523$	−666456.	−	242570.i	−0.106541	−	0.0387778i	−0.394741	+	0.918793i	$0.629166\pi$
$524$		0			0
$525$	1.07214e7	+	1.85700e7i	1.69767	+	2.94045i
$526$		0			0
$527$	−4.78445e6	−	4.01463e6i	−0.750423	−	0.629679i
$528$		0			0
$529$	−67857.1	+	384837.i	−0.0105428	+	0.0597912i
$530$		0			0
$531$	−1.29579e6			−0.199433
$532$		0			0
$533$	4.47883e6			0.682883
$534$		0			0
$535$	459997.	−	2.60877e6i	0.0694817	−	0.394050i
$536$		0			0
$537$	−5.81667e6	−	4.88077e6i	−0.870440	−	0.730386i
$538$		0			0
$539$	1.00919e6	+	1.74796e6i	0.149623	+	0.259155i
$540$		0			0
$541$	7.56664e6	+	2.75403e6i	1.11150	+	0.404554i	0.831544	−	0.555459i	$-0.187457\pi$
$541$	7.56664e6	+	2.75403e6i	1.11150	+	0.404554i	0.279958	+	0.960012i	$0.409680\pi$
$542$		0			0
$543$	−402423.	+	697018.i	−0.0585711	+	0.101448i
$544$		0			0
$545$	3.29979e6	+	1.87141e7i	0.475878	+	2.69884i
$546$		0			0
$547$	−2.77516e6	+	2.32864e6i	−0.396570	+	0.332762i	−0.819166	−	0.573556i	$-0.805563\pi$
$547$	−2.77516e6	+	2.32864e6i	−0.396570	+	0.332762i	0.422596	+	0.906318i	$0.361119\pi$
$548$		0			0
$549$	2.28718e6	−	832464.i	0.323869	−	0.117878i
$550$		0			0
$551$	−479558.	+	2.33133e6i	−0.0672918	+	0.327134i
$552$		0			0
$553$	5.09264e6	−	1.85357e6i	0.708158	−	0.257748i
$554$		0			0
$555$	−1.60943e7	+	1.35047e7i	−2.21789	+	1.86103i
$556$		0			0
$557$	−1.52751e6	−	8.66294e6i	−0.208615	−	1.18312i	−0.891648	−	0.452729i	$-0.850451\pi$
$557$	−1.52751e6	−	8.66294e6i	−0.208615	−	1.18312i	0.683033	−	0.730388i	$-0.260661\pi$
$558$		0			0
$559$	2.10083e6	−	3.63874e6i	0.284355	−	0.492518i
$560$		0			0
$561$	9.66125e6	+	3.51641e6i	1.29606	+	0.471729i
$562$		0			0
$563$	4.81553e6	+	8.34074e6i	0.640284	+	1.10900i	0.985369	+	0.170433i	$0.0545167\pi$
$563$	4.81553e6	+	8.34074e6i	0.640284	+	1.10900i	−0.345085	+	0.938571i	$0.612150\pi$
$564$		0			0
$565$	−1.00776e7	−	8.45614e6i	−1.32812	−	1.11443i
$566$		0			0
$567$	1.37827e6	−	7.81658e6i	0.180044	−	1.02108i
$568$		0			0
$569$	8.21966e6			1.06432			0.532161	−	0.846643i	$-0.321380\pi$
$569$	8.21966e6			1.06432			0.532161	+	0.846643i	$0.321380\pi$
$570$		0			0
$571$	5.96008e6			0.765000			0.382500	−	0.923955i	$-0.375063\pi$
$571$	5.96008e6			0.765000			0.382500	+	0.923955i	$0.375063\pi$
$572$		0			0
$573$	1.40857e6	−	7.98841e6i	0.179223	−	1.01642i
$574$		0			0
$575$	1.65174e7	+	1.38598e7i	2.08340	+	1.74818i
$576$		0			0
$577$	−2.78470e6	−	4.82324e6i	−0.348208	−	0.603113i	0.637723	−	0.770265i	$-0.279876\pi$
$577$	−2.78470e6	−	4.82324e6i	−0.348208	−	0.603113i	−0.985931	+	0.167152i	$0.946543\pi$
$578$		0			0
$579$	−2.22450e6	−	809653.i	−0.275763	−	0.100370i
$580$		0			0
$581$	302163.	−	523361.i	0.0371365	−	0.0643222i
$582$		0			0
$583$	2.27163e6	+	1.28830e7i	0.276800	+	1.56981i
$584$		0			0
$585$	1.11288e7	−	9.33819e6i	1.34450	−	1.12817i
$586$		0			0
$587$	9.34356e6	−	3.40078e6i	1.11922	−	0.407364i	0.284856	−	0.958570i	$-0.408054\pi$
$587$	9.34356e6	−	3.40078e6i	1.11922	−	0.407364i	0.834369	+	0.551206i	$0.185832\pi$
$588$		0			0
$589$	−9.84983e6	+	7.80026e6i	−1.16988	+	0.926447i
$590$		0			0
$591$	3.21147e6	−	1.16888e6i	0.378212	−	0.137658i
$592$		0			0
$593$	−1.17739e7	+	9.87946e6i	−1.37494	+	1.15371i	−0.403894	+	0.914806i	$0.632343\pi$
$593$	−1.17739e7	+	9.87946e6i	−1.37494	+	1.15371i	−0.971043	+	0.238903i	$0.923212\pi$
$594$		0			0
$595$	1.72664e6	+	9.79228e6i	0.199945	+	1.13394i
$596$		0			0
$597$	5.02815e6	−	8.70901e6i	0.577394	−	1.00008i
$598$		0			0
$599$	−6.99902e6	−	2.54744e6i	−0.797022	−	0.290092i	−0.0887702	−	0.996052i	$-0.528294\pi$
$599$	−6.99902e6	−	2.54744e6i	−0.797022	−	0.290092i	−0.708252	+	0.705960i	$0.750516\pi$
$600$		0			0
$601$	−6.85981e6	−	1.18815e7i	−0.774687	−	1.34180i	−0.934970	−	0.354726i	$-0.884574\pi$
$601$	−6.85981e6	−	1.18815e7i	−0.774687	−	1.34180i	0.160284	−	0.987071i	$-0.448759\pi$
$602$		0			0
$603$	−8.89163e6	−	7.46096e6i	−0.995837	−	0.835606i
$604$		0			0
$605$	4.38438e6	−	2.48651e7i	0.486990	−	2.76186i
$606$		0			0
$607$	4.24872e6			0.468044			0.234022	−	0.972231i	$-0.424811\pi$
$607$	4.24872e6			0.468044			0.234022	+	0.972231i	$0.424811\pi$
$608$		0			0
$609$	−3.69855e6			−0.404099
$610$		0			0
$611$	−423473.	+	2.40164e6i	−0.0458905	+	0.260258i
$612$		0			0
$613$	1.06663e7	+	8.95005e6i	1.14646	+	0.961998i	0.999631	−	0.0271629i	$-0.00864729\pi$
$613$	1.06663e7	+	8.95005e6i	1.14646	+	0.961998i	0.146834	+	0.989161i	$0.453092\pi$
$614$		0			0
$615$	−7.58105e6	−	1.31308e7i	−0.808242	−	1.39992i
$616$		0			0
$617$	1.18529e7	+	4.31411e6i	1.25347	+	0.456224i	0.881572	−	0.472050i	$-0.156486\pi$
$617$	1.18529e7	+	4.31411e6i	1.25347	+	0.456224i	0.371895	+	0.928275i	$0.378708\pi$
$618$		0			0
$619$	−600080.	+	1.03937e6i	−0.0629481	+	0.109029i	−0.895782	−	0.444494i	$-0.853384\pi$
$619$	−600080.	+	1.03937e6i	−0.0629481	+	0.109029i	0.832834	+	0.553523i	$0.186717\pi$
$620$		0			0
$621$	−411175.	−	2.33189e6i	−0.0427856	−	0.242649i
$622$		0			0
$623$	−6.52060e6	+	5.47144e6i	−0.673082	+	0.564783i
$624$		0			0
$625$	−3.73362e7	+	1.35893e7i	−3.82323	+	1.39154i
$626$		0			0
$627$	1.08448e7	−	1.76116e7i	1.10167	−	1.78908i
$628$		0			0
$629$	−6.74967e6	+	2.45668e6i	−0.680230	+	0.247583i
$630$		0			0
$631$	−1.16187e7	+	9.74921e6i	−1.16167	+	0.974756i	−0.999927	−	0.0120770i	$-0.996156\pi$
$631$	−1.16187e7	+	9.74921e6i	−1.16167	+	0.974756i	−0.161742	+	0.986833i	$0.551711\pi$
$632$		0			0
$633$	1.44921e6	+	8.21887e6i	0.143755	+	0.815273i
$634$		0			0
$635$	5.77389e6	−	1.00007e7i	0.568244	−	0.984227i
$636$		0			0
$637$	2.04590e6	+	744645.i	0.199772	+	0.0727111i
$638$		0			0
$639$	1.26032e6	+	2.18294e6i	0.122104	+	0.211490i
$640$		0			0
$641$	8.64196e6	+	7.25147e6i	0.830744	+	0.697077i	0.955462	−	0.295115i	$-0.0953580\pi$
$641$	8.64196e6	+	7.25147e6i	0.830744	+	0.697077i	−0.124717	+	0.992192i	$0.539802\pi$
$642$		0			0
$643$	−1.25941e6	+	7.14247e6i	−0.120127	+	0.681273i	0.863957	+	0.503566i	$0.167979\pi$
$643$	−1.25941e6	+	7.14247e6i	−0.120127	+	0.681273i	−0.984083	+	0.177707i	$0.943132\pi$
$644$		0			0
$645$	−1.42238e7			−1.34622
$646$		0			0
$647$	−6.97273e6			−0.654850			−0.327425	−	0.944877i	$-0.606181\pi$
$647$	−6.97273e6			−0.654850			−0.327425	+	0.944877i	$0.606181\pi$
$648$		0			0
$649$	−715289.	+	4.05661e6i	−0.0666607	+	0.378052i
$650$		0			0
$651$	−1.49562e7	−	1.25498e7i	−1.38315	−	1.16060i
$652$		0			0
$653$	−1.03642e7	−	1.79513e7i	−0.951159	−	1.64746i	−0.742922	−	0.669378i	$-0.766561\pi$
$653$	−1.03642e7	−	1.79513e7i	−0.951159	−	1.64746i	−0.208237	−	0.978078i	$-0.566773\pi$
$654$		0			0
$655$	−2.87917e7	−	1.04793e7i	−2.62219	−	0.954399i
$656$		0			0
$657$	4.41009e6	−	7.63851e6i	0.398597	−	0.690391i
$658$		0			0
$659$	2.24220e6	+	1.27162e7i	0.201123	+	1.14062i	0.903425	+	0.428745i	$0.141044\pi$
$659$	2.24220e6	+	1.27162e7i	0.201123	+	1.14062i	−0.702303	+	0.711878i	$0.747845\pi$
$660$		0			0
$661$	1.04863e7	−	8.79909e6i	0.933513	−	0.783311i	−0.0429314	−	0.999078i	$-0.513670\pi$
$661$	1.04863e7	−	8.79909e6i	0.933513	−	0.783311i	0.976445	+	0.215767i	$0.0692252\pi$
$662$		0			0
$663$	1.04215e7	−	3.79311e6i	0.920759	−	0.335129i
$664$		0			0
$665$	1.99949e7	+	566779.i	1.75334	+	0.0497004i
$666$		0			0
$667$	−3.49481e6	+	1.27201e6i	−0.304165	+	0.110707i
$668$		0			0
$669$	−7.25102e6	+	6.08433e6i	−0.626375	+	0.525591i
$670$		0			0
$671$	−1.34358e6	−	7.61980e6i	−0.115201	−	0.653337i
$672$		0			0
$673$	2.63236e6	−	4.55939e6i	0.224031	−	0.388033i	−0.731997	−	0.681308i	$-0.761412\pi$
$673$	2.63236e6	−	4.55939e6i	0.224031	−	0.388033i	0.956028	+	0.293274i	$0.0947450\pi$
$674$		0			0
$675$	7.93585e6	+	2.88841e6i	0.670400	+	0.244006i
$676$		0			0
$677$	−363309.	−	629270.i	−0.0304652	−	0.0527673i	0.850391	−	0.526152i	$-0.176366\pi$
$677$	−363309.	−	629270.i	−0.0304652	−	0.0527673i	−0.880856	+	0.473384i	$0.843032\pi$
$678$		0			0
$679$	1.12459e7	+	9.43647e6i	0.936098	+	0.785480i
$680$		0			0
$681$	−5.19327e6	+	2.94525e7i	−0.429115	+	2.43363i
$682$		0			0
$683$	−1.46770e7			−1.20388			−0.601942	−	0.798540i	$-0.705606\pi$
$683$	−1.46770e7			−1.20388			−0.601942	+	0.798540i	$0.705606\pi$
$684$		0			0
$685$	−128452.			−0.0104596
$686$		0			0
$687$	3.80699e6	−	2.15905e7i	0.307744	−	1.74530i
$688$		0			0
$689$	1.08098e7	+	9.07050e6i	0.867500	+	0.727919i
$690$		0			0
$691$	7.31140e6	+	1.26637e7i	0.582513	+	1.00894i	0.995180	+	0.0980601i	$0.0312637\pi$
$691$	7.31140e6	+	1.26637e7i	0.582513	+	1.00894i	−0.412668	+	0.910882i	$0.635403\pi$
$692$		0			0
$693$	1.35255e7	+	4.92286e6i	1.06984	+	0.389390i
$694$		0			0
$695$	−1.53500e7	+	2.65870e7i	−1.20544	+	2.08789i
$696$		0			0
$697$	−900134.	−	5.10491e6i	−0.0701819	−	0.398021i
$698$		0			0
$699$	−8.34009e6	+	6.99817e6i	−0.645621	+	0.541741i
$700$		0			0
$701$	−3.42531e6	+	1.24671e6i	−0.263272	+	0.0958232i	−0.470284	−	0.882515i	$-0.655848\pi$
$701$	−3.42531e6	+	1.24671e6i	−0.263272	+	0.0958232i	0.207012	+	0.978338i	$0.433626\pi$
$702$		0			0
$703$	2.10495e6	+	1.42956e7i	0.160640	+	1.09097i
$704$		0			0
$705$	7.75776e6	−	2.82359e6i	0.587846	−	0.213958i
$706$		0			0
$707$	1.45755e7	−	1.22303e7i	1.09667	−	0.920214i
$708$		0			0
$709$	−1.50845e6	−	8.55486e6i	−0.112698	−	0.639142i	−0.987864	−	0.155320i	$-0.950359\pi$
$709$	−1.50845e6	−	8.55486e6i	−0.112698	−	0.639142i	0.875166	−	0.483822i	$-0.160752\pi$
$710$		0			0
$711$	−4.58208e6	+	7.93639e6i	−0.339929	+	0.588775i
$712$		0			0
$713$	−1.84485e7	−	6.71470e6i	−1.35906	−	0.494656i
$714$		0			0
$715$	−2.30910e7	−	3.99948e7i	−1.68919	−	2.92576i
$716$		0			0
$717$	−670031.	−	562223.i	−0.0486740	−	0.0408423i
$718$		0			0
$719$	−2.29895e6	+	1.30380e7i	−0.165847	+	0.940566i	0.782339	+	0.622852i	$0.214026\pi$
$719$	−2.29895e6	+	1.30380e7i	−0.165847	+	0.940566i	−0.948187	+	0.317714i	$0.897085\pi$
$720$		0			0
$721$	−2.85723e6			−0.204695
$722$		0			0
$723$	2.21837e7			1.57829
$724$		0			0
$725$	2.30335e6	−	1.30629e7i	0.162748	−	0.922987i
$726$		0			0
$727$	2.22708e6	+	1.86874e6i	0.156279	+	0.131133i	0.717574	−	0.696482i	$-0.245252\pi$
$727$	2.22708e6	+	1.86874e6i	0.156279	+	0.131133i	−0.561296	+	0.827615i	$0.689697\pi$
$728$		0			0
$729$	4.25611e6	+	7.37180e6i	0.296616	+	0.513753i
$730$		0			0
$731$	−4.56961e6	−	1.66320e6i	−0.316290	−	0.115120i
$732$		0			0
$733$	−544211.	+	942601.i	−0.0374117	+	0.0647989i	−0.884125	−	0.467251i	$-0.845245\pi$
$733$	−544211.	+	942601.i	−0.0374117	+	0.0647989i	0.846713	+	0.532049i	$0.178578\pi$
$734$		0			0
$735$	−1.27986e6	−	7.25845e6i	−0.0873865	−	0.495593i
$736$		0			0
$737$	−2.82657e7	+	2.37177e7i	−1.91686	+	1.60844i
$738$		0			0
$739$	−3.62337e6	+	1.31880e6i	−0.244063	+	0.0888316i	−0.461155	−	0.887319i	$-0.652565\pi$
$739$	−3.62337e6	+	1.31880e6i	−0.244063	+	0.0888316i	0.217092	+	0.976151i	$0.430343\pi$
$740$		0			0
$741$	−3.25004e6	−	2.20724e7i	−0.217442	−	1.47674i
$742$		0			0
$743$	2.15124e6	−	782987.i	0.142961	−	0.0520334i	−0.269549	−	0.962987i	$-0.586875\pi$
$743$	2.15124e6	−	782987.i	0.142961	−	0.0520334i	0.412510	+	0.910953i	$0.364652\pi$
$744$		0			0
$745$	3.88301e7	−	3.25824e7i	2.56318	−	2.15076i
$746$		0			0
$747$	177450.	+	1.00637e6i	0.0116352	+	0.0659867i
$748$		0			0
$749$	1.41554e6	−	2.45179e6i	0.0921972	−	0.159690i
$750$		0			0
$751$	1.81046e6	+	658954.i	0.117136	+	0.0426339i	0.399923	−	0.916549i	$-0.369037\pi$
$751$	1.81046e6	+	658954.i	0.117136	+	0.0426339i	−0.282787	+	0.959183i	$0.591259\pi$
$752$		0			0
$753$	1.59333e7	+	2.75973e7i	1.02404	+	1.77369i
$754$		0			0
$755$	−3.50349e6	−	2.93978e6i	−0.223683	−	0.187692i
$756$		0			0
$757$	−1.30252e6	+	7.38697e6i	−0.0826124	+	0.468518i	0.915234	+	0.402923i	$0.132006\pi$
$757$	−1.30252e6	+	7.38697e6i	−0.0826124	+	0.468518i	−0.997846	+	0.0655954i	$0.979105\pi$
$758$		0			0
$759$	3.23180e7			2.03629
$760$		0			0
$761$	−170158.			−0.0106510			−0.00532552	−	0.999986i	$-0.501695\pi$
$761$	−170158.			−0.0106510			−0.00532552	+	0.999986i	$0.501695\pi$
$762$		0			0
$763$	−3.52659e6	+	2.00003e7i	−0.219302	+	1.24373i
$764$		0			0
$765$	−1.28802e7	−	1.08077e7i	−0.795734	−	0.667700i
$766$		0			0
$767$	2.22166e6	+	3.84803e6i	0.136361	+	0.236184i
$768$		0			0
$769$	2.51964e7	+	9.17074e6i	1.53646	+	0.559227i	0.965194	−	0.261535i	$-0.0842286\pi$
$769$	2.51964e7	+	9.17074e6i	1.53646	+	0.559227i	0.571270	+	0.820762i	$0.306451\pi$
$770$		0			0
$771$	−1.70597e7	+	2.95483e7i	−1.03356	+	1.79018i
$772$		0			0
$773$	−1.27917e6	−	7.25451e6i	−0.0769978	−	0.436676i	−0.998798	−	0.0490113i	$-0.984393\pi$
$773$	−1.27917e6	−	7.25451e6i	−0.0769978	−	0.436676i	0.921800	−	0.387665i	$-0.126718\pi$
$774$		0			0
$775$	5.36390e7	−	4.50084e7i	3.20794	−	2.69178i
$776$		0			0
$777$	−2.10995e7	+	7.67959e6i	−1.25378	+	0.456337i
$778$		0			0
$779$	−1.04238e7	−	295473.i	−0.615433	−	0.0174452i
$780$		0			0
$781$	7.52965e6	−	2.74057e6i	0.441720	−	0.160773i
$782$		0			0
$783$	−1.11586e6	+	936321.i	−0.0650439	+	0.0545783i
$784$		0			0
$785$	−2.49062e6	−	1.41250e7i	−0.144256	−	0.818116i
$786$		0			0
$787$	−1.02494e7	+	1.77524e7i	−0.589875	+	1.02169i	0.404374	+	0.914594i	$0.367489\pi$
$787$	−1.02494e7	+	1.77524e7i	−0.589875	+	1.02169i	−0.994248	+	0.107099i	$0.965844\pi$
$788$		0			0
$789$	1.87394e7	+	6.82058e6i	1.07168	+	0.390058i
$790$		0			0
$791$	−7.02979e6	−	1.21760e7i	−0.399486	−	0.691929i
$792$		0			0
$793$	−6.39356e6	−	5.36483e6i	−0.361044	−	0.302952i
$794$		0			0
$795$	8.29523e6	−	4.70446e7i	0.465491	−	2.63993i
$796$		0			0
$797$	3.03226e7			1.69091			0.845456	−	0.534045i	$-0.179329\pi$
$797$	3.03226e7			1.69091			0.845456	+	0.534045i	$0.179329\pi$
$798$		0			0
$799$	2.82246e6			0.156409
$800$		0			0
$801$	2.49942e6	−	1.41749e7i	0.137644	−	0.780620i
$802$		0			0
$803$	−2.14788e7	−	1.80229e7i	−1.17550	−	0.986358i
$804$		0			0
$805$	1.56278e7	+	2.70682e7i	0.849981	+	1.47221i
$806$		0			0
$807$	1.36149e7	+	4.95544e6i	0.735923	+	0.267854i
$808$		0			0
$809$	7.77348e6	−	1.34641e7i	0.417584	−	0.723277i	−0.578112	−	0.815958i	$-0.696210\pi$
$809$	7.77348e6	−	1.34641e7i	0.417584	−	0.723277i	0.995696	+	0.0926807i	$0.0295436\pi$
$810$		0			0
$811$	4.88755e6	+	2.77187e7i	0.260939	+	1.47986i	0.780355	+	0.625337i	$0.215038\pi$
$811$	4.88755e6	+	2.77187e7i	0.260939	+	1.47986i	−0.519416	+	0.854521i	$0.673851\pi$
$812$		0			0
$813$	−2.92370e7	+	2.45328e7i	−1.55134	+	1.30173i
$814$		0			0
$815$	1.69447e7	−	6.16735e6i	0.893591	−	0.325240i
$816$		0			0
$817$	−5.12940e6	+	8.33001e6i	−0.268851	+	0.436607i
$818$		0			0
$819$	1.45898e7	−	5.31024e6i	0.760044	−	0.276633i
$820$		0			0
$821$	9.26473e6	−	7.77403e6i	0.479705	−	0.402521i	−0.370614	−	0.928787i	$-0.620853\pi$
$821$	9.26473e6	−	7.77403e6i	0.479705	−	0.402521i	0.850320	+	0.526266i	$0.176408\pi$
$822$		0			0
$823$	190625.	+	1.08109e6i	0.00981027	+	0.0556368i	0.989320	−	0.145760i	$-0.0465629\pi$
$823$	190625.	+	1.08109e6i	0.00981027	+	0.0556368i	−0.979510	+	0.201397i	$0.935452\pi$
$824$		0			0
$825$	−5.76323e7	+	9.98220e7i	−2.94802	+	5.10612i
$826$		0			0
$827$	1.52717e7	+	5.55843e6i	0.776467	+	0.282611i	0.699698	−	0.714438i	$-0.253318\pi$
$827$	1.52717e7	+	5.55843e6i	0.776467	+	0.282611i	0.0767681	+	0.997049i	$0.475540\pi$
$828$		0			0
$829$	9.84609e6	+	1.70539e7i	0.497597	+	0.861863i	0.999996	−	0.00277304i	$-0.000882687\pi$
$829$	9.84609e6	+	1.70539e7i	0.497597	+	0.861863i	−0.502400	+	0.864636i	$0.667549\pi$
$830$		0			0
$831$	1.75828e7	+	1.47538e7i	0.883255	+	0.741139i
$832$		0			0
$833$	437563.	−	2.48154e6i	0.0218488	−	0.123911i
$834$		0			0
$835$	1.69254e7			0.840086
$836$		0			0
$837$	−7.68943e6			−0.379385
$838$		0			0
$839$	1.25283e6	−	7.10518e6i	0.0614453	−	0.348474i	−0.938549	−	0.345146i	$-0.887830\pi$
$839$	1.25283e6	−	7.10518e6i	0.0614453	−	0.348474i	0.999994	−	0.00332811i	$-0.00105937\pi$
$840$		0			0
$841$	−1.39598e7	−	1.17137e7i	−0.680596	−	0.571088i
$842$		0			0
$843$	−8.54356e6	−	1.47979e7i	−0.414066	−	0.717184i
$844$		0			0
$845$	−8.76016e6	−	3.18844e6i	−0.422056	−	0.153616i
$846$		0			0
$847$	1.34920e7	−	2.33688e7i	0.646201	−	1.11925i
$848$		0			0
$849$	−6.13798e6	−	3.48102e7i	−0.292251	−	1.65744i
$850$		0			0
$851$	−1.72961e7	+	1.45131e7i	−0.818697	+	0.686969i
$852$		0			0
$853$	−2.78616e7	+	1.01408e7i	−1.31109	+	0.477199i	−0.900594	−	0.434662i	$-0.856868\pi$
$853$	−2.78616e7	+	1.01408e7i	−1.31109	+	0.477199i	−0.410500	+	0.911861i	$0.634646\pi$
$854$		0			0
$855$	−2.65166e7	+	2.09990e7i	−1.24052	+	0.982388i
$856$		0			0
$857$	−3.56746e7	+	1.29845e7i	−1.65923	+	0.603911i	−0.990242	−	0.139360i	$-0.955496\pi$
$857$	−3.56746e7	+	1.29845e7i	−1.65923	+	0.603911i	−0.668991	+	0.743271i	$0.733273\pi$
$858$		0			0
$859$	2.19021e7	−	1.83781e7i	1.01275	−	0.849800i	0.0240525	−	0.999711i	$-0.492343\pi$
$859$	2.19021e7	−	1.83781e7i	1.01275	−	0.849800i	0.988700	+	0.149911i	$0.0478987\pi$
$860$		0			0
$861$	−2.81383e6	−	1.59580e7i	−0.129357	−	0.733619i
$862$		0			0
$863$	2.01235e7	−	3.48550e7i	0.919766	−	1.59308i	0.119997	−	0.992774i	$-0.461712\pi$
$863$	2.01235e7	−	3.48550e7i	0.919766	−	1.59308i	0.799769	−	0.600307i	$-0.204955\pi$
$864$		0			0
$865$	−3.34599e7	−	1.21784e7i	−1.52049	−	0.553414i
$866$		0			0
$867$	8.47538e6	+	1.46798e7i	0.382923	+	0.663242i
$868$		0			0
$869$	2.23164e7	+	1.87257e7i	1.00248	+	0.841180i
$870$		0			0
$871$	−6.91150e6	+	3.91971e7i	−0.308693	+	1.75069i
$872$		0			0
$873$	−2.48243e7			−1.10241
$874$		0			0
$875$	−7.17510e7			−3.16817
$876$		0			0
$877$	−2.28743e6	+	1.29726e7i	−0.100426	+	0.569547i	0.892522	+	0.451003i	$0.148934\pi$
$877$	−2.28743e6	+	1.29726e7i	−0.100426	+	0.569547i	−0.992949	+	0.118544i	$0.962177\pi$
$878$		0			0
$879$	1.43785e7	+	1.20650e7i	0.627683	+	0.526688i
$880$		0			0
$881$	−1.78039e7	−	3.08372e7i	−0.772813	−	1.33855i	−0.936015	−	0.351959i	$-0.885516\pi$
$881$	−1.78039e7	−	3.08372e7i	−0.772813	−	1.33855i	0.163202	−	0.986593i	$-0.447818\pi$
$882$		0			0
$883$	1.42165e7	+	5.17437e6i	0.613606	+	0.223334i	0.630081	−	0.776530i	$-0.283022\pi$
$883$	1.42165e7	+	5.17437e6i	0.613606	+	0.223334i	−0.0164741	+	0.999864i	$0.505244\pi$
$884$		0			0
$885$	7.52095e6	−	1.30267e7i	0.322786	−	0.559082i
$886$		0			0
$887$	−7.60616e6	−	4.31367e7i	−0.324606	−	1.84093i	−0.512431	−	0.858729i	$-0.671255\pi$
$887$	−7.60616e6	−	4.31367e7i	−0.324606	−	1.84093i	0.187825	−	0.982203i	$-0.439856\pi$
$888$		0			0
$889$	9.45411e6	−	7.93294e6i	0.401205	−	0.336651i
$890$		0			0
$891$	4.00927e7	−	1.45925e7i	1.69188	−	0.615795i
$892$		0			0
$893$	1.14401e6	−	5.56149e6i	0.0480064	−	0.233379i
$894$		0			0
$895$	3.70941e7	−	1.35011e7i	1.54792	−	0.563395i
$896$		0			0
$897$	2.67051e7	−	2.24083e7i	1.10819	−	0.929881i
$898$		0			0
$899$	2.09723e6	+	1.18940e7i	0.0865460	+	0.490827i
$900$		0			0
$901$	8.16594e6	−	1.41438e7i	0.335115	−	0.580437i
$902$		0			0
$903$	−1.42846e7	−	5.19918e6i	−0.582975	−	0.212186i
$904$		0			0
$905$	−2.09210e6	−	3.62362e6i	−0.0849102	−	0.147069i
$906$		0			0
$907$	−1.76046e7	−	1.47720e7i	−0.710571	−	0.596240i	0.214188	−	0.976792i	$-0.431289\pi$
$907$	−1.76046e7	−	1.47720e7i	−0.710571	−	0.596240i	−0.924759	+	0.380552i	$0.875734\pi$
$908$		0			0
$909$	−5.58696e6	+	3.16852e7i	−0.224267	+	1.27188i
$910$		0			0
$911$	−3.73713e7			−1.49191			−0.745955	−	0.665997i	$-0.768006\pi$
$911$	−3.73713e7			−1.49191			−0.745955	+	0.665997i	$0.768006\pi$
$912$		0			0
$913$	3.24851e6			0.128976
$914$		0			0
$915$	−4.90630e6	+	2.78250e7i	−0.193732	+	1.09871i
$916$		0			0
$917$	−2.50844e7	−	2.10483e7i	−0.985099	−	0.826596i
$918$		0			0
$919$	1.05977e7	+	1.83558e7i	0.413927	+	0.716942i	0.995315	−	0.0966840i	$-0.0308236\pi$
$919$	1.05977e7	+	1.83558e7i	0.413927	+	0.716942i	−0.581388	+	0.813626i	$0.697490\pi$
$920$		0			0
$921$	1.17789e7	+	4.28718e6i	0.457570	+	0.166542i
$922$		0			0
$923$	4.32171e6	−	7.48542e6i	0.166975	−	0.289209i
$924$		0			0
$925$	−1.39835e7	−	7.93042e7i	−0.537354	−	3.04749i
$926$		0			0
$927$	3.70113e6	−	3.10561e6i	0.141460	−	0.118699i
$928$		0			0
$929$	3.44216e7	−	1.25284e7i	1.30855	−	0.476274i	0.408780	−	0.912633i	$-0.365954\pi$
$929$	3.44216e7	−	1.25284e7i	1.30855	−	0.476274i	0.899773	+	0.436359i	$0.143732\pi$
$930$		0			0
$931$	−4.71237e6	−	1.86801e6i	−0.178183	−	0.0706327i
$932$		0			0
$933$	−1.83918e7	+	6.69405e6i	−0.691702	+	0.251759i
$934$		0			0
$935$	−4.09449e7	+	3.43569e7i	−1.53169	+	1.28524i
$936$		0			0
$937$	−1.54093e6	−	8.73905e6i	−0.0573369	−	0.325173i	0.942625	−	0.333852i	$-0.108349\pi$
$937$	−1.54093e6	−	8.73905e6i	−0.0573369	−	0.325173i	−0.999962	+	0.00867859i	$0.997237\pi$
$938$		0			0
$939$	1.26131e7	−	2.18465e7i	0.466829	−	0.808572i
$940$		0			0
$941$	3.88967e7	+	1.41572e7i	1.43199	+	0.521200i	0.937500	−	0.347986i	$-0.113134\pi$
$941$	3.88967e7	+	1.41572e7i	1.43199	+	0.521200i	0.494486	+	0.869186i	$0.335356\pi$
$942$		0			0
$943$	−8.14711e6	−	1.41112e7i	−0.298349	−	0.516755i
$944$		0			0
$945$	9.37782e6	+	7.86893e6i	0.341604	+	0.286639i
$946$		0			0
$947$	980220.	−	5.55910e6i	0.0355180	−	0.201433i	−0.961885	−	0.273454i	$-0.911834\pi$
$947$	980220.	−	5.55910e6i	0.0355180	−	0.201433i	0.997403	+	0.0720214i	$0.0229450\pi$
$948$		0			0
$949$	−3.02449e7			−1.09015
$950$		0			0
$951$	−3.88394e7			−1.39258
$952$		0			0
$953$	−9.24319e6	+	5.24207e7i	−0.329678	+	1.86969i	0.144849	+	0.989454i	$0.453730\pi$
$953$	−9.24319e6	+	5.24207e7i	−0.329678	+	1.86969i	−0.474527	+	0.880241i	$0.657381\pi$
$954$		0			0
$955$	3.23044e7	+	2.71066e7i	1.14618	+	0.961759i
$956$		0			0
$957$	−9.94066e6	−	1.72177e7i	−0.350861	−	0.607710i
$958$		0			0
$959$	−129001.	−	46952.5i	−0.00452946	−	0.00164859i
$960$		0			0
$961$	−1.75628e7	+	3.04197e7i	−0.613460	+	1.06254i
$962$		0			0
$963$	831300.	+	4.71454e6i	0.0288863	+	0.163822i
$964$		0			0
$965$	9.42756e6	−	7.91066e6i	0.325898	−	0.273460i
$966$		0			0
$967$	−9.92120e6	+	3.61102e6i	−0.341191	+	0.124183i	−0.506932	−	0.861986i	$-0.669221\pi$
$967$	−9.92120e6	+	3.61102e6i	−0.341191	+	0.124183i	0.165741	+	0.986169i	$0.446998\pi$
$968$		0			0
$969$	−2.45046e7	+	8.14036e6i	−0.838375	+	0.278506i
$970$		0			0
$971$	1.04641e7	−	3.80862e6i	0.356167	−	0.129634i	−0.157739	−	0.987481i	$-0.550420\pi$
$971$	1.04641e7	−	3.80862e6i	0.356167	−	0.129634i	0.513906	+	0.857847i	$0.328198\pi$
$972$		0			0
$973$	−2.51340e7	+	2.10899e7i	−0.851097	+	0.714155i
$974$		0			0
$975$	2.15905e7	+	1.22446e8i	0.727362	+	4.12508i
$976$		0			0
$977$	6.07125e6	−	1.05157e7i	0.203489	−	0.352454i	−0.746161	−	0.665765i	$-0.768105\pi$
$977$	6.07125e6	−	1.05157e7i	0.203489	−	0.352454i	0.949650	+	0.313312i	$0.101438\pi$
$978$		0			0
$979$	−4.29965e7	−	1.56495e7i	−1.43376	−	0.521846i
$980$		0			0
$981$	−1.71708e7	−	2.97406e7i	−0.569662	−	0.986684i
$982$		0			0
$983$	−1.08445e7	−	9.09963e6i	−0.357953	−	0.300359i	0.446021	−	0.895023i	$-0.352841\pi$
$983$	−1.08445e7	−	9.09963e6i	−0.357953	−	0.300359i	−0.803974	+	0.594664i	$0.797285\pi$
$984$		0			0
$985$	−3.08522e6	+	1.74972e7i	−0.101320	+	0.574615i
$986$		0			0
$987$	8.82304e6			0.288287
$988$		0			0
$989$	−1.52859e7			−0.496935
$990$		0			0
$991$	−6.27622e6	+	3.55942e7i	−0.203008	+	1.15132i	0.697535	+	0.716551i	$0.254280\pi$
$991$	−6.27622e6	+	3.55942e7i	−0.203008	+	1.15132i	−0.900543	+	0.434766i	$0.856831\pi$
$992$		0			0
$993$	4.51893e7	+	3.79184e7i	1.45433	+	1.22033i
$994$		0			0
$995$	2.61401e7	+	4.52759e7i	0.837045	+	1.44980i
$996$		0			0
$997$	−1.32682e7	−	4.82923e6i	−0.422741	−	0.153865i	0.121885	−	0.992544i	$-0.461106\pi$
$997$	−1.32682e7	−	4.82923e6i	−0.422741	−	0.153865i	−0.544626	+	0.838679i	$0.683328\pi$
$998$		0			0
$999$	−4.42163e6	+	7.65849e6i	−0.140174	+	0.242789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.i.a.5.7	✓	48
19.4	even	9	inner	76.6.i.a.61.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.i.a.5.7	✓	48	1.1	even	1	trivial
76.6.i.a.61.7	yes	48	19.4	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)

\(f(q)\)	\(=\)	\(q+(3.64287 - 20.6597i) q^{3} +(83.5459 + 70.1033i) q^{5} +(58.2786 + 100.941i) q^{7} +(-185.208 - 67.4103i) q^{9} +O(q^{10})\)	\(q+(3.64287 - 20.6597i) q^{3} +(83.5459 + 70.1033i) q^{5} +(58.2786 + 100.941i) q^{7} +(-185.208 - 67.4103i) q^{9} +(-313.273 + 542.605i) q^{11} +(117.360 + 665.581i) q^{13} +(1752.66 - 1470.66i) q^{15} +(735.035 - 267.531i) q^{17} +(-229.227 - 1556.78i) q^{19} +(2297.72 - 836.303i) q^{21} +(1883.53 - 1580.47i) q^{23} +(1522.79 + 8636.17i) q^{25} +(481.513 - 834.005i) q^{27} +(-1421.36 - 517.334i) q^{29} +(-3992.33 - 6914.92i) q^{31} +(10068.8 + 8448.77i) q^{33} +(-2207.40 + 12518.8i) q^{35} -9182.79 q^{37} +14178.2 q^{39} +(1150.76 - 6526.29i) q^{41} +(-4762.40 - 3996.13i) q^{43} +(-10747.7 - 18615.6i) q^{45} +(3390.72 + 1234.12i) q^{47} +(1610.71 - 2789.84i) q^{49} +(-2849.48 - 16160.2i) q^{51} +(15994.4 - 13420.9i) q^{53} +(-64211.1 + 23370.9i) q^{55} +(-32997.6 - 935.355i) q^{57} +(6177.95 - 2248.59i) q^{59} +(-9460.05 + 7937.92i) q^{61} +(-3989.18 - 22623.8i) q^{63} +(-36854.5 + 63833.9i) q^{65} +(55339.9 + 20142.1i) q^{67} +(-25790.6 - 44670.6i) q^{69} +(-9796.94 - 8220.61i) q^{71} +(-7770.94 + 44071.2i) q^{73} +183968. q^{75} -73028.4 q^{77} +(8073.99 - 45789.9i) q^{79} +(-52165.1 - 43771.7i) q^{81} +(-2592.40 - 4490.17i) q^{83} +(80163.9 + 29177.3i) q^{85} +(-15865.8 + 27480.4i) q^{87} +(12681.3 + 71919.5i) q^{89} +(-60345.1 + 50635.6i) q^{91} +(-157404. + 57290.3i) q^{93} +(89984.2 - 146132. i) q^{95} +(118356. - 43077.9i) q^{97} +(94597.8 - 79377.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) \) 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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