LMFDB - Embedded newform 76.6.i.a.17.1

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			17.1
Character	$\chi$	$=$	76.17
Dual form			76.6.i.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-16.5327 - 13.8726i) q^{3} +(17.0893 - 6.21998i) q^{5} +(-92.6180 - 160.419i) q^{7} +(38.6850 + 219.393i) q^{9} +O(q^{10})$	\(q+(-16.5327 - 13.8726i) q^{3} +(17.0893 - 6.21998i) q^{5} +(-92.6180 - 160.419i) q^{7} +(38.6850 + 219.393i) q^{9} +(107.339 - 185.917i) q^{11} +(-318.074 + 266.896i) q^{13} +(-368.819 - 134.239i) q^{15} +(-270.266 + 1532.75i) q^{17} +(-287.327 + 1547.11i) q^{19} +(-694.201 + 3937.01i) q^{21} +(1754.94 + 638.746i) q^{23} +(-2140.53 + 1796.12i) q^{25} +(-218.216 + 377.960i) q^{27} +(-754.646 - 4279.81i) q^{29} +(-2536.15 - 4392.74i) q^{31} +(-4353.75 + 1584.63i) q^{33} +(-2580.58 - 2165.36i) q^{35} +33.9163 q^{37} +8961.15 q^{39} +(9726.48 + 8161.49i) q^{41} +(-4690.09 + 1707.05i) q^{43} +(2025.72 + 3508.65i) q^{45} +(-2242.48 - 12717.7i) q^{47} +(-8752.70 + 15160.1i) q^{49} +(25731.4 - 21591.2i) q^{51} +(-24560.0 - 8939.11i) q^{53} +(677.947 - 3844.83i) q^{55} +(26212.6 - 21591.9i) q^{57} +(-3322.45 + 18842.6i) q^{59} +(29662.1 + 10796.1i) q^{61} +(31612.0 - 26525.6i) q^{63} +(-3775.56 + 6539.47i) q^{65} +(-5288.86 - 29994.6i) q^{67} +(-20152.8 - 34905.7i) q^{69} +(-34086.9 + 12406.6i) q^{71} +(-62821.4 - 52713.4i) q^{73} +60305.6 q^{75} -39766.1 q^{77} +(8486.16 + 7120.74i) q^{79} +(59721.3 - 21736.8i) q^{81} +(7468.07 + 12935.1i) q^{83} +(4915.05 + 27874.6i) q^{85} +(-46895.7 + 81225.7i) q^{87} +(-73562.7 + 61726.4i) q^{89} +(72274.6 + 26305.8i) q^{91} +(-19009.2 + 107807. i) q^{93} +(4712.78 + 28226.1i) q^{95} +(-11066.5 + 62761.3i) q^{97} +(44941.3 + 16357.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

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
$3$	−16.5327	−	13.8726i	−1.06057	−	0.889926i	−0.0664069	−	0.997793i	$-0.521154\pi$
$3$	−16.5327	−	13.8726i	−1.06057	−	0.889926i	−0.994165	+	0.107867i	$0.965598\pi$
$4$		0			0
$5$	17.0893	−	6.21998i	0.305702	−	0.111266i	−0.184614	−	0.982811i	$-0.559104\pi$
$5$	17.0893	−	6.21998i	0.305702	−	0.111266i	0.490316	+	0.871545i	$0.336881\pi$
$6$		0			0
$7$	−92.6180	−	160.419i	−0.714415	−	1.23740i	−0.963185	−	0.268840i	$-0.913360\pi$
$7$	−92.6180	−	160.419i	−0.714415	−	1.23740i	0.248770	−	0.968563i	$-0.419974\pi$
$8$		0			0
$9$	38.6850	+	219.393i	0.159197	+	0.902854i
$10$		0			0
$11$	107.339	−	185.917i	0.267471	−	0.463273i	−0.700737	−	0.713419i	$-0.747146\pi$
$11$	107.339	−	185.917i	0.267471	−	0.463273i	0.968208	+	0.250147i	$0.0804788\pi$
$12$		0			0
$13$	−318.074	+	266.896i	−0.521999	+	0.438009i	−0.865328	−	0.501206i	$-0.832890\pi$
$13$	−318.074	+	266.896i	−0.521999	+	0.438009i	0.343329	+	0.939215i	$0.388445\pi$
$14$		0			0
$15$	−368.819	−	134.239i	−0.423238	−	0.154046i
$16$		0			0
$17$	−270.266	+	1532.75i	−0.226813	+	1.28632i	0.632375	+	0.774662i	$0.282080\pi$
$17$	−270.266	+	1532.75i	−0.226813	+	1.28632i	−0.859188	+	0.511659i	$0.829031\pi$
$18$		0			0
$19$	−287.327	+	1547.11i	−0.182596	+	0.983188i
$19$	−287.327	+	1547.11i	−0.182596	+	0.983188i
$20$		0			0
$21$	−694.201	+	3937.01i	−0.343508	+	1.94813i
$22$		0			0
$23$	1754.94	+	638.746i	0.691740	+	0.251773i	0.663880	−	0.747839i	$-0.268909\pi$
$23$	1754.94	+	638.746i	0.691740	+	0.251773i	0.0278598	+	0.999612i	$0.491131\pi$
$24$		0			0
$25$	−2140.53	+	1796.12i	−0.684971	+	0.574759i
$26$		0			0
$27$	−218.216	+	377.960i	−0.0576071	+	0.0997785i
$28$		0			0
$29$	−754.646	−	4279.81i	−0.166628	−	0.944995i	−0.947370	−	0.320141i	$-0.896270\pi$
$29$	−754.646	−	4279.81i	−0.166628	−	0.944995i	0.780742	−	0.624854i	$-0.214842\pi$
$30$		0			0
$31$	−2536.15	−	4392.74i	−0.473992	−	0.820977i	0.525565	−	0.850753i	$-0.323854\pi$
$31$	−2536.15	−	4392.74i	−0.473992	−	0.820977i	−0.999557	+	0.0297760i	$0.990521\pi$
$32$		0			0
$33$	−4353.75	+	1584.63i	−0.695950	+	0.253305i
$34$		0			0
$35$	−2580.58	−	2165.36i	−0.356079	−	0.298786i
$36$		0			0
$37$	33.9163			0.00407290			0.00203645	−	0.999998i	$-0.499352\pi$
$37$	33.9163			0.00407290			0.00203645	+	0.999998i	$0.499352\pi$
$38$		0			0
$39$	8961.15			0.943414
$40$		0			0
$41$	9726.48	+	8161.49i	0.903642	+	0.758245i	0.970899	−	0.239490i	$-0.0769803\pi$
$41$	9726.48	+	8161.49i	0.903642	+	0.758245i	−0.0672571	+	0.997736i	$0.521425\pi$
$42$		0			0
$43$	−4690.09	+	1707.05i	−0.386821	+	0.140791i	−0.528108	−	0.849177i	$-0.677098\pi$
$43$	−4690.09	+	1707.05i	−0.386821	+	0.140791i	0.141287	+	0.989969i	$0.454876\pi$
$44$		0			0
$45$	2025.72	+	3508.65i	0.149124	+	0.258291i
$46$		0			0
$47$	−2242.48	−	12717.7i	−0.148076	−	0.839779i	−0.964846	−	0.262816i	$-0.915349\pi$
$47$	−2242.48	−	12717.7i	−0.148076	−	0.839779i	0.816770	−	0.576963i	$-0.195762\pi$
$48$		0			0
$49$	−8752.70	+	15160.1i	−0.520777	+	0.902013i
$50$		0			0
$51$	25731.4	−	21591.2i	1.38528	−	1.16239i
$52$		0			0
$53$	−24560.0	−	8939.11i	−1.20099	−	0.437124i	−0.337419	−	0.941354i	$-0.609554\pi$
$53$	−24560.0	−	8939.11i	−1.20099	−	0.437124i	−0.863569	+	0.504230i	$0.831776\pi$
$54$		0			0
$55$	677.947	−	3844.83i	0.0302196	−	0.171384i
$56$		0			0
$57$	26212.6	−	21591.9i	1.06862	−	0.880245i
$58$		0			0
$59$	−3322.45	+	18842.6i	−0.124259	+	0.704710i	0.857486	+	0.514508i	$0.172025\pi$
$59$	−3322.45	+	18842.6i	−0.124259	+	0.704710i	−0.981745	+	0.190202i	$0.939086\pi$
$60$		0			0
$61$	29662.1	+	10796.1i	1.02065	+	0.371487i	0.797514	−	0.603300i	$-0.206148\pi$
$61$	29662.1	+	10796.1i	1.02065	+	0.371487i	0.223138	+	0.974787i	$0.428370\pi$
$62$		0			0
$63$	31612.0	−	26525.6i	1.00346	−	0.842003i
$64$		0			0
$65$	−3775.56	+	6539.47i	−0.110840	+	0.191981i
$66$		0			0
$67$	−5288.86	−	29994.6i	−0.143938	−	0.816313i	−0.968214	−	0.250124i	$-0.919529\pi$
$67$	−5288.86	−	29994.6i	−0.143938	−	0.816313i	0.824276	−	0.566189i	$-0.191583\pi$
$68$		0			0
$69$	−20152.8	−	34905.7i	−0.509581	−	0.882620i
$70$		0			0
$71$	−34086.9	+	12406.6i	−0.802494	+	0.292084i	−0.710519	−	0.703678i	$-0.751540\pi$
$71$	−34086.9	+	12406.6i	−0.802494	+	0.292084i	−0.0919742	+	0.995761i	$0.529318\pi$
$72$		0			0
$73$	−62821.4	−	52713.4i	−1.37975	−	1.15775i	−0.969305	−	0.245862i	$-0.920929\pi$
$73$	−62821.4	−	52713.4i	−1.37975	−	1.15775i	−0.410445	−	0.911886i	$-0.634626\pi$
$74$		0			0
$75$	60305.6			1.23795
$76$		0			0
$77$	−39766.1			−0.764340
$78$		0			0
$79$	8486.16	+	7120.74i	0.152983	+	0.128368i	0.716067	−	0.698032i	$-0.245941\pi$
$79$	8486.16	+	7120.74i	0.152983	+	0.128368i	−0.563084	+	0.826400i	$0.690385\pi$
$80$		0			0
$81$	59721.3	−	21736.8i	1.01138	−	0.368114i
$82$		0			0
$83$	7468.07	+	12935.1i	0.118991	+	0.206098i	0.919368	−	0.393399i	$-0.128701\pi$
$83$	7468.07	+	12935.1i	0.118991	+	0.206098i	−0.800377	+	0.599497i	$0.795367\pi$
$84$		0			0
$85$	4915.05	+	27874.6i	0.0737872	+	0.418468i
$86$		0			0
$87$	−46895.7	+	81225.7i	−0.664255	+	1.15052i
$88$		0			0
$89$	−73562.7	+	61726.4i	−0.984425	+	0.826030i	−0.984751	−	0.173969i	$-0.944341\pi$
$89$	−73562.7	+	61726.4i	−0.984425	+	0.826030i	0.000326264		1.00000i	$0.499896\pi$
$90$		0			0
$91$	72274.6	+	26305.8i	0.914918	+	0.333003i
$92$		0			0
$93$	−19009.2	+	107807.i	−0.227907	+	1.29252i
$94$		0			0
$95$	4712.78	+	28226.1i	0.0535758	+	0.320879i
$96$		0			0
$97$	−11066.5	+	62761.3i	−0.119421	+	0.677271i	0.865045	+	0.501695i	$0.167290\pi$
$97$	−11066.5	+	62761.3i	−0.119421	+	0.677271i	−0.984466	+	0.175576i	$0.943821\pi$
$98$		0			0
$99$	44941.3	+	16357.3i	0.460848	+	0.167735i
$100$		0			0
$101$	−36817.5	+	30893.5i	−0.359129	+	0.301345i	−0.804444	−	0.594029i	$-0.797536\pi$
$101$	−36817.5	+	30893.5i	−0.359129	+	0.301345i	0.445314	+	0.895374i	$0.353092\pi$
$102$		0			0
$103$	−33680.8	+	58336.8i	−0.312816	+	0.541813i	−0.978971	−	0.204000i	$-0.934606\pi$
$103$	−33680.8	+	58336.8i	−0.312816	+	0.541813i	0.666155	+	0.745813i	$0.267939\pi$
$104$		0			0
$105$	12624.7	+	71598.5i	0.111751	+	0.633769i
$106$		0			0
$107$	−104101.	−	180308.i	−0.879011	−	1.52249i	−0.852427	−	0.522846i	$-0.824870\pi$
$107$	−104101.	−	180308.i	−0.879011	−	1.52249i	−0.0265842	−	0.999647i	$-0.508463\pi$
$108$		0			0
$109$	−3826.82	+	1392.85i	−0.0308512	+	0.0112289i	−0.357400	−	0.933952i	$-0.616337\pi$
$109$	−3826.82	+	1392.85i	−0.0308512	+	0.0112289i	0.326548	+	0.945180i	$0.394114\pi$
$110$		0			0
$111$	−560.728	−	470.506i	−0.00431961	−	0.00362458i
$112$		0			0
$113$	−172879.			−1.27364			−0.636819	−	0.771013i	$-0.719750\pi$
$113$	−172879.			−1.27364			−0.636819	+	0.771013i	$0.719750\pi$
$114$		0			0
$115$	33963.6			0.239480
$116$		0			0
$117$	−70859.9	−	59458.5i	−0.478559	−	0.401559i
$118$		0			0
$119$	270914.	−	98604.7i	1.75374	−	0.638308i
$120$		0			0
$121$	57482.2	+	99562.0i	0.356919	+	0.618202i
$122$		0			0
$123$	−47584.1	−	269863.i	−0.283595	−	1.60835i
$124$		0			0
$125$	−53823.9	+	93225.8i	−0.308106	+	0.533656i
$126$		0			0
$127$	−247017.	+	207272.i	−1.35900	+	1.14033i	−0.382704	+	0.923871i	$0.625007\pi$
$127$	−247017.	+	207272.i	−1.35900	+	1.14033i	−0.976291	+	0.216462i	$0.930548\pi$
$128$		0			0
$129$	101221.	+	36841.5i	0.535546	+	0.194923i
$130$		0			0
$131$	60080.8	−	340735.i	0.305885	−	1.73476i	−0.313426	−	0.949612i	$-0.601477\pi$
$131$	60080.8	−	340735.i	0.305885	−	1.73476i	0.619311	−	0.785146i	$-0.287412\pi$
$132$		0			0
$133$	274797.	−	97197.4i	1.34705	−	0.476459i
$134$		0			0
$135$	−1378.24	+	7816.36i	−0.00650862	+	0.0369122i
$136$		0			0
$137$	−94710.1	−	34471.7i	−0.431117	−	0.156914i	0.117341	−	0.993092i	$-0.462563\pi$
$137$	−94710.1	−	34471.7i	−0.431117	−	0.156914i	−0.548458	+	0.836178i	$0.684785\pi$
$138$		0			0
$139$	226390.	−	189964.i	0.993851	−	0.833940i	0.00773009	−	0.999970i	$-0.497539\pi$
$139$	226390.	−	189964.i	0.993851	−	0.833940i	0.986121	+	0.166030i	$0.0530950\pi$
$140$		0			0
$141$	−139353.	+	241367.i	−0.590296	+	1.02242i
$142$		0			0
$143$	15478.6	+	87783.6i	0.0632983	+	0.358983i
$144$		0			0
$145$	−39516.7	−	68444.9i	−0.156085	−	0.270347i
$146$		0			0
$147$	355016.	−	129215.i	1.35505	−	0.493197i
$148$		0			0
$149$	122658.	+	102922.i	0.452615	+	0.379789i	0.840405	−	0.541958i	$-0.182317\pi$
$149$	122658.	+	102922.i	0.452615	+	0.379789i	−0.387790	+	0.921748i	$0.626761\pi$
$150$		0			0
$151$	−315290.			−1.12530			−0.562649	−	0.826696i	$-0.690218\pi$
$151$	−315290.			−1.12530			−0.562649	+	0.826696i	$0.690218\pi$
$152$		0			0
$153$	−346731.			−1.19747
$154$		0			0
$155$	−70663.7	−	59293.9i	−0.236247	−	0.198235i
$156$		0			0
$157$	497814.	−	181190.i	1.61183	−	0.586657i	0.630026	−	0.776574i	$-0.283044\pi$
$157$	497814.	−	181190.i	1.61183	−	0.586657i	0.981800	+	0.189917i	$0.0608219\pi$
$158$		0			0
$159$	282035.	+	488498.i	0.884727	+	1.53239i
$160$		0			0
$161$	−60072.0	−	340685.i	−0.182645	−	1.03583i
$162$		0			0
$163$	170727.	−	295707.i	0.503306	−	0.871752i	−0.496687	−	0.867930i	$-0.665450\pi$
$163$	170727.	−	295707.i	0.503306	−	0.871752i	0.999993	−	0.00382173i	$-0.00121650\pi$
$164$		0			0
$165$	−64545.9	+	54160.4i	−0.184569	+	0.154872i
$166$		0			0
$167$	−95436.5	−	34736.0i	−0.264803	−	0.0963805i	0.206207	−	0.978508i	$-0.433888\pi$
$167$	−95436.5	−	34736.0i	−0.264803	−	0.0963805i	−0.471010	+	0.882128i	$0.656110\pi$
$168$		0			0
$169$	−34536.6	+	195867.i	−0.0930172	+	0.527527i
$170$		0			0
$171$	−350540.	−	3187.75i	−0.916744	−	0.00833670i
$172$		0			0
$173$	43202.3	−	245012.i	0.109747	−	0.622405i	−0.879471	−	0.475953i	$-0.842103\pi$
$173$	43202.3	−	245012.i	0.109747	−	0.622405i	0.989218	−	0.146452i	$-0.0467855\pi$
$174$		0			0
$175$	486384.	+	177029.i	1.20056	+	0.436969i
$176$		0			0
$177$	316324.	−	265427.i	0.758925	−	0.636814i
$178$		0			0
$179$	−331263.	+	573765.i	−0.772753	+	1.33845i	0.163295	+	0.986577i	$0.447788\pi$
$179$	−331263.	+	573765.i	−0.772753	+	1.33845i	−0.936049	+	0.351871i	$0.885546\pi$
$180$		0			0
$181$	−122306.	−	693629.i	−0.277492	−	1.57373i	−0.730935	−	0.682447i	$-0.760916\pi$
$181$	−122306.	−	693629.i	−0.277492	−	1.57373i	0.453443	−	0.891285i	$-0.350196\pi$
$182$		0			0
$183$	−340625.	−	589979.i	−0.751880	−	1.30229i
$184$		0			0
$185$	579.605	−	210.959i	0.00124509	−	0.000453177i
$186$		0			0
$187$	255954.	+	214771.i	0.535252	+	0.449130i
$188$		0			0
$189$	80842.8			0.164622
$190$		0			0
$191$	−730125.			−1.44815			−0.724075	−	0.689721i	$-0.757733\pi$
$191$	−730125.			−1.44815			−0.724075	+	0.689721i	$0.757733\pi$
$192$		0			0
$193$	268839.	+	225583.i	0.519516	+	0.435925i	0.864463	−	0.502697i	$-0.167659\pi$
$193$	268839.	+	225583.i	0.519516	+	0.435925i	−0.344947	+	0.938622i	$0.612103\pi$
$194$		0			0
$195$	153139.	−	55738.2i	0.288403	−	0.104970i
$196$		0			0
$197$	−302321.	−	523636.i	−0.555013	−	0.961311i	−0.997903	−	0.0647347i	$-0.979380\pi$
$197$	−302321.	−	523636.i	−0.555013	−	0.961311i	0.442889	−	0.896576i	$-0.353953\pi$
$198$		0			0
$199$	2245.00	+	12732.0i	0.00401868	+	0.0227911i	0.986751	−	0.162241i	$-0.0518722\pi$
$199$	2245.00	+	12732.0i	0.00401868	+	0.0227911i	−0.982732	+	0.185032i	$0.940761\pi$
$200$		0			0
$201$	−328664.	+	569262.i	−0.573801	+	0.993853i
$202$		0			0
$203$	−616670.	+	517448.i	−1.05030	+	0.881305i
$204$		0			0
$205$	216983.	+	78975.3i	0.360612	+	0.131252i
$206$		0			0
$207$	−72246.8	+	409732.i	−0.117191	+	0.664621i
$208$		0			0
$209$	256792.	+	219484.i	0.406645	+	0.347566i
$210$		0			0
$211$	−105477.	+	598191.i	−0.163100	+	0.924983i	0.787903	+	0.615800i	$0.211167\pi$
$211$	−105477.	+	598191.i	−0.163100	+	0.924983i	−0.951002	+	0.309184i	$0.899944\pi$
$212$		0			0
$213$	735660.	+	267758.i	1.11104	+	0.404384i
$214$		0			0
$215$	−69532.4	+	58344.6i	−0.102587	+	0.0860804i
$216$		0			0
$217$	−469786.	+	813694.i	−0.677253	+	1.17304i
$218$		0			0
$219$	307336.	+	1.74299e6i	0.433015	+	2.45575i
$220$		0			0
$221$	−323121.	−	559661.i	−0.445025	−	0.770805i
$222$		0			0
$223$	−439331.	+	159903.i	−0.591602	+	0.215325i	−0.620434	−	0.784259i	$-0.713043\pi$
$223$	−439331.	+	159903.i	−0.591602	+	0.215325i	0.0288320	+	0.999584i	$0.490821\pi$
$224$		0			0
$225$	−476864.	−	400136.i	−0.627969	−	0.526928i
$226$		0			0
$227$	−301861.			−0.388814			−0.194407	−	0.980921i	$-0.562278\pi$
$227$	−301861.			−0.388814			−0.194407	+	0.980921i	$0.562278\pi$
$228$		0			0
$229$	1.09881e6			1.38463			0.692313	−	0.721598i	$-0.256592\pi$
$229$	1.09881e6			1.38463			0.692313	+	0.721598i	$0.256592\pi$
$230$		0			0
$231$	657441.	+	551659.i	0.810638	+	0.680206i
$232$		0			0
$233$	−166874.	+	60737.2i	−0.201372	+	0.0732935i	−0.440737	−	0.897636i	$-0.645283\pi$
$233$	−166874.	+	60737.2i	−0.201372	+	0.0732935i	0.239365	+	0.970930i	$0.423061\pi$
$234$		0			0
$235$	−117426.	−	203388.i	−0.138706	−	0.240246i
$236$		0			0
$237$	−41516.2	−	235450.i	−0.0480116	−	0.272287i
$238$		0			0
$239$	116816.	−	202331.i	0.132284	−	0.229123i	−0.792273	−	0.610167i	$-0.791102\pi$
$239$	116816.	−	202331.i	0.132284	−	0.229123i	0.924557	+	0.381045i	$0.124436\pi$
$240$		0			0
$241$	791942.	−	664518.i	0.878315	−	0.736994i	−0.0875166	−	0.996163i	$-0.527893\pi$
$241$	791942.	−	664518.i	0.878315	−	0.736994i	0.965832	+	0.259169i	$0.0834486\pi$
$242$		0			0
$243$	−1.18924e6	−	432848.i	−1.29197	−	0.470240i
$244$		0			0
$245$	−55281.5	+	313517.i	−0.0588389	+	0.333692i
$246$		0			0
$247$	−321525.	−	568781.i	−0.335330	−	0.593202i
$248$		0			0
$249$	55975.5	−	317453.i	0.0572136	−	0.324475i
$250$		0			0
$251$	−1.16252e6	−	423122.i	−1.16470	−	0.423917i	−0.313928	−	0.949447i	$-0.601645\pi$
$251$	−1.16252e6	−	423122.i	−1.16470	−	0.423917i	−0.850775	+	0.525530i	$0.823867\pi$
$252$		0			0
$253$	307127.	−	257710.i	0.301659	−	0.253122i
$254$		0			0
$255$	305434.	−	529027.i	0.294149	−	0.509480i
$256$		0			0
$257$	−166782.	−	945869.i	−0.157513	−	0.893301i	−0.956452	−	0.291889i	$-0.905716\pi$
$257$	−166782.	−	945869.i	−0.157513	−	0.893301i	0.798939	−	0.601412i	$-0.205395\pi$
$258$		0			0
$259$	−3141.26	−	5440.82i	−0.00290974	−	0.00503982i
$260$		0			0
$261$	909769.	−	331129.i	0.826666	−	0.300882i
$262$		0			0
$263$	−1.04243e6	−	874704.i	−0.929304	−	0.779779i	0.0463880	−	0.998923i	$-0.485229\pi$
$263$	−1.04243e6	−	874704.i	−0.929304	−	0.779779i	−0.975692	+	0.219145i	$0.929673\pi$
$264$		0			0
$265$	−475314.			−0.415782
$266$		0			0
$267$	2.07249e6			1.77916
$268$		0			0
$269$	1.73934e6	+	1.45948e6i	1.46556	+	1.22975i	0.920144	+	0.391581i	$0.128072\pi$
$269$	1.73934e6	+	1.45948e6i	1.46556	+	1.22975i	0.545413	+	0.838167i	$0.316373\pi$
$270$		0			0
$271$	881034.	−	320670.i	0.728734	−	0.265238i	0.0491053	−	0.998794i	$-0.484363\pi$
$271$	881034.	−	320670.i	0.728734	−	0.265238i	0.679629	+	0.733556i	$0.262141\pi$
$272$		0			0
$273$	−829964.	−	1.43754e6i	−0.673989	−	1.16738i
$274$		0			0
$275$	104166.	+	590755.i	0.0830605	+	0.471059i
$276$		0			0
$277$	−417874.	+	723778.i	−0.327224	+	0.566769i	−0.981960	−	0.189089i	$-0.939447\pi$
$277$	−417874.	+	723778.i	−0.327224	+	0.566769i	0.654736	+	0.755858i	$0.272780\pi$
$278$		0			0
$279$	865627.	−	726348.i	0.665764	−	0.558642i
$280$		0			0
$281$	−1.47381e6	−	536423.i	−1.11346	−	0.405268i	−0.281201	−	0.959649i	$-0.590733\pi$
$281$	−1.47381e6	−	536423.i	−1.11346	−	0.405268i	−0.832263	+	0.554381i	$0.812955\pi$
$282$		0			0
$283$	−359924.	+	2.04123e6i	−0.267143	+	1.51504i	0.495719	+	0.868483i	$0.334905\pi$
$283$	−359924.	+	2.04123e6i	−0.267143	+	1.51504i	−0.762862	+	0.646561i	$0.776206\pi$
$284$		0			0
$285$	313654.	−	532032.i	0.228738	−	0.387994i
$286$		0			0
$287$	408411.	−	2.31622e6i	0.292680	−	1.65987i
$288$		0			0
$289$	−942056.	−	342880.i	−0.663486	−	0.241489i
$290$		0			0
$291$	1.05362e6	−	884092.i	0.729376	−	0.612019i
$292$		0			0
$293$	126571.	−	219228.i	0.0861324	−	0.149186i	−0.819741	−	0.572735i	$-0.805883\pi$
$293$	126571.	−	219228.i	0.0861324	−	0.149186i	0.905873	+	0.423549i	$0.139216\pi$
$294$		0			0
$295$	60422.2	+	342671.i	0.0404242	+	0.229257i
$296$		0			0
$297$	46846.1	+	81139.8i	0.0308164	+	0.0533756i
$298$		0			0
$299$	−728680.	+	265218.i	−0.471366	+	0.171563i
$300$		0			0
$301$	708231.	+	594277.i	0.450567	+	0.378070i
$302$		0			0
$303$	1.03726e6			0.649057
$304$		0			0
$305$	574056.			0.353349
$306$		0			0
$307$	−1.45169e6	−	1.21811e6i	−0.879078	−	0.737634i	0.0869114	−	0.996216i	$-0.472300\pi$
$307$	−1.45169e6	−	1.21811e6i	−0.879078	−	0.737634i	−0.965989	+	0.258582i	$0.916745\pi$
$308$		0			0
$309$	1.36612e6	−	497225.i	0.813938	−	0.296249i
$310$		0			0
$311$	486478.	+	842605.i	0.285209	+	0.493996i	0.972660	−	0.232235i	$-0.0746038\pi$
$311$	486478.	+	842605.i	0.285209	+	0.493996i	−0.687451	+	0.726231i	$0.741270\pi$
$312$		0			0
$313$	578383.	+	3.28017e6i	0.333699	+	1.89250i	0.439720	+	0.898135i	$0.355078\pi$
$313$	578383.	+	3.28017e6i	0.333699	+	1.89250i	−0.106022	+	0.994364i	$0.533811\pi$
$314$		0			0
$315$	375237.	−	649929.i	0.213073	−	0.369054i
$316$		0			0
$317$	559388.	−	469382.i	0.312655	−	0.262349i	−0.472933	−	0.881098i	$-0.656805\pi$
$317$	559388.	−	469382.i	0.312655	−	0.262349i	0.785588	+	0.618750i	$0.212360\pi$
$318$		0			0
$319$	−876692.	−	319090.i	−0.482359	−	0.175564i
$320$		0			0
$321$	−780268.	+	4.42512e6i	−0.422650	+	2.39697i
$322$		0			0
$323$	−2.29368e6	−	858530.i	−1.22328	−	0.457878i
$324$		0			0
$325$	201471.	−	1.14260e6i	0.105805	−	0.600047i
$326$		0			0
$327$	82590.0	+	30060.3i	0.0427128	+	0.0155462i
$328$		0			0
$329$	−1.83247e6	+	1.53763e6i	−0.933358	+	0.783180i
$330$		0			0
$331$	973238.	−	1.68570e6i	0.488258	−	0.845687i	−0.511651	−	0.859193i	$-0.670966\pi$
$331$	973238.	−	1.68570e6i	0.488258	−	0.845687i	0.999909	+	0.0135063i	$0.00429933\pi$
$332$		0			0
$333$	1312.05	+	7441.01i	0.000648396	+	0.00367724i
$334$		0			0
$335$	−276949.	−	479690.i	−0.134830	−	0.233533i
$336$		0			0
$337$	2.05743e6	−	748842.i	0.986846	−	0.359183i	0.202348	−	0.979314i	$-0.435143\pi$
$337$	2.05743e6	−	748842.i	0.986846	−	0.359183i	0.784498	+	0.620131i	$0.212921\pi$
$338$		0			0
$339$	2.85815e6	+	2.39828e6i	1.35079	+	1.13344i
$340$		0			0
$341$	−1.08891e6			−0.507115
$342$		0			0
$343$	129370.			0.0593744
$344$		0			0
$345$	−561510.	−	471163.i	−0.253986	−	0.213120i
$346$		0			0
$347$	−2.28044e6	+	830011.i	−1.01670	+	0.370050i	−0.796004	−	0.605292i	$-0.793056\pi$
$347$	−2.28044e6	+	830011.i	−1.01670	+	0.370050i	−0.220700	+	0.975342i	$0.570834\pi$
$348$		0			0
$349$	−1.65873e6	−	2.87300e6i	−0.728973	−	1.26262i	−0.957318	−	0.289037i	$-0.906665\pi$
$349$	−1.65873e6	−	2.87300e6i	−0.728973	−	1.26262i	0.228345	−	0.973580i	$-0.426669\pi$
$350$		0			0
$351$	−31467.4	−	178460.i	−0.0136330	−	0.0773168i
$352$		0			0
$353$	1.26131e6	−	2.18466e6i	0.538749	−	0.933141i	−0.460222	−	0.887804i	$-0.652230\pi$
$353$	1.26131e6	−	2.18466e6i	0.538749	−	0.933141i	0.998972	−	0.0453374i	$-0.0144363\pi$
$354$		0			0
$355$	−505351.	+	424040.i	−0.212825	+	0.178581i
$356$		0			0
$357$	−5.84684e6	−	2.12808e6i	−2.42801	−	0.883724i
$358$		0			0
$359$	−573983.	+	3.25522e6i	−0.235051	+	1.33304i	0.607454	+	0.794355i	$0.292191\pi$
$359$	−573983.	+	3.25522e6i	−0.235051	+	1.33304i	−0.842505	+	0.538688i	$0.818920\pi$
$360$		0			0
$361$	−2.31099e6	−	889051.i	−0.933317	−	0.359053i
$362$		0			0
$363$	430847.	−	2.44345e6i	0.171615	−	0.973279i
$364$		0			0
$365$	−1.40145e6	−	510085.i	−0.550611	−	0.200406i
$366$		0			0
$367$	20776.9	−	17433.9i	0.00805222	−	0.00675661i	−0.638753	−	0.769412i	$-0.720549\pi$
$367$	20776.9	−	17433.9i	0.00805222	−	0.00675661i	0.646805	+	0.762656i	$0.276105\pi$
$368$		0			0
$369$	−1.41431e6	+	2.44965e6i	−0.540727	+	0.936567i
$370$		0			0
$371$	840695.	+	4.76782e6i	0.317106	+	1.79839i
$372$		0			0
$373$	2.45951e6	+	4.26000e6i	0.915329	+	1.58540i	0.806419	+	0.591345i	$0.201403\pi$
$373$	2.45951e6	+	4.26000e6i	0.915329	+	1.58540i	0.108910	+	0.994052i	$0.465264\pi$
$374$		0			0
$375$	2.18314e6	−	794597.i	0.801683	−	0.291789i
$376$		0			0
$377$	1.38230e6	+	1.15989e6i	0.500897	+	0.420302i
$378$		0			0
$379$	−1.21025e6			−0.432791			−0.216396	−	0.976306i	$-0.569430\pi$
$379$	−1.21025e6			−0.432791			−0.216396	+	0.976306i	$0.569430\pi$
$380$		0			0
$381$	6.95926e6			2.45612
$382$		0			0
$383$	4.18047e6	+	3.50783e6i	1.45622	+	1.22192i	0.927875	+	0.372891i	$0.121633\pi$
$383$	4.18047e6	+	3.50783e6i	1.45622	+	1.22192i	0.528349	+	0.849027i	$0.322811\pi$
$384$		0			0
$385$	−679574.	+	247345.i	−0.233660	+	0.0850454i
$386$		0			0
$387$	−555953.	−	962938.i	−0.188695	−	0.326829i
$388$		0			0
$389$	149883.	+	850029.i	0.0502202	+	0.284813i	0.999567	−	0.0294167i	$-0.00936497\pi$
$389$	149883.	+	850029.i	0.0502202	+	0.284813i	−0.949347	+	0.314229i	$0.898254\pi$
$390$		0			0
$391$	−1.45334e6	+	2.51726e6i	−0.480756	+	0.832694i
$392$		0			0
$393$	−5.72017e6	+	4.79979e6i	−1.86822	+	1.56762i
$394$		0			0
$395$	189313.	+	68904.3i	0.0610503	+	0.0222205i
$396$		0			0
$397$	335321.	−	1.90170e6i	0.106779	−	0.605572i	−0.883716	−	0.468023i	$-0.844966\pi$
$397$	335321.	−	1.90170e6i	0.106779	−	0.605572i	0.990495	−	0.137549i	$-0.0439225\pi$
$398$		0			0
$399$	−5.89152e6	−	2.20521e6i	−1.85266	−	0.693455i
$400$		0			0
$401$	427729.	−	2.42577e6i	0.132834	−	0.753337i	−0.843510	−	0.537113i	$-0.819515\pi$
$401$	427729.	−	2.42577e6i	0.132834	−	0.753337i	0.976344	−	0.216224i	$-0.0693740\pi$
$402$		0			0
$403$	1.97909e6	+	720329.i	0.607019	+	0.220937i
$404$		0			0
$405$	885390.	−	742930.i	0.268224	−	0.225066i
$406$		0			0
$407$	3640.54	−	6305.61i	0.00108938	−	0.00188687i
$408$		0			0
$409$	162994.	+	924382.i	0.0481795	+	0.273239i	0.999375	−	0.0353494i	$-0.0112544\pi$
$409$	162994.	+	924382.i	0.0481795	+	0.273239i	−0.951196	+	0.308589i	$0.900143\pi$
$410$		0			0
$411$	1.08760e6	+	1.88378e6i	0.317589	+	0.550080i
$412$		0			0
$413$	3.33043e6	−	1.21218e6i	0.960783	−	0.349696i
$414$		0			0
$415$	208080.	+	174600.i	0.0593075	+	0.0497649i
$416$		0			0
$417$	−6.37813e6			−1.79620
$418$		0			0
$419$	715148.			0.199003			0.0995017	−	0.995037i	$-0.468275\pi$
$419$	715148.			0.199003			0.0995017	+	0.995037i	$0.468275\pi$
$420$		0			0
$421$	418023.	+	350763.i	0.114946	+	0.0964515i	0.698449	−	0.715660i	$-0.253874\pi$
$421$	418023.	+	350763.i	0.114946	+	0.0964515i	−0.583503	+	0.812111i	$0.698318\pi$
$422$		0			0
$423$	2.70344e6	−	983970.i	0.734624	−	0.267381i
$424$		0			0
$425$	−2.17450e6	−	3.76634e6i	−0.583964	−	1.01146i
$426$		0			0
$427$	−1.01534e6	−	5.75829e6i	−0.269490	−	1.52835i
$428$		0			0
$429$	961881.	−	1.66603e6i	0.252335	−	0.437058i
$430$		0			0
$431$	5.61843e6	−	4.71442e6i	1.45687	−	1.22246i	0.529506	−	0.848306i	$-0.322377\pi$
$431$	5.61843e6	−	4.71442e6i	1.45687	−	1.22246i	0.927366	−	0.374154i	$-0.122067\pi$
$432$		0			0
$433$	−677794.	−	246697.i	−0.173731	−	0.0632330i	0.253690	−	0.967286i	$-0.418356\pi$
$433$	−677794.	−	246697.i	−0.173731	−	0.0632330i	−0.427421	+	0.904053i	$0.640578\pi$
$434$		0			0
$435$	−296190.	+	1.67978e6i	−0.0750494	+	0.425626i
$436$		0			0
$437$	−1.49245e6	+	2.53155e6i	−0.373849	+	0.634137i
$438$		0			0
$439$	561812.	−	3.18620e6i	0.139133	−	0.789062i	−0.832759	−	0.553635i	$-0.813240\pi$
$439$	561812.	−	3.18620e6i	0.139133	−	0.789062i	0.971892	−	0.235427i	$-0.0756488\pi$
$440$		0			0
$441$	−3.66463e6	−	1.33382e6i	−0.897292	−	0.326587i
$442$		0			0
$443$	5.79583e6	−	4.86328e6i	1.40316	−	1.17739i	0.443478	−	0.896285i	$-0.353744\pi$
$443$	5.79583e6	−	4.86328e6i	1.40316	−	1.17739i	0.959678	−	0.281103i	$-0.0907002\pi$
$444$		0			0
$445$	−873195.	+	1.51242e6i	−0.209031	+	0.362053i
$446$		0			0
$447$	−600068.	−	3.40315e6i	−0.142047	−	0.805588i
$448$		0			0
$449$	−425393.	−	736803.i	−0.0995806	−	0.172479i	0.811931	−	0.583754i	$-0.198417\pi$
$449$	−425393.	−	736803.i	−0.0995806	−	0.172479i	−0.911511	+	0.411275i	$0.865083\pi$
$450$		0			0
$451$	2.56139e6	−	932269.i	0.592972	−	0.215824i
$452$		0			0
$453$	5.21259e6	+	4.37388e6i	1.19346	+	1.00143i
$454$		0			0
$455$	1.39874e6			0.316744
$456$		0			0
$457$	3.57687e6			0.801147			0.400574	−	0.916265i	$-0.368811\pi$
$457$	3.57687e6			0.801147			0.400574	+	0.916265i	$0.368811\pi$
$458$		0			0
$459$	−520343.	−	436620.i	−0.115281	−	0.0967324i
$460$		0			0
$461$	3.94449e6	−	1.43568e6i	0.864448	−	0.314633i	0.128531	−	0.991705i	$-0.458974\pi$
$461$	3.94449e6	−	1.43568e6i	0.864448	−	0.314633i	0.735917	+	0.677072i	$0.236752\pi$
$462$		0			0
$463$	−3.12019e6	−	5.40434e6i	−0.676440	−	1.17163i	−0.976046	−	0.217565i	$-0.930189\pi$
$463$	−3.12019e6	−	5.40434e6i	−0.676440	−	1.17163i	0.299606	−	0.954063i	$-0.403145\pi$
$464$		0			0
$465$	345702.	+	1.96057e6i	0.0741429	+	0.420485i
$466$		0			0
$467$	2.52384e6	−	4.37142e6i	0.535512	−	0.927534i	−0.463626	−	0.886031i	$-0.653452\pi$
$467$	2.52384e6	−	4.37142e6i	0.535512	−	0.927534i	0.999138	−	0.0415034i	$-0.0132147\pi$
$468$		0			0
$469$	−4.32187e6	+	3.62648e6i	−0.907276	+	0.761295i
$470$		0			0
$471$	−1.07438e7	−	3.91041e6i	−2.23154	−	0.812214i
$472$		0			0
$473$	−186060.	+	1.05520e6i	−0.0382385	+	0.216861i
$474$		0			0
$475$	−2.16376e6	−	3.82771e6i	−0.440023	−	0.778404i
$476$		0			0
$477$	1.01108e6	−	5.73411e6i	0.203465	−	1.15391i
$478$		0			0
$479$	7.88321e6	+	2.86925e6i	1.56987	+	0.571387i	0.972971	−	0.230928i	$-0.0741763\pi$
$479$	7.88321e6	+	2.86925e6i	1.56987	+	0.571387i	0.596901	+	0.802315i	$0.296399\pi$
$480$		0			0
$481$	−10787.9	+	9052.12i	−0.00212605	+	0.00178397i
$482$		0			0
$483$	−3.73303e6	+	6.46580e6i	−0.728105	+	1.26111i
$484$		0			0
$485$	201256.	+	1.14138e6i	0.0388503	+	0.220331i
$486$		0			0
$487$	−1.80494e6	−	3.12624e6i	−0.344858	−	0.597311i	0.640470	−	0.767983i	$-0.278739\pi$
$487$	−1.80494e6	−	3.12624e6i	−0.344858	−	0.597311i	−0.985328	+	0.170672i	$0.945406\pi$
$488$		0			0
$489$	−6.92479e6	+	2.52042e6i	−1.30959	+	0.476651i
$490$		0			0
$491$	−1.13684e6	−	953919.i	−0.212811	−	0.178570i	0.530151	−	0.847903i	$-0.322135\pi$
$491$	−1.13684e6	−	953919.i	−0.212811	−	0.178570i	−0.742962	+	0.669334i	$0.766580\pi$
$492$		0			0
$493$	6.76384e6			1.25336
$494$		0			0
$495$	869756.			0.159545
$496$		0			0
$497$	5.14732e6	+	4.31911e6i	0.934739	+	0.784339i
$498$		0			0
$499$	3.14449e6	−	1.14450e6i	0.565326	−	0.205762i	−0.0435166	−	0.999053i	$-0.513856\pi$
$499$	3.14449e6	−	1.14450e6i	0.565326	−	0.205762i	0.608843	+	0.793291i	$0.291634\pi$
$500$		0			0
$501$	1.09594e6	+	1.89823e6i	0.195071	+	0.337874i
$502$		0			0
$503$	1.17470e6	+	6.66206e6i	0.207017	+	1.17405i	0.894233	+	0.447601i	$0.147722\pi$
$503$	1.17470e6	+	6.66206e6i	0.207017	+	1.17405i	−0.687216	+	0.726453i	$0.741167\pi$
$504$		0			0
$505$	−437026.	+	756952.i	−0.0762569	+	0.132081i
$506$		0			0
$507$	3.28816e6	−	2.75909e6i	0.568111	−	0.476702i
$508$		0			0
$509$	695885.	+	253281.i	0.119054	+	0.0433320i	0.400860	−	0.916139i	$-0.368711\pi$
$509$	695885.	+	253281.i	0.119054	+	0.0433320i	−0.281806	+	0.959471i	$0.590934\pi$
$510$		0			0
$511$	−2.63784e6	+	1.49600e7i	−0.446886	+	2.53442i
$512$		0			0
$513$	−522046.	−	446201.i	−0.0875822	−	0.0748578i
$514$		0			0
$515$	−212726.	+	1.20643e6i	−0.0353429	+	0.200439i
$516$		0			0
$517$	−2.60514e6	−	948195.i	−0.428653	−	0.156017i
$518$		0			0
$519$	−4.11320e6	+	3.45139e6i	−0.670289	+	0.562439i
$520$		0			0
$521$	−4.40631e6	+	7.63196e6i	−0.711183	+	1.23180i	0.253231	+	0.967406i	$0.418507\pi$
$521$	−4.40631e6	+	7.63196e6i	−0.711183	+	1.23180i	−0.964414	+	0.264399i	$0.914827\pi$
$522$		0			0
$523$	1.50040e6	+	8.50919e6i	0.239857	+	1.36030i	0.832139	+	0.554567i	$0.187116\pi$
$523$	1.50040e6	+	8.50919e6i	0.239857	+	1.36030i	−0.592282	+	0.805731i	$0.701773\pi$
$524$		0			0
$525$	−5.58539e6	−	9.67417e6i	−0.884413	−	1.53185i
$526$		0			0
$527$	7.41841e6	−	2.70008e6i	1.16355	−	0.423497i
$528$		0			0
$529$	−2.25871e6	−	1.89528e6i	−0.350930	−	0.294465i
$530$		0			0
$531$	−4.26247e6			−0.656031
$532$		0			0
$533$	−5.27201e6			−0.803819
$534$		0			0
$535$	−2.90052e6	−	2.43382e6i	−0.438118	−	0.367625i
$536$		0			0
$537$	1.34363e7	−	4.89040e6i	2.01068	−	0.731828i
$538$		0			0
$539$	1.87901e6	+	3.25455e6i	0.278585	+	0.482524i
$540$		0			0
$541$	−783205.	−	4.44178e6i	−0.115049	−	0.652475i	−0.986726	−	0.162394i	$-0.948078\pi$
$541$	−783205.	−	4.44178e6i	−0.115049	−	0.652475i	0.871677	−	0.490081i	$-0.163033\pi$
$542$		0			0
$543$	−7.60038e6	+	1.31642e7i	−1.10621	+	1.91600i
$544$		0			0
$545$	−56734.0	+	47605.5i	−0.00818187	+	0.00686540i
$546$		0			0
$547$	−6.26270e6	−	2.27944e6i	−0.894939	−	0.325731i	−0.146716	−	0.989179i	$-0.546870\pi$
$547$	−6.26270e6	−	2.27944e6i	−0.894939	−	0.325731i	−0.748223	+	0.663448i	$0.769093\pi$
$548$		0			0
$549$	−1.22112e6	+	6.92532e6i	−0.172913	+	0.980639i
$550$		0			0
$551$	6.83816e6	+	62185.0i	0.959534	+	0.00872582i
$552$		0			0
$553$	356331.	−	2.02085e6i	0.0495496	−	0.281010i
$554$		0			0
$555$	−12509.0	−	4552.89i	−0.00172381	−	0.000627415i
$556$		0			0
$557$	6.16086e6	−	5.16958e6i	0.841402	−	0.706020i	−0.116477	−	0.993193i	$-0.537160\pi$
$557$	6.16086e6	−	5.16958e6i	0.841402	−	0.706020i	0.957879	+	0.287174i	$0.0927157\pi$
$558$		0			0
$559$	1.03619e6	−	1.79474e6i	0.140252	−	0.242924i
$560$		0			0
$561$	−1.25218e6	−	7.10148e6i	−0.167981	−	0.952669i
$562$		0			0
$563$	−3.97212e6	−	6.87992e6i	−0.528143	−	0.914771i	−0.999462	−	0.0328080i	$-0.989555\pi$
$563$	−3.97212e6	−	6.87992e6i	−0.528143	−	0.914771i	0.471318	−	0.881963i	$-0.343778\pi$
$564$		0			0
$565$	−2.95437e6	+	1.07530e6i	−0.389354	+	0.141713i
$566$		0			0
$567$	−9.01826e6	−	7.56722e6i	−1.17805	−	0.988504i
$568$		0			0
$569$	−1.10265e7			−1.42777			−0.713883	−	0.700265i	$-0.753065\pi$
$569$	−1.10265e7			−1.42777			−0.713883	+	0.700265i	$0.753065\pi$
$570$		0			0
$571$	−1.93966e6			−0.248963			−0.124482	−	0.992222i	$-0.539727\pi$
$571$	−1.93966e6			−0.248963			−0.124482	+	0.992222i	$0.539727\pi$
$572$		0			0
$573$	1.20709e7	+	1.01287e7i	1.53587	+	1.28875i
$574$		0			0
$575$	−4.90378e6	+	1.78483e6i	−0.618530	+	0.225127i
$576$		0			0
$577$	4.83163e6	+	8.36863e6i	0.604163	+	1.04644i	0.992183	+	0.124790i	$0.0398258\pi$
$577$	4.83163e6	+	8.36863e6i	0.604163	+	1.04644i	−0.388020	+	0.921651i	$0.626841\pi$
$578$		0			0
$579$	−1.31522e6	−	7.45897e6i	−0.163043	−	0.924661i
$580$		0			0
$581$	1.38336e6	−	2.39604e6i	0.170017	−	0.294479i
$582$		0			0
$583$	−4.29818e6	+	3.60660e6i	−0.523737	+	0.439467i
$584$		0			0
$585$	−1.58077e6	−	575355.i	−0.190977	−	0.0695098i
$586$		0			0
$587$	−968493.	+	5.49260e6i	−0.116012	+	0.657934i	0.870233	+	0.492641i	$0.163968\pi$
$587$	−968493.	+	5.49260e6i	−0.116012	+	0.657934i	−0.986244	+	0.165294i	$0.947143\pi$
$588$		0			0
$589$	7.52475e6	−	2.66155e6i	0.893724	−	0.316115i
$590$		0			0
$591$	−2.26599e6	+	1.28511e7i	−0.266864	+	1.51346i
$592$		0			0
$593$	−7.93353e6	−	2.88757e6i	−0.926467	−	0.337206i	−0.165659	−	0.986183i	$-0.552975\pi$
$593$	−7.93353e6	−	2.88757e6i	−0.926467	−	0.337206i	−0.760808	+	0.648977i	$0.775197\pi$
$594$		0			0
$595$	4.01640e6	−	3.37016e6i	0.465099	−	0.390264i
$596$		0			0
$597$	139510.	−	241639.i	0.0160203	−	0.0277479i
$598$		0			0
$599$	2.33109e6	+	1.32202e7i	0.265455	+	1.50547i	0.767736	+	0.640766i	$0.221383\pi$
$599$	2.33109e6	+	1.32202e7i	0.265455	+	1.50547i	−0.502281	+	0.864704i	$0.667506\pi$
$600$		0			0
$601$	−6.15660e6	−	1.06636e7i	−0.695273	−	1.20425i	−0.970089	−	0.242751i	$-0.921950\pi$
$601$	−6.15660e6	−	1.06636e7i	−0.695273	−	1.20425i	0.274816	−	0.961497i	$-0.411383\pi$
$602$		0			0
$603$	6.37603e6	−	2.32068e6i	0.714096	−	0.259910i
$604$		0			0
$605$	1.60160e6	+	1.34390e6i	0.177896	+	0.149272i
$606$		0			0
$607$	−1.00810e7			−1.11053			−0.555266	−	0.831673i	$-0.687384\pi$
$607$	−1.00810e7			−1.11053			−0.555266	+	0.831673i	$0.687384\pi$
$608$		0			0
$609$	1.73735e7			1.89821
$610$		0			0
$611$	4.10758e6	+	3.44667e6i	0.445127	+	0.373506i
$612$		0			0
$613$	2.53346e6	−	922102.i	0.272309	−	0.0991124i	−0.202256	−	0.979333i	$-0.564827\pi$
$613$	2.53346e6	−	922102.i	0.272309	−	0.0991124i	0.474565	+	0.880220i	$0.342605\pi$
$614$		0			0
$615$	−2.49172e6	−	4.31578e6i	−0.265651	−	0.460121i
$616$		0			0
$617$	1.33623e6	+	7.57813e6i	0.141308	+	0.801400i	0.970257	+	0.242076i	$0.0778282\pi$
$617$	1.33623e6	+	7.57813e6i	0.141308	+	0.801400i	−0.828949	+	0.559324i	$0.811061\pi$
$618$		0			0
$619$	−8.28561e6	+	1.43511e7i	−0.869156	+	1.50542i	−0.00629600	+	0.999980i	$0.502004\pi$
$619$	−8.28561e6	+	1.43511e7i	−0.869156	+	1.50542i	−0.862860	+	0.505443i	$0.831329\pi$
$620$		0			0
$621$	−624376.	+	523914.i	−0.0649706	+	0.0545168i
$622$		0			0
$623$	1.67153e7	+	6.08388e6i	1.72542	+	0.628002i
$624$		0			0
$625$	1.17636e6	−	6.67149e6i	0.120460	−	0.683160i
$626$		0			0
$627$	−1.20065e6	−	7.19102e6i	−0.121969	−	0.730503i
$628$		0			0
$629$	−9166.41	+	51985.3i	−0.000923788	+	0.00523906i
$630$		0			0
$631$	8.16546e6	+	2.97198e6i	0.816408	+	0.297148i	0.716268	−	0.697825i	$-0.245849\pi$
$631$	8.16546e6	+	2.97198e6i	0.816408	+	0.297148i	0.100140	+	0.994973i	$0.468071\pi$
$632$		0			0
$633$	1.00423e7	−	8.42647e6i	0.996146	−	0.835865i
$634$		0			0
$635$	−2.93211e6	+	5.07857e6i	−0.288567	+	0.499813i
$636$		0			0
$637$	−1.26217e6	−	7.15810e6i	−0.123245	−	0.698955i
$638$		0			0
$639$	−4.04058e6	−	6.99849e6i	−0.391464	−	0.678035i
$640$		0			0
$641$	−4.46130e6	+	1.62378e6i	−0.428861	+	0.156092i	−0.547427	−	0.836854i	$-0.684392\pi$
$641$	−4.46130e6	+	1.62378e6i	−0.428861	+	0.156092i	0.118566	+	0.992946i	$0.462170\pi$
$642$		0			0
$643$	−1.01365e7	−	8.50555e6i	−0.966856	−	0.811288i	0.0151991	−	0.999884i	$-0.495162\pi$
$643$	−1.01365e7	−	8.50555e6i	−0.966856	−	0.811288i	−0.982055	+	0.188596i	$0.939606\pi$
$644$		0			0
$645$	1.95895e6			0.185406
$646$		0			0
$647$	−1.09494e7			−1.02833			−0.514163	−	0.857693i	$-0.671897\pi$
$647$	−1.09494e7			−1.02833			−0.514163	+	0.857693i	$0.671897\pi$
$648$		0			0
$649$	3.14652e6	+	2.64024e6i	0.293237	+	0.246055i
$650$		0			0
$651$	1.90549e7	−	6.93540e6i	1.76219	−	0.641385i
$652$		0			0
$653$	−4.84673e6	−	8.39478e6i	−0.444801	−	0.770418i	0.553238	−	0.833024i	$-0.313392\pi$
$653$	−4.84673e6	−	8.39478e6i	−0.444801	−	0.770418i	−0.998038	+	0.0626059i	$0.980059\pi$
$654$		0			0
$655$	−1.09263e6	−	6.19662e6i	−0.0995108	−	0.564354i
$656$		0			0
$657$	9.13473e6	−	1.58218e7i	0.825624	−	1.43002i
$658$		0			0
$659$	−4.53873e6	+	3.80845e6i	−0.407119	+	0.341613i	−0.823238	−	0.567697i	$-0.807835\pi$
$659$	−4.53873e6	+	3.80845e6i	−0.407119	+	0.341613i	0.416119	+	0.909310i	$0.363390\pi$
$660$		0			0
$661$	−8.42106e6	−	3.06502e6i	−0.749658	−	0.272853i	−0.0611963	−	0.998126i	$-0.519492\pi$
$661$	−8.42106e6	−	3.06502e6i	−0.749658	−	0.272853i	−0.688462	+	0.725272i	$0.741714\pi$
$662$		0			0
$663$	−2.42189e6	+	1.37352e7i	−0.213979	+	1.21353i
$664$		0			0
$665$	4.09152e6	−	3.37027e6i	0.358782	−	0.295536i
$666$		0			0
$667$	1.40935e6	−	7.99284e6i	0.122661	−	0.695643i
$668$		0			0
$669$	9.48159e6	+	3.45102e6i	0.819060	+	0.298114i
$670$		0			0
$671$	5.19109e6	−	4.35584e6i	0.445094	−	0.373478i
$672$		0			0
$673$	−3.16540e6	+	5.48263e6i	−0.269396	+	0.466607i	−0.968706	−	0.248211i	$-0.920157\pi$
$673$	−3.16540e6	+	5.48263e6i	−0.269396	+	0.466607i	0.699310	+	0.714818i	$0.253491\pi$
$674$		0			0
$675$	−211765.	−	1.20098e6i	−0.0178894	−	0.101456i
$676$		0			0
$677$	−1.00287e7	−	1.73702e7i	−0.840955	−	1.45658i	−0.889088	−	0.457737i	$-0.848660\pi$
$677$	−1.00287e7	−	1.73702e7i	−0.840955	−	1.45658i	0.0481324	−	0.998841i	$-0.484673\pi$
$678$		0			0
$679$	1.10931e7	−	4.03755e6i	0.923374	−	0.336081i
$680$		0			0
$681$	4.99057e6	+	4.18759e6i	0.412366	+	0.346016i
$682$		0			0
$683$	4.18639e6			0.343391			0.171695	−	0.985150i	$-0.445076\pi$
$683$	4.18639e6			0.343391			0.171695	+	0.985150i	$0.445076\pi$
$684$		0			0
$685$	−1.83294e6			−0.149252
$686$		0			0
$687$	−1.81662e7	−	1.52433e7i	−1.46849	−	1.23221i
$688$		0			0
$689$	1.01977e7	−	3.71167e6i	0.818380	−	0.297866i
$690$		0			0
$691$	5.52964e6	+	9.57762e6i	0.440557	+	0.763067i	0.997731	−	0.0673289i	$-0.0214477\pi$
$691$	5.52964e6	+	9.57762e6i	0.440557	+	0.763067i	−0.557174	+	0.830396i	$0.688114\pi$
$692$		0			0
$693$	−1.53835e6	−	8.72443e6i	−0.121681	−	0.690087i
$694$		0			0
$695$	2.68727e6	−	4.65449e6i	0.211033	−	0.365519i
$696$		0			0
$697$	−1.51383e7	+	1.27025e7i	−1.18031	+	0.990394i
$698$		0			0
$699$	3.60146e6	+	1.31082e6i	0.278795	+	0.101473i
$700$		0			0
$701$	3.34964e6	−	1.89967e7i	0.257456	−	1.46010i	−0.532234	−	0.846597i	$-0.678647\pi$
$701$	3.34964e6	−	1.89967e7i	0.257456	−	1.46010i	0.789689	−	0.613507i	$-0.210242\pi$
$702$		0			0
$703$	−9745.06	+	52472.2i	−0.000743697	+	0.00400443i
$704$		0			0
$705$	−880147.	+	4.99156e6i	−0.0666934	+	0.378237i
$706$		0			0
$707$	8.36588e6	+	3.04493e6i	0.629453	+	0.229102i
$708$		0			0
$709$	−1.27087e7	+	1.06639e7i	−0.949478	+	0.796707i	−0.979210	−	0.202851i	$-0.934979\pi$
$709$	−1.27087e7	+	1.06639e7i	−0.949478	+	0.796707i	0.0297315	+	0.999558i	$0.490535\pi$
$710$		0			0
$711$	−1.23396e6	+	2.13727e6i	−0.0915431	+	0.158557i
$712$		0			0
$713$	−1.64495e6	−	9.32895e6i	−0.121179	−	0.687241i
$714$		0			0
$715$	810531.	+	1.40388e6i	0.0592931	+	0.102699i
$716$		0			0
$717$	−4.73814e6	+	1.72454e6i	−0.344199	+	0.125278i
$718$		0			0
$719$	8.94784e6	+	7.50813e6i	0.645500	+	0.541639i	0.905702	−	0.423916i	$-0.139345\pi$
$719$	8.94784e6	+	7.50813e6i	0.645500	+	0.541639i	−0.260202	+	0.965554i	$0.583789\pi$
$720$		0			0
$721$	1.24778e7			0.893922
$722$		0			0
$723$	−2.23115e7			−1.58739
$724$		0			0
$725$	9.30241e6	+	7.80565e6i	0.657280	+	0.551523i
$726$		0			0
$727$	−1.81999e6	+	662421.i	−0.127712	+	0.0464834i	−0.405086	−	0.914279i	$-0.632758\pi$
$727$	−1.81999e6	+	662421.i	−0.127712	+	0.0464834i	0.277373	+	0.960762i	$0.410536\pi$
$728$		0			0
$729$	5.93481e6	+	1.02794e7i	0.413607	+	0.716388i
$730$		0			0
$731$	−1.34892e6	−	7.65011e6i	−0.0933669	−	0.529510i
$732$		0			0
$733$	−4.19699e6	+	7.26941e6i	−0.288522	+	0.499734i	−0.973457	−	0.228870i	$-0.926497\pi$
$733$	−4.19699e6	+	7.26941e6i	−0.288522	+	0.499734i	0.684935	+	0.728604i	$0.259830\pi$
$734$		0			0
$735$	5.26324e6	−	4.41638e6i	0.359364	−	0.301542i
$736$		0			0
$737$	−6.14421e6	−	2.23631e6i	−0.416675	−	0.151657i
$738$		0			0
$739$	2.00935e6	−	1.13956e7i	0.135346	−	0.767584i	−0.839272	−	0.543711i	$-0.817019\pi$
$739$	2.00935e6	−	1.13956e7i	0.135346	−	0.767584i	0.974618	−	0.223873i	$-0.0718702\pi$
$740$		0			0
$741$	−2.57478e6	+	1.38639e7i	−0.172264	+	0.927553i
$742$		0			0
$743$	2.55970e6	−	1.45168e7i	0.170105	−	0.964712i	−0.773539	−	0.633749i	$-0.781515\pi$
$743$	2.55970e6	−	1.45168e7i	0.170105	−	0.964712i	0.943644	−	0.330963i	$-0.107374\pi$
$744$		0			0
$745$	2.73630e6	+	995933.i	0.180623	+	0.0657415i
$746$		0			0
$747$	−2.54897e6	+	2.13884e6i	−0.167133	+	0.140241i
$748$		0			0
$749$	−1.92832e7	+	3.33995e7i	−1.25596	+	2.17538i
$750$		0			0
$751$	−1.70521e6	−	9.67074e6i	−0.110326	−	0.625691i	−0.988959	−	0.148192i	$-0.952655\pi$
$751$	−1.70521e6	−	9.67074e6i	−0.110326	−	0.625691i	0.878632	−	0.477499i	$-0.158457\pi$
$752$		0			0
$753$	1.33497e7	+	2.31224e7i	0.857997	+	1.48609i
$754$		0			0
$755$	−5.38807e6	+	1.96110e6i	−0.344006	+	0.125208i
$756$		0			0
$757$	1.32786e7	+	1.11421e7i	0.842195	+	0.706685i	0.958056	−	0.286580i	$-0.0925184\pi$
$757$	1.32786e7	+	1.11421e7i	0.842195	+	0.706685i	−0.115861	+	0.993265i	$0.536963\pi$
$758$		0			0
$759$	−8.65274e6			−0.545192
$760$		0			0
$761$	−9.96741e6			−0.623908			−0.311954	−	0.950097i	$-0.600984\pi$
$761$	−9.96741e6			−0.623908			−0.311954	+	0.950097i	$0.600984\pi$
$762$		0			0
$763$	577872.	+	484892.i	0.0359352	+	0.0301532i
$764$		0			0
$765$	−5.92537e6	+	2.15666e6i	−0.366068	+	0.133238i
$766$		0			0
$767$	−3.97222e6	−	6.88008e6i	−0.243806	−	0.422285i
$768$		0			0
$769$	3.52845e6	+	2.00108e7i	0.215163	+	1.22025i	0.880623	+	0.473818i	$0.157125\pi$
$769$	3.52845e6	+	2.00108e7i	0.215163	+	1.22025i	−0.665459	+	0.746434i	$0.731764\pi$
$770$		0			0
$771$	−1.03643e7	+	1.79514e7i	−0.627918	+	1.08759i
$772$		0			0
$773$	−4.32321e6	+	3.62761e6i	−0.260230	+	0.218359i	−0.763563	−	0.645734i	$-0.776552\pi$
$773$	−4.32321e6	+	3.62761e6i	−0.260230	+	0.218359i	0.503332	+	0.864093i	$0.332107\pi$
$774$		0			0
$775$	1.33186e7	+	4.84758e6i	0.796535	+	0.289915i
$776$		0			0
$777$	−23544.7	+	133529.i	−0.00139908	+	0.00793455i
$778$		0			0
$779$	−1.54214e7	+	1.27029e7i	−0.910499	+	0.749997i
$780$		0			0
$781$	−1.35226e6	+	7.66904e6i	−0.0793290	+	0.449897i
$782$		0			0
$783$	1.78228e6	+	648695.i	0.103889	+	0.0378126i
$784$		0			0
$785$	7.38028e6	−	6.19279e6i	0.427463	−	0.358684i
$786$		0			0
$787$	1.04324e7	−	1.80695e7i	0.600410	−	1.03994i	−0.392348	−	0.919817i	$-0.628337\pi$
$787$	1.04324e7	−	1.80695e7i	0.600410	−	1.03994i	0.992759	−	0.120125i	$-0.0383294\pi$
$788$		0			0
$789$	5.09980e6	+	2.89224e7i	0.291649	+	1.65402i
$790$		0			0
$791$	1.60117e7	+	2.77331e7i	0.909906	+	1.57600i
$792$		0			0
$793$	−1.23162e7	+	4.48273e6i	−0.695495	+	0.253139i
$794$		0			0
$795$	7.85821e6	+	6.59382e6i	0.440967	+	0.370015i
$796$		0			0
$797$	−3.50950e6			−0.195704			−0.0978520	−	0.995201i	$-0.531197\pi$
$797$	−3.50950e6			−0.195704			−0.0978520	+	0.995201i	$0.531197\pi$
$798$		0			0
$799$	2.00992e7			1.11381
$800$		0			0
$801$	−1.63881e7	−	1.37513e7i	−0.902502	−	0.757289i
$802$		0			0
$803$	−1.65435e7	+	6.02134e6i	−0.905395	+	0.329537i
$804$		0			0
$805$	−3.14564e6	−	5.44842e6i	−0.171088	−	0.296333i
$806$		0			0
$807$	−8.50921e6	−	4.82581e7i	−0.459944	−	2.60847i
$808$		0			0
$809$	5.36926e6	−	9.29983e6i	0.288432	−	0.499579i	−0.685004	−	0.728540i	$-0.740199\pi$
$809$	5.36926e6	−	9.29983e6i	0.288432	−	0.499579i	0.973436	+	0.228961i	$0.0735328\pi$
$810$		0			0
$811$	−5.20532e6	+	4.36778e6i	−0.277904	+	0.233189i	−0.771077	−	0.636742i	$-0.780282\pi$
$811$	−5.20532e6	+	4.36778e6i	−0.277904	+	0.233189i	0.493173	+	0.869932i	$0.335837\pi$
$812$		0			0
$813$	−1.90144e7	−	6.92066e6i	−1.00892	−	0.367216i
$814$		0			0
$815$	1.07830e6	−	6.11533e6i	0.0568650	−	0.322497i
$816$		0			0
$817$	−1.29341e6	−	7.74656e6i	−0.0677923	−	0.406026i
$818$		0			0
$819$	−2.97538e6	+	1.68742e7i	−0.155000	+	0.879050i
$820$		0			0
$821$	−3.22864e7	−	1.17513e7i	−1.67171	−	0.608454i	−0.679576	−	0.733605i	$-0.737836\pi$
$821$	−3.22864e7	−	1.17513e7i	−1.67171	−	0.608454i	−0.992138	+	0.125151i	$0.960059\pi$
$822$		0			0
$823$	1.52514e7	−	1.27975e7i	0.784894	−	0.658604i	−0.159582	−	0.987185i	$-0.551015\pi$
$823$	1.52514e7	−	1.27975e7i	0.784894	−	0.658604i	0.944476	+	0.328581i	$0.106570\pi$
$824$		0			0
$825$	6.47315e6	−	1.12118e7i	0.331116	−	0.573510i
$826$		0			0
$827$	102834.	+	583203.i	0.00522847	+	0.0296521i	0.987310	−	0.158802i	$-0.0507633\pi$
$827$	102834.	+	583203.i	0.00522847	+	0.0296521i	−0.982082	+	0.188455i	$0.939652\pi$
$828$		0			0
$829$	1.40762e6	+	2.43806e6i	0.0711374	+	0.123214i	0.899400	−	0.437126i	$-0.144004\pi$
$829$	1.40762e6	+	2.43806e6i	0.0711374	+	0.123214i	−0.828263	+	0.560340i	$0.810670\pi$
$830$		0			0
$831$	1.69492e7	−	6.16902e6i	0.851428	−	0.309894i
$832$		0			0
$833$	−2.08712e7	−	1.75130e7i	−1.04216	−	0.874475i
$834$		0			0
$835$	−1.84700e6			−0.0916748
$836$		0			0
$837$	2.21371e6			0.109221
$838$		0			0
$839$	−1.48642e7	−	1.24725e7i	−0.729013	−	0.611715i	0.200849	−	0.979622i	$-0.435630\pi$
$839$	−1.48642e7	−	1.24725e7i	−0.729013	−	0.611715i	−0.929862	+	0.367908i	$0.880074\pi$
$840$		0			0
$841$	1.52688e6	−	555738.i	0.0744413	−	0.0270944i
$842$		0			0
$843$	1.69245e7	+	2.93141e7i	0.820250	+	1.42072i
$844$		0			0
$845$	628083.	+	3.56204e6i	0.0302605	+	0.171616i
$846$		0			0
$847$	1.06478e7	−	1.84425e7i	0.509976	−	0.883305i
$848$		0			0
$849$	3.42676e7	−	2.87539e7i	1.63160	−	1.36908i
$850$		0			0
$851$	59521.1	+	21663.9i	0.00281739	+	0.00102545i
$852$		0			0
$853$	3.78417e6	−	2.14611e7i	0.178073	−	1.00990i	−0.756464	−	0.654035i	$-0.773075\pi$
$853$	3.78417e6	−	2.14611e7i	0.178073	−	1.00990i	0.934537	−	0.355866i	$-0.115814\pi$
$854$		0			0
$855$	−6.01031e6	+	2.12588e6i	−0.281178	+	0.0994542i
$856$		0			0
$857$	−100216.	+	568351.i	−0.00466104	+	0.0264341i	−0.987050	−	0.160415i	$-0.948717\pi$
$857$	−100216.	+	568351.i	−0.00466104	+	0.0264341i	0.982389	+	0.186850i	$0.0598277\pi$
$858$		0			0
$859$	5.53782e6	+	2.01560e6i	0.256069	+	0.0932013i	0.466865	−	0.884329i	$-0.345383\pi$
$859$	5.53782e6	+	2.01560e6i	0.256069	+	0.0932013i	−0.210796	+	0.977530i	$0.567606\pi$
$860$		0			0
$861$	−3.88840e7	+	3.26275e7i	−1.78757	+	1.49995i
$862$		0			0
$863$	6.07495e6	−	1.05221e7i	0.277661	−	0.480924i	−0.693142	−	0.720801i	$-0.743774\pi$
$863$	6.07495e6	−	1.05221e7i	0.277661	−	0.480924i	0.970803	+	0.239878i	$0.0771073\pi$
$864$		0			0
$865$	−785678.	−	4.45580e6i	−0.0357030	−	0.202482i
$866$		0			0
$867$	1.08181e7	+	1.87375e7i	0.488768	+	0.846571i
$868$		0			0
$869$	2.23476e6	−	813386.i	0.100388	−	0.0365382i
$870$		0			0
$871$	9.68769e6	+	8.12894e6i	0.432688	+	0.363069i
$872$		0			0
$873$	−1.41975e7			−0.630488
$874$		0			0
$875$	1.99403e7			0.880463
$876$		0			0
$877$	9.25529e6	+	7.76611e6i	0.406342	+	0.340961i	0.822939	−	0.568130i	$-0.192333\pi$
$877$	9.25529e6	+	7.76611e6i	0.406342	+	0.340961i	−0.416597	+	0.909091i	$0.636777\pi$
$878$		0			0
$879$	−5.13382e6	+	1.86856e6i	−0.224114	+	0.0815708i
$880$		0			0
$881$	−1.47705e7	−	2.55833e7i	−0.641146	−	1.11050i	−0.985177	−	0.171539i	$-0.945126\pi$
$881$	−1.47705e7	−	2.55833e7i	−0.641146	−	1.11050i	0.344032	−	0.938958i	$-0.388207\pi$
$882$		0			0
$883$	5.44168e6	+	3.08613e7i	0.234872	+	1.33203i	0.842883	+	0.538097i	$0.180857\pi$
$883$	5.44168e6	+	3.08613e7i	0.234872	+	1.33203i	−0.608011	+	0.793929i	$0.708032\pi$
$884$		0			0
$885$	3.75479e6	−	6.50349e6i	0.161149	−	0.279118i
$886$		0			0
$887$	−5.64474e6	+	4.73650e6i	−0.240899	+	0.202138i	−0.755241	−	0.655447i	$-0.772480\pi$
$887$	−5.64474e6	+	4.73650e6i	−0.240899	+	0.202138i	0.514343	+	0.857585i	$0.328036\pi$
$888$		0			0
$889$	5.61287e7	+	2.04292e7i	2.38194	+	0.866954i
$890$		0			0
$891$	2.36920e6	−	1.34364e7i	0.0999786	−	0.567007i
$892$		0			0
$893$	2.03200e7	+	184787.i	0.852699	+	0.00775428i
$894$		0			0
$895$	−2.09224e6	+	1.18657e7i	−0.0873079	+	0.495148i
$896$		0			0
$897$	1.57263e7	+	5.72390e6i	0.652597	+	0.237526i
$898$		0			0
$899$	−1.68862e7	+	1.41692e7i	−0.696840	+	0.584718i
$900$		0			0
$901$	2.03392e7	−	3.52285e7i	0.834682	−	1.44571i
$902$		0			0
$903$	−3.46482e6	−	1.96500e7i	−0.141404	−	0.801942i
$904$		0			0
$905$	−6.40447e6	−	1.10929e7i	−0.259933	−	0.450218i
$906$		0			0
$907$	−1.61833e7	+	5.89023e6i	−0.653203	+	0.237747i	−0.647299	−	0.762236i	$-0.724102\pi$
$907$	−1.61833e7	+	5.89023e6i	−0.653203	+	0.237747i	−0.00590416	+	0.999983i	$0.501879\pi$
$908$		0			0
$909$	−8.20212e6	−	6.88240e6i	−0.329243	−	0.276268i
$910$		0			0
$911$	4.31231e7			1.72153			0.860764	−	0.509004i	$-0.169986\pi$
$911$	4.31231e7			1.72153			0.860764	+	0.509004i	$0.169986\pi$
$912$		0			0
$913$	3.20646e6			0.127306
$914$		0			0
$915$	−9.49068e6	−	7.96363e6i	−0.374753	−	0.314455i
$916$		0			0
$917$	−6.02250e7	+	2.19201e7i	−2.36512	+	0.860834i
$918$		0			0
$919$	−1.77789e7	−	3.07940e7i	−0.694411	−	1.20275i	−0.970379	−	0.241588i	$-0.922332\pi$
$919$	−1.77789e7	−	3.07940e7i	−0.694411	−	1.20275i	0.275968	−	0.961167i	$-0.411002\pi$
$920$		0			0
$921$	7.10197e6	+	4.02773e7i	0.275886	+	1.56463i
$922$		0			0
$923$	7.53088e6	−	1.30439e7i	0.290966	−	0.503967i
$924$		0			0
$925$	−72599.0	+	60917.8i	−0.00278982	+	0.00234094i
$926$		0			0
$927$	−1.41016e7	−	5.13258e6i	−0.538977	−	0.196172i
$928$		0			0
$929$	−2.75211e6	+	1.56080e7i	−0.104623	+	0.593346i	0.886747	+	0.462254i	$0.152959\pi$
$929$	−2.75211e6	+	1.56080e7i	−0.104623	+	0.593346i	−0.991370	+	0.131091i	$0.958152\pi$
$930$		0			0
$931$	−2.09395e7	−	1.78973e7i	−0.791756	−	0.676726i
$932$		0			0
$933$	3.64631e6	−	2.06792e7i	0.137135	−	0.777732i
$934$		0			0
$935$	5.70994e6	+	2.07825e6i	0.213601	+	0.0777443i
$936$		0			0
$937$	816887.	−	685449.i	0.0303957	−	0.0255051i	−0.627463	−	0.778646i	$-0.715907\pi$
$937$	816887.	−	685449.i	0.0303957	−	0.0255051i	0.657859	+	0.753141i	$0.271462\pi$
$938$		0			0
$939$	3.59422e7	−	6.22537e7i	1.33027	−	2.30410i
$940$		0			0
$941$	−4.83721e6	−	2.74332e7i	−0.178083	−	1.00996i	−0.934525	−	0.355896i	$-0.884176\pi$
$941$	−4.83721e6	−	2.74332e7i	−0.178083	−	1.00996i	0.756443	−	0.654060i	$-0.226936\pi$
$942$		0			0
$943$	1.18563e7	+	2.05357e7i	0.434179	+	0.752021i
$944$		0			0
$945$	1.38154e6	−	502841.i	0.0503251	−	0.0183169i
$946$		0			0
$947$	−1.07632e7	−	9.03137e6i	−0.390001	−	0.327249i	0.426613	−	0.904434i	$-0.359707\pi$
$947$	−1.07632e7	−	9.03137e6i	−0.390001	−	0.327249i	−0.816613	+	0.577185i	$0.804151\pi$
$948$		0			0
$949$	3.40508e7			1.22733
$950$		0			0
$951$	−1.57597e7			−0.565064
$952$		0			0
$953$	−6.01258e6	−	5.04516e6i	−0.214451	−	0.179946i	0.529234	−	0.848476i	$-0.322479\pi$
$953$	−6.01258e6	−	5.04516e6i	−0.214451	−	0.179946i	−0.743685	+	0.668530i	$0.766924\pi$
$954$		0			0
$955$	−1.24773e7	+	4.54136e6i	−0.442703	+	0.161131i
$956$		0			0
$957$	1.00675e7	+	1.74374e7i	0.355337	+	0.615462i
$958$		0			0
$959$	3.24195e6	+	1.83860e7i	0.113831	+	0.645567i
$960$		0			0
$961$	1.45047e6	−	2.51228e6i	0.0506640	−	0.0877526i
$962$		0			0
$963$	3.55312e7	−	2.98142e7i	1.23465	−	1.03600i
$964$		0			0
$965$	5.99738e6	+	2.18287e6i	0.207321	+	0.0754586i
$966$		0			0
$967$	−955958.	+	5.42151e6i	−0.0328755	+	0.186446i	−0.996823	−	0.0796453i	$-0.974621\pi$
$967$	−955958.	+	5.42151e6i	−0.0328755	+	0.186446i	0.963948	+	0.266092i	$0.0857324\pi$
$968$		0			0
$969$	2.60106e7	+	4.60130e7i	0.889901	+	1.57424i
$970$		0			0
$971$	2.29383e6	−	1.30090e7i	0.0780752	−	0.442787i	−0.920562	−	0.390597i	$-0.872269\pi$
$971$	2.29383e6	−	1.30090e7i	0.0780752	−	0.442787i	0.998637	−	0.0521900i	$-0.0166201\pi$
$972$		0			0
$973$	−5.14417e7	−	1.87233e7i	−1.74194	−	0.634015i
$974$		0			0
$975$	−1.91816e7	+	1.60953e7i	−0.646211	+	0.542235i
$976$		0			0
$977$	2.17762e7	−	3.77175e7i	0.729871	−	1.26417i	−0.227067	−	0.973879i	$-0.572914\pi$
$977$	2.17762e7	−	3.77175e7i	0.729871	−	1.26417i	0.956938	−	0.290294i	$-0.0937531\pi$
$978$		0			0
$979$	3.57982e6	+	2.03022e7i	0.119373	+	0.676996i
$980$		0			0
$981$	−453622.	−	785697.i	−0.0150495	−	0.0260665i
$982$		0			0
$983$	−3.18118e7	+	1.15786e7i	−1.05004	+	0.382183i	−0.808677	−	0.588253i	$-0.799816\pi$
$983$	−3.18118e7	+	1.15786e7i	−1.05004	+	0.382183i	−0.241361	+	0.970435i	$0.577594\pi$
$984$		0			0
$985$	−8.42346e6	−	7.06812e6i	−0.276630	−	0.232120i
$986$		0			0
$987$	5.16266e7			1.68687
$988$		0			0
$989$	−9.32121e6			−0.303027
$990$		0			0
$991$	1.36635e6	+	1.14651e6i	0.0441956	+	0.0370845i	0.664618	−	0.747183i	$-0.268594\pi$
$991$	1.36635e6	+	1.14651e6i	0.0441956	+	0.0370845i	−0.620422	+	0.784268i	$0.713039\pi$
$992$		0			0
$993$	−3.94752e7	+	1.43678e7i	−1.27043	+	0.462399i
$994$		0			0
$995$	117558.	+	203617.i	0.00376440	+	0.00652014i
$996$		0			0
$997$	6.61966e6	+	3.75420e7i	0.210910	+	1.19613i	0.887864	+	0.460107i	$0.152189\pi$
$997$	6.61966e6	+	3.75420e7i	0.210910	+	1.19613i	−0.676953	+	0.736026i	$0.736700\pi$
$998$		0			0
$999$	−7401.06	+	12819.0i	−0.000234628	+	0.000406388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.i.a.17.1	yes	48
19.9	even	9	inner	76.6.i.a.9.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.i.a.9.1	✓	48	19.9	even	9	inner
76.6.i.a.17.1	yes	48	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-16.5327 - 13.8726i) q^{3} +(17.0893 - 6.21998i) q^{5} +(-92.6180 - 160.419i) q^{7} +(38.6850 + 219.393i) q^{9} +O(q^{10})\)	\(q+(-16.5327 - 13.8726i) q^{3} +(17.0893 - 6.21998i) q^{5} +(-92.6180 - 160.419i) q^{7} +(38.6850 + 219.393i) q^{9} +(107.339 - 185.917i) q^{11} +(-318.074 + 266.896i) q^{13} +(-368.819 - 134.239i) q^{15} +(-270.266 + 1532.75i) q^{17} +(-287.327 + 1547.11i) q^{19} +(-694.201 + 3937.01i) q^{21} +(1754.94 + 638.746i) q^{23} +(-2140.53 + 1796.12i) q^{25} +(-218.216 + 377.960i) q^{27} +(-754.646 - 4279.81i) q^{29} +(-2536.15 - 4392.74i) q^{31} +(-4353.75 + 1584.63i) q^{33} +(-2580.58 - 2165.36i) q^{35} +33.9163 q^{37} +8961.15 q^{39} +(9726.48 + 8161.49i) q^{41} +(-4690.09 + 1707.05i) q^{43} +(2025.72 + 3508.65i) q^{45} +(-2242.48 - 12717.7i) q^{47} +(-8752.70 + 15160.1i) q^{49} +(25731.4 - 21591.2i) q^{51} +(-24560.0 - 8939.11i) q^{53} +(677.947 - 3844.83i) q^{55} +(26212.6 - 21591.9i) q^{57} +(-3322.45 + 18842.6i) q^{59} +(29662.1 + 10796.1i) q^{61} +(31612.0 - 26525.6i) q^{63} +(-3775.56 + 6539.47i) q^{65} +(-5288.86 - 29994.6i) q^{67} +(-20152.8 - 34905.7i) q^{69} +(-34086.9 + 12406.6i) q^{71} +(-62821.4 - 52713.4i) q^{73} +60305.6 q^{75} -39766.1 q^{77} +(8486.16 + 7120.74i) q^{79} +(59721.3 - 21736.8i) q^{81} +(7468.07 + 12935.1i) q^{83} +(4915.05 + 27874.6i) q^{85} +(-46895.7 + 81225.7i) q^{87} +(-73562.7 + 61726.4i) q^{89} +(72274.6 + 26305.8i) q^{91} +(-19009.2 + 107807. i) q^{93} +(4712.78 + 28226.1i) q^{95} +(-11066.5 + 62761.3i) q^{97} +(44941.3 + 16357.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) \) 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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