LMFDB - Embedded newform 162.7.d.c.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,7,Mod(53,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	162.d (of order $6$, degree $2$, not 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:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.1
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	162.53
Dual form			162.7.d.c.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(29.3939 + 16.9706i) q^{5} +(102.500 + 177.535i) q^{7} +181.019i q^{8} +O(q^{10})$	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(29.3939 + 16.9706i) q^{5} +(102.500 + 177.535i) q^{7} +181.019i q^{8} -192.000 q^{10} +(911.210 - 526.087i) q^{11} +(1020.50 - 1767.56i) q^{13} +(-1004.29 - 579.828i) q^{14} +(-512.000 - 886.810i) q^{16} +8247.69i q^{17} -1501.00 q^{19} +(940.604 - 543.058i) q^{20} +(-2976.00 + 5154.58i) q^{22} +(-6143.32 - 3546.85i) q^{23} +(-7236.50 - 12534.0i) q^{25} +11545.6i q^{26} +6560.00 q^{28} +(24632.1 - 14221.3i) q^{29} +(17495.0 - 30302.2i) q^{31} +(5016.55 + 2896.31i) q^{32} +(-23328.0 - 40405.3i) q^{34} +6957.93i q^{35} -57625.0 q^{37} +(7353.37 - 4245.47i) q^{38} +(-3072.00 + 5320.86i) q^{40} +(116341. + 67169.5i) q^{41} +(31283.0 + 54183.7i) q^{43} -33669.6i q^{44} +40128.0 q^{46} +(-44943.2 + 25948.0i) q^{47} +(37812.0 - 65492.3i) q^{49} +(70902.9 + 40935.8i) q^{50} +(-32656.0 - 56561.9i) q^{52} +77182.1i q^{53} +35712.0 q^{55} +(-32137.3 + 18554.5i) q^{56} +(-80448.0 + 139340. i) q^{58} +(321540. + 185641. i) q^{59} +(30648.5 + 53084.8i) q^{61} +197933. i q^{62} -32768.0 q^{64} +(59992.9 - 34636.9i) q^{65} +(-33845.5 + 58622.1i) q^{67} +(228567. + 131963. i) q^{68} +(-19680.0 - 34086.8i) q^{70} +509524. i q^{71} +423983. q^{73} +(282304. - 162988. i) q^{74} +(-24016.0 + 41596.9i) q^{76} +(186798. + 107848. i) q^{77} +(353766. + 612742. i) q^{79} -34755.7i q^{80} -759936. q^{82} +(745605. - 430475. i) q^{83} +(-139968. + 242432. i) q^{85} +(-306510. - 176963. i) q^{86} +(95232.0 + 164947. i) q^{88} +667656. i q^{89} +418405. q^{91} +(-196586. + 113499. i) q^{92} +(146784. - 254237. i) q^{94} +(-44120.2 - 25472.8i) q^{95} +(-263076. - 455660. i) q^{97} +427794. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 64 q^{4} + 410 q^{7}+O(q^{10}) $ 4 * q + 64 * q^4 + 410 * q^7	$ 4 q + 64 q^{4} + 410 q^{7} - 768 q^{10} + 4082 q^{13} - 2048 q^{16} - 6004 q^{19} - 11904 q^{22} - 28946 q^{25} + 26240 q^{28} + 69980 q^{31} - 93312 q^{34} - 230500 q^{37} - 12288 q^{40} + 125132 q^{43} + 160512 q^{46} + 151248 q^{49} - 130624 q^{52} + 142848 q^{55} - 321792 q^{58} + 122594 q^{61} - 131072 q^{64} - 135382 q^{67} - 78720 q^{70} + 1695932 q^{73} - 96064 q^{76} + 1415066 q^{79} - 3039744 q^{82} - 559872 q^{85} + 380928 q^{88} + 1673620 q^{91} + 587136 q^{94} - 1052302 q^{97}+O(q^{100}) $ 4 * q + 64 * q^4 + 410 * q^7 - 768 * q^10 + 4082 * q^13 - 2048 * q^16 - 6004 * q^19 - 11904 * q^22 - 28946 * q^25 + 26240 * q^28 + 69980 * q^31 - 93312 * q^34 - 230500 * q^37 - 12288 * q^40 + 125132 * q^43 + 160512 * q^46 + 151248 * q^49 - 130624 * q^52 + 142848 * q^55 - 321792 * q^58 + 122594 * q^61 - 131072 * q^64 - 135382 * q^67 - 78720 * q^70 + 1695932 * q^73 - 96064 * q^76 + 1415066 * q^79 - 3039744 * q^82 - 559872 * q^85 + 380928 * q^88 + 1673620 * q^91 + 587136 * q^94 - 1052302 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−4.89898	+	2.82843i	−0.612372	+	0.353553i
$2$	−4.89898	+	2.82843i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	16.0000	−	27.7128i	0.250000	−	0.433013i
$5$	29.3939	+	16.9706i	0.235151	+	0.135765i	0.612946	−	0.790125i	$-0.289984\pi$
$5$	29.3939	+	16.9706i	0.235151	+	0.135765i	−0.377795	+	0.925889i	$0.623318\pi$
$6$		0			0
$7$	102.500	+	177.535i	0.298834	+	0.517595i	0.975869	−	0.218355i	$-0.0700690\pi$
$7$	102.500	+	177.535i	0.298834	+	0.517595i	−0.677036	+	0.735950i	$0.736736\pi$
$8$			181.019i			0.353553i
$9$		0			0
$10$	−192.000			−0.192000
$11$	911.210	−	526.087i	0.684606	−	0.395257i	−0.116982	−	0.993134i	$-0.537322\pi$
$11$	911.210	−	526.087i	0.684606	−	0.395257i	0.801588	+	0.597877i	$0.203989\pi$
$12$		0			0
$13$	1020.50	−	1767.56i	0.464497	−	0.804532i	−0.534682	−	0.845054i	$-0.679568\pi$
$13$	1020.50	−	1767.56i	0.464497	−	0.804532i	0.999179	+	0.0405211i	$0.0129018\pi$
$14$	−1004.29	−	579.828i	−0.365995	−	0.211307i
$15$		0			0
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$			8247.69i			1.67875i	0.543554	+	0.839374i	$0.317078\pi$
$17$			8247.69i			1.67875i	−0.543554	+	0.839374i	$0.682922\pi$
$18$		0			0
$19$	−1501.00			−0.218837			−0.109418	−	0.993996i	$-0.534899\pi$
$19$	−1501.00			−0.218837			−0.109418	+	0.993996i	$0.534899\pi$
$20$	940.604	−	543.058i	0.117576	−	0.0678823i
$21$		0			0
$22$	−2976.00	+	5154.58i	−0.279489	+	0.484089i
$23$	−6143.32	−	3546.85i	−0.504917	−	0.291514i	0.225825	−	0.974168i	$-0.427492\pi$
$23$	−6143.32	−	3546.85i	−0.504917	−	0.291514i	−0.730742	+	0.682654i	$0.760826\pi$
$24$		0			0
$25$	−7236.50	−	12534.0i	−0.463136	−	0.802175i
$26$			11545.6i			0.656898i
$27$		0			0
$28$	6560.00			0.298834
$29$	24632.1	−	14221.3i	1.00997	−	0.583104i	0.0987845	−	0.995109i	$-0.468505\pi$
$29$	24632.1	−	14221.3i	1.00997	−	0.583104i	0.911182	+	0.412005i	$0.135171\pi$
$30$		0			0
$31$	17495.0	−	30302.2i	0.587258	−	1.01716i	−0.407332	−	0.913280i	$-0.633541\pi$
$31$	17495.0	−	30302.2i	0.587258	−	1.01716i	0.994590	−	0.103880i	$-0.0331259\pi$
$32$	5016.55	+	2896.31i	0.153093	+	0.0883883i
$33$		0			0
$34$	−23328.0	−	40405.3i	−0.593527	−	1.02802i
$35$			6957.93i			0.162284i
$36$		0			0
$37$	−57625.0			−1.13764			−0.568821	−	0.822461i	$-0.692600\pi$
$37$	−57625.0			−1.13764			−0.568821	+	0.822461i	$0.692600\pi$
$38$	7353.37	−	4245.47i	0.134009	−	0.0773704i
$39$		0			0
$40$	−3072.00	+	5320.86i	−0.0480000	+	0.0831384i
$41$	116341.	+	67169.5i	1.68803	+	0.974587i	0.956022	+	0.293294i	$0.0947516\pi$
$41$	116341.	+	67169.5i	1.68803	+	0.974587i	0.732011	+	0.681292i	$0.238582\pi$
$42$		0			0
$43$	31283.0	+	54183.7i	0.393462	+	0.681497i	0.992904	−	0.118922i	$-0.0379439\pi$
$43$	31283.0	+	54183.7i	0.393462	+	0.681497i	−0.599441	+	0.800419i	$0.704611\pi$
$44$		−	33669.6i		−	0.395257i
$45$		0			0
$46$	40128.0			0.412263
$47$	−44943.2	+	25948.0i	−0.432883	+	0.249925i	−0.700574	−	0.713580i	$-0.747073\pi$
$47$	−44943.2	+	25948.0i	−0.432883	+	0.249925i	0.267691	+	0.963505i	$0.413739\pi$
$48$		0			0
$49$	37812.0	−	65492.3i	0.321397	−	0.556675i
$50$	70902.9	+	40935.8i	0.567223	+	0.327487i
$51$		0			0
$52$	−32656.0	−	56561.9i	−0.232249	−	0.402266i
$53$			77182.1i			0.518429i	0.965820	+	0.259214i	$0.0834636\pi$
$53$			77182.1i			0.518429i	−0.965820	+	0.259214i	$0.916536\pi$
$54$		0			0
$55$	35712.0			0.214648
$56$	−32137.3	+	18554.5i	−0.182998	+	0.105654i
$57$		0			0
$58$	−80448.0	+	139340.i	−0.412317	+	0.714154i
$59$	321540.	+	185641.i	1.56559	+	0.903895i	0.996673	+	0.0815006i	$0.0259712\pi$
$59$	321540.	+	185641.i	1.56559	+	0.903895i	0.568918	+	0.822394i	$0.307362\pi$
$60$		0			0
$61$	30648.5	+	53084.8i	0.135027	+	0.233873i	0.925608	−	0.378484i	$-0.123555\pi$
$61$	30648.5	+	53084.8i	0.135027	+	0.233873i	−0.790581	+	0.612358i	$0.790221\pi$
$62$			197933.i			0.830508i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	59992.9	−	34636.9i	0.218454	−	0.126124i
$66$		0			0
$67$	−33845.5	+	58622.1i	−0.112532	+	0.194911i	−0.916791	−	0.399368i	$-0.869229\pi$
$67$	−33845.5	+	58622.1i	−0.112532	+	0.194911i	0.804258	+	0.594280i	$0.202563\pi$
$68$	228567.	+	131963.i	0.726920	+	0.419687i
$69$		0			0
$70$	−19680.0	−	34086.8i	−0.0573761	−	0.0993783i
$71$			509524.i			1.42361i	0.702379	+	0.711803i	$0.252121\pi$
$71$			509524.i			1.42361i	−0.702379	+	0.711803i	$0.747879\pi$
$72$		0			0
$73$	423983.			1.08988			0.544941	−	0.838474i	$-0.316552\pi$
$73$	423983.			1.08988			0.544941	+	0.838474i	$0.316552\pi$
$74$	282304.	−	162988.i	0.696661	−	0.402217i
$75$		0			0
$76$	−24016.0	+	41596.9i	−0.0547091	+	0.0947590i
$77$	186798.	+	107848.i	0.409167	+	0.236232i
$78$		0			0
$79$	353766.	+	612742.i	0.717522	+	1.24279i	0.961979	+	0.273125i	$0.0880572\pi$
$79$	353766.	+	612742.i	0.717522	+	1.24279i	−0.244456	+	0.969660i	$0.578609\pi$
$80$		−	34755.7i		−	0.0678823i
$81$		0			0
$82$	−759936.			−1.37827
$83$	745605.	−	430475.i	1.30399	−	0.752860i	0.322905	−	0.946431i	$-0.395341\pi$
$83$	745605.	−	430475.i	1.30399	−	0.752860i	0.981086	+	0.193572i	$0.0620073\pi$
$84$		0			0
$85$	−139968.	+	242432.i	−0.227915	+	0.394760i
$86$	−306510.	−	176963.i	−0.481891	−	0.278220i
$87$		0			0
$88$	95232.0	+	164947.i	0.139745	+	0.242045i
$89$			667656.i			0.947071i	0.880775	+	0.473536i	$0.157022\pi$
$89$			667656.i			0.947071i	−0.880775	+	0.473536i	$0.842978\pi$
$90$		0			0
$91$	418405.			0.555230
$92$	−196586.	+	113499.i	−0.252458	+	0.145757i
$93$		0			0
$94$	146784.	−	254237.i	0.176724	−	0.306095i
$95$	−44120.2	−	25472.8i	−0.0514596	−	0.0297102i
$96$		0			0
$97$	−263076.	−	455660.i	−0.288247	−	0.499259i	0.685144	−	0.728407i	$-0.259739\pi$
$97$	−263076.	−	455660.i	−0.288247	−	0.499259i	−0.973391	+	0.229149i	$0.926406\pi$
$98$			427794.i			0.454524i
$99$		0			0
$100$	−463136.			−0.463136
$101$	−77129.5	+	44530.8i	−0.0748612	+	0.0432211i	−0.536963	−	0.843606i	$-0.680429\pi$
$101$	−77129.5	+	44530.8i	−0.0748612	+	0.0432211i	0.462102	+	0.886827i	$0.347095\pi$
$102$		0			0
$103$	142626.	−	247036.i	0.130523	−	0.226073i	−0.793355	−	0.608759i	$-0.791668\pi$
$103$	142626.	−	247036.i	0.130523	−	0.226073i	0.923878	+	0.382686i	$0.125001\pi$
$104$	319962.	+	184730.i	0.284445	+	0.164225i
$105$		0			0
$106$	−218304.	−	378114.i	−0.183292	−	0.317471i
$107$		−	1.33684e6i		−	1.09126i	−0.838027	−	0.545629i	$-0.816291\pi$
$107$		−	1.33684e6i		−	1.09126i	0.838027	−	0.545629i	$-0.183709\pi$
$108$		0			0
$109$	2.21292e6			1.70878			0.854391	−	0.519631i	$-0.173931\pi$
$109$	2.21292e6			1.70878			0.854391	+	0.519631i	$0.173931\pi$
$110$	−174952.	+	101009.i	−0.131444	+	0.0758894i
$111$		0			0
$112$	104960.	−	181796.i	0.0747085	−	0.129399i
$113$	384854.	+	222196.i	0.266723	+	0.153993i	0.627398	−	0.778699i	$-0.284120\pi$
$113$	384854.	+	222196.i	0.266723	+	0.153993i	−0.360674	+	0.932692i	$0.617453\pi$
$114$		0			0
$115$	−120384.	−	208511.i	−0.0791544	−	0.137100i
$116$		−	910165.i		−	0.583104i
$117$		0			0
$118$	−2.10029e6			−1.27830
$119$	−1.46426e6	+	845389.i	−0.868913	+	0.501667i
$120$		0			0
$121$	−332244.	+	575464.i	−0.187543	+	0.324835i
$122$	−300293.	−	173374.i	−0.165373	−	0.0954783i
$123$		0			0
$124$	−559840.	−	969671.i	−0.293629	−	0.508580i
$125$		−	1.02156e6i		−	0.523039i
$126$		0			0
$127$	−330478.			−0.161336			−0.0806680	−	0.996741i	$-0.525705\pi$
$127$	−330478.			−0.161336			−0.0806680	+	0.996741i	$0.525705\pi$
$128$	160530.	−	92681.9i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−195936.	+	339371.i	−0.0891834	+	0.154470i
$131$	−1.07446e6	−	620342.i	−0.477945	−	0.275942i	0.241615	−	0.970372i	$-0.422323\pi$
$131$	−1.07446e6	−	620342.i	−0.477945	−	0.275942i	−0.719560	+	0.694431i	$0.755656\pi$
$132$		0			0
$133$	−153852.	−	266480.i	−0.0653958	−	0.113269i
$134$		−	382918.i		−	0.159144i
$135$		0			0
$136$	−1.49299e6			−0.593527
$137$	−2.09199e6	+	1.20781e6i	−0.813576	+	0.469718i	−0.848196	−	0.529682i	$-0.822311\pi$
$137$	−2.09199e6	+	1.20781e6i	−0.813576	+	0.469718i	0.0346200	+	0.999401i	$0.488978\pi$
$138$		0			0
$139$	2.55445e6	−	4.42443e6i	0.951157	−	1.64745i	0.208231	−	0.978080i	$-0.433229\pi$
$139$	2.55445e6	−	4.42443e6i	0.951157	−	1.64745i	0.742926	−	0.669373i	$-0.233437\pi$
$140$	192824.	+	111327.i	0.0702711	+	0.0405710i
$141$		0			0
$142$	−1.44115e6	−	2.49615e6i	−0.503321	−	0.871777i
$143$		−	2.14749e6i		−	0.734383i
$144$		0			0
$145$	965376.			0.316659
$146$	−2.07708e6	+	1.19921e6i	−0.667414	+	0.385332i
$147$		0			0
$148$	−922000.	+	1.59695e6i	−0.284411	+	0.492614i
$149$	−4.60649e6	−	2.65956e6i	−1.39255	−	0.803990i	−0.398955	−	0.916971i	$-0.630627\pi$
$149$	−4.60649e6	−	2.65956e6i	−1.39255	−	0.803990i	−0.993597	+	0.112980i	$0.963960\pi$
$150$		0			0
$151$	2.48349e6	+	4.30153e6i	0.721326	+	1.24937i	0.960468	+	0.278389i	$0.0898004\pi$
$151$	2.48349e6	+	4.30153e6i	0.721326	+	1.24937i	−0.239142	+	0.970985i	$0.576866\pi$
$152$		−	271710.i		−	0.0773704i
$153$		0			0
$154$	−1.22016e6			−0.334083
$155$	1.02849e6	−	593800.i	0.276189	−	0.159458i
$156$		0			0
$157$	−413101.	+	715512.i	−0.106747	+	0.184892i	−0.914451	−	0.404697i	$-0.867377\pi$
$157$	−413101.	+	715512.i	−0.106747	+	0.184892i	0.807703	+	0.589589i	$0.200710\pi$
$158$	−3.46619e6	−	2.00121e6i	−0.878782	−	0.507365i
$159$		0			0
$160$	98304.0	+	170268.i	0.0240000	+	0.0415692i
$161$		−	1.45421e6i		−	0.348457i
$162$		0			0
$163$	1.90160e6			0.439094			0.219547	−	0.975602i	$-0.429542\pi$
$163$	1.90160e6			0.439094			0.219547	+	0.975602i	$0.429542\pi$
$164$	3.72291e6	−	2.14942e6i	0.844017	−	0.487293i
$165$		0			0
$166$	−2.43514e6	+	4.21778e6i	−0.532352	+	0.922061i
$167$	−5.05789e6	−	2.92018e6i	−1.08598	−	0.626988i	−0.153474	−	0.988153i	$-0.549046\pi$
$167$	−5.05789e6	−	2.92018e6i	−1.08598	−	0.626988i	−0.932502	+	0.361164i	$0.882379\pi$
$168$		0			0
$169$	330564.	+	572554.i	0.0684850	+	0.118619i
$170$		−	1.58356e6i		−	0.322320i
$171$		0			0
$172$	2.00211e6			0.393462
$173$	3.35331e6	−	1.93604e6i	0.647643	−	0.373917i	−0.139910	−	0.990164i	$-0.544681\pi$
$173$	3.35331e6	−	1.93604e6i	0.647643	−	0.373917i	0.787553	+	0.616247i	$0.211348\pi$
$174$		0			0
$175$	1.48348e6	−	2.56947e6i	0.276801	−	0.479434i
$176$	−933079.	−	538714.i	−0.171151	−	0.0988143i
$177$		0			0
$178$	−1.88842e6	−	3.27083e6i	−0.334840	−	0.579960i
$179$			3.25305e6i			0.567195i	0.958943	+	0.283597i	$0.0915279\pi$
$179$			3.25305e6i			0.567195i	−0.958943	+	0.283597i	$0.908472\pi$
$180$		0			0
$181$	4.83110e6			0.814724			0.407362	−	0.913267i	$-0.366449\pi$
$181$	4.83110e6			0.814724			0.407362	+	0.913267i	$0.366449\pi$
$182$	−2.04976e6	+	1.18343e6i	−0.340007	+	0.196303i
$183$		0			0
$184$	642048.	−	1.11206e6i	0.103066	−	0.178515i
$185$	−1.69382e6	−	977929.i	−0.267518	−	0.154451i
$186$		0			0
$187$	4.33901e6	+	7.51538e6i	0.663538	+	1.14928i
$188$			1.66067e6i			0.249925i
$189$		0			0
$190$	288192.			0.0420166
$191$	−1.72621e6	+	996630.i	−0.247739	+	0.143032i	−0.618729	−	0.785605i	$-0.712352\pi$
$191$	−1.72621e6	+	996630.i	−0.247739	+	0.143032i	0.370989	+	0.928637i	$0.379019\pi$
$192$		0			0
$193$	−5.80510e6	+	1.00547e7i	−0.807491	+	1.39861i	0.107106	+	0.994248i	$0.465841\pi$
$193$	−5.80510e6	+	1.00547e7i	−0.807491	+	1.39861i	−0.914597	+	0.404367i	$0.867492\pi$
$194$	2.57760e6	+	1.48818e6i	0.353029	+	0.203822i
$195$		0			0
$196$	−1.20998e6	−	2.09575e6i	−0.160698	−	0.278338i
$197$		−	4.62309e6i		−	0.604691i	−0.953198	−	0.302345i	$-0.902230\pi$
$197$		−	4.62309e6i		−	0.604691i	0.953198	−	0.302345i	$-0.0977696\pi$
$198$		0			0
$199$	−9.03916e6			−1.14701			−0.573507	−	0.819201i	$-0.694417\pi$
$199$	−9.03916e6			−1.14701			−0.573507	+	0.819201i	$0.694417\pi$
$200$	2.26889e6	−	1.30995e6i	0.283612	−	0.163743i
$201$		0			0
$202$	251904.	−	436311.i	0.0305619	−	0.0529348i
$203$	5.04957e6	+	2.91537e6i	0.603624	+	0.348503i
$204$		0			0
$205$	2.27981e6	+	3.94874e6i	0.264629	+	0.458350i
$206$			1.61363e6i			0.184588i
$207$		0			0
$208$	−2.08998e6			−0.232249
$209$	−1.36773e6	+	789657.i	−0.149817	+	0.0864967i
$210$		0			0
$211$	5.47667e6	−	9.48588e6i	0.583001	−	1.00979i	−0.412120	−	0.911130i	$-0.635212\pi$
$211$	5.47667e6	−	9.48588e6i	0.583001	−	1.00979i	0.995121	−	0.0986584i	$-0.0314551\pi$
$212$	2.13893e6	+	1.23491e6i	0.224486	+	0.129607i
$213$		0			0
$214$	3.78115e6	+	6.54915e6i	0.385818	+	0.668257i
$215$			2.12356e6i			0.213673i
$216$		0			0
$217$	7.17295e6			0.701970
$218$	−1.08411e7	+	6.25909e6i	−1.04641	+	0.604146i
$219$		0			0
$220$	571392.	−	989680.i	0.0536619	−	0.0929452i
$221$	1.45783e7	+	8.41677e6i	1.35061	+	0.779774i
$222$		0			0
$223$	−6.18660e6	−	1.07155e7i	−0.557876	−	0.966269i	−0.997674	−	0.0681724i	$-0.978283\pi$
$223$	−6.18660e6	−	1.07155e7i	−0.557876	−	0.966269i	0.439798	−	0.898097i	$-0.355050\pi$
$224$			1.18749e6i			0.105654i
$225$		0			0
$226$	−2.51386e6			−0.217779
$227$	−5.33275e6	+	3.07887e6i	−0.455905	+	0.263217i	−0.710321	−	0.703878i	$-0.751450\pi$
$227$	−5.33275e6	+	3.07887e6i	−0.455905	+	0.263217i	0.254416	+	0.967095i	$0.418117\pi$
$228$		0			0
$229$	−2.77895e6	+	4.81328e6i	−0.231406	+	0.400807i	−0.958222	−	0.286025i	$-0.907666\pi$
$229$	−2.77895e6	+	4.81328e6i	−0.231406	+	0.400807i	0.726816	+	0.686832i	$0.240999\pi$
$230$	1.17952e6	+	680995.i	0.0969440	+	0.0559706i
$231$		0			0
$232$	2.57434e6	+	4.45888e6i	0.206159	+	0.357077i
$233$			1.17231e7i			0.926778i	0.886155	+	0.463389i	$0.153367\pi$
$233$			1.17231e7i			0.926778i	−0.886155	+	0.463389i	$0.846633\pi$
$234$		0			0
$235$	−1.76141e6			−0.135724
$236$	1.02893e7	−	5.94051e6i	0.782796	−	0.451947i
$237$		0			0
$238$	4.78224e6	−	8.28308e6i	0.354732	−	0.614414i
$239$	1.53042e7	+	8.83589e6i	1.12103	+	0.647227i	0.941664	−	0.336555i	$-0.109262\pi$
$239$	1.53042e7	+	8.83589e6i	1.12103	+	0.647227i	0.179367	+	0.983782i	$0.442595\pi$
$240$		0			0
$241$	−1.07844e7	−	1.86791e7i	−0.770451	−	1.33446i	−0.937316	−	0.348480i	$-0.886698\pi$
$241$	−1.07844e7	−	1.86791e7i	−0.770451	−	1.33446i	0.166866	−	0.985980i	$-0.446635\pi$
$242$		−	3.75892e6i		−	0.265226i
$243$		0			0
$244$	1.96150e6			0.135027
$245$	2.22288e6	−	1.28338e6i	0.151154	−	0.0872685i
$246$		0			0
$247$	−1.53177e6	+	2.65310e6i	−0.101649	+	0.176061i
$248$	5.48529e6	+	3.16693e6i	0.359621	+	0.207627i
$249$		0			0
$250$	2.88941e6	+	5.00460e6i	0.184922	+	0.320294i
$251$		−	1.51574e6i		−	0.0958527i	−0.998851	−	0.0479263i	$-0.984739\pi$
$251$		−	1.51574e6i		−	0.0958527i	0.998851	−	0.0479263i	$-0.0152613\pi$
$252$		0			0
$253$	−7.46381e6			−0.460892
$254$	1.61900e6	−	934733.i	0.0987977	−	0.0570409i
$255$		0			0
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	1.00354e7	+	5.79392e6i	0.591199	+	0.341329i	0.765571	−	0.643351i	$-0.222456\pi$
$257$	1.00354e7	+	5.79392e6i	0.591199	+	0.341329i	−0.174372	+	0.984680i	$0.555790\pi$
$258$		0			0
$259$	−5.90656e6	−	1.02305e7i	−0.339966	−	0.588838i
$260$		−	2.21676e6i		−	0.126124i
$261$		0			0
$262$	7.01837e6			0.390240
$263$	2.25139e7	−	1.29984e7i	1.23761	−	0.714535i	0.269006	−	0.963138i	$-0.413305\pi$
$263$	2.25139e7	−	1.29984e7i	1.23761	−	0.714535i	0.968605	+	0.248603i	$0.0799715\pi$
$264$		0			0
$265$	−1.30982e6	+	2.26868e6i	−0.0703842	+	0.121909i
$266$	1.50744e6	+	870321.i	0.0800931	+	0.0462418i
$267$		0			0
$268$	1.08306e6	+	1.87591e6i	0.0562661	+	0.0974557i
$269$			8.77605e6i			0.450861i	0.974259	+	0.225430i	$0.0723788\pi$
$269$			8.77605e6i			0.450861i	−0.974259	+	0.225430i	$0.927621\pi$
$270$		0			0
$271$	1.16794e7			0.586831			0.293416	−	0.955985i	$-0.405208\pi$
$271$	1.16794e7			0.586831			0.293416	+	0.955985i	$0.405208\pi$
$272$	7.31414e6	−	4.22282e6i	0.363460	−	0.209844i
$273$		0			0
$274$	6.83242e6	−	1.18341e7i	0.332141	−	0.575285i
$275$	−1.31879e7	−	7.61406e6i	−0.634131	−	0.366116i
$276$		0			0
$277$	−5.71151e6	−	9.89262e6i	−0.268727	−	0.465449i	0.699806	−	0.714333i	$-0.253270\pi$
$277$	−5.71151e6	−	9.89262e6i	−0.268727	−	0.465449i	−0.968533	+	0.248884i	$0.919936\pi$
$278$			2.89003e7i			1.34514i
$279$		0			0
$280$	−1.25952e6			−0.0573761
$281$	1.04576e7	−	6.03768e6i	0.471316	−	0.272114i	−0.245474	−	0.969403i	$-0.578944\pi$
$281$	1.04576e7	−	6.03768e6i	0.471316	−	0.272114i	0.716790	+	0.697289i	$0.245610\pi$
$282$		0			0
$283$	−1.94454e6	+	3.36804e6i	−0.0857942	+	0.148600i	−0.905729	−	0.423857i	$-0.860676\pi$
$283$	−1.94454e6	+	3.36804e6i	−0.0857942	+	0.148600i	0.819935	+	0.572456i	$0.194009\pi$
$284$	1.41203e7	+	8.15239e6i	0.616439	+	0.355901i
$285$		0			0
$286$	6.07402e6	+	1.05205e7i	0.259644	+	0.449716i
$287$			2.75395e7i			1.16496i
$288$		0			0
$289$	−4.38869e7			−1.81820
$290$	−4.72936e6	+	2.73050e6i	−0.193914	+	0.111956i
$291$		0			0
$292$	6.78373e6	−	1.17498e7i	0.272471	−	0.471933i
$293$	−2.31342e7	−	1.33566e7i	−0.919713	−	0.530997i	−0.0361697	−	0.999346i	$-0.511516\pi$
$293$	−2.31342e7	−	1.33566e7i	−0.919713	−	0.530997i	−0.883544	+	0.468349i	$0.844849\pi$
$294$		0			0
$295$	6.30086e6	+	1.09134e7i	0.245434	+	0.425104i
$296$		−	1.04312e7i		−	0.402217i
$297$		0			0
$298$	3.00895e7			1.13701
$299$	−1.25385e7	+	7.23912e6i	−0.469065	+	0.270815i
$300$		0			0
$301$	−6.41302e6	+	1.11077e7i	−0.235160	+	0.407308i
$302$	−2.43331e7	−	1.40487e7i	−0.883440	−	0.510055i
$303$		0			0
$304$	768512.	+	1.33110e6i	0.0273546	+	0.0473795i
$305$			2.08049e6i			0.0733273i
$306$		0			0
$307$	−1.79714e7			−0.621108			−0.310554	−	0.950556i	$-0.600515\pi$
$307$	−1.79714e7			−0.621108			−0.310554	+	0.950556i	$0.600515\pi$
$308$	5.97754e6	−	3.45113e6i	0.204583	−	0.118116i
$309$		0			0
$310$	−3.35904e6	+	5.81803e6i	−0.112754	+	0.195295i
$311$	3.59069e7	+	2.07308e7i	1.19370	+	0.689185i	0.959144	−	0.282917i	$-0.0913020\pi$
$311$	3.59069e7	+	2.07308e7i	1.19370	+	0.689185i	0.234559	+	0.972102i	$0.424635\pi$
$312$		0			0
$313$	1.13070e6	+	1.95843e6i	0.0368735	+	0.0638668i	0.883873	−	0.467727i	$-0.154927\pi$
$313$	1.13070e6	+	1.95843e6i	0.0368735	+	0.0638668i	−0.847000	+	0.531593i	$0.821593\pi$
$314$		−	4.67370e6i		−	0.150964i
$315$		0			0
$316$	2.26411e7			0.717522
$317$	−9.86582e6	+	5.69603e6i	−0.309710	+	0.178811i	−0.646797	−	0.762662i	$-0.723892\pi$
$317$	−9.86582e6	+	5.69603e6i	−0.309710	+	0.178811i	0.337087	+	0.941474i	$0.390558\pi$
$318$		0			0
$319$	1.49633e7	−	2.59172e7i	0.460952	−	0.798393i
$320$	−963179.	−	556091.i	−0.0293939	−	0.0169706i
$321$		0			0
$322$	4.11312e6	+	7.12413e6i	0.123198	+	0.213385i
$323$		−	1.23798e7i		−	0.367372i
$324$		0			0
$325$	−2.95394e7			−0.860501
$326$	−9.31591e6	+	5.37855e6i	−0.268889	+	0.155243i
$327$		0			0
$328$	−1.21590e7	+	2.10600e7i	−0.344568	+	0.596810i
$329$	−9.21336e6	−	5.31934e6i	−0.258720	−	0.149372i
$330$		0			0
$331$	−7.03387e6	−	1.21830e7i	−0.193959	−	0.335947i	0.752600	−	0.658478i	$-0.228800\pi$
$331$	−7.03387e6	−	1.21830e7i	−0.193959	−	0.335947i	−0.946559	+	0.322531i	$0.895466\pi$
$332$		−	2.75504e7i		−	0.752860i
$333$		0			0
$334$	3.30380e7			0.886696
$335$	−1.98970e6	+	1.14875e6i	−0.0529241	+	0.0305557i
$336$		0			0
$337$	−2.39591e7	+	4.14983e7i	−0.626008	+	1.08428i	0.362336	+	0.932047i	$0.381979\pi$
$337$	−2.39591e7	+	4.14983e7i	−0.626008	+	1.08428i	−0.988345	+	0.152231i	$0.951354\pi$
$338$	−3.23885e6	−	1.86995e6i	−0.0838766	−	0.0484262i
$339$		0			0
$340$	4.47898e6	+	7.75781e6i	0.113957	+	0.197380i
$341$		−	3.68156e7i		−	0.928472i
$342$		0			0
$343$	3.96210e7			0.981844
$344$	−9.80831e6	+	5.66283e6i	−0.240945	+	0.139110i
$345$		0			0
$346$	−1.09519e7	+	1.89692e7i	−0.264399	+	0.457953i
$347$	−3.68196e7	−	2.12578e7i	−0.881233	−	0.508780i	−0.0101680	−	0.999948i	$-0.503237\pi$
$347$	−3.68196e7	−	2.12578e7i	−0.881233	−	0.508780i	−0.871065	+	0.491168i	$0.836570\pi$
$348$		0			0
$349$	4.06997e7	+	7.04940e7i	0.957448	+	1.65835i	0.728663	+	0.684872i	$0.240142\pi$
$349$	4.06997e7	+	7.04940e7i	0.957448	+	1.65835i	0.228785	+	0.973477i	$0.426525\pi$
$350$			1.67837e7i			0.391456i
$351$		0			0
$352$	6.09485e6			0.139745
$353$	−3.30207e7	+	1.90645e7i	−0.750693	+	0.433413i	−0.825944	−	0.563752i	$-0.809358\pi$
$353$	−3.30207e7	+	1.90645e7i	−0.750693	+	0.433413i	0.0752511	+	0.997165i	$0.476024\pi$
$354$		0			0
$355$	−8.64691e6	+	1.49769e7i	−0.193275	+	0.334762i
$356$	1.85026e7	+	1.06825e7i	0.410094	+	0.236768i
$357$		0			0
$358$	−9.20102e6	−	1.59366e7i	−0.200534	−	0.347334i
$359$		−	7.04340e7i		−	1.52230i	−0.648579	−	0.761148i	$-0.724636\pi$
$359$		−	7.04340e7i		−	1.52230i	0.648579	−	0.761148i	$-0.275364\pi$
$360$		0			0
$361$	−4.47929e7			−0.952111
$362$	−2.36675e7	+	1.36644e7i	−0.498915	+	0.288048i
$363$		0			0
$364$	6.69448e6	−	1.15952e7i	0.138807	−	0.240422i
$365$	1.24625e7	+	7.19523e6i	0.256287	+	0.147967i
$366$		0			0
$367$	−1.93498e7	−	3.35148e7i	−0.391452	−	0.678014i	0.601190	−	0.799106i	$-0.294694\pi$
$367$	−1.93498e7	−	3.35148e7i	−0.391452	−	0.678014i	−0.992641	+	0.121092i	$0.961360\pi$
$368$			7.26394e6i			0.145757i
$369$		0			0
$370$	1.10640e7			0.218427
$371$	−1.37025e7	+	7.91117e6i	−0.268336	+	0.154924i
$372$		0			0
$373$	2.88381e7	−	4.99491e7i	0.555700	−	0.962500i	−0.442149	−	0.896942i	$-0.645784\pi$
$373$	2.88381e7	−	4.99491e7i	0.555700	−	0.962500i	0.997849	−	0.0655585i	$-0.0208829\pi$
$374$	−4.25134e7	−	2.45451e7i	−0.812664	−	0.469192i
$375$		0			0
$376$	−4.69709e6	−	8.13560e6i	−0.0883619	−	0.153047i
$377$		−	5.80515e7i		−	1.08340i
$378$		0			0
$379$	4.45022e7			0.817455			0.408728	−	0.912656i	$-0.365973\pi$
$379$	4.45022e7			0.817455			0.408728	+	0.912656i	$0.365973\pi$
$380$	−1.41185e6	+	815130.i	−0.0257298	+	0.0148551i
$381$		0			0
$382$	5.63779e6	−	9.76494e6i	0.101139	−	0.175178i
$383$	−9.36936e7	−	5.40940e7i	−1.66768	−	0.962837i	−0.968883	−	0.247520i	$-0.920384\pi$
$383$	−9.36936e7	−	5.40940e7i	−1.66768	−	0.962837i	−0.698800	−	0.715317i	$-0.746282\pi$
$384$		0			0
$385$	3.66048e6	+	6.34014e6i	0.0641440	+	0.111101i
$386$		−	6.56772e7i		−	1.14196i
$387$		0			0
$388$	−1.68368e7			−0.288247
$389$	7.41575e6	−	4.28149e6i	0.125981	−	0.0727354i	−0.435685	−	0.900099i	$-0.643494\pi$
$389$	7.41575e6	−	4.28149e6i	0.125981	−	0.0727354i	0.561666	+	0.827364i	$0.310160\pi$
$390$		0			0
$391$	2.92533e7	−	5.06682e7i	0.489378	−	0.847628i
$392$	1.18554e7	+	6.84470e6i	0.196814	+	0.113631i
$393$		0			0
$394$	1.30761e7	+	2.26484e7i	0.213790	+	0.370296i
$395$			2.40145e7i			0.389656i
$396$		0			0
$397$	−8.09229e7			−1.29330			−0.646651	−	0.762786i	$-0.723831\pi$
$397$	−8.09229e7			−1.29330			−0.646651	+	0.762786i	$0.723831\pi$
$398$	4.42826e7	−	2.55666e7i	0.702400	−	0.405531i
$399$		0			0
$400$	−7.41018e6	+	1.28348e7i	−0.115784	+	0.200544i
$401$	−4.36170e7	−	2.51823e7i	−0.676429	−	0.390537i	0.122079	−	0.992520i	$-0.461044\pi$
$401$	−4.36170e7	−	2.51823e7i	−0.676429	−	0.390537i	−0.798508	+	0.601984i	$0.794377\pi$
$402$		0			0
$403$	−3.57073e7	−	6.18468e7i	−0.545559	−	0.944936i
$404$			2.84997e6i			0.0432211i
$405$		0			0
$406$	−3.29837e7			−0.492857
$407$	−5.25085e7	+	3.03158e7i	−0.778836	+	0.449661i
$408$		0			0
$409$	−3.11297e7	+	5.39183e7i	−0.454994	+	0.788072i	−0.998688	−	0.0512112i	$-0.983692\pi$
$409$	−3.11297e7	+	5.39183e7i	−0.454994	+	0.788072i	0.543694	+	0.839283i	$0.317025\pi$
$410$	−2.23375e7	−	1.28965e7i	−0.324102	−	0.187121i
$411$		0			0
$412$	−4.56405e6	−	7.90516e6i	−0.0652617	−	0.113037i
$413$			7.61128e7i			1.08046i
$414$		0			0
$415$	2.92216e7			0.408846
$416$	1.02388e7	−	5.91137e6i	0.142223	−	0.0821123i
$417$		0			0
$418$	4.46698e6	−	7.73703e6i	0.0611624	−	0.105936i
$419$	1.03266e7	+	5.96208e6i	0.140384	+	0.0810505i	0.568547	−	0.822651i	$-0.307506\pi$
$419$	1.03266e7	+	5.96208e6i	0.140384	+	0.0810505i	−0.428163	+	0.903701i	$0.640839\pi$
$420$		0			0
$421$	2.80026e7	+	4.85019e7i	0.375277	+	0.649999i	0.990368	−	0.138457i	$-0.0442142\pi$
$421$	2.80026e7	+	4.85019e7i	0.375277	+	0.649999i	−0.615091	+	0.788456i	$0.710881\pi$
$422$			6.19615e7i			0.824488i
$423$		0			0
$424$	−1.39715e7			−0.183292
$425$	1.03376e8	−	5.96844e7i	1.34665	−	0.777489i
$426$		0			0
$427$	−6.28294e6	+	1.08824e7i	−0.0807011	+	0.139778i
$428$	−3.70476e7	−	2.13894e7i	−0.472529	−	0.272815i
$429$		0			0
$430$	−6.00634e6	−	1.04033e7i	−0.0755447	−	0.130847i
$431$			2.91184e6i			0.0363694i	0.999835	+	0.0181847i	$0.00578869\pi$
$431$			2.91184e6i			0.0363694i	−0.999835	+	0.0181847i	$0.994211\pi$
$432$		0			0
$433$	5.23835e7			0.645254			0.322627	−	0.946526i	$-0.395434\pi$
$433$	5.23835e7			0.645254			0.322627	+	0.946526i	$0.395434\pi$
$434$	−3.51401e7	+	2.02882e7i	−0.429867	+	0.248184i
$435$		0			0
$436$	3.54068e7	−	6.13263e7i	0.427195	−	0.739924i
$437$	9.22112e6	+	5.32382e6i	0.110494	+	0.0637939i
$438$		0			0
$439$	−7.23044e7	−	1.25235e8i	−0.854616	−	1.48024i	−0.877000	−	0.480490i	$-0.840459\pi$
$439$	−7.23044e7	−	1.25235e8i	−0.854616	−	1.48024i	0.0223839	−	0.999749i	$-0.492874\pi$
$440$			6.46456e6i			0.0758894i
$441$		0			0
$442$	−9.52249e7			−1.10277
$443$	7.69878e7	−	4.44489e7i	0.885545	−	0.511270i	0.0130624	−	0.999915i	$-0.495842\pi$
$443$	7.69878e7	−	4.44489e7i	0.885545	−	0.511270i	0.872483	+	0.488645i	$0.162509\pi$
$444$		0			0
$445$	−1.13305e7	+	1.96250e7i	−0.128579	+	0.222705i
$446$	6.06161e7	+	3.49967e7i	0.683256	+	0.394478i
$447$		0			0
$448$	−3.35872e6	−	5.81747e6i	−0.0373542	−	0.0646994i
$449$			9.48526e7i			1.04788i	0.851756	+	0.523939i	$0.175538\pi$
$449$			9.48526e7i			1.04788i	−0.851756	+	0.523939i	$0.824462\pi$
$450$		0			0
$451$	1.41348e8			1.54085
$452$	1.23153e7	−	7.11026e6i	0.133362	−	0.0769963i
$453$		0			0
$454$	1.74167e7	−	3.01666e7i	0.186122	−	0.322373i
$455$	1.22985e7	+	7.10057e6i	0.130563	+	0.0753805i
$456$		0			0
$457$	5.90119e6	+	1.02212e7i	0.0618288	+	0.107091i	0.895283	−	0.445498i	$-0.146973\pi$
$457$	5.90119e6	+	1.02212e7i	0.0618288	+	0.107091i	−0.833454	+	0.552589i	$0.813640\pi$
$458$		−	3.14402e7i		−	0.327257i
$459$		0			0
$460$	−7.70458e6			−0.0791544
$461$	−1.28196e8	+	7.40142e7i	−1.30850	+	0.755461i	−0.981845	−	0.189684i	$-0.939254\pi$
$461$	−1.28196e8	+	7.40142e7i	−1.30850	+	0.755461i	−0.326652	+	0.945145i	$0.605920\pi$
$462$		0			0
$463$	3.06114e7	−	5.30205e7i	0.308418	−	0.534196i	−0.669598	−	0.742724i	$-0.733534\pi$
$463$	3.06114e7	−	5.30205e7i	0.308418	−	0.534196i	0.978017	+	0.208527i	$0.0668670\pi$
$464$	−2.52232e7	−	1.45626e7i	−0.252492	−	0.145776i
$465$		0			0
$466$	−3.31580e7	−	5.74314e7i	−0.327666	−	0.567533i
$467$		−	5.91925e7i		−	0.581187i	−0.956847	−	0.290593i	$-0.906147\pi$
$467$		−	5.91925e7i		−	0.581187i	0.956847	−	0.290593i	$-0.0938527\pi$
$468$		0			0
$469$	−1.38767e7			−0.134514
$470$	8.62910e6	−	4.98201e6i	0.0831136	−	0.0479857i
$471$		0			0
$472$	−3.36046e7	+	5.82049e7i	−0.319575	+	0.553520i
$473$	5.70108e7	+	3.29152e7i	0.538733	+	0.311038i
$474$		0			0
$475$	1.08620e7	+	1.88135e7i	0.101351	+	0.175545i
$476$			5.41049e7i			0.501667i
$477$		0			0
$478$	−9.99667e7			−0.915317
$479$	5.31167e7	−	3.06669e7i	0.483308	−	0.279038i	−0.238486	−	0.971146i	$-0.576651\pi$
$479$	5.31167e7	−	3.06669e7i	0.483308	−	0.279038i	0.721794	+	0.692108i	$0.243318\pi$
$480$		0			0
$481$	−5.88063e7	+	1.01856e8i	−0.528432	+	0.915270i
$482$	1.05665e8	+	6.10058e7i	0.943606	+	0.544791i
$483$		0			0
$484$	1.06318e7	+	1.84149e7i	0.0937717	+	0.162417i
$485$		−	1.78582e7i		−	0.156535i
$486$		0			0
$487$	1.20027e8			1.03918			0.519592	−	0.854415i	$-0.326084\pi$
$487$	1.20027e8			1.03918			0.519592	+	0.854415i	$0.326084\pi$
$488$	−9.60937e6	+	5.54797e6i	−0.0826866	+	0.0477392i
$489$		0			0
$490$	−7.25990e6	+	1.25745e7i	−0.0617082	+	0.106882i
$491$	1.89139e8	+	1.09200e8i	1.59786	+	0.922522i	0.991900	+	0.127024i	$0.0405426\pi$
$491$	1.89139e8	+	1.09200e8i	1.59786	+	0.922522i	0.605956	+	0.795498i	$0.292791\pi$
$492$		0			0
$493$	1.17293e8	+	2.03158e8i	0.978886	+	1.69548i
$494$		−	1.73300e7i		−	0.143753i
$495$		0			0
$496$	−3.58298e7			−0.293629
$497$	−9.04585e7	+	5.22262e7i	−0.736852	+	0.425422i
$498$		0			0
$499$	9.59663e7	−	1.66219e8i	0.772355	−	1.33776i	−0.163914	−	0.986475i	$-0.552412\pi$
$499$	9.59663e7	−	1.66219e8i	0.772355	−	1.33776i	0.936269	−	0.351284i	$-0.114255\pi$
$500$	−2.83103e7	−	1.63450e7i	−0.226482	−	0.130760i
$501$		0			0
$502$	4.28717e6	+	7.42559e6i	0.0338890	+	0.0586976i
$503$			2.12153e8i			1.66704i	0.552491	+	0.833519i	$0.313678\pi$
$503$			2.12153e8i			1.66704i	−0.552491	+	0.833519i	$0.686322\pi$
$504$		0			0
$505$	−3.02285e6			−0.0234716
$506$	3.65650e7	−	2.11108e7i	0.282237	−	0.162950i
$507$		0			0
$508$	−5.28765e6	+	9.15847e6i	−0.0403340	+	0.0698606i
$509$	6.15952e6	+	3.55620e6i	0.0467082	+	0.0269670i	0.523172	−	0.852227i	$-0.324748\pi$
$509$	6.15952e6	+	3.55620e6i	0.0467082	+	0.0269670i	−0.476464	+	0.879194i	$0.658082\pi$
$510$		0			0
$511$	4.34583e7	+	7.52719e7i	0.325694	+	0.564118i
$512$		−	5.93164e6i		−	0.0441942i
$513$		0			0
$514$	−6.55507e7			−0.482712
$515$	8.38469e6	−	4.84090e6i	0.0613854	−	0.0354409i
$516$		0			0
$517$	−2.73018e7	+	4.72881e7i	−0.197570	+	0.342201i
$518$	5.78723e7	+	3.34126e7i	0.416372	+	0.240392i
$519$		0			0
$520$	6.26995e6	+	1.08599e7i	0.0445917	+	0.0772351i
$521$		−	2.39355e8i		−	1.69251i	−0.532781	−	0.846253i	$-0.678853\pi$
$521$		−	2.39355e8i		−	1.69251i	0.532781	−	0.846253i	$-0.321147\pi$
$522$		0			0
$523$	1.44195e8			1.00796			0.503982	−	0.863714i	$-0.331868\pi$
$523$	1.44195e8			1.00796			0.503982	+	0.863714i	$0.331868\pi$
$524$	−3.43828e7	+	1.98509e7i	−0.238972	+	0.137971i
$525$		0			0
$526$	−7.35302e7	+	1.27358e8i	−0.505253	+	0.875124i
$527$	2.49923e8	+	1.44293e8i	1.70756	+	0.985859i
$528$		0			0
$529$	−4.88577e7	−	8.46240e7i	−0.330039	−	0.571645i
$530$		−	1.48190e7i		−	0.0995383i
$531$		0			0
$532$	−9.84656e6			−0.0653958
$533$	2.37452e8	−	1.37093e8i	1.56817	−	0.905385i
$534$		0			0
$535$	2.26869e7	−	3.92949e7i	0.148154	−	0.256611i
$536$	−1.06117e7	−	6.12669e6i	−0.0689116	−	0.0397861i
$537$		0			0
$538$	−2.48224e7	−	4.29937e7i	−0.159403	−	0.276095i
$539$		−	7.95697e7i		−	0.508138i
$540$		0			0
$541$	−2.23812e8			−1.41348			−0.706742	−	0.707472i	$-0.749836\pi$
$541$	−2.23812e8			−1.41348			−0.706742	+	0.707472i	$0.749836\pi$
$542$	−5.72172e7	+	3.30344e7i	−0.359359	+	0.207476i
$543$		0			0
$544$	−2.38879e7	+	4.13750e7i	−0.148382	+	0.257005i
$545$	6.50464e7	+	3.75545e7i	0.401822	+	0.231992i
$546$		0			0
$547$	1.08691e8	+	1.88258e8i	0.664097	+	1.15025i	0.979529	+	0.201302i	$0.0645172\pi$
$547$	1.08691e8	+	1.88258e8i	0.664097	+	1.15025i	−0.315432	+	0.948948i	$0.602149\pi$
$548$			7.73000e7i			0.469718i
$549$		0			0
$550$	8.61433e7			0.517766
$551$	−3.69727e7	+	2.13462e7i	−0.221018	+	0.127605i
$552$		0			0
$553$	−7.25221e7	+	1.25612e8i	−0.428840	+	0.742772i
$554$	5.59611e7	+	3.23092e7i	0.329122	+	0.190019i
$555$		0			0
$556$	−8.17423e7	−	1.41582e8i	−0.475579	−	0.823727i
$557$			3.00003e8i			1.73604i	0.496528	+	0.868021i	$0.334608\pi$
$557$			3.00003e8i			1.73604i	−0.496528	+	0.868021i	$0.665392\pi$
$558$		0			0
$559$	1.27697e8			0.731048
$560$	6.17036e6	−	3.56246e6i	0.0351355	−	0.0202855i
$561$		0			0
$562$	−3.41543e7	+	5.91570e7i	−0.192414	+	0.333271i
$563$	−2.66439e8	−	1.53828e8i	−1.49304	−	0.862009i	−0.493074	−	0.869987i	$-0.664127\pi$
$563$	−2.66439e8	−	1.53828e8i	−1.49304	−	0.862009i	−0.999968	+	0.00797863i	$0.997460\pi$
$564$		0			0
$565$	7.54157e6	+	1.30624e7i	0.0418135	+	0.0724231i
$566$		−	2.20000e7i		−	0.121331i
$567$		0			0
$568$	−9.22337e7			−0.503321
$569$	−2.44559e7	+	1.41196e7i	−0.132754	+	0.0766455i	−0.564906	−	0.825155i	$-0.691088\pi$
$569$	−2.44559e7	+	1.41196e7i	−0.132754	+	0.0766455i	0.432152	+	0.901801i	$0.357754\pi$
$570$		0			0
$571$	9.89628e7	−	1.71409e8i	0.531574	−	0.920713i	−0.467747	−	0.883862i	$-0.654934\pi$
$571$	9.89628e7	−	1.71409e8i	0.531574	−	0.920713i	0.999321	−	0.0368506i	$-0.0117326\pi$
$572$	−5.95130e7	−	3.43598e7i	−0.317997	−	0.183596i
$573$		0			0
$574$	−7.78934e7	−	1.34915e8i	−0.411875	−	0.713388i
$575$			1.02667e8i			0.540042i
$576$		0			0
$577$	1.56557e8			0.814978			0.407489	−	0.913210i	$-0.366405\pi$
$577$	1.56557e8			0.814978			0.407489	+	0.913210i	$0.366405\pi$
$578$	2.15001e8	−	1.24131e8i	1.11341	−	0.642830i
$579$		0			0
$580$	1.54460e7	−	2.67533e7i	0.0791649	−	0.137118i
$581$	1.52849e8	+	8.82474e7i	0.779353	+	0.449960i
$582$		0			0
$583$	4.06045e7	+	7.03291e7i	0.204913	+	0.354919i
$584$			7.67491e7i			0.385332i
$585$		0			0
$586$	1.51112e8			0.750943
$587$	6.68861e6	−	3.86167e6i	0.0330690	−	0.0190924i	−0.483374	−	0.875414i	$-0.660589\pi$
$587$	6.68861e6	−	3.86167e6i	0.0330690	−	0.0190924i	0.516443	+	0.856321i	$0.327256\pi$
$588$		0			0
$589$	−2.62600e7	+	4.54836e7i	−0.128514	+	0.222592i
$590$	−6.17356e7	−	3.56431e7i	−0.300594	−	0.173548i
$591$		0			0
$592$	2.95040e7	+	5.11024e7i	0.142205	+	0.246307i
$593$			2.02243e8i			0.969861i	0.874553	+	0.484930i	$0.161155\pi$
$593$			2.02243e8i			0.969861i	−0.874553	+	0.484930i	$0.838845\pi$
$594$		0			0
$595$	−5.73869e7			−0.272434
$596$	−1.47408e8	+	8.51059e7i	−0.696276	+	0.401995i
$597$		0			0
$598$	4.09506e7	−	7.09286e7i	0.191495	−	0.331679i
$599$	−2.87407e8	−	1.65935e8i	−1.33726	−	0.772070i	−0.350863	−	0.936427i	$-0.614112\pi$
$599$	−2.87407e8	−	1.65935e8i	−1.33726	−	0.772070i	−0.986401	+	0.164357i	$0.947445\pi$
$600$		0			0
$601$	4.82333e7	+	8.35425e7i	0.222190	+	0.384844i	0.955473	−	0.295080i	$-0.0953463\pi$
$601$	4.82333e7	+	8.35425e7i	0.222190	+	0.384844i	−0.733283	+	0.679924i	$0.762013\pi$
$602$		−	7.25550e7i		−	0.332566i
$603$		0			0
$604$	1.58943e8			0.721326
$605$	−1.95319e7	+	1.12768e7i	−0.0882020	+	0.0509235i
$606$		0			0
$607$	8.42770e7	−	1.45972e8i	0.376828	−	0.652685i	−0.613771	−	0.789484i	$-0.710348\pi$
$607$	8.42770e7	−	1.45972e8i	0.376828	−	0.652685i	0.990599	+	0.136799i	$0.0436815\pi$
$608$	−7.52985e6	−	4.34736e6i	−0.0335024	−	0.0193426i
$609$		0			0
$610$	−5.88451e6	−	1.01923e7i	−0.0259251	−	0.0449036i
$611$			1.05920e8i			0.464358i
$612$		0			0
$613$	−3.19543e8			−1.38723			−0.693614	−	0.720347i	$-0.743983\pi$
$613$	−3.19543e8			−1.38723			−0.693614	+	0.720347i	$0.743983\pi$
$614$	8.80416e7	−	5.08308e7i	0.380349	−	0.219595i
$615$		0			0
$616$	−1.95226e7	+	3.38141e7i	−0.0835208	+	0.144662i
$617$	−1.87744e8	−	1.08394e8i	−0.799301	−	0.461477i	0.0439255	−	0.999035i	$-0.486014\pi$
$617$	−1.87744e8	−	1.08394e8i	−0.799301	−	0.461477i	−0.843227	+	0.537558i	$0.819347\pi$
$618$		0			0
$619$	−1.37724e8	−	2.38546e8i	−0.580683	−	1.00577i	−0.995399	−	0.0958210i	$-0.969452\pi$
$619$	−1.37724e8	−	2.38546e8i	−0.580683	−	1.00577i	0.414716	−	0.909951i	$-0.363881\pi$
$620$		−	3.80032e7i		−	0.159458i
$621$		0			0
$622$	−2.34543e8			−0.974655
$623$	−1.18532e8	+	6.84347e7i	−0.490200	+	0.283017i
$624$		0			0
$625$	−9.57339e7	+	1.65816e8i	−0.392126	+	0.679182i
$626$	−1.10786e7	−	6.39621e6i	−0.0451607	−	0.0260735i
$627$		0			0
$628$	1.32192e7	+	2.28964e7i	0.0533737	+	0.0924460i
$629$		−	4.75273e8i		−	1.90982i
$630$		0			0
$631$	−2.56044e8			−1.01912			−0.509562	−	0.860434i	$-0.670192\pi$
$631$	−2.56044e8			−1.01912			−0.509562	+	0.860434i	$0.670192\pi$
$632$	−1.10918e8	+	6.40386e7i	−0.439391	+	0.253682i
$633$		0			0
$634$	3.22216e7	−	5.58095e7i	0.126439	−	0.218998i
$635$	−9.71403e6	−	5.60840e6i	−0.0379383	−	0.0219037i
$636$		0			0
$637$	−7.71743e7	−	1.33670e8i	−0.298576	−	0.517148i
$638$			1.69291e8i			0.651885i
$639$		0			0
$640$	6.29146e6			0.0240000
$641$	1.37601e8	−	7.94439e7i	0.522453	−	0.301638i	−0.215485	−	0.976507i	$-0.569133\pi$
$641$	1.37601e8	−	7.94439e7i	0.522453	−	0.301638i	0.737938	+	0.674869i	$0.235800\pi$
$642$		0			0
$643$	1.57338e8	−	2.72517e8i	0.591833	−	1.02509i	−0.402152	−	0.915573i	$-0.631738\pi$
$643$	1.57338e8	−	2.72517e8i	0.591833	−	1.02509i	0.993985	−	0.109513i	$-0.0349290\pi$
$644$	−4.03002e7	−	2.32673e7i	−0.150886	−	0.0871142i
$645$		0			0
$646$	3.50153e7	+	6.06483e7i	0.129885	+	0.224968i
$647$		−	5.06718e8i		−	1.87091i	−0.353442	−	0.935457i	$-0.614989\pi$
$647$		−	5.06718e8i		−	1.87091i	0.353442	−	0.935457i	$-0.385011\pi$
$648$		0			0
$649$	3.90654e8			1.42908
$650$	1.44713e8	−	8.35500e7i	0.526947	−	0.304233i
$651$		0			0
$652$	3.04256e7	−	5.26988e7i	0.109773	−	0.190133i
$653$	−2.86560e8	−	1.65445e8i	−1.02914	−	0.594176i	−0.112404	−	0.993663i	$-0.535855\pi$
$653$	−2.86560e8	−	1.65445e8i	−1.02914	−	0.594176i	−0.916739	+	0.399487i	$0.869188\pi$
$654$		0			0
$655$	−2.10551e7	−	3.64685e7i	−0.0749262	−	0.129776i
$656$		−	1.37563e8i		−	0.487293i
$657$		0			0
$658$	6.01814e7			0.211244
$659$	−1.25671e8	+	7.25563e7i	−0.439116	+	0.253524i	−0.703223	−	0.710970i	$-0.748256\pi$
$659$	−1.25671e8	+	7.25563e7i	−0.439116	+	0.253524i	0.264106	+	0.964494i	$0.414923\pi$
$660$		0			0
$661$	3.58816e7	−	6.21488e7i	0.124242	−	0.215193i	−0.797195	−	0.603722i	$-0.793684\pi$
$661$	3.58816e7	−	6.21488e7i	0.124242	−	0.215193i	0.921436	+	0.388529i	$0.127017\pi$
$662$	6.89175e7	+	3.97896e7i	0.237550	+	0.137150i
$663$		0			0
$664$	7.79244e7	+	1.34969e8i	0.266176	+	0.461030i
$665$		−	1.04439e7i		−	0.0355137i
$666$		0			0
$667$	−2.01764e8			−0.679932
$668$	−1.61853e8	+	9.34456e7i	−0.542988	+	0.313494i
$669$		0			0
$670$	6.49834e6	−	1.12554e7i	0.0216062	−	0.0374230i
$671$	5.58545e7	+	3.22476e7i	0.184880	+	0.106741i
$672$		0			0
$673$	−2.76558e8	−	4.79013e8i	−0.907281	−	1.57146i	−0.817826	−	0.575465i	$-0.804821\pi$
$673$	−2.76558e8	−	4.79013e8i	−0.907281	−	1.57146i	−0.0894545	−	0.995991i	$-0.528512\pi$
$674$		−	2.71066e8i		−	0.885310i
$675$		0			0
$676$	2.11561e7			0.0684850
$677$	−2.69501e8	+	1.55596e8i	−0.868548	+	0.501456i	−0.866865	−	0.498542i	$-0.833869\pi$
$677$	−2.69501e8	+	1.55596e8i	−0.868548	+	0.501456i	−0.00168257	+	0.999999i	$0.500536\pi$
$678$		0			0
$679$	5.39305e7	−	9.34103e7i	0.172276	−	0.298391i
$680$	−4.38848e7	−	2.53369e7i	−0.139569	−	0.0805799i
$681$		0			0
$682$	1.04130e8	+	1.80359e8i	0.328264	+	0.568571i
$683$			6.40636e7i			0.201071i	0.994933	+	0.100535i	$0.0320556\pi$
$683$			6.40636e7i			0.201071i	−0.994933	+	0.100535i	$0.967944\pi$
$684$		0			0
$685$	−8.19890e7			−0.255084
$686$	−1.94102e8	+	1.12065e8i	−0.601254	+	0.347134i
$687$		0			0
$688$	3.20338e7	−	5.54842e7i	0.0983656	−	0.170374i
$689$	1.36424e8	+	7.87644e7i	0.417093	+	0.240809i
$690$		0			0
$691$	−1.16895e7	−	2.02469e7i	−0.0354293	−	0.0613654i	0.847767	−	0.530369i	$-0.177947\pi$
$691$	−1.16895e7	−	2.02469e7i	−0.0354293	−	0.0613654i	−0.883196	+	0.469003i	$0.844613\pi$
$692$		−	1.23906e8i		−	0.373917i
$693$		0			0
$694$	2.40505e8			0.719523
$695$	1.50170e8	−	8.67008e7i	0.447331	−	0.258267i
$696$		0			0
$697$	−5.53993e8	+	9.59545e8i	−1.63609	+	2.83378i
$698$	−3.98774e8	−	2.30233e8i	−1.17263	−	0.677018i
$699$		0			0
$700$	−4.74714e7	−	8.22229e7i	−0.138401	−	0.239717i
$701$		−	4.68576e8i		−	1.36027i	−0.733086	−	0.680136i	$-0.761921\pi$
$701$		−	4.68576e8i		−	1.36027i	0.733086	−	0.680136i	$-0.238079\pi$
$702$		0			0
$703$	8.64951e7			0.248958
$704$	−2.98585e7	+	1.72388e7i	−0.0855757	+	0.0494072i
$705$		0			0
$706$	1.07845e8	−	1.86793e8i	0.306469	−	0.530820i
$707$	−1.58116e7	−	9.12881e6i	−0.0447421	−	0.0258319i
$708$		0			0
$709$	8.00513e7	+	1.38653e8i	0.224610	+	0.389037i	0.956202	−	0.292706i	$-0.0945557\pi$
$709$	8.00513e7	+	1.38653e8i	0.224610	+	0.389037i	−0.731592	+	0.681743i	$0.761222\pi$
$710$		−	9.78286e7i		−	0.273332i
$711$		0			0
$712$	−1.20859e8			−0.334840
$713$	−2.14955e8	+	1.24104e8i	−0.593033	+	0.342387i
$714$		0			0
$715$	3.64441e7	−	6.31230e7i	0.0997032	−	0.172691i
$716$	9.01513e7	+	5.20489e7i	0.245602	+	0.141799i
$717$		0			0
$718$	1.99217e8	+	3.45055e8i	0.538213	+	0.932212i
$719$		−	5.03559e7i		−	0.135477i	−0.997703	−	0.0677383i	$-0.978422\pi$
$719$		−	5.03559e7i		−	0.135477i	0.997703	−	0.0677383i	$-0.0215783\pi$
$720$		0			0
$721$	5.84769e7			0.156019
$722$	2.19439e8	−	1.26693e8i	0.583046	−	0.336622i
$723$		0			0
$724$	7.72976e7	−	1.33883e8i	0.203681	−	0.352786i
$725$	−3.56500e8	−	2.05825e8i	−0.935504	−	0.540113i
$726$		0			0
$727$	−8.20132e7	−	1.42051e8i	−0.213442	−	0.369693i	0.739347	−	0.673324i	$-0.235134\pi$
$727$	−8.20132e7	−	1.42051e8i	−0.213442	−	0.369693i	−0.952790	+	0.303631i	$0.901801\pi$
$728$			7.57394e7i			0.196303i
$729$		0			0
$730$	−8.14047e7			−0.209258
$731$	−4.46891e8	+	2.58013e8i	−1.14406	+	0.660524i
$732$		0			0
$733$	−4.30100e7	+	7.44956e7i	−0.109209	+	0.189155i	−0.915450	−	0.402432i	$-0.868165\pi$
$733$	−4.30100e7	+	7.44956e7i	−0.109209	+	0.189155i	0.806241	+	0.591587i	$0.201498\pi$
$734$	1.89588e8	+	1.09459e8i	0.479428	+	0.276798i
$735$		0			0
$736$	−2.05455e7	−	3.55859e7i	−0.0515328	−	0.0892575i
$737$			7.12228e7i			0.177917i
$738$		0			0
$739$	2.22107e8			0.550338			0.275169	−	0.961396i	$-0.411266\pi$
$739$	2.22107e8			0.550338			0.275169	+	0.961396i	$0.411266\pi$
$740$	−5.42023e7	+	3.12937e7i	−0.133759	+	0.0772257i
$741$		0			0
$742$	4.47523e7	−	7.75133e7i	0.109548	−	0.189742i
$743$	1.59614e8	+	9.21532e7i	0.389139	+	0.224669i	0.681787	−	0.731551i	$-0.261203\pi$
$743$	1.59614e8	+	9.21532e7i	0.389139	+	0.224669i	−0.292648	+	0.956220i	$0.594536\pi$
$744$		0			0
$745$	−9.02684e7	−	1.56349e8i	−0.218307	−	0.378118i
$746$			3.26266e8i			0.785878i
$747$		0			0
$748$	2.77697e8			0.663538
$749$	2.37336e8	−	1.37026e8i	0.564831	−	0.326105i
$750$		0			0
$751$	1.30919e8	−	2.26758e8i	0.309088	−	0.535357i	−0.669075	−	0.743195i	$-0.733309\pi$
$751$	1.30919e8	−	2.26758e8i	0.309088	−	0.535357i	0.978163	+	0.207838i	$0.0666428\pi$
$752$	4.60219e7	+	2.65707e7i	0.108221	+	0.0624813i
$753$		0			0
$754$	1.64194e8	+	2.84393e8i	0.383040	+	0.663445i
$755$			1.68585e8i			0.391722i
$756$		0			0
$757$	−6.61933e8			−1.52590			−0.762951	−	0.646456i	$-0.776250\pi$
$757$	−6.61933e8			−1.52590			−0.762951	+	0.646456i	$0.776250\pi$
$758$	−2.18015e8	+	1.25871e8i	−0.500587	+	0.289014i
$759$		0			0
$760$	4.61107e6	−	7.98661e6i	0.0105042	−	0.0181937i
$761$	−1.70270e8	−	9.83054e7i	−0.386353	−	0.223061i	0.294226	−	0.955736i	$-0.404938\pi$
$761$	−1.70270e8	−	9.83054e7i	−0.386353	−	0.223061i	−0.680579	+	0.732675i	$0.738272\pi$
$762$		0			0
$763$	2.26825e8	+	3.92872e8i	0.510642	+	0.884458i
$764$			6.37843e7i			0.143032i
$765$		0			0
$766$	6.12004e8			1.36166
$767$	6.56262e8	−	3.78893e8i	1.45443	−	0.839713i
$768$		0			0
$769$	−5.15557e7	+	8.92971e7i	−0.113370	+	0.196362i	−0.917127	−	0.398595i	$-0.869498\pi$
$769$	−5.15557e7	+	8.92971e7i	−0.113370	+	0.196362i	0.803757	+	0.594958i	$0.202831\pi$
$770$	−3.58652e7	−	2.07068e7i	−0.0785600	−	0.0453566i
$771$		0			0
$772$	1.85763e8	+	3.21751e8i	0.403745	+	0.699307i
$773$			6.91840e8i			1.49785i	0.662657	+	0.748923i	$0.269429\pi$
$773$			6.91840e8i			1.49785i	−0.662657	+	0.748923i	$0.730571\pi$
$774$		0			0
$775$	−5.06410e8			−1.08792
$776$	8.24833e7	−	4.76218e7i	0.176515	−	0.101911i
$777$		0			0
$778$	−2.42197e7	+	4.19498e7i	−0.0514317	+	0.0890823i
$779$	−1.74628e8	−	1.00821e8i	−0.369403	−	0.213275i
$780$		0			0
$781$	2.68054e8	+	4.64284e8i	0.562691	+	0.974609i
$782$			3.30963e8i			0.692086i
$783$		0			0
$784$	−7.74390e7			−0.160698
$785$	−2.42853e7	+	1.40211e7i	−0.0502035	+	0.0289850i
$786$		0			0
$787$	−2.98954e8	+	5.17803e8i	−0.613310	+	1.06228i	0.377368	+	0.926063i	$0.376829\pi$
$787$	−2.98954e8	+	5.17803e8i	−0.613310	+	1.06228i	−0.990678	+	0.136221i	$0.956504\pi$
$788$	−1.28119e8	−	7.39694e7i	−0.261839	−	0.151173i
$789$		0			0
$790$	−6.79232e7	−	1.17646e8i	−0.137764	−	0.238615i
$791$			9.11002e7i			0.184073i
$792$		0			0
$793$	1.25107e8			0.250878
$794$	3.96440e8	−	2.28884e8i	0.791982	−	0.457251i
$795$		0			0
$796$	−1.44627e8	+	2.50500e8i	−0.286753	+	0.496672i
$797$	4.56600e8	+	2.63618e8i	0.901906	+	0.520716i	0.877818	−	0.478994i	$-0.158998\pi$
$797$	4.56600e8	+	2.63618e8i	0.901906	+	0.520716i	0.0240879	+	0.999710i	$0.492332\pi$
$798$		0			0
$799$	−2.14011e8	−	3.70678e8i	−0.419562	−	0.726702i
$800$		−	8.38366e7i		−	0.163743i
$801$		0			0
$802$	2.84905e8			0.552302
$803$	3.86338e8	−	2.23052e8i	0.746140	−	0.430784i
$804$		0			0
$805$	2.46787e7	−	4.27448e7i	0.0473080	−	0.0819399i
$806$	3.49859e8	+	2.01991e8i	0.668171	+	0.385769i
$807$		0			0
$808$	−8.06093e6	−	1.39619e7i	−0.0152810	−	0.0264674i
$809$			4.15867e8i			0.785433i	0.919660	+	0.392717i	$0.128465\pi$
$809$			4.15867e8i			0.785433i	−0.919660	+	0.392717i	$0.871535\pi$
$810$		0			0
$811$	8.91737e7			0.167176			0.0835880	−	0.996500i	$-0.473362\pi$
$811$	8.91737e7			0.167176			0.0835880	+	0.996500i	$0.473362\pi$
$812$	1.61586e8	−	9.32919e7i	0.301812	−	0.174251i
$813$		0			0
$814$	1.71492e8	−	2.97033e8i	0.317959	−	0.550721i
$815$	5.58955e7	+	3.22713e7i	0.103253	+	0.0596133i
$816$		0			0
$817$	−4.69558e7	−	8.13298e7i	−0.0861039	−	0.149136i
$818$		−	3.52193e8i		−	0.643458i
$819$		0			0
$820$	1.45908e8			0.264629
$821$	1.37118e8	−	7.91654e7i	0.247780	−	0.143056i	−0.370967	−	0.928646i	$-0.620974\pi$
$821$	1.37118e8	−	7.91654e7i	0.247780	−	0.143056i	0.618747	+	0.785590i	$0.287640\pi$
$822$		0			0
$823$	3.02933e8	−	5.24695e8i	0.543434	−	0.941255i	−0.455270	−	0.890353i	$-0.650457\pi$
$823$	3.02933e8	−	5.24695e8i	0.543434	−	0.941255i	0.998704	−	0.0509014i	$-0.0162094\pi$
$824$	4.47184e7	+	2.58182e7i	0.0799290	+	0.0461470i
$825$		0			0
$826$	−2.15280e8	−	3.72875e8i	−0.381999	−	0.661642i
$827$			4.44267e7i			0.0785466i	0.999229	+	0.0392733i	$0.0125043\pi$
$827$			4.44267e7i			0.0785466i	−0.999229	+	0.0392733i	$0.987496\pi$
$828$		0			0
$829$	−2.98743e8			−0.524365			−0.262183	−	0.965018i	$-0.584442\pi$
$829$	−2.98743e8			−0.524365			−0.262183	+	0.965018i	$0.584442\pi$
$830$	−1.43156e8	+	8.26513e7i	−0.250366	+	0.144549i
$831$		0			0
$832$	−3.34397e7	+	5.79193e7i	−0.0580621	+	0.100567i
$833$	5.40160e8	+	3.11862e8i	0.934518	+	0.539544i
$834$		0			0
$835$	−9.91140e7	−	1.71671e8i	−0.170246	−	0.294874i
$836$			5.05381e7i			0.0864967i
$837$		0			0
$838$	−6.74532e7			−0.114623
$839$	−2.41704e8	+	1.39548e8i	−0.409260	+	0.236286i	−0.690472	−	0.723360i	$-0.742597\pi$
$839$	−2.41704e8	+	1.39548e8i	−0.409260	+	0.236286i	0.281212	+	0.959646i	$0.409264\pi$
$840$		0			0
$841$	1.07081e8	−	1.85470e8i	0.180021	−	0.311806i
$842$	−2.74368e8	−	1.58407e8i	−0.459619	−	0.265361i
$843$		0			0
$844$	−1.75254e8	−	3.03548e8i	−0.291501	−	0.504894i
$845$			2.24394e7i			0.0371913i
$846$		0			0
$847$	−1.36220e8			−0.224177
$848$	6.84459e7	−	3.95172e7i	0.112243	−	0.0648036i
$849$		0			0
$850$	−3.37626e8	+	5.84786e8i	−0.549768	+	0.952226i
$851$	3.54009e8	+	2.04387e8i	0.574415	+	0.331638i
$852$		0			0
$853$	−1.22254e8	−	2.11750e8i	−0.196977	−	0.341174i	0.750570	−	0.660791i	$-0.229779\pi$
$853$	−1.22254e8	−	2.11750e8i	−0.196977	−	0.341174i	−0.947547	+	0.319617i	$0.896446\pi$
$854$		−	7.10834e7i		−	0.114129i
$855$		0			0
$856$	2.41994e8			0.385818
$857$	−2.33813e8	+	1.34992e8i	−0.371473	+	0.214470i	−0.674102	−	0.738639i	$-0.735469\pi$
$857$	−2.33813e8	+	1.34992e8i	−0.371473	+	0.214470i	0.302629	+	0.953108i	$0.402136\pi$
$858$		0			0
$859$	−6.88616e6	+	1.19272e7i	−0.0108642	+	0.0188173i	−0.871406	−	0.490562i	$-0.836792\pi$
$859$	−6.88616e6	+	1.19272e7i	−0.0108642	+	0.0188173i	0.860542	+	0.509379i	$0.170125\pi$
$860$	5.88498e7	+	3.39770e7i	0.0925230	+	0.0534182i
$861$		0			0
$862$	−8.23594e6	−	1.42651e7i	−0.0128585	−	0.0222716i
$863$			4.03111e8i			0.627180i	0.949559	+	0.313590i	$0.101532\pi$
$863$			4.03111e8i			0.627180i	−0.949559	+	0.313590i	$0.898468\pi$
$864$		0			0
$865$	1.31422e8			0.203059
$866$	−2.56625e8	+	1.48163e8i	−0.395136	+	0.228132i
$867$		0			0
$868$	1.14767e8	−	1.98783e8i	0.175493	−	0.303962i
$869$	6.44711e8	+	3.72224e8i	0.982440	+	0.567212i
$870$		0			0
$871$	6.90787e7	+	1.19648e8i	0.104542	+	0.181072i
$872$			4.00582e8i			0.604146i
$873$		0			0
$874$	−6.02321e7			−0.0902181
$875$	1.81363e8	−	1.04710e8i	0.270722	−	0.156302i
$876$		0			0
$877$	2.24825e8	−	3.89408e8i	0.333308	−	0.577306i	−0.649851	−	0.760062i	$-0.725169\pi$
$877$	2.24825e8	−	3.89408e8i	0.333308	−	0.577306i	0.983158	+	0.182756i	$0.0585019\pi$
$878$	7.08436e8	+	4.09016e8i	1.04669	+	0.604305i
$879$		0			0
$880$	−1.82845e7	−	3.16698e7i	−0.0268310	−	0.0464726i
$881$		−	1.62295e7i		−	0.0237344i	−0.999930	−	0.0118672i	$-0.996222\pi$
$881$		−	1.62295e7i		−	0.0237344i	0.999930	−	0.0118672i	$-0.00377753\pi$
$882$		0			0
$883$	−2.08844e8			−0.303347			−0.151673	−	0.988431i	$-0.548466\pi$
$883$	−2.08844e8			−0.303347			−0.151673	+	0.988431i	$0.548466\pi$
$884$	4.66505e8	−	2.69337e8i	0.675304	−	0.389887i
$885$		0			0
$886$	−2.51441e8	+	4.35509e8i	−0.361522	+	0.626175i
$887$	−4.93999e6	−	2.85211e6i	−0.00707873	−	0.00408691i	0.496456	−	0.868062i	$-0.334634\pi$
$887$	−4.93999e6	−	2.85211e6i	−0.00707873	−	0.00408691i	−0.503535	+	0.863975i	$0.667968\pi$
$888$		0			0
$889$	−3.38740e7	−	5.86715e7i	−0.0482127	−	0.0835068i
$890$		−	1.28190e8i		−	0.181838i
$891$		0			0
$892$	−3.95942e8			−0.557876
$893$	6.74598e7	−	3.89479e7i	0.0947307	−	0.0546928i
$894$		0			0
$895$	−5.52061e7	+	9.56198e7i	−0.0770049	+	0.133376i
$896$	3.29086e7	+	1.89998e7i	0.0457494	+	0.0264134i
$897$		0			0
$898$	−2.68284e8	−	4.64681e8i	−0.370481	−	0.641691i
$899$		−	9.95209e8i		−	1.36973i
$900$		0			0
$901$	−6.36574e8			−0.870312
$902$	−6.92461e8	+	3.99793e8i	−0.943574	+	0.544773i
$903$		0			0
$904$	−4.02217e7	+	6.96660e7i	−0.0544446	+	0.0943009i
$905$	1.42005e8	+	8.19865e7i	0.191583	+	0.110611i
$906$		0			0
$907$	6.61190e7	+	1.14521e8i	0.0886144	+	0.153485i	0.906926	−	0.421291i	$-0.138423\pi$
$907$	6.61190e7	+	1.14521e8i	0.0886144	+	0.153485i	−0.818311	+	0.574775i	$0.805089\pi$
$908$			1.97048e8i			0.263217i
$909$		0			0
$910$	−8.03338e7			−0.106604
$911$	−7.94695e8	+	4.58817e8i	−1.05110	+	0.606854i	−0.922958	−	0.384901i	$-0.874236\pi$
$911$	−7.94695e8	+	4.58817e8i	−1.05110	+	0.606854i	−0.128145	+	0.991755i	$0.540902\pi$
$912$		0			0
$913$	4.52935e8	−	7.84507e8i	0.595146	−	1.03082i
$914$	−5.78196e7	−	3.33822e7i	−0.0757245	−	0.0437196i
$915$		0			0
$916$	8.89264e7	+	1.54025e8i	0.115703	+	0.200403i
$917$		−	2.54340e8i		−	0.329843i
$918$		0			0
$919$	5.69732e8			0.734047			0.367024	−	0.930212i	$-0.380377\pi$
$919$	5.69732e8			0.734047			0.367024	+	0.930212i	$0.380377\pi$
$920$	3.77446e7	−	2.17918e7i	0.0484720	−	0.0279853i
$921$		0			0
$922$	4.18687e8	−	7.25188e8i	0.534192	−	0.925247i
$923$	9.00613e8	+	5.19969e8i	1.14534	+	0.661261i
$924$		0			0
$925$	4.17003e8	+	7.22271e8i	0.526883	+	0.912588i
$926$			3.46329e8i			0.436170i
$927$		0			0
$928$	1.64758e8			0.206159
$929$	7.11434e8	−	4.10746e8i	0.887334	−	0.512303i	0.0142647	−	0.999898i	$-0.495459\pi$
$929$	7.11434e8	−	4.10746e8i	0.887334	−	0.512303i	0.873070	+	0.487596i	$0.162126\pi$
$930$		0			0
$931$	−5.67558e7	+	9.83040e7i	−0.0703333	+	0.121821i
$932$	3.24881e8	+	1.87570e8i	0.401307	+	0.231695i
$933$		0			0
$934$	1.67422e8	+	2.89983e8i	0.205481	+	0.355903i
$935$			2.94542e8i			0.360339i
$936$		0			0
$937$	6.62725e8			0.805591			0.402796	−	0.915290i	$-0.368039\pi$
$937$	6.62725e8			0.805591			0.402796	+	0.915290i	$0.368039\pi$
$938$	6.79814e7	−	3.92491e7i	0.0823724	−	0.0475577i
$939$		0			0
$940$	−2.81825e7	+	4.88136e7i	−0.0339310	+	0.0587702i
$941$	−1.11503e8	−	6.43765e7i	−0.133819	−	0.0772607i	0.431596	−	0.902067i	$-0.357951\pi$
$941$	−1.11503e8	−	6.43765e7i	−0.133819	−	0.0772607i	−0.565415	+	0.824806i	$0.691284\pi$
$942$		0			0
$943$	−4.76480e8	−	8.25287e8i	−0.568211	−	0.984170i
$944$		−	3.80193e8i		−	0.451947i
$945$		0			0
$946$	−3.72393e8			−0.439874
$947$	2.13619e8	−	1.23333e8i	0.251530	−	0.145221i	−0.368934	−	0.929455i	$-0.620277\pi$
$947$	2.13619e8	−	1.23333e8i	0.251530	−	0.145221i	0.620465	+	0.784234i	$0.286944\pi$
$948$		0			0
$949$	4.32675e8	−	7.49414e8i	0.506247	−	0.876846i
$950$	−1.06425e8	−	6.14447e7i	−0.124129	−	0.0716660i
$951$		0			0
$952$	−1.53032e8	−	2.65059e8i	−0.177366	−	0.307207i
$953$			2.79388e8i			0.322797i	0.986889	+	0.161398i	$0.0516004\pi$
$953$			2.79388e8i			0.322797i	−0.986889	+	0.161398i	$0.948400\pi$
$954$		0			0
$955$	−6.76535e7			−0.0776748
$956$	4.89735e8	−	2.82749e8i	0.560515	−	0.323614i
$957$		0			0
$958$	−1.73478e8	+	3.00473e8i	−0.197310	+	0.341751i
$959$	−4.28858e8	−	2.47601e8i	−0.486248	−	0.280736i
$960$		0			0
$961$	−1.68398e8	−	2.91674e8i	−0.189744	−	0.328646i
$962$		−	6.65317e8i		−	0.747315i
$963$		0			0
$964$	−6.90202e8			−0.770451
$965$	−3.41269e8	+	1.97031e8i	−0.379764	+	0.219257i
$966$		0			0
$967$	−7.25321e8	+	1.25629e9i	−0.802142	+	1.38935i	0.116062	+	0.993242i	$0.462973\pi$
$967$	−7.25321e8	+	1.25629e9i	−0.802142	+	1.38935i	−0.918204	+	0.396108i	$0.870361\pi$
$968$	−1.04170e8	−	6.01427e7i	−0.114846	−	0.0663066i
$969$		0			0
$970$	5.05105e7	+	8.74867e7i	0.0553435	+	0.0958577i
$971$			1.50823e9i			1.64744i	0.566999	+	0.823719i	$0.308104\pi$
$971$			1.50823e9i			1.64744i	−0.566999	+	0.823719i	$0.691896\pi$
$972$		0			0
$973$	1.04732e9			1.13695
$974$	−5.88010e8	+	3.39488e8i	−0.636368	+	0.367407i
$975$		0			0
$976$	3.13841e7	−	5.43588e7i	0.0337567	−	0.0584683i
$977$	−1.05626e9	−	6.09831e8i	−1.13263	−	0.653922i	−0.188032	−	0.982163i	$-0.560211\pi$
$977$	−1.05626e9	−	6.09831e8i	−1.13263	−	0.653922i	−0.944594	+	0.328241i	$0.893544\pi$
$978$		0			0
$979$	3.51245e8	+	6.08375e8i	0.374337	+	0.648370i
$980$		−	8.21364e7i		−	0.0872685i
$981$		0			0
$982$	−1.23545e9			−1.30464
$983$	−8.80047e8	+	5.08095e8i	−0.926499	+	0.534915i	−0.885703	−	0.464253i	$-0.846323\pi$
$983$	−8.80047e8	+	5.08095e8i	−0.926499	+	0.534915i	−0.0407967	+	0.999167i	$0.512990\pi$
$984$		0			0
$985$	7.84564e7	−	1.35890e8i	0.0820955	−	0.142194i
$986$	−1.14923e9	−	6.63510e8i	−1.19889	−	0.692177i
$987$		0			0
$988$	4.90167e7	+	8.48993e7i	0.0508245	+	0.0880306i
$989$		−	4.43824e8i		−	0.458799i
$990$		0			0
$991$	7.53703e8			0.774425			0.387213	−	0.921990i	$-0.373438\pi$
$991$	7.53703e8			0.774425			0.387213	+	0.921990i	$0.373438\pi$
$992$	1.75529e8	−	1.01342e8i	0.179810	−	0.103814i
$993$		0			0
$994$	2.95436e8	−	5.11710e8i	0.300818	−	0.521033i
$995$	−2.65696e8	−	1.53400e8i	−0.269721	−	0.155724i
$996$		0			0
$997$	4.09571e8	+	7.09398e8i	0.413280	+	0.715822i	0.995246	−	0.0973913i	$-0.0310498\pi$
$997$	4.09571e8	+	7.09398e8i	0.413280	+	0.715822i	−0.581966	+	0.813213i	$0.697716\pi$
$998$			1.08573e9i			1.09228i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.d.c.53.1		4
3.2	odd	2	inner	162.7.d.c.53.2		4
9.2	odd	6	inner	162.7.d.c.107.1		4
9.4	even	3		54.7.b.a.53.1	✓	2
9.5	odd	6		54.7.b.a.53.2	yes	2
9.7	even	3	inner	162.7.d.c.107.2		4
36.23	even	6		432.7.e.f.161.2		2
36.31	odd	6		432.7.e.f.161.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.7.b.a.53.1	✓	2	9.4	even	3
54.7.b.a.53.2	yes	2	9.5	odd	6
162.7.d.c.53.1		4	1.1	even	1	trivial
162.7.d.c.53.2		4	3.2	odd	2	inner
162.7.d.c.107.1		4	9.2	odd	6	inner
162.7.d.c.107.2		4	9.7	even	3	inner
432.7.e.f.161.1		2	36.31	odd	6
432.7.e.f.161.2		2	36.23	even	6

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(29.3939 + 16.9706i) q^{5} +(102.500 + 177.535i) q^{7} +181.019i q^{8} +O(q^{10})\)	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(29.3939 + 16.9706i) q^{5} +(102.500 + 177.535i) q^{7} +181.019i q^{8} -192.000 q^{10} +(911.210 - 526.087i) q^{11} +(1020.50 - 1767.56i) q^{13} +(-1004.29 - 579.828i) q^{14} +(-512.000 - 886.810i) q^{16} +8247.69i q^{17} -1501.00 q^{19} +(940.604 - 543.058i) q^{20} +(-2976.00 + 5154.58i) q^{22} +(-6143.32 - 3546.85i) q^{23} +(-7236.50 - 12534.0i) q^{25} +11545.6i q^{26} +6560.00 q^{28} +(24632.1 - 14221.3i) q^{29} +(17495.0 - 30302.2i) q^{31} +(5016.55 + 2896.31i) q^{32} +(-23328.0 - 40405.3i) q^{34} +6957.93i q^{35} -57625.0 q^{37} +(7353.37 - 4245.47i) q^{38} +(-3072.00 + 5320.86i) q^{40} +(116341. + 67169.5i) q^{41} +(31283.0 + 54183.7i) q^{43} -33669.6i q^{44} +40128.0 q^{46} +(-44943.2 + 25948.0i) q^{47} +(37812.0 - 65492.3i) q^{49} +(70902.9 + 40935.8i) q^{50} +(-32656.0 - 56561.9i) q^{52} +77182.1i q^{53} +35712.0 q^{55} +(-32137.3 + 18554.5i) q^{56} +(-80448.0 + 139340. i) q^{58} +(321540. + 185641. i) q^{59} +(30648.5 + 53084.8i) q^{61} +197933. i q^{62} -32768.0 q^{64} +(59992.9 - 34636.9i) q^{65} +(-33845.5 + 58622.1i) q^{67} +(228567. + 131963. i) q^{68} +(-19680.0 - 34086.8i) q^{70} +509524. i q^{71} +423983. q^{73} +(282304. - 162988. i) q^{74} +(-24016.0 + 41596.9i) q^{76} +(186798. + 107848. i) q^{77} +(353766. + 612742. i) q^{79} -34755.7i q^{80} -759936. q^{82} +(745605. - 430475. i) q^{83} +(-139968. + 242432. i) q^{85} +(-306510. - 176963. i) q^{86} +(95232.0 + 164947. i) q^{88} +667656. i q^{89} +418405. q^{91} +(-196586. + 113499. i) q^{92} +(146784. - 254237. i) q^{94} +(-44120.2 - 25472.8i) q^{95} +(-263076. - 455660. i) q^{97} +427794. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 64 q^{4} + 410 q^{7}+O(q^{10}) \) 4 * q + 64 * q^4 + 410 * q^7	\( 4 q + 64 q^{4} + 410 q^{7} - 768 q^{10} + 4082 q^{13} - 2048 q^{16} - 6004 q^{19} - 11904 q^{22} - 28946 q^{25} + 26240 q^{28} + 69980 q^{31} - 93312 q^{34} - 230500 q^{37} - 12288 q^{40} + 125132 q^{43} + 160512 q^{46} + 151248 q^{49} - 130624 q^{52} + 142848 q^{55} - 321792 q^{58} + 122594 q^{61} - 131072 q^{64} - 135382 q^{67} - 78720 q^{70} + 1695932 q^{73} - 96064 q^{76} + 1415066 q^{79} - 3039744 q^{82} - 559872 q^{85} + 380928 q^{88} + 1673620 q^{91} + 587136 q^{94} - 1052302 q^{97}+O(q^{100}) \) 4 * q + 64 * q^4 + 410 * q^7 - 768 * q^10 + 4082 * q^13 - 2048 * q^16 - 6004 * q^19 - 11904 * q^22 - 28946 * q^25 + 26240 * q^28 + 69980 * q^31 - 93312 * q^34 - 230500 * q^37 - 12288 * q^40 + 125132 * q^43 + 160512 * q^46 + 151248 * q^49 - 130624 * q^52 + 142848 * q^55 - 321792 * q^58 + 122594 * q^61 - 131072 * q^64 - 135382 * q^67 - 78720 * q^70 + 1695932 * q^73 - 96064 * q^76 + 1415066 * q^79 - 3039744 * q^82 - 559872 * q^85 + 380928 * q^88 + 1673620 * q^91 + 587136 * q^94 - 1052302 * q^97

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