LMFDB - Embedded newform 108.5.f.a.19.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(19,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.f (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:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.14
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85603 - 3.54333i) q^{2} +(-9.11034 - 13.1530i) q^{4} +(14.8847 + 25.7811i) q^{5} +(-51.8739 - 29.9494i) q^{7} +(-63.5145 + 7.86857i) q^{8} +O(q^{10})$	\(q+(1.85603 - 3.54333i) q^{2} +(-9.11034 - 13.1530i) q^{4} +(14.8847 + 25.7811i) q^{5} +(-51.8739 - 29.9494i) q^{7} +(-63.5145 + 7.86857i) q^{8} +(118.977 - 4.89106i) q^{10} +(-195.278 - 112.744i) q^{11} +(-85.8824 - 148.753i) q^{13} +(-202.400 + 128.219i) q^{14} +(-90.0035 + 239.657i) q^{16} +99.0725 q^{17} +169.267i q^{19} +(203.494 - 430.653i) q^{20} +(-761.929 + 482.678i) q^{22} +(-310.777 + 179.427i) q^{23} +(-130.609 + 226.221i) q^{25} +(-686.480 + 28.2206i) q^{26} +(78.6636 + 955.147i) q^{28} +(-9.01635 + 15.6168i) q^{29} +(671.898 - 387.920i) q^{31} +(682.133 + 763.721i) q^{32} +(183.881 - 351.046i) q^{34} -1783.15i q^{35} +609.762 q^{37} +(599.768 + 314.164i) q^{38} +(-1148.25 - 1520.35i) q^{40} +(-206.545 - 357.747i) q^{41} +(265.498 + 153.286i) q^{43} +(296.127 + 3595.63i) q^{44} +(58.9591 + 1434.21i) q^{46} +(-2270.59 - 1310.93i) q^{47} +(593.432 + 1027.85i) q^{49} +(559.161 + 882.661i) q^{50} +(-1174.13 + 2484.80i) q^{52} -2034.30 q^{53} -6712.63i q^{55} +(3530.40 + 1494.05i) q^{56} +(38.6008 + 60.9330i) q^{58} +(2250.48 - 1299.32i) q^{59} +(708.681 - 1227.47i) q^{61} +(-127.469 - 3100.74i) q^{62} +(3972.17 - 999.536i) q^{64} +(2556.67 - 4428.28i) q^{65} +(5191.93 - 2997.56i) q^{67} +(-902.584 - 1303.10i) q^{68} +(-6318.29 - 3309.57i) q^{70} -1239.44i q^{71} -5060.60 q^{73} +(1131.73 - 2160.59i) q^{74} +(2226.37 - 1542.08i) q^{76} +(6753.22 + 11696.9i) q^{77} +(1635.99 + 944.538i) q^{79} +(-7518.28 + 1246.83i) q^{80} +(-1650.97 + 67.8700i) q^{82} +(5831.54 + 3366.84i) q^{83} +(1474.66 + 2554.19i) q^{85} +(1035.91 - 656.246i) q^{86} +(13290.1 + 5624.30i) q^{88} -9436.67 q^{89} +10288.5i q^{91} +(5191.29 + 2453.01i) q^{92} +(-8859.31 + 5612.33i) q^{94} +(-4363.88 + 2519.49i) q^{95} +(7297.91 - 12640.4i) q^{97} +(4743.45 - 195.000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.85603	−	3.54333i	0.464006	−	0.885832i
$2$	1.85603	−	3.54333i	0.464006	−	0.885832i
$3$		0			0
$3$		0			0
$4$	−9.11034	−	13.1530i	−0.569396	−	0.822063i
$5$	14.8847	+	25.7811i	0.595388	+	1.03124i	0.993492	+	0.113902i	$0.0363350\pi$
$5$	14.8847	+	25.7811i	0.595388	+	1.03124i	−0.398104	+	0.917340i	$0.630332\pi$
$6$		0			0
$7$	−51.8739	−	29.9494i	−1.05865	−	0.611212i	−0.133592	−	0.991036i	$-0.542651\pi$
$7$	−51.8739	−	29.9494i	−1.05865	−	0.611212i	−0.925059	+	0.379824i	$0.875984\pi$
$8$	−63.5145	+	7.86857i	−0.992413	+	0.122946i
$9$		0			0
$10$	118.977	−	4.89106i	1.18977	−	0.0489106i
$11$	−195.278	−	112.744i	−1.61387	−	0.931767i	−0.988462	−	0.151467i	$-0.951600\pi$
$11$	−195.278	−	112.744i	−1.61387	−	0.931767i	−0.625406	−	0.780300i	$-0.715066\pi$
$12$		0			0
$13$	−85.8824	−	148.753i	−0.508180	−	0.880194i	−0.999955	−	0.00947137i	$-0.996985\pi$
$13$	−85.8824	−	148.753i	−0.508180	−	0.880194i	0.491775	−	0.870722i	$-0.336348\pi$
$14$	−202.400	+	128.219i	−1.03265	+	0.654180i
$15$		0			0
$16$	−90.0035	+	239.657i	−0.351576	+	0.936159i
$17$	99.0725			0.342812			0.171406	−	0.985201i	$-0.445169\pi$
$17$	99.0725			0.342812			0.171406	+	0.985201i	$0.445169\pi$
$18$		0			0
$19$			169.267i			0.468884i	0.972130	+	0.234442i	$0.0753262\pi$
$19$			169.267i			0.468884i	−0.972130	+	0.234442i	$0.924674\pi$
$20$	203.494	−	430.653i	0.508735	−	1.07663i
$21$		0			0
$22$	−761.929	+	482.678i	−1.57423	+	0.997270i
$23$	−310.777	+	179.427i	−0.587480	+	0.339182i	−0.764101	−	0.645097i	$-0.776817\pi$
$23$	−310.777	+	179.427i	−0.587480	+	0.339182i	0.176620	+	0.984279i	$0.443484\pi$
$24$		0			0
$25$	−130.609	+	226.221i	−0.208974	+	0.361953i
$26$	−686.480	+	28.2206i	−1.01550	+	0.0417465i
$27$		0			0
$28$	78.6636	+	955.147i	0.100336	+	1.21830i
$29$	−9.01635	+	15.6168i	−0.0107210	+	0.0185693i	−0.871336	−	0.490687i	$-0.836746\pi$
$29$	−9.01635	+	15.6168i	−0.0107210	+	0.0185693i	0.860615	+	0.509256i	$0.170079\pi$
$30$		0			0
$31$	671.898	−	387.920i	0.699165	−	0.403663i	−0.107871	−	0.994165i	$-0.534403\pi$
$31$	671.898	−	387.920i	0.699165	−	0.403663i	0.807036	+	0.590502i	$0.201070\pi$
$32$	682.133	+	763.721i	0.666146	+	0.745821i
$33$		0			0
$34$	183.881	−	351.046i	0.159067	−	0.303673i
$35$		−	1783.15i		−	1.45563i
$36$		0			0
$37$	609.762			0.445407			0.222703	−	0.974886i	$-0.428512\pi$
$37$	609.762			0.445407			0.222703	+	0.974886i	$0.428512\pi$
$38$	599.768	+	314.164i	0.415352	+	0.217565i
$39$		0			0
$40$	−1148.25	−	1520.35i	−0.717659	−	0.950218i
$41$	−206.545	−	357.747i	−0.122871	−	0.212818i	0.798028	−	0.602620i	$-0.205877\pi$
$41$	−206.545	−	357.747i	−0.122871	−	0.212818i	−0.920899	+	0.389802i	$0.872543\pi$
$42$		0			0
$43$	265.498	+	153.286i	0.143590	+	0.0829019i	0.570074	−	0.821593i	$-0.306915\pi$
$43$	265.498	+	153.286i	0.143590	+	0.0829019i	−0.426484	+	0.904495i	$0.640248\pi$
$44$	296.127	+	3595.63i	0.152958	+	1.85725i
$45$		0			0
$46$	58.9591	+	1434.21i	0.0278635	+	0.677791i
$47$	−2270.59	−	1310.93i	−1.02788	−	0.593447i	−0.111504	−	0.993764i	$-0.535567\pi$
$47$	−2270.59	−	1310.93i	−1.02788	−	0.593447i	−0.916377	+	0.400317i	$0.868900\pi$
$48$		0			0
$49$	593.432	+	1027.85i	0.247160	+	0.428094i
$50$	559.161	+	882.661i	0.223665	+	0.353064i
$51$		0			0
$52$	−1174.13	+	2484.80i	−0.434219	+	0.918935i
$53$	−2034.30			−0.724209			−0.362104	−	0.932138i	$-0.617942\pi$
$53$	−2034.30			−0.724209			−0.362104	+	0.932138i	$0.617942\pi$
$54$		0			0
$55$		−	6712.63i		−	2.21905i
$56$	3530.40	+	1494.05i	1.12577	+	0.476418i
$57$		0			0
$58$	38.6008	+	60.9330i	0.0114747	+	0.0181133i
$59$	2250.48	−	1299.32i	0.646505	−	0.373260i	−0.140611	−	0.990065i	$-0.544907\pi$
$59$	2250.48	−	1299.32i	0.646505	−	0.373260i	0.787116	+	0.616805i	$0.211573\pi$
$60$		0			0
$61$	708.681	−	1227.47i	0.190455	−	0.329877i	−0.754946	−	0.655786i	$-0.772337\pi$
$61$	708.681	−	1227.47i	0.190455	−	0.329877i	0.945401	+	0.325910i	$0.105670\pi$
$62$	−127.469	−	3100.74i	−0.0331606	−	0.806645i
$63$		0			0
$64$	3972.17	−	999.536i	0.969768	−	0.244027i
$65$	2556.67	−	4428.28i	0.605129	−	1.04811i
$66$		0			0
$67$	5191.93	−	2997.56i	1.15659	−	0.667758i	0.206106	−	0.978530i	$-0.433921\pi$
$67$	5191.93	−	2997.56i	1.15659	−	0.667758i	0.950485	+	0.310772i	$0.100588\pi$
$68$	−902.584	−	1303.10i	−0.195196	−	0.281813i
$69$		0			0
$70$	−6318.29	−	3309.57i	−1.28945	−	0.675423i
$71$		−	1239.44i		−	0.245872i	−0.992415	−	0.122936i	$-0.960769\pi$
$71$		−	1239.44i		−	0.245872i	0.992415	−	0.122936i	$-0.0392310\pi$
$72$		0			0
$73$	−5060.60			−0.949633			−0.474817	−	0.880085i	$-0.657486\pi$
$73$	−5060.60			−0.949633			−0.474817	+	0.880085i	$0.657486\pi$
$74$	1131.73	−	2160.59i	0.206672	−	0.394555i
$75$		0			0
$76$	2226.37	−	1542.08i	0.385452	−	0.266980i
$77$	6753.22	+	11696.9i	1.13901	+	1.97283i
$78$		0			0
$79$	1635.99	+	944.538i	0.262135	+	0.151344i	0.625308	−	0.780378i	$-0.284973\pi$
$79$	1635.99	+	944.538i	0.262135	+	0.151344i	−0.363173	+	0.931722i	$0.618307\pi$
$80$	−7518.28	+	1246.83i	−1.17473	+	0.194818i
$81$		0			0
$82$	−1650.97	+	67.8700i	−0.245534	+	0.0100937i
$83$	5831.54	+	3366.84i	0.846500	+	0.488727i	0.859469	−	0.511189i	$-0.170795\pi$
$83$	5831.54	+	3366.84i	0.846500	+	0.488727i	−0.0129681	+	0.999916i	$0.504128\pi$
$84$		0			0
$85$	1474.66	+	2554.19i	0.204106	+	0.353522i
$86$	1035.91	−	656.246i	0.140064	−	0.0887298i
$87$		0			0
$88$	13290.1	+	5624.30i	1.71618	+	0.726279i
$89$	−9436.67			−1.19135			−0.595674	−	0.803226i	$-0.703115\pi$
$89$	−9436.67			−1.19135			−0.595674	+	0.803226i	$0.703115\pi$
$90$		0			0
$91$			10288.5i			1.24242i
$92$	5191.29	+	2453.01i	0.613338	+	0.289817i
$93$		0			0
$94$	−8859.31	+	5612.33i	−1.00264	+	0.635166i
$95$	−4363.88	+	2519.49i	−0.483533	+	0.279168i
$96$		0			0
$97$	7297.91	−	12640.4i	0.775631	−	1.34343i	−0.158808	−	0.987309i	$-0.550765\pi$
$97$	7297.91	−	12640.4i	0.775631	−	1.34343i	0.934439	−	0.356123i	$-0.115902\pi$
$98$	4743.45	−	195.000i	0.493904	−	0.0203040i
$99$		0			0
$100$	4165.37	−	343.050i	0.416537	−	0.0343050i
$101$	3230.71	−	5595.76i	0.316705	−	0.548550i	−0.663093	−	0.748537i	$-0.730757\pi$
$101$	3230.71	−	5595.76i	0.316705	−	0.548550i	0.979799	+	0.199987i	$0.0640900\pi$
$102$		0			0
$103$	−13991.6	+	8078.04i	−1.31884	+	0.761432i	−0.983542	−	0.180680i	$-0.942170\pi$
$103$	−13991.6	+	8078.04i	−1.31884	+	0.761432i	−0.335298	+	0.942112i	$0.608837\pi$
$104$	6625.25	+	8772.18i	0.612541	+	0.811037i
$105$		0			0
$106$	−3775.72	+	7208.20i	−0.336037	+	0.641527i
$107$			3065.27i			0.267732i	0.990999	+	0.133866i	$0.0427392\pi$
$107$			3065.27i			0.267732i	−0.990999	+	0.133866i	$0.957261\pi$
$108$		0			0
$109$	−17728.8			−1.49220			−0.746098	−	0.665836i	$-0.768075\pi$
$109$	−17728.8			−1.49220			−0.746098	+	0.665836i	$0.768075\pi$
$110$	−23785.1	−	12458.8i	−1.96571	−	1.02965i
$111$		0			0
$112$	11846.4	−	9736.37i	0.944388	−	0.776178i
$113$	−7396.56	−	12811.2i	−0.579259	−	1.00331i	−0.995565	−	0.0940814i	$-0.970009\pi$
$113$	−7396.56	−	12811.2i	−0.579259	−	1.00331i	0.416305	−	0.909225i	$-0.363325\pi$
$114$		0			0
$115$	−9251.65	−	5341.44i	−0.699558	−	0.403890i
$116$	287.550	−	23.6819i	0.0213696	−	0.00175995i
$117$		0			0
$118$	−426.951	−	10385.8i	−0.0306629	−	0.745890i
$119$	−5139.28	−	2967.16i	−0.362918	−	0.209531i
$120$		0			0
$121$	18101.8	+	31353.3i	1.23638	+	2.14147i
$122$	−3034.00	−	4789.31i	−0.203843	−	0.321776i
$123$		0			0
$124$	−11223.5	−	5303.40i	−0.729939	−	0.344914i
$125$	10829.6			0.693094
$126$		0			0
$127$			18478.7i			1.14568i	0.819667	+	0.572841i	$0.194159\pi$
$127$			18478.7i			1.14568i	−0.819667	+	0.572841i	$0.805841\pi$
$128$	3830.77	−	15929.9i	0.233812	−	0.972282i
$129$		0			0
$130$	−10945.6	−	17278.1i	−0.647669	−	1.02237i
$131$	−7205.95	+	4160.35i	−0.419902	+	0.242431i	−0.695036	−	0.718975i	$-0.744611\pi$
$131$	−7205.95	+	4160.35i	−0.419902	+	0.242431i	0.275133	+	0.961406i	$0.411278\pi$
$132$		0			0
$133$	5069.44	−	8780.53i	0.286587	−	0.496384i
$134$	−984.989	−	23960.3i	−0.0548557	−	1.33439i
$135$		0			0
$136$	−6292.54	+	779.559i	−0.340211	+	0.0421474i
$137$	−10703.4	+	18538.7i	−0.570268	+	0.987732i	0.426271	+	0.904596i	$0.359827\pi$
$137$	−10703.4	+	18538.7i	−0.570268	+	0.987732i	−0.996538	+	0.0831367i	$0.973506\pi$
$138$		0			0
$139$	−15783.6	+	9112.67i	−0.816915	+	0.471646i	−0.849351	−	0.527828i	$-0.823007\pi$
$139$	−15783.6	+	9112.67i	−0.816915	+	0.471646i	0.0324367	+	0.999474i	$0.489673\pi$
$140$	−23453.8	+	16245.1i	−1.19662	+	0.828832i
$141$		0			0
$142$	−4391.75	−	2300.44i	−0.217802	−	0.114086i
$143$			38730.8i			1.89402i
$144$		0			0
$145$	−536.823			−0.0255326
$146$	−9392.60	+	17931.3i	−0.440636	+	0.841215i
$147$		0			0
$148$	−5555.13	−	8020.20i	−0.253613	−	0.366152i
$149$	−8119.72	−	14063.8i	−0.365736	−	0.633474i	0.623158	−	0.782096i	$-0.285850\pi$
$149$	−8119.72	−	14063.8i	−0.365736	−	0.633474i	−0.988894	+	0.148622i	$0.952516\pi$
$150$		0			0
$151$	21240.4	+	12263.2i	0.931557	+	0.537835i	0.887304	−	0.461186i	$-0.152576\pi$
$151$	21240.4	+	12263.2i	0.931557	+	0.537835i	0.0442533	+	0.999020i	$0.485909\pi$
$152$	−1331.89	−	10750.9i	−0.0576476	−	0.465326i
$153$		0			0
$154$	53980.1	−	2219.08i	2.27611	−	0.0935690i
$155$	20002.0	+	11548.2i	0.832549	+	0.480672i
$156$		0			0
$157$	−19827.0	−	34341.4i	−0.804375	−	1.39322i	−0.916712	−	0.399548i	$-0.869167\pi$
$157$	−19827.0	−	34341.4i	−0.804375	−	1.39322i	0.112337	−	0.993670i	$-0.464166\pi$
$158$	6383.24	−	4043.75i	0.255698	−	0.161983i
$159$		0			0
$160$	−9536.19	+	28953.9i	−0.372507	+	1.13101i
$161$	21494.9			0.829248
$162$		0			0
$163$		−	25324.6i		−	0.953162i	−0.879130	−	0.476581i	$-0.841876\pi$
$163$		−	25324.6i		−	0.953162i	0.879130	−	0.476581i	$-0.158124\pi$
$164$	−2823.75	+	5975.89i	−0.104988	+	0.222185i
$165$		0			0
$166$	22753.3	−	14414.1i	0.825712	−	0.523084i
$167$	24109.7	−	13919.8i	0.864490	−	0.499113i	−0.00102363	−	0.999999i	$-0.500326\pi$
$167$	24109.7	−	13919.8i	0.864490	−	0.499113i	0.865513	+	0.500886i	$0.166992\pi$
$168$		0			0
$169$	−471.081	+	815.937i	−0.0164939	+	0.0285682i
$170$	11787.4	−	484.569i	0.407867	−	0.0167671i
$171$		0			0
$172$	−402.612	−	4888.59i	−0.0136091	−	0.165244i
$173$	−11027.3	+	19099.8i	−0.368448	+	0.638170i	−0.989323	−	0.145739i	$-0.953444\pi$
$173$	−11027.3	+	19099.8i	−0.368448	+	0.638170i	0.620875	+	0.783909i	$0.286777\pi$
$174$		0			0
$175$	13550.4	−	7823.30i	0.442461	−	0.255455i
$176$	44595.5	−	36652.4i	1.43968	−	1.18325i
$177$		0			0
$178$	−17514.7	+	33437.2i	−0.552794	+	1.05533i
$179$		−	52513.4i		−	1.63895i	−0.573118	−	0.819473i	$-0.694266\pi$
$179$		−	52513.4i		−	1.63895i	0.573118	−	0.819473i	$-0.305734\pi$
$180$		0			0
$181$	−7223.25			−0.220483			−0.110242	−	0.993905i	$-0.535162\pi$
$181$	−7223.25			−0.220483			−0.110242	+	0.993905i	$0.535162\pi$
$182$	36455.5	+	19095.7i	1.10058	+	0.576492i
$183$		0			0
$184$	18327.0	−	13841.6i	0.541322	−	0.408837i
$185$	9076.12	+	15720.3i	0.265190	+	0.459322i
$186$		0			0
$187$	−19346.7	−	11169.8i	−0.553252	−	0.319420i
$188$	3443.21	+	41808.1i	0.0974200	+	1.18289i
$189$		0			0
$190$	827.894	+	20138.9i	0.0229334	+	0.557864i
$191$	9164.94	+	5291.38i	0.251225	+	0.145045i	0.620325	−	0.784345i	$-0.287001\pi$
$191$	9164.94	+	5291.38i	0.251225	+	0.145045i	−0.369100	+	0.929390i	$0.620334\pi$
$192$		0			0
$193$	19543.2	+	33849.9i	0.524665	+	0.908746i	0.999588	+	0.0287188i	$0.00914273\pi$
$193$	19543.2	+	33849.9i	0.524665	+	0.908746i	−0.474923	+	0.880028i	$0.657524\pi$
$194$	−31243.8	−	49319.7i	−0.830157	−	1.31044i
$195$		0			0
$196$	8113.02	−	17169.5i	0.211189	−	0.446937i
$197$	10820.0			0.278802			0.139401	−	0.990236i	$-0.455482\pi$
$197$	10820.0			0.278802			0.139401	+	0.990236i	$0.455482\pi$
$198$		0			0
$199$			807.389i			0.0203881i	0.999948	+	0.0101940i	$0.00324492\pi$
$199$			807.389i			0.0203881i	−0.999948	+	0.0101940i	$0.996755\pi$
$200$	6515.50	−	15396.0i	0.162888	−	0.384900i
$201$		0			0
$202$	−13831.3	−	21833.3i	−0.338970	−	0.535078i
$203$	935.426	−	540.068i	0.0226996	−	0.0131056i
$204$		0			0
$205$	6148.73	−	10649.9i	0.146311	−	0.253419i
$206$	2654.41	+	64569.8i	0.0625510	+	1.52158i
$207$		0			0
$208$	43379.3	−	7194.03i	1.00267	−	0.166282i
$209$	19083.8	−	33054.1i	0.436890	−	0.756716i
$210$		0			0
$211$	52683.9	−	30417.0i	1.18335	−	0.683207i	0.226562	−	0.973997i	$-0.427251\pi$
$211$	52683.9	−	30417.0i	1.18335	−	0.683207i	0.956787	+	0.290790i	$0.0939181\pi$
$212$	18533.2	+	26757.2i	0.412361	+	0.595345i
$213$		0			0
$214$	10861.2	+	5689.21i	0.237166	+	0.124229i
$215$			9126.44i			0.197435i
$216$		0			0
$217$	−46471.9			−0.986895
$218$	−32905.1	+	62818.9i	−0.692389	+	1.32184i
$219$		0			0
$220$	−88291.3	+	61154.3i	−1.82420	+	1.26352i
$221$	−8508.59	−	14737.3i	−0.174210	−	0.301741i
$222$		0			0
$223$	9292.11	+	5364.80i	0.186855	+	0.107881i	0.590509	−	0.807031i	$-0.298927\pi$
$223$	9292.11	+	5364.80i	0.186855	+	0.107881i	−0.403654	+	0.914912i	$0.632260\pi$
$224$	−12511.9	−	60046.6i	−0.249361	−	1.19672i
$225$		0			0
$226$	−59122.5	+	2430.48i	−1.15754	+	0.0475856i
$227$	−65585.2	−	37865.7i	−1.27278	−	0.734842i	−0.297272	−	0.954793i	$-0.596077\pi$
$227$	−65585.2	−	37865.7i	−1.27278	−	0.734842i	−0.975511	+	0.219951i	$0.929410\pi$
$228$		0			0
$229$	26683.3	+	46216.8i	0.508825	+	0.881311i	0.999948	+	0.0102204i	$0.00325330\pi$
$229$	26683.3	+	46216.8i	0.508825	+	0.881311i	−0.491123	+	0.871090i	$0.663413\pi$
$230$	−36097.8	+	22867.8i	−0.682378	+	0.432283i
$231$		0			0
$232$	449.787	−	1062.84i	0.00835662	−	0.0197465i
$233$	−56485.5			−1.04046			−0.520230	−	0.854026i	$-0.674154\pi$
$233$	−56485.5			−1.04046			−0.520230	+	0.854026i	$0.674154\pi$
$234$		0			0
$235$		−	78050.9i		−	1.41333i
$236$	−37592.6	−	17763.4i	−0.674961	−	0.318935i
$237$		0			0
$238$	−20052.3	+	12703.0i	−0.354005	+	0.224260i
$239$	−41561.8	+	23995.7i	−0.727610	+	0.420086i	−0.817547	−	0.575862i	$-0.804667\pi$
$239$	−41561.8	+	23995.7i	−0.727610	+	0.420086i	0.0899375	+	0.995947i	$0.471333\pi$
$240$		0			0
$241$	32075.1	−	55555.6i	0.552247	−	0.956520i	−0.445865	−	0.895100i	$-0.647104\pi$
$241$	32075.1	−	55555.6i	0.552247	−	0.956520i	0.998112	−	0.0614196i	$-0.0195628\pi$
$242$	144692.	−	5948.19i	2.47067	−	0.101567i
$243$		0			0
$244$	−22601.3	+	1861.39i	−0.379624	+	0.0312649i
$245$	−17666.1	+	30598.6i	−0.294313	+	0.509764i
$246$		0			0
$247$	25178.9	−	14537.1i	0.412708	−	0.238277i
$248$	−39622.8	+	29925.4i	−0.644232	+	0.486561i
$249$		0			0
$250$	20100.0	−	38372.8i	0.321600	−	0.613965i
$251$		−	65230.8i		−	1.03539i	−0.855564	−	0.517696i	$-0.826790\pi$
$251$		−	65230.8i		−	1.03539i	0.855564	−	0.517696i	$-0.173210\pi$
$252$		0			0
$253$	80917.3			1.26415
$254$	65476.1	+	34296.9i	1.01488	+	0.531604i
$255$		0			0
$256$	−49334.7	−	43139.9i	−0.752788	−	0.658263i
$257$	−21657.9	−	37512.6i	−0.327907	−	0.567951i	0.654190	−	0.756331i	$-0.273010\pi$
$257$	−21657.9	−	37512.6i	−0.327907	−	0.567951i	−0.982096	+	0.188380i	$0.939676\pi$
$258$		0			0
$259$	−31630.7	−	18262.0i	−0.471530	−	0.272238i
$260$	−81537.3	+	6715.22i	−1.20617	+	0.0993376i
$261$		0			0
$262$	1367.08	+	33254.7i	0.0199155	+	0.484452i
$263$	−73443.4	−	42402.6i	−1.06180	−	0.613029i	−0.135868	−	0.990727i	$-0.543382\pi$
$263$	−73443.4	−	42402.6i	−1.06180	−	0.613029i	−0.925929	+	0.377698i	$0.876716\pi$
$264$		0			0
$265$	−30280.0	−	52446.5i	−0.431185	−	0.746835i
$266$	−21703.3	−	34259.6i	−0.306734	−	0.484193i
$267$		0			0
$268$	−86727.3	−	40980.8i	−1.20750	−	0.570572i
$269$	66685.5			0.921567			0.460784	−	0.887513i	$-0.347568\pi$
$269$	66685.5			0.921567			0.460784	+	0.887513i	$0.347568\pi$
$270$		0			0
$271$			122426.i			1.66700i	0.552516	+	0.833502i	$0.313668\pi$
$271$			122426.i			1.66700i	−0.552516	+	0.833502i	$0.686332\pi$
$272$	−8916.88	+	23743.4i	−0.120524	+	0.320926i
$273$		0			0
$274$	45823.2	+	72333.9i	0.610357	+	0.963475i
$275$	51010.0	−	29450.6i	0.674512	−	0.389430i
$276$		0			0
$277$	−68726.1	+	119037.i	−0.895699	+	1.55140i	−0.0627613	+	0.998029i	$0.519991\pi$
$277$	−68726.1	+	119037.i	−0.895699	+	1.55140i	−0.832937	+	0.553367i	$0.813343\pi$
$278$	2994.39	+	72839.8i	0.0387453	+	0.942496i
$279$		0			0
$280$	14030.8	+	113256.i	0.178965	+	1.44459i
$281$	7001.61	−	12127.2i	0.0886718	−	0.153584i	−0.818278	−	0.574822i	$-0.805071\pi$
$281$	7001.61	−	12127.2i	0.0886718	−	0.153584i	0.906950	+	0.421238i	$0.138404\pi$
$282$		0			0
$283$	−99634.2	+	57523.8i	−1.24404	+	0.718249i	−0.969915	−	0.243444i	$-0.921723\pi$
$283$	−99634.2	+	57523.8i	−1.24404	+	0.718249i	−0.274129	+	0.961693i	$0.588389\pi$
$284$	−16302.4	+	11291.7i	−0.202123	+	0.139999i
$285$		0			0
$286$	137236.	+	71885.5i	1.67778	+	0.878838i
$287$			24743.6i			0.300400i
$288$		0			0
$289$	−73705.6			−0.882480
$290$	−996.357	+	1902.14i	−0.0118473	+	0.0226176i
$291$		0			0
$292$	46103.7	+	66562.1i	0.540717	+	0.780659i
$293$	14259.3	+	24697.8i	0.166097	+	0.287689i	0.937044	−	0.349210i	$-0.113550\pi$
$293$	14259.3	+	24697.8i	0.166097	+	0.287689i	−0.770947	+	0.636899i	$0.780217\pi$
$294$		0			0
$295$	66995.6	+	38679.9i	0.769843	+	0.444469i
$296$	−38728.7	+	4797.95i	−0.442027	+	0.0547611i
$297$		0			0
$298$	−64902.9	+	2668.11i	−0.730856	+	0.0300449i
$299$	53380.6	+	30819.3i	0.597092	+	0.344731i
$300$		0			0
$301$	−9181.62	−	15903.0i	−0.101341	−	0.175528i
$302$	82875.2	−	52501.0i	0.908679	−	0.575644i
$303$		0			0
$304$	−40566.0	−	15234.6i	−0.438950	−	0.164848i
$305$	42194.0			0.453577
$306$		0			0
$307$		−	115338.i		−	1.22376i	−0.790952	−	0.611879i	$-0.790414\pi$
$307$		−	115338.i		−	1.22376i	0.790952	−	0.611879i	$-0.209586\pi$
$308$	92325.6	−	195388.i	0.973242	−	2.05966i
$309$		0			0
$310$	78043.1	−	49439.9i	0.812103	−	0.514463i
$311$	−85566.6	+	49401.9i	−0.884674	+	0.510767i	−0.872197	−	0.489155i	$-0.837305\pi$
$311$	−85566.6	+	49401.9i	−0.884674	+	0.510767i	−0.0124776	+	0.999922i	$0.503972\pi$
$312$		0			0
$313$	37066.1	−	64200.3i	0.378345	−	0.655313i	−0.612477	−	0.790489i	$-0.709827\pi$
$313$	37066.1	−	64200.3i	0.378345	−	0.655313i	0.990822	+	0.135176i	$0.0431600\pi$
$314$	−158482.	+	6515.09i	−1.60739	+	0.0660786i
$315$		0			0
$316$	−2480.88	−	30123.2i	−0.0248445	−	0.301667i
$317$	−1057.30	+	1831.29i	−0.0105215	+	0.0182238i	−0.871238	−	0.490860i	$-0.836682\pi$
$317$	−1057.30	+	1831.29i	−0.0105215	+	0.0182238i	0.860717	+	0.509084i	$0.170016\pi$
$318$		0			0
$319$	3521.39	−	2033.08i	0.0346045	−	0.0199789i
$320$	84893.7	+	87529.0i	0.829040	+	0.854775i
$321$		0			0
$322$	39895.2	−	76163.6i	0.384777	−	0.734575i
$323$			16769.7i			0.160739i
$324$		0			0
$325$	44868.0			0.424785
$326$	−89733.2	−	47003.1i	−0.844342	−	0.442273i
$327$		0			0
$328$	15933.6	+	21096.9i	0.148104	+	0.196097i
$329$	78522.8	+	136006.i	0.725444	+	1.25651i
$330$		0			0
$331$	12334.0	+	7121.02i	0.112576	+	0.0649960i	0.555231	−	0.831696i	$-0.312630\pi$
$331$	12334.0	+	7121.02i	0.112576	+	0.0649960i	−0.442655	+	0.896692i	$0.645963\pi$
$332$	−8843.19	−	107375.i	−0.0802292	−	0.974156i
$333$		0			0
$334$	−4573.98	−	111264.i	−0.0410017	−	0.997384i
$335$	154561.	+	89235.7i	1.37724	+	0.795150i
$336$		0			0
$337$	−37711.8	−	65318.7i	−0.332061	−	0.575146i	0.650855	−	0.759202i	$-0.274411\pi$
$337$	−37711.8	−	65318.7i	−0.332061	−	0.575146i	−0.982916	+	0.184056i	$0.941077\pi$
$338$	2016.79	+	3183.59i	0.0176534	+	0.0278666i
$339$		0			0
$340$	20160.7	−	42665.9i	0.174400	−	0.369082i
$341$	−174942.			−1.50448
$342$		0			0
$343$			72725.3i			0.618155i
$344$	−18069.1	−	7646.75i	−0.152693	−	0.0646190i
$345$		0			0
$346$	47209.9	+	74522.9i	0.394349	+	0.622498i
$347$	128553.	−	74220.2i	1.06764	−	0.616401i	0.140103	−	0.990137i	$-0.455257\pi$
$347$	128553.	−	74220.2i	1.06764	−	0.616401i	0.927535	+	0.373736i	$0.121923\pi$
$348$		0			0
$349$	11665.4	−	20205.1i	0.0957745	−	0.165886i	−0.814157	−	0.580645i	$-0.802801\pi$
$349$	11665.4	−	20205.1i	0.0957745	−	0.165886i	0.909932	+	0.414758i	$0.136134\pi$
$350$	−2570.71	−	62533.6i	−0.0209854	−	0.510478i
$351$		0			0
$352$	−47100.8	−	226044.i	−0.380140	−	1.82435i
$353$	9687.21	−	16778.7i	0.0777409	−	0.134651i	−0.824534	−	0.565812i	$-0.808563\pi$
$353$	9687.21	−	16778.7i	0.0777409	−	0.134651i	0.902275	+	0.431161i	$0.141896\pi$
$354$		0			0
$355$	31954.1	−	18448.7i	0.253554	−	0.146389i
$356$	85971.3	+	124121.i	0.678349	+	0.979364i
$357$		0			0
$358$	−186072.	−	97466.3i	−1.45183	−	0.760481i
$359$			139927.i			1.08571i	0.839827	+	0.542854i	$0.182656\pi$
$359$			139927.i			1.08571i	−0.839827	+	0.542854i	$0.817344\pi$
$360$		0			0
$361$	101670.			0.780148
$362$	−13406.5	+	25594.4i	−0.102306	+	0.195311i
$363$		0			0
$364$	135325.	−	93731.7i	1.02135	−	0.707431i
$365$	−75325.5	−	130468.i	−0.565400	−	0.979302i
$366$		0			0
$367$	−79304.5	−	45786.5i	−0.588797	−	0.339942i	0.175825	−	0.984421i	$-0.443741\pi$
$367$	−79304.5	−	45786.5i	−0.588797	−	0.339942i	−0.764622	+	0.644479i	$0.777074\pi$
$368$	−15029.9	−	90628.9i	−0.110984	−	0.669224i
$369$		0			0
$370$	72547.7	−	2982.38i	0.529932	−	0.0217851i
$371$	105527.	+	60926.1i	0.766684	+	0.442645i
$372$		0			0
$373$	−42790.4	−	74115.1i	−0.307559	−	0.532708i	0.670269	−	0.742118i	$-0.266179\pi$
$373$	−42790.4	−	74115.1i	−0.307559	−	0.532708i	−0.977828	+	0.209411i	$0.932845\pi$
$374$	−75486.3	+	47820.2i	−0.539666	+	0.341875i
$375$		0			0
$376$	154530.	+	65396.4i	1.09304	+	0.462571i
$377$	3097.38			0.0217928
$378$		0			0
$379$			39838.1i			0.277345i	0.990338	+	0.138672i	$0.0442835\pi$
$379$			39838.1i			0.277345i	−0.990338	+	0.138672i	$0.955716\pi$
$380$	72895.3	+	34444.8i	0.504815	+	0.238537i
$381$		0			0
$382$	35759.4	−	22653.4i	0.245055	−	0.155241i
$383$	−147816.	+	85341.8i	−1.00769	+	0.581787i	−0.910513	−	0.413480i	$-0.864313\pi$
$383$	−147816.	+	85341.8i	−1.00769	+	0.581787i	−0.0971722	+	0.995268i	$0.530980\pi$
$384$		0			0
$385$	−201039.	+	348210.i	−1.35631	+	2.34920i
$386$	156214.	−	6421.84i	1.04844	−	0.0431007i
$387$		0			0
$388$	−232745.	+	19168.3i	−1.54603	+	0.127327i
$389$	107907.	−	186901.i	0.713103	−	1.23513i	−0.250583	−	0.968095i	$-0.580622\pi$
$389$	107907.	−	186901.i	0.713103	−	1.23513i	0.963687	−	0.267036i	$-0.0860443\pi$
$390$		0			0
$391$	−30789.5	+	17776.3i	−0.201395	+	0.116275i
$392$	−45779.3	−	60614.2i	−0.297918	−	0.394459i
$393$		0			0
$394$	20082.3	−	38338.9i	0.129366	−	0.246972i
$395$			56236.6i			0.360434i
$396$		0			0
$397$	292553.			1.85620			0.928098	−	0.372336i	$-0.121443\pi$
$397$	292553.			1.85620			0.928098	+	0.372336i	$0.121443\pi$
$398$	2860.84	+	1498.53i	0.0180604	+	0.00946021i
$399$		0			0
$400$	−42460.1	−	51661.9i	−0.265376	−	0.322887i
$401$	102157.	+	176941.i	0.635300	+	1.10037i	0.986452	+	0.164053i	$0.0524567\pi$
$401$	102157.	+	176941.i	0.635300	+	1.10037i	−0.351152	+	0.936318i	$0.614210\pi$
$402$		0			0
$403$	−115408.	−	66631.1i	−0.710604	−	0.410267i
$404$	−103034.	+	8485.63i	−0.631274	+	0.0519902i
$405$		0			0
$406$	−177.464	−	4316.90i	−0.00107661	−	0.0261891i
$407$	−119073.	−	68746.9i	−0.718827	−	0.415015i
$408$		0			0
$409$	−17364.4	−	30076.0i	−0.103804	−	0.179793i	0.809445	−	0.587196i	$-0.199768\pi$
$409$	−17364.4	−	30076.0i	−0.103804	−	0.179793i	−0.913249	+	0.407402i	$0.866435\pi$
$410$	−26323.9	−	41553.5i	−0.156597	−	0.247195i
$411$		0			0
$412$	233718.	+	110438.i	1.37689	+	0.650613i
$413$	−155655.			−0.912564
$414$		0			0
$415$			200458.i			1.16393i
$416$	55022.3	−	167059.i	0.317945	−	0.965349i
$417$		0			0
$418$	−81701.5	−	128969.i	−0.467603	−	0.738132i
$419$	277682.	−	160320.i	1.58169	−	0.913187i	0.587073	−	0.809534i	$-0.300280\pi$
$419$	277682.	−	160320.i	1.58169	−	0.913187i	0.994614	−	0.103653i	$-0.0330530\pi$
$420$		0			0
$421$	−67885.7	+	117582.i	−0.383014	+	0.663399i	−0.991491	−	0.130172i	$-0.958447\pi$
$421$	−67885.7	+	117582.i	−0.383014	+	0.663399i	0.608478	+	0.793571i	$0.291780\pi$
$422$	−9994.93	−	243131.i	−0.0561248	−	1.36526i
$423$		0			0
$424$	129208.	−	16007.0i	0.718714	−	0.0890388i
$425$	−12939.7	+	22412.3i	−0.0716386	+	0.124082i
$426$		0			0
$427$	−73524.1	+	42449.2i	−0.403250	+	0.232816i
$428$	40317.5	−	27925.6i	0.220093	−	0.152446i
$429$		0			0
$430$	32338.0	+	16938.9i	0.174894	+	0.0916112i
$431$			31343.0i			0.168728i	0.996435	+	0.0843638i	$0.0268858\pi$
$431$			31343.0i			0.168728i	−0.996435	+	0.0843638i	$0.973114\pi$
$432$		0			0
$433$	101022.			0.538815			0.269407	−	0.963026i	$-0.413172\pi$
$433$	101022.			0.538815			0.269407	+	0.963026i	$0.413172\pi$
$434$	−86253.1	+	164665.i	−0.457926	+	0.874223i
$435$		0			0
$436$	161515.	+	233187.i	0.849651	+	1.22668i
$437$	−30371.1	−	52604.3i	−0.159037	−	0.275460i
$438$		0			0
$439$	157593.	+	90986.2i	0.817724	+	0.472113i	0.849631	−	0.527378i	$-0.176825\pi$
$439$	157593.	+	90986.2i	0.817724	+	0.472113i	−0.0319068	+	0.999491i	$0.510158\pi$
$440$	52818.8	+	426349.i	0.272824	+	2.20222i
$441$		0			0
$442$	−68011.3	+	2795.89i	−0.348126	+	0.0143112i
$443$	−32206.4	−	18594.4i	−0.164110	−	0.0947490i	0.415696	−	0.909504i	$-0.363538\pi$
$443$	−32206.4	−	18594.4i	−0.164110	−	0.0947490i	−0.579806	+	0.814755i	$0.696872\pi$
$444$		0			0
$445$	−140462.	−	243287.i	−0.709315	−	1.22857i
$446$	36255.7	−	22967.8i	0.182266	−	0.115465i
$447$		0			0
$448$	−235987.	−	67114.3i	−1.17580	−	0.334395i
$449$	20385.0			0.101115			0.0505577	−	0.998721i	$-0.483900\pi$
$449$	20385.0			0.101115			0.0505577	+	0.998721i	$0.483900\pi$
$450$		0			0
$451$			93146.9i			0.457947i
$452$	−101121.	+	214002.i	−0.494953	+	1.04747i
$453$		0			0
$454$	−255898.	+	162110.i	−1.24153	+	0.786501i
$455$	−265249.	+	153141.i	−1.28124	+	0.739724i
$456$		0			0
$457$	139829.	−	242191.i	0.669521	−	1.15964i	−0.308517	−	0.951219i	$-0.599833\pi$
$457$	139829.	−	242191.i	0.669521	−	1.15964i	0.978038	−	0.208426i	$-0.0668340\pi$
$458$	213286.	−	8768.03i	1.01679	−	0.0417995i
$459$		0			0
$460$	14029.6	+	170349.i	0.0663023	+	0.805054i
$461$	−80298.4	+	139081.i	−0.377838	+	0.654434i	−0.990747	−	0.135719i	$-0.956666\pi$
$461$	−80298.4	+	139081.i	−0.377838	+	0.654434i	0.612910	+	0.790153i	$0.289999\pi$
$462$		0			0
$463$	−85869.5	+	49576.8i	−0.400569	+	0.231268i	−0.686729	−	0.726913i	$-0.740954\pi$
$463$	−85869.5	+	49576.8i	−0.400569	+	0.231268i	0.286161	+	0.958182i	$0.407621\pi$
$464$	−2931.16	−	3566.39i	−0.0136146	−	0.0165651i
$465$		0			0
$466$	−104839.	+	200147.i	−0.482780	+	0.921673i
$467$		−	278790.i		−	1.27833i	−0.769068	−	0.639167i	$-0.779279\pi$
$467$		−	278790.i		−	1.27833i	0.769068	−	0.639167i	$-0.220721\pi$
$468$		0			0
$469$	−359101.			−1.63257
$470$	−276560.	−	144865.i	−1.25197	−	0.655792i
$471$		0			0
$472$	−132714.	+	100234.i	−0.595709	+	0.449913i
$473$	−34564.0	−	59866.6i	−0.154490	−	0.267585i
$474$		0			0
$475$	−38291.7	−	22107.7i	−0.169714	−	0.0979844i
$476$	7793.40	+	94628.8i	0.0343964	+	0.417647i
$477$		0			0
$478$	7884.90	+	191804.i	0.0345096	+	0.839462i
$479$	27705.5	+	15995.8i	0.120752	+	0.0697163i	0.559160	−	0.829060i	$-0.311124\pi$
$479$	27705.5	+	15995.8i	0.120752	+	0.0697163i	−0.438407	+	0.898776i	$0.644457\pi$
$480$		0			0
$481$	−52367.8	−	90703.7i	−0.226347	−	0.392044i
$482$	−137320.	−	216765.i	−0.591070	−	0.933029i
$483$		0			0
$484$	247477.	−	523733.i	1.05644	−	2.23573i
$485$	434509.			1.84721
$486$		0			0
$487$		−	346823.i		−	1.46235i	−0.682192	−	0.731173i	$-0.738973\pi$
$487$		−	346823.i		−	1.46235i	0.682192	−	0.731173i	$-0.261027\pi$
$488$	−35353.1	+	83538.5i	−0.148452	+	0.350790i
$489$		0			0
$490$	75632.1	+	119389.i	0.315003	+	0.497246i
$491$	−207830.	+	119991.i	−0.862076	+	0.497720i	−0.864707	−	0.502277i	$-0.832496\pi$
$491$	−207830.	+	119991.i	−0.862076	+	0.497720i	0.00263098	+	0.999997i	$0.499163\pi$
$492$		0			0
$493$	−893.273	+	1547.19i	−0.00367528	+	0.00636577i
$494$	−4776.82	−	116198.i	−0.0195743	−	0.476152i
$495$		0			0
$496$	32494.6	+	195939.i	0.132083	+	0.796448i
$497$	−37120.5	+	64294.7i	−0.150280	+	0.260293i
$498$		0			0
$499$	295354.	−	170523.i	1.18616	−	0.684828i	0.228726	−	0.973491i	$-0.426544\pi$
$499$	295354.	−	170523.i	1.18616	−	0.684828i	0.957431	+	0.288663i	$0.0932107\pi$
$500$	−98661.2	−	142442.i	−0.394645	−	0.569767i
$501$		0			0
$502$	−231134.	−	121070.i	−0.917184	−	0.480429i
$503$			3886.22i			0.0153600i	0.999971	+	0.00768001i	$0.00244465\pi$
$503$			3886.22i			0.0153600i	−0.999971	+	0.00768001i	$0.997555\pi$
$504$		0			0
$505$	192353.			0.754250
$506$	150185.	−	286716.i	0.586576	−	1.11983i
$507$		0			0
$508$	243051.	−	168347.i	0.941823	−	0.652347i
$509$	98673.1	+	170907.i	0.380858	+	0.659666i	0.991185	−	0.132484i	$-0.0422952\pi$
$509$	98673.1	+	170907.i	0.380858	+	0.659666i	−0.610327	+	0.792150i	$0.708962\pi$
$510$		0			0
$511$	262513.	+	151562.i	1.00533	+	0.580427i
$512$	−244425.	+	94740.3i	−0.932409	+	0.361405i
$513$		0			0
$514$	−173117.	+	7116.71i	−0.655260	+	0.0269372i
$515$	−416521.	−	240478.i	−1.57044	−	0.906696i
$516$		0			0
$517$	295597.	+	511990.i	1.10591	+	1.91549i
$518$	−123416.	+	78183.2i	−0.459950	+	0.291376i
$519$		0			0
$520$	−127541.	+	301377.i	−0.471676	+	1.11456i
$521$	−229165.			−0.844255			−0.422127	−	0.906536i	$-0.638717\pi$
$521$	−229165.			−0.844255			−0.422127	+	0.906536i	$0.638717\pi$
$522$		0			0
$523$		−	346673.i		−	1.26741i	−0.773575	−	0.633705i	$-0.781533\pi$
$523$		−	346673.i		−	1.26741i	0.773575	−	0.633705i	$-0.218467\pi$
$524$	120370.	+	56877.7i	0.438384	+	0.207147i
$525$		0			0
$526$	−286559.	+	181534.i	−1.03572	+	0.656124i
$527$	66566.6	−	38432.2i	0.239682	−	0.138380i
$528$		0			0
$529$	−75532.2	+	130826.i	−0.269911	+	0.467500i
$530$	−242035.	+	9949.89i	−0.861642	+	0.0354215i
$531$		0			0
$532$	−161675.	+	13315.2i	−0.571241	+	0.0470460i
$533$	−35477.2	+	61448.4i	−0.124881	+	0.216300i
$534$		0			0
$535$	−79025.8	+	45625.6i	−0.276097	+	0.159405i
$536$	−306176.	+	231242.i	−1.06572	+	0.804890i
$537$		0			0
$538$	123770.	−	236289.i	0.427613	−	0.816353i
$539$		−	267623.i		−	0.921184i
$540$		0			0
$541$	−287354.			−0.981799			−0.490900	−	0.871216i	$-0.663332\pi$
$541$	−287354.			−0.981799			−0.490900	+	0.871216i	$0.663332\pi$
$542$	433797.	+	227227.i	1.47669	+	0.773501i
$543$		0			0
$544$	67580.7	+	75663.8i	0.228362	+	0.255676i
$545$	−263888.	−	457067.i	−0.888436	−	1.53882i
$546$		0			0
$547$	−486589.	−	280932.i	−1.62625	−	0.938917i	−0.985198	−	0.171421i	$-0.945164\pi$
$547$	−486589.	−	280932.i	−1.62625	−	0.938917i	−0.641054	−	0.767496i	$-0.721502\pi$
$548$	341352.	−	28112.9i	1.13669	−	0.0936148i
$549$		0			0
$550$	−9677.37	−	235406.i	−0.0319913	−	0.778203i
$551$	−2643.40	−	1526.17i	−0.00870684	−	0.00502689i
$552$		0			0
$553$	−56576.7	−	97993.6i	−0.185006	−	0.320441i
$554$	294230.	+	464455.i	0.958666	+	1.51330i
$555$		0			0
$556$	263653.	+	124583.i	0.852871	+	0.403002i
$557$	393303.			1.26770			0.633850	−	0.773456i	$-0.281474\pi$
$557$	393303.			1.26770			0.633850	+	0.773456i	$0.281474\pi$
$558$		0			0
$559$		−	52658.1i		−	0.168516i
$560$	427344.	+	160490.i	1.36270	+	0.511766i
$561$		0			0
$562$	−29975.3	−	47317.3i	−0.0949054	−	0.149812i
$563$	481867.	−	278206.i	1.52023	−	0.877707i	0.520518	−	0.853851i	$-0.325739\pi$
$563$	481867.	−	278206.i	1.52023	−	0.877707i	0.999715	−	0.0238561i	$-0.00759436\pi$
$564$		0			0
$565$	220191.	−	381382.i	0.689768	−	1.19471i
$566$	18902.1	+	459802.i	0.0590035	+	1.43529i
$567$		0			0
$568$	9752.64	+	78722.5i	0.0302291	+	0.244007i
$569$	91030.8	−	157670.i	0.281167	−	0.486995i	−0.690506	−	0.723327i	$-0.742612\pi$
$569$	91030.8	−	157670.i	0.281167	−	0.486995i	0.971672	+	0.236332i	$0.0759453\pi$
$570$		0			0
$571$	190279.	−	109858.i	0.583604	−	0.336944i	−0.178960	−	0.983856i	$-0.557273\pi$
$571$	190279.	−	109858.i	0.583604	−	0.336944i	0.762565	+	0.646912i	$0.223940\pi$
$572$	509427.	−	352851.i	1.55701	−	1.07845i
$573$		0			0
$574$	87674.8	+	45924.8i	0.266104	+	0.139387i
$575$		−	93739.0i		−	0.283521i
$576$		0			0
$577$	9527.81			0.0286181			0.0143091	−	0.999898i	$-0.495445\pi$
$577$	9527.81			0.0286181			0.0143091	+	0.999898i	$0.495445\pi$
$578$	−136800.	+	261163.i	−0.409477	+	0.781729i
$579$		0			0
$580$	4890.64	+	7060.84i	0.0145382	+	0.0209894i
$581$	−201670.	−	349302.i	−0.597432	−	1.03478i
$582$		0			0
$583$	397254.	+	229355.i	1.16878	+	0.674794i
$584$	321421.	−	39819.7i	0.942429	−	0.116754i
$585$		0			0
$586$	113978.	−	4685.55i	0.331914	−	0.0136447i
$587$	−8948.63	−	5166.49i	−0.0259705	−	0.0149941i	0.486959	−	0.873425i	$-0.338106\pi$
$587$	−8948.63	−	5166.49i	−0.0259705	−	0.0149941i	−0.512929	+	0.858431i	$0.671440\pi$
$588$		0			0
$589$	65662.1	+	113730.i	0.189271	+	0.327827i
$590$	261401.	−	165596.i	0.750937	−	0.475715i
$591$		0			0
$592$	−54880.7	+	146134.i	−0.156594	+	0.416972i
$593$	−143639.			−0.408473			−0.204236	−	0.978922i	$-0.565471\pi$
$593$	−143639.			−0.408473			−0.204236	+	0.978922i	$0.565471\pi$
$594$		0			0
$595$		−	176661.i		−	0.499008i
$596$	−111007.	+	234924.i	−0.312507	+	0.661356i
$597$		0			0
$598$	208279.	−	131943.i	0.582428	−	0.368965i
$599$	305650.	−	176467.i	0.851865	−	0.491824i	−0.00941494	−	0.999956i	$-0.502997\pi$
$599$	305650.	−	176467.i	0.851865	−	0.491824i	0.861280	+	0.508131i	$0.169664\pi$
$600$		0			0
$601$	−17733.8	+	30715.9i	−0.0490969	+	0.0850382i	−0.889529	−	0.456878i	$-0.848968\pi$
$601$	−17733.8	+	30715.9i	−0.0490969	+	0.0850382i	0.840433	+	0.541916i	$0.182301\pi$
$602$	−73390.9	+	3017.04i	−0.202511	+	0.00832509i
$603$		0			0
$604$	−32209.8	−	391097.i	−0.0882907	−	1.07204i
$605$	−538881.	+	933369.i	−1.47225	+	2.55001i
$606$		0			0
$607$	424309.	−	244975.i	1.15161	−	0.664881i	0.202330	−	0.979317i	$-0.435149\pi$
$607$	424309.	−	244975.i	1.15161	−	0.664881i	0.949279	+	0.314436i	$0.101815\pi$
$608$	−129273.	+	115463.i	−0.349703	+	0.312345i
$609$		0			0
$610$	78313.2	−	149507.i	0.210463	−	0.401793i
$611$			450342.i			1.20631i
$612$		0			0
$613$	284390.			0.756821			0.378410	−	0.925638i	$-0.376471\pi$
$613$	284390.			0.756821			0.378410	+	0.925638i	$0.376471\pi$
$614$	−408680.	−	214070.i	−1.08404	−	0.567831i
$615$		0			0
$616$	−520965.	−	689785.i	−1.37293	−	1.81783i
$617$	98237.4	+	170152.i	0.258052	+	0.446958i	0.965720	−	0.259586i	$-0.0835862\pi$
$617$	98237.4	+	170152.i	0.258052	+	0.446958i	−0.707668	+	0.706545i	$0.750253\pi$
$618$		0			0
$619$	−58731.2	−	33908.5i	−0.153281	−	0.0884967i	0.421398	−	0.906876i	$-0.361540\pi$
$619$	−58731.2	−	33908.5i	−0.153281	−	0.0884967i	−0.574679	+	0.818379i	$0.694873\pi$
$620$	−30331.8	−	368294.i	−0.0789069	−	0.958101i
$621$		0			0
$622$	16233.3	+	394882.i	0.0419590	+	1.02067i
$623$	489517.	+	282623.i	1.26122	+	0.728167i
$624$		0			0
$625$	242826.	+	420586.i	0.621634	+	1.07670i
$626$	−158687.	−	250495.i	−0.404942	−	0.639219i
$627$		0			0
$628$	−271062.	+	573647.i	−0.687306	+	1.45454i
$629$	60410.6			0.152691
$630$		0			0
$631$			716972.i			1.80071i	0.435158	+	0.900354i	$0.356692\pi$
$631$			716972.i			1.80071i	−0.435158	+	0.900354i	$0.643308\pi$
$632$	−111341.	−	47118.9i	−0.278754	−	0.117967i
$633$		0			0
$634$	4526.49	+	7145.27i	0.0112612	+	0.0177762i
$635$	−476401.	+	275050.i	−1.18148	+	0.682125i
$636$		0			0
$637$	101931.	−	176549.i	0.251204	−	0.435098i
$638$	−668.061	−	16250.9i	−0.00164125	−	0.0399241i
$639$		0			0
$640$	467709.	−	138350.i	1.14187	−	0.337769i
$641$	321445.	−	556760.i	0.782332	−	1.35504i	−0.148248	−	0.988950i	$-0.547363\pi$
$641$	321445.	−	556760.i	0.782332	−	1.35504i	0.930580	−	0.366089i	$-0.119303\pi$
$642$		0			0
$643$	1326.59	−	765.910i	0.00320861	−	0.00185249i	−0.498395	−	0.866950i	$-0.666077\pi$
$643$	1326.59	−	765.910i	0.00320861	−	0.00185249i	0.501603	+	0.865098i	$0.332744\pi$
$644$	−195826.	−	282723.i	−0.472171	−	0.681695i
$645$		0			0
$646$	59420.6	+	31125.0i	0.142387	+	0.0745838i
$647$			106720.i			0.254938i	0.991843	+	0.127469i	$0.0406854\pi$
$647$			106720.i			0.254938i	−0.991843	+	0.127469i	$0.959315\pi$
$648$		0			0
$649$	−585960.			−1.39116
$650$	83276.1	−	158982.i	0.197103	−	0.376288i
$651$		0			0
$652$	−333094.	+	230715.i	−0.783560	+	0.542727i
$653$	114833.	+	198896.i	0.269301	+	0.466444i	0.968682	−	0.248306i	$-0.0798739\pi$
$653$	114833.	+	198896.i	0.269301	+	0.466444i	−0.699380	+	0.714750i	$0.746541\pi$
$654$		0			0
$655$	−214517.	−	123851.i	−0.500010	−	0.288681i
$656$	104326.	−	17301.5i	0.242430	−	0.0402046i
$657$		0			0
$658$	627652.	−	25802.3i	1.44966	−	0.0595946i
$659$	337909.	+	195092.i	0.778089	+	0.449230i	0.835753	−	0.549106i	$-0.185032\pi$
$659$	337909.	+	195092.i	0.778089	+	0.449230i	−0.0576633	+	0.998336i	$0.518365\pi$
$660$		0			0
$661$	−223443.	−	387014.i	−0.511403	−	0.885776i	−0.999913	−	0.0132177i	$-0.995793\pi$
$661$	−223443.	−	387014.i	−0.511403	−	0.885776i	0.488509	−	0.872559i	$-0.337541\pi$
$662$	48124.3	−	30486.5i	0.109812	−	0.0695651i
$663$		0			0
$664$	−396879.	−	167957.i	−0.900166	−	0.380945i
$665$	301829.			0.682523
$666$		0			0
$667$		−	6471.12i		−	0.0145455i
$668$	−402735.	−	190302.i	−0.902540	−	0.426472i
$669$		0			0
$670$	603060.	−	382036.i	1.34342	−	0.851048i
$671$	−276780.	+	159799.i	−0.614737	+	0.354919i
$672$		0			0
$673$	−169746.	+	294009.i	−0.374774	+	0.649128i	−0.990293	−	0.138994i	$-0.955613\pi$
$673$	−169746.	+	294009.i	−0.374774	+	0.649128i	0.615519	+	0.788122i	$0.288946\pi$
$674$	−301440.	+	12392.0i	−0.663561	+	0.0272785i
$675$		0			0
$676$	15023.7	−	1237.32i	0.0328764	−	0.00270762i
$677$	266702.	−	461941.i	0.581900	−	1.00788i	−0.413354	−	0.910570i	$-0.635643\pi$
$677$	266702.	−	461941.i	0.581900	−	1.00788i	0.995254	−	0.0973098i	$-0.0310238\pi$
$678$		0			0
$679$	−757142.	+	437136.i	−1.64224	+	0.948150i
$680$	−113760.	−	150625.i	−0.246022	−	0.325746i
$681$		0			0
$682$	−324698.	+	619878.i	−0.698089	+	1.33272i
$683$		−	175866.i		−	0.376999i	−0.982073	−	0.188500i	$-0.939638\pi$
$683$		−	175866.i		−	0.376999i	0.982073	−	0.188500i	$-0.0603624\pi$
$684$		0			0
$685$	−637265.			−1.35812
$686$	257689.	+	134980.i	0.547581	+	0.286828i
$687$		0			0
$688$	−60631.7	+	49832.2i	−0.128092	+	0.105277i
$689$	174711.	+	302608.i	0.368028	+	0.637444i
$690$		0			0
$691$	203114.	+	117268.i	0.425386	+	0.245597i	0.697379	−	0.716702i	$-0.254349\pi$
$691$	203114.	+	117268.i	0.425386	+	0.245597i	−0.271993	+	0.962299i	$0.587683\pi$
$692$	351682.	−	28963.7i	0.734409	−	0.0604842i
$693$		0			0
$694$	−24388.5	−	593261.i	−0.0506368	−	1.23176i
$695$	−469869.	−	271279.i	−0.972762	−	0.561625i
$696$		0			0
$697$	−20463.0	−	35442.9i	−0.0421214	−	0.0729565i
$698$	−49942.0	−	78835.6i	−0.102507	−	0.161812i
$699$		0			0
$700$	−226348.	−	106955.i	−0.461935	−	0.218276i
$701$	−192485.			−0.391707			−0.195853	−	0.980633i	$-0.562748\pi$
$701$	−192485.			−0.391707			−0.195853	+	0.980633i	$0.562748\pi$
$702$		0			0
$703$			103213.i			0.208844i
$704$	−888369.	−	252650.i	−1.79245	−	0.509770i
$705$		0			0
$706$	−41472.9	−	65466.7i	−0.0832060	−	0.131344i
$707$	−335179.	+	193516.i	−0.670561	+	0.387148i
$708$		0			0
$709$	300439.	−	520376.i	0.597674	−	1.03520i	−0.395489	−	0.918471i	$-0.629425\pi$
$709$	300439.	−	520376.i	0.597674	−	1.03520i	0.993164	−	0.116731i	$-0.0372417\pi$
$710$	−6062.18	−	147465.i	−0.0120258	−	0.292532i
$711$		0			0
$712$	599365.	−	74253.1i	1.18231	−	0.146472i
$713$	−139207.	+	241114.i	−0.273831	+	0.474288i
$714$		0			0
$715$	−998522.	+	576497.i	−1.95320	+	1.12768i
$716$	−690710.	+	478415.i	−1.34732	+	0.933209i
$717$		0			0
$718$	495808.	+	259708.i	0.961755	+	0.503776i
$719$			37302.4i			0.0721571i	0.999349	+	0.0360786i	$0.0114867\pi$
$719$			37302.4i			0.0721571i	−0.999349	+	0.0360786i	$0.988513\pi$
$720$		0			0
$721$	967729.			1.86159
$722$	188702.	−	360249.i	0.361994	−	0.691080i
$723$		0			0
$724$	65806.3	+	95007.6i	0.125542	+	0.181251i
$725$	−2355.23	−	4079.37i	−0.00448081	−	0.00776099i
$726$		0			0
$727$	−647844.	−	374033.i	−1.22575	−	0.707686i	−0.259611	−	0.965713i	$-0.583594\pi$
$727$	−647844.	−	374033.i	−1.22575	−	0.707686i	−0.966138	+	0.258027i	$0.916928\pi$
$728$	−80955.8	−	653469.i	−0.152751	−	1.23300i
$729$		0			0
$730$	−602095.	+	24751.7i	−1.12985	+	0.0464471i
$731$	26303.6	+	15186.4i	0.0492244	+	0.0284197i
$732$		0			0
$733$	131709.	+	228126.i	0.245136	+	0.424588i	0.962170	−	0.272450i	$-0.0878341\pi$
$733$	131709.	+	228126.i	0.245136	+	0.424588i	−0.717034	+	0.697038i	$0.754501\pi$
$734$	−309428.	+	196021.i	−0.574337	+	0.363840i
$735$		0			0
$736$	−349024.	−	114954.i	−0.644317	−	0.212211i
$737$	−1.35183e6			−2.48878
$738$		0			0
$739$			288908.i			0.529018i	0.964383	+	0.264509i	$0.0852099\pi$
$739$			288908.i			0.529018i	−0.964383	+	0.264509i	$0.914790\pi$
$740$	124083.	−	262596.i	0.226594	−	0.479539i
$741$		0			0
$742$	411742.	−	260837.i	0.747855	−	0.473763i
$743$	271416.	−	156702.i	0.491651	−	0.283855i	−0.233608	−	0.972331i	$-0.575053\pi$
$743$	271416.	−	156702.i	0.491651	−	0.283855i	0.725259	+	0.688476i	$0.241720\pi$
$744$		0			0
$745$	241719.	−	418670.i	0.435510	−	0.754326i
$746$	−342034.	+	14060.8i	−0.614599	+	0.0252657i
$747$		0			0
$748$	29338.1	+	356228.i	0.0524359	+	0.636685i
$749$	91802.9	−	159007.i	0.163641	−	0.283435i
$750$		0			0
$751$	204539.	−	118091.i	0.362658	−	0.209381i	−0.307588	−	0.951520i	$-0.599522\pi$
$751$	204539.	−	118091.i	0.362658	−	0.209381i	0.670246	+	0.742139i	$0.266189\pi$
$752$	518533.	−	426174.i	0.916940	−	0.753618i
$753$		0			0
$754$	5748.83	−	10975.0i	0.0101120	−	0.0193047i
$755$			730134.i			1.28088i
$756$		0			0
$757$	−1.00219e6			−1.74888			−0.874438	−	0.485137i	$-0.838770\pi$
$757$	−1.00219e6			−1.74888			−0.874438	+	0.485137i	$0.838770\pi$
$758$	141159.	+	73940.5i	0.245681	+	0.128690i
$759$		0			0
$760$	257345.	−	194361.i	0.445542	−	0.336498i
$761$	456412.	+	790529.i	0.788112	+	1.36505i	0.927122	+	0.374759i	$0.122275\pi$
$761$	456412.	+	790529.i	0.788112	+	1.36505i	−0.139010	+	0.990291i	$0.544392\pi$
$762$		0			0
$763$	919661.	+	530967.i	1.57971	+	0.912049i
$764$	−13898.1	−	168753.i	−0.0238105	−	0.289111i
$765$		0			0
$766$	28043.0	+	682158.i	0.0477933	+	1.16259i
$767$	−386554.	−	223177.i	−0.657082	−	0.379366i
$768$		0			0
$769$	104325.	+	180697.i	0.176416	+	0.305561i	0.940650	−	0.339378i	$-0.110216\pi$
$769$	104325.	+	180697.i	0.176416	+	0.305561i	−0.764235	+	0.644938i	$0.776883\pi$
$770$	860689.	+	1.35863e6i	1.45166	+	2.29151i
$771$		0			0
$772$	267183.	−	565437.i	0.448305	−	0.948744i
$773$	661279.			1.10669			0.553345	−	0.832952i	$-0.313351\pi$
$773$	661279.			1.10669			0.553345	+	0.832952i	$0.313351\pi$
$774$		0			0
$775$			202663.i			0.337420i
$776$	−364061.	+	860269.i	−0.604576	+	1.42860i
$777$		0			0
$778$	−461973.	−	729245.i	−0.763234	−	1.20480i
$779$	60554.8	−	34961.3i	0.0997869	−	0.0576120i
$780$		0			0
$781$	−139739.	+	242036.i	−0.229096	+	0.396805i
$782$	5841.23	+	142090.i	0.00955192	+	0.232355i
$783$		0			0
$784$	−299743.	+	49709.5i	−0.487660	+	0.0808736i
$785$	590239.	−	1.02232e6i	0.957830	−	1.65901i
$786$		0			0
$787$	−33656.2	+	19431.4i	−0.0543395	+	0.0313729i	−0.526924	−	0.849913i	$-0.676655\pi$
$787$	−33656.2	+	19431.4i	−0.0543395	+	0.0313729i	0.472584	+	0.881286i	$0.343321\pi$
$788$	−98574.1	−	142316.i	−0.158749	−	0.229193i
$789$		0			0
$790$	199265.	+	104377.i	0.319283	+	0.167243i
$791$			886090.i			1.41620i
$792$		0			0
$793$	−243453.			−0.387141
$794$	542986.	−	1.03661e6i	0.861287	−	1.64428i
$795$		0			0
$796$	10619.6	−	7355.58i	0.0167603	−	0.0116089i
$797$	−321301.	−	556510.i	−0.505820	−	0.876105i	−0.999977	−	0.00673297i	$-0.997857\pi$
$797$	−321301.	−	556510.i	−0.505820	−	0.876105i	0.494158	−	0.869372i	$-0.335477\pi$
$798$		0			0
$799$	−224953.	−	129877.i	−0.352369	−	0.203441i
$800$	−261862.	+	54564.2i	−0.409160	+	0.0852566i
$801$		0			0
$802$	816565.	−	33568.3i	1.26953	−	0.0521893i
$803$	988223.	+	570551.i	1.53258	+	0.884837i
$804$		0			0
$805$	319946.	+	554163.i	0.493725	+	0.855156i
$806$	−450297.	+	285261.i	−0.693152	+	0.439109i
$807$		0			0
$808$	−161166.	+	380833.i	−0.246860	+	0.583326i
$809$	−737297.			−1.12654			−0.563269	−	0.826274i	$-0.690456\pi$
$809$	−737297.			−1.12654			−0.563269	+	0.826274i	$0.690456\pi$
$810$		0			0
$811$			823394.i			1.25189i	0.779867	+	0.625945i	$0.215286\pi$
$811$			823394.i			1.25189i	−0.779867	+	0.625945i	$0.784714\pi$
$812$	−15625.6	−	7383.47i	−0.0236987	−	0.0111982i
$813$		0			0
$814$	−464595.	+	294319.i	−0.701174	+	0.444190i
$815$	652894.	−	376949.i	0.982941	−	0.567501i
$816$		0			0
$817$	−25946.2	+	44940.1i	−0.0388713	+	0.0673271i
$818$	−138798.	+	5705.87i	−0.207432	+	0.00852738i
$819$		0			0
$820$	−196096.	+	16150.0i	−0.291635	+	0.0240184i
$821$	−290123.	+	502508.i	−0.430424	+	0.745516i	−0.996910	−	0.0785556i	$-0.974969\pi$
$821$	−290123.	+	502508.i	−0.430424	+	0.745516i	0.566486	+	0.824071i	$0.308303\pi$
$822$		0			0
$823$	400074.	−	230983.i	0.590664	−	0.341020i	−0.174696	−	0.984622i	$-0.555894\pi$
$823$	400074.	−	230983.i	0.590664	−	0.341020i	0.765360	+	0.643602i	$0.222561\pi$
$824$	825104.	−	623166.i	1.21522	−	0.917802i
$825$		0			0
$826$	−288900.	+	551537.i	−0.423435	+	0.808378i
$827$		−	1.11437e6i		−	1.62936i	−0.579912	−	0.814679i	$-0.696913\pi$
$827$		−	1.11437e6i		−	1.62936i	0.579912	−	0.814679i	$-0.303087\pi$
$828$		0			0
$829$	915553.			1.33222			0.666108	−	0.745856i	$-0.267959\pi$
$829$	915553.			1.33222			0.666108	+	0.745856i	$0.267959\pi$
$830$	710287.	+	372055.i	1.03105	+	0.540071i
$831$		0			0
$832$	−489823.	−	505029.i	−0.707608	−	0.729574i
$833$	58792.8	+	101832.i	0.0847294	+	0.146756i
$834$		0			0
$835$	717733.	+	414383.i	1.02941	+	0.594332i
$836$	−608621.	+	50124.6i	−0.870832	+	0.0717197i
$837$		0			0
$838$	−52680.6	−	1.28148e6i	−0.0750175	−	1.82483i
$839$	489653.	+	282701.i	0.695608	+	0.401610i	0.805710	−	0.592311i	$-0.201784\pi$
$839$	489653.	+	282701.i	0.695608	+	0.401610i	−0.110101	+	0.993920i	$0.535118\pi$
$840$		0			0
$841$	353478.	+	612242.i	0.499770	+	0.865627i
$842$	290632.	+	458776.i	0.409939	+	0.647107i
$843$		0			0
$844$	−880044.	−	415842.i	−1.23543	−	0.583772i
$845$	−28047.6			−0.0392810
$846$		0			0
$847$		−	2.16856e6i		−	3.02276i
$848$	183094.	−	487534.i	0.254615	−	0.677975i
$849$		0			0
$850$	55397.5	+	87447.5i	0.0766748	+	0.121035i
$851$	−189500.	+	109408.i	−0.261668	+	0.151074i
$852$		0			0
$853$	−100990.	+	174919.i	−0.138796	+	0.240402i	−0.927041	−	0.374959i	$-0.877657\pi$
$853$	−100990.	+	174919.i	−0.138796	+	0.240402i	0.788245	+	0.615362i	$0.210990\pi$
$854$	13948.6	+	339307.i	0.0191256	+	0.465240i
$855$		0			0
$856$	−24119.3	−	194689.i	−0.0329167	−	0.265701i
$857$	−252164.	+	436762.i	−0.343338	+	0.594679i	−0.985050	−	0.172266i	$-0.944891\pi$
$857$	−252164.	+	436762.i	−0.343338	+	0.594679i	0.641712	+	0.766946i	$0.278224\pi$
$858$		0			0
$859$	662245.	−	382348.i	0.897496	−	0.518170i	0.0211092	−	0.999777i	$-0.493280\pi$
$859$	662245.	−	382348.i	0.897496	−	0.518170i	0.876387	+	0.481608i	$0.159947\pi$
$860$	120040.	−	83144.9i	0.162304	−	0.112419i
$861$		0			0
$862$	111059.	+	58173.5i	0.149464	+	0.0782907i
$863$		−	1.21817e6i		−	1.63564i	−0.575477	−	0.817818i	$-0.695183\pi$
$863$		−	1.21817e6i		−	1.63564i	0.575477	−	0.817818i	$-0.304817\pi$
$864$		0			0
$865$	−656551.			−0.877477
$866$	187499.	−	357953.i	0.250013	−	0.477299i
$867$		0			0
$868$	423375.	+	611246.i	0.561934	+	0.811290i
$869$	−212982.	−	368895.i	−0.282035	−	0.488498i
$870$		0			0
$871$	−891792.	−	514876.i	−1.17551	−	0.678682i
$872$	1.12603e6	−	139500.i	1.48088	−	0.183460i
$873$		0			0
$874$	−242764.	+	9979.83i	−0.317805	+	0.0130647i
$875$	−561773.	−	324340.i	−0.733744	−	0.423627i
$876$		0			0
$877$	−225455.	−	390499.i	−0.293130	−	0.507716i	0.681418	−	0.731894i	$-0.261364\pi$
$877$	−225455.	−	390499.i	−0.293130	−	0.507716i	−0.974548	+	0.224178i	$0.928030\pi$
$878$	614890.	−	389530.i	0.797642	−	0.505303i
$879$		0			0
$880$	1.60873e6	+	604161.i	2.07739	+	0.780166i
$881$	1.04312e6			1.34395			0.671974	−	0.740575i	$-0.265447\pi$
$881$	1.04312e6			1.34395			0.671974	+	0.740575i	$0.265447\pi$
$882$		0			0
$883$		−	303710.i		−	0.389527i	−0.980850	−	0.194763i	$-0.937606\pi$
$883$		−	303710.i		−	0.389527i	0.980850	−	0.194763i	$-0.0623939\pi$
$884$	−116324.	+	246175.i	−0.148855	+	0.315021i
$885$		0			0
$886$	−125662.	+	79606.3i	−0.160080	+	0.101410i
$887$	−587624.	+	339265.i	−0.746882	+	0.431213i	−0.824566	−	0.565765i	$-0.808581\pi$
$887$	−587624.	+	339265.i	−0.746882	+	0.431213i	0.0776839	+	0.996978i	$0.475248\pi$
$888$		0			0
$889$	553426.	−	958562.i	0.700255	−	1.21288i
$890$	−1.12275e6	+	46155.3i	−1.41743	+	0.0582696i
$891$		0			0
$892$	−14090.9	−	171094.i	−0.0177097	−	0.215034i
$893$	221896.	−	384336.i	0.278258	−	0.481956i
$894$		0			0
$895$	1.35385e6	−	781647.i	1.69015	−	0.975808i
$896$	−675807.	+	711615.i	−0.841795	+	0.886398i
$897$		0			0
$898$	37835.0	−	72230.6i	0.0469182	−	0.0895712i
$899$			13990.5i			0.0173107i
$900$		0			0
$901$	−201543.			−0.248267
$902$	330050.	+	172883.i	0.405664	+	0.212490i
$903$		0			0
$904$	570594.	+	755497.i	0.698217	+	0.924477i
$905$	−107516.	−	186223.i	−0.131273	−	0.227372i
$906$		0			0
$907$	−1.02766e6	−	593322.i	−1.24921	−	0.721233i	−0.278260	−	0.960506i	$-0.589758\pi$
$907$	−1.02766e6	−	593322.i	−1.24921	−	0.721233i	−0.970952	+	0.239273i	$0.923091\pi$
$908$	99456.1	+	1.20761e6i	0.120631	+	1.46472i
$909$		0			0
$910$	50321.7	+	1.22410e6i	0.0607676	+	1.47820i
$911$	−754071.	−	435363.i	−0.908606	−	0.524584i	−0.0286234	−	0.999590i	$-0.509112\pi$
$911$	−754071.	−	435363.i	−0.908606	−	0.524584i	−0.879982	+	0.475007i	$0.842446\pi$
$912$		0			0
$913$	−759181.	−	1.31494e6i	−0.910760	−	1.57748i
$914$	−598635.	−	944971.i	−0.716588	−	1.13117i
$915$		0			0
$916$	364797.	−	772016.i	0.434770	−	0.920101i
$917$	498400.			0.592706
$918$		0			0
$919$			60879.9i			0.0720847i	0.999350	+	0.0360423i	$0.0114751\pi$
$919$			60879.9i			0.0720847i	−0.999350	+	0.0360423i	$0.988525\pi$
$920$	629643.	+	266462.i	0.743907	+	0.314818i
$921$		0			0
$922$	343773.	+	542662.i	0.404399	+	0.638362i
$923$	−184370.	+	106446.i	−0.216415	+	0.124947i
$924$		0			0
$925$	−79640.2	+	137941.i	−0.0930783	+	0.161216i
$926$	16290.7	+	396280.i	0.0189985	+	0.462147i
$927$		0			0
$928$	−18077.2	+	3766.75i	−0.0209911	+	0.00437392i
$929$	−470405.	+	814765.i	−0.545055	+	0.944063i	0.453548	+	0.891232i	$0.350158\pi$
$929$	−470405.	+	814765.i	−0.545055	+	0.944063i	−0.998603	+	0.0528314i	$0.983175\pi$
$930$		0			0
$931$	−173982.	+	100448.i	−0.200726	+	0.115889i
$932$	514602.	+	742955.i	0.592434	+	0.855324i
$933$		0			0
$934$	−987846.	−	517442.i	−1.13239	−	0.593155i
$935$		−	665037.i		−	0.760717i
$936$		0			0
$937$	−634530.			−0.722725			−0.361362	−	0.932425i	$-0.617688\pi$
$937$	−634530.			−0.722725			−0.361362	+	0.932425i	$0.617688\pi$
$938$	−666501.	+	1.27241e6i	−0.757521	+	1.44618i
$939$		0			0
$940$	−1.02660e6	+	711070.i	−1.16184	+	0.804742i
$941$	34049.0	+	58974.5i	0.0384525	+	0.0666017i	0.884611	−	0.466329i	$-0.154424\pi$
$941$	34049.0	+	58974.5i	0.0384525	+	0.0666017i	−0.846159	+	0.532931i	$0.821091\pi$
$942$		0			0
$943$	128379.	+	74119.7i	0.144368	+	0.0833509i
$944$	108839.	+	656287.i	0.122135	+	0.736461i
$945$		0			0
$946$	−276279.	+	11357.6i	−0.308720	+	0.0126912i
$947$	−461349.	−	266360.i	−0.514434	−	0.297009i	0.220220	−	0.975450i	$-0.429322\pi$
$947$	−461349.	−	266360.i	−0.514434	−	0.297009i	−0.734654	+	0.678442i	$0.762656\pi$
$948$		0			0
$949$	434616.	+	752777.i	0.482585	+	0.835861i
$950$	−149405.	+	94647.6i	−0.165546	+	0.104873i
$951$		0			0
$952$	349766.	+	148019.i	0.385925	+	0.163321i
$953$	−72542.5			−0.0798742			−0.0399371	−	0.999202i	$-0.512716\pi$
$953$	−72542.5			−0.0798742			−0.0399371	+	0.999202i	$0.512716\pi$
$954$		0			0
$955$			315042.i			0.345432i
$956$	694258.	+	328054.i	0.759635	+	0.358946i
$957$		0			0
$958$	108100.	−	68481.1i	0.117787	−	0.0746173i
$959$	1.11045e6	−	641118.i	1.20743	−	0.697109i
$960$		0			0
$961$	−160796.	+	278507.i	−0.174112	+	0.301571i
$962$	−418589.	+	17207.9i	−0.452311	+	0.0185942i
$963$		0			0
$964$	−1.02294e6	+	84246.8i	−1.10077	+	0.0906566i
$965$	−581791.	+	1.00769e6i	−0.624759	+	1.08211i
$966$		0			0
$967$	−705768.	+	407475.i	−0.754760	+	0.435761i	−0.827411	−	0.561596i	$-0.810187\pi$
$967$	−705768.	+	407475.i	−0.754760	+	0.435761i	0.0726511	+	0.997357i	$0.476854\pi$
$968$	−1.39643e6	−	1.84895e6i	−1.49029	−	1.97322i
$969$		0			0
$970$	806460.	−	1.53961e6i	0.857115	−	1.63631i
$971$			939538.i			0.996496i	0.867034	+	0.498248i	$0.166023\pi$
$971$			939538.i			0.996496i	−0.867034	+	0.498248i	$0.833977\pi$
$972$		0			0
$973$	1.09168e6			1.15310
$974$	−1.22891e6	−	643713.i	−1.29539	−	0.678538i
$975$		0			0
$976$	230388.	+	280317.i	0.241858	+	0.294273i
$977$	870579.	+	1.50789e6i	0.912051	+	1.57972i	0.811162	+	0.584821i	$0.198835\pi$
$977$	870579.	+	1.50789e6i	0.912051	+	1.57972i	0.100889	+	0.994898i	$0.467831\pi$
$978$		0			0
$979$	1.84277e6	+	1.06393e6i	1.92268	+	1.11006i
$980$	563408.	−	46401.0i	0.586639	−	0.0483142i
$981$		0			0
$982$	39428.5	+	959116.i	0.0408872	+	0.994599i
$983$	−1.07730e6	−	621978.i	−1.11488	−	0.643677i	−0.174792	−	0.984605i	$-0.555925\pi$
$983$	−1.07730e6	−	621978.i	−1.11488	−	0.643677i	−0.940089	+	0.340929i	$0.889259\pi$
$984$		0			0
$985$	161053.	+	278952.i	0.165995	+	0.287513i
$986$	3824.28	+	6036.79i	0.00393365	+	0.00620944i
$987$		0			0
$988$	−420595.	−	198741.i	−0.430873	−	0.203598i
$989$	−110014.			−0.112475
$990$		0			0
$991$		−	766088.i		−	0.780066i	−0.920801	−	0.390033i	$-0.872464\pi$
$991$		−	766088.i		−	0.780066i	0.920801	−	0.390033i	$-0.127536\pi$
$992$	754587.	+	248529.i	0.766807	+	0.252554i
$993$		0			0
$994$	158920.	+	250863.i	0.160845	+	0.253900i
$995$	−20815.3	+	12017.7i	−0.0210251	+	0.0121388i
$996$		0			0
$997$	−192679.	+	333731.i	−0.193841	+	0.335742i	−0.946520	−	0.322645i	$-0.895428\pi$
$997$	−192679.	+	333731.i	−0.193841	+	0.335742i	0.752679	+	0.658388i	$0.228761\pi$
$998$	−56033.2	−	1.36303e6i	−0.0562580	−	1.36850i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.19.14		44
3.2	odd	2		36.5.f.a.7.9	yes	44
4.3	odd	2	inner	108.5.f.a.19.15		44
9.2	odd	6		324.5.d.f.163.21		22
9.4	even	3	inner	108.5.f.a.91.15		44
9.5	odd	6		36.5.f.a.31.8	yes	44
9.7	even	3		324.5.d.e.163.2		22
12.11	even	2		36.5.f.a.7.8	✓	44
36.7	odd	6		324.5.d.e.163.1		22
36.11	even	6		324.5.d.f.163.22		22
36.23	even	6		36.5.f.a.31.9	yes	44
36.31	odd	6	inner	108.5.f.a.91.14		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.8	✓	44	12.11	even	2
36.5.f.a.7.9	yes	44	3.2	odd	2
36.5.f.a.31.8	yes	44	9.5	odd	6
36.5.f.a.31.9	yes	44	36.23	even	6
108.5.f.a.19.14		44	1.1	even	1	trivial
108.5.f.a.19.15		44	4.3	odd	2	inner
108.5.f.a.91.14		44	36.31	odd	6	inner
108.5.f.a.91.15		44	9.4	even	3	inner
324.5.d.e.163.1		22	36.7	odd	6
324.5.d.e.163.2		22	9.7	even	3
324.5.d.f.163.21		22	9.2	odd	6
324.5.d.f.163.22		22	36.11	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.85603 - 3.54333i) q^{2} +(-9.11034 - 13.1530i) q^{4} +(14.8847 + 25.7811i) q^{5} +(-51.8739 - 29.9494i) q^{7} +(-63.5145 + 7.86857i) q^{8} +O(q^{10})\)	\(q+(1.85603 - 3.54333i) q^{2} +(-9.11034 - 13.1530i) q^{4} +(14.8847 + 25.7811i) q^{5} +(-51.8739 - 29.9494i) q^{7} +(-63.5145 + 7.86857i) q^{8} +(118.977 - 4.89106i) q^{10} +(-195.278 - 112.744i) q^{11} +(-85.8824 - 148.753i) q^{13} +(-202.400 + 128.219i) q^{14} +(-90.0035 + 239.657i) q^{16} +99.0725 q^{17} +169.267i q^{19} +(203.494 - 430.653i) q^{20} +(-761.929 + 482.678i) q^{22} +(-310.777 + 179.427i) q^{23} +(-130.609 + 226.221i) q^{25} +(-686.480 + 28.2206i) q^{26} +(78.6636 + 955.147i) q^{28} +(-9.01635 + 15.6168i) q^{29} +(671.898 - 387.920i) q^{31} +(682.133 + 763.721i) q^{32} +(183.881 - 351.046i) q^{34} -1783.15i q^{35} +609.762 q^{37} +(599.768 + 314.164i) q^{38} +(-1148.25 - 1520.35i) q^{40} +(-206.545 - 357.747i) q^{41} +(265.498 + 153.286i) q^{43} +(296.127 + 3595.63i) q^{44} +(58.9591 + 1434.21i) q^{46} +(-2270.59 - 1310.93i) q^{47} +(593.432 + 1027.85i) q^{49} +(559.161 + 882.661i) q^{50} +(-1174.13 + 2484.80i) q^{52} -2034.30 q^{53} -6712.63i q^{55} +(3530.40 + 1494.05i) q^{56} +(38.6008 + 60.9330i) q^{58} +(2250.48 - 1299.32i) q^{59} +(708.681 - 1227.47i) q^{61} +(-127.469 - 3100.74i) q^{62} +(3972.17 - 999.536i) q^{64} +(2556.67 - 4428.28i) q^{65} +(5191.93 - 2997.56i) q^{67} +(-902.584 - 1303.10i) q^{68} +(-6318.29 - 3309.57i) q^{70} -1239.44i q^{71} -5060.60 q^{73} +(1131.73 - 2160.59i) q^{74} +(2226.37 - 1542.08i) q^{76} +(6753.22 + 11696.9i) q^{77} +(1635.99 + 944.538i) q^{79} +(-7518.28 + 1246.83i) q^{80} +(-1650.97 + 67.8700i) q^{82} +(5831.54 + 3366.84i) q^{83} +(1474.66 + 2554.19i) q^{85} +(1035.91 - 656.246i) q^{86} +(13290.1 + 5624.30i) q^{88} -9436.67 q^{89} +10288.5i q^{91} +(5191.29 + 2453.01i) q^{92} +(-8859.31 + 5612.33i) q^{94} +(-4363.88 + 2519.49i) q^{95} +(7297.91 - 12640.4i) q^{97} +(4743.45 - 195.000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

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