LMFDB - Embedded newform 108.5.f.a.19.12

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			19.12
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.485844 + 3.97038i) q^{2} +(-15.5279 + 3.85798i) q^{4} +(-1.01545 - 1.75881i) q^{5} +(-20.0352 - 11.5673i) q^{7} +(-22.8618 - 59.7774i) q^{8} +O(q^{10})$	\(q+(0.485844 + 3.97038i) q^{2} +(-15.5279 + 3.85798i) q^{4} +(-1.01545 - 1.75881i) q^{5} +(-20.0352 - 11.5673i) q^{7} +(-22.8618 - 59.7774i) q^{8} +(6.48981 - 4.88624i) q^{10} +(4.32958 + 2.49968i) q^{11} +(-137.824 - 238.718i) q^{13} +(36.1928 - 85.1675i) q^{14} +(226.232 - 119.813i) q^{16} +266.009 q^{17} -367.194i q^{19} +(22.5533 + 23.3931i) q^{20} +(-7.82120 + 18.4045i) q^{22} +(-544.473 + 314.352i) q^{23} +(310.438 - 537.694i) q^{25} +(880.842 - 663.194i) q^{26} +(355.732 + 102.321i) q^{28} +(319.481 - 553.357i) q^{29} +(-1191.19 + 687.735i) q^{31} +(585.616 + 840.018i) q^{32} +(129.239 + 1056.16i) q^{34} +46.9843i q^{35} +1466.19 q^{37} +(1457.90 - 178.399i) q^{38} +(-81.9222 + 100.911i) q^{40} +(-593.019 - 1027.14i) q^{41} +(-1430.33 - 825.804i) q^{43} +(-76.8730 - 22.1114i) q^{44} +(-1512.63 - 2009.04i) q^{46} +(307.864 + 177.745i) q^{47} +(-932.893 - 1615.82i) q^{49} +(2285.68 + 971.322i) q^{50} +(3061.09 + 3175.07i) q^{52} -5297.49 q^{53} -10.1532i q^{55} +(-233.424 + 1462.10i) q^{56} +(2352.26 + 999.617i) q^{58} +(-5223.32 + 3015.68i) q^{59} +(-833.364 + 1443.43i) q^{61} +(-3309.31 - 4395.36i) q^{62} +(-3050.68 + 2733.24i) q^{64} +(-279.907 + 484.814i) q^{65} +(1908.36 - 1101.79i) q^{67} +(-4130.57 + 1026.26i) q^{68} +(-186.546 + 22.8270i) q^{70} -524.299i q^{71} -1492.29 q^{73} +(712.338 + 5821.33i) q^{74} +(1416.63 + 5701.76i) q^{76} +(-57.8293 - 100.163i) q^{77} +(-4448.35 - 2568.25i) q^{79} +(-440.456 - 276.236i) q^{80} +(3790.02 - 2853.54i) q^{82} +(6918.39 + 3994.33i) q^{83} +(-270.120 - 467.861i) q^{85} +(2583.84 - 6080.19i) q^{86} +(50.4426 - 315.958i) q^{88} +8860.17 q^{89} +6377.03i q^{91} +(7241.77 - 6981.79i) q^{92} +(-556.144 + 1308.70i) q^{94} +(-645.826 + 372.868i) q^{95} +(-3409.33 + 5905.14i) q^{97} +(5962.18 - 4488.98i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.485844	+	3.97038i	0.121461	+	0.992596i
$2$	0.485844	+	3.97038i	0.121461	+	0.992596i
$3$		0			0
$3$		0			0
$4$	−15.5279	+	3.85798i	−0.970494	+	0.241124i
$5$	−1.01545	−	1.75881i	−0.0406181	−	0.0703525i	0.845002	−	0.534764i	$-0.179599\pi$
$5$	−1.01545	−	1.75881i	−0.0406181	−	0.0703525i	−0.885620	+	0.464411i	$0.846266\pi$
$6$		0			0
$7$	−20.0352	−	11.5673i	−0.408882	−	0.236068i	0.281427	−	0.959583i	$-0.409192\pi$
$7$	−20.0352	−	11.5673i	−0.408882	−	0.236068i	−0.690309	+	0.723514i	$0.742526\pi$
$8$	−22.8618	−	59.7774i	−0.357216	−	0.934022i
$9$		0			0
$10$	6.48981	−	4.88624i	0.0648981	−	0.0488624i
$11$	4.32958	+	2.49968i	0.0357816	+	0.0206585i	0.517784	−	0.855511i	$-0.326757\pi$
$11$	4.32958	+	2.49968i	0.0357816	+	0.0206585i	−0.482002	+	0.876170i	$0.660090\pi$
$12$		0			0
$13$	−137.824	−	238.718i	−0.815527	−	1.41253i	−0.908949	−	0.416908i	$-0.863114\pi$
$13$	−137.824	−	238.718i	−0.815527	−	1.41253i	0.0934218	−	0.995627i	$-0.470219\pi$
$14$	36.1928	−	85.1675i	0.184657	−	0.434528i
$15$		0			0
$16$	226.232	−	119.813i	0.883719	−	0.468018i
$17$	266.009			0.920447			0.460224	−	0.887803i	$-0.347769\pi$
$17$	266.009			0.920447			0.460224	+	0.887803i	$0.347769\pi$
$18$		0			0
$19$		−	367.194i		−	1.01716i	−0.861015	−	0.508579i	$-0.830171\pi$
$19$		−	367.194i		−	1.01716i	0.861015	−	0.508579i	$-0.169829\pi$
$20$	22.5533	+	23.3931i	0.0563832	+	0.0584828i
$21$		0			0
$22$	−7.82120	+	18.4045i	−0.0161595	+	0.0380259i
$23$	−544.473	+	314.352i	−1.02925	+	0.594238i	−0.916770	−	0.399416i	$-0.869213\pi$
$23$	−544.473	+	314.352i	−1.02925	+	0.594238i	−0.112481	+	0.993654i	$0.535880\pi$
$24$		0			0
$25$	310.438	−	537.694i	0.496700	−	0.860310i
$26$	880.842	−	663.194i	1.30302	−	0.981057i
$27$		0			0
$28$	355.732	+	102.321i	0.453739	+	0.130512i
$29$	319.481	−	553.357i	0.379882	−	0.657975i	−0.611163	−	0.791505i	$-0.709298\pi$
$29$	319.481	−	553.357i	0.379882	−	0.657975i	0.991045	+	0.133530i	$0.0426312\pi$
$30$		0			0
$31$	−1191.19	+	687.735i	−1.23953	+	0.715645i	−0.968999	−	0.247065i	$-0.920534\pi$
$31$	−1191.19	+	687.735i	−1.23953	+	0.715645i	−0.270535	+	0.962710i	$0.587201\pi$
$32$	585.616	+	840.018i	0.571891	+	0.820330i
$33$		0			0
$34$	129.239	+	1056.16i	0.111799	+	0.913633i
$35$			46.9843i			0.0383545i
$36$		0			0
$37$	1466.19			1.07099			0.535496	−	0.844538i	$-0.320125\pi$
$37$	1466.19			1.07099			0.535496	+	0.844538i	$0.320125\pi$
$38$	1457.90	−	178.399i	1.00963	−	0.123545i
$39$		0			0
$40$	−81.9222	+	100.911i	−0.0512014	+	0.0630692i
$41$	−593.019	−	1027.14i	−0.352777	−	0.611028i	0.633958	−	0.773368i	$-0.281429\pi$
$41$	−593.019	−	1027.14i	−0.352777	−	0.611028i	−0.986735	+	0.162339i	$0.948096\pi$
$42$		0			0
$43$	−1430.33	−	825.804i	−0.773572	−	0.446622i	0.0605755	−	0.998164i	$-0.480706\pi$
$43$	−1430.33	−	825.804i	−0.773572	−	0.446622i	−0.834147	+	0.551542i	$0.814040\pi$
$44$	−76.8730	−	22.1114i	−0.0397071	−	0.0114212i
$45$		0			0
$46$	−1512.63	−	2009.04i	−0.714852	−	0.949453i
$47$	307.864	+	177.745i	0.139368	+	0.0804642i	0.568063	−	0.822985i	$-0.307693\pi$
$47$	307.864	+	177.745i	0.139368	+	0.0804642i	−0.428695	+	0.903449i	$0.641026\pi$
$48$		0			0
$49$	−932.893	−	1615.82i	−0.388544	−	0.672977i
$50$	2285.68	+	971.322i	0.914270	+	0.388529i
$51$		0			0
$52$	3061.09	+	3175.07i	1.13206	+	1.17421i
$53$	−5297.49			−1.88590			−0.942950	−	0.332934i	$-0.891961\pi$
$53$	−5297.49			−1.88590			−0.942950	+	0.332934i	$0.891961\pi$
$54$		0			0
$55$		−	10.1532i		−	0.00335644i
$56$	−233.424	+	1462.10i	−0.0744338	+	0.466232i
$57$		0			0
$58$	2352.26	+	999.617i	0.699245	+	0.297151i
$59$	−5223.32	+	3015.68i	−1.50052	+	0.866327i	−0.500522	+	0.865724i	$0.666859\pi$
$59$	−5223.32	+	3015.68i	−1.50052	+	0.866327i	−1.00000		0.000603027i	$0.999808\pi$
$60$		0			0
$61$	−833.364	+	1443.43i	−0.223962	+	0.387914i	−0.956008	−	0.293342i	$-0.905233\pi$
$61$	−833.364	+	1443.43i	−0.223962	+	0.387914i	0.732045	+	0.681256i	$0.238566\pi$
$62$	−3309.31	−	4395.36i	−0.860902	−	1.14343i
$63$		0			0
$64$	−3050.68	+	2733.24i	−0.744794	+	0.667295i
$65$	−279.907	+	484.814i	−0.0662502	+	0.114749i
$66$		0			0
$67$	1908.36	−	1101.79i	0.425119	−	0.245443i	−0.272146	−	0.962256i	$-0.587733\pi$
$67$	1908.36	−	1101.79i	0.425119	−	0.245443i	0.697265	+	0.716813i	$0.254400\pi$
$68$	−4130.57	+	1026.26i	−0.893289	+	0.221942i
$69$		0			0
$70$	−186.546	+	22.8270i	−0.0380705	+	0.00465858i
$71$		−	524.299i		−	0.104007i	−0.998647	−	0.0520035i	$-0.983439\pi$
$71$		−	524.299i		−	0.104007i	0.998647	−	0.0520035i	$-0.0165607\pi$
$72$		0			0
$73$	−1492.29			−0.280032			−0.140016	−	0.990149i	$-0.544715\pi$
$73$	−1492.29			−0.280032			−0.140016	+	0.990149i	$0.544715\pi$
$74$	712.338	+	5821.33i	0.130084	+	1.06306i
$75$		0			0
$76$	1416.63	+	5701.76i	0.245261	+	0.987146i
$77$	−57.8293	−	100.163i	−0.00975364	−	0.0168938i
$78$		0			0
$79$	−4448.35	−	2568.25i	−0.712762	−	0.411513i	0.0993209	−	0.995055i	$-0.468333\pi$
$79$	−4448.35	−	2568.25i	−0.712762	−	0.411513i	−0.812083	+	0.583542i	$0.801666\pi$
$80$	−440.456	−	276.236i	−0.0688212	−	0.0431619i
$81$		0			0
$82$	3790.02	−	2853.54i	0.563656	−	0.424382i
$83$	6918.39	+	3994.33i	1.00427	+	0.579813i	0.909508	−	0.415687i	$-0.136459\pi$
$83$	6918.39	+	3994.33i	1.00427	+	0.579813i	0.0947580	+	0.995500i	$0.469792\pi$
$84$		0			0
$85$	−270.120	−	467.861i	−0.0373868	−	0.0647558i
$86$	2583.84	−	6080.19i	0.349356	−	0.822092i
$87$		0			0
$88$	50.4426	−	315.958i	0.00651376	−	0.0408004i
$89$	8860.17			1.11857			0.559283	−	0.828977i	$-0.311076\pi$
$89$	8860.17			1.11857			0.559283	+	0.828977i	$0.311076\pi$
$90$		0			0
$91$			6377.03i			0.770080i
$92$	7241.77	−	6981.79i	0.855597	−	0.824881i
$93$		0			0
$94$	−556.144	+	1308.70i	−0.0629407	+	0.148110i
$95$	−645.826	+	372.868i	−0.0715596	+	0.0413150i
$96$		0			0
$97$	−3409.33	+	5905.14i	−0.362348	+	0.627606i	−0.988347	−	0.152219i	$-0.951358\pi$
$97$	−3409.33	+	5905.14i	−0.362348	+	0.627606i	0.625999	+	0.779824i	$0.284692\pi$
$98$	5962.18	−	4488.98i	0.620802	−	0.467408i
$99$		0			0
$100$	−2746.04	+	9546.92i	−0.274604	+	0.954692i
$101$	1545.53	−	2676.93i	0.151507	−	0.262418i	−0.780274	−	0.625437i	$-0.784921\pi$
$101$	1545.53	−	2676.93i	0.151507	−	0.262418i	0.931782	+	0.363019i	$0.118254\pi$
$102$		0			0
$103$	9409.35	−	5432.49i	0.886922	−	0.512065i	0.0139875	−	0.999902i	$-0.495547\pi$
$103$	9409.35	−	5432.49i	0.886922	−	0.512065i	0.872934	+	0.487838i	$0.162214\pi$
$104$	−11119.1	+	13696.3i	−1.02802	+	1.26630i
$105$		0			0
$106$	−2573.76	−	21033.1i	−0.229063	−	1.87194i
$107$		−	14106.5i		−	1.23212i	−0.787699	−	0.616060i	$-0.788728\pi$
$107$		−	14106.5i		−	1.23212i	0.787699	−	0.616060i	$-0.211272\pi$
$108$		0			0
$109$	16328.3			1.37432			0.687160	−	0.726506i	$-0.258857\pi$
$109$	16328.3			1.37432			0.687160	+	0.726506i	$0.258857\pi$
$110$	40.3122	−	4.93288i	0.00333159	−	0.000407676i
$111$		0			0
$112$	−5918.52	−	216.430i	−0.471821	−	0.0172536i
$113$	5911.44	+	10238.9i	0.462952	+	0.801857i	0.999107	−	0.0422631i	$-0.0134568\pi$
$113$	5911.44	+	10238.9i	0.462952	+	0.801857i	−0.536154	+	0.844120i	$0.680123\pi$
$114$		0			0
$115$	1105.77	+	638.418i	0.0836123	+	0.0482736i
$116$	−2826.03	+	9825.03i	−0.210020	+	0.730160i
$117$		0			0
$118$	−14511.1	−	19273.4i	−1.04217	−	1.38419i
$119$	−5329.56	−	3077.02i	−0.376354	−	0.217288i
$120$		0			0
$121$	−7308.00	−	12657.8i	−0.499146	−	0.864547i
$122$	−6135.85	−	2607.49i	−0.412245	−	0.175188i
$123$		0			0
$124$	15843.5	−	15274.7i	1.03040	−	0.993411i
$125$	−2530.25			−0.161936
$126$		0			0
$127$			20979.9i			1.30076i	0.759609	+	0.650379i	$0.225390\pi$
$127$			20979.9i			1.30076i	−0.759609	+	0.650379i	$0.774610\pi$
$128$	−12334.2	−	10784.4i	−0.752817	−	0.658229i
$129$		0			0
$130$	−2060.89	−	875.796i	−0.121946	−	0.0518222i
$131$	24723.9	−	14274.3i	1.44070	−	0.831789i	0.442804	−	0.896618i	$-0.353984\pi$
$131$	24723.9	−	14274.3i	1.44070	−	0.831789i	0.997896	+	0.0648298i	$0.0206504\pi$
$132$		0			0
$133$	−4247.46	+	7356.81i	−0.240119	+	0.415898i
$134$	5301.70	+	7041.62i	0.295261	+	0.392160i
$135$		0			0
$136$	−6081.45	−	15901.3i	−0.328798	−	0.859718i
$137$	−309.436	+	535.959i	−0.0164866	+	0.0285556i	−0.874151	−	0.485654i	$-0.838581\pi$
$137$	−309.436	+	535.959i	−0.0164866	+	0.0285556i	0.857664	+	0.514210i	$0.171915\pi$
$138$		0			0
$139$	16819.9	−	9710.99i	0.870552	−	0.502613i	0.00302027	−	0.999995i	$-0.499039\pi$
$139$	16819.9	−	9710.99i	0.870552	−	0.502613i	0.867532	+	0.497382i	$0.165705\pi$
$140$	−181.264	−	729.568i	−0.00924818	−	0.0372228i
$141$		0			0
$142$	2081.67	−	254.728i	0.103237	−	0.0126328i
$143$		−	1378.07i		−	0.0673903i
$144$		0			0
$145$	−1297.67			−0.0617203
$146$	−725.022	−	5924.98i	−0.0340130	−	0.277959i
$147$		0			0
$148$	−22766.8	+	5656.52i	−1.03939	+	0.258241i
$149$	309.641	+	536.313i	0.0139471	+	0.0241572i	0.872915	−	0.487873i	$-0.162227\pi$
$149$	309.641	+	536.313i	0.0139471	+	0.0241572i	−0.858968	+	0.512030i	$0.828894\pi$
$150$		0			0
$151$	3758.08	+	2169.73i	0.164821	+	0.0951593i	0.580141	−	0.814516i	$-0.302997\pi$
$151$	3758.08	+	2169.73i	0.164821	+	0.0951593i	−0.415321	+	0.909675i	$0.636331\pi$
$152$	−21949.9	+	8394.72i	−0.950048	+	0.363345i
$153$		0			0
$154$	369.591	−	278.268i	0.0155840	−	0.0117334i
$155$	2419.20	+	1396.72i	0.100695	+	0.0581362i
$156$		0			0
$157$	3103.88	+	5376.08i	0.125923	+	0.218105i	0.922093	−	0.386967i	$-0.126477\pi$
$157$	3103.88	+	5376.08i	0.125923	+	0.218105i	−0.796170	+	0.605073i	$0.793144\pi$
$158$	8035.75	−	18909.4i	0.321894	−	0.757468i
$159$		0			0
$160$	882.770	−	1882.99i	0.0344832	−	0.0735541i
$161$	14544.9			0.561123
$162$		0			0
$163$		−	15857.0i		−	0.596824i	−0.954437	−	0.298412i	$-0.903543\pi$
$163$		−	15857.0i		−	0.596824i	0.954437	−	0.298412i	$-0.0964569\pi$
$164$	13171.0	+	13661.5i	0.489702	+	0.507937i
$165$		0			0
$166$	−12497.8	+	29409.3i	−0.453541	+	1.06725i
$167$	−362.861	+	209.498i	−0.0130109	+	0.00751186i	−0.506491	−	0.862245i	$-0.669058\pi$
$167$	−362.861	+	209.498i	−0.0130109	+	0.00751186i	0.493480	+	0.869757i	$0.335724\pi$
$168$		0			0
$169$	−23710.4	+	41067.7i	−0.830169	+	1.43789i
$170$	1726.35	−	1299.79i	0.0597353	−	0.0449753i
$171$		0			0
$172$	25396.0	+	7304.81i	0.858438	+	0.246918i
$173$	−9600.40	+	16628.4i	−0.320772	+	0.555594i	−0.980648	−	0.195781i	$-0.937276\pi$
$173$	−9600.40	+	16628.4i	−0.320772	+	0.555594i	0.659875	+	0.751375i	$0.270609\pi$
$174$		0			0
$175$	−12439.4	+	7181.88i	−0.406184	+	0.234510i
$176$	1278.98	+	46.7701i	0.0412895	+	0.00150988i
$177$		0			0
$178$	4304.66	+	35178.3i	0.135862	+	1.11028i
$179$			49821.7i			1.55494i	0.628922	+	0.777468i	$0.283496\pi$
$179$			49821.7i			1.55494i	−0.628922	+	0.777468i	$0.716504\pi$
$180$		0			0
$181$	13970.7			0.426443			0.213222	−	0.977004i	$-0.431604\pi$
$181$	13970.7			0.426443			0.213222	+	0.977004i	$0.431604\pi$
$182$	−25319.3	+	3098.24i	−0.764378	+	0.0935347i
$183$		0			0
$184$	31238.8	+	25360.6i	0.922696	+	0.749071i
$185$	−1488.84	−	2578.75i	−0.0435016	−	0.0753469i
$186$		0			0
$187$	1151.71	+	664.939i	0.0329351	+	0.0190151i
$188$	−5466.22	−	1572.28i	−0.154658	−	0.0444851i
$189$		0			0
$190$	−1794.20	−	2383.02i	−0.0497008	−	0.0660117i
$191$	−26994.8	−	15585.5i	−0.739969	−	0.427221i	0.0820893	−	0.996625i	$-0.473841\pi$
$191$	−26994.8	−	15585.5i	−0.739969	−	0.427221i	−0.822058	+	0.569404i	$0.807174\pi$
$192$		0			0
$193$	−13498.2	−	23379.5i	−0.362377	−	0.627655i	0.625975	−	0.779843i	$-0.284701\pi$
$193$	−13498.2	−	23379.5i	−0.362377	−	0.627655i	−0.988351	+	0.152189i	$0.951368\pi$
$194$	−25102.1	−	10667.4i	−0.666970	−	0.283436i
$195$		0			0
$196$	20719.7	+	21491.2i	0.539350	+	0.559434i
$197$	−10416.4			−0.268402			−0.134201	−	0.990954i	$-0.542847\pi$
$197$	−10416.4			−0.268402			−0.134201	+	0.990954i	$0.542847\pi$
$198$		0			0
$199$			8438.68i			0.213093i	0.994308	+	0.106546i	$0.0339793\pi$
$199$			8438.68i			0.213093i	−0.994308	+	0.106546i	$0.966021\pi$
$200$	−39239.1	−	6264.51i	−0.980978	−	0.156613i
$201$		0			0
$202$	11379.3	+	4835.76i	0.278878	+	0.118512i
$203$	−12801.7	+	7391.09i	−0.310654	+	0.179356i
$204$		0			0
$205$	−1204.36	+	2086.02i	−0.0286583	+	0.0496376i
$206$	26140.6	+	34719.4i	0.616000	+	0.818159i
$207$		0			0
$208$	−59781.7	−	37492.7i	−1.38179	−	0.866602i
$209$	917.868	−	1589.79i	0.0210130	−	0.0363956i
$210$		0			0
$211$	19871.6	−	11472.8i	0.446341	−	0.257695i	−0.259943	−	0.965624i	$-0.583704\pi$
$211$	19871.6	−	11472.8i	0.446341	−	0.257695i	0.706284	+	0.707929i	$0.250370\pi$
$212$	82259.0	−	20437.6i	1.83026	−	0.454735i
$213$		0			0
$214$	56008.4	−	6853.58i	1.22300	−	0.149655i
$215$			3354.25i			0.0725637i
$216$		0			0
$217$	31821.1			0.675764
$218$	7933.01	+	64829.6i	0.166926	+	1.36414i
$219$		0			0
$220$	39.1709	+	157.658i	0.000809316	+	0.00325740i
$221$	−36662.5	−	63501.3i	−0.750650	−	1.30016i
$222$		0			0
$223$	−55651.0	−	32130.1i	−1.11909	−	0.646105i	−0.177919	−	0.984045i	$-0.556936\pi$
$223$	−55651.0	−	32130.1i	−1.11909	−	0.646105i	−0.941167	+	0.337941i	$0.890270\pi$
$224$	−2016.17	−	23604.0i	−0.0401820	−	0.470423i
$225$		0			0
$226$	−37780.4	+	28445.2i	−0.739690	+	0.556919i
$227$	5807.02	+	3352.69i	0.112694	+	0.0650641i	0.555288	−	0.831658i	$-0.312608\pi$
$227$	5807.02	+	3352.69i	0.112694	+	0.0650641i	−0.442593	+	0.896722i	$0.645941\pi$
$228$		0			0
$229$	−17775.1	−	30787.4i	−0.338955	−	0.587087i	0.645281	−	0.763945i	$-0.276740\pi$
$229$	−17775.1	−	30787.4i	−0.338955	−	0.587087i	−0.984236	+	0.176858i	$0.943407\pi$
$230$	−1997.53	+	4700.51i	−0.0377605	+	0.0888566i
$231$		0			0
$232$	−40382.2	−	6447.00i	−0.750263	−	0.119779i
$233$	−62439.9			−1.15014			−0.575070	−	0.818105i	$-0.695025\pi$
$233$	−62439.9			−1.15014			−0.575070	+	0.818105i	$0.695025\pi$
$234$		0			0
$235$		−	721.967i		−	0.0130732i
$236$	69472.8	−	66978.7i	1.24736	−	1.20258i
$237$		0			0
$238$	9627.62	−	22655.3i	0.169967	−	0.399960i
$239$	−3250.59	+	1876.73i	−0.0569070	+	0.0328553i	−0.528184	−	0.849130i	$-0.677127\pi$
$239$	−3250.59	+	1876.73i	−0.0569070	+	0.0328553i	0.471277	+	0.881985i	$0.343793\pi$
$240$		0			0
$241$	44832.6	−	77652.3i	0.771898	−	1.33697i	−0.164624	−	0.986356i	$-0.552641\pi$
$241$	44832.6	−	77652.3i	0.771898	−	1.33697i	0.936522	−	0.350610i	$-0.114026\pi$
$242$	46705.9	−	35165.3i	0.797519	−	0.600460i
$243$		0			0
$244$	7371.68	−	25628.5i	0.123819	−	0.430471i
$245$	−1894.62	+	3281.57i	−0.0315638	+	0.0546701i
$246$		0			0
$247$	−87655.9	+	50608.2i	−1.43677	+	0.829520i
$248$	68343.8	+	55483.5i	1.11121	+	0.902112i
$249$		0			0
$250$	−1229.31	−	10046.1i	−0.0196689	−	0.160737i
$251$			9246.49i			0.146767i	0.997304	+	0.0733836i	$0.0233798\pi$
$251$			9246.49i			0.146767i	−0.997304	+	0.0733836i	$0.976620\pi$
$252$		0			0
$253$	−3143.12			−0.0491043
$254$	−83298.4	+	10193.0i	−1.29113	+	0.157992i
$255$		0			0
$256$	36825.9	−	54210.9i	0.561918	−	0.827193i
$257$	7624.85	+	13206.6i	0.115442	+	0.199952i	0.917956	−	0.396681i	$-0.129838\pi$
$257$	7624.85	+	13206.6i	0.115442	+	0.199952i	−0.802514	+	0.596633i	$0.796505\pi$
$258$		0			0
$259$	−29375.4	−	16959.9i	−0.437909	−	0.252827i
$260$	2475.97	−	8608.02i	0.0366268	−	0.127338i
$261$		0			0
$262$	68686.5	+	91228.1i	1.00062	+	1.32900i
$263$	−89478.0	−	51660.2i	−1.29361	−	0.746869i	−0.314322	−	0.949317i	$-0.601777\pi$
$263$	−89478.0	−	51660.2i	−1.29361	−	0.746869i	−0.979293	+	0.202448i	$0.935110\pi$
$264$		0			0
$265$	5379.35	+	9317.30i	0.0766016	+	0.132678i
$266$	−31273.0	−	13289.8i	−0.441983	−	0.187825i
$267$		0			0
$268$	−25382.2	+	24470.9i	−0.353394	+	0.340707i
$269$	86017.8			1.18873			0.594366	−	0.804195i	$-0.297403\pi$
$269$	86017.8			1.18873			0.594366	+	0.804195i	$0.297403\pi$
$270$		0			0
$271$			15629.0i			0.212810i	0.994323	+	0.106405i	$0.0339340\pi$
$271$			15629.0i			0.212810i	−0.994323	+	0.106405i	$0.966066\pi$
$272$	60179.8	−	31871.3i	0.813417	−	0.430786i
$273$		0			0
$274$	−2278.30	−	968.188i	−0.0303466	−	0.0128961i
$275$	2688.13	−	1551.99i	0.0355455	−	0.0205222i
$276$		0			0
$277$	28307.3	−	49029.7i	0.368926	−	0.638998i	−0.620472	−	0.784228i	$-0.713059\pi$
$277$	28307.3	−	49029.7i	0.368926	−	0.638998i	0.989398	+	0.145231i	$0.0463924\pi$
$278$	46728.2	+	62063.6i	0.604630	+	0.803059i
$279$		0			0
$280$	2808.60	−	1074.15i	0.0358240	−	0.0137008i
$281$	55533.5	−	96186.8i	0.703303	−	1.21816i	−0.263998	−	0.964523i	$-0.585041\pi$
$281$	55533.5	−	96186.8i	0.703303	−	1.21816i	0.967301	−	0.253633i	$-0.0816255\pi$
$282$		0			0
$283$	78979.6	−	45598.9i	0.986148	−	0.569353i	0.0820271	−	0.996630i	$-0.473861\pi$
$283$	78979.6	−	45598.9i	0.986148	−	0.569353i	0.904121	+	0.427278i	$0.140527\pi$
$284$	2022.73	+	8141.27i	0.0250785	+	0.100938i
$285$		0			0
$286$	5471.45	−	669.525i	0.0668914	−	0.00818530i
$287$			27438.6i			0.333118i
$288$		0			0
$289$	−12760.0			−0.152776
$290$	−630.465	−	5152.25i	−0.00749661	−	0.0612633i
$291$		0			0
$292$	23172.2	−	5757.23i	0.271770	−	0.0675224i
$293$	41507.5	+	71893.1i	0.483494	+	0.837436i	0.999820	−	0.0189556i	$-0.00603412\pi$
$293$	41507.5	+	71893.1i	0.483494	+	0.837436i	−0.516326	+	0.856392i	$0.672701\pi$
$294$		0			0
$295$	10608.0	+	6124.56i	0.121897	+	0.0703770i
$296$	−33519.7	−	87644.8i	−0.382575	−	1.00033i
$297$		0			0
$298$	−1978.93	+	1489.96i	−0.0222843	+	0.0167780i
$299$	150083.	+	86650.5i	1.67876	+	0.969234i
$300$		0			0
$301$	19104.7	+	33090.3i	0.210866	+	0.365231i
$302$	−6788.81	+	15975.2i	−0.0744355	+	0.175159i
$303$		0			0
$304$	−43994.5	−	83071.0i	−0.476048	−	0.898882i
$305$	3384.96			0.0363876
$306$		0			0
$307$		−	65201.8i		−	0.691803i	−0.938271	−	0.345902i	$-0.887573\pi$
$307$		−	65201.8i		−	0.691803i	0.938271	−	0.345902i	$-0.112427\pi$
$308$	1284.40	+	1332.22i	0.0135393	+	0.0140435i
$309$		0			0
$310$	−4370.18	+	10283.7i	−0.0454753	+	0.107011i
$311$	−115786.	+	66849.3i	−1.19712	+	0.691156i	−0.959911	−	0.280303i	$-0.909565\pi$
$311$	−115786.	+	66849.3i	−1.19712	+	0.691156i	−0.237206	+	0.971459i	$0.576232\pi$
$312$		0			0
$313$	−5620.04	+	9734.19i	−0.0573655	+	0.0993599i	−0.893282	−	0.449497i	$-0.851603\pi$
$313$	−5620.04	+	9734.19i	−0.0573655	+	0.0993599i	0.835917	+	0.548857i	$0.184937\pi$
$314$	−19837.1	+	14935.5i	−0.201196	+	0.151482i
$315$		0			0
$316$	78981.8	+	22718.0i	0.790957	+	0.227508i
$317$	−19603.1	+	33953.5i	−0.195077	+	0.337883i	−0.946926	−	0.321452i	$-0.895829\pi$
$317$	−19603.1	+	33953.5i	−0.195077	+	0.337883i	0.751849	+	0.659336i	$0.229162\pi$
$318$		0			0
$319$	2766.43	−	1597.20i	0.0271856	−	0.0156956i
$320$	7905.07	+	2590.10i	0.0771979	+	0.0252939i
$321$		0			0
$322$	7066.54	+	57748.7i	0.0681546	+	0.556968i
$323$		−	97677.0i		−	0.936240i
$324$		0			0
$325$	−171143.			−1.62029
$326$	62958.4	−	7704.04i	0.592405	−	0.0724908i
$327$		0			0
$328$	−47842.2	+	58931.4i	−0.444696	+	0.547771i
$329$	−4112.08	−	7122.34i	−0.0379901	−	0.0658007i
$330$		0			0
$331$	64736.6	+	37375.7i	0.590873	+	0.341141i	0.765443	−	0.643504i	$-0.222520\pi$
$331$	64736.6	+	37375.7i	0.590873	+	0.341141i	−0.174570	+	0.984645i	$0.555853\pi$
$332$	−122838.	−	35332.7i	−1.11444	−	0.320553i
$333$		0			0
$334$	−1008.08	−	1338.92i	−0.00903656	−	0.0120022i
$335$	−3875.69	−	2237.63i	−0.0345350	−	0.0199388i
$336$		0			0
$337$	70909.1	+	122818.i	0.624370	+	1.08144i	0.988662	+	0.150156i	$0.0479775\pi$
$337$	70909.1	+	122818.i	0.624370	+	1.08144i	−0.364293	+	0.931285i	$0.618689\pi$
$338$	−174574.	−	74187.1i	−1.52808	−	0.649374i
$339$		0			0
$340$	5999.39	+	6222.78i	0.0518978	+	0.0538303i
$341$	−6876.48			−0.0591367
$342$		0			0
$343$			98710.7i			0.839027i
$344$	−16664.4	+	104381.i	−0.140823	+	0.882073i
$345$		0			0
$346$	−70685.3	−	30038.5i	−0.590442	−	0.250914i
$347$	158508.	−	91514.6i	1.31641	−	0.760032i	0.333264	−	0.942834i	$-0.391850\pi$
$347$	158508.	−	91514.6i	1.31641	−	0.760032i	0.983150	+	0.182802i	$0.0585168\pi$
$348$		0			0
$349$	−67279.0	+	116531.i	−0.552368	+	0.956729i	0.445735	+	0.895165i	$0.352942\pi$
$349$	−67279.0	+	116531.i	−0.552368	+	0.956729i	−0.998103	+	0.0615644i	$0.980391\pi$
$350$	−34558.4	−	45899.8i	−0.282110	−	0.374693i
$351$		0			0
$352$	435.691	+	5100.77i	0.00351636	+	0.0411671i
$353$	−100139.	+	173446.i	−0.803626	+	1.39192i	0.113589	+	0.993528i	$0.463765\pi$
$353$	−100139.	+	173446.i	−0.803626	+	1.39192i	−0.917215	+	0.398393i	$0.869568\pi$
$354$		0			0
$355$	−922.144	+	532.400i	−0.00731715	+	0.00422456i
$356$	−137580.	+	34182.3i	−1.08556	+	0.269713i
$357$		0			0
$358$	−197811.	+	24205.6i	−1.54342	+	0.188864i
$359$		−	161179.i		−	1.25060i	−0.780385	−	0.625300i	$-0.784977\pi$
$359$		−	161179.i		−	1.25060i	0.780385	−	0.625300i	$-0.215023\pi$
$360$		0			0
$361$	−4510.46			−0.0346104
$362$	6787.59	+	55469.1i	0.0517962	+	0.423286i
$363$		0			0
$364$	−24602.4	−	99022.0i	−0.185684	−	0.747358i
$365$	1515.35	+	2624.66i	0.0113744	+	0.0197010i
$366$		0			0
$367$	172828.	+	99782.5i	1.28317	+	0.740836i	0.977426	−	0.211279i	$-0.0677627\pi$
$367$	172828.	+	99782.5i	1.28317	+	0.740836i	0.305740	+	0.952115i	$0.401096\pi$
$368$	−85514.0	+	136351.i	−0.631454	+	1.00685i
$369$		0			0
$370$	9515.28	−	7164.14i	0.0695053	−	0.0523312i
$371$	106136.	+	61277.9i	0.771111	+	0.445201i
$372$		0			0
$373$	2894.35	+	5013.15i	0.0208033	+	0.0360324i	0.876240	−	0.481876i	$-0.160044\pi$
$373$	2894.35	+	5013.15i	0.0208033	+	0.0360324i	−0.855436	+	0.517908i	$0.826711\pi$
$374$	−2080.51	+	4895.78i	−0.0148740	+	0.0350008i
$375$		0			0
$376$	3586.83	−	22466.9i	0.0253709	−	0.158916i
$377$	−176129.			−1.23922
$378$		0			0
$379$		−	217930.i		−	1.51719i	−0.651565	−	0.758593i	$-0.725887\pi$
$379$		−	217930.i		−	1.51719i	0.651565	−	0.758593i	$-0.274113\pi$
$380$	8589.81	−	8281.44i	0.0594862	−	0.0573507i
$381$		0			0
$382$	48765.0	−	114752.i	0.334181	−	0.786381i
$383$	−60187.2	+	34749.1i	−0.410305	+	0.236890i	−0.690921	−	0.722930i	$-0.742795\pi$
$383$	−60187.2	+	34749.1i	−0.410305	+	0.236890i	0.280616	+	0.959820i	$0.409461\pi$
$384$		0			0
$385$	−117.446	+	203.422i	−0.000792348	+	0.00137239i
$386$	86267.6	−	64951.7i	0.578993	−	0.435929i
$387$		0			0
$388$	30157.9	−	104848.i	0.200326	−	0.696458i
$389$	28733.0	−	49767.0i	0.189881	−	0.328884i	−0.755329	−	0.655345i	$-0.772523\pi$
$389$	28733.0	−	49767.0i	0.189881	−	0.328884i	0.945210	+	0.326462i	$0.105856\pi$
$390$		0			0
$391$	−144835.	+	83620.5i	−0.947371	+	0.546965i
$392$	−75261.8	+	92706.5i	−0.489782	+	0.603306i
$393$		0			0
$394$	−5060.76	−	41357.2i	−0.0326004	−	0.266415i
$395$			10431.7i			0.0668595i
$396$		0			0
$397$	13255.8			0.0841056			0.0420528	−	0.999115i	$-0.486610\pi$
$397$	13255.8			0.0841056			0.0420528	+	0.999115i	$0.486610\pi$
$398$	−33504.8	+	4099.89i	−0.211515	+	0.0258825i
$399$		0			0
$400$	5808.42	−	158838.i	0.0363026	−	0.992737i
$401$	−2687.66	−	4655.16i	−0.0167142	−	0.0289498i	0.857547	−	0.514405i	$-0.171987\pi$
$401$	−2687.66	−	4655.16i	−0.0167142	−	0.0289498i	−0.874262	+	0.485455i	$0.838654\pi$
$402$		0			0
$403$	328350.	+	189573.i	2.02175	+	1.16726i
$404$	−13671.3	+	47529.7i	−0.0837618	+	0.291208i
$405$		0			0
$406$	−35565.1	−	47236.9i	−0.215761	−	0.286569i
$407$	6347.97	+	3665.00i	0.0383218	+	0.0221251i
$408$		0			0
$409$	120347.	+	208446.i	0.719427	+	1.24608i	0.961227	+	0.275758i	$0.0889289\pi$
$409$	120347.	+	208446.i	0.719427	+	1.24608i	−0.241800	+	0.970326i	$0.577738\pi$
$410$	−8867.43	−	3768.31i	−0.0527509	−	0.0224170i
$411$		0			0
$412$	−125149.	+	120656.i	−0.737282	+	0.710814i
$413$	139534.			0.818049
$414$		0			0
$415$		−	16224.2i		−	0.0942035i
$416$	119816.	−	255572.i	0.692352	−	1.47682i
$417$		0			0
$418$	6758.04	+	2871.90i	0.0386784	+	0.0164368i
$419$	30669.6	−	17707.1i	0.174695	−	0.100860i	−0.410103	−	0.912039i	$-0.634507\pi$
$419$	30669.6	−	17707.1i	0.174695	−	0.100860i	0.584798	+	0.811179i	$0.301174\pi$
$420$		0			0
$421$	82548.0	−	142977.i	0.465739	−	0.806683i	−0.533496	−	0.845803i	$-0.679122\pi$
$421$	82548.0	−	142977.i	0.465739	−	0.806683i	0.999235	+	0.0391198i	$0.0124554\pi$
$422$	55206.1	+	73323.7i	0.310000	+	0.411737i
$423$		0			0
$424$	121110.	+	316670.i	0.673673	+	1.76147i
$425$	82579.3	−	143032.i	0.457187	−	0.791870i
$426$		0			0
$427$	33393.2	−	19279.6i	0.183148	−	0.105741i
$428$	54422.7	+	219045.i	0.297093	+	1.19577i
$429$		0			0
$430$	−13317.7	+	1629.65i	−0.0720264	+	0.00881366i
$431$		−	161673.i		−	0.870327i	−0.900351	−	0.435163i	$-0.856691\pi$
$431$		−	161673.i		−	0.870327i	0.900351	−	0.435163i	$-0.143309\pi$
$432$		0			0
$433$	−61835.3			−0.329808			−0.164904	−	0.986310i	$-0.552731\pi$
$433$	−61835.3			−0.329808			−0.164904	+	0.986310i	$0.552731\pi$
$434$	15460.1	+	126342.i	0.0820791	+	0.670761i
$435$		0			0
$436$	−253544.	+	62994.2i	−1.33377	+	0.331381i
$437$	115428.	+	199927.i	0.604434	+	1.04691i
$438$		0			0
$439$	−268021.	−	154742.i	−1.39072	−	0.802933i	−0.397326	−	0.917677i	$-0.630062\pi$
$439$	−268021.	−	154742.i	−1.39072	−	0.802933i	−0.993395	+	0.114744i	$0.963395\pi$
$440$	−606.933	+	232.121i	−0.00313499	+	0.00119897i
$441$		0			0
$442$	234312.	−	176416.i	1.19936	−	0.903011i
$443$	−40615.5	−	23449.4i	−0.206959	−	0.119488i	0.392938	−	0.919565i	$-0.371459\pi$
$443$	−40615.5	−	23449.4i	−0.206959	−	0.119488i	−0.599897	+	0.800077i	$0.704792\pi$
$444$		0			0
$445$	−8997.07	−	15583.4i	−0.0454340	−	0.0786940i
$446$	100531.	−	236566.i	0.505396	−	1.18928i
$447$		0			0
$448$	92737.3	−	19472.8i	0.462060	−	0.0970226i
$449$	124857.			0.619328			0.309664	−	0.950846i	$-0.399783\pi$
$449$	124857.			0.619328			0.309664	+	0.950846i	$0.399783\pi$
$450$		0			0
$451$		−	5929.43i		−	0.0291514i
$452$	−131294.	−	136183.i	−0.642639	−	0.666569i
$453$		0			0
$454$	−10490.1	+	24685.0i	−0.0508944	+	0.119763i
$455$	11216.0	−	6475.56i	0.0541771	−	0.0312791i
$456$		0			0
$457$	62748.5	−	108684.i	0.300449	−	0.520393i	−0.675789	−	0.737095i	$-0.736197\pi$
$457$	62748.5	−	108684.i	0.300449	−	0.520393i	0.976238	+	0.216703i	$0.0695302\pi$
$458$	113602.	−	85532.1i	0.541571	−	0.407754i
$459$		0			0
$460$	−19633.3	−	5647.25i	−0.0927852	−	0.0266883i
$461$	51647.4	−	89455.9i	0.243022	−	0.420927i	−0.718551	−	0.695474i	$-0.755194\pi$
$461$	51647.4	−	89455.9i	0.243022	−	0.420927i	0.961574	+	0.274547i	$0.0885278\pi$
$462$		0			0
$463$	−277564.	+	160252.i	−1.29480	+	0.747552i	−0.979501	−	0.201442i	$-0.935437\pi$
$463$	−277564.	+	160252.i	−1.29480	+	0.747552i	−0.315297	+	0.948993i	$0.602104\pi$
$464$	5977.62	−	163465.i	0.0277646	−	0.759257i
$465$		0			0
$466$	−30336.1	−	247910.i	−0.139697	−	1.14162i
$467$			427381.i			1.95967i	0.199820	+	0.979833i	$0.435964\pi$
$467$			427381.i			1.95967i	−0.199820	+	0.979833i	$0.564036\pi$
$468$		0			0
$469$	−50979.2			−0.231765
$470$	2866.49	−	350.764i	0.0129764	−	0.00158788i
$471$		0			0
$472$	299684.	+	243292.i	1.34518	+	1.09205i
$473$	−4128.49	−	7150.76i	−0.0184531	−	0.0319617i
$474$		0			0
$475$	−197438.	−	113991.i	−0.875071	−	0.505223i
$476$	94627.9	+	27218.4i	0.417643	+	0.120129i
$477$		0			0
$478$	−9030.61	−	11994.3i	−0.0395240	−	0.0524951i
$479$	−166330.	−	96030.5i	−0.724935	−	0.418541i	0.0916316	−	0.995793i	$-0.470792\pi$
$479$	−166330.	−	96030.5i	−0.724935	−	0.418541i	−0.816566	+	0.577252i	$0.804125\pi$
$480$		0			0
$481$	−202076.	−	350006.i	−0.873422	−	1.51281i
$482$	330091.	+	140276.i	1.42082	+	0.603793i
$483$		0			0
$484$	162312.	+	168356.i	0.692882	+	0.718682i
$485$	13848.1			0.0588715
$486$		0			0
$487$		−	52885.1i		−	0.222985i	−0.993765	−	0.111492i	$-0.964437\pi$
$487$		−	52885.1i		−	0.222985i	0.993765	−	0.111492i	$-0.0355631\pi$
$488$	105337.	+	16816.9i	0.442323	+	0.0706167i
$489$		0			0
$490$	−13949.6	−	5928.02i	−0.0580991	−	0.0246898i
$491$	6368.89	−	3677.08i	0.0264180	−	0.0152525i	−0.486733	−	0.873551i	$-0.661811\pi$
$491$	6368.89	−	3677.08i	0.0264180	−	0.0152525i	0.513151	+	0.858298i	$0.328478\pi$
$492$		0			0
$493$	84984.9	−	147198.i	0.349662	−	0.605632i
$494$	−243521.	−	323440.i	−0.997890	−	1.32538i
$495$		0			0
$496$	−187086.	+	298308.i	−0.760465	+	1.21255i
$497$	−6064.75	+	10504.4i	−0.0245527	+	0.0425266i
$498$		0			0
$499$	359442.	−	207524.i	1.44354	−	0.833426i	0.445452	−	0.895306i	$-0.353043\pi$
$499$	359442.	−	207524.i	1.44354	−	0.833426i	0.998084	+	0.0618804i	$0.0197097\pi$
$500$	39289.5	−	9761.65i	0.157158	−	0.0390466i
$501$		0			0
$502$	−36712.1	+	4492.35i	−0.145681	+	0.0178265i
$503$			53242.3i			0.210436i	0.994449	+	0.105218i	$0.0335541\pi$
$503$			53242.3i			0.210436i	−0.994449	+	0.105218i	$0.966446\pi$
$504$		0			0
$505$	−6277.63			−0.0246157
$506$	−1527.07	−	12479.4i	−0.00596426	−	0.0487408i
$507$		0			0
$508$	−80940.1	−	325775.i	−0.313644	−	1.26238i
$509$	−248630.	−	430640.i	−0.959662	−	1.66218i	−0.723319	−	0.690515i	$-0.757384\pi$
$509$	−248630.	−	430640.i	−0.959662	−	1.66218i	−0.236344	−	0.971669i	$-0.575949\pi$
$510$		0			0
$511$	29898.4	+	17261.9i	0.114500	+	0.0661068i
$512$	233130.	+	119875.i	0.889320	+	0.457286i
$513$		0			0
$514$	−48730.9	+	36689.9i	−0.184450	+	0.138874i
$515$	−19109.5	−	11032.9i	−0.0720501	−	0.0415981i
$516$		0			0
$517$	888.614	+	1539.12i	0.00332454	+	0.00575828i
$518$	53065.4	−	124871.i	0.197766	−	0.465375i
$519$		0			0
$520$	35380.1	+	5648.42i	0.130843	+	0.0208891i
$521$	58965.8			0.217233			0.108616	−	0.994084i	$-0.465358\pi$
$521$	58965.8			0.217233			0.108616	+	0.994084i	$0.465358\pi$
$522$		0			0
$523$		−	117488.i		−	0.429527i	−0.976666	−	0.214763i	$-0.931102\pi$
$523$		−	117488.i		−	0.429527i	0.976666	−	0.214763i	$-0.0688980\pi$
$524$	−328840.	+	317035.i	−1.19763	+	1.15463i
$525$		0			0
$526$	161638.	−	380361.i	0.584215	−	1.37475i
$527$	−316868.	+	182944.i	−1.14093	+	0.658714i
$528$		0			0
$529$	57713.8	−	99963.2i	0.206238	−	0.357214i
$530$	−34379.8	+	25884.8i	−0.122391	+	0.0921497i
$531$		0			0
$532$	37571.7	−	130623.i	0.132751	−	0.461525i
$533$	−163465.	+	283129.i	−0.575399	+	0.996620i
$534$		0			0
$535$	−24810.8	+	14324.5i	−0.0866828	+	0.0500463i
$536$	−109491.	−	88887.9i	−0.381108	−	0.309395i
$537$		0			0
$538$	41791.3	+	341524.i	0.144385	+	1.17993i
$539$		−	9327.75i		−	0.0321070i
$540$		0			0
$541$	−16461.8			−0.0562448			−0.0281224	−	0.999604i	$-0.508953\pi$
$541$	−16461.8			−0.0562448			−0.0281224	+	0.999604i	$0.508953\pi$
$542$	−62053.1	+	7593.26i	−0.211235	+	0.0258482i
$543$		0			0
$544$	155779.	+	223453.i	0.526395	+	0.755071i
$545$	−16580.6	−	28718.4i	−0.0558222	−	0.0966869i
$546$		0			0
$547$	−337391.	−	194793.i	−1.12761	−	0.651026i	−0.184277	−	0.982874i	$-0.558994\pi$
$547$	−337391.	−	194793.i	−1.12761	−	0.651026i	−0.943333	+	0.331848i	$0.892328\pi$
$548$	2737.18	−	9516.13i	0.00911470	−	0.0316883i
$549$		0			0
$550$	7468.01	+	9918.87i	0.0246876	+	0.0327897i
$551$	−203189.	−	117312.i	−0.669265	−	0.386400i
$552$		0			0
$553$	59415.7	+	102911.i	0.194290	+	0.336521i
$554$	208420.	+	88570.1i	0.679077	+	0.288581i
$555$		0			0
$556$	−223714.	+	215682.i	−0.723674	+	0.697694i
$557$	−434133.			−1.39931			−0.699653	−	0.714483i	$-0.746662\pi$
$557$	−434133.			−1.39931			−0.699653	+	0.714483i	$0.746662\pi$
$558$		0			0
$559$			455263.i			1.45693i
$560$	5629.31	+	10629.3i	0.0179506	+	0.0338946i
$561$		0			0
$562$	408879.	+	173758.i	1.29456	+	0.550137i
$563$	192477.	−	111127.i	0.607244	−	0.350592i	−0.164642	−	0.986353i	$-0.552647\pi$
$563$	192477.	−	111127.i	0.607244	−	0.350592i	0.771886	+	0.635761i	$0.219314\pi$
$564$		0			0
$565$	12005.6	−	20794.2i	0.0376084	−	0.0651397i
$566$	219417.	+	291425.i	0.684916	+	0.909692i
$567$		0			0
$568$	−31341.2	+	11986.4i	−0.0971448	+	0.0371529i
$569$	1962.56	−	3399.25i	0.00606175	−	0.0104993i	−0.862979	−	0.505240i	$-0.831404\pi$
$569$	1962.56	−	3399.25i	0.00606175	−	0.0104993i	0.869040	+	0.494741i	$0.164737\pi$
$570$		0			0
$571$	−331554.	+	191423.i	−1.01691	+	0.587112i	−0.913207	−	0.407496i	$-0.866402\pi$
$571$	−331554.	+	191423.i	−1.01691	+	0.587112i	−0.103702	+	0.994608i	$0.533069\pi$
$572$	5316.54	+	21398.5i	0.0162494	+	0.0654020i
$573$		0			0
$574$	−108942.	+	13330.9i	−0.330652	+	0.0404609i
$575$			390347.i			1.18063i
$576$		0			0
$577$	18219.2			0.0547239			0.0273620	−	0.999626i	$-0.491289\pi$
$577$	18219.2			0.0547239			0.0273620	+	0.999626i	$0.491289\pi$
$578$	−6199.39	−	50662.3i	−0.0185564	−	0.151645i
$579$		0			0
$580$	20150.1	−	5006.38i	0.0598992	−	0.0148822i
$581$	−92407.6	−	160055.i	−0.273751	−	0.474150i
$582$		0			0
$583$	−22935.9	−	13242.0i	−0.0674806	−	0.0389599i
$584$	34116.5	+	89205.4i	0.100032	+	0.261556i
$585$		0			0
$586$	−265277.	+	199730.i	−0.772510	+	0.581630i
$587$	45835.0	+	26462.8i	0.133021	+	0.0767998i	0.565034	−	0.825068i	$-0.308863\pi$
$587$	45835.0	+	26462.8i	0.133021	+	0.0767998i	−0.432013	+	0.901868i	$0.642196\pi$
$588$		0			0
$589$	252532.	+	437399.i	0.727924	+	1.26080i
$590$	−19163.0	+	45093.6i	−0.0550503	+	0.129542i
$591$		0			0
$592$	331698.	−	175668.i	0.946455	−	0.501243i
$593$	−216280.			−0.615046			−0.307523	−	0.951541i	$-0.599500\pi$
$593$	−216280.			−0.615046			−0.307523	+	0.951541i	$0.599500\pi$
$594$		0			0
$595$			12498.3i			0.0353033i
$596$	−6877.16	−	7133.24i	−0.0193605	−	0.0200814i
$597$		0			0
$598$	−271119.	+	637986.i	−0.758154	+	1.78406i
$599$	260151.	−	150198.i	0.725057	−	0.418612i	−0.0915543	−	0.995800i	$-0.529184\pi$
$599$	260151.	−	150198.i	0.725057	−	0.418612i	0.816611	+	0.577188i	$0.195850\pi$
$600$		0			0
$601$	−255485.	+	442514.i	−0.707322	+	1.22512i	0.258525	+	0.966005i	$0.416764\pi$
$601$	−255485.	+	442514.i	−0.707322	+	1.22512i	−0.965847	+	0.259113i	$0.916570\pi$
$602$	−122099.	+	91929.8i	−0.336915	+	0.253667i
$603$		0			0
$604$	−66725.9	−	19192.8i	−0.182903	−	0.0526094i
$605$	−14841.8	+	25706.8i	−0.0405487	+	0.0702324i
$606$		0			0
$607$	154217.	−	89037.5i	0.418558	−	0.241655i	−0.275902	−	0.961186i	$-0.588976\pi$
$607$	154217.	−	89037.5i	0.418558	−	0.241655i	0.694460	+	0.719531i	$0.255643\pi$
$608$	308450.	−	215035.i	0.834405	−	0.581703i
$609$		0			0
$610$	1644.56	+	13439.6i	0.00441968	+	0.0361182i
$611$		−	97990.4i		−	0.262483i
$612$		0			0
$613$	570495.			1.51821			0.759103	−	0.650970i	$-0.225638\pi$
$613$	570495.			1.51821			0.759103	+	0.650970i	$0.225638\pi$
$614$	258876.	−	31677.9i	0.686681	−	0.0840272i
$615$		0			0
$616$	−4665.42	+	5746.80i	−0.0122950	+	0.0151448i
$617$	107951.	+	186976.i	0.283567	+	0.491153i	0.972261	−	0.233900i	$-0.0751488\pi$
$617$	107951.	+	186976.i	0.283567	+	0.491153i	−0.688694	+	0.725052i	$0.741815\pi$
$618$		0			0
$619$	158318.	+	91404.9i	0.413189	+	0.238555i	0.692159	−	0.721745i	$-0.256660\pi$
$619$	158318.	+	91404.9i	0.413189	+	0.238555i	−0.278970	+	0.960300i	$0.589993\pi$
$620$	−42953.6	−	12355.0i	−0.111742	−	0.0321410i
$621$		0			0
$622$	−321672.	−	427238.i	−0.831442	−	1.10431i
$623$	−177515.	−	102489.i	−0.457362	−	0.264058i
$624$		0			0
$625$	−191454.	−	331608.i	−0.490123	−	0.848918i
$626$	−41378.9	−	17584.4i	−0.105592	−	0.0448724i
$627$		0			0
$628$	−68937.6	−	71504.6i	−0.174798	−	0.181307i
$629$	390019.			0.985791
$630$		0			0
$631$		−	153307.i		−	0.385037i	−0.981293	−	0.192518i	$-0.938335\pi$
$631$		−	153307.i		−	0.385037i	0.981293	−	0.192518i	$-0.0616655\pi$
$632$	−51826.4	+	324626.i	−0.129753	+	0.812734i
$633$		0			0
$634$	−144333.	−	61335.7i	−0.359076	−	0.152593i
$635$	36899.8	−	21304.1i	0.0915117	−	0.0528343i
$636$		0			0
$637$	−257150.	+	445397.i	−0.633736	+	1.09766i
$638$	7685.56	+	10207.8i	0.0188814	+	0.0250779i
$639$		0			0
$640$	−6443.06	+	32644.5i	−0.0157301	+	0.0796986i
$641$	196626.	−	340566.i	0.478547	−	0.828869i	−0.521150	−	0.853465i	$-0.674497\pi$
$641$	196626.	−	340566.i	0.478547	−	0.828869i	0.999697	+	0.0245966i	$0.00783012\pi$
$642$		0			0
$643$	384971.	−	222263.i	0.931120	−	0.537583i	0.0439545	−	0.999034i	$-0.486004\pi$
$643$	384971.	−	222263.i	0.931120	−	0.537583i	0.887166	+	0.461451i	$0.152671\pi$
$644$	−225851.	+	56113.7i	−0.544566	+	0.135300i
$645$		0			0
$646$	387815.	−	47455.8i	0.929309	−	0.113717i
$647$			152505.i			0.364314i	0.983269	+	0.182157i	$0.0583079\pi$
$647$			152505.i			0.364314i	−0.983269	+	0.182157i	$0.941692\pi$
$648$		0			0
$649$	−30153.0			−0.0715881
$650$	−83148.9	−	679504.i	−0.196802	−	1.60829i
$651$		0			0
$652$	61176.0	+	246226.i	0.143908	+	0.579214i
$653$	−149617.	−	259144.i	−0.350876	−	0.607736i	0.635527	−	0.772079i	$-0.280783\pi$
$653$	−149617.	−	259144.i	−0.350876	−	0.607736i	−0.986403	+	0.164343i	$0.947450\pi$
$654$		0			0
$655$	−50211.7	−	28989.8i	−0.117037	−	0.0675713i
$656$	−257224.	−	161321.i	−0.597728	−	0.374871i
$657$		0			0
$658$	26280.6	−	19786.9i	0.0606992	−	0.0457010i
$659$	361192.	+	208535.i	0.831702	+	0.480183i	0.854435	−	0.519558i	$-0.173903\pi$
$659$	361192.	+	208535.i	0.831702	+	0.480183i	−0.0227330	+	0.999742i	$0.507237\pi$
$660$		0			0
$661$	−379775.	−	657790.i	−0.869208	−	1.50551i	−0.862808	−	0.505532i	$-0.831296\pi$
$661$	−379775.	−	657790.i	−0.869208	−	1.50551i	−0.00639999	−	0.999980i	$-0.502037\pi$
$662$	−116944.	+	275188.i	−0.266847	+	0.627933i
$663$		0			0
$664$	80604.0	−	504881.i	0.182819	−	1.14512i
$665$	17252.3			0.0390126
$666$		0			0
$667$			401718.i			0.902962i
$668$	4826.24	−	4652.98i	0.0108157	−	0.0104275i
$669$		0			0
$670$	7001.28	−	16475.1i	0.0155965	−	0.0367011i
$671$	−7216.22	+	4166.29i	−0.0160275	+	0.00925346i
$672$		0			0
$673$	18836.0	−	32624.9i	0.0415871	−	0.0720309i	−0.844483	−	0.535583i	$-0.820092\pi$
$673$	18836.0	−	32624.9i	0.0415871	−	0.0720309i	0.886070	+	0.463552i	$0.153425\pi$
$674$	−453184.	+	341207.i	−0.997597	+	0.751100i
$675$		0			0
$676$	209735.	−	729170.i	0.458964	−	1.59564i
$677$	−347010.	+	601039.i	−0.757120	+	1.31137i	0.187193	+	0.982323i	$0.440061\pi$
$677$	−347010.	+	601039.i	−0.757120	+	1.31137i	−0.944313	+	0.329047i	$0.893272\pi$
$678$		0			0
$679$	136614.	−	78873.9i	0.296315	−	0.171078i
$680$	−21792.1	+	26843.2i	−0.0471282	+	0.0580519i
$681$		0			0
$682$	−3340.90	−	27302.3i	−0.00718281	−	0.0586989i
$683$		−	357197.i		−	0.765714i	−0.923808	−	0.382857i	$-0.874940\pi$
$683$		−	357197.i		−	0.765714i	0.923808	−	0.382857i	$-0.125060\pi$
$684$		0			0
$685$	1256.87			0.00267861
$686$	−391920.	+	47958.0i	−0.832815	+	0.101909i
$687$		0			0
$688$	−422529.	−	15451.1i	−0.892647	−	0.0326425i
$689$	730122.	+	1.26461e6i	1.53800	+	2.66390i
$690$		0			0
$691$	384473.	+	221976.i	0.805212	+	0.464889i	0.845290	−	0.534307i	$-0.179427\pi$
$691$	384473.	+	221976.i	0.805212	+	0.464889i	−0.0400786	+	0.999197i	$0.512761\pi$
$692$	84922.2	−	295242.i	0.177341	−	0.616547i
$693$		0			0
$694$	440359.	+	584876.i	0.914297	+	1.21435i
$695$	−34159.6	−	19722.1i	−0.0707202	−	0.0408304i
$696$		0			0
$697$	−157749.	−	273228.i	−0.324713	−	0.562420i
$698$	−495358.	−	210508.i	−1.01674	−	0.432073i
$699$		0			0
$700$	165450.	−	159510.i	0.337653	−	0.325531i
$701$	483771.			0.984474			0.492237	−	0.870461i	$-0.336179\pi$
$701$	483771.			0.984474			0.492237	+	0.870461i	$0.336179\pi$
$702$		0			0
$703$		−	538375.i		−	1.08937i
$704$	−20040.4	+	4208.04i	−0.0404353	+	0.00849053i
$705$		0			0
$706$	−737299.	−	313323.i	−1.47922	−	0.628612i
$707$	−61929.9	+	35755.3i	−0.123897	+	0.0715321i
$708$		0			0
$709$	−79169.5	+	137126.i	−0.157494	+	0.272788i	−0.933965	−	0.357366i	$-0.883675\pi$
$709$	−79169.5	+	137126.i	−0.157494	+	0.272788i	0.776470	+	0.630154i	$0.217008\pi$
$710$	−2561.85	−	3402.60i	−0.00508203	−	0.00674986i
$711$		0			0
$712$	−202559.	−	529638.i	−0.399569	−	1.04477i
$713$	432382.	−	748907.i	0.850527	−	1.47316i
$714$		0			0
$715$	−2423.76	+	1399.36i	−0.00474108	+	0.00273726i
$716$	−192211.	−	773627.i	−0.374932	−	1.50906i
$717$		0			0
$718$	639941.	−	78307.7i	1.24134	−	0.151899i
$719$		−	781622.i		−	1.51196i	−0.654597	−	0.755978i	$-0.727162\pi$
$719$		−	781622.i		−	1.51196i	0.654597	−	0.755978i	$-0.272838\pi$
$720$		0			0
$721$	−251358.			−0.483529
$722$	−2191.38	−	17908.3i	−0.00420381	−	0.0343541i
$723$		0			0
$724$	−216936.	+	53898.7i	−0.413861	+	0.102826i
$725$	−198358.	−	343566.i	−0.377375	−	0.653633i
$726$		0			0
$727$	51590.1	+	29785.6i	0.0976107	+	0.0563556i	0.548011	−	0.836471i	$-0.315385\pi$
$727$	51590.1	+	29785.6i	0.0976107	+	0.0563556i	−0.450400	+	0.892827i	$0.648719\pi$
$728$	381202.	−	145790.i	0.719271	−	0.275085i
$729$		0			0
$730$	−9684.71	+	7291.71i	−0.0181736	+	0.0136831i
$731$	−380482.	−	219672.i	−0.712032	−	0.411092i
$732$		0			0
$733$	106923.	+	185196.i	0.199004	+	0.344685i	0.948206	−	0.317657i	$-0.102896\pi$
$733$	106923.	+	185196.i	0.199004	+	0.344685i	−0.749202	+	0.662342i	$0.769563\pi$
$734$	−312207.	+	734674.i	−0.579497	+	1.36365i
$735$		0			0
$736$	−582914.	−	273278.i	−1.07609	−	0.504486i
$737$	11016.5			0.0202819
$738$		0			0
$739$			218903.i			0.400832i	0.979711	+	0.200416i	$0.0642294\pi$
$739$			218903.i			0.400832i	−0.979711	+	0.200416i	$0.935771\pi$
$740$	33067.3	+	34298.7i	0.0603860	+	0.0626345i
$741$		0			0
$742$	−191731.	+	451174.i	−0.348245	+	0.819476i
$743$	431487.	−	249119.i	0.781610	−	0.451263i	−0.0553907	−	0.998465i	$-0.517640\pi$
$743$	431487.	−	249119.i	0.781610	−	0.451263i	0.837001	+	0.547202i	$0.184307\pi$
$744$		0			0
$745$	628.850	−	1089.20i	0.00113301	−	0.00196243i
$746$	−18497.9	+	13927.3i	−0.0332388	+	0.0250258i
$747$		0			0
$748$	−20448.9	−	5881.85i	−0.0365483	−	0.0105126i
$749$	−163175.	+	282628.i	−0.290864	+	0.503792i
$750$		0			0
$751$	534346.	−	308505.i	0.947421	−	0.546994i	0.0551419	−	0.998479i	$-0.482439\pi$
$751$	534346.	−	308505.i	0.947421	−	0.546994i	0.892279	+	0.451485i	$0.149106\pi$
$752$	90944.9	+	3325.69i	0.160821	+	0.00588093i
$753$		0			0
$754$	−85571.1	−	699299.i	−0.150517	−	1.23004i
$755$		−	8813.01i		−	0.0154607i
$756$		0			0
$757$	483106.			0.843045			0.421523	−	0.906818i	$-0.361496\pi$
$757$	483106.			0.843045			0.421523	+	0.906818i	$0.361496\pi$
$758$	865266.	−	105880.i	1.50595	−	0.184279i
$759$		0			0
$760$	37053.8	+	30081.4i	0.0641513	+	0.0520799i
$761$	−68847.3	−	119247.i	−0.118882	−	0.205910i	0.800443	−	0.599409i	$-0.204598\pi$
$761$	−68847.3	−	119247.i	−0.118882	−	0.205910i	−0.919325	+	0.393499i	$0.871264\pi$
$762$		0			0
$763$	−327141.	−	188875.i	−0.561935	−	0.324433i
$764$	479301.	+	137864.i	0.821148	+	0.236192i
$765$		0			0
$766$	−167209.	−	222084.i	−0.284972	−	0.378494i
$767$	1.43980e6	+	831268.i	2.44743	+	1.41303i
$768$		0			0
$769$	173385.	+	300311.i	0.293196	+	0.507830i	0.974564	−	0.224111i	$-0.0719478\pi$
$769$	173385.	+	300311.i	0.293196	+	0.507830i	−0.681368	+	0.731941i	$0.738614\pi$
$770$	−864.724	−	367.473i	−0.00145847	−	0.000619790i
$771$		0			0
$772$	299796.	+	310959.i	0.503027	+	0.521758i
$773$	456941.			0.764717			0.382358	−	0.924014i	$-0.375112\pi$
$773$	456941.			0.764717			0.382358	+	0.924014i	$0.375112\pi$
$774$		0			0
$775$			853996.i			1.42185i
$776$	430938.	+	68799.0i	0.715634	+	0.114251i
$777$		0			0
$778$	211554.	+	89902.1i	0.349512	+	0.148529i
$779$	−377159.	+	217753.i	−0.621512	+	0.358830i
$780$		0			0
$781$	1310.58	−	2269.99i	0.00214863	−	0.00372154i
$782$	−402373.	−	534424.i	−0.657984	−	0.873922i
$783$		0			0
$784$	−404646.	−	253777.i	−0.658329	−	0.412877i
$785$	6303.68	−	10918.3i	0.0102295	−	0.0177180i
$786$		0			0
$787$	−602982.	+	348132.i	−0.973543	+	0.562075i	−0.900314	−	0.435240i	$-0.856663\pi$
$787$	−602982.	+	348132.i	−0.973543	+	0.562075i	−0.0732283	+	0.997315i	$0.523330\pi$
$788$	161745.	−	40186.4i	0.260483	−	0.0647182i
$789$		0			0
$790$	−41418.1	+	5068.21i	−0.0663645	+	0.00812082i
$791$		−	273518.i		−	0.437153i
$792$		0			0
$793$	459430.			0.730589
$794$	6440.25	+	52630.6i	0.0102156	+	0.0834829i
$795$		0			0
$796$	−32556.3	−	131035.i	−0.0513817	−	0.206805i
$797$	65680.3	+	113762.i	0.103399	+	0.179093i	0.913083	−	0.407773i	$-0.133695\pi$
$797$	65680.3	+	113762.i	0.103399	+	0.179093i	−0.809684	+	0.586867i	$0.800361\pi$
$798$		0			0
$799$	81894.7	+	47281.9i	0.128281	+	0.0740631i
$800$	633470.	−	54108.9i	0.989796	−	0.0845451i
$801$		0			0
$802$	17177.0	−	12932.7i	0.0267053	−	0.0201067i
$803$	−6461.00	−	3730.26i	−0.0100200	−	0.00578506i
$804$		0			0
$805$	−14769.6	−	25581.7i	−0.0227917	−	0.0394764i
$806$	−593151.	+	1.39578e6i	−0.913051	+	2.14855i
$807$		0			0
$808$	−195353.	−	31188.1i	−0.299225	−	0.0477712i
$809$	−796199.			−1.21653			−0.608267	−	0.793732i	$-0.708135\pi$
$809$	−796199.			−1.21653			−0.608267	+	0.793732i	$0.708135\pi$
$810$		0			0
$811$		−	116976.i		−	0.177851i	−0.996038	−	0.0889253i	$-0.971657\pi$
$811$		−	116976.i		−	0.177851i	0.996038	−	0.0889253i	$-0.0283432\pi$
$812$	170270.	−	164157.i	0.258241	−	0.248970i
$813$		0			0
$814$	−11467.3	+	26984.5i	−0.0173067	+	0.0407254i
$815$	−27889.5	+	16102.0i	−0.0419881	+	0.0242418i
$816$		0			0
$817$	−303230.	+	525210.i	−0.454285	+	0.786845i
$818$	−769142.	+	579094.i	−1.14948	+	0.865451i
$819$		0			0
$820$	10653.4	−	37037.9i	0.0158439	−	0.0550832i
$821$	146773.	−	254219.i	0.217751	−	0.377157i	−0.736369	−	0.676580i	$-0.763461\pi$
$821$	146773.	−	254219.i	0.217751	−	0.377157i	0.954120	+	0.299424i	$0.0967945\pi$
$822$		0			0
$823$	198711.	−	114726.i	0.293375	−	0.169380i	−0.346088	−	0.938202i	$-0.612490\pi$
$823$	198711.	−	114726.i	0.293375	−	0.169380i	0.639463	+	0.768822i	$0.279157\pi$
$824$	−539855.	−	438270.i	−0.795102	−	0.645487i
$825$		0			0
$826$	67791.7	+	554003.i	0.0993611	+	0.811992i
$827$		−	673431.i		−	0.984651i	−0.870411	−	0.492326i	$-0.836147\pi$
$827$		−	673431.i		−	0.984651i	0.870411	−	0.492326i	$-0.163853\pi$
$828$		0			0
$829$	268282.			0.390375			0.195188	−	0.980766i	$-0.437468\pi$
$829$	268282.			0.390375			0.195188	+	0.980766i	$0.437468\pi$
$830$	64416.3	−	7882.43i	0.0935060	−	0.0114421i
$831$		0			0
$832$	1.07293e6	+	351546.i	1.54998	+	0.507850i
$833$	−248158.	−	429823.i	−0.357634	−	0.619440i
$834$		0			0
$835$	736.936	+	425.470i	0.00105696	+	0.000610234i
$836$	−8119.18	+	28227.3i	−0.0116172	+	0.0403884i
$837$		0			0
$838$	85204.7	+	113167.i	0.121332	+	0.161151i
$839$	−867924.	−	501096.i	−1.23299	−	0.711865i	−0.265334	−	0.964156i	$-0.585482\pi$
$839$	−867924.	−	501096.i	−1.23299	−	0.711865i	−0.967651	+	0.252292i	$0.918816\pi$
$840$		0			0
$841$	149504.	+	258949.i	0.211379	+	0.366119i
$842$	607780.	+	258283.i	0.857279	+	0.364310i
$843$		0			0
$844$	−264302.	+	254813.i	−0.371035	+	0.357715i
$845$	96307.2			0.134879
$846$		0			0
$847$			338137.i			0.471330i
$848$	−1.19846e6	+	634707.i	−1.66661	+	0.882636i
$849$		0			0
$850$	608011.	+	258381.i	0.841538	+	0.357620i
$851$	−798300.	+	460899.i	−1.10232	+	0.636424i
$852$		0			0
$853$	−205795.	+	356448.i	−0.282837	+	0.489889i	−0.972082	−	0.234640i	$-0.924609\pi$
$853$	−205795.	+	356448.i	−0.282837	+	0.489889i	0.689245	+	0.724528i	$0.257942\pi$
$854$	92771.3	+	123217.i	0.127203	+	0.168949i
$855$		0			0
$856$	−843253.	+	322501.i	−1.15083	+	0.440133i
$857$	−460403.	+	797442.i	−0.626869	+	1.08577i	0.361307	+	0.932447i	$0.382331\pi$
$857$	−460403.	+	797442.i	−0.626869	+	1.08577i	−0.988176	+	0.153322i	$0.951003\pi$
$858$		0			0
$859$	520799.	−	300684.i	0.705804	−	0.407496i	−0.103702	−	0.994608i	$-0.533069\pi$
$859$	520799.	−	300684.i	0.705804	−	0.407496i	0.809505	+	0.587112i	$0.199735\pi$
$860$	−12940.6	−	52084.6i	−0.0174968	−	0.0704226i
$861$		0			0
$862$	641903.	−	78547.8i	0.863883	−	0.105711i
$863$			1.01872e6i			1.36783i	0.729560	+	0.683917i	$0.239725\pi$
$863$			1.01872e6i			1.36783i	−0.729560	+	0.683917i	$0.760275\pi$
$864$		0			0
$865$	38994.9			0.0521166
$866$	−30042.3	−	245510.i	−0.0400588	−	0.327366i
$867$		0			0
$868$	−494115.	+	122765.i	−0.655826	+	0.162943i
$869$	−12839.6	−	22238.9i	−0.0170025	−	0.0294492i
$870$		0			0
$871$	−526036.	−	303707.i	−0.693392	−	0.400330i
$872$	−373294.	−	976063.i	−0.490929	−	1.28365i
$873$		0			0
$874$	−737709.	+	555428.i	−0.965744	+	0.727118i
$875$	50694.1	+	29268.3i	0.0662128	+	0.0382280i
$876$		0			0
$877$	−432672.	−	749411.i	−0.562549	−	0.974363i	−0.997273	−	0.0737993i	$-0.976488\pi$
$877$	−432672.	−	749411.i	−0.562549	−	0.974363i	0.434724	−	0.900564i	$-0.356846\pi$
$878$	484169.	−	1.13933e6i	0.628070	−	1.47795i
$879$		0			0
$880$	−1216.48	−	2296.98i	−0.00157087	−	0.00296615i
$881$	−1.46275e6			−1.88459			−0.942296	−	0.334780i	$-0.891338\pi$
$881$	−1.46275e6			−1.88459			−0.942296	+	0.334780i	$0.891338\pi$
$882$		0			0
$883$			162909.i			0.208941i	0.994528	+	0.104470i	$0.0333148\pi$
$883$			162909.i			0.208941i	−0.994528	+	0.104470i	$0.966685\pi$
$884$	814278.	+	844599.i	1.04200	+	1.08080i
$885$		0			0
$886$	73370.2	−	172652.i	0.0934657	−	0.219940i
$887$	−192525.	+	111154.i	−0.244703	+	0.141280i	−0.617337	−	0.786699i	$-0.711788\pi$
$887$	−192525.	+	111154.i	−0.244703	+	0.141280i	0.372633	+	0.927979i	$0.378455\pi$
$888$		0			0
$889$	242682.	−	420338.i	0.307068	−	0.531857i
$890$	57500.8	−	43292.9i	0.0725929	−	0.0546559i
$891$		0			0
$892$	988102.	+	284213.i	1.24186	+	0.357203i
$893$	65267.1	−	113046.i	0.0818448	−	0.141759i
$894$		0			0
$895$	87627.1	−	50591.5i	0.109394	−	0.0631585i
$896$	122370.	+	358742.i	0.152427	+	0.446854i
$897$		0			0
$898$	60661.2	+	495731.i	0.0752243	+	0.614743i
$899$			878873.i			1.08744i
$900$		0			0
$901$	−1.40918e6			−1.73587
$902$	23542.1	−	2880.78i	0.0289356	−	0.00354077i
$903$		0			0
$904$	476909.	−	587450.i	0.583578	−	0.718844i
$905$	−14186.6	−	24571.9i	−0.0173213	−	0.0300014i
$906$		0			0
$907$	−1.03664e6	−	598505.i	−1.26013	−	0.727534i	−0.287028	−	0.957922i	$-0.592667\pi$
$907$	−1.03664e6	−	598505.i	−1.26013	−	0.727534i	−0.973099	+	0.230388i	$0.926001\pi$
$908$	−103106.	−	29656.8i	−0.125058	−	0.0359711i
$909$		0			0
$910$	31159.7	+	41385.7i	0.0376280	+	0.0499767i
$911$	806036.	+	465365.i	0.971220	+	0.560734i	0.899608	−	0.436698i	$-0.143852\pi$
$911$	806036.	+	465365.i	0.971220	+	0.560734i	0.0716123	+	0.997433i	$0.477186\pi$
$912$		0			0
$913$	19969.1	+	34587.5i	0.0239562	+	0.0414933i
$914$	462001.	+	196332.i	0.553033	+	0.235017i
$915$		0			0
$916$	394788.	+	409489.i	0.470515	+	0.488035i
$917$	−660464.			−0.785435
$918$		0			0
$919$		−	1.46503e6i		−	1.73467i	−0.497725	−	0.867335i	$-0.665831\pi$
$919$		−	1.46503e6i		−	1.73467i	0.497725	−	0.867335i	$-0.334169\pi$
$920$	12883.0	−	80695.6i	0.0152210	−	0.0953398i
$921$		0			0
$922$	380267.	+	161598.i	0.447329	+	0.190097i
$923$	−125160.	+	72261.0i	−0.146913	+	0.0848205i
$924$		0			0
$925$	455160.	−	788360.i	0.531962	−	0.921385i
$926$	−771115.	−	1.02418e6i	−0.899284	−	1.19441i
$927$		0			0
$928$	651923.	−	55685.1i	0.757008	−	0.0646611i
$929$	493591.	−	854925.i	0.571921	−	0.990596i	−0.424448	−	0.905452i	$-0.639532\pi$
$929$	493591.	−	854925.i	0.571921	−	0.990596i	0.996369	−	0.0851437i	$-0.0271349\pi$
$930$		0			0
$931$	−593319.	+	342553.i	−0.684524	+	0.395210i
$932$	969561.	−	240892.i	1.11620	−	0.277326i
$933$		0			0
$934$	−1.69687e6	+	207641.i	−1.94516	+	0.238023i
$935$		−	2700.85i		−	0.00308942i
$936$		0			0
$937$	−287243.			−0.327167			−0.163584	−	0.986529i	$-0.552305\pi$
$937$	−287243.			−0.327167			−0.163584	+	0.986529i	$0.552305\pi$
$938$	−24768.0	−	202407.i	−0.0281504	−	0.230049i
$939$		0			0
$940$	2785.33	+	11210.6i	0.00315226	+	0.0126875i
$941$	−149097.	−	258244.i	−0.168380	−	0.291643i	0.769470	−	0.638683i	$-0.220520\pi$
$941$	−149097.	−	258244.i	−0.168380	−	0.291643i	−0.937850	+	0.347040i	$0.887187\pi$
$942$		0			0
$943$	645766.	+	372833.i	0.726193	+	0.419267i
$944$	−820364.	+	1.30806e6i	−0.920583	+	1.46786i
$945$		0			0
$946$	26385.5	−	19865.9i	0.0294837	−	0.0221986i
$947$	−904210.	−	522046.i	−1.00825	−	0.582115i	−0.0975732	−	0.995228i	$-0.531108\pi$
$947$	−904210.	−	522046.i	−1.00825	−	0.582115i	−0.910680	+	0.413113i	$0.864441\pi$
$948$		0			0
$949$	205674.	+	356238.i	0.228374	+	0.395555i
$950$	356664.	−	839287.i	0.395195	−	0.929957i
$951$		0			0
$952$	−62093.0	+	388933.i	−0.0685124	+	0.429142i
$953$	1.38691e6			1.52708			0.763539	−	0.645762i	$-0.223460\pi$
$953$	1.38691e6			1.52708			0.763539	+	0.645762i	$0.223460\pi$
$954$		0			0
$955$			63305.1i			0.0694115i
$956$	43234.4	−	41682.3i	0.0473058	−	0.0456075i
$957$		0			0
$958$	300468.	−	707049.i	0.327391	−	0.770404i
$959$	12399.2	−	7158.71i	0.0134821	−	0.00778391i
$960$		0			0
$961$	484199.	−	838657.i	0.524297	−	0.908109i
$962$	1.29148e6	−	972367.i	1.39552	−	1.05070i
$963$		0			0
$964$	−396576.	+	1.37874e6i	−0.426748	+	1.48364i
$965$	−27413.5	+	47481.5i	−0.0294381	+	0.0509882i
$966$		0			0
$967$	−697159.	+	402505.i	−0.745554	+	0.430446i	−0.824085	−	0.566466i	$-0.808310\pi$
$967$	−697159.	+	402505.i	−0.745554	+	0.430446i	0.0785311	+	0.996912i	$0.474977\pi$
$968$	−589578.	+	726234.i	−0.629203	+	0.775043i
$969$		0			0
$970$	6728.00	+	54982.1i	0.00715060	+	0.0584356i
$971$		−	643421.i		−	0.682428i	−0.939986	−	0.341214i	$-0.889162\pi$
$971$		−	643421.i		−	0.682428i	0.939986	−	0.341214i	$-0.110838\pi$
$972$		0			0
$973$	−449321.			−0.474604
$974$	209974.	−	25693.9i	0.221334	−	0.0270840i
$975$		0			0
$976$	−15592.6	+	426397.i	−0.0163688	+	0.447625i
$977$	−63505.8	−	109995.i	−0.0665311	−	0.115235i	0.830841	−	0.556510i	$-0.187860\pi$
$977$	−63505.8	−	109995.i	−0.0665311	−	0.115235i	−0.897372	+	0.441275i	$0.854526\pi$
$978$		0			0
$979$	38360.8	+	22147.6i	0.0400241	+	0.0231079i
$980$	16759.2	−	58265.3i	0.0174502	−	0.0606678i
$981$		0			0
$982$	17693.7	+	23500.5i	0.0183483	+	0.0243699i
$983$	158662.	+	91603.6i	0.164197	+	0.0947994i	0.579847	−	0.814725i	$-0.303112\pi$
$983$	158662.	+	91603.6i	0.164197	+	0.0947994i	−0.415650	+	0.909525i	$0.636446\pi$
$984$		0			0
$985$	10577.4	+	18320.6i	0.0109020	+	0.0188828i
$986$	625723.	+	265907.i	0.643618	+	0.273512i
$987$		0			0
$988$	1.16587e6	−	1.12401e6i	1.19436	−	1.15148i
$989$	1.03837e6			1.06160
$990$		0			0
$991$		−	684255.i		−	0.696740i	−0.937357	−	0.348370i	$-0.886735\pi$
$991$		−	684255.i		−	0.696740i	0.937357	−	0.348370i	$-0.113265\pi$
$992$	−1.27529e6	−	597874.i	−1.29594	−	0.607556i
$993$		0			0
$994$	−44653.2	−	18975.8i	−0.0451939	−	0.0192056i
$995$	14842.1	−	8569.07i	0.0149916	−	0.00865541i
$996$		0			0
$997$	271816.	−	470800.i	0.273455	−	0.473637i	−0.696289	−	0.717761i	$-0.745167\pi$
$997$	271816.	−	470800.i	0.273455	−	0.473637i	0.969744	+	0.244124i	$0.0785003\pi$
$998$	998582.	+	1.32630e6i	1.00259	+	1.33162i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.19.12		44
3.2	odd	2		36.5.f.a.7.11	✓	44
4.3	odd	2	inner	108.5.f.a.19.3		44
9.2	odd	6		324.5.d.f.163.6		22
9.4	even	3	inner	108.5.f.a.91.3		44
9.5	odd	6		36.5.f.a.31.20	yes	44
9.7	even	3		324.5.d.e.163.17		22
12.11	even	2		36.5.f.a.7.20	yes	44
36.7	odd	6		324.5.d.e.163.18		22
36.11	even	6		324.5.d.f.163.5		22
36.23	even	6		36.5.f.a.31.11	yes	44
36.31	odd	6	inner	108.5.f.a.91.12		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.11	✓	44	3.2	odd	2
36.5.f.a.7.20	yes	44	12.11	even	2
36.5.f.a.31.11	yes	44	36.23	even	6
36.5.f.a.31.20	yes	44	9.5	odd	6
108.5.f.a.19.3		44	4.3	odd	2	inner
108.5.f.a.19.12		44	1.1	even	1	trivial
108.5.f.a.91.3		44	9.4	even	3	inner
108.5.f.a.91.12		44	36.31	odd	6	inner
324.5.d.e.163.17		22	9.7	even	3
324.5.d.e.163.18		22	36.7	odd	6
324.5.d.f.163.5		22	36.11	even	6
324.5.d.f.163.6		22	9.2	odd	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)

\(f(q)\)	\(=\)	\(q+(0.485844 + 3.97038i) q^{2} +(-15.5279 + 3.85798i) q^{4} +(-1.01545 - 1.75881i) q^{5} +(-20.0352 - 11.5673i) q^{7} +(-22.8618 - 59.7774i) q^{8} +O(q^{10})\)	\(q+(0.485844 + 3.97038i) q^{2} +(-15.5279 + 3.85798i) q^{4} +(-1.01545 - 1.75881i) q^{5} +(-20.0352 - 11.5673i) q^{7} +(-22.8618 - 59.7774i) q^{8} +(6.48981 - 4.88624i) q^{10} +(4.32958 + 2.49968i) q^{11} +(-137.824 - 238.718i) q^{13} +(36.1928 - 85.1675i) q^{14} +(226.232 - 119.813i) q^{16} +266.009 q^{17} -367.194i q^{19} +(22.5533 + 23.3931i) q^{20} +(-7.82120 + 18.4045i) q^{22} +(-544.473 + 314.352i) q^{23} +(310.438 - 537.694i) q^{25} +(880.842 - 663.194i) q^{26} +(355.732 + 102.321i) q^{28} +(319.481 - 553.357i) q^{29} +(-1191.19 + 687.735i) q^{31} +(585.616 + 840.018i) q^{32} +(129.239 + 1056.16i) q^{34} +46.9843i q^{35} +1466.19 q^{37} +(1457.90 - 178.399i) q^{38} +(-81.9222 + 100.911i) q^{40} +(-593.019 - 1027.14i) q^{41} +(-1430.33 - 825.804i) q^{43} +(-76.8730 - 22.1114i) q^{44} +(-1512.63 - 2009.04i) q^{46} +(307.864 + 177.745i) q^{47} +(-932.893 - 1615.82i) q^{49} +(2285.68 + 971.322i) q^{50} +(3061.09 + 3175.07i) q^{52} -5297.49 q^{53} -10.1532i q^{55} +(-233.424 + 1462.10i) q^{56} +(2352.26 + 999.617i) q^{58} +(-5223.32 + 3015.68i) q^{59} +(-833.364 + 1443.43i) q^{61} +(-3309.31 - 4395.36i) q^{62} +(-3050.68 + 2733.24i) q^{64} +(-279.907 + 484.814i) q^{65} +(1908.36 - 1101.79i) q^{67} +(-4130.57 + 1026.26i) q^{68} +(-186.546 + 22.8270i) q^{70} -524.299i q^{71} -1492.29 q^{73} +(712.338 + 5821.33i) q^{74} +(1416.63 + 5701.76i) q^{76} +(-57.8293 - 100.163i) q^{77} +(-4448.35 - 2568.25i) q^{79} +(-440.456 - 276.236i) q^{80} +(3790.02 - 2853.54i) q^{82} +(6918.39 + 3994.33i) q^{83} +(-270.120 - 467.861i) q^{85} +(2583.84 - 6080.19i) q^{86} +(50.4426 - 315.958i) q^{88} +8860.17 q^{89} +6377.03i q^{91} +(7241.77 - 6981.79i) q^{92} +(-556.144 + 1308.70i) q^{94} +(-645.826 + 372.868i) q^{95} +(-3409.33 + 5905.14i) q^{97} +(5962.18 - 4488.98i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 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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