LMFDB - Embedded newform 108.5.f.a.19.3

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			19.3
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.68138 + 1.56444i) q^{2} +(11.1051 - 11.5186i) q^{4} +(-1.01545 - 1.75881i) q^{5} +(20.0352 + 11.5673i) q^{7} +(-22.8618 + 59.7774i) q^{8} +O(q^{10})$	\(q+(-3.68138 + 1.56444i) q^{2} +(11.1051 - 11.5186i) q^{4} +(-1.01545 - 1.75881i) q^{5} +(20.0352 + 11.5673i) q^{7} +(-22.8618 + 59.7774i) q^{8} +(6.48981 + 4.88624i) q^{10} +(-4.32958 - 2.49968i) q^{11} +(-137.824 - 238.718i) q^{13} +(-91.8536 - 11.2399i) q^{14} +(-9.35520 - 255.829i) q^{16} +266.009 q^{17} +367.194i q^{19} +(-31.5357 - 7.83518i) q^{20} +(19.8494 + 2.42891i) q^{22} +(544.473 - 314.352i) q^{23} +(310.438 - 537.694i) q^{25} +(880.842 + 663.194i) q^{26} +(355.732 - 102.321i) q^{28} +(319.481 - 553.357i) q^{29} +(1191.19 - 687.735i) q^{31} +(434.669 + 927.167i) q^{32} +(-979.280 + 416.155i) q^{34} -46.9843i q^{35} +1466.19 q^{37} +(-574.453 - 1351.78i) q^{38} +(128.352 - 20.4914i) q^{40} +(-593.019 - 1027.14i) q^{41} +(1430.33 + 825.804i) q^{43} +(-76.8730 + 22.1114i) q^{44} +(-1512.63 + 2009.04i) q^{46} +(-307.864 - 177.745i) q^{47} +(-932.893 - 1615.82i) q^{49} +(-301.649 + 2465.11i) q^{50} +(-4280.24 - 1063.44i) q^{52} -5297.49 q^{53} +10.1532i q^{55} +(-1149.51 + 933.203i) q^{56} +(-310.436 + 2536.92i) q^{58} +(5223.32 - 3015.68i) q^{59} +(-833.364 + 1443.43i) q^{61} +(-3309.31 + 4395.36i) q^{62} +(-3050.68 - 2733.24i) q^{64} +(-279.907 + 484.814i) q^{65} +(-1908.36 + 1101.79i) q^{67} +(2954.05 - 3064.05i) q^{68} +(73.5040 + 172.967i) q^{70} +524.299i q^{71} -1492.29 q^{73} +(-5397.59 + 2293.76i) q^{74} +(4229.55 + 4077.71i) q^{76} +(-57.8293 - 100.163i) q^{77} +(4448.35 + 2568.25i) q^{79} +(-440.456 + 276.236i) q^{80} +(3790.02 + 2853.54i) q^{82} +(-6918.39 - 3994.33i) q^{83} +(-270.120 - 467.861i) q^{85} +(-6557.52 - 802.424i) q^{86} +(248.406 - 201.664i) q^{88} +8860.17 q^{89} -6377.03i q^{91} +(2425.53 - 9762.46i) q^{92} +(1411.44 + 172.713i) q^{94} +(645.826 - 372.868i) q^{95} +(-3409.33 + 5905.14i) q^{97} +(5962.18 + 4488.98i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.68138	+	1.56444i	−0.920344	+	0.391110i
$2$	−3.68138	+	1.56444i	−0.920344	+	0.391110i
$3$		0			0
$3$		0			0
$4$	11.1051	−	11.5186i	0.694066	−	0.719911i
$5$	−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	0.690309	−	0.723514i	$-0.257474\pi$
$7$	20.0352	+	11.5673i	0.408882	+	0.236068i	−0.281427	+	0.959583i	$0.590808\pi$
$8$	−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	0.482002	−	0.876170i	$-0.339910\pi$
$11$	−4.32958	−	2.49968i	−0.0357816	−	0.0206585i	−0.517784	+	0.855511i	$0.673243\pi$
$12$		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	$-0.470219\pi$
$14$	−91.8536	−	11.2399i	−0.468641	−	0.0573462i
$15$		0			0
$16$	−9.35520	−	255.829i	−0.0365438	−	0.999332i
$17$	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	$0.169829\pi$
$19$			367.194i			1.01716i	−0.861015	+	0.508579i	$0.830171\pi$
$20$	−31.5357	−	7.83518i	−0.0788392	−	0.0195879i
$21$		0			0
$22$	19.8494	+	2.42891i	0.0410111	+	0.00501841i
$23$	544.473	−	314.352i	1.02925	−	0.594238i	0.112481	−	0.993654i	$-0.464120\pi$
$23$	544.473	−	314.352i	1.02925	−	0.594238i	0.916770	+	0.399416i	$0.130787\pi$
$24$		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	0.270535	−	0.962710i	$-0.412799\pi$
$31$	1191.19	−	687.735i	1.23953	−	0.715645i	0.968999	+	0.247065i	$0.0794660\pi$
$32$	434.669	+	927.167i	0.424481	+	0.905437i
$33$		0			0
$34$	−979.280	+	416.155i	−0.847128	+	0.359996i
$35$		−	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	$0.320125\pi$
$38$	−574.453	−	1351.78i	−0.397820	−	0.936135i
$39$		0			0
$40$	128.352	−	20.4914i	0.0802202	−	0.0128071i
$41$	−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	0.834147	−	0.551542i	$-0.185960\pi$
$43$	1430.33	+	825.804i	0.773572	+	0.446622i	−0.0605755	+	0.998164i	$0.519294\pi$
$44$	−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	0.428695	−	0.903449i	$-0.358974\pi$
$47$	−307.864	−	177.745i	−0.139368	−	0.0804642i	−0.568063	+	0.822985i	$0.692307\pi$
$48$		0			0
$49$	−932.893	−	1615.82i	−0.388544	−	0.672977i
$50$	−301.649	+	2465.11i	−0.120660	+	0.986046i
$51$		0			0
$52$	−4280.24	−	1063.44i	−1.58293	−	0.393286i
$53$	−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
$56$	−1149.51	+	933.203i	−0.366552	+	0.297578i
$57$		0			0
$58$	−310.436	+	2536.92i	−0.0922818	+	0.754139i
$59$	5223.32	−	3015.68i	1.50052	−	0.866327i	0.500522	−	0.865724i	$-0.333141\pi$
$59$	5223.32	−	3015.68i	1.50052	−	0.866327i	1.00000		0.000603027i	$-0.000191950\pi$
$60$		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	−0.697265	−	0.716813i	$-0.745600\pi$
$67$	−1908.36	+	1101.79i	−0.425119	+	0.245443i	0.272146	+	0.962256i	$0.412267\pi$
$68$	2954.05	−	3064.05i	0.638852	−	0.662640i
$69$		0			0
$70$	73.5040	+	172.967i	0.0150008	+	0.0352993i
$71$			524.299i			0.104007i	0.998647	+	0.0520035i	$0.0165607\pi$
$71$			524.299i			0.104007i	−0.998647	+	0.0520035i	$0.983439\pi$
$72$		0			0
$73$	−1492.29			−0.280032			−0.140016	−	0.990149i	$-0.544715\pi$
$73$	−1492.29			−0.280032			−0.140016	+	0.990149i	$0.544715\pi$
$74$	−5397.59	+	2293.76i	−0.985680	+	0.418875i
$75$		0			0
$76$	4229.55	+	4077.71i	0.732263	+	0.705975i
$77$	−57.8293	−	100.163i	−0.00975364	−	0.0168938i
$78$		0			0
$79$	4448.35	+	2568.25i	0.712762	+	0.411513i	0.812083	−	0.583542i	$-0.198334\pi$
$79$	4448.35	+	2568.25i	0.712762	+	0.411513i	−0.0993209	+	0.995055i	$0.531667\pi$
$80$	−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	−0.0947580	−	0.995500i	$-0.530208\pi$
$83$	−6918.39	−	3994.33i	−1.00427	−	0.579813i	−0.909508	+	0.415687i	$0.863541\pi$
$84$		0			0
$85$	−270.120	−	467.861i	−0.0373868	−	0.0647558i
$86$	−6557.52	−	802.424i	−0.886630	−	0.108494i
$87$		0			0
$88$	248.406	−	201.664i	0.0320773	−	0.0260413i
$89$	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
$92$	2425.53	−	9762.46i	0.286570	−	1.15341i
$93$		0			0
$94$	1411.44	+	172.713i	0.159737	+	0.0195465i
$95$	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	−0.872934	−	0.487838i	$-0.837786\pi$
$103$	−9409.35	+	5432.49i	−0.886922	+	0.512065i	−0.0139875	+	0.999902i	$0.504453\pi$
$104$	17420.9	−	2781.23i	1.61066	−	0.257141i
$105$		0			0
$106$	19502.1	−	8287.61i	1.73568	−	0.737594i
$107$			14106.5i			1.23212i	0.787699	+	0.616060i	$0.211272\pi$
$107$			14106.5i			1.23212i	−0.787699	+	0.616060i	$0.788728\pi$
$108$		0			0
$109$	16328.3			1.37432			0.687160	−	0.726506i	$-0.258857\pi$
$109$	16328.3			1.37432			0.687160	+	0.726506i	$0.258857\pi$
$110$	−15.8841	−	37.3778i	−0.00131273	−	0.00308908i
$111$		0			0
$112$	2771.83	−	5233.81i	0.220968	−	0.417236i
$113$	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
$122$	809.770	−	6617.55i	0.0544054	−	0.444608i
$123$		0			0
$124$	5306.53	−	21358.2i	0.345118	−	1.38906i
$125$	−2530.25			−0.161936
$126$		0			0
$127$		−	20979.9i		−	1.30076i	−0.759609	−	0.650379i	$-0.774610\pi$
$127$		−	20979.9i		−	1.30076i	0.759609	−	0.650379i	$-0.225390\pi$
$128$	15506.7	+	5289.48i	0.946452	+	0.322844i
$129$		0			0
$130$	271.983	−	2222.68i	0.0160936	−	0.131519i
$131$	−24723.9	+	14274.3i	−1.44070	+	0.831789i	−0.997896	−	0.0648298i	$-0.979350\pi$
$131$	−24723.9	+	14274.3i	−1.44070	+	0.831789i	−0.442804	+	0.896618i	$0.646016\pi$
$132$		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	−0.867532	−	0.497382i	$-0.834295\pi$
$139$	−16819.9	+	9710.99i	−0.870552	+	0.502613i	−0.00302027	+	0.999995i	$0.500961\pi$
$140$	−541.192	−	521.763i	−0.0276118	−	0.0266206i
$141$		0			0
$142$	−820.234	−	1930.14i	−0.0406781	−	0.0957222i
$143$			1378.07i			0.0673903i
$144$		0			0
$145$	−1297.67			−0.0617203
$146$	5493.69	−	2334.60i	0.257726	−	0.109523i
$147$		0			0
$148$	16282.1	−	16888.4i	0.743339	−	0.771018i
$149$	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	0.415321	−	0.909675i	$-0.363669\pi$
$151$	−3758.08	−	2169.73i	−0.164821	−	0.0951593i	−0.580141	+	0.814516i	$0.697003\pi$
$152$	−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	$0.793144\pi$
$158$	−20393.9	−	2495.54i	−0.816933	−	0.0999657i
$159$		0			0
$160$	1189.33	−	1705.99i	0.0464582	−	0.0666404i
$161$	14544.9			0.561123
$162$		0			0
$163$			15857.0i			0.596824i	0.954437	+	0.298412i	$0.0964569\pi$
$163$			15857.0i			0.596824i	−0.954437	+	0.298412i	$0.903543\pi$
$164$	−18416.7	−	4575.71i	−0.684737	−	0.170126i
$165$		0			0
$166$	31718.1	+	3881.25i	1.15104	+	0.140849i
$167$	362.861	−	209.498i	0.0130109	−	0.00751186i	−0.493480	−	0.869757i	$-0.664276\pi$
$167$	362.861	−	209.498i	0.0130109	−	0.00751186i	0.506491	+	0.862245i	$0.330942\pi$
$168$		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
$176$	−598.987	+	1131.02i	−0.0193371	+	0.0365127i
$177$		0			0
$178$	−32617.6	+	13861.2i	−1.02947	+	0.437482i
$179$		−	49821.7i		−	1.55494i	−0.628922	−	0.777468i	$-0.716504\pi$
$179$		−	49821.7i		−	1.55494i	0.628922	−	0.777468i	$-0.283496\pi$
$180$		0			0
$181$	13970.7			0.426443			0.213222	−	0.977004i	$-0.431604\pi$
$181$	13970.7			0.426443			0.213222	+	0.977004i	$0.431604\pi$
$182$	9976.48	+	23476.3i	0.301186	+	0.708738i
$183$		0			0
$184$	6343.50	+	39733.9i	0.187367	+	1.17361i
$185$	−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	0.822058	−	0.569404i	$-0.192826\pi$
$191$	26994.8	+	15585.5i	0.739969	+	0.427221i	−0.0820893	+	0.996625i	$0.526159\pi$
$192$		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	$0.951368\pi$
$194$	3312.81	−	27072.7i	0.0880224	−	0.719331i
$195$		0			0
$196$	−28971.8	−	7198.16i	−0.754159	−	0.187374i
$197$	−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	$-0.966021\pi$
$199$		−	8438.68i		−	0.213093i	0.994308	−	0.106546i	$-0.0339793\pi$
$200$	25044.8	+	30849.8i	0.626119	+	0.771245i
$201$		0			0
$202$	−1501.77	+	12272.7i	−0.0368045	+	0.300771i
$203$	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	−0.706284	−	0.707929i	$-0.749630\pi$
$211$	−19871.6	+	11472.8i	−0.446341	+	0.257695i	0.259943	+	0.965624i	$0.416296\pi$
$212$	−58829.0	+	61019.6i	−1.30894	+	1.35768i
$213$		0			0
$214$	−22068.8	−	51931.5i	−0.481894	−	1.13397i
$215$		−	3354.25i		−	0.0725637i
$216$		0			0
$217$	31821.1			0.675764
$218$	−60110.6	+	25544.6i	−1.26485	+	0.537510i
$219$		0			0
$220$	116.951	+	112.752i	0.00241634	+	0.00232959i
$221$	−36662.5	−	63501.3i	−0.750650	−	1.30016i
$222$		0			0
$223$	55651.0	+	32130.1i	1.11909	+	0.646105i	0.941167	−	0.337941i	$-0.109730\pi$
$223$	55651.0	+	32130.1i	1.11909	+	0.646105i	0.177919	+	0.984045i	$0.443064\pi$
$224$	−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	0.442593	−	0.896722i	$-0.354059\pi$
$227$	−5807.02	−	3352.69i	−0.112694	−	0.0650641i	−0.555288	+	0.831658i	$0.687392\pi$
$228$		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	$0.943407\pi$
$230$	5069.53	+	620.344i	0.0958323	+	0.0117267i
$231$		0			0
$232$	25774.4	+	31748.5i	0.478864	+	0.589857i
$233$	−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
$236$	23268.9	−	93654.5i	0.417784	−	1.68153i
$237$		0			0
$238$	−24433.9	−	2989.91i	−0.431359	−	0.0527841i
$239$	3250.59	−	1876.73i	0.0569070	−	0.0328553i	−0.471277	−	0.881985i	$-0.656207\pi$
$239$	3250.59	−	1876.73i	0.0569070	−	0.0328553i	0.528184	+	0.849130i	$0.322873\pi$
$240$		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
$248$	13878.2	+	86929.3i	0.225647	+	1.41339i
$249$		0			0
$250$	9314.81	−	3958.42i	0.149037	−	0.0633348i
$251$		−	9246.49i		−	0.146767i	−0.997304	−	0.0733836i	$-0.976620\pi$
$251$		−	9246.49i		−	0.146767i	0.997304	−	0.0733836i	$-0.0233798\pi$
$252$		0			0
$253$	−3143.12			−0.0491043
$254$	32821.8	+	77235.1i	0.508739	+	1.19715i
$255$		0			0
$256$	−65361.0	+	4786.66i	−0.997329	+	0.0730387i
$257$	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	0.979293	−	0.202448i	$-0.0648896\pi$
$263$	89478.0	+	51660.2i	1.29361	+	0.746869i	0.314322	+	0.949317i	$0.398223\pi$
$264$		0			0
$265$	5379.35	+	9317.30i	0.0766016	+	0.132678i
$266$	4127.21	−	33728.1i	0.0583301	−	0.476682i
$267$		0			0
$268$	−8501.38	+	34217.1i	−0.118364	+	0.476402i
$269$	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	$-0.966066\pi$
$271$		−	15629.0i		−	0.212810i	0.994323	−	0.106405i	$-0.0339340\pi$
$272$	−2488.57	−	68052.9i	−0.0336366	−	0.919833i
$273$		0			0
$274$	300.676	−	2457.16i	0.00400495	−	0.0327290i
$275$	−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	−0.904121	−	0.427278i	$-0.859473\pi$
$283$	−78979.6	+	45598.9i	−0.986148	+	0.569353i	−0.0820271	+	0.996630i	$0.526139\pi$
$284$	6039.18	+	5822.37i	0.0748758	+	0.0721877i
$285$		0			0
$286$	−2155.90	−	5073.18i	−0.0263570	−	0.0620223i
$287$		−	27438.6i		−	0.333118i
$288$		0			0
$289$	−12760.0			−0.152776
$290$	4777.21	−	2030.12i	0.0568039	−	0.0241394i
$291$		0			0
$292$	−16572.0	+	17189.1i	−0.194361	+	0.201598i
$293$	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
$302$	17229.3	+	2108.30i	0.188910	+	0.0231163i
$303$		0			0
$304$	93938.9	−	3435.17i	1.01648	−	0.0371708i
$305$	3384.96			0.0363876
$306$		0			0
$307$			65201.8i			0.691803i	0.938271	+	0.345902i	$0.112427\pi$
$307$			65201.8i			0.691803i	−0.938271	+	0.345902i	$0.887573\pi$
$308$	−1795.94	−	446.209i	−0.0189317	−	0.00470367i
$309$		0			0
$310$	11091.1	+	1357.18i	0.115412	+	0.0141226i
$311$	115786.	−	66849.3i	1.19712	−	0.691156i	0.237206	−	0.971459i	$-0.423768\pi$
$311$	115786.	−	66849.3i	1.19712	−	0.691156i	0.959911	+	0.280303i	$0.0904350\pi$
$312$		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
$320$	−1709.44	+	8141.04i	−0.0166938	+	0.0795023i
$321$		0			0
$322$	−53545.1	+	22754.5i	−0.516426	+	0.219461i
$323$			97677.0i			0.936240i
$324$		0			0
$325$	−171143.			−1.62029
$326$	−24807.3	−	58375.6i	−0.233424	−	0.549283i
$327$		0			0
$328$	74957.2	−	11966.9i	0.696732	−	0.111233i
$329$	−4112.08	−	7122.34i	−0.0379901	−	0.0658007i
$330$		0			0
$331$	−64736.6	−	37375.7i	−0.590873	−	0.341141i	0.174570	−	0.984645i	$-0.444147\pi$
$331$	−64736.6	−	37375.7i	−0.590873	−	0.341141i	−0.765443	+	0.643504i	$0.777480\pi$
$332$	−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	$0.618689\pi$
$338$	23039.2	−	188279.i	0.201666	−	1.64804i
$339$		0			0
$340$	−8388.78	−	2084.23i	−0.0725673	−	0.0180297i
$341$	−6876.48			−0.0591367
$342$		0			0
$343$		−	98710.7i		−	0.839027i
$344$	−82064.4	+	66622.3i	−0.693487	+	0.562993i
$345$		0			0
$346$	9328.60	−	76234.5i	0.0779227	−	0.636795i
$347$	−158508.	+	91514.6i	−1.31641	+	0.760032i	−0.983150	−	0.182802i	$-0.941483\pi$
$347$	−158508.	+	91514.6i	−1.31641	+	0.760032i	−0.333264	+	0.942834i	$0.608150\pi$
$348$		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
$356$	98392.7	−	102056.i	0.776359	−	0.805268i
$357$		0			0
$358$	77943.1	+	183413.i	0.608151	+	1.43108i
$359$			161179.i			1.25060i	0.780385	+	0.625300i	$0.215023\pi$
$359$			161179.i			1.25060i	−0.780385	+	0.625300i	$0.784977\pi$
$360$		0			0
$361$	−4510.46			−0.0346104
$362$	−51431.4	+	21856.3i	−0.392474	+	0.166786i
$363$		0			0
$364$	−73454.3	−	70817.3i	−0.554389	−	0.534487i
$365$	1515.35	+	2624.66i	0.0113744	+	0.0197010i
$366$		0			0
$367$	−172828.	−	99782.5i	−1.28317	−	0.740836i	−0.305740	−	0.952115i	$-0.598904\pi$
$367$	−172828.	−	99782.5i	−1.28317	−	0.740836i	−0.977426	+	0.211279i	$0.932237\pi$
$368$	−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	$0.826711\pi$
$374$	5280.12	+	646.113i	0.0377486	+	0.00461919i
$375$		0			0
$376$	17663.5	−	14339.7i	0.124940	−	0.101430i
$377$	−176129.			−1.23922
$378$		0			0
$379$			217930.i			1.51719i	0.651565	+	0.758593i	$0.274113\pi$
$379$			217930.i			1.51719i	−0.651565	+	0.758593i	$0.725887\pi$
$380$	2877.03	−	11579.7i	0.0199240	−	0.0801919i
$381$		0			0
$382$	−123760.	−	15144.2i	−0.848116	−	0.103781i
$383$	60187.2	−	34749.1i	0.410305	−	0.236890i	−0.280616	−	0.959820i	$-0.590539\pi$
$383$	60187.2	−	34749.1i	0.410305	−	0.236890i	0.690921	+	0.722930i	$0.257205\pi$
$384$		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
$392$	117917.	−	18825.4i	0.767369	−	0.122510i
$393$		0			0
$394$	38346.8	−	16295.9i	0.247023	−	0.104975i
$395$		−	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	$0.486610\pi$
$398$	13201.8	+	31066.0i	0.0833426	+	0.196119i
$399$		0			0
$400$	−140462.	−	74388.7i	−0.877887	−	0.464930i
$401$	−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	$0.577738\pi$
$410$	1170.27	−	9563.57i	0.00696173	−	0.0568922i
$411$		0			0
$412$	−41916.9	+	168711.i	−0.246942	+	0.993912i
$413$	139534.			0.818049
$414$		0			0
$415$			16224.2i			0.0942035i
$416$	161424.	−	231549.i	0.932784	−	1.33800i
$417$		0			0
$418$	−891.882	+	7288.58i	−0.00510452	+	0.0417148i
$419$	−30669.6	+	17707.1i	−0.174695	+	0.100860i	−0.584798	−	0.811179i	$-0.698826\pi$
$419$	−30669.6	+	17707.1i	−0.174695	+	0.100860i	0.410103	+	0.912039i	$0.365493\pi$
$420$		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
$428$	162487.	+	156654.i	0.887017	+	0.855173i
$429$		0			0
$430$	5247.53	+	12348.3i	0.0283803	+	0.0667835i
$431$			161673.i			0.870327i	0.900351	+	0.435163i	$0.143309\pi$
$431$			161673.i			0.870327i	−0.900351	+	0.435163i	$0.856691\pi$
$432$		0			0
$433$	−61835.3			−0.329808			−0.164904	−	0.986310i	$-0.552731\pi$
$433$	−61835.3			−0.329808			−0.164904	+	0.986310i	$0.552731\pi$
$434$	−117145.	+	49782.1i	−0.621936	+	0.264298i
$435$		0			0
$436$	181327.	−	188079.i	0.953869	−	0.989388i
$437$	115428.	+	199927.i	0.604434	+	1.04691i
$438$		0			0
$439$	268021.	+	154742.i	1.39072	+	0.802933i	0.993395	−	0.114744i	$-0.0366049\pi$
$439$	268021.	+	154742.i	1.39072	+	0.802933i	0.397326	+	0.917677i	$0.369938\pi$
$440$	−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	0.599897	−	0.800077i	$-0.295208\pi$
$443$	40615.5	+	23449.4i	0.206959	+	0.119488i	−0.392938	+	0.919565i	$0.628541\pi$
$444$		0			0
$445$	−8997.07	−	15583.4i	−0.0454340	−	0.0786940i
$446$	−255138.	−	31220.5i	−1.28264	−	0.156953i
$447$		0			0
$448$	−29504.7	−	90049.2i	−0.147006	−	0.448667i
$449$	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
$452$	183585.	+	45612.4i	0.898585	+	0.223257i
$453$		0			0
$454$	26622.9	+	3257.77i	0.129165	+	0.0158055i
$455$	−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	0.315297	−	0.948993i	$-0.397896\pi$
$463$	277564.	−	160252.i	1.29480	−	0.747552i	0.979501	+	0.201442i	$0.0645626\pi$
$464$	−144554.	−	76555.7i	−0.671418	−	0.355584i
$465$		0			0
$466$	229865.	−	97683.4i	1.05852	−	0.449831i
$467$		−	427381.i		−	1.95967i	−0.199820	−	0.979833i	$-0.564036\pi$
$467$		−	427381.i		−	1.95967i	0.199820	−	0.979833i	$-0.435964\pi$
$468$		0			0
$469$	−50979.2			−0.231765
$470$	−1129.47	−	2657.83i	−0.00511305	−	0.0120318i
$471$		0			0
$472$	60855.3	+	381180.i	0.273158	+	1.71099i
$473$	−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	0.816566	−	0.577252i	$-0.195875\pi$
$479$	166330.	+	96030.5i	0.724935	+	0.418541i	−0.0916316	+	0.995793i	$0.529208\pi$
$480$		0			0
$481$	−202076.	−	350006.i	−0.873422	−	1.51281i
$482$	−43563.3	+	356005.i	−0.187511	+	1.53237i
$483$		0			0
$484$	−226956.	−	56388.2i	−0.968838	−	0.240712i
$485$	13848.1			0.0588715
$486$		0			0
$487$			52885.1i			0.222985i	0.993765	+	0.111492i	$0.0355631\pi$
$487$			52885.1i			0.222985i	−0.993765	+	0.111492i	$0.964437\pi$
$488$	−67232.2	−	82815.7i	−0.282317	−	0.347755i
$489$		0			0
$490$	1840.98	−	15044.7i	0.00766754	−	0.0626602i
$491$	−6368.89	+	3677.08i	−0.0264180	+	0.0152525i	−0.513151	−	0.858298i	$-0.671522\pi$
$491$	−6368.89	+	3677.08i	−0.0264180	+	0.0152525i	0.486733	+	0.873551i	$0.338189\pi$
$492$		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	−0.998084	−	0.0618804i	$-0.980290\pi$
$499$	−359442.	+	207524.i	−1.44354	+	0.833426i	−0.445452	+	0.895306i	$0.646957\pi$
$500$	−28098.6	+	29144.9i	−0.112394	+	0.116580i
$501$		0			0
$502$	14465.6	+	34039.8i	0.0574021	+	0.135076i
$503$		−	53242.3i		−	0.210436i	−0.994449	−	0.105218i	$-0.966446\pi$
$503$		−	53242.3i		−	0.210436i	0.994449	−	0.105218i	$-0.0335541\pi$
$504$		0			0
$505$	−6277.63			−0.0246157
$506$	11571.0	−	4917.22i	0.0451929	−	0.0192052i
$507$		0			0
$508$	−241659.	−	232984.i	−0.936431	−	0.902813i
$509$	−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
$518$	−134675.	−	16479.7i	−0.501910	−	0.0614173i
$519$		0			0
$520$	−22581.7	−	27815.8i	−0.0835123	−	0.102869i
$521$	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	$0.0688980\pi$
$523$			117488.i			0.429527i	−0.976666	+	0.214763i	$0.931102\pi$
$524$	−110140.	+	443301.i	−0.401128	+	1.61449i
$525$		0			0
$526$	−410222.	−	50197.6i	−1.48268	−	0.181431i
$527$	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
$536$	−22233.7	−	139266.i	−0.0773896	−	0.484747i
$537$		0			0
$538$	−316664.	+	134570.i	−1.09404	+	0.464925i
$539$			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	$0.508953\pi$
$542$	24450.6	+	57536.2i	0.0832322	+	0.195859i
$543$		0			0
$544$	115626.	+	246635.i	0.390713	+	0.833407i
$545$	−16580.6	−	28718.4i	−0.0558222	−	0.0966869i
$546$		0			0
$547$	337391.	+	194793.i	1.12761	+	0.651026i	0.943333	−	0.331848i	$-0.107672\pi$
$547$	337391.	+	194793.i	1.12761	+	0.651026i	0.184277	+	0.982874i	$0.441006\pi$
$548$	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
$554$	−27505.9	+	224782.i	−0.0896202	+	0.732388i
$555$		0			0
$556$	−74929.6	+	301583.i	−0.242384	+	0.975567i
$557$	−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
$560$	−12019.9	+	439.547i	−0.0383289	+	0.00140162i
$561$		0			0
$562$	−53961.3	+	440979.i	−0.170848	+	1.39619i
$563$	−192477.	+	111127.i	−0.607244	+	0.350592i	−0.771886	−	0.635761i	$-0.780686\pi$
$563$	−192477.	+	111127.i	−0.607244	+	0.350592i	0.164642	+	0.986353i	$0.447353\pi$
$564$		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	0.103702	−	0.994608i	$-0.466931\pi$
$571$	331554.	−	191423.i	1.01691	−	0.587112i	0.913207	+	0.407496i	$0.133598\pi$
$572$	15873.3	+	15303.5i	0.0485151	+	0.0467734i
$573$		0			0
$574$	42926.0	+	101012.i	0.130286	+	0.306583i
$575$		−	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	$0.491289\pi$
$578$	46974.5	−	19962.3i	0.140607	−	0.0597524i
$579$		0			0
$580$	−14410.7	+	14947.3i	−0.0428380	+	0.0444331i
$581$	−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	0.432013	−	0.901868i	$-0.357804\pi$
$587$	−45835.0	−	26462.8i	−0.133021	−	0.0767998i	−0.565034	+	0.825068i	$0.691137\pi$
$588$		0			0
$589$	252532.	+	437399.i	0.727924	+	1.26080i
$590$	48633.7	+	5951.16i	0.139712	+	0.0170961i
$591$		0			0
$592$	−13716.5	−	375093.i	−0.0391380	−	1.07028i
$593$	−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
$596$	9616.14	+	2389.17i	0.0270713	+	0.00672597i
$597$		0			0
$598$	688072.	+	84197.3i	1.92412	+	0.235448i
$599$	−260151.	+	150198.i	−0.725057	+	0.418612i	−0.816611	−	0.577188i	$-0.804150\pi$
$599$	−260151.	+	150198.i	−0.725057	+	0.418612i	0.0915543	+	0.995800i	$0.470816\pi$
$600$		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	−0.694460	−	0.719531i	$-0.744357\pi$
$607$	−154217.	+	89037.5i	−0.418558	+	0.241655i	0.275902	+	0.961186i	$0.411024\pi$
$608$	−340450.	+	159608.i	−0.920972	+	0.431765i
$609$		0			0
$610$	−12461.3	+	5295.56i	−0.0334892	+	0.0142316i
$611$			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	$0.225638\pi$
$614$	−102004.	−	240032.i	−0.270571	−	0.636697i
$615$		0			0
$616$	7309.59	−	1166.97i	0.0192633	−	0.00307538i
$617$	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	0.278970	−	0.960300i	$-0.410007\pi$
$619$	−158318.	−	91404.9i	−0.413189	−	0.238555i	−0.692159	+	0.721745i	$0.743340\pi$
$620$	−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
$626$	5460.93	−	44627.4i	0.0139353	−	0.113881i
$627$		0			0
$628$	96393.6	+	23949.4i	0.244415	+	0.0607261i
$629$	390019.			0.985791
$630$		0			0
$631$			153307.i			0.385037i	0.981293	+	0.192518i	$0.0616655\pi$
$631$			153307.i			0.385037i	−0.981293	+	0.192518i	$0.938335\pi$
$632$	−255221.	+	207196.i	−0.638972	+	0.518736i
$633$		0			0
$634$	19048.1	−	155664.i	0.0473885	−	0.387265i
$635$	−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	−0.887166	−	0.461451i	$-0.847329\pi$
$643$	−384971.	+	222263.i	−0.931120	+	0.537583i	−0.0439545	+	0.999034i	$0.513996\pi$
$644$	161522.	−	167536.i	0.389456	−	0.403958i
$645$		0			0
$646$	−152810.	−	359586.i	−0.366173	−	0.861663i
$647$		−	152505.i		−	0.364314i	−0.983269	−	0.182157i	$-0.941692\pi$
$647$		−	152505.i		−	0.364314i	0.983269	−	0.182157i	$-0.0583079\pi$
$648$		0			0
$649$	−30153.0			−0.0715881
$650$	630042.	−	267743.i	1.49122	−	0.633711i
$651$		0			0
$652$	182650.	+	176093.i	0.429660	+	0.414235i
$653$	−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	0.0227330	−	0.999742i	$-0.492763\pi$
$659$	−361192.	−	208535.i	−0.831702	−	0.480183i	−0.854435	+	0.519558i	$0.826097\pi$
$660$		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	$-0.502037\pi$
$662$	296792.	+	36317.5i	0.677230	+	0.0828706i
$663$		0			0
$664$	396938.	−	322246.i	0.900298	−	0.730888i
$665$	17252.3			0.0390126
$666$		0			0
$667$		−	401718.i		−	0.902962i
$668$	1616.48	−	6506.14i	0.00362257	−	0.0145804i
$669$		0			0
$670$	−17768.5	−	2174.28i	−0.0395824	−	0.00484358i
$671$	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
$680$	34142.9	−	5450.90i	0.0738385	−	0.0117883i
$681$		0			0
$682$	25314.9	−	10757.8i	0.0544261	−	0.0231289i
$683$			357197.i			0.765714i	0.923808	+	0.382857i	$0.125060\pi$
$683$			357197.i			0.765714i	−0.923808	+	0.382857i	$0.874940\pi$
$684$		0			0
$685$	1256.87			0.00267861
$686$	154427.	+	363391.i	0.328152	+	0.772194i
$687$		0			0
$688$	197884.	−	373647.i	0.418054	−	0.789376i
$689$	730122.	+	1.26461e6i	1.53800	+	2.66390i
$690$		0			0
$691$	−384473.	−	221976.i	−0.805212	−	0.464889i	0.0400786	−	0.999197i	$-0.487239\pi$
$691$	−384473.	−	221976.i	−0.805212	−	0.464889i	−0.845290	+	0.534307i	$0.820573\pi$
$692$	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
$698$	65374.2	−	534247.i	0.134182	−	1.09656i
$699$		0			0
$700$	55415.0	−	223039.i	0.113092	−	0.455182i
$701$	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
$704$	6375.91	+	19459.5i	0.0128646	+	0.0392632i
$705$		0			0
$706$	97304.0	−	795181.i	0.195219	−	1.59535i
$707$	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
$716$	−573875.	−	553273.i	−1.11942	−	1.07923i
$717$		0			0
$718$	−252154.	−	593359.i	−0.489122	−	1.15098i
$719$			781622.i			1.51196i	0.654597	+	0.755978i	$0.272838\pi$
$719$			781622.i			1.51196i	−0.654597	+	0.755978i	$0.727162\pi$
$720$		0			0
$721$	−251358.			−0.483529
$722$	16604.7	−	7056.34i	0.0318535	−	0.0135365i
$723$		0			0
$724$	155146.	−	160923.i	0.295980	−	0.307001i
$725$	−198358.	−	343566.i	−0.377375	−	0.653633i
$726$		0			0
$727$	−51590.1	−	29785.6i	−0.0976107	−	0.0563556i	0.450400	−	0.892827i	$-0.351281\pi$
$727$	−51590.1	−	29785.6i	−0.0976107	−	0.0563556i	−0.548011	+	0.836471i	$0.684615\pi$
$728$	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	$0.769563\pi$
$734$	792350.	+	96957.5i	1.47070	+	0.179966i
$735$		0			0
$736$	528122.	+	368179.i	0.974943	+	0.679678i
$737$	11016.5			0.0202819
$738$		0			0
$739$		−	218903.i		−	0.400832i	−0.979711	−	0.200416i	$-0.935771\pi$
$739$		−	218903.i		−	0.400832i	0.979711	−	0.200416i	$-0.0642294\pi$
$740$	−46237.2	−	11487.8i	−0.0844361	−	0.0209785i
$741$		0			0
$742$	486594.	+	59543.1i	0.883810	+	0.108149i
$743$	−431487.	+	249119.i	−0.781610	+	0.451263i	−0.837001	−	0.547202i	$-0.815693\pi$
$743$	−431487.	+	249119.i	−0.781610	+	0.451263i	0.0553907	+	0.998465i	$0.482360\pi$
$744$		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	−0.892279	−	0.451485i	$-0.850894\pi$
$751$	−534346.	+	308505.i	−0.947421	+	0.546994i	−0.0551419	+	0.998479i	$0.517561\pi$
$752$	−42592.3	+	80423.4i	−0.0753174	+	0.142215i
$753$		0			0
$754$	648396.	−	275543.i	1.14051	−	0.484670i
$755$			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	$0.361496\pi$
$758$	−340938.	−	802283.i	−0.593386	−	1.39633i
$759$		0			0
$760$	7524.32	+	47130.2i	0.0130269	+	0.0815966i
$761$	−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	$0.738614\pi$
$770$	114.121	−	932.610i	0.000192479	−	0.00157296i
$771$		0			0
$772$	−419197.	−	104151.i	−0.703369	−	0.174755i
$773$	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
$776$	−275050.	−	338803.i	−0.456761	−	0.562632i
$777$		0			0
$778$	−27919.5	+	228162.i	−0.0461263	+	0.376951i
$779$	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	0.0732283	−	0.997315i	$-0.476670\pi$
$787$	602982.	−	348132.i	0.973543	−	0.562075i	0.900314	+	0.435240i	$0.143337\pi$
$788$	−115675.	+	119982.i	−0.186289	+	0.193226i
$789$		0			0
$790$	16319.8	+	38403.2i	0.0261494	+	0.0615337i
$791$			273518.i			0.437153i
$792$		0			0
$793$	459430.			0.730589
$794$	−48799.6	+	20737.9i	−0.0774061	+	0.0328945i
$795$		0			0
$796$	−97201.6	−	93712.1i	−0.153408	−	0.147900i
$797$	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
$806$	1.50536e6	+	184206.i	2.31723	+	0.283552i
$807$		0			0
$808$	124686.	+	153587.i	0.190984	+	0.235251i
$809$	−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	$0.0283432\pi$
$811$			116976.i			0.177851i	−0.996038	+	0.0889253i	$0.971657\pi$
$812$	57029.3	−	229536.i	0.0864940	−	0.348128i
$813$		0			0
$814$	29102.9	+	3561.24i	0.0439226	+	0.00537468i
$815$	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	−0.639463	−	0.768822i	$-0.720843\pi$
$823$	−198711.	+	114726.i	−0.293375	+	0.169380i	0.346088	+	0.938202i	$0.387510\pi$
$824$	−109626.	−	686663.i	−0.161457	−	1.01132i
$825$		0			0
$826$	−513676.	+	218292.i	−0.752886	+	0.319947i
$827$			673431.i			0.984651i	0.870411	+	0.492326i	$0.163853\pi$
$827$			673431.i			0.984651i	−0.870411	+	0.492326i	$0.836147\pi$
$828$		0			0
$829$	268282.			0.390375			0.195188	−	0.980766i	$-0.437468\pi$
$829$	268282.			0.390375			0.195188	+	0.980766i	$0.437468\pi$
$830$	−25381.8	−	59727.4i	−0.0368439	−	0.0866996i
$831$		0			0
$832$	−232017.	+	1.10496e6i	−0.335177	+	1.59624i
$833$	−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	0.967651	−	0.252292i	$-0.0811843\pi$
$839$	867924.	+	501096.i	1.23299	+	0.711865i	0.265334	+	0.964156i	$0.414518\pi$
$840$		0			0
$841$	149504.	+	258949.i	0.211379	+	0.366119i
$842$	−80210.9	+	655494.i	−0.113138	+	0.924581i
$843$		0			0
$844$	−88524.0	+	356299.i	−0.124273	+	0.500183i
$845$	96307.2			0.134879
$846$		0			0
$847$		−	338137.i		−	0.471330i
$848$	49559.1	+	1.35525e6i	0.0689179	+	1.88464i
$849$		0			0
$850$	−80241.4	+	655743.i	−0.111061	+	0.907603i
$851$	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	−0.809505	−	0.587112i	$-0.800265\pi$
$859$	−520799.	+	300684.i	−0.705804	+	0.407496i	0.103702	+	0.994608i	$0.466931\pi$
$860$	−38636.2	−	37249.2i	−0.0522394	−	0.0503640i
$861$		0			0
$862$	−252927.	−	595178.i	−0.340393	−	0.801000i
$863$		−	1.01872e6i		−	1.36783i	−0.729560	−	0.683917i	$-0.760275\pi$
$863$		−	1.01872e6i		−	1.36783i	0.729560	−	0.683917i	$-0.239725\pi$
$864$		0			0
$865$	38994.9			0.0521166
$866$	227639.	−	96737.6i	0.303536	−	0.128991i
$867$		0			0
$868$	353375.	−	366533.i	0.469025	−	0.486490i
$869$	−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	$-0.356846\pi$
$878$	−1.22877e6	−	150361.i	−1.59398	−	0.195050i
$879$		0			0
$880$	2597.49	−	94.9854i	0.00335419	−	0.000122657i
$881$	−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	$-0.966685\pi$
$883$		−	162909.i		−	0.208941i	0.994528	−	0.104470i	$-0.0333148\pi$
$884$	−1.13858e6	−	282886.i	−1.45700	−	0.361999i
$885$		0			0
$886$	−186206.	−	22785.5i	−0.237206	−	0.0290262i
$887$	192525.	−	111154.i	0.244703	−	0.141280i	−0.372633	−	0.927979i	$-0.621545\pi$
$887$	192525.	−	111154.i	0.244703	−	0.141280i	0.617337	+	0.786699i	$0.288212\pi$
$888$		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
$896$	249494.	+	285347.i	0.310774	+	0.355432i
$897$		0			0
$898$	−459646.	+	195332.i	−0.569995	+	0.242225i
$899$		−	878873.i		−	1.08744i
$900$		0			0
$901$	−1.40918e6			−1.73587
$902$	−9276.24	−	21828.5i	−0.0114014	−	0.0268294i
$903$		0			0
$904$	−747202.	+	119290.i	−0.914326	+	0.145972i
$905$	−14186.6	−	24571.9i	−0.0173213	−	0.0300014i
$906$		0			0
$907$	1.03664e6	+	598505.i	1.26013	+	0.727534i	0.973099	−	0.230388i	$-0.0739995\pi$
$907$	1.03664e6	+	598505.i	1.26013	+	0.727534i	0.287028	+	0.957922i	$0.407333\pi$
$908$	−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	−0.0716123	−	0.997433i	$-0.522814\pi$
$911$	−806036.	−	465365.i	−0.971220	−	0.560734i	−0.899608	+	0.436698i	$0.856148\pi$
$912$		0			0
$913$	19969.1	+	34587.5i	0.0239562	+	0.0414933i
$914$	−60972.0	+	498271.i	−0.0729857	+	0.596449i
$915$		0			0
$916$	−552022.	−	137152.i	−0.657908	−	0.163460i
$917$	−660464.			−0.785435
$918$		0			0
$919$			1.46503e6i			1.73467i	0.497725	+	0.867335i	$0.334169\pi$
$919$			1.46503e6i			1.73467i	−0.497725	+	0.867335i	$0.665831\pi$
$920$	63442.9	−	51504.8i	0.0749562	−	0.0608516i
$921$		0			0
$922$	−50185.2	+	410120.i	−0.0590355	+	0.482446i
$923$	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
$932$	−693399.	+	719219.i	−0.798273	+	0.827998i
$933$		0			0
$934$	668612.	+	1.57335e6i	0.766444	+	1.80357i
$935$			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	$0.552305\pi$
$938$	187674.	−	79753.9i	0.213303	−	0.0906455i
$939$		0			0
$940$	8316.04	+	8017.49i	0.00941154	+	0.00907367i
$941$	−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	0.910680	−	0.413113i	$-0.135559\pi$
$947$	904210.	+	522046.i	1.00825	+	0.582115i	0.0975732	+	0.995228i	$0.468892\pi$
$948$		0			0
$949$	205674.	+	356238.i	0.228374	+	0.395555i
$950$	−905175.	−	110764.i	−1.00296	−	0.122730i
$951$		0			0
$952$	−305780.	+	248241.i	−0.337392	+	0.273905i
$953$	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
$956$	14480.7	−	58283.3i	0.0158444	−	0.0637717i
$957$		0			0
$958$	−762556.	−	93311.7i	−0.830885	−	0.101673i
$959$	−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	−0.0785311	−	0.996912i	$-0.525023\pi$
$967$	697159.	−	402505.i	0.745554	−	0.430446i	0.824085	+	0.566466i	$0.191690\pi$
$968$	923727.	−	147473.i	0.985809	−	0.157384i
$969$		0			0
$970$	−50979.9	+	21664.4i	−0.0541821	+	0.0230252i
$971$			643421.i			0.682428i	0.939986	+	0.341214i	$0.110838\pi$
$971$			643421.i			0.682428i	−0.939986	+	0.341214i	$0.889162\pi$
$972$		0			0
$973$	−449321.			−0.474604
$974$	−82735.5	−	194690.i	−0.0872116	−	0.205223i
$975$		0			0
$976$	377067.	+	199695.i	0.395839	+	0.209637i
$977$	−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	0.415650	−	0.909525i	$-0.363554\pi$
$983$	−158662.	−	91603.6i	−0.164197	−	0.0947994i	−0.579847	+	0.814725i	$0.696888\pi$
$984$		0			0
$985$	10577.4	+	18320.6i	0.0109020	+	0.0188828i
$986$	−82578.9	+	674846.i	−0.0849406	+	0.694146i
$987$		0			0
$988$	390490.	−	1.57168e6i	0.400034	−	1.61009i
$989$	1.03837e6			1.06160
$990$		0			0
$991$			684255.i			0.696740i	0.937357	+	0.348370i	$0.113265\pi$
$991$			684255.i			0.696740i	−0.937357	+	0.348370i	$0.886735\pi$
$992$	1.15542e6	+	805497.i	1.17413	+	0.818542i
$993$		0			0
$994$	5893.04	−	48158.7i	0.00596440	−	0.0487419i
$995$	−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.19.3		44
3.2	odd	2		36.5.f.a.7.20	yes	44
4.3	odd	2	inner	108.5.f.a.19.12		44
9.2	odd	6		324.5.d.f.163.5		22
9.4	even	3	inner	108.5.f.a.91.12		44
9.5	odd	6		36.5.f.a.31.11	yes	44
9.7	even	3		324.5.d.e.163.18		22
12.11	even	2		36.5.f.a.7.11	✓	44
36.7	odd	6		324.5.d.e.163.17		22
36.11	even	6		324.5.d.f.163.6		22
36.23	even	6		36.5.f.a.31.20	yes	44
36.31	odd	6	inner	108.5.f.a.91.3		44

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

\(f(q)\)	\(=\)	\(q+(-3.68138 + 1.56444i) q^{2} +(11.1051 - 11.5186i) q^{4} +(-1.01545 - 1.75881i) q^{5} +(20.0352 + 11.5673i) q^{7} +(-22.8618 + 59.7774i) q^{8} +O(q^{10})\)	\(q+(-3.68138 + 1.56444i) q^{2} +(11.1051 - 11.5186i) q^{4} +(-1.01545 - 1.75881i) q^{5} +(20.0352 + 11.5673i) q^{7} +(-22.8618 + 59.7774i) q^{8} +(6.48981 + 4.88624i) q^{10} +(-4.32958 - 2.49968i) q^{11} +(-137.824 - 238.718i) q^{13} +(-91.8536 - 11.2399i) q^{14} +(-9.35520 - 255.829i) q^{16} +266.009 q^{17} +367.194i q^{19} +(-31.5357 - 7.83518i) q^{20} +(19.8494 + 2.42891i) q^{22} +(544.473 - 314.352i) q^{23} +(310.438 - 537.694i) q^{25} +(880.842 + 663.194i) q^{26} +(355.732 - 102.321i) q^{28} +(319.481 - 553.357i) q^{29} +(1191.19 - 687.735i) q^{31} +(434.669 + 927.167i) q^{32} +(-979.280 + 416.155i) q^{34} -46.9843i q^{35} +1466.19 q^{37} +(-574.453 - 1351.78i) q^{38} +(128.352 - 20.4914i) q^{40} +(-593.019 - 1027.14i) q^{41} +(1430.33 + 825.804i) q^{43} +(-76.8730 + 22.1114i) q^{44} +(-1512.63 + 2009.04i) q^{46} +(-307.864 - 177.745i) q^{47} +(-932.893 - 1615.82i) q^{49} +(-301.649 + 2465.11i) q^{50} +(-4280.24 - 1063.44i) q^{52} -5297.49 q^{53} +10.1532i q^{55} +(-1149.51 + 933.203i) q^{56} +(-310.436 + 2536.92i) q^{58} +(5223.32 - 3015.68i) q^{59} +(-833.364 + 1443.43i) q^{61} +(-3309.31 + 4395.36i) q^{62} +(-3050.68 - 2733.24i) q^{64} +(-279.907 + 484.814i) q^{65} +(-1908.36 + 1101.79i) q^{67} +(2954.05 - 3064.05i) q^{68} +(73.5040 + 172.967i) q^{70} +524.299i q^{71} -1492.29 q^{73} +(-5397.59 + 2293.76i) q^{74} +(4229.55 + 4077.71i) q^{76} +(-57.8293 - 100.163i) q^{77} +(4448.35 + 2568.25i) q^{79} +(-440.456 + 276.236i) q^{80} +(3790.02 + 2853.54i) q^{82} +(-6918.39 - 3994.33i) q^{83} +(-270.120 - 467.861i) q^{85} +(-6557.52 - 802.424i) q^{86} +(248.406 - 201.664i) q^{88} +8860.17 q^{89} -6377.03i q^{91} +(2425.53 - 9762.46i) q^{92} +(1411.44 + 172.713i) q^{94} +(645.826 - 372.868i) q^{95} +(-3409.33 + 5905.14i) q^{97} +(5962.18 + 4488.98i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 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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