LMFDB - Embedded newform 108.5.f.a.19.18

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			19.18
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.05951 - 2.57671i) q^{2} +(2.72116 - 15.7669i) q^{4} +(-14.3046 - 24.7763i) q^{5} +(22.2124 + 12.8243i) q^{7} +(-32.3013 - 55.2506i) q^{8} +O(q^{10})$	\(q+(3.05951 - 2.57671i) q^{2} +(2.72116 - 15.7669i) q^{4} +(-14.3046 - 24.7763i) q^{5} +(22.2124 + 12.8243i) q^{7} +(-32.3013 - 55.2506i) q^{8} +(-107.606 - 38.9445i) q^{10} +(-93.9677 - 54.2523i) q^{11} +(44.2246 + 76.5993i) q^{13} +(101.004 - 17.9987i) q^{14} +(-241.191 - 85.8084i) q^{16} -504.169 q^{17} -191.405i q^{19} +(-429.571 + 158.119i) q^{20} +(-427.287 + 76.1421i) q^{22} +(831.897 - 480.296i) q^{23} +(-96.7443 + 167.566i) q^{25} +(332.680 + 120.402i) q^{26} +(262.643 - 315.324i) q^{28} +(396.671 - 687.053i) q^{29} +(-285.428 + 164.792i) q^{31} +(-959.027 + 358.946i) q^{32} +(-1542.51 + 1299.10i) q^{34} -733.789i q^{35} +209.943 q^{37} +(-493.194 - 585.604i) q^{38} +(-906.848 + 1590.65i) q^{40} +(528.200 + 914.869i) q^{41} +(2887.45 + 1667.07i) q^{43} +(-1111.09 + 1333.95i) q^{44} +(1307.61 - 3613.02i) q^{46} +(977.185 + 564.178i) q^{47} +(-871.573 - 1509.61i) q^{49} +(135.779 + 761.951i) q^{50} +(1328.08 - 488.847i) q^{52} -1138.62 q^{53} +3104.23i q^{55} +(-8.93796 - 1641.49i) q^{56} +(-556.720 - 3124.15i) q^{58} +(4037.49 - 2331.05i) q^{59} +(2799.84 - 4849.46i) q^{61} +(-448.648 + 1239.65i) q^{62} +(-2009.25 + 3569.33i) q^{64} +(1265.23 - 2191.45i) q^{65} +(6127.74 - 3537.85i) q^{67} +(-1371.92 + 7949.19i) q^{68} +(-1890.76 - 2245.03i) q^{70} +4433.42i q^{71} -1953.21 q^{73} +(642.322 - 540.962i) q^{74} +(-3017.86 - 520.842i) q^{76} +(-1391.50 - 2410.15i) q^{77} +(-1523.90 - 879.826i) q^{79} +(1324.12 + 7203.27i) q^{80} +(3973.38 + 1438.03i) q^{82} +(-2621.64 - 1513.61i) q^{83} +(7211.95 + 12491.5i) q^{85} +(13129.7 - 2339.71i) q^{86} +(37.8113 + 6944.19i) q^{88} +559.336 q^{89} +2268.61i q^{91} +(-5309.06 - 14423.4i) q^{92} +(4443.42 - 791.814i) q^{94} +(-4742.31 + 2737.97i) q^{95} +(1100.89 - 1906.79i) q^{97} +(-6556.40 - 2372.87i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.05951	−	2.57671i	0.764877	−	0.644177i
$2$	3.05951	−	2.57671i	0.764877	−	0.644177i
$3$		0			0
$3$		0			0
$4$	2.72116	−	15.7669i	0.170072	−	0.985432i
$5$	−14.3046	−	24.7763i	−0.572185	−	0.991053i	−0.996341	−	0.0854642i	$-0.972763\pi$
$5$	−14.3046	−	24.7763i	−0.572185	−	0.991053i	0.424156	−	0.905589i	$-0.360571\pi$
$6$		0			0
$7$	22.2124	+	12.8243i	0.453314	+	0.261721i	0.709229	−	0.704978i	$-0.249043\pi$
$7$	22.2124	+	12.8243i	0.453314	+	0.261721i	−0.255915	+	0.966699i	$0.582377\pi$
$8$	−32.3013	−	55.2506i	−0.504708	−	0.863290i
$9$		0			0
$10$	−107.606	−	38.9445i	−1.07606	−	0.389445i
$11$	−93.9677	−	54.2523i	−0.776593	−	0.448366i	0.0586287	−	0.998280i	$-0.481327\pi$
$11$	−93.9677	−	54.2523i	−0.776593	−	0.448366i	−0.835221	+	0.549914i	$0.814661\pi$
$12$		0			0
$13$	44.2246	+	76.5993i	0.261684	+	0.453250i	0.966690	−	0.255952i	$-0.0823888\pi$
$13$	44.2246	+	76.5993i	0.261684	+	0.453250i	−0.705005	+	0.709202i	$0.749055\pi$
$14$	101.004	−	17.9987i	0.515324	−	0.0918302i
$15$		0			0
$16$	−241.191	−	85.8084i	−0.942151	−	0.335189i
$17$	−504.169			−1.74453			−0.872265	−	0.489034i	$-0.837349\pi$
$17$	−504.169			−1.74453			−0.872265	+	0.489034i	$0.837349\pi$
$18$		0			0
$19$		−	191.405i		−	0.530207i	−0.964220	−	0.265104i	$-0.914594\pi$
$19$		−	191.405i		−	0.530207i	0.964220	−	0.265104i	$-0.0854062\pi$
$20$	−429.571	+	158.119i	−1.07393	+	0.395298i
$21$		0			0
$22$	−427.287	+	76.1421i	−0.882825	+	0.157318i
$23$	831.897	−	480.296i	1.57258	−	0.907932i	0.576733	−	0.816933i	$-0.304327\pi$
$23$	831.897	−	480.296i	1.57258	−	0.907932i	0.995851	−	0.0909988i	$-0.0290059\pi$
$24$		0			0
$25$	−96.7443	+	167.566i	−0.154791	+	0.268106i
$26$	332.680	+	120.402i	0.492129	+	0.178110i
$27$		0			0
$28$	262.643	−	315.324i	0.335004	−	0.402199i
$29$	396.671	−	687.053i	0.471665	−	0.816948i	−0.527809	−	0.849363i	$-0.676986\pi$
$29$	396.671	−	687.053i	0.471665	−	0.816948i	0.999475	+	0.0324147i	$0.0103197\pi$
$30$		0			0
$31$	−285.428	+	164.792i	−0.297011	+	0.171480i	−0.641099	−	0.767458i	$-0.721521\pi$
$31$	−285.428	+	164.792i	−0.297011	+	0.171480i	0.344088	+	0.938937i	$0.388188\pi$
$32$	−959.027	+	358.946i	−0.936550	+	0.350534i
$33$		0			0
$34$	−1542.51	+	1299.10i	−1.33435	+	1.12379i
$35$		−	733.789i		−	0.599011i
$36$		0			0
$37$	209.943			0.153355			0.0766775	−	0.997056i	$-0.475569\pi$
$37$	209.943			0.153355			0.0766775	+	0.997056i	$0.475569\pi$
$38$	−493.194	−	585.604i	−0.341547	−	0.405543i
$39$		0			0
$40$	−906.848	+	1590.65i	−0.566780	+	0.994154i
$41$	528.200	+	914.869i	0.314218	+	0.544241i	0.979271	−	0.202555i	$-0.0649245\pi$
$41$	528.200	+	914.869i	0.314218	+	0.544241i	−0.665053	+	0.746796i	$0.731591\pi$
$42$		0			0
$43$	2887.45	+	1667.07i	1.56163	+	0.901608i	0.997093	+	0.0762001i	$0.0242788\pi$
$43$	2887.45	+	1667.07i	1.56163	+	0.901608i	0.564537	+	0.825407i	$0.309055\pi$
$44$	−1111.09	+	1333.95i	−0.573911	+	0.689024i
$45$		0			0
$46$	1307.61	−	3613.02i	0.617964	−	1.70748i
$47$	977.185	+	564.178i	0.442365	+	0.255400i	0.704600	−	0.709604i	$-0.251126\pi$
$47$	977.185	+	564.178i	0.442365	+	0.255400i	−0.262235	+	0.965004i	$0.584460\pi$
$48$		0			0
$49$	−871.573	−	1509.61i	−0.363004	−	0.628742i
$50$	135.779	+	761.951i	0.0543116	+	0.304780i
$51$		0			0
$52$	1328.08	−	488.847i	0.491152	−	0.180787i
$53$	−1138.62			−0.405346			−0.202673	−	0.979247i	$-0.564963\pi$
$53$	−1138.62			−0.405346			−0.202673	+	0.979247i	$0.564963\pi$
$54$		0			0
$55$			3104.23i			1.02619i
$56$	−8.93796	−	1641.49i	−0.00285011	−	0.523434i
$57$		0			0
$58$	−556.720	−	3124.15i	−0.165493	−	0.928700i
$59$	4037.49	−	2331.05i	1.15987	−	0.669648i	0.208593	−	0.978002i	$-0.433111\pi$
$59$	4037.49	−	2331.05i	1.15987	−	0.669648i	0.951272	+	0.308354i	$0.0997781\pi$
$60$		0			0
$61$	2799.84	−	4849.46i	0.752442	−	1.30327i	−0.194193	−	0.980963i	$-0.562209\pi$
$61$	2799.84	−	4849.46i	0.752442	−	1.30327i	0.946636	−	0.322305i	$-0.104458\pi$
$62$	−448.648	+	1239.65i	−0.116714	+	0.322488i
$63$		0			0
$64$	−2009.25	+	3569.33i	−0.490540	+	0.871419i
$65$	1265.23	−	2191.45i	0.299463	−	0.518686i
$66$		0			0
$67$	6127.74	−	3537.85i	1.36506	−	0.788116i	0.374764	−	0.927120i	$-0.377724\pi$
$67$	6127.74	−	3537.85i	1.36506	−	0.788116i	0.990292	+	0.139004i	$0.0443902\pi$
$68$	−1371.92	+	7949.19i	−0.296696	+	1.71911i
$69$		0			0
$70$	−1890.76	−	2245.03i	−0.385869	−	0.458170i
$71$			4433.42i			0.879472i	0.898127	+	0.439736i	$0.144928\pi$
$71$			4433.42i			0.879472i	−0.898127	+	0.439736i	$0.855072\pi$
$72$		0			0
$73$	−1953.21			−0.366524			−0.183262	−	0.983064i	$-0.558666\pi$
$73$	−1953.21			−0.366524			−0.183262	+	0.983064i	$0.558666\pi$
$74$	642.322	−	540.962i	0.117298	−	0.0987878i
$75$		0			0
$76$	−3017.86	−	520.842i	−0.522483	−	0.0901735i
$77$	−1391.50	−	2410.15i	−0.234694	−	0.406501i
$78$		0			0
$79$	−1523.90	−	879.826i	−0.244176	−	0.140975i	0.372918	−	0.927864i	$-0.378357\pi$
$79$	−1523.90	−	879.826i	−0.244176	−	0.140975i	−0.617095	+	0.786889i	$0.711690\pi$
$80$	1324.12	+	7203.27i	0.206894	+	1.12551i
$81$		0			0
$82$	3973.38	+	1438.03i	0.590925	+	0.213865i
$83$	−2621.64	−	1513.61i	−0.380555	−	0.219714i	0.297505	−	0.954720i	$-0.403846\pi$
$83$	−2621.64	−	1513.61i	−0.380555	−	0.219714i	−0.678060	+	0.735007i	$0.737179\pi$
$84$		0			0
$85$	7211.95	+	12491.5i	0.998193	+	1.72892i
$86$	13129.7	−	2339.71i	1.77525	−	0.316348i
$87$		0			0
$88$	37.8113	+	6944.19i	0.00488266	+	0.896719i
$89$	559.336			0.0706144			0.0353072	−	0.999377i	$-0.488759\pi$
$89$	559.336			0.0706144			0.0353072	+	0.999377i	$0.488759\pi$
$90$		0			0
$91$			2268.61i			0.273953i
$92$	−5309.06	−	14423.4i	−0.627252	−	1.70409i
$93$		0			0
$94$	4443.42	−	791.814i	0.502877	−	0.0896122i
$95$	−4742.31	+	2737.97i	−0.525463	+	0.303376i
$96$		0			0
$97$	1100.89	−	1906.79i	0.117004	−	0.202656i	−0.801575	−	0.597894i	$-0.796004\pi$
$97$	1100.89	−	1906.79i	0.117004	−	0.202656i	0.918579	+	0.395238i	$0.129338\pi$
$98$	−6556.40	−	2372.87i	−0.682674	−	0.247071i
$99$		0			0
$100$	2378.74	+	1981.33i	0.237874	+	0.198133i
$101$	−365.841	+	633.655i	−0.0358632	+	0.0621170i	−0.883400	−	0.468620i	$-0.844751\pi$
$101$	−365.841	+	633.655i	−0.0358632	+	0.0621170i	0.847537	+	0.530737i	$0.178085\pi$
$102$		0			0
$103$	−8533.78	+	4926.98i	−0.804391	+	0.464415i	−0.845004	−	0.534760i	$-0.820402\pi$
$103$	−8533.78	+	4926.98i	−0.804391	+	0.464415i	0.0406134	+	0.999175i	$0.487069\pi$
$104$	2803.64	−	4917.69i	0.259212	−	0.454668i
$105$		0			0
$106$	−3483.60	+	2933.88i	−0.310039	+	0.261114i
$107$			804.642i			0.0702806i	0.999382	+	0.0351403i	$0.0111878\pi$
$107$			804.642i			0.0702806i	−0.999382	+	0.0351403i	$0.988812\pi$
$108$		0			0
$109$	−17324.9			−1.45820			−0.729102	−	0.684405i	$-0.760062\pi$
$109$	−17324.9			−1.45820			−0.729102	+	0.684405i	$0.760062\pi$
$110$	7998.70	+	9497.42i	0.661050	+	0.784911i
$111$		0			0
$112$	−4256.99	−	4999.12i	−0.339364	−	0.398527i
$113$	8573.94	+	14850.5i	0.671465	+	1.16301i	0.977489	+	0.210988i	$0.0676680\pi$
$113$	8573.94	+	14850.5i	0.671465	+	1.16301i	−0.306024	+	0.952024i	$0.598999\pi$
$114$		0			0
$115$	−23799.9	−	13740.9i	−1.79962	−	1.03901i
$116$	−9753.31	−	8123.85i	−0.724829	−	0.603734i
$117$		0			0
$118$	6346.30	−	17535.3i	0.455782	−	1.25936i
$119$	−11198.8	−	6465.63i	−0.790820	−	0.456580i
$120$		0			0
$121$	−1433.88	−	2483.55i	−0.0979359	−	0.169630i
$122$	−3929.52	−	22051.3i	−0.264010	−	1.48155i
$123$		0			0
$124$	1821.56	+	4948.74i	0.118468	+	0.321848i
$125$	−12345.2			−0.790094
$126$		0			0
$127$		−	9591.51i		−	0.594675i	−0.954772	−	0.297337i	$-0.903901\pi$
$127$		−	9591.51i		−	0.594675i	0.954772	−	0.297337i	$-0.0960986\pi$
$128$	3049.81	+	16097.6i	0.186146	+	0.982522i
$129$		0			0
$130$	−1775.73	−	9964.88i	−0.105073	−	0.589638i
$131$	−3933.27	+	2270.88i	−0.229198	+	0.132328i	−0.610202	−	0.792246i	$-0.708912\pi$
$131$	−3933.27	+	2270.88i	−0.229198	+	0.132328i	0.381004	+	0.924573i	$0.375578\pi$
$132$		0			0
$133$	2454.64	−	4251.56i	0.138766	−	0.240350i
$134$	9631.84	−	26613.5i	0.536414	−	1.48215i
$135$		0			0
$136$	16285.3	+	27855.6i	0.880478	+	1.50604i
$137$	−2450.82	+	4244.95i	−0.130578	+	0.226168i	−0.923900	−	0.382635i	$-0.875017\pi$
$137$	−2450.82	+	4244.95i	−0.130578	+	0.226168i	0.793321	+	0.608803i	$0.208350\pi$
$138$		0			0
$139$	7491.80	−	4325.39i	0.387754	−	0.223870i	−0.293432	−	0.955980i	$-0.594798\pi$
$139$	7491.80	−	4325.39i	0.387754	−	0.223870i	0.681187	+	0.732110i	$0.261464\pi$
$140$	−11569.6	−	1996.75i	−0.590285	−	0.101875i
$141$		0			0
$142$	11423.6	+	13564.1i	0.566535	+	0.672687i
$143$		−	9597.15i		−	0.469321i
$144$		0			0
$145$	−22696.9			−1.07952
$146$	−5975.85	+	5032.84i	−0.280346	+	0.236106i
$147$		0			0
$148$	571.288	−	3310.15i	0.0260814	−	0.151121i
$149$	−6346.46	−	10992.4i	−0.285863	−	0.495130i	0.686955	−	0.726700i	$-0.258947\pi$
$149$	−6346.46	−	10992.4i	−0.285863	−	0.495130i	−0.972818	+	0.231570i	$0.925614\pi$
$150$		0			0
$151$	−11055.3	−	6382.78i	−0.484860	−	0.279934i	0.237579	−	0.971368i	$-0.423646\pi$
$151$	−11055.3	−	6382.78i	−0.484860	−	0.279934i	−0.722440	+	0.691434i	$0.756979\pi$
$152$	−10575.2	+	6182.63i	−0.457723	+	0.267600i
$153$		0			0
$154$	−10467.5	−	3788.37i	−0.441370	−	0.159739i
$155$	8165.87	+	4714.57i	0.339891	+	0.196236i
$156$		0			0
$157$	20283.0	+	35131.2i	0.822873	+	1.42526i	0.903534	+	0.428516i	$0.140963\pi$
$157$	20283.0	+	35131.2i	0.822873	+	1.42526i	−0.0806612	+	0.996742i	$0.525703\pi$
$158$	−6929.45	+	1234.82i	−0.277578	+	0.0494641i
$159$		0			0
$160$	22611.9	+	18626.6i	0.883277	+	0.727601i
$161$	24637.9			0.950499
$162$		0			0
$163$			6872.98i			0.258684i	0.991600	+	0.129342i	$0.0412865\pi$
$163$			6872.98i			0.258684i	−0.991600	+	0.129342i	$0.958713\pi$
$164$	15862.0	−	5838.58i	0.589752	−	0.217080i
$165$		0			0
$166$	−11921.1	+	2124.32i	−0.432612	+	0.0770910i
$167$	−30405.5	+	17554.6i	−1.09023	+	0.629447i	−0.933639	−	0.358216i	$-0.883385\pi$
$167$	−30405.5	+	17554.6i	−1.09023	+	0.629447i	−0.156595	+	0.987663i	$0.550052\pi$
$168$		0			0
$169$	10368.9	−	17959.4i	0.363043	−	0.628809i
$170$	54251.8	+	19634.6i	1.87723	+	0.679398i
$171$		0			0
$172$	34141.8	−	40989.9i	1.15406	−	1.38554i
$173$	1491.72	−	2583.74i	0.0498420	−	0.0863290i	−0.840028	−	0.542543i	$-0.817462\pi$
$173$	1491.72	−	2583.74i	0.0498420	−	0.0863290i	0.889870	+	0.456214i	$0.150795\pi$
$174$		0			0
$175$	−4297.84	+	2481.36i	−0.140338	+	0.0810240i
$176$	18008.8	+	21148.4i	0.581380	+	0.682734i
$177$		0			0
$178$	1711.29	−	1441.25i	0.0540113	−	0.0454881i
$179$			45199.3i			1.41067i	0.708874	+	0.705335i	$0.249203\pi$
$179$			45199.3i			1.41067i	−0.708874	+	0.705335i	$0.750797\pi$
$180$		0			0
$181$	27600.9			0.842492			0.421246	−	0.906946i	$-0.361593\pi$
$181$	27600.9			0.842492			0.421246	+	0.906946i	$0.361593\pi$
$182$	5845.53	+	6940.81i	0.176474	+	0.209540i
$183$		0			0
$184$	−53408.0	−	30448.6i	−1.57750	−	0.899356i
$185$	−3003.16	−	5201.62i	−0.0877474	−	0.151983i
$186$		0			0
$187$	47375.6	+	27352.3i	1.35479	+	0.782188i
$188$	11554.4	−	13872.0i	0.326913	−	0.392484i
$189$		0			0
$190$	−7454.16	+	20596.4i	−0.206487	+	0.570537i
$191$	16300.9	+	9411.33i	0.446833	+	0.257979i	0.706492	−	0.707721i	$-0.250277\pi$
$191$	16300.9	+	9411.33i	0.446833	+	0.257979i	−0.259659	+	0.965700i	$0.583610\pi$
$192$		0			0
$193$	−4727.11	−	8187.59i	−0.126906	−	0.219807i	0.795571	−	0.605861i	$-0.207171\pi$
$193$	−4727.11	−	8187.59i	−0.126906	−	0.219807i	−0.922476	+	0.386054i	$0.873838\pi$
$194$	−1545.08	−	8670.52i	−0.0410532	−	0.230378i
$195$		0			0
$196$	−26173.5	+	9634.13i	−0.681319	+	0.250784i
$197$	21650.0			0.557860			0.278930	−	0.960311i	$-0.410020\pi$
$197$	21650.0			0.557860			0.278930	+	0.960311i	$0.410020\pi$
$198$		0			0
$199$			25261.4i			0.637898i	0.947772	+	0.318949i	$0.103330\pi$
$199$			25261.4i			0.637898i	−0.947772	+	0.318949i	$0.896670\pi$
$200$	12383.1	−	67.4262i	0.309577	−	0.00168566i
$201$		0			0
$202$	513.451	+	2881.34i	0.0125834	+	0.0706141i
$203$	17622.0	−	10174.1i	0.427625	−	0.246889i
$204$		0			0
$205$	15111.4	−	26173.7i	0.359581	−	0.622813i
$206$	−13413.8	+	37063.2i	−0.316094	+	0.873390i
$207$		0			0
$208$	−4093.70	−	22269.9i	−0.0946214	−	0.514744i
$209$	−10384.1	+	17985.9i	−0.237727	+	0.411755i
$210$		0			0
$211$	18674.0	−	10781.5i	0.419443	−	0.242166i	−0.275396	−	0.961331i	$-0.588809\pi$
$211$	18674.0	−	10781.5i	0.419443	−	0.242166i	0.694839	+	0.719165i	$0.255476\pi$
$212$	−3098.35	+	17952.4i	−0.0689380	+	0.399440i
$213$		0			0
$214$	2073.33	+	2461.81i	0.0452731	+	0.0537559i
$215$		−	95387.3i		−	2.06354i
$216$		0			0
$217$	−8453.38			−0.179519
$218$	−53005.7	+	44641.3i	−1.11535	+	0.939342i
$219$		0			0
$220$	48944.2	+	8447.10i	1.01124	+	0.174527i
$221$	−22296.7	−	38619.0i	−0.456516	−	0.790709i
$222$		0			0
$223$	16709.5	+	9647.22i	0.336011	+	0.193996i	0.658507	−	0.752575i	$-0.271188\pi$
$223$	16709.5	+	9647.22i	0.336011	+	0.193996i	−0.322496	+	0.946571i	$0.604522\pi$
$224$	−25905.5	−	4325.83i	−0.516293	−	0.0862130i
$225$		0			0
$226$	64497.4	+	23342.7i	1.26277	+	0.457018i
$227$	56144.4	+	32415.0i	1.08957	+	0.629063i	0.933462	−	0.358677i	$-0.116772\pi$
$227$	56144.4	+	32415.0i	1.08957	+	0.629063i	0.156107	+	0.987740i	$0.450105\pi$
$228$		0			0
$229$	−19575.4	−	33905.7i	−0.373285	−	0.646549i	0.616784	−	0.787133i	$-0.288435\pi$
$229$	−19575.4	−	33905.7i	−0.373285	−	0.646549i	−0.990069	+	0.140584i	$0.955102\pi$
$230$	−108222.	+	19285.1i	−2.04579	+	0.364558i
$231$		0			0
$232$	−50773.1	+	276.461i	−0.943317	+	0.00513639i
$233$	2307.53			0.0425045			0.0212522	−	0.999774i	$-0.493235\pi$
$233$	2307.53			0.0425045			0.0212522	+	0.999774i	$0.493235\pi$
$234$		0			0
$235$		−	32281.4i		−	0.584543i
$236$	−25766.7	−	70001.9i	−0.462632	−	1.25686i
$237$		0			0
$238$	−50922.8	+	9074.40i	−0.898998	+	0.160201i
$239$	65999.7	−	38104.9i	1.15544	−	0.667091i	0.205230	−	0.978714i	$-0.434206\pi$
$239$	65999.7	−	38104.9i	1.15544	−	0.667091i	0.950206	+	0.311623i	$0.100872\pi$
$240$		0			0
$241$	−8157.12	+	14128.5i	−0.140444	+	0.243256i	−0.927664	−	0.373416i	$-0.878186\pi$
$241$	−8157.12	+	14128.5i	−0.140444	+	0.243256i	0.787220	+	0.616672i	$0.211520\pi$
$242$	−10786.3	−	3903.75i	−0.184180	−	0.0666579i
$243$		0			0
$244$	−68842.2	−	57340.9i	−1.15631	−	0.963130i
$245$	−24935.0	+	43188.8i	−0.415411	+	0.719513i
$246$		0			0
$247$	14661.5	−	8464.81i	0.240317	−	0.138747i
$248$	18324.5	+	10447.1i	0.297941	+	0.169860i
$249$		0			0
$250$	−37770.3	+	31810.0i	−0.604324	+	0.508960i
$251$		−	33833.6i		−	0.537033i	−0.963275	−	0.268517i	$-0.913467\pi$
$251$		−	33833.6i		−	0.537033i	0.963275	−	0.268517i	$-0.0865334\pi$
$252$		0			0
$253$	−104229.			−1.62834
$254$	−24714.5	−	29345.3i	−0.383076	−	0.454853i
$255$		0			0
$256$	50809.8	+	41392.4i	0.775297	+	0.631597i
$257$	−28773.1	−	49836.4i	−0.435632	−	0.754537i	0.561715	−	0.827331i	$-0.310142\pi$
$257$	−28773.1	−	49836.4i	−0.435632	−	0.754537i	−0.997347	+	0.0727940i	$0.976808\pi$
$258$		0			0
$259$	4663.34	+	2692.38i	0.0695180	+	0.0401362i
$260$	−31109.5	−	25912.1i	−0.460199	−	0.383315i
$261$		0			0
$262$	−6182.49	+	17082.6i	−0.0900659	+	0.248859i
$263$	−68019.2	−	39270.9i	−0.983378	−	0.567753i	−0.0800895	−	0.996788i	$-0.525521\pi$
$263$	−68019.2	−	39270.9i	−0.983378	−	0.567753i	−0.903288	+	0.429034i	$0.858854\pi$
$264$		0			0
$265$	16287.5	+	28210.7i	0.231933	+	0.401719i
$266$	−3445.04	−	19332.6i	−0.0486890	−	0.273229i
$267$		0			0
$268$	−39106.4	−	106242.i	−0.544476	−	1.47921i
$269$	5376.96			0.0743074			0.0371537	−	0.999310i	$-0.488171\pi$
$269$	5376.96			0.0743074			0.0371537	+	0.999310i	$0.488171\pi$
$270$		0			0
$271$			108113.i			1.47211i	0.676924	+	0.736053i	$0.263312\pi$
$271$			108113.i			1.47211i	−0.676924	+	0.736053i	$0.736688\pi$
$272$	121601.	+	43261.9i	1.64361	+	0.584747i
$273$		0			0
$274$	3439.68	+	19302.5i	0.0458160	+	0.257106i
$275$	18181.7	−	10497.2i	0.240419	−	0.138806i
$276$		0			0
$277$	21971.1	−	38055.1i	0.286347	−	0.495968i	−0.686588	−	0.727047i	$-0.740892\pi$
$277$	21971.1	−	38055.1i	0.286347	−	0.495968i	0.972935	+	0.231079i	$0.0742255\pi$
$278$	11775.9	−	32537.8i	0.152372	−	0.421015i
$279$		0			0
$280$	−40542.2	+	23702.3i	−0.517120	+	0.302326i
$281$	25435.7	−	44055.9i	0.322130	−	0.557945i	−0.658798	−	0.752320i	$-0.728935\pi$
$281$	25435.7	−	44055.9i	0.322130	−	0.557945i	0.980927	+	0.194375i	$0.0622680\pi$
$282$		0			0
$283$	22858.8	−	13197.5i	0.285418	−	0.164786i	−0.350456	−	0.936579i	$-0.613973\pi$
$283$	22858.8	−	13197.5i	0.285418	−	0.164786i	0.635873	+	0.771793i	$0.280640\pi$
$284$	69901.3	+	12064.0i	0.866659	+	0.149574i
$285$		0			0
$286$	−24729.0	−	29362.5i	−0.302326	−	0.358973i
$287$			27095.2i			0.328950i
$288$		0			0
$289$	170665.			2.04338
$290$	−69441.2	+	58483.2i	−0.825699	+	0.695401i
$291$		0			0
$292$	−5314.98	+	30796.0i	−0.0623356	+	0.361184i
$293$	65395.3	+	113268.i	0.761748	+	1.31939i	0.941949	+	0.335757i	$0.108992\pi$
$293$	65395.3	+	113268.i	0.761748	+	1.31939i	−0.180201	+	0.983630i	$0.557675\pi$
$294$		0			0
$295$	−115510.	−	66689.5i	−1.32731	−	0.766325i
$296$	−6781.44	−	11599.5i	−0.0773995	−	0.132390i
$297$		0			0
$298$	−47741.2	−	17278.3i	−0.537602	−	0.194567i
$299$	73580.7	+	42481.8i	0.823041	+	0.475183i
$300$		0			0
$301$	42758.2	+	74059.3i	0.471939	+	0.817423i
$302$	−50270.3	+	8958.12i	−0.551186	+	0.0982207i
$303$		0			0
$304$	−16424.1	+	46165.0i	−0.177720	+	0.499535i
$305$	−160202.			−1.72214
$306$		0			0
$307$		−	54227.3i		−	0.575362i	−0.957726	−	0.287681i	$-0.907116\pi$
$307$		−	54227.3i		−	0.575362i	0.957726	−	0.287681i	$-0.0928843\pi$
$308$	−41787.0	+	15381.2i	−0.440494	+	0.162140i
$309$		0			0
$310$	37131.6	−	6616.81i	0.386385	−	0.0688534i
$311$	−117745.	+	67980.1i	−1.21737	+	0.702847i	−0.964354	−	0.264616i	$-0.914755\pi$
$311$	−117745.	+	67980.1i	−1.21737	+	0.702847i	−0.253013	+	0.967463i	$0.581422\pi$
$312$		0			0
$313$	−82194.2	+	142364.i	−0.838981	+	1.45316i	0.0517658	+	0.998659i	$0.483515\pi$
$313$	−82194.2	+	142364.i	−0.838981	+	1.45316i	−0.890747	+	0.454499i	$0.849818\pi$
$314$	152579.	+	55220.7i	1.54751	+	0.560070i
$315$		0			0
$316$	−18018.9	+	21633.1i	−0.180449	+	0.216643i
$317$	60309.5	−	104459.i	0.600160	−	1.03951i	−0.392637	−	0.919694i	$-0.628437\pi$
$317$	60309.5	−	104459.i	0.600160	−	1.03951i	0.992796	−	0.119814i	$-0.0382297\pi$
$318$		0			0
$319$	−74548.4	+	43040.6i	−0.732584	+	0.422957i
$320$	117176.	−	1276.10i	1.14430	−	0.0124619i
$321$		0			0
$322$	75379.8	−	63484.6i	0.727015	−	0.612290i
$323$			96500.4i			0.924962i
$324$		0			0
$325$	−17113.9			−0.162025
$326$	17709.6	+	21027.9i	0.166638	+	0.197861i
$327$		0			0
$328$	33485.5	−	58734.8i	0.311250	−	0.545944i
$329$	14470.4	+	25063.5i	0.133687	+	0.231553i
$330$		0			0
$331$	100184.	+	57841.2i	0.914412	+	0.527936i	0.881848	−	0.471534i	$-0.156299\pi$
$331$	100184.	+	57841.2i	0.914412	+	0.527936i	0.0325639	+	0.999470i	$0.489633\pi$
$332$	−30998.8	+	37216.5i	−0.281235	+	0.337644i
$333$		0			0
$334$	−47792.7	+	132055.i	−0.428419	+	1.18375i
$335$	−175310.	−	101215.i	−1.56213	−	0.901895i
$336$		0			0
$337$	−93868.0	−	162584.i	−0.826528	−	1.43159i	−0.900746	−	0.434347i	$-0.856979\pi$
$337$	−93868.0	−	162584.i	−0.826528	−	1.43159i	0.0742175	−	0.997242i	$-0.476354\pi$
$338$	−14552.5	−	81664.4i	−0.127381	−	0.714825i
$339$		0			0
$340$	216576.	−	79718.9i	1.87350	−	0.689610i
$341$	35761.3			0.307542
$342$		0			0
$343$		−	106292.i		−	0.903465i
$344$	−1161.87	−	213382.i	−0.00981841	−	1.80319i
$345$		0			0
$346$	−2093.61	−	11748.7i	−0.0174881	−	0.0981381i
$347$	117124.	−	67621.8i	0.972721	−	0.561601i	0.0726566	−	0.997357i	$-0.476852\pi$
$347$	117124.	−	67621.8i	0.972721	−	0.561601i	0.900065	+	0.435756i	$0.143519\pi$
$348$		0			0
$349$	−1651.44	+	2860.38i	−0.0135585	+	0.0234841i	−0.872725	−	0.488212i	$-0.837649\pi$
$349$	−1651.44	+	2860.38i	−0.0135585	+	0.0234841i	0.859167	+	0.511696i	$0.170983\pi$
$350$	−6755.54	+	18666.0i	−0.0551472	+	0.152376i
$351$		0			0
$352$	109591.	+	18300.1i	0.884485	+	0.147695i
$353$	21366.4	−	37007.7i	0.171467	−	0.296990i	−0.767466	−	0.641090i	$-0.778483\pi$
$353$	21366.4	−	37007.7i	0.171467	−	0.296990i	0.938933	+	0.344100i	$0.111816\pi$
$354$		0			0
$355$	109844.	−	63418.4i	0.871603	−	0.503220i
$356$	1522.04	−	8819.00i	0.0120095	−	0.0695856i
$357$		0			0
$358$	116465.	+	138287.i	0.908721	+	1.07899i
$359$			175816.i			1.36418i	0.731270	+	0.682088i	$0.238928\pi$
$359$			175816.i			1.36418i	−0.731270	+	0.682088i	$0.761072\pi$
$360$		0			0
$361$	93685.2			0.718880
$362$	84445.1	−	71119.4i	0.644402	−	0.542714i
$363$		0			0
$364$	35768.9	+	6173.23i	0.269962	+	0.0465918i
$365$	27939.9	+	48393.3i	0.209719	+	0.363245i
$366$		0			0
$367$	6867.31	+	3964.84i	0.0509864	+	0.0294370i	0.525277	−	0.850932i	$-0.323962\pi$
$367$	6867.31	+	3964.84i	0.0509864	+	0.0294370i	−0.474290	+	0.880369i	$0.657295\pi$
$368$	−241859.	+	44459.1i	−1.78594	+	0.328296i
$369$		0			0
$370$	−22591.2	−	8176.13i	−0.165020	−	0.0597234i
$371$	−25291.4	−	14602.0i	−0.183749	−	0.106087i
$372$		0			0
$373$	−123336.	−	213624.i	−0.886486	−	1.53544i	−0.844001	−	0.536342i	$-0.819806\pi$
$373$	−123336.	−	213624.i	−0.886486	−	1.53544i	−0.0424851	−	0.999097i	$-0.513527\pi$
$374$	215425.	−	38388.5i	1.54011	−	0.274447i
$375$		0			0
$376$	−393.206	−	72213.7i	−0.00278128	−	0.510792i
$377$	70170.4			0.493709
$378$		0			0
$379$		−	147423.i		−	1.02633i	−0.858291	−	0.513163i	$-0.828474\pi$
$379$		−	147423.i		−	1.02633i	0.858291	−	0.513163i	$-0.171526\pi$
$380$	30264.8	+	82222.0i	0.209590	+	0.569404i
$381$		0			0
$382$	74123.0	−	13208.6i	0.507956	−	0.0905172i
$383$	−105968.	+	61180.9i	−0.722402	+	0.417079i	−0.815636	−	0.578565i	$-0.803613\pi$
$383$	−105968.	+	61180.9i	−0.722402	+	0.417079i	0.0932341	+	0.995644i	$0.470280\pi$
$384$		0			0
$385$	−39809.7	+	68952.5i	−0.268576	+	0.465188i
$386$	−35559.6	−	12869.6i	−0.238662	−	0.0863755i
$387$		0			0
$388$	−27068.6	−	22546.3i	−0.179805	−	0.149765i
$389$	−91728.1	+	158878.i	−0.606182	+	1.04994i	0.385682	+	0.922632i	$0.373966\pi$
$389$	−91728.1	+	158878.i	−0.606182	+	1.04994i	−0.991863	+	0.127306i	$0.959367\pi$
$390$		0			0
$391$	−419417.	+	242150.i	−2.74342	+	1.58391i
$392$	−55253.8	+	96917.3i	−0.359575	+	0.630709i
$393$		0			0
$394$	66238.3	−	55785.7i	0.426694	−	0.359361i
$395$			50342.3i			0.322656i
$396$		0			0
$397$	81466.1			0.516887			0.258444	−	0.966026i	$-0.416790\pi$
$397$	81466.1			0.516887			0.258444	+	0.966026i	$0.416790\pi$
$398$	65091.2	+	77287.4i	0.410919	+	0.487913i
$399$		0			0
$400$	37712.4	−	32113.9i	0.235702	−	0.200712i
$401$	100584.	+	174217.i	0.625518	+	1.08343i	0.988440	+	0.151610i	$0.0484459\pi$
$401$	100584.	+	174217.i	0.625518	+	1.08343i	−0.362922	+	0.931820i	$0.618221\pi$
$402$		0			0
$403$	−25245.9	−	14575.7i	−0.155446	−	0.0897469i
$404$	8995.27	+	7492.45i	0.0551127	+	0.0459051i
$405$		0			0
$406$	27699.0	−	76534.4i	0.168040	−	0.464306i
$407$	−19727.9	−	11389.9i	−0.119094	−	0.0687592i
$408$		0			0
$409$	70320.1	+	121798.i	0.420371	+	0.728104i	0.995976	−	0.0896241i	$-0.0285666\pi$
$409$	70320.1	+	121798.i	0.420371	+	0.728104i	−0.575605	+	0.817728i	$0.695233\pi$
$410$	−21208.6	−	119016.i	−0.126166	−	0.708009i
$411$		0			0
$412$	54461.5	+	147958.i	0.320845	+	0.871656i
$413$	119576.			0.701044
$414$		0			0
$415$			86606.3i			0.502867i
$416$	−69907.7	−	57586.6i	−0.403960	−	0.332763i
$417$		0			0
$418$	14574.0	+	81784.8i	0.0834114	+	0.468080i
$419$	−133102.	+	76846.6i	−0.758154	+	0.437720i	−0.828633	−	0.559793i	$-0.810881\pi$
$419$	−133102.	+	76846.6i	−0.758154	+	0.437720i	0.0704785	+	0.997513i	$0.477547\pi$
$420$		0			0
$421$	−77206.0	+	133725.i	−0.435599	+	0.754479i	−0.997344	−	0.0728309i	$-0.976797\pi$
$421$	−77206.0	+	133725.i	−0.435599	+	0.754479i	0.561746	+	0.827310i	$0.310130\pi$
$422$	29352.6	−	81103.5i	0.164825	−	0.455422i
$423$		0			0
$424$	36778.8	+	62909.2i	0.204581	+	0.349931i
$425$	48775.5	−	84481.6i	0.270037	−	0.467718i
$426$		0			0
$427$	124382.	−	71812.1i	0.682186	−	0.393860i
$428$	12686.7	+	2189.56i	0.0692567	+	0.0119528i
$429$		0			0
$430$	−245785.	−	291838.i	−1.32929	−	1.57836i
$431$		−	191579.i		−	1.03132i	−0.856793	−	0.515660i	$-0.827547\pi$
$431$		−	191579.i		−	1.03132i	0.856793	−	0.515660i	$-0.172453\pi$
$432$		0			0
$433$	−53963.8			−0.287824			−0.143912	−	0.989591i	$-0.545968\pi$
$433$	−53963.8			−0.287824			−0.143912	+	0.989591i	$0.545968\pi$
$434$	−25863.2	+	21781.9i	−0.137310	+	0.115642i
$435$		0			0
$436$	−47143.8	+	273160.i	−0.248000	+	1.43696i
$437$	−91930.9	−	159229.i	−0.481392	−	0.833795i
$438$		0			0
$439$	−14586.4	−	8421.44i	−0.0756864	−	0.0436976i	0.461679	−	0.887047i	$-0.347247\pi$
$439$	−14586.4	−	8421.44i	−0.0756864	−	0.0436976i	−0.537366	+	0.843349i	$0.680580\pi$
$440$	171511.	−	100271.i	0.885902	−	0.517928i
$441$		0			0
$442$	−167727.	−	60703.0i	−0.858534	−	0.310718i
$443$	140111.	+	80892.9i	0.713943	+	0.412195i	0.812519	−	0.582934i	$-0.198095\pi$
$443$	140111.	+	80892.9i	0.713943	+	0.412195i	−0.0985761	+	0.995130i	$0.531429\pi$
$444$		0			0
$445$	−8001.09	−	13858.3i	−0.0404045	−	0.0699826i
$446$	75980.8	−	13539.7i	0.381974	−	0.0680674i
$447$		0			0
$448$	−90404.5	+	53516.1i	−0.450437	+	0.266642i
$449$	−127200.			−0.630949			−0.315475	−	0.948934i	$-0.602164\pi$
$449$	−127200.			−0.630949			−0.315475	+	0.948934i	$0.602164\pi$
$450$		0			0
$451$		−	114624.i		−	0.563538i
$452$	257477.	−	94774.0i	1.26027	−	0.463887i
$453$		0			0
$454$	255298.	−	45493.9i	1.23861	−	0.220720i
$455$	56207.7	−	32451.5i	0.271502	−	0.156752i
$456$		0			0
$457$	9423.93	−	16322.7i	0.0451232	−	0.0781556i	−0.842582	−	0.538569i	$-0.818965\pi$
$457$	9423.93	−	16322.7i	0.0451232	−	0.0781556i	0.887705	+	0.460413i	$0.152299\pi$
$458$	−147256.	−	53294.4i	−0.702009	−	0.254068i
$459$		0			0
$460$	−281415.	+	337860.i	−1.32994	+	1.59669i
$461$	−29335.9	+	50811.3i	−0.138038	+	0.239088i	−0.926754	−	0.375669i	$-0.877413\pi$
$461$	−29335.9	+	50811.3i	−0.138038	+	0.239088i	0.788716	+	0.614758i	$0.210746\pi$
$462$		0			0
$463$	41167.7	−	23768.2i	0.192041	−	0.110875i	−0.400897	−	0.916123i	$-0.631301\pi$
$463$	41167.7	−	23768.2i	0.192041	−	0.110875i	0.592938	+	0.805248i	$0.297968\pi$
$464$	−154628.	+	131673.i	−0.718212	+	0.611591i
$465$		0			0
$466$	7059.89	−	5945.82i	0.0325107	−	0.0273804i
$467$		−	150686.i		−	0.690936i	−0.938431	−	0.345468i	$-0.887720\pi$
$467$		−	150686.i		−	0.690936i	0.938431	−	0.345468i	$-0.112280\pi$
$468$		0			0
$469$	181482.			0.825066
$470$	−83179.7	−	98765.1i	−0.376549	−	0.447103i
$471$		0			0
$472$	−259208.	−	147778.i	−1.16349	−	0.663323i
$473$	−180885.	−	313302.i	−0.808500	−	1.40036i
$474$		0			0
$475$	32072.9	+	18517.3i	0.142152	+	0.0820712i
$476$	−132417.	+	158976.i	−0.584425	+	0.701647i
$477$		0			0
$478$	103741.	−	286644.i	0.454041	−	1.25455i
$479$	−47830.3	−	27614.8i	−0.208464	−	0.120357i	0.392133	−	0.919908i	$-0.371737\pi$
$479$	−47830.3	−	27614.8i	−0.208464	−	0.120357i	−0.600598	+	0.799551i	$0.705071\pi$
$480$		0			0
$481$	9284.65	+	16081.5i	0.0401306	+	0.0695082i
$482$	11448.4	+	64244.9i	0.0492776	+	0.276531i
$483$		0			0
$484$	−43059.7	+	15849.7i	−0.183815	+	0.0676598i
$485$	−62991.1			−0.267791
$486$		0			0
$487$			2975.59i			0.0125463i	0.999980	+	0.00627313i	$0.00199681\pi$
$487$			2975.59i			0.0125463i	−0.999980	+	0.00627313i	$0.998003\pi$
$488$	−358374.	+	1951.36i	−1.50486	+	0.00819402i
$489$		0			0
$490$	34995.9	+	196387.i	0.145755	+	0.817937i
$491$	234443.	−	135356.i	0.972467	−	0.561454i	0.0724794	−	0.997370i	$-0.476909\pi$
$491$	234443.	−	135356.i	0.972467	−	0.561454i	0.899987	+	0.435916i	$0.143576\pi$
$492$		0			0
$493$	−199989.	+	346391.i	−0.822834	+	1.42519i
$494$	23045.5	−	63676.5i	0.0944350	−	0.260931i
$495$		0			0
$496$	82983.0	−	15254.1i	0.337307	−	0.0620047i
$497$	−56855.6	+	98476.8i	−0.230176	+	0.398677i
$498$		0			0
$499$	226339.	−	130677.i	0.908988	−	0.524805i	0.0288827	−	0.999583i	$-0.490805\pi$
$499$	226339.	−	130677.i	0.908988	−	0.524805i	0.880105	+	0.474778i	$0.157472\pi$
$500$	−33593.2	+	194646.i	−0.134373	+	0.778583i
$501$		0			0
$502$	−87179.4	−	103514.i	−0.345944	−	0.410764i
$503$		−	283008.i		−	1.11857i	−0.828976	−	0.559284i	$-0.811076\pi$
$503$		−	283008.i		−	1.11857i	0.828976	−	0.559284i	$-0.188924\pi$
$504$		0			0
$505$	20932.9			0.0820816
$506$	−318888.	+	268567.i	−1.24548	+	1.04894i
$507$		0			0
$508$	−151228.	−	26100.0i	−0.586011	−	0.101138i
$509$	−106839.	−	185051.i	−0.412378	−	0.714259i	0.582772	−	0.812636i	$-0.301968\pi$
$509$	−106839.	−	185051.i	−0.412378	−	0.714259i	−0.995149	+	0.0983769i	$0.968635\pi$
$510$		0			0
$511$	−43385.4	−	25048.6i	−0.166151	−	0.0959271i
$512$	262109.	−	4281.91i	0.999867	−	0.0163342i
$513$		0			0
$514$	−216445.	−	78335.0i	−0.819260	−	0.296503i
$515$	244145.	+	140957.i	0.920520	+	0.531463i
$516$		0			0
$517$	−61215.9	−	106029.i	−0.229025	−	0.396683i
$518$	21205.0	−	3778.71i	0.0790275	−	0.0140826i
$519$		0			0
$520$	−161947.	+	881.808i	−0.598918	+	0.00326113i
$521$	−168525.			−0.620854			−0.310427	−	0.950597i	$-0.600472\pi$
$521$	−168525.			−0.620854			−0.310427	+	0.950597i	$0.600472\pi$
$522$		0			0
$523$			231592.i			0.846681i	0.905971	+	0.423340i	$0.139143\pi$
$523$			231592.i			0.846681i	−0.905971	+	0.423340i	$0.860857\pi$
$524$	25101.6	+	68194.9i	0.0914196	+	0.248364i
$525$		0			0
$526$	−309295.	+	55116.1i	−1.11790	+	0.199208i
$527$	143904.	−	83082.9i	0.518145	−	0.299151i
$528$		0			0
$529$	321448.	−	556764.i	1.14868	−	1.98957i
$530$	122522.	+	44342.8i	0.436178	+	0.157860i
$531$		0			0
$532$	−60354.5	−	50271.2i	−0.213249	−	0.177622i
$533$	−46718.9	+	80919.5i	−0.164452	+	0.284839i
$534$		0			0
$535$	19936.1	−	11510.1i	0.0696518	−	0.0402135i
$536$	−393402.	−	224284.i	−1.36933	−	0.780671i
$537$		0			0
$538$	16450.8	−	13854.8i	0.0568360	−	0.0478671i
$539$			189139.i			0.651035i
$540$		0			0
$541$	−3552.06			−0.0121363			−0.00606815	−	0.999982i	$-0.501932\pi$
$541$	−3552.06			−0.0121363			−0.00606815	+	0.999982i	$0.501932\pi$
$542$	278575.	+	330772.i	0.948296	+	1.12598i
$543$		0			0
$544$	483512.	−	180970.i	1.63384	−	0.611516i
$545$	247826.	+	429248.i	0.834362	+	1.44516i
$546$		0			0
$547$	444293.	+	256513.i	1.48489	+	0.857302i	0.999852	−	0.0171904i	$-0.00547213\pi$
$547$	444293.	+	256513.i	1.48489	+	0.857302i	0.485039	+	0.874493i	$0.338805\pi$
$548$	60260.6	+	50193.0i	0.200665	+	0.167141i
$549$		0			0
$550$	28578.7	−	78965.1i	0.0944752	−	0.261042i
$551$	−131505.	−	75924.6i	−0.433152	−	0.250080i
$552$		0			0
$553$	−22566.4	−	39086.1i	−0.0737924	−	0.127812i
$554$	−30836.1	−	173043.i	−0.100471	−	0.563813i
$555$		0			0
$556$	−47811.7	−	129893.i	−0.154662	−	0.420180i
$557$	269383.			0.868281			0.434141	−	0.900845i	$-0.357052\pi$
$557$	269383.			0.868281			0.434141	+	0.900845i	$0.357052\pi$
$558$		0			0
$559$			294903.i			0.943746i
$560$	−62965.2	+	176983.i	−0.200782	+	0.564359i
$561$		0			0
$562$	−35698.5	−	200330.i	−0.113026	−	0.634267i
$563$	−48439.2	+	27966.4i	−0.152820	+	0.0882307i	−0.574460	−	0.818533i	$-0.694788\pi$
$563$	−48439.2	+	27966.4i	−0.152820	+	0.0882307i	0.421640	+	0.906763i	$0.361455\pi$
$564$		0			0
$565$	245294.	−	424861.i	0.768404	−	1.33092i
$566$	35930.5	−	99278.4i	0.112158	−	0.309900i
$567$		0			0
$568$	244949.	−	143205.i	0.759239	−	0.443877i
$569$	212266.	−	367655.i	0.655625	−	1.13558i	−0.326111	−	0.945331i	$-0.605738\pi$
$569$	212266.	−	367655.i	0.655625	−	1.13558i	0.981737	−	0.190245i	$-0.0609282\pi$
$570$		0			0
$571$	25297.4	−	14605.5i	0.0775897	−	0.0447964i	−0.460703	−	0.887554i	$-0.652403\pi$
$571$	25297.4	−	14605.5i	0.0775897	−	0.0447964i	0.538293	+	0.842758i	$0.319069\pi$
$572$	−151317.	−	26115.3i	−0.462484	−	0.0798185i
$573$		0			0
$574$	69816.5	+	82898.1i	0.211902	+	0.251606i
$575$			185863.i			0.562158i
$576$		0			0
$577$	−494524.			−1.48537			−0.742687	−	0.669639i	$-0.766449\pi$
$577$	−494524.			−1.48537			−0.742687	+	0.669639i	$0.766449\pi$
$578$	522152.	−	439755.i	1.56294	−	1.31630i
$579$		0			0
$580$	−61761.7	+	357860.i	−0.183596	+	1.06379i
$581$	−38822.0	−	67241.7i	−0.115007	−	0.199199i
$582$		0			0
$583$	106993.	+	61772.5i	0.314788	+	0.181743i
$584$	63091.1	+	107916.i	0.184988	+	0.316417i
$585$		0			0
$586$	491936.	+	178040.i	1.43256	+	0.518467i
$587$	208206.	+	120208.i	0.604251	+	0.348865i	0.770712	−	0.637183i	$-0.219901\pi$
$587$	208206.	+	120208.i	0.604251	+	0.348865i	−0.166461	+	0.986048i	$0.553234\pi$
$588$		0			0
$589$	31541.9	+	54632.2i	0.0909197	+	0.157477i
$590$	−525241.	+	93597.5i	−1.50888	+	0.268881i
$591$		0			0
$592$	−50636.3	−	18014.9i	−0.144484	−	0.0514029i
$593$	470902.			1.33912			0.669562	−	0.742756i	$-0.266482\pi$
$593$	470902.			1.33912			0.669562	+	0.742756i	$0.266482\pi$
$594$		0			0
$595$			369954.i			1.04499i
$596$	−190586.	+	70152.0i	−0.536534	+	0.197491i
$597$		0			0
$598$	334584.	−	59622.5i	0.935626	−	0.166728i
$599$	−8669.92	+	5005.58i	−0.0241636	+	0.0139509i	−0.512033	−	0.858966i	$-0.671108\pi$
$599$	−8669.92	+	5005.58i	−0.0241636	+	0.0139509i	0.487870	+	0.872917i	$0.337774\pi$
$600$		0			0
$601$	−196449.	+	340259.i	−0.543876	+	0.942021i	0.454800	+	0.890593i	$0.349711\pi$
$601$	−196449.	+	340259.i	−0.543876	+	0.942021i	−0.998677	+	0.0514280i	$0.983623\pi$
$602$	321648.	+	116410.i	0.887540	+	0.321215i
$603$		0			0
$604$	−130720.	+	156939.i	−0.358317	+	0.430188i
$605$	−41022.2	+	71052.5i	−0.112075	+	0.194119i
$606$		0			0
$607$	375426.	−	216752.i	1.01894	−	0.588283i	0.105141	−	0.994457i	$-0.466471\pi$
$607$	375426.	−	216752.i	1.01894	−	0.588283i	0.913796	+	0.406174i	$0.133137\pi$
$608$	68704.1	+	183562.i	0.185855	+	0.496566i
$609$		0			0
$610$	−490140.	+	412795.i	−1.31723	+	1.10937i
$611$			99802.2i			0.267336i
$612$		0			0
$613$	301951.			0.803555			0.401778	−	0.915737i	$-0.368393\pi$
$613$	301951.			0.803555			0.401778	+	0.915737i	$0.368393\pi$
$614$	−139728.	−	165909.i	−0.370635	−	0.440081i
$615$		0			0
$616$	−88214.7	+	154732.i	−0.232477	+	0.407773i
$617$	98373.3	+	170388.i	0.258409	+	0.447577i	0.965816	−	0.259229i	$-0.0834686\pi$
$617$	98373.3	+	170388.i	0.258409	+	0.447577i	−0.707407	+	0.706806i	$0.750135\pi$
$618$		0			0
$619$	−536199.	−	309575.i	−1.39941	−	0.807949i	−0.405078	−	0.914282i	$-0.632756\pi$
$619$	−536199.	−	309575.i	−1.39941	−	0.807949i	−0.994331	+	0.106333i	$0.966089\pi$
$620$	96554.8	−	115921.i	0.251183	−	0.301565i
$621$		0			0
$622$	−185077.	+	511380.i	−0.478378	+	1.32179i
$623$	12424.2	+	7173.12i	0.0320105	+	0.0184813i
$624$		0			0
$625$	237059.	+	410598.i	0.606870	+	1.05113i
$626$	115358.	+	647355.i	0.294374	+	1.65194i
$627$		0			0
$628$	609103.	−	224203.i	1.54444	−	0.568488i
$629$	−105847.			−0.267532
$630$		0			0
$631$		−	308766.i		−	0.775479i	−0.921769	−	0.387740i	$-0.873256\pi$
$631$		−	308766.i		−	0.775479i	0.921769	−	0.387740i	$-0.126744\pi$
$632$	613.198	+	112616.i	0.00153521	+	0.281946i
$633$		0			0
$634$	−84643.3	−	474993.i	−0.210578	−	1.18170i
$635$	−237642.	+	137203.i	−0.589354	+	0.340264i
$636$		0			0
$637$	77090.0	−	133524.i	0.189985	−	0.329064i
$638$	−117178.	+	323772.i	−0.287877	+	0.795424i
$639$		0			0
$640$	355214.	−	305834.i	0.867222	−	0.746665i
$641$	−171200.	+	296528.i	−0.416666	+	0.721687i	−0.995602	−	0.0936860i	$-0.970135\pi$
$641$	−171200.	+	296528.i	−0.416666	+	0.721687i	0.578935	+	0.815373i	$0.303468\pi$
$642$		0			0
$643$	−478867.	+	276474.i	−1.15823	+	0.668702i	−0.950878	−	0.309566i	$-0.899816\pi$
$643$	−478867.	+	276474.i	−1.15823	+	0.668702i	−0.207347	+	0.978267i	$0.566483\pi$
$644$	67043.5	−	388463.i	0.161654	−	0.936652i
$645$		0			0
$646$	248653.	+	295244.i	0.595839	+	0.707482i
$647$		−	576814.i		−	1.37793i	−0.724794	−	0.688965i	$-0.758065\pi$
$647$		−	576814.i		−	1.37793i	0.724794	−	0.688965i	$-0.241935\pi$
$648$		0			0
$649$	−505858.			−1.20099
$650$	−52360.1	+	44097.6i	−0.123929	+	0.104373i
$651$		0			0
$652$	108366.	+	18702.4i	0.254915	+	0.0439950i
$653$	−286795.	−	496744.i	−0.672583	−	1.16495i	−0.977169	−	0.212463i	$-0.931852\pi$
$653$	−286795.	−	496744.i	−0.672583	−	1.16495i	0.304586	−	0.952485i	$-0.401482\pi$
$654$		0			0
$655$	112528.	+	64968.0i	0.262288	+	0.151432i
$656$	−48893.4	−	265982.i	−0.113617	−	0.618080i
$657$		0			0
$658$	108854.	+	39395.9i	0.251415	+	0.0909911i
$659$	299298.	+	172800.i	0.689180	+	0.397899i	0.803305	−	0.595568i	$-0.203073\pi$
$659$	299298.	+	172800.i	0.689180	+	0.397899i	−0.114125	+	0.993466i	$0.536406\pi$
$660$		0			0
$661$	187583.	+	324904.i	0.429330	+	0.743622i	0.996814	−	0.0797628i	$-0.0254163\pi$
$661$	187583.	+	324904.i	0.429330	+	0.743622i	−0.567484	+	0.823385i	$0.692083\pi$
$662$	455553.	−	81179.1i	1.03950	−	0.185237i
$663$		0			0
$664$	1054.91	+	193739.i	0.00239266	+	0.439421i
$665$	−140451.			−0.317600
$666$		0			0
$667$		−	762077.i		−	1.71296i
$668$	194044.	+	527170.i	0.434858	+	1.18140i
$669$		0			0
$670$	−797164.	+	142054.i	−1.77582	+	0.316449i
$671$	−526189.	+	303795.i	−1.16868	+	0.674739i
$672$		0			0
$673$	286866.	−	496866.i	0.633358	−	1.09701i	−0.353503	−	0.935433i	$-0.615010\pi$
$673$	286866.	−	496866.i	0.633358	−	1.09701i	0.986861	−	0.161574i	$-0.0516571\pi$
$674$	−706121.	−	255557.i	−1.55439	−	0.562558i
$675$		0			0
$676$	−254949.	−	212355.i	−0.557904	−	0.464697i
$677$	−13789.2	+	23883.6i	−0.0300859	+	0.0521103i	−0.880676	−	0.473719i	$-0.842911\pi$
$677$	−13789.2	+	23883.6i	−0.0300859	+	0.0521103i	0.850590	+	0.525829i	$0.176245\pi$
$678$		0			0
$679$	48906.7	−	28236.3i	0.106079	−	0.0612447i
$680$	457205.	−	801955.i	0.988765	−	1.73433i
$681$		0			0
$682$	109412.	−	92146.5i	0.235232	−	0.198112i
$683$			1038.30i			0.00222578i	0.999999	+	0.00111289i	$0.000354244\pi$
$683$			1038.30i			0.00222578i	−0.999999	+	0.00111289i	$0.999646\pi$
$684$		0			0
$685$	140232.			0.298859
$686$	−273883.	−	325200.i	−0.581992	−	0.691040i
$687$		0			0
$688$	−553378.	−	649850.i	−1.16908	−	1.37289i
$689$	−50354.8	−	87217.2i	−0.106073	−	0.183723i
$690$		0			0
$691$	−289343.	−	167052.i	−0.605978	−	0.349862i	0.165411	−	0.986225i	$-0.447105\pi$
$691$	−289343.	−	167052.i	−0.605978	−	0.349862i	−0.771390	+	0.636363i	$0.780438\pi$
$692$	−36678.4	−	30550.6i	−0.0765945	−	0.0637981i
$693$		0			0
$694$	184101.	−	508685.i	0.382241	−	1.05616i
$695$	−214335.	−	123746.i	−0.443734	−	0.256190i
$696$		0			0
$697$	−266302.	−	461249.i	−0.548162	−	0.949445i
$698$	2317.77	+	13006.6i	0.00475729	+	0.0266965i
$699$		0			0
$700$	27428.3	+	74515.9i	0.0559761	+	0.152073i
$701$	−177927.			−0.362082			−0.181041	−	0.983476i	$-0.557947\pi$
$701$	−177927.			−0.362082			−0.181041	+	0.983476i	$0.557947\pi$
$702$		0			0
$703$		−	40184.1i		−	0.0813100i
$704$	382449.	−	226396.i	0.771664	−	0.456796i
$705$		0			0
$706$	−29987.3	−	168280.i	−0.0601629	−	0.337616i
$707$	−16252.4	+	9383.33i	−0.0325146	+	0.0187723i
$708$		0			0
$709$	−362484.	+	627841.i	−0.721102	+	1.24899i	0.239456	+	0.970907i	$0.423031\pi$
$709$	−362484.	+	627841.i	−0.721102	+	1.24899i	−0.960558	+	0.278079i	$0.910302\pi$
$710$	172657.	−	477064.i	0.342506	−	0.946368i
$711$		0			0
$712$	−18067.3	−	30903.7i	−0.0356396	−	0.0609607i
$713$	−158298.	+	274180.i	−0.311383	+	0.539332i
$714$		0			0
$715$	−237782.	+	137284.i	−0.465122	+	0.268538i
$716$	712652.	+	122994.i	1.39012	+	0.239916i
$717$		0			0
$718$	453027.	+	537911.i	0.878770	+	1.04343i
$719$			536436.i			1.03767i	0.854874	+	0.518836i	$0.173634\pi$
$719$			536436.i			1.03767i	−0.854874	+	0.518836i	$0.826366\pi$
$720$		0			0
$721$	−252741.			−0.486189
$722$	286630.	−	241399.i	0.549855	−	0.463086i
$723$		0			0
$724$	75106.3	−	435181.i	0.143284	−	0.830218i
$725$	76751.2	+	132937.i	0.146019	+	0.252912i
$726$		0			0
$727$	−375814.	−	216977.i	−0.711057	−	0.410529i	0.100395	−	0.994948i	$-0.467989\pi$
$727$	−375814.	−	216977.i	−0.711057	−	0.410529i	−0.811452	+	0.584418i	$0.801323\pi$
$728$	125342.	−	73278.9i	0.236501	−	0.138266i
$729$		0			0
$730$	210178.	+	76066.7i	0.394403	+	0.142741i
$731$	−1.45577e6	−	840486.i	−2.72431	−	1.57288i
$732$		0			0
$733$	390208.	+	675860.i	0.726254	+	1.25791i	0.958456	+	0.285241i	$0.0920735\pi$
$733$	390208.	+	675860.i	0.726254	+	1.25791i	−0.232202	+	0.972667i	$0.574593\pi$
$734$	31226.8	−	5564.59i	0.0579610	−	0.0103286i
$735$		0			0
$736$	−625411.	+	759223.i	−1.15454	+	1.40157i
$737$	−767746.			−1.41346
$738$		0			0
$739$			215142.i			0.393947i	0.980409	+	0.196973i	$0.0631112\pi$
$739$			215142.i			0.393947i	−0.980409	+	0.196973i	$0.936889\pi$
$740$	−90185.5	+	33196.1i	−0.164692	+	0.0606210i
$741$		0			0
$742$	−115004.	+	20493.6i	−0.208884	+	0.0372230i
$743$	250360.	−	144546.i	0.453511	−	0.261835i	−0.255801	−	0.966730i	$-0.582339\pi$
$743$	250360.	−	144546.i	0.453511	−	0.261835i	0.709312	+	0.704895i	$0.249006\pi$
$744$		0			0
$745$	−181567.	+	314484.i	−0.327133	+	0.566612i
$746$	−927794.	−	335784.i	−1.66715	−	0.603367i
$747$		0			0
$748$	560178.	−	672537.i	1.00120	−	1.20202i
$749$	−10319.0	+	17873.0i	−0.0183939	+	0.0318592i
$750$		0			0
$751$	−593117.	+	342436.i	−1.05162	+	0.607156i	−0.923104	−	0.384551i	$-0.874356\pi$
$751$	−593117.	+	342436.i	−1.05162	+	0.607156i	−0.128521	+	0.991707i	$0.541023\pi$
$752$	−187277.	−	219925.i	−0.331168	−	0.388901i
$753$		0			0
$754$	214687.	−	180809.i	0.377627	−	0.318036i
$755$			365213.i			0.640697i
$756$		0			0
$757$	−646906.			−1.12888			−0.564442	−	0.825472i	$-0.690909\pi$
$757$	−646906.			−1.12888			−0.564442	+	0.825472i	$0.690909\pi$
$758$	−379865.	−	451040.i	−0.661136	−	0.785013i
$759$		0			0
$760$	304457.	+	173575.i	0.527108	+	0.300511i
$761$	383411.	+	664087.i	0.662057	+	1.14672i	0.980074	+	0.198631i	$0.0636495\pi$
$761$	383411.	+	664087.i	0.662057	+	1.14672i	−0.318018	+	0.948085i	$0.603017\pi$
$762$		0			0
$763$	−384828.	−	222181.i	−0.661025	−	0.381643i
$764$	192745.	−	231405.i	0.330214	−	0.396448i
$765$		0			0
$766$	−166566.	+	460233.i	−0.283876	+	0.784369i
$767$	357113.	+	206179.i	0.607037	+	0.350473i
$768$		0			0
$769$	289867.	+	502065.i	0.490170	+	0.848999i	0.999936	−	0.0113137i	$-0.00360135\pi$
$769$	289867.	+	502065.i	0.490170	+	0.848999i	−0.509766	+	0.860313i	$0.670268\pi$
$770$	55872.2	+	313538.i	0.0942355	+	0.528822i
$771$		0			0
$772$	−141956.	+	52252.2i	−0.238188	+	0.0876738i
$773$	885783.			1.48241			0.741205	−	0.671279i	$-0.234255\pi$
$773$	885783.			1.48241			0.741205	+	0.671279i	$0.234255\pi$
$774$		0			0
$775$		−	63770.7i		−	0.106174i
$776$	−140912.	+	767.268i	−0.234004	+	0.00127416i
$777$		0			0
$778$	128739.	+	722444.i	0.212691	+	1.19356i
$779$	175110.	−	101100.i	0.288561	−	0.166601i
$780$		0			0
$781$	240523.	−	416598.i	0.394325	−	0.682991i
$782$	−659257.	+	1.82157e6i	−1.07806	+	2.97875i
$783$		0			0
$784$	80678.1	+	438892.i	0.131257	+	0.714045i
$785$	580281.	−	1.00508e6i	0.941671	−	1.63102i
$786$		0			0
$787$	910515.	−	525686.i	1.47007	−	0.848744i	0.470633	−	0.882329i	$-0.344026\pi$
$787$	910515.	−	525686.i	1.47007	−	0.848744i	0.999436	+	0.0335849i	$0.0106924\pi$
$788$	58913.0	−	341353.i	0.0948765	−	0.549733i
$789$		0			0
$790$	129717.	+	154023.i	0.207847	+	0.246792i
$791$			439820.i			0.702946i
$792$		0			0
$793$	495287.			0.787609
$794$	249246.	−	209914.i	0.395355	−	0.332967i
$795$		0			0
$796$	398294.	+	68740.2i	0.628605	+	0.108489i
$797$	−47409.2	−	82115.1i	−0.0746356	−	0.129273i	0.826292	−	0.563242i	$-0.190446\pi$
$797$	−47409.2	−	82115.1i	−0.0746356	−	0.129273i	−0.900928	+	0.433969i	$0.857113\pi$
$798$		0			0
$799$	−492666.	−	284441.i	−0.771719	−	0.445552i
$800$	32633.2	−	195426.i	0.0509894	−	0.305354i
$801$		0			0
$802$	756643.	+	273841.i	1.17636	+	0.425745i
$803$	183538.	+	105966.i	0.284640	+	0.164337i
$804$		0			0
$805$	−352436.	−	610436.i	−0.543861	−	0.941995i
$806$	−114797.	+	20456.8i	−0.176710	+	0.0314896i
$807$		0			0
$808$	46826.9	−	254.974i	0.0717254	−	0.000390547i
$809$	209085.			0.319467			0.159734	−	0.987160i	$-0.448937\pi$
$809$	209085.			0.319467			0.159734	+	0.987160i	$0.448937\pi$
$810$		0			0
$811$			577209.i			0.877589i	0.898587	+	0.438794i	$0.144594\pi$
$811$			577209.i			0.877589i	−0.898587	+	0.438794i	$0.855406\pi$
$812$	−112461.	−	305530.i	−0.170566	−	0.463384i
$813$		0			0
$814$	−89706.0	+	15985.5i	−0.135386	+	0.0241256i
$815$	170287.	−	98315.3i	0.256370	−	0.148015i
$816$		0			0
$817$	319086.	−	552673.i	0.478039	−	0.827987i
$818$	528983.	+	191447.i	0.790560	+	0.286116i
$819$		0			0
$820$	−371558.	−	309483.i	−0.552585	−	0.460266i
$821$	−367923.	+	637262.i	−0.545847	+	0.945435i	0.452706	+	0.891660i	$0.350459\pi$
$821$	−367923.	+	637262.i	−0.545847	+	0.945435i	−0.998553	+	0.0537749i	$0.982875\pi$
$822$		0			0
$823$	148172.	−	85547.4i	0.218760	−	0.126301i	−0.386616	−	0.922241i	$-0.626356\pi$
$823$	148172.	−	85547.4i	0.218760	−	0.126301i	0.605376	+	0.795940i	$0.293023\pi$
$824$	547871.	+	312348.i	0.806908	+	0.460029i
$825$		0			0
$826$	365845.	−	308114.i	0.536212	−	0.451597i
$827$		−	1.03882e6i		−	1.51890i	−0.650563	−	0.759452i	$-0.725467\pi$
$827$		−	1.03882e6i		−	1.51890i	0.650563	−	0.759452i	$-0.274533\pi$
$828$		0			0
$829$	−802150.			−1.16720			−0.583601	−	0.812040i	$-0.698357\pi$
$829$	−802150.			−1.16720			−0.583601	+	0.812040i	$0.698357\pi$
$830$	223159.	+	264972.i	0.323935	+	0.384631i
$831$		0			0
$832$	−362267.	+	3945.22i	−0.523337	+	0.00569934i
$833$	439420.	+	761098.i	0.633272	+	1.09686i
$834$		0			0
$835$	869879.	+	502225.i	1.24763	+	0.720320i
$836$	255325.	+	212668.i	0.365326	+	0.304292i
$837$		0			0
$838$	−209216.	+	578078.i	−0.297925	+	0.823187i
$839$	487546.	+	281485.i	0.692615	+	0.399881i	0.804591	−	0.593830i	$-0.202385\pi$
$839$	487546.	+	281485.i	0.692615	+	0.399881i	−0.111976	+	0.993711i	$0.535718\pi$
$840$		0			0
$841$	38945.5	+	67455.6i	0.0550637	+	0.0953732i
$842$	108357.	+	608069.i	0.152839	+	0.857686i
$843$		0			0
$844$	−119175.	−	323770.i	−0.167302	−	0.454518i
$845$	−593291.			−0.830910
$846$		0			0
$847$		−	73554.1i		−	0.102527i
$848$	274623.	+	97702.8i	0.381897	+	0.135867i
$849$		0			0
$850$	−68455.5	−	384152.i	−0.0947481	−	0.531698i
$851$	174651.	−	100835.i	0.241164	−	0.139236i
$852$		0			0
$853$	331406.	−	574011.i	0.455472	−	0.788901i	−0.543243	−	0.839575i	$-0.682804\pi$
$853$	331406.	−	574011.i	0.455472	−	0.788901i	0.998715	+	0.0506745i	$0.0161371\pi$
$854$	195509.	−	540206.i	0.268072	−	0.740703i
$855$		0			0
$856$	44456.9	−	25991.0i	0.0606725	−	0.0354712i
$857$	566602.	−	981383.i	0.771465	−	1.33622i	−0.165294	−	0.986244i	$-0.552857\pi$
$857$	566602.	−	981383.i	0.771465	−	1.33622i	0.936760	−	0.349973i	$-0.113809\pi$
$858$		0			0
$859$	−347489.	+	200623.i	−0.470928	+	0.271890i	−0.716628	−	0.697456i	$-0.754315\pi$
$859$	−347489.	+	200623.i	−0.470928	+	0.271890i	0.245700	+	0.969346i	$0.420982\pi$
$860$	−1.50396e6	−	259564.i	−2.03348	−	0.350952i
$861$		0			0
$862$	−493643.	−	586137.i	−0.664352	−	0.788832i
$863$			1.22445e6i			1.64407i	0.569437	+	0.822035i	$0.307161\pi$
$863$			1.22445e6i			1.64407i	−0.569437	+	0.822035i	$0.692839\pi$
$864$		0			0
$865$	−85354.1			−0.114075
$866$	−165103.	+	139049.i	−0.220150	+	0.185409i
$867$		0			0
$868$	−23003.0	+	133284.i	−0.0305312	+	0.176904i
$869$	95465.2	+	165351.i	0.126417	+	0.218961i
$870$		0			0
$871$	541994.	+	312920.i	0.714427	+	0.412475i
$872$	559618.	+	957212.i	0.735967	+	1.25885i
$873$		0			0
$874$	−691550.	−	250283.i	−0.905317	−	0.327649i
$875$	−274217.	−	158319.i	−0.358161	−	0.206784i
$876$		0			0
$877$	−65931.0	−	114196.i	−0.0857216	−	0.148474i	0.819977	−	0.572397i	$-0.193986\pi$
$877$	−65931.0	−	114196.i	−0.0857216	−	0.148474i	−0.905698	+	0.423922i	$0.860653\pi$
$878$	−66326.6	+	11819.3i	−0.0860397	+	0.0153322i
$879$		0			0
$880$	266369.	−	748712.i	0.343969	−	0.966828i
$881$	−510450.			−0.657660			−0.328830	−	0.944389i	$-0.606654\pi$
$881$	−510450.			−0.657660			−0.328830	+	0.944389i	$0.606654\pi$
$882$		0			0
$883$			233561.i			0.299557i	0.988720	+	0.149778i	$0.0478560\pi$
$883$			233561.i			0.299557i	−0.988720	+	0.149778i	$0.952144\pi$
$884$	−669575.	+	246462.i	−0.856830	+	0.315388i
$885$		0			0
$886$	637107.	−	113532.i	0.811605	−	0.144627i
$887$	554282.	−	320015.i	0.704504	−	0.406746i	−0.104519	−	0.994523i	$-0.533330\pi$
$887$	554282.	−	320015.i	0.704504	−	0.406746i	0.809023	+	0.587777i	$0.199997\pi$
$888$		0			0
$889$	123005.	−	213050.i	0.155639	−	0.269574i
$890$	−60188.2	−	21783.1i	−0.0759856	−	0.0275004i
$891$		0			0
$892$	197576.	−	237205.i	0.248316	−	0.298122i
$893$	107986.	−	187038.i	0.135415	−	0.234545i
$894$		0			0
$895$	1.11987e6	−	646558.i	1.39805	−	0.807164i
$896$	−138698.	+	396679.i	−0.172764	+	0.494109i
$897$		0			0
$898$	−389169.	+	327757.i	−0.482598	+	0.406443i
$899$			261472.i			0.323524i
$900$		0			0
$901$	574055.			0.707137
$902$	−295353.	−	350694.i	−0.363018	−	0.431037i
$903$		0			0
$904$	543549.	−	953406.i	0.665123	−	1.16665i
$905$	−394820.	−	683849.i	−0.482061	−	0.834954i
$906$		0			0
$907$	379256.	+	218964.i	0.461018	+	0.266169i	0.712472	−	0.701700i	$-0.247575\pi$
$907$	379256.	+	218964.i	0.461018	+	0.266169i	−0.251454	+	0.967869i	$0.580909\pi$
$908$	663862.	−	797017.i	0.805204	−	0.966710i
$909$		0			0
$910$	88349.7	−	244116.i	0.106690	−	0.294791i
$911$	666090.	+	384567.i	0.802594	+	0.463378i	0.844377	−	0.535749i	$-0.179971\pi$
$911$	666090.	+	384567.i	0.802594	+	0.463378i	−0.0417834	+	0.999127i	$0.513304\pi$
$912$		0			0
$913$	164233.	+	284460.i	0.197024	+	0.341256i
$914$	−13226.3	−	74222.2i	−0.0158324	−	0.0888467i
$915$		0			0
$916$	−587855.	+	216382.i	−0.700615	+	0.257887i
$917$	−116490.			−0.138532
$918$		0			0
$919$			1.37883e6i			1.63260i	0.577626	+	0.816301i	$0.303979\pi$
$919$			1.37883e6i			1.63260i	−0.577626	+	0.816301i	$0.696021\pi$
$920$	9576.76	+	1.75881e6i	0.0113147	+	2.07799i
$921$		0			0
$922$	41172.4	+	231048.i	0.0484334	+	0.271794i
$923$	−339597.	+	196066.i	−0.398621	+	0.230144i
$924$		0			0
$925$	−20310.8	+	35179.3i	−0.0237380	+	0.0411153i
$926$	64709.1	−	178796.i	0.0754646	−	0.208514i
$927$		0			0
$928$	−133802.	+	801287.i	−0.155370	+	0.930448i
$929$	−130885.	+	226699.i	−0.151656	+	0.262675i	−0.931836	−	0.362879i	$-0.881794\pi$
$929$	−130885.	+	226699.i	−0.151656	+	0.262675i	0.780181	+	0.625554i	$0.215127\pi$
$930$		0			0
$931$	−288946.	+	166823.i	−0.333363	+	0.192467i
$932$	6279.14	−	36382.6i	0.00722883	−	0.0418853i
$933$		0			0
$934$	−388273.	−	461023.i	−0.445085	−	0.528481i
$935$		−	1.56506e6i		−	1.79022i
$936$		0			0
$937$	1.29656e6			1.47677			0.738384	−	0.674380i	$-0.235589\pi$
$937$	1.29656e6			1.47677			0.738384	+	0.674380i	$0.235589\pi$
$938$	555246.	−	467627.i	0.631073	−	0.531488i
$939$		0			0
$940$	−508978.	−	87842.7i	−0.576027	−	0.0994146i
$941$	−211160.	−	365741.i	−0.238470	−	0.413042i	0.721806	−	0.692096i	$-0.243312\pi$
$941$	−211160.	−	365741.i	−0.238470	−	0.413042i	−0.960275	+	0.279054i	$0.909979\pi$
$942$		0			0
$943$	878816.	+	507385.i	0.988267	+	0.570576i
$944$	−1.17383e6	+	215776.i	−1.31723	+	0.242136i
$945$		0			0
$946$	−1.36071e6	−	492462.i	−1.52048	−	0.550288i
$947$	−844845.	−	487772.i	−0.942057	−	0.543897i	−0.0514525	−	0.998675i	$-0.516385\pi$
$947$	−844845.	−	487772.i	−0.942057	−	0.543897i	−0.890605	+	0.454779i	$0.849718\pi$
$948$		0			0
$949$	−86379.8	−	149614.i	−0.0959135	−	0.166127i
$950$	145841.	−	25988.7i	0.161597	−	0.0287964i
$951$		0			0
$952$	4506.24	+	827589.i	0.00497211	+	0.913147i
$953$	−1.52194e6			−1.67576			−0.837878	−	0.545857i	$-0.816204\pi$
$953$	−1.52194e6			−1.67576			−0.837878	+	0.545857i	$0.816204\pi$
$954$		0			0
$955$		−	538502.i		−	0.590447i
$956$	−421201.	−	1.14430e6i	−0.460865	−	1.25206i
$957$		0			0
$958$	−217492.	+	38756.9i	−0.236981	+	0.0422297i
$959$	−108877.	+	62860.3i	−0.118386	+	0.0683501i
$960$		0			0
$961$	−407448.	+	705720.i	−0.441190	+	0.764163i
$962$	69843.8	+	25277.6i	0.0754705	+	0.0273140i
$963$		0			0
$964$	200567.	+	167058.i	0.215826	+	0.179769i
$965$	−135239.	+	234241.i	−0.145227	+	0.251540i
$966$		0			0
$967$	1.31627e6	−	759947.i	1.40764	−	0.812700i	0.412478	−	0.910967i	$-0.364663\pi$
$967$	1.31627e6	−	759947.i	1.40764	−	0.812700i	0.995160	+	0.0982670i	$0.0313299\pi$
$968$	−90901.4	+	159445.i	−0.0970108	+	0.170161i
$969$		0			0
$970$	−192722.	+	162310.i	−0.204827	+	0.172505i
$971$		−	606895.i		−	0.643687i	−0.946793	−	0.321844i	$-0.895697\pi$
$971$		−	606895.i		−	0.643687i	0.946793	−	0.321844i	$-0.104303\pi$
$972$		0			0
$973$	221881.			0.234366
$974$	7667.21	+	9103.82i	0.00808201	+	0.00959634i
$975$		0			0
$976$	−1.09142e6	+	929395.i	−1.14576	+	0.975665i
$977$	−440254.	−	762542.i	−0.461226	−	0.798867i	0.537796	−	0.843075i	$-0.319257\pi$
$977$	−440254.	−	762542.i	−0.461226	−	0.798867i	−0.999022	+	0.0442080i	$0.985924\pi$
$978$		0			0
$979$	−52559.6	−	30345.3i	−0.0548386	−	0.0316611i
$980$	613101.	+	510672.i	0.638381	+	0.531728i
$981$		0			0
$982$	368508.	−	1.01821e6i	0.382141	−	1.05588i
$983$	1.55074e6	+	895318.i	1.60484	+	0.926553i	0.990501	+	0.137509i	$0.0439095\pi$
$983$	1.55074e6	+	895318.i	1.60484	+	0.926553i	0.614336	+	0.789044i	$0.289424\pi$
$984$		0			0
$985$	−309695.	−	536407.i	−0.319199	−	0.552869i
$986$	280681.	+	1.57510e6i	0.288708	+	1.62015i
$987$		0			0
$988$	−93567.6	−	254200.i	−0.0958543	−	0.260413i
$989$	3.20275e6			3.27439
$990$		0			0
$991$		−	1.12180e6i		−	1.14227i	−0.820858	−	0.571133i	$-0.806504\pi$
$991$		−	1.12180e6i		−	1.14227i	0.820858	−	0.571133i	$-0.193496\pi$
$992$	214582.	−	260493.i	0.218057	−	0.264712i
$993$		0			0
$994$	79795.9	+	447791.i	0.0807621	+	0.453213i
$995$	625885.	−	361355.i	0.632191	−	0.364996i
$996$		0			0
$997$	−420584.	+	728473.i	−0.423119	+	0.732864i	−0.996243	−	0.0866051i	$-0.972398\pi$
$997$	−420584.	+	728473.i	−0.423119	+	0.732864i	0.573124	+	0.819469i	$0.305731\pi$
$998$	355769.	−	983016.i	0.357197	−	0.986960i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.19.18		44
3.2	odd	2		36.5.f.a.7.5	✓	44
4.3	odd	2	inner	108.5.f.a.19.13		44
9.2	odd	6		324.5.d.f.163.20		22
9.4	even	3	inner	108.5.f.a.91.13		44
9.5	odd	6		36.5.f.a.31.10	yes	44
9.7	even	3		324.5.d.e.163.3		22
12.11	even	2		36.5.f.a.7.10	yes	44
36.7	odd	6		324.5.d.e.163.4		22
36.11	even	6		324.5.d.f.163.19		22
36.23	even	6		36.5.f.a.31.5	yes	44
36.31	odd	6	inner	108.5.f.a.91.18		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.5	✓	44	3.2	odd	2
36.5.f.a.7.10	yes	44	12.11	even	2
36.5.f.a.31.5	yes	44	36.23	even	6
36.5.f.a.31.10	yes	44	9.5	odd	6
108.5.f.a.19.13		44	4.3	odd	2	inner
108.5.f.a.19.18		44	1.1	even	1	trivial
108.5.f.a.91.13		44	9.4	even	3	inner
108.5.f.a.91.18		44	36.31	odd	6	inner
324.5.d.e.163.3		22	9.7	even	3
324.5.d.e.163.4		22	36.7	odd	6
324.5.d.f.163.19		22	36.11	even	6
324.5.d.f.163.20		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)

\(f(q)\)	\(=\)	\(q+(3.05951 - 2.57671i) q^{2} +(2.72116 - 15.7669i) q^{4} +(-14.3046 - 24.7763i) q^{5} +(22.2124 + 12.8243i) q^{7} +(-32.3013 - 55.2506i) q^{8} +O(q^{10})\)	\(q+(3.05951 - 2.57671i) q^{2} +(2.72116 - 15.7669i) q^{4} +(-14.3046 - 24.7763i) q^{5} +(22.2124 + 12.8243i) q^{7} +(-32.3013 - 55.2506i) q^{8} +(-107.606 - 38.9445i) q^{10} +(-93.9677 - 54.2523i) q^{11} +(44.2246 + 76.5993i) q^{13} +(101.004 - 17.9987i) q^{14} +(-241.191 - 85.8084i) q^{16} -504.169 q^{17} -191.405i q^{19} +(-429.571 + 158.119i) q^{20} +(-427.287 + 76.1421i) q^{22} +(831.897 - 480.296i) q^{23} +(-96.7443 + 167.566i) q^{25} +(332.680 + 120.402i) q^{26} +(262.643 - 315.324i) q^{28} +(396.671 - 687.053i) q^{29} +(-285.428 + 164.792i) q^{31} +(-959.027 + 358.946i) q^{32} +(-1542.51 + 1299.10i) q^{34} -733.789i q^{35} +209.943 q^{37} +(-493.194 - 585.604i) q^{38} +(-906.848 + 1590.65i) q^{40} +(528.200 + 914.869i) q^{41} +(2887.45 + 1667.07i) q^{43} +(-1111.09 + 1333.95i) q^{44} +(1307.61 - 3613.02i) q^{46} +(977.185 + 564.178i) q^{47} +(-871.573 - 1509.61i) q^{49} +(135.779 + 761.951i) q^{50} +(1328.08 - 488.847i) q^{52} -1138.62 q^{53} +3104.23i q^{55} +(-8.93796 - 1641.49i) q^{56} +(-556.720 - 3124.15i) q^{58} +(4037.49 - 2331.05i) q^{59} +(2799.84 - 4849.46i) q^{61} +(-448.648 + 1239.65i) q^{62} +(-2009.25 + 3569.33i) q^{64} +(1265.23 - 2191.45i) q^{65} +(6127.74 - 3537.85i) q^{67} +(-1371.92 + 7949.19i) q^{68} +(-1890.76 - 2245.03i) q^{70} +4433.42i q^{71} -1953.21 q^{73} +(642.322 - 540.962i) q^{74} +(-3017.86 - 520.842i) q^{76} +(-1391.50 - 2410.15i) q^{77} +(-1523.90 - 879.826i) q^{79} +(1324.12 + 7203.27i) q^{80} +(3973.38 + 1438.03i) q^{82} +(-2621.64 - 1513.61i) q^{83} +(7211.95 + 12491.5i) q^{85} +(13129.7 - 2339.71i) q^{86} +(37.8113 + 6944.19i) q^{88} +559.336 q^{89} +2268.61i q^{91} +(-5309.06 - 14423.4i) q^{92} +(4443.42 - 791.814i) q^{94} +(-4742.31 + 2737.97i) q^{95} +(1100.89 - 1906.79i) q^{97} +(-6556.40 - 2372.87i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 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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