LMFDB - Embedded newform 108.5.f.a.91.13

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			91.13
Character	$\chi$	$=$	108.91
Dual form			108.5.f.a.19.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.701741 + 3.93796i) q^{2} +(-15.0151 + 5.52686i) q^{4} +(-14.3046 + 24.7763i) q^{5} +(-22.2124 + 12.8243i) q^{7} +(-32.3013 - 55.2506i) q^{8} +O(q^{10})$	\(q+(0.701741 + 3.93796i) q^{2} +(-15.0151 + 5.52686i) q^{4} +(-14.3046 + 24.7763i) q^{5} +(-22.2124 + 12.8243i) q^{7} +(-32.3013 - 55.2506i) q^{8} +(-107.606 - 38.9445i) q^{10} +(93.9677 - 54.2523i) q^{11} +(44.2246 - 76.5993i) q^{13} +(-66.0891 - 78.4722i) q^{14} +(194.908 - 165.973i) q^{16} -504.169 q^{17} -191.405i q^{19} +(77.8502 - 451.079i) q^{20} +(279.585 + 331.970i) q^{22} +(-831.897 - 480.296i) q^{23} +(-96.7443 - 167.566i) q^{25} +(332.680 + 120.402i) q^{26} +(262.643 - 315.324i) q^{28} +(396.671 + 687.053i) q^{29} +(285.428 + 164.792i) q^{31} +(790.370 + 651.069i) q^{32} +(-353.796 - 1985.40i) q^{34} -733.789i q^{35} +209.943 q^{37} +(753.745 - 134.317i) q^{38} +(1830.96 - 9.96965i) q^{40} +(528.200 - 914.869i) q^{41} +(-2887.45 + 1667.07i) q^{43} +(-1111.09 + 1333.95i) q^{44} +(1307.61 - 3613.02i) q^{46} +(-977.185 + 564.178i) q^{47} +(-871.573 + 1509.61i) q^{49} +(591.979 - 498.563i) q^{50} +(-240.684 + 1394.57i) q^{52} -1138.62 q^{53} +3104.23i q^{55} +(1426.04 + 813.005i) q^{56} +(-2427.23 + 2044.21i) q^{58} +(-4037.49 - 2331.05i) q^{59} +(2799.84 + 4849.46i) q^{61} +(-448.648 + 1239.65i) q^{62} +(-2009.25 + 3569.33i) q^{64} +(1265.23 + 2191.45i) q^{65} +(-6127.74 - 3537.85i) q^{67} +(7570.16 - 2786.47i) q^{68} +(2889.63 - 514.930i) q^{70} +4433.42i q^{71} -1953.21 q^{73} +(147.326 + 826.748i) q^{74} +(1057.87 + 2873.97i) q^{76} +(-1391.50 + 2410.15i) q^{77} +(1523.90 - 879.826i) q^{79} +(1324.12 + 7203.27i) q^{80} +(3973.38 + 1438.03i) q^{82} +(2621.64 - 1513.61i) q^{83} +(7211.95 - 12491.5i) q^{85} +(-8591.12 - 10200.8i) q^{86} +(-6032.75 - 3439.35i) q^{88} +559.336 q^{89} +2268.61i q^{91} +(15145.6 + 2613.92i) q^{92} +(-2907.44 - 3452.21i) q^{94} +(4742.31 + 2737.97i) q^{95} +(1100.89 + 1906.79i) q^{97} +(-6556.40 - 2372.87i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.701741	+	3.93796i	0.175435	+	0.984491i
$2$	0.701741	+	3.93796i	0.175435	+	0.984491i
$3$		0			0
$3$		0			0
$4$	−15.0151	+	5.52686i	−0.938445	+	0.345429i
$5$	−14.3046	+	24.7763i	−0.572185	+	0.991053i	0.424156	+	0.905589i	$0.360571\pi$
$5$	−14.3046	+	24.7763i	−0.572185	+	0.991053i	−0.996341	+	0.0854642i	$0.972763\pi$
$6$		0			0
$7$	−22.2124	+	12.8243i	−0.453314	+	0.261721i	−0.709229	−	0.704978i	$-0.750957\pi$
$7$	−22.2124	+	12.8243i	−0.453314	+	0.261721i	0.255915	+	0.966699i	$0.417623\pi$
$8$	−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	$-0.518673\pi$
$11$	93.9677	−	54.2523i	0.776593	−	0.448366i	0.835221	+	0.549914i	$0.185339\pi$
$12$		0			0
$13$	44.2246	−	76.5993i	0.261684	−	0.453250i	−0.705005	−	0.709202i	$-0.749055\pi$
$13$	44.2246	−	76.5993i	0.261684	−	0.453250i	0.966690	+	0.255952i	$0.0823888\pi$
$14$	−66.0891	−	78.4722i	−0.337189	−	0.400369i
$15$		0			0
$16$	194.908	−	165.973i	0.761358	−	0.648332i
$17$	−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	$-0.0854062\pi$
$20$	77.8502	−	451.079i	0.194625	−	1.12770i
$21$		0			0
$22$	279.585	+	331.970i	0.577654	+	0.685889i
$23$	−831.897	−	480.296i	−1.57258	−	0.907932i	−0.995851	−	0.0909988i	$-0.970994\pi$
$23$	−831.897	−	480.296i	−1.57258	−	0.907932i	−0.576733	−	0.816933i	$-0.695673\pi$
$24$		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	0.999475	−	0.0324147i	$-0.0103197\pi$
$29$	396.671	+	687.053i	0.471665	+	0.816948i	−0.527809	+	0.849363i	$0.676986\pi$
$30$		0			0
$31$	285.428	+	164.792i	0.297011	+	0.171480i	0.641099	−	0.767458i	$-0.278479\pi$
$31$	285.428	+	164.792i	0.297011	+	0.171480i	−0.344088	+	0.938937i	$0.611812\pi$
$32$	790.370	+	651.069i	0.771846	+	0.635809i
$33$		0			0
$34$	−353.796	−	1985.40i	−0.306052	−	1.71747i
$35$		−	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	$0.475569\pi$
$38$	753.745	−	134.317i	0.521984	−	0.0930171i
$39$		0			0
$40$	1830.96	−	9.96965i	1.14435	−	0.00623103i
$41$	528.200	−	914.869i	0.314218	−	0.544241i	−0.665053	−	0.746796i	$-0.731591\pi$
$41$	528.200	−	914.869i	0.314218	−	0.544241i	0.979271	+	0.202555i	$0.0649245\pi$
$42$		0			0
$43$	−2887.45	+	1667.07i	−1.56163	+	0.901608i	−0.564537	+	0.825407i	$0.690945\pi$
$43$	−2887.45	+	1667.07i	−1.56163	+	0.901608i	−0.997093	+	0.0762001i	$0.975721\pi$
$44$	−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	$-0.748874\pi$
$47$	−977.185	+	564.178i	−0.442365	+	0.255400i	0.262235	+	0.965004i	$0.415540\pi$
$48$		0			0
$49$	−871.573	+	1509.61i	−0.363004	+	0.628742i
$50$	591.979	−	498.563i	0.236792	−	0.199425i
$51$		0			0
$52$	−240.684	+	1394.57i	−0.0890104	+	0.515744i
$53$	−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
$56$	1426.04	+	813.005i	0.454732	+	0.259249i
$57$		0			0
$58$	−2427.23	+	2044.21i	−0.721531	+	0.607672i
$59$	−4037.49	−	2331.05i	−1.15987	−	0.669648i	−0.208593	−	0.978002i	$-0.566889\pi$
$59$	−4037.49	−	2331.05i	−1.15987	−	0.669648i	−0.951272	+	0.308354i	$0.900222\pi$
$60$		0			0
$61$	2799.84	+	4849.46i	0.752442	+	1.30327i	0.946636	+	0.322305i	$0.104458\pi$
$61$	2799.84	+	4849.46i	0.752442	+	1.30327i	−0.194193	+	0.980963i	$0.562209\pi$
$62$	−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	$-0.622276\pi$
$67$	−6127.74	−	3537.85i	−1.36506	−	0.788116i	−0.990292	+	0.139004i	$0.955610\pi$
$68$	7570.16	−	2786.47i	1.63715	−	0.602611i
$69$		0			0
$70$	2889.63	−	514.930i	0.589721	−	0.105088i
$71$			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	$0.558666\pi$
$74$	147.326	+	826.748i	0.0269039	+	0.150977i
$75$		0			0
$76$	1057.87	+	2873.97i	0.183149	+	0.497570i
$77$	−1391.50	+	2410.15i	−0.234694	+	0.406501i
$78$		0			0
$79$	1523.90	−	879.826i	0.244176	−	0.140975i	−0.372918	−	0.927864i	$-0.621643\pi$
$79$	1523.90	−	879.826i	0.244176	−	0.140975i	0.617095	+	0.786889i	$0.288310\pi$
$80$	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	$-0.596154\pi$
$83$	2621.64	−	1513.61i	0.380555	−	0.219714i	0.678060	+	0.735007i	$0.262821\pi$
$84$		0			0
$85$	7211.95	−	12491.5i	0.998193	−	1.72892i
$86$	−8591.12	−	10200.8i	−1.16159	−	1.37924i
$87$		0			0
$88$	−6032.75	−	3439.35i	−0.779023	−	0.444131i
$89$	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
$92$	15145.6	+	2613.92i	1.78941	+	0.308828i
$93$		0			0
$94$	−2907.44	−	3452.21i	−0.329045	−	0.390698i
$95$	4742.31	+	2737.97i	0.525463	+	0.303376i
$96$		0			0
$97$	1100.89	+	1906.79i	0.117004	+	0.202656i	0.918579	−	0.395238i	$-0.129338\pi$
$97$	1100.89	+	1906.79i	0.117004	+	0.202656i	−0.801575	+	0.597894i	$0.796004\pi$
$98$	−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	0.847537	−	0.530737i	$-0.178085\pi$
$101$	−365.841	−	633.655i	−0.0358632	−	0.0621170i	−0.883400	+	0.468620i	$0.844751\pi$
$102$		0			0
$103$	8533.78	+	4926.98i	0.804391	+	0.464415i	0.845004	−	0.534760i	$-0.179598\pi$
$103$	8533.78	+	4926.98i	0.804391	+	0.464415i	−0.0406134	+	0.999175i	$0.512931\pi$
$104$	−5660.67	+	30.8225i	−0.523361	+	0.00284971i
$105$		0			0
$106$	−799.013	−	4483.83i	−0.0711119	−	0.399059i
$107$			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	$0.760062\pi$
$110$	−12224.4	+	2178.37i	−1.01028	+	0.180030i
$111$		0			0
$112$	−2200.87	+	6186.22i	−0.175452	+	0.493161i
$113$	8573.94	−	14850.5i	0.671465	−	1.16301i	−0.306024	−	0.952024i	$-0.598999\pi$
$113$	8573.94	−	14850.5i	0.671465	−	1.16301i	0.977489	−	0.210988i	$-0.0676680\pi$
$114$		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
$122$	−17132.2	+	14428.7i	−1.15105	+	0.969412i
$123$		0			0
$124$	−5196.51	−	896.848i	−0.337963	−	0.0583278i
$125$	−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	$-0.0960986\pi$
$128$	−15465.9	−	5407.61i	−0.943962	−	0.330054i
$129$		0			0
$130$	−7741.98	+	6520.27i	−0.458105	+	0.385815i
$131$	3933.27	+	2270.88i	0.229198	+	0.132328i	0.610202	−	0.792246i	$-0.291088\pi$
$131$	3933.27	+	2270.88i	0.229198	+	0.132328i	−0.381004	+	0.924573i	$0.624422\pi$
$132$		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	0.793321	−	0.608803i	$-0.208350\pi$
$137$	−2450.82	−	4244.95i	−0.130578	−	0.226168i	−0.923900	+	0.382635i	$0.875017\pi$
$138$		0			0
$139$	−7491.80	−	4325.39i	−0.387754	−	0.223870i	0.293432	−	0.955980i	$-0.405202\pi$
$139$	−7491.80	−	4325.39i	−0.387754	−	0.223870i	−0.681187	+	0.732110i	$0.738536\pi$
$140$	4055.55	+	11017.9i	0.206916	+	0.562139i
$141$		0			0
$142$	−17458.6	+	3111.11i	−0.865832	+	0.154290i
$143$		−	9597.15i		−	0.469321i
$144$		0			0
$145$	−22696.9			−1.07952
$146$	−1370.65	−	7691.66i	−0.0643013	−	0.360840i
$147$		0			0
$148$	−3152.32	+	1160.33i	−0.143915	+	0.0529733i
$149$	−6346.46	+	10992.4i	−0.285863	+	0.495130i	−0.972818	−	0.231570i	$-0.925614\pi$
$149$	−6346.46	+	10992.4i	−0.285863	+	0.495130i	0.686955	+	0.726700i	$0.258947\pi$
$150$		0			0
$151$	11055.3	−	6382.78i	0.484860	−	0.279934i	−0.237579	−	0.971368i	$-0.576354\pi$
$151$	11055.3	−	6382.78i	0.484860	−	0.279934i	0.722440	+	0.691434i	$0.243021\pi$
$152$	−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	−0.0806612	−	0.996742i	$-0.525703\pi$
$157$	20283.0	−	35131.2i	0.822873	−	1.42526i	0.903534	−	0.428516i	$-0.140963\pi$
$158$	4534.11	+	5383.67i	0.181626	+	0.215657i
$159$		0			0
$160$	−27437.0	+	10269.2i	−1.07176	+	0.401140i
$161$	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	$0.958713\pi$
$164$	−2874.63	+	16656.2i	−0.106879	+	0.619280i
$165$		0			0
$166$	7800.24	+	9261.78i	0.283069	+	0.336108i
$167$	30405.5	+	17554.6i	1.09023	+	0.629447i	0.933639	−	0.358216i	$-0.116615\pi$
$167$	30405.5	+	17554.6i	1.09023	+	0.629447i	0.156595	+	0.987663i	$0.449948\pi$
$168$		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	0.889870	−	0.456214i	$-0.150795\pi$
$173$	1491.72	+	2583.74i	0.0498420	+	0.0863290i	−0.840028	+	0.542543i	$0.817462\pi$
$174$		0			0
$175$	4297.84	+	2481.36i	0.140338	+	0.0810240i
$176$	9310.60	−	26170.3i	0.300575	−	0.844857i
$177$		0			0
$178$	392.509	+	2202.65i	0.0123883	+	0.0695192i
$179$			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	$0.361593\pi$
$182$	−8933.68	+	1591.97i	−0.269704	+	0.0480610i
$183$		0			0
$184$	334.744	+	61477.0i	0.00988728	+	1.81584i
$185$	−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	$-0.749723\pi$
$191$	−16300.9	+	9411.33i	−0.446833	+	0.257979i	0.259659	+	0.965700i	$0.416390\pi$
$192$		0			0
$193$	−4727.11	+	8187.59i	−0.126906	+	0.219807i	−0.922476	−	0.386054i	$-0.873838\pi$
$193$	−4727.11	+	8187.59i	−0.126906	+	0.219807i	0.795571	+	0.605861i	$0.207171\pi$
$194$	−6736.35	+	5673.33i	−0.178987	+	0.150742i
$195$		0			0
$196$	4743.37	−	27484.0i	0.123474	−	0.715432i
$197$	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	$0.896670\pi$
$200$	−6133.15	+	10757.8i	−0.153329	+	0.268944i
$201$		0			0
$202$	2238.58	−	1885.33i	0.0548619	−	0.0462045i
$203$	−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	$-0.411191\pi$
$211$	−18674.0	−	10781.5i	−0.419443	−	0.242166i	−0.694839	+	0.719165i	$0.744524\pi$
$212$	17096.4	−	6292.97i	0.380394	−	0.140018i
$213$		0			0
$214$	−3168.65	+	564.650i	−0.0691906	+	0.0123297i
$215$		−	95387.3i		−	2.06354i
$216$		0			0
$217$	−8453.38			−0.179519
$218$	−12157.6	−	68224.9i	−0.255821	−	1.43559i
$219$		0			0
$220$	−17156.7	−	46610.4i	−0.354477	−	0.963025i
$221$	−22296.7	+	38619.0i	−0.456516	+	0.790709i
$222$		0			0
$223$	−16709.5	+	9647.22i	−0.336011	+	0.193996i	−0.658507	−	0.752575i	$-0.728812\pi$
$223$	−16709.5	+	9647.22i	−0.336011	+	0.193996i	0.322496	+	0.946571i	$0.395478\pi$
$224$	−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	$-0.883228\pi$
$227$	−56144.4	+	32415.0i	−1.08957	+	0.629063i	−0.156107	+	0.987740i	$0.549895\pi$
$228$		0			0
$229$	−19575.4	+	33905.7i	−0.373285	+	0.646549i	−0.990069	−	0.140584i	$-0.955102\pi$
$229$	−19575.4	+	33905.7i	−0.373285	+	0.646549i	0.616784	+	0.787133i	$0.288435\pi$
$230$	70812.6	+	84080.7i	1.33861	+	1.58943i
$231$		0			0
$232$	25147.1	−	44109.0i	0.467210	−	0.819504i
$233$	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
$236$	73506.8	+	12686.3i	1.31979	+	0.227777i
$237$		0			0
$238$	33320.1	+	39563.3i	0.588237	+	0.698455i
$239$	−65999.7	−	38104.9i	−1.15544	−	0.667091i	−0.205230	−	0.978714i	$-0.565794\pi$
$239$	−65999.7	−	38104.9i	−1.15544	−	0.667091i	−0.950206	+	0.311623i	$0.899128\pi$
$240$		0			0
$241$	−8157.12	−	14128.5i	−0.140444	−	0.243256i	0.787220	−	0.616672i	$-0.211520\pi$
$241$	−8157.12	−	14128.5i	−0.140444	−	0.243256i	−0.927664	+	0.373416i	$0.878186\pi$
$242$	−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
$248$	−114.852	−	21093.0i	−0.00186739	−	0.342954i
$249$		0			0
$250$	−8663.15	−	48615.0i	−0.138610	−	0.777840i
$251$		−	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
$254$	37771.0	−	6730.76i	0.585452	−	0.104327i
$255$		0			0
$256$	10441.9	−	64698.8i	0.159331	−	0.987225i
$257$	−28773.1	+	49836.4i	−0.435632	+	0.754537i	−0.997347	−	0.0727940i	$-0.976808\pi$
$257$	−28773.1	+	49836.4i	−0.435632	+	0.754537i	0.561715	+	0.827331i	$0.310142\pi$
$258$		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	$-0.474479\pi$
$263$	68019.2	−	39270.9i	0.983378	−	0.567753i	0.903288	+	0.429034i	$0.141146\pi$
$264$		0			0
$265$	16287.5	−	28210.7i	0.231933	−	0.401719i
$266$	−15020.0	+	12649.8i	−0.212278	+	0.178780i
$267$		0			0
$268$	111562.	+	19254.1i	1.55327	+	0.268073i
$269$	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	$0.736688\pi$
$272$	−98266.4	+	83678.5i	−1.32821	+	1.13103i
$273$		0			0
$274$	14996.6	−	12630.1i	0.199752	−	0.168231i
$275$	−18181.7	−	10497.2i	−0.240419	−	0.138806i
$276$		0			0
$277$	21971.1	+	38055.1i	0.286347	+	0.495968i	0.972935	−	0.231079i	$-0.0742255\pi$
$277$	21971.1	+	38055.1i	0.286347	+	0.495968i	−0.686588	+	0.727047i	$0.740892\pi$
$278$	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	0.980927	−	0.194375i	$-0.0622680\pi$
$281$	25435.7	+	44055.9i	0.322130	+	0.557945i	−0.658798	+	0.752320i	$0.728935\pi$
$282$		0			0
$283$	−22858.8	−	13197.5i	−0.285418	−	0.164786i	0.350456	−	0.936579i	$-0.386027\pi$
$283$	−22858.8	−	13197.5i	−0.285418	−	0.164786i	−0.635873	+	0.771793i	$0.719360\pi$
$284$	−24502.9	−	66568.3i	−0.303795	−	0.825336i
$285$		0			0
$286$	37793.2	−	6734.71i	0.462042	−	0.0823355i
$287$			27095.2i			0.328950i
$288$		0			0
$289$	170665.			2.04338
$290$	−15927.3	−	89379.5i	−0.189386	−	1.06278i
$291$		0			0
$292$	29327.6	−	10795.1i	0.343963	−	0.126608i
$293$	65395.3	−	113268.i	0.761748	−	1.31939i	−0.180201	−	0.983630i	$-0.557675\pi$
$293$	65395.3	−	113268.i	0.761748	−	1.31939i	0.941949	−	0.335757i	$-0.108992\pi$
$294$		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
$302$	32893.1	+	39056.3i	0.360654	+	0.428230i
$303$		0			0
$304$	−31768.0	−	37306.2i	−0.343750	−	0.403677i
$305$	−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	$-0.0928843\pi$
$308$	7572.97	−	43879.3i	0.0798297	−	0.462549i
$309$		0			0
$310$	−24296.1	−	28848.5i	−0.252821	−	0.300193i
$311$	117745.	+	67980.1i	1.21737	+	0.702847i	0.964354	−	0.264616i	$-0.0852451\pi$
$311$	117745.	+	67980.1i	1.21737	+	0.702847i	0.253013	+	0.967463i	$0.418578\pi$
$312$		0			0
$313$	−82194.2	−	142364.i	−0.838981	−	1.45316i	−0.890747	−	0.454499i	$-0.849818\pi$
$313$	−82194.2	−	142364.i	−0.838981	−	1.45316i	0.0517658	−	0.998659i	$-0.483515\pi$
$314$	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	0.992796	+	0.119814i	$0.0382297\pi$
$317$	60309.5	+	104459.i	0.600160	+	1.03951i	−0.392637	+	0.919694i	$0.628437\pi$
$318$		0			0
$319$	74548.4	+	43040.6i	0.732584	+	0.422957i
$320$	−59693.4	−	100840.i	−0.582943	−	0.984763i
$321$		0			0
$322$	17289.4	+	97023.1i	0.166751	+	0.935758i
$323$			96500.4i			0.924962i
$324$		0			0
$325$	−17113.9			−0.162025
$326$	−27065.5	+	4823.05i	−0.254672	+	0.0453823i
$327$		0			0
$328$	−67608.6	+	368.131i	−0.628426	+	0.00342180i
$329$	14470.4	−	25063.5i	0.133687	−	0.231553i
$330$		0			0
$331$	−100184.	+	57841.2i	−0.914412	+	0.527936i	−0.881848	−	0.471534i	$-0.843701\pi$
$331$	−100184.	+	57841.2i	−0.914412	+	0.527936i	−0.0325639	+	0.999470i	$0.510367\pi$
$332$	−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	0.0742175	+	0.997242i	$0.476354\pi$
$337$	−93868.0	+	162584.i	−0.826528	+	1.43159i	−0.900746	+	0.434347i	$0.856979\pi$
$338$	−63447.2	+	53435.1i	−0.555366	+	0.467728i
$339$		0			0
$340$	−39249.7	+	227420.i	−0.339530	+	1.96730i
$341$	35761.3			0.307542
$342$		0			0
$343$		−	106292.i		−	0.903465i
$344$	185375.	+	105685.i	1.56652	+	0.893091i
$345$		0			0
$346$	−9127.87	+	7687.47i	−0.0762460	+	0.0642142i
$347$	−117124.	−	67621.8i	−0.972721	−	0.561601i	−0.0726566	−	0.997357i	$-0.523148\pi$
$347$	−117124.	−	67621.8i	−0.972721	−	0.561601i	−0.900065	+	0.435756i	$0.856481\pi$
$348$		0			0
$349$	−1651.44	−	2860.38i	−0.0135585	−	0.0234841i	0.859167	−	0.511696i	$-0.170983\pi$
$349$	−1651.44	−	2860.38i	−0.0135585	−	0.0234841i	−0.872725	+	0.488212i	$0.837649\pi$
$350$	−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	0.938933	−	0.344100i	$-0.111816\pi$
$353$	21366.4	+	37007.7i	0.171467	+	0.296990i	−0.767466	+	0.641090i	$0.778483\pi$
$354$		0			0
$355$	−109844.	−	63418.4i	−0.871603	−	0.503220i
$356$	−8398.50	+	3091.38i	−0.0662677	+	0.0243922i
$357$		0			0
$358$	−177993.	+	31718.2i	−1.38879	+	0.247481i
$359$			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
$362$	19368.7	+	108691.i	0.147803	+	0.829426i
$363$		0			0
$364$	−12538.3	−	34063.4i	−0.0946313	−	0.257090i
$365$	27939.9	−	48393.3i	0.209719	−	0.363245i
$366$		0			0
$367$	−6867.31	+	3964.84i	−0.0509864	+	0.0294370i	−0.525277	−	0.850932i	$-0.676038\pi$
$367$	−6867.31	+	3964.84i	−0.0509864	+	0.0294370i	0.474290	+	0.880369i	$0.342705\pi$
$368$	−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	−0.0424851	+	0.999097i	$0.513527\pi$
$373$	−123336.	+	213624.i	−0.886486	+	1.53544i	−0.844001	+	0.536342i	$0.819806\pi$
$374$	−140958.	−	167369.i	−1.00773	−	1.19655i
$375$		0			0
$376$	62735.5	+	35766.3i	0.443749	+	0.252987i
$377$	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	$-0.171526\pi$
$380$	−86338.7	−	14900.9i	−0.597914	−	0.103192i
$381$		0			0
$382$	−48500.5	−	57588.0i	−0.332368	−	0.394644i
$383$	105968.	+	61180.9i	0.722402	+	0.417079i	0.815636	−	0.578565i	$-0.196387\pi$
$383$	105968.	+	61180.9i	0.722402	+	0.417079i	−0.0932341	+	0.995644i	$0.529720\pi$
$384$		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	−0.991863	−	0.127306i	$-0.959367\pi$
$389$	−91728.1	−	158878.i	−0.606182	−	1.04994i	0.385682	−	0.922632i	$-0.373966\pi$
$390$		0			0
$391$	419417.	+	242150.i	2.74342	+	1.58391i
$392$	111560.	−	607.446i	0.725998	−	0.00395308i
$393$		0			0
$394$	15192.7	+	85256.9i	0.0978684	+	0.549208i
$395$			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	$0.416790\pi$
$398$	−99478.5	+	17727.0i	−0.628005	+	0.111910i
$399$		0			0
$400$	−46667.6	−	16602.9i	−0.291673	−	0.103768i
$401$	100584.	−	174217.i	0.625518	−	1.08343i	−0.362922	−	0.931820i	$-0.618221\pi$
$401$	100584.	−	174217.i	0.625518	−	1.08343i	0.988440	−	0.151610i	$-0.0484459\pi$
$402$		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	−0.575605	−	0.817728i	$-0.695233\pi$
$409$	70320.1	−	121798.i	0.420371	−	0.728104i	0.995976	+	0.0896241i	$0.0285666\pi$
$410$	−92466.8	+	77875.3i	−0.550070	+	0.463268i
$411$		0			0
$412$	−155367.	−	26814.2i	−0.915299	−	0.157968i
$413$	119576.			0.701044
$414$		0			0
$415$			86606.3i			0.502867i
$416$	84825.3	−	31748.5i	0.490161	−	0.183458i
$417$		0			0
$418$	63540.7	−	53513.8i	0.363663	−	0.306276i
$419$	133102.	+	76846.6i	0.758154	+	0.437720i	0.828633	−	0.559793i	$-0.189119\pi$
$419$	133102.	+	76846.6i	0.758154	+	0.437720i	−0.0704785	+	0.997513i	$0.522453\pi$
$420$		0			0
$421$	−77206.0	−	133725.i	−0.435599	−	0.754479i	0.561746	−	0.827310i	$-0.310130\pi$
$421$	−77206.0	−	133725.i	−0.435599	−	0.754479i	−0.997344	+	0.0728309i	$0.976797\pi$
$422$	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
$428$	−4447.15	−	12081.8i	−0.0242769	−	0.0659544i
$429$		0			0
$430$	375632.	−	66937.2i	2.03154	−	0.362019i
$431$		−	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	$0.545968\pi$
$434$	−5932.08	−	33289.1i	−0.0314940	−	0.176735i
$435$		0			0
$436$	260136.	−	95752.5i	1.36844	−	0.503706i
$437$	−91930.9	+	159229.i	−0.481392	+	0.833795i
$438$		0			0
$439$	14586.4	−	8421.44i	0.0756864	−	0.0436976i	−0.461679	−	0.887047i	$-0.652753\pi$
$439$	14586.4	−	8421.44i	0.0756864	−	0.0436976i	0.537366	+	0.843349i	$0.319420\pi$
$440$	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	$-0.801905\pi$
$443$	−140111.	+	80892.9i	−0.713943	+	0.412195i	0.0985761	+	0.995130i	$0.468571\pi$
$444$		0			0
$445$	−8001.09	+	13858.3i	−0.0404045	+	0.0699826i
$446$	−49716.1	−	59031.5i	−0.249935	−	0.296766i
$447$		0			0
$448$	−1144.04	−	105051.i	−0.00570015	−	0.523411i
$449$	−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
$452$	−46662.0	+	270369.i	−0.228395	+	1.32337i
$453$		0			0
$454$	−167048.	−	198348.i	−0.810456	−	0.962311i
$455$	−56207.7	−	32451.5i	−0.271502	−	0.156752i
$456$		0			0
$457$	9423.93	+	16322.7i	0.0451232	+	0.0781556i	0.887705	−	0.460413i	$-0.152299\pi$
$457$	9423.93	+	16322.7i	0.0451232	+	0.0781556i	−0.842582	+	0.538569i	$0.818965\pi$
$458$	−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	0.788716	−	0.614758i	$-0.210746\pi$
$461$	−29335.9	−	50811.3i	−0.138038	−	0.239088i	−0.926754	+	0.375669i	$0.877413\pi$
$462$		0			0
$463$	−41167.7	−	23768.2i	−0.192041	−	0.110875i	0.400897	−	0.916123i	$-0.368699\pi$
$463$	−41167.7	−	23768.2i	−0.192041	−	0.110875i	−0.592938	+	0.805248i	$0.702032\pi$
$464$	191346.	+	68075.3i	0.888760	+	0.316194i
$465$		0			0
$466$	1619.29	+	9086.96i	0.00745679	+	0.0418453i
$467$		−	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
$470$	127123.	−	22653.2i	0.575478	−	0.102550i
$471$		0			0
$472$	1624.63	+	298370.i	0.00729240	+	1.33928i
$473$	−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	$-0.628263\pi$
$479$	47830.3	−	27614.8i	0.208464	−	0.120357i	0.600598	+	0.799551i	$0.294929\pi$
$480$		0			0
$481$	9284.65	−	16081.5i	0.0401306	−	0.0695082i
$482$	49913.5	−	42037.0i	0.214844	−	0.180941i
$483$		0			0
$484$	7803.61	−	45215.7i	0.0333123	−	0.193018i
$485$	−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	$0.998003\pi$
$488$	177497.	−	311337.i	0.745335	−	1.30735i
$489$		0			0
$490$	152578.	−	128501.i	0.635476	−	0.535196i
$491$	−234443.	−	135356.i	−0.972467	−	0.561454i	−0.0724794	−	0.997370i	$-0.523091\pi$
$491$	−234443.	−	135356.i	−0.972467	−	0.561454i	−0.899987	+	0.435916i	$0.856424\pi$
$492$		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	$-0.509195\pi$
$499$	−226339.	−	130677.i	−0.908988	−	0.524805i	−0.880105	+	0.474778i	$0.842528\pi$
$500$	185365.	−	68230.3i	0.741459	−	0.272921i
$501$		0			0
$502$	133236.	−	23742.5i	0.528704	−	0.0942146i
$503$		−	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
$506$	−73141.5	−	410448.i	−0.285669	−	1.60309i
$507$		0			0
$508$	53010.9	+	144018.i	0.205418	+	0.558069i
$509$	−106839.	+	185051.i	−0.412378	+	0.714259i	−0.995149	−	0.0983769i	$-0.968635\pi$
$509$	−106839.	+	185051.i	−0.412378	+	0.714259i	0.582772	+	0.812636i	$0.301968\pi$
$510$		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
$518$	−13874.9	−	16474.7i	−0.0517097	−	0.0613985i
$519$		0			0
$520$	80210.0	−	140691.i	0.296635	−	0.520309i
$521$	−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	$0.860857\pi$
$524$	−71609.4	−	12358.8i	−0.260800	−	0.0450105i
$525$		0			0
$526$	202379.	+	240299.i	0.731467	+	0.868522i
$527$	−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
$536$	2465.72	+	452838.i	0.00858250	+	1.57621i
$537$		0			0
$538$	3773.23	+	21174.3i	0.0130361	+	0.0731550i
$539$			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	$0.501932\pi$
$542$	−425745.	+	75867.3i	−1.44927	+	0.258259i
$543$		0			0
$544$	−398480.	−	328249.i	−1.34651	−	1.10919i
$545$	247826.	−	429248.i	0.834362	−	1.44516i
$546$		0			0
$547$	−444293.	+	256513.i	−1.48489	+	0.857302i	−0.999852	−	0.0171904i	$-0.994528\pi$
$547$	−444293.	+	256513.i	−1.48489	+	0.857302i	−0.485039	+	0.874493i	$0.661195\pi$
$548$	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
$554$	−134442.	+	113226.i	−0.438041	+	0.368917i
$555$		0			0
$556$	136396.	+	23540.1i	0.441217	+	0.0761482i
$557$	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
$560$	−121789.	−	143021.i	−0.388358	−	0.456062i
$561$		0			0
$562$	−155641.	+	131081.i	−0.492779	+	0.415017i
$563$	48439.2	+	27966.4i	0.152820	+	0.0882307i	0.574460	−	0.818533i	$-0.305212\pi$
$563$	48439.2	+	27966.4i	0.152820	+	0.0882307i	−0.421640	+	0.906763i	$0.638545\pi$
$564$		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	0.981737	+	0.190245i	$0.0609282\pi$
$569$	212266.	+	367655.i	0.655625	+	1.13558i	−0.326111	+	0.945331i	$0.605738\pi$
$570$		0			0
$571$	−25297.4	−	14605.5i	−0.0775897	−	0.0447964i	0.460703	−	0.887554i	$-0.347597\pi$
$571$	−25297.4	−	14605.5i	−0.0775897	−	0.0447964i	−0.538293	+	0.842758i	$0.680931\pi$
$572$	53042.1	+	144102.i	0.162117	+	0.440432i
$573$		0			0
$574$	−106700.	+	19013.9i	−0.323848	+	0.0577094i
$575$			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	$0.766449\pi$
$578$	119763.	+	672074.i	0.358482	+	2.01169i
$579$		0			0
$580$	340796.	−	125443.i	1.01307	−	0.372897i
$581$	−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	$-0.780099\pi$
$587$	−208206.	+	120208.i	−0.604251	+	0.348865i	0.166461	+	0.986048i	$0.446766\pi$
$588$		0			0
$589$	31541.9	−	54632.2i	0.0909197	−	0.157477i
$590$	343678.	+	408074.i	0.987298	+	1.17229i
$591$		0			0
$592$	40919.5	−	34844.9i	0.116758	−	0.0994250i
$593$	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
$596$	34539.4	−	200128.i	0.0972349	−	0.563398i
$597$		0			0
$598$	−218926.	−	259947.i	−0.612203	−	0.726912i
$599$	8669.92	+	5005.58i	0.0241636	+	0.0139509i	0.512033	−	0.858966i	$-0.328892\pi$
$599$	8669.92	+	5005.58i	0.0241636	+	0.0139509i	−0.487870	+	0.872917i	$0.662226\pi$
$600$		0			0
$601$	−196449.	−	340259.i	−0.543876	−	0.942021i	−0.998677	−	0.0514280i	$-0.983623\pi$
$601$	−196449.	−	340259.i	−0.543876	−	0.942021i	0.454800	−	0.890593i	$-0.349711\pi$
$602$	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	$-0.533529\pi$
$607$	−375426.	−	216752.i	−1.01894	−	0.588283i	−0.913796	+	0.406174i	$0.866863\pi$
$608$	124618.	−	151281.i	0.337111	−	0.409238i
$609$		0			0
$610$	−112421.	−	630872.i	−0.302125	−	1.69544i
$611$			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	$0.368393\pi$
$614$	213545.	−	38053.5i	0.566439	−	0.100939i
$615$		0			0
$616$	178109.	−	969.810i	0.469380	−	0.00255579i
$617$	98373.3	−	170388.i	0.258409	−	0.447577i	−0.707407	−	0.706806i	$-0.750135\pi$
$617$	98373.3	−	170388.i	0.258409	−	0.447577i	0.965816	+	0.259229i	$0.0834686\pi$
$618$		0			0
$619$	536199.	−	309575.i	1.39941	−	0.807949i	0.405078	−	0.914282i	$-0.367244\pi$
$619$	536199.	−	309575.i	1.39941	−	0.807949i	0.994331	+	0.106333i	$0.0339110\pi$
$620$	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
$626$	502947.	−	423581.i	1.28343	−	1.08090i
$627$		0			0
$628$	−110386.	+	639600.i	−0.279896	+	1.62177i
$629$	−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	$-0.126744\pi$
$632$	−97835.0	−	55777.0i	−0.244940	−	0.139644i
$633$		0			0
$634$	−369034.	+	310800.i	−0.918096	+	0.773218i
$635$	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	0.578935	−	0.815373i	$-0.303468\pi$
$641$	−171200.	−	296528.i	−0.416666	−	0.721687i	−0.995602	+	0.0936860i	$0.970135\pi$
$642$		0			0
$643$	478867.	+	276474.i	1.15823	+	0.668702i	0.950878	−	0.309566i	$-0.100184\pi$
$643$	478867.	+	276474.i	1.15823	+	0.668702i	0.207347	+	0.978267i	$0.433517\pi$
$644$	−369941.	+	136170.i	−0.891991	+	0.328330i
$645$		0			0
$646$	−380015.	+	67718.3i	−0.910617	+	0.162271i
$647$		−	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
$650$	−12009.5	−	67394.0i	−0.0284250	−	0.159512i
$651$		0			0
$652$	−37986.0	−	103199.i	−0.0893569	−	0.242761i
$653$	−286795.	+	496744.i	−0.672583	+	1.16495i	0.304586	+	0.952485i	$0.401482\pi$
$653$	−286795.	+	496744.i	−0.672583	+	1.16495i	−0.977169	+	0.212463i	$0.931852\pi$
$654$		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	$-0.796927\pi$
$659$	−299298.	+	172800.i	−0.689180	+	0.397899i	0.114125	+	0.993466i	$0.463594\pi$
$660$		0			0
$661$	187583.	−	324904.i	0.429330	−	0.743622i	−0.567484	−	0.823385i	$-0.692083\pi$
$661$	187583.	−	324904.i	0.429330	−	0.743622i	0.996814	+	0.0797628i	$0.0254163\pi$
$662$	−298080.	−	353931.i	−0.680168	−	0.807612i
$663$		0			0
$664$	−168310.	−	95955.8i	−0.381746	−	0.217638i
$665$	−140451.			−0.317600
$666$		0			0
$667$		−	762077.i		−	1.71296i
$668$	−553565.	−	95537.8i	−1.24055	−	0.214103i
$669$		0			0
$670$	521604.	+	619337.i	1.16196	+	1.37968i
$671$	526189.	+	303795.i	1.16868	+	0.674739i
$672$		0			0
$673$	286866.	+	496866.i	0.633358	+	1.09701i	0.986861	+	0.161574i	$0.0516571\pi$
$673$	286866.	+	496866.i	0.633358	+	1.09701i	−0.353503	+	0.935433i	$0.615010\pi$
$674$	−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	0.850590	−	0.525829i	$-0.176245\pi$
$677$	−13789.2	−	23883.6i	−0.0300859	−	0.0521103i	−0.880676	+	0.473719i	$0.842911\pi$
$678$		0			0
$679$	−48906.7	−	28236.3i	−0.106079	−	0.0612447i
$680$	−923116.	+	5026.39i	−1.99636	+	0.0108702i
$681$		0			0
$682$	25095.2	+	140827.i	0.0539538	+	0.302773i
$683$			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
$686$	418573.	−	74589.3i	0.889454	−	0.158500i
$687$		0			0
$688$	−286098.	+	804164.i	−0.604418	+	1.69890i
$689$	−50354.8	+	87217.2i	−0.106073	+	0.183723i
$690$		0			0
$691$	289343.	−	167052.i	0.605978	−	0.349862i	−0.165411	−	0.986225i	$-0.552895\pi$
$691$	289343.	−	167052.i	0.605978	−	0.349862i	0.771390	+	0.636363i	$0.219562\pi$
$692$	−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
$698$	10105.2	−	8510.57i	0.0207412	−	0.0174682i
$699$		0			0
$700$	−78246.8	−	13504.3i	−0.159687	−	0.0275599i
$701$	−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
$704$	4839.78	+	444408.i	0.00976517	+	0.896679i
$705$		0			0
$706$	−130741.	+	110110.i	−0.262303	+	0.220911i
$707$	16252.4	+	9383.33i	0.0325146	+	0.0187723i
$708$		0			0
$709$	−362484.	−	627841.i	−0.721102	−	1.24899i	−0.960558	−	0.278079i	$-0.910302\pi$
$709$	−362484.	−	627841.i	−0.721102	−	1.24899i	0.239456	−	0.970907i	$-0.423031\pi$
$710$	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
$716$	−249810.	−	678672.i	−0.487286	−	1.32384i
$717$		0			0
$718$	−692358.	+	123378.i	−1.34302	+	0.239325i
$719$			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
$722$	65742.8	+	368929.i	0.126117	+	0.707731i
$723$		0			0
$724$	−414431.	+	152546.i	−0.790632	+	0.291021i
$725$	76751.2	−	132937.i	0.146019	−	0.252912i
$726$		0			0
$727$	375814.	−	216977.i	0.711057	−	0.410529i	−0.100395	−	0.994948i	$-0.532011\pi$
$727$	375814.	−	216977.i	0.711057	−	0.410529i	0.811452	+	0.584418i	$0.198677\pi$
$728$	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	−0.232202	−	0.972667i	$-0.574593\pi$
$733$	390208.	−	675860.i	0.726254	−	1.25791i	0.958456	−	0.285241i	$-0.0920735\pi$
$734$	−20432.5	−	24260.9i	−0.0379253	−	0.0450314i
$735$		0			0
$736$	−344801.	−	921234.i	−0.636521	−	1.70065i
$737$	−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	$0.936889\pi$
$740$	16344.1	−	94700.9i	0.0298468	−	0.172938i
$741$		0			0
$742$	75250.1	+	89349.7i	0.136678	+	0.162288i
$743$	−250360.	−	144546.i	−0.453511	−	0.261835i	0.255801	−	0.966730i	$-0.417661\pi$
$743$	−250360.	−	144546.i	−0.453511	−	0.261835i	−0.709312	+	0.704895i	$0.750994\pi$
$744$		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	$-0.125644\pi$
$751$	593117.	+	342436.i	1.05162	+	0.607156i	0.128521	+	0.991707i	$0.458977\pi$
$752$	−96822.4	+	272149.i	−0.171214	+	0.481250i
$753$		0			0
$754$	49241.5	+	276329.i	0.0866141	+	0.486052i
$755$			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	$0.690909\pi$
$758$	580545.	−	103452.i	1.01041	−	0.180054i
$759$		0			0
$760$	−1908.24	−	350455.i	−0.00330374	−	0.606744i
$761$	383411.	−	664087.i	0.662057	−	1.14672i	−0.318018	−	0.948085i	$-0.603017\pi$
$761$	383411.	−	664087.i	0.662057	−	1.14672i	0.980074	−	0.198631i	$-0.0636495\pi$
$762$		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	−0.509766	−	0.860313i	$-0.670268\pi$
$769$	289867.	−	502065.i	0.490170	−	0.848999i	0.999936	+	0.0113137i	$0.00360135\pi$
$770$	243596.	−	205156.i	0.410855	−	0.346021i
$771$		0			0
$772$	25726.4	−	149064.i	0.0431662	−	0.250114i
$773$	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
$776$	69791.3	−	122417.i	0.115899	−	0.203291i
$777$		0			0
$778$	561285.	−	472713.i	0.927309	−	0.780977i
$779$	−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	$-0.655974\pi$
$787$	−910515.	−	525686.i	−1.47007	−	0.848744i	−0.999436	+	0.0335849i	$0.989308\pi$
$788$	−325077.	+	119657.i	−0.523521	+	0.192701i
$789$		0			0
$790$	−198246.	+	35327.3i	−0.317651	+	0.0566052i
$791$			439820.i			0.702946i
$792$		0			0
$793$	495287.			0.787609
$794$	57168.1	+	320811.i	0.0906803	+	0.508871i
$795$		0			0
$796$	−139616.	−	379303.i	−0.220348	−	0.598632i
$797$	−47409.2	+	82115.1i	−0.0746356	+	0.129273i	−0.900928	−	0.433969i	$-0.857113\pi$
$797$	−47409.2	+	82115.1i	−0.0746356	+	0.129273i	0.826292	+	0.563242i	$0.190446\pi$
$798$		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
$806$	75114.7	+	89189.0i	0.115626	+	0.137291i
$807$		0			0
$808$	−23192.7	+	40680.8i	−0.0355245	+	0.0623113i
$809$	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	$0.855406\pi$
$812$	320827.	+	55370.4i	0.486585	+	0.0839781i
$813$		0			0
$814$	58696.8	+	69694.9i	0.0885862	+	0.105185i
$815$	−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	−0.998553	−	0.0537749i	$-0.982875\pi$
$821$	−367923.	−	637262.i	−0.545847	−	0.945435i	0.452706	−	0.891660i	$-0.350459\pi$
$822$		0			0
$823$	−148172.	−	85547.4i	−0.218760	−	0.126301i	0.386616	−	0.922241i	$-0.373644\pi$
$823$	−148172.	−	85547.4i	−0.218760	−	0.126301i	−0.605376	+	0.795940i	$0.706977\pi$
$824$	−3433.88	−	630644.i	−0.00505743	−	0.928817i
$825$		0			0
$826$	83911.7	+	470888.i	0.122988	+	0.690172i
$827$		−	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	$0.698357\pi$
$830$	−341052.	+	60775.2i	−0.495068	+	0.0882206i
$831$		0			0
$832$	184550.	+	311760.i	0.266604	+	0.450374i
$833$	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	$-0.797615\pi$
$839$	−487546.	+	281485.i	−0.692615	+	0.399881i	0.111976	+	0.993711i	$0.464282\pi$
$840$		0			0
$841$	38945.5	−	67455.6i	0.0550637	−	0.0953732i
$842$	472424.	−	397874.i	0.666358	−	0.561205i
$843$		0			0
$844$	339980.	+	58676.0i	0.477275	+	0.0823713i
$845$	−593291.			−0.830910
$846$		0			0
$847$		−	73554.1i		−	0.102527i
$848$	−221925.	+	188979.i	−0.308613	+	0.262798i
$849$		0			0
$850$	−298458.	+	251360.i	−0.413090	+	0.347903i
$851$	−174651.	−	100835.i	−0.241164	−	0.139236i
$852$		0			0
$853$	331406.	+	574011.i	0.455472	+	0.788901i	0.998715	−	0.0506745i	$-0.0161371\pi$
$853$	331406.	+	574011.i	0.455472	+	0.788901i	−0.543243	+	0.839575i	$0.682804\pi$
$854$	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	0.936760	+	0.349973i	$0.113809\pi$
$857$	566602.	+	981383.i	0.771465	+	1.33622i	−0.165294	+	0.986244i	$0.552857\pi$
$858$		0			0
$859$	347489.	+	200623.i	0.470928	+	0.271890i	0.716628	−	0.697456i	$-0.245685\pi$
$859$	347489.	+	200623.i	0.470928	+	0.271890i	−0.245700	+	0.969346i	$0.579018\pi$
$860$	527193.	+	1.43225e6i	0.712808	+	1.93652i
$861$		0			0
$862$	754431.	−	134439.i	1.01532	−	0.180930i
$863$			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
$866$	−37868.6	−	212508.i	−0.0504945	−	0.283360i
$867$		0			0
$868$	126928.	−	46720.7i	0.168469	−	0.0620111i
$869$	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	−0.905698	−	0.423922i	$-0.860653\pi$
$877$	−65931.0	+	114196.i	−0.0857216	+	0.148474i	0.819977	+	0.572397i	$0.193986\pi$
$878$	43399.2	+	51530.9i	0.0562979	+	0.0668465i
$879$		0			0
$880$	515219.	+	605039.i	0.665314	+	0.781300i
$881$	−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	$0.952144\pi$
$884$	121346.	−	703100.i	0.155281	−	0.899730i
$885$		0			0
$886$	−416875.	−	494985.i	−0.531053	−	0.630557i
$887$	−554282.	−	320015.i	−0.704504	−	0.406746i	0.104519	−	0.994523i	$-0.466670\pi$
$887$	−554282.	−	320015.i	−0.704504	−	0.406746i	−0.809023	+	0.587777i	$0.800003\pi$
$888$		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
$896$	412883.	−	78223.6i	0.514293	−	0.0974365i
$897$		0			0
$898$	−89261.5	−	500909.i	−0.110691	−	0.621164i
$899$			261472.i			0.323524i
$900$		0			0
$901$	574055.			0.707137
$902$	451386.	−	80436.5i	0.554798	−	0.0988645i
$903$		0			0
$904$	−1.09745e6	+	5975.64i	−1.34291	+	0.00731219i
$905$	−394820.	+	683849.i	−0.482061	+	0.834954i
$906$		0			0
$907$	−379256.	+	218964.i	−0.461018	+	0.266169i	−0.712472	−	0.701700i	$-0.752425\pi$
$907$	−379256.	+	218964.i	−0.461018	+	0.266169i	0.251454	+	0.967869i	$0.419091\pi$
$908$	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	$-0.820029\pi$
$911$	−666090.	+	384567.i	−0.802594	+	0.463378i	0.0417834	+	0.999127i	$0.486696\pi$
$912$		0			0
$913$	164233.	−	284460.i	0.197024	−	0.341256i
$914$	−57665.1	+	48565.4i	−0.0690273	+	0.0581346i
$915$		0			0
$916$	106536.	−	617288.i	0.126971	−	0.735694i
$917$	−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	$0.696021\pi$
$920$	−1.52796e6	−	871111.i	−1.80525	−	1.02920i
$921$		0			0
$922$	179507.	−	151180.i	0.211164	−	0.177841i
$923$	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	0.780181	−	0.625554i	$-0.215127\pi$
$929$	−130885.	−	226699.i	−0.151656	−	0.262675i	−0.931836	+	0.362879i	$0.881794\pi$
$930$		0			0
$931$	288946.	+	166823.i	0.333363	+	0.192467i
$932$	−34647.8	+	12753.4i	−0.0398881	+	0.0146823i
$933$		0			0
$934$	593394.	−	105742.i	0.680220	−	0.121215i
$935$		−	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	$0.235589\pi$
$938$	127354.	+	714671.i	0.144746	+	0.812270i
$939$		0			0
$940$	178415.	+	484709.i	0.201918	+	0.548562i
$941$	−211160.	+	365741.i	−0.238470	+	0.413042i	−0.960275	−	0.279054i	$-0.909979\pi$
$941$	−211160.	+	365741.i	−0.238470	+	0.413042i	0.721806	+	0.692096i	$0.243312\pi$
$942$		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	$-0.483615\pi$
$947$	844845.	−	487772.i	0.942057	−	0.543897i	0.890605	+	0.454779i	$0.150282\pi$
$948$		0			0
$949$	−86379.8	+	149614.i	−0.0959135	+	0.166127i
$950$	−95427.4	−	113308.i	−0.105737	−	0.125549i
$951$		0			0
$952$	−718966.	−	409892.i	−0.793294	−	0.452267i
$953$	−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
$956$	1.20159e6	+	207379.i	1.31475	+	0.226907i
$957$		0			0
$958$	142311.	+	168976.i	0.155062	+	0.184117i
$959$	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	$-0.635337\pi$
$967$	−1.31627e6	−	759947.i	−1.40764	−	0.812700i	−0.995160	+	0.0982670i	$0.968670\pi$
$968$	183534.	−	999.347i	0.195869	−	0.00106651i
$969$		0			0
$970$	−44203.5	−	248057.i	−0.0469800	−	0.263638i
$971$		−	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
$974$	−11717.7	+	2088.09i	−0.0123517	+	0.00220106i
$975$		0			0
$976$	1.35059e6	+	480499.i	1.41783	+	0.504421i
$977$	−440254.	+	762542.i	−0.461226	+	0.798867i	−0.999022	−	0.0442080i	$-0.985924\pi$
$977$	−440254.	+	762542.i	−0.461226	+	0.798867i	0.537796	+	0.843075i	$0.319257\pi$
$978$		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	−0.614336	+	0.789044i	$0.710576\pi$
$983$	−1.55074e6	+	895318.i	−1.60484	+	0.926553i	−0.990501	+	0.137509i	$0.956091\pi$
$984$		0			0
$985$	−309695.	+	536407.i	−0.319199	+	0.552869i
$986$	1.22374e6	−	1.03063e6i	1.25873	−	1.06010i
$987$		0			0
$988$	266928.	+	46068.1i	0.273451	+	0.0471940i
$989$	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	$-0.193496\pi$
$992$	118303.	+	316080.i	0.120219	+	0.321198i
$993$		0			0
$994$	347900.	−	293001.i	0.352113	−	0.296549i
$995$	−625885.	−	361355.i	−0.632191	−	0.364996i
$996$		0			0
$997$	−420584.	−	728473.i	−0.423119	−	0.732864i	0.573124	−	0.819469i	$-0.305731\pi$
$997$	−420584.	−	728473.i	−0.423119	−	0.732864i	−0.996243	+	0.0866051i	$0.972398\pi$
$998$	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.91.13		44
3.2	odd	2		36.5.f.a.31.10	yes	44
4.3	odd	2	inner	108.5.f.a.91.18		44
9.2	odd	6		36.5.f.a.7.5	✓	44
9.4	even	3		324.5.d.e.163.3		22
9.5	odd	6		324.5.d.f.163.20		22
9.7	even	3	inner	108.5.f.a.19.18		44
12.11	even	2		36.5.f.a.31.5	yes	44
36.7	odd	6	inner	108.5.f.a.19.13		44
36.11	even	6		36.5.f.a.7.10	yes	44
36.23	even	6		324.5.d.f.163.19		22
36.31	odd	6		324.5.d.e.163.4		22

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.701741 + 3.93796i) q^{2} +(-15.0151 + 5.52686i) q^{4} +(-14.3046 + 24.7763i) q^{5} +(-22.2124 + 12.8243i) q^{7} +(-32.3013 - 55.2506i) q^{8} +O(q^{10})\)	\(q+(0.701741 + 3.93796i) q^{2} +(-15.0151 + 5.52686i) q^{4} +(-14.3046 + 24.7763i) q^{5} +(-22.2124 + 12.8243i) q^{7} +(-32.3013 - 55.2506i) q^{8} +(-107.606 - 38.9445i) q^{10} +(93.9677 - 54.2523i) q^{11} +(44.2246 - 76.5993i) q^{13} +(-66.0891 - 78.4722i) q^{14} +(194.908 - 165.973i) q^{16} -504.169 q^{17} -191.405i q^{19} +(77.8502 - 451.079i) q^{20} +(279.585 + 331.970i) q^{22} +(-831.897 - 480.296i) q^{23} +(-96.7443 - 167.566i) q^{25} +(332.680 + 120.402i) q^{26} +(262.643 - 315.324i) q^{28} +(396.671 + 687.053i) q^{29} +(285.428 + 164.792i) q^{31} +(790.370 + 651.069i) q^{32} +(-353.796 - 1985.40i) q^{34} -733.789i q^{35} +209.943 q^{37} +(753.745 - 134.317i) q^{38} +(1830.96 - 9.96965i) q^{40} +(528.200 - 914.869i) q^{41} +(-2887.45 + 1667.07i) q^{43} +(-1111.09 + 1333.95i) q^{44} +(1307.61 - 3613.02i) q^{46} +(-977.185 + 564.178i) q^{47} +(-871.573 + 1509.61i) q^{49} +(591.979 - 498.563i) q^{50} +(-240.684 + 1394.57i) q^{52} -1138.62 q^{53} +3104.23i q^{55} +(1426.04 + 813.005i) q^{56} +(-2427.23 + 2044.21i) q^{58} +(-4037.49 - 2331.05i) q^{59} +(2799.84 + 4849.46i) q^{61} +(-448.648 + 1239.65i) q^{62} +(-2009.25 + 3569.33i) q^{64} +(1265.23 + 2191.45i) q^{65} +(-6127.74 - 3537.85i) q^{67} +(7570.16 - 2786.47i) q^{68} +(2889.63 - 514.930i) q^{70} +4433.42i q^{71} -1953.21 q^{73} +(147.326 + 826.748i) q^{74} +(1057.87 + 2873.97i) q^{76} +(-1391.50 + 2410.15i) q^{77} +(1523.90 - 879.826i) q^{79} +(1324.12 + 7203.27i) q^{80} +(3973.38 + 1438.03i) q^{82} +(2621.64 - 1513.61i) q^{83} +(7211.95 - 12491.5i) q^{85} +(-8591.12 - 10200.8i) q^{86} +(-6032.75 - 3439.35i) q^{88} +559.336 q^{89} +2268.61i q^{91} +(15145.6 + 2613.92i) q^{92} +(-2907.44 - 3452.21i) q^{94} +(4742.31 + 2737.97i) q^{95} +(1100.89 + 1906.79i) q^{97} +(-6556.40 - 2372.87i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 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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