LMFDB - Embedded newform 108.4.i.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	108.13
Dual form			108.4.i.a.25.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173032 + 5.19327i) q^{3} +(6.54095 + 5.48851i) q^{5} +(11.9650 + 4.35489i) q^{7} +(-26.9401 - 1.79720i) q^{9} +O(q^{10})$	\(q+(-0.173032 + 5.19327i) q^{3} +(6.54095 + 5.48851i) q^{5} +(11.9650 + 4.35489i) q^{7} +(-26.9401 - 1.79720i) q^{9} +(-7.56521 + 6.34796i) q^{11} +(-6.10231 + 34.6079i) q^{13} +(-29.6351 + 33.0192i) q^{15} +(-44.7027 + 77.4273i) q^{17} +(-1.00444 - 1.73974i) q^{19} +(-24.6865 + 61.3838i) q^{21} +(33.9901 - 12.3714i) q^{23} +(-9.04572 - 51.3009i) q^{25} +(13.9949 - 139.596i) q^{27} +(40.5831 + 230.158i) q^{29} +(113.063 - 41.1517i) q^{31} +(-31.6577 - 40.3866i) q^{33} +(54.3604 + 94.1550i) q^{35} +(98.7263 - 170.999i) q^{37} +(-178.672 - 37.6792i) q^{39} +(-4.40922 + 25.0059i) q^{41} +(410.543 - 344.487i) q^{43} +(-166.350 - 159.617i) q^{45} +(-17.7125 - 6.44681i) q^{47} +(-138.558 - 116.264i) q^{49} +(-394.366 - 245.551i) q^{51} +366.433 q^{53} -84.3245 q^{55} +(9.20873 - 4.91529i) q^{57} +(-122.347 - 102.661i) q^{59} +(385.626 + 140.356i) q^{61} +(-314.511 - 138.825i) q^{63} +(-229.861 + 192.876i) q^{65} +(152.450 - 864.586i) q^{67} +(58.3667 + 178.661i) q^{69} +(69.1038 - 119.691i) q^{71} +(554.236 + 959.964i) q^{73} +(267.984 - 38.1002i) q^{75} +(-118.162 + 43.0075i) q^{77} +(-48.8286 - 276.921i) q^{79} +(722.540 + 96.8338i) q^{81} +(168.981 + 958.337i) q^{83} +(-717.359 + 261.097i) q^{85} +(-1202.29 + 170.934i) q^{87} +(530.757 + 919.298i) q^{89} +(-223.728 + 387.508i) q^{91} +(194.148 + 594.289i) q^{93} +(2.97859 - 16.8924i) q^{95} +(-158.761 + 133.216i) q^{97} +(215.216 - 157.419i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) $ 54 * q + 12 * q^5 - 48 * q^9	$ 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) $ 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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			0
$2$		0			0
$3$	−0.173032	+	5.19327i	−0.0333000	+	0.999445i
$3$	−0.173032	+	5.19327i	−0.0333000	+	0.999445i
$4$		0			0
$5$	6.54095	+	5.48851i	0.585040	+	0.490907i	0.886598	−	0.462541i	$-0.153062\pi$
$5$	6.54095	+	5.48851i	0.585040	+	0.490907i	−0.301558	+	0.953448i	$0.597507\pi$
$6$		0			0
$7$	11.9650	+	4.35489i	0.646048	+	0.235142i	0.644201	−	0.764856i	$-0.277190\pi$
$7$	11.9650	+	4.35489i	0.646048	+	0.235142i	0.00184654	+	0.999998i	$0.499412\pi$
$8$		0			0
$9$	−26.9401	−	1.79720i	−0.997782	−	0.0665631i
$10$		0			0
$11$	−7.56521	+	6.34796i	−0.207363	+	0.173998i	−0.740555	−	0.671996i	$-0.765437\pi$
$11$	−7.56521	+	6.34796i	−0.207363	+	0.173998i	0.533191	+	0.845995i	$0.320993\pi$
$12$		0			0
$13$	−6.10231	+	34.6079i	−0.130191	+	0.738347i	0.847898	+	0.530159i	$0.177868\pi$
$13$	−6.10231	+	34.6079i	−0.130191	+	0.738347i	−0.978089	+	0.208188i	$0.933243\pi$
$14$		0			0
$15$	−29.6351	+	33.0192i	−0.510117	+	0.568369i
$16$		0			0
$17$	−44.7027	+	77.4273i	−0.637764	+	1.10464i	0.348158	+	0.937436i	$0.386807\pi$
$17$	−44.7027	+	77.4273i	−0.637764	+	1.10464i	−0.985922	+	0.167204i	$0.946526\pi$
$18$		0			0
$19$	−1.00444	−	1.73974i	−0.0121281	−	0.0210065i	0.859898	−	0.510466i	$-0.170527\pi$
$19$	−1.00444	−	1.73974i	−0.0121281	−	0.0210065i	−0.872026	+	0.489460i	$0.837194\pi$
$20$		0			0
$21$	−24.6865	+	61.3838i	−0.256525	+	0.637859i
$22$		0			0
$23$	33.9901	−	12.3714i	0.308149	−	0.112157i	−0.183317	−	0.983054i	$-0.558683\pi$
$23$	33.9901	−	12.3714i	0.308149	−	0.112157i	0.491466	+	0.870897i	$0.336461\pi$
$24$		0			0
$25$	−9.04572	−	51.3009i	−0.0723658	−	0.410407i
$26$		0			0
$27$	13.9949	−	139.596i	0.0997524	−	0.995012i
$28$		0			0
$29$	40.5831	+	230.158i	0.259865	+	1.47377i	0.783269	+	0.621683i	$0.213551\pi$
$29$	40.5831	+	230.158i	0.259865	+	1.47377i	−0.523404	+	0.852085i	$0.675338\pi$
$30$		0			0
$31$	113.063	−	41.1517i	0.655057	−	0.238421i	0.00695640	−	0.999976i	$-0.497786\pi$
$31$	113.063	−	41.1517i	0.655057	−	0.238421i	0.648101	+	0.761554i	$0.275563\pi$
$32$		0			0
$33$	−31.6577	−	40.3866i	−0.166997	−	0.213042i
$34$		0			0
$35$	54.3604	+	94.1550i	0.262531	+	0.454717i
$36$		0			0
$37$	98.7263	−	170.999i	0.438662	−	0.759785i	−0.558924	−	0.829219i	$-0.688786\pi$
$37$	98.7263	−	170.999i	0.438662	−	0.759785i	0.997587	+	0.0694333i	$0.0221191\pi$
$38$		0			0
$39$	−178.672	−	37.6792i	−0.733602	−	0.154705i
$40$		0			0
$41$	−4.40922	+	25.0059i	−0.0167952	+	0.0952504i	−0.992053	−	0.125820i	$-0.959844\pi$
$41$	−4.40922	+	25.0059i	−0.0167952	+	0.0952504i	0.975258	+	0.221070i	$0.0709550\pi$
$42$		0			0
$43$	410.543	−	344.487i	1.45598	−	1.22171i	0.527918	−	0.849296i	$-0.322973\pi$
$43$	410.543	−	344.487i	1.45598	−	1.22171i	0.928065	−	0.372419i	$-0.121471\pi$
$44$		0			0
$45$	−166.350	−	159.617i	−0.551067	−	0.528761i
$46$		0			0
$47$	−17.7125	−	6.44681i	−0.0549708	−	0.0200077i	0.314388	−	0.949294i	$-0.398201\pi$
$47$	−17.7125	−	6.44681i	−0.0549708	−	0.0200077i	−0.369359	+	0.929287i	$0.620423\pi$
$48$		0			0
$49$	−138.558	−	116.264i	−0.403959	−	0.338962i
$50$		0			0
$51$	−394.366	−	245.551i	−1.08279	−	0.674195i
$52$		0			0
$53$	366.433			0.949687			0.474844	−	0.880070i	$-0.342505\pi$
$53$	366.433			0.949687			0.474844	+	0.880070i	$0.342505\pi$
$54$		0			0
$55$	−84.3245			−0.206733
$56$		0			0
$57$	9.20873	−	4.91529i	0.0213987	−	0.0114219i
$58$		0			0
$59$	−122.347	−	102.661i	−0.269969	−	0.226531i	0.497745	−	0.867323i	$-0.334161\pi$
$59$	−122.347	−	102.661i	−0.269969	−	0.226531i	−0.767714	+	0.640793i	$0.778606\pi$
$60$		0			0
$61$	385.626	+	140.356i	0.809415	+	0.294603i	0.713382	−	0.700775i	$-0.247162\pi$
$61$	385.626	+	140.356i	0.809415	+	0.294603i	0.0960331	+	0.995378i	$0.469385\pi$
$62$		0			0
$63$	−314.511	−	138.825i	−0.628963	−	0.277624i
$64$		0			0
$65$	−229.861	+	192.876i	−0.438627	+	0.368051i
$66$		0			0
$67$	152.450	−	864.586i	0.277981	−	1.57651i	−0.451351	−	0.892346i	$-0.649058\pi$
$67$	152.450	−	864.586i	0.277981	−	1.57651i	0.729332	−	0.684160i	$-0.239831\pi$
$68$		0			0
$69$	58.3667	+	178.661i	0.101834	+	0.311713i
$70$		0			0
$71$	69.1038	−	119.691i	0.115509	−	0.200067i	−0.802474	−	0.596687i	$-0.796484\pi$
$71$	69.1038	−	119.691i	0.115509	−	0.200067i	0.917983	+	0.396620i	$0.129817\pi$
$72$		0			0
$73$	554.236	+	959.964i	0.888608	+	1.53911i	0.841522	+	0.540223i	$0.181660\pi$
$73$	554.236	+	959.964i	0.888608	+	1.53911i	0.0470856	+	0.998891i	$0.485007\pi$
$74$		0			0
$75$	267.984	−	38.1002i	0.412589	−	0.0586591i
$76$		0			0
$77$	−118.162	+	43.0075i	−0.174881	+	0.0636515i
$78$		0			0
$79$	−48.8286	−	276.921i	−0.0695399	−	0.394380i	−0.999634	−	0.0270585i	$-0.991386\pi$
$79$	−48.8286	−	276.921i	−0.0695399	−	0.394380i	0.930094	−	0.367322i	$-0.119725\pi$
$80$		0			0
$81$	722.540	+	96.8338i	0.991139	+	0.132831i
$82$		0			0
$83$	168.981	+	958.337i	0.223470	+	1.26736i	0.865588	+	0.500757i	$0.166945\pi$
$83$	168.981	+	958.337i	0.223470	+	1.26736i	−0.642118	+	0.766606i	$0.721944\pi$
$84$		0			0
$85$	−717.359	+	261.097i	−0.915394	+	0.333176i
$86$		0			0
$87$	−1202.29	+	170.934i	−1.48160	+	0.210644i
$88$		0			0
$89$	530.757	+	919.298i	0.632136	+	1.09489i	0.987114	+	0.160017i	$0.0511549\pi$
$89$	530.757	+	919.298i	0.632136	+	1.09489i	−0.354978	+	0.934875i	$0.615512\pi$
$90$		0			0
$91$	−223.728	+	387.508i	−0.257726	+	0.446394i
$92$		0			0
$93$	194.148	+	594.289i	0.216476	+	0.662634i
$94$		0			0
$95$	2.97859	−	16.8924i	0.00321681	−	0.0182434i
$96$		0			0
$97$	−158.761	+	133.216i	−0.166183	+	0.139444i	−0.722087	−	0.691803i	$-0.756817\pi$
$97$	−158.761	+	133.216i	−0.166183	+	0.139444i	0.555904	+	0.831247i	$0.312372\pi$
$98$		0			0
$99$	215.216	−	157.419i	0.218485	−	0.159810i
$100$		0			0
$101$	−1263.16	−	459.753i	−1.24445	−	0.452942i	−0.365927	−	0.930644i	$-0.619248\pi$
$101$	−1263.16	−	459.753i	−1.24445	−	0.452942i	−0.878522	+	0.477701i	$0.841470\pi$
$102$		0			0
$103$	−725.221	−	608.533i	−0.693768	−	0.582141i	0.226225	−	0.974075i	$-0.427362\pi$
$103$	−725.221	−	608.533i	−0.693768	−	0.582141i	−0.919993	+	0.391934i	$0.871806\pi$
$104$		0			0
$105$	−498.378	+	266.016i	−0.463207	+	0.247243i
$106$		0			0
$107$	1007.69			0.910439			0.455219	−	0.890379i	$-0.349561\pi$
$107$	1007.69			0.910439			0.455219	+	0.890379i	$0.349561\pi$
$108$		0			0
$109$	−542.749			−0.476935			−0.238467	−	0.971151i	$-0.576645\pi$
$109$	−542.749			−0.476935			−0.238467	+	0.971151i	$0.576645\pi$
$110$		0			0
$111$	870.961	+	542.301i	0.744757	+	0.463720i
$112$		0			0
$113$	−1544.12	−	1295.67i	−1.28548	−	1.07864i	−0.992464	−	0.122535i	$-0.960898\pi$
$113$	−1544.12	−	1295.67i	−1.28548	−	1.07864i	−0.293013	−	0.956109i	$-0.594658\pi$
$114$		0			0
$115$	290.228	+	105.634i	0.235339	+	0.0856562i
$116$		0			0
$117$	226.595	−	921.375i	0.179048	−	0.728044i
$118$		0			0
$119$	−872.054	+	731.740i	−0.671774	+	0.563685i
$120$		0			0
$121$	−214.190	+	1214.73i	−0.160924	+	0.912646i
$122$		0			0
$123$	−129.100	−	27.2251i	−0.0946383	−	0.0199577i
$124$		0			0
$125$	756.060	−	1309.53i	0.540993	−	0.937027i
$126$		0			0
$127$	731.061	+	1266.24i	0.510797	+	0.884726i	0.999922	+	0.0125122i	$0.00398286\pi$
$127$	731.061	+	1266.24i	0.510797	+	0.884726i	−0.489125	+	0.872214i	$0.662684\pi$
$128$		0			0
$129$	1717.98	+	2191.67i	1.17255	+	1.49586i
$130$		0			0
$131$	1594.59	−	580.385i	1.06351	−	0.387087i	0.249766	−	0.968306i	$-0.419646\pi$
$131$	1594.59	−	580.385i	1.06351	−	0.387087i	0.813747	+	0.581219i	$0.197424\pi$
$132$		0			0
$133$	−4.44170	−	25.1901i	−0.00289582	−	0.0164230i
$134$		0			0
$135$	857.716	−	836.282i	0.546818	−	0.533153i
$136$		0			0
$137$	−323.495	−	1834.63i	−0.201737	−	1.14411i	−0.902492	−	0.430707i	$-0.858264\pi$
$137$	−323.495	−	1834.63i	−0.201737	−	1.14411i	0.700755	−	0.713402i	$-0.252847\pi$
$138$		0			0
$139$	−999.280	+	363.708i	−0.609768	+	0.221938i	−0.628402	−	0.777889i	$-0.716291\pi$
$139$	−999.280	+	363.708i	−0.609768	+	0.221938i	0.0186335	+	0.999826i	$0.494068\pi$
$140$		0			0
$141$	36.5448	−	90.8701i	0.0218272	−	0.0542741i
$142$		0			0
$143$	−173.525	−	300.554i	−0.101475	−	0.175759i
$144$		0			0
$145$	−997.772	+	1728.19i	−0.571452	+	0.989783i
$146$		0			0
$147$	627.765	−	699.451i	0.352225	−	0.392447i
$148$		0			0
$149$	578.529	−	3281.00i	0.318087	−	1.80396i	−0.236278	−	0.971685i	$-0.575928\pi$
$149$	578.529	−	3281.00i	0.318087	−	1.80396i	0.554365	−	0.832274i	$-0.312961\pi$
$150$		0			0
$151$	1959.73	−	1644.41i	1.05616	−	0.886224i	0.0624329	−	0.998049i	$-0.480114\pi$
$151$	1959.73	−	1644.41i	1.05616	−	0.886224i	0.993728	+	0.111825i	$0.0356696\pi$
$152$		0			0
$153$	1343.45	−	2005.56i	0.709878	−	1.05974i
$154$		0			0
$155$	965.403	+	351.378i	0.500278	+	0.182086i
$156$		0			0
$157$	−2145.49	−	1800.28i	−1.09063	−	0.915144i	−0.0938671	−	0.995585i	$-0.529923\pi$
$157$	−2145.49	−	1800.28i	−1.09063	−	0.915144i	−0.996759	+	0.0804405i	$0.974367\pi$
$158$		0			0
$159$	−63.4046	+	1902.98i	−0.0316246	+	0.949160i
$160$		0			0
$161$	460.567			0.225452
$162$		0			0
$163$	−1529.32			−0.734879			−0.367440	−	0.930047i	$-0.619766\pi$
$163$	−1529.32			−0.734879			−0.367440	+	0.930047i	$0.619766\pi$
$164$		0			0
$165$	14.5908	−	437.920i	0.00688422	−	0.206618i
$166$		0			0
$167$	−2951.09	−	2476.26i	−1.36744	−	1.14742i	−0.973607	−	0.228233i	$-0.926705\pi$
$167$	−2951.09	−	2476.26i	−1.36744	−	1.14742i	−0.393831	−	0.919183i	$-0.628850\pi$
$168$		0			0
$169$	904.034	+	329.041i	0.411486	+	0.149769i
$170$		0			0
$171$	23.9330	+	48.6739i	0.0107029	+	0.0217672i
$172$		0			0
$173$	−1403.86	+	1177.98i	−0.616956	+	0.517688i	−0.896845	−	0.442345i	$-0.854147\pi$
$173$	−1403.86	+	1177.98i	−0.616956	+	0.517688i	0.279889	+	0.960032i	$0.409702\pi$
$174$		0			0
$175$	115.178	−	653.206i	0.0497522	−	0.282159i
$176$		0			0
$177$	554.316	−	617.615i	0.235395	−	0.262276i
$178$		0			0
$179$	−191.456	+	331.612i	−0.0799448	+	0.138469i	−0.903226	−	0.429165i	$-0.858808\pi$
$179$	−191.456	+	331.612i	−0.0799448	+	0.138469i	0.823281	+	0.567634i	$0.192141\pi$
$180$		0			0
$181$	150.411	+	260.519i	0.0617677	+	0.106985i	0.895256	−	0.445553i	$-0.146993\pi$
$181$	150.411	+	260.519i	0.0617677	+	0.106985i	−0.833488	+	0.552538i	$0.813660\pi$
$182$		0			0
$183$	−795.634	+	1978.37i	−0.321393	+	0.799156i
$184$		0			0
$185$	1584.29	−	576.636i	0.629619	−	0.229163i
$186$		0			0
$187$	−153.321	−	869.525i	−0.0599568	−	0.340032i
$188$		0			0
$189$	775.375	−	1609.32i	0.298414	−	0.619369i
$190$		0			0
$191$	566.341	+	3211.88i	0.214550	+	1.21677i	0.881686	+	0.471836i	$0.156409\pi$
$191$	566.341	+	3211.88i	0.214550	+	1.21677i	−0.667136	+	0.744936i	$0.732480\pi$
$192$		0			0
$193$	−1782.33	+	648.714i	−0.664739	+	0.241945i	−0.652281	−	0.757977i	$-0.726188\pi$
$193$	−1782.33	+	648.714i	−0.664739	+	0.241945i	−0.0124579	+	0.999922i	$0.503966\pi$
$194$		0			0
$195$	−961.885	−	1227.10i	−0.353241	−	0.450639i
$196$		0			0
$197$	−486.365	−	842.409i	−0.175899	−	0.304666i	0.764573	−	0.644537i	$-0.222950\pi$
$197$	−486.365	−	842.409i	−0.175899	−	0.304666i	−0.940472	+	0.339871i	$0.889616\pi$
$198$		0			0
$199$	−1402.61	+	2429.40i	−0.499641	+	0.865403i	−1.00000		0.000414695i	$-0.999868\pi$
$199$	−1402.61	+	2429.40i	−0.499641	+	0.865403i	0.500359	+	0.865818i	$0.333201\pi$
$200$		0			0
$201$	4463.65	+	941.314i	1.56638	+	0.330324i
$202$		0			0
$203$	−516.738	+	2930.57i	−0.178660	+	1.01323i
$204$		0			0
$205$	−166.086	+	139.362i	−0.0565850	+	0.0474804i
$206$		0			0
$207$	−937.933	+	272.200i	−0.314931	+	0.0913971i
$208$		0			0
$209$	18.6426	+	6.78534i	0.00617002	+	0.00224570i
$210$		0			0
$211$	−6.10520	−	5.12287i	−0.00199194	−	0.00167144i	0.641791	−	0.766880i	$-0.278192\pi$
$211$	−6.10520	−	5.12287i	−0.00199194	−	0.00167144i	−0.643783	+	0.765208i	$0.722636\pi$
$212$		0			0
$213$	609.632	+	379.585i	0.196109	+	0.122107i
$214$		0			0
$215$	4576.06			1.45156
$216$		0			0
$217$	1532.01			0.479261
$218$		0			0
$219$	−5081.25	+	2712.19i	−1.56785	+	0.836862i
$220$		0			0
$221$	−2406.81	−	2019.55i	−0.732577	−	0.614705i
$222$		0			0
$223$	3121.71	+	1136.21i	0.937422	+	0.341194i	0.765147	−	0.643855i	$-0.222666\pi$
$223$	3121.71	+	1136.21i	0.937422	+	0.341194i	0.172275	+	0.985049i	$0.444888\pi$
$224$		0			0
$225$	151.495	+	1398.31i	0.0448873	+	0.414314i
$226$		0			0
$227$	−2498.72	+	2096.68i	−0.730599	+	0.613046i	−0.930295	−	0.366812i	$-0.880449\pi$
$227$	−2498.72	+	2096.68i	−0.730599	+	0.613046i	0.199696	+	0.979858i	$0.436005\pi$
$228$		0			0
$229$	0.498021	−	2.82442i	0.000143712	−	0.000815033i	−0.984736	−	0.174056i	$-0.944313\pi$
$229$	0.498021	−	2.82442i	0.000143712	−	0.000815033i	0.984880	+	0.173241i	$0.0554238\pi$
$230$		0			0
$231$	−202.904	−	621.090i	−0.0577926	−	0.176904i
$232$		0			0
$233$	−419.561	+	726.702i	−0.117967	+	0.204325i	−0.918962	−	0.394346i	$-0.870971\pi$
$233$	−419.561	+	726.702i	−0.117967	+	0.204325i	0.800995	+	0.598671i	$0.204304\pi$
$234$		0			0
$235$	−80.4729	−	139.383i	−0.0223382	−	0.0386909i
$236$		0			0
$237$	1446.57	−	205.664i	0.396477	−	0.0563684i
$238$		0			0
$239$	928.725	−	338.028i	0.251356	−	0.0914863i	−0.213269	−	0.976993i	$-0.568411\pi$
$239$	928.725	−	338.028i	0.251356	−	0.0914863i	0.464626	+	0.885507i	$0.346189\pi$
$240$		0			0
$241$	157.896	+	895.472i	0.0422032	+	0.239346i	0.998611	−	0.0526883i	$-0.0167790\pi$
$241$	157.896	+	895.472i	0.0422032	+	0.239346i	−0.956408	+	0.292034i	$0.905668\pi$
$242$		0			0
$243$	−627.907	+	3735.59i	−0.165762	+	0.986166i
$244$		0			0
$245$	−268.185	−	1520.95i	−0.0699335	−	0.396612i
$246$		0			0
$247$	66.3381	−	24.1451i	0.0170890	−	0.00621990i
$248$		0			0
$249$	−5006.14	+	711.739i	−1.27410	+	0.181143i
$250$		0			0
$251$	2208.59	+	3825.39i	0.555398	+	0.961977i	0.997872	+	0.0651964i	$0.0207674\pi$
$251$	2208.59	+	3825.39i	0.555398	+	0.961977i	−0.442475	+	0.896781i	$0.645899\pi$
$252$		0			0
$253$	−178.609	+	309.360i	−0.0443837	+	0.0768748i
$254$		0			0
$255$	−1231.82	−	3770.62i	−0.302509	−	0.925981i
$256$		0			0
$257$	−1181.55	+	6700.91i	−0.286782	+	1.62642i	0.412066	+	0.911154i	$0.364807\pi$
$257$	−1181.55	+	6700.91i	−0.286782	+	1.62642i	−0.698848	+	0.715270i	$0.746304\pi$
$258$		0			0
$259$	1925.94	−	1616.06i	0.462054	−	0.387710i
$260$		0			0
$261$	−679.672	−	6273.42i	−0.161190	−	1.48780i
$262$		0			0
$263$	817.417	+	297.515i	0.191650	+	0.0697551i	0.436062	−	0.899916i	$-0.356373\pi$
$263$	817.417	+	297.515i	0.191650	+	0.0697551i	−0.244412	+	0.969671i	$0.578595\pi$
$264$		0			0
$265$	2396.82	+	2011.17i	0.555605	+	0.466208i
$266$		0			0
$267$	−4866.00	+	2597.30i	−1.11533	+	0.595325i
$268$		0			0
$269$	−4222.12			−0.956977			−0.478489	−	0.878094i	$-0.658815\pi$
$269$	−4222.12			−0.956977			−0.478489	+	0.878094i	$0.658815\pi$
$270$		0			0
$271$	7100.72			1.59165			0.795826	−	0.605525i	$-0.207037\pi$
$271$	7100.72			1.59165			0.795826	+	0.605525i	$0.207037\pi$
$272$		0			0
$273$	−1973.72	−	1228.93i	−0.437564	−	0.272448i
$274$		0			0
$275$	394.089	+	330.680i	0.0864162	+	0.0725118i
$276$		0			0
$277$	−6209.30	−	2260.00i	−1.34686	−	0.490218i	−0.434895	−	0.900481i	$-0.643215\pi$
$277$	−6209.30	−	2260.00i	−1.34686	−	0.490218i	−0.911967	+	0.410263i	$0.865437\pi$
$278$		0			0
$279$	−3119.90	+	905.434i	−0.669475	+	0.194290i
$280$		0			0
$281$	1603.24	−	1345.28i	0.340360	−	0.285596i	−0.456546	−	0.889700i	$-0.650913\pi$
$281$	1603.24	−	1345.28i	0.340360	−	0.285596i	0.796905	+	0.604104i	$0.206469\pi$
$282$		0			0
$283$	1511.14	−	8570.09i	0.317413	−	1.80014i	−0.240946	−	0.970538i	$-0.577458\pi$
$283$	1511.14	−	8570.09i	0.317413	−	1.80014i	0.558359	−	0.829599i	$-0.311431\pi$
$284$		0			0
$285$	87.2114	+	18.3915i	0.0181262	+	0.00382253i
$286$		0			0
$287$	−161.654	+	279.993i	−0.0332479	+	0.0575870i
$288$		0			0
$289$	−1540.16	−	2667.64i	−0.313487	−	0.542975i
$290$		0			0
$291$	−664.358	−	847.540i	−0.133833	−	0.170734i
$292$		0			0
$293$	7336.53	−	2670.28i	1.46282	−	0.532421i	0.516676	−	0.856181i	$-0.327169\pi$
$293$	7336.53	−	2670.28i	1.46282	−	0.532421i	0.946139	+	0.323760i	$0.104947\pi$
$294$		0			0
$295$	−236.807	−	1343.00i	−0.0467371	−	0.265059i
$296$		0			0
$297$	780.279	+	1144.91i	0.152446	+	0.223686i
$298$		0			0
$299$	220.730	+	1251.82i	0.0426928	+	0.242123i
$300$		0			0
$301$	6412.34	−	2333.90i	1.22791	−	0.446923i
$302$		0			0
$303$	2606.19	−	6480.39i	0.494131	−	1.22868i
$304$		0			0
$305$	1752.01	+	3034.58i	0.328918	+	0.569703i
$306$		0			0
$307$	2400.44	−	4157.68i	0.446255	−	0.772936i	−0.551884	−	0.833921i	$-0.686091\pi$
$307$	2400.44	−	4157.68i	0.446255	−	0.772936i	0.998139	+	0.0609852i	$0.0194242\pi$
$308$		0			0
$309$	3285.76	−	3660.97i	0.604920	−	0.673998i
$310$		0			0
$311$	−1262.48	+	7159.88i	−0.230189	+	1.30546i	0.622325	+	0.782759i	$0.286188\pi$
$311$	−1262.48	+	7159.88i	−0.230189	+	1.30546i	−0.852513	+	0.522705i	$0.824923\pi$
$312$		0			0
$313$	22.5342	−	18.9084i	0.00406935	−	0.00341459i	−0.640751	−	0.767749i	$-0.721377\pi$
$313$	22.5342	−	18.9084i	0.00406935	−	0.00341459i	0.644820	+	0.764334i	$0.276932\pi$
$314$		0			0
$315$	−1295.26	−	2634.24i	−0.231681	−	0.471183i
$316$		0			0
$317$	−3605.13	−	1312.16i	−0.638752	−	0.232487i	0.00228399	−	0.999997i	$-0.499273\pi$
$317$	−3605.13	−	1312.16i	−0.638752	−	0.232487i	−0.641036	+	0.767511i	$0.721495\pi$
$318$		0			0
$319$	−1768.05	−	1483.57i	−0.310320	−	0.260389i
$320$		0			0
$321$	−174.362	+	5233.20i	−0.0303176	+	0.909934i
$322$		0			0
$323$	179.604			0.0309395
$324$		0			0
$325$	1830.62			0.312444
$326$		0			0
$327$	93.9129	−	2818.64i	0.0158819	−	0.476670i
$328$		0			0
$329$	−183.854	−	154.272i	−0.0308091	−	0.0258519i
$330$		0			0
$331$	2593.45	+	943.938i	0.430661	+	0.156748i	0.548250	−	0.836315i	$-0.315294\pi$
$331$	2593.45	+	943.938i	0.430661	+	0.156748i	−0.117589	+	0.993062i	$0.537516\pi$
$332$		0			0
$333$	−2967.02	+	4429.30i	−0.488263	+	0.728902i
$334$		0			0
$335$	5742.45	−	4818.49i	0.936548	−	0.785857i
$336$		0			0
$337$	−1738.35	+	9858.65i	−0.280990	+	1.59358i	0.438275	+	0.898841i	$0.355590\pi$
$337$	−1738.35	+	9858.65i	−0.280990	+	1.59358i	−0.719266	+	0.694735i	$0.755522\pi$
$338$		0			0
$339$	6995.96	−	7794.86i	1.12085	−	1.24885i
$340$		0			0
$341$	−594.118	+	1029.04i	−0.0943499	+	0.163419i
$342$		0			0
$343$	−3335.21	−	5776.75i	−0.525027	−	0.909374i
$344$		0			0
$345$	−598.807	+	1488.96i	−0.0934455	+	0.232356i
$346$		0			0
$347$	376.101	−	136.890i	0.0581849	−	0.0211776i	−0.312764	−	0.949831i	$-0.601255\pi$
$347$	376.101	−	136.890i	0.0581849	−	0.0211776i	0.370949	+	0.928653i	$0.379033\pi$
$348$		0			0
$349$	−124.917	−	708.438i	−0.0191594	−	0.108659i	0.973728	−	0.227713i	$-0.0731248\pi$
$349$	−124.917	−	708.438i	−0.0191594	−	0.108659i	−0.992888	+	0.119054i	$0.962014\pi$
$350$		0			0
$351$	4745.74	+	1336.19i	0.721678	+	0.203193i
$352$		0			0
$353$	−27.6907	−	157.042i	−0.00417515	−	0.0236784i	0.982649	−	0.185475i	$-0.0593823\pi$
$353$	−27.6907	−	157.042i	−0.00417515	−	0.0236784i	−0.986824	+	0.161796i	$0.948271\pi$
$354$		0			0
$355$	1108.93	−	403.618i	0.165791	−	0.0603431i
$356$		0			0
$357$	−3649.23	−	4655.43i	−0.541002	−	0.690172i
$358$		0			0
$359$	−4825.04	−	8357.21i	−0.709348	−	1.22863i	−0.965099	−	0.261884i	$-0.915656\pi$
$359$	−4825.04	−	8357.21i	−0.709348	−	1.22863i	0.255752	−	0.966743i	$-0.417677\pi$
$360$		0			0
$361$	3427.48	−	5936.57i	0.499706	−	0.865516i
$362$		0			0
$363$	−6271.37	−	1322.53i	−0.906781	−	0.191226i
$364$		0			0
$365$	−1643.54	+	9321.00i	−0.235691	+	1.33667i
$366$		0			0
$367$	−6305.46	+	5290.91i	−0.896845	+	0.752543i	−0.969571	−	0.244809i	$-0.921275\pi$
$367$	−6305.46	+	5290.91i	−0.896845	+	0.752543i	0.0727258	+	0.997352i	$0.476830\pi$
$368$		0			0
$369$	163.726	−	665.738i	0.0230981	−	0.0939212i
$370$		0			0
$371$	4384.36	+	1595.78i	0.613543	+	0.223311i
$372$		0			0
$373$	5136.29	+	4309.86i	0.712995	+	0.598274i	0.925438	−	0.378899i	$-0.123697\pi$
$373$	5136.29	+	4309.86i	0.712995	+	0.598274i	−0.212443	+	0.977174i	$0.568142\pi$
$374$		0			0
$375$	6669.95	+	4153.02i	0.918492	+	0.571896i
$376$		0			0
$377$	−8212.94			−1.12198
$378$		0			0
$379$	−7620.82			−1.03286			−0.516432	−	0.856328i	$-0.672740\pi$
$379$	−7620.82			−1.03286			−0.516432	+	0.856328i	$0.672740\pi$
$380$		0			0
$381$	−6702.40	+	3577.50i	−0.901245	+	0.481052i
$382$		0			0
$383$	−8850.82	−	7426.72i	−1.18082	−	0.990829i	−0.999973	−	0.00731893i	$-0.997670\pi$
$383$	−8850.82	−	7426.72i	−1.18082	−	0.990829i	−0.180851	−	0.983510i	$-0.557885\pi$
$384$		0			0
$385$	−1008.94	−	367.224i	−0.133559	−	0.0486116i
$386$		0			0
$387$	−11679.2	+	8542.68i	−1.53407	+	1.12209i
$388$		0			0
$389$	596.696	−	500.687i	0.0777729	−	0.0652592i	−0.603072	−	0.797686i	$-0.706057\pi$
$389$	596.696	−	500.687i	0.0777729	−	0.0652592i	0.680845	+	0.732427i	$0.261613\pi$
$390$		0			0
$391$	−561.566	+	3184.80i	−0.0726333	+	0.411924i
$392$		0			0
$393$	2738.18	+	8381.58i	0.351458	+	1.07581i
$394$		0			0
$395$	1200.50	−	2079.32i	0.152920	−	0.264866i
$396$		0			0
$397$	420.795	+	728.838i	0.0531967	+	0.0921394i	0.891398	−	0.453222i	$-0.149726\pi$
$397$	420.795	+	728.838i	0.0531967	+	0.0921394i	−0.838201	+	0.545362i	$0.816392\pi$
$398$		0			0
$399$	131.588	−	18.7082i	0.0165103	−	0.00234733i
$400$		0			0
$401$	14884.6	−	5417.54i	1.85362	−	0.674661i	0.870364	−	0.492409i	$-0.163883\pi$
$401$	14884.6	−	5417.54i	1.85362	−	0.674661i	0.983252	−	0.182252i	$-0.0583388\pi$
$402$		0			0
$403$	734.227	+	4164.01i	0.0907555	+	0.514700i
$404$		0			0
$405$	4194.63	+	4599.05i	0.514648	+	0.564269i
$406$		0			0
$407$	338.610	+	1920.35i	0.0412390	+	0.233878i
$408$		0			0
$409$	4496.30	−	1636.52i	0.543588	−	0.197850i	−0.0556071	−	0.998453i	$-0.517709\pi$
$409$	4496.30	−	1636.52i	0.543588	−	0.197850i	0.599196	+	0.800603i	$0.295487\pi$
$410$		0			0
$411$	9583.70	−	1362.55i	1.15019	−	0.163527i
$412$		0			0
$413$	−1016.79	−	1761.14i	−0.121146	−	0.209831i
$414$		0			0
$415$	−4154.55	+	7195.88i	−0.491418	+	0.851161i
$416$		0			0
$417$	−1715.93	−	5252.46i	−0.201509	−	0.616821i
$418$		0			0
$419$	−1644.96	+	9329.01i	−0.191793	+	1.08771i	0.725119	+	0.688624i	$0.241785\pi$
$419$	−1644.96	+	9329.01i	−0.191793	+	1.08771i	−0.916912	+	0.399090i	$0.869326\pi$
$420$		0			0
$421$	−7997.87	+	6711.01i	−0.925873	+	0.776900i	−0.975072	−	0.221889i	$-0.928778\pi$
$421$	−7997.87	+	6711.01i	−0.925873	+	0.776900i	0.0491989	+	0.998789i	$0.484333\pi$
$422$		0			0
$423$	465.590	+	205.511i	0.0535171	+	0.0236224i
$424$		0			0
$425$	4376.46	+	1592.90i	0.499504	+	0.181805i
$426$		0			0
$427$	4002.77	+	3358.72i	0.453647	+	0.380655i
$428$		0			0
$429$	1590.88	−	849.155i	0.179041	−	0.0955655i
$430$		0			0
$431$	−8608.62			−0.962094			−0.481047	−	0.876695i	$-0.659743\pi$
$431$	−8608.62			−0.962094			−0.481047	+	0.876695i	$0.659743\pi$
$432$		0			0
$433$	−4458.02			−0.494778			−0.247389	−	0.968916i	$-0.579573\pi$
$433$	−4458.02			−0.494778			−0.247389	+	0.968916i	$0.579573\pi$
$434$		0			0
$435$	−8802.32	−	5480.73i	−0.970205	−	0.604095i
$436$		0			0
$437$	−55.6640	−	46.7076i	−0.00609330	−	0.00511288i
$438$		0			0
$439$	−621.671	−	226.270i	−0.0675871	−	0.0245997i	0.308005	−	0.951385i	$-0.400339\pi$
$439$	−621.671	−	226.270i	−0.0675871	−	0.0245997i	−0.375592	+	0.926785i	$0.622561\pi$
$440$		0			0
$441$	3523.82	+	3381.18i	0.380501	+	0.365099i
$442$		0			0
$443$	12445.6	−	10443.1i	1.33478	−	1.12001i	0.351847	−	0.936057i	$-0.385554\pi$
$443$	12445.6	−	10443.1i	1.33478	−	1.12001i	0.982934	−	0.183957i	$-0.0588908\pi$
$444$		0			0
$445$	−1573.92	+	8926.14i	−0.167665	+	0.950876i
$446$		0			0
$447$	16939.0	+	3572.17i	1.79237	+	0.377982i
$448$		0			0
$449$	−6286.72	+	10888.9i	−0.660777	+	1.14450i	0.319635	+	0.947541i	$0.396440\pi$
$449$	−6286.72	+	10888.9i	−0.660777	+	1.14450i	−0.980412	+	0.196959i	$0.936894\pi$
$450$		0			0
$451$	−125.380	−	217.164i	−0.0130907	−	0.0226738i
$452$		0			0
$453$	8200.75	+	10461.9i	0.850562	+	1.08509i
$454$		0			0
$455$	−3590.23	+	1306.74i	−0.369918	+	0.134639i
$456$		0			0
$457$	344.908	+	1956.07i	0.0353044	+	0.200221i	0.997358	−	0.0726379i	$-0.0231418\pi$
$457$	344.908	+	1956.07i	0.0353044	+	0.200221i	−0.962054	+	0.272859i	$0.912031\pi$
$458$		0			0
$459$	10183.0	+	7323.92i	1.03551	+	0.744774i
$460$		0			0
$461$	−2257.12	−	12800.8i	−0.228036	−	1.29326i	−0.856795	−	0.515657i	$-0.827548\pi$
$461$	−2257.12	−	12800.8i	−0.228036	−	1.29326i	0.628759	−	0.777600i	$-0.283563\pi$
$462$		0			0
$463$	−11058.6	+	4024.98i	−1.11001	+	0.404010i	−0.830997	−	0.556277i	$-0.812229\pi$
$463$	−11058.6	+	4024.98i	−1.11001	+	0.404010i	−0.279013	+	0.960287i	$0.590007\pi$
$464$		0			0
$465$	−1991.85	+	4952.80i	−0.198644	+	0.493937i
$466$		0			0
$467$	−8253.92	−	14296.2i	−0.817871	−	1.41659i	−0.907248	−	0.420597i	$-0.861821\pi$
$467$	−8253.92	−	14296.2i	−0.817871	−	1.41659i	0.0893763	−	0.995998i	$-0.471513\pi$
$468$		0			0
$469$	5589.23	−	9680.84i	0.550292	−	0.953133i
$470$		0			0
$471$	9720.56	−	10830.6i	0.950955	−	1.05955i
$472$		0			0
$473$	−919.056	+	5212.23i	−0.0893409	+	0.506677i
$474$		0			0
$475$	−80.1642	+	67.2657i	−0.00774355	+	0.00649761i
$476$		0			0
$477$	−9871.74	−	658.555i	−0.947581	−	0.0632141i
$478$		0			0
$479$	−8477.76	−	3085.65i	−0.808682	−	0.294336i	−0.0956026	−	0.995420i	$-0.530478\pi$
$479$	−8477.76	−	3085.65i	−0.808682	−	0.294336i	−0.713079	+	0.701083i	$0.752700\pi$
$480$		0			0
$481$	5315.46	+	4460.20i	0.503876	+	0.422802i
$482$		0			0
$483$	−79.6929	+	2391.85i	−0.00750756	+	0.225327i
$484$		0			0
$485$	−1769.61			−0.165678
$486$		0			0
$487$	−14156.8			−1.31726			−0.658632	−	0.752465i	$-0.728865\pi$
$487$	−14156.8			−1.31726			−0.658632	+	0.752465i	$0.728865\pi$
$488$		0			0
$489$	264.621	−	7942.16i	0.0244715	−	0.734472i
$490$		0			0
$491$	−3325.98	−	2790.83i	−0.305702	−	0.256514i	0.477011	−	0.878897i	$-0.341720\pi$
$491$	−3325.98	−	2790.83i	−0.305702	−	0.256514i	−0.782713	+	0.622383i	$0.786165\pi$
$492$		0			0
$493$	−19634.7	−	7146.44i	−1.79372	−	0.652859i
$494$		0			0
$495$	2271.71	+	151.548i	0.206275	+	0.0137608i
$496$		0			0
$497$	1348.07	−	1131.16i	0.121668	−	0.102092i
$498$		0			0
$499$	1245.95	−	7066.16i	0.111777	−	0.633917i	−0.876519	−	0.481367i	$-0.840140\pi$
$499$	1245.95	−	7066.16i	0.111777	−	0.633917i	0.988296	−	0.152550i	$-0.0487485\pi$
$500$		0			0
$501$	13370.5	−	14897.3i	1.19232	−	1.32847i
$502$		0			0
$503$	8090.46	−	14013.1i	0.717168	−	1.24217i	−0.244949	−	0.969536i	$-0.578771\pi$
$503$	8090.46	−	14013.1i	0.717168	−	1.24217i	0.962117	−	0.272636i	$-0.0878954\pi$
$504$		0			0
$505$	−5738.92	−	9940.10i	−0.505700	−	0.875898i
$506$		0			0
$507$	−1865.23	+	4637.96i	−0.163388	+	0.406270i
$508$		0			0
$509$	16489.7	−	6001.77i	1.43594	−	0.522640i	0.497313	−	0.867571i	$-0.334320\pi$
$509$	16489.7	−	6001.77i	1.43594	−	0.522640i	0.938628	+	0.344931i	$0.112098\pi$
$510$		0			0
$511$	2450.87	+	13899.6i	0.212172	+	1.20329i
$512$		0			0
$513$	−256.918	+	115.868i	−0.0221115	+	0.00997216i
$514$		0			0
$515$	−1403.70	−	7960.76i	−0.120105	−	0.681152i
$516$		0			0
$517$	174.923	−	63.6666i	0.0148802	−	0.00541597i
$518$		0			0
$519$	−5874.64	−	7494.45i	−0.496856	−	0.633853i
$520$		0			0
$521$	525.762	+	910.646i	0.0442112	+	0.0765761i	0.887284	−	0.461223i	$-0.152589\pi$
$521$	525.762	+	910.646i	0.0442112	+	0.0765761i	−0.843073	+	0.537799i	$0.819256\pi$
$522$		0			0
$523$	5220.14	−	9041.55i	0.436445	−	0.755946i	−0.560967	−	0.827838i	$-0.689571\pi$
$523$	5220.14	−	9041.55i	0.436445	−	0.755946i	0.997412	+	0.0718925i	$0.0229039\pi$
$524$		0			0
$525$	3372.35	+	711.176i	0.280345	+	0.0591205i
$526$		0			0
$527$	−1867.97	+	10593.8i	−0.154402	+	0.875659i
$528$		0			0
$529$	−8318.18	+	6979.79i	−0.683668	+	0.573665i
$530$		0			0
$531$	3111.53	+	2985.58i	0.254291	+	0.243998i
$532$		0			0
$533$	−838.496	−	305.188i	−0.0681413	−	0.0248014i
$534$		0			0
$535$	6591.24	+	5530.71i	0.532643	+	0.446941i
$536$		0			0
$537$	−1689.02	−	1051.66i	−0.135730	−	0.0845115i
$538$		0			0
$539$	1786.26			0.142745
$540$		0			0
$541$	19911.0			1.58233			0.791165	−	0.611603i	$-0.209475\pi$
$541$	19911.0			1.58233			0.791165	+	0.611603i	$0.209475\pi$
$542$		0			0
$543$	−1378.97	+	736.047i	−0.108982	+	0.0581709i
$544$		0			0
$545$	−3550.09	−	2978.88i	−0.279026	−	0.234131i
$546$		0			0
$547$	181.433	+	66.0364i	0.0141820	+	0.00516181i	0.349101	−	0.937085i	$-0.386487\pi$
$547$	181.433	+	66.0364i	0.0141820	+	0.00516181i	−0.334919	+	0.942247i	$0.608709\pi$
$548$		0			0
$549$	−10136.6	−	4474.27i	−0.788011	−	0.347827i
$550$		0			0
$551$	359.651	−	301.783i	0.0278070	−	0.0233329i
$552$		0			0
$553$	621.728	−	3525.99i	0.0478093	−	0.271140i
$554$		0			0
$555$	2720.49	+	8327.44i	0.208069	+	0.636901i
$556$		0			0
$557$	−5088.83	+	8814.12i	−0.387111	+	0.670496i	−0.992060	−	0.125769i	$-0.959860\pi$
$557$	−5088.83	+	8814.12i	−0.387111	+	0.670496i	0.604949	+	0.796264i	$0.293194\pi$
$558$		0			0
$559$	9416.71	+	16310.2i	0.712494	+	1.23408i
$560$		0			0
$561$	4542.21	−	645.780i	0.341840	−	0.0486005i
$562$		0			0
$563$	10169.9	−	3701.53i	0.761295	−	0.277089i	0.0679443	−	0.997689i	$-0.478356\pi$
$563$	10169.9	−	3701.53i	0.761295	−	0.277089i	0.693351	+	0.720600i	$0.256134\pi$
$564$		0			0
$565$	−2988.72	−	16949.9i	−0.222542	−	1.26210i
$566$		0			0
$567$	8223.47	+	4305.20i	0.609089	+	0.318874i
$568$		0			0
$569$	−2827.77	−	16037.1i	−0.208341	−	1.18156i	−0.892095	−	0.451849i	$-0.850765\pi$
$569$	−2827.77	−	16037.1i	−0.208341	−	1.18156i	0.683753	−	0.729713i	$-0.260346\pi$
$570$		0			0
$571$	13023.1	−	4740.01i	0.954464	−	0.347396i	0.182602	−	0.983187i	$-0.441548\pi$
$571$	13023.1	−	4740.01i	0.954464	−	0.347396i	0.771862	+	0.635791i	$0.219326\pi$
$572$		0			0
$573$	−16778.2	+	2385.40i	−1.22324	+	0.173912i
$574$		0			0
$575$	−942.129	−	1631.82i	−0.0683296	−	0.118350i
$576$		0			0
$577$	8766.90	−	15184.7i	0.632532	−	1.09558i	−0.354501	−	0.935056i	$-0.615349\pi$
$577$	8766.90	−	15184.7i	0.632532	−	1.09558i	0.987032	−	0.160521i	$-0.0513175\pi$
$578$		0			0
$579$	−3060.55	−	9368.35i	−0.219675	−	0.672427i
$580$		0			0
$581$	−2151.61	+	12202.4i	−0.153638	+	0.871324i
$582$		0			0
$583$	−2772.14	+	2326.10i	−0.196930	+	0.165244i
$584$		0			0
$585$	6539.12	−	4783.00i	0.462152	−	0.338039i
$586$		0			0
$587$	17793.1	+	6476.17i	1.25111	+	0.455367i	0.880777	−	0.473532i	$-0.157021\pi$
$587$	17793.1	+	6476.17i	1.25111	+	0.455367i	0.370333	+	0.928899i	$0.379243\pi$
$588$		0			0
$589$	−185.158	−	155.366i	−0.0129530	−	0.0108689i
$590$		0			0
$591$	4459.01	−	2380.06i	0.310354	−	0.165656i
$592$		0			0
$593$	8252.04			0.571451			0.285726	−	0.958311i	$-0.407765\pi$
$593$	8252.04			0.571451			0.285726	+	0.958311i	$0.407765\pi$
$594$		0			0
$595$	−9720.22			−0.669732
$596$		0			0
$597$	−12373.8	−	7704.51i	−0.848285	−	0.528182i
$598$		0			0
$599$	−12055.4	−	10115.7i	−0.822320	−	0.690008i	0.131194	−	0.991357i	$-0.458119\pi$
$599$	−12055.4	−	10115.7i	−0.822320	−	0.690008i	−0.953514	+	0.301348i	$0.902563\pi$
$600$		0			0
$601$	3323.58	+	1209.69i	0.225577	+	0.0821033i	0.452336	−	0.891848i	$-0.350591\pi$
$601$	3323.58	+	1209.69i	0.225577	+	0.0821033i	−0.226759	+	0.973951i	$0.572813\pi$
$602$		0			0
$603$	−5660.85	+	23018.1i	−0.382301	+	1.55451i
$604$		0			0
$605$	−8068.07	+	6769.92i	−0.542171	+	0.454936i
$606$		0			0
$607$	−202.364	+	1147.67i	−0.0135317	+	0.0767419i	−0.990826	−	0.135145i	$-0.956850\pi$
$607$	−202.364	+	1147.67i	−0.0135317	+	0.0767419i	0.977294	+	0.211887i	$0.0679610\pi$
$608$		0			0
$609$	−15129.8	−	3190.64i	−1.00672	−	0.212301i
$610$		0			0
$611$	331.198	−	573.651i	0.0219293	−	0.0379827i
$612$		0			0
$613$	−1701.46	−	2947.01i	−0.112107	−	0.194174i	0.804513	−	0.593935i	$-0.202426\pi$
$613$	−1701.46	−	2947.01i	−0.112107	−	0.194174i	−0.916619	+	0.399761i	$0.869093\pi$
$614$		0			0
$615$	−695.008	−	886.642i	−0.0455698	−	0.0581347i
$616$		0			0
$617$	−6455.20	+	2349.50i	−0.421194	+	0.153302i	−0.543917	−	0.839139i	$-0.683059\pi$
$617$	−6455.20	+	2349.50i	−0.421194	+	0.153302i	0.122723	+	0.992441i	$0.460837\pi$
$618$		0			0
$619$	1533.49	+	8696.87i	0.0995739	+	0.564712i	0.993249	+	0.115998i	$0.0370066\pi$
$619$	1533.49	+	8696.87i	0.0995739	+	0.564712i	−0.893676	+	0.448714i	$0.851882\pi$
$620$		0			0
$621$	−1251.31	−	4918.04i	−0.0808591	−	0.317800i
$622$		0			0
$623$	2347.05	+	13310.8i	0.150935	+	0.855994i
$624$		0			0
$625$	6013.91	−	2188.88i	0.384890	−	0.140089i
$626$		0			0
$627$	−38.4639	+	95.6419i	−0.00244992	+	0.00609182i
$628$		0			0
$629$	8826.66	+	15288.2i	0.559526	+	0.969128i
$630$		0			0
$631$	−14372.3	+	24893.6i	−0.906739	+	1.57052i	−0.0881735	+	0.996105i	$0.528103\pi$
$631$	−14372.3	+	24893.6i	−0.906739	+	1.57052i	−0.818566	+	0.574413i	$0.805230\pi$
$632$		0			0
$633$	27.6608	−	30.8195i	0.00173684	−	0.00193518i
$634$		0			0
$635$	−2167.91	+	12294.8i	−0.135482	+	0.768354i
$636$		0			0
$637$	4869.17	−	4085.72i	0.302863	−	0.254132i
$638$		0			0
$639$	−2076.77	+	3100.30i	−0.128569	+	0.191934i
$640$		0			0
$641$	383.429	+	139.557i	0.0236264	+	0.00859932i	0.353806	−	0.935319i	$-0.384887\pi$
$641$	383.429	+	139.557i	0.0236264	+	0.00859932i	−0.330180	+	0.943918i	$0.607109\pi$
$642$		0			0
$643$	−19820.7	−	16631.6i	−1.21563	−	1.02004i	−0.999041	−	0.0437759i	$-0.986061\pi$
$643$	−19820.7	−	16631.6i	−1.21563	−	1.02004i	−0.216593	−	0.976262i	$-0.569494\pi$
$644$		0			0
$645$	−791.805	+	23764.7i	−0.0483369	+	1.45075i
$646$		0			0
$647$	−17713.1			−1.07631			−0.538156	−	0.842845i	$-0.680879\pi$
$647$	−17713.1			−1.07631			−0.538156	+	0.842845i	$0.680879\pi$
$648$		0			0
$649$	1577.26			0.0953976
$650$		0			0
$651$	−265.087	+	7956.15i	−0.0159594	+	0.478995i
$652$		0			0
$653$	15919.4	+	13357.9i	0.954017	+	0.800516i	0.979970	−	0.199147i	$-0.0638173\pi$
$653$	15919.4	+	13357.9i	0.954017	+	0.800516i	−0.0259520	+	0.999663i	$0.508262\pi$
$654$		0			0
$655$	13615.6	+	4955.67i	0.812222	+	0.295625i
$656$		0			0
$657$	−13205.9	−	26857.6i	−0.784189	−	1.59485i
$658$		0			0
$659$	−17125.5	+	14370.0i	−1.01232	+	0.849434i	−0.988643	−	0.150286i	$-0.951981\pi$
$659$	−17125.5	+	14370.0i	−1.01232	+	0.849434i	−0.0236732	+	0.999720i	$0.507536\pi$
$660$		0			0
$661$	−651.001	+	3692.01i	−0.0383071	+	0.217251i	−0.997952	−	0.0639633i	$-0.979626\pi$
$661$	−651.001	+	3692.01i	−0.0383071	+	0.217251i	0.959645	+	0.281214i	$0.0907370\pi$
$662$		0			0
$663$	10904.5	−	12149.8i	0.638759	−	0.711701i
$664$		0			0
$665$	109.203	−	189.146i	0.00636800	−	0.0110297i
$666$		0			0
$667$	4226.80	+	7321.03i	0.245371	+	0.424995i
$668$		0			0
$669$	−6440.80	+	16015.3i	−0.372221	+	0.925540i
$670$		0			0
$671$	−3808.32	+	1386.11i	−0.219104	+	0.0797472i
$672$		0			0
$673$	−1678.26	−	9517.90i	−0.0961252	−	0.545153i	−0.994397	−	0.105712i	$-0.966288\pi$
$673$	−1678.26	−	9517.90i	−0.0961252	−	0.545153i	0.898271	−	0.439441i	$-0.144823\pi$
$674$		0			0
$675$	−7288.01	+	544.801i	−0.415578	+	0.0310658i
$676$		0			0
$677$	2125.75	+	12055.7i	0.120678	+	0.684400i	0.983781	+	0.179372i	$0.0574067\pi$
$677$	2125.75	+	12055.7i	0.120678	+	0.684400i	−0.863103	+	0.505028i	$0.831482\pi$
$678$		0			0
$679$	−2479.72	+	902.543i	−0.140151	+	0.0510109i
$680$		0			0
$681$	−10456.3	−	13339.3i	−0.588377	−	0.750608i
$682$		0			0
$683$	9922.08	+	17185.5i	0.555868	+	0.962791i	0.997835	+	0.0657604i	$0.0209473\pi$
$683$	9922.08	+	17185.5i	0.555868	+	0.962791i	−0.441968	+	0.897031i	$0.645719\pi$
$684$		0			0
$685$	7953.41	−	13775.7i	0.443627	−	0.768384i
$686$		0			0
$687$	14.5818	+	3.07507i	0.000809796	+	0.000170773i
$688$		0			0
$689$	−2236.09	+	12681.5i	−0.123640	+	0.701199i
$690$		0			0
$691$	22107.7	−	18550.5i	1.21710	−	1.02127i	0.218129	−	0.975920i	$-0.430005\pi$
$691$	22107.7	−	18550.5i	1.21710	−	1.02127i	0.998971	−	0.0453479i	$-0.0144396\pi$
$692$		0			0
$693$	3260.60	−	946.266i	0.178730	−	0.0518697i
$694$		0			0
$695$	−8532.45	−	3105.56i	−0.465690	−	0.169497i
$696$		0			0
$697$	−1739.04	−	1459.22i	−0.0945060	−	0.0793000i
$698$		0			0
$699$	−3701.36	−	2304.64i	−0.200284	−	0.124706i
$700$		0			0
$701$	12315.2			0.663538			0.331769	−	0.943361i	$-0.392355\pi$
$701$	12315.2			0.663538			0.331769	+	0.943361i	$0.392355\pi$
$702$		0			0
$703$	−396.658			−0.0212806
$704$		0			0
$705$	737.779	−	393.800i	0.0394133	−	0.0210374i
$706$		0			0
$707$	−13111.5	−	11001.9i	−0.697467	−	0.585245i
$708$		0			0
$709$	18496.8	+	6732.27i	0.979776	+	0.356609i	0.781753	−	0.623588i	$-0.214326\pi$
$709$	18496.8	+	6732.27i	0.979776	+	0.356609i	0.198023	+	0.980197i	$0.436548\pi$
$710$		0			0
$711$	817.765	+	7548.04i	0.0431345	+	0.398134i
$712$		0			0
$713$	3333.94	−	2797.50i	0.175115	−	0.146939i
$714$		0			0
$715$	514.574	−	2918.30i	0.0269147	−	0.152641i
$716$		0			0
$717$	1594.77	+	4881.61i	0.0830654	+	0.254264i
$718$		0			0
$719$	3523.96	−	6103.67i	0.182784	−	0.316590i	−0.760044	−	0.649872i	$-0.774823\pi$
$719$	3523.96	−	6103.67i	0.182784	−	0.316590i	0.942827	+	0.333281i	$0.108156\pi$
$720$		0			0
$721$	−6027.15	−	10439.3i	−0.311322	−	0.539225i
$722$		0			0
$723$	−4677.75	+	665.050i	−0.240619	+	0.0342095i
$724$		0			0
$725$	11440.2	−	4163.89i	0.586039	−	0.213301i
$726$		0			0
$727$	−598.760	−	3395.73i	−0.0305458	−	0.173234i	0.965718	−	0.259592i	$-0.0835881\pi$
$727$	−598.760	−	3395.73i	−0.0305458	−	0.173234i	−0.996264	+	0.0863584i	$0.972477\pi$
$728$		0			0
$729$	−19291.3	−	3907.27i	−0.980099	−	0.198510i
$730$		0			0
$731$	8320.29	+	47186.7i	0.420981	+	2.38750i
$732$		0			0
$733$	708.598	−	257.909i	0.0357062	−	0.0129960i	−0.324105	−	0.946021i	$-0.605063\pi$
$733$	708.598	−	257.909i	0.0357062	−	0.0129960i	0.359812	+	0.933025i	$0.382841\pi$
$734$		0			0
$735$	7945.12	−	1129.58i	0.398721	−	0.0566875i
$736$		0			0
$737$	4335.04	+	7508.52i	0.216667	+	0.375278i
$738$		0			0
$739$	−9360.22	+	16212.4i	−0.465929	+	0.807012i	−0.999243	−	0.0389052i	$-0.987613\pi$
$739$	−9360.22	+	16212.4i	−0.465929	+	0.807012i	0.533314	+	0.845917i	$0.320946\pi$
$740$		0			0
$741$	113.913	+	348.690i	0.00564739	+	0.0172867i
$742$		0			0
$743$	4145.09	−	23508.0i	0.204668	−	1.16073i	−0.693292	−	0.720656i	$-0.743841\pi$
$743$	4145.09	−	23508.0i	0.204668	−	1.16073i	0.897961	−	0.440076i	$-0.145048\pi$
$744$		0			0
$745$	21791.9	−	18285.6i	1.07167	−	0.899238i
$746$		0			0
$747$	−2830.03	−	26121.4i	−0.138615	−	1.27943i
$748$		0			0
$749$	12057.0	+	4388.38i	0.588187	+	0.214082i
$750$		0			0
$751$	2631.87	+	2208.40i	0.127880	+	0.107304i	0.704485	−	0.709719i	$-0.251178\pi$
$751$	2631.87	+	2208.40i	0.127880	+	0.107304i	−0.576604	+	0.817024i	$0.695623\pi$
$752$		0			0
$753$	−20248.4	+	10807.9i	−0.979939	+	0.523056i
$754$		0			0
$755$	21843.8			1.05295
$756$		0			0
$757$	16653.4			0.799573			0.399786	−	0.916608i	$-0.369084\pi$
$757$	16653.4			0.799573			0.399786	+	0.916608i	$0.369084\pi$
$758$		0			0
$759$	−1575.69	−	981.096i	−0.0753542	−	0.0469190i
$760$		0			0
$761$	−15257.9	−	12802.9i	−0.726806	−	0.609862i	0.202453	−	0.979292i	$-0.435109\pi$
$761$	−15257.9	−	12802.9i	−0.726806	−	0.609862i	−0.929259	+	0.369430i	$0.879553\pi$
$762$		0			0
$763$	−6493.97	−	2363.61i	−0.308123	−	0.112147i
$764$		0			0
$765$	19795.0	−	5744.75i	0.935541	−	0.271506i
$766$		0			0
$767$	4299.48	−	3607.69i	0.202406	−	0.169839i
$768$		0			0
$769$	3628.05	−	20575.7i	0.170131	−	0.964861i	−0.773484	−	0.633816i	$-0.781488\pi$
$769$	3628.05	−	20575.7i	0.170131	−	0.964861i	0.943615	−	0.331045i	$-0.107401\pi$
$770$		0			0
$771$	−34595.2	−	7295.58i	−1.61597	−	0.340783i
$772$		0			0
$773$	−8425.94	+	14594.1i	−0.392057	+	0.679062i	−0.992721	−	0.120439i	$-0.961570\pi$
$773$	−8425.94	+	14594.1i	−0.392057	+	0.679062i	0.600664	+	0.799502i	$0.294903\pi$
$774$		0			0
$775$	−3133.86	−	5428.00i	−0.145254	−	0.251586i
$776$		0			0
$777$	8059.36	+	10281.6i	0.372108	+	0.474709i
$778$		0			0
$779$	47.9325	−	17.4460i	0.00220457	−	0.000802398i
$780$		0			0
$781$	237.011	+	1344.16i	0.0108591	+	0.0615848i
$782$		0			0
$783$	32697.2	−	2444.22i	1.49234	−	0.111557i
$784$		0			0
$785$	−4152.68	−	23551.0i	−0.188810	−	1.07079i
$786$		0			0
$787$	−11260.1	+	4098.33i	−0.510010	+	0.185628i	−0.584191	−	0.811616i	$-0.698588\pi$
$787$	−11260.1	+	4098.33i	−0.510010	+	0.185628i	0.0741808	+	0.997245i	$0.476366\pi$
$788$		0			0
$789$	−1686.52	+	4193.59i	−0.0760983	+	0.189221i
$790$		0			0
$791$	−12832.9	−	22227.2i	−0.576845	−	0.999125i
$792$		0			0
$793$	−7210.65	+	12489.2i	−0.322898	+	0.559275i
$794$		0			0
$795$	−10859.3	+	12099.3i	−0.484451	+	0.539772i
$796$		0			0
$797$	7532.17	−	42717.0i	0.334759	−	1.89851i	−0.0948385	−	0.995493i	$-0.530233\pi$
$797$	7532.17	−	42717.0i	0.334759	−	1.89851i	0.429598	−	0.903020i	$-0.358655\pi$
$798$		0			0
$799$	1290.95	−	1083.24i	0.0571598	−	0.0479627i
$800$		0			0
$801$	−12646.5	−	25719.9i	−0.557855	−	1.13454i
$802$		0			0
$803$	−10286.7	−	3744.06i	−0.452068	−	0.164539i
$804$		0			0
$805$	3012.55	+	2527.83i	0.131899	+	0.110676i
$806$		0			0
$807$	730.561	−	21926.6i	0.0318674	−	0.956447i
$808$		0			0
$809$	−5452.36			−0.236953			−0.118476	−	0.992957i	$-0.537801\pi$
$809$	−5452.36			−0.236953			−0.118476	+	0.992957i	$0.537801\pi$
$810$		0			0
$811$	17403.7			0.753548			0.376774	−	0.926305i	$-0.377033\pi$
$811$	17403.7			0.753548			0.376774	+	0.926305i	$0.377033\pi$
$812$		0			0
$813$	−1228.65	+	36875.9i	−0.0530021	+	1.59077i
$814$		0			0
$815$	−10003.2	−	8393.67i	−0.429934	−	0.360758i
$816$		0			0
$817$	−1011.68	−	368.222i	−0.0433222	−	0.0157680i
$818$		0			0
$819$	6723.68	−	10037.4i	0.286868	−	0.428249i
$820$		0			0
$821$	−31338.9	+	26296.5i	−1.33220	+	1.11785i	−0.348640	+	0.937257i	$0.613356\pi$
$821$	−31338.9	+	26296.5i	−1.33220	+	1.11785i	−0.983558	+	0.180591i	$0.942199\pi$
$822$		0			0
$823$	1104.56	−	6264.27i	0.0467831	−	0.265320i	−0.952440	−	0.304726i	$-0.901435\pi$
$823$	1104.56	−	6264.27i	0.0467831	−	0.265320i	0.999223	+	0.0394053i	$0.0125463\pi$
$824$		0			0
$825$	−1785.50	+	1989.39i	−0.0753492	+	0.0839536i
$826$		0			0
$827$	9552.52	−	16545.5i	0.401661	−	0.695698i	−0.592265	−	0.805743i	$-0.701766\pi$
$827$	9552.52	−	16545.5i	0.401661	−	0.695698i	0.993927	+	0.110045i	$0.0350996\pi$
$828$		0			0
$829$	11338.5	+	19638.8i	0.475033	+	0.822781i	0.999591	−	0.0285937i	$-0.00910290\pi$
$829$	11338.5	+	19638.8i	0.475033	+	0.822781i	−0.524558	+	0.851374i	$0.675770\pi$
$830$		0			0
$831$	12811.2	−	31855.5i	0.534797	−	1.32979i
$832$		0			0
$833$	15195.9	−	5530.86i	0.632061	−	0.230051i
$834$		0			0
$835$	−5711.96	−	32394.1i	−0.236731	−	1.34257i
$836$		0			0
$837$	−4162.32	−	16359.1i	−0.171889	−	0.675573i
$838$		0			0
$839$	−409.589	−	2322.89i	−0.0168541	−	0.0955842i	0.975220	−	0.221236i	$-0.0710090\pi$
$839$	−409.589	−	2322.89i	−0.0168541	−	0.0955842i	−0.992074	+	0.125651i	$0.959898\pi$
$840$		0			0
$841$	−28407.6	+	10339.5i	−1.16477	+	0.423941i
$842$		0			0
$843$	6708.97	+	8558.82i	0.274103	+	0.349681i
$844$		0			0
$845$	4107.29	+	7114.04i	0.167213	+	0.289622i
$846$		0			0
$847$	−7852.80	+	13601.5i	−0.318566	+	0.551773i
$848$		0			0
$849$	44245.3	+	9330.65i	1.78857	+	0.377181i
$850$		0			0
$851$	1240.22	−	7033.66i	0.0499581	−	0.283327i
$852$		0			0
$853$	−18056.3	+	15151.1i	−0.724780	+	0.608163i	−0.928703	−	0.370824i	$-0.879075\pi$
$853$	−18056.3	+	15151.1i	−0.724780	+	0.608163i	0.203923	+	0.978987i	$0.434631\pi$
$854$		0			0
$855$	−110.603	+	449.730i	−0.00442401	+	0.0179888i
$856$		0			0
$857$	−15096.0	−	5494.49i	−0.601714	−	0.219006i	0.0231598	−	0.999732i	$-0.492627\pi$
$857$	−15096.0	−	5494.49i	−0.601714	−	0.219006i	−0.624874	+	0.780726i	$0.714850\pi$
$858$		0			0
$859$	−22951.6	−	19258.7i	−0.911639	−	0.764956i	0.0607910	−	0.998151i	$-0.480638\pi$
$859$	−22951.6	−	19258.7i	−0.911639	−	0.764956i	−0.972430	+	0.233194i	$0.925082\pi$
$860$		0			0
$861$	−1426.11	−	887.962i	−0.0564479	−	0.0351471i
$862$		0			0
$863$	34109.9			1.34544			0.672719	−	0.739898i	$-0.265126\pi$
$863$	34109.9			1.34544			0.672719	+	0.739898i	$0.265126\pi$
$864$		0			0
$865$	−15647.9			−0.615081
$866$		0			0
$867$	14120.3	−	7536.88i	0.553113	−	0.295232i
$868$		0			0
$869$	2127.28	+	1785.00i	0.0830416	+	0.0696801i
$870$		0			0
$871$	28991.2	+	10551.9i	1.12782	+	0.410492i
$872$		0			0
$873$	4516.46	−	3303.54i	0.175096	−	0.128073i
$874$		0			0
$875$	14749.1	−	12376.0i	0.569841	−	0.478154i
$876$		0			0
$877$	−2513.11	+	14252.6i	−0.0967638	+	0.548775i	0.897429	+	0.441159i	$0.145433\pi$
$877$	−2513.11	+	14252.6i	−0.0967638	+	0.548775i	−0.994193	+	0.107615i	$0.965678\pi$
$878$		0			0
$879$	12598.0	+	38562.6i	0.483414	+	1.47973i
$880$		0			0
$881$	−3372.51	+	5841.37i	−0.128970	+	0.223383i	−0.923278	−	0.384133i	$-0.874501\pi$
$881$	−3372.51	+	5841.37i	−0.128970	+	0.223383i	0.794308	+	0.607516i	$0.207834\pi$
$882$		0			0
$883$	−7289.54	−	12625.9i	−0.277817	−	0.481193i	0.693025	−	0.720914i	$-0.256278\pi$
$883$	−7289.54	−	12625.9i	−0.277817	−	0.481193i	−0.970842	+	0.239720i	$0.922944\pi$
$884$		0			0
$885$	7015.54	−	997.421i	0.266469	−	0.0378847i
$886$		0			0
$887$	−11377.1	+	4140.92i	−0.430671	+	0.156751i	−0.548254	−	0.836312i	$-0.684707\pi$
$887$	−11377.1	+	4140.92i	−0.430671	+	0.156751i	0.117584	+	0.993063i	$0.462485\pi$
$888$		0			0
$889$	3232.81	+	18334.2i	0.121963	+	0.691685i
$890$		0			0
$891$	−6080.86	+	3854.09i	−0.228638	+	0.144912i
$892$		0			0
$893$	6.57531	+	37.2905i	0.000246399	+	0.00139740i
$894$		0			0
$895$	−3072.36	+	1118.25i	−0.114746	+	0.0417642i
$896$		0			0
$897$	−6539.25	+	929.706i	−0.243410	+	0.0346064i
$898$		0			0
$899$	14059.8	+	24352.4i	0.521604	+	0.903445i
$900$		0			0
$901$	−16380.5	+	28371.9i	−0.605677	+	1.04906i
$902$		0			0
$903$	11011.0	+	33704.8i	0.405786	+	1.24211i
$904$		0			0
$905$	−446.033	+	2529.58i	−0.0163830	+	0.0929127i
$906$		0			0
$907$	15986.2	−	13414.0i	0.585239	−	0.491073i	−0.301424	−	0.953490i	$-0.597462\pi$
$907$	15986.2	−	13414.0i	0.585239	−	0.491073i	0.886663	+	0.462417i	$0.153018\pi$
$908$		0			0
$909$	33203.5	+	14656.0i	1.21154	+	0.534772i
$910$		0			0
$911$	−40925.5	−	14895.7i	−1.48839	−	0.541729i	−0.535365	−	0.844621i	$-0.679826\pi$
$911$	−40925.5	−	14895.7i	−1.48839	−	0.541729i	−0.953025	+	0.302892i	$0.902048\pi$
$912$		0			0
$913$	−7361.86	−	6177.33i	−0.266859	−	0.223921i
$914$		0			0
$915$	−16062.5	+	8573.60i	−0.580340	+	0.309764i
$916$		0			0
$917$	21606.8			0.778101
$918$		0			0
$919$	241.628			0.00867310			0.00433655	−	0.999991i	$-0.498620\pi$
$919$	241.628			0.00867310			0.00433655	+	0.999991i	$0.498620\pi$
$920$		0			0
$921$	21176.6	+	13185.5i	0.757647	+	0.471746i
$922$		0			0
$923$	3720.57	+	3121.93i	0.132681	+	0.111332i
$924$		0			0
$925$	−9665.44	−	3517.93i	−0.343565	−	0.125048i
$926$		0			0
$927$	18443.9	+	17697.3i	0.653481	+	0.627029i
$928$		0			0
$929$	−248.263	+	208.317i	−0.00876775	+	0.00735702i	−0.647161	−	0.762353i	$-0.724044\pi$
$929$	−248.263	+	208.317i	−0.00876775	+	0.00735702i	0.638393	+	0.769710i	$0.279599\pi$
$930$		0			0
$931$	−63.0958	+	357.834i	−0.00222114	+	0.0125967i
$932$		0			0
$933$	−36964.7	−	7795.29i	−1.29708	−	0.273533i
$934$		0			0
$935$	3769.53	−	6529.02i	0.131847	−	0.228366i
$936$		0			0
$937$	15521.6	+	26884.2i	0.541162	+	0.937320i	0.998838	+	0.0482011i	$0.0153488\pi$
$937$	15521.6	+	26884.2i	0.541162	+	0.937320i	−0.457675	+	0.889119i	$0.651318\pi$
$938$		0			0
$939$	94.2973	+	120.298i	0.00327718	+	0.00418080i
$940$		0			0
$941$	−41340.5	+	15046.7i	−1.43216	+	0.521263i	−0.937550	−	0.347852i	$-0.886911\pi$
$941$	−41340.5	+	15046.7i	−1.43216	+	0.521263i	−0.494610	+	0.869115i	$0.664689\pi$
$942$		0			0
$943$	159.488	+	904.503i	0.00550758	+	0.0312351i
$944$		0			0
$945$	13904.5	−	6270.83i	0.478637	−	0.215862i
$946$		0			0
$947$	3654.72	+	20726.9i	0.125409	+	0.711230i	0.981064	+	0.193683i	$0.0620434\pi$
$947$	3654.72	+	20726.9i	0.125409	+	0.711230i	−0.855655	+	0.517546i	$0.826845\pi$
$948$		0			0
$949$	−36604.5	+	13322.9i	−1.25209	+	0.455723i
$950$		0			0
$951$	7438.21	−	18495.4i	0.253628	−	0.630656i
$952$		0			0
$953$	−12519.2	−	21684.0i	−0.425538	−	0.737054i	0.570932	−	0.820997i	$-0.306582\pi$
$953$	−12519.2	−	21684.0i	−0.425538	−	0.737054i	−0.996471	+	0.0839433i	$0.973249\pi$
$954$		0			0
$955$	−13924.0	+	24117.1i	−0.471802	+	0.817185i
$956$		0			0
$957$	8010.53	−	8925.28i	0.270579	−	0.301477i
$958$		0			0
$959$	4119.01	−	23360.1i	0.138696	−	0.786586i
$960$		0			0
$961$	−11731.4	+	9843.79i	−0.393789	+	0.330428i
$962$		0			0
$963$	−27147.3	−	1811.02i	−0.908420	−	0.0606017i
$964$		0			0
$965$	−15218.6	−	5539.11i	−0.507672	−	0.184777i
$966$		0			0
$967$	−16449.7	−	13802.9i	−0.547038	−	0.459019i	0.326899	−	0.945059i	$-0.393996\pi$
$967$	−16449.7	−	13802.9i	−0.547038	−	0.459019i	−0.873936	+	0.486040i	$0.838441\pi$
$968$		0			0
$969$	−31.0773	+	932.734i	−0.00103029	+	0.0309223i
$970$		0			0
$971$	−2611.91			−0.0863236			−0.0431618	−	0.999068i	$-0.513743\pi$
$971$	−2611.91			−0.0863236			−0.0431618	+	0.999068i	$0.513743\pi$
$972$		0			0
$973$	−13540.3			−0.446126
$974$		0			0
$975$	−316.755	+	9506.89i	−0.0104044	+	0.312271i
$976$		0			0
$977$	5137.13	+	4310.56i	0.168220	+	0.141154i	0.723011	−	0.690836i	$-0.242757\pi$
$977$	5137.13	+	4310.56i	0.168220	+	0.141154i	−0.554791	+	0.831990i	$0.687202\pi$
$978$		0			0
$979$	−9850.95	−	3585.45i	−0.321591	−	0.117050i
$980$		0			0
$981$	14621.7	+	975.430i	0.475877	+	0.0317463i
$982$		0			0
$983$	7814.81	−	6557.41i	0.253564	−	0.212766i	−0.507141	−	0.861863i	$-0.669298\pi$
$983$	7814.81	−	6557.41i	0.253564	−	0.212766i	0.760705	+	0.649097i	$0.224853\pi$
$984$		0			0
$985$	1442.28	−	8179.57i	0.0466546	−	0.264592i
$986$		0			0
$987$	832.987	−	928.109i	0.0268635	−	0.0299311i
$988$		0			0
$989$	9692.64	−	16788.1i	0.311636	−	0.539769i
$990$		0			0
$991$	16979.4	+	29409.2i	0.544268	+	0.942699i	0.998653	+	0.0518937i	$0.0165257\pi$
$991$	16979.4	+	29409.2i	0.544268	+	0.942699i	−0.454385	+	0.890805i	$0.650141\pi$
$992$		0			0
$993$	−5350.88	+	13305.1i	−0.171002	+	0.425203i
$994$		0			0
$995$	−22508.2	+	8192.30i	−0.717143	+	0.261019i
$996$		0			0
$997$	5475.70	+	31054.3i	0.173939	+	0.986457i	0.939361	+	0.342929i	$0.111419\pi$
$997$	5475.70	+	31054.3i	0.173939	+	0.986457i	−0.765422	+	0.643528i	$0.777470\pi$
$998$		0			0
$999$	−22489.2	−	16174.9i	−0.712238	−	0.512265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.i.a.13.5	✓	54
3.2	odd	2		324.4.i.a.253.4		54
27.2	odd	18		324.4.i.a.73.4		54
27.25	even	9	inner	108.4.i.a.25.5	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.13.5	✓	54	1.1	even	1	trivial
108.4.i.a.25.5	yes	54	27.25	even	9	inner
324.4.i.a.73.4		54	27.2	odd	18
324.4.i.a.253.4		54	3.2	odd	2

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173032 + 5.19327i) q^{3} +(6.54095 + 5.48851i) q^{5} +(11.9650 + 4.35489i) q^{7} +(-26.9401 - 1.79720i) q^{9} +O(q^{10})\)	\(q+(-0.173032 + 5.19327i) q^{3} +(6.54095 + 5.48851i) q^{5} +(11.9650 + 4.35489i) q^{7} +(-26.9401 - 1.79720i) q^{9} +(-7.56521 + 6.34796i) q^{11} +(-6.10231 + 34.6079i) q^{13} +(-29.6351 + 33.0192i) q^{15} +(-44.7027 + 77.4273i) q^{17} +(-1.00444 - 1.73974i) q^{19} +(-24.6865 + 61.3838i) q^{21} +(33.9901 - 12.3714i) q^{23} +(-9.04572 - 51.3009i) q^{25} +(13.9949 - 139.596i) q^{27} +(40.5831 + 230.158i) q^{29} +(113.063 - 41.1517i) q^{31} +(-31.6577 - 40.3866i) q^{33} +(54.3604 + 94.1550i) q^{35} +(98.7263 - 170.999i) q^{37} +(-178.672 - 37.6792i) q^{39} +(-4.40922 + 25.0059i) q^{41} +(410.543 - 344.487i) q^{43} +(-166.350 - 159.617i) q^{45} +(-17.7125 - 6.44681i) q^{47} +(-138.558 - 116.264i) q^{49} +(-394.366 - 245.551i) q^{51} +366.433 q^{53} -84.3245 q^{55} +(9.20873 - 4.91529i) q^{57} +(-122.347 - 102.661i) q^{59} +(385.626 + 140.356i) q^{61} +(-314.511 - 138.825i) q^{63} +(-229.861 + 192.876i) q^{65} +(152.450 - 864.586i) q^{67} +(58.3667 + 178.661i) q^{69} +(69.1038 - 119.691i) q^{71} +(554.236 + 959.964i) q^{73} +(267.984 - 38.1002i) q^{75} +(-118.162 + 43.0075i) q^{77} +(-48.8286 - 276.921i) q^{79} +(722.540 + 96.8338i) q^{81} +(168.981 + 958.337i) q^{83} +(-717.359 + 261.097i) q^{85} +(-1202.29 + 170.934i) q^{87} +(530.757 + 919.298i) q^{89} +(-223.728 + 387.508i) q^{91} +(194.148 + 594.289i) q^{93} +(2.97859 - 16.8924i) q^{95} +(-158.761 + 133.216i) q^{97} +(215.216 - 157.419i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 54 * q + 12 * q^5 - 48 * q^9	\( 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) \) 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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