LMFDB - Embedded newform 108.4.i.a.25.5

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			25.5
Character	$\chi$	$=$	108.25
Dual form			108.4.i.a.13.5

$q$-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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

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	−0.301558	−	0.953448i	$-0.597507\pi$
$5$	6.54095	−	5.48851i	0.585040	−	0.490907i	0.886598	+	0.462541i	$0.153062\pi$
$6$		0			0
$7$	11.9650	−	4.35489i	0.646048	−	0.235142i	0.00184654	−	0.999998i	$-0.499412\pi$
$7$	11.9650	−	4.35489i	0.646048	−	0.235142i	0.644201	+	0.764856i	$0.277190\pi$
$8$		0			0
$9$	−26.9401	+	1.79720i	−0.997782	+	0.0665631i
$10$		0			0
$11$	−7.56521	−	6.34796i	−0.207363	−	0.173998i	0.533191	−	0.845995i	$-0.320993\pi$
$11$	−7.56521	−	6.34796i	−0.207363	−	0.173998i	−0.740555	+	0.671996i	$0.765437\pi$
$12$		0			0
$13$	−6.10231	−	34.6079i	−0.130191	−	0.738347i	−0.978089	−	0.208188i	$-0.933243\pi$
$13$	−6.10231	−	34.6079i	−0.130191	−	0.738347i	0.847898	−	0.530159i	$-0.177868\pi$
$14$		0			0
$15$	−29.6351	−	33.0192i	−0.510117	−	0.568369i
$16$		0			0
$17$	−44.7027	−	77.4273i	−0.637764	−	1.10464i	−0.985922	−	0.167204i	$-0.946526\pi$
$17$	−44.7027	−	77.4273i	−0.637764	−	1.10464i	0.348158	−	0.937436i	$-0.386807\pi$
$18$		0			0
$19$	−1.00444	+	1.73974i	−0.0121281	+	0.0210065i	−0.872026	−	0.489460i	$-0.837194\pi$
$19$	−1.00444	+	1.73974i	−0.0121281	+	0.0210065i	0.859898	+	0.510466i	$0.170527\pi$
$20$		0			0
$21$	−24.6865	−	61.3838i	−0.256525	−	0.637859i
$22$		0			0
$23$	33.9901	+	12.3714i	0.308149	+	0.112157i	0.491466	−	0.870897i	$-0.336461\pi$
$23$	33.9901	+	12.3714i	0.308149	+	0.112157i	−0.183317	+	0.983054i	$0.558683\pi$
$24$		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	−0.523404	−	0.852085i	$-0.675338\pi$
$29$	40.5831	−	230.158i	0.259865	−	1.47377i	0.783269	−	0.621683i	$-0.213551\pi$
$30$		0			0
$31$	113.063	+	41.1517i	0.655057	+	0.238421i	0.648101	−	0.761554i	$-0.275563\pi$
$31$	113.063	+	41.1517i	0.655057	+	0.238421i	0.00695640	+	0.999976i	$0.497786\pi$
$32$		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	0.997587	−	0.0694333i	$-0.0221191\pi$
$37$	98.7263	+	170.999i	0.438662	+	0.759785i	−0.558924	+	0.829219i	$0.688786\pi$
$38$		0			0
$39$	−178.672	+	37.6792i	−0.733602	+	0.154705i
$40$		0			0
$41$	−4.40922	−	25.0059i	−0.0167952	−	0.0952504i	0.975258	−	0.221070i	$-0.0709550\pi$
$41$	−4.40922	−	25.0059i	−0.0167952	−	0.0952504i	−0.992053	+	0.125820i	$0.959844\pi$
$42$		0			0
$43$	410.543	+	344.487i	1.45598	+	1.22171i	0.928065	+	0.372419i	$0.121471\pi$
$43$	410.543	+	344.487i	1.45598	+	1.22171i	0.527918	+	0.849296i	$0.322973\pi$
$44$		0			0
$45$	−166.350	+	159.617i	−0.551067	+	0.528761i
$46$		0			0
$47$	−17.7125	+	6.44681i	−0.0549708	+	0.0200077i	−0.369359	−	0.929287i	$-0.620423\pi$
$47$	−17.7125	+	6.44681i	−0.0549708	+	0.0200077i	0.314388	+	0.949294i	$0.398201\pi$
$48$		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	−0.767714	−	0.640793i	$-0.778606\pi$
$59$	−122.347	+	102.661i	−0.269969	+	0.226531i	0.497745	+	0.867323i	$0.334161\pi$
$60$		0			0
$61$	385.626	−	140.356i	0.809415	−	0.294603i	0.0960331	−	0.995378i	$-0.469385\pi$
$61$	385.626	−	140.356i	0.809415	−	0.294603i	0.713382	+	0.700775i	$0.247162\pi$
$62$		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	0.729332	+	0.684160i	$0.239831\pi$
$67$	152.450	+	864.586i	0.277981	+	1.57651i	−0.451351	+	0.892346i	$0.649058\pi$
$68$		0			0
$69$	58.3667	−	178.661i	0.101834	−	0.311713i
$70$		0			0
$71$	69.1038	+	119.691i	0.115509	+	0.200067i	0.917983	−	0.396620i	$-0.129817\pi$
$71$	69.1038	+	119.691i	0.115509	+	0.200067i	−0.802474	+	0.596687i	$0.796484\pi$
$72$		0			0
$73$	554.236	−	959.964i	0.888608	−	1.53911i	0.0470856	−	0.998891i	$-0.485007\pi$
$73$	554.236	−	959.964i	0.888608	−	1.53911i	0.841522	−	0.540223i	$-0.181660\pi$
$74$		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	0.930094	+	0.367322i	$0.119725\pi$
$79$	−48.8286	+	276.921i	−0.0695399	+	0.394380i	−0.999634	+	0.0270585i	$0.991386\pi$
$80$		0			0
$81$	722.540	−	96.8338i	0.991139	−	0.132831i
$82$		0			0
$83$	168.981	−	958.337i	0.223470	−	1.26736i	−0.642118	−	0.766606i	$-0.721944\pi$
$83$	168.981	−	958.337i	0.223470	−	1.26736i	0.865588	−	0.500757i	$-0.166945\pi$
$84$		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	−0.354978	−	0.934875i	$-0.615512\pi$
$89$	530.757	−	919.298i	0.632136	−	1.09489i	0.987114	−	0.160017i	$-0.0511549\pi$
$90$		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	0.555904	−	0.831247i	$-0.312372\pi$
$97$	−158.761	−	133.216i	−0.166183	−	0.139444i	−0.722087	+	0.691803i	$0.756817\pi$
$98$		0			0
$99$	215.216	+	157.419i	0.218485	+	0.159810i
$100$		0			0
$101$	−1263.16	+	459.753i	−1.24445	+	0.452942i	−0.878522	−	0.477701i	$-0.841470\pi$
$101$	−1263.16	+	459.753i	−1.24445	+	0.452942i	−0.365927	+	0.930644i	$0.619248\pi$
$102$		0			0
$103$	−725.221	+	608.533i	−0.693768	+	0.582141i	−0.919993	−	0.391934i	$-0.871806\pi$
$103$	−725.221	+	608.533i	−0.693768	+	0.582141i	0.226225	+	0.974075i	$0.427362\pi$
$104$		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	−0.293013	+	0.956109i	$0.594658\pi$
$113$	−1544.12	+	1295.67i	−1.28548	+	1.07864i	−0.992464	+	0.122535i	$0.960898\pi$
$114$		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	−0.489125	−	0.872214i	$-0.662684\pi$
$127$	731.061	−	1266.24i	0.510797	−	0.884726i	0.999922	−	0.0125122i	$-0.00398286\pi$
$128$		0			0
$129$	1717.98	−	2191.67i	1.17255	−	1.49586i
$130$		0			0
$131$	1594.59	+	580.385i	1.06351	+	0.387087i	0.813747	−	0.581219i	$-0.197424\pi$
$131$	1594.59	+	580.385i	1.06351	+	0.387087i	0.249766	+	0.968306i	$0.419646\pi$
$132$		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	0.700755	+	0.713402i	$0.252847\pi$
$137$	−323.495	+	1834.63i	−0.201737	+	1.14411i	−0.902492	+	0.430707i	$0.858264\pi$
$138$		0			0
$139$	−999.280	−	363.708i	−0.609768	−	0.221938i	0.0186335	−	0.999826i	$-0.494068\pi$
$139$	−999.280	−	363.708i	−0.609768	−	0.221938i	−0.628402	+	0.777889i	$0.716291\pi$
$140$		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	0.554365	+	0.832274i	$0.312961\pi$
$149$	578.529	+	3281.00i	0.318087	+	1.80396i	−0.236278	+	0.971685i	$0.575928\pi$
$150$		0			0
$151$	1959.73	+	1644.41i	1.05616	+	0.886224i	0.993728	−	0.111825i	$-0.0356696\pi$
$151$	1959.73	+	1644.41i	1.05616	+	0.886224i	0.0624329	+	0.998049i	$0.480114\pi$
$152$		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	−0.996759	−	0.0804405i	$-0.974367\pi$
$157$	−2145.49	+	1800.28i	−1.09063	+	0.915144i	−0.0938671	+	0.995585i	$0.529923\pi$
$158$		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	−0.393831	+	0.919183i	$0.628850\pi$
$167$	−2951.09	+	2476.26i	−1.36744	+	1.14742i	−0.973607	+	0.228233i	$0.926705\pi$
$168$		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	0.279889	−	0.960032i	$-0.409702\pi$
$173$	−1403.86	−	1177.98i	−0.616956	−	0.517688i	−0.896845	+	0.442345i	$0.854147\pi$
$174$		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	0.823281	−	0.567634i	$-0.192141\pi$
$179$	−191.456	−	331.612i	−0.0799448	−	0.138469i	−0.903226	+	0.429165i	$0.858808\pi$
$180$		0			0
$181$	150.411	−	260.519i	0.0617677	−	0.106985i	−0.833488	−	0.552538i	$-0.813660\pi$
$181$	150.411	−	260.519i	0.0617677	−	0.106985i	0.895256	+	0.445553i	$0.146993\pi$
$182$		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	−0.667136	−	0.744936i	$-0.732480\pi$
$191$	566.341	−	3211.88i	0.214550	−	1.21677i	0.881686	−	0.471836i	$-0.156409\pi$
$192$		0			0
$193$	−1782.33	−	648.714i	−0.664739	−	0.241945i	−0.0124579	−	0.999922i	$-0.503966\pi$
$193$	−1782.33	−	648.714i	−0.664739	−	0.241945i	−0.652281	+	0.757977i	$0.726188\pi$
$194$		0			0
$195$	−961.885	+	1227.10i	−0.353241	+	0.450639i
$196$		0			0
$197$	−486.365	+	842.409i	−0.175899	+	0.304666i	−0.940472	−	0.339871i	$-0.889616\pi$
$197$	−486.365	+	842.409i	−0.175899	+	0.304666i	0.764573	+	0.644537i	$0.222950\pi$
$198$		0			0
$199$	−1402.61	−	2429.40i	−0.499641	−	0.865403i	0.500359	−	0.865818i	$-0.333201\pi$
$199$	−1402.61	−	2429.40i	−0.499641	−	0.865403i	−1.00000		0.000414695i	$0.999868\pi$
$200$		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	−0.643783	−	0.765208i	$-0.722636\pi$
$211$	−6.10520	+	5.12287i	−0.00199194	+	0.00167144i	0.641791	+	0.766880i	$0.278192\pi$
$212$		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	0.172275	−	0.985049i	$-0.444888\pi$
$223$	3121.71	−	1136.21i	0.937422	−	0.341194i	0.765147	+	0.643855i	$0.222666\pi$
$224$		0			0
$225$	151.495	−	1398.31i	0.0448873	−	0.414314i
$226$		0			0
$227$	−2498.72	−	2096.68i	−0.730599	−	0.613046i	0.199696	−	0.979858i	$-0.436005\pi$
$227$	−2498.72	−	2096.68i	−0.730599	−	0.613046i	−0.930295	+	0.366812i	$0.880449\pi$
$228$		0			0
$229$	0.498021	+	2.82442i	0.000143712	+	0.000815033i	0.984880	−	0.173241i	$-0.0554238\pi$
$229$	0.498021	+	2.82442i	0.000143712	+	0.000815033i	−0.984736	+	0.174056i	$0.944313\pi$
$230$		0			0
$231$	−202.904	+	621.090i	−0.0577926	+	0.176904i
$232$		0			0
$233$	−419.561	−	726.702i	−0.117967	−	0.204325i	0.800995	−	0.598671i	$-0.204304\pi$
$233$	−419.561	−	726.702i	−0.117967	−	0.204325i	−0.918962	+	0.394346i	$0.870971\pi$
$234$		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	0.464626	−	0.885507i	$-0.346189\pi$
$239$	928.725	+	338.028i	0.251356	+	0.0914863i	−0.213269	+	0.976993i	$0.568411\pi$
$240$		0			0
$241$	157.896	−	895.472i	0.0422032	−	0.239346i	−0.956408	−	0.292034i	$-0.905668\pi$
$241$	157.896	−	895.472i	0.0422032	−	0.239346i	0.998611	+	0.0526883i	$0.0167790\pi$
$242$		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	−0.442475	−	0.896781i	$-0.645899\pi$
$251$	2208.59	−	3825.39i	0.555398	−	0.961977i	0.997872	−	0.0651964i	$-0.0207674\pi$
$252$		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	−0.698848	−	0.715270i	$-0.746304\pi$
$257$	−1181.55	−	6700.91i	−0.286782	−	1.62642i	0.412066	−	0.911154i	$-0.364807\pi$
$258$		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	−0.244412	−	0.969671i	$-0.578595\pi$
$263$	817.417	−	297.515i	0.191650	−	0.0697551i	0.436062	+	0.899916i	$0.356373\pi$
$264$		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	−0.911967	−	0.410263i	$-0.865437\pi$
$277$	−6209.30	+	2260.00i	−1.34686	+	0.490218i	−0.434895	+	0.900481i	$0.643215\pi$
$278$		0			0
$279$	−3119.90	−	905.434i	−0.669475	−	0.194290i
$280$		0			0
$281$	1603.24	+	1345.28i	0.340360	+	0.285596i	0.796905	−	0.604104i	$-0.206469\pi$
$281$	1603.24	+	1345.28i	0.340360	+	0.285596i	−0.456546	+	0.889700i	$0.650913\pi$
$282$		0			0
$283$	1511.14	+	8570.09i	0.317413	+	1.80014i	0.558359	+	0.829599i	$0.311431\pi$
$283$	1511.14	+	8570.09i	0.317413	+	1.80014i	−0.240946	+	0.970538i	$0.577458\pi$
$284$		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	0.946139	−	0.323760i	$-0.104947\pi$
$293$	7336.53	+	2670.28i	1.46282	+	0.532421i	0.516676	+	0.856181i	$0.327169\pi$
$294$		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	0.998139	−	0.0609852i	$-0.0194242\pi$
$307$	2400.44	+	4157.68i	0.446255	+	0.772936i	−0.551884	+	0.833921i	$0.686091\pi$
$308$		0			0
$309$	3285.76	+	3660.97i	0.604920	+	0.673998i
$310$		0			0
$311$	−1262.48	−	7159.88i	−0.230189	−	1.30546i	−0.852513	−	0.522705i	$-0.824923\pi$
$311$	−1262.48	−	7159.88i	−0.230189	−	1.30546i	0.622325	−	0.782759i	$-0.286188\pi$
$312$		0			0
$313$	22.5342	+	18.9084i	0.00406935	+	0.00341459i	0.644820	−	0.764334i	$-0.276932\pi$
$313$	22.5342	+	18.9084i	0.00406935	+	0.00341459i	−0.640751	+	0.767749i	$0.721377\pi$
$314$		0			0
$315$	−1295.26	+	2634.24i	−0.231681	+	0.471183i
$316$		0			0
$317$	−3605.13	+	1312.16i	−0.638752	+	0.232487i	−0.641036	−	0.767511i	$-0.721495\pi$
$317$	−3605.13	+	1312.16i	−0.638752	+	0.232487i	0.00228399	+	0.999997i	$0.499273\pi$
$318$		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	−0.117589	−	0.993062i	$-0.537516\pi$
$331$	2593.45	−	943.938i	0.430661	−	0.156748i	0.548250	+	0.836315i	$0.315294\pi$
$332$		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	−0.719266	−	0.694735i	$-0.755522\pi$
$337$	−1738.35	−	9858.65i	−0.280990	−	1.59358i	0.438275	−	0.898841i	$-0.355590\pi$
$338$		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	0.370949	−	0.928653i	$-0.379033\pi$
$347$	376.101	+	136.890i	0.0581849	+	0.0211776i	−0.312764	+	0.949831i	$0.601255\pi$
$348$		0			0
$349$	−124.917	+	708.438i	−0.0191594	+	0.108659i	−0.992888	−	0.119054i	$-0.962014\pi$
$349$	−124.917	+	708.438i	−0.0191594	+	0.108659i	0.973728	+	0.227713i	$0.0731248\pi$
$350$		0			0
$351$	4745.74	−	1336.19i	0.721678	−	0.203193i
$352$		0			0
$353$	−27.6907	+	157.042i	−0.00417515	+	0.0236784i	−0.986824	−	0.161796i	$-0.948271\pi$
$353$	−27.6907	+	157.042i	−0.00417515	+	0.0236784i	0.982649	+	0.185475i	$0.0593823\pi$
$354$		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	0.255752	+	0.966743i	$0.417677\pi$
$359$	−4825.04	+	8357.21i	−0.709348	+	1.22863i	−0.965099	+	0.261884i	$0.915656\pi$
$360$		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	0.0727258	−	0.997352i	$-0.476830\pi$
$367$	−6305.46	−	5290.91i	−0.896845	−	0.752543i	−0.969571	+	0.244809i	$0.921275\pi$
$368$		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	−0.212443	−	0.977174i	$-0.568142\pi$
$373$	5136.29	−	4309.86i	0.712995	−	0.598274i	0.925438	+	0.378899i	$0.123697\pi$
$374$		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	−0.180851	+	0.983510i	$0.557885\pi$
$383$	−8850.82	+	7426.72i	−1.18082	+	0.990829i	−0.999973	+	0.00731893i	$0.997670\pi$
$384$		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	0.680845	−	0.732427i	$-0.261613\pi$
$389$	596.696	+	500.687i	0.0777729	+	0.0652592i	−0.603072	+	0.797686i	$0.706057\pi$
$390$		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	−0.838201	−	0.545362i	$-0.816392\pi$
$397$	420.795	−	728.838i	0.0531967	−	0.0921394i	0.891398	+	0.453222i	$0.149726\pi$
$398$		0			0
$399$	131.588	+	18.7082i	0.0165103	+	0.00234733i
$400$		0			0
$401$	14884.6	+	5417.54i	1.85362	+	0.674661i	0.983252	+	0.182252i	$0.0583388\pi$
$401$	14884.6	+	5417.54i	1.85362	+	0.674661i	0.870364	+	0.492409i	$0.163883\pi$
$402$		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	0.599196	−	0.800603i	$-0.295487\pi$
$409$	4496.30	+	1636.52i	0.543588	+	0.197850i	−0.0556071	+	0.998453i	$0.517709\pi$
$410$		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	−0.916912	−	0.399090i	$-0.869326\pi$
$419$	−1644.96	−	9329.01i	−0.191793	−	1.08771i	0.725119	−	0.688624i	$-0.241785\pi$
$420$		0			0
$421$	−7997.87	−	6711.01i	−0.925873	−	0.776900i	0.0491989	−	0.998789i	$-0.484333\pi$
$421$	−7997.87	−	6711.01i	−0.925873	−	0.776900i	−0.975072	+	0.221889i	$0.928778\pi$
$422$		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	−0.375592	−	0.926785i	$-0.622561\pi$
$439$	−621.671	+	226.270i	−0.0675871	+	0.0245997i	0.308005	+	0.951385i	$0.400339\pi$
$440$		0			0
$441$	3523.82	−	3381.18i	0.380501	−	0.365099i
$442$		0			0
$443$	12445.6	+	10443.1i	1.33478	+	1.12001i	0.982934	+	0.183957i	$0.0588908\pi$
$443$	12445.6	+	10443.1i	1.33478	+	1.12001i	0.351847	+	0.936057i	$0.385554\pi$
$444$		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	−0.980412	−	0.196959i	$-0.936894\pi$
$449$	−6286.72	−	10888.9i	−0.660777	−	1.14450i	0.319635	−	0.947541i	$-0.396440\pi$
$450$		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	−0.962054	−	0.272859i	$-0.912031\pi$
$457$	344.908	−	1956.07i	0.0353044	−	0.200221i	0.997358	+	0.0726379i	$0.0231418\pi$
$458$		0			0
$459$	10183.0	−	7323.92i	1.03551	−	0.744774i
$460$		0			0
$461$	−2257.12	+	12800.8i	−0.228036	+	1.29326i	0.628759	+	0.777600i	$0.283563\pi$
$461$	−2257.12	+	12800.8i	−0.228036	+	1.29326i	−0.856795	+	0.515657i	$0.827548\pi$
$462$		0			0
$463$	−11058.6	−	4024.98i	−1.11001	−	0.404010i	−0.279013	−	0.960287i	$-0.590007\pi$
$463$	−11058.6	−	4024.98i	−1.11001	−	0.404010i	−0.830997	+	0.556277i	$0.812229\pi$
$464$		0			0
$465$	−1991.85	−	4952.80i	−0.198644	−	0.493937i
$466$		0			0
$467$	−8253.92	+	14296.2i	−0.817871	+	1.41659i	0.0893763	+	0.995998i	$0.471513\pi$
$467$	−8253.92	+	14296.2i	−0.817871	+	1.41659i	−0.907248	+	0.420597i	$0.861821\pi$
$468$		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	−0.713079	−	0.701083i	$-0.752700\pi$
$479$	−8477.76	+	3085.65i	−0.808682	+	0.294336i	−0.0956026	+	0.995420i	$0.530478\pi$
$480$		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	−0.782713	−	0.622383i	$-0.786165\pi$
$491$	−3325.98	+	2790.83i	−0.305702	+	0.256514i	0.477011	+	0.878897i	$0.341720\pi$
$492$		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	0.988296	+	0.152550i	$0.0487485\pi$
$499$	1245.95	+	7066.16i	0.111777	+	0.633917i	−0.876519	+	0.481367i	$0.840140\pi$
$500$		0			0
$501$	13370.5	+	14897.3i	1.19232	+	1.32847i
$502$		0			0
$503$	8090.46	+	14013.1i	0.717168	+	1.24217i	0.962117	+	0.272636i	$0.0878954\pi$
$503$	8090.46	+	14013.1i	0.717168	+	1.24217i	−0.244949	+	0.969536i	$0.578771\pi$
$504$		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	0.938628	−	0.344931i	$-0.112098\pi$
$509$	16489.7	+	6001.77i	1.43594	+	0.522640i	0.497313	+	0.867571i	$0.334320\pi$
$510$		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	−0.843073	−	0.537799i	$-0.819256\pi$
$521$	525.762	−	910.646i	0.0442112	−	0.0765761i	0.887284	+	0.461223i	$0.152589\pi$
$522$		0			0
$523$	5220.14	+	9041.55i	0.436445	+	0.755946i	0.997412	−	0.0718925i	$-0.0229039\pi$
$523$	5220.14	+	9041.55i	0.436445	+	0.755946i	−0.560967	+	0.827838i	$0.689571\pi$
$524$		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	−0.334919	−	0.942247i	$-0.608709\pi$
$547$	181.433	−	66.0364i	0.0141820	−	0.00516181i	0.349101	+	0.937085i	$0.386487\pi$
$548$		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	0.604949	−	0.796264i	$-0.293194\pi$
$557$	−5088.83	−	8814.12i	−0.387111	−	0.670496i	−0.992060	+	0.125769i	$0.959860\pi$
$558$		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	0.693351	−	0.720600i	$-0.256134\pi$
$563$	10169.9	+	3701.53i	0.761295	+	0.277089i	0.0679443	+	0.997689i	$0.478356\pi$
$564$		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	0.683753	+	0.729713i	$0.260346\pi$
$569$	−2827.77	+	16037.1i	−0.208341	+	1.18156i	−0.892095	+	0.451849i	$0.850765\pi$
$570$		0			0
$571$	13023.1	+	4740.01i	0.954464	+	0.347396i	0.771862	−	0.635791i	$-0.219326\pi$
$571$	13023.1	+	4740.01i	0.954464	+	0.347396i	0.182602	+	0.983187i	$0.441548\pi$
$572$		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	0.987032	+	0.160521i	$0.0513175\pi$
$577$	8766.90	+	15184.7i	0.632532	+	1.09558i	−0.354501	+	0.935056i	$0.615349\pi$
$578$		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	0.370333	−	0.928899i	$-0.379243\pi$
$587$	17793.1	−	6476.17i	1.25111	−	0.455367i	0.880777	+	0.473532i	$0.157021\pi$
$588$		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	−0.953514	−	0.301348i	$-0.902563\pi$
$599$	−12055.4	+	10115.7i	−0.822320	+	0.690008i	0.131194	+	0.991357i	$0.458119\pi$
$600$		0			0
$601$	3323.58	−	1209.69i	0.225577	−	0.0821033i	−0.226759	−	0.973951i	$-0.572813\pi$
$601$	3323.58	−	1209.69i	0.225577	−	0.0821033i	0.452336	+	0.891848i	$0.350591\pi$
$602$		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	0.977294	−	0.211887i	$-0.0679610\pi$
$607$	−202.364	−	1147.67i	−0.0135317	−	0.0767419i	−0.990826	+	0.135145i	$0.956850\pi$
$608$		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	−0.916619	−	0.399761i	$-0.869093\pi$
$613$	−1701.46	+	2947.01i	−0.112107	+	0.194174i	0.804513	+	0.593935i	$0.202426\pi$
$614$		0			0
$615$	−695.008	+	886.642i	−0.0455698	+	0.0581347i
$616$		0			0
$617$	−6455.20	−	2349.50i	−0.421194	−	0.153302i	0.122723	−	0.992441i	$-0.460837\pi$
$617$	−6455.20	−	2349.50i	−0.421194	−	0.153302i	−0.543917	+	0.839139i	$0.683059\pi$
$618$		0			0
$619$	1533.49	−	8696.87i	0.0995739	−	0.564712i	−0.893676	−	0.448714i	$-0.851882\pi$
$619$	1533.49	−	8696.87i	0.0995739	−	0.564712i	0.993249	−	0.115998i	$-0.0370066\pi$
$620$		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	−0.818566	−	0.574413i	$-0.805230\pi$
$631$	−14372.3	−	24893.6i	−0.906739	−	1.57052i	−0.0881735	−	0.996105i	$-0.528103\pi$
$632$		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	−0.330180	−	0.943918i	$-0.607109\pi$
$641$	383.429	−	139.557i	0.0236264	−	0.00859932i	0.353806	+	0.935319i	$0.384887\pi$
$642$		0			0
$643$	−19820.7	+	16631.6i	−1.21563	+	1.02004i	−0.216593	+	0.976262i	$0.569494\pi$
$643$	−19820.7	+	16631.6i	−1.21563	+	1.02004i	−0.999041	+	0.0437759i	$0.986061\pi$
$644$		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	−0.0259520	−	0.999663i	$-0.508262\pi$
$653$	15919.4	−	13357.9i	0.954017	−	0.800516i	0.979970	+	0.199147i	$0.0638173\pi$
$654$		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	−0.0236732	−	0.999720i	$-0.507536\pi$
$659$	−17125.5	−	14370.0i	−1.01232	−	0.849434i	−0.988643	+	0.150286i	$0.951981\pi$
$660$		0			0
$661$	−651.001	−	3692.01i	−0.0383071	−	0.217251i	0.959645	−	0.281214i	$-0.0907370\pi$
$661$	−651.001	−	3692.01i	−0.0383071	−	0.217251i	−0.997952	+	0.0639633i	$0.979626\pi$
$662$		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	0.898271	+	0.439441i	$0.144823\pi$
$673$	−1678.26	+	9517.90i	−0.0961252	+	0.545153i	−0.994397	+	0.105712i	$0.966288\pi$
$674$		0			0
$675$	−7288.01	−	544.801i	−0.415578	−	0.0310658i
$676$		0			0
$677$	2125.75	−	12055.7i	0.120678	−	0.684400i	−0.863103	−	0.505028i	$-0.831482\pi$
$677$	2125.75	−	12055.7i	0.120678	−	0.684400i	0.983781	−	0.179372i	$-0.0574067\pi$
$678$		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	−0.441968	−	0.897031i	$-0.645719\pi$
$683$	9922.08	−	17185.5i	0.555868	−	0.962791i	0.997835	−	0.0657604i	$-0.0209473\pi$
$684$		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	0.998971	+	0.0453479i	$0.0144396\pi$
$691$	22107.7	+	18550.5i	1.21710	+	1.02127i	0.218129	+	0.975920i	$0.430005\pi$
$692$		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	0.198023	−	0.980197i	$-0.436548\pi$
$709$	18496.8	−	6732.27i	0.979776	−	0.356609i	0.781753	+	0.623588i	$0.214326\pi$
$710$		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	0.942827	−	0.333281i	$-0.108156\pi$
$719$	3523.96	+	6103.67i	0.182784	+	0.316590i	−0.760044	+	0.649872i	$0.774823\pi$
$720$		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	−0.996264	−	0.0863584i	$-0.972477\pi$
$727$	−598.760	+	3395.73i	−0.0305458	+	0.173234i	0.965718	+	0.259592i	$0.0835881\pi$
$728$		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	0.359812	−	0.933025i	$-0.382841\pi$
$733$	708.598	+	257.909i	0.0357062	+	0.0129960i	−0.324105	+	0.946021i	$0.605063\pi$
$734$		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	0.533314	−	0.845917i	$-0.320946\pi$
$739$	−9360.22	−	16212.4i	−0.465929	−	0.807012i	−0.999243	+	0.0389052i	$0.987613\pi$
$740$		0			0
$741$	113.913	−	348.690i	0.00564739	−	0.0172867i
$742$		0			0
$743$	4145.09	+	23508.0i	0.204668	+	1.16073i	0.897961	+	0.440076i	$0.145048\pi$
$743$	4145.09	+	23508.0i	0.204668	+	1.16073i	−0.693292	+	0.720656i	$0.743841\pi$
$744$		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	−0.576604	−	0.817024i	$-0.695623\pi$
$751$	2631.87	−	2208.40i	0.127880	−	0.107304i	0.704485	+	0.709719i	$0.251178\pi$
$752$		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	−0.929259	−	0.369430i	$-0.879553\pi$
$761$	−15257.9	+	12802.9i	−0.726806	+	0.609862i	0.202453	+	0.979292i	$0.435109\pi$
$762$		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	0.943615	+	0.331045i	$0.107401\pi$
$769$	3628.05	+	20575.7i	0.170131	+	0.964861i	−0.773484	+	0.633816i	$0.781488\pi$
$770$		0			0
$771$	−34595.2	+	7295.58i	−1.61597	+	0.340783i
$772$		0			0
$773$	−8425.94	−	14594.1i	−0.392057	−	0.679062i	0.600664	−	0.799502i	$-0.294903\pi$
$773$	−8425.94	−	14594.1i	−0.392057	−	0.679062i	−0.992721	+	0.120439i	$0.961570\pi$
$774$		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	0.0741808	−	0.997245i	$-0.476366\pi$
$787$	−11260.1	−	4098.33i	−0.510010	−	0.185628i	−0.584191	+	0.811616i	$0.698588\pi$
$788$		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	0.429598	+	0.903020i	$0.358655\pi$
$797$	7532.17	+	42717.0i	0.334759	+	1.89851i	−0.0948385	+	0.995493i	$0.530233\pi$
$798$		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	−0.983558	−	0.180591i	$-0.942199\pi$
$821$	−31338.9	−	26296.5i	−1.33220	−	1.11785i	−0.348640	−	0.937257i	$-0.613356\pi$
$822$		0			0
$823$	1104.56	+	6264.27i	0.0467831	+	0.265320i	0.999223	−	0.0394053i	$-0.0125463\pi$
$823$	1104.56	+	6264.27i	0.0467831	+	0.265320i	−0.952440	+	0.304726i	$0.901435\pi$
$824$		0			0
$825$	−1785.50	−	1989.39i	−0.0753492	−	0.0839536i
$826$		0			0
$827$	9552.52	+	16545.5i	0.401661	+	0.695698i	0.993927	−	0.110045i	$-0.0350996\pi$
$827$	9552.52	+	16545.5i	0.401661	+	0.695698i	−0.592265	+	0.805743i	$0.701766\pi$
$828$		0			0
$829$	11338.5	−	19638.8i	0.475033	−	0.822781i	−0.524558	−	0.851374i	$-0.675770\pi$
$829$	11338.5	−	19638.8i	0.475033	−	0.822781i	0.999591	+	0.0285937i	$0.00910290\pi$
$830$		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	−0.992074	−	0.125651i	$-0.959898\pi$
$839$	−409.589	+	2322.89i	−0.0168541	+	0.0955842i	0.975220	+	0.221236i	$0.0710090\pi$
$840$		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	0.203923	−	0.978987i	$-0.434631\pi$
$853$	−18056.3	−	15151.1i	−0.724780	−	0.608163i	−0.928703	+	0.370824i	$0.879075\pi$
$854$		0			0
$855$	−110.603	−	449.730i	−0.00442401	−	0.0179888i
$856$		0			0
$857$	−15096.0	+	5494.49i	−0.601714	+	0.219006i	−0.624874	−	0.780726i	$-0.714850\pi$
$857$	−15096.0	+	5494.49i	−0.601714	+	0.219006i	0.0231598	+	0.999732i	$0.492627\pi$
$858$		0			0
$859$	−22951.6	+	19258.7i	−0.911639	+	0.764956i	−0.972430	−	0.233194i	$-0.925082\pi$
$859$	−22951.6	+	19258.7i	−0.911639	+	0.764956i	0.0607910	+	0.998151i	$0.480638\pi$
$860$		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	−0.994193	−	0.107615i	$-0.965678\pi$
$877$	−2513.11	−	14252.6i	−0.0967638	−	0.548775i	0.897429	−	0.441159i	$-0.145433\pi$
$878$		0			0
$879$	12598.0	−	38562.6i	0.483414	−	1.47973i
$880$		0			0
$881$	−3372.51	−	5841.37i	−0.128970	−	0.223383i	0.794308	−	0.607516i	$-0.207834\pi$
$881$	−3372.51	−	5841.37i	−0.128970	−	0.223383i	−0.923278	+	0.384133i	$0.874501\pi$
$882$		0			0
$883$	−7289.54	+	12625.9i	−0.277817	+	0.481193i	−0.970842	−	0.239720i	$-0.922944\pi$
$883$	−7289.54	+	12625.9i	−0.277817	+	0.481193i	0.693025	+	0.720914i	$0.256278\pi$
$884$		0			0
$885$	7015.54	+	997.421i	0.266469	+	0.0378847i
$886$		0			0
$887$	−11377.1	−	4140.92i	−0.430671	−	0.156751i	0.117584	−	0.993063i	$-0.462485\pi$
$887$	−11377.1	−	4140.92i	−0.430671	−	0.156751i	−0.548254	+	0.836312i	$0.684707\pi$
$888$		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	0.886663	−	0.462417i	$-0.153018\pi$
$907$	15986.2	+	13414.0i	0.585239	+	0.491073i	−0.301424	+	0.953490i	$0.597462\pi$
$908$		0			0
$909$	33203.5	−	14656.0i	1.21154	−	0.534772i
$910$		0			0
$911$	−40925.5	+	14895.7i	−1.48839	+	0.541729i	−0.953025	−	0.302892i	$-0.902048\pi$
$911$	−40925.5	+	14895.7i	−1.48839	+	0.541729i	−0.535365	+	0.844621i	$0.679826\pi$
$912$		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	0.638393	−	0.769710i	$-0.279599\pi$
$929$	−248.263	−	208.317i	−0.00876775	−	0.00735702i	−0.647161	+	0.762353i	$0.724044\pi$
$930$		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	−0.457675	−	0.889119i	$-0.651318\pi$
$937$	15521.6	−	26884.2i	0.541162	−	0.937320i	0.998838	−	0.0482011i	$-0.0153488\pi$
$938$		0			0
$939$	94.2973	−	120.298i	0.00327718	−	0.00418080i
$940$		0			0
$941$	−41340.5	−	15046.7i	−1.43216	−	0.521263i	−0.494610	−	0.869115i	$-0.664689\pi$
$941$	−41340.5	−	15046.7i	−1.43216	−	0.521263i	−0.937550	+	0.347852i	$0.886911\pi$
$942$		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	−0.855655	−	0.517546i	$-0.826845\pi$
$947$	3654.72	−	20726.9i	0.125409	−	0.711230i	0.981064	−	0.193683i	$-0.0620434\pi$
$948$		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	−0.996471	−	0.0839433i	$-0.973249\pi$
$953$	−12519.2	+	21684.0i	−0.425538	+	0.737054i	0.570932	+	0.820997i	$0.306582\pi$
$954$		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	−0.873936	−	0.486040i	$-0.838441\pi$
$967$	−16449.7	+	13802.9i	−0.547038	+	0.459019i	0.326899	+	0.945059i	$0.393996\pi$
$968$		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	−0.554791	−	0.831990i	$-0.687202\pi$
$977$	5137.13	−	4310.56i	0.168220	−	0.141154i	0.723011	+	0.690836i	$0.242757\pi$
$978$		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	0.760705	−	0.649097i	$-0.224853\pi$
$983$	7814.81	+	6557.41i	0.253564	+	0.212766i	−0.507141	+	0.861863i	$0.669298\pi$
$984$		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	−0.454385	−	0.890805i	$-0.650141\pi$
$991$	16979.4	−	29409.2i	0.544268	−	0.942699i	0.998653	−	0.0518937i	$-0.0165257\pi$
$992$		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	−0.765422	−	0.643528i	$-0.777470\pi$
$997$	5475.70	−	31054.3i	0.173939	−	0.986457i	0.939361	−	0.342929i	$-0.111419\pi$
$998$		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.25.5	yes	54
3.2	odd	2		324.4.i.a.73.4		54
27.13	even	9	inner	108.4.i.a.13.5	✓	54
27.14	odd	18		324.4.i.a.253.4		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.13.5	✓	54	27.13	even	9	inner
108.4.i.a.25.5	yes	54	1.1	even	1	trivial
324.4.i.a.73.4		54	3.2	odd	2
324.4.i.a.253.4		54	27.14	odd	18

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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