LMFDB - Embedded newform 108.3.k.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(5,108)]

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, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.k (of order $18$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	108.41
Dual form			108.3.k.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.78257 - 1.12129i) q^{3} +(-2.69546 + 3.21232i) q^{5} +(11.1367 + 4.05342i) q^{7} +(6.48544 + 6.24012i) q^{9} +O(q^{10})$	\(q+(-2.78257 - 1.12129i) q^{3} +(-2.69546 + 3.21232i) q^{5} +(11.1367 + 4.05342i) q^{7} +(6.48544 + 6.24012i) q^{9} +(7.66419 + 9.13382i) q^{11} +(-0.429892 + 2.43804i) q^{13} +(11.1022 - 5.91614i) q^{15} +(-11.9968 - 6.92637i) q^{17} +(1.88960 + 3.27289i) q^{19} +(-26.4436 - 23.7663i) q^{21} +(9.18883 + 25.2461i) q^{23} +(1.28769 + 7.30285i) q^{25} +(-11.0493 - 24.6356i) q^{27} +(-40.6205 + 7.16249i) q^{29} +(32.7920 - 11.9353i) q^{31} +(-11.0845 - 34.0093i) q^{33} +(-43.0393 + 24.8488i) q^{35} +(33.5308 - 58.0771i) q^{37} +(3.92995 - 6.30200i) q^{39} +(5.01099 + 0.883573i) q^{41} +(-35.5382 + 29.8201i) q^{43} +(-37.5265 + 4.01333i) q^{45} +(31.9088 - 87.6686i) q^{47} +(70.0593 + 58.7867i) q^{49} +(25.6156 + 32.7250i) q^{51} +51.4760i q^{53} -49.9992 q^{55} +(-1.58812 - 11.2258i) q^{57} +(9.45130 - 11.2636i) q^{59} +(-48.1278 - 17.5171i) q^{61} +(46.9324 + 95.7824i) q^{63} +(-6.67301 - 7.95258i) q^{65} +(2.35762 - 13.3707i) q^{67} +(2.73949 - 80.5524i) q^{69} +(-27.9939 - 16.1623i) q^{71} +(-20.3025 - 35.1650i) q^{73} +(4.60549 - 21.7646i) q^{75} +(48.3304 + 132.787i) q^{77} +(12.9014 + 73.1676i) q^{79} +(3.12181 + 80.9398i) q^{81} +(150.972 - 26.6204i) q^{83} +(54.5866 - 19.8679i) q^{85} +(121.061 + 25.6170i) q^{87} +(-18.0718 + 10.4337i) q^{89} +(-14.6700 + 25.4091i) q^{91} +(-104.629 - 3.55830i) q^{93} +(-15.6069 - 2.75192i) q^{95} +(-36.5526 + 30.6713i) q^{97} +(-7.29054 + 107.062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q - 9 * q^5 + 6 * q^9	$ 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) $ 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$

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
$3$	−2.78257	−	1.12129i	−0.927525	−	0.373762i
$3$	−2.78257	−	1.12129i	−0.927525	−	0.373762i
$4$		0			0
$5$	−2.69546	+	3.21232i	−0.539091	+	0.642464i	−0.964984	−	0.262310i	$-0.915516\pi$
$5$	−2.69546	+	3.21232i	−0.539091	+	0.642464i	0.425892	+	0.904774i	$0.359960\pi$
$6$		0			0
$7$	11.1367	+	4.05342i	1.59095	+	0.579060i	0.977549	−	0.210708i	$-0.0675769\pi$
$7$	11.1367	+	4.05342i	1.59095	+	0.579060i	0.613406	+	0.789768i	$0.289799\pi$
$8$		0			0
$9$	6.48544	+	6.24012i	0.720604	+	0.693347i
$10$		0			0
$11$	7.66419	+	9.13382i	0.696744	+	0.830347i	0.992154	−	0.125023i	$-0.0399006\pi$
$11$	7.66419	+	9.13382i	0.696744	+	0.830347i	−0.295410	+	0.955371i	$0.595456\pi$
$12$		0			0
$13$	−0.429892	+	2.43804i	−0.0330686	+	0.187542i	−0.996868	−	0.0790884i	$-0.974799\pi$
$13$	−0.429892	+	2.43804i	−0.0330686	+	0.187542i	0.963799	+	0.266630i	$0.0859102\pi$
$14$		0			0
$15$	11.1022	−	5.91614i	0.740149	−	0.394410i
$16$		0			0
$17$	−11.9968	−	6.92637i	−0.705695	−	0.407433i	0.103770	−	0.994601i	$-0.466910\pi$
$17$	−11.9968	−	6.92637i	−0.705695	−	0.407433i	−0.809465	+	0.587168i	$0.800243\pi$
$18$		0			0
$19$	1.88960	+	3.27289i	0.0994528	+	0.172257i	0.911458	−	0.411392i	$-0.134957\pi$
$19$	1.88960	+	3.27289i	0.0994528	+	0.172257i	−0.812005	+	0.583650i	$0.801624\pi$
$20$		0			0
$21$	−26.4436	−	23.7663i	−1.25922	−	1.13173i
$22$		0			0
$23$	9.18883	+	25.2461i	0.399514	+	1.09766i	0.962522	+	0.271204i	$0.0874219\pi$
$23$	9.18883	+	25.2461i	0.399514	+	1.09766i	−0.563008	+	0.826452i	$0.690356\pi$
$24$		0			0
$25$	1.28769	+	7.30285i	0.0515076	+	0.292114i
$26$		0			0
$27$	−11.0493	−	24.6356i	−0.409232	−	0.912431i
$28$		0			0
$29$	−40.6205	+	7.16249i	−1.40071	+	0.246982i	−0.822434	−	0.568861i	$-0.807384\pi$
$29$	−40.6205	+	7.16249i	−1.40071	+	0.246982i	−0.578273	+	0.815843i	$0.696273\pi$
$30$		0			0
$31$	32.7920	−	11.9353i	1.05781	−	0.385010i	0.246203	−	0.969218i	$-0.420817\pi$
$31$	32.7920	−	11.9353i	1.05781	−	0.385010i	0.811604	+	0.584208i	$0.198595\pi$
$32$		0			0
$33$	−11.0845	−	34.0093i	−0.335895	−	1.03058i
$34$		0			0
$35$	−43.0393	+	24.8488i	−1.22970	+	0.709965i
$36$		0			0
$37$	33.5308	−	58.0771i	0.906238	−	1.56965i	0.0869922	−	0.996209i	$-0.472274\pi$
$37$	33.5308	−	58.0771i	0.906238	−	1.56965i	0.819246	−	0.573442i	$-0.194392\pi$
$38$		0			0
$39$	3.92995	−	6.30200i	0.100768	−	0.161590i
$40$		0			0
$41$	5.01099	+	0.883573i	0.122219	+	0.0215506i	0.234423	−	0.972135i	$-0.424680\pi$
$41$	5.01099	+	0.883573i	0.122219	+	0.0215506i	−0.112204	+	0.993685i	$0.535791\pi$
$42$		0			0
$43$	−35.5382	+	29.8201i	−0.826470	+	0.693490i	−0.954478	−	0.298283i	$-0.903586\pi$
$43$	−35.5382	+	29.8201i	−0.826470	+	0.693490i	0.128008	+	0.991773i	$0.459142\pi$
$44$		0			0
$45$	−37.5265	+	4.01333i	−0.833922	+	0.0891851i
$46$		0			0
$47$	31.9088	−	87.6686i	0.678910	−	1.86529i	0.224579	−	0.974456i	$-0.427899\pi$
$47$	31.9088	−	87.6686i	0.678910	−	1.86529i	0.454331	−	0.890833i	$-0.349878\pi$
$48$		0			0
$49$	70.0593	+	58.7867i	1.42978	+	1.19973i
$50$		0			0
$51$	25.6156	+	32.7250i	0.502267	+	0.641667i
$52$		0			0
$53$			51.4760i			0.971245i	0.874169	+	0.485622i	$0.161407\pi$
$53$			51.4760i			0.971245i	−0.874169	+	0.485622i	$0.838593\pi$
$54$		0			0
$55$	−49.9992			−0.909077
$56$		0			0
$57$	−1.58812	−	11.2258i	−0.0278617	−	0.196945i
$58$		0			0
$59$	9.45130	−	11.2636i	0.160192	−	0.190909i	−0.679978	−	0.733232i	$-0.738011\pi$
$59$	9.45130	−	11.2636i	0.160192	−	0.190909i	0.840170	+	0.542323i	$0.182455\pi$
$60$		0			0
$61$	−48.1278	−	17.5171i	−0.788980	−	0.287165i	−0.0840678	−	0.996460i	$-0.526791\pi$
$61$	−48.1278	−	17.5171i	−0.788980	−	0.287165i	−0.704912	+	0.709295i	$0.749013\pi$
$62$		0			0
$63$	46.9324	+	95.7824i	0.744959	+	1.52036i
$64$		0			0
$65$	−6.67301	−	7.95258i	−0.102662	−	0.122347i
$66$		0			0
$67$	2.35762	−	13.3707i	0.0351884	−	0.199563i	−0.962146	−	0.272536i	$-0.912138\pi$
$67$	2.35762	−	13.3707i	0.0351884	−	0.199563i	0.997334	+	0.0729728i	$0.0232486\pi$
$68$		0			0
$69$	2.73949	−	80.5524i	0.0397027	−	1.16743i
$70$		0			0
$71$	−27.9939	−	16.1623i	−0.394281	−	0.227638i	0.289733	−	0.957108i	$-0.406434\pi$
$71$	−27.9939	−	16.1623i	−0.394281	−	0.227638i	−0.684013	+	0.729470i	$0.739767\pi$
$72$		0			0
$73$	−20.3025	−	35.1650i	−0.278117	−	0.481713i	0.692800	−	0.721130i	$-0.256377\pi$
$73$	−20.3025	−	35.1650i	−0.278117	−	0.481713i	−0.970917	+	0.239417i	$0.923044\pi$
$74$		0			0
$75$	4.60549	−	21.7646i	0.0614065	−	0.290195i
$76$		0			0
$77$	48.3304	+	132.787i	0.627667	+	1.72450i
$78$		0			0
$79$	12.9014	+	73.1676i	0.163309	+	0.926172i	0.950791	+	0.309834i	$0.100273\pi$
$79$	12.9014	+	73.1676i	0.163309	+	0.926172i	−0.787481	+	0.616338i	$0.788615\pi$
$80$		0			0
$81$	3.12181	+	80.9398i	0.0385408	+	0.999257i
$82$		0			0
$83$	150.972	−	26.6204i	1.81894	−	0.320728i	0.842857	−	0.538138i	$-0.180872\pi$
$83$	150.972	−	26.6204i	1.81894	−	0.320728i	0.976080	+	0.217411i	$0.0697611\pi$
$84$		0			0
$85$	54.5866	−	19.8679i	0.642196	−	0.233740i
$86$		0			0
$87$	121.061	+	25.6170i	1.39150	+	0.294449i
$88$		0			0
$89$	−18.0718	+	10.4337i	−0.203054	+	0.117233i	−0.598079	−	0.801437i	$-0.704069\pi$
$89$	−18.0718	+	10.4337i	−0.203054	+	0.117233i	0.395025	+	0.918670i	$0.370736\pi$
$90$		0			0
$91$	−14.6700	+	25.4091i	−0.161209	+	0.279221i
$92$		0			0
$93$	−104.629	−	3.55830i	−1.12504	−	0.0382613i
$94$		0			0
$95$	−15.6069	−	2.75192i	−0.164283	−	0.0289676i
$96$		0			0
$97$	−36.5526	+	30.6713i	−0.376831	+	0.316199i	−0.811457	−	0.584412i	$-0.801325\pi$
$97$	−36.5526	+	30.6713i	−0.376831	+	0.316199i	0.434626	+	0.900611i	$0.356881\pi$
$98$		0			0
$99$	−7.29054	+	107.062i	−0.0736418	+	1.08144i
$100$		0			0
$101$	16.2462	−	44.6361i	0.160854	−	0.441942i	−0.832915	−	0.553400i	$-0.813330\pi$
$101$	16.2462	−	44.6361i	0.160854	−	0.441942i	0.993769	+	0.111458i	$0.0355522\pi$
$102$		0			0
$103$	−80.7592	−	67.7650i	−0.784070	−	0.657912i	0.160200	−	0.987085i	$-0.448786\pi$
$103$	−80.7592	−	67.7650i	−0.784070	−	0.657912i	−0.944270	+	0.329172i	$0.893230\pi$
$104$		0			0
$105$	147.623	−	20.8842i	1.40593	−	0.198897i
$106$		0			0
$107$		−	189.677i		−	1.77268i	−0.463031	−	0.886342i	$-0.653238\pi$
$107$		−	189.677i		−	1.77268i	0.463031	−	0.886342i	$-0.346762\pi$
$108$		0			0
$109$	−86.7332			−0.795718			−0.397859	−	0.917447i	$-0.630247\pi$
$109$	−86.7332			−0.795718			−0.397859	+	0.917447i	$0.630247\pi$
$110$		0			0
$111$	−158.423	+	124.006i	−1.42723	+	1.11717i
$112$		0			0
$113$	99.7785	−	118.911i	0.882996	−	1.05231i	−0.115263	−	0.993335i	$-0.536771\pi$
$113$	99.7785	−	118.911i	0.882996	−	1.05231i	0.998259	−	0.0589785i	$-0.0187844\pi$
$114$		0			0
$115$	−105.867	−	38.5323i	−0.920579	−	0.335063i
$116$		0			0
$117$	−18.0017	+	13.1292i	−0.153861	+	0.112215i
$118$		0			0
$119$	−105.529	−	125.765i	−0.886801	−	1.05685i
$120$		0			0
$121$	−3.67551	+	20.8449i	−0.0303761	+	0.172271i
$122$		0			0
$123$	−12.9527	−	8.07736i	−0.105307	−	0.0656696i
$124$		0			0
$125$	−117.719	−	67.9654i	−0.941756	−	0.543723i
$126$		0			0
$127$	−100.294	−	173.715i	−0.789720	−	1.36784i	−0.926138	−	0.377184i	$-0.876892\pi$
$127$	−100.294	−	173.715i	−0.789720	−	1.36784i	0.136418	−	0.990651i	$-0.456441\pi$
$128$		0			0
$129$	132.324	−	43.1281i	1.02577	−	0.334327i
$130$		0			0
$131$	36.8927	+	101.362i	0.281624	+	0.773755i	0.997169	+	0.0751889i	$0.0239560\pi$
$131$	36.8927	+	101.362i	0.281624	+	0.773755i	−0.715546	+	0.698566i	$0.753822\pi$
$132$		0			0
$133$	7.77752	+	44.1085i	0.0584776	+	0.331643i
$134$		0			0
$135$	108.920	+	30.9105i	0.806817	+	0.228967i
$136$		0			0
$137$	85.3702	−	15.0531i	0.623140	−	0.109876i	0.146842	−	0.989160i	$-0.453089\pi$
$137$	85.3702	−	15.0531i	0.623140	−	0.109876i	0.476299	+	0.879284i	$0.341978\pi$
$138$		0			0
$139$	−57.5515	+	20.9470i	−0.414040	+	0.150698i	−0.540637	−	0.841256i	$-0.681817\pi$
$139$	−57.5515	+	20.9470i	−0.414040	+	0.150698i	0.126597	+	0.991954i	$0.459594\pi$
$140$		0			0
$141$	−187.090	+	208.165i	−1.32688	+	1.47635i
$142$		0			0
$143$	−25.5634	+	14.7590i	−0.178765	+	0.103210i
$144$		0			0
$145$	86.4826	−	149.792i	0.596432	−	1.03305i
$146$		0			0
$147$	−129.028	−	242.135i	−0.877745	−	1.64718i
$148$		0			0
$149$	0.691518	+	0.121933i	0.00464106	+	0.000818344i	0.175968	−	0.984396i	$-0.443694\pi$
$149$	0.691518	+	0.121933i	0.00464106	+	0.000818344i	−0.171327	+	0.985214i	$0.554806\pi$
$150$		0			0
$151$	−96.5772	+	81.0379i	−0.639584	+	0.536675i	−0.903890	−	0.427764i	$-0.859301\pi$
$151$	−96.5772	+	81.0379i	−0.639584	+	0.536675i	0.264306	+	0.964439i	$0.414857\pi$
$152$		0			0
$153$	−34.5833	−	119.782i	−0.226034	−	0.782890i
$154$		0			0
$155$	−50.0494	+	137.510i	−0.322899	+	0.887158i
$156$		0			0
$157$	158.053	+	132.622i	1.00671	+	0.844729i	0.987900	−	0.155095i	$-0.0495682\pi$
$157$	158.053	+	132.622i	1.00671	+	0.844729i	0.0188086	+	0.999823i	$0.494013\pi$
$158$		0			0
$159$	57.7193	−	143.236i	0.363014	−	0.900853i
$160$		0			0
$161$			318.404i			1.97766i
$162$		0			0
$163$	105.377			0.646484			0.323242	−	0.946316i	$-0.395227\pi$
$163$	105.377			0.646484			0.323242	+	0.946316i	$0.395227\pi$
$164$		0			0
$165$	139.127	+	56.0634i	0.843191	+	0.339778i
$166$		0			0
$167$	134.126	−	159.846i	0.803152	−	0.957159i	−0.196576	−	0.980489i	$-0.562982\pi$
$167$	134.126	−	159.846i	0.803152	−	0.957159i	0.999728	+	0.0233298i	$0.00742678\pi$
$168$		0			0
$169$	153.049	+	55.7052i	0.905614	+	0.329617i
$170$		0			0
$171$	−8.16832	+	33.0175i	−0.0477679	+	0.193085i
$172$		0			0
$173$	−85.3497	−	101.716i	−0.493351	−	0.587953i	0.460715	−	0.887548i	$-0.347593\pi$
$173$	−85.3497	−	101.716i	−0.493351	−	0.587953i	−0.954066	+	0.299595i	$0.903148\pi$
$174$		0			0
$175$	−15.2609	+	86.5491i	−0.0872054	+	0.494566i
$176$		0			0
$177$	−38.9287	+	20.7443i	−0.219936	+	0.117199i
$178$		0			0
$179$	123.118	+	71.0820i	0.687808	+	0.397106i	0.802790	−	0.596261i	$-0.203348\pi$
$179$	123.118	+	71.0820i	0.687808	+	0.397106i	−0.114982	+	0.993368i	$0.536681\pi$
$180$		0			0
$181$	−1.37020	−	2.37326i	−0.00757019	−	0.0131119i	0.862215	−	0.506542i	$-0.169076\pi$
$181$	−1.37020	−	2.37326i	−0.00757019	−	0.0131119i	−0.869786	+	0.493430i	$0.835743\pi$
$182$		0			0
$183$	114.277	+	102.708i	0.624467	+	0.561243i
$184$		0			0
$185$	96.1813	+	264.256i	0.519899	+	1.42841i
$186$		0			0
$187$	−28.6817	−	162.662i	−0.153378	−	0.869849i
$188$		0			0
$189$	−23.1935	−	319.146i	−0.122717	−	1.68861i
$190$		0			0
$191$	−37.1032	+	6.54229i	−0.194258	+	0.0342528i	−0.269930	−	0.962880i	$-0.587001\pi$
$191$	−37.1032	+	6.54229i	−0.194258	+	0.0342528i	0.0756728	+	0.997133i	$0.475890\pi$
$192$		0			0
$193$	116.274	−	42.3202i	0.602455	−	0.219276i	−0.0227435	−	0.999741i	$-0.507240\pi$
$193$	116.274	−	42.3202i	0.602455	−	0.219276i	0.625199	+	0.780466i	$0.285018\pi$
$194$		0			0
$195$	9.65103	+	29.6110i	0.0494925	+	0.151851i
$196$		0			0
$197$	−50.1629	+	28.9616i	−0.254634	+	0.147013i	−0.621884	−	0.783109i	$-0.713633\pi$
$197$	−50.1629	+	28.9616i	−0.254634	+	0.147013i	0.367250	+	0.930122i	$0.380299\pi$
$198$		0			0
$199$	−155.640	+	269.577i	−0.782112	+	1.35466i	0.148597	+	0.988898i	$0.452524\pi$
$199$	−155.640	+	269.577i	−0.782112	+	1.35466i	−0.930709	+	0.365761i	$0.880809\pi$
$200$		0			0
$201$	−21.5527	+	34.5615i	−0.107227	+	0.171948i
$202$		0			0
$203$	−481.410	−	84.8856i	−2.37148	−	0.418156i
$204$		0			0
$205$	−16.3452	+	13.7153i	−0.0797328	+	0.0669038i
$206$		0			0
$207$	−97.9451	+	221.071i	−0.473165	+	1.06798i
$208$		0			0
$209$	−15.4117	+	42.3433i	−0.0737402	+	0.202600i
$210$		0			0
$211$	−26.9821	−	22.6407i	−0.127877	−	0.107302i	0.576606	−	0.817022i	$-0.304377\pi$
$211$	−26.9821	−	22.6407i	−0.127877	−	0.107302i	−0.704483	+	0.709720i	$0.748821\pi$
$212$		0			0
$213$	59.7726	+	76.3620i	0.280623	+	0.358507i
$214$		0			0
$215$		−	194.539i		−	0.904832i
$216$		0			0
$217$	413.573			1.90587
$218$		0			0
$219$	17.0633	+	120.614i	0.0779146	+	0.550750i
$220$		0			0
$221$	22.0441	−	26.2711i	0.0997471	−	0.118874i
$222$		0			0
$223$	218.300	+	79.4546i	0.978923	+	0.356299i	0.781421	−	0.624004i	$-0.214495\pi$
$223$	218.300	+	79.4546i	0.978923	+	0.356299i	0.197502	+	0.980303i	$0.436717\pi$
$224$		0			0
$225$	−37.2194	+	55.3975i	−0.165420	+	0.246211i
$226$		0			0
$227$	272.310	+	324.527i	1.19960	+	1.42963i	0.875232	+	0.483703i	$0.160708\pi$
$227$	272.310	+	324.527i	1.19960	+	1.42963i	0.324372	+	0.945930i	$0.394847\pi$
$228$		0			0
$229$	46.3777	−	263.021i	0.202523	−	1.14856i	−0.698768	−	0.715349i	$-0.746268\pi$
$229$	46.3777	−	263.021i	0.202523	−	1.14856i	0.901291	−	0.433215i	$-0.142621\pi$
$230$		0			0
$231$	14.4088	−	423.681i	0.0623760	−	1.83412i
$232$		0			0
$233$	62.0180	+	35.8061i	0.266172	+	0.153674i	0.627147	−	0.778901i	$-0.284223\pi$
$233$	62.0180	+	35.8061i	0.266172	+	0.153674i	−0.360975	+	0.932576i	$0.617556\pi$
$234$		0			0
$235$	195.611	+	338.808i	0.832387	+	1.44174i
$236$		0			0
$237$	46.1426	−	218.060i	0.194695	−	0.920086i
$238$		0			0
$239$	34.3802	+	94.4587i	0.143850	+	0.395225i	0.990604	−	0.136760i	$-0.0436688\pi$
$239$	34.3802	+	94.4587i	0.143850	+	0.395225i	−0.846754	+	0.531984i	$0.821447\pi$
$240$		0			0
$241$	−5.20365	−	29.5114i	−0.0215919	−	0.122454i	0.972107	−	0.234539i	$-0.0753581\pi$
$241$	−5.20365	−	29.5114i	−0.0215919	−	0.122454i	−0.993699	+	0.112085i	$0.964247\pi$
$242$		0			0
$243$	82.0700	−	228.721i	0.337737	−	0.941241i
$244$		0			0
$245$	−377.684	+	66.5958i	−1.54157	+	0.271820i
$246$		0			0
$247$	−8.79176	+	3.19994i	−0.0355942	+	0.0129552i
$248$		0			0
$249$	−449.939	−	95.2092i	−1.80698	−	0.382366i
$250$		0			0
$251$	138.355	−	79.8791i	0.551214	−	0.318243i	−0.198398	−	0.980122i	$-0.563574\pi$
$251$	138.355	−	79.8791i	0.551214	−	0.318243i	0.749611	+	0.661878i	$0.230240\pi$
$252$		0			0
$253$	−160.168	+	277.420i	−0.633077	+	1.09652i
$254$		0			0
$255$	−174.169	−	5.92327i	−0.683015	−	0.0232285i
$256$		0			0
$257$	−438.482	−	77.3162i	−1.70616	−	0.300841i	−0.766318	−	0.642462i	$-0.777913\pi$
$257$	−438.482	−	77.3162i	−1.70616	−	0.300841i	−0.939838	+	0.341621i	$0.889024\pi$
$258$		0			0
$259$	608.833	−	510.872i	2.35071	−	1.97248i
$260$		0			0
$261$	−308.137	−	207.025i	−1.18060	−	0.793199i
$262$		0			0
$263$	−33.6999	+	92.5896i	−0.128136	+	0.352052i	−0.987127	−	0.159940i	$-0.948870\pi$
$263$	−33.6999	+	92.5896i	−0.128136	+	0.352052i	0.858990	+	0.511992i	$0.171092\pi$
$264$		0			0
$265$	−165.357	−	138.751i	−0.623990	−	0.523590i
$266$		0			0
$267$	61.9853	−	8.76905i	0.232155	−	0.0328429i
$268$		0			0
$269$			46.7784i			0.173898i	0.996213	+	0.0869488i	$0.0277116\pi$
$269$			46.7784i			0.173898i	−0.996213	+	0.0869488i	$0.972288\pi$
$270$		0			0
$271$	−262.335			−0.968026			−0.484013	−	0.875061i	$-0.660821\pi$
$271$	−262.335			−0.968026			−0.484013	+	0.875061i	$0.660821\pi$
$272$		0			0
$273$	69.3112	−	54.2536i	0.253887	−	0.198731i
$274$		0			0
$275$	−56.8338	+	67.7319i	−0.206669	+	0.246298i
$276$		0			0
$277$	−321.656	−	117.073i	−1.16121	−	0.422647i	−0.311682	−	0.950186i	$-0.600892\pi$
$277$	−321.656	−	117.073i	−1.16121	−	0.422647i	−0.849531	+	0.527539i	$0.823115\pi$
$278$		0			0
$279$	287.148	+	127.220i	1.02921	+	0.455987i
$280$		0			0
$281$	164.193	+	195.677i	0.584316	+	0.696361i	0.974503	−	0.224375i	$-0.0720341\pi$
$281$	164.193	+	195.677i	0.584316	+	0.696361i	−0.390187	+	0.920736i	$0.627590\pi$
$282$		0			0
$283$	−8.52103	+	48.3252i	−0.0301097	+	0.170760i	−0.996154	−	0.0876142i	$-0.972076\pi$
$283$	−8.52103	+	48.3252i	−0.0301097	+	0.170760i	0.966045	+	0.258375i	$0.0831868\pi$
$284$		0			0
$285$	40.3417	+	25.1572i	0.141550	+	0.0882710i
$286$		0			0
$287$	52.2243	+	30.1517i	0.181966	+	0.105058i
$288$		0			0
$289$	−48.5508	−	84.0925i	−0.167996	−	0.290978i
$290$		0			0
$291$	136.102	−	44.3592i	0.467703	−	0.152437i
$292$		0			0
$293$	−105.146	−	288.885i	−0.358859	−	0.985956i	−0.979426	−	0.201803i	$-0.935320\pi$
$293$	−105.146	−	288.885i	−0.358859	−	0.985956i	0.620567	−	0.784153i	$-0.286902\pi$
$294$		0			0
$295$	10.7068	+	60.7212i	0.0362942	+	0.205835i
$296$		0			0
$297$	140.334	−	289.734i	0.472504	−	0.975535i
$298$		0			0
$299$	−65.5012	+	11.5496i	−0.219067	+	0.0386275i
$300$		0			0
$301$	−516.651	+	188.046i	−1.71645	+	0.624736i
$302$		0			0
$303$	−95.2562	+	105.987i	−0.314377	+	0.349791i
$304$		0			0
$305$	185.997	−	107.385i	0.609825	−	0.352083i
$306$		0			0
$307$	139.540	−	241.691i	0.454528	−	0.787266i	−0.544133	−	0.838999i	$-0.683141\pi$
$307$	139.540	−	241.691i	0.454528	−	0.787266i	0.998661	+	0.0517333i	$0.0164746\pi$
$308$		0			0
$309$	148.734	+	279.115i	0.481341	+	0.903285i
$310$		0			0
$311$	−296.031	−	52.1983i	−0.951869	−	0.167840i	−0.323911	−	0.946087i	$-0.604998\pi$
$311$	−296.031	−	52.1983i	−0.951869	−	0.167840i	−0.627958	+	0.778247i	$0.716109\pi$
$312$		0			0
$313$	−187.281	+	157.148i	−0.598342	+	0.502069i	−0.890912	−	0.454175i	$-0.849934\pi$
$313$	−187.281	+	157.148i	−0.598342	+	0.502069i	0.292570	+	0.956244i	$0.405490\pi$
$314$		0			0
$315$	−434.188	−	107.415i	−1.37838	−	0.341001i
$316$		0			0
$317$	107.090	−	294.227i	0.337823	−	0.928161i	−0.648188	−	0.761480i	$-0.724473\pi$
$317$	107.090	−	294.227i	0.337823	−	0.928161i	0.986011	−	0.166681i	$-0.0533049\pi$
$318$		0			0
$319$	−376.744	−	316.126i	−1.18102	−	0.990990i
$320$		0			0
$321$	−212.682	+	527.791i	−0.662562	+	1.64421i
$322$		0			0
$323$		−	52.3524i		−	0.162082i
$324$		0			0
$325$	−18.3582			−0.0564868
$326$		0			0
$327$	241.342	+	97.2527i	0.738048	+	0.297409i
$328$		0			0
$329$	710.715	−	846.997i	2.16023	−	2.57446i
$330$		0			0
$331$	404.100	+	147.080i	1.22085	+	0.444352i	0.870453	−	0.492251i	$-0.163826\pi$
$331$	404.100	+	147.080i	1.22085	+	0.444352i	0.350393	+	0.936603i	$0.386048\pi$
$332$		0			0
$333$	579.870	−	167.419i	1.74135	−	0.502760i
$334$		0			0
$335$	36.5963	+	43.6137i	0.109243	+	0.130190i
$336$		0			0
$337$	−85.6983	+	486.019i	−0.254297	+	1.44219i	0.543572	+	0.839363i	$0.317071\pi$
$337$	−85.6983	+	486.019i	−0.254297	+	1.44219i	−0.797870	+	0.602830i	$0.794040\pi$
$338$		0			0
$339$	−410.975	+	219.000i	−1.21232	+	0.646017i
$340$		0			0
$341$	360.339	+	208.042i	1.05671	+	0.610093i
$342$		0			0
$343$	251.581	+	435.751i	0.733473	+	1.27041i
$344$		0			0
$345$	251.376	+	225.926i	0.728626	+	0.654857i
$346$		0			0
$347$	177.696	+	488.217i	0.512093	+	1.40696i	0.879051	+	0.476727i	$0.158177\pi$
$347$	177.696	+	488.217i	0.512093	+	1.40696i	−0.366958	+	0.930238i	$0.619601\pi$
$348$		0			0
$349$	−42.2124	−	239.399i	−0.120952	−	0.685956i	−0.983630	−	0.180201i	$-0.942325\pi$
$349$	−42.2124	−	239.399i	−0.120952	−	0.685956i	0.862677	−	0.505755i	$-0.168786\pi$
$350$		0			0
$351$	64.8126	−	16.3479i	0.184651	−	0.0465751i
$352$		0			0
$353$	−631.952	+	111.430i	−1.79023	+	0.315666i	−0.967520	−	0.252793i	$-0.918651\pi$
$353$	−631.952	+	111.430i	−1.79023	+	0.315666i	−0.822711	+	0.568460i	$0.807540\pi$
$354$		0			0
$355$	127.375	−	46.3607i	0.358803	−	0.130593i
$356$		0			0
$357$	152.625	+	468.279i	0.427520	+	1.31171i
$358$		0			0
$359$	287.633	−	166.065i	0.801207	−	0.462577i	−0.0426860	−	0.999089i	$-0.513592\pi$
$359$	287.633	−	166.065i	0.801207	−	0.462577i	0.843893	+	0.536511i	$0.180258\pi$
$360$		0			0
$361$	173.359	−	300.266i	0.480218	−	0.831762i
$362$		0			0
$363$	33.6004	−	53.8810i	0.0925631	−	0.148433i
$364$		0			0
$365$	167.686	+	29.5676i	0.459414	+	0.0810070i
$366$		0			0
$367$	54.4378	−	45.6788i	0.148332	−	0.124465i	−0.565602	−	0.824678i	$-0.691356\pi$
$367$	54.4378	−	45.6788i	0.148332	−	0.124465i	0.713934	+	0.700213i	$0.246912\pi$
$368$		0			0
$369$	26.9849	+	36.9995i	0.0731297	+	0.100270i
$370$		0			0
$371$	−208.654	+	573.271i	−0.562409	+	1.54521i
$372$		0			0
$373$	251.356	+	210.913i	0.673878	+	0.565450i	0.914210	−	0.405240i	$-0.132812\pi$
$373$	251.356	+	210.913i	0.673878	+	0.565450i	−0.240333	+	0.970691i	$0.577257\pi$
$374$		0			0
$375$	251.355	+	321.116i	0.670279	+	0.856309i
$376$		0			0
$377$		−	102.114i		−	0.270858i
$378$		0			0
$379$	−77.9266			−0.205611			−0.102806	−	0.994701i	$-0.532782\pi$
$379$	−77.9266			−0.205611			−0.102806	+	0.994701i	$0.532782\pi$
$380$		0			0
$381$	84.2925	+	595.834i	0.221240	+	1.56387i
$382$		0			0
$383$	132.591	−	158.016i	0.346192	−	0.412575i	−0.564651	−	0.825330i	$-0.690989\pi$
$383$	132.591	−	158.016i	0.346192	−	0.412575i	0.910842	+	0.412755i	$0.135433\pi$
$384$		0			0
$385$	−556.826	−	202.668i	−1.44630	−	0.526410i
$386$		0			0
$387$	−416.562	−	28.3663i	−1.07639	−	0.0732979i
$388$		0			0
$389$	−6.12284	−	7.29692i	−0.0157400	−	0.0187582i	0.758117	−	0.652119i	$-0.226120\pi$
$389$	−6.12284	−	7.29692i	−0.0157400	−	0.0187582i	−0.773857	+	0.633360i	$0.781675\pi$
$390$		0			0
$391$	64.6270	−	366.518i	0.165287	−	0.937386i
$392$		0			0
$393$	10.9989	−	323.414i	0.0279871	−	0.822937i
$394$		0			0
$395$	−269.813	−	155.777i	−0.683071	−	0.394371i
$396$		0			0
$397$	−38.5291	−	66.7344i	−0.0970507	−	0.168097i	0.813412	−	0.581688i	$-0.197608\pi$
$397$	−38.5291	−	66.7344i	−0.0970507	−	0.168097i	−0.910463	+	0.413591i	$0.864274\pi$
$398$		0			0
$399$	27.8167	−	131.456i	0.0697160	−	0.329464i
$400$		0			0
$401$	−113.749	−	312.524i	−0.283664	−	0.779361i	−0.996918	−	0.0784548i	$-0.975001\pi$
$401$	−113.749	−	312.524i	−0.283664	−	0.779361i	0.713253	−	0.700906i	$-0.247221\pi$
$402$		0			0
$403$	15.0017	+	85.0791i	0.0372252	+	0.211114i
$404$		0			0
$405$	−268.419	−	208.142i	−0.662764	−	0.513930i
$406$		0			0
$407$	787.452	−	138.849i	1.93477	−	0.341152i
$408$		0			0
$409$	−395.056	+	143.789i	−0.965906	+	0.351561i	−0.776345	−	0.630308i	$-0.782929\pi$
$409$	−395.056	+	143.789i	−0.965906	+	0.351561i	−0.189561	+	0.981869i	$0.560706\pi$
$410$		0			0
$411$	−254.428	−	53.8381i	−0.619046	−	0.130993i
$412$		0			0
$413$	150.912	−	87.1293i	0.365405	−	0.210967i
$414$		0			0
$415$	−321.425	+	556.724i	−0.774517	+	1.34150i
$416$		0			0
$417$	183.629	+	6.24499i	0.440357	+	0.0149760i
$418$		0			0
$419$	−154.222	−	27.1934i	−0.368071	−	0.0649008i	−0.0134462	−	0.999910i	$-0.504280\pi$
$419$	−154.222	−	27.1934i	−0.368071	−	0.0649008i	−0.354624	+	0.935009i	$0.615391\pi$
$420$		0			0
$421$	19.9240	−	16.7182i	0.0473253	−	0.0397107i	−0.618818	−	0.785534i	$-0.712388\pi$
$421$	19.9240	−	16.7182i	0.0473253	−	0.0397107i	0.666144	+	0.745824i	$0.267944\pi$
$422$		0			0
$423$	754.005	−	369.455i	1.78252	−	0.873415i
$424$		0			0
$425$	35.1341	−	96.5300i	0.0826684	−	0.227129i
$426$		0			0
$427$	−464.980	−	390.164i	−1.08894	−	0.913733i
$428$		0			0
$429$	87.6811	−	12.4042i	0.204385	−	0.0289143i
$430$		0			0
$431$		−	209.889i		−	0.486982i	−0.969903	−	0.243491i	$-0.921707\pi$
$431$		−	209.889i		−	0.486982i	0.969903	−	0.243491i	$-0.0782927\pi$
$432$		0			0
$433$	−405.331			−0.936100			−0.468050	−	0.883702i	$-0.655043\pi$
$433$	−405.331			−0.936100			−0.468050	+	0.883702i	$0.655043\pi$
$434$		0			0
$435$	−408.604	+	319.836i	−0.939320	+	0.735256i
$436$		0			0
$437$	−65.2644	+	77.7791i	−0.149347	+	0.177984i
$438$		0			0
$439$	119.203	+	43.3863i	0.271533	+	0.0988299i	0.474198	−	0.880418i	$-0.342738\pi$
$439$	119.203	+	43.3863i	0.271533	+	0.0988299i	−0.202665	+	0.979248i	$0.564960\pi$
$440$		0			0
$441$	87.5290	+	818.436i	0.198478	+	1.85586i
$442$		0			0
$443$	−226.993	−	270.519i	−0.512399	−	0.610653i	0.446367	−	0.894850i	$-0.352718\pi$
$443$	−226.993	−	270.519i	−0.512399	−	0.610653i	−0.958766	+	0.284197i	$0.908273\pi$
$444$		0			0
$445$	15.1952	−	86.1760i	0.0341464	−	0.193654i
$446$		0			0
$447$	−1.78748	−	1.11468i	−0.00399883	−	0.00249369i
$448$		0			0
$449$	422.525	+	243.945i	0.941036	+	0.543307i	0.890285	−	0.455404i	$-0.150505\pi$
$449$	422.525	+	243.945i	0.941036	+	0.543307i	0.0507511	+	0.998711i	$0.483838\pi$
$450$		0			0
$451$	30.3348	+	52.5414i	0.0672611	+	0.116500i
$452$		0			0
$453$	359.600	−	117.203i	0.793819	−	0.258727i
$454$		0			0
$455$	−42.0800	−	115.614i	−0.0924836	−	0.254096i
$456$		0			0
$457$	−43.5060	−	246.735i	−0.0951992	−	0.539901i	−0.994686	−	0.102954i	$-0.967171\pi$
$457$	−43.5060	−	246.735i	−0.0951992	−	0.539901i	0.899487	−	0.436948i	$-0.143941\pi$
$458$		0			0
$459$	−38.0795	+	372.080i	−0.0829618	+	0.810633i
$460$		0			0
$461$	455.801	−	80.3699i	0.988721	−	0.174338i	0.344177	−	0.938905i	$-0.388158\pi$
$461$	455.801	−	80.3699i	0.988721	−	0.174338i	0.644545	+	0.764567i	$0.277047\pi$
$462$		0			0
$463$	−406.424	+	147.926i	−0.877806	+	0.319495i	−0.741324	−	0.671147i	$-0.765802\pi$
$463$	−406.424	+	147.926i	−0.877806	+	0.319495i	−0.136482	+	0.990643i	$0.543580\pi$
$464$		0			0
$465$	293.453	−	326.511i	0.631083	−	0.702174i
$466$		0			0
$467$	55.4592	−	32.0194i	0.118756	−	0.0685640i	−0.439445	−	0.898269i	$-0.644825\pi$
$467$	55.4592	−	32.0194i	0.118756	−	0.0685640i	0.558202	+	0.829705i	$0.311492\pi$
$468$		0			0
$469$	80.4534	−	139.349i	0.171542	−	0.297120i
$470$		0			0
$471$	−291.087	−	546.254i	−0.618020	−	1.15978i
$472$		0			0
$473$	−544.743	−	96.0528i	−1.15168	−	0.203071i
$474$		0			0
$475$	−21.4682	+	18.0140i	−0.0451962	+	0.0379241i
$476$		0			0
$477$	−321.216	+	333.844i	−0.673409	+	0.699883i
$478$		0			0
$479$	−59.8876	+	164.540i	−0.125026	+	0.343507i	−0.986376	−	0.164505i	$-0.947397\pi$
$479$	−59.8876	+	164.540i	−0.125026	+	0.343507i	0.861350	+	0.508012i	$0.169620\pi$
$480$		0			0
$481$	127.180	+	106.716i	0.264407	+	0.221864i
$482$		0			0
$483$	357.022	−	885.982i	0.739175	−	1.83433i
$484$		0			0
$485$		−	200.092i		−	0.412560i
$486$		0			0
$487$	−28.7536			−0.0590424			−0.0295212	−	0.999564i	$-0.509398\pi$
$487$	−28.7536			−0.0590424			−0.0295212	+	0.999564i	$0.509398\pi$
$488$		0			0
$489$	−293.219	−	118.158i	−0.599630	−	0.241631i
$490$		0			0
$491$	−496.568	+	591.786i	−1.01134	+	1.20527i	−0.0327461	+	0.999464i	$0.510425\pi$
$491$	−496.568	+	591.786i	−1.01134	+	1.20527i	−0.978593	+	0.205804i	$0.934019\pi$
$492$		0			0
$493$	536.927	+	195.425i	1.08910	+	0.396401i
$494$		0			0
$495$	−324.267	−	312.001i	−0.655085	−	0.630306i
$496$		0			0
$497$	−246.247	−	293.466i	−0.495467	−	0.590474i
$498$		0			0
$499$	101.012	−	572.868i	0.202429	−	1.14803i	−0.699006	−	0.715116i	$-0.746374\pi$
$499$	101.012	−	572.868i	0.202429	−	1.14803i	0.901435	−	0.432915i	$-0.142515\pi$
$500$		0			0
$501$	−552.449	+	294.388i	−1.10269	+	0.587601i
$502$		0			0
$503$	−491.674	−	283.868i	−0.977484	−	0.564351i	−0.0759745	−	0.997110i	$-0.524207\pi$
$503$	−491.674	−	283.868i	−0.977484	−	0.564351i	−0.901510	+	0.432759i	$0.857540\pi$
$504$		0			0
$505$	99.5946	+	172.503i	0.197217	+	0.341590i
$506$		0			0
$507$	−363.408	−	326.615i	−0.716782	−	0.644212i
$508$		0			0
$509$	175.613	+	482.494i	0.345016	+	0.947925i	0.983916	+	0.178634i	$0.0571679\pi$
$509$	175.613	+	482.494i	0.345016	+	0.947925i	−0.638899	+	0.769291i	$0.720610\pi$
$510$		0			0
$511$	−83.5643	−	473.917i	−0.163531	−	0.927430i
$512$		0			0
$513$	59.7510	−	82.7146i	0.116474	−	0.161237i
$514$		0			0
$515$	435.366	−	76.7667i	0.845370	−	0.149062i
$516$		0			0
$517$	1045.30	−	380.459i	2.02186	−	0.735898i
$518$		0			0
$519$	123.439	+	378.733i	0.237841	+	0.729737i
$520$		0			0
$521$	−616.698	+	356.051i	−1.18368	+	0.683398i	−0.956863	−	0.290539i	$-0.906165\pi$
$521$	−616.698	+	356.051i	−1.18368	+	0.683398i	−0.226817	+	0.973937i	$0.572832\pi$
$522$		0			0
$523$	101.608	−	175.990i	0.194279	−	0.336502i	−0.752385	−	0.658724i	$-0.771096\pi$
$523$	101.608	−	175.990i	0.194279	−	0.336502i	0.946664	+	0.322222i	$0.104430\pi$
$524$		0			0
$525$	139.511	−	223.717i	0.265735	−	0.426128i
$526$		0			0
$527$	−476.068	−	83.9437i	−0.903355	−	0.159286i
$528$		0			0
$529$	−147.693	+	123.929i	−0.279193	+	0.234271i
$530$		0			0
$531$	131.582	−	14.0723i	0.247801	−	0.0265015i
$532$		0			0
$533$	−4.30837	+	11.8372i	−0.00808325	+	0.0222085i
$534$		0			0
$535$	609.304	+	511.267i	1.13889	+	0.955639i
$536$		0			0
$537$	−262.881	−	335.841i	−0.489536	−	0.625402i
$538$		0			0
$539$			1090.46i			2.02312i
$540$		0			0
$541$	96.3158			0.178033			0.0890165	−	0.996030i	$-0.471628\pi$
$541$	96.3158			0.178033			0.0890165	+	0.996030i	$0.471628\pi$
$542$		0			0
$543$	1.15159	+	8.14017i	0.00212079	+	0.0149911i
$544$		0			0
$545$	233.786	−	278.615i	0.428965	−	0.511220i
$546$		0			0
$547$	242.175	+	88.1443i	0.442732	+	0.161141i	0.553761	−	0.832676i	$-0.313192\pi$
$547$	242.175	+	88.1443i	0.442732	+	0.161141i	−0.111028	+	0.993817i	$0.535414\pi$
$548$		0			0
$549$	−202.821	−	413.929i	−0.369437	−	0.753969i
$550$		0			0
$551$	−100.199	−	119.412i	−0.181849	−	0.216719i
$552$		0			0
$553$	−152.900	+	867.139i	−0.276492	+	1.56806i
$554$		0			0
$555$	28.6748	−	843.159i	0.0516662	−	1.51920i
$556$		0			0
$557$	−251.062	−	144.951i	−0.450740	−	0.260235i	0.257403	−	0.966304i	$-0.417133\pi$
$557$	−251.062	−	144.951i	−0.450740	−	0.260235i	−0.708143	+	0.706069i	$0.750467\pi$
$558$		0			0
$559$	−57.4250	−	99.4630i	−0.102728	−	0.177930i
$560$		0			0
$561$	−102.581	+	484.779i	−0.182855	+	0.864133i
$562$		0			0
$563$	20.9437	+	57.5424i	0.0372002	+	0.102207i	0.956902	−	0.290411i	$-0.0937919\pi$
$563$	20.9437	+	57.5424i	0.0372002	+	0.102207i	−0.919702	+	0.392617i	$0.871570\pi$
$564$		0			0
$565$	113.033	+	641.041i	0.200058	+	1.13459i
$566$		0			0
$567$	−293.317	+	914.055i	−0.517313	+	1.61209i
$568$		0			0
$569$	−482.543	+	85.0854i	−0.848055	+	0.149535i	−0.580755	−	0.814079i	$-0.697242\pi$
$569$	−482.543	+	85.0854i	−0.848055	+	0.149535i	−0.267300	+	0.963613i	$0.586131\pi$
$570$		0			0
$571$	717.627	−	261.195i	1.25679	−	0.457434i	0.374099	−	0.927389i	$-0.377952\pi$
$571$	717.627	−	261.195i	1.25679	−	0.457434i	0.882690	+	0.469955i	$0.155730\pi$
$572$		0			0
$573$	110.578	+	23.3989i	0.192981	+	0.0408357i
$574$		0			0
$575$	−172.536	+	99.6138i	−0.300063	+	0.173241i
$576$		0			0
$577$	130.453	−	225.951i	0.226088	−	0.391595i	−0.730557	−	0.682851i	$-0.760740\pi$
$577$	130.453	−	225.951i	0.226088	−	0.391595i	0.956645	+	0.291256i	$0.0940730\pi$
$578$		0			0
$579$	−370.994	−	12.6170i	−0.640749	−	0.0217911i
$580$		0			0
$581$	1789.23	+	315.489i	3.07957	+	0.543011i
$582$		0			0
$583$	−470.172	+	394.521i	−0.806470	+	0.676709i
$584$		0			0
$585$	6.34768	−	93.2164i	0.0108507	−	0.159344i
$586$		0			0
$587$	−96.4128	+	264.892i	−0.164247	+	0.451264i	−0.994325	−	0.106382i	$-0.966073\pi$
$587$	−96.4128	+	264.892i	−0.164247	+	0.451264i	0.830079	+	0.557646i	$0.188295\pi$
$588$		0			0
$589$	101.027	+	84.7716i	0.171523	+	0.143925i
$590$		0			0
$591$	172.056	−	24.3408i	0.291127	−	0.0411857i
$592$		0			0
$593$		−	248.742i		−	0.419463i	−0.977759	−	0.209731i	$-0.932741\pi$
$593$		−	248.742i		−	0.419463i	0.977759	−	0.209731i	$-0.0672590\pi$
$594$		0			0
$595$	688.447			1.15705
$596$		0			0
$597$	735.354	−	575.601i	1.23175	−	0.964155i
$598$		0			0
$599$	−204.393	+	243.586i	−0.341224	+	0.406655i	−0.909179	−	0.416404i	$-0.863290\pi$
$599$	−204.393	+	243.586i	−0.341224	+	0.406655i	0.567956	+	0.823059i	$0.307734\pi$
$600$		0			0
$601$	−775.786	−	282.363i	−1.29083	−	0.469822i	−0.396828	−	0.917893i	$-0.629889\pi$
$601$	−775.786	−	282.363i	−1.29083	−	0.469822i	−0.893998	+	0.448071i	$0.852111\pi$
$602$		0			0
$603$	98.7253	−	72.0033i	0.163724	−	0.119408i
$604$		0			0
$605$	−57.0532	−	67.9933i	−0.0943027	−	0.112386i
$606$		0			0
$607$	−70.3046	+	398.717i	−0.115823	+	0.656865i	0.870516	+	0.492139i	$0.163785\pi$
$607$	−70.3046	+	398.717i	−0.115823	+	0.656865i	−0.986339	+	0.164726i	$0.947326\pi$
$608$		0			0
$609$	1244.38	+	775.999i	2.04331	+	1.27422i
$610$		0			0
$611$	200.022	+	115.483i	0.327369	+	0.189006i
$612$		0			0
$613$	−309.729	−	536.467i	−0.505268	−	0.875150i	−0.999981	−	0.00609364i	$-0.998060\pi$
$613$	−309.729	−	536.467i	−0.505268	−	0.875150i	0.494713	−	0.869056i	$-0.335273\pi$
$614$		0			0
$615$	60.8606	−	19.8361i	0.0989603	−	0.0322538i
$616$		0			0
$617$	275.916	+	758.074i	0.447190	+	1.22865i	0.934672	+	0.355512i	$0.115694\pi$
$617$	275.916	+	758.074i	0.447190	+	1.22865i	−0.487481	+	0.873133i	$0.662084\pi$
$618$		0			0
$619$	155.014	+	879.129i	0.250427	+	1.42024i	0.807544	+	0.589807i	$0.200796\pi$
$619$	155.014	+	879.129i	0.250427	+	1.42024i	−0.557118	+	0.830434i	$0.688093\pi$
$620$		0			0
$621$	520.423	−	505.323i	0.838041	−	0.813725i
$622$		0			0
$623$	−243.552	+	42.9448i	−0.390934	+	0.0689322i
$624$		0			0
$625$	361.427	−	131.549i	0.578283	−	0.210478i
$626$		0			0
$627$	90.3632	−	100.543i	0.144120	−	0.160355i
$628$		0			0
$629$	−804.527	+	464.494i	−1.27906	+	0.738464i
$630$		0			0
$631$	415.342	−	719.393i	0.658228	−	1.14008i	−0.322846	−	0.946452i	$-0.604640\pi$
$631$	415.342	−	719.393i	0.658228	−	1.14008i	0.981074	−	0.193633i	$-0.0620271\pi$
$632$		0			0
$633$	49.6931	+	93.2541i	0.0785041	+	0.147321i
$634$		0			0
$635$	828.368	+	146.064i	1.30452	+	0.230021i
$636$		0			0
$637$	−173.442	+	145.535i	−0.272280	+	0.228470i
$638$		0			0
$639$	−80.6982	−	279.505i	−0.126288	−	0.437410i
$640$		0			0
$641$	243.303	−	668.469i	0.379567	−	1.04285i	−0.591969	−	0.805961i	$-0.701649\pi$
$641$	243.303	−	668.469i	0.379567	−	1.04285i	0.971536	−	0.236892i	$-0.0761287\pi$
$642$		0			0
$643$	693.699	+	582.082i	1.07885	+	0.905260i	0.995825	−	0.0912875i	$-0.0290982\pi$
$643$	693.699	+	582.082i	1.07885	+	0.905260i	0.0830225	+	0.996548i	$0.473543\pi$
$644$		0			0
$645$	−218.134	+	541.319i	−0.338192	+	0.839254i
$646$		0			0
$647$			175.592i			0.271394i	0.990750	+	0.135697i	$0.0433273\pi$
$647$			175.592i			0.271394i	−0.990750	+	0.135697i	$0.956673\pi$
$648$		0			0
$649$	175.316			0.270133
$650$		0			0
$651$	−1150.80	−	463.733i	−1.76774	−	0.712340i
$652$		0			0
$653$	−649.581	+	774.140i	−0.994764	+	1.18551i	−0.0121359	+	0.999926i	$0.503863\pi$
$653$	−649.581	+	774.140i	−0.994764	+	1.18551i	−0.982628	+	0.185587i	$0.940581\pi$
$654$		0			0
$655$	−425.050	−	154.705i	−0.648931	−	0.236191i
$656$		0			0
$657$	87.7632	−	354.751i	0.133582	−	0.539956i
$658$		0			0
$659$	−168.977	−	201.379i	−0.256414	−	0.305582i	0.622445	−	0.782663i	$-0.286139\pi$
$659$	−168.977	−	201.379i	−0.256414	−	0.305582i	−0.878859	+	0.477081i	$0.841695\pi$
$660$		0			0
$661$	86.6822	−	491.599i	0.131138	−	0.743721i	−0.846334	−	0.532653i	$-0.821195\pi$
$661$	86.6822	−	491.599i	0.131138	−	0.743721i	0.977472	−	0.211067i	$-0.0676939\pi$
$662$		0			0
$663$	−90.7968	+	48.3837i	−0.136948	+	0.0729769i
$664$		0			0
$665$	−162.655	−	93.9086i	−0.244593	−	0.141216i
$666$		0			0
$667$	−554.080	−	959.694i	−0.830704	−	1.43882i
$668$		0			0
$669$	−518.344	−	465.865i	−0.774804	−	0.696360i
$670$		0			0
$671$	−208.862	−	573.844i	−0.311270	−	0.855208i
$672$		0			0
$673$	155.048	+	879.320i	0.230383	+	1.30657i	0.852122	+	0.523343i	$0.175316\pi$
$673$	155.048	+	879.320i	0.230383	+	1.30657i	−0.621739	+	0.783225i	$0.713573\pi$
$674$		0			0
$675$	165.682	−	112.414i	0.245455	−	0.166539i
$676$		0			0
$677$	−308.774	+	54.4452i	−0.456092	+	0.0804213i	−0.396974	−	0.917830i	$-0.629940\pi$
$677$	−308.774	+	54.4452i	−0.456092	+	0.0804213i	−0.0591175	+	0.998251i	$0.518829\pi$
$678$		0			0
$679$	−531.398	+	193.413i	−0.782619	+	0.284850i
$680$		0			0
$681$	−393.836	−	1208.36i	−0.578320	−	1.77439i
$682$		0			0
$683$	−421.298	+	243.237i	−0.616835	+	0.356130i	−0.775636	−	0.631181i	$-0.782571\pi$
$683$	−421.298	+	243.237i	−0.616835	+	0.356130i	0.158801	+	0.987311i	$0.449237\pi$
$684$		0			0
$685$	−181.756	+	314.811i	−0.265338	+	0.459579i
$686$		0			0
$687$	−423.971	+	679.873i	−0.617134	+	0.989626i
$688$		0			0
$689$	−125.500	−	22.1291i	−0.182149	−	0.0321177i
$690$		0			0
$691$	473.285	−	397.134i	0.684928	−	0.574723i	−0.232513	−	0.972593i	$-0.574695\pi$
$691$	473.285	−	397.134i	0.684928	−	0.574723i	0.917442	+	0.397870i	$0.130251\pi$
$692$		0			0
$693$	−515.161	+	1162.77i	−0.743378	+	1.67787i
$694$		0			0
$695$	87.8391	−	241.336i	0.126387	−	0.347246i
$696$		0			0
$697$	−53.9960	−	45.3080i	−0.0774692	−	0.0650044i
$698$		0			0
$699$	−132.421	−	169.173i	−0.189443	−	0.242022i
$700$		0			0
$701$		−	297.109i		−	0.423836i	−0.977287	−	0.211918i	$-0.932029\pi$
$701$		−	297.109i		−	0.423836i	0.977287	−	0.211918i	$-0.0679709\pi$
$702$		0			0
$703$	253.440			0.360512
$704$		0			0
$705$	−164.401	−	1162.09i	−0.233193	−	1.64836i
$706$		0			0
$707$	361.858	−	431.246i	0.511822	−	0.609966i
$708$		0			0
$709$	827.896	+	301.330i	1.16770	+	0.425006i	0.851841	−	0.523801i	$-0.175486\pi$
$709$	827.896	+	301.330i	1.16770	+	0.425006i	0.315855	+	0.948807i	$0.397709\pi$
$710$		0			0
$711$	−372.903	+	555.030i	−0.524477	+	0.780634i
$712$		0			0
$713$	602.640	+	718.198i	0.845217	+	1.00729i
$714$		0			0
$715$	21.4943	−	121.900i	0.0300619	−	0.170490i
$716$		0			0
$717$	10.2498	−	301.388i	0.0142955	−	0.420346i
$718$		0			0
$719$	−1021.09	−	589.526i	−1.42015	−	0.819925i	−0.423840	−	0.905737i	$-0.639318\pi$
$719$	−1021.09	−	589.526i	−1.42015	−	0.819925i	−0.996311	+	0.0858124i	$0.972651\pi$
$720$		0			0
$721$	−624.709	−	1082.03i	−0.866448	−	1.50073i
$722$		0			0
$723$	−18.6111	+	87.9524i	−0.0257415	+	0.121649i
$724$		0			0
$725$	−104.613	−	287.422i	−0.144294	−	0.396445i
$726$		0			0
$727$	−111.710	−	633.537i	−0.153658	−	0.871441i	−0.960002	−	0.279993i	$-0.909668\pi$
$727$	−111.710	−	633.537i	−0.153658	−	0.871441i	0.806344	−	0.591447i	$-0.201443\pi$
$728$		0			0
$729$	−484.828	+	544.411i	−0.665059	+	0.746791i
$730$		0			0
$731$	632.890	−	111.596i	0.865787	−	0.152662i
$732$		0			0
$733$	−177.435	+	64.5811i	−0.242067	+	0.0881052i	−0.460205	−	0.887813i	$-0.652224\pi$
$733$	−177.435	+	64.5811i	−0.242067	+	0.0881052i	0.218138	+	0.975918i	$0.430002\pi$
$734$		0			0
$735$	1125.61	+	238.183i	1.53144	+	0.324059i
$736$		0			0
$737$	140.195	−	80.9418i	0.190224	−	0.109826i
$738$		0			0
$739$	−455.604	+	789.129i	−0.616514	+	1.06783i	0.373603	+	0.927589i	$0.378122\pi$
$739$	−455.604	+	789.129i	−0.616514	+	1.06783i	−0.990117	+	0.140244i	$0.955211\pi$
$740$		0			0
$741$	28.0518	+	0.954005i	0.0378566	+	0.00128746i
$742$		0			0
$743$	293.238	+	51.7058i	0.394668	+	0.0695906i	0.367460	−	0.930039i	$-0.380227\pi$
$743$	293.238	+	51.7058i	0.394668	+	0.0695906i	0.0272075	+	0.999630i	$0.491339\pi$
$744$		0			0
$745$	−2.25565	+	1.89271i	−0.00302771	+	0.00254055i
$746$		0			0
$747$	1145.23	+	769.437i	1.53311	+	1.03004i
$748$		0			0
$749$	768.841	−	2112.37i	1.02649	−	2.82026i
$750$		0			0
$751$	−4.07029	−	3.41538i	−0.00541983	−	0.00454777i	0.640074	−	0.768314i	$-0.278904\pi$
$751$	−4.07029	−	3.41538i	−0.00541983	−	0.00454777i	−0.645494	+	0.763766i	$0.723348\pi$
$752$		0			0
$753$	−474.549	+	67.1344i	−0.630212	+	0.0891560i
$754$		0			0
$755$		−	528.671i		−	0.700227i
$756$		0			0
$757$	−678.131			−0.895813			−0.447907	−	0.894080i	$-0.647830\pi$
$757$	−678.131			−0.895813			−0.447907	+	0.894080i	$0.647830\pi$
$758$		0			0
$759$	756.747	−	592.347i	0.997032	−	0.780430i
$760$		0			0
$761$	−587.824	+	700.542i	−0.772436	+	0.920554i	−0.998566	−	0.0535434i	$-0.982948\pi$
$761$	−587.824	+	700.542i	−0.772436	+	0.920554i	0.226129	+	0.974097i	$0.427393\pi$
$762$		0			0
$763$	−965.920	−	351.566i	−1.26595	−	0.460768i
$764$		0			0
$765$	477.996	+	211.775i	0.624832	+	0.276830i
$766$		0			0
$767$	23.3981	+	27.8848i	0.0305060	+	0.0363557i
$768$		0			0
$769$	61.7617	−	350.268i	0.0803143	−	0.455485i	−0.917955	−	0.396684i	$-0.870161\pi$
$769$	61.7617	−	350.268i	0.0803143	−	0.455485i	0.998270	−	0.0588015i	$-0.0187279\pi$
$770$		0			0
$771$	1133.42	+	706.801i	1.47006	+	0.916733i
$772$		0			0
$773$	−630.397	−	363.960i	−0.815520	−	0.470841i	0.0333493	−	0.999444i	$-0.489383\pi$
$773$	−630.397	−	363.960i	−0.815520	−	0.470841i	−0.848869	+	0.528603i	$0.822716\pi$
$774$		0			0
$775$	129.388	+	224.106i	0.166952	+	0.289169i
$776$		0			0
$777$	−2266.96	+	738.862i	−2.91757	+	0.950917i
$778$		0			0
$779$	6.57695	+	18.0700i	0.00844281	+	0.0231964i
$780$		0			0
$781$	−66.9271	−	379.562i	−0.0856941	−	0.485995i
$782$		0			0
$783$	625.279	+	921.571i	0.798568	+	1.17697i
$784$		0			0
$785$	−852.051	+	150.240i	−1.08542	+	0.191388i
$786$		0			0
$787$	−43.1913	+	15.7203i	−0.0548809	+	0.0199750i	−0.369315	−	0.929304i	$-0.620408\pi$
$787$	−43.1913	+	15.7203i	−0.0548809	+	0.0199750i	0.314434	+	0.949279i	$0.398185\pi$
$788$		0			0
$789$	197.592	−	219.850i	0.250433	−	0.278644i
$790$		0			0
$791$	1593.20	−	919.834i	2.01416	−	1.16288i
$792$		0			0
$793$	63.3971	−	109.807i	0.0799459	−	0.138470i
$794$		0			0
$795$	304.539	+	571.498i	0.383068	+	0.718866i
$796$		0			0
$797$	388.808	+	68.5573i	0.487839	+	0.0860192i	0.412157	−	0.911113i	$-0.364775\pi$
$797$	388.808	+	68.5573i	0.487839	+	0.0860192i	0.0756820	+	0.997132i	$0.475887\pi$
$798$		0			0
$799$	−990.029	+	830.733i	−1.23908	+	1.03972i
$800$		0			0
$801$	−182.311	−	45.1026i	−0.227604	−	0.0563079i
$802$		0			0
$803$	165.589	−	454.951i	0.206213	−	0.566564i
$804$		0			0
$805$	−1022.82	−	858.244i	−1.27058	−	1.06614i
$806$		0			0
$807$	52.4520	−	130.164i	0.0649963	−	0.161294i
$808$		0			0
$809$			333.349i			0.412050i	0.978547	+	0.206025i	$0.0660529\pi$
$809$			333.349i			0.412050i	−0.978547	+	0.206025i	$0.933947\pi$
$810$		0			0
$811$	−1156.01			−1.42541			−0.712705	−	0.701464i	$-0.752530\pi$
$811$	−1156.01			−1.42541			−0.712705	+	0.701464i	$0.752530\pi$
$812$		0			0
$813$	729.967	+	294.152i	0.897868	+	0.361811i
$814$		0			0
$815$	−284.039	+	338.504i	−0.348514	+	0.415343i
$816$		0			0
$817$	−164.751	−	59.9644i	−0.201654	−	0.0733959i
$818$		0			0
$819$	−253.697	+	73.2470i	−0.309765	+	0.0894347i
$820$		0			0
$821$	796.964	+	949.784i	0.970723	+	1.15686i	0.987598	+	0.157005i	$0.0501839\pi$
$821$	796.964	+	949.784i	0.970723	+	1.15686i	−0.0168748	+	0.999858i	$0.505372\pi$
$822$		0			0
$823$	8.27963	−	46.9561i	0.0100603	−	0.0570548i	−0.979364	−	0.202103i	$-0.935223\pi$
$823$	8.27963	−	46.9561i	0.0100603	−	0.0570548i	0.989425	+	0.145048i	$0.0463336\pi$
$824$		0			0
$825$	234.091	−	124.742i	0.283747	−	0.151203i
$826$		0			0
$827$	914.751	+	528.132i	1.10611	+	0.638612i	0.937819	−	0.347126i	$-0.112842\pi$
$827$	914.751	+	528.132i	1.10611	+	0.638612i	0.168289	+	0.985738i	$0.446176\pi$
$828$		0			0
$829$	644.247	+	1115.87i	0.777137	+	1.34604i	0.933585	+	0.358355i	$0.116662\pi$
$829$	644.247	+	1115.87i	0.777137	+	1.34604i	−0.156448	+	0.987686i	$0.550004\pi$
$830$		0			0
$831$	763.759	+	686.433i	0.919084	+	0.826032i
$832$		0			0
$833$	−433.310	−	1190.51i	−0.520180	−	1.42918i
$834$		0			0
$835$	151.943	+	861.713i	0.181968	+	1.03199i
$836$		0			0
$837$	−656.361	−	675.975i	−0.784183	−	0.807616i
$838$		0			0
$839$	938.482	−	165.480i	1.11857	−	0.197234i	0.416358	−	0.909201i	$-0.363306\pi$
$839$	938.482	−	165.480i	1.11857	−	0.197234i	0.702214	+	0.711966i	$0.252195\pi$
$840$		0			0
$841$	808.443	−	294.249i	0.961288	−	0.349880i
$842$		0			0
$843$	−237.468	−	728.594i	−0.281694	−	0.864287i
$844$		0			0
$845$	−591.479	+	341.491i	−0.699976	+	0.404131i
$846$		0			0
$847$	−125.426	+	217.244i	−0.148083	+	0.256487i
$848$		0			0
$849$	77.8967	−	124.914i	0.0917511	−	0.147131i
$850$		0			0
$851$	1774.33	+	312.862i	2.08499	+	0.367640i
$852$		0			0
$853$	−267.861	+	224.762i	−0.314022	+	0.263496i	−0.786152	−	0.618033i	$-0.787930\pi$
$853$	−267.861	+	224.762i	−0.314022	+	0.263496i	0.472130	+	0.881529i	$0.343485\pi$
$854$		0			0
$855$	−84.0454	−	115.236i	−0.0982987	−	0.134779i
$856$		0			0
$857$	−207.031	+	568.812i	−0.241576	+	0.663725i	0.758353	+	0.651844i	$0.226004\pi$
$857$	−207.031	+	568.812i	−0.241576	+	0.663725i	−0.999929	+	0.0118810i	$0.996218\pi$
$858$		0			0
$859$	292.005	+	245.021i	0.339936	+	0.285240i	0.796734	−	0.604330i	$-0.206559\pi$
$859$	292.005	+	245.021i	0.339936	+	0.285240i	−0.456798	+	0.889571i	$0.651004\pi$
$860$		0			0
$861$	−111.509	−	142.458i	−0.129511	−	0.165456i
$862$		0			0
$863$		−	634.987i		−	0.735791i	−0.929867	−	0.367895i	$-0.880078\pi$
$863$		−	634.987i		−	0.735791i	0.929867	−	0.367895i	$-0.119922\pi$
$864$		0			0
$865$	556.800			0.643700
$866$		0			0
$867$	40.8046	+	288.433i	0.0470641	+	0.332679i
$868$		0			0
$869$	−569.421	+	678.609i	−0.655260	+	0.780908i
$870$		0			0
$871$	31.5849	+	11.4960i	0.0362628	+	0.0131986i
$872$		0			0
$873$	−428.452	−	29.1760i	−0.490781	−	0.0334204i
$874$		0			0
$875$	−1035.51	−	1234.08i	−1.18344	−	1.41037i
$876$		0			0
$877$	−59.6958	+	338.552i	−0.0680682	+	0.386034i	0.931673	+	0.363297i	$0.118349\pi$
$877$	−59.6958	+	338.552i	−0.0680682	+	0.386034i	−0.999741	+	0.0227366i	$0.992762\pi$
$878$		0			0
$879$	−31.3473	+	921.743i	−0.0356625	+	1.04863i
$880$		0			0
$881$	960.802	+	554.720i	1.09058	+	0.629648i	0.933731	−	0.357975i	$-0.116533\pi$
$881$	960.802	+	554.720i	1.09058	+	0.629648i	0.156850	+	0.987622i	$0.449866\pi$
$882$		0			0
$883$	−444.061	−	769.135i	−0.502900	−	0.871048i	−0.999994	−	0.00335171i	$-0.998933\pi$
$883$	−444.061	−	769.135i	−0.502900	−	0.871048i	0.497095	−	0.867696i	$-0.334400\pi$
$884$		0			0
$885$	38.2934	−	180.967i	0.0432694	−	0.204482i
$886$		0			0
$887$	−103.989	−	285.707i	−0.117237	−	0.322105i	0.867170	−	0.498012i	$-0.165936\pi$
$887$	−103.989	−	285.707i	−0.117237	−	0.322105i	−0.984407	+	0.175907i	$0.943714\pi$
$888$		0			0
$889$	−412.807	−	2341.15i	−0.464350	−	2.63346i
$890$		0			0
$891$	−715.364	+	648.852i	−0.802877	+	0.728229i
$892$		0			0
$893$	347.224	−	61.2250i	0.388829	−	0.0685611i
$894$		0			0
$895$	−560.197	+	203.895i	−0.625918	+	0.227815i
$896$		0			0
$897$	195.212	+	41.3078i	0.217628	+	0.0460511i
$898$		0			0
$899$	−1246.54	+	719.691i	−1.38659	+	0.800546i
$900$		0			0
$901$	356.542	−	617.548i	0.395718	−	0.685403i
$902$		0			0
$903$	1648.47	+	56.0625i	1.82555	+	0.0620847i
$904$		0			0
$905$	11.3170	+	1.99549i	0.0125050	+	0.00220497i
$906$		0			0
$907$	−441.779	+	370.697i	−0.487077	+	0.408706i	−0.852977	−	0.521948i	$-0.825206\pi$
$907$	−441.779	+	370.697i	−0.487077	+	0.408706i	0.365900	+	0.930654i	$0.380761\pi$
$908$		0			0
$909$	383.899	−	188.106i	0.422331	−	0.206938i
$910$		0			0
$911$	−137.001	+	376.407i	−0.150385	+	0.413180i	−0.991895	−	0.127062i	$-0.959445\pi$
$911$	−137.001	+	376.407i	−0.150385	+	0.413180i	0.841509	+	0.540243i	$0.181667\pi$
$912$		0			0
$913$	1400.22	+	1174.93i	1.53365	+	1.28688i
$914$		0			0
$915$	−637.959	+	90.2520i	−0.697223	+	0.0986361i
$916$		0			0
$917$			1278.38i			1.39409i
$918$		0			0
$919$	356.293			0.387696			0.193848	−	0.981032i	$-0.437903\pi$
$919$	356.293			0.387696			0.193848	+	0.981032i	$0.437903\pi$
$920$		0			0
$921$	−659.285	+	516.058i	−0.715836	+	0.560323i
$922$		0			0
$923$	51.4387	−	61.3023i	0.0557299	−	0.0664163i
$924$		0			0
$925$	467.306	+	170.085i	0.505195	+	0.183876i
$926$		0			0
$927$	−100.897	−	943.432i	−0.108842	−	1.01773i
$928$		0			0
$929$	165.109	+	196.769i	0.177727	+	0.211807i	0.847552	−	0.530712i	$-0.178075\pi$
$929$	165.109	+	196.769i	0.177727	+	0.211807i	−0.669825	+	0.742519i	$0.733631\pi$
$930$		0			0
$931$	−60.0182	+	340.380i	−0.0644663	+	0.365607i
$932$		0			0
$933$	765.200	+	477.181i	0.820150	+	0.511448i
$934$		0			0
$935$	599.832	+	346.313i	0.641532	+	0.370388i
$936$		0			0
$937$	784.782	+	1359.28i	0.837547	+	1.45067i	0.891939	+	0.452155i	$0.149345\pi$
$937$	784.782	+	1359.28i	0.837547	+	1.45067i	−0.0543920	+	0.998520i	$0.517322\pi$
$938$		0			0
$939$	697.331	−	227.279i	0.742631	−	0.242044i
$940$		0			0
$941$	−448.091	−	1231.12i	−0.476186	−	1.30831i	−0.912707	−	0.408616i	$-0.866012\pi$
$941$	−448.091	−	1231.12i	−0.476186	−	1.30831i	0.436521	−	0.899694i	$-0.356211\pi$
$942$		0			0
$943$	23.7384	+	134.627i	0.0251732	+	0.142765i
$944$		0			0
$945$	1087.72	+	785.740i	1.15102	+	0.831471i
$946$		0			0
$947$	−445.411	+	78.5381i	−0.470339	+	0.0829335i	−0.403794	−	0.914850i	$-0.632309\pi$
$947$	−445.411	+	78.5381i	−0.470339	+	0.0829335i	−0.0665453	+	0.997783i	$0.521198\pi$
$948$		0			0
$949$	94.4617	−	34.3812i	0.0995381	−	0.0362289i
$950$		0			0
$951$	−627.898	+	698.630i	−0.660250	+	0.734627i
$952$		0			0
$953$	1446.87	−	835.352i	1.51823	−	0.876550i	0.518460	−	0.855102i	$-0.326506\pi$
$953$	1446.87	−	835.352i	1.51823	−	0.876550i	0.999770	−	0.0214481i	$-0.00682765\pi$
$954$		0			0
$955$	78.9941	−	136.822i	0.0827164	−	0.143269i
$956$		0			0
$957$	693.851	+	1302.08i	0.725027	+	1.36059i
$958$		0			0
$959$	1011.76	+	178.400i	1.05501	+	0.186027i
$960$		0			0
$961$	196.695	−	165.046i	0.204677	−	0.171744i
$962$		0			0
$963$	1183.61	−	1230.14i	1.22908	−	1.27740i
$964$		0			0
$965$	−177.465	+	487.581i	−0.183902	+	0.505266i
$966$		0			0
$967$	−920.878	−	772.708i	−0.952304	−	0.799078i	0.0273800	−	0.999625i	$-0.491284\pi$
$967$	−920.878	−	772.708i	−0.952304	−	0.799078i	−0.979684	+	0.200547i	$0.935728\pi$
$968$		0			0
$969$	−58.7019	+	145.674i	−0.0605799	+	0.150335i
$970$		0			0
$971$		−	482.574i		−	0.496987i	−0.968634	−	0.248493i	$-0.920065\pi$
$971$		−	482.574i		−	0.496987i	0.968634	−	0.248493i	$-0.0799354\pi$
$972$		0			0
$973$	−725.840			−0.745982
$974$		0			0
$975$	51.0831	+	20.5848i	0.0523929	+	0.0211126i
$976$		0			0
$977$	380.969	−	454.021i	0.389937	−	0.464709i	−0.534987	−	0.844860i	$-0.679683\pi$
$977$	380.969	−	454.021i	0.389937	−	0.464709i	0.924924	+	0.380151i	$0.124128\pi$
$978$		0			0
$979$	−233.805	−	85.0982i	−0.238821	−	0.0869236i
$980$		0			0
$981$	−562.503	−	541.226i	−0.573398	−	0.551708i
$982$		0			0
$983$	−1099.90	−	1310.81i	−1.11892	−	1.33348i	−0.936666	−	0.350224i	$-0.886105\pi$
$983$	−1099.90	−	1310.81i	−1.11892	−	1.33348i	−0.182253	−	0.983252i	$-0.558339\pi$
$984$		0			0
$985$	42.1781	−	239.204i	0.0428204	−	0.242847i
$986$		0			0
$987$	−2927.34	+	1559.92i	−2.96590	+	1.58046i
$988$		0			0
$989$	−1079.39	−	623.189i	−1.09140	−	0.630120i
$990$		0			0
$991$	−256.814	−	444.815i	−0.259146	−	0.448855i	0.706867	−	0.707346i	$-0.250108\pi$
$991$	−256.814	−	444.815i	−0.259146	−	0.448855i	−0.966014	+	0.258492i	$0.916775\pi$
$992$		0			0
$993$	−959.520	−	862.374i	−0.966284	−	0.868453i
$994$		0			0
$995$	−446.446	−	1226.60i	−0.448689	−	1.23276i
$996$		0			0
$997$	291.959	+	1655.78i	0.292838	+	1.66076i	0.675863	+	0.737027i	$0.263771\pi$
$997$	291.959	+	1655.78i	0.292838	+	1.66076i	−0.383026	+	0.923738i	$0.625118\pi$
$998$		0			0
$999$	−1801.26	−	184.344i	−1.80306	−	0.184529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.k.a.41.1	yes	36
3.2	odd	2		324.3.k.a.233.5		36
4.3	odd	2		432.3.bc.b.257.6		36
27.2	odd	18	inner	108.3.k.a.29.1	✓	36
27.5	odd	18		2916.3.c.b.1457.10		36
27.22	even	9		2916.3.c.b.1457.27		36
27.25	even	9		324.3.k.a.89.5		36
108.83	even	18		432.3.bc.b.353.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.29.1	✓	36	27.2	odd	18	inner
108.3.k.a.41.1	yes	36	1.1	even	1	trivial
324.3.k.a.89.5		36	27.25	even	9
324.3.k.a.233.5		36	3.2	odd	2
432.3.bc.b.257.6		36	4.3	odd	2
432.3.bc.b.353.6		36	108.83	even	18
2916.3.c.b.1457.10		36	27.5	odd	18
2916.3.c.b.1457.27		36	27.22	even	9

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.78257 - 1.12129i) q^{3} +(-2.69546 + 3.21232i) q^{5} +(11.1367 + 4.05342i) q^{7} +(6.48544 + 6.24012i) q^{9} +O(q^{10})\)	\(q+(-2.78257 - 1.12129i) q^{3} +(-2.69546 + 3.21232i) q^{5} +(11.1367 + 4.05342i) q^{7} +(6.48544 + 6.24012i) q^{9} +(7.66419 + 9.13382i) q^{11} +(-0.429892 + 2.43804i) q^{13} +(11.1022 - 5.91614i) q^{15} +(-11.9968 - 6.92637i) q^{17} +(1.88960 + 3.27289i) q^{19} +(-26.4436 - 23.7663i) q^{21} +(9.18883 + 25.2461i) q^{23} +(1.28769 + 7.30285i) q^{25} +(-11.0493 - 24.6356i) q^{27} +(-40.6205 + 7.16249i) q^{29} +(32.7920 - 11.9353i) q^{31} +(-11.0845 - 34.0093i) q^{33} +(-43.0393 + 24.8488i) q^{35} +(33.5308 - 58.0771i) q^{37} +(3.92995 - 6.30200i) q^{39} +(5.01099 + 0.883573i) q^{41} +(-35.5382 + 29.8201i) q^{43} +(-37.5265 + 4.01333i) q^{45} +(31.9088 - 87.6686i) q^{47} +(70.0593 + 58.7867i) q^{49} +(25.6156 + 32.7250i) q^{51} +51.4760i q^{53} -49.9992 q^{55} +(-1.58812 - 11.2258i) q^{57} +(9.45130 - 11.2636i) q^{59} +(-48.1278 - 17.5171i) q^{61} +(46.9324 + 95.7824i) q^{63} +(-6.67301 - 7.95258i) q^{65} +(2.35762 - 13.3707i) q^{67} +(2.73949 - 80.5524i) q^{69} +(-27.9939 - 16.1623i) q^{71} +(-20.3025 - 35.1650i) q^{73} +(4.60549 - 21.7646i) q^{75} +(48.3304 + 132.787i) q^{77} +(12.9014 + 73.1676i) q^{79} +(3.12181 + 80.9398i) q^{81} +(150.972 - 26.6204i) q^{83} +(54.5866 - 19.8679i) q^{85} +(121.061 + 25.6170i) q^{87} +(-18.0718 + 10.4337i) q^{89} +(-14.6700 + 25.4091i) q^{91} +(-104.629 - 3.55830i) q^{93} +(-15.6069 - 2.75192i) q^{95} +(-36.5526 + 30.6713i) q^{97} +(-7.29054 + 107.062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q - 9 * q^5 + 6 * q^9	\( 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) \) 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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