LMFDB - Embedded newform 819.2.et.b.136.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			136.7
Character	$\chi$	$=$	819.136
Dual form			819.2.et.b.271.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56744 - 1.56744i) q^{2} -2.91373i q^{4} +(0.784926 - 2.92938i) q^{5} +(2.25305 + 1.38700i) q^{7} +(-1.43221 - 1.43221i) q^{8} +O(q^{10})$	\(q+(1.56744 - 1.56744i) q^{2} -2.91373i q^{4} +(0.784926 - 2.92938i) q^{5} +(2.25305 + 1.38700i) q^{7} +(-1.43221 - 1.43221i) q^{8} +(-3.36131 - 5.82195i) q^{10} +(0.188977 - 0.705270i) q^{11} +(-2.65012 - 2.44476i) q^{13} +(5.70555 - 1.35749i) q^{14} +1.33764 q^{16} -3.24611 q^{17} +(3.85949 - 1.03415i) q^{19} +(-8.53543 - 2.28706i) q^{20} +(-0.809258 - 1.40168i) q^{22} +5.96750i q^{23} +(-3.63505 - 2.09870i) q^{25} +(-7.98592 + 0.321882i) q^{26} +(4.04133 - 6.56478i) q^{28} +(-2.78094 + 4.81672i) q^{29} +(3.99535 - 1.07055i) q^{31} +(4.96110 - 4.96110i) q^{32} +(-5.08807 + 5.08807i) q^{34} +(5.83152 - 5.51136i) q^{35} +(-6.97285 - 6.97285i) q^{37} +(4.42855 - 7.67048i) q^{38} +(-5.31969 + 3.07132i) q^{40} +(-2.46389 + 0.660198i) q^{41} +(-5.73009 + 3.30827i) q^{43} +(-2.05497 - 0.550626i) q^{44} +(9.35370 + 9.35370i) q^{46} +(1.69510 + 0.454201i) q^{47} +(3.15248 + 6.24995i) q^{49} +(-8.98729 + 2.40814i) q^{50} +(-7.12338 + 7.72173i) q^{52} +(-3.37073 + 5.83828i) q^{53} +(-1.91767 - 1.10717i) q^{55} +(-1.24038 - 5.21333i) q^{56} +(3.19097 + 11.9089i) q^{58} +(2.33153 - 2.33153i) q^{59} +(6.30371 + 3.63945i) q^{61} +(4.58444 - 7.94048i) q^{62} -12.8772i q^{64} +(-9.24179 + 5.84425i) q^{65} +(-6.27534 - 1.68147i) q^{67} +9.45827i q^{68} +(0.501828 - 17.7793i) q^{70} +(8.06938 + 2.16218i) q^{71} +(1.62921 + 6.08031i) q^{73} -21.8590 q^{74} +(-3.01323 - 11.2455i) q^{76} +(1.40398 - 1.32690i) q^{77} +(7.87501 + 13.6399i) q^{79} +(1.04995 - 3.91846i) q^{80} +(-2.82718 + 4.89682i) q^{82} +(-10.4223 - 10.4223i) q^{83} +(-2.54795 + 9.50909i) q^{85} +(-3.79606 + 14.1671i) q^{86} +(-1.28075 + 0.739443i) q^{88} +(6.62546 - 6.62546i) q^{89} +(-2.57998 - 9.18388i) q^{91} +17.3877 q^{92} +(3.36890 - 1.94504i) q^{94} -12.1177i q^{95} +(2.37570 - 8.86623i) q^{97} +(14.7377 + 4.85508i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.56744	−	1.56744i	1.10835	−	1.10835i	0.114979	−	0.993368i	$-0.463320\pi$
$2$	1.56744	−	1.56744i	1.10835	−	1.10835i	0.993368	−	0.114979i	$-0.0366800\pi$
$3$		0			0
$3$		0			0
$4$		−	2.91373i		−	1.45686i
$5$	0.784926	−	2.92938i	0.351029	−	1.31006i	−0.534379	−	0.845245i	$-0.679454\pi$
$5$	0.784926	−	2.92938i	0.351029	−	1.31006i	0.885408	−	0.464815i	$-0.153879\pi$
$6$		0			0
$7$	2.25305	+	1.38700i	0.851574	+	0.524235i
$7$	2.25305	+	1.38700i	0.851574	+	0.524235i
$8$	−1.43221	−	1.43221i	−0.506364	−	0.506364i
$9$		0			0
$10$	−3.36131	−	5.82195i	−1.06294	−	1.84106i
$11$	0.188977	−	0.705270i	0.0569786	−	0.212647i	−0.931567	−	0.363570i	$-0.881558\pi$
$11$	0.188977	−	0.705270i	0.0569786	−	0.212647i	0.988546	+	0.150923i	$0.0482245\pi$
$12$		0			0
$13$	−2.65012	−	2.44476i	−0.735011	−	0.678055i
$13$	−2.65012	−	2.44476i	−0.735011	−	0.678055i
$14$	5.70555	−	1.35749i	1.52487	−	0.362804i
$15$		0			0
$16$	1.33764			0.334410
$17$	−3.24611			−0.787296			−0.393648	−	0.919261i	$-0.628787\pi$
$17$	−3.24611			−0.787296			−0.393648	+	0.919261i	$0.628787\pi$
$18$		0			0
$19$	3.85949	−	1.03415i	0.885428	−	0.237250i	0.212680	−	0.977122i	$-0.431781\pi$
$19$	3.85949	−	1.03415i	0.885428	−	0.237250i	0.672747	+	0.739872i	$0.265114\pi$
$20$	−8.53543	−	2.28706i	−1.90858	−	0.511402i
$21$		0			0
$22$	−0.809258	−	1.40168i	−0.172534	−	0.298839i
$23$			5.96750i			1.24431i	0.782894	+	0.622155i	$0.213743\pi$
$23$			5.96750i			1.24431i	−0.782894	+	0.622155i	$0.786257\pi$
$24$		0			0
$25$	−3.63505	−	2.09870i	−0.727009	−	0.419739i
$26$	−7.98592	+	0.321882i	−1.56617	+	0.0631262i
$27$		0			0
$28$	4.04133	−	6.56478i	0.763740	−	1.24063i
$29$	−2.78094	+	4.81672i	−0.516407	+	0.894443i	0.483412	+	0.875393i	$0.339397\pi$
$29$	−2.78094	+	4.81672i	−0.516407	+	0.894443i	−0.999819	+	0.0190499i	$0.993936\pi$
$30$		0			0
$31$	3.99535	−	1.07055i	0.717585	−	0.192276i	0.118491	−	0.992955i	$-0.462194\pi$
$31$	3.99535	−	1.07055i	0.717585	−	0.192276i	0.599094	+	0.800679i	$0.295528\pi$
$32$	4.96110	−	4.96110i	0.877007	−	0.877007i
$33$		0			0
$34$	−5.08807	+	5.08807i	−0.872597	+	0.872597i
$35$	5.83152	−	5.51136i	0.985707	−	0.931590i
$36$		0			0
$37$	−6.97285	−	6.97285i	−1.14633	−	1.14633i	−0.987269	−	0.159061i	$-0.949153\pi$
$37$	−6.97285	−	6.97285i	−1.14633	−	1.14633i	−0.159061	−	0.987269i	$-0.550847\pi$
$38$	4.42855	−	7.67048i	0.718406	−	1.24432i
$39$		0			0
$40$	−5.31969	+	3.07132i	−0.841116	+	0.485619i
$41$	−2.46389	+	0.660198i	−0.384795	+	0.103106i	−0.446031	−	0.895018i	$-0.647163\pi$
$41$	−2.46389	+	0.660198i	−0.384795	+	0.103106i	0.0612351	+	0.998123i	$0.480496\pi$
$42$		0			0
$43$	−5.73009	+	3.30827i	−0.873831	+	0.504507i	−0.868619	−	0.495480i	$-0.834992\pi$
$43$	−5.73009	+	3.30827i	−0.873831	+	0.504507i	−0.00521150	+	0.999986i	$0.501659\pi$
$44$	−2.05497	−	0.550626i	−0.309798	−	0.0830101i
$45$		0			0
$46$	9.35370	+	9.35370i	1.37913	+	1.37913i
$47$	1.69510	+	0.454201i	0.247256	+	0.0662521i	0.380318	−	0.924856i	$-0.375814\pi$
$47$	1.69510	+	0.454201i	0.247256	+	0.0662521i	−0.133062	+	0.991108i	$0.542481\pi$
$48$		0			0
$49$	3.15248	+	6.24995i	0.450355	+	0.892850i
$50$	−8.98729	+	2.40814i	−1.27099	+	0.340562i
$51$		0			0
$52$	−7.12338	+	7.72173i	−0.987835	+	1.07081i
$53$	−3.37073	+	5.83828i	−0.463005	+	0.801949i	−0.999109	−	0.0422032i	$-0.986562\pi$
$53$	−3.37073	+	5.83828i	−0.463005	+	0.801949i	0.536104	+	0.844152i	$0.319896\pi$
$54$		0			0
$55$	−1.91767	−	1.10717i	−0.258579	−	0.149291i
$56$	−1.24038	−	5.21333i	−0.165752	−	0.696661i
$57$		0			0
$58$	3.19097	+	11.9089i	0.418995	+	1.56371i
$59$	2.33153	−	2.33153i	0.303540	−	0.303540i	−0.538857	−	0.842397i	$-0.681144\pi$
$59$	2.33153	−	2.33153i	0.303540	−	0.303540i	0.842397	+	0.538857i	$0.181144\pi$
$60$		0			0
$61$	6.30371	+	3.63945i	0.807108	+	0.465984i	0.845951	−	0.533261i	$-0.179034\pi$
$61$	6.30371	+	3.63945i	0.807108	+	0.465984i	−0.0388426	+	0.999245i	$0.512367\pi$
$62$	4.58444	−	7.94048i	0.582224	−	1.00844i
$63$		0			0
$64$		−	12.8772i		−	1.60964i
$65$	−9.24179	+	5.84425i	−1.14630	+	0.724891i
$66$		0			0
$67$	−6.27534	−	1.68147i	−0.766655	−	0.205424i	−0.145762	−	0.989320i	$-0.546563\pi$
$67$	−6.27534	−	1.68147i	−0.766655	−	0.205424i	−0.620893	+	0.783895i	$0.713230\pi$
$68$			9.45827i			1.14698i
$69$		0			0
$70$	0.501828	−	17.7793i	0.0599800	−	2.12503i
$71$	8.06938	+	2.16218i	0.957659	+	0.256604i	0.703609	−	0.710587i	$-0.251571\pi$
$71$	8.06938	+	2.16218i	0.957659	+	0.256604i	0.254050	+	0.967191i	$0.418237\pi$
$72$		0			0
$73$	1.62921	+	6.08031i	0.190685	+	0.711646i	0.993342	+	0.115205i	$0.0367525\pi$
$73$	1.62921	+	6.08031i	0.190685	+	0.711646i	−0.802657	+	0.596441i	$0.796581\pi$
$74$	−21.8590			−2.54106
$75$		0			0
$76$	−3.01323	−	11.2455i	−0.345641	−	1.28995i
$77$	1.40398	−	1.32690i	0.159998	−	0.151214i
$78$		0			0
$79$	7.87501	+	13.6399i	0.886008	+	1.53461i	0.844554	+	0.535471i	$0.179866\pi$
$79$	7.87501	+	13.6399i	0.886008	+	1.53461i	0.0414546	+	0.999140i	$0.486801\pi$
$80$	1.04995	−	3.91846i	0.117388	−	0.438097i
$81$		0			0
$82$	−2.82718	+	4.89682i	−0.312210	+	0.540763i
$83$	−10.4223	−	10.4223i	−1.14399	−	1.14399i	−0.987713	−	0.156277i	$-0.950051\pi$
$83$	−10.4223	−	10.4223i	−1.14399	−	1.14399i	−0.156277	−	0.987713i	$-0.549949\pi$
$84$		0			0
$85$	−2.54795	+	9.50909i	−0.276364	+	1.03141i
$86$	−3.79606	+	14.1671i	−0.409339	+	1.52768i
$87$		0			0
$88$	−1.28075	+	0.739443i	−0.136529	+	0.0788249i
$89$	6.62546	−	6.62546i	0.702297	−	0.702297i	−0.262606	−	0.964903i	$-0.584582\pi$
$89$	6.62546	−	6.62546i	0.702297	−	0.702297i	0.964903	+	0.262606i	$0.0845820\pi$
$90$		0			0
$91$	−2.57998	−	9.18388i	−0.270455	−	0.962733i
$92$	17.3877			1.81279
$93$		0			0
$94$	3.36890	−	1.94504i	0.347476	−	0.200615i
$95$		−	12.1177i		−	1.24324i
$96$		0			0
$97$	2.37570	−	8.86623i	0.241216	−	0.900230i	−0.734032	−	0.679115i	$-0.762364\pi$
$97$	2.37570	−	8.86623i	0.241216	−	0.900230i	0.975248	−	0.221115i	$-0.0709695\pi$
$98$	14.7377	+	4.85508i	1.48874	+	0.490438i
$99$		0			0
$100$	−6.11503	+	10.5915i	−0.611503	+	1.05915i
$101$	6.10920	+	10.5814i	0.607888	+	1.05289i	0.991588	+	0.129435i	$0.0413163\pi$
$101$	6.10920	+	10.5814i	0.607888	+	1.05289i	−0.383700	+	0.923458i	$0.625350\pi$
$102$		0			0
$103$	0.347680	+	0.602200i	0.0342580	+	0.0593366i	0.882646	−	0.470038i	$-0.155760\pi$
$103$	0.347680	+	0.602200i	0.0342580	+	0.0593366i	−0.848388	+	0.529375i	$0.822427\pi$
$104$	0.294113	+	7.29697i	0.0288401	+	0.715526i
$105$		0			0
$106$	3.86773	+	14.4346i	0.375667	+	1.40201i
$107$	13.7976			1.33386			0.666930	−	0.745120i	$-0.267608\pi$
$107$	13.7976			1.33386			0.666930	+	0.745120i	$0.267608\pi$
$108$		0			0
$109$	−3.39308	−	12.6631i	−0.324998	−	1.21291i	−0.914314	−	0.405006i	$-0.867269\pi$
$109$	−3.39308	−	12.6631i	−0.324998	−	1.21291i	0.589316	−	0.807903i	$-0.299397\pi$
$110$	−4.74126	+	1.27042i	−0.452061	+	0.121129i
$111$		0			0
$112$	3.01377	+	1.85530i	0.284775	+	0.175310i
$113$	5.92811	+	10.2678i	0.557670	+	0.965912i	0.997690	+	0.0679248i	$0.0216378\pi$
$113$	5.92811	+	10.2678i	0.557670	+	0.965912i	−0.440021	+	0.897988i	$0.645029\pi$
$114$		0			0
$115$	17.4811	+	4.68405i	1.63012	+	0.436790i
$116$	14.0346	+	8.10290i	1.30308	+	0.752335i
$117$		0			0
$118$		−	7.30907i		−	0.672855i
$119$	−7.31364	−	4.50234i	−0.670441	−	0.412728i
$120$		0			0
$121$	9.06459	+	5.23344i	0.824053	+	0.475767i
$122$	15.5853	−	4.17607i	1.41103	−	0.378084i
$123$		0			0
$124$	−3.11929	−	11.6414i	−0.280121	−	1.04542i
$125$	1.72116	−	1.72116i	0.153945	−	0.153945i
$126$		0			0
$127$	−3.91434	−	2.25995i	−0.347342	−	0.200538i	0.316172	−	0.948702i	$-0.397602\pi$
$127$	−3.91434	−	2.25995i	−0.347342	−	0.200538i	−0.663514	+	0.748164i	$0.730936\pi$
$128$	−10.2620	−	10.2620i	−0.907038	−	0.907038i
$129$		0			0
$130$	−5.32544	+	23.6465i	−0.467072	+	2.07393i
$131$	−10.9818	+	6.34037i	−0.959488	+	0.553960i	−0.896015	−	0.444023i	$-0.853551\pi$
$131$	−10.9818	+	6.34037i	−0.959488	+	0.553960i	−0.0634723	+	0.997984i	$0.520217\pi$
$132$		0			0
$133$	10.1300	+	3.02311i	0.878381	+	0.262137i
$134$	−12.4718	+	7.20061i	−1.07740	+	0.622038i
$135$		0			0
$136$	4.64912	+	4.64912i	0.398659	+	0.398659i
$137$	7.16928	+	7.16928i	0.612513	+	0.612513i	0.943600	−	0.331087i	$-0.107415\pi$
$137$	7.16928	+	7.16928i	0.612513	+	0.612513i	−0.331087	+	0.943600i	$0.607415\pi$
$138$		0			0
$139$	0.0630104	−	0.0363791i	0.00534447	−	0.00308563i	−0.497325	−	0.867564i	$-0.665684\pi$
$139$	0.0630104	−	0.0363791i	0.00534447	−	0.00308563i	0.502670	+	0.864478i	$0.332351\pi$
$140$	−16.0586	−	16.9915i	−1.35720	−	1.43604i
$141$		0			0
$142$	16.0374	−	9.25917i	1.34582	−	0.777012i
$143$	−2.22503	+	1.40705i	−0.186066	+	0.117663i
$144$		0			0
$145$	11.9272	+	11.9272i	0.990500	+	0.990500i
$146$	12.0842	+	6.97682i	1.00010	+	0.577406i
$147$		0			0
$148$	−20.3170	+	20.3170i	−1.67005	+	1.67005i
$149$	0.322028	+	1.20183i	0.0263816	+	0.0984574i	0.977861	−	0.209254i	$-0.0671035\pi$
$149$	0.322028	+	1.20183i	0.0263816	+	0.0984574i	−0.951480	+	0.307711i	$0.900437\pi$
$150$		0			0
$151$	−0.716844	+	0.192078i	−0.0583359	+	0.0156311i	−0.287869	−	0.957670i	$-0.592947\pi$
$151$	−0.716844	+	0.192078i	−0.0583359	+	0.0156311i	0.229533	+	0.973301i	$0.426280\pi$
$152$	−7.00874	−	4.04650i	−0.568484	−	0.328214i
$153$		0			0
$154$	0.120819	−	4.28049i	0.00973586	−	0.344932i
$155$		−	12.5442i		−	1.00757i
$156$		0			0
$157$	−7.82322	−	4.51674i	−0.624361	−	0.360475i	0.154204	−	0.988039i	$-0.450719\pi$
$157$	−7.82322	−	4.51674i	−0.624361	−	0.360475i	−0.778565	+	0.627564i	$0.784052\pi$
$158$	33.7233	+	9.03614i	2.68289	+	0.718877i
$159$		0			0
$160$	−10.6389	−	18.4271i	−0.841076	−	1.45679i
$161$	−8.27690	+	13.4451i	−0.652311	+	1.05962i
$162$		0			0
$163$	−2.20381	+	0.590509i	−0.172616	+	0.0462523i	−0.344092	−	0.938936i	$-0.611813\pi$
$163$	−2.20381	+	0.590509i	−0.172616	+	0.0462523i	0.171476	+	0.985188i	$0.445146\pi$
$164$	1.92364	+	7.17912i	0.150211	+	0.560595i
$165$		0			0
$166$	−32.6725			−2.53588
$167$	0.729973	+	2.72430i	0.0564870	+	0.210812i	0.988401	−	0.151867i	$-0.0485286\pi$
$167$	0.729973	+	2.72430i	0.0564870	+	0.210812i	−0.931914	+	0.362680i	$0.881862\pi$
$168$		0			0
$169$	1.04626	+	12.9578i	0.0804816	+	0.996756i
$170$	10.9112	+	18.8987i	0.836847	+	1.44946i
$171$		0			0
$172$	9.63940	+	16.6959i	0.734998	+	1.27305i
$173$	2.31972	−	4.01787i	0.176365	−	0.305473i	−0.764268	−	0.644899i	$-0.776899\pi$
$173$	2.31972	−	4.01787i	0.176365	−	0.305473i	0.940633	+	0.339426i	$0.110233\pi$
$174$		0			0
$175$	−5.27907	−	9.77027i	−0.399060	−	0.738563i
$176$	0.252783	−	0.943397i	0.0190542	−	0.0711113i
$177$		0			0
$178$		−	20.7700i		−	1.55678i
$179$	−12.1991	+	7.04316i	−0.911804	+	0.526430i	−0.881011	−	0.473096i	$-0.843137\pi$
$179$	−12.1991	+	7.04316i	−0.911804	+	0.526430i	−0.0307928	+	0.999526i	$0.509803\pi$
$180$		0			0
$181$	−19.3214			−1.43615			−0.718075	−	0.695966i	$-0.754976\pi$
$181$	−19.3214			−1.43615			−0.718075	+	0.695966i	$0.754976\pi$
$182$	−18.4391	−	10.3512i	−1.36680	−	0.767283i
$183$		0			0
$184$	8.54675	−	8.54675i	0.630075	−	0.630075i
$185$	−25.8993	+	14.9530i	−1.90416	+	1.09936i
$186$		0			0
$187$	−0.613438	+	2.28938i	−0.0448590	+	0.167416i
$188$	1.32342	−	4.93907i	0.0965203	−	0.360219i
$189$		0			0
$190$	−18.9937	−	18.9937i	−1.37795	−	1.37795i
$191$	3.84651	−	6.66236i	0.278324	−	0.482071i	−0.692644	−	0.721279i	$-0.743554\pi$
$191$	3.84651	−	6.66236i	0.278324	−	0.482071i	0.970968	+	0.239208i	$0.0768878\pi$
$192$		0			0
$193$	2.07797	−	7.75507i	0.149575	−	0.558222i	−0.849934	−	0.526889i	$-0.823358\pi$
$193$	2.07797	−	7.75507i	0.149575	−	0.558222i	0.999509	−	0.0313328i	$-0.00997516\pi$
$194$	−10.1735	−	17.6210i	−0.730416	−	1.26512i
$195$		0			0
$196$	18.2107	−	9.18549i	1.30076	−	0.656106i
$197$	1.52597	+	5.69500i	0.108721	+	0.405752i	0.998741	−	0.0501699i	$-0.0159763\pi$
$197$	1.52597	+	5.69500i	0.108721	+	0.405752i	−0.890020	+	0.455922i	$0.849310\pi$
$198$		0			0
$199$	8.74035			0.619587			0.309794	−	0.950804i	$-0.399740\pi$
$199$	8.74035			0.619587			0.309794	+	0.950804i	$0.399740\pi$
$200$	2.20039	+	8.21195i	0.155591	+	0.580673i
$201$		0			0
$202$	26.1616	+	7.00997i	1.84072	+	0.493220i
$203$	−12.9464	+	6.99518i	−0.908657	+	0.490965i
$204$		0			0
$205$			7.73589i			0.540298i
$206$	1.48888	+	0.398944i	0.103735	+	0.0277958i
$207$		0			0
$208$	−3.54491	−	3.27021i	−0.245795	−	0.226749i
$209$		−	2.91741i		−	0.201802i
$210$		0			0
$211$	−10.0859	+	17.4692i	−0.694340	+	1.20263i	0.276063	+	0.961140i	$0.410970\pi$
$211$	−10.0859	+	17.4692i	−0.694340	+	1.20263i	−0.970403	+	0.241492i	$0.922363\pi$
$212$	17.0112	+	9.82140i	1.16833	+	0.674536i
$213$		0			0
$214$	21.6268	−	21.6268i	1.47838	−	1.47838i
$215$	5.19349	+	19.3824i	0.354193	+	1.32187i
$216$		0			0
$217$	10.4866	+	3.12952i	0.711875	+	0.212446i
$218$	−25.1671	−	14.5303i	−1.70453	−	0.984113i
$219$		0			0
$220$	−3.22599	+	5.58758i	−0.217496	+	0.376715i
$221$	8.60257	+	7.93596i	0.578671	+	0.533831i
$222$		0			0
$223$	12.7683	−	3.42126i	0.855031	−	0.229105i	0.195427	−	0.980718i	$-0.437391\pi$
$223$	12.7683	−	3.42126i	0.855031	−	0.229105i	0.659604	+	0.751613i	$0.270724\pi$
$224$	18.0586	−	4.29659i	1.20659	−	0.287078i
$225$		0			0
$226$	25.3861	+	6.80218i	1.68866	+	0.452474i
$227$	−5.38732	−	5.38732i	−0.357569	−	0.357569i	0.505347	−	0.862916i	$-0.331364\pi$
$227$	−5.38732	−	5.38732i	−0.357569	−	0.357569i	−0.862916	+	0.505347i	$0.831364\pi$
$228$		0			0
$229$	−28.2478	−	7.56897i	−1.86667	−	0.500171i	−0.999999	−	0.00128230i	$-0.999592\pi$
$229$	−28.2478	−	7.56897i	−1.86667	−	0.500171i	−0.866666	−	0.498889i	$-0.833742\pi$
$230$	34.7425	−	20.0586i	2.29085	−	1.32263i
$231$		0			0
$232$	10.8815	−	2.91568i	0.714404	−	0.191424i
$233$	0.786647	−	0.454171i	0.0515350	−	0.0297537i	−0.474011	−	0.880519i	$-0.657194\pi$
$233$	0.786647	−	0.454171i	0.0515350	−	0.0297537i	0.525546	+	0.850765i	$0.323861\pi$
$234$		0			0
$235$	2.66106	−	4.60909i	0.173588	−	0.300664i
$236$	−6.79346	−	6.79346i	−0.442216	−	0.442216i
$237$		0			0
$238$	−18.5208	+	4.40655i	−1.20053	+	0.285635i
$239$	−7.05491	+	7.05491i	−0.456344	+	0.456344i	−0.897453	−	0.441109i	$-0.854585\pi$
$239$	−7.05491	+	7.05491i	−0.456344	+	0.456344i	0.441109	+	0.897453i	$0.354585\pi$
$240$		0			0
$241$	5.10472	−	5.10472i	0.328824	−	0.328824i	−0.523315	−	0.852139i	$-0.675305\pi$
$241$	5.10472	−	5.10472i	0.328824	−	0.328824i	0.852139	+	0.523315i	$0.175305\pi$
$242$	22.4113	−	6.00509i	1.44065	−	0.386021i
$243$		0			0
$244$	10.6044	−	18.3673i	0.678876	−	1.17585i
$245$	20.7830	−	4.32909i	1.32777	−	0.276575i
$246$		0			0
$247$	−12.7564	−	6.69493i	−0.811667	−	0.425988i
$248$	−7.25545	−	4.18894i	−0.460722	−	0.265998i
$249$		0			0
$250$		−	5.39563i		−	0.341249i
$251$	2.92724	+	5.07013i	0.184766	+	0.320023i	0.943498	−	0.331380i	$-0.107514\pi$
$251$	2.92724	+	5.07013i	0.184766	+	0.320023i	−0.758732	+	0.651403i	$0.774181\pi$
$252$		0			0
$253$	4.20870	+	1.12772i	0.264599	+	0.0708990i
$254$	−9.67782	+	2.59316i	−0.607240	+	0.162710i
$255$		0			0
$256$	−6.41568			−0.400980
$257$	−15.9760			−0.996558			−0.498279	−	0.867017i	$-0.666034\pi$
$257$	−15.9760			−0.996558			−0.498279	+	0.867017i	$0.666034\pi$
$258$		0			0
$259$	−6.03888	−	25.3815i	−0.375238	−	1.57713i
$260$	17.0286	+	26.9281i	1.05607	+	1.67001i
$261$		0			0
$262$	−7.27522	+	27.1515i	−0.449465	+	1.67743i
$263$	−12.0727	−	20.9106i	−0.744437	−	1.28940i	−0.950457	−	0.310856i	$-0.899384\pi$
$263$	−12.0727	−	20.9106i	−0.744437	−	1.28940i	0.206020	−	0.978548i	$-0.433949\pi$
$264$		0			0
$265$	14.4568	+	14.4568i	0.888073	+	0.888073i
$266$	20.6167	−	11.1396i	1.26409	−	0.683013i
$267$		0			0
$268$	−4.89935	+	18.2846i	−0.299276	+	1.11691i
$269$		−	29.4878i		−	1.79790i	−0.438047	−	0.898952i	$-0.644330\pi$
$269$		−	29.4878i		−	1.79790i	0.438047	−	0.898952i	$-0.355670\pi$
$270$		0			0
$271$	0.604773	−	0.604773i	0.0367374	−	0.0367374i	−0.688499	−	0.725237i	$-0.741730\pi$
$271$	0.604773	−	0.604773i	0.0367374	−	0.0367374i	0.725237	+	0.688499i	$0.241730\pi$
$272$	−4.34212			−0.263280
$273$		0			0
$274$	22.4748			1.35775
$275$	−2.16709	+	2.16709i	−0.130680	+	0.130680i
$276$		0			0
$277$			14.2038i			0.853426i	0.904387	+	0.426713i	$0.140329\pi$
$277$			14.2038i			0.853426i	−0.904387	+	0.426713i	$0.859671\pi$
$278$	0.0417430	−	0.155787i	0.00250358	−	0.00934348i
$279$		0			0
$280$	−16.2454	−	0.458535i	−0.970851	−	0.0274027i
$281$	−1.82178	−	1.82178i	−0.108679	−	0.108679i	0.650676	−	0.759355i	$-0.274485\pi$
$281$	−1.82178	−	1.82178i	−0.108679	−	0.108679i	−0.759355	+	0.650676i	$0.774485\pi$
$282$		0			0
$283$	−9.55836	−	16.5556i	−0.568185	−	0.984126i	−0.996746	−	0.0806125i	$-0.974312\pi$
$283$	−9.55836	−	16.5556i	−0.568185	−	0.984126i	0.428560	−	0.903513i	$-0.359021\pi$
$284$	6.30002	−	23.5120i	0.373837	−	1.39518i
$285$		0			0
$286$	−1.28214	+	5.69306i	−0.0758144	+	0.336637i
$287$	−6.46697	−	1.92995i	−0.381733	−	0.113921i
$288$		0			0
$289$	−6.46280			−0.380165
$290$	37.3903			2.19563
$291$		0			0
$292$	17.7164	−	4.74709i	1.03677	−	0.277802i
$293$	−0.0611926	−	0.0163965i	−0.00357491	−	0.000957894i	0.257031	−	0.966403i	$-0.417256\pi$
$293$	−0.0611926	−	0.0163965i	−0.00357491	−	0.000957894i	−0.260606	+	0.965445i	$0.583922\pi$
$294$		0			0
$295$	−4.99987	−	8.66004i	−0.291104	−	0.504207i
$296$			19.9732i			1.16092i
$297$		0			0
$298$	2.38855	+	1.37903i	0.138365	+	0.0798850i
$299$	14.5891	−	15.8146i	0.843712	−	0.914582i
$300$		0			0
$301$	−17.4988	−	0.493911i	−1.00861	−	0.0284685i
$302$	−0.822539	+	1.42468i	−0.0473318	+	0.0819810i
$303$		0			0
$304$	5.16261	−	1.38332i	0.296096	−	0.0793387i
$305$	15.6093	−	15.6093i	0.893785	−	0.893785i
$306$		0			0
$307$	−4.12063	+	4.12063i	−0.235177	+	0.235177i	−0.814849	−	0.579673i	$-0.803180\pi$
$307$	−4.12063	+	4.12063i	−0.235177	+	0.235177i	0.579673	+	0.814849i	$0.303180\pi$
$308$	−3.86623	−	4.09082i	−0.220299	−	0.233096i
$309$		0			0
$310$	−19.6623	−	19.6623i	−1.11674	−	1.11674i
$311$	−2.60731	+	4.51600i	−0.147847	+	0.256079i	−0.930432	−	0.366466i	$-0.880568\pi$
$311$	−2.60731	+	4.51600i	−0.147847	+	0.256079i	0.782584	+	0.622544i	$0.213901\pi$
$312$		0			0
$313$	−14.7297	+	8.50419i	−0.832571	+	0.480685i	−0.854732	−	0.519069i	$-0.826279\pi$
$313$	−14.7297	+	8.50419i	−0.832571	+	0.480685i	0.0221612	+	0.999754i	$0.492945\pi$
$314$	−19.3421	+	5.18271i	−1.09154	+	0.292477i
$315$		0			0
$316$	39.7430	−	22.9457i	2.23572	−	1.29079i
$317$	−3.82263	−	1.02427i	−0.214700	−	0.0575288i	0.149866	−	0.988706i	$-0.452116\pi$
$317$	−3.82263	−	1.02427i	−0.214700	−	0.0575288i	−0.364566	+	0.931178i	$0.618783\pi$
$318$		0			0
$319$	2.87156	+	2.87156i	0.160776	+	0.160776i
$320$	−37.7221	−	10.1076i	−2.10873	−	0.565033i
$321$		0			0
$322$	8.10083	+	34.0479i	0.451441	+	1.89742i
$323$	−12.5283	+	3.35695i	−0.697094	+	0.186786i
$324$		0			0
$325$	4.50249	+	14.4486i	0.249753	+	0.801465i
$326$	−2.52875	+	4.37993i	−0.140055	+	0.242582i
$327$		0			0
$328$	4.47437	+	2.58328i	0.247056	+	0.142638i
$329$	3.18918	+	3.37444i	0.175825	+	0.186039i
$330$		0			0
$331$	−3.47024	−	12.9511i	−0.190742	−	0.711858i	−0.993328	−	0.115322i	$-0.963210\pi$
$331$	−3.47024	−	12.9511i	−0.190742	−	0.711858i	0.802586	−	0.596536i	$-0.203457\pi$
$332$	−30.3676	+	30.3676i	−1.66664	+	1.66664i
$333$		0			0
$334$	5.41436	+	3.12598i	0.296260	+	0.171046i
$335$	−9.85135	+	17.0630i	−0.538237	+	0.932253i
$336$		0			0
$337$		−	15.2503i		−	0.830737i	−0.909653	−	0.415368i	$-0.863653\pi$
$337$		−	15.2503i		−	0.830737i	0.909653	−	0.415368i	$-0.136347\pi$
$338$	21.9506	+	18.6707i	1.19395	+	1.01555i
$339$		0			0
$340$	27.7069	+	7.42404i	1.50262	+	0.402625i
$341$		−	3.02011i		−	0.163548i
$342$		0			0
$343$	−1.56594	+	18.4539i	−0.0845529	+	0.996419i
$344$	12.9449	+	3.46857i	0.697941	+	0.187013i
$345$		0			0
$346$	−2.66175	−	9.93378i	−0.143096	−	0.534043i
$347$	−9.79224			−0.525675			−0.262838	−	0.964840i	$-0.584658\pi$
$347$	−9.79224			−0.525675			−0.262838	+	0.964840i	$0.584658\pi$
$348$		0			0
$349$	−1.16556	−	4.34994i	−0.0623911	−	0.232847i	0.927688	−	0.373356i	$-0.121793\pi$
$349$	−1.16556	−	4.34994i	−0.0623911	−	0.232847i	−0.990079	+	0.140509i	$0.955126\pi$
$350$	−23.5889	−	7.03968i	−1.26088	−	0.376287i
$351$		0			0
$352$	−2.56138	−	4.43645i	−0.136522	−	0.236463i
$353$	−4.38567	+	16.3675i	−0.233425	+	0.871156i	0.745427	+	0.666587i	$0.232246\pi$
$353$	−4.38567	+	16.3675i	−0.233425	+	0.871156i	−0.978852	+	0.204568i	$0.934421\pi$
$354$		0			0
$355$	12.6677	−	21.9412i	0.672333	−	1.16452i
$356$	−19.3048	−	19.3048i	−1.02315	−	1.02315i
$357$		0			0
$358$	−8.08163	+	30.1611i	−0.427128	+	1.59406i
$359$	4.12643	−	15.4000i	0.217784	−	0.812782i	−0.767383	−	0.641189i	$-0.778442\pi$
$359$	4.12643	−	15.4000i	0.217784	−	0.812782i	0.985168	−	0.171594i	$-0.0548917\pi$
$360$		0			0
$361$	−2.62828	+	1.51744i	−0.138330	+	0.0798651i
$362$	−30.2851	+	30.2851i	−1.59175	+	1.59175i
$363$		0			0
$364$	−26.7594	+	7.51736i	−1.40257	+	0.394017i
$365$	19.0904			0.999235
$366$		0			0
$367$	−20.7903	+	12.0033i	−1.08524	+	0.626565i	−0.932306	−	0.361671i	$-0.882207\pi$
$367$	−20.7903	+	12.0033i	−1.08524	+	0.626565i	−0.152937	+	0.988236i	$0.548873\pi$
$368$			7.98237i			0.416110i
$369$		0			0
$370$	−17.1577	+	64.0335i	−0.891987	+	3.32894i
$371$	−15.6921	+	8.47875i	−0.814693	+	0.440195i
$372$		0			0
$373$	7.17404	−	12.4258i	0.371458	−	0.643384i	−0.618332	−	0.785917i	$-0.712191\pi$
$373$	7.17404	−	12.4258i	0.371458	−	0.643384i	0.989790	+	0.142533i	$0.0455247\pi$
$374$	2.62694	+	4.54999i	0.135836	+	0.235274i
$375$		0			0
$376$	−1.77724	−	3.07826i	−0.0916540	−	0.158749i
$377$	19.1456	−	5.96616i	0.986047	−	0.307273i
$378$		0			0
$379$	−2.18843	−	8.16732i	−0.112412	−	0.419527i	0.886668	−	0.462406i	$-0.153014\pi$
$379$	−2.18843	−	8.16732i	−0.112412	−	0.419527i	−0.999080	+	0.0428788i	$0.986347\pi$
$380$	−35.3076			−1.81124
$381$		0			0
$382$	−4.41366	−	16.4720i	−0.225823	−	0.842781i
$383$	−18.9731	+	5.08381i	−0.969478	+	0.259771i	−0.708607	−	0.705603i	$-0.750676\pi$
$383$	−18.9731	+	5.08381i	−0.969478	+	0.259771i	−0.260870	+	0.965374i	$0.584010\pi$
$384$		0			0
$385$	−2.78498	−	5.15431i	−0.141936	−	0.262688i
$386$	−8.89852	−	15.4127i	−0.452923	−	0.784485i
$387$		0			0
$388$	−25.8338	−	6.92215i	−1.31151	−	0.351419i
$389$	4.88185	+	2.81854i	0.247520	+	0.142906i	0.618628	−	0.785684i	$-0.287689\pi$
$389$	4.88185	+	2.81854i	0.247520	+	0.142906i	−0.371108	+	0.928590i	$0.621022\pi$
$390$		0			0
$391$		−	19.3712i		−	0.979641i
$392$	4.43623	−	13.4663i	0.224064	−	0.680151i
$393$		0			0
$394$	11.3184	+	6.53470i	0.570214	+	0.329213i
$395$	46.1379	−	12.3626i	2.32145	−	0.622030i
$396$		0			0
$397$	−3.51692	−	13.1253i	−0.176509	−	0.658740i	−0.996290	−	0.0860629i	$-0.972571\pi$
$397$	−3.51692	−	13.1253i	−0.176509	−	0.658740i	0.819781	−	0.572678i	$-0.194095\pi$
$398$	13.7000	−	13.7000i	0.686717	−	0.686717i
$399$		0			0
$400$	−4.86238	−	2.80730i	−0.243119	−	0.140365i
$401$	−5.57129	−	5.57129i	−0.278217	−	0.278217i	0.554180	−	0.832397i	$-0.313032\pi$
$401$	−5.57129	−	5.57129i	−0.278217	−	0.278217i	−0.832397	+	0.554180i	$0.813032\pi$
$402$		0			0
$403$	−13.2054	−	6.93059i	−0.657807	−	0.345237i
$404$	30.8315	−	17.8005i	1.53392	−	0.885610i
$405$		0			0
$406$	−9.32813	+	31.2572i	−0.462947	+	1.55127i
$407$	−6.23545	+	3.60004i	−0.309080	+	0.178447i
$408$		0			0
$409$	2.68114	+	2.68114i	0.132574	+	0.132574i	0.770280	−	0.637706i	$-0.220117\pi$
$409$	2.68114	+	2.68114i	0.132574	+	0.132574i	−0.637706	+	0.770280i	$0.720117\pi$
$410$	12.1255	+	12.1255i	0.598838	+	0.598838i
$411$		0			0
$412$	1.75465	−	1.01305i	0.0864453	−	0.0499092i
$413$	8.48689	−	2.01924i	0.417613	−	0.0993602i
$414$		0			0
$415$	−38.7115	+	22.3501i	−1.90027	+	1.09712i
$416$	−25.2762	+	1.01879i	−1.23927	+	0.0499502i
$417$		0			0
$418$	−4.57287	−	4.57287i	−0.223666	−	0.223666i
$419$	3.07221	+	1.77374i	0.150087	+	0.0866528i	0.573163	−	0.819441i	$-0.305716\pi$
$419$	3.07221	+	1.77374i	0.150087	+	0.0866528i	−0.423076	+	0.906094i	$0.639050\pi$
$420$		0			0
$421$	−21.1170	+	21.1170i	−1.02918	+	1.02918i	−0.0296199	+	0.999561i	$0.509430\pi$
$421$	−21.1170	+	21.1170i	−1.02918	+	1.02918i	−0.999561	+	0.0296199i	$0.990570\pi$
$422$	11.5730	+	43.1910i	0.563364	+	2.10250i
$423$		0			0
$424$	13.1893	−	3.53406i	0.640528	−	0.171629i
$425$	11.7997	+	6.81259i	0.572372	+	0.330459i
$426$		0			0
$427$	9.15469	+	16.9431i	0.443027	+	0.819934i
$428$		−	40.2024i		−	1.94325i
$429$		0			0
$430$	38.5212	+	22.2402i	1.85766	+	1.07252i
$431$	−15.5793	−	4.17446i	−0.750428	−	0.201077i	−0.136720	−	0.990610i	$-0.543656\pi$
$431$	−15.5793	−	4.17446i	−0.750428	−	0.201077i	−0.613708	+	0.789533i	$0.710323\pi$
$432$		0			0
$433$	14.9794	+	25.9452i	0.719866	+	1.24684i	0.961052	+	0.276366i	$0.0891302\pi$
$433$	14.9794	+	25.9452i	0.719866	+	1.24684i	−0.241186	+	0.970479i	$0.577537\pi$
$434$	21.3424	−	11.5317i	1.02447	−	0.553540i
$435$		0			0
$436$	−36.8970	+	9.88651i	−1.76704	+	0.473478i
$437$	6.17128	+	23.0315i	0.295212	+	1.10175i
$438$		0			0
$439$	4.51920			0.215690			0.107845	−	0.994168i	$-0.465605\pi$
$439$	4.51920			0.215690			0.107845	+	0.994168i	$0.465605\pi$
$440$	1.16082	+	4.33222i	0.0553397	+	0.206531i
$441$		0			0
$442$	25.9231	−	1.04486i	1.23304	−	0.0496990i
$443$	−16.8631	−	29.2078i	−0.801191	−	1.38770i	−0.918833	−	0.394648i	$-0.870867\pi$
$443$	−16.8631	−	29.2078i	−0.801191	−	1.38770i	0.117641	−	0.993056i	$-0.462467\pi$
$444$		0			0
$445$	−14.2080	−	24.6090i	−0.673524	−	1.16658i
$446$	14.6510	−	25.3762i	0.693743	−	1.20160i
$447$		0			0
$448$	17.8606	−	29.0129i	0.843832	−	1.37073i
$449$	0.999901	−	3.73168i	0.0471882	−	0.176109i	−0.938310	−	0.345796i	$-0.887609\pi$
$449$	0.999901	−	3.73168i	0.0471882	−	0.176109i	0.985498	+	0.169687i	$0.0542757\pi$
$450$		0			0
$451$			1.86247i			0.0877004i
$452$	29.9176	−	17.2729i	1.40720	−	0.812449i
$453$		0			0
$454$	−16.8886			−0.792620
$455$	−28.9282	+	0.349075i	−1.35617	+	0.0163649i
$456$		0			0
$457$	0.367380	−	0.367380i	0.0171853	−	0.0171853i	−0.698462	−	0.715647i	$-0.746132\pi$
$457$	0.367380	−	0.367380i	0.0171853	−	0.0171853i	0.715647	+	0.698462i	$0.246132\pi$
$458$	−56.1405	+	32.4128i	−2.62328	+	1.51455i
$459$		0			0
$460$	13.6480	−	50.9352i	0.636343	−	2.37487i
$461$	−7.57790	+	28.2811i	−0.352938	+	1.31718i	0.530122	+	0.847922i	$0.322146\pi$
$461$	−7.57790	+	28.2811i	−0.352938	+	1.31718i	−0.883060	+	0.469261i	$0.844520\pi$
$462$		0			0
$463$	15.0661	+	15.0661i	0.700181	+	0.700181i	0.964449	−	0.264268i	$-0.0851303\pi$
$463$	15.0661	+	15.0661i	0.700181	+	0.700181i	−0.264268	+	0.964449i	$0.585130\pi$
$464$	−3.71989	+	6.44304i	−0.172692	+	0.299111i
$465$		0			0
$466$	0.521136	−	1.94491i	0.0241412	−	0.0900961i
$467$	−2.14169	−	3.70951i	−0.0991054	−	0.171656i	0.812209	−	0.583366i	$-0.198265\pi$
$467$	−2.14169	−	3.70951i	−0.0991054	−	0.171656i	−0.911315	+	0.411711i	$0.864931\pi$
$468$		0			0
$469$	−11.8065	−	12.4923i	−0.545172	−	0.576841i
$470$	−3.05342	−	11.3955i	−0.140844	−	0.525636i
$471$		0			0
$472$	−6.67851			−0.307404
$473$	1.25037	+	4.66645i	0.0574921	+	0.214564i
$474$		0			0
$475$	−16.1998	−	4.34072i	−0.743297	−	0.199166i
$476$	−13.1186	+	21.3100i	−0.601289	+	0.976741i
$477$		0			0
$478$			22.1163i			1.01158i
$479$	−10.8652	−	2.91131i	−0.496442	−	0.133021i	0.00190599	−	0.999998i	$-0.499393\pi$
$479$	−10.8652	−	2.91131i	−0.496442	−	0.133021i	−0.498348	+	0.866977i	$0.666060\pi$
$480$		0			0
$481$	1.43191	+	35.5259i	0.0652895	+	1.61984i
$482$		−	16.0027i		−	0.728902i
$483$		0			0
$484$	15.2488	−	26.4117i	0.693129	−	1.20053i
$485$	−24.1078	−	13.9187i	−1.09468	−	0.632014i
$486$		0			0
$487$	4.97171	−	4.97171i	0.225290	−	0.225290i	−0.585432	−	0.810722i	$-0.699075\pi$
$487$	4.97171	−	4.97171i	0.225290	−	0.225290i	0.810722	+	0.585432i	$0.199075\pi$
$488$	−3.81580	−	14.2407i	−0.172733	−	0.644648i
$489$		0			0
$490$	25.7904	−	39.3616i	1.16509	−	1.77818i
$491$	0.343800	+	0.198493i	0.0155155	+	0.00895787i	0.507738	−	0.861512i	$-0.330482\pi$
$491$	0.343800	+	0.198493i	0.0155155	+	0.00895787i	−0.492222	+	0.870470i	$0.663815\pi$
$492$		0			0
$493$	9.02721	−	15.6356i	0.406565	−	0.704192i
$494$	−30.4887	+	9.50091i	−1.37175	+	0.427466i
$495$		0			0
$496$	5.34434	−	1.43201i	0.239968	−	0.0642992i
$497$	15.1818	+	16.0637i	0.680997	+	0.720556i
$498$		0			0
$499$	1.91022	+	0.511843i	0.0855133	+	0.0229132i	0.301322	−	0.953522i	$-0.402572\pi$
$499$	1.91022	+	0.511843i	0.0855133	+	0.0229132i	−0.215809	+	0.976436i	$0.569239\pi$
$500$	−5.01500	−	5.01500i	−0.224277	−	0.224277i
$501$		0			0
$502$	12.5354	+	3.35884i	0.559481	+	0.149913i
$503$	4.35557	−	2.51469i	0.194205	−	0.112124i	−0.399745	−	0.916627i	$-0.630901\pi$
$503$	4.35557	−	2.51469i	0.194205	−	0.112124i	0.593950	+	0.804502i	$0.297568\pi$
$504$		0			0
$505$	35.7924	−	9.59053i	1.59274	−	0.426773i
$506$	8.36451	−	4.82925i	0.371848	−	0.214687i
$507$		0			0
$508$	−6.58487	+	11.4053i	−0.292156	+	0.506030i
$509$	−4.21429	−	4.21429i	−0.186795	−	0.186795i	0.607514	−	0.794309i	$-0.292167\pi$
$509$	−4.21429	−	4.21429i	−0.186795	−	0.186795i	−0.794309	+	0.607514i	$0.792167\pi$
$510$		0			0
$511$	−4.76266	+	15.9590i	−0.210688	+	0.705983i
$512$	10.4677	−	10.4677i	0.462613	−	0.462613i
$513$		0			0
$514$	−25.0415	+	25.0415i	−1.10453	+	1.10453i
$515$	2.03698	−	0.545807i	0.0897600	−	0.0240511i
$516$		0			0
$517$	0.640669	−	1.10967i	0.0281766	−	0.0488033i
$518$	−49.2495	−	30.3184i	−2.16390	−	1.33211i
$519$		0			0
$520$	21.6065	+	4.86601i	0.947506	+	0.213389i
$521$	17.6087	+	10.1664i	0.771453	+	0.445399i	0.833393	−	0.552681i	$-0.186395\pi$
$521$	17.6087	+	10.1664i	0.771453	+	0.445399i	−0.0619398	+	0.998080i	$0.519729\pi$
$522$		0			0
$523$			27.0854i			1.18436i	0.805806	+	0.592180i	$0.201733\pi$
$523$			27.0854i			1.18436i	−0.805806	+	0.592180i	$0.798267\pi$
$524$	18.4741	+	31.9981i	0.807045	+	1.39784i
$525$		0			0
$526$	−51.6994	−	13.8528i	−2.25420	−	0.604011i
$527$	−12.9693	+	3.47512i	−0.564952	+	0.151379i
$528$		0			0
$529$	−12.6111			−0.548309
$530$	45.3202			1.96858
$531$		0			0
$532$	8.80852	−	29.5160i	0.381898	−	1.27968i
$533$	8.14364	+	4.27403i	0.352740	+	0.185129i
$534$		0			0
$535$	10.8301	−	40.4183i	0.468224	−	1.74744i
$536$	6.57940	+	11.3959i	0.284187	+	0.492226i
$537$		0			0
$538$	−46.2204	−	46.2204i	−1.99270	−	1.99270i
$539$	5.00365	−	1.04226i	0.215522	−	0.0448933i
$540$		0			0
$541$	8.82915	−	32.9508i	0.379595	−	1.41667i	−0.466919	−	0.884300i	$-0.654636\pi$
$541$	8.82915	−	32.9508i	0.379595	−	1.41667i	0.846513	−	0.532367i	$-0.178697\pi$
$542$		−	1.89589i		−	0.0814355i
$543$		0			0
$544$	−16.1043	+	16.1043i	−0.690464	+	0.690464i
$545$	−39.7585			−1.70307
$546$		0			0
$547$	−12.5750			−0.537669			−0.268834	−	0.963186i	$-0.586638\pi$
$547$	−12.5750			−0.537669			−0.268834	+	0.963186i	$0.586638\pi$
$548$	20.8893	−	20.8893i	0.892348	−	0.892348i
$549$		0			0
$550$			6.79355i			0.289678i
$551$	−5.75180	+	21.4660i	−0.245035	+	0.914482i
$552$		0			0
$553$	−1.17571	+	41.6541i	−0.0499961	+	1.77131i
$554$	22.2637	+	22.2637i	0.945892	+	0.945892i
$555$		0			0
$556$	−0.105999	−	0.183595i	−0.00449535	−	0.00778617i
$557$	7.89194	−	29.4531i	0.334392	−	1.24797i	−0.570134	−	0.821551i	$-0.693109\pi$
$557$	7.89194	−	29.4531i	0.334392	−	1.24797i	0.904527	−	0.426417i	$-0.140224\pi$
$558$		0			0
$559$	23.2734	+	5.24141i	0.984358	+	0.221688i
$560$	7.80048	−	7.37222i	0.329630	−	0.311533i
$561$		0			0
$562$	−5.71107			−0.240907
$563$	32.2270			1.35821			0.679104	−	0.734042i	$-0.262369\pi$
$563$	32.2270			1.35821			0.679104	+	0.734042i	$0.262369\pi$
$564$		0			0
$565$	34.7314	−	9.30625i	1.46116	−	0.391517i
$566$	−40.9320	−	10.9677i	−1.72050	−	0.461006i
$567$		0			0
$568$	−8.46038	−	14.6538i	−0.354989	−	0.614860i
$569$		−	8.01324i		−	0.335932i	−0.985793	−	0.167966i	$-0.946280\pi$
$569$		−	8.01324i		−	0.335932i	0.985793	−	0.167966i	$-0.0537199\pi$
$570$		0			0
$571$	20.5058	+	11.8390i	0.858139	+	0.495447i	0.863389	−	0.504539i	$-0.168338\pi$
$571$	20.5058	+	11.8390i	0.858139	+	0.495447i	−0.00524963	+	0.999986i	$0.501671\pi$
$572$	4.09975	+	6.48313i	0.171419	+	0.271073i
$573$		0			0
$574$	−13.1617	+	7.11150i	−0.549357	+	0.296828i
$575$	12.5240	−	21.6922i	0.522286	−	0.904626i
$576$		0			0
$577$	41.4172	−	11.0977i	1.72422	−	0.462004i	0.745382	−	0.666638i	$-0.232267\pi$
$577$	41.4172	−	11.0977i	1.72422	−	0.462004i	0.978839	+	0.204634i	$0.0656004\pi$
$578$	−10.1300	+	10.1300i	−0.421354	+	0.421354i
$579$		0			0
$580$	34.7526	−	34.7526i	1.44302	−	1.44302i
$581$	−9.02625	−	37.9375i	−0.374472	−	1.57391i
$582$		0			0
$583$	3.48057	+	3.48057i	0.144151	+	0.144151i
$584$	6.37492	−	11.0417i	0.263796	−	0.456908i
$585$		0			0
$586$	−0.121616	+	0.0702151i	−0.00502392	+	0.00290056i
$587$	31.0661	−	8.32414i	1.28224	−	0.343574i	0.447530	−	0.894269i	$-0.352304\pi$
$587$	31.0661	−	8.32414i	1.28224	−	0.343574i	0.834707	+	0.550695i	$0.185637\pi$
$588$		0			0
$589$	14.3129	−	8.26355i	0.589752	−	0.340494i
$590$	−21.4111	−	5.73708i	−0.881480	−	0.236192i
$591$		0			0
$592$	−9.32716	−	9.32716i	−0.383344	−	0.383344i
$593$	−33.1918	−	8.89371i	−1.36302	−	0.365221i	−0.498097	−	0.867121i	$-0.665968\pi$
$593$	−33.1918	−	8.89371i	−1.36302	−	0.365221i	−0.864926	+	0.501900i	$0.832634\pi$
$594$		0			0
$595$	−18.9297	+	17.8905i	−0.776043	+	0.733438i
$596$	3.50180	−	0.938303i	0.143439	−	0.0384344i
$597$		0			0
$598$	−1.92083	−	47.6560i	−0.0785486	−	1.94880i
$599$	2.36262	−	4.09217i	0.0965339	−	0.167202i	−0.813714	−	0.581266i	$-0.802558\pi$
$599$	2.36262	−	4.09217i	0.0965339	−	0.167202i	0.910248	+	0.414064i	$0.135891\pi$
$600$		0			0
$601$	2.81859	+	1.62731i	0.114973	+	0.0663794i	0.556383	−	0.830926i	$-0.312189\pi$
$601$	2.81859	+	1.62731i	0.114973	+	0.0663794i	−0.441411	+	0.897305i	$0.645522\pi$
$602$	−28.2024	+	26.6540i	−1.14944	+	1.08634i
$603$		0			0
$604$	0.559662	+	2.08869i	0.0227723	+	0.0849875i
$605$	22.4458	−	22.4458i	0.912551	−	0.912551i
$606$		0			0
$607$	−13.6571	−	7.88495i	−0.554326	−	0.320040i	0.196539	−	0.980496i	$-0.437030\pi$
$607$	−13.6571	−	7.88495i	−0.554326	−	0.320040i	−0.750865	+	0.660456i	$0.770363\pi$
$608$	14.0168	−	24.2778i	0.568457	−	0.984596i
$609$		0			0
$610$		−	48.9332i		−	1.98125i
$611$	−3.38181	−	5.34781i	−0.136813	−	0.216349i
$612$		0			0
$613$	−12.8002	−	3.42979i	−0.516993	−	0.138528i	−0.00911789	−	0.999958i	$-0.502902\pi$
$613$	−12.8002	−	3.42979i	−0.516993	−	0.138528i	−0.507876	+	0.861430i	$0.669569\pi$
$614$			12.9177i			0.521314i
$615$		0			0
$616$	−3.91121	−	0.110396i	−0.157587	−	0.00444797i
$617$	36.8780	+	9.88144i	1.48465	+	0.397812i	0.907928	−	0.419126i	$-0.137663\pi$
$617$	36.8780	+	9.88144i	1.48465	+	0.397812i	0.576726	+	0.816938i	$0.304330\pi$
$618$		0			0
$619$	4.73495	+	17.6711i	0.190314	+	0.710261i	0.993430	+	0.114439i	$0.0365070\pi$
$619$	4.73495	+	17.6711i	0.190314	+	0.710261i	−0.803117	+	0.595822i	$0.796826\pi$
$620$	−36.5504			−1.46790
$621$		0			0
$622$	2.99175	+	11.1653i	0.119958	+	0.447690i
$623$	24.1170	−	5.73802i	0.966226	−	0.229889i
$624$		0			0
$625$	−14.1844	−	24.5682i	−0.567377	−	0.982726i
$626$	−9.75809	+	36.4177i	−0.390012	+	1.45554i
$627$		0			0
$628$	−13.1606	+	22.7948i	−0.525163	+	0.909610i
$629$	22.6346	+	22.6346i	0.902501	+	0.902501i
$630$		0			0
$631$	8.97429	−	33.4925i	0.357261	−	1.33332i	−0.520354	−	0.853950i	$-0.674200\pi$
$631$	8.97429	−	33.4925i	0.357261	−	1.33332i	0.877615	−	0.479366i	$-0.159133\pi$
$632$	8.25659	−	30.8140i	0.328430	−	1.22572i
$633$		0			0
$634$	−7.59722	+	4.38626i	−0.301724	+	0.174201i
$635$	−9.69271	+	9.69271i	−0.384644	+	0.384644i
$636$		0			0
$637$	6.92519	−	24.2702i	0.274386	−	0.961620i
$638$	9.00199			0.356392
$639$		0			0
$640$	−38.1161	+	22.0063i	−1.50667	+	0.869877i
$641$			15.7583i			0.622414i	0.950342	+	0.311207i	$0.100733\pi$
$641$			15.7583i			0.622414i	−0.950342	+	0.311207i	$0.899267\pi$
$642$		0			0
$643$	−7.83090	+	29.2253i	−0.308821	+	1.15253i	0.620786	+	0.783980i	$0.286814\pi$
$643$	−7.83090	+	29.2253i	−0.308821	+	1.15253i	−0.929606	+	0.368554i	$0.879853\pi$
$644$	39.1754	+	24.1167i	1.54373	+	0.950330i
$645$		0			0
$646$	−14.3755	+	24.8992i	−0.565598	+	0.979645i
$647$	−22.4737	−	38.9255i	−0.883531	−	1.53032i	−0.847388	−	0.530974i	$-0.821826\pi$
$647$	−22.4737	−	38.9255i	−0.883531	−	1.53032i	−0.0361431	−	0.999347i	$-0.511507\pi$
$648$		0			0
$649$	−1.20376	−	2.08497i	−0.0472515	−	0.0818421i
$650$	29.7047	+	15.5900i	1.16511	+	0.611488i
$651$		0			0
$652$	1.72058	+	6.42131i	0.0673833	+	0.251478i
$653$	4.80782			0.188145			0.0940723	−	0.995565i	$-0.470012\pi$
$653$	4.80782			0.188145			0.0940723	+	0.995565i	$0.470012\pi$
$654$		0			0
$655$	9.95343	+	37.1467i	0.388913	+	1.45144i
$656$	−3.29580	+	0.883107i	−0.128679	+	0.0344796i
$657$		0			0
$658$	10.2881	+	0.290386i	0.401071	+	0.0113204i
$659$	1.29400	+	2.24128i	0.0504072	+	0.0873078i	0.890128	−	0.455710i	$-0.150615\pi$
$659$	1.29400	+	2.24128i	0.0504072	+	0.0873078i	−0.839721	+	0.543018i	$0.817281\pi$
$660$		0			0
$661$	−1.14316	−	0.306308i	−0.0444637	−	0.0119140i	0.236519	−	0.971627i	$-0.423994\pi$
$661$	−1.14316	−	0.306308i	−0.0444637	−	0.0119140i	−0.280982	+	0.959713i	$0.590660\pi$
$662$	−25.7395	−	14.8607i	−1.00039	−	0.577577i
$663$		0			0
$664$			29.8538i			1.15855i
$665$	16.8071	−	27.3017i	0.651753	−	1.05871i
$666$		0			0
$667$	−28.7438	−	16.5953i	−1.11297	−	0.642571i
$668$	7.93786	−	2.12694i	0.307125	−	0.0822939i
$669$		0			0
$670$	11.3039	+	42.1867i	0.436707	+	1.62981i
$671$	3.75805	−	3.75805i	0.145078	−	0.145078i
$672$		0			0
$673$	28.3877	+	16.3896i	1.09426	+	0.631774i	0.934709	−	0.355415i	$-0.115660\pi$
$673$	28.3877	+	16.3896i	1.09426	+	0.631774i	0.159556	+	0.987189i	$0.448994\pi$
$674$	−23.9039	−	23.9039i	−0.920744	−	0.920744i
$675$		0			0
$676$	37.7556	−	3.04852i	1.45214	−	0.117251i
$677$	−6.57450	+	3.79579i	−0.252678	+	0.145884i	−0.620990	−	0.783818i	$-0.713269\pi$
$677$	−6.57450	+	3.79579i	−0.252678	+	0.145884i	0.368312	+	0.929702i	$0.379936\pi$
$678$		0			0
$679$	17.6500	−	16.6810i	0.677345	−	0.640158i
$680$	17.2683	−	9.96984i	0.662208	−	0.382326i
$681$		0			0
$682$	−4.73383	−	4.73383i	−0.181268	−	0.181268i
$683$	−16.7687	−	16.7687i	−0.641635	−	0.641635i	0.309322	−	0.950957i	$-0.399898\pi$
$683$	−16.7687	−	16.7687i	−0.641635	−	0.641635i	−0.950957	+	0.309322i	$0.899898\pi$
$684$		0			0
$685$	26.6289	−	15.3742i	1.01744	−	0.587418i
$686$	26.4709	+	31.3799i	1.01066	+	1.19809i
$687$		0			0
$688$	−7.66480	+	4.42528i	−0.292218	+	0.168712i
$689$	23.2060	−	7.23149i	0.884080	−	0.275498i
$690$		0			0
$691$	2.45150	+	2.45150i	0.0932596	+	0.0932596i	0.752197	−	0.658938i	$-0.228994\pi$
$691$	2.45150	+	2.45150i	0.0932596	+	0.0932596i	−0.658938	+	0.752197i	$0.728994\pi$
$692$	−11.7070	−	6.75903i	−0.445033	−	0.256940i
$693$		0			0
$694$	−15.3487	+	15.3487i	−0.582630	+	0.582630i
$695$	−0.0571097	−	0.213136i	−0.00216630	−	0.00808473i
$696$		0			0
$697$	7.99806	−	2.14307i	0.302948	−	0.0811747i
$698$	−8.64521	−	4.99131i	−0.327226	−	0.188924i
$699$		0			0
$700$	−28.4679	+	15.3818i	−1.07599	+	0.581376i
$701$			40.4604i			1.52817i	0.645116	+	0.764085i	$0.276809\pi$
$701$			40.4604i			1.52817i	−0.645116	+	0.764085i	$0.723191\pi$
$702$		0			0
$703$	−34.1226	−	19.7007i	−1.28696	−	0.743026i
$704$	−9.08187	−	2.43348i	−0.342286	−	0.0917153i
$705$		0			0
$706$	18.7808	+	32.5294i	0.706826	+	1.22426i
$707$	−0.912077	+	32.3140i	−0.0343022	+	1.21529i
$708$		0			0
$709$	37.1048	−	9.94221i	1.39350	−	0.373388i	0.517495	−	0.855686i	$-0.326865\pi$
$709$	37.1048	−	9.94221i	1.39350	−	0.373388i	0.876007	+	0.482299i	$0.160198\pi$
$710$	−14.5355	−	54.2473i	−0.545508	−	2.03587i
$711$		0			0
$712$	−18.9782			−0.711237
$713$	6.38851	+	23.8422i	0.239252	+	0.892899i
$714$		0			0
$715$	2.37530	+	7.62239i	0.0888310	+	0.285061i
$716$	20.5219	+	35.5449i	0.766938	+	1.32837i
$717$		0			0
$718$	−17.6707	−	30.6065i	−0.659464	−	1.14223i
$719$	21.3049	−	36.9012i	0.794540	−	1.37618i	−0.128591	−	0.991698i	$-0.541045\pi$
$719$	21.3049	−	36.9012i	0.794540	−	1.37618i	0.923131	−	0.384486i	$-0.125621\pi$
$720$		0			0
$721$	−0.0519072	+	1.83902i	−0.00193313	+	0.0684887i
$722$	−1.74118	+	6.49816i	−0.0647999	+	0.241836i
$723$		0			0
$724$			56.2974i			2.09227i
$725$	20.2177	−	11.6727i	0.750865	−	0.433512i
$726$		0			0
$727$	−23.6095			−0.875628			−0.437814	−	0.899066i	$-0.644247\pi$
$727$	−23.6095			−0.875628			−0.437814	+	0.899066i	$0.644247\pi$
$728$	−9.45821	+	16.8484i	−0.350545	+	0.624442i
$729$		0			0
$730$	29.9230	−	29.9230i	1.10750	−	1.10750i
$731$	18.6005	−	10.7390i	0.687964	−	0.397196i
$732$		0			0
$733$	−6.59668	+	24.6192i	−0.243654	+	0.909329i	0.730401	+	0.683018i	$0.239333\pi$
$733$	−6.59668	+	24.6192i	−0.243654	+	0.909329i	−0.974055	+	0.226311i	$0.927334\pi$
$734$	−13.7731	+	51.4019i	−0.508374	+	1.89728i
$735$		0			0
$736$	29.6054	+	29.6054i	1.09127	+	1.09127i
$737$	−2.37178	+	4.10805i	−0.0873658	+	0.151322i
$738$		0			0
$739$	7.03335	−	26.2488i	0.258726	−	0.965579i	−0.707253	−	0.706960i	$-0.750066\pi$
$739$	7.03335	−	26.2488i	0.258726	−	0.965579i	0.965979	−	0.258619i	$-0.0832673\pi$
$740$	43.5689	+	75.4636i	1.60163	+	2.77410i
$741$		0			0
$742$	−11.3065	+	37.8863i	−0.415074	+	1.39085i
$743$	7.41429	+	27.6705i	0.272004	+	1.01513i	0.957823	+	0.287360i	$0.0927777\pi$
$743$	7.41429	+	27.6705i	0.272004	+	1.01513i	−0.685818	+	0.727773i	$0.740556\pi$
$744$		0			0
$745$	3.77338			0.138246
$746$	−8.23182	−	30.7216i	−0.301388	−	1.12480i
$747$		0			0
$748$	6.67064	+	1.78739i	0.243903	+	0.0653535i
$749$	31.0866	+	19.1372i	1.13588	+	0.699257i
$750$		0			0
$751$			19.8037i			0.722648i	0.932440	+	0.361324i	$0.117675\pi$
$751$			19.8037i			0.722648i	−0.932440	+	0.361324i	$0.882325\pi$
$752$	2.26744	+	0.607558i	0.0826849	+	0.0221554i
$753$		0			0
$754$	20.6579	−	39.3611i	0.752317	−	1.43345i
$755$			2.25068i			0.0819105i
$756$		0			0
$757$	16.3218	−	28.2703i	0.593228	−	1.02750i	−0.400567	−	0.916268i	$-0.631187\pi$
$757$	16.3218	−	28.2703i	0.593228	−	1.02750i	0.993794	−	0.111233i	$-0.0354799\pi$
$758$	−16.2320	−	9.37155i	−0.589573	−	0.340390i
$759$		0			0
$760$	−17.3551	+	17.3551i	−0.629535	+	0.629535i
$761$	6.44626	+	24.0578i	0.233677	+	0.872094i	0.978741	+	0.205101i	$0.0657522\pi$
$761$	6.44626	+	24.0578i	0.233677	+	0.872094i	−0.745064	+	0.666993i	$0.767581\pi$
$762$		0			0
$763$	9.91894	−	33.2369i	0.359090	−	1.20326i
$764$	−19.4123	−	11.2077i	−0.702312	−	0.405480i
$765$		0			0
$766$	−21.7705	+	37.7077i	−0.786601	+	1.36243i
$767$	−11.8789	+	0.478793i	−0.428922	+	0.0172882i
$768$		0			0
$769$	−52.0116	+	13.9365i	−1.87559	+	0.502562i	−0.875783	+	0.482705i	$0.839654\pi$
$769$	−52.0116	+	13.9365i	−1.87559	+	0.502562i	−0.999803	+	0.0198562i	$0.993679\pi$
$770$	−12.4444	−	3.71379i	−0.448463	−	0.133836i
$771$		0			0
$772$	−22.5962	−	6.05463i	−0.813254	−	0.217911i
$773$	−23.3186	−	23.3186i	−0.838711	−	0.838711i	0.149979	−	0.988689i	$-0.452080\pi$
$773$	−23.3186	−	23.3186i	−0.838711	−	0.838711i	−0.988689	+	0.149979i	$0.952080\pi$
$774$		0			0
$775$	−16.7700	−	4.49352i	−0.602397	−	0.161412i
$776$	−16.1009	+	9.29584i	−0.577987	+	0.333701i
$777$		0			0
$778$	12.0699	−	3.23412i	0.432727	−	0.115949i
$779$	−8.82663	+	5.09606i	−0.316247	+	0.182585i
$780$		0			0
$781$	3.04985	−	5.28249i	0.109132	−	0.189022i
$782$	−30.3631	−	30.3631i	−1.08578	−	1.08578i
$783$		0			0
$784$	4.21689	+	8.36018i	0.150603	+	0.298578i
$785$	−19.3719	+	19.3719i	−0.691413	+	0.691413i
$786$		0			0
$787$	1.78895	−	1.78895i	0.0637690	−	0.0637690i	−0.674503	−	0.738272i	$-0.735642\pi$
$787$	1.78895	−	1.78895i	0.0637690	−	0.0637690i	0.738272	+	0.674503i	$0.235642\pi$
$788$	16.5937	−	4.44627i	0.591126	−	0.158392i
$789$		0			0
$790$	52.9406	−	91.6959i	1.88354	−	3.26239i
$791$	−0.885042	+	31.3561i	−0.0314685	+	1.11490i
$792$		0			0
$793$	−7.80799	−	25.0561i	−0.277270	−	0.889767i
$794$	−26.0857	−	15.0606i	−0.925746	−	0.534480i
$795$		0			0
$796$		−	25.4670i		−	0.902655i
$797$	15.5118	+	26.8672i	0.549456	+	0.951686i	0.998312	+	0.0580819i	$0.0184985\pi$
$797$	15.5118	+	26.8672i	0.549456	+	0.951686i	−0.448855	+	0.893604i	$0.648168\pi$
$798$		0			0
$799$	−5.50248	−	1.47439i	−0.194664	−	0.0521600i
$800$	−28.4457	+	7.62199i	−1.00571	+	0.269478i
$801$		0			0
$802$	−17.4653			−0.616722
$803$	4.59614			0.162194
$804$		0			0
$805$	32.8891	+	34.7996i	1.15919	+	1.22653i
$806$	−31.5619	+	9.83535i	−1.11172	+	0.346435i
$807$		0			0
$808$	6.40521	−	23.9046i	0.225335	−	0.840960i
$809$	1.72648	+	2.99036i	0.0607000	+	0.105135i	0.894778	−	0.446510i	$-0.147333\pi$
$809$	1.72648	+	2.99036i	0.0607000	+	0.105135i	−0.834079	+	0.551646i	$0.814000\pi$
$810$		0			0
$811$	27.5137	+	27.5137i	0.966135	+	0.966135i	0.999445	−	0.0333099i	$-0.0106048\pi$
$811$	27.5137	+	27.5137i	0.966135	+	0.966135i	−0.0333099	+	0.999445i	$0.510605\pi$
$812$	20.3821	+	37.7222i	0.715270	+	1.32379i
$813$		0			0
$814$	−4.13084	+	15.4165i	−0.144786	+	0.540349i
$815$			6.91931i			0.242373i
$816$		0			0
$817$	−18.6940	+	18.6940i	−0.654020	+	0.654020i
$818$	8.40504			0.293875
$819$		0			0
$820$	22.5403			0.787141
$821$	12.7874	−	12.7874i	0.446284	−	0.446284i	−0.447833	−	0.894117i	$-0.647804\pi$
$821$	12.7874	−	12.7874i	0.446284	−	0.446284i	0.894117	+	0.447833i	$0.147804\pi$
$822$		0			0
$823$		−	51.6586i		−	1.80071i	−0.435159	−	0.900353i	$-0.643308\pi$
$823$		−	51.6586i		−	1.80071i	0.435159	−	0.900353i	$-0.356692\pi$
$824$	0.364527	−	1.36043i	0.0126989	−	0.0473929i
$825$		0			0
$826$	10.1377	−	16.4677i	0.352734	−	0.572985i
$827$	−34.2663	−	34.2663i	−1.19156	−	1.19156i	−0.976630	−	0.214927i	$-0.931049\pi$
$827$	−34.2663	−	34.2663i	−1.19156	−	1.19156i	−0.214927	−	0.976630i	$-0.568951\pi$
$828$		0			0
$829$	−7.28433	−	12.6168i	−0.252995	−	0.438201i	0.711354	−	0.702834i	$-0.248082\pi$
$829$	−7.28433	−	12.6168i	−0.252995	−	0.438201i	−0.964349	+	0.264633i	$0.914749\pi$
$830$	−25.6455	+	95.7102i	−0.890167	+	3.32215i
$831$		0			0
$832$	−31.4816	+	34.1260i	−1.09143	+	1.18311i
$833$	−10.2333	−	20.2880i	−0.354563	−	0.702937i
$834$		0			0
$835$	8.55348			0.296005
$836$	−8.50055			−0.293998
$837$		0			0
$838$	7.59572	−	2.03527i	0.262390	−	0.0703072i
$839$	−46.6633	−	12.5034i	−1.61100	−	0.431665i	−0.662658	−	0.748922i	$-0.730572\pi$
$839$	−46.6633	−	12.5034i	−1.61100	−	0.431665i	−0.948340	+	0.317257i	$0.897238\pi$
$840$		0			0
$841$	−0.967215	−	1.67527i	−0.0333522	−	0.0577678i
$842$			66.1993i			2.28138i
$843$		0			0
$844$	50.9006	+	29.3875i	1.75207	+	1.01156i
$845$	38.7797	+	7.10604i	1.33406	+	0.244455i
$846$		0			0
$847$	13.1642	+	24.3638i	0.452328	+	0.837149i
$848$	−4.50882	+	7.80951i	−0.154834	+	0.268180i
$849$		0			0
$850$	29.1737	−	7.81707i	1.00065	−	0.268123i
$851$	41.6105	−	41.6105i	1.42639	−	1.42639i
$852$		0			0
$853$	−36.7362	+	36.7362i	−1.25783	+	1.25783i	−0.305696	+	0.952129i	$0.598889\pi$
$853$	−36.7362	+	36.7362i	−1.25783	+	1.25783i	−0.952129	+	0.305696i	$0.901111\pi$
$854$	40.9067	+	12.2079i	1.39980	+	0.417744i
$855$		0			0
$856$	−19.7611	−	19.7611i	−0.675420	−	0.675420i
$857$	3.64891	−	6.32009i	0.124644	−	0.215890i	−0.796950	−	0.604046i	$-0.793554\pi$
$857$	3.64891	−	6.32009i	0.124644	−	0.215890i	0.921594	+	0.388156i	$0.126888\pi$
$858$		0			0
$859$	35.5603	−	20.5307i	1.21330	−	0.700500i	0.249825	−	0.968291i	$-0.419627\pi$
$859$	35.5603	−	20.5307i	1.21330	−	0.700500i	0.963477	+	0.267791i	$0.0862937\pi$
$860$	56.4750	−	15.1324i	1.92578	−	0.516012i
$861$		0			0
$862$	−30.9628	+	17.8764i	−1.05460	+	0.608872i
$863$	52.4930	+	14.0655i	1.78688	+	0.478794i	0.991810	−	0.127720i	$-0.0407660\pi$
$863$	52.4930	+	14.0655i	1.78688	+	0.478794i	0.795073	+	0.606514i	$0.207433\pi$
$864$		0			0
$865$	−9.94907	−	9.94907i	−0.338278	−	0.338278i
$866$	64.1468	+	17.1881i	2.17980	+	0.584075i
$867$		0			0
$868$	9.11859	−	30.5550i	0.309505	−	1.03711i
$869$	11.1080	−	2.97639i	0.376814	−	0.100967i
$870$		0			0
$871$	12.5196	+	19.7978i	0.424210	+	0.670824i
$872$	−13.2767	+	22.9960i	−0.449606	+	0.778741i
$873$		0			0
$874$	45.7736	+	26.4274i	1.54832	+	0.893920i
$875$	6.26511	−	1.49062i	0.211799	−	0.0503922i
$876$		0			0
$877$	11.0381	+	41.1947i	0.372729	+	1.39105i	0.856634	+	0.515925i	$0.172552\pi$
$877$	11.0381	+	41.1947i	0.372729	+	1.39105i	−0.483905	+	0.875121i	$0.660782\pi$
$878$	7.08357	−	7.08357i	0.239059	−	0.239059i
$879$		0			0
$880$	−2.56516	−	1.48099i	−0.0864714	−	0.0499243i
$881$	−13.6175	+	23.5863i	−0.458786	+	0.794641i	−0.998897	−	0.0469528i	$-0.985049\pi$
$881$	−13.6175	+	23.5863i	−0.458786	+	0.794641i	0.540111	+	0.841594i	$0.318382\pi$
$882$		0			0
$883$			21.3903i			0.719842i	0.932983	+	0.359921i	$0.117196\pi$
$883$			21.3903i			0.719842i	−0.932983	+	0.359921i	$0.882804\pi$
$884$	23.1232	−	25.0655i	0.777719	−	0.843046i
$885$		0			0
$886$	−72.2133	−	19.3495i	−2.42605	−	0.650059i
$887$		−	15.8366i		−	0.531741i	−0.964009	−	0.265871i	$-0.914341\pi$
$887$		−	15.8366i		−	0.531741i	0.964009	−	0.265871i	$-0.0856594\pi$
$888$		0			0
$889$	−5.68468	−	10.5210i	−0.190658	−	0.352861i
$890$	−60.8433	−	16.3029i	−2.03947	−	0.546475i
$891$		0			0
$892$	−9.96864	−	37.2035i	−0.333775	−	1.24566i
$893$	7.01194			0.234646
$894$		0			0
$895$	11.0567	+	41.2642i	0.369585	+	1.37931i
$896$	−8.88743	−	37.3540i	−0.296908	−	1.24791i
$897$		0			0
$898$	−4.28190	−	7.41646i	−0.142889	−	0.247491i
$899$	−5.95426	+	22.2216i	−0.198586	+	0.741132i
$900$		0			0
$901$	10.9417	−	18.9517i	0.364523	−	0.631371i
$902$	2.91931	+	2.91931i	0.0972024	+	0.0972024i
$903$		0			0
$904$	6.21535	−	23.1960i	0.206720	−	0.771488i
$905$	−15.1659	+	56.5998i	−0.504131	+	1.88144i
$906$		0			0
$907$	−22.5733	+	13.0327i	−0.749533	+	0.432743i	−0.825525	−	0.564365i	$-0.809121\pi$
$907$	−22.5733	+	13.0327i	−0.749533	+	0.432743i	0.0759921	+	0.997108i	$0.475788\pi$
$908$	−15.6972	+	15.6972i	−0.520929	+	0.520929i
$909$		0			0
$910$	−44.7960	+	45.8903i	−1.48497	+	1.52125i
$911$	45.9225			1.52148			0.760739	−	0.649057i	$-0.224837\pi$
$911$	45.9225			1.52148			0.760739	+	0.649057i	$0.224837\pi$
$912$		0			0
$913$	−9.32006	+	5.38094i	−0.308449	+	0.178083i
$914$		−	1.15169i		−	0.0380946i
$915$		0			0
$916$	−22.0539	+	82.3063i	−0.728682	+	2.71948i
$917$	−33.5367	−	0.946590i	−1.10748	−	0.0312591i
$918$		0			0
$919$	−1.32248	+	2.29060i	−0.0436245	+	0.0755598i	−0.887013	−	0.461744i	$-0.847224\pi$
$919$	−1.32248	+	2.29060i	−0.0436245	+	0.0755598i	0.843389	+	0.537304i	$0.180557\pi$
$920$	−18.3281	−	31.7453i	−0.604261	−	1.04661i
$921$		0			0
$922$	32.4510	+	56.2068i	1.06872	+	1.85107i
$923$	−16.0988	−	25.4578i	−0.529898	−	0.837953i
$924$		0			0
$925$	10.7128	+	39.9805i	0.352233	+	1.31455i
$926$	47.2304			1.55209
$927$		0			0
$928$	10.0997	+	37.6927i	0.331540	+	1.23732i
$929$	15.8375	−	4.24365i	0.519612	−	0.139230i	0.0105250	−	0.999945i	$-0.496650\pi$
$929$	15.8375	−	4.24365i	0.519612	−	0.139230i	0.509087	+	0.860715i	$0.329983\pi$
$930$		0			0
$931$	18.6303	+	20.8615i	0.610585	+	0.683707i
$932$	−1.32333	−	2.29208i	−0.0433472	−	0.0750795i
$933$		0			0
$934$	−9.17139	−	2.45747i	−0.300097	−	0.0804108i
$935$	6.22497	+	3.59399i	0.203578	+	0.117536i
$936$		0			0
$937$		−	17.9634i		−	0.586840i	−0.955984	−	0.293420i	$-0.905207\pi$
$937$		−	17.9634i		−	0.586840i	0.955984	−	0.293420i	$-0.0947934\pi$
$938$	−38.0869	−	1.07502i	−1.24358	−	0.0351006i
$939$		0			0
$940$	−13.4296	−	7.75361i	−0.438027	−	0.252895i
$941$	−50.6367	+	13.5681i	−1.65071	+	0.442307i	−0.959812	−	0.280645i	$-0.909452\pi$
$941$	−50.6367	+	13.5681i	−1.65071	+	0.442307i	−0.690899	+	0.722952i	$0.742785\pi$
$942$		0			0
$943$	−3.93974	−	14.7033i	−0.128295	−	0.478805i
$944$	3.11875	−	3.11875i	0.101507	−	0.101507i
$945$		0			0
$946$	9.27425	+	5.35449i	0.301532	+	0.174090i
$947$	−6.25266	−	6.25266i	−0.203184	−	0.203184i	0.598179	−	0.801363i	$-0.295891\pi$
$947$	−6.25266	−	6.25266i	−0.203184	−	0.203184i	−0.801363	+	0.598179i	$0.795891\pi$
$948$		0			0
$949$	10.5473	−	20.0966i	0.342380	−	0.652363i
$950$	−32.1960	+	18.5884i	−1.04458	+	0.603086i
$951$		0			0
$952$	4.02640	+	16.9230i	0.130496	+	0.548478i
$953$	21.4513	−	12.3849i	0.694877	−	0.401188i	−0.110559	−	0.993870i	$-0.535264\pi$
$953$	21.4513	−	12.3849i	0.694877	−	0.401188i	0.805437	+	0.592682i	$0.201931\pi$
$954$		0			0
$955$	−16.4974	−	16.4974i	−0.533842	−	0.533842i
$956$	20.5561	+	20.5561i	0.664832	+	0.664832i
$957$		0			0
$958$	−21.5938	+	12.4672i	−0.697664	+	0.402797i
$959$	6.20900	+	26.0965i	0.200499	+	0.842701i
$960$		0			0
$961$	−12.0301	+	6.94557i	−0.388067	+	0.224051i
$962$	57.9290	+	53.4402i	1.86771	+	1.72298i
$963$		0			0
$964$	−14.8738	−	14.8738i	−0.479052	−	0.479052i
$965$	−21.0865	−	12.1743i	−0.678799	−	0.391905i
$966$		0			0
$967$	0.370336	−	0.370336i	0.0119092	−	0.0119092i	−0.701127	−	0.713036i	$-0.747319\pi$
$967$	0.370336	−	0.370336i	0.0119092	−	0.0119092i	0.713036	+	0.701127i	$0.247319\pi$
$968$	−5.48702	−	20.4778i	−0.176360	−	0.658183i
$969$		0			0
$970$	−59.6042	+	15.9709i	−1.91378	+	0.512795i
$971$	−28.8662	−	16.6659i	−0.926359	−	0.534834i	−0.0407007	−	0.999171i	$-0.512959\pi$
$971$	−28.8662	−	16.6659i	−0.926359	−	0.534834i	−0.885658	+	0.464338i	$0.846292\pi$
$972$		0			0
$973$	0.192423	+	0.00543124i	0.00616881	+	0.000174118i
$974$		−	15.5857i		−	0.499398i
$975$		0			0
$976$	8.43210	+	4.86828i	0.269905	+	0.155830i
$977$	−30.7510	−	8.23970i	−0.983811	−	0.263611i	−0.269162	−	0.963095i	$-0.586747\pi$
$977$	−30.7510	−	8.23970i	−0.983811	−	0.263611i	−0.714649	+	0.699484i	$0.753413\pi$
$978$		0			0
$979$	−3.42068	−	5.92479i	−0.109325	−	0.189357i
$980$	−12.6138	−	60.5559i	−0.402933	−	1.93439i
$981$		0			0
$982$	0.850011	−	0.227760i	0.0271250	−	0.00726811i
$983$	−12.7899	−	47.7326i	−0.407935	−	1.52243i	−0.798577	−	0.601892i	$-0.794414\pi$
$983$	−12.7899	−	47.7326i	−0.407935	−	1.52243i	0.390642	−	0.920543i	$-0.372253\pi$
$984$		0			0
$985$	17.8806			0.569724
$986$	−10.3582	−	38.6574i	−0.329873	−	1.23110i
$987$		0			0
$988$	−19.5072	+	37.1686i	−0.620607	+	1.18249i
$989$	−19.7421	−	34.1944i	−0.627763	−	1.08732i
$990$		0			0
$991$	−21.3389	−	36.9601i	−0.677853	−	1.17408i	−0.975626	−	0.219439i	$-0.929577\pi$
$991$	−21.3389	−	36.9601i	−0.677853	−	1.17408i	0.297774	−	0.954637i	$-0.403756\pi$
$992$	14.5102	−	25.1324i	0.460699	−	0.797955i
$993$		0			0
$994$	48.9754	+	1.38235i	1.55341	+	0.0438456i
$995$	6.86053	−	25.6038i	0.217493	−	0.811696i
$996$		0			0
$997$		−	5.47320i		−	0.173338i	−0.996237	−	0.0866689i	$-0.972378\pi$
$997$		−	5.47320i		−	0.173338i	0.996237	−	0.0866689i	$-0.0276222\pi$
$998$	3.79644	−	2.19188i	0.120174	−	0.0693826i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.b.136.7		28
3.2	odd	2		91.2.ba.a.45.1	yes	28
7.5	odd	6		819.2.gh.b.19.1		28
13.11	odd	12		819.2.gh.b.388.1		28
21.2	odd	6		637.2.x.a.19.7		28
21.5	even	6		91.2.w.a.19.7	✓	28
21.11	odd	6		637.2.bd.b.97.1		28
21.17	even	6		637.2.bd.a.97.1		28
21.20	even	2		637.2.bb.a.227.1		28
39.11	even	12		91.2.w.a.24.7	yes	28
91.89	even	12	inner	819.2.et.b.271.7		28
273.11	even	12		637.2.bd.a.440.1		28
273.89	odd	12		91.2.ba.a.89.1	yes	28
273.128	even	12		637.2.bb.a.362.1		28
273.167	odd	12		637.2.x.a.570.7		28
273.206	odd	12		637.2.bd.b.440.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.7	✓	28	21.5	even	6
91.2.w.a.24.7	yes	28	39.11	even	12
91.2.ba.a.45.1	yes	28	3.2	odd	2
91.2.ba.a.89.1	yes	28	273.89	odd	12
637.2.x.a.19.7		28	21.2	odd	6
637.2.x.a.570.7		28	273.167	odd	12
637.2.bb.a.227.1		28	21.20	even	2
637.2.bb.a.362.1		28	273.128	even	12
637.2.bd.a.97.1		28	21.17	even	6
637.2.bd.a.440.1		28	273.11	even	12
637.2.bd.b.97.1		28	21.11	odd	6
637.2.bd.b.440.1		28	273.206	odd	12
819.2.et.b.136.7		28	1.1	even	1	trivial
819.2.et.b.271.7		28	91.89	even	12	inner
819.2.gh.b.19.1		28	7.5	odd	6
819.2.gh.b.388.1		28	13.11	odd	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.56744 - 1.56744i) q^{2} -2.91373i q^{4} +(0.784926 - 2.92938i) q^{5} +(2.25305 + 1.38700i) q^{7} +(-1.43221 - 1.43221i) q^{8} +O(q^{10})\)	\(q+(1.56744 - 1.56744i) q^{2} -2.91373i q^{4} +(0.784926 - 2.92938i) q^{5} +(2.25305 + 1.38700i) q^{7} +(-1.43221 - 1.43221i) q^{8} +(-3.36131 - 5.82195i) q^{10} +(0.188977 - 0.705270i) q^{11} +(-2.65012 - 2.44476i) q^{13} +(5.70555 - 1.35749i) q^{14} +1.33764 q^{16} -3.24611 q^{17} +(3.85949 - 1.03415i) q^{19} +(-8.53543 - 2.28706i) q^{20} +(-0.809258 - 1.40168i) q^{22} +5.96750i q^{23} +(-3.63505 - 2.09870i) q^{25} +(-7.98592 + 0.321882i) q^{26} +(4.04133 - 6.56478i) q^{28} +(-2.78094 + 4.81672i) q^{29} +(3.99535 - 1.07055i) q^{31} +(4.96110 - 4.96110i) q^{32} +(-5.08807 + 5.08807i) q^{34} +(5.83152 - 5.51136i) q^{35} +(-6.97285 - 6.97285i) q^{37} +(4.42855 - 7.67048i) q^{38} +(-5.31969 + 3.07132i) q^{40} +(-2.46389 + 0.660198i) q^{41} +(-5.73009 + 3.30827i) q^{43} +(-2.05497 - 0.550626i) q^{44} +(9.35370 + 9.35370i) q^{46} +(1.69510 + 0.454201i) q^{47} +(3.15248 + 6.24995i) q^{49} +(-8.98729 + 2.40814i) q^{50} +(-7.12338 + 7.72173i) q^{52} +(-3.37073 + 5.83828i) q^{53} +(-1.91767 - 1.10717i) q^{55} +(-1.24038 - 5.21333i) q^{56} +(3.19097 + 11.9089i) q^{58} +(2.33153 - 2.33153i) q^{59} +(6.30371 + 3.63945i) q^{61} +(4.58444 - 7.94048i) q^{62} -12.8772i q^{64} +(-9.24179 + 5.84425i) q^{65} +(-6.27534 - 1.68147i) q^{67} +9.45827i q^{68} +(0.501828 - 17.7793i) q^{70} +(8.06938 + 2.16218i) q^{71} +(1.62921 + 6.08031i) q^{73} -21.8590 q^{74} +(-3.01323 - 11.2455i) q^{76} +(1.40398 - 1.32690i) q^{77} +(7.87501 + 13.6399i) q^{79} +(1.04995 - 3.91846i) q^{80} +(-2.82718 + 4.89682i) q^{82} +(-10.4223 - 10.4223i) q^{83} +(-2.54795 + 9.50909i) q^{85} +(-3.79606 + 14.1671i) q^{86} +(-1.28075 + 0.739443i) q^{88} +(6.62546 - 6.62546i) q^{89} +(-2.57998 - 9.18388i) q^{91} +17.3877 q^{92} +(3.36890 - 1.94504i) q^{94} -12.1177i q^{95} +(2.37570 - 8.86623i) q^{97} +(14.7377 + 4.85508i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

Introduction

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