LMFDB - Embedded newform 945.2.bv.e.262.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(73,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 9, 2]))

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

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

chi := DirichletCharacter("945.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bv (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			262.20
Character	$\chi$	$=$	945.262
Dual form			945.2.bv.e.523.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0825718 + 0.0825718i) q^{2} -1.98636i q^{4} +(-1.53930 - 1.62190i) q^{5} +(2.61528 - 0.400384i) q^{7} +(0.329161 - 0.329161i) q^{8} +O(q^{10})$	\(q+(0.0825718 + 0.0825718i) q^{2} -1.98636i q^{4} +(-1.53930 - 1.62190i) q^{5} +(2.61528 - 0.400384i) q^{7} +(0.329161 - 0.329161i) q^{8} +(0.00682007 - 0.261026i) q^{10} +(-0.455930 - 0.789693i) q^{11} +(1.53935 - 5.74495i) q^{13} +(0.249009 + 0.182888i) q^{14} -3.91837 q^{16} +(0.884052 + 3.29933i) q^{17} +(-0.815184 - 1.41194i) q^{19} +(-3.22168 + 3.05761i) q^{20} +(0.0275595 - 0.102853i) q^{22} +(0.844982 + 3.15352i) q^{23} +(-0.261101 + 4.99318i) q^{25} +(0.601478 - 0.347264i) q^{26} +(-0.795308 - 5.19490i) q^{28} +(-5.74244 - 3.31540i) q^{29} -1.16339i q^{31} +(-0.981869 - 0.981869i) q^{32} +(-0.199433 + 0.345429i) q^{34} +(-4.67509 - 3.62541i) q^{35} +(-0.935230 + 3.49032i) q^{37} +(0.0492752 - 0.183898i) q^{38} +(-1.04054 - 0.0271873i) q^{40} +(5.95218 - 3.43649i) q^{41} +(-1.11001 - 4.14262i) q^{43} +(-1.56862 + 0.905642i) q^{44} +(-0.190620 + 0.330163i) q^{46} +(-4.13109 + 4.13109i) q^{47} +(6.67939 - 2.09423i) q^{49} +(-0.433855 + 0.390736i) q^{50} +(-11.4116 - 3.05772i) q^{52} +(-3.64349 - 13.5977i) q^{53} +(-0.578988 + 1.95505i) q^{55} +(0.729058 - 0.992640i) q^{56} +(-0.200405 - 0.747922i) q^{58} -4.13313 q^{59} +7.18890i q^{61} +(0.0960635 - 0.0960635i) q^{62} +7.67459i q^{64} +(-11.6873 + 6.34654i) q^{65} +(-10.7674 - 10.7674i) q^{67} +(6.55366 - 1.75605i) q^{68} +(-0.0866741 - 0.685386i) q^{70} -7.48342 q^{71} +(3.70949 - 0.993956i) q^{73} +(-0.365426 + 0.210979i) q^{74} +(-2.80463 + 1.61925i) q^{76} +(-1.50856 - 1.88272i) q^{77} +9.14441i q^{79} +(6.03155 + 6.35519i) q^{80} +(0.775240 + 0.207725i) q^{82} +(10.7518 - 2.88094i) q^{83} +(3.99035 - 6.51250i) q^{85} +(0.250408 - 0.433720i) q^{86} +(-0.410011 - 0.109862i) q^{88} +(1.92701 + 3.33768i) q^{89} +(1.72566 - 15.6410i) q^{91} +(6.26403 - 1.67844i) q^{92} -0.682222 q^{94} +(-1.03521 + 3.49555i) q^{95} +(1.83106 + 6.83360i) q^{97} +(0.724453 + 0.378604i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8}+O(q^{10}) $ 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8	$ 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8} - 24 q^{10} + 16 q^{11} - 152 q^{16} + 6 q^{17} - 60 q^{20} + 8 q^{22} - 8 q^{23} + 2 q^{25} + 36 q^{26} + 22 q^{28} - 12 q^{32} + 36 q^{35} - 4 q^{37} + 18 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 44 q^{50} + 54 q^{52} - 8 q^{53} - 148 q^{56} + 28 q^{58} + 124 q^{65} - 24 q^{67} - 42 q^{68} - 34 q^{70} + 40 q^{71} + 36 q^{73} + 96 q^{76} - 58 q^{77} - 36 q^{80} - 66 q^{82} + 138 q^{83} - 20 q^{85} + 16 q^{86} + 46 q^{88} - 48 q^{91} + 26 q^{92} - 188 q^{95} + 48 q^{97} - 102 q^{98}+O(q^{100}) $ 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8 - 24 * q^10 + 16 * q^11 - 152 * q^16 + 6 * q^17 - 60 * q^20 + 8 * q^22 - 8 * q^23 + 2 * q^25 + 36 * q^26 + 22 * q^28 - 12 * q^32 + 36 * q^35 - 4 * q^37 + 18 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 44 * q^50 + 54 * q^52 - 8 * q^53 - 148 * q^56 + 28 * q^58 + 124 * q^65 - 24 * q^67 - 42 * q^68 - 34 * q^70 + 40 * q^71 + 36 * q^73 + 96 * q^76 - 58 * q^77 - 36 * q^80 - 66 * q^82 + 138 * q^83 - 20 * q^85 + 16 * q^86 + 46 * q^88 - 48 * q^91 + 26 * q^92 - 188 * q^95 + 48 * q^97 - 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0825718	+	0.0825718i	0.0583871	+	0.0583871i	0.735697	−	0.677310i	$-0.236855\pi$
$2$	0.0825718	+	0.0825718i	0.0583871	+	0.0583871i	−0.677310	+	0.735697i	$0.736855\pi$
$3$		0			0
$3$		0			0
$4$		−	1.98636i		−	0.993182i
$5$	−1.53930	−	1.62190i	−0.688397	−	0.725335i
$5$	−1.53930	−	1.62190i	−0.688397	−	0.725335i
$6$		0			0
$7$	2.61528	−	0.400384i	0.988483	−	0.151331i
$7$	2.61528	−	0.400384i	0.988483	−	0.151331i
$8$	0.329161	−	0.329161i	0.116376	−	0.116376i
$9$		0			0
$10$	0.00682007	−	0.261026i	0.00215670	−	0.0825436i
$11$	−0.455930	−	0.789693i	−0.137468	−	0.238101i	0.789070	−	0.614304i	$-0.210563\pi$
$11$	−0.455930	−	0.789693i	−0.137468	−	0.238101i	−0.926538	+	0.376202i	$0.877230\pi$
$12$		0			0
$13$	1.53935	−	5.74495i	0.426940	−	1.59336i	−0.332709	−	0.943030i	$-0.607963\pi$
$13$	1.53935	−	5.74495i	0.426940	−	1.59336i	0.759649	−	0.650333i	$-0.225371\pi$
$14$	0.249009	+	0.182888i	0.0665504	+	0.0488789i
$15$		0			0
$16$	−3.91837			−0.979592
$17$	0.884052	+	3.29933i	0.214414	+	0.800204i	0.986372	+	0.164530i	$0.0526109\pi$
$17$	0.884052	+	3.29933i	0.214414	+	0.800204i	−0.771958	+	0.635674i	$0.780722\pi$
$18$		0			0
$19$	−0.815184	−	1.41194i	−0.187016	−	0.323921i	0.757238	−	0.653139i	$-0.226548\pi$
$19$	−0.815184	−	1.41194i	−0.187016	−	0.323921i	−0.944254	+	0.329218i	$0.893215\pi$
$20$	−3.22168	+	3.05761i	−0.720389	+	0.683703i
$21$		0			0
$22$	0.0275595	−	0.102853i	0.00587570	−	0.0219284i
$23$	0.844982	+	3.15352i	0.176191	+	0.657553i	0.996346	+	0.0854118i	$0.0272206\pi$
$23$	0.844982	+	3.15352i	0.176191	+	0.657553i	−0.820155	+	0.572142i	$0.806113\pi$
$24$		0			0
$25$	−0.261101	+	4.99318i	−0.0522203	+	0.998636i
$26$	0.601478	−	0.347264i	0.117960	−	0.0681040i
$27$		0			0
$28$	−0.795308	−	5.19490i	−0.150299	−	0.981744i
$29$	−5.74244	−	3.31540i	−1.06635	−	0.615655i	−0.139164	−	0.990269i	$-0.544442\pi$
$29$	−5.74244	−	3.31540i	−1.06635	−	0.615655i	−0.927181	+	0.374615i	$0.877775\pi$
$30$		0			0
$31$		−	1.16339i		−	0.208952i	−0.994527	−	0.104476i	$-0.966684\pi$
$31$		−	1.16339i		−	0.208952i	0.994527	−	0.104476i	$-0.0333165\pi$
$32$	−0.981869	−	0.981869i	−0.173572	−	0.173572i
$33$		0			0
$34$	−0.199433	+	0.345429i	−0.0342026	+	0.0592406i
$35$	−4.67509	−	3.62541i	−0.790234	−	0.612805i
$36$		0			0
$37$	−0.935230	+	3.49032i	−0.153751	+	0.573806i	0.845458	+	0.534042i	$0.179327\pi$
$37$	−0.935230	+	3.49032i	−0.153751	+	0.573806i	−0.999209	+	0.0397644i	$0.987339\pi$
$38$	0.0492752	−	0.183898i	0.00799349	−	0.0298321i
$39$		0			0
$40$	−1.04054	−	0.0271873i	−0.164524	−	0.00429869i
$41$	5.95218	−	3.43649i	0.929575	−	0.536690i	0.0428978	−	0.999079i	$-0.486341\pi$
$41$	5.95218	−	3.43649i	0.929575	−	0.536690i	0.886677	+	0.462389i	$0.153008\pi$
$42$		0			0
$43$	−1.11001	−	4.14262i	−0.169275	−	0.631744i	−0.997456	−	0.0712831i	$-0.977291\pi$
$43$	−1.11001	−	4.14262i	−0.169275	−	0.631744i	0.828181	−	0.560461i	$-0.189376\pi$
$44$	−1.56862	+	0.905642i	−0.236478	+	0.136531i
$45$		0			0
$46$	−0.190620	+	0.330163i	−0.0281053	+	0.0486799i
$47$	−4.13109	+	4.13109i	−0.602581	+	0.602581i	−0.940997	−	0.338416i	$-0.890109\pi$
$47$	−4.13109	+	4.13109i	−0.602581	+	0.602581i	0.338416	+	0.940997i	$0.390109\pi$
$48$		0			0
$49$	6.67939	−	2.09423i	0.954198	−	0.299176i
$50$	−0.433855	+	0.390736i	−0.0613564	+	0.0552584i
$51$		0			0
$52$	−11.4116	−	3.05772i	−1.58250	−	0.424029i
$53$	−3.64349	−	13.5977i	−0.500472	−	1.86779i	−0.496926	−	0.867793i	$-0.665538\pi$
$53$	−3.64349	−	13.5977i	−0.500472	−	1.86779i	−0.00354619	−	0.999994i	$-0.501129\pi$
$54$		0			0
$55$	−0.578988	+	1.95505i	−0.0780707	+	0.263618i
$56$	0.729058	−	0.992640i	0.0974245	−	0.132647i
$57$		0			0
$58$	−0.200405	−	0.747922i	−0.0263145	−	0.0982070i
$59$	−4.13313			−0.538088			−0.269044	−	0.963128i	$-0.586708\pi$
$59$	−4.13313			−0.538088			−0.269044	+	0.963128i	$0.586708\pi$
$60$		0			0
$61$			7.18890i			0.920444i	0.887804	+	0.460222i	$0.152230\pi$
$61$			7.18890i			0.920444i	−0.887804	+	0.460222i	$0.847770\pi$
$62$	0.0960635	−	0.0960635i	0.0122001	−	0.0122001i
$63$		0			0
$64$			7.67459i			0.959324i
$65$	−11.6873	+	6.34654i	−1.44963	+	0.787191i
$66$		0			0
$67$	−10.7674	−	10.7674i	−1.31544	−	1.31544i	−0.917342	−	0.398099i	$-0.869670\pi$
$67$	−10.7674	−	10.7674i	−1.31544	−	1.31544i	−0.398099	−	0.917342i	$-0.630330\pi$
$68$	6.55366	−	1.75605i	0.794748	−	0.212952i
$69$		0			0
$70$	−0.0866741	−	0.685386i	−0.0103595	−	0.0819193i
$71$	−7.48342			−0.888118			−0.444059	−	0.895997i	$-0.646462\pi$
$71$	−7.48342			−0.888118			−0.444059	+	0.895997i	$0.646462\pi$
$72$		0			0
$73$	3.70949	−	0.993956i	0.434163	−	0.116334i	−0.0351165	−	0.999383i	$-0.511180\pi$
$73$	3.70949	−	0.993956i	0.434163	−	0.116334i	0.469280	+	0.883050i	$0.344514\pi$
$74$	−0.365426	+	0.210979i	−0.0424799	+	0.0245258i
$75$		0			0
$76$	−2.80463	+	1.61925i	−0.321713	+	0.185741i
$77$	−1.50856	−	1.88272i	−0.171917	−	0.214556i
$78$		0			0
$79$			9.14441i			1.02883i	0.857542	+	0.514413i	$0.171990\pi$
$79$			9.14441i			1.02883i	−0.857542	+	0.514413i	$0.828010\pi$
$80$	6.03155	+	6.35519i	0.674348	+	0.710532i
$81$		0			0
$82$	0.775240	+	0.207725i	0.0856109	+	0.0229394i
$83$	10.7518	−	2.88094i	1.18017	−	0.316224i	0.385174	−	0.922844i	$-0.374142\pi$
$83$	10.7518	−	2.88094i	1.18017	−	0.316224i	0.794992	+	0.606620i	$0.207475\pi$
$84$		0			0
$85$	3.99035	−	6.51250i	0.432814	−	0.706380i
$86$	0.250408	−	0.433720i	0.0270022	−	0.0467692i
$87$		0			0
$88$	−0.410011	−	0.109862i	−0.0437073	−	0.0117113i
$89$	1.92701	+	3.33768i	0.204262	+	0.353793i	0.949897	−	0.312562i	$-0.101187\pi$
$89$	1.92701	+	3.33768i	0.204262	+	0.353793i	−0.745635	+	0.666355i	$0.767854\pi$
$90$		0			0
$91$	1.72566	−	15.6410i	0.180898	−	1.63962i
$92$	6.26403	−	1.67844i	0.653070	−	0.174990i
$93$		0			0
$94$	−0.682222			−0.0703658
$95$	−1.03521	+	3.49555i	−0.106210	+	0.358635i
$96$		0			0
$97$	1.83106	+	6.83360i	0.185916	+	0.693847i	0.994433	+	0.105374i	$0.0336040\pi$
$97$	1.83106	+	6.83360i	0.185916	+	0.693847i	−0.808517	+	0.588473i	$0.799729\pi$
$98$	0.724453	+	0.378604i	0.0731808	+	0.0382448i
$99$		0			0
$100$	9.91827	+	0.518642i	0.991827	+	0.0518642i
$101$	12.6902	−	7.32668i	1.26272	−	0.729032i	0.289120	−	0.957293i	$-0.406637\pi$
$101$	12.6902	−	7.32668i	1.26272	−	0.729032i	0.973600	+	0.228261i	$0.0733038\pi$
$102$		0			0
$103$	3.89828	−	1.04454i	0.384109	−	0.102922i	−0.0615970	−	0.998101i	$-0.519619\pi$
$103$	3.89828	−	1.04454i	0.384109	−	0.102922i	0.445706	+	0.895179i	$0.352953\pi$
$104$	−1.38432	−	2.39771i	−0.135744	−	0.235115i
$105$		0			0
$106$	0.821936	−	1.42364i	0.0798335	−	0.138276i
$107$	2.26902	−	8.46809i	0.219354	−	0.818641i	−0.765234	−	0.643752i	$-0.777377\pi$
$107$	2.26902	−	8.46809i	0.219354	−	0.818641i	0.984588	−	0.174889i	$-0.0559566\pi$
$108$		0			0
$109$	10.4090	+	6.00964i	0.997001	+	0.575619i	0.907360	−	0.420355i	$-0.138095\pi$
$109$	10.4090	+	6.00964i	0.997001	+	0.575619i	0.0896413	+	0.995974i	$0.471428\pi$
$110$	−0.209240	+	0.113624i	−0.0199502	+	0.0108336i
$111$		0			0
$112$	−10.2476	+	1.56885i	−0.968310	+	0.148242i
$113$	−11.6182	−	3.11308i	−1.09294	−	0.292853i	−0.333056	−	0.942907i	$-0.608080\pi$
$113$	−11.6182	−	3.11308i	−1.09294	−	0.292853i	−0.759888	+	0.650054i	$0.774746\pi$
$114$		0			0
$115$	3.81400	−	6.22469i	0.355657	−	0.580455i
$116$	−6.58559	+	11.4066i	−0.611457	+	1.05907i
$117$		0			0
$118$	−0.341280	−	0.341280i	−0.0314174	−	0.0314174i
$119$	3.63304	+	8.27470i	0.333040	+	0.758541i
$120$		0			0
$121$	5.08426	−	8.80619i	0.462205	−	0.800563i
$122$	−0.593600	+	0.593600i	−0.0537420	+	0.0537420i
$123$		0			0
$124$	−2.31092			−0.207527
$125$	8.50034	−	7.26253i	0.760293	−	0.649580i
$126$		0			0
$127$	8.68253	+	8.68253i	0.770450	+	0.770450i	0.978185	−	0.207735i	$-0.0666091\pi$
$127$	8.68253	+	8.68253i	0.770450	+	0.770450i	−0.207735	+	0.978185i	$0.566609\pi$
$128$	−2.59744	+	2.59744i	−0.229584	+	0.229584i
$129$		0			0
$130$	−1.48908	−	0.440992i	−0.130601	−	0.0386776i
$131$	11.3602	+	6.55882i	0.992546	+	0.573047i	0.906034	−	0.423204i	$-0.139095\pi$
$131$	11.3602	+	6.55882i	0.992546	+	0.573047i	0.0865118	+	0.996251i	$0.472428\pi$
$132$		0			0
$133$	−2.69725	−	3.36623i	−0.233881	−	0.291889i
$134$		−	1.77816i		−	0.153610i
$135$		0			0
$136$	1.37701	+	0.795014i	0.118077	+	0.0681719i
$137$	3.98207	−	14.8613i	0.340211	−	1.26968i	−0.557898	−	0.829910i	$-0.688392\pi$
$137$	3.98207	−	14.8613i	0.340211	−	1.26968i	0.898108	−	0.439774i	$-0.144942\pi$
$138$		0			0
$139$	4.93784	+	8.55258i	0.418822	+	0.725421i	0.995821	−	0.0913239i	$-0.0291099\pi$
$139$	4.93784	+	8.55258i	0.418822	+	0.725421i	−0.576999	+	0.816745i	$0.695777\pi$
$140$	−7.20137	+	9.28642i	−0.608627	+	0.784846i
$141$		0			0
$142$	−0.617919	−	0.617919i	−0.0518546	−	0.0518546i
$143$	−5.23859	+	1.40367i	−0.438073	+	0.117381i
$144$		0			0
$145$	3.46211	+	14.4171i	0.287513	+	1.19727i
$146$	0.388372	+	0.224227i	0.0321419	+	0.0185571i
$147$		0			0
$148$	6.93306	+	1.85771i	0.569894	+	0.152703i
$149$	12.7119	+	7.33921i	1.04140	+	0.601252i	0.920229	−	0.391380i	$-0.128002\pi$
$149$	12.7119	+	7.33921i	1.04140	+	0.601252i	0.121169	+	0.992632i	$0.461336\pi$
$150$		0			0
$151$	5.63119	+	9.75351i	0.458260	+	0.793729i	0.998869	−	0.0475446i	$-0.0151396\pi$
$151$	5.63119	+	9.75351i	0.458260	+	0.793729i	−0.540609	+	0.841274i	$0.681806\pi$
$152$	−0.733083	−	0.196429i	−0.0594609	−	0.0159325i
$153$		0			0
$154$	0.0308949	−	0.280025i	0.00248958	−	0.0225650i
$155$	−1.88691	+	1.79081i	−0.151560	+	0.143842i
$156$		0			0
$157$	2.39683	−	2.39683i	0.191288	−	0.191288i	−0.604965	−	0.796252i	$-0.706813\pi$
$157$	2.39683	−	2.39683i	0.191288	−	0.191288i	0.796252	+	0.604965i	$0.206813\pi$
$158$	−0.755070	+	0.755070i	−0.0600702	+	0.0600702i
$159$		0			0
$160$	−0.0810981	+	3.10388i	−0.00641137	+	0.245384i
$161$	3.47248	+	7.90901i	0.273670	+	0.623317i
$162$		0			0
$163$	−18.6846	−	5.00653i	−1.46349	−	0.392142i	−0.562798	−	0.826595i	$-0.690275\pi$
$163$	−18.6846	−	5.00653i	−1.46349	−	0.392142i	−0.900695	+	0.434453i	$0.856942\pi$
$164$	−6.82613	−	11.8232i	−0.533031	−	0.923237i
$165$		0			0
$166$	1.12568	+	0.649913i	0.0873698	+	0.0504430i
$167$	−8.86226	−	2.37464i	−0.685782	−	0.183755i	−0.100929	−	0.994894i	$-0.532181\pi$
$167$	−8.86226	−	2.37464i	−0.685782	−	0.183755i	−0.584854	+	0.811139i	$0.698848\pi$
$168$		0			0
$169$	−19.3765	−	11.1870i	−1.49050	−	0.860541i
$170$	0.867239	−	0.208259i	0.0665142	−	0.0159727i
$171$		0			0
$172$	−8.22876	+	2.20489i	−0.627437	+	0.168121i
$173$	10.5199	+	10.5199i	0.799814	+	0.799814i	0.983066	−	0.183252i	$-0.0586626\pi$
$173$	10.5199	+	10.5199i	0.799814	+	0.799814i	−0.183252	+	0.983066i	$0.558663\pi$
$174$		0			0
$175$	1.31633	+	13.1631i	0.0995055	+	0.995037i
$176$	1.78650	+	3.09431i	0.134662	+	0.233242i
$177$		0			0
$178$	−0.116481	+	0.434714i	−0.00873065	+	0.0325832i
$179$	6.51864	+	3.76354i	0.487226	+	0.281300i	0.723423	−	0.690405i	$-0.242568\pi$
$179$	6.51864	+	3.76354i	0.487226	+	0.281300i	−0.236197	+	0.971705i	$0.575901\pi$
$180$		0			0
$181$		−	1.22694i		−	0.0911977i	−0.998960	−	0.0455989i	$-0.985480\pi$
$181$		−	1.22694i		−	0.0911977i	0.998960	−	0.0455989i	$-0.0145196\pi$
$182$	1.43400	−	1.14901i	0.106295	−	0.0851706i
$183$		0			0
$184$	1.31615	+	0.759880i	0.0970279	+	0.0560191i
$185$	7.10055	−	3.85582i	0.522043	−	0.283485i
$186$		0			0
$187$	2.20239	−	2.20239i	0.161055	−	0.161055i
$188$	8.20584	+	8.20584i	0.598472	+	0.598472i
$189$		0			0
$190$	−0.374112	+	0.203155i	−0.0271410	+	0.0147384i
$191$	−0.709532			−0.0513399			−0.0256700	−	0.999670i	$-0.508172\pi$
$191$	−0.709532			−0.0513399			−0.0256700	+	0.999670i	$0.508172\pi$
$192$		0			0
$193$	−6.82635	+	6.82635i	−0.491372	+	0.491372i	−0.908738	−	0.417366i	$-0.862953\pi$
$193$	−6.82635	+	6.82635i	−0.491372	+	0.491372i	0.417366	+	0.908738i	$0.362953\pi$
$194$	−0.413069	+	0.715456i	−0.0296566	+	0.0513668i
$195$		0			0
$196$	−4.15991	−	13.2677i	−0.297136	−	0.947692i
$197$	−1.83581	−	1.83581i	−0.130796	−	0.130796i	0.638678	−	0.769474i	$-0.279482\pi$
$197$	−1.83581	−	1.83581i	−0.130796	−	0.130796i	−0.769474	+	0.638678i	$0.779482\pi$
$198$		0			0
$199$	2.12679	−	3.68372i	0.150764	−	0.261132i	−0.780744	−	0.624851i	$-0.785160\pi$
$199$	2.12679	−	3.68372i	0.150764	−	0.261132i	0.931509	+	0.363719i	$0.118493\pi$
$200$	1.55762	+	1.72950i	0.110140	+	0.122294i
$201$		0			0
$202$	1.65283	+	0.442874i	0.116293	+	0.0311605i
$203$	−16.3455	−	6.37152i	−1.14723	−	0.447193i
$204$		0			0
$205$	−14.7358	−	4.36403i	−1.02920	−	0.304797i
$206$	0.408138	+	0.235638i	0.0284363	+	0.0164177i
$207$		0			0
$208$	−6.03176	+	22.5108i	−0.418227	+	1.56085i
$209$	−0.743333	+	1.28749i	−0.0514174	+	0.0890575i
$210$		0			0
$211$	0.624913	+	1.08238i	0.0430208	+	0.0745142i	0.886734	−	0.462280i	$-0.152968\pi$
$211$	0.624913	+	1.08238i	0.0430208	+	0.0745142i	−0.843713	+	0.536794i	$0.819635\pi$
$212$	−27.0100	+	7.23730i	−1.85505	+	0.497060i
$213$		0			0
$214$	0.886582	−	0.511868i	0.0606055	−	0.0349906i
$215$	−5.01027	+	8.17707i	−0.341697	+	0.557672i
$216$		0			0
$217$	−0.465804	−	3.04260i	−0.0316208	−	0.206545i
$218$	0.363263	+	1.35572i	0.0246033	+	0.0918206i
$219$		0			0
$220$	3.88343	+	1.15008i	0.261821	+	0.0775384i
$221$	20.3153			1.36656
$222$		0			0
$223$	26.8379	−	7.19120i	1.79720	−	0.481558i	0.803664	−	0.595083i	$-0.202881\pi$
$223$	26.8379	−	7.19120i	1.79720	−	0.481558i	0.993535	+	0.113525i	$0.0362143\pi$
$224$	−2.96099	−	2.17474i	−0.197839	−	0.145306i
$225$		0			0
$226$	−0.702280	−	1.21638i	−0.0467149	−	0.0809127i
$227$	−2.59488	−	0.695297i	−0.172229	−	0.0461485i	0.171674	−	0.985154i	$-0.445082\pi$
$227$	−2.59488	−	0.695297i	−0.172229	−	0.0461485i	−0.343903	+	0.939005i	$0.611749\pi$
$228$		0			0
$229$	1.35564	−	2.34803i	0.0895831	−	0.155162i	−0.817752	−	0.575571i	$-0.804780\pi$
$229$	1.35564	−	2.34803i	0.0895831	−	0.155162i	0.907335	+	0.420408i	$0.138113\pi$
$230$	0.828912	−	0.199055i	0.0546568	−	0.0131253i
$231$		0			0
$232$	−2.98149	+	0.798888i	−0.195744	+	0.0524496i
$233$	10.1849	+	2.72904i	0.667236	+	0.178785i	0.576509	−	0.817091i	$-0.304414\pi$
$233$	10.1849	+	2.72904i	0.667236	+	0.178785i	0.0907264	+	0.995876i	$0.471081\pi$
$234$		0			0
$235$	13.0592	+	0.341210i	0.851887	+	0.0222581i
$236$			8.20990i			0.534419i
$237$		0			0
$238$	−0.383270	+	0.983244i	−0.0248437	+	0.0637342i
$239$	19.4428	−	11.2253i	1.25765	−	0.726104i	0.285032	−	0.958518i	$-0.407996\pi$
$239$	19.4428	−	11.2253i	1.25765	−	0.726104i	0.972617	+	0.232414i	$0.0746626\pi$
$240$		0			0
$241$	7.94408	−	4.58651i	0.511723	−	0.295443i	−0.221819	−	0.975088i	$-0.571199\pi$
$241$	7.94408	−	4.58651i	0.511723	−	0.295443i	0.733542	+	0.679645i	$0.237866\pi$
$242$	1.14696	−	0.307327i	0.0737293	−	0.0197557i
$243$		0			0
$244$	14.2798			0.914168
$245$	−13.6782	−	7.60962i	−0.873869	−	0.486161i
$246$		0			0
$247$	−9.36638	+	2.50971i	−0.595969	+	0.159689i
$248$	−0.382944	−	0.382944i	−0.0243170	−	0.0243170i
$249$		0			0
$250$	1.30157	+	0.102208i	0.0823184	+	0.00646420i
$251$		−	10.9957i		−	0.694041i	−0.937858	−	0.347020i	$-0.887193\pi$
$251$		−	10.9957i		−	0.694041i	0.937858	−	0.347020i	$-0.112807\pi$
$252$		0			0
$253$	2.10506	−	2.10506i	0.132344	−	0.132344i
$254$			1.43386i			0.0899687i
$255$		0			0
$256$	14.9202			0.932514
$257$	−1.62431	−	6.06202i	−0.101322	−	0.378138i	0.896580	−	0.442882i	$-0.146044\pi$
$257$	−1.62431	−	6.06202i	−0.101322	−	0.378138i	−0.997902	+	0.0647433i	$0.979377\pi$
$258$		0			0
$259$	−1.04842	+	9.50263i	−0.0651456	+	0.590465i
$260$	12.6065	+	23.2151i	0.781824	+	1.43974i
$261$		0			0
$262$	0.396459	+	1.47961i	0.0244933	+	0.0914104i
$263$	27.0712	+	7.25371i	1.66928	+	0.447283i	0.964917	−	0.262555i	$-0.0845650\pi$
$263$	27.0712	+	7.25371i	1.66928	+	0.447283i	0.704365	+	0.709838i	$0.251232\pi$
$264$		0			0
$265$	−16.4456	+	26.8403i	−1.01025	+	1.64879i
$266$	0.0552389	−	0.500673i	0.00338691	−	0.0306982i
$267$		0			0
$268$	−21.3879	+	21.3879i	−1.30647	+	1.30647i
$269$	−7.45736	+	12.9165i	−0.454683	+	0.787535i	−0.998670	−	0.0515593i	$-0.983581\pi$
$269$	−7.45736	+	12.9165i	−0.454683	+	0.787535i	0.543987	+	0.839094i	$0.316914\pi$
$270$		0			0
$271$	−13.3846	+	7.72761i	−0.813058	+	0.469419i	−0.848017	−	0.529970i	$-0.822203\pi$
$271$	−13.3846	+	7.72761i	−0.813058	+	0.469419i	0.0349588	+	0.999389i	$0.488870\pi$
$272$	−3.46404	−	12.9280i	−0.210038	−	0.783874i
$273$		0			0
$274$	1.55593	−	0.898315i	0.0939970	−	0.0542692i
$275$	4.06212	−	2.07035i	0.244955	−	0.124847i
$276$		0			0
$277$	−4.82001	+	17.9885i	−0.289607	+	1.08083i	0.655800	+	0.754934i	$0.272331\pi$
$277$	−4.82001	+	17.9885i	−0.289607	+	1.08083i	−0.945407	+	0.325892i	$0.894335\pi$
$278$	−0.298476	+	1.11393i	−0.0179014	+	0.0668090i
$279$		0			0
$280$	−2.73220	+	0.345514i	−0.163280	+	0.0206484i
$281$	−3.78805	+	6.56109i	−0.225976	+	0.391402i	−0.956612	−	0.291366i	$-0.905890\pi$
$281$	−3.78805	+	6.56109i	−0.225976	+	0.391402i	0.730636	+	0.682767i	$0.239224\pi$
$282$		0			0
$283$	−9.76300	−	9.76300i	−0.580350	−	0.580350i	0.354649	−	0.934999i	$-0.384600\pi$
$283$	−9.76300	−	9.76300i	−0.580350	−	0.580350i	−0.934999	+	0.354649i	$0.884600\pi$
$284$			14.8648i			0.882063i
$285$		0			0
$286$	−0.548463	−	0.316655i	−0.0324313	−	0.0187242i
$287$	14.1907	−	11.3706i	0.837651	−	0.671183i
$288$		0			0
$289$	4.61843	−	2.66645i	0.271672	−	0.156850i
$290$	−0.904569	+	1.47631i	−0.0531181	+	0.0866922i
$291$		0			0
$292$	−1.97436	−	7.36840i	−0.115541	−	0.431203i
$293$	−0.623080	+	2.32537i	−0.0364007	+	0.135849i	−0.981735	−	0.190254i	$-0.939069\pi$
$293$	−0.623080	+	2.32537i	−0.0364007	+	0.135849i	0.945334	+	0.326103i	$0.105736\pi$
$294$		0			0
$295$	6.36213	+	6.70351i	0.370418	+	0.390294i
$296$	0.841038	+	1.45672i	0.0488843	+	0.0846702i
$297$		0			0
$298$	0.443631	+	1.65566i	0.0256989	+	0.0959095i
$299$	19.4175			1.12294
$300$		0			0
$301$	−4.56163	−	10.3897i	−0.262928	−	0.598852i
$302$	−0.340387	+	1.27034i	−0.0195871	+	0.0731000i
$303$		0			0
$304$	3.19419	+	5.53250i	0.183199	+	0.317311i
$305$	11.6597	−	11.0659i	0.667630	−	0.633631i
$306$		0			0
$307$	−9.67145	+	9.67145i	−0.551979	+	0.551979i	−0.927012	−	0.375033i	$-0.877632\pi$
$307$	−9.67145	+	9.67145i	−0.551979	+	0.551979i	0.375033	+	0.927012i	$0.377632\pi$
$308$	−3.73977	+	2.99656i	−0.213093	+	0.170745i
$309$		0			0
$310$	−0.303676	−	0.00793443i	−0.0172476	−	0.000450645i
$311$		−	26.6121i		−	1.50903i	−0.656281	−	0.754516i	$-0.727872\pi$
$311$		−	26.6121i		−	1.50903i	0.656281	−	0.754516i	$-0.272128\pi$
$312$		0			0
$313$	0.524423	+	0.524423i	0.0296422	+	0.0296422i	0.721773	−	0.692130i	$-0.243328\pi$
$313$	0.524423	+	0.524423i	0.0296422	+	0.0296422i	−0.692130	+	0.721773i	$0.743328\pi$
$314$	0.395821			0.0223374
$315$		0			0
$316$	18.1641			1.02181
$317$	−5.05102	−	5.05102i	−0.283694	−	0.283694i	0.550887	−	0.834580i	$-0.314290\pi$
$317$	−5.05102	−	5.05102i	−0.283694	−	0.283694i	−0.834580	+	0.550887i	$0.814290\pi$
$318$		0			0
$319$			6.04636i			0.338531i
$320$	12.4474	−	11.8135i	0.695830	−	0.660395i
$321$		0			0
$322$	−0.366332	+	0.939790i	−0.0204149	+	0.0523725i
$323$	3.93778	−	3.93778i	0.219104	−	0.219104i
$324$		0			0
$325$	28.2836	+	9.18629i	1.56889	+	0.509564i
$326$	−1.12942	−	1.95622i	−0.0625530	−	0.108345i
$327$		0			0
$328$	0.828067	−	3.09039i	0.0457224	−	0.170638i
$329$	−9.14993	+	12.4580i	−0.504452	+	0.686830i
$330$		0			0
$331$	−7.27514			−0.399878			−0.199939	−	0.979808i	$-0.564074\pi$
$331$	−7.27514			−0.399878			−0.199939	+	0.979808i	$0.564074\pi$
$332$	−5.72260	−	21.3570i	−0.314068	−	1.17212i
$333$		0			0
$334$	−0.535695	−	0.927851i	−0.0293119	−	0.0507697i
$335$	−0.889337	+	34.0377i	−0.0485897	+	1.85968i
$336$		0			0
$337$	3.44698	−	12.8643i	0.187769	−	0.700763i	−0.806252	−	0.591572i	$-0.798507\pi$
$337$	3.44698	−	12.8643i	0.187769	−	0.700763i	0.994021	−	0.109191i	$-0.0348259\pi$
$338$	−0.676220	−	2.52369i	−0.0367815	−	0.137270i
$339$		0			0
$340$	−12.9362	−	7.92628i	−0.701563	−	0.429863i
$341$	−0.918724	+	0.530426i	−0.0497517	+	0.0287242i
$342$		0			0
$343$	16.6300	−	8.15132i	0.897934	−	0.440130i
$344$	−1.72896	−	0.998218i	−0.0932195	−	0.0538203i
$345$		0			0
$346$			1.73729i			0.0933975i
$347$	−8.46204	−	8.46204i	−0.454266	−	0.454266i	0.442502	−	0.896768i	$-0.354091\pi$
$347$	−8.46204	−	8.46204i	−0.454266	−	0.454266i	−0.896768	+	0.442502i	$0.854091\pi$
$348$		0			0
$349$	15.7451	−	27.2713i	0.842814	−	1.45980i	−0.0446913	−	0.999001i	$-0.514230\pi$
$349$	15.7451	−	27.2713i	0.842814	−	1.45980i	0.887506	−	0.460797i	$-0.152436\pi$
$350$	−0.978209	+	1.19559i	−0.0522875	+	0.0639071i
$351$		0			0
$352$	−0.327712	+	1.22304i	−0.0174671	+	0.0651882i
$353$	8.74262	−	32.6279i	0.465323	−	1.73661i	−0.190494	−	0.981688i	$-0.561009\pi$
$353$	8.74262	−	32.6279i	0.465323	−	1.73661i	0.655817	−	0.754920i	$-0.272324\pi$
$354$		0			0
$355$	11.5192	+	12.1373i	0.611378	+	0.644183i
$356$	6.62984	−	3.82774i	0.351381	−	0.202870i
$357$		0			0
$358$	0.227494	+	0.849018i	0.0120234	+	0.0448720i
$359$	−18.7587	+	10.8303i	−0.990044	+	0.571602i	−0.905288	−	0.424799i	$-0.860345\pi$
$359$	−18.7587	+	10.8303i	−0.990044	+	0.571602i	−0.0847568	+	0.996402i	$0.527011\pi$
$360$		0			0
$361$	8.17095	−	14.1525i	0.430050	−	0.744869i
$362$	0.101311	−	0.101311i	0.00532477	−	0.00532477i
$363$		0			0
$364$	−31.0687	−	3.42779i	−1.62844	−	0.179665i
$365$	−7.32212	−	4.48642i	−0.383257	−	0.234830i
$366$		0			0
$367$	18.0591	+	4.83891i	0.942676	+	0.252589i	0.697252	−	0.716826i	$-0.254406\pi$
$367$	18.0591	+	4.83891i	0.942676	+	0.252589i	0.245424	+	0.969416i	$0.421073\pi$
$368$	−3.31095	−	12.3566i	−0.172595	−	0.644134i
$369$		0			0
$370$	0.904687	+	0.267923i	0.0470324	+	0.0139287i
$371$	−14.9730	−	34.1030i	−0.777362	−	1.77054i
$372$		0			0
$373$	−4.78044	−	17.8408i	−0.247522	−	0.923763i	−0.972099	−	0.234570i	$-0.924632\pi$
$373$	−4.78044	−	17.8408i	−0.247522	−	0.923763i	0.724578	−	0.689193i	$-0.242035\pi$
$374$	0.363710			0.0188070
$375$		0			0
$376$			2.71959i			0.140252i
$377$	−27.8865	+	27.8865i	−1.43623	+	1.43623i
$378$		0			0
$379$			2.41029i			0.123808i	0.998082	+	0.0619042i	$0.0197173\pi$
$379$			2.41029i			0.123808i	−0.998082	+	0.0619042i	$0.980283\pi$
$380$	6.94343	+	2.05630i	0.356190	+	0.105486i
$381$		0			0
$382$	−0.0585873	−	0.0585873i	−0.00299759	−	0.00299759i
$383$	19.9514	−	5.34597i	1.01947	−	0.273166i	0.289889	−	0.957060i	$-0.406382\pi$
$383$	19.9514	−	5.34597i	1.01947	−	0.273166i	0.729581	+	0.683894i	$0.239715\pi$
$384$		0			0
$385$	−0.731447	+	5.34481i	−0.0372780	+	0.272397i
$386$	−1.12733			−0.0573795
$387$		0			0
$388$	13.5740	−	3.63715i	0.689116	−	0.184648i
$389$	−13.9223	+	8.03806i	−0.705890	+	0.407546i	−0.809537	−	0.587068i	$-0.800282\pi$
$389$	−13.9223	+	8.03806i	−0.705890	+	0.407546i	0.103648	+	0.994614i	$0.466949\pi$
$390$		0			0
$391$	−9.65747	+	5.57574i	−0.488399	+	0.281977i
$392$	1.50925	−	2.88793i	0.0762289	−	0.145863i
$393$		0			0
$394$		−	0.303172i		−	0.0152736i
$395$	14.8313	−	14.0760i	0.746244	−	0.708241i
$396$		0			0
$397$	−19.8438	−	5.31714i	−0.995934	−	0.266860i	−0.276193	−	0.961102i	$-0.589073\pi$
$397$	−19.8438	−	5.31714i	−0.995934	−	0.266860i	−0.719741	+	0.694243i	$0.755739\pi$
$398$	0.479784	−	0.128558i	0.0240494	−	0.00644402i
$399$		0			0
$400$	1.02309	−	19.5651i	0.0511546	−	0.978256i
$401$	−11.0213	+	19.0895i	−0.550379	+	0.953285i	0.447868	+	0.894100i	$0.352184\pi$
$401$	−11.0213	+	19.0895i	−0.550379	+	0.953285i	−0.998247	+	0.0591852i	$0.981150\pi$
$402$		0			0
$403$	−6.68364	−	1.79088i	−0.332936	−	0.0892099i
$404$	−14.5535	−	25.2073i	−0.724061	−	1.25411i
$405$		0			0
$406$	−0.823572	−	1.87579i	−0.0408732	−	0.0930938i
$407$	3.18268	−	0.852798i	0.157760	−	0.0422716i
$408$		0			0
$409$	8.90743			0.440444			0.220222	−	0.975450i	$-0.429322\pi$
$409$	8.90743			0.440444			0.220222	+	0.975450i	$0.429322\pi$
$410$	−0.856420	−	1.57711i	−0.0422955	−	0.0778879i
$411$		0			0
$412$	−2.07484	−	7.74340i	−0.102220	−	0.381490i
$413$	−10.8093	+	1.65484i	−0.531891	+	0.0814293i
$414$		0			0
$415$	−21.2229	−	13.0037i	−1.04179	−	0.638327i
$416$	−7.15223	+	4.12934i	−0.350667	+	0.202458i
$417$		0			0
$418$	−0.167689	+	0.0449320i	−0.00820192	+	0.00219770i
$419$	0.233728	+	0.404828i	0.0114183	+	0.0197771i	0.871678	−	0.490079i	$-0.163032\pi$
$419$	0.233728	+	0.404828i	0.0114183	+	0.0197771i	−0.860260	+	0.509856i	$0.829699\pi$
$420$		0			0
$421$	−4.23449	+	7.33434i	−0.206376	+	0.357454i	−0.950570	−	0.310509i	$-0.899500\pi$
$421$	−4.23449	+	7.33434i	−0.206376	+	0.357454i	0.744194	+	0.667963i	$0.232834\pi$
$422$	−0.0377740	+	0.140974i	−0.00183881	+	0.00686253i
$423$		0			0
$424$	−5.67513	−	3.27654i	−0.275609	−	0.159123i
$425$	−16.7049	+	3.55277i	−0.810309	+	0.172335i
$426$		0			0
$427$	2.87832	+	18.8010i	0.139292	+	0.909844i
$428$	−16.8207	−	4.50709i	−0.813059	−	0.217859i
$429$		0			0
$430$	−1.08890	+	0.261489i	−0.0525115	+	0.0126101i
$431$	−16.9162	+	29.2997i	−0.814825	+	1.41132i	0.0946293	+	0.995513i	$0.469833\pi$
$431$	−16.9162	+	29.2997i	−0.814825	+	1.41132i	−0.909454	+	0.415805i	$0.863500\pi$
$432$		0			0
$433$	−26.2098	−	26.2098i	−1.25956	−	1.25956i	−0.951303	−	0.308258i	$-0.900254\pi$
$433$	−26.2098	−	26.2098i	−1.25956	−	1.25956i	−0.308258	−	0.951303i	$-0.599746\pi$
$434$	0.212771	−	0.289695i	0.0102133	−	0.0139058i
$435$		0			0
$436$	11.9373	−	20.6760i	0.571694	−	0.990203i
$437$	3.76376	−	3.76376i	0.180045	−	0.180045i
$438$		0			0
$439$	17.9196			0.855257			0.427628	−	0.903955i	$-0.359349\pi$
$439$	17.9196			0.855257			0.427628	+	0.903955i	$0.359349\pi$
$440$	0.452945	+	0.834106i	0.0215933	+	0.0397644i
$441$		0			0
$442$	1.67747	+	1.67747i	0.0797893	+	0.0797893i
$443$	−21.0509	+	21.0509i	−1.00016	+	1.00016i	−0.000156112		1.00000i	$0.500050\pi$
$443$	−21.0509	+	21.0509i	−1.00016	+	1.00016i	−1.00000		0.000156112i	$0.999950\pi$
$444$		0			0
$445$	2.44712	−	8.26310i	0.116005	−	0.391708i
$446$	2.80984	+	1.62226i	0.133050	+	0.0768164i
$447$		0			0
$448$	3.07278	+	20.0712i	0.145175	+	0.948275i
$449$		−	31.1166i		−	1.46848i	−0.678889	−	0.734240i	$-0.737538\pi$
$449$		−	31.1166i		−	1.46848i	0.678889	−	0.734240i	$-0.262462\pi$
$450$		0			0
$451$	−5.42755	−	3.13360i	−0.255573	−	0.147555i
$452$	−6.18370	+	23.0779i	−0.290857	+	1.08549i
$453$		0			0
$454$	−0.156852	−	0.271676i	−0.00736144	−	0.0127504i
$455$	−28.0244	+	21.2774i	−1.31380	+	0.997498i
$456$		0			0
$457$	−4.40646	−	4.40646i	−0.206126	−	0.206126i	0.596493	−	0.802618i	$-0.296560\pi$
$457$	−4.40646	−	4.40646i	−0.206126	−	0.206126i	−0.802618	+	0.596493i	$0.796560\pi$
$458$	0.305819	−	0.0819439i	0.0142900	−	0.00382899i
$459$		0			0
$460$	−12.3645	−	7.57598i	−0.576497	−	0.353232i
$461$	−3.59037	−	2.07290i	−0.167220	−	0.0965446i	0.414054	−	0.910252i	$-0.364112\pi$
$461$	−3.59037	−	2.07290i	−0.167220	−	0.0965446i	−0.581274	+	0.813708i	$0.697446\pi$
$462$		0			0
$463$	18.4450	+	4.94233i	0.857214	+	0.229690i	0.660551	−	0.750781i	$-0.270323\pi$
$463$	18.4450	+	4.94233i	0.857214	+	0.229690i	0.196663	+	0.980471i	$0.436990\pi$
$464$	22.5010	+	12.9910i	1.04458	+	0.603090i
$465$		0			0
$466$	0.615645	+	1.06633i	0.0285192	+	0.0493967i
$467$	37.2688	+	9.98615i	1.72459	+	0.462104i	0.978926	−	0.204214i	$-0.0654638\pi$
$467$	37.2688	+	9.98615i	1.72459	+	0.462104i	0.745668	+	0.666317i	$0.232130\pi$
$468$		0			0
$469$	−32.4707	−	23.8486i	−1.49936	−	1.10123i
$470$	1.05015	+	1.10649i	0.0484396	+	0.0510388i
$471$		0			0
$472$	−1.36047	+	1.36047i	−0.0626205	+	0.0626205i
$473$	−2.76531	+	2.76531i	−0.127149	+	0.127149i
$474$		0			0
$475$	7.26291	−	3.70170i	0.333245	−	0.169846i
$476$	16.4366	−	7.21654i	0.753369	−	0.330769i
$477$		0			0
$478$	2.53232	+	0.678532i	0.115825	+	0.0310353i
$479$	15.4248	+	26.7165i	0.704776	+	1.22071i	0.966772	+	0.255639i	$0.0822858\pi$
$479$	15.4248	+	26.7165i	0.704776	+	1.22071i	−0.261996	+	0.965069i	$0.584381\pi$
$480$		0			0
$481$	18.6121	+	10.7457i	0.848638	+	0.489962i
$482$	1.03467	+	0.277240i	0.0471281	+	0.0126279i
$483$		0			0
$484$	−17.4923	−	10.0992i	−0.795104	−	0.459054i
$485$	8.26485	−	13.4888i	0.375287	−	0.612493i
$486$		0			0
$487$	0.230491	−	0.0617598i	0.0104445	−	0.00279861i	−0.253593	−	0.967311i	$-0.581612\pi$
$487$	0.230491	−	0.0617598i	0.0104445	−	0.00279861i	0.264038	+	0.964512i	$0.414946\pi$
$488$	2.36631	+	2.36631i	0.107118	+	0.107118i
$489$		0			0
$490$	−0.501095	−	1.75778i	−0.0226371	−	0.0794082i
$491$	13.2996	+	23.0356i	0.600204	+	1.03958i	0.992790	+	0.119868i	$0.0382473\pi$
$491$	13.2996	+	23.0356i	0.600204	+	1.03958i	−0.392586	+	0.919715i	$0.628419\pi$
$492$		0			0
$493$	5.86197	−	21.8772i	0.264010	−	0.985299i
$494$	−0.980631	−	0.566167i	−0.0441207	−	0.0254731i
$495$		0			0
$496$			4.55861i			0.204687i
$497$	−19.5712	+	2.99624i	−0.877890	+	0.134400i
$498$		0			0
$499$	−7.52176	−	4.34269i	−0.336720	−	0.194405i	0.322101	−	0.946705i	$-0.395611\pi$
$499$	−7.52176	−	4.34269i	−0.336720	−	0.194405i	−0.658821	+	0.752300i	$0.728944\pi$
$500$	−14.4260	−	16.8848i	−0.645151	−	0.755109i
$501$		0			0
$502$	0.907932	−	0.907932i	0.0405230	−	0.0405230i
$503$	−0.792859	−	0.792859i	−0.0353518	−	0.0353518i	0.689210	−	0.724562i	$-0.257958\pi$
$503$	−0.792859	−	0.792859i	−0.0353518	−	0.0353518i	−0.724562	+	0.689210i	$0.757958\pi$
$504$		0			0
$505$	−31.4171	−	9.30420i	−1.39804	−	0.414032i
$506$	0.347637			0.0154543
$507$		0			0
$508$	17.2467	−	17.2467i	0.765197	−	0.765197i
$509$	−17.0474	+	29.5270i	−0.755614	+	1.30876i	0.189455	+	0.981889i	$0.439328\pi$
$509$	−17.0474	+	29.5270i	−0.755614	+	1.30876i	−0.945069	+	0.326872i	$0.894005\pi$
$510$		0			0
$511$	9.30340	−	4.08469i	0.411558	−	0.180696i
$512$	6.42687	+	6.42687i	0.284030	+	0.284030i
$513$		0			0
$514$	0.366429	−	0.634674i	0.0161625	−	0.0279943i
$515$	−7.69477	−	4.71475i	−0.339072	−	0.207757i
$516$		0			0
$517$	5.14577	+	1.37881i	0.226311	+	0.0606398i
$518$	−0.871219	+	0.698079i	−0.0382792	+	0.0306718i
$519$		0			0
$520$	−1.75796	+	5.93602i	−0.0770915	+	0.260312i
$521$	−24.3965	−	14.0853i	−1.06883	−	0.617088i	−0.140967	−	0.990014i	$-0.545021\pi$
$521$	−24.3965	−	14.0853i	−1.06883	−	0.617088i	−0.927861	+	0.372926i	$0.878355\pi$
$522$		0			0
$523$	−1.21481	+	4.53372i	−0.0531198	+	0.198246i	−0.987386	−	0.158330i	$-0.949389\pi$
$523$	−1.21481	+	4.53372i	−0.0531198	+	0.198246i	0.934266	+	0.356576i	$0.116056\pi$
$524$	13.0282	−	22.5655i	0.569140	−	0.985779i
$525$		0			0
$526$	1.63637	+	2.83427i	0.0713490	+	0.123580i
$527$	3.83841	−	1.02850i	0.167204	−	0.0448022i
$528$		0			0
$529$	10.6879	−	6.17067i	0.464692	−	0.268290i
$530$	−3.57420	+	0.858308i	−0.155253	+	0.0372825i
$531$		0			0
$532$	−6.68656	+	5.35772i	−0.289899	+	0.232287i
$533$	−10.5800	−	39.4850i	−0.458269	−	1.71028i
$534$		0			0
$535$	−17.2271	+	9.35483i	−0.744791	+	0.404444i
$536$	−7.08839			−0.306172
$537$		0			0
$538$	−1.68231	+	0.450773i	−0.0725295	+	0.0194342i
$539$	−4.69913	−	4.31984i	−0.202406	−	0.186069i
$540$		0			0
$541$	3.90106	+	6.75684i	0.167720	+	0.290499i	0.937618	−	0.347668i	$-0.113026\pi$
$541$	3.90106	+	6.75684i	0.167720	+	0.290499i	−0.769898	+	0.638167i	$0.779693\pi$
$542$	−1.74328	−	0.467109i	−0.0748801	−	0.0200641i
$543$		0			0
$544$	2.37148	−	4.10753i	0.101676	−	0.176109i
$545$	−6.27557	−	26.1330i	−0.268816	−	1.11941i
$546$		0			0
$547$	21.1697	−	5.67241i	0.905153	−	0.242535i	0.223925	−	0.974606i	$-0.428113\pi$
$547$	21.1697	−	5.67241i	0.905153	−	0.242535i	0.681228	+	0.732072i	$0.261446\pi$
$548$	−29.5199	−	7.90983i	−1.26103	−	0.337891i
$549$		0			0
$550$	0.506369	+	0.164464i	0.0215916	+	0.00701279i
$551$			10.8106i			0.460549i
$552$		0			0
$553$	3.66127	+	23.9152i	0.155693	+	1.01698i
$554$	−1.88334	+	1.08735i	−0.0800156	+	0.0461970i
$555$		0			0
$556$	16.9885	−	9.80834i	0.720475	−	0.415966i
$557$	−14.7100	+	3.94152i	−0.623281	+	0.167008i	−0.556619	−	0.830768i	$-0.687902\pi$
$557$	−14.7100	+	3.94152i	−0.623281	+	0.167008i	−0.0666620	+	0.997776i	$0.521235\pi$
$558$		0			0
$559$	−25.5079			−1.07887
$560$	18.3187	+	14.2057i	0.774107	+	0.600299i
$561$		0			0
$562$	−0.854546	+	0.228975i	−0.0360469	+	0.00965873i
$563$	26.0894	+	26.0894i	1.09954	+	1.09954i	0.994465	+	0.105071i	$0.0335071\pi$
$563$	26.0894	+	26.0894i	1.09954	+	1.09954i	0.105071	+	0.994465i	$0.466493\pi$
$564$		0			0
$565$	12.8348	+	23.6354i	0.539962	+	0.994349i
$566$		−	1.61230i		−	0.0677699i
$567$		0			0
$568$	−2.46325	+	2.46325i	−0.103356	+	0.103356i
$569$			2.46664i			0.103407i	0.998662	+	0.0517034i	$0.0164651\pi$
$569$			2.46664i			0.103407i	−0.998662	+	0.0517034i	$0.983535\pi$
$570$		0			0
$571$	−8.81458			−0.368879			−0.184439	−	0.982844i	$-0.559047\pi$
$571$	−8.81458			−0.368879			−0.184439	+	0.982844i	$0.559047\pi$
$572$	2.78821	+	10.4057i	0.116581	+	0.435086i
$573$		0			0
$574$	2.11064	+	0.232866i	0.0880964	+	0.00971962i
$575$	−15.9667	+	3.39576i	−0.665857	+	0.141613i
$576$		0			0
$577$	−0.825534	−	3.08094i	−0.0343674	−	0.128261i	0.946611	−	0.322379i	$-0.104482\pi$
$577$	−0.825534	−	3.08094i	−0.0343674	−	0.128261i	−0.980978	+	0.194117i	$0.937816\pi$
$578$	0.601526	+	0.161178i	0.0250202	+	0.00670413i
$579$		0			0
$580$	28.6375	−	6.87701i	1.18911	−	0.285552i
$581$	26.9655	−	11.8393i	1.11872	−	0.491178i
$582$		0			0
$583$	−9.07683	+	9.07683i	−0.375924	+	0.375924i
$584$	0.893849	−	1.54819i	0.0369877	−	0.0640647i
$585$		0			0
$586$	−0.243459	+	0.140561i	−0.0100572	+	0.00580652i
$587$	0.184728	+	0.689415i	0.00762455	+	0.0284552i	0.969633	−	0.244563i	$-0.0786446\pi$
$587$	0.184728	+	0.689415i	0.00762455	+	0.0284552i	−0.962009	+	0.273019i	$0.911978\pi$
$588$		0			0
$589$	−1.64264	+	0.948380i	−0.0676839	+	0.0390773i
$590$	−0.0281883	+	1.07885i	−0.00116049	+	0.0444157i
$591$		0			0
$592$	3.66457	−	13.6764i	0.150613	−	0.562096i
$593$	5.80070	−	21.6485i	0.238206	−	0.888998i	−0.738471	−	0.674285i	$-0.764452\pi$
$593$	5.80070	−	21.6485i	0.238206	−	0.888998i	0.976677	−	0.214713i	$-0.0688815\pi$
$594$		0			0
$595$	7.82837	−	18.6297i	0.320932	−	0.763742i
$596$	14.5783	−	25.2504i	0.597152	−	1.03430i
$597$		0			0
$598$	1.60334	+	1.60334i	0.0655654	+	0.0655654i
$599$			2.33386i			0.0953591i	0.998863	+	0.0476796i	$0.0151826\pi$
$599$			2.33386i			0.0953591i	−0.998863	+	0.0476796i	$0.984817\pi$
$600$		0			0
$601$	−4.89779	−	2.82774i	−0.199785	−	0.115346i	0.396770	−	0.917918i	$-0.370131\pi$
$601$	−4.89779	−	2.82774i	−0.199785	−	0.115346i	−0.596555	+	0.802572i	$0.703464\pi$
$602$	0.481233	−	1.23456i	0.0196136	−	0.0503168i
$603$		0			0
$604$	19.3740	−	11.1856i	0.788317	−	0.455135i
$605$	−22.1089	+	5.30924i	−0.898856	+	0.215851i
$606$		0			0
$607$	−2.09856	−	7.83195i	−0.0851781	−	0.317889i	0.910170	−	0.414235i	$-0.135951\pi$
$607$	−2.09856	−	7.83195i	−0.0851781	−	0.317889i	−0.995348	+	0.0963465i	$0.969284\pi$
$608$	−0.585936	+	2.18674i	−0.0237629	+	0.0886842i
$609$		0			0
$610$	1.87649	+	0.0490288i	0.0759768	+	0.00198512i
$611$	17.3737	+	30.0921i	0.702864	+	1.21740i
$612$		0			0
$613$	−3.44755	−	12.8664i	−0.139245	−	0.519670i	−0.999944	−	0.0105563i	$-0.996640\pi$
$613$	−3.44755	−	12.8664i	−0.139245	−	0.519670i	0.860699	−	0.509114i	$-0.170027\pi$
$614$	−1.59718			−0.0644569
$615$		0			0
$616$	−1.11628	−	0.123158i	−0.0449762	−	0.00496219i
$617$	−0.531453	+	1.98341i	−0.0213955	+	0.0798490i	−0.975798	−	0.218673i	$-0.929827\pi$
$617$	−0.531453	+	1.98341i	−0.0213955	+	0.0798490i	0.954403	+	0.298522i	$0.0964937\pi$
$618$		0			0
$619$	22.7489	+	39.4022i	0.914355	+	1.58371i	0.807843	+	0.589398i	$0.200635\pi$
$619$	22.7489	+	39.4022i	0.914355	+	1.58371i	0.106512	+	0.994311i	$0.466032\pi$
$620$	3.55721	+	3.74808i	0.142861	+	0.150527i
$621$		0			0
$622$	2.19741	−	2.19741i	0.0881080	−	0.0881080i
$623$	6.37602	+	7.95742i	0.255450	+	0.318807i
$624$		0			0
$625$	−24.8637	−	2.60745i	−0.994546	−	0.104298i
$626$			0.0866051i			0.00346144i
$627$		0			0
$628$	−4.76097	−	4.76097i	−0.189983	−	0.189983i
$629$	−12.3425			−0.492128
$630$		0			0
$631$	−35.3686			−1.40800			−0.704000	−	0.710200i	$-0.748605\pi$
$631$	−35.3686			−1.40800			−0.704000	+	0.710200i	$0.748605\pi$
$632$	3.00999	+	3.00999i	0.119731	+	0.119731i
$633$		0			0
$634$		−	0.834143i		−	0.0331281i
$635$	0.717140	−	27.4472i	0.0284588	−	1.08921i
$636$		0			0
$637$	−1.74931	−	41.5965i	−0.0693102	−	1.64811i
$638$	−0.499259	+	0.499259i	−0.0197658	+	0.0197658i
$639$		0			0
$640$	8.21103	+	0.214538i	0.324570	+	0.00848034i
$641$	−5.92125	−	10.2559i	−0.233875	−	0.405084i	0.725070	−	0.688675i	$-0.241807\pi$
$641$	−5.92125	−	10.2559i	−0.233875	−	0.405084i	−0.958945	+	0.283591i	$0.908474\pi$
$642$		0			0
$643$	−0.689615	+	2.57368i	−0.0271958	+	0.101496i	−0.978190	−	0.207714i	$-0.933398\pi$
$643$	−0.689615	+	2.57368i	−0.0271958	+	0.101496i	0.950994	+	0.309210i	$0.100064\pi$
$644$	15.7102	−	6.89761i	0.619068	−	0.271804i
$645$		0			0
$646$	0.650300			0.0255857
$647$	1.45165	+	5.41764i	0.0570703	+	0.212989i	0.988572	−	0.150747i	$-0.0481677\pi$
$647$	1.45165	+	5.41764i	0.0570703	+	0.212989i	−0.931502	+	0.363736i	$0.881501\pi$
$648$		0			0
$649$	1.88442	+	3.26390i	0.0739698	+	0.128119i
$650$	1.57690	+	3.09396i	0.0618512	+	0.121355i
$651$		0			0
$652$	−9.94479	+	37.1145i	−0.389468	+	1.45351i
$653$	2.37893	+	8.87828i	0.0930946	+	0.347434i	0.996724	−	0.0808821i	$-0.0257737\pi$
$653$	2.37893	+	8.87828i	0.0930946	+	0.347434i	−0.903629	+	0.428316i	$0.859107\pi$
$654$		0			0
$655$	−6.84906	−	28.5211i	−0.267615	−	1.11441i
$656$	−23.3228	+	13.4655i	−0.910604	+	0.525738i
$657$		0			0
$658$	−1.78420	+	0.273151i	−0.0695555	+	0.0106485i
$659$	16.3480	+	9.43850i	0.636826	+	0.367672i	0.783391	−	0.621529i	$-0.213488\pi$
$659$	16.3480	+	9.43850i	0.636826	+	0.367672i	−0.146565	+	0.989201i	$0.546822\pi$
$660$		0			0
$661$			14.9804i			0.582670i	0.956621	+	0.291335i	$0.0940995\pi$
$661$			14.9804i			0.582670i	−0.956621	+	0.291335i	$0.905900\pi$
$662$	−0.600721	−	0.600721i	−0.0233477	−	0.0233477i
$663$		0			0
$664$	2.59079	−	4.48738i	0.100542	−	0.174144i
$665$	−1.30780	+	9.55631i	−0.0507143	+	0.370578i
$666$		0			0
$667$	5.60291	−	20.9103i	0.216945	−	0.809652i
$668$	−4.71689	+	17.6037i	−0.182502	+	0.681107i
$669$		0			0
$670$	−2.88399	+	2.73712i	−0.111418	+	0.105744i
$671$	5.67702	−	3.27763i	0.219159	−	0.126532i
$672$		0			0
$673$	−9.75822	−	36.4182i	−0.376152	−	1.40382i	−0.851655	−	0.524103i	$-0.824401\pi$
$673$	−9.75822	−	36.4182i	−0.376152	−	1.40382i	0.475503	−	0.879714i	$-0.342266\pi$
$674$	1.34685	−	0.777605i	0.0518788	−	0.0299522i
$675$		0			0
$676$	−22.2215	+	38.4888i	−0.854674	+	1.48034i
$677$	2.90409	−	2.90409i	0.111613	−	0.111613i	−0.649095	−	0.760708i	$-0.724852\pi$
$677$	2.90409	−	2.90409i	0.111613	−	0.111613i	0.760708	+	0.649095i	$0.224852\pi$
$678$		0			0
$679$	7.52479	+	17.1387i	0.288775	+	0.657721i
$680$	−0.830195	−	3.45713i	−0.0318365	−	0.132575i
$681$		0			0
$682$	−0.119659	−	0.0320625i	−0.00458197	−	0.00122774i
$683$	−3.62156	−	13.5159i	−0.138575	−	0.517170i	−0.999958	−	0.00921262i	$-0.997067\pi$
$683$	−3.62156	−	13.5159i	−0.138575	−	0.517170i	0.861382	−	0.507957i	$-0.169599\pi$
$684$		0			0
$685$	−30.2331	+	16.4175i	−1.15515	+	0.627280i
$686$	2.04624	+	0.700097i	0.0781256	+	0.0267298i
$687$		0			0
$688$	4.34944	+	16.2323i	0.165821	+	0.618852i
$689$	−83.7267			−3.18973
$690$		0			0
$691$		−	17.5908i		−	0.669187i	−0.942363	−	0.334593i	$-0.891401\pi$
$691$		−	17.5908i		−	0.669187i	0.942363	−	0.334593i	$-0.108599\pi$
$692$	20.8964	−	20.8964i	0.794360	−	0.794360i
$693$		0			0
$694$		−	1.39745i		−	0.0530465i
$695$	6.27059	−	21.1737i	0.237857	−	0.803163i
$696$		0			0
$697$	16.6002	+	16.6002i	0.628776	+	0.628776i
$698$	3.55194	−	0.951738i	0.134443	−	0.0360238i
$699$		0			0
$700$	26.1467	−	2.61472i	0.988253	−	0.0988270i
$701$	23.5988			0.891314			0.445657	−	0.895204i	$-0.352970\pi$
$701$	23.5988			0.891314			0.445657	+	0.895204i	$0.352970\pi$
$702$		0			0
$703$	5.69051	−	1.52477i	0.214622	−	0.0575077i
$704$	6.06057	−	3.49907i	0.228416	−	0.131876i
$705$		0			0
$706$	3.41604	−	1.97225i	0.128564	−	0.0742266i
$707$	30.2549	−	24.2423i	1.13785	−	0.911724i
$708$		0			0
$709$			26.1939i			0.983734i	0.870670	+	0.491867i	$0.163685\pi$
$709$			26.1939i			0.983734i	−0.870670	+	0.491867i	$0.836315\pi$
$710$	−0.0510375	+	1.95337i	−0.00191540	+	0.0733085i
$711$		0			0
$712$	1.73293	+	0.464337i	0.0649443	+	0.0174018i
$713$	3.66878	−	0.983047i	0.137397	−	0.0368154i
$714$		0			0
$715$	10.3404	+	6.33577i	0.386708	+	0.236944i
$716$	7.47576	−	12.9484i	0.279382	−	0.483904i
$717$		0			0
$718$	−2.44322	−	0.654658i	−0.0911800	−	0.0244316i
$719$	−4.74507	−	8.21871i	−0.176961	−	0.306506i	0.763877	−	0.645362i	$-0.223293\pi$
$719$	−4.74507	−	8.21871i	−0.176961	−	0.306506i	−0.940838	+	0.338856i	$0.889960\pi$
$720$		0			0
$721$	9.77688	−	4.29258i	0.364110	−	0.159864i
$722$	1.84329	−	0.493907i	0.0686001	−	0.0183813i
$723$		0			0
$724$	−2.43715			−0.0905759
$725$	18.0538	−	27.8074i	0.670499	−	1.03274i
$726$		0			0
$727$	0.342271	+	1.27737i	0.0126941	+	0.0473752i	0.971982	−	0.235054i	$-0.0755266\pi$
$727$	0.342271	+	1.27737i	0.0126941	+	0.0473752i	−0.959288	+	0.282429i	$0.908860\pi$
$728$	−4.58039	−	5.71643i	−0.169760	−	0.211865i
$729$		0			0
$730$	−0.234149	−	0.975052i	−0.00866625	−	0.0360883i
$731$	12.6866	−	7.32459i	0.469229	−	0.270910i
$732$		0			0
$733$	−48.3039	+	12.9430i	−1.78415	+	0.478060i	−0.991329	−	0.131400i	$-0.958053\pi$
$733$	−48.3039	+	12.9430i	−1.78415	+	0.478060i	−0.792816	+	0.609461i	$0.791386\pi$
$734$	1.09161	+	1.89073i	0.0402921	+	0.0697880i
$735$		0			0
$736$	2.26668	−	3.92600i	0.0835508	−	0.144714i
$737$	−3.59375	+	13.4121i	−0.132378	+	0.494040i
$738$		0			0
$739$	35.4720	+	20.4798i	1.30486	+	0.753361i	0.981233	−	0.192825i	$-0.0617649\pi$
$739$	35.4720	+	20.4798i	1.30486	+	0.753361i	0.323626	+	0.946185i	$0.395098\pi$
$740$	−7.65905	−	14.1043i	−0.281552	−	0.518483i
$741$		0			0
$742$	1.57959	−	4.05230i	0.0579887	−	0.148764i
$743$	−17.0232	−	4.56136i	−0.624522	−	0.167340i	−0.0673394	−	0.997730i	$-0.521451\pi$
$743$	−17.0232	−	4.56136i	−0.624522	−	0.167340i	−0.557183	+	0.830390i	$0.688118\pi$
$744$		0			0
$745$	−7.66398	−	31.9146i	−0.280787	−	1.16926i
$746$	1.07842	−	1.86788i	0.0394838	−	0.0683879i
$747$		0			0
$748$	−4.37475	−	4.37475i	−0.159957	−	0.159957i
$749$	2.54363	−	23.0549i	0.0929423	−	0.842408i
$750$		0			0
$751$	−19.9021	+	34.4714i	−0.726238	+	1.25788i	0.232225	+	0.972662i	$0.425400\pi$
$751$	−19.9021	+	34.4714i	−0.726238	+	1.25788i	−0.958462	+	0.285219i	$0.907934\pi$
$752$	16.1871	−	16.1871i	0.590283	−	0.590283i
$753$		0			0
$754$	−4.60527			−0.167714
$755$	7.15109	−	24.1468i	0.260255	−	0.878792i
$756$		0			0
$757$	5.50745	+	5.50745i	0.200172	+	0.200172i	0.800074	−	0.599902i	$-0.204794\pi$
$757$	5.50745	+	5.50745i	0.200172	+	0.200172i	−0.599902	+	0.800074i	$0.704794\pi$
$758$	−0.199022	+	0.199022i	−0.00722881	+	0.00722881i
$759$		0			0
$760$	0.809848	+	1.49135i	0.0293763	+	0.0540969i
$761$	−32.5147	−	18.7724i	−1.17866	−	0.680498i	−0.222954	−	0.974829i	$-0.571570\pi$
$761$	−32.5147	−	18.7724i	−1.17866	−	0.680498i	−0.955704	+	0.294331i	$0.904903\pi$
$762$		0			0
$763$	29.6286	+	11.5493i	1.07263	+	0.418112i
$764$			1.40939i			0.0509899i
$765$		0			0
$766$	2.08885	+	1.20600i	0.0754732	+	0.0435745i
$767$	−6.36235	+	23.7446i	−0.229731	+	0.857369i
$768$		0			0
$769$	16.8089	+	29.1138i	0.606143	+	1.04987i	0.991870	+	0.127258i	$0.0406175\pi$
$769$	16.8089	+	29.1138i	0.606143	+	1.04987i	−0.385727	+	0.922613i	$0.626049\pi$
$770$	−0.501728	+	0.380934i	−0.0180810	+	0.0137279i
$771$		0			0
$772$	13.5596	+	13.5596i	0.488022	+	0.488022i
$773$	23.9006	−	6.40415i	0.859645	−	0.230341i	0.198040	−	0.980194i	$-0.436542\pi$
$773$	23.9006	−	6.40415i	0.859645	−	0.230341i	0.661605	+	0.749853i	$0.269876\pi$
$774$		0			0
$775$	5.80903	+	0.303764i	0.208667	+	0.0109115i
$776$	2.85207	+	1.64664i	0.102383	+	0.0591110i
$777$		0			0
$778$	−1.81331	−	0.485874i	−0.0650102	−	0.0174194i
$779$	−9.70425	−	5.60275i	−0.347691	−	0.200739i
$780$		0			0
$781$	3.41191	+	5.90960i	0.122088	+	0.211462i
$782$	−1.25783	−	0.337035i	−0.0449800	−	0.0120524i
$783$		0			0
$784$	−26.1723	+	8.20597i	−0.934725	+	0.293070i
$785$	−7.57685	−	0.197968i	−0.270429	−	0.00706576i
$786$		0			0
$787$	−8.22532	+	8.22532i	−0.293201	+	0.293201i	−0.838343	−	0.545142i	$-0.816476\pi$
$787$	−8.22532	+	8.22532i	−0.293201	+	0.293201i	0.545142	+	0.838343i	$0.316476\pi$
$788$	−3.64658	+	3.64658i	−0.129904	+	0.129904i
$789$		0			0
$790$	2.38693	+	0.0623656i	0.0849231	+	0.00221887i
$791$	−31.6312	−	3.48985i	−1.12467	−	0.124085i
$792$		0			0
$793$	41.2999	+	11.0663i	1.46660	+	0.392975i
$794$	−1.19950	−	2.07759i	−0.0425685	−	0.0737308i
$795$		0			0
$796$	−7.31720	−	4.22459i	−0.259351	−	0.149737i
$797$	12.2523	+	3.28298i	0.433997	+	0.116289i	0.469202	−	0.883091i	$-0.344542\pi$
$797$	12.2523	+	3.28298i	0.433997	+	0.116289i	−0.0352047	+	0.999380i	$0.511208\pi$
$798$		0			0
$799$	−17.2819	−	9.97770i	−0.611389	−	0.352986i
$800$	5.15901	−	4.64628i	0.182399	−	0.164271i
$801$		0			0
$802$	−2.48631	+	0.666204i	−0.0877946	+	0.0235245i
$803$	−2.47619	−	2.47619i	−0.0873827	−	0.0873827i
$804$		0			0
$805$	7.48241	−	17.8064i	0.263720	−	0.627592i
$806$	−0.404004	−	0.699756i	−0.0142304	−	0.0246478i
$807$		0			0
$808$	1.76546	−	6.58878i	0.0621086	−	0.231792i
$809$	37.6915	+	21.7612i	1.32516	+	0.765083i	0.984547	−	0.175120i	$-0.0560312\pi$
$809$	37.6915	+	21.7612i	1.32516	+	0.765083i	0.340616	+	0.940203i	$0.389365\pi$
$810$		0			0
$811$			10.3140i			0.362172i	0.983467	+	0.181086i	$0.0579613\pi$
$811$			10.3140i			0.362172i	−0.983467	+	0.181086i	$0.942039\pi$
$812$	−12.6562	+	32.4682i	−0.444144	+	1.13941i
$813$		0			0
$814$	0.333217	+	0.192383i	0.0116792	+	0.00674302i
$815$	20.6412	+	38.0111i	0.723029	+	1.33147i
$816$		0			0
$817$	−4.94427	+	4.94427i	−0.172978	+	0.172978i
$818$	0.735503	+	0.735503i	0.0257162	+	0.0257162i
$819$		0			0
$820$	−8.66855	+	29.2708i	−0.302719	+	1.02218i
$821$	−32.0365			−1.11808			−0.559041	−	0.829140i	$-0.688831\pi$
$821$	−32.0365			−1.11808			−0.559041	+	0.829140i	$0.688831\pi$
$822$		0			0
$823$	−17.5073	+	17.5073i	−0.610266	+	0.610266i	−0.943015	−	0.332750i	$-0.892024\pi$
$823$	−17.5073	+	17.5073i	−0.610266	+	0.610266i	0.332750	+	0.943015i	$0.392024\pi$
$824$	0.939340	−	1.62698i	0.0327235	−	0.0566787i
$825$		0			0
$826$	−1.02919	−	0.755900i	−0.0358100	−	0.0263011i
$827$	12.7443	+	12.7443i	0.443164	+	0.443164i	0.893074	−	0.449910i	$-0.148544\pi$
$827$	12.7443	+	12.7443i	0.443164	+	0.443164i	−0.449910	+	0.893074i	$0.648544\pi$
$828$		0			0
$829$	−13.7029	+	23.7341i	−0.475921	+	0.824319i	−0.999619	−	0.0275844i	$-0.991218\pi$
$829$	−13.7029	+	23.7341i	−0.475921	+	0.824319i	0.523699	+	0.851904i	$0.324552\pi$
$830$	−0.678672	−	2.82615i	−0.0235571	−	0.0980971i
$831$		0			0
$832$	44.0901	+	11.8139i	1.52855	+	0.409574i
$833$	12.8145	+	20.1861i	0.443995	+	0.699406i
$834$		0			0
$835$	9.79028	+	18.0290i	0.338807	+	0.623918i
$836$	2.55742	+	1.47653i	0.0884503	+	0.0510668i
$837$		0			0
$838$	−0.0141281	+	0.0527267i	−0.000488046	+	0.00182141i
$839$	15.4515	−	26.7627i	0.533444	−	0.923952i	−0.465793	−	0.884894i	$-0.654231\pi$
$839$	15.4515	−	26.7627i	0.533444	−	0.923952i	0.999237	−	0.0390586i	$-0.0124359\pi$
$840$		0			0
$841$	7.48378	+	12.9623i	0.258061	+	0.446975i
$842$	−0.955259	+	0.255961i	−0.0329204	+	0.00882099i
$843$		0			0
$844$	2.15000	−	1.24131i	0.0740062	−	0.0427275i
$845$	11.6821	+	48.6469i	0.401876	+	1.67351i
$846$		0			0
$847$	9.77090	−	25.0663i	0.335732	−	0.861289i
$848$	14.2765	+	53.2808i	0.490258	+	1.82967i
$849$		0			0
$850$	−1.67272	−	1.08600i	−0.0573737	−	0.0372495i
$851$	−11.7970			−0.404398
$852$		0			0
$853$	10.6135	−	2.84389i	0.363400	−	0.0973729i	−0.0724984	−	0.997369i	$-0.523097\pi$
$853$	10.6135	−	2.84389i	0.363400	−	0.0973729i	0.435899	+	0.899996i	$0.356431\pi$
$854$	−1.31476	+	1.79010i	−0.0449903	+	0.0612559i
$855$		0			0
$856$	−2.04049	−	3.53424i	−0.0697426	−	0.120798i
$857$	14.2499	+	3.81825i	0.486768	+	0.130429i	0.493852	−	0.869546i	$-0.335588\pi$
$857$	14.2499	+	3.81825i	0.486768	+	0.130429i	−0.00708450	+	0.999975i	$0.502255\pi$
$858$		0			0
$859$	1.93946	−	3.35925i	0.0661736	−	0.114616i	−0.831040	−	0.556212i	$-0.812254\pi$
$859$	1.93946	−	3.35925i	0.0661736	−	0.114616i	0.897214	+	0.441596i	$0.145588\pi$
$860$	16.2426	+	9.95221i	0.553869	+	0.339368i
$861$		0			0
$862$	−3.81613	+	1.02253i	−0.129978	+	0.0348275i
$863$	16.4466	+	4.40686i	0.559850	+	0.150011i	0.527638	−	0.849470i	$-0.323078\pi$
$863$	16.4466	+	4.40686i	0.559850	+	0.150011i	0.0322127	+	0.999481i	$0.489745\pi$
$864$		0			0
$865$	0.868899	−	33.2555i	0.0295434	−	1.13072i
$866$		−	4.32837i		−	0.147084i
$867$		0			0
$868$	−6.04371	+	0.925256i	−0.205137	+	0.0314052i
$869$	7.22128	−	4.16921i	0.244965	−	0.141431i
$870$		0			0
$871$	−78.4327	+	45.2831i	−2.65759	+	1.53436i
$872$	5.40438	−	1.44810i	0.183015	−	0.0490388i
$873$		0			0
$874$	0.621560			0.0210246
$875$	19.3230	−	22.3969i	0.653235	−	0.757155i
$876$		0			0
$877$	8.44765	−	2.26354i	0.285257	−	0.0764344i	−0.113353	−	0.993555i	$-0.536159\pi$
$877$	8.44765	−	2.26354i	0.285257	−	0.0764344i	0.398610	+	0.917120i	$0.369493\pi$
$878$	1.47965	+	1.47965i	0.0499359	+	0.0499359i
$879$		0			0
$880$	2.26869	−	7.66059i	0.0764775	−	0.258239i
$881$			32.4079i			1.09185i	0.837835	+	0.545924i	$0.183821\pi$
$881$			32.4079i			1.09185i	−0.837835	+	0.545924i	$0.816179\pi$
$882$		0			0
$883$	−29.8636	+	29.8636i	−1.00499	+	1.00499i	−0.00500145	+	0.999987i	$0.501592\pi$
$883$	−29.8636	+	29.8636i	−1.00499	+	1.00499i	−0.999987	+	0.00500145i	$0.998408\pi$
$884$		−	40.3536i		−	1.35724i
$885$		0			0
$886$	−3.47641			−0.116792
$887$	13.9325	+	51.9969i	0.467808	+	1.74588i	0.647407	+	0.762144i	$0.275853\pi$
$887$	13.9325	+	51.9969i	0.467808	+	1.74588i	−0.179599	+	0.983740i	$0.557480\pi$
$888$		0			0
$889$	26.1836	+	19.2309i	0.878170	+	0.644984i
$890$	0.884362	−	0.480236i	0.0296439	−	0.0160975i
$891$		0			0
$892$	−14.2843	−	53.3098i	−0.478275	−	1.78495i
$893$	9.20044	+	2.46525i	0.307881	+	0.0824964i
$894$		0			0
$895$	−3.93008	−	16.3658i	−0.131368	−	0.547048i
$896$	−5.75307	+	7.83301i	−0.192197	+	0.261683i
$897$		0			0
$898$	2.56935	−	2.56935i	0.0857403	−	0.0857403i
$899$	−3.85712	+	6.68072i	−0.128642	+	0.222815i
$900$		0			0
$901$	41.6422	−	24.0421i	1.38730	−	0.800959i
$902$	−0.189416	−	0.706909i	−0.00630686	−	0.0235375i
$903$		0			0
$904$	−4.84895	+	2.79954i	−0.161274	+	0.0931114i
$905$	−1.98997	+	1.88863i	−0.0661489	+	0.0627802i
$906$		0			0
$907$	−1.45032	+	5.41268i	−0.0481572	+	0.179725i	−0.985815	−	0.167834i	$-0.946323\pi$
$907$	−1.45032	+	5.41268i	−0.0481572	+	0.179725i	0.937658	+	0.347559i	$0.112989\pi$
$908$	−1.38111	+	5.15438i	−0.0458339	+	0.171054i
$909$		0			0
$910$	−4.07093	−	0.557115i	−0.134950	−	0.0184682i
$911$	−20.2824	+	35.1302i	−0.671987	+	1.16392i	0.305353	+	0.952239i	$0.401226\pi$
$911$	−20.2824	+	35.1302i	−0.671987	+	1.16392i	−0.977340	+	0.211676i	$0.932108\pi$
$912$		0			0
$913$	−7.17713	−	7.17713i	−0.237528	−	0.237528i
$914$		−	0.727699i		−	0.0240701i
$915$		0			0
$916$	−4.66405	−	2.69279i	−0.154105	−	0.0889723i
$917$	32.3362	+	12.6047i	1.06783	+	0.416244i
$918$		0			0
$919$	15.0280	−	8.67643i	0.495729	−	0.286209i	−0.231219	−	0.972902i	$-0.574271\pi$
$919$	15.0280	−	8.67643i	0.495729	−	0.286209i	0.726948	+	0.686693i	$0.240938\pi$
$920$	−0.793505	−	3.30434i	−0.0261611	−	0.108941i
$921$		0			0
$922$	−0.125300	−	0.467626i	−0.00412654	−	0.0154005i
$923$	−11.5196	+	42.9919i	−0.379173	+	1.41509i
$924$		0			0
$925$	−17.1836	−	5.58110i	−0.564994	−	0.183505i
$926$	1.11494	+	1.93114i	0.0366393	+	0.0634611i
$927$		0			0
$928$	2.38304	+	8.89362i	0.0782271	+	0.291947i
$929$	31.4728			1.03259			0.516294	−	0.856412i	$-0.327311\pi$
$929$	31.4728			1.03259			0.516294	+	0.856412i	$0.327311\pi$
$930$		0			0
$931$	−8.40186	−	7.72371i	−0.275360	−	0.253134i
$932$	5.42086	−	20.2309i	0.177566	−	0.662686i
$933$		0			0
$934$	2.25278	+	3.90193i	0.0737131	+	0.127675i
$935$	−6.96219	−	0.181908i	−0.227688	−	0.00594902i
$936$		0			0
$937$	12.3936	−	12.3936i	0.404882	−	0.404882i	−0.475067	−	0.879950i	$-0.657576\pi$
$937$	12.3936	−	12.3936i	0.404882	−	0.404882i	0.879950	+	0.475067i	$0.157576\pi$
$938$	−0.711946	−	4.65039i	−0.0232459	−	0.151840i
$939$		0			0
$940$	0.677767	−	25.9403i	0.0221063	−	0.846079i
$941$			16.5978i			0.541072i	0.962710	+	0.270536i	$0.0872010\pi$
$941$			16.5978i			0.541072i	−0.962710	+	0.270536i	$0.912799\pi$
$942$		0			0
$943$	15.8665	+	15.8665i	0.516685	+	0.516685i
$944$	16.1951			0.527107
$945$		0			0
$946$	−0.456674			−0.0148477
$947$	38.5504	+	38.5504i	1.25272	+	1.25272i	0.954496	+	0.298223i	$0.0963938\pi$
$947$	38.5504	+	38.5504i	1.25272	+	1.25272i	0.298223	+	0.954496i	$0.403606\pi$
$948$		0			0
$949$		−	22.8409i		−	0.741447i
$950$	0.905368	+	0.294056i	0.0293740	+	0.00954043i
$951$		0			0
$952$	3.91957	+	1.52786i	0.127034	+	0.0495181i
$953$	−34.1611	+	34.1611i	−1.10659	+	1.10659i	−0.112990	+	0.993596i	$0.536043\pi$
$953$	−34.1611	+	34.1611i	−1.10659	+	1.10659i	−0.993596	+	0.112990i	$0.963957\pi$
$954$		0			0
$955$	1.09218	+	1.15079i	0.0353422	+	0.0372386i
$956$	−22.2975	−	38.6204i	−0.721153	−	1.24907i
$957$		0			0
$958$	−0.932377	+	3.47968i	−0.0301237	+	0.112423i
$959$	4.46401	−	40.4607i	0.144150	−	1.30655i
$960$		0			0
$961$	29.6465			0.956339
$962$	0.649542	+	2.42413i	0.0209421	+	0.0781569i
$963$		0			0
$964$	−9.11049	−	15.7798i	−0.293429	−	0.508234i
$965$	21.5795	+	0.563827i	0.694668	+	0.0181502i
$966$		0			0
$967$	8.03134	−	29.9734i	0.258270	−	0.963878i	−0.707971	−	0.706241i	$-0.750389\pi$
$967$	8.03134	−	29.9734i	0.258270	−	0.963878i	0.966242	−	0.257637i	$-0.0829439\pi$
$968$	−1.22512	−	4.57220i	−0.0393767	−	0.146956i
$969$		0			0
$970$	1.79623	−	0.431348i	0.0576736	−	0.0138497i
$971$	23.0153	−	13.2879i	0.738595	−	0.426428i	−0.0829632	−	0.996553i	$-0.526438\pi$
$971$	23.0153	−	13.2879i	0.738595	−	0.426428i	0.821558	+	0.570125i	$0.193105\pi$
$972$		0			0
$973$	16.3381	+	20.3904i	0.523777	+	0.653685i
$974$	0.0241317	+	0.0139324i	0.000773228	+	0.000446424i
$975$		0			0
$976$		−	28.1688i		−	0.901660i
$977$	−35.7147	−	35.7147i	−1.14261	−	1.14261i	−0.987970	−	0.154644i	$-0.950577\pi$
$977$	−35.7147	−	35.7147i	−1.14261	−	1.14261i	−0.154644	−	0.987970i	$-0.549423\pi$
$978$		0			0
$979$	1.75716	−	3.04349i	0.0561591	−	0.0972704i
$980$	−15.1155	+	27.1699i	−0.482846	+	0.867911i
$981$		0			0
$982$	−0.803919	+	3.00027i	−0.0256541	+	0.0957424i
$983$	0.144078	−	0.537708i	0.00459539	−	0.0171502i	−0.963590	−	0.267384i	$-0.913841\pi$
$983$	0.144078	−	0.537708i	0.00459539	−	0.0171502i	0.968185	+	0.250234i	$0.0805075\pi$
$984$		0			0
$985$	−0.151630	+	5.80335i	−0.00483132	+	0.184910i
$986$	2.29047	−	1.32240i	0.0729435	−	0.0421139i
$987$		0			0
$988$	4.98521	+	18.6050i	0.158601	+	0.591905i
$989$	12.1259	−	7.00088i	0.385581	−	0.222615i
$990$		0			0
$991$	−22.8617	+	39.5976i	−0.726226	+	1.25786i	0.232241	+	0.972658i	$0.425394\pi$
$991$	−22.8617	+	39.5976i	−0.726226	+	1.25786i	−0.958467	+	0.285202i	$0.907939\pi$
$992$	−1.14230	+	1.14230i	−0.0362681	+	0.0362681i
$993$		0			0
$994$	−1.86344	−	1.36863i	−0.0591046	−	0.0434102i
$995$	−9.24839	+	2.22091i	−0.293194	+	0.0704075i
$996$		0			0
$997$	−43.0999	−	11.5486i	−1.36499	−	0.365747i	−0.499341	−	0.866405i	$-0.666425\pi$
$997$	−43.0999	−	11.5486i	−1.36499	−	0.365747i	−0.865645	+	0.500658i	$0.833091\pi$
$998$	−0.262501	−	0.979668i	−0.00830933	−	0.0310109i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bv.e.262.20		160
3.2	odd	2		315.2.bs.e.52.21	✓	160
5.3	odd	4	inner	945.2.bv.e.73.20		160
7.5	odd	6		945.2.cj.e.397.20		160
9.4	even	3		945.2.cj.e.577.21		160
9.5	odd	6		315.2.cg.e.157.20	yes	160
15.8	even	4		315.2.bs.e.178.21	yes	160
21.5	even	6		315.2.cg.e.187.21	yes	160
35.33	even	12		945.2.cj.e.208.21		160
45.13	odd	12		945.2.cj.e.388.20		160
45.23	even	12		315.2.cg.e.283.21	yes	160
63.5	even	6		315.2.bs.e.292.21	yes	160
63.40	odd	6	inner	945.2.bv.e.712.20		160
105.68	odd	12		315.2.cg.e.313.20	yes	160
315.68	odd	12		315.2.bs.e.103.21	yes	160
315.103	even	12	inner	945.2.bv.e.523.20		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.21	✓	160	3.2	odd	2
315.2.bs.e.103.21	yes	160	315.68	odd	12
315.2.bs.e.178.21	yes	160	15.8	even	4
315.2.bs.e.292.21	yes	160	63.5	even	6
315.2.cg.e.157.20	yes	160	9.5	odd	6
315.2.cg.e.187.21	yes	160	21.5	even	6
315.2.cg.e.283.21	yes	160	45.23	even	12
315.2.cg.e.313.20	yes	160	105.68	odd	12
945.2.bv.e.73.20		160	5.3	odd	4	inner
945.2.bv.e.262.20		160	1.1	even	1	trivial
945.2.bv.e.523.20		160	315.103	even	12	inner
945.2.bv.e.712.20		160	63.40	odd	6	inner
945.2.cj.e.208.21		160	35.33	even	12
945.2.cj.e.388.20		160	45.13	odd	12
945.2.cj.e.397.20		160	7.5	odd	6
945.2.cj.e.577.21		160	9.4	even	3

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bv (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0825718 + 0.0825718i) q^{2} -1.98636i q^{4} +(-1.53930 - 1.62190i) q^{5} +(2.61528 - 0.400384i) q^{7} +(0.329161 - 0.329161i) q^{8} +O(q^{10})\)	\(q+(0.0825718 + 0.0825718i) q^{2} -1.98636i q^{4} +(-1.53930 - 1.62190i) q^{5} +(2.61528 - 0.400384i) q^{7} +(0.329161 - 0.329161i) q^{8} +(0.00682007 - 0.261026i) q^{10} +(-0.455930 - 0.789693i) q^{11} +(1.53935 - 5.74495i) q^{13} +(0.249009 + 0.182888i) q^{14} -3.91837 q^{16} +(0.884052 + 3.29933i) q^{17} +(-0.815184 - 1.41194i) q^{19} +(-3.22168 + 3.05761i) q^{20} +(0.0275595 - 0.102853i) q^{22} +(0.844982 + 3.15352i) q^{23} +(-0.261101 + 4.99318i) q^{25} +(0.601478 - 0.347264i) q^{26} +(-0.795308 - 5.19490i) q^{28} +(-5.74244 - 3.31540i) q^{29} -1.16339i q^{31} +(-0.981869 - 0.981869i) q^{32} +(-0.199433 + 0.345429i) q^{34} +(-4.67509 - 3.62541i) q^{35} +(-0.935230 + 3.49032i) q^{37} +(0.0492752 - 0.183898i) q^{38} +(-1.04054 - 0.0271873i) q^{40} +(5.95218 - 3.43649i) q^{41} +(-1.11001 - 4.14262i) q^{43} +(-1.56862 + 0.905642i) q^{44} +(-0.190620 + 0.330163i) q^{46} +(-4.13109 + 4.13109i) q^{47} +(6.67939 - 2.09423i) q^{49} +(-0.433855 + 0.390736i) q^{50} +(-11.4116 - 3.05772i) q^{52} +(-3.64349 - 13.5977i) q^{53} +(-0.578988 + 1.95505i) q^{55} +(0.729058 - 0.992640i) q^{56} +(-0.200405 - 0.747922i) q^{58} -4.13313 q^{59} +7.18890i q^{61} +(0.0960635 - 0.0960635i) q^{62} +7.67459i q^{64} +(-11.6873 + 6.34654i) q^{65} +(-10.7674 - 10.7674i) q^{67} +(6.55366 - 1.75605i) q^{68} +(-0.0866741 - 0.685386i) q^{70} -7.48342 q^{71} +(3.70949 - 0.993956i) q^{73} +(-0.365426 + 0.210979i) q^{74} +(-2.80463 + 1.61925i) q^{76} +(-1.50856 - 1.88272i) q^{77} +9.14441i q^{79} +(6.03155 + 6.35519i) q^{80} +(0.775240 + 0.207725i) q^{82} +(10.7518 - 2.88094i) q^{83} +(3.99035 - 6.51250i) q^{85} +(0.250408 - 0.433720i) q^{86} +(-0.410011 - 0.109862i) q^{88} +(1.92701 + 3.33768i) q^{89} +(1.72566 - 15.6410i) q^{91} +(6.26403 - 1.67844i) q^{92} -0.682222 q^{94} +(-1.03521 + 3.49555i) q^{95} +(1.83106 + 6.83360i) q^{97} +(0.724453 + 0.378604i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8}+O(q^{10}) \) 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8	\( 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8} - 24 q^{10} + 16 q^{11} - 152 q^{16} + 6 q^{17} - 60 q^{20} + 8 q^{22} - 8 q^{23} + 2 q^{25} + 36 q^{26} + 22 q^{28} - 12 q^{32} + 36 q^{35} - 4 q^{37} + 18 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 44 q^{50} + 54 q^{52} - 8 q^{53} - 148 q^{56} + 28 q^{58} + 124 q^{65} - 24 q^{67} - 42 q^{68} - 34 q^{70} + 40 q^{71} + 36 q^{73} + 96 q^{76} - 58 q^{77} - 36 q^{80} - 66 q^{82} + 138 q^{83} - 20 q^{85} + 16 q^{86} + 46 q^{88} - 48 q^{91} + 26 q^{92} - 188 q^{95} + 48 q^{97} - 102 q^{98}+O(q^{100}) \) 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8 - 24 * q^10 + 16 * q^11 - 152 * q^16 + 6 * q^17 - 60 * q^20 + 8 * q^22 - 8 * q^23 + 2 * q^25 + 36 * q^26 + 22 * q^28 - 12 * q^32 + 36 * q^35 - 4 * q^37 + 18 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 44 * q^50 + 54 * q^52 - 8 * q^53 - 148 * q^56 + 28 * q^58 + 124 * q^65 - 24 * q^67 - 42 * q^68 - 34 * q^70 + 40 * q^71 + 36 * q^73 + 96 * q^76 - 58 * q^77 - 36 * q^80 - 66 * q^82 + 138 * q^83 - 20 * q^85 + 16 * q^86 + 46 * q^88 - 48 * q^91 + 26 * q^92 - 188 * q^95 + 48 * q^97 - 102 * q^98

Introduction

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