LMFDB - Embedded newform 945.2.bv.e.523.20

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			523.20
Character	$\chi$	$=$	945.523
Dual form			945.2.bv.e.262.20

$q$-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 $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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	−0.677310	−	0.735697i	$-0.736855\pi$
$2$	0.0825718	−	0.0825718i	0.0583871	−	0.0583871i	0.735697	+	0.677310i	$0.236855\pi$
$3$		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	−0.926538	−	0.376202i	$-0.877230\pi$
$11$	−0.455930	+	0.789693i	−0.137468	+	0.238101i	0.789070	+	0.614304i	$0.210563\pi$
$12$		0			0
$13$	1.53935	+	5.74495i	0.426940	+	1.59336i	0.759649	+	0.650333i	$0.225371\pi$
$13$	1.53935	+	5.74495i	0.426940	+	1.59336i	−0.332709	+	0.943030i	$0.607963\pi$
$14$	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	−0.771958	−	0.635674i	$-0.780722\pi$
$17$	0.884052	−	3.29933i	0.214414	−	0.800204i	0.986372	−	0.164530i	$-0.0526109\pi$
$18$		0			0
$19$	−0.815184	+	1.41194i	−0.187016	+	0.323921i	−0.944254	−	0.329218i	$-0.893215\pi$
$19$	−0.815184	+	1.41194i	−0.187016	+	0.323921i	0.757238	+	0.653139i	$0.226548\pi$
$20$	−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	−0.820155	−	0.572142i	$-0.806113\pi$
$23$	0.844982	−	3.15352i	0.176191	−	0.657553i	0.996346	−	0.0854118i	$-0.0272206\pi$
$24$		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	−0.927181	−	0.374615i	$-0.877775\pi$
$29$	−5.74244	+	3.31540i	−1.06635	+	0.615655i	−0.139164	+	0.990269i	$0.544442\pi$
$30$		0			0
$31$			1.16339i			0.208952i	0.994527	+	0.104476i	$0.0333165\pi$
$31$			1.16339i			0.208952i	−0.994527	+	0.104476i	$0.966684\pi$
$32$	−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	−0.999209	−	0.0397644i	$-0.987339\pi$
$37$	−0.935230	−	3.49032i	−0.153751	−	0.573806i	0.845458	−	0.534042i	$-0.179327\pi$
$38$	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	0.886677	−	0.462389i	$-0.153008\pi$
$41$	5.95218	+	3.43649i	0.929575	+	0.536690i	0.0428978	+	0.999079i	$0.486341\pi$
$42$		0			0
$43$	−1.11001	+	4.14262i	−0.169275	+	0.631744i	0.828181	+	0.560461i	$0.189376\pi$
$43$	−1.11001	+	4.14262i	−0.169275	+	0.631744i	−0.997456	+	0.0712831i	$0.977291\pi$
$44$	−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	0.338416	−	0.940997i	$-0.390109\pi$
$47$	−4.13109	−	4.13109i	−0.602581	−	0.602581i	−0.940997	+	0.338416i	$0.890109\pi$
$48$		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	−0.00354619	+	0.999994i	$0.501129\pi$
$53$	−3.64349	+	13.5977i	−0.500472	+	1.86779i	−0.496926	+	0.867793i	$0.665538\pi$
$54$		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	$-0.847770\pi$
$61$		−	7.18890i		−	0.920444i	0.887804	−	0.460222i	$-0.152230\pi$
$62$	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	−0.398099	+	0.917342i	$0.630330\pi$
$67$	−10.7674	+	10.7674i	−1.31544	+	1.31544i	−0.917342	+	0.398099i	$0.869670\pi$
$68$	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	0.469280	−	0.883050i	$-0.344514\pi$
$73$	3.70949	+	0.993956i	0.434163	+	0.116334i	−0.0351165	+	0.999383i	$0.511180\pi$
$74$	−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	$-0.828010\pi$
$79$		−	9.14441i		−	1.02883i	0.857542	−	0.514413i	$-0.171990\pi$
$80$	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	0.794992	−	0.606620i	$-0.207475\pi$
$83$	10.7518	+	2.88094i	1.18017	+	0.316224i	0.385174	+	0.922844i	$0.374142\pi$
$84$		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	−0.745635	−	0.666355i	$-0.767854\pi$
$89$	1.92701	−	3.33768i	0.204262	−	0.353793i	0.949897	+	0.312562i	$0.101187\pi$
$90$		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	−0.808517	−	0.588473i	$-0.799729\pi$
$97$	1.83106	−	6.83360i	0.185916	−	0.693847i	0.994433	−	0.105374i	$-0.0336040\pi$
$98$	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	0.973600	−	0.228261i	$-0.0733038\pi$
$101$	12.6902	+	7.32668i	1.26272	+	0.729032i	0.289120	+	0.957293i	$0.406637\pi$
$102$		0			0
$103$	3.89828	+	1.04454i	0.384109	+	0.102922i	0.445706	−	0.895179i	$-0.352953\pi$
$103$	3.89828	+	1.04454i	0.384109	+	0.102922i	−0.0615970	+	0.998101i	$0.519619\pi$
$104$	−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	0.984588	+	0.174889i	$0.0559566\pi$
$107$	2.26902	+	8.46809i	0.219354	+	0.818641i	−0.765234	+	0.643752i	$0.777377\pi$
$108$		0			0
$109$	10.4090	−	6.00964i	0.997001	−	0.575619i	0.0896413	−	0.995974i	$-0.471428\pi$
$109$	10.4090	−	6.00964i	0.997001	−	0.575619i	0.907360	+	0.420355i	$0.138095\pi$
$110$	−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	−0.759888	−	0.650054i	$-0.774746\pi$
$113$	−11.6182	+	3.11308i	−1.09294	+	0.292853i	−0.333056	+	0.942907i	$0.608080\pi$
$114$		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	−0.207735	−	0.978185i	$-0.566609\pi$
$127$	8.68253	−	8.68253i	0.770450	−	0.770450i	0.978185	+	0.207735i	$0.0666091\pi$
$128$	−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	0.0865118	−	0.996251i	$-0.472428\pi$
$131$	11.3602	−	6.55882i	0.992546	−	0.573047i	0.906034	+	0.423204i	$0.139095\pi$
$132$		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	0.898108	+	0.439774i	$0.144942\pi$
$137$	3.98207	+	14.8613i	0.340211	+	1.26968i	−0.557898	+	0.829910i	$0.688392\pi$
$138$		0			0
$139$	4.93784	−	8.55258i	0.418822	−	0.725421i	−0.576999	−	0.816745i	$-0.695777\pi$
$139$	4.93784	−	8.55258i	0.418822	−	0.725421i	0.995821	+	0.0913239i	$0.0291099\pi$
$140$	−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	0.121169	−	0.992632i	$-0.461336\pi$
$149$	12.7119	−	7.33921i	1.04140	−	0.601252i	0.920229	+	0.391380i	$0.128002\pi$
$150$		0			0
$151$	5.63119	−	9.75351i	0.458260	−	0.793729i	−0.540609	−	0.841274i	$-0.681806\pi$
$151$	5.63119	−	9.75351i	0.458260	−	0.793729i	0.998869	+	0.0475446i	$0.0151396\pi$
$152$	−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	0.796252	−	0.604965i	$-0.206813\pi$
$157$	2.39683	+	2.39683i	0.191288	+	0.191288i	−0.604965	+	0.796252i	$0.706813\pi$
$158$	−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	−0.900695	−	0.434453i	$-0.856942\pi$
$163$	−18.6846	+	5.00653i	−1.46349	+	0.392142i	−0.562798	+	0.826595i	$0.690275\pi$
$164$	−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	−0.584854	−	0.811139i	$-0.698848\pi$
$167$	−8.86226	+	2.37464i	−0.685782	+	0.183755i	−0.100929	+	0.994894i	$0.532181\pi$
$168$		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	−0.183252	−	0.983066i	$-0.558663\pi$
$173$	10.5199	−	10.5199i	0.799814	−	0.799814i	0.983066	+	0.183252i	$0.0586626\pi$
$174$		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	−0.236197	−	0.971705i	$-0.575901\pi$
$179$	6.51864	−	3.76354i	0.487226	−	0.281300i	0.723423	+	0.690405i	$0.242568\pi$
$180$		0			0
$181$			1.22694i			0.0911977i	0.998960	+	0.0455989i	$0.0145196\pi$
$181$			1.22694i			0.0911977i	−0.998960	+	0.0455989i	$0.985480\pi$
$182$	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	0.417366	−	0.908738i	$-0.362953\pi$
$193$	−6.82635	−	6.82635i	−0.491372	−	0.491372i	−0.908738	+	0.417366i	$0.862953\pi$
$194$	−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	−0.769474	−	0.638678i	$-0.779482\pi$
$197$	−1.83581	+	1.83581i	−0.130796	+	0.130796i	0.638678	+	0.769474i	$0.279482\pi$
$198$		0			0
$199$	2.12679	+	3.68372i	0.150764	+	0.261132i	0.931509	−	0.363719i	$-0.118493\pi$
$199$	2.12679	+	3.68372i	0.150764	+	0.261132i	−0.780744	+	0.624851i	$0.785160\pi$
$200$	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	−0.843713	−	0.536794i	$-0.819635\pi$
$211$	0.624913	−	1.08238i	0.0430208	−	0.0745142i	0.886734	+	0.462280i	$0.152968\pi$
$212$	−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	0.993535	−	0.113525i	$-0.0362143\pi$
$223$	26.8379	+	7.19120i	1.79720	+	0.481558i	0.803664	+	0.595083i	$0.202881\pi$
$224$	−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	−0.343903	−	0.939005i	$-0.611749\pi$
$227$	−2.59488	+	0.695297i	−0.172229	+	0.0461485i	0.171674	+	0.985154i	$0.445082\pi$
$228$		0			0
$229$	1.35564	+	2.34803i	0.0895831	+	0.155162i	0.907335	−	0.420408i	$-0.138113\pi$
$229$	1.35564	+	2.34803i	0.0895831	+	0.155162i	−0.817752	+	0.575571i	$0.804780\pi$
$230$	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	0.0907264	−	0.995876i	$-0.471081\pi$
$233$	10.1849	−	2.72904i	0.667236	−	0.178785i	0.576509	+	0.817091i	$0.304414\pi$
$234$		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	0.972617	−	0.232414i	$-0.0746626\pi$
$239$	19.4428	+	11.2253i	1.25765	+	0.726104i	0.285032	+	0.958518i	$0.407996\pi$
$240$		0			0
$241$	7.94408	+	4.58651i	0.511723	+	0.295443i	0.733542	−	0.679645i	$-0.237866\pi$
$241$	7.94408	+	4.58651i	0.511723	+	0.295443i	−0.221819	+	0.975088i	$0.571199\pi$
$242$	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	$0.112807\pi$
$251$			10.9957i			0.694041i	−0.937858	+	0.347020i	$0.887193\pi$
$252$		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	−0.997902	−	0.0647433i	$-0.979377\pi$
$257$	−1.62431	+	6.06202i	−0.101322	+	0.378138i	0.896580	+	0.442882i	$0.146044\pi$
$258$		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	0.704365	−	0.709838i	$-0.251232\pi$
$263$	27.0712	−	7.25371i	1.66928	−	0.447283i	0.964917	+	0.262555i	$0.0845650\pi$
$264$		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	0.543987	−	0.839094i	$-0.316914\pi$
$269$	−7.45736	−	12.9165i	−0.454683	−	0.787535i	−0.998670	+	0.0515593i	$0.983581\pi$
$270$		0			0
$271$	−13.3846	−	7.72761i	−0.813058	−	0.469419i	0.0349588	−	0.999389i	$-0.488870\pi$
$271$	−13.3846	−	7.72761i	−0.813058	−	0.469419i	−0.848017	+	0.529970i	$0.822203\pi$
$272$	−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	−0.945407	−	0.325892i	$-0.894335\pi$
$277$	−4.82001	−	17.9885i	−0.289607	−	1.08083i	0.655800	−	0.754934i	$-0.272331\pi$
$278$	−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	0.730636	−	0.682767i	$-0.239224\pi$
$281$	−3.78805	−	6.56109i	−0.225976	−	0.391402i	−0.956612	+	0.291366i	$0.905890\pi$
$282$		0			0
$283$	−9.76300	+	9.76300i	−0.580350	+	0.580350i	−0.934999	−	0.354649i	$-0.884600\pi$
$283$	−9.76300	+	9.76300i	−0.580350	+	0.580350i	0.354649	+	0.934999i	$0.384600\pi$
$284$		−	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	0.945334	−	0.326103i	$-0.105736\pi$
$293$	−0.623080	−	2.32537i	−0.0364007	−	0.135849i	−0.981735	+	0.190254i	$0.939069\pi$
$294$		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	0.375033	−	0.927012i	$-0.377632\pi$
$307$	−9.67145	−	9.67145i	−0.551979	−	0.551979i	−0.927012	+	0.375033i	$0.877632\pi$
$308$	−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	$0.272128\pi$
$311$			26.6121i			1.50903i	−0.656281	+	0.754516i	$0.727872\pi$
$312$		0			0
$313$	0.524423	−	0.524423i	0.0296422	−	0.0296422i	−0.692130	−	0.721773i	$-0.743328\pi$
$313$	0.524423	−	0.524423i	0.0296422	−	0.0296422i	0.721773	+	0.692130i	$0.243328\pi$
$314$	0.395821			0.0223374
$315$		0			0
$316$	18.1641			1.02181
$317$	−5.05102	+	5.05102i	−0.283694	+	0.283694i	−0.834580	−	0.550887i	$-0.814290\pi$
$317$	−5.05102	+	5.05102i	−0.283694	+	0.283694i	0.550887	+	0.834580i	$0.314290\pi$
$318$		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	0.994021	+	0.109191i	$0.0348259\pi$
$337$	3.44698	+	12.8643i	0.187769	+	0.700763i	−0.806252	+	0.591572i	$0.798507\pi$
$338$	−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	−0.896768	−	0.442502i	$-0.854091\pi$
$347$	−8.46204	+	8.46204i	−0.454266	+	0.454266i	0.442502	+	0.896768i	$0.354091\pi$
$348$		0			0
$349$	15.7451	+	27.2713i	0.842814	+	1.45980i	0.887506	+	0.460797i	$0.152436\pi$
$349$	15.7451	+	27.2713i	0.842814	+	1.45980i	−0.0446913	+	0.999001i	$0.514230\pi$
$350$	−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	0.655817	+	0.754920i	$0.272324\pi$
$353$	8.74262	+	32.6279i	0.465323	+	1.73661i	−0.190494	+	0.981688i	$0.561009\pi$
$354$		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	−0.0847568	−	0.996402i	$-0.527011\pi$
$359$	−18.7587	−	10.8303i	−0.990044	−	0.571602i	−0.905288	+	0.424799i	$0.860345\pi$
$360$		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	0.245424	−	0.969416i	$-0.421073\pi$
$367$	18.0591	−	4.83891i	0.942676	−	0.252589i	0.697252	+	0.716826i	$0.254406\pi$
$368$	−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	0.724578	+	0.689193i	$0.242035\pi$
$373$	−4.78044	+	17.8408i	−0.247522	+	0.923763i	−0.972099	+	0.234570i	$0.924632\pi$
$374$	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	$-0.980283\pi$
$379$		−	2.41029i		−	0.123808i	0.998082	−	0.0619042i	$-0.0197173\pi$
$380$	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	0.729581	−	0.683894i	$-0.239715\pi$
$383$	19.9514	+	5.34597i	1.01947	+	0.273166i	0.289889	+	0.957060i	$0.406382\pi$
$384$		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	0.103648	−	0.994614i	$-0.466949\pi$
$389$	−13.9223	−	8.03806i	−0.705890	−	0.407546i	−0.809537	+	0.587068i	$0.800282\pi$
$390$		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	−0.719741	−	0.694243i	$-0.755739\pi$
$397$	−19.8438	+	5.31714i	−0.995934	+	0.266860i	−0.276193	+	0.961102i	$0.589073\pi$
$398$	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	−0.998247	−	0.0591852i	$-0.981150\pi$
$401$	−11.0213	−	19.0895i	−0.550379	−	0.953285i	0.447868	−	0.894100i	$-0.352184\pi$
$402$		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	−0.860260	−	0.509856i	$-0.829699\pi$
$419$	0.233728	−	0.404828i	0.0114183	−	0.0197771i	0.871678	+	0.490079i	$0.163032\pi$
$420$		0			0
$421$	−4.23449	−	7.33434i	−0.206376	−	0.357454i	0.744194	−	0.667963i	$-0.232834\pi$
$421$	−4.23449	−	7.33434i	−0.206376	−	0.357454i	−0.950570	+	0.310509i	$0.899500\pi$
$422$	−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	−0.909454	−	0.415805i	$-0.863500\pi$
$431$	−16.9162	−	29.2997i	−0.814825	−	1.41132i	0.0946293	−	0.995513i	$-0.469833\pi$
$432$		0			0
$433$	−26.2098	+	26.2098i	−1.25956	+	1.25956i	−0.308258	+	0.951303i	$0.599746\pi$
$433$	−26.2098	+	26.2098i	−1.25956	+	1.25956i	−0.951303	+	0.308258i	$0.900254\pi$
$434$	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	−1.00000		0.000156112i	$-0.999950\pi$
$443$	−21.0509	−	21.0509i	−1.00016	−	1.00016i	−0.000156112	−	1.00000i	$-0.500050\pi$
$444$		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	$0.262462\pi$
$449$			31.1166i			1.46848i	−0.678889	+	0.734240i	$0.737538\pi$
$450$		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	−0.802618	−	0.596493i	$-0.796560\pi$
$457$	−4.40646	+	4.40646i	−0.206126	+	0.206126i	0.596493	+	0.802618i	$0.296560\pi$
$458$	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	−0.581274	−	0.813708i	$-0.697446\pi$
$461$	−3.59037	+	2.07290i	−0.167220	+	0.0965446i	0.414054	+	0.910252i	$0.364112\pi$
$462$		0			0
$463$	18.4450	−	4.94233i	0.857214	−	0.229690i	0.196663	−	0.980471i	$-0.436990\pi$
$463$	18.4450	−	4.94233i	0.857214	−	0.229690i	0.660551	+	0.750781i	$0.270323\pi$
$464$	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	0.745668	−	0.666317i	$-0.232130\pi$
$467$	37.2688	−	9.98615i	1.72459	−	0.462104i	0.978926	+	0.204214i	$0.0654638\pi$
$468$		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	−0.261996	−	0.965069i	$-0.584381\pi$
$479$	15.4248	−	26.7165i	0.704776	−	1.22071i	0.966772	−	0.255639i	$-0.0822858\pi$
$480$		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	0.264038	−	0.964512i	$-0.414946\pi$
$487$	0.230491	+	0.0617598i	0.0104445	+	0.00279861i	−0.253593	+	0.967311i	$0.581612\pi$
$488$	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	−0.392586	−	0.919715i	$-0.628419\pi$
$491$	13.2996	−	23.0356i	0.600204	−	1.03958i	0.992790	−	0.119868i	$-0.0382473\pi$
$492$		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	−0.658821	−	0.752300i	$-0.728944\pi$
$499$	−7.52176	+	4.34269i	−0.336720	+	0.194405i	0.322101	+	0.946705i	$0.395611\pi$
$500$	−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	−0.724562	−	0.689210i	$-0.757958\pi$
$503$	−0.792859	+	0.792859i	−0.0353518	+	0.0353518i	0.689210	+	0.724562i	$0.257958\pi$
$504$		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	−0.945069	−	0.326872i	$-0.894005\pi$
$509$	−17.0474	−	29.5270i	−0.755614	−	1.30876i	0.189455	−	0.981889i	$-0.439328\pi$
$510$		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	−0.927861	−	0.372926i	$-0.878355\pi$
$521$	−24.3965	+	14.0853i	−1.06883	+	0.617088i	−0.140967	+	0.990014i	$0.545021\pi$
$522$		0			0
$523$	−1.21481	−	4.53372i	−0.0531198	−	0.198246i	0.934266	−	0.356576i	$-0.116056\pi$
$523$	−1.21481	−	4.53372i	−0.0531198	−	0.198246i	−0.987386	+	0.158330i	$0.949389\pi$
$524$	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	−0.769898	−	0.638167i	$-0.779693\pi$
$541$	3.90106	−	6.75684i	0.167720	−	0.290499i	0.937618	+	0.347668i	$0.113026\pi$
$542$	−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	0.681228	−	0.732072i	$-0.261446\pi$
$547$	21.1697	+	5.67241i	0.905153	+	0.242535i	0.223925	+	0.974606i	$0.428113\pi$
$548$	−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	−0.0666620	−	0.997776i	$-0.521235\pi$
$557$	−14.7100	−	3.94152i	−0.623281	−	0.167008i	−0.556619	+	0.830768i	$0.687902\pi$
$558$		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	0.105071	−	0.994465i	$-0.466493\pi$
$563$	26.0894	−	26.0894i	1.09954	−	1.09954i	0.994465	−	0.105071i	$-0.0335071\pi$
$564$		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	$-0.983535\pi$
$569$		−	2.46664i		−	0.103407i	0.998662	−	0.0517034i	$-0.0164651\pi$
$570$		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	−0.980978	−	0.194117i	$-0.937816\pi$
$577$	−0.825534	+	3.08094i	−0.0343674	+	0.128261i	0.946611	+	0.322379i	$0.104482\pi$
$578$	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	−0.962009	−	0.273019i	$-0.911978\pi$
$587$	0.184728	−	0.689415i	0.00762455	−	0.0284552i	0.969633	+	0.244563i	$0.0786446\pi$
$588$		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	0.976677	+	0.214713i	$0.0688815\pi$
$593$	5.80070	+	21.6485i	0.238206	+	0.888998i	−0.738471	+	0.674285i	$0.764452\pi$
$594$		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	$-0.984817\pi$
$599$		−	2.33386i		−	0.0953591i	0.998863	−	0.0476796i	$-0.0151826\pi$
$600$		0			0
$601$	−4.89779	+	2.82774i	−0.199785	+	0.115346i	−0.596555	−	0.802572i	$-0.703464\pi$
$601$	−4.89779	+	2.82774i	−0.199785	+	0.115346i	0.396770	+	0.917918i	$0.370131\pi$
$602$	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	−0.995348	−	0.0963465i	$-0.969284\pi$
$607$	−2.09856	+	7.83195i	−0.0851781	+	0.317889i	0.910170	+	0.414235i	$0.135951\pi$
$608$	−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	0.860699	+	0.509114i	$0.170027\pi$
$613$	−3.44755	+	12.8664i	−0.139245	+	0.519670i	−0.999944	+	0.0105563i	$0.996640\pi$
$614$	−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	0.954403	−	0.298522i	$-0.0964937\pi$
$617$	−0.531453	−	1.98341i	−0.0213955	−	0.0798490i	−0.975798	+	0.218673i	$0.929827\pi$
$618$		0			0
$619$	22.7489	−	39.4022i	0.914355	−	1.58371i	0.106512	−	0.994311i	$-0.466032\pi$
$619$	22.7489	−	39.4022i	0.914355	−	1.58371i	0.807843	−	0.589398i	$-0.200635\pi$
$620$	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	−0.958945	−	0.283591i	$-0.908474\pi$
$641$	−5.92125	+	10.2559i	−0.233875	+	0.405084i	0.725070	+	0.688675i	$0.241807\pi$
$642$		0			0
$643$	−0.689615	−	2.57368i	−0.0271958	−	0.101496i	0.950994	−	0.309210i	$-0.100064\pi$
$643$	−0.689615	−	2.57368i	−0.0271958	−	0.101496i	−0.978190	+	0.207714i	$0.933398\pi$
$644$	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	−0.931502	−	0.363736i	$-0.881501\pi$
$647$	1.45165	−	5.41764i	0.0570703	−	0.212989i	0.988572	+	0.150747i	$0.0481677\pi$
$648$		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	−0.903629	−	0.428316i	$-0.859107\pi$
$653$	2.37893	−	8.87828i	0.0930946	−	0.347434i	0.996724	+	0.0808821i	$0.0257737\pi$
$654$		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	−0.146565	−	0.989201i	$-0.546822\pi$
$659$	16.3480	−	9.43850i	0.636826	−	0.367672i	0.783391	+	0.621529i	$0.213488\pi$
$660$		0			0
$661$		−	14.9804i		−	0.582670i	−0.956621	−	0.291335i	$-0.905900\pi$
$661$		−	14.9804i		−	0.582670i	0.956621	−	0.291335i	$-0.0940995\pi$
$662$	−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	0.475503	+	0.879714i	$0.342266\pi$
$673$	−9.75822	+	36.4182i	−0.376152	+	1.40382i	−0.851655	+	0.524103i	$0.824401\pi$
$674$	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	0.760708	−	0.649095i	$-0.224852\pi$
$677$	2.90409	+	2.90409i	0.111613	+	0.111613i	−0.649095	+	0.760708i	$0.724852\pi$
$678$		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	0.861382	+	0.507957i	$0.169599\pi$
$683$	−3.62156	+	13.5159i	−0.138575	+	0.517170i	−0.999958	+	0.00921262i	$0.997067\pi$
$684$		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	$0.108599\pi$
$691$			17.5908i			0.669187i	−0.942363	+	0.334593i	$0.891401\pi$
$692$	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	$-0.836315\pi$
$709$		−	26.1939i		−	0.983734i	0.870670	−	0.491867i	$-0.163685\pi$
$710$	−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	−0.940838	−	0.338856i	$-0.889960\pi$
$719$	−4.74507	+	8.21871i	−0.176961	+	0.306506i	0.763877	+	0.645362i	$0.223293\pi$
$720$		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	−0.959288	−	0.282429i	$-0.908860\pi$
$727$	0.342271	−	1.27737i	0.0126941	−	0.0473752i	0.971982	+	0.235054i	$0.0755266\pi$
$728$	−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	−0.792816	−	0.609461i	$-0.791386\pi$
$733$	−48.3039	−	12.9430i	−1.78415	−	0.478060i	−0.991329	+	0.131400i	$0.958053\pi$
$734$	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	0.323626	−	0.946185i	$-0.395098\pi$
$739$	35.4720	−	20.4798i	1.30486	−	0.753361i	0.981233	+	0.192825i	$0.0617649\pi$
$740$	−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	−0.557183	−	0.830390i	$-0.688118\pi$
$743$	−17.0232	+	4.56136i	−0.624522	+	0.167340i	−0.0673394	+	0.997730i	$0.521451\pi$
$744$		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	−0.958462	−	0.285219i	$-0.907934\pi$
$751$	−19.9021	−	34.4714i	−0.726238	−	1.25788i	0.232225	−	0.972662i	$-0.425400\pi$
$752$	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	−0.599902	−	0.800074i	$-0.704794\pi$
$757$	5.50745	−	5.50745i	0.200172	−	0.200172i	0.800074	+	0.599902i	$0.204794\pi$
$758$	−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	−0.955704	−	0.294331i	$-0.904903\pi$
$761$	−32.5147	+	18.7724i	−1.17866	+	0.680498i	−0.222954	+	0.974829i	$0.571570\pi$
$762$		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	−0.385727	−	0.922613i	$-0.626049\pi$
$769$	16.8089	−	29.1138i	0.606143	−	1.04987i	0.991870	−	0.127258i	$-0.0406175\pi$
$770$	−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	0.661605	−	0.749853i	$-0.269876\pi$
$773$	23.9006	+	6.40415i	0.859645	+	0.230341i	0.198040	+	0.980194i	$0.436542\pi$
$774$		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	0.545142	−	0.838343i	$-0.316476\pi$
$787$	−8.22532	−	8.22532i	−0.293201	−	0.293201i	−0.838343	+	0.545142i	$0.816476\pi$
$788$	−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	−0.0352047	−	0.999380i	$-0.511208\pi$
$797$	12.2523	−	3.28298i	0.433997	−	0.116289i	0.469202	+	0.883091i	$0.344542\pi$
$798$		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	0.340616	−	0.940203i	$-0.389365\pi$
$809$	37.6915	−	21.7612i	1.32516	−	0.765083i	0.984547	+	0.175120i	$0.0560312\pi$
$810$		0			0
$811$		−	10.3140i		−	0.362172i	−0.983467	−	0.181086i	$-0.942039\pi$
$811$		−	10.3140i		−	0.362172i	0.983467	−	0.181086i	$-0.0579613\pi$
$812$	−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	0.332750	−	0.943015i	$-0.392024\pi$
$823$	−17.5073	−	17.5073i	−0.610266	−	0.610266i	−0.943015	+	0.332750i	$0.892024\pi$
$824$	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	−0.449910	−	0.893074i	$-0.648544\pi$
$827$	12.7443	−	12.7443i	0.443164	−	0.443164i	0.893074	+	0.449910i	$0.148544\pi$
$828$		0			0
$829$	−13.7029	−	23.7341i	−0.475921	−	0.824319i	0.523699	−	0.851904i	$-0.324552\pi$
$829$	−13.7029	−	23.7341i	−0.475921	−	0.824319i	−0.999619	+	0.0275844i	$0.991218\pi$
$830$	−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	0.999237	+	0.0390586i	$0.0124359\pi$
$839$	15.4515	+	26.7627i	0.533444	+	0.923952i	−0.465793	+	0.884894i	$0.654231\pi$
$840$		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	0.435899	−	0.899996i	$-0.356431\pi$
$853$	10.6135	+	2.84389i	0.363400	+	0.0973729i	−0.0724984	+	0.997369i	$0.523097\pi$
$854$	−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	−0.00708450	−	0.999975i	$-0.502255\pi$
$857$	14.2499	−	3.81825i	0.486768	−	0.130429i	0.493852	+	0.869546i	$0.335588\pi$
$858$		0			0
$859$	1.93946	+	3.35925i	0.0661736	+	0.114616i	0.897214	−	0.441596i	$-0.145588\pi$
$859$	1.93946	+	3.35925i	0.0661736	+	0.114616i	−0.831040	+	0.556212i	$0.812254\pi$
$860$	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	0.0322127	−	0.999481i	$-0.489745\pi$
$863$	16.4466	−	4.40686i	0.559850	−	0.150011i	0.527638	+	0.849470i	$0.323078\pi$
$864$		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	0.398610	−	0.917120i	$-0.369493\pi$
$877$	8.44765	+	2.26354i	0.285257	+	0.0764344i	−0.113353	+	0.993555i	$0.536159\pi$
$878$	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	$-0.816179\pi$
$881$		−	32.4079i		−	1.09185i	0.837835	−	0.545924i	$-0.183821\pi$
$882$		0			0
$883$	−29.8636	−	29.8636i	−1.00499	−	1.00499i	−0.999987	−	0.00500145i	$-0.998408\pi$
$883$	−29.8636	−	29.8636i	−1.00499	−	1.00499i	−0.00500145	−	0.999987i	$-0.501592\pi$
$884$			40.3536i			1.35724i
$885$		0			0
$886$	−3.47641			−0.116792
$887$	13.9325	−	51.9969i	0.467808	−	1.74588i	−0.179599	−	0.983740i	$-0.557480\pi$
$887$	13.9325	−	51.9969i	0.467808	−	1.74588i	0.647407	−	0.762144i	$-0.275853\pi$
$888$		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	0.937658	−	0.347559i	$-0.112989\pi$
$907$	−1.45032	−	5.41268i	−0.0481572	−	0.179725i	−0.985815	+	0.167834i	$0.946323\pi$
$908$	−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	−0.977340	−	0.211676i	$-0.932108\pi$
$911$	−20.2824	−	35.1302i	−0.671987	−	1.16392i	0.305353	−	0.952239i	$-0.401226\pi$
$912$		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	0.726948	−	0.686693i	$-0.240938\pi$
$919$	15.0280	+	8.67643i	0.495729	+	0.286209i	−0.231219	+	0.972902i	$0.574271\pi$
$920$	−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	0.879950	−	0.475067i	$-0.157576\pi$
$937$	12.3936	+	12.3936i	0.404882	+	0.404882i	−0.475067	+	0.879950i	$0.657576\pi$
$938$	−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	$-0.912799\pi$
$941$		−	16.5978i		−	0.541072i	0.962710	−	0.270536i	$-0.0872010\pi$
$942$		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	0.298223	−	0.954496i	$-0.403606\pi$
$947$	38.5504	−	38.5504i	1.25272	−	1.25272i	0.954496	−	0.298223i	$-0.0963938\pi$
$948$		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	−0.993596	−	0.112990i	$-0.963957\pi$
$953$	−34.1611	−	34.1611i	−1.10659	−	1.10659i	−0.112990	−	0.993596i	$-0.536043\pi$
$954$		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	0.966242	+	0.257637i	$0.0829439\pi$
$967$	8.03134	+	29.9734i	0.258270	+	0.963878i	−0.707971	+	0.706241i	$0.750389\pi$
$968$	−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	0.821558	−	0.570125i	$-0.193105\pi$
$971$	23.0153	+	13.2879i	0.738595	+	0.426428i	−0.0829632	+	0.996553i	$0.526438\pi$
$972$		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	−0.154644	+	0.987970i	$0.549423\pi$
$977$	−35.7147	+	35.7147i	−1.14261	+	1.14261i	−0.987970	+	0.154644i	$0.950577\pi$
$978$		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	0.968185	−	0.250234i	$-0.0805075\pi$
$983$	0.144078	+	0.537708i	0.00459539	+	0.0171502i	−0.963590	+	0.267384i	$0.913841\pi$
$984$		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	−0.958467	−	0.285202i	$-0.907939\pi$
$991$	−22.8617	−	39.5976i	−0.726226	−	1.25786i	0.232241	−	0.972658i	$-0.425394\pi$
$992$	−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	−0.865645	−	0.500658i	$-0.833091\pi$
$997$	−43.0999	+	11.5486i	−1.36499	+	0.365747i	−0.499341	+	0.866405i	$0.666425\pi$
$998$	−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.523.20		160
3.2	odd	2		315.2.bs.e.103.21	yes	160
5.2	odd	4	inner	945.2.bv.e.712.20		160
7.3	odd	6		945.2.cj.e.388.20		160
9.2	odd	6		315.2.cg.e.313.20	yes	160
9.7	even	3		945.2.cj.e.208.21		160
15.2	even	4		315.2.bs.e.292.21	yes	160
21.17	even	6		315.2.cg.e.283.21	yes	160
35.17	even	12		945.2.cj.e.577.21		160
45.2	even	12		315.2.cg.e.187.21	yes	160
45.7	odd	12		945.2.cj.e.397.20		160
63.38	even	6		315.2.bs.e.178.21	yes	160
63.52	odd	6	inner	945.2.bv.e.73.20		160
105.17	odd	12		315.2.cg.e.157.20	yes	160
315.52	even	12	inner	945.2.bv.e.262.20		160
315.227	odd	12		315.2.bs.e.52.21	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.21	✓	160	315.227	odd	12
315.2.bs.e.103.21	yes	160	3.2	odd	2
315.2.bs.e.178.21	yes	160	63.38	even	6
315.2.bs.e.292.21	yes	160	15.2	even	4
315.2.cg.e.157.20	yes	160	105.17	odd	12
315.2.cg.e.187.21	yes	160	45.2	even	12
315.2.cg.e.283.21	yes	160	21.17	even	6
315.2.cg.e.313.20	yes	160	9.2	odd	6
945.2.bv.e.73.20		160	63.52	odd	6	inner
945.2.bv.e.262.20		160	315.52	even	12	inner
945.2.bv.e.523.20		160	1.1	even	1	trivial
945.2.bv.e.712.20		160	5.2	odd	4	inner
945.2.cj.e.208.21		160	9.7	even	3
945.2.cj.e.388.20		160	7.3	odd	6
945.2.cj.e.397.20		160	45.7	odd	12
945.2.cj.e.577.21		160	35.17	even	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
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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