LMFDB - Embedded newform 945.2.bv.e.73.20

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			73.20
Character	$\chi$	$=$	945.73
Dual form			945.2.bv.e.712.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0825718 - 0.0825718i) q^{2} +1.98636i q^{4} +(-2.17426 - 0.522126i) q^{5} +(-0.400384 - 2.61528i) q^{7} +(0.329161 + 0.329161i) q^{8} +O(q^{10})$	\(q+(0.0825718 - 0.0825718i) q^{2} +1.98636i q^{4} +(-2.17426 - 0.522126i) q^{5} +(-0.400384 - 2.61528i) q^{7} +(0.329161 + 0.329161i) q^{8} +(-0.222645 + 0.136419i) q^{10} +(-0.455930 - 0.789693i) q^{11} +(5.74495 + 1.53935i) q^{13} +(-0.249009 - 0.182888i) q^{14} -3.91837 q^{16} +(3.29933 - 0.884052i) q^{17} +(0.815184 + 1.41194i) q^{19} +(1.03713 - 4.31886i) q^{20} +(-0.102853 - 0.0275595i) q^{22} +(-3.15352 + 0.844982i) q^{23} +(4.45477 + 2.27047i) q^{25} +(0.601478 - 0.347264i) q^{26} +(5.19490 - 0.795308i) q^{28} +(5.74244 + 3.31540i) q^{29} -1.16339i q^{31} +(-0.981869 + 0.981869i) q^{32} +(0.199433 - 0.345429i) q^{34} +(-0.494969 + 5.89534i) q^{35} +(3.49032 + 0.935230i) q^{37} +(0.183898 + 0.0492752i) q^{38} +(-0.543817 - 0.887544i) q^{40} +(5.95218 - 3.43649i) q^{41} +(4.14262 - 1.11001i) q^{43} +(1.56862 - 0.905642i) q^{44} +(-0.190620 + 0.330163i) q^{46} +(4.13109 + 4.13109i) q^{47} +(-6.67939 + 2.09423i) q^{49} +(0.555315 - 0.180362i) q^{50} +(-3.05772 + 11.4116i) q^{52} +(13.5977 - 3.64349i) q^{53} +(0.578988 + 1.95505i) q^{55} +(0.729058 - 0.992640i) q^{56} +(0.747922 - 0.200405i) q^{58} +4.13313 q^{59} +7.18890i q^{61} +(-0.0960635 - 0.0960635i) q^{62} -7.67459i q^{64} +(-11.6873 - 6.34654i) q^{65} +(-10.7674 + 10.7674i) q^{67} +(1.75605 + 6.55366i) q^{68} +(0.445918 + 0.527659i) q^{70} -7.48342 q^{71} +(0.993956 + 3.70949i) q^{73} +(0.365426 - 0.210979i) q^{74} +(-2.80463 + 1.61925i) q^{76} +(-1.88272 + 1.50856i) q^{77} -9.14441i q^{79} +(8.51953 + 2.04588i) q^{80} +(0.207725 - 0.775240i) q^{82} +(2.88094 + 10.7518i) q^{83} +(-7.63516 + 0.199491i) q^{85} +(0.250408 - 0.433720i) q^{86} +(0.109862 - 0.410011i) q^{88} +(-1.92701 - 3.33768i) q^{89} +(1.72566 - 15.6410i) q^{91} +(-1.67844 - 6.26403i) q^{92} +0.682222 q^{94} +(-1.03521 - 3.49555i) q^{95} +(6.83360 - 1.83106i) q^{97} +(-0.378604 + 0.724453i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

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

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
$5$	−2.17426	−	0.522126i	−0.972356	−	0.233502i
$5$	−2.17426	−	0.522126i	−0.972356	−	0.233502i
$6$		0			0
$7$	−0.400384	−	2.61528i	−0.151331	−	0.988483i
$7$	−0.400384	−	2.61528i	−0.151331	−	0.988483i
$8$	0.329161	+	0.329161i	0.116376	+	0.116376i
$9$		0			0
$10$	−0.222645	+	0.136419i	−0.0704065	+	0.0431396i
$11$	−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
$13$	5.74495	+	1.53935i	1.59336	+	0.426940i	0.943030	−	0.332709i	$-0.107963\pi$
$13$	5.74495	+	1.53935i	1.59336	+	0.426940i	0.650333	+	0.759649i	$0.274629\pi$
$14$	−0.249009	−	0.182888i	−0.0665504	−	0.0488789i
$15$		0			0
$16$	−3.91837			−0.979592
$17$	3.29933	−	0.884052i	0.800204	−	0.214414i	0.164530	−	0.986372i	$-0.447389\pi$
$17$	3.29933	−	0.884052i	0.800204	−	0.214414i	0.635674	+	0.771958i	$0.280722\pi$
$18$		0			0
$19$	0.815184	+	1.41194i	0.187016	+	0.323921i	0.944254	−	0.329218i	$-0.106785\pi$
$19$	0.815184	+	1.41194i	0.187016	+	0.323921i	−0.757238	+	0.653139i	$0.773452\pi$
$20$	1.03713	−	4.31886i	0.231910	−	0.965727i
$21$		0			0
$22$	−0.102853	−	0.0275595i	−0.0219284	−	0.00587570i
$23$	−3.15352	+	0.844982i	−0.657553	+	0.176191i	−0.572142	−	0.820155i	$-0.693887\pi$
$23$	−3.15352	+	0.844982i	−0.657553	+	0.176191i	−0.0854118	+	0.996346i	$0.527221\pi$
$24$		0			0
$25$	4.45477	+	2.27047i	0.890954	+	0.454094i
$26$	0.601478	−	0.347264i	0.117960	−	0.0681040i
$27$		0			0
$28$	5.19490	−	0.795308i	0.981744	−	0.150299i
$29$	5.74244	+	3.31540i	1.06635	+	0.615655i	0.927181	−	0.374615i	$-0.122225\pi$
$29$	5.74244	+	3.31540i	1.06635	+	0.615655i	0.139164	+	0.990269i	$0.455558\pi$
$30$		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
$35$	−0.494969	+	5.89534i	−0.0836650	+	0.996494i
$36$		0			0
$37$	3.49032	+	0.935230i	0.573806	+	0.153751i	0.534042	−	0.845458i	$-0.320673\pi$
$37$	3.49032	+	0.935230i	0.573806	+	0.153751i	0.0397644	+	0.999209i	$0.487339\pi$
$38$	0.183898	+	0.0492752i	0.0298321	+	0.00799349i
$39$		0			0
$40$	−0.543817	−	0.887544i	−0.0859850	−	0.140333i
$41$	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
$43$	4.14262	−	1.11001i	0.631744	−	0.169275i	0.0712831	−	0.997456i	$-0.477291\pi$
$43$	4.14262	−	1.11001i	0.631744	−	0.169275i	0.560461	+	0.828181i	$0.310624\pi$
$44$	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	$-0.109891\pi$
$47$	4.13109	+	4.13109i	0.602581	+	0.602581i	−0.338416	+	0.940997i	$0.609891\pi$
$48$		0			0
$49$	−6.67939	+	2.09423i	−0.954198	+	0.299176i
$50$	0.555315	−	0.180362i	0.0785334	−	0.0255070i
$51$		0			0
$52$	−3.05772	+	11.4116i	−0.424029	+	1.58250i
$53$	13.5977	−	3.64349i	1.86779	−	0.500472i	0.867793	−	0.496926i	$-0.165538\pi$
$53$	13.5977	−	3.64349i	1.86779	−	0.500472i	0.999994	−	0.00354619i	$-0.00112879\pi$
$54$		0			0
$55$	0.578988	+	1.95505i	0.0780707	+	0.263618i
$56$	0.729058	−	0.992640i	0.0974245	−	0.132647i
$57$		0			0
$58$	0.747922	−	0.200405i	0.0982070	−	0.0263145i
$59$	4.13313			0.538088			0.269044	−	0.963128i	$-0.413292\pi$
$59$	4.13313			0.538088			0.269044	+	0.963128i	$0.413292\pi$
$60$		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	−0.398099	+	0.917342i	$0.630330\pi$
$67$	−10.7674	+	10.7674i	−1.31544	+	1.31544i	−0.917342	+	0.398099i	$0.869670\pi$
$68$	1.75605	+	6.55366i	0.212952	+	0.794748i
$69$		0			0
$70$	0.445918	+	0.527659i	0.0532974	+	0.0630673i
$71$	−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
$73$	0.993956	+	3.70949i	0.116334	+	0.434163i	0.999383	−	0.0351165i	$-0.0111802\pi$
$73$	0.993956	+	3.70949i	0.116334	+	0.434163i	−0.883050	+	0.469280i	$0.844514\pi$
$74$	0.365426	−	0.210979i	0.0424799	−	0.0245258i
$75$		0			0
$76$	−2.80463	+	1.61925i	−0.321713	+	0.185741i
$77$	−1.88272	+	1.50856i	−0.214556	+	0.171917i
$78$		0			0
$79$		−	9.14441i		−	1.02883i	−0.857542	−	0.514413i	$-0.828010\pi$
$79$		−	9.14441i		−	1.02883i	0.857542	−	0.514413i	$-0.171990\pi$
$80$	8.51953	+	2.04588i	0.952513	+	0.228736i
$81$		0			0
$82$	0.207725	−	0.775240i	0.0229394	−	0.0856109i
$83$	2.88094	+	10.7518i	0.316224	+	1.18017i	0.922844	+	0.385174i	$0.125858\pi$
$83$	2.88094	+	10.7518i	0.316224	+	1.18017i	−0.606620	+	0.794992i	$0.707475\pi$
$84$		0			0
$85$	−7.63516	+	0.199491i	−0.828150	+	0.0216379i
$86$	0.250408	−	0.433720i	0.0270022	−	0.0467692i
$87$		0			0
$88$	0.109862	−	0.410011i	0.0117113	−	0.0437073i
$89$	−1.92701	−	3.33768i	−0.204262	−	0.353793i	0.745635	−	0.666355i	$-0.232146\pi$
$89$	−1.92701	−	3.33768i	−0.204262	−	0.353793i	−0.949897	+	0.312562i	$0.898813\pi$
$90$		0			0
$91$	1.72566	−	15.6410i	0.180898	−	1.63962i
$92$	−1.67844	−	6.26403i	−0.174990	−	0.653070i
$93$		0			0
$94$	0.682222			0.0703658
$95$	−1.03521	−	3.49555i	−0.106210	−	0.358635i
$96$		0			0
$97$	6.83360	−	1.83106i	0.693847	−	0.185916i	0.105374	−	0.994433i	$-0.466396\pi$
$97$	6.83360	−	1.83106i	0.693847	−	0.185916i	0.588473	+	0.808517i	$0.299729\pi$
$98$	−0.378604	+	0.724453i	−0.0382448	+	0.0731808i
$99$		0			0
$100$	−4.50998	+	8.84879i	−0.450998	+	0.884879i
$101$	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
$103$	1.04454	+	3.89828i	0.102922	+	0.384109i	0.998101	−	0.0615970i	$-0.0196194\pi$
$103$	1.04454	+	3.89828i	0.102922	+	0.384109i	−0.895179	+	0.445706i	$0.852953\pi$
$104$	1.38432	+	2.39771i	0.135744	+	0.235115i
$105$		0			0
$106$	0.821936	−	1.42364i	0.0798335	−	0.138276i
$107$	−8.46809	−	2.26902i	−0.818641	−	0.219354i	−0.174889	−	0.984588i	$-0.555957\pi$
$107$	−8.46809	−	2.26902i	−0.818641	−	0.219354i	−0.643752	+	0.765234i	$0.722623\pi$
$108$		0			0
$109$	−10.4090	−	6.00964i	−0.997001	−	0.575619i	−0.0896413	−	0.995974i	$-0.528572\pi$
$109$	−10.4090	−	6.00964i	−0.997001	−	0.575619i	−0.907360	+	0.420355i	$0.861905\pi$
$110$	0.209240	+	0.113624i	0.0199502	+	0.0108336i
$111$		0			0
$112$	1.56885	+	10.2476i	0.148242	+	0.968310i
$113$	3.11308	−	11.6182i	0.292853	−	1.09294i	−0.650054	−	0.759888i	$-0.725254\pi$
$113$	3.11308	−	11.6182i	0.292853	−	1.09294i	0.942907	−	0.333056i	$-0.108080\pi$
$114$		0			0
$115$	7.29773	−	0.190675i	0.680517	−	0.0177805i
$116$	−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	0.906034	−	0.423204i	$-0.139095\pi$
$131$	11.3602	+	6.55882i	0.992546	+	0.573047i	0.0865118	+	0.996251i	$0.472428\pi$
$132$		0			0
$133$	3.36623	−	2.69725i	0.291889	−	0.233881i
$134$			1.77816i			0.153610i
$135$		0			0
$136$	1.37701	+	0.795014i	0.118077	+	0.0681719i
$137$	−14.8613	−	3.98207i	−1.26968	−	0.340211i	−0.439774	−	0.898108i	$-0.644942\pi$
$137$	−14.8613	−	3.98207i	−1.26968	−	0.340211i	−0.829910	+	0.557898i	$0.811608\pi$
$138$		0			0
$139$	−4.93784	−	8.55258i	−0.418822	−	0.725421i	0.576999	−	0.816745i	$-0.304223\pi$
$139$	−4.93784	−	8.55258i	−0.418822	−	0.725421i	−0.995821	+	0.0913239i	$0.970890\pi$
$140$	−11.7103	−	0.983188i	−0.989700	−	0.0830946i
$141$		0			0
$142$	−0.617919	+	0.617919i	−0.0518546	+	0.0518546i
$143$	−1.40367	−	5.23859i	−0.117381	−	0.438073i
$144$		0			0
$145$	−10.7545	−	10.2068i	−0.893111	−	0.847629i
$146$	0.388372	+	0.224227i	0.0321419	+	0.0185571i
$147$		0			0
$148$	−1.85771	+	6.93306i	−0.152703	+	0.569894i
$149$	−12.7119	−	7.33921i	−1.04140	−	0.601252i	−0.121169	−	0.992632i	$-0.538664\pi$
$149$	−12.7119	−	7.33921i	−1.04140	−	0.601252i	−0.920229	+	0.391380i	$0.871998\pi$
$150$		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	$0.681806\pi$
$152$	−0.196429	+	0.733083i	−0.0159325	+	0.0594609i
$153$		0			0
$154$	−0.0308949	+	0.280025i	−0.00248958	+	0.0225650i
$155$	−0.607438	+	2.52951i	−0.0487906	+	0.203176i
$156$		0			0
$157$	−2.39683	−	2.39683i	−0.191288	−	0.191288i	0.604965	−	0.796252i	$-0.293187\pi$
$157$	−2.39683	−	2.39683i	−0.191288	−	0.191288i	−0.796252	+	0.604965i	$0.793187\pi$
$158$	−0.755070	−	0.755070i	−0.0600702	−	0.0600702i
$159$		0			0
$160$	2.64749	−	1.62217i	0.209303	−	0.128244i
$161$	3.47248	+	7.90901i	0.273670	+	0.623317i
$162$		0			0
$163$	5.00653	−	18.6846i	0.392142	−	1.46349i	−0.434453	−	0.900695i	$-0.643058\pi$
$163$	5.00653	−	18.6846i	0.392142	−	1.46349i	0.826595	−	0.562798i	$-0.190275\pi$
$164$	6.82613	+	11.8232i	0.533031	+	0.923237i
$165$		0			0
$166$	1.12568	+	0.649913i	0.0873698	+	0.0504430i
$167$	−2.37464	+	8.86226i	−0.183755	+	0.685782i	0.811139	+	0.584854i	$0.198848\pi$
$167$	−2.37464	+	8.86226i	−0.183755	+	0.685782i	−0.994894	+	0.100929i	$0.967819\pi$
$168$		0			0
$169$	19.3765	+	11.1870i	1.49050	+	0.860541i
$170$	−0.613977	+	0.646921i	−0.0470899	+	0.0496166i
$171$		0			0
$172$	2.20489	+	8.22876i	0.168121	+	0.627437i
$173$	−10.5199	+	10.5199i	−0.799814	+	0.799814i	−0.983066	−	0.183252i	$-0.941337\pi$
$173$	−10.5199	+	10.5199i	−0.799814	+	0.799814i	0.183252	+	0.983066i	$0.441337\pi$
$174$		0			0
$175$	4.15430	−	12.5595i	0.314035	−	0.949411i
$176$	1.78650	+	3.09431i	0.134662	+	0.233242i
$177$		0			0
$178$	−0.434714	−	0.116481i	−0.0325832	−	0.00873065i
$179$	−6.51864	−	3.76354i	−0.487226	−	0.281300i	0.236197	−	0.971705i	$-0.424099\pi$
$179$	−6.51864	−	3.76354i	−0.487226	−	0.281300i	−0.723423	+	0.690405i	$0.757432\pi$
$180$		0			0
$181$		−	1.22694i		−	0.0911977i	−0.998960	−	0.0455989i	$-0.985480\pi$
$181$		−	1.22694i		−	0.0911977i	0.998960	−	0.0455989i	$-0.0145196\pi$
$182$	−1.14901	−	1.43400i	−0.0851706	−	0.106295i
$183$		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	$-0.881507\pi$
$199$	−2.12679	+	3.68372i	−0.150764	+	0.261132i	0.780744	+	0.624851i	$0.214840\pi$
$200$	0.718987	+	2.21369i	0.0508401	+	0.156531i
$201$		0			0
$202$	0.442874	−	1.65283i	0.0311605	−	0.116293i
$203$	6.37152	−	16.3455i	0.447193	−	1.14723i
$204$		0			0
$205$	−14.7358	+	4.36403i	−1.02920	+	0.304797i
$206$	0.408138	+	0.235638i	0.0284363	+	0.0164177i
$207$		0			0
$208$	−22.5108	−	6.03176i	−1.56085	−	0.418227i
$209$	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	$0.819635\pi$
$212$	7.23730	+	27.0100i	0.497060	+	1.85505i
$213$		0			0
$214$	−0.886582	+	0.511868i	−0.0606055	+	0.0349906i
$215$	−9.58669	+	0.250481i	−0.653807	+	0.0170826i
$216$		0			0
$217$	−3.04260	+	0.465804i	−0.206545	+	0.0316208i
$218$	−1.35572	+	0.363263i	−0.0918206	+	0.0246033i
$219$		0			0
$220$	−3.88343	+	1.15008i	−0.261821	+	0.0775384i
$221$	20.3153			1.36656
$222$		0			0
$223$	7.19120	+	26.8379i	0.481558	+	1.79720i	0.595083	+	0.803664i	$0.297119\pi$
$223$	7.19120	+	26.8379i	0.481558	+	1.79720i	−0.113525	+	0.993535i	$0.536214\pi$
$224$	2.96099	+	2.17474i	0.197839	+	0.145306i
$225$		0			0
$226$	−0.702280	−	1.21638i	−0.0467149	−	0.0809127i
$227$	−0.695297	+	2.59488i	−0.0461485	+	0.172229i	−0.985154	−	0.171674i	$-0.945082\pi$
$227$	−0.695297	+	2.59488i	−0.0461485	+	0.172229i	0.939005	+	0.343903i	$0.111749\pi$
$228$		0			0
$229$	−1.35564	+	2.34803i	−0.0895831	+	0.155162i	−0.907335	−	0.420408i	$-0.861887\pi$
$229$	−1.35564	+	2.34803i	−0.0895831	+	0.155162i	0.817752	+	0.575571i	$0.195220\pi$
$230$	0.586843	−	0.618331i	0.0386952	−	0.0407716i
$231$		0			0
$232$	0.798888	+	2.98149i	0.0524496	+	0.195744i
$233$	−2.72904	+	10.1849i	−0.178785	+	0.667236i	0.817091	+	0.576509i	$0.195586\pi$
$233$	−2.72904	+	10.1849i	−0.178785	+	0.667236i	−0.995876	+	0.0907264i	$0.971081\pi$
$234$		0			0
$235$	−6.82509	−	11.1390i	−0.445220	−	0.726627i
$236$			8.20990i			0.534419i
$237$		0			0
$238$	−0.983244	−	0.383270i	−0.0637342	−	0.0248437i
$239$	−19.4428	+	11.2253i	−1.25765	+	0.726104i	−0.972617	−	0.232414i	$-0.925337\pi$
$239$	−19.4428	+	11.2253i	−1.25765	+	0.726104i	−0.285032	+	0.958518i	$0.592004\pi$
$240$		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	$0.237866\pi$
$242$	−0.307327	−	1.14696i	−0.0197557	−	0.0737293i
$243$		0			0
$244$	−14.2798			−0.914168
$245$	15.6161	−	1.06591i	0.997679	−	0.0680988i
$246$		0			0
$247$	2.50971	+	9.36638i	0.159689	+	0.595969i
$248$	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
$257$	−6.06202	+	1.62431i	−0.378138	+	0.101322i	−0.442882	−	0.896580i	$-0.646044\pi$
$257$	−6.06202	+	1.62431i	−0.378138	+	0.101322i	0.0647433	+	0.997902i	$0.479377\pi$
$258$		0			0
$259$	1.04842	−	9.50263i	0.0651456	−	0.590465i
$260$	12.6065	−	23.2151i	0.781824	−	1.43974i
$261$		0			0
$262$	1.47961	−	0.396459i	0.0914104	−	0.0244933i
$263$	−7.25371	+	27.0712i	−0.447283	+	1.66928i	0.262555	+	0.964917i	$0.415435\pi$
$263$	−7.25371	+	27.0712i	−0.447283	+	1.66928i	−0.709838	+	0.704365i	$0.751232\pi$
$264$		0			0
$265$	−31.4672	+	0.822174i	−1.93302	+	0.0505058i
$266$	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	$-0.683086\pi$
$269$	7.45736	−	12.9165i	0.454683	−	0.787535i	0.998670	+	0.0515593i	$0.0164191\pi$
$270$		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	$0.488870\pi$
$272$	−12.9280	+	3.46404i	−0.783874	+	0.210038i
$273$		0			0
$274$	−1.55593	+	0.898315i	−0.0939970	+	0.0542692i
$275$	−0.238088	−	4.55307i	−0.0143572	−	0.274561i
$276$		0			0
$277$	17.9885	+	4.82001i	1.08083	+	0.289607i	0.754934	−	0.655800i	$-0.227669\pi$
$277$	17.9885	+	4.82001i	1.08083	+	0.289607i	0.325892	+	0.945407i	$0.394335\pi$
$278$	−1.11393	−	0.298476i	−0.0668090	−	0.0179014i
$279$		0			0
$280$	−2.10344	+	1.77759i	−0.125705	+	0.106231i
$281$	−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	$-0.615400\pi$
$283$	9.76300	−	9.76300i	0.580350	−	0.580350i	0.934999	+	0.354649i	$0.115400\pi$
$284$		−	14.8648i		−	0.882063i
$285$		0			0
$286$	−0.548463	−	0.316655i	−0.0324313	−	0.0187242i
$287$	−11.3706	−	14.1907i	−0.671183	−	0.837651i
$288$		0			0
$289$	−4.61843	+	2.66645i	−0.271672	+	0.156850i
$290$	−1.73081	+	0.0452226i	−0.101637	+	0.00265556i
$291$		0			0
$292$	−7.36840	+	1.97436i	−0.431203	+	0.115541i
$293$	−2.32537	−	0.623080i	−0.135849	−	0.0364007i	0.190254	−	0.981735i	$-0.439069\pi$
$293$	−2.32537	−	0.623080i	−0.135849	−	0.0364007i	−0.326103	+	0.945334i	$0.605736\pi$
$294$		0			0
$295$	−8.98648	−	2.15801i	−0.523213	−	0.125644i
$296$	0.841038	+	1.45672i	0.0488843	+	0.0846702i
$297$		0			0
$298$	−1.65566	+	0.443631i	−0.0959095	+	0.0256989i
$299$	−19.4175			−1.12294
$300$		0			0
$301$	−4.56163	−	10.3897i	−0.262928	−	0.598852i
$302$	1.27034	+	0.340387i	0.0731000	+	0.0195871i
$303$		0			0
$304$	−3.19419	−	5.53250i	−0.183199	−	0.317311i
$305$	3.75351	−	15.6305i	0.214925	−	0.895000i
$306$		0			0
$307$	9.67145	+	9.67145i	0.551979	+	0.551979i	0.927012	−	0.375033i	$-0.122368\pi$
$307$	9.67145	+	9.67145i	0.551979	+	0.551979i	−0.375033	+	0.927012i	$0.622368\pi$
$308$	−2.99656	−	3.73977i	−0.170745	−	0.213093i
$309$		0			0
$310$	0.158709	+	0.259024i	0.00901408	+	0.0147116i
$311$		−	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	$-0.756672\pi$
$313$	−0.524423	+	0.524423i	−0.0296422	+	0.0296422i	0.692130	+	0.721773i	$0.256672\pi$
$314$	−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
$320$	−4.00710	+	16.6865i	−0.224004	+	0.932804i
$321$		0			0
$322$	0.939790	+	0.366332i	0.0523725	+	0.0204149i
$323$	3.93778	+	3.93778i	0.219104	+	0.219104i
$324$		0			0
$325$	22.0974	+	19.9012i	1.22574	+	1.10392i
$326$	−1.12942	−	1.95622i	−0.0625530	−	0.108345i
$327$		0			0
$328$	3.09039	+	0.828067i	0.170638	+	0.0457224i
$329$	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	$0.564074\pi$
$332$	−21.3570	+	5.72260i	−1.17212	+	0.314068i
$333$		0			0
$334$	0.535695	+	0.927851i	0.0293119	+	0.0507697i
$335$	29.0329	−	17.7891i	1.58624	−	0.971920i
$336$		0			0
$337$	−12.8643	−	3.44698i	−0.700763	−	0.187769i	−0.109191	−	0.994021i	$-0.534826\pi$
$337$	−12.8643	−	3.44698i	−0.700763	−	0.187769i	−0.591572	+	0.806252i	$0.701493\pi$
$338$	2.52369	−	0.676220i	0.137270	−	0.0367815i
$339$		0			0
$340$	−0.396262	−	15.1662i	−0.0214903	−	0.822503i
$341$	−0.918724	+	0.530426i	−0.0497517	+	0.0287242i
$342$		0			0
$343$	8.15132	+	16.6300i	0.440130	+	0.897934i
$344$	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	0.0446913	+	0.999001i	$0.485770\pi$
$349$	−15.7451	+	27.2713i	−0.842814	+	1.45980i	−0.887506	+	0.460797i	$0.847564\pi$
$350$	−0.694035	−	1.38009i	−0.0370977	−	0.0737689i
$351$		0			0
$352$	1.22304	+	0.327712i	0.0651882	+	0.0174671i
$353$	32.6279	+	8.74262i	1.73661	+	0.465323i	0.981688	−	0.190494i	$-0.0610091\pi$
$353$	32.6279	+	8.74262i	1.73661	+	0.465323i	0.754920	+	0.655817i	$0.227676\pi$
$354$		0			0
$355$	16.2709	+	3.90728i	0.863567	+	0.207377i
$356$	6.62984	−	3.82774i	0.351381	−	0.202870i
$357$		0			0
$358$	−0.849018	+	0.227494i	−0.0448720	+	0.0120234i
$359$	18.7587	−	10.8303i	0.990044	−	0.571602i	0.0847568	−	0.996402i	$-0.472989\pi$
$359$	18.7587	−	10.8303i	0.990044	−	0.571602i	0.905288	+	0.424799i	$0.139655\pi$
$360$		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
$365$	−0.224292	−	8.58435i	−0.0117400	−	0.449326i
$366$		0			0
$367$	4.83891	−	18.0591i	0.252589	−	0.942676i	−0.716826	−	0.697252i	$-0.754406\pi$
$367$	4.83891	−	18.0591i	0.252589	−	0.942676i	0.969416	−	0.245424i	$-0.0789273\pi$
$368$	12.3566	−	3.31095i	0.644134	−	0.172595i
$369$		0			0
$370$	−0.904687	+	0.267923i	−0.0470324	+	0.0139287i
$371$	−14.9730	−	34.1030i	−0.777362	−	1.77054i
$372$		0			0
$373$	17.8408	−	4.78044i	0.923763	−	0.247522i	0.234570	−	0.972099i	$-0.424632\pi$
$373$	17.8408	−	4.78044i	0.923763	−	0.247522i	0.689193	+	0.724578i	$0.257965\pi$
$374$	−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
$383$	5.34597	+	19.9514i	0.273166	+	1.01947i	0.957060	+	0.289889i	$0.0936183\pi$
$383$	5.34597	+	19.9514i	0.273166	+	1.01947i	−0.683894	+	0.729581i	$0.739715\pi$
$384$		0			0
$385$	4.88118	−	2.29698i	0.248768	−	0.117065i
$386$	−1.12733			−0.0573795
$387$		0			0
$388$	3.63715	+	13.5740i	0.184648	+	0.689116i
$389$	13.9223	−	8.03806i	0.705890	−	0.407546i	−0.103648	−	0.994614i	$-0.533051\pi$
$389$	13.9223	−	8.03806i	0.705890	−	0.407546i	0.809537	+	0.587068i	$0.199718\pi$
$390$		0			0
$391$	−9.65747	+	5.57574i	−0.488399	+	0.281977i
$392$	−2.88793	−	1.50925i	−0.145863	−	0.0762289i
$393$		0			0
$394$			0.303172i			0.0152736i
$395$	−4.77453	+	19.8823i	−0.240233	+	1.00039i
$396$		0			0
$397$	−5.31714	+	19.8438i	−0.266860	+	0.995934i	0.694243	+	0.719741i	$0.255739\pi$
$397$	−5.31714	+	19.8438i	−0.266860	+	0.995934i	−0.961102	+	0.276193i	$0.910927\pi$
$398$	0.128558	+	0.479784i	0.00644402	+	0.0240494i
$399$		0			0
$400$	−17.4554	−	8.89653i	−0.872772	−	0.444827i
$401$	−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
$403$	1.79088	−	6.68364i	0.0892099	−	0.332936i
$404$	14.5535	+	25.2073i	0.724061	+	1.25411i
$405$		0			0
$406$	−0.823572	−	1.87579i	−0.0408732	−	0.0930938i
$407$	−0.852798	−	3.18268i	−0.0422716	−	0.157760i
$408$		0			0
$409$	−8.90743			−0.440444			−0.220222	−	0.975450i	$-0.570678\pi$
$409$	−8.90743			−0.440444			−0.220222	+	0.975450i	$0.570678\pi$
$410$	−0.856420	+	1.57711i	−0.0422955	+	0.0778879i
$411$		0			0
$412$	−7.74340	+	2.07484i	−0.381490	+	0.102220i
$413$	−1.65484	−	10.8093i	−0.0814293	−	0.531891i
$414$		0			0
$415$	−0.650101	−	24.8814i	−0.0319122	−	1.22138i
$416$	−7.15223	+	4.12934i	−0.350667	+	0.202458i
$417$		0			0
$418$	−0.0449320	−	0.167689i	−0.00219770	−	0.00820192i
$419$	−0.233728	−	0.404828i	−0.0114183	−	0.0197771i	0.860260	−	0.509856i	$-0.170301\pi$
$419$	−0.233728	−	0.404828i	−0.0114183	−	0.0197771i	−0.871678	+	0.490079i	$0.836968\pi$
$420$		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	$0.232834\pi$
$422$	0.140974	+	0.0377740i	0.00686253	+	0.00183881i
$423$		0			0
$424$	5.67513	+	3.27654i	0.275609	+	0.159123i
$425$	16.7049	+	3.55277i	0.810309	+	0.172335i
$426$		0			0
$427$	18.8010	−	2.87832i	0.909844	−	0.139292i
$428$	4.50709	−	16.8207i	0.217859	−	0.813059i
$429$		0			0
$430$	−0.770907	+	0.812272i	−0.0371764	+	0.0391713i
$431$	−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	0.308258	−	0.951303i	$-0.400254\pi$
$433$	26.2098	−	26.2098i	1.25956	−	1.25956i	0.951303	−	0.308258i	$-0.0997462\pi$
$434$	−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	$-0.640651\pi$
$439$	−17.9196			−0.855257			−0.427628	+	0.903955i	$0.640651\pi$
$440$	−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
$448$	−20.0712	+	3.07278i	−0.948275	+	0.145175i
$449$			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
$452$	23.0779	+	6.18370i	1.08549	+	0.290857i
$453$		0			0
$454$	0.156852	+	0.271676i	0.00736144	+	0.0127504i
$455$	−11.9186	+	33.1065i	−0.558752	+	1.55206i
$456$		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	$0.296560\pi$
$458$	0.0819439	+	0.305819i	0.00382899	+	0.0142900i
$459$		0			0
$460$	0.378750	+	14.4960i	0.0176593	+	0.675877i
$461$	−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
$463$	−4.94233	+	18.4450i	−0.229690	+	0.857214i	0.750781	+	0.660551i	$0.229677\pi$
$463$	−4.94233	+	18.4450i	−0.229690	+	0.857214i	−0.980471	+	0.196663i	$0.936990\pi$
$464$	−22.5010	−	12.9910i	−1.04458	−	0.603090i
$465$		0			0
$466$	0.615645	+	1.06633i	0.0285192	+	0.0493967i
$467$	9.98615	−	37.2688i	0.462104	−	1.72459i	−0.204214	−	0.978926i	$-0.565464\pi$
$467$	9.98615	−	37.2688i	0.462104	−	1.72459i	0.666317	−	0.745668i	$-0.267870\pi$
$468$		0			0
$469$	32.4707	+	23.8486i	1.49936	+	1.10123i
$470$	−1.48333	−	0.356206i	−0.0684207	−	0.0164305i
$471$		0			0
$472$	1.36047	+	1.36047i	0.0626205	+	0.0626205i
$473$	−2.76531	−	2.76531i	−0.127149	−	0.127149i
$474$		0			0
$475$	0.425691	+	8.14072i	0.0195321	+	0.373522i
$476$	16.4366	−	7.21654i	0.753369	−	0.330769i
$477$		0			0
$478$	−0.678532	+	2.53232i	−0.0310353	+	0.115825i
$479$	−15.4248	−	26.7165i	−0.704776	−	1.22071i	−0.966772	−	0.255639i	$-0.917714\pi$
$479$	−15.4248	−	26.7165i	−0.704776	−	1.22071i	0.261996	−	0.965069i	$-0.415619\pi$
$480$		0			0
$481$	18.6121	+	10.7457i	0.848638	+	0.489962i
$482$	0.277240	−	1.03467i	0.0126279	−	0.0471281i
$483$		0			0
$484$	17.4923	+	10.0992i	0.795104	+	0.459054i
$485$	−15.8140	+	0.413188i	−0.718078	+	0.0187619i
$486$		0			0
$487$	−0.0617598	−	0.230491i	−0.00279861	−	0.0104445i	0.964512	−	0.264038i	$-0.0850543\pi$
$487$	−0.0617598	−	0.230491i	−0.00279861	−	0.0104445i	−0.967311	+	0.253593i	$0.918388\pi$
$488$	−2.36631	+	2.36631i	−0.107118	+	0.107118i
$489$		0			0
$490$	1.20144	−	1.37747i	0.0542754	−	0.0622276i
$491$	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
$493$	21.8772	+	5.86197i	0.985299	+	0.264010i
$494$	0.980631	+	0.566167i	0.0441207	+	0.0254731i
$495$		0			0
$496$			4.55861i			0.204687i
$497$	2.99624	+	19.5712i	0.134400	+	0.877890i
$498$		0			0
$499$	7.52176	+	4.34269i	0.336720	+	0.194405i	0.658821	−	0.752300i	$-0.271056\pi$
$499$	7.52176	+	4.34269i	0.336720	+	0.194405i	−0.322101	+	0.946705i	$0.604389\pi$
$500$	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	$-0.742042\pi$
$503$	0.792859	−	0.792859i	0.0353518	−	0.0353518i	0.724562	+	0.689210i	$0.242042\pi$
$504$		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	$-0.560672\pi$
$509$	17.0474	−	29.5270i	0.755614	−	1.30876i	0.945069	−	0.326872i	$-0.105995\pi$
$510$		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
$515$	−0.235707	−	9.02124i	−0.0103865	−	0.397523i
$516$		0			0
$517$	1.37881	−	5.14577i	0.0606398	−	0.226311i
$518$	−0.698079	−	0.871219i	−0.0306718	−	0.0382792i
$519$		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
$523$	−4.53372	−	1.21481i	−0.198246	−	0.0531198i	0.158330	−	0.987386i	$-0.449389\pi$
$523$	−4.53372	−	1.21481i	−0.198246	−	0.0531198i	−0.356576	+	0.934266i	$0.616056\pi$
$524$	−13.0282	+	22.5655i	−0.569140	+	0.985779i
$525$		0			0
$526$	1.63637	+	2.83427i	0.0713490	+	0.123580i
$527$	−1.02850	−	3.83841i	−0.0448022	−	0.167204i
$528$		0			0
$529$	−10.6879	+	6.17067i	−0.464692	+	0.268290i
$530$	−2.53042	+	2.66619i	−0.109914	+	0.115812i
$531$		0			0
$532$	5.35772	+	6.68656i	0.232287	+	0.289899i
$533$	39.4850	−	10.5800i	1.71028	−	0.458269i
$534$		0			0
$535$	17.2271	+	9.35483i	0.744791	+	0.404444i
$536$	−7.08839			−0.306172
$537$		0			0
$538$	−0.450773	−	1.68231i	−0.0194342	−	0.0725295i
$539$	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	$0.779693\pi$
$542$	−0.467109	+	1.74328i	−0.0200641	+	0.0748801i
$543$		0			0
$544$	−2.37148	+	4.10753i	−0.101676	+	0.176109i
$545$	19.4940	+	18.5013i	0.835032	+	0.792508i
$546$		0			0
$547$	−5.67241	−	21.1697i	−0.242535	−	0.905153i	−0.974606	−	0.223925i	$-0.928113\pi$
$547$	−5.67241	−	21.1697i	−0.242535	−	0.905153i	0.732072	−	0.681228i	$-0.238554\pi$
$548$	7.90983	−	29.5199i	0.337891	−	1.26103i
$549$		0			0
$550$	−0.395615	−	0.356296i	−0.0168691	−	0.0151925i
$551$			10.8106i			0.460549i
$552$		0			0
$553$	−23.9152	+	3.66127i	−1.01698	+	0.155693i
$554$	1.88334	−	1.08735i	0.0800156	−	0.0461970i
$555$		0			0
$556$	16.9885	−	9.80834i	0.720475	−	0.415966i
$557$	3.94152	+	14.7100i	0.167008	+	0.623281i	0.997776	+	0.0666620i	$0.0212349\pi$
$557$	3.94152	+	14.7100i	0.167008	+	0.623281i	−0.830768	+	0.556619i	$0.812098\pi$
$558$		0			0
$559$	25.5079			1.07887
$560$	1.93947	−	23.1001i	0.0819576	−	0.976158i
$561$		0			0
$562$	0.228975	+	0.854546i	0.00965873	+	0.0360469i
$563$	−26.0894	+	26.0894i	−1.09954	+	1.09954i	−0.105071	+	0.994465i	$0.533507\pi$
$563$	−26.0894	+	26.0894i	−1.09954	+	1.09954i	−0.994465	+	0.105071i	$0.966493\pi$
$564$		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	$0.559047\pi$
$572$	10.4057	−	2.78821i	0.435086	−	0.116581i
$573$		0			0
$574$	−2.11064	−	0.232866i	−0.0880964	−	0.00971962i
$575$	−15.9667	−	3.39576i	−0.665857	−	0.141613i
$576$		0			0
$577$	−3.08094	+	0.825534i	−0.128261	+	0.0343674i	−0.322379	−	0.946611i	$-0.604482\pi$
$577$	−3.08094	+	0.825534i	−0.128261	+	0.0343674i	0.194117	+	0.980978i	$0.437816\pi$
$578$	−0.161178	+	0.601526i	−0.00670413	+	0.0250202i
$579$		0			0
$580$	20.2744	−	21.3623i	0.841850	−	0.887022i
$581$	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
$587$	0.689415	−	0.184728i	0.0284552	−	0.00762455i	−0.244563	−	0.969633i	$-0.578645\pi$
$587$	0.689415	−	0.184728i	0.0284552	−	0.00762455i	0.273019	+	0.962009i	$0.411978\pi$
$588$		0			0
$589$	1.64264	−	0.948380i	0.0676839	−	0.0390773i
$590$	−0.920221	+	0.563839i	−0.0378849	+	0.0232129i
$591$		0			0
$592$	−13.6764	−	3.66457i	−0.562096	−	0.150613i
$593$	21.6485	+	5.80070i	0.888998	+	0.238206i	0.674285	−	0.738471i	$-0.264452\pi$
$593$	21.6485	+	5.80070i	0.888998	+	0.238206i	0.214713	+	0.976677i	$0.431119\pi$
$594$		0			0
$595$	3.57872	+	19.8882i	0.146713	+	0.815337i
$596$	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	0.396770	−	0.917918i	$-0.370131\pi$
$601$	−4.89779	−	2.82774i	−0.199785	−	0.115346i	−0.596555	+	0.802572i	$0.703464\pi$
$602$	−1.23456	−	0.481233i	−0.0503168	−	0.0196136i
$603$		0			0
$604$	−19.3740	+	11.1856i	−0.788317	+	0.455135i
$605$	−15.6524	+	16.4923i	−0.636361	+	0.670507i
$606$		0			0
$607$	−7.83195	+	2.09856i	−0.317889	+	0.0851781i	−0.414235	−	0.910170i	$-0.635951\pi$
$607$	−7.83195	+	2.09856i	−0.317889	+	0.0851781i	0.0963465	+	0.995348i	$0.469284\pi$
$608$	−2.18674	−	0.585936i	−0.0886842	−	0.0237629i
$609$		0			0
$610$	−0.980704	−	1.60057i	−0.0397076	−	0.0648053i
$611$	17.3737	+	30.0921i	0.702864	+	1.21740i
$612$		0			0
$613$	12.8664	−	3.44755i	0.519670	−	0.139245i	0.0105563	−	0.999944i	$-0.496640\pi$
$613$	12.8664	−	3.44755i	0.519670	−	0.139245i	0.509114	+	0.860699i	$0.329973\pi$
$614$	1.59718			0.0644569
$615$		0			0
$616$	−1.11628	−	0.123158i	−0.0449762	−	0.00496219i
$617$	1.98341	+	0.531453i	0.0798490	+	0.0213955i	0.298522	−	0.954403i	$-0.403506\pi$
$617$	1.98341	+	0.531453i	0.0798490	+	0.0213955i	−0.218673	+	0.975798i	$0.570173\pi$
$618$		0			0
$619$	−22.7489	−	39.4022i	−0.914355	−	1.58371i	−0.807843	−	0.589398i	$-0.799365\pi$
$619$	−22.7489	−	39.4022i	−0.914355	−	1.58371i	−0.106512	−	0.994311i	$-0.533968\pi$
$620$	−5.02454	−	1.20659i	−0.201790	−	0.0484579i
$621$		0			0
$622$	−2.19741	−	2.19741i	−0.0881080	−	0.0881080i
$623$	−7.95742	+	6.37602i	−0.318807	+	0.255450i
$624$		0			0
$625$	14.6899	+	20.2288i	0.587598	+	0.809153i
$626$			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
$635$	−23.4114	+	14.3447i	−0.929054	+	0.569251i
$636$		0			0
$637$	−41.5965	+	1.74931i	−1.64811	+	0.0693102i
$638$	−0.499259	−	0.499259i	−0.0197658	−	0.0197658i
$639$		0			0
$640$	4.29131	+	7.00369i	0.169629	+	0.276845i
$641$	−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
$643$	−2.57368	−	0.689615i	−0.101496	−	0.0271958i	0.207714	−	0.978190i	$-0.433398\pi$
$643$	−2.57368	−	0.689615i	−0.101496	−	0.0271958i	−0.309210	+	0.950994i	$0.600064\pi$
$644$	−15.7102	+	6.89761i	−0.619068	+	0.271804i
$645$		0			0
$646$	0.650300			0.0255857
$647$	5.41764	−	1.45165i	0.212989	−	0.0570703i	−0.150747	−	0.988572i	$-0.548168\pi$
$647$	5.41764	−	1.45165i	0.212989	−	0.0570703i	0.363736	+	0.931502i	$0.381501\pi$
$648$		0			0
$649$	−1.88442	−	3.26390i	−0.0739698	−	0.128119i
$650$	3.46790	−	0.181342i	0.136022	−	0.00711282i
$651$		0			0
$652$	37.1145	+	9.94479i	1.45351	+	0.389468i
$653$	−8.87828	+	2.37893i	−0.347434	+	0.0930946i	−0.428316	−	0.903629i	$-0.640893\pi$
$653$	−8.87828	+	2.37893i	−0.347434	+	0.0930946i	0.0808821	+	0.996724i	$0.474226\pi$
$654$		0			0
$655$	−21.2755	−	20.1920i	−0.831301	−	0.788967i
$656$	−23.3228	+	13.4655i	−0.910604	+	0.525738i
$657$		0			0
$658$	−0.273151	−	1.78420i	−0.0106485	−	0.0695555i
$659$	−16.3480	−	9.43850i	−0.636826	−	0.367672i	0.146565	−	0.989201i	$-0.453178\pi$
$659$	−16.3480	−	9.43850i	−0.636826	−	0.367672i	−0.783391	+	0.621529i	$0.786512\pi$
$660$		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
$665$	−8.72735	+	4.10692i	−0.338432	+	0.159259i
$666$		0			0
$667$	−20.9103	−	5.60291i	−0.809652	−	0.216945i
$668$	−17.6037	−	4.71689i	−0.681107	−	0.182502i
$669$		0			0
$670$	0.928423	−	3.86617i	0.0358681	−	0.149363i
$671$	5.67702	−	3.27763i	0.219159	−	0.126532i
$672$		0			0
$673$	36.4182	−	9.75822i	1.40382	−	0.376152i	0.524103	−	0.851655i	$-0.324401\pi$
$673$	36.4182	−	9.75822i	1.40382	−	0.376152i	0.879714	+	0.475503i	$0.157734\pi$
$674$	−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	$-0.275148\pi$
$677$	−2.90409	−	2.90409i	−0.111613	−	0.111613i	−0.760708	+	0.649095i	$0.775148\pi$
$678$		0			0
$679$	−7.52479	−	17.1387i	−0.288775	−	0.657721i
$680$	−2.57886	−	2.44753i	−0.0988949	−	0.0938586i
$681$		0			0
$682$	−0.0320625	+	0.119659i	−0.00122774	+	0.00458197i
$683$	13.5159	−	3.62156i	0.517170	−	0.138575i	0.00921262	−	0.999958i	$-0.497067\pi$
$683$	13.5159	−	3.62156i	0.517170	−	0.138575i	0.507957	+	0.861382i	$0.330401\pi$
$684$		0			0
$685$	30.2331	+	16.4175i	1.15515	+	0.627280i
$686$	2.04624	+	0.700097i	0.0781256	+	0.0267298i
$687$		0			0
$688$	−16.2323	+	4.34944i	−0.618852	+	0.165821i
$689$	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
$698$	0.951738	+	3.55194i	0.0360238	+	0.134443i
$699$		0			0
$700$	24.9478	+	8.25194i	0.942938	+	0.311894i
$701$	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
$703$	1.52477	+	5.69051i	0.0575077	+	0.214622i
$704$	−6.06057	+	3.49907i	−0.228416	+	0.131876i
$705$		0			0
$706$	3.41604	−	1.97225i	0.128564	−	0.0742266i
$707$	−24.2423	−	30.2549i	−0.911724	−	1.13785i
$708$		0			0
$709$		−	26.1939i		−	0.983734i	−0.870670	−	0.491867i	$-0.836315\pi$
$709$		−	26.1939i		−	0.983734i	0.870670	−	0.491867i	$-0.163685\pi$
$710$	1.66615	−	1.02088i	0.0625293	−	0.0383130i
$711$		0			0
$712$	0.464337	−	1.73293i	0.0174018	−	0.0649443i
$713$	0.983047	+	3.66878i	0.0368154	+	0.137397i
$714$		0			0
$715$	0.316747	+	12.1229i	0.0118457	+	0.453371i
$716$	7.47576	−	12.9484i	0.279382	−	0.483904i
$717$		0			0
$718$	0.654658	−	2.44322i	0.0244316	−	0.0911800i
$719$	4.74507	+	8.21871i	0.176961	+	0.306506i	0.940838	−	0.338856i	$-0.110040\pi$
$719$	4.74507	+	8.21871i	0.176961	+	0.306506i	−0.763877	+	0.645362i	$0.776707\pi$
$720$		0			0
$721$	9.77688	−	4.29258i	0.364110	−	0.159864i
$722$	−0.493907	−	1.84329i	−0.0183813	−	0.0686001i
$723$		0			0
$724$	2.43715			0.0905759
$725$	18.0538	+	27.8074i	0.670499	+	1.03274i
$726$		0			0
$727$	1.27737	−	0.342271i	0.0473752	−	0.0126941i	−0.235054	−	0.971982i	$-0.575527\pi$
$727$	1.27737	−	0.342271i	0.0473752	−	0.0126941i	0.282429	+	0.959288i	$0.408860\pi$
$728$	5.71643	−	4.58039i	0.211865	−	0.169760i
$729$		0			0
$730$	−0.727345	−	0.690305i	−0.0269203	−	0.0255493i
$731$	12.6866	−	7.32459i	0.469229	−	0.270910i
$732$		0			0
$733$	−12.9430	−	48.3039i	−0.478060	−	1.78415i	−0.609461	−	0.792816i	$-0.708614\pi$
$733$	−12.9430	−	48.3039i	−0.478060	−	1.78415i	0.131400	−	0.991329i	$-0.458053\pi$
$734$	−1.09161	−	1.89073i	−0.0402921	−	0.0697880i
$735$		0			0
$736$	2.26668	−	3.92600i	0.0835508	−	0.144714i
$737$	13.4121	+	3.59375i	0.494040	+	0.132378i
$738$		0			0
$739$	−35.4720	−	20.4798i	−1.30486	−	0.753361i	−0.323626	−	0.946185i	$-0.604902\pi$
$739$	−35.4720	−	20.4798i	−1.30486	−	0.753361i	−0.981233	+	0.192825i	$0.938235\pi$
$740$	7.65905	−	14.1043i	0.281552	−	0.518483i
$741$		0			0
$742$	−4.05230	−	1.57959i	−0.148764	−	0.0579887i
$743$	4.56136	−	17.0232i	0.167340	−	0.624522i	−0.830390	−	0.557183i	$-0.811882\pi$
$743$	4.56136	−	17.0232i	0.167340	−	0.624522i	0.997730	−	0.0673394i	$-0.0214510\pi$
$744$		0			0
$745$	23.8069	+	22.5945i	0.872217	+	0.827799i
$746$	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	−0.599902	−	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	−0.222954	−	0.974829i	$-0.571570\pi$
$761$	−32.5147	−	18.7724i	−1.17866	−	0.680498i	−0.955704	+	0.294331i	$0.904903\pi$
$762$		0			0
$763$	−11.5493	+	29.6286i	−0.418112	+	1.07263i
$764$		−	1.40939i		−	0.0509899i
$765$		0			0
$766$	2.08885	+	1.20600i	0.0754732	+	0.0435745i
$767$	23.7446	+	6.36235i	0.857369	+	0.229731i
$768$		0			0
$769$	−16.8089	−	29.1138i	−0.606143	−	1.04987i	−0.991870	−	0.127258i	$-0.959383\pi$
$769$	−16.8089	−	29.1138i	−0.606143	−	1.04987i	0.385727	−	0.922613i	$-0.373951\pi$
$770$	0.213381	−	0.592714i	0.00768973	−	0.0213599i
$771$		0			0
$772$	13.5596	−	13.5596i	0.488022	−	0.488022i
$773$	6.40415	+	23.9006i	0.230341	+	0.859645i	0.980194	+	0.198040i	$0.0634577\pi$
$773$	6.40415	+	23.9006i	0.230341	+	0.859645i	−0.749853	+	0.661605i	$0.769876\pi$
$774$		0			0
$775$	2.64145	−	5.18265i	0.0948836	−	0.186166i
$776$	2.85207	+	1.64664i	0.102383	+	0.0591110i
$777$		0			0
$778$	0.485874	−	1.81331i	0.0174194	−	0.0650102i
$779$	9.70425	+	5.60275i	0.347691	+	0.200739i
$780$		0			0
$781$	3.41191	+	5.90960i	0.122088	+	0.211462i
$782$	−0.337035	+	1.25783i	−0.0120524	+	0.0449800i
$783$		0			0
$784$	26.1723	−	8.20597i	0.934725	−	0.293070i
$785$	3.95987	+	6.46276i	0.141334	+	0.230666i
$786$		0			0
$787$	8.22532	+	8.22532i	0.293201	+	0.293201i	0.838343	−	0.545142i	$-0.183524\pi$
$787$	8.22532	+	8.22532i	0.293201	+	0.293201i	−0.545142	+	0.838343i	$0.683524\pi$
$788$	−3.64658	−	3.64658i	−0.129904	−	0.129904i
$789$		0			0
$790$	1.24747	+	2.03596i	0.0443831	+	0.0724361i
$791$	−31.6312	−	3.48985i	−1.12467	−	0.124085i
$792$		0			0
$793$	−11.0663	+	41.2999i	−0.392975	+	1.46660i
$794$	1.19950	+	2.07759i	0.0425685	+	0.0737308i
$795$		0			0
$796$	−7.31720	−	4.22459i	−0.259351	−	0.149737i
$797$	3.28298	−	12.2523i	0.116289	−	0.433997i	−0.883091	−	0.469202i	$-0.844542\pi$
$797$	3.28298	−	12.2523i	0.116289	−	0.433997i	0.999380	+	0.0352047i	$0.0112083\pi$
$798$		0			0
$799$	17.2819	+	9.97770i	0.611389	+	0.352986i
$800$	−6.60330	+	2.14470i	−0.233462	+	0.0758265i
$801$		0			0
$802$	0.666204	+	2.48631i	0.0235245	+	0.0877946i
$803$	2.47619	−	2.47619i	0.0873827	−	0.0873827i
$804$		0			0
$805$	−3.42056	−	19.0093i	−0.120559	−	0.669989i
$806$	−0.404004	−	0.699756i	−0.0142304	−	0.0246478i
$807$		0			0
$808$	6.58878	+	1.76546i	0.231792	+	0.0621086i
$809$	−37.6915	−	21.7612i	−1.32516	−	0.765083i	−0.340616	−	0.940203i	$-0.610635\pi$
$809$	−37.6915	−	21.7612i	−1.32516	−	0.765083i	−0.984547	+	0.175120i	$0.943969\pi$
$810$		0			0
$811$			10.3140i			0.362172i	0.983467	+	0.181086i	$0.0579613\pi$
$811$			10.3140i			0.362172i	−0.983467	+	0.181086i	$0.942039\pi$
$812$	32.4682	+	12.6562i	1.13941	+	0.444144i
$813$		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	$-0.675448\pi$
$829$	13.7029	−	23.7341i	0.475921	−	0.824319i	0.999619	+	0.0275844i	$0.00878151\pi$
$830$	−2.10818	−	2.00082i	−0.0731761	−	0.0694496i
$831$		0			0
$832$	11.8139	−	44.0901i	0.409574	−	1.52855i
$833$	−20.1861	+	12.8145i	−0.699406	+	0.443995i
$834$		0			0
$835$	9.79028	−	18.0290i	0.338807	−	0.623918i
$836$	2.55742	+	1.47653i	0.0884503	+	0.0510668i
$837$		0			0
$838$	−0.0527267	−	0.0141281i	−0.00182141	−	0.000488046i
$839$	−15.4515	+	26.7627i	−0.533444	+	0.923952i	0.465793	+	0.884894i	$0.345769\pi$
$839$	−15.4515	+	26.7627i	−0.533444	+	0.923952i	−0.999237	+	0.0390586i	$0.987564\pi$
$840$		0			0
$841$	7.48378	+	12.9623i	0.258061	+	0.446975i
$842$	0.255961	+	0.955259i	0.00882099	+	0.0329204i
$843$		0			0
$844$	−2.15000	+	1.24131i	−0.0740062	+	0.0427275i
$845$	−36.2884	−	34.4404i	−1.24836	−	1.18479i
$846$		0			0
$847$	−25.0663	−	9.77090i	−0.861289	−	0.335732i
$848$	−53.2808	+	14.2765i	−1.82967	+	0.490258i
$849$		0			0
$850$	1.67272	−	1.08600i	0.0573737	−	0.0372495i
$851$	−11.7970			−0.404398
$852$		0			0
$853$	2.84389	+	10.6135i	0.0973729	+	0.363400i	0.997369	−	0.0724984i	$-0.0230972\pi$
$853$	2.84389	+	10.6135i	0.0973729	+	0.363400i	−0.899996	+	0.435899i	$0.856431\pi$
$854$	1.31476	−	1.79010i	0.0449903	−	0.0612559i
$855$		0			0
$856$	−2.04049	−	3.53424i	−0.0697426	−	0.120798i
$857$	3.81825	−	14.2499i	0.130429	−	0.486768i	−0.869546	−	0.493852i	$-0.835588\pi$
$857$	3.81825	−	14.2499i	0.130429	−	0.486768i	0.999975	+	0.00708450i	$0.00225509\pi$
$858$		0			0
$859$	−1.93946	+	3.35925i	−0.0661736	+	0.114616i	−0.897214	−	0.441596i	$-0.854412\pi$
$859$	−1.93946	+	3.35925i	−0.0661736	+	0.114616i	0.831040	+	0.556212i	$0.187746\pi$
$860$	−0.497546	−	19.0426i	−0.0169662	−	0.649349i
$861$		0			0
$862$	1.02253	+	3.81613i	0.0348275	+	0.129978i
$863$	−4.40686	+	16.4466i	−0.150011	+	0.559850i	0.849470	+	0.527638i	$0.176922\pi$
$863$	−4.40686	+	16.4466i	−0.150011	+	0.559850i	−0.999481	+	0.0322127i	$0.989745\pi$
$864$		0			0
$865$	28.3657	−	17.3802i	0.964462	−	0.590946i
$866$		−	4.32837i		−	0.147084i
$867$		0			0
$868$	−0.925256	−	6.04371i	−0.0314052	−	0.205137i
$869$	−7.22128	+	4.16921i	−0.244965	+	0.141431i
$870$		0			0
$871$	−78.4327	+	45.2831i	−2.65759	+	1.53436i
$872$	−1.44810	−	5.40438i	−0.0490388	−	0.183015i
$873$		0			0
$874$	−0.621560			−0.0210246
$875$	−15.5902	+	25.1386i	−0.527043	+	0.849838i
$876$		0			0
$877$	−2.26354	−	8.44765i	−0.0764344	−	0.285257i	0.917120	−	0.398610i	$-0.130507\pi$
$877$	−2.26354	−	8.44765i	−0.0764344	−	0.285257i	−0.993555	+	0.113353i	$0.963841\pi$
$878$	−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	−0.999987	−	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
$887$	51.9969	−	13.9325i	1.74588	−	0.467808i	0.762144	−	0.647407i	$-0.224147\pi$
$887$	51.9969	−	13.9325i	1.74588	−	0.467808i	0.983740	+	0.179599i	$0.0574801\pi$
$888$		0			0
$889$	−26.1836	−	19.2309i	−0.878170	−	0.644984i
$890$	0.884362	+	0.480236i	0.0296439	+	0.0160975i
$891$		0			0
$892$	−53.3098	+	14.2843i	−1.78495	+	0.478275i
$893$	−2.46525	+	9.20044i	−0.0824964	+	0.307881i
$894$		0			0
$895$	12.2081	+	11.5864i	0.408073	+	0.387292i
$896$	−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
$902$	−0.706909	+	0.189416i	−0.0235375	+	0.00630686i
$903$		0			0
$904$	4.84895	−	2.79954i	0.161274	−	0.0931114i
$905$	−0.640617	+	2.66768i	−0.0212948	+	0.0886767i
$906$		0			0
$907$	5.41268	+	1.45032i	0.179725	+	0.0481572i	0.347559	−	0.937658i	$-0.387011\pi$
$907$	5.41268	+	1.45032i	0.179725	+	0.0481572i	−0.167834	+	0.985815i	$0.553677\pi$
$908$	−5.15438	−	1.38111i	−0.171054	−	0.0458339i
$909$		0			0
$910$	1.74952	+	3.71780i	0.0579961	+	0.123244i
$911$	−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
$917$	12.6047	−	32.3362i	0.416244	−	1.06783i
$918$		0			0
$919$	−15.0280	+	8.67643i	−0.495729	+	0.286209i	−0.726948	−	0.686693i	$-0.759062\pi$
$919$	−15.0280	+	8.67643i	−0.495729	+	0.286209i	0.231219	+	0.972902i	$0.425729\pi$
$920$	2.46489	+	2.33937i	0.0812651	+	0.0771267i
$921$		0			0
$922$	−0.467626	+	0.125300i	−0.0154005	+	0.00412654i
$923$	−42.9919	−	11.5196i	−1.41509	−	0.379173i
$924$		0			0
$925$	13.4252	+	12.0909i	0.441417	+	0.397547i
$926$	1.11494	+	1.93114i	0.0366393	+	0.0634611i
$927$		0			0
$928$	−8.89362	+	2.38304i	−0.291947	+	0.0782271i
$929$	−31.4728			−1.03259			−0.516294	−	0.856412i	$-0.672689\pi$
$929$	−31.4728			−1.03259			−0.516294	+	0.856412i	$0.672689\pi$
$930$		0			0
$931$	−8.40186	−	7.72371i	−0.275360	−	0.253134i
$932$	−20.2309	−	5.42086i	−0.662686	−	0.177566i
$933$		0			0
$934$	−2.25278	−	3.90193i	−0.0737131	−	0.127675i
$935$	3.63863	+	5.93848i	0.118996	+	0.194209i
$936$		0			0
$937$	−12.3936	−	12.3936i	−0.404882	−	0.404882i	0.475067	−	0.879950i	$-0.342424\pi$
$937$	−12.3936	−	12.3936i	−0.404882	−	0.404882i	−0.879950	+	0.475067i	$0.842424\pi$
$938$	4.65039	−	0.711946i	0.151840	−	0.0232459i
$939$		0			0
$940$	22.1261	−	13.5571i	0.721673	−	0.442184i
$941$			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	0.298223	−	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
$950$	0.707344	+	0.637043i	0.0229493	+	0.0206684i
$951$		0			0
$952$	1.52786	−	3.91957i	0.0495181	−	0.127034i
$953$	−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
$955$	1.54270	+	0.370465i	0.0499207	+	0.0119880i
$956$	−22.2975	−	38.6204i	−0.721153	−	1.24907i
$957$		0			0
$958$	−3.47968	−	0.932377i	−0.112423	−	0.0301237i
$959$	−4.46401	+	40.4607i	−0.144150	+	1.30655i
$960$		0			0
$961$	29.6465			0.956339
$962$	2.42413	−	0.649542i	0.0781569	−	0.0209421i
$963$		0			0
$964$	9.11049	+	15.7798i	0.293429	+	0.508234i
$965$	11.2780	+	18.4065i	0.363052	+	0.592525i
$966$		0			0
$967$	−29.9734	−	8.03134i	−0.963878	−	0.258270i	−0.257637	−	0.966242i	$-0.582944\pi$
$967$	−29.9734	−	8.03134i	−0.963878	−	0.258270i	−0.706241	+	0.707971i	$0.749611\pi$
$968$	4.57220	−	1.22512i	0.146956	−	0.0393767i
$969$		0			0
$970$	−1.27167	+	1.33991i	−0.0408310	+	0.0430219i
$971$	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
$973$	−20.3904	+	16.3381i	−0.653685	+	0.523777i
$974$	−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
$980$	2.11729	+	31.0193i	0.0676345	+	0.990876i
$981$		0			0
$982$	3.00027	+	0.803919i	0.0957424	+	0.0256541i
$983$	0.537708	+	0.144078i	0.0171502	+	0.00459539i	0.267384	−	0.963590i	$-0.413841\pi$
$983$	0.537708	+	0.144078i	0.0171502	+	0.00459539i	−0.250234	+	0.968185i	$0.580507\pi$
$984$		0			0
$985$	4.95003	−	3.03299i	0.157721	−	0.0966391i
$986$	2.29047	−	1.32240i	0.0729435	−	0.0421139i
$987$		0			0
$988$	−18.6050	+	4.98521i	−0.591905	+	0.158601i
$989$	−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
$995$	6.54756	−	6.89888i	0.207572	−	0.218709i
$996$		0			0
$997$	−11.5486	+	43.0999i	−0.365747	+	1.36499i	0.500658	+	0.865645i	$0.333091\pi$
$997$	−11.5486	+	43.0999i	−0.365747	+	1.36499i	−0.866405	+	0.499341i	$0.833575\pi$
$998$	0.979668	−	0.262501i	0.0310109	−	0.00830933i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bv.e.73.20		160
3.2	odd	2		315.2.bs.e.178.21	yes	160
5.2	odd	4	inner	945.2.bv.e.262.20		160
7.5	odd	6		945.2.cj.e.208.21		160
9.4	even	3		945.2.cj.e.388.20		160
9.5	odd	6		315.2.cg.e.283.21	yes	160
15.2	even	4		315.2.bs.e.52.21	✓	160
21.5	even	6		315.2.cg.e.313.20	yes	160
35.12	even	12		945.2.cj.e.397.20		160
45.22	odd	12		945.2.cj.e.577.21		160
45.32	even	12		315.2.cg.e.157.20	yes	160
63.5	even	6		315.2.bs.e.103.21	yes	160
63.40	odd	6	inner	945.2.bv.e.523.20		160
105.47	odd	12		315.2.cg.e.187.21	yes	160
315.257	odd	12		315.2.bs.e.292.21	yes	160
315.292	even	12	inner	945.2.bv.e.712.20		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.21	✓	160	15.2	even	4
315.2.bs.e.103.21	yes	160	63.5	even	6
315.2.bs.e.178.21	yes	160	3.2	odd	2
315.2.bs.e.292.21	yes	160	315.257	odd	12
315.2.cg.e.157.20	yes	160	45.32	even	12
315.2.cg.e.187.21	yes	160	105.47	odd	12
315.2.cg.e.283.21	yes	160	9.5	odd	6
315.2.cg.e.313.20	yes	160	21.5	even	6
945.2.bv.e.73.20		160	1.1	even	1	trivial
945.2.bv.e.262.20		160	5.2	odd	4	inner
945.2.bv.e.523.20		160	63.40	odd	6	inner
945.2.bv.e.712.20		160	315.292	even	12	inner
945.2.cj.e.208.21		160	7.5	odd	6
945.2.cj.e.388.20		160	9.4	even	3
945.2.cj.e.397.20		160	35.12	even	12
945.2.cj.e.577.21		160	45.22	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.0825718 - 0.0825718i) q^{2} +1.98636i q^{4} +(-2.17426 - 0.522126i) q^{5} +(-0.400384 - 2.61528i) q^{7} +(0.329161 + 0.329161i) q^{8} +O(q^{10})\)	\(q+(0.0825718 - 0.0825718i) q^{2} +1.98636i q^{4} +(-2.17426 - 0.522126i) q^{5} +(-0.400384 - 2.61528i) q^{7} +(0.329161 + 0.329161i) q^{8} +(-0.222645 + 0.136419i) q^{10} +(-0.455930 - 0.789693i) q^{11} +(5.74495 + 1.53935i) q^{13} +(-0.249009 - 0.182888i) q^{14} -3.91837 q^{16} +(3.29933 - 0.884052i) q^{17} +(0.815184 + 1.41194i) q^{19} +(1.03713 - 4.31886i) q^{20} +(-0.102853 - 0.0275595i) q^{22} +(-3.15352 + 0.844982i) q^{23} +(4.45477 + 2.27047i) q^{25} +(0.601478 - 0.347264i) q^{26} +(5.19490 - 0.795308i) q^{28} +(5.74244 + 3.31540i) q^{29} -1.16339i q^{31} +(-0.981869 + 0.981869i) q^{32} +(0.199433 - 0.345429i) q^{34} +(-0.494969 + 5.89534i) q^{35} +(3.49032 + 0.935230i) q^{37} +(0.183898 + 0.0492752i) q^{38} +(-0.543817 - 0.887544i) q^{40} +(5.95218 - 3.43649i) q^{41} +(4.14262 - 1.11001i) q^{43} +(1.56862 - 0.905642i) q^{44} +(-0.190620 + 0.330163i) q^{46} +(4.13109 + 4.13109i) q^{47} +(-6.67939 + 2.09423i) q^{49} +(0.555315 - 0.180362i) q^{50} +(-3.05772 + 11.4116i) q^{52} +(13.5977 - 3.64349i) q^{53} +(0.578988 + 1.95505i) q^{55} +(0.729058 - 0.992640i) q^{56} +(0.747922 - 0.200405i) q^{58} +4.13313 q^{59} +7.18890i q^{61} +(-0.0960635 - 0.0960635i) q^{62} -7.67459i q^{64} +(-11.6873 - 6.34654i) q^{65} +(-10.7674 + 10.7674i) q^{67} +(1.75605 + 6.55366i) q^{68} +(0.445918 + 0.527659i) q^{70} -7.48342 q^{71} +(0.993956 + 3.70949i) q^{73} +(0.365426 - 0.210979i) q^{74} +(-2.80463 + 1.61925i) q^{76} +(-1.88272 + 1.50856i) q^{77} -9.14441i q^{79} +(8.51953 + 2.04588i) q^{80} +(0.207725 - 0.775240i) q^{82} +(2.88094 + 10.7518i) q^{83} +(-7.63516 + 0.199491i) q^{85} +(0.250408 - 0.433720i) q^{86} +(0.109862 - 0.410011i) q^{88} +(-1.92701 - 3.33768i) q^{89} +(1.72566 - 15.6410i) q^{91} +(-1.67844 - 6.26403i) q^{92} +0.682222 q^{94} +(-1.03521 - 3.49555i) q^{95} +(6.83360 - 1.83106i) q^{97} +(-0.378604 + 0.724453i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8}+O(q^{10}) \) 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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