LMFDB - Embedded newform 945.2.cj.e.388.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(208,945)]

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, 10]))

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

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

chi := DirichletCharacter("945.208");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cj (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			388.20
Character	$\chi$	$=$	945.388
Dual form			945.2.cj.e.397.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0302234 + 0.112795i) q^{2} +(1.72024 - 0.993182i) q^{4} +(0.634953 + 2.14402i) q^{5} +(2.46509 + 0.960898i) q^{7} +(0.329161 + 0.329161i) q^{8} +O(q^{10})$	\(q+(0.0302234 + 0.112795i) q^{2} +(1.72024 - 0.993182i) q^{4} +(0.634953 + 2.14402i) q^{5} +(2.46509 + 0.960898i) q^{7} +(0.329161 + 0.329161i) q^{8} +(-0.222645 + 0.136419i) q^{10} +0.911859 q^{11} +(-1.53935 - 5.74495i) q^{13} +(-0.0338813 + 0.307092i) q^{14} +(1.95918 - 3.39341i) q^{16} +(3.29933 - 0.884052i) q^{17} +(0.815184 + 1.41194i) q^{19} +(3.22168 + 3.05761i) q^{20} +(0.0275595 + 0.102853i) q^{22} +(2.30853 + 2.30853i) q^{23} +(-4.19367 + 2.72271i) q^{25} +(0.601478 - 0.347264i) q^{26} +(5.19490 - 0.795308i) q^{28} +(-5.74244 + 3.31540i) q^{29} +(-1.00753 + 0.581697i) q^{31} +(1.34126 + 0.359389i) q^{32} +(0.199433 + 0.345429i) q^{34} +(-0.494969 + 5.89534i) q^{35} +(3.49032 + 0.935230i) q^{37} +(-0.134622 + 0.134622i) q^{38} +(-0.496727 + 0.914731i) q^{40} +(-5.95218 - 3.43649i) q^{41} +(-1.11001 + 4.14262i) q^{43} +(1.56862 - 0.905642i) q^{44} +(-0.190620 + 0.330163i) q^{46} +(-5.64317 + 1.51208i) q^{47} +(5.15335 + 4.73740i) q^{49} +(-0.433855 - 0.390736i) q^{50} +(-8.35384 - 8.35384i) q^{52} +(13.5977 - 3.64349i) q^{53} +(0.578988 + 1.95505i) q^{55} +(0.495122 + 1.12770i) q^{56} +(-0.547517 - 0.547517i) q^{58} +(-2.06657 - 3.57940i) q^{59} +(-6.22577 - 3.59445i) q^{61} +(-0.0960635 - 0.0960635i) q^{62} -7.67459i q^{64} +(11.3399 - 6.94819i) q^{65} +(14.7085 + 3.94113i) q^{67} +(4.79761 - 4.79761i) q^{68} +(-0.679925 + 0.122347i) q^{70} -7.48342 q^{71} +(0.993956 + 3.70949i) q^{73} +0.421958i q^{74} +(2.80463 + 1.61925i) q^{76} +(2.24782 + 0.876203i) q^{77} +(7.91929 + 4.57221i) q^{79} +(8.51953 + 2.04588i) q^{80} +(0.207725 - 0.775240i) q^{82} +(-10.7518 - 2.88094i) q^{83} +(3.99035 + 6.51250i) q^{85} -0.500816 q^{86} +(0.300149 + 0.300149i) q^{88} +(-1.92701 - 3.33768i) q^{89} +(1.72566 - 15.6410i) q^{91} +(6.26403 + 1.67844i) q^{92} +(-0.341111 - 0.590822i) q^{94} +(-2.50963 + 2.64429i) q^{95} +(-1.83106 + 6.83360i) q^{97} +(-0.378604 + 0.724453i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8}+O(q^{10}) $ 160 * q + 2 * q^2 + 6 * q^7 + 16 * q^8	$ 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8} - 24 q^{10} - 32 q^{11} + 76 q^{16} + 6 q^{17} + 60 q^{20} + 8 q^{22} + 16 q^{23} - 4 q^{25} + 36 q^{26} + 22 q^{28} + 48 q^{31} + 6 q^{32} + 36 q^{35} - 4 q^{37} - 12 q^{41} - 4 q^{43} - 16 q^{46} + 54 q^{47} + 44 q^{50} - 8 q^{53} + 92 q^{56} - 56 q^{58} - 24 q^{61} - 62 q^{65} + 12 q^{67} + 2 q^{70} + 40 q^{71} + 36 q^{73} - 96 q^{76} + 110 q^{77} - 36 q^{80} - 66 q^{82} - 138 q^{83} - 20 q^{85} - 32 q^{86} - 92 q^{88} - 48 q^{91} + 26 q^{92} + 94 q^{95} - 48 q^{97} - 102 q^{98}+O(q^{100}) $ 160 * q + 2 * q^2 + 6 * q^7 + 16 * q^8 - 24 * q^10 - 32 * q^11 + 76 * q^16 + 6 * q^17 + 60 * q^20 + 8 * q^22 + 16 * q^23 - 4 * q^25 + 36 * q^26 + 22 * q^28 + 48 * q^31 + 6 * q^32 + 36 * q^35 - 4 * q^37 - 12 * q^41 - 4 * q^43 - 16 * q^46 + 54 * q^47 + 44 * q^50 - 8 * q^53 + 92 * q^56 - 56 * q^58 - 24 * q^61 - 62 * q^65 + 12 * q^67 + 2 * q^70 + 40 * q^71 + 36 * q^73 - 96 * q^76 + 110 * q^77 - 36 * q^80 - 66 * q^82 - 138 * q^83 - 20 * q^85 - 32 * q^86 - 92 * q^88 - 48 * q^91 + 26 * q^92 + 94 * q^95 - 48 * q^97 - 102 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.0302234	+	0.112795i	0.0213712	+	0.0797582i	0.975788	−	0.218719i	$-0.0701879\pi$
$2$	0.0302234	+	0.112795i	0.0213712	+	0.0797582i	−0.954417	+	0.298477i	$0.903521\pi$
$3$		0			0
$3$		0			0
$4$	1.72024	−	0.993182i	0.860121	−	0.496591i
$5$	0.634953	+	2.14402i	0.283960	+	0.958836i
$5$	0.634953	+	2.14402i	0.283960	+	0.958836i
$6$		0			0
$7$	2.46509	+	0.960898i	0.931717	+	0.363185i
$7$	2.46509	+	0.960898i	0.931717	+	0.363185i
$8$	0.329161	+	0.329161i	0.116376	+	0.116376i
$9$		0			0
$10$	−0.222645	+	0.136419i	−0.0704065	+	0.0431396i
$11$	0.911859			0.274936			0.137468	−	0.990506i	$-0.456104\pi$
$11$	0.911859			0.274936			0.137468	+	0.990506i	$0.456104\pi$
$12$		0			0
$13$	−1.53935	−	5.74495i	−0.426940	−	1.59336i	−0.759649	−	0.650333i	$-0.774629\pi$
$13$	−1.53935	−	5.74495i	−0.426940	−	1.59336i	0.332709	−	0.943030i	$-0.392037\pi$
$14$	−0.0338813	+	0.307092i	−0.00905515	+	0.0820738i
$15$		0			0
$16$	1.95918	−	3.39341i	0.489796	−	0.848352i
$17$	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	$0.773452\pi$
$20$	3.22168	+	3.05761i	0.720389	+	0.683703i
$21$		0			0
$22$	0.0275595	+	0.102853i	0.00587570	+	0.0219284i
$23$	2.30853	+	2.30853i	0.481363	+	0.481363i	0.905567	−	0.424204i	$-0.139446\pi$
$23$	2.30853	+	2.30853i	0.481363	+	0.481363i	−0.424204	+	0.905567i	$0.639446\pi$
$24$		0			0
$25$	−4.19367	+	2.72271i	−0.838734	+	0.544542i
$26$	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	$-0.877775\pi$
$29$	−5.74244	+	3.31540i	−1.06635	+	0.615655i	−0.139164	+	0.990269i	$0.544442\pi$
$30$		0			0
$31$	−1.00753	+	0.581697i	−0.180957	+	0.104476i	−0.587742	−	0.809048i	$-0.699983\pi$
$31$	−1.00753	+	0.581697i	−0.180957	+	0.104476i	0.406785	+	0.913524i	$0.366650\pi$
$32$	1.34126	+	0.359389i	0.237103	+	0.0635316i
$33$		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	$0.487339\pi$
$38$	−0.134622	+	0.134622i	−0.0218386	+	0.0218386i
$39$		0			0
$40$	−0.496727	+	0.914731i	−0.0785394	+	0.144632i
$41$	−5.95218	−	3.43649i	−0.929575	−	0.536690i	−0.0428978	−	0.999079i	$-0.513659\pi$
$41$	−5.95218	−	3.43649i	−0.929575	−	0.536690i	−0.886677	+	0.462389i	$0.846992\pi$
$42$		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
$47$	−5.64317	+	1.51208i	−0.823141	+	0.220560i	−0.645719	−	0.763575i	$-0.723442\pi$
$47$	−5.64317	+	1.51208i	−0.823141	+	0.220560i	−0.177422	+	0.984135i	$0.556776\pi$
$48$		0			0
$49$	5.15335	+	4.73740i	0.736193	+	0.676772i
$50$	−0.433855	−	0.390736i	−0.0613564	−	0.0552584i
$51$		0			0
$52$	−8.35384	−	8.35384i	−1.15847	−	1.15847i
$53$	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
$56$	0.495122	+	1.12770i	0.0661635	+	0.150696i
$57$		0			0
$58$	−0.547517	−	0.547517i	−0.0718925	−	0.0718925i
$59$	−2.06657	−	3.57940i	−0.269044	−	0.465998i	0.699571	−	0.714563i	$-0.253374\pi$
$59$	−2.06657	−	3.57940i	−0.269044	−	0.465998i	−0.968615	+	0.248565i	$0.920041\pi$
$60$		0			0
$61$	−6.22577	−	3.59445i	−0.797128	−	0.460222i	0.0453379	−	0.998972i	$-0.485564\pi$
$61$	−6.22577	−	3.59445i	−0.797128	−	0.460222i	−0.842466	+	0.538750i	$0.818897\pi$
$62$	−0.0960635	−	0.0960635i	−0.0122001	−	0.0122001i
$63$		0			0
$64$		−	7.67459i		−	0.959324i
$65$	11.3399	−	6.94819i	1.40654	−	0.861817i
$66$		0			0
$67$	14.7085	+	3.94113i	1.79693	+	0.481485i	0.993491	−	0.113907i	$-0.0363366\pi$
$67$	14.7085	+	3.94113i	1.79693	+	0.481485i	0.803435	+	0.595392i	$0.203003\pi$
$68$	4.79761	−	4.79761i	0.581796	−	0.581796i
$69$		0			0
$70$	−0.679925	+	0.122347i	−0.0812666	+	0.0146233i
$71$	−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	$0.844514\pi$
$74$			0.421958i			0.0490516i
$75$		0			0
$76$	2.80463	+	1.61925i	0.321713	+	0.185741i
$77$	2.24782	+	0.876203i	0.256162	+	0.0998526i
$78$		0			0
$79$	7.91929	+	4.57221i	0.890990	+	0.514413i	0.874266	−	0.485447i	$-0.161343\pi$
$79$	7.91929	+	4.57221i	0.890990	+	0.514413i	0.0167239	+	0.999860i	$0.494676\pi$
$80$	8.51953	+	2.04588i	0.952513	+	0.228736i
$81$		0			0
$82$	0.207725	−	0.775240i	0.0229394	−	0.0856109i
$83$	−10.7518	−	2.88094i	−1.18017	−	0.316224i	−0.385174	−	0.922844i	$-0.625858\pi$
$83$	−10.7518	−	2.88094i	−1.18017	−	0.316224i	−0.794992	+	0.606620i	$0.792525\pi$
$84$		0			0
$85$	3.99035	+	6.51250i	0.432814	+	0.706380i
$86$	−0.500816			−0.0540044
$87$		0			0
$88$	0.300149	+	0.300149i	0.0319959	+	0.0319959i
$89$	−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
$92$	6.26403	+	1.67844i	0.653070	+	0.174990i
$93$		0			0
$94$	−0.341111	−	0.590822i	−0.0351829	−	0.0609386i
$95$	−2.50963	+	2.64429i	−0.257482	+	0.271298i
$96$		0			0
$97$	−1.83106	+	6.83360i	−0.185916	+	0.693847i	0.808517	+	0.588473i	$0.200271\pi$
$97$	−1.83106	+	6.83360i	−0.185916	+	0.693847i	−0.994433	+	0.105374i	$0.966396\pi$
$98$	−0.378604	+	0.724453i	−0.0382448	+	0.0731808i
$99$		0			0
$100$	−4.50998	+	8.84879i	−0.450998	+	0.884879i
$101$			14.6534i			1.45806i	0.684480	+	0.729032i	$0.260029\pi$
$101$			14.6534i			1.45806i	−0.684480	+	0.729032i	$0.739971\pi$
$102$		0			0
$103$	2.85374	−	2.85374i	0.281187	−	0.281187i	−0.552395	−	0.833582i	$-0.686286\pi$
$103$	2.85374	−	2.85374i	0.281187	−	0.281187i	0.833582	+	0.552395i	$0.186286\pi$
$104$	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	$0.861905\pi$
$110$	−0.203021	+	0.124395i	−0.0193573	+	0.0118606i
$111$		0			0
$112$	8.09029	−	6.48248i	0.764460	−	0.612537i
$113$	−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
$115$	−3.48374	+	6.41536i	−0.324860	+	0.598235i
$116$	−6.58559	+	11.4066i	−0.611457	+	1.05907i
$117$		0			0
$118$	0.341280	−	0.341280i	0.0314174	−	0.0314174i
$119$	8.98262	+	0.991047i	0.823436	+	0.0908491i
$120$		0			0
$121$	−10.1685			−0.924410
$122$	0.217273	−	0.810873i	0.0196709	−	0.0734130i
$123$		0			0
$124$	−1.15546	+	2.00132i	−0.103764	+	0.179724i
$125$	−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	$0.0666091\pi$
$128$	3.54817	−	0.950730i	0.313617	−	0.0840335i
$129$		0			0
$130$	1.12645	+	1.06909i	0.0987963	+	0.0937651i
$131$		−	13.1176i		−	1.14609i	−0.819523	−	0.573047i	$-0.805761\pi$
$131$		−	13.1176i		−	1.14609i	0.819523	−	0.573047i	$-0.194239\pi$
$132$		0			0
$133$	0.652773	+	4.26387i	0.0566026	+	0.369724i
$134$			1.77816i			0.153610i
$135$		0			0
$136$	1.37701	+	0.795014i	0.118077	+	0.0681719i
$137$	10.8792	−	10.8792i	0.929473	−	0.929473i	−0.0681985	−	0.997672i	$-0.521725\pi$
$137$	10.8792	−	10.8792i	0.929473	−	0.929473i	0.997672	+	0.0681985i	$0.0217251\pi$
$138$		0			0
$139$	−4.93784	+	8.55258i	−0.418822	+	0.725421i	−0.995821	−	0.0913239i	$-0.970890\pi$
$139$	−4.93784	+	8.55258i	−0.418822	+	0.725421i	0.576999	+	0.816745i	$0.304223\pi$
$140$	5.00368	+	10.6330i	0.422888	+	0.898652i
$141$		0			0
$142$	−0.226174	−	0.844093i	−0.0189801	−	0.0708347i
$143$	−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
$148$	6.93306	−	1.85771i	0.569894	−	0.152703i
$149$			14.6784i			1.20250i	0.799060	+	0.601252i	$0.205331\pi$
$149$			14.6784i			1.20250i	−0.799060	+	0.601252i	$0.794669\pi$
$150$		0			0
$151$	−11.2624			−0.916519			−0.458260	−	0.888818i	$-0.651527\pi$
$151$	−11.2624			−0.916519			−0.458260	+	0.888818i	$0.651527\pi$
$152$	−0.196429	+	0.733083i	−0.0159325	+	0.0594609i
$153$		0			0
$154$	−0.0308949	+	0.280025i	−0.00248958	+	0.0225650i
$155$	−1.88691	−	1.79081i	−0.151560	−	0.143842i
$156$		0			0
$157$	−0.877299	+	3.27413i	−0.0700161	+	0.261304i	−0.992057	−	0.125789i	$-0.959854\pi$
$157$	−0.877299	+	3.27413i	−0.0700161	+	0.261304i	0.922041	+	0.387092i	$0.126521\pi$
$158$	−0.276375	+	1.03145i	−0.0219872	+	0.0820574i
$159$		0			0
$160$	0.0810981	+	3.10388i	0.00641137	+	0.245384i
$161$	3.47248	+	7.90901i	0.273670	+	0.623317i
$162$		0			0
$163$	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	$-0.190275\pi$
$164$	−13.6523			−1.06606
$165$		0			0
$166$		−	1.29983i		−	0.100886i
$167$	8.86226	−	2.37464i	0.685782	−	0.183755i	0.100929	−	0.994894i	$-0.467819\pi$
$167$	8.86226	−	2.37464i	0.685782	−	0.183755i	0.584854	+	0.811139i	$0.301152\pi$
$168$		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
$173$	−3.85055	−	14.3705i	−0.292752	−	1.09257i	−0.942986	−	0.332832i	$-0.891996\pi$
$173$	−3.85055	−	14.3705i	−0.292752	−	1.09257i	0.650234	−	0.759734i	$-0.274671\pi$
$174$		0			0
$175$	−12.9540	+	2.68204i	−0.979232	+	0.202743i
$176$	1.78650	−	3.09431i	0.134662	−	0.233242i
$177$		0			0
$178$	0.318233	−	0.318233i	0.0238526	−	0.0238526i
$179$	−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	$-0.0145196\pi$
$182$	1.81638	−	0.278077i	0.134639	−	0.0206125i
$183$		0			0
$184$			1.51976i			0.112038i
$185$	0.211040	+	8.07716i	0.0155160	+	0.593845i
$186$		0			0
$187$	3.00852	−	0.806130i	0.220005	−	0.0589501i
$188$	−8.20584	+	8.20584i	−0.598472	+	0.598472i
$189$		0			0
$190$	−0.374112	−	0.203155i	−0.0271410	−	0.0147384i
$191$	0.354766	−	0.614473i	0.0256700	−	0.0444617i	−0.852905	−	0.522066i	$-0.825161\pi$
$191$	0.354766	−	0.614473i	0.0256700	−	0.0444617i	0.878575	+	0.477604i	$0.158495\pi$
$192$		0			0
$193$	−2.49862	+	9.32497i	−0.179855	+	0.671226i	0.815819	+	0.578307i	$0.196286\pi$
$193$	−2.49862	+	9.32497i	−0.179855	+	0.671226i	−0.995674	+	0.0929191i	$0.970380\pi$
$194$	−0.826138			−0.0593132
$195$		0			0
$196$	13.5701	+	3.03126i	0.969294	+	0.216519i
$197$	−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	$0.214840\pi$
$200$	−2.27660	−	0.484183i	−0.160980	−	0.0342369i
$201$		0			0
$202$	−1.65283	+	0.442874i	−0.116293	+	0.0311605i
$203$	−17.3414	+	2.65487i	−1.21713	+	0.186335i
$204$		0			0
$205$	3.58856	−	14.9436i	0.250636	−	1.04371i
$206$	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	−0.843713	−	0.536794i	$-0.819635\pi$
$211$	0.624913	−	1.08238i	0.0430208	−	0.0745142i	0.886734	+	0.462280i	$0.152968\pi$
$212$	19.7727	−	19.7727i	1.35799	−	1.35799i
$213$		0			0
$214$		−	1.02374i		−	0.0699812i
$215$	−9.58669	+	0.250481i	−0.653807	+	0.0170826i
$216$		0			0
$217$	−3.04260	+	0.465804i	−0.206545	+	0.0316208i
$218$	0.363263	−	1.35572i	0.0246033	−	0.0918206i
$219$		0			0
$220$	2.93772	+	2.78811i	0.198061	+	0.187974i
$221$	−10.1577	−	17.5936i	−0.683279	−	1.18347i
$222$		0			0
$223$	−26.8379	−	7.19120i	−1.79720	−	0.481558i	−0.803664	−	0.595083i	$-0.797119\pi$
$223$	−26.8379	−	7.19120i	−1.79720	−	0.481558i	−0.993535	+	0.113525i	$0.963786\pi$
$224$	2.96099	+	2.17474i	0.197839	+	0.145306i
$225$		0			0
$226$	−0.702280	−	1.21638i	−0.0467149	−	0.0809127i
$227$	−1.89959	−	1.89959i	−0.126080	−	0.126080i	0.641251	−	0.767331i	$-0.278416\pi$
$227$	−1.89959	−	1.89959i	−0.126080	−	0.126080i	−0.767331	+	0.641251i	$0.778416\pi$
$228$		0			0
$229$	2.71128			0.179166			0.0895831	−	0.995979i	$-0.471447\pi$
$229$	2.71128			0.179166			0.0895831	+	0.995979i	$0.471447\pi$
$230$	−0.828912	−	0.199055i	−0.0546568	−	0.0131253i
$231$		0			0
$232$	−2.98149	−	0.798888i	−0.195744	−	0.0524496i
$233$	−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
$236$	−7.10998	−	4.10495i	−0.462820	−	0.267210i
$237$		0			0
$238$	0.159700	+	1.04315i	0.0103518	+	0.0676173i
$239$	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
$241$			9.17303i			0.590887i	0.955360	+	0.295443i	$0.0954674\pi$
$241$			9.17303i			0.590887i	−0.955360	+	0.295443i	$0.904533\pi$
$242$	−0.307327	−	1.14696i	−0.0197557	−	0.0737293i
$243$		0			0
$244$	−14.2798			−0.914168
$245$	−6.88496	+	14.0569i	−0.439864	+	0.898064i
$246$		0			0
$247$	6.85667	−	6.85667i	0.436279	−	0.436279i
$248$	−0.523111	−	0.140167i	−0.0332176	−	0.00890063i
$249$		0			0
$250$	0.562269	−	1.17829i	0.0355610	−	0.0745219i
$251$		−	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
$254$	1.24176	+	0.716932i	0.0779151	+	0.0449843i
$255$		0			0
$256$	−7.46011	−	12.9213i	−0.466257	−	0.807581i
$257$	4.43771	+	4.43771i	0.276817	+	0.276817i	0.831837	−	0.555020i	$-0.187290\pi$
$257$	4.43771	+	4.43771i	0.276817	+	0.276817i	−0.555020	+	0.831837i	$0.687290\pi$
$258$		0			0
$259$	7.70531	+	5.65927i	0.478785	+	0.351650i
$260$	12.6065	−	23.2151i	0.781824	−	1.43974i
$261$		0			0
$262$	1.47961	−	0.396459i	0.0914104	−	0.0244933i
$263$	−19.8175	−	19.8175i	−1.22200	−	1.22200i	−0.966920	−	0.255079i	$-0.917898\pi$
$263$	−19.8175	−	19.8175i	−1.22200	−	1.22200i	−0.255079	−	0.966920i	$-0.582102\pi$
$264$		0			0
$265$	16.4456	+	26.8403i	1.01025	+	1.64879i
$266$	−0.461215	+	0.202498i	−0.0282789	+	0.0124160i
$267$		0			0
$268$	29.2164	−	7.82851i	1.78468	−	0.478202i
$269$	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	$0.488870\pi$
$272$	3.46404	−	12.9280i	0.210038	−	0.783874i
$273$		0			0
$274$	1.55593	+	0.898315i	0.0939970	+	0.0542692i
$275$	−3.82403	+	2.48273i	−0.230598	+	0.149714i
$276$		0			0
$277$	−13.1685	+	13.1685i	−0.791220	+	0.791220i	−0.981692	−	0.190473i	$-0.938998\pi$
$277$	−13.1685	+	13.1685i	−0.791220	+	0.791220i	0.190473	+	0.981692i	$0.438998\pi$
$278$	−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	0.730636	−	0.682767i	$-0.239224\pi$
$281$	−3.78805	−	6.56109i	−0.225976	−	0.391402i	−0.956612	+	0.291366i	$0.905890\pi$
$282$		0			0
$283$	−13.3365	−	3.57351i	−0.792773	−	0.212423i	−0.160365	−	0.987058i	$-0.551267\pi$
$283$	−13.3365	−	3.57351i	−0.792773	−	0.212423i	−0.632409	+	0.774635i	$0.717934\pi$
$284$	−12.8733	+	7.43239i	−0.763889	+	0.441031i
$285$		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
$290$	0.826242	−	1.52154i	0.0485186	−	0.0893478i
$291$		0			0
$292$	5.39404	+	5.39404i	0.315663	+	0.315663i
$293$	0.623080	+	2.32537i	0.0364007	+	0.135849i	0.981735	−	0.190254i	$-0.0609310\pi$
$293$	0.623080	+	2.32537i	0.0364007	+	0.135849i	−0.945334	+	0.326103i	$0.894264\pi$
$294$		0			0
$295$	6.36213	−	6.70351i	0.370418	−	0.390294i
$296$	0.841038	+	1.45672i	0.0488843	+	0.0846702i
$297$		0			0
$298$	−1.65566	+	0.443631i	−0.0959095	+	0.0256989i
$299$	9.70876	−	16.8161i	0.561472	−	0.972498i
$300$		0			0
$301$	−6.71692	+	9.14534i	−0.387157	+	0.527128i
$302$	−0.340387	−	1.27034i	−0.0195871	−	0.0731000i
$303$		0			0
$304$	6.38838			0.366399
$305$	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	$0.622368\pi$
$308$	4.73702	−	0.725208i	0.269916	−	0.0413226i
$309$		0			0
$310$	0.144966	−	0.266958i	0.00823354	−	0.0151622i
$311$	−23.0467	+	13.3060i	−1.30686	+	0.754516i	−0.981571	−	0.191098i	$-0.938795\pi$
$311$	−23.0467	+	13.3060i	−1.30686	+	0.754516i	−0.325290	+	0.945614i	$0.605462\pi$
$312$		0			0
$313$	−0.191952	−	0.716376i	−0.0108498	−	0.0404919i	0.960289	−	0.279008i	$-0.0900057\pi$
$313$	−0.191952	−	0.716376i	−0.0108498	−	0.0404919i	−0.971139	+	0.238516i	$0.923339\pi$
$314$	−0.395821			−0.0223374
$315$		0			0
$316$	18.1641			1.02181
$317$	−1.84880	−	6.89982i	−0.103839	−	0.387533i	0.894372	−	0.447324i	$-0.147623\pi$
$317$	−1.84880	−	6.89982i	−0.103839	−	0.387533i	−0.998211	+	0.0597917i	$0.980956\pi$
$318$		0			0
$319$	−5.23630	+	3.02318i	−0.293176	+	0.169266i
$320$	16.4545	−	4.87301i	0.919834	−	0.272409i
$321$		0			0
$322$	−0.787148	+	0.630716i	−0.0438660	+	0.0351484i
$323$	3.93778	+	3.93778i	0.219104	+	0.219104i
$324$		0			0
$325$	22.0974	+	19.9012i	1.22574	+	1.10392i
$326$	2.25885			0.125106
$327$		0			0
$328$	−0.828067	−	3.09039i	−0.0457224	−	0.170638i
$329$	−15.3639	−	1.69509i	−0.847038	−	0.0934532i
$330$		0			0
$331$	3.63757	−	6.30046i	0.199939	−	0.346304i	−0.748569	−	0.663056i	$-0.769259\pi$
$331$	3.63757	−	6.30046i	0.199939	−	0.346304i	0.948508	+	0.316752i	$0.102592\pi$
$332$	−21.3570	+	5.72260i	−1.17212	+	0.314068i
$333$		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	$0.798507\pi$
$338$	−1.84747	−	1.84747i	−0.100489	−	0.100489i
$339$		0			0
$340$	13.3325	+	7.23993i	0.723054	+	0.392640i
$341$	−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
$346$	1.50454	−	0.868647i	0.0808846	−	0.0466988i
$347$	11.5594	+	3.09732i	0.620539	+	0.166273i	0.555373	−	0.831602i	$-0.312576\pi$
$347$	11.5594	+	3.09732i	0.620539	+	0.166273i	0.0651661	+	0.997874i	$0.479242\pi$
$348$		0			0
$349$	−15.7451	−	27.2713i	−0.842814	−	1.45980i	−0.887506	−	0.460797i	$-0.847564\pi$
$349$	−15.7451	−	27.2713i	−0.842814	−	1.45980i	0.0446913	−	0.999001i	$-0.485770\pi$
$350$	−0.694035	−	1.38009i	−0.0370977	−	0.0737689i
$351$		0			0
$352$	1.22304	+	0.327712i	0.0651882	+	0.0174671i
$353$	−23.8853	+	23.8853i	−1.27129	+	1.27129i	−0.325871	+	0.945414i	$0.605658\pi$
$353$	−23.8853	+	23.8853i	−1.27129	+	1.27129i	−0.945414	+	0.325871i	$0.894342\pi$
$354$		0			0
$355$	−4.75162	−	16.0446i	−0.252190	−	0.851560i
$356$	−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	$-0.472989\pi$
$359$	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
$362$	0.138393	−	0.0370823i	0.00727377	−	0.00194900i
$363$		0			0
$364$	−12.5658	−	28.6202i	−0.658627	−	1.50010i
$365$	−7.32212	+	4.48642i	−0.383257	+	0.234830i
$366$		0			0
$367$	13.2202	+	13.2202i	0.690087	+	0.690087i	0.962251	−	0.272164i	$-0.0877394\pi$
$367$	13.2202	+	13.2202i	0.690087	+	0.690087i	−0.272164	+	0.962251i	$0.587739\pi$
$368$	12.3566	−	3.31095i	0.644134	−	0.172595i
$369$		0			0
$370$	−0.904687	+	0.267923i	−0.0470324	+	0.0139287i
$371$	37.0206	+	4.08446i	1.92201	+	0.212054i
$372$		0			0
$373$	−13.0604	−	13.0604i	−0.676242	−	0.676242i	0.282906	−	0.959148i	$-0.408702\pi$
$373$	−13.0604	−	13.0604i	−0.676242	−	0.676242i	−0.959148	+	0.282906i	$0.908702\pi$
$374$	0.181855	+	0.314982i	0.00940351	+	0.0162874i
$375$		0			0
$376$	−2.35523	−	1.35979i	−0.121462	−	0.0701260i
$377$	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	$-0.0197173\pi$
$380$	−1.69091	+	7.04133i	−0.0867416	+	0.361213i
$381$		0			0
$382$	0.0800318	+	0.0214445i	0.00409478	+	0.00109719i
$383$	14.6055	−	14.6055i	0.746304	−	0.746304i	−0.227479	−	0.973783i	$-0.573048\pi$
$383$	14.6055	−	14.6055i	0.746304	−	0.746304i	0.973783	+	0.227479i	$0.0730483\pi$
$384$		0			0
$385$	−0.451342	+	5.37572i	−0.0230025	+	0.273972i
$386$	−1.12733			−0.0573795
$387$		0			0
$388$	3.63715	+	13.5740i	0.184648	+	0.689116i
$389$			16.0761i			0.815091i	0.913185	+	0.407546i	$0.133615\pi$
$389$			16.0761i			0.815091i	−0.913185	+	0.407546i	$0.866385\pi$
$390$		0			0
$391$	9.65747	+	5.57574i	0.488399	+	0.281977i
$392$	0.136914	+	3.25565i	0.00691520	+	0.164435i
$393$		0			0
$394$	−0.262554	−	0.151586i	−0.0132273	−	0.00763678i
$395$	−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	$0.910927\pi$
$398$	−0.479784	−	0.128558i	−0.0240494	−	0.00644402i
$399$		0			0
$400$	1.02309	+	19.5651i	0.0511546	+	0.978256i
$401$	22.0427			1.10076			0.550379	−	0.834915i	$-0.314483\pi$
$401$	22.0427			1.10076			0.550379	+	0.834915i	$0.314483\pi$
$402$		0			0
$403$	4.89276	+	4.89276i	0.243726	+	0.243726i
$404$	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
$409$	4.45372	+	7.71406i	0.220222	+	0.381436i	0.954875	−	0.297007i	$-0.0959885\pi$
$409$	4.45372	+	7.71406i	0.220222	+	0.381436i	−0.734653	+	0.678443i	$0.762655\pi$
$410$	1.79403	−	0.0468743i	0.0886007	−	0.00231496i
$411$		0			0
$412$	2.07484	−	7.74340i	0.102220	−	0.381490i
$413$	−1.65484	−	10.8093i	−0.0814293	−	0.531891i
$414$		0			0
$415$	−0.650101	−	24.8814i	−0.0319122	−	1.22138i
$416$		−	8.25869i		−	0.404916i
$417$		0			0
$418$	−0.122757	+	0.122757i	−0.00600422	+	0.00600422i
$419$	−0.233728	+	0.404828i	−0.0114183	+	0.0197771i	−0.871678	−	0.490079i	$-0.836968\pi$
$419$	−0.233728	+	0.404828i	−0.0114183	+	0.0197771i	0.860260	+	0.509856i	$0.170301\pi$
$420$		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	$0.899500\pi$
$422$	0.140974	+	0.0377740i	0.00686253	+	0.00183881i
$423$		0			0
$424$	5.67513	+	3.27654i	0.275609	+	0.159123i
$425$	−11.4293	+	12.6905i	−0.554401	+	0.615581i
$426$		0			0
$427$	−11.8932	−	14.8430i	−0.575552	−	0.718302i
$428$	−16.8207	+	4.50709i	−0.813059	+	0.217859i
$429$		0			0
$430$	−0.317995	−	1.07376i	−0.0153351	−	0.0517814i
$431$	−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	$-0.0997462\pi$
$434$	−0.144498	−	0.329112i	−0.00693613	−	0.0157979i
$435$		0			0
$436$	−23.8746			−1.14339
$437$	−1.37763	+	5.14139i	−0.0659010	+	0.245946i
$438$		0			0
$439$	8.95981	−	15.5188i	0.427628	−	0.740674i	−0.569034	−	0.822314i	$-0.692683\pi$
$439$	8.95981	−	15.5188i	0.427628	−	0.740674i	0.996662	+	0.0816404i	$0.0260159\pi$
$440$	−0.452945	+	0.834106i	−0.0215933	+	0.0397644i
$441$		0			0
$442$	1.67747	−	1.67747i	0.0797893	−	0.0797893i
$443$	28.7560	−	7.70515i	1.36624	−	0.366083i	0.500135	−	0.865947i	$-0.333284\pi$
$443$	28.7560	−	7.70515i	1.36624	−	0.366083i	0.866103	+	0.499865i	$0.166617\pi$
$444$		0			0
$445$	5.93249	−	6.25082i	0.281227	−	0.296317i
$446$		−	3.24453i		−	0.153633i
$447$		0			0
$448$	7.37450	−	18.9186i	0.348412	−	0.893818i
$449$			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
$452$	−16.8942	+	16.8942i	−0.794636	+	0.794636i
$453$		0			0
$454$	0.156852	−	0.271676i	0.00736144	−	0.0127504i
$455$	34.6304	−	6.23145i	1.62350	−	0.292135i
$456$		0			0
$457$	−1.61288	−	6.01934i	−0.0754472	−	0.281573i	0.917887	−	0.396842i	$-0.129894\pi$
$457$	−1.61288	−	6.01934i	−0.0754472	−	0.281573i	−0.993334	+	0.115269i	$0.963227\pi$
$458$	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	$-0.635888\pi$
$461$	3.59037	−	2.07290i	0.167220	−	0.0965446i	0.581274	+	0.813708i	$0.302554\pi$
$462$		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	$0.270323\pi$
$464$			25.9819i			1.20618i
$465$		0			0
$466$	−1.23129			−0.0570384
$467$	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
$470$	1.05015	−	1.10649i	0.0484396	−	0.0510388i
$471$		0			0
$472$	0.497965	−	1.85843i	0.0229207	−	0.0855412i
$473$	−1.01217	+	3.77749i	−0.0465399	+	0.173689i
$474$		0			0
$475$	−7.26291	−	3.70170i	−0.333245	−	0.169846i
$476$	16.4366	−	7.21654i	0.753369	−	0.330769i
$477$		0			0
$478$	−0.678532	+	2.53232i	−0.0310353	+	0.115825i
$479$	30.8496			1.40955			0.704776	−	0.709430i	$-0.251048\pi$
$479$	30.8496			1.40955			0.704776	+	0.709430i	$0.251048\pi$
$480$		0			0
$481$		−	21.4914i		−	0.979923i
$482$	−1.03467	+	0.277240i	−0.0471281	+	0.0126279i
$483$		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	$0.918388\pi$
$488$	−0.866128	−	3.23243i	−0.0392078	−	0.146325i
$489$		0			0
$490$	−1.79364	−	0.351742i	−0.0810284	−	0.0158901i
$491$	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
$493$	−16.0152	+	16.0152i	−0.721289	+	0.721289i
$494$	0.980631	+	0.566167i	0.0441207	+	0.0254731i
$495$		0			0
$496$			4.55861i			0.204687i
$497$	−18.4473	−	7.19080i	−0.827475	−	0.322551i
$498$		0			0
$499$		−	8.68538i		−	0.388811i	−0.980921	−	0.194405i	$-0.937722\pi$
$499$		−	8.68538i		−	0.388811i	0.980921	−	0.194405i	$-0.0622777\pi$
$500$	−21.8356	−	4.05092i	−0.976520	−	0.181163i
$501$		0			0
$502$	1.24026	−	0.332326i	0.0553555	−	0.0148324i
$503$	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
$506$	−0.173818	+	0.301062i	−0.00772717	+	0.0133838i
$507$		0			0
$508$	6.31272	−	23.5594i	0.280082	−	1.04528i
$509$	−34.0949			−1.51123			−0.755614	−	0.655017i	$-0.772661\pi$
$509$	−34.0949			−1.51123			−0.755614	+	0.655017i	$0.772661\pi$
$510$		0			0
$511$	−1.11425	+	10.0993i	−0.0492916	+	0.446768i
$512$	6.42687	−	6.42687i	0.284030	−	0.284030i
$513$		0			0
$514$	−0.366429	+	0.634674i	−0.0161625	+	0.0279943i
$515$	7.93047	+	4.30649i	0.349458	+	0.189767i
$516$		0			0
$517$	−5.14577	+	1.37881i	−0.226311	+	0.0606398i
$518$	−0.405458	+	1.04016i	−0.0178148	+	0.0457022i
$519$		0			0
$520$	6.01972	+	1.44558i	0.263982	+	0.0633927i
$521$	−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
$527$	−2.80991	+	2.80991i	−0.122402	+	0.122402i
$528$		0			0
$529$		−	12.3413i		−	0.536580i
$530$	−2.53042	+	2.66619i	−0.109914	+	0.115812i
$531$		0			0
$532$	5.35772	+	6.68656i	0.232287	+	0.289899i
$533$	−10.5800	+	39.4850i	−0.458269	+	1.71028i
$534$		0			0
$535$	−0.512016	−	19.5965i	−0.0221364	−	0.847230i
$536$	3.54420	+	6.13873i	0.153086	+	0.265153i
$537$		0			0
$538$	1.68231	+	0.450773i	0.0725295	+	0.0194342i
$539$	4.69913	+	4.31984i	0.202406	+	0.186069i
$540$		0			0
$541$	3.90106	+	6.75684i	0.167720	+	0.290499i	0.937618	−	0.347668i	$-0.113026\pi$
$541$	3.90106	+	6.75684i	0.167720	+	0.290499i	−0.769898	+	0.638167i	$0.779693\pi$
$542$	−1.27617	−	1.27617i	−0.0548160	−	0.0548160i
$543$		0			0
$544$	4.74297			0.203353
$545$	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	$0.428113\pi$
$548$	7.90983	−	29.5199i	0.337891	−	1.26103i
$549$		0			0
$550$	−0.395615	−	0.356296i	−0.0168691	−	0.0151925i
$551$	−9.36230	−	5.40532i	−0.398847	−	0.230275i
$552$		0			0
$553$	15.1284	+	18.8805i	0.643323	+	0.802882i
$554$	−1.88334	−	1.08735i	−0.0800156	−	0.0461970i
$555$		0			0
$556$			19.6167i			0.831932i
$557$	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
$560$	19.0355	+	13.2297i	0.804399	+	0.559056i
$561$		0			0
$562$	0.625571	−	0.625571i	0.0263881	−	0.0263881i
$563$	35.6387	+	9.54937i	1.50199	+	0.402458i	0.913767	−	0.406238i	$-0.133160\pi$
$563$	35.6387	+	9.54937i	1.50199	+	0.402458i	0.588227	+	0.808696i	$0.299826\pi$
$564$		0			0
$565$	−14.0515	−	22.9329i	−0.591151	−	0.964796i
$566$		−	1.61230i		−	0.0677699i
$567$		0			0
$568$	−2.46325	−	2.46325i	−0.103356	−	0.103356i
$569$	2.13617	+	1.23332i	0.0895530	+	0.0517034i	0.544108	−	0.839015i	$-0.316868\pi$
$569$	2.13617	+	1.23332i	0.0895530	+	0.0517034i	−0.454555	+	0.890719i	$0.650202\pi$
$570$		0			0
$571$	4.40729	+	7.63365i	0.184439	+	0.319458i	0.943387	−	0.331693i	$-0.107620\pi$
$571$	4.40729	+	7.63365i	0.184439	+	0.319458i	−0.758948	+	0.651151i	$0.774286\pi$
$572$	−7.61753	−	7.61753i	−0.318505	−	0.318505i
$573$		0			0
$574$	1.25699	−	1.71143i	0.0524656	−	0.0714339i
$575$	−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	$0.437816\pi$
$578$	−0.440347	−	0.440347i	−0.0183160	−	0.0183160i
$579$		0			0
$580$	−28.6375	−	6.87701i	−1.18911	−	0.285552i
$581$	−23.7359	−	17.4332i	−0.984732	−	0.723250i
$582$		0			0
$583$	12.3992	−	3.32235i	0.513522	−	0.137598i
$584$	−0.893849	+	1.54819i	−0.0369877	+	0.0640647i
$585$		0			0
$586$	−0.243459	+	0.140561i	−0.0100572	+	0.00580652i
$587$	−0.184728	+	0.689415i	−0.00762455	+	0.0284552i	−0.969633	−	0.244563i	$-0.921355\pi$
$587$	−0.184728	+	0.689415i	−0.00762455	+	0.0284552i	0.962009	+	0.273019i	$0.0880220\pi$
$588$		0			0
$589$	−1.64264	−	0.948380i	−0.0676839	−	0.0390773i
$590$	0.948409	+	0.515015i	0.0390454	+	0.0212028i
$591$		0			0
$592$	10.0118	−	10.0118i	0.411483	−	0.411483i
$593$	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
$598$	2.19020	+	0.586863i	0.0895640	+	0.0239986i
$599$	−2.02119	+	1.16693i	−0.0825834	+	0.0476796i	−0.540723	−	0.841201i	$-0.681849\pi$
$599$	−2.02119	+	1.16693i	−0.0825834	+	0.0476796i	0.458140	+	0.888880i	$0.348516\pi$
$600$		0			0
$601$	4.89779	−	2.82774i	0.199785	−	0.115346i	−0.396770	−	0.917918i	$-0.629869\pi$
$601$	4.89779	−	2.82774i	0.199785	−	0.115346i	0.596555	+	0.802572i	$0.296536\pi$
$602$	−1.23456	−	0.481233i	−0.0503168	−	0.0196136i
$603$		0			0
$604$	−19.3740	+	11.1856i	−0.788317	+	0.455135i
$605$	−6.45653	−	21.8015i	−0.262495	−	0.886358i
$606$		0			0
$607$	5.73338	+	5.73338i	0.232711	+	0.232711i	0.813823	−	0.581112i	$-0.197382\pi$
$607$	5.73338	+	5.73338i	0.232711	+	0.232711i	−0.581112	+	0.813823i	$0.697382\pi$
$608$	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
$613$	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	$0.329973\pi$
$614$	−0.798589	+	1.38320i	−0.0322284	+	0.0558213i
$615$		0			0
$616$	0.451482	+	1.02831i	0.0181907	+	0.0414316i
$617$	−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
$619$	45.4978			1.82871			0.914355	−	0.404913i	$-0.132698\pi$
$619$	45.4978			1.82871			0.914355	+	0.404913i	$0.132698\pi$
$620$	−5.02454	−	1.20659i	−0.201790	−	0.0484579i
$621$		0			0
$622$	−2.19741	−	2.19741i	−0.0881080	−	0.0881080i
$623$	−1.54309	−	10.0793i	−0.0618224	−	0.403820i
$624$		0			0
$625$	10.1737	−	22.8363i	0.406948	−	0.913451i
$626$	0.0750023	−	0.0433026i	0.00299769	−	0.00173072i
$627$		0			0
$628$	1.74264	+	6.50361i	0.0695387	+	0.259522i
$629$	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	$0.748605\pi$
$632$	1.10173	+	4.11172i	0.0438245	+	0.163555i
$633$		0			0
$634$	0.722389	−	0.417072i	0.0286898	−	0.0165640i
$635$	24.1286	+	13.1025i	0.957512	+	0.519959i
$636$		0			0
$637$	19.2833	−	36.8983i	0.764032	−	1.46196i
$638$	−0.499259	−	0.499259i	−0.0197658	−	0.0197658i
$639$		0			0
$640$	4.29131	+	7.00369i	0.169629	+	0.276845i
$641$	11.8425			0.467751			0.233875	−	0.972267i	$-0.424859\pi$
$641$	11.8425			0.467751			0.233875	+	0.972267i	$0.424859\pi$
$642$		0			0
$643$	0.689615	+	2.57368i	0.0271958	+	0.101496i	0.978190	−	0.207714i	$-0.0666022\pi$
$643$	0.689615	+	2.57368i	0.0271958	+	0.101496i	−0.950994	+	0.309210i	$0.899936\pi$
$644$	13.8286	+	10.1566i	0.544923	+	0.400226i
$645$		0			0
$646$	−0.325150	+	0.563176i	−0.0127929	+	0.0221579i
$647$	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
$650$	−1.57690	+	3.09396i	−0.0618512	+	0.121355i
$651$		0			0
$652$	−9.94479	−	37.1145i	−0.389468	−	1.45351i
$653$	6.49935	+	6.49935i	0.254339	+	0.254339i	0.822747	−	0.568408i	$-0.192440\pi$
$653$	6.49935	+	6.49935i	0.254339	+	0.254339i	−0.568408	+	0.822747i	$0.692440\pi$
$654$		0			0
$655$	28.1245	−	8.32909i	1.09892	−	0.325445i
$656$	−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	$-0.546822\pi$
$659$	16.3480	−	9.43850i	0.636826	−	0.367672i	0.783391	+	0.621529i	$0.213488\pi$
$660$		0			0
$661$	12.9734	−	7.49021i	0.504607	−	0.291335i	−0.226007	−	0.974126i	$-0.572567\pi$
$661$	12.9734	−	7.49021i	0.504607	−	0.291335i	0.730614	+	0.682790i	$0.239234\pi$
$662$	0.820601	+	0.219879i	0.0318936	+	0.00854585i
$663$		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
$668$	12.8868	−	12.8868i	0.498605	−	0.498605i
$669$		0			0
$670$	−3.81241	+	1.12905i	−0.147286	+	0.0436189i
$671$	−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
$677$	3.96706	−	1.06297i	0.152467	−	0.0408533i	−0.181778	−	0.983340i	$-0.558185\pi$
$677$	3.96706	−	1.06297i	0.152467	−	0.0408533i	0.334245	+	0.942486i	$0.391519\pi$
$678$		0			0
$679$	−11.0801	+	15.0860i	−0.425216	+	0.578947i
$680$	−0.830195	+	3.45713i	−0.0318365	+	0.132575i
$681$		0			0
$682$	−0.0875964	−	0.0875964i	−0.00335424	−	0.00335424i
$683$	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
$686$	−1.62942	+	1.42204i	−0.0622115	+	0.0542939i
$687$		0			0
$688$	11.8829	+	11.8829i	0.453031	+	0.453031i
$689$	−41.8634	−	72.5095i	−1.59487	−	2.76239i
$690$		0			0
$691$	15.2341	+	8.79542i	0.579533	+	0.334593i	0.760948	−	0.648813i	$-0.224734\pi$
$691$	15.2341	+	8.79542i	0.579533	+	0.334593i	−0.181415	+	0.983407i	$0.558068\pi$
$692$	−20.8964	−	20.8964i	−0.794360	−	0.794360i
$693$		0			0
$694$			1.39745i			0.0530465i
$695$	−21.4722	−	5.15634i	−0.814488	−	0.195591i
$696$		0			0
$697$	−22.6762	−	6.07608i	−0.858923	−	0.230148i
$698$	2.60020	−	2.60020i	0.0984189	−	0.0984189i
$699$		0			0
$700$	−19.6203	+	17.4795i	−0.741577	+	0.660661i
$701$	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
$704$		−	6.99814i		−	0.263752i
$705$		0			0
$706$	−3.41604	−	1.97225i	−0.128564	−	0.0742266i
$707$	−14.0804	+	36.1219i	−0.529547	+	1.35850i
$708$		0			0
$709$	22.6846	+	13.0970i	0.851939	+	0.491867i	0.861305	−	0.508089i	$-0.169648\pi$
$709$	22.6846	+	13.0970i	0.851939	+	0.491867i	−0.00936569	+	0.999956i	$0.502981\pi$
$710$	1.66615	−	1.02088i	0.0625293	−	0.0383130i
$711$		0			0
$712$	0.464337	−	1.73293i	0.0174018	−	0.0649443i
$713$	−3.66878	−	0.983047i	−0.137397	−	0.0368154i
$714$		0			0
$715$	10.3404	−	6.33577i	0.386708	−	0.236944i
$716$	−14.9515			−0.558764
$717$		0			0
$718$	1.78856	+	1.78856i	0.0667484	+	0.0667484i
$719$	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
$722$	1.84329	+	0.493907i	0.0686001	+	0.0183813i
$723$		0			0
$724$	−1.21857	−	2.11063i	−0.0452880	−	0.0784411i
$725$	15.0550	−	29.5387i	0.559130	−	1.09704i
$726$		0			0
$727$	−0.342271	+	1.27737i	−0.0126941	+	0.0473752i	−0.971982	−	0.235054i	$-0.924473\pi$
$727$	−0.342271	+	1.27737i	−0.0126941	+	0.0473752i	0.959288	+	0.282429i	$0.0911401\pi$
$728$	5.71643	−	4.58039i	0.211865	−	0.169760i
$729$		0			0
$730$	−0.727345	−	0.690305i	−0.0269203	−	0.0255493i
$731$			14.6492i			0.541819i
$732$		0			0
$733$	−35.3609	+	35.3609i	−1.30609	+	1.30609i	−0.381869	+	0.924217i	$0.624719\pi$
$733$	−35.3609	+	35.3609i	−1.30609	+	1.30609i	−0.924217	+	0.381869i	$0.875281\pi$
$734$	−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	$0.938235\pi$
$740$	8.38513	+	13.6851i	0.308244	+	0.503073i
$741$		0			0
$742$	0.658180	+	4.29919i	0.0241625	+	0.157828i
$743$	−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
$745$	−31.4709	+	9.32012i	−1.15300	+	0.341463i
$746$	1.07842	−	1.86788i	0.0394838	−	0.0683879i
$747$		0			0
$748$	4.37475	−	4.37475i	0.159957	−	0.159957i
$749$	−18.6943	−	13.7303i	−0.683075	−	0.501694i
$750$		0			0
$751$	39.8042			1.45248			0.726238	−	0.687443i	$-0.241267\pi$
$751$	39.8042			1.45248			0.726238	+	0.687443i	$0.241267\pi$
$752$	−5.92490	+	22.1120i	−0.216059	+	0.806342i
$753$		0			0
$754$	−2.30264	+	3.98828i	−0.0838571	+	0.145245i
$755$	−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	$0.204794\pi$
$758$	0.271869	−	0.0728472i	0.00987474	−	0.00264593i
$759$		0			0
$760$	−1.69647	+	0.0443253i	−0.0615374	+	0.00160785i
$761$			37.5448i			1.36100i	0.732750	+	0.680498i	$0.238237\pi$
$761$			37.5448i			1.36100i	−0.732750	+	0.680498i	$0.761763\pi$
$762$		0			0
$763$	−19.8845	−	24.8163i	−0.719866	−	0.898410i
$764$		−	1.40939i		−	0.0509899i
$765$		0			0
$766$	2.08885	+	1.20600i	0.0754732	+	0.0435745i
$767$	−17.3823	+	17.3823i	−0.627638	+	0.627638i
$768$		0			0
$769$	−16.8089	+	29.1138i	−0.606143	+	1.04987i	0.385727	+	0.922613i	$0.373951\pi$
$769$	−16.8089	+	29.1138i	−0.606143	+	1.04987i	−0.991870	+	0.127258i	$0.959383\pi$
$770$	−0.619996	+	0.111563i	−0.0223431	+	0.00402046i
$771$		0			0
$772$	4.96317	+	18.5228i	0.178628	+	0.666650i
$773$	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
$778$	−1.81331	+	0.485874i	−0.0650102	+	0.0174194i
$779$		−	11.2055i		−	0.401479i
$780$		0			0
$781$	−6.82382			−0.244176
$782$	−0.337035	+	1.25783i	−0.0120524	+	0.0449800i
$783$		0			0
$784$	26.1723	−	8.20597i	0.934725	−	0.293070i
$785$	−7.57685	+	0.197968i	−0.270429	+	0.00706576i
$786$		0			0
$787$	3.01068	−	11.2360i	0.107319	−	0.400520i	−0.891279	−	0.453456i	$-0.850191\pi$
$787$	3.01068	−	11.2360i	0.107319	−	0.400520i	0.998598	+	0.0529354i	$0.0168578\pi$
$788$	−1.33474	+	4.98132i	−0.0475482	+	0.177452i
$789$		0			0
$790$	−2.38693	+	0.0623656i	−0.0849231	+	0.00221887i
$791$	−31.6312	−	3.48985i	−1.12467	−	0.124085i
$792$		0			0
$793$	−11.0663	+	41.2999i	−0.392975	+	1.46660i
$794$	−2.39899			−0.0851370
$795$		0			0
$796$			8.44918i			0.299473i
$797$	−12.2523	+	3.28298i	−0.433997	+	0.116289i	−0.469202	−	0.883091i	$-0.655458\pi$
$797$	−12.2523	+	3.28298i	−0.433997	+	0.116289i	0.0352047	+	0.999380i	$0.488792\pi$
$798$		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
$803$	0.906347	+	3.38253i	0.0319843	+	0.119367i
$804$		0			0
$805$	−14.7522	+	12.4669i	−0.519948	+	0.439402i
$806$	−0.404004	+	0.699756i	−0.0142304	+	0.0246478i
$807$		0			0
$808$	−4.82332	+	4.82332i	−0.169684	+	0.169684i
$809$	−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	$0.942039\pi$
$812$	−27.1947	+	21.7902i	−0.954345	+	0.764686i
$813$		0			0
$814$			0.384766i			0.0134860i
$815$	43.2392	−	1.12975i	1.51460	−	0.0395735i
$816$		0			0
$817$	−6.75400	+	1.80973i	−0.236293	+	0.0633144i
$818$	−0.735503	+	0.735503i	−0.0257162	+	0.0257162i
$819$		0			0
$820$	−8.66855	−	29.2708i	−0.302719	−	1.02218i
$821$	16.0183	−	27.7444i	0.559041	−	0.968287i	−0.438536	−	0.898714i	$-0.644503\pi$
$821$	16.0183	−	27.7444i	0.559041	−	0.968287i	0.997577	−	0.0695735i	$-0.0221638\pi$
$822$		0			0
$823$	−6.40811	+	23.9154i	−0.223373	+	0.833638i	0.759677	+	0.650300i	$0.225357\pi$
$823$	−6.40811	+	23.9154i	−0.223373	+	0.833638i	−0.983050	+	0.183338i	$0.941310\pi$
$824$	1.87868			0.0654469
$825$		0			0
$826$	1.16922	−	0.513351i	0.0406824	−	0.0178618i
$827$	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	$0.00878151\pi$
$830$	2.78685	−	0.825328i	0.0967331	−	0.0286476i
$831$		0			0
$832$	−44.0901	+	11.8139i	−1.52855	+	0.409574i
$833$	21.1907	+	11.0744i	0.734214	+	0.383705i
$834$		0			0
$835$	10.7184	+	17.4931i	0.370925	+	0.605374i
$836$	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	−0.999237	−	0.0390586i	$-0.987564\pi$
$839$	−15.4515	−	26.7627i	−0.533444	−	0.923952i	0.465793	−	0.884894i	$-0.345769\pi$
$840$		0			0
$841$	7.48378	−	12.9623i	0.258061	−	0.446975i
$842$	0.699298	−	0.699298i	0.0240994	−	0.0240994i
$843$		0			0
$844$		−	2.48261i		−	0.0854550i
$845$	−36.2884	−	34.4404i	−1.24836	−	1.18479i
$846$		0			0
$847$	−25.0663	−	9.77090i	−0.861289	−	0.335732i
$848$	14.2765	−	53.2808i	0.490258	−	1.82967i
$849$		0			0
$850$	−1.77686	−	0.905615i	−0.0609458	−	0.0310623i
$851$	5.89852	+	10.2165i	0.202199	+	0.350219i
$852$		0			0
$853$	−10.6135	−	2.84389i	−0.363400	−	0.0973729i	0.0724984	−	0.997369i	$-0.476903\pi$
$853$	−10.6135	−	2.84389i	−0.363400	−	0.0973729i	−0.435899	+	0.899996i	$0.643569\pi$
$854$	1.31476	−	1.79010i	0.0449903	−	0.0612559i
$855$		0			0
$856$	−2.04049	−	3.53424i	−0.0697426	−	0.120798i
$857$	10.4317	+	10.4317i	0.356339	+	0.356339i	0.862461	−	0.506123i	$-0.168922\pi$
$857$	10.4317	+	10.4317i	0.356339	+	0.356339i	−0.506123	+	0.862461i	$0.668922\pi$
$858$		0			0
$859$	3.87893			0.132347			0.0661736	−	0.997808i	$-0.478921\pi$
$859$	3.87893			0.132347			0.0661736	+	0.997808i	$0.478921\pi$
$860$	−16.2426	+	9.95221i	−0.553869	+	0.339368i
$861$		0			0
$862$	−3.81613	−	1.02253i	−0.129978	−	0.0348275i
$863$	−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
$866$	3.74848	+	2.16419i	0.127379	+	0.0735421i
$867$		0			0
$868$	−4.77138	+	3.82315i	−0.161951	+	0.129766i
$869$	7.22128	+	4.16921i	0.244965	+	0.141431i
$870$		0			0
$871$		−	90.5663i		−	3.06872i
$872$	−1.44810	−	5.40438i	−0.0490388	−	0.183015i
$873$		0			0
$874$	−0.621560			−0.0210246
$875$	−13.9756	−	26.0707i	−0.472460	−	0.881352i
$876$		0			0
$877$	−6.18411	+	6.18411i	−0.208823	+	0.208823i	−0.803767	−	0.594944i	$-0.797174\pi$
$877$	−6.18411	+	6.18411i	−0.208823	+	0.208823i	0.594944	+	0.803767i	$0.297174\pi$
$878$	2.02125	+	0.541591i	0.0682137	+	0.0182778i
$879$		0			0
$880$	7.76861	+	1.86555i	0.261880	+	0.0628878i
$881$			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	$-0.501592\pi$
$884$	−34.9473	−	20.1768i	−1.17540	−	0.678620i
$885$		0			0
$886$	1.73821	+	3.01066i	0.0583962	+	0.101145i
$887$	−38.0643	−	38.0643i	−1.27808	−	1.27808i	−0.941743	−	0.336332i	$-0.890813\pi$
$887$	−38.0643	−	38.0643i	−1.27808	−	1.27808i	−0.336332	−	0.941743i	$-0.609187\pi$
$888$		0			0
$889$	29.7463	−	13.0602i	0.997658	−	0.438025i
$890$	0.884362	+	0.480236i	0.0296439	+	0.0160975i
$891$		0			0
$892$	−53.3098	+	14.2843i	−1.78495	+	0.478275i
$893$	−6.73519	−	6.73519i	−0.225384	−	0.225384i
$894$		0			0
$895$	3.93008	−	16.3658i	0.131368	−	0.547048i
$896$	9.66012	+	1.06580i	0.322722	+	0.0356057i
$897$		0			0
$898$	−3.50980	+	0.940447i	−0.117123	+	0.0313831i
$899$	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
$905$	2.63059	−	0.779050i	0.0874437	−	0.0258965i
$906$		0			0
$907$	−3.96235	+	3.96235i	−0.131568	+	0.131568i	−0.769824	−	0.638256i	$-0.779656\pi$
$907$	−3.96235	+	3.96235i	−0.131568	+	0.131568i	0.638256	+	0.769824i	$0.279656\pi$
$908$	−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	−0.977340	−	0.211676i	$-0.932108\pi$
$911$	−20.2824	−	35.1302i	−0.671987	−	1.16392i	0.305353	−	0.952239i	$-0.401226\pi$
$912$		0			0
$913$	−9.80415	−	2.62701i	−0.324470	−	0.0869414i
$914$	0.630206	−	0.363850i	0.0208454	−	0.0120351i
$915$		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	$0.425729\pi$
$920$	−3.25840	+	0.964976i	−0.107426	+	0.0318143i
$921$		0			0
$922$	0.342326	+	0.342326i	0.0112739	+	0.0112739i
$923$	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
$928$	−8.89362	+	2.38304i	−0.291947	+	0.0782271i
$929$	15.7364	−	27.2562i	0.516294	−	0.894247i	−0.483527	−	0.875329i	$-0.660645\pi$
$929$	15.7364	−	27.2562i	0.516294	−	0.894247i	0.999821	−	0.0189177i	$-0.00602206\pi$
$930$		0			0
$931$	−2.48800	+	11.1381i	−0.0815409	+	0.365036i
$932$	5.42086	+	20.2309i	0.177566	+	0.662686i
$933$		0			0
$934$	4.50556			0.147426
$935$	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	$0.842424\pi$
$938$	−1.70863	+	4.38333i	−0.0557887	+	0.143121i
$939$		0			0
$940$	−22.8038	−	12.3832i	−0.743779	−	0.403895i
$941$	14.3741	−	8.29889i	0.468582	−	0.270536i	−0.247064	−	0.968999i	$-0.579466\pi$
$941$	14.3741	−	8.29889i	0.468582	−	0.270536i	0.715646	+	0.698463i	$0.246132\pi$
$942$		0			0
$943$	−5.80755	−	21.6741i	−0.189120	−	0.705805i
$944$	−16.1951			−0.527107
$945$		0			0
$946$	−0.456674			−0.0148477
$947$	14.1104	+	52.6608i	0.458527	+	1.71125i	0.677507	+	0.735517i	$0.263061\pi$
$947$	14.1104	+	52.6608i	0.458527	+	1.71125i	−0.218980	+	0.975729i	$0.570273\pi$
$948$		0			0
$949$	19.7808	−	11.4205i	0.642112	−	0.370724i
$950$	0.198024	−	0.931099i	0.00642475	−	0.0302088i
$951$		0			0
$952$	2.63052	+	3.28294i	0.0852555	+	0.106401i
$953$	−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
$956$	44.5950			1.44231
$957$		0			0
$958$	0.932377	+	3.47968i	0.0301237	+	0.112423i
$959$	37.2720	−	16.3644i	1.20358	−	0.528435i
$960$		0			0
$961$	−14.8233	+	25.6746i	−0.478170	+	0.828214i
$962$	2.42413	−	0.649542i	0.0781569	−	0.0209421i
$963$		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	$0.750389\pi$
$968$	−3.34708	−	3.34708i	−0.107579	−	0.107579i
$969$		0			0
$970$	−0.524559	−	1.77126i	−0.0168426	−	0.0568717i
$971$	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
$976$	−24.3949	+	14.0844i	−0.780860	+	0.450830i
$977$	48.7872	+	13.0725i	1.56084	+	0.418226i	0.932929	−	0.360060i	$-0.117244\pi$
$977$	48.7872	+	13.0725i	1.56084	+	0.418226i	0.627911	+	0.778285i	$0.283910\pi$
$978$		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
$983$	−0.393629	+	0.393629i	−0.0125548	+	0.0125548i	−0.713356	−	0.700802i	$-0.752826\pi$
$983$	−0.393629	+	0.393629i	−0.0125548	+	0.0125548i	0.700802	+	0.713356i	$0.252826\pi$
$984$		0			0
$985$	−5.10166	−	2.77036i	−0.162552	−	0.0882710i
$986$	−2.29047	−	1.32240i	−0.0729435	−	0.0421139i
$987$		0			0
$988$	4.98521	−	18.6050i	0.158601	−	0.591905i
$989$	−12.1259	+	7.00088i	−0.385581	+	0.222615i
$990$		0			0
$991$	−22.8617	+	39.5976i	−0.726226	+	1.25786i	0.232241	+	0.972658i	$0.425394\pi$
$991$	−22.8617	+	39.5976i	−0.726226	+	1.25786i	−0.958467	+	0.285202i	$0.907939\pi$
$992$	−1.56041	+	0.418111i	−0.0495431	+	0.0132750i
$993$		0			0
$994$	0.253548	−	2.29810i	0.00804204	−	0.0728912i
$995$	−9.24839	−	2.22091i	−0.293194	−	0.0704075i
$996$		0			0
$997$	−31.5513	−	31.5513i	−0.999239	−	0.999239i	0.000760425	−	1.00000i	$-0.499758\pi$
$997$	−31.5513	−	31.5513i	−0.999239	−	0.999239i	−1.00000		0.000760425i	$0.999758\pi$
$998$	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.cj.e.388.20		160
3.2	odd	2		315.2.cg.e.283.21	yes	160
5.2	odd	4	inner	945.2.cj.e.577.21		160
7.5	odd	6		945.2.bv.e.523.20		160
9.2	odd	6		315.2.bs.e.178.21	yes	160
9.7	even	3		945.2.bv.e.73.20		160
15.2	even	4		315.2.cg.e.157.20	yes	160
21.5	even	6		315.2.bs.e.103.21	yes	160
35.12	even	12		945.2.bv.e.712.20		160
45.2	even	12		315.2.bs.e.52.21	✓	160
45.7	odd	12		945.2.bv.e.262.20		160
63.47	even	6		315.2.cg.e.313.20	yes	160
63.61	odd	6	inner	945.2.cj.e.208.21		160
105.47	odd	12		315.2.bs.e.292.21	yes	160
315.47	odd	12		315.2.cg.e.187.21	yes	160
315.187	even	12	inner	945.2.cj.e.397.20		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.21	✓	160	45.2	even	12
315.2.bs.e.103.21	yes	160	21.5	even	6
315.2.bs.e.178.21	yes	160	9.2	odd	6
315.2.bs.e.292.21	yes	160	105.47	odd	12
315.2.cg.e.157.20	yes	160	15.2	even	4
315.2.cg.e.187.21	yes	160	315.47	odd	12
315.2.cg.e.283.21	yes	160	3.2	odd	2
315.2.cg.e.313.20	yes	160	63.47	even	6
945.2.bv.e.73.20		160	9.7	even	3
945.2.bv.e.262.20		160	45.7	odd	12
945.2.bv.e.523.20		160	7.5	odd	6
945.2.bv.e.712.20		160	35.12	even	12
945.2.cj.e.208.21		160	63.61	odd	6	inner
945.2.cj.e.388.20		160	1.1	even	1	trivial
945.2.cj.e.397.20		160	315.187	even	12	inner
945.2.cj.e.577.21		160	5.2	odd	4	inner

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.cj (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0302234 + 0.112795i) q^{2} +(1.72024 - 0.993182i) q^{4} +(0.634953 + 2.14402i) q^{5} +(2.46509 + 0.960898i) q^{7} +(0.329161 + 0.329161i) q^{8} +O(q^{10})\)	\(q+(0.0302234 + 0.112795i) q^{2} +(1.72024 - 0.993182i) q^{4} +(0.634953 + 2.14402i) q^{5} +(2.46509 + 0.960898i) q^{7} +(0.329161 + 0.329161i) q^{8} +(-0.222645 + 0.136419i) q^{10} +0.911859 q^{11} +(-1.53935 - 5.74495i) q^{13} +(-0.0338813 + 0.307092i) q^{14} +(1.95918 - 3.39341i) q^{16} +(3.29933 - 0.884052i) q^{17} +(0.815184 + 1.41194i) q^{19} +(3.22168 + 3.05761i) q^{20} +(0.0275595 + 0.102853i) q^{22} +(2.30853 + 2.30853i) q^{23} +(-4.19367 + 2.72271i) q^{25} +(0.601478 - 0.347264i) q^{26} +(5.19490 - 0.795308i) q^{28} +(-5.74244 + 3.31540i) q^{29} +(-1.00753 + 0.581697i) q^{31} +(1.34126 + 0.359389i) q^{32} +(0.199433 + 0.345429i) q^{34} +(-0.494969 + 5.89534i) q^{35} +(3.49032 + 0.935230i) q^{37} +(-0.134622 + 0.134622i) q^{38} +(-0.496727 + 0.914731i) q^{40} +(-5.95218 - 3.43649i) q^{41} +(-1.11001 + 4.14262i) q^{43} +(1.56862 - 0.905642i) q^{44} +(-0.190620 + 0.330163i) q^{46} +(-5.64317 + 1.51208i) q^{47} +(5.15335 + 4.73740i) q^{49} +(-0.433855 - 0.390736i) q^{50} +(-8.35384 - 8.35384i) q^{52} +(13.5977 - 3.64349i) q^{53} +(0.578988 + 1.95505i) q^{55} +(0.495122 + 1.12770i) q^{56} +(-0.547517 - 0.547517i) q^{58} +(-2.06657 - 3.57940i) q^{59} +(-6.22577 - 3.59445i) q^{61} +(-0.0960635 - 0.0960635i) q^{62} -7.67459i q^{64} +(11.3399 - 6.94819i) q^{65} +(14.7085 + 3.94113i) q^{67} +(4.79761 - 4.79761i) q^{68} +(-0.679925 + 0.122347i) q^{70} -7.48342 q^{71} +(0.993956 + 3.70949i) q^{73} +0.421958i q^{74} +(2.80463 + 1.61925i) q^{76} +(2.24782 + 0.876203i) q^{77} +(7.91929 + 4.57221i) q^{79} +(8.51953 + 2.04588i) q^{80} +(0.207725 - 0.775240i) q^{82} +(-10.7518 - 2.88094i) q^{83} +(3.99035 + 6.51250i) q^{85} -0.500816 q^{86} +(0.300149 + 0.300149i) q^{88} +(-1.92701 - 3.33768i) q^{89} +(1.72566 - 15.6410i) q^{91} +(6.26403 + 1.67844i) q^{92} +(-0.341111 - 0.590822i) q^{94} +(-2.50963 + 2.64429i) q^{95} +(-1.83106 + 6.83360i) q^{97} +(-0.378604 + 0.724453i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8}+O(q^{10}) \) 160 * q + 2 * q^2 + 6 * q^7 + 16 * q^8	\( 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8} - 24 q^{10} - 32 q^{11} + 76 q^{16} + 6 q^{17} + 60 q^{20} + 8 q^{22} + 16 q^{23} - 4 q^{25} + 36 q^{26} + 22 q^{28} + 48 q^{31} + 6 q^{32} + 36 q^{35} - 4 q^{37} - 12 q^{41} - 4 q^{43} - 16 q^{46} + 54 q^{47} + 44 q^{50} - 8 q^{53} + 92 q^{56} - 56 q^{58} - 24 q^{61} - 62 q^{65} + 12 q^{67} + 2 q^{70} + 40 q^{71} + 36 q^{73} - 96 q^{76} + 110 q^{77} - 36 q^{80} - 66 q^{82} - 138 q^{83} - 20 q^{85} - 32 q^{86} - 92 q^{88} - 48 q^{91} + 26 q^{92} + 94 q^{95} - 48 q^{97} - 102 q^{98}+O(q^{100}) \) 160 * q + 2 * q^2 + 6 * q^7 + 16 * q^8 - 24 * q^10 - 32 * q^11 + 76 * q^16 + 6 * q^17 + 60 * q^20 + 8 * q^22 + 16 * q^23 - 4 * q^25 + 36 * q^26 + 22 * q^28 + 48 * q^31 + 6 * q^32 + 36 * q^35 - 4 * q^37 - 12 * q^41 - 4 * q^43 - 16 * q^46 + 54 * q^47 + 44 * q^50 - 8 * q^53 + 92 * q^56 - 56 * q^58 - 24 * q^61 - 62 * q^65 + 12 * q^67 + 2 * q^70 + 40 * q^71 + 36 * q^73 - 96 * q^76 + 110 * q^77 - 36 * q^80 - 66 * q^82 - 138 * q^83 - 20 * q^85 - 32 * q^86 - 92 * q^88 - 48 * q^91 + 26 * q^92 + 94 * q^95 - 48 * q^97 - 102 * q^98

Introduction

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