LMFDB - Embedded newform 387.2.bc.a.233.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(26,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 17]))

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

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

chi := DirichletCharacter("387.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.bc (of order $42$, degree $12$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			233.2
Character	$\chi$	$=$	387.233
Dual form			387.2.bc.a.98.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15365 - 1.03715i) q^{2} +(2.31558 + 2.90364i) q^{4} +(3.04753 - 2.82769i) q^{5} +(-1.76335 - 1.01807i) q^{7} +(-0.911635 - 3.99413i) q^{8} +O(q^{10})$	\(q+(-2.15365 - 1.03715i) q^{2} +(2.31558 + 2.90364i) q^{4} +(3.04753 - 2.82769i) q^{5} +(-1.76335 - 1.01807i) q^{7} +(-0.911635 - 3.99413i) q^{8} +(-9.49606 + 2.92915i) q^{10} +(-3.31643 - 2.64476i) q^{11} +(4.78379 + 1.47560i) q^{13} +(2.74176 + 4.02142i) q^{14} +(-0.526312 + 2.30592i) q^{16} +(2.10399 - 2.26756i) q^{17} +(0.730589 + 0.286735i) q^{19} +(15.2674 + 2.30119i) q^{20} +(4.39944 + 9.13553i) q^{22} +(-0.641577 + 4.25659i) q^{23} +(0.917932 - 12.2490i) q^{25} +(-8.77221 - 8.13943i) q^{26} +(-1.12706 - 7.47756i) q^{28} +(-4.18505 + 2.85332i) q^{29} +(-0.630084 - 8.40788i) q^{31} +(-1.58362 + 1.98580i) q^{32} +(-6.88304 + 2.70140i) q^{34} +(-8.25266 + 1.88362i) q^{35} +(-1.83774 + 1.06102i) q^{37} +(-1.27605 - 1.37526i) q^{38} +(-14.0724 - 9.59442i) q^{40} +(3.36429 - 6.98603i) q^{41} +(0.170121 + 6.55523i) q^{43} -15.7539i q^{44} +(5.79644 - 8.50181i) q^{46} +(-4.61679 + 3.68177i) q^{47} +(-1.42706 - 2.47174i) q^{49} +(-14.6808 + 25.4280i) q^{50} +(6.79261 + 17.3073i) q^{52} +(-2.59603 - 8.41613i) q^{53} +(-17.5855 + 1.31785i) q^{55} +(-2.45878 + 7.97117i) q^{56} +(11.9724 - 1.80456i) q^{58} +(-4.46065 - 1.01811i) q^{59} +(-0.719441 - 0.0539146i) q^{61} +(-7.36321 + 18.7612i) q^{62} +(9.73212 - 4.68674i) q^{64} +(18.7513 - 9.03015i) q^{65} +(3.21120 - 8.18201i) q^{67} +(11.4561 + 0.858517i) q^{68} +(19.7270 + 4.50255i) q^{70} +(7.32896 - 1.10466i) q^{71} +(-4.31622 + 13.9929i) q^{73} +(5.05828 - 0.379065i) q^{74} +(0.859159 + 2.78532i) q^{76} +(3.15547 + 8.04001i) q^{77} +(1.58429 - 2.74407i) q^{79} +(4.91649 + 8.51562i) q^{80} +(-14.4910 + 11.5562i) q^{82} +(4.42760 - 6.49410i) q^{83} -12.8599i q^{85} +(6.43234 - 14.2941i) q^{86} +(-7.54017 + 15.6573i) q^{88} +(7.63906 + 5.20822i) q^{89} +(-6.93323 - 7.47225i) q^{91} +(-13.8452 + 7.99354i) q^{92} +(13.7615 - 3.14097i) q^{94} +(3.03729 - 1.19205i) q^{95} +(0.938409 - 1.17673i) q^{97} +(0.509841 + 6.80335i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 24 q^{4} - 6 q^{7}+O(q^{10}) $ 168 * q - 24 * q^4 - 6 * q^7	$ 168 q - 24 q^{4} - 6 q^{7} + 8 q^{10} + 26 q^{13} - 8 q^{16} + 24 q^{19} + 14 q^{25} + 32 q^{31} - 48 q^{34} - 78 q^{37} - 244 q^{40} - 32 q^{43} - 92 q^{46} + 54 q^{49} + 76 q^{52} - 96 q^{55} - 20 q^{58} - 96 q^{64} - 18 q^{67} + 140 q^{70} + 10 q^{73} - 16 q^{76} - 168 q^{88} - 38 q^{91} - 112 q^{94} - 40 q^{97}+O(q^{100}) $ 168 * q - 24 * q^4 - 6 * q^7 + 8 * q^10 + 26 * q^13 - 8 * q^16 + 24 * q^19 + 14 * q^25 + 32 * q^31 - 48 * q^34 - 78 * q^37 - 244 * q^40 - 32 * q^43 - 92 * q^46 + 54 * q^49 + 76 * q^52 - 96 * q^55 - 20 * q^58 - 96 * q^64 - 18 * q^67 + 140 * q^70 + 10 * q^73 - 16 * q^76 - 168 * q^88 - 38 * q^91 - 112 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$-1$

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 $

$2$	−2.15365	−	1.03715i	−1.52286	−	0.733372i	−0.529491	−	0.848315i	$-0.677617\pi$
$2$	−2.15365	−	1.03715i	−1.52286	−	0.733372i	−0.993372	+	0.114943i	$0.963331\pi$
$3$		0			0
$3$		0			0
$4$	2.31558	+	2.90364i	1.15779	+	1.45182i
$5$	3.04753	−	2.82769i	1.36290	−	1.26458i	0.430765	−	0.902464i	$-0.358244\pi$
$5$	3.04753	−	2.82769i	1.36290	−	1.26458i	0.932132	−	0.362120i	$-0.117947\pi$
$6$		0			0
$7$	−1.76335	−	1.01807i	−0.666484	−	0.384795i	0.128259	−	0.991741i	$-0.459061\pi$
$7$	−1.76335	−	1.01807i	−0.666484	−	0.384795i	−0.794743	+	0.606946i	$0.792394\pi$
$8$	−0.911635	−	3.99413i	−0.322312	−	1.41214i
$9$		0			0
$10$	−9.49606	+	2.92915i	−3.00292	+	0.926277i
$11$	−3.31643	−	2.64476i	−0.999941	−	0.797427i	−0.0206302	−	0.999787i	$-0.506567\pi$
$11$	−3.31643	−	2.64476i	−0.999941	−	0.797427i	−0.979311	+	0.202361i	$0.935139\pi$
$12$		0			0
$13$	4.78379	+	1.47560i	1.32678	+	0.409259i	0.875542	−	0.483142i	$-0.160505\pi$
$13$	4.78379	+	1.47560i	1.32678	+	0.409259i	0.451243	+	0.892401i	$0.350981\pi$
$14$	2.74176	+	4.02142i	0.732766	+	1.07477i
$15$		0			0
$16$	−0.526312	+	2.30592i	−0.131578	+	0.576481i
$17$	2.10399	−	2.26756i	0.510292	−	0.549963i	−0.424376	−	0.905486i	$-0.639507\pi$
$17$	2.10399	−	2.26756i	0.510292	−	0.549963i	0.934668	+	0.355523i	$0.115697\pi$
$18$		0			0
$19$	0.730589	+	0.286735i	0.167609	+	0.0657815i	0.447662	−	0.894203i	$-0.352257\pi$
$19$	0.730589	+	0.286735i	0.167609	+	0.0657815i	−0.280053	+	0.959984i	$0.590352\pi$
$20$	15.2674	+	2.30119i	3.41389	+	0.514562i
$21$		0			0
$22$	4.39944	+	9.13553i	0.937963	+	1.94770i
$23$	−0.641577	+	4.25659i	−0.133778	+	0.887560i	0.816766	+	0.576970i	$0.195765\pi$
$23$	−0.641577	+	4.25659i	−0.133778	+	0.887560i	−0.950544	+	0.310591i	$0.899473\pi$
$24$		0			0
$25$	0.917932	−	12.2490i	0.183586	−	2.44979i
$26$	−8.77221	−	8.13943i	−1.72037	−	1.59627i
$27$		0			0
$28$	−1.12706	−	7.47756i	−0.212994	−	1.41313i
$29$	−4.18505	+	2.85332i	−0.777144	+	0.529847i	−0.885708	−	0.464242i	$-0.846327\pi$
$29$	−4.18505	+	2.85332i	−0.777144	+	0.529847i	0.108565	+	0.994089i	$0.465374\pi$
$30$		0			0
$31$	−0.630084	−	8.40788i	−0.113166	−	1.51010i	−0.707978	−	0.706235i	$-0.750392\pi$
$31$	−0.630084	−	8.40788i	−0.113166	−	1.51010i	0.594811	−	0.803865i	$-0.297227\pi$
$32$	−1.58362	+	1.98580i	−0.279947	+	0.351043i
$33$		0			0
$34$	−6.88304	+	2.70140i	−1.18043	+	0.463285i
$35$	−8.25266	+	1.88362i	−1.39495	+	0.318389i
$36$		0			0
$37$	−1.83774	+	1.06102i	−0.302122	+	0.174430i	−0.643396	−	0.765534i	$-0.722475\pi$
$37$	−1.83774	+	1.06102i	−0.302122	+	0.174430i	0.341274	+	0.939964i	$0.389142\pi$
$38$	−1.27605	−	1.37526i	−0.207003	−	0.223096i
$39$		0			0
$40$	−14.0724	−	9.59442i	−2.22505	−	1.51701i
$41$	3.36429	−	6.98603i	0.525414	−	1.09103i	−0.454340	−	0.890828i	$-0.650125\pi$
$41$	3.36429	−	6.98603i	0.525414	−	1.09103i	0.979754	−	0.200205i	$-0.0641609\pi$
$42$		0			0
$43$	0.170121	+	6.55523i	0.0259432	+	0.999663i
$43$	0.170121	+	6.55523i	0.0259432	+	0.999663i
$44$		−	15.7539i		−	2.37499i
$45$		0			0
$46$	5.79644	−	8.50181i	0.854638	−	1.25352i
$47$	−4.61679	+	3.68177i	−0.673428	+	0.537041i	−0.899419	−	0.437088i	$-0.856010\pi$
$47$	−4.61679	+	3.68177i	−0.673428	+	0.537041i	0.225990	+	0.974130i	$0.427438\pi$
$48$		0			0
$49$	−1.42706	−	2.47174i	−0.203866	−	0.353106i
$50$	−14.6808	+	25.4280i	−2.07619	+	3.59606i
$51$		0			0
$52$	6.79261	+	17.3073i	0.941965	+	2.40009i
$53$	−2.59603	−	8.41613i	−0.356592	−	1.15604i	−0.939223	−	0.343307i	$-0.888453\pi$
$53$	−2.59603	−	8.41613i	−0.356592	−	1.15604i	0.582631	−	0.812737i	$-0.302023\pi$
$54$		0			0
$55$	−17.5855	+	1.31785i	−2.37123	+	0.177699i
$56$	−2.45878	+	7.97117i	−0.328568	+	1.06519i
$57$		0			0
$58$	11.9724	−	1.80456i	1.57206	−	0.236950i
$59$	−4.46065	−	1.01811i	−0.580727	−	0.132547i	−0.0779408	−	0.996958i	$-0.524835\pi$
$59$	−4.46065	−	1.01811i	−0.580727	−	0.132547i	−0.502786	+	0.864411i	$0.667692\pi$
$60$		0			0
$61$	−0.719441	−	0.0539146i	−0.0921149	−	0.00690306i	0.0285929	−	0.999591i	$-0.490897\pi$
$61$	−0.719441	−	0.0539146i	−0.0921149	−	0.00690306i	−0.120708	+	0.992688i	$0.538516\pi$
$62$	−7.36321	+	18.7612i	−0.935129	+	2.38267i
$63$		0			0
$64$	9.73212	−	4.68674i	1.21651	−	0.585843i
$65$	18.7513	−	9.03015i	2.32581	−	1.12005i
$66$		0			0
$67$	3.21120	−	8.18201i	0.392311	−	0.999591i	−0.589167	−	0.808012i	$-0.700544\pi$
$67$	3.21120	−	8.18201i	0.392311	−	0.999591i	0.981477	−	0.191579i	$-0.0613609\pi$
$68$	11.4561	+	0.858517i	1.38926	+	0.104110i
$69$		0			0
$70$	19.7270	+	4.50255i	2.35782	+	0.538158i
$71$	7.32896	−	1.10466i	0.869788	−	0.131099i	0.301040	−	0.953611i	$-0.402666\pi$
$71$	7.32896	−	1.10466i	0.869788	−	0.131099i	0.568748	+	0.822512i	$0.307428\pi$
$72$		0			0
$73$	−4.31622	+	13.9929i	−0.505176	+	1.63774i	0.239927	+	0.970791i	$0.422876\pi$
$73$	−4.31622	+	13.9929i	−0.505176	+	1.63774i	−0.745103	+	0.666949i	$0.767600\pi$
$74$	5.05828	−	0.379065i	0.588013	−	0.0440655i
$75$		0			0
$76$	0.859159	+	2.78532i	0.0985523	+	0.319499i
$77$	3.15547	+	8.04001i	0.359599	+	0.916244i
$78$		0			0
$79$	1.58429	−	2.74407i	0.178246	−	0.308731i	−0.763034	−	0.646359i	$-0.776291\pi$
$79$	1.58429	−	2.74407i	0.178246	−	0.308731i	0.941280	+	0.337627i	$0.109624\pi$
$80$	4.91649	+	8.51562i	0.549681	+	0.952075i
$81$		0			0
$82$	−14.4910	+	11.5562i	−1.60027	+	1.27617i
$83$	4.42760	−	6.49410i	0.485992	−	0.712820i	−0.502418	−	0.864625i	$-0.667556\pi$
$83$	4.42760	−	6.49410i	0.485992	−	0.712820i	0.988410	+	0.151805i	$0.0485085\pi$
$84$		0			0
$85$		−	12.8599i		−	1.39485i
$86$	6.43234	−	14.2941i	0.693617	−	1.54138i
$87$		0			0
$88$	−7.54017	+	15.6573i	−0.803785	+	1.66908i
$89$	7.63906	+	5.20822i	0.809739	+	0.552070i	0.895923	−	0.444209i	$-0.146515\pi$
$89$	7.63906	+	5.20822i	0.809739	+	0.552070i	−0.0861847	+	0.996279i	$0.527468\pi$
$90$		0			0
$91$	−6.93323	−	7.47225i	−0.726800	−	0.783304i
$92$	−13.8452	+	7.99354i	−1.44346	+	0.833384i
$93$		0			0
$94$	13.7615	−	3.14097i	1.41939	−	0.323967i
$95$	3.03729	−	1.19205i	0.311620	−	0.122302i
$96$		0			0
$97$	0.938409	−	1.17673i	0.0952810	−	0.119479i	−0.731905	−	0.681406i	$-0.761369\pi$
$97$	0.938409	−	1.17673i	0.0952810	−	0.119479i	0.827186	+	0.561928i	$0.189940\pi$
$98$	0.509841	+	6.80335i	0.0515017	+	0.687242i
$99$		0			0
$100$	37.6921	−	25.6980i	3.76921	−	2.56980i
$101$	1.18249	+	7.84532i	0.117662	+	0.780638i	0.967367	+	0.253379i	$0.0815421\pi$
$101$	1.18249	+	7.84532i	0.117662	+	0.780638i	−0.849705	+	0.527259i	$0.823220\pi$
$102$		0			0
$103$	1.39397	+	1.29342i	0.137352	+	0.127444i	0.745857	−	0.666106i	$-0.232040\pi$
$103$	1.39397	+	1.29342i	0.137352	+	0.127444i	−0.608505	+	0.793550i	$0.708230\pi$
$104$	1.53269	−	20.4523i	0.150293	−	2.00551i
$105$		0			0
$106$	−3.13779	+	20.8179i	−0.304769	+	2.02201i
$107$	2.79159	+	5.79679i	0.269873	+	0.560397i	0.991227	−	0.132169i	$-0.0421943\pi$
$107$	2.79159	+	5.79679i	0.269873	+	0.560397i	−0.721354	+	0.692566i	$0.756480\pi$
$108$		0			0
$109$	3.64539	+	0.549454i	0.349165	+	0.0526281i	0.321283	−	0.946983i	$-0.395886\pi$
$109$	3.64539	+	0.549454i	0.349165	+	0.0526281i	0.0278814	+	0.999611i	$0.491124\pi$
$110$	39.2399	+	15.4005i	3.74138	+	1.46838i
$111$		0			0
$112$	3.27567	−	3.53033i	0.309521	−	0.333585i
$113$	−1.26307	+	5.53385i	−0.118819	+	0.520581i	0.880129	+	0.474734i	$0.157456\pi$
$113$	−1.26307	+	5.53385i	−0.118819	+	0.520581i	−0.998948	+	0.0458470i	$0.985401\pi$
$114$		0			0
$115$	10.0811	+	14.7863i	0.940068	+	1.37883i
$116$	−17.9758	−	5.54480i	−1.66901	−	0.514822i
$117$		0			0
$118$	8.55076	+	6.81900i	0.787161	+	0.627740i
$119$	−6.01860	+	1.85649i	−0.551724	+	0.170184i
$120$		0			0
$121$	1.55620	+	6.81815i	0.141472	+	0.619831i
$122$	1.49351	+	0.862278i	0.135216	+	0.0780669i
$123$		0			0
$124$	22.9545	−	21.2986i	2.06137	−	1.91267i
$125$	−18.8786	−	23.6731i	−1.68856	−	2.11738i
$126$		0			0
$127$	12.3895	+	5.96649i	1.09939	+	0.529441i	0.893468	−	0.449127i	$-0.148265\pi$
$127$	12.3895	+	5.96649i	1.09939	+	0.529441i	0.205927	+	0.978567i	$0.433979\pi$
$128$	−20.7406			−1.83323
$129$		0			0
$130$	−49.7494			−4.36331
$131$	11.2029	+	5.39504i	0.978803	+	0.471367i	0.853693	−	0.520776i	$-0.174357\pi$
$131$	11.2029	+	5.39504i	0.978803	+	0.471367i	0.125110	+	0.992143i	$0.460072\pi$
$132$		0			0
$133$	−0.996368	−	1.24941i	−0.0863961	−	0.108337i
$134$	−15.4017	+	14.2907i	−1.33051	+	1.23453i
$135$		0			0
$136$	−10.9750	−	6.33642i	−0.941098	−	0.543343i
$137$	3.86004	+	16.9119i	0.329785	+	1.44488i	0.819539	+	0.573023i	$0.194230\pi$
$137$	3.86004	+	16.9119i	0.329785	+	1.44488i	−0.489754	+	0.871861i	$0.662913\pi$
$138$		0			0
$139$	−10.3012	+	3.17751i	−0.873739	+	0.269513i	−0.699017	−	0.715105i	$-0.746379\pi$
$139$	−10.3012	+	3.17751i	−0.873739	+	0.269513i	−0.174722	+	0.984618i	$0.555903\pi$
$140$	−24.5790	−	19.6011i	−2.07730	−	1.65660i
$141$		0			0
$142$	−16.9297	−	5.22213i	−1.42071	−	0.438232i
$143$	−11.9625	−	17.5457i	−1.00035	−	1.46725i
$144$		0			0
$145$	−4.68575	+	20.5296i	−0.389130	+	1.70489i
$146$	23.8083	−	25.6592i	1.97039	−	2.12357i
$147$		0			0
$148$	−7.33623	−	2.87926i	−0.603034	−	0.236674i
$149$	15.9320	+	2.40136i	1.30520	+	0.196727i	0.764573	−	0.644537i	$-0.222950\pi$
$149$	15.9320	+	2.40136i	1.30520	+	0.196727i	0.540625	+	0.841264i	$0.318188\pi$
$150$		0			0
$151$	−1.79330	−	3.72383i	−0.145937	−	0.303041i	0.815168	−	0.579225i	$-0.196645\pi$
$151$	−1.79330	−	3.72383i	−0.145937	−	0.303041i	−0.961105	+	0.276183i	$0.910930\pi$
$152$	0.479228	−	3.17947i	0.0388705	−	0.257889i
$153$		0			0
$154$	1.54286	−	20.5881i	0.124327	−	1.65903i
$155$	−25.6951	−	23.8416i	−2.06388	−	1.91500i
$156$		0			0
$157$	0.210829	+	1.39876i	0.0168260	+	0.111633i	0.995667	−	0.0929880i	$-0.0296418\pi$
$157$	0.210829	+	1.39876i	0.0168260	+	0.111633i	−0.978841	+	0.204621i	$0.934404\pi$
$158$	−6.25800	+	4.26663i	−0.497860	+	0.339435i
$159$		0			0
$160$	0.789098	+	10.5298i	0.0623836	+	0.832452i
$161$	5.46484	−	6.85269i	0.430690	−	0.540068i
$162$		0			0
$163$	18.4804	−	7.25303i	1.44750	−	0.568101i	0.493990	−	0.869467i	$-0.335538\pi$
$163$	18.4804	−	7.25303i	1.44750	−	0.568101i	0.953509	+	0.301366i	$0.0974426\pi$
$164$	28.0752	−	6.40797i	2.19230	−	0.500379i
$165$		0			0
$166$	−16.2708	+	9.39397i	−1.26286	+	0.729114i
$167$	2.44570	+	2.63584i	0.189254	+	0.203967i	0.820550	−	0.571575i	$-0.193667\pi$
$167$	2.44570	+	2.63584i	0.189254	+	0.203967i	−0.631296	+	0.775542i	$0.717477\pi$
$168$		0			0
$169$	9.96614	+	6.79480i	0.766626	+	0.522677i
$170$	−13.3376	+	27.6957i	−1.02294	+	2.12417i
$171$		0			0
$172$	−18.6401	+	15.6731i	−1.42129	+	1.19506i
$173$			18.7366i			1.42452i	0.701916	+	0.712260i	$0.252328\pi$
$173$			18.7366i			1.42452i	−0.701916	+	0.712260i	$0.747672\pi$
$174$		0			0
$175$	−14.0889	+	20.6647i	−1.06502	+	1.56210i
$176$	7.84410	−	6.25546i	0.591271	−	0.471523i
$177$		0			0
$178$	−11.0502	−	19.1395i	−0.828248	−	1.43457i
$179$	5.33990	−	9.24898i	0.399123	−	0.691301i	−0.594495	−	0.804099i	$-0.702648\pi$
$179$	5.33990	−	9.24898i	0.399123	−	0.691301i	0.993618	+	0.112798i	$0.0359813\pi$
$180$		0			0
$181$	−7.97248	−	20.3136i	−0.592590	−	1.50989i	−0.840887	−	0.541211i	$-0.817966\pi$
$181$	−7.97248	−	20.3136i	−0.592590	−	1.50989i	0.248297	−	0.968684i	$-0.420129\pi$
$182$	7.18198	+	23.2834i	0.532364	+	1.72588i
$183$		0			0
$184$	17.5863	−	1.31791i	1.29648	−	0.0971575i
$185$	−2.60032	+	8.43004i	−0.191180	+	0.619789i
$186$		0			0
$187$	−12.9749	+	1.95565i	−0.948817	+	0.143011i
$188$	−21.3811	−	4.88009i	−1.55937	−	0.355917i
$189$		0			0
$190$	−7.77760	−	0.582851i	−0.564247	−	0.0422844i
$191$	−8.14790	+	20.7605i	−0.589562	+	1.50218i	0.255120	+	0.966909i	$0.417885\pi$
$191$	−8.14790	+	20.7605i	−0.589562	+	1.50218i	−0.844682	+	0.535269i	$0.820210\pi$
$192$		0			0
$193$	7.96764	−	3.83701i	0.573523	−	0.276194i	−0.124559	−	0.992212i	$-0.539751\pi$
$193$	7.96764	−	3.83701i	0.573523	−	0.276194i	0.698082	+	0.716018i	$0.254037\pi$
$194$	−3.24145	+	1.56100i	−0.232722	+	0.112073i
$195$		0			0
$196$	3.87258	−	9.86718i	0.276613	−	0.704799i
$197$	20.8145	+	1.55983i	1.48297	+	0.111133i	0.791454	−	0.611228i	$-0.209324\pi$
$197$	20.8145	+	1.55983i	1.48297	+	0.111133i	0.691516	+	0.722362i	$0.256943\pi$
$198$		0			0
$199$	2.50457	+	0.571651i	0.177544	+	0.0405233i	0.310369	−	0.950616i	$-0.399548\pi$
$199$	2.50457	+	0.571651i	0.177544	+	0.0405233i	−0.132824	+	0.991140i	$0.542405\pi$
$200$	−49.7608	+	7.50023i	−3.51862	+	0.530347i
$201$		0			0
$202$	5.59006	−	18.1225i	0.393315	−	1.27510i
$203$	10.2846	−	0.770723i	0.721836	−	0.0540942i
$204$		0			0
$205$	−9.50156	−	30.8033i	−0.663618	−	2.15140i
$206$	−1.66068	−	4.23133i	−0.115705	−	0.294811i
$207$		0			0
$208$	−5.92039	+	10.2544i	−0.410505	+	0.711016i
$209$	−1.66460	−	2.88317i	−0.115143	−	0.199433i
$210$		0			0
$211$	−7.73093	+	6.16521i	−0.532219	+	0.424431i	−0.852373	−	0.522935i	$-0.824837\pi$
$211$	−7.73093	+	6.16521i	−0.532219	+	0.424431i	0.320153	+	0.947366i	$0.396266\pi$
$212$	18.4261	−	27.0261i	1.26551	−	1.85616i
$213$		0			0
$214$		−	15.3796i		−	1.05133i
$215$	19.0546	+	19.4962i	1.29952	+	1.32963i
$216$		0			0
$217$	−7.44877	+	15.4675i	−0.505655	+	1.05000i
$218$	−7.28104	−	4.96413i	−0.493134	−	0.336213i
$219$		0			0
$220$	−44.5471	−	48.0104i	−3.00337	−	3.23686i
$221$	13.4110	−	7.74287i	0.902124	−	0.520842i
$222$		0			0
$223$	21.1197	−	4.82043i	1.41428	−	0.322800i	0.553955	−	0.832547i	$-0.313118\pi$
$223$	21.1197	−	4.82043i	1.41428	−	0.322800i	0.860325	+	0.509746i	$0.170261\pi$
$224$	4.81416	−	1.88942i	0.321660	−	0.126242i
$225$		0			0
$226$	8.45962	−	10.6080i	0.562725	−	0.705635i
$227$	−1.45082	−	19.3599i	−0.0962945	−	1.28496i	−0.810797	−	0.585328i	$-0.800966\pi$
$227$	−1.45082	−	19.3599i	−0.0962945	−	1.28496i	0.714502	−	0.699633i	$-0.246653\pi$
$228$		0			0
$229$	2.76623	−	1.88598i	0.182798	−	0.124629i	−0.468464	−	0.883483i	$-0.655192\pi$
$229$	2.76623	−	1.88598i	0.182798	−	0.124629i	0.651262	+	0.758853i	$0.274240\pi$
$230$	−6.37571	−	42.3001i	−0.420402	−	2.78918i
$231$		0			0
$232$	15.2118	+	14.1145i	0.998701	+	0.926659i
$233$	0.317399	−	4.23539i	0.0207935	−	0.277470i	−0.977109	−	0.212738i	$-0.931762\pi$
$233$	0.317399	−	4.23539i	0.0207935	−	0.277470i	0.997903	−	0.0647315i	$-0.0206191\pi$
$234$		0			0
$235$	−3.65889	+	24.2752i	−0.238680	+	1.58354i
$236$	−7.37273	−	15.3096i	−0.479924	−	0.996572i
$237$		0			0
$238$	14.8874	+	2.24392i	0.965009	+	0.145452i
$239$	−10.1347	−	3.97757i	−0.655559	−	0.257288i	0.0141634	−	0.999900i	$-0.495492\pi$
$239$	−10.1347	−	3.97757i	−0.655559	−	0.257288i	−0.669722	+	0.742612i	$0.733587\pi$
$240$		0			0
$241$	−7.76376	+	8.36734i	−0.500108	+	0.538988i	−0.931771	−	0.363047i	$-0.881736\pi$
$241$	−7.76376	+	8.36734i	−0.500108	+	0.538988i	0.431663	+	0.902035i	$0.357927\pi$
$242$	3.71990	−	16.2979i	0.239124	−	1.04767i
$243$		0			0
$244$	−1.50937	−	2.21384i	−0.0966275	−	0.141727i
$245$	−11.3383	−	3.49742i	−0.724381	−	0.223442i
$246$		0			0
$247$	3.07188	+	2.44974i	0.195459	+	0.155873i
$248$	−33.0078	+	10.1816i	−2.09600	+	0.646530i
$249$		0			0
$250$	16.1057	+	70.5635i	1.01861	+	4.46283i
$251$	10.4948	+	6.05918i	0.662427	+	0.382452i	0.793201	−	0.608960i	$-0.208413\pi$
$251$	10.4948	+	6.05918i	0.662427	+	0.382452i	−0.130774	+	0.991412i	$0.541746\pi$
$252$		0			0
$253$	13.3854	−	12.4199i	0.841534	−	0.780830i
$254$	−20.4947	−	25.6995i	−1.28595	−	1.61253i
$255$		0			0
$256$	25.2038	+	12.1375i	1.57524	+	0.758594i
$257$	2.17013			0.135369			0.0676844	−	0.997707i	$-0.478439\pi$
$257$	2.17013			0.135369			0.0676844	+	0.997707i	$0.478439\pi$
$258$		0			0
$259$	4.32077			0.268479
$260$	69.6404	+	33.5370i	4.31891	+	2.07988i
$261$		0			0
$262$	−18.5318	−	23.2381i	−1.14490	−	1.43565i
$263$	14.7605	−	13.6958i	0.910172	−	0.844516i	−0.0781429	−	0.996942i	$-0.524899\pi$
$263$	14.7605	−	13.6958i	0.910172	−	0.844516i	0.988315	+	0.152426i	$0.0487086\pi$
$264$		0			0
$265$	−31.7097	−	18.3076i	−1.94791	−	1.12463i
$266$	0.850017	+	3.72417i	0.0521179	+	0.228343i
$267$		0			0
$268$	31.1934	−	9.62188i	1.90544	−	0.587750i
$269$	−11.5232	−	9.18946i	−0.702583	−	0.560292i	0.205716	−	0.978612i	$-0.434048\pi$
$269$	−11.5232	−	9.18946i	−0.702583	−	0.560292i	−0.908300	+	0.418320i	$0.862619\pi$
$270$		0			0
$271$	14.8432	+	4.57853i	0.901662	+	0.278126i	0.710720	−	0.703475i	$-0.248369\pi$
$271$	14.8432	+	4.57853i	0.901662	+	0.278126i	0.190943	+	0.981601i	$0.438846\pi$
$272$	4.12146	+	6.04507i	0.249900	+	0.366536i
$273$		0			0
$274$	9.22694	−	40.4259i	0.557420	−	2.44222i
$275$	−35.4399	+	38.1951i	−2.13710	+	2.30325i
$276$		0			0
$277$	1.81284	+	0.711488i	0.108923	+	0.0427492i	0.419177	−	0.907905i	$-0.362319\pi$
$277$	1.81284	+	0.711488i	0.108923	+	0.0427492i	−0.310254	+	0.950654i	$0.600414\pi$
$278$	25.4808	+	3.84061i	1.52824	+	0.230345i
$279$		0			0
$280$	15.0468	+	31.2451i	0.899220	+	1.86725i
$281$	0.250380	−	1.66116i	0.0149364	−	0.0990965i	−0.980120	−	0.198403i	$-0.936424\pi$
$281$	0.250380	−	1.66116i	0.0149364	−	0.0990965i	0.995057	+	0.0993068i	$0.0316625\pi$
$282$		0			0
$283$	−2.08142	+	27.7747i	−0.123728	+	1.65103i	0.497546	+	0.867438i	$0.334235\pi$
$283$	−2.08142	+	27.7747i	−0.123728	+	1.65103i	−0.621273	+	0.783594i	$0.713384\pi$
$284$	20.1783	+	18.7227i	1.19736	+	1.11099i
$285$		0			0
$286$	7.56557	+	50.1943i	0.447362	+	2.96805i
$287$	−13.0447	+	8.89373i	−0.770004	+	0.524980i
$288$		0			0
$289$	0.555351	+	7.41065i	0.0326677	+	0.435920i
$290$	31.3837	−	39.3539i	1.84291	−	2.31094i
$291$		0			0
$292$	−50.6248	+	19.8688i	−2.96259	+	1.16273i
$293$	−29.2810	+	6.68320i	−1.71061	+	0.390437i	−0.962103	−	0.272686i	$-0.912088\pi$
$293$	−29.2810	+	6.68320i	−1.71061	+	0.390437i	−0.748511	+	0.663122i	$0.769231\pi$
$294$		0			0
$295$	−16.4729	+	9.51062i	−0.959088	+	0.553730i
$296$	5.91319	+	6.37291i	0.343697	+	0.370418i
$297$		0			0
$298$	−31.8214	−	21.6955i	−1.84336	−	1.25678i
$299$	−9.35021	+	19.4159i	−0.540737	+	1.12285i
$300$		0			0
$301$	6.37371	−	11.7324i	0.367375	−	0.676243i
$302$			9.87976i			0.568516i
$303$		0			0
$304$	−1.04571	+	1.53377i	−0.0599754	+	0.0879677i
$305$	−2.34497	+	1.87005i	−0.134273	+	0.107079i
$306$		0			0
$307$	8.02244	+	13.8953i	0.457865	+	0.793045i	0.998848	−	0.0479883i	$-0.0152810\pi$
$307$	8.02244	+	13.8953i	0.457865	+	0.793045i	−0.540983	+	0.841033i	$0.681948\pi$
$308$	−16.0386	+	27.7796i	−0.913882	+	1.58289i
$309$		0			0
$310$	30.6112	+	77.9961i	1.73860	+	4.42988i
$311$	3.59633	+	11.6590i	0.203929	+	0.661121i	0.998541	+	0.0540035i	$0.0171982\pi$
$311$	3.59633	+	11.6590i	0.203929	+	0.661121i	−0.794612	+	0.607118i	$0.792326\pi$
$312$		0			0
$313$	−1.18689	+	0.0889449i	−0.0670868	+	0.00502746i	−0.108231	−	0.994126i	$-0.534519\pi$
$313$	−1.18689	+	0.0889449i	−0.0670868	+	0.00502746i	0.0411444	+	0.999153i	$0.486900\pi$
$314$	0.996665	−	3.23111i	0.0562450	−	0.182342i
$315$		0			0
$316$	11.6363	−	1.75389i	0.654594	−	0.0986641i
$317$	25.0907	+	5.72679i	1.40923	+	0.321649i	0.858407	−	0.512970i	$-0.171455\pi$
$317$	25.0907	+	5.72679i	1.40923	+	0.321649i	0.550828	+	0.834619i	$0.314312\pi$
$318$		0			0
$319$	21.4258	+	1.60564i	1.19961	+	0.0898985i
$320$	16.4062	−	41.8024i	0.917137	−	2.33683i
$321$		0			0
$322$	−18.8766	+	9.09049i	−1.05195	+	0.506593i
$323$	2.18734	−	1.05337i	0.121707	−	0.0586109i
$324$		0			0
$325$	22.4658	−	57.2419i	1.24618	−	3.17521i
$326$	−47.3229	−	3.54636i	−2.62097	−	0.196415i
$327$		0			0
$328$	−30.9701	−	7.06873i	−1.71004	−	0.390305i
$329$	11.8893	−	1.79203i	0.655480	−	0.0987977i
$330$		0			0
$331$	−5.65311	+	18.3269i	−0.310723	+	1.00734i	0.656695	+	0.754156i	$0.271954\pi$
$331$	−5.65311	+	18.3269i	−0.310723	+	1.00734i	−0.967418	+	0.253183i	$0.918522\pi$
$332$	29.1090	−	2.18142i	1.59756	−	0.119721i
$333$		0			0
$334$	−2.53344	−	8.21323i	−0.138624	−	0.449408i
$335$	−13.3500	−	34.0152i	−0.729388	−	1.85845i
$336$		0			0
$337$	−7.75049	+	13.4242i	−0.422196	+	0.731265i	−0.996154	−	0.0876199i	$-0.972074\pi$
$337$	−7.75049	+	13.4242i	−0.422196	+	0.731265i	0.573958	+	0.818885i	$0.305407\pi$
$338$	−14.4164	−	24.9700i	−0.784150	−	1.35819i
$339$		0			0
$340$	37.3405	−	29.7780i	2.02507	−	1.61494i
$341$	−20.1472	+	29.5506i	−1.09103	+	1.60025i
$342$		0			0
$343$			20.0644i			1.08338i
$344$	26.0274	−	6.65547i	1.40330	−	0.358839i
$345$		0			0
$346$	19.4326	−	40.3522i	1.04470	−	2.16935i
$347$	−15.8754	−	10.8237i	−0.852238	−	0.581046i	0.0565053	−	0.998402i	$-0.482004\pi$
$347$	−15.8754	−	10.8237i	−0.852238	−	0.581046i	−0.908743	+	0.417357i	$0.862957\pi$
$348$		0			0
$349$	−0.0149764	−	0.0161407i	−0.000801666	−	0.000863991i	0.732651	−	0.680605i	$-0.238283\pi$
$349$	−0.0149764	−	0.0161407i	−0.000801666	−	0.000863991i	−0.733453	+	0.679741i	$0.762092\pi$
$350$	51.7750	−	29.8923i	2.76749	−	1.59781i
$351$		0			0
$352$	10.5039	−	2.39745i	0.559862	−	0.127785i
$353$	2.49546	−	0.979396i	0.132820	−	0.0521280i	−0.298000	−	0.954566i	$-0.596320\pi$
$353$	2.49546	−	0.979396i	0.132820	−	0.0521280i	0.430820	+	0.902438i	$0.358224\pi$
$354$		0			0
$355$	19.2116	−	24.0906i	1.01964	−	1.27859i
$356$	2.56602	+	34.2411i	0.135999	+	1.81477i
$357$		0			0
$358$	−21.0928	+	14.3809i	−1.11479	+	0.760052i
$359$	−3.79676	−	25.1898i	−0.200385	−	1.32947i	−0.832255	−	0.554393i	$-0.812950\pi$
$359$	−3.79676	−	25.1898i	−0.200385	−	1.32947i	0.631870	−	0.775075i	$-0.282288\pi$
$360$		0			0
$361$	−13.4764	−	12.5043i	−0.709286	−	0.658122i
$362$	−3.89813	+	52.0170i	−0.204881	+	2.73395i
$363$		0			0
$364$	5.64229	−	37.4342i	0.295736	−	1.96208i
$365$	26.4137	+	54.8486i	1.38256	+	2.87091i
$366$		0			0
$367$	−10.2975	−	1.55210i	−0.537525	−	0.0810188i	−0.125331	−	0.992115i	$-0.539999\pi$
$367$	−10.2975	−	1.55210i	−0.537525	−	0.0810188i	−0.412194	+	0.911096i	$0.635237\pi$
$368$	−9.47769	−	3.71972i	−0.494059	−	0.193904i
$369$		0			0
$370$	14.3434	−	15.4585i	0.745676	−	0.803648i
$371$	−3.99050	+	17.4835i	−0.207177	+	0.907700i
$372$		0			0
$373$	−4.48110	−	6.57257i	−0.232023	−	0.340315i	0.692516	−	0.721402i	$-0.256502\pi$
$373$	−4.48110	−	6.57257i	−0.232023	−	0.340315i	−0.924539	+	0.381087i	$0.875550\pi$
$374$	29.9717	+	9.24504i	1.54980	+	0.478050i
$375$		0			0
$376$	18.9143	+	15.0837i	0.975431	+	0.777880i
$377$	−24.2307	+	7.47420i	−1.24795	+	0.384941i
$378$		0			0
$379$	2.37369	+	10.3998i	0.121928	+	0.534203i	0.998589	+	0.0530946i	$0.0169085\pi$
$379$	2.37369	+	10.3998i	0.121928	+	0.534203i	−0.876661	+	0.481108i	$0.840234\pi$
$380$	10.4944	+	6.05892i	0.538349	+	0.310816i
$381$		0			0
$382$	39.0794	−	36.2604i	1.99948	−	1.85524i
$383$	−2.87583	−	3.60618i	−0.146948	−	0.184267i	0.702910	−	0.711279i	$-0.251884\pi$
$383$	−2.87583	−	3.60618i	−0.146948	−	0.184267i	−0.849858	+	0.527012i	$0.823312\pi$
$384$		0			0
$385$	32.3511	+	15.5795i	1.64876	+	0.794003i
$386$	−21.1391			−1.07595
$387$		0			0
$388$	5.58975			0.283777
$389$	−6.28087	−	3.02471i	−0.318453	−	0.153359i	0.267828	−	0.963467i	$-0.413694\pi$
$389$	−6.28087	−	3.02471i	−0.318453	−	0.153359i	−0.586281	+	0.810108i	$0.699408\pi$
$390$		0			0
$391$	8.30219	+	10.4106i	0.419860	+	0.526487i
$392$	−8.57152	+	7.95320i	−0.432927	+	0.401697i
$393$		0			0
$394$	−43.2094	−	24.9470i	−2.17686	−	1.25681i
$395$	−2.93122	−	12.8425i	−0.147486	−	0.646176i
$396$		0			0
$397$	−10.4881	+	3.23514i	−0.526381	+	0.162367i	−0.546545	−	0.837430i	$-0.684057\pi$
$397$	−10.4881	+	3.23514i	−0.526381	+	0.162367i	0.0201639	+	0.999797i	$0.493581\pi$
$398$	−4.80109	−	3.82874i	−0.240657	−	0.191917i
$399$		0			0
$400$	27.7620	+	8.56345i	1.38810	+	0.428172i
$401$	−3.40902	−	5.00011i	−0.170238	−	0.249694i	0.731633	−	0.681699i	$-0.238759\pi$
$401$	−3.40902	−	5.00011i	−0.170238	−	0.249694i	−0.901871	+	0.432005i	$0.857806\pi$
$402$		0			0
$403$	9.39252	−	41.1513i	0.467875	−	2.04989i
$404$	−20.0418	+	21.6000i	−0.997118	+	1.07464i
$405$		0			0
$406$	−22.9488	−	9.00674i	−1.13893	−	0.446997i
$407$	8.90086	+	1.34159i	0.441199	+	0.0665001i
$408$		0			0
$409$	−0.0848887	−	0.176273i	−0.00419747	−	0.00871614i	0.898860	−	0.438237i	$-0.144397\pi$
$409$	−0.0848887	−	0.176273i	−0.00419747	−	0.00871614i	−0.903057	+	0.429521i	$0.858683\pi$
$410$	−11.4844	+	76.1942i	−0.567175	+	3.76296i
$411$		0			0
$412$	−0.527771	+	7.04261i	−0.0260014	+	0.346964i
$413$	6.82918	+	6.33655i	0.336042	+	0.311801i
$414$		0			0
$415$	−4.87008	−	32.3109i	−0.239063	−	1.58608i
$416$	−10.5060	+	7.16284i	−0.515097	+	0.351187i
$417$		0			0
$418$	0.594705	+	7.93579i	0.0290880	+	0.388152i
$419$	−3.11657	+	3.90805i	−0.152254	+	0.190921i	−0.852109	−	0.523364i	$-0.824677\pi$
$419$	−3.11657	+	3.90805i	−0.152254	+	0.190921i	0.699855	+	0.714285i	$0.253248\pi$
$420$		0			0
$421$	5.06007	−	1.98593i	0.246613	−	0.0967885i	−0.238815	−	0.971065i	$-0.576759\pi$
$421$	5.06007	−	1.98593i	0.246613	−	0.0967885i	0.485428	+	0.874277i	$0.338664\pi$
$422$	23.0440	−	5.25964i	1.12176	−	0.256035i
$423$		0			0
$424$	−31.2485	+	18.0413i	−1.51756	+	0.876165i
$425$	−25.8439	−	27.8531i	−1.25361	−	1.35107i
$426$		0			0
$427$	1.21374	+	0.827512i	0.0587369	+	0.0400461i
$428$	−10.3677	+	21.5287i	−0.501140	+	1.04063i
$429$		0			0
$430$	−20.8167	−	61.7505i	−1.00387	−	2.97787i
$431$			10.1175i			0.487344i	0.969858	+	0.243672i	$0.0783520\pi$
$431$			10.1175i			0.487344i	−0.969858	+	0.243672i	$0.921648\pi$
$432$		0			0
$433$	9.28376	−	13.6168i	0.446149	−	0.654381i	−0.535620	−	0.844459i	$-0.679922\pi$
$433$	9.28376	−	13.6168i	0.446149	−	0.654381i	0.981769	+	0.190079i	$0.0608743\pi$
$434$	32.0841	−	25.5862i	1.54009	−	1.22818i
$435$		0			0
$436$	6.84575	+	11.8572i	0.327852	+	0.567857i
$437$	−1.68924	+	2.92585i	−0.0808074	+	0.139963i
$438$		0			0
$439$	−13.4676	−	34.3149i	−0.642774	−	1.63776i	−0.764061	−	0.645144i	$-0.776797\pi$
$439$	−13.4676	−	34.3149i	−0.642774	−	1.63776i	0.121287	−	0.992617i	$-0.461298\pi$
$440$	21.2952	+	69.0375i	1.01521	+	3.29123i
$441$		0			0
$442$	−36.9132	+	2.76626i	−1.75578	+	0.131578i
$443$	6.36694	−	20.6411i	0.302503	−	0.980690i	−0.668920	−	0.743334i	$-0.733243\pi$
$443$	6.36694	−	20.6411i	0.302503	−	0.980690i	0.971423	−	0.237355i	$-0.0762806\pi$
$444$		0			0
$445$	38.0075	−	5.72871i	1.80173	−	0.271567i
$446$	−50.4840	−	11.5226i	−2.39049	−	0.545613i
$447$		0			0
$448$	−21.9326	−	1.64362i	−1.03622	−	0.0776537i
$449$	11.6258	−	29.6221i	0.548655	−	1.39795i	−0.340456	−	0.940260i	$-0.610581\pi$
$449$	11.6258	−	29.6221i	0.548655	−	1.39795i	0.889111	−	0.457691i	$-0.151323\pi$
$450$		0			0
$451$	−29.6338	+	14.2709i	−1.39540	+	0.671990i
$452$	−18.9930	+	9.14657i	−0.893358	+	0.430218i
$453$		0			0
$454$	−16.9544	+	43.1992i	−0.795711	+	2.02744i
$455$	−42.2585	−	3.16684i	−1.98111	−	0.148464i
$456$		0			0
$457$	−24.7470	−	5.64834i	−1.15762	−	0.264218i	−0.399747	−	0.916625i	$-0.630902\pi$
$457$	−24.7470	−	5.64834i	−1.15762	−	0.264218i	−0.757869	+	0.652407i	$0.773759\pi$
$458$	−7.91354	+	1.19277i	−0.369776	+	0.0557347i
$459$		0			0
$460$	−19.5904	+	63.5106i	−0.913409	+	2.96120i
$461$	4.87982	−	0.365692i	0.227276	−	0.0170320i	0.0393947	−	0.999224i	$-0.487457\pi$
$461$	4.87982	−	0.365692i	0.227276	−	0.0170320i	0.187881	+	0.982192i	$0.439838\pi$
$462$		0			0
$463$	3.09414	+	10.0309i	0.143797	+	0.466178i	0.998607	−	0.0527629i	$-0.0168028\pi$
$463$	3.09414	+	10.0309i	0.143797	+	0.466178i	−0.854810	+	0.518941i	$0.826327\pi$
$464$	−4.37689	−	11.1521i	−0.203192	−	0.517724i
$465$		0			0
$466$	−5.07628	+	8.79238i	−0.235154	+	0.407299i
$467$	3.47230	+	6.01421i	0.160679	+	0.278304i	0.935112	−	0.354351i	$-0.115298\pi$
$467$	3.47230	+	6.01421i	0.160679	+	0.278304i	−0.774433	+	0.632655i	$0.781965\pi$
$468$		0			0
$469$	−13.9923	+	11.1585i	−0.646106	+	0.515252i
$470$	33.0569	−	48.4855i	1.52480	−	2.23647i
$471$		0			0
$472$			18.7446i			0.862789i
$473$	16.7728	−	22.1899i	0.771216	−	1.02029i
$474$		0			0
$475$	4.18284	−	8.68575i	0.191922	−	0.398529i
$476$	−19.3271	−	13.1770i	−0.885857	−	0.603967i
$477$		0			0
$478$	17.7013	+	19.0775i	0.809638	+	0.872583i
$479$	−5.71586	+	3.30005i	−0.261164	+	0.150783i	−0.624866	−	0.780732i	$-0.714846\pi$
$479$	−5.71586	+	3.30005i	−0.261164	+	0.150783i	0.363701	+	0.931516i	$0.381513\pi$
$480$		0			0
$481$	−10.3570	+	2.36391i	−0.472238	+	0.107785i
$482$	25.3986	−	9.96821i	1.15687	−	0.454040i
$483$		0			0
$484$	−16.1939	+	20.3066i	−0.736088	+	0.923026i
$485$	−0.467597	−	6.23965i	−0.0212325	−	0.283328i
$486$		0			0
$487$	−8.73970	+	5.95863i	−0.396034	+	0.270011i	−0.744920	−	0.667154i	$-0.767512\pi$
$487$	−8.73970	+	5.95863i	−0.396034	+	0.270011i	0.348886	+	0.937165i	$0.386560\pi$
$488$	0.440525	+	2.92269i	0.0199416	+	0.132304i
$489$		0			0
$490$	20.7915	+	19.2917i	0.939266	+	0.871512i
$491$	−1.26133	+	16.8313i	−0.0569232	+	0.759587i	0.893586	+	0.448892i	$0.148181\pi$
$491$	−1.26133	+	16.8313i	−0.0569232	+	0.759587i	−0.950509	+	0.310696i	$0.899438\pi$
$492$		0			0
$493$	−2.33522	+	15.4932i	−0.105173	+	0.697777i
$494$	−4.07503	−	8.46188i	−0.183344	−	0.380718i
$495$		0			0
$496$	19.7195	+	2.97224i	0.885434	+	0.133458i
$497$	−14.0482	−	5.51350i	−0.630146	−	0.247314i
$498$		0			0
$499$	21.9415	−	23.6474i	0.982238	−	1.05860i	−0.0160359	−	0.999871i	$-0.505105\pi$
$499$	21.9415	−	23.6474i	0.982238	−	1.05860i	0.998274	−	0.0587294i	$-0.0187049\pi$
$500$	25.0231	−	109.634i	1.11907	−	4.90296i
$501$		0			0
$502$	−16.3179	−	23.9340i	−0.728306	−	1.06823i
$503$	−1.10193	−	0.339900i	−0.0491326	−	0.0151554i	0.270091	−	0.962835i	$-0.412946\pi$
$503$	−1.10193	−	0.339900i	−0.0491326	−	0.0151554i	−0.319224	+	0.947679i	$0.603422\pi$
$504$		0			0
$505$	25.7878	+	20.5651i	1.14754	+	0.915136i
$506$	−41.7088	+	12.8654i	−1.85418	+	0.571939i
$507$		0			0
$508$	11.3644	+	49.7906i	0.504213	+	2.20910i
$509$	25.4868	+	14.7148i	1.12968	+	0.652223i	0.943855	−	0.330359i	$-0.107170\pi$
$509$	25.4868	+	14.7148i	1.12968	+	0.652223i	0.185829	+	0.982582i	$0.440503\pi$
$510$		0			0
$511$	21.8567	−	20.2801i	0.966885	−	0.897139i
$512$	−15.8288	−	19.8487i	−0.699541	−	0.877197i
$513$		0			0
$514$	−4.67370	−	2.25074i	−0.206148	−	0.0992757i
$515$	7.90558			0.348361
$516$		0			0
$517$	25.0487			1.10164
$518$	−9.30543	−	4.48126i	−0.408857	−	0.196895i
$519$		0			0
$520$	−53.1620	−	66.6630i	−2.33131	−	2.92337i
$521$	−4.68971	+	4.35141i	−0.205460	+	0.190639i	−0.776190	−	0.630498i	$-0.782851\pi$
$521$	−4.68971	+	4.35141i	−0.205460	+	0.190639i	0.570731	+	0.821137i	$0.306660\pi$
$522$		0			0
$523$	−18.8055	−	10.8573i	−0.822305	−	0.474758i	0.0289056	−	0.999582i	$-0.490798\pi$
$523$	−18.8055	−	10.8573i	−0.822305	−	0.474758i	−0.851211	+	0.524824i	$0.824131\pi$
$524$	10.2759	+	45.0218i	0.448907	+	1.96679i
$525$		0			0
$526$	−45.9935	+	14.1871i	−2.00541	+	0.618588i
$527$	−20.3910	−	16.2613i	−0.888248	−	0.708354i
$528$		0			0
$529$	4.27125	+	1.31751i	0.185707	+	0.0572829i
$530$	49.3041	+	72.3159i	2.14163	+	3.14120i
$531$		0			0
$532$	1.32066	−	5.78619i	0.0572579	−	0.250863i
$533$	26.4027	−	28.4553i	1.14363	−	1.23254i
$534$		0			0
$535$	24.8990	+	9.77214i	1.07648	+	0.422486i
$536$	−35.6075	−	5.36696i	−1.53801	−	0.231818i
$537$		0			0
$538$	15.2862	+	31.7422i	0.659036	+	1.36850i
$539$	−1.80443	+	11.9716i	−0.0777223	+	0.515654i
$540$		0			0
$541$	−0.114593	+	1.52913i	−0.00492672	+	0.0657426i	−0.999125	−	0.0418182i	$-0.986685\pi$
$541$	−0.114593	+	1.52913i	−0.00492672	+	0.0657426i	0.994199	+	0.107561i	$0.0343040\pi$
$542$	−27.2186	−	25.2552i	−1.16914	−	1.08480i
$543$		0			0
$544$	1.17099	+	7.76904i	0.0502060	+	0.333095i
$545$	12.6631	−	8.63357i	0.542428	−	0.369821i
$546$		0			0
$547$	0.146864	+	1.95976i	0.00627944	+	0.0837934i	0.999463	−	0.0327674i	$-0.0104321\pi$
$547$	0.146864	+	1.95976i	0.00627944	+	0.0837934i	−0.993184	+	0.116561i	$0.962813\pi$
$548$	−40.1680	+	50.3690i	−1.71589	+	2.15166i
$549$		0			0
$550$	115.939	−	45.5027i	4.94366	−	1.94024i
$551$	−3.87570	+	0.884602i	−0.165110	+	0.0376853i
$552$		0			0
$553$	−5.58731	+	3.22583i	−0.237597	+	0.137176i
$554$	−3.16632	−	3.41248i	−0.134524	−	0.144982i
$555$		0			0
$556$	−33.0796	−	22.5533i	−1.40289	−	0.956473i
$557$	10.8308	−	22.4905i	0.458918	−	0.952952i	−0.535208	−	0.844720i	$-0.679767\pi$
$557$	10.8308	−	22.4905i	0.458918	−	0.952952i	0.994126	−	0.108232i	$-0.0345189\pi$
$558$		0			0
$559$	−8.85910	+	31.6099i	−0.374700	+	1.33696i
$560$		−	20.0214i		−	0.846057i
$561$		0			0
$562$	−2.26209	+	3.31788i	−0.0954207	+	0.139956i
$563$	−30.0977	+	24.0021i	−1.26846	+	1.01157i	−0.269647	+	0.962959i	$0.586907\pi$
$563$	−30.0977	+	24.0021i	−1.26846	+	1.01157i	−0.998818	+	0.0486077i	$0.984522\pi$
$564$		0			0
$565$	11.7988	+	20.4362i	0.496380	+	0.859756i
$566$	33.2890	−	57.6582i	1.39924	−	2.42356i
$567$		0			0
$568$	−11.0935	−	28.2658i	−0.465473	−	1.18601i
$569$	3.95319	+	12.8159i	0.165727	+	0.537272i	0.999899	−	0.0142319i	$-0.00453031\pi$
$569$	3.95319	+	12.8159i	0.165727	+	0.537272i	−0.834172	+	0.551504i	$0.814054\pi$
$570$		0			0
$571$	18.8058	−	1.40930i	0.786996	−	0.0589772i	0.324832	−	0.945772i	$-0.394692\pi$
$571$	18.8058	−	1.40930i	0.786996	−	0.0589772i	0.462164	+	0.886794i	$0.347073\pi$
$572$	23.2465	−	75.3632i	0.971984	−	3.15109i
$573$		0			0
$574$	37.3179	−	5.62476i	1.55762	−	0.234773i
$575$	51.5498	+	11.7659i	2.14978	+	0.490672i
$576$		0			0
$577$	−41.8889	−	3.13914i	−1.74386	−	0.130684i	−0.835667	−	0.549237i	$-0.814919\pi$
$577$	−41.8889	−	3.13914i	−1.74386	−	0.130684i	−0.908193	+	0.418552i	$0.862538\pi$
$578$	6.48988	−	16.5359i	0.269943	−	0.687805i
$579$		0			0
$580$	−70.4608	+	33.9321i	−2.92572	+	1.40895i
$581$	−14.4189	+	6.94376i	−0.598196	+	0.288076i
$582$		0			0
$583$	−13.6491	+	34.7774i	−0.565289	+	1.44033i
$584$	59.8242	+	4.48320i	2.47554	+	0.185516i
$585$		0			0
$586$	69.9926	+	15.9753i	2.89137	+	0.659936i
$587$	1.97011	−	0.296946i	0.0813150	−	0.0122563i	−0.108259	−	0.994123i	$-0.534527\pi$
$587$	1.97011	−	0.296946i	0.0813150	−	0.0122563i	0.189574	+	0.981866i	$0.439289\pi$
$588$		0			0
$589$	1.95050	−	6.32338i	0.0803691	−	0.260550i
$590$	45.3408	−	3.39782i	1.86665	−	0.139886i
$591$		0			0
$592$	−1.47940	−	4.79610i	−0.0608030	−	0.197119i
$593$	−6.21357	−	15.8319i	−0.255161	−	0.650139i	0.744690	−	0.667411i	$-0.232597\pi$
$593$	−6.21357	−	15.8319i	−0.255161	−	0.650139i	−0.999851	+	0.0172712i	$0.994502\pi$
$594$		0			0
$595$	−13.0923	+	22.6765i	−0.536731	+	0.929645i
$596$	29.9190	+	51.8212i	1.22553	+	2.12268i
$597$		0			0
$598$	40.2742	−	32.1176i	1.64694	−	1.31339i
$599$	−18.7088	+	27.4407i	−0.764419	+	1.12120i	0.224750	+	0.974417i	$0.427844\pi$
$599$	−18.7088	+	27.4407i	−0.764419	+	1.12120i	−0.989169	+	0.146781i	$0.953109\pi$
$600$		0			0
$601$		−	6.73555i		−	0.274749i	−0.990519	−	0.137374i	$-0.956134\pi$
$601$		−	6.73555i		−	0.274749i	0.990519	−	0.137374i	$-0.0438664\pi$
$602$	−25.8949	+	18.6570i	−1.05540	+	0.760403i
$603$		0			0
$604$	6.66014	−	13.8299i	0.270997	−	0.562732i
$605$	24.0222	+	16.3781i	0.976641	+	0.665863i
$606$		0			0
$607$	−19.1094	−	20.5950i	−0.775626	−	0.835926i	0.214409	−	0.976744i	$-0.431217\pi$
$607$	−19.1094	−	20.5950i	−0.775626	−	0.835926i	−0.990036	+	0.140818i	$0.955027\pi$
$608$	−1.72637	+	0.996723i	−0.0700137	+	0.0404224i
$609$		0			0
$610$	6.98977	−	1.59537i	0.283008	−	0.0645946i
$611$	−27.5186	+	10.8003i	−1.11328	+	0.436932i
$612$		0			0
$613$	3.00715	−	3.77085i	0.121458	−	0.152303i	−0.717385	−	0.696677i	$-0.754661\pi$
$613$	3.00715	−	3.77085i	0.121458	−	0.152303i	0.838843	+	0.544374i	$0.183233\pi$
$614$	−2.86614	−	38.2460i	−0.115668	−	1.54348i
$615$		0			0
$616$	29.2362	−	19.9329i	1.17796	−	0.803121i
$617$	−3.92171	−	26.0189i	−0.157882	−	1.04748i	−0.917680	−	0.397320i	$-0.869940\pi$
$617$	−3.92171	−	26.0189i	−0.157882	−	1.04748i	0.759798	−	0.650159i	$-0.225298\pi$
$618$		0			0
$619$	−32.4417	−	30.1015i	−1.30394	−	1.20988i	−0.962907	−	0.269832i	$-0.913032\pi$
$619$	−32.4417	−	30.1015i	−1.30394	−	1.20988i	−0.341035	−	0.940050i	$-0.610778\pi$
$620$	9.72839	−	129.816i	0.390702	−	5.21355i
$621$		0			0
$622$	4.34683	−	28.8394i	0.174292	−	1.15635i
$623$	−8.16800	−	16.9610i	−0.327244	−	0.679529i
$624$		0			0
$625$	−63.7430	−	9.60771i	−2.54972	−	0.384308i
$626$	2.64839	+	1.03942i	0.105851	+	0.0415435i
$627$		0			0
$628$	−3.57331	+	3.85111i	−0.142590	+	0.153676i
$629$	−1.46065	+	6.39954i	−0.0582400	+	0.255166i
$630$		0			0
$631$	12.1711	+	17.8518i	0.484525	+	0.710667i	0.988190	−	0.153232i	$-0.0489680\pi$
$631$	12.1711	+	17.8518i	0.484525	+	0.710667i	−0.503666	+	0.863899i	$0.668016\pi$
$632$	−12.4045	−	3.82627i	−0.493423	−	0.152201i
$633$		0			0
$634$	−48.0972	−	38.3562i	−1.91018	−	1.52332i
$635$	54.6289	−	16.8508i	2.16788	−	0.668703i
$636$		0			0
$637$	−3.17945	−	13.9301i	−0.125974	−	0.551930i
$638$	−44.4784	−	25.6796i	−1.76092	−	1.01667i
$639$		0			0
$640$	−63.2075	+	58.6480i	−2.49850	+	2.31827i
$641$	17.5598	+	22.0193i	0.693570	+	0.869709i	0.996525	−	0.0832955i	$-0.0265445\pi$
$641$	17.5598	+	22.0193i	0.693570	+	0.869709i	−0.302955	+	0.953005i	$0.597973\pi$
$642$		0			0
$643$	22.0774	+	10.6319i	0.870646	+	0.419281i	0.815199	−	0.579181i	$-0.196627\pi$
$643$	22.0774	+	10.6319i	0.870646	+	0.419281i	0.0554467	+	0.998462i	$0.482342\pi$
$644$	32.5520			1.28273
$645$		0			0
$646$	−5.80326			−0.228326
$647$	8.82373	+	4.24928i	0.346897	+	0.167057i	0.599216	−	0.800587i	$-0.295479\pi$
$647$	8.82373	+	4.24928i	0.346897	+	0.167057i	−0.252319	+	0.967644i	$0.581193\pi$
$648$		0			0
$649$	12.1008	+	15.1739i	0.474996	+	0.595626i
$650$	−107.752	+	99.9790i	−4.22637	+	3.92150i
$651$		0			0
$652$	63.8530	+	36.8656i	2.50068	+	1.44377i
$653$	5.60922	+	24.5756i	0.219506	+	0.961717i	0.957845	+	0.287287i	$0.0927534\pi$
$653$	5.60922	+	24.5756i	0.219506	+	0.961717i	−0.738339	+	0.674430i	$0.764389\pi$
$654$		0			0
$655$	49.3967	−	15.2369i	1.93009	−	0.595354i
$656$	14.3386	+	11.4346i	0.559827	+	0.446447i
$657$		0			0
$658$	−27.4641	−	8.47155i	−1.07066	−	0.330255i
$659$	−9.36282	−	13.7327i	−0.364723	−	0.534951i	0.599385	−	0.800461i	$-0.295412\pi$
$659$	−9.36282	−	13.7327i	−0.364723	−	0.534951i	−0.964108	+	0.265510i	$0.914460\pi$
$660$		0			0
$661$	−6.79754	+	29.7820i	−0.264394	+	1.15838i	0.652036	+	0.758188i	$0.273915\pi$
$661$	−6.79754	+	29.7820i	−0.264394	+	1.15838i	−0.916430	+	0.400196i	$0.868942\pi$
$662$	31.1825	−	33.6068i	1.21194	−	1.30616i
$663$		0			0
$664$	−29.9747	−	11.7642i	−1.16324	−	0.456539i
$665$	−6.56940	−	0.990178i	−0.254751	−	0.0383975i
$666$		0			0
$667$	−9.46036	−	19.6446i	−0.366307	−	0.760644i
$668$	−1.99032	+	13.2049i	−0.0770078	+	0.510913i
$669$		0			0
$670$	−6.52746	+	87.1028i	−0.252178	+	3.36508i
$671$	2.24338	+	2.08155i	0.0866048	+	0.0803575i
$672$		0			0
$673$	5.44046	+	36.0951i	0.209714	+	1.39136i	0.807575	+	0.589764i	$0.200779\pi$
$673$	5.44046	+	36.0951i	0.209714	+	1.39136i	−0.597861	+	0.801600i	$0.703983\pi$
$674$	30.6148	−	20.8728i	1.17924	−	0.803990i
$675$		0			0
$676$	3.34770	+	44.6720i	0.128758	+	1.71815i
$677$	7.43954	−	9.32889i	0.285925	−	0.358538i	−0.618039	−	0.786147i	$-0.712073\pi$
$677$	7.43954	−	9.32889i	0.285925	−	0.358538i	0.903964	+	0.427609i	$0.140644\pi$
$678$		0			0
$679$	−2.85274	+	1.11962i	−0.109478	+	0.0429670i
$680$	−51.3641	+	11.7235i	−1.96972	+	0.449576i
$681$		0			0
$682$	74.0384	−	42.7461i	2.83508	−	1.63683i
$683$	−11.4414	−	12.3309i	−0.437793	−	0.471829i	0.475156	−	0.879901i	$-0.342392\pi$
$683$	−11.4414	−	12.3309i	−0.437793	−	0.471829i	−0.912950	+	0.408073i	$0.866201\pi$
$684$		0			0
$685$	59.5854	+	40.6246i	2.27664	+	1.55219i
$686$	20.8097	−	43.2118i	0.794518	−	1.64983i
$687$		0			0
$688$	−15.2054	−	3.05781i	−0.579700	−	0.116578i
$689$		−	44.0917i		−	1.67976i
$690$		0			0
$691$	−2.40348	+	3.52526i	−0.0914326	+	0.134107i	−0.869230	−	0.494408i	$-0.835385\pi$
$691$	−2.40348	+	3.52526i	−0.0914326	+	0.134107i	0.777797	+	0.628515i	$0.216337\pi$
$692$	−54.4044	+	43.3861i	−2.06815	+	1.64929i
$693$		0			0
$694$	22.9644	+	39.7756i	0.871718	+	1.50986i
$695$	−22.4083	+	38.8123i	−0.849994	+	1.47223i
$696$		0			0
$697$	−8.76279	−	22.3272i	−0.331914	−	0.845704i
$698$	0.0155137	+	0.0502941i	0.000587201	+	0.00190366i
$699$		0			0
$700$	−92.6268	+	6.94142i	−3.50096	+	0.262361i
$701$	−3.56571	+	11.5598i	−0.134675	+	0.436606i	−0.997640	−	0.0686573i	$-0.978129\pi$
$701$	−3.56571	+	11.5598i	−0.134675	+	0.436606i	0.862965	+	0.505264i	$0.168605\pi$
$702$		0			0
$703$	−1.64686	+	0.248224i	−0.0621125	+	0.00936196i
$704$	−44.6712	−	10.1959i	−1.68361	−	0.384273i
$705$		0			0
$706$	−6.39014	−	0.478874i	−0.240496	−	0.0180227i
$707$	5.90195	−	15.0379i	0.221966	−	0.565559i
$708$		0			0
$709$	4.45609	−	2.14594i	0.167352	−	0.0805925i	−0.348332	−	0.937371i	$-0.613252\pi$
$709$	4.45609	−	2.14594i	0.167352	−	0.0805925i	0.515684	+	0.856779i	$0.327538\pi$
$710$	−66.3605	+	31.9575i	−2.49047	+	1.19934i
$711$		0			0
$712$	13.8383	−	35.2594i	0.518612	−	1.32140i
$713$	36.1931	+	2.71230i	1.35544	+	0.101576i
$714$		0			0
$715$	−86.0700	−	19.6449i	−3.21884	−	0.734678i
$716$	39.2207	−	5.91156i	1.46575	−	0.220926i
$717$		0			0
$718$	−17.9486	+	58.1879i	−0.669836	+	2.17155i
$719$	39.3559	−	2.94932i	1.46773	−	0.109991i	0.683266	−	0.730169i	$-0.260559\pi$
$719$	39.3559	−	2.94932i	1.46773	−	0.109991i	0.784461	+	0.620178i	$0.212940\pi$
$720$		0			0
$721$	−1.14127	−	3.69992i	−0.0425033	−	0.137792i
$722$	16.0548	+	40.9070i	0.597498	+	1.52240i
$723$		0			0
$724$	40.5224	−	70.1868i	1.50600	−	2.60847i
$725$	31.1085	+	53.8816i	1.15534	+	2.00111i
$726$		0			0
$727$	−34.5775	+	27.5746i	−1.28241	+	1.02269i	−0.284458	+	0.958688i	$0.591814\pi$
$727$	−34.5775	+	27.5746i	−1.28241	+	1.02269i	−0.997950	+	0.0639979i	$0.979615\pi$
$728$	−23.5246	+	34.5042i	−0.871879	+	1.27881i
$729$		0			0
$730$		−	145.520i		−	5.38593i
$731$	15.2223	+	13.4064i	0.563017	+	0.495852i
$732$		0			0
$733$	−13.9740	+	29.0174i	−0.516142	+	1.07178i	0.466198	+	0.884680i	$0.345623\pi$
$733$	−13.9740	+	29.0174i	−0.516142	+	1.07178i	−0.982341	+	0.187100i	$0.940091\pi$
$734$	20.5675	+	14.0227i	0.759159	+	0.517586i
$735$		0			0
$736$	−7.43671	−	8.01486i	−0.274121	−	0.295432i
$737$	−32.2892	+	18.6422i	−1.18939	+	0.686693i
$738$		0			0
$739$	−47.7029	+	10.8879i	−1.75478	+	0.400517i	−0.974406	−	0.224796i	$-0.927828\pi$
$739$	−47.7029	+	10.8879i	−1.75478	+	0.400517i	−0.780374	+	0.625313i	$0.784971\pi$
$740$	−30.4990	+	11.9700i	−1.12117	+	0.440026i
$741$		0			0
$742$	26.7271	−	33.5148i	0.981184	−	1.23037i
$743$	1.21764	+	16.2483i	0.0446709	+	0.596092i	0.973957	+	0.226732i	$0.0728041\pi$
$743$	1.21764	+	16.2483i	0.0446709	+	0.596092i	−0.929286	+	0.369360i	$0.879577\pi$
$744$		0			0
$745$	55.3435	−	37.7326i	2.02763	−	1.38241i
$746$	2.83404	+	18.8026i	0.103761	+	0.688412i
$747$		0			0
$748$	−35.7228	−	33.1459i	−1.30616	−	1.21193i
$749$	0.978998	−	13.0638i	0.0357718	−	0.477341i
$750$		0			0
$751$	3.85098	−	25.5496i	0.140524	−	0.932317i	−0.801795	−	0.597600i	$-0.796121\pi$
$751$	3.85098	−	25.5496i	0.140524	−	0.932317i	0.942319	−	0.334717i	$-0.108641\pi$
$752$	−6.06000	−	12.5837i	−0.220986	−	0.458881i
$753$		0			0
$754$	59.9365	+	9.03397i	2.18276	+	0.328998i
$755$	−15.9950	−	6.27758i	−0.582118	−	0.228464i
$756$		0			0
$757$	−24.6609	+	26.5781i	−0.896315	+	0.965997i	−0.999589	−	0.0286554i	$-0.990877\pi$
$757$	−24.6609	+	26.5781i	−0.896315	+	0.965997i	0.103275	+	0.994653i	$0.467068\pi$
$758$	5.67401	−	24.8595i	0.206089	−	0.902937i
$759$		0			0
$760$	−7.53011	−	11.0446i	−0.273146	−	0.400631i
$761$	−11.6265	−	3.58631i	−0.421461	−	0.130004i	0.0767679	−	0.997049i	$-0.475540\pi$
$761$	−11.6265	−	3.58631i	−0.421461	−	0.130004i	−0.498229	+	0.867045i	$0.666016\pi$
$762$		0			0
$763$	−5.86872	−	4.68014i	−0.212462	−	0.169433i
$764$	−79.1482	+	24.4140i	−2.86348	+	0.883267i
$765$		0			0
$766$	2.45342	+	10.7491i	0.0886455	+	0.388381i
$767$	−19.8365	−	11.4526i	−0.716254	−	0.413529i
$768$		0			0
$769$	1.74990	−	1.62367i	0.0631030	−	0.0585510i	−0.647991	−	0.761648i	$-0.724391\pi$
$769$	1.74990	−	1.62367i	0.0631030	−	0.0585510i	0.711094	+	0.703097i	$0.248200\pi$
$770$	−53.5149	−	67.1056i	−1.92854	−	2.41832i
$771$		0			0
$772$	29.5910	+	14.2503i	1.06500	+	0.512878i
$773$	−17.4255			−0.626750			−0.313375	−	0.949629i	$-0.601460\pi$
$773$	−17.4255			−0.626750			−0.313375	+	0.949629i	$0.601460\pi$
$774$		0			0
$775$	−103.566			−3.72021
$776$	−5.55550	−	2.67539i	−0.199431	−	0.0960408i
$777$		0			0
$778$	10.3898	+	13.0283i	0.372491	+	0.467089i
$779$	4.46105	−	4.13925i	0.159834	−	0.148304i
$780$		0			0
$781$	−27.2276	−	15.7198i	−0.974279	−	0.562500i
$782$	−7.08272	−	31.0314i	−0.253278	−	1.10968i
$783$		0			0
$784$	6.45073	−	1.98979i	0.230383	−	0.0710638i
$785$	4.59778	+	3.66661i	0.164102	+	0.130867i
$786$		0			0
$787$	27.8005	+	8.57533i	0.990982	+	0.305678i	0.747525	−	0.664234i	$-0.231242\pi$
$787$	27.8005	+	8.57533i	0.990982	+	0.305678i	0.243458	+	0.969912i	$0.421718\pi$
$788$	43.6683	+	64.0496i	1.55562	+	2.28167i
$789$		0			0
$790$	−7.00671	+	30.6984i	−0.249288	+	1.09220i
$791$	7.86109	−	8.47224i	0.279508	−	0.301238i
$792$		0			0
$793$	−3.36210	−	1.31953i	−0.119392	−	0.0468577i
$794$	25.9430	+	3.91028i	0.920682	+	0.138771i
$795$		0			0
$796$	4.13965	+	8.59607i	0.146726	+	0.304680i
$797$	1.26219	−	8.37409i	0.0447091	−	0.296626i	−0.955290	−	0.295669i	$-0.904457\pi$
$797$	1.26219	−	8.37409i	0.0447091	−	0.296626i	1.00000		0.000956528i	$-0.000304472\pi$
$798$		0			0
$799$	−1.36504	+	18.2152i	−0.0482917	+	0.644409i
$800$	22.8703	+	21.2205i	0.808587	+	0.750259i
$801$		0			0
$802$	2.15600	+	14.3041i	0.0761311	+	0.505097i
$803$	51.3223	−	34.9909i	1.81112	−	1.23480i
$804$		0			0
$805$	−2.72306	−	36.3367i	−0.0959751	−	1.28070i
$806$	−62.9081	+	78.8843i	−2.21584	+	2.77858i
$807$		0			0
$808$	30.2573	−	11.8751i	1.06445	−	0.417764i
$809$	4.82188	−	1.10056i	0.169528	−	0.0386937i	−0.136914	−	0.990583i	$-0.543718\pi$
$809$	4.82188	−	1.10056i	0.169528	−	0.0386937i	0.306442	+	0.951889i	$0.400861\pi$
$810$		0			0
$811$	35.9239	−	20.7407i	1.26146	−	0.728304i	0.288102	−	0.957600i	$-0.406976\pi$
$811$	35.9239	−	20.7407i	1.26146	−	0.728304i	0.973357	+	0.229296i	$0.0736425\pi$
$812$	26.0526	+	28.0781i	0.914268	+	0.985347i
$813$		0			0
$814$	−17.7780	−	12.1208i	−0.623117	−	0.424834i
$815$	35.8103	−	74.3609i	1.25438	−	2.60475i
$816$		0			0
$817$	−1.75533	+	4.83796i	−0.0614111	+	0.169259i
$818$			0.467673i			0.0163518i
$819$		0			0
$820$	67.4401	−	98.9165i	2.35511	−	3.45431i
$821$	41.6436	−	33.2097i	1.45337	−	1.15902i	0.496675	−	0.867937i	$-0.334554\pi$
$821$	41.6436	−	33.2097i	1.45337	−	1.15902i	0.956696	−	0.291088i	$-0.0940173\pi$
$822$		0			0
$823$	16.1049	+	27.8946i	0.561383	+	0.972344i	0.997376	+	0.0723937i	$0.0230638\pi$
$823$	16.1049	+	27.8946i	0.561383	+	0.972344i	−0.435993	+	0.899950i	$0.643603\pi$
$824$	3.89529	−	6.74685i	0.135699	−	0.235038i
$825$		0			0
$826$	−8.13576	−	20.7296i	−0.283079	−	0.721274i
$827$	0.0850810	+	0.275826i	0.00295856	+	0.00959140i	0.957040	−	0.289956i	$-0.0936406\pi$
$827$	0.0850810	+	0.275826i	0.00295856	+	0.00959140i	−0.954081	+	0.299547i	$0.903164\pi$
$828$		0			0
$829$	10.9509	−	0.820656i	0.380340	−	0.0285026i	0.116812	−	0.993154i	$-0.462733\pi$
$829$	10.9509	−	0.820656i	0.380340	−	0.0285026i	0.263529	+	0.964652i	$0.415114\pi$
$830$	−23.0226	+	74.6374i	−0.799126	+	2.59070i
$831$		0			0
$832$	53.4722	−	8.05963i	1.85381	−	0.279418i
$833$	−8.60734	−	1.96457i	−0.298227	−	0.0680683i
$834$		0			0
$835$	14.9067	+	1.11710i	0.515867	+	0.0386589i
$836$	4.51719	−	11.5096i	0.156230	−	0.398068i
$837$		0			0
$838$	10.7652	−	5.18426i	0.371878	−	0.179087i
$839$	−15.4847	+	7.45706i	−0.534593	+	0.257446i	−0.681646	−	0.731682i	$-0.738735\pi$
$839$	−15.4847	+	7.45706i	−0.534593	+	0.257446i	0.147053	+	0.989129i	$0.453021\pi$
$840$		0			0
$841$	−1.22169	+	3.11282i	−0.0421273	+	0.107339i
$842$	−12.9573	−	0.971019i	−0.446540	−	0.0334635i
$843$		0			0
$844$	−35.8031	−	8.17183i	−1.23239	−	0.281286i
$845$	49.5858	−	7.47385i	1.70580	−	0.257108i
$846$		0			0
$847$	4.19724	−	13.6071i	0.144219	−	0.467546i
$848$	20.7733	−	1.55674i	0.713357	−	0.0534587i
$849$		0			0
$850$	26.7711	+	86.7898i	0.918241	+	2.97686i
$851$	−3.33726	−	8.50321i	−0.114400	−	0.291486i
$852$		0			0
$853$	18.4631	−	31.9791i	0.632166	−	1.09494i	−0.354942	−	0.934888i	$-0.615499\pi$
$853$	18.4631	−	31.9791i	0.632166	−	1.09494i	0.987108	−	0.160055i	$-0.0511672\pi$
$854$	−1.75572	−	3.04100i	−0.0600795	−	0.104061i
$855$		0			0
$856$	20.6083	−	16.4345i	0.704376	−	0.561721i
$857$	−3.11840	+	4.57385i	−0.106522	+	0.156240i	−0.875799	−	0.482677i	$-0.839665\pi$
$857$	−3.11840	+	4.57385i	−0.106522	+	0.156240i	0.769276	+	0.638916i	$0.220617\pi$
$858$		0			0
$859$		−	50.5326i		−	1.72415i	−0.506779	−	0.862076i	$-0.669164\pi$
$859$		−	50.5326i		−	1.72415i	0.506779	−	0.862076i	$-0.330836\pi$
$860$	−12.4875	+	100.473i	−0.425821	+	3.42609i
$861$		0			0
$862$	10.4933	−	21.7896i	0.357404	−	0.742158i
$863$	21.5039	+	14.6611i	0.732001	+	0.499070i	0.871037	−	0.491217i	$-0.163448\pi$
$863$	21.5039	+	14.6611i	0.732001	+	0.499070i	−0.139036	+	0.990287i	$0.544400\pi$
$864$		0			0
$865$	52.9815	+	57.1004i	1.80142	+	1.94147i
$866$	−34.1166	+	19.6972i	−1.15933	+	0.669339i
$867$		0			0
$868$	−62.1603	+	14.1877i	−2.10986	+	0.481561i
$869$	−12.5116	+	4.91043i	−0.424426	+	0.166575i
$870$		0			0
$871$	27.4351	−	34.4025i	0.929603	−	1.16569i
$872$	−1.12867	−	15.0611i	−0.0382216	−	0.510032i
$873$		0			0
$874$	6.67258	−	4.54929i	0.225703	−	0.153882i
$875$	9.18881	+	60.9638i	0.310638	+	2.06095i
$876$		0			0
$877$	6.43846	+	5.97402i	0.217411	+	0.201728i	0.781358	−	0.624083i	$-0.214527\pi$
$877$	6.43846	+	5.97402i	0.217411	+	0.201728i	−0.563947	+	0.825811i	$0.690718\pi$
$878$	−6.58497	+	87.8703i	−0.222232	+	2.96548i
$879$		0			0
$880$	6.21660	−	41.2444i	0.209561	−	1.39035i
$881$	−15.3089	−	31.7894i	−0.515771	−	1.07101i	−0.982440	−	0.186578i	$-0.940260\pi$
$881$	−15.3089	−	31.7894i	−0.515771	−	1.07101i	0.466669	−	0.884432i	$-0.345454\pi$
$882$		0			0
$883$	45.0712	+	6.79339i	1.51677	+	0.228616i	0.854024	−	0.520233i	$-0.174155\pi$
$883$	45.0712	+	6.79339i	1.51677	+	0.228616i	0.662741	+	0.748849i	$0.269393\pi$
$884$	53.5368	+	21.0116i	1.80064	+	0.706698i
$885$		0			0
$886$	−35.1200	+	37.8504i	−1.17988	+	1.27161i
$887$	2.67196	−	11.7066i	0.0897157	−	0.393070i	−0.910055	−	0.414488i	$-0.863961\pi$
$887$	2.67196	−	11.7066i	0.0897157	−	0.393070i	0.999771	+	0.0214176i	$0.00681795\pi$
$888$		0			0
$889$	−15.7728	−	23.1345i	−0.529003	−	0.775905i
$890$	−87.7966	−	27.0817i	−2.94295	−	0.907779i
$891$		0			0
$892$	62.9011	+	50.1619i	2.10608	+	1.67955i
$893$	−4.42867	+	1.36606i	−0.148200	+	0.0457136i
$894$		0			0
$895$	−9.87979	−	43.2862i	−0.330245	−	1.44690i
$896$	36.5729	+	21.1154i	1.22182	+	0.705416i
$897$		0			0
$898$	−55.7603	+	51.7380i	−1.86075	+	1.72652i
$899$	26.6273	+	33.3896i	0.888069	+	1.11360i
$900$		0			0
$901$	−24.5461	−	11.8208i	−0.817748	−	0.393807i
$902$	78.6220			2.61783
$903$		0			0
$904$	23.2544			0.773430
$905$	−81.7369	−	39.3624i	−2.71703	−	1.30845i
$906$		0			0
$907$	−9.85860	−	12.3623i	−0.327349	−	0.410483i	0.590737	−	0.806865i	$-0.298837\pi$
$907$	−9.85860	−	12.3623i	−0.327349	−	0.410483i	−0.918086	+	0.396381i	$0.870266\pi$
$908$	52.8546	−	49.0419i	1.75404	−	1.62751i
$909$		0			0
$910$	87.7257	+	50.6484i	2.90808	+	1.67898i
$911$	−3.56505	−	15.6195i	−0.118115	−	0.517497i	−0.999022	−	0.0442075i	$-0.985924\pi$
$911$	−3.56505	−	15.6195i	−0.118115	−	0.517497i	0.880907	−	0.473289i	$-0.156933\pi$
$912$		0			0
$913$	−31.8592	+	9.82726i	−1.05439	+	0.325235i
$914$	47.4383	+	37.8308i	1.56912	+	1.25133i
$915$		0			0
$916$	11.8816	+	3.66500i	0.392580	+	0.121095i
$917$	−14.2621	−	20.9187i	−0.470977	−	0.690797i
$918$		0			0
$919$	−10.1702	+	44.5585i	−0.335483	+	1.46985i	0.472861	+	0.881137i	$0.343221\pi$
$919$	−10.1702	+	44.5585i	−0.335483	+	1.46985i	−0.808344	+	0.588711i	$0.799636\pi$
$920$	49.8681	−	53.7450i	1.64410	−	1.77192i
$921$		0			0
$922$	−10.8887	−	4.27351i	−0.358601	−	0.140740i
$923$	36.6903	+	5.53017i	1.20767	+	0.182028i
$924$		0			0
$925$	11.3094	+	23.4843i	0.371852	+	0.772159i
$926$	3.73985	−	24.8123i	0.122899	−	0.815381i
$927$		0			0
$928$	0.961417	−	12.8292i	0.0315601	−	0.421140i
$929$	−3.12247	−	2.89723i	−0.102445	−	0.0950550i	0.627288	−	0.778788i	$-0.284165\pi$
$929$	−3.12247	−	2.89723i	−0.102445	−	0.0950550i	−0.729733	+	0.683733i	$0.760355\pi$
$930$		0			0
$931$	−0.333860	−	2.21502i	−0.0109418	−	0.0725943i
$932$	13.0330	−	8.88575i	0.426910	−	0.291063i
$933$		0			0
$934$	−1.24054	−	16.5538i	−0.0405916	−	0.541657i
$935$	−34.0114	+	42.6489i	−1.11229	+	1.39477i
$936$		0			0
$937$	13.3180	−	5.22692i	0.435079	−	0.170756i	−0.137685	−	0.990476i	$-0.543966\pi$
$937$	13.3180	−	5.22692i	0.435079	−	0.170756i	0.572764	+	0.819720i	$0.305871\pi$
$938$	41.7077	−	9.51950i	1.36180	−	0.310823i
$939$		0			0
$940$	−78.9588	+	45.5869i	−2.57535	+	1.48688i
$941$	−1.88885	−	2.03569i	−0.0615746	−	0.0663616i	0.701513	−	0.712656i	$-0.252508\pi$
$941$	−1.88885	−	2.03569i	−0.0615746	−	0.0663616i	−0.763088	+	0.646295i	$0.776318\pi$
$942$		0			0
$943$	27.5782	+	18.8025i	0.898069	+	0.612293i
$944$	4.69538	−	9.75006i	0.152822	−	0.317338i
$945$		0			0
$946$	−59.1371	+	30.3935i	−1.92271	+	0.988177i
$947$		−	3.91259i		−	0.127142i	−0.997977	−	0.0635710i	$-0.979751\pi$
$947$		−	3.91259i		−	0.127142i	0.997977	−	0.0635710i	$-0.0202489\pi$
$948$		0			0
$949$	−41.2958	+	60.5699i	−1.34052	+	1.96618i
$950$	−18.0168	+	14.3679i	−0.584541	+	0.466156i
$951$		0			0
$952$	12.9019	+	22.3467i	0.418151	+	0.724259i
$953$	−9.43823	+	16.3475i	−0.305734	+	0.529547i	−0.977425	−	0.211285i	$-0.932235\pi$
$953$	−9.43823	+	16.3475i	−0.305734	+	0.529547i	0.671690	+	0.740832i	$0.265569\pi$
$954$		0			0
$955$	33.8734	+	86.3081i	1.09612	+	2.79286i
$956$	−11.9182	−	38.6379i	−0.385462	−	1.24964i
$957$		0			0
$958$	15.7326	−	1.17900i	0.508298	−	0.0380916i
$959$	10.4110	−	33.7515i	0.336187	−	1.08989i
$960$		0			0
$961$	−39.6417	+	5.97503i	−1.27877	+	0.192743i
$962$	24.7571	+	5.65064i	0.798201	+	0.182184i
$963$		0			0
$964$	−42.2733	−	3.16795i	−1.36153	−	0.102033i
$965$	13.4317	−	34.2235i	0.432382	−	1.10169i
$966$		0			0
$967$	−22.4112	+	10.7927i	−0.720696	+	0.347069i	−0.758017	−	0.652234i	$-0.773832\pi$
$967$	−22.4112	+	10.7927i	−0.720696	+	0.347069i	0.0373213	+	0.999303i	$0.488117\pi$
$968$	25.8139	−	12.4313i	0.829690	−	0.399558i
$969$		0			0
$970$	−5.46438	+	13.9230i	−0.175451	+	0.447041i
$971$	20.9303	+	1.56851i	0.671686	+	0.0503359i	0.406207	−	0.913781i	$-0.366851\pi$
$971$	20.9303	+	1.56851i	0.671686	+	0.0503359i	0.265479	+	0.964117i	$0.414470\pi$
$972$		0			0
$973$	21.3996	+	4.88432i	0.686040	+	0.156584i
$974$	25.0022	−	3.76848i	0.801123	−	0.120750i
$975$		0			0
$976$	0.502973	−	1.63060i	0.0160998	−	0.0521942i
$977$	−49.8246	+	3.73384i	−1.59403	+	0.119456i	−0.841928	−	0.539591i	$-0.818579\pi$
$977$	−49.8246	+	3.73384i	−1.59403	+	0.119456i	−0.752102	+	0.659047i	$0.770960\pi$
$978$		0			0
$979$	−11.5599	−	37.4762i	−0.369455	−	1.19774i
$980$	−16.0996	−	41.0210i	−0.514282	−	1.31037i
$981$		0			0
$982$	20.1730	−	34.9407i	0.643746	−	1.11500i
$983$	−13.6604	−	23.6604i	−0.435698	−	0.754651i	0.561654	−	0.827372i	$-0.310165\pi$
$983$	−13.6604	−	23.6604i	−0.435698	−	0.754651i	−0.997352	+	0.0727209i	$0.976832\pi$
$984$		0			0
$985$	67.8435	−	54.1034i	2.16167	−	1.72388i
$986$	21.0979	−	30.9450i	0.671895	−	0.985488i
$987$		0			0
$988$			14.5922i			0.464239i
$989$	−28.0121	−	3.48155i	−0.890732	−	0.110707i
$990$		0			0
$991$	6.08857	−	12.6430i	0.193410	−	0.401620i	−0.781600	−	0.623779i	$-0.785596\pi$
$991$	6.08857	−	12.6430i	0.193410	−	0.401620i	0.975010	+	0.222160i	$0.0713106\pi$
$992$	17.6942	+	12.0637i	0.561790	+	0.383022i
$993$		0			0
$994$	24.5366	+	26.4441i	0.778253	+	0.838757i
$995$	9.24920	−	5.34003i	0.293219	−	0.169290i
$996$		0			0
$997$	−8.78347	+	2.00477i	−0.278175	+	0.0634917i	−0.359332	−	0.933210i	$-0.616996\pi$
$997$	−8.78347	+	2.00477i	−0.278175	+	0.0634917i	0.0811572	+	0.996701i	$0.474138\pi$
$998$	−71.7802	+	28.1717i	−2.27216	+	0.891758i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.bc.a.233.2	yes	168
3.2	odd	2	inner	387.2.bc.a.233.13	yes	168
43.12	odd	42	inner	387.2.bc.a.98.13	yes	168
129.98	even	42	inner	387.2.bc.a.98.2	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.bc.a.98.2	✓	168	129.98	even	42	inner
387.2.bc.a.98.13	yes	168	43.12	odd	42	inner
387.2.bc.a.233.2	yes	168	1.1	even	1	trivial
387.2.bc.a.233.13	yes	168	3.2	odd	2	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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.bc (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15365 - 1.03715i) q^{2} +(2.31558 + 2.90364i) q^{4} +(3.04753 - 2.82769i) q^{5} +(-1.76335 - 1.01807i) q^{7} +(-0.911635 - 3.99413i) q^{8} +O(q^{10})\)	\(q+(-2.15365 - 1.03715i) q^{2} +(2.31558 + 2.90364i) q^{4} +(3.04753 - 2.82769i) q^{5} +(-1.76335 - 1.01807i) q^{7} +(-0.911635 - 3.99413i) q^{8} +(-9.49606 + 2.92915i) q^{10} +(-3.31643 - 2.64476i) q^{11} +(4.78379 + 1.47560i) q^{13} +(2.74176 + 4.02142i) q^{14} +(-0.526312 + 2.30592i) q^{16} +(2.10399 - 2.26756i) q^{17} +(0.730589 + 0.286735i) q^{19} +(15.2674 + 2.30119i) q^{20} +(4.39944 + 9.13553i) q^{22} +(-0.641577 + 4.25659i) q^{23} +(0.917932 - 12.2490i) q^{25} +(-8.77221 - 8.13943i) q^{26} +(-1.12706 - 7.47756i) q^{28} +(-4.18505 + 2.85332i) q^{29} +(-0.630084 - 8.40788i) q^{31} +(-1.58362 + 1.98580i) q^{32} +(-6.88304 + 2.70140i) q^{34} +(-8.25266 + 1.88362i) q^{35} +(-1.83774 + 1.06102i) q^{37} +(-1.27605 - 1.37526i) q^{38} +(-14.0724 - 9.59442i) q^{40} +(3.36429 - 6.98603i) q^{41} +(0.170121 + 6.55523i) q^{43} -15.7539i q^{44} +(5.79644 - 8.50181i) q^{46} +(-4.61679 + 3.68177i) q^{47} +(-1.42706 - 2.47174i) q^{49} +(-14.6808 + 25.4280i) q^{50} +(6.79261 + 17.3073i) q^{52} +(-2.59603 - 8.41613i) q^{53} +(-17.5855 + 1.31785i) q^{55} +(-2.45878 + 7.97117i) q^{56} +(11.9724 - 1.80456i) q^{58} +(-4.46065 - 1.01811i) q^{59} +(-0.719441 - 0.0539146i) q^{61} +(-7.36321 + 18.7612i) q^{62} +(9.73212 - 4.68674i) q^{64} +(18.7513 - 9.03015i) q^{65} +(3.21120 - 8.18201i) q^{67} +(11.4561 + 0.858517i) q^{68} +(19.7270 + 4.50255i) q^{70} +(7.32896 - 1.10466i) q^{71} +(-4.31622 + 13.9929i) q^{73} +(5.05828 - 0.379065i) q^{74} +(0.859159 + 2.78532i) q^{76} +(3.15547 + 8.04001i) q^{77} +(1.58429 - 2.74407i) q^{79} +(4.91649 + 8.51562i) q^{80} +(-14.4910 + 11.5562i) q^{82} +(4.42760 - 6.49410i) q^{83} -12.8599i q^{85} +(6.43234 - 14.2941i) q^{86} +(-7.54017 + 15.6573i) q^{88} +(7.63906 + 5.20822i) q^{89} +(-6.93323 - 7.47225i) q^{91} +(-13.8452 + 7.99354i) q^{92} +(13.7615 - 3.14097i) q^{94} +(3.03729 - 1.19205i) q^{95} +(0.938409 - 1.17673i) q^{97} +(0.509841 + 6.80335i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 24 q^{4} - 6 q^{7}+O(q^{10}) \) 168 * q - 24 * q^4 - 6 * q^7	\( 168 q - 24 q^{4} - 6 q^{7} + 8 q^{10} + 26 q^{13} - 8 q^{16} + 24 q^{19} + 14 q^{25} + 32 q^{31} - 48 q^{34} - 78 q^{37} - 244 q^{40} - 32 q^{43} - 92 q^{46} + 54 q^{49} + 76 q^{52} - 96 q^{55} - 20 q^{58} - 96 q^{64} - 18 q^{67} + 140 q^{70} + 10 q^{73} - 16 q^{76} - 168 q^{88} - 38 q^{91} - 112 q^{94} - 40 q^{97}+O(q^{100}) \) 168 * q - 24 * q^4 - 6 * q^7 + 8 * q^10 + 26 * q^13 - 8 * q^16 + 24 * q^19 + 14 * q^25 + 32 * q^31 - 48 * q^34 - 78 * q^37 - 244 * q^40 - 32 * q^43 - 92 * q^46 + 54 * q^49 + 76 * q^52 - 96 * q^55 - 20 * q^58 - 96 * q^64 - 18 * q^67 + 140 * q^70 + 10 * q^73 - 16 * q^76 - 168 * q^88 - 38 * q^91 - 112 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

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