LMFDB - Embedded newform 900.2.bj.f.127.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.5
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31411 - 0.522605i) q^{2} +(1.45377 + 1.37352i) q^{4} +(1.83309 - 1.28054i) q^{5} +(-1.46352 + 1.46352i) q^{7} +(-1.19260 - 2.56470i) q^{8} +O(q^{10})$	\(q+(-1.31411 - 0.522605i) q^{2} +(1.45377 + 1.37352i) q^{4} +(1.83309 - 1.28054i) q^{5} +(-1.46352 + 1.46352i) q^{7} +(-1.19260 - 2.56470i) q^{8} +(-3.07810 + 0.724779i) q^{10} +(-0.716610 - 0.986329i) q^{11} +(0.610002 - 0.0966148i) q^{13} +(2.68808 - 1.15838i) q^{14} +(0.226878 + 3.99356i) q^{16} +(2.23367 - 4.38383i) q^{17} +(-1.11648 - 3.43617i) q^{19} +(4.42373 + 0.656192i) q^{20} +(0.426243 + 1.67065i) q^{22} +(-6.81819 - 1.07989i) q^{23} +(1.72046 - 4.69468i) q^{25} +(-0.852100 - 0.191828i) q^{26} +(-4.13780 + 0.117442i) q^{28} +(-0.953684 - 0.309871i) q^{29} +(10.1146 - 3.28642i) q^{31} +(1.78891 - 5.36654i) q^{32} +(-5.22631 + 4.59351i) q^{34} +(-0.808681 + 4.55687i) q^{35} +(-0.749924 - 4.73483i) q^{37} +(-0.328585 + 5.09899i) q^{38} +(-5.47034 - 3.17418i) q^{40} +(4.46659 + 3.24517i) q^{41} +(2.74571 + 2.74571i) q^{43} +(0.312960 - 2.41817i) q^{44} +(8.39548 + 4.98232i) q^{46} +(-0.593032 - 1.16389i) q^{47} +2.71620i q^{49} +(-4.71434 + 5.27020i) q^{50} +(1.01950 + 0.697395i) q^{52} +(-2.82569 - 5.54573i) q^{53} +(-2.57664 - 0.890388i) q^{55} +(5.49890 + 2.00811i) q^{56} +(1.09131 + 0.905605i) q^{58} +(10.5976 + 7.69958i) q^{59} +(7.64473 - 5.55422i) q^{61} +(-15.0092 - 0.967209i) q^{62} +(-5.15541 + 6.11733i) q^{64} +(0.994471 - 0.958232i) q^{65} +(-7.24032 - 3.68913i) q^{67} +(9.26853 - 3.30507i) q^{68} +(3.44414 - 5.56560i) q^{70} +(-12.8093 - 4.16201i) q^{71} +(1.08745 - 6.86590i) q^{73} +(-1.48897 + 6.61400i) q^{74} +(3.09656 - 6.52891i) q^{76} +(2.49229 + 0.394740i) q^{77} +(2.17258 - 6.68651i) q^{79} +(5.52978 + 7.03004i) q^{80} +(-4.17364 - 6.59877i) q^{82} +(3.19885 - 6.27810i) q^{83} +(-1.51912 - 10.8963i) q^{85} +(-2.17324 - 5.04309i) q^{86} +(-1.67501 + 3.01419i) q^{88} +(-8.41934 - 11.5882i) q^{89} +(-0.751354 + 1.03415i) q^{91} +(-8.42880 - 10.9348i) q^{92} +(0.171053 + 1.83940i) q^{94} +(-6.44675 - 4.86913i) q^{95} +(3.66823 - 1.86906i) q^{97} +(1.41950 - 3.56938i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8}+O(q^{10}) $ 240 * q - 12 * q^8	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{20}\right)$

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 $

$2$	−1.31411	−	0.522605i	−0.929216	−	0.369538i
$2$	−1.31411	−	0.522605i	−0.929216	−	0.369538i
$3$		0			0
$3$		0			0
$4$	1.45377	+	1.37352i	0.726884	+	0.686761i
$5$	1.83309	−	1.28054i	0.819784	−	0.572673i
$5$	1.83309	−	1.28054i	0.819784	−	0.572673i
$6$		0			0
$7$	−1.46352	+	1.46352i	−0.553160	+	0.553160i	−0.927351	−	0.374192i	$-0.877920\pi$
$7$	−1.46352	+	1.46352i	−0.553160	+	0.553160i	0.374192	+	0.927351i	$0.377920\pi$
$8$	−1.19260	−	2.56470i	−0.421648	−	0.906760i
$9$		0			0
$10$	−3.07810	+	0.724779i	−0.973380	+	0.229195i
$11$	−0.716610	−	0.986329i	−0.216066	−	0.297389i	0.687202	−	0.726467i	$-0.258839\pi$
$11$	−0.716610	−	0.986329i	−0.216066	−	0.297389i	−0.903268	+	0.429077i	$0.858839\pi$
$12$		0			0
$13$	0.610002	−	0.0966148i	0.169184	−	0.0267961i	−0.0712677	−	0.997457i	$-0.522704\pi$
$13$	0.610002	−	0.0966148i	0.169184	−	0.0267961i	0.240452	+	0.970661i	$0.422704\pi$
$14$	2.68808	−	1.15838i	0.718418	−	0.309591i
$15$		0			0
$16$	0.226878	+	3.99356i	0.0567196	+	0.998390i
$17$	2.23367	−	4.38383i	0.541746	−	1.06324i	−0.444162	−	0.895946i	$-0.646499\pi$
$17$	2.23367	−	4.38383i	0.541746	−	1.06324i	0.985908	−	0.167289i	$-0.0535014\pi$
$18$		0			0
$19$	−1.11648	−	3.43617i	−0.256138	−	0.788312i	−0.993603	−	0.112927i	$-0.963977\pi$
$19$	−1.11648	−	3.43617i	−0.256138	−	0.788312i	0.737465	−	0.675385i	$-0.236023\pi$
$20$	4.42373	+	0.656192i	0.989177	+	0.146729i
$21$		0			0
$22$	0.426243	+	1.67065i	0.0908753	+	0.356183i
$23$	−6.81819	−	1.07989i	−1.42169	−	0.225174i	−0.602236	−	0.798318i	$-0.705723\pi$
$23$	−6.81819	−	1.07989i	−1.42169	−	0.225174i	−0.819454	+	0.573145i	$0.805723\pi$
$24$		0			0
$25$	1.72046	−	4.69468i	0.344092	−	0.938936i
$26$	−0.852100	−	0.191828i	−0.167111	−	0.0376205i
$27$		0			0
$28$	−4.13780	+	0.117442i	−0.781971	+	0.0221944i
$29$	−0.953684	−	0.309871i	−0.177095	−	0.0575416i	0.219127	−	0.975696i	$-0.429679\pi$
$29$	−0.953684	−	0.309871i	−0.177095	−	0.0575416i	−0.396222	+	0.918155i	$0.629679\pi$
$30$		0			0
$31$	10.1146	−	3.28642i	1.81663	−	0.590259i	0.816717	−	0.577038i	$-0.195791\pi$
$31$	10.1146	−	3.28642i	1.81663	−	0.590259i	0.999913	−	0.0132212i	$-0.00420855\pi$
$32$	1.78891	−	5.36654i	0.316238	−	0.948680i
$33$		0			0
$34$	−5.22631	+	4.59351i	−0.896304	+	0.787780i
$35$	−0.808681	+	4.55687i	−0.136692	+	0.770251i
$36$		0			0
$37$	−0.749924	−	4.73483i	−0.123287	−	0.778402i	−0.969416	−	0.245424i	$-0.921073\pi$
$37$	−0.749924	−	4.73483i	−0.123287	−	0.778402i	0.846129	−	0.532978i	$-0.178927\pi$
$38$	−0.328585	+	5.09899i	−0.0533036	+	0.827165i
$39$		0			0
$40$	−5.47034	−	3.17418i	−0.864937	−	0.501881i
$41$	4.46659	+	3.24517i	0.697564	+	0.506810i	0.879138	−	0.476568i	$-0.158119\pi$
$41$	4.46659	+	3.24517i	0.697564	+	0.506810i	−0.181574	+	0.983377i	$0.558119\pi$
$42$		0			0
$43$	2.74571	+	2.74571i	0.418717	+	0.418717i	0.884761	−	0.466044i	$-0.154321\pi$
$43$	2.74571	+	2.74571i	0.418717	+	0.418717i	−0.466044	+	0.884761i	$0.654321\pi$
$44$	0.312960	−	2.41817i	0.0471805	−	0.364553i
$45$		0			0
$46$	8.39548	+	4.98232i	1.23785	+	0.734603i
$47$	−0.593032	−	1.16389i	−0.0865026	−	0.169771i	0.843703	−	0.536811i	$-0.180371\pi$
$47$	−0.593032	−	1.16389i	−0.0865026	−	0.169771i	−0.930205	+	0.367040i	$0.880371\pi$
$48$		0			0
$49$			2.71620i			0.388028i
$50$	−4.71434	+	5.27020i	−0.666708	+	0.745319i
$51$		0			0
$52$	1.01950	+	0.697395i	0.141380	+	0.0967113i
$53$	−2.82569	−	5.54573i	−0.388139	−	0.761765i	0.611425	−	0.791302i	$-0.290597\pi$
$53$	−2.82569	−	5.54573i	−0.388139	−	0.761765i	−0.999564	+	0.0295374i	$0.990597\pi$
$54$		0			0
$55$	−2.57664	−	0.890388i	−0.347434	−	0.120060i
$56$	5.49890	+	2.00811i	0.734822	+	0.268345i
$57$		0			0
$58$	1.09131	+	0.905605i	0.143295	+	0.118912i
$59$	10.5976	+	7.69958i	1.37969	+	1.00240i	0.996909	+	0.0785588i	$0.0250318\pi$
$59$	10.5976	+	7.69958i	1.37969	+	1.00240i	0.382776	+	0.923841i	$0.374968\pi$
$60$		0			0
$61$	7.64473	−	5.55422i	0.978807	−	0.711145i	0.0213655	−	0.999772i	$-0.493199\pi$
$61$	7.64473	−	5.55422i	0.978807	−	0.711145i	0.957442	+	0.288627i	$0.0931986\pi$
$62$	−15.0092	−	0.967209i	−1.90616	−	0.122836i
$63$		0			0
$64$	−5.15541	+	6.11733i	−0.644427	+	0.764666i
$65$	0.994471	−	0.958232i	0.123349	−	0.118854i
$66$		0			0
$67$	−7.24032	−	3.68913i	−0.884546	−	0.450699i	−0.0481602	−	0.998840i	$-0.515336\pi$
$67$	−7.24032	−	3.68913i	−0.884546	−	0.450699i	−0.836386	+	0.548141i	$0.815336\pi$
$68$	9.26853	−	3.30507i	1.12397	−	0.400799i
$69$		0			0
$70$	3.44414	−	5.56560i	0.411653	−	0.665217i
$71$	−12.8093	−	4.16201i	−1.52019	−	0.493940i	−0.574360	−	0.818603i	$-0.694749\pi$
$71$	−12.8093	−	4.16201i	−1.52019	−	0.493940i	−0.945830	+	0.324663i	$0.894749\pi$
$72$		0			0
$73$	1.08745	−	6.86590i	0.127277	−	0.803592i	−0.838630	−	0.544701i	$-0.816643\pi$
$73$	1.08745	−	6.86590i	0.127277	−	0.803592i	0.965907	−	0.258891i	$-0.0833570\pi$
$74$	−1.48897	+	6.61400i	−0.173089	+	0.768862i
$75$		0			0
$76$	3.09656	−	6.52891i	0.355199	−	0.748917i
$77$	2.49229	+	0.394740i	0.284023	+	0.0449848i
$78$		0			0
$79$	2.17258	−	6.68651i	0.244434	−	0.752291i	−0.751295	−	0.659967i	$-0.770570\pi$
$79$	2.17258	−	6.68651i	0.244434	−	0.752291i	0.995729	−	0.0923241i	$-0.0294296\pi$
$80$	5.52978	+	7.03004i	0.618249	+	0.785983i
$81$		0			0
$82$	−4.17364	−	6.59877i	−0.460902	−	0.728712i
$83$	3.19885	−	6.27810i	0.351119	−	0.689111i	−0.646130	−	0.763227i	$-0.723614\pi$
$83$	3.19885	−	6.27810i	0.351119	−	0.689111i	0.997250	+	0.0741166i	$0.0236137\pi$
$84$		0			0
$85$	−1.51912	−	10.8963i	−0.164772	−	1.18187i
$86$	−2.17324	−	5.04309i	−0.234347	−	0.543810i
$87$		0			0
$88$	−1.67501	+	3.01419i	−0.178557	+	0.321313i
$89$	−8.41934	−	11.5882i	−0.892448	−	1.22835i	−0.972815	−	0.231585i	$-0.925609\pi$
$89$	−8.41934	−	11.5882i	−0.892448	−	1.22835i	0.0803663	−	0.996765i	$-0.474391\pi$
$90$		0			0
$91$	−0.751354	+	1.03415i	−0.0787633	+	0.108408i
$92$	−8.42880	−	10.9348i	−0.878763	−	1.14004i
$93$		0			0
$94$	0.171053	+	1.83940i	0.0176428	+	0.189720i
$95$	−6.44675	−	4.86913i	−0.661423	−	0.499563i
$96$		0			0
$97$	3.66823	−	1.86906i	0.372453	−	0.189774i	−0.257737	−	0.966215i	$-0.582977\pi$
$97$	3.66823	−	1.86906i	0.372453	−	0.189774i	0.630190	+	0.776441i	$0.282977\pi$
$98$	1.41950	−	3.56938i	0.143391	−	0.360562i
$99$		0			0
$100$	8.94939	−	4.46188i	0.894939	−	0.446188i
$101$	14.2792			1.42083			0.710417	−	0.703781i	$-0.248506\pi$
$101$	14.2792			1.42083			0.710417	+	0.703781i	$0.248506\pi$
$102$		0			0
$103$	−11.1840	+	5.69852i	−1.10199	+	0.561492i	−0.907771	−	0.419467i	$-0.862217\pi$
$103$	−11.1840	+	5.69852i	−1.10199	+	0.561492i	−0.194219	+	0.980958i	$0.562217\pi$
$104$	−0.975276	−	1.44925i	−0.0956337	−	0.142111i
$105$		0			0
$106$	0.815039	+	8.76442i	0.0791636	+	0.851276i
$107$	3.88843	−	3.88843i	0.375909	−	0.375909i	−0.493715	−	0.869624i	$-0.664361\pi$
$107$	3.88843	−	3.88843i	0.375909	−	0.375909i	0.869624	+	0.493715i	$0.164361\pi$
$108$		0			0
$109$	−3.30533	+	4.54940i	−0.316593	+	0.435753i	−0.937423	−	0.348192i	$-0.886796\pi$
$109$	−3.30533	+	4.54940i	−0.316593	+	0.435753i	0.620830	+	0.783945i	$0.286796\pi$
$110$	2.92067	+	2.51663i	0.278475	+	0.239952i
$111$		0			0
$112$	−6.17671	−	5.51263i	−0.583644	−	0.520894i
$113$	−6.70930	+	1.06265i	−0.631158	+	0.0999656i	−0.463813	−	0.885933i	$-0.653519\pi$
$113$	−6.70930	+	1.06265i	−0.631158	+	0.0999656i	−0.167345	+	0.985898i	$0.553519\pi$
$114$		0			0
$115$	−13.8812	+	6.75138i	−1.29443	+	0.629569i
$116$	−0.960821	−	1.76039i	−0.0892100	−	0.163448i
$117$		0			0
$118$	−9.90252	−	15.6564i	−0.911601	−	1.44129i
$119$	3.14681	+	9.68488i	0.288467	+	0.887811i
$120$		0			0
$121$	2.93987	−	9.04800i	0.267261	−	0.822545i
$122$	−12.9487	+	3.30368i	−1.17232	+	0.299101i
$123$		0			0
$124$	19.2182	+	9.11488i	1.72585	+	0.818541i
$125$	−2.85794	−	10.8089i	−0.255622	−	0.966777i
$126$		0			0
$127$	−2.16580	+	13.6743i	−0.192183	+	1.21340i	0.683296	+	0.730142i	$0.260546\pi$
$127$	−2.16580	+	13.6743i	−0.192183	+	1.21340i	−0.875479	+	0.483256i	$0.839454\pi$
$128$	9.97173	−	5.34459i	0.881384	−	0.472400i
$129$		0			0
$130$	−1.80762	+	0.739506i	−0.158539	+	0.0648590i
$131$	1.62756	−	0.528826i	0.142201	−	0.0462038i	−0.237052	−	0.971497i	$-0.576181\pi$
$131$	1.62756	−	0.528826i	0.142201	−	0.0462038i	0.379253	+	0.925293i	$0.376181\pi$
$132$		0			0
$133$	6.66292	+	3.39493i	0.577748	+	0.294377i
$134$	7.58662	+	8.63175i	0.655384	+	0.745670i
$135$		0			0
$136$	−13.9071	−	0.500556i	−1.19253	−	0.0429224i
$137$	0.0719242	+	0.454112i	0.00614490	+	0.0387974i	0.990570	−	0.137006i	$-0.0437478\pi$
$137$	0.0719242	+	0.454112i	0.00614490	+	0.0387974i	−0.984425	+	0.175803i	$0.943748\pi$
$138$		0			0
$139$	−3.76808	+	2.73767i	−0.319604	+	0.232206i	−0.736007	−	0.676974i	$-0.763291\pi$
$139$	−3.76808	+	2.73767i	−0.319604	+	0.232206i	0.416402	+	0.909180i	$0.363291\pi$
$140$	−7.43459	+	5.51388i	−0.628337	+	0.466008i
$141$		0			0
$142$	14.6578	+	12.1636i	1.23005	+	1.02074i
$143$	−0.532427	−	0.532427i	−0.0445238	−	0.0445238i
$144$		0			0
$145$	−2.14499	+	0.653204i	−0.178132	+	0.0542456i
$146$	−5.01718	+	8.45423i	−0.415225	+	0.699677i
$147$		0			0
$148$	5.41318	−	7.91338i	0.444961	−	0.650476i
$149$			19.6344i			1.60852i	0.594281	+	0.804258i	$0.297437\pi$
$149$			19.6344i			1.60852i	−0.594281	+	0.804258i	$0.702563\pi$
$150$		0			0
$151$		−	23.7781i		−	1.93504i	−0.252799	−	0.967519i	$-0.581351\pi$
$151$		−	23.7781i		−	1.93504i	0.252799	−	0.967519i	$-0.418649\pi$
$152$	−7.48126	+	6.96142i	−0.606810	+	0.564646i
$153$		0			0
$154$	−3.06885	−	1.82122i	−0.247295	−	0.146758i
$155$	14.3326	−	18.9764i	1.15122	−	1.52422i
$156$		0			0
$157$	2.38350	+	2.38350i	0.190224	+	0.190224i	0.795793	−	0.605569i	$-0.207054\pi$
$157$	2.38350	+	2.38350i	0.190224	+	0.190224i	−0.605569	+	0.795793i	$0.707054\pi$
$158$	−6.34941	+	7.65140i	−0.505132	+	0.608713i
$159$		0			0
$160$	−3.59280	−	12.1281i	−0.284036	−	0.958814i
$161$	11.5590	−	8.39812i	0.910979	−	0.661865i
$162$		0			0
$163$	0.927372	+	5.85520i	0.0726374	+	0.458614i	0.997020	+	0.0771471i	$0.0245811\pi$
$163$	0.927372	+	5.85520i	0.0726374	+	0.458614i	−0.924382	+	0.381467i	$0.875419\pi$
$164$	2.03607	+	10.8527i	0.158991	+	0.847451i
$165$		0			0
$166$	−7.48461	+	6.57837i	−0.580918	+	0.510580i
$167$	11.9576	+	6.09269i	0.925305	+	0.471467i	0.850644	−	0.525742i	$-0.176212\pi$
$167$	11.9576	+	6.09269i	0.925305	+	0.471467i	0.0746615	+	0.997209i	$0.476212\pi$
$168$		0			0
$169$	−12.0010	+	3.89935i	−0.923151	+	0.299950i
$170$	−3.69816	+	15.1128i	−0.283636	+	1.15910i
$171$		0			0
$172$	0.220332	+	7.76292i	0.0168002	+	0.591917i
$173$	−2.52253	+	15.9266i	−0.191785	+	1.21088i	0.684473	+	0.729038i	$0.260032\pi$
$173$	−2.52253	+	15.9266i	−0.191785	+	1.21088i	−0.876258	+	0.481842i	$0.839968\pi$
$174$		0			0
$175$	4.35284	+	9.38871i	0.329044	+	0.709720i
$176$	3.77638	−	3.08560i	0.284655	−	0.232586i
$177$		0			0
$178$	5.00787	+	19.6282i	0.375355	+	1.47120i
$179$	−1.87266	+	5.76347i	−0.139970	+	0.430782i	−0.996330	−	0.0855968i	$-0.972720\pi$
$179$	−1.87266	+	5.76347i	−0.139970	+	0.430782i	0.856360	+	0.516379i	$0.172720\pi$
$180$		0			0
$181$	7.06640	+	21.7482i	0.525242	+	1.61653i	0.763837	+	0.645409i	$0.223313\pi$
$181$	7.06640	+	21.7482i	0.525242	+	1.61653i	−0.238596	+	0.971119i	$0.576687\pi$
$182$	1.52781	−	0.966324i	0.113249	−	0.0716287i
$183$		0			0
$184$	5.36175	+	18.7745i	0.395274	+	1.38408i
$185$	−7.43780	−	7.71909i	−0.546838	−	0.567518i
$186$		0			0
$187$	−5.92457	+	0.938360i	−0.433248	+	0.0686197i
$188$	0.736498	−	2.50657i	0.0537147	−	0.182810i
$189$		0			0
$190$	5.92711	+	9.76768i	0.429997	+	0.708622i
$191$	4.71698	−	6.49237i	0.341309	−	0.469771i	−0.603514	−	0.797352i	$-0.706233\pi$
$191$	4.71698	−	6.49237i	0.341309	−	0.469771i	0.944823	+	0.327581i	$0.106233\pi$
$192$		0			0
$193$	7.12358	−	7.12358i	0.512767	−	0.512767i	−0.402606	−	0.915373i	$-0.631896\pi$
$193$	7.12358	−	7.12358i	0.512767	−	0.512767i	0.915373	+	0.402606i	$0.131896\pi$
$194$	−5.79724	+	0.539109i	−0.416218	+	0.0387058i
$195$		0			0
$196$	−3.73076	+	3.94872i	−0.266483	+	0.282051i
$197$	−13.3419	+	6.79803i	−0.950570	+	0.484339i	−0.859292	−	0.511486i	$-0.829095\pi$
$197$	−13.3419	+	6.79803i	−0.950570	+	0.484339i	−0.0912781	+	0.995825i	$0.529095\pi$
$198$		0			0
$199$	4.76131			0.337520			0.168760	−	0.985657i	$-0.446024\pi$
$199$	4.76131			0.337520			0.168760	+	0.985657i	$0.446024\pi$
$200$	−14.0923	+	1.18640i	−0.996475	+	0.0838914i
$201$		0			0
$202$	−18.7644	−	7.46239i	−1.32026	−	0.525052i
$203$	1.84924	−	0.942236i	0.129791	−	0.0661320i
$204$		0			0
$205$	12.3432	+	0.229069i	0.862088	+	0.0159988i
$206$	17.6750	−	1.64367i	1.23148	−	0.114520i
$207$		0			0
$208$	0.524233	+	2.41416i	0.0363490	+	0.167392i
$209$	−2.58912	+	3.56361i	−0.179093	+	0.246500i
$210$		0			0
$211$	0.683337	+	0.940532i	0.0470428	+	0.0647489i	0.831890	−	0.554940i	$-0.187259\pi$
$211$	0.683337	+	0.940532i	0.0470428	+	0.0647489i	−0.784848	+	0.619689i	$0.787259\pi$
$212$	3.50928	−	11.9434i	0.241019	−	0.820273i
$213$		0			0
$214$	−7.14194	+	3.07771i	−0.488213	+	0.210388i
$215$	8.54912	+	1.51716i	0.583045	+	0.103470i
$216$		0			0
$217$	−9.99315	+	19.6127i	−0.678379	+	1.33139i
$218$	6.72110	−	4.25102i	0.455211	−	0.287916i
$219$		0			0
$220$	−2.52287	−	4.83349i	−0.170092	−	0.325874i
$221$	0.939002	−	2.88995i	0.0631641	−	0.194399i
$222$		0			0
$223$	21.2551	+	3.36648i	1.42335	+	0.225436i	0.820147	−	0.572152i	$-0.193891\pi$
$223$	21.2551	+	3.36648i	1.42335	+	0.225436i	0.603202	+	0.797589i	$0.293891\pi$
$224$	5.23595	+	10.4722i	0.349841	+	0.699702i
$225$		0			0
$226$	9.37210	+	2.10988i	0.623423	+	0.140347i
$227$	1.05635	−	6.66952i	0.0701123	−	0.442672i	−0.927513	−	0.373792i	$-0.878057\pi$
$227$	1.05635	−	6.66952i	0.0701123	−	0.442672i	0.997625	−	0.0688800i	$-0.0219425\pi$
$228$		0			0
$229$	−19.0806	−	6.19967i	−1.26088	−	0.409686i	−0.399075	−	0.916918i	$-0.630669\pi$
$229$	−19.0806	−	6.19967i	−1.26088	−	0.409686i	−0.861809	+	0.507232i	$0.830669\pi$
$230$	21.7697	−	1.61765i	1.43545	−	0.106665i
$231$		0			0
$232$	0.342637	+	2.81547i	0.0224952	+	0.184845i
$233$	4.84966	+	2.47103i	0.317712	+	0.161882i	0.605573	−	0.795790i	$-0.292944\pi$
$233$	4.84966	+	2.47103i	0.317712	+	0.161882i	−0.287861	+	0.957672i	$0.592944\pi$
$234$		0			0
$235$	−2.57749	−	1.37412i	−0.168137	−	0.0896378i
$236$	4.83085	+	25.7494i	0.314462	+	1.67614i
$237$		0			0
$238$	0.926120	−	14.3715i	0.0600314	−	0.931568i
$239$	−11.2896	+	8.20235i	−0.730261	+	0.530566i	−0.889646	−	0.456651i	$-0.849049\pi$
$239$	−11.2896	+	8.20235i	−0.730261	+	0.530566i	0.159385	+	0.987217i	$0.449049\pi$
$240$		0			0
$241$	13.3980	+	9.73420i	0.863040	+	0.627035i	0.928710	−	0.370806i	$-0.120919\pi$
$241$	13.3980	+	9.73420i	0.863040	+	0.627035i	−0.0656704	+	0.997841i	$0.520919\pi$
$242$	−8.59185	+	10.3537i	−0.552305	+	0.665559i
$243$		0			0
$244$	18.7425	+	2.42565i	1.19987	+	0.155287i
$245$	3.47819	+	4.97904i	0.222213	+	0.318099i
$246$		0			0
$247$	−1.01304	−	1.98820i	−0.0644582	−	0.126506i
$248$	−20.4913	−	22.0215i	−1.30120	−	1.39837i
$249$		0			0
$250$	−1.89314	+	15.6976i	−0.119733	+	0.992806i
$251$			22.8681i			1.44342i	0.692195	+	0.721711i	$0.256644\pi$
$251$			22.8681i			1.44342i	−0.692195	+	0.721711i	$0.743356\pi$
$252$		0			0
$253$	3.82085	+	7.49883i	0.240215	+	0.471448i
$254$	9.99236	−	16.8377i	0.626976	−	1.05649i
$255$		0			0
$256$	−15.8971	+	1.81210i	−0.993566	+	0.113256i
$257$	17.5555	+	17.5555i	1.09508	+	1.09508i	0.994977	+	0.100106i	$0.0319182\pi$
$257$	17.5555	+	17.5555i	1.09508	+	1.09508i	0.100106	+	0.994977i	$0.468082\pi$
$258$		0			0
$259$	8.02707	+	5.83201i	0.498778	+	0.362383i
$260$	2.76188	−	0.0271194i	0.171285	−	0.00168188i
$261$		0			0
$262$	−2.41516	−	0.155636i	−0.149209	−	0.00961522i
$263$	1.08432	+	6.84611i	0.0668619	+	0.422149i	0.998302	+	0.0582542i	$0.0185534\pi$
$263$	1.08432	+	6.84611i	0.0668619	+	0.422149i	−0.931440	+	0.363895i	$0.881447\pi$
$264$		0			0
$265$	−12.2813	−	6.54745i	−0.754432	−	0.402206i
$266$	−6.98160	−	7.94338i	−0.428069	−	0.487040i
$267$		0			0
$268$	−5.45865	−	15.3079i	−0.333440	−	0.935077i
$269$	−26.2916	+	8.54266i	−1.60303	+	0.520855i	−0.967854	−	0.251514i	$-0.919072\pi$
$269$	−26.2916	+	8.54266i	−1.60303	+	0.520855i	−0.635174	+	0.772369i	$0.719072\pi$
$270$		0			0
$271$	14.4397	+	4.69173i	0.877147	+	0.285002i	0.712772	−	0.701396i	$-0.247439\pi$
$271$	14.4397	+	4.69173i	0.877147	+	0.285002i	0.164375	+	0.986398i	$0.447439\pi$
$272$	18.0139	+	7.92572i	1.09225	+	0.480567i
$273$		0			0
$274$	0.142805	−	0.634340i	0.00862716	−	0.0383219i
$275$	−5.86339	+	1.66731i	−0.353576	+	0.100543i
$276$		0			0
$277$	−18.0952	−	2.86600i	−1.08723	−	0.172201i	−0.413009	−	0.910727i	$-0.635522\pi$
$277$	−18.0952	−	2.86600i	−1.08723	−	0.172201i	−0.674225	+	0.738526i	$0.735522\pi$
$278$	6.38239	−	1.62838i	0.382790	−	0.0976636i
$279$		0			0
$280$	12.6514	−	3.36049i	0.756069	−	0.200828i
$281$	4.45191	+	13.7016i	0.265579	+	0.817368i	0.991559	+	0.129653i	$0.0413863\pi$
$281$	4.45191	+	13.7016i	0.265579	+	0.817368i	−0.725980	+	0.687715i	$0.758614\pi$
$282$		0			0
$283$	13.2557	−	26.0158i	0.787971	−	1.54648i	−0.0487251	−	0.998812i	$-0.515516\pi$
$283$	13.2557	−	26.0158i	0.787971	−	1.54648i	0.836696	−	0.547668i	$-0.184484\pi$
$284$	−12.9052	−	23.6445i	−0.765783	−	1.40304i
$285$		0			0
$286$	0.421418	+	0.977916i	0.0249190	+	0.0578254i
$287$	−11.2863	+	1.78758i	−0.666211	+	0.105517i
$288$		0			0
$289$	−4.23634	−	5.83082i	−0.249197	−	0.342990i
$290$	3.16012	+	0.262603i	0.185569	+	0.0154206i
$291$		0			0
$292$	11.0114	−	8.48778i	0.644391	−	0.496710i
$293$	−3.00790	+	3.00790i	−0.175723	+	0.175723i	−0.789489	−	0.613765i	$-0.789654\pi$
$293$	−3.00790	+	3.00790i	−0.175723	+	0.175723i	0.613765	+	0.789489i	$0.289654\pi$
$294$		0			0
$295$	29.2859	+	0.543495i	1.70509	+	0.0316435i
$296$	−11.2491	+	7.57009i	−0.653840	+	0.440003i
$297$		0			0
$298$	10.2611	−	25.8018i	0.594407	−	1.49466i
$299$	−4.26344			−0.246561
$300$		0			0
$301$	−8.03683			−0.463235
$302$	−12.4266	+	31.2471i	−0.715070	+	1.79807i
$303$		0			0
$304$	13.4693	−	5.23833i	0.772515	−	0.300439i
$305$	6.90112	−	19.9707i	0.395157	−	1.14352i
$306$		0			0
$307$	22.9222	−	22.9222i	1.30824	−	1.30824i	0.385554	−	0.922685i	$-0.374010\pi$
$307$	22.9222	−	22.9222i	1.30824	−	1.30824i	0.922685	−	0.385554i	$-0.125990\pi$
$308$	3.08103	+	3.99707i	0.175558	+	0.227754i
$309$		0			0
$310$	−28.7517	+	17.4468i	−1.63299	+	0.990909i
$311$	−5.82470	−	8.01702i	−0.330289	−	0.454603i	0.611285	−	0.791411i	$-0.290653\pi$
$311$	−5.82470	−	8.01702i	−0.330289	−	0.454603i	−0.941574	+	0.336807i	$0.890653\pi$
$312$		0			0
$313$	−12.2798	+	1.94493i	−0.694097	+	0.109934i	−0.493508	−	0.869741i	$-0.664286\pi$
$313$	−12.2798	+	1.94493i	−0.694097	+	0.109934i	−0.200589	+	0.979675i	$0.564286\pi$
$314$	−1.88655	−	4.37781i	−0.106464	−	0.247054i
$315$		0			0
$316$	12.3425	−	6.73654i	0.694319	−	0.378960i
$317$	−1.92273	+	3.77356i	−0.107991	+	0.211944i	−0.938678	−	0.344796i	$-0.887948\pi$
$317$	−1.92273	+	3.77356i	−0.107991	+	0.211944i	0.830687	+	0.556740i	$0.187948\pi$
$318$		0			0
$319$	0.377785	+	1.16270i	0.0211519	+	0.0650988i
$320$	−1.61690	+	17.8153i	−0.0903872	+	0.995907i
$321$		0			0
$322$	−19.5787	+	4.99524i	−1.09108	+	0.278374i
$323$	−17.5575	−	2.78083i	−0.976924	−	0.154730i
$324$		0			0
$325$	0.595908	−	3.02998i	0.0330550	−	0.168073i
$326$	1.84129	−	8.17902i	0.101980	−	0.452994i
$327$		0			0
$328$	2.99604	−	15.3257i	0.165429	−	0.846218i
$329$	2.57130	+	0.835465i	0.141760	+	0.0460607i
$330$		0			0
$331$	−8.18304	+	2.65883i	−0.449781	+	0.146143i	−0.525144	−	0.851014i	$-0.675988\pi$
$331$	−8.18304	+	2.65883i	−0.449781	+	0.146143i	0.0753630	+	0.997156i	$0.475988\pi$
$332$	13.2735	−	4.73320i	0.728477	−	0.259768i
$333$		0			0
$334$	−12.5295	−	14.2556i	−0.685584	−	0.780030i
$335$	−17.9962	+	2.50897i	−0.983240	+	0.137080i
$336$		0			0
$337$	0.107869	+	0.681059i	0.00587601	+	0.0370997i	0.990452	−	0.137857i	$-0.0440215\pi$
$337$	0.107869	+	0.681059i	0.00587601	+	0.0370997i	−0.984576	+	0.174957i	$0.944021\pi$
$338$	17.8084	+	1.14760i	0.968650	+	0.0624210i
$339$		0			0
$340$	12.7578	−	17.9272i	0.691890	−	0.972238i
$341$	−10.4897	−	7.62121i	−0.568049	−	0.412711i
$342$		0			0
$343$	−14.2199	−	14.2199i	−0.767802	−	0.767802i
$344$	3.76740	−	10.3165i	0.203125	−	0.556227i
$345$		0			0
$346$	11.6382	−	19.6111i	0.625675	−	1.05430i
$347$	11.6804	+	22.9240i	0.627035	+	1.23063i	0.957942	+	0.286962i	$0.0926455\pi$
$347$	11.6804	+	22.9240i	0.627035	+	1.23063i	−0.330907	+	0.943663i	$0.607355\pi$
$348$		0			0
$349$			29.6548i			1.58739i	0.608318	+	0.793694i	$0.291845\pi$
$349$			29.6548i			1.58739i	−0.608318	+	0.793694i	$0.708155\pi$
$350$	−0.813520	−	14.6126i	−0.0434845	−	0.781077i
$351$		0			0
$352$	−6.57513	+	2.08126i	−0.350455	+	0.110932i
$353$	15.1420	+	29.7179i	0.805928	+	1.58172i	0.813368	+	0.581750i	$0.197632\pi$
$353$	15.1420	+	29.7179i	0.805928	+	1.58172i	−0.00744012	+	0.999972i	$0.502368\pi$
$354$		0			0
$355$	−28.8103	+	8.77347i	−1.52909	+	0.465647i
$356$	3.67692	−	28.4107i	0.194876	−	1.50577i
$357$		0			0
$358$	5.47291	−	6.59516i	0.289252	−	0.348565i
$359$	−5.20850	−	3.78419i	−0.274894	−	0.199722i	0.441793	−	0.897117i	$-0.354342\pi$
$359$	−5.20850	−	3.78419i	−0.274894	−	0.199722i	−0.716687	+	0.697395i	$0.754342\pi$
$360$		0			0
$361$	4.81056	−	3.49508i	0.253187	−	0.183951i
$362$	2.07968	−	32.2724i	0.109305	−	1.69620i
$363$		0			0
$364$	−2.51272	+	0.471412i	−0.131702	+	0.0247087i
$365$	−6.79862	−	13.9783i	−0.355856	−	0.731660i
$366$		0			0
$367$	−8.78476	−	4.47606i	−0.458561	−	0.233648i	0.209422	−	0.977825i	$-0.432842\pi$
$367$	−8.78476	−	4.47606i	−0.458561	−	0.233648i	−0.667982	+	0.744177i	$0.732842\pi$
$368$	2.76573	−	27.4738i	0.144173	−	1.43217i
$369$		0			0
$370$	5.74005	+	14.0308i	0.298411	+	0.729424i
$371$	12.2518	+	3.98084i	0.636081	+	0.206675i
$372$		0			0
$373$	−1.58263	+	9.99236i	−0.0819457	+	0.517385i	0.912236	+	0.409666i	$0.134355\pi$
$373$	−1.58263	+	9.99236i	−0.0819457	+	0.517385i	−0.994181	+	0.107719i	$0.965645\pi$
$374$	8.27593	+	1.86311i	0.427938	+	0.0963389i
$375$		0			0
$376$	−2.27779	+	2.90901i	−0.117468	+	0.150021i
$377$	−0.611687	−	0.0968817i	−0.0315035	−	0.00498966i
$378$		0			0
$379$	−5.72788	+	17.6286i	−0.294221	+	0.905521i	0.689260	+	0.724514i	$0.257936\pi$
$379$	−5.72788	+	17.6286i	−0.294221	+	0.905521i	−0.983482	+	0.181007i	$0.942064\pi$
$380$	−2.68422	−	15.9333i	−0.137698	−	0.817363i
$381$		0			0
$382$	−9.59158	+	6.06656i	−0.490748	+	0.310392i
$383$	−4.71055	+	9.24497i	−0.240698	+	0.472396i	−0.979478	−	0.201550i	$-0.935402\pi$
$383$	−4.71055	+	9.24497i	−0.240698	+	0.472396i	0.738781	+	0.673946i	$0.235402\pi$
$384$		0			0
$385$	5.07408	−	2.46787i	0.258599	−	0.125774i
$386$	−13.0840	+	5.63835i	−0.665958	+	0.286984i
$387$		0			0
$388$	7.89995	+	2.32122i	0.401059	+	0.117842i
$389$	−16.6111	−	22.8633i	−0.842217	−	1.15921i	−0.985524	−	0.169535i	$-0.945774\pi$
$389$	−16.6111	−	22.8633i	−0.842217	−	1.15921i	0.143307	−	0.989678i	$-0.454226\pi$
$390$		0			0
$391$	−19.9637	+	27.4777i	−1.00961	+	1.38960i
$392$	6.96625	−	3.23934i	0.351849	−	0.163611i
$393$		0			0
$394$	21.0854	−	1.96081i	1.06227	−	0.0987844i
$395$	−4.57977	−	15.0390i	−0.230433	−	0.756697i
$396$		0			0
$397$	−13.0371	+	6.64271i	−0.654311	+	0.333388i	−0.749436	−	0.662077i	$-0.769675\pi$
$397$	−13.0371	+	6.64271i	−0.654311	+	0.333388i	0.0951247	+	0.995465i	$0.469675\pi$
$398$	−6.25688	−	2.48829i	−0.313629	−	0.124727i
$399$		0			0
$400$	19.1388	+	5.80564i	0.956941	+	0.290282i
$401$	18.3995			0.918829			0.459415	−	0.888222i	$-0.348059\pi$
$401$	18.3995			0.918829			0.459415	+	0.888222i	$0.348059\pi$
$402$		0			0
$403$	5.85239	−	2.98194i	0.291528	−	0.148541i
$404$	20.7586	+	19.6128i	1.03278	+	0.975773i
$405$		0			0
$406$	−2.92252	+	0.271777i	−0.145042	+	0.0134881i
$407$	−4.13270	+	4.13270i	−0.204850	+	0.204850i
$408$		0			0
$409$	1.04712	−	1.44123i	0.0517766	−	0.0712643i	−0.782344	−	0.622847i	$-0.785976\pi$
$409$	1.04712	−	1.44123i	0.0517766	−	0.0712643i	0.834120	+	0.551583i	$0.185976\pi$
$410$	−16.1006	−	6.75165i	−0.795153	−	0.333440i
$411$		0			0
$412$	−24.0859	−	7.07710i	−1.18663	−	0.348664i
$413$	−26.7783	+	4.24127i	−1.31767	+	0.208699i
$414$		0			0
$415$	−2.17553	−	15.6046i	−0.106793	−	0.765998i
$416$	0.572753	−	3.44644i	0.0280815	−	0.168975i
$417$		0			0
$418$	5.26474	−	3.32989i	0.257507	−	0.162870i
$419$	−12.5557	−	38.6425i	−0.613386	−	1.88781i	−0.423108	−	0.906079i	$-0.639061\pi$
$419$	−12.5557	−	38.6425i	−0.613386	−	1.88781i	−0.190279	−	0.981730i	$-0.560939\pi$
$420$		0			0
$421$	2.89797	−	8.91902i	0.141238	−	0.434687i	−0.855270	−	0.518183i	$-0.826609\pi$
$421$	2.89797	−	8.91902i	0.141238	−	0.434687i	0.996508	+	0.0834962i	$0.0266087\pi$
$422$	−0.406452	−	1.59308i	−0.0197858	−	0.0775498i
$423$		0			0
$424$	−10.8532	+	13.8609i	−0.527080	+	0.673145i
$425$	−16.7377	−	18.0286i	−0.811900	−	0.874515i
$426$		0			0
$427$	−3.05951	+	19.3170i	−0.148060	+	0.934814i
$428$	10.9937	−	0.312031i	0.531401	−	0.0150826i
$429$		0			0
$430$	−10.4416	−	6.46154i	−0.503539	−	0.311603i
$431$	−3.54339	+	1.15132i	−0.170679	+	0.0554571i	−0.393110	−	0.919491i	$-0.628601\pi$
$431$	−3.54339	+	1.15132i	−0.170679	+	0.0554571i	0.222431	+	0.974948i	$0.428601\pi$
$432$		0			0
$433$	−5.53878	−	2.82215i	−0.266177	−	0.135624i	0.315809	−	0.948823i	$-0.397724\pi$
$433$	−5.53878	−	2.82215i	−0.266177	−	0.135624i	−0.581986	+	0.813199i	$0.697724\pi$
$434$	23.3818	−	20.5507i	1.12236	−	0.986466i
$435$		0			0
$436$	−11.0539	+	2.07382i	−0.529385	+	0.0993181i
$437$	3.90167	+	24.6342i	0.186642	+	1.17841i
$438$		0			0
$439$	−0.813614	+	0.591125i	−0.0388317	+	0.0282129i	−0.607032	−	0.794678i	$-0.707640\pi$
$439$	−0.813614	+	0.591125i	−0.0388317	+	0.0282129i	0.568200	+	0.822890i	$0.307640\pi$
$440$	0.789318	+	7.67020i	0.0376293	+	0.365662i
$441$		0			0
$442$	−2.74426	+	3.30698i	−0.130531	+	0.157297i
$443$	10.2940	+	10.2940i	0.489083	+	0.489083i	0.908017	−	0.418934i	$-0.137596\pi$
$443$	10.2940	+	10.2940i	0.489083	+	0.489083i	−0.418934	+	0.908017i	$0.637596\pi$
$444$		0			0
$445$	−30.2726	−	10.4610i	−1.43506	−	0.495901i
$446$	−26.1722	−	15.5320i	−1.23929	−	0.735460i
$447$		0			0
$448$	−1.40779	−	16.4979i	−0.0665117	−	0.779454i
$449$		−	18.2346i		−	0.860542i	−0.902700	−	0.430271i	$-0.858418\pi$
$449$		−	18.2346i		−	0.860542i	0.902700	−	0.430271i	$-0.141582\pi$
$450$		0			0
$451$		−	6.73104i		−	0.316952i
$452$	−11.2133	−	7.67052i	−0.527431	−	0.360791i
$453$		0			0
$454$	−4.87369	+	8.21243i	−0.228733	+	0.385428i
$455$	−0.0530363	+	2.85783i	−0.00248638	+	0.133977i
$456$		0			0
$457$	20.4576	+	20.4576i	0.956967	+	0.956967i	0.999112	−	0.0421448i	$-0.0134191\pi$
$457$	20.4576	+	20.4576i	0.956967	+	0.956967i	−0.0421448	+	0.999112i	$0.513419\pi$
$458$	21.8341	+	18.1187i	1.02024	+	0.846631i
$459$		0			0
$460$	−29.4532	−	9.25121i	−1.37326	−	0.431340i
$461$	−1.26163	+	0.916631i	−0.0587602	+	0.0426918i	−0.616778	−	0.787137i	$-0.711562\pi$
$461$	−1.26163	+	0.916631i	−0.0587602	+	0.0426918i	0.558017	+	0.829829i	$0.311562\pi$
$462$		0			0
$463$	1.78849	+	11.2921i	0.0831181	+	0.524787i	0.993755	+	0.111581i	$0.0355913\pi$
$463$	1.78849	+	11.2921i	0.0831181	+	0.524787i	−0.910637	+	0.413207i	$0.864409\pi$
$464$	1.02112	−	3.87890i	0.0474042	−	0.180073i
$465$		0			0
$466$	−5.08161	−	5.78166i	−0.235401	−	0.267830i
$467$	24.5198	+	12.4935i	1.13464	+	0.578129i	0.917391	−	0.397987i	$-0.130291\pi$
$467$	24.5198	+	12.4935i	1.13464	+	0.578129i	0.217251	+	0.976116i	$0.430291\pi$
$468$		0			0
$469$	15.9955	−	5.19726i	0.738604	−	0.239987i
$470$	2.66897	+	3.15275i	0.123111	+	0.145426i
$471$		0			0
$472$	7.10850	−	36.3621i	0.327195	−	1.67370i
$473$	0.740570	−	4.67578i	0.0340515	−	0.214992i
$474$		0			0
$475$	−18.0526	−	0.670280i	−0.828310	−	0.0307546i
$476$	−8.72766	+	18.4018i	−0.400032	+	0.843443i
$477$		0			0
$478$	19.1223	−	4.87880i	0.874634	−	0.223151i
$479$	0.100925	−	0.310615i	0.00461137	−	0.0141923i	−0.948724	−	0.316105i	$-0.897625\pi$
$479$	0.100925	−	0.310615i	0.00461137	−	0.0141923i	0.953336	+	0.301912i	$0.0976250\pi$
$480$		0			0
$481$	−0.914910	−	2.81580i	−0.0417163	−	0.128390i
$482$	−12.5193	−	19.7937i	−0.570237	−	0.901577i
$483$		0			0
$484$	16.7015	−	9.11570i	0.759159	−	0.414350i
$485$	4.33082	−	8.12346i	0.196652	−	0.368867i
$486$		0			0
$487$	5.27724	−	0.835833i	0.239135	−	0.0378752i	−0.0357166	−	0.999362i	$-0.511371\pi$
$487$	5.27724	−	0.835833i	0.239135	−	0.0378752i	0.274851	+	0.961487i	$0.411371\pi$
$488$	−23.3620	−	12.9825i	−1.05755	−	0.587690i
$489$		0			0
$490$	−1.96864	−	8.36073i	−0.0889343	−	0.377699i
$491$	21.9210	−	30.1717i	0.989282	−	1.36163i	0.0576063	−	0.998339i	$-0.481653\pi$
$491$	21.9210	−	30.1717i	0.989282	−	1.36163i	0.931676	−	0.363291i	$-0.118347\pi$
$492$		0			0
$493$	−3.48864	+	3.48864i	−0.157121	+	0.157121i
$494$	0.292200	+	3.14214i	0.0131467	+	0.141371i
$495$		0			0
$496$	15.4193	+	39.6475i	0.692347	+	1.78023i
$497$	24.8380	−	12.6556i	1.11414	−	0.567680i
$498$		0			0
$499$	13.5542			0.606769			0.303385	−	0.952868i	$-0.401883\pi$
$499$	13.5542			0.606769			0.303385	+	0.952868i	$0.401883\pi$
$500$	10.6915	−	19.6391i	0.478137	−	0.878285i
$501$		0			0
$502$	11.9510	−	30.0512i	0.533399	−	1.34125i
$503$	31.6307	−	16.1167i	1.41034	−	0.718606i	0.427668	−	0.903936i	$-0.359335\pi$
$503$	31.6307	−	16.1167i	1.41034	−	0.718606i	0.982676	+	0.185330i	$0.0593353\pi$
$504$		0			0
$505$	26.1751	−	18.2850i	1.16478	−	0.813673i
$506$	−1.10208	−	11.8511i	−0.0489934	−	0.526845i
$507$		0			0
$508$	−21.9305	+	16.9045i	−0.973009	+	0.750015i
$509$	−5.94794	+	8.18664i	−0.263638	+	0.362866i	−0.920229	−	0.391380i	$-0.871998\pi$
$509$	−5.94794	+	8.18664i	−0.263638	+	0.362866i	0.656591	+	0.754247i	$0.271998\pi$
$510$		0			0
$511$	8.45689	+	11.6399i	0.374111	+	0.514919i
$512$	21.8375	+	5.92658i	0.965089	+	0.261920i
$513$		0			0
$514$	−13.8953	−	32.2445i	−0.612894	−	1.42224i
$515$	−13.2041	+	24.7674i	−0.581842	+	1.09138i
$516$		0			0
$517$	−0.723006	+	1.41898i	−0.0317978	+	0.0624067i
$518$	−7.50061	−	11.8589i	−0.329558	−	0.521050i
$519$		0			0
$520$	−3.64359	−	1.40774i	−0.159782	−	0.0617333i
$521$	11.1158	−	34.2110i	0.486994	−	1.49881i	−0.342079	−	0.939671i	$-0.611131\pi$
$521$	11.1158	−	34.2110i	0.486994	−	1.49881i	0.829072	−	0.559141i	$-0.188869\pi$
$522$		0			0
$523$	−22.2065	−	3.51717i	−0.971023	−	0.153795i	−0.349282	−	0.937018i	$-0.613574\pi$
$523$	−22.2065	−	3.51717i	−0.971023	−	0.153795i	−0.621741	+	0.783223i	$0.713574\pi$
$524$	3.09245	+	1.46670i	0.135094	+	0.0640730i
$525$		0			0
$526$	2.15290	−	9.56321i	0.0938710	−	0.416976i
$527$	8.18553	−	51.6814i	0.356567	−	2.25128i
$528$		0			0
$529$	23.4472	+	7.61845i	1.01944	+	0.331237i
$530$	12.7172	+	15.0223i	0.552400	+	0.652528i
$531$		0			0
$532$	5.02333	+	14.0871i	0.217789	+	0.610753i
$533$	3.03816	+	1.54802i	0.131597	+	0.0670521i
$534$		0			0
$535$	2.14858	−	12.1071i	0.0928914	−	0.523437i
$536$	−0.826717	+	22.9689i	−0.0357088	+	0.992107i
$537$		0			0
$538$	39.0145	+	2.51414i	1.68203	+	0.108392i
$539$	2.67906	−	1.94645i	0.115395	−	0.0838397i
$540$		0			0
$541$	16.8088	+	12.2123i	0.722666	+	0.525048i	0.887235	−	0.461318i	$-0.152623\pi$
$541$	16.8088	+	12.2123i	0.722666	+	0.525048i	−0.164569	+	0.986366i	$0.552623\pi$
$542$	−16.5234	−	13.7117i	−0.709739	−	0.588968i
$543$		0			0
$544$	−19.5302	−	19.8294i	−0.837350	−	0.850179i
$545$	−0.233316	+	12.5721i	−0.00999414	+	0.538528i
$546$		0			0
$547$	1.88617	+	3.70181i	0.0806466	+	0.158278i	0.927808	−	0.373057i	$-0.121690\pi$
$547$	1.88617	+	3.70181i	0.0806466	+	0.158278i	−0.847162	+	0.531335i	$0.821690\pi$
$548$	−0.519171	+	0.758962i	−0.0221779	+	0.0324213i
$549$		0			0
$550$	8.57649	+	0.873208i	0.365703	+	0.0372337i
$551$			3.62299i			0.154345i
$552$		0			0
$553$	6.60624	+	12.9655i	0.280926	+	0.551348i
$554$	22.2813	+	13.2229i	0.946640	+	0.561786i
$555$		0			0
$556$	−9.23815	−	1.19560i	−0.391785	−	0.0507048i
$557$	12.9204	+	12.9204i	0.547455	+	0.547455i	0.925704	−	0.378249i	$-0.123474\pi$
$557$	12.9204	+	12.9204i	0.547455	+	0.547455i	−0.378249	+	0.925704i	$0.623474\pi$
$558$		0			0
$559$	1.94016	+	1.40961i	0.0820602	+	0.0596202i
$560$	−18.3816	−	2.19566i	−0.776764	−	0.0927838i
$561$		0			0
$562$	1.31022	−	20.3320i	0.0552682	−	0.857653i
$563$	−0.508973	−	3.21353i	−0.0214506	−	0.135434i	0.974639	−	0.223783i	$-0.0718408\pi$
$563$	−0.508973	−	3.21353i	−0.0214506	−	0.135434i	−0.996090	+	0.0883493i	$0.971841\pi$
$564$		0			0
$565$	−10.9380	+	10.5394i	−0.460166	+	0.443397i
$566$	−31.0155	+	27.2601i	−1.30368	+	1.14583i
$567$		0			0
$568$	4.60210	+	37.8158i	0.193100	+	1.58672i
$569$	18.5217	−	6.01805i	0.776468	−	0.252290i	0.106137	−	0.994352i	$-0.466152\pi$
$569$	18.5217	−	6.01805i	0.776468	−	0.252290i	0.670332	+	0.742062i	$0.266152\pi$
$570$		0			0
$571$	−39.3841	−	12.7967i	−1.64817	−	0.535525i	−0.669832	−	0.742513i	$-0.733634\pi$
$571$	−39.3841	−	12.7967i	−1.64817	−	0.535525i	−0.978343	+	0.206989i	$0.933634\pi$
$572$	−0.0427251	−	1.50532i	−0.00178642	−	0.0629408i
$573$		0			0
$574$	15.7657	+	3.54922i	0.658046	+	0.148142i
$575$	−16.8002	+	30.1513i	−0.700616	+	1.25740i
$576$		0			0
$577$	24.3357	+	3.85440i	1.01311	+	0.160461i	0.640849	−	0.767667i	$-0.278583\pi$
$577$	24.3357	+	3.85440i	1.01311	+	0.160461i	0.372261	+	0.928128i	$0.378583\pi$
$578$	2.51980	+	9.87628i	0.104810	+	0.410799i
$579$		0			0
$580$	−4.01551	−	1.99659i	−0.166735	−	0.0829037i
$581$	4.50655	+	13.8697i	0.186963	+	0.575413i
$582$		0			0
$583$	−3.44500	+	6.76119i	−0.142677	+	0.280020i
$584$	−18.9059	+	5.39928i	−0.782331	+	0.223424i
$585$		0			0
$586$	5.52465	−	2.38076i	0.228221	−	0.0983484i
$587$	−38.9053	+	6.16199i	−1.60579	+	0.254333i	−0.894003	−	0.448060i	$-0.852115\pi$
$587$	−38.9053	+	6.16199i	−1.60579	+	0.254333i	−0.711789	+	0.702393i	$0.752115\pi$
$588$		0			0
$589$	−22.5854	−	31.0862i	−0.930617	−	1.28088i
$590$	−38.2008	−	16.0192i	−1.57270	−	0.659499i
$591$		0			0
$592$	18.7387	−	4.06910i	0.770156	−	0.167239i
$593$	22.6547	−	22.6547i	0.930317	−	0.930317i	−0.0674081	−	0.997725i	$-0.521473\pi$
$593$	22.6547	−	22.6547i	0.930317	−	0.930317i	0.997725	+	0.0674081i	$0.0214730\pi$
$594$		0			0
$595$	18.1702	+	13.7237i	0.744906	+	0.562616i
$596$	−26.9683	+	28.5439i	−1.10467	+	1.16920i
$597$		0			0
$598$	5.60262	+	2.22810i	0.229108	+	0.0911136i
$599$	33.3301			1.36183			0.680916	−	0.732361i	$-0.261582\pi$
$599$	33.3301			1.36183			0.680916	+	0.732361i	$0.261582\pi$
$600$		0			0
$601$	−30.1376			−1.22934			−0.614669	−	0.788785i	$-0.710710\pi$
$601$	−30.1376			−1.22934			−0.614669	+	0.788785i	$0.710710\pi$
$602$	10.5613	+	4.20009i	0.430445	+	0.171183i
$603$		0			0
$604$	32.6598	−	34.5679i	1.32891	−	1.40655i
$605$	−6.19722	−	20.3504i	−0.251953	−	0.827363i
$606$		0			0
$607$	16.1185	−	16.1185i	0.654230	−	0.654230i	−0.299779	−	0.954009i	$-0.596913\pi$
$607$	16.1185	−	16.1185i	0.654230	−	0.654230i	0.954009	+	0.299779i	$0.0969129\pi$
$608$	−20.4377	−	0.155376i	−0.828857	−	0.00630134i
$609$		0			0
$610$	−19.5057	+	22.6372i	−0.789761	+	0.916553i
$611$	−0.474199	−	0.652680i	−0.0191841	−	0.0264046i
$612$		0			0
$613$	−41.4745	+	6.56892i	−1.67514	+	0.265316i	−0.920478	−	0.390795i	$-0.872200\pi$
$613$	−41.4745	+	6.56892i	−1.67514	+	0.265316i	−0.754664	+	0.656112i	$0.772200\pi$
$614$	−42.1016	+	18.1430i	−1.69908	+	0.732193i
$615$		0			0
$616$	−1.95991	−	6.86275i	−0.0789671	−	0.276508i
$617$	−10.3229	+	20.2599i	−0.415585	+	0.815632i	0.584406	+	0.811461i	$0.301327\pi$
$617$	−10.3229	+	20.2599i	−0.415585	+	0.815632i	−0.999991	+	0.00417035i	$0.998673\pi$
$618$		0			0
$619$	−4.80555	−	14.7900i	−0.193151	−	0.594459i	−0.999993	−	0.00369144i	$-0.998825\pi$
$619$	−4.80555	−	14.7900i	−0.193151	−	0.594459i	0.806842	−	0.590768i	$-0.201175\pi$
$620$	46.9007	−	7.90115i	1.88358	−	0.317318i
$621$		0			0
$622$	3.46456	+	13.5793i	0.138916	+	0.544479i
$623$	29.2815	+	4.63774i	1.17314	+	0.185807i
$624$		0			0
$625$	−19.0800	−	16.1540i	−0.763201	−	0.646161i
$626$	17.1535	+	3.86165i	0.685591	+	0.154343i
$627$		0			0
$628$	0.191266	+	6.73884i	0.00763235	+	0.268909i
$629$	−22.4318	−	7.28854i	−0.894415	−	0.290613i
$630$		0			0
$631$	9.56990	−	3.10945i	0.380972	−	0.123785i	−0.112270	−	0.993678i	$-0.535812\pi$
$631$	9.56990	−	3.10945i	0.380972	−	0.123785i	0.493241	+	0.869893i	$0.335812\pi$
$632$	−19.7399	+	2.40231i	−0.785212	+	0.0955586i
$633$		0			0
$634$	4.49876	−	3.95405i	0.178669	−	0.157035i
$635$	13.5403	+	27.8396i	0.537331	+	1.10478i
$636$		0			0
$637$	0.262425	+	1.65689i	0.0103977	+	0.0656482i
$638$	0.111184	−	1.72535i	0.00440181	−	0.0683073i
$639$		0			0
$640$	11.4352	−	22.5663i	0.452014	−	0.892011i
$641$	2.79699	+	2.03213i	0.110474	+	0.0802644i	0.641651	−	0.766997i	$-0.278250\pi$
$641$	2.79699	+	2.03213i	0.110474	+	0.0802644i	−0.531176	+	0.847261i	$0.678250\pi$
$642$		0			0
$643$	17.1130	+	17.1130i	0.674871	+	0.674871i	0.958835	−	0.283964i	$-0.0916496\pi$
$643$	17.1130	+	17.1130i	0.674871	+	0.674871i	−0.283964	+	0.958835i	$0.591650\pi$
$644$	28.3391	+	3.66765i	1.11672	+	0.144526i
$645$		0			0
$646$	21.6192	+	12.8299i	0.850594	+	0.504787i
$647$	−16.5566	−	32.4942i	−0.650909	−	1.27748i	−0.946666	−	0.322217i	$-0.895572\pi$
$647$	−16.5566	−	32.4942i	−0.650909	−	1.27748i	0.295757	−	0.955263i	$-0.404428\pi$
$648$		0			0
$649$		−	15.9703i		−	0.626888i
$650$	−2.36657	+	3.67031i	−0.0928247	+	0.143961i
$651$		0			0
$652$	−6.69405	+	9.78586i	−0.262159	+	0.383244i
$653$	18.6301	+	36.5636i	0.729051	+	1.43084i	0.895623	+	0.444813i	$0.146730\pi$
$653$	18.6301	+	36.5636i	0.729051	+	1.43084i	−0.166573	+	0.986029i	$0.553270\pi$
$654$		0			0
$655$	2.30629	−	3.05354i	0.0901141	−	0.119312i
$656$	−11.9464	+	18.5738i	−0.466428	+	0.725187i
$657$		0			0
$658$	−2.94235	−	2.44167i	−0.114705	−	0.0951861i
$659$	−25.5515	−	18.5642i	−0.995344	−	0.723160i	−0.0342591	−	0.999413i	$-0.510907\pi$
$659$	−25.5515	−	18.5642i	−0.995344	−	0.723160i	−0.961085	+	0.276253i	$0.910907\pi$
$660$		0			0
$661$	−6.57518	+	4.77715i	−0.255745	+	0.185810i	−0.708269	−	0.705943i	$-0.750524\pi$
$661$	−6.57518	+	4.77715i	−0.255745	+	0.185810i	0.452524	+	0.891752i	$0.350524\pi$
$662$	12.1429	+	0.782506i	0.471949	+	0.0304130i
$663$		0			0
$664$	−19.9164	−	0.716848i	−0.772906	−	0.0278191i
$665$	16.5611	−	2.30888i	0.642211	−	0.0895347i
$666$		0			0
$667$	6.16777	+	3.14263i	0.238817	+	0.121683i
$668$	9.01510	+	25.2813i	0.348805	+	0.978165i
$669$		0			0
$670$	24.9602	+	6.10787i	0.964298	+	0.235968i
$671$	−10.9566	−	3.56001i	−0.422974	−	0.137433i
$672$		0			0
$673$	−4.92681	+	31.1067i	−0.189915	+	1.19907i	0.689952	+	0.723855i	$0.257631\pi$
$673$	−4.92681	+	31.1067i	−0.189915	+	1.19907i	−0.879867	+	0.475220i	$0.842369\pi$
$674$	0.214173	−	0.951360i	0.00824965	−	0.0366450i
$675$		0			0
$676$	−22.8025	−	10.8148i	−0.877017	−	0.415955i
$677$	4.81004	+	0.761836i	0.184865	+	0.0292797i	0.248180	−	0.968714i	$-0.420167\pi$
$677$	4.81004	+	0.761836i	0.184865	+	0.0292797i	−0.0633155	+	0.997994i	$0.520167\pi$
$678$		0			0
$679$	−2.63314	+	8.10396i	−0.101050	+	0.311001i
$680$	−26.1340	+	16.8910i	−1.00219	+	0.647740i
$681$		0			0
$682$	9.80172	+	15.4971i	0.375327	+	0.593413i
$683$	−3.12436	+	6.13190i	−0.119550	+	0.234631i	−0.943025	−	0.332723i	$-0.892033\pi$
$683$	−3.12436	+	6.13190i	−0.119550	+	0.234631i	0.823474	+	0.567353i	$0.192033\pi$
$684$		0			0
$685$	0.713350	+	0.740327i	0.0272557	+	0.0282865i
$686$	11.2551	+	26.1179i	0.429722	+	0.997185i
$687$		0			0
$688$	−10.3422	+	11.5881i	−0.394294	+	0.441792i
$689$	−2.25948	−	3.10990i	−0.0860792	−	0.118478i
$690$		0			0
$691$	6.99922	−	9.63360i	0.266263	−	0.366480i	−0.654861	−	0.755750i	$-0.727273\pi$
$691$	6.99922	−	9.63360i	0.266263	−	0.366480i	0.921124	+	0.389270i	$0.127273\pi$
$692$	−25.5428	+	19.6889i	−0.970990	+	0.748459i
$693$		0			0
$694$	−3.36907	−	36.2289i	−0.127888	−	1.37523i
$695$	−3.40156	+	9.84356i	−0.129028	+	0.373387i
$696$		0			0
$697$	24.2032	−	12.3321i	0.916760	−	0.467113i
$698$	15.4978	−	38.9697i	0.586600	−	1.47503i
$699$		0			0
$700$	−6.56757	+	19.6277i	−0.248231	+	0.741858i
$701$	−33.9745			−1.28320			−0.641600	−	0.767040i	$-0.721729\pi$
$701$	−33.9745			−1.28320			−0.641600	+	0.767040i	$0.721729\pi$
$702$		0			0
$703$	−15.4324	+	7.86322i	−0.582045	+	0.296567i
$704$	9.72812	+	0.701193i	0.366642	+	0.0264272i
$705$		0			0
$706$	−4.36754	−	46.9658i	−0.164375	−	1.76758i
$707$	−20.8979	+	20.8979i	−0.785948	+	0.785948i
$708$		0			0
$709$	−9.76306	+	13.4377i	−0.366659	+	0.504663i	−0.951989	−	0.306132i	$-0.900965\pi$
$709$	−9.76306	+	13.4377i	−0.366659	+	0.504663i	0.585330	+	0.810795i	$0.300965\pi$
$710$	42.4450	+	3.52713i	1.59293	+	0.132371i
$711$		0			0
$712$	−19.6795	+	35.4132i	−0.737520	+	1.32717i
$713$	−72.5120	+	11.4848i	−2.71560	+	0.430108i
$714$		0			0
$715$	−1.65778	−	0.294197i	−0.0619974	−	0.0110023i
$716$	−10.6387	+	5.80660i	−0.397586	+	0.217003i
$717$		0			0
$718$	4.86689	+	7.69483i	0.181631	+	0.287169i
$719$	11.5947	+	35.6849i	0.432410	+	1.33082i	0.895717	+	0.444624i	$0.146663\pi$
$719$	11.5947	+	35.6849i	0.432410	+	1.33082i	−0.463307	+	0.886198i	$0.653337\pi$
$720$		0			0
$721$	8.02809	−	24.7079i	0.298982	−	0.920171i
$722$	−8.14815	+	2.07889i	−0.303243	+	0.0773682i
$723$		0			0
$724$	−19.5987	+	41.3226i	−0.728378	+	1.53574i
$725$	−3.09552	+	3.94412i	−0.114965	+	0.146481i
$726$		0			0
$727$	−5.20051	+	32.8348i	−0.192876	+	1.21777i	0.681241	+	0.732059i	$0.261441\pi$
$727$	−5.20051	+	32.8348i	−0.192876	+	1.21777i	−0.874118	+	0.485715i	$0.838559\pi$
$728$	3.54835	+	0.693673i	0.131511	+	0.0257092i
$729$		0			0
$730$	1.62897	+	21.9221i	0.0602911	+	0.811372i
$731$	18.1698	−	5.90372i	0.672033	−	0.218357i
$732$		0			0
$733$	28.4963	+	14.5196i	1.05254	+	0.536294i	0.892607	−	0.450835i	$-0.148874\pi$
$733$	28.4963	+	14.5196i	1.05254	+	0.536294i	0.159928	+	0.987129i	$0.448874\pi$
$734$	9.20493	+	10.4730i	0.339760	+	0.386565i
$735$		0			0
$736$	−17.9924	+	34.6582i	−0.663210	+	1.27752i
$737$	1.54979	+	9.78500i	0.0570873	+	0.360435i
$738$		0			0
$739$	−14.5373	+	10.5619i	−0.534762	+	0.388527i	−0.822136	−	0.569291i	$-0.807218\pi$
$739$	−14.5373	+	10.5619i	−0.534762	+	0.388527i	0.287374	+	0.957818i	$0.407218\pi$
$740$	−0.210501	−	21.4377i	−0.00773818	−	0.788067i
$741$		0			0
$742$	−14.0198	−	11.6341i	−0.514682	−	0.427102i
$743$	13.7539	+	13.7539i	0.504581	+	0.504581i	0.912858	−	0.408277i	$-0.133870\pi$
$743$	13.7539	+	13.7539i	0.504581	+	0.504581i	−0.408277	+	0.912858i	$0.633870\pi$
$744$		0			0
$745$	25.1426	+	35.9917i	0.921153	+	1.31864i
$746$	7.30182	−	12.3040i	0.267338	−	0.450480i
$747$		0			0
$748$	−9.90181	−	6.77337i	−0.362046	−	0.247659i
$749$			11.3816i			0.415875i
$750$		0			0
$751$			1.95838i			0.0714623i	0.999361	+	0.0357311i	$0.0113760\pi$
$751$			1.95838i			0.0714623i	−0.999361	+	0.0357311i	$0.988624\pi$
$752$	4.51352	−	2.63237i	0.164591	−	0.0959927i
$753$		0			0
$754$	0.753193	+	0.446984i	0.0274297	+	0.0162782i
$755$	−30.4487	−	43.5875i	−1.10814	−	1.58631i
$756$		0			0
$757$	−17.8464	−	17.8464i	−0.648640	−	0.648640i	0.304025	−	0.952664i	$-0.401670\pi$
$757$	−17.8464	−	17.8464i	−0.648640	−	0.648640i	−0.952664	+	0.304025i	$0.901670\pi$
$758$	16.7399	−	20.1725i	0.608019	−	0.732698i
$759$		0			0
$760$	−4.79949	+	22.3409i	−0.174096	+	0.810391i
$761$	9.56396	−	6.94862i	0.346693	−	0.251887i	−0.400787	−	0.916171i	$-0.631263\pi$
$761$	9.56396	−	6.94862i	0.346693	−	0.251887i	0.747481	+	0.664284i	$0.231263\pi$
$762$		0			0
$763$	−1.82072	−	11.4956i	−0.0659145	−	0.416168i
$764$	15.7748	−	2.95952i	0.570712	−	0.107072i
$765$		0			0
$766$	11.0216	−	9.68714i	0.398228	−	0.350011i
$767$	7.20842	+	3.67288i	0.260281	+	0.132620i
$768$		0			0
$769$	19.4145	−	6.30814i	0.700103	−	0.227477i	0.0627276	−	0.998031i	$-0.480020\pi$
$769$	19.4145	−	6.30814i	0.700103	−	0.227477i	0.637375	+	0.770553i	$0.280020\pi$
$770$	−7.95761	+	0.591311i	−0.286773	+	0.0213094i
$771$		0			0
$772$	20.1404	−	0.571638i	0.724870	−	0.0205737i
$773$	3.16880	−	20.0070i	0.113974	−	0.719603i	−0.862834	−	0.505487i	$-0.831313\pi$
$773$	3.16880	−	20.0070i	0.113974	−	0.719603i	0.976808	−	0.214116i	$-0.0686870\pi$
$774$		0			0
$775$	1.97301	−	53.1388i	0.0708725	−	1.90880i
$776$	−9.16832	−	7.17890i	−0.329123	−	0.257707i
$777$		0			0
$778$	9.88038	+	38.7259i	0.354229	+	1.38839i
$779$	6.16410	−	18.9711i	0.220852	−	0.679711i
$780$		0			0
$781$	5.07419	+	15.6168i	0.181569	+	0.558812i
$782$	40.5944	−	25.6755i	1.45165	−	0.918155i
$783$		0			0
$784$	−10.8473	+	0.616246i	−0.387404	+	0.0220088i
$785$	7.42134	+	1.31702i	0.264879	+	0.0470065i
$786$		0			0
$787$	49.0348	−	7.76635i	1.74790	−	0.276841i	0.801071	−	0.598570i	$-0.204264\pi$
$787$	49.0348	−	7.76635i	1.74790	−	0.276841i	0.946832	+	0.321729i	$0.104264\pi$
$788$	−28.7332	−	8.44261i	−1.02358	−	0.300755i
$789$		0			0
$790$	−1.84117	+	22.1564i	−0.0655059	+	0.788288i
$791$	8.26401	−	11.3744i	0.293834	−	0.404428i
$792$		0			0
$793$	4.12668	−	4.12668i	0.146543	−	0.146543i
$794$	20.6036	−	1.91601i	0.731195	−	0.0679968i
$795$		0			0
$796$	6.92184	+	6.53976i	0.245338	+	0.231796i
$797$	−10.0858	+	5.13896i	−0.357257	+	0.182031i	−0.623402	−	0.781902i	$-0.714250\pi$
$797$	−10.0858	+	5.13896i	−0.357257	+	0.182031i	0.266145	+	0.963933i	$0.414250\pi$
$798$		0			0
$799$	−6.42694			−0.227369
$800$	−22.1164	−	17.6313i	−0.781935	−	0.623361i
$801$		0			0
$802$	−24.1790	−	9.61570i	−0.853791	−	0.339542i
$803$	−7.55131	+	3.84758i	−0.266480	+	0.135778i
$804$		0			0
$805$	10.4347	−	30.1963i	0.367774	−	1.06428i
$806$	−9.24905	+	0.860106i	−0.325784	+	0.0302960i
$807$		0			0
$808$	−17.0294	−	36.6219i	−0.599091	−	1.28836i
$809$	9.99015	−	13.7503i	0.351235	−	0.483434i	−0.596446	−	0.802653i	$-0.703421\pi$
$809$	9.99015	−	13.7503i	0.351235	−	0.483434i	0.947681	+	0.319220i	$0.103421\pi$
$810$		0			0
$811$	13.4786	+	18.5517i	0.473299	+	0.651440i	0.977200	−	0.212322i	$-0.0681024\pi$
$811$	13.4786	+	18.5517i	0.473299	+	0.651440i	−0.503901	+	0.863761i	$0.668102\pi$
$812$	3.98255	+	1.17018i	0.139760	+	0.0410653i
$813$		0			0
$814$	7.59059	−	3.27105i	0.266050	−	0.114650i
$815$	9.19774	+	9.54559i	0.322183	+	0.334367i
$816$		0			0
$817$	6.36921	−	12.5003i	0.222830	−	0.437329i
$818$	−2.12922	+	1.34671i	−0.0744465	+	0.0470865i
$819$		0			0
$820$	17.6295	+	17.2867i	0.615650	+	0.603677i
$821$	−6.99281	+	21.5217i	−0.244051	+	0.751111i	0.751740	+	0.659459i	$0.229215\pi$
$821$	−6.99281	+	21.5217i	−0.244051	+	0.751111i	−0.995791	+	0.0916520i	$0.970785\pi$
$822$		0			0
$823$	−53.8434	−	8.52795i	−1.87686	−	0.297266i	−0.889646	−	0.456652i	$-0.849049\pi$
$823$	−53.8434	−	8.52795i	−1.87686	−	0.297266i	−0.987216	+	0.159386i	$0.949049\pi$
$824$	27.9530	+	21.8875i	0.973789	+	0.762488i
$825$		0			0
$826$	37.4061	+	8.42100i	1.30153	+	0.293004i
$827$	−2.96544	+	18.7231i	−0.103119	+	0.651065i	0.880941	+	0.473226i	$0.156911\pi$
$827$	−2.96544	+	18.7231i	−0.103119	+	0.651065i	−0.984060	+	0.177839i	$0.943089\pi$
$828$		0			0
$829$	−3.94785	−	1.28273i	−0.137114	−	0.0445512i	0.239656	−	0.970858i	$-0.422965\pi$
$829$	−3.94785	−	1.28273i	−0.137114	−	0.0445512i	−0.376770	+	0.926307i	$0.622965\pi$
$830$	−5.29615	+	21.6431i	−0.183832	+	0.751242i
$831$		0			0
$832$	−2.55379	+	4.22967i	−0.0885366	+	0.146637i
$833$	11.9074	+	6.06710i	0.412566	+	0.210213i
$834$		0			0
$835$	29.7213	−	4.14363i	1.02855	−	0.143396i
$836$	−8.65867	+	1.62446i	−0.299466	+	0.0561830i
$837$		0			0
$838$	−3.69520	+	57.3422i	−0.127649	+	1.98085i
$839$	2.92007	−	2.12156i	0.100812	−	0.0732443i	−0.536237	−	0.844067i	$-0.680155\pi$
$839$	2.92007	−	2.12156i	0.100812	−	0.0732443i	0.637049	+	0.770823i	$0.280155\pi$
$840$		0			0
$841$	−22.6480	−	16.4547i	−0.780965	−	0.567405i
$842$	−8.46938	+	10.2061i	−0.291874	+	0.351725i
$843$		0			0
$844$	−0.298429	+	2.30589i	−0.0102723	+	0.0793721i
$845$	−17.0056	+	22.5155i	−0.585012	+	0.774558i
$846$		0			0
$847$	8.93938	+	17.5445i	0.307161	+	0.602837i
$848$	21.5061	−	12.5428i	0.738524	−	0.430721i
$849$		0			0
$850$	12.5734	+	32.4388i	0.431264	+	1.11264i
$851$			33.0928i			1.13441i
$852$		0			0
$853$	−2.88314	−	5.65849i	−0.0987169	−	0.193743i	0.836366	−	0.548171i	$-0.184676\pi$
$853$	−2.88314	−	5.65849i	−0.0987169	−	0.193743i	−0.935083	+	0.354428i	$0.884676\pi$
$854$	14.1157	−	23.7857i	0.483029	−	0.813930i
$855$		0			0
$856$	−14.6100	−	5.33533i	−0.499360	−	0.182358i
$857$	−0.669915	−	0.669915i	−0.0228838	−	0.0228838i	0.695572	−	0.718456i	$-0.255151\pi$
$857$	−0.669915	−	0.669915i	−0.0228838	−	0.0228838i	−0.718456	+	0.695572i	$0.755151\pi$
$858$		0			0
$859$	6.89179	+	5.00718i	0.235145	+	0.170843i	0.699117	−	0.715007i	$-0.253576\pi$
$859$	6.89179	+	5.00718i	0.235145	+	0.170843i	−0.463973	+	0.885849i	$0.653576\pi$
$860$	10.3446	+	13.9480i	0.352747	+	0.475623i
$861$		0			0
$862$	5.25809	+	0.338838i	0.179091	+	0.0115409i
$863$	1.83066	+	11.5583i	0.0623164	+	0.393451i	0.999057	+	0.0434252i	$0.0138270\pi$
$863$	1.83066	+	11.5583i	0.0623164	+	0.393451i	−0.936740	+	0.350025i	$0.886173\pi$
$864$		0			0
$865$	15.7706	+	32.4252i	0.536216	+	1.10249i
$866$	5.80369	+	6.60321i	0.197217	+	0.224386i
$867$		0			0
$868$	−41.4661	+	14.7864i	−1.40745	+	0.501884i
$869$	−8.15198	+	2.64874i	−0.276537	+	0.0898523i
$870$		0			0
$871$	−4.77303	−	1.55085i	−0.161728	−	0.0525486i
$872$	15.6098	+	3.05158i	0.528614	+	0.103340i
$873$		0			0
$874$	7.74672	−	34.4110i	0.262037	−	1.16397i
$875$	20.0017	+	11.6364i	0.676182	+	0.393382i
$876$		0			0
$877$	27.8979	+	4.41859i	0.942044	+	0.149205i	0.608522	−	0.793537i	$-0.291763\pi$
$877$	27.8979	+	4.41859i	0.942044	+	0.149205i	0.333522	+	0.942742i	$0.391763\pi$
$878$	1.37810	−	0.351604i	0.0465087	−	0.0118661i
$879$		0			0
$880$	2.97124	−	10.4920i	0.100160	−	0.353685i
$881$	−7.87708	−	24.2432i	−0.265386	−	0.816773i	−0.991604	−	0.129309i	$-0.958724\pi$
$881$	−7.87708	−	24.2432i	−0.265386	−	0.816773i	0.726219	−	0.687464i	$-0.241276\pi$
$882$		0			0
$883$	−7.98248	+	15.6665i	−0.268632	+	0.527219i	−0.985434	−	0.170057i	$-0.945605\pi$
$883$	−7.98248	+	15.6665i	−0.268632	+	0.527219i	0.716803	+	0.697276i	$0.245605\pi$
$884$	5.33450	−	2.91158i	0.179419	−	0.0979269i
$885$		0			0
$886$	−8.14775	−	18.9071i	−0.273729	−	0.635198i
$887$	24.9107	−	3.94547i	0.836421	−	0.132476i	0.276491	−	0.961016i	$-0.410828\pi$
$887$	24.9107	−	3.94547i	0.836421	−	0.132476i	0.559929	+	0.828540i	$0.310828\pi$
$888$		0			0
$889$	−16.8430	−	23.1823i	−0.564895	−	0.777511i
$890$	34.3145	+	29.5676i	1.15022	+	0.991107i
$891$		0			0
$892$	26.2761	+	34.0885i	0.879788	+	1.14137i
$893$	−3.33722	+	3.33722i	−0.111676	+	0.111676i
$894$		0			0
$895$	3.94756	+	12.9630i	0.131952	+	0.433305i
$896$	−6.77192	+	22.4158i	−0.226234	+	0.748859i
$897$		0			0
$898$	−9.52948	+	23.9622i	−0.318003	+	0.799629i
$899$	−10.6645			−0.355680
$900$		0			0
$901$	−30.6232			−1.02021
$902$	−3.51768	+	8.84532i	−0.117126	+	0.294517i
$903$		0			0
$904$	10.7269	+	15.9401i	0.356771	+	0.530158i
$905$	40.8027	+	30.8176i	1.35633	+	1.02441i
$906$		0			0
$907$	20.9210	−	20.9210i	0.694669	−	0.694669i	−0.268586	−	0.963256i	$-0.586556\pi$
$907$	20.9210	−	20.9210i	0.694669	−	0.694669i	0.963256	+	0.268586i	$0.0865565\pi$
$908$	10.6964	−	8.24502i	0.354973	−	0.273620i
$909$		0			0
$910$	1.56321	−	3.72778i	0.0518200	−	0.123575i
$911$	−16.8211	−	23.1523i	−0.557309	−	0.767070i	0.433672	−	0.901071i	$-0.357218\pi$
$911$	−16.8211	−	23.1523i	−0.557309	−	0.767070i	−0.990981	+	0.134000i	$0.957218\pi$
$912$		0			0
$913$	−8.48459	+	1.34383i	−0.280799	+	0.0444742i
$914$	−16.1923	−	37.5748i	−0.535593	−	1.24286i
$915$		0			0
$916$	−19.2234	−	35.2205i	−0.635160	−	1.16372i
$917$	−1.60802	+	3.15592i	−0.0531016	+	0.104218i
$918$		0			0
$919$	−7.46481	−	22.9743i	−0.246241	−	0.757853i	−0.995430	−	0.0954962i	$-0.969556\pi$
$919$	−7.46481	−	22.9743i	−0.246241	−	0.757853i	0.749188	−	0.662357i	$-0.230444\pi$
$920$	33.8700	+	27.5495i	1.11666	+	0.908280i
$921$		0			0
$922$	2.13696	−	0.545217i	0.0703771	−	0.0179558i
$923$	−8.21583	−	1.30126i	−0.270427	−	0.0428315i
$924$		0			0
$925$	−23.5187	−	4.62544i	−0.773291	−	0.152083i
$926$	3.55103	−	15.7737i	0.116694	−	0.518356i
$927$		0			0
$928$	−3.36899	+	4.56366i	−0.110593	+	0.149809i
$929$	29.1865	+	9.48327i	0.957579	+	0.311136i	0.745791	−	0.666180i	$-0.232072\pi$
$929$	29.1865	+	9.48327i	0.957579	+	0.311136i	0.211787	+	0.977316i	$0.432072\pi$
$930$		0			0
$931$	9.33333	−	3.03258i	0.305888	−	0.0993889i
$932$	3.65627	+	10.2534i	0.119765	+	0.335862i
$933$		0			0
$934$	−25.6926	−	29.2320i	−0.840686	−	0.956499i
$935$	−9.65869	+	9.30672i	−0.315873	+	0.304362i
$936$		0			0
$937$	−5.74987	−	36.3032i	−0.187840	−	1.18598i	−0.883790	−	0.467885i	$-0.845016\pi$
$937$	−5.74987	−	36.3032i	−0.187840	−	1.18598i	0.695950	−	0.718091i	$-0.254984\pi$
$938$	−23.7360	−	1.52958i	−0.775007	−	0.0499424i
$939$		0			0
$940$	−1.85968	−	5.53788i	−0.0606560	−	0.180626i
$941$	17.5281	+	12.7349i	0.571401	+	0.415147i	0.835614	−	0.549317i	$-0.185112\pi$
$941$	17.5281	+	12.7349i	0.571401	+	0.415147i	−0.264213	+	0.964464i	$0.585112\pi$
$942$		0			0
$943$	−26.9496	−	26.9496i	−0.877599	−	0.877599i
$944$	−28.3444	+	44.0689i	−0.922531	+	1.43432i
$945$		0			0
$946$	−3.41678	+	5.75746i	−0.111089	+	0.187191i
$947$	−15.1008	−	29.6371i	−0.490711	−	0.963075i	−0.995032	−	0.0995587i	$-0.968257\pi$
$947$	−15.1008	−	29.6371i	−0.490711	−	0.963075i	0.504320	−	0.863517i	$-0.331743\pi$
$948$		0			0
$949$		−	4.29327i		−	0.139366i
$950$	23.3728	+	10.3152i	0.758314	+	0.334670i
$951$		0			0
$952$	21.0860	−	19.6208i	0.683400	−	0.635914i
$953$	−12.4971	−	24.5269i	−0.404819	−	0.794503i	0.595139	−	0.803623i	$-0.297097\pi$
$953$	−12.4971	−	24.5269i	−0.404819	−	0.794503i	−0.999958	+	0.00911989i	$0.997097\pi$
$954$		0			0
$955$	0.332961	−	17.9414i	0.0107744	−	0.580569i
$956$	−27.6785	−	3.58215i	−0.895187	−	0.115855i
$957$		0			0
$958$	−0.294955	+	0.355438i	−0.00952957	+	0.0114837i
$959$	−0.769866	−	0.559340i	−0.0248603	−	0.0180620i
$960$		0			0
$961$	66.4244	−	48.2601i	2.14272	−	1.55678i
$962$	−0.269262	+	4.17841i	−0.00868136	+	0.134717i
$963$		0			0
$964$	6.10741	+	32.5537i	0.196706	+	1.04848i
$965$	3.93619	−	22.1802i	0.126711	−	0.714006i
$966$		0			0
$967$	−35.2063	−	17.9385i	−1.13216	−	0.576863i	−0.215487	−	0.976507i	$-0.569134\pi$
$967$	−35.2063	−	17.9385i	−1.13216	−	0.576863i	−0.916671	+	0.399644i	$0.869134\pi$
$968$	−26.7115	+	3.25073i	−0.858541	+	0.104483i
$969$		0			0
$970$	−9.93654	+	8.41181i	−0.319043	+	0.270087i
$971$	15.6458	+	5.08364i	0.502099	+	0.163142i	0.549106	−	0.835753i	$-0.314968\pi$
$971$	15.6458	+	5.08364i	0.502099	+	0.163142i	−0.0470070	+	0.998895i	$0.514968\pi$
$972$		0			0
$973$	1.50803	−	9.52131i	0.0483451	−	0.305239i
$974$	−7.37169	−	1.65954i	−0.236204	−	0.0531751i
$975$		0			0
$976$	23.9155	+	29.2696i	0.765518	+	0.936896i
$977$	1.13863	+	0.180341i	0.0364279	+	0.00576961i	0.174622	−	0.984636i	$-0.444130\pi$
$977$	1.13863	+	0.180341i	0.0364279	+	0.00576961i	−0.138194	+	0.990405i	$0.544130\pi$
$978$		0			0
$979$	−5.39642	+	16.6085i	−0.172470	+	0.530809i
$980$	−1.78235	+	12.0157i	−0.0569351	+	0.383829i
$981$		0			0
$982$	−44.5745	+	28.1929i	−1.42243	+	0.899671i
$983$	0.911754	−	1.78942i	0.0290804	−	0.0570735i	−0.876009	−	0.482294i	$-0.839804\pi$
$983$	0.911754	−	1.78942i	0.0290804	−	0.0570735i	0.905090	+	0.425221i	$0.139804\pi$
$984$		0			0
$985$	−15.7518	+	29.5462i	−0.501894	+	0.941419i
$986$	6.40764	−	2.76127i	0.204061	−	0.0879369i
$987$		0			0
$988$	1.25812	−	4.28182i	0.0400260	−	0.136223i
$989$	−15.7557	−	21.6858i	−0.501002	−	0.689570i
$990$		0			0
$991$	−14.2213	+	19.5739i	−0.451754	+	0.621786i	−0.972773	−	0.231759i	$-0.925552\pi$
$991$	−14.2213	+	19.5739i	−0.451754	+	0.621786i	0.521019	+	0.853545i	$0.325552\pi$
$992$	0.457359	−	60.1594i	0.0145212	−	1.91006i
$993$		0			0
$994$	−39.2537	+	3.65036i	−1.24505	+	0.115782i
$995$	8.72793	−	6.09703i	0.276694	−	0.193289i
$996$		0			0
$997$	38.9735	−	19.8580i	1.23430	−	0.628909i	0.289699	−	0.957118i	$-0.406445\pi$
$997$	38.9735	−	19.8580i	1.23430	−	0.628909i	0.944605	+	0.328209i	$0.106445\pi$
$998$	−17.8117	−	7.08349i	−0.563819	−	0.224224i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.127.5		240
3.2	odd	2		300.2.w.a.127.26	✓	240
4.3	odd	2	inner	900.2.bj.f.127.1		240
12.11	even	2		300.2.w.a.127.30	yes	240
25.13	odd	20	inner	900.2.bj.f.163.1		240
75.38	even	20		300.2.w.a.163.30	yes	240
100.63	even	20	inner	900.2.bj.f.163.5		240
300.263	odd	20		300.2.w.a.163.26	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.26	✓	240	3.2	odd	2
300.2.w.a.127.30	yes	240	12.11	even	2
300.2.w.a.163.26	yes	240	300.263	odd	20
300.2.w.a.163.30	yes	240	75.38	even	20
900.2.bj.f.127.1		240	4.3	odd	2	inner
900.2.bj.f.127.5		240	1.1	even	1	trivial
900.2.bj.f.163.1		240	25.13	odd	20	inner
900.2.bj.f.163.5		240	100.63	even	20	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31411 - 0.522605i) q^{2} +(1.45377 + 1.37352i) q^{4} +(1.83309 - 1.28054i) q^{5} +(-1.46352 + 1.46352i) q^{7} +(-1.19260 - 2.56470i) q^{8} +O(q^{10})\)	\(q+(-1.31411 - 0.522605i) q^{2} +(1.45377 + 1.37352i) q^{4} +(1.83309 - 1.28054i) q^{5} +(-1.46352 + 1.46352i) q^{7} +(-1.19260 - 2.56470i) q^{8} +(-3.07810 + 0.724779i) q^{10} +(-0.716610 - 0.986329i) q^{11} +(0.610002 - 0.0966148i) q^{13} +(2.68808 - 1.15838i) q^{14} +(0.226878 + 3.99356i) q^{16} +(2.23367 - 4.38383i) q^{17} +(-1.11648 - 3.43617i) q^{19} +(4.42373 + 0.656192i) q^{20} +(0.426243 + 1.67065i) q^{22} +(-6.81819 - 1.07989i) q^{23} +(1.72046 - 4.69468i) q^{25} +(-0.852100 - 0.191828i) q^{26} +(-4.13780 + 0.117442i) q^{28} +(-0.953684 - 0.309871i) q^{29} +(10.1146 - 3.28642i) q^{31} +(1.78891 - 5.36654i) q^{32} +(-5.22631 + 4.59351i) q^{34} +(-0.808681 + 4.55687i) q^{35} +(-0.749924 - 4.73483i) q^{37} +(-0.328585 + 5.09899i) q^{38} +(-5.47034 - 3.17418i) q^{40} +(4.46659 + 3.24517i) q^{41} +(2.74571 + 2.74571i) q^{43} +(0.312960 - 2.41817i) q^{44} +(8.39548 + 4.98232i) q^{46} +(-0.593032 - 1.16389i) q^{47} +2.71620i q^{49} +(-4.71434 + 5.27020i) q^{50} +(1.01950 + 0.697395i) q^{52} +(-2.82569 - 5.54573i) q^{53} +(-2.57664 - 0.890388i) q^{55} +(5.49890 + 2.00811i) q^{56} +(1.09131 + 0.905605i) q^{58} +(10.5976 + 7.69958i) q^{59} +(7.64473 - 5.55422i) q^{61} +(-15.0092 - 0.967209i) q^{62} +(-5.15541 + 6.11733i) q^{64} +(0.994471 - 0.958232i) q^{65} +(-7.24032 - 3.68913i) q^{67} +(9.26853 - 3.30507i) q^{68} +(3.44414 - 5.56560i) q^{70} +(-12.8093 - 4.16201i) q^{71} +(1.08745 - 6.86590i) q^{73} +(-1.48897 + 6.61400i) q^{74} +(3.09656 - 6.52891i) q^{76} +(2.49229 + 0.394740i) q^{77} +(2.17258 - 6.68651i) q^{79} +(5.52978 + 7.03004i) q^{80} +(-4.17364 - 6.59877i) q^{82} +(3.19885 - 6.27810i) q^{83} +(-1.51912 - 10.8963i) q^{85} +(-2.17324 - 5.04309i) q^{86} +(-1.67501 + 3.01419i) q^{88} +(-8.41934 - 11.5882i) q^{89} +(-0.751354 + 1.03415i) q^{91} +(-8.42880 - 10.9348i) q^{92} +(0.171053 + 1.83940i) q^{94} +(-6.44675 - 4.86913i) q^{95} +(3.66823 - 1.86906i) q^{97} +(1.41950 - 3.56938i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 240 * q - 12 * q^8	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

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