LMFDB - Embedded newform 630.2.ce.b.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(53,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("630.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.ce (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.6040479020157644046336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 $ x^16 - 7x^12 - 32x^8 - 567*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.3
Root			$0.912166 + 1.47240i$ of defining polynomial
Character	$\chi$	$=$	630.107
Dual form			630.2.ce.b.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-1.21358 + 1.87809i) q^{5} +(0.576028 + 2.58228i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-1.21358 + 1.87809i) q^{5} +(0.576028 + 2.58228i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.12819 - 0.686141i) q^{10} +(-1.41864 + 0.819051i) q^{11} +(1.00000 - 1.00000i) q^{13} +(-2.34521 + 1.22474i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.23769 - 0.599587i) q^{17} +(0.274205 + 0.158312i) q^{19} +(0.111944 - 2.23326i) q^{20} +(-1.15831 - 1.15831i) q^{22} +(-8.03324 + 2.15250i) q^{23} +(-2.05446 - 4.55842i) q^{25} +(1.22474 + 0.707107i) q^{26} +(-1.79000 - 1.94831i) q^{28} +1.19033 q^{29} +(1.50000 + 2.59808i) q^{31} +(0.965926 + 0.258819i) q^{32} -2.31662i q^{34} +(-5.54882 - 2.05197i) q^{35} +(-6.83013 + 1.83013i) q^{37} +(-0.0819485 + 0.305836i) q^{38} +(2.18614 - 0.469882i) q^{40} +2.82843i q^{41} +(5.63325 - 5.63325i) q^{43} +(0.819051 - 1.41864i) q^{44} +(-4.15831 - 7.20241i) q^{46} +(1.63486 + 6.10139i) q^{47} +(-6.33638 + 2.97494i) q^{49} +(3.87137 - 3.16426i) q^{50} +(-0.366025 + 1.36603i) q^{52} +(-3.01091 + 11.2369i) q^{53} +(0.183375 - 3.65831i) q^{55} +(1.41864 - 2.23326i) q^{56} +(0.308079 + 1.14977i) q^{58} +(-1.04294 - 1.80642i) q^{59} +(0.158312 - 0.274205i) q^{61} +(-2.12132 + 2.12132i) q^{62} +1.00000i q^{64} +(0.664513 + 3.09167i) q^{65} +(-0.963836 + 3.59709i) q^{67} +(2.23769 - 0.599587i) q^{68} +(0.545910 - 5.89084i) q^{70} -7.51884i q^{71} +(12.7267 + 3.41012i) q^{73} +(-3.53553 - 6.12372i) q^{74} -0.316625 q^{76} +(-2.93220 - 3.19153i) q^{77} +(8.34264 + 4.81662i) q^{79} +(1.01969 + 1.99004i) q^{80} +(-2.73205 + 0.732051i) q^{82} +(10.0879 + 10.0879i) q^{83} +(3.84169 - 3.47494i) q^{85} +(6.89929 + 3.98331i) q^{86} +(1.58228 + 0.423972i) q^{88} +(7.74273 - 13.4108i) q^{89} +(3.15831 + 2.00626i) q^{91} +(5.88074 - 5.88074i) q^{92} +(-5.47036 + 3.15831i) q^{94} +(-0.630095 + 0.322858i) q^{95} +(-9.15831 - 9.15831i) q^{97} +(-4.51355 - 5.35051i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{7}+O(q^{10}) $ 16 * q + 12 * q^7	$ 16 q + 12 q^{7} + 16 q^{13} + 8 q^{16} + 8 q^{22} - 12 q^{28} + 24 q^{31} - 40 q^{37} + 12 q^{40} - 16 q^{43} - 40 q^{46} + 8 q^{52} + 56 q^{55} - 20 q^{58} - 24 q^{61} - 32 q^{67} + 4 q^{70} + 48 q^{73} + 48 q^{76} - 16 q^{82} + 88 q^{85} - 4 q^{88} + 24 q^{91} - 120 q^{97}+O(q^{100}) $ 16 * q + 12 * q^7 + 16 * q^13 + 8 * q^16 + 8 * q^22 - 12 * q^28 + 24 * q^31 - 40 * q^37 + 12 * q^40 - 16 * q^43 - 40 * q^46 + 8 * q^52 + 56 * q^55 - 20 * q^58 - 24 * q^61 - 32 * q^67 + 4 * q^70 + 48 * q^73 + 48 * q^76 - 16 * q^82 + 88 * q^85 - 4 * q^88 + 24 * q^91 - 120 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.21358	+	1.87809i	−0.542729	+	0.839908i
$5$	−1.21358	+	1.87809i	−0.542729	+	0.839908i
$6$		0			0
$7$	0.576028	+	2.58228i	0.217718	+	0.976012i
$7$	0.576028	+	2.58228i	0.217718	+	0.976012i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−2.12819	−	0.686141i	−0.672994	−	0.216977i
$11$	−1.41864	+	0.819051i	−0.427735	+	0.246953i	−0.698381	−	0.715726i	$-0.746096\pi$
$11$	−1.41864	+	0.819051i	−0.427735	+	0.246953i	0.270646	+	0.962679i	$0.412763\pi$
$12$		0			0
$13$	1.00000	−	1.00000i	0.277350	−	0.277350i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	1.00000	−	1.00000i	0.277350	−	0.277350i	0.832050	+	0.554700i	$0.187167\pi$
$14$	−2.34521	+	1.22474i	−0.626783	+	0.327327i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.23769	−	0.599587i	−0.542719	−	0.145421i	−0.0229637	−	0.999736i	$-0.507310\pi$
$17$	−2.23769	−	0.599587i	−0.542719	−	0.145421i	−0.519755	+	0.854315i	$0.673977\pi$
$18$		0			0
$19$	0.274205	+	0.158312i	0.0629070	+	0.0363194i	0.531124	−	0.847294i	$-0.321770\pi$
$19$	0.274205	+	0.158312i	0.0629070	+	0.0363194i	−0.468217	+	0.883614i	$0.655103\pi$
$20$	0.111944	−	2.23326i	0.0250314	−	0.499373i
$21$		0			0
$22$	−1.15831	−	1.15831i	−0.246953	−	0.246953i
$23$	−8.03324	+	2.15250i	−1.67505	+	0.448827i	−0.966464	−	0.256801i	$-0.917332\pi$
$23$	−8.03324	+	2.15250i	−1.67505	+	0.448827i	−0.708582	+	0.705628i	$0.750665\pi$
$24$		0			0
$25$	−2.05446	−	4.55842i	−0.410891	−	0.911684i
$26$	1.22474	+	0.707107i	0.240192	+	0.138675i
$27$		0			0
$28$	−1.79000	−	1.94831i	−0.338278	−	0.368196i
$29$	1.19033			0.221038			0.110519	−	0.993874i	$-0.464749\pi$
$29$	1.19033			0.221038			0.110519	+	0.993874i	$0.464749\pi$
$30$		0			0
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	0.968709	−	0.248199i	$-0.0798387\pi$
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	−0.699301	+	0.714827i	$0.746505\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$		0			0
$34$		−	2.31662i		−	0.397298i
$35$	−5.54882	−	2.05197i	−0.937922	−	0.346846i
$36$		0			0
$37$	−6.83013	+	1.83013i	−1.12287	+	0.300871i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	−6.83013	+	1.83013i	−1.12287	+	0.300871i	−0.350823	+	0.936442i	$0.614098\pi$
$38$	−0.0819485	+	0.305836i	−0.0132938	+	0.0496132i
$39$		0			0
$40$	2.18614	−	0.469882i	0.345659	−	0.0742949i
$41$			2.82843i			0.441726i	0.975305	+	0.220863i	$0.0708874\pi$
$41$			2.82843i			0.441726i	−0.975305	+	0.220863i	$0.929113\pi$
$42$		0			0
$43$	5.63325	−	5.63325i	0.859063	−	0.859063i	−0.132165	−	0.991228i	$-0.542193\pi$
$43$	5.63325	−	5.63325i	0.859063	−	0.859063i	0.991228	+	0.132165i	$0.0421929\pi$
$44$	0.819051	−	1.41864i	0.123477	−	0.213868i
$45$		0			0
$46$	−4.15831	−	7.20241i	−0.613110	−	1.06194i
$47$	1.63486	+	6.10139i	0.238469	+	0.889979i	0.976554	+	0.215272i	$0.0690637\pi$
$47$	1.63486	+	6.10139i	0.238469	+	0.889979i	−0.738085	+	0.674708i	$0.764270\pi$
$48$		0			0
$49$	−6.33638	+	2.97494i	−0.905198	+	0.424991i
$50$	3.87137	−	3.16426i	0.547494	−	0.447494i
$51$		0			0
$52$	−0.366025	+	1.36603i	−0.0507586	+	0.189434i
$53$	−3.01091	+	11.2369i	−0.413580	+	1.54350i	0.374084	+	0.927395i	$0.377957\pi$
$53$	−3.01091	+	11.2369i	−0.413580	+	1.54350i	−0.787663	+	0.616106i	$0.788709\pi$
$54$		0			0
$55$	0.183375	−	3.65831i	0.0247263	−	0.493287i
$56$	1.41864	−	2.23326i	0.189573	−	0.298432i
$57$		0			0
$58$	0.308079	+	1.14977i	0.0404528	+	0.150972i
$59$	−1.04294	−	1.80642i	−0.135779	−	0.235176i	0.790116	−	0.612958i	$-0.210020\pi$
$59$	−1.04294	−	1.80642i	−0.135779	−	0.235176i	−0.925895	+	0.377782i	$0.876687\pi$
$60$		0			0
$61$	0.158312	−	0.274205i	0.0202698	−	0.0351084i	−0.855713	−	0.517451i	$-0.826881\pi$
$61$	0.158312	−	0.274205i	0.0202698	−	0.0351084i	0.875982	+	0.482343i	$0.160214\pi$
$62$	−2.12132	+	2.12132i	−0.269408	+	0.269408i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	0.664513	+	3.09167i	0.0824227	+	0.383474i
$66$		0			0
$67$	−0.963836	+	3.59709i	−0.117751	+	0.439454i	−0.999478	−	0.0323066i	$-0.989715\pi$
$67$	−0.963836	+	3.59709i	−0.117751	+	0.439454i	0.881727	+	0.471761i	$0.156381\pi$
$68$	2.23769	−	0.599587i	0.271359	−	0.0727106i
$69$		0			0
$70$	0.545910	−	5.89084i	0.0652487	−	0.704090i
$71$		−	7.51884i		−	0.892322i	−0.894953	−	0.446161i	$-0.852791\pi$
$71$		−	7.51884i		−	0.892322i	0.894953	−	0.446161i	$-0.147209\pi$
$72$		0			0
$73$	12.7267	+	3.41012i	1.48955	+	0.399125i	0.909586	−	0.415516i	$-0.136399\pi$
$73$	12.7267	+	3.41012i	1.48955	+	0.399125i	0.579967	+	0.814640i	$0.303065\pi$
$74$	−3.53553	−	6.12372i	−0.410997	−	0.711868i
$75$		0			0
$76$	−0.316625			−0.0363194
$77$	−2.93220	−	3.19153i	−0.334155	−	0.363708i
$78$		0			0
$79$	8.34264	+	4.81662i	0.938620	+	0.541913i	0.889528	−	0.456882i	$-0.151034\pi$
$79$	8.34264	+	4.81662i	0.938620	+	0.541913i	0.0490927	+	0.998794i	$0.484367\pi$
$80$	1.01969	+	1.99004i	0.114004	+	0.222493i
$81$		0			0
$82$	−2.73205	+	0.732051i	−0.301705	+	0.0808415i
$83$	10.0879	+	10.0879i	1.10730	+	1.10730i	0.993505	+	0.113790i	$0.0362992\pi$
$83$	10.0879	+	10.0879i	1.10730	+	1.10730i	0.113790	+	0.993505i	$0.463701\pi$
$84$		0			0
$85$	3.84169	−	3.47494i	0.416690	−	0.376910i
$86$	6.89929	+	3.98331i	0.743970	+	0.429531i
$87$		0			0
$88$	1.58228	+	0.423972i	0.168672	+	0.0451955i
$89$	7.74273	−	13.4108i	0.820728	−	1.42154i	−0.0844133	−	0.996431i	$-0.526902\pi$
$89$	7.74273	−	13.4108i	0.820728	−	1.42154i	0.905141	−	0.425111i	$-0.139765\pi$
$90$		0			0
$91$	3.15831	+	2.00626i	0.331081	+	0.210313i
$92$	5.88074	−	5.88074i	0.613110	−	0.613110i
$93$		0			0
$94$	−5.47036	+	3.15831i	−0.564224	+	0.325755i
$95$	−0.630095	+	0.322858i	−0.0646463	+	0.0331245i
$96$		0			0
$97$	−9.15831	−	9.15831i	−0.929886	−	0.929886i	0.0678124	−	0.997698i	$-0.478398\pi$
$97$	−9.15831	−	9.15831i	−0.929886	−	0.929886i	−0.997698	+	0.0678124i	$0.978398\pi$
$98$	−4.51355	−	5.35051i	−0.455937	−	0.540483i
$99$		0			0
$100$	4.05842	+	2.92048i	0.405842	+	0.292048i
$101$	9.73657	−	5.62141i	0.968825	−	0.559351i	0.0699470	−	0.997551i	$-0.477717\pi$
$101$	9.73657	−	5.62141i	0.968825	−	0.559351i	0.898878	+	0.438200i	$0.144384\pi$
$102$		0			0
$103$	3.52601	+	13.1593i	0.347428	+	1.29662i	0.889749	+	0.456449i	$0.150879\pi$
$103$	3.52601	+	13.1593i	0.347428	+	1.29662i	−0.542321	+	0.840171i	$0.682454\pi$
$104$	−1.41421			−0.138675
$105$		0			0
$106$	−11.6332			−1.12992
$107$	−0.0949220	−	0.354254i	−0.00917646	−	0.0342470i	0.961186	−	0.275902i	$-0.0889765\pi$
$107$	−0.0949220	−	0.354254i	−0.00917646	−	0.0342470i	−0.970362	+	0.241655i	$0.922310\pi$
$108$		0			0
$109$	−8.02502	+	4.63325i	−0.768658	+	0.443785i	−0.832396	−	0.554182i	$-0.813031\pi$
$109$	−8.02502	+	4.63325i	−0.768658	+	0.443785i	0.0637378	+	0.997967i	$0.479698\pi$
$110$	3.58112	−	0.769714i	0.341446	−	0.0733894i
$111$		0			0
$112$	2.52434	+	0.792287i	0.238528	+	0.0748641i
$113$	−1.41421	−	1.41421i	−0.133038	−	0.133038i	0.637452	−	0.770490i	$-0.279988\pi$
$113$	−1.41421	−	1.41421i	−0.133038	−	0.133038i	−0.770490	+	0.637452i	$0.779988\pi$
$114$		0			0
$115$	5.70637	−	17.6994i	0.532122	−	1.65048i
$116$	−1.03085	+	0.595163i	−0.0957123	+	0.0552595i
$117$		0			0
$118$	1.47494	−	1.47494i	0.135779	−	0.135779i
$119$	0.259332	−	6.12372i	0.0237729	−	0.561361i
$120$		0			0
$121$	−4.15831	+	7.20241i	−0.378028	+	0.654764i
$122$	0.305836	+	0.0819485i	0.0276891	+	0.00741927i
$123$		0			0
$124$	−2.59808	−	1.50000i	−0.233314	−	0.134704i
$125$	11.0544	+	1.67355i	0.988734	+	0.149686i
$126$		0			0
$127$	11.7916	+	11.7916i	1.04633	+	1.04633i	0.998873	+	0.0474587i	$0.0151123\pi$
$127$	11.7916	+	11.7916i	1.04633	+	1.04633i	0.0474587	+	0.998873i	$0.484888\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$		0			0
$130$	−2.81433	+	1.44205i	−0.246834	+	0.126476i
$131$	14.8908	+	8.59723i	1.30102	+	0.751143i	0.980579	−	0.196126i	$-0.0628362\pi$
$131$	14.8908	+	8.59723i	1.30102	+	0.751143i	0.320439	+	0.947269i	$0.396170\pi$
$132$		0			0
$133$	−0.250858	+	0.799268i	−0.0217521	+	0.0693053i
$134$	−3.72398			−0.321703
$135$		0			0
$136$	1.15831	+	2.00626i	0.0993245	+	0.172035i
$137$	−17.3867	−	4.65874i	−1.48544	−	0.398023i	−0.577247	−	0.816569i	$-0.695873\pi$
$137$	−17.3867	−	4.65874i	−1.48544	−	0.398023i	−0.908196	+	0.418546i	$0.862540\pi$
$138$		0			0
$139$			13.2665i			1.12525i	0.826712	+	0.562625i	$0.190208\pi$
$139$			13.2665i			1.12525i	−0.826712	+	0.562625i	$0.809792\pi$
$140$	5.83141	−	0.997353i	0.492844	−	0.0842917i
$141$		0			0
$142$	7.26264	−	1.94602i	0.609468	−	0.163306i
$143$	−0.599587	+	2.23769i	−0.0501400	+	0.187125i
$144$		0			0
$145$	−1.44455	+	2.23554i	−0.119964	+	0.185652i
$146$			13.1757i			1.09043i
$147$		0			0
$148$	5.00000	−	5.00000i	0.410997	−	0.410997i
$149$	3.53553	−	6.12372i	0.289642	−	0.501675i	−0.684082	−	0.729405i	$-0.739797\pi$
$149$	3.53553	−	6.12372i	0.289642	−	0.501675i	0.973724	+	0.227730i	$0.0731303\pi$
$150$		0			0
$151$	−11.6583	−	20.1928i	−0.948740	−	1.64327i	−0.748084	−	0.663604i	$-0.769026\pi$
$151$	−11.6583	−	20.1928i	−0.948740	−	1.64327i	−0.200656	−	0.979662i	$-0.564307\pi$
$152$	−0.0819485	−	0.305836i	−0.00664690	−	0.0248066i
$153$		0			0
$154$	2.32387	−	3.65831i	0.187263	−	0.294795i
$155$	−6.69979	−	0.335831i	−0.538140	−	0.0269746i
$156$		0			0
$157$	−3.77615	+	14.0928i	−0.301369	+	1.12473i	0.634657	+	0.772794i	$0.281142\pi$
$157$	−3.77615	+	14.0928i	−0.301369	+	1.12473i	−0.936026	+	0.351931i	$0.885525\pi$
$158$	−2.49327	+	9.30500i	−0.198354	+	0.740266i
$159$		0			0
$160$	−1.65831	+	1.50000i	−0.131101	+	0.118585i
$161$	−10.1857	−	19.5042i	−0.802749	−	1.53715i
$162$		0			0
$163$	4.37396	+	16.3238i	0.342595	+	1.27858i	0.895397	+	0.445269i	$0.146892\pi$
$163$	4.37396	+	16.3238i	0.342595	+	1.27858i	−0.552802	+	0.833313i	$0.686441\pi$
$164$	−1.41421	−	2.44949i	−0.110432	−	0.191273i
$165$		0			0
$166$	−7.13325	+	12.3552i	−0.553648	+	0.958946i
$167$	−5.65685	+	5.65685i	−0.437741	+	0.437741i	−0.891251	−	0.453510i	$-0.850171\pi$
$167$	−5.65685	+	5.65685i	−0.437741	+	0.437741i	0.453510	+	0.891251i	$0.350171\pi$
$168$		0			0
$169$			11.0000i			0.846154i
$170$	4.35083	+	2.81141i	0.333694	+	0.215625i
$171$		0			0
$172$	−2.06191	+	7.69516i	−0.157219	+	0.586751i
$173$	19.2217	−	5.15043i	1.46140	−	0.391580i	0.561425	−	0.827528i	$-0.310253\pi$
$173$	19.2217	−	5.15043i	1.46140	−	0.391580i	0.899972	+	0.435947i	$0.143587\pi$
$174$		0			0
$175$	10.5877	−	7.93097i	0.800356	−	0.599525i
$176$			1.63810i			0.123477i
$177$		0			0
$178$	14.9578	+	4.00793i	1.12114	+	0.300407i
$179$	−0.707107	−	1.22474i	−0.0528516	−	0.0915417i	0.838389	−	0.545072i	$-0.183498\pi$
$179$	−0.707107	−	1.22474i	−0.0528516	−	0.0915417i	−0.891241	+	0.453530i	$0.850164\pi$
$180$		0			0
$181$	11.3668			0.844884			0.422442	−	0.906390i	$-0.361173\pi$
$181$	11.3668			0.844884			0.422442	+	0.906390i	$0.361173\pi$
$182$	−1.12046	+	3.56995i	−0.0830542	+	0.264623i
$183$		0			0
$184$	7.20241	+	4.15831i	0.530969	+	0.306555i
$185$	4.85175	−	15.0486i	0.356708	−	1.10640i
$186$		0			0
$187$	3.66556	−	0.982183i	0.268052	−	0.0718244i
$188$	−4.46653	−	4.46653i	−0.325755	−	0.325755i
$189$		0			0
$190$	−0.474937	−	0.525063i	−0.0344556	−	0.0380921i
$191$	1.67392	+	0.966438i	0.121121	+	0.0699290i	0.559336	−	0.828941i	$-0.311056\pi$
$191$	1.67392	+	0.966438i	0.121121	+	0.0699290i	−0.438216	+	0.898870i	$0.644389\pi$
$192$		0			0
$193$	−3.38083	−	0.905890i	−0.243357	−	0.0652074i	0.135079	−	0.990835i	$-0.456871\pi$
$193$	−3.38083	−	0.905890i	−0.243357	−	0.0652074i	−0.378436	+	0.925627i	$0.623538\pi$
$194$	6.47590	−	11.2166i	0.464943	−	0.805305i
$195$		0			0
$196$	4.00000	−	5.74456i	0.285714	−	0.410326i
$197$	−9.82861	+	9.82861i	−0.700259	+	0.700259i	−0.964466	−	0.264207i	$-0.914890\pi$
$197$	−9.82861	+	9.82861i	−0.700259	+	0.700259i	0.264207	+	0.964466i	$0.414890\pi$
$198$		0			0
$199$	7.47661	−	4.31662i	0.530003	−	0.305997i	−0.211015	−	0.977483i	$-0.567677\pi$
$199$	7.47661	−	4.31662i	0.530003	−	0.305997i	0.741018	+	0.671485i	$0.234343\pi$
$200$	−1.77057	+	4.67601i	−0.125198	+	0.330644i
$201$		0			0
$202$	7.94987	+	7.94987i	0.559351	+	0.559351i
$203$	0.685661	+	3.07376i	0.0481240	+	0.215736i
$204$		0			0
$205$	−5.31205	−	3.43252i	−0.371009	−	0.239737i
$206$	−11.7983	+	6.81174i	−0.822025	+	0.474596i
$207$		0			0
$208$	−0.366025	−	1.36603i	−0.0253793	−	0.0947168i
$209$	−0.518663			−0.0358767
$210$		0			0
$211$	14.9499			1.02919			0.514596	−	0.857433i	$-0.327942\pi$
$211$	14.9499			1.02919			0.514596	+	0.857433i	$0.327942\pi$
$212$	−3.01091	−	11.2369i	−0.206790	−	0.771750i
$213$		0			0
$214$	0.317615	−	0.183375i	0.0217117	−	0.0125353i
$215$	3.74337	+	17.4161i	0.255296	+	1.18777i
$216$		0			0
$217$	−5.84493	+	5.36999i	−0.396780	+	0.364539i
$218$	−6.55240	−	6.55240i	−0.443785	−	0.443785i
$219$		0			0
$220$	1.67035	+	3.25988i	0.112615	+	0.219781i
$221$	−2.83727	+	1.63810i	−0.190856	+	0.110191i
$222$		0			0
$223$	−12.8417	+	12.8417i	−0.859943	+	0.859943i	−0.991331	−	0.131388i	$-0.958057\pi$
$223$	−12.8417	+	12.8417i	−0.859943	+	0.859943i	0.131388	+	0.991331i	$0.458057\pi$
$224$	−0.111944	+	2.64338i	−0.00747956	+	0.176618i
$225$		0			0
$226$	1.00000	−	1.73205i	0.0665190	−	0.115214i
$227$	22.5221	+	6.03479i	1.49485	+	0.400543i	0.911370	−	0.411588i	$-0.135026\pi$
$227$	22.5221	+	6.03479i	1.49485	+	0.400543i	0.583476	+	0.812130i	$0.301692\pi$
$228$		0			0
$229$	−22.5167	−	13.0000i	−1.48794	−	0.859064i	−0.488037	−	0.872823i	$-0.662287\pi$
$229$	−22.5167	−	13.0000i	−1.48794	−	0.859064i	−0.999905	+	0.0137585i	$0.995620\pi$
$230$	18.5732	+	0.930994i	1.22468	+	0.0613879i
$231$		0			0
$232$	−0.841688	−	0.841688i	−0.0552595	−	0.0552595i
$233$	−1.01434	+	0.271793i	−0.0664518	+	0.0178057i	−0.291892	−	0.956451i	$-0.594285\pi$
$233$	−1.01434	+	0.271793i	−0.0664518	+	0.0178057i	0.225440	+	0.974257i	$0.427618\pi$
$234$		0			0
$235$	−13.4430	−	4.33409i	−0.876925	−	0.282725i
$236$	1.80642	+	1.04294i	0.117588	+	0.0678895i
$237$		0			0
$238$	5.98218	−	1.33444i	0.387767	−	0.0864990i
$239$	−10.3473			−0.669309			−0.334655	−	0.942341i	$-0.608620\pi$
$239$	−10.3473			−0.669309			−0.334655	+	0.942341i	$0.608620\pi$
$240$		0			0
$241$	−13.2916	−	23.0217i	−0.856185	−	1.48296i	−0.875542	−	0.483143i	$-0.839495\pi$
$241$	−13.2916	−	23.0217i	−0.856185	−	1.48296i	0.0193567	−	0.999813i	$-0.493838\pi$
$242$	−8.03324	−	2.15250i	−0.516396	−	0.138368i
$243$		0			0
$244$			0.316625i			0.0202698i
$245$	2.10249	−	15.5106i	0.134323	−	0.990938i
$246$		0			0
$247$	0.432518	−	0.115893i	0.0275204	−	0.00737408i
$248$	0.776457	−	2.89778i	0.0493051	−	0.184009i
$249$		0			0
$250$	1.24456	+	11.1109i	0.0787131	+	0.702712i
$251$		−	15.7093i		−	0.991565i	−0.868447	−	0.495783i	$-0.834881\pi$
$251$		−	15.7093i		−	0.991565i	0.868447	−	0.495783i	$-0.165119\pi$
$252$		0			0
$253$	9.63325	−	9.63325i	0.605637	−	0.605637i
$254$	−8.33789	+	14.4417i	−0.523166	+	0.906150i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.36307	−	5.08705i	−0.0850260	−	0.317321i	0.910293	−	0.413964i	$-0.135856\pi$
$257$	−1.36307	−	5.08705i	−0.0850260	−	0.317321i	−0.995319	+	0.0966430i	$0.969189\pi$
$258$		0			0
$259$	−8.66025	−	16.5831i	−0.538122	−	1.03043i
$260$	−2.12132	−	2.34521i	−0.131559	−	0.145444i
$261$		0			0
$262$	−4.45025	+	16.6086i	−0.274937	+	1.02608i
$263$	−7.13904	+	26.6433i	−0.440212	+	1.64289i	0.288065	+	0.957611i	$0.406988\pi$
$263$	−7.13904	+	26.6433i	−0.440212	+	1.64289i	−0.728277	+	0.685283i	$0.759679\pi$
$264$		0			0
$265$	−17.4499	−	19.2916i	−1.07194	−	1.18507i
$266$	−0.836960	−	0.0354442i	−0.0513173	−	0.00217322i
$267$		0			0
$268$	−0.963836	−	3.59709i	−0.0588757	−	0.219727i
$269$	13.7709	+	23.8518i	0.839624	+	1.45427i	0.890209	+	0.455552i	$0.150558\pi$
$269$	13.7709	+	23.8518i	0.839624	+	1.45427i	−0.0505850	+	0.998720i	$0.516109\pi$
$270$		0			0
$271$	−5.34169	+	9.25207i	−0.324484	+	0.562023i	−0.981408	−	0.191934i	$-0.938524\pi$
$271$	−5.34169	+	9.25207i	−0.324484	+	0.562023i	0.656923	+	0.753957i	$0.271857\pi$
$272$	−1.63810	+	1.63810i	−0.0993245	+	0.0993245i
$273$		0			0
$274$		−	18.0000i		−	1.08742i
$275$	6.64811	+	4.78404i	0.400896	+	0.288489i
$276$		0			0
$277$	4.85588	−	18.1224i	0.291761	−	1.08887i	−0.651994	−	0.758224i	$-0.726067\pi$
$277$	4.85588	−	18.1224i	0.291761	−	1.08887i	0.943756	−	0.330644i	$-0.107266\pi$
$278$	−12.8145	+	3.43362i	−0.768560	+	0.205935i
$279$		0			0
$280$	2.47265	+	5.37457i	0.147769	+	0.321192i
$281$		−	19.7990i		−	1.18111i	−0.806998	−	0.590554i	$-0.798909\pi$
$281$		−	19.7990i		−	1.18111i	0.806998	−	0.590554i	$-0.201091\pi$
$282$		0			0
$283$	−7.26264	−	1.94602i	−0.431719	−	0.115679i	0.0364138	−	0.999337i	$-0.488407\pi$
$283$	−7.26264	−	1.94602i	−0.431719	−	0.115679i	−0.468133	+	0.883658i	$0.655073\pi$
$284$	3.75942	+	6.51151i	0.223081	+	0.386387i
$285$		0			0
$286$	−2.31662			−0.136985
$287$	−7.30380	+	1.62925i	−0.431130	+	0.0961718i
$288$		0			0
$289$	−10.0747	−	5.81662i	−0.592629	−	0.342154i
$290$	−2.53325	−	0.816731i	−0.148757	−	0.0479601i
$291$		0			0
$292$	−12.7267	+	3.41012i	−0.744776	+	0.199562i
$293$	0.707107	+	0.707107i	0.0413096	+	0.0413096i	0.727460	−	0.686150i	$-0.240701\pi$
$293$	0.707107	+	0.707107i	0.0413096	+	0.0413096i	−0.686150	+	0.727460i	$0.740701\pi$
$294$		0			0
$295$	4.65831	+	0.233501i	0.271217	+	0.0135949i
$296$	6.12372	+	3.53553i	0.355934	+	0.205499i
$297$		0			0
$298$	6.83013	+	1.83013i	0.395659	+	0.106016i
$299$	−5.88074	+	10.1857i	−0.340092	+	0.589057i
$300$		0			0
$301$	17.7916	+	11.3017i	1.02549	+	0.651421i
$302$	16.4873	−	16.4873i	0.948740	−	0.948740i
$303$		0			0
$304$	0.274205	−	0.158312i	0.0157267	−	0.00907984i
$305$	0.322858	+	0.630095i	0.0184868	+	0.0360791i
$306$		0			0
$307$	−9.00000	−	9.00000i	−0.513657	−	0.513657i	0.401988	−	0.915645i	$-0.368319\pi$
$307$	−9.00000	−	9.00000i	−0.513657	−	0.513657i	−0.915645	+	0.401988i	$0.868319\pi$
$308$	4.13512	+	1.29785i	0.235620	+	0.0739517i
$309$		0			0
$310$	−1.40965	−	6.55842i	−0.0800625	−	0.372493i
$311$	4.51119	−	2.60454i	0.255806	−	0.147690i	−0.366614	−	0.930373i	$-0.619483\pi$
$311$	4.51119	−	2.60454i	0.255806	−	0.147690i	0.622420	+	0.782683i	$0.286150\pi$
$312$		0			0
$313$	−2.00397	−	7.47890i	−0.113271	−	0.422733i	0.885881	−	0.463913i	$-0.153555\pi$
$313$	−2.00397	−	7.47890i	−0.113271	−	0.422733i	−0.999152	+	0.0411802i	$0.986888\pi$
$314$	−14.5899			−0.823356
$315$		0			0
$316$	−9.63325			−0.541913
$317$	−4.12813	−	15.4064i	−0.231859	−	0.865309i	−0.979540	−	0.201251i	$-0.935499\pi$
$317$	−4.12813	−	15.4064i	−0.231859	−	0.865309i	0.747681	−	0.664058i	$-0.231167\pi$
$318$		0			0
$319$	−1.68864	+	0.974937i	−0.0945457	+	0.0545860i
$320$	−1.87809	−	1.21358i	−0.104989	−	0.0678411i
$321$		0			0
$322$	16.2034	−	14.8867i	0.902978	−	0.829605i
$323$	−0.518663	−	0.518663i	−0.0288592	−	0.0288592i
$324$		0			0
$325$	−6.61288	−	2.50397i	−0.366816	−	0.138895i
$326$	−14.6355	+	8.44984i	−0.810588	+	0.467993i
$327$		0			0
$328$	2.00000	−	2.00000i	0.110432	−	0.110432i
$329$	−14.8138	+	7.73625i	−0.816711	+	0.426513i
$330$		0			0
$331$	8.31662	−	14.4048i	0.457123	−	0.791760i	−0.541684	−	0.840582i	$-0.682213\pi$
$331$	8.31662	−	14.4048i	0.457123	−	0.791760i	0.998808	+	0.0488216i	$0.0155466\pi$
$332$	−13.7804	−	3.69244i	−0.756297	−	0.202649i
$333$		0			0
$334$	−6.92820	−	4.00000i	−0.379094	−	0.218870i
$335$	−5.58597	−	6.17552i	−0.305194	−	0.337405i
$336$		0			0
$337$	−6.10819	−	6.10819i	−0.332734	−	0.332734i	0.520890	−	0.853624i	$-0.325600\pi$
$337$	−6.10819	−	6.10819i	−0.332734	−	0.332734i	−0.853624	+	0.520890i	$0.825600\pi$
$338$	−10.6252	+	2.84701i	−0.577934	+	0.154857i
$339$		0			0
$340$	−1.58953	+	4.93023i	−0.0862044	+	0.267379i
$341$	−4.25591	−	2.45715i	−0.230471	−	0.133062i
$342$		0			0
$343$	−11.3321	−	14.6487i	−0.611874	−	0.790955i
$344$	−7.96662			−0.429531
$345$		0			0
$346$	9.94987	+	17.2337i	0.534909	+	0.926489i
$347$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$347$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$348$		0			0
$349$			4.00000i			0.214115i	0.994253	+	0.107058i	$0.0341429\pi$
$349$			4.00000i			0.214115i	−0.994253	+	0.107058i	$0.965857\pi$
$350$	10.4010	+	8.17426i	0.555958	+	0.436933i
$351$		0			0
$352$	−1.58228	+	0.423972i	−0.0843360	+	0.0225978i
$353$	6.18571	−	23.0854i	0.329232	−	1.22871i	−0.580756	−	0.814077i	$-0.697243\pi$
$353$	6.18571	−	23.0854i	0.329232	−	1.22871i	0.909988	−	0.414634i	$-0.136090\pi$
$354$		0			0
$355$	14.1211	+	9.12470i	0.749469	+	0.484289i
$356$			15.4855i			0.820728i
$357$		0			0
$358$	1.00000	−	1.00000i	0.0528516	−	0.0528516i
$359$	6.10463	−	10.5735i	0.322190	−	0.558049i	−0.658750	−	0.752362i	$-0.728914\pi$
$359$	6.10463	−	10.5735i	0.322190	−	0.558049i	0.980940	+	0.194313i	$0.0622477\pi$
$360$		0			0
$361$	−9.44987	−	16.3677i	−0.497362	−	0.861456i
$362$	2.94193	+	10.9794i	0.154624	+	0.577066i
$363$		0			0
$364$	−3.73831	−	0.158312i	−0.195941	−	0.00829782i
$365$	−21.8494	+	19.7635i	−1.14365	+	1.03447i
$366$		0			0
$367$	1.27192	−	4.74685i	0.0663934	−	0.247784i	−0.924751	−	0.380573i	$-0.875727\pi$
$367$	1.27192	−	4.74685i	0.0663934	−	0.247784i	0.991144	+	0.132789i	$0.0423934\pi$
$368$	−2.15250	+	8.03324i	−0.112207	+	0.418762i
$369$		0			0
$370$	15.7916	+	0.791562i	0.820964	+	0.0411513i
$371$	−30.7511	−	1.30227i	−1.59652	−	0.0676105i
$372$		0			0
$373$	−3.54436	−	13.2277i	−0.183520	−	0.684906i	−0.994943	−	0.100446i	$-0.967973\pi$
$373$	−3.54436	−	13.2277i	−0.183520	−	0.684906i	0.811422	−	0.584460i	$-0.198694\pi$
$374$	1.89743	+	3.28645i	0.0981139	+	0.169938i
$375$		0			0
$376$	3.15831	−	5.47036i	0.162878	−	0.282112i
$377$	1.19033	−	1.19033i	0.0613049	−	0.0613049i
$378$		0			0
$379$			17.3668i			0.892070i	0.895016	+	0.446035i	$0.147164\pi$
$379$			17.3668i			0.892070i	−0.895016	+	0.446035i	$0.852836\pi$
$380$	0.384249	−	0.594650i	0.0197116	−	0.0305049i
$381$		0			0
$382$	−0.500265	+	1.86702i	−0.0255958	+	0.0955248i
$383$	1.93185	−	0.517638i	0.0987130	−	0.0264501i	−0.209124	−	0.977889i	$-0.567061\pi$
$383$	1.93185	−	0.517638i	0.0987130	−	0.0264501i	0.307837	+	0.951439i	$0.400395\pi$
$384$		0			0
$385$	9.55243	−	1.63376i	0.486837	−	0.0832643i
$386$		−	3.50009i		−	0.178150i
$387$		0			0
$388$	12.5105	+	3.35217i	0.635124	+	0.170181i
$389$	10.3118	+	17.8606i	0.522830	+	0.905569i	0.999647	+	0.0265660i	$0.00845720\pi$
$389$	10.3118	+	17.8606i	0.522830	+	0.905569i	−0.476817	+	0.879003i	$0.658209\pi$
$390$		0			0
$391$	19.2665			0.974349
$392$	6.58410	+	2.37690i	0.332547	+	0.120052i
$393$		0			0
$394$	−12.0375	−	6.94987i	−0.606442	−	0.350130i
$395$	−19.1705	+	9.82289i	−0.964573	+	0.494243i
$396$		0			0
$397$	29.0506	−	7.78408i	1.45801	−	0.390672i	0.559206	−	0.829029i	$-0.311106\pi$
$397$	29.0506	−	7.78408i	1.45801	−	0.390672i	0.898801	+	0.438357i	$0.144439\pi$
$398$	6.10463	+	6.10463i	0.305997	+	0.305997i
$399$		0			0
$400$	−4.97494	−	0.500000i	−0.248747	−	0.0250000i
$401$	−6.06233	−	3.50009i	−0.302738	−	0.174786i	0.340934	−	0.940087i	$-0.389257\pi$
$401$	−6.06233	−	3.50009i	−0.302738	−	0.174786i	−0.643672	+	0.765301i	$0.722590\pi$
$402$		0			0
$403$	4.09808	+	1.09808i	0.204140	+	0.0546991i
$404$	−5.62141	+	9.73657i	−0.279676	+	0.484412i
$405$		0			0
$406$	−2.79156	+	1.45785i	−0.138543	+	0.0723517i
$407$	8.19051	−	8.19051i	0.405988	−	0.405988i
$408$		0			0
$409$	−22.3864	+	12.9248i	−1.10694	+	0.639091i	−0.938035	−	0.346542i	$-0.887356\pi$
$409$	−22.3864	+	12.9248i	−1.10694	+	0.639091i	−0.168903	+	0.985633i	$0.554023\pi$
$410$	1.94070	−	6.01944i	0.0958443	−	0.297279i
$411$		0			0
$412$	−9.63325	−	9.63325i	−0.474596	−	0.474596i
$413$	4.06393	−	3.73371i	0.199973	−	0.183724i
$414$		0			0
$415$	−31.1886	+	6.70357i	−1.53099	+	0.329065i
$416$	1.22474	−	0.707107i	0.0600481	−	0.0346688i
$417$		0			0
$418$	−0.134240	−	0.500990i	−0.00656589	−	0.0245042i
$419$	−24.9372			−1.21826			−0.609130	−	0.793070i	$-0.708481\pi$
$419$	−24.9372			−1.21826			−0.609130	+	0.793070i	$0.708481\pi$
$420$		0			0
$421$	1.58312			0.0771567			0.0385784	−	0.999256i	$-0.487717\pi$
$421$	1.58312			0.0771567			0.0385784	+	0.999256i	$0.487717\pi$
$422$	3.86931	+	14.4405i	0.188355	+	0.702951i
$423$		0			0
$424$	10.0747	−	5.81662i	0.489270	−	0.282480i
$425$	1.86406	+	11.4321i	0.0904203	+	0.554541i
$426$		0			0
$427$	0.799268	+	0.250858i	0.0386793	+	0.0121399i
$428$	0.259332	+	0.259332i	0.0125353	+	0.0125353i
$429$		0			0
$430$	−15.8539	+	8.12345i	−0.764541	+	0.391747i
$431$	35.4562	−	20.4707i	1.70787	−	0.986037i	0.770669	−	0.637236i	$-0.219922\pi$
$431$	35.4562	−	20.4707i	1.70787	−	0.986037i	0.937197	−	0.348800i	$-0.113411\pi$
$432$		0			0
$433$	−25.9499	+	25.9499i	−1.24707	+	1.24707i	−0.290064	+	0.957007i	$0.593677\pi$
$433$	−25.9499	+	25.9499i	−1.24707	+	1.24707i	−0.957007	+	0.290064i	$0.906323\pi$
$434$	−6.69979	−	4.25591i	−0.321600	−	0.204290i
$435$		0			0
$436$	4.63325	−	8.02502i	0.221892	−	0.384329i
$437$	−2.54352	−	0.681535i	−0.121673	−	0.0326022i
$438$		0			0
$439$	24.7537	+	14.2916i	1.18143	+	0.682099i	0.956345	−	0.292240i	$-0.0944006\pi$
$439$	24.7537	+	14.2916i	1.18143	+	0.682099i	0.225085	+	0.974339i	$0.427734\pi$
$440$	−2.71648	+	2.45715i	−0.129503	+	0.117140i
$441$		0			0
$442$	−2.31662	−	2.31662i	−0.110191	−	0.110191i
$443$	−1.98027	+	0.530612i	−0.0940854	+	0.0252101i	−0.305555	−	0.952175i	$-0.598842\pi$
$443$	−1.98027	+	0.530612i	−0.0940854	+	0.0252101i	0.211469	+	0.977385i	$0.432175\pi$
$444$		0			0
$445$	15.7903	+	30.8166i	0.748532	+	1.46085i
$446$	−15.7278	−	9.08044i	−0.744732	−	0.429972i
$447$		0			0
$448$	−2.58228	+	0.576028i	−0.122001	+	0.0272148i
$449$	23.4521			1.10677			0.553386	−	0.832925i	$-0.313335\pi$
$449$	23.4521			1.10677			0.553386	+	0.832925i	$0.313335\pi$
$450$		0			0
$451$	−2.31662	−	4.01251i	−0.109086	−	0.188942i
$452$	1.93185	+	0.517638i	0.0908667	+	0.0243476i
$453$		0			0
$454$			23.3166i			1.09430i
$455$	−7.60079	+	3.49685i	−0.356331	+	0.163935i
$456$		0			0
$457$	−17.4051	+	4.66369i	−0.814177	+	0.218158i	−0.641799	−	0.766873i	$-0.721812\pi$
$457$	−17.4051	+	4.66369i	−0.814177	+	0.218158i	−0.172378	+	0.985031i	$0.555145\pi$
$458$	6.72930	−	25.1141i	0.314439	−	1.17350i
$459$		0			0
$460$	3.90783	+	18.1813i	0.182204	+	0.847708i
$461$			28.2134i			1.31403i	0.753878	+	0.657014i	$0.228181\pi$
$461$			28.2134i			1.31403i	−0.753878	+	0.657014i	$0.771819\pi$
$462$		0			0
$463$	14.3668	−	14.3668i	0.667680	−	0.667680i	−0.289499	−	0.957178i	$-0.593489\pi$
$463$	14.3668	−	14.3668i	0.667680	−	0.667680i	0.957178	+	0.289499i	$0.0934886\pi$
$464$	0.595163	−	1.03085i	0.0276297	−	0.0478561i
$465$		0			0
$466$	−0.525063	−	0.909435i	−0.0243231	−	0.0421288i
$467$	3.76142	+	14.0378i	0.174058	+	0.649592i	0.996710	+	0.0810475i	$0.0258266\pi$
$467$	3.76142	+	14.0378i	0.174058	+	0.649592i	−0.822653	+	0.568544i	$0.807507\pi$
$468$		0			0
$469$	−9.84389	−	0.416876i	−0.454549	−	0.0192495i
$470$	0.707107	−	14.1067i	0.0326164	−	0.650693i
$471$		0			0
$472$	−0.539864	+	2.01480i	−0.0248493	+	0.0927388i
$473$	−3.37762	+	12.6055i	−0.155303	+	0.579599i
$474$		0			0
$475$	0.158312	−	1.57519i	0.00726387	−	0.0722746i
$476$	2.83727	+	5.43297i	0.130046	+	0.249020i
$477$		0			0
$478$	−2.67807	−	9.99470i	−0.122492	−	0.457147i
$479$	0.483219	+	0.836960i	0.0220789	+	0.0382417i	0.876854	−	0.480757i	$-0.159638\pi$
$479$	0.483219	+	0.836960i	0.0220789	+	0.0382417i	−0.854775	+	0.518999i	$0.826305\pi$
$480$		0			0
$481$	−5.00000	+	8.66025i	−0.227980	+	0.394874i
$482$	18.7971	−	18.7971i	0.856185	−	0.856185i
$483$		0			0
$484$		−	8.31662i		−	0.378028i
$485$	28.3145	−	6.08582i	1.28569	−	0.276343i
$486$		0			0
$487$	0.558212	−	2.08327i	0.0252950	−	0.0944022i	−0.952124	−	0.305711i	$-0.901106\pi$
$487$	0.558212	−	2.08327i	0.0252950	−	0.0944022i	0.977419	+	0.211309i	$0.0677726\pi$
$488$	−0.305836	+	0.0819485i	−0.0138445	+	0.00370964i
$489$		0			0
$490$	15.5263	−	1.98359i	0.701406	−	0.0896097i
$491$		−	9.60472i		−	0.433455i	−0.976232	−	0.216727i	$-0.930462\pi$
$491$		−	9.60472i		−	0.433455i	0.976232	−	0.216727i	$-0.0695383\pi$
$492$		0			0
$493$	−2.66358	−	0.713704i	−0.119962	−	0.0321436i
$494$	0.223888	+	0.387785i	0.0100732	+	0.0174473i
$495$		0			0
$496$	3.00000			0.134704
$497$	19.4158	−	4.33107i	0.870917	−	0.194275i
$498$		0			0
$499$	19.0526	+	11.0000i	0.852910	+	0.492428i	0.861632	−	0.507534i	$-0.169443\pi$
$499$	19.0526	+	11.0000i	0.852910	+	0.492428i	−0.00872186	+	0.999962i	$0.502776\pi$
$500$	−10.4101	+	4.07786i	−0.465556	+	0.182367i
$501$		0			0
$502$	15.1741	−	4.06588i	0.677252	−	0.181469i
$503$	−11.0189	−	11.0189i	−0.491310	−	0.491310i	0.417409	−	0.908719i	$-0.362938\pi$
$503$	−11.0189	−	11.0189i	−0.491310	−	0.491310i	−0.908719	+	0.417409i	$0.862938\pi$
$504$		0			0
$505$	−1.25856	+	25.1082i	−0.0560053	+	1.11730i
$506$	11.7983	+	6.81174i	0.524497	+	0.302819i
$507$		0			0
$508$	−16.1076	−	4.31601i	−0.714658	−	0.191492i
$509$	0.371275	−	0.643068i	0.0164565	−	0.0285035i	−0.857680	−	0.514184i	$-0.828095\pi$
$509$	0.371275	−	0.643068i	0.0164565	−	0.0285035i	0.874136	+	0.485681i	$0.161428\pi$
$510$		0			0
$511$	−1.47494	+	34.8284i	−0.0652474	+	1.54072i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	4.56092	−	2.63325i	0.201174	−	0.116148i
$515$	−28.9934	−	9.34762i	−1.27760	−	0.411905i
$516$		0			0
$517$	−7.31662	−	7.31662i	−0.321785	−	0.321785i
$518$	13.7766	−	12.6572i	0.605310	−	0.556125i
$519$		0			0
$520$	1.71626	−	2.65602i	0.0752629	−	0.116474i
$521$	−9.73657	+	5.62141i	−0.426567	+	0.246278i	−0.697883	−	0.716212i	$-0.745874\pi$
$521$	−9.73657	+	5.62141i	−0.426567	+	0.246278i	0.271316	+	0.962490i	$0.412541\pi$
$522$		0			0
$523$	−1.71423	−	6.39761i	−0.0749582	−	0.279748i	0.918266	−	0.395965i	$-0.129590\pi$
$523$	−1.71423	−	6.39761i	−0.0749582	−	0.279748i	−0.993224	+	0.116217i	$0.962923\pi$
$524$	−17.1945			−0.751143
$525$		0			0
$526$	−27.5831			−1.20268
$527$	−1.79876	−	6.71306i	−0.0783552	−	0.292426i
$528$		0			0
$529$	39.9811	−	23.0831i	1.73831	−	1.00361i
$530$	14.1179	−	21.8483i	0.613241	−	0.949030i
$531$		0			0
$532$	−0.182385	−	0.817615i	−0.00790738	−	0.0354481i
$533$	2.82843	+	2.82843i	0.122513	+	0.122513i
$534$		0			0
$535$	0.780516	+	0.251642i	0.0337447	+	0.0108794i
$536$	3.22506	−	1.86199i	0.139301	−	0.0804257i
$537$		0			0
$538$	−19.4749	+	19.4749i	−0.839624	+	0.839624i
$539$	6.55240	−	9.41017i	0.282232	−	0.405325i
$540$		0			0
$541$	−1.79156	+	3.10308i	−0.0770253	+	0.133412i	−0.901965	−	0.431809i	$-0.857876\pi$
$541$	−1.79156	+	3.10308i	−0.0770253	+	0.133412i	0.824940	+	0.565220i	$0.191209\pi$
$542$	−10.3193	−	2.76506i	−0.443254	−	0.118770i
$543$		0			0
$544$	−2.00626	−	1.15831i	−0.0860175	−	0.0496622i
$545$	1.03733	−	20.6945i	0.0444342	−	0.886457i
$546$		0			0
$547$	3.31662	+	3.31662i	0.141809	+	0.141809i	0.774447	−	0.632639i	$-0.218028\pi$
$547$	3.31662	+	3.31662i	0.141809	+	0.141809i	−0.632639	+	0.774447i	$0.718028\pi$
$548$	17.3867	−	4.65874i	0.742722	−	0.199012i
$549$		0			0
$550$	−2.90037	+	7.65978i	−0.123672	+	0.326614i
$551$	0.326393	+	0.188443i	0.0139048	+	0.00802796i
$552$		0			0
$553$	−7.63230	+	24.3176i	−0.324558	+	1.03409i
$554$	18.7617			0.797107
$555$		0			0
$556$	−6.63325	−	11.4891i	−0.281312	−	0.487247i
$557$	−9.40184	−	2.51922i	−0.398369	−	0.106743i	0.0540720	−	0.998537i	$-0.482780\pi$
$557$	−9.40184	−	2.51922i	−0.398369	−	0.106743i	−0.452441	+	0.891794i	$0.649447\pi$
$558$		0			0
$559$		−	11.2665i		−	0.476522i
$560$	−4.55147	+	3.77944i	−0.192335	+	0.159710i
$561$		0			0
$562$	19.1244	−	5.12436i	0.806712	−	0.216158i
$563$	3.61049	−	13.4745i	0.152164	−	0.567884i	−0.847167	−	0.531326i	$-0.821694\pi$
$563$	3.61049	−	13.4745i	0.152164	−	0.567884i	0.999332	−	0.0365582i	$-0.0116394\pi$
$564$		0			0
$565$	4.37228	−	0.939764i	0.183943	−	0.0395362i
$566$		−	7.51884i		−	0.316041i
$567$		0			0
$568$	−5.31662	+	5.31662i	−0.223081	+	0.223081i
$569$	5.62141	−	9.73657i	0.235662	−	0.408178i	−0.723803	−	0.690007i	$-0.757608\pi$
$569$	5.62141	−	9.73657i	0.235662	−	0.408178i	0.959465	+	0.281828i	$0.0909409\pi$
$570$		0			0
$571$	9.42481	+	16.3243i	0.394416	+	0.683149i	0.993026	−	0.117892i	$-0.0376135\pi$
$571$	9.42481	+	16.3243i	0.394416	+	0.683149i	−0.598610	+	0.801040i	$0.704280\pi$
$572$	−0.599587	−	2.23769i	−0.0250700	−	0.0935624i
$573$		0			0
$574$	−3.46410	−	6.63325i	−0.144589	−	0.276866i
$575$	26.3160	+	32.1967i	1.09745	+	1.34269i
$576$		0			0
$577$	4.20012	−	15.6751i	0.174853	−	0.652561i	−0.821723	−	0.569887i	$-0.806987\pi$
$577$	4.20012	−	15.6751i	0.174853	−	0.652561i	0.996577	−	0.0826745i	$-0.0263462\pi$
$578$	3.01091	−	11.2369i	0.125237	−	0.467392i
$579$		0			0
$580$	0.133250	−	2.65831i	0.00553289	−	0.110380i
$581$	−20.2390	+	31.8609i	−0.839655	+	1.32181i
$582$		0			0
$583$	−4.93217	−	18.4071i	−0.204270	−	0.762344i
$584$	−6.58785	−	11.4105i	−0.272607	−	0.472169i
$585$		0			0
$586$	−0.500000	+	0.866025i	−0.0206548	+	0.0357752i
$587$	8.22595	−	8.22595i	0.339521	−	0.339521i	−0.516666	−	0.856187i	$-0.672827\pi$
$587$	8.22595	−	8.22595i	0.339521	−	0.339521i	0.856187	+	0.516666i	$0.172827\pi$
$588$		0			0
$589$			0.949874i			0.0391389i
$590$	0.980115	+	4.56002i	0.0403507	+	0.187733i
$591$		0			0
$592$	−1.83013	+	6.83013i	−0.0752178	+	0.280716i
$593$	20.9445	−	5.61207i	0.860089	−	0.230460i	0.198292	−	0.980143i	$-0.436461\pi$
$593$	20.9445	−	5.61207i	0.860089	−	0.230460i	0.661797	+	0.749683i	$0.269794\pi$
$594$		0			0
$595$	11.1862	+	7.91867i	0.458589	+	0.324634i
$596$			7.07107i			0.289642i
$597$		0			0
$598$	−11.3607	−	3.04410i	−0.464574	−	0.124482i
$599$	2.38065	+	4.12341i	0.0972708	+	0.168478i	0.910554	−	0.413390i	$-0.135655\pi$
$599$	2.38065	+	4.12341i	0.0972708	+	0.168478i	−0.813283	+	0.581868i	$0.802322\pi$
$600$		0			0
$601$	31.6332			1.29035			0.645174	−	0.764036i	$-0.276785\pi$
$601$	31.6332			1.29035			0.645174	+	0.764036i	$0.276785\pi$
$602$	−6.31185	+	20.1104i	−0.257252	+	0.819640i
$603$		0			0
$604$	20.1928	+	11.6583i	0.821633	+	0.474370i
$605$	−8.48035	−	16.5504i	−0.344775	−	0.672869i
$606$		0			0
$607$	19.3406	−	5.18230i	0.785011	−	0.210343i	0.156018	−	0.987754i	$-0.450134\pi$
$607$	19.3406	−	5.18230i	0.785011	−	0.210343i	0.628993	+	0.777411i	$0.283467\pi$
$608$	0.223888	+	0.223888i	0.00907984	+	0.00907984i
$609$		0			0
$610$	−0.525063	+	0.474937i	−0.0212592	+	0.0192296i
$611$	7.73625	+	4.46653i	0.312975	+	0.180696i
$612$		0			0
$613$	40.4798	+	10.8465i	1.63496	+	0.438087i	0.955348	−	0.295483i	$-0.0954804\pi$
$613$	40.4798	+	10.8465i	1.63496	+	0.438087i	0.679614	+	0.733569i	$0.262147\pi$
$614$	6.36396	−	11.0227i	0.256829	−	0.444840i
$615$		0			0
$616$	−0.183375	+	4.33013i	−0.00738840	+	0.174466i
$617$	−24.7133	+	24.7133i	−0.994920	+	0.994920i	−0.999987	−	0.00506744i	$-0.998387\pi$
$617$	−24.7133	+	24.7133i	−0.994920	+	0.994920i	0.00506744	+	0.999987i	$0.498387\pi$
$618$		0			0
$619$	23.8877	−	13.7916i	0.960127	−	0.554330i	0.0639150	−	0.997955i	$-0.479641\pi$
$619$	23.8877	−	13.7916i	0.960127	−	0.554330i	0.896212	+	0.443626i	$0.146308\pi$
$620$	5.97011	−	3.05906i	0.239765	−	0.122855i
$621$		0			0
$622$	3.68338	+	3.68338i	0.147690	+	0.147690i
$623$	39.0905	+	12.2689i	1.56613	+	0.491544i
$624$		0			0
$625$	−16.5584	+	18.7302i	−0.662337	+	0.749206i
$626$	6.70540	−	3.87137i	0.268002	−	0.154731i
$627$		0			0
$628$	−3.77615	−	14.0928i	−0.150685	−	0.562363i
$629$	16.3810			0.653154
$630$		0			0
$631$	21.5330			0.857215			0.428608	−	0.903491i	$-0.359004\pi$
$631$	21.5330			0.857215			0.428608	+	0.903491i	$0.359004\pi$
$632$	−2.49327	−	9.30500i	−0.0991769	−	0.370133i
$633$		0			0
$634$	13.8130	−	7.97494i	0.548584	−	0.316725i
$635$	−36.4556	+	7.83565i	−1.44670	+	0.310948i
$636$		0			0
$637$	−3.36145	+	9.31132i	−0.133185	+	0.368928i
$638$	−1.37877	−	1.37877i	−0.0545860	−	0.0545860i
$639$		0			0
$640$	0.686141	−	2.12819i	0.0271221	−	0.0841243i
$641$	2.51088	−	1.44966i	0.0991738	−	0.0572580i	−0.449593	−	0.893234i	$-0.648431\pi$
$641$	2.51088	−	1.44966i	0.0991738	−	0.0572580i	0.548767	+	0.835976i	$0.315098\pi$
$642$		0			0
$643$	−31.8997	+	31.8997i	−1.25800	+	1.25800i	−0.305958	+	0.952045i	$0.598977\pi$
$643$	−31.8997	+	31.8997i	−1.25800	+	1.25800i	−0.952045	+	0.305958i	$0.901023\pi$
$644$	18.5732	+	11.7983i	0.731887	+	0.464917i
$645$		0			0
$646$	0.366750	−	0.635230i	0.0144296	−	0.0249928i
$647$	13.7320	+	3.67947i	0.539859	+	0.144655i	0.518437	−	0.855116i	$-0.326514\pi$
$647$	13.7320	+	3.67947i	0.539859	+	0.144655i	0.0214219	+	0.999771i	$0.493181\pi$
$648$		0			0
$649$	2.95910	+	1.70844i	0.116155	+	0.0670621i
$650$	0.707107	−	7.03562i	0.0277350	−	0.275960i
$651$		0			0
$652$	−11.9499	−	11.9499i	−0.467993	−	0.467993i
$653$	−10.2225	+	2.73911i	−0.400038	+	0.107190i	−0.453228	−	0.891395i	$-0.649728\pi$
$653$	−10.2225	+	2.73911i	−0.400038	+	0.107190i	0.0531903	+	0.998584i	$0.483061\pi$
$654$		0			0
$655$	−34.2176	+	17.5329i	−1.33699	+	0.685069i
$656$	2.44949	+	1.41421i	0.0956365	+	0.0552158i
$657$		0			0
$658$	−11.3067	−	12.3067i	−0.440783	−	0.479767i
$659$	28.8029			1.12200			0.561002	−	0.827815i	$-0.310416\pi$
$659$	28.8029			1.12200			0.561002	+	0.827815i	$0.310416\pi$
$660$		0			0
$661$	−0.891813	−	1.54467i	−0.0346875	−	0.0600805i	0.848160	−	0.529739i	$-0.177710\pi$
$661$	−0.891813	−	1.54467i	−0.0346875	−	0.0600805i	−0.882848	+	0.469659i	$0.844377\pi$
$662$	16.0665	+	4.30500i	0.624442	+	0.167319i
$663$		0			0
$664$		−	14.2665i		−	0.553648i
$665$	−1.19666	−	1.44111i	−0.0464046	−	0.0558838i
$666$		0			0
$667$	−9.56218	+	2.56218i	−0.370249	+	0.0992079i
$668$	2.07055	−	7.72741i	0.0801121	−	0.298982i
$669$		0			0
$670$	4.51934	−	6.99397i	0.174597	−	0.270201i
$671$			0.518663i			0.0200228i
$672$		0			0
$673$	−25.7414	+	25.7414i	−0.992259	+	0.992259i	−0.999970	−	0.00771082i	$-0.997546\pi$
$673$	−25.7414	+	25.7414i	−0.992259	+	0.992259i	0.00771082	+	0.999970i	$0.497546\pi$
$674$	4.31914	−	7.48097i	0.166367	−	0.288156i
$675$		0			0
$676$	−5.50000	−	9.52628i	−0.211538	−	0.366395i
$677$	−3.44660	−	12.8629i	−0.132463	−	0.494360i	0.867532	−	0.497381i	$-0.165705\pi$
$677$	−3.44660	−	12.8629i	−0.132463	−	0.494360i	−0.999995	+	0.00302107i	$0.999038\pi$
$678$		0			0
$679$	18.3739	−	28.9248i	0.705126	−	1.11003i
$680$	−5.17364	−	0.259332i	−0.198400	−	0.00994492i
$681$		0			0
$682$	1.27192	−	4.74685i	0.0487042	−	0.181766i
$683$	12.1126	−	45.2048i	0.463476	−	1.72972i	−0.198418	−	0.980118i	$-0.563580\pi$
$683$	12.1126	−	45.2048i	0.463476	−	1.72972i	0.661894	−	0.749598i	$-0.269753\pi$
$684$		0			0
$685$	29.8496	−	27.0000i	1.14050	−	1.03162i
$686$	11.2166	−	14.7373i	0.428252	−	0.562673i
$687$		0			0
$688$	−2.06191	−	7.69516i	−0.0786097	−	0.293375i
$689$	8.22595	+	14.2478i	0.313384	+	0.542797i
$690$		0			0
$691$	−24.0000	+	41.5692i	−0.913003	+	1.58137i	−0.103204	+	0.994660i	$0.532909\pi$
$691$	−24.0000	+	41.5692i	−0.913003	+	1.58137i	−0.809799	+	0.586707i	$0.800424\pi$
$692$	−14.0712	+	14.0712i	−0.534909	+	0.534909i
$693$		0			0
$694$		0			0
$695$	−24.9157	−	16.0999i	−0.945106	−	0.610705i
$696$		0			0
$697$	1.69589	−	6.32914i	0.0642363	−	0.239733i
$698$	−3.86370	+	1.03528i	−0.146243	+	0.0391858i
$699$		0			0
$700$	−5.20375	+	12.1623i	−0.196683	+	0.459691i
$701$			22.2618i			0.840815i	0.907335	+	0.420407i	$0.138113\pi$
$701$			22.2618i			0.840815i	−0.907335	+	0.420407i	$0.861887\pi$
$702$		0			0
$703$	−2.16259	−	0.579464i	−0.0815635	−	0.0218549i
$704$	−0.819051	−	1.41864i	−0.0308691	−	0.0534669i
$705$		0			0
$706$	23.8997			0.899479
$707$	20.1246	+	21.9045i	0.756864	+	0.823803i
$708$		0			0
$709$	9.75707	+	5.63325i	0.366435	+	0.211561i	0.671900	−	0.740642i	$-0.265479\pi$
$709$	9.75707	+	5.63325i	0.366435	+	0.211561i	−0.305465	+	0.952203i	$0.598812\pi$
$710$	−5.15898	+	16.0016i	−0.193613	+	0.600528i
$711$		0			0
$712$	−14.9578	+	4.00793i	−0.560568	+	0.150204i
$713$	−17.6422	−	17.6422i	−0.660707	−	0.660707i
$714$		0			0
$715$	−3.47494	−	3.84169i	−0.129955	−	0.143671i
$716$	1.22474	+	0.707107i	0.0457709	+	0.0264258i
$717$		0			0
$718$	11.7932	+	3.15999i	0.440120	+	0.117930i
$719$	16.0041	−	27.7200i	0.596853	−	1.03378i	−0.396429	−	0.918065i	$-0.629751\pi$
$719$	16.0041	−	27.7200i	0.596853	−	1.03378i	0.993282	−	0.115715i	$-0.0369158\pi$
$720$		0			0
$721$	−31.9499	+	16.6853i	−1.18988	+	0.621392i
$722$	13.3641	−	13.3641i	0.497362	−	0.497362i
$723$		0			0
$724$	−9.84389	+	5.68338i	−0.365845	+	0.211221i
$725$	−2.44547	−	5.42601i	−0.0908226	−	0.201517i
$726$		0			0
$727$	−7.89181	−	7.89181i	−0.292691	−	0.292691i	0.545451	−	0.838142i	$-0.316358\pi$
$727$	−7.89181	−	7.89181i	−0.292691	−	0.292691i	−0.838142	+	0.545451i	$0.816358\pi$
$728$	−0.814627	−	3.65190i	−0.0301921	−	0.135348i
$729$		0			0
$730$	−24.7452	−	15.9897i	−0.915860	−	0.591807i
$731$	−15.9831	+	9.22783i	−0.591155	+	0.341304i
$732$		0			0
$733$	−11.8104	−	44.0769i	−0.436226	−	1.62802i	−0.738116	−	0.674673i	$-0.764284\pi$
$733$	−11.8104	−	44.0769i	−0.436226	−	1.62802i	0.301891	−	0.953342i	$-0.402382\pi$
$734$	4.91430			0.181390
$735$		0			0
$736$	−8.31662			−0.306555
$737$	−1.57886	−	5.89239i	−0.0581581	−	0.217049i
$738$		0			0
$739$	22.4298	−	12.9499i	0.825095	−	0.476369i	−0.0270753	−	0.999633i	$-0.508619\pi$
$739$	22.4298	−	12.9499i	0.825095	−	0.476369i	0.852170	+	0.523265i	$0.175286\pi$
$740$	3.32257	+	15.4583i	0.122140	+	0.568260i
$741$		0			0
$742$	−6.70108	−	30.0404i	−0.246004	−	1.10282i
$743$	7.00018	+	7.00018i	0.256812	+	0.256812i	0.823756	−	0.566944i	$-0.191875\pi$
$743$	7.00018	+	7.00018i	0.256812	+	0.256812i	−0.566944	+	0.823756i	$0.691875\pi$
$744$		0			0
$745$	7.21027	+	14.0717i	0.264164	+	0.515546i
$746$	11.8597	−	6.84718i	0.434213	−	0.250693i
$747$		0			0
$748$	−2.68338	+	2.68338i	−0.0981139	+	0.0981139i
$749$	0.860106	−	0.449176i	0.0314276	−	0.0164125i
$750$		0			0
$751$	−0.500000	+	0.866025i	−0.0182453	+	0.0316017i	−0.875004	−	0.484116i	$-0.839141\pi$
$751$	−0.500000	+	0.866025i	−0.0182453	+	0.0316017i	0.856759	+	0.515718i	$0.172475\pi$
$752$	6.10139	+	1.63486i	0.222495	+	0.0596173i
$753$		0			0
$754$	1.45785	+	0.841688i	0.0530916	+	0.0306525i
$755$	52.0722	+	2.61015i	1.89510	+	0.0949931i
$756$		0			0
$757$	14.2665	+	14.2665i	0.518525	+	0.518525i	0.917125	−	0.398600i	$-0.130504\pi$
$757$	14.2665	+	14.2665i	0.518525	+	0.518525i	−0.398600	+	0.917125i	$0.630504\pi$
$758$	−16.7750	+	4.49485i	−0.609295	+	0.163260i
$759$		0			0
$760$	0.673839	+	0.217249i	0.0244427	+	0.00788045i
$761$	−34.6192	−	19.9874i	−1.25495	−	0.724544i	−0.282859	−	0.959161i	$-0.591283\pi$
$761$	−34.6192	−	19.9874i	−1.25495	−	0.724544i	−0.972088	+	0.234618i	$0.924616\pi$
$762$		0			0
$763$	−16.5870	−	18.0540i	−0.600490	−	0.653599i
$764$	−1.93288			−0.0699290
$765$		0			0
$766$	1.00000	+	1.73205i	0.0361315	+	0.0625815i
$767$	−2.84936	−	0.763484i	−0.102884	−	0.0275678i
$768$		0			0
$769$			22.3668i			0.806566i	0.915075	+	0.403283i	$0.132131\pi$
$769$			22.3668i			0.806566i	−0.915075	+	0.403283i	$0.867869\pi$
$770$	4.05045	+	8.80409i	0.145968	+	0.317277i
$771$		0			0
$772$	3.38083	−	0.905890i	0.121679	−	0.0326037i
$773$	−0.327794	+	1.22334i	−0.0117899	+	0.0440006i	−0.971570	−	0.236752i	$-0.923917\pi$
$773$	−0.327794	+	1.22334i	−0.0117899	+	0.0440006i	0.959780	+	0.280752i	$0.0905839\pi$
$774$		0			0
$775$	8.76144	−	12.1753i	0.314720	−	0.437348i
$776$			12.9518i			0.464943i
$777$		0			0
$778$	−14.5831	+	14.5831i	−0.522830	+	0.522830i
$779$	−0.447775	+	0.775569i	−0.0160432	+	0.0277876i
$780$		0			0
$781$	6.15831	+	10.6665i	0.220362	+	0.381678i
$782$	4.98654	+	18.6100i	0.178318	+	0.665493i
$783$		0			0
$784$	−0.591820	+	6.97494i	−0.0211364	+	0.249105i
$785$	−21.8849	−	24.1946i	−0.781104	−	0.863543i
$786$		0			0
$787$	−0.750398	+	2.80052i	−0.0267488	+	0.0998279i	−0.978010	−	0.208559i	$-0.933123\pi$
$787$	−0.750398	+	2.80052i	−0.0267488	+	0.0998279i	0.951261	+	0.308387i	$0.0997892\pi$
$788$	3.59752	−	13.4261i	0.128156	−	0.478286i
$789$		0			0
$790$	−14.4499	−	15.9749i	−0.514103	−	0.568363i
$791$	2.83727	−	4.46653i	0.100882	−	0.158811i
$792$		0			0
$793$	−0.115893	−	0.432518i	−0.00411547	−	0.0153591i
$794$	15.0377	+	26.0460i	0.533667	+	0.924339i
$795$		0			0
$796$	−4.31662	+	7.47661i	−0.152999	+	0.265002i
$797$	3.83031	−	3.83031i	0.135677	−	0.135677i	−0.636007	−	0.771683i	$-0.719415\pi$
$797$	3.83031	−	3.83031i	0.135677	−	0.135677i	0.771683	+	0.636007i	$0.219415\pi$
$798$		0			0
$799$		−	14.6332i		−	0.517687i
$800$	−0.804646	−	4.93483i	−0.0284485	−	0.174473i
$801$		0			0
$802$	1.81178	−	6.76165i	0.0639762	−	0.238762i
$803$	−20.8477	+	5.58612i	−0.735699	+	0.197130i
$804$		0			0
$805$	48.9919	+	4.54013i	1.72674	+	0.160019i
$806$			4.24264i			0.149441i
$807$		0			0
$808$	−10.8597	−	2.90986i	−0.382044	−	0.102368i
$809$	17.9370	+	31.0678i	0.630631	+	1.09229i	0.987423	+	0.158102i	$0.0505373\pi$
$809$	17.9370	+	31.0678i	0.630631	+	1.09229i	−0.356791	+	0.934184i	$0.616129\pi$
$810$		0			0
$811$	10.1003			0.354668			0.177334	−	0.984151i	$-0.443253\pi$
$811$	10.1003			0.354668			0.177334	+	0.984151i	$0.443253\pi$
$812$	−2.13068	−	2.31912i	−0.0747722	−	0.0813853i
$813$		0			0
$814$	10.0313	+	5.79156i	0.351596	+	0.202994i
$815$	−35.9658	−	11.5956i	−1.25983	−	0.406175i
$816$		0			0
$817$	2.43648	−	0.652853i	0.0852416	−	0.0228404i
$818$	−18.2784	−	18.2784i	−0.639091	−	0.639091i
$819$		0			0
$820$	6.31662	+	0.316625i	0.220586	+	0.0110570i
$821$	18.1159	+	10.4592i	0.632249	+	0.365029i	0.781623	−	0.623752i	$-0.214392\pi$
$821$	18.1159	+	10.4592i	0.632249	+	0.365029i	−0.149374	+	0.988781i	$0.547726\pi$
$822$		0			0
$823$	−25.8175	−	6.91779i	−0.899943	−	0.241139i	−0.220951	−	0.975285i	$-0.570916\pi$
$823$	−25.8175	−	6.91779i	−0.899943	−	0.241139i	−0.678992	+	0.734146i	$0.737583\pi$
$824$	6.81174	−	11.7983i	0.237298	−	0.411012i
$825$		0			0
$826$	4.65831	+	2.95910i	0.162083	+	0.102960i
$827$	−23.1106	+	23.1106i	−0.803636	+	0.803636i	−0.983662	−	0.180026i	$-0.942382\pi$
$827$	−23.1106	+	23.1106i	−0.803636	+	0.803636i	0.180026	+	0.983662i	$0.442382\pi$
$828$		0			0
$829$	37.1089	−	21.4248i	1.28884	−	0.744114i	0.310396	−	0.950607i	$-0.399538\pi$
$829$	37.1089	−	21.4248i	1.28884	−	0.744114i	0.978448	+	0.206493i	$0.0662050\pi$
$830$	−14.5473	−	28.3908i	−0.504946	−	0.985460i
$831$		0			0
$832$	1.00000	+	1.00000i	0.0346688	+	0.0346688i
$833$	15.9626	−	2.85777i	0.553071	−	0.0990159i
$834$		0			0
$835$	−3.75906	−	17.4891i	−0.130087	−	0.605236i
$836$	0.449176	−	0.259332i	0.0155351	−	0.00896917i
$837$		0			0
$838$	−6.45422	−	24.0875i	−0.222957	−	0.832088i
$839$	−41.3182			−1.42646			−0.713231	−	0.700929i	$-0.752769\pi$
$839$	−41.3182			−1.42646			−0.713231	+	0.700929i	$0.752769\pi$
$840$		0			0
$841$	−27.5831			−0.951142
$842$	0.409743	+	1.52918i	0.0141207	+	0.0526990i
$843$		0			0
$844$	−12.9470	+	7.47494i	−0.445653	+	0.257298i
$845$	−20.6590	−	13.3494i	−0.710691	−	0.459232i
$846$		0			0
$847$	−20.9940	−	6.58915i	−0.721361	−	0.226406i
$848$	8.22595	+	8.22595i	0.282480	+	0.282480i
$849$		0			0
$850$	−10.5602	+	4.75940i	−0.362210	+	0.163246i
$851$	50.9287	−	29.4037i	1.74581	−	1.00795i
$852$		0			0
$853$	22.3166	−	22.3166i	0.764107	−	0.764107i	−0.212955	−	0.977062i	$-0.568309\pi$
$853$	22.3166	−	22.3166i	0.764107	−	0.764107i	0.977062	+	0.212955i	$0.0683089\pi$
$854$	−0.0354442	+	0.836960i	−0.00121287	+	0.0286402i
$855$		0			0
$856$	−0.183375	+	0.317615i	−0.00626764	+	0.0108559i
$857$	48.6021	+	13.0229i	1.66022	+	0.444854i	0.962447	−	0.271468i	$-0.0875092\pi$
$857$	48.6021	+	13.0229i	1.66022	+	0.444854i	0.697770	+	0.716322i	$0.254176\pi$
$858$		0			0
$859$	−40.5730	−	23.4248i	−1.38433	−	0.799244i	−0.391663	−	0.920109i	$-0.628100\pi$
$859$	−40.5730	−	23.4248i	−1.38433	−	0.799244i	−0.992669	+	0.120865i	$0.961433\pi$
$860$	−11.9499	−	13.2111i	−0.407489	−	0.450496i
$861$		0			0
$862$	28.9499	+	28.9499i	0.986037	+	0.986037i
$863$	−51.9663	+	13.9243i	−1.76895	+	0.473990i	−0.988500	−	0.151223i	$-0.951679\pi$
$863$	−51.9663	+	13.9243i	−1.76895	+	0.473990i	−0.780455	+	0.625213i	$0.785012\pi$
$864$		0			0
$865$	−13.6540	+	42.3505i	−0.464251	+	1.43996i
$866$	−31.7820	−	18.3493i	−1.08000	−	0.623536i
$867$		0			0
$868$	2.37686	−	7.57301i	0.0806759	−	0.257045i
$869$	−15.7802			−0.535308
$870$		0			0
$871$	2.63325	+	4.56092i	0.0892243	+	0.154541i
$872$	8.95075	+	2.39835i	0.303111	+	0.0812183i
$873$		0			0
$874$		−	2.63325i		−	0.0890710i
$875$	2.04606	+	29.5096i	0.0691696	+	0.997605i
$876$		0			0
$877$	38.1118	−	10.2120i	1.28694	−	0.344835i	0.450444	−	0.892804i	$-0.351266\pi$
$877$	38.1118	−	10.2120i	1.28694	−	0.344835i	0.836499	+	0.547969i	$0.184599\pi$
$878$	−7.39786	+	27.6092i	−0.249666	+	0.931765i
$879$		0			0
$880$	−3.07650	−	1.98796i	−0.103709	−	0.0670142i
$881$			1.93288i			0.0651203i	0.999470	+	0.0325601i	$0.0103660\pi$
$881$			1.93288i			0.0651203i	−0.999470	+	0.0325601i	$0.989634\pi$
$882$		0			0
$883$	10.3166	−	10.3166i	0.347182	−	0.347182i	−0.511877	−	0.859059i	$-0.671050\pi$
$883$	10.3166	−	10.3166i	0.347182	−	0.347182i	0.859059	+	0.511877i	$0.171050\pi$
$884$	1.63810	−	2.83727i	0.0550953	−	0.0954279i
$885$		0			0
$886$	−1.02506	−	1.77546i	−0.0344377	−	0.0596478i
$887$	−4.90459	−	18.3042i	−0.164680	−	0.614594i	−0.998081	−	0.0619250i	$-0.980276\pi$
$887$	−4.90459	−	18.3042i	−0.164680	−	0.614594i	0.833401	−	0.552669i	$-0.186391\pi$
$888$		0			0
$889$	−23.6569	+	37.2414i	−0.793427	+	1.24904i
$890$	−25.6797	+	23.2282i	−0.860787	+	0.778611i
$891$		0			0
$892$	4.70038	−	17.5421i	0.157380	−	0.587352i
$893$	−0.517638	+	1.93185i	−0.0173221	+	0.0646470i
$894$		0			0
$895$	3.15831	+	0.158312i	0.105571	+	0.00529180i
$896$	−1.22474	−	2.34521i	−0.0409159	−	0.0783479i
$897$		0			0
$898$	6.06984	+	22.6530i	0.202553	+	0.755939i
$899$	1.78549	+	3.09256i	0.0595494	+	0.103143i
$900$		0			0
$901$	13.4749	−	23.3393i	0.448915	−	0.777544i
$902$	3.27620	−	3.27620i	0.109086	−	0.109086i
$903$		0			0
$904$			2.00000i			0.0665190i
$905$	−13.7944	+	21.3478i	−0.458543	+	0.709625i
$906$		0			0
$907$	−14.7386	+	55.0051i	−0.489386	+	1.82641i	0.0700554	+	0.997543i	$0.477682\pi$
$907$	−14.7386	+	55.0051i	−0.489386	+	1.82641i	−0.559441	+	0.828870i	$0.688984\pi$
$908$	−22.5221	+	6.03479i	−0.747423	+	0.200271i
$909$		0			0
$910$	−5.34493	−	6.43675i	−0.177183	−	0.213376i
$911$			40.4226i			1.33926i	0.742694	+	0.669631i	$0.233548\pi$
$911$			40.4226i			1.33926i	−0.742694	+	0.669631i	$0.766452\pi$
$912$		0			0
$913$	−22.5737	−	6.04859i	−0.747079	−	0.200179i
$914$	−9.00956	−	15.6050i	−0.298010	−	0.516168i
$915$		0			0
$916$	26.0000			0.859064
$917$	−13.6229	+	43.4046i	−0.449869	+	1.43335i
$918$		0			0
$919$	−6.29297	−	3.63325i	−0.207586	−	0.119850i	0.392603	−	0.919708i	$-0.371575\pi$
$919$	−6.29297	−	3.63325i	−0.207586	−	0.119850i	−0.600189	+	0.799858i	$0.704908\pi$
$920$	−16.5504	+	8.48035i	−0.545650	+	0.279589i
$921$		0			0
$922$	−27.2520	+	7.30216i	−0.897498	+	0.240484i
$923$	−7.51884	−	7.51884i	−0.247486	−	0.247486i
$924$		0			0
$925$	22.3747	+	27.3747i	0.735675	+	0.900074i
$926$	17.5956	+	10.1588i	0.578227	+	0.333840i
$927$		0			0
$928$	1.14977	+	0.308079i	0.0377429	+	0.0101132i
$929$	−28.2488	+	48.9284i	−0.926814	+	1.60529i	−0.138196	+	0.990405i	$0.544131\pi$
$929$	−28.2488	+	48.9284i	−0.926814	+	1.60529i	−0.788618	+	0.614884i	$0.789203\pi$
$930$		0			0
$931$	−2.20844	−	0.187385i	−0.0723786	−	0.00614129i
$932$	0.742551	−	0.742551i	0.0243231	−	0.0243231i
$933$		0			0
$934$	−12.5859	+	7.26650i	−0.411825	+	0.237767i
$935$	−2.60381	+	8.07621i	−0.0851537	+	0.264120i
$936$		0			0
$937$	−16.3747	−	16.3747i	−0.534938	−	0.534938i	0.387100	−	0.922038i	$-0.373477\pi$
$937$	−16.3747	−	16.3747i	−0.534938	−	0.534938i	−0.922038	+	0.387100i	$0.873477\pi$
$938$	−2.14512	−	9.61637i	−0.0700405	−	0.313986i
$939$		0			0
$940$	13.8090	−	2.96807i	0.450401	−	0.0968077i
$941$	−32.3637	+	18.6852i	−1.05502	+	0.609119i	−0.924052	−	0.382267i	$-0.875143\pi$
$941$	−32.3637	+	18.6852i	−1.05502	+	0.609119i	−0.130973	+	0.991386i	$0.541810\pi$
$942$		0			0
$943$	−6.08819	−	22.7214i	−0.198259	−	0.739912i
$944$	−2.08588			−0.0678895
$945$		0			0
$946$	−13.0501			−0.424296
$947$	2.94193	+	10.9794i	0.0955999	+	0.356784i	0.997110	−	0.0759749i	$-0.0242069\pi$
$947$	2.94193	+	10.9794i	0.0955999	+	0.356784i	−0.901510	+	0.432759i	$0.857540\pi$
$948$		0			0
$949$	16.1369	−	9.31662i	0.523825	−	0.302430i
$950$	1.56249	−	0.254771i	0.0506939	−	0.00826585i
$951$		0			0
$952$	−4.51350	+	4.14675i	−0.146283	+	0.134397i
$953$	−36.8517	−	36.8517i	−1.19374	−	1.19374i	−0.976008	−	0.217734i	$-0.930133\pi$
$953$	−36.8517	−	36.8517i	−1.19374	−	1.19374i	−0.217734	−	0.976008i	$-0.569867\pi$
$954$		0			0
$955$	−3.84649	+	1.97093i	−0.124470	+	0.0637777i
$956$	8.96100	−	5.17364i	0.289819	−	0.167327i
$957$		0			0
$958$	−0.683375	+	0.683375i	−0.0220789	+	0.0220789i
$959$	2.01499	−	47.5809i	0.0650674	−	1.53647i
$960$		0			0
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$	−9.65926	−	2.58819i	−0.311427	−	0.0834466i
$963$		0			0
$964$	23.0217	+	13.2916i	0.741478	+	0.428092i
$965$	5.80424	−	5.25013i	0.186845	−	0.169008i
$966$		0			0
$967$	−28.6913	−	28.6913i	−0.922650	−	0.922650i	0.0745657	−	0.997216i	$-0.476243\pi$
$967$	−28.6913	−	28.6913i	−0.922650	−	0.922650i	−0.997216	+	0.0745657i	$0.976243\pi$
$968$	8.03324	−	2.15250i	0.258198	−	0.0691840i
$969$		0			0
$970$	13.2068	+	25.7746i	0.424044	+	0.827571i
$971$	−35.9765	−	20.7710i	−1.15454	−	0.666574i	−0.204551	−	0.978856i	$-0.565573\pi$
$971$	−35.9765	−	20.7710i	−1.15454	−	0.666574i	−0.949990	+	0.312282i	$0.898907\pi$
$972$		0			0
$973$	−34.2579	+	7.64188i	−1.09826	+	0.244987i
$974$	2.15676			0.0691072
$975$		0			0
$976$	−0.158312	−	0.274205i	−0.00506746	−	0.00877709i
$977$	17.6925	+	4.74069i	0.566033	+	0.151668i	0.530477	−	0.847700i	$-0.322013\pi$
$977$	17.6925	+	4.74069i	0.566033	+	0.151668i	0.0355565	+	0.999368i	$0.488680\pi$
$978$		0			0
$979$			25.3668i			0.810725i
$980$	5.93450	+	14.4838i	0.189571	+	0.462669i
$981$		0			0
$982$	9.27745	−	2.48588i	0.296055	−	0.0793278i
$983$	−9.12764	+	34.0648i	−0.291127	+	1.08650i	0.653119	+	0.757256i	$0.273460\pi$
$983$	−9.12764	+	34.0648i	−0.291127	+	1.08650i	−0.944245	+	0.329243i	$0.893206\pi$
$984$		0			0
$985$	−6.53124	−	30.3868i	−0.208103	−	0.968204i
$986$		−	2.75754i		−	0.0878179i
$987$		0			0
$988$	−0.316625	+	0.316625i	−0.0100732	+	0.0100732i
$989$	−33.1277	+	57.3788i	−1.05340	+	1.82454i
$990$		0			0
$991$	−5.34169	−	9.25207i	−0.169684	−	0.293902i	0.768625	−	0.639700i	$-0.220941\pi$
$991$	−5.34169	−	9.25207i	−0.169684	−	0.293902i	−0.938309	+	0.345798i	$0.887608\pi$
$992$	0.776457	+	2.89778i	0.0246525	+	0.0920045i
$993$		0			0
$994$	9.20866	+	17.6332i	0.292081	+	0.559293i
$995$	−0.966438	+	19.2803i	−0.0306382	+	0.611227i
$996$		0			0
$997$	−0.616158	+	2.29953i	−0.0195139	+	0.0728270i	−0.974996	−	0.222222i	$-0.928669\pi$
$997$	−0.616158	+	2.29953i	−0.0195139	+	0.0728270i	0.955482	+	0.295049i	$0.0953358\pi$
$998$	−5.69402	+	21.2504i	−0.180241	+	0.672669i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ce.b.107.3	yes	16
3.2	odd	2	inner	630.2.ce.b.107.2	yes	16
5.3	odd	4	inner	630.2.ce.b.233.3	yes	16
7.4	even	3	inner	630.2.ce.b.557.2	yes	16
15.8	even	4	inner	630.2.ce.b.233.2	yes	16
21.11	odd	6	inner	630.2.ce.b.557.3	yes	16
35.18	odd	12	inner	630.2.ce.b.53.2	✓	16
105.53	even	12	inner	630.2.ce.b.53.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.b.53.2	✓	16	35.18	odd	12	inner
630.2.ce.b.53.3	yes	16	105.53	even	12	inner
630.2.ce.b.107.2	yes	16	3.2	odd	2	inner
630.2.ce.b.107.3	yes	16	1.1	even	1	trivial
630.2.ce.b.233.2	yes	16	15.8	even	4	inner
630.2.ce.b.233.3	yes	16	5.3	odd	4	inner
630.2.ce.b.557.2	yes	16	7.4	even	3	inner
630.2.ce.b.557.3	yes	16	21.11	odd	6	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-1.21358 + 1.87809i) q^{5} +(0.576028 + 2.58228i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-1.21358 + 1.87809i) q^{5} +(0.576028 + 2.58228i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.12819 - 0.686141i) q^{10} +(-1.41864 + 0.819051i) q^{11} +(1.00000 - 1.00000i) q^{13} +(-2.34521 + 1.22474i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.23769 - 0.599587i) q^{17} +(0.274205 + 0.158312i) q^{19} +(0.111944 - 2.23326i) q^{20} +(-1.15831 - 1.15831i) q^{22} +(-8.03324 + 2.15250i) q^{23} +(-2.05446 - 4.55842i) q^{25} +(1.22474 + 0.707107i) q^{26} +(-1.79000 - 1.94831i) q^{28} +1.19033 q^{29} +(1.50000 + 2.59808i) q^{31} +(0.965926 + 0.258819i) q^{32} -2.31662i q^{34} +(-5.54882 - 2.05197i) q^{35} +(-6.83013 + 1.83013i) q^{37} +(-0.0819485 + 0.305836i) q^{38} +(2.18614 - 0.469882i) q^{40} +2.82843i q^{41} +(5.63325 - 5.63325i) q^{43} +(0.819051 - 1.41864i) q^{44} +(-4.15831 - 7.20241i) q^{46} +(1.63486 + 6.10139i) q^{47} +(-6.33638 + 2.97494i) q^{49} +(3.87137 - 3.16426i) q^{50} +(-0.366025 + 1.36603i) q^{52} +(-3.01091 + 11.2369i) q^{53} +(0.183375 - 3.65831i) q^{55} +(1.41864 - 2.23326i) q^{56} +(0.308079 + 1.14977i) q^{58} +(-1.04294 - 1.80642i) q^{59} +(0.158312 - 0.274205i) q^{61} +(-2.12132 + 2.12132i) q^{62} +1.00000i q^{64} +(0.664513 + 3.09167i) q^{65} +(-0.963836 + 3.59709i) q^{67} +(2.23769 - 0.599587i) q^{68} +(0.545910 - 5.89084i) q^{70} -7.51884i q^{71} +(12.7267 + 3.41012i) q^{73} +(-3.53553 - 6.12372i) q^{74} -0.316625 q^{76} +(-2.93220 - 3.19153i) q^{77} +(8.34264 + 4.81662i) q^{79} +(1.01969 + 1.99004i) q^{80} +(-2.73205 + 0.732051i) q^{82} +(10.0879 + 10.0879i) q^{83} +(3.84169 - 3.47494i) q^{85} +(6.89929 + 3.98331i) q^{86} +(1.58228 + 0.423972i) q^{88} +(7.74273 - 13.4108i) q^{89} +(3.15831 + 2.00626i) q^{91} +(5.88074 - 5.88074i) q^{92} +(-5.47036 + 3.15831i) q^{94} +(-0.630095 + 0.322858i) q^{95} +(-9.15831 - 9.15831i) q^{97} +(-4.51355 - 5.35051i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{7}+O(q^{10}) \) 16 * q + 12 * q^7	\( 16 q + 12 q^{7} + 16 q^{13} + 8 q^{16} + 8 q^{22} - 12 q^{28} + 24 q^{31} - 40 q^{37} + 12 q^{40} - 16 q^{43} - 40 q^{46} + 8 q^{52} + 56 q^{55} - 20 q^{58} - 24 q^{61} - 32 q^{67} + 4 q^{70} + 48 q^{73} + 48 q^{76} - 16 q^{82} + 88 q^{85} - 4 q^{88} + 24 q^{91} - 120 q^{97}+O(q^{100}) \) 16 * q + 12 * q^7 + 16 * q^13 + 8 * q^16 + 8 * q^22 - 12 * q^28 + 24 * q^31 - 40 * q^37 + 12 * q^40 - 16 * q^43 - 40 * q^46 + 8 * q^52 + 56 * q^55 - 20 * q^58 - 24 * q^61 - 32 * q^67 + 4 * q^70 + 48 * q^73 + 48 * q^76 - 16 * q^82 + 88 * q^85 - 4 * q^88 + 24 * q^91 - 120 * q^97

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