LMFDB - Embedded newform 630.2.ce.b.233.3

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			233.3
Root			$1.73122 + 0.0537601i$ of defining polynomial
Character	$\chi$	$=$	630.233
Dual form			630.2.ce.b.557.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.01969 - 1.99004i) q^{5} +(2.58228 - 0.576028i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.01969 - 1.99004i) q^{5} +(2.58228 - 0.576028i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.469882 - 2.18614i) q^{10} +(-1.41864 + 0.819051i) q^{11} +(1.00000 + 1.00000i) q^{13} +(2.34521 - 1.22474i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.599587 + 2.23769i) q^{17} +(-0.274205 - 0.158312i) q^{19} +(-0.111944 - 2.23326i) q^{20} +(-1.15831 + 1.15831i) q^{22} +(-2.15250 - 8.03324i) q^{23} +(-2.92048 - 4.05842i) q^{25} +(1.22474 + 0.707107i) q^{26} +(1.94831 - 1.79000i) q^{28} -1.19033 q^{29} +(1.50000 + 2.59808i) q^{31} +(0.258819 - 0.965926i) q^{32} +2.31662i q^{34} +(1.48680 - 5.72620i) q^{35} +(1.83013 + 6.83013i) q^{37} +(-0.305836 - 0.0819485i) q^{38} +(-0.686141 - 2.12819i) q^{40} +2.82843i q^{41} +(5.63325 + 5.63325i) q^{43} +(-0.819051 + 1.41864i) q^{44} +(-4.15831 - 7.20241i) q^{46} +(6.10139 - 1.63486i) q^{47} +(6.33638 - 2.97494i) q^{49} +(-3.87137 - 3.16426i) q^{50} +(1.36603 + 0.366025i) q^{52} +(-11.2369 - 3.01091i) q^{53} +(0.183375 + 3.65831i) q^{55} +(1.41864 - 2.23326i) q^{56} +(-1.14977 + 0.308079i) q^{58} +(1.04294 + 1.80642i) q^{59} +(0.158312 - 0.274205i) q^{61} +(2.12132 + 2.12132i) q^{62} -1.00000i q^{64} +(3.00972 - 0.970349i) q^{65} +(3.59709 + 0.963836i) q^{67} +(0.599587 + 2.23769i) q^{68} +(-0.0459101 - 5.91590i) q^{70} -7.51884i q^{71} +(-3.41012 + 12.7267i) q^{73} +(3.53553 + 6.12372i) q^{74} -0.316625 q^{76} +(-3.19153 + 2.93220i) q^{77} +(-8.34264 - 4.81662i) q^{79} +(-1.21358 - 1.87809i) q^{80} +(0.732051 + 2.73205i) q^{82} +(-10.0879 + 10.0879i) q^{83} +(3.84169 + 3.47494i) q^{85} +(6.89929 + 3.98331i) q^{86} +(-0.423972 + 1.58228i) q^{88} +(-7.74273 + 13.4108i) q^{89} +(3.15831 + 2.00626i) q^{91} +(-5.88074 - 5.88074i) q^{92} +(5.47036 - 3.15831i) q^{94} +(-0.594650 + 0.384249i) q^{95} +(-9.15831 + 9.15831i) q^{97} +(5.35051 - 4.51355i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.01969	−	1.99004i	0.456017	−	0.889971i
$5$	1.01969	−	1.99004i	0.456017	−	0.889971i
$6$		0			0
$7$	2.58228	−	0.576028i	0.976012	−	0.217718i
$7$	2.58228	−	0.576028i	0.976012	−	0.217718i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	0.469882	−	2.18614i	0.148590	−	0.691318i
$11$	−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	0.832050	−	0.554700i	$-0.187167\pi$
$13$	1.00000	+	1.00000i	0.277350	+	0.277350i	−0.554700	+	0.832050i	$0.687167\pi$
$14$	2.34521	−	1.22474i	0.626783	−	0.327327i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.599587	+	2.23769i	−0.145421	+	0.542719i	0.854315	+	0.519755i	$0.173977\pi$
$17$	−0.599587	+	2.23769i	−0.145421	+	0.542719i	−0.999736	+	0.0229637i	$0.992690\pi$
$18$		0			0
$19$	−0.274205	−	0.158312i	−0.0629070	−	0.0363194i	0.468217	−	0.883614i	$-0.344897\pi$
$19$	−0.274205	−	0.158312i	−0.0629070	−	0.0363194i	−0.531124	+	0.847294i	$0.678230\pi$
$20$	−0.111944	−	2.23326i	−0.0250314	−	0.499373i
$21$		0			0
$22$	−1.15831	+	1.15831i	−0.246953	+	0.246953i
$23$	−2.15250	−	8.03324i	−0.448827	−	1.67505i	−0.705628	−	0.708582i	$-0.749335\pi$
$23$	−2.15250	−	8.03324i	−0.448827	−	1.67505i	0.256801	−	0.966464i	$-0.417332\pi$
$24$		0			0
$25$	−2.92048	−	4.05842i	−0.584096	−	0.811684i
$26$	1.22474	+	0.707107i	0.240192	+	0.138675i
$27$		0			0
$28$	1.94831	−	1.79000i	0.368196	−	0.338278i
$29$	−1.19033			−0.221038			−0.110519	−	0.993874i	$-0.535251\pi$
$29$	−1.19033			−0.221038			−0.110519	+	0.993874i	$0.535251\pi$
$30$		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	$0.746505\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$		0			0
$34$			2.31662i			0.397298i
$35$	1.48680	−	5.72620i	0.251315	−	0.967905i
$36$		0			0
$37$	1.83013	+	6.83013i	0.300871	+	1.12287i	0.936442	+	0.350823i	$0.114098\pi$
$37$	1.83013	+	6.83013i	0.300871	+	1.12287i	−0.635571	+	0.772043i	$0.719235\pi$
$38$	−0.305836	−	0.0819485i	−0.0496132	−	0.0132938i
$39$		0			0
$40$	−0.686141	−	2.12819i	−0.108488	−	0.336497i
$41$			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	0.991228	−	0.132165i	$-0.0421929\pi$
$43$	5.63325	+	5.63325i	0.859063	+	0.859063i	−0.132165	+	0.991228i	$0.542193\pi$
$44$	−0.819051	+	1.41864i	−0.123477	+	0.213868i
$45$		0			0
$46$	−4.15831	−	7.20241i	−0.613110	−	1.06194i
$47$	6.10139	−	1.63486i	0.889979	−	0.238469i	0.215272	−	0.976554i	$-0.430936\pi$
$47$	6.10139	−	1.63486i	0.889979	−	0.238469i	0.674708	+	0.738085i	$0.264270\pi$
$48$		0			0
$49$	6.33638	−	2.97494i	0.905198	−	0.424991i
$50$	−3.87137	−	3.16426i	−0.547494	−	0.447494i
$51$		0			0
$52$	1.36603	+	0.366025i	0.189434	+	0.0507586i
$53$	−11.2369	−	3.01091i	−1.54350	−	0.413580i	−0.616106	−	0.787663i	$-0.711291\pi$
$53$	−11.2369	−	3.01091i	−1.54350	−	0.413580i	−0.927395	+	0.374084i	$0.877957\pi$
$54$		0			0
$55$	0.183375	+	3.65831i	0.0247263	+	0.493287i
$56$	1.41864	−	2.23326i	0.189573	−	0.298432i
$57$		0			0
$58$	−1.14977	+	0.308079i	−0.150972	+	0.0404528i
$59$	1.04294	+	1.80642i	0.135779	+	0.235176i	0.925895	−	0.377782i	$-0.123313\pi$
$59$	1.04294	+	1.80642i	0.135779	+	0.235176i	−0.790116	+	0.612958i	$0.789980\pi$
$60$		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
$65$	3.00972	−	0.970349i	0.373310	−	0.120357i
$66$		0			0
$67$	3.59709	+	0.963836i	0.439454	+	0.117751i	0.471761	−	0.881727i	$-0.343619\pi$
$67$	3.59709	+	0.963836i	0.439454	+	0.117751i	−0.0323066	+	0.999478i	$0.510285\pi$
$68$	0.599587	+	2.23769i	0.0727106	+	0.271359i
$69$		0			0
$70$	−0.0459101	−	5.91590i	−0.00548731	−	0.707085i
$71$		−	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
$73$	−3.41012	+	12.7267i	−0.399125	+	1.48955i	0.415516	+	0.909586i	$0.363601\pi$
$73$	−3.41012	+	12.7267i	−0.399125	+	1.48955i	−0.814640	+	0.579967i	$0.803065\pi$
$74$	3.53553	+	6.12372i	0.410997	+	0.711868i
$75$		0			0
$76$	−0.316625			−0.0363194
$77$	−3.19153	+	2.93220i	−0.363708	+	0.334155i
$78$		0			0
$79$	−8.34264	−	4.81662i	−0.938620	−	0.541913i	−0.0490927	−	0.998794i	$-0.515633\pi$
$79$	−8.34264	−	4.81662i	−0.938620	−	0.541913i	−0.889528	+	0.456882i	$0.848966\pi$
$80$	−1.21358	−	1.87809i	−0.135682	−	0.209977i
$81$		0			0
$82$	0.732051	+	2.73205i	0.0808415	+	0.301705i
$83$	−10.0879	+	10.0879i	−1.10730	+	1.10730i	−0.113790	+	0.993505i	$0.536299\pi$
$83$	−10.0879	+	10.0879i	−1.10730	+	1.10730i	−0.993505	+	0.113790i	$0.963701\pi$
$84$		0			0
$85$	3.84169	+	3.47494i	0.416690	+	0.376910i
$86$	6.89929	+	3.98331i	0.743970	+	0.429531i
$87$		0			0
$88$	−0.423972	+	1.58228i	−0.0451955	+	0.168672i
$89$	−7.74273	+	13.4108i	−0.820728	+	1.42154i	0.0844133	+	0.996431i	$0.473098\pi$
$89$	−7.74273	+	13.4108i	−0.820728	+	1.42154i	−0.905141	+	0.425111i	$0.860235\pi$
$90$		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
$95$	−0.594650	+	0.384249i	−0.0610098	+	0.0394231i
$96$		0			0
$97$	−9.15831	+	9.15831i	−0.929886	+	0.929886i	−0.997698	−	0.0678124i	$-0.978398\pi$
$97$	−9.15831	+	9.15831i	−0.929886	+	0.929886i	0.0678124	+	0.997698i	$0.478398\pi$
$98$	5.35051	−	4.51355i	0.540483	−	0.455937i
$99$		0			0
$100$	−4.55842	−	2.05446i	−0.455842	−	0.205446i
$101$	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
$103$	−13.1593	+	3.52601i	−1.29662	+	0.347428i	−0.840171	−	0.542321i	$-0.817546\pi$
$103$	−13.1593	+	3.52601i	−1.29662	+	0.347428i	−0.456449	+	0.889749i	$0.650879\pi$
$104$	1.41421			0.138675
$105$		0			0
$106$	−11.6332			−1.12992
$107$	−0.354254	+	0.0949220i	−0.0342470	+	0.00917646i	−0.275902	−	0.961186i	$-0.588976\pi$
$107$	−0.354254	+	0.0949220i	−0.0342470	+	0.00917646i	0.241655	+	0.970362i	$0.422310\pi$
$108$		0			0
$109$	8.02502	−	4.63325i	0.768658	−	0.443785i	−0.0637378	−	0.997967i	$-0.520302\pi$
$109$	8.02502	−	4.63325i	0.768658	−	0.443785i	0.832396	+	0.554182i	$0.186969\pi$
$110$	1.12397	+	3.48620i	0.107166	+	0.332396i
$111$		0			0
$112$	0.792287	−	2.52434i	0.0748641	−	0.238528i
$113$	1.41421	−	1.41421i	0.133038	−	0.133038i	−0.637452	−	0.770490i	$-0.720012\pi$
$113$	1.41421	−	1.41421i	0.133038	−	0.133038i	0.770490	+	0.637452i	$0.220012\pi$
$114$		0			0
$115$	−18.1813	−	3.90783i	−1.69542	−	0.364407i
$116$	−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
$122$	0.0819485	−	0.305836i	0.00741927	−	0.0276891i
$123$		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	0.0474587	−	0.998873i	$-0.484888\pi$
$127$	11.7916	−	11.7916i	1.04633	−	1.04633i	0.998873	−	0.0474587i	$-0.0151123\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$		0			0
$130$	2.65602	−	1.71626i	0.232949	−	0.150526i
$131$	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
$133$	−0.799268	−	0.250858i	−0.0693053	−	0.0217521i
$134$	3.72398			0.321703
$135$		0			0
$136$	1.15831	+	2.00626i	0.0993245	+	0.172035i
$137$	−4.65874	+	17.3867i	−0.398023	+	1.48544i	0.418546	+	0.908196i	$0.362540\pi$
$137$	−4.65874	+	17.3867i	−0.398023	+	1.48544i	−0.816569	+	0.577247i	$0.804127\pi$
$138$		0			0
$139$		−	13.2665i		−	1.12525i	−0.826712	−	0.562625i	$-0.809792\pi$
$139$		−	13.2665i		−	1.12525i	0.826712	−	0.562625i	$-0.190208\pi$
$140$	−1.57549	−	5.70244i	−0.133154	−	0.481944i
$141$		0			0
$142$	−1.94602	−	7.26264i	−0.163306	−	0.609468i
$143$	−2.23769	−	0.599587i	−0.187125	−	0.0501400i
$144$		0			0
$145$	−1.21376	+	2.36879i	−0.100797	+	0.196717i
$146$			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	−0.973724	−	0.227730i	$-0.926870\pi$
$149$	−3.53553	+	6.12372i	−0.289642	+	0.501675i	0.684082	+	0.729405i	$0.260203\pi$
$150$		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	$-0.564307\pi$
$152$	−0.305836	+	0.0819485i	−0.0248066	+	0.00664690i
$153$		0			0
$154$	−2.32387	+	3.65831i	−0.187263	+	0.294795i
$155$	6.69979	−	0.335831i	0.538140	−	0.0269746i
$156$		0			0
$157$	14.0928	+	3.77615i	1.12473	+	0.301369i	0.772794	−	0.634657i	$-0.218858\pi$
$157$	14.0928	+	3.77615i	1.12473	+	0.301369i	0.351931	+	0.936026i	$0.385525\pi$
$158$	−9.30500	−	2.49327i	−0.740266	−	0.198354i
$159$		0			0
$160$	−1.65831	−	1.50000i	−0.131101	−	0.118585i
$161$	−10.1857	−	19.5042i	−0.802749	−	1.53715i
$162$		0			0
$163$	−16.3238	+	4.37396i	−1.27858	+	0.342595i	−0.833313	−	0.552802i	$-0.813559\pi$
$163$	−16.3238	+	4.37396i	−1.27858	+	0.342595i	−0.445269	+	0.895397i	$0.646892\pi$
$164$	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	$-0.149829\pi$
$167$	5.65685	+	5.65685i	0.437741	+	0.437741i	−0.453510	+	0.891251i	$0.649829\pi$
$168$		0			0
$169$		−	11.0000i		−	0.846154i
$170$	4.61017	+	2.36223i	0.353584	+	0.181175i
$171$		0			0
$172$	7.69516	+	2.06191i	0.586751	+	0.157219i
$173$	5.15043	+	19.2217i	0.391580	+	1.46140i	0.827528	+	0.561425i	$0.189747\pi$
$173$	5.15043	+	19.2217i	0.391580	+	1.46140i	−0.435947	+	0.899972i	$0.643587\pi$
$174$		0			0
$175$	−9.87928	−	8.79772i	−0.746803	−	0.665045i
$176$			1.63810i			0.123477i
$177$		0			0
$178$	−4.00793	+	14.9578i	−0.300407	+	1.12114i
$179$	0.707107	+	1.22474i	0.0528516	+	0.0915417i	0.891241	−	0.453530i	$-0.149836\pi$
$179$	0.707107	+	1.22474i	0.0528516	+	0.0915417i	−0.838389	+	0.545072i	$0.816502\pi$
$180$		0			0
$181$	11.3668			0.844884			0.422442	−	0.906390i	$-0.361173\pi$
$181$	11.3668			0.844884			0.422442	+	0.906390i	$0.361173\pi$
$182$	3.56995	+	1.12046i	0.264623	+	0.0830542i
$183$		0			0
$184$	−7.20241	−	4.15831i	−0.530969	−	0.306555i
$185$	15.4583	+	3.32257i	1.13652	+	0.244280i
$186$		0			0
$187$	−0.982183	−	3.66556i	−0.0718244	−	0.268052i
$188$	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
$193$	0.905890	−	3.38083i	0.0652074	−	0.243357i	−0.925627	−	0.378436i	$-0.876462\pi$
$193$	0.905890	−	3.38083i	0.0652074	−	0.243357i	0.990835	+	0.135079i	$0.0431287\pi$
$194$	−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	$-0.0851102\pi$
$197$	9.82861	+	9.82861i	0.700259	+	0.700259i	−0.264207	+	0.964466i	$0.585110\pi$
$198$		0			0
$199$	−7.47661	+	4.31662i	−0.530003	+	0.305997i	−0.741018	−	0.671485i	$-0.765657\pi$
$199$	−7.47661	+	4.31662i	−0.530003	+	0.305997i	0.211015	+	0.977483i	$0.432323\pi$
$200$	−4.93483	−	0.804646i	−0.348945	−	0.0568970i
$201$		0			0
$202$	7.94987	−	7.94987i	0.559351	−	0.559351i
$203$	−3.07376	+	0.685661i	−0.215736	+	0.0481240i
$204$		0			0
$205$	5.62867	+	2.88411i	0.393123	+	0.201435i
$206$	−11.7983	+	6.81174i	−0.822025	+	0.474596i
$207$		0			0
$208$	1.36603	−	0.366025i	0.0947168	−	0.0253793i
$209$	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	$0.327942\pi$
$212$	−11.2369	+	3.01091i	−0.771750	+	0.206790i
$213$		0			0
$214$	−0.317615	+	0.183375i	−0.0217117	+	0.0125353i
$215$	16.9545	−	5.46622i	1.15629	−	0.372793i
$216$		0			0
$217$	5.36999	+	5.84493i	0.364539	+	0.396780i
$218$	6.55240	−	6.55240i	0.443785	−	0.443785i
$219$		0			0
$220$	1.98796	+	3.07650i	0.134028	+	0.207418i
$221$	−2.83727	+	1.63810i	−0.190856	+	0.110191i
$222$		0			0
$223$	−12.8417	−	12.8417i	−0.859943	−	0.859943i	0.131388	−	0.991331i	$-0.458057\pi$
$223$	−12.8417	−	12.8417i	−0.859943	−	0.859943i	−0.991331	+	0.131388i	$0.958057\pi$
$224$	0.111944	−	2.64338i	0.00747956	−	0.176618i
$225$		0			0
$226$	1.00000	−	1.73205i	0.0665190	−	0.115214i
$227$	6.03479	−	22.5221i	0.400543	−	1.49485i	−0.411588	−	0.911370i	$-0.635026\pi$
$227$	6.03479	−	22.5221i	0.400543	−	1.49485i	0.812130	−	0.583476i	$-0.198308\pi$
$228$		0			0
$229$	22.5167	+	13.0000i	1.48794	+	0.859064i	0.999905	−	0.0137585i	$-0.00437961\pi$
$229$	22.5167	+	13.0000i	1.48794	+	0.859064i	0.488037	+	0.872823i	$0.337713\pi$
$230$	−18.5732	+	0.930994i	−1.22468	+	0.0613879i
$231$		0			0
$232$	−0.841688	+	0.841688i	−0.0552595	+	0.0552595i
$233$	−0.271793	−	1.01434i	−0.0178057	−	0.0664518i	0.956451	−	0.291892i	$-0.0942847\pi$
$233$	−0.271793	−	1.01434i	−0.0178057	−	0.0664518i	−0.974257	+	0.225440i	$0.927618\pi$
$234$		0			0
$235$	2.96807	−	13.8090i	0.193615	−	0.900802i
$236$	1.80642	+	1.04294i	0.117588	+	0.0678895i
$237$		0			0
$238$	1.33444	+	5.98218i	0.0864990	+	0.387767i
$239$	10.3473			0.669309			0.334655	−	0.942341i	$-0.391380\pi$
$239$	10.3473			0.669309			0.334655	+	0.942341i	$0.391380\pi$
$240$		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	$-0.493838\pi$
$242$	−2.15250	+	8.03324i	−0.138368	+	0.516396i
$243$		0			0
$244$		−	0.316625i		−	0.0202698i
$245$	0.540890	−	15.6431i	0.0345562	−	0.999403i
$246$		0			0
$247$	−0.115893	−	0.432518i	−0.00737408	−	0.0275204i
$248$	2.89778	+	0.776457i	0.184009	+	0.0493051i
$249$		0			0
$250$	−10.2446	+	4.47760i	−0.647923	+	0.283189i
$251$		−	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
$257$	−5.08705	+	1.36307i	−0.317321	+	0.0850260i	−0.413964	−	0.910293i	$-0.635856\pi$
$257$	−5.08705	+	1.36307i	−0.317321	+	0.0850260i	0.0966430	+	0.995319i	$0.469189\pi$
$258$		0			0
$259$	8.66025	+	16.5831i	0.538122	+	1.03043i
$260$	2.12132	−	2.34521i	0.131559	−	0.145444i
$261$		0			0
$262$	16.6086	+	4.45025i	1.02608	+	0.274937i
$263$	−26.6433	−	7.13904i	−1.64289	−	0.440212i	−0.685283	−	0.728277i	$-0.740321\pi$
$263$	−26.6433	−	7.13904i	−1.64289	−	0.440212i	−0.957611	+	0.288065i	$0.906988\pi$
$264$		0			0
$265$	−17.4499	+	19.2916i	−1.07194	+	1.18507i
$266$	−0.836960	−	0.0354442i	−0.0513173	−	0.00217322i
$267$		0			0
$268$	3.59709	−	0.963836i	0.219727	−	0.0588757i
$269$	−13.7709	−	23.8518i	−0.839624	−	1.45427i	−0.890209	−	0.455552i	$-0.849442\pi$
$269$	−13.7709	−	23.8518i	−0.839624	−	1.45427i	0.0505850	−	0.998720i	$-0.483891\pi$
$270$		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
$275$	7.46716	+	3.36541i	0.450286	+	0.202942i
$276$		0			0
$277$	−18.1224	−	4.85588i	−1.08887	−	0.291761i	−0.330644	−	0.943756i	$-0.607266\pi$
$277$	−18.1224	−	4.85588i	−1.08887	−	0.291761i	−0.758224	+	0.651994i	$0.773933\pi$
$278$	−3.43362	−	12.8145i	−0.205935	−	0.768560i
$279$		0			0
$280$	−2.99771	−	5.10037i	−0.179147	−	0.304805i
$281$		−	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
$283$	1.94602	−	7.26264i	0.115679	−	0.431719i	−0.883658	−	0.468133i	$-0.844927\pi$
$283$	1.94602	−	7.26264i	0.115679	−	0.431719i	0.999337	+	0.0364138i	$0.0115934\pi$
$284$	−3.75942	−	6.51151i	−0.223081	−	0.386387i
$285$		0			0
$286$	−2.31662			−0.136985
$287$	1.62925	+	7.30380i	0.0961718	+	0.431130i
$288$		0			0
$289$	10.0747	+	5.81662i	0.592629	+	0.342154i
$290$	−0.559313	+	2.60222i	−0.0328440	+	0.152808i
$291$		0			0
$292$	3.41012	+	12.7267i	0.199562	+	0.744776i
$293$	−0.707107	+	0.707107i	−0.0413096	+	0.0413096i	−0.727460	−	0.686150i	$-0.759299\pi$
$293$	−0.707107	+	0.707107i	−0.0413096	+	0.0413096i	0.686150	+	0.727460i	$0.259299\pi$
$294$		0			0
$295$	4.65831	−	0.233501i	0.271217	−	0.0135949i
$296$	6.12372	+	3.53553i	0.355934	+	0.205499i
$297$		0			0
$298$	−1.83013	+	6.83013i	−0.106016	+	0.395659i
$299$	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
$305$	−0.384249	−	0.594650i	−0.0220020	−	0.0340496i
$306$		0			0
$307$	−9.00000	+	9.00000i	−0.513657	+	0.513657i	−0.915645	−	0.401988i	$-0.868319\pi$
$307$	−9.00000	+	9.00000i	−0.513657	+	0.513657i	0.401988	+	0.915645i	$0.368319\pi$
$308$	−1.29785	+	4.13512i	−0.0739517	+	0.235620i
$309$		0			0
$310$	6.38458	−	2.05842i	0.362620	−	0.116911i
$311$	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
$313$	7.47890	−	2.00397i	0.422733	−	0.113271i	−0.0411802	−	0.999152i	$-0.513112\pi$
$313$	7.47890	−	2.00397i	0.422733	−	0.113271i	0.463913	+	0.885881i	$0.346445\pi$
$314$	14.5899			0.823356
$315$		0			0
$316$	−9.63325			−0.541913
$317$	−15.4064	+	4.12813i	−0.865309	+	0.231859i	−0.664058	−	0.747681i	$-0.731167\pi$
$317$	−15.4064	+	4.12813i	−0.865309	+	0.231859i	−0.201251	+	0.979540i	$0.564501\pi$
$318$		0			0
$319$	1.68864	−	0.974937i	0.0945457	−	0.0545860i
$320$	−1.99004	−	1.01969i	−0.111246	−	0.0570022i
$321$		0			0
$322$	−14.8867	−	16.2034i	−0.829605	−	0.902978i
$323$	0.518663	−	0.518663i	0.0288592	−	0.0288592i
$324$		0			0
$325$	1.13794	−	6.97890i	0.0631216	−	0.387120i
$326$	−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	$0.0155466\pi$
$332$	−3.69244	+	13.7804i	−0.202649	+	0.756297i
$333$		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	−0.853624	−	0.520890i	$-0.825600\pi$
$337$	−6.10819	+	6.10819i	−0.332734	+	0.332734i	0.520890	+	0.853624i	$0.325600\pi$
$338$	−2.84701	−	10.6252i	−0.154857	−	0.577934i
$339$		0			0
$340$	5.06447	+	1.08854i	0.274659	+	0.0590344i
$341$	−4.25591	−	2.45715i	−0.230471	−	0.133062i
$342$		0			0
$343$	14.6487	−	11.3321i	0.790955	−	0.611874i
$344$	7.96662			0.429531
$345$		0			0
$346$	9.94987	+	17.2337i	0.534909	+	0.926489i
$347$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$347$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$348$		0			0
$349$		−	4.00000i		−	0.214115i	−0.994253	−	0.107058i	$-0.965857\pi$
$349$		−	4.00000i		−	0.214115i	0.994253	−	0.107058i	$-0.0341429\pi$
$350$	−11.8197	−	5.94100i	−0.631788	−	0.317560i
$351$		0			0
$352$	0.423972	+	1.58228i	0.0225978	+	0.0843360i
$353$	23.0854	+	6.18571i	1.22871	+	0.329232i	0.814077	−	0.580756i	$-0.197243\pi$
$353$	23.0854	+	6.18571i	1.22871	+	0.329232i	0.414634	+	0.909988i	$0.363910\pi$
$354$		0			0
$355$	−14.9628	−	7.66686i	−0.794141	−	0.406915i
$356$			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	−0.980940	−	0.194313i	$-0.937752\pi$
$359$	−6.10463	+	10.5735i	−0.322190	+	0.558049i	0.658750	+	0.752362i	$0.271086\pi$
$360$		0			0
$361$	−9.44987	−	16.3677i	−0.497362	−	0.861456i
$362$	10.9794	−	2.94193i	0.577066	−	0.154624i
$363$		0			0
$364$	3.73831	+	0.158312i	0.195941	+	0.00829782i
$365$	21.8494	+	19.7635i	1.14365	+	1.03447i
$366$		0			0
$367$	−4.74685	−	1.27192i	−0.247784	−	0.0663934i	0.132789	−	0.991144i	$-0.457607\pi$
$367$	−4.74685	−	1.27192i	−0.247784	−	0.0663934i	−0.380573	+	0.924751i	$0.624273\pi$
$368$	−8.03324	−	2.15250i	−0.418762	−	0.112207i
$369$		0			0
$370$	15.7916	−	0.791562i	0.820964	−	0.0411513i
$371$	−30.7511	−	1.30227i	−1.59652	−	0.0676105i
$372$		0			0
$373$	13.2277	−	3.54436i	0.684906	−	0.183520i	0.100446	−	0.994943i	$-0.467973\pi$
$373$	13.2277	−	3.54436i	0.684906	−	0.183520i	0.584460	+	0.811422i	$0.301306\pi$
$374$	−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	$-0.852836\pi$
$379$		−	17.3668i		−	0.892070i	0.895016	−	0.446035i	$-0.147164\pi$
$380$	−0.322858	+	0.630095i	−0.0165623	+	0.0323232i
$381$		0			0
$382$	1.86702	+	0.500265i	0.0955248	+	0.0255958i
$383$	0.517638	+	1.93185i	0.0264501	+	0.0987130i	0.977889	−	0.209124i	$-0.0670614\pi$
$383$	0.517638	+	1.93185i	0.0264501	+	0.0987130i	−0.951439	+	0.307837i	$0.900395\pi$
$384$		0			0
$385$	2.58082	+	9.34117i	0.131531	+	0.476070i
$386$		−	3.50009i		−	0.178150i
$387$		0			0
$388$	−3.35217	+	12.5105i	−0.170181	+	0.635124i
$389$	−10.3118	−	17.8606i	−0.522830	−	0.905569i	−0.999647	−	0.0265660i	$-0.991543\pi$
$389$	−10.3118	−	17.8606i	−0.522830	−	0.905569i	0.476817	−	0.879003i	$-0.341791\pi$
$390$		0			0
$391$	19.2665			0.974349
$392$	2.37690	−	6.58410i	0.120052	−	0.332547i
$393$		0			0
$394$	12.0375	+	6.94987i	0.606442	+	0.350130i
$395$	−18.0921	+	11.6907i	−0.910314	+	0.588223i
$396$		0			0
$397$	−7.78408	−	29.0506i	−0.390672	−	1.45801i	−0.829029	−	0.559206i	$-0.811106\pi$
$397$	−7.78408	−	29.0506i	−0.390672	−	1.45801i	0.438357	−	0.898801i	$-0.355561\pi$
$398$	−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
$403$	−1.09808	+	4.09808i	−0.0546991	+	0.204140i
$404$	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	0.168903	−	0.985633i	$-0.445977\pi$
$409$	22.3864	−	12.9248i	1.10694	−	0.639091i	0.938035	+	0.346542i	$0.112644\pi$
$410$	6.18334	+	1.32903i	0.305373	+	0.0656360i
$411$		0			0
$412$	−9.63325	+	9.63325i	−0.474596	+	0.474596i
$413$	3.73371	+	4.06393i	0.183724	+	0.199973i
$414$		0			0
$415$	9.78883	+	30.3619i	0.480515	+	1.49041i
$416$	1.22474	−	0.707107i	0.0600481	−	0.0346688i
$417$		0			0
$418$	0.500990	−	0.134240i	0.0245042	−	0.00656589i
$419$	24.9372			1.21826			0.609130	−	0.793070i	$-0.291519\pi$
$419$	24.9372			1.21826			0.609130	+	0.793070i	$0.291519\pi$
$420$		0			0
$421$	1.58312			0.0771567			0.0385784	−	0.999256i	$-0.487717\pi$
$421$	1.58312			0.0771567			0.0385784	+	0.999256i	$0.487717\pi$
$422$	14.4405	−	3.86931i	0.702951	−	0.188355i
$423$		0			0
$424$	−10.0747	+	5.81662i	−0.489270	+	0.282480i
$425$	10.8326	−	4.10175i	0.525456	−	0.198964i
$426$		0			0
$427$	0.250858	−	0.799268i	0.0121399	−	0.0386793i
$428$	−0.259332	+	0.259332i	−0.0125353	+	0.0125353i
$429$		0			0
$430$	14.9620	−	9.66811i	0.721534	−	0.466238i
$431$	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	−0.957007	−	0.290064i	$-0.906323\pi$
$433$	−25.9499	−	25.9499i	−1.24707	−	1.24707i	−0.290064	−	0.957007i	$-0.593677\pi$
$434$	6.69979	+	4.25591i	0.321600	+	0.204290i
$435$		0			0
$436$	4.63325	−	8.02502i	0.221892	−	0.384329i
$437$	−0.681535	+	2.54352i	−0.0326022	+	0.121673i
$438$		0			0
$439$	−24.7537	−	14.2916i	−1.18143	−	0.682099i	−0.225085	−	0.974339i	$-0.572266\pi$
$439$	−24.7537	−	14.2916i	−1.18143	−	0.682099i	−0.956345	+	0.292240i	$0.905599\pi$
$440$	2.71648	+	2.45715i	0.129503	+	0.117140i
$441$		0			0
$442$	−2.31662	+	2.31662i	−0.110191	+	0.110191i
$443$	−0.530612	−	1.98027i	−0.0252101	−	0.0940854i	0.952175	−	0.305555i	$-0.0988419\pi$
$443$	−0.530612	−	1.98027i	−0.0252101	−	0.0940854i	−0.977385	+	0.211469i	$0.932175\pi$
$444$		0			0
$445$	18.7928	+	29.0831i	0.890865	+	1.37867i
$446$	−15.7278	−	9.08044i	−0.744732	−	0.429972i
$447$		0			0
$448$	−0.576028	−	2.58228i	−0.0272148	−	0.122001i
$449$	−23.4521			−1.10677			−0.553386	−	0.832925i	$-0.686665\pi$
$449$	−23.4521			−1.10677			−0.553386	+	0.832925i	$0.686665\pi$
$450$		0			0
$451$	−2.31662	−	4.01251i	−0.109086	−	0.188942i
$452$	0.517638	−	1.93185i	0.0243476	−	0.0908667i
$453$		0			0
$454$		−	23.3166i		−	1.09430i
$455$	7.21301	−	4.23940i	0.338151	−	0.198746i
$456$		0			0
$457$	4.66369	+	17.4051i	0.218158	+	0.814177i	0.985031	+	0.172378i	$0.0551451\pi$
$457$	4.66369	+	17.4051i	0.218158	+	0.814177i	−0.766873	+	0.641799i	$0.778188\pi$
$458$	25.1141	+	6.72930i	1.17350	+	0.314439i
$459$		0			0
$460$	−17.6994	+	5.70637i	−0.825238	+	0.266061i
$461$			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	0.957178	−	0.289499i	$-0.0934886\pi$
$463$	14.3668	+	14.3668i	0.667680	+	0.667680i	−0.289499	+	0.957178i	$0.593489\pi$
$464$	−0.595163	+	1.03085i	−0.0276297	+	0.0478561i
$465$		0			0
$466$	−0.525063	−	0.909435i	−0.0243231	−	0.0421288i
$467$	14.0378	−	3.76142i	0.649592	−	0.174058i	0.0810475	−	0.996710i	$-0.474173\pi$
$467$	14.0378	−	3.76142i	0.649592	−	0.174058i	0.568544	+	0.822653i	$0.307507\pi$
$468$		0			0
$469$	9.84389	+	0.416876i	0.454549	+	0.0192495i
$470$	−0.707107	−	14.1067i	−0.0326164	−	0.650693i
$471$		0			0
$472$	2.01480	+	0.539864i	0.0927388	+	0.0248493i
$473$	−12.6055	−	3.37762i	−0.579599	−	0.155303i
$474$		0			0
$475$	0.158312	+	1.57519i	0.00726387	+	0.0722746i
$476$	2.83727	+	5.43297i	0.130046	+	0.249020i
$477$		0			0
$478$	9.99470	−	2.67807i	0.457147	−	0.122492i
$479$	−0.483219	−	0.836960i	−0.0220789	−	0.0382417i	0.854775	−	0.518999i	$-0.173695\pi$
$479$	−0.483219	−	0.836960i	−0.0220789	−	0.0382417i	−0.876854	+	0.480757i	$0.840362\pi$
$480$		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
$485$	8.88676	+	27.5640i	0.403527	+	1.25162i
$486$		0			0
$487$	−2.08327	−	0.558212i	−0.0944022	−	0.0252950i	0.211309	−	0.977419i	$-0.432227\pi$
$487$	−2.08327	−	0.558212i	−0.0944022	−	0.0252950i	−0.305711	+	0.952124i	$0.598894\pi$
$488$	−0.0819485	−	0.305836i	−0.00370964	−	0.0138445i
$489$		0			0
$490$	−3.52628	−	15.2501i	−0.159301	−	0.688929i
$491$		−	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
$493$	0.713704	−	2.66358i	0.0321436	−	0.119962i
$494$	−0.223888	−	0.387785i	−0.0100732	−	0.0174473i
$495$		0			0
$496$	3.00000			0.134704
$497$	−4.33107	−	19.4158i	−0.194275	−	0.870917i
$498$		0			0
$499$	−19.0526	−	11.0000i	−0.852910	−	0.492428i	0.00872186	−	0.999962i	$-0.497224\pi$
$499$	−19.0526	−	11.0000i	−0.852910	−	0.492428i	−0.861632	+	0.507534i	$0.830557\pi$
$500$	−8.73660	+	6.97652i	−0.390713	+	0.312000i
$501$		0			0
$502$	−4.06588	−	15.1741i	−0.181469	−	0.677252i
$503$	11.0189	−	11.0189i	0.491310	−	0.491310i	−0.417409	−	0.908719i	$-0.637062\pi$
$503$	11.0189	−	11.0189i	0.491310	−	0.491310i	0.908719	+	0.417409i	$0.137062\pi$
$504$		0			0
$505$	−1.25856	−	25.1082i	−0.0560053	−	1.11730i
$506$	11.7983	+	6.81174i	0.524497	+	0.302819i
$507$		0			0
$508$	4.31601	−	16.1076i	0.191492	−	0.714658i
$509$	−0.371275	+	0.643068i	−0.0164565	+	0.0285035i	−0.874136	−	0.485681i	$-0.838572\pi$
$509$	−0.371275	+	0.643068i	−0.0164565	+	0.0285035i	0.857680	+	0.514184i	$0.171905\pi$
$510$		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
$515$	−6.40142	+	29.7828i	−0.282080	+	1.31239i
$516$		0			0
$517$	−7.31662	+	7.31662i	−0.321785	+	0.321785i
$518$	12.6572	+	13.7766i	0.556125	+	0.605310i
$519$		0			0
$520$	1.44205	−	2.81433i	0.0632382	−	0.123417i
$521$	−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
$523$	6.39761	−	1.71423i	0.279748	−	0.0749582i	−0.116217	−	0.993224i	$-0.537077\pi$
$523$	6.39761	−	1.71423i	0.279748	−	0.0749582i	0.395965	+	0.918266i	$0.370410\pi$
$524$	17.1945			0.751143
$525$		0			0
$526$	−27.5831			−1.20268
$527$	−6.71306	+	1.79876i	−0.292426	+	0.0783552i
$528$		0			0
$529$	−39.9811	+	23.0831i	−1.73831	+	1.00361i
$530$	−11.8623	+	23.1506i	−0.515264	+	1.00560i
$531$		0			0
$532$	−0.817615	+	0.182385i	−0.0354481	+	0.00790738i
$533$	−2.82843	+	2.82843i	−0.122513	+	0.122513i
$534$		0			0
$535$	−0.172329	+	0.801768i	−0.00745045	+	0.0346635i
$536$	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	$0.191209\pi$
$542$	−2.76506	+	10.3193i	−0.118770	+	0.443254i
$543$		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	−0.632639	−	0.774447i	$-0.718028\pi$
$547$	3.31662	−	3.31662i	0.141809	−	0.141809i	0.774447	+	0.632639i	$0.218028\pi$
$548$	4.65874	+	17.3867i	0.199012	+	0.742722i
$549$		0			0
$550$	8.08375	+	1.31809i	0.344692	+	0.0562036i
$551$	0.326393	+	0.188443i	0.0139048	+	0.00802796i
$552$		0			0
$553$	−24.3176	−	7.63230i	−1.03409	−	0.324558i
$554$	−18.7617			−0.797107
$555$		0			0
$556$	−6.63325	−	11.4891i	−0.281312	−	0.487247i
$557$	−2.51922	+	9.40184i	−0.106743	+	0.398369i	−0.998537	−	0.0540720i	$-0.982780\pi$
$557$	−2.51922	+	9.40184i	−0.106743	+	0.398369i	0.891794	+	0.452441i	$0.149447\pi$
$558$		0			0
$559$			11.2665i			0.476522i
$560$	−4.21564	−	4.15071i	−0.178143	−	0.175400i
$561$		0			0
$562$	−5.12436	−	19.1244i	−0.216158	−	0.806712i
$563$	13.4745	+	3.61049i	0.567884	+	0.152164i	0.531326	−	0.847167i	$-0.321694\pi$
$563$	13.4745	+	3.61049i	0.567884	+	0.152164i	0.0365582	+	0.999332i	$0.488361\pi$
$564$		0			0
$565$	−1.37228	−	4.25639i	−0.0577323	−	0.179068i
$566$		−	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	−0.959465	−	0.281828i	$-0.909059\pi$
$569$	−5.62141	+	9.73657i	−0.235662	+	0.408178i	0.723803	+	0.690007i	$0.242392\pi$
$570$		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	$0.704280\pi$
$572$	−2.23769	+	0.599587i	−0.0935624	+	0.0250700i
$573$		0			0
$574$	3.46410	+	6.63325i	0.144589	+	0.276866i
$575$	−26.3160	+	32.1967i	−1.09745	+	1.34269i
$576$		0			0
$577$	−15.6751	−	4.20012i	−0.652561	−	0.174853i	−0.0826745	−	0.996577i	$-0.526346\pi$
$577$	−15.6751	−	4.20012i	−0.652561	−	0.174853i	−0.569887	+	0.821723i	$0.693013\pi$
$578$	11.2369	+	3.01091i	0.467392	+	0.125237i
$579$		0			0
$580$	0.133250	+	2.65831i	0.00553289	+	0.110380i
$581$	−20.2390	+	31.8609i	−0.839655	+	1.32181i
$582$		0			0
$583$	18.4071	−	4.93217i	0.762344	−	0.204270i
$584$	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	$-0.327173\pi$
$587$	−8.22595	−	8.22595i	−0.339521	−	0.339521i	−0.856187	+	0.516666i	$0.827173\pi$
$588$		0			0
$589$		−	0.949874i		−	0.0391389i
$590$	4.43915	−	1.43120i	0.182757	−	0.0589218i
$591$		0			0
$592$	6.83013	+	1.83013i	0.280716	+	0.0752178i
$593$	5.61207	+	20.9445i	0.230460	+	0.860089i	0.980143	+	0.198292i	$0.0635393\pi$
$593$	5.61207	+	20.9445i	0.230460	+	0.860089i	−0.749683	+	0.661797i	$0.769794\pi$
$594$		0			0
$595$	11.9220	+	6.76035i	0.488754	+	0.277148i
$596$			7.07107i			0.289642i
$597$		0			0
$598$	3.04410	−	11.3607i	0.124482	−	0.464574i
$599$	−2.38065	−	4.12341i	−0.0972708	−	0.168478i	0.813283	−	0.581868i	$-0.197678\pi$
$599$	−2.38065	−	4.12341i	−0.0972708	−	0.168478i	−0.910554	+	0.413390i	$0.864345\pi$
$600$		0			0
$601$	31.6332			1.29035			0.645174	−	0.764036i	$-0.276785\pi$
$601$	31.6332			1.29035			0.645174	+	0.764036i	$0.276785\pi$
$602$	20.1104	+	6.31185i	0.819640	+	0.257252i
$603$		0			0
$604$	−20.1928	−	11.6583i	−0.821633	−	0.474370i
$605$	10.0929	+	15.6194i	0.410334	+	0.635018i
$606$		0			0
$607$	−5.18230	−	19.3406i	−0.210343	−	0.785011i	−0.987754	−	0.156018i	$-0.950134\pi$
$607$	−5.18230	−	19.3406i	−0.210343	−	0.785011i	0.777411	−	0.628993i	$-0.216533\pi$
$608$	−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
$613$	−10.8465	+	40.4798i	−0.438087	+	1.63496i	0.295483	+	0.955348i	$0.404520\pi$
$613$	−10.8465	+	40.4798i	−0.438087	+	1.63496i	−0.733569	+	0.679614i	$0.762147\pi$
$614$	−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	$-0.00161302\pi$
$617$	24.7133	+	24.7133i	0.994920	+	0.994920i	−0.00506744	+	0.999987i	$0.501613\pi$
$618$		0			0
$619$	−23.8877	+	13.7916i	−0.960127	+	0.554330i	−0.896212	−	0.443626i	$-0.853692\pi$
$619$	−23.8877	+	13.7916i	−0.960127	+	0.554330i	−0.0639150	+	0.997955i	$0.520359\pi$
$620$	5.63427	−	3.64073i	0.226278	−	0.146215i
$621$		0			0
$622$	3.68338	−	3.68338i	0.147690	−	0.147690i
$623$	−12.2689	+	39.0905i	−0.491544	+	1.56613i
$624$		0			0
$625$	−7.94158	+	23.7051i	−0.317663	+	0.948204i
$626$	6.70540	−	3.87137i	0.268002	−	0.154731i
$627$		0			0
$628$	14.0928	−	3.77615i	0.562363	−	0.150685i
$629$	−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	$0.359004\pi$
$632$	−9.30500	+	2.49327i	−0.370133	+	0.0991769i
$633$		0			0
$634$	−13.8130	+	7.97494i	−0.548584	+	0.316725i
$635$	−11.4419	−	35.4893i	−0.454059	−	1.40835i
$636$		0			0
$637$	9.31132	+	3.36145i	0.368928	+	0.133185i
$638$	1.37877	−	1.37877i	0.0545860	−	0.0545860i
$639$		0			0
$640$	−2.18614	−	0.469882i	−0.0864148	−	0.0185737i
$641$	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	−0.952045	−	0.305958i	$-0.901023\pi$
$643$	−31.8997	−	31.8997i	−1.25800	−	1.25800i	−0.305958	−	0.952045i	$-0.598977\pi$
$644$	−18.5732	−	11.7983i	−0.731887	−	0.464917i
$645$		0			0
$646$	0.366750	−	0.635230i	0.0144296	−	0.0249928i
$647$	3.67947	−	13.7320i	0.144655	−	0.539859i	−0.855116	−	0.518437i	$-0.826514\pi$
$647$	3.67947	−	13.7320i	0.144655	−	0.539859i	0.999771	−	0.0214219i	$-0.00681934\pi$
$648$		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
$653$	−2.73911	−	10.2225i	−0.107190	−	0.400038i	0.891395	−	0.453228i	$-0.149728\pi$
$653$	−2.73911	−	10.2225i	−0.107190	−	0.400038i	−0.998584	+	0.0531903i	$0.983061\pi$
$654$		0			0
$655$	32.2928	−	20.8668i	1.26178	−	0.815334i
$656$	2.44949	+	1.41421i	0.0956365	+	0.0552158i
$657$		0			0
$658$	12.3067	−	11.3067i	0.479767	−	0.440783i
$659$	−28.8029			−1.12200			−0.561002	−	0.827815i	$-0.689584\pi$
$659$	−28.8029			−1.12200			−0.561002	+	0.827815i	$0.689584\pi$
$660$		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	$0.844377\pi$
$662$	4.30500	−	16.0665i	0.167319	−	0.624442i
$663$		0			0
$664$			14.2665i			0.553648i
$665$	−1.31422	+	1.33478i	−0.0509632	+	0.0517604i
$666$		0			0
$667$	2.56218	+	9.56218i	0.0992079	+	0.370249i
$668$	7.72741	+	2.07055i	0.298982	+	0.0801121i
$669$		0			0
$670$	3.79729	−	7.41085i	0.146702	−	0.286306i
$671$			0.518663i			0.0200228i
$672$		0			0
$673$	−25.7414	−	25.7414i	−0.992259	−	0.992259i	0.00771082	−	0.999970i	$-0.497546\pi$
$673$	−25.7414	−	25.7414i	−0.992259	−	0.992259i	−0.999970	+	0.00771082i	$0.997546\pi$
$674$	−4.31914	+	7.48097i	−0.166367	+	0.288156i
$675$		0			0
$676$	−5.50000	−	9.52628i	−0.211538	−	0.366395i
$677$	−12.8629	+	3.44660i	−0.494360	+	0.132463i	−0.497381	−	0.867532i	$-0.665705\pi$
$677$	−12.8629	+	3.44660i	−0.494360	+	0.132463i	0.00302107	+	0.999995i	$0.499038\pi$
$678$		0			0
$679$	−18.3739	+	28.9248i	−0.705126	+	1.11003i
$680$	5.17364	−	0.259332i	0.198400	−	0.00994492i
$681$		0			0
$682$	−4.74685	−	1.27192i	−0.181766	−	0.0487042i
$683$	45.2048	+	12.1126i	1.72972	+	0.463476i	0.980118	−	0.198418i	$-0.0635803\pi$
$683$	45.2048	+	12.1126i	1.72972	+	0.463476i	0.749598	+	0.661894i	$0.230247\pi$
$684$		0			0
$685$	29.8496	+	27.0000i	1.14050	+	1.03162i
$686$	11.2166	−	14.7373i	0.428252	−	0.562673i
$687$		0			0
$688$	7.69516	−	2.06191i	0.293375	−	0.0786097i
$689$	−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
$695$	−26.4008	−	13.5277i	−1.00144	−	0.513133i
$696$		0			0
$697$	−6.32914	−	1.69589i	−0.239733	−	0.0642363i
$698$	−1.03528	−	3.86370i	−0.0391858	−	0.146243i
$699$		0			0
$700$	−12.9546	−	2.67941i	−0.489637	−	0.101272i
$701$			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
$703$	0.579464	−	2.16259i	0.0218549	−	0.0815635i
$704$	0.819051	+	1.41864i	0.0308691	+	0.0534669i
$705$		0			0
$706$	23.8997			0.899479
$707$	21.9045	−	20.1246i	0.823803	−	0.756864i
$708$		0			0
$709$	−9.75707	−	5.63325i	−0.366435	−	0.211561i	0.305465	−	0.952203i	$-0.401188\pi$
$709$	−9.75707	−	5.63325i	−0.366435	−	0.211561i	−0.671900	+	0.740642i	$0.734521\pi$
$710$	−16.4372	−	3.53297i	−0.616879	−	0.132590i
$711$		0			0
$712$	4.00793	+	14.9578i	0.150204	+	0.560568i
$713$	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
$718$	−3.15999	+	11.7932i	−0.117930	+	0.440120i
$719$	−16.0041	+	27.7200i	−0.596853	+	1.03378i	0.396429	+	0.918065i	$0.370249\pi$
$719$	−16.0041	+	27.7200i	−0.596853	+	1.03378i	−0.993282	+	0.115715i	$0.963084\pi$
$720$		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
$725$	3.47632	+	4.83085i	0.129107	+	0.179413i
$726$		0			0
$727$	−7.89181	+	7.89181i	−0.292691	+	0.292691i	−0.838142	−	0.545451i	$-0.816358\pi$
$727$	−7.89181	+	7.89181i	−0.292691	+	0.292691i	0.545451	+	0.838142i	$0.316358\pi$
$728$	3.65190	−	0.814627i	0.135348	−	0.0301921i
$729$		0			0
$730$	26.2201	+	13.4351i	0.970450	+	0.497254i
$731$	−15.9831	+	9.22783i	−0.591155	+	0.341304i
$732$		0			0
$733$	44.0769	−	11.8104i	1.62802	−	0.436226i	0.674673	−	0.738116i	$-0.264284\pi$
$733$	44.0769	−	11.8104i	1.62802	−	0.436226i	0.953342	+	0.301891i	$0.0976178\pi$
$734$	−4.91430			−0.181390
$735$		0			0
$736$	−8.31662			−0.306555
$737$	−5.89239	+	1.57886i	−0.217049	+	0.0581581i
$738$		0			0
$739$	−22.4298	+	12.9499i	−0.825095	+	0.476369i	−0.852170	−	0.523265i	$-0.824714\pi$
$739$	−22.4298	+	12.9499i	−0.825095	+	0.476369i	0.0270753	+	0.999633i	$0.491381\pi$
$740$	15.0486	−	4.85175i	0.553198	−	0.178354i
$741$		0			0
$742$	−30.0404	+	6.70108i	−1.10282	+	0.246004i
$743$	−7.00018	+	7.00018i	−0.256812	+	0.256812i	−0.823756	−	0.566944i	$-0.808125\pi$
$743$	−7.00018	+	7.00018i	−0.256812	+	0.256812i	0.566944	+	0.823756i	$0.308125\pi$
$744$		0			0
$745$	8.58129	+	13.2801i	0.314394	+	0.486546i
$746$	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	$0.172475\pi$
$752$	1.63486	−	6.10139i	0.0596173	−	0.222495i
$753$		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	−0.398600	−	0.917125i	$-0.630504\pi$
$757$	14.2665	−	14.2665i	0.518525	−	0.518525i	0.917125	+	0.398600i	$0.130504\pi$
$758$	−4.49485	−	16.7750i	−0.163260	−	0.609295i
$759$		0			0
$760$	−0.148776	+	0.692186i	−0.00539668	+	0.0251082i
$761$	−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
$763$	18.0540	−	16.5870i	0.653599	−	0.600490i
$764$	1.93288			0.0699290
$765$		0			0
$766$	1.00000	+	1.73205i	0.0361315	+	0.0625815i
$767$	−0.763484	+	2.84936i	−0.0275678	+	0.102884i
$768$		0			0
$769$		−	22.3668i		−	0.806566i	−0.915075	−	0.403283i	$-0.867869\pi$
$769$		−	22.3668i		−	0.806566i	0.915075	−	0.403283i	$-0.132131\pi$
$770$	4.91055	+	8.35492i	0.176964	+	0.301090i
$771$		0			0
$772$	−0.905890	−	3.38083i	−0.0326037	−	0.121679i
$773$	−1.22334	−	0.327794i	−0.0440006	−	0.0117899i	0.236752	−	0.971570i	$-0.423917\pi$
$773$	−1.22334	−	0.327794i	−0.0440006	−	0.0117899i	−0.280752	+	0.959780i	$0.590584\pi$
$774$		0			0
$775$	6.16337	−	13.6753i	0.221395	−	0.491230i
$776$			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
$782$	18.6100	−	4.98654i	0.665493	−	0.178318i
$783$		0			0
$784$	0.591820	−	6.97494i	0.0211364	−	0.249105i
$785$	21.8849	−	24.1946i	0.781104	−	0.863543i
$786$		0			0
$787$	2.80052	+	0.750398i	0.0998279	+	0.0267488i	0.308387	−	0.951261i	$-0.400211\pi$
$787$	2.80052	+	0.750398i	0.0998279	+	0.0267488i	−0.208559	+	0.978010i	$0.566877\pi$
$788$	13.4261	+	3.59752i	0.478286	+	0.128156i
$789$		0			0
$790$	−14.4499	+	15.9749i	−0.514103	+	0.568363i
$791$	2.83727	−	4.46653i	0.100882	−	0.158811i
$792$		0			0
$793$	0.432518	−	0.115893i	0.0153591	−	0.00411547i
$794$	−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	$-0.280585\pi$
$797$	−3.83031	−	3.83031i	−0.135677	−	0.135677i	−0.771683	+	0.636007i	$0.780585\pi$
$798$		0			0
$799$			14.6332i			0.517687i
$800$	−4.67601	+	1.77057i	−0.165322	+	0.0625992i
$801$		0			0
$802$	−6.76165	−	1.81178i	−0.238762	−	0.0639762i
$803$	−5.58612	−	20.8477i	−0.197130	−	0.735699i
$804$		0			0
$805$	−49.2003	+	0.381817i	−1.73408	+	0.0134573i
$806$			4.24264i			0.149441i
$807$		0			0
$808$	2.90986	−	10.8597i	0.102368	−	0.382044i
$809$	−17.9370	−	31.0678i	−0.630631	−	1.09229i	−0.987423	−	0.158102i	$-0.949463\pi$
$809$	−17.9370	−	31.0678i	−0.630631	−	1.09229i	0.356791	−	0.934184i	$-0.383871\pi$
$810$		0			0
$811$	10.1003			0.354668			0.177334	−	0.984151i	$-0.443253\pi$
$811$	10.1003			0.354668			0.177334	+	0.984151i	$0.443253\pi$
$812$	−2.31912	+	2.13068i	−0.0813853	+	0.0747722i
$813$		0			0
$814$	−10.0313	−	5.79156i	−0.351596	−	0.202994i
$815$	−7.94085	+	36.9451i	−0.278156	+	1.29413i
$816$		0			0
$817$	−0.652853	−	2.43648i	−0.0228404	−	0.0852416i
$818$	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
$823$	6.91779	−	25.8175i	0.241139	−	0.899943i	−0.734146	−	0.678992i	$-0.762417\pi$
$823$	6.91779	−	25.8175i	0.241139	−	0.899943i	0.975285	−	0.220951i	$-0.0709161\pi$
$824$	−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	$-0.0576183\pi$
$827$	23.1106	+	23.1106i	0.803636	+	0.803636i	−0.180026	+	0.983662i	$0.557618\pi$
$828$		0			0
$829$	−37.1089	+	21.4248i	−1.28884	+	0.744114i	−0.978448	−	0.206493i	$-0.933795\pi$
$829$	−37.1089	+	21.4248i	−1.28884	+	0.744114i	−0.310396	+	0.950607i	$0.600462\pi$
$830$	17.3135	+	26.7938i	0.600961	+	0.930026i
$831$		0			0
$832$	1.00000	−	1.00000i	0.0346688	−	0.0346688i
$833$	2.85777	+	15.9626i	0.0990159	+	0.553071i
$834$		0			0
$835$	17.0256	−	5.48913i	0.589194	−	0.189959i
$836$	0.449176	−	0.259332i	0.0155351	−	0.00896917i
$837$		0			0
$838$	24.0875	−	6.45422i	0.832088	−	0.222957i
$839$	41.3182			1.42646			0.713231	−	0.700929i	$-0.247231\pi$
$839$	41.3182			1.42646			0.713231	+	0.700929i	$0.247231\pi$
$840$		0			0
$841$	−27.5831			−0.951142
$842$	1.52918	−	0.409743i	0.0526990	−	0.0141207i
$843$		0			0
$844$	12.9470	−	7.47494i	0.445653	−	0.257298i
$845$	−21.8904	−	11.2165i	−0.753052	−	0.385861i
$846$		0			0
$847$	−6.58915	+	20.9940i	−0.226406	+	0.721361i
$848$	−8.22595	+	8.22595i	−0.282480	+	0.282480i
$849$		0			0
$850$	9.40184	−	6.76566i	0.322480	−	0.232060i
$851$	50.9287	−	29.4037i	1.74581	−	1.00795i
$852$		0			0
$853$	22.3166	+	22.3166i	0.764107	+	0.764107i	0.977062	−	0.212955i	$-0.0683089\pi$
$853$	22.3166	+	22.3166i	0.764107	+	0.764107i	−0.212955	+	0.977062i	$0.568309\pi$
$854$	0.0354442	−	0.836960i	0.00121287	−	0.0286402i
$855$		0			0
$856$	−0.183375	+	0.317615i	−0.00626764	+	0.0108559i
$857$	13.0229	−	48.6021i	0.444854	−	1.66022i	−0.271468	−	0.962447i	$-0.587509\pi$
$857$	13.0229	−	48.6021i	0.444854	−	1.66022i	0.716322	−	0.697770i	$-0.245824\pi$
$858$		0			0
$859$	40.5730	+	23.4248i	1.38433	+	0.799244i	0.992669	−	0.120865i	$-0.0385667\pi$
$859$	40.5730	+	23.4248i	1.38433	+	0.799244i	0.391663	+	0.920109i	$0.371900\pi$
$860$	11.9499	−	13.2111i	0.407489	−	0.450496i
$861$		0			0
$862$	28.9499	−	28.9499i	0.986037	−	0.986037i
$863$	−13.9243	−	51.9663i	−0.473990	−	1.76895i	−0.625213	−	0.780455i	$-0.714988\pi$
$863$	−13.9243	−	51.9663i	−0.473990	−	1.76895i	0.151223	−	0.988500i	$-0.451679\pi$
$864$		0			0
$865$	43.5036	+	9.35053i	1.47917	+	0.317928i
$866$	−31.7820	−	18.3493i	−1.08000	−	0.623536i
$867$		0			0
$868$	7.57301	+	2.37686i	0.257045	+	0.0806759i
$869$	15.7802			0.535308
$870$		0			0
$871$	2.63325	+	4.56092i	0.0892243	+	0.154541i
$872$	2.39835	−	8.95075i	0.0812183	−	0.303111i
$873$		0			0
$874$			2.63325i			0.0890710i
$875$	−27.5815	+	10.6892i	−0.932426	+	0.361361i
$876$		0			0
$877$	−10.2120	−	38.1118i	−0.344835	−	1.28694i	−0.892804	−	0.450444i	$-0.851266\pi$
$877$	−10.2120	−	38.1118i	−0.344835	−	1.28694i	0.547969	−	0.836499i	$-0.315401\pi$
$878$	−27.6092	−	7.39786i	−0.931765	−	0.249666i
$879$		0			0
$880$	3.25988	+	1.67035i	0.109891	+	0.0563074i
$881$			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	0.859059	−	0.511877i	$-0.171050\pi$
$883$	10.3166	+	10.3166i	0.347182	+	0.347182i	−0.511877	+	0.859059i	$0.671050\pi$
$884$	−1.63810	+	2.83727i	−0.0550953	+	0.0954279i
$885$		0			0
$886$	−1.02506	−	1.77546i	−0.0344377	−	0.0596478i
$887$	−18.3042	+	4.90459i	−0.614594	+	0.164680i	−0.552669	−	0.833401i	$-0.686391\pi$
$887$	−18.3042	+	4.90459i	−0.614594	+	0.164680i	−0.0619250	+	0.998081i	$0.519724\pi$
$888$		0			0
$889$	23.6569	−	37.2414i	0.793427	−	1.24904i
$890$	25.6797	+	23.2282i	0.860787	+	0.778611i
$891$		0			0
$892$	−17.5421	−	4.70038i	−0.587352	−	0.157380i
$893$	−1.93185	−	0.517638i	−0.0646470	−	0.0173221i
$894$		0			0
$895$	3.15831	−	0.158312i	0.105571	−	0.00529180i
$896$	−1.22474	−	2.34521i	−0.0409159	−	0.0783479i
$897$		0			0
$898$	−22.6530	+	6.06984i	−0.755939	+	0.202553i
$899$	−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
$905$	11.5905	−	22.6202i	0.385282	−	0.751922i
$906$		0			0
$907$	55.0051	+	14.7386i	1.82641	+	0.489386i	0.997543	−	0.0700554i	$-0.0223176\pi$
$907$	55.0051	+	14.7386i	1.82641	+	0.489386i	0.828870	+	0.559441i	$0.188984\pi$
$908$	−6.03479	−	22.5221i	−0.200271	−	0.747423i
$909$		0			0
$910$	5.86999	−	5.96181i	0.194588	−	0.197632i
$911$			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
$913$	6.04859	−	22.5737i	0.200179	−	0.747079i
$914$	9.00956	+	15.6050i	0.298010	+	0.516168i
$915$		0			0
$916$	26.0000			0.859064
$917$	43.4046	+	13.6229i	1.43335	+	0.449869i
$918$		0			0
$919$	6.29297	+	3.63325i	0.207586	+	0.119850i	0.600189	−	0.799858i	$-0.295092\pi$
$919$	6.29297	+	3.63325i	0.207586	+	0.119850i	−0.392603	+	0.919708i	$0.628425\pi$
$920$	−15.6194	+	10.0929i	−0.514956	+	0.332752i
$921$		0			0
$922$	7.30216	+	27.2520i	0.240484	+	0.897498i
$923$	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
$928$	−0.308079	+	1.14977i	−0.0101132	+	0.0377429i
$929$	28.2488	−	48.9284i	0.926814	−	1.60529i	0.138196	−	0.990405i	$-0.455869\pi$
$929$	28.2488	−	48.9284i	0.926814	−	1.60529i	0.788618	−	0.614884i	$-0.210797\pi$
$930$		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
$935$	−8.29611	−	1.78314i	−0.271312	−	0.0583149i
$936$		0			0
$937$	−16.3747	+	16.3747i	−0.534938	+	0.534938i	−0.922038	−	0.387100i	$-0.873477\pi$
$937$	−16.3747	+	16.3747i	−0.534938	+	0.534938i	0.387100	+	0.922038i	$0.373477\pi$
$938$	9.61637	−	2.14512i	0.313986	−	0.0700405i
$939$		0			0
$940$	−4.33409	−	13.4430i	−0.141363	−	0.438462i
$941$	−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
$943$	22.7214	−	6.08819i	0.739912	−	0.198259i
$944$	2.08588			0.0678895
$945$		0			0
$946$	−13.0501			−0.424296
$947$	10.9794	−	2.94193i	0.356784	−	0.0955999i	−0.0759749	−	0.997110i	$-0.524207\pi$
$947$	10.9794	−	2.94193i	0.356784	−	0.0955999i	0.432759	+	0.901510i	$0.357540\pi$
$948$		0			0
$949$	−16.1369	+	9.31662i	−0.523825	+	0.302430i
$950$	0.560607	+	1.48054i	0.0181885	+	0.0480351i
$951$		0			0
$952$	4.14675	+	4.51350i	0.134397	+	0.146283i
$953$	36.8517	−	36.8517i	1.19374	−	1.19374i	0.217734	−	0.976008i	$-0.430133\pi$
$953$	36.8517	−	36.8517i	1.19374	−	1.19374i	0.976008	−	0.217734i	$-0.0698667\pi$
$954$		0			0
$955$	3.63012	−	2.34570i	0.117468	−	0.0759050i
$956$	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
$962$	−2.58819	+	9.65926i	−0.0834466	+	0.311427i
$963$		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	−0.997216	−	0.0745657i	$-0.976243\pi$
$967$	−28.6913	+	28.6913i	−0.922650	+	0.922650i	0.0745657	+	0.997216i	$0.476243\pi$
$968$	2.15250	+	8.03324i	0.0691840	+	0.258198i
$969$		0			0
$970$	15.7180	+	24.3247i	0.504676	+	0.781019i
$971$	−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
$973$	−7.64188	−	34.2579i	−0.244987	−	1.09826i
$974$	−2.15676			−0.0691072
$975$		0			0
$976$	−0.158312	−	0.274205i	−0.00506746	−	0.00877709i
$977$	4.74069	−	17.6925i	0.151668	−	0.566033i	−0.847700	−	0.530477i	$-0.822013\pi$
$977$	4.74069	−	17.6925i	0.151668	−	0.566033i	0.999368	−	0.0355565i	$-0.0113204\pi$
$978$		0			0
$979$		−	25.3668i		−	0.810725i
$980$	−7.35314	−	13.8178i	−0.234887	−	0.441393i
$981$		0			0
$982$	−2.48588	−	9.27745i	−0.0793278	−	0.296055i
$983$	−34.0648	−	9.12764i	−1.08650	−	0.291127i	−0.329243	−	0.944245i	$-0.606794\pi$
$983$	−34.0648	−	9.12764i	−1.08650	−	0.291127i	−0.757256	+	0.653119i	$0.773460\pi$
$984$		0			0
$985$	29.5814	−	9.53718i	0.942541	−	0.303880i
$986$		−	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	$0.887608\pi$
$992$	2.89778	−	0.776457i	0.0920045	−	0.0246525i
$993$		0			0
$994$	−9.20866	−	17.6332i	−0.292081	−	0.559293i
$995$	0.966438	+	19.2803i	0.0306382	+	0.611227i
$996$		0			0
$997$	2.29953	+	0.616158i	0.0728270	+	0.0195139i	0.295049	−	0.955482i	$-0.404664\pi$
$997$	2.29953	+	0.616158i	0.0728270	+	0.0195139i	−0.222222	+	0.974996i	$0.571331\pi$
$998$	−21.2504	−	5.69402i	−0.672669	−	0.180241i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.b.53.2	✓	16	7.4	even	3	inner
630.2.ce.b.53.3	yes	16	21.11	odd	6	inner
630.2.ce.b.107.2	yes	16	15.2	even	4	inner
630.2.ce.b.107.3	yes	16	5.2	odd	4	inner
630.2.ce.b.233.2	yes	16	3.2	odd	2	inner
630.2.ce.b.233.3	yes	16	1.1	even	1	trivial
630.2.ce.b.557.2	yes	16	35.32	odd	12	inner
630.2.ce.b.557.3	yes	16	105.32	even	12	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)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.01969 - 1.99004i) q^{5} +(2.58228 - 0.576028i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.01969 - 1.99004i) q^{5} +(2.58228 - 0.576028i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.469882 - 2.18614i) q^{10} +(-1.41864 + 0.819051i) q^{11} +(1.00000 + 1.00000i) q^{13} +(2.34521 - 1.22474i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.599587 + 2.23769i) q^{17} +(-0.274205 - 0.158312i) q^{19} +(-0.111944 - 2.23326i) q^{20} +(-1.15831 + 1.15831i) q^{22} +(-2.15250 - 8.03324i) q^{23} +(-2.92048 - 4.05842i) q^{25} +(1.22474 + 0.707107i) q^{26} +(1.94831 - 1.79000i) q^{28} -1.19033 q^{29} +(1.50000 + 2.59808i) q^{31} +(0.258819 - 0.965926i) q^{32} +2.31662i q^{34} +(1.48680 - 5.72620i) q^{35} +(1.83013 + 6.83013i) q^{37} +(-0.305836 - 0.0819485i) q^{38} +(-0.686141 - 2.12819i) q^{40} +2.82843i q^{41} +(5.63325 + 5.63325i) q^{43} +(-0.819051 + 1.41864i) q^{44} +(-4.15831 - 7.20241i) q^{46} +(6.10139 - 1.63486i) q^{47} +(6.33638 - 2.97494i) q^{49} +(-3.87137 - 3.16426i) q^{50} +(1.36603 + 0.366025i) q^{52} +(-11.2369 - 3.01091i) q^{53} +(0.183375 + 3.65831i) q^{55} +(1.41864 - 2.23326i) q^{56} +(-1.14977 + 0.308079i) q^{58} +(1.04294 + 1.80642i) q^{59} +(0.158312 - 0.274205i) q^{61} +(2.12132 + 2.12132i) q^{62} -1.00000i q^{64} +(3.00972 - 0.970349i) q^{65} +(3.59709 + 0.963836i) q^{67} +(0.599587 + 2.23769i) q^{68} +(-0.0459101 - 5.91590i) q^{70} -7.51884i q^{71} +(-3.41012 + 12.7267i) q^{73} +(3.53553 + 6.12372i) q^{74} -0.316625 q^{76} +(-3.19153 + 2.93220i) q^{77} +(-8.34264 - 4.81662i) q^{79} +(-1.21358 - 1.87809i) q^{80} +(0.732051 + 2.73205i) q^{82} +(-10.0879 + 10.0879i) q^{83} +(3.84169 + 3.47494i) q^{85} +(6.89929 + 3.98331i) q^{86} +(-0.423972 + 1.58228i) q^{88} +(-7.74273 + 13.4108i) q^{89} +(3.15831 + 2.00626i) q^{91} +(-5.88074 - 5.88074i) q^{92} +(5.47036 - 3.15831i) q^{94} +(-0.594650 + 0.384249i) q^{95} +(-9.15831 + 9.15831i) q^{97} +(5.35051 - 4.51355i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{7}+O(q^{10}) \) 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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