LMFDB - Embedded newform 624.2.bv.g.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(49,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("624.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bv (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.649638144.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 14x^{6} + 75x^{4} - 170x^{2} + 169 $ x^8 - 14x^6 + 75x^4 - 170*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$-2.34138 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	624.49
Dual form			624.2.bv.g.433.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{3} -0.475353i q^{5} +(-3.94508 - 2.27769i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.43069 - 0.826009i) q^{11} +(2.88139 - 2.16739i) q^{13} +(0.411667 - 0.237676i) q^{15} +(3.96973 - 6.87577i) q^{17} +(2.25402 + 1.30136i) q^{19} -4.55539i q^{21} +(-1.90604 - 3.30136i) q^{23} +4.77404 q^{25} -1.00000 q^{27} +(-0.411667 - 0.713029i) q^{29} -1.79260i q^{31} +(1.43069 + 0.826009i) q^{33} +(-1.08271 + 1.87530i) q^{35} +(-1.62174 + 0.936315i) q^{37} +(3.31771 + 1.41167i) q^{39} +(-9.26841 + 5.35112i) q^{41} +(4.94508 - 8.56513i) q^{43} +(0.411667 + 0.237676i) q^{45} +7.29869i q^{47} +(6.87577 + 11.9092i) q^{49} +7.93945 q^{51} -10.0063 q^{53} +(-0.392645 - 0.680082i) q^{55} +2.60272i q^{57} +(-1.28744 - 0.743302i) q^{59} +(5.87014 - 10.1674i) q^{61} +(3.94508 - 2.27769i) q^{63} +(-1.03027 - 1.36968i) q^{65} +(-2.87826 + 1.66176i) q^{67} +(1.90604 - 3.30136i) q^{69} +(-1.65130 - 0.953379i) q^{71} +6.14686i q^{73} +(2.38702 + 4.13444i) q^{75} -7.52558 q^{77} +10.7515 q^{79} +(-0.500000 - 0.866025i) q^{81} -14.7628i q^{83} +(-3.26841 - 1.88702i) q^{85} +(0.411667 - 0.713029i) q^{87} +(-6.32548 + 3.65202i) q^{89} +(-16.3040 + 1.98758i) q^{91} +(1.55243 - 0.896298i) q^{93} +(0.618606 - 1.07146i) q^{95} +(-3.62423 - 2.09245i) q^{97} +1.65202i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{15} + 12 q^{17} - 6 q^{19} + 2 q^{23} - 4 q^{25} - 8 q^{27} + 6 q^{29} + 6 q^{33} - 10 q^{35} - 24 q^{41} + 8 q^{43} - 6 q^{45} + 18 q^{49} + 24 q^{51}+ \cdots - 66 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^9 + 6 * q^11 - 6 * q^13 - 6 * q^15 + 12 * q^17 - 6 * q^19 + 2 * q^23 - 4 * q^25 - 8 * q^27 + 6 * q^29 + 6 * q^33 - 10 * q^35 - 24 * q^41 + 8 * q^43 - 6 * q^45 + 18 * q^49 + 24 * q^51 + 4 * q^53 + 10 * q^55 + 36 * q^59 + 2 * q^61 - 28 * q^65 - 36 * q^67 - 2 * q^69 - 6 * q^71 - 2 * q^75 + 56 * q^77 + 12 * q^79 - 4 * q^81 + 24 * q^85 - 6 * q^87 - 12 * q^89 - 38 * q^91 - 6 * q^93 + 34 * q^95 - 66 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$		−	0.475353i		−	0.212584i	−0.994335	−	0.106292i	$-0.966102\pi$
$5$		−	0.475353i		−	0.212584i	0.994335	−	0.106292i	$-0.0338979\pi$
$6$		0			0
$7$	−3.94508	−	2.27769i	−1.49110	−	0.860887i	−0.491152	−	0.871074i	$-0.663424\pi$
$7$	−3.94508	−	2.27769i	−1.49110	−	0.860887i	−0.999948	+	0.0101870i	$0.996757\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	1.43069	−	0.826009i	0.431369	−	0.249051i	−0.268561	−	0.963263i	$-0.586548\pi$
$11$	1.43069	−	0.826009i	0.431369	−	0.249051i	0.699930	+	0.714212i	$0.253215\pi$
$12$		0			0
$13$	2.88139	−	2.16739i	0.799155	−	0.601125i
$13$	2.88139	−	2.16739i	0.799155	−	0.601125i
$14$		0			0
$15$	0.411667	−	0.237676i	0.106292	−	0.0613678i
$16$		0			0
$17$	3.96973	−	6.87577i	0.962800	−	1.66762i	0.247388	−	0.968917i	$-0.420428\pi$
$17$	3.96973	−	6.87577i	0.962800	−	1.66762i	0.715412	−	0.698702i	$-0.246239\pi$
$18$		0			0
$19$	2.25402	+	1.30136i	0.517109	+	0.298553i	0.735751	−	0.677252i	$-0.236829\pi$
$19$	2.25402	+	1.30136i	0.517109	+	0.298553i	−0.218642	+	0.975805i	$0.570163\pi$
$20$		0			0
$21$		−	4.55539i		−	0.994067i
$22$		0			0
$23$	−1.90604	−	3.30136i	−0.397437	−	0.688381i	0.595972	−	0.803005i	$-0.296767\pi$
$23$	−1.90604	−	3.30136i	−0.397437	−	0.688381i	−0.993409	+	0.114624i	$0.963434\pi$
$24$		0			0
$25$	4.77404			0.954808
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−0.411667	−	0.713029i	−0.0764447	−	0.132406i	0.825269	−	0.564740i	$-0.191024\pi$
$29$	−0.411667	−	0.713029i	−0.0764447	−	0.132406i	−0.901714	+	0.432334i	$0.857690\pi$
$30$		0			0
$31$		−	1.79260i		−	0.321960i	−0.986958	−	0.160980i	$-0.948535\pi$
$31$		−	1.79260i		−	0.321960i	0.986958	−	0.160980i	$-0.0514654\pi$
$32$		0			0
$33$	1.43069	+	0.826009i	0.249051	+	0.143790i
$34$		0			0
$35$	−1.08271	+	1.87530i	−0.183011	+	0.316984i
$36$		0			0
$37$	−1.62174	+	0.936315i	−0.266613	+	0.153929i	−0.627348	−	0.778739i	$-0.715859\pi$
$37$	−1.62174	+	0.936315i	−0.266613	+	0.153929i	0.360734	+	0.932669i	$0.382526\pi$
$38$		0			0
$39$	3.31771	+	1.41167i	0.531259	+	0.226048i
$40$		0			0
$41$	−9.26841	+	5.35112i	−1.44748	+	0.835705i	−0.998331	−	0.0577505i	$-0.981607\pi$
$41$	−9.26841	+	5.35112i	−1.44748	+	0.835705i	−0.449152	+	0.893455i	$0.648274\pi$
$42$		0			0
$43$	4.94508	−	8.56513i	0.754118	−	1.30617i	−0.191694	−	0.981455i	$-0.561398\pi$
$43$	4.94508	−	8.56513i	0.754118	−	1.30617i	0.945812	−	0.324715i	$-0.105268\pi$
$44$		0			0
$45$	0.411667	+	0.237676i	0.0613678	+	0.0354307i
$46$		0			0
$47$			7.29869i			1.06462i	0.846549	+	0.532311i	$0.178676\pi$
$47$			7.29869i			1.06462i	−0.846549	+	0.532311i	$0.821324\pi$
$48$		0			0
$49$	6.87577	+	11.9092i	0.982253	+	1.70131i
$50$		0			0
$51$	7.93945			1.11175
$52$		0			0
$53$	−10.0063			−1.37447			−0.687234	−	0.726436i	$-0.741175\pi$
$53$	−10.0063			−1.37447			−0.687234	+	0.726436i	$0.741175\pi$
$54$		0			0
$55$	−0.392645	−	0.680082i	−0.0529443	−	0.0917022i
$56$		0			0
$57$			2.60272i			0.344739i
$58$		0			0
$59$	−1.28744	−	0.743302i	−0.167610	−	0.0967696i	0.413848	−	0.910346i	$-0.364184\pi$
$59$	−1.28744	−	0.743302i	−0.167610	−	0.0967696i	−0.581458	+	0.813576i	$0.697518\pi$
$60$		0			0
$61$	5.87014	−	10.1674i	0.751595	−	1.30180i	−0.195455	−	0.980713i	$-0.562618\pi$
$61$	5.87014	−	10.1674i	0.751595	−	1.30180i	0.947049	−	0.321088i	$-0.104048\pi$
$62$		0			0
$63$	3.94508	−	2.27769i	0.497033	−	0.286962i
$64$		0			0
$65$	−1.03027	−	1.36968i	−0.127790	−	0.169888i
$66$		0			0
$67$	−2.87826	+	1.66176i	−0.351635	+	0.203016i	−0.665405	−	0.746482i	$-0.731741\pi$
$67$	−2.87826	+	1.66176i	−0.351635	+	0.203016i	0.313770	+	0.949499i	$0.398408\pi$
$68$		0			0
$69$	1.90604	−	3.30136i	0.229460	−	0.397437i
$70$		0			0
$71$	−1.65130	−	0.953379i	−0.195973	−	0.113145i	0.398803	−	0.917037i	$-0.369426\pi$
$71$	−1.65130	−	0.953379i	−0.195973	−	0.113145i	−0.594776	+	0.803892i	$0.702759\pi$
$72$		0			0
$73$			6.14686i			0.719435i	0.933061	+	0.359718i	$0.117127\pi$
$73$			6.14686i			0.719435i	−0.933061	+	0.359718i	$0.882873\pi$
$74$		0			0
$75$	2.38702	+	4.13444i	0.275629	+	0.477404i
$76$		0			0
$77$	−7.52558			−0.857619
$78$		0			0
$79$	10.7515			1.20964			0.604821	−	0.796361i	$-0.293245\pi$
$79$	10.7515			1.20964			0.604821	+	0.796361i	$0.293245\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	14.7628i		−	1.62043i	−0.586135	−	0.810213i	$-0.699351\pi$
$83$		−	14.7628i		−	1.62043i	0.586135	−	0.810213i	$-0.300649\pi$
$84$		0			0
$85$	−3.26841	−	1.88702i	−0.354509	−	0.204676i
$86$		0			0
$87$	0.411667	−	0.713029i	0.0441354	−	0.0764447i
$88$		0			0
$89$	−6.32548	+	3.65202i	−0.670500	+	0.387113i	−0.796266	−	0.604947i	$-0.793194\pi$
$89$	−6.32548	+	3.65202i	−0.670500	+	0.387113i	0.125766	+	0.992060i	$0.459861\pi$
$90$		0			0
$91$	−16.3040	+	1.98758i	−1.70912	+	0.208355i
$92$		0			0
$93$	1.55243	−	0.896298i	0.160980	−	0.0929418i
$94$		0			0
$95$	0.618606	−	1.07146i	0.0634676	−	0.109929i
$96$		0			0
$97$	−3.62423	−	2.09245i	−0.367985	−	0.212456i	0.304593	−	0.952483i	$-0.401480\pi$
$97$	−3.62423	−	2.09245i	−0.367985	−	0.212456i	−0.672578	+	0.740026i	$0.734813\pi$
$98$		0			0
$99$			1.65202i			0.166034i
$100$		0			0
$101$	−2.75965	−	4.77985i	−0.274595	−	0.475613i	0.695438	−	0.718587i	$-0.255211\pi$
$101$	−2.75965	−	4.77985i	−0.274595	−	0.475613i	−0.970033	+	0.242973i	$0.921877\pi$
$102$		0			0
$103$	11.8902			1.17157			0.585786	−	0.810466i	$-0.300786\pi$
$103$	11.8902			1.17157			0.585786	+	0.810466i	$0.300786\pi$
$104$		0			0
$105$	−2.16541			−0.211323
$106$		0			0
$107$	2.98412	+	5.16864i	0.288486	+	0.499672i	0.973448	−	0.228906i	$-0.0735150\pi$
$107$	2.98412	+	5.16864i	0.288486	+	0.499672i	−0.684963	+	0.728578i	$0.740182\pi$
$108$		0			0
$109$			9.79260i			0.937961i	0.883209	+	0.468980i	$0.155378\pi$
$109$			9.79260i			0.937961i	−0.883209	+	0.468980i	$0.844622\pi$
$110$		0			0
$111$	−1.62174	−	0.936315i	−0.153929	−	0.0888711i
$112$		0			0
$113$	0.969727	−	1.67962i	0.0912243	−	0.158005i	−0.816802	−	0.576918i	$-0.804255\pi$
$113$	0.969727	−	1.67962i	0.0912243	−	0.158005i	0.908027	+	0.418913i	$0.137589\pi$
$114$		0			0
$115$	−1.56931	+	0.906042i	−0.146339	+	0.0844888i
$116$		0			0
$117$	0.436315	+	3.57905i	0.0403373	+	0.330884i
$118$		0			0
$119$	−31.3218	+	18.0836i	−2.87126	+	1.65772i
$120$		0			0
$121$	−4.13542	+	7.16276i	−0.375947	+	0.651160i
$122$		0			0
$123$	−9.26841	−	5.35112i	−0.835705	−	0.482494i
$124$		0			0
$125$		−	4.64611i		−	0.415561i
$126$		0			0
$127$	4.43631	+	7.68392i	0.393659	+	0.681838i	0.992929	−	0.118709i	$-0.0378756\pi$
$127$	4.43631	+	7.68392i	0.393659	+	0.681838i	−0.599270	+	0.800547i	$0.704542\pi$
$128$		0			0
$129$	9.89016			0.870780
$130$		0			0
$131$	3.97750			0.347516			0.173758	−	0.984788i	$-0.444409\pi$
$131$	3.97750			0.347516			0.173758	+	0.984788i	$0.444409\pi$
$132$		0			0
$133$	−5.92820	−	10.2679i	−0.514040	−	0.890344i
$134$		0			0
$135$			0.475353i			0.0409118i
$136$		0			0
$137$	15.1527	+	8.74840i	1.29458	+	0.747426i	0.979462	−	0.201627i	$-0.0646227\pi$
$137$	15.1527	+	8.74840i	1.29458	+	0.747426i	0.315118	+	0.949053i	$0.397956\pi$
$138$		0			0
$139$	−10.1386	+	17.5605i	−0.859941	+	1.48946i	0.0120427	+	0.999927i	$0.496167\pi$
$139$	−10.1386	+	17.5605i	−0.859941	+	1.48946i	−0.871984	+	0.489534i	$0.837167\pi$
$140$		0			0
$141$	−6.32085	+	3.64934i	−0.532311	+	0.307330i
$142$		0			0
$143$	2.33210	−	5.48091i	0.195020	−	0.458337i
$144$		0			0
$145$	−0.338940	+	0.195687i	−0.0281474	+	0.0162509i
$146$		0			0
$147$	−6.87577	+	11.9092i	−0.567104	+	0.982253i
$148$		0			0
$149$	6.65516	+	3.84236i	0.545212	+	0.314778i	0.747188	−	0.664612i	$-0.231403\pi$
$149$	6.65516	+	3.84236i	0.545212	+	0.314778i	−0.201977	+	0.979390i	$0.564737\pi$
$150$		0			0
$151$		−	1.65202i		−	0.134439i	−0.997738	−	0.0672196i	$-0.978587\pi$
$151$		−	1.65202i		−	0.134439i	0.997738	−	0.0672196i	$-0.0214128\pi$
$152$		0			0
$153$	3.96973	+	6.87577i	0.320933	+	0.555873i
$154$		0			0
$155$	−0.852115			−0.0684436
$156$		0			0
$157$	−13.4855			−1.07626			−0.538132	−	0.842861i	$-0.680870\pi$
$157$	−13.4855			−1.07626			−0.538132	+	0.842861i	$0.680870\pi$
$158$		0			0
$159$	−5.00314	−	8.66569i	−0.396775	−	0.687234i
$160$		0			0
$161$			17.3655i			1.36859i
$162$		0			0
$163$	16.4045	+	9.47117i	1.28490	+	0.741839i	0.977741	−	0.209818i	$-0.0672870\pi$
$163$	16.4045	+	9.47117i	1.28490	+	0.741839i	0.307163	+	0.951657i	$0.400620\pi$
$164$		0			0
$165$	0.392645	−	0.680082i	0.0305674	−	0.0529443i
$166$		0			0
$167$	2.42015	−	1.39728i	0.187277	−	0.108125i	−0.403430	−	0.915010i	$-0.632182\pi$
$167$	2.42015	−	1.39728i	0.187277	−	0.108125i	0.590707	+	0.806886i	$0.298849\pi$
$168$		0			0
$169$	3.60487	−	12.4902i	0.277298	−	0.960784i
$170$		0			0
$171$	−2.25402	+	1.30136i	−0.172370	+	0.0995176i
$172$		0			0
$173$	3.47535	−	6.01949i	0.264226	−	0.457653i	−0.703134	−	0.711057i	$-0.748217\pi$
$173$	3.47535	−	6.01949i	0.264226	−	0.457653i	0.967361	+	0.253404i	$0.0815501\pi$
$174$		0			0
$175$	−18.8340	−	10.8738i	−1.42371	−	0.821982i
$176$		0			0
$177$		−	1.48660i		−	0.111740i
$178$		0			0
$179$	−4.97287	−	8.61326i	−0.371689	−	0.643785i	0.618136	−	0.786071i	$-0.287888\pi$
$179$	−4.97287	−	8.61326i	−0.371689	−	0.643785i	−0.989826	+	0.142286i	$0.954555\pi$
$180$		0			0
$181$	12.9887			0.965446			0.482723	−	0.875773i	$-0.339648\pi$
$181$	12.9887			0.965446			0.482723	+	0.875773i	$0.339648\pi$
$182$		0			0
$183$	11.7403			0.867867
$184$		0			0
$185$	0.445080	+	0.770901i	0.0327229	+	0.0566777i
$186$		0			0
$187$		−	13.1161i		−	0.959146i
$188$		0			0
$189$	3.94508	+	2.27769i	0.286962	+	0.165678i
$190$		0			0
$191$	−5.82333	+	10.0863i	−0.421362	+	0.729820i	−0.996073	−	0.0885364i	$-0.971781\pi$
$191$	−5.82333	+	10.0863i	−0.421362	+	0.729820i	0.574711	+	0.818356i	$0.305114\pi$
$192$		0			0
$193$	0.538044	−	0.310640i	0.0387292	−	0.0223603i	−0.480510	−	0.876989i	$-0.659549\pi$
$193$	0.538044	−	0.310640i	0.0387292	−	0.0223603i	0.519240	+	0.854629i	$0.326215\pi$
$194$		0			0
$195$	0.671040	−	1.57708i	0.0480542	−	0.112937i
$196$		0			0
$197$	−1.60770	+	0.928203i	−0.114544	+	0.0661317i	−0.556177	−	0.831064i	$-0.687732\pi$
$197$	−1.60770	+	0.928203i	−0.114544	+	0.0661317i	0.441634	+	0.897195i	$0.354399\pi$
$198$		0			0
$199$	−6.89578	+	11.9438i	−0.488829	+	0.846677i	−0.999917	−	0.0128512i	$-0.995909\pi$
$199$	−6.89578	+	11.9438i	−0.488829	+	0.846677i	0.511088	+	0.859528i	$0.329243\pi$
$200$		0			0
$201$	−2.87826	−	1.66176i	−0.203016	−	0.117212i
$202$		0			0
$203$			3.75061i			0.263241i
$204$		0			0
$205$	2.54367	+	4.40576i	0.177658	+	0.307712i
$206$		0			0
$207$	3.81208			0.264958
$208$		0			0
$209$	4.29974			0.297420
$210$		0			0
$211$	11.4313	+	19.7997i	0.786966	+	1.36307i	0.927817	+	0.373034i	$0.121683\pi$
$211$	11.4313	+	19.7997i	0.786966	+	1.36307i	−0.140851	+	0.990031i	$0.544984\pi$
$212$		0			0
$213$		−	1.90676i		−	0.130649i
$214$		0			0
$215$	−4.07146	−	2.35066i	−0.277671	−	0.160313i
$216$		0			0
$217$	−4.08298	+	7.07194i	−0.277171	+	0.480074i
$218$		0			0
$219$	−5.32333	+	3.07343i	−0.359718	+	0.207683i
$220$		0			0
$221$	−3.46410	−	28.4157i	−0.233021	−	1.91145i
$222$		0			0
$223$	6.39821	−	3.69401i	0.428456	−	0.247369i	−0.270233	−	0.962795i	$-0.587101\pi$
$223$	6.39821	−	3.69401i	0.428456	−	0.247369i	0.698689	+	0.715426i	$0.253767\pi$
$224$		0			0
$225$	−2.38702	+	4.13444i	−0.159135	+	0.275629i
$226$		0			0
$227$	−8.27690	−	4.77867i	−0.549357	−	0.317172i	0.199505	−	0.979897i	$-0.436066\pi$
$227$	−8.27690	−	4.77867i	−0.549357	−	0.317172i	−0.748863	+	0.662725i	$0.769400\pi$
$228$		0			0
$229$		−	17.6017i		−	1.16315i	−0.813492	−	0.581575i	$-0.802437\pi$
$229$		−	17.6017i		−	1.16315i	0.813492	−	0.581575i	$-0.197563\pi$
$230$		0			0
$231$	−3.76279	−	6.51734i	−0.247573	−	0.428810i
$232$		0			0
$233$	−19.3391			−1.26695			−0.633473	−	0.773765i	$-0.718371\pi$
$233$	−19.3391			−1.26695			−0.633473	+	0.773765i	$0.718371\pi$
$234$		0			0
$235$	3.46945			0.226322
$236$		0			0
$237$	5.37577	+	9.31111i	0.349194	+	0.604821i
$238$		0			0
$239$			18.6417i			1.20583i	0.797805	+	0.602916i	$0.205994\pi$
$239$			18.6417i			1.20583i	−0.797805	+	0.602916i	$0.794006\pi$
$240$		0			0
$241$	−0.0524342	−	0.0302729i	−0.00337758	−	0.00195005i	0.498310	−	0.866999i	$-0.333954\pi$
$241$	−0.0524342	−	0.0302729i	−0.00337758	−	0.00195005i	−0.501688	+	0.865049i	$0.667287\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	5.66106	−	3.26841i	0.361672	−	0.208811i
$246$		0			0
$247$	9.31529	−	1.13561i	0.592717	−	0.0722569i
$248$		0			0
$249$	12.7850	−	7.38139i	0.810213	−	0.467777i
$250$		0			0
$251$	9.29869	−	16.1058i	0.586928	−	1.01659i	−0.407704	−	0.913114i	$-0.633671\pi$
$251$	9.29869	−	16.1058i	0.586928	−	1.01659i	0.994632	−	0.103475i	$-0.0329962\pi$
$252$		0			0
$253$	−5.45391	−	3.14882i	−0.342884	−	0.197964i
$254$		0			0
$255$		−	3.77404i		−	0.236340i
$256$		0			0
$257$	14.9531	+	25.8996i	0.932750	+	1.61557i	0.778597	+	0.627524i	$0.215932\pi$
$257$	14.9531	+	25.8996i	0.932750	+	1.61557i	0.154154	+	0.988047i	$0.450735\pi$
$258$		0			0
$259$	8.53055			0.530063
$260$		0			0
$261$	0.823335			0.0509631
$262$		0			0
$263$	−5.03341	−	8.71813i	−0.310373	−	0.537583i	0.668070	−	0.744099i	$-0.267121\pi$
$263$	−5.03341	−	8.71813i	−0.310373	−	0.537583i	−0.978443	+	0.206516i	$0.933787\pi$
$264$		0			0
$265$			4.75651i			0.292190i
$266$		0			0
$267$	−6.32548	−	3.65202i	−0.387113	−	0.223500i
$268$		0			0
$269$	−14.0668	+	24.3645i	−0.857669	+	1.48553i	0.0164768	+	0.999864i	$0.494755\pi$
$269$	−14.0668	+	24.3645i	−0.857669	+	1.48553i	−0.874146	+	0.485663i	$0.838578\pi$
$270$		0			0
$271$	22.5593	−	13.0246i	1.37038	−	0.791188i	0.379402	−	0.925232i	$-0.376130\pi$
$271$	22.5593	−	13.0246i	1.37038	−	0.791188i	0.990975	+	0.134044i	$0.0427962\pi$
$272$		0			0
$273$	−9.87328	−	13.1259i	−0.597558	−	0.794413i
$274$		0			0
$275$	6.83017	−	3.94340i	0.411875	−	0.237796i
$276$		0			0
$277$	−3.92578	+	6.79965i	−0.235877	+	0.408551i	−0.959527	−	0.281616i	$-0.909130\pi$
$277$	−3.92578	+	6.79965i	−0.235877	+	0.408551i	0.723650	+	0.690167i	$0.242463\pi$
$278$		0			0
$279$	1.55243	+	0.896298i	0.0929418	+	0.0536600i
$280$		0			0
$281$		−	1.26064i		−	0.0752037i	−0.999293	−	0.0376018i	$-0.988028\pi$
$281$		−	1.26064i		−	0.0752037i	0.999293	−	0.0376018i	$-0.0119719\pi$
$282$		0			0
$283$	1.30966	+	2.26840i	0.0778513	+	0.134842i	0.902323	−	0.431061i	$-0.141861\pi$
$283$	1.30966	+	2.26840i	0.0778513	+	0.134842i	−0.824471	+	0.565904i	$0.808527\pi$
$284$		0			0
$285$	1.23721			0.0732861
$286$		0			0
$287$	48.7528			2.87779
$288$		0			0
$289$	−23.0175	−	39.8674i	−1.35397	−	2.34514i
$290$		0			0
$291$		−	4.18490i		−	0.245323i
$292$		0			0
$293$	22.0305	+	12.7193i	1.28703	+	0.743070i	0.978124	−	0.208021i	$-0.0667023\pi$
$293$	22.0305	+	12.7193i	1.28703	+	0.743070i	0.308910	+	0.951091i	$0.400036\pi$
$294$		0			0
$295$	−0.353330	+	0.611986i	−0.0205717	+	0.0356312i
$296$		0			0
$297$	−1.43069	+	0.826009i	−0.0830170	+	0.0479299i
$298$		0			0
$299$	−12.6474	−	5.38139i	−0.731417	−	0.311214i
$300$		0			0
$301$	−39.0175	+	22.5267i	−2.24893	+	1.29842i
$302$		0			0
$303$	2.75965	−	4.77985i	0.158538	−	0.274595i
$304$		0			0
$305$	−4.83309	−	2.79039i	−0.276742	−	0.159777i
$306$		0			0
$307$		−	15.5100i		−	0.885203i	−0.896718	−	0.442601i	$-0.854056\pi$
$307$		−	15.5100i		−	0.885203i	0.896718	−	0.442601i	$-0.145944\pi$
$308$		0			0
$309$	5.94508	+	10.2972i	0.338204	+	0.585786i
$310$		0			0
$311$	−19.0829			−1.08209			−0.541047	−	0.840993i	$-0.681972\pi$
$311$	−19.0829			−1.08209			−0.541047	+	0.840993i	$0.681972\pi$
$312$		0			0
$313$	12.3406			0.697535			0.348767	−	0.937209i	$-0.386600\pi$
$313$	12.3406			0.697535			0.348767	+	0.937209i	$0.386600\pi$
$314$		0			0
$315$	−1.08271	−	1.87530i	−0.0610036	−	0.105661i
$316$		0			0
$317$		−	19.5636i		−	1.09880i	−0.835559	−	0.549401i	$-0.814856\pi$
$317$		−	19.5636i		−	1.09880i	0.835559	−	0.549401i	$-0.185144\pi$
$318$		0			0
$319$	−1.17794	−	0.680082i	−0.0659518	−	0.0380773i
$320$		0			0
$321$	−2.98412	+	5.16864i	−0.166557	+	0.288486i
$322$		0			0
$323$	17.8957	−	10.3321i	0.995745	−	0.574893i
$324$		0			0
$325$	13.7559	−	10.3472i	0.763040	−	0.573959i
$326$		0			0
$327$	−8.48064	+	4.89630i	−0.468980	+	0.270766i
$328$		0			0
$329$	16.6242	−	28.7939i	0.916520	−	1.58746i
$330$		0			0
$331$	−22.2820	−	12.8645i	−1.22473	−	0.707099i	−0.258808	−	0.965929i	$-0.583330\pi$
$331$	−22.2820	−	12.8645i	−1.22473	−	0.707099i	−0.965923	+	0.258830i	$0.916663\pi$
$332$		0			0
$333$		−	1.87263i		−	0.102619i
$334$		0			0
$335$	0.789923	+	1.36819i	0.0431581	+	0.0747520i
$336$		0			0
$337$	4.90141			0.266997			0.133498	−	0.991049i	$-0.457379\pi$
$337$	4.90141			0.266997			0.133498	+	0.991049i	$0.457379\pi$
$338$		0			0
$339$	1.93945			0.105337
$340$		0			0
$341$	−1.48070	−	2.56465i	−0.0801844	−	0.138884i
$342$		0			0
$343$		−	30.7559i		−	1.66066i
$344$		0			0
$345$	−1.56931	−	0.906042i	−0.0844888	−	0.0487797i
$346$		0			0
$347$	9.48091	−	16.4214i	0.508962	−	0.881548i	−0.490984	−	0.871169i	$-0.663363\pi$
$347$	9.48091	−	16.4214i	0.508962	−	0.881548i	0.999946	−	0.0103797i	$-0.00330403\pi$
$348$		0			0
$349$	10.4045	−	6.00707i	0.556943	−	0.321551i	−0.194975	−	0.980808i	$-0.562462\pi$
$349$	10.4045	−	6.00707i	0.556943	−	0.321551i	0.751918	+	0.659257i	$0.229129\pi$
$350$		0			0
$351$	−2.88139	+	2.16739i	−0.153797	+	0.115687i
$352$		0			0
$353$	12.3074	−	7.10567i	0.655056	−	0.378197i	−0.135334	−	0.990800i	$-0.543211\pi$
$353$	12.3074	−	7.10567i	0.655056	−	0.378197i	0.790391	+	0.612603i	$0.209878\pi$
$354$		0			0
$355$	−0.453191	+	0.784950i	−0.0240529	+	0.0416608i
$356$		0			0
$357$	−31.3218	−	18.0836i	−1.65772	−	0.957088i
$358$		0			0
$359$		−	14.2766i		−	0.753488i	−0.926317	−	0.376744i	$-0.877044\pi$
$359$		−	14.2766i		−	0.753488i	0.926317	−	0.376744i	$-0.122956\pi$
$360$		0			0
$361$	−6.11292	−	10.5879i	−0.321732	−	0.557257i
$362$		0			0
$363$	−8.27084			−0.434106
$364$		0			0
$365$	2.92192			0.152941
$366$		0			0
$367$	8.61854	+	14.9278i	0.449884	+	0.779222i	0.998378	−	0.0569323i	$-0.0181319\pi$
$367$	8.61854	+	14.9278i	0.449884	+	0.779222i	−0.548494	+	0.836155i	$0.684799\pi$
$368$		0			0
$369$		−	10.7022i		−	0.557137i
$370$		0			0
$371$	39.4756	+	22.7912i	2.04947	+	1.18326i
$372$		0			0
$373$	−4.76528	+	8.25370i	−0.246737	+	0.427360i	−0.962618	−	0.270861i	$-0.912692\pi$
$373$	−4.76528	+	8.25370i	−0.246737	+	0.427360i	0.715882	+	0.698221i	$0.246025\pi$
$374$		0			0
$375$	4.02365	−	2.32306i	0.207781	−	0.119962i
$376$		0			0
$377$	−2.73159	−	1.16227i	−0.140684	−	0.0598602i
$378$		0			0
$379$	1.95064	−	1.12620i	0.100198	−	0.0578492i	−0.449064	−	0.893500i	$-0.648242\pi$
$379$	1.95064	−	1.12620i	0.100198	−	0.0578492i	0.549262	+	0.835651i	$0.314909\pi$
$380$		0			0
$381$	−4.43631	+	7.68392i	−0.227279	+	0.393659i
$382$		0			0
$383$	32.9004	+	18.9950i	1.68113	+	0.970601i	0.960913	+	0.276852i	$0.0892910\pi$
$383$	32.9004	+	18.9950i	1.68113	+	0.970601i	0.720217	+	0.693749i	$0.244042\pi$
$384$		0			0
$385$			3.57730i			0.182316i
$386$		0			0
$387$	4.94508	+	8.56513i	0.251373	+	0.435390i
$388$		0			0
$389$	32.0413			1.62456			0.812280	−	0.583267i	$-0.198226\pi$
$389$	32.0413			1.62456			0.812280	+	0.583267i	$0.198226\pi$
$390$		0			0
$391$	−30.2659			−1.53061
$392$		0			0
$393$	1.98875	+	3.44461i	0.100319	+	0.173758i
$394$		0			0
$395$		−	5.11077i		−	0.257151i
$396$		0			0
$397$	30.0512	+	17.3501i	1.50823	+	0.870776i	0.999954	+	0.00957973i	$0.00304937\pi$
$397$	30.0512	+	17.3501i	1.50823	+	0.870776i	0.508273	+	0.861196i	$0.330284\pi$
$398$		0			0
$399$	5.92820	−	10.2679i	0.296781	−	0.514040i
$400$		0			0
$401$	−24.9439	+	14.4013i	−1.24564	+	0.719169i	−0.970236	−	0.242161i	$-0.922144\pi$
$401$	−24.9439	+	14.4013i	−1.24564	+	0.719169i	−0.275401	+	0.961329i	$0.588811\pi$
$402$		0			0
$403$	−3.88525	−	5.16518i	−0.193538	−	0.257296i
$404$		0			0
$405$	−0.411667	+	0.237676i	−0.0204559	+	0.0118102i
$406$		0			0
$407$	−1.54681	+	2.67915i	−0.0766725	+	0.132801i
$408$		0			0
$409$	25.4140	+	14.6728i	1.25664	+	0.725521i	0.972420	−	0.233238i	$-0.0749320\pi$
$409$	25.4140	+	14.6728i	1.25664	+	0.725521i	0.284220	+	0.958759i	$0.408265\pi$
$410$		0			0
$411$			17.4968i			0.863053i
$412$		0			0
$413$	3.38603	+	5.86477i	0.166615	+	0.288586i
$414$		0			0
$415$	−7.01753			−0.344477
$416$		0			0
$417$	−20.2771			−0.992975
$418$		0			0
$419$	−11.3709	−	19.6949i	−0.555503	−	0.962159i	−0.997864	−	0.0653223i	$-0.979192\pi$
$419$	−11.3709	−	19.6949i	−0.555503	−	0.962159i	0.442361	−	0.896837i	$-0.354141\pi$
$420$		0			0
$421$			0.831698i			0.0405345i	0.999795	+	0.0202672i	$0.00645170\pi$
$421$			0.831698i			0.0405345i	−0.999795	+	0.0202672i	$0.993548\pi$
$422$		0			0
$423$	−6.32085	−	3.64934i	−0.307330	−	0.177437i
$424$		0			0
$425$	18.9516	−	32.8252i	0.919289	−	1.59226i
$426$		0			0
$427$	−46.3164	+	26.7408i	−2.24141	+	1.29408i
$428$		0			0
$429$	5.91266	−	0.720800i	0.285466	−	0.0348005i
$430$		0			0
$431$	−22.7562	+	13.1383i	−1.09613	+	0.632849i	−0.935201	−	0.354118i	$-0.884781\pi$
$431$	−22.7562	+	13.1383i	−1.09613	+	0.632849i	−0.160925	+	0.986967i	$0.551448\pi$
$432$		0			0
$433$	−2.73224	+	4.73238i	−0.131303	+	0.227423i	−0.924179	−	0.381959i	$-0.875249\pi$
$433$	−2.73224	+	4.73238i	−0.131303	+	0.227423i	0.792876	+	0.609383i	$0.208583\pi$
$434$		0			0
$435$	−0.338940	−	0.195687i	−0.0162509	−	0.00938248i
$436$		0			0
$437$		−	9.92180i		−	0.474624i
$438$		0			0
$439$	6.65230	+	11.5221i	0.317497	+	0.549920i	0.979965	−	0.199169i	$-0.0638244\pi$
$439$	6.65230	+	11.5221i	0.317497	+	0.549920i	−0.662468	+	0.749090i	$0.730491\pi$
$440$		0			0
$441$	−13.7515			−0.654835
$442$		0			0
$443$	14.0879			0.669336			0.334668	−	0.942336i	$-0.391376\pi$
$443$	14.0879			0.669336			0.334668	+	0.942336i	$0.391376\pi$
$444$		0			0
$445$	1.73600	+	3.00683i	0.0822941	+	0.142538i
$446$		0			0
$447$			7.68471i			0.363474i
$448$		0			0
$449$	−7.89016	−	4.55539i	−0.372360	−	0.214982i	0.302129	−	0.953267i	$-0.402303\pi$
$449$	−7.89016	−	4.55539i	−0.372360	−	0.214982i	−0.674489	+	0.738285i	$0.735636\pi$
$450$		0			0
$451$	−8.84015	+	15.3116i	−0.416266	+	0.720994i
$452$		0			0
$453$	1.43069	−	0.826009i	0.0672196	−	0.0388093i
$454$		0			0
$455$	0.944802	+	7.75014i	0.0442930	+	0.363332i
$456$		0			0
$457$	−7.42323	+	4.28580i	−0.347244	+	0.200481i	−0.663471	−	0.748202i	$-0.730917\pi$
$457$	−7.42323	+	4.28580i	−0.347244	+	0.200481i	0.316227	+	0.948684i	$0.397584\pi$
$458$		0			0
$459$	−3.96973	+	6.87577i	−0.185291	+	0.320933i
$460$		0			0
$461$	34.2647	+	19.7827i	1.59587	+	0.921374i	0.992272	+	0.124083i	$0.0395989\pi$
$461$	34.2647	+	19.7827i	1.59587	+	0.921374i	0.603595	+	0.797291i	$0.293734\pi$
$462$		0			0
$463$			11.4836i			0.533688i	0.963740	+	0.266844i	$0.0859808\pi$
$463$			11.4836i			0.533688i	−0.963740	+	0.266844i	$0.914019\pi$
$464$		0			0
$465$	−0.426058	−	0.737954i	−0.0197580	−	0.0342218i
$466$		0			0
$467$	25.9125			1.19909			0.599545	−	0.800341i	$-0.295348\pi$
$467$	25.9125			1.19909			0.599545	+	0.800341i	$0.295348\pi$
$468$		0			0
$469$	15.1399			0.699097
$470$		0			0
$471$	−6.74277	−	11.6788i	−0.310691	−	0.538132i
$472$		0			0
$473$		−	16.3387i		−	0.751255i
$474$		0			0
$475$	10.7608	+	6.21275i	0.493739	+	0.285061i
$476$		0			0
$477$	5.00314	−	8.66569i	0.229078	−	0.396775i
$478$		0			0
$479$	−29.7135	+	17.1551i	−1.35764	+	0.783836i	−0.989306	−	0.145856i	$-0.953407\pi$
$479$	−29.7135	+	17.1551i	−1.35764	+	0.783836i	−0.368338	+	0.929692i	$0.620073\pi$
$480$		0			0
$481$	−2.64353	+	6.21284i	−0.120535	+	0.283281i
$482$		0			0
$483$	−15.0390	+	8.68276i	−0.684297	+	0.395079i
$484$		0			0
$485$	−0.994652	+	1.72279i	−0.0451648	+	0.0782278i
$486$		0			0
$487$	−35.2110	−	20.3291i	−1.59556	−	0.921199i	−0.992328	−	0.123636i	$-0.960545\pi$
$487$	−35.2110	−	20.3291i	−1.59556	−	0.921199i	−0.603235	−	0.797563i	$-0.706122\pi$
$488$		0			0
$489$			18.9423i			0.856602i
$490$		0			0
$491$	8.44822	+	14.6327i	0.381263	+	0.660367i	0.991243	−	0.132050i	$-0.0421560\pi$
$491$	8.44822	+	14.6327i	0.381263	+	0.660367i	−0.609980	+	0.792417i	$0.708823\pi$
$492$		0			0
$493$	−6.53683			−0.294404
$494$		0			0
$495$	0.785291			0.0352962
$496$		0			0
$497$	4.34301	+	7.52231i	0.194811	+	0.337422i
$498$		0			0
$499$		−	24.6899i		−	1.10527i	−0.833422	−	0.552637i	$-0.813622\pi$
$499$		−	24.6899i		−	1.10527i	0.833422	−	0.552637i	$-0.186378\pi$
$500$		0			0
$501$	2.42015	+	1.39728i	0.108125	+	0.0624257i
$502$		0			0
$503$	−15.7181	+	27.2246i	−0.700837	+	1.21388i	0.267337	+	0.963603i	$0.413856\pi$
$503$	−15.7181	+	27.2246i	−0.700837	+	1.21388i	−0.968173	+	0.250281i	$0.919477\pi$
$504$		0			0
$505$	−2.27212	+	1.31181i	−0.101108	+	0.0583746i
$506$		0			0
$507$	12.6193	−	3.12319i	0.560441	−	0.138706i
$508$		0			0
$509$	−22.9856	+	13.2707i	−1.01882	+	0.588216i	−0.913762	−	0.406251i	$-0.866836\pi$
$509$	−22.9856	+	13.2707i	−1.01882	+	0.588216i	−0.105058	+	0.994466i	$0.533503\pi$
$510$		0			0
$511$	14.0007	−	24.2498i	0.619352	−	1.07275i
$512$		0			0
$513$	−2.25402	−	1.30136i	−0.0995176	−	0.0574565i
$514$		0			0
$515$		−	5.65202i		−	0.249058i
$516$		0			0
$517$	6.02878	+	10.4422i	0.265145	+	0.459245i
$518$		0			0
$519$	6.95071			0.305102
$520$		0			0
$521$	16.0605			0.703625			0.351813	−	0.936070i	$-0.385565\pi$
$521$	16.0605			0.703625			0.351813	+	0.936070i	$0.385565\pi$
$522$		0			0
$523$	0.497514	+	0.861719i	0.0217548	+	0.0376804i	0.876698	−	0.481041i	$-0.159741\pi$
$523$	0.497514	+	0.861719i	0.0217548	+	0.0376804i	−0.854943	+	0.518722i	$0.826408\pi$
$524$		0			0
$525$		−	21.7476i		−	0.949143i
$526$		0			0
$527$	−12.3255	−	7.11612i	−0.536906	−	0.309983i
$528$		0			0
$529$	4.23401	−	7.33352i	0.184087	−	0.318849i
$530$		0			0
$531$	1.28744	−	0.743302i	0.0558700	−	0.0322565i
$532$		0			0
$533$	−15.1080	+	35.5069i	−0.654400	+	1.53798i
$534$		0			0
$535$	2.45693	−	1.41851i	0.106222	−	0.0613274i
$536$		0			0
$537$	4.97287	−	8.61326i	0.214595	−	0.371689i
$538$		0			0
$539$	19.6742	+	11.3589i	0.847427	+	0.489262i
$540$		0			0
$541$			10.8825i			0.467874i	0.972252	+	0.233937i	$0.0751610\pi$
$541$			10.8825i			0.467874i	−0.972252	+	0.233937i	$0.924839\pi$
$542$		0			0
$543$	6.49437	+	11.2486i	0.278700	+	0.482723i
$544$		0			0
$545$	4.65494			0.199396
$546$		0			0
$547$	−18.1985			−0.778111			−0.389056	−	0.921214i	$-0.627199\pi$
$547$	−18.1985			−0.778111			−0.389056	+	0.921214i	$0.627199\pi$
$548$		0			0
$549$	5.87014	+	10.1674i	0.250532	+	0.433933i
$550$		0			0
$551$		−	2.14291i		−	0.0912911i
$552$		0			0
$553$	−42.4157	−	24.4887i	−1.80370	−	1.04137i
$554$		0			0
$555$	−0.445080	+	0.770901i	−0.0188926	+	0.0327229i
$556$		0			0
$557$	4.84699	−	2.79841i	0.205373	−	0.118572i	−0.393786	−	0.919202i	$-0.628835\pi$
$557$	4.84699	−	2.79841i	0.205373	−	0.118572i	0.599159	+	0.800630i	$0.295502\pi$
$558$		0			0
$559$	−4.31522	−	35.3974i	−0.182514	−	1.49715i
$560$		0			0
$561$	11.3589	−	6.55806i	0.479573	−	0.276881i
$562$		0			0
$563$	12.2381	−	21.1971i	0.515776	−	0.893351i	−0.484056	−	0.875037i	$-0.660837\pi$
$563$	12.2381	−	21.1971i	0.515776	−	0.893351i	0.999832	−	0.0183136i	$-0.00582972\pi$
$564$		0			0
$565$	−0.798410	−	0.460962i	−0.0335894	−	0.0193928i
$566$		0			0
$567$			4.55539i			0.191308i
$568$		0			0
$569$	−8.93411	−	15.4743i	−0.374537	−	0.648717i	0.615720	−	0.787965i	$-0.288865\pi$
$569$	−8.93411	−	15.4743i	−0.374537	−	0.648717i	−0.990258	+	0.139247i	$0.955532\pi$
$570$		0			0
$571$	1.74669			0.0730968			0.0365484	−	0.999332i	$-0.488364\pi$
$571$	1.74669			0.0730968			0.0365484	+	0.999332i	$0.488364\pi$
$572$		0			0
$573$	−11.6467			−0.486547
$574$		0			0
$575$	−9.09952	−	15.7608i	−0.379476	−	0.657272i
$576$		0			0
$577$		−	10.6236i		−	0.442267i	−0.975244	−	0.221133i	$-0.929024\pi$
$577$		−	10.6236i		−	0.442267i	0.975244	−	0.221133i	$-0.0709756\pi$
$578$		0			0
$579$	0.538044	+	0.310640i	0.0223603	+	0.0129097i
$580$		0			0
$581$	−33.6251	+	58.2404i	−1.39500	+	2.41622i
$582$		0			0
$583$	−14.3159	+	8.26528i	−0.592903	+	0.342313i
$584$		0			0
$585$	1.70131	−	0.207403i	0.0703406	−	0.00857507i
$586$		0			0
$587$	−38.8023	+	22.4025i	−1.60154	+	0.924651i	−0.610364	+	0.792121i	$0.708977\pi$
$587$	−38.8023	+	22.4025i	−1.60154	+	0.924651i	−0.991179	+	0.132530i	$0.957690\pi$
$588$		0			0
$589$	2.33282	−	4.04056i	0.0961220	−	0.166488i
$590$		0			0
$591$	−1.60770	−	0.928203i	−0.0661317	−	0.0381812i
$592$		0			0
$593$		−	34.9834i		−	1.43660i	−0.695736	−	0.718298i	$-0.744921\pi$
$593$		−	34.9834i		−	1.43660i	0.695736	−	0.718298i	$-0.255079\pi$
$594$		0			0
$595$	8.59610	+	14.8889i	0.352406	+	0.610385i
$596$		0			0
$597$	−13.7916			−0.564451
$598$		0			0
$599$	−21.9569			−0.897133			−0.448566	−	0.893749i	$-0.648065\pi$
$599$	−21.9569			−0.897133			−0.448566	+	0.893749i	$0.648065\pi$
$600$		0			0
$601$	2.88702	+	5.00047i	0.117764	+	0.203973i	0.918881	−	0.394534i	$-0.129094\pi$
$601$	2.88702	+	5.00047i	0.117764	+	0.203973i	−0.801117	+	0.598507i	$0.795761\pi$
$602$		0			0
$603$		−	3.32352i		−	0.135344i
$604$		0			0
$605$	3.40483	+	1.96578i	0.138426	+	0.0799204i
$606$		0			0
$607$	−9.72276	+	16.8403i	−0.394635	+	0.683527i	−0.993054	−	0.117656i	$-0.962462\pi$
$607$	−9.72276	+	16.8403i	−0.394635	+	0.683527i	0.598420	+	0.801183i	$0.295795\pi$
$608$		0			0
$609$	−3.24812	+	1.87530i	−0.131621	+	0.0759911i
$610$		0			0
$611$	15.8191	+	21.0304i	0.639971	+	0.850799i
$612$		0			0
$613$	−8.21222	+	4.74133i	−0.331689	+	0.191500i	−0.656591	−	0.754247i	$-0.728002\pi$
$613$	−8.21222	+	4.74133i	−0.331689	+	0.191500i	0.324902	+	0.945748i	$0.394669\pi$
$614$		0			0
$615$	−2.54367	+	4.40576i	−0.102571	+	0.177658i
$616$		0			0
$617$	−37.6567	−	21.7411i	−1.51600	−	0.875263i	−0.999824	−	0.0187816i	$-0.994021\pi$
$617$	−37.6567	−	21.7411i	−1.51600	−	0.875263i	−0.516177	−	0.856482i	$-0.672645\pi$
$618$		0			0
$619$			5.40607i			0.217288i	0.994081	+	0.108644i	$0.0346509\pi$
$619$			5.40607i			0.217288i	−0.994081	+	0.108644i	$0.965349\pi$
$620$		0			0
$621$	1.90604	+	3.30136i	0.0764868	+	0.132479i
$622$		0			0
$623$	33.2727			1.33304
$624$		0			0
$625$	21.6617			0.866466
$626$		0			0
$627$	2.14987	+	3.72369i	0.0858576	+	0.148710i
$628$		0			0
$629$			14.8677i			0.592812i
$630$		0			0
$631$	14.4714	+	8.35505i	0.576096	+	0.332609i	0.759581	−	0.650413i	$-0.225404\pi$
$631$	14.4714	+	8.35505i	0.576096	+	0.332609i	−0.183484	+	0.983023i	$0.558738\pi$
$632$		0			0
$633$	−11.4313	+	19.7997i	−0.454355	+	0.786966i
$634$		0			0
$635$	3.65257	−	2.10881i	0.144948	−	0.0836857i
$636$		0			0
$637$	45.6236	+	19.4126i	1.80767	+	0.769155i
$638$		0			0
$639$	1.65130	−	0.953379i	0.0653245	−	0.0377151i
$640$		0			0
$641$	0.0468720	−	0.0811847i	0.00185133	−	0.00320660i	−0.865098	−	0.501602i	$-0.832744\pi$
$641$	0.0468720	−	0.0811847i	0.00185133	−	0.00320660i	0.866950	+	0.498396i	$0.166077\pi$
$642$		0			0
$643$	14.8696	+	8.58496i	0.586399	+	0.338558i	0.763672	−	0.645604i	$-0.223394\pi$
$643$	14.8696	+	8.58496i	0.586399	+	0.338558i	−0.177273	+	0.984162i	$0.556728\pi$
$644$		0			0
$645$		−	4.70131i		−	0.185114i
$646$		0			0
$647$	16.1224	+	27.9248i	0.633837	+	1.09784i	0.986760	+	0.162185i	$0.0518543\pi$
$647$	16.1224	+	27.9248i	0.633837	+	1.09784i	−0.352923	+	0.935652i	$0.614812\pi$
$648$		0			0
$649$	−2.45590			−0.0964023
$650$		0			0
$651$	−8.16597			−0.320050
$652$		0			0
$653$	−3.32119	−	5.75247i	−0.129968	−	0.225111i	0.793696	−	0.608315i	$-0.208154\pi$
$653$	−3.32119	−	5.75247i	−0.129968	−	0.225111i	−0.923664	+	0.383203i	$0.874821\pi$
$654$		0			0
$655$		−	1.89071i		−	0.0738763i
$656$		0			0
$657$	−5.32333	−	3.07343i	−0.207683	−	0.119906i
$658$		0			0
$659$	−4.78529	+	8.28837i	−0.186408	+	0.322869i	−0.944050	−	0.329802i	$-0.893018\pi$
$659$	−4.78529	+	8.28837i	−0.186408	+	0.322869i	0.757642	+	0.652671i	$0.226351\pi$
$660$		0			0
$661$	−25.6891	+	14.8316i	−0.999189	+	0.576882i	−0.908008	−	0.418953i	$-0.862397\pi$
$661$	−25.6891	+	14.8316i	−0.999189	+	0.576882i	−0.0911805	+	0.995834i	$0.529064\pi$
$662$		0			0
$663$	22.8767	−	17.2079i	0.888457	−	0.668298i
$664$		0			0
$665$	−4.88090	+	2.81799i	−0.189273	+	0.109277i
$666$		0			0
$667$	−1.56931	+	2.71813i	−0.0607640	+	0.105246i
$668$		0			0
$669$	6.39821	+	3.69401i	0.247369	+	0.142819i
$670$		0			0
$671$		−	19.3952i		−	0.748742i
$672$		0			0
$673$	5.57180	+	9.65064i	0.214777	+	0.372005i	0.953204	−	0.302329i	$-0.0977642\pi$
$673$	5.57180	+	9.65064i	0.214777	+	0.372005i	−0.738427	+	0.674334i	$0.764431\pi$
$674$		0			0
$675$	−4.77404			−0.183753
$676$		0			0
$677$	−5.44763			−0.209369			−0.104685	−	0.994505i	$-0.533383\pi$
$677$	−5.44763			−0.209369			−0.104685	+	0.994505i	$0.533383\pi$
$678$		0			0
$679$	9.53192	+	16.5098i	0.365802	+	0.633587i
$680$		0			0
$681$		−	9.55734i		−	0.366238i
$682$		0			0
$683$	−25.3654	−	14.6447i	−0.970579	−	0.560364i	−0.0711666	−	0.997464i	$-0.522672\pi$
$683$	−25.3654	−	14.6447i	−0.970579	−	0.560364i	−0.899413	+	0.437100i	$0.856006\pi$
$684$		0			0
$685$	4.15857	−	7.20286i	0.158891	−	0.275207i
$686$		0			0
$687$	15.2435	−	8.80083i	0.581575	−	0.335773i
$688$		0			0
$689$	−28.8320	+	21.6875i	−1.09841	+	0.826227i
$690$		0			0
$691$	20.5580	−	11.8692i	0.782063	−	0.451524i	−0.0550979	−	0.998481i	$-0.517547\pi$
$691$	20.5580	−	11.8692i	0.782063	−	0.451524i	0.837161	+	0.546957i	$0.184214\pi$
$692$		0			0
$693$	3.76279	−	6.51734i	0.142937	−	0.247573i
$694$		0			0
$695$	8.34743	+	4.81939i	0.316636	+	0.182810i
$696$		0			0
$697$			84.9700i			3.21847i
$698$		0			0
$699$	−9.66955	−	16.7481i	−0.365736	−	0.633473i
$700$		0			0
$701$	7.62417			0.287961			0.143980	−	0.989581i	$-0.454010\pi$
$701$	7.62417			0.287961			0.143980	+	0.989581i	$0.454010\pi$
$702$		0			0
$703$	−4.87394			−0.183824
$704$		0			0
$705$	1.73472	+	3.00463i	0.0653335	+	0.113161i
$706$		0			0
$707$			25.1425i			0.945582i
$708$		0			0
$709$	−26.4127	−	15.2494i	−0.991950	−	0.572702i	−0.0860931	−	0.996287i	$-0.527438\pi$
$709$	−26.4127	−	15.2494i	−0.991950	−	0.572702i	−0.905857	+	0.423585i	$0.860772\pi$
$710$		0			0
$711$	−5.37577	+	9.31111i	−0.201607	+	0.349194i
$712$		0			0
$713$	−5.91801	+	3.41676i	−0.221631	+	0.127959i
$714$		0			0
$715$	−2.60537	−	1.10857i	−0.0974352	−	0.0414582i
$716$		0			0
$717$	−16.1442	+	9.32085i	−0.602916	+	0.348093i
$718$		0			0
$719$	3.31529	−	5.74224i	0.123639	−	0.214150i	−0.797561	−	0.603238i	$-0.793877\pi$
$719$	3.31529	−	5.74224i	0.123639	−	0.214150i	0.921200	+	0.389089i	$0.127210\pi$
$720$		0			0
$721$	−46.9076	−	27.0821i	−1.74693	−	1.00859i
$722$		0			0
$723$		−	0.0605458i		−	0.00225172i
$724$		0			0
$725$	−1.96532	−	3.40403i	−0.0729900	−	0.126422i
$726$		0			0
$727$	−17.4607			−0.647583			−0.323792	−	0.946128i	$-0.604958\pi$
$727$	−17.4607			−0.647583			−0.323792	+	0.946128i	$0.604958\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−39.2612	−	68.0025i	−1.45213	−	2.51516i
$732$		0			0
$733$		−	23.3284i		−	0.861653i	−0.902435	−	0.430826i	$-0.858222\pi$
$733$		−	23.3284i		−	0.861653i	0.902435	−	0.430826i	$-0.141778\pi$
$734$		0			0
$735$	5.66106	+	3.26841i	0.208811	+	0.120557i
$736$		0			0
$737$	−2.74526	+	4.75493i	−0.101123	+	0.175150i
$738$		0			0
$739$	1.88090	−	1.08594i	0.0691899	−	0.0399468i	−0.465006	−	0.885308i	$-0.653948\pi$
$739$	1.88090	−	1.08594i	0.0691899	−	0.0399468i	0.534196	+	0.845361i	$0.320614\pi$
$740$		0			0
$741$	5.64111	+	7.49947i	0.207231	+	0.275500i
$742$		0			0
$743$	40.3332	−	23.2864i	1.47968	−	0.854296i	0.479948	−	0.877297i	$-0.340656\pi$
$743$	40.3332	−	23.2864i	1.47968	−	0.854296i	0.999735	+	0.0230015i	$0.00732227\pi$
$744$		0			0
$745$	1.82647	−	3.16355i	0.0669168	−	0.115903i
$746$		0			0
$747$	12.7850	+	7.38139i	0.467777	+	0.270071i
$748$		0			0
$749$		−	27.1876i		−	0.993414i
$750$		0			0
$751$	21.1998	+	36.7191i	0.773590	+	1.33990i	0.935583	+	0.353106i	$0.114874\pi$
$751$	21.1998	+	36.7191i	0.773590	+	1.33990i	−0.161993	+	0.986792i	$0.551792\pi$
$752$		0			0
$753$	18.5974			0.677726
$754$		0			0
$755$	−0.785291			−0.0285797
$756$		0			0
$757$	0.402625	+	0.697367i	0.0146337	+	0.0253462i	0.873250	−	0.487273i	$-0.162008\pi$
$757$	0.402625	+	0.697367i	0.0146337	+	0.0253462i	−0.858616	+	0.512620i	$0.828675\pi$
$758$		0			0
$759$		−	6.29763i		−	0.228589i
$760$		0			0
$761$	1.04395	+	0.602723i	0.0378430	+	0.0218487i	0.518802	−	0.854894i	$-0.326378\pi$
$761$	1.04395	+	0.602723i	0.0378430	+	0.0218487i	−0.480959	+	0.876743i	$0.659711\pi$
$762$		0			0
$763$	22.3045	−	38.6326i	0.807478	−	1.39859i
$764$		0			0
$765$	3.26841	−	1.88702i	0.118170	−	0.0682254i
$766$		0			0
$767$	−5.32063	+	0.648627i	−0.192117	+	0.0234206i
$768$		0			0
$769$	−13.1878	+	7.61397i	−0.475564	+	0.274567i	−0.718566	−	0.695459i	$-0.755201\pi$
$769$	−13.1878	+	7.61397i	−0.475564	+	0.274567i	0.243002	+	0.970026i	$0.421868\pi$
$770$		0			0
$771$	−14.9531	+	25.8996i	−0.538524	+	0.932750i
$772$		0			0
$773$	15.7092	+	9.06971i	0.565021	+	0.326215i	0.755158	−	0.655543i	$-0.227560\pi$
$773$	15.7092	+	9.06971i	0.565021	+	0.326215i	−0.190137	+	0.981757i	$0.560893\pi$
$774$		0			0
$775$		−	8.55793i		−	0.307410i
$776$		0			0
$777$	4.26528	+	7.38767i	0.153016	+	0.265031i
$778$		0			0
$779$	−27.8550			−0.998008
$780$		0			0
$781$	−3.15000			−0.112716
$782$		0			0
$783$	0.411667	+	0.713029i	0.0147118	+	0.0254816i
$784$		0			0
$785$			6.41039i			0.228797i
$786$		0			0
$787$	−15.1991	−	8.77521i	−0.541790	−	0.312802i	0.204014	−	0.978968i	$-0.434601\pi$
$787$	−15.1991	−	8.77521i	−0.541790	−	0.312802i	−0.745804	+	0.666166i	$0.767934\pi$
$788$		0			0
$789$	5.03341	−	8.71813i	0.179194	−	0.310373i
$790$		0			0
$791$	−7.65130	+	4.41748i	−0.272049	+	0.157068i
$792$		0			0
$793$	−5.12246	−	42.0191i	−0.181904	−	1.49214i
$794$		0			0
$795$	−4.11926	+	2.37826i	−0.146095	+	0.0843480i
$796$		0			0
$797$	9.67937	−	16.7652i	0.342861	−	0.593852i	−0.642102	−	0.766619i	$-0.721937\pi$
$797$	9.67937	−	16.7652i	0.342861	−	0.593852i	0.984963	+	0.172767i	$0.0552708\pi$
$798$		0			0
$799$	50.1841	+	28.9738i	1.77539	+	1.02502i
$800$		0			0
$801$		−	7.30404i		−	0.258075i
$802$		0			0
$803$	5.07736	+	8.79424i	0.179176	+	0.310342i
$804$		0			0
$805$	8.25474			0.290941
$806$		0			0
$807$	−28.1336			−0.990351
$808$		0			0
$809$	−5.23429	−	9.06605i	−0.184028	−	0.318745i	0.759221	−	0.650833i	$-0.225580\pi$
$809$	−5.23429	−	9.06605i	−0.184028	−	0.318745i	−0.943248	+	0.332088i	$0.892247\pi$
$810$		0			0
$811$			38.1332i			1.33904i	0.742795	+	0.669518i	$0.233500\pi$
$811$			38.1332i			1.33904i	−0.742795	+	0.669518i	$0.766500\pi$
$812$		0			0
$813$	22.5593	+	13.0246i	0.791188	+	0.456793i
$814$		0			0
$815$	4.50215	−	7.79794i	0.157703	−	0.273150i
$816$		0			0
$817$	22.2927	−	12.8707i	0.779921	−	0.450288i
$818$		0			0
$819$	6.43069	−	15.1134i	0.224706	−	0.528107i
$820$		0			0
$821$	9.47772	−	5.47196i	0.330775	−	0.190973i	−0.325410	−	0.945573i	$-0.605502\pi$
$821$	9.47772	−	5.47196i	0.330775	−	0.190973i	0.656185	+	0.754600i	$0.272169\pi$
$822$		0			0
$823$	19.7578	−	34.2215i	0.688714	−	1.19289i	−0.283540	−	0.958960i	$-0.591509\pi$
$823$	19.7578	−	34.2215i	0.688714	−	1.19289i	0.972254	−	0.233928i	$-0.0751578\pi$
$824$		0			0
$825$	6.83017	+	3.94340i	0.237796	+	0.137292i
$826$		0			0
$827$		−	38.3552i		−	1.33374i	−0.745174	−	0.666870i	$-0.767633\pi$
$827$		−	38.3552i		−	1.33374i	0.745174	−	0.666870i	$-0.232367\pi$
$828$		0			0
$829$	0.548578	+	0.950166i	0.0190529	+	0.0330006i	0.875395	−	0.483409i	$-0.160602\pi$
$829$	0.548578	+	0.950166i	0.0190529	+	0.0330006i	−0.856342	+	0.516410i	$0.827268\pi$
$830$		0			0
$831$	−7.85156			−0.272368
$832$		0			0
$833$	109.180			3.78285
$834$		0			0
$835$	−0.664199	−	1.15043i	−0.0229856	−	0.0398122i
$836$		0			0
$837$			1.79260i			0.0619612i
$838$		0			0
$839$	−9.92981	−	5.73298i	−0.342815	−	0.197924i	0.318701	−	0.947855i	$-0.396753\pi$
$839$	−9.92981	−	5.73298i	−0.342815	−	0.197924i	−0.661516	+	0.749931i	$0.730087\pi$
$840$		0			0
$841$	14.1611	−	24.5277i	0.488312	−	0.845782i
$842$		0			0
$843$	1.09175	−	0.630322i	0.0376018	−	0.0217094i
$844$		0			0
$845$	−5.93725	−	1.71358i	−0.204247	−	0.0589491i
$846$		0			0
$847$	32.6291	−	18.8384i	1.12115	−	0.647296i
$848$		0			0
$849$	−1.30966	+	2.26840i	−0.0449474	+	0.0778513i
$850$		0			0
$851$	6.18223	+	3.56931i	0.211924	+	0.122354i
$852$		0			0
$853$		−	18.6403i		−	0.638232i	−0.947716	−	0.319116i	$-0.896614\pi$
$853$		−	18.6403i		−	0.638232i	0.947716	−	0.319116i	$-0.103386\pi$
$854$		0			0
$855$	0.618606	+	1.07146i	0.0211559	+	0.0366430i
$856$		0			0
$857$	−41.9413			−1.43269			−0.716344	−	0.697747i	$-0.754186\pi$
$857$	−41.9413			−1.43269			−0.716344	+	0.697747i	$0.754186\pi$
$858$		0			0
$859$	−8.80656			−0.300476			−0.150238	−	0.988650i	$-0.548004\pi$
$859$	−8.80656			−0.300476			−0.150238	+	0.988650i	$0.548004\pi$
$860$		0			0
$861$	24.3764	+	42.2212i	0.830746	+	1.43889i
$862$		0			0
$863$			20.0833i			0.683643i	0.939765	+	0.341822i	$0.111044\pi$
$863$			20.0833i			0.683643i	−0.939765	+	0.341822i	$0.888956\pi$
$864$		0			0
$865$	−2.86138	−	1.65202i	−0.0972898	−	0.0561703i
$866$		0			0
$867$	23.0175	−	39.8674i	0.781714	−	1.35397i
$868$		0			0
$869$	15.3821	−	8.88087i	0.521802	−	0.301263i
$870$		0			0
$871$	−4.69171	+	11.0265i	−0.158972	+	0.373618i
$872$		0			0
$873$	3.62423	−	2.09245i	0.122662	−	0.0708187i
$874$		0			0
$875$	−10.5824	+	18.3293i	−0.357751	+	0.619643i
$876$		0			0
$877$	−29.0698	−	16.7835i	−0.981617	−	0.566737i	−0.0788594	−	0.996886i	$-0.525128\pi$
$877$	−29.0698	−	16.7835i	−0.981617	−	0.566737i	−0.902758	+	0.430149i	$0.858461\pi$
$878$		0			0
$879$			25.4386i			0.858023i
$880$		0			0
$881$	17.6280	+	30.5326i	0.593903	+	1.02867i	0.993701	+	0.112067i	$0.0357471\pi$
$881$	17.6280	+	30.5326i	0.593903	+	1.02867i	−0.399797	+	0.916604i	$0.630920\pi$
$882$		0			0
$883$	−7.59185			−0.255486			−0.127743	−	0.991807i	$-0.540773\pi$
$883$	−7.59185			−0.255486			−0.127743	+	0.991807i	$0.540773\pi$
$884$		0			0
$885$	−0.706661			−0.0237541
$886$		0			0
$887$	15.9073	+	27.5523i	0.534115	+	0.925115i	0.999206	+	0.0398516i	$0.0126885\pi$
$887$	15.9073	+	27.5523i	0.534115	+	0.925115i	−0.465090	+	0.885263i	$0.653978\pi$
$888$		0			0
$889$		−	40.4182i		−	1.35558i
$890$		0			0
$891$	−1.43069	−	0.826009i	−0.0479299	−	0.0276723i
$892$		0			0
$893$	−9.49823	+	16.4514i	−0.317846	+	0.550526i
$894$		0			0
$895$	−4.09433	+	2.36386i	−0.136858	+	0.0790153i
$896$		0			0
$897$	−1.66327	−	13.6437i	−0.0555349	−	0.455548i
$898$		0			0
$899$	−1.27817	+	0.737954i	−0.0426295	+	0.0246121i
$900$		0			0
$901$	−39.7222	+	68.8009i	−1.32334	+	2.29209i
$902$		0			0
$903$	−39.0175	−	22.5267i	−1.29842	−	0.749643i
$904$		0			0
$905$		−	6.17424i		−	0.205239i
$906$		0			0
$907$	−12.4320	−	21.5328i	−0.412796	−	0.714984i	0.582398	−	0.812904i	$-0.302115\pi$
$907$	−12.4320	−	21.5328i	−0.412796	−	0.714984i	−0.995194	+	0.0979194i	$0.968781\pi$
$908$		0			0
$909$	5.51930			0.183064
$910$		0			0
$911$	−28.9183			−0.958105			−0.479052	−	0.877786i	$-0.659020\pi$
$911$	−28.9183			−0.958105			−0.479052	+	0.877786i	$0.659020\pi$
$912$		0			0
$913$	−12.1942	−	21.1210i	−0.403569	−	0.699002i
$914$		0			0
$915$		−	5.58078i		−	0.184495i
$916$		0			0
$917$	−15.6915	−	9.05952i	−0.518181	−	0.299172i
$918$		0			0
$919$	−9.62560	+	16.6720i	−0.317519	+	0.549960i	−0.979970	−	0.199146i	$-0.936183\pi$
$919$	−9.62560	+	16.6720i	−0.317519	+	0.549960i	0.662451	+	0.749106i	$0.269516\pi$
$920$		0			0
$921$	13.4321	−	7.75500i	0.442601	−	0.255536i
$922$		0			0
$923$	−6.82439	+	0.831947i	−0.224628	+	0.0273839i
$924$		0			0
$925$	−7.74227	+	4.47000i	−0.254564	+	0.146973i
$926$		0			0
$927$	−5.94508	+	10.2972i	−0.195262	+	0.338204i
$928$		0			0
$929$	13.1348	+	7.58336i	0.430938	+	0.248802i	0.699746	−	0.714392i	$-0.253296\pi$
$929$	13.1348	+	7.58336i	0.430938	+	0.248802i	−0.268808	+	0.963194i	$0.586630\pi$
$930$		0			0
$931$			35.7914i			1.17302i
$932$		0			0
$933$	−9.54146	−	16.5263i	−0.312373	−	0.541047i
$934$		0			0
$935$	−6.23478			−0.203899
$936$		0			0
$937$	49.2136			1.60774			0.803869	−	0.594807i	$-0.202771\pi$
$937$	49.2136			1.60774			0.803869	+	0.594807i	$0.202771\pi$
$938$		0			0
$939$	6.17032	+	10.6873i	0.201361	+	0.348767i
$940$		0			0
$941$		−	46.2058i		−	1.50627i	−0.657868	−	0.753133i	$-0.728541\pi$
$941$		−	46.2058i		−	1.50627i	0.657868	−	0.753133i	$-0.271459\pi$
$942$		0			0
$943$	35.3320	+	20.3989i	1.15057	+	0.664280i
$944$		0			0
$945$	1.08271	−	1.87530i	0.0352205	−	0.0610036i
$946$		0			0
$947$	−17.6367	+	10.1826i	−0.573117	+	0.330889i	−0.758393	−	0.651797i	$-0.774015\pi$
$947$	−17.6367	+	10.1826i	−0.573117	+	0.330889i	0.185277	+	0.982686i	$0.440682\pi$
$948$		0			0
$949$	13.3226	+	17.7115i	0.432470	+	0.574940i
$950$		0			0
$951$	16.9426	−	9.78181i	0.549401	−	0.317197i
$952$		0			0
$953$	15.8233	−	27.4068i	0.512568	−	0.887794i	−0.487326	−	0.873220i	$-0.662028\pi$
$953$	15.8233	−	27.4068i	0.512568	−	0.887794i	0.999894	−	0.0145737i	$-0.00463912\pi$
$954$		0			0
$955$	4.79455	+	2.76814i	0.155148	+	0.0895748i
$956$		0			0
$957$		−	1.36016i		−	0.0439678i
$958$		0			0
$959$	−39.8523	−	69.0263i	−1.28690	−	2.22897i
$960$		0			0
$961$	27.7866			0.896342
$962$		0			0
$963$	−5.96823			−0.192324
$964$		0			0
$965$	−0.147663	−	0.255761i	−0.00475345	−	0.00823322i
$966$		0			0
$967$			16.7482i			0.538585i	0.963058	+	0.269293i	$0.0867899\pi$
$967$			16.7482i			0.538585i	−0.963058	+	0.269293i	$0.913210\pi$
$968$		0			0
$969$	17.8957	+	10.3321i	0.574893	+	0.331915i
$970$		0			0
$971$	−2.70131	+	4.67881i	−0.0866892	+	0.150150i	−0.906110	−	0.423043i	$-0.860962\pi$
$971$	−2.70131	+	4.67881i	−0.0866892	+	0.150150i	0.819421	+	0.573193i	$0.194295\pi$
$972$		0			0
$973$	79.9948	−	46.1850i	2.56452	−	1.48062i
$974$		0			0
$975$	15.8389	+	6.73936i	0.507250	+	0.215832i
$976$		0			0
$977$	−33.3556	+	19.2579i	−1.06714	+	0.616114i	−0.927399	−	0.374074i	$-0.877961\pi$
$977$	−33.3556	+	19.2579i	−1.06714	+	0.616114i	−0.139742	+	0.990188i	$0.544627\pi$
$978$		0			0
$979$	−6.03320	+	10.4498i	−0.192822	+	0.333977i
$980$		0			0
$981$	−8.48064	−	4.89630i	−0.270766	−	0.156327i
$982$		0			0
$983$		−	32.5378i		−	1.03779i	−0.854837	−	0.518897i	$-0.826343\pi$
$983$		−	32.5378i		−	1.03779i	0.854837	−	0.518897i	$-0.173657\pi$
$984$		0			0
$985$	0.441224	+	0.764222i	0.0140586	+	0.0243501i
$986$		0			0
$987$	33.2483			1.05831
$988$		0			0
$989$	−37.7021			−1.19886
$990$		0			0
$991$	−0.491235	−	0.850844i	−0.0156046	−	0.0270280i	0.858118	−	0.513453i	$-0.171634\pi$
$991$	−0.491235	−	0.850844i	−0.0156046	−	0.0270280i	−0.873722	+	0.486425i	$0.838301\pi$
$992$		0			0
$993$		−	25.7291i		−	0.816487i
$994$		0			0
$995$	5.67754	+	3.27793i	0.179990	+	0.103917i
$996$		0			0
$997$	25.0536	−	43.3942i	0.793457	−	1.37431i	−0.130358	−	0.991467i	$-0.541613\pi$
$997$	25.0536	−	43.3942i	0.793457	−	1.37431i	0.923814	−	0.382840i	$-0.125054\pi$
$998$		0			0
$999$	1.62174	−	0.936315i	0.0513097	−	0.0296237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.bv.g.49.2		8
3.2	odd	2		1872.2.by.m.1297.3		8
4.3	odd	2		312.2.bf.b.49.2	✓	8
12.11	even	2		936.2.bi.c.361.3		8
13.2	odd	12		8112.2.a.cs.1.2		4
13.4	even	6	inner	624.2.bv.g.433.3		8
13.11	odd	12		8112.2.a.cq.1.3		4
39.17	odd	6		1872.2.by.m.433.2		8
52.3	odd	6		4056.2.c.p.337.4		8
52.11	even	12		4056.2.a.bd.1.3		4
52.15	even	12		4056.2.a.be.1.2		4
52.23	odd	6		4056.2.c.p.337.5		8
52.43	odd	6		312.2.bf.b.121.3	yes	8
156.95	even	6		936.2.bi.c.433.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bf.b.49.2	✓	8	4.3	odd	2
312.2.bf.b.121.3	yes	8	52.43	odd	6
624.2.bv.g.49.2		8	1.1	even	1	trivial
624.2.bv.g.433.3		8	13.4	even	6	inner
936.2.bi.c.361.3		8	12.11	even	2
936.2.bi.c.433.2		8	156.95	even	6
1872.2.by.m.433.2		8	39.17	odd	6
1872.2.by.m.1297.3		8	3.2	odd	2
4056.2.a.bd.1.3		4	52.11	even	12
4056.2.a.be.1.2		4	52.15	even	12
4056.2.c.p.337.4		8	52.3	odd	6
4056.2.c.p.337.5		8	52.23	odd	6
8112.2.a.cq.1.3		4	13.11	odd	12
8112.2.a.cs.1.2		4	13.2	odd	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} -0.475353i q^{5} +(-3.94508 - 2.27769i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.43069 - 0.826009i) q^{11} +(2.88139 - 2.16739i) q^{13} +(0.411667 - 0.237676i) q^{15} +(3.96973 - 6.87577i) q^{17} +(2.25402 + 1.30136i) q^{19} -4.55539i q^{21} +(-1.90604 - 3.30136i) q^{23} +4.77404 q^{25} -1.00000 q^{27} +(-0.411667 - 0.713029i) q^{29} -1.79260i q^{31} +(1.43069 + 0.826009i) q^{33} +(-1.08271 + 1.87530i) q^{35} +(-1.62174 + 0.936315i) q^{37} +(3.31771 + 1.41167i) q^{39} +(-9.26841 + 5.35112i) q^{41} +(4.94508 - 8.56513i) q^{43} +(0.411667 + 0.237676i) q^{45} +7.29869i q^{47} +(6.87577 + 11.9092i) q^{49} +7.93945 q^{51} -10.0063 q^{53} +(-0.392645 - 0.680082i) q^{55} +2.60272i q^{57} +(-1.28744 - 0.743302i) q^{59} +(5.87014 - 10.1674i) q^{61} +(3.94508 - 2.27769i) q^{63} +(-1.03027 - 1.36968i) q^{65} +(-2.87826 + 1.66176i) q^{67} +(1.90604 - 3.30136i) q^{69} +(-1.65130 - 0.953379i) q^{71} +6.14686i q^{73} +(2.38702 + 4.13444i) q^{75} -7.52558 q^{77} +10.7515 q^{79} +(-0.500000 - 0.866025i) q^{81} -14.7628i q^{83} +(-3.26841 - 1.88702i) q^{85} +(0.411667 - 0.713029i) q^{87} +(-6.32548 + 3.65202i) q^{89} +(-16.3040 + 1.98758i) q^{91} +(1.55243 - 0.896298i) q^{93} +(0.618606 - 1.07146i) q^{95} +(-3.62423 - 2.09245i) q^{97} +1.65202i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{15} + 12 q^{17} - 6 q^{19} + 2 q^{23} - 4 q^{25} - 8 q^{27} + 6 q^{29} + 6 q^{33} - 10 q^{35} - 24 q^{41} + 8 q^{43} - 6 q^{45} + 18 q^{49} + 24 q^{51}+ \cdots - 66 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^9 + 6 * q^11 - 6 * q^13 - 6 * q^15 + 12 * q^17 - 6 * q^19 + 2 * q^23 - 4 * q^25 - 8 * q^27 + 6 * q^29 + 6 * q^33 - 10 * q^35 - 24 * q^41 + 8 * q^43 - 6 * q^45 + 18 * q^49 + 24 * q^51 + 4 * q^53 + 10 * q^55 + 36 * q^59 + 2 * q^61 - 28 * q^65 - 36 * q^67 - 2 * q^69 - 6 * q^71 - 2 * q^75 + 56 * q^77 + 12 * q^79 - 4 * q^81 + 24 * q^85 - 6 * q^87 - 12 * q^89 - 38 * q^91 - 6 * q^93 + 34 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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