LMFDB - Embedded newform 1344.2.bb.e.607.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(31,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 1]))

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

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

chi := DirichletCharacter("1344.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.bb (of order $6$, degree $2$, 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 84x^{8} - 187x^{6} + 141x^{4} + 108x^{2} + 16 $ x^12 - 15x^10 + 84x^8 - 187x^6 + 141x^4 + 108*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.6
Root			$-2.43956 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1344.607
Dual form			1344.2.bb.e.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{3} +(1.10074 - 1.90653i) q^{5} +(-2.43956 - 1.02398i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{3} +(1.10074 - 1.90653i) q^{5} +(-2.43956 - 1.02398i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-0.332992 - 0.576760i) q^{11} +2.15352 q^{13} -2.20147i q^{15} +(2.72545 - 1.57354i) q^{17} +(2.77256 + 1.60074i) q^{19} +(-2.62471 + 0.332992i) q^{21} +(-0.907554 - 0.523976i) q^{23} +(0.0767598 + 0.132952i) q^{25} -1.00000i q^{27} -2.79812i q^{29} +(-4.17161 - 7.22545i) q^{31} +(-0.576760 - 0.332992i) q^{33} +(-4.63756 + 3.52398i) q^{35} +(-7.52766 - 4.34609i) q^{37} +(1.86500 - 1.07676i) q^{39} -9.75826i q^{41} -4.21314 q^{43} +(-1.10074 - 1.90653i) q^{45} +(3.97157 - 6.87897i) q^{47} +(4.90294 + 4.99611i) q^{49} +(1.57354 - 2.72545i) q^{51} +(-0.851311 + 0.491505i) q^{53} -1.46615 q^{55} +3.20147 q^{57} +(-12.7309 + 7.35016i) q^{59} +(1.20147 - 2.08101i) q^{61} +(-2.10657 + 1.60074i) q^{63} +(2.37046 - 4.10575i) q^{65} +(1.04051 + 1.80221i) q^{67} -1.04795 q^{69} +4.95205i q^{71} +(3.37414 - 1.94806i) q^{73} +(0.132952 + 0.0767598i) q^{75} +(0.221768 + 1.74802i) q^{77} +(-7.66765 - 4.42692i) q^{79} +(-0.500000 - 0.866025i) q^{81} +8.70032i q^{83} -6.92820i q^{85} +(-1.39906 - 2.42324i) q^{87} +(8.30704 + 4.79607i) q^{89} +(-5.25365 - 2.20515i) q^{91} +(-7.22545 - 4.17161i) q^{93} +(6.10371 - 3.52398i) q^{95} +3.49604i q^{97} -0.665985 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} + 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^5 + 6 * q^9	$ 12 q - 6 q^{5} + 6 q^{9} - 12 q^{17} - 6 q^{21} - 12 q^{25} + 6 q^{33} + 12 q^{37} + 6 q^{45} - 18 q^{49} - 42 q^{53} - 24 q^{61} + 48 q^{65} - 36 q^{73} + 54 q^{77} - 6 q^{81} + 48 q^{89} - 42 q^{93}+O(q^{100}) $ 12 * q - 6 * q^5 + 6 * q^9 - 12 * q^17 - 6 * q^21 - 12 * q^25 + 6 * q^33 + 12 * q^37 + 6 * q^45 - 18 * q^49 - 42 * q^53 - 24 * q^61 + 48 * q^65 - 36 * q^73 + 54 * q^77 - 6 * q^81 + 48 * q^89 - 42 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		0			0
$5$	1.10074	−	1.90653i	0.492264	−	0.852627i	−0.507696	−	0.861536i	$-0.669503\pi$
$5$	1.10074	−	1.90653i	0.492264	−	0.852627i	0.999960	+	0.00890964i	$0.00283606\pi$
$6$		0			0
$7$	−2.43956	−	1.02398i	−0.922069	−	0.387027i
$7$	−2.43956	−	1.02398i	−0.922069	−	0.387027i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−0.332992	−	0.576760i	−0.100401	−	0.173900i	0.811449	−	0.584423i	$-0.198679\pi$
$11$	−0.332992	−	0.576760i	−0.100401	−	0.173900i	−0.911850	+	0.410524i	$0.865346\pi$
$12$		0			0
$13$	2.15352			0.597279			0.298639	−	0.954366i	$-0.403467\pi$
$13$	2.15352			0.597279			0.298639	+	0.954366i	$0.403467\pi$
$14$		0			0
$15$		−	2.20147i		−	0.568418i
$16$		0			0
$17$	2.72545	−	1.57354i	0.661018	−	0.381639i	−0.131646	−	0.991297i	$-0.542026\pi$
$17$	2.72545	−	1.57354i	0.661018	−	0.381639i	0.792665	+	0.609658i	$0.208693\pi$
$18$		0			0
$19$	2.77256	+	1.60074i	0.636068	+	0.367234i	0.783098	−	0.621898i	$-0.213638\pi$
$19$	2.77256	+	1.60074i	0.636068	+	0.367234i	−0.147030	+	0.989132i	$0.546971\pi$
$20$		0			0
$21$	−2.62471	+	0.332992i	−0.572759	+	0.0726649i
$22$		0			0
$23$	−0.907554	−	0.523976i	−0.189238	−	0.109257i	0.402388	−	0.915469i	$-0.368180\pi$
$23$	−0.907554	−	0.523976i	−0.189238	−	0.109257i	−0.591626	+	0.806213i	$0.701514\pi$
$24$		0			0
$25$	0.0767598	+	0.132952i	0.0153520	+	0.0265904i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		−	2.79812i		−	0.519597i	−0.965663	−	0.259799i	$-0.916344\pi$
$29$		−	2.79812i		−	0.519597i	0.965663	−	0.259799i	$-0.0836562\pi$
$30$		0			0
$31$	−4.17161	−	7.22545i	−0.749244	−	1.29773i	−0.948185	−	0.317717i	$-0.897084\pi$
$31$	−4.17161	−	7.22545i	−0.749244	−	1.29773i	0.198941	−	0.980011i	$-0.436250\pi$
$32$		0			0
$33$	−0.576760	−	0.332992i	−0.100401	−	0.0579665i
$34$		0			0
$35$	−4.63756	+	3.52398i	−0.783891	+	0.595661i
$36$		0			0
$37$	−7.52766	−	4.34609i	−1.23754	−	0.714494i	−0.268949	−	0.963155i	$-0.586676\pi$
$37$	−7.52766	−	4.34609i	−1.23754	−	0.714494i	−0.968591	+	0.248661i	$0.920010\pi$
$38$		0			0
$39$	1.86500	−	1.07676i	0.298639	−	0.172420i
$40$		0			0
$41$		−	9.75826i		−	1.52398i	−0.647587	−	0.761992i	$-0.724222\pi$
$41$		−	9.75826i		−	1.52398i	0.647587	−	0.761992i	$-0.275778\pi$
$42$		0			0
$43$	−4.21314			−0.642498			−0.321249	−	0.946995i	$-0.604103\pi$
$43$	−4.21314			−0.642498			−0.321249	+	0.946995i	$0.604103\pi$
$44$		0			0
$45$	−1.10074	−	1.90653i	−0.164088	−	0.284209i
$46$		0			0
$47$	3.97157	−	6.87897i	0.579314	−	1.00340i	−0.416245	−	0.909253i	$-0.636654\pi$
$47$	3.97157	−	6.87897i	0.579314	−	1.00340i	0.995558	−	0.0941480i	$-0.0300127\pi$
$48$		0			0
$49$	4.90294	+	4.99611i	0.700421	+	0.713730i
$50$		0			0
$51$	1.57354	−	2.72545i	0.220339	−	0.381639i
$52$		0			0
$53$	−0.851311	+	0.491505i	−0.116937	+	0.0675134i	−0.557327	−	0.830293i	$-0.688173\pi$
$53$	−0.851311	+	0.491505i	−0.116937	+	0.0675134i	0.440391	+	0.897806i	$0.354840\pi$
$54$		0			0
$55$	−1.46615			−0.197695
$56$		0			0
$57$	3.20147			0.424045
$58$		0			0
$59$	−12.7309	+	7.35016i	−1.65742	+	0.956909i	−0.683515	+	0.729937i	$0.739550\pi$
$59$	−12.7309	+	7.35016i	−1.65742	+	0.956909i	−0.973901	+	0.226973i	$0.927117\pi$
$60$		0			0
$61$	1.20147	−	2.08101i	0.153833	−	0.266446i	−0.778801	−	0.627272i	$-0.784172\pi$
$61$	1.20147	−	2.08101i	0.153833	−	0.266446i	0.932633	+	0.360825i	$0.117505\pi$
$62$		0			0
$63$	−2.10657	+	1.60074i	−0.265403	+	0.201674i
$64$		0			0
$65$	2.37046	−	4.10575i	0.294019	−	0.509256i
$66$		0			0
$67$	1.04051	+	1.80221i	0.127118	+	0.220175i	0.922559	−	0.385856i	$-0.126094\pi$
$67$	1.04051	+	1.80221i	0.127118	+	0.220175i	−0.795441	+	0.606031i	$0.792761\pi$
$68$		0			0
$69$	−1.04795			−0.126159
$70$		0			0
$71$			4.95205i			0.587700i	0.955852	+	0.293850i	$0.0949366\pi$
$71$			4.95205i			0.587700i	−0.955852	+	0.293850i	$0.905063\pi$
$72$		0			0
$73$	3.37414	−	1.94806i	0.394913	−	0.228003i	−0.289374	−	0.957216i	$-0.593447\pi$
$73$	3.37414	−	1.94806i	0.394913	−	0.228003i	0.684287	+	0.729213i	$0.260114\pi$
$74$		0			0
$75$	0.132952	+	0.0767598i	0.0153520	+	0.00886346i
$76$		0			0
$77$	0.221768	+	1.74802i	0.0252728	+	0.199205i
$78$		0			0
$79$	−7.66765	−	4.42692i	−0.862678	−	0.498068i	0.00222998	−	0.999998i	$-0.499290\pi$
$79$	−7.66765	−	4.42692i	−0.862678	−	0.498068i	−0.864908	+	0.501930i	$0.832624\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			8.70032i			0.954984i	0.878636	+	0.477492i	$0.158454\pi$
$83$			8.70032i			0.954984i	−0.878636	+	0.477492i	$0.841546\pi$
$84$		0			0
$85$		−	6.92820i		−	0.751469i
$86$		0			0
$87$	−1.39906	−	2.42324i	−0.149995	−	0.259799i
$88$		0			0
$89$	8.30704	+	4.79607i	0.880544	+	0.508383i	0.870838	−	0.491570i	$-0.163577\pi$
$89$	8.30704	+	4.79607i	0.880544	+	0.508383i	0.00970652	+	0.999953i	$0.496910\pi$
$90$		0			0
$91$	−5.25365	−	2.20515i	−0.550732	−	0.231163i
$92$		0			0
$93$	−7.22545	−	4.17161i	−0.749244	−	0.432576i
$94$		0			0
$95$	6.10371	−	3.52398i	0.626227	−	0.361552i
$96$		0			0
$97$			3.49604i			0.354969i	0.984124	+	0.177484i	$0.0567959\pi$
$97$			3.49604i			0.354969i	−0.984124	+	0.177484i	$0.943204\pi$
$98$		0			0
$99$	−0.665985			−0.0669340
$100$		0			0
$101$	7.40294	+	12.8223i	0.736621	+	1.27586i	0.954009	+	0.299779i	$0.0969129\pi$
$101$	7.40294	+	12.8223i	0.736621	+	1.27586i	−0.217388	+	0.976085i	$0.569754\pi$
$102$		0			0
$103$	1.04051	−	1.80221i	0.102524	−	0.177577i	−0.810200	−	0.586154i	$-0.800641\pi$
$103$	1.04051	−	1.80221i	0.102524	−	0.177577i	0.912724	+	0.408577i	$0.133975\pi$
$104$		0			0
$105$	−2.25426	+	5.37063i	−0.219993	+	0.524120i
$106$		0			0
$107$	1.82347	−	3.15835i	0.176282	−	0.305329i	−0.764322	−	0.644834i	$-0.776926\pi$
$107$	1.82347	−	3.15835i	0.176282	−	0.305329i	0.940604	+	0.339505i	$0.110260\pi$
$108$		0			0
$109$	−8.22062	+	4.74618i	−0.787392	+	0.454601i	−0.839044	−	0.544064i	$-0.816885\pi$
$109$	−8.22062	+	4.74618i	−0.787392	+	0.454601i	0.0516513	+	0.998665i	$0.483552\pi$
$110$		0			0
$111$	−8.69219			−0.825026
$112$		0			0
$113$	20.2568			1.90560			0.952799	−	0.303601i	$-0.0981891\pi$
$113$	20.2568			1.90560			0.952799	+	0.303601i	$0.0981891\pi$
$114$		0			0
$115$	−1.99795	+	1.15352i	−0.186310	+	0.107566i
$116$		0			0
$117$	1.07676	−	1.86500i	0.0995465	−	0.172420i
$118$		0			0
$119$	−8.26017	+	1.04795i	−0.757209	+	0.0960657i
$120$		0			0
$121$	5.27823	−	9.14217i	0.479839	−	0.831106i
$122$		0			0
$123$	−4.87913	−	8.45090i	−0.439936	−	0.761992i
$124$		0			0
$125$	11.3453			1.01476
$126$		0			0
$127$			12.4509i			1.10484i	0.833566	+	0.552419i	$0.186295\pi$
$127$			12.4509i			1.10484i	−0.833566	+	0.552419i	$0.813705\pi$
$128$		0			0
$129$	−3.64869	+	2.10657i	−0.321249	+	0.185473i
$130$		0			0
$131$	15.0215	+	8.67267i	1.31243	+	0.757734i	0.982499	−	0.186269i	$-0.0596396\pi$
$131$	15.0215	+	8.67267i	1.31243	+	0.757734i	0.329936	+	0.944003i	$0.392973\pi$
$132$		0			0
$133$	−5.12471	−	6.74413i	−0.444369	−	0.584790i
$134$		0			0
$135$	−1.90653	−	1.10074i	−0.164088	−	0.0947363i
$136$		0			0
$137$	−8.20147	−	14.2054i	−0.700699	−	1.21365i	−0.968221	−	0.250095i	$-0.919538\pi$
$137$	−8.20147	−	14.2054i	−0.700699	−	1.21365i	0.267522	−	0.963552i	$-0.413795\pi$
$138$		0			0
$139$		−	17.6044i		−	1.49319i	−0.665280	−	0.746594i	$-0.731688\pi$
$139$		−	17.6044i		−	1.49319i	0.665280	−	0.746594i	$-0.268312\pi$
$140$		0			0
$141$		−	7.94315i		−	0.668934i
$142$		0			0
$143$	−0.717106	−	1.24206i	−0.0599674	−	0.103867i
$144$		0			0
$145$	−5.33470	−	3.07999i	−0.443022	−	0.255779i
$146$		0			0
$147$	6.74413	+	1.87529i	0.556247	+	0.154671i
$148$		0			0
$149$	17.4509	+	10.0753i	1.42963	+	0.825399i	0.997091	−	0.0762148i	$-0.0242835\pi$
$149$	17.4509	+	10.0753i	1.42963	+	0.825399i	0.432542	+	0.901614i	$0.357617\pi$
$150$		0			0
$151$	9.31027	−	5.37529i	0.757659	−	0.437435i	−0.0707955	−	0.997491i	$-0.522554\pi$
$151$	9.31027	−	5.37529i	0.757659	−	0.437435i	0.828455	+	0.560056i	$0.189220\pi$
$152$		0			0
$153$		−	3.14708i		−	0.254426i
$154$		0			0
$155$	−18.3674			−1.47530
$156$		0			0
$157$	6.15352	+	10.6582i	0.491104	+	0.850618i	0.999948	−	0.0102416i	$-0.00326005\pi$
$157$	6.15352	+	10.6582i	0.491104	+	0.850618i	−0.508843	+	0.860859i	$0.669927\pi$
$158$		0			0
$159$	−0.491505	+	0.851311i	−0.0389789	+	0.0675134i
$160$		0			0
$161$	1.67750	+	2.20759i	0.132205	+	0.173982i
$162$		0			0
$163$	4.87913	−	8.45090i	0.382163	−	0.661925i	−0.609208	−	0.793010i	$-0.708513\pi$
$163$	4.87913	−	8.45090i	0.382163	−	0.661925i	0.991371	+	0.131085i	$0.0418460\pi$
$164$		0			0
$165$	−1.26972	+	0.733074i	−0.0988476	+	0.0570697i
$166$		0			0
$167$	3.94724			0.305447			0.152723	−	0.988269i	$-0.451196\pi$
$167$	3.94724			0.305447			0.152723	+	0.988269i	$0.451196\pi$
$168$		0			0
$169$	−8.36235			−0.643258
$170$		0			0
$171$	2.77256	−	1.60074i	0.212023	−	0.122411i
$172$		0			0
$173$	−5.47602	+	9.48475i	−0.416334	+	0.721112i	−0.995568	−	0.0940497i	$-0.970019\pi$
$173$	−5.47602	+	9.48475i	−0.416334	+	0.721112i	0.579233	+	0.815162i	$0.303352\pi$
$174$		0			0
$175$	−0.0511208	−	0.402945i	−0.00386437	−	0.0304598i
$176$		0			0
$177$	−7.35016	+	12.7309i	−0.552472	+	0.956909i
$178$		0			0
$179$	6.45267	+	11.1763i	0.482295	+	0.835359i	0.999793	−	0.0203248i	$-0.00647002\pi$
$179$	6.45267	+	11.1763i	0.482295	+	0.835359i	−0.517498	+	0.855684i	$0.673137\pi$
$180$		0			0
$181$	−2.15352			−0.160070			−0.0800349	−	0.996792i	$-0.525503\pi$
$181$	−2.15352			−0.160070			−0.0800349	+	0.996792i	$0.525503\pi$
$182$		0			0
$183$		−	2.40294i		−	0.177631i
$184$		0			0
$185$	−16.5719	+	9.56781i	−1.21839	+	0.703439i
$186$		0			0
$187$	−1.81511	−	1.04795i	−0.132734	−	0.0766339i
$188$		0			0
$189$	−1.02398	+	2.43956i	−0.0744833	+	0.177452i
$190$		0			0
$191$	15.5449	+	8.97487i	1.12479	+	0.649399i	0.942620	−	0.333868i	$-0.108354\pi$
$191$	15.5449	+	8.97487i	1.12479	+	0.649399i	0.182172	+	0.983267i	$0.441687\pi$
$192$		0			0
$193$	−9.85499	−	17.0693i	−0.709378	−	1.22868i	−0.965088	−	0.261925i	$-0.915643\pi$
$193$	−9.85499	−	17.0693i	−0.709378	−	1.22868i	0.255710	−	0.966753i	$-0.417691\pi$
$194$		0			0
$195$		−	4.74091i		−	0.339504i
$196$		0			0
$197$		−	3.78113i		−	0.269394i	−0.990887	−	0.134697i	$-0.956994\pi$
$197$		−	3.78113i		−	0.269394i	0.990887	−	0.134697i	$-0.0430061\pi$
$198$		0			0
$199$	−6.52812	−	11.3070i	−0.462766	−	0.801535i	0.536331	−	0.844008i	$-0.319810\pi$
$199$	−6.52812	−	11.3070i	−0.462766	−	0.801535i	−0.999098	+	0.0424728i	$0.986476\pi$
$200$		0			0
$201$	1.80221	+	1.04051i	0.127118	+	0.0733916i
$202$		0			0
$203$	−2.86521	+	6.82618i	−0.201098	+	0.479104i
$204$		0			0
$205$	−18.6044	−	10.7413i	−1.29939	−	0.750203i
$206$		0			0
$207$	−0.907554	+	0.523976i	−0.0630793	+	0.0364189i
$208$		0			0
$209$		−	2.13213i		−	0.147483i
$210$		0			0
$211$	27.9428			1.92366			0.961831	−	0.273645i	$-0.0882293\pi$
$211$	27.9428			1.92366			0.961831	+	0.273645i	$0.0882293\pi$
$212$		0			0
$213$	2.47602	+	4.28860i	0.169654	+	0.293850i
$214$		0			0
$215$	−4.63756	+	8.03249i	−0.316279	+	0.547811i
$216$		0			0
$217$	2.77823	+	21.8986i	0.188599	+	1.48657i
$218$		0			0
$219$	1.94806	−	3.37414i	0.131638	−	0.228003i
$220$		0			0
$221$	5.86931	−	3.38865i	0.394812	−	0.227945i
$222$		0			0
$223$	21.5145			1.44072			0.720358	−	0.693603i	$-0.243978\pi$
$223$	21.5145			1.44072			0.720358	+	0.693603i	$0.243978\pi$
$224$		0			0
$225$	0.153520			0.0102346
$226$		0			0
$227$	−5.76311	+	3.32733i	−0.382511	+	0.220843i	−0.678910	−	0.734221i	$-0.737547\pi$
$227$	−5.76311	+	3.32733i	−0.382511	+	0.220843i	0.296399	+	0.955064i	$0.404214\pi$
$228$		0			0
$229$	3.72177	−	6.44629i	0.245941	−	0.425983i	−0.716455	−	0.697634i	$-0.754236\pi$
$229$	3.72177	−	6.44629i	0.245941	−	0.425983i	0.962396	+	0.271651i	$0.0875696\pi$
$230$		0			0
$231$	1.06607	+	1.40294i	0.0701420	+	0.0923070i
$232$		0			0
$233$	1.42807	−	2.47349i	0.0935560	−	0.162044i	−0.815449	−	0.578829i	$-0.803510\pi$
$233$	1.42807	−	2.47349i	0.0935560	−	0.162044i	0.909005	+	0.416785i	$0.136843\pi$
$234$		0			0
$235$	−8.74331	−	15.1439i	−0.570351	−	0.987876i
$236$		0			0
$237$	−8.85384			−0.575119
$238$		0			0
$239$			18.0000i			1.16432i	0.813073	+	0.582162i	$0.197793\pi$
$239$			18.0000i			1.16432i	−0.813073	+	0.582162i	$0.802207\pi$
$240$		0			0
$241$	−24.1715	+	13.9554i	−1.55702	+	0.898948i	−0.559485	+	0.828841i	$0.689001\pi$
$241$	−24.1715	+	13.9554i	−1.55702	+	0.898948i	−0.997539	+	0.0701077i	$0.977666\pi$
$242$		0			0
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	14.9221	−	3.84821i	0.953337	−	0.245853i
$246$		0			0
$247$	5.97075	+	3.44722i	0.379910	+	0.219341i
$248$		0			0
$249$	4.35016	+	7.53470i	0.275680	+	0.477492i
$250$		0			0
$251$			8.20147i			0.517672i	0.965921	+	0.258836i	$0.0833390\pi$
$251$			8.20147i			0.517672i	−0.965921	+	0.258836i	$0.916661\pi$
$252$		0			0
$253$			0.697921i			0.0438779i
$254$		0			0
$255$	−3.46410	−	6.00000i	−0.216930	−	0.375735i
$256$		0			0
$257$	5.12103	+	2.95663i	0.319441	+	0.184429i	0.651143	−	0.758955i	$-0.274290\pi$
$257$	5.12103	+	2.95663i	0.319441	+	0.184429i	−0.331702	+	0.943384i	$0.607623\pi$
$258$		0			0
$259$	13.9139	+	18.3107i	0.864568	+	1.13777i
$260$		0			0
$261$	−2.42324	−	1.39906i	−0.149995	−	0.0865995i
$262$		0			0
$263$	26.4128	−	15.2494i	1.62868	−	0.940320i	0.644195	−	0.764861i	$-0.277193\pi$
$263$	26.4128	−	15.2494i	1.62868	−	0.940320i	0.984487	−	0.175458i	$-0.0561408\pi$
$264$		0			0
$265$			2.16407i			0.132938i
$266$		0			0
$267$	9.59214			0.587030
$268$		0			0
$269$	0.471193	+	0.816130i	0.0287291	+	0.0497603i	0.880033	−	0.474913i	$-0.157521\pi$
$269$	0.471193	+	0.816130i	0.0287291	+	0.0497603i	−0.851303	+	0.524674i	$0.824187\pi$
$270$		0			0
$271$	−10.0912	+	17.4786i	−0.613000	+	1.06175i	0.377732	+	0.925915i	$0.376704\pi$
$271$	−10.0912	+	17.4786i	−0.613000	+	1.06175i	−0.990732	+	0.135832i	$0.956629\pi$
$272$		0			0
$273$	−5.65237	+	0.717106i	−0.342097	+	0.0434012i
$274$		0			0
$275$	0.0511208	−	0.0885439i	0.00308270	−	0.00533940i
$276$		0			0
$277$	−14.0768	+	8.12722i	−0.845791	+	0.488317i	−0.859228	−	0.511592i	$-0.829056\pi$
$277$	−14.0768	+	8.12722i	−0.845791	+	0.488317i	0.0134378	+	0.999910i	$0.495722\pi$
$278$		0			0
$279$	−8.34323			−0.499496
$280$		0			0
$281$	−20.7556			−1.23818			−0.619089	−	0.785321i	$-0.712498\pi$
$281$	−20.7556			−1.23818			−0.619089	+	0.785321i	$0.712498\pi$
$282$		0			0
$283$	6.85152	−	3.95573i	0.407281	−	0.235144i	−0.282340	−	0.959314i	$-0.591111\pi$
$283$	6.85152	−	3.95573i	0.407281	−	0.235144i	0.689621	+	0.724171i	$0.257777\pi$
$284$		0			0
$285$	3.52398	−	6.10371i	0.208742	−	0.361552i
$286$		0			0
$287$	−9.99222	+	23.8059i	−0.589822	+	1.40522i
$288$		0			0
$289$	−3.54795	+	6.14523i	−0.208703	+	0.361484i
$290$		0			0
$291$	1.74802	+	3.02766i	0.102471	+	0.177484i
$292$		0			0
$293$	−2.75057			−0.160690			−0.0803451	−	0.996767i	$-0.525602\pi$
$293$	−2.75057			−0.160690			−0.0803451	+	0.996767i	$0.525602\pi$
$294$		0			0
$295$			32.3624i			1.88421i
$296$		0			0
$297$	−0.576760	+	0.332992i	−0.0334670	+	0.0193222i
$298$		0			0
$299$	−1.95443	−	1.12839i	−0.113028	−	0.0652567i
$300$		0			0
$301$	10.2782	+	4.31416i	0.592427	+	0.248664i
$302$		0			0
$303$	12.8223	+	7.40294i	0.736621	+	0.425288i
$304$		0			0
$305$	−2.64501	−	4.58129i	−0.151453	−	0.262324i
$306$		0			0
$307$		−	15.7962i		−	0.901538i	−0.892641	−	0.450769i	$-0.851150\pi$
$307$		−	15.7962i		−	0.901538i	0.892641	−	0.450769i	$-0.148850\pi$
$308$		0			0
$309$		−	2.08101i		−	0.118385i
$310$		0			0
$311$	3.54716	+	6.14386i	0.201141	+	0.348386i	0.948896	−	0.315588i	$-0.102202\pi$
$311$	3.54716	+	6.14386i	0.201141	+	0.348386i	−0.747755	+	0.663974i	$0.768868\pi$
$312$		0			0
$313$	16.5553	+	9.55822i	0.935762	+	0.540262i	0.888629	−	0.458626i	$-0.151658\pi$
$313$	16.5553	+	9.55822i	0.935762	+	0.540262i	0.0471325	+	0.998889i	$0.484992\pi$
$314$		0			0
$315$	0.733074	+	5.77823i	0.0413040	+	0.325566i
$316$		0			0
$317$	19.9295	+	11.5063i	1.11935	+	0.646257i	0.941235	−	0.337753i	$-0.109667\pi$
$317$	19.9295	+	11.5063i	1.11935	+	0.646257i	0.178115	+	0.984010i	$0.443000\pi$
$318$		0			0
$319$	−1.61384	+	0.931752i	−0.0903578	+	0.0521681i
$320$		0			0
$321$		−	3.64695i		−	0.203553i
$322$		0			0
$323$	10.0753			0.560604
$324$		0			0
$325$	0.165304	+	0.286314i	0.00916940	+	0.0158819i
$326$		0			0
$327$	−4.74618	+	8.22062i	−0.262464	+	0.454601i
$328$		0			0
$329$	−16.7328	+	12.7149i	−0.922510	+	0.700994i
$330$		0			0
$331$	−7.25160	+	12.5601i	−0.398584	+	0.690368i	−0.993551	−	0.113382i	$-0.963832\pi$
$331$	−7.25160	+	12.5601i	−0.398584	+	0.690368i	0.594967	+	0.803750i	$0.297165\pi$
$332$		0			0
$333$	−7.52766	+	4.34609i	−0.412513	+	0.238165i
$334$		0			0
$335$	4.58129			0.250303
$336$		0			0
$337$	−1.59476			−0.0868719			−0.0434359	−	0.999056i	$-0.513830\pi$
$337$	−1.59476			−0.0868719			−0.0434359	+	0.999056i	$0.513830\pi$
$338$		0			0
$339$	17.5429	−	10.1284i	0.952799	−	0.550099i
$340$		0			0
$341$	−2.77823	+	4.81204i	−0.150450	+	0.260587i
$342$		0			0
$343$	−6.84515	−	17.2088i	−0.369603	−	0.929190i
$344$		0			0
$345$	−1.15352	+	1.99795i	−0.0621034	+	0.107566i
$346$		0			0
$347$	−13.6468	−	23.6369i	−0.732597	−	1.26890i	−0.955770	−	0.294117i	$-0.904975\pi$
$347$	−13.6468	−	23.6369i	−0.732597	−	1.26890i	0.223172	−	0.974779i	$-0.428359\pi$
$348$		0			0
$349$	18.8059			1.00666			0.503328	−	0.864095i	$-0.332109\pi$
$349$	18.8059			1.00666			0.503328	+	0.864095i	$0.332109\pi$
$350$		0			0
$351$		−	2.15352i		−	0.114946i
$352$		0			0
$353$	−15.7351	+	9.08467i	−0.837495	+	0.483528i	−0.856412	−	0.516293i	$-0.827312\pi$
$353$	−15.7351	+	9.08467i	−0.837495	+	0.483528i	0.0189167	+	0.999821i	$0.493978\pi$
$354$		0			0
$355$	9.44123	+	5.45090i	0.501089	+	0.289304i
$356$		0			0
$357$	−6.62954	+	5.03764i	−0.350873	+	0.266620i
$358$		0			0
$359$	13.2543	+	7.65237i	0.699535	+	0.403877i	0.807174	−	0.590313i	$-0.200996\pi$
$359$	13.2543	+	7.65237i	0.699535	+	0.403877i	−0.107639	+	0.994190i	$0.534329\pi$
$360$		0			0
$361$	−4.37529	−	7.57822i	−0.230278	−	0.398854i
$362$		0			0
$363$		−	10.5565i		−	0.554071i
$364$		0			0
$365$		−	8.57720i		−	0.448951i
$366$		0			0
$367$	−10.3508	−	17.9281i	−0.540306	−	0.935838i	−0.998886	−	0.0471846i	$-0.984975\pi$
$367$	−10.3508	−	17.9281i	−0.540306	−	0.935838i	0.458580	−	0.888653i	$-0.348358\pi$
$368$		0			0
$369$	−8.45090	−	4.87913i	−0.439936	−	0.253997i
$370$		0			0
$371$	2.58012	−	0.327335i	0.133953	−	0.0169944i
$372$		0			0
$373$	18.2856	+	10.5572i	0.946792	+	0.546631i	0.892083	−	0.451872i	$-0.149243\pi$
$373$	18.2856	+	10.5572i	0.946792	+	0.546631i	0.0547092	+	0.998502i	$0.482577\pi$
$374$		0			0
$375$	9.82534	−	5.67267i	0.507379	−	0.292935i
$376$		0			0
$377$		−	6.02580i		−	0.310344i
$378$		0			0
$379$	8.04294			0.413138			0.206569	−	0.978432i	$-0.433770\pi$
$379$	8.04294			0.413138			0.206569	+	0.978432i	$0.433770\pi$
$380$		0			0
$381$	6.22545	+	10.7828i	0.318939	+	0.552419i
$382$		0			0
$383$	0.558593	−	0.967512i	0.0285428	−	0.0494376i	−0.851401	−	0.524515i	$-0.824247\pi$
$383$	0.558593	−	0.967512i	0.0285428	−	0.0494376i	0.879944	+	0.475078i	$0.157580\pi$
$384$		0			0
$385$	3.57676	+	1.50130i	0.182289	+	0.0765133i
$386$		0			0
$387$	−2.10657	+	3.64869i	−0.107083	+	0.185473i
$388$		0			0
$389$	−30.3299	+	17.5110i	−1.53779	+	0.887841i	−0.538817	+	0.842423i	$0.681129\pi$
$389$	−30.3299	+	17.5110i	−1.53779	+	0.887841i	−0.998968	+	0.0454180i	$0.985538\pi$
$390$		0			0
$391$	−3.29799			−0.166786
$392$		0			0
$393$	17.3453			0.874956
$394$		0			0
$395$	−16.8801	+	9.74574i	−0.849331	+	0.490362i
$396$		0			0
$397$	−12.6715	+	21.9477i	−0.635965	+	1.10152i	0.350345	+	0.936621i	$0.386064\pi$
$397$	−12.6715	+	21.9477i	−0.635965	+	1.10152i	−0.986310	+	0.164903i	$0.947269\pi$
$398$		0			0
$399$	−7.81020	−	3.27823i	−0.390999	−	0.164117i
$400$		0			0
$401$	18.0804	−	31.3162i	0.902894	−	1.56386i	0.0791748	−	0.996861i	$-0.474771\pi$
$401$	18.0804	−	31.3162i	0.902894	−	1.56386i	0.823719	−	0.566998i	$-0.191895\pi$
$402$		0			0
$403$	−8.98365	−	15.5601i	−0.447508	−	0.775106i
$404$		0			0
$405$	−2.20147			−0.109392
$406$		0			0
$407$			5.78887i			0.286943i
$408$		0			0
$409$	−14.6535	+	8.46021i	−0.724570	+	0.418331i	−0.816432	−	0.577441i	$-0.804051\pi$
$409$	−14.6535	+	8.46021i	−0.724570	+	0.418331i	0.0918625	+	0.995772i	$0.470718\pi$
$410$		0			0
$411$	−14.2054	−	8.20147i	−0.700699	−	0.404549i
$412$		0			0
$413$	38.5841	−	4.89510i	1.89860	−	0.240872i
$414$		0			0
$415$	16.5874	+	9.57676i	0.814245	+	0.470105i
$416$		0			0
$417$	−8.80221	−	15.2459i	−0.431046	−	0.746594i
$418$		0			0
$419$			3.69296i			0.180413i	0.995923	+	0.0902065i	$0.0287527\pi$
$419$			3.69296i			0.180413i	−0.995923	+	0.0902065i	$0.971247\pi$
$420$		0			0
$421$			15.6204i			0.761291i	0.924721	+	0.380646i	$0.124298\pi$
$421$			15.6204i			0.761291i	−0.924721	+	0.380646i	$0.875702\pi$
$422$		0			0
$423$	−3.97157	−	6.87897i	−0.193105	−	0.334467i
$424$		0			0
$425$	0.418410	+	0.241569i	0.0202958	+	0.0117178i
$426$		0			0
$427$	−5.06197	+	3.84648i	−0.244966	+	0.186144i
$428$		0			0
$429$	−1.24206	−	0.717106i	−0.0599674	−	0.0346222i
$430$		0			0
$431$	8.10166	−	4.67750i	0.390243	−	0.225307i	−0.292022	−	0.956412i	$-0.594328\pi$
$431$	8.10166	−	4.67750i	0.390243	−	0.225307i	0.682266	+	0.731104i	$0.260995\pi$
$432$		0			0
$433$			23.9444i			1.15070i	0.817909	+	0.575348i	$0.195133\pi$
$433$			23.9444i			1.15070i	−0.817909	+	0.575348i	$0.804867\pi$
$434$		0			0
$435$	−6.15998			−0.295348
$436$		0			0
$437$	−1.67750	−	2.90551i	−0.0802455	−	0.138989i
$438$		0			0
$439$	−7.92718	+	13.7303i	−0.378344	+	0.655310i	−0.990821	−	0.135177i	$-0.956840\pi$
$439$	−7.92718	+	13.7303i	−0.378344	+	0.655310i	0.612478	+	0.790488i	$0.290173\pi$
$440$		0			0
$441$	6.77823	−	1.74802i	0.322773	−	0.0832390i
$442$		0			0
$443$	14.0309	−	24.3022i	0.666628	−	1.15463i	−0.312214	−	0.950012i	$-0.601071\pi$
$443$	14.0309	−	24.3022i	0.666628	−	1.15463i	0.978841	−	0.204621i	$-0.0655962\pi$
$444$		0			0
$445$	18.2877	−	10.5584i	0.866921	−	0.500517i
$446$		0			0
$447$	20.1506			0.953089
$448$		0			0
$449$	34.3527			1.62120			0.810602	−	0.585598i	$-0.199140\pi$
$449$	34.3527			1.62120			0.810602	+	0.585598i	$0.199140\pi$
$450$		0			0
$451$	−5.62817	+	3.24943i	−0.265020	+	0.153009i
$452$		0			0
$453$	5.37529	−	9.31027i	0.252553	−	0.437435i
$454$		0			0
$455$	−9.98707	+	7.58895i	−0.468201	+	0.355776i
$456$		0			0
$457$	1.79738	−	3.11315i	0.0840778	−	0.145627i	−0.820920	−	0.571043i	$-0.806539\pi$
$457$	1.79738	−	3.11315i	0.0840778	−	0.145627i	0.904998	+	0.425416i	$0.139872\pi$
$458$		0			0
$459$	−1.57354	−	2.72545i	−0.0734465	−	0.127213i
$460$		0			0
$461$	−29.4006			−1.36932			−0.684662	−	0.728860i	$-0.740050\pi$
$461$	−29.4006			−1.36932			−0.684662	+	0.728860i	$0.740050\pi$
$462$		0			0
$463$		−	9.29738i		−	0.432086i	−0.976384	−	0.216043i	$-0.930685\pi$
$463$		−	9.29738i		−	0.432086i	0.976384	−	0.216043i	$-0.0693151\pi$
$464$		0			0
$465$	−15.9066	+	9.18369i	−0.737652	+	0.425884i
$466$		0			0
$467$	12.8658	+	7.42807i	0.595358	+	0.343730i	0.767213	−	0.641392i	$-0.221643\pi$
$467$	12.8658	+	7.42807i	0.595358	+	0.343730i	−0.171855	+	0.985122i	$0.554976\pi$
$468$		0			0
$469$	−0.692961	−	5.46206i	−0.0319980	−	0.252214i
$470$		0			0
$471$	10.6582	+	6.15352i	0.491104	+	0.283539i
$472$		0			0
$473$	1.40294	+	2.42997i	0.0645075	+	0.111730i
$474$		0			0
$475$			0.491489i			0.0225510i
$476$		0			0
$477$			0.983009i			0.0450089i
$478$		0			0
$479$	−13.6468	−	23.6369i	−0.623537	−	1.08000i	−0.988822	−	0.149102i	$-0.952362\pi$
$479$	−13.6468	−	23.6369i	−0.623537	−	1.08000i	0.365285	−	0.930896i	$-0.380972\pi$
$480$		0			0
$481$	−16.2110	−	9.35940i	−0.739156	−	0.426752i
$482$		0			0
$483$	2.55655	+	1.07308i	0.116327	+	0.0488268i
$484$		0			0
$485$	6.66530	+	3.84821i	0.302656	+	0.174738i
$486$		0			0
$487$	−4.63557	+	2.67635i	−0.210058	+	0.121277i	−0.601338	−	0.798995i	$-0.705366\pi$
$487$	−4.63557	+	2.67635i	−0.210058	+	0.121277i	0.391281	+	0.920271i	$0.372032\pi$
$488$		0			0
$489$		−	9.75826i		−	0.441284i
$490$		0			0
$491$	17.3524			0.783105			0.391552	−	0.920156i	$-0.371938\pi$
$491$	17.3524			0.783105			0.391552	+	0.920156i	$0.371938\pi$
$492$		0			0
$493$	−4.40294	−	7.62612i	−0.198299	−	0.343463i
$494$		0			0
$495$	−0.733074	+	1.26972i	−0.0329492	+	0.0570697i
$496$		0			0
$497$	5.07078	−	12.0808i	0.227456	−	0.541900i
$498$		0			0
$499$	−11.7818	+	20.4066i	−0.527424	+	0.913526i	0.472065	+	0.881564i	$0.343509\pi$
$499$	−11.7818	+	20.4066i	−0.527424	+	0.913526i	−0.999489	+	0.0319621i	$0.989824\pi$
$500$		0			0
$501$	3.41841	−	1.97362i	0.152723	−	0.0881748i
$502$		0			0
$503$	1.79991			0.0802538			0.0401269	−	0.999195i	$-0.487224\pi$
$503$	1.79991			0.0802538			0.0401269	+	0.999195i	$0.487224\pi$
$504$		0			0
$505$	32.5948			1.45045
$506$		0			0
$507$	−7.24201	+	4.18118i	−0.321629	+	0.185693i
$508$		0			0
$509$	−19.8107	+	34.3132i	−0.878095	+	1.52090i	−0.0246656	+	0.999696i	$0.507852\pi$
$509$	−19.8107	+	34.3132i	−0.878095	+	1.52090i	−0.853429	+	0.521209i	$0.825481\pi$
$510$		0			0
$511$	−10.2262	+	1.29738i	−0.452380	+	0.0573926i
$512$		0			0
$513$	1.60074	−	2.77256i	0.0706742	−	0.122411i
$514$		0			0
$515$	−2.29064	−	3.96751i	−0.100938	−	0.174829i
$516$		0			0
$517$	−5.29002			−0.232655
$518$		0			0
$519$			10.9520i			0.480742i
$520$		0			0
$521$	−25.4412	+	14.6885i	−1.11460	+	0.643515i	−0.940017	−	0.341127i	$-0.889191\pi$
$521$	−25.4412	+	14.6885i	−1.11460	+	0.643515i	−0.174584	+	0.984642i	$0.555858\pi$
$522$		0			0
$523$	−37.5094	−	21.6561i	−1.64017	−	0.946953i	−0.980771	−	0.195160i	$-0.937477\pi$
$523$	−37.5094	−	21.6561i	−1.64017	−	0.946953i	−0.659399	−	0.751793i	$-0.729189\pi$
$524$		0			0
$525$	−0.245744	−	0.323400i	−0.0107252	−	0.0141143i
$526$		0			0
$527$	−22.7390	−	13.1284i	−0.990528	−	0.571882i
$528$		0			0
$529$	−10.9509	−	18.9675i	−0.476126	−	0.824674i
$530$		0			0
$531$			14.7003i			0.637940i
$532$		0			0
$533$		−	21.0146i		−	0.910243i
$534$		0			0
$535$	−4.01433	−	6.95302i	−0.173555	−	0.300605i
$536$		0			0
$537$	11.1763	+	6.45267i	0.482295	+	0.278453i
$538$		0			0
$539$	1.24891	−	4.49149i	0.0537945	−	0.193462i
$540$		0			0
$541$	−21.7794	−	12.5743i	−0.936369	−	0.540613i	−0.0475486	−	0.998869i	$-0.515141\pi$
$541$	−21.7794	−	12.5743i	−0.936369	−	0.540613i	−0.888820	+	0.458256i	$0.848474\pi$
$542$		0			0
$543$	−1.86500	+	1.07676i	−0.0800349	+	0.0462082i
$544$		0			0
$545$			20.8972i			0.895136i
$546$		0			0
$547$	18.0184			0.770412			0.385206	−	0.922831i	$-0.374130\pi$
$547$	18.0184			0.770412			0.385206	+	0.922831i	$0.374130\pi$
$548$		0			0
$549$	−1.20147	−	2.08101i	−0.0512776	−	0.0888154i
$550$		0			0
$551$	4.47905	−	7.75794i	0.190814	−	0.330499i
$552$		0			0
$553$	14.1727	+	18.6513i	0.602683	+	0.793132i
$554$		0			0
$555$	−9.56781	+	16.5719i	−0.406131	+	0.703439i
$556$		0			0
$557$	−4.55744	+	2.63124i	−0.193105	+	0.111489i	−0.593435	−	0.804882i	$-0.702229\pi$
$557$	−4.55744	+	2.63124i	−0.193105	+	0.111489i	0.400330	+	0.916371i	$0.368895\pi$
$558$		0			0
$559$	−9.07309			−0.383751
$560$		0			0
$561$	−2.09591			−0.0884892
$562$		0			0
$563$	−15.0650	+	8.69779i	−0.634915	+	0.366568i	−0.782653	−	0.622458i	$-0.786134\pi$
$563$	−15.0650	+	8.69779i	−0.634915	+	0.366568i	0.147738	+	0.989027i	$0.452801\pi$
$564$		0			0
$565$	22.2974	−	38.6202i	0.938058	−	1.62476i
$566$		0			0
$567$	0.332992	+	2.62471i	0.0139844	+	0.110228i
$568$		0			0
$569$	5.75057	−	9.96029i	0.241077	−	0.417557i	−0.719945	−	0.694032i	$-0.755833\pi$
$569$	5.75057	−	9.96029i	0.241077	−	0.417557i	0.961021	+	0.276475i	$0.0891661\pi$
$570$		0			0
$571$	16.6928	+	28.9128i	0.698573	+	1.20996i	0.968961	+	0.247213i	$0.0795148\pi$
$571$	16.6928	+	28.9128i	0.698573	+	1.20996i	−0.270388	+	0.962752i	$0.587152\pi$
$572$		0			0
$573$	17.9497			0.749861
$574$		0			0
$575$		−	0.160881i		−	0.00670921i
$576$		0			0
$577$	1.50000	−	0.866025i	0.0624458	−	0.0360531i	−0.468452	−	0.883489i	$-0.655188\pi$
$577$	1.50000	−	0.866025i	0.0624458	−	0.0360531i	0.530898	+	0.847436i	$0.321855\pi$
$578$		0			0
$579$	−17.0693	−	9.85499i	−0.709378	−	0.409559i
$580$		0			0
$581$	8.90892	−	21.2250i	0.369604	−	0.880561i
$582$		0			0
$583$	0.566960	+	0.327335i	0.0234811	+	0.0135568i
$584$		0			0
$585$	−2.37046	−	4.10575i	−0.0980063	−	0.169752i
$586$		0			0
$587$			9.46056i			0.390479i	0.980756	+	0.195240i	$0.0625484\pi$
$587$			9.46056i			0.390479i	−0.980756	+	0.195240i	$0.937452\pi$
$588$		0			0
$589$		−	26.7106i		−	1.10059i
$590$		0			0
$591$	−1.89056	−	3.27455i	−0.0777674	−	0.134697i
$592$		0			0
$593$	37.3527	+	21.5656i	1.53389	+	0.885593i	0.999177	+	0.0405595i	$0.0129140\pi$
$593$	37.3527	+	21.5656i	1.53389	+	0.885593i	0.534714	+	0.845033i	$0.320419\pi$
$594$		0			0
$595$	−7.09432	+	16.9018i	−0.290839	+	0.692906i
$596$		0			0
$597$	−11.3070	−	6.52812i	−0.462766	−	0.267178i
$598$		0			0
$599$	10.5752	−	6.10557i	0.432089	−	0.249467i	−0.268147	−	0.963378i	$-0.586411\pi$
$599$	10.5752	−	6.10557i	0.432089	−	0.249467i	0.700236	+	0.713911i	$0.253078\pi$
$600$		0			0
$601$		−	24.8788i		−	1.01483i	−0.861703	−	0.507413i	$-0.830602\pi$
$601$		−	24.8788i		−	1.01483i	0.861703	−	0.507413i	$-0.169398\pi$
$602$		0			0
$603$	2.08101			0.0847453
$604$		0			0
$605$	−11.6199	−	20.1262i	−0.472415	−	0.818247i
$606$		0			0
$607$	2.78852	−	4.82987i	0.113183	−	0.196038i	−0.803869	−	0.594806i	$-0.797229\pi$
$607$	2.78852	−	4.82987i	0.113183	−	0.196038i	0.917052	+	0.398768i	$0.130562\pi$
$608$		0			0
$609$	0.931752	+	7.34425i	0.0377565	+	0.297604i
$610$		0			0
$611$	8.55286	−	14.8140i	0.346012	−	0.599310i
$612$		0			0
$613$	−21.7483	+	12.5564i	−0.878405	+	0.507147i	−0.870132	−	0.492819i	$-0.835967\pi$
$613$	−21.7483	+	12.5564i	−0.878405	+	0.507147i	−0.00827253	+	0.999966i	$0.502633\pi$
$614$		0			0
$615$	−21.4825			−0.866259
$616$		0			0
$617$	4.11523			0.165673			0.0828364	−	0.996563i	$-0.473602\pi$
$617$	4.11523			0.165673			0.0828364	+	0.996563i	$0.473602\pi$
$618$		0			0
$619$	−7.18773	+	4.14984i	−0.288899	+	0.166796i	−0.637445	−	0.770496i	$-0.720009\pi$
$619$	−7.18773	+	4.14984i	−0.288899	+	0.166796i	0.348546	+	0.937292i	$0.386675\pi$
$620$		0			0
$621$	−0.523976	+	0.907554i	−0.0210264	+	0.0364189i
$622$		0			0
$623$	−15.3545	−	20.2065i	−0.615165	−	0.809558i
$624$		0			0
$625$	12.1044	−	20.9655i	0.484177	−	0.838619i
$626$		0			0
$627$	−1.06607	−	1.84648i	−0.0425746	−	0.0737413i
$628$		0			0
$629$	−27.3550			−1.09071
$630$		0			0
$631$			6.53944i			0.260331i	0.991492	+	0.130166i	$0.0415509\pi$
$631$			6.53944i			0.260331i	−0.991492	+	0.130166i	$0.958449\pi$
$632$		0			0
$633$	24.1992	−	13.9714i	0.961831	−	0.555313i
$634$		0			0
$635$	23.7380	+	13.7052i	0.942015	+	0.543872i
$636$		0			0
$637$	10.5586	+	10.7592i	0.418346	+	0.426296i
$638$		0			0
$639$	4.28860	+	2.47602i	0.169654	+	0.0979500i
$640$		0			0
$641$	−2.72545	−	4.72062i	−0.107649	−	0.186453i	0.807169	−	0.590321i	$-0.200999\pi$
$641$	−2.72545	−	4.72062i	−0.107649	−	0.186453i	−0.914817	+	0.403868i	$0.867666\pi$
$642$		0			0
$643$			26.1992i			1.03319i	0.856229	+	0.516597i	$0.172802\pi$
$643$			26.1992i			1.03319i	−0.856229	+	0.516597i	$0.827198\pi$
$644$		0			0
$645$			9.27512i			0.365207i
$646$		0			0
$647$	−2.56415	−	4.44124i	−0.100807	−	0.174603i	0.811210	−	0.584755i	$-0.198809\pi$
$647$	−2.56415	−	4.44124i	−0.100807	−	0.174603i	−0.912017	+	0.410151i	$0.865476\pi$
$648$		0			0
$649$	8.47855	+	4.89510i	0.332812	+	0.192149i
$650$		0			0
$651$	13.3553	+	17.5756i	0.523436	+	0.688842i
$652$		0			0
$653$	−36.3707	−	20.9986i	−1.42330	−	0.821740i	−0.426716	−	0.904386i	$-0.640330\pi$
$653$	−36.3707	−	20.9986i	−1.42330	−	0.821740i	−0.996579	+	0.0826459i	$0.973663\pi$
$654$		0			0
$655$	33.0694	−	19.0926i	1.29213	−	0.746011i
$656$		0			0
$657$		−	3.89612i		−	0.152002i
$658$		0			0
$659$	−1.18106			−0.0460075			−0.0230038	−	0.999735i	$-0.507323\pi$
$659$	−1.18106			−0.0460075			−0.0230038	+	0.999735i	$0.507323\pi$
$660$		0			0
$661$	15.7867	+	27.3434i	0.614033	+	1.06354i	0.990553	+	0.137128i	$0.0437872\pi$
$661$	15.7867	+	27.3434i	0.614033	+	1.06354i	−0.376520	+	0.926408i	$0.622879\pi$
$662$		0			0
$663$	3.38865	−	5.86931i	0.131604	−	0.227945i
$664$		0			0
$665$	−18.4989	+	2.34691i	−0.717355	+	0.0910095i
$666$		0			0
$667$	−1.46615	+	2.53944i	−0.0567694	+	0.0983276i
$668$		0			0
$669$	18.6321	−	10.7572i	0.720358	−	0.415899i
$670$		0			0
$671$	−1.60032			−0.0617798
$672$		0			0
$673$	19.5948			0.755322			0.377661	−	0.925944i	$-0.376728\pi$
$673$	19.5948			0.755322			0.377661	+	0.925944i	$0.376728\pi$
$674$		0			0
$675$	0.132952	−	0.0767598i	0.00511732	−	0.00295449i
$676$		0			0
$677$	8.08527	−	14.0041i	0.310742	−	0.538221i	−0.667781	−	0.744358i	$-0.732756\pi$
$677$	8.08527	−	14.0041i	0.310742	−	0.538221i	0.978523	+	0.206136i	$0.0660891\pi$
$678$		0			0
$679$	3.57986	−	8.52881i	0.137382	−	0.327306i
$680$		0			0
$681$	−3.32733	+	5.76311i	−0.127504	+	0.220843i
$682$		0			0
$683$	−2.65557	−	4.59959i	−0.101613	−	0.175998i	0.810737	−	0.585411i	$-0.199067\pi$
$683$	−2.65557	−	4.59959i	−0.101613	−	0.175998i	−0.912349	+	0.409413i	$0.865734\pi$
$684$		0			0
$685$	−36.1106			−1.37972
$686$		0			0
$687$		−	7.44354i		−	0.283989i
$688$		0			0
$689$	−1.83331	+	1.05846i	−0.0698437	+	0.0403243i
$690$		0			0
$691$	−14.7308	−	8.50483i	−0.560386	−	0.323539i	0.192914	−	0.981216i	$-0.438206\pi$
$691$	−14.7308	−	8.50483i	−0.560386	−	0.323539i	−0.753300	+	0.657677i	$0.771539\pi$
$692$		0			0
$693$	1.62471	+	0.681953i	0.0617177	+	0.0259052i
$694$		0			0
$695$	−33.5634	−	19.3778i	−1.27313	−	0.735043i
$696$		0			0
$697$	−15.3550	−	26.5956i	−0.581612	−	1.00738i
$698$		0			0
$699$		−	2.85614i		−	0.108029i
$700$		0			0
$701$		−	21.1336i		−	0.798204i	−0.916907	−	0.399102i	$-0.869322\pi$
$701$		−	21.1336i		−	0.798204i	0.916907	−	0.399102i	$-0.130678\pi$
$702$		0			0
$703$	−13.9139	−	24.0996i	−0.524773	−	0.908933i
$704$		0			0
$705$	−15.1439	−	8.74331i	−0.570351	−	0.329292i
$706$		0			0
$707$	−4.93025	−	38.8612i	−0.185421	−	1.46153i
$708$		0			0
$709$	5.16318	+	2.98096i	0.193907	+	0.111952i	0.593810	−	0.804605i	$-0.297623\pi$
$709$	5.16318	+	2.98096i	0.193907	+	0.111952i	−0.399903	+	0.916557i	$0.630956\pi$
$710$		0			0
$711$	−7.66765	+	4.42692i	−0.287559	+	0.166023i
$712$		0			0
$713$			8.74331i			0.327440i
$714$		0			0
$715$	−3.15738			−0.118079
$716$		0			0
$717$	9.00000	+	15.5885i	0.336111	+	0.582162i
$718$		0			0
$719$	7.99427	−	13.8465i	0.298136	−	0.516387i	−0.677574	−	0.735455i	$-0.736968\pi$
$719$	7.99427	−	13.8465i	0.298136	−	0.516387i	0.975709	+	0.219068i	$0.0703018\pi$
$720$		0			0
$721$	−4.38380	+	3.33115i	−0.163261	+	0.124059i
$722$		0			0
$723$	−13.9554	+	24.1715i	−0.519008	+	0.898948i
$724$		0			0
$725$	0.372015	−	0.214783i	0.0138163	−	0.00797683i
$726$		0			0
$727$	−7.01126			−0.260033			−0.130017	−	0.991512i	$-0.541503\pi$
$727$	−7.01126			−0.260033			−0.130017	+	0.991512i	$0.541503\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−11.4827	+	6.62954i	−0.424703	+	0.245203i
$732$		0			0
$733$	22.3239	−	38.6661i	0.824552	−	1.42817i	−0.0777100	−	0.996976i	$-0.524761\pi$
$733$	22.3239	−	38.6661i	0.824552	−	1.42817i	0.902262	−	0.431189i	$-0.141906\pi$
$734$		0			0
$735$	10.9988	−	10.7937i	0.405697	−	0.398132i
$736$		0			0
$737$	0.692961	−	1.20024i	0.0255255	−	0.0442115i
$738$		0			0
$739$	−25.2700	−	43.7690i	−0.929573	−	1.61007i	−0.784036	−	0.620715i	$-0.786842\pi$
$739$	−25.2700	−	43.7690i	−0.929573	−	1.61007i	−0.145537	−	0.989353i	$-0.546491\pi$
$740$		0			0
$741$	6.89443			0.253273
$742$		0			0
$743$		−	35.1895i		−	1.29098i	−0.763770	−	0.645489i	$-0.776654\pi$
$743$		−	35.1895i		−	1.29098i	0.763770	−	0.645489i	$-0.223346\pi$
$744$		0			0
$745$	38.4177	−	22.1805i	1.40751	−	0.812629i
$746$		0			0
$747$	7.53470	+	4.35016i	0.275680	+	0.159164i
$748$		0			0
$749$	−7.68256	+	5.83780i	−0.280715	+	0.213309i
$750$		0			0
$751$	19.4430	+	11.2254i	0.709487	+	0.409622i	0.810871	−	0.585225i	$-0.198994\pi$
$751$	19.4430	+	11.2254i	0.709487	+	0.409622i	−0.101384	+	0.994847i	$0.532327\pi$
$752$		0			0
$753$	4.10074	+	7.10268i	0.149439	+	0.258836i
$754$		0			0
$755$		−	23.6671i		−	0.861334i
$756$		0			0
$757$			31.3430i			1.13918i	0.821928	+	0.569591i	$0.192898\pi$
$757$			31.3430i			1.13918i	−0.821928	+	0.569591i	$0.807102\pi$
$758$		0			0
$759$	0.348960	+	0.604417i	0.0126665	+	0.0219389i
$760$		0			0
$761$	−27.9896	−	16.1598i	−1.01462	−	0.585792i	−0.102080	−	0.994776i	$-0.532550\pi$
$761$	−27.9896	−	16.1598i	−1.01462	−	0.585792i	−0.912542	+	0.408984i	$0.865883\pi$
$762$		0			0
$763$	24.9147	−	3.16088i	0.901973	−	0.114432i
$764$		0			0
$765$	−6.00000	−	3.46410i	−0.216930	−	0.125245i
$766$		0			0
$767$	−27.4161	+	15.8287i	−0.989939	+	0.571542i
$768$		0			0
$769$		−	33.0367i		−	1.19133i	−0.803231	−	0.595667i	$-0.796888\pi$
$769$		−	33.0367i		−	1.19133i	0.803231	−	0.595667i	$-0.203112\pi$
$770$		0			0
$771$	5.91326			0.212961
$772$		0			0
$773$	−23.5948	−	40.8673i	−0.848644	−	1.46990i	−0.882418	−	0.470466i	$-0.844086\pi$
$773$	−23.5948	−	40.8673i	−0.848644	−	1.46990i	0.0337739	−	0.999429i	$-0.489247\pi$
$774$		0			0
$775$	0.640424	−	1.10925i	0.0230047	−	0.0398453i
$776$		0			0
$777$	21.2052	+	8.90060i	0.760731	+	0.319307i
$778$		0			0
$779$	15.6204	−	27.0553i	0.559659	−	0.969357i
$780$		0			0
$781$	2.85614	−	1.64899i	0.102201	−	0.0590056i
$782$		0			0
$783$	−2.79812			−0.0999965
$784$		0			0
$785$	27.0936			0.967012
$786$		0			0
$787$	−19.4143	+	11.2088i	−0.692044	+	0.399552i	−0.804377	−	0.594119i	$-0.797501\pi$
$787$	−19.4143	+	11.2088i	−0.692044	+	0.399552i	0.112333	+	0.993671i	$0.464168\pi$
$788$		0			0
$789$	15.2494	−	26.4128i	0.542894	−	0.940320i
$790$		0			0
$791$	−49.4177	−	20.7425i	−1.75709	−	0.737517i
$792$		0			0
$793$	2.58739	−	4.48150i	0.0918811	−	0.159143i
$794$		0			0
$795$	1.08203	+	1.87414i	0.0383758	+	0.0664688i
$796$		0			0
$797$	−9.08854			−0.321933			−0.160966	−	0.986960i	$-0.551461\pi$
$797$	−9.08854			−0.321933			−0.160966	+	0.986960i	$0.551461\pi$
$798$		0			0
$799$		−	24.9977i		−	0.884355i
$800$		0			0
$801$	8.30704	−	4.79607i	0.293515	−	0.169461i
$802$		0			0
$803$	−2.24712	−	1.29738i	−0.0792993	−	0.0457835i
$804$		0			0
$805$	6.05531	−	0.768227i	0.213422	−	0.0270764i
$806$		0			0
$807$	0.816130	+	0.471193i	0.0287291	+	0.0165868i
$808$		0			0
$809$	−6.87897	−	11.9147i	−0.241852	−	0.418899i	0.719390	−	0.694606i	$-0.244421\pi$
$809$	−6.87897	−	11.9147i	−0.241852	−	0.418899i	−0.961242	+	0.275707i	$0.911088\pi$
$810$		0			0
$811$			9.20883i			0.323366i	0.986843	+	0.161683i	$0.0516922\pi$
$811$			9.20883i			0.323366i	−0.986843	+	0.161683i	$0.948308\pi$
$812$		0			0
$813$			20.1825i			0.707831i
$814$		0			0
$815$	−10.7413	−	18.6044i	−0.376250	−	0.651684i
$816$		0			0
$817$	−11.6812	−	6.74413i	−0.408673	−	0.235947i
$818$		0			0
$819$	−4.53654	+	3.44722i	−0.158520	+	0.120455i
$820$		0			0
$821$	29.0048	+	16.7459i	1.01228	+	0.584438i	0.911857	−	0.410508i	$-0.134649\pi$
$821$	29.0048	+	16.7459i	1.01228	+	0.584438i	0.100418	+	0.994945i	$0.467982\pi$
$822$		0			0
$823$	36.3691	−	20.9977i	1.26775	−	0.731934i	0.293185	−	0.956056i	$-0.405285\pi$
$823$	36.3691	−	20.9977i	1.26775	−	0.731934i	0.974561	+	0.224122i	$0.0719513\pi$
$824$		0			0
$825$		−	0.102242i		−	0.00355960i
$826$		0			0
$827$	6.17518			0.214732			0.107366	−	0.994220i	$-0.465758\pi$
$827$	6.17518			0.214732			0.107366	+	0.994220i	$0.465758\pi$
$828$		0			0
$829$	16.8250	+	29.1418i	0.584358	+	1.01214i	0.994955	+	0.100320i	$0.0319868\pi$
$829$	16.8250	+	29.1418i	0.584358	+	1.01214i	−0.410598	+	0.911817i	$0.634680\pi$
$830$		0			0
$831$	−8.12722	+	14.0768i	−0.281930	+	0.488317i
$832$		0			0
$833$	21.2243	+	5.90167i	0.735378	+	0.204481i
$834$		0			0
$835$	4.34487	−	7.52553i	0.150360	−	0.260432i
$836$		0			0
$837$	−7.22545	+	4.17161i	−0.249748	+	0.144192i
$838$		0			0
$839$	29.1087			1.00494			0.502471	−	0.864594i	$-0.332424\pi$
$839$	29.1087			1.00494			0.502471	+	0.864594i	$0.332424\pi$
$840$		0			0
$841$	21.1705			0.730019
$842$		0			0
$843$	−17.9749	+	10.3778i	−0.619089	+	0.357431i
$844$		0			0
$845$	−9.20475	+	15.9431i	−0.316653	+	0.548459i
$846$		0			0
$847$	−22.2379	+	16.8981i	−0.764105	+	0.580626i
$848$		0			0
$849$	3.95573	−	6.85152i	0.135760	−	0.235144i
$850$		0			0
$851$	4.55450	+	7.88863i	0.156126	+	0.270419i
$852$		0			0
$853$	22.3453			0.765090			0.382545	−	0.923937i	$-0.375048\pi$
$853$	22.3453			0.765090			0.382545	+	0.923937i	$0.375048\pi$
$854$		0			0
$855$		−	7.04795i		−	0.241035i
$856$		0			0
$857$	−32.5948	+	18.8186i	−1.11342	+	0.642831i	−0.939712	−	0.341967i	$-0.888907\pi$
$857$	−32.5948	+	18.8186i	−1.11342	+	0.642831i	−0.173704	+	0.984798i	$0.555574\pi$
$858$		0			0
$859$	15.2355	+	8.79623i	0.519829	+	0.300123i	0.736865	−	0.676040i	$-0.236305\pi$
$859$	15.2355	+	8.79623i	0.519829	+	0.300123i	−0.217036	+	0.976164i	$0.569639\pi$
$860$		0			0
$861$	3.24943	+	25.6126i	0.110740	+	0.872876i
$862$		0			0
$863$	−26.6619	−	15.3933i	−0.907583	−	0.523993i	−0.0279305	−	0.999610i	$-0.508892\pi$
$863$	−26.6619	−	15.3933i	−0.907583	−	0.523993i	−0.879653	+	0.475616i	$0.842225\pi$
$864$		0			0
$865$	12.0553	+	20.8804i	0.409893	+	0.709955i
$866$		0			0
$867$			7.09591i			0.240990i
$868$		0			0
$869$			5.89652i			0.200026i
$870$		0			0
$871$	2.24075	+	3.88109i	0.0759249	+	0.131506i
$872$		0			0
$873$	3.02766	+	1.74802i	0.102471	+	0.0591615i
$874$		0			0
$875$	−27.6777	−	11.6174i	−0.935676	−	0.392738i
$876$		0			0
$877$	−45.5159	−	26.2786i	−1.53696	−	0.887365i	−0.999014	−	0.0443869i	$-0.985867\pi$
$877$	−45.5159	−	26.2786i	−1.53696	−	0.887365i	−0.537947	−	0.842978i	$-0.680800\pi$
$878$		0			0
$879$	−2.38207	+	1.37529i	−0.0803451	+	0.0463873i
$880$		0			0
$881$			3.08321i			0.103876i	0.998650	+	0.0519379i	$0.0165398\pi$
$881$			3.08321i			0.103876i	−0.998650	+	0.0519379i	$0.983460\pi$
$882$		0			0
$883$	−33.1222			−1.11465			−0.557326	−	0.830294i	$-0.688173\pi$
$883$	−33.1222			−1.11465			−0.557326	+	0.830294i	$0.688173\pi$
$884$		0			0
$885$	16.1812	+	28.0266i	0.543924	+	0.942105i
$886$		0			0
$887$	−15.4375	+	26.7386i	−0.518342	+	0.897795i	0.481431	+	0.876484i	$0.340117\pi$
$887$	−15.4375	+	26.7386i	−0.518342	+	0.897795i	−0.999773	+	0.0213107i	$0.993216\pi$
$888$		0			0
$889$	12.7494	−	30.3748i	0.427602	−	1.01874i
$890$		0			0
$891$	−0.332992	+	0.576760i	−0.0111557	+	0.0193222i
$892$		0			0
$893$	22.0228	−	12.7149i	0.736966	−	0.425487i
$894$		0			0
$895$	28.4107			0.949666
$896$		0			0
$897$	−2.25679			−0.0753519
$898$		0			0
$899$	−20.2176	+	11.6727i	−0.674296	+	0.389305i
$900$		0			0
$901$	−1.54680	+	2.67914i	−0.0515315	+	0.0892551i
$902$		0			0
$903$	11.0583	−	1.40294i	0.367997	−	0.0466871i
$904$		0			0
$905$	−2.37046	+	4.10575i	−0.0787967	+	0.136480i
$906$		0			0
$907$	13.3629	+	23.1452i	0.443708	+	0.768525i	0.997961	−	0.0638231i	$-0.0203294\pi$
$907$	13.3629	+	23.1452i	0.443708	+	0.768525i	−0.554253	+	0.832348i	$0.686996\pi$
$908$		0			0
$909$	14.8059			0.491080
$910$		0			0
$911$			51.6768i			1.71213i	0.516870	+	0.856064i	$0.327097\pi$
$911$			51.6768i			1.71213i	−0.516870	+	0.856064i	$0.672903\pi$
$912$		0			0
$913$	5.01800	−	2.89714i	0.166071	−	0.0958814i
$914$		0			0
$915$	−4.58129	−	2.64501i	−0.151453	−	0.0874413i
$916$		0			0
$917$	−27.7653	−	36.5392i	−0.916891	−	1.20663i
$918$		0			0
$919$	3.20457	+	1.85016i	0.105709	+	0.0610312i	0.551922	−	0.833895i	$-0.313894\pi$
$919$	3.20457	+	1.85016i	0.105709	+	0.0610312i	−0.446213	+	0.894927i	$0.647228\pi$
$920$		0			0
$921$	−7.89811	−	13.6799i	−0.260252	−	0.450769i
$922$		0			0
$923$			10.6643i			0.351021i
$924$		0			0
$925$		−	1.33442i		−	0.0438755i
$926$		0			0
$927$	−1.04051	−	1.80221i	−0.0341747	−	0.0591923i
$928$		0			0
$929$	44.6922	+	25.8031i	1.46630	+	0.846571i	0.999290	−	0.0376787i	$-0.0119963\pi$
$929$	44.6922	+	25.8031i	1.46630	+	0.846571i	0.467014	+	0.884250i	$0.345330\pi$
$930$		0			0
$931$	5.59623	+	21.7003i	0.183409	+	0.711199i
$932$		0			0
$933$	6.14386	+	3.54716i	0.201141	+	0.116129i
$934$		0			0
$935$	−3.99591	+	2.30704i	−0.130680	+	0.0754482i
$936$		0			0
$937$		−	3.23013i		−	0.105524i	−0.998607	−	0.0527619i	$-0.983198\pi$
$937$		−	3.23013i		−	0.105524i	0.998607	−	0.0527619i	$-0.0168024\pi$
$938$		0			0
$939$	19.1164			0.623841
$940$		0			0
$941$	−19.4557	−	33.6983i	−0.634239	−	1.09853i	−0.986676	−	0.162698i	$-0.947980\pi$
$941$	−19.4557	−	33.6983i	−0.634239	−	1.09853i	0.352437	−	0.935835i	$-0.385353\pi$
$942$		0			0
$943$	−5.11310	+	8.85614i	−0.166505	+	0.288396i
$944$		0			0
$945$	3.52398	+	4.63756i	0.114635	+	0.150860i
$946$		0			0
$947$	28.3915	−	49.1756i	0.922601	−	1.59799i	0.127227	−	0.991874i	$-0.459392\pi$
$947$	28.3915	−	49.1756i	0.922601	−	1.59799i	0.795374	−	0.606119i	$-0.207274\pi$
$948$		0			0
$949$	7.26627	−	4.19518i	0.235873	−	0.136181i
$950$		0			0
$951$	23.0125			0.746233
$952$		0			0
$953$	−33.1779			−1.07474			−0.537369	−	0.843347i	$-0.680582\pi$
$953$	−33.1779			−1.07474			−0.537369	+	0.843347i	$0.680582\pi$
$954$		0			0
$955$	34.2217	−	19.7579i	1.10739	−	0.639352i
$956$		0			0
$957$	−0.931752	+	1.61384i	−0.0301193	+	0.0521681i
$958$		0			0
$959$	5.46206	+	43.0530i	0.176379	+	1.39025i
$960$		0			0
$961$	−19.3047	+	33.4368i	−0.622734	+	1.07861i
$962$		0			0
$963$	−1.82347	−	3.15835i	−0.0587606	−	0.101776i
$964$		0			0
$965$	−43.3910			−1.39681
$966$		0			0
$967$		−	15.4679i		−	0.497415i	−0.968579	−	0.248707i	$-0.919994\pi$
$967$		−	15.4679i		−	0.497415i	0.968579	−	0.248707i	$-0.0800058\pi$
$968$		0			0
$969$	8.72545	−	5.03764i	0.280302	−	0.161832i
$970$		0			0
$971$	44.9546	+	25.9546i	1.44266	+	0.832922i	0.998027	−	0.0627890i	$-0.0199995\pi$
$971$	44.9546	+	25.9546i	1.44266	+	0.832922i	0.444636	+	0.895711i	$0.353333\pi$
$972$		0			0
$973$	−18.0265	+	42.9471i	−0.577903	+	1.37682i
$974$		0			0
$975$	0.286314	+	0.165304i	0.00916940	+	0.00529395i
$976$		0			0
$977$	7.90179	+	13.6863i	0.252801	+	0.437864i	0.964296	−	0.264827i	$-0.0853149\pi$
$977$	7.90179	+	13.6863i	0.252801	+	0.437864i	−0.711495	+	0.702691i	$0.751982\pi$
$978$		0			0
$979$		−	6.38822i		−	0.204168i
$980$		0			0
$981$			9.49235i			0.303067i
$982$		0			0
$983$	13.9638	+	24.1860i	0.445376	+	0.771414i	0.998078	−	0.0619649i	$-0.0197367\pi$
$983$	13.9638	+	24.1860i	0.445376	+	0.771414i	−0.552702	+	0.833379i	$0.686403\pi$
$984$		0			0
$985$	−7.20883	−	4.16202i	−0.229693	−	0.132613i
$986$		0			0
$987$	−8.13360	+	19.3778i	−0.258895	+	0.616803i
$988$		0			0
$989$	3.82365	+	2.20759i	0.121585	+	0.0701972i
$990$		0			0
$991$	−46.9027	+	27.0793i	−1.48991	+	0.860202i	−0.999934	−	0.0115316i	$-0.996329\pi$
$991$	−46.9027	+	27.0793i	−1.48991	+	0.860202i	−0.489980	+	0.871734i	$0.662996\pi$
$992$		0			0
$993$			14.5032i			0.460245i
$994$		0			0
$995$	−28.7430			−0.911213
$996$		0			0
$997$	14.8730	+	25.7608i	0.471032	+	0.815852i	0.999451	−	0.0331321i	$-0.0105482\pi$
$997$	14.8730	+	25.7608i	0.471032	+	0.815852i	−0.528419	+	0.848984i	$0.677215\pi$
$998$		0			0
$999$	−4.34609	+	7.52766i	−0.137504	+	0.238165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.bb.e.607.6	yes	12
4.3	odd	2	inner	1344.2.bb.e.607.3	yes	12
7.3	odd	6		1344.2.bb.h.31.4	yes	12
8.3	odd	2		1344.2.bb.h.607.4	yes	12
8.5	even	2		1344.2.bb.h.607.1	yes	12
28.3	even	6		1344.2.bb.h.31.1	yes	12
56.3	even	6	inner	1344.2.bb.e.31.6	yes	12
56.45	odd	6	inner	1344.2.bb.e.31.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1344.2.bb.e.31.3	✓	12	56.45	odd	6	inner
1344.2.bb.e.31.6	yes	12	56.3	even	6	inner
1344.2.bb.e.607.3	yes	12	4.3	odd	2	inner
1344.2.bb.e.607.6	yes	12	1.1	even	1	trivial
1344.2.bb.h.31.1	yes	12	28.3	even	6
1344.2.bb.h.31.4	yes	12	7.3	odd	6
1344.2.bb.h.607.1	yes	12	8.5	even	2
1344.2.bb.h.607.4	yes	12	8.3	odd	2

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(1.10074 - 1.90653i) q^{5} +(-2.43956 - 1.02398i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{3} +(1.10074 - 1.90653i) q^{5} +(-2.43956 - 1.02398i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-0.332992 - 0.576760i) q^{11} +2.15352 q^{13} -2.20147i q^{15} +(2.72545 - 1.57354i) q^{17} +(2.77256 + 1.60074i) q^{19} +(-2.62471 + 0.332992i) q^{21} +(-0.907554 - 0.523976i) q^{23} +(0.0767598 + 0.132952i) q^{25} -1.00000i q^{27} -2.79812i q^{29} +(-4.17161 - 7.22545i) q^{31} +(-0.576760 - 0.332992i) q^{33} +(-4.63756 + 3.52398i) q^{35} +(-7.52766 - 4.34609i) q^{37} +(1.86500 - 1.07676i) q^{39} -9.75826i q^{41} -4.21314 q^{43} +(-1.10074 - 1.90653i) q^{45} +(3.97157 - 6.87897i) q^{47} +(4.90294 + 4.99611i) q^{49} +(1.57354 - 2.72545i) q^{51} +(-0.851311 + 0.491505i) q^{53} -1.46615 q^{55} +3.20147 q^{57} +(-12.7309 + 7.35016i) q^{59} +(1.20147 - 2.08101i) q^{61} +(-2.10657 + 1.60074i) q^{63} +(2.37046 - 4.10575i) q^{65} +(1.04051 + 1.80221i) q^{67} -1.04795 q^{69} +4.95205i q^{71} +(3.37414 - 1.94806i) q^{73} +(0.132952 + 0.0767598i) q^{75} +(0.221768 + 1.74802i) q^{77} +(-7.66765 - 4.42692i) q^{79} +(-0.500000 - 0.866025i) q^{81} +8.70032i q^{83} -6.92820i q^{85} +(-1.39906 - 2.42324i) q^{87} +(8.30704 + 4.79607i) q^{89} +(-5.25365 - 2.20515i) q^{91} +(-7.22545 - 4.17161i) q^{93} +(6.10371 - 3.52398i) q^{95} +3.49604i q^{97} -0.665985 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} + 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^5 + 6 * q^9	\( 12 q - 6 q^{5} + 6 q^{9} - 12 q^{17} - 6 q^{21} - 12 q^{25} + 6 q^{33} + 12 q^{37} + 6 q^{45} - 18 q^{49} - 42 q^{53} - 24 q^{61} + 48 q^{65} - 36 q^{73} + 54 q^{77} - 6 q^{81} + 48 q^{89} - 42 q^{93}+O(q^{100}) \) 12 * q - 6 * q^5 + 6 * q^9 - 12 * q^17 - 6 * q^21 - 12 * q^25 + 6 * q^33 + 12 * q^37 + 6 * q^45 - 18 * q^49 - 42 * q^53 - 24 * q^61 + 48 * q^65 - 36 * q^73 + 54 * q^77 - 6 * q^81 + 48 * q^89 - 42 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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