LMFDB - Embedded newform 1344.2.s.d.239.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (of order $4$, 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.17
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.d.911.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.945839 + 1.45100i) q^{3} +(-1.69539 - 1.69539i) q^{5} -1.00000 q^{7} +(-1.21078 + 2.74482i) q^{9} +O(q^{10})$	\(q+(0.945839 + 1.45100i) q^{3} +(-1.69539 - 1.69539i) q^{5} -1.00000 q^{7} +(-1.21078 + 2.74482i) q^{9} +(0.445358 - 0.445358i) q^{11} +(-1.51259 - 1.51259i) q^{13} +(0.856437 - 4.06356i) q^{15} -1.39276i q^{17} +(-0.965003 + 0.965003i) q^{19} +(-0.945839 - 1.45100i) q^{21} -6.04660i q^{23} +0.748676i q^{25} +(-5.12792 + 0.839319i) q^{27} +(4.93200 - 4.93200i) q^{29} -0.470285i q^{31} +(1.06745 + 0.224976i) q^{33} +(1.69539 + 1.69539i) q^{35} +(1.47646 - 1.47646i) q^{37} +(0.764098 - 3.62544i) q^{39} +8.35300 q^{41} +(-8.97272 - 8.97272i) q^{43} +(6.70626 - 2.60079i) q^{45} -4.84660 q^{47} +1.00000 q^{49} +(2.02089 - 1.31733i) q^{51} +(-3.42232 - 3.42232i) q^{53} -1.51011 q^{55} +(-2.31295 - 0.487478i) q^{57} +(6.61989 - 6.61989i) q^{59} +(-8.04415 - 8.04415i) q^{61} +(1.21078 - 2.74482i) q^{63} +5.12887i q^{65} +(-4.38159 + 4.38159i) q^{67} +(8.77359 - 5.71911i) q^{69} -12.3448i q^{71} +14.0195i q^{73} +(-1.08633 + 0.708126i) q^{75} +(-0.445358 + 0.445358i) q^{77} +16.5847i q^{79} +(-6.06803 - 6.64673i) q^{81} +(-9.24664 - 9.24664i) q^{83} +(-2.36127 + 2.36127i) q^{85} +(11.8212 + 2.49143i) q^{87} -5.25384 q^{89} +(1.51259 + 1.51259i) q^{91} +(0.682381 - 0.444814i) q^{93} +3.27211 q^{95} +5.17660 q^{97} +(0.683197 + 1.76166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{7}+O(q^{10}) $ 48 * q - 48 * q^7	$ 48 q - 48 q^{7} - 8 q^{19} + 12 q^{27} + 16 q^{37} + 24 q^{39} + 48 q^{43} + 20 q^{45} + 48 q^{49} + 32 q^{55} + 8 q^{61} + 16 q^{67} - 28 q^{69} + 12 q^{75} - 48 q^{85} - 56 q^{87} - 64 q^{93} - 32 q^{99}+O(q^{100}) $ 48 * q - 48 * q^7 - 8 * q^19 + 12 * q^27 + 16 * q^37 + 24 * q^39 + 48 * q^43 + 20 * q^45 + 48 * q^49 + 32 * q^55 + 8 * q^61 + 16 * q^67 - 28 * q^69 + 12 * q^75 - 48 * q^85 - 56 * q^87 - 64 * q^93 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.945839	+	1.45100i	0.546080	+	0.837733i
$3$	0.945839	+	1.45100i	0.546080	+	0.837733i
$4$		0			0
$5$	−1.69539	−	1.69539i	−0.758200	−	0.758200i	0.217794	−	0.975995i	$-0.430114\pi$
$5$	−1.69539	−	1.69539i	−0.758200	−	0.758200i	−0.975995	+	0.217794i	$0.930114\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$		0			0
$9$	−1.21078	+	2.74482i	−0.403593	+	0.914939i
$10$		0			0
$11$	0.445358	−	0.445358i	0.134281	−	0.134281i	−0.636772	−	0.771052i	$-0.719731\pi$
$11$	0.445358	−	0.445358i	0.134281	−	0.134281i	0.771052	+	0.636772i	$0.219731\pi$
$12$		0			0
$13$	−1.51259	−	1.51259i	−0.419518	−	0.419518i	0.465519	−	0.885038i	$-0.345868\pi$
$13$	−1.51259	−	1.51259i	−0.419518	−	0.419518i	−0.885038	+	0.465519i	$0.845868\pi$
$14$		0			0
$15$	0.856437	−	4.06356i	0.221131	−	1.04921i
$16$		0			0
$17$		−	1.39276i		−	0.337795i	−0.985634	−	0.168897i	$-0.945979\pi$
$17$		−	1.39276i		−	0.337795i	0.985634	−	0.168897i	$-0.0540207\pi$
$18$		0			0
$19$	−0.965003	+	0.965003i	−0.221387	+	0.221387i	−0.809082	−	0.587695i	$-0.800035\pi$
$19$	−0.965003	+	0.965003i	−0.221387	+	0.221387i	0.587695	+	0.809082i	$0.300035\pi$
$20$		0			0
$21$	−0.945839	−	1.45100i	−0.206399	−	0.316633i
$22$		0			0
$23$		−	6.04660i		−	1.26080i	−0.776269	−	0.630402i	$-0.782890\pi$
$23$		−	6.04660i		−	1.26080i	0.776269	−	0.630402i	$-0.217110\pi$
$24$		0			0
$25$			0.748676i			0.149735i
$26$		0			0
$27$	−5.12792	+	0.839319i	−0.986868	+	0.161527i
$28$		0			0
$29$	4.93200	−	4.93200i	0.915849	−	0.915849i	−0.0808754	−	0.996724i	$-0.525772\pi$
$29$	4.93200	−	4.93200i	0.915849	−	0.915849i	0.996724	+	0.0808754i	$0.0257716\pi$
$30$		0			0
$31$		−	0.470285i		−	0.0844657i	−0.999108	−	0.0422328i	$-0.986553\pi$
$31$		−	0.470285i		−	0.0844657i	0.999108	−	0.0422328i	$-0.0134471\pi$
$32$		0			0
$33$	1.06745	+	0.224976i	0.185819	+	0.0391633i
$34$		0			0
$35$	1.69539	+	1.69539i	0.286573	+	0.286573i
$36$		0			0
$37$	1.47646	−	1.47646i	0.242729	−	0.242729i	−0.575249	−	0.817978i	$-0.695095\pi$
$37$	1.47646	−	1.47646i	0.242729	−	0.242729i	0.817978	+	0.575249i	$0.195095\pi$
$38$		0			0
$39$	0.764098	−	3.62544i	0.122354	−	0.580535i
$40$		0			0
$41$	8.35300			1.30452			0.652260	−	0.757996i	$-0.273821\pi$
$41$	8.35300			1.30452			0.652260	+	0.757996i	$0.273821\pi$
$42$		0			0
$43$	−8.97272	−	8.97272i	−1.36833	−	1.36833i	−0.862827	−	0.505500i	$-0.831308\pi$
$43$	−8.97272	−	8.97272i	−1.36833	−	1.36833i	−0.505500	−	0.862827i	$-0.668692\pi$
$44$		0			0
$45$	6.70626	−	2.60079i	0.999711	−	0.387703i
$46$		0			0
$47$	−4.84660			−0.706949			−0.353475	−	0.935444i	$-0.615000\pi$
$47$	−4.84660			−0.706949			−0.353475	+	0.935444i	$0.615000\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	2.02089	−	1.31733i	0.282982	−	0.184463i
$52$		0			0
$53$	−3.42232	−	3.42232i	−0.470092	−	0.470092i	0.431852	−	0.901944i	$-0.357860\pi$
$53$	−3.42232	−	3.42232i	−0.470092	−	0.470092i	−0.901944	+	0.431852i	$0.857860\pi$
$54$		0			0
$55$	−1.51011			−0.203623
$56$		0			0
$57$	−2.31295	−	0.487478i	−0.306358	−	0.0645681i
$58$		0			0
$59$	6.61989	−	6.61989i	0.861836	−	0.861836i	−0.129715	−	0.991551i	$-0.541406\pi$
$59$	6.61989	−	6.61989i	0.861836	−	0.861836i	0.991551	+	0.129715i	$0.0414064\pi$
$60$		0			0
$61$	−8.04415	−	8.04415i	−1.02995	−	1.02995i	−0.999537	−	0.0304110i	$-0.990318\pi$
$61$	−8.04415	−	8.04415i	−1.02995	−	1.02995i	−0.0304110	−	0.999537i	$-0.509682\pi$
$62$		0			0
$63$	1.21078	−	2.74482i	0.152544	−	0.345814i
$64$		0			0
$65$			5.12887i			0.636158i
$66$		0			0
$67$	−4.38159	+	4.38159i	−0.535296	+	0.535296i	−0.922144	−	0.386847i	$-0.873564\pi$
$67$	−4.38159	+	4.38159i	−0.535296	+	0.535296i	0.386847	+	0.922144i	$0.373564\pi$
$68$		0			0
$69$	8.77359	−	5.71911i	1.05622	−	0.688500i
$70$		0			0
$71$		−	12.3448i		−	1.46506i	−0.680737	−	0.732528i	$-0.738340\pi$
$71$		−	12.3448i		−	1.46506i	0.680737	−	0.732528i	$-0.261660\pi$
$72$		0			0
$73$			14.0195i			1.64086i	0.571750	+	0.820428i	$0.306265\pi$
$73$			14.0195i			1.64086i	−0.571750	+	0.820428i	$0.693735\pi$
$74$		0			0
$75$	−1.08633	+	0.708126i	−0.125438	+	0.0817674i
$76$		0			0
$77$	−0.445358	+	0.445358i	−0.0507533	+	0.0507533i
$78$		0			0
$79$			16.5847i			1.86592i	0.359974	+	0.932962i	$0.382786\pi$
$79$			16.5847i			1.86592i	−0.359974	+	0.932962i	$0.617214\pi$
$80$		0			0
$81$	−6.06803	−	6.64673i	−0.674226	−	0.738525i
$82$		0			0
$83$	−9.24664	−	9.24664i	−1.01495	−	1.01495i	−0.999887	−	0.0150642i	$-0.995205\pi$
$83$	−9.24664	−	9.24664i	−1.01495	−	1.01495i	−0.0150642	−	0.999887i	$-0.504795\pi$
$84$		0			0
$85$	−2.36127	+	2.36127i	−0.256116	+	0.256116i
$86$		0			0
$87$	11.8212	+	2.49143i	1.26736	+	0.267110i
$88$		0			0
$89$	−5.25384			−0.556906			−0.278453	−	0.960450i	$-0.589822\pi$
$89$	−5.25384			−0.556906			−0.278453	+	0.960450i	$0.589822\pi$
$90$		0			0
$91$	1.51259	+	1.51259i	0.158563	+	0.158563i
$92$		0			0
$93$	0.682381	−	0.444814i	0.0707597	−	0.0461250i
$94$		0			0
$95$	3.27211			0.335711
$96$		0			0
$97$	5.17660			0.525604			0.262802	−	0.964850i	$-0.415353\pi$
$97$	5.17660			0.525604			0.262802	+	0.964850i	$0.415353\pi$
$98$		0			0
$99$	0.683197	+	1.76166i	0.0686638	+	0.177053i
$100$		0			0
$101$	2.41310	+	2.41310i	0.240112	+	0.240112i	0.816896	−	0.576784i	$-0.195693\pi$
$101$	2.41310	+	2.41310i	0.240112	+	0.240112i	−0.576784	+	0.816896i	$0.695693\pi$
$102$		0			0
$103$	5.77249			0.568780			0.284390	−	0.958709i	$-0.408209\pi$
$103$	5.77249			0.568780			0.284390	+	0.958709i	$0.408209\pi$
$104$		0			0
$105$	−0.856437	+	4.06356i	−0.0835797	+	0.396563i
$106$		0			0
$107$	11.2943	−	11.2943i	1.09186	−	1.09186i	0.0965337	−	0.995330i	$-0.469224\pi$
$107$	11.2943	−	11.2943i	1.09186	−	1.09186i	0.995330	−	0.0965337i	$-0.0307756\pi$
$108$		0			0
$109$	−7.78278	−	7.78278i	−0.745455	−	0.745455i	0.228167	−	0.973622i	$-0.426727\pi$
$109$	−7.78278	−	7.78278i	−0.745455	−	0.745455i	−0.973622	+	0.228167i	$0.926727\pi$
$110$		0			0
$111$	3.53883	+	0.745845i	0.335891	+	0.0707925i
$112$		0			0
$113$		−	1.12705i		−	0.106024i	−0.998594	−	0.0530119i	$-0.983118\pi$
$113$		−	1.12705i		−	0.106024i	0.998594	−	0.0530119i	$-0.0168821\pi$
$114$		0			0
$115$	−10.2513	+	10.2513i	−0.955941	+	0.955941i
$116$		0			0
$117$	5.98321	−	2.32038i	0.553148	−	0.214519i
$118$		0			0
$119$			1.39276i			0.127674i
$120$		0			0
$121$			10.6033i			0.963937i
$122$		0			0
$123$	7.90059	+	12.1202i	0.712372	+	1.09284i
$124$		0			0
$125$	−7.20764	+	7.20764i	−0.644671	+	0.644671i
$126$		0			0
$127$		−	2.20449i		−	0.195617i	−0.995205	−	0.0978084i	$-0.968817\pi$
$127$		−	2.20449i		−	0.195617i	0.995205	−	0.0978084i	$-0.0311832\pi$
$128$		0			0
$129$	4.53263	−	21.5061i	0.399076	−	1.89351i
$130$		0			0
$131$	10.5553	+	10.5553i	0.922222	+	0.922222i	0.997186	−	0.0749639i	$-0.0238841\pi$
$131$	10.5553	+	10.5553i	0.922222	+	0.922222i	−0.0749639	+	0.997186i	$0.523884\pi$
$132$		0			0
$133$	0.965003	−	0.965003i	0.0836764	−	0.0836764i
$134$		0			0
$135$	10.1168	+	7.27084i	0.870714	+	0.625774i
$136$		0			0
$137$	11.4183			0.975529			0.487764	−	0.872975i	$-0.337813\pi$
$137$	11.4183			0.975529			0.487764	+	0.872975i	$0.337813\pi$
$138$		0			0
$139$	−6.59016	−	6.59016i	−0.558970	−	0.558970i	0.370044	−	0.929014i	$-0.379342\pi$
$139$	−6.59016	−	6.59016i	−0.558970	−	0.558970i	−0.929014	+	0.370044i	$0.879342\pi$
$140$		0			0
$141$	−4.58410	−	7.03240i	−0.386051	−	0.592235i
$142$		0			0
$143$	−1.34729			−0.112666
$144$		0			0
$145$	−16.7233			−1.38879
$146$		0			0
$147$	0.945839	+	1.45100i	0.0780115	+	0.119676i
$148$		0			0
$149$	7.72246	+	7.72246i	0.632649	+	0.632649i	0.948732	−	0.316083i	$-0.102368\pi$
$149$	7.72246	+	7.72246i	0.632649	+	0.632649i	−0.316083	+	0.948732i	$0.602368\pi$
$150$		0			0
$151$	20.3662			1.65738			0.828690	−	0.559709i	$-0.189087\pi$
$151$	20.3662			1.65738			0.828690	+	0.559709i	$0.189087\pi$
$152$		0			0
$153$	3.82288	+	1.68633i	0.309062	+	0.136332i
$154$		0			0
$155$	−0.797315	+	0.797315i	−0.0640419	+	0.0640419i
$156$		0			0
$157$	10.2467	+	10.2467i	0.817779	+	0.817779i	0.985786	−	0.168007i	$-0.0537331\pi$
$157$	10.2467	+	10.2467i	0.817779	+	0.817779i	−0.168007	+	0.985786i	$0.553733\pi$
$158$		0			0
$159$	1.72881	−	8.20274i	0.137104	−	0.650520i
$160$		0			0
$161$			6.04660i			0.476539i
$162$		0			0
$163$	−1.79718	+	1.79718i	−0.140766	+	0.140766i	−0.773978	−	0.633212i	$-0.781736\pi$
$163$	−1.79718	+	1.79718i	−0.140766	+	0.140766i	0.633212	+	0.773978i	$0.281736\pi$
$164$		0			0
$165$	−1.42832	−	2.19116i	−0.111195	−	0.170582i
$166$		0			0
$167$			16.1405i			1.24899i	0.781028	+	0.624496i	$0.214696\pi$
$167$			16.1405i			1.24899i	−0.781028	+	0.624496i	$0.785304\pi$
$168$		0			0
$169$		−	8.42412i		−	0.648009i
$170$		0			0
$171$	−1.48035	−	3.81716i	−0.113205	−	0.291906i
$172$		0			0
$173$	−9.68789	+	9.68789i	−0.736557	+	0.736557i	−0.971910	−	0.235353i	$-0.924375\pi$
$173$	−9.68789	+	9.68789i	−0.736557	+	0.736557i	0.235353	+	0.971910i	$0.424375\pi$
$174$		0			0
$175$		−	0.748676i		−	0.0565946i
$176$		0			0
$177$	15.8668	+	3.34408i	1.19262	+	0.251357i
$178$		0			0
$179$	−5.28473	−	5.28473i	−0.394999	−	0.394999i	0.481466	−	0.876465i	$-0.340105\pi$
$179$	−5.28473	−	5.28473i	−0.394999	−	0.394999i	−0.876465	+	0.481466i	$0.840105\pi$
$180$		0			0
$181$	−11.8638	+	11.8638i	−0.881829	+	0.881829i	−0.993720	−	0.111892i	$-0.964309\pi$
$181$	−11.8638	+	11.8638i	−0.881829	+	0.881829i	0.111892	+	0.993720i	$0.464309\pi$
$182$		0			0
$183$	4.06356	−	19.2805i	0.300387	−	1.42526i
$184$		0			0
$185$	−5.00635			−0.368074
$186$		0			0
$187$	−0.620279	−	0.620279i	−0.0453593	−	0.0453593i
$188$		0			0
$189$	5.12792	−	0.839319i	0.373001	−	0.0610515i
$190$		0			0
$191$	−12.2503			−0.886404			−0.443202	−	0.896422i	$-0.646157\pi$
$191$	−12.2503			−0.886404			−0.443202	+	0.896422i	$0.646157\pi$
$192$		0			0
$193$	−10.1400			−0.729892			−0.364946	−	0.931029i	$-0.618913\pi$
$193$	−10.1400			−0.729892			−0.364946	+	0.931029i	$0.618913\pi$
$194$		0			0
$195$	−7.44196	+	4.85108i	−0.532930	+	0.347393i
$196$		0			0
$197$	−19.2804	−	19.2804i	−1.37367	−	1.37367i	−0.854931	−	0.518741i	$-0.826401\pi$
$197$	−19.2804	−	19.2804i	−1.37367	−	1.37367i	−0.518741	−	0.854931i	$-0.673599\pi$
$198$		0			0
$199$	−10.4170			−0.738438			−0.369219	−	0.929342i	$-0.620375\pi$
$199$	−10.4170			−0.738438			−0.369219	+	0.929342i	$0.620375\pi$
$200$		0			0
$201$	−10.5019	−	2.21339i	−0.740750	−	0.156121i
$202$		0			0
$203$	−4.93200	+	4.93200i	−0.346158	+	0.346158i
$204$		0			0
$205$	−14.1616	−	14.1616i	−0.989087	−	0.989087i
$206$		0			0
$207$	16.5968	+	7.32109i	1.15356	+	0.508851i
$208$		0			0
$209$			0.859544i			0.0594559i
$210$		0			0
$211$	−3.35351	+	3.35351i	−0.230865	+	0.230865i	−0.813054	−	0.582188i	$-0.802197\pi$
$211$	−3.35351	+	3.35351i	−0.230865	+	0.230865i	0.582188	+	0.813054i	$0.302197\pi$
$212$		0			0
$213$	17.9122	−	11.6762i	1.22733	−	0.800038i
$214$		0			0
$215$			30.4245i			2.07493i
$216$		0			0
$217$			0.470285i			0.0319250i
$218$		0			0
$219$	−20.3422	+	13.2602i	−1.37460	+	0.896039i
$220$		0			0
$221$	−2.10669	+	2.10669i	−0.141711	+	0.141711i
$222$		0			0
$223$		−	12.3063i		−	0.824088i	−0.911164	−	0.412044i	$-0.864815\pi$
$223$		−	12.3063i		−	0.824088i	0.911164	−	0.412044i	$-0.135185\pi$
$224$		0			0
$225$	−2.05498	−	0.906480i	−0.136998	−	0.0604320i
$226$		0			0
$227$	−5.20817	−	5.20817i	−0.345678	−	0.345678i	0.512819	−	0.858497i	$-0.328601\pi$
$227$	−5.20817	−	5.20817i	−0.345678	−	0.345678i	−0.858497	+	0.512819i	$0.828601\pi$
$228$		0			0
$229$	12.4704	−	12.4704i	0.824068	−	0.824068i	−0.162620	−	0.986689i	$-0.551995\pi$
$229$	12.4704	−	12.4704i	0.824068	−	0.824068i	0.986689	+	0.162620i	$0.0519946\pi$
$230$		0			0
$231$	−1.06745	−	0.224976i	−0.0702331	−	0.0148023i
$232$		0			0
$233$	2.99215			0.196022			0.0980110	−	0.995185i	$-0.468752\pi$
$233$	2.99215			0.196022			0.0980110	+	0.995185i	$0.468752\pi$
$234$		0			0
$235$	8.21687	+	8.21687i	0.536009	+	0.536009i
$236$		0			0
$237$	−24.0643	+	15.6865i	−1.56315	+	1.01894i
$238$		0			0
$239$	4.27730			0.276675			0.138338	−	0.990385i	$-0.455824\pi$
$239$	4.27730			0.276675			0.138338	+	0.990385i	$0.455824\pi$
$240$		0			0
$241$	−25.2132			−1.62413			−0.812063	−	0.583569i	$-0.801656\pi$
$241$	−25.2132			−1.62413			−0.812063	+	0.583569i	$0.801656\pi$
$242$		0			0
$243$	3.90500	−	15.0914i	0.250506	−	0.968115i
$244$		0			0
$245$	−1.69539	−	1.69539i	−0.108314	−	0.108314i
$246$		0			0
$247$	2.91932			0.185752
$248$		0			0
$249$	4.67101	−	22.1627i	0.296013	−	1.40450i
$250$		0			0
$251$	−11.5897	+	11.5897i	−0.731533	+	0.731533i	−0.970923	−	0.239391i	$-0.923052\pi$
$251$	−11.5897	+	11.5897i	−0.731533	+	0.731533i	0.239391	+	0.970923i	$0.423052\pi$
$252$		0			0
$253$	−2.69290	−	2.69290i	−0.169301	−	0.169301i
$254$		0			0
$255$	−5.65958	−	1.19281i	−0.354417	−	0.0746969i
$256$		0			0
$257$			18.3388i			1.14394i	0.820274	+	0.571970i	$0.193821\pi$
$257$			18.3388i			1.14394i	−0.820274	+	0.571970i	$0.806179\pi$
$258$		0			0
$259$	−1.47646	+	1.47646i	−0.0917428	+	0.0917428i
$260$		0			0
$261$	7.56587	+	19.5090i	0.468316	+	1.20758i
$262$		0			0
$263$		−	5.86015i		−	0.361352i	−0.983543	−	0.180676i	$-0.942171\pi$
$263$		−	5.86015i		−	0.361352i	0.983543	−	0.180676i	$-0.0578286\pi$
$264$		0			0
$265$			11.6043i			0.712848i
$266$		0			0
$267$	−4.96929	−	7.62330i	−0.304115	−	0.466539i
$268$		0			0
$269$	−1.15567	+	1.15567i	−0.0704624	+	0.0704624i	−0.741460	−	0.670997i	$-0.765866\pi$
$269$	−1.15567	+	1.15567i	−0.0704624	+	0.0704624i	0.670997	+	0.741460i	$0.265866\pi$
$270$		0			0
$271$		−	6.87631i		−	0.417706i	−0.977947	−	0.208853i	$-0.933027\pi$
$271$		−	6.87631i		−	0.417706i	0.977947	−	0.208853i	$-0.0669731\pi$
$272$		0			0
$273$	−0.764098	+	3.62544i	−0.0462453	+	0.219422i
$274$		0			0
$275$	0.333429	+	0.333429i	0.0201065	+	0.0201065i
$276$		0			0
$277$	2.82011	−	2.82011i	0.169444	−	0.169444i	−0.617291	−	0.786735i	$-0.711770\pi$
$277$	2.82011	−	2.82011i	0.169444	−	0.169444i	0.786735	+	0.617291i	$0.211770\pi$
$278$		0			0
$279$	1.29085	+	0.569411i	0.0772809	+	0.0340897i
$280$		0			0
$281$	25.8107			1.53974			0.769868	−	0.638203i	$-0.220322\pi$
$281$	25.8107			1.53974			0.769868	+	0.638203i	$0.220322\pi$
$282$		0			0
$283$	−8.51014	−	8.51014i	−0.505875	−	0.505875i	0.407383	−	0.913258i	$-0.366442\pi$
$283$	−8.51014	−	8.51014i	−0.505875	−	0.505875i	−0.913258	+	0.407383i	$0.866442\pi$
$284$		0			0
$285$	3.09489	+	4.74781i	0.183325	+	0.281236i
$286$		0			0
$287$	−8.35300			−0.493062
$288$		0			0
$289$	15.0602			0.885895
$290$		0			0
$291$	4.89623	+	7.51122i	0.287022	+	0.440316i
$292$		0			0
$293$	−8.85088	−	8.85088i	−0.517074	−	0.517074i	0.399611	−	0.916685i	$-0.369145\pi$
$293$	−8.85088	−	8.85088i	−0.517074	−	0.517074i	−0.916685	+	0.399611i	$0.869145\pi$
$294$		0			0
$295$	−22.4465			−1.30689
$296$		0			0
$297$	−1.90996	+	2.65756i	−0.110827	+	0.154207i
$298$		0			0
$299$	−9.14605	+	9.14605i	−0.528930	+	0.528930i
$300$		0			0
$301$	8.97272	+	8.97272i	0.517179	+	0.517179i
$302$		0			0
$303$	−1.21899	+	5.78380i	−0.0700293	+	0.332270i
$304$		0			0
$305$			27.2759i			1.56181i
$306$		0			0
$307$	14.6474	−	14.6474i	0.835971	−	0.835971i	−0.152355	−	0.988326i	$-0.548686\pi$
$307$	14.6474	−	14.6474i	0.835971	−	0.835971i	0.988326	+	0.152355i	$0.0486857\pi$
$308$		0			0
$309$	5.45984	+	8.37586i	0.310600	+	0.476486i
$310$		0			0
$311$			18.9809i			1.07631i	0.842846	+	0.538155i	$0.180879\pi$
$311$			18.9809i			1.07631i	−0.842846	+	0.538155i	$0.819121\pi$
$312$		0			0
$313$			1.41725i			0.0801077i	0.999198	+	0.0400539i	$0.0127529\pi$
$313$			1.41725i			0.0801077i	−0.999198	+	0.0400539i	$0.987247\pi$
$314$		0			0
$315$	−6.70626	+	2.60079i	−0.377855	+	0.146538i
$316$		0			0
$317$	−7.89489	+	7.89489i	−0.443421	+	0.443421i	−0.893160	−	0.449739i	$-0.851517\pi$
$317$	−7.89489	+	7.89489i	−0.443421	+	0.443421i	0.449739	+	0.893160i	$0.351517\pi$
$318$		0			0
$319$		−	4.39301i		−	0.245961i
$320$		0			0
$321$	27.0706	+	5.70541i	1.51093	+	0.318445i
$322$		0			0
$323$	1.34402	+	1.34402i	0.0747833	+	0.0747833i
$324$		0			0
$325$	1.13244	−	1.13244i	0.0628166	−	0.0628166i
$326$		0			0
$327$	3.93153	−	18.6540i	0.217414	−	1.03157i
$328$		0			0
$329$	4.84660			0.267202
$330$		0			0
$331$	−12.2512	−	12.2512i	−0.673384	−	0.673384i	0.285111	−	0.958495i	$-0.407970\pi$
$331$	−12.2512	−	12.2512i	−0.673384	−	0.673384i	−0.958495	+	0.285111i	$0.907970\pi$
$332$		0			0
$333$	2.26495	+	5.84028i	0.124118	+	0.320045i
$334$		0			0
$335$	14.8570			0.811723
$336$		0			0
$337$	21.2205			1.15596			0.577978	−	0.816052i	$-0.303842\pi$
$337$	21.2205			1.15596			0.577978	+	0.816052i	$0.303842\pi$
$338$		0			0
$339$	1.63534	−	1.06601i	0.0888197	−	0.0578976i
$340$		0			0
$341$	−0.209445	−	0.209445i	−0.0113421	−	0.0113421i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−24.5707	−	5.17853i	−1.32284	−	0.278803i
$346$		0			0
$347$	5.77536	−	5.77536i	0.310038	−	0.310038i	−0.534886	−	0.844924i	$-0.679646\pi$
$347$	5.77536	−	5.77536i	0.310038	−	0.310038i	0.844924	+	0.534886i	$0.179646\pi$
$348$		0			0
$349$	23.8646	+	23.8646i	1.27744	+	1.27744i	0.942093	+	0.335352i	$0.108855\pi$
$349$	23.8646	+	23.8646i	1.27744	+	1.27744i	0.335352	+	0.942093i	$0.391145\pi$
$350$		0			0
$351$	9.02601	+	6.48691i	0.481773	+	0.346246i
$352$		0			0
$353$			0.589919i			0.0313982i	0.999877	+	0.0156991i	$0.00499739\pi$
$353$			0.589919i			0.0313982i	−0.999877	+	0.0156991i	$0.995003\pi$
$354$		0			0
$355$	−20.9292	+	20.9292i	−1.11081	+	1.11081i
$356$		0			0
$357$	−2.02089	+	1.31733i	−0.106957	+	0.0697205i
$358$		0			0
$359$			4.56354i			0.240855i	0.992722	+	0.120427i	$0.0384265\pi$
$359$			4.56354i			0.240855i	−0.992722	+	0.120427i	$0.961574\pi$
$360$		0			0
$361$			17.1375i			0.901976i
$362$		0			0
$363$	−15.3854	+	10.0290i	−0.807522	+	0.526387i
$364$		0			0
$365$	23.7684	−	23.7684i	1.24410	−	1.24410i
$366$		0			0
$367$		−	19.3900i		−	1.01215i	−0.862489	−	0.506076i	$-0.831096\pi$
$367$		−	19.3900i		−	1.01215i	0.862489	−	0.506076i	$-0.168904\pi$
$368$		0			0
$369$	−10.1136	+	22.9274i	−0.526495	+	1.19356i
$370$		0			0
$371$	3.42232	+	3.42232i	0.177678	+	0.177678i
$372$		0			0
$373$	−19.5876	+	19.5876i	−1.01421	+	1.01421i	−0.0143107	+	0.999898i	$0.504555\pi$
$373$	−19.5876	+	19.5876i	−1.01421	+	1.01421i	−0.999898	+	0.0143107i	$0.995445\pi$
$374$		0			0
$375$	−17.2755	−	3.64099i	−0.892104	−	0.188020i
$376$		0			0
$377$	−14.9202			−0.768431
$378$		0			0
$379$	21.9568	+	21.9568i	1.12785	+	1.12785i	0.990527	+	0.137320i	$0.0438487\pi$
$379$	21.9568	+	21.9568i	1.12785	+	1.12785i	0.137320	+	0.990527i	$0.456151\pi$
$380$		0			0
$381$	3.19870	−	2.08509i	0.163875	−	0.106822i
$382$		0			0
$383$	−33.3358			−1.70338			−0.851690	−	0.524046i	$-0.824422\pi$
$383$	−33.3358			−1.70338			−0.851690	+	0.524046i	$0.824422\pi$
$384$		0			0
$385$	1.51011			0.0769623
$386$		0			0
$387$	35.4924	−	13.7645i	1.80418	−	0.699688i
$388$		0			0
$389$	−8.17897	−	8.17897i	−0.414690	−	0.414690i	0.468679	−	0.883369i	$-0.344730\pi$
$389$	−8.17897	−	8.17897i	−0.414690	−	0.414690i	−0.883369	+	0.468679i	$0.844730\pi$
$390$		0			0
$391$	−8.42148			−0.425893
$392$		0			0
$393$	−5.33209	+	25.2994i	−0.268969	+	1.27618i
$394$		0			0
$395$	28.1175	−	28.1175i	1.41474	−	1.41474i
$396$		0			0
$397$	10.0314	+	10.0314i	0.503462	+	0.503462i	0.912512	−	0.409050i	$-0.134140\pi$
$397$	10.0314	+	10.0314i	0.503462	+	0.503462i	−0.409050	+	0.912512i	$0.634140\pi$
$398$		0			0
$399$	2.31295	+	0.487478i	0.115792	+	0.0244044i
$400$		0			0
$401$		−	15.4592i		−	0.771993i	−0.922500	−	0.385997i	$-0.873858\pi$
$401$		−	15.4592i		−	0.771993i	0.922500	−	0.385997i	$-0.126142\pi$
$402$		0			0
$403$	−0.711350	+	0.711350i	−0.0354349	+	0.0354349i
$404$		0			0
$405$	−0.981113	+	21.5564i	−0.0487519	+	1.07115i
$406$		0			0
$407$		−	1.31511i		−	0.0651875i
$408$		0			0
$409$		−	12.5042i		−	0.618292i	−0.951015	−	0.309146i	$-0.899957\pi$
$409$		−	12.5042i		−	0.618292i	0.951015	−	0.309146i	$-0.100043\pi$
$410$		0			0
$411$	10.7998	+	16.5679i	0.532717	+	0.817232i
$412$		0			0
$413$	−6.61989	+	6.61989i	−0.325743	+	0.325743i
$414$		0			0
$415$			31.3533i			1.53907i
$416$		0			0
$417$	3.32906	−	15.7955i	0.163025	−	0.773510i
$418$		0			0
$419$	19.2109	+	19.2109i	0.938516	+	0.938516i	0.998216	−	0.0597005i	$-0.0190146\pi$
$419$	19.2109	+	19.2109i	0.938516	+	0.938516i	−0.0597005	+	0.998216i	$0.519015\pi$
$420$		0			0
$421$	0.650536	−	0.650536i	0.0317052	−	0.0317052i	−0.691076	−	0.722782i	$-0.742863\pi$
$421$	0.650536	−	0.650536i	0.0317052	−	0.0317052i	0.722782	+	0.691076i	$0.242863\pi$
$422$		0			0
$423$	5.86816	−	13.3030i	0.285320	−	0.646815i
$424$		0			0
$425$	1.04273			0.0505797
$426$		0			0
$427$	8.04415	+	8.04415i	0.389284	+	0.389284i
$428$		0			0
$429$	−1.27432	−	1.95492i	−0.0615248	−	0.0943843i
$430$		0			0
$431$	9.29584			0.447765			0.223882	−	0.974616i	$-0.428127\pi$
$431$	9.29584			0.447765			0.223882	+	0.974616i	$0.428127\pi$
$432$		0			0
$433$	13.5879			0.652991			0.326495	−	0.945199i	$-0.394132\pi$
$433$	13.5879			0.652991			0.326495	+	0.945199i	$0.394132\pi$
$434$		0			0
$435$	−15.8175	−	24.2654i	−0.758393	−	1.16344i
$436$		0			0
$437$	5.83499	+	5.83499i	0.279125	+	0.279125i
$438$		0			0
$439$	0.193033			0.00921297			0.00460649	−	0.999989i	$-0.498534\pi$
$439$	0.193033			0.00921297			0.00460649	+	0.999989i	$0.498534\pi$
$440$		0			0
$441$	−1.21078	+	2.74482i	−0.0576561	+	0.130706i
$442$		0			0
$443$	−5.02164	+	5.02164i	−0.238585	+	0.238585i	−0.816264	−	0.577679i	$-0.803959\pi$
$443$	−5.02164	+	5.02164i	−0.238585	+	0.238585i	0.577679	+	0.816264i	$0.303959\pi$
$444$		0			0
$445$	8.90730	+	8.90730i	0.422246	+	0.422246i
$446$		0			0
$447$	−3.90106	+	18.5095i	−0.184514	+	0.875467i
$448$		0			0
$449$		−	36.2149i		−	1.70909i	−0.519379	−	0.854544i	$-0.673837\pi$
$449$		−	36.2149i		−	1.70909i	0.519379	−	0.854544i	$-0.326163\pi$
$450$		0			0
$451$	3.72008	−	3.72008i	0.175172	−	0.175172i
$452$		0			0
$453$	19.2632	+	29.5513i	0.905062	+	1.38844i
$454$		0			0
$455$		−	5.12887i		−	0.240445i
$456$		0			0
$457$		−	28.6790i		−	1.34155i	−0.741663	−	0.670773i	$-0.765963\pi$
$457$		−	28.6790i		−	1.34155i	0.741663	−	0.670773i	$-0.234037\pi$
$458$		0			0
$459$	1.16897	+	7.14198i	0.0545630	+	0.333359i
$460$		0			0
$461$	11.2373	−	11.2373i	0.523375	−	0.523375i	−0.395214	−	0.918589i	$-0.629329\pi$
$461$	11.2373	−	11.2373i	0.523375	−	0.523375i	0.918589	+	0.395214i	$0.129329\pi$
$462$		0			0
$463$			8.11410i			0.377094i	0.982064	+	0.188547i	$0.0603778\pi$
$463$			8.11410i			0.377094i	−0.982064	+	0.188547i	$0.939622\pi$
$464$		0			0
$465$	−1.91103	−	0.402769i	−0.0886220	−	0.0186780i
$466$		0			0
$467$	11.8202	+	11.8202i	0.546973	+	0.546973i	0.925564	−	0.378591i	$-0.123591\pi$
$467$	11.8202	+	11.8202i	0.546973	+	0.546973i	−0.378591	+	0.925564i	$0.623591\pi$
$468$		0			0
$469$	4.38159	−	4.38159i	0.202323	−	0.202323i
$470$		0			0
$471$	−5.17621	+	24.5597i	−0.238507	+	1.13165i
$472$		0			0
$473$	−7.99215			−0.367479
$474$		0			0
$475$	−0.722474	−	0.722474i	−0.0331494	−	0.0331494i
$476$		0			0
$477$	13.5373	−	5.24997i	0.619831	−	0.240380i
$478$		0			0
$479$	−28.2089			−1.28890			−0.644449	−	0.764647i	$-0.722913\pi$
$479$	−28.2089			−1.28890			−0.644449	+	0.764647i	$0.722913\pi$
$480$		0			0
$481$	−4.46657			−0.203658
$482$		0			0
$483$	−8.77359	+	5.71911i	−0.399212	+	0.260228i
$484$		0			0
$485$	−8.77634	−	8.77634i	−0.398513	−	0.398513i
$486$		0			0
$487$	−1.26539			−0.0573402			−0.0286701	−	0.999589i	$-0.509127\pi$
$487$	−1.26539			−0.0573402			−0.0286701	+	0.999589i	$0.509127\pi$
$488$		0			0
$489$	−4.30753	−	0.907856i	−0.194793	−	0.0410547i
$490$		0			0
$491$	21.3825	−	21.3825i	0.964980	−	0.964980i	−0.0344277	−	0.999407i	$-0.510961\pi$
$491$	21.3825	−	21.3825i	0.964980	−	0.964980i	0.999407	+	0.0344277i	$0.0109608\pi$
$492$		0			0
$493$	−6.86911	−	6.86911i	−0.309369	−	0.309369i
$494$		0			0
$495$	1.82841	−	4.14497i	0.0821808	−	0.186303i
$496$		0			0
$497$			12.3448i			0.553739i
$498$		0			0
$499$	9.37843	−	9.37843i	0.419836	−	0.419836i	−0.465311	−	0.885147i	$-0.654057\pi$
$499$	9.37843	−	9.37843i	0.419836	−	0.419836i	0.885147	+	0.465311i	$0.154057\pi$
$500$		0			0
$501$	−23.4199	+	15.2664i	−1.04632	+	0.682050i
$502$		0			0
$503$			19.7856i			0.882195i	0.897459	+	0.441098i	$0.145411\pi$
$503$			19.7856i			0.882195i	−0.897459	+	0.441098i	$0.854589\pi$
$504$		0			0
$505$		−	8.18227i		−	0.364106i
$506$		0			0
$507$	12.2234	−	7.96786i	0.542858	−	0.353865i
$508$		0			0
$509$	12.5552	−	12.5552i	0.556501	−	0.556501i	−0.371809	−	0.928309i	$-0.621262\pi$
$509$	12.5552	−	12.5552i	0.556501	−	0.556501i	0.928309	+	0.371809i	$0.121262\pi$
$510$		0			0
$511$		−	14.0195i		−	0.620185i
$512$		0			0
$513$	4.13851	−	5.75840i	0.182720	−	0.254240i
$514$		0			0
$515$	−9.78660	−	9.78660i	−0.431249	−	0.431249i
$516$		0			0
$517$	−2.15847	+	2.15847i	−0.0949296	+	0.0949296i
$518$		0			0
$519$	−23.2203	−	4.89391i	−1.01926	−	0.214819i
$520$		0			0
$521$	−7.36126			−0.322503			−0.161251	−	0.986913i	$-0.551553\pi$
$521$	−7.36126			−0.322503			−0.161251	+	0.986913i	$0.551553\pi$
$522$		0			0
$523$	19.9496	+	19.9496i	0.872334	+	0.872334i	0.992726	−	0.120392i	$-0.0384152\pi$
$523$	19.9496	+	19.9496i	0.872334	+	0.872334i	−0.120392	+	0.992726i	$0.538415\pi$
$524$		0			0
$525$	1.08633	−	0.708126i	0.0474111	−	0.0309052i
$526$		0			0
$527$	−0.654996			−0.0285321
$528$		0			0
$529$	−13.5614			−0.589625
$530$		0			0
$531$	10.1552	+	26.1856i	0.440696	+	1.13636i
$532$		0			0
$533$	−12.6347	−	12.6347i	−0.547270	−	0.547270i
$534$		0			0
$535$	−38.2965			−1.65570
$536$		0			0
$537$	2.66962	−	12.6666i	0.115203	−	0.546605i
$538$		0			0
$539$	0.445358	−	0.445358i	0.0191829	−	0.0191829i
$540$		0			0
$541$	−19.1432	−	19.1432i	−0.823032	−	0.823032i	0.163509	−	0.986542i	$-0.447719\pi$
$541$	−19.1432	−	19.1432i	−0.823032	−	0.823032i	−0.986542	+	0.163509i	$0.947719\pi$
$542$		0			0
$543$	−28.4355	−	5.99308i	−1.22029	−	0.257188i
$544$		0			0
$545$			26.3896i			1.13041i
$546$		0			0
$547$	23.1275	−	23.1275i	0.988862	−	0.988862i	−0.0110764	−	0.999939i	$-0.503526\pi$
$547$	23.1275	−	23.1275i	0.988862	−	0.988862i	0.999939	+	0.0110764i	$0.00352580\pi$
$548$		0			0
$549$	31.8194	−	12.3400i	1.35802	−	0.526660i
$550$		0			0
$551$			9.51878i			0.405514i
$552$		0			0
$553$		−	16.5847i		−	0.705253i
$554$		0			0
$555$	−4.73520	−	7.26419i	−0.200998	−	0.308348i
$556$		0			0
$557$	7.81224	−	7.81224i	0.331015	−	0.331015i	−0.521957	−	0.852972i	$-0.674798\pi$
$557$	7.81224	−	7.81224i	0.331015	−	0.331015i	0.852972	+	0.521957i	$0.174798\pi$
$558$		0			0
$559$			27.1442i			1.14808i
$560$		0			0
$561$	0.313338	−	1.48671i	0.0132292	−	0.0627688i
$562$		0			0
$563$	−5.29314	−	5.29314i	−0.223079	−	0.223079i	0.586715	−	0.809794i	$-0.300421\pi$
$563$	−5.29314	−	5.29314i	−0.223079	−	0.223079i	−0.809794	+	0.586715i	$0.800421\pi$
$564$		0			0
$565$	−1.91079	+	1.91079i	−0.0803873	+	0.0803873i
$566$		0			0
$567$	6.06803	+	6.64673i	0.254833	+	0.279136i
$568$		0			0
$569$	−10.7397			−0.450231			−0.225115	−	0.974332i	$-0.572276\pi$
$569$	−10.7397			−0.450231			−0.225115	+	0.974332i	$0.572276\pi$
$570$		0			0
$571$	9.64927	+	9.64927i	0.403809	+	0.403809i	0.879573	−	0.475764i	$-0.157828\pi$
$571$	9.64927	+	9.64927i	0.403809	+	0.403809i	−0.475764	+	0.879573i	$0.657828\pi$
$572$		0			0
$573$	−11.5868	−	17.7752i	−0.484048	−	0.742569i
$574$		0			0
$575$	4.52694			0.188787
$576$		0			0
$577$	−38.6282			−1.60811			−0.804056	−	0.594554i	$-0.797329\pi$
$577$	−38.6282			−1.60811			−0.804056	+	0.594554i	$0.797329\pi$
$578$		0			0
$579$	−9.59079	−	14.7131i	−0.398580	−	0.611455i
$580$		0			0
$581$	9.24664	+	9.24664i	0.383615	+	0.383615i
$582$		0			0
$583$	−3.04832			−0.126249
$584$		0			0
$585$	−14.0778	−	6.20992i	−0.582045	−	0.256749i
$586$		0			0
$587$	9.36336	−	9.36336i	0.386467	−	0.386467i	−0.486958	−	0.873425i	$-0.661894\pi$
$587$	9.36336	−	9.36336i	0.386467	−	0.386467i	0.873425	+	0.486958i	$0.161894\pi$
$588$		0			0
$589$	0.453826	+	0.453826i	0.0186996	+	0.0186996i
$590$		0			0
$591$	9.73964	−	46.2120i	0.400635	−	1.90091i
$592$		0			0
$593$		−	29.8401i		−	1.22539i	−0.790320	−	0.612694i	$-0.790086\pi$
$593$		−	29.8401i		−	1.22539i	0.790320	−	0.612694i	$-0.209914\pi$
$594$		0			0
$595$	2.36127	−	2.36127i	0.0968028	−	0.0968028i
$596$		0			0
$597$	−9.85276	−	15.1150i	−0.403246	−	0.618614i
$598$		0			0
$599$		−	8.61900i		−	0.352163i	−0.984376	−	0.176081i	$-0.943658\pi$
$599$		−	8.61900i		−	0.352163i	0.984376	−	0.176081i	$-0.0563422\pi$
$600$		0			0
$601$		−	37.6975i		−	1.53771i	−0.639421	−	0.768857i	$-0.720826\pi$
$601$		−	37.6975i		−	1.53771i	0.639421	−	0.768857i	$-0.279174\pi$
$602$		0			0
$603$	−6.72152	−	17.3318i	−0.273722	−	0.705805i
$604$		0			0
$605$	17.9767	−	17.9767i	0.730858	−	0.730858i
$606$		0			0
$607$			9.27459i			0.376444i	0.982127	+	0.188222i	$0.0602724\pi$
$607$			9.27459i			0.376444i	−0.982127	+	0.188222i	$0.939728\pi$
$608$		0			0
$609$	−11.8212	−	2.49143i	−0.479018	−	0.100958i
$610$		0			0
$611$	7.33094	+	7.33094i	0.296578	+	0.296578i
$612$		0			0
$613$	23.9007	−	23.9007i	0.965339	−	0.965339i	−0.0340804	−	0.999419i	$-0.510850\pi$
$613$	23.9007	−	23.9007i	0.965339	−	0.965339i	0.999419	+	0.0340804i	$0.0108502\pi$
$614$		0			0
$615$	7.15382	−	33.9429i	0.288470	−	1.36871i
$616$		0			0
$617$	17.9544			0.722817			0.361409	−	0.932408i	$-0.382296\pi$
$617$	17.9544			0.722817			0.361409	+	0.932408i	$0.382296\pi$
$618$		0			0
$619$	14.4355	+	14.4355i	0.580214	+	0.580214i	0.934962	−	0.354748i	$-0.115433\pi$
$619$	14.4355	+	14.4355i	0.580214	+	0.580214i	−0.354748	+	0.934962i	$0.615433\pi$
$620$		0			0
$621$	5.07503	+	31.0065i	0.203654	+	1.24425i
$622$		0			0
$623$	5.25384			0.210491
$624$		0			0
$625$	28.1829			1.12731
$626$		0			0
$627$	−1.24719	+	0.812990i	−0.0498082	+	0.0324677i
$628$		0			0
$629$	−2.05636	−	2.05636i	−0.0819925	−	0.0819925i
$630$		0			0
$631$	12.7763			0.508616			0.254308	−	0.967123i	$-0.418152\pi$
$631$	12.7763			0.508616			0.254308	+	0.967123i	$0.418152\pi$
$632$		0			0
$633$	−8.03782	−	1.69405i	−0.319475	−	0.0673325i
$634$		0			0
$635$	−3.73746	+	3.73746i	−0.148317	+	0.148317i
$636$		0			0
$637$	−1.51259	−	1.51259i	−0.0599312	−	0.0599312i
$638$		0			0
$639$	33.8842	+	14.9468i	1.34044	+	0.591286i
$640$		0			0
$641$			1.57497i			0.0622075i	0.999516	+	0.0311038i	$0.00990224\pi$
$641$			1.57497i			0.0622075i	−0.999516	+	0.0311038i	$0.990098\pi$
$642$		0			0
$643$	32.8549	−	32.8549i	1.29567	−	1.29567i	0.364444	−	0.931225i	$-0.381259\pi$
$643$	32.8549	−	32.8549i	1.29567	−	1.29567i	0.931225	−	0.364444i	$-0.118741\pi$
$644$		0			0
$645$	−44.1458	+	28.7766i	−1.73824	+	1.13308i
$646$		0			0
$647$		−	28.8641i		−	1.13477i	−0.823454	−	0.567383i	$-0.807956\pi$
$647$		−	28.8641i		−	1.13477i	0.823454	−	0.567383i	$-0.192044\pi$
$648$		0			0
$649$		−	5.89644i		−	0.231456i
$650$		0			0
$651$	−0.682381	+	0.444814i	−0.0267446	+	0.0174336i
$652$		0			0
$653$	−11.3854	+	11.3854i	−0.445546	+	0.445546i	−0.893871	−	0.448325i	$-0.852021\pi$
$653$	−11.3854	+	11.3854i	−0.445546	+	0.445546i	0.448325	+	0.893871i	$0.352021\pi$
$654$		0			0
$655$		−	35.7907i		−	1.39846i
$656$		0			0
$657$	−38.4809	−	16.9745i	−1.50128	−	0.662237i
$658$		0			0
$659$	−6.17983	−	6.17983i	−0.240732	−	0.240732i	0.576421	−	0.817153i	$-0.304449\pi$
$659$	−6.17983	−	6.17983i	−0.240732	−	0.240732i	−0.817153	+	0.576421i	$0.804449\pi$
$660$		0			0
$661$	−15.1242	+	15.1242i	−0.588263	+	0.588263i	−0.937161	−	0.348898i	$-0.886556\pi$
$661$	−15.1242	+	15.1242i	−0.588263	+	0.588263i	0.348898	+	0.937161i	$0.386556\pi$
$662$		0			0
$663$	−5.04938	−	1.06421i	−0.196102	−	0.0413304i
$664$		0			0
$665$	−3.27211			−0.126887
$666$		0			0
$667$	−29.8218	−	29.8218i	−1.15471	−	1.15471i
$668$		0			0
$669$	17.8563	−	11.6397i	0.690366	−	0.450018i
$670$		0			0
$671$	−7.16506			−0.276604
$672$		0			0
$673$	−10.6946			−0.412248			−0.206124	−	0.978526i	$-0.566085\pi$
$673$	−10.6946			−0.412248			−0.206124	+	0.978526i	$0.566085\pi$
$674$		0			0
$675$	−0.628378	−	3.83915i	−0.0241863	−	0.147769i
$676$		0			0
$677$	−8.78670	−	8.78670i	−0.337700	−	0.337700i	0.517801	−	0.855501i	$-0.326751\pi$
$677$	−8.78670	−	8.78670i	−0.337700	−	0.337700i	−0.855501	+	0.517801i	$0.826751\pi$
$678$		0			0
$679$	−5.17660			−0.198660
$680$		0			0
$681$	2.63095	−	12.4831i	0.100818	−	0.478354i
$682$		0			0
$683$	12.9374	−	12.9374i	0.495037	−	0.495037i	−0.414852	−	0.909889i	$-0.636167\pi$
$683$	12.9374	−	12.9374i	0.495037	−	0.495037i	0.909889	+	0.414852i	$0.136167\pi$
$684$		0			0
$685$	−19.3584	−	19.3584i	−0.739646	−	0.739646i
$686$		0			0
$687$	29.8895	+	6.29952i	1.14036	+	0.240342i
$688$		0			0
$689$			10.3532i			0.394424i
$690$		0			0
$691$	−10.0400	+	10.0400i	−0.381940	+	0.381940i	−0.871801	−	0.489861i	$-0.837048\pi$
$691$	−10.0400	+	10.0400i	−0.381940	+	0.381940i	0.489861	+	0.871801i	$0.337048\pi$
$692$		0			0
$693$	−0.683197	−	1.76166i	−0.0259525	−	0.0669198i
$694$		0			0
$695$			22.3457i			0.847622i
$696$		0			0
$697$		−	11.6338i		−	0.440660i
$698$		0			0
$699$	2.83009	+	4.34159i	0.107044	+	0.164214i
$700$		0			0
$701$	−25.2156	+	25.2156i	−0.952381	+	0.952381i	−0.998917	−	0.0465357i	$-0.985182\pi$
$701$	−25.2156	+	25.2156i	−0.952381	+	0.952381i	0.0465357	+	0.998917i	$0.485182\pi$
$702$		0			0
$703$			2.84958i			0.107474i
$704$		0			0
$705$	−4.15081	+	19.6945i	−0.156328	+	0.741737i
$706$		0			0
$707$	−2.41310	−	2.41310i	−0.0907539	−	0.0907539i
$708$		0			0
$709$	−18.4484	+	18.4484i	−0.692844	+	0.692844i	−0.962857	−	0.270013i	$-0.912972\pi$
$709$	−18.4484	+	18.4484i	−0.692844	+	0.692844i	0.270013	+	0.962857i	$0.412972\pi$
$710$		0			0
$711$	−45.5220	−	20.0804i	−1.70721	−	0.753074i
$712$		0			0
$713$	−2.84362			−0.106495
$714$		0			0
$715$	2.28418	+	2.28418i	0.0854236	+	0.0854236i
$716$		0			0
$717$	4.04563	+	6.20634i	0.151087	+	0.231780i
$718$		0			0
$719$	30.2998			1.12999			0.564996	−	0.825094i	$-0.308878\pi$
$719$	30.2998			1.12999			0.564996	+	0.825094i	$0.308878\pi$
$720$		0			0
$721$	−5.77249			−0.214979
$722$		0			0
$723$	−23.8476	−	36.5843i	−0.886904	−	1.36058i
$724$		0			0
$725$	3.69247	+	3.69247i	0.137135	+	0.137135i
$726$		0			0
$727$	14.0577			0.521373			0.260686	−	0.965424i	$-0.416051\pi$
$727$	14.0577			0.521373			0.260686	+	0.965424i	$0.416051\pi$
$728$		0			0
$729$	25.5911	−	8.60792i	0.947818	−	0.318812i
$730$		0			0
$731$	−12.4969	+	12.4969i	−0.462214	+	0.462214i
$732$		0			0
$733$	32.7566	+	32.7566i	1.20989	+	1.20989i	0.971061	+	0.238831i	$0.0767642\pi$
$733$	32.7566	+	32.7566i	1.20989	+	1.20989i	0.238831	+	0.971061i	$0.423236\pi$
$734$		0			0
$735$	0.856437	−	4.06356i	0.0315902	−	0.149887i
$736$		0			0
$737$			3.90275i			0.143760i
$738$		0			0
$739$	1.60188	−	1.60188i	0.0589260	−	0.0589260i	−0.677030	−	0.735956i	$-0.736733\pi$
$739$	1.60188	−	1.60188i	0.0589260	−	0.0589260i	0.735956	+	0.677030i	$0.236733\pi$
$740$		0			0
$741$	2.76120	+	4.23592i	0.101435	+	0.155610i
$742$		0			0
$743$		−	31.9687i		−	1.17282i	−0.810015	−	0.586409i	$-0.800541\pi$
$743$		−	31.9687i		−	1.17282i	0.810015	−	0.586409i	$-0.199459\pi$
$744$		0			0
$745$		−	26.1851i		−	0.959349i
$746$		0			0
$747$	36.5760	−	14.1847i	1.33824	−	0.518991i
$748$		0			0
$749$	−11.2943	+	11.2943i	−0.412686	+	0.412686i
$750$		0			0
$751$			15.0201i			0.548093i	0.961716	+	0.274046i	$0.0883622\pi$
$751$			15.0201i			0.548093i	−0.961716	+	0.274046i	$0.911638\pi$
$752$		0			0
$753$	−27.7785	−	5.85460i	−1.01230	−	0.213353i
$754$		0			0
$755$	−34.5286	−	34.5286i	−1.25663	−	1.25663i
$756$		0			0
$757$	5.17499	−	5.17499i	0.188088	−	0.188088i	−0.606781	−	0.794869i	$-0.707539\pi$
$757$	5.17499	−	5.17499i	0.188088	−	0.188088i	0.794869	+	0.606781i	$0.207539\pi$
$758$		0			0
$759$	1.36034	−	6.45445i	0.0493772	−	0.234282i
$760$		0			0
$761$	11.6404			0.421966			0.210983	−	0.977490i	$-0.432334\pi$
$761$	11.6404			0.421966			0.210983	+	0.977490i	$0.432334\pi$
$762$		0			0
$763$	7.78278	+	7.78278i	0.281755	+	0.281755i
$764$		0			0
$765$	−3.62228	−	9.34024i	−0.130964	−	0.337697i
$766$		0			0
$767$	−20.0264			−0.723112
$768$		0			0
$769$	40.3055			1.45345			0.726726	−	0.686927i	$-0.241041\pi$
$769$	40.3055			1.45345			0.726726	+	0.686927i	$0.241041\pi$
$770$		0			0
$771$	−26.6095	+	17.3455i	−0.958317	+	0.624683i
$772$		0			0
$773$	−17.0980	−	17.0980i	−0.614971	−	0.614971i	0.329266	−	0.944237i	$-0.393199\pi$
$773$	−17.0980	−	17.0980i	−0.614971	−	0.614971i	−0.944237	+	0.329266i	$0.893199\pi$
$774$		0			0
$775$	0.352091			0.0126475
$776$		0			0
$777$	−3.53883	−	0.745845i	−0.126955	−	0.0267570i
$778$		0			0
$779$	−8.06067	+	8.06067i	−0.288803	+	0.288803i
$780$		0			0
$781$	−5.49785	−	5.49785i	−0.196729	−	0.196729i
$782$		0			0
$783$	−21.1514	+	29.4304i	−0.755888	+	1.05176i
$784$		0			0
$785$		−	34.7444i		−	1.24008i
$786$		0			0
$787$	−26.8062	+	26.8062i	−0.955536	+	0.955536i	−0.999053	−	0.0435165i	$-0.986144\pi$
$787$	−26.8062	+	26.8062i	−0.955536	+	0.955536i	0.0435165	+	0.999053i	$0.486144\pi$
$788$		0			0
$789$	8.50305	−	5.54276i	0.302717	−	0.197327i
$790$		0			0
$791$			1.12705i			0.0400733i
$792$		0			0
$793$			24.3351i			0.864164i
$794$		0			0
$795$	−16.8378	+	10.9758i	−0.597176	+	0.389272i
$796$		0			0
$797$	30.6309	−	30.6309i	1.08500	−	1.08500i	0.0889663	−	0.996035i	$-0.471644\pi$
$797$	30.6309	−	30.6309i	1.08500	−	1.08500i	0.996035	−	0.0889663i	$-0.0283563\pi$
$798$		0			0
$799$			6.75017i			0.238804i
$800$		0			0
$801$	6.36124	−	14.4208i	0.224763	−	0.509535i
$802$		0			0
$803$	6.24369	+	6.24369i	0.220335	+	0.220335i
$804$		0			0
$805$	10.2513	−	10.2513i	0.361312	−	0.361312i
$806$		0			0
$807$	−2.76995	−	0.583795i	−0.0975068	−	0.0205506i
$808$		0			0
$809$	5.88033			0.206742			0.103371	−	0.994643i	$-0.467037\pi$
$809$	5.88033			0.206742			0.103371	+	0.994643i	$0.467037\pi$
$810$		0			0
$811$	18.5431	+	18.5431i	0.651137	+	0.651137i	0.953267	−	0.302130i	$-0.0976977\pi$
$811$	18.5431	+	18.5431i	0.651137	+	0.651137i	−0.302130	+	0.953267i	$0.597698\pi$
$812$		0			0
$813$	9.97750	−	6.50388i	0.349926	−	0.228101i
$814$		0			0
$815$	6.09382			0.213457
$816$		0			0
$817$	17.3174			0.605859
$818$		0			0
$819$	−5.98321	+	2.32038i	−0.209070	+	0.0810805i
$820$		0			0
$821$	17.7928	+	17.7928i	0.620972	+	0.620972i	0.945780	−	0.324808i	$-0.105300\pi$
$821$	17.7928	+	17.7928i	0.620972	+	0.620972i	−0.324808	+	0.945780i	$0.605300\pi$
$822$		0			0
$823$	3.21292			0.111995			0.0559977	−	0.998431i	$-0.482166\pi$
$823$	3.21292			0.111995			0.0559977	+	0.998431i	$0.482166\pi$
$824$		0			0
$825$	−0.168434	+	0.799174i	−0.00586412	+	0.0278237i
$826$		0			0
$827$	7.63626	−	7.63626i	0.265539	−	0.265539i	−0.561761	−	0.827300i	$-0.689876\pi$
$827$	7.63626	−	7.63626i	0.265539	−	0.265539i	0.827300	+	0.561761i	$0.189876\pi$
$828$		0			0
$829$	17.7711	+	17.7711i	0.617217	+	0.617217i	0.944817	−	0.327600i	$-0.106240\pi$
$829$	17.7711	+	17.7711i	0.617217	+	0.617217i	−0.327600	+	0.944817i	$0.606240\pi$
$830$		0			0
$831$	6.75933	+	1.42460i	0.234479	+	0.0494187i
$832$		0			0
$833$		−	1.39276i		−	0.0482564i
$834$		0			0
$835$	27.3645	−	27.3645i	0.946987	−	0.946987i
$836$		0			0
$837$	0.394719	+	2.41158i	0.0136435	+	0.0833565i
$838$		0			0
$839$			8.70592i			0.300562i	0.988643	+	0.150281i	$0.0480178\pi$
$839$			8.70592i			0.300562i	−0.988643	+	0.150281i	$0.951982\pi$
$840$		0			0
$841$		−	19.6492i		−	0.677558i
$842$		0			0
$843$	24.4127	+	37.4512i	0.840820	+	1.28989i
$844$		0			0
$845$	−14.2821	+	14.2821i	−0.491321	+	0.491321i
$846$		0			0
$847$		−	10.6033i		−	0.364334i
$848$		0			0
$849$	4.29896	−	20.3974i	0.147540	−	0.700037i
$850$		0			0
$851$	−8.92757	−	8.92757i	−0.306033	−	0.306033i
$852$		0			0
$853$	−19.8103	+	19.8103i	−0.678291	+	0.678291i	−0.959613	−	0.281323i	$-0.909227\pi$
$853$	−19.8103	+	19.8103i	−0.678291	+	0.678291i	0.281323	+	0.959613i	$0.409227\pi$
$854$		0			0
$855$	−3.96180	+	8.98133i	−0.135491	+	0.307155i
$856$		0			0
$857$	51.7656			1.76828			0.884139	−	0.467224i	$-0.154746\pi$
$857$	51.7656			1.76828			0.884139	+	0.467224i	$0.154746\pi$
$858$		0			0
$859$	−1.55742	−	1.55742i	−0.0531386	−	0.0531386i	0.680038	−	0.733177i	$-0.261963\pi$
$859$	−1.55742	−	1.55742i	−0.0531386	−	0.0531386i	−0.733177	+	0.680038i	$0.761963\pi$
$860$		0			0
$861$	−7.90059	−	12.1202i	−0.269251	−	0.413054i
$862$		0			0
$863$	19.0224			0.647530			0.323765	−	0.946138i	$-0.395051\pi$
$863$	19.0224			0.647530			0.323765	+	0.946138i	$0.395051\pi$
$864$		0			0
$865$	32.8495			1.11692
$866$		0			0
$867$	14.2445	+	21.8523i	0.483770	+	0.742143i
$868$		0			0
$869$	7.38614	+	7.38614i	0.250557	+	0.250557i
$870$		0			0
$871$	13.2551			0.449133
$872$		0			0
$873$	−6.26771	+	14.2088i	−0.212130	+	0.480895i
$874$		0			0
$875$	7.20764	−	7.20764i	0.243663	−	0.243663i
$876$		0			0
$877$	8.86901	+	8.86901i	0.299485	+	0.299485i	0.840812	−	0.541327i	$-0.182078\pi$
$877$	8.86901	+	8.86901i	0.299485	+	0.299485i	−0.541327	+	0.840812i	$0.682078\pi$
$878$		0			0
$879$	4.47109	−	21.2141i	0.150806	−	0.715534i
$880$		0			0
$881$			30.7009i			1.03434i	0.855883	+	0.517170i	$0.173014\pi$
$881$			30.7009i			1.03434i	−0.855883	+	0.517170i	$0.826986\pi$
$882$		0			0
$883$	22.6512	−	22.6512i	0.762275	−	0.762275i	−0.214458	−	0.976733i	$-0.568799\pi$
$883$	22.6512	−	22.6512i	0.762275	−	0.762275i	0.976733	+	0.214458i	$0.0687987\pi$
$884$		0			0
$885$	−21.2308	−	32.5698i	−0.713666	−	1.09482i
$886$		0			0
$887$			11.9499i			0.401239i	0.979669	+	0.200620i	$0.0642955\pi$
$887$			11.9499i			0.401239i	−0.979669	+	0.200620i	$0.935704\pi$
$888$		0			0
$889$			2.20449i			0.0739362i
$890$		0			0
$891$	−5.66262	−	0.257727i	−0.189705	−	0.00863418i
$892$		0			0
$893$	4.67698	−	4.67698i	0.156509	−	0.156509i
$894$		0			0
$895$			17.9193i			0.598977i
$896$		0			0
$897$	−21.9216	−	4.62020i	−0.731940	−	0.154264i
$898$		0			0
$899$	−2.31944	−	2.31944i	−0.0773578	−	0.0773578i
$900$		0			0
$901$	−4.76649	+	4.76649i	−0.158795	+	0.158795i
$902$		0			0
$903$	−4.53263	+	21.5061i	−0.150837	+	0.715679i
$904$		0			0
$905$	40.2274			1.33721
$906$		0			0
$907$	−41.0833	−	41.0833i	−1.36415	−	1.36415i	−0.868554	−	0.495595i	$-0.834950\pi$
$907$	−41.0833	−	41.0833i	−1.36415	−	1.36415i	−0.495595	−	0.868554i	$-0.665050\pi$
$908$		0			0
$909$	−9.54523	+	3.70178i	−0.316595	+	0.122780i
$910$		0			0
$911$	21.3664			0.707902			0.353951	−	0.935264i	$-0.384838\pi$
$911$	21.3664			0.707902			0.353951	+	0.935264i	$0.384838\pi$
$912$		0			0
$913$	−8.23614			−0.272576
$914$		0			0
$915$	−39.5772	+	25.7986i	−1.30838	+	0.852876i
$916$		0			0
$917$	−10.5553	−	10.5553i	−0.348567	−	0.348567i
$918$		0			0
$919$	−29.4386			−0.971090			−0.485545	−	0.874212i	$-0.661379\pi$
$919$	−29.4386			−0.971090			−0.485545	+	0.874212i	$0.661379\pi$
$920$		0			0
$921$	35.1074	+	7.39924i	1.15683	+	0.243813i
$922$		0			0
$923$	−18.6727	+	18.6727i	−0.614618	+	0.614618i
$924$		0			0
$925$	1.10539	+	1.10539i	0.0363450	+	0.0363450i
$926$		0			0
$927$	−6.98920	+	15.8444i	−0.229556	+	0.520399i
$928$		0			0
$929$		−	16.0304i		−	0.525940i	−0.964804	−	0.262970i	$-0.915298\pi$
$929$		−	16.0304i		−	0.525940i	0.964804	−	0.262970i	$-0.0847021\pi$
$930$		0			0
$931$	−0.965003	+	0.965003i	−0.0316267	+	0.0316267i
$932$		0			0
$933$	−27.5413	+	17.9529i	−0.901660	+	0.587752i
$934$		0			0
$935$			2.10323i			0.0687828i
$936$		0			0
$937$			10.2290i			0.334167i	0.985943	+	0.167084i	$0.0534350\pi$
$937$			10.2290i			0.334167i	−0.985943	+	0.167084i	$0.946565\pi$
$938$		0			0
$939$	−2.05642	+	1.34049i	−0.0671089	+	0.0437452i
$940$		0			0
$941$	13.7787	−	13.7787i	0.449172	−	0.449172i	−0.445907	−	0.895079i	$-0.647119\pi$
$941$	13.7787	−	13.7787i	0.449172	−	0.449172i	0.895079	+	0.445907i	$0.147119\pi$
$942$		0			0
$943$		−	50.5073i		−	1.64474i
$944$		0			0
$945$	−10.1168	−	7.27084i	−0.329099	−	0.236520i
$946$		0			0
$947$	−18.3826	−	18.3826i	−0.597354	−	0.597354i	0.342253	−	0.939608i	$-0.388810\pi$
$947$	−18.3826	−	18.3826i	−0.597354	−	0.597354i	−0.939608	+	0.342253i	$0.888810\pi$
$948$		0			0
$949$	21.2058	−	21.2058i	0.688369	−	0.688369i
$950$		0			0
$951$	−18.9228	−	3.98816i	−0.613612	−	0.129325i
$952$		0			0
$953$	−32.8708			−1.06479			−0.532394	−	0.846497i	$-0.678708\pi$
$953$	−32.8708			−1.06479			−0.532394	+	0.846497i	$0.678708\pi$
$954$		0			0
$955$	20.7691	+	20.7691i	0.672071	+	0.672071i
$956$		0			0
$957$	6.37424	−	4.15508i	0.206050	−	0.134315i
$958$		0			0
$959$	−11.4183			−0.368715
$960$		0			0
$961$	30.7788			0.992866
$962$		0			0
$963$	17.3259	+	44.6758i	0.558320	+	1.43966i
$964$		0			0
$965$	17.1912	+	17.1912i	0.553404	+	0.553404i
$966$		0			0
$967$	55.1646			1.77398			0.886988	−	0.461793i	$-0.152794\pi$
$967$	55.1646			1.77398			0.886988	+	0.461793i	$0.152794\pi$
$968$		0			0
$969$	−0.678942	+	3.22140i	−0.0218108	+	0.103486i
$970$		0			0
$971$	7.89937	−	7.89937i	0.253503	−	0.253503i	−0.568902	−	0.822405i	$-0.692632\pi$
$971$	7.89937	−	7.89937i	0.253503	−	0.253503i	0.822405	+	0.568902i	$0.192632\pi$
$972$		0			0
$973$	6.59016	+	6.59016i	0.211271	+	0.211271i
$974$		0			0
$975$	2.71428	+	0.572062i	0.0869264	+	0.0183206i
$976$		0			0
$977$			13.4649i			0.430780i	0.976528	+	0.215390i	$0.0691023\pi$
$977$			13.4649i			0.430780i	−0.976528	+	0.215390i	$0.930898\pi$
$978$		0			0
$979$	−2.33984	+	2.33984i	−0.0747817	+	0.0747817i
$980$		0			0
$981$	30.7855	−	11.9391i	0.982906	−	0.381185i
$982$		0			0
$983$			2.38464i			0.0760581i	0.999277	+	0.0380291i	$0.0121079\pi$
$983$			2.38464i			0.0760581i	−0.999277	+	0.0380291i	$0.987892\pi$
$984$		0			0
$985$			65.3755i			2.08304i
$986$		0			0
$987$	4.58410	+	7.03240i	0.145914	+	0.223844i
$988$		0			0
$989$	−54.2544	+	54.2544i	−1.72519	+	1.72519i
$990$		0			0
$991$		−	42.9802i		−	1.36531i	−0.730741	−	0.682655i	$-0.760825\pi$
$991$		−	42.9802i		−	1.36531i	0.730741	−	0.682655i	$-0.239175\pi$
$992$		0			0
$993$	6.18876	−	29.3640i	0.196394	−	0.931838i
$994$		0			0
$995$	17.6608	+	17.6608i	0.559884	+	0.559884i
$996$		0			0
$997$	−1.43276	+	1.43276i	−0.0453761	+	0.0453761i	−0.729431	−	0.684055i	$-0.760215\pi$
$997$	−1.43276	+	1.43276i	−0.0453761	+	0.0453761i	0.684055	+	0.729431i	$0.260215\pi$
$998$		0			0
$999$	−6.33195	+	8.81039i	−0.200334	+	0.278749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.d.239.17		48
3.2	odd	2	inner	1344.2.s.d.239.4		48
4.3	odd	2		336.2.s.d.323.23	yes	48
12.11	even	2		336.2.s.d.323.2	yes	48
16.5	even	4		336.2.s.d.155.2	✓	48
16.11	odd	4	inner	1344.2.s.d.911.4		48
48.5	odd	4		336.2.s.d.155.23	yes	48
48.11	even	4	inner	1344.2.s.d.911.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.2	✓	48	16.5	even	4
336.2.s.d.155.23	yes	48	48.5	odd	4
336.2.s.d.323.2	yes	48	12.11	even	2
336.2.s.d.323.23	yes	48	4.3	odd	2
1344.2.s.d.239.4		48	3.2	odd	2	inner
1344.2.s.d.239.17		48	1.1	even	1	trivial
1344.2.s.d.911.4		48	16.11	odd	4	inner
1344.2.s.d.911.17		48	48.11	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.945839 + 1.45100i) q^{3} +(-1.69539 - 1.69539i) q^{5} -1.00000 q^{7} +(-1.21078 + 2.74482i) q^{9} +O(q^{10})\)	\(q+(0.945839 + 1.45100i) q^{3} +(-1.69539 - 1.69539i) q^{5} -1.00000 q^{7} +(-1.21078 + 2.74482i) q^{9} +(0.445358 - 0.445358i) q^{11} +(-1.51259 - 1.51259i) q^{13} +(0.856437 - 4.06356i) q^{15} -1.39276i q^{17} +(-0.965003 + 0.965003i) q^{19} +(-0.945839 - 1.45100i) q^{21} -6.04660i q^{23} +0.748676i q^{25} +(-5.12792 + 0.839319i) q^{27} +(4.93200 - 4.93200i) q^{29} -0.470285i q^{31} +(1.06745 + 0.224976i) q^{33} +(1.69539 + 1.69539i) q^{35} +(1.47646 - 1.47646i) q^{37} +(0.764098 - 3.62544i) q^{39} +8.35300 q^{41} +(-8.97272 - 8.97272i) q^{43} +(6.70626 - 2.60079i) q^{45} -4.84660 q^{47} +1.00000 q^{49} +(2.02089 - 1.31733i) q^{51} +(-3.42232 - 3.42232i) q^{53} -1.51011 q^{55} +(-2.31295 - 0.487478i) q^{57} +(6.61989 - 6.61989i) q^{59} +(-8.04415 - 8.04415i) q^{61} +(1.21078 - 2.74482i) q^{63} +5.12887i q^{65} +(-4.38159 + 4.38159i) q^{67} +(8.77359 - 5.71911i) q^{69} -12.3448i q^{71} +14.0195i q^{73} +(-1.08633 + 0.708126i) q^{75} +(-0.445358 + 0.445358i) q^{77} +16.5847i q^{79} +(-6.06803 - 6.64673i) q^{81} +(-9.24664 - 9.24664i) q^{83} +(-2.36127 + 2.36127i) q^{85} +(11.8212 + 2.49143i) q^{87} -5.25384 q^{89} +(1.51259 + 1.51259i) q^{91} +(0.682381 - 0.444814i) q^{93} +3.27211 q^{95} +5.17660 q^{97} +(0.683197 + 1.76166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{7}+O(q^{10}) \) 48 * q - 48 * q^7	\( 48 q - 48 q^{7} - 8 q^{19} + 12 q^{27} + 16 q^{37} + 24 q^{39} + 48 q^{43} + 20 q^{45} + 48 q^{49} + 32 q^{55} + 8 q^{61} + 16 q^{67} - 28 q^{69} + 12 q^{75} - 48 q^{85} - 56 q^{87} - 64 q^{93} - 32 q^{99}+O(q^{100}) \) 48 * q - 48 * q^7 - 8 * q^19 + 12 * q^27 + 16 * q^37 + 24 * q^39 + 48 * q^43 + 20 * q^45 + 48 * q^49 + 32 * q^55 + 8 * q^61 + 16 * q^67 - 28 * q^69 + 12 * q^75 - 48 * q^85 - 56 * q^87 - 64 * q^93 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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