LMFDB - Embedded newform 3150.2.bp.c.899.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(899,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3150.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bp (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	3150.899
Dual form			3150.2.bp.c.1349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.189469 - 2.63896i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.189469 - 2.63896i) q^{7} +1.00000 q^{8} +(4.67303 + 2.69798i) q^{11} -2.51764 q^{13} +(-2.19067 + 1.48356i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.89658 - 2.24969i) q^{17} +(2.48004 - 1.43185i) q^{19} -5.39595i q^{22} +(0.133975 + 0.232051i) q^{23} +(1.25882 + 2.18034i) q^{26} +(2.38014 + 1.15539i) q^{28} -8.89898i q^{29} +(4.18154 + 2.41421i) q^{31} +(-0.500000 + 0.866025i) q^{32} +4.49938i q^{34} +(-5.64444 + 3.25882i) q^{37} +(-2.48004 - 1.43185i) q^{38} -0.760279 q^{41} +5.86370i q^{43} +(-4.67303 + 2.69798i) q^{44} +(0.133975 - 0.232051i) q^{46} +(6.92418 - 3.99768i) q^{47} +(-6.92820 + 1.00000i) q^{49} +(1.25882 - 2.18034i) q^{52} +(4.19918 - 7.27319i) q^{53} +(-0.189469 - 2.63896i) q^{56} +(-7.70674 + 4.44949i) q^{58} +(6.33573 - 10.9738i) q^{59} +(-2.27035 + 1.31079i) q^{61} -4.82843i q^{62} +1.00000 q^{64} +(-8.50643 - 4.91119i) q^{67} +(3.89658 - 2.24969i) q^{68} +4.76268i q^{71} +(5.82843 - 10.0951i) q^{73} +(5.64444 + 3.25882i) q^{74} +2.86370i q^{76} +(6.23445 - 12.8431i) q^{77} +(4.29618 + 7.44120i) q^{79} +(0.380139 + 0.658421i) q^{82} +9.45001i q^{83} +(5.07812 - 2.93185i) q^{86} +(4.67303 + 2.69798i) q^{88} +(-3.98502 - 6.90226i) q^{89} +(0.477014 + 6.64394i) q^{91} -0.267949 q^{92} +(-6.92418 - 3.99768i) q^{94} +6.16353 q^{97} +(4.33013 + 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 24 q^{11} - 16 q^{13} - 4 q^{16} - 24 q^{17} + 8 q^{23} + 8 q^{26} - 4 q^{32} + 32 q^{41} - 24 q^{44} + 8 q^{46} - 12 q^{47} + 8 q^{52} - 4 q^{53} + 24 q^{59} + 8 q^{64} - 48 q^{67} + 24 q^{68} + 24 q^{73} + 4 q^{77} + 24 q^{79} - 16 q^{82} + 24 q^{88} + 16 q^{89} - 20 q^{91} - 16 q^{92} + 12 q^{94} + 48 q^{97}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 24 * q^11 - 16 * q^13 - 4 * q^16 - 24 * q^17 + 8 * q^23 + 8 * q^26 - 4 * q^32 + 32 * q^41 - 24 * q^44 + 8 * q^46 - 12 * q^47 + 8 * q^52 - 4 * q^53 + 24 * q^59 + 8 * q^64 - 48 * q^67 + 24 * q^68 + 24 * q^73 + 4 * q^77 + 24 * q^79 - 16 * q^82 + 24 * q^88 + 16 * q^89 - 20 * q^91 - 16 * q^92 + 12 * q^94 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.189469	−	2.63896i	−0.0716124	−	0.997433i
$7$	−0.189469	−	2.63896i	−0.0716124	−	0.997433i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	4.67303	+	2.69798i	1.40897	+	0.813471i	0.995289	−	0.0969504i	$-0.0309088\pi$
$11$	4.67303	+	2.69798i	1.40897	+	0.813471i	0.413683	+	0.910421i	$0.364242\pi$
$12$		0			0
$13$	−2.51764			−0.698267			−0.349134	−	0.937073i	$-0.613524\pi$
$13$	−2.51764			−0.698267			−0.349134	+	0.937073i	$0.613524\pi$
$14$	−2.19067	+	1.48356i	−0.585481	+	0.396499i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.89658	−	2.24969i	−0.945058	−	0.545630i	−0.0535160	−	0.998567i	$-0.517043\pi$
$17$	−3.89658	−	2.24969i	−0.945058	−	0.545630i	−0.891542	+	0.452937i	$0.850376\pi$
$18$		0			0
$19$	2.48004	−	1.43185i	0.568960	−	0.328489i	−0.187774	−	0.982212i	$-0.560127\pi$
$19$	2.48004	−	1.43185i	0.568960	−	0.328489i	0.756734	+	0.653723i	$0.226794\pi$
$20$		0			0
$21$		0			0
$22$		−	5.39595i		−	1.15042i
$23$	0.133975	+	0.232051i	0.0279356	+	0.0483859i	0.879655	−	0.475612i	$-0.157773\pi$
$23$	0.133975	+	0.232051i	0.0279356	+	0.0483859i	−0.851720	+	0.523998i	$0.824440\pi$
$24$		0			0
$25$		0			0
$26$	1.25882	+	2.18034i	0.246875	+	0.427600i
$27$		0			0
$28$	2.38014	+	1.15539i	0.449804	+	0.218349i
$29$		−	8.89898i		−	1.65250i	−0.563304	−	0.826250i	$-0.690470\pi$
$29$		−	8.89898i		−	1.65250i	0.563304	−	0.826250i	$-0.309530\pi$
$30$		0			0
$31$	4.18154	+	2.41421i	0.751027	+	0.433606i	0.826065	−	0.563575i	$-0.190574\pi$
$31$	4.18154	+	2.41421i	0.751027	+	0.433606i	−0.0750380	+	0.997181i	$0.523908\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$			4.49938i			0.771637i
$35$		0			0
$36$		0			0
$37$	−5.64444	+	3.25882i	−0.927940	+	0.535747i	−0.886160	−	0.463380i	$-0.846636\pi$
$37$	−5.64444	+	3.25882i	−0.927940	+	0.535747i	−0.0417807	+	0.999127i	$0.513303\pi$
$38$	−2.48004	−	1.43185i	−0.402316	−	0.232277i
$39$		0			0
$40$		0			0
$41$	−0.760279			−0.118736			−0.0593678	−	0.998236i	$-0.518908\pi$
$41$	−0.760279			−0.118736			−0.0593678	+	0.998236i	$0.518908\pi$
$42$		0			0
$43$			5.86370i			0.894206i	0.894482	+	0.447103i	$0.147544\pi$
$43$			5.86370i			0.894206i	−0.894482	+	0.447103i	$0.852456\pi$
$44$	−4.67303	+	2.69798i	−0.704486	+	0.406735i
$45$		0			0
$46$	0.133975	−	0.232051i	0.0197535	−	0.0342140i
$47$	6.92418	−	3.99768i	1.01000	−	0.583121i	0.0988053	−	0.995107i	$-0.468498\pi$
$47$	6.92418	−	3.99768i	1.01000	−	0.583121i	0.911190	+	0.411986i	$0.135165\pi$
$48$		0			0
$49$	−6.92820	+	1.00000i	−0.989743	+	0.142857i
$50$		0			0
$51$		0			0
$52$	1.25882	−	2.18034i	0.174567	−	0.302359i
$53$	4.19918	−	7.27319i	0.576802	−	0.999050i	−0.419042	−	0.907967i	$-0.637634\pi$
$53$	4.19918	−	7.27319i	0.576802	−	0.999050i	0.995843	−	0.0910826i	$-0.0290327\pi$
$54$		0			0
$55$		0			0
$56$	−0.189469	−	2.63896i	−0.0253188	−	0.352646i
$57$		0			0
$58$	−7.70674	+	4.44949i	−1.01194	+	0.584247i
$59$	6.33573	−	10.9738i	0.824842	−	1.42867i	−0.0771977	−	0.997016i	$-0.524597\pi$
$59$	6.33573	−	10.9738i	0.824842	−	1.42867i	0.902040	−	0.431653i	$-0.142069\pi$
$60$		0			0
$61$	−2.27035	+	1.31079i	−0.290689	+	0.167829i	−0.638253	−	0.769827i	$-0.720342\pi$
$61$	−2.27035	+	1.31079i	−0.290689	+	0.167829i	0.347564	+	0.937656i	$0.387009\pi$
$62$		−	4.82843i		−	0.613211i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−8.50643	−	4.91119i	−1.03923	−	0.599997i	−0.119612	−	0.992821i	$-0.538165\pi$
$67$	−8.50643	−	4.91119i	−1.03923	−	0.599997i	−0.919614	+	0.392824i	$0.871498\pi$
$68$	3.89658	−	2.24969i	0.472529	−	0.272815i
$69$		0			0
$70$		0			0
$71$			4.76268i			0.565226i	0.959234	+	0.282613i	$0.0912013\pi$
$71$			4.76268i			0.565226i	−0.959234	+	0.282613i	$0.908799\pi$
$72$		0			0
$73$	5.82843	−	10.0951i	0.682166	−	1.18155i	−0.292153	−	0.956372i	$-0.594372\pi$
$73$	5.82843	−	10.0951i	0.682166	−	1.18155i	0.974319	−	0.225174i	$-0.0722951\pi$
$74$	5.64444	+	3.25882i	0.656153	+	0.378830i
$75$		0			0
$76$			2.86370i			0.328489i
$77$	6.23445	−	12.8431i	0.710482	−	1.46361i
$78$		0			0
$79$	4.29618	+	7.44120i	0.483358	+	0.837200i	0.999817	−	0.0191114i	$-0.00608373\pi$
$79$	4.29618	+	7.44120i	0.483358	+	0.837200i	−0.516460	+	0.856312i	$0.672750\pi$
$80$		0			0
$81$		0			0
$82$	0.380139	+	0.658421i	0.0419794	+	0.0727104i
$83$			9.45001i			1.03727i	0.854995	+	0.518636i	$0.173560\pi$
$83$			9.45001i			1.03727i	−0.854995	+	0.518636i	$0.826440\pi$
$84$		0			0
$85$		0			0
$86$	5.07812	−	2.93185i	0.547587	−	0.316150i
$87$		0			0
$88$	4.67303	+	2.69798i	0.498147	+	0.287605i
$89$	−3.98502	−	6.90226i	−0.422412	−	0.731638i	0.573763	−	0.819021i	$-0.305483\pi$
$89$	−3.98502	−	6.90226i	−0.422412	−	0.731638i	−0.996175	+	0.0873828i	$0.972150\pi$
$90$		0			0
$91$	0.477014	+	6.64394i	0.0500046	+	0.696474i
$92$	−0.267949			−0.0279356
$93$		0			0
$94$	−6.92418	−	3.99768i	−0.714175	−	0.412329i
$95$		0			0
$96$		0			0
$97$	6.16353			0.625812			0.312906	−	0.949784i	$-0.398698\pi$
$97$	6.16353			0.625812			0.312906	+	0.949784i	$0.398698\pi$
$98$	4.33013	+	5.50000i	0.437409	+	0.555584i
$99$		0			0
$100$		0			0
$101$	7.02458	−	12.1669i	0.698972	−	1.21065i	−0.269852	−	0.962902i	$-0.586975\pi$
$101$	7.02458	−	12.1669i	0.698972	−	1.21065i	0.968823	−	0.247753i	$-0.0796920\pi$
$102$		0			0
$103$	−7.08845	−	12.2776i	−0.698446	−	1.20974i	−0.969005	−	0.247040i	$-0.920542\pi$
$103$	−7.08845	−	12.2776i	−0.698446	−	1.20974i	0.270560	−	0.962703i	$-0.412791\pi$
$104$	−2.51764			−0.246875
$105$		0			0
$106$	−8.39836			−0.815721
$107$	0.820863	+	1.42178i	0.0793559	+	0.137448i	0.902972	−	0.429699i	$-0.141380\pi$
$107$	0.820863	+	1.42178i	0.0793559	+	0.137448i	−0.823616	+	0.567147i	$0.808047\pi$
$108$		0			0
$109$	−9.94887	+	17.2319i	−0.952929	+	1.65052i	−0.213890	+	0.976858i	$0.568613\pi$
$109$	−9.94887	+	17.2319i	−0.952929	+	1.65052i	−0.739039	+	0.673663i	$0.764720\pi$
$110$		0			0
$111$		0			0
$112$	−2.19067	+	1.48356i	−0.206999	+	0.140184i
$113$	−5.95867			−0.560545			−0.280272	−	0.959921i	$-0.590425\pi$
$113$	−5.95867			−0.560545			−0.280272	+	0.959921i	$0.590425\pi$
$114$		0			0
$115$		0			0
$116$	7.70674	+	4.44949i	0.715553	+	0.413125i
$117$		0			0
$118$	−12.6715			−1.16650
$119$	−5.19856	+	10.7091i	−0.476551	+	0.981706i
$120$		0			0
$121$	9.05816	+	15.6892i	0.823469	+	1.42629i
$122$	2.27035	+	1.31079i	0.205548	+	0.118673i
$123$		0			0
$124$	−4.18154	+	2.41421i	−0.375513	+	0.216803i
$125$		0			0
$126$		0			0
$127$		−	14.5103i		−	1.28758i	−0.765200	−	0.643792i	$-0.777360\pi$
$127$		−	14.5103i		−	1.28758i	0.765200	−	0.643792i	$-0.222640\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	−7.73325	−	13.3944i	−0.675657	−	1.17027i	−0.976276	−	0.216529i	$-0.930527\pi$
$131$	−7.73325	−	13.3944i	−0.675657	−	1.17027i	0.300619	−	0.953744i	$-0.402807\pi$
$132$		0			0
$133$	−4.24849	−	6.27343i	−0.368391	−	0.543975i
$134$			9.82237i			0.848524i
$135$		0			0
$136$	−3.89658	−	2.24969i	−0.334129	−	0.192909i
$137$	4.31079	−	7.46651i	0.368296	−	0.637907i	−0.621004	−	0.783808i	$-0.713275\pi$
$137$	4.31079	−	7.46651i	0.368296	−	0.637907i	0.989299	+	0.145901i	$0.0466081\pi$
$138$		0			0
$139$			10.2512i			0.869495i	0.900552	+	0.434748i	$0.143162\pi$
$139$			10.2512i			0.869495i	−0.900552	+	0.434748i	$0.856838\pi$
$140$		0			0
$141$		0			0
$142$	4.12460	−	2.38134i	0.346129	−	0.199838i
$143$	−11.7650	−	6.79253i	−0.983839	−	0.568020i
$144$		0			0
$145$		0			0
$146$	−11.6569			−0.964728
$147$		0			0
$148$		−	6.51764i		−	0.535747i
$149$	−7.96640	+	4.59940i	−0.652633	+	0.376798i	−0.789464	−	0.613797i	$-0.789641\pi$
$149$	−7.96640	+	4.59940i	−0.652633	+	0.376798i	0.136831	+	0.990594i	$0.456308\pi$
$150$		0			0
$151$	6.37429	−	11.0406i	0.518733	−	0.898471i	−0.481030	−	0.876704i	$-0.659737\pi$
$151$	6.37429	−	11.0406i	0.518733	−	0.898471i	0.999763	−	0.0217674i	$-0.00692931\pi$
$152$	2.48004	−	1.43185i	0.201158	−	0.116139i
$153$		0			0
$154$	−14.2397	+	1.02236i	−1.14747	+	0.0823845i
$155$		0			0
$156$		0			0
$157$	−6.92236	+	11.9899i	−0.552464	+	0.956896i	0.445632	+	0.895216i	$0.352979\pi$
$157$	−6.92236	+	11.9899i	−0.552464	+	0.956896i	−0.998096	+	0.0616798i	$0.980354\pi$
$158$	4.29618	−	7.44120i	0.341786	−	0.591990i
$159$		0			0
$160$		0			0
$161$	0.586988	−	0.397520i	0.0462612	−	0.0313289i
$162$		0			0
$163$	17.8444	−	10.3025i	1.39768	−	0.806954i	0.403535	−	0.914964i	$-0.367781\pi$
$163$	17.8444	−	10.3025i	1.39768	−	0.806954i	0.994150	+	0.108010i	$0.0344480\pi$
$164$	0.380139	−	0.658421i	0.0296839	−	0.0514140i
$165$		0			0
$166$	8.18394	−	4.72500i	0.635197	−	0.366731i
$167$		−	6.84961i		−	0.530038i	−0.964243	−	0.265019i	$-0.914622\pi$
$167$		−	6.84961i		−	0.530038i	0.964243	−	0.265019i	$-0.0853783\pi$
$168$		0			0
$169$	−6.66150			−0.512423
$170$		0			0
$171$		0			0
$172$	−5.07812	−	2.93185i	−0.387203	−	0.223552i
$173$	11.0488	−	6.37902i	0.840024	−	0.484988i	−0.0172486	−	0.999851i	$-0.505491\pi$
$173$	11.0488	−	6.37902i	0.840024	−	0.484988i	0.857272	+	0.514863i	$0.172157\pi$
$174$		0			0
$175$		0			0
$176$		−	5.39595i		−	0.406735i
$177$		0			0
$178$	−3.98502	+	6.90226i	−0.298690	+	0.517347i
$179$	−16.3390	−	9.43331i	−1.22123	−	0.705079i	−0.256052	−	0.966663i	$-0.582422\pi$
$179$	−16.3390	−	9.43331i	−1.22123	−	0.705079i	−0.965181	+	0.261584i	$0.915755\pi$
$180$		0			0
$181$		−	25.5498i		−	1.89910i	−0.313615	−	0.949550i	$-0.601540\pi$
$181$		−	25.5498i		−	1.89910i	0.313615	−	0.949550i	$-0.398460\pi$
$182$	5.51532	−	3.73508i	0.408822	−	0.276862i
$183$		0			0
$184$	0.133975	+	0.232051i	0.00987674	+	0.0171070i
$185$		0			0
$186$		0			0
$187$	−12.1392	−	21.0257i	−0.887707	−	1.53755i
$188$			7.99536i			0.583121i
$189$		0			0
$190$		0			0
$191$	7.00657	−	4.04524i	0.506977	−	0.292704i	−0.224613	−	0.974448i	$-0.572112\pi$
$191$	7.00657	−	4.04524i	0.506977	−	0.292704i	0.731590	+	0.681745i	$0.238778\pi$
$192$		0			0
$193$	−12.2343	−	7.06350i	−0.880648	−	0.508442i	−0.00977575	−	0.999952i	$-0.503112\pi$
$193$	−12.2343	−	7.06350i	−0.880648	−	0.508442i	−0.870872	+	0.491510i	$0.836445\pi$
$194$	−3.08176	−	5.33777i	−0.221258	−	0.383230i
$195$		0			0
$196$	2.59808	−	6.50000i	0.185577	−	0.464286i
$197$	−14.2738			−1.01697			−0.508483	−	0.861072i	$-0.669793\pi$
$197$	−14.2738			−1.01697			−0.508483	+	0.861072i	$0.669793\pi$
$198$		0			0
$199$	−3.06742	−	1.77098i	−0.217444	−	0.125541i	0.387322	−	0.921944i	$-0.373400\pi$
$199$	−3.06742	−	1.77098i	−0.217444	−	0.125541i	−0.604766	+	0.796403i	$0.706733\pi$
$200$		0			0
$201$		0			0
$202$	−14.0492			−0.988495
$203$	−23.4840	+	1.68608i	−1.64826	+	0.118339i
$204$		0			0
$205$		0			0
$206$	−7.08845	+	12.2776i	−0.493876	+	0.855418i
$207$		0			0
$208$	1.25882	+	2.18034i	0.0872834	+	0.151179i
$209$	15.4524			1.06887
$210$		0			0
$211$	−3.92340			−0.270098			−0.135049	−	0.990839i	$-0.543119\pi$
$211$	−3.92340			−0.270098			−0.135049	+	0.990839i	$0.543119\pi$
$212$	4.19918	+	7.27319i	0.288401	+	0.499525i
$213$		0			0
$214$	0.820863	−	1.42178i	0.0561131	−	0.0971907i
$215$		0			0
$216$		0			0
$217$	5.57874	−	11.4923i	0.378709	−	0.780150i
$218$	19.8977			1.34764
$219$		0			0
$220$		0			0
$221$	9.81017	+	5.66390i	0.659903	+	0.380995i
$222$		0			0
$223$	−14.6904			−0.983740			−0.491870	−	0.870669i	$-0.663686\pi$
$223$	−14.6904			−0.983740			−0.491870	+	0.870669i	$0.663686\pi$
$224$	2.38014	+	1.15539i	0.159030	+	0.0771980i
$225$		0			0
$226$	2.97934	+	5.16036i	0.198182	+	0.343262i
$227$	19.7303	+	11.3913i	1.30955	+	0.756068i	0.982021	−	0.188774i	$-0.0604514\pi$
$227$	19.7303	+	11.3913i	1.30955	+	0.756068i	0.327527	+	0.944842i	$0.393785\pi$
$228$		0			0
$229$	17.5089	−	10.1087i	1.15702	−	0.668005i	0.206431	−	0.978461i	$-0.433815\pi$
$229$	17.5089	−	10.1087i	1.15702	−	0.668005i	0.950588	+	0.310456i	$0.100482\pi$
$230$		0			0
$231$		0			0
$232$		−	8.89898i		−	0.584247i
$233$	1.31543	+	2.27840i	0.0861769	+	0.149263i	0.905892	−	0.423509i	$-0.139202\pi$
$233$	1.31543	+	2.27840i	0.0861769	+	0.149263i	−0.819715	+	0.572771i	$0.805868\pi$
$234$		0			0
$235$		0			0
$236$	6.33573	+	10.9738i	0.412421	+	0.714334i
$237$		0			0
$238$	11.8737	−	0.852491i	0.769656	−	0.0552588i
$239$		−	16.8766i		−	1.09165i	−0.837898	−	0.545827i	$-0.816216\pi$
$239$		−	16.8766i		−	1.09165i	0.837898	−	0.545827i	$-0.183784\pi$
$240$		0			0
$241$	−12.5793	−	7.26268i	−0.810306	−	0.467831i	0.0367560	−	0.999324i	$-0.488298\pi$
$241$	−12.5793	−	7.26268i	−0.810306	−	0.467831i	−0.847062	+	0.531494i	$0.821631\pi$
$242$	9.05816	−	15.6892i	0.582280	−	1.00854i
$243$		0			0
$244$		−	2.62158i		−	0.167829i
$245$		0			0
$246$		0			0
$247$	−6.24384	+	3.60488i	−0.397286	+	0.229373i
$248$	4.18154	+	2.41421i	0.265528	+	0.153303i
$249$		0			0
$250$		0			0
$251$	−15.7243			−0.992507			−0.496254	−	0.868178i	$-0.665291\pi$
$251$	−15.7243			−0.992507			−0.496254	+	0.868178i	$0.665291\pi$
$252$		0			0
$253$			1.44584i			0.0908993i
$254$	−12.5663	+	7.25517i	−0.788481	+	0.455230i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	17.0275	−	9.83083i	1.06215	−	0.613230i	0.136121	−	0.990692i	$-0.456536\pi$
$257$	17.0275	−	9.83083i	1.06215	−	0.613230i	0.926025	+	0.377462i	$0.123203\pi$
$258$		0			0
$259$	9.66933	+	14.2780i	0.600823	+	0.887192i
$260$		0			0
$261$		0			0
$262$	−7.73325	+	13.3944i	−0.477762	+	0.827508i
$263$	2.16088	−	3.74275i	0.133245	−	0.230788i	−0.791680	−	0.610935i	$-0.790794\pi$
$263$	2.16088	−	3.74275i	0.133245	−	0.230788i	0.924926	+	0.380148i	$0.124127\pi$
$264$		0			0
$265$		0			0
$266$	−3.30871	+	6.81601i	−0.202870	+	0.417917i
$267$		0			0
$268$	8.50643	−	4.91119i	0.519613	−	0.299999i
$269$	8.79895	−	15.2402i	0.536482	−	0.929214i	−0.462608	−	0.886563i	$-0.653086\pi$
$269$	8.79895	−	15.2402i	0.536482	−	0.929214i	0.999090	−	0.0426509i	$-0.0135803\pi$
$270$		0			0
$271$	−9.12436	+	5.26795i	−0.554265	+	0.320005i	−0.750840	−	0.660484i	$-0.770351\pi$
$271$	−9.12436	+	5.26795i	−0.554265	+	0.320005i	0.196575	+	0.980489i	$0.437018\pi$
$272$			4.49938i			0.272815i
$273$		0			0
$274$	−8.62158			−0.520849
$275$		0			0
$276$		0			0
$277$	−2.61489	−	1.50971i	−0.157114	−	0.0907097i	0.419382	−	0.907810i	$-0.362247\pi$
$277$	−2.61489	−	1.50971i	−0.157114	−	0.0907097i	−0.576496	+	0.817100i	$0.695580\pi$
$278$	8.87780	−	5.12560i	0.532455	−	0.307413i
$279$		0			0
$280$		0			0
$281$			10.6880i			0.637591i	0.947824	+	0.318795i	$0.103278\pi$
$281$			10.6880i			0.637591i	−0.947824	+	0.318795i	$0.896722\pi$
$282$		0			0
$283$	−8.78434	+	15.2149i	−0.522175	+	0.904434i	0.477492	+	0.878636i	$0.341546\pi$
$283$	−8.78434	+	15.2149i	−0.522175	+	0.904434i	−0.999667	+	0.0257976i	$0.991787\pi$
$284$	−4.12460	−	2.38134i	−0.244750	−	0.141307i
$285$		0			0
$286$			13.5851i			0.803301i
$287$	0.144049	+	2.00634i	0.00850295	+	0.118431i
$288$		0			0
$289$	1.62220	+	2.80973i	0.0954235	+	0.165278i
$290$		0			0
$291$		0			0
$292$	5.82843	+	10.0951i	0.341083	+	0.590773i
$293$		−	14.6710i		−	0.857086i	−0.903521	−	0.428543i	$-0.859027\pi$
$293$		−	14.6710i		−	0.857086i	0.903521	−	0.428543i	$-0.140973\pi$
$294$		0			0
$295$		0			0
$296$	−5.64444	+	3.25882i	−0.328076	+	0.189415i
$297$		0			0
$298$	7.96640	+	4.59940i	0.461481	+	0.266436i
$299$	−0.337300	−	0.584220i	−0.0195065	−	0.0337863i
$300$		0			0
$301$	15.4741	−	1.11099i	0.891911	−	0.0640363i
$302$	−12.7486			−0.733599
$303$		0			0
$304$	−2.48004	−	1.43185i	−0.142240	−	0.0821223i
$305$		0			0
$306$		0			0
$307$	−21.2772			−1.21435			−0.607177	−	0.794567i	$-0.707698\pi$
$307$	−21.2772			−1.21435			−0.607177	+	0.794567i	$0.707698\pi$
$308$	8.00524	+	11.8208i	0.456141	+	0.673550i
$309$		0			0
$310$		0			0
$311$	5.91724	−	10.2490i	0.335536	−	0.581165i	−0.648052	−	0.761596i	$-0.724416\pi$
$311$	5.91724	−	10.2490i	0.335536	−	0.581165i	0.983588	+	0.180431i	$0.0577493\pi$
$312$		0			0
$313$	2.25485	+	3.90551i	0.127452	+	0.220753i	0.922689	−	0.385546i	$-0.125987\pi$
$313$	2.25485	+	3.90551i	0.127452	+	0.220753i	−0.795237	+	0.606299i	$0.792654\pi$
$314$	13.8447			0.781302
$315$		0			0
$316$	−8.59235			−0.483358
$317$	9.19151	+	15.9202i	0.516247	+	0.894165i	0.999822	+	0.0188626i	$0.00600451\pi$
$317$	9.19151	+	15.9202i	0.516247	+	0.894165i	−0.483576	+	0.875303i	$0.660662\pi$
$318$		0			0
$319$	24.0092	−	41.5852i	1.34426	−	2.32833i
$320$		0			0
$321$		0			0
$322$	−0.637756	−	0.309587i	−0.0355408	−	0.0172526i
$323$	−12.8849			−0.716934
$324$		0			0
$325$		0			0
$326$	−17.8444	−	10.3025i	−0.988313	−	0.570603i
$327$		0			0
$328$	−0.760279			−0.0419794
$329$	−11.8616	−	17.5152i	−0.653952	−	0.965644i
$330$		0			0
$331$	−3.98066	−	6.89471i	−0.218797	−	0.378967i	0.735643	−	0.677369i	$-0.236880\pi$
$331$	−3.98066	−	6.89471i	−0.218797	−	0.378967i	−0.954440	+	0.298401i	$0.903547\pi$
$332$	−8.18394	−	4.72500i	−0.449152	−	0.259318i
$333$		0			0
$334$	−5.93193	+	3.42480i	−0.324581	+	0.187397i
$335$		0			0
$336$		0			0
$337$		−	6.89417i		−	0.375549i	−0.982212	−	0.187775i	$-0.939873\pi$
$337$		−	6.89417i		−	0.375549i	0.982212	−	0.187775i	$-0.0601275\pi$
$338$	3.33075	+	5.76903i	0.181169	+	0.313794i
$339$		0			0
$340$		0			0
$341$	13.0270	+	22.5634i	0.705451	+	1.22188i
$342$		0			0
$343$	3.95164	+	18.0938i	0.213368	+	0.976972i
$344$			5.86370i			0.316150i
$345$		0			0
$346$	−11.0488	−	6.37902i	−0.593986	−	0.342938i
$347$	−8.17789	+	14.1645i	−0.439012	+	0.760392i	−0.997614	−	0.0690448i	$-0.978005\pi$
$347$	−8.17789	+	14.1645i	−0.439012	+	0.760392i	0.558601	+	0.829436i	$0.311338\pi$
$348$		0			0
$349$			24.5851i			1.31601i	0.753014	+	0.658004i	$0.228599\pi$
$349$			24.5851i			1.31601i	−0.753014	+	0.658004i	$0.771401\pi$
$350$		0			0
$351$		0			0
$352$	−4.67303	+	2.69798i	−0.249073	+	0.143803i
$353$	11.8802	+	6.85906i	0.632321	+	0.365071i	0.781651	−	0.623717i	$-0.214378\pi$
$353$	11.8802	+	6.85906i	0.632321	+	0.365071i	−0.149329	+	0.988788i	$0.547711\pi$
$354$		0			0
$355$		0			0
$356$	7.97005			0.422412
$357$		0			0
$358$			18.8666i			0.997132i
$359$	−10.3059	+	5.95011i	−0.543924	+	0.314035i	−0.746668	−	0.665197i	$-0.768348\pi$
$359$	−10.3059	+	5.95011i	−0.543924	+	0.314035i	0.202744	+	0.979232i	$0.435014\pi$
$360$		0			0
$361$	−5.39960	+	9.35238i	−0.284190	+	0.492231i
$362$	−22.1268	+	12.7749i	−1.16296	+	0.671433i
$363$		0			0
$364$	−5.99233	−	2.90887i	−0.314083	−	0.152466i
$365$		0			0
$366$		0			0
$367$	6.29461	−	10.9026i	0.328576	−	0.569110i	−0.653654	−	0.756794i	$-0.726765\pi$
$367$	6.29461	−	10.9026i	0.328576	−	0.569110i	0.982230	+	0.187684i	$0.0600980\pi$
$368$	0.133975	−	0.232051i	0.00698391	−	0.0120965i
$369$		0			0
$370$		0			0
$371$	−19.9893	−	9.70342i	−1.03779	−	0.503776i
$372$		0			0
$373$	23.5331	−	13.5868i	1.21850	−	0.703499i	0.253900	−	0.967230i	$-0.418286\pi$
$373$	23.5331	−	13.5868i	1.21850	−	0.703499i	0.964596	+	0.263731i	$0.0849531\pi$
$374$	−12.1392	+	21.0257i	−0.627704	+	1.08722i
$375$		0			0
$376$	6.92418	−	3.99768i	0.357087	−	0.206164i
$377$			22.4044i			1.15389i
$378$		0			0
$379$	−15.7335			−0.808174			−0.404087	−	0.914721i	$-0.632411\pi$
$379$	−15.7335			−0.808174			−0.404087	+	0.914721i	$0.632411\pi$
$380$		0			0
$381$		0			0
$382$	−7.00657	−	4.04524i	−0.358487	−	0.206973i
$383$	13.6669	−	7.89060i	0.698347	−	0.403191i	−0.108384	−	0.994109i	$-0.534568\pi$
$383$	13.6669	−	7.89060i	0.698347	−	0.403191i	0.806732	+	0.590918i	$0.201234\pi$
$384$		0			0
$385$		0			0
$386$			14.1270i			0.719046i
$387$		0			0
$388$	−3.08176	+	5.33777i	−0.156453	+	0.270984i
$389$	−13.7556	−	7.94182i	−0.697438	−	0.402666i	0.108954	−	0.994047i	$-0.465250\pi$
$389$	−13.7556	−	7.94182i	−0.697438	−	0.402666i	−0.806393	+	0.591381i	$0.798583\pi$
$390$		0			0
$391$		−	1.20560i		−	0.0609700i
$392$	−6.92820	+	1.00000i	−0.349927	+	0.0505076i
$393$		0			0
$394$	7.13689	+	12.3615i	0.359552	+	0.622762i
$395$		0			0
$396$		0			0
$397$	18.6806	+	32.3557i	0.937550	+	1.62388i	0.770022	+	0.638017i	$0.220245\pi$
$397$	18.6806	+	32.3557i	0.937550	+	1.62388i	0.167528	+	0.985867i	$0.446422\pi$
$398$			3.54195i			0.177542i
$399$		0			0
$400$		0			0
$401$	−24.4856	+	14.1368i	−1.22275	+	0.705957i	−0.965504	−	0.260389i	$-0.916149\pi$
$401$	−24.4856	+	14.1368i	−1.22275	+	0.705957i	−0.257249	+	0.966345i	$0.582816\pi$
$402$		0			0
$403$	−10.5276	−	6.07812i	−0.524417	−	0.302773i
$404$	7.02458	+	12.1669i	0.349486	+	0.605327i
$405$		0			0
$406$	13.2022	+	19.4947i	0.655214	+	0.967507i
$407$	−35.1689			−1.74326
$408$		0			0
$409$	−13.8647	−	8.00481i	−0.685567	−	0.395812i	0.116382	−	0.993204i	$-0.462870\pi$
$409$	−13.8647	−	8.00481i	−0.685567	−	0.395812i	−0.801949	+	0.597392i	$0.796204\pi$
$410$		0			0
$411$		0			0
$412$	14.1769			0.698446
$413$	−30.1599	−	14.6405i	−1.48407	−	0.720414i
$414$		0			0
$415$		0			0
$416$	1.25882	−	2.18034i	0.0617187	−	0.106900i
$417$		0			0
$418$	−7.72620	−	13.3822i	−0.377901	−	0.654544i
$419$	29.5137			1.44184			0.720919	−	0.693020i	$-0.243720\pi$
$419$	29.5137			1.44184			0.720919	+	0.693020i	$0.243720\pi$
$420$		0			0
$421$	0.309114			0.0150653			0.00753265	−	0.999972i	$-0.497602\pi$
$421$	0.309114			0.0150653			0.00753265	+	0.999972i	$0.497602\pi$
$422$	1.96170	+	3.39776i	0.0954939	+	0.165400i
$423$		0			0
$424$	4.19918	−	7.27319i	0.203930	−	0.353217i
$425$		0			0
$426$		0			0
$427$	3.88928	+	5.74301i	0.188215	+	0.277924i
$428$	−1.64173			−0.0793559
$429$		0			0
$430$		0			0
$431$	−7.63843	−	4.41005i	−0.367930	−	0.212425i	0.304624	−	0.952473i	$-0.401469\pi$
$431$	−7.63843	−	4.41005i	−0.367930	−	0.212425i	−0.672554	+	0.740048i	$0.734803\pi$
$432$		0			0
$433$	9.56388			0.459611			0.229805	−	0.973237i	$-0.426191\pi$
$433$	9.56388			0.459611			0.229805	+	0.973237i	$0.426191\pi$
$434$	−12.7420	+	0.914836i	−0.611636	+	0.0439135i
$435$		0			0
$436$	−9.94887	−	17.2319i	−0.476464	−	0.825260i
$437$	0.664525	+	0.383663i	0.0317885	+	0.0183531i
$438$		0			0
$439$	31.3336	−	18.0905i	1.49547	−	0.863412i	0.495487	−	0.868615i	$-0.334990\pi$
$439$	31.3336	−	18.0905i	1.49547	−	0.863412i	0.999986	+	0.00520362i	$0.00165637\pi$
$440$		0			0
$441$		0			0
$442$		−	11.3278i		−	0.538809i
$443$	−2.04284	−	3.53830i	−0.0970582	−	0.168110i	0.813408	−	0.581694i	$-0.197610\pi$
$443$	−2.04284	−	3.53830i	−0.0970582	−	0.168110i	−0.910466	+	0.413584i	$0.864277\pi$
$444$		0			0
$445$		0			0
$446$	7.34519	+	12.7222i	0.347805	+	0.602415i
$447$		0			0
$448$	−0.189469	−	2.63896i	−0.00895155	−	0.124679i
$449$			19.9377i			0.940918i	0.882422	+	0.470459i	$0.155912\pi$
$449$			19.9377i			0.940918i	−0.882422	+	0.470459i	$0.844088\pi$
$450$		0			0
$451$	−3.55281	−	2.05121i	−0.167295	−	0.0965879i
$452$	2.97934	−	5.16036i	0.140136	−	0.242723i
$453$		0			0
$454$		−	22.7826i		−	1.06924i
$455$		0			0
$456$		0			0
$457$	−17.4283	+	10.0623i	−0.815264	+	0.470693i	−0.848780	−	0.528745i	$-0.822663\pi$
$457$	−17.4283	+	10.0623i	−0.815264	+	0.470693i	0.0335168	+	0.999438i	$0.489329\pi$
$458$	−17.5089	−	10.1087i	−0.818136	−	0.472351i
$459$		0			0
$460$		0			0
$461$	0.909299			0.0423503			0.0211751	−	0.999776i	$-0.493259\pi$
$461$	0.909299			0.0423503			0.0211751	+	0.999776i	$0.493259\pi$
$462$		0			0
$463$		−	21.4280i		−	0.995843i	−0.867222	−	0.497922i	$-0.834097\pi$
$463$		−	21.4280i		−	0.995843i	0.867222	−	0.497922i	$-0.165903\pi$
$464$	−7.70674	+	4.44949i	−0.357777	+	0.206562i
$465$		0			0
$466$	1.31543	−	2.27840i	0.0609363	−	0.105545i
$467$	−10.9917	+	6.34607i	−0.508636	+	0.293661i	−0.732273	−	0.681012i	$-0.761540\pi$
$467$	−10.9917	+	6.34607i	−0.508636	+	0.293661i	0.223637	+	0.974672i	$0.428207\pi$
$468$		0			0
$469$	−11.3487	+	23.3786i	−0.524035	+	1.07952i
$470$		0			0
$471$		0			0
$472$	6.33573	−	10.9738i	0.291626	−	0.505111i
$473$	−15.8201	+	27.4013i	−0.727411	+	1.25991i
$474$		0			0
$475$		0			0
$476$	−6.67511	−	9.85666i	−0.305953	−	0.451779i
$477$		0			0
$478$	−14.6155	+	8.43828i	−0.668499	+	0.385958i
$479$	6.43828	−	11.1514i	0.294172	−	0.509522i	−0.680620	−	0.732637i	$-0.738289\pi$
$479$	6.43828	−	11.1514i	0.294172	−	0.509522i	0.974792	+	0.223115i	$0.0716227\pi$
$480$		0			0
$481$	14.2107	−	8.20453i	0.647950	−	0.374094i
$482$			14.5254i			0.661612i
$483$		0			0
$484$	−18.1163			−0.823469
$485$		0			0
$486$		0			0
$487$	18.0301	+	10.4097i	0.817022	+	0.471708i	0.849388	−	0.527768i	$-0.176971\pi$
$487$	18.0301	+	10.4097i	0.817022	+	0.471708i	−0.0323665	+	0.999476i	$0.510304\pi$
$488$	−2.27035	+	1.31079i	−0.102774	+	0.0593366i
$489$		0			0
$490$		0			0
$491$		−	27.3271i		−	1.23325i	−0.787256	−	0.616627i	$-0.788499\pi$
$491$		−	27.3271i		−	1.23325i	0.787256	−	0.616627i	$-0.211501\pi$
$492$		0			0
$493$	−20.0199	+	34.6755i	−0.901653	+	1.56171i
$494$	6.24384	+	3.60488i	0.280924	+	0.162191i
$495$		0			0
$496$		−	4.82843i		−	0.216803i
$497$	12.5685	−	0.902379i	0.563775	−	0.0404772i
$498$		0			0
$499$	16.6802	+	28.8909i	0.746708	+	1.29334i	0.949393	+	0.314092i	$0.101700\pi$
$499$	16.6802	+	28.8909i	0.746708	+	1.29334i	−0.202685	+	0.979244i	$0.564967\pi$
$500$		0			0
$501$		0			0
$502$	7.86214	+	13.6176i	0.350904	+	0.607784i
$503$		−	16.2936i		−	0.726494i	−0.931693	−	0.363247i	$-0.881668\pi$
$503$		−	16.2936i		−	0.726494i	0.931693	−	0.363247i	$-0.118332\pi$
$504$		0			0
$505$		0			0
$506$	1.25214	−	0.722921i	0.0556642	−	0.0321377i
$507$		0			0
$508$	12.5663	+	7.25517i	0.557540	+	0.321896i
$509$	12.3400	+	21.3735i	0.546961	+	0.947365i	0.998481	+	0.0551036i	$0.0175489\pi$
$509$	12.3400	+	21.3735i	0.546961	+	0.947365i	−0.451519	+	0.892261i	$0.649118\pi$
$510$		0			0
$511$	−27.7449	−	13.4683i	−1.22736	−	0.595801i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−17.0275	−	9.83083i	−0.751051	−	0.433619i
$515$		0			0
$516$		0			0
$517$	43.1426			1.89741
$518$	7.53044	−	15.5129i	0.330869	−	0.681597i
$519$		0			0
$520$		0			0
$521$	−0.141663	+	0.245367i	−0.00620635	+	0.0107497i	−0.869112	−	0.494616i	$-0.835309\pi$
$521$	−0.141663	+	0.245367i	−0.00620635	+	0.0107497i	0.862906	+	0.505365i	$0.168642\pi$
$522$		0			0
$523$	5.64083	+	9.77021i	0.246656	+	0.427222i	0.962596	−	0.270941i	$-0.0873347\pi$
$523$	5.64083	+	9.77021i	0.246656	+	0.427222i	−0.715940	+	0.698162i	$0.754001\pi$
$524$	15.4665			0.675657
$525$		0			0
$526$	−4.32175			−0.188437
$527$	−10.8625	−	18.8143i	−0.473176	−	0.819565i
$528$		0			0
$529$	11.4641	−	19.8564i	0.498439	−	0.863322i
$530$		0			0
$531$		0			0
$532$	7.55719	−	0.542582i	0.327646	−	0.0235239i
$533$	1.91411			0.0829092
$534$		0			0
$535$		0			0
$536$	−8.50643	−	4.91119i	−0.367422	−	0.212131i
$537$		0			0
$538$	−17.5979			−0.758700
$539$	−35.0737	−	14.0191i	−1.51073	−	0.603845i
$540$		0			0
$541$	17.4125	+	30.1593i	0.748621	+	1.29665i	0.948484	+	0.316826i	$0.102617\pi$
$541$	17.4125	+	30.1593i	0.748621	+	1.29665i	−0.199862	+	0.979824i	$0.564049\pi$
$542$	9.12436	+	5.26795i	0.391925	+	0.226278i
$543$		0			0
$544$	3.89658	−	2.24969i	0.167064	−	0.0964546i
$545$		0			0
$546$		0			0
$547$			35.4261i			1.51471i	0.653002	+	0.757356i	$0.273509\pi$
$547$			35.4261i			1.51471i	−0.653002	+	0.757356i	$0.726491\pi$
$548$	4.31079	+	7.46651i	0.184148	+	0.318953i
$549$		0			0
$550$		0			0
$551$	−12.7420	−	22.0698i	−0.542828	−	0.940206i
$552$		0			0
$553$	18.8230	−	12.7473i	0.800436	−	0.542071i
$554$			3.01942i			0.128283i
$555$		0			0
$556$	−8.87780	−	5.12560i	−0.376503	−	0.217374i
$557$	4.07093	−	7.05105i	0.172491	−	0.298763i	−0.766799	−	0.641887i	$-0.778152\pi$
$557$	4.07093	−	7.05105i	0.172491	−	0.298763i	0.939290	+	0.343124i	$0.111485\pi$
$558$		0			0
$559$		−	14.7627i		−	0.624395i
$560$		0			0
$561$		0			0
$562$	9.25605	−	5.34398i	0.390443	−	0.225422i
$563$	17.6821	+	10.2088i	0.745212	+	0.430248i	0.823961	−	0.566646i	$-0.191759\pi$
$563$	17.6821	+	10.2088i	0.745212	+	0.430248i	−0.0787491	+	0.996894i	$0.525093\pi$
$564$		0			0
$565$		0			0
$566$	17.5687			0.738467
$567$		0			0
$568$			4.76268i			0.199838i
$569$	22.5542	−	13.0217i	0.945520	−	0.545896i	0.0538334	−	0.998550i	$-0.482856\pi$
$569$	22.5542	−	13.0217i	0.945520	−	0.545896i	0.891686	+	0.452654i	$0.149523\pi$
$570$		0			0
$571$	6.18811	−	10.7181i	0.258964	−	0.448539i	−0.707000	−	0.707213i	$-0.749952\pi$
$571$	6.18811	−	10.7181i	0.258964	−	0.448539i	0.965965	+	0.258674i	$0.0832855\pi$
$572$	11.7650	−	6.79253i	0.491920	−	0.284010i
$573$		0			0
$574$	1.66552	−	1.12792i	0.0695175	−	0.0470786i
$575$		0			0
$576$		0			0
$577$	−13.4753	+	23.3399i	−0.560985	+	0.971654i	0.436426	+	0.899740i	$0.356244\pi$
$577$	−13.4753	+	23.3399i	−0.560985	+	0.971654i	−0.997411	+	0.0719139i	$0.977089\pi$
$578$	1.62220	−	2.80973i	0.0674746	−	0.116869i
$579$		0			0
$580$		0			0
$581$	24.9382	−	1.79048i	1.03461	−	0.0742816i
$582$		0			0
$583$	39.2458	−	22.6586i	1.62539	−	0.938422i
$584$	5.82843	−	10.0951i	0.241182	−	0.417740i
$585$		0			0
$586$	−12.7054	+	7.33548i	−0.524856	+	0.303026i
$587$			35.3511i			1.45910i	0.683930	+	0.729548i	$0.260269\pi$
$587$			35.3511i			1.45910i	−0.683930	+	0.729548i	$0.739731\pi$
$588$		0			0
$589$	13.8272			0.569739
$590$		0			0
$591$		0			0
$592$	5.64444	+	3.25882i	0.231985	+	0.133937i
$593$	−25.4711	+	14.7057i	−1.04597	+	0.603893i	−0.921519	−	0.388333i	$-0.873051\pi$
$593$	−25.4711	+	14.7057i	−1.04597	+	0.603893i	−0.124454	+	0.992225i	$0.539718\pi$
$594$		0			0
$595$		0			0
$596$		−	9.19881i		−	0.376798i
$597$		0			0
$598$	−0.337300	+	0.584220i	−0.0137932	+	0.0238905i
$599$	26.5494	+	15.3283i	1.08478	+	0.626298i	0.932182	−	0.361990i	$-0.117903\pi$
$599$	26.5494	+	15.3283i	1.08478	+	0.626298i	0.152598	+	0.988288i	$0.451236\pi$
$600$		0			0
$601$			34.3407i			1.40078i	0.713758	+	0.700392i	$0.246992\pi$
$601$			34.3407i			1.40078i	−0.713758	+	0.700392i	$0.753008\pi$
$602$	−8.69918	−	12.8454i	−0.354552	−	0.523541i
$603$		0			0
$604$	6.37429	+	11.0406i	0.259366	+	0.449236i
$605$		0			0
$606$		0			0
$607$	16.3087	+	28.2475i	0.661950	+	1.14653i	0.980103	+	0.198492i	$0.0636042\pi$
$607$	16.3087	+	28.2475i	0.661950	+	1.14653i	−0.318153	+	0.948040i	$0.603062\pi$
$608$			2.86370i			0.116139i
$609$		0			0
$610$		0			0
$611$	−17.4326	+	10.0647i	−0.705247	+	0.407174i
$612$		0			0
$613$	−13.8537	−	7.99843i	−0.559545	−	0.323054i	0.193418	−	0.981117i	$-0.438043\pi$
$613$	−13.8537	−	7.99843i	−0.559545	−	0.323054i	−0.752963	+	0.658063i	$0.771376\pi$
$614$	10.6386	+	18.4266i	0.429339	+	0.743636i
$615$		0			0
$616$	6.23445	−	12.8431i	0.251193	−	0.517464i
$617$	25.1429			1.01221			0.506107	−	0.862471i	$-0.331084\pi$
$617$	25.1429			1.01221			0.506107	+	0.862471i	$0.331084\pi$
$618$		0			0
$619$	−32.3379	−	18.6703i	−1.29977	−	0.750423i	−0.319406	−	0.947618i	$-0.603483\pi$
$619$	−32.3379	−	18.6703i	−1.29977	−	0.750423i	−0.980364	+	0.197195i	$0.936817\pi$
$620$		0			0
$621$		0			0
$622$	−11.8345			−0.474519
$623$	−17.4597	+	11.8241i	−0.699510	+	0.473722i
$624$		0			0
$625$		0			0
$626$	2.25485	−	3.90551i	0.0901219	−	0.156096i
$627$		0			0
$628$	−6.92236	−	11.9899i	−0.276232	−	0.478448i
$629$	29.3253			1.16928
$630$		0			0
$631$	49.5015			1.97062			0.985311	−	0.170767i	$-0.0546245\pi$
$631$	49.5015			1.97062			0.985311	+	0.170767i	$0.0546245\pi$
$632$	4.29618	+	7.44120i	0.170893	+	0.295995i
$633$		0			0
$634$	9.19151	−	15.9202i	0.365041	−	0.632270i
$635$		0			0
$636$		0			0
$637$	17.4427	−	2.51764i	0.691105	−	0.0997525i
$638$	−48.0185			−1.90107
$639$		0			0
$640$		0			0
$641$	31.4439	+	18.1542i	1.24196	+	0.717046i	0.969493	−	0.245119i	$-0.0788271\pi$
$641$	31.4439	+	18.1542i	1.24196	+	0.717046i	0.272467	+	0.962165i	$0.412160\pi$
$642$		0			0
$643$	10.2653			0.404824			0.202412	−	0.979300i	$-0.435122\pi$
$643$	10.2653			0.404824			0.202412	+	0.979300i	$0.435122\pi$
$644$	0.0507680	+	0.707107i	0.00200054	+	0.0278639i
$645$		0			0
$646$	6.44244	+	11.1586i	0.253474	+	0.439031i
$647$	18.8980	+	10.9108i	0.742956	+	0.428946i	0.823143	−	0.567834i	$-0.192218\pi$
$647$	18.8980	+	10.9108i	0.742956	+	0.428946i	−0.0801869	+	0.996780i	$0.525552\pi$
$648$		0			0
$649$	59.2142	−	34.1873i	2.32436	−	1.34197i
$650$		0			0
$651$		0			0
$652$			20.6050i			0.806954i
$653$	23.6457	+	40.9556i	0.925329	+	1.60272i	0.791032	+	0.611775i	$0.209544\pi$
$653$	23.6457	+	40.9556i	0.925329	+	1.60272i	0.134297	+	0.990941i	$0.457122\pi$
$654$		0			0
$655$		0			0
$656$	0.380139	+	0.658421i	0.0148419	+	0.0257070i
$657$		0			0
$658$	−9.23779	+	19.0301i	−0.360127	+	0.741869i
$659$			3.58255i			0.139556i	0.997563	+	0.0697782i	$0.0222291\pi$
$659$			3.58255i			0.139556i	−0.997563	+	0.0697782i	$0.977771\pi$
$660$		0			0
$661$	−1.41761	−	0.818459i	−0.0551388	−	0.0318344i	0.472177	−	0.881504i	$-0.343468\pi$
$661$	−1.41761	−	0.818459i	−0.0551388	−	0.0318344i	−0.527316	+	0.849669i	$0.676802\pi$
$662$	−3.98066	+	6.89471i	−0.154713	+	0.267970i
$663$		0			0
$664$			9.45001i			0.366731i
$665$		0			0
$666$		0			0
$667$	2.06502	−	1.19224i	0.0799577	−	0.0461636i
$668$	5.93193	+	3.42480i	0.229513	+	0.132510i
$669$		0			0
$670$		0			0
$671$	−14.1459			−0.546097
$672$		0			0
$673$			2.02242i			0.0779587i	0.999240	+	0.0389794i	$0.0124107\pi$
$673$			2.02242i			0.0779587i	−0.999240	+	0.0389794i	$0.987589\pi$
$674$	−5.97053	+	3.44709i	−0.229976	+	0.132777i
$675$		0			0
$676$	3.33075	−	5.76903i	0.128106	−	0.221886i
$677$	19.8169	−	11.4413i	0.761626	−	0.439725i	−0.0682532	−	0.997668i	$-0.521743\pi$
$677$	19.8169	−	11.4413i	0.761626	−	0.439725i	0.829879	+	0.557943i	$0.188409\pi$
$678$		0			0
$679$	−1.16780	−	16.2653i	−0.0448159	−	0.624205i
$680$		0			0
$681$		0			0
$682$	13.0270	−	22.5634i	0.498829	−	0.863997i
$683$	−15.7026	+	27.1977i	−0.600844	+	1.04069i	0.391850	+	0.920029i	$0.371835\pi$
$683$	−15.7026	+	27.1977i	−0.600844	+	1.04069i	−0.992694	+	0.120663i	$0.961498\pi$
$684$		0			0
$685$		0			0
$686$	13.6938	−	12.4691i	0.522834	−	0.476073i
$687$		0			0
$688$	5.07812	−	2.93185i	0.193601	−	0.111776i
$689$	−10.5720	+	18.3113i	−0.402762	+	0.697604i
$690$		0			0
$691$	29.3677	−	16.9554i	1.11720	−	0.645015i	0.176515	−	0.984298i	$-0.443518\pi$
$691$	29.3677	−	16.9554i	1.11720	−	0.645015i	0.940684	+	0.339283i	$0.110184\pi$
$692$			12.7580i			0.484988i
$693$		0			0
$694$	16.3558			0.620857
$695$		0			0
$696$		0			0
$697$	2.96248	+	1.71039i	0.112212	+	0.0647857i
$698$	21.2913	−	12.2925i	0.805887	−	0.465279i
$699$		0			0
$700$		0			0
$701$			10.5296i			0.397699i	0.980030	+	0.198849i	$0.0637205\pi$
$701$			10.5296i			0.397699i	−0.980030	+	0.198849i	$0.936280\pi$
$702$		0			0
$703$	−9.33229	+	16.1640i	−0.351974	+	0.609637i
$704$	4.67303	+	2.69798i	0.176122	+	0.101684i
$705$		0			0
$706$		−	13.7181i		−	0.516288i
$707$	−33.4390	−	16.2323i	−1.25760	−	0.610479i
$708$		0			0
$709$	7.52572	+	13.0349i	0.282634	+	0.489537i	0.972033	−	0.234845i	$-0.0754584\pi$
$709$	7.52572	+	13.0349i	0.282634	+	0.489537i	−0.689398	+	0.724382i	$0.742125\pi$
$710$		0			0
$711$		0			0
$712$	−3.98502	−	6.90226i	−0.149345	−	0.258673i
$713$			1.29377i			0.0484522i
$714$		0			0
$715$		0			0
$716$	16.3390	−	9.43331i	0.610616	−	0.352539i
$717$		0			0
$718$	10.3059	+	5.95011i	0.384613	+	0.222056i
$719$	12.2137	+	21.1547i	0.455494	+	0.788938i	0.998716	−	0.0506506i	$-0.0161295\pi$
$719$	12.2137	+	21.1547i	0.455494	+	0.788938i	−0.543223	+	0.839589i	$0.682796\pi$
$720$		0			0
$721$	−31.0569	+	21.0323i	−1.15662	+	0.783285i
$722$	10.7992			0.401905
$723$		0			0
$724$	22.1268	+	12.7749i	0.822335	+	0.474775i
$725$		0			0
$726$		0			0
$727$	−43.7349			−1.62204			−0.811019	−	0.585020i	$-0.801087\pi$
$727$	−43.7349			−1.62204			−0.811019	+	0.585020i	$0.801087\pi$
$728$	0.477014	+	6.64394i	0.0176793	+	0.246241i
$729$		0			0
$730$		0			0
$731$	13.1915	−	22.8484i	0.487906	−	0.845077i
$732$		0			0
$733$	−22.3596	−	38.7280i	−0.825872	−	1.43045i	−0.901251	−	0.433297i	$-0.857350\pi$
$733$	−22.3596	−	38.7280i	−0.825872	−	1.43045i	0.0753789	−	0.997155i	$-0.475983\pi$
$734$	−12.5892			−0.464677
$735$		0			0
$736$	−0.267949			−0.00987674
$737$	−26.5005	−	45.9003i	−0.976160	−	1.69076i
$738$		0			0
$739$	−10.7360	+	18.5954i	−0.394932	+	0.684042i	−0.993092	−	0.117334i	$-0.962565\pi$
$739$	−10.7360	+	18.5954i	−0.394932	+	0.684042i	0.598161	+	0.801376i	$0.295898\pi$
$740$		0			0
$741$		0			0
$742$	1.59123	+	22.1629i	0.0584157	+	0.813626i
$743$	29.5637			1.08459			0.542293	−	0.840190i	$-0.317556\pi$
$743$	29.5637			1.08459			0.542293	+	0.840190i	$0.317556\pi$
$744$		0			0
$745$		0			0
$746$	−23.5331	−	13.5868i	−0.861607	−	0.497449i
$747$		0			0
$748$	24.2784			0.887707
$749$	3.59648	−	2.43561i	0.131413	−	0.0889951i
$750$		0			0
$751$	−0.596750	−	1.03360i	−0.0217757	−	0.0377166i	0.854932	−	0.518740i	$-0.173599\pi$
$751$	−0.596750	−	1.03360i	−0.0217757	−	0.0377166i	−0.876708	+	0.481023i	$0.840265\pi$
$752$	−6.92418	−	3.99768i	−0.252499	−	0.145780i
$753$		0			0
$754$	19.4028	−	11.2022i	0.706608	−	0.407960i
$755$		0			0
$756$		0			0
$757$		−	26.8915i		−	0.977386i	−0.872456	−	0.488693i	$-0.837474\pi$
$757$		−	26.8915i		−	0.977386i	0.872456	−	0.488693i	$-0.162526\pi$
$758$	7.86673	+	13.6256i	0.285732	+	0.494903i
$759$		0			0
$760$		0			0
$761$	0.939574	+	1.62739i	0.0340595	+	0.0589928i	0.882553	−	0.470213i	$-0.155823\pi$
$761$	0.939574	+	1.62739i	0.0340595	+	0.0589928i	−0.848493	+	0.529206i	$0.822490\pi$
$762$		0			0
$763$	47.3594	+	22.9897i	1.71452	+	0.832284i
$764$			8.09049i			0.292704i
$765$		0			0
$766$	−13.6669	−	7.89060i	−0.493806	−	0.285099i
$767$	−15.9511	+	27.6281i	−0.575960	+	0.997592i
$768$		0			0
$769$		−	50.6544i		−	1.82664i	−0.407239	−	0.913322i	$-0.633508\pi$
$769$		−	50.6544i		−	1.82664i	0.407239	−	0.913322i	$-0.366492\pi$
$770$		0			0
$771$		0			0
$772$	12.2343	−	7.06350i	0.440324	−	0.254221i
$773$	−42.1499	−	24.3353i	−1.51603	−	0.875279i	−0.999823	−	0.0188128i	$-0.994011\pi$
$773$	−42.1499	−	24.3353i	−1.51603	−	0.875279i	−0.516204	−	0.856466i	$-0.672655\pi$
$774$		0			0
$775$		0			0
$776$	6.16353			0.221258
$777$		0			0
$778$			15.8836i			0.569456i
$779$	−1.88552	+	1.08861i	−0.0675558	+	0.0390034i
$780$		0			0
$781$	−12.8496	+	22.2562i	−0.459795	+	0.796388i
$782$	−1.04408	+	0.602802i	−0.0373364	+	0.0215562i
$783$		0			0
$784$	4.33013	+	5.50000i	0.154647	+	0.196429i
$785$		0			0
$786$		0			0
$787$	7.47307	−	12.9437i	0.266386	−	0.461395i	−0.701540	−	0.712630i	$-0.747504\pi$
$787$	7.47307	−	12.9437i	0.266386	−	0.461395i	0.967926	+	0.251236i	$0.0808370\pi$
$788$	7.13689	−	12.3615i	0.254241	−	0.440359i
$789$		0			0
$790$		0			0
$791$	1.12898	+	15.7247i	0.0401420	+	0.559105i
$792$		0			0
$793$	5.71593	−	3.30009i	0.202979	−	0.117190i
$794$	18.6806	−	32.3557i	0.662948	−	1.14826i
$795$		0			0
$796$	3.06742	−	1.77098i	0.108722	−	0.0627706i
$797$			15.0557i			0.533301i	0.963793	+	0.266650i	$0.0859169\pi$
$797$			15.0557i			0.533301i	−0.963793	+	0.266650i	$0.914083\pi$
$798$		0			0
$799$	−35.9741			−1.27267
$800$		0			0
$801$		0			0
$802$	24.4856	+	14.1368i	0.864617	+	0.499187i
$803$	54.4729	−	31.4499i	1.92231	−	1.10984i
$804$		0			0
$805$		0			0
$806$			12.1562i			0.428185i
$807$		0			0
$808$	7.02458	−	12.1669i	0.247124	−	0.428031i
$809$	30.7426	+	17.7493i	1.08085	+	0.624031i	0.931127	−	0.364696i	$-0.118827\pi$
$809$	30.7426	+	17.7493i	1.08085	+	0.624031i	0.149727	+	0.988727i	$0.452160\pi$
$810$		0			0
$811$		−	24.5935i		−	0.863594i	−0.901971	−	0.431797i	$-0.857880\pi$
$811$		−	24.5935i		−	0.863594i	0.901971	−	0.431797i	$-0.142120\pi$
$812$	10.2818	−	21.1808i	0.360822	−	0.743301i
$813$		0			0
$814$	17.5844	+	30.4571i	0.616334	+	1.06752i
$815$		0			0
$816$		0			0
$817$	8.39595	+	14.5422i	0.293737	+	0.508768i
$818$			16.0096i			0.559763i
$819$		0			0
$820$		0			0
$821$	12.3035	−	7.10342i	0.429395	−	0.247911i	−0.269694	−	0.962946i	$-0.586923\pi$
$821$	12.3035	−	7.10342i	0.429395	−	0.247911i	0.699089	+	0.715035i	$0.253589\pi$
$822$		0			0
$823$	1.63780	+	0.945584i	0.0570901	+	0.0329610i	0.528273	−	0.849074i	$-0.322840\pi$
$823$	1.63780	+	0.945584i	0.0570901	+	0.0329610i	−0.471183	+	0.882035i	$0.656173\pi$
$824$	−7.08845	−	12.2776i	−0.246938	−	0.427709i
$825$		0			0
$826$	2.40085	+	33.4395i	0.0835361	+	1.16351i
$827$	−31.9280			−1.11024			−0.555122	−	0.831769i	$-0.687329\pi$
$827$	−31.9280			−1.11024			−0.555122	+	0.831769i	$0.687329\pi$
$828$		0			0
$829$	−3.38864	−	1.95643i	−0.117692	−	0.0679497i	0.439998	−	0.897999i	$-0.354979\pi$
$829$	−3.38864	−	1.95643i	−0.117692	−	0.0679497i	−0.557691	+	0.830049i	$0.688312\pi$
$830$		0			0
$831$		0			0
$832$	−2.51764			−0.0872834
$833$	29.2460	+	11.6897i	1.01331	+	0.405025i
$834$		0			0
$835$		0			0
$836$	−7.72620	+	13.3822i	−0.267216	+	0.462832i
$837$		0			0
$838$	−14.7568	−	25.5596i	−0.509766	−	0.882941i
$839$	−15.3513			−0.529984			−0.264992	−	0.964251i	$-0.585369\pi$
$839$	−15.3513			−0.529984			−0.264992	+	0.964251i	$0.585369\pi$
$840$		0			0
$841$	−50.1918			−1.73075
$842$	−0.154557	−	0.267701i	−0.00532639	−	0.00922557i
$843$		0			0
$844$	1.96170	−	3.39776i	0.0675244	−	0.116956i
$845$		0			0
$846$		0			0
$847$	39.6869	−	26.8767i	1.36366	−	0.923495i
$848$	−8.39836			−0.288401
$849$		0			0
$850$		0			0
$851$	−1.51242	−	0.873198i	−0.0518452	−	0.0299328i
$852$		0			0
$853$	−22.2302			−0.761148			−0.380574	−	0.924750i	$-0.624274\pi$
$853$	−22.2302			−0.761148			−0.380574	+	0.924750i	$0.624274\pi$
$854$	3.02896	−	6.23972i	0.103649	−	0.213519i
$855$		0			0
$856$	0.820863	+	1.42178i	0.0280565	+	0.0485953i
$857$	−45.7432	−	26.4098i	−1.56256	−	0.902143i	−0.996997	−	0.0774356i	$-0.975327\pi$
$857$	−45.7432	−	26.4098i	−1.56256	−	0.902143i	−0.565560	−	0.824707i	$-0.691340\pi$
$858$		0			0
$859$	15.2916	−	8.82859i	0.521742	−	0.301228i	−0.215905	−	0.976414i	$-0.569270\pi$
$859$	15.2916	−	8.82859i	0.521742	−	0.301228i	0.737647	+	0.675187i	$0.235937\pi$
$860$		0			0
$861$		0			0
$862$			8.82010i			0.300414i
$863$	−8.22446	−	14.2452i	−0.279964	−	0.484912i	0.691412	−	0.722461i	$-0.256989\pi$
$863$	−8.22446	−	14.2452i	−0.279964	−	0.484912i	−0.971375	+	0.237549i	$0.923656\pi$
$864$		0			0
$865$		0			0
$866$	−4.78194	−	8.28256i	−0.162497	−	0.281453i
$867$		0			0
$868$	7.16328	+	10.5775i	0.243138	+	0.359024i
$869$			46.3639i			1.57279i
$870$		0			0
$871$	21.4161	+	12.3646i	0.725657	+	0.418958i
$872$	−9.94887	+	17.2319i	−0.336911	+	0.583547i
$873$		0			0
$874$		−	0.767327i		−	0.0259552i
$875$		0			0
$876$		0			0
$877$	46.9521	−	27.1078i	1.58546	−	0.915366i	0.591418	−	0.806365i	$-0.298568\pi$
$877$	46.9521	−	27.1078i	1.58546	−	0.915366i	0.994042	−	0.109001i	$-0.0347652\pi$
$878$	−31.3336	−	18.0905i	−1.05746	−	0.610524i
$879$		0			0
$880$		0			0
$881$	50.1647			1.69009			0.845046	−	0.534694i	$-0.179573\pi$
$881$	50.1647			1.69009			0.845046	+	0.534694i	$0.179573\pi$
$882$		0			0
$883$			0.841563i			0.0283208i	0.999900	+	0.0141604i	$0.00450755\pi$
$883$			0.841563i			0.0283208i	−0.999900	+	0.0141604i	$0.995492\pi$
$884$	−9.81017	+	5.66390i	−0.329952	+	0.190498i
$885$		0			0
$886$	−2.04284	+	3.53830i	−0.0686305	+	0.118872i
$887$	−34.7262	+	20.0492i	−1.16599	+	0.673185i	−0.952732	−	0.303811i	$-0.901741\pi$
$887$	−34.7262	+	20.0492i	−1.16599	+	0.673185i	−0.213258	+	0.976996i	$0.568408\pi$
$888$		0			0
$889$	−38.2922	+	2.74926i	−1.28428	+	0.0922071i
$890$		0			0
$891$		0			0
$892$	7.34519	−	12.7222i	0.245935	−	0.425972i
$893$	11.4482	−	19.8288i	0.383098	−	0.663546i
$894$		0			0
$895$		0			0
$896$	−2.19067	+	1.48356i	−0.0731852	+	0.0495624i
$897$		0			0
$898$	17.2665	−	9.96885i	0.576192	−	0.332665i
$899$	21.4840	−	37.2114i	0.716533	−	1.24107i
$900$		0			0
$901$	−32.7248	+	18.8937i	−1.09022	+	0.629440i
$902$			4.10243i			0.136596i
$903$		0			0
$904$	−5.95867			−0.198182
$905$		0			0
$906$		0			0
$907$	39.1348	+	22.5945i	1.29945	+	0.750238i	0.980309	−	0.197469i	$-0.0632720\pi$
$907$	39.1348	+	22.5945i	1.29945	+	0.750238i	0.319142	+	0.947707i	$0.396605\pi$
$908$	−19.7303	+	11.3913i	−0.654774	+	0.378034i
$909$		0			0
$910$		0			0
$911$		−	58.2281i		−	1.92918i	−0.263746	−	0.964592i	$-0.584958\pi$
$911$		−	58.2281i		−	1.92918i	0.263746	−	0.964592i	$-0.415042\pi$
$912$		0			0
$913$	−25.4959	+	44.1602i	−0.843791	+	1.46149i
$914$	17.4283	+	10.0623i	0.576478	+	0.332830i
$915$		0			0
$916$			20.2175i			0.668005i
$917$	−33.8820	+	22.9455i	−1.11888	+	0.757729i
$918$		0			0
$919$	6.61745	+	11.4618i	0.218290	+	0.378089i	0.954285	−	0.298898i	$-0.0966190\pi$
$919$	6.61745	+	11.4618i	0.218290	+	0.378089i	−0.735996	+	0.676986i	$0.763286\pi$
$920$		0			0
$921$		0			0
$922$	−0.454649	−	0.787476i	−0.0149731	−	0.0259341i
$923$		−	11.9907i		−	0.394679i
$924$		0			0
$925$		0			0
$926$	−18.5572	+	10.7140i	−0.609827	+	0.352084i
$927$		0			0
$928$	7.70674	+	4.44949i	0.252986	+	0.146062i
$929$	10.4434	+	18.0885i	0.342637	+	0.593464i	0.984921	−	0.173002i	$-0.0553467\pi$
$929$	10.4434	+	18.0885i	0.342637	+	0.593464i	−0.642285	+	0.766466i	$0.722013\pi$
$930$		0			0
$931$	−15.7504	+	12.4002i	−0.516197	+	0.406400i
$932$	−2.63087			−0.0861769
$933$		0			0
$934$	10.9917	+	6.34607i	0.359660	+	0.207650i
$935$		0			0
$936$		0			0
$937$	23.2465			0.759430			0.379715	−	0.925103i	$-0.376022\pi$
$937$	23.2465			0.759430			0.379715	+	0.925103i	$0.376022\pi$
$938$	25.9208	−	1.86103i	0.846345	−	0.0607649i
$939$		0			0
$940$		0			0
$941$	−0.752551	+	1.30346i	−0.0245325	+	0.0424915i	−0.878031	−	0.478604i	$-0.841143\pi$
$941$	−0.752551	+	1.30346i	−0.0245325	+	0.0424915i	0.853499	+	0.521095i	$0.174476\pi$
$942$		0			0
$943$	−0.101858	−	0.176423i	−0.00331695	−	0.00574513i
$944$	−12.6715			−0.412421
$945$		0			0
$946$	31.6403			1.02871
$947$	12.1314	+	21.0122i	0.394218	+	0.682805i	0.993001	−	0.118106i	$-0.0376823\pi$
$947$	12.1314	+	21.0122i	0.394218	+	0.682805i	−0.598783	+	0.800911i	$0.704349\pi$
$948$		0			0
$949$	−14.6739	+	25.4159i	−0.476334	+	0.825035i
$950$		0			0
$951$		0			0
$952$	−5.19856	+	10.7091i	−0.168486	+	0.347085i
$953$	−56.7061			−1.83689			−0.918446	−	0.395547i	$-0.870555\pi$
$953$	−56.7061			−1.83689			−0.918446	+	0.395547i	$0.870555\pi$
$954$		0			0
$955$		0			0
$956$	14.6155	+	8.43828i	0.472700	+	0.272913i
$957$		0			0
$958$	−12.8766			−0.416023
$959$	−20.5206	−	9.96132i	−0.662643	−	0.321668i
$960$		0			0
$961$	−3.84315	−	6.65652i	−0.123972	−	0.214727i
$962$	−14.2107	−	8.20453i	−0.458170	−	0.264525i
$963$		0			0
$964$	12.5793	−	7.26268i	0.405153	−	0.233915i
$965$		0			0
$966$		0			0
$967$			7.23556i			0.232680i	0.993209	+	0.116340i	$0.0371162\pi$
$967$			7.23556i			0.232680i	−0.993209	+	0.116340i	$0.962884\pi$
$968$	9.05816	+	15.6892i	0.291140	+	0.504270i
$969$		0			0
$970$		0			0
$971$	19.3560	+	33.5256i	0.621163	+	1.07589i	0.989269	+	0.146103i	$0.0466730\pi$
$971$	19.3560	+	33.5256i	0.621163	+	1.07589i	−0.368106	+	0.929784i	$0.619994\pi$
$972$		0			0
$973$	27.0525	−	1.94228i	0.867263	−	0.0622667i
$974$		−	20.8194i		−	0.667096i
$975$		0			0
$976$	2.27035	+	1.31079i	0.0726722	+	0.0419573i
$977$	9.08052	−	15.7279i	0.290512	−	0.503181i	−0.683419	−	0.730026i	$-0.739508\pi$
$977$	9.08052	−	15.7279i	0.290512	−	0.503181i	0.973931	+	0.226845i	$0.0728412\pi$
$978$		0			0
$979$		−	43.0060i		−	1.37448i
$980$		0			0
$981$		0			0
$982$	−23.6659	+	13.6635i	−0.755211	+	0.436021i
$983$	14.2026	+	8.19988i	0.452993	+	0.261536i	0.709093	−	0.705115i	$-0.249104\pi$
$983$	14.2026	+	8.19988i	0.452993	+	0.261536i	−0.256100	+	0.966650i	$0.582438\pi$
$984$		0			0
$985$		0			0
$986$	40.0399			1.27513
$987$		0			0
$988$		−	7.20977i		−	0.229373i
$989$	−1.36068	+	0.785587i	−0.0432670	+	0.0249802i
$990$		0			0
$991$	5.44584	−	9.43247i	0.172993	−	0.299632i	−0.766472	−	0.642278i	$-0.777990\pi$
$991$	5.44584	−	9.43247i	0.172993	−	0.299632i	0.939465	+	0.342645i	$0.111323\pi$
$992$	−4.18154	+	2.41421i	−0.132764	+	0.0766514i
$993$		0			0
$994$	−7.06574	−	10.4335i	−0.224112	−	0.330930i
$995$		0			0
$996$		0			0
$997$	−17.7740	+	30.7856i	−0.562910	+	0.974988i	0.434331	+	0.900753i	$0.356985\pi$
$997$	−17.7740	+	30.7856i	−0.562910	+	0.974988i	−0.997241	+	0.0742349i	$0.976349\pi$
$998$	16.6802	−	28.8909i	0.528002	−	0.914527i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bp.c.899.2		8
3.2	odd	2		3150.2.bp.d.899.2		8
5.2	odd	4		3150.2.bf.c.1151.4		8
5.3	odd	4		630.2.be.b.521.1	yes	8
5.4	even	2		3150.2.bp.f.899.3		8
7.5	odd	6		3150.2.bp.a.1349.3		8
15.2	even	4		3150.2.bf.b.1151.2		8
15.8	even	4		630.2.be.a.521.3	yes	8
15.14	odd	2		3150.2.bp.a.899.3		8
21.5	even	6		3150.2.bp.f.1349.3		8
35.3	even	12		4410.2.b.e.881.1		8
35.12	even	12		3150.2.bf.b.1601.2		8
35.18	odd	12		4410.2.b.b.881.1		8
35.19	odd	6		3150.2.bp.d.1349.2		8
35.33	even	12		630.2.be.a.341.3	✓	8
105.38	odd	12		4410.2.b.b.881.8		8
105.47	odd	12		3150.2.bf.c.1601.4		8
105.53	even	12		4410.2.b.e.881.8		8
105.68	odd	12		630.2.be.b.341.1	yes	8
105.89	even	6	inner	3150.2.bp.c.1349.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.be.a.341.3	✓	8	35.33	even	12
630.2.be.a.521.3	yes	8	15.8	even	4
630.2.be.b.341.1	yes	8	105.68	odd	12
630.2.be.b.521.1	yes	8	5.3	odd	4
3150.2.bf.b.1151.2		8	15.2	even	4
3150.2.bf.b.1601.2		8	35.12	even	12
3150.2.bf.c.1151.4		8	5.2	odd	4
3150.2.bf.c.1601.4		8	105.47	odd	12
3150.2.bp.a.899.3		8	15.14	odd	2
3150.2.bp.a.1349.3		8	7.5	odd	6
3150.2.bp.c.899.2		8	1.1	even	1	trivial
3150.2.bp.c.1349.2		8	105.89	even	6	inner
3150.2.bp.d.899.2		8	3.2	odd	2
3150.2.bp.d.1349.2		8	35.19	odd	6
3150.2.bp.f.899.3		8	5.4	even	2
3150.2.bp.f.1349.3		8	21.5	even	6
4410.2.b.b.881.1		8	35.18	odd	12
4410.2.b.b.881.8		8	105.38	odd	12
4410.2.b.e.881.1		8	35.3	even	12
4410.2.b.e.881.8		8	105.53	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.189469 - 2.63896i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.189469 - 2.63896i) q^{7} +1.00000 q^{8} +(4.67303 + 2.69798i) q^{11} -2.51764 q^{13} +(-2.19067 + 1.48356i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.89658 - 2.24969i) q^{17} +(2.48004 - 1.43185i) q^{19} -5.39595i q^{22} +(0.133975 + 0.232051i) q^{23} +(1.25882 + 2.18034i) q^{26} +(2.38014 + 1.15539i) q^{28} -8.89898i q^{29} +(4.18154 + 2.41421i) q^{31} +(-0.500000 + 0.866025i) q^{32} +4.49938i q^{34} +(-5.64444 + 3.25882i) q^{37} +(-2.48004 - 1.43185i) q^{38} -0.760279 q^{41} +5.86370i q^{43} +(-4.67303 + 2.69798i) q^{44} +(0.133975 - 0.232051i) q^{46} +(6.92418 - 3.99768i) q^{47} +(-6.92820 + 1.00000i) q^{49} +(1.25882 - 2.18034i) q^{52} +(4.19918 - 7.27319i) q^{53} +(-0.189469 - 2.63896i) q^{56} +(-7.70674 + 4.44949i) q^{58} +(6.33573 - 10.9738i) q^{59} +(-2.27035 + 1.31079i) q^{61} -4.82843i q^{62} +1.00000 q^{64} +(-8.50643 - 4.91119i) q^{67} +(3.89658 - 2.24969i) q^{68} +4.76268i q^{71} +(5.82843 - 10.0951i) q^{73} +(5.64444 + 3.25882i) q^{74} +2.86370i q^{76} +(6.23445 - 12.8431i) q^{77} +(4.29618 + 7.44120i) q^{79} +(0.380139 + 0.658421i) q^{82} +9.45001i q^{83} +(5.07812 - 2.93185i) q^{86} +(4.67303 + 2.69798i) q^{88} +(-3.98502 - 6.90226i) q^{89} +(0.477014 + 6.64394i) q^{91} -0.267949 q^{92} +(-6.92418 - 3.99768i) q^{94} +6.16353 q^{97} +(4.33013 + 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 24 q^{11} - 16 q^{13} - 4 q^{16} - 24 q^{17} + 8 q^{23} + 8 q^{26} - 4 q^{32} + 32 q^{41} - 24 q^{44} + 8 q^{46} - 12 q^{47} + 8 q^{52} - 4 q^{53} + 24 q^{59} + 8 q^{64} - 48 q^{67} + 24 q^{68} + 24 q^{73} + 4 q^{77} + 24 q^{79} - 16 q^{82} + 24 q^{88} + 16 q^{89} - 20 q^{91} - 16 q^{92} + 12 q^{94} + 48 q^{97}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 24 * q^11 - 16 * q^13 - 4 * q^16 - 24 * q^17 + 8 * q^23 + 8 * q^26 - 4 * q^32 + 32 * q^41 - 24 * q^44 + 8 * q^46 - 12 * q^47 + 8 * q^52 - 4 * q^53 + 24 * q^59 + 8 * q^64 - 48 * q^67 + 24 * q^68 + 24 * q^73 + 4 * q^77 + 24 * q^79 - 16 * q^82 + 24 * q^88 + 16 * q^89 - 20 * q^91 - 16 * q^92 + 12 * q^94 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more