LMFDB - Embedded newform 260.2.z.a.49.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(49,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("260.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.z (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 21x^{12} - 22x^{10} - 26x^{8} - 198x^{6} + 1701x^{4} - 5103x^{2} + 6561 $ x^16 - 7x^14 + 21x^12 - 22x^10 - 26x^8 - 198x^6 + 1701x^4 - 5103*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.8
Root			$0.517063 + 1.65307i$ of defining polynomial
Character	$\chi$	$=$	260.49
Dual form			260.2.z.a.69.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.86320 - 1.65307i) q^{3} +(-0.877236 + 2.05681i) q^{5} +(0.517063 - 0.895580i) q^{7} +(3.96529 - 6.86809i) q^{9} +O(q^{10})$	\(q+(2.86320 - 1.65307i) q^{3} +(-0.877236 + 2.05681i) q^{5} +(0.517063 - 0.895580i) q^{7} +(3.96529 - 6.86809i) q^{9} +(-2.96091 + 1.70948i) q^{11} +(3.57672 + 0.455025i) q^{13} +(0.888345 + 7.33919i) q^{15} +(2.07508 + 1.19805i) q^{17} +(-5.37246 - 3.10179i) q^{19} -3.41897i q^{21} +(-6.28304 + 3.62751i) q^{23} +(-3.46091 - 3.60861i) q^{25} -16.3012i q^{27} +(0.902796 + 1.56369i) q^{29} +5.80053i q^{31} +(-5.65180 + 9.78921i) q^{33} +(1.38845 + 1.84913i) q^{35} +(-0.713520 - 1.23585i) q^{37} +(10.9931 - 4.60975i) q^{39} +(-3.60158 + 2.07937i) q^{41} +(1.86864 + 1.07886i) q^{43} +(10.6478 + 14.1808i) q^{45} +3.50894 q^{47} +(2.96529 + 5.13604i) q^{49} +7.92183 q^{51} -4.55382i q^{53} +(-0.918661 - 7.58965i) q^{55} -20.5099 q^{57} +(-5.06250 - 2.92283i) q^{59} +(-1.90280 + 3.29574i) q^{61} +(-4.10061 - 7.10247i) q^{63} +(-4.07353 + 6.95747i) q^{65} +(-3.80822 - 6.59603i) q^{67} +(-11.9931 + 20.7726i) q^{69} +(9.49745 + 5.48336i) q^{71} +7.15345 q^{73} +(-15.8746 - 4.61105i) q^{75} +3.53565i q^{77} -12.8524 q^{79} +(-15.0512 - 26.0694i) q^{81} -0.706694 q^{83} +(-4.28448 + 3.21707i) q^{85} +(5.16978 + 2.98477i) q^{87} +(5.06250 - 2.92283i) q^{89} +(2.25690 - 2.96796i) q^{91} +(9.58870 + 16.6081i) q^{93} +(11.0927 - 8.32912i) q^{95} +(7.99794 - 13.8528i) q^{97} +27.1144i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{9}+O(q^{10}) $ 16 * q + 10 * q^9	$ 16 q + 10 q^{9} - 6 q^{11} + 6 q^{15} - 18 q^{19} - 14 q^{25} + 12 q^{29} + 18 q^{39} - 48 q^{41} + 45 q^{45} - 6 q^{49} + 44 q^{51} + 2 q^{55} - 30 q^{59} - 28 q^{61} - 15 q^{65} - 34 q^{69} - 18 q^{71} - 42 q^{75} - 16 q^{79} - 44 q^{81} - 45 q^{85} + 30 q^{89} - 10 q^{91}+O(q^{100}) $ 16 * q + 10 * q^9 - 6 * q^11 + 6 * q^15 - 18 * q^19 - 14 * q^25 + 12 * q^29 + 18 * q^39 - 48 * q^41 + 45 * q^45 - 6 * q^49 + 44 * q^51 + 2 * q^55 - 30 * q^59 - 28 * q^61 - 15 * q^65 - 34 * q^69 - 18 * q^71 - 42 * q^75 - 16 * q^79 - 44 * q^81 - 45 * q^85 + 30 * q^89 - 10 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.86320	−	1.65307i	1.65307	−	0.954401i	0.677273	−	0.735732i	$-0.263162\pi$
$3$	2.86320	−	1.65307i	1.65307	−	0.954401i	0.975799	−	0.218669i	$-0.0701715\pi$
$4$		0			0
$5$	−0.877236	+	2.05681i	−0.392312	+	0.919832i
$5$	−0.877236	+	2.05681i	−0.392312	+	0.919832i
$6$		0			0
$7$	0.517063	−	0.895580i	0.195432	−	0.338497i	−0.751610	−	0.659607i	$-0.770723\pi$
$7$	0.517063	−	0.895580i	0.195432	−	0.338497i	0.947042	+	0.321110i	$0.104056\pi$
$8$		0			0
$9$	3.96529	−	6.86809i	1.32176	−	2.28936i
$10$		0			0
$11$	−2.96091	+	1.70948i	−0.892749	+	0.515429i	−0.874841	−	0.484411i	$-0.839034\pi$
$11$	−2.96091	+	1.70948i	−0.892749	+	0.515429i	−0.0179086	+	0.999840i	$0.505701\pi$
$12$		0			0
$13$	3.57672	+	0.455025i	0.992005	+	0.126201i
$13$	3.57672	+	0.455025i	0.992005	+	0.126201i
$14$		0			0
$15$	0.888345	+	7.33919i	0.229370	+	1.89497i
$16$		0			0
$17$	2.07508	+	1.19805i	0.503280	+	0.290569i	0.730067	−	0.683375i	$-0.239489\pi$
$17$	2.07508	+	1.19805i	0.503280	+	0.290569i	−0.226787	+	0.973944i	$0.572822\pi$
$18$		0			0
$19$	−5.37246	−	3.10179i	−1.23253	−	0.711600i	−0.264972	−	0.964256i	$-0.585363\pi$
$19$	−5.37246	−	3.10179i	−1.23253	−	0.711600i	−0.967556	+	0.252656i	$0.918696\pi$
$20$		0			0
$21$		−	3.41897i		−	0.746080i
$22$		0			0
$23$	−6.28304	+	3.62751i	−1.31010	+	0.756389i	−0.982113	−	0.188292i	$-0.939705\pi$
$23$	−6.28304	+	3.62751i	−1.31010	+	0.756389i	−0.327991	+	0.944681i	$0.606371\pi$
$24$		0			0
$25$	−3.46091	−	3.60861i	−0.692183	−	0.721722i
$26$		0			0
$27$		−	16.3012i		−	3.13717i
$28$		0			0
$29$	0.902796	+	1.56369i	0.167645	+	0.290370i	0.937591	−	0.347739i	$-0.113050\pi$
$29$	0.902796	+	1.56369i	0.167645	+	0.290370i	−0.769946	+	0.638109i	$0.779717\pi$
$30$		0			0
$31$			5.80053i			1.04181i	0.853616	+	0.520903i	$0.174405\pi$
$31$			5.80053i			1.04181i	−0.853616	+	0.520903i	$0.825595\pi$
$32$		0			0
$33$	−5.65180	+	9.78921i	−0.983852	+	1.70408i
$34$		0			0
$35$	1.38845	+	1.84913i	0.234691	+	0.312561i
$36$		0			0
$37$	−0.713520	−	1.23585i	−0.117302	−	0.203173i	0.801396	−	0.598135i	$-0.204091\pi$
$37$	−0.713520	−	1.23585i	−0.117302	−	0.203173i	−0.918698	+	0.394962i	$0.870758\pi$
$38$		0			0
$39$	10.9931	−	4.60975i	1.76030	−	0.738151i
$40$		0			0
$41$	−3.60158	+	2.07937i	−0.562472	+	0.324744i	−0.754137	−	0.656717i	$-0.771945\pi$
$41$	−3.60158	+	2.07937i	−0.562472	+	0.324744i	0.191665	+	0.981460i	$0.438611\pi$
$42$		0			0
$43$	1.86864	+	1.07886i	0.284965	+	0.164525i	0.635669	−	0.771962i	$-0.280724\pi$
$43$	1.86864	+	1.07886i	0.284965	+	0.164525i	−0.350704	+	0.936486i	$0.614058\pi$
$44$		0			0
$45$	10.6478	+	14.1808i	1.58729	+	2.11394i
$46$		0			0
$47$	3.50894			0.511832			0.255916	−	0.966699i	$-0.417623\pi$
$47$	3.50894			0.511832			0.255916	+	0.966699i	$0.417623\pi$
$48$		0			0
$49$	2.96529	+	5.13604i	0.423613	+	0.733719i
$50$		0			0
$51$	7.92183			1.10928
$52$		0			0
$53$		−	4.55382i		−	0.625515i	−0.949833	−	0.312757i	$-0.898747\pi$
$53$		−	4.55382i		−	0.625515i	0.949833	−	0.312757i	$-0.101253\pi$
$54$		0			0
$55$	−0.918661	−	7.58965i	−0.123872	−	1.02339i
$56$		0			0
$57$	−20.5099			−2.71661
$58$		0			0
$59$	−5.06250	−	2.92283i	−0.659081	−	0.380520i	0.132846	−	0.991137i	$-0.457588\pi$
$59$	−5.06250	−	2.92283i	−0.659081	−	0.380520i	−0.791927	+	0.610616i	$0.790922\pi$
$60$		0			0
$61$	−1.90280	+	3.29574i	−0.243628	+	0.421976i	−0.961745	−	0.273946i	$-0.911671\pi$
$61$	−1.90280	+	3.29574i	−0.243628	+	0.421976i	0.718117	+	0.695922i	$0.245004\pi$
$62$		0			0
$63$	−4.10061	−	7.10247i	−0.516629	−	0.894827i
$64$		0			0
$65$	−4.07353	+	6.95747i	−0.505259	+	0.862968i
$66$		0			0
$67$	−3.80822	−	6.59603i	−0.465248	−	0.805833i	0.533965	−	0.845507i	$-0.320702\pi$
$67$	−3.80822	−	6.59603i	−0.465248	−	0.805833i	−0.999213	+	0.0396734i	$0.987368\pi$
$68$		0			0
$69$	−11.9931	+	20.7726i	−1.44380	+	2.50073i
$70$		0			0
$71$	9.49745	+	5.48336i	1.12714	+	0.650755i	0.943214	−	0.332185i	$-0.107786\pi$
$71$	9.49745	+	5.48336i	1.12714	+	0.650755i	0.183926	+	0.982940i	$0.441119\pi$
$72$		0			0
$73$	7.15345			0.837248			0.418624	−	0.908160i	$-0.362513\pi$
$73$	7.15345			0.837248			0.418624	+	0.908160i	$0.362513\pi$
$74$		0			0
$75$	−15.8746	−	4.61105i	−1.83304	−	0.532438i
$76$		0			0
$77$			3.53565i			0.402924i
$78$		0			0
$79$	−12.8524			−1.44601			−0.723005	−	0.690843i	$-0.757240\pi$
$79$	−12.8524			−1.44601			−0.723005	+	0.690843i	$0.757240\pi$
$80$		0			0
$81$	−15.0512	−	26.0694i	−1.67236	−	2.89660i
$82$		0			0
$83$	−0.706694			−0.0775698			−0.0387849	−	0.999248i	$-0.512349\pi$
$83$	−0.706694			−0.0775698			−0.0387849	+	0.999248i	$0.512349\pi$
$84$		0			0
$85$	−4.28448	+	3.21707i	−0.464718	+	0.348940i
$86$		0			0
$87$	5.16978	+	2.98477i	0.554258	+	0.320001i
$88$		0			0
$89$	5.06250	−	2.92283i	0.536623	−	0.309820i	−0.207086	−	0.978323i	$-0.566398\pi$
$89$	5.06250	−	2.92283i	0.536623	−	0.309820i	0.743709	+	0.668503i	$0.233065\pi$
$90$		0			0
$91$	2.25690	−	2.96796i	0.236588	−	0.311127i
$92$		0			0
$93$	9.58870	+	16.6081i	0.994302	+	1.72218i
$94$		0			0
$95$	11.0927	−	8.32912i	1.13809	−	0.854550i
$96$		0			0
$97$	7.99794	−	13.8528i	0.812068	−	1.40654i	−0.0993461	−	0.995053i	$-0.531675\pi$
$97$	7.99794	−	13.8528i	0.812068	−	1.40654i	0.911414	−	0.411490i	$-0.134992\pi$
$98$		0			0
$99$			27.1144i			2.72510i
$100$		0			0
$101$	2.99562	+	5.18857i	0.298076	+	0.516282i	0.975696	−	0.219130i	$-0.0703219\pi$
$101$	2.99562	+	5.18857i	0.298076	+	0.516282i	−0.677620	+	0.735412i	$0.736989\pi$
$102$		0			0
$103$		−	11.7096i		−	1.15378i	−0.816822	−	0.576890i	$-0.804266\pi$
$103$		−	11.7096i		−	1.15378i	0.816822	−	0.576890i	$-0.195734\pi$
$104$		0			0
$105$	7.03216	+	2.99924i	0.686269	+	0.292696i
$106$		0			0
$107$	−11.7452	+	6.78110i	−1.13545	+	0.655554i	−0.945300	−	0.326201i	$-0.894231\pi$
$107$	−11.7452	+	6.78110i	−1.13545	+	0.655554i	−0.190152	+	0.981755i	$0.560898\pi$
$108$		0			0
$109$		−	1.39533i		−	0.133648i	−0.997765	−	0.0668240i	$-0.978713\pi$
$109$		−	1.39533i		−	0.133648i	0.997765	−	0.0668240i	$-0.0212866\pi$
$110$		0			0
$111$	−4.08591	−	2.35900i	−0.387817	−	0.223906i
$112$		0			0
$113$	3.65133	+	2.10810i	0.343488	+	0.198313i	0.661813	−	0.749669i	$-0.269787\pi$
$113$	3.65133	+	2.10810i	0.343488	+	0.198313i	−0.318325	+	0.947982i	$0.603120\pi$
$114$		0			0
$115$	−1.94939	−	16.1052i	−0.181782	−	1.50182i
$116$		0			0
$117$	17.3079	−	22.7609i	1.60012	−	2.10425i
$118$		0			0
$119$	2.14589	−	1.23893i	0.196714	−	0.113573i
$120$		0			0
$121$	0.344677	−	0.596999i	0.0313343	−	0.0542726i
$122$		0			0
$123$	−6.87471	+	11.9073i	−0.619871	+	1.07365i
$124$		0			0
$125$	10.4583	−	3.95283i	0.935415	−	0.353552i
$126$		0			0
$127$	5.16978	−	2.98477i	0.458744	−	0.264856i	−0.252772	−	0.967526i	$-0.581342\pi$
$127$	5.16978	−	2.98477i	0.458744	−	0.264856i	0.711516	+	0.702670i	$0.248009\pi$
$128$		0			0
$129$	7.13374			0.628091
$130$		0			0
$131$	19.0556			1.66489			0.832447	−	0.554105i	$-0.186940\pi$
$131$	19.0556			1.66489			0.832447	+	0.554105i	$0.186940\pi$
$132$		0			0
$133$	−5.55581	+	3.20765i	−0.481750	+	0.278138i
$134$		0			0
$135$	33.5285	+	14.3000i	2.88567	+	1.23075i
$136$		0			0
$137$	0.231497	−	0.400964i	0.0197781	−	0.0342567i	−0.855967	−	0.517031i	$-0.827037\pi$
$137$	0.231497	−	0.400964i	0.0197781	−	0.0342567i	0.875745	+	0.482774i	$0.160371\pi$
$138$		0			0
$139$	4.65970	−	8.07084i	0.395231	−	0.684559i	−0.597900	−	0.801571i	$-0.703998\pi$
$139$	4.65970	−	8.07084i	0.395231	−	0.684559i	0.993131	+	0.117011i	$0.0373314\pi$
$140$		0			0
$141$	10.0468	−	5.80053i	0.846095	−	0.488493i
$142$		0			0
$143$	−11.3682	+	4.76707i	−0.950659	+	0.398642i
$144$		0			0
$145$	−4.00817	+	0.485154i	−0.332861	+	0.0402899i
$146$		0			0
$147$	16.9805	+	9.80368i	1.40053	+	0.808594i
$148$		0			0
$149$	−9.44524	−	5.45321i	−0.773784	−	0.446744i	0.0604387	−	0.998172i	$-0.480750\pi$
$149$	−9.44524	−	5.45321i	−0.773784	−	0.446744i	−0.834223	+	0.551427i	$0.814083\pi$
$150$		0			0
$151$		−	4.85943i		−	0.395455i	−0.980257	−	0.197727i	$-0.936644\pi$
$151$		−	4.85943i		−	0.395455i	0.980257	−	0.197727i	$-0.0633561\pi$
$152$		0			0
$153$	16.4566	−	9.50121i	1.33044	−	0.768127i
$154$		0			0
$155$	−11.9306	−	5.08844i	−0.958287	−	0.408713i
$156$		0			0
$157$			8.80782i			0.702940i	0.936199	+	0.351470i	$0.114318\pi$
$157$			8.80782i			0.702940i	−0.936199	+	0.351470i	$0.885682\pi$
$158$		0			0
$159$	−7.52779	−	13.0385i	−0.596992	−	1.03402i
$160$		0			0
$161$			7.50261i			0.591289i
$162$		0			0
$163$	9.30996	−	16.1253i	0.729212	−	1.26303i	−0.228004	−	0.973660i	$-0.573220\pi$
$163$	9.30996	−	16.1253i	0.729212	−	1.26303i	0.957217	−	0.289372i	$-0.0934466\pi$
$164$		0			0
$165$	−15.1766	−	20.2121i	−1.18149	−	1.57351i
$166$		0			0
$167$	7.18849	+	12.4508i	0.556262	+	0.963474i	0.997804	+	0.0662334i	$0.0210982\pi$
$167$	7.18849	+	12.4508i	0.556262	+	0.963474i	−0.441542	+	0.897240i	$0.645568\pi$
$168$		0			0
$169$	12.5859	+	3.25499i	0.968147	+	0.250384i
$170$		0			0
$171$	−42.6068	+	24.5990i	−3.25822	+	1.88113i
$172$		0			0
$173$	−18.9947	−	10.9666i	−1.44414	−	0.833773i	−0.446014	−	0.895026i	$-0.647157\pi$
$173$	−18.9947	−	10.9666i	−1.44414	−	0.833773i	−0.998122	+	0.0612532i	$0.980490\pi$
$174$		0			0
$175$	−5.02131	+	1.23365i	−0.379575	+	0.0932548i
$176$		0			0
$177$	−19.3266			−1.45268
$178$		0			0
$179$	−5.06250	−	8.76850i	−0.378389	−	0.655388i	0.612439	−	0.790518i	$-0.290188\pi$
$179$	−5.06250	−	8.76850i	−0.378389	−	0.655388i	−0.990828	+	0.135129i	$0.956855\pi$
$180$		0			0
$181$	0.272578			0.0202606			0.0101303	−	0.999949i	$-0.496775\pi$
$181$	0.272578			0.0202606			0.0101303	+	0.999949i	$0.496775\pi$
$182$		0			0
$183$			12.5818i			0.930076i
$184$		0			0
$185$	3.16784	−	0.383439i	0.232904	−	0.0281910i
$186$		0			0
$187$	−8.19217			−0.599071
$188$		0			0
$189$	−14.5990	−	8.42876i	−1.06192	−	0.613102i
$190$		0			0
$191$	7.39587	−	12.8100i	0.535147	−	0.926901i	−0.464010	−	0.885830i	$-0.653590\pi$
$191$	7.39587	−	12.8100i	0.535147	−	0.926901i	0.999156	−	0.0410710i	$-0.0130770\pi$
$192$		0			0
$193$	3.50212	+	6.06585i	0.252088	+	0.436629i	0.964101	−	0.265538i	$-0.0855494\pi$
$193$	3.50212	+	6.06585i	0.252088	+	0.436629i	−0.712013	+	0.702167i	$0.752216\pi$
$194$		0			0
$195$	−0.162148	+	26.6545i	−0.0116117	+	1.90877i
$196$		0			0
$197$	−4.81643	−	8.34230i	−0.343157	−	0.594365i	0.641861	−	0.766821i	$-0.278163\pi$
$197$	−4.81643	−	8.34230i	−0.343157	−	0.594365i	−0.985017	+	0.172457i	$0.944829\pi$
$198$		0			0
$199$	1.96091	−	3.39640i	0.139006	−	0.240765i	−0.788115	−	0.615528i	$-0.788943\pi$
$199$	1.96091	−	3.39640i	0.139006	−	0.240765i	0.927120	+	0.374763i	$0.122276\pi$
$200$		0			0
$201$	−21.8074	−	12.5905i	−1.53818	−	0.888067i
$202$		0			0
$203$	1.86721			0.131052
$204$		0			0
$205$	−1.11744	−	9.23186i	−0.0780451	−	0.644781i
$206$		0			0
$207$			57.5366i			3.99907i
$208$		0			0
$209$	21.2099			1.46712
$210$		0			0
$211$	7.29429	+	12.6341i	0.502160	+	0.869766i	0.999997	+	0.00249580i	$0.000794440\pi$
$211$	7.29429	+	12.6341i	0.502160	+	0.869766i	−0.497837	+	0.867271i	$0.665872\pi$
$212$		0			0
$213$	36.2575			2.48433
$214$		0			0
$215$	−3.85825	+	2.89702i	−0.263131	+	0.197575i
$216$		0			0
$217$	5.19484	+	2.99924i	0.352649	+	0.203602i
$218$		0			0
$219$	20.4818	−	11.8252i	1.38403	−	0.799070i
$220$		0			0
$221$	6.87684	+	5.22929i	0.462586	+	0.351760i
$222$		0			0
$223$	−1.50165	−	2.60093i	−0.100558	−	0.174171i	0.811357	−	0.584551i	$-0.198729\pi$
$223$	−1.50165	−	2.60093i	−0.100558	−	0.174171i	−0.911915	+	0.410380i	$0.865396\pi$
$224$		0			0
$225$	−38.5078	+	9.46067i	−2.56719	+	0.630711i
$226$		0			0
$227$	5.84058	−	10.1162i	0.387653	−	0.671435i	−0.604480	−	0.796620i	$-0.706619\pi$
$227$	5.84058	−	10.1162i	0.387653	−	0.671435i	0.992133	+	0.125185i	$0.0399526\pi$
$228$		0			0
$229$		−	18.5293i		−	1.22445i	−0.790684	−	0.612224i	$-0.790275\pi$
$229$		−	18.5293i		−	1.22445i	0.790684	−	0.612224i	$-0.209725\pi$
$230$		0			0
$231$	5.84468	+	10.1233i	0.384552	+	0.666063i
$232$		0			0
$233$		−	11.1750i		−	0.732097i	−0.930596	−	0.366048i	$-0.880710\pi$
$233$		−	11.1750i		−	0.732097i	0.930596	−	0.366048i	$-0.119290\pi$
$234$		0			0
$235$	−3.07817	+	7.21722i	−0.200798	+	0.470800i
$236$		0			0
$237$	−36.7991	+	21.2460i	−2.39036	+	1.38007i
$238$		0			0
$239$			2.16507i			0.140047i	0.997545	+	0.0700235i	$0.0223074\pi$
$239$			2.16507i			0.140047i	−0.997545	+	0.0700235i	$0.977693\pi$
$240$		0			0
$241$	16.7318	+	9.66011i	1.07779	+	0.622262i	0.930299	−	0.366801i	$-0.119547\pi$
$241$	16.7318	+	9.66011i	1.07779	+	0.622262i	0.147491	+	0.989063i	$0.452880\pi$
$242$		0			0
$243$	−43.8375	−	25.3096i	−2.81218	−	1.62361i
$244$		0			0
$245$	−13.1651	+	1.59352i	−0.841087	+	0.101806i
$246$		0			0
$247$	−17.8044	−	13.5389i	−1.13287	−	0.861457i
$248$		0			0
$249$	−2.02341	+	1.16822i	−0.128228	+	0.0740327i
$250$		0			0
$251$	−3.87684	+	6.71488i	−0.244704	+	0.423840i	−0.962048	−	0.272879i	$-0.912024\pi$
$251$	−3.87684	+	6.71488i	−0.244704	+	0.423840i	0.717344	+	0.696719i	$0.245357\pi$
$252$		0			0
$253$	12.4024	−	21.4815i	0.779730	−	1.35053i
$254$		0			0
$255$	−6.94931	+	16.2937i	−0.435183	+	1.02035i
$256$		0			0
$257$	15.4216	−	8.90366i	0.961973	−	0.555395i	0.0651933	−	0.997873i	$-0.479234\pi$
$257$	15.4216	−	8.90366i	0.961973	−	0.555395i	0.896780	+	0.442477i	$0.145900\pi$
$258$		0			0
$259$	−1.47574			−0.0916980
$260$		0			0
$261$	14.3194			0.886348
$262$		0			0
$263$	−14.3815	+	8.30316i	−0.886801	+	0.511995i	−0.872895	−	0.487908i	$-0.837760\pi$
$263$	−14.3815	+	8.30316i	−0.886801	+	0.511995i	−0.0139065	+	0.999903i	$0.504427\pi$
$264$		0			0
$265$	9.36633	+	3.99477i	0.575369	+	0.245397i
$266$		0			0
$267$	9.66330	−	16.7373i	0.591385	−	1.02431i
$268$		0			0
$269$	−2.96967	+	5.14362i	−0.181064	+	0.313612i	−0.942243	−	0.334930i	$-0.891287\pi$
$269$	−2.96967	+	5.14362i	−0.181064	+	0.313612i	0.761179	+	0.648542i	$0.224621\pi$
$270$		0			0
$271$	−8.37246	+	4.83384i	−0.508591	+	0.293635i	−0.732254	−	0.681031i	$-0.761532\pi$
$271$	−8.37246	+	4.83384i	−0.508591	+	0.293635i	0.223663	+	0.974666i	$0.428198\pi$
$272$		0			0
$273$	1.55572	−	12.2287i	0.0941562	−	0.740115i
$274$		0			0
$275$	16.4163	+	4.76841i	0.989942	+	0.287546i
$276$		0			0
$277$	17.9423	+	10.3590i	1.07805	+	0.622411i	0.930369	−	0.366624i	$-0.119487\pi$
$277$	17.9423	+	10.3590i	1.07805	+	0.622411i	0.147679	+	0.989035i	$0.452820\pi$
$278$		0			0
$279$	39.8386	+	23.0008i	2.38507	+	1.37702i
$280$		0			0
$281$			27.7700i			1.65662i	0.560272	+	0.828309i	$0.310697\pi$
$281$			27.7700i			1.65662i	−0.560272	+	0.828309i	$0.689303\pi$
$282$		0			0
$283$	−22.1502	+	12.7885i	−1.31670	+	0.760194i	−0.983196	−	0.182556i	$-0.941563\pi$
$283$	−22.1502	+	12.7885i	−1.31670	+	0.760194i	−0.333500	+	0.942750i	$0.608230\pi$
$284$		0			0
$285$	17.9921	−	42.1850i	1.06576	−	2.49882i
$286$		0			0
$287$			4.30067i			0.253861i
$288$		0			0
$289$	−5.62937	−	9.75035i	−0.331139	−	0.573550i
$290$		0			0
$291$		−	52.8847i		−	3.10016i
$292$		0			0
$293$	−14.1987	+	24.5929i	−0.829497	+	1.43673i	0.0689370	+	0.997621i	$0.478039\pi$
$293$	−14.1987	+	24.5929i	−0.829497	+	1.43673i	−0.898434	+	0.439109i	$0.855294\pi$
$294$		0			0
$295$	10.4527	−	7.84856i	0.608580	−	0.456961i
$296$		0			0
$297$	27.8667	+	48.2665i	1.61699	+	2.80071i
$298$		0			0
$299$	−24.1233	+	10.1157i	−1.39509	+	0.585005i
$300$		0			0
$301$	1.93241	−	1.11568i	0.111382	−	0.0643067i
$302$		0			0
$303$	17.1542	+	9.90396i	0.985481	+	0.568968i
$304$		0			0
$305$	−5.10950	−	6.80483i	−0.292569	−	0.389643i
$306$		0			0
$307$	−11.5519			−0.659302			−0.329651	−	0.944103i	$-0.606931\pi$
$307$	−11.5519			−0.659302			−0.329651	+	0.944103i	$0.606931\pi$
$308$		0			0
$309$	−19.3568	−	33.5269i	−1.10117	−	1.90728i
$310$		0			0
$311$	−1.03807			−0.0588634			−0.0294317	−	0.999567i	$-0.509370\pi$
$311$	−1.03807			−0.0588634			−0.0294317	+	0.999567i	$0.509370\pi$
$312$		0			0
$313$			29.6339i			1.67501i	0.546432	+	0.837504i	$0.315986\pi$
$313$			29.6339i			1.67501i	−0.546432	+	0.837504i	$0.684014\pi$
$314$		0			0
$315$	18.2056	−	2.20363i	1.02577	−	0.124161i
$316$		0			0
$317$	−20.4445			−1.14828			−0.574138	−	0.818759i	$-0.694663\pi$
$317$	−20.4445			−1.14828			−0.574138	+	0.818759i	$0.694663\pi$
$318$		0			0
$319$	−5.34620	−	3.08663i	−0.299330	−	0.172818i
$320$		0			0
$321$	−22.4193	+	38.8313i	−1.25132	+	2.16735i
$322$		0			0
$323$	−7.43219	−	12.8729i	−0.413538	−	0.716269i
$324$		0			0
$325$	−10.7367	−	14.4818i	−0.595567	−	0.803306i
$326$		0			0
$327$	−2.30657	−	3.99510i	−0.127554	−	0.220930i
$328$		0			0
$329$	1.81435	−	3.14254i	0.100028	−	0.173254i
$330$		0			0
$331$	4.39587	+	2.53796i	0.241619	+	0.139499i	0.615921	−	0.787808i	$-0.288784\pi$
$331$	4.39587	+	2.53796i	0.241619	+	0.139499i	−0.374302	+	0.927307i	$0.622118\pi$
$332$		0			0
$333$	−11.3173			−0.620182
$334$		0			0
$335$	16.9075	−	2.04650i	0.923754	−	0.111812i
$336$		0			0
$337$			10.4909i			0.571473i	0.958308	+	0.285737i	$0.0922382\pi$
$337$			10.4909i			0.571473i	−0.958308	+	0.285737i	$0.907762\pi$
$338$		0			0
$339$	13.9393			0.757081
$340$		0			0
$341$	−9.91593	−	17.1749i	−0.536977	−	0.930072i
$342$		0			0
$343$	13.3719			0.722012
$344$		0			0
$345$	−32.2045	−	42.8899i	−1.73383	−	2.30912i
$346$		0			0
$347$	27.6247	+	15.9491i	1.48297	+	0.856193i	0.999813	−	0.0193399i	$-0.00615647\pi$
$347$	27.6247	+	15.9491i	1.48297	+	0.856193i	0.483158	+	0.875533i	$0.339490\pi$
$348$		0			0
$349$	−28.4661	+	16.4349i	−1.52376	+	0.879741i	−0.524151	+	0.851625i	$0.675617\pi$
$349$	−28.4661	+	16.4349i	−1.52376	+	0.879741i	−0.999605	+	0.0281153i	$0.991049\pi$
$350$		0			0
$351$	7.41745	−	58.3049i	0.395914	−	3.11209i
$352$		0			0
$353$	−13.6825	−	23.6988i	−0.728245	−	1.26136i	−0.957624	−	0.288021i	$-0.907003\pi$
$353$	−13.6825	−	23.6988i	−0.728245	−	1.26136i	0.229379	−	0.973337i	$-0.426330\pi$
$354$		0			0
$355$	−19.6097	+	14.7242i	−1.04078	+	0.781481i
$356$		0			0
$357$	4.09609	−	7.09463i	0.216788	−	0.375488i
$358$		0			0
$359$		−	0.625579i		−	0.0330168i	−0.999864	−	0.0165084i	$-0.994745\pi$
$359$		−	0.625579i		−	0.0330168i	0.999864	−	0.0165084i	$-0.00525502\pi$
$360$		0			0
$361$	9.74225	+	16.8741i	0.512750	+	0.888109i
$362$		0			0
$363$		−	2.27911i		−	0.119622i
$364$		0			0
$365$	−6.27526	+	14.7133i	−0.328462	+	0.770127i
$366$		0			0
$367$	−3.44490	+	1.98891i	−0.179822	+	0.103820i	−0.587209	−	0.809435i	$-0.699773\pi$
$367$	−3.44490	+	1.98891i	−0.179822	+	0.103820i	0.407387	+	0.913256i	$0.366440\pi$
$368$		0			0
$369$			32.9813i			1.71694i
$370$		0			0
$371$	−4.07831	−	2.35461i	−0.211735	−	0.122245i
$372$		0			0
$373$	24.4645	+	14.1246i	1.26672	+	0.731343i	0.974367	−	0.224966i	$-0.0722271\pi$
$373$	24.4645	+	14.1246i	1.26672	+	0.731343i	0.292357	+	0.956309i	$0.405560\pi$
$374$		0			0
$375$	23.4098	−	28.6060i	1.20888	−	1.47721i
$376$		0			0
$377$	2.51754	+	6.00368i	0.129660	+	0.309205i
$378$		0			0
$379$	−14.1642	+	8.17771i	−0.727567	+	0.420061i	−0.817531	−	0.575884i	$-0.804658\pi$
$379$	−14.1642	+	8.17771i	−0.727567	+	0.420061i	0.0899646	+	0.995945i	$0.471325\pi$
$380$		0			0
$381$	9.86809	−	17.0920i	0.505557	−	0.875651i
$382$		0			0
$383$	10.4332	−	18.0708i	0.533111	−	0.923376i	−0.466141	−	0.884710i	$-0.654356\pi$
$383$	10.4332	−	18.0708i	0.533111	−	0.923376i	0.999252	−	0.0386654i	$-0.0123106\pi$
$384$		0			0
$385$	−7.27215	−	3.10160i	−0.370623	−	0.158072i
$386$		0			0
$387$	14.8194	−	8.55600i	0.753314	−	0.434926i
$388$		0			0
$389$	−3.54177			−0.179575			−0.0897874	−	0.995961i	$-0.528619\pi$
$389$	−3.54177			−0.179575			−0.0897874	+	0.995961i	$0.528619\pi$
$390$		0			0
$391$	−17.3837			−0.879133
$392$		0			0
$393$	54.5600	−	31.5002i	2.75219	−	1.58898i
$394$		0			0
$395$	11.2746	−	26.4349i	0.567286	−	1.33009i
$396$		0			0
$397$	−13.8394	+	23.9705i	−0.694578	+	1.20305i	0.275744	+	0.961231i	$0.411076\pi$
$397$	−13.8394	+	23.9705i	−0.694578	+	1.20305i	−0.970323	+	0.241814i	$0.922258\pi$
$398$		0			0
$399$	−10.6049	+	18.3683i	−0.530911	+	0.919565i
$400$		0			0
$401$	10.6799	−	6.16604i	0.533328	−	0.307917i	−0.209043	−	0.977907i	$-0.567035\pi$
$401$	10.6799	−	6.16604i	0.533328	−	0.307917i	0.742371	+	0.669989i	$0.233701\pi$
$402$		0			0
$403$	−2.63939	+	20.7469i	−0.131477	+	1.03348i
$404$		0			0
$405$	66.8233	−	8.08837i	3.32047	−	0.401914i
$406$		0			0
$407$	4.22534	+	2.43950i	0.209442	+	0.120922i
$408$		0			0
$409$	31.2917	+	18.0663i	1.54728	+	0.893321i	0.998348	+	0.0574521i	$0.0182976\pi$
$409$	31.2917	+	18.0663i	1.54728	+	0.893321i	0.548929	+	0.835869i	$0.315036\pi$
$410$		0			0
$411$		−	1.53072i		−	0.0755049i
$412$		0			0
$413$	−5.23526	+	3.02258i	−0.257610	+	0.148731i
$414$		0			0
$415$	0.619938	−	1.45353i	0.0304315	−	0.0713512i
$416$		0			0
$417$		−	30.8113i		−	1.50883i
$418$		0			0
$419$	6.26566	+	10.8524i	0.306097	+	0.530176i	0.977505	−	0.210912i	$-0.0676434\pi$
$419$	6.26566	+	10.8524i	0.306097	+	0.530176i	−0.671408	+	0.741088i	$0.734310\pi$
$420$		0			0
$421$			7.74907i			0.377667i	0.982009	+	0.188833i	$0.0604706\pi$
$421$			7.74907i			0.377667i	−0.982009	+	0.188833i	$0.939529\pi$
$422$		0			0
$423$	13.9140	−	24.0997i	0.676521	−	1.17177i
$424$		0			0
$425$	−2.85838	−	11.6345i	−0.138652	−	0.564356i
$426$		0			0
$427$	1.96773	+	3.40821i	0.0952252	+	0.164935i
$428$		0			0
$429$	−24.6693	+	32.4416i	−1.19104	+	1.56629i
$430$		0			0
$431$	−18.9375	+	10.9336i	−0.912188	+	0.526652i	−0.881134	−	0.472866i	$-0.843219\pi$
$431$	−18.9375	+	10.9336i	−0.912188	+	0.526652i	−0.0310532	+	0.999518i	$0.509886\pi$
$432$		0			0
$433$	−0.219232	−	0.126574i	−0.0105356	−	0.00608275i	0.494723	−	0.869051i	$-0.335270\pi$
$433$	−0.219232	−	0.126574i	−0.0105356	−	0.00608275i	−0.505259	+	0.862968i	$0.668603\pi$
$434$		0			0
$435$	−10.6742	+	8.01489i	−0.511790	+	0.384285i
$436$		0			0
$437$	45.0072			2.15299
$438$		0			0
$439$	6.98432	+	12.0972i	0.333344	+	0.577368i	0.983165	−	0.182719i	$-0.0584897\pi$
$439$	6.98432	+	12.0972i	0.333344	+	0.577368i	−0.649822	+	0.760087i	$0.725156\pi$
$440$		0			0
$441$	47.0330			2.23967
$442$		0			0
$443$		−	28.5957i		−	1.35862i	−0.733851	−	0.679310i	$-0.762279\pi$
$443$		−	28.5957i		−	1.35862i	0.733851	−	0.679310i	$-0.237721\pi$
$444$		0			0
$445$	1.57070	+	12.9766i	0.0744585	+	0.615149i
$446$		0			0
$447$	−36.0582			−1.70549
$448$		0			0
$449$	15.7293	+	9.08129i	0.742309	+	0.428572i	0.822908	−	0.568174i	$-0.192350\pi$
$449$	15.7293	+	9.08129i	0.742309	+	0.428572i	−0.0805990	+	0.996747i	$0.525683\pi$
$450$		0			0
$451$	7.10932	−	12.3137i	0.334765	−	0.579829i
$452$		0			0
$453$	−8.03298	−	13.9135i	−0.377422	−	0.653715i
$454$		0			0
$455$	4.12470	+	7.24562i	0.193369	+	0.339680i
$456$		0			0
$457$	−4.53992	−	7.86337i	−0.212368	−	0.367833i	0.740087	−	0.672511i	$-0.234784\pi$
$457$	−4.53992	−	7.86337i	−0.212368	−	0.367833i	−0.952455	+	0.304678i	$0.901451\pi$
$458$		0			0
$459$	19.5296	−	33.8263i	0.911564	−	1.57888i
$460$		0			0
$461$	−32.7734	−	18.9217i	−1.52641	−	0.881273i	−0.999509	−	0.0313456i	$-0.990021\pi$
$461$	−32.7734	−	18.9217i	−1.52641	−	0.881273i	−0.526900	−	0.849927i	$-0.676646\pi$
$462$		0			0
$463$	15.5694			0.723570			0.361785	−	0.932262i	$-0.382167\pi$
$463$	15.5694			0.723570			0.361785	+	0.932262i	$0.382167\pi$
$464$		0			0
$465$	−42.5712	+	5.15288i	−1.97419	+	0.238959i
$466$		0			0
$467$		−	4.19255i		−	0.194008i	−0.995284	−	0.0970040i	$-0.969074\pi$
$467$		−	4.19255i		−	0.194008i	0.995284	−	0.0970040i	$-0.0309260\pi$
$468$		0			0
$469$	−7.87636			−0.363697
$470$		0			0
$471$	14.5599	+	25.2186i	0.670887	+	1.16201i
$472$		0			0
$473$	−7.37719			−0.339204
$474$		0			0
$475$	7.40048	+	30.1222i	0.339557	+	1.38210i
$476$		0			0
$477$	−31.2760	−	18.0572i	−1.43203	−	0.826783i
$478$		0			0
$479$	−10.7058	+	6.18102i	−0.489162	+	0.282418i	−0.724227	−	0.689562i	$-0.757803\pi$
$479$	−10.7058	+	6.18102i	−0.489162	+	0.282418i	0.235064	+	0.971980i	$0.424470\pi$
$480$		0			0
$481$	−1.98972	−	4.74497i	−0.0907234	−	0.216352i
$482$		0			0
$483$	12.4024	+	21.4815i	0.564327	+	0.977443i
$484$		0			0
$485$	21.4766	+	28.6024i	0.975200	+	1.29877i
$486$		0			0
$487$	0.695283	−	1.20427i	0.0315063	−	0.0545705i	−0.849842	−	0.527037i	$-0.823303\pi$
$487$	0.695283	−	1.20427i	0.0315063	−	0.0545705i	0.881349	+	0.472467i	$0.156636\pi$
$488$		0			0
$489$		−	61.5601i		−	2.78384i
$490$		0			0
$491$	−2.90025	−	5.02338i	−0.130886	−	0.226702i	0.793132	−	0.609050i	$-0.208449\pi$
$491$	−2.90025	−	5.02338i	−0.130886	−	0.226702i	−0.924019	+	0.382348i	$0.875116\pi$
$492$		0			0
$493$			4.32637i			0.194850i
$494$		0			0
$495$	−55.7692	−	23.7857i	−2.50664	−	1.06909i
$496$		0			0
$497$	9.82157	−	5.67049i	0.440558	−	0.254356i
$498$		0			0
$499$			27.8242i			1.24558i	0.782388	+	0.622792i	$0.214002\pi$
$499$			27.8242i			1.24558i	−0.782388	+	0.622792i	$0.785998\pi$
$500$		0			0
$501$	41.1642	+	23.7662i	1.83908	+	1.06179i
$502$		0			0
$503$	8.71140	+	5.02953i	0.388422	+	0.224256i	0.681476	−	0.731840i	$-0.261338\pi$
$503$	8.71140	+	5.02953i	0.388422	+	0.224256i	−0.293054	+	0.956096i	$0.594672\pi$
$504$		0			0
$505$	−13.2998	+	1.60982i	−0.591832	+	0.0716360i
$506$		0			0
$507$	41.4168	−	11.4857i	1.83938	−	0.510097i
$508$		0			0
$509$	2.00505	−	1.15762i	0.0888724	−	0.0513105i	−0.454905	−	0.890540i	$-0.650327\pi$
$509$	2.00505	−	1.15762i	0.0888724	−	0.0513105i	0.543778	+	0.839229i	$0.316994\pi$
$510$		0			0
$511$	3.69878	−	6.40648i	0.163625	−	0.283406i
$512$		0			0
$513$	−50.5630	+	87.5777i	−2.23241	+	3.86665i
$514$		0			0
$515$	24.0844	+	10.2721i	1.06128	+	0.452642i
$516$		0			0
$517$	−10.3897	+	5.99849i	−0.456938	+	0.263813i
$518$		0			0
$519$	−72.5141			−3.18301
$520$		0			0
$521$	−2.78299			−0.121925			−0.0609626	−	0.998140i	$-0.519417\pi$
$521$	−2.78299			−0.121925			−0.0609626	+	0.998140i	$0.519417\pi$
$522$		0			0
$523$	−23.6078	+	13.6300i	−1.03230	+	0.595997i	−0.917642	−	0.397408i	$-0.869910\pi$
$523$	−23.6078	+	13.6300i	−1.03230	+	0.595997i	−0.114655	+	0.993405i	$0.536576\pi$
$524$		0			0
$525$	−12.3377	+	11.8328i	−0.538463	+	0.516424i
$526$		0			0
$527$	−6.94931	+	12.0366i	−0.302717	+	0.524321i
$528$		0			0
$529$	14.8177	−	25.6650i	0.644248	−	1.11587i
$530$		0			0
$531$	−40.1485	+	23.1798i	−1.74230	+	1.00592i
$532$		0			0
$533$	−13.8280	+	5.79854i	−0.598958	+	0.251162i
$534$		0			0
$535$	−3.64410	−	30.1063i	−0.157548	−	1.30161i
$536$		0			0
$537$	−28.9899	−	16.7373i	−1.25101	−	0.722269i
$538$		0			0
$539$	−17.5599	−	10.1382i	−0.756361	−	0.436685i
$540$		0			0
$541$		−	22.5466i		−	0.969353i	−0.874693	−	0.484677i	$-0.838937\pi$
$541$		−	22.5466i		−	0.969353i	0.874693	−	0.484677i	$-0.161063\pi$
$542$		0			0
$543$	0.780447	−	0.450591i	0.0334922	−	0.0193367i
$544$		0			0
$545$	2.86992	+	1.22403i	0.122934	+	0.0524317i
$546$		0			0
$547$		−	1.51141i		−	0.0646233i	−0.999478	−	0.0323117i	$-0.989713\pi$
$547$		−	1.51141i		−	0.0646233i	0.999478	−	0.0323117i	$-0.0102869\pi$
$548$		0			0
$549$	15.0903	+	26.1371i	0.644038	+	1.11551i
$550$		0			0
$551$		−	11.2011i		−	0.477185i
$552$		0			0
$553$	−6.64551	+	11.5104i	−0.282596	+	0.489470i
$554$		0			0
$555$	8.43631	−	6.33452i	0.358101	−	0.268886i
$556$		0			0
$557$	−17.5294	−	30.3618i	−0.742745	−	1.28647i	−0.951241	−	0.308449i	$-0.900190\pi$
$557$	−17.5294	−	30.3618i	−0.742745	−	1.28647i	0.208496	−	0.978023i	$-0.433143\pi$
$558$		0			0
$559$	6.19271	+	4.70907i	0.261924	+	0.199172i
$560$		0			0
$561$	−23.4559	+	13.5422i	−0.990307	+	0.571754i
$562$		0			0
$563$	−18.4393	−	10.6460i	−0.777125	−	0.448674i	0.0582852	−	0.998300i	$-0.481437\pi$
$563$	−18.4393	−	10.6460i	−0.777125	−	0.448674i	−0.835411	+	0.549626i	$0.814770\pi$
$564$		0			0
$565$	−7.53903	+	5.66079i	−0.317169	+	0.238151i
$566$		0			0
$567$	−31.1297			−1.30732
$568$		0			0
$569$	0.488701	+	0.846455i	0.0204874	+	0.0354853i	0.876087	−	0.482152i	$-0.160145\pi$
$569$	0.488701	+	0.846455i	0.0204874	+	0.0354853i	−0.855600	+	0.517638i	$0.826812\pi$
$570$		0			0
$571$	−24.5468			−1.02725			−0.513625	−	0.858015i	$-0.671698\pi$
$571$	−24.5468			−1.02725			−0.513625	+	0.858015i	$0.671698\pi$
$572$		0			0
$573$		−	48.9036i		−	2.04298i
$574$		0			0
$575$	34.8353	+	10.1185i	1.45273	+	0.421971i
$576$		0			0
$577$	−23.8270			−0.991932			−0.495966	−	0.868342i	$-0.665186\pi$
$577$	−23.8270			−0.991932			−0.495966	+	0.868342i	$0.665186\pi$
$578$		0			0
$579$	20.0546	+	11.5785i	0.833439	+	0.481186i
$580$		0			0
$581$	−0.365406	+	0.632901i	−0.0151596	+	0.0262572i
$582$		0			0
$583$	7.78468	+	13.4835i	0.322409	+	0.558428i
$584$		0			0
$585$	31.6318	+	55.5657i	1.30781	+	2.29736i
$586$		0			0
$587$	−7.63094	−	13.2172i	−0.314963	−	0.545532i	0.664467	−	0.747318i	$-0.268659\pi$
$587$	−7.63094	−	13.2172i	−0.314963	−	0.545532i	−0.979430	+	0.201786i	$0.935325\pi$
$588$		0			0
$589$	17.9921	−	31.1632i	0.741350	−	1.28406i
$590$		0			0
$591$	−27.5809	−	15.9238i	−1.13452	−	0.655018i
$592$		0			0
$593$	−35.9654			−1.47692			−0.738461	−	0.674296i	$-0.764447\pi$
$593$	−35.9654			−1.47692			−0.738461	+	0.674296i	$0.764447\pi$
$594$		0			0
$595$	0.665790	+	5.50052i	0.0272947	+	0.225500i
$596$		0			0
$597$		−	12.9661i		−	0.530668i
$598$		0			0
$599$	6.60243			0.269768			0.134884	−	0.990861i	$-0.456934\pi$
$599$	6.60243			0.269768			0.134884	+	0.990861i	$0.456934\pi$
$600$		0			0
$601$	−14.9409	−	25.8783i	−0.609451	−	1.05560i	−0.991331	−	0.131388i	$-0.958057\pi$
$601$	−14.9409	−	25.8783i	−0.609451	−	1.05560i	0.381881	−	0.924212i	$-0.375277\pi$
$602$		0			0
$603$	−60.4028			−2.45979
$604$		0			0
$605$	0.925548	+	1.23264i	0.0376289	+	0.0501141i
$606$		0			0
$607$	21.2089	+	12.2450i	0.860843	+	0.497008i	0.864294	−	0.502986i	$-0.167765\pi$
$607$	21.2089	+	12.2450i	0.860843	+	0.497008i	−0.00345162	+	0.999994i	$0.501099\pi$
$608$		0			0
$609$	5.34620	−	3.08663i	0.216639	−	0.125077i
$610$		0			0
$611$	12.5505	+	1.59666i	0.507740	+	0.0645938i
$612$		0			0
$613$	16.3530	+	28.3242i	0.660490	+	1.14400i	0.980487	+	0.196584i	$0.0629848\pi$
$613$	16.3530	+	28.3242i	0.660490	+	1.14400i	−0.319997	+	0.947419i	$0.603682\pi$
$614$		0			0
$615$	−18.4604	−	24.5855i	−0.744394	−	0.991383i
$616$		0			0
$617$	−7.18390	+	12.4429i	−0.289213	+	0.500932i	−0.973622	−	0.228167i	$-0.926727\pi$
$617$	−7.18390	+	12.4429i	−0.289213	+	0.500932i	0.684409	+	0.729098i	$0.260060\pi$
$618$		0			0
$619$			11.1681i			0.448883i	0.974488	+	0.224442i	$0.0720558\pi$
$619$			11.1681i			0.448883i	−0.974488	+	0.224442i	$0.927944\pi$
$620$		0			0
$621$	59.1329	+	102.421i	2.37292	+	4.11002i
$622$		0			0
$623$		−	6.04516i		−	0.242194i
$624$		0			0
$625$	−1.04414	+	24.9782i	−0.0417655	+	0.999127i
$626$		0			0
$627$	60.7282	−	35.0614i	2.42525	−	1.40022i
$628$		0			0
$629$		−	3.41932i		−	0.136337i
$630$		0			0
$631$	36.0259	+	20.7996i	1.43417	+	0.828018i	0.997435	−	0.0715729i	$-0.0228019\pi$
$631$	36.0259	+	20.7996i	1.43417	+	0.828018i	0.436734	+	0.899591i	$0.356135\pi$
$632$		0			0
$633$	41.7701	+	24.1160i	1.66021	+	0.958524i
$634$		0			0
$635$	1.60399	+	13.2516i	0.0636524	+	0.525873i
$636$		0			0
$637$	8.26901	+	19.7195i	0.327630	+	0.781313i
$638$		0			0
$639$	75.3203	−	43.4862i	2.97963	−	1.72029i
$640$		0			0
$641$	2.68565	−	4.65169i	0.106077	−	0.183731i	−0.808101	−	0.589044i	$-0.799504\pi$
$641$	2.68565	−	4.65169i	0.106077	−	0.183731i	0.914178	+	0.405314i	$0.132838\pi$
$642$		0			0
$643$	8.77839	−	15.2046i	0.346186	−	0.599612i	−0.639383	−	0.768889i	$-0.720810\pi$
$643$	8.77839	−	15.2046i	0.346186	−	0.599612i	0.985568	+	0.169277i	$0.0541433\pi$
$644$		0			0
$645$	−6.25798	+	14.6727i	−0.246408	+	0.577738i
$646$		0			0
$647$	−32.6893	+	18.8732i	−1.28515	+	0.741982i	−0.977785	−	0.209610i	$-0.932781\pi$
$647$	−32.6893	+	18.8732i	−1.28515	+	0.741982i	−0.307365	+	0.951592i	$0.599447\pi$
$648$		0			0
$649$	19.9862			0.784525
$650$		0			0
$651$	19.8319			0.777272
$652$		0			0
$653$	−11.0118	+	6.35766i	−0.430925	+	0.248794i	−0.699741	−	0.714397i	$-0.746701\pi$
$653$	−11.0118	+	6.35766i	−0.430925	+	0.248794i	0.268816	+	0.963192i	$0.413368\pi$
$654$		0			0
$655$	−16.7162	+	39.1936i	−0.653157	+	1.53142i
$656$		0			0
$657$	28.3655	−	49.1305i	1.10664	−	1.91676i
$658$		0			0
$659$	11.0625	−	19.1608i	0.430934	−	0.746399i	−0.566020	−	0.824391i	$-0.691518\pi$
$659$	11.0625	−	19.1608i	0.430934	−	0.746399i	0.996954	+	0.0779923i	$0.0248510\pi$
$660$		0			0
$661$	0.612035	−	0.353359i	0.0238054	−	0.0137441i	−0.488050	−	0.872816i	$-0.662292\pi$
$661$	0.612035	−	0.353359i	0.0238054	−	0.0137441i	0.511855	+	0.859072i	$0.328958\pi$
$662$		0			0
$663$	28.3342	+	3.60463i	1.10041	+	0.139992i
$664$		0			0
$665$	−1.72376	−	14.2411i	−0.0668445	−	0.552246i
$666$		0			0
$667$	−11.3446	−	6.54981i	−0.439265	−	0.253610i
$668$		0			0
$669$	−8.59903	−	4.96466i	−0.332458	−	0.191945i
$670$		0			0
$671$		−	13.0112i		−	0.502292i
$672$		0			0
$673$	23.3244	−	13.4663i	0.899090	−	0.519090i	0.0221849	−	0.999754i	$-0.492938\pi$
$673$	23.3244	−	13.4663i	0.899090	−	0.519090i	0.876905	+	0.480664i	$0.159604\pi$
$674$		0			0
$675$	−58.8247	+	56.4171i	−2.26416	+	2.17150i
$676$		0			0
$677$		−	21.5208i		−	0.827111i	−0.910479	−	0.413556i	$-0.864287\pi$
$677$		−	21.5208i		−	0.827111i	0.910479	−	0.413556i	$-0.135713\pi$
$678$		0			0
$679$	−8.27088	−	14.3256i	−0.317407	−	0.549766i
$680$		0			0
$681$		−	38.6196i		−	1.47991i
$682$		0			0
$683$	10.2786	−	17.8031i	0.393300	−	0.681215i	−0.599583	−	0.800313i	$-0.704667\pi$
$683$	10.2786	−	17.8031i	0.393300	−	0.681215i	0.992883	+	0.119098i	$0.0380001\pi$
$684$		0			0
$685$	0.621628	+	0.827884i	0.0237512	+	0.0316318i
$686$		0			0
$687$	−30.6302	−	53.0531i	−1.16862	−	2.02410i
$688$		0			0
$689$	2.07210	−	16.2877i	0.0789407	−	0.620514i
$690$		0			0
$691$	17.2344	−	9.95031i	0.655629	−	0.378528i	−0.134980	−	0.990848i	$-0.543097\pi$
$691$	17.2344	−	9.95031i	0.655629	−	0.378528i	0.790610	+	0.612321i	$0.209764\pi$
$692$		0			0
$693$	24.2831	+	14.0199i	0.922440	+	0.532571i
$694$		0			0
$695$	12.5125	+	16.6641i	0.474626	+	0.632106i
$696$		0			0
$697$	−9.96475			−0.377442
$698$		0			0
$699$	−18.4730	−	31.9962i	−0.698714	−	1.21021i
$700$		0			0
$701$	2.37131			0.0895631			0.0447816	−	0.998997i	$-0.485741\pi$
$701$	2.37131			0.0895631			0.0447816	+	0.998997i	$0.485741\pi$
$702$		0			0
$703$			8.85276i			0.333888i
$704$		0			0
$705$	3.11715	+	25.7528i	0.117399	+	0.969907i
$706$		0			0
$707$	6.19571			0.233014
$708$		0			0
$709$	−0.916777	−	0.529301i	−0.0344303	−	0.0198783i	0.482686	−	0.875793i	$-0.339661\pi$
$709$	−0.916777	−	0.529301i	−0.0344303	−	0.0198783i	−0.517116	+	0.855915i	$0.672995\pi$
$710$		0			0
$711$	−50.9636	+	88.2715i	−1.91128	+	3.31044i
$712$		0			0
$713$	−21.0415	−	36.4450i	−0.788011	−	1.36487i
$714$		0			0
$715$	0.167682	−	27.5641i	0.00627095	−	1.03084i
$716$		0			0
$717$	3.57902	+	6.19905i	0.133661	+	0.231508i
$718$		0			0
$719$	−5.60426	+	9.70687i	−0.209004	+	0.362005i	−0.951401	−	0.307955i	$-0.900355\pi$
$719$	−5.60426	+	9.70687i	−0.209004	+	0.362005i	0.742397	+	0.669960i	$0.233689\pi$
$720$		0			0
$721$	−10.4869	−	6.05460i	−0.390551	−	0.225485i
$722$		0			0
$723$	63.8754			2.37555
$724$		0			0
$725$	2.51824	−	8.66963i	0.0935252	−	0.321982i
$726$		0			0
$727$		−	38.9060i		−	1.44294i	−0.692443	−	0.721472i	$-0.743466\pi$
$727$		−	38.9060i		−	1.44294i	0.692443	−	0.721472i	$-0.256534\pi$
$728$		0			0
$729$	−77.0471			−2.85360
$730$		0			0
$731$	2.58505	+	4.47745i	0.0956117	+	0.165604i
$732$		0			0
$733$	24.7392			0.913765			0.456882	−	0.889527i	$-0.348966\pi$
$733$	24.7392			0.913765			0.456882	+	0.889527i	$0.348966\pi$
$734$		0			0
$735$	−35.0602	+	26.3254i	−1.29321	+	0.971028i
$736$		0			0
$737$	22.5516	+	13.0202i	0.830700	+	0.479605i
$738$		0			0
$739$	0.302370	−	0.174574i	0.0111229	−	0.00642179i	−0.494428	−	0.869218i	$-0.664623\pi$
$739$	0.302370	−	0.174574i	0.0111229	−	0.00642179i	0.505551	+	0.862797i	$0.331289\pi$
$740$		0			0
$741$	−73.3584	−	9.33253i	−2.69489	−	0.342839i
$742$		0			0
$743$	3.85776	+	6.68184i	0.141528	+	0.245133i	0.928072	−	0.372401i	$-0.121465\pi$
$743$	3.85776	+	6.68184i	0.141528	+	0.245133i	−0.786544	+	0.617534i	$0.788132\pi$
$744$		0			0
$745$	19.5019	−	14.6433i	0.714495	−	0.536489i
$746$		0			0
$747$	−2.80225	+	4.85364i	−0.102529	+	0.177585i
$748$		0			0
$749$			14.0250i			0.512463i
$750$		0			0
$751$	1.71161	+	2.96460i	0.0624575	+	0.108180i	0.895563	−	0.444934i	$-0.146773\pi$
$751$	1.71161	+	2.96460i	0.0624575	+	0.108180i	−0.833106	+	0.553114i	$0.813440\pi$
$752$		0			0
$753$			25.6348i			0.934183i
$754$		0			0
$755$	9.99491	+	4.26286i	0.363752	+	0.155142i
$756$		0			0
$757$	−9.76835	+	5.63976i	−0.355037	+	0.204981i	−0.666901	−	0.745146i	$-0.732380\pi$
$757$	−9.76835	+	5.63976i	−0.355037	+	0.204981i	0.311865	+	0.950127i	$0.399046\pi$
$758$		0			0
$759$		−	82.0079i		−	2.97670i
$760$		0			0
$761$	−33.1329	−	19.1293i	−1.20107	−	0.693435i	−0.240273	−	0.970705i	$-0.577237\pi$
$761$	−33.1329	−	19.1293i	−1.20107	−	0.693435i	−0.960792	+	0.277270i	$0.910570\pi$
$762$		0			0
$763$	−1.24963	−	0.721472i	−0.0452395	−	0.0261190i
$764$		0			0
$765$	5.10586	+	42.1828i	0.184603	+	1.52512i
$766$		0			0
$767$	−16.7772	−	12.7577i	−0.605789	−	0.460655i
$768$		0			0
$769$	33.7503	−	19.4857i	1.21707	−	0.702674i	0.252777	−	0.967525i	$-0.418656\pi$
$769$	33.7503	−	19.4857i	1.21707	−	0.702674i	0.964289	+	0.264851i	$0.0853228\pi$
$770$		0			0
$771$	29.4368	−	50.9860i	1.06014	−	1.83622i
$772$		0			0
$773$	14.4410	−	25.0126i	0.519407	−	0.899640i	−0.480338	−	0.877083i	$-0.659486\pi$
$773$	14.4410	−	25.0126i	0.519407	−	0.899640i	0.999746	−	0.0225567i	$-0.00718064\pi$
$774$		0			0
$775$	20.9319	−	20.0752i	0.751895	−	0.721121i
$776$		0			0
$777$	−4.22534	+	2.43950i	−0.151583	+	0.0875167i
$778$		0			0
$779$	25.7991			0.924350
$780$		0			0
$781$	−37.4949			−1.34167
$782$		0			0
$783$	25.4900	−	14.7167i	0.910939	−	0.525931i
$784$		0			0
$785$	−18.1160	−	7.72653i	−0.646587	−	0.275772i
$786$		0			0
$787$	1.52068	−	2.63389i	0.0542062	−	0.0938879i	−0.837649	−	0.546209i	$-0.816070\pi$
$787$	1.52068	−	2.63389i	0.0542062	−	0.0938879i	0.891855	+	0.452321i	$0.149404\pi$
$788$		0			0
$789$	−27.4514	+	47.5473i	−0.977297	+	1.69273i
$790$		0			0
$791$	3.77594	−	2.18004i	0.134257	−	0.0775132i
$792$		0			0
$793$	−8.30542	+	10.9221i	−0.294934	+	0.387856i
$794$		0			0
$795$	33.4213	−	4.04536i	1.18533	−	0.143474i
$796$		0			0
$797$	36.6254	+	21.1457i	1.29734	+	0.749018i	0.979944	−	0.199275i	$-0.0638589\pi$
$797$	36.6254	+	21.1457i	1.29734	+	0.749018i	0.317394	+	0.948294i	$0.397192\pi$
$798$		0			0
$799$	7.28133	+	4.20388i	0.257595	+	0.148723i
$800$		0			0
$801$		−	46.3595i		−	1.63803i
$802$		0			0
$803$	−21.1807	+	12.2287i	−0.747452	+	0.431542i
$804$		0			0
$805$	−15.4314	−	6.58156i	−0.543887	−	0.231970i
$806$		0			0
$807$			19.6363i			0.691230i
$808$		0			0
$809$	17.6250	+	30.5274i	0.619662	+	1.07329i	0.989547	+	0.144208i	$0.0460635\pi$
$809$	17.6250	+	30.5274i	0.619662	+	1.07329i	−0.369886	+	0.929077i	$0.620603\pi$
$810$		0			0
$811$			30.1607i			1.05908i	0.848284	+	0.529542i	$0.177636\pi$
$811$			30.1607i			1.05908i	−0.848284	+	0.529542i	$0.822364\pi$
$812$		0			0
$813$	−15.9814	+	27.6806i	−0.560492	+	0.970800i
$814$		0			0
$815$	24.9997	+	33.2945i	0.875700	+	1.16626i
$816$		0			0
$817$	−6.69281	−	11.5923i	−0.234152	−	0.405563i
$818$		0			0
$819$	−11.4350	−	27.2694i	−0.399570	−	0.952872i
$820$		0			0
$821$	3.92434	−	2.26572i	0.136960	−	0.0790741i	−0.429954	−	0.902851i	$-0.641470\pi$
$821$	3.92434	−	2.26572i	0.136960	−	0.0790741i	0.566915	+	0.823777i	$0.308137\pi$
$822$		0			0
$823$	−17.2729	−	9.97249i	−0.602094	−	0.347619i	0.167771	−	0.985826i	$-0.446343\pi$
$823$	−17.2729	−	9.97249i	−0.602094	−	0.347619i	−0.769865	+	0.638207i	$0.779676\pi$
$824$		0			0
$825$	54.8858	−	13.4845i	1.91088	−	0.469469i
$826$		0			0
$827$	12.3377			0.429025			0.214512	−	0.976721i	$-0.431184\pi$
$827$	12.3377			0.429025			0.214512	+	0.976721i	$0.431184\pi$
$828$		0			0
$829$	18.7968	+	32.5570i	0.652840	+	1.13075i	0.982431	+	0.186628i	$0.0597559\pi$
$829$	18.7968	+	32.5570i	0.652840	+	1.13075i	−0.329591	+	0.944124i	$0.606911\pi$
$830$		0			0
$831$	68.4966			2.37612
$832$		0			0
$833$			14.2102i			0.492355i
$834$		0			0
$835$	−31.9150	+	3.86303i	−1.10446	+	0.133686i
$836$		0			0
$837$	94.5557			3.26832
$838$		0			0
$839$	−20.7606	−	11.9861i	−0.716736	−	0.413808i	0.0968144	−	0.995302i	$-0.469135\pi$
$839$	−20.7606	−	11.9861i	−0.716736	−	0.413808i	−0.813550	+	0.581495i	$0.802468\pi$
$840$		0			0
$841$	12.8699	−	22.2914i	0.443790	−	0.768667i
$842$		0			0
$843$	45.9058	+	79.5111i	1.58108	+	2.73851i
$844$		0			0
$845$	−17.7357	+	23.0314i	−0.610127	+	0.792304i
$846$		0			0
$847$	−0.356440	−	0.617372i	−0.0122474	−	0.0212132i
$848$		0			0
$849$	−42.2804	+	73.2319i	−1.45106	+	2.51331i
$850$		0			0
$851$	8.96614	+	5.17660i	0.307355	+	0.177452i
$852$		0			0
$853$	−38.8952			−1.33175			−0.665873	−	0.746065i	$-0.731941\pi$
$853$	−38.8952			−1.33175			−0.665873	+	0.746065i	$0.731941\pi$
$854$		0			0
$855$	−13.2193	−	109.213i	−0.452090	−	3.73501i
$856$		0			0
$857$		−	44.4570i		−	1.51862i	−0.650727	−	0.759312i	$-0.725536\pi$
$857$		−	44.4570i		−	1.51862i	0.650727	−	0.759312i	$-0.274464\pi$
$858$		0			0
$859$	−46.8129			−1.59724			−0.798618	−	0.601838i	$-0.794435\pi$
$859$	−46.8129			−1.59724			−0.798618	+	0.601838i	$0.794435\pi$
$860$		0			0
$861$	7.10932	+	12.3137i	0.242285	+	0.419650i
$862$		0			0
$863$	−28.9384			−0.985073			−0.492537	−	0.870292i	$-0.663930\pi$
$863$	−28.9384			−0.985073			−0.492537	+	0.870292i	$0.663930\pi$
$864$		0			0
$865$	39.2189	−	29.4481i	1.33348	−	1.00126i
$866$		0			0
$867$	−32.2361	−	18.6115i	−1.09479	−	0.632079i
$868$		0			0
$869$	38.0549	−	21.9710i	1.29092	−	0.745315i
$870$		0			0
$871$	−10.6196	−	25.3250i	−0.359831	−	0.858105i
$872$		0			0
$873$	−63.4283	−	109.861i	−2.14672	−	3.71824i
$874$		0			0
$875$	1.86750	−	11.4101i	0.0631331	−	0.385731i
$876$		0			0
$877$	−0.912276	+	1.58011i	−0.0308054	+	0.0533565i	−0.881017	−	0.473084i	$-0.843141\pi$
$877$	−0.912276	+	1.58011i	−0.0308054	+	0.0533565i	0.850212	+	0.526441i	$0.176474\pi$
$878$		0			0
$879$			93.8858i			3.16669i
$880$		0			0
$881$	−5.47740	−	9.48714i	−0.184538	−	0.319630i	0.758882	−	0.651228i	$-0.225746\pi$
$881$	−5.47740	−	9.48714i	−0.184538	−	0.319630i	−0.943421	+	0.331598i	$0.892412\pi$
$882$		0			0
$883$			15.8747i			0.534227i	0.963665	+	0.267113i	$0.0860698\pi$
$883$			15.8747i			0.534227i	−0.963665	+	0.267113i	$0.913930\pi$
$884$		0			0
$885$	16.9540	−	39.7511i	0.569902	−	1.33622i
$886$		0			0
$887$	5.15751	−	2.97769i	0.173172	−	0.0999811i	−0.410908	−	0.911677i	$-0.634788\pi$
$887$	5.15751	−	2.97769i	0.173172	−	0.0999811i	0.584081	+	0.811695i	$0.301455\pi$
$888$		0			0
$889$		−	6.17327i		−	0.207045i
$890$		0			0
$891$	89.1306	+	51.4596i	2.98599	+	1.72396i
$892$		0			0
$893$	−18.8517	−	10.8840i	−0.630847	−	0.364220i
$894$		0			0
$895$	22.4761	−	2.72054i	0.751294	−	0.0909375i
$896$		0			0
$897$	−52.3480	+	68.8408i	−1.74785	+	2.29853i
$898$		0			0
$899$	−9.07023	+	5.23670i	−0.302509	+	0.174654i
$900$		0			0
$901$	5.45569	−	9.44953i	0.181755	−	0.314809i
$902$		0			0
$903$	3.68860	−	6.38884i	0.122749	−	0.212607i
$904$		0			0
$905$	−0.239115	+	0.560641i	−0.00794847	+	0.0186363i
$906$		0			0
$907$	33.0723	−	19.0943i	1.09815	−	0.634015i	0.162413	−	0.986723i	$-0.448072\pi$
$907$	33.0723	−	19.0943i	1.09815	−	0.634015i	0.935734	+	0.352707i	$0.114739\pi$
$908$		0			0
$909$	47.5141			1.57594
$910$		0			0
$911$	33.7516			1.11824			0.559121	−	0.829086i	$-0.311139\pi$
$911$	33.7516			1.11824			0.559121	+	0.829086i	$0.311139\pi$
$912$		0			0
$913$	2.09246	−	1.20808i	0.0692504	−	0.0399817i
$914$		0			0
$915$	−25.8784	−	11.0372i	−0.855514	−	0.364880i
$916$		0			0
$917$	9.85294	−	17.0658i	0.325373	−	0.563562i
$918$		0			0
$919$	−10.5062	+	18.1973i	−0.346568	+	0.600273i	−0.985637	−	0.168876i	$-0.945986\pi$
$919$	−10.5062	+	18.1973i	−0.346568	+	0.600273i	0.639070	+	0.769149i	$0.279320\pi$
$920$		0			0
$921$	−33.0755	+	19.0961i	−1.08987	+	0.629239i
$922$		0			0
$923$	31.4747	+	23.9340i	1.03600	+	0.787798i
$924$		0			0
$925$	−1.99028	+	6.85199i	−0.0654400	+	0.225292i
$926$		0			0
$927$	−80.4225	−	46.4319i	−2.64142	−	1.52502i
$928$		0			0
$929$	−33.3099	−	19.2315i	−1.09286	−	0.630965i	−0.158526	−	0.987355i	$-0.550674\pi$
$929$	−33.3099	−	19.2315i	−1.09286	−	0.630965i	−0.934337	+	0.356390i	$0.884008\pi$
$930$		0			0
$931$		−	36.7909i		−	1.20577i
$932$		0			0
$933$	−2.97220	+	1.71600i	−0.0973054	+	0.0561793i
$934$		0			0
$935$	7.18647	−	16.8497i	0.235023	−	0.551045i
$936$		0			0
$937$			45.7434i			1.49437i	0.664615	+	0.747186i	$0.268596\pi$
$937$			45.7434i			1.49437i	−0.664615	+	0.747186i	$0.731404\pi$
$938$		0			0
$939$	48.9870	+	84.8479i	1.59863	+	2.76891i
$940$		0			0
$941$		−	58.6037i		−	1.91043i	−0.295917	−	0.955214i	$-0.595625\pi$
$941$		−	58.6037i		−	1.91043i	0.295917	−	0.955214i	$-0.404375\pi$
$942$		0			0
$943$	15.0859	−	26.1296i	0.491265	−	0.850896i
$944$		0			0
$945$	30.1431	−	22.6334i	0.980556	−	0.736265i
$946$		0			0
$947$	20.3516	+	35.2500i	0.661338	+	1.14547i	0.980264	+	0.197692i	$0.0633446\pi$
$947$	20.3516	+	35.2500i	0.661338	+	1.14547i	−0.318926	+	0.947780i	$0.603322\pi$
$948$		0			0
$949$	25.5859	+	3.25499i	0.830554	+	0.105662i
$950$		0			0
$951$	−58.5367	+	33.7962i	−1.89818	+	1.09592i
$952$		0			0
$953$	−2.60814	−	1.50581i	−0.0844859	−	0.0487779i	0.457162	−	0.889384i	$-0.348866\pi$
$953$	−2.60814	−	1.50581i	−0.0844859	−	0.0487779i	−0.541648	+	0.840606i	$0.682199\pi$
$954$		0			0
$955$	19.8598	+	26.4493i	0.642649	+	0.855879i
$956$		0			0
$957$	−20.4097			−0.659752
$958$		0			0
$959$	−0.239397	−	0.414647i	−0.00773052	−	0.0133897i
$960$		0			0
$961$	−2.64620			−0.0853612
$962$		0			0
$963$			107.556i			3.46595i
$964$		0			0
$965$	−15.5485	+	1.88201i	−0.500523	+	0.0605839i
$966$		0			0
$967$	37.8156			1.21607			0.608033	−	0.793912i	$-0.291959\pi$
$967$	37.8156			1.21607			0.608033	+	0.793912i	$0.291959\pi$
$968$		0			0
$969$	−42.5597	−	24.5719i	−1.36722	−	0.789362i
$970$		0			0
$971$	−12.8681	+	22.2882i	−0.412957	+	0.715262i	−0.995212	−	0.0977445i	$-0.968837\pi$
$971$	−12.8681	+	22.2882i	−0.412957	+	0.715262i	0.582255	+	0.813006i	$0.302171\pi$
$972$		0			0
$973$	−4.81872	−	8.34626i	−0.154481	−	0.267569i
$974$		0			0
$975$	−54.6809	−	23.7158i	−1.75119	−	0.759513i
$976$		0			0
$977$	12.0613	+	20.8908i	0.385875	+	0.668355i	0.991890	−	0.127098i	$-0.0405663\pi$
$977$	12.0613	+	20.8908i	0.385875	+	0.668355i	−0.606015	+	0.795453i	$0.707233\pi$
$978$		0			0
$979$	−9.99308	+	17.3085i	−0.319380	+	0.553183i
$980$		0			0
$981$	−9.58322	−	5.53288i	−0.305969	−	0.176651i
$982$		0			0
$983$	−22.5964			−0.720715			−0.360357	−	0.932814i	$-0.617345\pi$
$983$	−22.5964			−0.720715			−0.360357	+	0.932814i	$0.617345\pi$
$984$		0			0
$985$	21.3837	−	2.58831i	0.681340	−	0.0824703i
$986$		0			0
$987$		−	11.9970i		−	0.381868i
$988$		0			0
$989$	−15.6543			−0.497779
$990$		0			0
$991$	−7.57562	−	13.1214i	−0.240648	−	0.416814i	0.720251	−	0.693713i	$-0.244026\pi$
$991$	−7.57562	−	13.1214i	−0.240648	−	0.416814i	−0.960899	+	0.276899i	$0.910693\pi$
$992$		0			0
$993$	16.7817			0.532552
$994$		0			0
$995$	5.26556	+	7.01267i	0.166930	+	0.222317i
$996$		0			0
$997$	−46.3633	−	26.7679i	−1.46834	−	0.847747i	−0.468970	−	0.883214i	$-0.655375\pi$
$997$	−46.3633	−	26.7679i	−1.46834	−	0.847747i	−0.999371	+	0.0354673i	$0.988708\pi$
$998$		0			0
$999$	−20.1459	+	11.6312i	−0.637388	+	0.367996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.z.a.49.8	yes	16
3.2	odd	2		2340.2.cr.a.829.6		16
4.3	odd	2		1040.2.df.d.49.1		16
5.2	odd	4		1300.2.y.e.101.1		16
5.3	odd	4		1300.2.y.e.101.8		16
5.4	even	2	inner	260.2.z.a.49.1	✓	16
13.2	odd	12		3380.2.c.e.2029.16		16
13.3	even	3		3380.2.d.d.1689.15		16
13.4	even	6	inner	260.2.z.a.69.1	yes	16
13.10	even	6		3380.2.d.d.1689.16		16
13.11	odd	12		3380.2.c.e.2029.15		16
15.14	odd	2		2340.2.cr.a.829.3		16
20.19	odd	2		1040.2.df.d.49.8		16
39.17	odd	6		2340.2.cr.a.1369.3		16
52.43	odd	6		1040.2.df.d.849.8		16
65.4	even	6	inner	260.2.z.a.69.8	yes	16
65.17	odd	12		1300.2.y.e.901.1		16
65.24	odd	12		3380.2.c.e.2029.1		16
65.29	even	6		3380.2.d.d.1689.2		16
65.43	odd	12		1300.2.y.e.901.8		16
65.49	even	6		3380.2.d.d.1689.1		16
65.54	odd	12		3380.2.c.e.2029.2		16
195.134	odd	6		2340.2.cr.a.1369.6		16
260.199	odd	6		1040.2.df.d.849.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.z.a.49.1	✓	16	5.4	even	2	inner
260.2.z.a.49.8	yes	16	1.1	even	1	trivial
260.2.z.a.69.1	yes	16	13.4	even	6	inner
260.2.z.a.69.8	yes	16	65.4	even	6	inner
1040.2.df.d.49.1		16	4.3	odd	2
1040.2.df.d.49.8		16	20.19	odd	2
1040.2.df.d.849.1		16	260.199	odd	6
1040.2.df.d.849.8		16	52.43	odd	6
1300.2.y.e.101.1		16	5.2	odd	4
1300.2.y.e.101.8		16	5.3	odd	4
1300.2.y.e.901.1		16	65.17	odd	12
1300.2.y.e.901.8		16	65.43	odd	12
2340.2.cr.a.829.3		16	15.14	odd	2
2340.2.cr.a.829.6		16	3.2	odd	2
2340.2.cr.a.1369.3		16	39.17	odd	6
2340.2.cr.a.1369.6		16	195.134	odd	6
3380.2.c.e.2029.1		16	65.24	odd	12
3380.2.c.e.2029.2		16	65.54	odd	12
3380.2.c.e.2029.15		16	13.11	odd	12
3380.2.c.e.2029.16		16	13.2	odd	12
3380.2.d.d.1689.1		16	65.49	even	6
3380.2.d.d.1689.2		16	65.29	even	6
3380.2.d.d.1689.15		16	13.3	even	3
3380.2.d.d.1689.16		16	13.10	even	6

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.86320 - 1.65307i) q^{3} +(-0.877236 + 2.05681i) q^{5} +(0.517063 - 0.895580i) q^{7} +(3.96529 - 6.86809i) q^{9} +O(q^{10})\)	\(q+(2.86320 - 1.65307i) q^{3} +(-0.877236 + 2.05681i) q^{5} +(0.517063 - 0.895580i) q^{7} +(3.96529 - 6.86809i) q^{9} +(-2.96091 + 1.70948i) q^{11} +(3.57672 + 0.455025i) q^{13} +(0.888345 + 7.33919i) q^{15} +(2.07508 + 1.19805i) q^{17} +(-5.37246 - 3.10179i) q^{19} -3.41897i q^{21} +(-6.28304 + 3.62751i) q^{23} +(-3.46091 - 3.60861i) q^{25} -16.3012i q^{27} +(0.902796 + 1.56369i) q^{29} +5.80053i q^{31} +(-5.65180 + 9.78921i) q^{33} +(1.38845 + 1.84913i) q^{35} +(-0.713520 - 1.23585i) q^{37} +(10.9931 - 4.60975i) q^{39} +(-3.60158 + 2.07937i) q^{41} +(1.86864 + 1.07886i) q^{43} +(10.6478 + 14.1808i) q^{45} +3.50894 q^{47} +(2.96529 + 5.13604i) q^{49} +7.92183 q^{51} -4.55382i q^{53} +(-0.918661 - 7.58965i) q^{55} -20.5099 q^{57} +(-5.06250 - 2.92283i) q^{59} +(-1.90280 + 3.29574i) q^{61} +(-4.10061 - 7.10247i) q^{63} +(-4.07353 + 6.95747i) q^{65} +(-3.80822 - 6.59603i) q^{67} +(-11.9931 + 20.7726i) q^{69} +(9.49745 + 5.48336i) q^{71} +7.15345 q^{73} +(-15.8746 - 4.61105i) q^{75} +3.53565i q^{77} -12.8524 q^{79} +(-15.0512 - 26.0694i) q^{81} -0.706694 q^{83} +(-4.28448 + 3.21707i) q^{85} +(5.16978 + 2.98477i) q^{87} +(5.06250 - 2.92283i) q^{89} +(2.25690 - 2.96796i) q^{91} +(9.58870 + 16.6081i) q^{93} +(11.0927 - 8.32912i) q^{95} +(7.99794 - 13.8528i) q^{97} +27.1144i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{9}+O(q^{10}) \) 16 * q + 10 * q^9	\( 16 q + 10 q^{9} - 6 q^{11} + 6 q^{15} - 18 q^{19} - 14 q^{25} + 12 q^{29} + 18 q^{39} - 48 q^{41} + 45 q^{45} - 6 q^{49} + 44 q^{51} + 2 q^{55} - 30 q^{59} - 28 q^{61} - 15 q^{65} - 34 q^{69} - 18 q^{71} - 42 q^{75} - 16 q^{79} - 44 q^{81} - 45 q^{85} + 30 q^{89} - 10 q^{91}+O(q^{100}) \) 16 * q + 10 * q^9 - 6 * q^11 + 6 * q^15 - 18 * q^19 - 14 * q^25 + 12 * q^29 + 18 * q^39 - 48 * q^41 + 45 * q^45 - 6 * q^49 + 44 * q^51 + 2 * q^55 - 30 * q^59 - 28 * q^61 - 15 * q^65 - 34 * q^69 - 18 * q^71 - 42 * q^75 - 16 * q^79 - 44 * q^81 - 45 * q^85 + 30 * q^89 - 10 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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