LMFDB - Embedded newform 260.2.z.a.69.1

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			69.1
Root			$-0.517063 + 1.65307i$ of defining polynomial
Character	$\chi$	$=$	260.69
Dual form			260.2.z.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.86320 - 1.65307i) q^{3} +(0.877236 - 2.05681i) q^{5} +(-0.517063 - 0.895580i) q^{7} +(3.96529 + 6.86809i) q^{9} +O(q^{10})$	\(q+(-2.86320 - 1.65307i) q^{3} +(0.877236 - 2.05681i) q^{5} +(-0.517063 - 0.895580i) q^{7} +(3.96529 + 6.86809i) q^{9} +(-2.96091 - 1.70948i) q^{11} +(-3.57672 + 0.455025i) q^{13} +(-5.91176 + 4.43893i) q^{15} +(-2.07508 + 1.19805i) q^{17} +(-5.37246 + 3.10179i) q^{19} +3.41897i q^{21} +(6.28304 + 3.62751i) q^{23} +(-3.46091 - 3.60861i) q^{25} -16.3012i q^{27} +(0.902796 - 1.56369i) q^{29} -5.80053i q^{31} +(5.65180 + 9.78921i) q^{33} +(-2.29562 + 0.277865i) q^{35} +(0.713520 - 1.23585i) q^{37} +(10.9931 + 4.60975i) q^{39} +(-3.60158 - 2.07937i) q^{41} +(-1.86864 + 1.07886i) q^{43} +(17.6048 - 2.13091i) q^{45} -3.50894 q^{47} +(2.96529 - 5.13604i) q^{49} +7.92183 q^{51} -4.55382i q^{53} +(-6.11350 + 4.59041i) q^{55} +20.5099 q^{57} +(-5.06250 + 2.92283i) q^{59} +(-1.90280 - 3.29574i) q^{61} +(4.10061 - 7.10247i) q^{63} +(-2.20173 + 7.75580i) q^{65} +(3.80822 - 6.59603i) q^{67} +(-11.9931 - 20.7726i) q^{69} +(9.49745 - 5.48336i) q^{71} -7.15345 q^{73} +(3.94401 + 16.0533i) q^{75} +3.53565i q^{77} -12.8524 q^{79} +(-15.0512 + 26.0694i) q^{81} +0.706694 q^{83} +(0.643819 + 5.31901i) q^{85} +(-5.16978 + 2.98477i) q^{87} +(5.06250 + 2.92283i) q^{89} +(2.25690 + 2.96796i) q^{91} +(-9.58870 + 16.6081i) q^{93} +(1.66687 + 13.7711i) q^{95} +(-7.99794 - 13.8528i) q^{97} -27.1144i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

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

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	−0.975799	−	0.218669i	$-0.929828\pi$
$3$	−2.86320	−	1.65307i	−1.65307	−	0.954401i	−0.677273	−	0.735732i	$-0.736838\pi$
$4$		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	$-0.229277\pi$
$7$	−0.517063	−	0.895580i	−0.195432	−	0.338497i	−0.947042	+	0.321110i	$0.895944\pi$
$8$		0			0
$9$	3.96529	+	6.86809i	1.32176	+	2.28936i
$10$		0			0
$11$	−2.96091	−	1.70948i	−0.892749	−	0.515429i	−0.0179086	−	0.999840i	$-0.505701\pi$
$11$	−2.96091	−	1.70948i	−0.892749	−	0.515429i	−0.874841	+	0.484411i	$0.839034\pi$
$12$		0			0
$13$	−3.57672	+	0.455025i	−0.992005	+	0.126201i
$13$	−3.57672	+	0.455025i	−0.992005	+	0.126201i
$14$		0			0
$15$	−5.91176	+	4.43893i	−1.52641	+	1.14613i
$16$		0			0
$17$	−2.07508	+	1.19805i	−0.503280	+	0.290569i	−0.730067	−	0.683375i	$-0.760511\pi$
$17$	−2.07508	+	1.19805i	−0.503280	+	0.290569i	0.226787	+	0.973944i	$0.427178\pi$
$18$		0			0
$19$	−5.37246	+	3.10179i	−1.23253	+	0.711600i	−0.967556	−	0.252656i	$-0.918696\pi$
$19$	−5.37246	+	3.10179i	−1.23253	+	0.711600i	−0.264972	+	0.964256i	$0.585363\pi$
$20$		0			0
$21$			3.41897i			0.746080i
$22$		0			0
$23$	6.28304	+	3.62751i	1.31010	+	0.756389i	0.982113	−	0.188292i	$-0.0602952\pi$
$23$	6.28304	+	3.62751i	1.31010	+	0.756389i	0.327991	+	0.944681i	$0.393629\pi$
$24$		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	−0.769946	−	0.638109i	$-0.779717\pi$
$29$	0.902796	−	1.56369i	0.167645	−	0.290370i	0.937591	+	0.347739i	$0.113050\pi$
$30$		0			0
$31$		−	5.80053i		−	1.04181i	−0.853616	−	0.520903i	$-0.825595\pi$
$31$		−	5.80053i		−	1.04181i	0.853616	−	0.520903i	$-0.174405\pi$
$32$		0			0
$33$	5.65180	+	9.78921i	0.983852	+	1.70408i
$34$		0			0
$35$	−2.29562	+	0.277865i	−0.388031	+	0.0469677i
$36$		0			0
$37$	0.713520	−	1.23585i	0.117302	−	0.203173i	−0.801396	−	0.598135i	$-0.795909\pi$
$37$	0.713520	−	1.23585i	0.117302	−	0.203173i	0.918698	+	0.394962i	$0.129242\pi$
$38$		0			0
$39$	10.9931	+	4.60975i	1.76030	+	0.738151i
$40$		0			0
$41$	−3.60158	−	2.07937i	−0.562472	−	0.324744i	0.191665	−	0.981460i	$-0.438611\pi$
$41$	−3.60158	−	2.07937i	−0.562472	−	0.324744i	−0.754137	+	0.656717i	$0.771945\pi$
$42$		0			0
$43$	−1.86864	+	1.07886i	−0.284965	+	0.164525i	−0.635669	−	0.771962i	$-0.719276\pi$
$43$	−1.86864	+	1.07886i	−0.284965	+	0.164525i	0.350704	+	0.936486i	$0.385942\pi$
$44$		0			0
$45$	17.6048	−	2.13091i	2.62437	−	0.317657i
$46$		0			0
$47$	−3.50894			−0.511832			−0.255916	−	0.966699i	$-0.582377\pi$
$47$	−3.50894			−0.511832			−0.255916	+	0.966699i	$0.582377\pi$
$48$		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
$55$	−6.11350	+	4.59041i	−0.824344	+	0.618971i
$56$		0			0
$57$	20.5099			2.71661
$58$		0			0
$59$	−5.06250	+	2.92283i	−0.659081	+	0.380520i	−0.791927	−	0.610616i	$-0.790922\pi$
$59$	−5.06250	+	2.92283i	−0.659081	+	0.380520i	0.132846	+	0.991137i	$0.457588\pi$
$60$		0			0
$61$	−1.90280	−	3.29574i	−0.243628	−	0.421976i	0.718117	−	0.695922i	$-0.245004\pi$
$61$	−1.90280	−	3.29574i	−0.243628	−	0.421976i	−0.961745	+	0.273946i	$0.911671\pi$
$62$		0			0
$63$	4.10061	−	7.10247i	0.516629	−	0.894827i
$64$		0			0
$65$	−2.20173	+	7.75580i	−0.273091	+	0.961988i
$66$		0			0
$67$	3.80822	−	6.59603i	0.465248	−	0.805833i	−0.533965	−	0.845507i	$-0.679298\pi$
$67$	3.80822	−	6.59603i	0.465248	−	0.805833i	0.999213	+	0.0396734i	$0.0126318\pi$
$68$		0			0
$69$	−11.9931	−	20.7726i	−1.44380	−	2.50073i
$70$		0			0
$71$	9.49745	−	5.48336i	1.12714	−	0.650755i	0.183926	−	0.982940i	$-0.441119\pi$
$71$	9.49745	−	5.48336i	1.12714	−	0.650755i	0.943214	+	0.332185i	$0.107786\pi$
$72$		0			0
$73$	−7.15345			−0.837248			−0.418624	−	0.908160i	$-0.637487\pi$
$73$	−7.15345			−0.837248			−0.418624	+	0.908160i	$0.637487\pi$
$74$		0			0
$75$	3.94401	+	16.0533i	0.455415	+	1.85368i
$76$		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	$-0.487651\pi$
$83$	0.706694			0.0775698			0.0387849	+	0.999248i	$0.487651\pi$
$84$		0			0
$85$	0.643819	+	5.31901i	0.0698320	+	0.576927i
$86$		0			0
$87$	−5.16978	+	2.98477i	−0.554258	+	0.320001i
$88$		0			0
$89$	5.06250	+	2.92283i	0.536623	+	0.309820i	0.743709	−	0.668503i	$-0.233065\pi$
$89$	5.06250	+	2.92283i	0.536623	+	0.309820i	−0.207086	+	0.978323i	$0.566398\pi$
$90$		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
$95$	1.66687	+	13.7711i	0.171018	+	1.41289i
$96$		0			0
$97$	−7.99794	−	13.8528i	−0.812068	−	1.40654i	−0.911414	−	0.411490i	$-0.865008\pi$
$97$	−7.99794	−	13.8528i	−0.812068	−	1.40654i	0.0993461	−	0.995053i	$-0.468325\pi$
$98$		0			0
$99$		−	27.1144i		−	2.72510i
$100$		0			0
$101$	2.99562	−	5.18857i	0.298076	−	0.516282i	−0.677620	−	0.735412i	$-0.736989\pi$
$101$	2.99562	−	5.18857i	0.298076	−	0.516282i	0.975696	+	0.219130i	$0.0703219\pi$
$102$		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	$-0.105769\pi$
$107$	11.7452	+	6.78110i	1.13545	+	0.655554i	0.190152	+	0.981755i	$0.439102\pi$
$108$		0			0
$109$			1.39533i			0.133648i	0.997765	+	0.0668240i	$0.0212866\pi$
$109$			1.39533i			0.133648i	−0.997765	+	0.0668240i	$0.978713\pi$
$110$		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	$-0.730213\pi$
$113$	−3.65133	+	2.10810i	−0.343488	+	0.198313i	0.318325	+	0.947982i	$0.396880\pi$
$114$		0			0
$115$	12.9728	−	9.74081i	1.20972	−	0.908336i
$116$		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	$-0.418658\pi$
$127$	−5.16978	−	2.98477i	−0.458744	−	0.264856i	−0.711516	+	0.702670i	$0.751991\pi$
$128$		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	$-0.172963\pi$
$137$	−0.231497	−	0.400964i	−0.0197781	−	0.0342567i	−0.875745	+	0.482774i	$0.839629\pi$
$138$		0			0
$139$	4.65970	+	8.07084i	0.395231	+	0.684559i	0.993131	−	0.117011i	$-0.0373314\pi$
$139$	4.65970	+	8.07084i	0.395231	+	0.684559i	−0.597900	+	0.801571i	$0.703998\pi$
$140$		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
$145$	−2.42424	−	3.22860i	−0.201322	−	0.268121i
$146$		0			0
$147$	−16.9805	+	9.80368i	−1.40053	+	0.808594i
$148$		0			0
$149$	−9.44524	+	5.45321i	−0.773784	+	0.446744i	−0.834223	−	0.551427i	$-0.814083\pi$
$149$	−9.44524	+	5.45321i	−0.773784	+	0.446744i	0.0604387	+	0.998172i	$0.480750\pi$
$150$		0			0
$151$			4.85943i			0.395455i	0.980257	+	0.197727i	$0.0633561\pi$
$151$			4.85943i			0.395455i	−0.980257	+	0.197727i	$0.936644\pi$
$152$		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	−0.957217	−	0.289372i	$-0.906553\pi$
$163$	−9.30996	−	16.1253i	−0.729212	−	1.26303i	0.228004	−	0.973660i	$-0.426780\pi$
$164$		0			0
$165$	25.0925	−	3.03723i	1.95345	−	0.236448i
$166$		0			0
$167$	−7.18849	+	12.4508i	−0.556262	+	0.963474i	0.441542	+	0.897240i	$0.354432\pi$
$167$	−7.18849	+	12.4508i	−0.556262	+	0.963474i	−0.997804	+	0.0662334i	$0.978902\pi$
$168$		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	$-0.352843\pi$
$173$	18.9947	−	10.9666i	1.44414	−	0.833773i	0.998122	+	0.0612532i	$0.0195097\pi$
$174$		0			0
$175$	−1.44229	+	4.96540i	−0.109027	+	0.375349i
$176$		0			0
$177$	19.3266			1.45268
$178$		0			0
$179$	−5.06250	+	8.76850i	−0.378389	+	0.655388i	−0.990828	−	0.135129i	$-0.956855\pi$
$179$	−5.06250	+	8.76850i	−0.378389	+	0.655388i	0.612439	+	0.790518i	$0.290188\pi$
$180$		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
$185$	−1.91599	−	2.55171i	−0.140866	−	0.187605i
$186$		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	0.999156	+	0.0410710i	$0.0130770\pi$
$191$	7.39587	+	12.8100i	0.535147	+	0.926901i	−0.464010	+	0.885830i	$0.653590\pi$
$192$		0			0
$193$	−3.50212	+	6.06585i	−0.252088	+	0.436629i	−0.964101	−	0.265538i	$-0.914451\pi$
$193$	−3.50212	+	6.06585i	−0.252088	+	0.436629i	0.712013	+	0.702167i	$0.247784\pi$
$194$		0			0
$195$	19.1249	−	18.5668i	1.36956	−	1.32960i
$196$		0			0
$197$	4.81643	−	8.34230i	0.343157	−	0.594365i	−0.641861	−	0.766821i	$-0.721837\pi$
$197$	4.81643	−	8.34230i	0.343157	−	0.594365i	0.985017	+	0.172457i	$0.0551705\pi$
$198$		0			0
$199$	1.96091	+	3.39640i	0.139006	+	0.240765i	0.927120	−	0.374763i	$-0.122276\pi$
$199$	1.96091	+	3.39640i	0.139006	+	0.240765i	−0.788115	+	0.615528i	$0.788943\pi$
$200$		0			0
$201$	−21.8074	+	12.5905i	−1.53818	+	0.888067i
$202$		0			0
$203$	−1.86721			−0.131052
$204$		0			0
$205$	−7.43631	+	5.58366i	−0.519374	+	0.389980i
$206$		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	−0.497837	−	0.867271i	$-0.665872\pi$
$211$	7.29429	−	12.6341i	0.502160	−	0.869766i	0.999997	−	0.00249580i	$-0.000794440\pi$
$212$		0			0
$213$	−36.2575			−2.48433
$214$		0			0
$215$	0.579770	+	4.78986i	0.0395400	+	0.326665i
$216$		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	$-0.801271\pi$
$223$	1.50165	−	2.60093i	0.100558	−	0.174171i	0.911915	+	0.410380i	$0.134604\pi$
$224$		0			0
$225$	11.0607	−	38.0791i	0.737381	−	2.53860i
$226$		0			0
$227$	−5.84058	−	10.1162i	−0.387653	−	0.671435i	0.604480	−	0.796620i	$-0.293381\pi$
$227$	−5.84058	−	10.1162i	−0.387653	−	0.671435i	−0.992133	+	0.125185i	$0.960047\pi$
$228$		0			0
$229$			18.5293i			1.22445i	0.790684	+	0.612224i	$0.209725\pi$
$229$			18.5293i			1.22445i	−0.790684	+	0.612224i	$0.790275\pi$
$230$		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	$-0.977693\pi$
$239$		−	2.16507i		−	0.140047i	0.997545	−	0.0700235i	$-0.0223074\pi$
$240$		0			0
$241$	16.7318	−	9.66011i	1.07779	−	0.622262i	0.147491	−	0.989063i	$-0.452880\pi$
$241$	16.7318	−	9.66011i	1.07779	−	0.622262i	0.930299	+	0.366801i	$0.119547\pi$
$242$		0			0
$243$	43.8375	−	25.3096i	2.81218	−	1.62361i
$244$		0			0
$245$	−7.96258	−	10.6045i	−0.508710	−	0.677500i
$246$		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	0.717344	−	0.696719i	$-0.245357\pi$
$251$	−3.87684	−	6.71488i	−0.244704	−	0.423840i	−0.962048	+	0.272879i	$0.912024\pi$
$252$		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	$-0.520766\pi$
$257$	−15.4216	−	8.90366i	−0.961973	−	0.555395i	−0.896780	+	0.442477i	$0.854100\pi$
$258$		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	$-0.162240\pi$
$263$	14.3815	+	8.30316i	0.886801	+	0.511995i	0.0139065	+	0.999903i	$0.495573\pi$
$264$		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	0.761179	−	0.648542i	$-0.224621\pi$
$269$	−2.96967	−	5.14362i	−0.181064	−	0.313612i	−0.942243	+	0.334930i	$0.891287\pi$
$270$		0			0
$271$	−8.37246	−	4.83384i	−0.508591	−	0.293635i	0.223663	−	0.974666i	$-0.428198\pi$
$271$	−8.37246	−	4.83384i	−0.508591	−	0.293635i	−0.732254	+	0.681031i	$0.761532\pi$
$272$		0			0
$273$	−1.55572	−	12.2287i	−0.0941562	−	0.740115i
$274$		0			0
$275$	4.07861	+	16.6012i	0.245949	+	1.00109i
$276$		0			0
$277$	−17.9423	+	10.3590i	−1.07805	+	0.622411i	−0.930369	−	0.366624i	$-0.880513\pi$
$277$	−17.9423	+	10.3590i	−1.07805	+	0.622411i	−0.147679	+	0.989035i	$0.547180\pi$
$278$		0			0
$279$	39.8386	−	23.0008i	2.38507	−	1.37702i
$280$		0			0
$281$		−	27.7700i		−	1.65662i	−0.560272	−	0.828309i	$-0.689303\pi$
$281$		−	27.7700i		−	1.65662i	0.560272	−	0.828309i	$-0.310697\pi$
$282$		0			0
$283$	22.1502	+	12.7885i	1.31670	+	0.760194i	0.983196	−	0.182556i	$-0.0584370\pi$
$283$	22.1502	+	12.7885i	1.31670	+	0.760194i	0.333500	+	0.942750i	$0.391770\pi$
$284$		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	0.898434	+	0.439109i	$0.144706\pi$
$293$	14.1987	+	24.5929i	0.829497	+	1.43673i	−0.0689370	+	0.997621i	$0.521961\pi$
$294$		0			0
$295$	1.57070	+	12.9766i	0.0914499	+	0.755526i
$296$		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
$305$	−8.44790	+	1.02254i	−0.483726	+	0.0585507i
$306$		0			0
$307$	11.5519			0.659302			0.329651	−	0.944103i	$-0.393069\pi$
$307$	11.5519			0.659302			0.329651	+	0.944103i	$0.393069\pi$
$308$		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
$315$	−11.0112	−	14.6647i	−0.620411	−	0.826263i
$316$		0			0
$317$	20.4445			1.14828			0.574138	−	0.818759i	$-0.305337\pi$
$317$	20.4445			1.14828			0.574138	+	0.818759i	$0.305337\pi$
$318$		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
$325$	14.0207	+	11.3322i	0.777731	+	0.628597i
$326$		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	−0.374302	−	0.927307i	$-0.622118\pi$
$331$	4.39587	−	2.53796i	0.241619	−	0.139499i	0.615921	+	0.787808i	$0.288784\pi$
$332$		0			0
$333$	11.3173			0.620182
$334$		0			0
$335$	−10.2261	−	13.6191i	−0.558709	−	0.744088i
$336$		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
$345$	−53.2460	+	6.44497i	−2.86667	+	0.346985i
$346$		0			0
$347$	−27.6247	+	15.9491i	−1.48297	+	0.856193i	−0.999813	−	0.0193399i	$-0.993844\pi$
$347$	−27.6247	+	15.9491i	−1.48297	+	0.856193i	−0.483158	+	0.875533i	$0.660510\pi$
$348$		0			0
$349$	−28.4661	−	16.4349i	−1.52376	−	0.879741i	−0.999605	−	0.0281153i	$-0.991049\pi$
$349$	−28.4661	−	16.4349i	−1.52376	−	0.879741i	−0.524151	−	0.851625i	$-0.675617\pi$
$350$		0			0
$351$	7.41745	+	58.3049i	0.395914	+	3.11209i
$352$		0			0
$353$	13.6825	−	23.6988i	0.728245	−	1.26136i	−0.229379	−	0.973337i	$-0.573670\pi$
$353$	13.6825	−	23.6988i	0.728245	−	1.26136i	0.957624	−	0.288021i	$-0.0929971\pi$
$354$		0			0
$355$	−2.94671	−	24.3446i	−0.156395	−	1.29208i
$356$		0			0
$357$	−4.09609	−	7.09463i	−0.216788	−	0.375488i
$358$		0			0
$359$			0.625579i			0.0330168i	0.999864	+	0.0165084i	$0.00525502\pi$
$359$			0.625579i			0.0330168i	−0.999864	+	0.0165084i	$0.994745\pi$
$360$		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	$-0.300227\pi$
$367$	3.44490	+	1.98891i	0.179822	+	0.103820i	−0.407387	+	0.913256i	$0.633560\pi$
$368$		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	$-0.927773\pi$
$373$	−24.4645	+	14.1246i	−1.26672	+	0.731343i	−0.292357	+	0.956309i	$0.594440\pi$
$374$		0			0
$375$	36.4784	+	5.97048i	1.88374	+	0.308314i
$376$		0			0
$377$	−2.51754	+	6.00368i	−0.129660	+	0.309205i
$378$		0			0
$379$	−14.1642	−	8.17771i	−0.727567	−	0.420061i	0.0899646	−	0.995945i	$-0.471325\pi$
$379$	−14.1642	−	8.17771i	−0.727567	−	0.420061i	−0.817531	+	0.575884i	$0.804658\pi$
$380$		0			0
$381$	9.86809	+	17.0920i	0.505557	+	0.875651i
$382$		0			0
$383$	−10.4332	−	18.0708i	−0.533111	−	0.923376i	−0.999252	−	0.0386654i	$-0.987689\pi$
$383$	−10.4332	−	18.0708i	−0.533111	−	0.923376i	0.466141	−	0.884710i	$-0.345644\pi$
$384$		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	0.970323	+	0.241814i	$0.0777424\pi$
$397$	13.8394	+	23.9705i	0.694578	+	1.20305i	−0.275744	+	0.961231i	$0.588924\pi$
$398$		0			0
$399$	−10.6049	−	18.3683i	−0.530911	−	0.919565i
$400$		0			0
$401$	10.6799	+	6.16604i	0.533328	+	0.307917i	0.742371	−	0.669989i	$-0.233701\pi$
$401$	10.6799	+	6.16604i	0.533328	+	0.307917i	−0.209043	+	0.977907i	$0.567035\pi$
$402$		0			0
$403$	2.63939	+	20.7469i	0.131477	+	1.03348i
$404$		0			0
$405$	40.4164	+	53.8265i	2.00831	+	2.67466i
$406$		0			0
$407$	−4.22534	+	2.43950i	−0.209442	+	0.120922i
$408$		0			0
$409$	31.2917	−	18.0663i	1.54728	−	0.893321i	0.548929	−	0.835869i	$-0.315036\pi$
$409$	31.2917	−	18.0663i	1.54728	−	0.893321i	0.998348	−	0.0574521i	$-0.0182976\pi$
$410$		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	−0.671408	−	0.741088i	$-0.734310\pi$
$419$	6.26566	−	10.8524i	0.306097	−	0.530176i	0.977505	+	0.210912i	$0.0676434\pi$
$420$		0			0
$421$		−	7.74907i		−	0.377667i	−0.982009	−	0.188833i	$-0.939529\pi$
$421$		−	7.74907i		−	0.377667i	0.982009	−	0.188833i	$-0.0604706\pi$
$422$		0			0
$423$	−13.9140	−	24.0997i	−0.676521	−	1.17177i
$424$		0			0
$425$	11.5050	+	3.34181i	0.558072	+	0.162102i
$426$		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	−0.0310532	−	0.999518i	$-0.509886\pi$
$431$	−18.9375	−	10.9336i	−0.912188	−	0.526652i	−0.881134	+	0.472866i	$0.843219\pi$
$432$		0			0
$433$	0.219232	−	0.126574i	0.0105356	−	0.00608275i	−0.494723	−	0.869051i	$-0.664730\pi$
$433$	0.219232	−	0.126574i	0.0105356	−	0.00608275i	0.505259	+	0.862968i	$0.331397\pi$
$434$		0			0
$435$	1.60399	+	13.2516i	0.0769054	+	0.635365i
$436$		0			0
$437$	−45.0072			−2.15299
$438$		0			0
$439$	6.98432	−	12.0972i	0.333344	−	0.577368i	−0.649822	−	0.760087i	$-0.725156\pi$
$439$	6.98432	−	12.0972i	0.333344	−	0.577368i	0.983165	+	0.182719i	$0.0584897\pi$
$440$		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
$445$	10.4527	−	7.84856i	0.495506	−	0.372058i
$446$		0			0
$447$	36.0582			1.70549
$448$		0			0
$449$	15.7293	−	9.08129i	0.742309	−	0.428572i	−0.0805990	−	0.996747i	$-0.525683\pi$
$449$	15.7293	−	9.08129i	0.742309	−	0.428572i	0.822908	+	0.568174i	$0.192350\pi$
$450$		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
$455$	8.08437	−	2.03841i	0.379001	−	0.0955621i
$456$		0			0
$457$	4.53992	−	7.86337i	0.212368	−	0.367833i	−0.740087	−	0.672511i	$-0.765216\pi$
$457$	4.53992	−	7.86337i	0.212368	−	0.367833i	0.952455	+	0.304678i	$0.0985490\pi$
$458$		0			0
$459$	19.5296	+	33.8263i	0.911564	+	1.57888i
$460$		0			0
$461$	−32.7734	+	18.9217i	−1.52641	+	0.881273i	−0.526900	+	0.849927i	$0.676646\pi$
$461$	−32.7734	+	18.9217i	−1.52641	+	0.881273i	−0.999509	+	0.0313456i	$0.990021\pi$
$462$		0			0
$463$	−15.5694			−0.723570			−0.361785	−	0.932262i	$-0.617833\pi$
$463$	−15.5694			−0.723570			−0.361785	+	0.932262i	$0.617833\pi$
$464$		0			0
$465$	25.7481	+	34.2913i	1.19404	+	1.59022i
$466$		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
$475$	29.7868	+	8.65209i	1.36671	+	0.396985i
$476$		0			0
$477$	31.2760	−	18.0572i	1.43203	−	0.826783i
$478$		0			0
$479$	−10.7058	−	6.18102i	−0.489162	−	0.282418i	0.235064	−	0.971980i	$-0.424470\pi$
$479$	−10.7058	−	6.18102i	−0.489162	−	0.282418i	−0.724227	+	0.689562i	$0.757803\pi$
$480$		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
$485$	−35.5087	+	4.29802i	−1.61237	+	0.195163i
$486$		0			0
$487$	−0.695283	−	1.20427i	−0.0315063	−	0.0545705i	0.849842	−	0.527037i	$-0.176697\pi$
$487$	−0.695283	−	1.20427i	−0.0315063	−	0.0545705i	−0.881349	+	0.472467i	$0.843364\pi$
$488$		0			0
$489$			61.5601i			2.78384i
$490$		0			0
$491$	−2.90025	+	5.02338i	−0.130886	+	0.226702i	−0.924019	−	0.382348i	$-0.875116\pi$
$491$	−2.90025	+	5.02338i	−0.130886	+	0.226702i	0.793132	+	0.609050i	$0.208449\pi$
$492$		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	$-0.785998\pi$
$499$		−	27.8242i		−	1.24558i	0.782388	−	0.622792i	$-0.214002\pi$
$500$		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	$-0.738662\pi$
$503$	−8.71140	+	5.02953i	−0.388422	+	0.224256i	0.293054	+	0.956096i	$0.405328\pi$
$504$		0			0
$505$	−8.04403	−	10.7130i	−0.357954	−	0.476723i
$506$		0			0
$507$	−41.4168	−	11.4857i	−1.83938	−	0.510097i
$508$		0			0
$509$	2.00505	+	1.15762i	0.0888724	+	0.0513105i	0.543778	−	0.839229i	$-0.316994\pi$
$509$	2.00505	+	1.15762i	0.0888724	+	0.0513105i	−0.454905	+	0.890540i	$0.650327\pi$
$510$		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	$-0.130090\pi$
$523$	23.6078	+	13.6300i	1.03230	+	0.595997i	0.114655	+	0.993405i	$0.463424\pi$
$524$		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
$535$	24.2507	−	18.2090i	1.04845	−	0.787244i
$536$		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	$0.161063\pi$
$541$			22.5466i			0.969353i	−0.874693	+	0.484677i	$0.838937\pi$
$542$		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
$555$	1.26770	+	10.4733i	0.0538110	+	0.444568i
$556$		0			0
$557$	17.5294	−	30.3618i	0.742745	−	1.28647i	−0.208496	−	0.978023i	$-0.566857\pi$
$557$	17.5294	−	30.3618i	0.742745	−	1.28647i	0.951241	−	0.308449i	$-0.0998100\pi$
$558$		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	$-0.518563\pi$
$563$	18.4393	−	10.6460i	0.777125	−	0.448674i	0.835411	+	0.549626i	$0.185230\pi$
$564$		0			0
$565$	1.13287	+	9.35938i	0.0476602	+	0.393752i
$566$		0			0
$567$	31.1297			1.30732
$568$		0			0
$569$	0.488701	−	0.846455i	0.0204874	−	0.0354853i	−0.855600	−	0.517638i	$-0.826812\pi$
$569$	0.488701	−	0.846455i	0.0204874	−	0.0354853i	0.876087	+	0.482152i	$0.160145\pi$
$570$		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
$575$	−8.65477	−	35.2275i	−0.360929	−	1.46909i
$576$		0			0
$577$	23.8270			0.991932			0.495966	−	0.868342i	$-0.334814\pi$
$577$	23.8270			0.991932			0.495966	+	0.868342i	$0.334814\pi$
$578$		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
$585$	−61.9980	+	15.6323i	−2.56330	+	0.646316i
$586$		0			0
$587$	7.63094	−	13.2172i	0.314963	−	0.545532i	−0.664467	−	0.747318i	$-0.731341\pi$
$587$	7.63094	−	13.2172i	0.314963	−	0.545532i	0.979430	+	0.201786i	$0.0646746\pi$
$588$		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	$-0.235553\pi$
$593$	35.9654			1.47692			0.738461	+	0.674296i	$0.235553\pi$
$594$		0			0
$595$	4.43070	−	3.32685i	0.181641	−	0.136388i
$596$		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	0.381881	+	0.924212i	$0.375277\pi$
$601$	−14.9409	+	25.8783i	−0.609451	+	1.05560i	−0.991331	+	0.131388i	$0.958057\pi$
$602$		0			0
$603$	60.4028			2.45979
$604$		0			0
$605$	1.53028	−	0.185226i	0.0622145	−	0.00753053i
$606$		0			0
$607$	−21.2089	+	12.2450i	−0.860843	+	0.497008i	−0.864294	−	0.502986i	$-0.832235\pi$
$607$	−21.2089	+	12.2450i	−0.860843	+	0.497008i	0.00345162	+	0.999994i	$0.498901\pi$
$608$		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	0.319997	+	0.947419i	$0.396318\pi$
$613$	−16.3530	+	28.3242i	−0.660490	+	1.14400i	−0.980487	+	0.196584i	$0.937015\pi$
$614$		0			0
$615$	30.5218	−	3.69440i	1.23076	−	0.148973i
$616$		0			0
$617$	7.18390	+	12.4429i	0.289213	+	0.500932i	0.973622	−	0.228167i	$-0.0732731\pi$
$617$	7.18390	+	12.4429i	0.289213	+	0.500932i	−0.684409	+	0.729098i	$0.739940\pi$
$618$		0			0
$619$		−	11.1681i		−	0.448883i	−0.974488	−	0.224442i	$-0.927944\pi$
$619$		−	11.1681i		−	0.448883i	0.974488	−	0.224442i	$-0.0720558\pi$
$620$		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	0.436734	−	0.899591i	$-0.356135\pi$
$631$	36.0259	−	20.7996i	1.43417	−	0.828018i	0.997435	+	0.0715729i	$0.0228019\pi$
$632$		0			0
$633$	−41.7701	+	24.1160i	−1.66021	+	0.958524i
$634$		0			0
$635$	−10.6742	+	8.01489i	−0.423593	+	0.318061i
$636$		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	0.914178	−	0.405314i	$-0.132838\pi$
$641$	2.68565	+	4.65169i	0.106077	+	0.183731i	−0.808101	+	0.589044i	$0.799504\pi$
$642$		0			0
$643$	−8.77839	−	15.2046i	−0.346186	−	0.599612i	0.639383	−	0.768889i	$-0.279190\pi$
$643$	−8.77839	−	15.2046i	−0.346186	−	0.599612i	−0.985568	+	0.169277i	$0.945857\pi$
$644$		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	$-0.0672193\pi$
$647$	32.6893	+	18.8732i	1.28515	+	0.741982i	0.307365	+	0.951592i	$0.400553\pi$
$648$		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	$-0.253299\pi$
$653$	11.0118	+	6.35766i	0.430925	+	0.248794i	−0.268816	+	0.963192i	$0.586632\pi$
$654$		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	0.996954	−	0.0779923i	$-0.0248510\pi$
$659$	11.0625	+	19.1608i	0.430934	+	0.746399i	−0.566020	+	0.824391i	$0.691518\pi$
$660$		0			0
$661$	0.612035	+	0.353359i	0.0238054	+	0.0137441i	0.511855	−	0.859072i	$-0.328958\pi$
$661$	0.612035	+	0.353359i	0.0238054	+	0.0137441i	−0.488050	+	0.872816i	$0.662292\pi$
$662$		0			0
$663$	−28.3342	+	3.60463i	−1.10041	+	0.139992i
$664$		0			0
$665$	11.4713	−	8.61336i	0.444837	−	0.334012i
$666$		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	$-0.507062\pi$
$673$	−23.3244	−	13.4663i	−0.899090	−	0.519090i	−0.876905	+	0.480664i	$0.840396\pi$
$674$		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	$-0.295333\pi$
$683$	−10.2786	−	17.8031i	−0.393300	−	0.681215i	−0.992883	+	0.119098i	$0.962000\pi$
$684$		0			0
$685$	−1.02778	+	0.124404i	−0.0392696	+	0.00475324i
$686$		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	0.790610	−	0.612321i	$-0.209764\pi$
$691$	17.2344	+	9.95031i	0.655629	+	0.378528i	−0.134980	+	0.990848i	$0.543097\pi$
$692$		0			0
$693$	−24.2831	+	14.0199i	−0.922440	+	0.532571i
$694$		0			0
$695$	20.6878	−	2.50408i	0.784733	−	0.0949851i
$696$		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
$705$	20.7440	−	15.5759i	0.781265	−	0.586624i
$706$		0			0
$707$	−6.19571			−0.233014
$708$		0			0
$709$	−0.916777	+	0.529301i	−0.0344303	+	0.0198783i	−0.517116	−	0.855915i	$-0.672995\pi$
$709$	−0.916777	+	0.529301i	−0.0344303	+	0.0198783i	0.482686	+	0.875793i	$0.339661\pi$
$710$		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
$715$	19.7776	−	19.2004i	0.739639	−	0.718055i
$716$		0			0
$717$	−3.57902	+	6.19905i	−0.133661	+	0.231508i
$718$		0			0
$719$	−5.60426	−	9.70687i	−0.209004	−	0.362005i	0.742397	−	0.669960i	$-0.233689\pi$
$719$	−5.60426	−	9.70687i	−0.209004	−	0.362005i	−0.951401	+	0.307955i	$0.900355\pi$
$720$		0			0
$721$	−10.4869	+	6.05460i	−0.390551	+	0.225485i
$722$		0			0
$723$	−63.8754			−2.37555
$724$		0			0
$725$	−8.76724	+	2.15395i	−0.325607	+	0.0799958i
$726$		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	$-0.651034\pi$
$733$	−24.7392			−0.913765			−0.456882	+	0.889527i	$0.651034\pi$
$734$		0			0
$735$	5.26840	+	43.5257i	0.194328	+	1.60547i
$736$		0			0
$737$	−22.5516	+	13.0202i	−0.830700	+	0.479605i
$738$		0			0
$739$	0.302370	+	0.174574i	0.0111229	+	0.00642179i	0.505551	−	0.862797i	$-0.331289\pi$
$739$	0.302370	+	0.174574i	0.0111229	+	0.00642179i	−0.494428	+	0.869218i	$0.664623\pi$
$740$		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	$-0.878535\pi$
$743$	−3.85776	+	6.68184i	−0.141528	+	0.245133i	0.786544	+	0.617534i	$0.211868\pi$
$744$		0			0
$745$	2.93050	+	24.2108i	0.107365	+	0.887015i
$746$		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	−0.833106	−	0.553114i	$-0.813440\pi$
$751$	1.71161	−	2.96460i	0.0624575	−	0.108180i	0.895563	+	0.444934i	$0.146773\pi$
$752$		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	$-0.267620\pi$
$757$	9.76835	+	5.63976i	0.355037	+	0.204981i	−0.311865	+	0.950127i	$0.600954\pi$
$758$		0			0
$759$			82.0079i			2.97670i
$760$		0			0
$761$	−33.1329	+	19.1293i	−1.20107	+	0.693435i	−0.960792	−	0.277270i	$-0.910570\pi$
$761$	−33.1329	+	19.1293i	−1.20107	+	0.693435i	−0.240273	+	0.970705i	$0.577237\pi$
$762$		0			0
$763$	1.24963	−	0.721472i	0.0452395	−	0.0261190i
$764$		0			0
$765$	−33.9785	+	25.5132i	−1.22849	+	0.922432i
$766$		0			0
$767$	16.7772	−	12.7577i	0.605789	−	0.460655i
$768$		0			0
$769$	33.7503	+	19.4857i	1.21707	+	0.702674i	0.964289	−	0.264851i	$-0.0853228\pi$
$769$	33.7503	+	19.4857i	1.21707	+	0.702674i	0.252777	+	0.967525i	$0.418656\pi$
$770$		0			0
$771$	29.4368	+	50.9860i	1.06014	+	1.83622i
$772$		0			0
$773$	−14.4410	−	25.0126i	−0.519407	−	0.899640i	−0.999746	−	0.0225567i	$-0.992819\pi$
$773$	−14.4410	−	25.0126i	−0.519407	−	0.899640i	0.480338	−	0.877083i	$-0.340514\pi$
$774$		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	$-0.183930\pi$
$787$	−1.52068	−	2.63389i	−0.0542062	−	0.0938879i	−0.891855	+	0.452321i	$0.850596\pi$
$788$		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
$795$	20.2141	+	26.9211i	0.716919	+	0.954791i
$796$		0			0
$797$	−36.6254	+	21.1457i	−1.29734	+	0.749018i	−0.979944	−	0.199275i	$-0.936141\pi$
$797$	−36.6254	+	21.1457i	−1.29734	+	0.749018i	−0.317394	+	0.948294i	$0.602808\pi$
$798$		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	−0.369886	−	0.929077i	$-0.620603\pi$
$809$	17.6250	−	30.5274i	0.619662	−	1.07329i	0.989547	−	0.144208i	$-0.0460635\pi$
$810$		0			0
$811$		−	30.1607i		−	1.05908i	−0.848284	−	0.529542i	$-0.822364\pi$
$811$		−	30.1607i		−	1.05908i	0.848284	−	0.529542i	$-0.177636\pi$
$812$		0			0
$813$	15.9814	+	27.6806i	0.560492	+	0.970800i
$814$		0			0
$815$	−41.3337	+	5.00308i	−1.44786	+	0.175250i
$816$		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	0.566915	−	0.823777i	$-0.308137\pi$
$821$	3.92434	+	2.26572i	0.136960	+	0.0790741i	−0.429954	+	0.902851i	$0.641470\pi$
$822$		0			0
$823$	17.2729	−	9.97249i	0.602094	−	0.347619i	−0.167771	−	0.985826i	$-0.553657\pi$
$823$	17.2729	−	9.97249i	0.602094	−	0.347619i	0.769865	+	0.638207i	$0.220324\pi$
$824$		0			0
$825$	15.7650	−	54.2748i	0.548868	−	1.88960i
$826$		0			0
$827$	−12.3377			−0.429025			−0.214512	−	0.976721i	$-0.568816\pi$
$827$	−12.3377			−0.429025			−0.214512	+	0.976721i	$0.568816\pi$
$828$		0			0
$829$	18.7968	−	32.5570i	0.652840	−	1.13075i	−0.329591	−	0.944124i	$-0.606911\pi$
$829$	18.7968	−	32.5570i	0.652840	−	1.13075i	0.982431	−	0.186628i	$-0.0597559\pi$
$830$		0			0
$831$	68.4966			2.37612
$832$		0			0
$833$			14.2102i			0.492355i
$834$		0			0
$835$	19.3030	+	25.7076i	0.668006	+	0.889650i
$836$		0			0
$837$	−94.5557			−3.26832
$838$		0			0
$839$	−20.7606	+	11.9861i	−0.716736	+	0.413808i	−0.813550	−	0.581495i	$-0.802468\pi$
$839$	−20.7606	+	11.9861i	−0.716736	+	0.413808i	0.0968144	+	0.995302i	$0.469135\pi$
$840$		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
$845$	4.34591	−	28.7422i	0.149504	−	0.988761i
$846$		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	$-0.268059\pi$
$853$	38.8952			1.33175			0.665873	+	0.746065i	$0.268059\pi$
$854$		0			0
$855$	−87.9717	+	66.0548i	−3.00857	+	2.25903i
$856$		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	$-0.336070\pi$
$863$	28.9384			0.985073			0.492537	+	0.870292i	$0.336070\pi$
$864$		0			0
$865$	−5.89333	−	48.6886i	−0.200379	−	1.65546i
$866$		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
$875$	8.94766	+	7.32234i	0.302486	+	0.247540i
$876$		0			0
$877$	0.912276	+	1.58011i	0.0308054	+	0.0533565i	0.881017	−	0.473084i	$-0.156859\pi$
$877$	0.912276	+	1.58011i	0.0308054	+	0.0533565i	−0.850212	+	0.526441i	$0.823526\pi$
$878$		0			0
$879$		−	93.8858i		−	3.16669i
$880$		0			0
$881$	−5.47740	+	9.48714i	−0.184538	+	0.319630i	−0.943421	−	0.331598i	$-0.892412\pi$
$881$	−5.47740	+	9.48714i	−0.184538	+	0.319630i	0.758882	+	0.651228i	$0.225746\pi$
$882$		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	$-0.365212\pi$
$887$	−5.15751	−	2.97769i	−0.173172	−	0.0999811i	−0.584081	+	0.811695i	$0.698545\pi$
$888$		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
$895$	13.5941	+	18.1046i	0.454401	+	0.605171i
$896$		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	$-0.551928\pi$
$907$	−33.0723	−	19.0943i	−1.09815	−	0.634015i	−0.935734	+	0.352707i	$0.885261\pi$
$908$		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	0.639070	−	0.769149i	$-0.279320\pi$
$919$	−10.5062	−	18.1973i	−0.346568	−	0.600273i	−0.985637	+	0.168876i	$0.945986\pi$
$920$		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
$925$	−6.92914	+	1.70237i	−0.227829	+	0.0559734i
$926$		0			0
$927$	80.4225	−	46.4319i	2.64142	−	1.52502i
$928$		0			0
$929$	−33.3099	+	19.2315i	−1.09286	+	0.630965i	−0.934337	−	0.356390i	$-0.884008\pi$
$929$	−33.3099	+	19.2315i	−1.09286	+	0.630965i	−0.158526	+	0.987355i	$0.550674\pi$
$930$		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	$0.404375\pi$
$941$			58.6037i			1.91043i	−0.295917	+	0.955214i	$0.595625\pi$
$942$		0			0
$943$	−15.0859	−	26.1296i	−0.491265	−	0.850896i
$944$		0			0
$945$	4.52953	+	37.4214i	0.147346	+	1.21732i
$946$		0			0
$947$	−20.3516	+	35.2500i	−0.661338	+	1.14547i	0.318926	+	0.947780i	$0.396678\pi$
$947$	−20.3516	+	35.2500i	−0.661338	+	1.14547i	−0.980264	+	0.197692i	$0.936655\pi$
$948$		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	$-0.651134\pi$
$953$	2.60814	−	1.50581i	0.0844859	−	0.0487779i	0.541648	+	0.840606i	$0.317801\pi$
$954$		0			0
$955$	32.8357	−	3.97447i	1.06254	−	0.128611i
$956$		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
$965$	9.40409	+	12.5244i	0.302729	+	0.403173i
$966$		0			0
$967$	−37.8156			−1.21607			−0.608033	−	0.793912i	$-0.708041\pi$
$967$	−37.8156			−1.21607			−0.608033	+	0.793912i	$0.708041\pi$
$968$		0			0
$969$	−42.5597	+	24.5719i	−1.36722	+	0.789362i
$970$		0			0
$971$	−12.8681	−	22.2882i	−0.412957	−	0.715262i	0.582255	−	0.813006i	$-0.302171\pi$
$971$	−12.8681	−	22.2882i	−0.412957	−	0.715262i	−0.995212	+	0.0977445i	$0.968837\pi$
$972$		0			0
$973$	4.81872	−	8.34626i	0.154481	−	0.267569i
$974$		0			0
$975$	−21.4113	−	55.6237i	−0.685711	−	1.78138i
$976$		0			0
$977$	−12.0613	+	20.8908i	−0.385875	+	0.668355i	−0.991890	−	0.127098i	$-0.959434\pi$
$977$	−12.0613	+	20.8908i	−0.385875	+	0.668355i	0.606015	+	0.795453i	$0.292767\pi$
$978$		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	$-0.382655\pi$
$983$	22.5964			0.720715			0.360357	+	0.932814i	$0.382655\pi$
$984$		0			0
$985$	−12.9334	−	17.2246i	−0.412091	−	0.548823i
$986$		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	−0.960899	−	0.276899i	$-0.910693\pi$
$991$	−7.57562	+	13.1214i	−0.240648	+	0.416814i	0.720251	+	0.693713i	$0.244026\pi$
$992$		0			0
$993$	−16.7817			−0.532552
$994$		0			0
$995$	8.70593	−	1.05378i	0.275997	−	0.0334070i
$996$		0			0
$997$	46.3633	−	26.7679i	1.46834	−	0.847747i	0.468970	−	0.883214i	$-0.344625\pi$
$997$	46.3633	−	26.7679i	1.46834	−	0.847747i	0.999371	+	0.0354673i	$0.0112920\pi$
$998$		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.69.1	yes	16
3.2	odd	2		2340.2.cr.a.1369.3		16
4.3	odd	2		1040.2.df.d.849.8		16
5.2	odd	4		1300.2.y.e.901.1		16
5.3	odd	4		1300.2.y.e.901.8		16
5.4	even	2	inner	260.2.z.a.69.8	yes	16
13.4	even	6		3380.2.d.d.1689.15		16
13.6	odd	12		3380.2.c.e.2029.15		16
13.7	odd	12		3380.2.c.e.2029.16		16
13.9	even	3		3380.2.d.d.1689.16		16
13.10	even	6	inner	260.2.z.a.49.8	yes	16
15.14	odd	2		2340.2.cr.a.1369.6		16
20.19	odd	2		1040.2.df.d.849.1		16
39.23	odd	6		2340.2.cr.a.829.6		16
52.23	odd	6		1040.2.df.d.49.1		16
65.4	even	6		3380.2.d.d.1689.2		16
65.9	even	6		3380.2.d.d.1689.1		16
65.19	odd	12		3380.2.c.e.2029.1		16
65.23	odd	12		1300.2.y.e.101.8		16
65.49	even	6	inner	260.2.z.a.49.1	✓	16
65.59	odd	12		3380.2.c.e.2029.2		16
65.62	odd	12		1300.2.y.e.101.1		16
195.179	odd	6		2340.2.cr.a.829.3		16
260.179	odd	6		1040.2.df.d.49.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.z.a.49.1	✓	16	65.49	even	6	inner
260.2.z.a.49.8	yes	16	13.10	even	6	inner
260.2.z.a.69.1	yes	16	1.1	even	1	trivial
260.2.z.a.69.8	yes	16	5.4	even	2	inner
1040.2.df.d.49.1		16	52.23	odd	6
1040.2.df.d.49.8		16	260.179	odd	6
1040.2.df.d.849.1		16	20.19	odd	2
1040.2.df.d.849.8		16	4.3	odd	2
1300.2.y.e.101.1		16	65.62	odd	12
1300.2.y.e.101.8		16	65.23	odd	12
1300.2.y.e.901.1		16	5.2	odd	4
1300.2.y.e.901.8		16	5.3	odd	4
2340.2.cr.a.829.3		16	195.179	odd	6
2340.2.cr.a.829.6		16	39.23	odd	6
2340.2.cr.a.1369.3		16	3.2	odd	2
2340.2.cr.a.1369.6		16	15.14	odd	2
3380.2.c.e.2029.1		16	65.19	odd	12
3380.2.c.e.2029.2		16	65.59	odd	12
3380.2.c.e.2029.15		16	13.6	odd	12
3380.2.c.e.2029.16		16	13.7	odd	12
3380.2.d.d.1689.1		16	65.9	even	6
3380.2.d.d.1689.2		16	65.4	even	6
3380.2.d.d.1689.15		16	13.4	even	6
3380.2.d.d.1689.16		16	13.9	even	3

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)

\(f(q)\)	\(=\)	\(q+(-2.86320 - 1.65307i) q^{3} +(0.877236 - 2.05681i) q^{5} +(-0.517063 - 0.895580i) q^{7} +(3.96529 + 6.86809i) q^{9} +O(q^{10})\)	\(q+(-2.86320 - 1.65307i) q^{3} +(0.877236 - 2.05681i) q^{5} +(-0.517063 - 0.895580i) q^{7} +(3.96529 + 6.86809i) q^{9} +(-2.96091 - 1.70948i) q^{11} +(-3.57672 + 0.455025i) q^{13} +(-5.91176 + 4.43893i) q^{15} +(-2.07508 + 1.19805i) q^{17} +(-5.37246 + 3.10179i) q^{19} +3.41897i q^{21} +(6.28304 + 3.62751i) q^{23} +(-3.46091 - 3.60861i) q^{25} -16.3012i q^{27} +(0.902796 - 1.56369i) q^{29} -5.80053i q^{31} +(5.65180 + 9.78921i) q^{33} +(-2.29562 + 0.277865i) q^{35} +(0.713520 - 1.23585i) q^{37} +(10.9931 + 4.60975i) q^{39} +(-3.60158 - 2.07937i) q^{41} +(-1.86864 + 1.07886i) q^{43} +(17.6048 - 2.13091i) q^{45} -3.50894 q^{47} +(2.96529 - 5.13604i) q^{49} +7.92183 q^{51} -4.55382i q^{53} +(-6.11350 + 4.59041i) q^{55} +20.5099 q^{57} +(-5.06250 + 2.92283i) q^{59} +(-1.90280 - 3.29574i) q^{61} +(4.10061 - 7.10247i) q^{63} +(-2.20173 + 7.75580i) q^{65} +(3.80822 - 6.59603i) q^{67} +(-11.9931 - 20.7726i) q^{69} +(9.49745 - 5.48336i) q^{71} -7.15345 q^{73} +(3.94401 + 16.0533i) q^{75} +3.53565i q^{77} -12.8524 q^{79} +(-15.0512 + 26.0694i) q^{81} +0.706694 q^{83} +(0.643819 + 5.31901i) q^{85} +(-5.16978 + 2.98477i) q^{87} +(5.06250 + 2.92283i) q^{89} +(2.25690 + 2.96796i) q^{91} +(-9.58870 + 16.6081i) q^{93} +(1.66687 + 13.7711i) q^{95} +(-7.99794 - 13.8528i) q^{97} -27.1144i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more